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FOR EDVCATION
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LIBRARY
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THE AMERICAN MUSEUM

oF
NATURAL HISTORY

KONINKLIJKE AKADEMIE
VAN WETENSCHAPPEN

-- TE AMSTERDAM -:-

PROCEEDINGS OF THE
SECTION OF SCIENCES

. .
/ 7
heer Vary, Vier

ee AIC +

4 ( ee er APE AY Pan | “

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‚ VOLUME XXIII
— (2%? PART) —
— (Nos. 6—8) —

PUBLISHED BY
“KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN”, AMSTERDAM
JUNE 1922

2Y — A 4 BOS buarel. >
(Translated from: „Verslagen van de Gewone Vergaderingen der Wis- en
Natuurkundige Afdeeling” Dl. XXVIII en XXIX).

Proceedings N°.
N°.
ib

NS.

CONTENTS.

ee

ar oh ee

NV

+
yoy

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS

VOLUME XxXIll
No.6.

President: Prof. H. A. LORENTZ.

Secretary: Prof. P. ZEEMAN.

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

Natuurkundige Afdeeling," Vols. XXVIII and XXIX).

CONTENTS.

G. KRUTKOW: “On the determination of quanta-conditions by means of adiabatic invariants”.
(Communicated by Prof. P. EHRENFEST), p. 826.

H. ZWAARDEMAKER: “On Sensibilization to Radioactivity by the Action of Hormones”, p. 838.

M. W. WOERDEMAN: “An Inquiry into the Distribution of Potassium-compounds in the Electric
Organ of the Thorn-back (Raja Clavata)”. (Communicated by Prof. H. ZWAARDEMAKER), p. 842.
(With one plate). ;

ALPH. DEUMENS: “Extinction by a Blackened Photographic Plate as Function of Wavelength,
Quantity of Silver, and Size of the Grains’. (Communicated by Prof. W. H. JULIUS), p. 848,

W. DE SITTER: “On the possibility of statistical equilibrium of the universe”, p. 866.

J. K. A. WERTHEIM SALOMONSON: “The Mechanism of the Automatic Current Interrupter”, p. 869.

J. F. VAN BEMMELEN: “The wing-design of mimetic butterflies”, p. 877.

J. J. VAN LAAR: “On the Equation of State for Arbitrary Temperatures and Volumes. Analogy
with Planck’s Formula” Il. (Communicated by Prof. H. A. LORENTZ), p. 887.

R. MAGNUS and A. DE KLEYN: “The function of the Otolithes”, p. 907. (With two plates).

B. P. HAALMEIJER: “On elementary surfaces of the third order”. (Fifth communication). (Communi-
cated by Prof. HENDRIK DE VRIES), p. 920.

W. H. KEESOM: “The quadrupole moments of the oxygen and nitrogen molecules”. (Communicated
by Prof. H. KAMERLINGH ONNES), p. 939.

W. H. KEESOM: “The cohesion forces in the theory of VAN DER WAALS”. (Communicated by Prof.
H. KAMERLINGH ONNES), p. 943.

L. E. J. BROUWER: “Intuitionistische Mengenlehre”, p. 949.

L. E. J. BROUWER: “Besitzt jede reelle Zahl eine Dezimalbruchentwickelung ?” p. 955.

Erratum, p. 964.

54
Proceedings Royal Acad. Amsterdam. Vol. XXIII

Physics. — “On the determination of quanta-conditions by means
of adiabatic invariants.” By G. Krurkow. (Communicated by
Prof. P. EHRENFEST.)

(Communicated at the meeting of September 25, 1920).

In a series of papers Enrenrest has shown that only such functions
of the general co-ordinates of a mechanical system may be quanti-
cized as are adiabatic invariants’). These functions can always be
found ®). Moreover, as we shall see, theory may answer the question
as to the number of essential adiabatic invariants, which in accord-
ance with the quanta-hypothesis have to assume discontinuous values.
If we suppose that the “density of probability” of the motion ot
the system, when not adiabatically acted upon, does not depend
explicitly on the time, and if then by means of some hypothesis or
some theorem which is derived from the properties of the system,
we replace the time-mean of a phase-function by a numerical mean,
it follows immediately that the number of essential invariants is
equal to the number of determining quantities of the system which
is left after the numerical mean has been determined (comp.
equations (12) sqq. below). By the determination of the adiabatic
invariants and the separation of the essential ones the uncertainty
as to the choice of the forms of motion which are admissible on
the quanta-hypothesis, becomes materially lessened. Still we must
not expect that the adiabatic invariants which we have found are
necessarily those which have to be quanticized: any arbitrary fune-
tion of those quantities is again an adiabatic invariant and has thus
equal claims to being selected. However, this liberty of choice can
be somewhat restricted; there is a further condition to which we
may subject the quania-functions. This condition is of the nature of
a hypothesis, but we may give it a simple statistical interpretation.
In every case, where the theory of quanta has been applied with
success *), the condition is fulfilled. It was introduced by PLaNcK as
a fundamental theorem for a complete determination of the quantities

1) P. EHRENFEST. These Proc. XIX N°. 3, p. 576. Ann. der Phys. 51 (1916)
Deel.

*) G. Krutxow. Proc. Amst XXI p. 1112. 1919.

3) My knowledge of the literature of the subject does not, however, extend
beyond the beginning of 1917.

827

which have to be quanticized'). A new proof will be given by
establishing a connection between the adiabatic invarianis and the
phase-space (below 18’).

This connection, which will be found to arise in a natural way,
with a concept derived from statistical mechanics, strengthens the bond
between it and the theory of quanta, a bond which, as it seems to
me, has gone into the background in the latest development of the
theory or at least has not been sufficiently emphasized, although in my
opinion it is of great importance. In view of this connection I think
that the only justification of the expression ‘‘action-quantum” is the
fact that it recalls to our mind the dimensions of the phase-extension.

Another conception of great importance to the theory of quanta
which will find a place in our classification is PLANCK’s*) coherence
of degrees of freedom. To me it seems of fundamental importance.
Its meaning will be found to appear very clearly by a juxtaposition
of the properties of a conditionally periodic system and a BOLTZMANN
“ergode’’.

This coherence of degrees of freedom must be very clearly distin-
guished from what is called ‘degeneration’ *). For instance from our
point of view an ergodic system is to the highest degree coherent,
but could in no case be called degenerated. For a degenerated system
the number of essential adiabatic invariants is greater than that of
the degrees of freedom, for a coherent system it is smaller.

The question arises: must the supernumerary adiabatic invariants
of a degenerated system be quanticised or, as suspected by Scnwarz-
SCHILD *), is the number of quanta-conditions smaller for such a
system for the normal case without degeneration?

For the solution of these questions the three steps which have
been taken viz. (1) establishment of the adiabatic invariants (2)
selection of the essential ones and (3) “normalisation” of the latter
are insufficient. In order to get nearer to the solution we must, I
think, take into account, that the quanta-functions must have a
meaning which is independent of the system of co-ordinates. We may
undoubtedly postulate this: if the quanta-laws are really physical
laws, they must necessarily satisfy this condition. The question is,
how to formulate this new invariance of the quanta-functions? I
shall not try to discuss it here in general; but only remark that

1) M. PLANCK. Ann. d. Phys. 50 (1916) p. 392.
*) M. PLANCK, l.c.
8) K. SCHWARZSCHILD. Sitzungsber. Berlin 1916. P. Epstein Ann. d. Phys.
51 (1916). p. 168.
*) K. SCHWARZSCHILD, l.c.
54*

828

we may return from the canonical equations which are so convenient
in the theory of quanta to the equations on cartesian co-ordinates.
Here the invariance in question means: invariance with respect to
the groups of rotations and translations; vector-analysis thus provides
the means of testing hypothetical quanta-quantities for the new
postulata *).

The above mentioned means enable us in special cases to separate
the quanta-quantities without ambiguity, for instance for the mecha-
nical systems considered by PLaNnck in the paper quoted. In some
cases, however, an ambiguity remains, which we may get rid of in
the following manner: by putting all but one of the quanta-quantities
equal to nought, a “singular motion” must be obtained. In this manner
we are able to make a connection between the methods sketched
out above and Pranck’s theory on the physical structure of the
phase-space, PLANCK'’s singular motions forming the last step in the
series. We may recapitulate as follows:

The quanta-quantities are (a) functions of the integrals of the
equations of motion (8) adiabatic invariants which (y) must be
“normalized” and (d) have a meaning which is independent of the
system of co-ordinates and finally (e) yield singular motions in
Pianck’s sense of the expression.

$ 1. The fundamental equation.
Let a mechanical system of n degrees of freedom be given by
its canonical equations of motion

ND
: 0g .

We shall consider a number of systems and introduce a function
o(pigi,t) which may be called the density of probability: @ must
satisfy the fundamental equation of statistical mechanics *) :

do % dop. dug.
—~-+ 2 | — == 0 ae

or, using (1):

dg Bui dor do : do
= = | —P. SS). ) SS eee IP ‘
Ot i = (5 urn òg, i) dt (2 )

o is therefore a function of the integrals of the equation (1).

1) In the theory of the ZEEMAN-effect as given by SOMMERFELD and DEBIJE
(Phys. Zschr. 17. (1916) a difficulty is met with here. This may, I think, be
evaded in different ways, but I am not able to give a uniquely determined
solution.

2) J. W. Gisps. Scientific papers. II’ p. 16; Statistical Mechanics. Chapter I.

829

If we suppose that the condition is stationary :
do
=

it follows that: @ is a function of those integrals which do not
contain ¢ explicitly, ie. of (2n—1) integrals, if only, as we shall
suppose all the time, H does not depend on ¢ explicitly.

We are at liberty to understand by o the density of probability
a posteriori or a priori. When applied to the theory of quanta our
result expresses the fact, that the quanta-quantities are functions of the
(2n—1) integrals of equations (1) which are independent of t.

Replacing the 2n-dimensional phase-space (pi,q;) by the corrre-
sponding integral space (c;,t;)*) the “‘path” of the system is a straight
line parallel to the t-axis. We can describe these lines either by
making ¢ increase, i.e. by following a definite system in its motion,
or by keeping ¢ constant and varying r, i.e. considering together
all the systems with given c,...cn?f,....t» and all possible values
Ott.

fo ee 3)

§ 2. H contains a variable parameter.

If H contains a parameter which may either have a constant
value as in the case just considered or vary slowly ®), the quantities
c, and ¢, are no longer constant, but variable; they have to satisfy
the following “equations of motion’’*):

A 0K : Ook
SS SS = —j . . . . . . 3
Bi at, ; t de. ( )
where:
Vv.
K = €, + & i), ep an oh tere (4)
0a

1) As in a previous communication we write the integrals of equations (1)
in the form:
Cg = Coach oe ee
and

“OV OV OV

a zet rt, ao = ae ae de
2 n

where c,...,¢n,T,h,...,¢ represent the 2m integration-constants and V
Jacosi’s. characteristic function. Comp. Proc. XXI, p. 1112, 1919.

*) The slowness is expressed in the fact, that H contains only a, not the
correspondiug momentum.

3) Proc. le.

ET tny

830

or putting a = const. approximately and representing the derivatives
with respect to a by dashes:

fr (a EEEN |
inter OEeDn emule ee 5) §=1,2,...50 F:
( ae ). ie
zo Tapirepitivio v haine hd
tan

Since the equations have the canonical. form, we have as the
fundamental A

3 (ee dr tn

Here we may not as before take 20. A further difficulty
a

presents itself: starting from a special line parallel to the ¢,-axis in

the (c;, ti) space -— a special ‘‘stream-line’ — if we now vary a

as equation (3) or (3’) show, the stream-line becomes broken up.
If we then keep a constant again and take together the points, that
lie on a straight line, @ will vary along this stream-line, since it
contains points of different origin. Thus on the new line @ is not
stationary, but explicitly dependent on ¢,.

We now form *) the time-mean of 9, which we shall call @ and

the difference e—o. Since fa (o—o) = 0, the quantity e—e in its

dependence on ¢, shows elevations and depressions round about Q,
the sum of the surfaces of the former being equal to that of the

latter. Each point carries its g—g value along with it and hence
the curve shifts regularly with the time ¢,. A stationary curve
represents the tendency towards condensation (in an elevation) or
rarefaction (in a depression) for the points of the stream-line, on the
supposition of the change of a being sufficiently small. If we make
our moving curve slide along the stationary one, in the course of
time elevations will cover depressions ‘and vice versa. A further
small change of a may therefore produce a diminution of the diffe-

rence g—o. By this reasoning it becomes clear that starting from
a stationary density a sufficiently slow change of a will to a corre-
sponding degree of approximation produce a stationary density *).

1) For the method now following comp. J. W. Grsss. Statistical Mechanics.
Chapter XIII.

8) Comp. J. M. Burcers. Proc. Amst. XX (1916) 149, Ann. d. Phys. 1917
(2) and my paper in the Proc. Amst. |. c.

831

We will therefore suppose that a changes slowly in the sense of
the theory of adiabatic invariants. Let Da be the total change of a, i.e.

De = if dt

and let De; and Dt, represent the corresponding changes of ¢; and ¢z;_
considering further that

a= const,

we find

De, _ 0 (OV mes 6
meme) TTT

where the horizontal line indicates the time-mean. If in equation
(5) we take c’; and ¢’; to mean these time-means, we obtain
0 n (de De. Ao Dt.
Ee hes ees ie 1843 beurre (D)
da ix1 \de, Da dt, Da
Since @ is independent of ¢, the corresponding term under the

summation-sign in (7) must be omitted.

§ 3. Phase-space and adiabatic invariants.
The stationary density @ need not depend on all the variables

Cowie) oa Pres bo ee ges og tn
For example in a conditionally-periodic system without commen-
surable relations between the periodicity-moduli @ depends on the
quantities c; only. This follows from the theorem which allows us
to replace the time-average by an averaging over a @-cell*). For
an ergodic (or quasi ergodic) system in consequence of the ergode-
hypothesis 9 depends on the energy c, only. We shall here suppose,
that @ depends on & quantities (k Sn), which we shall indicate by
Ein Cay = wann Oke
These integrals may be called essential integrals. Our supposition
with regard to o comes to the same as assuming that for our sys-
tem the time-mean may be replaced by a definite numerical mean.
To compute this we proceed as follows.
Suppose the system of equations
Etn ee er ane is |)
to be soluble with respect to p‚, ps, --- «> Pk, thus

1) J. M. Burgers. lc. and my paper l.c.

832
P, =k (M4: Sr ae Fy Pra Py CHE .+¢)) (i= 100.1, Be. 2)
Introducing the differentials de, ....dc, instead of the differentials
dp,.... dp, into the phase-integral

Laffer ef dood dad sel add BQ)

we find
I deed d dp d shi ee
= ffe, … de ffe dp, Ee TEN )
r=ff dy... dolen) sn ze HEAO)

Ò(p,,---p‚)
hsl fig +0 RE PETER CN mere LIE)

In (11) the integration has to be carried out, the limits being
determined by (8). From the (p;,q;)-space or the (c;, f;)-space we
may pass to the k-dimensional (c;,...cj)-space. A streamline of the
former space corresponds to a fixed point in the latter. The density
@ is replaced by ow in the c-space. Its elements therefore have the
weight w. For the iso-parametrie motion (a = const.) the c-space is
static i.e. each point is fixed. The integral (11) gives us the numerical
mean looked for, namely, if f is a ee. we have:

0(p,.--
oe bran Era -dqg/m. + + . (11)

Returning to equation (7) we now ren

where

k do De.
Be en eat aT ee yl UE
since 9 is a function of c,,...,cx only. Similarly the quantities
Deil ,, only depend on c,,..., Cz, as is easily seen from (6), if on

the right hand side we replace the time-mean by the numerical
mean (11'). Therefore 9 retains its property @ = @ (¢,-- ., Ck) when
a changes. Equation (12) expresses, that @ is a function of those &
integrals of the differential equations (6) which only contain the
quantities c,,...,cz. These integrals are obtained by integrating the
set of & differential equations which on the left side contain the
quantities De;/,, (¢=1,2,...,4). They are the essential adiabatic
invariants, and we have thus proved that @ is a function of the
essential adiabatic invariants.

833

Let us further consider the c-space. If a varies slowly, the fixed
points in it begin to move. Since in this motion the points do not
disappear nor new points are formed, the density gw must satisfy
the equation of continuity, i. e. our fundamental equation. As
@ = const. is certainly a possible solution, w itself must satisfy the
equation

dw k doc,

<= > ee — 0 . . . . . Ld . 13
where
zt De
Ct
in Da

Or with the notation
Dw dw k Qw De.

Da E da i=l de, Da É
in the equivalent forms
Dw k de’.
=

— See ee cea oe CLS
Da a ae dc. pee)
or
kde! 1D
iol Me ore (13")
i=1 00, w Da
For the quantity on the left side — the “divergence” — we
shall deduce another expression.
The essential adiabatic invariants — & in number — satisfy the
equations
Dv. ov. as)
SN Ch EN RPL ee omnes)

Das | tape Terdege
We shall suppose that the quantities vi can be expressed in the
quantities c,(2= 1,2...) or .
0(v,,.-+5%))

Ee oen Be

Ò(e‚,-.-,C) 7 ed

The properties of our system can be equally well described by
the quantities v; as by the quantities c;. The (v, .. . vz)-space has the

advantage over the c-space of being static, also with respect to the
action of adiabatic influences. Let us now examine the mutual
relation of the two spaces.

To this end we shall consider the D-derivative of the determi-
nant T:

(16)

834

Ov;
where v;,—— and V;, represents the corresponding sub-deter-

dc,
minant. We have identically
Dv. ov. dv —
__t—_ Sot Lo.
Da da de » dc)
hence
ò Dv, dv, ie dv, dc’)

a vn S= 0
dc, Da dadc, 8 ) derden a » Oe, Ven
and on the other hand

D dv. dv. 070

Da de, 5 Òa de,
From (a) and (6) it follows that

Sg 3)
bn Deen

(a)

(b)

(17)

(17)

(16)

(16°)

16”)

(18)

D Oer Do, a Ov. de”
Dad. 1 Das x Oc) Oey
or
EE kad)
—— =— 2 v, —.
Da esi es Oe
Substituting in (16) we obtain
De
Da th in do,
Since Ev; V;,=0 for 2u and equal to T for 2= u, (16’)
becomes
DT _ dc’;
pr cle, pn maa
Da 00)
Hence
> dc’; 1 DE
a d de; T Da
Comparing this result with (13°) it follows that
1 Deen 1 Dw
YT Da w Da
or
DD sl
og
Da To

In other words: Y/w is an adiabatic invariant or
Y=of(e,...,v), w= TF (v,,.- +0)
Substituting this value of w in the integral (10') we find

I de. de, YF B
eN: e, (rm) ff deden

(18)
(18°)

(19)

835

Tm fon fd do, Florent) cr ater eet celta LN)

Now we can always arrange, that F becomes equal to 1. We
have only to introduce, instead of one of the v;, the adiabatic
invariant

or

trae net (a. v‚)

and submit it to the condition

òr, ;
Ae” PMs PD AND ar TR Ee)
We then find
de. 7 Ov Oc 2 Ov *
) see cn
OE ates ton. 185) ar Br ò
Tm VE tg 1
DCE gn 3 de, v‚ x v,
or substituting for Y its value w/F:
or, F
T* = wow ——- = Py tins Mrt Ae Be wey bi!
a Ov, 1 ri en)

Calling the thus normalized set of essential adiabatic invariants

Colton et we find
dee es in are eR 4)

The v-space which is static with respect to adiabatic action is
“weightless”: its density @ is simply equal to y(v,,...,v,). The
quantities v,,...,v~% may be quanticized. Its property which is
expressed by eq. (22) is nothing but the fundamental law which
according to PLanck’s hypothesis the quanta-quantities have to obey ‘).
By our theorem (18") this hypothesis is connected with the adiabatic
invariants and thus finds a new confirmation. The property of the
v-space being “weightless” displays the character of this fundamental
law as a natural generalisation of the -old quanta-hy pothesis.

§ 4. On the coherence of degrees of freedom.

From the point of view now attained this very important con-
ception appears as a natural consequence of our suppositions. If the
number & — that of the essential integrals and adiabatic invariants
— is smaller than the number of degrees of freedom », as appears
from (22), some of the quantities v; must necessarily be of the dimen-

1) M. PLaANck. Lc.

836

sion Ap (p > 1), since the dimension of / is Jh". In order to illu-
strate this and the previous results we shall contrast the properties
of a BontzMann ergode and a conditionally periodic system without
commensurable relations:

ergode conditional periodic system
essential integrals
Ht 0 Heite ne

numerical mean

Op, Ogee, u
ff aen dn … dan SE ‚ (23) ffe aerden Ten (23')

density
e = 0(c,. 4) | oo lt ern)
essential adiabatic invariants

V= fap ..- dqn
H<e

vip dg = 1, 2, ape
1 2 2

0
density
vy=e¢(V) | 0 = 0 (P,P, ++. 5%)
The conditionally periodic system is what BOLTZMANN calls a sub-
ergode. On the other band the ergode appears as a coherent system

with a smallest value of 4, viz. k=—=1. These short indications may
suffice for the present.

$ 5. Degeneration.

A conditionally periodic system is called degenerated, if there
are commensurable relations between the periodicity moduli. It is
evident, that our system covers a lower set of points with its
orbital curve everywhere densely, than when there are no such
relations. Accordingly the; numerical mean will be of a lower
dimension and more quantities will remain free after the averaging
process. Thus besides the quantities c the quantities ¢ will play a
part: the number of essential adiabatic invariants becomes larger
than the numberof degrees of freedom. The question, whether these
supernumerary quantities have to be quanticized, we shall not discuss
here. A good instance for the discussion of the questions which may
arise here is afforded by the quanta-quantities in Epsrrin’s theory ')
of the Srark-effect for an infinitely weak external electric field; the
“parabolic” fquanta-quantities which are found in this case cannot

1) P. Epstein. Ann. d. Phys. 50. p. 490.

837

be represented as function of Sommurrenp’s “spherical” quanta-quan -
tities alone; other adiabatic invariants containing the quantities f,
and ¢, are essential in this case.

I am fully conscious of the fact, that by the above considerations
the difficulties which still beset the theory of quanta are in no way
removed, but only shifted. Still it seems to me that even the possi-
bility of such displacement deserves attention. Moreover | expect

that in special cases the general theory tentatively sketched out here
may be found useful.

Physical Laboratory of the University. Petrograd, April 1, 1920.

Physiology. — “On Sensibilization to Radioactivity by the action
of Hormones”. By Prof. H. ZWAARDEMAKER.

(Communicated at the meeting of Sept. 25, 1920).

Sensibilization of organisms or organs to the energy of light has
long since been a familiar process in physiology. It is especially
H. von Tappriner') who has called attention to some fluorescent
substances, which in the presence of oxygen largely increase the
deleterious influence of light. This noxious influence resembles the
influence of ultraviolet rays. Mr. and Mrs. Henri’) have detected
likewise an action of the colloidal selenium for the ultra-violet rays.

Long afterwards similar effects have been detected for the Röntgen-
rays. This is instanced by the use of enzytol (10°/, solution of boric
acid cholin) to increase the destruction of malignant tumors in
Röntgenization *)

In 1917) I have established sensibilization for Becequerel-rays.
Here also there were fluorescent substances which brought it about,
to wit fluorescein and eosin. The former had the stronger action
for the a-rays, the latter for the 3-rays. Their action took place
irrespective of the presence or the absence of light. In virtue of
standard experiments with adsorbentia (e.g. taleum venetum) I
correlated the sensibilization in these cases with a reinforcement of
the adsorptions, which the radioactive ions undergo through the
action of the sensibilizers. In these experiments we found a super-
session of fluorescein adsorption by eosin and not the reverse, running
parallel to a supersession of the sensibilization of fluorescein by
eosin and not the reverse‘). In general the adsorptions play a
prominent part in the action of radio-active atoms of the circulating
fluids, because the ions, moving freely in the fluid, exert an influence

!) H. von TAPPEINER, die photodynamische Erscheinung (Sensibilisierung durch
fluoreszierenden Stoffe). Ergebnisse der Physiol. Bd. 8. S. 698. 1909.

*) M. er Me. Victor Henri, Action photodynamique du sélénium colloidal, Soc.
de Biologie. C. R. du 24 févr. 1912. R

8) A full list of the literature on cholin-action is to be found in Dorn Strahlen-
therapie Bd. 8. S. 499.

*) Kon. Akad. v. Wetenschappen, Amsterdam 27 Sept 1917.

5) See for the technique A. M. SrreeF, Onderz. Physiol. Lab. Utrecht, 5e Reeks
XVIII p. 59.

839

only when attached through adsorption to the surfaces of the cells,
and not when they are located at various distances from the cells.
An improved adsorption, by which a larger number of a certain
group of ions attaches itself to the cells in a circulating fluid of
a given composition, improves the result elicited by these ions.

There is a simple means to detect sensibilizers for radioactivity.
One has only to start from radio-active antagonism ’).

We, therefore, preferred to experiment on the heart of a cold-
blooded animal, because the cells of this organ, the seat of automa-
tie movement, are washed directly by the circulating fluid.

The heart of an eel or a frog beats only when, given the further
necessary conditions, a radio-active component is present in the
circulating fluid in the proper dosage. It does not matter whether
the element under consideration is an «-rayer or a B-rayer (our
normal g-rayer is potassium). When applying the «- and the 3-rayer
simultaneously, the quanta may be counterbalanced so as to inhibit
each other’s effect completely. At such a moment there is a standstill.
A slight balance on the one side or the other will restore automaticity,

The dosage of «- and g-rayers in the circulating fluid must be
much smaller in summer than in winter. When taken alone, 5 mgr
of potassium chloride or 0,1 mgr of uranylnitrate per litre circulating
fluid is in summer sufficient to maintain the automaticity of sensitive
hearts. In winter at least 20 mgr of potassiumchloride or 10 mgr of
uranylnitrate per litre is needed. Accordingly the summer-, and the
winter-equilibria differ very much. In summer a combination of 20
to 30 mgr of potassiumchloride and 0,1 mgr of uranylnitrate (per
litre) may arrest the hearts action; in winter this result can be
achieved only by 40 mgr of potassiumchloride and 10 mgr of uranyl-
nitrate.

After having secured an equilibrium, no matter in what season, a
number of substances will give a shifting, which again restores
automaticity. Among the anorganie components it is especially the
caleium-ion to which we must ascribe a great influence; among the
organic substances | found a number of substances having in common
the property of considerable surface-activity (as observed for the
boundary layer air-water).

Shiftings may be observed on either side. When on the a-side,
so that a uranium-beat ensues, fresh potassium has to be added to
obtain a standstill again. When the shiftings are on the g-side,
uranium must be added to produce the same effect.

1) Kon. Akad. v. Wetensch. 27 April 1917. ©

840

The shifting does not at all prove that the substance, by which
it is generated, is a sensibilizer; it only renders this probable. To
ascertain this we have to find out the maximum-, and minimum-
doses, between which the automaticity of the organ can be main-
tained; the potassium limits are the most important. In summer
these extremes vary with the individuality of the animal, and range
from 5 to 20 and from 10 to 300 mgr. of potassium chloride per
Litre, a low threshold corresponding with a low upper-limit, ete. ;
in winter the extremes are more constant; 20—30 and 600—800
mgr. potassium chloride per litre. Similar observations were made
for the other radio-active elements, but I pass them over in silence,
since these elements do not occur in the animal organism. The
same holds good for the majority of the sensibilizers found by us.

An exception is afforded by cholin and adrenalin, both hormones
occurring in every organism. Their sensibilizing power for BECQUEREL
rays is very strong, even when the dosis of cholin is one mgr. per
litre of circulating fluid and of adrenalin 0,001 mgr. *)

In the presence of one of these hormones the potassium-dosis that
keeps up the heart’s action, may be reduced to half the normal
dosis, nay, to less even. In summer, therefore, these dosages are
extremely small, even '/, mgr. of KCl per litre. Then the greatest
purity of chemicals is of the utmost importance.

However, there is a difference: Cholin shifts a potassium-uranium
equilibrium towards the potassium-side, adrenalin towards the ura-
nium-side. Whether this difference will also manifest itself in normal
life is still an open guestion. For aught we know, there is nowhere
in the organism an a-rayer, unless it be the trace of rest-activity left
behind by emanation, when it is inspired and expired in minimal
quanta as an indifferent gas together with the atmospheric air.

Potassium, cholin, adrenalin are normal constituents of the organ-
ism. Accordingly, the study of their mutual relations is a true
physiological study. |

The bio-radio-activity of potassium has no temperature-coëfficient.
Both the velocity of effect and the dosage remain the same with
der lor ne

The small differences lie within the latitude of the experimental
errors. In this respect physiological radio-activity is analogous to
photo -hemical actions, whose temperature-coefficient is likewise

h W. LieBrecHT used for the same purpose but in another connection 0,05
mgr. per litre. (Arch. int. de Physol. T. 15, p. 357).

2) Summer- and winterdosage do not differ on account of the difference of
temperature. We mention the difference in hormones as a possible cause.

841

insignificant. Still, the two are not identical. On the contrary, phy-
sically corpuscular raying differs fundamentally from light-rays.
Nor have we succeeded, in spite of strenuous efforts, not even by
means of the most concentrated visible or ultraviolet light, in
achieving a recovery of automaticity in an organ perfused with a
potassium-free fluid. As regards the temperature-coefticient the ana-
logy between radio-biological and photo-chemical action is still a
matter of surprise, even though we are told by modern researchers
that in many cases the action of light rests on the liberation of
electrons.

These phenomena might be correlated by assuming that the
charged particles which send the radio-active radiation with great
velocity through the lipoid films on the surface of the cells, evoke’
inside the cells a catalytic effect, which we usually call a stimulus *).

1) On physiological radio-activity. Journal of Physiology. Vol. 53 p. 286.

55

Proceedings Royal Acad. Amsterdam. Vol. XXUL.

Histology. — “An Inquiry into the Distribution of Potasstum-
compounds in the Electric Organ of the Thorn-back (Raja
Clavata).” By M. W. WOERDEMAN. (Communicated by Prof.
H. ZWAARDEMAKER).

(Communicated at the meeting of October 30, 1920).

On Prof. ZwaarDEMakER’s suggestion I have latterly examined
different tissues and organs microchemically on the presence of
potassium-compounds. I intend to discuss the method and the results
of this inquiry more in detail; for the present I will publish
only my experience in the investigation of the electric organ of the
Thorn-back (Raja clavata).

ZWAARDEMAKER’S researches established that the function of organs,
perfused artificially with a salt-solution, largely depends on the
potassium-content of that solution, and that the potassium, being a
weakly radio-active element, plays such a prominent part in the
origin of the organic actions, on account of its very radio-activity.
It may be supposed, therefore, that the potassium compounds which
are normally to be found in the organs of animals or plants, take
an important part in the normal functions of these organs. We
presume, therefore, that information concerning the presence or the
absence of potassium-cumpounds in certain cells, tissues, or organs
will be gladly received.

Now, through chemical examination the quantum of potassium,
contained in various organs, has already been determined with great
accuracy. From this examination we do not learn, however, where
in the organ the potassium-compounds are located. MAcALLUM namely
has detected that in a number of tissues and organs the potassium-
salts are not distributed at random and irregularly, but that they
often occur there at definite places, bound to quite definite structures.
MacaLLum’s') reagent on potassium-compounds is a modification of
the mixture used for the first time by Dr Koninck?). MACALLUM’s
mixture of cobalt-salt and sodium-nitrite, added to a potassium-salt

‘) A. B. Macatium. On the distribution of potassium in animal and vegetable
cells. Journ. of Physiol Vol. XXXII, 1905 and Die Methoden und Ergebnisse der
Mikrochemie in der biologischen Forschung. Ergebn. der Physiologie, Jrg. 7
1908, p. 552.

3) DE Koninck. Zeitschr. f. analyt. Chemie. Bnd. 20. 1881, p. 390.

| B43

solution precipitates FrscHer’s crystalline salt (a potassium-cobalt
sodium-nitrite). Macarrum puts sections of frozen material or teased
out preparations of fresh tissue in his cobalt-nitrite-sodium-nitrite
mixture. In the tissues and in the cells the potassium-precipitate
can now be formed. After being thoroughly washed with distilled
water, by which the reagent is washed away, the tissue is subjected
to an after-treatment with ammonium sulphide, which renders FiscnEr’s
sali black (formation of cobalt-sulphide). Wherever microscopical
examination reveals black precipitates or black decoloration, we may
decide upon the presence of potassium-compounds.

If e.g. voluntary muscle-tissue is treated after Macuii.um’s method,
it will be seen that the potassium-compounds occur almost exclusively
in the doubly refracting discs of the muscular fibres. The discs
of single refraction do not contain any potassium. Now, because the
electric organs of the so-called electric fishes are developed (with a
few exceptions) from voluntary muscular tissue, and since nobody
has as yet studied the distribution of potassium-compounds in this
metamorphosed muscular tissue, we considered an inquiry into the
distribution of potassium compounds in the electric organs of some
consequence. I regret to say that, although Dr. C. KerBerrt, Director
of Natura Artis Magistra offered his kind assistance, the strong elec-
tric fishes could not be put at my disposal. But also the Thorn-back
(Raja clavata), occurring at the Dutch North Sea-coast, has an electric
organ, which, though its action is weak, largely resembles in struc-
ture the organs with stronger action. I, therefore, applied to the
Zoological Station at Helder, where, through the kindness of Dr.
Reprke and Dr. van Goor I was enabled to perform the potassium-
reaction in the living electric organ of a thornback. The tissue was
put in the reagent and afterwards made into sections with an ice-
microtome (spray from liquid carbon dioxide). Although it is better
to make the sections first and to treat them immediately after
with the reagent, [ followed the other way, because there was no
freezing microtome at the Station. This altered working-method,
however, did not lessen the value of the results. I took care to put
very small pieces of tissue in the reagent in order to allow the
reagent to permeate the tissue as effectually and as rapidly as possible.
As I do not see any difference between the outer and the central
parts of the preparations, the diffusion appears to have succeeded
well. Before reporting the results of this inquiry | may as well
remind the reader that the electric organ of the Thorn-back is situ-
ated within the. lower two-thirds of the tail. There it lies at the
side of the dorsal and ventral tail-muscles. It consists of a large

55*

844

number of so-called electric platelets disposed in rows running
parallel to the axis of the body. Each platelet (see fig. 1) consists
of 1. a so-called anterior cortical layer composed of a single layer
of cells; 2. an inner layer composed of numerous twisted lamellae

medullated nerve

posterior cortical layer
jelly-like
nonmedullated connective
nerve branchlets tissue

inner layer

anterior cortical layer

=

EN

Pe

nonmedullated
| nerve-fibre
posterior / B

cortical layer j anterior

lamellae cortical layer

of inner layer

Fig. 1. A. Sagittal section through electric organ of thorn-back.
(only two electric platelets have been represented).
B. Part of an electric platelet, more enlarged.
(Diagrams, made after picture of frozen sections).

M. W. WOERDEMAN: “An Inquiry into the Distribution of Potassium-
compounds in the electric organ of the Thorn-back (Raja Clavata)”’.

Electric platelet.

= bloodvessels.

medullated nerve.

Fig. 2. Microphoto of two electric platelets of Raja punctata. (Section of
frozen organ, treated with potassium-reagent) Exhibits a very black precipitate
in the electric platelets and little or no precipitate in the jelly-like connective
tissue between the platelets.
(Reichert. Objective 4. Ocul. 2).

remainder of striation.

Granular layer.

Juclei encircled
by granular
precipitate.

Nucleus encircled by
granular precipitate.

anterior cortical
layer.

Inner layer.

Posterior certical
layer.

Fig. 3. Microphoto of an electric platelet of Raja punctata. (frozen section,
treated with potassium-reagent).
(Oil-immersion '/ Leitz. Oculair 2).

Proceedings Royal Acad. Amsterdam. Vol. XXIII.

845

and 3. a posterior cortical layer. The latter consists, like the anterior
layer, of a single layer of cells, but this layer is folded in so many ways,
that in sections the impression is excited as if the posterior cortical layer
is provided with fringe-like prolongations. The entire platelet is enveloped
by a very thin homogeneous membrane (the electrolemma). A very
fine network of non-medullated nerve-fibres lies against the anterior
cortical layer. Where the fibres reach the cells of this layer, those
cells present peculiar rods. The inner layer is the most complicated.
To realize its structure we should bear in mind that each electric
platelet must be considered as a modified muscular fibre.

The lamellae of the inner layer are derived from the anisotropous-
and isotropous-dises of the striated muscle-fibre (see also ENGELMANN’S
researches in “Onderzoekingen Physiol. Lab. Utrecht 4e Reeks
III, p. 307).

The doubly refracting layers become thicker, they lose their
faculty of double refraction, while the isotropous discs remain visi-
ble as finer, dark stripes. The layers are sinuously disposed and
thus originates the complicate structure of the inner layer of the
electric platelet.

BaBvcHiN could distinguish in young living rays the gradual trans-
formation of the muscular fibres into electric platelets and was able
to demonstrate that electric stimulation still elicited contractions in
fibres which had not yet undergone a complete transformation. The
electric plate once being formed, contractility is lost, but the generation
of electricity, which is also a property of the muscular fibre, has
far more become a principal function. So the electric organ may
justly be looked upon as a highly interesting object with a view
to potassium-researches.

Let it be finally observed that all electric platelets are located in
a jelly-like connective tissue.

In successful preparations, treated after MacarLum, I was now
enabled to establish that the electric platelets contain a great many
potassium compounds, whereas the jelly in which they are lying is
almost destitute of potassium (see fig. 2). Whereas in the medullary
sheath of the medullated nerves a distinct reaction is found, by
which the neurokeratin-reticulum is disclosed, the non-medullated
fibres appeared to be entirely potassium-free. It follows that in
most preparations nothing is to be seen of the nerve-network which
lies against the anterior cortical layer. This confirms MAcALLUM’s
finding that no potassium-reaction occurs in the axis-cylinders of the
nervefibres. The electrolemma is colourless and therefore apparently
potassium-free. In the electric platelet itself the reaction reveals itself

846

most distinctly in the inner layer (Fig. 3). In the anterior and
posterior cortical layers we observe fine-granular, black precipitates,
above all round the nuclei. In the nuclei themselves there is no
reaction. Indeed, Macarrum could never observe a potassium-precipitate
in a nucleus. This justifies the assumption that the nucleus is potas-
sium-free, since so-called masked potassium-compounds (such as iron
in haemoglobin) are unknown.

Cell-boundaries between the various nuclei I did not detect, con-
sequently I would rather describe the anterior and posterior
cortical layer as a syncytium. It is very striking that there is a
considerable accumulation of black grains in that portion of the
anterior syncytium which leans on the inner-layer of the platelet.

A regular granular layer exists on the boundary between the
anterior syncytium and the inner layer. On the boundary between
the inner layer and posterior syneytium my preparations do not
reveal that accumulation of potassium-compounds. Although in some
parts of the anterior syncytium also rods could be distinguished,
they did not show any black coloration. The inner layer of the
electric platelet is highly potassium-rich and it is remarkable
that here also dark and light stripes occur, just as in voluntary
muscular tissue. The dark stripes are diffusely black; 1 did not see
any grains. — In pieces of voluntary muscuiar tissue taken from
the tail of the ray, which were also treated with the potassium-
reagent, the anisotropous discs were also diffusely black and the
isotropous layers completely colourless. Now, because the inner layer
of the platelet has arisen from the fibrillary part of a voluntary
muscular fibre, we can hardly be mistaken in conceiving the alter-
nation of dark and light stripes in the inner layer of the electric
platelet as a remainder of the alternation of anisotropous, potassium-
bearing and isotropous, potassiumfree discs of the muscular fibre.

In the jelly between the platelets 1 found only potassium deposits
in the protoplasm of the starshaped connective-tissue cells. They,
however, are poor in potassium and so the whole quantity of
potassium-compounds in the jelly is very small; anyhow, strikingly
small compared with the potassium-rich electric platelet. The same
pictures recurring in various preparations as described above, I may
be justified in considering the above-mentioned distribution of the
potassium-compounds to be not a casual, but a typical phenomenon.

According to MacaLLuM the forms under which potassium occurs
in the tissues are the following:

1st. as a local precipitate ;

2.4. as a series of local sharply outlined deposits;

847

3rd, as a so-called bio-chemical condensation.

According to this differentiation potassium occurs in the anterior,
and the posterior cortical layer as a local precipitate, in the inner
layer, however, in biochemical condensation.

The local precipitate is to be found especially round the nuclei
of the two cortical layers and on the boundary of the anterior
cortical layer and the inner layer, while in the latter the potassium
has been condensed in the originally doubly refracting discs.

The most interesting facts brought to light by this experimentation
are, in my judgment, 1%‘. the potassium-richness of the electric platelets
and the slight quantity of potassium in the surrounding jelly ;
2ed, the occurrence of a large precipitate of potassium on the boun-
dary between the anterior cortical layer, and the inner layer, and
3. the fact, that in the inner layer the peculiar distribution of the
potassium-compounds, found in voluntary muscular tissue, has been
maintained. The physiological explanation of these facts will, as I
hope, be given by those who are competent to do so.

Histological Laboratory of the Amsterdam University.

Physics. — ‘“Hivtinction by a Blackened Photographic Plate as Function
of Wavelength, Quantity of Silver, and Size of the Grains”.
By Avra. Drumens. (Communicated by Prof. W. H. Junius).

(Communicated at the meeting of Sept. 25, 1920).

Introduction. For the right understanding of the photographic process
knowledge of the final product: the blackened photographic plate,
is indispensable. In this communication we shall give an account of
a research of the blackened photographic plate.

We have set ourselves the task to investigate the blackening * for
different wave-lengths, to measure the quantity of silver present in
the examined plates per unit of area, and we have further deter-
mined the size of the silver grains ’).

The extinction of a photographic plate may be compared to that
of a fixed colloidal solution, e.g. milk-glass or ruby-glass, where
also small particles are steeped in another medium.

The quantities mentioned have been measured, because the extinc-
tion of a blackened photographic plate can be theoretically under-
stood by considering it as the result of the action of a great number
of irregularly distributed grains of silver, steeped in gelatine.

When the distribution and the nature of the silver in the plate
is known, the action on radiation of given wave-lengths can be
derived, and inversely something about the nature of the silver in
the plate can be inferred from this action for given radiation on
grains of given size.

In this communication we shall not enter further into the theo-
retical considerations, but reserve them for a following communication.

We now confine ourselves to the description of the experimental
methods used and of the results obtained by them.

') By blackening is understood Brigg’s logarithm of “2 in which J), resp. J,

is the intensity of the light that has traversed an unblackened, resp. blackened
part of the plate. :

The name “blackening” is not appropriate, because the photographic plate
is not black,

Hence it would be better to follow R. LUTHER (Zeitschr. f. phys. Chem.
1900) and speak of “the extinction” of the photographic plate.

*) Besides the extinction and silver content of a collargolsolution was,
examined.

849

The investigation of the blackening for different colours has, besides,
another practical use. Blackened photographic plates have often served
as light-reducers. Of late they have been used as such in different
researches in the Institute for Theoretical Physics. Compare Miss
RIw1in’s investigation *). It was, therefore, necessary to find a method
to gauge these reducers for different colours with regard to the
quantity of light that they allow to pass.

The attention may also be drawn to the fact that the law of
blackening that is found, can present differences when the plate is
measured for different colours.

For the blackening is dependent on the method by which it is
measured, in opposition to the number, the section, and the nature
of the grains of silver present in the photographic plate per unit of area.

The micro-photometers work with light of different colours, thus
e.g. that of Hartmann’) and all other visual ones chiefly with
yellow-green, that of Paur, Kocu ®) chiefly with light of short wave-
lengths, that of Morr *) for the greater part with red and ultra-red.

Differences in results may, therefore, always be interpreted by the
consideration that the blackened photographic plate is far from black.

$ 1. Determination of the Blackening for Different Parts
of the Spectrum.

1. Method of procedure. The determination of the blackening
takes place by means of the extinction meter of Morr, modified
according to the adjoined scheme. °) (fig. 1).

A Nitralamp Lp (25 candles, 4+ Volts) throws a beam of light
made parallel’) by lens Ls on the photographie plate Pt, which is
always put at the same place in the apparatus. A dish Ct filled
with a coloured liquid, and a colour-filter #7 enable us to throw
a beam of the desired colour on the plate. After this the beam
strikes the thermopile 7 and causes a thermo-current proportional
to the energy of the light that strikes it. The intensity is measured
by the aid of a compensation method. ;

1) These Proc. Vol. XXIII N° 5. p. 807.

*) Zeitschr. f. Instrum. Kunde 1899 p. 97.

4) Ann. der Physik Bd. 39, 1912, p. 705—751.

4) Dr. W. J. H. Morr. Een nieuwe registreerende microfotometer. Versl.
Kon. A. v. W. XXVIII (1919), p. 566.

5) Versl. Kon. Ak. v. W., 28, p. 1001—1006.

6) We choose a parallel beam to make the theory of the observed phenomenon
as simple as possible. We avoid then also the Callier effect (Zeitschr. f. Wiss.
Photabd: e75-p. 257 etc).

850

The decade resistance box Bé') brings the current of an accumu-
lator Ar to the strength at which the thermo-current is compen-

Wa--\2 Sz

Th Pt Fe Ct ip bs

Lp
é
Fig. 1.

ated. Then the galvanometer Gr is without current. The circuits
of accumulator and thermopile have the manganin wire AB, of about
0.1 ohm, in common. Shunt St protects the galvanometer Gr. against
too strong currents. The zero-position is obtained by bringing valve
Kp before the lamp, and by interrupting the current with the con-
tact key S/.

The blackening measurements are made in the following way:
We place the unblackened part of the photographic plate Pt in the
light path of the lamp Lp and determine the resistance R, in resis-
tance box Bk necessary to compensate the thermocurrent. Then we
shift Pé, till the blackened part of the plate is in the light path,
and compensate again, let us suppose with A, Ohm. The blackening

R
is then given by log = log B

In the measurements the following sources of error should be
taken into account:

1. The spectral distribution of energy of the lamp (Lp) changes
on protracted use. The same blackenings measured with an interval
of some hours’ burning of the lamp never gave differences greater
than the accuracy allowed by the method.

1) Every resistance of from 0,1 to 100.000 ohms can be inserted on the
decade resistance box.

851

2. The strength of current of the lamp may fluctuate; it must,
therefore, be continually controlled. Care has been taken that the
error in consequence of the fluctuations in the intensity of the lamp
remains at the most of the order of 1°/,.

As after a lamp has been lighted, the stationary and maximum
intensity is not reached until some time after, the observations are
always started half an hour after the lighting of the lamp, and the
lamp remains burning all through the series of observations.

3. When we allow light to fall on the thermopile Zh), the
galvanometer Gr reaches its position of equilibrium within 2 seconds.
When the radiation is continued, we see the deflection, after having
been constant for a moment, slowly diminish. This is a consequence
of the getting warm of the surroundings of those places of contact
in the thermopile that are not directly irradiated. *)

In order to minimize the influence of this error, the successive
manipulations in the measurements are performed with constant
intervals. ,

These intervals are marked by an electric clock, which every ten
seconds closes a mercury contact for a moment. This brings about
that via a relay through the key Wp, which can turn round a
horizontal axis at #, the circuit is closed and broken at C and D
alternately for ten seconds. Only during the 10 seconds that the
shunt St is cut out at C, and the accumulator current put in at D,
is the valve Ap open, and is the light admitted on the thermopile.

It will be at once clear that in these ten seconds the resistance
box BK cannot be adjusted so that the thermo-current is totally
compensated. Therefore it is ascertained through a preliminary in-
vestigation what value of the resistance is about required for every
blackening to compensate the thermo-current. The galvanometer shows,
therefore, a small deviation. As deviation is taken the difference
between the unshunted zero position (1), i.e. when valve Kp is
shut, key Wp is in position 1 and key S/ is out of the circuit, and
the unshunted state of equilibrium (3), i.e. when valve Kp is open,
key Wp in position 1 and key Sl is in the circuit *).

1) The thermopile is provided with a cylindrical tube in order to prevent
obliquely incident light.

?) This phenomenon is met with to a much smaller degree in the later
improved construction of the thermopile.

5) As has already been said there is every time a period of ten seconds;
this time is amply sufficient to allow the galvanometer with or without thermo-
pile to resume its state of equilibrium, and to read the position reached on
the graduated scale down to 0.1 m.m.

853

The correction of the resistance is calculated from the deviation in mm.

The influence of the error mentioned under 3 has been minimised
by this procedure, for:

1. the thermopile is irradiated always i the same way, and during
the same short time,

2. every observation is the mean of several measurements.

Besides every photographic plate is at least measured twice.

Il. The measurements. The first observations showed at once that
as was to be expected, the blackening is a function of the wave-
length of the light with which it is measured. Frequently repeated
observations confirmed the first results.

The following plates were used: Wellington plates, Speed 100,
and Speed 400, dimension 13 X 18 cm., always of the same emul-
sion number *).

Every period (1) and (3) of 10 seconds is succeeded by a period (2), in
which the key Wp is in position (2); hence the galvanometer is protected by
the shunt from too great deviations. -

In this period (2) of ten seconds the necessary manipulations, as the opening
and closing of valve Kp and key S/, the adjustment of the resistance box
BK to the resistance approximated before, and the noting down of the
observation, may be performed.

Every observation consists in the reading of 3 zero-positions (1) and 2
positions (3), and lasts therefore 90 seconds. The course of the observation
may be characterized by giving the periods (1) (2) and (3) in the right
succession, viz.:

H=2=—3)—2)=H)=2—3)=@)—()- By averaging the 3 positions (1)and
the 2 positions (3) and by subtraction, the sought small deviation is found
in m.m.

1) The plates Speed 100 are developed with hydroquinone according to
the recipe:

Ist solution: Hydroquinone 36 érms
Potassium meta bi-sulphite 36 „
Bromide of potassium OR
Water 3000 „

2nd solution: Potassium hydroxide N44 rhs
Water 3000 5

Used were equal volume parts of the two solutions.
The plates Speed 400 were developed with glycin according to the recipe:

Distilled water 3000 grms
Sodium sulphite (powder) 150 „
Glycin 30
Potassium carbonate tS Gere
As fixing bath is used in both cases:
Ist solution: Hyposulphite 1500 grms
Water 3000 „
2nd solution: Ammonium chloride 600 „
Water 30005

Mix A and B.

853

1. Plates developed with hydroquinone *).

The plates N°. 1—4 have been developed for 7 '/, minutes with
1 part of developer and 6 parts of water, plate 1 at 14.5°, plate
2—4 at 13°, the plates 5—10 have been developed at 13° for four
minutes with 1 part of developer and 3 parts of water. After
development all the plates were rinsed for '/, minute, fixed for
15 minutes, and rinsed for 2 hours.

In the plates 5—10 the two most uniformly blackened pieces of
15 cm? were chosen on each plate. These two pieces are denoted
by A and B in the adjoined tables. Of each piece of 15 cm?’ the
blackening is measured at three different spots. The area of the
beam of rays on the photographic plate amounting to about 4 cm’,
the blackening is directly determined on 12 em’ of the 15 cm’.
The blackening given is a mean of these three.

In the plates 2—4 two pieces of 65 cm’ are taken, because on
account of the slight blackening a larger area must be used in the
determination of silver to be described later. The blackening is
measured in four places in every piece. The blackening given is
the mean of these four.

In plate 1 the different blackenings — marked a, 8, y, and 0 in
the table — are so slight, that no determinations of silver can be
made with them.

Accordingly the blackening is measured only at one place, but
always twice.

2 Plates developed with glycin ’).

The plates N°. 11—19 have been developed at 18° for 7'/, minutes
with 1 part of glycin and 2 parts of water, and they have further
been treated in the same way as the plates 5—10 with hydroquinone.
As with glycin a cloud occurs near the blackened part, a very broad
region of the plate is left unilluminated in the plates developed
with glycin, and the resistance A, of the unblackened plate is
measured at a place sufficiently far from the clouded part of the plate.

The blackening is measured for all plates for the following colours.

a. For the whole spectrum except for ultra-red.
~The dish Ct in the light path of the lamp Zp is filled with a
3°/, copper-chloride solution; filter /’r is superfluous here.

6. For ultra-red; centre of the intensity estimated at 1,25 u. The

) We take Wellington plates, Speed -100, developed with Hydroquinone
and bromide of potassium to get plates with small grains.

*) We wish to make the blackening and the filter investigation for two
different developers. As second developer we take glycin without potassium
of bromide, because we then get a fairly constant and not too large grain.

854

dish in the light path of the lamp Lp is filled with an asphalt
solution; filter Fr is superfluous here.

c. For rays of 0,640 u to 0,535 u; centre of the intensity estimated
at 0,58 wu; we shall therefore indicate this wave-length region by
“yellow”.

d. For rays of from 0,590 u to 0,435 u, with the centre of
intensity estimated at 0,54 u. This region is indicated by “green”.

At c and d in the light path is placed a 3°/, copper-chloride
solution, and besides a coloured gelatine filter as is sold by the firm
Kipp, at c the filter 3Cc, at d the filter 5Ac.

e. For the whole spectrum, Neither dish Ct nor Pr is placed in
the light path.

We find in fig. 2 both for hydroquinone and for gelatine the ratio

b c .
7 and ji plotted against d as independent variable. Thus two curves
C (

120 | ake tei a ae
as Cea

HM, =Hydrochinon ;ultrarood. O

[y= : Geel MES
G,=Glycine —_,ultrarood. D
Gy = ; „geel .®
at ==] JE |
ES 04 06 08 10 12 LA 18 20 22 2

Fig. 2.

are obtained for glycin, denoted by the letters G, and G, and two
for hydroquinone, indicated by H, and H,’).
1) Only the four blackenings of plate 1 have been measured, besides for

b, c and d, also for the whole spectrum and for the whole spectrum except
ultra-red.

In fig. 2 only 5 and - of plate 1 have been plotted against d. All the

measurements, however, are found in the table 1 adjoined to this communication.

855

The points marked in fig. 2 have been obtained by taking the
mean everywhere of the values A and 5*) recorded in table I
(see the end of this communication).

It appears convincingly from fig. 2 that the blackening found is
a function of the wave-length with which the blackening has been
measured.

As we hope to demonstrate further in a following communication
and as appears from the measurements in § 3 — the strong deviation
of H, for blackening from O to 0,6 will have to be attributed to
the influence of the size of the grain of the silver.

160 — en :
Lb = Hydrochinon, utr
| ra EL

140 Gy = elycine wivaroot
(p= : geel

0.60 05 10
Fig. 3.

In order to make the survey of the efficiency of the photographic
plate as light-reducer clearer, the transparency for the measured
blackenings from fig. 2 has been derived in ratio to the transparency
for green, by the aid of the relation:

df? D
10%6—*d il (1)
Ti ee
in which D represents the transparency and the index 6 and d
means ultra-red and green.
(1) results immediately from the definition of the blackening.

1) Finally the same measurements b, c and d have been carried out for
collargol. As analogues of the blank plate serves a dish filled with pure water,
as analogues of the blackened plate serves a same dish filled with collargol-
solution. These observations are indicated in fig. 2 by C. 0.65 X 10-3 grams
of collargol are taken per cm° of water.

856

In fig. 3 the ratio of the transparency for yellow, resp. ultra red
to green has been plotted as ordinate against the blackening for
green as abscissa.

Hence it appears that for the region yellow-green the plates
developed with glycin with a blackening of from O to 1.0 to 8°/,
may be safely used as reducers. For the rest it is, however, advisable
always to gauge the plates with regard to their transparency for
the wave-length region for which they must be used. In the investi-
gation by Miss Riwiin cited above this has been done by the method
worked out by us’).

The mean error of the observations of blackening has the value
of 0,7°/, for blackenings of 2.0 to 0.1, the value of 3.3°/,7) of the
blackening for blackenings of 0.1 to 0.001. Also with blackenings
above 2.0 the accuracy becomes less.

§ 2. Determination of the Quantity of Silver Present per Unit
of Area on a Blackened Photographic Plate.

1. Method of procedure. It appears from the results of § 1 that
the quantity of silver present per unit of area on the photographic
plate cannot be proportional to the blackening.

The estimation of the silver was made with the extinction meter
of Mo11.*) in the form as it was used in Mr. Dirmarscn’s still un-
published investigation of the flaking of colloids. For particulars of
the research we refer to the publication of Mr. Dirmarscn’s results.
For our purpose it is sufficient to observe what follows.

The deviation of the galvanometer caused by change of the turbidity
in one of the dishes, is registered photographically *). Accordingly

') In our investigation it is impossible to reproduce all the blackenings that
are to be investigated, on one photographic plate. This is preferable especially
in a search for the law of blackening, properties of the blackening etc. As
the way in which the problem has been put, necessitates the determination
of the quantity of silver of the plates, and this requires a black plate of
sufficiently large area, we meet with practical difficulties when we wish to
represent all the blackenings on one plate. The same investigations have,
however, first been carried out with the different blackenings in small squares
on the same plate. The results obtained were the same. Hence the differences
found cannot be attributed to the use of different plates.

*) These slight blackenings can be measured with the same apparatus by a
somewhat more elaborate, but also more accurate way, which reduces the
mean error to 0.9%,

3) Versl. Kon. Akad. v. Wetensch. XXVIII 1920, p. 1001—1006.

‘) The error resulting from the changes in the dimensions of the registering
paper, which may appear after the development, appears to be smaller than 1 %,

857

the compensation switch described by Morr, has been omitted‘).
The variation of the turbidity with the time may be read from the
registered curve.

The use of the extinction meter of Morr for the estimation of
the silver-content of a solution’) is based on the fact that it becomes
turbid when a definite quantity of a sodium-chloride solution of a
given strength is added to it. The process that then takes place,
consists of two parts. First of all the silver and sodium ions join
to molecules of silver chloride, which takes place very quickly, and
then the molecular disperse solution which can be compared with a
finely divided sol, begins to flake slowly, and consequently becomes
turbid. After a considerable time the turbidity becomes constant.

Hence a method worked out with a view to the study of the
process of flaking, can also render good services for the investigation.

For liquids with equal silver content this turbidity is only dependent
on the time. When we, however, start from liquids with different
silver content, it appears from the shape of the registered curve
that this turbidity depends in a great degree on the silver concen-
tration. We have here, therefore, an accurate means to determine
the content of a silver solution. This method has been applied in
the following way:

The registered deviation of the galvanometer is plotted as function
of the time and the area described in ten minutes*) — called area
of flaking — is caleulated. This is done for different solutions of
known silver content. When we now plot the calculated areas
against the resp. silver contents, we get a gauging curve‘), from
which the content of a silver solution that is to be examined, can
be read after calculation of the area of flaking.

When the sketched method is applied unmodified to the photo-
graphic plate, we are confronted by the difficulty that the grains of
silver lie embedded in gelatine. When the silver of the plate is
dissolved in nitric acid, and when sodium chloride is added, the
gelatine or its reaction products appear to prevent the flaking for
the greater part. By varying all the circumstances and registering

1) Versl. Kon. Akad. v. Wetensch. XXVIII 1920, p. 1002—1003.

*) In our investigation this is always a silver nitrate solution.

35) In general the deviation of the galvanometer has already got near its
maximum after 10 minutes.

*) Instead of the area of flaking also the deviation reached after then minutes
might be used, but this method of procedure is less accurate. For the calculation
of the area of flaking comes to the same thing as the use of different deviations
separated from each other by equal time intervals.

56

Proceedings Royal Acad. Amsterdam. Vol. XXIII.

858

the areas of flaking corresponding to them, we found as the most
favourable conditions boiling of the pieces of the plate of 15 em’,
resp. 65 cm’ with nitric acid of 50°/, for 60 min, resp. 90 min.
The influence of the gelatine or of its reaction products then dis-
appears at 8°/,') for the pieces of 15 cm’, and at 17 °/,*) for those
of 65 cm’.

The content of the silver nitrate solutions thus obtained from the
photographic plate, can however not be read from the above described
curve of gauging. For this purpose we must first make comparable
silver-nitrate solutions of known content. This is done by developing,
fixing, and rinsing unilluminated photographic plates of the same
kind as has been used, in the same way as the blackened photo-
graphic plates for the estimation of silver of which they must serve.

Then pieces of 15 em?’ resp. 65 cm? of these unilluminated plates
are heated with the same quantity of nitric acid and a known
quantity of silvernitrate for 60 minutes resp. 90 minutes at 100°.
The silver solutions thus obtained contain, therefore, the gelatine and
its reaction products in the same form as the silver nitrate solutions
obtained from the blackened plates, hence they can serve for the
construction of the curves of gauging.

Fig. 4 gives two of the curves of gauging used; the area of
flaking in cm? has been plotted as ordinate against the number of
mg. AgNO, in 14 em? of solution as abscissa; / serves in the deter-
mination of the quantity of silver in plates of 15 em’, // in those
of 65 cm?. As was to be expected, / lies higher than // on account
of the smaller influence of the gelatine. That with zero silver a
small value is still found for the area of flaking (cf. fig. 4 pieces
AB 8 times enlarged), is a consequence of the turbidity through
small particles of dust, which are raised by the stirring after the
addition of the sodium chloride. The method has been used for
silver solutions with a silver content of 0.5 x 10-3 to 156 x 10-3
grams per liter; the sensitiveness of the method to detect traces of
silver extends, however, much further than 0.5 « 107% grams of Ag
per liter.

) The circumstances made it necessary for us to manufacture the dishes
ourselves. In this we met with the difficulty that all the well-known acid-proof
cementing substances were attacked by the acid after shorter or longer time.
At last we found a suitable cement in bakelite. When the recipe of BERTRAND—
GAUTHIER is applied, the influence of the gelatine can be quite eliminated,
hence for 100°. The acid-concentration required for this, however, attacks
also the bakelite in less than an hour.

2) More prolonged heating — which would enable us to carry up the
percentage higher — met with practical difficulties.

859

The mean error in the estimations of silver amounts to 3 °,,.
In the measurements attention should be paid to the following points.

pall,
:

{ —

40
JE on Ab 8x vergroot. ZB
wh by

130

120
118
100

90

—S

80
70
60

30

30 / I
/ 2
20 f af ak
5 OT le el Oka Za arl
005 0 05 020 Omg
A AMER Aven A ee A A RI
| 2 3 4
Fig. 4.

1. It appears experimentally that the area of flaking becomes
larger by ultra-violet rays. To obviate this complication a dish of
quinine-bisulphate has been placed in the light-path towards the
liquid to be measured.

2. The area of flaking is greatly dependent on the concentration
of the acid, Therefore the same acid concentration has always
been used.

3. The area of flaking increases with the temperature. At 17°
the area increases by 2,7°/, per degree of temperature increase.
Therefore the temperature of the liquid is always measured before
and after the flaking, and all the observations have always been
reduced to the same temperature.

4. In consequence of specks of dirt and premature flaking through
the everywhere present sodium chloride, the liquid which is to be
examined, will already exhibit a beginning turbidity. This error can
become pretty great, especially with small concentrations.

By means of suitable manipulations the extent of this effect can
be registered separately for every flaking. With only a few excep-
tions we find that this error is always smaller than 5°/,. In many

56*

860

cases it is no more than 2 or 3°/, owing to the many precautions
taken in the treatment of the plates. One of these is that all the
plates after having been fixed and rinsed for a long time, are once
more rinsed with distilled water for 10 or 12 hours, before they
are dissolved in nitric acid.

The extent of this error is then so perfectly accidental, both for
the gauging liquids and for the liquids under examination, that we
have not taken it into account. ')

§ 3. Measurements of the Cross Section of the Silver Grains
in the Photographic Plate.

The way in which the silver of the photographic plate acts on
the light, and the blackening observed in consequence of this, depends,
as is immediately seen, to a great extent on the way in which the
silver is distributed. The dimensions of the silver grains with respect
to the wave-length of the light used in the measurement of the
blackening, is of the greatest importance, If it is, therefore, required
to obtain results which are liable to theoretic discussion, it is
necessary to investigate, besides the blackening and the total quantity
of silver, also the distribution of the silver. In this we have con-
fined ourselves to the determination of the mean size of the silver
grains — for so far as this is possible — in the plates of which
the blackening and the total silver content was investigated before.

The measurement takes place with a Zeiss-microscope with oil-
emersion of numerical aperture of 1.3C, combined with an ocular
N°. 12. An ocular micrometer is gauged with a Zetss-object glass
micrometer. Thus it appears that a scalar division of the ocular
micrometer corresponds to 1.0 u.

The value of the cross-section of the grain is the mean of 40
observations. ”)

With the smallest blackenings of the plates developed with hydro-
quinone N°. 1, 2, and 3 the grain cannot be measured, it being so
small, that nothing is to be seen in the microscope but a faint
greyish tint. In plate 4 the grain bas been measured, but it is
already very diffuse. Of the plates 5, 6, and 7 the size of the grain

can very well be measured. For plate 8 — 0.49 u was found for
the cross-section — the result was more or less uncertain on account

') The quantity of silver of the collargol used has also been determined.

*) Of these 40 observations 20 were always by Dr. H. C. BURGER and 20
by me. The mean difference between the two series of observations amounted
to 5%,

861

of the great blackening. For this reason we have repeated the
measurements, after the grains of the plates have been mechanically
pressed out into thinner layers. After this operation we find 0.48u
for the cross section of the grain. It seems therefore that the pressing
out does not change the cross-section in the plates developed with
hydroquinone.

The size of the grain of the strongly blackened plates 9 and 10
has been determined in the same way.

O = zarteng voor ultraood

@ = mgAg per 100 cm

0.1 02 03 04 0.5 06
Fig. 5.

Fig. 5 gives the measured cross-sections of the grain of the plates
4--10 plotted against the quantity of silver found in § 2 in mg.
per 100 cm’, and against the blackening measured in $1 for ultra-
red. The lefthand vertical line is the axis of ordinates for the quan-
tity of silver, the righthand vertical line that for the blackening.

When of the plates N°. 3 and 2 the quantity of mg. of silver
per 100 cm.’ and the blackening of ultra-red are derived from table
1 (see the end of this paper), and the values A and B averaged,
two values of the size of the grain are found of every plate by
substitution in the curves of fig. 5, which must both pass through
the origin, and have therefore been continued to the origin.

The mean of this is 0.05 u for plate 3 and 0.03 u for plate 2.
As these quantities have been obtained by interpolation, they are
printed in italics in table I.

For the theory and the understanding of the action of the

862

blackened photographic plate on radiation of given wave-length especi-
ally investigations on plates with small and increasing size of the
grains will be the most interesting. It is in order to get those plates
with small, increasing grains that we have chosen the plates and
the developer used. It is seen from fig. 5 that this purpose has been
perfectly attained.

In fig. 6 the whole observing mate-
rial is brought in connection. As inde-
pendent variable the cross-section of
© gee! the grain has been chosen, as ordinate

: the ratio of the resp. blackening and
the quantity of silver in mg. per 100
em.” of plate.

As the grain of plates 3 and 2 has

EL

D groen

O uitraroomn

been found by interpolation, — these
030 = points are indicated on fig. 6 by a
vertical line over the circle — and as

we accordingly do not know in how
far this eross-section of the grain is
accurate, the curves have only been
continued up to the points obtained
from the observations of plate 4.

025 =

020 =| In the plates 10—4 the mean of the
values A and B has always been taken
for fig. 6.

It is self-evident that with equal
size and nature of the grains the
blackening must be proportional to the
quantity of silver per cm’. SHEPPARD
06 and Mers), Hurter and DriFFIELD *),

Fig. 6. Eper*) found this result; in our expe-
riments this appears not to be the case. This contradiction must
find its explanation in the fact that the said investigators had equal
grains in the different blackenings, whereas this was not the case
with us.

015

010

It appears clearly that really — depends in a high degree on the

size of the grain, as was derived by Nurrine *).

1) Zeitschr. f. Wiss. Phot. Bd. 3 1905, p. 282—289.

*) Jahrbuch f. Photographie und Reproduktionstechnik 1899, p. 219.

8) Beitrage zur Photochemie und Spectralanalyse Eder und Valenta II, p. 57—58.
t) Phil. Mag. 1913, Vol 26 p. 425.

863

The measurements of the grain of the plates developed with
glycin show that the grain is pretty well constant, and oscillates
within the errors of measurement round a value of 0.96 u with a
blackening of 1.3 to 0.15 (measured for green); for slighter blacken-
ings the valne descends to 0.9 u.

No measurements have been possible for greater blackenings,
because the grain itself seems to be broken up into smaller pieces,
when the layer of gelatine is pressed out.

In table II *) is found the ratio of blackening and silver content
for the three colours used. It is seen that this ratio decreases with
the blackening.

SUMMARY.

1. A method has been given to measure blackenings of photo-
grapbic plates up to a blackening of 0.001 for different wave-length
with an accuracy of 0.7°/, for the blackenings of from 2.0 to 0.1,
and of 3.3°/, for the blackenings of from 0.1 to 0.001.

2. It is found that the blackening of the blackened photographic
plate depends in a very great degree on the colour of the radiated
light; hence when used as reducer the plate must first be gauged
for the different colours.

3. Morr’s extinction meter has been applied to the silver analysis
of the photographic plate. The method has been used from 0.5 < 10—3
to 156 X 10-% grams of silver per Liter. The accuracy amounts to
3°/, on an average. |

4. The mean cross-sections of the grains of the examined plates
have been determined. As the ratio of blackening and silver content
present per unit of area in the photographic plate must be constant
for grains of the same size and nature, the curves of this ratio and
of not constant grain have been plotted.

Besides this ratio has been determined for plates with grains of
constant cross-section of the grains.

With great pleasure we acknowledge here our indebtedness to
Prof. L. S. Ornstein, Dr. W. J. H. Morr, and Dr. H. C. Buregr
for the great encouragement and assistance they gave us in the
execution of these researches.

1) The observations for collargol have been put together at the end of
Table II.

TABLE I. (Hydroquinone).

Cross- Ratio of the Ratio of the | Ratio of the
Number of | section of blackening for blackening for blackening for
the plate. the grain |ultra-red and mg. | yellow and m.g. « green and m.g.
vs. Ag per 100c.m?. | Ag. per 100 cm? Ag per 100 c.m.2.
10 A a == 05184 En 107156 a = 0.168
0.55 |
rop vat cn ee = 0.175 Fae = 0.152 me = 0.168
1.787 1.483 1.636
9A 656 0.187 Tice = 0.155 De 0.170
0.56 |
ede hep 1.483 1.602 1)
|
| 1.391 1.178 eer
8A En 0.211 TI 0.178 En 0.192
0.49 |
1.4 1.191 [aes
8B 6 = == 105223 6.32 7 0.188 =e == 05204
|
‚0.908 OET Id 4 0.869 _
7 A Ar 0.211 ETE 0.180 ade 0.202
0.42
‚0.943 0.781 0.880
0.559 _ 0.491 — 0.547
0.34 |
„55 0. :
6A ol = OL Doe ae OAT : = 0250
| 0.361 0.307 _ 0.356
5 A mee 0.212 a= 0.181 Dn 0.206
0.28 |
0.332 0.27 0.
(GF Ws Di -05148 ~ | 0.188 _
4A 0.532 — 0.241 0.532 > 0.279 0.532 = 0.354
LG an | |
| “0126. v> POs | 0.183
4B | oye 0.271 0.465 = 0.308 aa! 0.465 = 0.394
| | | |
0.0208 _ 0.0485 _ 0.0703 _
S.A | 0.205 =D S101 0.205 = 0.237 0.208 > 0.343
oars | h
| 0.0248 0.0547 0.0745
3 B | ed ee a
| 0.186 0.133 0.186 0.294 0.185 0.401
| | | |
| 0.0159 (0.0277 0.0364
2A e= | = 0.2 ee ==
| 000 NE rn eee
0.03 | | |
| (0.0182 0.0307 0.0390
ZB ee = ==
| 0-00 Cio 2 mm

') The estimation of silver failed.

TABLE I (Continuation).

Blackening for

Numer of Spinchenine Blackening for eee PEetenine fhe shale
the plate. for ultra-red. visible spectr. for yellow. | for green. spectrum.
|
l a 0.0013 0.0110 / 0.0088 0.0129 0.0025
ie. _ 0.0042 0.0206 0.0158 0.0206 0.00665
l y | 0.0111 0.0361 0.0267 0.0367 0.0130
10 | 0.0204 0.0542 — 0.0427 0.0567 0.0238
|
TABLE Im (Glycin),
aber ot | | Ratio of ee! | Ratio of blackening Ratio of blackening
rete: | for ultra-red and |‘ for yellow and for green and m.g.
pases \m.g. Ag per 100 c.m.2.m.g. Ag per 100 c.m.2, Ag per 100 c.m.2.
2.647 _ eA: ae 2.363 —
19 A sag 0.181 meel 0.151 oere 0.162
2.31 | 2.183 2.308 _.
19 B TW 0.163 | 14.95 = 0.153 14.05 = 0.162
2.05 1.756 1.879
18 A mee 0.184 | nz = 0.157 TE 0.168
2.080 ir 7 ax 1.929
18 B Ts = 0.170 TAG 0.152 at ate 0.166
1.428 | 120 1.280 _
17 A n= 0.142 | bos = 0.122 0.05 = 0127
1.408 1.208 1.219.
17 B | ES 0.149 Baj = 0.127 Ea 0.135
| 0.859 0.731 0: 750...
16 A | aia OnI25 6ikeT 0.107 TUR 0.109
16 B 0.874 0.750 0.767 ')
Wes 02220 : 0.195 0.193
15 A | 2.20 = 0.100 299 — 0.085 299 7 0.084
. [0258 0.203 0.199 _
15 B | 1095 = 0.114 905 = 0.099 nar 0.097
0.1163 0.106 0.102 _
14 0.936 ~ 0.124 0.936 — 0.113 0.036 — 0.109
0.090 0.078 0.076
13 | 0.855. = 0.105 0.855 — 0.091 0.855 0.089
| 0.0218 _ 0.0224 _ 0.0212
12 rc cr = 0.066 0.330 > 0.068 0.330 0.064
0.0203 0 0196 0.0187
11 en ek hage. é
mage OP pas ee yee
400105 3 Greil | 0.673
Collargol. | B 0.0015 RT 0.031 | Bb 0.110
1) The estimation of silver failed.

Utrecht, Aug. 1920. Institute for Theoretical Physics.

Astronomy. — “On the possibility of statistical equilibrium of the
universe’. By Prof. W. pr Sitter.

(Communicated at the meeting of Nov. 27, 1920).

EinsreiN has on several occasions expressed the opinion that the
existence of a finite amount of matter in the universe must neces-
sarily lead to the adoption of a finite three-dimensional space. In
his inaugural address at Leiden ') he says:

“Wir können aber auf Grund der relativistischen Gravitations-
“sleichungen behaupten, dass eine Abweichung vom euklidischen
“Verhalten bei Raumen von kosmischer Grössenordnung dann vor-
“handen sein muss, wenn eine noch so kleine positive mittlere
“Dichte der Materie in der Welt existiert. In diesem Falle muss die
“Welt notwendig räumlich geschlossen und von endlicher Grösse
“sein, wobei ihre Grösse durch den Wert jener mittleren Dichte
“bestimmt wird.”

It appears to me that this statement cannot be accepted unreser-
vedly. The gravitational field-equations are:

Ge (CS =e. ae ae

If we suppose all matter to be at rest and free from any strain
or internal forces, then the tensor 7’,, has the value

Dist 0, au other T=), Sb caer eee

o being the density in natural measure. We can pute =o, +0,
where the average value of o, is zero; y, is then the average den-
sity. If we neglect o, the equations (1) are satisfied by the g,,

.

implied by the line-element:

ds? = — dr? — R? sin? 5 dp? -+ sin? wp d6*|] + ce dt, . . (34)
if we take
2 1
40, = Ta" ye = (EINSTEIN) (27... u)

or by those of the line-element :
RE gld” SH sin? wy dO] + cos? zede, . (3B)

with

1) Aether und Relativitätstheorie. Berlin, Julius Springer, 1920, p. 13.

3
Di 0; a Re (DE. SERTER) oat... CEB)
For R =o both (A) and (B) degenerate into:
ds? = — dr? — r? [dw’? + sin? Wd} + cdt?, . . . (3C)
with
Bi 0, A == Du (NEWRON} Raut 5 fC)

It thus appears that EiNsTEIN's solution (A), in which three-dimen-
sional space is finite and closed, is the only one which admits of
a finite average density g,. But this is only true, if the tensor 7’,,
has the value (2), i.e. if the matter is at rest and in equilibrium.
If the matter is either in motion, or subjected to stresses or pres-
sures, the value (2) cannot be used; the equations (3) and (4) no
longer represent the exact solution, and we can have finite values
of o, also in the systems (B) and (C)'). EINsTEIN’s assertion can
thus only be maintained if we make the additional hypothesis that
for the whole universe, or for regions of very large, or ““cosmical”’,
size, we can still use the value (2) of the tensor 7’,,, i.e. if for
such regions we assume the matter to be in statistical equilibrium.

This result can also be expressed thus: If the system (A) is the
true one, then it is possible for the universe, or for large portions
of it, to be in statistical equilibrium. If either (B) or (C) is the true
system, then this is not possible. Now the possibility of statistical
equilibrium of large portions of the universe is, to my mind at least,
by no means self-evident, or even probable. The idea of evolution
in a determined sense appears to me to be rather opposed to the
actual existence, if not to the possibility, of equilibrium.

The systems (A) and (B), involving the introduction of the constant
4, originated from the wish to make the three-dimensional world
finite”). At the present time the choice between the systems (A),

1) Similarly in the system (A) the value of 0, differs from that given by (44).
See also: pe Sitter, On Einstein's theory of gravitation and its astronomical
consequences, Monthly Notices of the R. A. S. Vol. LXXVII, pp. 6—7, 18 and 20—23.

*) If we assume the three-dimensional line-element to be

do® = dr* + R? sin’ > [aep? + sin? pdé*],. . . - 5)

and gis =O, then no other solutions than (A) and (B) exist. Of the two possible
three-dimensional spaces of constant curvature having the line-element (5) we must
choose the so called elliptical space. The analogy with two-dimensional geometry
suggests the spherical space, but this analogy is misleading. The elliptical space
is really the one of which our ordinary euclidian geometry is the limiting case
for R=«. In our common geometry a plane has a line (and not a point) at

868

(B) and (C) is purely a matter of taste. There is no physical crite-
rion as yet available to decide between them. It is true that the
systems (B) and (C) do not satisfy Macn’s postulate that inertia
must be traceable to a material source. But this postulate is a purely
metaphysical one, and has no physical foundation whatever. It
appears to me to be the last remnant of the desire for a purely
mechanical interpretation of nature, which logically and historically
is based on the belief in forces at a distance, and the impossibility
of which has been so clearly demonstrated by EinsreiN in his Leiden
address.

The three systems differ however in their physical consequences
at large distances, and an experimental discrimination between them
may be possible in the future. The decision between (2) on the one,
and (A) and (C) on the other hand may be brought about by the
study of systematic radial motions of spiral nebulae *). The distinction
between (A) and (C) is more difficult, since they both have
is = 1, and differ only in the gi; with 7 and j different from 4,
the values of which at great distances it is not so easy to ascertain.
The decision between these two systems must, I fear, for a long
time be left to personal predilection.

infinity; two straight lines have only one (and not two) point of intersection,
which may be situated at infinity; if we go to infinity along one branch of a
hyperbola, we return along the other branch on the other (and not on the same)
side of the asymptote. All these are properties of the elliptical as contrasted with
the spherical space. The spherical is only a quite unnecessary reduplication
of the elliptical one.

1) See pe Sirrer, |. c. pp. 27—28. At that time (1917) the radial velocities of
only three spirals were known, of which one was negative; the mean being
+ 600 km/sec. Now the radial velocities of 25 spirals are known (see Mount
Wilson Publications, Nr. 161, p. 19) of which only three are negative, the mean
being + 560 km/sec (or + 677 km/sec if the four brightest are omitted). The
system (B) requires a (spurious) positive radial velocity for distant objects.

Physics. — “The Mechanism of the Automatic Current Interrupter’’.
By Prof. J. K. A. WeRTHEIM SALOMONSON.

(Communicated at the meeting of November 27, 1920).

~The mechanism of the automatic current interrupter as represented
by Hermnortz’s tuningfork interrupter, by Nurrrr-Wacnur’s hammer-
break, and by the ordinary electric bell, has not yet been explained
in an entirely satisfactory way. Lord Rarreien was the first to give
an explanation, without, however, entering into details. Later on
its mechanism was studied by Lippmann, Dvorak, Guinier, Bovassr
and others although no new points of view were opened. In this
paper | intend to submit a few considerations on this subject, prin-
cipally based on a research into the attraction by the electromagnet
on the armature during the working of the apparatus. As an indi-
cator for the attraction I used the number of lines of force passing
through the armature at each moment. These were measured by an
oscillographic method. This might have been done by the new
ABRAHAM-rheograph, but as I did not possess this instrument |
employed Dreuisnr’s method, described in the Physikalische Zeit-
schrift 1910, p. 513. The results of this method were compared
with those obtained by a new method, which I shall describe in
an appendix to this paper.

The interrupter used in my experiments has a horizontal horse-
shoe magnet. The cores turned from a solid bar of swedish iron
completely bored and slit lengthways, have a length of 5 cm and
a diameter of 1 cm. They are screwed at a distance of 3.2 cm
from each other into a yoke of 1.4 cm?’ transverse section, and are
each wound with 200 turns of well insulated copper wire of 1.2 ohm
resistance each. The armature measured 1.2 X 0.75 « 4.4 em. It is
screwed to a strong steel spring of 0.12 « 1.0 em. with a free
length of 1.3 em. Into the other end of the armature a brass bar
0.4 cm. in diameter and 5 em. in length was fixed, on which, if
desired, a small copper weight could be screwed. It was generally
used without weight and then made about 47 complete vibrations
per second, the platinum contact being so adjusted as to make and
break the current during one half of the periodic time. The arma-

870

ture was wound in its middle part with 40 turns of copper wire, the
ends of which were connected by means of two large spiral wind-
ings with a pair of fixed terminals, in such a way as not to
hamper its vibrations. If the interrupter is connected into a circuit
with an inductionless ballastresistance of abont 1 Ohm and with
two accumulator cells, the vibrations have an amplitude such as to
render the distance of the armature from the cores taken together,
variable from 2 millimeters to 7.6 millimeters. Without current the
sum of the airgaps has a length of 4.8 millimeter. The selfinduc-
tion of the electromagnet, which of course is not constant, has
during the passage of the current a mean vaiue of about 9.3
millihenry.

Whilst the interrupter was in action, oscillograms were taken of
the current through the electromagnet and at the same time the
magnetic density in the armature was oscillographically recorded.
For the current a high frequency DuppeLL oscillograph of the Cam-
bridge Instrument Cy was used, whilst the magnetic density was
recorded with a Sremens and Hatske oscillograph, or with a striug
galvanometer. On the oseillographic records time marks of 0.01
second were inscribed. For the stringgalvanometer records 0.001 second
marks were used.

871

In this way curves, as given in fig. 1, were obtained (2 times
enlargement of the original negative)
with the oscillograph, or as in fig. 7
with the stringgalvanometer.

We can divide one complete period
of the interrupter into 4 nearly equal
parts. The two first quarter periods
represent the time during which the
circuit is closed, the two last ones
the break period. During the 2rd and
3'¢ quarter period the armature mo-
ves towards the cores; during the
1st and 4 quarter period in an
opposite direction. We know that
the number of lines of force passing
through the armature determines the
force with which it is attracted by
the electromagnet. We may even
say that this attraction is very nearly
proportional to the square of that
number of lines of force. |

Our curves show that the attraction during the second quarter
period is very much greater than during the first. This fact was
pointed out by Lord Rayiuten and has practically formed the basis
of all later communications on this subject. But at the same time
we see that during the 3'¢ quarter period, the current being broken,
a strong attractive force still exists, which is notably stronger than
the attraction which during the 4!" quarter period works against the
movement of the armature. Even when the interrupter works under
very different conditions as to frequency, current-strength ete. this
fact remains unchanged. We may say that the attraction during any
part of the movement of the armature towards the pole pieces,
greatly exceeds the attractive force in any point during its course
away from the electromagnet. Consequently there is no need for
any retarding device for making the current with respect to the
movement of the armature — as suggested by Lord RayLriga — in
order to improve the working of the interrupter. Probably such a
device would not only be inconvenient, but would hamper the
working of the apparatus.

Can we explain the curve for the attraction? For the ascending
part this is certainly possible. We can even calculate it approximately.
We first suppose the selfinduction to be constant during the make

872

period. Applying the wellknown formula of Hermnortz:
R

Di =<
Sl L
[= R (1--e )

we compute the current strength in the magnet at every moment.
The current strength being known we try to calculate the number
of lines of force through the armature, assuming it to be proportional
to the current strength and inversely proportional to the length of
the airgap. We may do this as, practically, the total reluctance in
the: magnetic circuit is to be looked for in the airgaps. With small
magnetizing forces the permeability of the iron is so great that this
assumption is permittable. As an example we may take the moment
just before the breaking of the current. Using HerMmnoLtz’s formula
and supplying the real valne of the constants, we find /=1.13
ampere, whilst from the oscillographie record we find /=1.17
ampere. This makes the magnetising force: 0.42 X 400 X 1.17 =
590. As the airgap has a length of 0.48 cm we get 590 « 0.48 =
1225 lines of force through 1 cm? air-section. These lines start from
the pole pieces, which have a surface of 0.7 cm’; hence we find
for the magnetic density in the iron not more than 1750 lines per
em’?. This means that we may expect a permeability u of the order
of 3000. Taking u — 3000 we find that to force 1225 lines through
16.4 cm of iron of a section of 0.7 cm’, not quite 5 ampere turns
are needed. Consequently we have an error of not more than.1°/,, if
we consider the airgap only and disregard the ironpath.

In order to calculate the number of lines during the make-period,
we assume that the armature vibrates in such a way as to vary the
length of the airgaps periodically, according to the expression
a+bsin2 ant. Then we get as an approximate expression for the
number of lines of force:

E aes
Ord NE:
R

a+ 6b sin2 ar nt

B= for SEG

in which N is the number of turns of the magnetising coils, Z the
voltage of the galvanic battery, R the resistance of the circuit, L
the mean selfinduction, n the frequency of the interruptions, a the
mean length of the air-path, and 5 half the amplitude of the armature.
If we put in this formula the value already given for each of the
constants, we get as a result the curves in fig. 3, where [ represents
the current strength, IL the length of the airgap and III the number
of lines of force during the make period. If this last curve be

873

compared with the ascending part in the oscillographie record, we
see that they correspond fairly well. The constructed curve shows

f deter Pues
is Rl eas opi fi

1

Fig. 3.

a somewhat more rapid ascent in its first part, and also some difference
in the last part. But this can readily be explained. If we bad calcu-
lated the current strength, taking into account that the selfinduction
was greater at the beginning and at the end of the make period
and smaller in the middle, the curves might have agreed better
numerically : theoretically this point is of little or no interest.

The descending part of the curve, which embraces the two last
quarter periods, represents the magnetic attraction during the break
period. A quantitative explanation is as yet not possible, though
qualitatively there seems to be no difficulty. We know that the less
reluctance there is in the magnetic circuit, the longer will an electro-
magnet keep its magnetism after breaking the current. Immediately
after breaking the current the air-path is rather large and conse-
quently the reluctance is great and the magnetism disappears rapidly.
As the armature approaches the core, the magnetic circuit improves
and the magnetism disappears more slowly. The slope of the curve
is indeed least at the end of the 3'¢ quarter period. From then to
the end of the 4" quarter period the reluctance grows and the
descent becomes more rapid again, becoming nearly as fast as in the
commencement of the 3'¢ quarter period, though not quite, as at that
moment the direct action of the magnetomotive force is taken away.

57

Proceedings Royal Acad. Amsterdam. Vol XXIII.

874

New method for making oscillographic records of the number

of lines of force.

If we desire to make an oscillographic record of the number of
lines of force in an iron path or an airgap, a few insulated copper-
windings are laid round the iron or a small coil is placed in the
air gap. When the number of the lines of forces 6 varies, an

com wie doe ; : ,
electromotive force V = k- 7 generated. The terminals of the coil
(
are connected with a condenser of a capacity C. This takes up a
charge g = VC and tbrough the coil and the connecting wires with
a total resistance r we have a current t.

Now we can state:

dq db
ba ka and kandi ren en rie. Die RE
After substitution we get:
k oe =n, ay 4+ V
dt dt
and putting m= Ae

ey o
dt Cine:

which gives after integration:

Aly. ifs
B=AV+ =), Vidi ees Kanst.ait) srt. ceil sete Ss Bian
rc

875

EN V with respect to Ee
the electromotive force V is proportional to the magnetic induction.
Generally it will be impossible to measure V with an oscillographic
electrostatic instrument. But we can use a galvanometric oscillograph
at the terminals of C. We shall then get the connections shown in
fig. 5 and the differential equations become:

I dB
Saati, and &—-+4 ri Ri, ss. (4)

We eliminate t, and get

If we may disregard the expression

dB 4 dV f 1 1 \ (5)
DE | BROS rt
r Y
in which A en After integration this becomes:
gr er ns (6
zn — + — Lane da
eld A )

We find a linear expression connecting B and V if the integral
in (6) need not be considered. This is allowed if both RC and rC
are very large and if also the frequency per second is high enough.
With a periodic change of B, which
might be represented by a Fourier
series, the value for the integral during

one period = 0. We have only to
soe examine its value during one period.
j With a frequency of 50 per second

Fig. 6. and time constants CR and Cr of
0.2 second each we get for a potential curve as represented by the

;
EE TEE en
AT ee meen tn REC

57%

876

broken-line curve in fig. 6 the correction indicated by the full-line
curve. At the starting point and the end the correction is zero. At
the highest point with an ordinate « we get a correction:

a(5 + 5):2 X 200=1/,, a, or 2.5 °/,
of the maximum ordinate.

In my experiments I used a condenser of 2 mikrofarad, A and r
being 10° Ohm each. The oscillographic record was made with a
stringgalvanometer. Fig. 7 gives an example of the curves obtained
in this way.

Zoology. — “The wing-design of mimetic butterflies’. By Prof. J.
F. vaN BEMMELEN.

(Communicated at the meeting of Nov. 27, 1920).

In a paper: On the phylogenetic significance of the wing-markings
of Rhopalocera, read before the meeting of the second International
Entomological Congress at Oxford in 1912, | made the casual remark
that “while inspecting the series of butterflies in search for speci-
mens showing the primitive colour-pattern, | was greatly impressed
by the considerable percentage of mimetic forms among my harvest.
So the idea occurred to me that perhaps Mimetism might, at least
to a certain degree and for a limited number of cases, be explained
by supposing the resemblance between two or more non-related
forms to have started at an early period, when the ancestral types
of different butterfly-families looked more like each other than
nowadays, on account of the primitive colour-pattern common to
them all”.

Since those days I have tried to clear and widen my ideas about
the real character of the primitive colour-pattern, especially by a
detailed analysis of the wing-design in original forms such as the
Hepialids, and by its comparison to the pattern of the body. These
investigations have led me to a modified conception of primitiveness
in pattern: the occurrence of sets of uniform spots, regularly arran-
ged in rows between the wing-veins, and spread over the entire
wing-surface, appearing to me as a still more original condition
than the concentration of the markings in the shape of a stripe
along the middle-line of the internervural cells. But this does not
in the least weaken my conviction, that this latter arrangement has
retained a considerable amount of primitiveness also, and that its
origin lies far beyond the beginnings of genera, families, nay of the
whole order of Lepidoptera.

Since then the Groningen Zoological Laboratory has acquired the
magnificent collection of Lepidoptera left by the lamented Max
FürBriNGER in Heidelberg. Thereby I was enabled to study actual
specimens of mimetic butterflies in nature and this made me wish
to return to the question of Mimetism in general, but then
considered exclusively from a purely morphological standpoint. I desire
therefore to avoid carefully the biological side of the question,
though I may be allowed to express my conviction that the often

878 )

striking superficial similarity between forms belonging to widely
different groups, can hardly fail to provide certain advantages in
the strugele for existence either to one or to both of them, or at least
must have done so in former periods of their occurrence on earth.

I shall henceforth restrict myself to a careful comparative analysis
of the colour-pattern. But before entering on this task, T wish to
remark that the phenomenon of mimetic resemblance can never be
ascribed to the influence of a general law, and consequently the
different cases of Mimiery must be judged separately, quite independently
of each other That e.g. a Sesia resembles a wasp, cannot possibly
stand in any genetic connection to the mimetic similarity between
a Dismorphia and an Ithomiid or a Heliconid, or between a set of
species of the latter families amongst each other. Nor can this
occurrence of wasp-like Sphingids stand in any relation to the existence
of other members of that same group, which seem to have assumed
the habitus of humble- bees.

Mimetie resemblances consequently must be considered as of casual
origin, and the considerable number of conditions, which had to be
fulfilled before a real case of Mimicry could enter into existence,
make us readily understand the relative rareness of the phenomenon,
and its apparently capricious distribution over the animal kingdom
(as Reset has so judiciously pointed out).

Though, as mentioned before, I am inclined to acknowledge the
high probability, that in many cases the close superficial and simulating
resemblance existing between mimic and model is extremely useful
either to the mimic only or to all the members of the mimetic set,
I am also convinced that no impartial judgment can possibly be
formed without carefully abstaining from all considerations about this
hypothetical and problematic usefulness, and exclusively regarding
the mimetic forms from a purely morphological standpoint, that is
to say investigating them according to the very same principles and
rules that have proved useful for the understanding of the colour-
pattern of insects in general, and the laws that we could deduce
from this study. To this conclusion we are logically led by the
observation, that mimetic patterns do not differ in any special feature
from colour-designs in general, but on the contrary agree with the
non-mimetie patterns, at least when these are embraced in a general
view. Solely when we compare the mimetic forms with their nearest
allies: the non-mimetic members of the same genera, do we meet
with certain cases where they seem to depart widely from the
common generic type, though even this by no means can be called
the general rule. By the adherents of the Mimicry-hypothesis this

879

apparent diversion from the original pattern is attributed to the
influence of natural selection, leading gradually to a perfect though
wholly superficial and spurious similarity with the model.

In order to be able to accept this hypothesis, it is obvious
that we are obliged first to prove the assumed deviation from the
primitive common type of the genus or family. We ougbt to abstain
from accepting it a priori as a fixed truth, but should try to recon-
struct the original common genus- or family-type of colour-
design by a perfectly impartial comparative investigation of all the
existing members of the group, mimetic as well as non-mimetic,
judging them exclusively after the features of their markings, without
the least regard to any biological profit these markings might possibly
procure them.

The value of these considerations can best be appreciated by their
application to a few concrete examples.

In the famous paper of Barres on the resemblance between members
of the Pierid genus Dismorphia (Leptalis) and certain South-A merican
Ithomiids and Heliconids, the author figures a perfectly white species
of the said genus, side by side with the mimetic forms, and expressly
states that this represents the original type of that family. It neces-
sarily follows that he considers the mimetics as widely deviated
from this type. Punnett, in the chapter on “Mimicry Batesian and
Müllerian” of his valuable critical review ‘“Mimicry in Butterflies”,
expressly puts forward that this is the current view among the
supporters of the mimicry-theory, where he says: “We come back
to our Pierine, which must be assumed to show the general charac-
ters and coloration of the family of whites to which they belong”...
and “If however they could exchange their normal dress for one
resembling that of the Ithomiines”. (The italics are mine).

Doubtless Barns did not for a moment presume that the case
might as well be exactly the reverse: the mimetics representing the
more original, least altered forms, while the whites, under the pre-
vailing influence of albinism, have considerably departed from the
primitive condition.

To make a choice between these two opposite views, we must in
the first place undertake a careful and complete investigation of the
various colour-patterns of all the members of the genus Dismorphia
and different other genera of Pierids, and after that come to a clear
understanding about the real nature of the differences between the
mimetic and non-mimetic forms.

These differences can be summarized under three heads: those of
pattern, of hue and of shape.

880

Beginning with the first, we may start with the assertion, that a
really objective analysis of colour-patterns necessarily involves the
exact consideration of the whole complex of markings in all its
details. So we must as well pay attention to the underside as to
the upper surface, and attribute the same importance to those features,
in which the mimics differ from their models as to those in which
they agree with them. Viewed from this standpoint (which up till
now has very rarely been observed), we easily come to the con-
clusion, that all the elements, which enter in the composition of the
pattern of mimetic forms, can be traced back to those of their non-
mimetic congeners, and therefore may be counted among the cha-
racteristic features of the genus (or family) to which the mimics
belong.
_ The same remark holds good for the particular hues the mimics
display, and even for the apparently aberrant shapes they sometimes
assume. When e. g. the mimetic Dismorphia’s differ from the
majority of the species belonging to the genus by the greater
length and the more slender contour of their wings and body,
the question if such a form of butterfly might really be regarded
as aberrant, has carefully to be considered, instead of being
accepted as solved. That it deviates from the “common” type,
is obvious, but since when has mere commonness been regarded
as a proof of primitivity? Do the Monotremes represent a widely
aberrant and deeply modified type of Mammals, merely because
they are (at present) restricted to two families? The broad square
shape of the majority of Rhopalocera, with their rounded hind- and
triangular forewings, including a short body, may far more probably
be itself a modification of the narrow-winged form with slender
body, such as we find in so many Sphingids and Heterocera, especi-
ally in an eminently primitive family as the Hepialids. Even among —
Rhopalocera themselves this latter habitus is no rare exception, for
we find it prevailing in several families, e.g. the Ithomiids and
Heliconids. So in matter of shape the resemblance between these
“models” and their Dismorphian mimics can safely be attributed to
their both having remained faithful to the more ancient form of
Lepidopterous insects. Its antiquity may even reach far over the
limits of this order, for the same contours prevail among many
other, less specialised groups of insects, e.g. Odonata, Neuroptera or
Trichoptera. Coming once more to the question of colours, it is
easily conceivable that white need not at all be regarded as the most
primitive hue in the Pierid family, several other colours: red, yellow,
brown, black, occurring just as frequently, especially on the under-

881

side of the wings. Only its prevailing tendency to spread over large
parts of the wing-surface and obliterate the original pattern by
albinistie discoloration, gives to the white hue such a prominent
place in the colour-scale of this family. But the same role is played
by all the remaining shades in different cases. In this regard it
deserves our attention that Dixny, the eminent Pierid-specialist, in
his paper on the phylogeny of their colour-pattern, does not start
from a uniformly white groundform, but from a dark-hued regularly
spotted type as Eucheira socialis.

Out of the numerous instances of Mimiery the astonishing case of
Papilio dardanus “with his harem of different consorts, all tailless,
all unlike (the male) himself, and often wonderfully similar to
unpalatable forms found in the same localities’? (PUNNETT), seems to
to me especially fit to test the validity of my views. As Punnett
states: “From (a) long series of facts it is concluded that the male
of P. dardanus represents the original form of both sexes”.

According to my standpoint the only “facts” on which such a
conclusion should be based, are features relating to the colour-pattern
of the male and that of the different females, compared to each
other and to those of their fellow Papilionids. But the above-
mentioned “facts” are of an entirely different and wholly inadequate
character, for they are connected with the mimetic resemblance of
the females to Danaid models, and their apparent divergence from
the bulk of Papilionids.

An impartial scrutiny of the relation in pattern between the male
form and the manyfold females should be undertaken entirely
regardless of any such resemblances. When conscientiously remaining
true to this principle, and exclusively applying the general rules for
the consideration of the colour-pattern, we are forced to the conclusion,
that the male form, instead of being the original, is by far the
most-modified.

The opposite opinion seems chiefly to have root in the unconscious
susceptibility of the human mind to first impressions. We are so
accustomed to associate the type of a Papilionid butterfly with the
swallow-tail-image, that we involuntarily consider those members of
the family, which by their tails, their characteristic markings at the
inner angle of the hind-wings, their yellow and black hues, come
nearest to this apparent ground-form, as the original representatives
of the family. But when we cast a general look over the whole of
it, we encounter numbers of species in which the tails are absent,
either in both sexes or in one of them, and in the latter case it
need not exclusively be the female sex, which lacks tails: P. memnon

882

for instance showing the opposite case. It should also be taken into
account, that in closely-related groups, e.g. the Ornithoptera, Anti-
machus and Druryia, which for good reasons are considered highly
primitive in many features, there is not the slightest indication of
tails. And as to the original groundform of Rhopalocera in general,
this can scarcely be supposed to have carried such prominent
appendages at its hind-wings.

Though all males of P. dardanus, together with some of its (come
mimetic) female forms, can be considered as corresponding to only
one type, this type undoubtedly is subject to very wide variation, and
the trend of this variability lies in the direction of the pattern of the
mimetic females. So we might consider those males which in the
extension and the design of their markings come nearest to the
females as the least-altered ones, and this view is found to coincide
with the general assumption, that absence or restriction of markings
is a consequence of their obliteration by the transgression of hues
from their original centre over neighbouring areas.

In the male of P. dardanus it is the yellow shade which gets
the supremacy, and more or less reduces the black markings to
total extinction. Consequently racial forms in which the black shows
a greater extension, like meriones, tibullus and triment, represent the
less modified forms of the male type. Comparing these variations
with the mimetic females, we see that they agree with them to a
higher degree than the more-uniformly yellow males, and that the
special features in which this nearer agreement shows itself, are in
fact precisely those details of pattern, wherein these females seem
to deviate from the assumed specific Dardanus-type, and to simulate
their Danaid models. |

Let us consider e.g. the narrow black border along the front-
margin of the forewing of the male butterfly and those female forms,
which bear the masculine type. Some specimens of (he typical Dardanus
show a rather imperceptible thiekening in the middle of this rim,
proximad to the discoidal nervure. In bullus this thickening is much
more striking, in meriones and antinorw it can touch the back-limit
of the discoidal cell, and in ¢rimenz it stretches as a black crossbar
in an outward and backward direction up to the dark marginal
area along the outer wingborder, thereby cutting up the yellow area
into an antero-external and a postero-internal part. E. Haase: Unter-
suchungen über die Mimicry auf Grundlage eines natürlichen Systems
der Papilioniden (Bibl. Zool. III, 1893) in his Fig. 4 on page 13,
numbers this bar as N°. IV + V. Comparison with the female forms
cenea, acene, niavina, ruspinae, trophonius, trophonissa, hippocoon,

883

hippocoonides, clearly proves that in all of them this same oblique
dark crossbar is equally present, but that in its distal part, outside
the discoidal cell, it becomes broadened by junction with the nearest
distal dark marking along the discoidal nervure (Haasr’s Terminal-
band). In consequence of this junction the bar occupies the proximal
part of four successive internervural cells (R,, M,, M,, M,: Haasr’s
VR1+4+2+43-4 4).

By the occurrence of this crossbar the light-hued middle area of
the forewing is divided into a smaller apical blotch and a larger
more or less triangular field along the hinder (inner) margin, the
latter passing without interruption into the light area which fills the
proximal part of the hindwing. This division is one of the promi-
nent features on which the similarity with Danaids depends. But
it would be quite inadequate to ascribe the occurrence of this bar
to secondary deviation from the original specific type under the
influence of natural selection in connection with Protective Mimicry.
For the same bar occurs in the females of a considerable number
of nearly allied species, e.g. cynorta, homeyert, jacksoni, ucalegon,
auriger, adamastor, agamedes, whose males, at least part of them,
show an uninterrupted chain of light-hued internervural spots,
which increase in size from before backward, and on the hindwing
blend to the light middle-field. These spots are separated from
each other by longitudinal dark striae, caused by the more or less
pigmented wing-veins. The anterior light spot in the apical field
of the forewing of P. dardanus is the first of the series, it occupies
the interspace between the roots of nervus radialis 4 and 5 (radial
fork) and we get the impression that this position has something
to do with its more marked persistence, by means of which it
remains visible, when the other spots are effaced either by light or
by dark colour-overspreading. Yet this apical spot also is not
exempt from reduction or obliteration: in some specimens of all
forms of dardanus, male as well as female, it may be reduced to
a mere speck, or be wholly absent (comp. the figure of the tropho-
nius-female on Punnetr’s Pl. VIII).

Nor is the above-named dark cross-bar restricted to dardanus
and its nearest relatives, it occurs as well in a number of other
Papilionids, e.g. hesperus, pelodurus, and others.

In numerous other cases the tendency towards the formation of
the cross-bar is equally present, but does not lead to such a con-
spicuous partition between an anterior and a posterior light area.
In epiphorbas e.g. the forewing is almost entirely black, with the
exception of a hooked central green part. The foremost leg of this

884

hook is formed by the light blotch separating the terminal bar from
the third discoidal one, the hindmost leg by three remnants of the
above-mentioned chain of light areas in the internervural cells.

Traces of the bar can also be remarked in theorine, latreillanus,
ausorti, phoreas, oribazus, charopus, which means, that a tendency
towards interruption of the chain of light blotehes is manifest in
numerous and very different members of the Papilionid tribe. Nor
is this tendency restricted to the forms with tripartite wing-design,
it occurs as well in richly spotted forms e.g. cyrnus, demodocus, rex,
mimeticus, ridleyanus and even in regularly checked ones as anti-
machus. In the majority of these last-named butterflies the tendency
towards interruption of the light chain only shows itself in a reduc-
tion of one or two members of this chain to specks, one im ant-
machus and mimeticus, two in rev.

Applying the above considerations to other details of the pattern,
we are always led to the same conclusion. Especially convincing is
the careful analysis of the pattern on the underside of the different
dardanus-forms, and its comparison with that of the upperside. It
shows us, that the median dark striae in the internervural cells
have much better maintained themselves on the underside, but that
their remnants can be more or less retraced om the superior surface,
especially on that of the hindwings. Consequently such a condition
of this pattern, as is seen on both sides of the hindwings of the
hippocoon- or trophonissa-form, where these striae are sharp and run
without interruption through all the cells (thereby agreeing with
zalmoxis and similar forms) may, as I said before, be considered as
primitive. In regard to these striae two remarks may be offered.
The first refers to the pattern of the upperside of the male hindwing,
on which the submarginal bar presents all degrees of variation,
from a broad complete, uninterrupted belt to a few widely separated
irregular black markings. In the latter cases the reduction has either
led to the persistance of three blotches: an anterior (exterior), middle
and posterior (internal) one, or has only left the two extremes.
When the middle one is still present, this very often assumes the
character of an internervural stria, and thereby betrays its allegiance
to the markings on the underside.

The second remark refers to the colour-pattern of a near relative
of dardanus, viz. P. eynorta (alleged forms included, as norcyta,
Jacksoni fullehorni, echerioides, cypraeofila etc). Here also a similar
striking difference exists between male and female, though the latter
occurs only in a single form, which shows a mimetic resemblance
to Planemaepwea. The similarity chiefly depends on the presence

885

of the before-mentioned oblique dark cross-bar in the forepart of the
forewing, and on the series of black median striae in the inter-
nervural cells of the hindwing. The male differs from the female
by the absence of the cross-bar; the medial area of the forewing
thereby showing the uninterrupted chain of internervural light spaces,
which diminish in size towards the apex. In contrast with dardanus,
the root-part of the hindwings in cynorta is dark, which causes a
closer junction between the central chain of light markings on the
fore- and on the hindwings. When comparing these dark root-fields
with their counter-parts on the underside, they are seen to be present
also there, but tinged in a bright orange-brown hue, intersected by
a system of darker lines which mark the wing-veins and the inter-
nervural striae. As these lines reappear in the distal part of the
wing, it is evident that they are interrupted in the middle-area by
the white discoloration. So we are justified in assuming that in more
original forms both the veins and the striae will run uninterruptedly
over the whole surface of the hindwings (on upper- as well as on
underside) and we find the affirmation of this assumption in a great
many forms of butterflies, belonging to different groups, and counting
among them models as well as mimics (e.g. Planema tellus and
Pseudacraea terra, see Punnett, Plate IV, Fig. 3 and 8). In the
nireus and oribazus-groups e.g. the upper surface shows a tripartite
colour-pattern with light (azure) middle-bar, and black inner and
outer region, but only the slightest traces of nervural and interner-
vural striae, while these latter are distinctly marked and in complete
array on the underside of many of the appertaining forms (e.g. nireus).

When therefore it can be proved for every single detail in the
pattern of mimetic forms. that it belongs to the stock of generic,
familiar or ordinal hereditary features by which the outward appear-
ance of the several members of a group is effected, there is no
reason left for ascribing the total effect of the combination of all
these details to the influence of Protective Mimicry. Nor can the
phenomenon of Polygynomorphism itself be attributed to this cause,
it has to be considered as a peculiar complication of sexual difference
in general, occurring in certain groups of butterflies, as e.g. Papilionids.
That some of the polymorphic females may profit by their accidental
likeness to unpalatable forms, is indeed very probable, but this profit
can merely be a consequence of the casual similarity, never its
cause.

The phenomenon of Polygynomorphism itself should be classed
with other cases of Polymorphism, either in connection with sexuality
or independent of it, as seasonal, geographical, racial plurality of

856

type. In the end, it is of the same nature as specific differentiation
in general.

So in Hepialus humuli the white masculine form has evidently
lost the primitive specifie livery, which is still preserved by the
female and by the Shetland-male. |

Though in general my opinions on these subjects disagree with
those of Haase, I feel much satisfaction in making the following
quotation from the concluding passage of his “Resumption” (p. 112) :
“The mimetic transformation was preceded in most cases by atavistic
phenomena from the side of the females, which in the beginning
reached back to the patterns of the nearest relatives, but as the
process proceeded, passed over to those of more distanced forerunners
and in this way procured the material for the mimetic adaptation’.

So Haase attributes the uniforms of mimetic females to hereditary
influences, instead of considering them as the consequence of BERDE
deviations from the primitive specific type.

Groningen, Nov. 1920.

Physics. “On the Equation of State for Arbitrary Temperatures
and Volumes. Analogy with Planck's Formula.” 1. By Dr.
J. J. van Laar. (Communicated by Prof. H. A. Lorentz).

(Communicated at the meeting of November 27, 1920).

§ 7. Some Notes to § 1—6.

It will be soon two years ago that I wrote thé first part of this
Article’); studies of various kinds prevented me from continuing
the subject, and not until now could I take it up again.

Before I proceed to the derivation of the equation of state, based
on the found general expression (6) on p. 1194 loc. cit. for the
time-average of the square of velocity w,’, expressed in w,* (in which
u, represents the velocity with which the considered molecule passes
the neutral point in its motion to and fro between two neighbour-
ing molecules), I will add a few remarks to elucidate and complete
what was treated before.

1. In the first place a few words about the transition of some
‘linear’ quantities to the corresponding “spatial” quantities.

If we have linear quantities, we can consider all our velocities
as the components of the relative velocities directed normally; as we
always imagine a molecule moving rectilinearly to and fro between
two molecules at rest. We know that u=2u*, and that the mean
value of the component of u”, directed normally, in its turn is the
third part of this, so that we have (cf. also p. 1195 loc. eit):

CANS EN in
Hence we may write:
1 Nan”) - l te
| m3 m (uy eae Sy ot ee
or also, denoting the tüne-average by the index t:

il Ten
bd oe Nm (u?)t.

1 ee
En Nm (un ht == 5

3
In this 4, Nm (w°y;(="/,pv in ideal gases) ='*/, RT, so that we
may henceforth write:

1) These Proe., Vol. XXI, p. 1184.

888

1 =
3 Nn} (ur nite RT,

by which the transition in question has been accomplished. In what
follows u? will, however, always simply be written instead of (w,?),,
with omission of the indices r and » and of the usual mean-value
dash (the time-average is then denoted by w,*); the real mean
velocity square wu’, if it should occur, being expressed by (w’). Hence
we have:

'
oo Ce oe nt Be (ome Teel re)

Starting from the relation (ef. equation (a) on p. 1189 loc. cit.)
1 1
ry Nm == Thee u + Nf(l—ao)’,

in which 5 represents that distance from the centre of the moving
molecule to that of the molecule supposed stationary, towards which
it moves, at which the work of the attractive forces reaches its
maximum value (hence at which the attraction changes into repul-
sion) — we shall find, after multiplication by */,, for the real mean
squares of velocity :

1 1 3
a Nm lu) == a Nm (u,°) + a N f(l—o)’.

In this } Von (u,?) = FE represents the total Energy of the system
(the atom-energies within the molecule being left out of considera-
tion). Further */, Vm (u,?) = L, is the mean kinetic Energy at the
neutral point halfway between the two molecules at rest (where
the attractive forces neutralise each other), ?/, N f(/—o)?= A re-

presenting the maximum work of the attractive forces. We have
represented this last quantity by 4, in our first paper, but as this
way of representation can easily give rise to misunderstanding, we
shall substitute 4 for #, in what follows. We have therefore:

Eli AE Ee el

in which accordingly "DSE SNe te, =| Ne
Hence in the joint neutral points # — L, + the total potential
energy of the attractive forces; and in the joint points o in the
immediate neighbourhood of the molecules, with which the moving
molecule will impinge, / will be = L, + the total increment of
the kinetic energy in consequence of the attractive forces.

The quantity A, therefore, represents the fixed, invariable (poten-
tial or kinetic) energy of the attractive forces, which rise or fall

889

of temperature cannot increase or decrease. Change of tempe-
rature can only modify Z,, and consequently also £. Henceforth
E—A may always be written for Z,.

The work of the repulsive forces, which become active after the
attractive forces in the above-indicated point o have ceased to act,
has been left out of consideration in what precedes, because A is
entirely unaffected by it. For the diminished kinetic energy is simply
converted into a corresponding increase of the potential energy —
now of the repulsive forces — which reaches its culminating point
when u has become = 0 (culminating point of the collision). We
have, therefore, only to do with the maximum work of the attractive
forces.

2. In the first paper it has been shown that the calculation of
the time-average w,’ leads to the relation tes (6) on p. 1194)

Mv Vl? + log (p + VL 7 Ze dees
UW === U,

9 6
log (p + V1+ 9") \ B+ a

This becomes after division of numerator as denominator by

log (p + V1+ ¢’) bos
(1 E Te) ‘i LEGE
: log é
Pig A
LOT
Hels 2
Mmerwheh loc: eit): p= Lay The distance 6 —s’, during

We m
which the repulsive forces will act, follows from

2f pase 2e
u, + — (l—o)* — — (o—s')? =0, or ut (1+?) =— (os)
m m 5 m

ketel)

U ZE Us

at the culminating point of the collision. Hence we have for / —o
and o—s':

m ; a m Gs’ 4 a fi
lco=u p era Os =u Vlg’ Le AE == Ken Y oe (d)
»

whereas for the times ¢, and f, is found:

ee m t fl Gee fl
t =loalp + WI ld Ee ale oet a Ce ols hd
58

Proceedings Royal Acad. Amsterdam. Vol. X XIII.

890

a. At high temperatures where, in consequence of the equation
l—o

2f
WV, p becomes small when u, becomes large (supposing
U, m

/—o always remains comparatively small, which is fulfilled here,
because we always consider solid (at most liquid) systems), (c), (d)

and (e) with log (p + Vp”) = log (p + 1) =g pass into:

lake
2d | |
uz ee a ye ise ire eet | 4 t, En ir J high (c )
en | ea ae a Tee oa =a en
14 hart wl Lo 6& t, p e temp.)
p é

so that in the case of weak collisions (in which «, the constant of
the repulsive force, is not very much greater than f, the constant
of the attractive forces), in consequence of ~ in the denominators
of the second terms in numerator and denominator of the above
fraction for w,?, these latter terms will prevail; hence w,? will approach
to */, u,’ (cy = 6). Whereas in case of strong collisions, when € is
supposed very large with respect to /, or when p gradually increases
somewhat on decrease of temperature, the first terms prevail, so that
then uw? will more and more approach to w,*? (c, = 9).

The ratios (a—s’): (/—o) and ¢,:¢, will be great for p small and
j:€ not very much smaller than 1; smaller on the other hand for
somewhat larger p, and e much greater than f.

With regard to /—o and o—s’ themselves, it may be observed
that according to the supposition /—-o always remains finite, so that

m ;
o—s' =U, Y= can become large at increasing temperature and
€

finite «. But this increase’ is restricted first of all by this,
that wz, can never become too great, because then our suppositions
(solid state with small values of /— 6) would not be fulfilled ; and
secondly by this that with comparatively large values of w,, in
consequence of which 6—s’ would become too large, e will gradual-
ly greatly increase, so that the molecules can never approach each
other more closely than to a certain minimum distance. Only in case
of very strong collisions (¢ very large with respect to f) 6—-s’ can
approach to O at not too large values of u,

mts
It holds for ¢, and ¢, themselves, that ¢,=@ ye will always
ati

. m
approach O at high temperature, while /, = 4 |e remains
€

finite — unless e is very large, in which case ¢, can even become
much smaller than ¢,.

891

All these relations are graphically represented by Fig. fa and
. Fig. 16, in which the values of wu are given in function of the time.

High temperatures (uo large, p small).

distances 5
distances

finite comp. large

Repulsion

es he a

& small tz finite tb
small very small
Weak collisions. Strong collisions.
(*‘/f not very great; u = 1/5 92; co = 6). (e/s very great, or T somewhat lower;
Fig. 1e. up? = Uy"; Cy = 3).
Fig. 14.

In the so-called “weak” collisions the velocity of the colliding
molecule will not diminish suddenly, but gradually. This is among
others fulfilled when the attractive force is supposed to change into
a repulsive one already before the molecules collide. It may then be
further assumed that the repulsive force does not become infinite
before the impact itself, so that in general — unless the velocity is
infinitely great — the two molecules will never be in absolute contact.
Hence there is always between o and a value s’ somewhat greater
than s (the distance of the centres at contact) a certain space, in
which the decrease of velocity in consequence of the repulsive forces
can take place; and there always remains — even at 7’=0— some
distance, however slight, between the molecules, because of course
/ cannot become smaller than o.

It is self-evident that this somewhat modified way of considering
the matter is only of a formal nature. Theoretically there is nothing
changed when s is displaced to 6, and s’ from a point within s to
a point outside it; now, however, we need not think the molecule
greatly compressed in the weak collisions, as we had to do with
the former way of considering the matter.

The two above figures also show clearly why in the case of
Fig. 1a u,? approaches to '/, u,’, and in the case of Fig. 16 to w’,.
For as e.g. in the first case the time, during which the repulsive
forces act, is so much greater than that under the influence of the
attractive forces, the time-average will lie in the neighbourhood of

58*

892

iu”. In Fig. 15 on the other hand the “action” (energy X time)
of the repulsive forces will be very much smaller than that of the
attractive forces, with this result that now the time-average descends
but little below w,’.

With decreasing values of wu, (lower temperatures) the relations
of Fig. la will more and more shift in the direction of Fig. 16 in
consequence of the continual increase of , so that c, will descend
already to a smaller value from the limiting value 6, before the
temperature has fallen to such a low value, that w,* is in inverse
logarithmic dependence to w,* (see below) — in other words before
the region of quanta proper has been entered.

b. At low temperatures p will appear to be great; i.e. on the

l—o_ 2f
supposition that in @=—V / the quantity /—o does not approach
u

5 m
O to the same degree as w,, but much more slowly, so that (l—o) : u,
will approach oo. It is even probable that /—o does not become
=0 even at 7'=0, but approaches to a certain small limiting
value. This is in agreement with the permanent decrease of the
expansibility at very low temperatures, and with the remaining of
a certain finite zero-point energy A= ?/, Nf(/—o)? at T=0.
Our equation (c) now becomes:

gt hn VI) Me
AES fog Ep Flap) == st oe : aa » (¢,)
(eps # yp’ den El glt een

log2p 8 log2p €

which at very low temperatures, at which p approaches to 0, will
become nearer and nearer to

p pens)
7 = 2 — ‘ee itt er we '
Uy log CD x ( + Dik V 4 (very low temp), . (c‚)

because the finite term /og 2 can then also be omitted by the side of
log (29? +1) in log (4p* + 2) = log (2p* + 1) — log 2. But the

Ut

factor 1 + 3 aye can be omitted only when « is very large with
é

respect to f (strong collisions), which is, however, not very probable
in view of what was found at high temperatures — unless at high

temperatures p is so small, that notwithstanding « is very much
1 ef

Jr .
greater than f, the quantity Is Ve would yet remain compara-
€

Pp

tively great.

893

But at all events in the case (c,) or (c,') we? (proportional to the
temperature) will be very much greater than wu,’ (proportional to
L, = E—A4). Both — temperature and kinetic energy in the neutral
point — approach to 0, but the energy very much more rapidly to
A (the constant zero-point energy of the attractive forces that finally
remains) than the temperature to 0.

The relations (d) and (e) now become:

o—s' f m 43 EE f
= Jip at = log eq: ; — VL
l—o é af t, log 2p é

so that for a value of /—o remaining finite, the distance o—s’ will
not be very much smaller than /—o, unless again « is very much
larger than f. The time ¢, approaches (logarithmically) to oo, while

1 m
at finite ¢, (== Vee the ratio ¢,:¢, will approach logarith-

mically to 0. These relations are represented by the subjoined figure.

Low Temperatures (ug small, p large).
distances
nmmr sm |
€ bs!
finite small
times

her Os aa Ae

od

6 é3

great finite

ig.

As has been said both w,? and w,? approach to 0, and the reason
that u’ (i.e. the temperature) does not remain finite at w,? = 0
— since there isa finite increase of the square of velocity (originally = 0)
in consequence of the attraction forces — but likewise approaches
zero, lies in this that the time during which this increase takes place,
approaches o (though it be logarithmically). In the neutral point
the attraction is — 0; when the moving point has got somewhat
outside the neutral point, there will therefore be only very slowly
question of any action of a force (which then increases further
linearly with the deviation x, see p. 1188 loc. cit.), hence of acce-
leration.

8. When we now proceed from wu to 7, and from u,’ to
L,= E—A, we have therefore in the case of high temperatures
rome M= */, 1," :

i.e. (ef. Note 1)
ziet De ej es nea any:
2 a6 ca 3
Hence also

Eee Sabine ok ae aan eee
or

d
fae) SS oe ier oe en :
.=(%) Fen ie

If uw,’ were = u,’ instead of = '/, uw,” (strong collisions, cf. Fig. 15),
then Z would have become = A+ '/, RT, c, ='*/, R=3B.

All this applies to monatomic substances. In the case of multi-
atomic (n-atomie) substances it is necessary to take besides the energy
of the attractive forces A also the atomic energy A’ within the
molecule into consideration, so that H becomes = L, 4 A + A’,
Now L,=3RT, while A’ = 3(n—1)RT may be put, when 3(n—1)
represents the number of supplementary degrees of freedom. We
then find H=A-+ 3nRT, i.e. cy = 38nR = 6n (Neumann’s law) ').

At low temperatures we have:

SONG OR pees ty shore
log (4 p* + 2)
according to (c,), when we denote the factor

(+FDO

af

by 4; hence because u,? gy? = (—o)? —, and thus '/, Nmu,? g? =
m

— Nm u* =
2

= Nf (l— 6)? = /- As

1) It should be remembered that for gases H = A + 1/,R (3 + «) T may be put,
in which « also represents the number of supplementary degrees of freedom (see
among others Botrzmann, Gastheorie IJ, p. 124—125 and 128). But here u
is simply = for multi-atomic molecules, so that for mon-atomic molecules n
is still = 0, for di-atomie molecules however ” = 2, for tri-atomic ones» = 3, etc.
Hence when the term A, which approaches 0, is neglected, and also the quantity
e introduced by Botrzmann, referring to the potential energy of the intramolecular
movements, H becomes =!/,RT(3 4 n) for gases, leading to cv =!/,R(8-+ n),

2
hence (with cpy—cy = R) to “= ô
Cv d+ n

correction quantity e to 3 +).

. (Bottzmann adds the above mentioned

af
may Af (lg) des
us Os TINGE ht = apt io

7:
When we reverse the relation found for RT, omitting log 2 by

(I—6)
because p? =

0

A
the side of the so much larger term /og Gan 1), where B—A =

= L, is small compared with A, and putting also 6 =1 (which is
fulfilled for large values of ¢: f), we get:
2A

A
eRT sl

E=A+ (9)

As we already remarked in our first paper, it is indeed exceed-
ingly remarkable that (with the exception of a few numerical factors)
exactly the same relation between F and 7’ appears here as was
derived by Pranck on the ground of the hypothesis of “quanta”
drawn up by him. For this it was only required to take into account
the time averages in the ordinary dynamic ,relations, which gives
rise especially at low temperatures to a considerable difference between
ui” (the time average of the value of w,’, which has greatly increased
under the influence of the attractive forces) and w,’, both being very
slight and approaching to 0.

From (9) follows with 7/,A: R=a:

ep
(ele + DE ae (Ei) oss gw (9)
; e Een 1 ge (e it —1)?

which exponentially approaches to 0 (via to aR a 5) when 7’

approaches to 0.

There is, however, one great difference with Puanck’s formula.
Apart from this that in Pranck’s work the well-known quantity
Nhr appears instead of ?/,A4 = Nf (/—o)*, so that hy would have
to be hy=f(/—«c)?), our formula (g) is only valid for very low
_ temperatures, and (/) only for very high temperatures. This is of
course only owing to this that (c,) only ensues from the general
formula (c), when y is supposed to be small, whereas with large
values of ¢ the relation (c,) results from it. Accordingly our (g) may,

1) Cf. what has been said concerning /—c under b) of Note 2.

896

therefore, not be applied in case of high temperatures, whereas this
may be done with Pxranck’s formula: the latter holds (at small
volumes) both for low and for high temperatures.

It is, however, remarkable that if (g) were valid for high tempera-
tures (which is not the case according to us) H=A+3RT is duly
obtained as limiting value for Z, identical to(/). Our formula, from
which (f) ensues for high temperatures and (g) for low tempera-
tures, seems to be more general, and the approach to (f) takes
place in a somewhat different way than with PLanck’s formula.

At any rate it will have to be assumed — if p is to be small
at high temperature, and large at low temperature, and if Ais not
to become =O at 7'=0 — that with condensed (solid) systems

(/—o)? changes only comparatively slightly; and that it does so in
the same degree as the frequency v. Then PLANcx’s quantity 2 would
be related in a definite way with the constant of the attractive forces
J (being in its turn again in relation to e°‚ when e represents the
electric elementary quantum), and in consequence of this also with
%/,, at the absolute zero. There are very strong indications for this:
particularly the undeniable connection between the so-called chemical
constant and also the constant of the vapour-pressure on one side,
and the quantity “/,2 on the other side, as 1 demonstrated shortly
ago in a Paper in the Recueil des Tr. Ch. of March and May 1920
— while it is known that this chemical constant in its turn is again
in relation with h.
I hope to return to this special subject later on.

4. We will now discuss somewhat more fully the nature and
the way of acting of the forces assumed by us between the molecules.

In connection with what was already observed above, we might
assume that the attractive action of M, e.g. rapidly decreases at a
certain small distance from J/,, and disappears at a certain very
small distance o, being replaced by a rapidly increasing repulsive
force, which for «= s, when the moving molecule P would touch
the molecule M,, would become infinitely great. (Cf. further what
was already said on this head under a) of Note 2).

Thus no two separate forces are required, nor two separate Virial-
parts — an Attractive-Virial part and a Repulsive-Virial part —
but only one; which point of view was already set forth by me
some twenty years ago.') The difference with the assumption in the
first part of this paper lies, therefore, chiefly in this, that then the

1) See Arch. Teyler (2) T. VII, 3ième Partie, p. 1—34 (1901): „Sur l’influence
des corrections etc.” (particularly p. 28 et seq.).

897

attractive force continued to increase up to 6, after which it sud-
Total force F.

/; fa

Fig. 3.
denly (hence discontinuously) changed into a repulsive force, with
another constant of intensity ¢ than that of the attractive force vie
whereas now we suppose a continuous change of force at o with a
single constant f.
Analytically this may be expressed — as far as e.g. the action of a
force, exerted on P by M, is concerned —- by a formula of the form

: |,—6,—2

i, = (el, =F 2) pen aes (1a)
in which «= OP, and the indices 1 all refer to distances from M,,
measured towards the left; and this instead of simply PF, = /(e,—
—(/,—2,)) as we put formerly (loc. cit. p. 1188 et seq.), i.e. the
attractive force proportional to the distance from the moving point
P to the boundary of the sphere of attraction 9, (of M‚), so that
F,=0, when P lies on the boundary of this sphere or outside it.
In consequence of this the attraction, after having reached a maximum,
again becomes = 0 at 5, (hence (tr = /,—o,), reverses its sign, and
again changes into a repulsion, which would become infinite at s,
(« =/,—-s,). From the other molecule .M, P is subjected to an
attraction

’
ies &

: l,—o,+e
eee a) cares, (15)
in which # is again = OP, and the indices now refer to distances

from M,, measured to the right.

Hence after some reductions the total action exerted on P to the
right (see Fig. 3), (with omission of the indices, because /, = /, = /,
etc.) is now found to be:

Ff Ff! |. Be Ab lef)
(ls)? — a?
instead of simply (= F — F,=/. 2x, as before (p. 1188).

898

It is self-evident that the total attractive force will become = 0
somewhat earlier, when P moves towards M,, than at 6, (when
F, acts alone) — it does so at o', or simply o’ — because the
attractive force of JM, acts in opposite sense. In fact the above
quantity becomes = 0, when
tt = V (l—s)* — (gs) (6 —s8) = V (l—o)* — (0 +. o—2l) (o—s) = lo’

As in the case under consideration the molecule P will always
be within the spheres of attraction of the two molecules M, and M,,
2l is always <o-+s, hence a fortiori U <p + 6 (cf. p. 1187 Lc).
The value of z, is therefore < ]—o, i.e. F becomes — 0 in 0’,
on the left side of 6, *).

However, all such functions have the drawback, that the further
integrations become impossible to carry out by means of closed
forms; for both at high and at low temperatures (u, large or small)

x

the term of work "nf in Ve Deen Fdx can never be con-

sidered as permanently small with inci to wu,” between the limits
«= 0 and «=s’. For in the end (at the culmination point of the
collision) the quantity under the sign of the root becomes = 0 in
both cases (high and low temperature), hence the term of work
under consideration of the same order of magnitude as w,*. And at
low temperatures, which is justly the most important case in our
considerations, that term is almost everywhere of the order of
magnitude w‚* — except in the neighbourhood of the points O and
somewhere between o’ and s’, where this term becomes = 0 (Cf.
Fig. 3).

For this reason we were obliged in our first paper to consider
the attraction and the repulsion separately, and to assume, instead
of the course of F drawn in Fig. 3, a force which continues to
increase in direct rativ to w as far as o,, after which it suddenly
changes into a repulsive force, which likewise increases linearly as
the distance from P to 6, (P now thought on the righthand side
of 6,). This renders the integrations easy to carry out, and does not
touch the nature of the matter.

If it is thought desirable to avoid the introduction of a so-called
“sphere of attraction” — which at the same time offers the advan-

1) When the distance 7 of the molecules becomes too small, F will not first
become positive on the righthand side of O, become =O in oc’, and then negative
— but at once negative, i.e. there is already immediately repulsion on the right-
hand side of O. The same thing applies of course to the left side. We shall
return to all these different cases in our next paper on the calculation of the Virial.

899

tage that the assumption of a transition case (see p. 1186) becomes
unnecessary (viz. the case in which the moving molecule is always
within the sphere of attraction of J/,, but not always within that
of M,) — a plausible law of attraction must be substituted for g,—/, 4+ «
and 9,—/,—wz in the expressions for F,, and F,, so that we havee.g.:
| ge ae A

Gay eae fase!

through which we obtain with small values of a:

an \ x Se o—8
Be ea aca)

eg
In als (J—o) (l—s)

Fat inn f |» oP | 2
ml—s|l (l—a)(l—s) Hls Lo) (2)

i.e. again proportional to «. This first proportionality and the corre-

sponding quadratic form of the term of work [Fue continues to

exist whatever form is given to the expressions of the action of the force.
According to DeBrr') the exponent » would have the value 9
(for anomalous “Dipol” gases n would be =7 on the other hand;
cf. the note on p. 183 loe. cit.).
But also the above forms of F, and F;, are in a still greater
degree subject to the drawback, that they lead to integrations which
it is impossible to carry out in the further calculations.

5. However — without having recourse to the dualistic law of
force (one for the attraction and another for the repulsion) which
we have chosen for practical reasons — also (2) might be used for
the calculation of

le’ ls’

1 mens
Ri fm ri [vw Fre de, ed 100) (8)
0

daz
(==
Vu’ + w
0
L

in which wo, = — | Fdx; provided one is satisfied with a certain
Me

0
approximation in the logarithmic expression which is then obtained
for w,. We find namely:
2 Ls)’ — w?
eg 4. (4)
m (/—s)?
1) Desye, Die v. p. Waars'schen Kohäsionskräfte, Physik. Zeitschr. 21, p. 178— 187
(1920).

900

in which « changes in the above integrations from /—s’ to 0. And as
s’ is always >-s (only for an infinitely large value of wu, could s
be reached at the culmination of a collision), /—s’ is always < /—s.
Kspecially at lower temperatures, at which s’ remains comparatively
far from s, (/—s’): (/—s) can remain considerably smaller than 1
even at the extreme value of z. (If eg. l=1,2s, s’=1,1s, this
ratio becomes already '/,). We may therefore write in approximation
for the logarithmic term:

loo( 1 -— cs) Ze es et
(/—s)’ (ls)? 2 (l—-s)‘

so that with

(9 — s) (6—s)
Pader: . . ° ° 65 ° Fy . (5)
the following form is obtained for oi:
ER NS (1 x ree ‘a
Wy, = a tf) [ =f) (l—s)? an oe ee ( )

For the form under the sign of the root may therefore be written :

| fas 2
ws LE toer | |= we? Utp
2

Aa

Ls 2f
when again, as in the first paper, ee is put, and further
Us, m
. . x
y is substituted for ja Then:
Is’ l—s'
Ls l—s

ls (° dy

Ae (te) fra. dy.

Jay's

For the form under the sign of the root (1—v2,y?) (1 + w,7?) may
be written in this, when
w, — w, =p (le) ; vw, vw, ='/, PO,
. . . w
so that this form with yw, =z passes into (1—z’) ( +— Z|,
w,
which becomes with z=cosw:

3 Ws Î als ae os Ws
sin? W (1 + — (1 — sin’ w)=' sin wl = — sin ‘w )
w, ww,

0,
. dz
For dy we have further —— = —

1
Vw, Vw,

sin w dw, so that the

above integrals pass into

l—s BA
== —
u Vw, w ite, ln ‘1—F sin? wy a

0
l—s w u en
uw = — ef se V1— BF sin’? w dw,
Vw, w,tw, t
‘am

w,
w, + w,
to the limits of the integrals evidently zis also = O for y = O, hence
wy ='/,~7. And as at the upper limit w,? + w, becomes = 0 (culmi-

when =k? is put (hence 4? is always <1). With regard

nation point of the collision), also (1 — 2”) (1 + ze )=0 hence

z=1,y=0. Thus we have, after reversal of the limits, in conse-
quence of which the minus signs drop out:
Ig 7

sae frm vbw. ay
—s mu a dw ats 0
= jie Vw cians Ay pee te Ip 7 ;
Ly 1 10 w 1 {x
Aw
0

when for ¢ its value is substituted in the expression for u,?. Follow-
ing LrGENDRE and denoting the complete elliptical integral of the

Yor

d
1st kind, vin. [= by #’, or singly F, we have also:
0

Ig 7
2

Pp m w, + W,U es
t = —______ — FF, >= — — Tw Aw.dw,
les el iy, > F fo w Aw.dw
0

m l—s
2f is substituted for —— (see above). We have for the
; u

when pV
lo
modulus 4:

a es ee ‘1, [p(l—a) + Y p*?(1—a)* + 2a] .

WW, p Vp(l—e)' + Ze
when we calculate the quantities w, and w, + w, from the above
expressions for w,—w, and w,w,. Hence we may write:

1 1
kid MA ver Lj

2 va 2a
1 + —_—
p* (l—a)’

so that at low temperatures (large values of @) £* is always near
1 (provided a <1, in which case the + sign is valid).
We must now still reduce the last elliptical integral (the one with

902

sinty) to that of the 1st and the 2rd kind. According to known
formulae of reduction') we have:

D
: 1—k dp 2k?—1
for wAw.dp= | fz “+ aA dp sin eos pAw |
0 0

hence

Yom

eeu 1fl1—k? 2k?—1
f si WA w.dw = 5 Dek + a E |,

0

when the complete elliptical integral of the second kind, viz.
Ip 7

Jere is represented by Z. Hence we find finally :

en en ee RA ee ;
pe Pope SO oe Le eee es

because

p 2k*?—1 w,
mn = —, and kn
Vw, +w, VY p(1—a)? + 2a l—a w,-+w,

We shall now compare the found formulae (7) with those found
before, and again in the two limiting cases: high and low tempe-
ratures.

At high temperatures (p small) £7 approaches '/, (if a < 1), so that
then (7) reduces to

B=") ys epee ws? (lagh temp.);— “or ee
instead of w,2—7'/,u,? (weak collisions), as we found before. The

1) See among others Duriee, Th. der ellipt. Funct., p. 65, formule (29), i. e. (with
u =0,m =0)

sin Wp cos A yy fi _—_— 2 (1 nf" en : Ee vn fe ae = 1

from which the Lanett with sin*) can she expressed in an the others, that
with sin? being expressed in Fy and Ey by the formula (see p. 69)

Le
„ (ae wap ri
Aw

0
as can be easily verified by differentiation, after 2v=W1—k?sin*) has been

put everywhere in the denominator. (ne integral to be reduced by us then becomes

y
{> wy — k? sint p aw).
Aw
0

903

fall of the velocity during the action of the repulsive force —
expressed as function of the time — is now less great than in fig.
1“, so that the descending branch will be much more horizontal.
The natural consequence of this is, that the time average gets much
nearer to w,?. (c, would now become = '/, X °/, R = 4’/, instead of
6). However — the above calculation is certainly questionable at

high temperatures, because then log (2 re) may certainly not
—$

be expanded into a series, as at the culmination point of the impact
x would become —/—s(s’ = s). The expansion into a series up to
x* used by us, gives a too great value for w‚, hence also a too
great value for w,?. Instead of rather abruptly, the damping of this
exceedingly great velocity would take place during a much too long
interval — so great even that s’ would lie far inside s, which ig
of course impossible.

At low temperatures (p great) on the other hand there can be
no objection to applying the expansion into a series up to x*, because
then the velocity is so small that it will be reduced to O already
within a very short interval. Now the modulus & approaches to 1,

Wore
3 .

hence L/ of cosap dp = (sin we, i.e. also to 1 ; but F will approach to

0
d
Jae = log tg (45 + by) = log w—log 1,i.0. to log oo. As, however,
Li

at the same time 1—<4? approaches 0, we must examine what value
(l—k*) F assumes in (7), when 4? is near 1.
: 4
According to a well-known theorem’) /’ approaches to log ZE
a a
in this case.
Hence we get for ¢ and w,?, when & approaches 1, from (7):

1) Cf. among others Lamp, Treatise on Hydrodynamics, p. 170; Gay.ey, Ellipt.
funct., Art. 72; MaxweLL, Elect. and Magn. I, p. 311—3816; Durèae, p. 190
et seq., particularly p. 213; KircnHorr, Vorl. p. 270; etc. Better than Duriax’s
derivation, which is based on LANDEN’s transformation, is KirncHHOFF’s beautiful
derivation. The latter is founded on the splitting up of the integral into two parts, viz.

‘ar Uy Nar

f = af Ee J , in which 6 is a small quantity, which is, however, supposed

0 0 Ind
to be great with respect to W1-k? But in both derivations only the limiting
value of F is reached.

It is in my opinion a better method to start from Jacosi’s_ relation

1 4 m u
t = ——— log ———— Ce U : p
V1—a V1 —k? 27 3 (1—k ) log VTE
because ME approaches 1, and 1 may be omitted by the side of

2°—1 E 4
RO SRF Now from (6) follows for large values of

gere

ih a Ee:
fo et Ae ps ee Se
zl ai ne Pe
i 16

7 = Paap: log Een

1 32 (1—a)’
ee a ee,
2V (1—a) ee en : i) abies

4
so that we obtain with Ian

2

sn p „(low temp.) . .- (7°)

3 a

i == ies
32 (1—a)’
log | ———- p'
a
log qin)
F = — —— F’, in which F’ refers to the integral with the complementary
”

modulus kh’ =W1-—k*, and gq’ is one of the auxiliary quantities q and q’,

Ma (1 12 16 tc.
introduced by Jacostr. From the relation yk’ — Pind orde ree)
1+ 2q'+ 2q'*-}- 29" 4 etc.

1+ q%+4" ene

14 cia ip ) ‚from which
1+29¢'+2q‘+...

ele

Dal
SN me ne …. |. And from this follows:
13

‘ | 4 1 ' U
ma en Benen

1
follows first of all — k= 9)
i

128

1 1 9
Through expansion into series #'' — „rf! ge Tae ae + BEE is easily

1fgrc

dw F' 1
derived for Ff" = ,. So that from A= — —logq'
V 1—k? sin? wp [4% 2
0

1 9 4 1 EBser
finally ensues #’ = (: + mo Ee mn log oe ee dt pale

A ll
or approximated #’ — (2 + — ze) (tes 5 are | } the limiting value of which

4
is evidently log i

We may still point out that the auxiliary quantity q always remains very small.
q is=O0 for k’=0, but q’ is only 0,043 for k’ =1/.V2 (the same for k and q).
It is to this fact that the exceedingly strong convergence of the Jacosi series for
elliptical functions is owing.

905

A p'
Again t approaches logarithmically to oo and w;* to EERS wen,
ee
just as in (¢,), derived in $ 3 with two separate forces.
In order to render a comparison possible, we must now again
introduce the maximum work A performed by the attractive forces.

From (4°), i.e.

af xv a «a
(ls VL = 9) SS ee
mk [ EEN asl
tollows that this will be maximum, when ‘8 ee so that
(J—s)? a
2 En
(o) == =( ln

Multiplied by */, Nm, we get oe (Cf. Note 1)

TS 3
Nf (l— = = ==.
l—s)? 2
As further g? ee eae we get:
u. m
32 (1—a)*

2
= 64 X ed.

32 32 (1— a)
1! WN,
[2 4¥m x

peu,” = Nf(i—s)’.

Thus we find for 1/, Nm u; IRT, because '/, Vmu,?=?/,L,=
==, (EA):

1 2 16 <
RT= a en tee)
64 « °/, A lo 64 A '
eee 0 Te
: 7 ahs 6L :
as against R7’=— ne ae the former assumption of two separate
oo
has ETS

forces (see Note 3). The coefficients are different, but the logarithmic
relation has remained entirely the same.

As however our former assumption leads to better coefficients
than the assumption (2) of Note 4, elaborated by us in this paper,
and as it does so both for high and for low temperatures, we can
in future, by the side of the latter procedure, also base ourselves
on the supposition — which is simpler for the calculations — of
two separate forces, in which the repulsive force begins to act at
x=—=l—o, after the attractive force has reached its highest point.

I hope that the foregoing Notes go to clear up some of the diffi-
culties that might have presented themselves in the reading of my

59

Proceedings Royal Acad. Amsterdam. Vol. XXIII.

906

first paper.') Now we will proceed with the task which we had
set ourselves, and examine the Virial of attraction and of repulsion
with a view to the drawing up of the equation of state in case of
small volumes, especially at very low temperatures.
(To be concluded).
La Tour près Vevry, Autumn 1920.

I gratefully express my thanks again to the van ’r Horr-fund,
which has greatly facilitated the execution of this work.

1) Though not all the objections, which some time ago Prof. LORENTZ was so
kind as to communicate to me in a letter, may have been removed by this paper,
yet | hope that some have been solved. Nobody can be more fully conscious of
the great difficullies that are to be surmounted here, than the author himself.

In the autumn of 1919 I had the privilege of having a discussion with Prof.
EHRENFEST — to whom we owe the so important theory of the Adiabatic
Invariants (1916), which theory was later so felicitously continued by BuRGERS
(1917) and Krurkow (1919—1920) — on the contents of my first paper. He
advanced, among others, the objection that not all the molecules on approach
to other molecules would come in collision, after which they would again move
away from them, but that some of them would remain for a time in the
neighbourhood of them. This is perfectly true, but in case of gases we should
then have to do with association, a case that was purposely left out of conside-
ration by me as an unnecessary complication. But as we have to deal here not
with gases, but chiefly with solid bodies, where the molecules only move to and
fro between the neighbouring ones, this complication is, indeed, quite excluded.
Besides already for a long time all the more recent theories of structure have
rejected the idea of association in the solid, crystallized state, so that we are
justified in leaving it quite out of consideration. But in my opinion there are greater
difficulties, of an entirely different nature, to which I hope to return later.

Physiology. — “The function of the Otolithes’. By Prof. R. Maenus
and A. DE KLEYN.

(Communicated at the meeting of Sept. 25, 1920).

In the course of the last half century an infinite amount of literature
has appeared upon the functions of the vestibular organ. From the
first, anatomical research rendered it probable that a sharp distinction
had to be made between the sensory epithelium in the cristae
of the semi-circular canals covered by the so-called cupula and
which can move freely in the endolymph, and between the sensory
epithelium of the maculae of sacculus and utriculus which, covered
by the otolithes with their greater specific weight, appears specially
suited to react upon the greater or lesser pressure of the said
otolithes.

But, whereas our knowledge of the function of the semi-circular
canals is fairly extensive and, moreover, the anatomical data agree
fairly well with the clinical and experimental data, this is by no
means the case with respect to the knowledge and theories regarding
the function of the otolithes.

This is due to various causes. If, as has been supposed in particular
by Macu and Breuer, the function of the otolithes is determined by
the greater or lesser pressure upon the sensory epithelium beneath,
we may expect that the otolithes will have some influence upon
those reflexes which come into play by changes in the position of
the head, and that their influence will continue as long as this
position remains unchanged and the pressure of the otolithes is constant.
Or, in other words, that the otolithic reflexes are more particularly
tonic reflexes. Up till a few years ago, tonic reflexes of the labyrinth
were known only in the form of compensatory positions of the
eyeball, and therefore the function of the otolithes had to be studied
exclusively from these reflexes. As, however, our knowledge of these
positions was still far from complete, and sufficient investigations
had not been made, it is obvious that the literature on this subject
will contain opinions of a more or less speculative nature. Moreover,
the influence of the clinique was inhibitory. While, clinically, the
different vestibular reactions upon (rotatory) movements were in-
vestigated more and more carefully and began to assume an ever-
increasing importance in the diagnostics of the diseases of the labyrinth,

59*

908

in physiology also attention was concentrated almost exclusively upon
this species of labyrinth reflexes. Barany’s attempt to include the
compensatory positions of the eyeball in clinical research was not
imitated.

Besides by pressure, it is a priori very well imaginable that the
otolithes might react upon motion, if hereby the specifically heavier
otolithes by reason of their greater inertia undergo slight displacements
with respect to the underlying sensory epithelium. Macu and BrEUER,
upon purely theoretical grounds, believed this to be the case with
the labyrinthine reactions upon progressive movements. Experimental
data on this point were lacking, but, as it appeared to be physically
impossible that the canals played any part here, the cause had to be
ascribed to the otolithes. As will appear below, however, the opinion
held by Maca and Breuer, namely that for physical reasons the
canals cannot have anything to do with this, is erroneous, while
other experimental grounds will be furnished for the theory that in
the reactions upon progressive movements it is just the semi-circular
canals that play the chief part.

As now during the last ten years various other, hitherto unknown
tonic labyrinth reflexes were found at the Pharmacological Institute
of Utrecht, it was natural that these new experimental data should
be used for the further study of the function of the otolithes. For
this purpose the following method was adopted. If the tonic labyrinth
reflexes depend upon the greater or lesser pressure of the otolithes
upon the underlying sensory epithelium, it may be expected that
these reflexes will be at their maximum or minimum at the same
moment as this pressure is maximal or minimal. Whether the reflexes
will be the strongest under the greatest pressure or under the least,
cannot a priori be stated. This will depend upon whether the sensory
epithelium is excited most strongly by the pressing or the pulling of
the otolithes; it might be very well possible that pressure of the
otolithes gives rise to a certain reflex, whilst pulling might also excite
another reflex action, though a different one.

Therefore, to arrive at as unbiassed a conclusion as possible, all
the tonic labyrinth reflexes were first examined quantitatively as
exactly as possible, and in particular in what position of the head
the maximum and minimum of these reflexes were found.

The tonic reflexes examined were the newly found tonic labyrinth
reflexes on the muscles of the body and the so-called labyrinthine
“Stellreflexe’, while further the already long-known compensatory
“positions” of the eyeball were carefully examined quantitatively
as to their maxima and minima. This investigation was performed

909

upon different animals; the compensatory eye ‘positions’ only upon
rabbits and guinea-pigs, as in the case of animals with quick volun-
tary eye-movements, such as cats and dogs, these reflexes are not
so well suited for quantitative examination. In the Anatomical Insti-
tute, Messrs. pe Burrer and Koster kindly determined for us by
various methods the position of the otolithes in the rabbit head,
and constructed a model from which, in each position of the head,
the accompanying position of the otolithes could immediately be
seen, so that it was now possible to trace whether with the maxima
and minima of the tonic labyrinth reflexes also a typical position
of the otolithes was to be met with. This proved to be the case,
as this paper will further show.

It was finally desirable to answer the question as to the correct-
ness of the supposition that the tonic labyrinth reflexes are otolith
reflexes, and at the same time to investigate whether this is also
the case with the reactions upon progressive movement, as il is
fairly generally assumed to be according to the theory of Macu and
Breuer. For this purpose a method had to be employed whereby
the influence of the otolithes was in some way eliminated, while
keeping the semi-circular canals intact. The reflexes of the latter
should then be present and the otolith reflexes absent. This method
of control, as will be seen later, also confirmed the presupposed
function of the otolithes.

The result of the above-described investigations, shortly summarized,
was as follows:

A. PosiTION OF THE OTOLITHES WITH THE DIFFERENT TONIC
LABYRINTH REFLEXES IN THE RABBIT.

1. Tonie labyrinth reflexes upon the muscles of the body.
(Extremities and neck)

a. On the extremities.

When the tonus of the muscles of the extremities is examined in
the various positions of the head, it appears that the extensors attain
their maximal tonus whenever the head lies symmetrically on the
skull, the nose making an angle of 0° — 45° upwards (individual
differences). When the tonus of the extensors is minimal, the posi-
tion of the head differs from the former by 180°.

If the model of the rabbit’s skull with its otolithes be now put
into the same positions, it will appear that with the aforesaid
maximum and minimum, the utriculus otolithes also have a very
typical position (the individual variations anatomically found agree

910

with tbe variations found experimentally); this is not the case with
the sacculus otolithes.

In the position whereby the extensors have their maximal tension,
the utriculus otolithes stand horizontally and are hanging on the
epithelium in the position of the minimal tonus, the utriculus oto-
lithes also stand horizontally, but press upon the sensory epithelium.

It follows, therefore, that it is not by pressing that the utriculus
otolithes exhibit the greatest stimulus, but when hanging.

Just the reverse is the case with the tonus of the flexors; this
tonus is strongest when the otolithes press and weakest when
they hang.

The influence of the labyrinth upon the tonus of the flexors is,
however, much less than that upon the extensors, and can be demon-
strated only by special means, so that there is no room for doubt
that at all events the strongest stimuli proceed from the hanging
otolithes.

Experiments upon rabbits, where the labyrinth on one side had
been removed, sbowed that one labyrinth is connected with the
muscles of both extremities, so that each utriculus otolith exercises
its influence upon the muscles of both extremities.

b. On the neck.

For this the same holds as has been stated for the tonic labyrinth
reflexes upon the muscles of the extremities, with but one single
fundamental difference. Whereas, from experiments upon rabbits
with one labyrinth removed, it appeared that each labyrinth is in
conneetion with the muscles of both extremities, this is not the case
with the neck muscles, where the influence is uni-lateral. From
which it follows that one utrieulus otolith is connected with the
cervical muscles of one side of the body only.

Therefore, the fact that both utrieulus otolithes lie almost in one
plane, does not imply that the removal of one labyrinth will not
be followed bv any symptoms, as indeed is seen by the turning of
the neck after a uni-lateral labyrinth extirpation.

2. “Labyrinthstellreflexe’’.

By this word those reflexes are meant by which the head is
brought back from any abnormal position to the normal again. The
centres for these reflexes, like those of the other “Stellreflexe”’, lie
in the mesencephalon.

917

Examination of the labyrinthine “Stellreflexe” of rabbits after
uni-lateral labyrinth extirpation has shown that the ‘“Labyrinth-
Stellreflexe” are superimposed upon the turning of the neck above-
described and looked upon as utriculus-reaction, in such a way that
they try to bring the head into such a lateral position that the
intact labyrinth is uppermost. In this position the ‘‘Stellreflex’’
proceeding from the intact labyrinth has its minimum.

Whenever, on the contrary, the intact labyrinth is found under-
neath, the ‘“‘Stellreflex’’ has its maximum.

If the head be placed in any chosen position, the animal will
not rest until it has got its head back as far as possible into such
a position that the ‘Stellreflex’” proceeding from the intact labyrinth
is as small as possible. There is only perfect rest when, as has been
said above, the intact labyrinth is uppermost. If the model be
examined to see in what position the otolithes now are, it will be
seen that the sacculus otolith stands horizontally and presses upon
the sensory epithelium.

On the other hand, the greatest unrest is observed when the head
is placed into such a position that the intact sacculus otolith hangs
from the sensory epithelium.

Thus, in the case of the “Labyrinthstellreflexe”’ after uni-lateral
labyrinth extirpation, it can be proved with certainty that the
maximum stimulation proceeds from the otolith when it hangs, and
the minimum when it presses.

The ‘“Labyrinth-Stellreflexe’” on the head, by means of which,
when both labyrinths are intact, the head is invariably brought back
from an asymmetrical to a symmetrical position, are explained by
the coöperation of the stimuli from both labyrinths. The head comes
to rest in such a position that the stimuli arising from the two
sacculi are equally strong.

From the above it is clear that the maximum positions of the
right and left labyrinths differ for the above-described ‘‘Stellreflexe”
approximately 180°, from which it follows that they must be sacculus
reflexes and not utriculus reflexes, since the utriculus otolithes lie
almost in one horizontal plane, while the sacculus otolithes form an
angle of 120°—140°—150° with each other.

Besides the ‘Sacculusstellreflexe” just described, by which the
head is brought back from asymmetrical to symmetrical position,
we must assume that there are other labyrinthic ‘“Stellreflexe’, as
the head is not merely brought into an undetermined symmetric
posture, but always into such a position, that the vertex is above,
the lower jaw below, and the mouth rather under the horizontal

912

plane. Whether, in this case, the sacculi or the utriculi are the cause
of these reflexes, cannot yet be stated with certainty.

3. Tonic labyrinth reflexes upon the eye muscles.
a. Vertical deviations.

In these tonic labyrinth reflexes one does best to proceed from
the symptoms after uni-lateral labyrinth extirpation.

After uni-lateral labyrinth extirpation, the strongest vertical deviation
of the eyes will be found when the intact labyrinth is downwards,
with the head lying on the cheek. The rectus sup. of the same
side and the rectus inf. of the crossed side are then the most strongly
contracted. When the intact labyrinth is above, the rectus sup. of
the same side and the rectus inf. of the opposite side are least
contracted. A tonic influence of the intact labyrinth upon the rectus
sup. of the crossed side and the rectus inf. of the same side could
not be demonstrated.

With intact labyrinths and a normal position of the head, the
stimuli from both labyrinths upon the recti sup. and inf. of both
eyes are equally strong, so that the eyes in this case show no
vertical deviation.

As the maximum positions of the labyrinths differ about 180°
(maximum position of the right labyrinth when lying on the right
side, and of the left when lying upon the left side), these reflexes
cannot be utriculus reflexes, as then the maximum positions would
be the same.

On the other hand, in the maximum and minimum positions of
these reflexes the sacculus otolithes have again a very typical
position; in the maximum position the sacculus otolith is hanging,
whereas in the minimum position it presses.

After a uni-lateral labyrinth extirpation the vertical deviation is
maximal with the maximum position of the intact labyrinth, but
with the minimum position it is very slight or absent.

At all events it is certain that in the minimum position of the
intact labyrinth there is no vertical deviation to the other side, from
which we may fairly conclude that with the minimum position of the
sacculus otolithes the stimulus is really little or none, whereas with
the maximum position, on the other hand, it is very strong.

Thus in this case also, as with the ‘‘Labyrinthstellreflexe’, it can
be proved that the stimulus is strongest when the otolith hangs, and
weakest or nothing at all when the otolith presses.

913
b. Rotatory Deviations.

In the rotatory deviations the relations are much more compli-
cated than with the tonic labyrinth reflexes hitherto discussed. A
fuller discussion would, however, claim more space than we have
at our disposal, for which reason we shall merely mention the
results which the different considerations have led to.

The rotatory deviations of the eyes found with the compensatory
eye positions may perhaps be explained by the following hypothesis.
The foremost sacculus corners have their own innervation, are bent
laterally and thereby lie almost in one frontal plane. Each sacculus
corner has a functional connection with the obliquus sup. and inf.
of both eyes. When the otolith hangs from the sacculus corner, the
oblig. sup. of both eyes are the most strongly contracted and the
obliq. inf. the most relaxed. When the otolith presses upon the
sacculus corner, it is the obliq. inf. which is most contracted and
the obliq. sup. most relaxed. As the sacculus corners lie almost in
the same plane, no distinct change in the position of the maxima
and minima are to be found after uni-lateral extirpation. As each
sacculus corner influences the oblig. sup. of both eyes similarly and
the obliq. inf. reciprocally, the rotatory deviations remain qualita-
tively unchanged after uni-lateral extirpation, and are reduced quanti-
tatively to about the half.

Thus, with the rotatory deviations, it is not clear that the hanging
otolith exercises the strongest and the pressing otolith the weakest
stimuli, but it seems as if stimuli, even though opposed, are caused
by hanging as well as by pressing otoliths.

SUMMARY.

By means of a model, constructed in the Anatomical Institute of
Utrecht, of the otolithes in their correct position in the rabbit-skull,
an examination has been made as to whether the different tonic
labyrinth reflexes might be otolith reflexes. Experimentally in all
tonic labyrinth reflexes the position of the head has been determined,
whereby these reflexes have their maximum and minimum. The
following conclusions were arrived at:

1. The tonic labyrinth reflexes upon the muscles of the body
proceed from the utriculi. One utriculus macula is connected with
the muscles of both extremities; but, on the contrary, with the neck
(and trunk) muscles of one side of the body only.

2. The ‘Labyrinthstellreflexe” are reflexes of the sacculus. Whether
the utriculi also play a part is not certain.

914

3. Compensatory positions of the eyeball.

a. The vertical deviations are sacculus reflexes and are caused
by the main portion of the sacculus macula. One sacculus macula
is connected with the rectus sup. of the same side and with the
rectus inf. of the crossed side.

b. The rotatory deviations are probably produced in the sacculus
corners, which have their own innervation.

Stimuli proceed constantly from the maculae and do not alter as
long as the otolithes do not alter their position with respect to the
horizontal plane. When the otolith stands horizontally, the strongest
or the weakest stimuli are excited.-

In the case of the sacculus otolithes it can, with respect to the
“Labyrinthstellreflexe’” and of the vertical compensatory deviations
of the eyes, be proved with certainty, that the strongest stimulus
occurs when the otolith is hanging.

For the sacculus corners, on the contrary, things are somewhat
more complicated, and the stinuli occur when the otolithes press
as well as when they hang.

As our investigation is at present concerned with the rabbit, the
above holds good only for this species.

B. Isolated removal of the otolithes in guinea-pigs.

As has appeared from this and former communications, the dif-
ferent labyrinth reflexes may be divided into the following groups.

a. Reflexes upon movement.

1. Reactions and after-reactions of ‘the head and eyes upon
rotatory movements.
2. Reactions upon progressive movements.
b. Tome labyrinth reflexes.
1. Tonic reflexes upon the muscles of the body.
2. “Labyrinthstellreflexe’’.
3. Compensatory positions of the eyeball.

As regards the reactions and after-reactions upon rotatory move-
ments, these have long been known and are justly regarded by all
researchers as reflexes, of the semi-circular canals.

It was demonstrated above that the different tonic labyrinth reflexes
are probably otolith reflexes, and also that different otolithes may
be held responsible for the different reflexes.

But little experimental research has hitherto been devoted to the reactions
upon progressive movements. For some classes of animals, however, we were
able to demonstrate certain reactions upon progressive movements dependent
on the labyrinths. As the following investigations have been carried out

915

upon guinea-pigs, the reactions found in these animals may be shortly
recorded here.

Lift reactions.

The animal sits in a normal posture upon a plank held horizontally. If the
plank be moved vertically upwards, it will be seen that at the commencement
of the movement the fore-legs are bent sharply and the head droops.

When the movement of the plank ceases, the fore-legs will be stretched
straight out, the fore part of the body is lifted, and frequently too the head
is bent backwards. In strong reactions the hind-legs act too, till finally the
animal stands upon its four extended legs. The reverse reaction takes place
when the movement is downwards. When the movement commences, the
extremities, and especially the fore-legs, are extended, and the front part of
the body raised. On the cessation of the movement, the fore-legs are bent
and the head and front part of the body droop towards the plank.

Muscular vibrations.

The animal is held vertically in the air with the head upwards, the thumb
and little finger of the left hand lie round the belly, the fore and third fingers
support the fore-legs, with the hind-legs resting upon the palm of the hand,
while the thumb and forefinger of the right hand rest upon the neck and
shoulders of the animal. The head is in the normal position. One must wait
until the animal is perfectly quiet and the fingers of the right hand no longer
feel any muscular vibrations in the shoulder and neck muscles. Then, if the
animal be moved vertically (up and down), or horizontally (ventrally, dorsally,
to right and left), the right hand during these progressive movements will feel
a distinct muscular vibration. Closer attention will reveal that here, too, the
“vibration takes place at the commencement and end of the movement.

The spreading of the toes.

The guinea-pig is held vertically in the air, the right hand under the arm-
pits with the palm of the hand turned towards the back of the animal. The
toes of the hind feet are. then carefully stroked together. If the animal be
then moved even very slightly downwards, the toes of the hind feet will
immediately spread apart.

The reaction can be demonstrated with most, though not with all animals,
and occurs at the beginning of the movement. If the animal be moved in
the same way upwards, the toes will also be spread, this occurring some
times at the commencement and sometimes at the close of the movement.

All these reactions upon progressive movements are dependent upon the
labyrinths, and are not visible after a double labyrinth extirpation. We cannot
enter here into details, neither can we discuss the precautions to be observed
in the investigation. These will be given in more detail later, when also
some other labyrinthic reactions upon progressive movements will be described.

As was mentioned above, Macu and Brever believed on theoretical
considerations that it was physically impossible that the semi-circular -
canals had anything to do with these reactions, and therefore came
to the conclusion that only the otolithes were accountable for these

916

reactions. These considerations, however, Macu and Breuer based
upon the presupposition that the semi-circular canals are a closed
system with firm walls and filled with fluid, so that no endolymph
currents could be expected in progressive movements. In this they
overlooked the fact, however, that the endolymph of the semi-circular
canals is connected by the ductus endolymphaticus with the saccus-
endolymphaticus which lies in the cranial cavity, and also that the
perilymph is not surrounded everywhere by a firm wall, but that at
two parts there are elastic membranes, viz. the foramen rotundum
and the foramen ovale.

From researches made with the help of a model constructed with
due regard to the above by Prof. Ornstein and Dr. Bureer, it
appeared that under these circumstances with progressive movements
endolymph currents might well occur in the endolymph.

Thus it remained an open question whether the reactions upon
progressive mutions are reflexes of the semi-circular canals or of
the otolithes.

It therefore became desirable to find a method whereby either
the canals or the otolithes could be isolated. The latter proved to
be possible by employing a method of Wirrmaack’s, whereby normal
guinea-pigs are centrifugated in ether narcosis at a speed of 1000
metres per minute. Previous to the centrifugation, all the animals
to be experimented upon were carefully examined as to all labyrinth
reflexes in accordance with a certain scheme, and the result recorded.
The same examination was repeated after the centrifugation and
successively on the following days, so that the complete historia
morbi of each animal was obtained in this way. A clinical diagnosis
was then made regarding the condition of the canals and the various
otolithes, based upon the above-explained views regarding the function
of the semi-circular canals and the otolithes. After this the animals
were killed, the labyrinths fixed, and later carefully examined
microscopically in series-sections. In this way, it was possible to
compare the clinical and the anatomical diagnoses with each other.

The results obtained may be summed up as follows; for particulars
we refer again to the detailed communication to be published later.

SUMMARY.

1. By centrifugation of normal guinea-pigs, according to WITTMAACK’s
method, it was found possible to bring about in many of the animals
tested a condition in which the labyrinth reflexes upon movement
are normal (reactions and after-reactions of head and eyes upon

AGNUS and A. VE INET

GUINEA-PIG 2, a.
Right sacculus.

GUINEA-PIG 2, d
Right utriculus.
Membrane partially t

roceedings Royal Acad. Amsterda

‚ MAGNUS and A. DE KLEYN: “The function of the Otolithes’’.

GUINEA-PIG 2, a. GUINEA-PIG 2, 6."
Right sacculus. Left sacculus.

GUINEA-PIG 2, c. GUINEA-PIG 2, d.
Right utriculus. Left utriculus
Membrane partially torn off.

Proceedings Royal Acad. Amsterdam Vol. XXIII.

GUINEA-PIG 8, ¢

ight sacculus and right utricul
ranes. The tossed off sacculus
sacculus cavity

GUINEA-PIG 8

Left sacculus and left utrici
branes. The tossed off saccult
cavity of the sa

II

Ss 3 )
GUINEA-PIG 8, a. GUINEA-PIG 8, 5.

Right sacculus and right utriculus without mem- letmantcnitemwithontemem brane:
branes. The tossed off sacculus membrane in the

sacculus cavity.

GUINEA-PIG 8, c. GuUINEA-PIG 8, d.
Left jsacculus and left utriculus without mem- Right utriculus without membrane.

branes. The tossed off sacculus membrane in the
cavity of the sacculus.

SENN WD ARE Lhe EVEL Bip ais!

GUINEA-PIG 8, e.

Tossed off right utriculus mem
posterior vertical semi-circu

ceedings Royal Acad. Amsterdam

. MAGNUS and A. DE KLEYN: “The function of the Otolithes”.
Ill

GUINEA-PIG 8, e. GUINEA-PIG 8, f.
Tossed off right utriculus membrane in the Left utriculus (and left sacculus).
posterior vertical semi-circular canal. Without membrane.

GUINEA-PIG 8, g.

Tossed off left utriculus membrane in the
posterior vertical semi-circular canal.

| Proceedings Royal Acad. Amsterdam. Vol. XXIII.

917

rotatory movements and reactions upon progressive movements),
while all tonic labyrinth reflexes of the position are lacking.

2. If these animals be kept alive for some days, and examined
every day as to their labyrinth reflexes, it can be seen that in some
animals this condition remains unaltered, while in others the tonic
labyrinth reflexes return partially or even wholly.

3. A histologicai examination of one animal, where a complete
recovery had taken place, showed that all the otolithes were in
place with the exception of one utriculus otolith, which appeared
to be injured. This last, however, was in entire accordance with
the phenomena found clinically. The apparatus of the semi-circular
canals was likewise intact.

4. In one guinea-pig which, after two days, showed intact labyrinth
reactions upon movement (reactions and after-reactions upon rotatory
movements and reactions upon progressive movement), but, on the
other hand, no tonie labyrinth reflexes, all four otolithes were found,
upon histological examination, to be torn off, and were found in
Other places iu the labyrinth, while the canals with the cristae
appeared to be intact.

It follows from the above data that:

5. The labyrinth reflexes on movement, and in particular the
reactions and after-reactions of head and eyes on rotatory movements,
are reflexes of the semi-circular canals, and may be excited even
when the otholithes are lacking.

6. The same holds good for reactions upon progressive movements.

7. On the other hand, the tonic labyrinth reflexes (tonic labyrinth
reflexes upon the muscles of the body, ‘“abyrinthstell-reflexe” and
compensatory positions. of the eyeball) are otolith-reflexes, which
cannot be produced after the destruction of the otolith membranes.

8. In many cases, directly after the centrifugation, the function
of the otolithes is temporarily suspended owing to the strong mechanical
influences upon the specifical heavier otolith membranes, even
though the otolith membranes themselves still lie in their right places.
The function is only restored after various lengths of time.

9. It thus appears from these and previous data, that the reflexes
upon movement (reactions and after-reactions of head and eyes upon
rotatory movements and the reactions on progressive movements) are
excited by the semi-circular canals, while the otolith apparatus must
be held responsible for the tonic labyrinth reflexes (tonic labyrinth
reflexes on the muscles of the body, ‘Labyrinthstellreflexe” and
compensatory positions of the eyeball).

„10. This naturally does not exclude that the otolith apparatus

918

can be stimulated also by certain kinds of motion (centrifugal force,
inhibition in rapid progressive motions).

Finally some microphotos are reproduced for the further elucida-
tion of the above.

Guinea-pig 2.

After the. centrifugation of this animal the following clinical diagnosis was
made: All the labyrinth reflexes were present in a normal state. As, before
the centrifugation, the animal turned its head to the left when held up by
the pelvis with the head downwards, it had to be assumed that the right
utriculus had functioned before the centrifugation rather more than the left
one. After the centrifugation no further difference in the functioning of the
two utriculus otolithes was found, so that it seemed probable that the right
utriculus had been injured by the centrifugation. Further it had to be expected
that all the otolithes, as also the semi-circular canals, were intact.

The histological examination revealed the following facts:

Semt-circular canals with cristae normal.

Right sacculus (Fig. 2a.) quite intact. The photo shows the right
sacculus greatly magnified; the sensory epithelium with the intact otolith
membrane can be seen.

Left sacculus (Fig. 2b.) also quite intact. In the photo the intact otolith
membrane can be seen slightly magnified.

Right utriculus (Fig. 2c.), as was to be expected, was partly injured.
In the photo the otolith membrane can be seen in the region of the greatest
lesion, the part of the membrane that is turned towards the semi-circular
canals is still lying normally upon the sensory epithelium, the other portion
of the membrane has been torn off from the sensory epithelium.

Left utriculus. (Fig. 2d.) quite intact. In the photo the sensory
epithelium can be seen covered by the normal otolith membrane.

Thus we see complete accordance between the clinical and the
pathologic-anatomical diagnoses.

Cavia 8.

In this animal it appeared after the centrifugation that all the labyrinth
reflexes upon motion, i.e. the reactions and after-reactions of head and eyes
upon rotatory movements and the reactions upon progressive motion, were
present in the normal way, whereas the tonic labyrinth reflexes were all
lacking (tonic labyrinth reflexes on the muscles of the body, “Labyrinthstell-
reflexe”’ and compensatory positions of the eye).

The clinical diagnosis was as follows:

Semi-circular canals with ampullae intact; otolithes all tossed off.

Histologically the following was found:

Right sacculus (Fig. 8a.): The otolith membrane proved to be entirely
tossed off. In the photo the sensory epithelium can be seen slightly magnified
without otolith membrane, while the torn off membrane can be seen in the
corner of the sacculus.

Left sacculus (Fig. 8b. and 8c): In fig. 8b the sensory epithelium of
the left sacculus can be seen more strongly magnified. Nothing is left of an

919

otolith membrane; the difference between this and fig. 2a., where a normal
membrane is present, is clear. In fig. 8c. the sensory epithelium of the
sacculus, without otolith membrane can also be seen slightly magnified,
while the-torn off membrane lies in the corner of the sacculus.

Right utriculus (Fig. 8d.) In this photo, more strongly magnified, the
sensory epithelium of the utriculus can be seen covered with some fragments
of the otolith membrane in granular form. (Compare fig. 2d. with normal
otolith membrane). The torn off membrane itself was found in the posterior
vertical semi-circular canal (Fig. 8e.).

Left utriculus (Fig. 84): We see here, slightly magnified, the sensory
epithelium of the left utriculus covered with a few granules. The torn off
‘membrane was also in this side found in the posterior vertical canal (fig, 8g.
with the posterior vertical and with the horizontal canals).

Semi-circular canals with cristae quite intact. (The torn off
otolith membrane in the posterior vertical canals).

Thus here again is the most absolute agreement between the
clinical and the pathologic-anatomical diagnoses.

Three other cases, not described here, showed the same complete
agreement between the clinical and the microscopical investigations.

Pharmacological Institute of the Utrecht University.

Mathematics. — ‘On elementary surfaces of the third order”.
(Fifth communication). By Dr. B. P. HAALMEIJER. (Communicated
by Prof. Henprik DE Vries).

(Communicated at the meeting of November 27, 1920).

Some remarks from professor Ferix KrrIN caused me to go once
more through my former communications on this subject *), which
investigation showed me that several places require correcting and
supplementing.

$ 1. For surfaces of the third degree with 3 or 7 real lines *)
there are systems of planes, which, as far as the real part of the
section is concerned, have only one line in common with the surface.
Only a very artificial interpretation would enable us to bring these
surfaces under our definition of F* (comm. l.p. 102 and 103). This
difficulty disappears when point 2 of that definition is replaced by
the following condition (also preferable for other reasons): All plane
sections which exist, are elementary curves, amongst which the third
order occurs, but no higher order.

With regard to the counting of lines, we prescribe the following:

A line a is considered triple (resp. double) in a plane a, if every
line 6 (Fa) of a is limiting element of a sequence of lines, situated
in one plane and each of which has 3 (resp. 2, but for no sequence 3)
points in common with F®, which points converge towards the point
of intersection of a and 6.

In all other cases a is considered single in a.

The number of times a is counted on #* we put down as 1, plus
1 for every plane in which a counts double, plus 2 for every plane
in which a counts triple.

Theorem: No plane section of F* is of the second order.
Such a section would have one of the following forms:
1. Isolated point.

2. Oval.

3. Two different single lines.

+. One double line.

') These Proc. Vol. XX, p. 101—118, 304—321, 736--748 and 1246—1253,
*) Line stands for straight line.

921

First case. Let A be the point and a the corresponding plane.
There exists a plane 3 with a section of the third order and this
plane passes through A as a curve of the third order has at least
1 point in common with every line of its plane. The curve in @ has
only A in common with «, hence this curve passes at the point A
from one side of a to the other. Then however the plane a divides
the vicinity of A on £* into two parts with only one common limiting
point (A), and this contradicts point 1 of the definition of F’.’).

Second case. Let a be the plane of the oval, a a line intersecting
the oval at two different points A and B and 8 a plane through a.
Suppose the curve in 3 is of the third order, then one of the points
A and B, for instance A, counts double as point of intersection
with a. This is possible in three ways:

The curve in 2 has a for tangent at A.

A is cusp in 8, both branches coming from the same side of a.

A is ordinary double point, two branches coming from each
side of « °).

The two first possibilities do not agree with theorem 1 p. 311
comm. 2,*) for in « A is ordinary point of intersection of the oval
and a, and in 8 we can find lines converging towards a without
carrying points of 4” converging towards A.

Remains the third possibility. The two branches departing from
A in « are connected both above and below «a. The sector which
forms the connection above « cannot have 8 for tangent plane along
a branch in #, for in that case an infinite number of lines in 3
would belong to F*- *) It follows that this sector crosses 8 twice and
this is impossible as it connects two branches situated on different
sides of 9.

We conclude that the curve in 8 cannot be of the third order,
hence it must obviously be of tbe second. The only condition imposed
on @ was that this plane has two different points in common with
the oval in a. On the other hand there exist lines carrying 3 different
points of #*. Let y be a plane through such a line and intersecting
the oval in « at two different points. In y the curve must be of the

1) An analogous case was minutely dealt with in comm. 1 p. 104 and 105.

2) In case the curve in @ consists of a double line through A and a single one
through B, we can at once find another plane through a with a curve of the
third order and without a double line.

8) The demonstration there given made use of point 2 of the definition of F5
only so far as sections of order higher than the third were excluded.

4) This also holds when the curve in / has degenerated.

60
Proceedings Royal Acad. Amsterdam. Vol. XXIII.

922

second order, but at the same time have 3 different points in common
with a line and this of course cannot be.

Third case. Let a be the plane, b and c the lines and A their
point of intersection. If we exclude the point A, then along the rest
of 6 the sectors of /'* meet either everywhere from the same side,
or always from opposite sides of a’). The same holds for c. Now
if the sectors meet from the same side of « both along 6 and c,
then an infinite number of lines of a is contained in /’*. If the
sectors meet from the same side along b and from opposite sides
along c, then, according to our definitions, 6 counts double in «,
hence the section would be of the third order. Remains the possi-
bility that along 6 as well as c the sectors meet from different sides
of a. Let d be an arbitrary plane, not containing A, a the line of
intersection of d and @ and B and C the points of intersection of
a and ce resp. 6. The curve in d crosses a at B and C and has
no further points in common with a. For a curve of the third order
this would imply that either B or Cis double point and the reasoning
used for the second case reduces this to a contradiction. Hence the
curve in d is evidently of the second order. On the other hand there
exist lines not passing through A and carrying 3 different points of
F*. Thus in a plane through one of these lines and not containing
A we have once more constructed an impossibility.

Fourth case. Let a be the plane and a the double line. Along a
the sectors of F'? meet either everywhere from the same side, or
always from opposite sides of a. The former is impossible as the
space in which we work is supposed to be projective, and the
latter would imply that through every line (4 a) of a a plane 8
passes with a double point on a. This obviously would mean two
lines in 8. Hence /#'* would contain an infinite number of lines, a
possibility excluded throughout.

This completes our demonstration.

From the preceding theorem follows that a plane « with a double
line a contains besides a single line 6. Let a and 6 intersect at A.
We proceed to show that along a (point A excluded) the sectors of

1) Every point of b (4 A) is internal point of an interval along which the
sectors meet either from the same or from opposite sides of « Excluding an
arbitrarily small open segment of b round 4A, a finite number of these intervals
exist, such that every point of the rest of b is internal to at least one of them
(Borer-theorem). From this the property under consideration follows at once for
the entire line & (excluded point A).

923

F* meet everywhere from the same side of a. Suppose a carries a
point P, such that the branches meeting on a at P are connected
on both sides of a. Then there exists a plane through P, not con-
taining a and in which P is double point. The reasoning used for
the second case (p. 921) again reduces this to a contradiction. Hence
every point (F4) of a is internal to an interval along which the
sectors meet from the same side of «. The note at the bottom of
the preceding page completes the demonstration.

Along a triple line in @ the sectors obviously meet everywhere
from opposite sides of a.

$ 2. In this $ we intend to give some corrections and additions
to comm. 3 (p. 736—748).

p. 740 and 741. The reasoning sub II (p. 740) is incomplete and
starting at line 3 (p. 741) to be replaced by the following: Let d,
turning round c, converge towards a, first from one and then from
the other side. In both cases the loop of the curve in d contracts
towards A, for if the loops converged towards a finite segment of
a, then each of the converging planes would contain 3 branches,
with only one common point (A) and breadths larger than some
finite constant. These would converge towards a single linesegment
in the limiting plane, which circumstance contradicts the assumption
that #* is a twodimensional continnum. Hence only the principal
branches of the enrve in d converge towards a.

We consider a certain plane d. Let AP, AQ and AR be the
branches departing in d on the same side of c, AQ really being the
middle one. The two semilines in which A divides a, are connected
on that same side of. « by a sector which crosses d along the
branches AP, AQ and AR successively. If d converges from the
one side towards «, the outside branch on the side of AP converges
towards a and turning d in the opposite direction, the branch corre-
sponding to AQ merges in a. In both cases this is a principal branch
and as one of the outside branches belongs to the loop, there must
somewhere be a change from principal branch to loop branch, and
this means a degeneration. This contradicts the assumption that a
is the only line of #* through A.

p. 743 line 11 says: “If A is the only limiting point, then the
contracting ovals would give to A the character of a point of a
twodimensional continuum’. Here it has been overlooked that A does
not belong to the contracting region, defined by the ovals on F°,
but to these ovals themselves. This necessitates further consideration

60*

924

of the case. In every plane through a (Fe) lies an oval touching a
at A. Degeneration being excluded, the branches departing from A
on the oval, cannot pass from one side of a to the other, unless
their plane passes ¢. Let the semiplane in- which the oval touches
a, first turning one way and then the other, converge towards
e. If in both cases the ovals contracted towards A, then they
would suffice to give to A the character of a point of a two-
dimensional continuum and a sequence of points on a with A for
limiting point could not be fitted in anymore.

Considering ¢ has only « in common with /* there remains as
only possibility that when their plane turns one way, the ovals
contract towards A and in the other case towards the entire line a
(from both sides with branches connected via the line at infinity).
This means that A is cusp in every plane not containing a and
that every other point of a is point of inflexion in every plane
not containing a, with all tangents situated in ¢. Hence A is unt-
planar point and the vicinity on #* forms a twodimensional
continuum. According to our definitions a counts triple in e. Evidently
F* contains no further lines and as a counts single in every plane
apart from ¢, the total number of lines on F* is 3. The numbers of
lines being the principal object of the present investigation, we
exclude this case in what follows.

Above we excluded degenerations of the oval in planes through a
(Ge) on ground of the assumption that no second line of /? intersects
a. If we only assume that no second line passes through 4, then it
is possible for the oval to degenerate in two lines of which one
coincides with a and the other does not pass through A. Then in
a plane turning round a from the starting position e the following
changes take place: At first ovals have a for tangent at A, these
ovals extend and in a plane a occurs the generation in a and a
line not containing A. After that we find ovals again touching a
at A (but now from the other side) and when their plane converges
towards e‚ these ovals once more contract towards A. It can easily
be shown that no further degeneration takes place. A is another
kind of wniplanar point, with twodimensional vicinity on #”. In plane
x line a counts double. In « line a counts single and A can be con-
sidered as a point-oval. From the foregoing follows directly that #? con-
tains no further lines. The second line obviously does not count
double in any plane. It can also be easily shown that it does not
count triple in more than one plane, but we leave undecided if this
can happen in one plane. Hence the total number of lines on F” is

925

3 or 5 (and we leave undecided whether the case of 5 can occur
The occurrence of points as here described is again excluded in what
follows.

Comm. 4 p. 1247 line 14 we used some results of comm. 3.
These were deduced for points through which passes only 1 line of
F* and the application on points through which 2 lines pass, causes
incompleteness. Besides the note at the bottom of p. 1248 is not
quite correct. On these grounds comm. 4 requires alterations. One
of these will appear to be the extending of the numbers 3, 7, 15, 27
before mentioned to 3, 5'), 7, 9, 15, 27.

We shall now start on a minute consideration (§ § 3 and 4) of
points through which pass 2 or more lines of #%. This will permit
us to deal separately with several singularities. In the last part (§ 5)
we intend to point out further changes necessary in comm. 3 and 4.

$ 3. On points through which pass 2 different lines of F*, but
not 3 different lines situated in one plane.

Through A pass the lines BD and CE in a (fig. 1). We distinguish
2 cases :

1. Neither line counts double in «.

2. One of the lines counts double in a.

In the first case a contains a third line, not passing through A
and along each of the 4 branches departing from A in a, the sectors
of F* obviously meet from opposite sides of «a. It is easily shown
that each of these branches is connected with both surrounding ones,
the sectors lying alternately above and below a.

In the second case -let CZ count double. Then along AC the
sectors meet from one side of @ and along AZ from the other (via
the point at infinity this is the same side). Along AB and AD the
sectors meet everywhere from opposite sides of «. Here also it is
easily shown that each of the 4 branches meeting at A in a, is
connected with both surrounding ones, 2 successive sectors now lying
above and the other 2 below a.

First case. Let AB be connected with AC and AD with AEF
above a by / and /// respectively, and below @ AC with AD
and AK with AB by J/ and JV. To begin with we assume that
all plane branches departing from A on F* touch « at A. Then in
every plane, containing neither BD nor CE, A is ordinary point
with tangent in «. We proceed to show that in a plane 8 (Fa)

1) Further investigation will probably show that the number 5 can be left out.

926

through BD (or CE) no further branches depart from A. Suppose
a further branch leaves A in 8, then 3 contains an oval having BD
for tangent at A. Let this oval depart from A above a. Let AF and
AH be the branches of this oval and let AF’ depart on J, then AA
is situated on J//, for the assumption that both lie on J at once
gives a contradiction when we consider the section in a plane (# a)
through RS (fig. 1). Now let 8 turn round BD, in such a way
that the top part moves towards AC, then in every position before
a is reached, a branch departs from A on J and we keep ovals,
touching BD. From this it follows that in all these planes @ the
lines through A not coinciding with BD, carry only 1 other point
of F*. Now this is impossible as in every plane not containing BD
or CE, A is ordinary point with tangent in a and if this tangent
be slightly turned in that plane round A, we obtain 3 different
points of intersection with #”.

A point A as here described we call normal point of intersection
of 2 lines on F*.

We shall now consider the alternative, that a plane branch departs
from A not having a as tangent plane at A. Let us first assume
that a third line of F* (not situated in a) passes through A. Let this
line depart above « on / and below « on //. Let 8 denote the
plane through this line and BD. If every vicinity of 4 in 8 contains
points of /J7+ JV then the curve in 8 is composed of 3 lines
through A, which case shall be dealt with later. Remains the possi-
bility that //74+ AE + IV is situated entirely on one side of 8.
Then however of the 4 branches departing from A in 8, two opposite
ones are directly connected and this is impossible, as well when one
of the lines in 8 counts double, as when both count single.

Let a branch departing from A and not having « for tangent
plane, be situated on J, then through the line RS of « (fig. 1)
planes can be found in which at least 2 branches depart from A
on J, but in each of these planes at least 1 branch departs on JI
and / on ZV, hence A is ordinary double point and as RS is not
tangent, branches depart on J// and JV also, for which a is not
tangent plane. The same now follows for J/7/. Hence if a is turned
round a line through A in « (A BD or CE) out of its original
position, then at first A remains double point.

Now let « turn round RS in such a way that the back part
moves upwards. We proceed to show that there cannot be a last
position with double point in A and branches departing on /. Suppose
a plane 8 formed such a last position and let AN and AM be the

927

branches on J. Let PQ be a line through A in « inside “ BAC
(fig. 1) and y a plane through PQ, such that the branches AM and

Bigot;

AN depart to different sides. In y a branch departs from A on /
in front of 8. This branch has the line of intersection of Band y for
tangent, as otherwise 6 could not be the last plane with double point
in A and branches on /. In y also departs a branch on ///, hence
A is double point in y with the line of intersection of y and # as
one of the tangents. The character of the curve in >, however, requires
this line to carry a point of F* different from A, hence a contradiction
is obtained *).

Not all planes through RS show a double point at A, for the set
of planes with 2 branches on J and the set of those with 2 on ///
would be separated by a plane with 1 branch on / and /// each
and these would be lines. In every plane through RS however, 2
branches arrive at A from below «, hence a plane 8 through RS
exists in which A is either ordinary point or cusp. Let us assume
the first. Now let 8 turn round RS, then before «a is reached, A has
become double point. The assumption that no plane through RS
shows a cusp in A leads to an impossibility, for when $ turns, there
cannot be a first plane with double point in A (as shown above)
and that there cannot be a last position with an ordinary point in
A is proved by the reasoning of comm. 1 p. 113 and 114.

Hence there exists a plane through RS with a cusp in A. Let @
be this plane and 7U the cuspidal tangent.

In every plane Fe) through PQ (fig. 1), not containing TU, 2
branches arrive at A from below on // or JV and also 2 from

1) Somewhat analogous reasoning occurs in comm. 1. to which we do not
always refer, in order to avoid confusion.

928
above, namely 1 on Z and J/// each, hence A is always double point.
For the plane through PQ and 7’U remains only the possibility that
A is cusp with P'U for tangent. From this follows again that A is
double point in every plane through RS not containing TU. All
this can at once be extended to the following:

In every plane containing neither BD nor CE, A is double point,
except in the planes through TU, and in these A is cusp with TU
for tangent.

We note that no line through A carries 2 other points of F*.

There remain to be considered the sections in planes through BD
or CE. If such a plane does not pass through 7'U, then it obviously
contains a non-degenerated oval through A. For a plane through
TU and one of the lines in @ we shall show that the entire section
is situated on the line in «. Let us consider the plane @ through
CE and TU. The restcurve (that is the curve minus CZ) cannot
contain a line different from CE, for TU has only A in common
with F* and no third line passes through A. Neither can 8 contain
an oval not passing through A, as no line through A carries 2 other
points of F*. If there is an oval through A, then TU is tangent at
A. Let the branch AV of this oval (fig. 1) depart on / (above a).
Branches leaving from A on / all depart behind the plane through
RS and TU. This holds for every line RS inside / BAE, hence
no branch departing from A on / has a semitangent at A situated
outside trihedron AUCB. The branch AV cannot be isolated on
the frontside (that is the side on which D lies) of the plane 3
(through CE and TU), hence on that side of 8, AV is connected
with AC. Let y be a plane through BD, such that AC and AU
lie on different sides, then in this plane a branch departs from A
on the subsector of I joining AV to AC and the line of intersection
of 3 and y is tangent to this branch (as no semitangent is situated
outside trihedron AUCB). This tangent would;have only A in common
with #*, but in 8 it carries a second point of the oval, hence we
arrive at a contradiction.

We thus find that the plane through CE and 7'U contains no
points of F* not situated on CE and the corresponding thing holds
for the plane through BD and ZU. Hence all tangents at A are
situated in the planes through ZU and CEor BD respectively, and
on the other hand it is easily shown that every line through A in
one of these planes is tangent. Hence A 2s biplanar point and in each
of the tangent planes the entire section is situated on a single line. *)

1) A good drawing representing such a point can be found in table II joined to
a note of Krein, Math. Ann. 6, p. 551.

929

The above results show that here /* contains no line not situated
in a. If follows that none of the 3 lines in « counts double in any
plane. If none of them ever counts triple either, then the total
number of lines on F° is 8.

Let H and K represent the points of intersection of the third line
in a and CE and BD respectively. For each of these points two
possibilities exist, namely they can be normal point of intersection
of 2 lines or biplanar point of the same type as A. If both are
normal points, then the above deseribed character of such points
shows that none of the 3 lines in « counts triple in any plane. If
on the other hand A is biplanar and K normal, then the line
AH (= CE) counts triple in the plane through 7'U, in which plane
then also lies the cuspidal tangent at the biplanar point H. In this case
the total number of lines on F* would be5*). If lastly, Kis biplanar
also, then each of the 3 lines in « counts triple in a particular plane
and the total number of lines on F* becomes 9.

Second case. CE counts double in a. Suppose above a AB is
connected with AC by J and AC with AD by //. Below a AD
with AE and AH with AB by J/I and JV respectively (fig. 2). To
begin with we assume that every branch departing from A has «
for tangent plane. Then A is point of inflexion in every plane not
containing BD or CE. We consider a plane (4 a) through CE. If
in this plane a further branch leaves A, then in this plane an oval
touches CE at A. Let this oval depart from A above « and
let the branch leaving in the direction AZ at first lie on /. Now in
a plane (Ze) through the line AL of a (fig. 2), the branches
departing on // and {V form a point of inflexion at A, but at least
2 more branches depart on /, hence a contradiction has been obtained.

Let us consider a plane 2 through BD. If in 3 another branch
leaves A, then an oval touches BD at A. Let this oval
depart from A above a. If both branches of this oval at first lie
on /, then we get a contradiction as above. Hence one branch AF
would have to start on / and the other AH on J//. In § now depart
from A the branches AB and AD on the line and AF and AH on
the oval having this line for tangent. Former results’) show that
each of these 4 branches is connected with the 2 surrounding ones,
alternately on opposite sides of 8. Now AB and AD are connected
on that side of 8 where Z lies, hence AF and AH also, but then
inside every vicinity of A, / and // would be connected by a sector

1) We leave undecided whether this case can occur.
8) Comm. 3 p. 738 and 739.

930

not containing AC or AEF and this is impossible. This completes the
demonstration that in no plane Ge) through BD or CE a further
branch starts from A.

Once more we consider a plane (# a@) through CE. If in this plane
a further branch starts from a point (A A) of CE, then an oval
touches CE at that point, as every point (# A) of CE is isolated
on one side of «a. It can then be fairly easily shown that this
point is uniplanar point of the second kind described in § 2. Such
points however, we excluded, hence we conclude that in no plane
(Ka) through CE a further branch starts from any point of CE.

Let the planes 8,8, 2,.... all containing BD, converge towards
a in such a way that the top parts move towards AC (fig. 2). These
planes end up by containing ovals, converging towards CZ, inter-
secting AB and AD, and facing at these points of intersection A
with their convex sides. For if these ovals did not so face A, then
they would have points in common with every plane through CZ,
and in such a plane a further branch would depart from some
point of CH.

A point A as here described we shall call normal point of inter-
section of a double and a single line.

We now have to consider the case that a branch leaves A, for
instance on J, not having @ for tangent plane. We distinguish 2
possibilities :

1. Through A passes no line of F*, not situated in a.

2. Throagh A passes a line of F*, not situated in a.

1. Planes through line AL of a (fig. 2) can be found, in
which 2 branches depart on Z, and 1 branch on JJ and IV
each, and this means that A is double point with AZ as one of
the tangents. Hence a branch starts from A on 7 in the direction
AL, and it follows that in every plane Feu) through the line AM
of a (fig. 2) 2 branches leave from A on /. In each of these planes
A is double point and we conclude that no line ( CE or BD)

931

through 4 carries 2 other points of F*. Evidently every line inside
7 BAE can be taken as AM.

Every point (# A) of CE is isolated on one side of a, hence BD
is the only line of F° intersecting CE.

In an arbitrary plane (Xe) through AM, A is double point with
a tangent in a. Let 8 be the plane through the other tangent (A H)
and CE. The resteurve in @ contains no line different from CE, as
BD is the only line intersecting CH. Neither can the resteurve in 8
contain an oval not passing through A, as no line through A carries
2 other points of F*. An oval in 8 passing through A is also
impossible as the above mentioned tangent AH would also be tangent
to this oval, hence this oval would cross CE at a point different
from A and this would be irreconcilable with the way in which
the sectors meet along CEH. Hence 8 contains no points of F*,
not situated on CE. It follows directly that 3 is tangent plane at A,
hence A is a biplanar point.

As 8 contains no points of F* not situated on CE, BD is not
intersected by any line except CH. Above we found that CH has
no line of intersection except BD, hence CE and BD are the only
lines of F'*. It follows at once that neither counts double in any
plane (Zea). It can also be easily shown that neither counts triple
in any plane. Hence the total number of lines on F° is 3. In what
follows we exclude points as here described, and we leave undecided
whether they can occur. |

2. Through A passes a line 6 of F', not situated in «. Let this
line depart above « on /, then it leaves below a on JV, for if it
started on ///, we could at once find an infinite number of planes
in which 6 branches meet at A (2 on / and /// each and 1 on
II and JV each) and this would mean an infinite number of dege-
nerations. Besides it is evident that all branches leaving from A on
II and //T touch a at that point.

We consider the plane 8 through 6 and CZ. A reasoning analo-
gous to that of p. 926 shows that in 3 a third line passes through
A, again leaving on / and JV. Hence in 3 3 different lines pass
through A, which case shall be treated in § 4.

§ 4. On points through which pass 3 different lines of F’*, situated
m one plane.

Let A be a point throngh which 3 lines pass, situated in plane a.
Six branches start from A in a. Along none of these the sectors
meet from the same side of a, for in that case an infinite number

932

of lines in « would belong to F*. Two branches, separated by a
single one, cannot be directly connected, for if the joining sector
were situated above «, then the sector departing above a from the
branch in between, could not be fitted in on a twodimensional
continuum. All this leaves only 2 possibilities for connecting the 6
branches :

1. Every branch is connected with the 2 surrounding ones, altern-
ately above and below a.

2. A representative case of this possibility is that above a. AC'is
connected with AF, AD with AH and AA with AB, and below a.
AD with AH, AE with AF and AB with AC (fig. 4).

1. Suppose above a AB is connected with AC by /, AD with
AE by III, and AF with AH by V, below a AC with AD by
Il, AE with AF by /V and AH with AB by VI (fig. 3). To

Fig. 3.

begin with we assume that a branch departs from A, for instance
on /, not having « for tangent plane. Then a plane through A
inside / DAC can be found, in which 2 branches start from A on
I. Besides one branch on // and V each. The branch leaving on //
does not have « for tangent plane. Proceeding in this way we find
that a branch leaves on /// not touching a and lastly we show
that the same holds for /V. Then however an infinite number of
planes can be found in which 2 branches start on 7 and JV each
and one on // and V each. This means an infinite number of degene-
rations, which case we exclude.

Hence all branches starting from A have « for tangent plane.
This means that A is point of inflexion in every plane which does
not contain one of the lines in a, with all tangents in «e. We
proceed to show that in no plane through one of the lines in «
further branches depart from A. Suppose in a plane ? through BL
a further branch leaves 4, for instance above «. Then in 8 an oval
(with BE for tangent) leaves on / and J/J. Let 8 turn round BE,

933

in such a way that the top part moves towards C (fig. 3), then in
every position ? contains an oval, with BH for tangent at A and
departing on / and ///. Every line through A in one of these planes
has only one further point in common with #*. This contradicts
the above obtained result that in every plane not containing one of
the lines in «, A is point of inflexion with tangent in «a, for if the
tangent be slightly tnrned round A, we obtain 0 or 2 points of
intersection with #'*, different from A.

A point as here described we call normal point of intersection
of 3 lines situated in 1 plane.

2. Above « AC is connected with AF (1), AD with AE (LIL)
and AH with AB (V), below « AD with AH (11), AE with AF
JV) and AB with AC (VI) (fig. 4). On none of the sectors 4/1,
IV, V, and V/ can be situated a branch not having a as tangent
plane, for let such a branch start on ///, then at once an infinite
number of planes can be found in which 2 branches depart on
lll and one on 4, Il, TV and VJ, each. This makes 6 in all, in
other words it would mean degeneration. Hence in every plane

Fig. 4.

through A inside one of the angles FAM or HAD the line of inter-
section with « is one of the two tangents at the double point 4.

We consider an arbitrary plane @ through B£. In 8 a branch
leaves A on J and another on //, both situated on the restoval.
Let 8 turning round BE converge towards a, in such a way that
the top part moves towards / (fig. 4), then these branches converge
towards AF and AD respectively. If 8 turns the other way the
branches converge towards AC and AH respectively. It follows that
a position of ? exists in which the oval degenerates, hence a line

934

PQ passes through A, not situated in «, leaving on / (AP) and
on lI (AQ).

We note that no line through A carries 2 other points of F?
without belonging entirely to that surface.

Let y denote an arbitrary plane through PQ inside “FAH. The
part of the section in y which is not situated on PQ, can consist of:

1. Two different lines through A.

2. Nothing.

3. One line through A (possibly to be counted double).

4. An oval touching « at A.

No two planes y can contain a section falling sub 1, 2 or 3, for
then an infinite number of planes through A inside / EAD could
be found, each containing 2 lines not situated in @ and having only
A in common with #* (namely the lines of intersection with the
2 planes y) and this is impossible considering that in all those
planes A is double point with a tangent in a.

Hence it suffices to consider 4 cases. In the first 3 all planes y
except one, contain a non-degenerated oval and the excepted plane y
shows a section falling sub 1, 2 and 3 respectively. In the fourth
case every plane y contains a non-degenerated oval.

First case. In a plane 7 through PQ inside “FAH (fig. 4) the
curve consists of 3 different lines through A. In plane 8 through
PQ and BE no third line passes through A, for then sector / would
ercss this plane twice and this cannot be as sector / comes from
the one side of 8 (AF) and ends up at the other side (AC). Neither
PQ nor BE can count double in @, hence the curve in 8 consists
of 3 lines forming a triangle.

Almost the same reasoning holds for the plane through PQ and
DH) and substituting / for // and vice versa, also for the plane
through PQ and CF. Besides for PQ can be substituted either of
the remaining lines in y. Hence in all 15 lines on #* have been
found, namely 6 through A and 9 others.

From the foregoing follows at once that none of the 3 lines in
« can be intersected by other lines as those mentioned. Also it can
be easily shown that none of the 15 lines counts double or triple
in any plane. Hence the total number is 15.

Every line through A in a or y is tangent at that point and on
the other hand every tangent is situated in «a or y. Hence A is

‘) DH cannot count double in the plane through PQ, for then sector JJ could
not cross y three times, without passing more than once through the plane o
PQ and DH.

935

biplanar point and each tangent plane has 3 different lines in common
with F*"). We found A to be double point in every plane not
containing the line of intersection a of « and y. In every plane
(fa or y) through a, A is cusp, for in such a plane a is the only
line having no point but 4 in common with £*.

Points as here described are excluded in what follows.

Second case. The plane y bas no points in common with F'*, not
situated on PQ. This case can be dealt with in almost entirely the
same way as the first case’). Again A is biplanar point with a
and y for tangent planes. We find 7 lines, namely 3 in «, PQ and
3 more in the planes through PQ and the first 3. Of all these,
except PQ, it can be easily shown that in no plane they count double
or triple. For PQ remain the possibilities that this line counts single
or triple in y. Accordingly the total number of lines on F* is 7 or
9. In the last case PQ carries a second biplanar point of the same
type as A. We leave undecided whether this last case can occur.

Biplanar points as here described are excluded in what follows.
They are a cross-type of those immediately preceding and those
of p. 928. *)

Third case. In y the curve consists of 2 lines through A, one of
which counts double. The results of p. 931 show that through the
double one passes a plane containing 3 different lines through A.
Part of the reasoning given for the first case shows that this plane
cannot contain one of the lines in «a. Neither can it be situated
inside “ DAE or / EAF, for such planes always contain branches
touching @. Hence the above mentioned plane would lie inside
“4 FAH. Then however the double line is the intersection of 2
planes inside “ FAH, neither of which contains a non-degenerated
oval, and this is impossible according to the results of p. 934.

Fourth case. Every plane y contains a non-degenerated oval with
a for tangent plane at A. Obviously these ovals depart either all on
[or all on //. Let us assume the latter, then these ovals contract

1) A good drawing is to be found in table III of the above mentioned paper
of KLEIN.

4) That HD does not count double in the plane through PQ appears when we
bear in mind that every plane (4 y) through PQ inside L AH contains an oval
having « for tangent plane at A. In the planes on the side of y these ovals
depart on J, and in those on the other side of y they start on JJ, for otherwise
F3 could not be a twodimensional continuum.

3) For cubic surfaces, compare Krein, loc. cit, p. 557.

936

towards A when y converges towards the plane 8 through PQ and
CF, for the alternative demands the existence of points on PQ,
which can be points of inflexion with the tangent in 8, and this is
impossible as the line CF belongs to #*. Hence a finite vicinity of
A exists, inside which the converging planes contain no points of
1 not situated on PQ. This means that along AF the sectors / and
/V meet from the same side of 8, in other words CF counts double
in 8. From this it follows that CH is not intersected by any line,
not passing through A. In the same way as above we find the
total number of lines on F* to be 7 (CF counted double). A is
biplanar point, such that the line of intersection of the tangent
planes lies on the surface, and one of the tangent planes at A is
tangent plane all along this line. This case is excluded in what
follows and we leave undecided if it can occur.

§ 5 On surfaces F* on which the singularities described above
do not occur.

Except points lying on one line or no line at all, the surface can
contain what we called normal points of intersection of 2 or 3 lines,
and of a single and a double line.

In comm. 3 p. 736—744 we proved (theorem 1): that every point
on a line of F* has a tangent plane, provided this line is not inter-
sected by any other. Above (§ 2) we already did some supplementing
and brought forward two kinds of uniplanar points. Apart from this,
the demonstration can, with some small self evident alterations’) be
used to establish the following theorem: Lf a line of F'* counts double
in no plane, then every point of this line has a tangent plane provided
no second line passes through that point.

Theorem 2 of p. 744 (comm. 3) holds, with the same demon-
stration, when normal points of intersection are admitted.

We pass on to comm. 4 (p. 1246—1253). As the above described
singularities are excluded, theorem 1 (p. 1246) holds and can even
be extended to the following: The lines of F* passing through one
point, lie in one plane.

Apart from the occurrence of a plane « in which the curve is
composed of a double and a single line, the rest of comm. 4 can

1) Example of a necessary alteration: p. 739, J. 6 from bottom: If the rest-
curve consisted of 2 lines, these lines would have a normal point of intersection
at B. Hence in 2 the curve would have 0 for tangent at B, and this cannot be
as A is cusp in 2. If the restcurve in « is a double line through B, then a slight
turning of 6 round A in 2 would replace B by 2 points of intersection and this
again is impossible,

937

remain the same (see however the errata below). In §2 of comm. 4
occasionally the question arises if none of the lines can count double
or triple in any plane. Now the case of a double line will be dealt
with below and for a surface #”* without the singularities mentioned,
but with a line which counts triple in a certain plane, the total
number of lines is always 3.

We conclude by considering the case that the curve in a planea
consists of a single line a and a double line 5. The normal point
of intersection A of a and 6 has « as tangent plane. If « turns
round a, then (according to the results of p. 983) a non-degenerated
oval appears out of 6. The points of intersection of this oval and a
start from A to right and left, and at these points the oval faces A
with its convex sides (anyway at first). Obviously 6 cannot be
intersected by a line of #* not situated in «. Hence all further lines
intersect a. If such further lines exist, their number is at least 4,
which brings the total up to 7. If there are still more, the oval
degenerates in at least 4 planes through a different from a and then
the reasoniug on p 1251 (comm. 4) shows that #? contains lines
which do not intersect a: a contradiction. Hence for a surface F"
with a plane section consisting of a double and a single line, the
total number of lines is 3 or 7 (for it is easily shown that no further
multiplicity can increase these numbers).

ERRATA.

In comm. 1, p. 102 |. 22 for: “straight line and isolated point”;
read: “straight line and point-oval”.

In comm. 2, p. 309 1. 24—34: this part can be left out.

p. 311 1. 1214: the letter C to be replaced by D.

In comm. 3, p. 740 1. 25 for: “Liet c be a line through A in a,

not being tangent to the oval and not coinciding with
a or 6”; read: “Let c be a line through A in a, not
coinciding with a or 6 (6 is tangent to the oval)”.
p. 742 1. 7 from bottom, for: “It follows that A must
be cusp in every plane except a”; read: “It follows
that A must be cusp in every plane not containing
the line a’.

In comm. 4, p. 1251 1. 3 from bottom, for: “Now none of these
last 4 points can coincide with one of the first, because
in that case a line of /* would pass through that
point and through the point of intersection of 6, and
b',”; read: “Now none of these last 4 lines of inter-

61
Proceedings Royal Acad. Amsterdam. Vol. XXIII.

938

section of c can coincide with one of the first 4, for
in that case a line of #* would pass through the point
of intersection of 6, and 6',, without being situated in
the plane through these lines”.

_p. 1253 1. 2 from bottom, for: “cannot occur’; read:
“can only occur”.

Physics. — “The quadrupole moments of the oxygen and nitrogen
molecules”. By Prof. W. H. Krersom. (Communication N°. 6a
from the Laboratory of Physics and Physical Chemistry of
the Veterinary College at Utrecht). (Communicated by Prof.
KAMERLINGH ONNES).

(Communicated at the meeting of November 27, 1920).

§ 1. Introduction. In Suppl. N°. 39a to the communications from
the physical laboratory of Leiden ')it has been proved, that, as far as
the term with the second virial coefficient, the equation of state of
hydrogen can be accounted for in the temperature interval between
+ 100° C. and —100° C. (according to Suppl. Nr. 39c down to
still lower temperatures) by assuming the molecules to act on each
other as electric quadrupoles with constant quadrupole moment’).
Thereto the repulsions which predominate at small. distances had to
be replaced by the forces that would act when the molecules collided
as solid spheres of definite radius. At the same time the quadrupole
moment of the hydrogen molecules was determined. This proved
a configuration of the two nuclei and the two electrons constituting
a H,-molecule to be very well possible in such a way that it has
the demanded quadrupole moment. By these considerations it was evident
that the molecular attractions can be explained for homopolar molecules
too by the electric forces exerted by the nuclei and the electrons
constituting the molecules. To show this was for the moment the
principal purpose of those considerations.

A comparison of the quadrupole moment demanded by the equation
of state with that of the Bour-Drgijr model for the hydrogen molecule
was not made because of the many difficulties that arise against
this model, especially with respect to the magnetic properties”) Mean-
while Burergs*) has calculated the quadrupole moment of the hydrogen

1) These Proceedings, vol. 18, p 686.

2) The following Communication will treat the influence on the second virial
coefficient of the mobility of the electrons within the molecule, which finds its
expression in the dielectric constant.

8) Comp. Leiden Comm. N°. 39a, p. 15, note 1. At present this difficulty has
perhaps a somewhat smaller weight than was thought then. (Added in the trans-
lation).

4) J. M. Bureers, Diss. Leiden 1918, p. 186.

ol

940

molecule according to Bonr-DeBije and he found a remarkable
agreement with the value derived from the second virial coefficient
(Comm. Leiden, Suppl. N°. 39a):

from the equation of state *) 2,03 « 102 (e. st. e. cm’)

according to Borr-DrEBuE AO aes 5

However favourable this result may be for the Bonr-Drgije model,

still it seems probable that the always increasing objections against
this model?) will compel us to seek for another. The calculation
of the quadrupole moment from the equation of state retains
however its value. Abstracted from the incertainty caused by the
simplifying assumption on the repulsing forces, it gives namely
important data which will have to be taken into consideration in
the construction of the definite model of a molecule. In this sense
it seemed interesting to calculate the quadrupole moments for other
gases too. In § 2 this has been done for oxygen and for nitrogen.

§ 2. In the temperature interval in which the second virial coef-
ficient has been calculated for quadrupole molecules, we possess the
data comprised in table I for the second virial coefficients of oxygen
and nitrogen *).

The index © indicates here that the volume v in the equation
of state
|

pie aE Wales ese
ee |

is expressed in the theoretical normal volume as a unit *).

These data do not admit a control of the change of B for these
gases with the temperature compared with that of spherical quadru-
pole molecules. This would require more values of B espe-
cially for higher temperatures. Let us assume for the present that
this is the case for the considered temperature interval ®), then they

When we attend to the circumstance that the molecules are polarized in
their mutual electric fields, this value will still undergo a small alteration (comp.
Comm. N°. 66 especially § 4).

2) Comp Miss H. J. van Lezuwen, these Proc. Vol. XVIII, N°. 7, p. 1071. J. M.
BURGERS, these Proc. Vol. XIX, 2. p. 480. A. SoMMERFELD, Atombau und Spektra-
llinien. Braunschweig 1919, p. 288 and 533. Frl. G. Lasxi, Physik. ZS. 20 (1919),
p. 550. W. Lenz, Verh. D. physik. Ges. 21 (1919), p. 632.

3) These numbers are taken from the calculations by Mr. M. Daniers, phil.
nat. docts, where for the observations of AMAGAT were taken the virial coefficients
given by KAMERLINGH ONNES in Comm. Leiden N°. 71.

4) Comp. H. KAMERLINGH Onnes und W. H. Keesom, Die Zustandsgleichung.
Math Enz. V. 10, Leiden Suppl. N°. 23, Einheiten 0.

5) For hydrogen deviations occur in the corresponding interval already.

941

TABLE I.
Oxygen | Nitrogen
a LET y ;
T | Be X103 | T | Bo X10)
| | | | ARR
412.6 | + 0.213 | AMAGAT 1 472.5 | + 0.690 AMAGAT
372.6 | — 0.088 : | 372.45 | + 0.324 p
293.1 -— 0.848 | Onnes&HyNDMAN 290.6 lhe 0.298 Lepuc 1910
288.7 | — 0.694 : || 289.1 | — 0.234 AMAGAT
288.7 | — 0.739 | AMAGAT | 288.0 | — 0.316 | RAYLEIGH
288.1 | — 0.645 | Lepuc 1910 | 2731 | 0.312 | Amacar
284.3 — 0.791 | RAYLEIGH |
273.1 — 0.812 | ONNES & HYNDMAN
273.1 | — 0.928 AMAGAT |

suffice to determine the quadrupole moment, besides the diameter
of the molecules when regarded as spheres.

For this purpose we take the values of B/B,, for different values
of T/Tinv=o) for spherical quadrupole molecules from Comm.
Leiden, Suppl. N°. 39a and c.

Applying the method of the logarithmic diagrams (comp. Comm.
Leiden, Suppl. N°. 25) we found successively :

For oxygen:

for the inversion temperature of the Joule-Kelvin-effect for small
densities :

Tinv (o=20) = 728 (450° C),
for the potential energy of the molecules in contact (with the qua-
drupole axes mutually perpendicular and perpendicular to the line
connecting the centres):
e500) x10,
for the diameter of the molecule:
o = 2,65 « 10-8,
for the quadrupole moment:
u, = 3,55 X 10-% [e.st.e. X cm’).
For nitrogen:
T inv (e=0) = 604, (381°C.)
y = 4,77 X 10-44,
B AS Oe,
Bi 30. 102 Me steak em]:

942

§ 3. In order to form a better judgment of the value found
for the quadrupole moment of oxygen we must still investigate
whether the magnetic attraction between the paramagnetic oxygen
molecules contributes considerably to B. In this case the quadru-
pole moment ought to be smaller than the value found above with
neglect of this attraction. Calculation proves however that this
is not the case.

According to Weiss and Piccard’) oxygen should possess 14
magnetons per molecule. This involves a magnetic moment of the
O,-molecule

: . ie OO,

In Comm. Leiden Suppl. n°. 25 $ + has been shown that
u = 9,47 X 10-19 should be required in order to explain the molecular
attraction. The real magnetic moment has only zb of this value.
Taking into consideration, that the statistically remaining molecular
attraction is proportional to u“, we see that the contribution of the
magnetic moment to the molecular attraction does not come into
consideration here.

§ 4. We must expressly point out that the calculations of this
communication (as well as those for H,, Leiden Suppl. n°. 39) are
based on the supposition that the molecules collide as solid spheres
with constant diameter. If this were not the case and if the behaviour
at a collision should correspond to a value of o depending on the
temperature, this would become manifest in B by terms also depend-
ing on 7. The dependency of B on 7’ would then no longer be
due to molecular attraction exclusively as in this Comm. For the
same reason the values of the quadrupole moments would possibly
have to be altered considerably. .

.1).P. Weiss and A. Piccarp. C. R. 155 (1912), p. 1984.

Physics. — “The cohesion forces in the theory of VAN DER Waars”’.
By Prof. W. H. Kersom. (Communication N°. 65 from the
Laboratory of Physics and Physical Chemistry of the Veteri-
nary College at Utrecht). Communicated by Prof. KAMERLINGH
ONNES).

(Communicated at the meeting of November 27, 1920).

§ 1. (Introduction. Desise') has recently shown in an important
paper on the cohesion forces in the theory of vaN DER Waats that
these may be explained in this way that one molecule in the field
of neighbouring molecules obtains a bipole moment, and that because
of this bipole moment it is attracted by the inducing molecule.
DeBije considered especially those gases the molecules of which
possess no spontaneous bipole moment. In the calculation he assumed
that the field of the molecules could be treated in first approximation
as that of a quadrupole. Evidently neighbouring molecules will influence
their mutual direction in such a way that the cases of attraction
are more frequent than those of repulsion. In a preliminary orientating
calculation the mean mutual attraction of the molecules due to their
own quadrupole moment was neglected. In fact, this will be allowed,
as was already remarked by Desig, for sufficiently high temperatures.
Then this mean attraction vanishes namely as the heat movement
hinders the directing influences of the molecules mutually.

On the other hand we have shown (Comm. Leiden Suppl. N°. 39a) °)
that the molecular attraction in hydrogen, at least as far as to the
second virial coefficient, may be explained by the circumstance that
those molecules possess a quadrupole moment, while a contribution
to the attraction due to the mobility of theelectrons in the molecules
was neglected. In fact, Derije remarks rightly that in the calculation
of the molecular attraction we shall have to attend to the attraction
of the molecules mutually because of their quadrupole moments as
well as to that especially treated by DeBie and due to the polarisa-
bility of the molecules in an electric field.

In this paper we shall discuss principally the influence of the

1) P. Dezije, Physik. Z.S. 21 (1920), p. 178.
*) These Proceedings, vol. 18, p. 636, See also W. H. KEEsom and Miss C.
VAN LEEUWEN, these Proceedings, Vol. XVIII, NO, p. 1568.

944

molecular attraction on the equation of state, confining ourselves to
the second virial coefficient.

Now we may ask which of the two mentioned contributions to
the attraction will have the greatest influence on the second virial
coefficient at the temperatures for which the measurements on the
equation of state were made. It will appear that for these tempera-
tures the influence of the molecular attraction in B is principally
due to the spontaneous quadrupole moments of the molecules.

§ 2. Preliminary orientation. For shortness sake we shall denote
by the name ‘quadrupole attraction” the contribution to the attraction
due to the spontaneous quadrupole moments and by the name
“induced attraction” the part due to the forces exerted by the qua-
drupoles on the bipoles that are induced in the molecules. In the
same way we shall speak of “quadrupole terms’ for the terms in
the second virial coefficient due to the quadrupole attraction and
of “induced terms” for those caused by the induced attraction.

Between them this important difference exists, that at high tem-
peratures the quadrupole terms become proportional to 7-2,
while the induced terms become proportional to 7.

This comes to the same as saying that the Van per W aars attrac-
tion force in the case of quadrupole attraction becomes proportional
to 7-1, whereas in the case of induced attraction they become constant.

Now it has been shown already (Leiden Suppl. N°. 39a. See Fig.
2 there and comp. also Leiden Suppl. N°. 39c § 3) that for hydrogen
the second virial coefficient behaves more in agreement with the
hypothesis of quadrupole attraction than with that a, = const., as
would be demanded for high temperatures because of the induced
attraction. Therefore we may evidently expect that at least for
hydrogen, the quadrupole terms prevail.

We may compare the values derived by Denise for the quadrupole mo-
ment under the assumption that for high temperatures the induced attrac-
tion has only to be considered, with the quadrupole moment found in
Leiden Suppl. N°. 39a for hydrogen. This comparison is in agreement
with the above conclusion. For hydrogen Dusise finds (table I 1.c.) 3,20 X
10-26, while in the Leiden Suppl. N°. 39a a quadrupole moment of
2,03 > 10-2 has been shown to give already a quadrupole attrac-
tion sufficient to explain the experimentally found equation of state.
The first of the quadrupole terms being proportional to the fourth
power of the quadrupole moment, the quadrupole moments of
Draijer would therefore give a quadrupole attraction that would be
far too great.

945

The same conclusion is reached for oxygen and nitrogen, the
quadrupole moments of which have been calculated inthe preceding
paper (Comm. n°. 6a) with neglect of the induced attraction:

OBB 1152010, ‘Comm. N° 6a: 3,55. < 10-28
NE: PRO oe de

The conclusion that the quadrupole attraction for these gases
exceeds the induced attraction is confirmed when in the calculation
of the second virial coefficient the induced attraction is also attended
to. This has been done in ó 3.

6 3. The second virial coefficient for spherical polarisable quadru-
pole molecules. We suppose the state of polarisation of the molecules
(displacements of the electrons from their positions or paths of
equilibrium) to be at each moment in correspondence with the field
that surrounds the molecule at that moment. Further the molecule
to be isotropically polarisable, so that the induced bipole moment
has the direction of the electric field # and is equal to

Wes dee Amert ee eee! rei GL)

The index 1 indicates he that we have to do with a bipole
moment, while both here and further on quantities with the index
2 are due to the electrostatic induction.

The energy of the induced bipole in the field H (compare Desir
Keje:

lm 9
ne ke

When the induced bipole is placed at a point P of the field of
a zonal quadrupole A with quadrupole moment u, (Fig. 1), in such
a way that PA makes the angle 6 with the axis of the quadru-
pole, we find for the energy of the induced bipole

9 au,’
2 x ae

The calculation of the second virial coefficient may be analogous
to that of Leiden Suppl. N°. 39a $2. A pair of molecules that may

sint 0 + 4cos* 6}. . . (3)

1
add
=d

|

|

946

be considered as lying in their mutual spheres of action will be
characterized again by the distance 7 of their centres, the angles
0, and 9, of the quadrupole axes with the line connecting the
centres and by the angle p (see Fig. 2). The energy of this pair
will be obtained by adding to the quadrupole term given in the
cited paper:

3 3
gb1 => {1 — 5 cos* A, — 5 cos? A, — 15 cos* A, cos? 0, +

yr
+ 2 (4 cos 0, cos 0, + sin O, sin 8, cos p)°} . (4)

the induced term:
nen Aleta) oon ree
WITT gigs bsin* 0, + sin“ 0, + 4c0s* 0, +-4¢08*O,} . (5)

Still a term might be added, due to the forces exerted by the
two induced bipoles on each other. This term would contain a’.
For the moment we shall however omit terms with @’.

From Leiden Suppl. N°. 39a we take the notations

marine
TE | |
where for shortness sake v will be written for ,v, this being the
potential energy of the pair of molecules when in contact with the
mentioned (l.c.) direetions of the quadrupole axes for the case that
only the quadrupole attraction is taken into consideration.

Further

v 65 = diameter of the molecule, . . . (6)

GC
eh =e oa Win eren die
where heee
Wi A Bicosap. tr O c0s AP ae a EN
when

A = 2(1—3 cos? 8.) (1 —3 cos* O,) |
B= 16 sin O, cos 0, sin 0, cos 8, | hs RS etat
C = sin’ 0, sin’ 0,
We now introduce ;
X = sin' 0, + sin‘ 0, + 4 cos‘ 0, + 40086, . . . (10)
Then we have

: Sen Jato’
SU a th os ie Teeter aan ee

The second virial coefficient becomes

heey
Ba zn(; wot P') ee. eel)
2 \8

with

947

Cae oe 2 : Mags nour mA
P =e ff (ee = ta) r‘sin0, sind, dr dO, dO, dp . (13)

7 0 0 0
Developing into a series of ascending powers of kh, with neglect
of terms with a’ etc., we find P’ to be split up into:
Pa EY a ser vent eae meee €)
where ‚P’ may be taken from Leiden Suppl N°. 39a. After inte-
gration en respect to 7 we find:

nn 20
== zeef ff x 1 — ah WL sien vend, „sin0,d dÔ,dp.(15)
000 ,
Performing this integration we obtain
Fens Fae olan ea OA abe (16)
= a: Av) rs pb a oe st
and then *)
US LA SPE FEE „heil tje Go)”. el eer a)
Arg 5 3

These terms added to ,B of the Leiden Suppl. N°. 39a finally
give:

ded
B= jn. 0") 1 — 1,0667 (hv)? + 0,1741 (hv)... —

ts 24 ho [1 + 1,067 (hv). . - ] (18)

§ 4. Conclusions. In the first place we may remark, that for a
strong validity of the law of corresponding states the same value of

a
— would be required for different gases.
5

With DeBijr we derive the value of a from the molecular refrac-
tion (P,) for A==o, while the values of o are taken from the
Leiden Suppl. N°. 39a for H,, from the preceding Communication
(N°. 6a) for O, and for N,. In this way we obtain:

| Po 0
hydrogen | 2,03 2,32 XxX 10—8
oxygen | 3,98 2,65 “
nitrogen | 4,34 2,98 -

1) The first term of this result corresponds to a value for the VAN DER WAALS
attraction constant a that perfectly agrees with that Bn by DeBuje (l. c.
equation (18)).

948

For hydrogen we have then:

ice
Bat ens ede 1,0667 (ho)? + 0,1741 (ho)* …. —

|
— 0.1586 hy — 0,1638 (hr) … | … ne fe LD

For nitrogen the last row of terms is only slightly different, for
oxygen somewhat more.

The values of 5 used here being derived from calculations in
which the induced attraction has not been attended to, this expression
for B may be regarded as a first step only in a series of succeeding
approximations. In the Leiden Supplement N°. 39a, the value of
hv in the Joure-KeLviN point of inversion has been calculated starting
from eqation (19). When we wished to do this here, we should
first have to derive still some terms for the “induced part” of 5.
After this the experimental values of 7%,,(,—0) and Bi, would give
us corrected values for v and o. We may expect the alteration
of 6 in consequence of this correction to be rather small, so that also
the change of equation (19) due to it will be not considerable.

In this communication we will however confine ourselves to the
following statement: A comparison of the terms in question shows
that at least for the mentioned gases, unless the temperature be
very high, the “qwadrupole attraction” has considerably more in-
fluence in B than the “induced attraction’. For gases as the above
the cohesion forces introduced by van pER Waals into the equation
of state may therefore be ascribed principally to the forces exerted
by the molecules on each other because of their quadrupole moments

Mathematics. — “/ntuitionistische Mengenlehre’*). By Prof. L. E.J.
BROUWER.

(Communicated at the meeting of December 18, 1920.)

Im folgenden gebe ich eine referierende Einleitung zu den
beiden Teilen der Abhandlung: „Begründung der Mengenlehre un-
abhiingig vom logischen Satz vom ausgeschlossenen Dritten”’, welche
ich im November 1917 bzw. Oktober 1918 der Akademie vorgelegt
habe.

Seit 1907 habe ich in mehreren Schriften *) die beiden folgenden
Thesen verteidigt:

I. dass das Komprehensionsaxiom, auf Grund dessen alle Dinge,
welche eine bestimmte Eigenschaft besitzen, zu einer Menge vereinigt
werden (auch in der ilim später von ZERMELO gegebenen beschränkteren
Form *)) zur Begründung der Mengenlehre unzulässig bzw. unbrauchbar
sei und nur in einer konstruktiven Mengendefinition eine zuverlässige
Basis der Mathematik gefunden werden könne;

II. dass das von HirBerT 1900 formulierte Aaiom von der Lösbar-
keit jedes Problems*) mit dem logischen Satz vom ausgeschlossenen
Dritten äquivalent sei, mithin, weil für das genannte Axiom kein

1) Unter demselben Titel ist ein im wesentlichen gleichlautender Aufsatz im Bd. 28
(1920) des Jahresberichtes der Deutschen Mathematiker-Vereinigung erschienen.

2) Vgl. „Over de grondslagen der wiskunde’, Inauguraldissertation Amsterdam
1907, besonders auch die beigefiigten Thesen; , De onbetrouwbcarheid der logische
principes”, Tijdschrift voor wijsbegeerte 2 (1908), abgedruckt in , Wiskunde, waar-
heid, werkelijkheid”, Groningen 1919; „Over de grondslagen der wiskunde”,
N. Archief v. Wisk. (2) 8 (1908); Besprechung von Mannoury, „ Methodologisches
und Philosophisches zur Elementarmathematik’”, N. Archief v. Wisk. (2) 9 (1910);
,lntuitionisme en formalisme”, Antrittsrede Amsterdam 1912, abgedruckt in
» Wiskunde, waarheid, werkelijkheid’, obengenaunt; „Zntwitionism and forma-
lism”, Amer. Bull. 20 (1913); Besprechung von SCHOENFLIES-HAHN, „Die Ent-
wickelung der Mengenlehre und ihrer Anwendungen’, Jahresber. d. D. M.-V. 23
(1914); „Addenda en corrigenda over de grondslagen der wiskunde’, Versl. Kon.
Akad. v. Wetensch. Amsterdam 25 (1917), abgedruckt in N. Archief y Wisk. (2)
12 (1918).

3) Vgl. Math. Ann. 65, S. 263.

4) Vgl. z. B. Archiv d. Math. u. Phys. (3) 1, S. 52. Nach der hier geäusserten
Ansicht HiLBERTs entspricht das Axiom einer von jedem Mathematiker geteilten
Ueberzeugung. In seinem neulich in Math. Ann. 78 abgedruckten Vortrag „Azio-
matisches Denken’ stellt er jedoch auf S. 412 die Frage nach der Lösbarkeit

950

zureichender Grund vorliege und die Logik auf der Mathematik
beruhe und nicht umgekehrt, der logische Satz vom ausgeschlossenen
Dritten ein wrerlaubtes mathematisches Beweismittel sei, dem kein
andrer als ein scholastischer und heuristischer Wert zugesprochen
werden könne, so dass Theoreme, bei deren Beweis seine Anwendung
nicht umgangen werden kann, jeden mathematischen Inhalt entbehren.
Von der in diesen beiden Thesen kondensierten @tuttionistischen
Auffassung der Mathematik habe ich übrigens in den in Anm. *)
zitierten Schriften bloss fragmentarische Konsequenzen gezogen, habe
auch in meinen gleichzeitigen philosophiefreien mathematischen
Arbeiten regelmässig die alten Methoden gebraucht, wobei ich aller-
dings bestrebt war, nur solche Resultate herzuleiten, von denen ich
hoffen konnte, dass sie nach Ausführung eines systematischen Auf-
baues der intuitionistischen Mengenlehre, im neuen Lehrgebaude,
eventuell in modifizierter Form, einen Platz finden und einen Wert
behaupten würden.
| Mit einem solchen systematischen Aufbau der intuitionistischen
Mengenlehre habe ich erst in der eingangs erwähnten Abhandlung
einen Anfang gemacht. Hier möchte ich kurz hinweisen auf einige
der am tiefsten einschneidenden, nicht nur formalen, sondern auch
inhaltlichen Aenderungen, welche die klassische Mengenlehre dabei
erfahren hat.

Die zugrunde gelegte Mengendefinition ist folgende:

Eine Menge ist ein Gesetz, auf Grund dessen, wenn immer wieder
ein willkürlicher Ziffernkomplex der Folge 1,2,3,4,5,.... gewahlt
wird, jede dieser Wahlen entweder ein bestimmtes Zeichen oder nichts
erzeugt oder aber die Hemmung des Prozesses und die definitive
Vernichtung seines Resultates herbeiführt, wobei für jedes n > 1 nach
jeder ungehemmten Folge von n—1 Wahlen wenigstens ein Ziffern-
komplex angegeben werden kann, der, wenn er als n-ter Ziffernkomplex

eines jeden mathematischen Problems als ein noch zu lösendes Problem. Seine
an diese Problemstellung anschliessenden Bemerkungen tiber die Endlichkeit des
vollen algebraischen Invariantensystems waren in meiner Terminologie so zu for-
mulieren, dass aus der Unmöglichkeit der Unendlichkeit einer Menge keineswegs
ihre Endlichkeit folgt.

Meiner Ueberzeugung nach sind das Lösbarkeitsaxiom und der Satz vom ausge
schlossenen Dritten beide falsch und ist der Glaube an diese Dogmen historisch
dadurch verursacht worden, dass man zunächst aus der Mathematik der Teilmengen
einer bestimmten endlichen Menge die klassische Logik abstrahiert, sodann dieser
Logik eine von der Mathematik unabhängige Existenz a priori zugeschrieben und
sie schliesslich auf Grund dieser vermeintlichen Apriorität unberechtigterweise auf
die Mathematik der unendlichen Mengen angewandt hat.

951

gewählt wird, nicht die Hemmung des Prozesses herbeiführt. Jede in
dieser Weise von einer in unbegrenzter Fortsetzung begriffenen Wahlfolge
erzeugte Zeichenfolge (welche also im allgemeinen einen wesentlich
unfertigen Charakter besitzt) heisst ein Element der Menge. Die ge-
meinsame Entstehungsart der Elemente der Menge M wird ebenfalls
kurz als die Menge M bezeichnet.

Auf diesen Mengenbegriff wird sodann die Definition des Begriffes
der mathematischen Spezies, der den Mengenbegriff als Sonderfall
enthalt, gegriindet.

In der Theorie der Kardinalzahlen, welche nunmehr zunächst
behandelt wird, tritt vor allem die Zerlegung des Gleichmüchtigkeits-
begriffes in den Vordergrund. Zwei für die klassische Mengenlebre
gleichmächtige Mengen oder Spezies können für die intuitionistische
Mengenlehre gleichmeichtig, halbgleichmichtig, diquivalent, von gleichem
Umfang, von gleicher Ausdehnung oder von gleichem Gewicht sein’).
Im Anschluss daran gibt es unter den fiir die klassische Theorie
abzählbaren Mengen oder Spezies für die intuitionistische Mengen-
lehre abzählbar unendliche, abziühlbare, zühlbare, auszühlbare, durch-
züählbare und aufzühlbare Mengen bzw. Spezies. Die klassischen
Kardinalzahlen a und c bleiben bestehen, dagegen wird das in der
klassischen Theorie durch die Menge aller Funktionen einer Varia-
blen gelieferte Beispiel einer Kardinalzahl >>ec hinfällig.

In der Theorie der geordneten Mengen wird für den geordneten
_Charakter einer Spezies die Existenz der ordnenden Kelation nur für
je zwei als verschieden erkannte Elemente gefordert. Weiter gestaltet
sich u.a. die Charakterisierung der Ordinalzahlen % und ¢ viel ver-
wickelter, als in der klassischen Theorie; erstere erhält folgende
Form: 3

Jede geordnete Spezies P, welche eine solche abzählbar unendliche,
im engern Sinne überall dichte Teilspezies M enthält, dass zwischen
je zwei Elementen®) von P Elemente von M liegen, dass die Spezies
der vor einem willkürlichen Elemente p von P liegenden Elemente von
M eine abtrennbare Teilspezies von M ist, von der entweder kein
Element existieren oder wenigstens ein Element bestimmt werden kann,
und dass zu jeder der Ordnungseigenschaft entsprechenden Funda-
mentalreihe von Relationen ,,nach’’ oder „nicht nach’ zu den Elementen

5) Erst diese Begriffszerlegung hat mir ermöglicht, den Mächtigkeitscharakter,
den ich in früheren Schriften nur für gewisse spezielle Mengen zulassen konnte,
auf alle Spezies auszudehnen und in dieser Weise gewissermassen die Existenzbe-
rechtigung der komprehensiven Auffassung der Spezies wiederherzustellen.

6) d. h. zwischen je zwei als verschieden erkannten Elementen.

952

von M') ein diese Relationen erfüllendes Element von P bestimmt
werden kann, besitzt die Ordinalzahl 9

In der Theorie der wohlgeordneten Mengen müssen allererst die
beiden Haupteigenschaften, dass je zwei wohlgeordnete Mengen ver-
gleichbar sind, und dass jede Teilmenge einer wohlgeordneten Menge
ein erstes Element besitzt, welche die wichtigsten Beweismittel der
klassischen Theorie bilden, preisgegeben werden; demzufolge hat
die hier aufzubauende neue konstruktive Theorie mit ihrer Vorgän-
gerin fast gar keine Aehnlichkeit mehr, weder äusserlich noch
innerlich. An die Stelle der letzteren Haupteigenschaft bringt sie
folgendes Theorem:

Ein Gesetz, welches in einer wohlgeordneten Spezies ein Element
bestimmt und jedem schon bestimmten Elemente entweder die Hemmung
des Prozesses oder ein ihm vorangehendes Element zuordnet, bestimmt
sicher ein Element, dem es die Hemmung des Prozesses zuordnet.

Der Theorie der ebenen Punktmengen wird die Menge Q derjeni-
gen Quadrate zugrunde gelegt, von denen ein Eekpunt in bezug auf
ein rechtwinkliges Koordinatensystem die Koordinaten «. 2” und
b.2-" und die (den Acbsen parallelen) Seiten die Lange 2—" oder
21—” besitzen. Sodann wird unter einem Punkte der Ebene eine un-
begrenzt fortgesetzte Folge von Quadraten von Q, deren jedes im
Innengebiete des nächstvorangehenden enthalten ist, verstanden.

Auf dieser Grundlage kommen aus der klassischen Theorie der
Punktmengen zahlreiche Theoreme in Fortfall.

Vom Canrrorschen Haupttheorem bleibt z.B. nur folgende negative
Teilaussage in Kraft:

Es kann keine abgeschlossene geordnete Punktmenge existieren, deren
Müächtigkeit grösser als die abzählbar unendliche ist und von der jeder
Punkt einerseits einen nächstfolgenden Punkt aufweist, andrerseits von
abzählbarer Ordnung ist bzw. von der Spezies der auf ihn folgenden
Punkte einen endlichen Abstand besitzt.

Auch diese Teilaussage muss indes nach einer von der üblichen,
auf dem Satz vom ausgeschlossenen Dritten beruhenden, völlig ver-
schiedenen Methode bewiesen werden, z.B. so:

Eine Punktmenge a, deren Mächtigkeit grösser als die abzdhlbar
unendliche ist, lässt sich nur so ordnen, dass endliche Mengen
tid, von endlichen Wahlfolgen, welche nicht Abschnitte von-
einander sind, der Reihe nach geordnet werden, und zwar in solcher

1) d. h. zu jeder der Ordnungseigenschaft entsprechenden unbegrenzten Folge von
Relationen „nach’’ oder „nicht nach” zu den einer Abzählung durch eine Fundamen-
talreihe unterzogenen Elementen von M.

953

Weise, dass man für jedes & sicher ist, dass S (ir, i42,...) von
jedem Reste jeder unbegrenzt fortgesetzten Wahlfolge einen Abschnitt
enthält. Indem wir nun in © (2,44, Ö42,… …) nur diejenigen Wahlfolgen
behalten, welche keine vorangehende Wahlfolge als Abschnitt enhalten,
bestimmen wir eine zählbare Menge von Wahifolgen jz. Alsdann
können wir an der Hand der fortschreitenden Konstruktion der, bei
der Herstellung eines willkürlichen 9, für jede dazu gehörige Wahlfolge
nur für höchstens einen einzigen als Fortsetzung davon erzeugten
Punkt (nämlich für denjenigen, der bestimmt wird, indem für u >>»
in jedem folgenden j, immer wieder die am höchsten geordnete Fort-
setzung der schon vorhandenen Wahlfolge zu wählen ist) sicherstellen,
dass er in der resultierenden Ordnung von a einen nächstfolgenden
Punkt aufweist. Die Kardinalzahl der Spezies der Punkte, für welche
diese Sicherkeit zu erlangen ist, kann mitbin unmöglich grösser als
die abzählbar unendliche sein °).

An die Stelle der positiven Aussage des Cantorschen Haupitheorems
tritt in der intuitionistischen Mengenlehre eine ausführliche Charakte-
risierung derjenigen Punktmengen und Punktspezies, welche die
betreffende Eigenschaft besitzen °).

8) Dieser Beweis findet sich schon in den beiden letzten der in Anm. 2) zitierten
Schriften; die daselbst gebrauchte Terminologie stimmt aber noch nicht mit der
in meiner Abhandlung eingeführten überein, während in meiner Besprechung des
SCHOENFLIESschen Buches die betreffende Stelle überdies einige Schreibfehler ent-
halt (S. 81 ist Z. 3 u. 19 statt ,Teilmenge zweiter Art”, „nicht-abzählbare Teil-
menge zweiter Art”, Z. 10 statt „von Gebieten e‚‚e,..…” „von einander enthal-
ERDER Gebiclen Cor tha,neen «und Z. 11: statt „zu: djs dass 2, „ZU tej, lon eo)!
zu lesen).

9) In meinen in Anm.?) zitierten Schriften (die letzte ausgenommen), in denen die
Konsequenzen des Intuitionismus sich noch weniger deutlich für mich abgezeichnet
hatten, haften der konstruktiven Mengendefinition noch zwei unnötige beschränkende
Voraussetzungen an; in meiner jetzigen Terminologie sind nämlich die daselbst
betrachteten Punktmengen erstens örtlich individualisiert, und lassen zweitens eine
vollständige innere Abbrechung zu. Die Folge davon ist, dass z. B. in meiner
Besprechung des ScrHoenrLiesschen Buches das Haupttheorem statt als falsch, als
selbstverständlich angeführt wird, und dass die daselbst gemachte Unterscheidung
zwischen wohlkonstruierten Punktmengen und Punktmengen im allgemeinen
(die gleichzeitig gemachte Zusammensetzung der wohlkonstruierten Punktmengen aus
solchen erster und solchen zweiter Art, von denen die ersteren einen besonderen Fal]
der letzteren darstellen, soll als unwesentlich zurückgenommen werden) sich erst nach
Fortschaffung der genannten beschränkenden Voraussetzungen mit der jetzigen
Unterscheidung zwischen Punktmengen und Punktspezies im wesentlichen deckt.

Zum a. a. O. gegebenen Beispiel einer nicht-wohlkonstruierten Punktmenge ist
zu bemerken, dass die daselbst zugrunde gelegte Funktion f (x) nicht das volle
Kontinuum zum Existenzbereich hat (vgl. meine gleichzeitig vorzulegende Mitteilung
über die Dezimalbruchentwickelung der reellen Zahlen), dass Z. 12 statt „rational”’,

62

Proceedings Royal Acad. Amsterdam. Vol. XXIII.

954

Die inneren Grenzmengen der klassischen Theorie, d. h. die Durch-
schnitte von Fundamentalreihen von Bereichen, werden in der intui-
tionistischen Mengenlehre, weil sie nicht notwendig Mengencharakter
besitzen, als innere Grenzspezies eingeführt. Dabei bleibt das Theorem
der klassischen Mengenlehre, dass der Durchschnitt zweier innerer
Grenzspezies wiederum eine innere Grenzspezies ist, bestehen; der
analoge Satz fiir die Vereinigung fallt aber fort, und von der Haupt-
eigenschaft der inneren Grenzmengen der klassischen Theorie, dass
zu einer willkiirlichen Punktmenge Q eine innere Grenzspezies existiert,
welche ausser ausschliesslich Grenzpunkte der finalen Kohärenz
von Q enthält, bleibt nur der folgende Bestandteil erhalten :

Zu jeder vollstandig abbrechbaren Punktmenge x existiert eine innere
Grenzspezies, welche mit der Vereinigung von x und einer Teilspezies
der Abschliessung der finalen Kohârenz von a örtlich kongruent ist
und eine mit x örtlich kongruente Punktmenge als Teilspezies enthält.

Die klassische Definition der Messbarkeit erleidet in der intuitio-
nistischen Mengenlehre nur eine geringe Aenderung; die Sicherkeit
der Messbarkeit verschwindet aber sowolil für die Bereiche wie für
die abgeschlossenen Punktspezies und inneren Grenzspezies, und die
Haupteigenschaft des klassischen Messbarkeitsbegriffes, dass die Ver-
einigung einer abzählbaren Menge messbarer Mengen ohne gemein-
same Punkte messbar und ihr Mass gleich der Summe der Masse
ihrer Komponenten ist, wird in der intuitionistischen Mengenlehre
folgendermassen formuliert: |

Wenn F eine solche Fundamentalreihe von messbaren Punktspezies
ist, dass die Inhalte der Vereinigungen ihrer Anfangssegmente eine
limitierte Folge i bilden, so ist auch die Vereinigung von F messbar
und ihr Inhalt gleich i.

Selbstverstandlich erleidet der Begriff des Punktes der Kbene eine
beträchtliche Verengerung, wenn in der betreffenden Definition statt
“unbegrenzt fortgesetzte Folge’, “Fundamentalreihe” gelesen wird.
Bemerkenswert ist aber, dass das lineare Analogon dieses engern
Punktbegriffes seinerseits noch erheblich mehr umfasst, als der
klassische lineare Punktbegriff, der auf dem Schnitte beruht, wie in
meiner gleichzeitig vorzulegenden Mitteilung über die Dezimalbruch-
entwickelung der reellen Zahlen näher erörtert wird.

„durch einen endlichen Dualbruch darstellbar" zu lesen ist, und dass man in der
Spezies der endlich definierbaren Punkte der Ebene ein viel einfacheres Beispiel
einer nicht-wohlkonstruierten Punktmenge besitzt.

Mathematics. — ‘“Besitzt jede reelle Zahl eine Dezimalbruch-
entwickelung?’*) By Prof. L. E. J. Brouwer.

(Communicated at the meeting of December 18, 1920).

ee i
Existenzbereich der unendlichen Dezimalbruchentwickelung
auf dem Kontinuum.

Versteben wir in der Menge der endlichen Dualbriiche 20 und <1
a+ 2

2

Endelemente besitzendes geschlossenes Intervall, unter einem Punkte
des Kontinuums eine in unbegrenzter Fortsetzung begriffene Folge
von Intervallen 2, deren jedes im Innern des nächstvorangehenden
enthalten ist*), unter a2 einen variablen Punkt des Kontinuums,
unter F,(v) einen n-stelligen Dezimalbruch mit der Eigenschaft,
dass jeder links von ihm liegende Punkt des Kontinuums links von
einem Intervalle von w liegt, während F(a) +10 " rechts von
einem Intervalle von z liegt, unter F'(wv) die eindeutige unendliche
Dezimalbruchentwickelung von z, so besitzt #,(x) die (übrigens
allen unstetigen Funktionen gemeinsame) Eigenschaft, dass ihr Exi-
stenzbereich G, nicht mit dem Kontinuum zusammenfallen *) kann.
Der Existenzbereich G=D(G,,G,,...) von F(x) kann also erst
recht nicht mit dem Kontinuum zusammentallen, obgleich er sich
(ebenso wie der Existenzbereich der regelmässigen Kettenbruchent-
wickelung von 2) dem Kontinuum so eng anschmiegt, dass er mit

als

. hd had .. a
unter einem Intervalle 2, ein zwei Dualbrüche 7 und

1) Ueber den Inhalt dieser Abhandlung wurde am 22. September 1920 auf der
Naturforscherversammlung in Bad Nauheim ein referierender Vortrag gehalten.

2) Vgl. meine in Bd. XII der Verhandelingen der Koninklijke Akademie van
Wetenschappen te Amsterdam (Eerste Sectie) erschienene Abhandlung: ,, Begriindung
der Mengenlehre unabhängig vom logischen Satz vom ausgeschlossenen Dritten’’,
2. Teil, S. 3, 4. Wie daselbst S. 4 Fussnote +) hervorgehoben und durch die
vorliegende Arbeit klar ins Licht gestellt wird, sind die beiden S. 9 des 1. Teiles
benutzten Begriffe der ,reellen Zahl” bedeutend enger als der hier definierte Begriff
des Punktes des Kontinuums. In einem ganz andern, aus dem Zusammenhang
ersichtlichen Sinne wird der Ausdruck ,reelle Zahl” der Expressivität wegen in
der Ueberschrift und im Schlussparagraphen der vorliegenden Arbeit gebraucht.

3) a. a. OF 2. Teil, S. 5.

956

demselben einerseits örtlich übereinstimmt*), andrerseits inhalts-
gleich *) ist’).

Die Definition des Punktes des Kontinuums erleidet indessen eine
erhebliche Einschränkung, wenn wir in derselben statt „in unbe-
grenzter Fortsetzung begriffene Folge’, ,,Fundamentalreihe” *) lesen.
Zweck der folgenden Paragraphen ist, klarzustellen, inwiefern fiir
diese Punkte des Kontinuums im engern Sinne, die unendliche Dezi-
malbruchentwickelung existiert.

§ 2.
Die Ergäünzungselemente der abzählbar unendlichen, überall
dicht geordneten Mengen.

Es sei eine abzählbar unendliche, im engern Sinne überall dicht
geordnete ®) Menge // gegeben. Es seien 9,,9,,9s---- die nach
irgend einem, H als abzählbar unendliche Menge charakterisieren-
den, Abzählungsgesetze y numerierten Elemente von H und es sei
S (91, ----9Y) =S gesetzt. Unter einem 7, bzw.y, verstehen wir
ein (eventuell aus einem einzigen Elemente bestehendes) geschlosse-
nes Intervall®) von H, deren Endelemente zu s, gehören, deren
Inneres aber höchstens ein bzw. kein einziges Element von s, enthalt.

Unter einem Ausfüllungselemente r von H verstehen wir erstens
eine jedenfalls ein Element besitzende Spezies von in unbegrenzter
Fortsetzung begriffenen Folgen #, Fat, Fafe... (4 eine für r
bestimmte positive ganze Zahl), wo jedes Fr, ein 2, und jedes Fatt
in F,4, enthalten ist, während r, für jedes v zu einer für 7 bestimmten
Spezies S, gehört, von der je zwei Elemente ein Element von s,
gemeinsam haben; zweitens eine jedenfalls ein Element besitzende
Spezies von in unbegrenzter Fortsetzung begriffenen Folgen 5,, &,, $,,...
von je ein bestimmbares Element besitzenden abtrennbaren Teil-

Warna Os 2. Weil, S220.

5 "aa. 0, Bx Fels S: 29, 30: -

3) Natiirlich kann auch der Existenzbereich einer mittels einer Funktion der
unendlichen Dezimalbruchentwickelung von x erklärten Funktion von 2 nicht über
G hinausgehen. Z. B. hat die im Jahresber. d. D. M.-V. 23, S. 80 von mir
definierte Funktion f(x) genau G zum Existenzbereich. Während aber die Funktion
F(x) des Textes in der auf dem Kontinuum überall dichten Punktmenge G
gleichmässig stetig ist und sich auf Grund dieser Eigenschaft zu einer auf dem
vollen Kontinuum existierenden Funktion v(x) = x erweitern lässt, ist für f(a)
jede Erweiterung auf das volle Kontinuum ausgeschlossen.

4) Vgl. ,,Begriindung der Mengenlehre usw.”, 1. Teil, S. 14.

i) tava O), GLa, -S.c16.

6y-a a: Os =a. Vell Aa. lo:

957

mengen ') von #H, wenn in jeder Folge jedes 5,44 in 5, enthalten
ist und eine Fundamentalreihe n,, n,, n,,... (‚41 > n,) von ganzen
positiven Zahlen und ein Ausfüllungselement erster Art r, von H
bestimmt sind mit der Higenschaft, dass zu jedem Elemente 5, &, 5,
von r ein Element fa, Ft1,/a+2,+--Vvon 7, existiert, so dass 5, zu
Fay gehört.

Unter einem Lrgdnzungselemente nullter Ordnung oder kurz einem
Ergünzungselemente r von H verstehen wir erstens eine Fundamen-
talreihe F,, Fagi, Fata... (a eine für » bestimmte positive ganze
Zahl), wo jedes r, ein 4 und jedes rf ‚41 in roy, enthalten ist;
zweitens eine jedenfalls ein Element besitzende Spezies von in unbe-
grenzter Fortsetzung begriffenen Folgen ¢,, 5, 6,,... von je ein bestimm-
bares Element besitzenden abtrennbaren Teilmengen von H, wenn
in jeder Folge jedes 54, in ¢,. enthalten ist und eine Fundamental-
reihe 7, 2, %,---(%41>%,) von ganzen positiven Zahlen und ein
Ergänzungselement erster Art F., Fati Fat2,.-. von H bestimmt
sind, so dass jedes §, von r zu Fay, gehört. *)

Wenn ‚r und ,r Ausfüllungselemente von H sind und jedes ‚r,
mit jedem ‚r, ein gemeinsames Element besitzt, so sagen wir, dass
‚rund ‚r in H zusammenfallen. Ein mit einem Ergänzungselemente
von H in H zusammenfallendes Ausfüllungselement von AH wird
gleichfalls als Ergdnzungselement von H bezeichnet.

Wenn das Element g von H zu jedem rf, des Ausfüllungselemen-
tes 7 von H gehört, so sagen wir, dass 7 und g in H zusammen-
Fallen.

Wenn ,r und ,r Ausfüllungselemente von H sind und man ein
‚Fm und ein ,f, ohne gemeinsame Elemente angeben kann, so sagen
wir, dass ‚r und ‚r m A örtlich verschieden sind.

Wenn man ein fr, des Ausfüllungselementes 7 von H angeben
kann, zu dem das Element g von H nicht gehört, so sagen wir,
dass r und g in H örtlich verschieden sind.

Das Ergänzungselement bzw. Ausfüllungselement + von H heisst ein
Ergénzungselement erster Ordnung von H, wenn für jedes Element g von
Hentweder die Relation g > r (d. h. jedes rechts von g gelegene Element
von H liegt rechts von einem bestimmbaren fr, von r), oder die
Relation g <r (d. h. jedes links von g gelegene Element von // liegt links
von einem bestimmbaren fr, von 7) hergeleitet werden kann, oder,
was auf dasselbe hinauskommt, wenn r mit einem Ergänzungsele-
mente 7’ von H, von dem jedes f', ein 7, ist, zusammenfällt.

Nod. a O.. Lay hel, -S: 4.

2) Ob der Begriff des Ausfüllungselementes sich auf den des Ergänzungselementes
zurückführen lässt, bleibe hier dahingestellt.

958

Die Ergänzungselemente erster Ordnung von H entsprechen den
Dedekindschen Schnitten von H.

Das Ergänzungselement erster Ordnung r von H heisst ein
Erginzungselement zweiter Ordnung von H, wenn fiir jedes Element
g von H die Relation g <r entweder hergeleitet, oder ad absurdum
geführt werden kann, oder, was auf dasselbe hinauskommt, wenn 7’
sich so wählen lässt, dass kein u mit der Eigenschaft, dass die
rechten Endelemente von ¢', und r', für jedes » > w identisch sind,
existieren kann.

Das Ergänzungselement zweiter Ordnung r von H heisst ein
Ergänzungselement dritter Ordnung von H, wenn für jedes Element
g von H entweder die Relation g >>r (d. h. man kann ein links
von g gelegenes r, von 7 bestimmen), oder die Relation g <r
hergeleitet werden kann, oder, was auf dasselbe hinauskommt, wenn
r’ sich so wählen lässt, dass zu jedem Ff’, ein solches fr’, bestimmt
werden kann, dessen rechtes Endelement links vom rechten End-
elemente von fF’, gelegen ist.

Ein Ergänzungselement dritter Ordnung von H heisst ein Ergänzungs-
element vierter Ordnung von H, wenn für jedes Element g von H
entweder die Relation g > 7, oder die Relation g=~r (d. h. g und
r fallen in H zusammen), oder schliesslich g <r (d. h. man kann
ein rechts von g gelegenes Ff, von 7 bestimmen) hergeleitet werden
kann, oder, was auf dasselbe hinauskommt, wenn 7’ sich so wählen
lässt, dass zu jedem Fr’, ein solches v >> u bestimmt werden kann,
dass die beiden Endelemente von fF’, von den beiden Endelementen
von Ff’, verschieden sind.

Die vorstehenden Definitionen der Ausfüllungselemente sowie der
Ergänzungselemente nullter, erster, zweiter, dritter und vierter Ord-
nung von H sind für gegebene ordnende Relationen in H offenbar
unabhängig vom Abzählungsgesetze y.

Sei M eine endliche Menge oder eine Fundamentalreihe von
Ergänzungselementen vierter Ordnung von H,, deren je zwei in H,
drtlich verschieden sind und deren jedes von jedem Elemente von H, in
H, ortlich verschieden ist. Die Vereinigung von M und H, bildet eine
abzählbar unendliche, im engern Sinne iiberall dicht geordnete Menge
H,+1. Jedes Ergänzungselement von H, ist gleichzeitig Erganzungs-
element von H,4; und jedes Ergänzungselement A-ter Ordnung von
H+, fällt in H‚41 zusammen mit einem Ergänzungselemente /-ter
Ordnung von A,

Die vorstehende Beziehung besteht sowohl zwischen der geordneten
Menge der endlichen Dualbrüche AH, und der geordneten Menge der

959

endlichen Dezimalbrüche H,, wie zwischen H, und der geordneten
Menge der rationalen Zahlen 4,.

§ 3.
Ergänzungselemente, Dezimalbruchentwickelungen und
Kettenbruchentwickelungen.

Ein Ergänzungselement erster Ordnung von H lässt in H die
Ortsbestimmung erster Ordnung zu, welche sich, wenn H als die
Menge der endlichen Dezimalbriiche gelesen wird, als die mehrdeutige
unendliche Dezimalbruchentwickelung herausstellt. Umgekehrt ist jedes
Ausfüllungselement von H, das in H die Ortsbestimmung erster
Ordnung zulässt, ein Ergänzungselement erster Ordnung von H.

Die Ortsbestimmung erster Ordnung in H kann für in H zusammen-
fallende Ergänzungselemente von A verschieden ausfallen.

Ein Ergänzungselement zweiter Ordnung von H lässt in H die
Ortsbestimmung zweiter Ordnung zu, welche sich, wenn H als die
Menge der endlichen Dezimalbrüche gelesen wird, als die eindeutige
unendliche Dezimalbruchentwickelung (für welche die Existenz einer
letzten von 9 verschiedenen Ziffer ausgeschlossen ist) herausstellt.
Umgekehrt ist jedes. Ausfüllungselement von H, das in H die
Ortsbestimmung zweiter Ordnung zulässt, ein Ergänzungselement
zweiter Ordnung von H.

Zwei Ergänzungselemente von H, für welche die Oene
zweiter Ordnung in A verschieden ausfällt, können in H nicht
zusammenfallen.

Ein Ergänzungselement dritter Ordnung von H lässt in H die
Ortsbestimmung dritter Ordnung zu, welche sich, wenn H als die
Menge der rationalen Zahlen gelesen wird, als die wnendliche reduziert-
regelmdssige Kettenbruchentwickelung herausstellt. Umgekehrt ist jedes
Ausfüllungselement von H, das in H die Ortsbestimmung dritter
Ordnung zulässt, ein Ergänzungselement dritter Ordnung von A.

Zwei Ergänzungselemente von H, für welche die Ortsbestimmung
dritter Ordnung in A verschieden ansfällt, sind in H örtlich verschieden.

Ein Ergänzungselement vierter Ordnung von M lässt in H die
Ortsbestimmung vierter Ordnung zu, welche sich, wenn H als die
Menge der rationalen Zahlen gelesen wird, als die eindeutige regel-
mässige Kettenbruchentwickelung (welche eventuell endlich ausfallen
kann) herausstellt. Umgekehrt ist jedes Ausfüllungselement von A,
das in A die Ortsbestimmung vierter Ordnung zulässt, ein Ergän-
zungselement vierter Ordnung von A.

Zwei Ergänzungselemente von H, für welche die Ortsbestimmung
vierter Ordnung in A verschieden ausfällt, sind in A örtlich verschieden.

960

§ 4.
Existenz der Dezimalbruchentwickelung reeller
algebraischer Zahlen.

Seien 7, und +, beliebige reelle algebraische Zahlen, d. h. je
einer algebraischen Gleichung mit ganzen rationalen Koeffizienten
genügende Ausfiillungselemente der von den rationalen Zahlen
gebildeten geordneten Menge H,. Alsdann kann man eine algebra-
ische Gleichung F («) =a, e+ a,ar-14+....4+a,444+a,=0
mit ganzen rationalen Koeffizienten und nicht verschwindender
Diskriminante D bestimmen, der sowohl 7, wie r, genügt. Seien
Wy, Wo, Wa die (mit jedem beliebigen Grade der Genauigkeit
approximierbaren) Wurzeln von F'(r)==0, so können w, und w,
für rs nicht in H, zusammenfallen. Sei g eine rationale Zabl,
welche die Moduln aller Wurzeln von F (7) = O übersteigt, und 6 =2o9,
so ist

| wp - w,| <b (r Fs).
Weil aber

iT i a
(w, —— wy) =a ane ’
MAD °

go ist andrerseits

| 2 > 2

| wy, — We | —————

! An? Sn
a, n bn n—2

so dass wir mittels hinreichend genauer Approximierung von r,
und r, entweder Sicherheit erlangen, dass r, und 7, mit derselben
Wurzel w, zusammenfallen, oder ein r, und r, trennendes rationales
Intervall bestimmen können. Indem wir dieses Resultat zunächst
spezialisieren für den Fall, dass r, eine rationale Zahl ist, ersehen
wir miihelos, dass 7, in H, entweder mit einem Elemente von A,
zusammenfallt oder von jedem Elemente von H, örtlich verschieden
ist, so dass 7, sich als Ergänzungselement vierter Ordnung von H,
erweist, mithin sowohl in einen eindeutigen unendlichen Dezimalbruch,
wie in einen eindeutigen regelmdssigen Kettenbruch entwickelt werden kann.

Setzen wir nun weiter voraus, dass weder r, noch r, mit einem
Elemente von H, zusammenfällt, so fallen sie entweder in H, zu-
sammen, oder sind in H, örtlich verschieden.

Hieraus folgern wir, dass die Spezies der reellen algebraischen
Zahlen eine abzählbar unendliche, im engern Sinne überall diclit
geordnete Menge H, bildet, welche zu H, die am Schluss von $ 2
erklärte Beziehung eines H.4; zu einem entsprechenden H, besitzt.

961
§ 5.
Existenz der Dezimalbruchentwickelung von =x.

Seien a und 5 ganze positive Zahlen und a< 6. Wir verstehen
unter AK, den unbedingt konvergenten *) unendlichen Kettenbruch

een),

und unter K, den unbedingt konvergenten unendlichen Kettenbruch

a? a? oo
(am 4 1)B (2 4 Db In
Alsdann gelten die Beziehungen

-=K 4
ee aaa yc
a’
Kn = > an |
é (2m = 1) 5 —_ Kn we ik )
Seien 2,,2,,2,,-.. reelle Variablen, welche durch die Beziehungen
a
Pe ST
b—«, |
RET
a
ON — TA AE ENE ee (m 2 ish

(2m + 1) b — ami
verbunden sind, und 2’, eine rationale Zahl zwischen O und 1, also
<4b. Mittels (+) leiten wir aus 2’, weitere rationale Zahlen

Pe B Od <2" 44, fe her... Von ‘diesen

fallen Ei Las. tr alle positiv aus, während 2',_1,
eten,

oma dr alle < 46: und a’ < Ti wird. Weiter kann man ein

kleinstes r>>a bestimmen mit der Eigenschaft, dass x,’ < 0 oder > 1
wird *).

Sei a eine (für das weitere hinreichend klein gewählte) positive
rationale Zahl und ya ein solches geschlossenes rationales Wert-
intervall von w,, dass sowohl 1, wie die auf Grund von (tf) ent-
sprechenden Wertintervalle 1041, Nate,--- Mr VON Tais Late,-.+ Lr
rechts vom Werte O und links vom Werte 1 liegen, während, wenn
wir noch die auf Grund von (f) entsprechenden Wertintervalle von
ey ino B emt Haers Neder Ne bezeichnen, jedes K, fir
O<v<r in »y enthalten ist und eine Entfernung > 2a von den
Endwerten von %, besitzt. Alsdann können wir eine solche ganze
nichtnegative Zahl s< r bestimmen, dass 2’,, 2’,,...2's_1 der Reihe
nach in 1), %,,...%s 4 enthalten sind, während a’, eine Entfernung
>a von K, besitzt.

1) Vgl. PRINGSHEM, Miinchener Berichte 28 (1898), S. 299 fgg.
aa. 8-0, B38.

962

Sei 3' eine solche positive rationale Zahl, dass für fos zu %, ge-
horige x, die Ungleichung

hdi

gilt, so besitzt w’, eine Entfernung > af' von K,.

Sei x," eine solche rationale Zahl, dass die auf Grund von (4)
entsprechende Zahl x, <0 oder 21 ausfällt. Alsdann können wir
eine solche ganze nichtnegative Zahl ¢< a bestimmen, dass w",,... v”;_4
der Reihe nach in %,...% 1 enthalten sind, während z,’ eine
Entfernung >a von K, besitzt.

Sei B’ eine solche positive rationale Zahl, dass für jedes zu 4,
gehorige «, die wale oar ical eee

”

ae
gilt, so besitzt a," eine Entfernung SS up von K,.

Zu einer beliebigen positiven rationalen Zahl 2, << 1 und einer
beliebigen positiven rationalen Zahl 7 kann man mithin eine solche
positive rationale Zahl 7, < 1 bestimmen, dass

|i— agi, | >i,

Insbesondere kann man zu einer beliebigen positiven rationalen
Zahl i,<1 eine solche positive rationale Zahl 7,< 1 bestimmen, dass
tg t, | = tay
mithin auch (weil im zwischen den Werten O und 2 enthaltenen
Wertegebiet von y die Ungleichung

'

d arctg y eS |
dy ie 9
besteht)

ud
— =—4,
so dass die Zahl x sich als nnen, vierter Ordnung von
H, erweist'), mithin sich sowohl in einen eindeutigen unendlichen
Dezimalbruch wie in einen eindeutigen regelmässigen Kettenbruch
entwickeln léisst.

Die Entwickelungen dieses und des vorangehenden Paragraphen
bieten Beispiele der Charakterisierung von Ergänzungselementen
bzw. Ausfüllungselementen 7 von H als Ergänzungselemente vierter

1) Die gleiche Eigenschaft der Zahl e ist eine unmittelbare Folge der regelmäs-
sigen Kettenbruchentwickelung

En te 1 le =
mo jee (ere ay |

963

Ordnung von A mittels positiver Rationalitätsbeweise in H (die ein
Element von H bestimmen, mit dem 7 zusammenfallt) oder post-
tiver Irrationalitütsbeweise in H (die r als von jedem Elemente von
H örtlich verschieden erkennen lassen). Hierzu ist zu bemerken,
dass sich aus einem negativen Rationalitits- bzw. lrrationalitdtsheweise
in H (der die Annahme, dass 7 von jedem Elemente von H örtlich
verschieden wäre bzw. mit einem Elemente von H zusammentfiele;
ad absurdum führt) nicht einmal folgern lässt, dass 7 Ergänzungs-
element erster Ordnung von #H ist. Eben deshalb haben wir in
diesem § den LampeErtschen negativen Irrationalitätsbeweis von 2
einer passenden Umarbeitung unterzogen und in die obige positive
Form gebracht. Die weiteren klassischen Beweise desselben Satzes
lassen sich übrigens in analoger Weise ergänzen.

§ 6.
Reelle Zahlen, welche keine Dezimalbruchentwickelung besitzen.

Sei c, die n-te Ziffer der unendlichen Dezimalbruchentwickelung
von a. Wir werden sagen, dass n sich im ersten Falle befindet,
wenn Cn Cnti,--+-Cn44 alle gleich sind, im zweiten Falle, wenn
Cn Cnti,+--+Cntg alle verschieden sind, und im dritten Falle, wenn
weder der erste, noch der zweite Fall vorliegt.

Wir definieren ein Ergänzungselement r der geordneten Menge
der endlichen Dezimalbrüche H, mittels der unendlichen Reihe

Go
Ld

ni
wo d,=0, wenn ” sich im ersten Falle befindet, a, = 10, wenn
n sich im zweiten Falle befindet, sonst a, = 9.

Dieses Ergänzungselement würde erst dann ein Ergänzungselement
erster Ordnung von H, darstellen, m. a. W. eine unendliche Dezimal-
bruchentwickelung zulassen, wenn man eine Methode besässe, für
jedes beliebige im dritten Falle befindliche n, entweder die Existenz
eines im zweiten Kalle befindlichen m >>n mit der Kigenschaft, dass
jede zwischen n und m liegende ganze Zahl sich im dritten Falle
befände, ad absurdum zu führen, oder die Existenz eines im ersten
Falle befindlichen m >> mit der Eigenschaft, dass jede zwischen n
und m liegende ganze Zahl sich im dritten Falle befände, ad absurdum
zu führen.

Wir definieren weiter ein Ergänzungselement erster Ordnung r
von H, mittels der unendlichen Reihe

oo
Bia, 10E

sd)

964

wo jedes a, entweder gleich O oder gleich 9 ist, während a, = 9
und ap: dann und nur dann von a, verschieden ist, wenn n sich
im zweiten Falle befindet.

Dieses Ergänzungselement erster Ordnung würde erst dann ein
Ergänzungselement zweiter Ordnung von H, darstellen, m. a. W.
die im $ 3 definierte eindeutige unendliche Dezimalbruchentwickelung
zulassen, wenn man eine Methode besässe, für jedes ganze positive
n mit der Eigenschaft, dass entweder keine oder eine gerade Anzahl
von ganzen positiven Zahlen <7 sich im zweiten Falle befindet,
entweder die Existenz oder die Abwesenheit eines im zweiten Falle
befindliehen m >> n ad absurdum zu führen.

Ein Ergänzungselement dritter Ordnung von H, würde dasselbe
Ergänzungselement erst dann darstellen, wenn man eine Methode
besässe, für jedes ganze positive n mit der Eigenschaft, dass entweder
keine oder eine gerade Anzahl von ganzen positiven Zahlen < x
sich im zweiten Falle befindet, entweder die Existenz eines im zweiten
Falle befindlichen m >n ad absurdum zu führen, oder ein im
zweiten Falle befindliches m >> n anzugeben.

Wir definieren schliesslich ein Erganzungselement dritter Ordnung
r von H, mittels der unendlichen Reihe

a2

a) —n—1l1
Di ead UD) ;

n=1

wo a,„=9, wenn vn sich im zweiten Falle befindet, sonst a, — 0.

Dieses Ergänzungselement dritter Ordnung würde erst dann ein
Ergänzungselement vierter Ordnung von H, darstellen, wenn man
eine Methode besässe, fiir jedes ganze positive 7, entweder die Existenz
eines im zweiten Falle befindlichen m >>n ad absurdum zu führen,
oder ein im zweiten Falle befindliches m >> n anzugeben.

Sämtliche Beispiele dieses $ fallen übrigens in H, zusammen mit
Ergänzungselementen vierter Ordnung der geordneten Menge der
endlichen Dualbrüche H,. .

Für Beispiele reeller Zahlen ohne Dezimalbruchentwickelung be-
steht bei der Weiterentwickelung der Mathematik stets die Möglich-
keit, dass sie einmal hinfällig werden; dann aber können sie immer
durch solehe, welche ihre Gültigkeit behalten haben, ersetzt werden.

ERRATUM.

Proceedings, Vol. XX (2), p. 1156, 1. 13 from the bottom: read
in the formula: ,,— 0.00003219 7°*” for ,,— 0.00005102 7'*”.

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS

VOLUME XXIII
Ne

President: Prof. H. A. LORENTZ.

Secretary: Prof. L. BOLK.

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

Natuurkundige Afdeeling,” Vols. XXVIII and XXIX).

CONTENTS.

A. SMITS and G. J. DE GRUYTER: “The Electromotive Behaviour of Aluminium”. II. (Communicated
by Prof. P. ZEEMAN), p. 966.

A. SMITS, L. v. D. LANDE, and P. BOUMAN: “The Existence of Hydrates in Aqueous Solutions”.
(Communicated by Prof. P. ZEEMAN), p. 969.

A. SMITS and R. PH. BECK: “The Electromotive Behaviour of Magnesium”. I. (Communicated by
Prof. P. ZEEMAN), p. 975.

A. SMITS and J. SPUYMAN: “A Thermo-electrical Differential Method for the Determination of
Transition Points of Metals at Comparatively Low Temperatures”. (Communicated by Prof. P.
ZEEMAN), p. 977.

BALTH. VAN DER POL JR.: “Discontinuities in the Magnetisation”. II. (Communicated by Prof. H. A.
LORENTZ), p. 980. (With one plate).

P. EHRENFEST: “Note on the paramagnetism of solids”, p. 989.

Miss J. E. VAN VEEN: “The identity of the genera Poloniella and Kloedenella” (Communicated by
Prof. J. W. MOLL), p. 993. (With one plate).

G. A. F. MOLENGRAAFF: “On Manganese Nodules in Mesozoic Deep-sea deposits of Dutch Timor”
with a preliminary communication on “Fossils of Cretaceous Age in those Deposits” by
Dr. L. F. DE BEAUFORT, p. 997. (With two plates). Thy

Eug. DUBOIS: “The Proto-Australian Fossil Man of Wadjak, Java”, p. 1013. (With one wake.

H. A. KRAMERS: “On the application of EINSTEIN’s theory of gravitation to a stationary field of
gravitation”. (Communicated by Prof. H. A, LORENTZ), p. 1052.

NIL RATAN DHAR: “Catalysis. Part XII. Some induced reactions and their mechanism”. (Communi-
cated by Prof. ERNST COHEN), p. 1074.

Proceedings Royal Acad. Amsterdam. Vol. XXIII.

Chemistry. — “The Electromotive Behaviour of Aluminium’. II. *).
By Prof. A. Smrrs and G. J. pe GRUITER. (Communicated by
Prof. P. Zeman).

(Communicated at the meeting of Nov. 27, 1920).

With a view to obtaining a better insight into the electromotive
behaviour of aluminium and its alloys with mercury, the melting-
point diagram was first determined. It was found that, as follows
from the subjoined T,X-figure 1, no compound occurs in the system

Ov 10) 20°. 30 408450) 2601207 80 790" 100
He MOL% AL
al

igst,
1) First communication, These Proc. XXII, N°. 9 and 10, p. 876.

967

Hg-Al, and that the melting-point line of aluminium consists of two
branches, in consequence of the occurrence of a transition point
lying at about 585°.

The determination of the melting-point diagram served by way
of orientation, and now that no compound appeared to exist, it was
certain that the EX-figure corresponding to the ordinary temperature,
must belong to the type I or II in Fig. 2.

S-.. € L
a 5 5 L
E
b b
ae AL 3Hg
Type 1. Fig. 2. Type 2.

Assuming, as has been done before, that GiBBs's paradox is also
applicable to the components of a mixed crystal phase present in
diluted state, the formula’):

0.058 “Ly
log

vF (MI)
was found for the exp. electric potential.

This formula already shows that when we first determine the
potential of Aluminium immersed in a non-aqueous solution of an
Al-salt, and then in an equivalent solution of an Al-salt + a Hg-salt,
the direction of the potential change will depend on which quantity
has decreased more, Ly or (Mr) ®).

If (Aly) has decreased more, the potential will be more negative,
if on the other hand (La;) has decreased more, the potential will

have become less negative.
It is evident that it is also possible to follow the opposite course;

— 2,8.

1) These Proc. XXI, N°. 4, p. 562.
2) Lm is now not a constant quantity, but decreases with greater mercury
content.

63%

968

electrodes with different quantities of mercury may be made before-
hand, and then they may be immersed in a non-aqueous solution
of an aluminium salt, to determine the electric potential.

Without entering here further into the method of experimenting,
we will state already now that the coexisting electrolyte is always
relatively richer in aluminium than the mixed crystal, so that it
could be deduced with certainty from this that the E,X-figure of
the system Al-Hg belongs to the second type. .

But what is remarkable is that though in virtue of the concen-
tration of the coexisting phases it would be expected that the potential
of the Aluminium in an Al-salt solution becomes less negative on
addition of a little of a mercury salt, just the reverse takes place,
and even to a very considerable degree.

This exceedingly remarkable phenomenon shows that, as was
already pre-supposed before, the mercury dissolved in aluminium is
a catalyst for the internal conversions in the aluminium. The metal
magnesium, which is being examined by Mr. Beck, behaves in an
analogous way, but the effects are less.

In a following communication we shall enter more deeply into
the interesting phenomenon mentioned here.

Laboratory for General and Inorganic
Chemistry of the University.
Amsterdam, June 1920.

Chemistry. — “The Ewistence of Hydrates in Aqueous Solutions”.
By Prof. A. Smits, L. v. p. LANDE, and P. Bouman. (Communi-
cated by Prof. P. ZEEMAN).

(Communicated at the meeting of December 18, 1920).

Since the research “On Retrogressive Melting-Point Lines”, in
which an indirect proof was given for the presence of hydrated
Na,SO, molecules in the aqueous solution, attemps have now and
then be made to find other methods, which might be able to give
an answer to the question whether formation of hydrates takes place
in the aqueous solution, also in cases of melting-point lines with
normal courses.

25

we
i=)

.

TWD IN MINUTEN.

EEE EEN ee er ME SS
HOG ib 20 JO 40 50 60 70 60
GRAMM FE‚CLgP100GR.OPL. — FeCl

Fig. 1.
1) Sirs, These Proc. Vol. 14 p. 170 (1911).

970

Thus at constant temperature different properties of aqueous
solutions of hydrate-forming substances, as e.g. spec. gravity, surface
tension, refraction ete. were studied as function of the concentration,
in which curves were obtained, which on the whole taught little or
nothing of importance. Also the determination of the viscosity for
a few systems yielded at first but inconclusive results; in the con-
viction, however, that nevertheless this method promised most on
the whole for the end we had in view, the investigation was con-
tinued with the favourable result that in a few cases curves were
obtained which very convincingly pleaded for the existence of
hydrates in the aqueous solutions.

The system H,O—FeCl, was chosen, of which part of the melting-
point figure, as it was studied by Baknvis KoozrBoom, has been
reproduced in Fig. 1.

The plan was to carry out the experiment at the temperature of
40°, because then, passing very close over the top of the compound

conc. in weight 0/) Fe,Cle (Times of outflow in minutes).

0 1.70
33.50 | 6.15
39.58 | 8.70
46.13 | 12.50
50.19 | 16.45
52.57 | 18.05
55.39 | 19.32
51.45 | 18.66
58.69 | 17.92
60.18 | 17.50
62.44 | 16.90
65.09 | 16.95
66.84 | 17.50
68.45 | 18.60
71.06 | 21.73
12.88 24.63
13.83 28.17
14.12 31.00 Gan

971

Fe,Cl, 12 aq. (melting point 37°), and over that of FeCl, 7 aq. (melting-
point 32.5°) there is the greatest chance that in this neighbourhood
the homogeneous solution will contain considerable hydrate concen-
trations. For at higher temperatures the hydrates will dissociate
more strongly as a rule, hence their concentrations will decrease.

The times of outflow found at 40° are recorded in the table of
the preceding page.

When these results are graphically represented, as has been done
in Fig.1, we get a curve of viscosity exhibiting a very pronounced
maximum and minimum, lying on the left and the right of the
concentration of the hydrate with 12 aq.

This peculiar shape of the viscosity curve must in my opinion
be interpreted in the following way.

When no hydrates were formed in the solution, the viscosity of
the solution with the Fe,Cl,-concentration would increase in an
ever greater degree, and in the end very high values would occur,
because the viscosity of supercooled liquid Fe,Cl, at 40° will be
exceedingly great.

At 6 a decrease of the viscosity is now found here, which in my
opinion must be ascribed to the increasing hydrate concentration.
When only the hydrate Fe,Cl, 12 aq conld exist in solution, it was
to be expected that the minimum would lie near the concentration
of this hydrate.

At 40°, however, we pass not only over the top of the melting-
point line of Fe,Cl, 12 H,O, but also, though not at such a small
distance, over that of the melting point line of Fe,Cl, 7 H‚O.

At the descent from 6 to c an appreciable increase of the con-
centration of the hydrate with 7 H,O will, therefore, also take place,
and when this gives also rise to a decrease in viscosity, the result
will be that the viscosity curve, which must finally ascend again in
consequence of the increase of the Fe,Cl, concentration, presents a
minimum, lying on the righthand side of the concentration of the
hydrate with 12 aq.

After this result had been obtained, and the plan had been formed
to examine also the system HO,—SO,, because this seemed to be
particularly suitable for this purpose, it appeared that KyretscH'),
who studied this system from different points of view, also gives a
viscosity line which presents a close resemblance with the curve
discussed above and of which up to now no notice had been
taken.

1) Ber. 34, 4102 (1901).

972

This circumstance brought, however, no change in our plan,
as it was our purpose to study the influence of the temperature
on the shape of the curve of viscosity in the system H,O—SO,.

It is seen from the subjoined 7—X figure of the system H,O—SO,,
which is not yet quite completed, that at 15° the tops of the compounds

H,SO,.H,O and H,SO, are passed at temperature distances of 6.47°,
resp. 4.65°.

Fig. 2.

The compounds H,SO, . 2 H,O and H,SO, . 4 H,O are, indeed,
also passed, but the melting-points of these compounds lie so far
below 15° (—38.9° resp. —25°) that it is not to be expected that the

973

curve of viscosity will still give any information about these hydrates
at 15°.

Also with a view to this the concentrations were examined between
61 and 83 weight °/, SO,

The investigation was carried out at three different temperatures,
viz. 15°, 40°, and 60° with the following result:

weight 0/0 Time of outflow Time of outflow | Time of outflow

SO, at 15° at 40° | at 60°
88,84 5 min. 21/5 sec. 2 min. 21!/s sec. | 1 min. 2045 sec.
82,13 | ZN 10 ME ay ISHS
81,72 Per bn |

81,55 ae ae, Den We Re | eee
81,42 te ae

80,53 ate weit ot AEN Sioa whe eee ee
17,55 pe ain ode zijnde
16,27 Amen lk

15,12 A panies EE
15,33 EERE,

75,19 A= tat

15,03 hrm er bom 1s. x
73,96 [neg dT ie bena loes.
12,69 ET ee ee
12,08 Re

69,72 Dee fc eae ee
69,60 i Sana’ tebe

64,78 eenden Sr. ie den
63,76 gS Se

63,28 | 1, > 90 » 59'/5 „

Fig. 3 represents these results graphically. It shows that the curve
of viscosity at 15° really has the same shape as that of the system
H,O—Fe,Cl, at 40°. The curves found at 40° and 60° show further
that the peculiar character of the shape of the curve of viscosity

974

becomes less and less pronounced at higher temperature, which can
be accounted for by the increasing dissociation of the hydrates on
increase of temperature.

300

iS)
bh
ee)

DOORSTR TIJD iN SEC
S
S

an
So

qn

ee ae ll

So

TEMPwGR C.

a
5

C 80
GEWA S03
Fig. 3.

Laboratory of General and Inorganic
Chemistry of the Unwersity.
Amsterdam, December 1920.

Chemistry. — “The Electromotwe Behaviour of Magnesium’. 1.
By Prof. A. Smits and R. Pa. Beck. (Communicated by Prof.
P. ZEEMAN.)

(Communicated at the meeting of Dec. 18, 1920).

As was stated before magnesium closely resembles aluminium in
its electromotive behaviour. Also the pure magnesium is as a rule
a state disturbed in a noble direction, which reaches internal equi-
librium by the absorption of small quantities of mercury; but in
this case with magnesium these phenomena are weaker than with
aluminium.

Our purpose was to examine the electromotive behaviour of mix-
tures of magnesium and mercury of different concentration in order
to be able to set forth still more clearly the particular influence of
small quantities of mercury.

Before proceeding to this research, it was desirable to determine
the melting-point diagram of the system Mg —Hg, which investigation
was attended with several difficulties, which we will, however, not
discuss here. The result to which this research led, is represented
in the adjoined 7,N-figure. It must be pointed out here that this
system had already been examined on the Hg-side by L. Campi and
G. Sprroni'), but that this research had been discontinued at the
very point where the difficulties set in, and the system becomes
most interesting.

We see from our diagram, which represents the situation of the
melting-point lines under the varying vapour pressure, that the
system Mg—Hg is very complicated, and contains several compounds.

In order to ascertain what corrections must be applied in the
concentration, in connection with the mercury in the vapour phase,
the determination of the vapour tension of the different mixtures
was undertaken, in which use was made of a glass spring indicator.
This investigation, which is now being continued with the mixtures
rich in mercury, however, yielded the result that for mixtures from
0 to 50 at. °/, Hg the vapour tensions are very small, even up to
the final temperatures of fusion.

1) Atti della R. Accad. dei Lincei 24, 734 (1915).

976

After ‘the 7,X-diagram found had given something of a general
insight, the investigation of the electromotive behaviour of Mg—Hg-

650

600

550

500

40 McHc M M
ary GHG die, me ; 90 Ms
se

mixtures was started, the results of which will be communicated
in a following publication.

Laboratory of General and Inorganic
Chemistry of the University.
Amsterdam, December 13 1920.

Chemistry. — “A Thermo-electrical Differential Method for the
Determination of Transition Points of Metals at Comparatively
Low Temperatures’. By Prof. A. Smits and J. Spuyman.
(Communicated by Prof. P. Zeeman).

(Communicated at the meeting of December 18, 1920).

This paper should be considered as a continuation of the publi-
cation “The Thermo-electrical Determination of Transition Points 1” ©).
In the latter paper it was already stated that the very favourable
results obtained by us on application of the thermo-electrical method
in the investigation of the combination, iron-tin, and copper-tin,
induced us to examine also other important metals in the same way,
starting with copper. Our purpose was to examine in the first place
whether copper shows a point of transition in the neighbourhood
of 70°. The arrangement which we used at first for this purpose is
represented in outline in the subjoined figure.

Cull Ag Cul Cull

q

Fig. 1.

The combination pure silver-pure copper (Cu 1), of which the
copper wire is passed through a glass capillary, was placed in a
wider tube 6, filled with an electrolyte, with which silver and copper
were in electromotive equilibrium. For this purpose we took a
solution of copper-sulphate, because the electrolyte, which is in

1) These Proc. Vol. XXIII, 5, p. 687.

978

electromotive equilibrium with copper and silver, contains but
exceedingly little silver.

As was shown before‘) there then exists between the copper and the
silver wire still a potential difference equal to the Volta-effect. Now
the tube 6 was placed in a thermostat a and the two soldering
places Ag—Cull and Cu l—Cu II in melting ice. After the thermostat
had been kept constant at a definite temperature for some time, the
electromotive force of the circuit was measured. This measurement,
ranging over a temperature interval of from 40°—80°, gave no
indications of a discontinuity in the neighbourhood of 60°, after
which it was resolved to apply a more accurate measurement,
which we found in a method, which we shall call the diferential
method. The arrangement of this differential method is given in
outline below in Fig. 2.

Cull Cul As Cul Cul

a
Fig. 2.

The two extremities of the silver wire, which are soldered to
wires of pure copper, are now both in the thermostat a, but the
capillary & is filled with a solution of copper sulphate, and c
contains anhydrous paraffin oil. Both solutions are under a nitrogen
atmosphere *).

The consideration that led to this arrangement, is as follows. So
long as no transition point is reached on change of temperature,
the electromotive force of the circuit will be very small, hence it
will change but exceedingly little with the temperature in the ther-
mostat; but when a transition temperature of silver or copper is
passed, it is probable that the thread of the differential thermoele-
ment, which is in electromotive equilibrium with the electrolyte, is

1) These Proc. Vol. XX1, 3, p. 386.

2) In reality the tubes b and c, which contain the metal wires immersed in a
liquid, have been first exhausted of air, then filled with nitrogen, and finally
fused to.

6 979

sooner transformed than the thread of the same combination which
is immersed in paraffin oil’).

If this is actually the case, the electromotive force of the differ-
ential thermo-element will undergo a rather sudden change, and the
initial point of this change will correspond with the transition point
of one of the metals of the element. On application of this simple
and very sensitive differential method it was found that the electro-
motive force was practically zero throughout the temperature range
that we examined, for it was less than 0,001 milli Volt. We did
not consider the investigation as finished then, and we once more
examined the same differential thermo-element Cu—Ag—Cu, taking
care that one pair of wires was not only immersed in a solution
of CuSO,, but in such a way that the etched copper wire, the
soldering place, and a small piece of the silver wire were in contact
with powdery copper.

This procedure in our experiment, however, did not bring about
the slightest change in the results, for now too the electromotive
force of the circuit between 40° and 80° remained certainly smaller
than 0,001 milli-Volt.

We will still mention here that the times of observation have
been taken very long here on purpose, and amount to 2x 24 hours.
Notwithstanding this prolonged heating at temperatures above and
below those at which dilatometrically indications were found for a
transition point, the electromotive force of the differential thermo-
element appeared to be smaller than 0,001 milli-Volt. In the first
place this result shows that both the silver wire and the copper
wire were very homogeneous, and in the second place that neither
the silver wire nor the etched copper wire, though they were in
contact with a solution of CuSO, and with fine copper powder over
a length of 20 cm., showed appreciable transformation.

The differential method discussed here is now being applied to
the other important metals. In the following paper also the theory
will be discussed.

Laboratory of General and Inorganic
Chemistry of the University.
Amsterdam, December 13, 1920.

1) For ConeN found that contact with an electrolyte has an accelerating effect
on the transformation of one metal modification into another. This accelerating
action must probably be ascribed to this, that when the stable modification has
appeared only in one point, this gives rise to local currents, which greatly promote
the transformation. ;

Physics. — ‘Discontinutties in the Magnetisation” II. By Dr. Bauru.
VAN DER Por Jr. (Communicated by Prof. H. A. Lorentz).

(Communicated at the meeting of Nov. 27, 1920).

In a previous paper’) under the same title, some preliminary
experiments were described about the discontinuities in the magnetic
induction which occur under certain circumstances in ferro magnetic
bodies, when the magnetic force is varied quite continuously. The
simplest method to observe these discontinuities is to connect a
coil surrounding the ferromagnetic substance to be investigated to
a telephone receiver (through a triode amplifier or even without one)
in which the discontinuities in the induction can be observed, if one
brings a permanent magnet slowly near the coil. In our previous
paper the attention has already been called to the fact that these
discontinuities can also be made visible galvanometrically and that
the phenomenon is especially conspicuous with nickelsteel.

Some further investigations on these discontinuities form the
contents of the present paper.

In order to determine on which part of a magnetic cycle the
discontinuities occur, some hysteresis curves were obtained by means
of an improvised magnetometer. Figure 1 relates to the above
mentioned nickelsteel which has the same thermal expansion coefficient
as glass. The cylindrical wire used has a diameter of 1.98 millimetres

Pa ee a ome
den
bed
Bees omer”

fo 1.

1000

1) These Proceedings Vol. XXIII, N°. 4, page 637 (1920).

981

and is 343 millimetres long. Figure 2 shows the hysteresis curve ot
a soft iron wire (diametre 1.82 millimetres, length 349 millimetres).

Fig. 2.

In order to obtain (for the determination of the part where the
discontinuities occur) a very gradual increase of the magnetising
current, two copper plates in series with the magnetising solenoid
were placed next to each other in a glass jar. With the aid of a
siphon arrangement this jar was gradually filled with a copper-
sulphate solution, which caused a decrease of the resistance and a
rather continuous increase of the current through it. After the Ni Fe
or Fe wire was put in the magnetising solenoid together with a
second induction solenoid closely surrounding the wire, we determined
with the aid of a telephone connected to the induction solenoid
through a three stage triode amplifier, the point on the hysteresis
curve where the discontinuities for the first time occur and the spot
where they disappear again.

It appeared that the discontinuities in the magnetic induction only
occur on the steep parts of the hysteresis curves, viz. in figure 1
and 2 on the parts A—S and C—D. The part from saturation to
where =O, and where therefore only the remanent magnetisation
is left, is, at any rate as far as can be observed, quite continuous.
However, as soon as H changes its sign and therefore the existing
magnetisation is reduced, the discontinuities begin to occur. They
are further audible over a certain distance, which however does not
reach quite to saturation. The rustling noise in the telephones, as

64

Proceedings Royal Acad. Amsterdam. Vol. XXIII.

982

soon as it appears for the first time at A and C' (fig. 1) or D (fig.
2) is still very weak at these points. Thereupon its intensity increases
and at B and D it gradually disappears again.

The electrolytic current control mentioned above, is not sufficiently
continuous for galvanometric observations. By using the following
method, however, we could obtain a very continuous current variation,
though the total magnitude of it was limited.

The magnetising coil M (fig. 3] is put in series with a precision

VODVOVO |

ammeter A, rheostat /?,, key S, commutator G, and battery K.
Moreover M is shunted by the variable resistance ft, while S is
put in parallel to a platinum wire DH, the latter being placed ina
glass tube. This tube has two connections. The one at D goes through
the tap # to a Gaedepump the other at H to a long capillary glass
tube. After S is closed, we can, by variation of A, and R,, and
with the aid of the commutator G submit the ferromagnetic wire
C a few times to a complete magnetic cycle. For the sake of
clearness the wire C’ has been drawn in fig. 3 outside the coil M,
though actually of course its place is inside. Thereupon, after the
pump has been working for some time, the current through M is
made zero and the key S is opened. With the aid of the resistances
the platinum wire DH is brought to a dull red heat and the magne-
tising current is brought to a value which brings the ferro magnetic
substance on the steep part of the hysteresis curve. After the tap
has been closed, the pressure of the air in DH slowly increases;
due to the leakage through the capillary tube, the platinum wire
gets colder, and the magnetising current through J/ increases very

Fig. 3.

983

continuously. By using this arrangement the magnetising current
could in one minute very gradually be increased e.g. from 0.200
Amp. to 0.230 Amp.

The discontinuities which occur in the magnetic induction in the
NiFe wire, the magnetic field being controlled by the thermal
method, are shown in fig. 4, which gives two photographic reproductions
on the same plate of the deflection of an ordinary StemeNs and HALSsKE
moving coil galvanometer. This galvanometer was connected (without
series resistance or triode amplifier) to a long secondary coil of
16500 turns (566 Ohm), which narrowly surrounded the NiFe wire
over its total length. In 6 seconds the field increased from 6.0 to
6.2 Gauss, it having been brought before a few times alternately
to + 36 Gauss. As the galvanometer was very damped, we can
consider the curves of fig. 4 to approximately represent a small
part of the hysteresis curve. (See appendix). The discontinuities in
the induction are very well visible; the upper curve e.g. shows 6
sudden increases of the 5.

Obviously the biggest discontinuities only are registered by a
moving coil galvanometer. However, the phenomenon can be followed
more in detail by using an EiNTHoveN string galvanometer. Various
photograms directly on bromide paper were obtained by using the
latter galvanometer, the bromide paper having been mounted on a
revolving cylinder, every point of which described a screw curve
with a pitch of 1 centimetre.

Figures 5 and 6 are parts of larger photograms. Figure 5 is
obtained with the above mentioned nickelsteel wire and figure 6
with a soft iron wire. In both cases the 566 ohm induction solenoid
surrounded the ferromagneticum over its total length, and in both
cases the sensitivity of the galvanometer was the same, viz. such,
that a deflection of 1,0 centimetre (the distances between the sub-
sequent pitches) corresponds to 0,18.10-° Amp. The width of either
photogram corresponds to one second. The photos were taken after
(in both cases) the material was brought on the steep part of the
hysteresis curve, where the discontinuities are most frequent. The
continuous increase of the field was obtained with the thermal current
control of fig. 3 such, that the field, when using nickelsteel, increased
in 37 seconds from 6.0 to 6.7 Gauss and, when using iron, in 60
seconds from 4,8 to 5,5 Gauss. In the photograms the time runs
from left to right aud the bottom part was described first. The time
in which the string reaches its new equilibrium position when a
constant current is made and broken, is shown at the bottom of
the photograms.

64*

984

The considerable difference between the discontinuities in the iron
and nickelsteel is very well marked in these figures. When using
nickelsteel the clapses are much stronger; the photograms therefore
confirm the observations made before with triode amplifier and
telephone. Apart from giving the intensity, the photograms also enable
us to count approximately the number of discontinuities.

Thus for nickelsteel 1554 clapses were found for a change of
field from 6.0 to 6.7 Gauss, and for iron 1546 clapses for a change
of field from 4.8 to 5.5 Gauss. Moreover the region on the hyste-
resis curve where the discontinuities occur (see fig. 1 and 2) being
known, as well as the fact that the number of clapses at A and C
in the figures mentioned does not reach its maximum value at
once, we can approximately estimate the number of clapses during
a complete reversal of the magnesitation. Thus we found:

for nickelsteel wire (dia. 1.98 mm., length 343 mm.) 5000 clapses,
soft iron wire (dia. 1,82 mm., length 349 mm.) 6500 clapses.

We did not examine more in detail the dependency of the number
of discontinuities upon the diameter and the length of the ferro-
magnetic wire. One should be inclined to expect this number to be
proportional to the volume or, if long iron filaments are magnetised
as a whole, to the diameter; but on the other hand eddy currents
will occur in the outer layers, if an ironerystal in the inner part
is suddenly remagnetised, which eddy currents may be expected to
reduce the suddenness of the currents in the induction solenoid, and
also the rustling noise in the telephone receiver. Very likely, owing
to these eddy currents, jumps of most different values appear on the
photograms, though possibly one definite intensity of magnetic moment
of the crystal is prevalent.

Finally, the assumption that, under certain circumstances, the mag-
netic moments of long filaments suddenly" change as a whole (see
Le.) was found confirmed by the following experiment.

The nickelsteel wire was brought into the magnetising solenoid,
and the current was controlled thermally in the way described
above. The nickelsteel core was surrounded by two small flat coils
of 3 mm. axial length, on either of these coils 2600 turns of ena-
melled copper wire of 0,05 mm. had been wound (the inner dia-
meter of the coil being 3,4 mm., the outer one 13.0 mm.). The
distance between the two coils could be given any arbitrary value.
Hither coil was connected to one of two identical moving coil
galvanometers. Both the galvanometer spots had the form of a line
inclined at 45° to the horizon. They were projected on the same
scale and formed together a cross. |X|

~

985

When now the coils were put immediately near each other, the
jumps in the galvanometer deflections occurred simultaneously, and
the galvanometer spots, in the form of a cross, moved as a whole.
With distances between the coils bigger than 10 em, the average
deflections of the galvanometer were the same, but the jumps were
quite incoherent. However, even up to a distance between the coils
of 7 centimeters, the bigger jumps occurred quite simultaneously,
which shows, that in the nickelsteel used, crystals exist, or at any
rate groups of crystals, which have to be considered as a magnetic
unity, having a length of 7 cm. Possibly these long crystals are
formed during the drawing process to which the wire is submitted
while being manufactured. An effort also to submit annealed or
electrolytic iron to this test did not succeed, as the discontinuities
in iron are too small to be detected with a moving coil galvano-
meter (a double-string galvanometer was not at our disposal).

Appendix. Interpretation of the galvanometer curves.

If in the galvanometer circuit with a total resistance ran E.M.F.
dN
on is induced (by varying the flux MN through the induction solenoid),
Q

we have the following ane

db aN

Ben LS Aas a mae aE
we 9 = Ki |
LT HE aa en |

where @ is the deflection of the system (moving coil or string), u
the elastic force or couple, f a friction constant, m the mass or

16
moment of inertia of the system, and eae the E. M.F. induced
(

dO
for a change of deflection ee

Neglecting the selfinductance L, the elimination of 7 yields the
following equation for the deflection
d’ do KdN
ucts On ee See
moet (f+ ate ae (1)

K
The term represents in the usual way the electromagnetic

damping of the galvanometer.
If we put (1) in the form

va 42 dé 9 dN'
ae ng
where
N' == — N
mr
K*
{+
Za ==
m
ME ee
m

we find, with the method of variation of the constants and with
inh iti dd)
the initial conditions (oo tij ôt):

t t

] F dN! bk dN'
== a ef Be dt — otf mes dhl Seep
(v,—~,) dt dt
0

0

where w, and 2, are the (negative) roots of
vt Zar dw? =0.

If we now suppose that at the time t— 0, N= 0, we have
t t

‘ dN' 3 Aas
en t e SS ap dt — N t 7 uv : en t N ent dt
0 0

Hence (2) becomes
t t

1 .
OZ, et fx’ edt — x, evst po ett dt
(7,-—2,) é :

Further, if we suppose the flux NM’ to increase with jumps, so
that the discontinuous increase at the time t=O is A,N’, at the
time t=, is A, N’ ete. and if we consider MN’ to remain constant
during the intervals between the discontinuities, we may in the
following way replace the integrals by summations

t

werf N'e-sutdt =
0
— A, N'(1—en!) — A, N' (Lendl tij AL (1 ent) . 2.
The deflection 6 can now be written as:

1 ee ti
Siew ed ee

= («,—2,) Ps

A ALN oa Re
€ REA VAL

¥

1

re

zere

BALTH. VAN DER POL Jr.: “Discontinuities in the Magne-

tisation.”

Ho
652 6.7 6.0

Fig. 4.

Figo:

Fis. 6.

Proceedings Royal Acad. Amsterdam. Vol. XXIII.

987

but with the restriction, that up to the time ¢= tj; the first k terms
only of the series are to be taken. Hence, with each discontinuity
the number of terms of the series expression for @ is increased by one.

2 de
For the velocity Fane get
C

dé 1 ; (>
— SS >» An N B a tn) ot uv, é

en es fy
dt (7,—#,) n

| RN
Immediately after the moment f, the velocity zi therefore in-
creased by the amount
1
—_——~ A;, N' (ae) = A; N'
(7,—#,)

Therefore, the effect of the 4’ discontinuity is, that the velocity
existing just before it occurred, is increased by the amount

K
Ay N= — A; N
rm

Hence every discontinuity in the magnetic induction causes a
proportional increase of the velocity of the galvanometer system.

Finally let us consider what becomes of the deflection 4 if, as
was the case with the moving coil galvanometer, the galvanometer
is greatly damped and therefore

DE a".

In this case a deflection, once obtained, decreases only very
slowly (as with the Grassot-fluxmeter).

Now the roots v, and w, are approximately

Tied 1 w?
oe. mn ee | ree
a aa

hence

i} zen )
. | ’ \ n
OS AN! te? « — e~2e(t+t,)

If the experiment does not last too long, we have for all values

to be considered

aa :
nn (hy)

7,

988

The other terms
en e—2a(t—t,)

every time disappear very soon after each discontinuity and produce
a small bend at the upper part of each jump. See e.g. fig. 4. The
more the galvanometer is damped, the greater therefore «, the smaller
these bends are and the quicker the galvanometer is able to follow
the sudden changes of the flux.

If we disregard these small bends the deflection of the greatly
damped galvanometer is simply given by

U

i
Ae Sn ie
2a 2a

and the galvanometer deflections are at any moment proportioual
to the flux going through the induction solenoid‘). If the H there-
fore increases proportionally to the time, the deflection of a greatly
damped galvanometer accurately describes a hysteresis curve. This
extreme case can be better approximated with a moving coil
galvanometer than with a string instrument. The curve described
by the image of the string galvanometer representing the solution
of (1) from which the function N has to be found back, does not
lead to such a simple interpretation.

Haarlem. Physical Laboratory, Teruem’s Institute.

1) This relation is obtained at once from (1) by neglecting the first and third
term of the left hand member.

Physics. — ‘Note on the paramagnetism of solids.” By Prof. P.
EHRENFEST.

(Communicated at the meeting of December 18, 1920).

1. The object of this note is to show that the validity of the
Curir-LANGEVIN law for the susceptibility of solid paramagnetic sub-
stances may be arrived at on a different theoretical basis from that
discussed by Welss') Srern*) and Lrnz*) (comp. section 3 of this
paper), namely on the following assumption : the atoms or molecules
of a solid paramagnetic substance contain electrons circulating in
definite, practically fixed orbits of lowest quantum-number (which
we shall call ‘‘rest-orbits’’), so that, in the absence of an external
magnetic field, there is no perceptible difference in the energy of
the two opposite (right and left) directions of circulation. It will be
further assumed, that with a magnetic field at a given tempera-
ture 7’ the statistical distribution between right and left which
corresponds to MH and 7’‘) will automatically establish itself. On
these assumptions the CUrIr-LANGEVIN law will be found to hold
c.f. § 4), and, in the case of a crystal symmetry or of acrystalline
powder of any crystalline structure, even with the correct numerical
factor 3 in the denominator.

2. LANGEVIN's theory explains the fact, that paramagnetic gases

1) P. Weiss, C. R. 156 (1913) 1674.

3) O. Stern. Z. f. Phys. 1 (1920) 147.

3) W. Lenz. Phys. Zschr. 21 (1920) 613.

4) If the motions of the electrons are not submitted to any limitations by means
of quantum-conditions and if the law of thermal statistics is applied to all the
degrees of freedom, the body is found to be wnmagnetic; comp. H. A. Lorentz.
Vortr. kinet. Theorie der Mat. u. Elektr. p. 188. (Teubner 1914); H. J. van LEEUWEN,
Vraagstukken uit de elektronentheorie van het magnetisme p. 54. [Dissertation
Leiden 1919). Accordingly in his theory of paramagnetism LANGEVIN assumes,
that the ampère currents, which represent the elementary magnets, are not sub-
jected to thermal statistics in their cyclic co-ordinates. But when, as in our case,
quantum conditions are introduced into the statistic scheme, the possibility of
paramagnetism returns, even if not a single degree of freedom remains outside
the scheme. To this circumstance my attention was drawn by Prof. N. Bork in
a conversation (1919).

990

and solutions of paramagnetic salts obey Curie's law, in these cases,
taking account of the smallness of

ull
a= 1
rT’ ( )
it gives at the limit the Curte-LANGEVIN relation
Nw’
ar (2)
3r 7

where X = molair susceptibility; MN = AvoGapro’s number 7 = —=

N

BoLTzMANN’s constant, j= magnetic moment of one molecule. Ex-
periment shows that this relation also holds for certain solid para-
magnetic substances. In particular KAMERLINGH Onnes has found that
gadolinium sulphate follows the law exactly down to the lowest
(Helium) temperatures. This is not what one would expect in view
of the assumption underlying the derivation of the formula, namely
that the orientation of the elementary magnets depends exclusively
on: (1) the thermal motions, (2) the directing influence of the external
field H. In solid (crystalline) bodies there must be additional forces
of a different nature which also play a part in the orientation of
the elementary magnets.

3. lt follows from the papers by Weiss, Stern, and Lenz, that in
the case of forces of that kind which depend on a crystalline structure
the same relation is obtained, if only it is assumed that:

1. The potential energy ® of the forces which try to keep the
axis of an elementary magnet parallel to a definite direction & is
centrally symmetrical, i. e. it is equal for any two opposite orien-
tations of the elementary magnets.

2. When the temperature or the field changes, the statistical
distribution of the orientations, which according to BoLTZMANN
corresponds to the new values of 7’ and H, and to ®, actually
establishes itself; this involves, that there is no retardation in the
necessary reversal of the elementary magnets (false equilibrium).

4. Let us now consider a solid body containing electrons whose
“rest-orbits’” satisfy the conditions mentioned in § 1. Fora particular
electron let the magnetic moment of its orbit be u and its projection
on the direction of the field + g cos 9, according to whether it
circulates to the right or left). At the temperatures considered we

1) Strictly speaking u itself depends on the orientation of the orbit relatively

to the field H, since the velocity of the electron is affected by it. In a magnetic
field it is not simply the mechanical momentum of the electron that is to be

991

can leave out of account the possibility of the electron jumping to
an orbit of higher quantum-number. Now the times during which
the electron moves to the right and to the left are in the ratio *)
et COSI + g—AC0S J anes AET eee (3)
rT
and the time-average of the projection of its magnetic moment on
the direction of H is therefore given by

os 3, G Ee 7
pe cos 9, et cos Fo — yr cos 1}, e— 48 Fo

et cos So + e— eos 3° (4)
Since a is small we may put
gede BN EE coe Os!) A mort u TRE)
hence (4) becomes
wr
79 6
cos? I, (6)
and the susceptibility y for N such electrons will be
Nu? $
En Ë COMO OBB, A HAA. sna)
rT

the mean being taken over the possible orientations of the ‘“‘rest-orbits”’
of the electrons. For a crystal of cubic symmetry or a powder of
arbitrary crystalline structure we have obviously

aes evel

i eee A Mh eins oe oats, Gate
or (8)

whereby equation (2) is arrived at.

5. Additional remarks.
1. According to the above theory the Röntgen-reflection of a
crystal would not be changed by magnetisation. By a very sensitive

h
taken equal to — or a multiple of it, but the electro-kinetic momentum of the
7

electron (reduced to mechanical units) has to be added. However, even with a very
high value of H, this term is small compared to the other. We may therefore
neglect this diamagnetic action, depending on induction, just as LANGEVIN did in
his fundamental theory.

1) In the power of e we must put the quantity which remains constant during
a “collision”. For an electron, which in a constant field H changes from a right-
hand to a left-hand motion, this quantity is not the sum of the mechanical and
electro-kinetic energies, but a kind of “RourH-Function” has to be taken. (Comp.
Dissertation by H. J. van Leeuwen. Leiden 1919, p.p. 11, 18, 52—54, an extract
of which is soon to appear in the Journal de Physique). A simple calcution on
this basis, with the approximation referred to in the previous footnote, gives the
ratio (3).

992

null-method Compron and Roeniry') have actually established the
absence of any such effect for the (ferro-magnetic) crystals of magnetite.

2. In the theory of Lanerevin-Wuiss the rotational movement of
the elementary magnets gives its own contribution to the kinetic
energy and therefore to the specific heat, whereas in our theory
the corresponding term does not occur. At first sight this appears
strange, since the form of equation (2) seems to point to equiparti-
tion. But a similar result will always be obtained, in cases, where
the lowest quantum-motions which are possible, possess a very small
difference of energy As with respect to each other (in our case
2 uHleos 9 with a field H). In those cases there is always a range
of temperatures 7, where 7’ is small enough for the higher quan-
tum-orbits to be disregarded, and at the same time large enough
with respect to Ae.

3. Although the transition between the right- and left-hand
motions requires an amount of energy small as compared to 77’,
still it may require the coincidence of favourable circumstances to
bring about the corresponding reversal of the motion (moment of
momentum). Since we are dealing with a quantic process, it is
probably difficult to treat this question quantitatively. In general we
may expect, that the corresponding retardations in the establishment
of the magnetisation would show themselves most easily at very low
temperatures and rapidly alternating fields’). (For light-vibrations
xy is always=0O). They would for instance give rise to a kind of
hysteresis and a corresponding development of heat, when gadolinium-
sulphate. is periodically magnetized in opposite directions.

Leiden. Physical Department.

1) A. H. Compton and O. Roanuey. Is the atom the ultimate magnetic particle?
Phys. Review. 16 (1920) 464.

2) The possibility of this retardation was pointed out by Lenz in his address
at Nauheim (lc. p. 615) from the point of view of the sudden reversals of the
magnetic atoms. Previously to this in the beginning of July 1920 the question was
discussed by Prof. KAMERLINGH ONNES and me, both from the point of view of
Weiss’ theory and of the assumptions ol this paper, together with the possibility
of testing it experimentally.

Palaeontology. — “The identity of the genera Poloniella and
Kloedenella” By Miss J. E. van Veen. (Communicated by
Prof. J.W. Mout.)

(Communicated at the meeting of December 18, 1920).

In the year 1896 a treatise appeared by Prof. Dr. Géricu about the
Palaeozoicum of the Polish middle mountain range. In this treatise
the author instituted the new genus Poloniella (4, p. 388) for a few
carapaces and valves of formerly unknown Ostracoda, originating
from the middle devonian Ostracoda marl of Dombrowa near Kielce.
These remains he united into one species viz. Poloniella devonica.

Some twelve years afterwards the two American palaeonotologists
Dr. UrricH and Dr. Basser supplied a contribution to the know-
ledge of the Beyrichiidae. On this occasion the new genus Kloede-
nella (8, p. 317) was founded also, under which group they intended
to bring together eight species at the least.

In 1914 Prof. Dr. Bonnema (2, p. 1087; 3, p. 1105) was able to
amplify the characteristics of the genus Kloedenella as given by
Unricn and Bassier as a resuit of his investigation into the nature
of the Ostracod, which Dr. Aurrt Krauser formerly described under
the name Beyrichia hieroglyphica.

In comparing what the above mentioned authors have said about
the genera Poloniella and Kloedenella, it is obvious that the latter
are identical. It should however be observed that what BoNNEMA
takes to be the anterior part of the carapace — and rightly in my
opinion — is considered the posterior part by the others. As a
natural result the valve, which is the left one, according to BONNEMA,
is called the right one by the others.

Thus Bonnema found as the most characteristic feature of the genus
Kloedenella that the right valve before the straight part of the hinge
line has a notch in which a process of the left valve fits. (fig. 3).

In the genus Poloniella a similar connection of the valves seems to
be present. GiricH does not mention this fact emphatically, but as he
writes: “Ganz am vorderen Ende jedoch tritt der linke Saum wieder
zurück und auf der hinteren Kantenhälfte springt der rechte Saum
sogar stark über”, | should conelude from this that it occurs here also.

Besides BONNEMA had found that in the genus Kloedenella the
right valve overlaps the left one at the hinge line, whereas the
Opposite is the case with the free edges. In accordance herewith,
GüricH writes ‘“.... greift am Schlossrande die linke Klappe in
einer gradlinigen Leiste vorspringend iiber den entsprechenden Rand

994

der rechten Klappe” and ‘Langs des Bauch-, Vorder- und Hinter-
randes greift die rechte Klappe über...”

The identity of the two genera, however, appears much more
clearly from the figures Géricn gives of his Poloniella devonica and
BoNNeMa of Aloedenella hreroglyphica and which are partly copied
on the accompanying plate. If we compare Fig. 1 of Poloniella
devonica with Fig. 2 of Kloedenella hieroglyphica and Fig. 7 of the
former with Fig. 8 of the latter, it appears that also of the former
the right valve has undoubtedly a notch in which a process of the
left valve fits. The fact that Güricu represents complete carapaces
of Poloniella devonica and loose valves of the other Ostracoda,
originating from the same locality, renders it also probable that in
Poloniella the connection of valves is present, which is characteristic
of the genus Kloedenella.

At the same time it is easy to see that the furrows on the lateral
sides of the carapaces of the Ostracoda correspond, when we only
assume that in Poloniella devonica the anterior and the posterior
furrows are joined at the ventral side, so that we cannot distinguish
here the two small furrows that are present in Kloedenella hieroglyphica.

If we compare the figures 7 and 9 of Poloniella devonica which
were given by GUricu, it strikes us immediately that the carapaces
illustrated are very different in thickness. This is easily explained
by assuming that the first comes of a male and the second of a
female individual, as has occurred in many other Ostracoda. (1, p. 79;
7, p. 66). The carapace of the female is taken to be thicker than
that of the male as a result of the stronger development of the
genital apparatus.

The same phenomenon appears also in Kloedenella hieroglyphica.
Among the material of this Ostracod, which is to be found in the
Mineralogical-geological Institute at Groningen, occur two kinds of
carapaces viz. thick ones which I think originating from females
(Fig. 10) and less thick ones originating from males (Fig. 8).

Thus we can see that in both genera Poloniella and Kloedenella
sexual dimorphism appears in the same manner.

I, therefore, do not doubt the identity of the genera Poloniella
and Kloedenella. The former being founded Beene latter, the genus
Kloedenella must be abandoned.

The criteria of the genus Poloniella are: carapace elongate and
small; the length usually less than 15 mm.; the thickness of the
carapace of the male individuals practically everywhere the same;
in the female much larger especially at the posterior end. At the
anterior and posterior ends the carapace is equal in height with the

995

males; with the females the posterior part is higher. The dorsal
edge straight; the ventral one convex or somewhat concave. The
anterior edge equally curved and passing almost unperceptibly into
the dorsal edge, as together with it a very obtuse angle is formed;
the posterior edge less curved and forming almost a right angle
with the dorsal edge. Valves unequal; the right one on the anterior
part with a half eireular noteh, in which a process of the left valve
fits. Owing to this peculiar connection of the valves complete carapaces
have generally been preserved. The sharp hinge line of the left
valve lies in a furrow on the hinge line of the right valve, the
latter being higher than the left one along the hinge line. The sharp
free edges of the right valve lie in a furrow on the free edges of
the left, so that with the free edges the left valve overlaps the right
one. The surface of the carapaces is different. On the anterior part
of each valve two more or less vertical furrows are found that are
separated by a narrow lobe. Also on the posterior part a furrow may
occur which can be linked to the anterior furrow below. For the
rest the surface is generally smooth and without ornamental markings.

Remains of these Ostracoda have been found in upper silurian,
devonian and probably also in carboniferous strata of the temperate
zones of the Northern Hemisphere.

In the foregoing we have seen that Poloniella devonica can easily
be derived from the upper silurian Poloniella hieroglyphica by
assuming that the two small furrows which are found below the
middle of the three larger ones, are joined together and with the
anterior and posterior furrow, through the disappearance of the
intermediate lobes. |

Poloniella hieroplyphica is sure to have found its origin in a
species of this genus which resembled to a degree the older but yet
upper silurian Poloniella Hallii Jones sp. (Fig. 12) (5, p. 15). Here
the two small furrows are wanting, bui the three larger ones are
already well developed. The occurrence of valves with one small
furrow in Poloniella hieroglyphica points to this fact also (Fig. 6).

The forms resembling Poloniella Halli: can be easily derived from
the type represented by Poloniella pennsylvanica (Fig. 13) (6 p. 341)
which occurs in under-devonian deposits and where no more than
two vertical furrows are present.

Finally I give my best thanks to Prof. Dr. J. H. Bonnema for
kindly putting the material of Poloniella hieroglyphica at my disposal,
and to Miss A. J. Porr, who has been so obliging as to make the

necessary drawings.
Mineral.-Geol. Inst. University at Groningen.

996

L 11E! RASP ARE:
1. BONNEMA, J. H. „Beitrag zur Kenntnis der Ostracoden der Kuckers schen
Schicht (C,)’.
Mitt. a. d. Mineral.-Geol. Institut d. R. Univ. zu Groningen, Bd. II,
Heft 15:S 184° Tat, IES VOLTS 1009
2. BONNEMA, J. H. „Bijdrage tot de kennis van het geslacht Kloedenella,
UrricH en BASSLER”'.
Kon. Akad. v. Wet. te Amsterdam. Versl. v. d. gew. Verg. d. Wis- en
Nat. Afd. v. 28 Maart 1914. Deel XXII blz. 1087—1092.
3. BONNEMA, J. H. „Contribution to the knowledge of the genus Kloedenella
UrricH and BASSLER.”
These Proceedings Amsterd. Meeting of 24 April 1914. Vol. XVI,
p. 1105—1109.
4. Güricn, G. Das Palaeozoïcum im Polnischen Mittelgebirge.
Verhandl. der Russisch-Kaiserl. Mineral. Gesellsch. zu St. Petersburg.
2e Serie, 32ter Band. 1896.
5. Jones, T. R. On some Palaeozotc Ostracoda from North America, Wales
and Ireland.
Quarterly journal of the geol. society of London. Vol. XLVI p. 15. Pl. IV
Nov. 6. 1889.
6. Jones, T. R. The American Geologist, Vol. IV., N°. 6, 1889. p. 337—342.
7. Moserec, J. C. och GRONWALL, K. A. Om Fyledalens Gotlandium.

Lunds Universitets Arsskrift, N. F. Afdl. 2. Bd. 5. N°. 1.
Kongl. fysiografiska Sällskapets. N. F. Bd. 10. N® 1.

8. UrricH, E. O. and Bassuer, R.S. “New American Palaeozoic Ostracoda.
Preliminary revision of the Beyrichtidae with descriptions of new
genera.”

Proc. of the U. S. Nat. Mus, Vol. XXXV, p. 227—340, with
pl. XXXVII—XLIV, 1908.

EXPLANATION OF THE PLATE.

Fig. 1. Carapace of Poloniella devonica G. GiiricH seen from the right
side. (After GiiRICH).

Fig. 2. Carapace of Poloniella hieroglyphica A. KRAUSE sp. seen from the
right side 40 X. (After BONNEMA).

Fig. 3. Right valve of Polontella hieroglyphica A. KRAUSE sp. 40 X.

Fig. 4. Carapace of Polonzella devonica G. GiiRiCH seen from the left side.
(After GiiRICH).

Fig. 5. Carapace of Poloniella hieroglyphica A. KRAUSE sp. seen from the
left side. 40 X. (After BONNEMA).

Fig. 6. Left valve of Poloniella hieroglyphica A. KRAUSE sp. 40 X.

Fig. 7. Carapace of Poloniella devonica G. Giiricu of a male individual
seen from the dorsal side. (After GiiRICH).

Fig. 8. Carapace of Poloniella hieroglyphica A. KRAUSE sp. of a male
individual seen from the dorsal side. 40 X. (After BONNEMA).

Fig. 9. Carapace of Poloniella devonica G. Giiricu of a female individual
seen from the ventral side. (After GiiRICH).

Fig. 10. Carapace of Poloniella hieroglyphica A. KRAUSE sp. of a female
individual seen from the dorsal side. 40 X.

Fig. 11. Transverse section at the height of the muscle impression of a
carapace of Poloniella hieroglyphica A. KRAUSE sp. seen from the posterior
end. 35 >. (After BONNEMA).

Fig. 12. Left valve of Poloniella Hallii Jones. sp. 15 X. (After JONES).

Fig. 13. Carapace of Poloniella pennsylvanica JONES sp. seen from the
riëht side, from the anterior end and from the ventral edge. 15 X (After JONES).

J. E. VAN VEEN: “The identity of the genera Poloniella and

Kloedenella”’.

Fig. 4. Bae os Fig. 6.

Fig. 10.

ws. a AA VET

Fig. 11. Fig. 12. Fig. 13.

Proceedings Royal Acad. Amsterdam. Vol. XXIII.

Geology. — “On Manganese Nodules in Mesozoic Deep-sea deposits
of Dutch Timor’. By Prof. G. A. F. Moneneraarr, with a
preliminary communication on “fossils of Cretaceous Age in
those Deposits’. By Dr. L. F. pr Braurort.

(Communicated at the meeting of November 27, 1920).

Deep-sea deposits, which resemble in nearly every respect the
recent deep-sea oozes have in tie latter three decades been observed ')
in many islands of the Kast-Indian Archipelago’), notably in the
islands Borneo, Rotti, and Timor. In Borneo they are of mesozoic,
probably of pre-cretaceous age, in Rotti partly of jurassic, and in
Timor, as had been accepted until now of triassie and of jurassic
age. Red clay-shale here and there containing radiolaria, being the
equivalent of the recent red clay, as well as chert and hornstone
with radiolaria, so-called radiolarites, being the equivalent of the
recent radiolaria-ooze, have been found and take up a foremost
place among the rocks composing the soil of these islands. Manga-
nese nodules are not wanting in the mesozoic deep-sea deposits and
I have succeeded in proving®) that they enclose numerous radiolaria,
and thus have been formed by the precipitation of manganese in
an ooze containing radiolaria. The nodules of manganese, which
had been found prior to those described in this paper, differ from
those of the recent deep-sea deposits in two respects. They do not
present, at least not distinctly, a concentric structure, and they
do not include other fossils besides radiolaria. Recent manganese
nodules from the deep-sea, on the contrary, have as a rule a con-
centric arrangement and not seldom the nuclei around which they
are grown, consist of fossil remains, as e.g. teeth of sharks. Shark’s
teeth devoid of any coating of manganese were frequently brought
up in great quantities by the Challenger-expedition from great depths
in the red clay, showing that in such cases these teeth were lying
loose on the bottom of the sea.

1) They are deposited in the deepest parts of the mesozoic Tethys-geosyn-
cline and considering their character of deep-sea deposits, comparatively
close to the land.

*) See References 1, 2, 7, 8, 9, 10, 11, 12.

8) G. A. F. MOLENGRAAFF, Ref. 9, pp. 426 and 427.

65

Proceedings Royal Acad. Amsterdam. Vol. XXIII.

998

The late Prof. Dr. H. G. Jonker *), who, in the year 1916, made
palaeontological explorations in the island of Timor, was fortunate
enough to make a discovery, which decidedly increases the know-
ledge of fossil deep-sea deposits.

In the bed of a little brook, discharging itself into the Noil Tobee,
also called Noil Toninu, on its right bank he found near its
mouth a good exposure of beds of red deep-sea clay, containing,
besides numerous nodules of manganese also teeth of L/asmabranchii,
especially of sharks. The Noil Tobee is a small river rising about
4*/, km. KH. N. B. of Niki-Niki in the district of Amanuban in
Central Timor and joins the Noil Bunu at 3 km. to the North of
its source, a little below the Fatu Toninu. The Noil Bunu flows
into the Noil Noni’), and this again into the Noil Benain, which
river discharges into the Timor sea, not far from Besikama. The
spot in the bed of the brooklet, where Jonker has found this red
clay, is situated about 480 m. above the sealevel.

Jonker had a clear vertical section dug out and entirely freed
from debris which had been transported by the brooklet. A sketch
taken from his diary is reproduced here without any alteration.

. Red clay.
P. Thin bedded limestone.
„CC. Boundary Plane between
ie andieP.

AB. 2 meters.

Fig. 1. Section in the Noil Tobee.

1) Prof. JoNKER by his sudden death on 19 Jan. 1917, was prevented
from preparing any of the results of his explorations for publication. His
collections are stored now in the geological and palaeontological museum of
the Technical High School at Delft. I have been able to make use of his
diary in preparing this article.

?) This portion of the Noil Noni is sometimes considered to form a part
of the Noil Benain.

999

A clay ranging in colour from yellow to red and brown, and con-
taining nodules of manganese overlies, apparently, quite conformably
a thin bedded limestone, which contains badly preserved shales of
Aviculidae (Halobia). The bedded limestone is well stratified, the clay,
on the contrary, is not distinctly stratified except in a portion of the
section, where brown and yellowish-red clay are found to alternate.
In the section the beds of the clay are apparently undisturbed, but
the polished slickensides, which traverse the clay, testify to its having
been exposed to considerable mountain-pressure. In consequence of
the large number of slickensides the clay is crumbly and it is
impossible to obtain a good-sized specimen without joints. The largest
entire specimen brought by Jonker, measures 8 X 6 > 2 cm. It is
represented on Pl. I fig. 2. The position of the limestone and the
clay is the same; both have a strike N. 35° W. and a dip 42°
towards S.W. The yellow clay which prevails in the lower portion
of the section is about 40 cm. thick and is followed by red, and
chocolate-brown clay rather more than 38 metres thick; with it the
section terminates against the surface soil.

Fig. 2. Manganese nodules in red deep-sea clay, Noil Tobee
Central-Timor.

Foto H. G. JONKER.

In the upper portion of the section the brown clay alternates
65*

1000

with bands of yellowish-red clay, which brings out the stratification
to greater advantage.

The manganese nodules are numerous and scattered over the entire
section, as can be seen in Fig. 2. In the red clay, however, they are
more numerous than in the yellow. The relation between these
nodules and the clay has been represented in figure 1 only
schematically. Compared with the given scale the nodules appear
much too large in the drawing. The largest have on an average a
longer axis of at most 10cm., all the others have varying smaller
dimensions. Small ones e.g. of a diameter of 1 or 2 cm. are as
numerous as larger ones.

Further upstream Jonker discovered another exposure of red deep-sea
clay with manganese nodules on the left bank of Noil Tobee, but
it is inferior to the one sketched above.

Teeth of Llasmobranchit especially of sharks are disseminated
in the red clay. Jonker has collected most of them as loose specimens
weathered out from the clay. In his collection there are two pieces
only in which a shark’s tooth constitutes the nucleus of a manganese
nodule. JONKER’s diary does not give more particulars about the
distribution of the shark’s teeth in the clay.

a. The red deep-sea clay.

The red deep-sea clay of Noil Tobee has apparently been altered
very little by diagenetic processes. It has a greasy feel resembling that
of soapstone and can be scratched with the nail; in a dry state
it is somewhat plastic, and distinctly so after moistening. Considering
it as a rock it could hardly claim the name of clayshale, the term
solid clay being more apprcpriate to its character. In this respect
it differs from all other deep-sea shales, hitherto discovered in
Timor and in other islands of the East-Indian Archipelago. In
Timor mesozoic red clayshale is an important constituent in the
structure of the soil, and is found in many places.

In all localities known to me the red deep-sea clay occurs as a
non-plastic, fairly hard clayshale, not unfrequently slightly schistose
through mountain-pressure, and always altered rather considerably
by diagenesis, maybe through silicification, maybe by calcification,

On microscopic examination I found in many cases that such
a clay-shale had first been silicified, whereas later a portion of the
silica has been dissolved again and leached from the rock whilst a
cement of lime had been introduced into the rock.

The locality Noil Tobee, discovered by Jonker, is the only one

1001

known until now where red deep-sea clay of mesozoic age is
found unmodified as a true clay. Up to this day fossil red deep-sea
clay in an equally unaltered state of preservation, has been found
only in one place, viz. the island of Barbados. But here it occurs in
much younger deposits, viz. in the so-called “oceanic beds” of miocene
age. Harrison ') describes it as “clays having a peculiarly greasy feel,
ranging in colour from a dark chocolate-red through various shades
of red and pink to yellow and greyish white”.

There is some difference in properties between the varieties
of the clay of Noil Tobee. The pale red variety displays most
distinctly the properties of a true clay and is also fractured least by
joints showing slickensides; it no doubt represents the purest and
least modified form in which the deep-sea clay here occurs. This
explains why ‘only this pale red variety has been used by me as a
material for an analysis as well as for microscopic examination.
The brown varieties have undergone a more marked modification ;
they are harder and very much fractured by minor polished fault-
planes.

An analysis of a sample of pure, pale red deep-sea clay of Noil
Tobee, carried out by Prof. H. ter Meuren at Delft, shows its
chemical composition to be as follows:

SiO, 57.6

TiO, 0.6

Al,O, Foe

Fe,O, (is

MnO, trace

CaO 1:2

MgO 1.4

K,O trace

Na,O 2.3
H,O below 110° 6.2 10.2
H,O above 110° 4.0

99.6

Trace of Sulphate.

In order to compare this composition with that of recent deep-sea
clay and that of the miocene deep-sea clay of Barbados, the results
of the analyses have to be brought first into intercomparable form

In the analyses of the numerous samples of recent red deep-sea
clay, collected by the Challenger-expedition, Brazier has not taken
into account the salts which had been dissolved in the seawater

1) A. J. JuKES BROWNE and I. B. Harrison. Lit. 3 p. 189.

1002

adhering to the clay. Such adhering connate salts of course can no more
be expected to occur in the samples of fossil deep-sea clay. The quantity
of this adhering salt is not inconsiderable and amounts to 3.61 °/,,
as shown by Harrison and Wi.iiAms') in material of the Challenger.
The constituents of this salt are NaCl, MgCl,, CaSO,, and a trace
of phosphate... Moreover Brazier has not determined the alkalis in
the samples of the Challenger, so that the figures assigned by him
to SiO, and other substances are too high. To meet this deticiency
in our knowledge of the chemical composition of the recent red
deep-sea clay, Harrison and Wirrrams®) have made a new analysis
of the typical red deep-sea clay collected by the Challenger determining
the percentage of the alkalis and mentioning separately the quantity and
the composition of the adhering sea salt. Leaving out the adhering
salt the analysis of the sample of deep-sea clay, examined by Har-
RISON and Winiiams would come to this:

SiO, 56.12

Al;O; 16.30

Ber, 10.94

MnO, ACG

CaO 1.65

MgO 1.43

K,O 1.95

Nar. Bot

H,O 6.92 whilst heating
an natter ey ALI
100.3 at 100°

Now we are enabled to compare the above analysis of recent red
clay with those of the fossil deep-sea clay, as soon as in both the amount
of water, escaping below and above 100°, has been taken into
account in the same way. Doing so it is desirable not to take into
account the water which escapes on heating to 100°, because this
was done neither in the analyses of the miocene deep-sea clay of
Barbados, nor in the most recent analyses of recent red deep-sea clay
made by G. Srrigur and discussed by CLARKE *).

The analysis referred to, of the cretaceous deep-sea clay of Noil
Tobee, recalculated in this way runs:

1) J. B. Harrison and A. J. JuKEs BROWNE. Lit. 6 p. 315.
Dj ‘Rei. 6 py 31 5<and 321.
5) F. M. CraRkKE. Ref. 4, p. 785.

1003

SiO, 61.3
Bei 0.7
Al,O, 20.4
~ Fe,O 7.6
MnO trace
CaO 1.3
MgO 1.5
K,O trace
Na,O 2.5
H,O 4.3 Eseapes on heating
99.6 above 110°C.

In this way we have obtained the following analyses in a com-
parable form:

1 | 2 3 4
SiO, 56.12 | 54.48 | 60.99 | 61.3
TiO, 2.01') 0.98 3.63')) 0.7
Al,O3 16.30 | 15.94 | 21.03 | 20.4
Fe,03 ) 8.66 6.95 1.6
FeO oaks 0.84
MnO, 1.62 121 1.24 trace
CaO 1.65 1.96 (tye 133
MgO 1.43 deelt 202 1.5
K,0 1.95 2.85 0.50 trace
Na,O 3.34 2.05 1.95 2.5
H‚O after drying at 100° 6.92 7.04 4.72 4.32)
[100.27 | 9932 | 100— | 986

1) In the samples 1 and 3 TiO, is determined from a separate
quantity making the figure for Al,O; too high, because TiO, is
comprised in it.

2) Dried at 110°.

1. Recent red deep-sea clay. Pacific Ocean. Challenger station 256. 30° 22’ N. Lat
and 154° 56’ W. Long. Depth 5310 m. Anal. Harrison and WILLIAMs.

2. Average composition of 51 samples of recent deep-sea clay. Anal. G. STEIGER.

Miocene red deep-sea clay. Mt. Hillaby, Barbados. Anal. J. B. Harrison.

4. Cretaceous red deep-sea clay. Noil Tobee. Central Timor. Anal. H. TER MEULEN.

>

On comparing the analysis 3 of the red clay of Barbados
with the analysis 4 of the red clay of Noil Tobee, it strikes us that

1004

the first-named contains 1.24°/, MnO,, whereas the second contains
only a trace. This may be accounted for by the fact that no manganese
nodules occur in the red clay of Barbados and thus the manganese
ore there is not concentrated, as is the case in the red clay of
Noil Tobee. For the rest the analyses 3 and 4 resemble each other
so much, that we may speak of an almost complete identity as to
chemical composition between the cretaceous deep-sea clay of Noil
Tobee of Central Timor and the miocene deep-sea clay of Mt Hillaby
in the island of Barbados. The differences between the fossil and
the recent deep-sea clay are slightly greater. This is easy to under-
stand, as the deposit, directly it had been raised by diastrophism
above the sea-level, must in some measure have been modified
through diagenetic processes, in spite of its being almost impervious
to water. By those processes a portion of the iron has been leached
out and removed from the rock, and silica has been introduced into it.
Taking this into consideration the chemical composition of the red
clay, as well of Barbados as of Central Timor, appears to resemble
fairly well that of the recent deep-sea clay brought up at different
stations by the Challenger, as is evidenced by the above analyses.
The accordance in composition with the samples of red deep-sea clay
collected by the Gazelle and analyzed by von Gümger ') is also great.

Microscopic composition of the red clay.

The microscopic examination of four thin slides of red clay of
Noil Tobee, carried out by Prof. H. A. Brouwer, yielded the following
results: ‘The major part consists of an extremely fine clay-mass,
which cannot be determined more precisely. It contains some larger
fragments of minerals and rocks which were recognized as

a. a polysynthetically twinned crystal of plagioclase ;

b. a small fragment of a voleanic rock with felsparlaths in the
groundmass ;

c. a strongly altered fragment of the groundmass probably of a
volcanic rock rich in glass ;

d. a fragment of a voleanic rock rich in glass, with felsparlaths,
featherlets of ore and much glass ;

e. some strongly altered (serpentinized) fragments, possibly of
olivine originating from a volcanic rock ;

f- an amorphous piece of quartz.

Ill-defined remains of radiolaria, the tests of which have mostly
disappeared, occur in a small quantity in all the slides”.

1) W. von GiimMBEL. Ref. 5, p. 85 and 87.

1005

In one of the sections a nodule of manganese was found to be
cut through. The concentration of the manganese ore appears to
be perfect in this clay since not a trace of scattered grains of
manganese has been found in any of the sections of the red clay
in the slide.

Besides the fragment of quartz mentioned sub f visible under
the microscope, I also observed with the naked eye some white points
which proved to be composed of diminutive pieces of quartz. These
fragments of quartz I consider to be erratic in the red clay, i. e.
to be constituents of terrigenous origin, which for some accidental
reason or Other have been deposited in the deep sea; they may
have been transported by floating treetrunks outside the littoral zone.
For Timor and the East-Indian Archipelago in general such an
interpretation is admissible, because also in the Mesozoicum this region
cannot at any time have been far remote from land.

b. The manganese nodules.

Jonker collected a large number of manganese nodules from the
deep-sea clay of Noil Tobee. The largest among them have the size
of lemons, the smallest are about equal in size to nuts; in the
fragments of red clay a good many occur no larger than peas. The
largest specimen measures 10 X 85 X 6 cm. Two types are found
in the collection, the first type being represented by 90 specimens,
the second by 2 speeimens only.

Type 1. Nearly all nodules are spherical or ellipsoidal. A few
are cylindrical in shape and evidently originated by the coalescence
of two individuals.

The surface is tubercular and finely granulated, reminding one
of shagreen (PI. II, fig. 4). The colour is black to brownish black;
the stripe is dark brown. The nodules are mostly dull, but display
a faint metallic lustre on the projecting parts of the relief, i.e. on
the granules and on the tubercles. Their hardness is less than 2.
The specific weight is + 1.7. This low value is due to the great
porosity of the nodules. As to physical properties the composing
material is analogous to Waad.

The manganese nodules possess a distinctly concentric structure.
A radial arrangement could hardly be perceived in some, in others not
at all. Several nodules in the collection were broken in two, and
show very well the concentric structure. (Plate II fig. 1 and 2). Some
of them are broken on purpose, but Jonker reports that just
below the surface he often found the nodules broken in two

1006

pieces. The nodules have often a white or gray nucleus free
from manganese in their centre, around which on all sides the
manganese has been precipitated in concentric, porous layers *). The
white nucleus is sharply contrasted with the dark envelope (Fig. 3

€

in the text and PI. II fig. 3).

4

Fig. 3. Manganese nodules with a white nucleus of chert containing
radiolaria for the greater part altered into amorphous silica.

In some of the specimens part of the nuclear mass is of a greenish
colour and dimly transparent. These parts can easily be recognized
as chert with a strong pocket lens.

The nuclei are always brittle and more or less friable. In one
case 1 succeeded in having a thin section made through an entire
nodule, nucleus and envelope, without interfering with the structure.
This slide is reproduced in PI. [ fig. I.

On microscopic examination this nucleus appeared to consist of
radiolarite, being converted for the greater part into white, amorphous
silica. In it the radiolaria are packed close together, their casts being
filled up with a crystalline mosaic of quartz. The concentric arrange-
ment and the porous character of the manganese envelope round this
nucleus are easily recognizable in this figure. In some other slides

'! Very rarely a white substance free from manganese, quite similar to
that of the nuclei, was found outside the centre of a nodule, between two
layers of the manganese envelope.

1007

made from these nodules I could state the presence of some radiolaria
also in the manganese substance itself.

The chemical composition is shown in the following analysis of
one of these nodules made by Prof. H. rrr Mrunun:

SiO, 24.4
Fe,O, 25.5
AO: 9.8
MnO FOS
CaO 15
BaO ().32
MgO 0.34
KO Ot
Na,O 1.46
NiO 0.28
CoO 0.16
CuO 0.12
Cl (oxyg. aed.) 0.60

H,O escaping below 110° Tove HEE
is above 110° 10.2 te
99.63

Traces of lead, sulphate and phosphate.

This substance might be called a Waad rich in iron and silica.
For the sake of comparison I give this analysis of a nodule of Noil
Tobee in the following table, after recalculation as if the material
had been dried at 110°, next to an analysis of manganese nodules
from the recent deep-sea clay brought up by the Challenger at four
different stations.

From this table it appears that the composition varies very much
in the different nodules *). On account of the high percentage of iron
they all might be called iron-manganese nodules. The composition
of the nodule of Noil Tobee lies, except for its contents of alumina,
within the extreme values, found on analyzing the nodules of
manganese of the present oceans.

Type 2. Among the manganese nodules of Noil Tobee there
are two of a different type, which I have named the second type.
One of them is broad and flat, measuring 10 >< 9'/, X 3*/, cm.;
the second is more spherical and smaller. They have a specific
gravity of 4.2 and their hardness is 6. Thus they are much heavier

1) An analysis made by A. SCHWAGER of a manganese nodule found in

red deep-sea clay by the Gazelle in the Pacific Ocean, is given by W. von
GiMBEL Ref. 5 p. 102.

1008

and harder than those of the first type. They have a smooth surface
and bear a close resemblance to the manganese nodules occurring
near Sua Lain in the island of Rotti }) in jurassic marls, which
enclose numerous radiolaria. They are also very much like those
which were collected in Timor near Mt Somoholle in deep-sea clay
of presumably triassic age.

Comparative table of analyses of manganese nodules in red clay.

Place |E | Stat AS | SAS GELDE Noll Tobee | z4 type
Depth in | 2600 | 2740 | 2350 | 2335 |
SiO, | 21.80 | 27.62 | 13.66 |. 20.01 26.5 2.9
Al,03 6.60 3.10 2.81 (BiB =|
22.30 23
Fe,0O; 17.82 | 46.40 | 17.88 2151
MnO, 39.32 | 25.48 | 14.82 | 38.15 18.3 57.7
MnO 10.5
CaO 2.21 2.91 3.53 3.58 1.63 5.6
BaO 0.35 11.7
MgO 0.89 127 0.74 | 0.33 0.37
K,0 | 0.16
Na,O 1.59 1.1
NiO trace | trace 0.30
CoO trace trace 0.17 0.3
CuO trace trace trace trace 0.13
Cl (oxyg. aeq) 0.65
CO, Ree
H2Oescaping
above 110° | 11.— | 15.20 | 14.40 | 11.35 11.1 + 15.3

When broken into halves these nodules look quite compact and
homogeneous and show no trace of a concentric structure. In
the last column of the above table the chemical composition of a
nodule of the second type from Sua Lain?) in the island of Rotti
is given. It differs much from that of the nodules of the first type.
These nodules of the second type of Noil Tobee have not been
examined any further, because JonKER’s notes do not tell us whether

1) Ref. 12 p. 326, 393; 2 p. 61 and 9 p. 1064.
3) The large percentage of BaO accounts for the high specific gravity,

1009

they originate from the red clay in situ or whether they have been
transported by the brooklet from a higher level.

c. The fossils in the red clay and in the manganese nodules.

- These fossils have been examined by Dr. L. F. pr Braurort, who
has summarized his results, thus far obtained, as follows:

“The fossils derived from the deep-sea deposits of Noil Tobee
consist for the greater part of tooth-fragments of Hlasmobranchu.
With a few exceptions only the crown of the teeth has been pre-
served and of these also the dentine has been dissolved, so that only
an enamel sheath remains.

This state of preservation, quite in keeping with what could be
anticipated in a deep-sea deposit, renders the determination of the
objects very difficult. In many cases it is even impossible to class
the fragments as a definite species or even as a definite genus.

By far the greater number of the teeth belong to sharks of the
Lamnidae. Thus far no older specimens of this family are known
than those belonging to the chalk, unless the genus Orthacodus of
the Upper-Jura be classified among the Lammnidae.

This genus, however, is not represented in the collection under |
consideration. We recognize in it tooth-fragments of Carcharodon
(known from Chalk and Tertiary deposits), Zamna (Cretaceous to
Recent), and Scapanorhynchus (know only from the Upper Chalk).

Furthermore I include a single fragment among the genus Memu-
pristis (Upper Chalk, Tertiary, and a single recent species) of the
family of Carcharidea.

Considered merely palaeontologically, the fossils mentioned above
might be believed to belong to the Upper Chalk. This view is sub-
stantiated in large measure by the presence in the collection of some
well-preserved teeth of the easily recognizable genus Ptychodus,
teeth of this genus, which is looked upon as a precursor of the
Myliobatidae, being found up to the present only in the Upper
Chalk of Europe and North-Aterica.

In the Timor-collection we find teeth of 3, perhaps of 4 species
of this genus. They may be assimilated to, or anyhow they are
closely related to the following species: P. decurrens Ag., P. dixoni
Dudley and P.rugosus Dixon. These three species, which according
to Smita Woopwarp (Quart. Journal Geol. Soe. London, Vol. 67.,
1911, p. 276) form an ascending progression, occur according to DiDLEY
(le. p. 263 seqq) in different layers of the Upper Chalk of England.

Over and above the teeth discussed, the collection also contains
some undetermined fish-teeth and a fragment of a tooth ofa reptile,

1010

furthermore some fin-spines presumably of Selachii and lastly some
fragments of bones, indeterminable thus far.

It may be that a closer investigation of these hitherto undetermined
pieces from the remarkable collection will reveal that still older
types are among them. As yet I can establish only with abso-
lute certainty that ‘an the deep-sea deposits of Timor there occur
types, known up to now either exclusively from the Upper Chalk
or from no older strata than the Upper Chalk.”

The above examination goes to show that the fossils found in the
red deep-sea clay and also in some of the manganese nodules
are of upper-cretaceous age. From this we can logically infer that
the deep-sea clay in which the teeth of Hlasmobranchii are formed,
is also of upper-cretaceous age. This result is divergent from what
might be concluded from the stratigraphy of the complex of layers,
to which the deep-sea clay belongs, as observed by Jonker. It is
evident both from the deseription and the section (fig. 1) that the
red clay directly and comformably overlies a well stratified bedded
limestone, in which are found not very well preserved, but clearly
recognizable, remains of Aviculidae (Halobia). These are only known
to. occur in deposits of triassic age, and Jonker, therefore, did not
hesitate to consider the red deep-sea clay with manganese nodules
as triassic.

Although I believe the palaeontological evidence to be conclusive,
it appears necessary to look for an explanation of this controversy.
Two ways in which the section (fig. 1) may be read deserve con-
sideration in order to account for the apparent contrariety.

First of all the cretaceous deep-sea clay, overlying directly conformably
the triassic bedded limestone, may not have been deposited there
originally, but may have been brought there afterwards by orogenetic
movements. The plane cc’ (fig. 1) in this ease would not be a partition-
plane between two superposed formations, but would represent the
tectonic contact of two formations of very different age. A large break
and a marked stratigraphic gap would then separate the two conform-
able, successive complexes of layers. Similar stratigraphic hiatus between
conformably superposed formations, are of frequent occurrence in
Timor with its chaotic tectonic, and are peculiar to regions, which
have been considerably disturbed by orogenetie movements with
considerable horizontal displacements, as BERTRAND has set forth as
early as the year 1890. Most often, however, the difference in age
between the conformably superposed formations is not so great as
must be assumed in the case of Noil Tobee. Frequently I encountered

Deep-

G. A. F. MOLENGRAAFF: “On Manganese Nodules in Mesozoic

sea deposits of Netherlands Timor’’.

Plate I.

G. A. F. MOLENGRAAFF: “On Manganese Nodules in Mesozoic Deep-
sea deposits of Netherlands Timor”.

Plate I.

Fig. 1.

Fig. 2.

Proceedings Royal Acad. Amsterdam. Vol. XXIII.

A. F. MOLENGRAAFF: “On Manganese Nodules in Mesozoic
Deep-sea deposits of Netherlands Timor”.
Plate II.

-roceedings Royal Acad. Amsterdam. Vol. XXIII.

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1011

upper-triassic deposits overlying permian deposits conformably ; in
the case of Noil Tobee it would appear that an upper-cretaceous
deposit is superposed conformably on an upper-triassic sediment. In
such a case certain characteristics of the plane of contact between
the two formations often reveal it to be a tectonic plane. In fact in
such cases the plane is as a rule more or less polished, slickensided
or plastered over with a thin layer of gouge. No mention is made
of it by Jonker in his notes about the geology of the place. Pro-
bably he conceived the plane cc’ between the red clay and the
bedded limestone to be a normal partition between two deposits in
normal succession.

Secondly it is possible, that the section after all represents a true
undisturbed succession; if so, the red clay with nodules of manga-
nese would embody the sum total of all that has been deposited
here, in the deep-sea, from upper-triassic to uppercretaceous time.
In such a case one might expect the fish-teeth, described above,
not to occur in the lowermost part of the section. The notes on
hand do not settle the question. An a priori rejection of this solu-
tion would not be warrantable either. True, the thickness of the red
clay (in the section rather more than 3 m.) is small if compared
with the enormous time its deposition must have taken, but then
also the process of sedimentation must have been extremely slow
in the deepest parts of the oceans far removed from the land, i.e.
in the areas of the red clay.

EXPLANATION OF THE PLATES.
PLATE ‘I.

Fig. 1. Section of a manganese nodule from the cretaceous deep-sea
clay of Noil Tobee.

K. Nucleus, consisting of modified radiolaria-chert.

CC Concentric shales of manganese ore.

B.O. Outer surface of the nodule.

Fig. 2. Fragment of red deep-sea clay of Noil Tobee, containing a small
manganese nodule with a large, white nucleus. Natural size.

PLATE II.

Fig. 1 and Fig. 2. Broken nodules manganese of Noil Tobee, clearly showing
concentric arrangement.

Fig. 3. Nodule of manganese showing concentric layers and a white nucleus.

Fig. 4. Nodule of manganese seen from the outside. The surface is mam-
millated and is like shagreen in appearance by numerous little rugosities.

1012

REFERENCES.

1. H. A. BROUWER. Geologisch overzicht van het oostelijk gedeelte van den
Oost-Indischen archipel. Jaarboek van het Mijnwezen, 46e Jaargang, 1917,
especially pp. 52, 61 and 63. Batavia 1919.

2. H. A. BROUWER. Voorloopig overzicht der geologie van het eiland Rotti.
T. K. Ned. Aardr. Gen. 2. XXXI p.611, 1914.

3. A. J. Jukes BROWNE and J. B. Harrison. On the geology of Barbados
Part Il. The oceanic deposits. Quart Journ. Geol. Soc. Vol. XLVIII p. 170, 1892.

4. F. W. CLARKE. The composition of the red clay. Journal of Geology XV.
p. 783, 1907. 2

5. W. von GüMmBeL. Die min. geol. Beschaffenheit der auf der Forschungs-
reise S.M.S. Gazelle gesammelten Meeresgrund-Ablagerungen. Forschungs-
reise S.M.S. Gazelle II. p. 69. Berlin 1888.

6. J.B. Harrison and A. J. JukES BROWNE. Notes on the chemical com-
position of some oceanic deposits. Quart Journ. Geol. Soc. Vol. LI p. 313, 1895.

7. G. A. F. MOLENGRAAFF. Geological exploration in Central Borneo
pp. 414—418 and Appendix I by E. J. Hinpe, Leiden 1902.

8. G. A. F. MOLENGRAAFF. On oceanic deep-sea deposits of Central-
Borneo. Proc. Royal Acad. Sc. Amsterdam XII p. 141—147, 1909.

9. G. A.F. MOLENGRAAFF. On the occurrence of nodules of manganese
in mesozoic deep-sea deposits from Borneo, Timor and Rotti, their significance
and mode of formation. Proc. Royal Acad. Sc. Amsterdam Vol. XVIII, pp.
415—430, 1915.

10. G.A. F. MOLENGRAAFF. L’expédition néerlandaise à Timor en 1910—1912
Archives Néerl. des Sciences exactes et naturelles III B, Tome II, p. 395, 1915.

11. G. A. F. MOLENGRAAFF. Folded mountain chains, overthrust sheets and
block-faulted mountains in the East Indian Archipelago. Compte Rendu XlIle
Congrès géologique international Toronto 1913, p. 690, Ottawa 1915.

12. R. D. M. VerBEeEK. Molukken-verslag. Jaarboek van het Mijnwezen,
37e Jaargang, pp. 694 and seq. Batavia 1908.

Palaeontology. — “The Proto-Australian Fossil Man of Wadjak,
Java’. By Prof. Eve. Dusots.

(Communicated at the meeting of May 29 and September 25, 1920).

Tjampur Darat or Wadjak, the capital of the district of Wadjak,
is a village (dessa), south-west of the town of Tulung Agung, and
about in the meridian of the Wilis-summit. There the plain of Kediri
has penetrated, past Mount Kelut, into the Gunung Kidul — the
Southern mountain range —, and has obtained a steep Eastern
boundary. The origin of this abrupt breaking off of the Tertiary
lime-stone mountains has been attributed, no doubt rightly, by
VERBEEK and Frnnema to a fault running along that escarpment,
through Tjampur Darat or Wadjak and Gamping *). In this southern
continuation of the plain of Kediri, separated from the Indian Ocean
by a mountain tract only 3 kilometers broad, lies the Rawa Bening
(Clear Lake), now for the greater part a marsh, the water of which
flows off through the Kali Tjampur, which, after uniting with the
Kali Bendo, coming from the West, to form the Kali-Ngrowo, falls
into the Brantas on the North of Tulung Agung. Repeated eruptions
of Kelut and other voleanoes must gradually have raised the bottom
of the lake with voleanic ashes. And while in the similar deposits
which were formed downstream, the river easily kept its bed deep,
the lake, which was probably very large at first and extended as
far as the foot of the lime-stone rocks, had to diminish in extent and
depth in course of time. Possibly the upheaval of Southern Java
may also have contributed to this effect.

On the slope of that part of the mountain that extends, almost
rectilinearly, over a distance of 800 meters in W.S. W. direction,
immediately on the south of Tjerme and at 2 kilometers distance
S.5. W. of Tjampur Darat, fossil human bones were found in 1889
and 1890. The plain lies there at the foot of the mountain 90 meters
above the level of the sea, the plateau more than 140 meters higher,
i.e. more than 230 meters above the level of the sea. Near the top
the rock rises up almost vertically, for the rest the gradient is on
an average 300, through the accumulation of fallen lime-stone blocks

1) Fault N°. XXXI on the map “Cvrr and Dit” of the Geological Atlas of Java
and Madura.
66
Proceedings Royal Acad. Amsterdam. Vol. XXIII.

1014

and smaller débris, and there are also some small irregular terrace-
shaped projections. Where the slope is not very steep and on the
plateau, the lime-stone is often covered with a yellowish clay, con-
taining more or less humus, a weathering product, no doubt, of
voleanic ashes fallen in former times. In such places where it is
somewhat protected against the direct action of the rain, this clay,
impregnated with calcite, can unite with fragments of lime-stone to
a breccia. Also many bones were wholly or partly inclosed in the
hardened clay of such a breccia. For the rest they lay in the loamy
clay, only superficially covered with a calcareous concretion.

The first find dates from 1889. In the beginning of this year,
when I was carrying out excavations in caves in the surroundings
of Pajakombo in the Padang Highlands in Sumatra, Dr. C. Pr.
SLUITER, then at Batavia and member of the board of the ‘“Natuur-
kundige Vereeniging in Nederlandsch-Indié”, had the kindness to
send me some fossil bones. These fossils had been found by Mr. B. D.
VAN RierscHoreN when exploring the described lime-stone rocks for
the establishment of marble quarries’), and had been sent to the said
Society. Mr. van RigerscHoten thought these bones to be remains of
“the skull of a man or a manlike animal”. After having prepared
and joined the very fragmentary remains, I recognized in them the
not entirely complete skull with right angular part of the lower
jaw’) and a few other fragments of the skeleton of a fossil man
greatly deviating from the Malay type. The resemblance with the
Papuan type seemed closest to me °).

This important find of Mr. van RierscHOreN induced me to carry
out excavations near Wadjak the following year. The finding-place
of the Wadjak skull I appeared to lie near the middle of the described
part of the mountain slope, and at about 50 meters above the plain,
in a terrace shaped projection, formed by blocks and smaller stones
with breccia and clay *). Here parts were found of a second fossil
skull, Wadjak II, with unmistakably similar characters as the first,
whieh, like the first skull, after further preparation, presented an
even closer resemblance with the Australian of the present time than

!) The marble exploitation company, formerly called ‘‘Wadjak”, is now conti-
nued under the name of “Marmoyo”.

2) Natuurkundig Tijdschrift van Nederlandsch-Indié. Batavia. Deel 49. (1889),
p. 209—211.

8) The rest of the lower jaw and most of the crowns of the teeth of the upper
jaw must have got lost in the digging.

4) | had at first erroneously taken an interstice between blocks for a crevice in
the rock.

1015

with the Papuan'). Besides a large part of the upper jaw and a
large part of the lower jaw (Fig. 4 to Fig. 7. The existing fragment
of the right ramus mandibulae is not represented), six loose teeth
(which are lost in the lower jaw), and several large and small
fragments of the calvaria, in which the most important morphological
characters can still be recognized, there were found some pieces of
other bones of the skeleton and a few fragments of bones of mammals,
as far as can be ascertained not different from species now living
in Java. All the bones met with were in the same condition of
fossilisation; all of them were found scattered in a detached, frag-
mentary state, quite encrusted, for so far as they were not enclosed
in a breccia, with an irregularly thick, yellowish-grey calcareous
concretion, forming a rough surface and containing some clay. This
so firmly adhered to the white bony substance lying under it, that
it mechanically constituted one whole with it; only the difference
in colour could serve at its removal. The incrustation was so thin,
in most places, that the general morphological characters of the bones
were hardly masked by it. That the specific weight of the bones of
these fossil australoid men is high, and the fossilisation very complete,
is at once perceived when they are taken in the hand; they are really
heavy and cold to the touch as stone. From the available remains,
the weight of the whole mandible of the Wadjak man II can be
calculated at 230 grams, i.e. about a hundred grams more than the
maximum of Australian aborigines. Partly this greater weight is,
indeed, to be attributed to the very great size and robustness of the
fossil mandible, but the specific weight is about 40 per cent. higher
than that of fresh bone. For the specific weight of powdered cortical
substance of a femur | find 2.78 at 15° C. The specific weight of
the cortical substance of recent long bones is 1.98, that of pure calcite
2.72, of apatite on an average 3.19, which is also about the maximum
of phosphorite. The fossil bones of Wadjak now contain only a very
small quantity of organic substance.

The specifie weight of the bones of the fossil man of La Chapelle-
aux-Saints, as deduced from a comparison of weight with recent
bones of the same dimensions’), has increased: only in the ratio of
about 1 : 1.20, instead of 1 : 1.40, which is about the ratio for
the fossil men of Wadjak. This may be partly owing to the more
favourable conditions of fossilisation of these latter bones, however
it certainly points to great age.

In the absence of direct data for the determination of the geolo-
1 Verslag van het Mijnwezen, over het Derde Kwartaal 1890. Batavia 1890.

’) M Bouvre, L'Homme fossile de La Chapelle-aux-Saints, p. 16. Paris 1913.
66*

1016

gical age — also artifacts were not found — another find near
Wadjak is of special importance. At the eastern corner of the
described rectilinear part of the mountain, at a height of about 120
meters above the plain, in the same kind of breccia and clay and
again on a small terrace-shaped projection (behind which was found
the entrance of a cave forty meters long, running in the shape
of a U, and almost entirely filled up with the same kind of clay,
in which nothing of any importance was found), I dug up some ©
parts of a human skeleton in the same year, which are in a very
different state of fossilisation, and have a quite different anthropo-
logical character. It is also certain that these remains were worked
as skeleton by a human hand, for the outer surface of the cranial
bones (not the inner surface), the teeth, and also other bones were
painted red with a firmly adhering ochre-layer. After this the bones
must have been broken, for the fragments were encrusted and partly
enclosed in breccia, in a similar way as those of the two Austra-
loids. They are however much less petrified and specifically lighter
than these. Besides, the skull was distinctly brachycephalic, in contrast
with those dolichocephalic australoid skulls. As this fossil man is
certainly prehistoric, the bones of two others, fossilized under similar
circumstances, but to a very much higher degree, must probably
date from Plistocene time.

The presence of human remains from very different periods may
be attributed to the circumstance that this mountain slope belonged
to the shore of a lake abounding in fish *), the fact that the bones
are broken in so many places may be accounted for in this way,
that in times lying widely apart, first the two proto-Australians living
there, and much later the skeleton placed before the cave which
was probably inhabited, were buried and crushed under falling stones
and rubble, possibly in earth-quakes. In the lime-stone mountains of
Sumatra I a few times witnessed close by the imposing phenomenon
of the spontaneous fall of lime-stone rock and rubble, and also once
in the Gunung Kidul (Southern Range) in Java. The large quantity
of rubble, at the foot and against the slope of these mountains, bears
witness to the frequency of the stone-falls. The fragmentary character
of the parts of the skeleton cannot be attributed to cannibalism ; the
fractures are too numerous. The lower jaw of Wadjak II, a very
strong bone, was, for instance, broken into at least five large pieces.
The fact that in both cases the remains were found on a flat —

1) Calcareous waters abound in fish as a rule. The Rawa Bening does so

still, and the number of water-fowl is enormous; it is also paradisical through its
uxuriant vegetation.

1017

part of the slope under a precipice, and the circumstance that
Wadjak I, to all appearance a woman, accompanied Wadjak II,
who was certainly a man, that also the skeleton was crushed on
the other flat part, in the front of the cave, are facts that quite fit
in with the other interpretation of the fragmentary state of the bones.
For the same reasons Carnivora (Tiger, Adjag) cannot have broken
the bones either. It is further easy to understand that in the progress
of the natural change of the mountain slope, many parts of the
crushed skeleton were lost.

The skull of Wadjak I is partially filled up with breccia mass,
and defective in some places; a few bones have also been slightly
dislocated. Consequently some measures can only be taken indirectly,
others not at all. After some correction, the former can generally,
i.e. when the amount of the dislocation is measurable, still be deter-
mined with sufficient certainty.

The general form and the principal dimensions at once show that
we have to do with a type deviating altogether from the Malay
race. This is already evident on comparison of the norma lateralis
with that of a typically Javanese skull placed at the same auricular-
bregma line (fig. 1). For further comparison with our fossil skull,
as far as its morphological characters are concerned, only the
Papuan (in general the Melanesian), the Australian, and the Tas-
manian are evidently to be taken into consideration, a group, which
morphologically has a great number of characters in common. That
the Wadjak man is no more closely related to Homo neandertalensis
than those recent human types needs hardly further demonstration
nowadays. *)

The fossil skull of Wadjak I is large, exceptionally large for a
woman, to whom it probably belonged (from the comparison with
Wadjak II). The greatest length of the calvaria is 200 mm. This
is probably never attained by female representatives of the said
recent races of man, hardly ever by male Australian skulls (Turner) *),
and exceeded by very few by a few millimeters (Duckworrn) °).

1) Cf. M. Boure, L'Homme fossile de La Chapelle-aux-Saints. Paris 1913.
Extrait des Annales de Paléontologie. (1911—1913), p. 231 et seq., and also the
treatise by Berry and RoBerrtson, the last-mentioned paper of note (4), p. 171
et sec., and A. Kerrr, The Antiquity of Man, Chapter VIII. London 1920.

4) W. Turner, Report on the Human Crania and other Bones of the Skeleton.
Challenger Reports, Vol. X. (1884); Vol. XVI. (1886).

5) W.L. H. Duckwortn, A Critical Study of the Collection of Crania of
Aboriginal Australians in the Cambridge University Museum, Journal of the Anthro-
pological Institute of Great Britain and Ireland, Vol. XXIII. (1894), p. 284, and
Notes on Crania of Australian Aborigines. Ibid., Vol. XX VI. (1897), p. 204.

1018

The greatest breadth is 145 mm. (measured directly, without the
necessary correction 150 mm.), the basi bregmatic height is 140 mm.
These measures, too, are near the maxima of the comparable group.
For the length-breadth index 72.5 is thus found, for the length-height
index 70, for the breadth-height index 96.7. Accordingly the skull
is dolichoeephalie and tapeinocephalic [Fig. 2. Norma frontalis, and
Fig. 3. Norma verticalis |.

According to the records of Berry, ROBERTSON, STUART Cross, and
Bicuner') these cranial measures, minima, means, and maxima
for 100 Australians, 86 Tasmanians, and 191 Papuans (unsexed),
in millimeters, and the mean indices, with which I compare Wadjak

I, were as follows:
eset

|

| Australians | Tasmanians | Papuans Wadjak I
|

|
Maximum CranialLength| 164 181.8 199 |163 180.3 198/157 177 197 200

Maxim. Cranial Breadth] 120 130.7 143 | 125 135.1 145/112 128.4 146 145
Basi-Bregmatic Height | 115 129.7 144|117 130.3 140/118 131.7 143 140

Length-Breadth Index Nila 74.94 72.54 72.5
Length-Height Index 71.38 72.19 74.41 70

Breadth-Height Index | 99.65 96.33 | 102.56 96.7

From this appears the close resemblance with this group of
modern human types. The approach is closest to the Australians
and the Tasmanians, least so to the Papuans. This applies also to
other morphological characters of the cranium. The cranial vault
has the characteristic rooflike appearance of Australian skulls, and
the side-walls are almost vertical (Fig. 2 Norma frontalis), but the
height of the cranium is nevertheless comparatively small; the
glabella and superciliary ridges are very pronounced; the forehead

1) A. W. D. Rosertson, Craniological Observations on the Lengths, Breadths and
Heights of a Hundred Australian Aboriginal Crania. Proceedings of the Royal
Society of Edinburgh, Vol. XXXI. (1912), p. 1. — RicHarp J. A. BERRY and
K. Stuart Cross, A Biometrical Study of the Relative Purity of Race of the
Tasmanian, Australian and Papuan. Ibid, p. 17. — Ricnarv J. A. Berry and
A. W. D. Rosertson, The Place in Nature of the Tasmanian Aboriginal as Deduced
from a Study of his Calvarium. Part I. His Relations to the Anthropoid Apes,
Pithecanthropus, Homo primigenius, Homo fossilis and Homo sapiens. Ibid. p. 41.
— L. W. G. BiicHNer, A Study of the Curvatures of the Tasmanian Aboriginal
Cranium. Proceedings of the Royal Society of Edinburgh, Vol XXXIV. (1914),
p. 128. — Ricnarp J. A. Berry and A. W. D. Ropertson, The Place in Nature
of the Tasmanian Aboriginal as Deduced from a Study of his Calvaria. Part II.
His Relation to the Australian Aboriginal. Ibid., p. 144.

1019

is more receding; the orbits are low in comparison with their
breadth (in all these respects Wadjak II still exceeds the first found
skull); the nasal bones are little prominent; the upper jaw is more
prognathous, and the floor of the nasal cavity passes gradually into
the incisive region; there is even an almost perfect sulcus praena-
salis (‘Affenrinne’) at both crania; the lower jaw is exceedingly
strong and the chin more pronounced. In all these characters the
fossil cranium is still somewhat nearer the Australian.

Berry, RoBurrsoN, and Stuart Cross have decisively shown, appa-
rently, that the present Papuan type is the least pure of the three
types mentioned, and, in their opinion, also the Australian is a hete-
rogeneous type, a view which was already accepted by many
anthropologists, contra SCHOETENSACK, Kraarscn*) and some others.

Berry supposes that a primitive Papuan race may be the common
stock type of the Tasmanian, who has remained purer, but varied
during the long time of his isolation, and also of the Australian
aboriginal, who is the result of the cross between Homo tasmanianus
and some unknown other race *).

G. Serci*) assumes as the common stock type a primitive Homo
tasmanianus, characterized by roof-like elevation of the sutura
sagittalis and lateral flattening of the cranial walls (lophocephaly),
who not improbably would have come from the American continent,
across the Pacific Ocean, in early Plistocene, or even late Pliocene

times. In Tasmania he then changed to the recent Tasmanian, whom

SERGI proposes to call Hesperanthropus tasmanianus. In Australia,
also according to Serat, crossing of the Homo tasmantanus took
place with another, as he supposes, Polynesian element, from which
arose the Australian aboriginal of to-day.

It seems to me that the fossil Homo wadjakensis of Java, who
in some respects possesses more “primitive” characters of the cranium
and the lower jaw than these present races, may be considered to
be such a stock type. He must then have wandered eastward from

1) O. Scuoetensack, Die Bedeutung Australiens fiir die Heranbildung des Menschen
aus einer niederen Form. Zeitschrift fiir Ethnologie. Jahrgang 23. (Berlin 1901),
p. 127.

H. Kraarscr in “Weltall und Menschheit”. Band II. Berlin 1902. — H. Ktaarscu.
The Skull of the Australian Aboriginal. Reports from the Pathological Laboratory
of the Lunacy Department. New South Wales Government. Vol. I, Part 3. Sydney 1908.

2) Ricuarp J. A. Berry, A Living Descendant of an Extinct (Tasmanian) Race,
Proceedings of the Royal Society of Victoria. Vol. XX. (New Series). Part. I. 1897.
Cf. also Proceedings of the Royal Society of Edinburgh. Vol. XX XIV. (1914), p. 186.

3) G. Serer, Tasmanier und Australier. Hesperanthropus tasmanianus spec.
Archiv. fiir Anthropologie. Neue Folge, Band XI. (1912), p. 201.

RE ET GE TD REE EEE ETN EEN ENNE EEN CSD IE IE NET ENT TT ES ET EET EEV TEEGEE NEE

1020

Asia. Though the resemblance to the recent Tasmanian is certainly
no less than to the present Australian, I have introduced him here
as proto-Australian, because the autochthone of the smallest continent
is mostly considered as the principal type of the group. This resem-
’ state may further appear from the more
detailed comparison and description.

As regards the form of the calvaria in the first place, Berry and
others, with the aid of determinations of minima, means, and maxima
for crania of Australians and Tasmanians, find what follows:

blance and this ‘primitive’

Australians Tasmanians Wadjak I
1. Maximum Cranial Length 164. 181.8 199 163 180.3 198 200
2, Glabella-Inion Length 162:" :119:5* 196 | 157" fis "158 192
3. Calvarial Height 195. 95.1 108 BT 97 108 100
4. Calvarial Height Index 449 53 61.5) 48.3 56.1 62.7 52
5. Distance of Foot-Point of Ca!varial Heightfrom | 88 101.1 123 | 85 101.9 115.5 123
Glabella
6. Distance Bregma Foot-Point from Glabella 51.5 61.2 74 | 43 58.1, 11,9 69
7. Calvarial Height Foot-Point Positional Index | 44.9 564 653 53.1 59 64.8 64
8. Bregma Foot-Point Positional Index 29.2 34.1 38.8) 26 34 40.6 36
9. Breadth-Calvarial Height Index 60:3 °72:7 ©85:4) "65:92 DASD 69
10. Nasion-Bregma Arc 116, 126:8 1143 | 113. ZO 143 136
11. Nasion-Bregma Chord 100 110.9 124.5) 97 109.5 120 119
12. Glabella-Lambda Chord 161. 178.7 194 )162 173.2 189 190
13. Glabella-Bregma Arc (Frontal Arc) 99. 110,2, ,128 >| 900 1119. 325 122
14. Glabella-Bregma Chord 5 1084121 a Sen 1052 STs 115
15. Greatest Distance Frontal Arc to Chord 13 19.6 28 | 10 18:91: /25 16
16. Index of Frontal Curvature (25: "181" 2D LOS PRI ZS 13.9
17. Bregma-Lambda Arc (Parietal Arc) 109 . 425.9. 147 | AAR: od25.8 145 130
18. Bregma-Lambda Chord 98 "16 137") OS es. eT 113
19. Greatest Distance Parietal Arc to Chord 17 23.2.6 430;5|°/09 23.3 28 23
20. Index of Parietal Curvature 153 95202252 173. 206. ZA 20.6
21. Glabella-Bregma Angle (BGI). 49° 548° 60°| 51.5° 56° 64° 54°
22. Frontal Curvature (Glabella-Bregma Frontal | 123.5° 139.6° 153° | 131.5° 139.5° 149° 148°
Angle)
23. Parietal Curvature (Bregma-Lambda Rate) 125°. 135.7% 145° | 125.59 13430 141 5°) 1382
ng

1021

Taking the dimensions of the fossil cranium into consideration,
the deviations from the Australians and Tasmanians are mostly slight.
Then the glabella-inion length, just as the glabella-lambda chord,
presents in proportion to the maximum cranial length, the closest
agreement with the Tasmanians, the calvarial height index with the
Australians. Both the glabella-lambda line and the glabella-inion line
are, with regard to the maxium cranial length, shorter in Tasmanian
and in Wadjak I than in the Australian. This is in connection with
the bulging out of the occiput. The latter is still more strongly
pronounced in Wadjak II, so that the lobus occipitalis of the
cerebrum ended more or less pointed.

An important difference consists in this that the top of the calva-
rial height (N°. 7 of the Table) lies relatively much more dorsally
in the fossil man of Wadjak I than, on an average, in those recent
races, particularly the Australian race. This means that the frontal
part of the cranium was comparatively low vaulted, which also
appears from the smallness of the index of frontal curvature (N°. 16),
and the considerable value of the angle of frontal curvature (N°. 22).
It is noteworthy that in all these respects the fossil cranium comes
as near, or nearer, to that of the Tasmanian as to that of the
Australian.

The comparatively lesser development of the frontal part of the
cranium may also be inferred from the measure of the minimum
frontal breadth; this is only 99 mm. for the Wadjak craninm, with
a maximum length of 200 mm. (in the second cranium, which was -
certainly still longer, 101 mm.), while in Australian crania the
maximum is 104, and the mean 98, according to Duckwortn’s
measurements, and Turner even met with a maximum of 108.
This latter went together with the greatest capacity found by TurNER
in Australian crania, 1514 cm.’ ’).

This relatively lesser development of the frontal part must have
an unfavourable influence on the capacity of the cranium, as actually
appears in the capacities of Australian crania, found by direct
measurement.

Nor may the unfavourable influence on the capacity of the roof-
like elevation, in comparison with equally high crania with rounded
vault, observed in Australian crania, be neglected, when the capacity
of Wadjak I has to be estimated, though it cannot be very great here.

1) Challenger Reports. Vol. X. (1884). Also in 1897 (Some Distinctive Characters
of Human Structure. Toronto Meeting of the British Association for the Advan-
cement of Science) TURNER had not found a greater capacity among 63 Australian
skulls than 1514 cm? of that cranium of Port Curtis in Queensland.

1022

The length of the basis of the cranium, the basi-nasal line, measures
107 mm. Dvekworrn found as a mean of 26 male Australian skulls
101 mm., of 5 female skulls 95 mm., and as maximum 109 mm.;
Frower *) found 102.5 mm. for 22 male Australian skulls, 100 mm.
for 9 male Tasmanian skulls, and 95.5 mm. for 14 female Austra-
lian and also for 4 female Tasmanian skulls. The proportions of
this dimension to the principal other dimensions of the fossil skull
do not deviate from the recent ones; this cannot be a cause of
deviation of the capacity.

Taking all this into consideration, and paying attention to the
thickness of the cranial walls, which is 10 mm. near the bregma
in Wadjak I, the capacity of the fossil cranium can, in approxima-
tion, be calculated from its length, breadth, and height.

Applying the methods of Manovuvrirr ’), of Lex ©), and of Froriep ‘)
I find, taking the above mentioned points into consideration, that
the capacity of the Wadjak I skull probably amounts to about
1550 em.

This is a high capacity in comparison with that of the Austra-
lians and Tasmanians. Turner (1897) determined the mean of male
Australian crania at 1280, and the maximum at 1514 cm”, of
female crania the mean at 1116 em.* and the maximum at 1240
cm”. The Tasmanian race had a capacity perhaps 50 cm.” higher.
Probably the Wadjak men were taller, at least heavier, than their
thin Australian descendants, so that they did not exceed these modern
races in the relative development of the neurocranium to the
splanehnocranium.

1) W. H. Frower, On the Size of the Teeth as a Character of Race. Journal
Anthrop. Institute of Great Britain and Ireland. Vol. XIV. (London 1885), p. 188.

1) L. MANouvrieR, Sur l’indice cubique du crane. Association francaise pour
l'avancement des Sciences, 1880, p. 869. — The mean coefficient 1.2 for male
Polynesians, Australians etc. was used, and the capacity calculated in Broca-
measure was reduced to real capacity.

8) Arice Lee, A First Study of the Correlation of the Human Skull. Philo-
sophical Transactions of the Royal Society of London. Series A, Vol. 196. (1901),
p. 225—264. Formulae and Tables, p. 243—247. The auricular height, which is
a necessary factor in these formulae, is 122 mm. in Wadjak I. The formula
(p. 243) for the male Naqada-Egyptian crania was used, with which the similarity
in form is relatively greatest (cf. chief dimensions p. 246). .

*) A. Frortep, Ueber die Bestimmung der Schädelkapazität durch Messung und
Berechnung. Zeitschrift fiir Morphologie und Anthropologie. Band 18, p. 347. (1910).
An equal result is also obtained by the method of H. WEtcKER (Die Kapazität
und die drei Hauptdurchmesser der Schädelkapsel bei den verschiedenen Nationen.
Archiv fiir Anthropologie. Braunschweig 1886. Band 16, p. 1), after some modi-
fications of the chief measures required by the particular shape of the fossil skull.

1023

To estimate this relative development Artnur KeitH*) has intro-
duced the comparison of the capacity with the “palatal area’, this
area being the space bounded by the outer margins of the crowns
of the teeth in the upper jaw and a line joining the posterior margin
of the upper third molar teeth. He found this area of the upper
dental arcade for a female chimpanzee skull, of a capacity of 320
em.*, equal to 36.5 cm.*; hence to 1 cm.’ of palatal area came
8.7 cm.* of brain capacity. The upper palatal area of a Tasmanian
skull was 36.8 cm.’, the capacity of this skull was 1350 cm.’,
which gives a ratio of 1:36.7. For the Homo neandertalensis of
Gibraltar*) Keira found for these values 31.6 cm.* and 1200 em.’,
and the ratio 1:38, but for the Aurignac-man of Combe-Capelle the
ratio is 1:53, about that of modern Englishmen, viz. 1 : 56.3,
with 26.6 cm.” palatal area and 1500 cm.’ capacity.

With pretty great accuracy — as only the crowns of the incisors
and the crown of the right m, fail — the palatal area of the
Wadjak-man II may be determined at 41.4cm.*. That of Wadjak I,
in which only few tooth-crowns have been left, measures about
35 cm”. Through its relatively small size this palate presents a
striking difference from that of Wadjak II, which is one of the
characters that lead me to assume that the first found fossil remains
belonged to a woman, the second to aman. Other female characters
of Wadjak I are: the more reduced form of the teeth (the upper
m, and m, are almost perfectly three-cusped), the smaller dimensions
of the comparable parts of the skull, though not in the same degree
smaller as the palate, the less pronounced superciliary ridges and
the forehead that does not recede so much, the orbits which are
higher with respect to their breadth, the somewhat slighter develop-
ment of the muscle attachments, the more rounded form of the
occiput, the somewhat slighter lophocephaly and dolichocephaly, in
so far as the latter can be judged from the fragments of the second
skull.

If for the fossil woman of Wadjak 44.3 em.” brain capacity comes
to 1 cm. of palatal area, it may be assumed that for the man, who
had a much larger palate, but probably also a larger neurocranium,
this ratio was smaller. Putting his cranial capacity 100 em.’ higher

1) ARTHUR Keir, The Antiquity of Man. (London 1920), p. 97, 151, 328.

2) For the Homo neandertalensis of La Chapelle-aux-Saints I calculate an upper
palatal area of 38 cm? after the reconstructive drawing of Bouvre, which with
1626 cm’ Broca- or 1530 real cranial capacity yields the ratio 1:40.38. But the
normal palatal area may have been somewhat larger than that of this man, who
had early lost his teeth for the greater part.

1024

than that of the woman, which is a plausible estimation, I find for
him the ratio 1 : 40. Thus much appears, at any rate, with certainty
that as regards the comparative size of the two chief parts of the
skull, the neurocranium and the splanchnocranium, Homo wajaken-
sis resembles those most primitive recent human types, and also the
Plistocene Homo neandertalensis.

In many more respects there is unmistakable resemblance between
Homo wadjakensis and the recent Australian group of races. But he
also presents deviations from this group, which are certainly partly
due to a more “primitive” condition.

Both these points may further appear from the description of some
other characters.

The strongly marked glabella and superciliary ridges, also of the
woman of Wadjak, though not in the same degree as of the man,
are certainly australoid characters, but the supraorbital borders and
also the lateral orbital borders are somewhat less massive and rounded
than in the Australian crania. The height of the orbit is 33 mm., the
breadth 42 mm. in Wadjak I, so that the orbital index is 78.6. For the
male cranium these dimensions and index are 30, 40, and 75; it
is remarkable that the orbit is smaller in the man, but the lower
index for the woman presents an important sexual difference
in the Australians, according to Turner. He found for the mean
orbital index of Australian crania 84, for that of twenty men 81.4,
and of nine women 90; Frower in fifty-one Australian crania
a mean index of 80.9, Quatrefages and Hamy in thirty-one
crania a mean index of 78.8. The inter-orbital breadth of Wadjak
II is at least 29 mm. Turner found as mean of male Australian
crania 24.5 mm., and as maximum 28 mm.

The root of the nose is deeply sunk (most in Wadjak II), and
the bridge of the nose is very flat, rounded from side to side.
The apertura piriformis of Wadjak I measures across 30, (Wadjak
II 32), the height is 27 mm., to which corresponds the index 111.
In Australian crania this index ranges between 82 and 130 according
to KLAatscH; in European crania it is on an average 70. The spina
nasalis is short and blunt. The nasal height is 50 in Wadjak I, the
nasal breadth 30 mm. (in Wadjak II 32), the nasal index 60. In
Australian crania the following values were found as means for
this nasal index: 57.9 by Quarrrraars and Hamy (N = 31), 56.9 by
Frower (N= 31), 53.4 by Turner (N = 29), 55.6 with the maxi-
mum 65.1 by Duckwortu (N = 38).

The sides of the nasal aperture are not sharp-edged, but, as
generally in Australian skulls, blunt and rounded off, especially near

EUG. DUBOIS: “The Proto-Australian Fossil Man of Wadjak, Java”.

PLATE I.

Figs 4:

Biss.

Proceedings Royal Acad. Amsterdam. Vol. XXIII.

PLATE II.

Fig. 4. Fig. 5.

Fig. 8.

1025

the floor of the nose. The more or less direct continuity of this floor
into the incisive region, which is frequently found in Australian
skulls, is a perfect one in Homo wadjakensis; from the outer edge
of the nasal aperture a linear elevation continues on to the latter
region, curved downward and inward, which is lost at 6 mm. below
the nasal floor. This is a transition form between the infantile type
of the lower edge of the nasal aperture and the suleus prae-
nasalis of the Anthropoids, which may be designated as ‘Affen-
rinne’, and which is undoubtedly in connection with the strong
alveolar prognathism of Homo wadjakensis *). The other prognathism,
which is indicated by the relative lengths of the basi-alveolar and
basi-nasal lines, Frower's ‘“gnathic index”, which he found to be
103,6 on an average in Australian skulls, while Turner met with
a (female) minimum of 92, and a (male) maximum of 108, cannot
be accurately determined in Wadjak I; it can, however, be indi-
cated by the index 91 approximatively. The smallness of this index
strengthens me again in the conviction that the first found fossil
skull must be considered as female. The alveolar prognathism (Fig. 1.
Norma lateralis of Wadjak [ and Fig. 4. Upper and lower jaw of
Wadjak II) is not slight.

A character which peculiarly distinguishes Homo wadjakensis is
the extraordinary great breadth of the dental arcade in the upper
jaw, compared with its length. (Fig. 6). The maximum width between
the outer edges of the crowns of the 2°¢ upper molar teeth is 81 mm.
for Wadjak I], 71 mm. for Wadjak 1. The length of the row of
five molars, Frower’s “dental length’, is only 50 mm. at the male
skull, and 47 mm. at the female skull. In Australian skulls TURNER *)
found as maximum of width on the second upper molars 73 mm.,
as maximum of dental length 51 mm. In the fossil Wadjak men
the breadths are to the lengths as 1.62 and 1.51:1. The palato-
maxillary breadth agrees about with the greatest breadth over the
molars. It is 82 mm. in Wadjak Il, and 70 mm. in Wadjak. I.
These breadths are to the dental lengths as 1.64:1 and 1.49.1.
Duckwortn determined the average of the palato-maxillary breadths
of eleven male Australian skulls at 64.9 mm., and the mean dental
length at 46.4 mm.; these dimensions are to each other as 1.40:1.

1) Cf. for these forms of the lower edge of the apertura piriformis: Ruporr
Martin, Lehrbuch der Anthropologie. Jena 1914, p. 845 el seq.
2) Sir Wittiam Turner, The Relation of the Dental Arcades in the Crania of
Australian Aborigines. Journal of Anatomy and Physiology. Vol. 25. (1891),
p. 461—472. P. Aprorr (Das Gebiss des Menschen und der Anthropomorphen, p. 28.
Berlin 1908) found for this dimension on the maxilla of a Melanesian 75.5 mm.

1026

In a female skull these. dimensions and ratio were 63 mm., 46 mm.
and 1.37:1. Greatest, viz. 1.52:1, was the ratio of a male skull
with 70 mm. palato-maxillary breadth, and 46 mm. dental length.
The mean dental length, determined by FLowrr') from twenty-two
male Australian skulls, was 45.9 mm., and from fourteen female
skulls 44 mm., from nine male Tasmanian skulls 47.5 mm., and
from four female skulls 44 mm.

Frower’s dental index (dental length > 100: basal length) was
44.8 for Australian, and 47.5 for Tasmanian male skulls, 46.1 for
Australian and 48.7 for Tasmanian female skulls. At the skull of
Wadjak I this index is 44, hence the dental length is relatively
small, probably still smaller in Wadjak II.

The breadth between the outer margins of the 2™" upper molars
at the fossil skull of Gibraltar is 71 mm. according to Kerrn, the
dental length, from his drawings (mean of left and right row of
teeth) 45 mm.?). The breadth is to the length as 1.57:4. Almost
perfectly the same ratio, 1.56:1 for 75 mm. breadth and 48 mm.
dental length, is presented by the upper dental arcade of the fossil
man of La Chapelle-aux-Saints in tbe reconstruction of Bourr*).
Accordingly Homo wadjakensis resembles Homo neandertalensis in
this large relative breadth of the upper dental arcade.

This, however, holds only for the greatest breadth (measured at
the molars) of the upper dental arcade; the form of this arcade is
very different. Whereas the curvature of the arcade of the Neander-
tal Man continues regularly forward, the arcade curve of the upper
teeth of Homo wadjakensis, especially of the male individual, changes
its form anteriorly to the molars. The three molars lie in a
parabolic line of greater parameter, the foremost half of the teeth
row (the praemolars, canini, and incisivi) in a similar line of smaller
parameter, so that for the row of the molars the dental arcade
narrows, but not gradually. The parabolic line of the foremost half
of the dental arcade departs only little from the almost uniform
line, in which the whole dental arcade of the lower jaw lies. In
fact, the front half of the dental arcade of the upper jaw projects
little at the praemolars (of course not at all at the incisivi) beyond
that of the lower jaw; the upper molars, however, project greatly
outside the lower molars. The width between the outer margins of

1) FLOWER, l.c., p. 186.

2) KEITH, l.c, 5 149 — 151.

8) MARCELLIN BouLe, L'Homme fossile de la ORDE: aux-Saints. Extrait des
Annales de Paléontologie. (1911—1913). Paris 19138, p. 100, fig. 60. The dental
index (FLOWER) was only 38.

1027

the lower 2"d molars is only 69 mm., the arcade in the upper jaw
being 12 mm. wider there than in the lower jaw, (in Australians
— which race surpasses others in this respect — TURNER found as
maximum 8 mm.). The consequence of this remarkable relation be-
tween the two dental arcades is that the lingual cusps of the crowns
of the molars in the upper jaw have been worn off obliquely from
inside: and above to outside and below on the buccal cusps of those
in the lower jaw, while on the other hand in the upper jaw the
buceal cusps, in the lower jaw the lingual cusps of the crowns of
the 2nd and 3rd molars are worn off very little, if at all, and the
crowns of the 1st molars at least unequally on the buccal and
lingual half, the lower ones very obliquely.

Dental arcades resembling the described type, though perhaps not
so pronounced, are not seldom met with in Australian and also in
Malay skulls; but the type of the Neandertal Man is an entirely
different one. Also the molar half of the upper dental arcade projects
but little outside that of the lower jaw; the two arcades have the
same shape, and cover each other much more, and the wear of the
crowns takes place over the whole grinding surface more equally,
horizontally. It may be assumed that the food of Homo neanderta-
lensis was of a different nature from that of Homo wadjakensis and
of the Australians. This race lives chiefly on animal food; very
probably the mode of living of Homo neandertalensis was more
vegetarian. In connection with this it is of importance that in an
examination with X-rays, made with the collaboration of my brother,
Dr. V. Dusois, it was found that the teeth of Homo wadjakensis
possess roots and pulp-cavities that agree in form and size with the
Australian type, and depart entirely from the taurodont type of the
Neandertal men.

The following remarks about the most important characters of
the teeth and the mandible may now precede a further discussion.

On the whole the teeth are large, though they are still surpassed
by those of many Australians. The 2"d and 3'¢ upper molars present
reduction phenomena, especially in Wadjak I.

The mandible (Fig. 7 and Fig. 8) is a very strong bone, clearly
built according to a type resembling a common Australian one. The
corpus mandibulae is, pretty uniformly, high (40 mm. at the symphysis
of Wadjak II. Average of 7 Australians 33 mm., maximum 42 mm.
according to Frizzt')) and thick. The ramus is very broad (at the

et E. Frizzt, Untersuchungen am menschlichen Unterkiefer mit spezieller Berück-
sichtigung der Regio mentalis. Archiv. für Anthropologie. N. F. Band IX. (1910),
p. 252—286.

1028

narrowest place 46.5 mm. in Wadjak IL. For 7 Australians, according
to Frizz, the breadth is on an average 37 mm., maximum 40 mm.).
This applies particularly to the mandible of Wadjak II, which 1
consider as male, but to a certain extent also to the other mandible,
of which only little is preserved.

The symphysial or mental angle (between the infradental-pogonium
line and the base line) measures 96°. Though there is a strongly
developed protuberantia mentalis, yet the perpendicular dropped
from the infradental point or incision, falls 3 mm. before its most
projecting point, the pogonium. When this projection, which makes
the impression of being a separate formation, is thought eliminated,
the angle of the chin would be 102°. The other symphysial or mental
angle, that with regard to the alveolar line, measures 80°. It would
attain 86°, when the protuberantial swelling did not exist. For the
Neandertal-mandibulae, which possess no or very small protube-
rantia, the angle is still considerably greater. La Naulette 94°, Spy
106°, Mauer 105°. From seven Australian mandibles Frizz (like
Wercerer from fifteen) found a mean of 83° for this angle, the maxi-
mum was 94°. But this greater angle of the Australians is also
partly owing to the mostly slight development of the protuberantia
mentalis. The true angle of inclination of the corpus mandibulae at
the symphysis (without that projection), can yet be called peculiarly
great in Wadjak Il. Hence Frizz’s “Korrekturvertikale” i.e. the
perpendicular drawn to the alveolar border line, close along the
deepest point of the chin concavity, only just intersects the protu-
berantia of Wadjak IL. Noteworthy of this fossil mandible is
further the relatively thin inferior border or base, and the situation
of the small fossae digastricae, behind this border, 23 mm. apart
from each other, reminding of the condition of Hylobates syndacty lus.

In comparison with the dentition of the Wadjak Man, another
find may be mentioned of a fossil man related to the present
Australian race, the skull of Talgai in Queensland, Australia, which
was discovered in 1684, mentioned by T. W. E. Davip and
J. T. Wirson *) in 1914, and elaborately described by Stewart ARTHUR
SmitH 7) in 1918. This skull of a “male youth” (for m, was still
unerupted), though cracked im situ into numerous fragments, which
are more or less considerably dislocated, but held in position by
thin layers of calcareous earthy matrix cementing them together,

1) Reports of the British Association for the Advancement of Science. Sydney
Meeting. (1914), p. 531. — Cf. also ,,Nature”. London 1915, p. 52.

*) Srewart ARTHUR SMITH, The Fossil Human Skull Found at Talgai, Queens-
land. Philosophical Transactions of the Royal Society of London. Series B, Vol. 208,
pp. 351—387. 7 Plates. Londen 1918.

1029

the condition resembling a coarse mosaic, can yet be clearly recog-
nized as not deviating, in its general features, from the present ab-
original Australian skull. The cranium as a whole, and the palatum,
however, hardly admit of any reliable measurements. They could
still be made at the tooth-crowns, each in itself, but most of them
have more or less receded from each other; the apparent palatal
area thus considerably exceeds the real, which, in my opinion,
was no larger than that of the Australian native of present times.
SMITH supposes that the (upper) canine tooth, in an analogous way
as in the dentition of Apes, though without a true diastema in
the maxilla, penetrated, almost ape-like, with its apex between
the lower canine and the lower first premolar. In my opinion
there is reason to doubt this, on the ground of a comparison
with the teeth of Wadjak Il. The facets on the upper canine,
which have been described by Smiru (loc.cit. p. 374 et seq. and figures
6, 21 and 22) and considered by him to have been caused
by the projecting between the said teeth in the mandible,
are identical in their position with facets on the upper canine in
the Wadjak maxilla. One of them, on the distal (posterior) surface,
can be clearly recognised as interstitial contact facet (Zsic-
MONDY) with the first premolar tooth (in the maxilla). The other
placed on the lingual slope of the narrow margin of the mesial
surface, by the side of the interstitial contact facet on the mesial
surface caused by the contact with the lateral incisor tooth, is to be
recognised, by comparison with Wadjak IJ, as belonging to the
general wear of the masticatory surface. In his reconstruction (Fig. 4)
SMITH lowers the upper canine tooth to nearly 7 mm. below the
level of the mesial margin of the upper premolar, till the upper
border of its crown gets very nearly ona level with the upper border
of the crown of the premolar. Erroneously, for the crown-border
of such a large upper canine tooth as the Talgai canine, is always
considerably above the level of the crown-border of the upper pre-
molar; in the maxilla of Wadjak Il the distance is 3 mm. The
upper canine, therefore, cannot have projected so far downward as
is required according to Smirn’s interpretation of the distal (posterior)
facet. The canine tooth of Wadjak II, which strikingly resembles
that of Talgai, is also equally broad as the latter, and if its wear
were as little advanced as that of the canine of the boy of Talgai, it
would no doubt be as pointed and little shorter than the latter.

If for those reasons I cannot agree with Smirn in ascribing to the
fossil skull of Queensland, which indeed he too considers as typically
Australian, “characters more ape-like than have been observed in

: 67

Proceedings Royal Acad. Amsterdam. Vol. XXIII.

1030

any living or extinet race, except that of Zoanthropus”’, this skull
is nevertheless of great importance, because several circumstances, men-
tioned by Sirs along with his valuable description, go to show that the
aboriginal Australian with Canis dingo already lived, in the smallest
continent, by the side of now extinct Marsupialia, which are generally
considered as Plistocene. As the said species of the true Canis genus, the
only large Placental Mammal of Australia besides Man, has most probably
come with the latter from Hast-Asia, the find of Talgai throws also
some more light on the geological age of the fossil Man of Wadjak.

But the “Talgai Man” does not at all indicate a nearer approach
to the common ancestor of modern mankind than do the Australian
aborigines of the present time.

If, however, the Australians may justly be considered as the most
“primitive”, the “lowest” type, ie. tbat of living races of Man
resembling most closely the common stock-type, it might have been
reasonably expected that the real predecessor of humanity would
be found in their fossil ancestors; unless the Australian type was
evolved already long ago and has since remained unchanged.

On account of the unmistakable morphological resemblance, also of
the geographical relation and the antiquity, the fossil man of Wadjak
may certainly be considered as an ancestor of the present Australian
racial group, a proto-Australian. The geographical relation is obvious,
and though there are no direct data for the determination of the
geological age, this must certainly be considerable; several indirect
data which I have mentioned, render it probable that a rather early
place in the Plistocene period may be assigned to our fossil Man.

The expectation, however, to find in him a distinctly lower type
than the Australian of the present time, has not been realised, for
this ancestor had reached the same stage in the evolutional scale
as the living race, at least almost.

Striking are the many points of resemblance on the skull and
the lower jaw of the Wadjak Man with the Australian group, especi-
ally the aboriginal of the largest insular country. The differences
may nearly all be attributed to more vigorous development and
greater perfection of the type, in surroundings more favour-
able than those in which the Australian native finds, and has found
for a long time, a scanty subsistence. Homo wadjakensis was an
optimate form. In the present race the type is evidently in a state
of decadence, as also Homo neandertalensis is the less vigorous and
less perfect descendant of Homo heidelbergensis. Judging from the
lower jaw, also of the latter, the type was purer and in this
sense more primitive in the older of the two forms.

1031

At the neurocranium of the Wadjak Man only the somewhat
smaller relative size of the frontal part and the jutting backward
of the occipital lobe of the cerebrum (‘‘pointed” in the Wadjak II
skull, because the occiput is not only flattened in vertical direction,
but is also relatively narrow) can be considered as primitive in the
true sense, i.e. phylogenetically. But even this is somewhat
doubtful, in my opinion, where the development of the total brain
volume was certainly no less than in the present Australians.

The powerful jaws give a truly bestial appearance to the splanchno-
cranium. But an absolutely large and strong masticatory apparatus
is no evidence as such of a phylogenetically primitive condition.
Thus the powerful masticatory apparatus of the Eskimos is only a
requirement of the way of living of the hyperboreans, namely their
feeding chiefly on raw meat and bacon. Besides, in proportion to
the brain capacity, the palatal area of Homo Wadjakensis is cer-
tainly no larger than that of the Australians, as was demonstrated
above. Taking into consideration that here a surface is compared
with a volume, it is found, that certainly in Wadjak I, and
probably also in Wadjak II the mean longitudinal dimension of the
masticatory apparatus, in proportion to that of the brain,
is smaller than in the compared Tasmanian.

The dimensions of the jaws and the teeth of the Wadjak Man,
taken each in itself, even remain all within the limits of other
pachygnathous and megadont fossil and living human types; the
deviations are never so considerable as to assume systematic signi-
ficance. The Wadjak Man is certainly megadont, as the Australian
racial group and also Homo neandertalensis, and even the Combe-
Capelle Man *). In the absolute strength of the masticatory apparatus,
taken as a whole, the Wadjak Man is, how-
ever, only equalled, not surpassed by Homo heidel-
bergensis. Just as in the whole build of the skeleton,
the Australian is a type diametrically opposite to
the Neandertalian, as Bouvre has demonstrated *),
in the same way Homo wadjakensis is so of Homo
heidelbergensis, at least certainly in the lower jaw
(compare especially the cross-sections of the
symphyses in the adjoined diagram). But these
have both the most powerful masticatory appara-

') The size of the teeth may appear from the subjoined comparative tables.
(See Tables following page). The maxima of the living races of man are taken
from DE TERRA, BLACK, MüHLREITER, ADLOFF.

2) L'Homme fossile de La Chapeile-aux-Saints, p. 281-234. Paris 1913.

67%

1032

tus known of their type, the former also of the Homo sapiens-type.
In contrast, however, with Homo heidelbergensis reduction pheno-

Maximum dimensions of crowns of teeth in the maxilla (mm.)

Wadjak All living

II (1) Talgai Capelle Krapina races
C sup. Mesio-distal 9.7 — 9.6 | 8 10.5 9.3
» y» Labio-lingual 10.2 — 10.9 9 fico 10.8
P, sup. Mesio-distal 83 — 8.6 | 6 8.2 9.5
» y Bucco-lingual 11.0 — 12.3 9 11.4 12.5
P‚ sup. Mesio-distal 8.0 (7.6) 8.1 6.5 -- 8.2
» y Bucco-lingual 10.8 (11.0) 11.0 9 — Md
M, sup. Mesio-distal 12.0 (11.2) 12.6 10.5 13.3 12.8
» y» Bucco-lingual 13.0 (13.8)| 13.1 12 18:34 14.5
M, sup. Mesio-distal 11.0 (10.6) 4-3 | “10.8 12.0 11.8
» » Bucco-lingual | 13.5 (14.2); 13.5 | 12 14.0 14.7
M3 sup. Mesio-distal 11.0 (8.2) — BZ — 1 ME
» » Buceco-lingual 13.0 (13.0) — |b ys, — 14.8

Maximum dimensions of crowns of teeth in the mandible (mm.)

RE IP tee Se ay All —
Wadjak | Combe- M 3 Be

auer | Krapina | Spy u living

I] (1) Capelle | races
I, inf. Mesio-distal 6.2 — 5) 55 | 652 6.0 6.5
, » Labio-lingual apa 6 7A | gn VY aot | Sn
I, inf. Mesio-distal 6.8 — 6 6.0 155 6.0 He? 4
» » Labio-lingual 1.6. = 6.5 7.8 8.2 8.0 7.6
C2 inf. Mesio-distal 8.4 — 8 Aad 8.4 125 9.0
» » Labio-lingual 95 — 9 9.0 10.0 9.0 10.0
P, inf. Mesio-distal 8.5 — 6 8.1 8.3 fe) 8.7
» » Bucco-lingual 9.0 — 9 9.0 10.0 9.0 9.8
P. inf. Mesio-distal 833: Aen 7) io 8.5 1.5 9.0
» » Bucco-lingual 8.5 — 9.5 9.2 9.9 9.0 10.5
M, inf. Mesio-distal 13.7 — 12 11.6 13.8 149 12.8
„ » Bucco-lingual 12.5 — 12 12 12.4 iW Wee) 12.2
M, inf. Mesio-distal 11.77 (120) 12 12.7 12:5 11.0 12:5
» » Bucco-lingual 11.0 (11.0) WL et ZE) 11.4 11.0 12.0
M3 inf. Mesio-distal | 12.0 (13.0) 11 1252 13.6 12.0 15.0
» » Bucco-lingual | 11.3 (11.0) 11 10.9 11.0 12.0 13.0

1033

mena occur at the crowns of the molars of Homo wadjakensis in
a no less degree than in recent men. The hindmost lingual cusps
of the second and the third molar of the upper jaw of Wadjak II,
and particularly of Wadjak I are little developed. In connection
with this the mesio-distal dimension is relatively small, especially
in m, of Wadjak I. In Wadjak II the crown of mm, shows on the
backside, in the middle a small accessory cusp, which reminds of
what has been described by Emir, Setunka about the Orang-utan,
and which was also found in Man in rare cases.

The total length of the canine of the upper jaw of Wadjak II
measured on the skiagram, is 29 mm. Münrreirer found 37 mm.
as maximum of all living races. Thus measured, the length of the
roots of the upper m, is 14 mm., of m, 16 mm., and the distance
of the root-ends resp. 9 and 7,5 mm.; this distance is about 10 mm.
in m,. In these respects, and in the vertical depth of the pulp-
cavities, which is 15 mm. in m,, 25 mm. in m,, the fossil form
of Java again resembles the Australians, and differs from Homo
neandertalensis (and heidelbergensis).

The folding of the enamel (crenation) is more composite than in
Kuropeans, but not to a higher degree than is also found in Australians.

The two premolars in the lower jaw of Wadjak II are not larger
and not more primitive of form than in the fossil mandibles already
known and those of the living races of Man. The crowns of the
(loose) incisors and canine, like those of the first premolar, are
larger, of the second premolar and of the molars on the other hand
smaller than in Homo heidelbergensis. The joint length of the two
back molars in the latter is 25 mm., in Wadjak II 24 mm., the
distance from the incision to the back margin of m, being 42 mm.
in Homo heidelbergensis and 47 mm. in Wadjak II. The length of
the dental arch was 58 mm. in the Heidelberg Man, and probably
60 mm. in Wadjak IL. In the Wadjak Man the front part, in Homo
heidelbergensis the back part of the dental series was larger. In the
latter the molars are all three five-cusped, and the crown of the
middle molar is the largest. In Wadjak II, on the contrary, only
the front molar is five-cusped; this is also the largest, the second
and third molars are four-cusped, and comparatively considerably
smaller; the middle one is the smallest. In the fragment that is
extant of the lower jaw of Wadjak I (the right back half of the
corpus mandibulae and the lower part of the ramus with the
angulus, in which the complete mm, and m,, besides the greater
(back) part of m,, with much less worn crowns than in Wadjak II),
m, has three buccal and two lingual cusps; this tooth-crown is also

1034

longer in mesio-distal direction, though the whole of the jaw must
have been less large than that of Wadjak II. All these differences
between Homo wadjakensis and Homo heidelbergensis are certainly
significant of a difference in function of the molars.

A five-cusped m, have on an average three of the four Australians
and one of the four representatives of the Malay race; in both races
m, is five-cusped in two out of three individuals on an average.
In this respect Papuans agree more closely with Malays than
with Australians. In Homo neandertalensis nine of the twelve
m, were found to be five-cusped, and m, nearly always four-cusped
(in ten out of eleven of these teeth); probably the crown of m, is
no less reduced. The two individuals of Homo wadjakensis,
therefore, in this respect, closely resemble Homo neandertalensis,
and are certainly less on the primitive side than the average Australian
native. As has been said, the lower molars of Homo heidelbergensis
on the other hand, are all three five-cusped, hence they present the
more primitive condition. From what is observed in the living races
it seems, however, that both the number of cusps and the size of
the dental crowns are in connection with the function.

Some of the most important characters of the maxilla and the
mandible of Homo wadjakensis I have already briefly described.
The following remarks may now be added.

The protuberantia mentalis, a low trigonal pyramid with rounded
edges and vertex, with its base put, as it were, on the uniformly
bent outer side of the corpus mandibulae, and rising 3 mm. above
this surface (ideal of the “e@minence triangulaire, plus au moins:
bombée a son centre, qui se superpose a la face anterieure de la
mandibule” of the European lower jaw, in the description of Topinard),
may be clearly recognised as a formation that has arisen independently
of the growth of the basal part of the corpus mandibulae. According
to KuaatscH’) such a “trigonal prominence” is also what is found,
as a rule, in Australian mandibles. The basal part is by no means
bent outward as in many modern lower jaws, but the external surface
of the corpus mandibulae is straight to the inferior border. The
internal surface at the chin, apart from the spina mentalis
placed on it, is only slightly convex, and inclines almost uniformly
from above downward. The spina is of a type frequently occurring
in Home sapiens, which | will designate as scissor-shaped of outline,
as it really presents a close resemblance with the outline of a

) H. KLAATSCH, The Skull of the Australian Aboriginal. Reports from the
Pathological Laboratory of the Lunacy Department. New South Wales Government.
Vol. I. Part Ul, p. 155. Sydney 1908.

1035

shorter or longer pair of tailor’s scissors; it consists of a median
crista geniohyoidea, 9 mm. long, and two round tuber-
cula genioglossa lying 6 mm. apart above it. The foramen
mentale is placed under the interval between p, and m,, and
directed backward.

An incisura submentalis, so considerable in the mandible
of Mauer (Homo heidelbergensis) (10 mm. deep), is scarcely percep-
tible (1 mm. deep) in that of Wadjak Il. The incisura prae-
angularis s. praemasseterica (Bonner) is, on the other
hand, uncommonly deep. There also exists a very considerable tuber
massetericum (Bonnet). These two prove that the musculus
masseter was exceedingly powerful.

In strength the lower jaw of Wadjak II is not inferior to that
of Homo heidelbergensis. This may already be inferred from the
vertical sections in the symphysis-line in comparison also with the
most frequently occurring Australian type and with the common
European lower jaw. (Fig. 8 of Plate II). For in the symphysis the
lower jaw has to resist the greatest violence.

The strength of this bone in Wadjak Il may further appear from
the following measures. The height of the corpus mandibulae at
the symphysis, 40 mm. in Wadjak II, is about 33.5 mm. in Homo
heidelbergensis, 36 mm. at the mandibula of Spy, 30 mm. at that
of La Naulette. The median thickness at the symphysis, 16 mm. in
Wadjak II (above the spina mentalis) is on the other hand
17.5 mm. in Homo heidelbergensis, but only 15 mm. at the mandibula
of Spy, and also at that of La Naulette. The height, measured
between p, and mm, is 37 mm. in Wadjak II, and the thickness
there 17 mm.; in Homo heidelbergensis these measures are resp.
33 and 19.4 mm.

The greatest thickness of the body of the lower jaw, under m,,
is 21 mm. in Wadjak II, which is equal to the “enorme Breite”
found by OeTTEKING, and also by GORVANOVIC-KRAMBERGER, each once,
in lower jaws of Eskimos, in which race this bone is peculiarly
strong as a rule’). The lower jaw of Mauer is 23.5 mm. thick at
the same place, that of La Naulette only 15, and of Spy 16 mm.,
Australians not seldom attaining 19 mm. he height at m, is about 35

1) B. OerrekiNg, Ein Beitrag zur Kraniologie der Eskimo. Abhandlungen und
Berichte des Königl. Zoologischen und Anthropologisch-Ethnographischen Museums
zu Dresden. Band XII (1908). NO. 8, p. 38.

K. Gorsanovic—Krampercer, Der Unterkiefer der Eskimos (Grönländer) als
Trager primitiver Merkmale. Sitzungsberichte der Königl. Preuss. Akademie der
Wissenschaften. Jahrgang 1909, p. 12821294. Taf. XV und XVI, p. 1283.

1036

mm. at the lower jaw of Wadjak II, at that of the Heidelberg
man 30 mm.

The condylar height of the ramus mandibulae of Wadjak II is
about 70 mm., the breadth, at the narrowest place, 46.5 mm. At
the lower jaw of the Heidelberg Man these dimensions are resp. 69
and 52 mm., but the angulus (s. arcus, BoNnNET) is, as it were, cut
off obliquely, just as in the Neandertal Man of La Chapelle-aux-
Saints, whereas it forms a round projection at the lower jaw of
Wadjak II. The external surface of the ramus cannot be measured
accurately, because this part of the lower jaw has broken off with
the loss of some parts that cannot be accurately determined, but it is
very large, and may be estimated at only 2 cm.’ less than that of
the Heidelberg Man. In the latter this surface is enlarged, it is true,
by the very considerable breadth of the processus coronoides, but on
the other hand the angular part is much larger in fthe Wadjak
Man. The outer surface of the ramus at an average European
lower jaw is 16 cm.’ smaller, at an Australian lower jaw (according
to Kuta) 12 cm.” smaller than at that of the Heidelberg Man. This
means that the area of attachment of the muscles of mastication of
the Wadjak Man is almost as large as that of the latter — in the
Heidelberg Man the musculus temporalis preponderated, in our Java-
nese Australian the masseter — and much larger than that of the
present European, and even of the Australian aborigines.

The condylus is in transversal direction as large as that of the
Mauer-mandibula, on the other hand in sagittal direction much
smaller and rounder. Also the glenoid fossa is of the present type.
The articulation was evidently, as in general in Homo sapiens,more hinge
joint, for movement up and down of the lower jaw, than gliding
joint, hence less adapted to grinding motion of the lower jaw than
that of Homo heidelbergensis. The important differences of the same
nature, which exist between the temporo-mandibular joint of Homo
neandertalensis and modern Man, have been set forth by Boure in
his masterly description of the fossil Man of La Chapelle-aux-
Saints. The very wide and shallow articular cavities of the latter
were certainly adapted to grinding movement, almost as in the
Anthropoids.

The processus coronoides is narrower, but higher and consequently
the incisura mandibulae is deeper than in Homo neandertalensis and
heidelbergensis.

The external surface of the ramus as a whole inclines somewhat
towards the outside from above downward, so that the two rami
diverge. This is still more pronounced for the regio angularis,

1037

because this is, besides, in itself strongly bent outward, which is
especially apparent when the posterior and inferior border are con-
sidered. This part of the ramus is thick and strong. This thickness
and the bending of the angular part of the ramus outward mean
strong development of the musculus masseter, absolute and in com-
parison with the musculus pterygoidens internus *). In the morpho-
logy of the ramus mandibulae described, as in that of the chin-region,
the lower jaw of Wadjak II represents very perfectly the type of
modern Man (Homo sapiens).

Entirely opposite to this is the type of the lower jaw of Homo
neandertalensis, which is exhibited in its greatest purity by the
Mauer mandible (Homo heidelbergensis). Here no protuberantia
mentalis (in the older form, the Heidelberg Man) or only traces of
it (in some representatives of the later form, the Neandertal Man
proper), nor outward bending of the inferior border of the corpus
mandibulae. On the other hand, on the inner side of the regio
mentalis, particularly in this most original and powerful jaw of the
type, a considerable strengthening of the arch of the mandible by
means of a torus mentalis internus, closely corresponding to that of
the Anthropoids and of most of the lower Monkeys, and in connection
with this no spina mentalis, or one that is only little developed.
The two rami converge from above downward, and the thin
pars angularis is bent inward (at least not outward). In the Homo
neandertalensis of La Chapelle-aux-Saints BouLe has also described
and drawn this important obliqueness of the rami mandibulae with
regard to the sagittal plane of the skull, and the greatly narrowed
pars angularis, which makes the said obliqueness more apparent, in
that it “se déjette en dedans, au lieu de se déjetter en dehors, comme
dans la plupart des mandibules humaines actuelles’’*); he has also
pointed out its occurrence in many cynomorphous Monkeys and in
the Orang-utan among the Anthropoid Apes, also seeing in this an
indication for the comparatively great strength of the musculi ptery-
goidei (which may also be inferred from the extensive surfaces of
their origin and insertion).

It is clear that thus in the Man of Wadjak, just as in a more or
less degree in general in Homo sapiens, the directions of the right
and the left musculus masseter, which muscles moreover had their

1) According to THEILE the musculus pterygoideus internus, in a strong Euro-
pean, has not even half the weight of the masseter, the musculus temporalis on
the other hand one and a half times the weight.

9) MARCELLIN Boure, L'Homme fossile de La Chapella-aux-Saints. Paris 1913,
p. 983—94 and p. 65, fig. 45.

1038

origin from much less projecting zygomatic arches, than in Homo
neandertalensis, strongly diverged from each other downward, which
must have gone together with peculiarly strong divergence in that
direction of the musculi pterygoidei interni. Jointly with the musculi
temporales and pterygoidei interni, the masseters drew, in their
principal action, not only the lower jaw upward at the angles, but
at the same time the two angles towards each other, through which
its arch was greatly strained, most at the symphysis, where the
curvature of the arch is greatest, and caused thereon the outside
of the lower jaw very considerable stretching strains. In general in
Homo sapiens the resulting contraction direction of all the muscles
of mastication is converging upward, and stretching strains arise of
this nature.

In the mandibular type of Homo neandertalensis, on the contrary,
strong strains must have arisen in the mandibular arch on the
inside of the symphysis, in consequence of the convergence of
the two musculi masseteres, which was still increased by the pecu-
liar projection of the zygomatic arches — the considerable phaenozygy.
The same we find in the Apes, for also those Anthropoids in which
the ramus mandibulae is not directed obliquely to the sagittal plane
from above outside to below inside, yet present convergence of the
two musculi masseteres in consequence of the projecting far beyond
the sides of the skull of the zygomatic arches, from which these
muscles take their origin; the phaenozygy is here still more con-
siderable than in Homo neandertalensis.

It will remain WatLkuHorr’s great merit that he was the first to
draw attention to muscular action as an explanation of the chin of
Homo sapiens. In his conception Homo neandertalensis and Homo
heidelbergensis must have been almost or entirely speechless, which,
taking the great brain-capacity of the Neandertal Man into consider-
ation, is very doubtful. But Vax pen BROEK is justly of opinion that
other muscles than those which are directly active in speech, namely
the facial (mimic) muscles and the muscles of mastication, may have
given rise to the particular form of the chin of modern Man. He
chiefly thinks of the facial (mimic) muscles *). Here stress may be
laid on the action of the muscles of mastication, by the side of
whose strength, which acts not less continually than the facial
muscles and which is to be measured by more than a hundred
kilograms even in Europeans, the power of the lingual and hyoid

1) A. J. P. van DEN Brork, Ueber Muskelinsertionen und Ursprünge am Unter-
kiefer; ein Beitrag zur Kinnfrage. Zeitschrift fiir Morphologie und Anthropologie.
Band 21, p. 227. Stuttgart 1920.

1039

muscles taken into consideration by Warknorr and of the facial
muscles, becomes negligible *). .

In order to be able to resist the stretching strains described above,
which are caused by the action of the masticatory muscles, the
lower jaw bad to be reinforced at the symphysis. This has happened:
first, by a general uniform heightening or thickening, both in the
mandibular type with stretching strains on the outside and in that
with stretching strains on the inside; secondly, through locally
restricted strengthening, and then: in the type of Homo sapiens
(and Homo wadjakensis) with stretching strains on the outside,
through: (a)a protuberantia mentalis, (6) the lower border bent
outward (torus marginalis), which is not found in the Wadjak-
Man; in the type of Homo neandertalensis (and Homo heidelbergensis)
and most Apes, with siretching strains on the inside, through: (a) a
torus mentalis internus, (ba lamina submentalis (Kutn’s
“simian plate, shelf or ledge”), which latter is only met with in
Monkeys, not in the Neandertal-Heidelberg Man *).

The existence of these strengthenings of the mandible need not
only be accepted as mechanically efficient and necessary, such a
growth of bony substance may also be considered as a definite

consequence of muscular action, which — as ArcHEL*) has
demonstrated — causes directly or indirectly stretching strain (“Zug”),

and with it physiological stimulation of the periost.

What then explains further the difference in direction of the
muscles of mastication, which is the cause of the two mandibular
types? Why is the direction of the musculus masseter slanting from
above and outside towards below and inside in the type of Homo
neandertalensis-heidelbergensis and the Monkeys, and on the contrary,
at least the resulting direction of contraction of the muscles of
mastication in the type Homo sapiens-wadjakensis from above and
inside downward and outside?

The explanation is to be found in the special function of the
masseter and the other muscles of mastication. A different direction

1) In the large Anthropoids (Orang-utan) the strength of the muscles of masti-
cation, estimated by their weight, is three times as great as in Europeans.

2) This torus mentalis internus is another than the torus mandibularis
met with by C. M. Fürsr (Verhandlungen der Anatomischen Gesellschaft 22.
Versammlung, p. 295. Jena 1908) in about 80°) of the lower jaws of Eskimos
examined by him, on the inside of the premolars.

3) O. Aicuet, Vorläufige Mitteilung über Entstehung und Bedeutung der Augen-
brauenwülste, zugleich ein Beitrag zur Abänderung der Knochenform durch plhysio-
logische Reizung des Periostes. Anatomischer Anzeiger, Band 49 (1916), p. 497.

1040

and unequal strength of them must go hand in hand with different
and unequally strong function. In the last-mentioned type, that of
modern Man, the musculus masseter is comparatively stronger, the
musculi pterygoidei are weaker than these muscles were in the type
of the Neandertal Man. The direction of the musculus pterygoideus
internus in modern Man is such that it strengthens the action of
the masseter to a considerable degree, thus helping to elevate the
lower jaw, whereas in the Neandertal type the more transverse
direction of this muscle (which is besides stronger), with regard to
the ramus, caused it and the musculus pterygoideus externus, with
the musculus temporalis, to be especially aetive in the grinding
movement. The latter muscle was more developed broadwise (in
sagittal direction), less as to its height (vertical direction) in Homo
neandertalensis, which could be inferred not only from the form of
its attachment area on the skull *, but also from its broad insertion,
appearing in the shortness, but considerable breadth of the processus
coronoides and the shallowness of the incisura mandibulae. The
backmost part of the muscle, active in the masticatory movement,
was evidently, compared with the type of Homo sapiens-wadja-
kensis, relatively stronger than the front part, which assists the
masseter.

Thus the masticatory apparatus of the type Homo neandertalensis-
heidelbergensis was undoubtedly more adapted for grinding move-
ment; that of Homo sapiens-wadjakensis, on the other hand, parti-
cularly suitable for biting, cutting, and crushing of the food. The
latter type was most perfect in the Wadjak Man. The lower dental
arch is here at the molars narrower by the width of a crown than
the upper dental arch, so that, as I have already mentioned, the
buccal cusps of the lower molars are worn off very obliquely against
the lingual cusps of the upper molars, whereas the lingual cusps
of the lower, and the buccal cusps of the upper molars have remained
intact (nm, and m,), or are worn off a good deal less (m,). Grinding
mastication, with horizontal movement of the lower jaw, as in the
other type, must not have been possible with this obliqueness of
the masticatory surfaces and great inequality of the two dental

1) Described by M. Bouts, loc. cit. p. 43, of the skull of La Chapelle-aux-
Saints. Compare also: R. VircHow (Zeitschrift fiir Ethnologie. Berliner Gesell-
schaft fiir Anthropologie, Ethnographie und Urgeschichte. 1872, p. 8) on the
Neandertal-skull and J. FRAIPONT (JULIEN FRaipont et Max LoHeEst, Recherches
ethnographiques sur des ossements humains découverts dans les dépots quaternaires
d'une grotte à Spy. Archives de Biologie. Vol. VII. (1886), p. 720. Gand 1887)
on the Spy-skulls.

1041

arches. This type of dental arch and teeth of the Wadjak Man, to
some extent analogous to that of the Carnivora among the Mammals,
was certainly particularly suitable for animal food. In the Australi-
ans, which live chiefly carnivorously, the difference in breadth of
the two dental arches is greater than in any other living race,
perhaps with the exception of the Eskimos, but even in Europeans
the upper dental arch is, as a rule, wider at the molars than the
lower arch; this is a general character of Homo sapiens ').

KraarscH considers this wide lateral prominence of the upper
dental arch of the Australians as a character of the primitive state;
the dentition of his Homo aurignacensis of Combe-Capelle had lost
this ‘Primitivitét’” of the Australians’). This can only refer to an
original type of Man, not to a prehuman stage; for in the Anthro-
poids and most other Monkeys the upper molars certainly do not
extend further beyond the lower ones than in modern Man. Such
conditions, with narrow lower dental arch and oblique wearing off
of the teeth, as are met with in the Wadjak Man, have even been
described of jaws of the Eskimos, who belong to the Mongoloids,
but feed chiefly on raw meat and bacon *).

Entirely different was the type of the relation of the dental arcades
in the Neandertal- (and probably also the Heidelberg-) Man. The two
dental arches must have covered each other perfectly or the upper
molars must have extended but little outside the lower ones, as in
most Monkeys; for the crown of these teeth were ground off horizontally,
at least uniformly over their entire breadth. The prematurity of
the wearing off in comparatively still young individuals, has struck many
investigators; it is universally attributed to coarseness and impurity
of the vegetable food, which was often mixed with small quantities
of earth. This renders it probable that Homo neandertalensis found
his food mostly on (or in) the ground; this can also be deduced
from particularities of his skull and skeleton, which will be discussed
further.

As meat and fish, in general animal food, contain the nourishing
substances in a relatively pure state, and are mostly not hard, they
need not be ground particularly fine to be digested. Biting off by the
front teeth, tearing, and crushing by the molars is sufficient; thus
the food can rapidly pass, almost linea recta, through the mouth-

1) Sir Wituiam Turner, The Relations of the Dental Arcades in the Crania of
Australian Aborigines. Journal of Anatomy and Physiology. Vol. 25 (1891),
p. 461—472.

3) In Praehistorische Zeitschrift. Band I (1910), p. 313. Berlin 1910.

5) K. GoRrsanovic-KRAMBERGER, |. c.

1042

cavity to the gullet. The direction in which the masticatory muscles
draw the lower jaw against the upper jaw, was in the Wadjak-Man
from below and outside towards above and inside, in which direction
the masticatory surfaces of the molars have been ground off against
each other. For such a jaw is also frequently active alternately left
and right, in which the half of the mandible which was first somewhat

abduced when the mouth was opened — in such a way that the
molar-crowns are directly above each other — is moved obliquely

from below and outside towards above and inside. Thus between
the bueeal crown-halves of the upper and lingual crown-halves of
the lower molars, which have remained unworn for the greater part,
and form two rows of cusps, pieces of meat and fish are stretched
in such a way that when the jaws are firmly closed, particles are
comparatively easily pinched off by the other crown-halves, which
have been ground off against each other.

The two sides can also act simultaneously, but
then more crushing. In any case these jaws are
almost as unsuited for grinding movement as those
of the Carnivora among the Mammals. The con-
verging direction of contraction of the masticatory
muscles and in connection with this the formation
of the chin in the type of Homo sapiens-wadjakensis is, therefore,
to be explained by the more carnivorous masticatory apparatus of
this type of Man.

_ Vegetable food, however, on which the men of the type Homo
neandertalensis-heidelbergensis cbiefly lived, like the Monkeys, is
generally much poorer in nourishing substances, contains them at
least in less concentrated condition, or else it is very hard. If suffi-
cient quantities of nourishing substances were to be absorbed and
digested, the masticatory apparatus had to be very active and the
food had first to be ground very fine. This took place through -
grinding mastication, in which the food was continually pushed
automatically by the tongue and the not masticating side of the
lower jaw — the grinding movement is chiefly alternately one-sided —
under the masticating teeth of the upper jaw of the other side
(which takes place on opening the mouth in the other type of
jaws and teeth). The direction of the movement of the lower jaw,
determined by the direction of contraction of the muscles of masti-
cation, had therefore to be from below and inside to above and
outside. And the directions of muscular contraction of the two sides
thus diverging in this diluvial type of Man, as in the Monkeys, led
to the formation of a torus mentalis internus, in the latter besides

1043

to a lamina submentalis, all this in connection with a more vegeta-
rian way of living.

Thus the comparison of the masticatory apparatus teaches us that
Homo wadjakensis and Homo neandertalensis were types of an
entirely opposite way of living. The former will have chiefly sub-
sisted by hunting and fishing, the other must have found his vege-
table food on, in or near the ground, for there can be no doubt of
his biped locomotion. The same contrast in mode of living can also
be deduced from a comparison of the neurocranium and the other
parts of the skeleton.

The most striking and important characters of the neurocranium
of Homo neandertalensis are the platy cephaly (with flattening
of the forehead and of the occiput, the latter leading to the formation
of a torus occipitalis transversus), and the torus supraorbitalis.
These two, in the first place, have been considered as simian morpho-
logical characters of the Neandertal Man, as attributes of low and
quantitatively small development of the brain. Chiefly in virtue of
these characters, G. SCHWALBw*) has tried to justify, with great con-
viction, the epithet primigentus, assigned by Wirser to this Plistocene
human type, by comparative measurements and morphological
investigations. Homo neandertalensis would be the direct stock form of
Homo sapiens, modern Man, from whom he would be distinguished
by essential peculiarities. The latter is diametrically opposed to what
Huxiey stated in his famous treatise “Evidence as to Man’s Place
in Nature” in 1863, and what, as far as platycephaly is concerned,
was again advocated by Sra, ten years ago, though with an entirely
different purpose in view, in an elaborate study’). In Huxrev’s
Opinion, and in that of others a torus supraorbitalis, though in a
less degree, would even be found in some cases among the present
Australians, the lowest and most primitive of living races. In both
conceptions a type might have been expected in the probably Plistocene

1) Especially in his “Studien zur Vorgeschichte des Menschen”, Zeitschrift für
Morphologie und Anthropologie. Sonderheft (228 pp.) Stuttgart 1906.

*) G. L. Sera, Sul significate della platicefalia con speciale considerazione della
razza di Neanderthal.Archivio per |’Antropologia e la Etnologia. Vol. 40, p. 381 —
432 (1910); Vol. 41, p. 40—82 (1911). Sera, indeed, considers the platycephaly
of the Neandertal Man as a typical property, but not as simian. It is sporadically
met with in living races, it would, however, have occurred constantly in this
diluvial Man, pathologically or semi-pathologically, then as a passive adaptation
to the glacial climate. The characters of the masticatory apparatus discussed here,
which are in connection with the form of the neurocranium are incompatible with
this conception; so is the fact that the typical masticatory apparatus of this fossil
Man in early diluvial time was more perfect (Homo heidelbergensis).

1044

anstraloid Man of Wadjak, which approaches somewhat nearer to the
type of the Neandertal Man. The contrary is found. Between the
Javanese proto-Australian and the Neandertal Man the contrast, as
regards the splanchnocranium, is still sharper than between the
latter and the Australian of the present time; attention may be
drawn here to the characters of the external nares. Nor is there
found a trace of a torus supra-orbitalis at the neurocranium of the
proto-Australian, or platycephaly; many an Australian of modern
times is in this respect even somewhat less far from the Neandertal
Man. Evidently the two types were distinct from the very beginning.
Indeed since it is known that the capacity of the brain of Homo
neandertalensis was not smaller than that of present Man, nay even
exceeded this, it will not do to consider his platycephaly and the
torus supraorbitalis attending it as characters of a still low and
simian brain-develupment. Homo neandertalensis was perfectly human,
and this resemblance in characters to the Apes can only be explained
as functional analogy.

The torus supraorbitalis of Homo neandertalensis cannot be
accounted for by his powerful masticatory apparatus, for in this
respect he is inferior to Homo wadjakensis, who nevertheless does
not possess a torus supraorbitalis. No more can such an explanation
apply to the Monkeys, among which this torus is almost universally
found.

It is an important fact that there is no torus supraorbitalis at the
skull of the Orang-utan, whereas this is strongly developed in the
other Anthropoid Apes. The neurocranium is also comparatively short
and round and less flattened in the Malay Ape. The primary devia-
tion is evidently the absence of the torus supraorbitalis. This can
again not be attributed to a difference in the comparative size of
the jaws, for this is certainly no less than in the Chimpanzee, and
equals in large individuals of Sumatra that of the Gorilla.

Now there is one organ in the Orang-utan very peculiarly deve-
loped, entirely different from what is found in the other Anthropoid
Apes, and this is in connection with the mechanism of the movements
of the skull, and indirectly with its shape. In all orang-utans, female
as well as male ones, the throat poach or laryngeal sac, properly two
sacs, homologue to the small ventricles of the mucous membrane of
the larynx, which are known by the name of ventriculi Morgagni
in the anatomy of Man, is or are not enclosed between the lower
jaw and the trachea, as in the Siamang, or (apart from axillary and
other deepseated recesses and c.q, of transverse sacs under the lower
jaw) restricted to the median front side of the neck only, as in the

1045

Chimpanzee or the Gorilla, but are developed to a large air-cushion
which, embracing the neck, extends far over the breast and the
shoulders, and on which the head rests in front and on the sides ').
Deniker and BovrarT, and also Heck are inclined to consider the
large laryngeal sacs of the Orang-utan as support for lower jaw
and parts of the head, the muscles of the neck being much less strong
than in the other large Anthropoids*). Probably not in contrast with
the much smaller laryngeal sacs of the other Anthropoids mentioned,
their functional meaning is certainly not connected with the voice,
for the Orang-utan is almost dumb. Nor is their large size in the
Orang-utan in connection with an extra-ordinary weight of the
head; that of many Chimpanzees is no less heavy, and the head of
the Gorilla is certainly generally heavier. The laryngeal sacs of the
Orang-utan grow with the general growth of the animal, and are
larger in males than in females, largest in gigantic old males. As
the head gets heavier, the laryngeal sacs increase in volume. They
support the head also on the side, and it seems that they can be
assisted in this by the cheek lobes, for where these occur, the
laryngeal sacs are comparatively less large *).

But in Anthropoids and other Apes, in contrast with what happens
in Homo sapiens, the head is not carried poised on the vertebral
column, but in most it is carried strongly hanging over; the centre
of gravity then lies far before the supporting line of the condyles,
and very powerful muscles of the neck carry this overhanging
weight. The muscles of the neck in the Orang-utan are directed
much less steeply with regard to the “horizontal planes” of the skull,
consequently the planum nuchale is steeper than in the other
Anthropoids, for instance in the Chimpanzee. The angle of the
basio-nasal line with the basio-inion line is about 30° smaller in the
Orang-utan, and the angle of the plane through the middle of the
condyles and the nasion with the condylo-inion-plane 22° smaller
than in the Chimpanzee. This means that only with an elevation of
the head of the Orang-utan of 22°, when in front it certainly rests

1) R. Fick (Vergleichend anatomische Studien an einem erwachsenen Orang-
Utang. Archiv fiir Anatomie und Entwickelungsgeschichte. (W. His), Jahrgang
1895, p. 75) found at the dead body that when the laryngeal sacs are swollen,
the head was greatly lifted up backward, without his seeing in this an indication
of the vainly sought functional meaning of that air sac.

9) Deniker and Bovutart in Nouvelles Archives du Muséum d'histoire naturelle,
Paris 1895. sér. 3, t. VII, p. 47—48. Breums Tierleben. Vierte Auflage. Säugetiere,
Bd. IV, Primates. Bearbeitet von L. Heck, p. 630. Leipzig. 1916.

5) Cf.: C. Kerpert, Reuzen-Orangoetans, in „Natuur- en Wetenschap”. Eerste
Jaargang, p. 7. Brugge 1914.

68

Proceedings Royal Acad. Amsterdam. Vol. XXIII.

1046

no longer on the air-cushion, the muscles of the neck pull at the
occiput in as favourable a direction, thus raising the front of the
head as in the Chimpanzee. But in the Orang-utan these muscles
then pull in the direction of the orbital arch of the frontal bone,
while through its elevation the front part of the head hangs much
less heavily at the occipital part of the cranium, which is besides
shorter; they draw in the Chimpanzee in the direction of the crown
of the cranium, the frontal part of the head still hanging with its full
weight at the occipital part of the cranium, which is besides longer.
When, as occurs frequently during locomotion, the body is moved
up with great velocity, or is checked in its speed obtained by
gravity, the heavy head will fall forward with great force through
inertia, unless it is stopped. This takes place in front in the Orang-
utan, by means of the elastic laryngeal air sac, in the other
Anthropoids and most lower Apes only by means of the muscles
of the neck, which acting behind the transverse axis of rotation,
pull the skull backward. The stretching strain thus arising between |
the front part and the back part of the calvaria, is comparatively
small in the Orang-utan, great in the other Anthropoids, whose
cranial vault would certainly run a risk of breaking, if there were
no mechanism to strengthen it, through transference and dispersion
of the excited strain. In Man of the present type the head turning
about the condylar axis, never hangs over forward so heavily,
because in the ordinary erect attitude it balances on the vertebral
column, the planum nuchale lies very flat, and the muscles of the
neck, which thus act almost straight downward, pull the head
backward, which causes the strain excited between the occiput and
the front to be much less great in all positions. However, also in
Man and in the Orang-utan, the cranial vault might possibly not
always be able to resist it, without the mechanism in question, now
to be described, which is however less strong here *).

Apparently the strain is borne certainly not entirely, probably
only for a very small part by the brittle bony substance, but for
the greater part by the very elastic apparatus of the musculus
epicranius or occipito-frontalis, the two-bellied flat muscle, whose
uniting tendon, the strong epicranial aponeurosis or galea aponeu-
rotica, which chiefly consists of longitudinal fibers, and is loosely

') The principal functional meaning of the air pouches, found in so many Monkeys,
most probably consists, in general, in this that they help the muscles of the neck
to prevent sudden stretching of the encephalon and the medulla spinalis of which
there might be a danger from the generally heavy front part of the head, and
the situation of the foramen occipitale under the back part of the cranium.

1047

attached to the calvarial bone upon which it glides, but firmly
bound to the hairy skin of the head, extends over the calvaria
between the fascia temporalis of the two sides, in which it is lost. The
backmost belly, formed on either side by the musculus occipitalis,
starts, in modern Man, in different extension and coherency from the
occipital bone, above the superior curved line, and laterally to the
basis of the mastoid process of the temporal bone, hence above the
muscles that pull the bead backward. The front muscle belly, formed
by the two musculi frontales, rises from the epicranial aponeurosis,
and its fibers terminate, in Man of the modern type, besides in the
skin of the root of the nose and of the brows over their entire
length, at the median part of the frontal bone and at the outside
of the orbital arch, but here in very various extension and coher-
ency; most uniform is still the lateral part of this attachment, namely
near and at the processus zygomaticus frontalis. More coherent is
this bony origin (directly or indirectly by fascia) in Apes that possess
a torus supraorbitalis *).

This apparatus must have a more important function and especi-
ally (in the Neandertal Man) have had a more important function
than elevating the eye-brows and wrinkling the forehead. Its principal
action apparently is, as was stated above, the distribution of the
strain, which is exited by the muscles of the neck, by transference
to the frontal orbital arches, and as stress, to the malar bones and
elastic zygomatic arches back to the occipital bone.’)

The functional significance of the torus supraorbitalis in most
Apes, and its absence in the Orang-utan and Homo sapiens thus |
becomes clear; besides, its formation can also be explained directly
mechanically by the application of Arcuer’s demonstration.

The validity of this view may also appear from what is found
in American Apes (Chrysothrix, Cebus, Ateles). Here the planum
nuchale, to which the muscles that draw the head back, are attached,
makes much smaller angles with the transversal glabella-inion plane,
hence no very great strain can arise in the cranial vault, and there
was not developed a torus supraorbitalis.

1) In an analogous way as the apparatus of the musculus epicranius protects
the calvaria from the violence of the cervical muscles, the strong fascia temporalis,
stretched out between the temporal crest and superior temporal line, and the
zygomatic arch, and serving for partial attachment of the musculus temporalis,
protects it against the violence of the latter muscle, and the zygomatic arch against
that of the musculus masseter. This apparatus, though exceedingly strong in the
Apes, does probably not contribute to the formation of the lateral part of the
torus supraorbitalis, but only of the temporal crest.

3) Cf. on those muscles in Apes and Man: G. Ruce, Untersuchungen über die
Gesichtsmuskulatur der Primaten, p. 37—51 and 84—983. Leipzig 1887.

68*

1048

Apparently the torus supraorbitalis of Homo neandertalensis must
be explained in a similar way, as mechanically efficient, and as
having arisen mechanico-physiologically, if the head was not carried
erect, resting in equilibrium on the vertebral column, as in Homo
sapiens-wadjakensis, but bent forward, supported by the muscles
of the neck. And actually a number of characters of the former,
of which some had been known already for some time, others were
. described by Marceriin Boure for the first time, from the fossil man
of La Chapelle-aux-Saints, could not be explained differently. The
characters of the occiput lead us to assume that in Neandertal Man
the muscles of the neck were very strong and supported the head
also in a position of rest. This latter appears-among others from
the steepness of the planum nuchale. For the glabella-inion-opisthion
angle or lower inion angle amounts to 51.5° at the Neandertal cal-
varia, to 54° at the skull of Spy I, to 53° in Spy II, to 44,5° at
the skull of La Chapelle-aux-Saints (Boure), to from 31° to 40° in
Homo sapiens; in Wadjak I this angle cannot be determined accurately ;
it is probably 40°, but the planum nuchale is still less steep as a
whole on account of the depression under the inion well-known
also of Australian skulls. The foramen occipitale is placed somewhat
further backward in the Neandertal Man than generally in modern
Man (and the Wadjak Man), and the angle of the plane of this
foramen with the plane of the orbital axes (Broca) is open in front,
in the same way, though not so widely, as in the Anthropoids,
in contrast with the angle open to the back of the modern type
of Man and of the Wadjak Man (not to be measured accurately
at the skull of the latter). Accordingly, the plane of the foramen
occipitale must turn strongly forward (16.5° in comparison with
the Australian skull, 22° with the European skull, according to
Boure), if the orbits are to assume the same direction with
regard to the vertical. The spinous processes of the two lowest
cervical and first dorsal vertebrae are not directed obliquely
downward, as in Homo sapiens, but about horizontally, as in the
Anthropoids, and the curvature of the cervical vertebral column
is little pronounced. The figure of Neandertal Man was short,
especially in the legs, but broad and thickset, the posture less per-
fectly vertical, with legs slightly bent in the hip and knee joints.
The mastoid processes are comparatively small, so that the musculi
sternocleidomastoidei, which turn the head, (hardly feasible with
bent head) were comparatively weak muscles. The orbits are (quite
different from those in the Wadjak Man) very large, deep, and
round; the eye-balls must have been large. Like arboreal animals,

1049

and those that move very rapidly (Horse, Ostrich), Homo neander-
talensis had large eyes, in order to be able to distinguish details in
the field of view sharply, as served his requirements when seeking
vegetable food on, in, or near the ground, at any rate in his close
neighbourhood, like the arboreal animals. It was different with the
hunting and fishing Wadjak Man, to whom the minute details in
his field of view were not so important. In accordance with his
mode of living, the latter, judging from the preserved parts of the .
femur and the tibia, was equally slenderly built as the Australian
aborigines are as a rule. He was, indeed, taller; therefore the bones
are absolutely heavier (thicker). The diaphysis of the femur meas-
ures in the middle, sagittally 30 mm. (Neandertal 30, Spy 31),
transversally 29 mm. (Neandertal and Spy 30); under the trochan-
ter minor, sagittally 28 mm., (Neandertal 29, Spy 27), transversally
33 mm. (Neandertal 34, Spy 35). The caput femoris has a vertical
diameter of 47 mm. (Neandertal 52, Spy 53) and the same transversal
diameter (Neandertal 50, Spy 52). The breadth of the proximal epiphysis
of the tibia is 75 mm. (Spy 81). Consequently the Wadjak Man was much
slenderer than the Neandertal Man (whose legs were much shorter).

In all these points the Neandertal Man was the direct opposite of
the Wadjak Man. The other peculiarity of the skull, so characteristic
of the former, of Pithecanthropus, and of the Apes, namely the
platycephaly, which generally goes together with a torus supraorbitalis,
and which, with this latter, is entirely absent in the Wadjak Man,
can now be explained as mechanically efficient: first to
obtain a longer lever for the force of the muscles of the neck
carrying the exceedingly heavy head, that hangs forwards, through
the ‘“chignon”-like bulging out of the occiput; secondly to get a
more favourable direction of the musculus epicranius in the conveyance
of the strain from the occipital bone to the frontal bone, in the
direction of the longitudinal axis of the calvaria and of the zygomatic
arches; thirdly to make the head, which was always to be carried
by muscular force, less top-heavy, by transference of brain below
the transversal glabella-inion plane (which I propose to demonstrate
further in a following communication). Also the physiological pressure
of the musculus epicranius, which worked exceedingly energically,
may be considered as a direct cause of the platycephaly — in an
analogous way as in the artificial deformation of the Marken skulls,
according to Barer’s investigation *).

1) J. A. J. Baran, Beiträge zur Kenntnis der niederländischen Anthropologie. II.

Schädel der Insel Marken. Zeitschrift für Morphologie und Anthropologie, Band 16, -
p. 465—524, with one table and 6 plates. Stuttgart 1914.

1050

It appears thus firmly established that Homo neandertalensis (with
Homo heidelbergensis) and Homo wadjakensis belong to two types
of Man opposite in every respect, and that it is especially impossible
to derive this form of the type Homo sapiens (though it is very old),
from the other type. They may, nay they must, indeed, have sprung
from a common Hominide branch in a time geologically much more
remote than that from which their fossil remains date. It need hardly
be said that the latter cannot be identified with the time of their
origin, nor without further proof, with the optimum of their existence,
nor with the end.

Homo heidelbergensis and Homo wadjakensis were both optimate
forms of their type. The best time of existence of the first type the
Neandertal Man. proper had certainly already long behind him.
From the Second or Mindel-Riss Interglacial period, from which the
lower jaw of Mauer (Homo heidelbergensis) dates, till the Third or
Riss-Wiirm Interglacial period, from which most fossil remains of
the Neandertal Man are, the type has greatly deteriorated, judging
from the masticatory apparatus. It then disappears soon, probably
in the last or Würm-Glacial period (Spy), making place in Europe
for several already very differentiated forms of the type Homo
sapiens (Cro-Magnon, Combe-Capelle, Grimaldi). In the vegetable
world which got poorer and poorer during the Plistocene epoch, a
Man specially equipped for a vegetarian mode of living must have
experienced greater and greater difficulty in finding his food, whereas
a carnivorous Man could always find an ample supply of food in
the animal world. The adaptation to the unfavourableness of the
climate by the assumption of a more carnivorous way of living,
could only be very limited in such a very specialised type as the
Neandertal Man; the very small morphological approach in the
masticatory apparatus to the type of Homo sapiens, may be accounted
for in this way. In the latter type, however, such an adaptation to
a more omnivorous way of living, was indeed possible, which
facilitated the feeding; it was still more improved by the use of
fire in the preparation of the food, all which contributed to the
development of the type Homo sapiens in his present form.

It needs no further argument that the Neandertal-Heidelberg type
cannot have arisen in the Plistocene epoch. It is also impossible
to assume this for the Homo sapiens type, because these two types
must certainly come from a common stock, as is proved by the
human shape of their bodies, and especially, because they had both
already reached the height of modern Man in the principal human
character, the very exceptionally large size of the encephalon; it is

1051

moreover impossible to assume this on account of the said early
differentiation of sapiens-forms, also manifest in the Wadjak Man,
probably the oldest, certainly the most primitive of the forms of
this type known up to now.

If therefore the Neandertal type and the Wadjak (sapiens) type
existed already before the Plistocene epoch as real Human beings,
which had a common human stock, it must have been in still earlier
times that their common ancestor sprang from a biped, though only
Man-like transitional type, possessing a less large encephalon.

EXPLANATION OF THE PLATES.

PEALE +I.
Fig. 1. Wadjak I. Norma lateralis of the skull. As horizontal the Frankfurt
plane. Stippled outline of a typical Javanese skull.
Fig. 2. Wadjak I. Norma frontalis of the skull. As horizontal the Frankfurt
plane.
Fig. 3. Wadjak I. Norma verticalis of the skull. As horizontal the Frankfurt
plane.

Figures 1—3 in 1/, natural size.

PLATE II.

Fig. 4. Wadjak II. Maxilla and mandibula. Left side. As horizontal the
alveolar plane.

Fig. 5. Wadjak II. Maxilla and mandibula. Facial view. As horizontal the
alveolar plane.

Fig. 6. Wadjak I. Maxilla from below. Alveolar plane. The crowns of the
right p, and of the left # and #3 must lie 1 mm. more to the outside, the
crown of the left p, 0.5 mm. in the figures 4, 5, and 6, on account of
deformation in correspondence to twice the amounts in the original.

Fig. 7. Wadjak II. Mandibula from above. Alveolar plane.

Figures 4—7 in !/, natural size.

Fig. 8. Vertical cross-sections in the symphysis line of the mandibula of
Wadjak II (full line), Homo heidelbergensis (broken line), and an Australian
(stippled line), by the side of it a Frenchman. The two latter according to
BOUuLE (loc. cit., p. 88, Fig. 56). All these from plaster casts, except the Mauer-
“jaw, which is from a figure of the original (O. SCHOETENSACK, Der Unterkiefer
des Homo Heidelbergensis. Jena 1908, Table 8, Fig. 20 and Table 13, Fig. 48).

Natural size.

Physics. — “On the application of Einstein's theory of gravitation
to a stationary field of gravitation.” By H. A. Kramers. (Com-
municated by Prof. H. A. Lorentz).

(Communicated at the meeting of September 25, 1920).

1. Definition and invariant properties of a stationarr
prop y
field of gravitation.

We will call a field of gravitation stationary when the expression
for the line element can be put into such a form ds’ = g,,dx,dz,')
(a, time-coordinate, 2,,2,,7, space-coordinates) that the gravitation
potentials g,, do not depend on the time z,. A special case of the
stationary field of gravitation, defined in this way, forms the so-
called “static” field of gravitation, which appears when it is possible
by a suitable transformation to make the quantities go1, gor and go3
equal to zero. It is simply seen, that when the line element of a
stationary field’ of gravitation is brought in the above mentioned
form, the most general transformation of coordinates, for which the
g””s remain independent of the time, and for which a point at rest
remains at rest, is given by the formulae

Br PUG eco ols (== 4,3) (1)
Ly = ast, i wp (e'‚, V's &',).
Here pz; and w are arbitrary functions of w',, 2',, z'‚, while a is
a positive constant. The quantities g,, and their derivatives show,
with regard to the transformation group expressed by (1), certain
invariant and covariant properties, which we will now investigate.
The line element may be written in the following form,

1
ds? =9,,dx,da,=-& Gy dapdx (+ — (goede, Horde, Hodes +954)’,
Joo
. (2)
gok Jol
Gri = — gu Hs

1) Just as EINSTEIN we have omitted the signs of summation for summations
which have to be extended over indices, which occur twice in a product.

1053

where the summation has to be extended over 4,/=1, 2, 3. When
in the following an index can assume one of the values 1, 2, 3,
we will denote this index by a Latin letter. If on the contrary an
index can assume one of the values 0, 1, 2, 3, it will always be
denoted by a Greek letter. In case of summation over an index,
occurring twice in a product, the sign of summation will be omitted
in both cases. If now we perform the transformation (1), the
expression Gy; dz, dx, becomes again a quadratic form of the diffe-

1
rentials of the space coordinates, and — (go, de)’ becomes again the

60
square of a linear differential form. Since the separation in two
parts of the expression of the line-element given by (2) is only
possible in one way, we may conclude, that the expressions
Joo

are invariants with regard to the transformation (1). Consequently
the quantities go./Vgoo possess the character of a vector, and from
this we conclude again, that the bilinear differentialform

g Eken EE APP att LAG
Ow, gs Ox,

is also invariant with regard to the transformation (1). The constant
s may be chosen arbitrarily, because the quantity g,, appears only
multiplied by a constant factor after the transformation. Choosing
the special value s=1, we see that all terms for which u = 0
or »=O become equal to zero, so that in this case we may omit
the index O under the summation, and we obtain the result, that
the expression

gol Ò (gok
4 hs En id 0x 5)

is invariant. As the coefficients of this differential form are anti-
symmetrical with regard to the indices & and /, we may consider the
expression (4) as a linear form of the differentials dj, —= derde dvd.

Gy der der and

s—}

00

IRE OG buds Ns tell)

Now for a threedimensional extension, the expression EWG Dandy,
remains invariant for an arbitrary transformation of coordinates,
where G represents the determinant of the coefficients Gj, in the
expression do? = Gj derde, for the invariant line-element, and where
under the summation the indices 4,/,m assume the sets of values
1,2,3 and 2,3,1 and 3,1,2. Consequently the quantities V Gdzyz
are transformed as the components of a covariant vector (if we, in
the usual way, call the transformation of the components de, of a

1054

small displacement contravariant). From the invariance of the
expression (4) we may thus conclude, that the quantities *)

Joel 9 (901 Ò (gok
Rn LA laki Sh a a. Gene
; G Ou}. (=) Ow) (=) (

where k‚lan again may assume the sets of values 1, 2,3 and 2, 3,1
and 3, 1, 2, with regard to the transformation (1) are the contra-
variant components of a vector in the three-dimensional extension
with the invariant line-element do? = Gj,da,da,;. The invariant ab-

solute value of this vector is given by R=V Gy, RER!

If the components 2” are everywhere equal to zero, we have to
do with a static field of gravitation. In fact, from (5) follows that
in this case the quantities gor/g,, may be deduced from a potential

p in such a way that gor == Yeo but from this follows again,

(pp
Dar,’
that the line element may be written in the form ds? = — Gij derde +
+ gsde,*, where x, = x, + Pp.

If the components Rr" are not equal to zero, these quantities deter-
mine in every point what might be called the “rotatory” properties
of the stationary field of gravitation. This may be illustrated by
considering the motion of a masspoint, the velocity of which is small]
compared with the velocity of light. In general the ‘‘worldline” of
a masspoint is determined by the equations

dv) | uv ) de, de, 0
ee azo A HOUTE
ds? (2 ds ds

If now we assume, that by a suitable transformation of the kind
(1), the line-element has been given the form ds? = da,’°—dx,*?—dw,’?—
dr,’ at a given point P of the worldline, it may be easily verified
that the equations (6), looking apart from small terms of the same
‘order of magnitude as the square of the velocity, in the point P
assume the simple form:

lk Ae (2 dn =) ETE EN

de,” Ue dx, Ow}
where klm just as before may assume the sets of values 1, 2, 3
and 2, 3, 1 and 3, 1, 2. From these equations we learn that the
“force” which the field of gravitation in the point P exerts on a
mass point of unit mass may be described as the sum of a Corio-
lis-force perpendicular to the velocity and proportional to it and of
a force, which may be derived from the potential 4 ,,.

1) If we admit only such transformations, for which the functional determinant
is positive, we may by the root-sign in this expression always understand the
positive root.

1055

If next we consider the motion of a mass-point in a conservative
field of force, such as would take place according to Newtonian
mechanics, we obtain equations of motion of the same form as (7),
if the Cartesian coordinates describing the position of the mass-point
refer to a system of coordinates which rotates uniformly in the
space. In fact, if the equations of motion in the non-rotating system
of coordinates. possess the form

/

they obtain in a system of coordinates vl, et! which rotates
round an axis through the origin with an angular velocity which,
considered as a vector, possesses the components — #', — FR? and
— R*,*) the form:
du!) pl d'n de | 0 (p—w)
= 5 == 2 R oe re Fins = ee Fi 3
dt dt Ox ke
Yp =$ (LJ (wt He Helt) — HRE! + Re, + Rk a)

rm

which coincides exactly with the form of the equations (7), if we
put t=a, and gy —w=b3g,,. The essential difference with the
equations of motion in the non-rotating system of coordinates lies
consequently in the appearance of the Coriolis-forces, and we are
justified in denoting in the following the vector RE as the “rotation-
vector”.

The character of the rotation-vector may also be examined in the
following way. We will try by a transformation of coordinates of
the form (1) to give the line-element of a stationary field of gravi-
tation such a form, that in a given point P not only the relations
Ins = Ems are valid, where the quantities «,, are defined by

Ei FS oe ey Srl, Ent Ap) pf 5 8)

4

but that at the same time the quantities e= Ju,k AS many of
them as possible become equal to zero. If it was possible to make all
the latter quantities equal to zero, we should obtain in this way a
system of coordinates, which is “geodetic” in P. Now it is always
possible in many ways by means of a transformation (1) to make
the quantities y,, assume the values &,, in the point P, but in general
it will not be possible to make all quantities Ju,k equal to zero. In

!) Here and in the following we will assume the usual rule, that to a
rotation in a plane corresponds a direction of the normal of this plane in
such a way, that, for a rotation in the X|, Xg-plane from the positive X-axis
to the positive x-axis through an angle smaller than z, the corresponding
„normal points to the same half-space as the positive x-axis.

1056

the first place this is easily seen to hold for the quantities goor,
because goo by the transformation (1) is only multiplied by a constant
factor; but neither the quantities go, can all of them at the same time
be reduced to zero, because this would mean, that the components of
the rotation-vector would be equal to zero, and this is in general
not the case. On the other hand it is obviously always possible to
perform such a special transformation, that the system of coordina-
tes in the three-dimensional extension with the line-element do? =
= Gi der da, becomes geodetic in the point P. In this way we get
ise = 0 and consequently also gui, = 9, since gz; = — Gy 5 seek
Oxy N Joo
and since the quantities gz. are equal to zero in the point P.

Let us now imagine, that by means of (1) the line-element has
been given such a form, that in a given point P the following
relations are valid

d) Juv = Ens

B) gki,v= 0 (9)

ec) gok,1 + 9ol,k= 0 |

As regards the third of these conditions it will be observed, that
it is always possible by a suitable transformation of the time to
effect, that the symmetrical quantities Az; == Gort + Goi,p become equal
to zero in P. In fact, it is easily shown that, if the conditions (a)
and (6) are already fulfilled, but not yet (c), the transformation
aw’, =a, + 4 (An)P (ar — (re) p) (wi — (2) Pp) leads us to the desired
purpose. Thereby we have denoted the value of a quantity in the
point P by adding the index P on the right below. Let us now
perform a transformation of coordinates, which corresponds to a
uniform rotation, around an axis through P, of the z,, 2,, 2,-space
(considered as a Euclidean space with the line-element do? = dv,’ +
de,” + dx,?), the angular velocity of which considered as a vector
has the components #', k?, and R*. After the performance of this
“rotation transformation’, which does not belong to the group
of transformations (1), the relations (a) and (6) are still valid,
but also all the quantities go, have become equal to zero. This
may be proved by a direct calculation, and the proof becomes
especially simple, if we assume, that in P the quantities /* and 2?
are equal to zero, so that we have to do with a uniform rotation
round the axis of the coordinate #, with an angular velocity
k?=w. Since in the point P the quantities A, reduce to
4 (Gom, Jolm), we have in consequence of relation (c), that of all

*

1057

quantities gox,, only the two quantities Joie and goo, are different
from zero in such a way that W = 902.1 = — Yos. The rotation-
transformation can now be written in the form

#, —(«,)p=2', cosw ax, —a2', sin wc,

©, — (e)P= et! sinw x, + 2', cosw a,

If now by means of this formula the line-element (2) is trans-
formed, and if we make use of the above mentioned relations (a),
(6) and (c) it is easy to verify:

That for the transformed quantities Ju» in the point P the rela-
tions (a) and (6) are still valid.

That, although the g,,’s will contain the time #,, their first derivatives
with respect to the time will be equal to zero in P, and that equally
all derivatives of Jor Joz and go3 have become equal to zero.

We thus see in the first place that, after the rotation-transforma-
tion, the equations for the world-line of a mass point, the velocity
of which is small compared with that of light, assume in the point
P the simple form

so that the term corresponding to a Coriolis-force appears no more,
which was naturally to be expected from the above considerations.
Let us further consider the special case, that in the point P the
mass point can remain in equilibrium; that is, that in this point the
quantities goo, in the original system of coordinates are equal to
zero. In this case we find, that in the new system of coordinates,
to which the rotation-transformation has given rise, all quantities
Yu», Without exception disappear in the point P, so that this system
of coordinates is geodetic in that point.

§ 2. On the field of gravitation, which is produced by
stationarily moving masses.

Let us consider a space-time-extension, for which the line-element
at large distances from the zero-point of the coordinates approaches
to ds? = dx,*—dz,?—dx,’—dz,? ') and in which there exist masses,
which perform stationary motions; that is, the components 7, of
the energy-tensor of matter do not depend on the time. The field
of gravitation, to which these masses give rise will then be stationary

') Here and in the following we shall always assume that the centimeter
has been chosen as unit of length. The unit of time is then determined by
the condition that the velocity of light is equal to 1.

1058

in the sense described in $ J, and is determined by the equations
of EINSTEIN
Ruy = 5 Om = BE 8 rx Dap, . . . . . (10)

in which Zw, is a tensor of the second order, which depends only
on the g’s and their derivatives:
ey

0 0 (uv
“Sich
mol © o\ le

while R=g” R,,. x is the gravitation constant of Einstein, which,
if we choose the gram as unit of mass, is equal to 7,4.10—%9. If
we assume that the g,,’s of the line-element which corresponds to
the field of gravitation, only differ little from ¢,,, there exists a
simple method indicated by Einstein to obtain in first approximation
a solution of the equations (10). This solution is obtained by writing

Duy = Evy + Yur Sy, guar” VE teal elgmmees (11)

where the functions y,, everywhere possess a very small value, and
introducing the quantities y',, defined by

no ur} (96

a

5]

o o

N

Vues = Yu — 4 Evy (E28 Yup)
which give

Vm = Ym — 4 Ee (Exp Yass. « + - » « (12)
the values of the y',, in the point w,, 2,, @, and at the moment

v, may be calculated as retardated potentials by means of the
formulae

TEN wv — 7 — Pr
Maun = TT tn f l ed : | dS s = . 5 (13)
i

Here dS represents the space-element de, dv, de, and r represents
the distance from that space-element to the point

Ly, Les LX, (7? = (x, — z,)* + @, — 4) + @, — 2,)’).
The addition [,—=.2,—7] means that everywhere the value of
T.,, at the moment x, —7 has to be used. If we apply the formulae
(13) to our case where the 7’,,’s do not depend on the time, we
may clearly omit the latter condition, and we obtain the usual
formulae for static potentials

Palas

7

We will now calculate the components of the rotation-vector in

the point w,,2,,2,. Neglecting small terms which relative to the
main terms are of the same order of magnitude as the y’,,’s, we
obtain for the w,-component of the rotation-vector

An te (Ei) () |
G Ox, Joo Oz, Joo
rot (t)-Poae

Ox, \7 de, \T

and analogous expressions for the components /? and 2. With
neglect of small terms of the same order of magnitude as the square
of the velocities of the masses we have further the formulae

n

where m is the density of mass of matter, and v,,v,,v, denote the
components of the velocity of matter. If we substitute these values
in the expression found above, we get

== Fen MN, T, == mv,, is

oe,

01

00 02

(ve) Vz — (re) V5 dS '

R' = 2x Im

(15)
ze

and correspondingly #? and &*. This formula teaches, that the con-
tribution of every mass particle to the rotation-vector in point P is
equal to the moment of momentum of the mass particle with respect
to the point P, divided by the cube of the distance from P, and
multiplied by twice the gravitation constant of EINSTEIN.

Formula (15) can be applied to a problem which has been treated
by H. Tuirrinc') in order to illustrate the influence of rotating
masses on the field of gravitation. A homogeneous spherical shell
with mass J/ and radius « rotates with constant angular velocity
w in a space, in which no other matter is present, and for which the
quantities g,, approach to ¢,, at infinite distance from the centre.
It is asked to determine the influence of the spherical shell on the
motion of a mass point, which is lying just at the centre OQ. The
field of gravitation produced by the shell is stationary. From symmetry
we may further conclude that in O a mass point can remain in

i ze San end
equilibrium; that means that in this point the quantities ae dis-
ee

appear. Approximately, that means omitting small terms proportional
to w’, g,, will even be constant in the space within the shell, and
0744, |
02,02)"
point at rest just outside O, will in general be proportional to w?*,
but cannot be determined if the constitution of the shell has not

which determine the force exerted on a mass

the quantities

1) H. TuHirriNG, Phys. Zeitschr. XIX,-p. 33 (1918).

1060

been defined in nearer details. The rotation-vector in O, however,
may directly be calculated approximately by means of (15). Its
direction is of course parallel to the axis of rotation. We intro-
duce a system of Cartesian coordinates «, y, z, the origin of which
coincides with O, and the z-axis of which coincides with the axis
of rotation. Let the mass of unit surface of the shell be denoted by
m. The contribution to the value of A? which is due to a ring of
the shell, the angular distance of which to the z-axis is equal to 9,
will then be equal to

2x X 2x a’? sin BAD Km A od dn sin? 9 dd
a

a’

and for A itself we thus get

xMo (. 4x M
kz = fein van =O foie eas MEN
a da

0

From this we learn that if in O we introduce a system of coor-
dinates, which rotates uniformly in the same sense as the shell with

4M. ee
an angular velocity equal to ae times that of the shell, the Coriolis-
a

forces will disappear from the equations of motion for a mass point
in O. This result is in agreement with the results obtained by
THiRRING in his above mentioned paper.

Another application of formula (15) may be obtained in connection
with the following problem. Let us imagine a uniformly rotating
sphere, such as eg. the earth, and let us suppose that the
FoucauLt’s pendulum experiments are performed at the northpole.
Then it will be found, that the plane in which the pendulum
moves, will not remain at rest with respect to the fixed stars, but
will rotate slowly in the same sense as the earth. The angular
velocity of this slow rotation is given by the absolute value of the
rotation vector at the pole, which by means of (15) may be found
by simple integration. We find

ce cee Oe Mele) Le

where M denotes the mass of the earth, which is supposed to be
homogeneous, while a and w represent the radius and the angular

dx M
velocity of the earth. The factor ~~ is of course so small (circa

5.10 10), that it will be impossible to detect this rotation of the
plane of the pendulum. Also at lower latitudes a similar influence

1061

on the result of Foucautt’s experiments must be expected, but we
will not enter here into this problem.

§ 3. Influence of a stationary field of gravitation on the motion
of a rigid body round its centre of gravitation.

In the former § we have given an example of the appearance of
the rotation-vector; the present § forms a direct continuation of § 1
and gives the necessary preparation for the treatment of the problem,
which will be discussed in § 4, and which deals with the influence
of the sun’s field of gravitation on the precession of the axis of
the earth.

If in the following we speak of a rigid body, we mean only a
body, which is practically rigid, and which can move in the way
well known from classical mechanics, characterised by 6 degrees of
freedom, without changes of form or the appearance of enormously
high stresses. Thus we will assume that the linear dimensions of
the body are so small, that the “geometry” inside the body, which
is determined by the quantities g,, and their derivatives deviates
very little from the Euclidean geometry, and also that the relative
velocities, which the different parts of the body possess relative to
each other, are very small compared with the velocity of light. For
such a rigid body it is possible directly to determine the values of
the components of the energy-tensor of matter to an approximation,
which may be exactly defined. In fact, if we introduce such a
system of coordinates that in every point within the body. the line
element only differs very little from ds* = d«,*—d2x,’—dz2,’—da,?
— as a consequence of the above mentioned assumptions this will
always be possible — and if we denote by v a small quantity of

dap
vy
parts of the body, we have — neglecting small terms, which relative
to the main terms are of the order v? and of the same order as
the small deviations of the g,,’s from the ¢,,’s (see (8)) —:
dat},
dx,
while the quantities 7’, (4,/= 1, 2,3) which are connected with the
stresses existing in the body, and which can only be determined, if
the constitution of the body is known more closely, will be small
compared with the quantities 7%, and may be considered as being
of the order of magnitude v?. The quantity m in the formulae (18)

represents the mass per unit of volume. Further it may be remarked,
69

of the different

the same order of magnitude as the velocity

(18)

1 ’
e= fj Tor == — m

Proceedings Royal Acad. Amsterdam. Vol. XXIII.

1062

that apart from the sign, we need not distinguish between covari-
ant, contravariant and mixed components of the energy-tensor *). Theore-
tically there will be a difference, but this difference will be of the same
order of magnitude as the small deviations of the g,,’s from the
é,, 8, and small terms of this order have already been neglected in
the establishment of the formulae (18).

In the former we have fixed the properties of a rigid body with
an approximation, sufficient for our purpose. Let us now imagine
such a body at a certain time to be placed in a stationary field of
gravitation in such a way, that its centre of gravitation is at rest
and coincides with a point P of the field, where all the derivatives

ò,
en are equal to zero, and we propose to discuss the influence, which
Lie

the stationary field of gravitation will have on the motions, which
will be executed by the body. We will begin by proving, that the

centre of gravity will remain at rest in P. For this purpose we will
use the equations of energy and impulse of matter:

Ohta entier |
Haes } Ju Tw —= 0, Rw) zZz Te —gq, . . rate (19)
02) Ou,

where g represents the determinant of the quantities g,,. We will
assume, that by means of a suitable transformation of the form (1)
the- coordinates in P are made to fulfill the conditions (9). Then the
gus may in the neighbourhood of P be represented by

02,02
Jok = (Jok,m) P&n + 4 (gom) P Gin Cyto es ans neee (20)
Oh) = Ex + 4 (art, mn)P Um Une | |

Oyu»
Joo = Foo + } (Joo,mn) P Um Uny Ypv‚mn =

Here we have assumed for the sake of simplicity, that the coordinates

» &, and x, are equal to zero in the point P and have neglected
small terms of the order of magnitude «*, z* ete, that is, terms
which would contain products of three or more «’;’s.

Let us now consider a closed surface in the «,-#,-«,-space, which
encloses the body under consideration, and in the inside of which
the relations (20) hold, and let us integrate both sides of (19) over
the space inside this surface. Then we get, denoting the space element
dx, de, de, by dS:

x

1 Ok ’k yt 7 der 00 ry my ;
yee = 71; aE nr ff = 1 = Too =m.
vO

1063

d »
aa ke is) a 1 (osn f Uh [oo dS ao (oep fret dS +e
Lo '

= (oare f a TAS +... OEY sp. Depa)

Here we have omitted terms, which would be of the order v?
(terms with 7%) and of the order x’. The left side of (21) represents,
apart from the sign, the variation with the time of the total
momentum of the body in the direction of the wi-axis. The integral
in the first term on the right side (order of magnitude x) represents
the total moment of the body with respect to a plane through P
perpendicular to the «k-axis and is eqnal to zero, because we have
assumed that P coincides with the centre of gravity. The integral
in the second term on the right side (order of magnitude v) is equal
to the total momentum of the body in the direction of the a,-axis
and is also equal to zero, because we have assumed that the centre
of gravity was at rest at the moment under consideration; finally
the third term is a small term of the order of magnitude zv and
may be neglected, since we already have omitted terms of the order
of magnitude #? and v°. From this we see that in first approximation
the momentum of the body remains zero in the course of time, and
that consequently also the centre of gravity remains at rest. (Here
it may be of interest to mention, that it is impossible to fix the
centre of gravity of a body in an invariant way; if we try to keep
to the classical definition, there always exists a small uncertainty
in the position of the centre of gravity, the order of magnitude of
which may be easily indicated). If we assume that the equilibrium
of the body in P is stable, equation (21) allows us also to calculate
the small oscillations, which the centre of gravity can perform in the
neighbourhood of P, but we shall not enter further into this point.

We will now proceed to consider the possible motion, characterised
by three degrees of freedom, of the rigid body round its centre of
gravity. This may be done most easily by calculating the rate of varia-
tion with the time of the moments of momentum of a body round
the axes of coordinates. For this purpose it will be of advantage to
introduce the system of coordinates, which was discussed at the
end of the first $, and which appears by the “rotation-transfor-
mation” mentioned there (see p. 1056). This new system of coordi-
nates rotates uniformly round tbe point ? with respect to a system
of coordinates, which is at rest in the stationary teld of gravitation,
with an angular velocity, the components of which coincide with
the components /?;, of the “rotation-vector’, and we shall investigate

69*

1064

the moment of momentum of the body with respect to these coor-
dinates. In the point P this system is geodetical at any moment,
but the quantities g,, will, in contrast to what was the case before,
depend on the time 2, and will be periodical with respect to the

F eee,
time in P with a period 7’=-—, where RF represents the absolute

R:
value of the rotation-vector. In the neighbourhood of P we have
now, instead of (20), the following formulae

Gus = Ep» +4 (Gusmn)P Em Ems - .. se « (22)
where the quantities (4, m.)p are periodical functions of the time.
In order now to determine the variation with the time of the moment
of momentum round the «,-axis we make again use of the impulse
equations (19), and get from these:

oT,’ or 4
a. ee ae Ee + $ (4%, Juv3 — Cy Joa) Te.
Integrating again over a closed surface in the «,—a,—.«#,-space,
which encloses the body, we find with neglect of terms of the order
av*,xv?,ev*, and higher orders:

Aas: —(fe. is = Bee) is) = —4 fie, PRB ee

— #, (Joork)p)ar TO dS. . . ee ree | (3)

The left side represents the variation with the time woth moment
of momentum of the body round the w‚-axis; the right side may
directly be interpreted as the 2,-component of the couple, which a
field of acceleration with potential + tg, exerts on the body, and

is obviously closely connected with the integrals fazer TdS, which

determine the ellipsoid of inertia of the body. In case of a homo-
geneous spherical body they are as is well known equal to zero. By
means of (23) and of the two analogous equations, which refer to
the moment round the «#,-axis and the z,-axis, the motion of the
body round its centre of gravity in the stationary field of gravita-
tion may thus be determined completely. It may be described as a
Poinsot-motion, which is more or less disturbed by the influence of
a field of acceleration with potential + 4 g,, (right side of (23)),
and on which is superposed a uniform rotation, the components of the
angular velocity of which are given by AZ, and R,. The latter rotation
is quite independent of the properties of the body, in contrast to the
influence of the field of acceleration, which is intimately connected
with these properties, and which e.g. disappears, if we have to
do with a homogeneous spherical body.

1065

Until now we have neglected the influence on the field of gravi-
tation due to the body itself, but in the applications to special cases
such a neglect might not be justifiable. When e.g. in the next
§ we will discuss the praecession of the axis of the earth, we have
to-do with a body, the “own” field of gravitation of which is much
stronger, e.g. at its surface, than the field of gravitation arising
from the sun (which appears as is well known in the forces, which
cause the tides). We might imagine that in such a case other forces
might influence the motion round the centre of gravity, which are
much stronger than the forces just considered, or which disturb
these forces essentially. A closer consideration shows, however, that
if the mass of the body is so small, that at large distances it can
only cause small changes in the original stationary field of gravitation,
the own field of gravitation will only cause a small change in the
motion of the body, which may be considered superposed on the
influences of the stationary field of gravitation considered above,
and which will be proportional to the mass of the body.

In order to show this let us first imagine the body placed in a
space, in which no other matter is present, and the line-element of
which approaches to ds? = der, — dx,? — da,’ — da,’ at infinite
distance from the origin. Then it is easily seen, that in first
approximation the own field of gravitation will have no influence
at all on the Pornsot-motion of the body, because the “forces”
determined by the g,,’s, which the different parts of the rigid body
exert on each other in first approximation will fulfill the principle
of action and reaction, just as is the case in Newton's theory of
gravitation. This may easily be proved by applying Einstein's
approximative solution of the field equations, described on page 1058,
on the impulse energy equations (19), but for the sake of brevity
we will not enter into this proof.

Let us again imagine the body placed in a stationary field
of gravitation with its centre of gravity at the point P. Let us
suppose, that the original values of the g,,’s only undergo small
changes A,, on account of the presence of the body, and let the
new values of the g,,’s be denoted by g',,, so that

Puss = Jp» + An . . . . . = . . (24)

Then we obtain, by applying the field-equations (10), for the 4,,’s
a set of 10 partial linear inhomogeneous differential-equations of the
second order, of which we will assume that there exists a regular
solution. (If necessary boundary conditions must be given. If the
stationary field of gravitation is such that the line-element every-

1066

where differs very little from ds? = da,? — dxv,? — dv,? — dz,’ and
becomes equal to this expression at infinity, the 4,,’s might simply
with a high degree of approximation be calculated by means of the
formulae (13) of Einstein). Inside the body and in its neighbourhood
this solution will be the same as in the absence of the stationary
field of gravitation, and just as before there will be no direct
influence of the own field of gravitation on the motion of the body.
Further it is easily seen, that the values of the A,,’s at large
distance from the body to a high degree of approximation will
depend only on the total mass of the body, because at such large
distances the influence of the body can be considered as that of a
singular point (or as a singular line in the space-time-extension)
characterised by the integrals of the quantities 7, over the volume
of the body. But, always neglecting small quantities of the order
vy? and higher orders, the integrals involving the 17%/s may be
neglected, while those of the 7%,’s disappear, because the centre of
gravitation is at rest; so that we only have to do with the integral
of 7, extended over the volume, that is with the total mass M of
the body. Thus we find that the body will exert small forces
proportional to M/ on the bodies, which give rise to the stationary
field of gravitation. The motion of these bodies will therefore undergo
a small perturbation, and as a consequence of this the g,,’s of the
stationary field of gravitation itself will again undergo a modification.
Instead of (24) we must therefore write

Os — Jp + Ais + Sis 2 . ° . ° « (25)

where the A's represent the modifications just mentioned. The
A's are terms, which will be small compared with the 4,,’s, and
which will be proportional to J/; in contrast to the terms 4,, they
will, however, in general have an influence on the motion of a
body, which clearly will be proportional to MM.

In order to discuss this influence we will confine ourselves, for
simplicity, to the case that the 4',,’s are independent of the time.

In this case the quantities aan will in general not be equal to zero
B
in the point P, so that there must be found a point P’ in the
neighbourhood of P, where the centre of gravity of the body may
remain at rest. Further in order to determine the components of
the rotation-vector we will have to introduce in the formulae (5)
instead of the quantities g,, the values of the quantities g,, + A',
and of their derivatives in the point P’. In this way a small modi-
fication proportional to M will be found in the values of the rotation-

1067

vector at the point, where the body is situated, and in consequence
of this a corresponding modification in the perturbing influence,
which the field of gravitation exerts on the motion of the body. It
will also be clear that the influence which according to equation
(23) is exerted on the motion of the body, will undergo a modi-
fication proportional to M.

The results of this § may be briefly stated as follows. If a rigid
body is situated in a stationary field of gravitation with its centre
of gravity at rest, the Pornsor-motion, which the body in the absence
of the field of gravitation would perform in the way well known
from classical mechanics, will be disturbed by a superposed uniform
rotation, which is independent of the properties of the body, and
at the same time by the influence of a conservative field of accel-
eration, an influence, which is closely connected with the properties
of the body (c.q. with the ellipsoid of inertia). The “own” field of
gravitation of the body will — in first approximation — have the
effect that all quantities, which characterise the position and the just
mentioned perturbations in the motion of the body, will undergo
small modifications proportional to the mass M/ of the body.

In practical applications all these influences may of course be of
quite different orders of magnitude, and it may happen that some
of them practically may be neglected, while others are so large,
that the approximation perhaps has to be carried on further than
indicated in this §.

- § 4. Influence of the field of gravitation of the sun on the
rotation of the earth.

The line element of the field of gravitation, to which the sun,
which is supposed to be at rest, gives rise, can be written in the
following: form, which for the first time was given by SCHWARZSCHILD:

a (1 oe “) dR= gee rin idee)

SUN r 1s a
x

where 7’ represents the time, the unit of time being chosen such that

the velocity of light at large distance from the sun approaches to

unity. 7, 7, p are polar coordinates, which determine the position

of a point in space, and «a is a constant, which is connected with

the mass Mz of the sun by the formulae

1068

e= ME dln eg alle fo: SD

where x again denotes the constant of gravitation (see p. 1058).

Let us now introduce a new system of coordinates, which rotates
round the axis of the original system of coordinates with an angular
velocity w. The line element in the new coordinates may then be
calculated by means of the transformation

p=ttotr
This gives

ise = (1 eae a r* sin? 0) ai?

i.
— 2r7 sin? Fw dpdl —

(28)

dr*

— rt (d9* + sin? 9 dp”) |
pps |
% |

The field of gravitation corresponding to this line element is
stationary. We will first try to find a point P, where a mass-point
can remain in equilibrium. In such a point the first derivatives of

a 3 . : .
grr = 1 ——7" sin? Jo" are equal to zero. This gives the following
7
conditions, which must be fulfilled by the coordinates of P:

0 0
TP ares 2r sin? JF w? —=0, Er = — 2r’ sin 3 cos 3 w° =—0.
Or "? 09

From this we see, that a mass-point can remain at rest at every
point P, which lies in the equatorial plane he and for which

the distance A from the sun fulfills the relation
2 AP wt 5+ staten ne en)

This relation gives us therefore the connection between the angular
velocity and the orbital radius of a planet, which moves in a circle
round the sun.

In order to discuss the rotation of such a planet round its
axis we shall begin by calculating the rotation-vector in P. In
order to find, by means of (5), its contravariant components we
want to know the value of the determinant G of the quantities

Gi = — Jui + ates
We find

1069

1 (r? sin? 3 w)?
Ge. SS SSS Gss — r, Guy — r sin? 9 a = == En ==
a a a Seating
1— — 1 — — — 7’ sin? 3} oa?
r 5
a
fue Ss
r
= sn? en a
a rds As
b— —— 7? in? do
r
1 1 — «/
- e I ie
GG == Gy, == 0, = —— . rr. sin? 9 ——____— - ==
1 a 1—*/,—r? sind w*
r
r* sin? }
OTN

Since the derivatives of grr are equal to zero in the point P, the
expressions (5) reduces in that point to

# 0901 Ògoz |

Rm p= 1 d
( ) 2 V9, Oxk

dar, |

This gives

PA

VG 09

r sin? 9 2) w

Vg,,@ Or Vrtsint JP A’
Consequently the rotation-vector in P is perpendicular to the

equatorial plane, and for its absolute value R we find

(9721707 9) = 0;

(R°)p =e

R= VGuRER RVG Azo, te (80)

According to § 1 p. 1057 this result means, that for an observer
placed at the earth the sun rotates with an angular velocity w with
respect to a system of coordinates, in which no Coriolis-forces are
present, i.e. in which the Galileian law of inertia holds. On the
other hand, from the point of view of the same observer, the sun
rotates in the same sense with respect to the fixed stars with an
angular velocity equal to the product of w and the ratio of the
time-unit of an observer on the earth and an observer, which is at
rest at infinite distance from the sun, since, according to the formulae
in the beginning of this §, w represents the angular velocity of
the earth round the sun, if the last mentioned time unit is used *).

1) Originally the writer had simply put the angular velocity of the sun with
respect to the fixed stars equal to », and as a consequence of this obtained
he result that EINSTEIN’s theory of gravitation did not claim a non-Newtonian

1070

From formulae (28) the ratio of the two time units in question is

« ; :
found to be equal to the value of Aa — —— rw’ sin? & at the point

r

€

; ' Xm
where the earth is situated. Since at this point r= A, oe a: the

oUt

° AA
It is therefore seen, that a system of coordinates in which the
law of inertia holds, at the point where the earth is situated will
sa 3 :
rotate with an angular velocity ia. Gee a v? w (where v is the velo-
city of the earth in its circular orbit) with respect to the fixed stars
in the same sense as that, in which the earth rotates round the sun.
From this result, and from the results in the former §, we may
therefore conclude that according to the gravitation theory of EiNsTerN
there will be a contribution to the precession of the axis of the
earth in progressive sense, which is independent of the constitution
of the body of the earth, and which amounts to an angle equal to
one and a half times the ratio of the velocity of the earth to the
velocity of light, i.e. to 0,019 are seconds anually. The existence of
a non-Newtonian precession of this kind has for the first time
been suggested in a paper by Professor Scnouren.') In this paper
attention was drawn to the circumstance, that the field of gravita-
tion of the sun is such, that a small body, which was made to
move geodetically along a circle round the sun with radius A, would
no longer have the same position as before at its return to the same

ratio in question is equal to 1 —

za
point, but tbat it would be turned by a small angle equal to 7

in the same sense as that, in which the body had moved along the
circle, and it was pointed out, that this result suggested a possible
precession of the axis of the earth with respect to the fixed stars.

Now it remains to investigate the influence, which what we have
called the “own” field of gravitation of the earth, may exert on its
motion. According to what has been said in the former $ (p. 1067),
we may expect, that this influence will cause perturbations as well
in the orbit of the earth as in its motion round the centre of gra-

precession of the kind described. I am indebted to Dr. FOKKER for the remark,
that in doing so I had overlooked the difference in the time unit, in which
the two angular velocities in question were expressed. Compare A. D. Fokker,
These Proc. Vol. XXIII. N°. 5, p. 729 (1920).

1, These Proc. Vol. XXI, p. 533 (1918).

1071

vity, and these perturbations will be small quantities proportional
to the mass M4 of the earth. From elassieal mechanies we know
already in first approximation the influence on the orbit: the sun is
not at rest, but deseribes round the centre of gravity O of sun and
earth an orbit similar to that of the earth, in sneh a way that its
distance to O is always equal to the distance of the earth to O

V4

multiphed by a Assuming that the orbit of the earth is again a

.
fr
2)

circle, we shall still have, that the product of the square of the
angular velocity w and the cube of the distance earth-sun will have

a
a constant value, but this value will no longer be equal to q? butto

z (1 +> If we again introduce a system of coor-
2 Mz :
dinates rotating with angular velocity @, with respect to whieh the
centre of gravity of the earth is at rest, the field of gravitation will
again be stationary in these rotating coordinates, (if we look apart
from the motion of the sun and of the earth round their respective
centres of gravity ')) but the distance from the earth to QO corre-
sponding to this angular velocity is no longer the same as when
the mass of the earth was neglected, but smaller in the proportion
2M 4 é : .
(1— ) Thus we have to do with a displacement of the point,
3Mz
where the centre of gravity of the earth may remain at rest, which
is a consequence of the own field of gravitation of the earth, and
which is proportional to the mass of the earth. According to the
considerations on p. 1066 such a displacement was to be expected.
We must further consider the possibility that the absolute value
of the rotation-vector at the centre of the earth is no longer exactly

; 4 Maz
equal to w, but may, e.g. be written in the form @ (1 +h 5 }
Mz

where & is a numerical factor of the same order of magnitude as
unity. Here it must be remembered, that when speaking of the
rotation-vector at the centre of the earth, we mean the quantity,
which according to the scheme indicated in the former $ (p. 1066)

1 From some interesting considerations by EINSTEIN, Berliner Berichte
1916 p. 695, it follows, that the field of gravitation in question may only be
regarded as stationary to a certain degree of approximation, because we must
expect that, analogous to what according to the classical theory of electrons
would take place in a system of moving electrified particles, a system as that
considered here will radiate energy in space in the form of socalled
gravitational waves.

1072

may be calculated by means of formula (5), if we so to say neglect
the field of gravitation, which is directly due to the earth, or, more
exactly, if we replace the g,,’s of the original stationary field of
gravitation by the quantities g,, + 4',,, where the A',,’s represent
the small terms proportional to M4, which are discussed on p. 1066.
We shall now prove, that the just mentioned factor & is equal to

; ze : a
zero, at any rate with neglect of small quantities of the order 4

This may most easily be proved by using the results of classical
mechanics, which — with neglect of small quantities of the relative

at
order of magnitude — — will coincide with the results of Ernsruin’s

4

theory of gravitation. In fact, it is well known, that according to
classical mechanics, the precession of the axis of rotation of the earth
will entirely be due to the inhomogeinity of the Newtonian field of
gravitation due to the sun at the place of the earth. In the mathematical
expression for this precession there will therefore, whether we take the
mass of the earth into account or not, not occur terms independent of
the constitution of the earth and of the kind discussed on p. 1070,
terms, which only appear, when the modifications in the phenomena
of gravitation required by EiNsreiN’s theory are taken into account.
Hence we have the result, mentioned above that, with neglect of

a
small quantities of the order —, that is of the same order as the

square of the velocity of the earth, the mentioned factor & will
be zero.

Consequently we find, that the influence of the earth’s own field
of gravitation on the non-Newtonian contribution to the precession
of the rotation-axis of the earth, considered in the present §, will
LE a
A Mz
thermore clear that, if the mass of the earth is not neglected, also
the contribution to the value of the precession, which is due to
the inhomogeinity of the sun’s field of gravitation at the place of
the earth will be altered by small quantities, which relative to the

at most be a small quantity of the order w > is fur-

M,
main term are of the order non and that this alteration will be
IVEY
the same as that calculated by means of Newtonian mechanics.
In connection with this result it might be of interest to draw
attention to the fact that we have made use of the circumstance,
that for the system under consideration, which consisted of bodies

moving under mutual gravitational influence, the results obtained

1073

on Newton's theory will differ from those obtained on EINsTEIN’s
theory only by small quantities of the same order as the square of
the velocities of the bodies. This circumstance is remarkable on
account of the fact, that in Einstein's theory all gravitational influ-
ence is propagated in space with the velocity of light, as it is
e.g. indicated by the formulae (13), which have the form of retarded
potentials. From this we might at first hand infer, that there might
be discrepancies between the results of Einstrin’s and of Newron’s
theories of the same order of magnitude as the first power of the
velocity of the earth. A closer consideration, into which for the —
sake of brevity we will not enter here, shows however, that for the
system under consideration small terms of this order will just com-
pensate each other, a circumstance which is completely analogous
to similar well-known phenomena with which we meet in the
theory of electrons, whose interaction may be calculated by means
of retarded potentials.

Conclusions of this paragraph.

It has been found that, in’ confirmation of an idea for the first
time put forward by Scuovuten, the gravitation theory of EINSTEIN
leads to the result, that theoretically there will exist a contribution
to the value of the precession of the rotation axis of the earth,
which did not appear on Newton’s theory, and which is independ-
ent of the constitution of the body of the earth, and which amounts .
to a progressive precession of 0,019 arc seconds annually. In the
calculations, the influence of the mass of the earth was neglected ;
if it is taken into account, there may arise a modification in the
value of the precession, which relative to the main term in the
expression for this precession is of the same order of magnitude
as the ratio of the mass of the earth to that of the sun. In the
considerations no regard has been paid to the contribution to the
precession arising from the influence of the moon.

Chemistry. — ‘Catalysis — Part XII. Some induced reactions and
their mechanisn’’. By Nit Ratan Duar. (Communicated by
Prof. Ernst COHEN).

(Communicated at the meeting of January 29, 1921).

When an aqueous solution of mercuric chloride is boiled with
oxalic acid, there is no reduction of the mercuric chloride to the
mercurous state, but as is well known this mixture of mercuric
chloride and oxalic acid decomposes at the ordinary ple in
sunlight according to the equation,

2HgCl, + H,C,0, = 2HgCl + 2HCI + 2C0,.

The same change, however, takes place in the dark as the author
has observed if a few drops of a deci-normal potassium permangan-
ate are added to the mixture. As soon as the color of the per-
manganate is discharged, mercurous chloride begins to separate out.

This phenomenon appears to be of general occurrence. Thus the
reduction of mercuric chloride and bromide by oxalic acid, tartaric
acid, citrie acid, malonic acid, malic acid, glycollic acid, cane sugar,
glycerine, lactic acid, hydroxylamine bydrochloride, hydrazinehydro-
chloride ete., the reduction of gold chloride by several reducing ©
agents, the reduction of silver nitrate, cupric chloride and selenious
acid (to selenium) by various organic acids, cane sugar etc. are
promoted by the addition of such oxidising agents as potassium
permanganate, potassium persulphate, manganese dioxide, potassium
nitrite, hydrogen peroxide, ceric salts etc.

It is a remarkable fact that this effect is particularly noticeable
in those reactions which are sensitive to light.

In all these instances, chemical changes are taking place in a
homogeneous system. I have also investigated several cases of induced
reactions taking place in heterogeneous systems, and I have made
a special study of oxidations effected by oxygen of the air. The
following are some of the experimental results obtained:

Primary change Induced change

Sodium sulphite + oxygen Sodium arsenite + oxygen
Sodium sulphite + oxygen Sodium nitrite + oxygen

Sodium sulphite + oxygen Sodium oxalate + oxygen

Sodium sulphite + oxygen Sodium formate + oxygen
Sodium sulphite + oxygen Ferrous ammonium sulphate + O,
Sulphurous acid + oxygen Ferrous ammonium sulphate + O,
Stannous chloride + oxygen Ferrous ammonium sulphate + Op,
Manganous hydroxide + oxygen Sodium arsenite + oxygen
_Cobaltous hydroxide + oxygen Sodium arsenite + oxygen
Acetaldehyde + oxygen Sodium arsenite + oxygen
Formaldehyde + oxygen Sodium arsenite + oxygen
Benzaldehyde + oxygen Sodium arsenite + oxygen
Ferrous ammonium sulphate + oxygen | Sodium oxalate + oxygen

Ferrous ammonium sulphate + oxygen | Sodium tartarate + oxygen
Ferrous ammonium sulphate + oxygen | Sodium citrate + oxygen

Ferrous hydroxyde + oxygen Sodium arsenite + oxygen
Ammoniacal cuprous hydroxide + oxygen | Sodium arsenite + oxygen.

In all these cases at first the primary change, that is, the oxidation
of the easily oxidisable substance takes place and this primary
change induces or promotes the secondary or the induced change
that is, the oxidation of the difficultly oxidisable substance. In other
words, the potential chemical change between oxygen and sodium
arsenite is activated by the previous oxidation of sodium sulphite.
The oxygen divides itself, as it were, between the two reducing
agents and the proportion in which it divides itself between the:
two reducing agents is the next point of“ interest.

It is well known that a solution of sodium arsenite is not oxidised
by atmospheric oxygen under ordinary conditions, On the other hand
a solution of sodium sulphite is readily oxidised to sodium sulphate.
Now if we mix the two together both the oxidations take place
simultaneously. At the same time a curious phenomenon takes place.
The velocity of the oxidation of sodium sulphite becomes very small
in. presence of sodium arsenite, that is, sodium arsenite which is
undergoing a slow oxidation acts as a powerful negative catalyst in
the oxidation of sodium sulphite. Similarly a solution of an oxalate
which also undergoes slow oxidation in presence of sodium sulphite
which itself is being oxidised, decreases to a marked extent the
oxidation of sodium sulphite by atmospheric oxygen. It appears,
probable, therefore that the phenomenon of negative catalysis is

1076

possible only when the catalyst is liable to be oxidised. These cases
are of great importance in connection with the controversial question
of negative catalysis.

In a previous paper (Jour. Chem. Soc. 1917, 111, 707) I have
shown that manganous salts act as a powerful negative catalyst in
the oxidations of formic and phosphorous acids by chromic acid and
manganous salts can easily pass into the manganic state. Moreover
it has been shown by myself as well as other investigators that
various organic substances notably hydroquinone, brucine ete. act
as negative catalysts in the oxidation of sodium sulphite by oxygen
and all these organic substances are themselves readily oxidised. It
is well known that the oxidation of phosphorus by oxygen of the
air is retarded by the vapours of various organic substances e.g.
ether, alcohol, turpentine ete. and the oxidation of chloroform is
retarded by the presence of a small quantity of alcohol. Now all
these negative catalysts are good reducing agents and are themselves
readily oxidised. Hence in oxidation reactions the phenomenon of
negative catalysis takes place when the catalyst itself is liable to
be readily oxidised.

A study of the slower oxidations that take place at ordinary
temperatures has not only shown that the process of oxidation is
complicated by the presence of water, but the question has been
raised that just so much oxygen takes part in the induced reaction
as combines with the substance undergoing oxidation.

SCHÖNBEIN (Jour. prakt. Chem. 1858, 75, 99; 1864, 93, 25; 105,
226, 1868) first noticed that when certain substances are undergoing
oxidation spontaneously by atmospherie oxygen, one part of the
oxygen combines directly with the substance undergoing oxidation
whilst another part of it is converted into ozone, hydrogen peroxide
or simultaneously oxidises some other substance. SCHÖNBEIN (loc. cit.)
still further demonstrated that just so much oxygen is rendered
active as is consumed by the substance which is being oxidised or
in all slow oxidations the same amount of oxygen is required as is
consumed in the formation of hydrogen peroxide from water or is
consumed in the induced oxidation.

Later investigators like Jorissen (Zeit. phys. Chem. 1897 23, 667)
EneLeR and Wip (Ber. 38, 1109, 1000) have verified the law of
ScHONBEIN in several cases. If we expose a mixture of sodium sulphite
and sodium arsenite to atmospheric oxygen according to SCHONBEIN
(loc. cit.) one atom of oxygen should go to oxidise sodium sulphite,
while the other atom would oxidise a molecule of sodium arsenite
in the same time. The oxidation of sodium arsenite is a very slow

1077

chemical change and in order that ScHÖNBRIN’s law be applicable, it
follows immediately that the oxidation of sodium sulphite, which is
fairly rapid, becomes a slow change and the velocity of this oxida-
tion becomes equal to that of the oxidation of sodium arsenite,
because the same amount of oxygen will be taken up by the reducing
agents in the same time. As a matter of fact from my experiments
I have observed that in presence of sodium arsenite or potassium
oxalate the velocity of the oxidation of sodium sulphite becomes
very small. We assume that a molecule of oxygen splits up in this
reaction into two atoms and each atom oxidises one of the reducing
agents. Now as a solution of sodium sulphite is much more readily
oxidised than a solution of sodium arsenite it becomes difficult to
understand why the other oxygen atom instead of attacking the
readily oxidisable nnacted sodium sulphite attacks the much more
diffieultly oxidisable sodium arsenite. Or if we assume that at first
a peroxide of the type of BopLANDErR’s benzoyl peroxide (Ahrens’
Sam. 8, 470 1899) is formed as a combination of the sodium sulphite
with a molecule of oxygen, we are still encountered with the same
difficulty. In this case we shall have to assume that this peroxide
instead of attacking the readily oxidisable and unattacked sodium
sulphite, will attack the less readily oxidisable sodium arsenite by
preference. It seems to me therefore that the only course left to us
is to find out the explanation in the view of the formation of a
complex of sulphite and arsenite or of sulphite and oxalate and that
this complex is oxidised as a whole. It is well known that complex
oxalates and sulphites do exist. OsrwaLp thinks that in order to
explain positive catalysis by the hypothesis of intermediate compound
formation it is necessary to show that the intermediate reactions
actually take place more readily than the direct reaction under the
given conditions, because if a reaction goes more slowly via the
intermediate product than the direct path, it will take the latter
and the possibility of intermediate products can have no influence
on the process. “Hence”, adds Osrwarp, ‘I see no possibility of
explaining retarding catalytic influences by the intermediate products”
(Nature, 1902, 65 522).

I have observed in a previous paper (Proc. Akad. Wet. Amsterdam
-1920) that in the oxidation of sulphites and sulphurous acid the
sulphite ion is the active agent. If we can decrease the sulphite ion
we can decrease the chemical change, and a solution of sulphurous
acid which is a weak acid containing few sulphite ions is oxidised
less readily than a solution of sodium sulphite of the same concen-
tration. On the addition of an arsenite to a sulphite a complex which

1078

itself is oxidised as a whole is formed. At the same time the velo-
city of the oxidation of the sulphite becomes less due to the decrease
in the concentration of the sulphite ions, arising out of the formation
of a complex of sulphite and arsenite or of sulpbite and oxalate.
Here it seems to me that the only plausible explanation of this
negative catalysis stands on the hypothesis of the formation of an
intermediate complex compound.

On investigating these various cases of induced reactions I was
naturally led to the more general conclusion that one chemical
change should) induce another chemical change of the same type
and 1 tried to verify this conclusion. I found that the reduction of
mercuric chloride by such different reducing agents as formic acid,
sulphurous acid, phosphorous acid etc. induce in all cases the
reduction of the same substance (e.g. mercuric chloride) by sodium
arsenite. I also investigated other changes, as for instance, the de-
composition of unstable substances. If is well known that ammonium
dichromate decomposes readily into nitrogen, water and chromium
oxide. Also the decomposition temperature of potassium persulphate
is lower than that of potassium, chlorate, and I have found that in
presence of decomposing ammonium dichromate or persulphate the
decomposition temperature of potassium chlorate is appreciably
lowered. In this connection it will be of interest to investigate
whether the presence of an easily decomposable explosive will lower
down the decomposition temperature of a difficultly decomposable
explosive, and this investigation will throw light on the stability of
mixed explosives. As far as my experiments go I am inclined to
the view that one chemical change will either promote or induce
another chemical change of the same nature.

A solution of ferrous ammonium sulphate is very slowly oxidised
by atmospheric oxygen. If an oxalate is added to this solution the
rate of oxidation is greatly increased, and the ferrous iron readily
passes into the ferric state in presence of atmospheric oxygen, and
the oxalate is also slowly oxidised. The same sort of behaviour is
noticeable if we add a tartrate or a citrate instead of an oxalate
to a ferrous salt solution. The potential reducing activity of iron is
increased by the addition of an oxalate or a tartrate. Hence soluti-
ons of ammoniuw ferro-oxalate, or ferro-citrate or ferro-tartrate are
better reducing agents than ferrous ammonium sulphate and are
largely used as developers in photography.

Now there is no chemical change between potassium oxalate and
mercuric chloride in the dark at the ordinary temperature, though
the following chemical change takes place in light

1079

K,C,0, + HgCl, = 2HgCl + 2KCI + 2CO,,

If to this mixture of oxalate and mercuric chloride one adds a
ferrous salt, one gets a slight precipitate of ferrous oxalate and at
the same time mercurous chloride is formed. A solution of ferrous salt
cannot reduce mercuric chloride at the ordinary-temperature, but in
presence of an oxalate it becomes a better reducing agent, and reduces
mercuric chloride to the mercurous state, and at the same time the
potential reducing power of an oxalate is activated in bringing forth
the reduction of mercuric chloride to the mercurous state. Evidently
the reducing power of the ferrous salt as also that of the oxalate
is activated by their mutual presence. Tartrates and citrates behave
in a similar manner in presence of ferrous salts.

Wintuer (Zeit. wiss. Phot. 1909, 7, 409) has brought forward
argument to show that the light sensitiveness of a mixture of an
oxalate and mercuric chloride is due to the presence of iron and
the investigator suggests that the purest mixtures of an oxalate and
mercuric chloride so far prepared have contained iron. In absence
of iron the mixture is not sensitive to visible rays. It seems to me
that the real function of iron, if it is present, is not that of a
photoferment or photocatalyst, as suggested by Winrner, but that
of an inductor. The ferrous salt in presence of an oxalate reduces
the mercuric chloride to the mercurous state and at the same time
activates the potential reducing power of the oxalate in inducing
the reduction of mercuric chloride to the mercurous state. This
induced reaction takes place also in the dark. Evidently the Winrarr
hypothesis seems to be doubtful.

Chemical Laboratory Muir Central College
Allahabad India.

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KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS

VOLUME XXIII
N°, 8.

President: Prof. H. A. LORENTZ.
Secretary: Prof. L. BOLK.

(Translated from: “Verslag van de gewone vergaderingen der Wis- en
Natuurkundige Afdeeling,” Vols. XXVIII and XXIX).

CONTENTS,

J. M. BURGERS: “Stationary streaming caused by a body in a fluid with friction”. (Communicated
by Prof P. EHRENFEST), p. 1082. (With one plate).

J. A. SCHOUTEN: “On geodesic precession”. (Communicated by Prof. H. A. LORENTZ), p. 1108.
W. H. JULIUS: “Mutual Influence of Neighbouring Fraunhofer Lines”, p. 1113.

D. VAN VUGT: “On the Homology of the M. marsupialis and the M. pyramidalis in Mammals”.
(Communicated by Prof. L. BOLK), p. 1119.

W.H. KEESOM: “On the deviations of liquid oxygen from the law of CURIE”. (Communicated by
Prof. H. KAMERLINGH ONNES), p. 1127.

L. RUTTEN: “Quaternary and Tertiary Limestones of North-New Guinea between the Tami-,
and the Biri-river basins”, p. 1137.

. RUTTEN: “On the Age of the Tertiary Oil-bearing Deposits of the Peninsula of Klias and
Pulu Labuan (N. W. Borneo)”, p. 1142.

A. H. SCHREINEMAKERS: “In-, mono- and divariant equilibria”. XXI, p. 1151.

. LANDSTEINER: “On the serological specificity of haemoglobin in different species of animals”.
(Communicated by Prof. C. H. H. SPRONCK), p. 1161.

K. LANDSTEINER: “On Heterogenetic Antigen”. (Communicated by Prof. C. H. H. SPRONCK), p. 1166.

W. STORM VAN LEEUWEN and F. VERZáR: “Concerning the Sensitivity to Poisons in Animals
suffering from Avitaminosis”. (Communicated by Prof. R. MAGNUS), p. 1170.

E. MATHIAS, C. A. CROMMELIN and H. KAMERLINGH ONNES: “The rectilinear diameter of hydrogen”.
(Communicated by Prof. H. KAMERLINGH ONNES), p. 1175.

H. KAMERLINGH ONNES and C. A. CROMMELIN: “Methods and apparatus used in the cryogenic
laboratory. XVIII. Improved form of a hydrogen vapour cryostat for temperatures between —
217° C. and — 253° C.”. (Communicated by Prof. H. KAMERLINGH ONNES), p. 1185

H. ZWAARDEMAKER: “On the Influence of the Season on Laboratory Animals”, p. 1192.

PAUL S. EPSTEIN: “On the principles of the theory of quanta’. (Communicated by Prof. P.
EHRENFEST), p. 1193.

. J. VAN VEEN: “Properties of Congruences of Rays’. (Communicated by Prof. J. CARDINAAL), p. 1206.

H
G. C. HERINGA: “Ombredanne's Theory of the “lames vasculaires” and the anatomy of the canalis
cruralis”. (Communicated by Prof. J. BOEKE), p. 1209.

J. W. N. LE HEUX: “Explanation of some Interference Curves of Uniaxial and Biaxial Crystals by
Superposition of elliptic Pencils”. (Communicated by Prof. HK. DE VRIES), p. 1223. (With one plate).

J. C. KLUYVER: “On analytic functions defined by certain LAMBERT series”, p. 1226.

H. A. BROUWER: “On the Composition and the Xenoliths of the Lavadome of the Galunggung”.
(West-Java). (Communicated by Prof. G. A. F. MOLENGRAAFF), p. 1234. (With one plate).

H. A. BROUWER: “On the Alkalirocks of the Serra do Gericino to the northwest of Rio de Janeiro
and the Resemblance between the Eruptive Rocks of Brazil and those of South-Africa”. (Com-
municated by Prof. G. A. F. MOLENGRAAFF), p. 1241.

S. VAN CREVELD and R. BRINKMAN: “A direct proof of the impermeability of the bloodcorpuscles
of man and of the rabbit to glucose”. (Communicated by Prof. H. J. HAMBURGER), p. 1256.

R. BRINKMAN and Miss E. VAN DAM: “The Significance of the concentration of calciumions for the
movements of the stomach caused by stimulation of the N. Vagus”. (Communicated by Prof.
H. J. HAMBURGER), p. 1262.

EuG. DUBOIS: “On the Significance of the Large Cranial Capacity of Homo Neandertalensis”, p. 1271.

W. E. DE MOL: “On the influence of circumstances of culture on the habitus and partial sterility
of the pollengrains of Hyacinthus orientalis”. (Communicated by Prof. A. H. BLAAUW), p. 1289.

M. PINKHOF: “A new method of recording the modifications in aperture of stomata”. (First Com-
munication). (Communicated by Prof. F. A. F. C. WENT), p. 1303.

EuG. DUBOIS: “On the Motion of Ground Water in Frost and Thawing Weather”, p. 1321.
JAN DE VRIES: “Two Representations of the Field of Circles on Point-Space”, p. 1323.

70

Am OT

Proceedings Royal Acad. Amsterdam. Vol. XXIII.

Physics. — “Stationary streaming caused by a body in a fluid
with friction”. By Prof. J. M. Burgers. (Communicated by
Prof. P. EHRENFEST).

(Communicated at the meetings of 18 Dec. 1920 and 29 Jan. 1921).

§ 1. In this paper a summary will be given of some types found
in the literature of the stationary streaming in a fluid caused by
the uniform rectilinear motion of a simple symmetrical body. The
fluid will be supposed to be incompressible, illimited in all directi-
ons and adhering to the sides of the body. Neither the possibility
of lability of the stationary (or laminary) currents will be attended
to, nor peculiarities or differences occurring when the body deviates
more or less from the spherical form or when we pass from the
three-dimensional problem to the two-dimensional one.

The body however is assumed to have in both cases its axis of
symmetry parallel with the direction of the current and to possess
no sharp edges.

The character of the streaming is wholly governed by the nwmber
of REYNOLDs:

yv

U is the velocity of the body with respect to the undisturbed
fluid; d is a dimension of the body f. i. the greatest dimension
perpendicular to the direction of the motion, u is the cinematic
coëfficient of friction of the fluid (== u/e)*). At one limit, friction
infinite or motion infinitely slow, A= 0, at the other limit, fluid
without friction, R = oo.

Remark. For shoriness sake the expression: absolute current is
used here to indicate the current seen by an observer for whom
the fluid at an infinite distance is at rest while the body is moving
with the velocity U. The streamlines are displaced with the body;

') This number of comparison was introduced by O. Reynorps in the investi-
gation of the flow through tubes, Phil. Trans. Lond. 174, p. 935, 1883. It is of
great importance for all model-experiments in hydrodynamics and in aerodynamics.
See f.i. L. Barrstow, Applied Aerodynamics, London 1920, Ch. VIII (p. 372) and
other new textbooks.

1083

in this case they are not identical with the paths of the particles
of the fluid.

By relative flow will be meant the image of the flow as seen by
an observer that regards the body as being at rest. This is therefore
the real stationary state’). As will be known both states may be
derived from each other by increasing or decreasing by U all
velocities parallel to the axis of motion.

In the diagrams of the distribution of the vortices the density of
the vorticity is indicated by vertical hatching. In some sketches the
“opposite” vorticity (see $ 3) is indicated by broken horizontal hatching.

§ 2. Introduction.

The state of flow is governed by the propagation or the dispersion
of the vorticity. This is caused by two phenomena: diffusion and
convection. The equation for the vortex motion which may be
deduced from the equations of Eurer:

Ov 1
QT) SS A at e . . .
di ° ve +r4Ov—(v.y)v . : (2)

by differentiation is:

raw MEIN COMPU) von ene CE)

The first term at the right hand, with the coefficiént of friction »,
gives the diffusion of the vorticity. As will be known the velocity of
diffusion has no definite value: it depends on the concentration gradient
of the diffusing matter or state. There is no diffusion front or a
propagation of waves.

Besides this term we see at the right hand side the convection
terms: — (Vv. 7) w + (W. 7) v, which express:

1° that the vorticity is carried along by the current;

2° that the vortex vectors turn with the fluid particles and are
deformated together with these.

In one case the last term fails: viz. in the plane or two dimen-
sional motion’). In this case the operation (W. 7) (the differentiation
in the direction of w) is zero. The first term is of more importance

1) Some investigators as f.i. |. AHLBORN speak of lines of force and of current
to indicate what has been called here absolute and relative flow.

’) In the original paper the three-dimensional motion was mentioned here too;
this is not correct, as has been remarked to me by Prof. Pranoprt.

70*

1084

and defines the true convection. Therefore we shall take this equation
for the vortex motion:
Ow
Br AM AV.) W iy Sela igh aad
It is evident that for a small velocity U and a high value of »
(2 therefore small) the vorticity will come everywhere by the
diffusion. When, on the contrary, U is great and » small (R there-
fore great) practically no eddies will diffuse against the current;
all is drawn back.

§ 3. Mlementary description of the flow for R not too small
(fig. 1—4).

I. When in a fluid originally at rest a body is suddenly set into
motion, we may consider a surface 6, that surrounds the body at
a very short distance e. Outside this surface we have, during the
first moments, only to do with pressure forces and as these are
continuous an irrotational motion (without vortices) will arise. Let
us consider the flow at a moment Tr after the beginning of the
motion of the body, then ¢« will be smaller as rt is smaller. The
initial flow (because of the condition of continuity) must therefore be
determined by the well-known boundary condition for the potential p :

aot ee Ves Oy i ae ae ee

where V, is the normal component of the velocity of the body at
the point in question of the surface. Thus, the original flow is the
irrotational motion of classic hydrodynamics (Pranptt1); this has been
proved experimentally *).

Between 6, and the body a thin vortex layer is formed, the
intensity of which is defined by:

op
fom = ELAN HERE er lar «aioe pests | (0)

1 L. PrANDTL, Verhandl. des III. internat. Mathematiker-Kongresses, Heidelberg
1904, p. 484.

H. Rusacu, Forschungsarbeiten herausgeg. v. Verein deutscher Ingenieure, 185.
1916.

Also in the limiting case of very great friction (R0) we find by the calcu-
lation method of Srokes that the original motion is the ordinary potential flow.
See A. B. Basset, Hydrodynamics Il (Cambridge 1888), p. 289 (Art. 505).

See in connexion with this also the note of 8 7.

1085

(s indicates here a tangential direction at a point of the surface) ').

Fig. 1 illustrates the “relative” flow for the two-dimensional case,
the body being a circular cylinder.

Il. The above mentioned vortex layer flows out by the diffusion,
becomes thicker; the vorticity comes into the current and is carried
along to the back of the body. See fig. 2 (the dotted circle in
the vortex region gives the direction of rotation). When the vorticity
behind the body has got a definite intensity, a part of the fluid
there begins to rotate as a whole or to flow in closed orbits
i.o.w. behind the body at both sides of the axis of symmetry
there are formed circular currents (see fig. 3) *). Behind the body
we therefore have a current towards the left; in front of it the
current remains as it was to the right. Therefore we must have at
both sides a point S, where the current leaves the surface (for solids
of revolution this will take place along a parallel circle).

At the back of the body a vortex layer is now formed the rotation
of which is opposite to that at the front (in the tigure indicated by
dotted, horizontal hatching).

III. After some time we might expect a stationary state to be
created, in the way as has been sketched in fig. 4, where the
diffusion and the convection neutralize each other. In reality
this is not the case. After passing a state as is represented by fig. 3.
the flow begins to fluctuate; it becomes more or less “turbulent”.
In stead of the regular vortex distribution a more or less irregular
one is formed; the vortices “coagulate” so to say, so that regions
with strong vortex motions (vortex cores) are formed, dispersed in
a mass with weaker vortex motion.

A more detailed discussion of these phenomena will be omitted
here *).

1) The limit of e for t=O is determined by the sphere of action of the mole-
cular forces at the surface of the body. As long as the fluid is treated as a conti-
nuum this may be regarded as infinitely small.

3) These considerations have of course the same purpose as those of PRANDTL
(Le); the above form has been chosen to illustrate the propagation of the vortex motion.

That the accumulation of vortices gives rise to circular currents in the fluid,
will probably only be true for high values of # (when the vortex motion is not too
diluted). Only in the limiting case of very great R it can be proved by means of
the formulae (see below, § 7 and 8).

On the photo's of RupacH le. we can see that the circular currents are
formed on a small scale behind the cylinder at both sides of the point where the
flow unites. Theoretically this has been investigated by BLAsius (see l.c. § 8).

3) This fluctuating motion may also be described in another way. When Ris high,
so that the velocity of diffusion of the vortex motion is small, then the vortex sheet

1086

ern RR ret

Fig.‘ 1.

Fin ———

formed in front of the body and leaving it at S to enter the fluid, is very thin,
so that it represents approximately a surface of discontinuity for the distribution
of the velocity. This sheet can be seen on photo’s of the flow in the immediate
neighbourhood of the body. Sometimes the stream lines are bent so sharply that
we may speak of a discontinuity.

Thus a vortex layer leaves the body at both sides; as will be known these
layers (at least for the two-dimensional flow) have the property to cur! themselves
in the way of spirals to a row of vortex threads. The vortex threads formed from
both layers are placed more or less regularly (von Karman, Phys. Zeitschrift 18
p. 49, 1912 and others).

This may be demonstrated by coloured fluid flowing from holes at the front
surface of the body. This fluid comes into the boundary or vortex layer, partici-
pates its motion and in this way makes its form manifest. Especially fine cinema-

1087
Laminary motion for different values of R.

§ 4. The flow round a sphere according to Stokus. The method
indicated by Stokes for the solution of the hydrodynamical equations
neglects the convection terms. It gives therefore the flow at the
end A0 of the series; the velocity U must be very small, so
that the influence of the friction dominates. Equation (4) is reduced
to the simple equation for the diffusion:

Ow

The most known solution of this equation is that for the stationary
motion of a sphere’). The vortex motion diffuses from the surface
symmetrically forward and backward; its intensity is given by:

sin Ó

3
Jl ZES Ua aT . . . . . . . : (8)
2 r

(a is the radius of the sphere; r and @ are polar coordinates with
the centre of the sphere as pole and the direction of motion as axis).
This distribution is represented in fig. 5.

The stream function for the absolute flow is:

3 2
Mani al» =) int 6 EI A es (8)

By means of this the figures 6 and 7 for absolute and relative
flow have been drawn. These figures too are symmetrical at both
sides.

§ 5. The motion according to OsreN.

OskEN has remarked that the considerations leading to the neglection
of the convection terms hold in the immediate neighbourhood of
the sphere; at great distances from it the velocity of diffusion dimi-
nishes to zero, while the convection current always keeps the same
velocity U: hence the convection will predominate here.

tographic photo’s are found in: E. F. Retr, Technical Report Advisory Committee
for Aeronautics, London 1912—13, p. 133 (Rep. N°. 76); and in L. BAIRsTOW,
Applied Aerodynamics, London 1920, p. 345, fig. 167 (photo by J. L. NAYLER, see
Techn. Rep. etc. Rep. N°. 382 of May 1917).

The vortex layer behaves as a so-called „filament-line”, (see L. Bairstow,
lic. p. 348).

1) See fi. H. LamB, Hydrodynamics, Cambridge 1916, p. 587. LAMB also gives
a fine diagram of the absolute flow.

1088

Fig. 5—7. Flow caused by a sphere for R—>0 according to STOKEs.

Fig. 6. Absolute flow.

ed

Fig. 7. Relative flow.

he)

Pen

J. M. BURGERS: “Stationary streaming caused by a body in a fluid with friction.”

Fig. 25.
fs Fig. 26.
= na En ee Eens is
TELL WHEE ES
R = szoo
GEER ITE CECFFEELEREEELEREEEER pa og

R »Booso

Fig: 25-28, Flow caused by a cylinder for high values of R, calculated according
to the method of § 7 and § 10.

Proceedings Royal Acad. Amsterdam. Vol. XXIII.

1089

To take this into consideration Osren has kept the constant trans-
lational current U in the equation; equation (4) has not been sim-
plified to (7) but to:

—= — UW) , a
vOw me, BEE (10)

In the nearest neighbourhood of the body this does not give an
amelioration, on the contrary rather a little change for the worse, but
the inaccuracy remains of the same order of magnitude as in Stokes’

Ua
solution viz. of the order —, or of the order of R.
Vv

For the stationary motion of a sphere OsreN finds in the imme-
diate neighbourhood of the sphere the same solution as Stokes and
therefore the same value of the resistance. This was also found by
Lams in another way. At a great distance however all has been
“drawn backward”. The distribution of the vorticity is defined by:

3 1 + U7r/2v U (r—a)

w= — Va?
2 r? 2v

„sin O, exp

RE 0

2aU

v

and represented in fig. 8 (the figures have been drawn for R=

= 0,4). The asymmetry between front and back side is evident.

Because of the exponential factor at the end of (41) w is very small
outside a parabolical space f.i. bounded by:

| 20v

ie

(where at the outside the exponential function is smaller than

0,000045). Here the motion becomes therefore nearly irrotational.
The stream function is given by:

NE

3 ge Ua
bil Et ear 1 — exp Eer * sin? 6 (12)
2 : 2v 4r

See fig. 9 and for the relative flow fig. 10. Fig. 11 gives on
a smaller scale (i.e. for higher values of r) the distribution of the
vorticity and the absolute flow; it shows that outside the para-
bolically bounded space the motion approaches a radial current

1) C. W. Osren, Arkiv f. Mat. Astron. och Fysik. Bd. 6, N°. 29 (1910).

H. Lamp, Phil. Mag. (6) 21, p. 112, 1911 and Hydrodynamics, p. 594 seqq.
LAMB gives a discussion of the character of the motion (from which these
remarks have been taken) and also gives a solution for the corresponding two-
dimensional problem. (In this last case Stokes’ method does not give a solution),

1090

Fig. 8—10. Flow caused by a sphere for R= 0,4 according to OSEEN and LAMB.

Fig. 8. Distribution of the vorticity.

ene

Fig. 9. Absolute flow.

Ee
STe = agli {a nn

a.

Fig. 10. Relative flow.

1091

(with v = 3va/2r*), while inside this space the fluid is carried along
with the sphere’).

Fig. 11. Flow caused by a sphere for R = 0,4
according to OsEEN and LAMB.
Distribution of the vorticity and absolute flow.
Radius of the sphere in this figure = ca 0,2 mm.

§ 6. Oszun’s limiting current for Ro.
In different papers OsreNn has investigated the properties of the
general solution of equation (10) and of the corresponding equations
for the velocity v and in two publications of 1914 and 1915 he
determined the limit to which the solution approaches when the
friction becomes zero and # therefore infinite’).

In this case the diffusion vanishes and as the only cause of the

1) The current given by (12) is no exact solution of the equations used (see
LAMB, le. p. 598). A more exact approximation has been given by R. W.
Burcess, American Journal of Mathematics 88, p. 81, 1916. — Lams’s method
has been applied to ellipsoids by B. Pat, Bull. Cale. Math. Soc. X, p. 81, 1919.

2) CG. W. Oseen, Zur Theorie des Flüssigkeitswiderstandes, Nov. Acta R. Soc.
Scient. Upsaliensis Ser. IV, Vol. 4, 1914.

1092

motion of the vortex elements is the translational current (according to
equation (10)) there will be formed in front of the body an infinitely
thin vortex layer (of finite total intensity) which extends itself
backward in a cylindrical sheet, parallel to the direction of the
current, which sheet surrounds the body along the parallel circle
of largest diameter. This is sketched in fig. 12, where the vortex
sheet has been indicated by a thick line. Outside the cylinder the
motion is grrotational, inside it generally not. Along the cylindrical
surface the w-component of the velocity changes abruptly.

For the stationary motion the following solution is found *) (the
formulae refer to the absolute flow; the system of coordinates w, y, z
moves with the body, the a-axis is in the direction of motion):

Let p be a potential function, then we have outside the considered
cylindrical space:

Vie © oa” oc awe fem)
and inside it
USM Oe Va er en ee) ae a)

where v*(y,z) indicates the value of yyw at the point at the back
of the body witb the y- and z-coordinates: y,z. Here (a, y, 2)
is defined by the following conditions (that follow from the equation
of continuity):
gp EN etek LA
further at the front of the body:
0
(52) ES U aster ko ieee Clay
On 0 :
and at the back:
dv, dv: ò ò
T= ty lle ick ane A
Oy dz :
At the back of the body we have
Vl. «(parallel to the c-axis) … erna fae)

Here the fluid sticks to the body. At the front on the contrary only

C. W. OSEEN, Beiträge zur Hydrodynamik I, Ann. de Phys. 46, p. 231, 1915.
In the following papers (p. 623 and 1130) OsEeEN treats the properties of the
solution of the non-simplified equations. These are written in the form:

Ov 1
Oak FT ptger)-uAv=A
Ot 2
Then the vector A=e(v>Xw) is treated as “external force". In the paper of

p. 231 A has not been considered.
1) C. W. OseenN, Ann. d. Phys., lc. p. 249.

1093

tae normal component of the velocity of the fluid has to correspond
to the normal component of the velocity of the body; the tangential
velocity is not bound, so that generally the fluid will slip along the
body. Here a boundary layer exists, and vorticity is formed *).

I have tried to represent this solution for the case of the two-
dimensional flow along a cylinder with circular section. The
radius of the cylinder and the velocity U have both been taken
= 1. The vortex domain lies therefore between y — + 1 and
y=—1. Equation (14c) gives then: dv,*/dy = 0; and as on the
v-axis vy* = (because of the symmetry) we have everywhere
v,* = 0. On the line y=--1 v changes abruptly by the amount:

1—v*; between y= -+1 and y= —1 the vorticity is:
dv* (16
1) === 6 . . . . . . . .
dy )
In order to find an approximate value for p‚ | have put:
N A, cosn@
a Ag lta ee Pe. eo GET)
1 ny

(6 =O is the point most in front of the circle, where «= +1;
at the opposite point 6 =a). Then the boundary conditions (146)

and (14c) become:
N

SOS: ao Acos mn Of CORONES)
0

N
ae E (n+1) Aycos(n+1)O=0 . (182)
0

By means of the method of least squares a solution has been
sought that for a given value of N satisfies as well as possible
(18a) and (186). For N==8 is found in this way:

A, = + 0,374
A, = + 0,375
A, == + 0,248
A, = + 0,086

With the aid of these numbers fig. 13 has been drawn for the
absolute flow and fig. 14 for the relative flow.

) Lc. p. 252; further also p. 623 and 1144.

OsSEEN considers moreover the following simple cases (lc. p. 249/250):

a. Body illimited in ‘backward direction (the thickness has no maximum at a
finite distance). Everywhere outside the body we have irrotational motion, defined by
(13a), (14a) and (145).

b. Body illimited in front direction. Then a solution of (144) and (14c) is given
by: p=0 (we have no front, so that (14b) vanishes). Outside the cylinder
v = 0; inside vy = U.

1094

Fig. 12—14. Flow caused by a cylinder for R = ox,
calculated with the formulae of OSEEN.

Fig. 12. Vortex layers.

Fig. 13. Absolute flow.

ones ae chs aa

TE Sr ews Wrs ESET

Fig. 14. Relative flow.

At a great distance from the cylinder we have a radial current,
which displaces totally: 227 A,—2,35; this amount comes back in
the wake stream between y=-+1 and y= — 1. In the wake at
a great distance from the cylinder 7g may be neglected, so that
v=1—-v*; and

1

2 ay (1—v*) = 2,36.
0

1095

The value of v* proves to be <0, so that tbe velocity in the
wake is >1. In the image of the relative flow a forward current
is therefore formed. The stream line for yO follows the z-axis
for x >1, the circle until about 6 = + 90°, then it leaves this and
approaches asymptotically to the lines y = + 1,18.

As further dv*/dy < 0 for y > 0 the direction of rotation of the
vorticity is here opposite to that in the boundary layer y= +1 U).

§ 7. Application of a method of calculation of Bousstnesg.

The limiting flow of OserN we discussed above is very different
from the flow which usually takes place in a fluid with infinite-
simal friction. The most typical particularity in the case of OsrEN
is the discontinuity of v at a cylindrical surface that surrounds the
body. The form of the surface of discontinuity is determined by the
way in which the convection of the vortex motion has been calculated:
the vorticity moves in the direction of the x-axis with the translational
current (/ only, so that it extends from the thickest part of the
body backward in an infinitesimally thin layer (fig. 12). When however
we attend to the elementary description of the initial development
motion of the (§ 3)*) we should expect fora great velocity and a small v
that the thin vortex layer at the surface of the body is slept back-
ward by the current along that surface viz. towards the point where

1) The degree of inaccuracy of this solution may be estimated by calculating the
value of the stream function ),,, for y=1 and 6 = 90°; it has the value 0,933
instead of 1,000. Further the values of v, are for 6 = 90°, 120°, 150° and 180°
resp.: 0,126, 0,074, 0,034 and O, instead of all being O. In order to avoid diffi-
culties the fears have been a little shaped.

An approximation to NV = 10, gave for A, till Ajo resp.:

+ 0,366; + 0,419; + 0,240; + 0,024; — 0,059; — 0,019;
+ 0,028; + 0,020; — 0,011; — 0,021; — 0,010.
From this follows:
Wats for ral; @ =90° : 0,977
v, for 6=90° (therefore y= 1) : 0,018.
In this case we have:
vA, == 1514905 22 A, = 2,30.

The general character of the motion therefore does not change by this closer
approximation.

2) Also in the limiting case of Osren the original flow, when it starts from

the state of rest, is the ordinary irrotational motion. According to Ann. d. Phys.,
Le. p. 246/247 the flow outside the space described by the body is everywhere

irrotational; the potential ¢ is determined by: Ao =O U cos (nx) at

one
>On

1096

the current originally closes, and that it moves further in the
direction of the axis of the current behind the body. Approximately
it will be confined to a small paraboloid round that axis and the
whole vortex region may be roughly represented by fig. 15.

In the limiting case R=o the vortex layer at the body will
be infinitely thin and the paraboloid will contract to the axis (see
fig. 16). The vortices from opposite parts of the surface of the body
having opposite signs, they will soon vanish in the axis. [nthe
limiting case R= we have therefore everywhere outside the body
irrotational motion, while at the surface of the body an infinitesimal
vortex layer is found’). The potential p of the current is determined
by the ordinary condition:

ae siet tn Sie AREA
On

for the absolute flow along the whole surface of the body. When
we wish to obtain a corresponding representation of the vorticity
distribution and yet to use as in Osnrn’s solution a linear equation,
equation (4) must be replaced by:

0

where v, is written for a known current, which at a great distance
from the body approaches the parallel current U, following however
the surface of the body in its immediate neighbourhood.

For v, we may e.g. take the ordinary irrotational current. In this
case (20) changes into an equation applied by Boussinesq in the
calculation of the transport of heat by a moving fluid’). It is

d00p dal?
the -front; REN ma (nx) at the back of the body. Behind the body we

therefore have:

i zoja n= cos (nat).

ae noon

As soon as the body is x into motion we shall have over the whole surface
0,
= = U cos (nx), so that ¢ is the ordinary potential; the space outside the region
n
described by the body is then the whole space outside the body, hence every-
where v = Vo.

1) Perhaps the a-axis behind the body must be regarded as a singular line in
the flow.

2) J. Boussinesq, Journa de Liouville (6) 1, p. 285, 1905. See also: A. RUSSELL,
Phil. Mag. (6) 20, p. 591, 1910, and L. V. Kine, Phil. Trans. London A 214,
p. 373, 1914.

1097

evident that neither this choice of v nor the method of OsreN gives
the true convection of the vorticity along the surface, as the con-
vection velocity must sink to zero there, which is not the case with
the value of v, taken above.

Boussinesq has shown that for the stationary two dimensional
flow equation (20) takes a simple form, when we take as coordinates
the stream function and the potential of the flow v, (here the relative
flow image is used). When as in the notation of Boussinesq Ua is
written for the stream-function, Up for the potential, then the equation

0—p (Ee de _ at (= aig =) (20%)
Ont Ov dx dydy) =
becomes:
8 dw 0?w Ow
= oa ae) Bag
or:
Ow pv (O?w dw
Ta (53 : =) GND oO

A difficulty in the solution of this equation is that the boundary
conditions are expressed in v and not in w. The limiting case
however treated by Boussinesq himself in the problem of heat
transport ') is simple: »/U is very small (this involves a very great
R), so that the vortex motion is confined to a very thin boundary
layer and the derivative of a quantity with respect to a (viz. in a
direction perpendicular to the boundary layer) will be much greater
than the derivative with respect to 8 (in the direction of the boun-
dary layer).

Then we may assume:

re (22)

and also:
ge 28
v= — De . = 5 5 5 A ° . ° ( )

where vs is the (true) velocity in the boundary layer parallel to
the surface.

By means of these formulae we can calculate the distribution of
the vorticity and the current in the boundary layer, when we suppose
the velocity outside the boundary layer to be known. In analogy

1) J. Boussinesg, le. p. 295/296. — Boussinesg also treats the problem for a
solid of rotation (p. 305). In thecalculation of the heat transport Kine uses the
complete equation (21) (}.c.)

71
Proceedings Royal Acad. Amsterdam. Vol. XXIII.

1098

Fig. 15—18. Flow produced by a cylinder for a high value of R,
calculated according to the method of § 7 and § 10.

car

; ERLE

Fig. 15. Distribution of the vorticity.

Fig. 16. Limit of fig. 15 for R =o.

Fig. 17. Absolute flow.

Fig. 18. Relative flow.

1099

with the above we shall assume an ordinary irrotational current
to exist outside the boundary layer.

From the calculation we see that an reversion of the direction of
the flow may take place in the boundary layer, when the outside
motion is retarded. In this case a counter current will be formed
behind the body and the current coming from the front leaves
the surface at a certain point. The place of this point depends on
the form of the body but not on R. The thickness of the layer, in
which these currents take place proves to be proportional toV rd/ U,
where d is a dimension of the body; the relative thickness is

1 a 1
therefore of the order: 7 Der In these two points
there is a qualitative agreement with the exact method of PRANDTL;
there is however no quantitative agreement.

For the details of the calculation see $10. The distribution of the
vorticity has been represented schematically in the above mentioned
fig. 15; fig. 17 gives a sketch of the image of the absolute flow;

fig. 18 of that of the relative flow.

$ 8. The method of Pranptu.

The method of PranNprL and his collaborators is the only method
of calculation in which equation (4) is not reduced artificially to a
linear equation, but where directly a solution of the quadratic
equation is sought for *). A detailed discussion of this method cannot
be given here; a few remarks only may find place:

a. The method has been worked out for the two-dimensional
and for the axial-symmetrical three-dimensional flow, for high values
of PR, so that the boundary layer is thin.

6. Because of this last circumstance PRrANDTL simplifies Eurer’s
equation to:

dv, Ov, Ov, 1 dp 07»,
s— + 2», — => ——-—-4 pv :

oy o dx Oy?
where the w-axis has been taken parallel to the surface of the
body, and the y-axis perpendicular to it. The pressure p is given
by the state outside the boundary layer and can be treated in this

(24)

1) L. Pranptt, Ueber Flüssigkeitsbewegung bei sehr kleiner Reibung, Verhandl.
d. III. internat. Mathematiker-Kongresses, Heidelberg 1904, p. 484.
H. Brastus, Zeitschr. f. Math. u. Phys. 56, p. 1, 1908 (dissert. Göttingen 1907)
en ibidem 58, p. 225, 1910.
E. Botrze, Dissert. Göttingen 1908.
K. Hiemenz, Dinglers Polytechn. Journal 826, p. 321, 1911.
FG he

1100

layer as independent of y, v, and wv, are connected by the equa-
tion of continuity.

0
For the vorticity w = — = we therefore have:
Y
Ow Ow Ow =) 25
DE =S Oy? En v, 55 + Vv, Oy - 5 e 4 = ( )

c. From the solutions of the equations (which for the greater
part must be obtained by numerical approximation) we find that in
the case of a retarded flow outside the boundary layer, there is a
point in this layer where the direction of the flow is reversed, so
that counter currents are formed and the currént coming from the
frontside leaves the surface. The place of this point is independent
from L.

The dimensions of the boundary Jayer in the direction of y are

1
given by the form of the body and are proportional to Dn times

the dimensions of the body.

Thus we find by both these methods (of $ 7 and $ 8) that for
high values of A a vortex sheet leaves the surface of the body at
both sides (eventually round the body) and emerges into the fluid
as has been indicated by Osten. For increasing values of R howe-
ver this sheet evidently does not only become thinner so that it
approaches to a surface of discontinuity, but it fits more closely
round the body so that the irrotational motion outside gradually
extends over a greater space and finally becomes the ordinary
irrotational flow *).

§ 9. Remark on the motion for mean values of R.

The calculation according to the methods of $ 6—8 teaches that
for high values of A there is formed behind the body a forward
current opposite to the original direction of the current, which is
in agreement with the experimental results *). For R—0O this does

1) The considered bodies must not have sharp edges (as was demanded in § 1).
Therefore the above remark does not say anything against HELMHOLTz’s disconti-
nuous flow along a plate with sharp edges.

2) In the image of the absolute flow the velocity immediately behind the body
is greater than U (the fluid “overtakes” the body), the stream-lines must therefore
be packed more closely together than in the original parallel flow. As to the
distribution of the vorticity: at the back of the body we havea layer of ‘‘opposite”
vortex motion (see above § 3, II).

Fig. 19—21. Sketch of the flow produced by a cylinder for a

mean value of R.
|

|

Er
mil oz WP

aS

Fig. 19. Distribution a the vorticity.

Fig. 20. Absolute flow.

Fig. 21. Relative flow.

1102

Fig. 22—24. Sketch of the flow produced by a cylinder for a
mean value of R (but higher than for fig. 19—21).

Fig. 22. Distribution of the vorticity.

ee

Fig. 23. Absolute flow.

Fig. 24. Relative flow.

1103

not occur’), so that the question arises: when does this reversion
of the flow begin, is it connected with a definite value of R?
Further, how far does the region of the counter currents extend;
is it at first a thin layer which becomes thicker with increasing R
and which afterwards diminishes again? That the length is finite,
is proved by the consideration that the differences in velocity are
finally quite dissolved by the friction, so that in the axis the current
must reassume the original direction.

A second question is the following: in the image of the absolute
flow the stream lines are not closed according to Stokes and OsEEN -
Lams, but they are for the ordinary irrotational motion (the limiting
current of §§ 7 and 8). Where is the passage from one case to
the other?

The figures 19— 24 are meant as a possible interpolation between
the considered limiting cases (they have been sketched for the two-
dimensional case). Of course they can by no means claim the name
of approximation ’). |

Such flows are observed at the beginning of the motion. After-
wards they change into a more or less irregular motion. It is
not known for which value of A the lability of the laminar one
begins *).

$ 10. Application of the method of $ 7 to the calculation of
the diffusion and the convection of the vorticity in the trrotational motion.
I. Notation. U=velocity of the indisturbed parallel current; v, V=
velocity of the irrotational motion, v U==velocity of the fluid in the

In the following cases: flow of Strokes round a sphere; of Osren
round a sphere and round a cylinder; and of Burgess round a sphere (see the
quotations of § 5) we see from the formulae given by the authors that in the
image of relative flow the velocity v on the axis behind the body has the same
value as that of the original current U.

2) The distribution of the vorticity given in the figures has not been derived by
calculation from the distribution of the velocities; they were only sketched on
view. Fig. 22 gives the beginning contraction of the vortices to a vortex sheet.
In Fig. 24 the length of the domain of the counter currents has been left
undetermined.

Theoretical and experimental investigations on the flow produced by a sphere
for medium values of R in a space bounded by solid walls have been made by
W. E. Wiutams, Phil. Mag. (6) 29, p. 526, 1915. In the paper several photo's
and drawings are represented.

8) The “coagulation’’ of the vorticity cannot increase or decrease its quantity.
Therefore even in the real, turbulent flow the “wake” must remain of finite length.
The figures 22—-24 may be said to represent the “mean state" of the fluctuating
current.

1104

boundary layer (parallel to the surface), wl —= vorticity. Further
aU is written for the stream function of v,U, and BU for the
potential.

The stream line «=O is the line of symmetry of the motion;
in front of the body it splits into two branches. These two unite
again at the back of the body. At the branch points the values of
8 are 8, and 8, For a circular cylinder we have f.i. (when the
radius of the section is a):

«=y(1-5) : p=e(1+5).
r r

The line a=O consists of the x-axis (y = 0) and the circle (r = a);
at the points of intersection a — +a, so that:
B= 2a; 8 at AE
II. The differential equation for the vortex motion in the boun-
dary layer is:
dw vy dw
08 Uda
which is a shortened form of equation (21). When the latter was
derived from equation (20*) it has been divided by:

sa alo Guan
(a) + (Qa

which quantity is different from zero everywhere but at the points
B, and 9,, where the stream line «a =O splits. When at these points
(21) is satisfied, then necessarily the original equation (20*) is also
satistied. In the neighbourhood of these two points — at least in
that of 8, — the boundary layer may no longer be treated as infi-
nitely thin, so that there the simplification of (21) is not allowed;
in the determination of v too we find here a difficulty. With increa-
sing A however the allowable limit of |—,| decreases.

III. As a solution of (22) we may take for B, <@ <8, and for
a 20 (that is for the left side of the surface of the body):

(22)

A (8) — a’

Inta bgg tE le, I
Vai. Ae ie

w=— fd

1
where k= v/U. Because of the symmetry the same expression may
hold for the right side of the surface, with the opposite sign.

A (5) determines the quantity of vorticity that leaves the surface
in the neighbourhood of the point B=6 in unit of time; it diffuses
in the direction perpendicular to the surface and at the same
time it is washed backward in the direction parallel to the sur-

1105

face. A is determined by the boundary condition for v. When the
boundary layer is sufficiently thin (as has heen assumed), we have
at all its points, except for the nearest neighbourhood of 8, and 9,:

rime RN Ee vat te Wi GEE)

where n is the normal to the surface, while V,U denotes the velo-
city of the potential current at the foot of the normal, which is a
function of 8. Then the velocity in the boundary layer is:

n a

B
1 1 a
~— ee ee a S kil: OUA SAAN
v= wdn = wda = a Pai saleete : :

0 0 A
At the surface (2 = 0),-v 0; when « increases indefinitely, we
come outside the boundary layer and we may put v= JV,, so that,

(IIL)

PB
Vir de Aen es Nps a Ee
At
whence A is given by:
ae a 4
a aaa Od

IV. Formulae (V), (1) and (111) roughly describe the flow in the
boundary layer (the velocity in the direction perpendicular to the
surface must be determined with the aid of the equation of conti-
nuity). From (///) we can immediately derive the occurring of the
reversed flow. The values of A at points near 8 namely are here
multiplied by a greater factor than at points situated more towards
the front, which is especially obvious for small values of «. At the
points 8, and 8, V,=0O; between these V, has a maximum at a
point Bn, so that according to (V) A is positive for 8 < Bp, negative
for 8 > Bm. For 8B >PB, in (111) these negative values of A will
count more than the positive ones; from a certain value of 8 they
will predominate, so that the sign of V is inverted.

When « approaches zero, we have:

B
ve 4 Soe d Li
if VakV, VBS
A
so that the point 8s where the current leaves the surface is given by
Ps
A
faro ROE
Vas 8

1106

From this equation we see that 8g is defined by the function A(§),
viz. by the form of the body; in this equation A does not occur.
4 2
For the circular cylinder we have: V,? = 4 — sep A=— zi and
a
8 (a—s)VB+ 2a
WZ Ss
: 3V ak a?

This expression is zero for Bs =a; i.e. 120° from the most forward
point of the circle. This is rather far backward; the experiments
and the calculations according to PRANDTIL’s theory give for this distance
somewhat less than 90°. This difference is caused by the calculation
of the convection, which keeps here a finite velocity up to the
surface so that gs is slept along too far by the flow.

According to (/) the order of magnitude of the thickness of the
boundary layer is of the order of «= of the order of Vk8 = of

va a
the order of [4 sao the order of ——.
U VR

V. Values of w and v for 8 > 6,

When we suppose, that (J) and (V’) may be used up till B=&,,
the distribution of w for 8 > 8, is found by the diffusion into each
other of the two distributions that exist in 8= —, for positive and
negative values of a respectively (which are equal and opposite).
This gives:

Bs ZN See
A — a? —
w= — ee ss exp ees Ay Ce eN (V/T)
V xk (B—E) 4k(8—S) 4k(8—B,)(8—S)

A
The distribution of the velocity is then found from:

1 Go
Ve f ede. lr aante IEEE)
0

where V,U is the velocity of the irrotational motion in the direction
of the a-axis (i.e. along the line a= 0).

With the aid of these formulae the distribution of the vorticity and
the flow in the boundary layer have been calculated by graphical
integration. In order to obtain everywhere abstract numbers, we
have put:

B= Ba ; §=Xa ; a=2CV ka;
Then (J) and (V/J) take the form
1 1
ws ze f aX. (XB,0 = Tet C)
where p and f are numerical quantities.

1107

In fig. 25 f(C) has been represented graphically for several
Values of B; C has been set out in vertical direction, f each time
from the C-line in horizontal direction (viz. parallel to the B-axis).
The most outward broken line gives the value f— ca. 0,01. The
“opposite” values of f occur for small values of C between
== 1 and B ca. 3:

In fig. 26 these distribution curves are given along the circum-
ference of the cylinder and along the z-axis behind it. Here k/a
has been taken equal to 0,000625, i.e. A= 3200, though this
makes the boundary layer already too thick to allow the appro-
ximation. The thick lines indicate the distribution of the velocity
for the same values of B. The region of negative velocities extends
from B= 1 till beyond 6—5; the limit has not been calculated,
as the determination of the integrals by means of the planimeter has
not been made with sufficient accurateness thereto.

Fig. 27 gives a sketch of the vortex region and of the stream
lines of the relative flow.

Fig. 28 is a sketch of the dimensions of the vortex region for
R= 80000 = 25 3200; the values of «a (and therefore the
thickness of the layer) are then divided by 5.

VI. When we use the complete equation (21) in stead of (22), (/)
is replaced by an expression with a Besselianfunction under the
sign of integration: (see the quoted paper of L. V. Kine).

Physics. — “On geodesic precession.” By Prof. J. A. ScHouren.
(Communicated by Prof. H. A. Lorentz).

(Communicated at the meeting of February 26, 1921).

In a preceeding communication [*) have demonstrated geometrically,
that a system of axes, moved geodesically along a closed curve in
a non-euclidean V,, will show a deviation when returned to its
starting point. For the special case that the linear element of the
V, is the spacial part of the linear element of ScHWARZsCHILD and
that the curve is a circle round the sun with a radius equal to the
mean radius of the orbit of the earth, this deviation is 0.013" after
one revolution.

Now if firstly the fourdimensional problem of the motion of a

material point in a static gravitational tield, neglecting as usual
3

a
quantities of order RY could be reduced to a problem of classical

mechanics (mechanics with the fundamental theorem: force = mass
XxX geodesic acceleration) in a threedimensional non-euclidean space,
and if secondly we could demonstrate that a geodesically moving
system of axes may be regarded in first approximation as an inertial-
system, than we might conclude for the earth to a deviation of the
ordinary precession to the amount of 0.013".

In the mean time Fokker’), starting with the complete linear
element of ScuwarzscnHiLD, has demonstrated with a fourdimensional
calculation, that, apart from other relativity-corrections on the ordinary
precession, a geodesic precession exists, that is exactly 1'/, & 0.013".

Now we can show that this difference is caused by the fact, that
the fourdimensional problem can be reduced then and only then

to a threedimensional one, when the square of the velocity is of
2

a
order Re the square of the real occuring velocity in general being

a
f order —.
of order —

The world-line of a material point is given by the equation:

|e Oe) a

1) Proc Kon. Akad., XXI 1918, p. 533—539.
2) Proc. Kon. Akad. XXIII, 1921, p. 729.

1109

Now if ds? has the form

d. 2 B 2 3 B #2 8 2 irre 3 2
o> Erik, — |dt?—dl* =| 1— — | dl — | 14 — ]dr*—9’ sin? Odp*—r* dh, (2)
r r

than (1) can be replaced by

BAC Ole
mof DDO 0
ORO IE

In this equation the second term and the two last terms only

then can be neglected with respect to the other terms, when id
~

9

diN® a
and consequently (5) is of order —. Then the equation changes
Pe

fen EN en a A80 Dn, O68

But this is the equation of classical mechanics in a threedimensional

into

space with the linear element d/ and a potential function U = 5 . (4) is
ae

equivalent to

0U da” Av | de) dev
ed :

Oana | uw | de dt

dl\? a
If = and consequently 1 is of order —, which in particular
r ip

holds for the linear element of ScawarzscHiLD, for which B—a, the
reduction to a threedimensional problem is not possible, at least
not in this way *).

Now we will demonstrate, that in the threedimensional problem

1) Hence the equations derived Proc. Kon. Akad. XXI 1918, 1176—1183 on
p. 1178—1180 hold only for velocities of order bef
r

1110

a geodesically moving system of axes is under certain conditions an
inertialsystem. Therefore we firstly write out the equations (4) for
the linear element d/.

Since

1” | Bett iy, at ka in” A, ki == 4 rein” "
r r r p

0
ia = — 1’ sind cos 6, fs | = + r* sin Ô cos 0, „ (6)
0 p
00 Or
tje [Je
the other symbols of CrrisrorreL being zero, we have
del jest BU, rt — sin? Og" — rt
# r
a % ay ae py Sites ae (7)
O=r sin? Op 2rsin® Or p + Ar’ sin 6 cos 6 pd
0=r 6 —r sin cos 6 gy? + rr.
A motion, satisfying these equations is the circular motion :
r= R= constant, p'=o' mi En (8)
SIRE WE rb ea et ae

When we consider only motions, deviating little from this circular

Jt
one, we can put sin 0 = 1, cosO =— — @ and neglect in the first

equation r? and 6%, in the second one cos@@ and in the third
one 7 @. Then these equations pass into:

belt

O=rpd2rgp (8)
0—6 — cos p'
Now we introduce the variables x, y and z by the equations:
REDE |
For 2R |
y Ree
daarden Oz | es ne AND
5 — 0 = cos = =

x, y, 2 form a rectangular system of axes moving with a velocity

1111

Rw,t along the orbit r=A, the axis of # having always the direction
of the radius and the axis of y the direction of the motion. Then
the equations pass into

o=(1 + 5) #— 20, y— 80? # (1 za)

% a : aes 11)
Ozi tot) (
0 =—z—w,?z )

or
a . L \

ik EEA vyd ll
F a : vg) toy EZ)
jl)
z= —w,7z.

We further pass to a system of axes x’, y’, 2’, which revolves with
respect to a,y,z around the ayis of z with an angular velocity w
in the sense of y to w, the axis of 2’ coinciding with the axis of z:

r= 2' coswt + y' sin wt
y= sinwtd gest). . . . , (13)
A MEL

Then the equations pass into:

a tho-w,(1- Et y'+ or(1 5) (2' cos? wt y' sin wt cos wt) +

+ in aa)

y'— +2.w—w ee 2430, jee z' cos wt sin wt + 'sin? wt) —(
y ° 0 OR y

+ o-ta(-s)b

1 MRE | : /
.

(14)

Being given a spherical body with centre in the origine of the
system x,y,z and so small, that the squares of its dimensions may
be neglected. Then, supposing the body with this neglection to be
rigid, in the expressions of the moments > m (y’ 2’— 2’ y’) cycl. the
terms with x’, y’, z’ will all contain an inertial product or a difference
of two equal inertial moments and consequently this terms will
vanish. The terms with 2’, y’ and z’ then and only then vanish for

1112

7
v

in such way that the terms with «’, y’ and 2’ vanish in the equations

(14), ie. if:
oz (1-55) = tbe a 3 (15)

But in this case w’, y’, 2’ is extactly a geodesically moving system
of axes as I demonstrated in the publication referred to on the

every kind of motion with respect to 2’, y’ and 2’ if w be choosen

. . : Ta
first page. After one revolution this system has turned over R’

This can of course also be calculated in the fourdimensional way.
Starting with the linear element (2) we find a precession passing
for 8=O (velocity approaching to zero) in the above calculated

value = and for gain’ 1°/, << this: value.

[t is worth observing the ordinary precession gets. possibly also
another value in relativistic mechanics than in classical mechanics,
a possibility pointed out by pe Sitter. By means of the equations
given by Fokker it will be possible to calculate the deviation caused
by this, at least so far as it is not influenced by forces caused by
the mutual attractions of the parts of the planet.

Physics. — Mutual Influence of Neighbouring Fraunhofer Lines” *).
By Prof. W. H. Junius.

(Communicated at the meeting of January 29, 1921.)

If the hypothesis holds good that the darkness of Fraunhofer lines
is not a pure absorption effect — as it is commonly supposed to be —
but chiefly due to anomalous dispersion (showing itself both in mole-
cular diffusion and irregular ray-curving), we may expect on theo-
retical grounds?) that neighbouring Fraunhofer lines will, as arule,
seem to repel each other. If, now, such a mutual influence is
actually found to exist, a mighty support will thus be given to the
said interpretation of the solar spectrum, as long as it remains
impossible to explain that phenomenon on the basis of the current
view that one is dealing with mere absorption lines.

In a communication on “The general relativity theory and the
solar spectrum”®) we have made use of the already reliable and
striking results obtained in a preliminary research on the manifes-
tations of mutual influence of Fraunhofer lines as appearing in the
limb-centre displacements measured by AbAms*) about the year
1910. At my request Dr. P. H. van Crrrerr and Dr. M. Minnagrt
have, however, once more examined the same data with the utmost
care, using still more rigorously defined criteria, in order that every
trace of bias might be avoided in selecting the lines. Besides, the
investigation has been extended over the observation son limb-centre
displacements published by EversHeD, Narayana Ayyer and Royps °)
in 1914—191L6. It will appear that this extension of the field has
led to a considerable corroboration of the former inferences, so as
to put the existence of mutual influence practically beyond doubt.

Care has been taken, of course, that during the act of selecting
lines that would probably be influenced, one was ignorant of the
observed displacements. Basing ourselves on the conception how,

1 This paper is an abstract of an ampler article that has since appeared in the
Astrophysical Journal 54, 92 (1921). (Note, added January 1922).

2) Cf. Astroph. Journ. 43, 49—53 (1916).

3) W. H. Junius and P. H. van Cittert. These Proc. 23, 522 (1920).

4) W. S. Apaus, Astroph. Journal 31, 30 (1910); Mt. Wilson Contrib. No. 43.

5) EversHep and Royps, Kodaik. Bull. 39 (1914); Narayana Ayyer, Kodaik.
Bull. 44 (1914); Royps, Kodaik. Bull. 53 (1916).

72
Proceedings Royal Acad. Amsterdam. Vol. XXIII.

1114

according to the dispersion theory, the asymmetry of the Fraunhofer
lines originates, we drew up a scheme of criteria which a line and
its surroundings would have to answer for giving reason to expect
either an increase or a decrease of its displacement towards the red,
owing to neighbour lines. In the tables containing the selected lines
(which will be printed in the Astrophysical Journal) we have men-
tioned the criteria and considerations applied with each line, as well as
the direction of the expected effect. Next to these data will be found
the actually observed displacements, under one of the headings d,
or d, according as a repulsion from the violet or from the red side
(i.e. an increased or a decreased amount of displacement towards
the red) was expected.

MOUNT WILSON KODAIKANAL
| 0.015
|
| 0.010
10.005
0
4000 5000 6000 4000 5000. + 6000 AE.

In the diagram abscissae represent wave-lengths, ordinates displa-
cements, positive when towards the red. The values of d, are cha-
racterized by full dots, the values of d, by circlets.

We have kept the Mount Wilson data separated from te Kodai-
kanal data in order to asceriain whether these two mutually inde-
pendent series of observations would yield similar results.

The outcome is very convincing: in both cases the full dots average
decidedly higher than the circlets, which means that the displace-
ment towards the red is generally greater for lines with companion
on the violet side than for lines with companion on the red side.

We need not wonder at finding some full dots yet to lie low and

1115

a few circlets high. Indeed, taking any dispersion line for itself, the
amount of its displacement towards the red will be determined by
the shape of the dispersion curve; this, however, does not depend
exclusively on the positions and intensities of the nearest companion
lines, but also on the value nm, which the index of refraction of the
medium would have for light of the small spectral region under
consideration, if this ‘where free from lines. Since n, varies along
the spectrum, there will be a corresponding fluctuation of the values
of the displacements, on which the influence of close neighbouring
lines superposes itself. Thus we conceive that the two swarms of
black dots and circlets must partially penetrate each other.

Let us next consider numerically, to which extent the displacement
of a line towards the red is modified, on the average, by the presence
of close companions.

For that purpose we make use of the two curves shown in the
diagram, which represent the general increase of the displacement
with wave-length. They are derived for Mount Wilson *) from 450,
for Kodaikanal from 392 measured displacements. (The second curve
lies sensibly lower than the first; this may be due to the accidental
fact that in the Kodaikanal material a greater number of very weak
lines, showing small displacements, have been included); These curves
define for every region in the spectrum an average or normal displa-
cement d. Now we have calculated for each influenced line the
value of the expression

which may be denominated “relative departure”.

With lines having a companion on the violet side, these depar-
tures are for the greater part positive, with lines having a com-
panion on the red side they are mainly negative, so that the first
group gives a positive, the second group a negative “sum of departures”’.

From the Mount Wilson data we derive (after applying a correction
explained in the original paper):

= D,= + 7,09 (25 lines) and SD, = — 7,09 (23 lines) . (1)
and from the Kodaikanal data
= D, = + 19,15 (36 lines) and =D, = — 19,16 (44 lines) . (2)

Hence the mean value of a relative departure (positive or negative)
is:
7,09 + 7,09 + 19,15 + 19,16

D= = 0,410,
128

1) Cf. Junius and van Cirtert, l.c.

72%

1116

which indicates that the limb—centre displacement of a line is
augmented or diminished by as much as */, (on an average) of its
normal amount if another line is near.

This comparatively great influence can only be explained as arising
from the modification which the neighbour line brings about in
the refracting power of the medium. The phenomenon thus proves
the efficiency of anomalous dispersion in the sun; it strongly suggests
that limb—centre shifts in general may be chiefly conditioned by
the shape of the dispersion curve of the gaseous mixture; and this
inference again vindicates our hypothesis that the distribution of the
light in Fraunhofer lines is dominated by anomalous dispersion.

Taking for granted the validity of this interpretation of the solar
spectrum we should expect, moreover, that in the spectrum of the
centre of the sun’s disk the Fraunhofer lines will also be generally
displaced towards the red with respect to the positions of their cores
(which are determined by the values of the free periods on the sun),
and that these shifts will be comparable in magnitude with the
limb— centre displacements.

There is strong reason, therefore, to ascribe the observed centre-
are displacements perhaps wholly, but at any rate for a considerable
part, to anomalous dispersion — an explanation, indeed, confirmed
by the fact that the principal characteristics of these displacements
are very similar to those of the limb—centre shifts *).

If we now imagine the observed centre— arc displacements to be
reduced by substracting from them the purely solar displacements
of the centre lines with respect to their cores (as mentioned above),
the remaining shifts — if any — will be so small, that the existence
of a gravitational displacement of the solar line-cores with respect

le)
to the terrestrial arc lines (expected to amount to from 0,008 A to

0,014 A in the visible spectrum) appears highly improbable.

Let us finally try to express numerically with how much confi-
dence we may assert that the observations really indicate the existence
of a mutual influence of Fraunhofer lines.

One might indeed suggest it to be an effect of mere chance that
the black dots in our diagram average so much higher than the
circlets. The probability of that supposed casual event can be calculated
according to the rules of the theory of errors.

From the equations (1), relating to the Mount Wilson measure-
ments, it follows that a line having a companion on the violet side
shows a mean relative departure

‘) Cf. Junius and van Cittert. These Proceedings 23, 530 (1921).

1117

2) nntsnoe
WE = + 0,284,
v 55 + 0,
and a line having a companion on the red side
se 09
Mes —= — 0,308.
23

Supposing, on the other band, that out of the 48 cases we had
chosen 25 cases without any guiding principle, entirely at random,
then the probable departure of the mean of those 25 cases would
have been 7,= ag 0,066 (in which 7, the probable departure
for a single line, depends on the “precision” of the entire group,
and proved to be — 0,329).

The mean relative departure Pp actually found is, therefore,
0,284
0,066
have been in case of random choice.

Conformably we find for a line with companion on the red side
(r’, being = 0,068).

D, = — 0,308 = — 4,50 r',.

= 4,30 times as great as the “probable” departure 7, would

The probability that a mean departure D, derived from cases
selected without guiding principle, would be included between + 4,307,
and —4,50r’, or, what is very nearly the same, between + 4,407",
and —4,40r", (putting 7", == 0,067) amounts to *)

4,40

2 SF
06 fe dt = 0,997,
Vn

0
so that only 0,003 in left for the probability that, by mere chance,

D would lie beyond those limits.

Applying the same argument to the equations (2) derived from
the Kodaikanal measurements, which include a greater number of
influenced lines, we find an even much smaller value for the pro-
bability that the observed considerable separation of the two swarms
of dots and cirelets would be purely accidental, namely 0,00001.

Since these latter data have been obtained independently of the
Mount Wilson measurements, we may value the probability of the
concurrence of those two casualities at 0,003 x 0,00001.

It has been established, therefore, with a probability of more than
107 to 1 that the guiding principle used in selecting the lines is

') Gf. Guauvener, Spherical and practical astronomy, Vol. Il, Table IX A.

1118

physically significant, and that neighbouring Fraunhofer lines really
seem to repel each other.

We have of course also considered the idea, that this phenomenon,
although undoubtedly involved in the observational results, might
be caused by systematic errors in the methods, applied in making,
or judging, or measuring the photographs.

The chance, however, for such errors to have appreciably affected
the result, is very small especially in the case of limb-—centre dis-
placements, because these displacements are usually derived from a
comparison between photographs, the density and general appearance
of which have been chosen as similar as possible. If, therefore, in
estimating the distance between the members of a close pair of
lines, a systematic error is made owing to their proximity, that
error will be very nearly the same in the limb spectrum as in the
centre spectrum, and will thus be eliminated in the limb-centre
differences.

As the distance between neighbouring lines is nevertheless found
to be greater in the limb spectrum than in the centre spectrum, it
is safe to say that influencing each other is a true property of
Fraunhofer lines. This property seems only explainable from the
point of view of the dispersion theory. |

The skilful collaboration of Dr. van Crrrert and Dr. Minnauer
in this research is highly appreciated.
Utrecht, January 1921. Heliophysical Observatory.

Anatomy. — “On the Homology of the M. marsupials and the
M. pyramidalis in Mammals’. By D. van Vuer. (Communi-
cated by Prof. L. Bork).

(Communicated at the meeting of January 29, 1921).

The name of M. pvramidalis designates in the Literature of
Anatomy a muscle found in the lower part of the anterior abdominal
wall of various classes of mammals. In the following classes of
mammals a M. pyramidalis has never been met with: Edentata,
Glires, Galeopithecidae, Ungulata, Sirenia and Cetaceae; while there
may be one in Monotremata, Marsupialia, Insectivora, Chiroptera
and Primates. A M. pyramidalis has also been described in Hyrax
and in Hyena’). Furthermore ErLeNBERGER and Baum *) describe a
M. praeputialis in the dog, which they look upon as the thoracic
portion of the M. pyramidalis.

This muscle being always designated by the same name, it is
evident that it is considered homologous in all the classes mentioned.
This, in fact, has been emphatically acknowledged by some writers.
EisLeR*) e.g. says: “Der M. pyramidalis ist ein typischer und groszer
Muskel bei den Säugern, die einen Beutelknochen besitzen”. In
Bronn’s Klassen und Ordnungen *) we read: “Dieser zwischen der
ventralen Wand der Rectusscheide und dem Rectus gelegene Muskel
ist als der Muskel des Beutelknochens anzusehen und ist deshalb
bei den aplacentalen Säugern am stärksten entwickelt”. WirpERsHEIM
maintains likewise: “Der Pyramidalis ist der eigentliche Muskel des
Beutelknochens” °) and “Bei den aplacentalen Säugethieren d.h. bei
Monotremen und Beutelthieren ist der M. pyramidalis im Anschlusz
an die Beutelknochen gewaltig entwickelt” °). Of the same opinion
are, amongst others, also GEGENBAUR, BARDELEBEN, RAUBER and Testvt.
Only Lorn’) records that Cuupzinsky holds another opinion, without
mentioning, however, what it actually is.

1) Bronn’s Klassen und Ordnungen. Mammalia II. pg. 788 sqq.

2) ELLENBERGER und Baum. Anatomie des Hundes, p. 167.

3) ErsLer. Die Muskeln des Stammes, p. 585.

4) Bronn l.c.

6) WiepersHerm. Vergleichende Anatomie der Wirbeltiere, p. 244.

6) - . Der Bau der Menschen als Zeugnis fiir seine Vergangenheit.

7) Lora. Muskelsystem des Negers. p. 98. Studien und Forschungen zur Menschen-
und Völkerkunde IX 1912.

1120

Be this as it may, no evidence has as yet been brought forward
for the homology of this muscle in placental and aplacental mam-
malia, ie. of M. pyramidalis and M. marsupialis: the mere fact
that the M. marsupialis of the aplacental mammalia occupies a place
similar to that of the M. pyramidalis of tbe other mammalia, and
that both are enclosed in the rectus-sheath, can hardly be deemed
sufficient evidence for the homology.

In this paper we publish the results of an inquiry into the
validity of this homology-hy pothesis.
The M. marsupialis generally arises from the medial border of
the os marsupiale, the lower fibers of the muscle running more or
less transversally, while those situated more proximally slope upward
towards the linea alba. This muscle lies before the M. rectus, being
separated from it only by a thin layer of loose connective tissue.
However, it seems that the M. marsupialis does not always lie before
the M. rectus, as W. Vrouk *) discovered that in Dendrolagus
inustus the M. pyramidalis was covered by the right abdominal

muscle.

The other abdominal muscles of the marsupials run as follows:
The M. obliquus externus always passes along in front of the M.
rectus and in front of the M. marsupialis. The course of the M.
obliquus internus, however, varies just as that of the M. transversus.
A general view of it is given in the diagrams in Fig. 1, which

|

' i}
i i i M. rectus

} hii

weer M. obl. ext.

— M. obl. int.

Sn M. transv.

a. Petrogale.
b. Didelphys.

c. Phascologale.
Belideus.

=—= =—_=----
eene eene > =

1) W. Vrouik. Ontleedkundige nasporingen omtrent Dendrolagus inustus. Kon,
Akad. v. Wet. A’dam Afd. Nat. Deel V.

1121

show the succession of the various muscles in a longitudinal section
of the inferior part of the abdomen.

With Phascologale penicillata (fig. 1c) the following relation exists :
The inferior portion of the M. obliquus internus inserts itself into
the lateral border of the Os marsupiale; the superior portion, unable
to attach itself to the Os marsupiale, extends along the upper border
of the M. marsupialis and is inserted into the linea alba. Moreover
a leaf is split from the aponeurosis, which passes with the aponeurosis
of the M. transversus behind the M. rectus. With Belideus ariel the
course of the M. obliquus internus and M. transversus was the
same as with Phascologale. Here also the M. marsupialis lies in
front of the M. rectus, the muscle-fibers, however, follow a more
oblique, proximal course than in the case of Phascologale.

Between M. marsupialis and M. rectus of Petrogale penicillata
(fig. 1a) runs the anterior leaf of the aponeurosis of the M. trans-
versus; this splitting into an anterior and a posterior leaf takes place
only in the inferior portion of the M. transversus. More towards
the cranium the M. transversus continues unsplit behind the M.
rectus. The M. -obliquus internus of this animal does not continue
between M. marsupialis and aponeurosis of the M. transversus, but
follows the latter muscle behind the. M. rectus. In Petrogale
xanthopus Parsons ') found nearly the same condition: “The internal
oblique is inserted into the last three ribs, dorsal to the lateral line
of the body it is fleshy, while ventrally it becomes aponeurotic and
blends with the transversalis. The transversalis.... passes-in the
anterior two thirds of the abdomen deep to the rectus, in the posterior
third it splits to enclose that muscle”.

On the M. obliquus internus and M. transversus of Didelphys
virginiana Erriorr Cours’) writes: ‘‘The lower border (of the internal
oblique) is fleshy and stretches nearly horizontally inward from
Poupart’s ligament to the upper part of the marsupial bone, a stout
bundle of fibres being inserted into the tip of that bone. The rest
of the muscle passes more and more directly upward, till its
posterior part is vertical. Its anterior margin ends along a linea
semilunaris by blending the aponeurosis with that of the transversalis’’.
Of the latter muscle Cours says: “There is no splitting of the
aponeurosis to get outside the rectus below” (fig. 10).

1) Parsons. On the anatomy of Petrogale xanthopus. Proceedings of the Zoolo-
gical Society of London. June 16, 1896.

2) Ermorr Cougs. The osteology and myology of Didelphys Virginiana. Memoirs
of the Boston Society of Natural- History, Vol. Il. Part. 1 1872.

1122

GEGENBAUR ‘) writes of the M. pyramidalis — also of that of
the Monotremata and of the Marsupials: — “allein seine Lage nicht
nur, sondern vielmehr sein Anschlusz an den Rectus so wie der
Einschlusz in eine mit dem Rectus gemeinsame Scheide macht seine
Entstehung aus dem Rectus wahrscheinlich und verweist auf die
Thatsache, dasz bereits bei Amphibien mehrfache Rectus-bildungen
vorkommen, von welchen die oberflächliche der Metamerie entbehrt,
gleich dem Pyramidalis der Säugethiere, welcher auch nicht mit
Unrecht als vorderer Rectus unterscheiden ward”. Also in Errmorr
Cours’s inquiry, quoted above, we find a differentiation between a
M. rectus externus and internus. This view is not plausible as
regards the M. marsupialis. As appears from the diagram of the
abdominal wall of Petrogale (fig. 1a) a leaf of the aponeurosis of
the M. transversus passes between M. rectus and M. marsupialis.
This renders it highly improbable that the M. marsupialis should
arise from the M. rectus. The diagrams of Phascologale and Belideus
(fig. 1c) also show that the M. marsupialis is not exactly invested
by the rectus-sheath — which according to GEGENBAUR would speak
for its arising from the M. rectus — but that it rather constitutes
a part of the sheath itself. The M. obliquus internus does not play
a part in the formation of the frontal leaf of the vagina muse.
recti, owing to its insertion into the lateral border of the Os marsu-
piale; now it is just the M. marsupialis which completes that same
part of the rectus-sheath. Again, the fibres of the inferior part of
the M.. marsupialis run at a right angle to the M. rectus which,
though this is not a cogent proof of the reverse, renders it by no
means plausible they should arise from the M. rectus.

The fibre-course of the M. marsupialis corresponds much more
to that of the M. obliquus internus. The fact that the M. marsu-
pialis completes, as it were, the M. obliquus internus, and the location
of this muscle between the M. obliquus externus and M. transversus
— which appears above all in Petrogale (fig. 1a) — renders it more
probable that the M. marsupialis is a part of the M. obliquus internus.
This conception helps us to realise the condition described by Vrouik
that the M. rectus overlies the M. pyramidalis of Dendrolagus inustus,
such being not at all extraordinary for a part of the M. obliquus
internus ”). |

This has been clearly demonstrated in a Didelphys marsupialis (fig. 2).

1) GEGENBAUER. Vergleichende Anatomie, I. 1898 p. 664.

*) For the course of the abdominal muscles relative to the M. rectus, we refer
to W. A. Mussera: “Over den bouw van den musculeuzen buikwand der Primaten.”
Kon. Akad. v. Wet A'dam 14 Mei 1915.

1125

The lower portion of the M. obliquus internus is inserted into
the lateral border of the Os marsupiale; the lower portion of the
M. marsupiale arises from the medial border of this bone. The
aponeurosis of the middle part of the M. obliquus internus does
not continue as far as the linea alba, but blends with the upper
portion of the M. marsupialis, so that this part of the aponeurosis
constitutes an intermediate tendon between the two muscles. The
upper part of the M. obliquus internus is inserted into the linea alba
and the lower ribs. Here, then, there is a close relation between the
two muscles, so that it might be called a Pars marsupialis musculi obliqui
interni. But in most cases the relation
between the two muscles is less distinct. In
the description Vrom gives us of Dendrola-
gus inustus, alluded to above, we read
that “Zij (de buidelspier) hecht zich aan
de witte lijn en slaat zich achter het
marsupiaalbeen om ten einde zich te ver-
eenigen met de peesplaat van M. obliquus
internus en transversus.” True, this des-
cription falls short of clearness, but it is
not impossible that in Dendralogus a con-
dition occurred such as I observed in
_Didelphys marsupialis.

Various opinions are prevalent concern-
ing tbe Ossa marsupialia. FLowsr *)
considers them as “Verknöcherungen der
inneren Sehne der äusseren schrägen
Bauchmuskel selbst, oder doch innig mit
ihr verbunden, und sie fallen daher unter
der Kategorie der Sesam beine’”’. Karz ”)

diene speaks of “Ossificationen in einer hintern

sehnig gedachten Partie des M. Pyrami-

Fig. 2. dalis”. Since Wri1epersnurm °) undertook

his extensive inquiries into the pelvic girdle, it is generally received

that the Oss marsupiale is a strongly developed Epipubis. In the

matter of homology of M. pyramidalis and M. marsupialis, the
significance of the Os marsupiale is immaterial.

1) Flower. Einleitung in der Osteologie der Säugethiere, 1888 p. 298.

*) Karz. Zur Kenntniss der Bauchdecke und der mit ihr verknüpften Organe bei
den Beutelthieren. Zeitschrift fur wiss. Zoöl. Bd. 36. 1882.

3) WrepersHerm. Die Phylogenie der Beutelknochen. Zeitschrift für wiss. Zoöl.
Bd. 53—1882. (Suppl.).

1124

Now concerning the M. pyramidalis the following facts may be
pointed out.

The M. pyramidalis in man is a small triangular muscle in the
anterior abdominal wall, arising from the pubic crest in front of
the rectus muscle. It is directed obliquely upwards, to be inserted
for a variable distance into the linea alba. Some superficial fibers
are also inserted into the posterior side of the ventral leaf of the
rectus-sheath *). This muscle is lodged right in front of the M. rectus
and is separated from it only by a thin layer of loose connective
tissue. Yet the connective tissue between the two muscles sometimes
seems to become a solid membrane, for we read in EisLER’s *) work:
“In der Regel findet sich zwischen Pyramidalis und Rectus nur
eine diinne Schicht lockeren Bindegewebes, doch schiebt sich gele-
gentlich von latera her ein aponeurolisches von der ventralen Rectus
scheidewand im besonderen von der Aponeurose des M. transversus
abdominis abgespaltenes Blatt zwischen beide, ohne aber eine voll-
ständige Abschlieszung des Pyramidalis herzustellen”’.

Krausk*) maintains even that the latter condition is the rule. Since,
however, the obturation (Abschlieszung) as HisLer remarks, js never
complete, and occurs only exceptionally, anyhow is not constant by
far, -— witness the different opinions prevailing in this respect —
it does not seem probable that the obturation is effected by a true
aponeurosis.

The M. pyramidalis is lacking bilaterally in + 16°/, of the Euro-
peans, in half the other cases it occurs only unilaterally. Further-
more the M. pyramidalis is absent in approximately 10°/, of the
Negroes and 4°/, of the Japanese.

The following remarks are still given by Santorini, CRUVEILHIER,
Quain and GRGENBAUR. In the absence of the M. pyramidalis the
caudal end of the M. rectus is broader and stronger; conversely,
MacALISTER *) reports that the insertion of the M. rectus is narrow
when the M. pyramidalis is strongly developed. We shall see that
these relations are of some consequence.

In man the aponeurosis of the M. obliquus internus continues as
far as the linea alba, without any junction between this aponeurosis
and the M. pyramidalis, as in the case of Didelphys. The direction
of the fibres of M. pyramidalis and of M. obliquus internus differs
rather much; moreover the aponeurosis of the M. transversus is

1) Erster. Die Muskeln des Stammes. p. 572.

3) KIsLer l.c.

3) Krause. Handbuch der menschlichen da 1879 Bd Il, p. 242.
4) Hisuer lc. p. 574.

1125

lying between the two muscles. For these several reasons we cannot
consider also the M. pyramidalis as a portion of the M. obliquus
internus, as the M. marsupialis is. From this it follows again that
the M. pyramidalis and the M. marsupialis cannot be homologous.

What then is the significance of the M pyramidalis of the Mono-
delphys? An answer to this question will be found in the following
record of an investigation into the mode of insertion of the M rectus
abdominis in some mammalia. In Tarsius spectrum the Os pubis
presents only a small place for insertion, which is narrower than the
breadth of the muscle. The insertion is nevertheless effected over
the whole breadth of the muscle because the inferior part of the
M. rectus bends round anteriorly and laterally at the linea alba,
so that a small triangular portion of the muscle is disposed in front
of the larger unbent portion of the M rectus. This portion bears
a close resemblance to a M. pyramidalis; however, it has not an
insertion of its own into the linea alba, but at the linea alba its
fibres merge directly into those of the M. rectus. We see then that
in Tarsius the M. rectus has a U-shaped insertion. However in case,
through some cause or other, such a triangular piece of muscle
should become independent and obtain an insertion of its own into
the linea alba, a M. pyramidalis is originated. In Insectivores such
a case is encountered in the crossing of the two Mm recti, as des-
eribed by Lrcun'). In the embryo the crossing commences in the
most caudal part. The Mm recti draw near to the middle line, the
right M. rectus splits up in two in order to allow the left M. rectus
to pass (at Talpa europea) or otherwise both Mm. recti split and
in this way a more complicate network is formed. The right M.
rectus then inserts itself into the left Os pubis and the left M. rectus
into the right Os pubis. As the embryo develops, the process
continues proximally, until the full-grown condition is reached. In
an investigation of embryos of Talpa I detected likewise a bending
of the medial border of the M. reetus anteriorly and laterally ; now
when the unbent parts of the rectus cross, the triangular anterior
layer must of necessity be disconnected from the rest of the M.
rectus and gets an insertion of its own, in other words it becomes
a M. pyramendalis. The impossibility of a connection between bent
and unbent pieces of the M. rectus is dictated here by the circum-
stance that the medial border of the M. rectus, along which the
bending took place anteriorly afd laterally, is shifted, after the
crossing, towards the opposite side. In embryos, in which the

_ 1) Lecue. Zur Anatomie der Beckenregion der Insectivera. Kon. Svenska Vet.
Akad. Handl. Bd 20, NO. 4, 1883.

1126

crossing of the Mm. recti began but was not entirely accomplished,
the bending of the M. rectus is discernible at a certain level, while
at a lower level, where the crossing had already been partly accom-
plished, the connection between the two pieces of the M. rectus has
been abolished.

How it is that in the Simiae and in man a bent piece of the M.
rectus is liberated as a M. pyramidalis, is not so easy to under-
stand as it is in Inseetivora. But, also in other regions of the human
system it occurs that the portion of a muscle with U-shaped inser-
tion, the insertion being one of the arms of the U, becomes inde-
pendent. This e.g. may be the case with the pars abdominalis of
the M. pectoralis major.

With this exposition of the origin of the M. pyramidalis in man
several facts are in perfect harmony. First of all the fact that
Santorini and other authors have established that the insertion of
the M. rectus into the Os pubis is narrow, when the M. pyramidalis
has a broad origin in this skeletal bone and conversely. In agree-
ment with this is also the fact that some fibres of the M. rectus
are regularly inserted into the inferior part of the linea alba, as is
described by Nicatsp'), as the rectus must of necessity obtain an
insertion, along the previous line of flexion, into the linea alba,
when the same happens with the M. pyramidalis. i

Because the function of the M. pyramidalis is very inconsiderable
this muscle disappears in many cases either on one side or on either
side, the only indication of its earlier existence and mode of origin
then being the insertion of fibres of the M. rectus into the inferior
part of the linea alba.

The question may be asked why in some animals the insertion
of the M. rectus is U-shaped. In this respect there may be relation-
ship between the breadth of the M. rectus on the one side and
on the other side the dimensions, the form and the size of the
pelvis i.e. the space for insertion. This, however, requires further
investigation. We only wish te observe that among the half-apes the
M. rectus has a simple, recti linear insertion in the Lemurinae and
that in the other half-apes the M. rectus presents a more compli-
cated mode of insertion. This, no doubt, has something to do with
the fact recorded by Weber’) that the Lemurinae have a wide
pelvis: ,,Gegeniiber dem weiten Becken der Lemurinae, haben die
nicht-madagassichen Prosimiae ein enges Becken.”

!) Eister. Die Muskeln des Stammes, p. 565
2) M. Weser. „Die Säugetiere”. p. 747.

Physics. — “On the deviations of liquid oxygen from the law of
Curie”. By Prof. W. H. Kexsom. (Communication N°. 8 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 February 26, 1921).

§ 1. Jntroduction. It will be well-known that the magnetic sus-
ceptibility of gaseous oxygen‘) follows the law of Curie

fil CF We Wipe Ee, ere cL)
but that for liquid oxygen *) we have the relation
Ae Ne ORNL ge AT Webel ars SAM 7)

where A is a constant viz. A— 71. An explanation of this pheno-
menon has been sought in different ways.

We may for this liquid base our considerations on the validity
of the fundamental idea of LANGeviN’s theory. Then the deviation
from the law of Curie might be caused by: —

1. a change of the number of elementary magnets e. g. by poly-
merisation of the oxygen molecules (KAMERLINGH ONNEs and PERRIER,
Leiden Comm. N°. 116). More recent experiments baving shown
that similar deviations also occur in the case of solids, for which
such a polymerisation, changing with the temperature, can hardly
be assumed, we should prefer to find another explanation for oxy-
gen also. |

2. a decrease of the magnetic moment of the oxygen molecules
or atoms, either by a slower circulation at lower temperatures of the
electrons which give rise to the magnetic moment or, in the case
of liquid oxygen, by the influence of the thermic pressure (KAMER-
LINGH OnnEs and Prrrizer, Leiden Comm. N°. 116). More recent
experiments on the susceptibility of gaseous oxygen down to 147° K.
on the one hand (KAMERLINGH OnNES and OosrerHUIS |. c.) and of

1) P. Curie. Ann. chim. phys. (7) 5 (1895), p. 289. H. KAMERLINGH ONNES
and E. OosrerHuis. Leiden Comm. No. 134d.

*) H. KAMERLINGH ONNES and A. PERRIER. Leiden Comm. No. 116. These
Proceedings Vol. XII 1910, p. 799. H. KAMERLINGH ONNEs and E. OosTER-
HUIS. Leiden Comm. No. 132e. These Proceedings Vol. XV 1913, p. 965.

For liquid mixtures of oxygen and nitrogen comp. A. PERRIER and H. KAMER-
LINGH ONNES. Leiden Comm. No. 139d. These Proceedings Vol. XVI 1914, p.901.

1128

liquid mixtures of oxygen and nitrogen (KAMERLINGH Onnes and
Perrine |. ¢.) on the other are not in favour of these explanations.
3. a change of the field of force, in which the separate oxygen
molecules are to be found, by an oppositely acting negative mole-
cular field (KAMERLINGH ONNES and Perrier, Leiden Comm. N°. 139d) *).
4. a change in the heat motion. We might for instance suppose
that this motion no longer follows the laws of equipartition, but
that, in agreement with the quantum-theory with assumption of a
zeropoint-energy, at low temperatures it neutralizes the magnetisation
to a higher degree than would be the case if the equipartition laws
were still valid. (Krusom, Leiden Comm. Suppl. N°. 36c) ’).
Without further discussing the arguments for or against the two
latter ways of explanation, we shall in this paper only treat a
question put by Prof. KAMrRLINGH ONNEs on occasion of discussions
held at Leiden on magnetic problems. This question may be formu-
lated in the following way. Might it not be possible that the occur-
rence of A in (2) was caused by what is left, when we take the
statistic mean, from a directing action of the couples of force,
exerted by the oxygen molecules on each other when, ina magnetic
field, the molecules come very near to each other? In our conside-
rations we shall assume that with sufficient approximation the forces
exerted by the oxygen molecules on each other may be treated as
forces exerted by electric quadrupoles, as has been proved to be

1) As to R. Gans, Ann. d. Phys. (4) 50, p. 163, 1916, comp. p. 1134, note 1.

*) This hypothesis has first been tried by OosrterHuis, Leiden Comm.
Suppl. No. 31, These Proceedings Vol. XVI (1913), p. 432, for paramag-
netic salts, afterwards by KEEsomM, Leiden Comm. Suppl. No. 32, These Pro-
ceedings October 1913, p. 454 and 468, for ferromagnetic substances. More
recently v. WEIJSSENHOFF (Ann. d. Phys. (4) 49, p. 149, 1916) and especially
REICHE (Ann. d. Phys. (4) 54, p. 401, 1917) have worked out the hypothesis
by the methods of the quantum theory which had then been developed much
further. They found a good agreement with the observations on the suscep-
tibility of paramagnetic salts, comp. also A. SMEKAL, Ann. d. Phys. (4), 57,
p. 376, 1918. LANGEVIN. too (Procés-Verbaux et Résumé des Communications
de la Soc. franc. de physique 1919, p. 18) adheres to this way of explaining
the deviations from the law of Curie. Especially from the results of the
investigations on crystal structure with the aid of Röntgen rays we can hardly
think any longer that in solids molecules rotate, in the heat motion, as a
whole like elementary magnets in the sense of the “magnetic molecule’, a
definition of which, in accordance with the ideas of Weiss, has been given
in Leiden Suppl. No. 32a, p. 11, note 3. Thus we shall have to consider
parts of the molecule, eventually atoms or parts of atoms, comp. O. STERN,
Zs. f. Phys. 1, p. 147, 1920. Comp. also W. LENz, Physik. Zs. p. 613, 1920,
P. EHRENFEST, Leiden Comm. Suppl. No. 446, These Proceedings Vol. XXIII
(1921), p. 989.

1129

permissible for the explanation of the molecular attraction in the
equation of state. In this paper it will be shown that very probably
the answer to the above question must be in the negative.

§ 2. Introductory considerations.

When in the gaseous state two oxygen molecules come so near
to each other that there arise mutual forces between them, these
forces will generally form a couple, so that the molecules have
a directing influence on each other. When we take the statistical
mean and when we treat the electric field of the molecule to the
first approximation as that of a quadrupole, it is due to this direc-
ting action that there remains an attraction between the molecules,
which becomes manifest in the equation of state as the attraction
term introduced by van per WaAALs. *)

When we desire to investigate what influence this directing
action will have on the susceptibility, we must take into consi-
deration the relative position of the electric quadrupolar axis and the
magnetie dipolar axis in the oxygen molecules. In doing this we shall
assume these two axes to have a fixed position in the molecule.

Then we may distinguish the following three cases:

a. the magnetic dipolar axis coincides with the quadrupolar
axis; 6. the magnetic dipolar axis is perpendicular to the quadru-
‚polar axis and c. they form an arbitrary angle with each other.

In this paper only the two extreme cases viz. a and 6 will be treated.

First we shall consider case a viz. where magnetic axis and
quadrupolar axis coincide. This assumption would seem the more
preferable, for all our considerations in this paper will be based
on the validity of the laws of equipartition; and in that case only
assumption « gives the right value for the specific heat in the
gaseous state.

First we shall investigate the influence on the susceptibility of
the mutual directing action, which the molecules also exert on
each other because of their quadrupolar forces, when the gas is
placed in a magnetic field. We may then imagine, that by these

attracting actions all molecules would be

8 anited to form double molecules as has been
represented in fig. 1 viz. that one of the two
electric poles of one molecule lies against the
7 equator of the other molecule (either one

Heet magnetic axis, or both may also have direc-

tions opposite to those indicated in the figure).

1) Comp. W. H. KeEsom. Comm. No. 65. These Proceedings 23, p. 943.
73

Proceedings Royal Acad. Amsterdam. Vol. XXIII.

1130

The magnetic moment of the double molecule will then be
u, V2, when that of a single molecule is u,. As in the formula of
LANGEVIN for the susceptibility

1 np?
the number of magnetic molecules is now reduced to half its
original value, the susceptibility is proved to have remained un-
changed.

It is only when we take into consideration that the directing
action of the quadrupoles, though the most considerable one for
small distances between the molecules, is not the only directing
influence and that at the same time we must consider the directing
„action of the external field or that of the action of the magnetic
dipoles on each other, that we fiud a change in the susceptibility.
The calculation and discussion of this change will be given in §§3
and 4 under the assumption that the quadrupolar axis and the mag-
netic dipolar axis coincide. In $$ 5 and 6 the case will be treated
in which these axes are perpendicular to each other.

§ 3. Spherical quadrupolar molecules, having a magnetic dipolar
moment in the direction of their quadrupolar axis, in a magnetic field.

We shall suppose the density of the gas to be such that we have
only to consider pairs of molecules and single molecules, while
collisions of three or more molecules are so rare that they may be
neglected.

In tig. 2 let OA be the direction of the line connecting the centres
of the two molecules of a pair, which line we shall draw in the
direction from the second molecule to the first one. Let OQ, and
OQ, be the directions of the quadrupolar axes of the first and the
second molecule, chosen in the sense that OQ, and OQ, at the same
time indicate the directions of the magnetic axes. Then a pair of
molecules is characterized and its orientation
with respect to the magnetic field is defined
by the codrdinates :

rw. Ps 0.

Here x may vary between O and a,
between 0 and 22, while for 7,6,,6, and p
we may refer to Leiden Comm. Suppl. N°.
39a § 2").

Fig. 2. The potential energy of the pair of mole-

1) These Proceedings 18, p. 636, 1915.

1131

cules due to the quadrupolar forces is then, according to the above
mentioned communication, *):

lg =v, —- ¥ > oS AV Meets)
r
in which
Pe AB cos P AG cos apel ee ER
and
A = 2 (13 cos* 0) (1-3 cos? 0)
B= 16 sin 9, cos G, sin 4, cos O, Ee a vee
C= sn Dan 0. |
Here
3,”
Me Fe. Mentha. guy dese (7)

(u, = quadrupolar moment) is the potential energy due to the qua-
drupolar forces, when the molecules are in contact while the two
quadrupolar axes are perpendicular to each other and to the line
connecting the centres ’).

The potential energy of the pair of molecules ane to the magnetic
dipoles is given by °*)

o?
i ae aed RE ih meres iy sO)
in which
ee
Un or . . . . . . . . . . (9)

(u, = magnetic dipolar moment), and
B= 2 cos 6, cos 0, + sinO, snO,cosp . . . . (10)

For the potential energy of the magnetic dipoles in the magnetic
field we find

Wy = RA eg dee. at =). on CLE)
in which

$2 = cos x (cos 0, — cos 6,) — sin x {sin O, cos Wp + sin O, cos (W + p)}. (12)

1) Comp. also these Communications No. 6b § 3, These Proceedings 23,
p. 943, 1920. As, in this paper, we have only to do with pairs of molecules
and not with groups of three and more, we shall simplify the notations for
the energy by writing for example for the potential energy of a definite pair
of molecules uw, while until now we have written zp).

3) In this paper we shall neglect the action of induction between the
molecules. In Comm. No. 66 it has been proved that this action is of no
importance compared with that of the quadrupoles.

5) Leiden Comm. Suppl. No. 246 § 6. These Proceedings June 1912, p. 256.

73*

1132

The total potential energy of the pair of molecules is then:
“tg Um Fr UH SG eee (13)
The two molecules of the pair together contribute to the mag-
netic moment in the direction of the field AZ the amount:
BO or ee
The number of pairs of molecules in the element
dr dy dO, dO, dw dp
of the x, x, 0, As, W, p-hyper-space is, according to Leiden Comm.
Suppl. N°. 246 equation (49):
NR Np je 7
———e r'siny sin 0, sin @, dr dy dO, dO,dpdp . . (15)
16 ” v
These pairs contribute to the magnetic moment in the direction
of H the amount:

nx 2n 2n

La ele —hu
se arf INNNE ‘ Qr’ sin y sind, sin, drdy dO, dO, dw dp.(16)
nv 4
¢ 00.0 0 0

Here n has been written for the number of molecules in the

volume v of the gas and 4 = a
The mean contribution of each single molecule is, when we
consider only the first two terms in the development:

1 1
pi hie, — em (hHu) 2 2 2 2. (IN)

Their number is found by diminishing n by twice the expression
(15), integrated over all variables. The contribution of the single
molecules added to (16) gives:

1 iat
gem, hip, E op a (itu, 7

THU Wn Br

B wad Le “2 + Sha, — Fe er | i

700000
sin y sin 0, sin 6, dr dy dO, dO, dw dy.

If the mutual action of the quadrupoles and of the dipoles were
neglected, then these molecules would give a magnetic moment
that might be obtained from (18) by substituting a MH tonen
This mutual action thus gives rise to an increase of the magnetic
moment of the gas. This increase has the value:

1133

omtnn An Wn

—hu rz —hu H ce
AM == — iene “oS |. En ‚Hu,

50000 (19)

2
i ips (hHu,)’ te sin x sin @, sin 6, dr dy dO, d6, dw dip,

in which we may take oo as upper limit for r. For the calculation
of (19) we develop the expression in series using (4), (8), and
(11). Viz:

hu H 2 2 5 1
— € Q + eae = 2+ a Hu, (2-38 2*) —

(20)
fi Ol) (423) — — WR (4308241529) .
hu He) o* pupae
é qo mls heg When mae "© +4 4 (hvg y pie U 4 +
a o° 1 os
de hv, hom. re WD $ (hom) . re DE 6 (Av,)" im Bar (21)

13 11

— 4 (Avg)? bd ° wtp thy (hUm)? se wo (he ) : Pp?
CO en ri? 2 q° m ee 6 m r ae

„We may then calculate the different terms of (19) separately.
The term 2 in Wh gives no contribution.

Only the term: 5 bin, (2—32’) in (20) can give a contribution

proportional with H.

We can easily prove that w/(2—32*) where / is a positive
integer, gives 0 when integrated with respect to y and w.

From this it is evident, that the directing action of the quadru-
polar forces on the susceptibility has no influence that might be
expressed in (2) by a A independent of H.

Of the terms written in (21) only ¥?® and ®° give contribu-
tions when multiplied by 2—3 (2?; viz when we put

1
Whip, BORLAND GAT Sk ble (OA
Rens Rt 23
Mm = OTE n0* (hvg)* . hom. habana
und
ln4
A M= 75 7 3 no? (hum )* Mebel ED: ae IC N (236)

Further W? gives when multiplied by 4—30 2? + 15 @*:

1134

0 = age eg 70" inal (hHu)' M . . . (23)

Of these contributions AM, is due to the directing action of the
quadrupoles, AM, to that of the magnetic dipoles, AM „ to the
combined action of the quadrupoles and dipoles. They form the first

terms of developments in ascending powers of h, hence of 7’—.

§ 4. The values derived in the preceeding § for the influence of
the above mentioned mutual directing actions on the magnetisation
become manifest in the susceptibility by the introduction into (2)
of the terms Agn, Am, Ag. These then become:

128 n 4 wn

Ee aoe pee AD
2205 » 3 KT) kT
ln 4 Um 8

A ee ER ree ah oe ee
75 asen. (=) Ge

128" n 4 PEEN
Arle Sg Ee GUL
q 11025» 3 °° (25) (Gr) sas

The sign of none of these A’s agrees‘) with that of the A found
experimentally for liquid oxygen (§ 1). Further A,,, and A,, prove
to be proportional to 7-2, An to 7-S and also to H*, while the
observations give no indications of such a dependence of A on 7’
and H.

To form us a better judgment of the magnitude of the influence
that might be exerted on the susceptibility by the above mentioned
mutual directing actions we shall calculate, for special circum-
stances, the values of the above derived A’s for oxygen. For this
purpose we may take from Comm. N°. 6a §2: vg = 5,7 x 10714
and 6 = 2,65 « 10-8; further from the same Comm. §3: u, == 2,6 Xx
2 10-9, so that according to (9): vn, = 3,7 X 10—".

Let us consider oxygen in the gaseous state at 90° K. under the

fate the = eee ay Olea te ent ae

v3
—16) . Vg — ky Pee : 7 i ain A,,, = —
10-16) : Uae iT 0.0030. By this we obtain A „== —0,0022,
Arme 2 C10.

Hu,

’

When further we put H = 55000, then
Ag = — 0,002.

!) That the mutual action of the magnetic dipoles has an effect in the
opposite direction, has already been remarked by LANGEVIN l.c. note 2
p. 1128. This result does not agree with that of Gans l.c. note 1, p. 1128.

= 0,12, which gives

1135

From these results we see that even in highly compressed oxygen
and, as regards to Ag, in the strongest fields, these A’s will be
negligible.

When we take into consideration that the contributions found in
(23a) and (23c) are only the first terms in series of ascending powers
of hv, ($4 the end) and that in our case Av, is about 4.7, then it
is evidently quite possible that the further terms in that development
will preponderate. Even then those terms might be almost negligible,
but further the value of A that we should obtain by using those
terms would show a still greater dependence on 7 than was the
case with the values given in (24) (unless over a certain temperature
interval a very special compensation might occur). Then it, would
still less agree with a value of A that may be regarded as constant
throughout a certain temperature region.

Thus an explanation of the experimental deviation from Curie'’s
law, based on the directing action of the electrostatic forces between
the molecules seems to be excluded, unless the directing action
occurring in the liquid state might preponderate to a special degree.

In the following §§ will be shown, that this conclusion remains
valid also when we suppose the magnetic dipolar axis to be per-
pendicular ') to the quadrupolar axis.

§ 5. Spherical quadrupolar molecules, with a magnetic dipolar
moment in a fixed direction perpendicular to the quadrupolar aavs,
in a magnetic field.

In Fig. 3 OQ, and OQ, again
represent the directions of the qua-
drupolar axes of the two molecules.
The directions of the magnetic dipo-
lar axes have now been indicated
'-by OB, and OB,, fixed by the angles
w, and w, (from O to 27) and
Ook = e= 00

We shall now follow step by step
the calculations of § 3, of the for-
mulae given there we have only to
change the following ones. We now
have the coördinates:

wr tn POD 0
The potential energy of the pair of molecules due to the mag-

Fig. 3.

) Comp. W. Pau. Jr., Physik. Zs. 21, p. 615, 1920.

1136

netic dipoles is now given by (8) and (9) if we merely substitute
in (10) 0,’,0,’ and p’ (fig. 3) for 6,,6, and g.
We thus find:

DP = 2cosw,cosw,sinO ,sinO, + cosp (sinw,sinw, + cosw,cosw,cosO ,cosO,) +

25
+ sin p (cos w, sin w, cos 0, — sin w, cos w, cos O,) (22)
Instead of (12) we obtain
2 = cosy (cos w, sin A, — cos w, sinG,) + siny {cos w, cos, cos | (26)

+ sina, sin + cos, cos A, cos (W + @) + sina, sin (W + g)i \
ab dw, dw,, while (16), (18) and (19) un-
dergo similar changes, where the integrations with respect to w,
and w, have to be extended from O0 to 22.

The term {2 in (20) again gives zero.

This is also the case with WY! (2—3 9’), / being a positive integer,
so that the conclusion drawn in § 3 remains valid here also.

Again we find contributions due to 2—3 2? multiplied by 4»
and ®? viz.

(15) is multiplied by

AMon = = —— — — XG" (AD) ROn MU, (Ale)
v

while for AJZ,, (236) is found again, as might have been expected
for this term is independent of the quadrupolar forces and hence
the situation of the dipolar axis with respect to the quadrupolar
axis is without influence on AM.

Further Y when multiplied by 4—380 2* + 15 2* gives a con-
tribution :

DM ae a OY, hog (ABG) MS. 878)
v

§ 6. The values of Am and A, corresponding to the AM, and
AM, found in § 4, may now easily be written down. Both have
now the sign agreeing with the observations.

For the circumstances chosen in § 4 we have now (for oxygen):
Agm = 0.0041, A, = 0.0013. From this we see that the conclusions
of § 4 are also valid assuming that the dipolar axis is perpendicular
to the quadrupolar axis.

Geology. — “Quaternary and Tertiary Limestones of North-New
Guinea between the Tami-, and the Biri-river basins’. By
Dr. L. Rurren. (Correspondent of the Academy).

(Communicated at the meeting of February 26, 1921).

In arranging the rocks, collected by the New Guinea-Expedition
of 1903, it appeared that in the coastal region of North-New Guinea
between the Tami-river and Walckenaers-bay, folded deposits of
tertiary age and limestones, belonging to a quaternary transgression,
are widely spread along with old basic eruptive rocks and scarce
mesozoic sediments *).

The tertiary deposits have afterwards been found in the region
of the 141% meridian comparatively far into the interior: limestones
with Lepidocyeclina were met with in the Upper course of the
Bewani-river (Basin of the Tami) and of the Keerom-river, about
66 km. from the coast’). It seems that tertiary deposits play an
important part in this zone, which lies between the coast and the
large central plain, through which the affluents of the Idenburg-river
are flowing.

As known, the Mamberamoriver equally breaks — about 300 km.
to the West — through a young folded mountainrange, called the Van
Rees-mountains, which are built up chiefly of young tertiary sand-
stones, shales and limestones with dykes of eruptive rocks.
Likewise it is known that older, basic eruptiva and mesozoic
sediments are of rare occurrence here’). The strike in the Van
Rees-mountains is S. 65° to 5.E., so it might be expected that the
tertiary folded mountains could also be found in the region between
the Van Rees-mountains and the Tami-river, while the a priori
conclusion might be made that here indications were tu be found
of the occurrence of older basic eruptiva.

For the “Bataafsche Petroleum-Maatschappij” I recently examined
a collection of limestones and marls, collected by Dr. W. van Horsr

1) A. WicHMANN. Nova Guinea. IV, 1917.
L. Rurren. Nova Guinea. VI. 1914.
2) L. ScHuLtTzg. Mitteilungen aus den Deutschen Schutzgebieten. Ergänz. Heft
11. Berlijn 1914.
8) J. van GexpeEr. Jaarb. Mijnw. Nederl. Indië. 1910. Wetensch. Gedeelte.
p. 87 —112.

1138

PeLLEKAAN in the territory between Tami- and Biri-river, and
originating from localities, at the farthest some 50 km. from the
shore. The results of this investigation, the publication of which
was so liberally permitted by the “Bataafsche Petroleum-Maatschappij’’,
evidenced that we were right in supposing that tertiary and especially
neogene sediments are widely spread over the whole coastal moun-
tain range between the Tami-, and the Biri-river, while also indi-
cations were present of the occurrence of older, basic eruptive rocks.

What has been stated above will appear from the following
description of a number of thin sections.

-R/Bo nuslle
IG.

JJ: £SO00 000

Previous investigations tended to show that eocene rocks are of
rare occurrence in the coastal region of North-New Guinea. Hitherto
we know only boulders of eocene reeflimestone from the Tawarin-
river *), which however cannot be derived from the present riverbasin.
WICHMANN suspects that their mother-rock is to be looked for in the
territory of the Sermuwai, which rises much farther in the interior’).

This hypothesis tallies with the fact that the collection Housr
PELLEKAAN also comprises only two eocene limestones, which were
found in the river Nanggoi in the South-Nimboran Mountains i.e. in
the basin of the river Sermuwai. They are two blackish-grey rocks
of reeflimestone. The one contains Alveolina s.str., the other Alveo-
lina s.str., Lithothamnium, Nummulites cf. Bagalensis Verb. and
Orthophragmina; their age is doubtless eocene.

By far the greater number of the collection are of oligomiocene
age, and belong to the Lepidocyclina-bearing neogene. They all

1) Nova Guinea. VI. p. 35.
3) Nova Guinea. IV. p. 266—267.

1139

indicate the occurrence of neogene deposits in litoral facies. The
material examined did not yield sufficient data to make a subdivision
into older and younger levels. The rocks comprised in this collection
are the following:

Pure, porous limestone, south of Nafri, Humboldt bay. No terri-
genous material. Contains: Lepidocyclina ef. Munieri Lem. et Douv.,
Globigerina, ? Cycloclypeus, ? Carpenteria and Corals.

Yellowish-grey, highly crystalline limestones from the Singringreng-
river, south of the Nimboran mountains. Contains large and small
Lepidocyclinae, Rotalidae and Lithothamnium.

Slightly porous limestone from the Sg. Tung, Botbotna moun-
tains with small Lepidocyclinae, Miogypsina, ? Carpenteria conoidea
Rutten, Nummulites ef. Cuminghii Carp., Amphistegina, Operculina,
? Cycloclypeus, Rotalidae, Lithothamnium and corals. From the same
river a greenish gray reeflimestone, including the same faunula as
the preceding and besides these fragments of serpentine-grains,
indicative of the occurrence in the vicinity of a subsoil of basic
eruptiva.

Two yellowish grey reeflimestones from the river Ohung, right
affluent of the river Sermuwai near the village of Sawé, with Lepi-
doeyelina cf. Munieri Lem. et Douv., Operculina, Amphistegina, ?
Cyeloelypeus, Nummulites cf. Cuminghii Carp., ? Carpenteria, Globi-
gerina, Orbulina, Lithothamnium and corals.

Four limestones from the river Buarim, southwestern affluent of
the river Sermuwai with Lepidocyclina ef. Munieri Lem. et Douv.,
Miogypsina, ? Carpenteria, Amphistegina, Gypsina cf. inhaerens, ?
Planorbulina larvata P. a. J., ? Cycloclypeus, Miliola, Globigerina,
Lithothamnium, Halimeda and corals.

A greenish calcareous rock from the river Gisé, north of the
Botbotna-mountains with an abundance of quartzgrains, and few
plagioclase splinters and serpentine grains. It contains small Lepi-
doeyelinae, ? Cycloclypeus, Amphistegina, Globigerina and Litho-
thamnium.

Different limestone-boulders from conglomerates at the middle
course of the Biri-river with Lepidocyclina, ? Miogypsina, Hetero-
stegina, Operculina, Cycloclypeus, Amphistegina, Globigerina, Carpen-
teria, Miliola, Lithothamnium, Halimeda and corals. One sample
contains serpentine grains.

A reeflimestone from the South-river, upper course of the Iware,
basin of the Biri, contains Cycloclypeus, Lepidocyclina ef. Munieri
Lem. et Douv., Heterostegina or Spiroclypeus and corals.

A very finely crystalline reeflimestone from Prauw-bivouac, Biri-

1140

river contains small Lepidocyclinae, Globigerina and: Lithothamnium.

Of a number of rocks, which are specially characterized by the
occurrence of numerous Globigerinae, the age cannot be established
with certainty. Since their localities are often the same as those of
the Lepidocyclina-bearing rocks it may be that some of them are
of the same age as these rocks and were formed under somewhat
different circumstances viz. in somewhat deeper water.

A marly limestone with many Globigerinae comes from the river
Urbiahua, Tamibasin.

A greyish green limestone with Globigerinae and a few quartz
splinters was found at Sentanilake opposite Dondai.

In the peninsula of Morni, Matterer bay a green marl-lime with
quartz- and plagioclase splinters and a few Globigerina was found.

The Ajer Dambé, Demta-bay, produced a grey marl-line rich in
grey Globigerina.

Tuffacous lime-sandstones with quartz-, plagioclase-, and serpentine-
grains and with scarce Globigerina originate from the vicinity of
the Muris-bay.

Brown marl-limes with pyrite-granules, Globigerina, Pulvinulina,
and Rotalidae were found in the Sg. Gauw, South Nimboran-mountains.

A limestone rich in pyrite with very many Globigerina, Amphi-
stegina, Operculina, and corals comes from the Sawé-hill, Sermuwai-
river. The facies of this rock is intermediate between the reeflimes
and the true Globigerina-rocks.

A limestone from the river Gemuwai appeared to be almost quite
a breccia of Globigerina and Pulvinulina.

Whereas it is possible that of the above Globigerina-rocks some
already belong to the quaternary transgression, this is far more
probable for some single limestones which, it is true, do not contain
characteristic fossils, but whose habitus gives the impression that
they are true ‘Karang’’-samples, “very young reeflimestones”. They
are porous limestones from the Muris- and Demta-bay.

Of four reeflimestones (Sekanto-river, Middle Biririver, Upper
Biririver and Iwarinriver in the Gautier Mountains the exact age
cannot be given, but they are certainly of post-cretaceous age.

It appears from the foregoing that all the limestones described
belong to the post-cretaceous system, while eocene rocks are only
very scarce. Two other rather considerably recrystallized limestones
(from village of Semenaré and from the Cyclop mountains) which
do not contain recognizable fossils, were the only ones in the col-
lection which probably were of pretertiary age, though they also
may be young.

1141

By far the majority of the rocks belong to the Lepidocyclina-
bearing tertiary and point to the vast diffusion of neogene deposits
in litoral facies.

Finally the assumption is admissible ‘that the material also contains
very young, most likely quaternary reeflimestones.

Utrecht, January 15, 1921.

Geology. — “On the Age of the Tertiary Oil-bearing Deposits of
the Peninsula of Klias and Pulu Labuan (N. W. Borneo).”
By Dr. L. Rurren. (Correspondent of the Academy).

(Communicated at the meeting of February 26, 1921).

On the geological map of Borneo published by Tx. Posewrrz *)
a broad band of tertiary deposits is marked along the north-west
coast of the island and on the island of Labuan. It extends
from South-Serawak to the Northern point of Borneo. It is not
known to which subdivisions of the Tertiary these deposits generally
belong. T. Britor?) who was the first to report the existence
of coal on the island of Labuan does not say anything about its
age. J. Mor.ny*) who described the coal formation of Labuan rather
minutely, is convinced that it is of tertiary age, but he does not
positively say to which subdivision of the Tertiary it belongs.
Ta. Posewirz‘), however, records that Morrey considered the tertiary
of Labuan to be eocene. C. Scumipt also says that nearly all older
writers took the tertiary of Labuan and of the Peninsula of Klias
to be eocene and even points to the petrographic analogy between
the deposits of Klias and the rocks of Pulu Laut, to the South-east
of Borneo®). A. V. Jenninas*) described eocene Orbitoids from more
Southern territories of North-West Borneo; they were found along
the Barram river near Langusan (Batu Gading) and to the South
of Barram river (Silungen). Nuwron and HorLAND?) demonstrated
that in these southern territories oligomiocene rocks must occur
along with eocene rocks; they found in boulders from the Sungei

1) Ta. Posewitz. Borneo. Berlin. 1889.

*) T. BeLtor. On the discovery of coal on the island of Labuan, Borneo. Quart.
Journ. Geol. Soc. London. 4. 1846. p. 50.

8) J. Morrrey. Report on the geological phenomena on the island of Labuan
etc. Journ. of the Indian Archipelago VI. 1852. p. 555—573. Cf. also: Quart.
Journ. Geol. Soc. London 9. 1853. p. 54—57.

4) Tu. Posewirz. lc. p. 174.

5) CG. Scumipt. Ueber die Geologie von NW-Borneo etc. Gerlands Beitr. zur
Geophysik. VII. 1905. p. 121—135. 1 pl.

6) A. V. Jennines. Note on the orbitoidal limestone of North Borneo. Geol.
Magazine. (3) V. 1888. p. 529—532.

7) R. B. Newron and R. Hottanp. On some tertiary Foraminifera from Borneo.
Ann. and Mag. Nat. Hist. (7) III. 1899. p. 245 — 264.

1143

Malinam (Melinan), an affluent of the Sungei Barram, oligomiocene
Orbitoides (Lepidocyclina Verbeeki Newt. and Holl.) as well as
eocene Orbitoides and Nummulites.

Whereas we know nothing about the nature of the sediments
from which the oligomiocene fossils described by Newton and
HorLanD originate, we have a fair knowledge of the composition
of the deposits of Brunei, Klias and Labuan which are considered
to be eocene. According to C. Scumipt’s (l.c.) descriptions and profiles
we have to do here with an oil-bearing formation of several thousands
of metres thickness, made up of a highly folded series of sand-
stones, marls, shales, limestones, conglomerates and coal. Numerous
oil-localities and important mud-voleanoes prove this formation to
have been rich in oil originally.

In 1914 I received from the late Dr. G. NierHAMMER some frag-
ments of limestone from the tertiary of the peninsula of Klias. Some
time ago Dr. W. Horz of Basle sent me a small collection of rocks
and boring-samples, some of which had been collected by NieTHAMMER,
others by himself. This small collection derives its interest from
belonging to different stratigraphic horizons. A fragment of lime-
stone originates from Pulu Burung to the south of Labuan; according
to C. Scumipr (lc.) the islet rests upon a syncline, so that the lime-
stone is sure to belong to the more recent horizons of the formation.
Another fragment was found by Horz on the small island on the
westcoast of Klias, which, according to Scumipr. was formed during
the eruption of a mud-voleano on the 21st of September 1897 on
the axis of a deeply folded anticline. Various pieces of limestone
were collected on Klias on the surface. From the boring 1 of the
Dutch Colonial Oil-Company on Klias I obtained samples, that were
brought up from depths of from 773 to 1480 feet. Finally Horz
collected a fragment of limestone on a cliff to the north of the
isle of Tega, situated to the North of Klias.

The rock I received from Dr. NieTHAMMER in 1914 is a yellowish-
grey, rather crystalline reef limestone on whose surface with the aid
of a loupe Cycloclypeus communis Martin, Heterostegina depressa
d’Orb., small Lepidocyclines and Corals can be recognized. In thin
sections it can be seen, that some of the Lepidocyclinae are charac-
terized by small dimensions, by scarce thick skeleton-columns centrally
arranged, and by median chambers, which become higher towards
the periphery, and on this account must be classed along with
L. Munieri Lem. et Douv. From one particular specimen we con-
cluded that the fossils are megalospherical and that the embryonic
chambers are of the kidney-shaped type. Furthermore the thin sections

1144

hi

reveal Lithothamnia and Lepidocyclina. Another Lepidocyclina being
of the shape of a double cone and microspherical, could be removed
from the roek; it is closely allied to L. acuta Rutten. From the
absence of Nummulites and large Lepidocyclinae on the one side
and of Miogypsina on the other, and from the presence of L. acuta
we are justified in concluding that the rock belongs to the middle
part of the Lepidocycline-bearing tertiary, and, therefore, is most
likely middle-old-miocene.

It is not impossible that the rock described is derived from the
same finding-place as another limestone of the Horz-collection, which
was found by NreTHAMMER at the Sungei Silico (N°. 499). Here also
may be recognized on the surface Heterostegina, small Lepidocyclinae
and a few larger, flat Lepidocyclinae. In the thin sections of the rock
it can be observed that the limestones are highly crystalline and
that they include numerous Lepidocyclinae. Besides these also Cyclo-
clypeus communis Martin, Heterostegina, Operculina, Carpenteria,
Rotalidae and Lithothamninm occur. Most of the Lepidocyclinae
belong to a small species; the horizontal diameter is from 2—3 mm. ;
the vertical one from 1—1} mm. The fossils are megalospherical
with kidney-shaped embryonic chambers; there are scarce, but very
thick, centrally arranged skeleton-columns; the median chambers
are higher towards the periphery, and often the plane of the median
chambers is continued out of the proper body of the fossil, forming
a collar round the lentoid centre. It is certain, that these fossils
must be grouped along with the Lepidocyclina Munieri Lem. et
Douv. Beyond these, some slightly larger, microspherical forms occur
(horizontal diameter 3—4 mm., vertical diameter 1—14 mm.) distin-
guished from the others by a flatter lentoid shape and by the occur-
rence of numerous skeleton-columns evenly distributed over the
whole body.

Lastly there are some sections of a still larger species, whose
diameter exceeds 6 mm., whose height, however, is no more than
14 mm. It is evident, then that the fossils are very flat and the height
of the chambers is accordingly insignificant. Probably they are
microspherical. True skeleton-columns there are none, but the vertical
walls between the lateral chambers are thickened rather considerably.
Whereas the two forms first described belong still to the “ordinary”
small Lepidocyclina, which characterize the middle-, and the most
recent part of. the Lepidocyclina-bearing tertiary, the last-described
form already begins to show analogies to the group of Lep. formosa
Schl. (flatness, larger diameter, absence of skeleton-columns) which
characterizes the lowermost part of the Lepidocyclina-bearing tertiary.

1145

The fossils of the limestone of Sg. Silico nevertheless differ from
the typical L. formosa in having a much smaller diameter. Also this
limestone may just as well be referred to the middle-old-miocene.

The limestone of Pulu Burung south of Labuan, which according
to C. Scamp (l.c.) appears in asyncline, is a true reeflime. J. Motrer
(Le), therefore, was wrong in considering the limestones of this
island to be the sedimentary products of calciferous sources. The
rock is grey, somewhat porous and fairly crystalline. In the thin
sections may be recognized Lithothamnium, Halimeda, Amphistegina,
Miliola, Textularidae, a very few Miogypsinae and a few small Lepi-
docyclinae with a diameter of only 14 mm., of which some still
possess strong columns, others are quite devoid of skeletons. The
presence of Miogypsina and of small degenerated Lepidocyclinae and
the absence of larger Lepidocyclinae points to the fact that the rock
must be referred to the youngest part of the Lepidocyclina-bearing
tertiary, which conclusion is substantiated by the geological obser-
vations in loco.

The rock of the New Island on the west coast of Klias on the
other hand certainly originates from the lower part of the sediment-
series. It is a brownish-gray Foraminifera breccia impregnated with
limonite. The limonitic substance has to some extent filled up the
hollows and the pores of the fossils, through which their structure
bas become very conspicuous. Besides corals, Lithothamnia, Oper-
culina, Heterostegina and Lepidoeyelina ef. Munieri Lem. et Douv.,
here also occur larger, megalospherical Lepidocyclinae of the Eulepi-
dina type. They differ little in size from the typical forms of
L. formosa Schl., with which they have in common the considerable
flatness, the structure of the embryonic chambers, the absence of
columns and the considerable thickness of the vertical walls between
the lateral chambers.

Two marly limestones, found by G. NierHammer in the rivulets
Napassu and Blanot, do not include any typical fossils.

The samples from the boring N° 1 of the Dutch Colonial Oi!
Company are chiefly hard, gray, sometimes somewhat marly clay-
shales, very much like the clayshales from the oldest miocene and
the oligocene of East-Borneo (samples of 773’, 825’, 830’, 975
980’, 1000’ and 1480’). Sometimes sands or sandstones appear
(1415—1420’). On various levels Foraminifera were found in the
marly clayshales, of which the samples presented faunulae that
differed with the depth at which they. were found. At 800’ 1300’,
1308—1312’, 138830—1335’, and at 1342’ we found besides indiffe-
rent forms such as Heterostegina and Cristellaria only small Lepi-

74

Proceedings Royal Acad. Amsterdam. Vol. XXIII.

1146

docyclinae, which belonged to various species (L. aff. Mumeri Lem.
et Douv., L. aff. inflata Provale, L. sp.). I shall not enter into their
specific determination or their description, since they are of no
special value for stratigraphy. At 1355’— 1370’ and at 1412—1415’
however we found along with small Lepidocyclinae also larger indi-
viduals, notably the same flat, column-less Kulepidines about 10 mm.
in diameter, which also occur in the limestone of New Island,
but along with them also other forms characterized by having
numerous columns diffused over the whole surface. The former are
allied to L. formosa, the latter are related te L. insulaenatalis JonEs
and CHapmaN. We see, therefore, that these larger forms begin to
appear only in the deeper horizons of the boring.

Whereas all the rocks, described above, certainly belong to one
and the same series of sediments, the habitus of the limestone, found
by Hotz on a lime reef to the north of Pulu Kalumpunian to the
north of Pulu Tega, is different. [t is a grey, pseudo-oolitic rock,
containing a great many Lithothamnia and some Miliolidae, but in
which the typical litoral Foraminifera of the oligomiocene are alto-
gether lacking. This limestone also may belong to the Tertiary, but
it is quite impossible to say to which subdivision.

Our examination of the rocks described above shows first of all
that the oil-formation of Northwest Borneo and more particularly
that of the peninsula of Klias and the island of Labuan is not, as
hitherto assumed, of eocene age, but that its anticlinal cores hardly
reach the oligocene'), the typical large Lepidoeyelina which characte-
rize the oligocene being absent here; neither do we find here reticu-
late Nummulites. (Deeper parts of the boring Klias I, rock from New
Island). The youngest rock examined (limestone from P. Burung
South of Labuan) — which, however, does not yet belong to the
youngest part of the sediments-series — must still be considered to
belong to the miocene s.str.; the fossils, however, prove the rock
to originate from the topmost part of the Lepidocyclina-bearing
tertiary.

It appears then, that a satisfactory stratigraphical concordance
exists between the oil-formations of Northwest- and those of kast-
Borneo.

Both formations originated in the same period of prolonged
sedimentation, attended with subsidence of the sedimentation-regions,

') It may be, of course, that the eocene is developed under the anticlinal cores.
As to this nothing can be said for certain, nor can anything be surmised on the
basis of the examined material.

1147

which probably begins in the oligocene (gas-, and oil-bearing layers
from the core of the Sangatta, Bungalun and Sekurau-anticline in
Kast-Borneo') and continues into the pliocene (oil-layers of P.
Tarakan).

MorLENGRAAFF®) demonstrated a short time ago that the tertiary
oil-deposits of the western part of the East-Indian Archipelago in
the E., S., and S.W., are marginal to the old ‘Sunda-land” and
suspects that genetically the oil-formation of North-West Borneo,
which occupies an analogous situation at the N.W. margin of this
land-mass, is closely related to the oil deposits on the Dutch terri-
tories. This view appears to be correct. According to MOLENGRAAFF’s
conception the origin of the material of the neogene sediments of
N.W. Borneo must be looked for in the South-East, in the old massif
of Borneo. Morrey’s (l.c.) view was diametrically opposite to this
conception. This writer considered the tertiary sediments of Labuan,
Brunei and Klias to be partly sedimentations at a south-eastern coast
of a South-Asiatie continent, partly delta-formations of an enormous
river, which he presumes to have come down from Central-Asia.
To this divergence of opinion we shall revert presently.

We will first call attention to the fact that the margins of the
oligomiocene “Sundaland” will be marked still better by the neogene
reeflimes than by the diffusion of the oil-, and coaldeposits ; the
former, whose facies agrees with those of the recent-tropical reeflimes,
having never been absent from a coastal fringe of any extent, the
latter originating only under certain favourable conditions of sedi-
mentation. The most inward oligomiocene reeflime stones, therefore,
will mark the nearest limit of the border of the island of Borneo
that was washed by the sea during the neogene.

When considering the island from this point of view we see that
there must have been periods in the neogene in which only compar-
atively small portions of Borneo emerged from the sealevel.

Beginning in the north we see that neogene reeflimes are known
of the islands of Balambangan and Banguey*). Of the vicinity of
Kudat | possess a Lepidocyclina-bearing limestone, found there by
Dr. W. Horz. Of the basin of the Sg. Kinebatangan miocene litoral
limes of the G. Gomanton have long been known‘). Of the Batu
Tjinagat the Geol. Institute of Utrecht possesses a Liepidocyclina-

1) L. Rurren. These Proceedings, XIX. 1917. p. 728.

2) G. A. F. Moreneraarr. These Proceedings. XXIII. 1920. p. 440—447.
8) L. Rurren. Samml. Geol. Reichsmus. Leiden. (1) X. 1915. p. 11—17.
4) R. Burren Newton and R. Horranp lc.

74*

1148

containing limestone. While these localities are all pretty near to
the coast and only little is known of the inland in these northern
regions, we see, that farther in the South of East Borneo the litoral
neogene limestones appear more and more towards the interior. Of
the basin of the Berau river I possess Lepidocyclina-bearing lime-
stones from the rivulets Birang and Lassan, collected by Dr. F. Wege.
As known, on Sangkulirang neogene sediments are widely diffused.
Towards the south, certainly as far as South of the Balikpapan Bay,
a coastal belt of rather more than 100 km. in breadth is built
up of folded neogene rocks. We know that not all these sediments
are of marine origin; important and numerous ingressions and
regressions must have taken place’). That these ingressions have
encroached far on the inland once at least, is borne out by the
findings of oligomiocene limestone near Udju Halang’*) and Kiham
Halo*) at the Upper-Mahakam-river. Contiguous with this towards
the south are the old neogene reeflimes of the Middle-Barito-river
near Batu Putihf) and of the Mahangjongriver in the basin of the
Sg. Kapuwas Murang®). Still farther to the south I do not know
of any occurrence of neogene coastal deposits.

When we cross to the Northwest coast of Borneo, we find farthest
into the inland the formation of neogene limestones at the Melinau
river, a left affluent of the Barram-river (BULLEN, Newton and HorLAND
Le). Data produced by J. Morrey (l.c.) seem to point to the existence
on the Redjang-river of neogene deposits of a litoral character. On
the other hand the rocks of Klias and Labuan described above are
all lying in the litoral zone.

On the accompanying map we have, on the basis of all these
data, indicated very roughly which territories of Borneo were not
covered by the sea during the farthest neogene ingression. We see
here a central landmass rather narrow in the North and broadening
towards the South-West, where it is connected with the old Sunda
continent’),

This sketehmap enables us to realize the stupendous changes
undergone by Borneo in the neogene. After the farthest old-

1) L. Rurren. These Proceedings l.c. 1916.

2) |. Provare. Rivista italiana di Paleontologia. XV. Catania 1909. p. 95.

3) N. Wine Easton. Tijdschr. Kon. Ned. Aardr. Gen. (2) 34. 1917. p. 680—695.

4, L. Rurren. Samml. Geol. Reichsm. Leiden. (1) IX. 1914. p. 320—3822.

5) L. Rurren. Samml Geol. Reichsm. Leiden. (1) IX. 1912. p. 218—217.

6) In several places the old central landmass of Borneo was no doubt still
smaller than is shown on the map; but no published data are at our disposal.
On the other hand it is probable that out of this central core, e.g. in the farthest
South East of the island, some territories were not transgressed by the sea.

1149

neogene ingression the central part of the island must have been

subjected to continual upheavals, for only in this way could it

Balaméa agar O Bangucy

7:8000 000.

Batoe Tpenagel

Er # ONE Nt Aiham Helo +

+ Oedjoe Hatlang

pads Ge Sey
Ve Np BaloeNverrp. SEAT

: ys eo ONS oe he + SI
bret reien 27° 5 4 Kiks 5 meyers ty LAP GRAMZOPZ.
bal, Gino mtD. lnedy
°
¢
> °
a had
9 E
6 d
3 qQ
3
ed
°
a
3
x

+ Oligomiocene limestones.

Central core not or only partly covered by the sea during the most significant
neogene ingression.

procure the incredible masses of detritus which were required for

building up the neogene deposits in the East, the South-East, and

the North-West, which are several thousands of metres thick and

which during ‘their deposition, when they had not yet been pushed
up by the latest folding-process, covered a much larger area than
at present. In the neogene period, therefore, the old centre of the
land of Borneo was a very pronounced geanticlinal region, whereas
the marginal zones in the N.W. and S.E. were true geosynclines.

It is probable that the material of the recent deposits in the eastern
syncline came from the West, i.e. entirely from the old Borneo

2

1150

centre; in fact in Sankulirang the deposits become more and more
pelagic, as the sediments lie more eastward, and point to an old
marine territory in Macassar Strait (L. Rurren, l.c. 1916). It does
not seem probable, though, that also the western geosyncline was
bounded in the N.W. by a deep sea. First of all there are factors
pointing to the smaller significance of this geosynclinal territory
than that of the East. The strike of the western geosyncline almost
coincided with the northwest coast of the island as is shown on the
map of C. Scumipr (le). In its south-western elongation nothing is
known of a continuation of the subsided area; we find ourselves
there in the old landmasses of Sambas') and the Natuna-Islands ’).
One is impressed with the idea that the subsided region, which
most likely extended from the Philippines as far as the northwest
coast of Borneo, terminated here. There is still something else. In
1914 1 obtained from Dr. NieTHAMMER a fragment of limestone from
a territory far removed from the Borneo-coast viz. the islet of Man-
galum (see sketchmap). It is an Operculina limestone, which, it is
true, includes only Operculina complanata Defr., and which on that
account may be quaternary as well as tertiary, but it bears a close
resemblance to a Lepidocyclina-bearing Operculina-limestone from
Pulu Labuansklambu near the northwestern point of Borneo. It cannot
be doubted, therefore, but that the the limestone from Mangalum is
still met with in Jitoral facies so far from the coast, so that it seems
highly improbable that the Northwestern geosyncline should have
been bounded in the North-West by a deep sea. It may be deemed
more probable that here lay a subsided area, which at one time
was alternately shallow sea, delta-territory or low land; that it was
bounded on the one side by the old land-centre of Borneo, on the
other by an old continent now transgressed by the Chinese Sea,
and formerly perhaps connected with Indo-China, which is also an
old continental region. According to this view both J. Morey and
MOLENGRAAFF would be right, the former in referring the source of
the material of the tertiary formations of Northwest Borneo to the
Northwest, the latter in looking for it in the South-east. Moreover
this view would also favour the conclusion that the central landmass
of Borneo, which had already to contribute so much detritus towards
the East and the South-East, was somewhat disburdened as to its
contribution towards the Northwest.
Utrecht, 2 Febr 1921.

1) N. Wine Easton. Versl. Geol. Sectie. Geol. Mijnbk. Gen. I. 1914. p. 179—189.
2) P G. Krause. Samml. Geol. Reichsmus. Leiden. (1) V. 1898. p. 221—236.

Chemistry. — ‘““/n-, mono- and divariant equilibria’. XXI. By
Prof. F. A. H. SCHREINEMAKERS.

(Communicated at the meeting of February 26, 1921).

Equilibria of n components in n phases, in which the quantity of
one of the components approaches to zero. The influence of a new
substance on an invariant (P or T) equilibrium. (Continuation).

In communication XX we have examined the influence of a new
substance on the invariant (P or 7’) equilibrium:

| yee OM a eer LY oe (1)

With this we have assumed that L, Z,...are liquids and F, F,...
solid substances of unvariable composition. The general form of this
equilibrium / is:

Disses Sy en oy bes Be
in which G is a gas and M, M,... are mixed crystals, which may
contain all components or not.

When we know the reaction, occurring in this invariant (P or 7’)
equilibrium, then we may deduce again with the aid of (12) and
(15) (XX) which influence has the addition of a new substance.
Now we shall consider some special cases of this equilibrium.

We take the unary equilibrium G +4 Z, viz. an unary liquid in
equilibrium with the vapour; this equilibrium is invariant (P or 7).
As the reaction is L, = G, it follows:

= (Aa) =a — a, = (4 H) = H — H, = (AV) = VV,
in which w, H and V relate to the vapour G.
Now it follows from (12) and (15) (XX):
RT (#@—a#,) RI? (#,—2)

(dT)p = — Beo ato. Wik (3)
RT («—2,)
(dP); = VZV, Er ie edt CE

Herein AW is the heat of evaporation of a molecular quantity
of liquid and V-—J, the increase of volume at the evaporation of
this quantity of liquid. Consequently we refind in (3)-and (4) the
known formula’s. We find, therefore, the rule well-known:

When, at addition of a new substance the concentration of this

1152

substance in the vapour (viz. 2) is larger (smaller) than in the liquid
(viz. w,) then the boiling-point under constant pressure is lowered
(raised) and the vapour-tension at constant 7’ is raised (lowered) ;

when the new substance is not volatile (consequently 2 = 0) then
the boiling-point under constant P is raised and the vaponr-tension
at constant 7’ is lowered.

We consider the invariant (P or 7’) equilibrium
BNG WD PTA AEN A VERA)

viz. a complex of liquids in equilibrium with their vapour G. We
write the reaction which may occur in £:

deiner Aad Phe A A tea een ANE ee ee
When all reaction-coefficients 4,4, ... are positive, then all liquids
take part in the formation of vapour in the ratio 4,:A,:a,...,

then we shall say that the vapour has a “average” composition.
When, however, in (6) one or more of the reaction-coefficients are
negative, then also one or more liquids arise at a time with the
vapour; the vapour has then a ‘‘non-average’ composition.

When we represent by AW the heat, wanted to form one quantity
of vapour, and the corresponding increase of volume by AV, then
AW and AV are positive, unless in very special cases.

Now we may write for (12) and (15) (XX):

he (ae) RT > (42)
———_———————— a —— en

(dT)p = — AW nd (dP)r = AV (7)

Herein is:
= (Ar) =a —(Aa, + Aye, + aa, He.) 2. « . (8)
Now we take a mixture of the liquids Z, Z,... in such a ratio
that it has the same composition as the vapour G. We call this
mixture or complex of phases the “reduced mixture’. As appears
from (6) this mixture has the composition:

An Ba Aa oR uae BY DNA oale sink ener (AN
in which one or more of the coefficients may also be negative.
When the vapour has an average composition, then all coefficients
in (9) are positive; when the vapour, however, has a non-average
composition, then one or more of the coefficients in (9) are negative.
When we put now:

AyHilot Acts dydgtenckiot VERN =) sibs
consequently c is the concentration of the new substance X in the
reduced mixture. Instead of (7) we may write now:

1153

RT? (c—2)
ll od

Hence follows the rule’):

when, on addition of a new substance the concentration of this
substance in the vapour (viz. 2) is larger (smaller) than in the
reduced mixture (viz. ce) then the boiling-point under constant pressure
is lowered (raised) and the vapour-tension is raised (lowered) at
constant temperature. :

Applying those and the following rules and formula (11) we have
to consider to following.

When the vapour has an average composition, then c is positive
when, however, the vapour has a non-average composition, then c
may be as well positive as negative; w—c is then always positive
when c is negative.

When we substitute in the rule above “reduced mixture” by
“liquid” then we refind the rule, which is true for the addition of
a new substance to the unary equilibrium Z + G.

When the added new substance is not volatile, then «=O; (LI)
passes then into:

d, GE 1
an oe AV ZOO

(d7)p =

RT RTe
ema is Le la Dye
Ca AV

When we keep in mind that c may be as well positive as nega-
tive, then we find the rule:

when the vapour has an average composition, then, on addition
of a new substance, the boiling-point under constant pressure shall
be raised and the vapour-tension at constant temperature shall be
lowered ;

when the vapour has a non-average composition, then for c >0
this rule is true also; for c << 0 however an opposite rule is true.

We may for some cases also represent the above results geome-
trically. Let us firstly consider the addition of a new substance to
the binary equilibrium H— L, + L, + G. In figs 1—4 the sides
ZX and ZY of the ternary concentration-diagram are partly drawn:
a,a, and a represent the two liquids and the vapour G of this
equilibrium #. In figs 1 and 3 this vapour a has an average, in
figs 2 and 4 a non-average composition. When, at constant 7 or
P, we add a new substance, then the liquids Z, and ZL, trace the
curves a, 6,c, and a,6,c,; the vapour traces curve abc. Each of the

(dT)p = (12)

1) This rule is deduced already formerly for a definite case, viz. the addition of
a new substance to the binary equilibrium Zj + Lj + G. F. A. H. ScoREINEMAKERS.
Zeitschr. f. Phys. Chem. 38 (1901) 252.

1154

phases oi the ternary equilibrium traces, therefore, a three-phases-
curve. Now we assume that on addition of very little of the new
substance the two liquids and the vapour are represented by the
points 6,6, and 6; consequently these points are situated in the
immediate vicinity of a,a, and a; for sake of clearness they are
drawn however in the figures on greater distance. Relating to the
situation of the vapour-point 5 with respect to the line 6, b, we shall
say that the three-phases-triangle 6, 6,6 turns his vapour-point in
figs 1 and 2 away from the side YZ of the components-triangle and
in figs 3 and 4 towards this side.
When we represent the reaction by

PAs Er ete Oe (he
then is:
Eke, Azo eer ea ees
in wich 4, and 2, are defined by
AAE Tani’ MA A ieee ct eee ey

so that 4, and 4, are linear functions of y. When we consider x
and y in (14) as running coördinates, then 2 (2.x) = 0 represents

Fig. 3.

1155

the equation of the straight line 6, 6,. When we put viz. c=2,
and y= y, then follows from (15) 4,=1 and 4,=0so that S (Az)
= 0; consequently the line goes through the point 6,. In the same
way it is apparent that this line goes through the point 6,. When
the point wy is not situated on the line 6, b,, then 2 (Ax) is not zero,
but positive or negative, in accordance to the situation of this point
on the one or on the other side of this line. Now we imagine in
the figs 1—4 a horizontal line drawn through a; as 6 is situated in
the immediate vicinity of a, this line goes also, by approximation,
through 6; we call 7 the point of intersection of this line with the
line 6, 6,. On this horizontal line in 7 consequently Z (Ax) = 0, at
the right of » 2 (Az) is > O at the left of r 2 (4x) is < 0. Conse-
quently when we trace the line 6, 6, in the direction from 6, towards
6,, then 2 (Av) is at the right of this line positive and negative at
the left of this line.

As in figs 1 and 2 the vapour point 6 is situated at the right of
the line 6,6, consequently (4x) is positive. Therefore, follows
from (7):
| EDA hen W(dP)n > AB LA (16)
which is also indicated in those figures. Hence follows: when we
trace the three phases-curves (viz. a6c, a,b,c, and a,6,c,) beginning
at their binary terminating-points (viz. aa, and a,) then the tempe-
rature decreases under constant pressure and the pressure increases
at constant temperature.

In figs 3 and 4 the vapour-point is situated at the left of the line
6, 6, so that 2 (4x) is negative. Now it follows from (7):

(ETT A05 eM AAP) Jrg DTZ)
which is also indicated in the figs 3 and 4. Hence it follows, there-
fore: when we trace the 3 three-phases-curves, beginning at their
binary terminating-points, then the temperature increases under
constant pressure and the pressure decreases at constant temperature.

We may summarise those results in the following way:

When we trace the three-phases-curves of the ternary equilibrium
L, + L,+ G beginning at their binary terminating-points.

then under constant P the temperature decreases and at constant
T the pressure increases, when the three-phases-triangle turns its
vapour-point away from the side (with the binary terminating-points)
(figs. 1 and 2)

and under constant P the temperature increases and at constant
T the pressure decreases, when the three-phases-triangle turns its
vapour-point towards the side (with the binary terminating-points)
(figs. 3 and 4).

1156

The previous rule is deduced in the supposition that the three-
phases-triangle is situated in the immediate vicinity of the side with
the binary terminating-points. As however by this is determined
the direction in which 7 and P increase or decrease along the
three-phases-curves, the rule remains also true, when the three-
phases-triangle moves further away from this side. When the three-
phases-triangle passes into a straight line, then on the three-phases-
curves a point of maximum or minimum pressure occurs.

The previous considerations are also valid when the added new
substance is not volatile. The threephases-curve a 6c, which indicates
the composition of the vapour, however, then not goes from a into
the triangle, but it falls on the side YZ. Of the three-phases-triangle
bb, 6, the angle-points 6, and 6, are situated, therefore, within the
concentration-diagram, but, as is drawn in fig. 5, the point b is
situated on YZ in the immediate vicinity of point a.

Now we shall indicate by s the point
of intersection of 6,6, with the side
YZ, in fig. 5 this point of intersection —
2 is drawn, inthe other figures, however,

it is not drawn. We may now disting-

uish two cases, viz.

1° the point a (and consequently

also 6) is situated on the other side of
s as the points a, and a,,.

2° the point a (and consequently

X also 6) is situated on the same side of
Fig. 5. s as the points a, and a,.

The first case is represented in fig. 5, the second in the figs. 3
and 4; we imagine, however, in the two latter figures the point
bon the side YZ in the immediate vicinity of point a. Now we
call those figures the new figures 3 and 4. In those new tigures 3
and 4, the three-phases-triangle 6, 6,6 turns, just as in the old
figures its vapour point 5 towards YZ; in the new figures (dP)r
and (d7’)p have consequently the same sign as is indicated in the
old figures.

Notwithstanding that also in fig. 5 the point 6 is situated on the
side YZ, it is yet apparent that we must say here, that the three-
phases-triangle turns its vapour-point 6 away from the side YZ.
Consequently (d7’)p and (dP)r must have the sign, indicated in
fig. 5.

Consequently on addition of a new substance, which is not volatile,

1157

in the case of the new figures 3 and 4 the boiling-point is raised
under constant P and at constant 7 the vapour-pressure is lowered;

in the case of fig. 5 under constant P the boiling-point is lowered
and at constant 7’ the vapour-pressure is raised.

Kasily we see that this all is also in accordance with the deduc-
tions from formula (12). In fig. 3 the vapour « has a mediate
composition and ¢ in formula (12) is, therefore, positive. In figs 4
and 5 the vapour has a not-mediate composition but e is in fig. 4
still positive, but negative in fig. 5.

The previous considerations are valid still also, when also one of
the components of the binary equilibrium H= L, + L,+ G is not
volatile. When Y is this component which is not-volatile, then in
the figs 1-—5 point a coincides with Z When also the new sub-
stance is not-volatile, then the vapour remains always represented
by point 7; when the new substance is volatile indeed, then the
vapour proceeds along the side ZX. Also in those cases, the boiling-
point shall be raised or lowered under constant P and the vapour-
pressure shall be lowered or raised at constant 7’, dependent on
the situation of the three-phases-triangle.

In a similar way we may deduce also the influence of a new
substance on the ternary, equilibrium H=—1,+ L, + L, + G.
When we represent the reaction by:

Ni li teh be ct Alacer. oreleiai ial (18)
then is:
= (A#) = 2 — 1,2, — 1,4, — 1,2,
and À, 4, and 2, are defined by:
4,+4,+4,=1 Aven allan delle =y » … (19)
dz tthe Agta at Avene

When. we take a regular tetrahedron for concentration-diagram,
then the phases of the ternary equilibrium / are represented by
four points on the side-plane YZU; we shall call those points a,
a, a, and a. When, at constant P, we add a new substance X,
then each phase traces a four-phases-curve; we call those curves
orbi en AS OE C4 sd, O, C,,jand.,a.be.

The four-phases-tetrahedron 6, 6,6, 6 turns now its vapour-point
b either towards the side-plane YZU or away from that plane.
Easily now we find the rule:

when we follow the four-phases-curves of the quaternary equili-
brium L,+ 4,+ Lig + G starting from their ternary terminating-
points, then

under constant P the temperature decreases and at constant 7’

1158

the pressure increases, when the four-phases-tetrahedron turns its
vapour-point away from the side (with the ternary terminating-points)

and under constant P the temperature increases and at constant
T the pressure decreases, when the four-phases-tetrahedron turns its
vapour-point towards the side (with the ternary terminating-points).

We now take en invarient (P or 7’) equilibrium, in which occur,
besides a liquid LZ yet also the mixed-crystals M, M,...; we repre-
sent this equilibrium by

U ROL AIEN BONNEN
and the occurring reaction by:
UI CUM AEM NAE EN ens

Of course one or more of the reaction-coefficients may be nega-
tive. When all coefficients are positive, so that the liquid has a
mediate composition, then (21) represents a congruent melting of the
mixed-erystals; when one or more of the coefficients are negative,
so that the liquid has a not-mediate composition then (21) represents
a conversion of the one of mixed-crystals in the other, with forma-
tion of liquid, consequently an incongruent melting.

We shall call a mixture of the mixed-crystals M, M,... taken
in such ratio, that it has the same composition as the liquid, the
“reduced complex of mixed-crystals’”. Now we have:

= (Aa) 2 — de, Ae, —1,8,—-..Sa—e . . (22)
in which, therefore, c represents the concentration of the new sub-
stance X in the reduced complex of mixed crystals; consequently
c may be as well positive as negative.

Therefore, we obtain again formula (11) in which AW is the
heat, which is necessary for the congruent or incongruent melting,
and AV the change in volume, occurring with this. We may assume
again that in general AW is positive; AV may be, however, posi-
tive or negative.

When we only consider the change of the congruent or incon-
gruent melting-point under constant pressure consequently, then
follows the rule:

when, on addition of a new substance, the concentration of that
substance in the liquid (viz) is greater (smaller) than in the reduced
complex of mixed crystals (viz c) than the (congruent or incongruent)
melting-point of the mixed crystals under constant pressure decreases
(increases).

When the new substance, which is added, does not occur in the
mixed-crystals, then, as #,a#,7,... are zero, also c=0. (11) then
passes into:

1159

RT’ RT «
ae yr ——— 4, 5 a)

en
B AV

AW

Hence it follows:

on addition of a new substance, which does not occur in the
mixed crystals, the (congruent or incongruent) melting-point of the
mixed-crystals under constant pressure is lowered.

We shall briefly consider more in detail the case that a new
substance is added to the binary invariant (P or 7’) equilibrium;
E=M, + M,+ L. For this we imagine that in the figs 1—4 the
points a, a, and a represent the two mixed-crystals M, and M, and
the liquid Z. In the figs 1 and 3 then a congruent melting takes
place and in the figs 2 ‘and 4 an incongruent melting.

When we add at constant 7’ or P a new substance, which occurs
also in the mixed-crystals, so that ternary mixed-crystals occur, then
M, and WM, trace the three-phases-curves a, b,c, and a,6,c,; the
liquid ZL traces the three-phases-curves abc. In figs 1 and 2 the
three-phases-triangle 6, 6,6 turns its liquid-point 6 away from the
side YZ of the components-triangle, in figs 3 and + towards this side.

In a similar-way as with the equilibrium Z, + Z,-+ G we now
find that also for the equilibrium M, + M,-+ L the sign of (d7’)p
must be the same as is indicated in the figs 1—4; this is also valid
for (dAP)r when AV is >0; for AV <0 we must take, however
the opposite sign for (dP)7.

Consequently we find the rule:

when we trace the threephases-curves of the equilibrium M, +
M,+ L starting from their binary terminating-points,

then under constant P the temperature decreases, when the three-
phases-triangle turns its liquid-point away from the side (with the
binary terminating points) (figs 1 and 2),

and under constant P the temperature increases, when the three-
phases-triangle turns its liquid-point towards the side (with the
binary terminating-points) (figs 3 and 4).

The reader himself may easely find the rule for the change of
pressure at constant 7’.

When the added new substance does not occur in the mixed-
crystals, so that those rest binary ones, then in the figs 1—4 the
curves a,b,c, and a,b,c, must coincide with the side YZ. The
three-phases-triangle 6, 6,6 is then always situated with the angle-
points 6, and 6, on the side YZ, while the liquid-point 6 is situated
within the concentration-diagram. Therefore, we imagine in the figs

1160

1 and 2 the points 6, and 6, on YZ in the vicinity of a, and a,
Then from fig. 1 a diagram arises, such
as is drawn in fig. 6.

As the three-phases-triangle now turns
always its liquid point away from the
side YZ, the temperature must, accor-
ding to the previous rule, decrease under
constant P, viz. when we trace the
curves starting from their binary termi-
nating-points. This is in accordance also
with the first formula (23).

In the previous communication XX

Fig. 6. we have deduced the relation:
es dP
(AP) ED) (ie da rode anke ek AU
dl ni)

Hence appears: when in the invariant (P or 7’) equilibrium
(which consequently is monovariant) the pressure increases at increase
of 7, then (dP)r and (d7’)p have opposite signs; when, however,
the pressure decreases at increase of 7’, then (dP)r and (d7’)p have
the same sign. We now may express this in the following way:

we add a new substance to an invariant (P or 7’) equilibrium;

when in this equilibrium the pressure increases at increase of
temperature, then the influence on the pressure at constant 7’ is
opposite to the influence on the temperature under constant P;

when in this equilibrium the pressure decreases at increase of
temperature, then the influence on the pressure at constant 7’ is
the same as the influence on the temperature under constant P.

It is evident that “influence” means here the sign of the change
of pressure of temperature.

Leiden. Inorg. Chem. Lab.

(To be continued).

Physiology. — “On the serological specificity of haemoglobin in
different species of animals”. By K. LANDSTEINER. (Communi-
cated by Prof. C. H. H. Spronck).

(Communicated at the meeting of January 29, 1921).

The knowledge of species-specificity is based principally on morpho-
logical facts, on the phenomena of inheritance and transplantation,
and on serological reactions. The first allow the direct inference
that species-specificity is a property of all the constituents of the
body; serological data, on the other hand — as far as animal
organisms are concerned — bear first of all on the proteins of the
blood serum.

Concerning these latter there exist numerous results of precipitin
tests, of which the greater part were carried out by Nurrats’),
and which may be summarised, that serological relationship in
general corresponds to the zoological classification and that the diffe-
rence of the precipitin reactions increase in a measure corresponding
to the difference in the scale of animal classification.

For the other constituents of the body an analogous relationship
is probable, and is often accepted as a matter of fact; this subject,
however has been far less thoroughly investigated than the properties
of the bloodserum.

Some proteins differ in a greater degree (protein of the eye-lens®)
and the horny substance*)) and others (casein®)) in a smaller
degree from the specificity type mentioned i.e. their specificity is
more or less independant of the animal species. In these cases we
cannot exclude the possibility that the species-specificie structure
although present is concealed by other structures.

Whether the haemagglutinating immune-sera with regard to their
group reactions correspond as well to the zoological classification,
as the before mentioned precipitins, is indeed still doubtful °).

1) NurrarL. Bloodimmunity and bloodrelationship, Cambridge (1904).

2) UHLENHUTH. Festschr. f. Rob. Koch.

8) Krusius. Arch. f. Augenheilk. 67. (1910).

4) VersELL. Zeitschr. f. Immunitätsf. 24. 267. (1915).

5) Cf. Lanpstemer u. Reien. Zeitschr. f. Hyg. 58. 227. (1907).
BROCKMANN. Zeitschr. f. lmmunitätsf. 9. 114 (1911).

75
Proceedings Royal Acad. Amsterdam. Vol. XXIII.

1162

The same applies to the immune sera against the cells of various
organs °). [

As far as the globulins of milk are concerned it may be accepted
as highly probable and experience goes to prove, that they behave
quite similarly to the serum-globulin, and the same may be said
for all proteins which have a very similar chemical composition as
the serum-proteins as regards the kind and quantity of the amino-
acids which build up their molecule.

But when one considers proteins such as haemoglobin which in
their chemical struetures i.e. in their construction out of amino-acids
differ widely from the proteins of the serum, a note-worthy problem
presents itself.

If these bebave in regard to the species specificity similarly to the
serum protein, two possibilities present themselves: either the
species-structure in such proteins and in serum proteins is realised
in wholly different and independent wavs, or else there is a relation
in this way that among the different proteins of a species one
corresponding smaller ov larger group (or several groups) of the
molecule is the bearer of the species-specificity.

In the latter case the problem would arise of demonstrating this
species-specific nucleus. In the other and perhaps less probable case
there would be a similarity of chemical structure of two homologous
proteins in related animal-species, but no chemical similarity would
be found between the different proteins of the same species. From
this it appears indicated to investigate the different proteins as to
their species-specificity and I have, therefore, undertaken the investi-
gation of the precipitins against haemoglobin. This substance is
well suited for the examination of the question raised because the
composition of its protein constituent i.e. of globin varies widely
from that of serum globulins and serum albumins.

LeBLANC*®), Ipk*) and Demees®) were the first to report on the
formation of precipitins against haemoglobin. THOMSEN °) investigated
the question of species-specificity and came to the conclusion that
anaphylaxis against erythrocytes is to a certain extent species-specific.
The greater number of his experiments, as also the researches of

1) SaLus. Bioch. Zeitschr. 60. 1. 1914.

2) La Cellule 18. 337. (1901).

Bee » 20. 263. (1902).

| » 84, 423. (1907).

5) Zeitschr. f. Immunitatsf. 3. 539. (1909). Cf. WeicHarpt. Zeitschr. f. Immunitatsf.
14. 609. (1912). On the specificity of haemoglobin crystals. cf. ReicHert a. BROWN,
Carnegie Institution Publication Washington 1909.

1163

BRADLEY and SANsuM *), were carried out with a blood solution and
not with isolated haemoglobin. In a second series of experiments
with erystallised haemoglobin these authors found that guinea pigs
sensitized with dog’s haemoglobin reacted sfrongly (no acute death)
on dog’s bloodsolution, in a lesser degree with such solutions from
pig, and turtle and not at all with those from fowl, calf, horse, goat,
rabbit, rat, guinea pig, sheep and man. This result does not allow
of a definite conclusion yet.

As the species differences of haemoglobin certainly are due to its
protein components, the experiments on globin ought to be mentioned
here. Browning and Witson *) found a strongly homologous reaction
with an immune serum against guinea pig globin, weak complement
fixation with rabbit-globin, and none with ox-globin. In a recent
publication *) these same anthors find that an immune serum against
ox-globin reacts also on globin of goats, guinea pigs and ducks but
not on rabbit-globin. On this point they state, “Thus while evidence
of species-speciticity exists in certain cases, there is also a wide
though not universal, community of antigenic properties shared by
the globin of widely separated animal-species’’.

It ought still to be mentioned that some time ago ScamipT and
Bennett *) on the ground of some previous (Forp and Harsrv) and
of their own negative findings, deny the ability of haemoglobin to
produce antibodies and they ascribe the positive results to impurities
in the injected materials.

BROWNING and Wirson, who themselves obtained a distinctly active
serum against haemoglobin, believe that they can explain the
negative results in this way, that haemoglobin possesses only a
weak antigenic property. I am inclined to agree with this view ‘),
as in my experiments with 5 animals with intensive immuni-
sation (2 gr. of haemoglobin and more) only one gave a good
active serum, 2 others very weak sera, whereas the sera of the
remaining two were not active at all. I have no cause to doubt
that the reactions obtained are really attributable to the haemoglobin,
seeing that the active sera gave only very weak haemolysis with

1) Journ. Biol. Chem. 18. 497. (1914).

®) Journ. of Path. a. Bact. 14. 174. (1909). Cf. Gay a. Roperrson J. Exper.
Med. 17. 535. (1913).

8) Journ. of Immunol. 5. 417 (1920).

4) Journ. infect. Dis. 25. 207, (1919).

5) Perhaps alteration occur during the process of isolation, which diminish the
antigenic properties.

15%

1164

horse blood and that only a long-continued standing produced a just
perceptible turbidity with dilntions of horse-serum *).

LEBLANC’s *) results also are in favour of the antigenic property
of haemoglobin, for he found, that the haemoglobin is carried down
with the precipitate produced by precipitin-serum.

As I intend further to pursue this investigation I shall perhaps
come back to this point later and also describe more fully the
results which are only shortly sammarised lere.

In my experiments I used for the immunisation of rabbits crystallised horse-
haemoglobin, prepared in the same manner as described by Ipe and Demesgs; i.e.
defribinated horse blood was centrifugalised, the sediment washed five times and
again centrifugalised, the bloodcorpuscles dissolved in etherised water of double
the volume of the original blood, kept in the icechest for one or two days, and
during this time repeatedly shaken, and finally decanted to get rid of any sediment
which might eventuaily still be present. In order to free it from stromata and
globulin, it was mixed with an equal volume of saturated ammonium sulphate
solution, the precipitate filtered off through a folded filter. To the clear filtrate
ammonium-sulphate crystals were added until the haemoglobin (standing in the
cold) was precipitated, the filtered precipitate washed with ammonium sulphate
solution, suspended or dissolved in water, some ether added and the mixture
dialysed. Finally 10/, of sodium chloride was added.

In the test tube experiments I took solutions which had been prepared from
very well washed blood corpuscles with water and ether, the water amounting
to twice the blood volume. The solutions were completely freed from susupended
matter by filtration through an asbestos filter. In the case of horseblood, moreover,
the solution of crystallised haemoglobin was used.

The tests for specificity gave the following result.

Technique of the experiments: The 5°/) haemoglobin solution was diluted to 1 :
500 and 0.2 ce. of this taken. To this were added 3 capillary drops of 0.04 ce.
each, of immune serum and left to stand one hour at room temperature and the
reading taken. Horse-serum diluted 500 times.

Tests were also made with all solutions in dilutions of 1 : 100 and 1 : 2.500.
They are not given in detail because they agree with the experiments of the 1:
500 dilution.

Haemoglobin solutions. serum
~ wv | = |
ag Sie Woe SAD ern EEN oh
cS i | 3 2 o
BA Sais) Se ENE
Gg ee RAG ap dan 0 of +] oo 0

1) A solution of the horse haemoglobin reacted in the same manner against an
ordinary anti-horse precipitin.
2) Ipe. le. p. 263.

1165

According to these tests, the species-specificity of haemoglobin is
certainly not much less marked than that of the serum-protein.

Somewhat striking is the fairly strong reaction with mouse-blood,
yet similar reactions are also known to occur in the case of pre-
cipitin reactions with serum albumin. It would be interesting to
prove, whether the group reaction mentioned also takes place with
Other precipitin sera against horse-haemoglobin. After the tests had
stood about 20 hours some further weak group-reactions were
observed.

A reaction for haemoglobin solutions generally succeeds with the
help of the inhibition test *). If to the tests, containing the quantities
of horse-haemoglobin and the corresponding immune-serum mentioned
above, 0.05 cc. of a 1°/, solution of haemoglobin belonging to
different animal species was added, an inhibition of the precipitation
took place, which as experiments with the addition of smaller
quantities of haemoglobin showed, was with one pul strongest
in the case of horse and ass haemoglobin.

Haemoglobin solutions.
| |
horse ass | dog | Ox sheep | rabbit aen | |_control
| my
0 | 0 | “0 | 0 | 0 | 0 | On te | tale

I also endeavoured to investigate by means of the inhibition
reaction the question of the presence of a common species-specific
group in serum-protein and haemoglobin. From this it appeared
that by the addition of 0.05 ee. of normal serum belonging to
different animal species, to the mixtures of haemoglobin and their
antibodies, the precipitation was inhibited.

When serum from 11 different species of animals were tested
simultaneously the inhibition was strongest and equally marked in
the case of the serum from the horse, ass and two other kinds of
serum. The result, therefore, does not yet permit of any definite
conclusions. It is, however, possible, that through further variation
(immune bodies against other kinds of haemoglobin) and perhaps
through modifications of the method of experiment, a positive result
will be obtained.

1) LANDSTEINER. Bioch. Z. 98, 115, 104, 280, HALBAN u. LANDSTEINER. Munch.
med. Woch. 1902. NO. 12.

Physiology. — ‘On Heterogenetic Antigen”. By K. LANDSTEINER.
(Communicated by Prof. C. H. H. Spronck).

(Communicated at the meeting of lebruary 26, 1921).

It is well known that Forssman ') discovered the fact, that by injection
of organs of guinea pigs into the rabbit the formation takes place
of a strongly active specific hemolysin against sheep’s blood. It soon
was observed that the same property may be ascribed to the organs
of a large number of animals, e.g. to those of the horse, the cat
and the fowl, whereas these active substances are absent in other
animal species.

These substances are generally called heterogenetic antigens; the
hemolysins generated by their injection are termed heterogenetic
antibodies.

A complete account of the investigations on this subject and their
results will be found in the publications referred to below. In this
paper I shall record only the results regarding the heterogenetic
antigen which are of special interest for my work.

Doerr and Pick?) found that the said substances of the organs
are resistant to the influence of alcohol; Sachs and Grorer’) record
the use of alcoholic extracts, FRIEDBERGER *) (Poor, Suro, SCHIFF) report
the solubility in alcohol of the heterogenetic antigen occurring in
the urine (see Dorrr and Pick) of animals. SorDELL and Frscaer ®)
found that the active constituents of the horse’s kidney can be split
into two fractions by treating with alcohol (and ether), the one of
which fractions, soluble in alcohol, combines in vitro with immune
bodies, but does not bring about immunization, while the part
that is insoluble in alcohol and ether, combines only inappreciably
in vitro; however, 7 generates immune bodies. (SorDELLI and
Pico®) also observed, just as Sacus and GutH’) did, a flocculation

1) J. ForssMan. Biochem. Zeitschr. 3%. pag. 78 (1911).

4) R. Doerr en R. Pick. Biochem. Zeitschr. 50. pag. 129 (1918). :

3) SacHs en GEORG. Zeitschr. f. Immun. 21. pag. 346 (1914).

4) FRIEDBERGER. Berl. Klin. Wochenschr. 1913, N. 34. Zeitschr. f. Immun. 18
pag. 269 (1913) 28. pag. 217 (1919).

6) SORDELLI en FiscHeER. Revista del Inst. Bacteriol. Buenos-Aires. Vol. I. 1918
pag. 229.

6) SoRDELLI en Pico. Revista del Inst. Bacteriol. Buenos-Aires Vol. I. 1919. p. 261.

7) SacHs en GurH. Mediz. Klinik 1920 No. 6.

1167

reaction of the alcoholic organ-extracts with the heterogenetic im-
mune serum).

It is evidently difficult to explain these results as it would seem
as if specific immune bodies against one substance are formed by
the injection of another.

In my experiments, which were performed for the greater part
without my having knowledge of the publications of Sorprrar and
his coworkers, I obtained results that agree with their observations
in main points, as I also found that the alcoholic extracts (and
the ether-extracts) of a horse's kidney — though in vitro their
capacity of combination is very great — do not bring about any
or any appreciable formation of antibodes. However, further exami-
nation induced me to give a modified explanation of this matter.

In my experiments preparations of horse’s kidney were injected
into rabbits. In one of these the procedure was as follows’):

The kidneys were twice ground finely then sifted through a course-mesh-, and
through a fine-mesh-sieve, emulsified with three times their volume of 0.9 per
cent salt solution, placed in the ice-chest for 24 hours, being shaken repeatedly,
and finally percolated (I). The turbid extract was digested with six times the
volume of 95°/, alcohol during two days at room temperature, subsequently
after filtration digested once more for 24 hours with 1 vol. of alcohol and the
insoluble precipitate was taken up in 0.9 per cent salt solution (Il). A third
portion was prepared like II, but here the substance that was obtained by
evaporating the alcoholic extracts to dryness, was emulsified in 0.9 per cent salt
solution, and was added to the suspension of the first precipitate (III). A fourth
portion was digested similarly as to II with alcohol at room-temperature, and then
the precipitate, obtained after filtration, was boiled for half an hour with one volume
of alcohol and the insoluble part was suspended 0.9 per cent salt solution (IV)
and finally the aqueous extract or the suspension was heated for half an hour in
boiling water (V).

All the suspensions were brought to the original volume of the extract, and
0.25 ¥/, phenol was added.

The following table shows the hemolytic action of rabbit’s sera, after
two intraperitioneal injections (at an interval of a week) of the five
extracts described above. The amount of every injection was about
equal to 1 grm of kidney-substance; allowance should here be made
to the fact that in percolating a large portion of the kidney-substance
is left behind.

The dilution of the sera was 1: 250; 0.5 ee. of this dilution
is added 0.5 ec. of guinea pig complement 1:10 and 0.05 °/,
sheep’s blood.

') The subject will be discussed at length elsewhere.

1168

In the following table the degree of hemolysis after one bour is
indicated as follows:

ce = complete; a.c. = almost complete; m — marked; d = distinct;
f= taint; dr = rangs n= none;

Injection of
preparation I {I | Ill | IV Vv
Number of Ae, oa SAT) DS) EE | | |
| | | | IK | |
the rabbits I | 2 | 3 | 4 | 7 | 8 9 me a il ss pe be 21 Pee a
BR 14) KE Pi abs, ie Ua: Wk,
c. jc ew Coke ob. | o. | d. kid | m. 0. | 0. (tr. | tr. ac. C. | c ls
| PSE Se PERU | | | ú

Sera 1, 2 and 4 also dissolved completely in dilutions of 1 : 1000,
1:500, 1:500. The experiment described here, indicate that the
kidney-substance, treated with alcohol at room temperature, has still
the power to generate hemolysins but in a much smaller degree than
the original emulsion. Under the actual conditions this immunizing
capacity was abolished almost completely by boiling with alcohol.
The antigenic property is still well preserved after boiling in aqueous
solution (Dorrr and Pick), although it should be noted that the
serum titre was lower than after the injection of the unheated
material. :

My investigation therefore proved that by treating with alcohol,
substances are brought into solution, which react with hemolysin in
vitro; that however, they have lost their immunizing capacity, and
that the residue which is left after aleohol-extraction, has a much
weaker antigenic property, which is all but abolished after heating
with alcohol.

It seems to me that the most obvious interpretation of the facts
recorded is, that the antigen is made up of a part, that is essential
to immunization and is probably built up of protein, and of anotber
part combined with this, which contains the specific reacting groups
and is perhaps a lipoid. Furthermore it appears, that the latter can
be separated from the former by means of alcohol.

This view is supported chiefly by results obtained in experiments
that I published some time ago’). These experiments proved that
there are substances which probably react specifically in vitro, without
being antigens.

As it will be convenient to have a special name for such

1) K. LANDSTEINER. Biochem. Zeitschr. 93. pag. 106 (1919) Biochem. Zeitschr.
104. pag. 280 (1920).

1169

substances which react specifically with immune serum which however
do not immunize and consequently are not antigens, I propose to
term them as haptens.

As to the chemical composition of these haptens from the horse’s
kidney, I obtained results from preliminary tests, which in some
way correspond with those achieved by Wernicke and Sorperur ?).
However, 1 was not able to prove, whether the data concerning
the solubility of this substance might be confirmed in all points.

If it is true that organs of different animal species, which possess
heterogenetic antigens, contain “compounds of protein and one or
similar haptens, it can be understood that material derived from
quite different sources should bring about the formation of antibodies
producing a similar effect.

The Hague. From the R. K. Hospital Laboratory.

1) WERNICKE en SoRDELLI. Revista del Inst. Bacteriol. Buenos-Aires Vol. IL
p. 281 1919.

Physiology. — “Concerning the Sensitivity to Poisons in Animals
suffering from Avitaminosis.” By W. Storm van LEEUWEN and
EF. Verzar. (Communicated by Prof. R. Magnus).

‘(Communicated at the meeting of November 27, 1920).

E1ikmMan found in 1893 that fowls, fed on polished rice, develop
polyneuritis, and that this disease could be prevented by an under-
milled rice-diet, or by adding to the -polished rice the “silverlayers”
detached from it. He found, moreover, that in man an abundant
diet of polished rice subserved the development of beri-beri, whereas
the disease was not produced, or if already produced, was cured
when the silverlayers had been added to the rice. Later on it
appeared that these findings bear on a special case of a general rule.
Not merely in unhusked rice, but also in all sorts of foodstuffs,
constituents occur that are essential for the normal growth and the
healthy condition of men and animals, even though these foodstuffs
contain an adequate amount of the- proper, long known nutritious
element. These constituents, whose real nature is unknown as yet,
are often classed together as “vitamins”.

Through the latest achievements in this field, notably of American
workers, our knowledge of these things has largely increased. We
now know that the term “vitamin” is not applied to a single sub-
stance, but that it includes various accessory foodstuffs, the fat
soluble A and the water soluble B, and perhaps a third substance
C’; we are also aware that according as various nutritious elements
are wanting in the foodstuffs, the symptoms of a disease may be
widely different and that these symptoms may also be very different
in different animals. Many experimental data concerning the occur-
rence of vitamins in various foodstuffs have been brought forward.
There is one thing, however, of which we must still admit great
ignorance, viz. the causation of the symptoms of the disease, reveal-
ing themselves in animals that suffer from a deficiency of vitamins.
Some hold that under certain conditions this deficiency brings about
a predi8position to infection with certain bacteria, but this supposi-
tion does not afford complete satisfaction and certainly does not
clarify every case.

The symptoms of avitaminosis that present themselves are disorders

1171

in the innervation of the striated muscles, disorders in the innerva-
tion of the unstriated muscular tissue (paralysis of the esophagus
and the gastro-intestinal canal in the fowl, among others) and also
trophical disorders. These disturbances are no doubt partly of a
nervous character; in animals suffering from avitaminoses, e.g. in
fowls attacked by polyneuritis, distinct anomalies occur in the peri-
pheral nerves. These anatomic anomalies, however, cannot be the
decisive factor in the origin of the avitaminosis, since very often in
animals, exhibiting marked symptoms of avitaminosis, an injection
of the vitamins concerned may exert a highly curative effect in a
very short time, so that the animal may practically be cured. This
leads to the conclusion that part of the disorders occurring with
avitaminosis are doubtless functional, i.e. the organs of the animal
do not react on the stimuli present at that moment, but may
recover, or nearly so, their normal function again through the addition
of a special substance: vitamin.

It should seem then that with avitaminosis the condition frequently
occurs that several striated and unstriated muscles do not indeed
react, but that they may be incited to reaction through the addition
of a special substance.

The question, therefore, arises: Why do these striped and smooth
muscles not react?

In our judgment three possibilities must be considered, anyhow so
far as the unstriated muscular tissue is concerned :

Firstly, the organs do not react, because the substance which has
to stimulate the organ is not present in an adequate amount.

Secondly: the organs do not react because their sensitivity to
stimulating substances, even if present in an adequate amount, is
lessened:

Thirdly: the sensitivity of the organs is normal, there is sufficient
quantum of stimulating substances, but specific (colloidal) substances
are wanting in the body of the animals, which have to facilitate or
to promote the action of the stimulating substances through the
organs.

An intimation that influences on the sensitivity of unstriated
muscular tissue are in operation in the symptoms of avitaminosis,
is found in a report by UntmMann'), who showed that in a vitamin-
preparation, orypan, there is a substance which plays an influence on
unstriated muscular tissue which resembles the influence of pilocarpin.

Without having taken any cognizance of UHLMANN’s researches,

1) Fr. ULHMANN. Beiträge zur Pharmakologie der Vitamine. Habilitationsschrift.

1157

Verzak and BöaeL had examined the influence of extracts, which
certainly contained fat soluble A or water soluble B on various
surviving organs, and had found this influence to be inappreciable.
However, since owing to external circumstances, they were not in
a position to examine also the ‘‘vitamin’’-properties of their extracts,
and since their extracts were most likely different from UHrMANN’s,
Untmann’s finding is by no means disqualified by their investigation.

We believe that prior to any endeavour to better understand the
action of vitamins, and to realize the significance of the observations
made by UHLMANN a.o., it is necessary to decide on the three possi-
bilities suggested above.

For this reason we narrowly considered the probability expressed
in the second question by trying to ascertain whether in animals
suffering from avitaminosis a lessened or anyhow altered reaction
on poisons could be demonstrated. Of course, if in this way an
altered reaction was found, it still remained for us to decide whether
this altered reaction rests on a modification of the sensitivity of
the organs (compare sub 2) or would prove to depend on the possi-
bility suggested sub 3.

We experimented with fowls and with cats.

The fowls were fed for some weeks on polished rice. As known,
these animals relish this food at first, but their appetite for it gradu-
ally diminishes and soon they most often show a disinclination to
eat it; then we had recourse to “forced feeding”. Their reaction on
poisons was not examined in these experiments until marked symp-
toms of polyneuritus made themselves evident; some animals were
already moribund during the experiment. We anaesthetized the
animals with ether, registered the bloodpressure and determined the
sensitivity to adrenalin, to cholin and to histamin intravenously ;
we also ascertained how strong the electric current had to be for
the vagus-stimulation to yield a distinct lowering of the bloodpressure,
and subsequently we endeavoured to determine the quantity of
atropin that was required to abolish this influence of the vagus on
the bloodpressure.

After this bloodpressure-experiment the animal was killed and the
gut, in some cases also the esophagus, was removed, put into Tyrode-
solution and the same day or the next we determined the sensitivity
of the surviving gut to pilocarpin, to atropin, afterwards also to
cholin and to histamin.

Not knowing the sensitivity of normal fowls to the above-mentioned
poisons we first examined four normal fowls.

1173

In the four cats which were examined, an avitaminosis was elicited
by means of a prolonged meat-diet, the meat being prepared in the
manner described by Vonarrin '). The meat deprived of its fat and
made alkaline, was heated to 120° in the autoclave for three hours.
This meat, when neutralised by the addition of acid, was relished
by the cats.

In our experiments with cats a special inquiry into the reaction
of normal animals was not necessary, because we had sufficient
data, already obtained in our laboratory, at our disposal.

We wish to call attention to the fact that, although the symptoms,
exhibited in our animals, depended for the major part, anyhow in
fowls, on a deficiency of water soluble B, the food was devoid not
only of one but of several vitamins, and there was also a deficiency
of other foodstuffs; but this did not matter iu our investigation,
considering that we only wished first to ascertain whether a deficiency
of vitamins would at all result in a difference in sensitivity. Had
this inquiry yielded positive results, we still should have had to find
the special vitamin, which was the determinant factor here. Seeing
that the result was negative a more detailed investigation was no
longer needed.

The results of our research will be published in extenso elsewhere.
Suffice it to say here that — beyond expectation — in morbid
animals the reaction did not in any respect differ from that found
in healthy animals. True, there occur rather marked individual
deviations in sensitivity to the poisons examined, but these were not
greater in the diseased animals than in the normal ones.

When we assume that many of the automatic functions of the
unstriated muscles are brought about by chemical stimuli, and when
we see moreover that in many unstriated muscles that function
has lost much of its activity in animals suffering from avitaminosis,
then the result of our researches compels us to believe that in these
diseased animals there is presumably a deficiency of stimulating
substances, and that the receptive organ is not the seat of the
disturbance, and also that the decrease in activity is not brought
about by a deficiency of (colloidal) substances that promote the action
of poisons.

We have already pointed out that UrrMmanN has established that
a vitamin-preparation (orypan), examined by him, acted pharmaco-
logically in a similar way to pilocarpin. On this finding is based

') Cart Voratiin and G. U. Lake, Experimental Mammalian polineuritis produced
by a deficient diet.

1174

the hypothesis that in the case of avitaminosis an impaired function
of many organs is caused by a deficiency of a substance, which is
supposed to be a constituent of “orypan”. We believe that this
problem is not. yet ripe for solution for the simple reason that only
few positive facts are known. We only wish to point out that the
above hypothesis migth be supported by the results of our research.

CONCLUSIONS.

When avitaminosis has been elicited in fowls through a polished
rice diet, or in cats fed on specially prepared meat, the sensitivity
of the animals to adrenalin, histamin, cholin, and atropin, and the
sensitivity of the surviving organs of those animals to histamin,
pilocarpin, atropin and cholin, is unmodified..

In two experiments it was proved that atropin (in doses of from
0,001 mgr. to 1 mgr. added to 75 ce. of Tyrode) had no inhibitive
effect on the guts of fowls suffering from avitaminosis; these guts
performed only faint spontaneous movements. The gut of normal
fowls displayed unmistakable inhibition on the application of atropin.
In view of Le Heux’s experience of the influence of cholin on the
inhibitory or the stimulating effect of atropin on the gut, this would
also lend support to the conception that in hens fed on polished
rice a stimulating substance in the gut is wanting.

Physics. — “The rectilinear diameter of hydrogen”. By E. Marnias,
. C. A. CROMMELIN and H. KAMERLINGH Onnes. Communication
N°. 1546 from the Physical Laboratory at Leiden. (Communi-
cated by Prof. H. KAMERLINGH ONNms).

(Communicated at the meeting of January 29, 1921).

$ 1. Zntroduction. This communication forms the continuation of
a series of contributions to the knowledge of the density-curves for
liquid and saturated vapour and of the diameters, in the case of
substances of low critical temperature and simple molecular struc-
ture. The investigation by means of the dilatometer-method was
started in the Leiden physical laboratory a considerable time ago
and has dealt successively with oxygen *), argon’) and nitrogen *).
Great importance was attached to the extension of the measurements
to hydrogen for the knowledge of its equation of state, especially
in connection with previous determinations of the liquid densities
between boiling point and melting point‘), of the critical point °)
and the various computations of the critical density °) °).

The research could not be carried out, however, until the experi-
mental difficulties had been overcome as regards the construction
of a transparent bath of constant and uniform temperature between
the critical point and the boiling point, i.e. between about — 240°
C. and — 253° C.

§ 2. The apparatus for the compression of hydrogen, the mea-
surement of the liquid and vapour volumes, the determination of
the vapour pressures and that of the volume of the gas under

1) E. MATHIAS and H. KAMERLINGH ONNES, these Proceedings 13, p. 939,
Leiden Comm. NO. 117.

2) E. Matuias, H. KAMERLINGH ONNEs and C. A. CROMMELIN, these Pro-
ceedings 15, p. 667, Leiden Comm. N°. 131a.

5) E. Matuias, H. KAMERLINGH ONNES and C. A. CROMMELIN, these Pro-
ceedings 17, p. 953, Leiden Comm. N°. 145c.

4) H. KAMERLINGH ONNES and C. A. CROMMELIN, these Proceedings, 16,
p. 245, Leiden Comm. N°. 137a.

5) H. KAMERLINGH ONNES, C. A. CROMMELIN and P.G. Catu, these Procee-
dings 20, p. 178, Leiden Comm. N°. 15lc.

6) J. J. VAN LAAR, Chem. Weekblad 16 (1919), p. 1557.

1176

normal conditions were exactly the same, as those used in the case
of nitrogen. For these we may therefore refer to the paper on the
diameter of nitrogen quoted above.

As regards the cryostat, only a small part of the temperature
range of the measurements might have been covered with a liquefied
gas, namely with neon (boiling point — 245°.92C., triple point —
248°.67)'). Uniform and constant temperatures over the whole range
can only be obtained by means of superheated vapour, as used in
the hydrogen vapour cryostat described on a former occasion *). But
this apparatus, being opaque, could not be used without alteration,
since the position of the meniscus in the dilatometer has to be read.

A description of the modified arrangement by which we succeeded
in obtaining a transparent bath of superheated hydrogen vapour
which answered all requirements, will be given in the next com-
munication *).

The hydrogen was freed from all impurities by freezing in liquid
hydrogen *) and is therefore to be looked upon as having been
absolutely pure.

§ 3. The experiments were also conducted in the same manner
as in the case of argon and nitrogen.

The quantity of liquid or vapour in the dilatometer was found
by reading the position of the meniscus on the scales of the upper
tube or the appendix at the bottom of the dilatometer ; the hydrogen
was then blown off into the carefully exhausted volumenometer and
the quantity collected was finally measured under normal conditions.

Although a series of vapour pressures of hydrogen between the
critical point and the boiling point was available’) for the purpose
of the necessary corrections, it seemed advisable to make measure-
ments of the pressure regularly during the experiments. For this

1) H. KAMERLINGH ONNES and C. A. CROMMELIN, these Proceedings 18, p. 515,
Leiden Comm. N°. 147d. In this paper on p. 518, line 8 from the bottom,
(Leiden Comm. p. 52, 1. 10) the pressure 76.00 should be replaced by 75.95
(one atmosphere at Leiden). The temperature of the boiling point — 2459.92
is correct.

2) H. KAMERLINGH ONNES, these Proceedings 19, p. 1049, Leiden Comm.
N°. 15la.

3) H. KAMERLINGH ONNES and C. A. CROMMELIN, these Proceedings 23,
p. 1185, Leiden Comm. N°. 154c.

4) H. KAMERLINGH ONNES, these Proceedings 11, p. 883, Leiden Comm.
NO, 1095.

5) P. G. Carn and H. KAMERLINGH ONNES, these Proceedings 20, pp. 991,
1155, Leiden Comm. No. 152a and P. G. Carn, Dissertation, Leiden 1917, p. 103.

BETE

purpose we used the open standard manometer *), since the pressures
were all below 12.80 atm. (critical pressure) and in our closed
hydrogen-manometer, which is otherwise much simpler in use, the
mercury does not become visible till 20 atmospheres.

To the results of these measurements and the use made of them
in the calculation of the corrections we shall return in diseussing
the calculations.

The temperature was measured and at the same time kept constant
by means of two platinum resistance thermometers Pt, and Pty,
which were compared with a helium thermometer shortly after the
measurements and under exactly the same conditions, i. e. in the
eryostat and at the same temperatures as had been used in the
diameter-measurements. The agreement of the two thermometers
was completely satisfactory. *)

The temperature to be taken for the glass capillary of the dilato-
meter was this time separately determined with a simple gas ther-
mometer in the form of a tube which was mounted beside the
capillary in question in the lid of the cryostat, and had been
similarly used in previous measurements *). In this manner the
temperature of the capillary is measnied in each determination
separately, instead of making an estimation or deriving it from
previous determinations; the method also simplifies the calculation
of the corrections, since only one temperature is dealt with, whereas
before the capillary had as a rule to be divided into three portions
each with its own mean temperature *).

A few days before the commencement of the real measurements
a “general rehearsal’ was held, chiefly to ascertain the degree of
constancy and uniformity of the temperature to be obtained with
the new cryostat, and the influence of various methods of illumi-
nation on the temperature. The filling of the dilatometer with liquid
hydrogen was found to proceed without a hiteh.

During the period of the measurements the illumination trials
were continued for the first ten days: a metal wire lamp behind
a vessel with alum solution was found to give no disturbance ; with
clear weather diffuse daylight was also sometimes used.

1) H. KAMERLINGH ONNES, these Proceedings 1, p. 213, Leiden. Comm. N°. 44.

*) Comp. fig. 2 of the next communication.

3) For instance by P. G. CatH and H. KAMERLINGH ONNEs, these Procee-
dings 20, p. 991, p. 1155, Leiden. Comm. N°. 152a and P. G. Catn, Disser-
tation, Leiden 1917, Figure on p. 101.

*) F. HENNING. Die Grundlagen, Methoden und Ergebnisse der Temperatur-
-messung (1915) pp. 46 and 47.

76

Proceedings Royal Acad. Amsterdam. Vol. XXIII.

1178

The first six experimental days were used for studying one definite
temperature, — 243°10, in order to obtain as much routine and
experience as possible, in the management of the eryostat (so dif-
ferent in principle from the ordinary liquid baths), as also in the
adjustment of the equilibrium and the taking of the readings.
Special attention was given to checking tbe equilibrium between
vapour and liquid. When this is reached, not only the hydrogen
meniscus in the dilatometer but also the mercury in the tube of
the compression cylinder remains at absolutely constant level, some-
times after considerable intervals of waiting. Both the liquid density
and that of the vapour were measured three times; moreover a
number of measurements of the vapour pressure were made under
various conditions (meniscus in appendix, bulb or tube).

In the discussion of our results it will appear that in a special
range of temperatures certain circumstances prevail which affect
the measurements of the vapour density and require to be more
fully investigated.

For the reduction of the experiments the pressure in the dilato-
meter has to be accurately known and for this purpose, as men-
tioned, during the measurements a great number of pressures were
determined, referring therefore to a meniscus sometimes in the
appendix and sometimes in the tube; moreover a number of readings
were taken with the hydrogen meniscus in the bulb of the dilato-
meter, in which case a proper equilibrium between liquid and
vapour can be better counted on. The measurements with the
meniscus in the appendix and the tube, i.e. with little or much
liquid, also serve to form an opinion as to possible deviations of
the temperature low down and high up in the eryostat, since the
absolute purity of the bydrogen could be assumed as certain. These
pressure measurements we would rather not call ‘‘vapour pressure
determinations’, since for determinations of that kind, when properly
conducted, stirring is an absolute necessity. We propose shortly in
the same cryostat to measure vapour pressures of hydrogen in a
piezometer with electro-magnetic stirrer.

The result of our pressure measurements was as follows: the
readings in the bulb, when plotted, lie on a smooth curve, which
as it seems to us cannot deviate appreciably from the true vapour
pressure curve; the readings in the appendix are a little less regular,
but they do not show any systematic deviations from the previous
ones; the observations in the tube, on the other hand, at correspond-
ing temperatures consistenly give slightly higher values.

From this we have to infer, that the temperature must have been

1179

slightly higher high up in the cryostat, than half way down and
below. We intend to check this result shortly by special measure-
ments in the eryostat. But although thus there appears to be a small
difference of temperature below and above, this causes but a very
small inaccuracy in our density determinations. The middle of the
resistance thermometers, which were mounted parallel to the dilato-
meter, was about on a level with the middle of the dilatometer;
hence the temperature indicated by the thermometers must be very
near the mean temperature of the dilatometer and this is the essential
quantity.

For the reduction of the ‘noxious’ volumes the pressures were
of course used as measured, without any correction.

It may be mentioned that for the whole series of measurements
no less than about 170 litres of liquid hydrogen and 400 litres of
liquid air were required.

§ 4. The calculations. For these we may again in many respects
refer to previous communications. The reduction to the normal con-
ditions of the gaseous volumes in the noxious spaces at low tempe-
rature gave no difficulties, since the thermal behaviour of hydrogen
at the temperatures and pressures of the experiments is accurately
known '). It was a great convenience, that these measurements have
been united in a special reduced equation of state for hydrogen
VII. H,.3.*); by using the coefficients in this equation the various
reductions could be accurately computed.

The volumes of the hydrogen menisci were found by using pre-
vious measurements in the Leiden laboratory concerning the capillary
constants of hydrogen *). For the manner in which these calculations
were made we refer chiefly to our paper on the diameter of argon.

For the density of hydrogen under normal conditions, i.e. the
mass of 1 litre of hydrogen at O° and 1 atmosphere Mortry’s value *)
0.089873 was taken, which appeared to us to deserve most confidence.

As regards the accuracy of our measurements it may be observed
that 0.1 of a mm. on the tube of the dilatometer corresponded to
an accuracy of the liquid volume of about '/,,,,; this accuracy

1) H. KAMERLINGH ONNES and C. BRAAK, these Proceedings 9, p. 754; 10,
p. 204, p. 413, Leiden Comm. Nrs. 97a, 99a, 100a.

*) Published by J. P. DALTON, these Proceedings 11, p. 863, Leiden Comm.
N° 109a.

3) H. KAMERLINGH ONNES and H. A. Kuypers, these Proceedings 17, p. 528,
Leiden Comm.°N®. 142d.

*) E. W. Mortey, Zs. f. phys. Chemie 20 (1896), p. 68, 242, 417 and
SMITHSONIAN Contr. to knowledge 1895.

76*

1180

corresponds to '/,,, of a degree in the temperature and to this same
amount the temperature in the eryostat could be kept constant for
a long time, when the conditions were favourable. The accuracy of
the measurements in the volumenometer could be made much higher
without any difficulty. Taking into account the specially favourable
conditions under which the measurements were made, we think
we may put the accuracy of our results for the liquid densities at
‘Ieeooe. AS regards the vapour densities we must suspend judgment,
as certain deviations are left as yet unexplained.

§ 5. Results. The results are plotted in fig. 1 and contained in
the following table. The plot as well as the table also give the
previous Leiden measurements of the liquid density between the

| vel: toc xe AE
0 | T | Pr |" F sd y(Q) | HO) | abs. in 0/0
| | | ENOTES SIE ce iss
= "240.57 32-52 0.04316 0.01922 0.03119 0.03128 —0.00009 —0.29
In a | | |
5 gs) 24183 31.26 5001 1366, 3184 _3178| + 6 + 19
a | | | |
Zó | 243.03 30.06 5402 1081 3241, 3225/4 16 + 49
=ro |
2932 l 244.30 28.79, 5740 806, 3213| 3275|— 23— 6
O5 s¢ |
E = fae
gEe 245.73 27.36) 6050, 613, 3382, 3331 + Dae
ES Of 247.79|25.30| 6416/ 405) 3411) 3412] — Ie 13
< | | | | |
= ‘|. 249.89 |23.20| 6724 264, 3494, 3495 | — f\asteny
5 —252.68| 20.41 0.07081 | 0.00135 | 0.03608) 3605 + 3) 4-1 8
| 253.24|19.85| 7137 | 116| 3627| 3627 0 0
05 | | |
ns 253.76|19.33; 7192 | 101] 3647| 3648|— el
Ze |
6& 255.19/ 17.90, 7344 | 64] 3704 3704 0 0
TO | | |
go 255.99/17.10| 7421 | 49| _3736| 3735 | + 1+ 3
ae | |
aje 256.75|16.34\ 7494 38| 3766) 3165 + Be m3
== | |
Zz 257.23/15.86| 7538 | 31| 3784) 3784 0 0
& |
ed 258.27| 14.82] 7631 | 20| 3826 3825.) + We See)
—_—— — — — ————_— ———— — = — Se! Se = — = = — — —— — —
6 = temperature on the Kwrvin-scale in degrees centigrade.
Orig. and OP rap, Are the densities of the liquid and vapour
respectively, in grammes per cm’.

y (Q) is the observed ordinate of the diameter, i.e. the mean
of the figures in the previous columns.

1181

boiling point and the triple point and the corresponding vapour
densities, as found by calculation. These values have also served in
the computation of the diameter constants.

in HEEE
Savane SMa,

(es) IN ie) + (oh) N yee oO
2 oa oo 2) Oe ©)
oO ©, ©, (2) oO ie) ©, oO

Fig. 1

From the values of y(Q) the equation of the diameter was deduced
by the method of least squares; the first three values nearest the
critical point were, however, left out of account, since they gave a

1182

somewhat considerable deviation from the straight line, as a preli-
minary plot has shown. In this manner the rectilinear character of
the diameter is duly observed and the critical density is found in
a more rational way than otherwise.

The equation of the diameter being written in the form

y=a-t bt
the coefficients are found as follows
a= — 0:063510.
b = — 0:00039402.

The 6%, 7% and 8 column of the table refer to this calculation ;
y(C) are the calculated values of y, O — C the differences, absolute
and in percentages of y(C) respectively.

§ 6. Discussion. From the last column it appears that the devia-
tions from the straight line are usually small, less than 7/100, except
near the critical point, where they rise to almost 1/20. The experi-
mental diameter evidently shows a small hump. A similar bump,
although very little marked, was previously found with argon, but
on the other hand it was very pronounced with nitrogen. The
maximum deviation there amounted to nearly Ys. The magnitude
of this deviation surprised us considerably at the time and made
us suspect some irregularity in our method of observation or cal-
culation as the cause. Since, however, we have now found a hump
of a similar character, although four times lower, with hydrogen,
we think we may infer that this result may be dune to some
systematic error, not yet explained, by which in some manner
(condensation on the wall?) a not quite correct vapour density is
observed.

The slope of the diameter is given by the coefficient

b = — 000039402

the smallest valne so far found for any substance.
The critical density as derived from the diameter, using — 239°-91 5)
as the critical temperature, is
rd = 0.038102

in complete accordance with the value previously calculated 0:0310.
A comparison of this value with the value to be derived from
the isothermals by means of the equation

(3 _ (dp
VA Jon dT coër.k.

1) These Proceedings 20, p. 178, Leiden Comm. N°. 151c.

1183

(as in the ease of argon) could not be made, since isothermals in
the neighbourhood of the critical point are not available.

The critical coefficient becomes

CE — 9.976
RT.
the smallest value yet found for any substance.

For a ready comparison with other substances of simple molecular
structure we subjoin the following table of the critical values, the
diameter slope and the eritical coefficient, as far as known at the
time with sufficient accuracy.

The numbers concerning xenon are taken from the measurements
of PATTERSON, Cripps and Gray!), the others from the Leiden
measurements.

| Op | Oka | 2 Kaa
x + 16:6 | 1°155 | 0-003055 | 3-607 |
O, | —118:82 | 0-4299 | 2265 | 3°419
Ar | —122:44 | 0-5308 26235 | 3-424
N, | —147:13 | 0:3110 | 1958 | 3-421
H, | —239:91 0-03102 | 03940 | 3-276

The data thus obtained, combined with the values of the vapour
pressure, allow a computation of the heat of evaporation L and

of the quantity
d A Pee Geene
—_—_{ — |= —_ zm — m
d log T\ T 7 Et iii ly

(m’ and m being the specific heats of the saturated vapour and the
liquid respectively).

In a later paper we hope to communicate the results of these
calculations not only for hydrogen, but also for oxygen, nitrogen
and argon.

For the investigation described in this paper we have had the
benefit of a grant from the BoNAPARTE-fund allowed by the “Aca-
démie des Sciences” of Paris, for which we wish here to express
our profound gratitude.

1) H. S. PATTERSON, R. S. Cripps and R. W. Gray, London Proc. R.S. 86
(1912) p. 579.

1184

We gladly thank all who have assisted us in carrying out the
measurements, in tbe first place Mr. F. M. Pennine, who was
entirely responsible for the regulation and measurement of the
temperatures and the calibration of the resistance thermometers,
and made all the calculations involved every time; further Miss
H. van per Horst, who assisted in the temperature measurements
and carried out and calculated the greater part of the observations
with the helium thermometer; finally to Mr. G. J. Fri, chief
mechanic of the cryogenic laboratory and to Messrs. L. and A.
OUWERKERK, with whom the far from simple management of the
vapour cryostat was in very able hands.

Physics. — “Methods and apparatus used in the cryogenic laboratory.
XVIII. Improved form of a hydrogen vapour cryostat for
temperatures between — 217° C. and — 258° C.”. By H.
KAMERLINGH ONNES and C. A. CROMMELIN. Communication
N°. 154c from the Physical Laboratory at Leiden. (Commu-
nicated by Prof. H. KAMERLINGH Onnus).

(Communicated at the meeting of January 29, 1921).

$ 1. Introduction. In a previous communication one of us has
described a hydrogen vapour cryostat for temperatures between the
melting point of oxygen and the boiling point of hydrogen *). During
the preliminary determinations of the critical points of neon’) and
of hydrogen’), made in this cryostai, it was found that in principle
the apparatus properly performed its function, but at the same time
we discovered certain faults and deficiencies. When therefore the
modification, which had been foreseen all the time and by which
it would become possible to take readings on a tube inside the
cryostat, became necessary, we resolved with the assistance of Mr.
Frrm, chief mechanic of the cryogenic laboratory, to revise the con-
struction in all details and rather than execute the modifications as
originally planned to build a new apparatus of somewhat larger
dimensions. This new cryostat which in the various measurements
has given almost complete satisfaction and may therefore be con-
sidered to have approached its final form, will be described in
this paper.

The apparatus is shown in fig. 1, partly in section, partly in
direct view, as appears easily from the different details. Moreover
three sections are given at different heights, a view of the turnable
drum and diagramatically the electric connections, as will be further
explained later on.

1) H. KAMERLINGH ONNEs, these Proceedings..19, p. 1049, Leiden Comm.
N°. 151a. ;

2) H. KAMERLINGH ONNES, C. A. CROMMELIN and P. G. Carn, these Proceedings
19, p. 1058, Leiden Comm. N°. 1515.

3) H. KAMERLINGH ONNES, C. A. CROMMELIN and P. G. Carn, these Proceedings
20, p. 178, Leiden Comm. N°. 15lc.

1186

ri oe NE ky A
KO og
ed, VSSD NY
REE, / A j = Z 4

W A 7
Reet =

1187

§ 2. Description of the cryostat *).

The eryostat consists of two vacuum vessels, viz. an evaporator
V and cryostat B, both enclosed in vacuum vessels with liquid
air V, and B, and closed by german silver lids or caps Vy and By.

The principle of the apparatus consists in the experimental space
E being kept at constant temperature by a current of gaseous
hydrogen, the temperature of which is kept at a definite value by
automatic regulation of an electric current through a heating wire.

Let us follow the gaseous hydrogen on its way through the
apparatus, as shown by the arrows. At 6, it enters under small
excess of pressure. For the manner in which the current is kept
constant and regulated. we refer to fig. 6 of the previous paper on
the vapour cryostat. It then flows through the copper spiral 6,,
which is cooled, as will appear presently, by the waste hydrogen,
and the tube 53 (of german silver in order to minimize the supply
of heat to the liquid hydrogen below) from which it escapes at
6, bubbling up through the liquid hydrogen which fills the evaporator.

In this manner a fairly strong and regular evaporation of the
liquid hydrogen is obtained; the hydrogen vapour passes into the
tube Ds, which continues as a spiral under the liquid hydrogen,
and hence into the double walled vacuum tube be which carries
the gas (cooled to about — 253°) to the lower end of the cryostat at 67.

Here it enters the spiral-shaped heating space £, (see also section
V—VI) and flows round a heating wire W, which heats the gas
to about the desired temperature by means of an automatically
regulated current. The space 4, communicates at the centre through
a hole with a second space KE, above it. Here the gas first passes
along a copper thermometer bulb H, (which serves for the regula-
tion of the temperature, as will be explained further down), then
along a resistance JW, and finally rises through 6, into a thickwalled
copper tube going four times up and down, the horizontal parts of
which are seen in section III—IV at bo, the vertical soldered on
the outside against the very thick copper mantle (for the purpose
of a uniform temperature) of the experimental space 4; this motion
up and down serves to communicate the required temperature to
the copper mantle. Finally the gas enters the experimental space
# with the measuring instruments (in the figure a dilatometer D

1) We here refer to Leiden Comm. N°. 15la (these Proceedings 19, p. 1049)
where many constructional details are mentioned and the principle of the
apparatus is explained; at the same time the present description is so arranged,
that it may be read and understood by itself.

1185

and two platinum resistance thermometers Pt, and Pt, as used
for the determination of the diameter of hydrogen *)) passes through
it and-by the holes in the lid # enters the space /#, above; it is
then carried through the vacuum tube 6,, into the space surrounding
the spiral 4,, by which the gas inside acquires a preliminary cooling,
and finally escapes by bj, to a gasometer.

The half automatic regulation of the temperature is very simple
in principle. By the resistance W, the gas is heated to the desired
temperature, the current being furnished by the accumulators A; (36
volts) and adjusted by the regulating resistance W 3. The gas-ther-
mometer //, already referred to, which is connected with the
manometer through the capillary. C, provides for the automatic
closing and opening of the current, in a manner easily understood
from the figure. As long as the temperature is too low, the mano-
meter being properly adjusted, there is electric contact at D; when
the temperature rises above the desired value, the contact is broken.
When the cryostat is in action and everything properly regulated,
the automatic arrangement is continually in action and the current
is opened and closed at regular intervals (of say 10 or 20 seconds).

When this arrangement was tested, it appeared from the readings
of the platinum resistance thermometers that owing to some inertia
in the automatic action small fluctuations of the temperature in the
experimental space of ‘02° to ‘03° were still present. With a view
to a still finer regulation the resistance W, was then introduced
in the space £5.

The current through this small resistance is furnished by an accu-
mulator A, aud is regulated by hand by the observer at the galvano-
meter by means of the regulating resistance W,. The deflection of
the galvanometer shows the small variations of temperature much
more quickly than the automatic regulator can act and the observer
is able by a change of W, at once to bring back the temperature
to the desired value. In this manner it is possible to keep the tem-
perature constant to .01°, sometimes during hours.

The connecting wires of the various resistances are only shown
diagrammatically in the figure. Thus ZL, represents the 4 wires of
the automatic regulator and the resistance W,, L, the eight wires
of two platinum resistance thermometers Pt, and Pt,

One of the principal desiderata in the previous simpler cryostat
was the possibility to make visual observations in the space #. The
apertures which had originally been made in the copper mantle for

1) E. Maruias, C. A. CROMMELIN and H. KAMERLINGH ONNES, these Pro-
ceedings 23, p. 1175, Leiden. Comm. N°. 1545.

1189

this purpose lad afterwards been closed again by copper plates for
safety, in order to avoid fluctuations of the temperature in consequence
of the presence of these apertures in connection with the small
heat-capacity of the gaseous hydrogen. On the latter account the
vapour cryostat requires much greater precautions than an ordinary
liquid cryostat and for this reason in our first trials all superfluous
complications were avoided. The difficulty which was then feared
(correctly, as we found later on) is met in the present model by
providing the copper mantle with two diametrically opposite narrow
glass windows and surrounding the mantle with a second one M
of german silver (also shown separately in the figure). In this mantle
two screw shaped slits have been cut. Thus a tield K is left clear
for ilJumination from behind and observation from the front.

The mantle M may be turned by means of a glass rod G and
the cogwheel 7’ which works in a rack fitted on the outside of the
mantle at the top: by this means AK may be moved vertically up
or down. An experimental tube mounted axially in the space #
may thus successively be observed from the bottom to the top. The
resistance thermometers which do not need to be seen may be
mounted excentrally.

In this manner the aperture for visual observation which might
produce fluctuations of the temperature by radiation is reduced toa
minimum, and moreover the mantle can be closed by turning far
enough as soon as an observation is finished.

We have systematically investigated whether the opening did still
cause any change of temperature and for this purpose have tried
various sources of light, for instance a metal wire lamp with or
without alum filter, diffuse daylight, ete. A lamp without a filter
immediately produces a rise in the temperature of a few hundredths
of a degree. When a heat filter (alum solution) was placed between
the lamp and the cryostat, and the light was used with caution, no
changes of the temperature of as much as .01° could be observed.

In the silver coating of the vessels B and B, narrow slots have
naturally also been left open, and similarly in the coating of vessel
V, in order that the evaporation of the liquid hydrogen may be
followed. V is for the greater part unsilvered.

The construction of these vessels, which was particularly difficult
in the case of the large outer ones, we thank to the exceptional
ability of the chief glassblower Mr. O. KessrLrING. It seems as if
with these largest vessels the limit of what can be done with cylin-
drical vessels has almost been reached. They have to be treated
with the utmost care and have to be very slowly cooled, at least

1190

for half an hour, before liquid air may be poured in: Even then it
has happened repeatedly that a vessel of this kind burst, specially
during the addition of liquid air in the narrow space between the
vessels.

To begin with we feared that the very low temperatures near
the boiling point of hydrogen would give difficulties and might

Fig. 2.

1191

possibly not be attainable at all’). This fear turned out to be
unfounded. Temperatures of — 250° and — 251° do not procure
any special difficulties.

It was mentioned above, that the temperature in the experimental
space could be kept constant to .01 of a degree during a long time.
In confirmation of this we here reproduce two curves drawn according
to the galvanometer-deflections of the two thermometers Pos and Pto;,
representing the deviations of the temperature as a function of the
time. They refer to an observation at — 244.°38. It must be men-
tioned, however, that the management of the eryostat is far from
easy or simple. A great deal of routine and experience is required
to work the cryostat in such a way that the above constancy of
the temperature is attained, and it is only after repeated vain efforts
that even our highly trained technical staff has now learned to
make the apparatus answer to the slightest hint.

Much is due to Mr. G. J. Frim, chief mechanic of the cryogenic
laboratory, under whose able guidance the apparatus was designed
and constructed, and further to Messrs. L. and A. Ouwerkerk both
attendants 1st class, under whose supervision the apparatus now
works so excellently.

1) Comp. Leiden Comm. No. 15la p. 4 note 1.

Physiology. — “On the Influence of the Season on Laboratory
Animals”. By Prof. H. ZWAARDEMAKER.

(Communicated at the meeting of January 29, 1921).

This technical subject appears to be of general application. In
previous publications the present writer and his co-workers have
superadded to J. Lons’s balancing of ions of the circulating fluids,

Na+ K

—- = constant, the balancing for-
Mg + Ca

expressed in the equation

Rt NO el
mula = constant. Im the latter formula the radio-
Ca + Sr + Ba
physiological antagonism between K and (UO), + 7h. need not be
taken into account *).

Moreover, in earlier discourses the replacement of potassium by
the other radio-active elements Rd, (U O),, U, Th, lo, Ra, Em, has
been repeatedly discussed *).

Now the present writer wishes to point out that the dosages in
which these elements are to be administered must be much smaller
in summer than in winter. Of course, this difference is not brought
about by the radio-active elements as such, but by the fact that in
summer the organs are more sensitized by certain substances *).

These substances can be washed out, so that in the transition
periods the functionating of a summer-organ during some hours’
perfusion with an artificial but nonetheless efficient circulating fluid,
suffices to transform a summer-organ into a winter-organ.

As regards sensitizing power, that of the washed-out substances
is analogous to that of adrenalin.

The organs operated upon were the hearts of frogs and of eels.

A detailed publication will appear elsewhere.

1) G. R. des Séances de la Soc. de Biologie 7 Juin 1919.
2) Journal of Physiology Vol. 53 p. 273 1920.
3) Proceedings of this Acad. 25 Sept. 1920.

Physics. — “On the principles of the theory of quanta. By Paur
S. Epstein. (Communicated by Prof. P. Esrenrust).

(Communicated at the meeting of January, 29, 1921.)

1. Introduction. The quantum-theory in the form, which in 1911
Pranck *) has given it, depends on the application of statistical mechanies
in the so-called “phase-space” of the canonical position- and impulse-
coordinates q,q,-...Qf; Pi P.--++- py, and consists in dividing this
space into elementary regions of probability. The method obtains
a considerable simplification for the soluble mechanical systems,
since for them each impulse-coordinate p; = p;(q;). Instead of the
2f-dimensional phase-space (f being the number of degrees of freedom
of the system) it is then sufficient to consider the f ‘‘phase-planes”
(pi, gi), which, as the author showed a few years ago’), gives great
advantages in the treatment of these systems. In each of these planes
the successive conditions of the system are represented by a curve.
For the class of the “conditioned-periodic motions”, the only ones
for which so far quantum-conditions have been established, the
curves in question are as a rule closed. The only exception is formed
by the “cyclic coordinates” which bear the character of a plane
angle; a cyclic coordinate varies from 0 to 2a and the corresponding
impulse is constant; hence the representive curve becomes a segment
of a straight line parallel to the axis of abscissae. *)

Puanck’s hypothesis, as extended by SommurreLp and the author,
consists in the assumption of the existence among the states of the
system of certain preferential or ‘‘stationary” motions, which are
represented by discrete curves in the diagram, the area of the phase-
plane between two successive stationary curves being equal to the

universal constant /
[fea SPT leh A rte 4

If the area of the narrowest of these curves (or for cyclic coor-

1) M. Pranck. Verhandelingen van het Solvay-congres.
2) P. S. Epstein. Ann. d. Phys. 50, p. 489; 51, p. 168, 1916.
3) This case was discussed for the first time by P. EHRENFEST. Verh. d.
D. phys. Ges. 15, p. 451. 1913.
(A
Proceedings Roval Acad. Amsterdam Vol. XXIII.

1194

dinates the one nearest the axis of abscissae) is equal to /,, that of
the (n + 1) st stationary orbit will be

[rig = hy + nh oo Lae ay ee aie ne

h, has therefore to be determined, in order that all the stationary
curves be fixed.

For this purpose Pranck') lays down the principle, that the
narrowest orbit must coincide with the natural boundary of the
phase-plane; i.e. if on any grounds, connected with the nature of
the system, the integral (1), which is essentially positive, cannot
fall below a definite value, the latter has to be taken as /,. In
most cases a lower limit of that kind does not exist and the integral

may be taken equal to zero, whence

Krk nd es

In his treatment of the relativistic Kepler-motion SOMMERFELD ”)
found the case to be different; he there gave a lower limit p, = xe°/c *)
for the constant azimuthal impulse; this would give h,=—= 2a p,. It
would therefore, as pointed out by PranckK, be necessary to take (2)
as the fundamental relation, whereas experiment (the Balmer-series)
can only be reconciled with supposition (2’). SOMMERFELD ‘) tried to
remove this contradiction by pointing out, that when the motion of
the nucleus is taken into account the numerical value of the limit-
ing impulse is smaller than xe°/c. In what follows we hope to prove
that the limitation of the phase-plane by the value p=p, is only
an apparent one, even if the motion of the nucleus is left out of
account, and that p can very well fall below this value: at the
same time the character of the motion is then essentially changed.

The admissibility of stationary orbits of azimuthal impulse p = 0
which on SOMMERFELD’s theory seemed to be excluded is thereby
proved in principle. As long as we are dealing with attractive forces
(nucleus and electron) these orbits are hardly of practical importance,
as they must lead to a collision of electron and nucleus. But the
case changes, when the forces are repulsive (nucleus and a-particle) ;
the orbits are then hyperbolic. If the quantization of such orbits is
admitted, interesting physical conclusions follow which appear to

1) M. PrANCK. Ann. d. Phys. 50, p. 385. 1916.
%) A. SOMMERFELD. Ann. d. Phys. 51, p. 57. 1916.
8) Here e is the charge of an electron, ze that of the atomic nucleus and
c the velocity of light.
4) A. SOMMERFELD. Miinchener Ber., p. 137, 1916.

1195

give an explanation of certain recent experimental results of RurnEr-
ForD’s’). The question raised by the author?) before as to the
quantization of non-periodic motions is therefore put once more
and discussed in a different manner (§ 4, 7).

§ 2. The apparent boundary of the phase-plane p= p,.
The relativistic Kepler-motion is given by the following equation
between the polar coordinates r,@ (cf. lc. p. 819).

1 B Vp—p,
tS =| te eo 5 me p=) | nen
r P —Po P ~

with the abbreviations
a
BS spe dre 1, ssi SS aia are idl

A=a(S+ 2m) ; ie
c

a represents the energy of the system, c the velocity of light,
m the mass of the moving particle. The positive sign of B refers
to the case of attraction, the negative sign to repulsion; p‚ is the
azimuth of the radius vector with respect to the aphelion.

For p >p, with negative energies (A < 0) and attracting forces
(B > 0) the orbit is an ellips with perihelion-motion. The procession
of the perihelion increases in speed, the smaller the difference p?— p,’,
and in the limiting case p =p, the orbit converges on the nucleus
in a manner similar to an Archimedian spiral’):

ay

ree vie :
an PP, EB 5 . ° ‘ 5 ° . (5)

But nothing prevents us from now taking p< p,; the expression
(3) then assumes the form:

2 2

5 Bat a nde et ey ies ae rand cng
eM Dd at sare | 4

The right-hand side of this expression for a very large positive

or negative value of ~ becomes exponentially infinite independently

of the value of the excentricity «. The two extremities of the orbit

thus approach logarithmic spirals. It further follows from (4) that

') E. RuTHERFORD. Phil. Mag. 37, p. 537, 1919.

4) P. S. Epstein. Ann. d. Phys. 50, p. 815, 1916. This paper will be
quoted here as l.c.
5) Comp. A. SOMMERFELD Ann. d. Physik. 51, p. 50 1916.
Ta

1196

: < > ) : ‘ :
for A=0, e=l. Thus with negative energy 7 always remains finite,
> &

the particle moves out from the centre and again returns to it.

When the energy disappears or becomes positive the orbit divides
into two branches which run from the centre to infinity or vice
versa. In the limiting case p=—=0 r is only finite for w =p, Le.
the motion is rectilinear.

Thus it is seen, that in reality there is not a limit p= p, atall:
with small positive values of p—p, tbe orbit encircles the centre
many times, while 7 diminishes, but remains at a finite distance
from it which passes through a minimum and then increases again.
For p=p, the curve runs into the centre as an Archimedian spiral.
The approach to the centre is even more rapid when p< p,, the
spiral becoming logarithmic. It must not be supposed that the particle
in its motion on the spiral will permanently remain near the centre:
for although the spiral encircles the point an infinite number of
times, its total length is finite and the time to describe it from a
finite distance, as a simple calculation shows, is also finite and
practically very small. Therefore the collision will oceur very soon.

§ 3. Quantization of the spiral orbits. In the last section we have
shown, that in the relativistic Kepler-motion, even with negative
energy, besides the ellips-like orbits other forms are possible which
are of finite length and are only once described.

The question now arises, whether these motions can be submitted
to quantum-conditions and in what manner this would have to be
done. Our answer to the first question is implicitly contained in the
above discussion: the disappearance of the limiting value /, in
assumption (2) we have explained by the fact that orbits have to
be taken into account for which pis less than the azimuthal quantum
po. It follows that these orbits join on continuously to the others
and must be equivalent to them from the point of view of the
quantum theory. Since for p >> p, the stationary motions are given
by the relation p= nh/2a0 (n=1,2,....), it follows that for p < p,
the only possible stationary condition is p=QO. This conclusion is
strengthened by the circumstance that when the movement of the
nucleus is taken into account (as proposed by SoOMMERFELD) similar
spiral-shaped orbits have to be considered in order to explain the
possibility of p= 0: this can be easily shown to be the case.

We have therefore only to discuss the quantisation of the radial
impulse: its dependence on the radius vector 7 and on the constants
of the problem is given by the equation (lc. p. 823).

1197

AERC? ER BW Pr
== a + 2B i + (p,’—p’) pho Sip banis (7)

which is represented graphically in Fig. 1 for p< p,. The curves
nearest the axis of ordinates correspond to large negative values of
the energy constant «. With increasing energy the curves bend out
more and more and for «—O they divide into two branches which
approach asymptotically to the axis of abscissae. For a positive the
asymptotes are straight lines parallel to this axis.

For small values of 7 (7) reduces to

amt |
Di pons EE Sh U OEE (|
r

ie. at a distance from the axis of abscissae the curves are hy perbolic.
The area of such a curve is logarithmically infinite and the difference
between the area of two curves is also always infinite, unless we
apply artificial means such as the formation of the principal values
of the integral. Since according to the quantum theory the areas
of two successive stationary curves must differ by the finite quantity A,
it follows that in this case the stationary energy stages must be
infinitely dense, ie. all values of the energy are “selected” in the
sense of the theory. Whereas the selected values of p form a series
of discrete numbers, those of « form a continuum. There are thus
an infinite number of motions which starting from the zero reach
as far as we like. All these orbits lead to a collision with the
nucleus and for this reason they are not very important physically.

Fig. 1.

1198

But for our purpose it is important that these orbits are possible
in principle irrespectively of how long an electron can move along it.

Fig. 2.

§ 4. Quantization of the hyperbolic curves. The problem becomes
of greater importance pbysically, if repulsive forces are considered,
so that the orbits are hyperbolic. The question, how these orbits
have to be quantizized was discussed by me several years ago (I.c.).
The method adopted then, which was explicitly stated to be provi-
sional, I do not wish to adhere to in all its particulars. But the
fundamental idea of submitting such orbits to quantum-conditions
still appears to me a sound one. Quite a long time ago I have in
the Munich colloquium developed certain views on this subject
which appear to me still to deserve attention. For simplicity we
shall here disregard the relativity correction (¢c =o): the radial
impulse according to (7) and (4) then assumes the form:

1 1
pa|/ 2ma+ dumei—p Whe strate
r r

For a <0 the motion is elliptical, for « =O parabolic, for a > 0
hyperbolic. The aspect of the curves in the phase-plane (p,7) is
seen in Fig. 2. The part of the plane, where « <0 is bounded by
the heavily drawn curve « == 0, both ends of which approach the
axis of abscissae asymptotically. Inside this region the curves are
elliptic and it is easy to fulfil the condition that the area between

1199

two successive curves be equal to h. In the region outside the curve
a =O each one of the curves possesses two asymptotes parallel to
the axis of abscissae. The strip between two curves whose energy-
constants differ by a finite amount has an infinite area. Just as in
the case of the spiral orbits we may conclude that the energy stages
of the stationary motions must be infinitely dense. very positive
value of the energy-constant is therefore a “selected” value in the
sense of the quantum theory. That hyperbolic orbits with all values
of the energy are present, was already enunciated by Bonr on the
ground of experimental results (by WaGner and others). From our
point of view this does not prove that the hyperbolic motion is
beyond the controll of the quantum theory; on the contrary this
fact is a natural inference of a consistent application of this theory.

This view naturally implies that the azimuthal impulse must also
be subjected to quantic conditions. What these are cannot immedi-
ately be deduced from the case of the elliptic motion. Two possibi-

lities seem to present themselves: we must extend the integral | pdp

either over the range of change of the codrdinate y, i.e. over the
angle enclosed between the asymptotes, or, as in the case of the
elliptic motion, from Oto 2. The former assumption would according
to 2’ give

nh (92)
P=): . ail eee’ ve Bh ES a
2p
the latter
nh
De gone (95)
7

In $ 7 we shall meet with an argument in favour of the second
assumption, but a decision between the two can ultimately only be
brought by experiment.

§ 5. Collision between an a-particle and an atomic nucleus. We
shall now investigate the case of repulsive forces in detail and
thereby take into account the motion of the nucleus, neglecting the
relativistie correction which is of no importance for our purpose.
In the usual manner by means of the principle of the centre of
mass we eliminate the co-ordinates of the one body and so reduce
the problem to that of a system of two degrees of freedom. We
shall choose as the variables the relative polar co-ordinates of the
two particles, i.e. their distance and the angle p under which the
«-particle appears for an observer moving with the atomic nucleus,

1200

and shall call p the impulse corresponding canonically to », m
and M/ the masses, e, # the charges of the a-particle and nucleus
respectively, and finally v the initial velocity of the «-particle, the
atom being originally supposed at rest. The equation to the orbit
then assumes the simple form

1 uel
i= [ecos (pp) Ty vers ont An, mall
p

1 1 Beare:
ae aes AE + (2) 4 sG

Hence the angle p between the axis and the asymptote of the
relative hyperbolic orbit of the «-particle is given by

where

cos Pp = —
€
or
Det
p= wilt (goes et cana wike
Ip = Ee (12)

We can now change to the absolute motion by considering, that
the centre of gravity of the two bodies must move uniformly;
originally this point moves in the direction of the « particle with
the velocity ™’/(474m) and this motion has therefore to be superposed
on the relative motion.” A simple calculation gives the following
result'): after a sufficient time both bodies have assumed a uniform
rectilinear motion. The direction of the final motion of the «-particle
encloses an angle ® with the initial direction (through this angle
the a-particle is deflected by the collision)

tgp
ty D= ok 2s ade, oar 5 Ava
(m—M) + (M + m) tq’? p

the velocity V obtaining the value

v= Vise Mie Dim Menai aa.) .. (A

M - m
The angle between the direction in which the atom is propelled
and the original direction of the @-particle is exactly equal to the
angle p of equation (12). The velocity of the atom is

w= 2v— cong, . ee), eee ee die

According to the view set forth in § 4 certain special motions of

') Comp. C. Darwin. Phil. Mag. 27, p. 499, 1914.

1201

the system are to be allowed, namely those for which the azimuthal
impulse p has a value satisfying the conditions (97,6). In these the
letter » represents a positive whole number, but ==0 which would
be excluded according to SOMMERFEILD must also be admitted on the
point of view explained in § 2. In the latter case the assumptions
(9a) and (96) both give p=0O; hence

ma as

PD Me wit te Eer A

in other words: the nuclei or “recoilrays’” as RuruerForp has called
them, have for n=O the direction of the primary a-rays.

$ 6. Recoil-rays of hydrogen. Whereas. the values (16) which
obtain for n==0, hold generally for all kinds of atoms, the results
are less general for n=—=1, 2 etc.; we shall only discuss the special
case of the collision with a hydrogen atom. On the assumption (9a)
we have according to (12)

Ee. hv
PGP rank wee) ond) SAS en rl)
on assumption (95)
= hv
WPS Pr . t . . ‘ é + (18)

In these expressions we may substitute 4 = 6.55 X 10-77 erg. sec.
H= 4.7710—-' e.s. units e=2#; for v we shall take the velocity
of the a-rays of RaC, for which RernerForD gives the value
1.92.109 ¢™/,... we then obtain

pty p = 13.8 hy or tg p= 4.40n ‘een eee, BETS)
The first of these equations gives

nl, @, = 842, u, == 0,;10'u,, == 0,001 Fe;
n=2, g,=86°,50'", u,=0,055u,, R, = 0,0002 R-
The velocities u,v, are computed from (15), the corresponding
ranges A, 2, from the empirical equation R: R, = u*: wu’.
Similarly the second hypothesis gives
ei == 17% va RDR
EN OOAD == 83 ION Ai OE Re 0 00NRE
On the view that the particles can only move on the special
orbits allowed by the quantum theory, we obtain the following
result: a portion of the recoil rays are emitted in the direction of
the primary rays (n=O); besides there are only particles which
start at considerable angles to that direction, the smallest angle in

1202

the one case (96) being 77° in the second (9a) even 84°. The corres-
ponding ranges are exceedingly much smaller than for the H-atoms
emitted in the direction of the primary @-particles.

These results agree with the result of RurHerrorD’s experiments’),
who found al! the H-atoms to be propelled in the direction of the
primary rays. The range of this secondary radiation was 28 cms,
which gives R, = 0.028 em. or R, = 0.3) em. according as we use
(9a) or (95). These values are too small for experimental verification,
and were bound to escape detection.

§ 7. Transition to the stationary orbits. Up to the present time
the quantum theory has only been applied to systems whose members
permanently move round each other at a finite distance, i.e. systems
which in the LAPLACE-sense are stable. My attempt of 1916 (lc.) to
apply the theory to the single passage of a particle through the
sphere of action of a nucleus has not met with much sympathy
among physicists. lt therefore seems necessary to submit the difference
between the two cases to a careful conceptual analysis.

The hypothesis of the theory as established by Bour consists of
two parts: 1. There are certain preferential or stationary orbits in
which the system moves without radiation. 2. If the initial state is
not a stationary one, the system passes into a stationary state with
the emission of energy in the form of radiation. It is quite possible,
that the real process is only formally represented by this division,
but it has been confirmed in:several cases and it forms for the
present the only basis on which we can erect our further structures.

As regards the existence of stationary orbits, there does not seem
to be any reason, why the quantum conditions shouid be solely
applicable to finite orbits. Our views on this point have been ex-
pounded in $$ 3 and 4; but we shall try to strengthen them from
a fresh point of view. The difference between motions which are
finite and those which reach to infinity is expressed analytically by
the fact, that for the former each cartesian co-ordinate may be
represented as a Fourter-series according to angular variables,
whereas this is impossible for the latter. Bonr has established a
relation between the terms of this Fourimr-series and the transitions
which on the quantum-theory are possible from one stationary orbit
to another.

In the case of the relativistie Kepler-motion the Cartesian co-
ordinates are e= rcosp, y=rsing. For shortness putting

1) E. RUTHERFORD, l.c.

1203

Vp--p,’
a (o—9,) — ENE (20)
it follows from (3) that
p* po cos@ p'—p, sing
e= : U — —. . (21)
B 1—€cosw B 1—€cos

For a motion of elliptic type (¢< 1) r and y are periodic in
p and w witb a period 27; p and w are therefore angular coordi-
nates of the problem and a Fourier-expansion is possible’). Passing
to the case ¢ >1 the angle w becomes limited and varies between

| ats
the limits + arc cos (~) = +y. Only between these limits «and y
é

have the meaning of the functions given in (21); hence they may
now be represented by a Fourrer-integral

2 en 2
ae DB on fear i
a sE

The case is different for p: this angle isi varies between two
Bin
Vp po
a physical periodicity: on changing @ by the amount 2a the same
point of space is reached, so that # and remain periodic with
respect to p. We may continue the dependence on in the ranges

extreme values == + p; but in contrast with w it possesses

PS pa and —a<p<— p, where no motion takes place, just
as we like. It would be simplest to assume the continuance of the
law expressed by cosp and sin p over the whole range from 0 to
2a, in which case we should get

te

* cossh
p) + cos (s p—q) | ds

& cos 2

“ahd

It seems to me that in this result lies a confirmation of the
reasoning of § 4. The coefficient of w is the number s which may
assume any value, whereas the coefficient of is the whole number
1. Extending Bour’s principles to this case we might conclude that
the radial quantum which is subordinated to yw underlies no limi-
tations, whereas the azimuthal quantic number can only change by

1) These coordinates are not linear functions of the time. If we wish them to
satify the latter condition, they have to be defined differently. But the conclusions
to be drawn remain valid with this change in the definition.

1204

| each time. In this way it is made probable, that the azimuthal
impulse possesses discrete special values and the analogy with the
case of the elliptic motion imparts special probability to the hypo--
thesis (96).

Although the existence of stationary orbits is thus rendered pro
bable, it does not follow that a particle which to begin with is not
moving in a stationary orbit will have time and opportunity to pass
into one. The giving off of energy requires time which is always
available in the case of stable motion (in Lapnacr’s sense). But for
hyperbolic motion the case is different: the energy is not limited
by any conditions, but the rotational impulse tends towards definite
values which can only be reached by the process of radiation of
electromagnetic moment of momentum. For this radiation the time
available is only the one motion past the nucleus, and it is thus
quite possible that the impulse lost by radiation is not sufficient and
that the particle returns to infinity without having reached a stationary
condition. On the basis of Maxwett’s theory this would even be the
usual case. Calculation gives for the radiated impulse (for p >> p,)

eu’ xe

2 /
elas (+55) b m1 ,
pv Pr ned HE xe
that is an amount of the order 10! erg sec., whereas the steps
of the constant p are about 10-°7 erg sec., or about 1000 times
larger. Under these circumstances no fraction of the particles worth
mentioning could attain stationary orbits.

On the other hand we have the experimental fact, mentioned in
the previous section, that the H-atoms are preferably emitted in the
direction of the incident a@-particles and it seems difficult to interpret
this otherwise than on the quantum-theory. One of the possible ex-
planations of Rurserrorp’s results seems therefore to be that the
radiation is really stronger than would follow from Maxwerr’s theory,
sufficiently so to carry a considerable portion of the systems into
the stationary condition. When we consider that even in the radiation
of the hydrogen spectrum, where the distances from the nucleus
are greater than 2 < 10-8 ems, a considerable deviation exists from
MaxweLr’s theory, the supposition in RUTHERFORD's case of a very
much larger deviation does not appear to us too hazardous. For
the distance from the nucleus is here of the order 3.5 < 10—13 and
thus the acceleration about 1.5 X 10° times larger than in the
emission of the hydrogen lines. Moreover Einstein *) has postulated
a complete breach with Maxwe..’s theory for elementary processes

3

C

1) A. EINSTEIN. Kleiner-Festschrift, Zürich 1918.

1205

of this kind and we further know from the existence of a limit
of the Röntgen-radiation on the side of the small wavelengths, that
they cannot take place in accordance with the theory. According
to RutHerrorp’s experiments the relative number of the emitted
recoil-rays is strongly dependent on the rapidity or range A of the
primary a-particles, as shown by the following table:

ie '720 5,3 4,5 3,7 3,0 ete.

Vi == 100 77 51 25 0.

This might be interpreted as indicating that the radiation of
rotational impulse decreases rapidly with the speed v, so that with
falling v there are less and less particles which are able to reach
the stationary orbit. If this view is correct, we would have in
RurnerForD’s table a new way along which to penetrate into the
riddle of the quantum theory.

Side by side with particles which have completed the transition
into the stationary orbit, others are to be expected, even with the
highest velocities, which owing to a higher initial impulse have not
succeeded in doing so. The directed radiation must therefore be
surrounded with a scattered radiation. According to a kind personal
communication of sir Ernest Rutarrrorp’s something of that kind
is found experimentally: a new experimental method has shown
that the recoil-rays are in reality less homogeneous than appeared
originally and that side by side with the rapid H-particles observed
at first, there are others of smaller speed’).

As suggested above it is probable that the large deviations from
Maxwerr’'s theory, as required for a sufficiently strong radiation,
are limited to the range of very high accelerations. This makes it
doubtful, whether a similar approach to the stationary orbit n = 1
is to be expected as to the orbit n = 0; for the range near it
correspondends to a much greater distance from the nuclens.

On a different occasion we hope to discuss the question, bow
the stationary orbits are distributed for nuclei other than of hydrogen.
We shall only mention here, that for heavy atoms the equations
(17) and (18) owing to the high value of the nucleus charge #
make the steps of the discrete angular distribution so small, that
the result cannot differ appreciably from a distribution in accordance
with classical statistics.

1) Cf. E. RUTHERFORD, Phil. Mag. 41 (6), p. 307, 1921.

Mathematics. — “Properties of Congruences of Rays’. By H. J.
VAN Vuen. (Communicated by Prof. J. Carprnaat).

(Communicated at the meeting of February 26, 1921).

§ 1. The rays of the space =, can be represented by a quadratic
hypersurface 07, in a five dimensional point-space 2,. By the aid
of this representation [ have derived the properties of a few com-
plexes of rays (Nieuw Archief voor Wiskunde R 2, dl. XI, p. 232;
id. dl. XII, p. 19; Handel. 17° Nederl. Natuur- en Geneesk. Congres
1919, p. 171). By the method followed there also the characteristic
numbers for an arbitrary complex of rays can be determined. In
what follows 1 shall make use of the representation mentioned to
derive some of the principal properties of congruences of rays.

§ 2. In the first place I consider an arbitrary congruence of the
field-degree p and the sheaf-degree q. This congruence is represented
in >, by a surface V, of O7,, which has p points in common with
any a-plane (representation of a field of rays) and g points with
any B-plane (representation of a sheaf of rays).

$ 8. Let P be an arbitrary point of V,. A hyperplane through
P cuts V, in a curve that has one tangent in P; the tangents in
P to V, form, therefore, a plane pencil. 2 of the straight lines
through P on O?, (images of plane pencils: of 2,) lie in a linear
space A, throngh P; for a ray of >, lies in 2 plane pencils of
a bilinear congruence to which it belongs. The straight lines of O°,
through P form accordingly a threedimensional quadratic cone. The
plane pencil and the cone lie in the hyperplane touching O?, at P
and have therefore two straight lines in common. Consequently :

Any ray of a congruence is intersected by 2 consecutive rays, or

On any ray of the congruence there le 2 focal points and through
any ray of the congruence there pass 2 focal planes.

The identity of the surface of the focal points with that of the
focal planes (the focal surface) can easily be demonstrated now in
=, (See e.g. Sturm, Liniengeometrie II).

§ 4. The hyperplane R, touching O?, at a point P, cuts V, in
a curve V,. This I project out of P on a linear space R, in A,

1207

Of the a- (9-) planes through P two cut a straight line of R,;
they intersect A, therefore in the a- and b-lines of a quadratic
surface O?. On O' lies the projection & of the curve V,; & has the
a- and 6-lines as p- and q-fold secants. The projections of % out of
a point O of U? on a plane r of R* gives a curve k’, which has
a p-fold and a q-fold point in the passages A, and B, of the a- and
b-lines through O. The straight line A,B, has only the points A,
and B, in common with 4’, hence &’ is of the order p+q. If r
is the number of double points of 4, hence also of 4’, the class of
Rs:

(PN hl Ook) ag (G1) ar’ "2e
so that out of A there can be drawn
2 (pq—r) — 2g = 2g (pl) — 20
and out of B
2 (pq—r) — 2p = 2p (q—1) — 2r
tangents to &’, touching this curve elsewhere.

These numbers are at the same time the numbers of b- and a-lines
touching & and also the numbers of the g- and the a-planes through
P that have two coinciding points in common with V,.

Now r is the number of bisecants of V, through P or the axis-
degree (rank) of the congruence in consideration, hence:

The focal surface of a congruence of the field-degree p, the sheaf-
degree q and the axis-degree r is of the order 2p(q—1)—2r and of
the class 2q(p—1)—2r.

§ 5. I shall now consider the complete congruence of intersection
of two complexes.

If these are of the order m and n, they have as images the
multiplicities which O*, has in common with two hypersurfaces
Vi and V,". These two hypersurfaces cut each other in a multi-
plicity V,m. The bisecants of V,”" passing through a point P and
cutting a plane zr lie in the linear space Rh, =(P, 2); they are also
the bisecants through P of a curve in PR, which is the complete
intersection of a surface of the mt» order and a surface of the nth
order. The number of these bisecants is 4 mn (m—1)(n—1), hence
the bisecants of V,”" through P form a cone of 3 dimensions and
of the order 5 mn (m—1)(n—1). By choosing P on O*, it appears
that through this point there pass mn(m—1)(n—1) bisecants of Vy
that lie on O?,, accordingly :

The congruence of intersection of a complex of the m* order and
a complex of the n™ order has the axis-degree mn (m—n)(n—1).

1208

$ 6. In order to find the order and the class of the focal surface
of the congruence of intersection of two complexes, [ pass two
a-planes a, and a, through a point P of O?,. The @-plane through
a ray a, of the plane pencil P, a, cuts «, in a straight line a,. A
plane y through a, which cuts «, in a straight line a’, and has two
coinciding points in common with )’,”", touches the curve which
the space R,=(a,«,) cuts out of V,”"; as this curve is the curve
of intersection of a surface of the m'* order and a surface of the
nt order, it has the rank mn (m+n—2); accordingly this is the
number of the planes through a, intersecting «, in a straight line
a,‘ and at the same time touching ),”". Between the rays a, and
a,! belonging to the same ray a,, there exists a [mn (m-—-+-n—2),
mn (m+n—2)| correspondence, hence there pass through P 2mn(m—+
n—2) 3-planes (and as many «-planes) touching V,”". or:

The focal surface of the congruence of intersection of a complex
of the m* and a complex of the n® order, has the order and the
class 2mn(m—+-n—2).

Of course this result can also be derived from § 4 and § 5.

Anatomy. — “OMBREDANNE's Theory of the “lames vasculaires”
and the anatomy of the canalis eruralis”. By G. C. Herinaa.
(Communicated by Prof. J. Boeke).

(Communicated at the meeting of December 18, 1920.)

When adopting the reasonable and general view tbat the muscular
fasciae are to be considered as compressions of loose connective
tissue, originated under mechanic influences exerted by the surrounding
individual muscles, a conception bas been propounded, which brings
before ‘our mind the ‘““muscle-compartments” in a clear and com-
prehensible way, and which is also of great practical value. Still,
it would seem that the scientific value of this view may justly be
contested. It would seem also that in order to obtain a clear notion
of the matter these formations of connective tissue themselves should
receive more of our attention than the spaces invested by the fasciae
and filled up with muscles.

I would call upon the reader to consider a fascia as a thin layer
of undifferentiated connective tissue, bounded on either side by a
lamina of fibrillary connective tissue. Further we conceive a blood-
vessel running in the middle layer and we imagine, in accordance
with the publica opinio, that the two plane faces have, as it were,
been attached through a polishing process to this interstitium of
connective tissue by the mechanic action of the surrounding muscles,
or by other tissues. This hypothesis approaches real facts, for a
similar position we observe of the vasa plantaria med. und lat. in
the septa intermuscularia pedis; a similar location we observe of
the vena jugularis ext. in the fascia superficialis colli, of the aa.
meningeae and the sinus durae matris in the hard cerebral membrane,
of the vena saphena magna in the fascia lata, of the vasa epigastrica
in the fascia transversalis"), and finally in a similar way numerous
nerves — suffice it to mention only the n. cutaneus femoris lateralis,
the branches of the n. femoralis, of the nervi superficialis colli —
are running in the fasciae, prior to their ultimate intrusion into the
skin.

The instances here enumerated, could easily be increased. They
lend support to the roughly phrased conception that, generally

1) Tesrur et Jacos, Traité d’Anat. topogr., p. 45.
78
Proceedings Royal Acad. Amsterdam. Vol. XXIII.

1210

speaking, an inner layer of vessel-conducting connective tissue is
the essential factor for the fasciae and „ot the polished fibrous tissue,
which for the knife and for the eye is their characteristic aspect.

This is analogized by the mesentery, in which the functional
essence is not constituted by the peritoneal epithelium lining it, but
in reality by the vessels contained in its connective tissuelike sub-
stvate'). The thought underlying the view set forth here, is by no
means new. It is OMBREDANNE's. This author has worked it out in
his thesis (Paris 1900), particularly for the abdomen and the pelvis,
but he also surmises its validity for the whole body :

“Il existe’, OMBREDANNE says, “entre le peritoine de l’abdomen et
du bassin une lame vasculaire, contenant les vaisseaux dans son
épaisseur, émettant une lame secondaire, quand l’artere émet une
série de branches dans un autre plan, que son plan de ramfication
principal émettant une gaine vasculaire periviscerale quand l'artêre
émet un bouquet de branches allant envelloper un organe, présen-
tant des renforcements du côté, d'où viennent les pressions, et
capable de se souder au niveau de ses plicatures”’.

We see then that according to his description the fascia pelvis is
such a “lame vasculaire” differentiated in the subperitoneal connec-
tive tissue, which “lame” is in the first instance attached to the
large vessels lying against the pelvic wall, but from which “lame”
determined by the outgoing ramifications, a number of lateral
septa are emanating, which, in a frontal arrangement, divide the
subperitoneal space into a number of partitions *) or leave the pelvis
along with the ontgoing vessels (vv glutaea, pudenda) and thus may
assume the character of intermuscular septa. There is, according to
OMBREDANNE, a Close relationship between vessels and connective
tissue, which invariably reveals itself in a condensation of the latter,
in continuous connection with the vascular adventitia®). Fundamen-
tally it is quite immaterial whether here, as in the case alluded to
in the outset, pressure or distension on the part of the environing
tissue influences the morphosis of the whole, or whether it does not.
In the region of the pelvic fasciae examined by OMBRRDANNR this
manifests itself e.g. by the fact that a rather smooth plane of con-

1) This parallel between fascia and mesentery, which also OMBREDANNE has
drawn, might still be extended, if, as is most likely, every fascia has u super-
ficial lining of endothelium.

2) A clear and concise compendium of it may be found in Trsrur-JAcoB.
Tome |I, p. 391-398.

5) In a section through the umbilical cord the more precise arrangement of
the connective tissue elements round the vessels is distinctly noticeable.

1211

nective tissue, the so-called muscular fascia of the M. levator ani,
lines the muscular bottom of the pelvis; that, however, the frontal
extensions, which do not undergo any pressure, gradually fade away
in the subperitoneal connective tissue.

My starting-point then was the fundamental idea of OMBREDANNE’s
reasoning, which runs as follows: “.... que les vaisseaux ne sont
nulle part libres entre deux feuillets fibreux, on entre un plan fibreux,
et un plan périostique; si l’on arrive a les isoler, a les disséquer,
comme on dit, c'est a l'aide du tranchant d’un scalpel”... “Nous
avons dit, que nous ne croyons pas les vaisseaux inclus libres entre
deux feuillets dans une gaine, mois plongés dans l’epaisseur d’une
lame: la formation de ces lames est la consequence méme de la
formation du tissu conjonctif. Ce tissu est essentiellement un tissu
de remplissage, de soutien; mais il n'existe que la, où il soutient
quelque chose’... “Lorsque une artere s’épanouit en un éventail
de branches, disposées dans un méme plan, il constitue a cette
-artere et à ses branches une lame vasculaire, qui pourra s’infléchir,
dont partiront des lames secondaires.”’

It was an investigation on a totally different basis which by
chance, as it were, led me in the direction of OMBREDANNE’S con-
ception of which | had some cognizance through Trsrur and Jacos’s
work. But for the very reason that the results of this investigation
compelled me to follow the general principle of OmBREDANNE’s con-
ception, | feel inclined to preface the publication of those results
with a few theoretical considerations.

In the year 1919 Fransen of Leyden wrote a thesis in which
the significance of the fasciae for the bloodstream in the venae was
emphatically brought forward. As shown by him: ‘over the whole
length of the lower extremities there exist formations of which the
principal components are fasciae connected with muscles; formations,
which guard the large venae and the arteriae from compression,
and through their relation to the environment can perform the
function of a suction-apparatus, by which the venous circulation of
the blood and the continuous supply of arterial blood is guaranteed
and promoted. Theorically as well as practically (with regard to
the pathogenesis and the therapy of the varices) FRANsEN’s clear
exposition is no doubt of great value. It seems to me that he has
hit the nail on the head in his roughly worded conclusion quoted
above. Still, I presume to raise an objection to the details of his
exposition, however cautiously they may have been laid before us.
Among the instances prefixed by FRANSEN to the conclusion just
quoted, we distinguish two groups of different nature. On the one

18

1212

hand he describes the vena femoralis as lying “in a prismatic space’,
bounded by fasciae, and in which a negative pressure is supposed
to arise with contraction of the M. sartorius through tension of the
fascia lata. On the other hand in the same demonstration the cir-
cumstance that the vena poplitea is kept open on leaving Hunters
canal, is correlated with an arcus tendineus stretched by adductor
fibres and grown into one with the vascular sheath. Then again,
according to the writer the same principle holds for the fossa
poplitea and for the fossa Scarpae. On the other hand again, the
arcus tendineus of the M. Soleus is supposed to act in the same
way for the vasa tibialia, passing below il, as above the M. adductor
magnus for the vv. poplitea. :

It is obvious that two different principles have been mixed np
here by the writer. Moreover the question arises whether these two
mechanisms to keep the venae open actually coincide.

Now, | think, some objections may at once be raised against
FRANSEN’S interpretation of the effect of a negative pressure in the
fossa Scarpae and the same applies of course to the fossa poplitea.

In the first place for a negative pressure-action to arise, as FRANSEN
conceives it, it is necessary for the “space” containing the vessels,
to be closed hermetically. It is both groundless and improbable to
suppose that such a closure should be brought about by the fasciae.

In the second place that “space” round the vessels is quite filled
with more or less closely woven connective, as is easily made out
by the study of transverse sections. And though the intercellular,
interfibullar groundsubstance of that connective tissue may be humid,
it would require special experimentation to see whether any negative
pressure could be propagated through such a colloidal medium.

In the third place, granting these two conditions to be fulfilled
and the influence upon the vena as supposed by FRANSEN to really
exist, two other conditions have to be satisfied for an effect on the
bloodstream im the vena:

a. change of place or form of the vena as a whole on one side
should be excluded. A ‘prismatic space’ could not satisfy this
condition

6. Since we cannot conceive of a sucking pump without valves,
there must needs be at least one valve proximad from Hyrrr’s
suction-apparatus. Now it is remarkable that on page 26 of his
thesis FRANSEN says, in agreement with Dergert: “No valves occur
(or if any, the are insufficient) in the vena fomoralis beyond the
outlet of the vena saphena magna.”

So it seems to me that FRANSEN’s view is open to controversy on

1213

several points, even though, for the rest, the anatomic relations
were such as he supposes them fo be. In fact, the last-named are
decidedly more complicated. It seems to me that, on arguments to
be brought up presently, we should really no longer consider the
“fossa” Scarpae as a space enclosed by walls independent of its
contents. There is, on the other hand, every reason to follow in
OMBREDANNE's track, and assume it to be a connective tissue enclosed
by muscles, carrying the vasa femoralia, besides the lymphatic
vessels, and the lymphatic glands, of which connective tissue the
superficial layers (i.e. those lying against the muscles) have been
compressed into fascia lata, deep and superficial layer. In other
words I am inclined to consider the fossa Scarpae, wall and con-
tents taken together, as a “lame vasculaire” which has adapted its
shape to the available space.

Still, although I cannot endorse Fransen’s exposition, I think
nonetheless that his pronouncement regarding the functional signi-
ficance of the fascia lata for the bloodstream in the vena femoralis,
is correct in so far as the fascia plays a part in keeping the vena
open. But this, I believe, to be the consequence of the direct con-
nection of the fascia lata with the connective tissue sheath of the
vessels themselves.

Now about the relations in Hunrer’s canal. Weil, it seems to me
that they may readily be looked upon from the same point of view
that we just now suggested for the fossa Scarpae. This could be
realised beforehand since HuntEr’s canal is direetly continuous with
the fossa Scarpae. FRANSEN points out, with reason, that HUNTER’s
canal is invested by three aponeurotic fasciae. Well then, here also
the vessels do not lie loose in that space, but wall and contents
again form one whole. Here again, just as with the fossa Scarpae,
the connective tissue layer bordering on the muscles, assumed the
character of a fascia, in this case complicated because muscle-fibers
attached themselves to this fascia and thus bestowed on it an apo-
neurotic character. It follows then in my opinion that FRANSEN’s
arcus tendineus is to be conceived as an aponeurotic fibre-bundle
fascie, closely related to the vessels.

As | alluded to above, the investigation which led me in the
direction of OMBREDANNE'’s theory was of quite a different nature, so
that in order to discuss this question I must call the reader’s
attention to a totally different matter. I was induced to undertake
my investigation by a question, put to me by Dr. La CHAPELLE,
at the time assistant at the surgical clinic of Leyden.

I will repeat the question here in its original form. The starting-

1214

point was the following observation made by Dr. La CHAPELLA:
“After reposition of the stump of a tied up hernial sac in non-
incarcerated hernia femoralis, a more or less sharp border may be
felt when passing the finger under Poupart’s ligament, the border
constituting an arch over the os. pubis. The question to be answered
runs as follows: Has this border, which will incarcerate the hernial
sac, even before Poupart’s ligament does so, been prefor-
med anatomically, and if so, what is it?

We might alter the question and say that we have to establish the
identity of a clinically tactily ligament, which being concentric
with Gimbernat’s ligament, but located on a deeper level,
narrows the entrance to the crural canal. Now, seeing that, as we
read in surgical manuals, the incarcerating factor proper of the hernia
femoralis is not known precisely, because after the removal of
Poupart-Gimbernat often still further cleaving of deeper fibers,
entwining the neck of the hernial sac, is required, we deemed it
worth our while to look into this matter from a practical as well
as from a theoretical point of view. This inquiry was begun by —
myself in conjunction with Dr. La Caapenia. Only a considerable
time later could I conelude it, thanks to Prof. vaN DEN Brork’s and
Prof. Baren’s kindness in granting me the loan of their material at
Utrecht. I also feel indebted to Dr. van Rissrr, at the time prosector
for pathological anatomy at Utrecht, for yielding me an opportunity
to verify the results obtained in the anatomical laboratory at an
obduction “ corpse. I thus examined three corpses in all, two male
bodies and one female, while of another female corpse sagittal frozen
sections through the pelvis were examined.

When removing from the triangle of Scarpa the skin and the
superficial layer of the fascia lata, and cautiously cleansing the
large deep lymphatic vessels, it will be seen that the latter disappear
into the medial upper angle of the regio, where by the aid of
Gimbernat’s ligament, the ligament of Poupart touches upon
the pecten ossis pubis and fastens itself to the fascia pectinea. This
convergency of the lymphatic vessels, besides the location im situ
of one or more of the lymphatic glands (Rosemiiller’s glands)
induce us to suspect Cloqnet’s septum to lie in that corner
of the inextricable fibrous tissue. This septum Cloqueti is described
as a subdivision of the fascia transversalis, which after fastening
itself to Poupart’s ligament extends to the os pubis and thus
obturates the entrance to the crural canal, as a vertical septum
pierced only by lymphatic vessels. But, if we closely consider what
our preparation reveals, there seems to be something wrong, viz.

1215

the entrance to the crural canal seems not to fill up all the space
between Poupart and the os pubis; as none of the lymphatic
vessels on its way to the pelvis passes directly beneath Poupart,
but they all dive down to a deeper level. And when palpating
cautiously along the frontal border of the complex of lymphatic
vessels, we feel that the frontal border of the entrance to the crural
canal is formed not by Poupart’s ligament but by another tightly
stretched connective tissue band, which runs parallel to Poupart,
but is about 1 ¢.m. lower and lies somewhat deeper, and is approxi-
mately concentric with the curving fibres of Gimbernat’s ligament;
it also appears that this frontal border as well as Gimbernat’s
ligament converged with the fascia pectinea.
Through this palpation we were able to corroborate to some
extent LA CHAPELLE’s finding and now it will not be difficult to
lay bare the bundle of fibres under consideration. If namely the
lymphatic vessels are prepared away, we can see this bundie as
well as when we felt it just now. (Fig. 1). We see then that the
entrance to the crural canal is bounded at the front by this strand,
which is separated from Poupart by a ioose- meshed connective tissue.

yy

—
a

Fase. lata

1216

Furthermore, if we expose the deeper layer entirely by cutting
Poupart through and folding the flap back, we see that what
seemed to be a strand of connective tissue, is in reality the sharp,
free lower border of a fascia, which descends from above behind
Poupart.

This being established it was not difficult to expose this fascial
leaf upwards, and to ascertain its continuity with the fascia trans-
versalis abdominis. When this fascia is laid bare by preparation,

li-t-fasc.su.

M-transv__ Jul |.
pf j-M-obl.ext.

en obl.int

Fig: 2.
Sagittal section of a female pelvis about the vv. femoralia.
Semi-schematic.

after removal of skin and muscles, it will be seen to descend
farther, after having: passed behind Poupart’s ligament, under
exchange of a more or less distinct supply of fibers, till it meets at
a right angle the vasa iliaca externa, which runs subperitonically
on the bottom of the pelvis. These vessels it envelops in the well-
known manner in which the fascia pelvis encloses the organs which
pierce the bottom of the pelvis; it envelops the vessels with a
fibrous formation, which partly runs proximally with the vessels

1217

partly accompanies them distally and passes with them to the crural
regio beneath Poupart’s ligament. The faszia layer, of which, as
described above, we could spy the free border after removal of the
fascia lata (superficial layer), is indeed nothing else but the lower
end of the fascia transversalis, which could not but pass on to the
thigh, because it had been inseparably attached to the vessels by
the formation of the vessel-sheath.

ftransv- | ben
M.Rectus-- îJ-M.obl. int.
HLL m_obl.ext.
i-F-fasc. sup.

Lig. Goeper

Fig. 3.
Paramedian sagittal section through a female pelvis. Showing semi-schematically
the insertion of THomson’s ligament on the os pubis. It is remarkable that, in
consequence of an exchange of fibers of the m. rectus and the f. transvers, a close
connection is brought about between THumson’s lig. and the insertion of m. rectus.

_ In harmony with this the free border of this extension of fascia,
just now described, and radiating out medially into the fascia pectina,
concurs in forming the vessel-sheath where it could no more be
separated from the fibers of the fascia lata.

When I had proceeded so far in my investigation, | felt justified
in establishing that the fascia transversalis, instead of inserting itself
to the os pubis and of forming CroQvet’s septum, terminates
medial to the femoral vessels with a free border, and that, therefore,
the lymphatic vessels, instead of piercing the fascia
(in loco Sept. of Croquwm), pass undermeath it to the

1218

subperifoneal areas of the pelvis. That more laterally the
fascia transversalis attaches itself the ruscular sheath of the femoral
vessels, did not surprise me as | was not ignorant of Testur-Jacos’s
description of the “insertion inférieure” of the fascia transversalis:
“Puis, continuant son traject descendant, ce fascia rencontre les
vaisseaux femoraux: il se fixe sur leur pourtour, en contractant avec
eux, avec la veine particulièrement, des adhérences intimes” (p. 43).

However my view was considerably altered when a close study
of the sagittal sections taught me the following facts:

1. That the free border alluded to was an artificial product
originated during the removal of the fascia lata for that there is a
continual relationship between tbe fascia transversalis and the
fascia lata.

Fig. 3 shows how some of the fibers of the fascia lata attach
themselves to Poupart, resp. blends with the fascia abdominis
superficialis; how others, the larger number of its fibers, running
along behind Poupart get connection with that lower end of the
fascia transversalis, which, as described above, reaches the crural
region together with the vessels. Thus formulated this remark may
sound strange to the reader; on closer inspection, however, our
representation is not so strange, not even new. Also in the litera-
ture mention is made everywhere of the junction of the fibers of
these two fasciae in the ligamentum inguinale, to which, from above,
the fascia transversalis, from below the superficial layer of the fascia
lata, attaches itself. And besides, already DerBer (Poirier. Traité,
T. 5, pag. 89) reports a concurrence of the f. transversalis with
the vessels on the thigh. ;

2. We saw just now that the fascia lata and transversalis were
connected when passing before the vessels, on the tacit understanding
that with f. lata we meant only the superficial leaf. Now the sagittal
sections afford us another datum of fundamental significance, viz.
that while passing behind the vessels the fascia transversa is in
precisely the same way connected with the deep layer of the fascia
lata, ie. with the layer that lines the bottom of the fossa scarpae.
This is no novelty either, since, as we know, Cooper’s ligament
lining the pecten ossis, is generally acknowledged to be an inter-
lacement of fascia transversa and deep fascia-lata-fibers.

When combining the facts mentioned under 1 and 2, we arrive
at the conclusion that, as said above, the fascia transversa,
on meeting the vasa iliaca, not merely attaches itself
to them, but forms round it a closed sheath. For further
illustration we add the following particular: .

1219

Just as Poupart’s and Cooper’s Ligament are formed by
transversal, fiber bundles interwoven where fascia-extensions, coming
from different directions, meet, we also find in a number of cases
a fully developed frontal fiber-bundle there where passing behind
Poupart f. transversalis and fascia lata become merged. This is
the very bundle felt by La CHAPELLE in vivo. It naturally runs
parallel to the ligamentum inguinale in a somewhat deeper level.
This ligament, which I observed most distinctly in two of the four
corpses examined, and which in the frontal section of the female
pelvis was highly conspicuous as a bundle of 2 mm in diameter
(see figs 2 and 3), is no doubt the same as THomson’s ligament
(Bandelette iliopubienne) described especially by French writers.

3. While then the fascia transversalis forms distally a closed
vascular sheath about the vasa femoralia, proximally te same thing
occurs, as pointed out above. This bears more particularly on
OmBREDANNE’S region. According to a number of authors the fascia
transversalis reaches no further down than to the upper limit of
the pelvis, which means to say down to the os pubis. It goes
without saying that this view is incompatible with the relation
described by me. Besides relying on direct observation of my
sagittal sections which in my judgment, proves irrefutably the con-
nection between fascia transversalis and fascia pelvis, I also call
to witness other authors making special mention of this connection.
First of all SpaLrrHortz in his well-known atlas (p. 613); secondly
Pau Dergert, whom we have referred to in connection with the
crural extension of the fascia transversalis. There we read: „En
bas il (F. tr.) descend seulement jusqu’ au pubis (CHARPeY, Piprre
Dergert); le plus souvent, si jen crois mes recherches, confirmées
par les récents travaux D’OMRREDANNE, il se continue jusqu’ au plancher
pelvien. Il recouvre alors sur la ligne mediane le pubis, qu’il sépare
de la vessie, latéralement le ligament de Gimbernat: plus en
dehors lorifice des vaisseaux fémoraux. Une partie de ce tissu
cellulaire suit les vaisseaux dans la cuisse, l'autre descend directe-
ment derrière lorifice en formant le septum crural. Par sa face
antérieure il adhère intimement aux arcade de Dovaras, en bas il
contracte avec la face postérieure du pubis des adhérences laches’, etc.
It will be remembered that in the exordium of this article we have
stated that OMBREDANNE has emphatically asserted that the vessels
in the subperitoneal pelvic connective tissue are not merely lined
by the fascia pelvis, but that this fascia provides them with a
complete sheath, that as OMBREDANNE puts it, then run 22to this
fascia. Now when correlating this deseription, which as already

1220

mentioned, was endorsed by many French authors, with my obser-
vations concerning the fascia transversalis, which yielded data quite
in keeping with OMBREDANNE’s conception, we conceive the following
image of the entire complex of fasciae in these regions and its
relation to the large vessels:

From their subperitoneal course along the floor of the pelvis, up
to the leg the vessels run through one continuous tubular sheath,
formed by a series of interconnected fascia-formations, in which,
however, as OMBREDANNE rightly points out, the vessels are not free
but are enclosed by, embedded in, massive connective tissue.
It seems, therefore, admissible to assume that these fasciae are,
indeed, nothing but compressions, (due to some mechanic cause),
of the vascular connective tissue, where its surface was exposed to
friction and pressure from environing elements. ')

Still there is one more item I should like to discuss in this con-
nection. The importance which OMBREDANNE ascribes to the vessels
in his treatise, and which reveals itself also in his terminology
(lames vasculaires) has caused him to be accused of one-sidedness.
That OMBREDANNW's conception requires, indeed, to be worked out
a little more, cannot be demonstrated better than in the very region
of Scarpa’s triangle. For, if we once more consider the boundary
of the ‘‘fascial tube’, the frontwall will be seen to be formed by
the superficial layer, the back-wall by the deep layer of the fascia
lata, both of which are continued in the fascia pelvis with the
co-operation of the fascia transversalis. It is clear, therefore, that
what is known in topographical anatomy as “Fossa Searpae’’ is
nothing else but a considerable distension of the ‘lame vasculaire”;
which distension may be explained by the presence of the large
number of lymphatic glands in situ, which will apparently occur
also in that “lame”. For the very reason that the lymphatic vessels
require so much space the ‘fascial tube’ cannot enfold the vessels
closely, on its passage under THomson’s ligament; this is why this
ligament of THomson, instead of uniting medially to the vessels
with the deep layer of the fascia lata, attaches itself only much
farther medially to the f. pectinea; and finally this is why we
observe on the medial side of the vessels a mass of connective tissue,
furrowed with lymphatic vessels, bridged over at the front by
THomson’s ligament, at the place where (in my judgment wrongly)

') The term „fascial tube” should not bring before our minds individual, inde-
pendent formations. | could not find a better expression. From what has been
said and will still be said, it will be clear to the reader, I hope, that it is just
the passive capacity of assimilation of the connective tissue that I wished to accentuate.

1221

observers presume to have detected the Septum of Cloquet. In
reality what has been described as such, is nothing but a mass of
connective tissue bundles filling up the space left between the
lymphatic vessels. | am firmly convinced that, together with the
vessels, also the lymphatic vessels run from the leg as far as the
pelvis and perhaps further, in a permanent connective tissue sub-
strate, surrounded by connected fasciae, which according as the
local relations vary, will be outlined more or less sharply.

In the foregoing I do not at all presume to have brought forward
new facts. Such facts as were disclosed in my preparations have
already been discussed by others. How could it be otherwise, con-
sidering that the same field bas already been worked up thoroughly
numberless times by numberless anatomists? If then, in spite of this
I have been bold enough to take up again the anatomy of the crural
canal, it is because I believe that the bringing together of some details,
about which some authors still disagree, may serve two purposes:

In the first place this inquiry may be conducive to increase the
appreciation of the connective tissue in the strict sense of the word,
also in macroscopic anatomy, without derogating from the fasciae.
We only wish to lay stress on the fact, that as OMBREDANNE argues,
the connective tissue is essentially a supporting tissue: ,,. . . mais
il n'existe que là vu il soutient quelque chose”. Moreover, apart
from the appreciation due to Fransren’s valuable work described
in his thesis, my paper may tend to forestall the view that the
fossae of the topographical anatomy are to be considered essentially
ag spaces, in which a vacuum could readily be induced.

In the second place what has been reported in this paper, may
be of some valne for applied anatomy, also in another respect. For
instance our conception of the canalis cruralis is somewhat modified
by it. Whereas hitherto it has been described as a region, more or
less independent, and enclosed by independent muscular fasciae, it
would be more proper, I think, to look upon this path, along which
the hernia proceeds, as a subdivision of a large continuous complex
of connective tissue. It is generally imagined that an entrance into
this forbidden space is made by forcing Cloquet’s septum, which
is Supposed to stand at the beginning of the tunnel. I, on the con-
trary, would contend that, since there is no real entrance of the
tunnel anyhow not in that sense, a spot must be found somewhere
else, when the intrusive peritoneum can press itself into the fascial
tube. Indeed, I believe to have found a ‘‘weak spot” in the fascial
wall, which may be deemed answerable for such a dereliction of
duty. When we consider that the fascia transversa, running across

1222

the os pubis, leaves the pelvis at the place, where the vasa femo-
ralia is located (see Fig. 4), while it covers the posterior part of

Fig. 4.
Front-view of the f. transversalis after detaching and folding back
all layers of the anterior abdominal wall lying before it.

this bone, i.e. the interior of the pelvic wall, medially behind the
corpus ossis pubis, we may naturally expect that in one spot or
other, situated between these two places, the fascia transversa must
cross the os pubis. Now, this crossing-point could easily be found
in our anatomical preparation, because at the same place a trans-
parent spot became at once conspicuous. Moreover this spot was
less resistant to the pressure of the palpating finger, so that it is
not out of the bounds of probabilities to state that there, that is
exactly on the inside of THomson’s ligament, the fascia yields to the
peritoneum and allows it to force its way into the canal. It should
be noticed that, if this supposition is correct, the hernial sac must
enter the canal from the medial side, on the medial side of the
vessels, consequently precisely at the spot where the septum femorale
is usually localized, so that my view does not clash with daily
experience. However, further investigations may throw more light
upon the matter.

Mathematics. — “Explanation of some Interference Curves of
Uniavial and Biaxial Crystals by Superposition of elliptic
Pencils”. By ‘J. W. N. re Heux. (Communicated by Prof.
Hk. pr Vrits).

(Communicated at the meeting of February 20, 1921).

In Lissasous’ “Etude optique des mouvements vibratoires’*), the
name of ‘Unisson” is given to the curve, resulting from the com-
position of two vibrations, which only differ in amplitude and in
phase.

When the amplitudes are supposed to be equal and not diminishing
with continued movement, when the directions are at right angles
and the difference of phase increases from 0° to 90° — the unisson
may be considered asa pencil of ellipses, whose envelope is a square ’).

The null-ellipse of this pencil is a diagonal d, of the square, the
end-ellipse is the circle, inscribed in the square. Let the other diagonal
be d,.’

Two equal unissons, U, and U,, partially covering each other,
produce certain ‘watered curves” (moiré), which may be divided
into two sets:

1°. those similiar to hyperbolas, when the exact covering of U,
and U, may be obtained by moving the centre of the pencil along
d, (fig. 1) and |

2°. those, similiar to lemniscates, when the exact covering may
be obtained by moving the centre along d, (fig. 2).

The “watered curves” *), above mentioned, bear a strong resemblance
to the interference curves of some crystals — it will be examined,
whether these interference curves may be explained by superposition
of two pencils of ellipses.

Theretore, the image of the hyperbolas will be compared to the
interference curves of a uniaxial crystal in convergent light, the
erystal-plate being cut parallel to the optic axis and the image of
the lemniscates to the interference curves of a biaxial crystal, the
plate being cut perpendicular to the first diameter.

1) Annales de Chimie et de Physique, 3i@me série. t. Ll. Octobre 1857.
2) Proc. Kon. Acad. v. Wet. pp. 857—870 March i914.
Mathésis, 3i¢me série t. X pp. 209—212, 1910.
3) On stereoscopic curves, see Comptes Rendus t. 130 p. 1616.
Also: Harmonic Vibrations and Vibration Figures by J. Gooup, C. E. BENHAM,
R. Kerr and Prof. L. R. WiLBERFORCE, Newton, London.

1224

The “‘isophase” surface of Bertin, by means of which interference
curves usually are explained, is the locus of points with a constant
difference of retardations :

1 1
2 Wm

In this formula d means the length of the way in the crystal,
supposing, with Brrtin'), that the bifurcation of the ray is neglected,
V the velocity of light in the medium, V, the velocity of the
ordinary and JV, that of the extra-ordinary ray in the erystal.

anh d d
V being constant, we may write ia a aT constant.
i 2

The centre of the ellipsoid of polarisation is supposed to be in
the centre of light in the lower side of the plate.

Let P be a point of the image of interference curves in the upper
side of the plate, where d= d,.

d s
Suppose Vv =m, then d, =mV,, so P lies on a surface p= m V,
1
(m = constant), homothetic with the blade 9 = V, of the surface of

the wave.

d
Suppose — =n, then d‚ =nV, and P lies also on the surface

Vi
vy=nV, (n=constant), homothethie with the blade 9 = V, of the
surface of the wave.

The surfaces 9 = mV, and 9=nV,, each being cut by the upper
side of the crystal plate in a pencil of curves C, and C,, when m
and n are variable, it is evident, that each curve of the image is
the locus of the points of intersection of those curves of the pencils,
which correspond to m—n = constant.

The forms, into which the wave is found to diverge, are a sphere
and an ellipsoid for uniaxial crystals; so the sections with the upper
side of a plate, cut parallel to the optic axis, are a circle and an
ellipse, having the same tangent in the extremities of the minor
axis of the ellipse (the section in the upper side is an approximate
form of that in the lower side of the plate).

For the wave in a biaxial crystal, we find two surfaces, which
are in fact one continuous surface. A plate, cut perpendicular to
the first diameter, gives two ellipses, one of which is wholly sur-
rounded by the other.

Thus, it may be said generally, that inter ference curves may be considered
as “watered figures’ of two concentric pencils of ellipses EK, and E,.

1) Ann. de Chim. et de Phys. (3). 63 pp. 57—92, 1861 en Sér 2. T 63. 1861.

ial Crystals

iax

ial and B

1ax

f some Interference-Curves of Un

by Superposition of Elliptic Pencils’’.

10n oO

W.N. LE HEUX: “Explanat

d

al
is sl
BP
Fa
(
_
nf
—
24
PS
©
>
&
iss}
: ke)
NS a
ANAASS bd
~ 55
N N A\ E
RAS <
NN 5
„Ap NEN NEEN N MS
\< NS ss
SRS AV ssz“~1 asx“ x
S as
SS n
SS ‘on
5
ae
o
o

TOC

1225

Now, it is possible by means of a simple algebraic transformation,
to derive these concentric pencils E,, and E,, from the excentric pencils
Ug sand .0-.

The curves of the new pencils however are composed of four
vibrations, which differ only in phase and whose directions two by
two are parallel to those of the compounding vibrations of the unissons.

To support these conclusions by experiment, | have made use of
an instrument') planned by myself, with four pendulems, two of
which describe a Iissasous-curve on a plane, which deseribes such
a curve itself. In our case, those two curves are unissons. The resulting
movement is a spiral, which may be considered as a pencil of concentric
circles. By altering the difference of phase, the circles are converted
into ellipses.

It is shown now by experiment, that always hyperbolas are
obtained by superposition of two pencils, which have for null-curves
a circle and an ellipse, having the same tangent in the extremilies
of the minor axis, and lemniscates, when the null-curves are two
ellipses, one of which is surrounded by the other.

Because the pencils U, and U,, by inversion, may be derived from
the pencils B, and E,, it is evident, that the ‘watered curves” of
the unissons are approximate images of interference curves of uniaxial
and biaxial crystals.

This theory is supported by further experiments. The centre of the
hyperbolas is displaced by a small rotation of one of the unissons.
The image resembles the interference-curves of a uniaxial erystal, cut
non-parallel to the optic axis (fig. 3).

With a small number of curves, the image of the lemniscates has
both poles surrounded by the inner curve, just as is taught in erystal-
opties. (fig. 4). Two concentric pencils of circles (each compounded »
of four vibrations), show the phaenomenon of Newton’s rings.

Probably it is also possible to obtain Airy’s spirals in this manner,
and the way, in which a certain image appears by superposition of
two pencils of ellipses may throw more light upon the phaenomena
of refraction and polarisation of light in crystals.

1) Other instruments are described in: Harmonic Vibrations and Vibration Figures

by Goorp etc.

Also: A. C. BANFIeLD. The Photo-Ratiograph, Illustrated London News,
Sept. 25th 1920. pg. 470. |

Comptes Rendus t. 130. pg. 1616.

H. J. Oosting. Hand. XIV Ned. Nat. en Geneesk. Congres March 1918. Ann.
d. Phys. u. Chem. N. F. 33. p. 415 1888; Maandbl. voor Natuurwetenschappen
1898; Zt. f.-d. Physik. u. Chem. Unterr. 8 p. 190 1895 and 11, p. 221 1898.

73
Proceedings Royal Acad. Amsterdam. Vol. XXIII.

Mathematics. — “On analytic functions defined by certain LamBert
series.” By J. C. Kiuyver.

(Communicated at the meeting of March 26, 1921).

The definition of the analytic function was based by Wetrrsrrass
on his theory of power-series. From a given analytic expression we
deduce an element of the analytic function, that is a power-series
converging within a determinate circle, and by the continuation of
this element an analytic function is defined existing within the
region that is covered by the set of the circles of convergence. One
and the same analytic expression in distinct regions may define
several functions. So, for instance, TANNERY’s series

n

n = 0 22
=
ni) ag
k=%
for: |zj <1 will represent the analytic function p,(2)—= = ==
Gl

z
TE whereas for |z| >>1 the expression defines the analytic func-
+z
k= 0 1
tion p‚ (2) = — JF e*k*= —

hil ars
defined in a separate region, can be continued over the whole plane,
but manifestly they remain everywhere essentially distinct.

In fact, from the general theory it follows that the concept of
an analytic function is not co-extensive with the concept of function-
ality as expressed by an analytic expression and it is precisely this
fundamental idea that, as Bors. repeatedly pointed out, sometimes
leads to conclusions which are not always in every respect satisfactory *).

Bore supposes that a given analytic expression F (z) defines a
function @, (z) inside a certain closed curve C and moreover a second
function g,(z) in the region outside C, the singularities of these
functions being everywhere-dense on the curve, so that C for both
functions constitutes a socalled natural limit. He then shows that
the series of polynomials representing ~, (2) under certain conditions
remains convergent, absolutely and uniformly, when the variable z
along certain radii crosses the boundary C. Otherwise said, it occurs

Both functions, each of them

1) Legons sur les Fonctions monogénes uniformes d'une variable complexe.
Chap. Ill.

1227

that the value of an analytic expression, coinciding at first with
that of the function ~, (z), can be made to change continuously into
the value of the function g,(z) and this possibility more or less
seems to be incompatible with the theory, according to which the
functions g, (z) and gy, (z) are wholly uneonnected.

In the present paper I propose to treat two simple examples in
which the transformation of ¢,(z) into a series of polynomials is
not necessary, and that, as I believe, yet give an insight into the
tendency of Borer’s remarks.

Let the given analytic expression be the series of LAMBERT

n=o, | gn

F (2) = = —

n=1 Nn 1— 2"

’

where the exponent s may supposed to be real.

Clearly, whatever be the value of s, we can expand F(z) into
an integral series, and as for |z| <1 we have
Lf. 2 1 1
wie a ee

F(z) defines an analytic function p‚(z) inside the circle C of radius
unity. However, if s >>1, we may write

n= 1 il gn n=o | “gn
Pg) = == j- —, —}|——O(s)— YS —.——

n=l ns ns all

erst ind
and from F(z) we derive also an integral series in —, that is a
z

second analytic function p‚(z) existing in the region outside C.
The functions p‚(e) and @,{z) represented in distinct regions by
the same analytic expression satisfy the relation

1
nl te(ZJ=—s (CD

but the main question is, whether either of them is, or is not an
analytic continuation of the other. The decision can be based on
a transformation of F(z). Corresponding to the rational numbers

a” the interval (0,1) we can arrange the so-called rational

on?
points a, =e ? on the circle C as a sequence (a,) and denoting
by g the denominator of the rational fraction that corresponds
to a, it will be seen that we have
— 1
F SE 1 EE EE
(z) 2$(s+ brie PES Dd

hor

1228

This series of fractions represents p‚(z), if |2|} <1, s > 0, on the
other hand it is equal to p‚(z) as soon as | zl > 1 and at the same
time s >1. We now can apply a theorem due to Goursat *) and
conclude that the points a, without exception are singular points
of the functions p‚(z) and p‚(z). Hence, as these points form a set
dense on ©, the continuation of either of the functions across the
circle is excluded. *)

By application of EtLer’s summation-formula we can calculate
the values taken by the functions p‚(2) and g,(z), when z along
the radius approaches one of the singular points. In this way find
in the first place, when z has a positive value a< 1, the following
asymptotic expression for p‚(2)
gin ae ~$(s +1) + (toe ‚) I’ (1—s) § (1 —s) — § §(s) +

log—

a“

; B, 3 6
ee 2 log - = fs S(s—1l) — — (tog, ) §(s—3) + — 5 (los - - ¢(s—5) —....

holding for all en values of s.
The result is less simple, when z tends along the radius to the
ong
point e 9 ef. Putting z— ge'®, | get for 0 < 1 and supposing
again s to be a non-integer *)

') Bulletin des Sciences Math., t. XI, p. 109. Sur les fonctions à espaces lacunaires.

n == 00 zn

2) This results also from one of the propositions concerning the series X /), Tb
n= EE

enunciated in a previous communication (Verslagen en Mededeelingen. XXVIII.
p. 269) according to which the continuation of the function across the circle is
impossible, as soon as 6, >0 and Lim b, —0.

n=
3) For integer values of s the result is obtained by making s tend to the
integer limit. So for instance, if s tends to zero, we ‘will find

1
C — log log —
wv

; B. 1 ig avs
y{e): = î rg Sng Nas Pd En log — ahs lair
log —
wv
and
Oe log | 1
nape FOB 7 108 °8 | Rn 8
Lim {p, (ge?) — = met = heot—.
p> 2q h=1 2

1
q log—
e
The former of these formulae was obtained by ScHL6MILcH, the latter | deduced
in a previous paper: On LAMBERT's series.

1229

1 a 1 \s—1 A
ORS (ere maar DE (tog, ) NN OSE
gett log —
QO
En — Sel - om
— 2 §{ s,— }cot—
I 2q° jesil q 9
Belketre. Sel 1,” )(Deotm,_18
EE Er CTU Rei pT Si ier Deb y
u 08 | chan sic (eo tet
Te 1 li 1 4
+ (ve) | Ben En (2 ‚Jo cot»), ‚tel

ne Bin
+ (teg, ) Jide 3) ges = sn Orcon ha tal +

des 4 eye
4
log. | | tue, ae „Jes cot»), hg tal +

In this formula ¢(p,@) stands for the function that, if pipe 1

n=O 1
and 0 < a <1, is represented by the series S ———
nzo (anp

It may be noticed that in both equations the absolute value of
the error committed by stopping at any particular stage in the series
is always less than a finite multiple of that of the last written term.

In particular we may deduce, supposing s > 1,

1
Lim dp, @) — — Eet = — 48),
I= 1
log—
wv
1 lil ] hy
Lim ie BED) er = — 486) + on e(") cot
pall gsi log je: Oil q
Q
(8 == Ar ®)
q
ori

Hence, as z approaches along the radius a rational point 2 ont, iti is
only the real part of the value of the function that increases inde-
Del
finitely and at all points e ke which correspond to the same deno-
minator q the real parts are ultimately equal.
The function p‚(z) behaves in quite similar manner because of

the relation

l
ns (2) tr O (el

1230

by means of which g, (z), as soon as z along the radius tends to
ani d:
e 9 from the outside of the circle, is expressed in p, EE

The rational points on C thus having been recognized as singula-
rities of g, (2) and p‚(z), we now must turn our attention to other
points on the curve, and as such | will consider the points e2/%,
where § is a root of an irreducible algebraic equation of degree
u>1 with integer coefficients. Evidently these points e?#ë which I
will call the algebraic points of order u on C, determine a new
enumerable set, everywhere-dense on the circle.

Let z=oe?"%, then it is readily seen that for all values of @

Sl zt if cos 22nd << 0,

——]
zn

1
ee 1) > |sin dang we Mh COS Arnen EE 0;

zn

Now in the latter case n& is an irrational number increasing with
the index n, hence there exists an integer 4, such that |nE—k|< 3:
But, as cos 2u(ns—k) = cos 2unE > 0, we must have |nS—k|< 4+
and sin 2u|n§—k| being the sine of an acute angle is greater than

2
the angle itself multiplied by —.
Jt

Therefore, if cos 2mn§ >>0, we may write
|sin21né|=sin 2a | n & —k|
and

Now according to LrouvirLe's known theorem about algebraic
numbers, we have
ä k
jn
n

where M is a finite number independent of n and only depending
on the coefficients of the equation of which § is a root.
In this way we conclude that

kiten 4
BD | get

1
zs Mnt'

and consequently that we have for all values of e = | z|

i zn | 1
a ve if ‘cos Za nE 0,

ns 1|—zn

vi ji, cos peor nd > 0.

ns 1— zn

1231

Therefore the series of LAMBERT F (2) converges absolutely on the
radius of the point e*5, as soon as s >u, the convergence being
then independent of @ and uniform on any segment of the radius.
Supposing z to move continuously along that radius, the value of
the analytic expression F(z) which for s< 1 is equal to that of
the funetion , (z) changes also continuously into the value of the
function , (z) as soon as @ becomes greater than unity. Besides, if
s is taken sufficiently above the number u, for instance, if we take
s > 2u—1, the series obtained by differentiating term-by-term the
series F(z) with regard to o in exactly the same way will give the

dp,(z) dp,(z)

dz dz
order of thought we may ascribe to the functions g, (z) and g, (z)
a common definite value at the point e?**, though of course that
point is not an ordinary point. Making wp, (e?**) and g, (e?*%) both

equal to the finite limit Lim F (ge), we obtain
eI

value of or that of according to the value of g. In this

z 5 cot ans

DE), C)=—35) + 5

= ns

and the series Fat hin
n==1 ns

Hence, we have established a certain connexion between the
functions g, (z) and p,(z) which according to Wererstrass’s theory
we must regard as essential distinct and in no wise connected. In
fact, we have shown that in this very special case in which the
classical continuation by means of power-series is impossible, a new
kind of continuation, as complete as could be desired, is furnished
by the series of LAMBERT along the radii of an enumerable infinite set.

The question arises, whether cases exist in which the continuation
by means of a series of LAMBERT is effected along the radii of a
set having the power c of the continuum. The answer is in the
affirmative, we only want to choose a LAMBERT series the coefficients
of which are decreasing more rapidly. For instance [ will consider
the series

will certainly be convergent, if only s >u.

n—o | gn
re fh n=1 nt 1—z"

Again in this new series the coefficients are positive and zero is
their common limit, hence according to the proposition mentioned
in the footnote on p. 1228, the rational points on the circle C are
singularities of the analytic functions w, (z) and w, (z) defined by
G (2) inside and outside C.

1232

Again some insight in the behaviour of these functions in the
neighbourhood of the singularities is obtained by the application of
Evrer’s summation-formula. Giving in the first place z the positive
value «<1, I find

1 B peep 1
wp, («) = —— {Li@) —Cj—4e—) +9) log — 7% -5e( log ) +
1 24 i U 4! U

log —
v
B, EAR
+- 6! . 52 é (toe) a” Oy le „js 6

and the absolute value of the error committed by stopping at any
particular stage in the series always will be less than that of the
last written term.

Ey}
osb

Putting then z= ¢e 7 — oe? and making @ tend to unity, we
will find

; il fe 1 h=q-1/h, te
Lim jw, (oef) — DT = ENT =— 4 (el) Ss (<- 5 oats
el Des (kg) ! kg h=1 \Q

The function w,(z) behaves in the neighbourhood of a singular
point in a similar manner because of the relation

(2+ w. (=) =d (el

Now, let § be a transcendental number of the interval (0,1) the
expansion of which in a continued fraction gives
FD atid WR 1
ata, da, ae ak
where all integers ay, are less than a given finite number J.
Evidently these numbers &, and therefore also the points e?™
form a set of power c, the set of points e?* however being not
dense on the circle. By the known properties of continued fractions

. . . Al
we have, & being an arbitrary integer, N the n-th convergent

AN n
| k | | Th Tne Ta
An+-2 1 i 1

eas (aneNi + Nn) > ZN No es an + IJN’ ee Bi aN

and as N, is manifestly always less than (/-+1)", we may write
k iL

Fae

1233

Determining then the integer & by the condition (ns — 4’ < 4 and
putting z= oe2*%, we get by the same reasoning as before

1
n> ’ if cos 2 ans < 0,
1 | | ke) 2n '
Ent ‘jens ; £0,
= 1 >a § n\> Gp let ‚if cos 22n§ >
and consequently
1 en | 1 ‘
tamer ag Gos
nl len, nl
1 ze | (/+ 1) 1) 2n+1 :
ae: ial ie f ed
nl 1—2"| On. nt ‚if cos 2 us >

Hence the series G(z) will converge absolutely on the radius of
the point e?** and the convergence will be uniform on any segment
of that radius.

Thus then, we have shown that in ‘this case the functions y, (2)
and w,(z) are connected at all points of an aggregate of power c
and that along the radii of these points the series of Lampert G (2)
procures a faultless continuation, whereas the analytic continuation
necessarily fails *).

The elementary examples I discussed show as well as the examples
of Borer that sometimes we are led to regard as a single function
a group of distinct analytic functions existing in separate regions.
And from the fact that in these cases a non-analytic continuation
can be effectuated, the question arises whether a certain extension
should not be given to the concept of functionality. Boren, made a
step in this direction by developing the theory of a class of non-
analytic, monogenic functions existing in a so-called domain of
Cauchy °).

1 1 ;
1) As we have — < — for all yalues of s, if only x is sufficiently large, we
nl ns

are certain that the series G(z) also furnishes the continuation along the radii of
algebraic points of order whatever.

*) Lecons sur les fonctions monogènes uniformes d'une variable complexe.
Chap. V.

Geology. — “On the Composition and the Xenoliths of the Lava-
dome of the Galunggung”’. (West-Java). By Prof. H. A. BROUWER.
(Communicated by Prof. G. A. F. MOrENGRAAFF).

(Communicated at the meeting of November 27, 1920).

During an eruption of the Galunggung, which commenced on
the 18% of July 1918 and produced only an inconsiderable fall of
ashes, a lavadome was formed in the crater, which formed on the
20" of July an islet in the eraterlake *), and which gradually grew
so large that the entire lake disappeared. On the 11'* of August
only the N. W. part of the Warirang-crater was covered with water’).

On a visit to the Galunggung-crater Dr. W. van BEMMELEN, on
my request, searched for xenoliths in the rocks of the dome, in
order to ascertain whether any crystallization had taken place in
the magma under the crater similar to that in the dome of the
Ruang (Sangi Islands) *). The collection transmitted to me through
the ‘Headoffice of the Mining Department” comprises numerous
samples of lava from the dome with fine-crystalline to coarse-grained
homoeogeneous xenoliths, which will be described lower down.

The lava of the dome.

All the rocks examined are brownish-red, porous hypersthene-
augiteandesites with phenocrysts of zonary plagioclases, among which
frequently narrow basic and more acid zones occur alternately, so
that the marginal zone, even in the case of markedly zonary struc-
ture, is often only little more acid than the central part; also the
succeeding zones differ but little as to basicity.

Carlsbad twins occur; in sections of the symmetrical zone we
determined that, on an average, the composition of the plagioclases
is like that of bytownite Ab,, Ah,,. Inclusions, among which some
of ore and of a glassy substance are generally few in number; a
zonary arrangement, the inclusions being limited to certain zones,
is sometimes met with. The hypersthene- and augite phenocrysts

1) R. D. M. VERBEEK et R. FENNEMA. Geologische Beschrijving van Java
en Madoera. II.

*) B. G. Escuer. De uitbarsting van den Goenoeng Galoenggoeng. De Taak
12 Oct. 1918 pp. 126—127 en Mededeeling namens B. G. EscHER door
G. A. F. MOLENGRAAFF. Versl. Geol. Sectie. Geol. Mijnb. Gen. II. Oct. 1919.

5) H. A. Brouwer. Crystallisation and Resorption in the magma of the
volcano Ruang. (Sangi Island). Proc. Kon. Akad. v. Wetensch. Vol. XXIII,
p. 561.

1235

are often accumulated; sometimes they are found together with
plagioclase- and larger ore crystals. Where the pyroxenes are con-
tiguous to groundmass they are commonly encircled by a narrow
zone of ore, which is lacking where they are in contact with
plagioclases. Apparently this is a chemical exchange between the
phenocrysts of pyroxene and the still liquid part of the enclosing
magma. In some samples of the dome resorbed brown amphiboles
were found; however, they exhibited no idiomorphous erystalform
and we venture to assume that they are not crystals formed in the
dome but fragments transported by tbe rising magma. Some of them
may be fragments of the same crystallization products, from which
the amphibole-rich homoeogeneous xenoliths originate.

The groundmass of the dome-roek is rich in glass and contains
lath-shaped plagioclase and grains or skeleton-shaped individuals of ore,
while pyroxene has not (or only to a small degree) crystallized in
this ground-mass.

The «xenoliths of the domerock.

Among them we distinguish the following types:

1. medium-grained, occasionally porphyric xenoliths, consisting of
plagioclase and amphibole with a small quantity of a more or less
devitrified glass.

2. medium-, to coarse-grained xenoliths, made up of plagioclase,
amphibole with little pyroxene and sometimes a little olivine. Glass
occurs also in these xenoliths.

3. medium-, to coarse-grained, sometimes porphyric xenoliths with
plagioclase, (little olivine), amphibole and much augite and hyper-
sthene. The olivine was seen ouly in some xenoliths, ore sometimes
occurs in a small quantity outside the resorption-rims of the amphibole.
The relative quantity of amphibole, augite, aud hypersthene is variable.
All xenoliths, in which the number of pyroxenes is not very small,
have been included here. Glass with microlites was observed only
in some xenolith and in a very small quantity.

4. porphyric xenoliths with phenocrysts of plagioclase in a fine-
grained groundmass in two generations with plagioclase, pyroxene
and ore. Larger pyroxene-crystals do not occur in the xenoliths, but
are accumulated in a small marginal zone against the enclosing rock.

D. fine-grained xenoliths, made up of plagioclase, augite, hyper-
sthene and little ore. Much glass with microlites is found in some
samples between the other minerals.

6. xenoliths of older andesites, some of them bearing amphibole,
others devoid of amphibole.

1236

The xenoliths mentioned sub 1 (Plate fig. 1 and 2) are first of all
characterized by plagioclases, which ave distinguished from those of
the phenoerysts of the enclosing rocks by the almost total absence
of the frequent alternation of more basic and more acid zones. The
crystals, often zonary and with a broad basic central part are chiefly
composed of basic bytownite, the marginal zone is more acid.

The amphibole is strongly pleochroitic, from a brownish red to
light-yellow, and invariably shows a resorption-rim, often only narrow
in many xenoliths and sometimes entirely absent where the crystals
are contiguous to plagioclase, while it is often well developed where
the amphibole is in contact with the glass-rich mass with microlites.
These narrow resorption rims are composed of a black mass of ore.
It is obvious that in part the amphibole has erystallized later than
the plagioclases, which form idiomorphous crystals and then guard
against resorption that portion of the amphibole with which they
are in contact. In the xenoliths with more strongly resorbed amphi-
bole, there occur entirely resorbed crystals, which can only be
recognized as original amphibole by their crystalform. In the erystals
that are partly unaltered, the resorption-rim consists only of a mass
of ore or a marginal zone of ore, separated from the intact part of
the crystal by an irregularly shaped pyroxene-rich zone, which is
sometimes lacking and which sometimes occurs mixed with un-
modified amphibole. Out of the resorption rims larger crystals of
ore do not occur in the xenoliths.

Some of the xenoliths with strongly resorbed amphiboles present
a porphyric structure, the groundmass, which contains large, more
or less idiomorphous amphibole crystals, consisting of plagioclase.
Between these smaller plagioclase crystals, as in the non-porphyric
xenoliths with larger plagioclases, more or less devitrified glass is
found. Plagioclase-microlites and ore-skeletons are easy to distinguish
in this mass; only a small number of pyroxene microlites’ are
distinguishable; the devitrification is sometimes complete.

The limit between the xenoliths and the enclosing lava is always
such that the lava has adapted itself to the shapes of the xenolith.
The erystal faces of the plagioclases and amphiboles have reached
full development at the margin of the xenoliths so that the boundary
line with the lava proceeds irregularly. Also the enclasped glassy
mass shows that the minerals had not been perfectly crystallized,
when the xenoliths were taken up in the enclosing magma, so they
were still molten to a certain extent and may therefore be considered
as an almost perfectly crystallized crust on the magma, which was
effused from a larger depth and has produced the dome. The

H. A. BROUWER

H. A. BROUWER: “On the Composition and the Xenoliths of the Lavadome of the Galunggung”. (West-Java).

Fig. 1. Magnification > 24. nicols. Xenolith with plagioclase and
amphibole. The amphibole is slightly resorbed. The enclasped glass-
bearing mass has partly disappeared in the section.

Fig. 2. Magn. X 24. > nicols. Ibid. Fig. 1.

Fig. 3. Magnification >< 42. nicols. Xenolith with plagioclase and Fig. 4. Magn. X 42. X nicols. Phenoc

vst with plagioclase with
pyroxene. In this xenolith amphibole occurs rarely. It is not visible

numerous inclusions of pyroxene and ore, Porphyric xenolith with
in the preparatton, while the enclasped glassmass with microlites has phenocrysts of plagioclase in a finely crystalline ground mass in two
partly disappeared.

generations with plagioclase, pyroxene and ore.

Proceedings Royal Acad. Amsterdam. Vol. XXIII.

1237

groundmass of the lava of the dome and the devitrified glass of
the xenoliths have then crystallized almost simultaneously.

The xenoliths mentioned sub 2 do not differ much from those just
described; they are all characterized by a small amount of pyroxene,
while also a small amount of olivine was found in some. The
amphiboles show a narrow resorption rim, which contains much
ore, mixed: with pyroxene (principally augite).

Veins. of the same composition as the resorption rim are found
in.the more central part of the crystals, which are larger than those
of the other minerals, which present an irregular outline and may
enclose all the other components entirely or partly, also olivine,
if it oceurs in the xenoliths. The olivine presents rounded shapes
without distinct crystal faces and has been altered to some degree
into a brownish red or black substance, rich in iron. The glass-bearing
mass is rich in laths of plagioclase and also contains many pyroxene-
microlites. The glass is very dark and the devitrified portion is
apparently rich in iron; ore hardly shows itself in separate grains.

The xenoliths with more pyroxene, mentioned sub 3 (Pl. fig. 3)
are distinguished from the preceding chiefly by the decrease of the
amount of amphibole and the increase of pyroxene. Various structures
occur. Pyroxene (augite as well as hypersthene) occurs occasionally
with a few larger amphibole-, and plagioclase-crystals in a finer
crystalline mixture, consisting mainly of plagioclase with little
pyroxene. The pyroxene (above all the augite) then exhibits similar
skeleton-like structures to those of the amphibole, and then incloses,
just like the last-named mineral, numerous plagioclase crystals, which
also penetrate into the augites with idiomorphous erystal form, so
that these are one of the last crystallisation products of the xenolith.
In connection with this the smaller plagioclases are entirely free
from enclosed dark minerals, the larger nearly so. It is these
xenoliths that contain olivine with rounded sbapes and mostly
enclosed by the amphibole. Devitrified glass occurs in small quantity.

In other xenoliths also bearing occasionally olivine, for the rest
little different from the others, the pyroxenes are chiefly restricted
to the fine-erystalline bulk of the xenolith, while only few larger
crystals occur with some of partly resorbed amphibole and of
plagioclase. A portion of the xenoliths of this group displays the
normal, medium grained structure without larger crystals; here we
find evidence of the posterior crystallization of the amphiboles,
because they occur in skeleton shaped crystals, which occasionally
enclose the pyroxene. The different stages of resorption of the
amphibole, mentioned already for the xenoliths described sub 1,

1238

were also met with here. No olivine was found in the samples of
the mediumgrained xenoliths examined.

The xenoliths mentioned sub 4, found only in some specimens,
are free from amphibole, just as those mentioned sub 3. They are
characterized by a remarkable structure, large plagioclase-phenocry sts
lying in a groundmass, consisting of smaller crystals of plagioclase,
few ore-crystals and very few of augite and hypersthene. The
latter in their turn are surrounded by a fine-crystalline mixture
of the same minerals, whose constituents — with the exception of
the small plagioclases — occur in a large number as inclusions
in the plagioclases of the first and te second generation (PI. fig. 4).
Zonary structure does not occur with these plagioclases or
only in a small measure and without the alternation of basic
and more acid zones, which distinguish them from those
of the enclosing lava. The fine-crystalline groundmass is almost
entirely absent in a narrow marginal zone of the xenolith where
this is contiguous to the enclosing lava. Here we see a mixture of
plagioclase, like those occurring everywhere in the xenolith as small-
sized phenocrysts, together with the angite-, hypersthene-, and ore-
crystals, which are seen only in small number in the central parts
of the xenoliths as small phenocrysts. It appears then that pyroxene
and ore are accumulated in the marginal zone. The structures
described heretofore point to the fact that the crystallization of the
xenoliths was still to take place for the most part, when they had
already been taken up in the enclosing lava. In an early stage the
plagioelases, the pyroxenes, and the ore-crystals of the second gene-
ration have crystallized. The latter two have accumulated in the
marginal zone of the xenolith. That the crystallization of the plagio-
clases was the first to be finished here, is proved by the idiomorph-
ous shape of the crystals relative to the pyroxenes in the marginal
zone and the enclosure of plagioclase by pyroxenes, which occurs
frequently here. In the central parts we see that the crystallization
of the ore and of the pyroxene of the fine-crystalline groundmass
had already begun during the crystallization of the plagioclases,
some of which have grown into larger phenocrysts. Then followed
the ultimate crystallization of the fine-crystalline groundmass, in
which oceurs the plagioclase in rounded shapes, which points to a
crystallization about simultaneous with that of the pyroxene. The
plagioclases of the marginal zones are poor in or destitute of in-
clusions and seem, therefore, to have erystallized before those of
the central part of the xenolith, or the crystallization of the fine-
crystalline groundmass has taken place in the marginal zone later

1239

and in a smaller degree, so that the quantity of it is small there.
The boundary between the xenolith and the enclosing lava, of which
the latter has adapted itself to the shapes of the crystals in the
xenolith, proves moreover that the xenolith has not been enclosed
at greater depth in a solid state, but that it has been taken up in
the enclosing lava as a partly crystallized mass. |

The “xenoliths mentioned sub 5 consist of plagioclase, augite and
hypersthene with a few ore-crystals, the interspaces being filled up
with various quantities of a partly devitrified, dark substance, against
which feldspar-mierolites stand out sharply outlined. The plagio-
clases and the pyroxenes present mostly idiomorphous outlines (espe-
cially the plagioclases); in contradistinction to that of the xenoliths
thus far described, the structure of the plagioclase is zonary with
frequent alternation of more acid and basic zones, like those of the
phenocrysts in the enclosing lava of the dome mentioned above.

The xenoliths of older andesites mentioned sub 6, display differ-
ences as regards mineralogical composition and structure. In some
of them a few plagioclase phenocrysts occur in a groundmass,
consisting of plagioclase and pyroxene with ore.

In others amphibole was observed, occasionally as phenocryst in
similar rocks to those mentioned above, sometimes in aureoles round
orecrystals, occurring porphyrically with plagioclase in a dark glass-
bearing groundmass. Frequently the microscopic aspect changes
considerably, e.g. as to the amount of ore and as regards the colour
of the groundmass, while the rocks give an impression of being
modified through contactmetamorphism, in which process recrystalli-
zations have taken place. The porphyrie plagioclases have been
strongly eroded by the clear mixture of which the present ground-
mass consists; we then suppose the groundmass to have been
entirely recrystallized and the phenocrysts only in their marginal
zone. The aureoles of amphibole round ore-erystals in a partly
devitrified groundmass find an explanation in the assumption that
what has taken place here is just the reverse of what happened
with the resorption of amphibole. The enclosed andesite fragment,
heated anew, has been for some time submitted to temperature-
and pressure-relations, which do not affect amphibole and this
mineral has crystallized instead of components that otherwise build
up resorption rims.

The various erystallizations in the Galunggung magma.

The boundaries of the homoeogeneous xenoliths relative to the
enclosing lava proves that the xenoliths had not crystallized com-
pletely when they were taken up in the lava. The residual magma

1240

has crystallized as a glass-bearing mass with microlites, just as the
groundmass of the enclosing rocks.

That in many xenoliths the amphiboles exhibit a resorption-rim
where they border on the glass-bearing mass alluded to, points out
that the amphibole remained stable down to the moment of the
eruption of the lava dome. After this the pressure in the lava and
the xenoliths decreased rapidly, which made the amphibole instable
and augite could crystallize during the time when the temperature
of the residual magma fell, and a complete solidification had not
yet been effected. This interval may have been longer or shorter
for different portions of the dome, hence the resorption in amphi-
boles of different xenoliths was varying. Already before we accounted
for the mineralogical differences between xenoliths and dome-lava -
of the Ruan!) we have assumed that during the eruption of the
voleano the outpouring magma enclosed fragments of its completely
or partly solidified dioritie crust. The same applies to dome and
xenoliths of the Galunggung. The occurrence of pyroxene-poor and
pyroxene-rich ampbibole-bearing xenoliths may be accounted for by
the assumption that they originate from zones at various depths in
this crust. It depends on the difference of pressure and temperature
of these zones whether amphibole only or first pyroxene and later,
on further cooling, amphibole has crystallized. *)

In that case the pyroxene-bearing xenoliths originate from deeper
zones according as they are richer in pyroxene, whereas at a greater
depth with a higher temperature much less crystalline components
and only pyroxenes occur in the outpouring magma, which does
not contain amphibole as phenocrysts.

The amphibole-free xenoliths with different structures described
above, may have crystallized already before the eruption at a great
depth, so above temperatures, at which the amphibole is stable,
while in that case complete crystallization has taken place after
the eruption had commenced, when the amphibole was not stable
either, in connection with the suddenly modified pressure and tem-
perature relations. Maybe some of these xenoliths have crystallized
at a pressure lower than that of the stage of stability of the
amphibole and may therefore belong to parts of the magma that
have cooled down more slowly, that could crystallize more com-
pletely along the walls of the vent and were only then carried
along by the outpouring magma.

') HA BROUWER, Crystallizations etc. loc. cit. p. 665.
3) F. Becker. Gesteine des Columbretes. Anhang. Tscherm. Min. u. Petrogr.
Mitt. XVI. 1897. blz. 327 e.v.

Geology. — “On the Alkalirocks of the Serra do Gericino to the
northwest of Rio de Janeiro and the Resemblance between
the Eruptive Rocks of Brazil and those of South-Africa.”
By Prof. H. A. Brouwer. (Communicated by Prof. G. A. F.
MOLENGRAAFF).

(Communicated at the meeting of January 29, 1921).

On the boundary between the State of Rio de Janeiro and the
Districto Federal lies near the station of Maxambomba of the E. F.
Central do Brazil, the Serra do Gericino'), extending in W.S.W.-
N.N.E. direction over a length of about twenty k.m. and a breadth
of about eight k.m. It is chiefly composed of nephelinesyenites like
the Tingua eruptive province which lies about 30 km. farther to
the North and of which the alkali-rocks have been described by
Graurr®) and Dursy*). As I could not personally visit the Serra do
Gericino during my stay in Brazil, several samples for further
investigation were sent me by GonzaGa DE Campos, Director of the
“Servico geologico e mineralogico do Brazil”.

Geological Survey.

The alkali-rocks constitute an eruptive centre amidst the old
gneisses of the mountain-range Serra do Mar, which runs parallel
to the Brazilian Coast. (Fig. 1). We only know that the gneisses
are intruded by alkali-rocks which consequently must be younger
than the gneisses. No data were obtained concerning the exact
geological age.

Coarse-grained, as well as dyke-, and effusive rocks occur, just
as in other Brazilian occurrences of alkali-rocks. Although nearly
the whole region and especially the highest parts consist of coarse-
grained rocks, the occurrence of effusive rocks allied to them, still

1) MarHias G. DE OLIVEIRA Roxo. Resumé of the preliminar note on the
Gericinó eruptive centre. Empresa Brasil Editora 1920.

*) Fr. GraEFF, Mineralogisch-petrographische Untersuchung von Eleolithsyeniten
von der Serra de Tingua. Neues Jahrb. f. Min., Geol. u. Pal. 1887. II, blz. 222 e.v.

3) O. E. DerBy. On nepheline rocks in Basil Quart. Journ. Geol. Soc. Vol.
XLIII. 1887, blz. 457; Vol. XLVII, 1891, blz. 251.

80
Proceedings Roval Acad. Amsterdam. Vol. XXIII.

1242

proves that the Serra do Gericino constitutes the strongly denuded
remnant of a voleano or group of volcanoes, like the Serra de Tingua
further northward. That remains of lava-flows have been preserved
only locally, and only between the eruptive rocks, whereas they
do not occur in the surrounding gneisses, points to the circum-
stance that these effusive rocks, which originally must have extended
far beyond the present mountain, have long been protected from
erosion through overhead stoping, the roof having locally sunk
down. These effusive rocks occur near the station of Maxambomba
of the E.F. Central do Brazil, and near the facenda D. Eugenia
close to the west of this station.

Dyke-rocks were e.g. met with near the station of Maxambomba
(tinguaite), near the facenda Mascarenhas and in the western part
of the eruptive province, between Cava and Ypiranga (aegerine- and
amphibole-Sölvsbergite). |

The coarse-grained rocks, which chiefly compose the eruptive
province, are generally characterised by table-shaped felspars; con-
sequently they belong to the foyaites as far as they contain nepheline.
Of the western part, known as Serra de Marapieu, samples of
nepheline-free umptekite were examined, while among the foyaites,
which seem to build up the greater part of the mountain-ridge
between the Serra de Marapicu and the station of Maxambomba,
also alkali-syenites (partly pulaskites) occur ')

The granular rocks.

The following types may be distinguished :

1. Foyaites.

2. Alkali-syenites.

3. Umptekites.

4. Pulaskites.

Foyaites.

They seem to be the most common rocks of the Serra do Gericino.

Type 1 is a pyroxene-amphibolafoyaite, collected near Cancella
Azul along the road which crosses the rivulet Cachoeira. The com-
posing minerals are light-coloured orthoclase and microperthite,

‘) Most of the samples received, which had been provisionally determined as
nepheline-syenite, belonged to the alkali-syenites. The typical foyaites originate
from Cancella Azul along the road intersecting the rivulet Cachoeira. Therefore,
because many of the rocks have apparently been mistaken for nepheline-syenites,
whereas they are actually alkali-syenites, the data occurring on a map on which
different types of nepheline-syenites have been separated cannot be relied on.

1243

=, KK X
=<

SS

Cee

zt
se ee
SN

oe

KEN \ —
sG
\ AEN ar Hit EN NN
DISTRICT ZA EEE Be
NY ie ns — N
x = ams

QW WL
x!
NIN MIN
WS

Archaeicum.

=| Foyaite, Umptekite, Atlantic Ocean.
Pulaskite, etc.

renner Granite.

Scale 1: 500.000

Fig. 1. Geological Sketchmap of the environs of the Serra do Gericinó to the
Northwest of Rio de Janeiro. R. C. = Rio Cachoeira, (compiled from observations
of Dr. MATHIAS DE OLIVEIRA Roxo). k

80*

1244

nepheline, sodalite, aegirineaugite, greenish-brown amphibole with a
slight quantum of analcite, lavenite, biotite, pyrite and magnetite,
while muscovite and calcite occur as secondary minerals.

Large extinction angles in sections normal to the obtuse bissectrix
point to Na-content of the orthoclase. Like the sodalite, the clear
nepheline, only slightly altered into secondary minerals (muscovite
and analcite), exhibits some idiomorphic crystals. The pyroxene is
for the greater part of zonary structure, the central part may be
very rich in augite-, the marginal zone very rich in aegirine mole-
cules, but in most erystals the extinction angles for central part
and margin do not vary much. The amphibole presents olive-green
or bluish-green colours, both kinds are found grown together some-
times with the pyroxene, in which the crystallographic axes of the
different minerals do not coincide. The large extinction angles point
to amphiboles similar to those described by Wericur’) and by
Ussina ?) and collected respectively from Brazilian and from Green-
land alkali-rocks. The lavenite forms highly pleochroie and with
strong birefringence crystals sometimes occurring with irregular
erystal-form between the other minerals, like the analcite, in so far
as this mineral is not an alteration-product of the felspathoids. The
absorption-scheme of the lavenite is ¢ (canary-coloured) > 6 =a
(bright yellow); the crystals are often (sometimes polysynthetically)
twinned; simple crystals also occur. The plane of optic axes is at
right angles to the twinning plane cf. (100) and the cleavage-lines ;
the axial angle is large. Sometimes the crystals are partly idiomor-
phic. Pyrite and magnetite occur in separated crystals, but often
the pyrite is enclosed by a margin of magnetite and both minerals
also occur grown together with the other dark minerals.

Type 2. This rock is more finely grained than the preceding
and is composed of white- to light flesh-coloured felspars (chiefly
microperthite) with grey or black greenish-coloured liebeneritepseudo-
morphs after original felspathoids. It was found near the facenda
D. Eugenia. Beyond strongly weathered ore no original dark minerals
can be recognized in the rock.

Alkalisyenites.

A rock, also collected near the facenda D. Eugenia, consisting
for the greater part of light-coloured microperthite which is rich in
albite and strongly weathered ore, contains only little of a substance

1) F. E. Wricur. Die syenitisch-theralitischen Eruptivgesteine der Insel Cabo
Frio, Brasilien, Tscherm. Min. u. Petr. Mitt. 1901, XX, blz. 249.

*) N. V. Ussine. Geology of the country around Julianehaab, Greenland, Med-
delelser om Grönland. Vol. XX XVIII, 1911.

1945

consisting of small muscovite-flakes, which may also be alteration
products of original felspathoids. These, however, were then present
only in a very smal] quantity.

Umptekites.

The Serra de Marapicu i.e. the Western part of the Serra do
Gericino seems to be chiefly built up of these rocks. The composing
minerals are for the greater part light-coloured microperthite and
amphibole, and small quantities of pyroxene, titanite, analcite mag-
netite and apatite.

The felspars are microperthites with a variable amount of acid
plagioclase, which is sometimes absent altogether. Large extinction
angles in sections normal to the obtuse bissectrix point to a Na-
content of the orthoclase. The amphibole differs from that of type1
of the foyaites, the extinction-angles remain smaller and frequently
varying colours occur in one and the same crystal; a greenish
variety in the marginal zone, a brownish in the central part, but
both varieties form separate crystals. The amphiboles are very much
like those which Wricnr*) has described in an umptekite near
Cabo Frio. In erystals of zonary structure we see in sections normal
to the acute negative bissectrix of a small axial angle the following
absorption: ¢ central part: reddish brown-green; margin: green)
+ = 6 (central part: brown with a greenish tint; margin: brownish-
green).

In sections parallel to the plane of symmetry the extinction-angle
increases towards the green marginal zone up to + 22°; we often
see for the absorption parallel to the c-axis a homogeneous light
yellow-brown colour, without any difference for central part and
marginal zone. The only slight quantity of pyroxene consists of a
green augite with extinction angles as high as 40° relative to the
cleavage lines Apatite is present in numerous idiomorphic crystals.

Pulaskites.

This term comprises the alkali-roeks rich in mica, sometimes with
a small amount of felspathoids.

Type 1. The felspars have a more reddish tint than those of the
rocks described above. The sample was collected along the road
from Maxambomba to Mascarenhas, close to the facenda D. Eugenia.
Biotite and titanite are visible macroscopically in numerous crystals.
The composing minirals are: microperthite and a small amount of
plagioclase, sodalite and analeite, biotite, augite with a margin of
aegirineaugite, apatite and ore. As secondary product occurs a chlo-

1) F. E. Wriaut. |. c. p. 246.

1246

ritie mineral of rather strong double refraction, which has been
formed to the cost of the pyroxene.

The large extinction angles in sections normal to the obtuse bis-
sectrix again point to a Na-content of the orthoclase of the micro-
perthites. The analcite has been formed partly at the cost of the
felspar, optic anomalies occur. The biotite is highly pleschroic, the
colour ranging from brownish black to brownish-yellow. The py-
roxene is almost colourless and is often encircled by a rim of green
aegirine augite, but both -also occur separately. Biotite, pyroxene,
titanomagnetite, titanite and apatite often are grown together, in these
intergrowths all or some of the minerals referred to occur.

Type 2. The felspars in this rock are partly green and the dark
minerals chiefly occur only in small crystals. It was found in that
part of the Serra do Gericino which is known as Serra de Cabucu,
along the road between Mascarenhas and Cabucu.

The felspars consist of orthoclase or microperthite, which is poor
in plagioclase. Not a trace of felspathoids is distinguishable. The
markedly pleochroic biotite (from brownblack to light brownish-
yellow) has often partly or completely been converted into green
mica, while at the same time grains of a light yellow-green highly
refracting, isotropous mineral having the properties of garnet, are
formed. These grains are also found scattered in the felspars and
the conversion may have taken place already before the complete
erystallization of the rock.

The rock contains also titanomagnetite which has been entirely
or partially converted into leucoxene.

The dyke-, and the effusive rocks.

We distinguish the following types of rocks:

1. Alkalisyeniteporphyries.

2. Nephdinesyeniteaplites.

3. Tinguaites.

4. Sölvsbergites.

5. Trachy tes.

Alkalisyeniteporphyries.

If these rocks contained originally felspathoids, the latter have
been completely converted into secondary minerals.

Type 1. A rock, collected where the. road to the facenda D.
Eugenia erosses the rivulet Cachoeira, contains white to bright
reddish felsparphenoerysts in a grey fine-grained ground mass.

The felsparphenocrysts consist of orthoclase in which felspar with
stronger double refraction is seen in small quantities. Pseudomorphs

1247

also occur. They consist of muscovite flakes; whether the original
mineral has partially belonged to felspathoids, which the form some-
times seems to suggest, could not be made out with certainty. In
the groundmass the same felspars occur, the laths contain more of
the strongest double-refracting felspar mentioned above, this felspar
sometimes exhibits polysynthetie twins and occurs also in a few
separate crystals. The groundmass contains also muscovite, calcite,
rather much apatite and ore, which occurs also in some larger
erystals, is strongly weathered and consists partly of pyrite.

Type 2. Near the facenda D. Eugenia a rock was collected with
white to faintly reddish coloured felsparphenoerysts in a light-gray,
finely crystalline groundmass. The rock is strongly sericitised, although
the felsparphenocrysts have been altered very little. Initially it may
have contained felspathoids. Ore, leucoxene and titanite occur.

Nephelinesyeniteaplites.

These rocks are known only as boulders near Mount Sapé in
the Serra di Marapucu (western part of the Serra di Gericino).
Macroscopirally it presents itself as a medium-, to fine-grained light-
grey rock, with numerous black points chiefly consisting of magnetite.
The constituents are: clear albite, less clear orthoclase and micro-
perthite, nepheline and analcite, magnetite and little pyrite, titanite
apatite and green or brownish biotite.

The nepheline is often enclosed by the felspars. The albite reveals
itself in a large quantity in polysynthetically twinned crystals. There
is an abundance of analcite; a Cl-reaction with a negative result
points to the absence of sodalite.

Tinguaites.

Typical tinguaites were collected near Maxambomba, the rocks
seem to form a dyke here and also a flow, the latter of a thickness
of more than 100 meters. Only a single sample was examined, most
likely several varieties and also typical effusive rocks occur here.

The sample contains in a grey finely-crystalline groundmass a
few phenocrysts of light-coloured felspar, consisting of Na-bearing
orthoclase or anorthoclase. They have been partially converted into
natrolite. Microscopically the groundmass seems to consists of felspar
laths aegirine, natrolite, analcite and a little nepheline. Some prisms
with high refractive indices and strong birefringence, which show
parallel extinction and are optically positive, point to zircon.

The colourless substance with low refractive index which exists
in large quantity between the felspar laths, is probably chiefly
composed of analcite, which is partially an alteration product of
original nepheline.

1248

Muscovite flakes also occur as alteration products of nepheline.
Larger crystals of aegirine show distinctly a higher augite content
in their central part the needles often show a sheaf-shaped or radial
arrangement.

Sölvsbergites.

Under this name we have grouped the rocks in which probably
felspathoids occurred, but in smaller quantity than in the tinguaites.
The felspathoids cannot be recognised any more as such, the second-
ary minerals, however, are indicative of their having been present
originally. Then the rocks approach the tinguaites.

ype 1 (with pyrowene). lt is distinguished from the above-mentioned
tinguaite by the dark grey colour of the finely crystalline ground-
mass, against which numerous white or light-red phenocrysts, which
no doubt consist for the greater part of felspar, are sharply outlined,
while also a few larger pyroxene crystals occur. It was collected
from a dyke between the Serra de Cabucu and the Serra de Marapicu.

Orthoclase is the predominant mineral of the phenocrysts; in
small quantity polysynthetically twinned felspars occur with small
extinction-angles. More or less regularly defined groups, consisting —
chiefly of acid plagioclase and cancrinite, sometimes mixed with
analcite, possibly point to original felspathoids. Beside larger crystals
of aegirine-augite with a high augite-content, which decreases in
zonary crystals in a narrow marginal zone, also a few phenocrysts
of brown amphibole and very little biotite occur together with larger
_ ore-crystals. The groundmass consists of numerous pyroxene-needles
sometimes of zonary structure and consisting of aegirine and aegirine-
augite. Sometimes the central part of zonary crystals is of a violet
colour with a great extinction-angle indicating the presence of titani-
ferous augite, which was also observed in some large crystals. Very
few amphibole prisms occur. In the colourless mass between them
felspar can be recognised, originally it probably consisted chiefly of
felspar and felspathoids; at present there is an abundance of cancrinite
and analcite as products of alteration. Inclosures of ore are numerous.

Type 2 (with amphibole). It was collected near type 1 also from
a dyke. It is a dark grey fine-crystalline rock with some felspar-
phenocrysts. Original felspathoids are not noticeable, but the cancrinite-
content of the groundmass points to their former existence. True
amphibolephenocrysts do not occur, though we do see accumulations
of brown-green amphibole and ore which sometimes show a regular
outline.

The groundmass is composed of a good many plagioclase-laths
which are sometimes polysynthetically twinned, of markedly pleo-

1249

chroie amphibole, the colour ranging from dark brownish green to
light brownish yellow, without large extinction-angles; of ore,
cancrinite, analcite, fluorite and little calcite.

Trachyte.

The grey, compact rock was collected from a lava flow more
than 100 M. in thickness, near the facenda D. Eugenia.

A microscopic examination shows beside portions, in which crystal-
line constituents with weak birefringence are scarcely visible, other
parts, in which distinctly felsparlaths without polysynthetic twins
and with nearly parallel extinction, have been largely developed.
There are also larger felsparcrystals; in sections normal to the acute
bissectrix they present a rather small axial angle. Some of the larger
felspars exhibit polysynthetie twins with small extinction-angles.
Parts with a more or less regular form and consisting of muscovite
flakes remind somewhat of liebeneritepseudomorphs after nepheline.
However, sometimes quartz occurs in large quantity mixed with
muscovite flakes. The quartz, which we take to be a secondary
product, also occurs scattered in the rock. Finally pyrite must be
mentioned as one of the composing minerals.

Resemblance between the Eruptive Rocks of Brazil
and those of South Africa.

Rocks, rich in alkalies, some of which have been described above,
are of frequent occurrence in Brazil as well as in South-Africa, and
the various types in both regions show many points of resemblance,
which will be discussed in detail lower down. This resemblance
exists also with regard to other eruptive rocks. On a journey through
Brazil in 1920 I was struck by the marked resemblance of some
groups of sedimentary rocks with which [ got acquainted in South
Africa in 1910. Anyhow the differences are not greater than are
known for adjacent regions of the African continent at a much
shorter distance.

As the principal groups of eruptive rocks whose resemblance in
composition and geological aspect will be discussed below, we mention:

1. Old granites, intrusive in rocks of probably archaean age.

2. Younger granites, intrusive in deposits of Devonian age and
older than permo-carboniferous rocks.

3. Younger rocks, rich in alkali, (nephelinesyenites, aikalisyenites
with accompanying abyssal- and effusive rocks).

4. Jurassic volcanic rocks and intrusive dolerites (the determination

1250

of age is connected with the prolonged denudation before Upper-
cretaceous time.

5. Kimberlites, alnoites ete. in pipes and dykes, younger than the
dolerites mentioned sub 4°).

Old Granites.

The archaean rocks classed together for Brazil under the term
Brazilian complex, are granites, gneisses, quartzites, marbles and
crystalline schists. They may be compared with the Malmesbury
system of the Southern Cape Colony, the Swarzland system of the
Transvaal and Rhodesia and the Fundamental complex with intrusive
old granites of South-West Africa. Both the east coast of Brazil in
the Serra do Mar and the opposite West Coast of South- and Central
Africa consist for the major part of these rocks and they often
impart to the landscape in both continents a similar topographic
aspect. As to the petrographic features of these rocks no data are
known sufficient for a minate comparison of the rocks near the
opposite shores.

Young granites.

An instance of this type in South Africa are the granites of the
“Bushveld Igneous Complex” in The Transvaal, occurring in com-
bination with the gabbros, norites and ultrabasie rocks, the Erongo
granite in Hereroland, and the Branaberg granite in the North
Western part of Damaraland. The first-named are intrusive in the
? Devonian Waterberg Sandstone; the Eronga-granite has intruded the
lowermost division of the ?Cambrian Nama System, hence they are
younger than the old granites from which they also differ in petro-
graphic composition, but their exact age is not known.

In Brazil the extensive granite areas and their contacts with the
environing sediments have been studied very little. However, here
also granites are known as intrusions in the algonkian or old-palae-
ozoic Minas Serie, as e.g. appears from the gold-bearing dyke of
Passagem’) in Minas Geraes, ultra-acid granite apophysis, and in-
trusive in the so-called itabirite-formation of the Minas Series. In
the neighbourhood a granite occurs and similar gold-bearing quartz-
dykes are known in several places in the States of Minas Geraes
and Goyaz. In the southern states mention is made of the occurrence

1) For the literature on parts of the coastal regions on either side of the
Atlantic Ocean we refer to: J. C. BRANNER. Geology of Brazil. Bull. Americ.
Geol. Soc. 1919. P. A. Wagner. The Geology and Mineral Industry of South-
West-Africa Geol. Surv. Memoir N°, 7, 1916.

3) E. Hussax. Der goldführende kiesige Quarzlagergang von Passagem in Minas
Geraes. Zeitschr. f. Prakt. Geol. 1898. Oktober, blz. 345 e.v. °

1251

of granites, intrusive in rocks of probably old-palaeozoic. For in-
stance by B. P. pr Oniverra, and according to a communication to
the present writer by GONZAGA pr Campos also in the State of Sao
Paulo granites have distinctly metamorphosed old-palaeozoic rocks.
As with the old granites, still too little is known of the petrographic
features of the Brazilian young granites to compare them with those
of South-Africa.

Alkali-rocks.

First of all we refer to places, where alkalirocks occur at or near
the opposite coasts, as in Brazil in a number of places in the Serra
do Mar’) (Itatiaya, Serra do Gericino, Serra de Tingue, Cabo Trio)
and in Africa near the coast of Liideritzland, and near Cape Cross
to the North of Swakopmund.®) It is most likely that similar rocks
occur out of these better known regions in a number of other
localities near the coasts. We know e.g. already pyroxene foyaite
from Angola and much farther northward different alkali-rocks, from
the Los Islands (9°13’ N.East).

Abyssal-roeks and the related dyke- and effusive-rocks are associated
with each other. They are in South-West Africa sy enites, nepheline-
__syenites, essexites, and theralites with phonolites, tinguaites, boston-
ites, camptonites, monchiquites alnoites. Similar rocks aré known to
occur in the Brazilian coastal region, we cite only the well-examined
foyaites, essexites, phonolites, and basic dyke-rovks, besides tinguaites
and bostonites in and near the State of Rio de Janeiro. The associa-
tion with the related effusive rocks points in both regions to the
circumstance that the alkalirocks are in part intrusive into their
own effusive rocks and that they have crystallized at a small depth
below the earth’s surface. Erosion caused the volcanoes to disappear,
which formerly existed near the two opposed coasts of the Atlantic
Ocean, as they now arise near the Kast-African Lake-region, where
also alkali-rocks are of frequent occurrence. Farther removed from the
two coasts alkalirocks exist in various localities. We confine ourselves
to mentioning only two largest eruptive provinces, hitherto examined
on both continents, viz that of Pocos de Caldas *) in the South of
the State of Minas Geraes, and the that of the Pilandsberg *) in the
district of Rustenburg (Transvaal). These two large provinces, the

1) O. E. Dersy. On Nepheline rocks in Brazil. 1. c.

*) E. Kayser. Bericht über geologische Studien während des Krieges in Süd-
West-Afrika. Abh. der Giessener Hochschulegesellsch. [l, 1920, blz. 18,

5) O. E. Dersy. loc. cit.

4) H. A. Brouwer. Geology of the alkali rocks in the Transvaal. Journ. of
Geology, 1917, XXV, p. 741 sqq.

1252

first with a diameter of about 25 to 30 k.m., the second of about
30 k.m., are both remnants of volcanic centres of large extent. In
both provinces the effusive-rocks include phonolites, leucite-rocks,
voleanic breccias and tuffs; among the abyssal-rocks foyaites and
syenites are known. In both provinces aegirine or aegirineaugite is
a common dark constituent and tinguaites occur as independent rocks
or as marginal zone of nephelinesyenites.

Volcanic rocks and intrusive dolerites.

The volcanic rocks of the Stormberg-series, whose lavas are widely
spread over the whole of South-Africa, point to a volcanic episode
in the mesozoic history of this country. At the same time and
shortly after this the instrusion of the so-called Karroo-dolorites
took place, which occur chiefly as dykes and intrusive sheets. Near
the westeoast the Kaoko-formation, composed of horizontal sandstones
and augiteporphyrite, extends over a wide area between 18° and
AS Lad,

In Brazil similar rocks have a great extent. Dykes and intrusive
sheets of diabase occur in various places in the states of Minas
Geraes and Sao Paulo in rocks of permian and of triassic age. Just
as in South-Africa a thick series of voleanie rock occurs in the
upper series of the Sta Catherina System, which is the equivalent
of the South-African Karroo-System. These rocks are considered to
be of Jurassic age and cover large surfaces in the States of Rio
Grande do Sul, Santa Catharina, Parana, Sao Paulo and Matto
Groso, even parts of The Argentine, Urugay and Paraguay.

Rocks like those in the above-named Kaoko-formation in South-
Africa occur also in Brazil near the opposite coast in the Southern
States of Santa Catherina, and Rio Grande do Sul. In both regions
these formations overlie for the greater part archaean rocks.

Kimberlites, Alnoites, etc.

The frequent occurrence of these rocks in South-Africa as far as
in the Congo State is well-known, in connection with the occurrence
of the diamond in some of these rocks, especially in some diamond-
pipes which are generally filled up by a volcanic breccia of
serpentinised ultrabasic material.

Suchlike rocks have been known long since in Brazil. They
have been described by Hussak ') as picriteporphyrite. He points out
a certain resemblance between the diamond-bearing deposit of Agua
Suja in West-Minas Geraes and the Kimberlites of South-Africa,
while later on Kimberlite was recognized in dykes in the State of

1) E. Hussax. Uber das Vorkomen von Palladium und Platin in Brasilien. Zeitschr.
f. prakt. Geol. XIV, 1906, blz. 284 e.v.

1253

Rio de Janeiro together with picrite porphyrites, alnoites and lim-
burgites, besides similar rocks in dykes and pipes in the Western
part of the State Minas Geraes ').

Just as the Kimberlite rocks near the West-Coast of South-Africa,
the known Brazilian rocks also belong nearly all to the basaltic
varieties, which are poor in mica. ;

Horizontal movement of the Atlantic Coasts.

The resemblance between some groups of sedimentary rocks on
either side of the Atlantic Ocean is also striking. We merely men-
tion the South-African Karroo System and the Brazilian Santa
Catharina System. The Orleans conglomerate in Sta. Catharina and
Rio Grande de Sul agrees with the Dwyka conglomerate of South-
Africa and in either continent the higher divisions are built up of
the above-named thick series of voleanic rocks, such as those of the
Drakensberg in Cape Colony and those of the Serra Geral in Rio
Grande de Sul.

When we reconstruct the volcanoes of alkali rocks which existed
in earlier periods along the present coasts, and imagine the two
continents to be brought close together, we obtain a configuration
similar to the aspect of the East-African Lake region, where at the
present day the voleanoe Kenia and Kilima Ndsjaro built up of
alkali-rich rocks, arise. This picture illustrates WEGENER’s*) inter-
pretation of the origin of the Atlantic Ocean *). More should be
known, than has been recorded in the foregoing, about the resem-

') KE. Rimann. Uber Kimberlite und Alnoite in Brasilien. Tscherm. Min. u. Petr.
Mitt. 1915. Id. A Kimberlita no Brazil. Annaes da Escola de Minas de Ouro
Preto. N°! TS: TOT.“ blz. 21 e.V.

2) A. Wecener. Die Entstehung der Kontinente und Ozeane, Die Wissenschaft,
Bd. 66, 1920.

3) Still other fissures of the African continent may be reconstructed of similar
character to, but of higher geological age than, those of the present East African
fractures. We refer to the system of dykes of alkalierocks with a uniform north-
western to northern trend, occurring on either side of the old volcanic centre of
the Pilands Berg in the Transvaal and can be traced over a distance of more
than 100 K.M., cutting through all older formations. In the part of the earth’s
crust, which has disappeared here through erosion the fault-system may have
‘ exhibited here an aspect similar to that of parts of the present East-African
fracture-system ; it seems however that the horizontal movements on either side
of these faults soon ceased and that they did not produce any considerable gaps.
Then the fissures will disappear at greater depths and many similar faults may
have existed in an earlier stage of erosion on the African Continent as intruded
or gaping, fissures, of which no trace is visible now. (Cf. fig. 2 and p. 765 in
H. A. Brouwer, Geology of the Alkali rocks ete. 1. c.)

1254

blance of the eruptive rocks and the petrographic provinces near
the opposed shores, to lend support to the above interpretation.
Still, in any case the resemblance of the rare eruptive rocks, is
striking. According to Wreener the present coastlines of Africa and
South-America represent the borders of a fissure, which is supposed
by that writer to have gratually widened to the present Atlantic
Ocean through horizontal movements of the two present continents.

This hypothesis is at variance
with the view that the Atlantic
Ocean should have arisen through
the subsidence of a continental
region, while Africa and America
are supposed not to have moved
in a horizontal direction.

The vertical movements executed
on the surface of the earth are
evidenced e.g. by upheaved shore-
terraces and reefeaps, drowned
river valleys etc. In connection
with this the genesis of sea-basins
is explained by vertical downward

movements, because the horizontal
movements are not established in
| a similar manner and consequently

eN escape our direct observation. But

with rising rows of islands the

| horizontal component of the rate

of movement is sometimes much

greater than the vertical one. The

latter is distinguishable by up-

Fig. 2. An older African fault- heavedecoralreefsand shore-deposits
system. whereas the former must be derived
cscs: The old Pilandsberg vulcano from far less distinguishable phe-
(Transvaal). nomena such as the form of the
reefcaps and the character of the
fault-movements.*) The mesozoic
rows of islands of the Tethys have
executed chiefly horizontal and far less significant vertical movements,

— —- Dikes of (nepheline) syenitic
rocks.
Scale + 1: 1100.000.

1) H. A. Brouwer. Uber die horizontale Bewegung der Inselreihen in den
Molukken. Nachr. Ges. der Wiss. zu Göttingen. 1920, Math. phys. Kl. Id. Breuken
en Verschuivingen nabij de oppervlakte van bewegende geantiklinalen. Versl. Kon.
Akad. v. Wet. Amsterdam, XXVIII, 1920, p. 1151.

1255

at present their masses overlie each other in the overthrust sheets
of the mountain chains. These movements are explained by the fact
that the old continental flocks of Eurasia and Indo-Africa have
moved towards each other, in which process continental areas have
executed horizontal movements. Similar movements may have co-
operated to originate the Atlantic Ocean. Whether horizontal or
vertical movements have prevailed may to some degree be made
out by comparing the geological composition and structure of the
opposed coastal regions. The points of similarity enumerated by
Wererner and contested by Sokraer *) have still retained their signi-
ficance in some measure and the concordance of the eruptive rocks
discussed by us does not clash with the prevalence of horizontal
movements.

!) W. Soeraer. Die atlantische „Spalte”. Zeitschr. der Deutschen Geol, Gesellsch.
1916, Monatsber. Bd. 68, S. 200 folg.

Physiology. — “A direct proof of the impermeability of the blood-
corpuscles of man and of the rabbit to glucose’. By S. van
Creverp and R. Brinkman. (Communicated by Prof. H. J.
HAMBURGER).

(Communicated at the meeting of December 18, 1920).

1. Introduction.

The question dealing with division of glucose between the red
bloodeorpuseles and the bloodplasma, which has been discussed so
often already in the literature, has come to the front again through
recent research.

In 1919 one of us together with Miss EK. van Dam published a
series of researches*) which clearly demonstrated that the permea-
bility of the bloodeorpuseles for glucose is intimately related to the
process of coagulation, and that the bloodcorpuscles of the frog and
of man are found to be impermeable to gluclose only when the
earliest incipiency of coagulation has been prevented. In the case
of the frog the physiological impermeability could be shown by
direct chemical analysis.

Such a direct chemical proof could at that time not be given for
the human bloodcorpuscles. In the osmotic experiments these blood-
corpuscles were invariably found to be impermeable in cases where
the blood had not yet coagulated, and it was held that all the
authors who had found the bloodcorpuscles to be permeable to sugar
had used blood of which the commencement of coagulation had not
been prevented.

Shortly after this publication there appeared an article by W. Farra
and M. Ricnter-QuirTNer’*) on the distribution of sugar, chlorides
and residual-N between plasma and bloodcorpuscles in the circu-
lating blood. Also these investigators came to the conclusion that in
man the sugar in the blood occurred only in the plasma. The
method used by them could be considered as a direct chemical one.
They determined the amount of sugar in the blood as a whole and
in the plasma, and from these two values calculated the volume of
the bloodcorpuscles, taking for granted that all the sugar occurred

1) BRINKMAN and v. Dam. Arch. Intern. de Physiologie XV. 105. 1919,
*) Fatra and RicHTER—QvuITTNER: Biochem. Zeitschr. 100. 140. 1919.

1257

in the plasma. The volume of the bloodeorpuseles found in this
way corresponded in a large number of cases to that determined
in the haematocrite.

The results of the Austrian investigators have, during the past
year, been contradicted from different quarters by others who had
used the same method, but had come to opposite results*). This
did not surprise us seeing that Farra and Ricurer-Qumrrner had
used hirudine to obtain the bloodplasma. Before them, however,
several other investigators had already used hirudine blood and had
found the bloodcorpusecles to be permeable.

The explanation of this we thought could be sought in the fact
that hirudine does not prevent the first phases of coagulation. Only
after this had been prevented in another way it was found by the
osmotic experiments that also in the hirudine blood the bloodcor-
puscles are impermeable to sugar’). If Farra and Ricnter-QuiTTnEr
in spite of using hirudine blood had obtained the same results, then,
we thought, it was to be attributed not to the hirudine but to the
Separation of the plasma and bloodcorpuscles by direct and rapid
centrifugalisation. Whether, by setting to work in this way, the
bloodcorpuscles are indeed found to be impermeable to sugar is,
however, still subject to grave doubt owing to the many failures of
experiments done with hirudine blood by- others.

The great theoretical and practical value of the question under
discussion demands however direct chemical proof which can be
regarded as being absolute. Also this we think cannot be said of
the experiments of Fauta and RicHrer-QUITTNER.

According to our train of thought such direct proofs could be
given only by examining plasma which was free from bloodcorpus-
cles and which had been drawn directly from the bloodvessels, or
had been obtained outside the body from blood which had remained
perfectly fluid without the addition of a single one of the substances
which prevent coagulation, for these, after all, do not prevent the
first phases of coagulation. The amount of sugar in the plasma ought,
if the bloodecorpuscles were impermeable, to be able to be calculated
approximately from the total amount of sugar in the blood, and the
volume of the bloodcorpuscles *).

1) See f. i Biochem. Zeitschr. 107. 246 and 248. 1920.

2) BRINKMAN and v. DAM l.c.

5) We say “approximately” because we want to take for granted for the time
being that the blood corpuscles have a share in the socalled restreduction. This
is however very small according to the investigation of R. Ear (Biochem. Zeitschr.
107, 229, 1920) when determined by the Bang-method which we used.

81

Proceedings Royal Acad. Amsterdam. Vol. X XIII.

1258

We have succeeded in obtaining plasma in both of these above-
mentioned ways, first from the rabbit and afterwards from man,
and in subsequently demonstrating in a direct chemical way the
impermeability of the bloodcorpuscles towards glucose.

Il. Determination of the amount of sugar in the bloodplasma
of the rabbit obtained from a vein isolated from the body.

To obtain blood-plasma from a blood-vessel our primary idea
was that we could make use of the property of the bloodcorpuscles
of female animals (especially pregnant ones) of settling rapidly
compared to those of male animals’). Aceordingly we several times
clamped the marginal vein of a she-rabbits ear which did not show
apparent anastomoses, the rabbit being bound on a rabbit plank
and the ear in question held vertically. We did not succeed, however,
in obtaining sedimentation in this way, probably because, after all,
there still existed small anastomoses on account of which the blood
could still circulate in the clamped vein.

By another method, however, the desired result was obtained
with the same animals.

Artuts *) has found that when blood is kept in a vein which is
taken from the body and ligated at both ends, the blood remains
fluid in this vein, and, what is of great importance with regard to
the question under discussion, shows no glycolysis. This method for
obtaining uncoagulable plasma has, practically speaking, up to the
present been followed only with the jugular of the horse and is
therefore known as the jugular-method.

We have applied it twice to obtain pure plasma from rabbits.
Here we set to work in the following way: The jugular on one
side/ was laid open over a length of at least 4 cms. and dissected
free from the neighbouring tissues and the greatest length between
two of its confluent veins was doubly ligated at both ends. This
part which was + 21!/, ems. long in both cases was then removed
from the body and held vertically. Seeing that it would take too
long to wait for the bloodeorpuscles to settle down when the vein
was hung up we placed it in a small centrifugal tube in which
the vein just reached to the bottom, and eentrifugalized rapidly.
After some minutes there could be seen through the wall of the

1) FäHRAEUS. Biochem. Zeitschr. 89. 355. 1918.
*) ArrHus. Arch. de Physiologie 1891— 1892,

1259

vein the distinet division between the dark mass of bloodcorpuscles
and the pale yellow translucent plasma. The bloodvessel was then
ligated in the lowest layer of plasma and a prick hole made in
the top portion from which the oozing plasma was caught up on
two pieces of Bang’s paper. In both cases we obtained enough
plasma to enable us to make a reliable double determination of the
plasma sugar. Simultaneously with this blood was drawn from a
vein in the ear of the same rabbit and in this the amount of blood
sugar and the relative volume of blood corpuscles was determined.
The result of both experiments was the following :

a. b. 6 d.
Total Volume Amount of plasma
Plasmasugar. ploddétsar of sugar calculated
Ba bloodcorpuscles.| from 6 and c.
Exper. I. 0.266 0/, 0.194 9%, 27 0.2657 9/,
ame | 0.255 » 0.1935 27 0.265

We have therefore obtained with the jugular-method the result
almost surprisingly accurate and accordanto that 7m the case of the
rabbit the blood sugar occurs almost exclusively im the plasma.
It can be remarked here still that both rabbits which were operated
upon under a light ether anaesthesia showed a pronounced hypergly-
caemia. This hyperglycaemia could therefore be reduced totally to
a hyperglucoplasmia.

UI. Zo show the impermeability of the bloodcorpyscles of man towards
sugar by the paraffin method.

To investigate also in the case of man the impermeability of the
blood corpuscles towards sugar along directly chemical lines we
first used the vein method for obtaining the plasma. Upon the
advise of Prof. HAMBURGER the umbilical cord was used as human
vein. Through the condencension of Prof. NisHorr and the house
obstetricians of the obstetrical clinic in Groningen we had for some
weeks at our disposal perfectly fresh umbilical cords. We tried
repeatedly to bring about in pieces of umbilical cord a division
between plasma and bloodcorpuscles in the large vein which could not
always be traced distinctly, because this vein could only with great
difficulty be dissected free from the neighbouring tissue with which

onl

1260

it was intimately connected. Neither by centrifugalizing in suitable
tubes nor by hanging up vertically pieces of ligated cord did we
succeed in this however in more than a few cases. The strong
contortions of the most umbilical cords and the consequent twistings
were the chief reasons for this. Only once up to this did we succeed
in bringing about in a cord with few contortions, the division and
comparing the plasma sugar with the quantity of sugar in the
blood of the cord as a whole and the relative volume of the blood
corpuscles. The concentration of the sugar in the plasma was found
to be markedly higher that that of the blood in the cord.

[t appeared that some of the large veins which are constantly
found on the surface of the foetal side of the placenta could be
more easily isolated and then centrifugalized. In these the blood
remained fluid for a markedly long time. Also in these cases we
can up to this boast of only one reliable determination for com-
paring the plasma and the blood as a whole. This however also
proved to be in favour of the plasma. We have not been able to
make a sufficient number of determinations by this method to come
to a conclusion through them whether human bloodeorpuscles are
permeable or impermeable to sugar.

We succeeded in doing this in the meantime by another method
viz the paraffin method; one way of keeping blood uncoagulated
without adding one of the known substances is by collecting it in
tubes which have been thoroughly cleaned and then waxed to make
them perfectly smooth. By using thus small and narrow waxed
tubes the blood collected in them can by rapid centrifugalization
be divided into its corpuscular and plasmatic parts which takes
place without the occurrence of coagulation. In larger tubes coagu-
lation took place fairly regularly during the process of centrifu-
galization. The way in which plasma was obtained now was
very simple. _

From a carefully cleaned finger tip in which a deep prick was
made with a needle, we allowed a few drops of blood to fall into
two tubes which had been waxed shortly before the experiment.
These were then rapidly centrifugalized for a period of from one
to two minutes and the plasma then sucked off by means of a waxed
pipette and dropped on Bane’s paper. At the same time blood was
collected for the determination of the total amount of bloodsugar
and the relative volume of the bloodcorpuscles.

From a number of these experiments conducted with different

persons at different times of the day the following results were
obtained : |

1261

Total Sugar in the Volume of the Calculated
bloodsugar. plasma. bloodcorpuscles. ih ee
0.117 0/, 0.178 °/, 38 0/, 0.188 °/,
0.103 0.161 39 0.169
0.110 0.165 38 0.180
0.135 0.223 43 0.237
0.137 0.192 38 0.221
0.111 0.188 41 0.190

In our opinion these results afford a direct chemical proof that
the bloodcorpuscles of man are free from sugar.

This decision will have to be taken into account in clinical
examinations so that besides the determination of the amount of
sugar in the whole of the blood the volume of the bloodcorpuscles
will have to be determined.

The contradiction which we find with the many authors on this
subject’) we hold has its origin in the following facts which we
wil] return to in extenso later:

1. Only in blood in which no signs of coagulation have appeared,
we find the bloodcorpuscles free from glucose (hirudine and other
substances which are supposed to make the blood uncoagulable, do
not arrest the very first phases of the process of coagulation).

2. The existence of a glucose-colloid-compound must be taken
into account.

3. Experiments which purpose the examination of the permeability
of the bloodcorpuseles towards glucose with the aid of the intro-
duction of fresh glucose must be judged with great care because the
relative permeabilities of the «- and $-modifications of the a-glucose
which result on solution of the latter are by no means equal ’).

Groningen, December 1920. Physiological Laboratory.

') See f.i. FALTA en RICHTER-QUITTNER. l.c.
R. Ear. Biochem. Zeitschr. 111. 189. 1920.

BONNIGER. ,, De 103. 306. 1920.

BRINKMAN en v. DAM. Biochem. Zeitschr. 105. 93., 108. 74. 1920.
HAGEDOORN. - En 107. 248. 1920.

FEIGL. re 112. 54. 1920.

M. B. WisHart. Journ. Biol. Chemistry. 44. 563. 1920.
TacHAU. Zeitschr. Klin. Med. 79. 421. 1914.
GRADWOHL and BLAivas. Journ. Lab. and Clin. Med. IL. No. 6. 1917.
4) HAMBURGER. Proceedings of the Royal Acad. of Sciences XXI. N°. 4, XXVIII
p. 318 and 327. |

Physiology. — The Significance of the concentration of calcium-
ions for the movements of the stomach caused by stimulation
of the N. Vagus’. By R. Brinkman and Miss E. van Dam.
(Communicated by Prof. H. J. HAMBURGER).

(Communicated at the meeting of December 18, 1920).

The great significance of the calcium-ion as an antagonist of the
Na- and K-ions has been set forth by numerous researches *) since
the fundamental experiments by Rineer and Logs. The physico-
chemical explanation of the action of calcium-ions must be sought
in the balancing effect that this ion has towards the monovalent
Na- and K-ions, as is very clearly illustrated, for instance, by the
researches of NrvscHLosz’), published but latily, about the influence
of salt-equilibration on the surface-tension of lecithine-soles in water.
From the table below one can form an idea of this action. In this
list it is stated how the strongly-increasing influence which definite
(physiological) NaCl-concentrations exercise on the surface-tension

TABEL I.
cena mac LRE EEN EEE Cale CS a Eh | hn ah
1 mol. 90.3 | 89.4 83.8 80.3 7618's nnNe | 82.7 88.8
Il, mol. SO 90.3 84.4 80.8 16.6 78.4 83.6 90.6
4 mol. 92.9 90.8 85.6 81.7 76.8 19.4 84.4 91.5
'/g mol. 94.5 oii 86.1 82.1 76.4 80.0 85.2 92.4
‘he mol. 92.9 89.7 84.4 81.2 76.0 79.8 | 84.9 91.0
"39 mol. 87.6 89.0 84 80.5 75.9 19.6 83.3 90.3
'/g4 mol. 83.6 88.3 83.6 80.1 75.7 78.5 82.5 89.4
1128 mol. 80.1 87.5 821 | 78.5 | 75.9 11.5 81.9 88.1

1) Summary in Héser: Physikalische Chemie der Zelle und Gewebe, Kap.
VIIL (1914); v. TscHeRMAK: Allgemeine Physiologie, p. 120 (1916); Bayurss:
Principles of General Physiology, p. 215 (1915); Héper: Pflüger's Archiv. 166,
581, 1917.

2) NeuscnLozs: Pflüger's Archiv. 181, 17, 1920.

1263

of lecithine-soles, is almost entirely neutralized by a definite con-
centration of Ca’-ions.

The surface-tension of a pure 1°/, lecithine-sole amounted to
75.9.*)

Consequently it appears from this table that the influence of a
definite concentration of an unbalanced NaCl-solution on the surface-
tension of a lecithine-sole, may be neutralized almost entirely by
the addition of Ca-ions, but it appears at the same time that only
one definite [Ca”] can do this and that this balancing effect can be
produced neither by a too large [Ca“] nor by a too small one. The
degree of this balancing [Ca’] depends on the ion-system present.

How we should explain this balancing is not known with certainty ;
it seems that LorB*) and others have modified the theory of the
electro-chemical ion-proteid-compound in favour of an ousting from
the surface. In a biological respect examples have of late come to
our knowledge from which it appears that also with the physiolo-
gical ion-balancing the degree of [Ca“] is decisive, and that very
slight fluctuations of these [Ca”| may have an important physiolo-
gical consequence. *)

It may be understood therefore that these [Ca”] should be kept
constant in the blood-plasm, as well as, e.g. the [H']. The buffer-
system by which this is principally effected has been indicated
by Rona and Takanasni*). According to these authors there is
for the free calcium-ion-concentration in the blood the equation:
Ke Ne Sn (K being about 350), a relation we could entirely

L
confirm by direct measurement of the [Ca”|.®) As the [H'] practi-
cally varies very little in physiological and also in pathological
cases, the |[Ca”] will consequently be controlled chiefly by the con-
centration of the bicarbonate-ions. An increase of the [Ca”] will
depend in the first place on a decrease of the [HCO’,], in other
words of an acidosis.

The main object of this communication is what influence the [Ca™]
and its fluctuations have on the irritability of the N. vagus. As a

1) Measured with the stalagmometer of TRaAuBE: Handbuch der Biochemische
Arbeitsmethoden V, Bd. 2. 1912.

2) LoeB: Journal of General Physiology, Vol. I en II.

8) HAMBURGER en BRINKMAN : Biochemische Zeitschrift 88, 97, 1918;

BRINKMAN: Biochem. Zeitschr. 95, 101, 1919.

4) Rona en TAKAHASHI: Biochemische Zeitschrift 49, 370, 1913.

5) BRINKMAN and miss vAN Dam, Verslagen Kon. Akad. v. Wetenschappen,
meeting of 25 Oct. 1919.

1264

test-organ we selected the perfused, surviving frog’s stomach, on
which we can easily study the influence of the N. vagus on the
motility. .

The general significance of the Ca-ions for the irritability of the
cerebro-spinal and the autonomic, central and peripheric nervous
system has been known for some time.

Locke’) demonstrated that the Ca-ion is necessary for conducting
the stimulus from a nerve to a voluntary muscle. OvERTON ’) proved
that it was equally indispensable for preserving the synapsis between
nerve-ending and ganglion-cell.

Busquet and Pacuon*) showed that the irritability of the N. vagus,
which soon disappears on perfusing the heart with a pure NaCl-
solution (Howerr)®), returns by adding small quantities of Ca. They
further found, as did also SaBBATAN1®) by testing many calcium-salts
of widely differing degree of dissociation, that we are definitely
concerned with an ion-influence and that undissociated Ca-salts were
of no importance for the balancing effect.

It is the concurring opinion of all investigators that the explana-
tion of this Ca-ion effect must be sought again in the influence on
the synapsis-colloids which is antagonistic to Na and K. From the
above-mentioned experiments of NeEuscHiosz°) as well as from said
physiological experiments °) it appeared also that this | Ca” ] must have
a very special constant value, and that slight variations of the physi-
ological [Ca”] may be of great influence. A total absence of Ca™-
ions will never occur in vivo, but especially these slight fluctuations
of |Ca”| are important under. physiological conditions.

It is true that in the literature of the subject there are indications
to be found that a too large quantity of Ca is as detrimental as a

1) Locke: Zentralblatt f. Physiologie 8, 166, 1894. See farther
CusHING: American Journal of Physiology, 6, 77, 1902;
Mines: Journal of Physiology, 42, 251, 1911.

2) OvERTON: Pfliiger’s Archiv. 105, 261 and 280, 1904.

3) Busqurr et PacHon: Journal de Physiologie et de Pathologie Gén. 11, 807
and 851, 1909.
Mines l.c.; Loewr: Archiv. f. Exp. Pathol. 70, 343, 1912.
HAGGAN and ORMOND: Amerc. Journ. o. Physiol. 30, 105, 1912.
CAZZOLA: Archivio di Fisiol. 11, 88, 1913.

*) HoweLL: Americ. Journ. o. Physiol. 15, 280, 1906.
6) SABBATANI: C. r. Soc. Biol. 54, 716, 1902.

6} NEUSCHLOSZ: le.

7) HAMBURGER and BRINKMAN: l.c.

1265

too small one’), but a careful study, showing the relation between
the [Ca] degree and the vagus-irritability, has not come to our
knowledge. For this reason we have tried to find this relation as
it was also done with the surviving frog’s kidney *) and the haemolysis ®).

The perfusions were done as follows:

The abdominal wall, thorax wall, and clavicula of the frog (d') are carefully
cut away, also the extremities are removed and the test object is nailed to a board.
For a better survey the intestines may also be removed as far as the duodenum
provided the mesogastrium is not injured. The canula is inserted into the a. coe-
liaca; the a. mesenterica is tied tight. In this way stomach + liver and gall-
bladder (art. hepatica) are perfused. The pressure may be regulated by the level
of the liquid-reservoir and the orifice of the canula.

Should it be desired to perfuse the whole of the intestines + portal circulation,
than the a. mesenterica is not tied; liver (arterial and venous), wall of gall-bladder,
stomach and intestines are then perfused. The proximal part of the v. abdominalis
must be tied.

The n. vagus is stimulated by inserting electrodes in the tubae Eustachii; this
is done most easily, by hammering 2 copper nails through the tubae into the board.

With this method of stimulation we always see (by very constant coils-distance)
the vagus-effects on heart and stomach-intestines.

The duration of each experiment was about 1'/, hours.

We have now observed the influence of the Ca-ion-concentration
in about 75 perfusions. Beforehand the irritability and the motility
of the stomach-wall of the newly-killed not-perfused frog was deter-
mined, which existed as much as possible under physiological conditions.

Afterwards the perfusions took place with the following solutions:

1. NaCl 0,6°/,.

2. NaCl 0,6°/,, then NaCl 0,5°/,, NaHCO, 0,20°/,, CaCl,.6 aq.
0,040°/,, KCl 0,020°/, Pr == + 8,6 *).

3. NaCl 0,6°/, + KCl 0,02°/,.

4. NaCl 0,6°/, + KCl 0,02 °/, + CaCl, .6aq. 0,005°/,, 0,010°/,,
0,012°/,, 0,014°/, ete., 0,020°/,, 0,025°/, etc.

5. NaCl 0,5°/,, NaHCO, 0,28°/,, CaCl,.6 aq. 0,040°/,, KCl 0,02°/,,
Py varying considerably: from 8,6 to 7,2.

6. NaCl 0,6°/,, CaCl,.6 aq 0,040°/,, KC10,02, Py=8,6, NaHCO,
0,05°/,, 0,010°/,, 0,0015°/, etc.

1) Josep E. MELTZER: Americ. Journ. o. Physiol. 29, 1, 1911.
BENDA: Zeitschr. f. Biol. 63, 11, 1914.

2) HAMBURGER u. BRINKMAN, l.c.
3) BRINKMAN: l.c.
4) Colorimetricai according to SORENSEN.

1266

1. The influence of a pure NaCt-solution on the motility and
the irritability of the vagus of the muscular-stomachwall.

When observing the stomach of a newly-killed frog, one often
notices spontaneous local contractions or peristaltic waves in both
directions. Stimulation of the vagus, brought about in the way
described above, causes strong peristaltic movements, especially in
the pyloric part; at the same time one can observe a frequent
lengthwise contraction. The stimnlation has a rather long after-
effect (5 minutes). It was constantly found that the minimum degree
of effective stimulation was with a coils-distance of 7 to 8 ¢.m.

[f the stomach is perfused with a 0.6 °/, NaCl solution Py = 8.6),
we see that the spontaneous peristalsis has disappeared after 5 to 10
minutes and that the stomach has become quite limp; the mechanical
irritability has completely disappeared.

The vagus-irritability is as follows: before the perfusion a vagus-
effect is observed with a coil-distance of 7 to 8 e.m.; after a 5
minutes perfusion a distance of 5 c.m.; after 10 minutes a distance
of 4 to 3 em.; after 15 to 20 minutes even the strongest stimulation
of the vagus takes no effect.

This disappearance of the vagus-irritability 1s reversible. If, after
half an hour’s perfusion with the pure NaCl solution, the liquid is
replaced by a well-equilibrated salt-solution (NaCl 0.5 °/,, NaHCO,
0.28 °/,, CaCl, 6 aq 0.040 °/,, KCl 0.020 °/,, Pa == 8.6) spontaneous
contractions are again observed after five minutes; after 10 minutes
vagus-effect occurs at 10 em. coil-distance, after 25 minutes vagus-
effect can be observed clearly at a coil-distance of 7 cm.

So it is clear that after half an hour’s perfusion with a pure
NaCl solution, the harmful action is still perfectly reversible.

2. The influence of NaCl + KCl.

Now we have tried to find out which ions of the physiological
solution in this respect caused the balancing effect. It soon appeared
that the addition of K-ions, to which one has to assign such an
important effect in heart-perfusion, have no effect of importance here.
A concentration of K-ions which can cause the return of the vagus-
irritability cannot be found.

3. The influence of NaCl + KCl+ Call. 6 aq.

The vagus-influence may be re-established by the addition of a
certain calcium-concentration to the (in itself insufficient) system of

1267

NaCl 0.6°/, + KCl 0.02 °/, (Py—= 8.6). The following experiments
give a brief survey of it:

a. unperfused stomach, vagus-effect at a distance of 8 em., after-
wards NaCl 0.6 °/, + KCl 0.02 °/,; after 10 minutes the vagus is
un-irritable, the stomach is limp. Then NaCl 0.6°/,, KCl 0.02 °/,,
CaCl, .6 aq 0.002 °/,; vagus-effect still fails to appear, stomach
remains limp, though somewhat less so than when it is perfused
with a pure NaCl solution ;

6. unperfused stomach, vagus-effect at 7.5 em., then NaCl 0.6°/,,
KCI 0.02 °/,; after 15 minutes the stomach is limp, stimulation of
vagus has no effect. Then NaCl 0.6 °/,, KCI 0.02 °/,, CaCl,.6 aq
0.004 °/,. Whereas the effect of this Ca-concentration on the perfused
heart is clearly visible, there is no effect whatever on the stomach,
except a slight tonie contraction.

c. Nor could a return of the vagus-irritability be established in
numerous perfusions, when to the NaCl 0.6 °/, + KCl 0.02 °/, was
added respectively CaCl, .6 aq 0.006°/,, 0.008°/,, 0.010°/,, ete. But

d. the addition of 0015°/, CaCl, .6 aq to NaCl 0.6°/,+ KC10.02°/,
caused the vagus-irritability to return completely. We must, however,
stress the fact, that, to obtain this result, one should take special
precautions. As namely the liquid does not possess at all a buffer-
system against H-ions, fluctuations of [H°] occur very easily. It is
necessary that the Py of this perfusion-liquid should be 8.6 and
remain constant during the experiment. The use of a rubber tube
is very dangerous in this experiment, as it nearly always makes
the liquid too acid.

These precautions being taken, one can always demonstrate that
a concentration of 0.015 °/, CaCl, .6 aq (and also 0.016 °/,) is able
to balance the concentration of alkali-ions; this concentration corre-
sponds to a free [Ca] of about 9 milligrammes per litre.

It is an interesting fact that exactly the same concentration of
Ca-ions proved necessary for the preservation of the impermeability
of the glomerulal membrane for physiological quantities of glucose.')

e. a concentration of CaCl,.6 aq of 0.020°/, and higher con-
centrations are unable to preserve or recall the vagus-irritability ;
then tonic contractions of the stomach-wall too disappear again
completely iu this case.

4. The influence of a concentration of hydrogen-ions.

By choosing the total quantity of Ca of the perfusion-liquid in

1) HAMBURGER and BRINKMANN, l.c.

1268

such a manner that a high free [Ca] cannot arise, it is possible to
investigate the influence of the [H') separately.

It appeared already in the above-mentioned perfusions with NaCl
0,6 °/,, KCI 0,02 °/,, CaCl,.6aq 0,015 °/,, that the [H') must be kept
within rather narrow limits.

When a bufter-system exists (NaHCO, + CO), the [|H] may vary
within the limits of this system, as appears from the following
experiments:

a. Perfusion with NaCl0,5°/,, NaHCO, 0,28°/,, KC1 0,020°/,, CaCl, .
Gaq 0,015°/,, Pm =8,6; there are strong spontaneous peristaltic
movements; vagus-irritability at a coil-distance of 7.5 em. Then the
same liquid but now with CO, passed through until Py — 7,1; the
stomach becomes limp in 10 minutes and can no longer be in-
fluenced by vagus-irritation.

6. Perfusion with NaCl 0,5°/,, NaHCO, 0,28°/,, KCl 0,02°/,, CaCl, .
6 aq 0,015°/,, Py—8,6; irritability at a distance of 8 cm., spon-
taneous contractions. Then Py= 8,3, constant irritability at 10 ¢m.’s
distance; spontaneous contractions of stomach. Then Py=— 7,7;
irritability at 14 em., spontaneous rapid peristalsis. Then Py = 7,3;
irritability at 14 em, stomach contracted spastically. Then Py == 7,1;
stomach not irritable, spontaneous movements have disappeared. Then
Py= 8,6; after 10 minutes’ vagus-stimulation at 8 em. spontaneous
movements of stomach.

This last survey is an example of many similar experiments, from
which it appears that the slight [H’] fluctuations do not let the
vagus-irritability disappear but certainly influence it.

The actions of the H' and the Ca“ cannot be separated here,
because their quantities are directly dependent on each other and
because in general the colloid-action of the Ca'-ions depends on the
H-ion-concentration which is present. The balancing effect of Ca’~-
ions can be indicated only with one definite H’-ion-concentration.

The fact that an alteration of the Ca’-ion-concentration in itself
induces a variation of the vagus-irritability, is shown by the last
series of experiments which correspond for the most part to condi-
tions as they occur physiologically and pathologically.

5. The influence of the NaHCO,-concentration.

When the NaHCO,-degree of a liquid is moditied systematically,
the H-ion-concentration remaining constant, one obtains likewise a

1269

modification of the Ca-ion-concentration, because the [HCO',| and
[Ca] are inversely proportional to each other, the influence of this
modification is great, as appears from the following examples:

a. Perfusion with NaCl 0,6 °/,, KCl 0,02 °/,, CaCl,.6 aq. 0,04°/,,
NaHCO, 0,05 °/,. Pir — 8,6. After 5 minutes the spontaneous con-
tractions have disappeared and the stomach is contracted spastically :
no effect of vagus-irritability is visible.

6. Perfusion with NaCl 0,6°/,, KCI 0,02 °/,, CaCl,.6 aq 0,04°/,,
NaHCO, 0,10°/,, Pa = 8,6. After 10 minutes the stomach is contracting
with intense spasms, especially the pyloric part of it. The vagus is
extremely irritable, at 15 em’s coil-distance deep waves arise in the
stomach-wall which last very long and are displaced very slightly ;
finally we have a very spastically contracted stomach (pylorospasmus).

c. Perfusion with NaCl 0,5 °/,, KCl 0,02 °/,, CaCl,. 6 aq 0,04 °/,,
NaHCO, 0,15 °/,, Po = 8,6. After 10 minutes the stomach shows
very slight peristalsis with intense spastic contractions in the pyloric
part. Vagus-irritability at 12 cm, tonic contractions lasting a very
long time.

d. Perfusion with NaCl 0,5 °/,, KCl 0,02 °/,, CaCl,. 6 aq. 0,04 °/,,
NaHCO, 0,20°/,, Pa= 8,6. With this liquid the spontaneous perist-
altic movements appear again; the vagus is irritable at a coil-distance
of 9 cm. and produces a series of peristaltic movements; the spastic
contractions are still present in a slight degree.

e. Perfusion with NaCl 0,5 °/,, KCl 0,02 °/,, CaCl,. 6aq. 0,04 °/,,
NaHCO, 0,28 °/,, Po = 8,6. With this liquid the vagus is irritable
at a coil-distance of 7 cm.; there are normal peristaltic movements
and no spastic contractions. The conditions are completely like dose
of the unperfused stomach.

From these experiments appears clearly the great influence which
a change in bicarbonate-concentration has on the irritability of the
n. vagus and on the spontaneous rhythmical movements of the
stomach-wall. The latter effect is probably also due to the influence
on the autonomous plexus of AurrBacH. It cannot be decided with
certainty whether we have to think here especially of a direct
influence of the HCO,-ions *) or only of the influence of the latter
on the [Ca™], but, in connection with the experiments with pure
NaCl + CaCl, solutions, the primary significance of the Ca-ions seems
to us by far the more probable.

We attach some significance to the fact that a decrease of | HCO,’],

1) Rona and NeukKircH: Pfliiger’s Archiv. 148, 285, 1912.

1270

so an acidose, can cause spastic concentration of the stomach and
an increased irritability of the n. vagus (vagotony). Whether a
decreased [Ca] can cause similar phenomena, has not yet been
investigated by us.

Physiological Laboratory of the Unwersity

of Groningen.
December 1920.

Paleontology. — ‘On the Significance of the Large Cranial Capacity
of Homo Neandertalensis’’. By Prof. Eve. Dusois.

(Communicated at the meeting of November 27, 1920).

Before the discovery of the fossil man of La Chapelle-aux-Saints
our knowledge of the most important character of Homo neander-
talensis, the cranial capacity, rested only on estimation, especially
from the capacity of the calvaria. SCHAAFFHAUSEN, Huxley and
SCHWALBE started from the supposition that the capacity of the
calvaria of the Neandertal Man, which is human as regards its size,
was in the same ratio to that of the whole skull as in Man of the
present type. It is not surprising, that their results are pretty well
concordant *).

First SCHAAFFHAUSEN*?) measured the capacity of the Neandertal
calvaria with water, on a level with the orbital plate of the frontal
bone, with the deepest notch in the squamous margin of the parietal,
and with the superior semicircular ridges of the occipital. He found
for it 1033 em.*, and estimating the capacity of the missing part at
215 em.* from other skulls, he found 1248 cm.’ for the total capa-
city of the skull. Later, anew measuring the calvaria with water,
“mit ihrem oberen Rande horizontal gestellt”, he found 930 em.” for
its capacity, and now for the whole capacity, through comparison
with the corresponding part and the whole of a “roh gebildeten
Schadel” of 1805 em.” capacity and of a negro skull, only 1098,
resp. 1099 ecm.*). Accepting the first calvaria measurement by
ScHAAFFHAUSEN, Huxrer *) estimated the capacity of the entire skull
at about 75 cubic inches (= 1229 em.*). ScnwarBeE *) measured the
capacity of the Neandertal calvaria with peas up to the transversal

!) M. Boure, Sur la capacité cranienne des Hommes fossiles du type de
Néanderthal. Comptes rendus. Académie des Sciences. Tome 148, p. 1352. Paris
1909.

2) SCHAAFFHAUSEN, Zur Kenntniss der ältesten Rassenschädel. Archiv für Ana-
tomie, Physiologie und wissenschaftliche Medicin (Johannes Müller). Jahrgang 1858.
Berlin, p. 455 and p. 464.

H. ScHAAFFHAUSEN, Der Neanderthaler Fund, p. 43. Bonn 1888.

3) T.H. Huxtey, Evidence as to Man's Place in Nature, p. 156 — 157. London 1863.

4) G. SorwaLBe, Der Neanderthalschädel. Bonner Jahrbticher, Heft 106, p. 50—
52. Bonn 1901. ScHWALBE erroneously rejects SCHAAFFHAUSEN's second deter-
mination, „weil sie durch Wasserfiillung ermittelt ist”, which would, indeed, also
be applicable to the first determination. In this procedure errors could be avoided.
It is not clear what caused ScHAAFFHAUSEN to arrive at so much lower capacity

1272

glabella-inion plane, and found, on comparison with the skull of a
New-lrelander, 1233 cm.’ for the capacity of the entire Neandertal
skull. His confidence .in these results was so great that he stated:
“An der Thatsache, dass die Capacität des Neanderthalschädels
nicht mehr als 1230 cm.’ beträgt, ist jedenfalls nicht zu zweifeln’’.
Yet it has turned out that his conclusion was erroneous.

SCHAAFFHAUSEN's measurements dit not refer to parts of the cra-
nial cavity that could be clearly defined. For this reason I measured
the capacity of the Neandertal calvaria, already in 1897, up to a
definite plane imaginable in the encephalon, the transversal plane
through the frontal pole of the hemispherical axis (which plane in
most human skulls, as also in those of Neandertal and of Spy and
in Pithecanthropus, corresponds to the boundary of the lowest and
middle third part of the area of the inferior frontal convolution) and
the middle of the upper rim of the right suleus transver$us of the
occipital bone (corresponding to the lower margin of the cerebrum).
First I then measured the capacity of the calvaria of the Spy-skulls
at Liege, in the laboratory of my regretted friend Julien FRAIPONT;
the following day at Bonn, in the Provincial-Museum, with the
permission of the director, Professor J. Krein, that of the Neandertal-
calvaria in perfectly the same way, with the same material (rape-
seed). | found 920 em°. for the Neandertal-calvaria, almost the same
capacity aS SCHAAFFHAUSEN found in his second measurement. This
concordance is probably owing to this that the upper rim of the
right sulcus transversus coincides in its horizontal course with the
edge of the fracture'). Thus I determined the capacity of the cal-
varia of Spy I at at least 900 cm’*., of Spy IL at at least 1050 cm’.
The two latter values can be so only approximately on account of
the incompleteness and partial reconstruction of the skull walls,
especially of Spy I.

of the fossil skull in his later comparison; probably because he took other limits
of the calvaria space in the modern skulls than in the fossil one.

J. Ranke (Der Mensch. Zweite Auflage. Band II, p 478. Leipzig 1894) estimated
the capacity, from the horizontal circumference and the breadth index according to
Wetcxer’s table, at 1532 cm’. L. Manouvrter (, Deuxiéme étude sur le Pithécanthropus”’
in Bulletin de la Société d’Anthropologie de Paris, 4e série, tome 6, p. 585. Paris
1895) estimated it at 1500 cm*. by assuming a basio-bregmatic height of 125 mm.
and a cubic index of 1.25. The latter estimation, in Broca-measure, corresponds
to a minimum of 1410 cm.* real capacity. RANKE supposes, certainly erroneously,
that the height, independent of the particular shape of the skull, is in the same
relation to the horizontal dimensions as in ordinary human skulls.

') Thus noted down at the time of my investigation. The protuberantia occipitalis
interna, which cannot be sharply defined, lies + 8 mm. higher.

1273

In order to compare as much as possible with homologous capa-
cities of recent men I chose three skulls of Kuropeans (Dutchmen)
of different sizes, and a skull of a Javanese, and determined the
capacities of the upper or calvarial part, to the same level, and of
the entire skulls, with water, by the halves which had been made
impermeable and were shut off by a glass plate.

DRR De J.
Cranial capacity 1260 1434 1500 1550 cm°
Calvarial capacity 884 1000 1070 1150 „
Ratio 142 1.43 1.40 1.35 mean 1.4.

Accordingly the calvarial capacities of the examined individuals
of the Neandertal-Man fall entirely within the range of the calvarial
capacity (which is as much as possible homologous) of large-brained
recent races. The total capacity was, therefore, certainly not smaller.’)
A simian flattened upper part of the skull must have gone together,
as in the Apes, with a comparatively larger lower part of the skull
than in the high-vaulted skull of recent Man.

According to the ratio found in recent Man the capacity of the
(entire) Neandertal-skull would have been 1288 cm’, in concordance
with the earlier and with ScuwaLsn’s estimations; that of Spy I
would at least be 1260, and that of Spy II at least 1470 em’.

But at the skulls of Apes (Gorilla gorilla, Simia satyrus, Hylobates
agilis, Semnopithecus entellus, Macacus cynomolgus) I found that
the ratio of these capacities, which were again as homologous as
possible and deviated little inter se, is 1.6 on an average. In the

8) Eve. Dugors, Remarks upon the Brain-Cast of Pithecanthropus erectus.
Proceedings of the Fourth International Congress of Zoology. Cambridge 1898.
p. 85—86. There too with regard to the same investigation made on skulls of
apes and on the calvaria of Pithecanthropus erectus. The results were in detail
as follows:

Pithecanthropus Gorilla & Anthropopithecus & | Simia satyrus 2
Capacity — 540 356 346
Calvaria 570 334 255 219
Ratio — 1.61 1.43 1.58

sed Semnopithecus Macacus
S l
Hylobates agilis | Symphalangus & ia eee RA,
114 128 116 di
73 62 72 48
1.56 2.06 1.61 1.60

The measurements of the capacities with rape-seed yielded average results equal
to those with water; the values found can in view of this, be considered as the
true capacities.

82

Proceedings Royal Acad. Amsterdam. Vol. XXIII.

1274

very flat-headed Siamang it has even risen to 2 (in contrast with -
1.56 in Hylobates agilis); in a female Chimpanzee I found on the
other hand 1.43.

These last ratios give rise to doubt whether the comparatively
small capacity of the upper part of the skull (calvaria) and the
platycephaly are really an indication in general of a low development
of the brain; they make it probable that here mechanic factors
lying outside the brain, which are in connection with the compara-
tively great size of the jaws or the poise of the head, if they are
not the only ones, at least preponderate. Actually the jaws of the
Siamang are comparatively much larger than those of the small
Hylobatides (the ratio capacity: palatal area was 6.7: 1 in Sympha-
langus syndactylus, 9.5:1 in Hylobates leuciscus); also the female
Chimpanzee has comparatively small jaws. And undoubtedly the head
poise of Homo neandertalensis was different from that of Homo sapiens.

The ratios found in skulls of Apes might have led us to expect
that in the platycephalic skulls of the Neandertal type the lower
part of the skull, hence the whole capacity of the skull in com-
parison with the calvaria, was more spacious than in skulls of the
Homo sapiens type.

This has actually appeared, after in 1909 Boure') with VerNneau
and River, through direct measurement with millet-seed, had deter-
mined the (total) skull capacity of the fossil man of La Chapelle-
Aux-Saints, and had found the considerable amount of 1626 cm?
Broca-measure, i.e. 1530 em° real capacity ’).

ScHwaALBE*) then concluded from this skull that it would not do
to calculate the missing part of the capacity of the Neandertal-skull
from the comparison with a skull of Homo sapiens, as he had done
before, and found that the Neandertal type is sharply distinguished
from that of Homo sapiens by the much more considerable relative
height of the lower part of the skull, measured by the perpendicular
of the basion to the glabella-inion line. He states from photograms
published by Bourke that the height of the lower part of the skull con-
stitutes a relatively much larger part of the total height (normal to
the glabella-inion line) than for instance in Australian skulls. The
calvarial height of the La Chapelle skull is 82 mm. according to

1) Comptes rendus. Académie des Sciences, loc. cit.

’) According to E. Scumipt’s Reductionstabelle fiir die Broca’sche Schrotmessungen.
Archiv für Anthropologie. Band 13. Supplement, p. 78. Braunschweig 1882.

5) G. Scnwarse, Kritische Besprechung von Boute’s Werk: ,L’Homme fossile de
La Chapelle aux-Saints’ mit eigenen Untersuchungen. Zeitschrift fiir Morphologie
und Anthropologie. Band 16, p. 593-594. Fig. 1—3. Stuttgart 1914.

1275

his measurement, which I, too, find from Bovutn’s figures 24, p. 34
and 1, Pl. III. The rest of his statements are difficult to follow ;
this calvarial height is for instance as ‘‘Unterschadel” added to an
“Oberschädel (Kalottenhöhe)” of 130 mm., which yields an (impossible)
total height of 212 mm. In reality the basion-bregma height is,
according to Boure's statement’), 131 mm., from which I find
135 mm. for the total height, hence 53 mm. for the height of the
lower part of the skull, or 39.3°/, of the total height, which latter
result is after all in good agreement with ScnwarBu'’s 38.7°/,. He
gives 12.7°/, height of the lower part of the skull for an Alsatian
man, 27.6°/, for an Australian. In his figures 1 (Alsatian) and 2
(Australian) I, however, measure ratios of 24.1 and 21.6°/,. Two
other Australians have 22.8 and 27.7°/. The skull of Wadjak I
gives the ratio 28.6°/,. I find 21.2°/, in a Javanese skull, 25,6°/, in
a Dutch skull of unknown origin. SCHWALBE finds 50°/, height of
the lower skull part fora full-grown chimpanzee, and 55°/, for a Macacus
nemestrinus. I determined the ratio 46.5°/, in a skull of Hylobates
agilis, and 60°/, in that of the Siamang, Hylobates (Sy mphalangus)
syndactylus. ScHwaLBE calculates 38.5°/, for the Neandertal skull;
but on comparison with the total height of 135 of the La Chapelle-
skull I find with ScHwaLBE's 80.5 mm. calvarial height of the
Neandertal man, 37°/,.

In this connection the comparative height of the lower part of
the skulls of Frisians of old mounds (“terpen”) and of the island
of Marken in the Zuiderzee, which have been excellently described
by Barer, gets particular significance *).

In this Barer has proved conclusively, what had already been

1) L'Homme fossile de la Chapelle-aux-Saints, p. 37.

’) J. A. J. Barae, Beiträge zur Kenntnis der niederländischen Anthropologie [,
Friesenschädel. Zeitschrift für Morphologie und Anthropologie. Band 16, p. 329—
396. Stuttgart 1913. Il. Schädel von der Insel Marken. Ibid., p. 465—521, Stutt-
gart 1914. With reproductions and tables. — From the island of Marken originates
also Blumenbach’s ‘‘Batavus genuinus’’, at whose forehead ScHAAFFHAUSEN, SPENGEL
and R. VircHow thought they could detect neandertaloid characteristics. On the
evidence of the “Batavus genuinus” Rup. WaaneRr- was even led to pronounce
the sentence: “Der Neanderthalschädel ist von einem alten Holländer”, with the
attenuating circumstance: “his zum Gorilla hat es doch noch entsetzlich weit hin”.
(H. ScHAAFFHAUSEN, Der Neanderthaler Fund, p. 21, footnote. Bonn 1888). This
large Marken skull cannot be called platycephalic, because the calvarial height
index is 54.8 (G. Scuwarse, Neanderthal Schädel und Friesenschädel. Globus.
Band 81, p. 173. Braunschweig 1901), which is about equal to the mean of
Australians and Tasmanians. Also the shape of the forehead should sooner be
called austroloid. The height of the lower part of the skull is 19.4 °/, of its total
height (measured on Scuwatse’s Abbildung 3, p. 172).

82*

1276

observed by Bork, that the Frisian skulls of the island of Marken, and
more particularly the female skulls, have become artificially deformed,
platycephalic through a particular kind of children’s caps; their calva-
rial height index is on an average 55.4 (in three female skulls 52.5)
as against 59.4 in the naturally formed old Frisian skulls from mounds.

It is very remarkable that also this artificial flattening is accom-
panied by an increase in height of the lower skull. On 28 of Barar’s
median curves of skulls of mound-Frisians the comparative height
of the lower skull (vertically below the glabella-inion line) can be
measured; I find the following values for this in percentages of
the total height of the’ skull: 25.1, 13.9, 21.3, 19.5, 19.9, 10.3,
23.0, 23.5, 21.2, 25.2, 21.5, 21.1, 24.0, 25.7, 23.7, 24.7, 24.8, 15.7,
22.6, 17.7, 12.8, 19.3, 16.5, 21.4, 25.5, 20.0, 24.4, 18.8. The mean
of these Frisian skulls is 20.8.

From 9 median curves of Marken skulls I find: 28.4, 28.4, 27.0,
23.0, 26.0, 26.3, 25.4, 22.9, 21.1. The three first, largest, values
are of female skulls. The mean of the nine Marken skulls is 25.4,
of the six male ones(?) alone 24.1, of the three female ones 27.9.

It thus appears that this artificial platycephaly is attended with
greater height of the lower skull. This can hardly be imagined in
another way than that through the pressure from above part of the
brain mass was forced downward. Therefore to the slight depression
of the upper part of the skull corresponds a proportionally slight
rise of the lower part of the skull; in the skull of La Chapelle-
aux-Saints to 40.5 calvarial height index 39.3 °/, height of the lower
part of the skull.

Now the greater height of the lower part of the skull, betow the
glabella-inion line in skulls of the Neandertal-type and in skulls of
Apes can certainly partly be accounted for by the relatively high
situation of the inion. In Spy [ I found this point 12 mm., in Spy
I] 14 mm. above the middle of the right suleus transversus, while
in skulls of the present type the two points lie mostly on the same
level’). In the skull of a » chimpanzee the inion lies 23 mm., in

1) J. Frarpont and M. Lonest (Recherches Ethnographiques sur des ossements
humains découverts dans les dépôts quaternaires d'une grotte 4 Spy. Archives de
Biologie. Vol VII, p. 622. Gand 1887) say that the protuberantia occipitalis
interna “est situee plus bas et en avant à un centimétre de distance environ”.

K. Gorsanovic—Kramperaer (Der diluviale Mensch von Krapina in Kroatien,
p- 112. Wiesbaden 1906) found the protuberantia occipitalis interna „etwa 2 cm.
abwärts vom Torus’, M. Bourk (loc. cit., p. 47) between the same points, “inion
interne” and ‘inion externe”, the distance of 24 mm. at the skull of La Chapelle-
aux-Saints, and Scuwatse (loc. eit, p. 50) in the Neandertal-calvaria the external
inion opposite the internal “nur um ein Geringes verschoben”’.

1277

that of a 2 orang utan 32 mm., of a £ Hylobates agilis and of a
J Siamang 5 mm., of a g Semnopithecus entellus 14 mm., and of
a & Macacus cynomologus 18 mm. above the right sulcus transversus.

But in this way the great height of the lower part of the skull
in the Neandertal type can only be accounted for for about a third
part, and there exists a considerable difference in the relative height
of the lower part of the skull between the two Hylobatides, though
the inion is situated at the same distance above the sulcus trans-
versus. It should be pointed out here that the platycephaly of the
Siamang is by no means to be explained by the greater size of its
body, for its weight is only the half more than that of the smaller
Hylobatides. In the development of the brain they are certainly all
about on a line, and yet the skull of the Siamang is in comparison
with the other Hylobatides as much flattened as that of the Nean-
dertal Man in comparison with recent Man (Fig. 1 and Fig. 2).

It may, therefore, be assumed that the homologous lower part of
the skull in relation to the whole is more capacious in Homo nean-
dertalensis than in Homo sapiens, not or not chiefly on account of
the upper part of the brain being less large in itself, but in con-
sequence of similar external causes as make the lower part more
spacious in the platycephalic Siamang than in his smaller relative.
Also in the skull of the Neandertal Man the flattening above must
have caused part of the brain to be displaced downward.In fact for the
physiological function of the brain the place which it occupies in
the skull is very indifferent; it is not so with the bone- and
muscle substance at the skull, whose funetion is directly dependent
on the place. This leads to the insight that the peculiar shape of
the skull of the Neandertal type was not determined, at least not -
chiefly, by the comparatively small size and low stage of develop-
ment of the encephalon, but by external mechanic factors, chiefly
in connection with the position and poise of the skull on the spinal
column — which I have referred in my communication of September
25, 1920 on the “Protoaustralian Fossil Man of Wadjak, Java’? —
just as the platycephaly in the Siamang, in contrast to the other
Hylobatides, can only be explained by its comparatively large jaws.

The capacity of the skull of 1288 cm.* to be calculated for the
man of the Neander-valley from the calvaria, in accordance with
the proportion in the recent human type, must then be much too
small. According to the ratio which exists in Apes between the
calvaria and the total capacity of the skull this fossil man would
have possessed a brain capacity of 1472 em*. Bourn’) calculated

1) M. Boure, L'Homme fossile de La Chapelle-aux-Saints, p. 189.

1278

1408 em.’ Broca (i.e. 1320 cm.’ real capacity) from the comparison
of the greatest length and breadth and a corresponding height of
the endocranial plaster casts of the Neandertal calvaria and the

een

Fig. 1. Median cross section of a skull of
Hylobates agilis. °%/3 natural size.

Le aca

Fig. 2. Median cross-section of the skull of Hylobates
(Symphalangus) syndactylus. */s nat. size.

La Chapelle skull in relation to its capacity. In this the relatively
more considerable breadth of the Neandertal calvaria in the frontal
region was not taken into account. Perhaps some measure did not
exactly correspond. Assuming similarity of form, the capacity as
computed from the relation of the calvarial heights of these skulls,
is 1450 cm’. On the strength of these and of the foregoing consi-
derations it seems to me that an estimation of the capacity of the
entire Neandertal-skull at 1400 cm’. at least cannot be far from
the truth. That of Spy I can have been but little smaller, and Spy
II must, in the same ratio, have reached a true capacity of 1600
cm’. By the method of the “cubic index” J. Fraipont had calculated
for Spy I 1562 em°. Broca-capacity (which corresponds to 1470 cm’.
real volume), for Spy Il 1723 cm’. Broca (i.e. 1620 cm’. real volume),

1279

unexpectedly high results, so much so that he was perplexed (‘‘effrayé’’)
by them, and deterred from publishing these values; he communi-
cated then, however, to Bourke in a letter *). At present these calcul-
ated capacities do not seem improbable to us at all; for the more
highly vaulted skull of Spy IL exceeds the La Chapelle skull only
by from 70 to 90 cm’.

SoLLas ?) calculated the capacity of the Gibraltar skull at about
1260 em°. from the right half, which had been partly reconstructed,
and of which he had measured the capacity with millet seed.
Comparison of the endocranial plaster cast (of this right half of the
skull) with that of the La Chapelle skull gave Bourr*) 1296 cm’.
Broca (= 1214 em’. real capacity), and by direct determination of
the capacity of such a cast Kerra *) found about 1200 cm’. cranial
capacity. No great value can be attached to these estimates from
the very incomplete fossil. More trustworthy is the result obtained
from the skull of La Quina, whose capacity Bourr*) put 1367 em’.
Broca (= 1282 ecm’. real capacity) from the less incomplete endo-
cranial plaster cast.

The two last-mentioned skulls are generally considered to be
female, the other skulls of the Neandertaltype are probably all
male. As the mean real capacity of the Kuropeans can be put about
1450 em°. for men, and 1300 cm’. for women, the absolute
capacity of the Neandertal Man appears to have been no less than
that of Europeans.

But the relative capacity must certainly have been greater
then, for Homo neandertalensis was a small type of men. After a
full discussion of the length dimensions of the skeleton Boure ®)
arrives at the estimate of 154 or 155 em. for the body length of
the fossil man of La Chapelle-aux-Saints in life, which was probably
also the mean male length of the species, hence as much as or a
few centimeters less than those of the smallest present human races,
except the “pygmies”, and 14 or 15 em. less than the mean of the
male Europeans. It is true that the Neandertal Man through his
compact stature, must have been comparatively heavy, but it is not
probable that this made him reach the mean body weight of the so

1) M. BouLg, loc. cit., p. 187.

2) W.J. Sorras, On the Cranial Characters of the Neandertal Race. Phil.
Transactions Roy. Society. Series B. Vol. 199, p. 329. London 1908.

3) M. Boure. loc. cit., p. 189.

4) A. Keitu, Antiquity of Man. (London 1920), p. 124.

5) M. Boure, loc. cit., p. 189.

6) Loe. cit, p. 115—118.

1280

much taller European; we may, therefore, assume that this brain
quantity, alsocalculated in relation to the body-
weight, exceeded thatofthe present European.

This bigh cephalisation of Homo neandertalensis can, in my
opinion, be explained by the fact that he was in possession of par-
ticularly powerful muscles, which may be inferred from the robust
character of his bones and the comparative shortness of his limbs,
especially of his legs '). In this respect the Neandertal Man resembles
the Japanese, the Eskimos, probably also the Chinese and Javanese,
in general the Mongolian race ’).

ManouvrieR®) was the first to point out that the cranial capacity
of men with thin limbs (as the Hindus and the Australians) is
comparatively small, of men with “carrure’ which are “trapus”
and “robustes” (mountaineers, Eskimos) comparatively large. About
the ‘“carrure” he says: “Ce facteur me paraît avoir une importance
considérable d’apres mes propres observations. Il est certainement
plus important que la longueur du corps, et cela s’expliquerait par
le fait que l'énergie motrice des muscles est bien plus en rapport
avec leur section transversale qu’avec leur longueur’’. (p. 686). He
sees a connection between the great cranial capacity of the Eskimos
and the fact that they are “trapus et actifs’. (p. 219). [lay particular
stress on the last word.

Later Matiecka‘) has demonstrated from Prague section reports
that there exist relations between the brain weight and muscularity
and also the more or less powerful build of the bones.

These relations of the brain weight and its dependence on the
build of the body, especially on its breadth, can be much better
studied now than formerly, by comparison of the human races.

In the first place it may now be considered as certain that among
the present human races it is not the Europeans, but the Mongoloids
that possess the greatest relative quantity of brain. The best data

1) M. Bouts, loc. cil., p. 125-170 and p. 120.

*) After what precedes it will be self-evident that it is not my intention, to have
recourse here to the well-worn path of relationship.

5) L. MANOUVvRIER, Sur l’interprétation de la quantité dans l’encéphale. Mémoires
de la Société d’Anthropologie de Paris. 2me série. Tome 3, p. 217—219. 1885,
— and under “Cerveau” in Dictionnaire de Physiologie par CHARLES RICHET,
p. 686—687. Paris 1898.

*) H. Matigcxa, Ueber das Hirngewicht, die Schädelkapacität und die Kopfform,
sowie deren Beziehungen zur psychischen Tatigkeit des Menschen. Sitzungsberichte
der Kön böhmischen Gesellschafft der Wissenschaften. Mathem.-Naturw. Classe.
Jahrgang 1902. XX, p. 13—14 and 44. Prague 1903.

1281

about the latter refer to the Japanese. They were supplied by Tacucut’s *)
researches referring to no less than 421 male and 176 female Japanese,
of whom most had died in the hospitals. The mean brain weight of
374 adult men was 1367 grams, of 150 adult women 1214 grams.
These are quantities that pretty closely agree with the means of the
Europeans obtained in the same way. But on an average the body
weight of the Japanese men is 8 kg., their length 10 cm. less, and the
Japanese women are on an average 7 kg. lighter and 10 cm. shorter’).

Accordingly these East-Asiaties have more brain-weight than the
Europeans, both per em. body length and in proportion to the body
weight. Still greater is the difference with regard to the muscle
length, with which, strictly speaking, the brain quantity can be
better compared than with the body length. The Japanese are built
more compactly; their arms, and especially their legs, are shorter
in proportion to the trunk and exceedingly muscular; to the great
strength of the muscles corresponds their considerable cross-section,
and also the robust build of the long bones is in connection with
this. In proportion to the muscle length the brain-mass is, therefore,
still considerably greater than in proportion to the body length;
the brain-mass is evidently proportional to the cross-section of the
muscles. Kagucut showed that, later than in Europeans, this great
brain quantity of the Japanese is not acquired until after childhood
and first youth, and according to Barrz the Japanese are later full-
grown in body-length and weight. Hence the large relative brain
quantity and the greater muscular power of the Japanese is certainly
not owing to a greater nu w ber of the neurones and of the muscle
fibers, but to larger separate cross-sections of these, larger
separate volume of those.

Still somewhat shorter tban the Japanese are the Eskimos, and
also still broader and more compactly built, still shorter of limbs,
especially of legs, and more muscular. Judging by the few deter-
minations of their brain weight, which we owe to the determinations
of CHupziNsKr, HRDIICKA, SPITZKA ®), this mean is certainly no less

1) E. A. Spirzxa, The Brain-Weight of the Japanese. Science. New Series,
Vol. 18, p. 371—373. Philadelphia 1903.

2) E. Baez, Die körperlichen Eigenschaften der Japaner. Mittheilungen der
deutschen Gesellschaft für Natur- und Völkerkunde Ostasiens. Erster Teil. Band III
(1880— 1884), p. 330—359. Berlin und Yokohama. — Zweiter Teil. Band IV
(1884—1888), p. 35—103). Higher weights and greater body lengths do not refer
to means for the whole people, but for definite classes or selected individuals.

5) E. A. Spirzka in American Journal of Anatomy. Baltimore. Vol. IL (1902—
1903), p. 26—31. Three male brains of an average weight of 1457 grams

1282

high, probably higher than in the Japanese. From the many available
determinations of the cranial capacity, which, however, mostly refer in-
differently to male and female skulls, the same statement may be deduced.

The brain-weights of the Chinese which are out of proportion
high to the length of the body, have been very striking in each
of the few determinations that could be made, and it was
ascertained many times that the mean cranial capacity is great. ’)

KOHLBRUGGE *) showed that also the Javanese, whose large cranial
capacity was already known, belong to the peoples with relatively
high brain weight. In this respect, too, they may be placed side by
side with the other mongoloids mentioned.

In the Australians, Negroes, Hindus on the other hand, a slender
figure, with long and thin legs and arms, is accompanied with a
brain weight which is low in proportion to the body length, and
small cranial capacity.

Comparison of the Neandertal Man with these present human races
renders it exceedingly probable, that also in him the great brain-
quantity was in relation with the thickset, strongly built body and
the short limbs, henee with great muscular force. We are particu-
larly justified in this assumption, because such a relation is frequently
met with in Mammals. .

Thus the Bears are distinguished from the other land-Carnivora
by their heavy, massive shape, and thick limbs, which are short in
proportion to the body, and with which they can exert a tremen-
dous force. The long bones of the limbs in the Bears are thicker
with respect to their length, in part somewhat prismatically shaped,
and the surfaces of attachment of the muscles still more developed
in cristae and apophyses, — in asimilar way as in the Neandertal Man.

(1398—1503), two female brains of an average weight of 1242 grams (1227—
1256). Also body lengths.

1) CROCHLEY—CLAPHAM: eleven male brains of an average weight of 1430
grams (1310—1587), cited in P. ToPiNARrD's, Eléments d’Anthropologie générale,
p. 571. (1885). — Kurz in Zeitschrift für Morphologie und Anthropologie, Bd. 16.
(1913), p. 284: of a man of a body weight of 160 em., 1454 grams; of a woman,
155 em. long, 1200 grams.

2) J. H. F. KoHLBruGGE, Die Gehirnfurchen der Javanen. Verhandelingen der
Kon. Akademie van Wetenschappen te Amsterdam. 2de Sectie, Deel 12, NO. 4
(1906), p. 13. The mean weight of 16 adult male brains (of the 19 determinations
1 exclude one of exceptionally high, and one of exceptionally low weight, and one
of a child of seven years old) was 1301 grams (the extremes were 1101 and
1458). This is a high brain weight with 50.27 kg. (living) body weight, which
is probably not reached by European men of equal living body weight. (Compare:
Eua. Durors, Ueber die Abhängigkeit des Hirngewichtes von der Körpergrösse
beim Menschen. Archiv für Anthropologie. Band 25, p. 432. Braunschweig 1898).

1283

According to the data about brain weight and body weight of
Bears, supplied by Max Weper, Ar. Hrpricka, W. T. BLANFORD and
others, and capacity determinations of my own, the cephalisation
of Ursus arctos, horribilis, tibetanus, and maritimus may be indicated
about by 0.5, i.e. one and a half times as high as of Felides (0.33),
and Canides (0.37), which means that in this ratio a Bear species
in the adult state with equal body weight, exceeds a Cat- or a
Dog species.

Fig. 3. Skeleton of the man of La Chapelle-aux-Saints
by the side of that of an Australian. (From Boure). !)

As regards their brain quantity the said Ursides are on a line with
the Monkey genus Semnopithecus, but Ursus malayanus is even
equal with the Anthropoid Apes. I see in this a very striking proof
of the truth of the conception that the quantity of the brain is
determined by the functional mechanism.

1) L’ Homme fossile de la Chapelle-aux-Saints, Fig. 99 (p. 232), Fig. 100 (p. 233).
Paris 1913.

1284

The Malay Bear or B ruwang is of comparatively small build,
and has still disproportionally shorter, at the same time still more
muscalar limbs than the other Bears. He uses his out of proportion
enormous claws as dexterously as powerfully. Considering the size
of his body he is by far the strongest of his race; he is also the
best climber and the swiftest runner. As regards motor mechanism
he may be called the most perfect of the Bears.

His very marked macrocephaly results from the very considerable
size of the encephalon, which also manifests itself in the brain-
weight and cranial capacity.

Weser') determined the body weight of a male Béruwang of
114 em. body length (from nose to rump), which had died in the
Amsterdam Zoological gardens, and was probably much too light,
at 20 kilograms, the brain weight at 325 grams. HRDLICKA®) found
for the brain weight of a female specimen from the Washington
Zoological Park, weighing 45.02 kilograms, 385.5 grams. According
to records by BrANForRD®) the weight of a female bear of Borneo
was 60 Ibs. or 27.215 kilograms, with 36 inches or 91.5 em. body
length (from nose to rump). The male body length is averagely 4
feet or 122 cm., and probably never becomes greater than 4'/, feet
or. 13%, cnr

l have been able to measure the capacity of five adult skulls
from the Museum of Natural History at Leiden, placed kindly at
my disposal for this purpose by the director Prof. E. D. van Oort:

N°. 1. (“b. Sumatra-Reinwardt’). Male skull. Basal (basion-inion)
length (Flower) 214 mm. Greatest breadth, across the zygomatic
arches, 190 mm. Middle-aged from the degree of wear of the teeth.
(BLANFORD measured at a “very old and large skull” 8.5 inches
basal length or 216 mm., and 8.3 inches or 211 mm. breadth].
Capacity (measured with mustard seed)*) 373 em’.

N°. 2. (“f. Borneo). Male skull. Middle age. Basal length 214 mm.
Greatest breadth 188 mm. Capacity 355 em’.

N°. 3. (“e. Borneo. S. Müller 1827”). Female skull. Middle age,
Basal length +187 mm. Greatest breadth, across the zygomata,
163 mm. Capacity 325 em’.

1) Max WEBER, Vorstudien über das Hirngewicht der Säugethiere, (Festschrift
für CARL GEGENBAUR), p. 113. Leipzig 1896.

2) Ar. Hrpiicka, Brain Weight in Vertebrates. Smithsonian Miscellaneous Col-
lections. Vol. 48, p. 94. Washington 1905.

5) W. T. BLANFoRD. Mammalia. The Fauna of British India including Ceylon
and Burma, p. 199. London 1891. i

4) With shot, by Broca’s method, | get 380 cm. Such a ratio applies also to
the following measureinents, which have all been made with mustard seed.

1285

N°’. 4. (‘‘a. Borneo. Reinwardt’). Female skeleton. Basal length
of skull 169 mm. Breadth across the zygomata 150 mm. Length of
the skeleton from alveolar point to caudal basis 89 cm. (measured
along the back). Somewhat below middle age, the cranial sutures
only commencing to obliterate. Capacity 278 em’.

N°. 5. (“907”). Balik Papan, Borneo. Female skull. With skeleton,
allowing to measure the length of the skeleton (along the back)
from alvesolar point to caudal basis, 109 em. Full-grown and middle-
aged, according to skeleton and skull. Basal length 199 mm. Breadth
across the zygomata 167 mm. Capacity 341 cm’*.’).

I determined the cranial capacity of a young female béruwang,
whose teeth, with the exception of the canini, had all erupted, and
which weighed 12 kilograms according to my estimation, when
kept in captivity in its native country at Bua in Sumatra for some
time, at 305 cm’.

l find 325 cm? for the capacity of a large male tiger, killed there,
the same value as for that of the female bear N°. 3 from Borneo,
with probably four times greater body weight. The skull of a female
orang utan of this island has a capacity of 380 cm*. The animal
probably weighed as much as a large Bornean bear with the same
cranial capacity.

With these data about brain weights and body weights, and
longitudinal dimensions of body and skeleton, determined directly,
and with the brain weights calculated by means of CokNeEvIN’s
comparisons”) I find that- the cephalisation-coefficient of Ursus
malayanus may be put at least at0.75, equal with that of the
Anthropoid Apes.

The relation between the muscular power (which is determined
by the cross-section of the muscles) and the rapidity of motion
which depends on it, and the quantity of brain manifests itself in
a very striking way in American Monkeys. The Howlers (Mycetes)
have much less brains in proportion to the size of their bodies than

1) No. 4 and 5 were not mentioned in the Dutch version of this communication.
Accordingly the coefficient of cephalisation of Ursus malayanus found here is
somewhat different from that in the Verslagen.

4) Cu. Cornevin, Examen comparé de la capacité cranienne dans les diverses
races des espéces domestiques. Journal de Médecine vétérinaire et de Zootechnie
publié al’Ecole de Lyon, 3me Série, Tome 14, p.8-31 and Etude sur le poids de l’encéphale
dans les diverses races des espèces domestiques. p. 248—262. — Irom his
recorded values | calculate 88°/, brain weight for capacities of a mean of 650,
and 93 °/, brain weight for an average capacity of 100 and less, say 91 °/) for
the capacities mentioned above.

1286

the species Cebus and Ateles living in the same country. FroweRr *)
determined the brain weight of an exceedingly emaciated old male
Mycetes seniculus, which had died in the London Zoological Gardens,
at 48 grams (740 grains), the body weight at 3444.5 grams (9 lbs.
9*/, ozs. avoirdupois). Spirzka’) found the brain weight of a
female Mycetes ursinus (which species is somewhat larger) to be
54 grams, Lreuw®) found 63 cm’. for the cranial capacity of Mycetes
ursinus in an adult male, and 54 em°. in an adult female specimen.
The body weight was only known of atrophical zoological garden
individuals. From Surinam [ received the skull and other parts of
the skeleton of a male Mycetes seniculus, killed in the natural
state, which weighed 6750 grams, though judging from the condition
of the skeleton, it was only almost full-grown. The cranial capa-
city is 54 em*., from which a brain weight of 50 grams can be
calculated and a cephalisation-coefficient 0.37, about the same as
that of Macacus cynomolgus. For the entirely full-grown state a
still somewhat lower value would certainly have been found *).

The Howling Monkeys, now, are described as being, in their free
state, exceedingly indolent animals, which remain very much at the
place where they are. All their movements are slow, almost creeping ;
they never play with each other, climb deliberately, and never
jump far—in sharp contrast to the lively, rapid movements, the
leaps and swings of the agile rovers of the genera of Cebus and
Ateles. The cephalisation coefficient of these is more than three
times as great as that of Mycetes.

Here, therefore, the same contrast as between swift and slow
species of Reptiles and Amphibians. Thus Hyla arborea has double
the cephalisation of Rana fusca. And as it is demonstrated there
(e.g. between Phrynosoma and Sceloporus) it may be assumed here
that the nerve fibers (and the muscle fibers) are thicker, the neurones
more voluminous in the more vigorous and quicker species ®).

1) W. H. FLower, On the Brain of the Red Howling Monkey (Mycetes seniculus
Linn.) Proceed. Zool. Soc. London. 1864, p. 335—338.

2) E. A. Sprrzka, Brain-Weights of Animals with Special Reference to the Weight
of the Brain in the Macaque Monkey. Journal of Comparative Neurology. Vol. 13,
p. 13, Philadelphia 1905.

3) W. Lecue, Ueber Beziehungen zwischen Gehirn und Schädel bei den Affen.
Zoologische Jahrbiicher. (SPENGEL). Supplement XV, Band 2, p. 17. Jena 1912.

4) What is urgently required is more data of body weights in the
free state. Especially nimble animals get much lighter in captivity; the
brain weights change less, and can also be calculated pretty accurately from
the cranial capacity.

5) Euc. Dusois, “The Significance of the Size of the Neurone and its Parts.“
These Proceedings, Vol. XXI, No. 5, p. 711.

1287

A contrast of the same nature, but not so great, exists between
the Orang utan and the Chimpanzee. The slow, clumsy, deliberate
movements, without jumps, of the Malay anthropoid are indeed
sharply distinguished from the mode of moving of his African rela-
tion, the Chimpanzee, which is an excellent climber, swings over
large distances from one branch to another, and jumps with wonder-
ful agility. But though the body weight of the Orang utan is cer-
tainly a third greater than that of the Chimpanzee, the brain weight
of the two species is the same in the females, in the males that of
the Orang utan is only little more.

SELENKA’) determined the mean capacity in the sexes of the Orang
utan at 455 and 390 cm’., and of the Chimpanzee at 420 and 390 cm’.
To him in the Anthropoids ‘““Muskelmasse und Hirngrösse” seem
“daher in direkter Beziehung zu stehen”, because the “rein geistigen
Fähigkeiten wohl als nabezu gleich angenommen werden dürfen.”
It also strikes him that in Orang utan “Skelet und Muskulatur des
Männchens” are “ausserordentlich viel stärker als die des Weibchens.”
It is now remarkable that according to Fick’s®) research the total
muscle weight in reference. to the body weight is much less, the
fat percentage on the other hand, greater in Orang utan than in Man.
We meet here with the same difference in the composition of the
body weight as between woman and man, and here too we see this
accompanied on one side by a brain weight low in comparison with
the body weight; for we may assume that the Chimpanzee, like
most other Apes, is more muscular than the Orang utan.*)

Among the American Monkeys, Saimiri (Chrysothrix) is further
much quicker and nimbler in its movements than Leontocebus
(Midas) and Callithrix (Hapale); accordingly its cephalisation coeffi-
cient is considerably higher.

In conclusion attention may still be drawn in this connection to
the high cephalisation of the Seals and to the considerably higher
cephalisation of the Toothed Whales than that of the Whalebone
Whales. For Balaenoptera musculus I calculated the coefficient 0.384 *).

1) Emit SELENKA, Menschenaffen. Zweite Lieferung, p. 99—100. Wiesbaden 1899.

*) R. Fick, Vergleichend anatomische Studien an einem erwachsenen Orang-
Utang. Archiv fiir Anatomie und Entwickelungsgeschichte. (W. His). Leipzig.
Jahrgang 1895, p. 68—69 and p. 73. The examined specimen was a male Orang utan.

3) Euc. DuBois, Comparison of the Brain Weight in Function of the Body-
Weight, between the Two Sexes. These Proc. Vol. XXI, No. 6 and 7, p. 850
seq. 1918. — H. WELCKER (loc. cit. p. 41) found the relative muscle weight
of a male “Inuus cynomolgus” greater than the mean of the male in Man.

4) The Significance of the Size of the Neurone and its Parts. These Proc. Vol.
XXI, No. 5, p. 724.

1288

Through accurate determination Wreer') found 1886 grams for the
brain weight of a fullgrown female specimen of Tursiops tursio, a
toothed whale of the Delphinidae family, the body weight being
432 times as much. From this the cephalisation-coefficient 0,981
can be calculated. The Odontocetes, among them especially the
Delphinidae, swim with extraordinary dexterity and swiftness, faster
than the fastest steamer, they even swim round a steamer at full
speed; the Mysticetes, on the contrary, cannot reach the speed of
an ordinary steamer. In connection with this the dorsal muscles of
the former are much more powerful, which is to be seen by the
great thickness of the back part of the body.

Thus the muscle apparatus of Homo neandertalensis was also
stronger than that of Homo sapiens, and among the races of modern
Man the Mongoloids possess the most powerful muscle apparatus.
In agreement with this Homo neandertalensis and the Mongoloids
possess also the relatively largest encephalon.

4) loc. cit, p. 113. The body weight with the brainratio 1: 432 is 815kg. The
value 278 is given, evidently a misprint.

Botany. — “On the influence of circumstances of culture on the
habitus and partial sterility of the pollengrains of Hyacinthus
orientalis”. By Dr. W. E. pr Mor. (Communicated by Prof.
A. H. Braauw.)

(Communicated at the meeting of February 26, 1921).
I. Introduction.

When, in the spring of 1919, it had become evident to me
that the nuclei of the single-flowered, rose-coloured hyacinth-variety
Nimrod possessed 19 chromosomes’), I thought it advisable to examine
the fertility of the pollen and to compare it with that of the Dutch
varieties with 24 chromosomes in the somatic cells, which number
IT at that time still considered as diploid. I chose for that purpose
the closed anthers, taken from growing Nimrod-plants that belonged
to the same grower as those of which I had fixed the root-tops in
behalf of my chromosome-examination. To my surprise the pollen-
grains in these anthers differed greatly from the aspect which hya-
cinth-pollen had always shown to me. I did not find one normal
fertile grain. The sterile pollengrains were elliptic, round or tri-
angular in shape and had various dimensions. The wartlike protu-
berances on the exine, which in normal cases cause the pollengrains,
when plunged into a drop of some liquid, to stick together to some
extent, were undeveloped, so that the pollen dispersed very easily.
Apart from these sterile pollengrains, there appeared in the prepa-
rations many that were much larger and globe-shaped, and were
full of large starchgrains. If the pollen was put into a diluted
solution of jodine in jodide of potassium, one saw at once the
abnormal pollengrains lying like intensely blue-black globes among
the yellow, shrivelled exines of the sterile pollengrains. In a drop
of water the exine usually burst rather soon and the starchgrains

1) Over het optreden van heteroploide Hollandsche varieteiten van Hyacinthus
orientalis L. en de chromosomengarnituur van deze plantensoort.

Verslagen van de Koninklijke Akademie van Wetenschappen te Amsterdam, Wis-
en Natuurkundige Afdeeling, Deel XXIX, p. 518.

Nieuwe banen voor het winnen van waardevolle varieteiten van bolgewassen,
p. 1%

83
Proceedings Royal Acad. Amsterdam. Vol XXIII.

1290

then floated loose in the preparation causing a bluish spine when
the light fell through it. There appeared to be starchgrains among
them, reaching the size of a small sterile pollengrain.

But moreover, numerous elliptic pollengrains occurred that had
germinated, not with a normal pollen-tube however, but with a
tube that had rather the shape of a bubble. This bubble was
sometimes smaller than the pollengrain itself, but often it was much
larger. It contained 2, 3, 4, 5 or more globe-shaped nuclei.

The closed anthers were slightly shrivelled, and the violet antho-
eyanin in their walls was slightly discoloured.

This observation stimulated me to try and find out whether in
literature any mention was made of phenomena like those observed
by me. I then, indeed, found that NEmrc (1898) had already observed
the same thing, also in the hyacinth. He however, had discovered it
in the partly petaloid anthers of a variety with double flowers. The
anthers were taken by him from young closed flower-buds, fixed,
bedded in paraffine, coloured, and made into microtome-series. He
also found the small sterile pollengrains without reservesubstance, and
the large, globe-shaped ones full of starchgrains. And here, too,
many pollengrains had developed in the closed anthers pollen-tubes
that often looked like large bubbles. He sometimes saw 8 nuclei
in them.

NEMEC supposed these deviations to be the consequence of the anthers
being petaloid from the fact that I found them in the anthers of a
single-flowered variety, one could infer that they were due to other
causes than the flowers being double. | therefore thought the phenomenon
was to be ascribed either to the peculiar bastardlike nature, of the
variety Nimrod — as the latter is supposed to be a product of
cross-fertilization between a French and a Dutch variety! — or to
the occurrence of the deviating number of chromosomes in the
somatic cells.

I now resolved to examine the pollen of a large number of varieties
Carefully I considered in what way this examination was to be
performed, in order to derive the most favourable results from it. In the
month of April and May 1919 I managed to perform it at Lisse, the
centre of the Dutch hyacinth-cultures, in the following way. I chose
varieties with the most diverging shapes, dimensions and flowering-
times, double-flowered as well as single-flowered ones. Moreover I
collected several times many racemes of one and the same variety,
cultivated by different growers under greatly diverging circumstances.
In this way I was able to come to palpable results. One of these
results, in my eys the most important, may be mentioned here.

1291
II. On the occurrence of pollengrains with 3 and more nuclei.

ScnürnHorr (1919) has drawn our attention to the fact that among
Monocotyledons as well as Dicotyledons pollengrains with 3 nuclei
—1 vegatative and 2 generative — occurs before the germination. He
wonders whether this early- division of the male sexual nucleus has
a biological or a systematical importance and concludes on p. 147,
after giving a general view of the orders of plants where pollen-
grains with 3 nuclei have been noticed: “Es ergibt sich also aus
dieser Aufstellung, dass dem Vorkommen von dreikernigen Pollen-
körnern keine besondere systematische Bedeutung zukommt. Eine
derartige Bedeutung liesze sich zur Not für die Monokotylen kon-
struieren, da bei den ersten Ordnungen das Vorkommen dreikerniger
Pollenkörner die Regel bildet, während sie bei den letzten Ordnun-
gen der Monokotylen fehlen”’. Of the Monocotyledons, according to
him, the Helobiae, the Glumiflorae and part of the Spadiciflorae
are characterized by pollengrains with 3 nuclei. The orders of the
Enantioblastae, the Liliflorae, the Scitamineae and the Gynandrae,
with the exception of the Juncaceae and other isolated cases, do not
possess them.

If we examine more closely some cases of the Monocotyledons,
we notice that ErrvinG saw, as early as 1878, 3 kernels in the
pollengrains of Andropogon campesiris, and that SrraspurcEr (1884)
saw that in many cases the generative nucleus was divided in the
pollengrain. Gotinsky (1893) found 2 sperm-nuclei in the pollen-
grains of Triticum, Scuarrner (1897) in Sagittaria variabilis. “The
division of the generative nucleus before pollination”, he says on
p. 254, “seems to be quite common in monocotyledons, and it is
probable that this condition will be found to be the rule rather than
the exception in this group’. According to the researches of CHAM-
BERLAIN (1897) the generative nucleus of Liliwm aurantiacum and of
Lilium tigrinum was divided in the pollengrain, “a condition not
uncommon, in monocotyledons”, he says. In 2 cases he also observed
in Zelium aurantiacum, that the divisions went still further, so that
3 generative nuclei were present. In Lilium Philadelphicum the
early division of the generative nucleus occured seldom. In Lilium
martagon it is perhaps out of the question. GuigNarD (1891) at least
notices that the generative nucleus is here only divided in the pollen-
tube. The vegetative nucleus is never divided. In 1899 this naturalist
saw 3 nuclei in the pollengrains of Najas major. Wineanp (1899)
observed 2 generative nuclei in Potamageton foliosus Raf. and
gives an enumeration of the cases at that time observed in Mono-

8 3*

1292

cotyledons. Mirsuck (1902) observed 3 nuclei, J vegetative and 2
generative in Ruppia rostellata Koch. Scnürnorr (1919) describes
explicitly the mechanism of division in the generative nucleus of
Sagittaria sagittifolia.

In germinated pollengrains of Monocotyledons more than 2 gene-
rative nuclei have sometimes been observed. Thus STRASBURGER
(1884) saw 4 of them in the pollen-tubes of Ornithogalum and of
Scilla. Tams (1901) caused ripe pollengrains of Scilla sibrica to
germinate in a 5°/, solution of cane-sugar and says: “ausnahmsweise
wurden in einem gekeimten Pollenkorn 5 Kerne beobachtet”.

In hyacinch-varieties, too, one may observe under particular cir-
cumstances, that they contain pollengrains with 2 generative nuclei.
I found them ia. in the single-flowered white variety La Neige.
The vegetative nucleus was large and round. The exine of the pollen-
grains was very transparent here, the wartlike protuberences were
almost entirely absent. This made it possible to observe the nuclei
closely, without having to colour them green first in a drop of
methylgreen acid of vinegar. Not nearly all pollengrains possessed 2
generative nuclei. That I ascribe the early division of the genera-
tive nucleus to external circumstances, may appear later on.

HL Further particulars concerning the occurrence
of pollengrains with several nuclei in

Dutch hyacinth-varieties.

By way of introduction 1 mentioned that I found pollengrains
with several nuclei in the variety Nimrod. When composing my
extensive tables, 1 indicated not only the percentage of sterility, but
also the origin of the racemes, the latter by indicating each parti-
cular category with a capital. Moreover | nearly always gave, with
each numeration a short description of the habitus of the pollengrains.
In this contribution I think it sufficient to take out of the tables in
question those varieties in which 1 found 7 the closed anthers pollen-
grains, germinated with abnormal pollen-tubes, in which lay several
nuclei. At the same time I mention the other numerations, bearing
on the same varieties, but in which no pollengrains with abnormal
tubes were found. Because NEMmrc (1898), as I said before, observed
before me in the pollen of double-flowered hyacinths the same phe-
nomenon, shall henceforth indicate it, in his honour, by the name:
‘“Nemec’s phenomenon’. In so far as l have fixed the number of
chromosomes of the varieties named below, | shall mention this.

1293

A. Single-flowered varieties.

Charles Dickens, single-flowered red.

1. The upper flowers of the raceme are much smaller than the
others and have green points at the lobes of the corolla. The pollen
of these flowers show Nemrc’s phenomenon. The pollengrains in the
lower flowers of the raceme are normally formed, 21°/, are sterile.
The pollen of the upper flowers disperse at once in a drop of water;
of the lower flowers it sticks together.

2. All flowers contain normal pollengrains, 27°/, of which are
sterile. The pollen sticks together.

Général Peélissier, single-flowered red, 16 chromosomes.

1. The upper flowers of the raceme, are small and green coloured,
show NeEmec’s phenomenon. The other flowers contain normal pollen,
14°/, of which is sterile.

2. Ibid. The stickiness of the pollen is as in Charles Dickens.

3. The sterility amounts to 6°/,.

Lady Derby, single-flowered red, 24 chromosomes.

1. The pollen in all flowers of different racemes gives the same
impression. The flowerbuds are still quite green and closed. The
pollengrains do not stick together. Only a few sterile grains are
present. They at once swell very strongly. In most of the pollen-
grains many starchgrains are present, which are often very large.
There occur pollengrains showing Nem«o’s phenomenon. The various
nuclei are clearly visible.

2. The pollengrains only swell after a long time; 4°/, are sterile.

3. The sterility is 34 °/,.

4. The racemes originate from water-cultures: the sterility is 6°/,.

5. The pollen is sterile for 4°/,.

Moreno, single-flowered red.

1. The anthers are shrivelled and discoloured and contain very
few pollengrains. These do not swell in water. They have a turbid
content. Further there are large globe-shaped pollengrains present
which soon burst. The preparation is then full of loose starchgrains.
Several normally formed pollengrains show NeMrc's phenomenon.
In some normal non-swelling pollengrains 2 globe-shaped nuclei of
equal size are clearly visible. I do not find one normal fertile grain.
Some starchgrains are as large as a small pollengrain.

2. The colour of the flower is orange-red. The dark streak that
runs over the middle of the lobes of the corolla is clearly outlined.
The sterility is 24°/,.

3. The colour of the flower is rose-red. The dark streak is dimly

1294

outlined. The sterility amounts to 40°/,. (The bulbs of these flowers
and those of the former bad been subjected to high temperatures).

4. The pollengrains stick together. They swell very soon; 11°/, are
sterile.

5. Like 4, but 15°/, are sterile.

6. The pollengrains are taken from the flowers of bulbs that have
not been planted. The flowers lay shrivelled up in the bulb. The
pollengrains are slightly smaller than usual for the rest they look
quite normal; 13°/, are sterile.

7. The pollengrains are taken from a budvariety-in-colour of
Moreno. The colour of the flower has become dark red from rose-
red; 59°/, of the pollengrains were sterile in the only raceme I had
at my disposal.

8. The pollen is not sticky, the sterile pollengrains are ellipsoidical,
triangular or globe-shaped; the sterility is 40°/,.

9. The sterility is 8°/,.

10. The sterility is 35°/,.

Nimrod, single-flowered red, 19 chromosomes.

1. The anthers are shrivelled and give the same impression as
those of the variety Moreno of the same grower (c.f. 1). The pollen
does not stick together. 1 do not find one fertile grain. The sterile
ones are elleptic, round or triangular.

2. The flowers are taken from a lot that blooms very early. The
anthers are badly developed. The pollen shows beautifully Nemnc’s
phenomenon.

3. The flowers are taken from a lot that blooms late, coming
from the same grower as those under 2. They are not yet open.
The pollen shows, as in 2, Nemec’s phenomenon.

4. All pollengrains, fertile as well as sterile, are normally formed ;
26°/, are sterile.

5. The flowers are taken from a lot that blooms early. The bulbs
have been planted medio October, and on April 4 1919, the date
when I cut the racemes, they have long roots. The anthers are
normally formed, not shrivelled. The pollengrains at once swell in
water, but they are sticky. Among the fertily pollengrains these are
some that contain a more or less wide zone of water round a
rounded mass of protoplasm. Some pollengrains have developed a
short, wide pollen-tube; 36°/, are sterile. —

6. The flowers are taken from a late-flowering lot of the same
grower. The bulbs were planted on November 7, and on April 5'k
the gemma rises only 2 cm. above the ground. The roots of the
bulbs are still very short. The sterile pollengrains are all ellipsoidical,

1295

not triangular. Some fertile pollengrains of a normal size contain
starchgrains. I find some large globe-shaped pollengrains, full of
starchgrains; 29°/, are sterile. | perform many more enumerations
in pollen of flowers from other racemes, out of this same lot. I
always find the same phenomenon and a sterility, from 29 to 30°/,.

Fics. im, 6:

8. The pollen is not sticky. The nuclei are clearly visible. The
sterile pollengrains are all ellipsoidical. In the preparations float
some starchgrains, 66°/, are sterile.

City of Haarlem, single-flowered yellow, 23 chromosomes.

1. The pollen is not sticky. The anthers are large and normally
developed, but they contain hardly any pollengrains. The few there
are, nearly all have abnormal pollen-tubes with several nuclei or
they are large, globe-shaped and filled with starchgrains. | examine
several racemes. Always the phenomenon is the same.

King of the Yellows, single-flowered yellow.

1. I examine the pollen in the anthers of green buds. Every-
where the pollen shows NEMmuc's phenomenon.

2. All pollengrains are normally formed. Only 2 °/, are sterile.

Yellow Hammer, single-flowered yellow, 16 chromosomes.

1. The pollengrains are all normal; 17'/,°/, are sterile.

2. Id. 14°/, are sterile.

3. The pollen is sticky; some pollengrains have a wide, abnormal
pollen-tube; 87 °/, are sterile.

4. The pollen is not sticky. The various preparations never show
a normal fertile pollengrain. The pollen shows perfectly Nemsc’s
phenomenon.

5. I examine the pollen in all flowers of one raceme.

Undermost flower: the anthers contain only few pollengrains,
which are all sterile.

Next flower: there are sterile pollengrains, others with abnormal
pollen tubes and others again that are large and globe-shaped, full
of starchgrains.

Next flower: pollen as in the preceding flower; besides there are
triangular, sterile pollengrains, while the 2 former flowers had only
ellipsoidical sterile ones.

Next flower: pollen as in the former, but besides some fertile
pollengrains present.

Next flower: as in the former, but more fertile pollengrains pre-
senteren 273/,°/,-

Next flower: as in the former, but the fertility is 35'/, °/,.

So if we compare the pollen of the various flowers, going from

1296

below to the top, we observe a gradual transition from pollen which
is sterile or which shows Némsgc’s phenomenon, to pollen which
consists of normally formed sterile and fertile pollengrains.

6. The examination again refers to all flowers of one raceme.

Undermost tlower: very few normal, fertile pollengrains. For the
rest: Nemsc’s phenomenon. The anthers are shrivelled and contain
only little pollen.

Next flower: like the preceding one; in the abnormal pollen-tubes
more than 3 nuclei are clearly visible.

Next 12 flowers: the number of normal fertile pollengrains pre-
ponderate.

7. The pollen is not sticky, but it gives a normal impression ;
36 °/, are sterile.

8. Besides normally formed fertile and sterile pollengrains there
occur large, globe-shaped ones and others, of normal size, full of
starchgrains; 15 °/, are sterile.

Marchioness of Lorne, single-flowered orange, 16 chromosomes.

1. In the great number of preparations only sterile pollengrains
occur and others that have developed abnormal pollen-tubes.

2. More than 90 °/, of the pollengrains are sterile.

a: Ad.

B. Double-flowered varieties.

La Virginité, double flowered white.

1. In a drop of water the pollengrains burst very soon. The
grey colour they show in their protoplasm, has then disappeared
and the empty, bright yellow coloured exines, on which the wartlike
protuberances are clearly visible, are left. | make some preparations
and leave the pollengrains in water for half a minute. If I look at
them then, it appears that some grains have germinated with an
abnormal, wide pollen-tube. The protoplasm is now entirely in-the
pollen-tube and encloses several nuclei.

Noble par Merite, double-flowered red.

1. The. flowers are doubled to such an extent that I find only
few pollengrains. 18 °/, of these are sterile.

2. The sterility is difficult to make out, because most of the
pollengrains are in a transition-stage from fertile to sterile.

3. Most of the pollengrains are sterile. In the fertile ones 2
nuclei are clearly visible. I observe almost exclusively pollengrains
that stick together in groups of four. These tetrads consist generally
of 1 fertile and 3 sterile pollengrains or of 4 sterils ones. The
sterile ones are fullgrown. Among the sterile as well as among the

1297

fertile ones I observe some that are filled with starchgrains. There
also occur pollengrains with abnormal pollentubes. Not in all anthers
I find germinated pollengrains. The sterility amounts to at least 50 °/,.

Bloksberg, double-flowered blue.

1. I examine the anthers out of a green bud. The pollen is not
sticky and clearly shows Némsc’s phenomenon. Van Speijk, double-
flowered blue, 21 chromosomes.

1. The anthers of a green bud are examined. The preparations are
entirely in accordance with the drawings Nemec has made of the
abnormal pollen-tubes with many nuclei, of the large globe-shaped
pollengrains full of starch and of the sterile pollengrains.

2. The petaloid anthers contain little pollen. but this normal; 25°/,
is sterile.

To this I join a table, which renders, in a surveyable form, the
content af the descriptions. Under the figures 1° — 10° the result of
the numeration is indicated for every variety, in accordance with what
stood behind the same figure in the descriptions. These figures indicate
the percentages of sterility; by the letter 2 Nemxc’s phenomenon is
indicated. The capital letter in parenthesis shows the origin of the
raceme from which the pollen was taken.

Further I put the number of chromosomen occuring in the somatic
cells, behind the varieties of which I know this number.

The principal conclusions down from the preceding examinations,
with a view to the purpose of this publication, are the following:

1°. The pollengrains in normally formed anthers, as well as those
in petaloid anthers, may germinate with abnormal pollentubes with
several nuclei. So Némsc’s opinion that this phenomenon should only
occur in double flowers, is inaccurate.

2°. The phenomenon has nothing to do either with the quaestion
of the hyacinth-varieties being heteroploid or not. It may be observed
in diploids as well as in heteroploids.

3. From the fact that in one and the same raceme or in different
racemes of the same variety we now find quite normal pollengrains,
now pollen showing Nemec’s phenomenon, we may infer that the
abnormally germinated pollengrains with several nuclei are caused
by eaternal and not by internal influences.

After a more superficial examination one would possibly be inclined
to ascribe this kind of deviations simply to wnder- or overfeeding,
causes that are also so often named to explain the abnormal increase
of the number of chromosomes. NEmrc thought that as the cause of
the existence of the abnormal pollentubes with several nuclei was
to be considered the overfeeding of the petaloid anthers. The finding

1298

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of the abnormal pollengrains in the uppermost flowers of the racemes
of Charles Dickens (1°) and Général Pélissier (1° and 2°) might be
an argument in favour of the fact that under feeding is the cause,
as the uppermost flowers are always in a far worse condition than
the undermost of the raceme. However, what [ have observed in
Yellow Hammer (5° and 6°) is not in accordance with this. For here
the wndermost flowers of the raceme are developed in the same way
as the uppermost of Charles Dickens and Général Pélisier though
the same rule holds good here as well, that the undermost flowers
are in a better condition with regard to the feeding than the upper-
most. So at any rate the causes must be considered to be of a more
complicated nature; of which presently more.

5’. The abnormal pollen-tubes may developed when the bud is
still green. In other cases they do not develop until the flowering-
time has set in.

6°. From the descriptions given, as well as from the large tables
not published here, we may conclude that between the aspect shown
by normal pollen, and Némsc’s phenomenon, there is as it were a
gradual transition, manifesting itself as follows:

a. Normal aspect of the pollen; fertile and sterile grains are present ;
the latter large and elliptic.

6. Besides the large ellipsoidical pollengrains there occur smaller
elliptic ones and others that are round or triangular.

c. the sterile pollengrains of various shapes and sizes get the
upper hand, which probable indicates and early dying off, partially ;
besides these there occur large, round pollengrains, filled with
starchgrains.

d. Nemxc’s phenomenon complete.

IV. On the conditions, under which Néimuc’s phenomenon may
come to exist.

I may here remind the reader that all the pollen-grains examined
originated from plants which, ou the ground of the various condi-
tions under which they had been cultivated, were classed by me in
13 different categories, from A to M. That I owe a considerable
part of my results to this arrangement, may appear from a glance
at the last table. This table shows clearly, that Némxc’s phenome-
non confined itself almost exclusively to the categories C and B.
Of the 20 times that this aspect was found it occured 11 times in
C, 6 times in B and once in D, K, in: H. Besides it immediately
struck the eye, that the pollen-aspects which showed one of the

1300

transitions outlined above of a normal aspect to NEmec's phenomenon
likewise manifested themselves most in the categories C and J.

As I had acquainted myself as carefully as possible with the
circumstances under which the plants belonging to the 13 categories,
had lived, from the moment when the bulbs were dug up in 1918
till the moment when the pollen was examined by me, it was not
difficult for me to decide under what conditions of culture hyacinth-
varieties are able to produce pollen that exhibits Nemxc’s phenomenon.

It may be considered as a well-known fact, that the growers dig
up their hyacinth-bulbs after the leaves have died off, towards the
end of June and in July, then lay the bulbs in artificially heated
barns to be dried, and plant them again in September. So, for
instance the bulbs, — I mention this in outline only — which were
classed by me under category D; were dug up in 1918 between
July 1 and July 25. The barn was heated from August 1. till
November 1, during the first weeks to 65° F., afterwards the tem-
perature was allowed to rise to 75° F. Between September 20 and
November 1 the bulbs were planted again.

All bulbs which (1) were treated in this way, be it that duration
of heating and degree of heating diverged a little, besides others
which (2) were housed in barns where there was no heating; (3)
were not dug up, so passed the resting-time outside; (4) were not
planted or placed upon glasses; (5) were cultivated on glasses; (6)
differed in age or size, never produced flowers the pollen of which
showed Némec’s phenomenon. It was different with those plants
which partially had suffered what is called “preparation”. The bulbs
chosen for that purpose, are dug up in an unripe state, heated pretty
strongly in the barn, and afterwards planted in pots or placed upon
glasses. When the bud begins to rise a little above ground, the
plant is exposed to a higher temperature a second time, the conse-
quence of which is that the flowers bloom very early. See for this:
A. H. Braauw: On the periodicity of Hyacinthus orientalis p. 51,
Vol. XVII of the “Communications of the Agricultural University”,
and my publication: “On the occurrence of heteroploid varieties of
Hyacinthus orientalis L. in the Dutch cultures”. Arch. Néerl. 1921
and Genetica 1921.

So the bulbs of the variety Nimrod (category B) in the flowers
of which 1 first. found pollen-grains which showed me NEmEc’s
phenomenon, were dug up on June 10%, the leaves still being a
fresh green not showing a trace of dying off.

They were exposed for 21 days to a temperature varying on an
indented line from 90° F. to 78° F.; afterwards till October 26 to

1301

a temperature fluctuating between 70° F. and 60° F. They were
not placed in pots, and afterwards not forced to early florescence,
but between October 26 and November 1 planted in the open ground
outside. In this way all bulbs had been treated which are grouped
under category B and developed abnormal pollen-tubes.

Very remarkable was the phenomenon that I observed in the
plants belonging to category C. These were all cultivated by the
same grower, of whom I examined 25 varieties (19 single-flowered
and 6 double-flowered), with which I effected 31 numerations.
Of six varieties 2 numerations were noted. These were varieties
which had been grown in 2 lots, under different conditions. In 21
of the 31 cases the pollen diverged more from the normal aspect
than that of the same varieties classed under all other categories.
In 5 cases I could not compare it with that of other categories
because for them I had no racemes at my disposal. In the remaining
cases it was found in the same condition or in one a little better
than that of any other category.

In a very striking manner it now appeared to me that the racemes
with pollen showing Némuc’s phenomenon or transitions from the
normal aspect to Nemuc’s phenomenon, always originated from bulbs
dug up in an unripe condition, between July 1 and 15. Immediately
after the digging up artificial heating was started, till September 20,
from 75° to 80° F.; afterwards till the planting time, which was in
October, from 70° to 75° F. The planting was done in the open ground.

My observations have induced me last sommer to purposely subject
several hyacinth-bulbs to various exterior influences. From these

Fig. 1. (Oe. 2, Obj. A. of Zeiss). Fig. 2. (Oc. 2, Obj. D. of Zeiss).

1302

experiments it has now, on the 3rd February, become evident to me
that it is possible, to cause the growth of pollen-grains that exhibit
Nemec’s phenomenon. To the great importance of deliberately produ-
cing pollen-grains with more than one nucleus — also SAKAMURA
(1920, p. 145) by his discovery of several nuclei in the pollen-
grains of Allium Cepa has come to the opinion that they owe their
origin to a modification of the exterior conditions of life — I hope
shortly to draw attention.

The diagrams 1 and 2 picture forth the pollen-grains of the variety
Yellow Hammer, as I found them now in all anthers of the plants
which are exposed to the same particular exterior circumstances.

REFERENCES.

CHAMBERLAIN, Cu. J., Contribution to the life history of Lilium philadelphi-
cum (The pollengrain), Bot. Gaz,, 23, 1897.

ELFVING, Fr, Studien über die Pollenkörner der Angtospermen, Jenaische
Zeitschr. f. Naturwiss., 13, 1878.

Gorinski, Ein Beitrag zur Entwicklungsgeschichte des Androeceums und
des Gynaeceums der Grédser, Bot. Centralbl., 55, 1893.

GUIGNARD, L., Le développement du pollen et la réduction chromatique
dans le Najas major, Arch. d’anat. microsc., II, 1899.

Murseck, Sv., Ueber die Embryologie von Ruppia rostellata Koch. K. Sv.
Vetensk. Handl., 36, 1902.

Nemec, B., Ueber den Pollen der petaloiden Antheren von Hyacinthus
orientalis L., Academie des Sciences de |’Empereur Francois Joseph I, V,
Bulletin Internal, (Sc. math. et nat.), 1898.

SAKAMURA, F. Experimentelle Studien über die Zell- und Kernteilung mit
besonderer Riicksicht auf Form, Grösze und Zahl der Chromosomen, Journal
of the College of Science, Imperial Univ. of Tokyo, Vol. XXXIX, Art. 11,
March 20th, 1920.

SCHAFFNER, J. H., Contribution to the Life-History of Sagittaria variabilis
Bot. Gaz., 23, 1897.

SCHNIEWIND—TuiEs, J., Die Reduction der Chromosomenzahl und die ihr
folgenden Kernteilungen in den Embryosackmutterzellen der Angiospermen,
Jena, 1901.

ScHürHorF, P. N., Ueber die Teilung des generativen Kerns vor der
Keimung des Pollenkorns, Arch. f. Zellf., 15, Heft 2, 1919.

STRASBURGER, E., Neue Untersuchungen über dem Befruchtungsvorgang der
Phanerogamen usw., Jena, 1884.

WieGcanp, K. M., The development of the microsporangium and microspores
in Convallaria and Potamogeton, Bot. Gaz., 28, 1899.

From the Laboratory for the Physiology of Plants of
Prof. Ep. VurscHarreLt, Hortus Botanicus.
Amsterdam, February 1921.

Botany. — “A new method of recording the modifications in
aperture of stomata.” (First Communication). By M. Pinknor.
(Communicated by Prof. F. A. F. C. Went).

(Communicated at the meeting of October 30, 1920).
§ 1. Zntroduction.

For organisms which, like the “higher” plants, live as a rule in
the (gaseous) atmosphere, the regulation of the gas interchange is an
essential point in the organisation. In connection with this the fact
must be pointed out, that among the vegetative organs, common to
all plants, the only part that is capable of quick response in con-
sequence of its specialised structure, and thus deserves the name of
“apparatus”, is the very part that has to regulate the gas interchange.
This organ is the stoma (Spaltöffnungsapparat).

Just as essential as the stomata themselves are for the plant, the
study of them is for the plant-physiologist. The finding of methods
to get acquainted with the behaviour of stomata by means of expe-
rimental researches, has been indeed a subject of constant care in
physiology. Much has already been done in this department, but
of course there are always improvements to be made and as an
attempt in that direction should be regarded the conception of a
self-recording type of an existing apparatus treated below.

After the exhaustive discussion, which van SrLOGTEREN, in the
introduction to his dissertation ') has devoted to the numerous direct
and indirect methods, invented to judge the aperture of stomata —
I think it to be superfluous to mention these methods again and I
restrict myself to quoting what vaN SLOGTEREN says about the poro-
meter-method of Darwin and Perrz and its advantages. *)

“... it is based on the following principle: a glass chamber is
fixed air-tight to a leaf and through a tube connected with this
chamber, the air is sucked out, so that the pressure in the chamber
is diminished. After the side-tube has been closed, the difference in
pressure inside and outside the chamber, can only be annulled,
when air is sucked through the leaf. From the time, necessary for
making equal the pressure, the degree of aperture of the stomata
is judged.

1) E v. SLtoareren, De gasbeweging door het blad in verband met stomata en
intercellulaire ruimten. Groningen 1917, p. 1 —13.
2) Le, pal.

1304 *

A great advantage of this method is, that the values found are
not directly connected with the transpiration...”

“An advantage offered by the porometer-method above all other
methods is, that it enables us to examine the stomata in the living
leaf, which remains attached to the plant, in circumstances more
normal than with the other methods. It enables us to observe the
same leaf a very long time consecutively without ifs experiencing
any injurious consequences”.

Finally van SLOGTEREN ') points out, that the porometer of DARWIN
and Prrrz should also be preferred, because it likewise indicates
small modifications in the aperture accurately and makes known
the average of thousands of stomata at the same time.

It might be expected, that after the method of Darwin and Prrtz’)
got known, attempts should be made, to make it capable of self-
recording. It may be said, that the phenomenon to be studied asks
for a continuous picture projected of its changes. Indeed some three
self-recording porometers have already been described (resp. by
Batis?), Jones *) and Lawnaw & Kuient *) of whieh Barrs's stoma-
tograph may be called the most successful. About these apparatus
VAN SLOGTEREN says‘): “There is a danger, that either a too great
pressure is used, or the apparatus is made so complicated that it
may give rise to all kinds of sources of error. A great advantage
of the original porometer of Darwin and Perrz is its very simplicity,
through which the influence of external factors exercised on the
apparatus, is so easily judged. Besides the plant is placed in quite
abnormal circumstances, if a continuous current of air is sucked
through the leaf, as is necessary in these methods”.

With the recording porometer, that Lam now going to describe, all
these objections have been avoided and the circumstances in which
the plant remains during the experiment, are even more favourable
than in the case of the original porometer.

§ 2. General description.

When a selfrecording apparatus is made, the purpose is a.o. to

Dele psa:

2) F, DARWIN and D. F. M. Pertz. On a New Method of Estimating the
Aperture of Stomata, Proc. Roy. Soc. Lond Serie B, Vol. 84, 1912.

3) W. L. Batis, The Stomatograph, Proc. Roy. Soc. Lond. B, 85, 1912, p. 33.

4) W. NeiLsoN Jones, A Selfrecording Porometer and Potometer, New Phytologist,
XIII, 1914, p. 353.

5) CG. G. P. Larpvaw and R. C. Knieur, A Description of a Recording Poro-
meter etc., Annals of Botany, XXX, 1916, p. 47.

Gen pt 6:

1305

replace the person, who works a similar non-recording apparatus.
In the simplest case his work consists in the reading and recording
the position of a hand and of a time designer (e.p. aneroid-barometer
and barograph). With the porometer of Darwin and Pertz however
the working of the apparatus is more complicated, for besides the fact
that for each observation two positions and two moments have to be
read and recorded, the apparatus has to be brought into its original
position after each observation. So there are several functions here,
which will have to be done automatically by. a selfrecording poro-
meter. In constructing the automatic apparatus I have tried to keep
the principle of the original porometer unaltered as far as possible.

The apparatus (see fig. 1 lower half) consists of a glass chamber
cemented to the leaf (1) [provided with the side-tube (2) indicated
by VAN SLOGTEREN *), which must for the present be considered closed,
just as the tube 18 in fig. 1], connected with a U-shaped manometer,
with distilled water. The closed limb M, has a side-tube with rubber
tube (8). In the case of the ordinary porometer the observer would,
in bringing about a certain pressure, push open the elastic clamp-cock
suck at the rubber tube and then let the elastic clamp recoil. In
this case however the rubber tube leads to the water-jet-air-pump
(P) and passes a compression cock, which as a rule closes it, but
at the required moments is pulled open by an electro-magnet K,,
so that the connection between air-pump and porometer is brought
about. When the required air-rarefaction has been attained, the
current of the magnet is broken, the clamp recoils and the rare-
faction can only be adjusted via the stomata.

Since the air-pump works continuously a very great rarefaction
would soon arise in the space outside the cock, which on opening
the cock would also appear in the porometer. To prevent this, the
tube leading from the air-pump is branched outside the cock and
a second rubber tube (4) runs between the movable part (5) of the
cock and a fixed metal block (6).

In the position of rest of the cock, this rubber tube is open and
connects the pump with the atmosphere (at 7). When however the
cock is pulled open, 4 is closed off, so that now the pump can
only work on the porometer (through 3). So the water-jet-air-pump
and the electro-magnetic clamp replace the sucking with the mouth
and the clamp cock of the ordinary porometer. 6

Now it should be looked to, that the electro-magnet works at the
right time. The open limb M, of the manometer is wider than M,

Wte p: 1S.
84

Proceedings Royal Acad. Amsterdam. Vol. XXIII.

1306

and on the water floats a glass floater, suspended on a cord, passing
over a pulley, and consequently in case of a change of water-level

Ne

AE 2 zn if il | U,
5 ay Pa apa ee Len (
cs : J) a

EEKE
un

Fig. 1. Scheme of the arrangement of the self-recording porometer. Expla
nation of letters and figures in the text.

sets the pulley in motion. The force, with which this takes place, is
exclusively dependent on the floating-power of the floater and quite

1307

independent of the difference in pressure to be adjusted. Therefore
pressures differing but little from the atmospheric can be
employed, which makes circumstances more natural for the plant.
Fig. 1 refers to a moment, when the difference in pressure is being
adjusted, so the water is falling in M, and rising in M, and the
pulley is moving as the arrow indicates. Now there turns on the
same shaft a second pulley and over this a cord passes, carrying
at either of its extremities a n-shaped fork of nickel wire. Such
a fork moves, when the pulley terns, in a vertical direction, with
each of its limbs in a glass tube, at the bottom of which is mercury,
which has been inserted into a circuit.

If the fork 8 dips into the mereury of contact C,, circuit I is
closed and the current passes through the solenoid 8, of the auto-
matie electric mercury-switech W (upper half of Fig. 1). The core
of soft iron is attracted, the switch is changed over and a.o. one of
the insulated iron forks dips into the mercury cups of contact C,,
in consequence of which circuit III is closed, the electro-magnet
opens the cock K,, the porometer is brought in connection with the
pump and the water rises in M, and falls in M,. The air-rarefaction
and with it the movement of the water and of the pulley continues
till the fork 9, which is sinking now, reaches the mercury in C,,
for in consequence of that circuit II is closed, solinoid 8, works
and, the switch changing over, circuit III is broken, the porometer-
space is closed by the clamp and the current of air passing through
the stomata rebegins the adjustment of the difference in pressure.
It is evident, that the degrees of air-rarefaction between which
we want to work, can be regulated by altering the place of the
mercury-contacts along their stand.

The preceding may be summarized as follows:

There are two alternate periods in the working of the apparatus:

Period I, of indefinite shorter or longer duration, in which the
position of the switch is such, that the current through the electro-
magnet is broken; the porometer-space consequently is closed by the
cock and the pressure is increased by the current of air through the
leaf from the lowest fixed limit to the highest.

Period LT, of a short duration, in which the position of the switeh
is such, that the current passes through the electro-magnet; the poro-
meter-space consequently is connected with the pump, which dimi-
nishes the pressure again to the lowest limit.

Each period begins with a contact, made by one of the forks (taking
part in the movement of the water in the manometer) through which
the switch is drawn in the required. position.

84*

1308

Now the purpose is to record the duration of period 1 every time.
The simplest method would be, to make the switch give a mark on
a revolving drum at each changing over, and next to measure the
distances of those marks and make a graphic of them. A similar
method has already been applied by Barus and by LatpLaw and
Kniaut, who employed drums, revolving rather quickly and falling
simultaneously, because otherwise the marks would come too close
together for them to be able to judge the distances.

The recording-apparatus to be discussed here, has been constructed
thus, that it gives the required data directly in a survey on a slowly
revolving drum, so that the modifications in the degree of aperture
of the stomata, for instance during 24 hours can be read, without
measuring or copying.

It consists firstly of a recording drum, turned round by the
clockwork U, in 24 hours (see fig. 1 at the top).

The tracing-pencil (11) is fastened to a trolley (12), which can be
moved on rail parallel to the descriptive line of the cylinder, being
attached with a cord to the disk (18), which is fixed on one shaft
with the cog-wheel T, of the second clockwork U,. T, however is
not constantly in connection with the rest of the cog-wheels of U,
In fact, the cog-wheel T,, that has to transmit the motion of the clock-
work to T,, does not turn in the frame of the clockwork, but in
a separate lever, which can be moved round the pivot 14 to
a small extent by alternate attraction of the cores of soft iron of
the solenoids S, and S, If 8, pulls down, T, goes up, the
motion of T,. is transmitted to T, and the trolley is drawn to the
left with a certain speed. If next 8, pulls, T, goes down, T, is
released and the trolly is drawn back to zero by the weight 15.

The intention with this arrangement is, that the trolley is only taken
along by the clockwork during the period 1 of the porometer, which
is to be recorded, and that during period 2 it has an opportunity
of running back to zero, to recommence its uniform movement with
the next period 1. The longer period 1 lasts, the longer the clock-
work continues pulling uninterruptedly and the longer therefore grows
the line, traced by the pencil towards the left. In this way the left
extremities of the lines thus obtained, give a distinct picture of the
course of the durations of the periods 1, i.e. of the degree of aperture
of the stomata.

For the changing over of the cog-wheels at the exact time the
automatic switch W cares, which itself is indeed changed over at the
alternation of the two periods. To its shaft namely some other iron
forks have been fixed insulatedly and these serve to close circuit

1309

V at the beginning of period 1 in the mercury-contact O,, in conse -
quence of which the solenoid S, (at the clockwork) works and
makes T, catch into T, — while at the beginning of period 2 in C,
circuit IV is closed, which by means of S, pulls down the cog-
wheel T,.

Thursday May 13 1920. Friday May 14.

ONE BeOne ah ae IS neder he SOF. ew 4s wih ea eS
BANNER Ch reek Ca
i)

ast mi he

Fig. 2. Course of the stomatal aperture in a leaf of Ficus elastica for
nearly 24 hours. The lengths of the lines denote the time, in which the
pressure in the porometer was increased from 5 to 1 cms. of water below
the height of the barometer.

Fig. 2 is a reproduction of a diagram, obtained with the aid of
the described arrangement. It is hardly necessary to point out, that the
distance between the lines is the smaller, the shorter the periods 1
are. If period 1 lasts longer than 16 minutes, the pencil goes no
farther, so that the line is, as it were cut off. There is however no
objection to this, because in such long periods the length may be
accurately read from the time-axis down to half-minutes.

The picture given by fig. 2 clearly shows how on May 13th at
5.30 p.m. a slow closure of the stomata had already set in, between 7
and 8 o’clock the closure went quicker and quicker, at 8.30 the
period was 5 times longer than at 5.30. Next the stomata remained
in the strongly-narrowed condition, till about midnight, then they
began to re-open, first very slowly, but between 4 and 6 o’clock
in the morning very fast.

From 7 to 9 o'clock they were more open than the previous
afternoon at 5.30. Between 9 and 2 the degree of aperture showed
fairly strong oscillations, which, in connection with observations |
shall no further discuss here, should probably be attributed more
to the influence of temperature than the light. At the maximal
aperture at 2 o'clock, period 1 was 16 times shorter than at the
greatest closure at 10 o’clock in the previous night. After 4 hours

1310

a slow closing set in, so that at about 5 o’clock the condition was
almost equal to that of 24 hours ago.

At first sight the results obtained in this way, seem satisfactory.
Undoubtedly the general course of the aperture of the stomata may
be read from the diagram. Yet the apparatus discussed above meets
with the same objection as the other recording porometers: the
uninterrupted flow of air through the leaf. This objection can be
removed, by introducing between every two observations a period
of rest, during which the pressure in the porometer is equal to that
of the atmosphere. For this purpose the following arrangement has
been added to the apparatus. (fig. 1. upper half). The circuit IIT,
enabling the electro-magnet to connect the porometer with the pump,
has not only been interrupted in contact C, (at the automatic switch),
but moreover at C, (mercury-cups in ebonite block, fixed to the
clockwork U,). Even if at the end of period 1 the connection in
C, is brought about, yet the current will not pass through the
magnet before C, has likewise been closed. This may be attained
by a fork (16), fixed to the cog-wheel T,. In the position as illus-
trated (during period 1), this cog-wheel is free from the clockwork
and is kept in this position by a weight, that keeps the fork 16
at a special distance from C,. At the end of period 1 T, goes down
and its teeth catch into those of T,. Now this latter turns slowly
back and after some time 16 reaches C,, the circuit III is
entirely closed and the reduction of the pressure in the porometer
may begin. As the rod, to which 16 has been fixed, insulated, can
be turned round the shaft of T, with friction, the angle through
which it has to be moved by the clockwork, may be taken arbi-
trarily and in this way the duration of the period of rest can be
determined.

Our purpose, viz. to have atmospheric pressure in the porometer
during the period of rest has not yet been attained, for at the beginning
of the period of rest there is still a difference in pressure and it would
take long to adjust this quite.

The porometer-space therefore should be brought into direct connection
with the atmosphere and this happens by means of the rubber tube 19
(Fig. 1. bottom half), attached to the side-tube 2 of the glass chamber
and which is not — as is the case with VAN SLOGTEREN’s porometer —
closed off with a common clamp, but runs through an electromagnetic
clamp. Tube 19 had been closed off between the frame 20 and
the fixed block 21, during period 1, because the armature 22 was
attracted by the electro-magnet K,. Circuit VI serves this purpose,
which can be interrupted at the mercury-contact C, of the switch,

1311

but in the illustration (period 1) is just kept closed by a fork. Is the
switch changed over at the end of period 1, VI is interrupted and
the frame 21 is pushed upward by the elasticity of the rubbertube
itself so that 19 is opened and the pressure inside and outside the
porometer becomes equal. When the period of rest is finished, 19
must be closed, otherwise the pump cannot reduce the pressure. In
order to attain this end, circuit VI has also been conducted past C,, so
that 19 is closed off, as soon as 16 dips into the mercury. As T,
(thus 16) is not released by T, before the switch has taken the
position illustrated in fig. 1, consequently the current VI is also
closed in C,, VI keeps going and the rubber tube 19 remains
closed, also during the transition from period 2 to 1.

The arrangement is such, that circuit III is entirely closed, when
both in C, and in C, contact has been made, whereas the current
already goes through VI, when in either of the contacts C, of C, the
fork dips into the mercury.

It had appeared in practice, that during the period of rest, in conse-
quence of the transpiration of the leaf, the air in the glass-chamber was
saturated with water-vapour, the result of which was, that the condition
of the glue-rim did not remain trustworthy. Therefore it was necessary
to renew the air during the rest and this could be attained, by giving
the waste rubber-tube 4, with an open end at 7, (where during
period 1 and the rest-period air is sucked in by the pump from
outside,) a side-limb (17) passing clamp K,, next past 18 and ending
at the bottom of the glass-chamber. If K, is open, a current of air
enters at 19, and passes through 2, 1, 18, 17, 4 to the pump.
Since 7 always remains open, the current of air through the chamber
is not too strong. When the period of rest is over, 17 in K, is closed
by the clamp at the same time as 19 and the circulation stops.

With the apparatus thus modified 3 periods are to be observed:

Period 1. Porometer-space closed. The air enters through stomata.

Period of rest. Porometer-space connected both with atmosphere
and pump. The air circulates.

Period 2. Porometer-space only connected with pump. The air
is rarified.

Fig. 3 is a photograph of a diagram, showing the periods of rest
between the observations. The laboratory possesses two recording-
porometers, writing on one drum, enabling us to examine two plants
simultaneously.

In this case Ficus elastica and Peperomia maculosa were treated.
It is striking, that in the case of Ficus, since the introduction of

1312

the period of rest, a much larger amplitude is to be noticed, than
in the case of uninterrupted recording, which proves the necessity

Thursday, October 21st 1920. Friday, October 22nd,

Peperomia maculosa
'

7106 Sa eM roel. Wee ES A EY Ge OG 19 Oi HEN Tora Soh eS." Gk 7 eke
MRE ot DOC IE SES es EEE ae AREER Se ERE: wa fer A
| bi dohakekodetestel | i} 1] I

EE
sf

Ficus elastica

Fig. 3. Course of the stomatal aperture in leaves of Peperomia maculosa
and Ficus elastica recorded simultaneously with intervals of 20 minutes for
nearly 26 hours. The lengths of the lines denote the time, in which the
pressure in the porometer is increased from 7 to 4 cms. of water below the
height of the barometer.

of the period of rest (ep. fig. 2 and fig. 3). If from 13 to 14 May
the rate of time between “most open” and “most closed” was 1: 16,
in fig. 3 it is 1:85. It is also remarkable, that even during the
night opening and closing may be noticed, which proves, that other
factors than light act a part.

Comparison between Ficus and Peperomia shows, how with the
latter the stomata check the current of air but very little in the
middle of the day, towards evening the closure is much quicker
with Ficus. What lasts still 5'/, min. at 4 o’clock, is done in 125 min.
between 5 and 7 o'clock. In the evening Peperomia gave a slower
closure than Ficus, in the morning however an opening at least
equally quick. The ratio of open and closed is particularly strong
in the case of Peperomia. At one o’clock in the afternoon the period
of fall is not yet '/, minute, about midnight 32 minutes. Here it is
not the place for a further inquiry into these results, which immediately
tempt to further physiological contemplations.

1313
§ 3. Particulars.

The practical execution of the system discussed has given various
experiences, which I will communicate here. In fig. 4 and 5 the

Photo J. QUELLE.
Fig. 4. Arrangement of two recording porometers, the chambers of which
have been fixed to one leaf of a Ficus elastica on either side of the middle-
vein. Explanation of letters and marks in the text. To the left a hygrograph
and behind it a thermograph. Through the opening at the top in the middle
something of the sunshine-autograph may be seen.

real arrangement of the parts has been illustrated, deviating here
and there from the schematic fig. 1. The signification of letters and
figures is the same throughout.

1. The glass chamber. At present I always use the model, as
illustrated by van SLOGTEREN on p. 18 of his dissertation, so the one
with the side-tube attached near the edge. In the case of Ficus
elastica I use chambers with wide mouths (diameter 4 centims),
because by doing so a greater number of stomata is set to work
and the falling of the water in the porometer goes quicker. Because
I use pressures, little below the atmospheric pressure, (viz. between
7 and 4 millims underpressure or between 5 and 1 millims under-
pressure) to make the condition of the plant differ as slightly as
possible from the natural condition, the fall-period is longer than

1314

for instance in the case of most of vAN SLOGTEREN’s experiments.
That is why measures such as the use of the large-surface-chambers

ern ee emt er

Photo J. QUELLE.

Fig. 5. Arrangement of the recording apparatus. To the left the recording
drum and in front of it one of the two writing clockworks (U2). The second
clock conformable to the first was too much to the left to be seen in the
photo only some parts belonging to it (112, 12e, 15) are visible. The clockwork
moving the drum should also be thought to the left. To the right the two
automatic mercury switches (the one in front of the other) and behind those
a resistance. Further explanation of the figures in the text.

and the diminution of the gas-contents of the porometer are to be
recommended.

The fixing of the chamber to the leaf remains a difficult question.

In 1914, when I was occupied with ordinary porometer-observa-
tions, I tried a number of glues, and just as VAN SLOGTEREN '), |
came to the conclusion, that ordinary Arabic gum is by far the best.
In 1919 on the advice of my colleague J. Heimans, I tried mixing
a small quantity of Sesame-oil with the gum and indeed this makes
the substance somewhat tougher and cracks do not so soon appear
in drying. Besides [ always add a trace of Thymol, to prevent its
decay. Too much thymol is injurious to the experimental plant.

1) Le, p. 20.

1315

It is my experience, that well-fixed chambers may remain fit for
use for 4 weeks, but they should be ventilated regularly between
the experiments. It is essential, that the air in the hothouse at least
in the first hours after attaching the chamber is fairly dry, other-
wise the glue remains soft too long, which may cause the leaf
to get slightly removed from the chamber.

Il. The manometer. The two limbs are of unequal diameter,
therefore the manometer should be tested before use in order to know
what distance in the narrow tube conforms with a change in
pressure of 1 cm of water. Fixing the water-level at zero is a very
simple thing and quickly done, in consequence of the presence of
a water-reservoir R (attached to the manameter by means of a
rubber tube with clamp) and of a drain with clamp. Practice teaches
that hardly any water evaporates from the manometer, so that the
apparatus can work 48 hours at a stretch, without the water-level
having to be fixed anew '). |

UL The electro-magnetic clamp K,. The whole apparatus is really
based upon the theorem, that the elastic clamps close the rubber
tubes absolutely and that at the points where the rubber tubes pass
over the glass tubes, leakage is impossible. What fig. 3 shows for
Ficus elastica between 5 and 7 p. m. is the best proof for the
practicability of this theorem.

About the structure of the clamp itself there is not much more
to be said, than can be seen in the picture. The electric current
however should be further discussed. It is yielded by a battery of
accumulators of 7 cells, therefore with a voltage of 14 Volt and
the force of the current is for the clamp K, only 1 Ampère. There
is a very small loss of electricity, for the time used for sucking up
the water in the manometer is at most 4 seconds. The current of
the battery is also used for the solenoids of the switch (circuit
I and II) and for the electromagnetic clamp K, (circuit VI).
Part of the apparatus being in the hothouse (everything below the
horizontal line in fig. 1) and the rest in a room of the laboratory
(switch, recording-apparatus and battery) an amount of connecting
Wire is necessary. A tube, containing 16 wires, joins the two localities
and the wires end on terminal boards with numbered terminals, from
which flexible wires lead towards the different apparatus. Two series-
switches have been inserted, which can close and break the current
if necessary botn in the hothouse and in the room.

1) The U-shaped manometer is therefore also to be preferred in case of the
non-recording porometer to the ordinary glass tube placed in a vessel of water.

1316

IV. The electro-magnetic clamp K,. Except during the period of
rest, this clamp must remain closed and consequently is in circuit.
Therefore it has been arranged in such a way, that a current of 0,45
Ampere is sufficient. For the rubber tubes 17 and 19 has been used
common bicycle valve-tube.

V. The: pulley-contact-arrangement. The pulley-shaft runs very
lightly between two conical pivots. The floater is made of glass
and contains mercury at the bottom. A thin cord runs over one
pulley and bears a weight at its other end. In fig. 4 to the right
is shown, that in the newest model the second pulley is larger,
which magnifies the movement of the forks 8 and 9 and enables
us to fix the contacts C, and C, more accurately.

As appears from the description, | have always used mercury
in the contact-arrangements, which was done because mercury-
contacts are absolutely trustworthy, contrary to brushes of other
metals and because force is not wanted for bringing about the
connection.

It would not be an easy matter to keep the mercury in the
glass tubes C, and C, clean, when soiled by sparks. With the
amperage used sparks only occur on breaking the current, therefore
it was necessary to break the cireuits [ and Il somewhere else
before the forks 8 or 9 rise out of the mercury. This end has been
attained by adding to

VI. the automatic mercury switch, an arrangement of levers (not
shown in fig. 1), by which, again with the aid of mercury-
contacts, the circuits | and II can be broken, when the switch has
reached the required position and further action of the solenoids
S, or S, is superfluous. With this arrangement a double purpose
has been attained: 18* the spark of breaking is removed to a place
where the mercury must not so anxiously be kept clean; 2rd the
loss of electricity in the solenoids is limited to a minimum. —
At the first trials of the switch it appeared, that in consequence
of the elastic fall of the iron forks in the mereury-cups, the switch
recoiled halfway after a moment. To prevent this, the clockmaker
J. Mussias devised a brake, consisting of a couple of metal springs,
checking the movement of the lever. One of them has been rendered
in the diagram as No. 23.

The mercury-cups of the contacts C, to C, are bored out in
ebonite blocks. At the bottom of the cavities there end the iron
screws of the “terminals” put up at the sides, carrying the current
to the mercury.

VIL The clockwork U,. The proportion of the cog-wheels and the

1317

outline of the pulley 18 is such, that the trolley is drawn on with
a speed of 1 mm. per minute.

[It is essential, that the lever, in which T, turns, is kept steadily
in the required position. Therefore after every movement it shoots
behind an elastic pawl. Consequently the solenoids S, and S, must
possess great strength in order to draw the lever back along
the pawl. The electric current yielded by the battery could not
perform this, and therefore use has been made for this arrangement
of the alternate current of 220 Volt taken from the plug-switch SC.
The circuits IV and V (drawn as an undulating line in the illus-
tration) carry the alternate current. Mr. Mrssias invented an arran-
gement, which prevented the current to pass longer than strictly
necessary. In fact, the vertical shaft, to which the cores of soft
iron are fixed in S, and S,, ends on both sides in a bone tip and
this breaks the current in a gold-contact when the extreme position
is reached. (This is not indicated in the picture).

VII. Lhe tracing-pencil. The tracing is done in recording-ink i.e.
with red, because the common lilae ink is not well reproduced in an
ordinary photograph. The glass needles are made according to a
model, used in the Royal Dutch Metereological Institute at De Bilt’).
Every needle consists of a bulb, (capable of containing ink enough
for recording during 48 hours), from which issues a pointed capil-
lary tube, which rests on the paper. This tube is fixed to the bulb
with the aid of sealing-wax. The whole is seized in a small clamp
at the end of the shaft of the trolley.

IX. The recording-drum revolves in 24 hours and has an outline of
72 ems. Each hour is therefore 3 cms. and the minutes of 4 mm.
are easily read. For paper millimeter-paper is used, so that after-
wards a scale has not to be added and the data can immediately
be accurately read. The paper is fastened round the drum by means
of narrow brass hoops.

The lines, written by the pencil when the trolley is drawn on
by the clockwork U,, form an angle with the ordinate, the tangent
of which is: the quotient of the distance, travelled by the recording-
drum in one minute and that which the trolley travels along its
rail in one minute, or >.

As has already been mentioned above, the trolley is stopped after
having run for 15 minutes. The clockwork need not stop, because
the shaft of T, turns with friction. During that time the pencil
writes a line parallel to the abscis (see fig. 2 and 3).

5 Dr. C. ScHoure, Director of the Institute, was kind enough to explain this
method to me.

1318

X. General remarks. The idea of using a tracing-pencil periodi-
cally moving backwards | got from the selfrecording anemometers
used in meteorology. There the distance travelled is automatically
differentiated as to time by the backward movement of the stiletto
every 5 minutes, so the velocity is recorded. In the case of my
apparatus the differentiation does not take place as usual according
to time, but the velocity is taken as “the time needed to travel a
certain distance”.

In this connection I want to point out, that the recording appa-
ratus by itself, therefore apart from the porometer, may be used
for all kinds of other physiological inquiries, in which velocities have
to be recorded. I hope soon to provide the ‘“arc-indicator of growth”
with an apparatus, enabling us to record the growth in the way
mentioned above. Then the alterations in rate of growth, which
are really wanted, may be directly read, while with the usual
method, they must be derived from the inclination of the curve.

It may not be undesirable to consider the advantages of recording-
instruments in general, apart from the special method followed here.
In the first place we have the uninterrupted observation, next a
great saving of time, for, when the construction is sufficiently sure,
an apparatus as the one under discussion can work for 24 hours,
without our having to look at it. Finally the accuracy with which
everything can be regulated. For instance it is impossible for an
experimentator to observe in the way followed here: an observation,
during which he must patiently wait, then waiting for exactly 20
minutes, another observation, another 20 minutes waiting — that
is slow work and not very encouraging which cannot be kept up
very long. Moreover with slow movement of the meniscus it cannot
be precisely stated, when the exact point is reached. The mercury-
contact tells us this with minute accuracy. Indeed working with
such slight differences in pressure (i.e. in circumstances so slightly
unfavourable for the plant) as is possible here, is almost impractic-
able for an ordinary observer.

Let us finally consider what advantages the apparatus discussed
here offers above the existing recording porometers and we find as
general advantage: the possibility of introducing periods of rest
with renewal of air between the observations.

Let us next consider separately the real porometer and the
recording apparatus. The porometer itself may be built almost equally
compactly as Baus’ stomatograph, and is therefore equally fit for
use in hothouses or outside among the plants. The mechanism, which
has to be in the immediate vicinity of the plant however is simpler

1319

and, on account of the mercury-contacts, works more accurately. As
a complication however it should be added, that the apparatus must
be connected with an air-pump by means of a tube. The porometer
of Lamraw and KNiGutT is in consequence of the necessity of placing
a bath of a constant temperature around the jar of Mariotte, only
practicable for laboratory-experiments of no long duration and is
consequently inferior to the apparatus of Barrs and of myself, in
spite of the pressure being almost constant. Moreover the forming
and getting loose of a drop of water seems to me a less accurate
measuring of time, than the change of level in a manometer. All
methods mentioned however are to be preferred to that of Jonmrs, in which
the recording-apparatus forms one inseparable whole with the porometer.

The advantage of the electric connection between porometer and
recording-apparatus, rendering an arbitrary distance between the two
possible, cannot be valued too high. The plant can be examined in
the most different circumstances, while the recording occurs in a fixed
place and the apparatus suffers no injury from uncommon temperature
or moisture.

The special adventages of the recording-method used have already
been mentioned: 1°. The fact that the readings can be taken much
more accurately, also of very short periods, without the unities along
the time-axis having to be particularly large; 2°. writing a directly
practicable graphic of the course of the phenomenon to be studied ;
3°. the fact that it can be used for recording other physiological pheno-
mena respecting velocities and gives a better survey of those, than has
been done hitherto. These properties of the recording-apparatus make
up for the fairly bigh costs of procuring, and make it an apparatus
that can be regularly used in the laboratory.

The observations with a recording-apparatus that may be left alone
for a whole day, require however, that the circumstances in which
the plant finds itself, are recorded uninterruptedly. Otherwise it cannotbe
controlled what the occurring phenoma are due to. It would be ideal
to record temperature, moisture ete. on one recording-drum with the
vital phenomenon to be examined. Until this has been achieved, we
must be satisfied with the existing apparatus for this purpose, the
only inconvenience of which is, that their drums revolving in one
week are too small for us to read the time accurately even for a
period of 5 minutes. Through the kindness of Prof. E. van EvERDINGEN,
Chief-Director of the Royal Dutch Meteorological Institute, | had some
apparatus in loan during my experiments. At present the Laboratory
of Plant Physiology possesses a thermograph, a hygrograph and a
sunshine-autograph.

1320

The results mentioned above would not have been attained, if I had
not been sustained by the confidence in the success of the undertaking,
which the director of the Laboratory, Prof. E. Verscaarreit, has
always shown, and by the aid in word and deed, I experienced from
Mr. J. VAN DER ZWAAL, instrumentmaker, and Mr. J. Mrssras, clockmaker,
in the technical execution of the plans.

October 1920.

(From the Laboratory of Plant-Physiology
of the University of Amsterdam).

Hydrology. — “On the Motion of Ground Water in Frost and

Thawing Weather.’ By Prof. Bue. Dugoss.
(Communicated at the meeting of January 29, 1921).

From small pools, from detached ditches, especially with high
sides, from wheel tracks, water is seen to disappear on prolonged
frost from under the ice formed, so that beneath the ice there are
air-filled spaces. The vanished water-layer can be from a few centi-
meters to some decimeters thick. The phenomenon is universally
known, but the question what happens to the water, has not been
answered as yet.

Other, equally common phenomena, are observed in thawing
weather. Before the frost the soil may have been fairly dry near
the surface, but without previous snow or rain it is found to be
muddy on the still frozen substratum, as soon as thaw has set in.
Not until the frost has quite gone from the ground, the superficial
soil resumes its former, less wet condition, because then the excess
of water sinks away. Whence this excess of water?

When the frost has gone from the ground, new-set plants that
had not yet properly taken root, may be found “frozen up’, that
is partly, in some cases of small plants entirely, uprooted. By
what cause?

Some winters, especially that of 1917/18, I had an opportunity to
make observations in the ‘‘sand-diluvium” of central Limburg, which,
I think, can throw some light on the causes of these phenomena.

The most important fact found, was that i thawing weather the
ground water rises. Without snow or rain, and without superficial
inflow of water, the level of the water, among others in ditches, after
the ice in them had melted, is seen to rise in the district mentioned
to such an amount as 1 em. per twenty-four hours.

Hence there is displacement of ground water, during frost upwards,
and during thaw downwards, and I imagine this to take place as
follows.

The pressing action of the surface tension of the water that sur-
rounds the ground grains, decreases with increasing diameter. Hence
in the state of equilibrium the coarse ground grains are covered
with thicker water layers than the fine ground grains. And just as

85

Proceedings Royal Acad. Amsterdam. Vol. XXIII.

1322

the liquid moves from a small soap-bubble towards a large one, in
the same way water that surrounds the ground grains moves from
the fine towards the coarse grains when the state of equilibrium has
not yet been reached. So far as | know, E. Ramann was the first
to point out this important influence of the grain-size on the moisture
of the soil.') In the capillary spaces between the grains the height
to which the water rises is also in inverse ratio to the cross-section
of those interstitial spaces.

Now it seems to me that the same influence manifests itself in
these phenomena of freezing and thawing of the ground.

For as soon as the frost penetrates into the ground, the ground
grains become larger in consequence of their water-envelopes getting
frozen, and then suck the water to them from the neighbouring,
still unfrozen grains; this water freezes again, and thus the diameter
of the solid grains gets greater and greater. In the same way the
capillary spaces get narrower, so that ground water rises in them.
The quantities of water that thus can be retained in the frozen
parts of the ground, must be very considerable.

This appears in thawing weather from the muddy state of the
ground at the surface, which thaws first. When also the lower
layers are thawed, the water that has risen during the frost, can
sink away, and return to the ground water.

Plants are not found uprooted through frost until it thaws. This
may be explained in this way: when the ground thaws, differences
of tension arise directed from below upward, through which the
plants that have not yet firmly taken root, are ejected.

1) In the third edition of his “Bodenkunde’’, p. 332, (Berlin 1911).

Mathematics. — “Two Representations of the Field of Circles on
Point-Space.” By Prof. Jan pr Vrins.

(Communicated at the meeting of January 29, 1921).

1. In 1917 these Proceedings (Vol. 19, p. 1130) contained a paper
of Dr. K. W. Warsrra on the representation of the circles of a plane
on the points of space. In this representation a pencil of circles is
replaced by a point-range, a net of circles by a field of points, and
two orthogonal circles are represented by two points that are har-
mouically separated by a paraboloid of revolution, the points of
which are the images of the point-circles of the field of cireles.

Lately this representation has been investigated more closely and
applied further by Dr. J. Smir in his thesis entitled: “A Representa-
tion of the Field of Circles on Point-Space” (Utrecht 1920). We
arrive also at this representation in the following way. Let A be
a point outside the plane ® of the circles c; through c and A a
sphere is passed. If we consider its centre as the image of c the
representation defined in this way shows all the above mentioned
peculiarities.

2. In order to arrive at another representation of the field of
circles we transform in the first place the plane ® by inversion
with centre N into a sphere 3; the circles c are in this way replaced
by circles c’ of B. Now we consider the pole C' of the plane y’ of
e’ as the image of the circle c. The point-circles P of ® are, evidently,
represented by the points P” of 8. A straight line l of ® is trans-
formed by the inversion into a circle 2 through A, is therefore
represented by a point L of the plane » touching 8 at N. N is
apparently the image of the straight line at infinity of ®.

3. A pencil of circles (c) is transformed by inversion into a
“pencil” (c’), i.e. a system of which there passes one circle through
any point of 8, so that the planes y’ of the circles c’ form a pencil,
pass therefore through a straight line 7’. But then the poles C lie
in a straight line » (the polar line of #/ with respect to @). Also in
this representation a pencil of circles is therefore transformed into
a point-range.

1524

If (c) has the base point B, and B, also the circles c’ pass through
two fixed points and the image r of (c) lies outside 3.

If on the contrary (c) has two point-cireles P, and P,, 7’ is the
intersection of the planes touching 8 at 7”, and 1’, and the image
r cuts the sphere.

The image of a pencil of concentrical circles is evidently a straight
line # through the point N.

A parabolical pencil of circles is represented by a tangent of B.
Any two circles of such a pencil touch at a point P; the images
of two touching circles are therefore joined by a tangent.

/

4. A net of circles [c] is transformed by inversion into a “net”
[c’]; the planes y’ pass through a fixed point S, consequently the
images C lie in a plane o, the polar plane of S.

The image of a net with base-point Pis the plane touching 8 at P’.

All the circles c cutting a circle c, at right angles, form a net
[c]; to this belong the points P of c,. As these points may be
considered as circles touching c,, they have their images in the points
of contact of the tangents of 8 meeting in the image C,. Consequently
the net is represented by the polar plane of C,. The images of two
orthogonal circles are therefore harmonically separated by B. The
sphere 8 plays here the same part as the paraboloid in the above
mentioned representation.

All the circles intersecting c, diametrically also form a net, [c*].
As [c*] has no circle in common with the net of the circles inter-
secting c, at right angles, the image o* is parallel to the plane o of
c,. To [c*] belongs also the circle c,: hence o* passes through C,

5. An arbitrary conic d* contains the image of a system (c),, with
index two; for the tangent plane o of a point A’ has two points
in common with d and these are images of two circles e through
the point R. The system (c), belongs to the net [c] which is repre-
sented by the plane of d’. °)

If the plane @ touching 8 at FR’ also touches J’, LF’ is the central
projection of a point R of the curve enveloped by (c),. Now let Z
be the image of the straight line / in ®; the enveloping cone of

8 the vertex of which is Z, has four tangent planes @ in common

N

1) The orthoptical circles of a pencil of conics form a system (c),. For through
a point of the straight line at infinity pass the degenerate circles consisting of
Il, and the director lines of the two parabolas. The point-circles of the system
are found in the double points of the three pairs of lines and in the centra (the
orthogonal circle of the net to which (c), belongs) having its centre in the point
of intersection of the two director lines.

1325

with the cone projecting d out of Z. From this it ensues that the
system (c), is enveloped by a curve of the fourth order.

The points of intersection of d’ with 2 are the image of four
point-circles belonging to (c),; the points of intersection of d? with
the plane » represent the two straight lines of (c),.

6. A twisted cubic d* is the image of a system (c), with inder
three. At such a system we can arrive in the following way. Let
us consider three projective pencils of circles (c,), (c,), (c,) in ®;
let c be the circle intersecting the homologous circles c,, c, and c,
at right angles. The image C of c is the point of intersection of
the polar planes y,, y,, 7, of the images C,, C,, C,. These planes
revolve round the polar lines 7,,7,,7, of the straight lines 7*,, 7*,,r*,
containing the images C,, C,, C,; the locus of the point C is accord-
ingly a twisted cubic, d*. Apparently we can inversely choose for
”,7,,7, three arbitrary chords of a given curve d*; their polar
lines with respect to 8 define in ® three projective pencils of circles,
which in their turn define the system (c), which has d* its image.

7. A plane curve d* is the image of a (c), belonging to the net
that is represented by the plane d of d*. A tangent plane o of 8
intersects d* in three points of the straight line dg; as a second
tangent plane to 8 can be passed through this straight line, the
system (c), is characterized by the property that the three circles
through a point P have another /* in common. If do is a tangent
to 8 the three circles touch in a point P; this point of contact lies
evidently on the orthogonal circle (diametrical circle) of the net.
In a special case the orthogonal circle can be replaced by a straight
line, containing in this case the centres of the circles of the system (c),.

8. Let O be the centre of the sphere 9. If the images C, and
C, of two circles c, and c, are such that “OC,C, is a right angle,
c, is intersected diametrically by c, ($ 4). If C, is fixed C, remains
on the sphere 7” having OC, as diameter. This sphere is apparently
the image of the twofold infinite system of circles c that are inter-
sected diametrically by the fixed circle c,. The intersection of two
tangent planes of 3 has two points in common with J"; hence through
two points there generally pass two circles of the system. A pencil
of circles contains also two circles of the system.

9. We arrive at another representation of the field of circles in
the following way. In the plane ® of the field there are assumed

1326

three arbitrary points K,L,M; the powers of the circle c with
respect to these points are considered to be the coordinates «, y, z
of a point C with respect to an orthogonal system of axes.

The plane «=O contains the images of the circles passing through
K. As a pencil of circles (c) sends one circle through A, the image
of (c) has one point in common with «=O and is therefore also
in this case a straight line. As further a pencil (c) has one circle
in common with a net [c], a net is represented by a plane.

A pencil (c) has two pointcircles; the locus of the images of the
pointeireles P is again a quadratic surface d°. We find its equation
by making use of the well known relation between the sides of the
complete quadrilateral PAK LM.) Substituting there AL* =A, LM*= f,
Mk? = g, we find after some reduction,

per + gy? + he? + (h—f—g) HMD) (fg) (ye + fe) +
+ (g—h—f) (ze + gy) + fgh = 0.

The plane «0 contains only the image of the point-circle K;
from this follows that ®* touches the coordinate planes.

Any circle concentrical with the circle KLM, has equal powers
relative to K, L and M, is therefore represented by a point of the
straight line &=y==z; as a concentrical pencil contains only one
point-cirele at finite distance, ®? must be an elliptical paraboloid
the diameters of which make equal angles with the three coordinate
axes. |
_ If we choose K,/, M in the angular points of an equilateral
triangle, so that f=g=h, ®° becomes apparently a paraboloid
of revolution.

1) See e.g. SALMON-FiepLeR, Anal. Geom. des Raumes | (1879) p. 74.

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KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS

VOLUME XXIII
Ne, 9.

President: Prof. H. A. LORENTZ.
Secretary: Prof. L. BOLK.

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

Natuurkundige Afdeeling," Vols. XXVIII and XXIX).

CONTENTS,

L. BOLK: “On the character of morphological modifications in consequence of affections of the
endocrine organs”, p. 1328.
Miss M. A. VAN HERWERDEN: “Concerning the Influence of the Adrenal Cortex upon the Growth

and the Reproduction of Lower Organisms and its presumable Antitoxic Action”. (Communi-
cated by Prof. C. A. PEKELHARING), p. 1339.

J. DE HAAN and S. VAN CREVELD: “The Interchange between Blood-plasm on one hand and Humor
aqueus and cerebro-spinal fluid on the other hand, studied from their sugar-percentages and
in connection with the problem of combined sugar”. (Communicated by Prof. H. J. HAMBUR-
GER), p. 1343.

A. DE KLEYN “Experiments on the Quick component Phase of Vestibular Nystagmus in the Rabbit”.
(Communicated by Prof. R. MAGNUS), p. 1357.

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”. I. (Communicated by Prof. P.
ZEEMAN), p. 1365.

F, ROELS and J. FELDBRUGGE: “On the Development of Attention from the 8th until and including
the 12th year of life”. (Communicated by Prof. C. WINKLER), p. 1371.

A. A. HIJMANS VAN DEN BERGH: “Concerning Sulphaemoglobinaemia”, p. 1392.

N. G. W. H. BEEGER: “Bestimmung der Klassenzahl aller Unterkörper des Kreiskörpers der m-ten
Einheitswurzeln.” (Verbesserung). (Communicated by Prof. W. KAPTEYN), p. 1399.

P. ZEEMAN, W. DE GROOT, Miss A. SNETHLAGE and G. C. DIBBETZ: “The Propagation of Light in

Moving, Transparent, Solid Substances. III. Measurements on the Fizeau-Effect in Flint Glass”,
p. 1402.

H. ZANSTRA: “Motion relativated by means of a hypothesis of A. FoPPL”. (Communicated by Prof.
P. EHRENFEST), p. 1412.

N. H. KOLKMEIJER: “Space-time-symmetry. I. General Considerations, p. 1419. Ibid. II. Discussion of
a special case. The tetrahedrical atom-models of LANDE, p. 1428. Ibid. III. Remarks on the

deduction of groups of space-time symmetry operations” (Communicated by Prof. H. KAMER-
LINGH ONNES), p. 1434.

K. KOMURO (Nagasaki): “On Smelling during complete Exhaustion (resp. adaptation) for a given
odour’. (Communicated by Prof. H. ZWAARDEMAKER), p. 1442.

H. J. PRINS: “On the Acceleration of Solubility of Metals in Acids by Reducible Compounds”.
(Communicated by Prof. J. BOESEKEN), p. 1449.

86
Proceedings Royal Acad. Amsterdam. Vol. X XIII.

Anatomy. — “On the character of morphological modifications in
consequence of affections of the endocrine organs”. By Prof. L. Bork.

(Communicated at the meeting of February 26, 1921).

By endocrine organs are meant a group of organs whose right
functioning is requisite for the regular development of the body.
Besides these organs exercise a regulating influence on the metabolic
processes in the body. This latter function, although hardly separable
from the former, bears a more physiological character, and therefore
is beyond the scope of the following considerations which treat
mainly of the significance of these glands for morphology.

The principal of these glands are: Hypophysis, Epiphysis, Glan-
dulae suprarenales, Glandula thyroidea, Thymus and the so-called
interstitial gland.

The influence of these glands appears from the fact that, if their
right funetioning is disturbed, whether by abnormal development,
or by affections at a later age, the regular morphogenesis of the
body is disturbed in some respect or other, or the adult body shows
characteristic variations in form. These variations differ greatly as
to their nature, and clinical observations as well as experimental
research have of late years enabled us to reduce definite metamor-
phoses to affections of one or more of these organs. The morphological
modifications are so divergent in character, that any relation or
connection between them seems wanting. And still, in this commu-
nication, the facts will be set forth in such a way, that a relation
will become evident, and at the same time a new perspective will
be opened on the part that these organs play, or rather have played.

For the better understanding what follows, it is desirable, in this
place already, to set forth this perspective, and to announce the
conclusion, to which the facts point. This conelusion runs as follows:
with abnormal functioning of the endocrine organs, such morpbo-
logical properties are developed again in the human body, as it had
lost during the last phase of its phylogenetic development. The
latest phase of his phylogenesis was that in which man got his
morphological specifically human characteristics, such as distinguished
him from his nearest relations, the Anthropoids and the other Pri-

1329

mates. Well then, affection of the endocrine organs asserts its influ-
ence in the first place on these specifically human characteristics.

From an a posteriori point of view, this is really quite natural
and perfectly logical. The endocrine organs regulate the development
of the form up to the most trifling details, and least considerable
properties, they control the morphogenesis. In the man of to-day
they co-operate in such a manner as to originate the Homo recens.
But in the ancestor of man, with his rather pithecoid characters,
their co-operation was such as to originate a more primitive form.
During evolution the activity of the endocrine organs must therefore
have undergone a modification, a morpbological character that in a
primitive form acquired a certain degree of development, in a higher
form must have altered its development. That alteration may be
either a regressive one — so retardation. or suppression of the
development -— or a progressive one, so a more forcible develop-
ment. What I will call the architectonic function of the endocrine
organs in man must be somewhat different from, say, that of Gorilla,
or Chimpanzee. If the endocrine organs control the morphogenesis,
then they must also adapt themselves in their function to the phy-
logenetic metamorphoses. Is it, however, really beyond all doubt,
that we have to speak of adaptation in this case? Did the endocrine
organs indeed play only the passive part of adaptation, in this
process, or was that part rather an active one, if not a directing,
then, at least, a regulating one? The question is one of biological
principle, for it is immediately related to the question of even
wider bearing, whether evolution has only been brought about by
the influence of external circumstances, or rather by such influence
in connection with an internal agent. In a former publication I
wrote in favour of the last named opinion and [ then pointed out
the possibility that the endocrine organs have played an important
part in evolution, It was then impossible to me to arrive at any
notion as to the nature of that relation between their function and
evolution. I believe now to have advanced a step, as it has become
evident to me, that, at least in the bringing about of the specifically
human characteristics, that influence has always acted in the same
direction.

The differences in form between related species may be brought
about either by something existant developing more strongly, or
being suppressed in its development. In this latter case, therefore.
the influence of the endocrine organs must have been a retardative
one. Well then, I propose to demonstrate that the development of

the specifically human characteristics is the result of a retardative
86*

1330

or suppressing activity of the endocrine organs, and that, in case of
affection or abnormal development of those organs that suppressing
influence is lost, so that the modifications which then appear in
the body, have a pithecoid character.

I hope further to draw your attention to phenomena from which
we may conclude that that retardative influence not only corcerns
the merely morphological faculties, but that the entire process of
development, the developmental rate of the human individual, as
compared to that of the other Primates, is retardated.

One of the first characteristics by which man is distinguished
from all other Primates is his hairlessness. On the cause of this
Darwin is not always of the same opinion. At one time he is inclined
to consider the nakedness of man as the result of sexual selection,
at other times he leaves scope for the possibility of climatological
influences, having been at work. I have no space for a criticism
of these opinions. I shall restrict myself to the observation that
the foetus of all Primates is hairless and that therefore, in the
genesis of man, the part played by the endocrine organs consisted
in suppressing the potentiality for hair-development, with the exception
of that part of the skin which covers the skull. The hairlessness
of man is therefore the persistance of a foetal character. It is a
well-known fact that now and then this suppressing influence on
the development of the hair-covering is removed and individuals are
born with a more or less complete hair-coat, the so-called hair-men.

Which of the endocrine organs was it, that had a suppressing
influence on the formation of the hair-covering in man? We can
indicate it with a good deal of certainty. This organ is the Hypo-
physis. For we know that with hyperfunction of this organ in man
as well as in woman, a hair-covering may be developed in an
extremely strong degree, so that the limbs and trunk in particular
are thickly covered with long hairs.

So we have here our first instance of an affection of an endocrine
organ influencing a specifically human character, and that in such
a way, that a pithecoid condition returns. However, an affection of
Hypophysis is present in yet another series of phenomena, which bear
the same character and manifest themselves in particular at the skull.

The skull of apes, especially of anthropoids, is distinguished from
man’s, by the marked development ef the jaws, the so-called supra-
orbital-ridges also attaining an extraordinary size. The anthropoids
are what is called markedly prognathic, man is orthognathic, whereas
his supraorbital-ridges have hardly come to any development at all.

Again orthognathy is a foetal character, not only of man, but

1331

also of apes. It is only gradually, that in the ape-foetus and the
young ape-child, the jaws extend forward. In man this growth is
ugain suppressed, he retains his foetal character. And this retardation
also takes place under the influence of hypophysis. For we know
that when this organ is affected, both jaws, but particularly the
lower jaw can enlarge considerably ; the suppressing influence there-
fore, which proceeded from this organ — and which, in normal
circumstances, keeps this potentiality of development in a latent
condition, for the whole of life — is removed, and the old pithecoid
factor of development tries to re-assert itself. Not only, however,
for the jaws, also for the frontal-ridges. Do not many historia morbi
of such patients mention a gradually stronger development of these
ridges ?

Not all human races however are equally orthognathic ; the stronger
prognathy of the “black” races is well-known. From this it might
be inferred that that suppressing influence acted less strongly in the
latter races than in the white ones. This assertion is supported by
another character to which I want to draw your attention, viz. the
colour of the human skin, and especiably that of the white races.

The colour of the skin is defined by the development to a more
or less degree of the so-called skin-pigment. This is developed in all
Primates, and as regards man, particularly in the black races. So
the hardly if at all pigmented skin of the white races has again
been brought about by a retardation or suppression of the develop-
ment of skin-pigment. And here again we have a persistence of a
foetal character. The white skin of man, therefore, is not a new-
acquired property, for it is a condition found temporarily in all
fetal primate individuals, the further developmental phase, which
follows in the other Primates and also in the black races, being
suppressed in the white races. And that this influence is active
already in negroes, is evident from the fact that negrochildren are
born with a white skin, and only become black shortly after birth.
Therefore the white has, in a way, retained a foetal character, which
the negro has lost, consequently the retardation process in the
white is stronger than in the black, in complete accordance with
what could be ascertained with regard to the development of the
jaws. So human evolution has, at least with regard to the morpho-
logical properties, progressed further in the white race than in the
black races. How far the same applies to the mental qualities may
here be left out of discussion.

So the whiteness of the human skin is again an instance of
retardation. Which endocrine organ is responsible here? To this

1332

question we can also give a rather exact answer. It is the adrenals.
Since long we have known a disease first described in 1855 by
Appison, and also named after him, the main symptom of which
is an abnormally strong development of pigment in the skin, so
that the latter acquires a colour between bronze and dark-brown.
This pigment is not of haematogeneous origin, for it is without iron,
as is the skin-pigment of the coloured races. With autopsy of persons
who have died of this disease, we find, almost without exception,
degeneration of the adrenals, generally of a tuberculous nature.

I proceed with another phenomenon. A typical difference between
man and the other Primates consists in the fact that the sutures of
the skull in primates close very early. With anthropoids, where they
remain longest open, they still disappear before the individual is
adult. In man, on the other hand, the sutures remain much longer,
and the closing bears more of the character of a symptom of senility.
The fact of the sutures remaining open is not to be ascribed to the
considerable development of the brain in man. If this were the case,
they might also close in man immediately after the termination of
the growth of the brain, that is, at a comparatively early age. The
fact of the sutures remaining open in man, is again to be considered
as the persistence of a foetal character, to which I drew attention,
a few years ago, in a monograph on this subject. This persistence
is again the consequence of a _ retardation or suppression of the
growing-together-process, which manifests itself in the other Primates
in an earlier or later phase of their development. This process
consists in the ossification of the fibrous tissue that separated
the parts of the skeleton, the adjoining parts of the skeleton
becoming one whole. This ossification-process is retarded in man and
shifted to a later phase of his life. Even in acentenarian WALDEYER
found sutures. Now by the influence of which endocrine gland was
this retardation brought about? The answer to this must be: under
the influence of Thymus. The significance of this organ is not yet
known in all respects, but we do know, that it is in the first place
the skeletogeneous processes in the body which are influenced by
this gland.

When thymus is removed experimentally in youthful animals, or
when this gland has from necessity to be removed surgically in
young human beings, serious disturbances appear after a short time
in the ostegeneous processes. Mostly affection of a rachitical nature
are the result. Now one of the symptoms of rachitis is the so-called
premature closure of the sutures of the skull, that is to say, the
sutures disappear even before the individual is adult, sometimes

1333

even at a very youthful age. Even in the rachitical hydrocephalus,
in whom the skull under the influence of the increased intracranial
pressure, may strongly increase in size, this premature ossification
may manifest itself. So here again we state that with affection of
one of the endocrine organs, by the removal of a retardation-process,
a specifically human character is lost, the bones of the skull growing
together, as is normal for other Primates.

So now we have met with four specifically human characters
which are to be considered as persisting foetal characteristics, and
which, when any of the endocrine organs is affected, can undergo
alterations in a pithecoid direction: his hairlessness, his orthognathy,
his white skin, his persisting sutures of the skull. Each of these characters
is the result of a retardation in the development and this retardative
influence is removed with degeneration of any of the endocrine
organs. I could bring under this group another phenomenon, viz.
the slight development and slender build of the hands and feet in
man, in contradistinction to those of the anthropomorphous apes.
If sufficient time were at my disposal I would prove by a somewhat
detailed anatomical demonstration, that in outward appearance as
well as in structure, especially the foot of man has retained a foetal
character. So here again we are confronted with a retardation in
development. And this retardative influence is bound at the function
of the Hypophysis. For with affection of this organ this retardative
influence can again be removed, hand and foot become inelegant
in shape, grow, and may considerably increase in size.

We now come to a second group of phenomena, in which that
retardative influence of the endocrine organs manifests itself in a
somewhat different manner.

The genital organs, especially in woman, differ from those
of the female individuals of the other Primates in a very
particular way by the presence of the so-called mons veneris and
Labia majora. These form therefore a specifically human character-
istie and a typical difference with the apes. The absence of these
characters in apes is still of some historical importance as far as,
at the time, Biscnorr the Munich anatomist, adduced this difference,
as well as the absence of a hymen in apes as a great argument
against the Darwinian theory about the relation between man
and the other Primates. Yet Biscnorr was wrong, for though it
may be true, that the organs mentioned are absent in born indi-
viduals, if we examine the foetal stages of development of these
animals, we obtain a different view. The organs mentioned originate
from a wall-shaped eminence, which is formed round the genital

1334

orifice, not only in man, but in all Primates. In the lower apes this
wall soon disappears, in the foetus of anthropoids on the other hand
it continues to exist, as appears from the observations of DENIKER,
Sperino, myself, and others, so that the older foetus of these apes
has, in front of the vestibulum a mons veneris and at the sides labia
majora, be it that they are not nearly so strongly developed as in man.
After birth these characters seem to disappear soon, also in anthro-
poids, in man they continue to exist. So we have here again a typical
human character, which is nothing but a persisting foetal property.

And here also we are struck by the fact that the difference
between man and the apes is the result of a developmental retard-
ation, but now of a somewhat different character from the preceding
cases. For though in the other Primates the genital wall disappears
at last, and the disappearance is therefore the normal process, it
continues to exist in man and increases in size in accordance with
the general growth. So here the retardation did not mean the sup-
pression of the coming about of a morphological character, but the
prevention of the disappearance of a very early condition. Which
endocrine organ may be thought of in relation to this phenomenon?
By many clinical observations we are able to answer also this
question. It is almost certain that we must here think of the influ-
ence of glandula thyroidea. Congenital absence, or too slight .
development of this gland is accompanied by an insufficient develop-
ment of the exterior genitals, the labia majora and the mons veneris
are sometimes missing. The genital apparatus therefore, has in
such cases, been formed as in the other Primates, the specifical
human character having developed in an insufficient manner. The
influence of Glandula thyroidea on this human character appears
further from the fact that after extirpation of this endocrine organ
atrophy of the genitals is resulting, adhibition of the extract of this
gland brings atrophied or insufficiently developed external genitals to
a stronger development.

The case that we have last discussed forms a welcome transition
to a specifical human charactar, that I now want to discuss briefly
and with which I shall conclude the casuistic part of my contribu-
tion. The specifically human character par excellence is the great
weight of the brain. Is this also the result of a retardative influence,
you will ask somewhat sceptically ? I reply, yes, however paradoxical
this may sound.

Let us therefore briefly take a nearer view of the part played
by the endocrine organs in morphogenesis. This part consists in these
organs ensuring a harmonious development of the form. An har-

1335

monious development is brought about when the rate of development
of each part of the body is exactly dosed and the duration of
development exactly limited. This rate and this duration are different
for each part and so in every stage of development there will be
a different correlation between the organs. As an instance I mention
the heart. In the tirst phase of embryonal development this organ
grows very rapidly, and is already completely formed when other
organs are stil more or less far removed from their final stages.
For each organ comes the moment when it has reached its definitive
size-relation to the whole, after which it further increases in size
in accordance with the general growth. If, for instance, the size-
correlation of the heart or the kidneys, as it exists in the beginning
of the second month of development in the human foetus, would be
made permanent, then individuals would be born with monstrously
developed heart or kidneys. But in the course of the further develop-
ment heart and kidneys decrease again in relative size.

Now this same point of view also applies to the brain. It also
increases enormously in size in the first developmental phase, not
only in man, but in all Primates. Of all Primates the foetus passes
a developmental stage in which with regard to the whole body the
brain has a monstrous degree of development. It afterwards decreases
relatively in size until a definite phase of development, after which
regularly to take part in the general growth. Now the difference
between man and the apes is, that this happens in man in an
earlier stage of development than in the other Primates, therefore
the correlative relation in him was fixed in a younger phase when
the brain was relatively larger. So here again the principle of retard-
ation finds expression. The sooner a limit is put to the relative
diminution in size, the larger the brain will become, the longer this
relative diminution lasts during the development, the smaller the
definitive weight of the brain becomes.

1 have done my best to give my view in as succinet a form as
possible; I hope that the intelligibility has not suffered too much
by doing so.

Under the influence of which organs stood this retardative process ?
In order to answer this question let us examine what is the con-
sequence if the correlation is not fixed at the point of time normal
for man, but, as in the other primates at a more or less later
moment in the development, when the brain in regard to the entire
organism has become relatively smaller.

Then also in man, therefore, a decreased mass-relation of the
brain to the whole is brought about, the wellknown microcephaly

1556

with the accompanying idiocy. And with this the answer has been
given to the question asked, for clinical observations of this disease
point most decidedly in the direction of glandula thyroidea.

It will not have eseaped the attentive hearer that in the preceding,
notone, but several points of view have been discussed collectively. The
first point of view I could summarize in this thesis: the specifically human
characters are persisting foetal properties; the second point of view in
this: the specifically human characters originate in the general develop-
mental process of primates having been retarded in certain parts;
the third view in this; this retardation is caused by the various
endocrine organs, and finally the fourth in this: with affection of
the endocrine organs this retardative influence is removed and the
human body recovers pithecoid properties. Now I cannot conclude
this contribution before, on the basis of the theses just mentioned,
opening up before you another point of view of more general bio-
logical interest. The specifically morphological characteristics of man
are a result of retardation; well then, this influence of the endo-
crine organs not only concerns the development of morphological
properties, but has stamped the entire developmental process of man
as such, his rate of development has been slackened, his youth, as
compared with the other Primates, has been lengthened, the adult
phase of his life also, and perhaps also his phase of senility. This
is an idea which I had carried about with me for years, but for
which I had really never been able to find a proper correlation to
other views or observations, until I at last found it in my view of
the significance of the endocrine organs for the bringing about of
the morphological properties during evolution.

Still this idea was formerly’ not a merely intuitive one, it was
founded on a fact. This was supplied by the peculiar behaviour of
the genital glands in human beings, particularly in woman. These
glands show the remarkable phenomenon that after that the specifical
elements have developed, and no longer increase by division —
which is already the case in the second year — a phase of rest
begins. The histological differentiation of the genital glands is finished
in the second year, but their function only begins at a later age —
say between the 12‘ and tbe 14th year. Between the histological
final stage and the beginning of the function a pause, a latent period
is shoved in. This latent phase in human beings has always seemed
something very remarkable to me. And, to put it briefly, it has
always seemed to me that a discongruency has arisen between the
sexual and the somatic development. How far this also occurs in
other mammals may here be left undiscussed; so much is certain

1337

however, that it is not the normal relation in mammals. This dis-
congruency can only have been brought about by a retardation of
the somatic development, not by an acceleration of the development
of the genital glands, as this would be absolutely useless. But with
this retardation of the rate of the somatic development the function
of the genital glands had of necessity to be suppressed so long, till
the body was sufficiently developed to be able to pass through the
whole physiological process which follows a conception. So I see
here again the activity of two influences: retardation in the develop-
mental rate of the body as a whole, and temporary suppression
of the function of the genital glands.

Here also I touched but slightly on my line of thought, to
conclude with the question: have we to do in this case also, with
the influence of an endocrine organ? The clinical observations gives
us again the answer to this, and refers us to those, happily rare, but
sad cases of so-called premature sexual development. Children in
whom puberty begins at the age of four or five, girls, as cases are
known, who conceive at the age of seven or eight.

How are these abnormal conditions to be explained? In my opinion
here also the solution of the problem is to be sought in the removal
of the retardative influence on the developmental rate of the sexual
development, which, as appears from what was said above, exists
in man. And like all those mentioned before, this retardative
influence also originates with an endocrine organ, for, as is proved
conclusively by autopsy, this premature sexual development is the
result of a degeneration of the pineal gland. With this I wish to
conclude my exposition. The abundance of matter has compelled
me to give my contribution in as succinct a form as possible. That
the subject-matter is not exhausted with what is here discussed,
will be clear to anybody more or less expert. For the perspectives
here opened up go in two directions. In the first place they give
to the physician a wider view of the character of the conditions
observed by him, and to the physiologist they submit the question
to examine whether in the province of metabolic phenomena, with
affection of the endocrine organs, he can make observations which
are parallel to the morphological consequences of these affections.
Personally I am more attracted by the second direction in which
the facts point. That is the general biological one. In the exposition
given it has been shown that the endocrine organs influence the
coming about of the evolutional development of a higher organism,
it is therefore, in my opinion, no longer to be denied, that internal
factors play a part in evolution.

1338

Still I must warn against a possible one-sided interpretation of
the part that these organs can play in the bringing about of morph-
ological differences. In the evolution of man this part was, say,
pre-eminently a retardative one. | have not been able to find any
indication of an activating influence. But this is not saying that in
other cases an activating influence may not exist, causing an accent-
uation in younger forms of characteristics which existed in prin-
ciple in their ancestors.

And, to conclude, another question, or rather a problem. I have
advanced a ground to prove that the developmental rate of man
has been retarded, a retardation which, by the way, is stronger in
the male than in the female sex. To this retardation-process he owes
it, I would observe, that he is born “nudus et inermis”, that, in
contradistinction to the other mammals, it is only rather a long
time after his birth, that his consciousness of self awakes, followed
by the longer infantile, puerile and juvenile phases.

This is a privilege which man has over other organisms. But —
would it be overbold to ‘attach to this view the remark, that he
has had to pay for this privilege with: greater sensitiveness to
disease-causing influences as a consequence of a weakened capacity
for resistance? A retardation of the vital processes means a decrease
of their intensity. A decreased intensity of the vital processes means
weakening of staying-power; weakening of staying-power means
increased sensitiveness to noxious influences. And is there any other
organism to be found, so sensitive to noxious influences, so subject
to disease as man? With this question I wish to close my contribution.

Physiology. — “Concerning the Influence of the Adrenal Cortex
upon the Growth and the Reproduction of Lower Organisms
and its presumable Antitoric Action’. By Miss M. A. vaN
HeRWERDEN. (Communicated by Prof. C. A. PEKELHARING).

(Communicated at the meeting of March 26, 1921).

I have been studying the influence of various tissue-extracts on
the cyclic reproduction in a race of Daphnia pulex bred for many
years in the laboratory. I thereby hit upon a phenomenon which
led me to make further experiments. Although these experiments
are still in progress, I consider it worth while to say a few words
about this problem here, as it is one of general importance.

The first time when I added a small quantity of dried adrenal
cortex from the ox to my Cladocera cultures, it appeared to produce
a peculiar effect. First of all the fecundity of parthenogenetic females
is considerably intensified, sexual maturity commences sooner than
in the control-animals (for which I always selected sisters from one
and the same brood) and the generations follow each other in quicker
succession. Not infrequently as many as three broods have been
deposited, while the control-sisters are still bearing their first. It also
often bappens that the first generations have reached maturity while
the ovary of the untreated sisters is still infantile. This great difference
may be seen as well when the control-culture contains only ditch-
water with unicellular algae, as when for purposes of comparison
an equal quantity of adrenal medulla was added insteadof cortex.

Furthermore there is another very remarkable influence of the
adrenal cortex upon the cultures, which is not exerted by the medulla.
It is to this phenomenon that I wish to call special attention. It is
well-known that Daphniae do not tolerate multicellular algae in the
culture-glasses. The presence of these long filaments invariably
occasion in my cultures depression, and ultimately induce death, if
the animals are not transmitted in time to fresh ditch-water with
unicellular algae. It now appeared that the addition of a small
quantum of dried adrenal cortex, or an aqueous extract of it, was
sufficient to ensure a healthy life to the Daphniae in a tangle of

1340

long algae even without cleaning the glasses regularly. More remarkable
still is that different mould-mycelia, (otherwise invariably destroying
a culture within a short time), do not at all affect the health of
Daphniae and do not interfere with their rapid reproduction in the
adrenal-cortex cultures where the moulds are speedily developed.

I have availed myself of the above phenomenon in keeping my
insufficiently cleaned cultures alive during the holidays. Such a
densely populated culture, which contains per 25 c.c. of ditchwater,
say, 5 mgrms of dried adrenal cortex, mocks at all the care gen-
erally bestowed upon an organism like Daphnia pulex, which needs
much oxygen and is otherwise greatly affected by impurity and
thrives best when transmitted to fresh ditchwater every week.

The fresh adrenal cortex of the ox was carefully separated from
the medulla, minced up, dried for 24 hrs in an incubator at a tem-
perature of 60° and then pulverized. By due caution one really
succeeds in getting cortex tissue free from the medulla.

Moreover an admixture of a minimal quantity of medulla gives
a pink colouration of the ditchwater *), so that any contamination
may be directly recognized.

Besides it has appeared that the medulla (if sufficiently free from
cortex tissue)*) lacks the influence upon Daphniae described above
and its prolongated action even seems often to be noxious.

The quantity of dried adrenal cortex, just giving a positive result,
amounted to 1 mgr. per 20 cc. of ditchwater. No experiments were
made with smaller quanta.

When we distribute sisters from the same brood over culture-
glasses to which respectively an equal quantum of fresh aqueous
extract ®) of dried adrenal cortex, adrenal medulla, thyroid gland
and hypophysis of the ox is added, the medulla appears to have
the least favourable effect. Thyroid-gland extract is often tolerated
less in the beginning than after prolonged administration (tachycardia),
the reproduction of Daphniae is much less intensive than in the
adrenal cortex cultures, stronger though than in the control-cultures,
and the same holds for the hypophysis-cultures.

The extremely rapid growth of algae in the culture-glasses to
which adrenal-corter is added, is very striking. By placing the

1) This is a very sensitive adrenalin-reaction, appearing in the presence of oxygen
(Bied] I, p. 527).

2) It is much more difficult to obtain adrenal medulla free from cortex-tissue
than vice versa.

3) 1 ee. of aqueous extract (prepared 24 hrs previously by adding 0,5 gr. to
25 c.c. of water at room-temperature was added to 10 c.c. of ditchwater.

1341

animals during the experiment in a badly lighted space it may be
observed, that only the addition of the adrenal-cortex tissue is
answerable for the favourable condition of the cultures, but „ot the
rapid growth of the algae. It has, for that matter, already been
stated that the growth of multicellular algae is just a factor which,
on the contrary, inhibits the development of Daphniae.

An aqueous extract of the dried adrenal-cortex (0,5 gr. per 25 cc),
which had been heated for 2 hours at 110° in the autoclave, proved
to have the same favourable influence as the non-heated extract on
the growth of the algae. Judging from the preliminary experiences
it also seemed to promote the reproduction of the Daphniae. Spon-
taneous growth of moulds does not occur in these cultures, so that
they have still to be infected in order to ascertain whether the pro-
longed heating leaves intact the substance, wich counteracts the
effect of moulds in the cultures.

In the spring of the year 1920 I noted an extraordinary difference
in the growth of eggs of the watersnail (Limnaea ovata), according as they
were treated with dried adrenal-cortex, or not. A mass of jelly containing
eggs, originating from a single female, has been cut in two halves,
each of which has been put in a glass filled with ditehwater. During
the experiment an equal amount of algae was added to each glass.
After the lapse of three weeks the size of all the young snails,
contained in the glass, to which a few milligrams of dried cortex
of the suprarenal capsule had been added, surpassed several times
the size of those of the controlculture or the adrenal medulla cultures.

It has been shown, that the adrenal cortex contains a substance,
soluble in water, which in these invertebrates exerts an influence
upon their fecundity and upon their health. Factors, which are in
other circumstances noxious to Daphniae, such as caused by over-
population, inadequate supply of oxygen, the growth of moulds and
of multicellular algae, are removed by the addition of very small
quantities of dried cortex of the suprarenal gland. This influence
seems to exist also among lower plants, witness the highly intensified
growth of unicellular and multicellular algae. Sexual maturity is
accelerated, the embryonal development is promoted, the broods
follow each otber in quicker succession. In the snail the rate of
growth of the tissues has largely increased during the embryonal
and the post-embryonal stage.

The study of adrenalin has pushed the question of the significance
of the adrenal-cortex tissue into the background for a considerable
length of time, until it was brought under our notice again, notably

1342

by A. Biepr. In addition to the connection between the function
of the cortex and that of the sexual organs, also the possibility of
an antitoxic action of the adrenal cortex has been empbasized. In
the latest edition of his Manual of Internal Secretion Brepu still
considers it as an open question whether, just as Cobra-poison in
vitro, also endogenous poisons can be counter-acted by adrenal-
cortex.

It seems to me that the result of adding small quantities of
adrenal cortex to the Daphnia cultures — in the case of over-
population and of mould infection — indeed points to an inhibitory
influence on the action of normal metabolic products. It is notable
that this occurs in lower organisms, which, so far as we know,
do not possess an organ corresponding to the suprarenal capsule of
the vertebrata. ;

Our deficient knowledge of the normal function of the adrenal
cortex justifies a further inquiry of this problem in different directions.

Physiology. — “The Interchange between Blood-plasm on one hand
and Humor aqueus and cerebro-spinal fluid on the other hand,
studied from their sugar-percentages and in connection with
the problem of combined sugar.” By J. pr Haan and S. van
CreveLp. (Communicated by Prof. H. J. Hampurcer.)

(Communicated at the meeting of March 26, 1921).

Humor aqueus and cerebro-spinal fluid are two very remarkable
tissue-liquids. They are so in the first place because they are almost
entirely free from colloids and secondly because of the great simi-
larity between their chemical composition and that of the blood. A
large part of the present-day investigators are of opinion that these
liquids must be regarded as formed by “active secretion” by certain
layers of cells, namely the epithelial layer of the corpus ciliare and
the chorioid plexus. HALLIBURTON and Dixon') a.o. have accepted
this secretion especially for the cerebro-spinal liquid „on account of
(among other things) the discongruity which would exist between
the specific action of certain substances on the secretion of the liquid
and the action of those substances on the pressure of the blood. It
is, however, exceedingly difficult to establish experimentally and
without any doubt, an increased formation of the liquid; and equally
difficult is the exact determination of the blood-pressure in the
vascular system, connected with the formation of the liquid. We
here only refer to the recent elaborate publications of BecutT?) in
which from his own researches this author reaches the conclusion
that all the phenomena which at first sight point to secretion, may
very well be explained in a mechanical way. For the rest we will
leave out of consideration the significance of the blood-pressure, nor
will we, in what follows, discuss the value of the argument that
the histological gland-strueture of the said epithelial cells should
furnish a proof for the secretion. Leaving elone the way the liquid
is formed and the place where it originates, in other words leaving
alone the direction of its movement, we wish to take as starting-
point for our researches the chemical composition of these liquids.

And then he who speaks of secretion here, will admit that the

1) Journ. of Physiology 47, p. 215, 1913 and 48, p. 128, 1914.
*) Americ. Journal of Physiology 51, 1, 1920.

87
Proceedings Royal Acad. Amsterdam. Vol. XXIII.

1344

secreting cells “produce” a substance which remarkably resembles
the blood-liquid and which therefore those cells hardly alter actively :
osmotic pressure, concentration of the various salts and crystalloids
and of the H-ions, they all oscillate within narrow limits round
values which are practically those always indicated for the blood.’)
When, however, one states that the secreting membrane actively
checks erystalloids (fluorescin for the liquid of the eye-chamber,
aceton and other substances in the cerebro-spinal fluid), then the
researches, justifying these conclusions, are nearly always open to
criticism both on account of the method used and or account of
their varying results’). The fact that these liquids contain only
traces of proteins and that ferments, immune bodies are practically
absent from them, does not tell at all for an active, vital stopping.
For every well-functioning dialysing-membrane, every ultra-filter will
do this too.

What follows here is the provisional brief communication *) of
the results of an investigation to find an answer to the question:
in how far can the said liquids be regarded as ultra-filtrates or,
rather, as dialysates? For the name ultra-filtrate indicates a liquid
which is pressed through by means of a super-pressure (in this case
the pressure of the blood) and with which a not unimportant speed
of circulation is supposed. Now it is very probable, especially for
the liquid of the eye-chamber that under physiological conditions
the movement of the liquid is very slow. When these liquids follow
the fluctuations in the composition of the blood, this will be the
consequence of a process, of diffusion for the greater part, and
further of direct filtration; consequently in our view a combination
of dialysis and ultra-filtration. In how far does the composition of
these liquids correspond to what we must expect if the separating
layer between the latter and the primary fluctuating liquid (blood)
acts as a simple dialysing-membrane? We need not find complete
similarity: for the liquid interacts not only with the blood, but also
with the remaining surroundings (cerebral tissue, tissues round the
eye-chamber). But it will be especially interesting to trace, which
changes should be attributed to the last-mentioned factor.

For the present we have limited our investigations to one of the
substances which oceur normally in the blood, namely: glucose.

1) See a.o. OSBORNE: Journ. of Physiology, 52, p. 347, 1918—1919.

*) We hope to have an opportunity of returning to this question in further
researches.

5) A more elaborate publication will appear in the Biochemische Zeitschrift.

1345

Our choice is explained by the fact that one of us *) (when he
was comparing the sugar-percentage of blood-serum and that of the
ultra-filtrate of this serum), made the unexpected discovery that in
the process of ultra-filtration a considerable portion of the substance,
causing the reduction, remains behind. The above-mentioned differ-
ence in the sugar-percentage between serum and its ultra-filtrate *)
has been described at about the same time by Rusznyak *). The
problem of combined sugar now again came to the fore. By the
researches of v. Hess and Mc. Gurean ©), using Ager’s °), method of
vivodiffusion, and of Mricmarris and Rona *) it seemed to have been
solved in this sense that all the sugar in the blood occurred in a
free state. Here we can leave out of consideration (as unsolved) the
question whether the reducing substance which remains behind in
ultra-filtration, is really combined sugar or whether it must be
accounted one of the substances which give the so-called ‘rest-
reduction”. We would only observe here that we should have to
accept that what does not pass the ultra-filter, is really glucose, if
we relied on the investigations of Ear’). This author found that of
the total reduction of the blood, determined by a slightly modified
method Bane (also used by us), only a very small part should be
ascribed to this rest-reduction. For convenience sake we shall call
the difference which was found, “combined sugar’.

When the difference in sugar-percentage between the serum
(containing colloids) and the ultra-filtrate (containing no colloids)
had been established, this problem presented itself to us: in how
for can those liquids of the body, containing like the ultra-filtrate
only insignificant quantities of albumen and colloids in general (such
as humor aqueus, cerebro-spinal fluid, amnion-liquid) be compared
with ultra-filtrates of the blood, also as regards their chemical com-

IS. VAN CREVELD: Communication “Physiologendag” 16 December 1920,
Amsterdam. Report to appear in Arch. Néerl. de Physiologie.

*) We wish to draw attention to a communication by HAMBURGER and
BRINKMAN (Biochem. Zeitschr. 88, 103, 1918). These authors did not find a
difference between the serum and its ultra-filtrate. But their results were
based only on provisional investigations, the chief aim of their researches
lying in a totally different field. Undoubtedly HAMBURGER and BRINKMAN
would by continuing their investigations have found the difference which is
mostly present and considerable.

8) RuszNyak. Biochem. Zeitschr. 113, 52, 1921. .

*) ABEL, ROWNTREE and TURNER, Journ. of Pharmac. and Exp. Ther. 5,
275 and 611, 1914.

5) v. Hess and Mc. Guiaan. Ibid. 6, 45, 1914.

6) MicH4ELIS and Rona. Biochem. Zeitschr. 14, 476, 1908.
1) Ear. Biochem. Zeitschr. 107, 229, 1920.

87*

1346

position? And especially: Is the “combined” sugar kept back here?
(We shall have to investigate whether the sugar is combined with
protein, or phosphatides or cholesterin). This we have investigated
most fully in the case of the liquid of the eye-chamber. The values
for the sugar-percentage of this liquid, mentioned in the literature
of the subject, did not help us much. We had to rely on our own
researches. In the first place one nearly always finds indicated (as
e.g. by OsBorNB')) that the sugar-percentage of the liquid of the
eye-chamber is about equal to that of the blood. Nearly always
however it is omitted to investigate blood and eye-chamber liquid
simultaneously. This may be called the first requisite, on account
of the important fluctuations of the sugar-percentage in the blood
which are found even under physiological conditions; and, where
this simultaneous investigation was performed, as in the very detailed
communication of Ask’) of comparatively recent date concerning the
eye-liquid, these researches have lost much of their significance in
the light of our present state of knowledge. For, the liquid with
which the humor aqueus must be compared, is not the total blood,
but only the blood-plasm, the sugar-percentages of which are quite
different. By investigations of most recent date, a.o. of one of us’),
it has been established without doubt that in the case of a number
of animals (in any case with man and the rabbit) the corpuscles
are free from sugar. The value found when determining the sugar-
percentage of the total blood, is therefore considerably lower than
the actual concentration of sugar in the plasm. And, consequently,
if one compares the sugar-percentage of the liquid of the eye-chamber
with that of the total blood or with that of a blood-liquid the
identity of which with blood-plasma is not entirely without doubt,
one arrives at conclusions which are quite wrong. Serum obtained
by the coagulation of blood, plasm obtained by blood-coagulating
means (hirudin, oxalate) show a lower blood-sugar percentage than
the plasm proper, because in these operations in an exceedingly
short space of time part of the sugar disappears in the corpuscles,
this being due to changed permeability-relations. In this way are
to be explained Ask’s results (differing from ours) and his conclu-

1) OSBORNE, l.c.

*) Ask, Biochem. Zeitschr. 59, 1 and 35, 1914.

8) S. vAN CREVELD and R. BRINKMAN: Proceedings of the Royal Acad. of
Sciences Section of Dec. 17 1920. Further BRINKMAN and Miss vAN Dam:
Arch. Internat. de Phys. XV, p. 105, 1919. In these articles elaborate
bibliographies.

1347

sions') based on them, although this investigator, besides examining
the total blood, has also tried to investigate bloodplasm.

The bloodplasm required for our purpose was obtained in the
way indicated by one of us’). Into a small paraffined tube one
drops rapidly a small quantity of blood from a punctioned ear-vein
of a rabbit, one centrifugates for a few moments and takes away
the topmost fluid plasm with a paraffined glass-pipette. The sugar-
percentage in this was determined by the latest method of Bane.
This method was used by us for all sugar-analyses and gave complete
satisfaction. The double-determinations agreed well. We believe that
this method, used for a long time already in this laboratory, gives
reliable results, provided some precautions are observed. These
precautions were that with each experiment the reduction of a0.1°/,
glucose-solution was determined and besides it a blind-determination
in duplicate of all reagents used. This was done especially with a
view to the varying titre of the thiosulfate-solution.

Using this method with a number of rabbits we have first of all
compared the sugar-percentage of the blood-plasm and that of the
aqueus humour, which was taken at about the same time (difference
in time 10 minutes at most).

The chamber-liquid was obtained very easily (after cocain-anaesthesia) by
inserting a glass capillary tube with ground point into the anterior eye-chamber.
In general we performed (besides the sugar-determination) also a determination
of the refraction of plasm and aqueus humour (refractometer of ABBE) to
obtain an idea of the albumen-percentage of these liquids.

In Table [ the values found for the sugar-percentage in blood-
plasm and that in aqueus humour (examined at the same time) are
laid down.

In considering this table we must bear in mind the just-mentioned
fact that the chamber-liquid flows very slowly under normal con-
ditions, so that we can almost neglect filtration as a factor for
establishing the equilibrium in the components of the liquids, but
that this equilibrium is a consequence of the slower process of
diffusion of the various dissolved components. It follows that (from
this point of view) we can expect any change (increase or decrease)
in sugar-percentage of blood-plasm to be followed somewhat more
slowly by a similar change in the sugar-percentage of the chamber-
liquid. Where it is known that important changes in blood-sugar-
percentage may take place in a very short time, there may be

1) We shall return to these conclusions in detail later on.
ACS GREVELD."1.C.

1348

TABLE I.
Sugar-percentage

Ne of Reb Min | ur | Piece | pierre
1 0.20 0.19 + 0.01
2 0.28 0.19 + 0.09
3 0.2 0.15 + 0.05
4 0.2 0.19 + 0.01
5 0.28 0.16 - + 0.12
6 0.27 0.21 + 0.06
7 0.24 0.22 + 0.02

8 0.22 0.19 + 0.03 ) ae = 0.044
9 0.25 0.17 + 0.08
10 0.20 0.19 1.0301
11 0.22 0.19 + 0.03
12 0.21 0.19 + 0.02
13 0.26 0.24 + 0.02
14 0.32 0.25 + 0.07

15 0.22 0.18 + 0.04 ||

moments that the difference in sugar-percentage between plasm and
chamber-liquid does not correspond to what we should expect after
the analogy of what was stated with ultra-filtration. With a rapid
drop in the sugar-percentage of blood it will therefore be quite
possible for the relations to be temporarily reversed, so that the
chamber-liquid shows the greater percentage. In this way we can
satisfactorily explain the very diverging differences in table I. But
when they are compared in a large number of experiments, we
may expect the chamber-liquid to show the lower figures in the
majority of cases. We may further expect that in the mean values
of a large number of figures the same relation between chamber-
liquid and plasm will be shown which we should expect if this
chamber-liquid was, not a dialysate, but a quickly-flowing ultra-
filtrate. And when we find a mean difference of 0.044 °/, between
blood-plasm of the ear-vein and chamber-liquid, we have a right to
conclude: Provisionally the phenomenon observed in vitro of the
combined bloodsugar which behaves as a colloid, is confirmed in vivo:

1349

the sugar-percentage of chamber-liquid corresponds to the free plasma-
sugar and follows its fluctuations.

When we look at Table II it becomes still more probable that
we have a case of “colloidal sugar” remaining behind. In Table II
we have examined not only plasm and primary chamber-liquid, but
also the so called ‘secondary chamber-liquid” which rapidly (in a
few minutes) after the punction regenerates. As is known, it has
more direct connection with the composition of the blood; it contains
e.g. more protein: WesseLY *) gives one to two percent; we found
(like Harn) *) much higher values, (on account of refraction-figures),
namely from 3 to 5°/,. The secondary liquid therefore, as regards
albumen-percentage, approaches blood-plasm and the more so, as the
primary liquid had been taken away more completely. Now it
appeared that this secondary liquid (coagulating rapidly in the case
of the rabbit), also ‘qua’ sugar-percentage, must be regarded as a
kind of rapidly entering blood plasm, consequently blood of which
only the cellular elements are kept back. For the sugar-percentage
of this regenerating liquid corresponds strikingly with that of blood
plasm, investigated at the same time.

In considering table II we must bear in mind that through
“psychic” stimuli (sympathicus-stimulation) during the experiment,
the sugar-percentage in the blood of the rabbit mostly increases.
As between 1 and 3 (see table II) generally 20 or 30 minutes
elapse, the sugar-percentage of 3 (as appears from the table) can
no longer be compared with the bloodplasm of 20 minutes before,
but with that of 4. Then there appears to be nearly complete
correspondence between bloodplasm and secondary chamber-liquid :
the secondary chamber-liquid therefore has obtained the “combined
sugar’ together with the plasma-colloids.

To get a further insight into the manner and the rapidity with
which fluctuations in the sugar-percentage of bloodplasm are followed
by the aqueus humour, we have, in the case of a number of rabbits,
traced the sugar percentage of the chamber-liquid at different times
during severe hyperglycaemia, caused by subconjunctival injection
of 0.75 ee. of a 1°/,, adrenalin-solution in both eyes. We shall
here mention a few brief results of a long series of experiments.
The sugar-percentage of the bloodplasm rises rapidly after the
injection, after 45 minutes already it reaches 0.6 to 0.7°/, and
- remains thus for one to two hours; then it decreases again rather

1) Ergebnisse d. Physiologie 4!, p. 565, 1905.
2) Klin. Monatsbl. f. Augenheilkunde 64, p. 187, 1920.

1350

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1351

quickly to the normal values. The chamber-liquid follows these
changes more slowly, here probably abnormally slowly, because, as
a second adrenalin-action, the blood-supply to the eyes had decreased
very considerably for the time being. Thus, for example, the sugar-
percentage in the bloodplasm rose in 30 minutes from 0.25 °/, to
0.38 °/,, in the chamber-liquid (first in the right eye, then the left)
it rose in the same time from 0.17 °/, to 0.24°/,; in another expe-
riment the sugar-percentage in the bloodplasm had increased in 2
hours after the injection from 0.21 to more than 0.6 °/,, in the
chamber-liquid from 0.19 °/, to 4°/,; the rapidly regenerating secondary
chamber-liquid then contained 0.63 °/, which corresponds strikingly
to the bloodplasm at that moment.

When in the second period the sugar-percentage of the blood-
plasm decreases, this decrease is followed more rapidly by the
chamber-liquid than the increase which preceded. This is to be
expected because in this period the blood-supply to the eyes and
consequently the rapidity of diffusion has become greater. Yet we —
succeeded in establishing a moment when the decrease in blood-
sugar-percentage outstripped the chamber-liquid, so that the relations
were reversed: 5 hours after the injection the sugar-percentage of
the plasm was 0.27°/,, that of the chamber-liquid was 0.32°/,.

It might also be possible to explain the great difference (0.6 and
0.4) which was established at the culminating-point of the hy per-
glycaemia, not by means of retarded diffusion (consequently : equili-
brium not yet reached), but by a relative increase also of the combined
sugar during the hyperglycaemia. The difference of 0.2°/, could then
correspond to the quantity of combined sugar and the 0.4°/, sugar
in the chamber-liquid would indicate the moment of the equilibrium
of the diffusion. But this supposition is no longer valid, for during
a separate experiment we have, (during the maximum of hyper-
glycaemia) taken off a slightly larger quantity of blood and we have
determined the sugar-percentage of this together with the sugar-
percentage of the ultra-filtrate, obtained from it; the same had been
done before with the normal blood-plasm. In the beginning the
sugar-percentage of the chamber-liquid was 0.24, of the blood-plasm
it was 0.26 and of the ultra-filtrate of the plasm it was 0.16; the
difference between the last two is therefore 0.09. This difference
now remained equal during the adrenalin-hyperglycaemia (0.63°/,
and 0.54°/,), while then the sugar-percentage in the chamber-liquid
was much lower (0:44°/,) than that in the plasm. Hence the quantity
of combined sugar does not increase during adrenalin-hyperglycaemia.

It will strike that in vitro in this experiment we find a quantity

1352

of combined sugar of 0.09°/, whereas the mean difference between
eye-chamber liquid and bloodplasm amounted to only 0.044 °/,.
This figure is really low; for as an average in eight experiments
we found a quantity of combined sugar of 0.075 °/, in ultra-filtrates
(in vitro) of serum of our test-rabbits. |

Now this difference between the processes in vitro and in vivo is
not yet such that on the strength of this we should no longer regard
the chamber-liquid as a kind of ultra-filtrate, but moreover we are
inclined to think that this difference is not essential. For in com-
paring the eye-chamber liquid and the plasm of the blood from an
ear-vein we found an average difference of 0.044 °/,. But the blood
which interacts with the eye-chamber liquid, will in no case be
venous blood, but it will agree more with the composition of arterial
blood. Now, as a consequence of the sugar-consumption of the
various organs, the sugar-percentage of venous-blood will be lower
than that of arterial blood; the magnitude of this difference will
depend on the intensity of the sugar-metabolism of the particular
organ. We may take for granted that this metabolism will be very
slight in the case of the tissues (cornea, crystalline-lens) ete., which
surround the eye-chamber, and also that the venous blood flowing
from it, would differ very little from arterial blood, supposing we
could investigate the former separately. This difference exists very
distinctly when we compare blood taken simultaneously from the a.
carotis and from the v. facialis posterior, the latter of which practi-
cally corresponds to the blood from an ear-vein. In three experi-
ments we found here differences of 0.09, 0.03 and 0.02, on the
average therefore over 0.04°/,. If, therefore, we increase the sugar-
percentage of the plasm from the ear-vein with this amount, the
sugar-percentage of the chamber-liquid will correspond very well to
what we should expect of an ultra-filtrate.

As regards the second liquid investigated by us, the cerebro-spinal
fluid, we can dispose only of a much smaller number of experi-
ments. The statements in the literature of the subject made it pro-
bable that here also we should find a sugar-percentage, lower and
even considerably lower than that in the blood-plasm. Thus for
example Fins and Myers’) state that with a number of patients the
sugar-percentage of the cerebro-spinal liquid amounted to only 57°/,
of that of the total blood. A similar statement we find in Weston’).

For the reasons given before, this difference would become more

') Proceedings Soc. Exp. Biol. 13, p. 126, 1916.
*) Journ. of Med. Research. 35, p. 199.

1353

striking still, when compared with bloodplasm instead of the total
blood.

As regards the technique to obtain cerebro-spinal liquid from rabbits, we
obtained it by puncturing (with a glass capillary tube); the ligament connecting
occiput and atlas after this had first been exposed by cutting the skin and
preparing the muscles of the neck under local anaesthesia (without adrenalin);
consequently obtaining the liquid of the fourth ventricle. The animals can
bear this quite well.

We have embodied the results in tables III and IV.

In examining these tables we must bear in mind that a compar-
ison of cerebro-spinal liquid and bloodplasm under physiological
conditions is much more troublesome than in the case of chamber-
liquid; the operation generally lasts half an hour, and, when the
liquid can be obtained, distinct hyperglycaemia has occurred in the
blood in the mean time (this appears from the tables). Hence in the
values found for cerebro-spinal liquid, which in themselves are not
abnormally low (average 0.18°/, in table III) there is already a
certain amount owing to the increase of the quantity of blood-sugar.
The value of this quantity cannot be given however, as we do not
know the rapidity of diffusion here. The physiological difference
with the bloodsugar-percentage is, therefore, fairly certainly smaller
than that which we find if we compare with the plasm, taken simul-
taneously (column 3). But it is most certainly larger than would
appear from a comparison with the plasm at the beginning of the
experiment (column 1). By means of a larger number of experiments
and by causing the operation to last as short as possible we may
probably obtain more accurate data here. We shall, besides, obtain
an insight into the rapidity of diffusion from an investigation of the
speed with which adrenalin-hyperglycaemia manifests itself in the
cerebro-spinal liquid and also of the degree of this manifestation.
Onr next experiments will lie in that direction ’).

On the strength of table IV we may accept as certain that the
sugar-percentage in cerebro-spinal liquid is considerably lower than
it is in the chamber-liquid which was investigated simultaneously
(cf. columns 3 and 4).

So we see here two “ultra-filtrates’ with diverging sugar-percent-
ages. Are we to think here of an “active” stopping of glucose by
the plexus chorioideus? It seems to us that we need not call in
the aid of a similar force, but that the cause should rather be

1) The results of these have been mentioned in the more detailed publication
in the “Biochemische Zeitschrift”. 123. 190. 1921.

1354

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looked for in the action of the entire surrounding tissues, which, in
the case of the eye-chamber, will fairly certainly show a smaller
metabolism than the cerebral tissues with which the cerebro-spinal
liquid is as much in interaction as it is with the blood.

A somewhat rapid sugar-consumption in the cerebral-tissues will
necessarily cause a continuous diffusion of glucose from the cerebro-
spinal liquid to this place of lower sugar-concentration. The quantity
of sugar in the cerebro-spinal liquid therefore remains constantly
lower than its value would be if it had interacted only with the
blood; lower also than is found in the chamber-liquid. Thus we
may expect for the same reasons that the blood itself will yield
more sugar in the brain than round the eye-chamber and that,
therefore the blood in a cerebral vein will show a greater decrease
in sugar-percentage than the blood flowing from the eye-chamber
and its surroundings.

A comparison of the ultra-filtrates of the blood from the a. carotis
and the v. facialis posterior taught us that the difference in sugar-
percentage between arterial and venous blood is almost completely
due to the free sugar, while the quantity of ‘combined sugar”
suffers hardly any modification ip passing the capillary tubes.

It looks tempting to suppose that the combined sugar plays a
part in the consumption of the sugar in the tissues: here the sugar
would continually be combined (adsorbed?) and be combusted in
that’ condition; this would continually cause the fixing of fresh “free”
sugar from the neighbourhood; this would cause the decrease of
concentration of free sugar on that spot, followed by diffusion from
the blood, ete. A correct opinion about this supposition can only
be pronounced when it is settled that the reducing substance, which
cannot be ultra-filtrated, is sugar and when it is further settled of
what kind the substance is to which this sugar is “combined”.

SUMMARY AND CONCLUSIONS.

We can sum up the results of our investigations as follows:

1. In the case of rabbits the sugar-percentage of tissue-liquids con-
taining practically no colloids (aqueus humour, cerebro-spinal fluid)
is as a rule smaller than that of blood-plasm, investigated at the
same time. This phenomenon is in agreement with the lower value
for the sugar-percentage which ultra-filtrates of serum in vitro show
when compared with this serum.

2. As regards the liquid of the eye-chamber, this difference of sugar-
percentage, compared with plasm of arterial blood, is the same as the

1356

quantity of “combined sugar” in bloodserum which does not ultra-
filtrate.

3. As to cerebro-spinal fluid, the results do not yet give sufficient
certainty concerning the exact proportions of its sugar-percentage
and that of blood-plasm; to all appearance it is considerably lower
than it is in the liquid of the eye-chamber. We wish to indicate the
possibility of accounting for this difference by assuming a larger
glucose-consumption in the cerebral tissues than occurs in the tissues
lining the eye-chamber.

4. Krom the fluctuations in the sugar-percentage of eye-chamber
liquid under normal conditions and with hyperglycaemia after
adrenalin-injection we must conclude that the equilibrium with the
blood is here chiefly caused by diffusion and hardly by the circulation
of liquid; such corresponds to what is accepted about the speed of
circulation of the eye-chamber liquid. On the other hand, the so-
called secondary liquid of the eye-chamber is, as regards its sugar-
percentage, perfectly equal to blood plasm at the same moment. This
is accounted for as follows: what has entered is practically blood-
plasm with a high percentage of colloids and a corresponding quantity
of combined sugar.

5. In comparing arterial blood from the a. carotis and venous
blood from the v. facialis posterior it appeared that the difference
of sugar-percentage between these two is to be ascribed to the
free sugar which is therefore yielded to the tissues. |

6. The hyperglycaemia caused by adrenalin-injection depends
entirely on an increase of the free sugar.

| Physiological Laboratory.
Groningen, March 1921.

Physiology. — ‘“Hwperiments on the Quick component Phase of
Vestibular Nystagmus in the Rabbit’. By A. pr Kueyn.
(Communicated by Prof. R. Maenus).

(Communicated at the meeting of March 26, 1921).

When cold water is allowed to run into the right external audi-
tory ‘canal, a nystagmus will appear whose immediate effect is a
slow deviation of both eyes towards the syringed, ergo the right side.

This deviation is succeeded by a quick movement of the two
eyes towards the non-syringed, i.e. the left side. Then again follows
the slow deviation to the right. These alternations of slow-, and
quick eye-movements will recur while the syringing continues, and
for some time after.

With every vestibular nystagmus the primary deflection is such
a slow deviation, the so-called slow component phase of the nystag-
mus; the rapid movement, the so-called quick component phase is
secondary.

It would be reasonable therefore to determine the direction of a
nystagmus by the direction of the slow component phase. However,
the quick eye-movements strike the observer more particularly, so
that what in the clinical and in the physiological literature is called
a nystagmus to the right is almost exclusively a nystagmus in which
the quick component phase: moves to the right; whereas by a
nystagmus to the left a nystagmus is meant in which the quick
component phase moves to the left. Although in strictness this does
not square with the theory, from a practical point of view it will
be well to adhere to this conception.

All researchers agree that the slow component phase arises from
a direct reflex from the labyrinth via the nucleus of the N. vestibu-
laris to the nuclei of the eye-muscle and the eye-muscles. As regards
the origin of the quick component phase, opinions differ widely.
Hardly any experiments have been made, so that we possess only
a large number of more or less probable theoretical speculations and
are still left much in the dark.

We have no intention to discuss these several theories. Only one
of them, viz. Bartets’ theory, we will test experimentally. BARTELS
assumes that the source of the reflex that gives rise to the quick

1358

phase must be looked for in the periphery. By stimulating the
labyrinth certain eye-muscles gradually contract and their antagonists
relax simultaneously (slow phase). This process is supposed to elicit
a reflex which causes a rapid contraction of the originally relaxed
eye-museles and a rapid relaxation of the originally contracted eye-
muscles (quick phase). He relinquished his primary view that, owing
to the contractions of the eye-museles, the terminal branches of the
trigeminus are stimulated and the reflex for the quick phase has its
origin here, and adopted the view that the proprioceptive nerve-
ends in the eye-muscles themselves, demonstrated experimentally by
Tozer and SHERRINGTON '), represent the beginning of the reflex arc
for the quick phase of the nystagmus.

Now it seems easy at first sight to test experimentally the validity
of Bartris’ conception. When isolating one of the eye-muscles and
recording during a nystagmus the movements of this muscle accord-
ing to Barrers’ method on a Kymograph we need only to paralyse
the proprioceptive nerve-ends in this muscle and see whether the
rapid phase disappears.

Bartets’) himself had tried this previously by injecting cocain
into one of the orbitae. This however engendered such a rapid
paralysis of all the eye-nerves that the problem could evidently
not be solved in this way.

However we now possess a means to paralyse the proprioceptive
nerve-ends in the muscle. LirJESTRAND and Maenus’*) have demonstrated
that after injections of certain doses of novocain the muscles at the
place where the nerves enter, the proprioceptive nerves are paralysed
while the motor nerves retain their functions.

If it should appear, however, that in these experiments the rapid
phase does not become extinct (or would with larger doses disappear
only simultaneously with the slow phase at the moment when the
entire eye-nerve has been paralysed) this could not be put forward
as an argument against the theory of BARTELS.

When a nystagmus occurs, contractions and relaxations of various
muscles of both eyes take place. If, therefore, one wishes to paralyse
the proprioceptive nerve fibers, which come into play for the reflex
of the rapid phase, it is not enough to inject novocain into the
isolated muscle, but one has to eliminate all proprioceptive fibers
of all eye-muscles.

1) Folia Neurobiologica. IV, p. 626.
*) Klin. Monatsblätter für Augenheilkunde 1914. Bd. LIII, p. 365.
3) Pflügers Archiv. Bd. 176, p. 168.

1359

This was effected in the following way: Tracheotomy was per-
formed in a rabbit under ether anaesthesia and the respiration was
maintained artificially. The vagi were severed and the carotids were
temporarily closed by a clamp. Subsequently the M. externus of
one eye, say the left one, was prepared and at its extremity a
thread was attached through which with the aid of a lever the
contractions of this muscle could be registered on a kymograph.
Then followed the extirpation of the eyeball.

Hereafter the skull-cap was removed, likewise the cerebrum and,
after a frontal section through the brainstem a little before the cor-
pora quadrigemina, part of the brainstem. Finally section of the
two N.N. occulomotorii and the two N.N. trochleares at the base
of the skull, and of the right N.N. abducens- and trigeminus at their
entry into the orbita. So all the eyemuscle-nerves and consequently
also all proprioceptive nerves of the eyemuscles were cut through
with the exception of one N. abducens, whose associated M. externus
was used for the registration of the nystagmus.

In some experiments also the two N.N. trigemini were severed
at their exit from the medulla, with a view to ascertain once more
whether a normal nystagmus could be evoked after severing both
trigemini. Of this little is known in the literature. Héegyrs') points
out that in experiments conducted in his laboratory by Keurtrsz and
v. Marscuanko, vestibular eye-movements still occurred after section
of the ganglion Gasseri; however, in his. description he does not
state clearly whether or no a quick phase came forward. Moreover
these experiments were made only unilaterally.

Kuro *) only states in his well-known communication on the ves-
tibular reflexes in rabbits: “Die Durchtrennung des N. vagus, glos-
sopharyngeus und trigeminus in der Schädelhöhle bleibt ohne
Hinfluss auf die Reaktion nach der Einspritzung”’.

Fig. 1 shows the nystagmus in a rabbit whose M. externus had
been isolated to the /eft and whose N.N. trigemini, N.N. oculomotorii,
N.N. trochleares and right N. abducens had been cut through. With
the contraction of the M. externus the curve ascends.

From this experiment it appears that deviation and nystagmus
are still demonstrable after severing both N.N. trigemint and all
the eyemuscle-nerves with the eaception of one N. abducens by douching
alternately the two meatus with cold water and registering the
movements of the still innervated M. externus. When syringing the

!) Ueber den Nerven mechanismus der assoziierten Augenbewegungen, tibersetzt
von MARTIN SUGAR. Urban und Schwarzenberg 1918, p. 82.
2) Pflügers Archiv. 1906. Bd. 114, p. 151.
88
Proceedings Roval Acad. Amsterdam. Vol. XXIII.

1360

d.

b.

Fig. la: Syringing of the left auditory meatus with cold water. It will be seen
that immediately after the douching a nystagmus appears, in which a slow
contraction is invariably followed by a quick relaxation.

Fig. 15: Illustrates the same with a quicker rotation of the kymograph. (The
lever is shifted more towards the timeline, so that the contraction of the M. externus
is not so small as it looks to be).

Fig. le: Syringing of the right meatus with cold water.

Here just the reverse takes place to Fig. la. Slow relaxations are followed by
rapid contractions. The intense relaxation is very apparent just at the beginning
of the douching.

Fig. 1d: Presents the same picture as Fig. lc at a later douching of the left

meatus, with which the alternating relaxations and contractions are still distinctly
visible.

1361

meatus at the prepared side a nystagmus is elicited in which slow
contractions of the muscle are followed by quick relaxations and
conversely, when syringing the other meatus a nystagmus occurs
in which slow relaxations are followed by quick contractions.

This finding calls in question the soundness of. Barters’ theory.
If stimulation of the proprioceptive nerve-fibers in the eyemuscles
were to generate the reflex for the quick phase, these nerve-fibers
would have to be stimulated by contraction as wellas by relaxation
of the muscle. Another theoretical, hitherto unrecorded objection is
this that with the compensatory eye-positions, in which also occur
considerable contractions and relaxations of the eyemuscles, only a
large deviation but not a nystagmus is observed.

Ovr doubt proved to be well-grounded, as borne out by the
following experiments in which novocain was injected into the
isolated M. externus.

Technical difficulties caused a failure of some experiments. Six
experiments succeeded to perfection and all yielded precisely the
same results.

In every one of them the left M. rectus externus was isolated
and the right N. trigeminus and all the eyemuscle-nerves were
severed with the exception of the left N. abducens.

Registration of the nystagmus evoked by syringing the left meatus
with cold water (slow contractions of the M. externus, followed by
quick relaxations). Hereafter injection of 0.75—1°/, of novocain into
the isolated M. externus (Lower concentrations of novocain did not
seem to distinctly influence the nystagmus). With the above-named
concentrations not only the proprioceptive nerves were paralysed
but also a paralysis of the motor eye-nerve manifested itself.

Also during the complete paralysis the syringing was continued;
after some time the eye-nerve recovered itself slowly. In this manner,
while syringing continually, we were also able to observe how this
recovery occurred.

Now if the theory of Barrers is correct we have after the novocain-
injection to expect at the moment when the proprioceptive nerve- -
fibers are paralysed but the motor nerve-fibers are still functionating,
a stage in which the quick phase of the nystagmus disappears, but
the deviation still persists. Not before the moment when also the
motor nerve-fibers are paralysed, will the deviation disappear also.
Likewise during the recovery a stage of deviation is to be expected
without a quick phase and only then, when the proprioceptive nerve-
fibers begin to functionate, a normal nystagmus with a quick phase.

A similar process has already long been known during narcosis.

88*

1362

Fig. 2.
Mee HA ee

f

TE
—

de p wiken”

Fig. 2: Illustrates such an experiment. Directly after syringing the left meatus
with cold water a deviation and a nystagmus is evoked, which soon attains a
constant intensity.

It will be observed that during the etherization (at first ether 4 to 10, then
rising slowly as high as 8 to 10), the muscle contracts more and more and the
rapid beats of the nystagmus become smaller, until ultimately the latter disappear
entirely and the isolated contracted muscle does not display any more relaxations.

After the syringing «is stopped the contraction decreases and gradually the slow
phase of the nystagmus disappears.

1363

The experiments with injections of novocain into the isolated muscle
present just the opposite picture.
This is instanced in Fig. 3.

Fig. 3: Deviation and nystagmus evoked by syringing the left meatus with
cold water. ;

After the injection with novocain the contractions of the muscle (slow phase)
slacken, every slow contraction is however invariably followed by a rapid relaxation
in the same measure as before the novocain-injection, so that ultimately minimal

1364

contractions and relaxations alternate, or in other words the quick phase of the
nystagmus does not disappear before the entire muscle is paralysed.

After the total disappearance of the nystagmus the kymograph is stopped (at
28 sec. past 12), and now after one or more minutes we ascertain whether
recovery of the function is already discernible. As shown by the curve at 37 sec.
past 12 new small minimal contractions recur. Every one of them is again followed
directly by a quick relaxation.

As stated above, five other quite successful experiments yielded
the same result.

CONCLUSIONS.

BARTELS assumes in his theory that the rapid phase of the vestibular
nystagmus is brought about by a reflex originating near the proprio-
ceptive nerve-fibers and that the terminal branches of the trigeminus
in the orbita play a part in this process.

As the facts brought out in the present investigations have proved
this not to be the case, his theory cannot be accepted.

The place where the reflex for the quick phase of the nystagmus
arises is therefore to be looked for more towards the centra in the
brainstem.

Physics. — “Research by means of Röntgen Rays on the Structure
of the Crystals of Lithium and Some of its Compounds with
Light Elements”. 1. By J. M. Brsvorr and A. Karssen. (Com-
municated by Prof. P. Zeeman).

(Communicated at the meeting of March 26, 1921).

(For some ten years the researches at the Laboratory for general
and inorganic chemistry of this University have for the greater part
been directed to the solid substance. With a view to extend the
methods of research also to those that make use of Röntgen rays,
hoping in this way finally to get more knowledge about the finer
internal states of equilibrium, steps were taken to get the required
Röntgen apparatus.

Through the great kindness of the municipality and of the Amster-
dam University Association we have now this institution at our
disposal, and we feel obliged to express our hearty thanks to
both bodies.

The task we have set to leads us to the typical allotropic sub-
stances, but first we wanted to examine some simple, but never-
theless very interesting cases, in which results could be expected
which are of importance for the knowledge of the nature of the
link. For these cases were chosen Li and LiH, with the result
described below. A. Smits].

I CITHIUME

1. Introduction. The investigation of Li and some of its compounds
with light elements is perhaps more suitable than many of the
compounds examined hitherto for drawing conclusions concerning
structure and binding of the particles on account of the small number
of electrons outside the nucleus of the component atoms’).

The notion e.g. that electrons and ions must be considered as
equivalent elements of the space lattice, which view offers inter
alia great advantages for the explanation of the structure of the

1, Thus DeBYE and SCHERRER could show for LiF, that there are no atoms,
but ions in the lattice-points. Physik. Zeitschr. 19, 474 (1918).

1366

erystal, and for the relation between infra-red and ultra-violet
frequencies, may be tested in a simple way in the case of lithium.
In the case of an equally simple lattice set with atoms of a higher
atomic number the problem will be more difficult to solve. Thus we
hope to make out presently for lithium hydride, whether possibly
negative hydrogen ions occur here’).

The simplicity of these substances in contrast with more intricate
compounds gives scope for hope that the result will be unequivocal.
Moreover the said lithium compounds have the advantage that in
using the method of DrByr and Scuerrer place and intensity of the
lines are much less influenced by the absorption in the. rod than
they are with heavier compounds. The latter, when results of rays
of different wave-lengths [Kcy- and Kg,-rays] are recorded, may
give rise to small changes in intensity relations even as far as
reversing them if intensity is slightly differing. So it lately appeared
to us with sodium bromate.

2. Apparatus. A Rausch von Traubenberg-Debye tube with
exchangeable anti-cathode was used, as described by Bir and Kouk-
MEYER ?). The required high voltage direct current was obtained by
rectifying transformed alternate current with a Snook. The radius of
the camera used was 5.0 em, the dimensions of the diaphragms were
the same as those described by Bist and KorkMerer. The sample
was rotated by means of a clockwork.

3. Photograms. After being cleaned under paraffin-oil and
washed with dry ether a rod of lithium, 1,5 to 2 mm. thick was
covered with a thin protecting layer of paraffin, and fastened by
means of a glass foot in the axis of the camera. Even after days
the surface remained bright metallic and shiny. A Cr-anticathode
was used. The exposure lasted + 12 hours with a mean current
of + 12 mA. parallel spark between plate and point 3 cm.
Then a film was made of a glass rod covered with paraffin
to be able tuo eliminate the interference lines caused by these
substances.

4. Observations and calculation.
In column 1 of Table I are recorded the distances on the film from
the middle of the image to the interference lines, expressed in mm., and

1) Compare Moers, Z. f. anorg. u. allg. Chemie 113, 179 (1920).
*) These Proc. Vol. 21, p. 405.

1367

TABLE I.
fain iii } Cr ‚radiation Cr ,-radiation
mm. and [103 sin? ~|——— ——
estimated 2 4E ee
intensity Eh? oles 2| hyhghg | Xh’ tale 2, hyhohg
calculated ‚calculated
1 2 3 4 5 6 i] 8
NM 170 oi a i 110
47 5 zs 214 2 213 110
10.4 m 428 4 427 200
81.0 zz 535 6 530 211
91.6 s _ 640 6 640 211
116.1 ms 852 8 854 220
1202 zz 879 10 884 310

: : 2% k ear
the estimated intensities; tm column 2 the values for 10°sin?— calculated
: 2

from this (on account of the slight absorption in the lithium correction
for the thickness of the rod was here unnecessary). In the well-
known way the values referring to p-lines have been separated by
the aid of the ratio 4g: Aa = 2,079 . 10-8: 2,284 .10-8. In corres-
pondence with the regular crystalline form a common factor for

vi
10° sin? = of the a-lines was found, great 218,4. In connection with

density, atomic weight, value of AvoGapro and wave-length (resp.
0,534, 6,94, 0,6062.10** and 2,284.10-8) it follows that if the
number of particles per cell is n, a value for the common factor
A is calculated for n = 2, which corresponds with the observation
and is equal to half the factor mentioned, while for A = 106,7
follows n=1,99; hence per cell (lattice parameter a=3.50 . 10- Sem.)
there are two particles. In connection with the intensities of the
diffraction lines, those of planes with odd > / being absent, it is
obvious that lithium crystallizes in centered cubes’).

Table Il gives the observed and calculated intensities, in which
only the factor of the number of planes, the factor of Lorentz, and
the structure factor (which in this case is the same for the planes with

1) Hurr already studied lithium, but could not decide between cubes with
two atoms per lattice-point and centered cubes. Phys. Rev. 10, 661 (1917).

1368

even > /, and zero for those with odd ZA) have been taken into ©
consideration. Hence absorption in the rod, temperature factor, and
polarisation factor are not taken into account. We hope to ascertain
in how far anything can be concluded with regard to the configu-

TABLE II.
Intensity
Planes

Observed | Calculated
100 —
110 zs 6.0
111 — aa
200 m 1.5
210 = ae
211 = 4.0
220 ms 1.5
221
300 | ie is

ration of the electrons outside the nucleus after photometry of the
film. It can, indeed, already be stated that it is not possible to satisfy
the erystallographical and intensity conditions by a model, in which
by the side of the Li-ion, the valency-electron occupies a definite
place in the space-lattice. We tested the arrangement which may be
obtained in the following way, and which is .the only one that
deserves consideration :

Draw the system of non-intersecting trigonal axes in the cell with
edge a’ = 2a and place the valency-electron on each axis in the
middle between the ions. That the intensities calculated for this
model are not in agreement with the observed intensities appears
from table III (supposition B; the effect of the distance of the
remaining electrons from the nucleus can be neglected in this case.)

On the other hand agreement with the observed intensities 7s
found, when in this model the valency-electron is placed not on
the trigonal axis, but revolving in circles normal to the trigonal
axis in the midst of the Li-ions (Table III, supposition C); here r
= radius of the path supposed circular. The weakening factor occur-

1369

ring in this case for the electron’) makes the calculated intensities,
1 2
for values of en +01, ie. r > + + of the distance between two

nuclei, differ but little from those found for case A (simply centred
cubic lattice; the intensities of column A are not essentially affected
by taking into account a weakening factor for the Li-atom.) The
choice between the two models that are in agreement with the Röntgen
investigation, viz. that with atoms in the lattice points and that with
ions between which binding circles, will be postponed till after
photometry of the film ’).

TABLE III 3)

Intensity |
Planes En Lal
Observed | Calculated
A B C
r
(7=01)
= = 16 8
220 zs 216 96 78
ae ze 14 0
400 m 54 6 20
332 CE. 4 '
422 Ss 144 64 dig
431
| - :
510
521
| ms 54 60 22
440

It is, however, very questionable whether a decision can be made
with sufficient probability along this line, i.a. on account of the un-

1) Cf. the analogous calculations on binding circles in diamond by Coster.
These Proc. Vol. 22, p. 536 and KOLKMEYER, Vol. 23, p. 120.

3) Possibly this choice will be still more difficult here than it is for dia-
mond, as the number of valency-electrons is here only !/; of the total number.

3) The planes for which the structure factor becomes zero independent of

the value of ul have not been included in the table.
a

1370

certainty of some intensity factors, e.g. those referring to the thermal
movement of the valency electrons.

For the value of the diameter of BraGe’s atomic domain ') follows
from the given structure 3.04.10-® which is in very good agreement
with the value given by Brace (3.00.10 ®).

5. Summary. Lithium erystallizes in centered cubes, lattice-para-
meter a= 3,50.10-8 em.; no lattice of stationary valency electrons.
Possibly binding circles normal to the trigonal axes.

In conclusion we express our great indebtedness to Prof. Smits
for his assistance and the great interest he has taken in this work.

Laboratory of Physical and Inorganic
Chemistry of the University.
Amsterdam, March 14% 1921.

Whilst this paper was being printed our attention was directed
by a paper of Trirrine (Z. f. Phys. 4, 1, 1921), to the appendix
of a paper by Hager (Sitz. Ber. der Preuss. Ak. d. Wiss. 51, 990,
1919), from which appears that at a meeting of the d. Chem. Ges.
Drayer already communicated the result of still unpublished in-
vestigation of Li, which agrees with our conclusion as to the
arrangement of the Li-particles, and the rejection of the lattice of
stationary electrons.

') Phil. Mag. August. (1920), p. 169.

Experimental Psychology. — “On the Development of Attention
from the 8 until and including the 12% year of life.” By
F. Rorrs and J. FrLpsruaes. (Communicated by Prof.
C. WinNkLER).

(Communicated at the meeting of February 26, 1921).

I.

The literature records little about the development of attention
in children, the writers having confined themselves only to the
value which the experimental investigation of attention in adults,
possesses for a proper notion of the development of attention in
children. Their investigations regarded the range of attention for
simultaneous and successive impressions, its intensity, the aptness
for distraction or the power of resistance to disturbing influences,
the degree of clearness of the several elements observed in one
action. True, in the first part of his “Vorlesungen zur Einführung
in die experimentelle Pädagogik und ihre psychologischen Grund-
lagen” *) Mreumann describes, on the basis of his own investigations,
the development of attention in young individuals in all these
respects, but for want of space he had to forego the publication
of his experimental results. Children were also experimented on
ao. by F. N. Freeman’), A. Kocn ®), J. Hasricn *), D. Karz *) and
M. v. KuvenBure ®); with exception of the first, all about attention
and conscious isolating abstraction, i.e. fixating of uniform elements
from simple pictures.

1) Leipzig 1916, p. 179 volg.

°) Untersuchungen über. den Aufmerksamkeitsumfang und die Zahlauffassung bei
Kindern und Erwachsenen. Pädagogische Arbeiten des Leipziger Lehrervereins I, 1910.

3) Experimentelle Untersuchungen über die Abstraktionsfähigkeit von Volks-
schulkindern. Zeitschrift fiir angewandte Psychologie 7, p. 332.

4) Experimentelle Untersuchungen über die Abstraktionsfahigkeit von Schülerinnen,
Ibid. 9, p. 189.

5) Studiën zur Kinderpsychologie. Wissenschaftliche Beiträge zur Pädagogik und
Psychologie. Heft 4, 1913.

6) Ueber Abstraktionsfähigkeit und die Entstehung von Relationen beim vorschul-
pflichtigen Kinde. Ibid. 17, p. 270; See also K. Bünrer: Die geistige Entwick-
lung des Kindes?. Jena 1921, p. 162.

1372

Experimental psychological investigation of children has been of
still rarer occurrence with regard to the process of the concentration
of attention in continued labour. Counterparts to the psychological
investigations of children by von Voss’), Rivers and KRAEPELIN ®),
AmbBerG*), WhryGanpt‘*) and other experimentalists of the München
school, do not exist. They would not, indeed, have satisfied us in
the form given to them by these authors. For, although the fluctu-
ations manifesting themselves in different places of their activity-
curve, whether they are due to the start, to accommodation, to
practice, to fatigue, to the final spurt etc., are chiefly put down to
the degree of attention, generally speaking, the task imposed upon
the subjects was too complicate to bring out the effect of attention
as clearly as possible. For this reason we have not made use of
KRAEPELIN’S cipher-tests but of the cancellation-test.

We need not enter into an argumentation about the well-grounded
validity of Bourbon and Binet’s ®) crossing-test, applied in the inquiry
into the process of a prolonged concentration of attention. It has an
advantage over KRAEPELIN’s cipher-test in that, unlike this test, it
does not put in requisition any other function except attention °).

In a previous investigation one of us established the advantages
of this test notably with regard to the attention in children ’). They
consist above all in the fact that the test may be classed among the
ordinary schooltasks, and that also young children take an interest
in it provided they can read. Besides this, the experiment may be
carried out, without any difficulty whatever, with several children
simultaneously.

The text consisted of a printed paper of 36 lines, comprising
1768 letters distributed over 304 meaningless words. Some twenty

1) Ueber die Schwankungen der geistigen Arbeitsleistung. Psychologische Arbeiten
2, p. 399.

*) Ueber Ermiidung und Erholung. Ibid. 1, p. 627.

3) Ueber den Einfluss von Arbeitspausen auf die geistige Leistungsfähigkeit.
Ibid. 1, p. 300.

t) Ueber den Einfluss des Arbeitswechsels auf fortlaufende geistige Arbeit.
Ibid. 2, p. 118.

5) Attention et adaptation. L'année psychologique 6, blz. 364; B. Bourbon:
Observations comparatives sur la reconnaissance, la discrimination et |l’association.
Revue philosophique 40, p. 209.

6) KRAEPELIN: Die Arbeitscurve. Philosophische Studien 19, blz. 459; vgl. ook
E. Meumann: Vorlesungen zur Einführung in die experimentelle Pädagogik und
ihre psychologischen Grundlagen III, Leipzig 1914, p. 390.

1) F. Roers en Jon. WeRKER: Proeven over opmerkzaamheid bij doove, slecht-

hoorende en normale kinderen. Tijdschrift voor Zielkunde en Opvoedingsleer 10,
p. 209.

1373

teachers of elementary middle-class schools assisted us. A special
procedure had been prescribed for them. The investigation was made
with a whole class of from 20 to 30 children at the same time.
The task was written on the blackboard and enjoined the pupils to
cross as quickly and as well as possible all the a’s, the e’s and the
h’s of which there were respectively 122, 331 and 59 in the piece.
The trialpaper was put before the pupils immediately before the
commencement of the experiment. As the letters to be crossed were
written distinctly at the top of it, there was no necessity for the
pupil to look at the blackboard in case he should waver.

Before starting the experiment proper the children had some
preparatory practice. A piece of paper was laid before them on
which were written similar meaningless words, in which they had
to cross the a’s, the e’s and the /’s with a pencil. This afforded an
Opportunity to give several hints necessary for an undisturbed and
uniform progress of the experiment. The children were enjoined to
cross out the letters only once with a single light stroke, and not
to return to words and lines that had already been read.

After the children had received all due information the real tests
commenced. The teacher gave the sign for starting and marked the
time. At intervals of a minute a signal sounded for the children to
indicate with a mark the place they had reached. When a pupil
was ready he had to turn over his paper, to put down his pencil
and fold his arms till the last of them had finished his task. In all
1123 children from 8—12 years were investigated: 596 boys and
547 girls. Of either sex + 100 children of the age of 8, 9, 10, 11
or 12 years were at our disposal. As we could make use only of
the experimental results of those children who had passed the age-
limit by no more than three months and as we also had to put
aside some unreliable results, no more than 1073 protocols were at
our diposal, distributed over the two sexes and the various ages
as follows:

Boys 558. Girls 513.

8 years 104 8 years 98
Or ie 111 Or 101
WO nes 112 LO; nia 107
dk 111 TEM 105
tiga 120 fd 102

1374

In making up the protocols we determined: 1° the time taken up
by the test, a fraction of a minute being eliminated; 2° the total
number of mistakes. We considered as mistakes: a letters which
should bave been struck out and were skipped; 6 letters that were
struck out by mistake. The mistakes sub a and 6 were added up.
Finally the mistakes made in every minute were cast up shia sub
a and 6 also put together).

Table I shows the time required for the test by the children of
various ages, boys and girls together and each sex separately. The
first column gives the arithmetical means (A. M.); the second the
mean deviations (M. D.) and the third the central values (C. V.).

TABEE

Age (years) Boys Girls | Children

on AMD Efe _ [AM | MD. | CV. | aM MD, CV. | AM | MD. | CV AM. | M.D. | GY.

14 Tel ie | 14
13.39] (2.3 13
[StS SAM 13 12527202 12
RAD ses 12 eZ enna 11

antenne 13 16 AEN 1)
10 11 2 11

10 EE Bia, AL NP 10.5: ed Onan
| |

From this it appears that for boys and girls together, as well as
for the two sexes separately, the time required for the labour de-
creases with the increase of age, leaving aside one exception: the
boys of 12 years. (The average decrease from 8—12 years is about
30 °/,). It should be observed that the working-times of the girls
are invariably longer than those of the boys. As to the amount of
work done in a certain time the boys are in advance of the girls
by two years: the mean working time of the boys of 8 years is
only little more than that of the girls of 10, while the mean time
of the boys of 10 is exactly equal to that of the girls of 12. These
data are substantiated by the mean deviation, which in all cases is
at most '/, of the arithmetic mean, and by the fact that the central
values are invariably equal to or smaller than the arithmetic means.
That the mean deviation lessens with the increase of years points to
the fact that with the increase of years a decrease is observable of
the individual differences regarding the working-speed in various
types of life-time.

1375

Table Il contains the average number of mistakes, with the mean
deviation and the central value, made by the children of different
ages, by boys and girls collectively and by each sex separately.

TABLE II.
Age (years) Boys | Girls | Children
| AM. | MD. | Cv. | AM. | MD. | CV. | AM. | MD. | CV.
8 50.5 | 23.1 | 47 53 | 25.3| 44 51.7 | 24.1 | 45.5
9 40 17.5 | 36 36.5 | 17.5 | 35 | 38.2| 17.2 | 36
10 40-3) Bie) 33-5 | 33.4 |. 12.2) al 36.1 | 16.9 |- 32
11 sorot 27 83°} TES) | SS ides) sp
12 23.5 | -f1.8 | *'92 27 14.8-| 25 25.2 | 13.3| 23

Also the number of mistakes, as well as the time-values decreases
rather regularly, both for the boys and the girls collectively and
for each sex separately, with the increase of years. The boys of
10 years form the only exception. While the average decrease of
the number of mistakes for the boys of 8—12 years is 46 °/,, that
for the girls is much larger, viz. 51°/,. Since the working-speed
in the same space of time increases for both categories only with
30°/,, the years seem to exert a greater influence upon accuracy
than upon speed. Boys of 8, 9 and 10 years generally make more
mistakes than girls of the same age. When considering the arith-
metic mean the boys of 8 years seem to form an exception to this
rule, but the rule holds good also for them when we consider the
central value. From the 11% year, however, the boys have the better
of the girls; however, the differences are generally inconsiderable.
For either sex and all lifetimes the central values are invariably
smaller than the arithmetical means. The mean deviations, on the
other hand, are rather considerable, as they amount to */,—’/, of
the arithmetical mean; here also they lessen with the increase of
age. As for accuracy the individual differences become less significant
as compared with the typical regularities, characterizing a certain age.

Times and mistakes per se do not throw much light upon the
nature and the quantity of the work done. To realize both we first
have to reduce the quantitative data of times and mistakes to one
experimental value, in which either the time values have been
reduced to mistake-values or the reverse. We followed the first
method and obtained our experimental value by adding to the average

89
Proceedings Royal Acad. Amsterdam. Vol XXIII.

1376

number of mistakes, made by children of a certain age and the
same sex, the average number of mistakes made during the minutes,
by which the working-time of the group of children under con-
sideration exceeded the minimum time required by a group of one
and the same sex for the performance of the task. The same method
was applied to the data of boys and girls taken together. Only, in
this case we added to the average number of mistakes, made by
children of a certain age, the average number of mistakes made by
them in the minutes they worked longer than the children of the
group that required the shortest time for the performance of the task.
The values thus obtained are collected in

TABLE lil.
Age (years) Boys Girls Children
8 61.4 62 61.7
9 45 41.5 46.25
10 39.5 40.6 40.05
11 29.7 38.8 34.35
12 22 29.6 25.8

The quality and the quantity of the work achieved being in
inverse proportion to the experimental value, it is evident from the
table that boys work better than girls of the same age. At 8-, 9-,
and 10 years the difference is not so great, but at 11-, and 12 years
it manifests itself distinctly. The proficiency exhibited with the
advance of years is best illustrated by a comparison of the experi-
mental values for boys and girls together: from 8—12 years it
amounts to as much as 58 °/).

In Table IV we have given in the first column in percentages of
the experimental values the superiority of the achievements of the
boys over those of the girls of the same age. In the next three
columns we have tabulated the progress made by the boys and
girls together, and the two sexes separately, from 8—9, from 9—10,
from 10—11, and from 11— 12 years. The increase of the achieve-
ment with every transition is expressed in percentages of the experi-
mental values. |

When examining tables II] and LV more closely we see, that the
achievements at 12 of boys and girls separately and of the two
sexes collectively surpass those at 8 resp. 2.8, 2.2, and 2.4 times.

1377

Broadly speaking the work done by boys of 11 years is equal to
the work done by girls of 12 years. Whereas with boys a slowing

TABLE IV.
Age (years) gein by the| Age | PEES | Progress of | Progress of
8 1
be Vas, Ue QI 23 25
9 5 =
9—10 13 15 14
10 2
et 10—11 25 5 15
11 24 ———
Mat 26 24 25
12 26

of the regular progress is observed between 9 and 10 years, with
girls it is not noticeable before the 10‘ year. Before and after that
time the yearly progress is much more considerable both with boys
and with girls.

Table V divides the children in quick, fairly quick and slow.
workers. The time required for the task varying from 6 to 18
minutes, these three categories corresponded respectively with the
three time-groups 6—9, 10—13, and 14—18 minutes‘).

For every age, for boys and girls separately, and for the two
sexes collectively, we give the percentages of the frequency, with
which quick, fairly quick and slow workers occur.

TABLE V.
Boys Girls Children
Age (years) | : en DE =

Quick Head Slow Quick ee ' Slow || Quick dr Slow

8 6 43 51 0 22 78 3 32.5 | 64.5

9 14 57 29 0 34 66 7 45.5 | 47.5

10 24 56 20 6 49 45 15 52.5 | 32.5

11 45 50 | 5 20 43 37 32.5) 46.5 | 21

12 Sy) a 40. 4 32 56 12 41 52.5 6.5

1) Vel. F. Roers en Jom. WERKER: Proeven over opmerkzaamheid bij doove,
slechthoorende en normale kinderen. |.c., p. 212 and 213.

89

1378

The percentage of quick workers increases regularly with age
for the boys and girls separately and for the two sexes collectively,
that of the slow workers lessens regularly. As to the fairly quick
workers the change in their percentage is not regular, neither for
the boys nor for the girls. The moving up from slow to fairly quick
workers is among the boys, with the exception of boys of from 8
to 9 years, invariably less considerable than from fairly quick workers
to quick ones. Among the girls, on the other hand, the transition
from the fairly-quick to the quick workers is more marked only
from 10—11 and from 11 to 12 years of age. The difference in
this respect between boys and girls manifest itself still more distinctly
by the fact, that of the 50°/, decrease in the percentage of slow
workers among the boys from 8—12 years, 44 °/, falls to the benefit
of quick workers and 6°/, to the fairly quick-ones; for the girls
these values are respectively 32°/, and 34 °/

This has been tabulated in

TABLE VI.
Boys Girls Children
Age (years) ; : d
Quick an ‘Slow Quick Bad ‘Siow Quick ae | Slow

8—9 Tig Ief | gore: | 412 | {2 |e 4E ae gy
go 18) tg’). 259 | Sgn 6 VU TRON or 5 NE
10= 11 — |) eat) EEG | fg (ie!) tg Gig Nitti 6 | ws
ese de | i” es Gia Sn eN Nee | 14.5
ns |

ean +44] +6 | —50 || +32| +34 | —66 |l+38 | +20 se

It illustrates how the decrease in the number of slow workers
for the boys and girls separately and for the two sexes collectively
benefits the groups of quick and fairly quick workers. The values
were obtained. by calculating the difference, positive and negative,
of the percentage of the quick, the fairly quick, and the slow
workers in two successive years. For each of the three several
groups the algebraic sum of these differences expresses the increase
or the decrease of the percentage of the quick, and the slow workers
in the five years.

1379

When reverting to Table V we see that more than half the
number of boys and rather more than */, of that of the girls of 8
years are slow Workers. Among the boys of 8 and 9 years there
are respectively 6 and 14°/, quick workers; among the girls of the
same age there are none. Since among the girls of 10 years there
is as large a percentage of quick workers as among the boys of 8,
the latter have the start of the former by two years. Later on this
advantage lessens: then the boys between 9 and 10 years are on
a level with the girls of 11; boys between 10 and 11 years on a
level with girls of 12.

Conversely, the percentage of slow workers among the girls is
invariably greater than that of the boys of the same age. In course
of time it also decreases far less rapidly among the girls. So also
here the boys are in advance of the girls. Among the boys of 9

TABLE VII.
8 Boys Girls Children
>
8 Quick ee, Slow || Quick cee Slow || Quick ee Slow
A.M. | 72 gants inde, jie 79 | 46 || (72) | 66 46
8 |MD.| 30 | 23 iS 42 i9 || Go) | 31 20
cv. | 61 40 | 40 || — 50 | 39 || (61) \ 51 40
|
eN fo 41 34 || (50) | 40 34
9 |MD.| 23 17 ig: || — 17 is (a3) fo. aT 15
Gives aac. | 435 agt en 43 42 || (44) | 39 32
AM.| 48 | 39 | 29 | 35 | 35 30 || 42 | 37 29
10 |MD.| 26 20 13 || 7 14 11 || 24 17 12
Ev APE asl 35 | ap gg) a4 21
| AES
AM.|-32 | ‘28 | 24 || 48 | 33 | 27 || 40 | 30 25
It | MD.| 14 14 B iA 14 12 || 16 14 12
CMaliae |x +25 22 || 46 | 31 24 || 35 | 26 23
AM.| 25.5 21 Bri: adam 25 19 || 30 23 13
12 |MD.| 13 Ee 15.5 | 8 || 13 13 8
cv.| 23 | 20 Te lage = 17.5 | 16.5| 28 | 20 18

1380

years e.g., there are fewer slow workers than among the girls of
11 years. Boys between 10 and 11 years are about on a par with
girls of 12. ;

For the bovs and girls separately and for the two sexes collect-
ively we have calculated the mean number of mistakes, made by
the quick, the fairly quick, and the slow workers of each lifetime.
The arithmetical mean, by the side of it the mean deviation and
central value is given for each of the three groups and for each
age in the columns of Table VII. Some figures in the column of
quick workers under the heading “children” have been put in
brackets to indicate that they are the results of calculation of the
data for boys, since among the girls of 8 or 9 years there are no
quick workers. (See Table VII p. 1379).

The average number of mistakes invariably increases at each
age for the boys and girls separately and for both sexes together
with the speed of working. There is only one exception; for the
girls of 10 years the mean number of mistakes of the quick workers
is as great as that of the fairly quick workers. The mean deviation
is rather high: */,—*/, of the arithmetical mean ; however the central
value is generally lower than the average.

In discussing the data of table IV we have already pointed out
a slowing in the regular progress of the boys between 9 and 10
years. Among the girls this occurs only between the age of 10 and
11. This phenomenon is corroborated by the data of table VII. In
all categories the decrease of the number of mistakes is least for
boys of 9—10 and for girls of 10—11. As to the quick workers
among the girls the mean number of mistakes made by girls of
11 is even greater than that made by girls of 10.

The above is elucidated by table VIIL which shows for boys and
for girls the decrease of the number of mistakes from year to year
in percentages for quick, fairly quick, and slow workers. We also
added the percentages of the total decrease of the number of mistakes
in the five years’). The slowing in the decrease of the mistakes of
boys of 9—10 and girls of 10—11 years, irrespective of their being
quick, fairly quick or slow workers, is conspicuous. The abrupt
fall among the boys of 8—9 years is striking, among the girls it
does not appear before a twelvemonth later.

The decrease of the number of mistakes in the five years is

1) Data concerning the total decrease of the number of mistakes in the five
years for slow workers among the boys and quick workers among the girls have
not been tabulated here, seeing that there were not enough slow workers among
the boys of 12 and no quick workers at all among the girls from 8—9 years.

1381

TABLE VIII.
Boys | Girls
Age (years) a
Quick | Fairly quick | Slow | Quick | Fairly quick | Slow
8—9 28 29 30 — 28 En ie.
Me 9 3 | 4 — 19 36
10—11 20 sone 19 si 12 11
11—12 28 20 aie — A 44 31
Degen, | et) 50% - - oo | 88%

largest among the girls; it progresses with the speed of working.
For the quick, and the fairly quick workers among the boys and
for the fairly quick, and the slow workers among the girls it
amounts resp. to 62°/,, 59°/,, 70°/, and 58°/,.

In Tables IX and X the data of the other tables are specified.
Table IX contains for the hoys and the girls separately and for the
two sexes collectively the percentage of children of each of the three
categories, that actually made from O—-10°/,, from 11—20°/,, from
21—30°/,, from 31—40°/, and from 41—50*/, of all the mistakes
that could be made.

In arranging the data for this table we considered as mistakes
the letters which should have been struck out and were skipped;
letters that were crossed mistakenly were left out of consideration.
We could readily do so because the latter are by far fewer in
number than the former. In fact they might have been left out of
consideration in all our calculations without interfering with the
accuracy of the experimental data. The scarcity of percentages in
the columns 31—40°/, and 41—50°/, is due to the fact that the
groups concerned did not yield enough cases of the percentages
under consideration to be worked out mathematically.

Table X gives for boys and girls separately in percentages the
increase of the percentage of children that made from 0—-10 °/, and
from 11—20°/, of the possible number of mistakes. As mistakes
were considered, just as in table IX letters that should have been
struck out but were skipped. No calculations were made from the

1382

TABLE IX.
Age (years) 0—10 11—20 21—30 | 31—40 41—50
B 58 37 2 2 1
8 G 60 30 6 4 —
C 59 33.5 4 3 0.5
B 16 22 2 — —
9 G 15 24 1 — ~~
8 159 23 15 — —
B 72 20 8 — —
10 G. 88 12 — — heli
c 80 16 4 — —
| Lt
B 86 * 14 — — —
11 G. 86 13 1 — —
C 86 13.5 0.5 — —
B 95 5 — = an!
12 G. 90 9 1 — —
C. 92.5 1 0.5 — —
TABLE X.
Boys Girls
Age (years) ~ rill se See ee ERS
Increase of Increase of Increase of Increase of
mistakes 0-100/9 mistakes 11-200/0 mistakes 0-100/o mistakes 11-200/o
8—9 + 18 | — 15 + 15 | — 6
9—10 aye — 2 + 13 | — 12
10—11 any Fe | 6 eZ maple ee EE
11—12 a — a0 + 4 eee Oe
Increase in
fivecyears + 37 | — 32 | + 30 | — 21

1383

data of the columns 31—40°/, and 41—50°/,, their number being
too small. Lastly we annexed the percentages of the total increase
of the number of mistakes in the five years.

The data of tables IX and X confirm in every respect the results
hitherto obtained. For boys and girls a constant increase is to be
observed of the number of cases in which from 0 to 10°/, of the
total number of possible mistakes was made; on the contrary a
constant decrease of the number of cases with 11-—20°/, of the
total number of possible mistakes. Here also the downward progress
among the boys from 9—10 years and the girls from 10-11 years
is remarkable. The increase and the decrease for boys is most
marked from 10 —11 years; whereas the girls present the best
results before the transition from 9—10 years, certainly with respect
to the decrease but to some extent also as regards the increase.
Let it finally be observed that, taking the five years together, the
increase and the decrease are invariably greater among the boys
than among the girls. This experience, of course, does not conflict
with the fact shown in table II, that the number of mistakes for
the boys from 8—12 years diminishes on an average with 45 °/,,
for the girls, however with 57 °/,.

In that table we recorded the absolute decrease of the mistakes;
here, however, the decrease of a certain group — the cases of
11—20 °/, of the total of the possible number of mistakes — to the
benefit of another group, viz. that of cases of 1—10°/, of the total
of the possible mistakes.

CONCLUSIONS.

1. The time, required for the work, decreases on an average
with 30°/, from the 8 to the 12‘ year.

2. The working times of the girls are invariably longer than
those of the boys. As regards speed of working the boys are
generally in advance of the girls by 2 years.

3. The accuracy of working increases from the 8 to the 12th
year for the boys with 46°/,, for the girls with 51°/,. Boys of 8,
9 and 10 years generally make more mistakes than girls of the
same age; after the eleventh year, however, the boys surpass
the girls.

4. By adding up to the mean number of mistakes, made by
children of a certain age and a definite sex, the mean number of
mistakes made in the minutes, by which the working time of the
category of children under consideration surpassed the smallest

1384

number of minutes, required by a group of the same sex for the
achievement of the same sex for the achievement of the task, we
obtained an experimental value, comprising the quantitative data
regarding time and mistakes. From these experimental values it
appears that boys always work better than girls. At 8, 9 and 10
years of age the difference is not so great. It is very conspicuous
however for the 11-, and 12-year old children. The improvement
in the work of 8—12 year old children is 58 °/,.

5. Among boys from 9—10 years a slowing is observed in the
regular progress; among the girls it appears a year later.

6. The percentage of quick workers increases regularly as they
grow older for the boys and girls separately and for the two sexes
collectively ; that of the slow workers decreases. The advance from
slow to fairly quick workers is among the boys (with the exception
of those from 8—9 years) invariably less than the advance from
the fairly quick-, to the quick workers. Among the girls, on the
contrary, the advance from the fairly quick-, to the quick workers
is most marked only from 10—11 and from 11— 12 years.

7. As regards the number quick workers among boys of 8 years,
the boys have the better of the girls. This superiority lessens later
on; then the boys from 9—10 years are on a par with girls of 12.
The same applies to the number of slow workers. Among the boys
of 9 years e.g. there are fewer slow workers than among the girls
of 11. Boys between 10—11 years are on a level with girls of about
12 years.

8. With one exception the accuracy of working decreases at each
age for the boys and girls separately and for the two sexes collectively.
The increase of accuracy in the five years is largest among the
girls; it augments with the speed of working.

9. For the quick-, the fairly quick, and the slow workers among
the boys a slowing of the regularly increasing accuracy is observed
from 9—10 years; for those among the girls a year later.

il.

In the Proceedings of the Meeting of Feb. 26. 1921 *) we published
under the same title the results of an inquiry into the phenomena
of attention, appearing during persistent labour. We now present a
sequel to it in a number of data concerning the types of workers
that acted as experimental subjects. For the technique and the
arrangement of the investigations I refer to our previous publication.

1!) Verslagen van de Kon. Akad. v. Wet. Wis- en Natk. Afd. Dl. XXIX, blz. 1077.

1385

In Table I we have grouped for every one of the three several
categories of quick, fairly quick, and slow workers among the boys
and girls separately and among the two sexes collectively, the num-
ber of minutes required for the task in three groups of consecutive
minutes. If the number of minutes was not divisible by 3, the first
and the last group were made equal so that the middle one was
one minute larger or smaller'). Then the average number of letters

TABLE I.

AL

a Boys Girls Children

Age 2
(years) 5 ; ; 3

: | : ;
A | Quick aes Slow | Quick ae Slow Pionero eS pe Slow
I 153 118 99 — 118 19 | (153) 118 90
8 Il 152 157 97 — 125 110 | (152) 142 106
Ill 198 127 103 | — 107 126 | (198) 119 171
I 172 127 105 — 126 87 | (172) 126 | 98
9 II 179 158 101 ao 135 120 | (179) 146 113
Ill 203 137 115 -- G17) 139 | (203) 129 127

et z
le
I 175 138 116 163 135 168 137 104
10 II 176 170 108 161 143 131 es i | 156 121
Ill 201 147 120 198 125 128 | 200 135 123
| |
I 191 151 127 174 142 105 181 146 115
11 II 192 185 avi 172 2150 134 181 171 125
Ill | 219 161 131 212 135 143 215 147 136
|

I 191 152 128 176 153 110 182 152 116
12 II 193 185 Np 176 157 152 183 170 134
Ill 220 163 130°} 219 | 137 132°) 207 147 130

*) Cf. F. Rorrs and Jon. Werker: Proeven over opmerkzaamheid bij doove,
slechthoorende en normale kinderen, l.c, p. 212 and 213.

F. Roes: Vergelijkend onderzoek van eenige met behulp der natuurlijke en
experimenteele leerwijze bij de studie van het geheugen verkregen resultaten. Ver-
slagen Kon. Akademie van Wet. 1917, deel XXV, blz. 1315 en 1316.

J. DAUBER: Zur Entwicklung der psychischen Leistungsfähigkeit. Fortschritte
der Psychologie und ihrer Anwendungen, 5, blz. 86, 108, 117 en 130.

1386

read
the values every group
working-rate of the quick,
as the labour proceeds.

for we

in a minute was calculated for every group.

By comparing
can conceive the changes in the

the fairly qaick and the slow-workers

The quick workers among the boys and the girls work invariably

harder in the third period than in the first and second;
two their working rate is about equal.

in the last
In course of time the differ-

ence ‚in working-rate with this category of boys and girls between
the first and the third period first decreases (from 8 to 10), then

remains constant (the differences

between the third and the first

periods are resp. 29, 18, 15, 15 and 15°/,). For the rapid workers
among the girls the difference in working-rate between the third,
and the first period decreases a little from the 10 to the 12% year,

although not much;

The fairly
and in the
girls we also find that they work

third harder

the differences are resp. 21, 22 and 24°/,.
quick boys always work hardest in the 2¢ period,
than in the first.

As to the fairly quick
hardest in the second period but,

contrary to the boys, they work quicker in the first period than in
the third. Since the changes in the working-rate in the three periods
with the fairly quick and the slow workers among the boys and
girls are not so simple as with the quick workers, we have tabulated
below for the quick, the fairly quick and the slow workers among
the boys and girls the percentage with which the working rate
increased from the first to the second and decreased from the second

TABLE II.
Boys Girls
Age (years) be Quick Fairy quick Slow Quick Fairly quick Slow
at | TI nn HIJ 111 oat I—I] an TI (III
8 —l +30 | +33 | —24 | — 2 ae [+e + 6) —17 | +39 | +14
9 Deg i ad i ee ae -|- | DS | 1 3R | +16
10 Hos | +14 | +23 | —16 | — 7} +11 | 1 | +23 | + 6 | —14 | +47 | — 7
11 40.9 | Hotes 15 | 4248 lush d Bind | +23 SLA) i218 | +28 | ts
12 +1 Heels +22 | —13 a ay 2 | | +4) 4] —19 490 | —1

1387

to the third period. The percentages express the increase or decrease
of working rate in the second, resp. the third period as compared
with the preceding period.

It now appears, that as regards the fairly-quick boys of 8 years,
there is a large increase from I—II, on the contrary a less consider-
able decrease from II to ILI. For the other ages the increase from
I to II is also larger than the decrease from II to III.

On the one side however the percentage of the increase in the
working-rate from I-—II, and on the other the percentage of decrease
from II to IIL remains approximately constant (resp. + 24, + 23,
+ 22, + 22 °/, and — 15, — 16, — 15, —13°/,). The percentages
with which the working-rate among the fairly-quick girls of differ-
ent ages increases from I to II and decreases from II to ITL do not
require special discussion.

With a few exceptions the slow boys and girls (the girls from
11—12 years) work hardest in the third period. But whereas the
boys work harder in the first period than in the second, the reverse
occurs with the girls. Just as in the case of the fairly-quick girls,
the percentages of increase and decrease in the working-rate of the
slow boys and girls of different ages from I to If and from II to III,
do not give rise to any further discussion. For the boys, with the
exception of those of 8 years, these percentages are approximately
constant. This constancy is however not noticeable among the slow girls.

It would be too bold to draw any conclusions from the changes
in the working-rates in connection with the influence exerted by
the various factors that come into play with persistently continued
labour, such as the start, the adaptation, practice, fatigue, abrupt
instinctive actions of the will, voluntary concentrations of longer
duration, the finish etc.') The task our experimental subjects were
directed to perform, was too simple and too uniform for such con-
clusions. Similarly our inquiry does not afford reliable evidence
relative to the problem of the working-types. Moreover, the factors
governing the working-process and to whose interference the differ-
ent types owe their existence, lacked scope to display the irinfluence to
the full during the comparatively short period required for our
experiments. Nevertheless some of the above regularities may be
classed with one of the types distinguished by Mrumann from a
quantitative point of view with persistently continued labour Mev-

1) Cf. Rivers und KRAEPELIN: Ueber Ermiidung und Erholung, Psychologische
Arbeiten 1, blz. 636 en 639; LrypLEy: Ueber Arbeit und Ruhe. Ibidem 3, blz.
513; v. Voss: Ueber die Schwankungen der geistigen Arbeitsleistung. lbidem 2.
blz. 399.

1388

MANN Observes: “Vielleicht können wir drei Hauptformen des Arbeits-
verlaufs unterscheiden, indem bei einigen Individuen die Arbeit mit
einer relativ grossen Leistung einsetzt und dann mit mancherlei
Schwankungen allmählich abnimmt, bei einer zweiten Gruppe von
Menschen erreicht die Arbeit erst nach längerer Zeit ihr Maximum,
um dann allmählig abzunehmen, bei einer dritten tritt das Arbeits-
maximum erst gegen das Ende einer längeren Arbeit ein. *) Con-
sidering that not any of the groups of boys and girls worked quickest
in the first period, we could not verify the first type. The fairly-
quick children, with the highest working-rate in the second period,
are no doubt to be classified with tbe second type. Nor can it be
doubted that Mbrumann’s third type is represented by the quick
workers among the boys and the girls that work hardest in the
third period and about equally hard in the first and second, as well
as by the slow girls that work quicker and quicker and by the
slow boys that, in spite of a fair start, begin to slacken a little in
the second period, but still reach their maximum in the third.

With regard to the types of workers we wish to say another word :
With the exception of the eight-year-old boys and girls among the
three categories and all the female subjects among the slow workers,
all the other groups, whichever may be the age of the children,
exhibit a striking constancy in the percentages of increase or decrease
of rate resp. from the first to the second and from the second to
the third. This appeared from a closer inspection of the data in
table IL. The conclusion therefore seems justifiable that the types are
formed after the 8" year and maintain themselves at the very least
until the 12th year. New experiments with older children will have
to show whether or no and if so when the type changes again.
We cannot find ont to what cause the exception of the slow workers
among the girls is to be ascribed.

Lastly we have given in Table III a survey of the mistakes made
in each category in the three periods established for Table I. A
comparison of the values for every group enables us to form an
idea of the changes in the accuracy of working among the three
categories of workers as the work progresses.

The quick workers among the boys and girls of different ages
most often make most mistakes in the third period; only the boys
from 9 to 12 and the girls of 12 years of age make most mistakes
in the second period; for the boys of 9 and the girls of 12 the

1) Vorlesungen zur Einführung in die experimentelle Pädagogik und ihre psycho-
logischen Grundlagen. Il, Leipzig 1913, blz. 389; vgl. ook LII, blz. 51.

1389

TABLE III.
eI Boys Girls Children
Age 8
SL a Quick rinks Slow Eee aati nf ofr fom | ES, peta es pie: | Slow | Quick fens Slow
I 25 28 31 — 23 29 0. (25) 27 31
8 Il 28 38 32 — 41 35 | (28) 38 33
Il 41 34 31 — 36 36 (47) 35 36
|
I 32 26 | 29 = 32 29 (32) 28 29
9 II 35 42 39 -- 38 34 | (35) 4l | 35
Ill 33 32 32 — 30 31 | (33) 31 36
eet en |
| 24 21 28 28 24 31 25 26 34
10 Il 37 38 34 28 42 34 35 40 30
Ill 39 35 38 dt 34 35 40 34 36
OAN ESE zaad len shoo loten aldeas vaan: ti hurt dike le
I ee, 26 31 29 23 28 25 24 29
11 II 38 44 45 33 37 39 36 38 42
HI 40 30 24 38 40 33 39 38 29
| aes
I 29 28 = 32 25 PAT | 31 26 29
12 I] 40 35 — 35 42 31 37 39 36
HI 31 37 — 33 33 36 32 35 35

difference in the percentage of the mistakes is however very small
in the second and the third periods. The smallest number of mistakes
by the quick workers among the boys and girls of all ages is made
in the first period. This phenomenon, which recurs with a single
exception also among the fairly quick and the slow workers of both
sexes, finds an explanation in the fact that the children are still
fresh in the first period and consequently the influence of fatigue
does not yet inhibit the favourable action of the start, the adaptation
and may be also that of practice. That most mistakes are made in
the third period is not surprising when we consider that, as appeared
in our discussion of the data of table I and II, the working rate of
the quick workers is just greatest in the third period and that, as we
stated before, the number of mistakes increases with the working-rate.

1390

The fairly-quick workers of either sex make the largest number
of mistakes in the second period — with the exception of the boys
of 12 and the girls of 11. Fewest mistakes were ever made in the
first period (one exception: the girls of 9). Here again the difference
in the percentage of the mistakes in the third and the second period
is very small, so that we find also for the fairly-quick workers that
the general rule (the number of mistakes increases with the working-
rate) not only holds for the working-time and the total number of
mistakes, but also for the groups into which we have split them
up. The slow workers among the boys and girls form an exception
to this almost general rule. Although they work hardest in the third
period, it is only the boys of 8 and 10, and the girls of 8, 9, and
10 that make most mistakes in this period. The boys of 9 and 11
and the girls of 11 and 12, on the contrary, make most mistakes in
the second period. And whereas the difference in the percentage of
mistakes is mostly small for the second and third period in the
exceptional cases of the other categories, it is here rather consider-
able except for the girls of 12.

The reasons for this deviation among the slow workers we were
not able to detect. Finally it is worth recording that also the slow
workers make fewest mistakes in the first period. Boys of 11 years
form the only exception in the 9 cases of slow workers.

CONCLUSIONS.

1. As regards the quick workers among the boys and girls more
work is done in the last period than in the first and the second;
in the latter two the rate is equal. With years this difference in
the working-rate, which occurs in this category of boys between the
third and the first period, first decreases (from 8 to 10); then it
remains constant. For the quick workers among the girls this differ-
ence increases a little, though not much. from 10—12.

2. The fairly-quick boys always work hardest in the second
period and in the third harder than in the first. The fairly-quick
girls also work hardest in the second period, but in the first harder
than in the third.

3. The slow boys and girls work quickest in the third period,
with the exception of a few. But whereas the boys work quicker
in the first than in the second, just the reverse is the case with
the girls.

4. We agree with Mrumann in distinguishing three principal forms:
“Indem bei einigen Individuen die Arbeit mit einer relativ grossen

1391

Leistung einsetzt und dann mit mancherlei Schwankungen allmahlig
abnimmt, bei einer zweiten Gruppe von Menschen erreicht die Arbeit
erst nach längerer zeit ihr Maximum, um dann allmablig abzunehmen,
bei einer dritten tritt das Arbeitsmaximum erst gegen das Ende
einer längeren zeit ein.” As not a single group of boys or girls
worked quickest in the first period, we could not verify experi-
mentally the occurrence of the first type. To the second type belong
no doubt the fairly-quick children with the greatest working-rate in
the second period, which ends more slowly with the boys than the
girls, but begins stronger with the latter than with the former. No
more can it be doubted but that Mrumann’s third type is represented
by the quick workers among the boys and the girls, that work
hardest in the third period and equally hard in the first and the
third, just as by the slow girls, that work quicker and quicker and
by the slow boys who, in spite of a fair start, begin to slacken a
little in the second period, but nevertheless attain their maximum
in tbe third.

5. After the 8 year the working-type is developed to maintain
itself at the very least till the 12? year. New inquiries with older
children will have to be made to ascertain whether or no, and if
so when, changes will occur still later.

6. The general rule that accuracy decreases with the working-rate
does not only hold good for the working-time and the total number
of mistakes, but also for the groups of the first, the second and the
third period into which we have split them up.

90
Proceedings Royal Acad. Amsterdam. Vol. XXIII.

Physiology. — ‘Concerning Sulphaemoglobinaemia.” By Prof. A. A.
HiJMANS VAN DEN BERGH.

(Communicated at the meeting of March 26, 1921).

The blue colour of the skin and the mucous membranes, called
cyanosis is almost exclusively due to a lowered oxygen, content
of the blood. Occasionally it is brought about by a slight
modification of the blood-pigment into the so-called methaemoglobin,
consequent on poisoning with some substances, such as_ nitrites,
nitrobenzol, anilin-derivatives and the like. We are greatly indebted
to Srokvis and to Tatma') for pointing out to us the fact that
in some cases of intestinal disease poisonous substances formed
in the intestinal canal are resorbed in the blood, and likewise evoke
methaemoglobinaemia with cyanosis. My own researches made in
19057) went to show that in these forms of enterogenous methae-
moglobinaemia nitrites are answerable for the formation of methae-
moglobin from the bloodpigment. In addition, on further investigation
I came across people exhibiting such a cyanosis, which, however,
appeared not to be due to the presence of methaemoglobin but to
a substance that possessed qualities which proved it to be sulphae-
moglobin i.e. the compound formed when allowing small quanta
of sulphuretted hydrogen to act upon haemoglobin. In all these cases
the serum was free from dissolved pigment, so that there was no
haemolysis. Afterwards we met with another form of methaemo-
and sulphaemoglobinaemia®), this time attended ‘with marked haemo-
lysis and most likely caused by anaerobe bacteria. So we know
already three forms of this cyanosis: the septic sulphaemoglobinaemia
with haemolysis; the intraglobular methaemoglobinaemia; and the
intraglobular sulphaemoglobinaemia. We now intend to record some
new researches concerning the intraglobular sulphaemoglobinaemia.

Our own observations together with those of various English physici-

1) Sroxvis, Festschr. f. Leyden, en Ned. Tijdschr. v. Geneesk. 1902, Il, 678.
TALMA, Ned. Tijdschr. v. Geneesk., 1902, II, 721.

2) HijMANs v. D. Ber@H, Deutsch. Arch. f. klin. Mediz. 1905, LX XXIII, 86.
HiyMANS v. D. BERGH en GRUTTERINK, Berlin. klin. Woch. 1906, I.

5) HijMmANs v. D. BERGH, Ned Tijdschr. v. Geneesk. 1918, I. 1774.

1398

ans, notably the contributions of Woop Crarke and HurtreY *) and of
Mackenzie Warris ®) seem to indicate that as a rule this sulphaemo-
globinaemia is presumably owing to a stasis in the large intestine.
That we had indeed to do with the sulphuretted hydrogen-compound
of haemoglobin was evident from the spectrum of the blood in these
conditions, which is quite similar to that of sulphaemoglobin:
besides the two familiar bands of the haemoglobin, a band is also
discernible in the red near 4 617. None of the other substances
examined by us displayed such a spectrum. It appeared moreover
that reducing substances, acting on the blood of these patients, did
not take this band away, whereas the band of the methaemoglobin,
which resembles most the sulphaemoglobin, disappears directly after
the addition of ammonium sulphid or of Srokes’ reagent. Chemically
however we could not demonstrate sulphuretted hydrogen in the
bloodserum. This was all the more surprising because according to
Erten Meymrr’s investigations the chemical methods to demonstrate
H,S are much more sensitive than the spectroscopic. This tallies
with the fact that in cadaveric blood drawn twice 24 hours after
death, sulphuretted hydrogen is chemically demonstrable in the
serum, while spectroscopically nothing might be seen of a sulphae-
moglobin-absorption band.

To my colleague Prof. Lameris I am especially indebted for the
observation of a young patient, who was suffering from an entero-
genous cyanosis due to snlphaemoglobinaemia, and who enabled us
to inspect more narrowly the above-named problem. This boy suffers
from the so-called Hirscusprune’s disease i.e. a marked dilatation
of the colon, existing from birth, and in large measure obstructed
defecation. The investigations, which I purpose to record here
have for the major portion been conducted by Dr. ENGELKrs.
In co-operation with him [ have tried to set at rest the above ques-
tion. To begin with it appeared that the boy’s blood presented a
marked sulfo-band. We could contirm the phenomenon detected by
West and CLARKE *®) that, in sulphaemoglobinaemia, on passing pure
carbon monoxid in a solution of sulphaemoglobin, the band in the
red is shifted 5 wavelengths to the right. In addition we could
superadd a new reaction on sulphaemoglobin to the previous one.
If namely a drop of a 1°/, sol. of potassium cyanid is added to a
sol. of SHb, the sulfo-band will persist at room-temperature for a
long time; the MHb-band disappears directly. Addition of a very

1) Woop CLARKE and Hurttey, Journ. Physiol. 1907, XXXVI, 62.

2) Mackenzie WALLIS, the Quarterly Journal of Medicine, 1913, VII, 73.
8) West and Woop CLARKE, Lancet, 1907, I, 272.

90*

1394

large quantity of a concentrated potassinm-cyanid solution also makes
the sulfo-band disappear, but then only after some minutes. If to an
SHb-solution an equal volume of a 1 °/, solution of CNK is added,
at a temperature of 37° the S-band disappears only after three hours.

By passing a current of CO, through a little serum from the boy
and collecting this in a solution of lead-acetate or even in the sen-
sitive reagent of Caro-FiscHpr we again failed to demonstrate sul-
phuretted hydrogen in the serum.

This induced us to discontinue the chemical tests with sulphuretted
hydrogen in the serum, and try another method. With due caution
to ensure sterility we allowed serum to act at 37° on a normal
haemoglobin solution. It then appeared that in the majority of the
tests a little sulphaemoglobin had been formed from the normal
haemoglobin after a sojourn of 2 X 24 hours in the incubator.
Now the idea suggested itself whether the serum might contain
bacteria to which the formation of sulphaemoglobin could be ascribed.
This idea had already occurred to GrBson *) regarding methaemoglo-
binaemia and, indeed, this author achieved a positive result. Later
experimenters, however, could not confirm it. A bacteriological
examination of our patient’s blood, carried out by Mr. ScHaar also
showed it to be sterile.

We now allowed very small quanta of hydrogen sulphid to act
upon normal haemoglobin-solutions; this yielded the sulphoband in
the incubator at 37° only after a good deal of time (24 hours), the
same result as had generally been obtained in the action of serum
from our patient on normal haemoglobin-solution. We were justified
in concluding from this fact, that small amounts of sulphuretted
hydrogen must be contained in the serum. Supposing that by passing
a current of carbon dioxid, too much of the small amounts of hydrogen
sulphid would get lost to recover the rest, we resolved to react
directly on the serum. Lead-salts did not answer our purpose as
they precipitate protein, which tampered with our result. Various
technical circumstances prevented us for the time from applying the
most sensitive reagent of Caro-Fiscurr. We then had recourse to
the reagent of Kran, consisting of a weak nitro-prussid-sodium
solution in a soda-alkaline or ammoniacal environment. When
adding such a solution to a solution containing a trace of hydrogen
sulphid, a beautiful red, violet-tinged coloration comes forth. This
reaction is believed to be less sensitive than the two others, never-
theless we obtained pronounced results, when we applied it as a

1) GiBson and DouerLas, Lancet, 1906, II. 72.

1395

ring-test on the patient’s serum. In that case the reaction was always
positive, so that in this way the presence of hydrogen sulphid in
the serum was established chemically. To make assurance double
sure possible sources of error had to be precluded. For acetone and
kreatinin also give a coloration with nitroprussid in ammoniacal
solution. We detected, however, that, as regards acetone, this reaction
turns out negative for a multiple of the largest possible quantities
occurring in the bloodserum. A negative result was likewise obtained
for two patients with pronounced acetonuria (diabetes). Similarly
kreatinin yields with this reagent a positive result only in a multiple
concentration of the largest possible quantities occurring in the serum.
Moreover the colour of the kreatinin-ring differs widely from that
of the hydrogen sulphid ring. Finally we have examined in the
same way the serum of a certain number of normal persons. The
result was negative.

In order to get more certainty that it was sulphaemoglobin we
had detected, we proceeded as follows. A little of the patient’s blood
was collected in a physiological common-salt solution and washed
out with it repeatedly, so that all the serum was removed. The
spectrum of the red bloodcorpuscles appeared to have retained the
sulpho-band, while the pipetted liquid did not yield a reaction with
Krat’s reagent.

We now added to a mixture of red bloodeorpuseles and physio-
logical saltsolution a little of a 2°/, potassium cyanid solution (neu-
tralized and in physiological NaCl solution to prevent haemolysis).
The mixture was placed some time in the incubator. After some
hours the HCN had expelled the H,S; the SHb-spectrum had made
room for that of CyHb and in the supernatant fluid we obtained a
positive reaction with nitroprussid *).

It would seem, then, that hereby the presence of H,S, be it only
in small quantities, in the serum as well as in the blood-pigment
of our patient, had been established.

Earlier experiments of Craupe BERNARD have demonstrated that
hydrogen sulphid injected intravenously into animals, is exhaled
through the lungs. Although, comparatively speaking the quantities
of H,S in the blood of our patient are not inconsiderable, we
did not succeed in demonstrating in this simple manner H,S in
the exhaled air. We did get a positive result, however, when the
boy had been breathing for + one hour in a specially contrived

1) When prosecuting our investigation we found this phenomenon to be of a
more complex nature than can be anticipated from the description given in this
paper.

1396

apparatus. Of course we endeavoured to preclude errors by control-
experiments with normal subjects and by taking due Measures.

It proved possible to determine the amount of Hb which is con-
verted to SHb. This determination is based on the now generally
received conception that haemoglobin is a well-defined substance
that contains to each molecule one atom of iron.

In a closed vessel supplied with pure oxygen, haemoglobin takes
up a constant amount of oxygen. The amount of iron in a given
quantity of haemoglobin and its loosely combined oxygen in an
environment of pure oxygen is constant: 2 atoms of O to 1 atom
of Fe, which is expressed in volumina: 401 ce of oxygen to one
gram of iron. The derivatives of the red blood-pigment, the methhb.,
the sulphhb., the cyanhb., the baematin are assumed not to take up
any oxygen from a gas-mixture. If, therefore, blood that contains
besides oxyhb., also SHb is brought into contact with an atmos-
phere of pure oxygen and the amount of loosely combined oxygen
and of iron is determined, the amount of the converted Hb may
be calculated from the difference between the known ratio of Fe:O
and of a pure OHb solution under the same conditions (401 : 1).

Now, Barcrort’s method affords a rather simple way to perform
an accurate gas-analysis of the blood, while the titanium method is
quite adapted for the iron-determination in this liquid. Dr. ENGrLKrs
used them in investigating the blood of our patient. It became evident
that the quantity of converted Hb varied at different times, as had
already been made out spectroscopically.

Once we found a quantity of converted Hb of 19°/,, another
time of 12.5 °/,.

In these inquiries the clinician meets with an impediment in that,
as a matter of course, he can work only with minimal quantities
and cannot often repeat an experiment. The field of research is
widened considerably when experimenting with animals. This
proved possible. At the outset of our investigation when we
had not yet succeeded in demonstrating chemically the presence
of H,S in the serum, we have injeeted intravenously some
of that serum into rabbits. To our great surprise we found already
after an hour in the blood of one of these rabbits a rather large
quantity of SHb. It was not necessary to look for the cause of this
surprisingly rapid action of such small amounts of the serum upon
rabbit’s blood, for on closer inspection we were still more surprised
at detecting in the blood of some perfectly healthy, fresh rabbits a
physiological amount of SHb which was distinetly demonstrable by
the spectroscope. We have subsequently examined about 26 rabbits.

1397

In 4 of them we found comperatively much SHb., in 13 a
small quantity and in 9 none at all. A quantitative determination
by gas-analysis and a Fe-determination in a rabbit with marked
S-band yielded the result:

aorta-blood . . . .°10:5-°/,.
vena-porta blood 12.5 °/,.

Now let us revert to the original question, why in the serum from
our patients (and the same will be the case with rabbits) so little
H,S is found with a more or less marked S-band., whereas in cadav-
eric blood the opposite ratio reveals itself. In my opinion this should
be interpreted as follows; the H,S that is taken up from the colon
by the blood, is first distributed over corpuscles and serum. In the
corpuscles it forms a solid compound, SHb, which does not dissociate,
consequently it does not give off H,S in the lungs. [t is most likely
destroyed slowly and removed from the blood, presumably together
with the remaining Hb-molecule. It is quite different with the H,S
in the plasma, which is there combined with alkali in solution.
Soon an equilibrium will be established between the gases dissolved
in the serum and those of the alveolar air, and since the alveolar air
is constantly refreshed by respiration and the atmospherical air does
practically not contain H,S, the H,S dissolved in the plasma will escape
from it. In serum or tissues part of it will be destroyed by oxydation.
Thus, in consequence of this process and of the respiration the serum
will, with the exception of a few traces only, be liberated from H,S. In
cadaveric blood more and more of H,S is taken up by the blood as
putrefaction progresses. Here again H,S is distributed over corpuscles
and serum. But respiration and oxydation are absent, the blood is
locked up in the vessels, so the dissolved H,S is not withdrawn
from the liquid. The quantities of H,S dissolved in the serum are
large enough to be demonstrated by the sensitive chemical reaction.
At the cadaveric temperature the quantity does not suffice to convert
Hb into SHb within a given lapse of time. With progressing putre-
faction and longer duration of the action the Shb-spectrum will
reveal itself.

In the course of our inquiry we saw three more patients, in
whom we noted marked Shb-aemie, consequent on a slowed
passage of the contents of the colon. The fact that sulphaemo-
globinaemia proved to be of more frequent occurrence than we had
originally supposed, and especially the otber fact that this blood
anomaly to a certain percentage, occurs in otherwise healthy rabbits,
enhance the significance of the results recorded in this paper.

1398

For it is really surprising that, with men in pathological and with
animals even in physiological condition, a substance is taken up by
the blood from the intestinal canal to the amount of 20°/,, which
is poisonous for the central nervous system, and which, by combining
with the respiratory pigment: renders part of it worthless.

The investigations described above do not yield conclusive evidence
for the Shb-aemia in patients with slowed progress of the contents
of the colon. We have been impressed with the idea that in patients
in whom there was an impediment in the advance of the intestinal
content, cyanosis was evolved in a comparatively short time —
almost rather abruptly. It still, looks as if another hitherto
unknown factor besides the resorption of H,S from the gut,
is instrumental to the origin of Shb-aemia. Whether this factor be
the presence of reducing substances, as Mackrnziz-Wattis concludes
from his interesting inquiry, will have to be made out by further
experiments. We were not so fortunate as to demonstrate such
reducing substances in the serum. Likewise the question whether
SHb-aemia occurs perhaps more frequently than spectrosopic exami-
nation could make out up to the present day, must be left for
subsequent investigation. In our judgment this spectroscopic result
cannot be achieved before about 10°/, of OHb have been converted
to SHb.

Mathematics. — “Bestimmung der Klassenzahl aller Unterkörper
des Kreiskörpers der m-ten Hinheitswurzeln.” (Verbesserung.)
By N. G. W.H. Bereer. (Communicated by Prof. W. Kapteyn.)

(Communicated at the meeting of November 26, 1921).

Anstatt von 4. § 4 meines Beitrages in diesen “Proceedings”
(Vol. XXII, S. 331 und 395) lese man Folgendes:

4. Der Grad der gemeinschaftliche Untergruppe, von g und der
Zerlegungsgruppe von /,, ist gleich d,d', wenn d, der gröszte ge-
meinschaftliche Teiler aller Zahlen 6;, bedeutet und d', der gröszte
gemeinschaftliche Teiler von f, mit den Summen:

4 pao bon + 2p (oe) eet + oet En Ne, p
2 n gh #7 Be n { 1 Pi
wo n nur die Werte durchlauft für welche bi, — 0 ist. Die Expo-
nenten ai sind bestimmt durch die Congruenz
lL +n a == A, "A “A,™.... (mod m)
2
wabrend die Zahl im linken Gliede in Satz 5 definirt ist.

Beweis: Die Substitutionen der Zerlegungsgruppe entstehen durch
Multiplizieren der Trägheitsgruppe (Satz 4) mit der zyklischen Gruppe
aus Satz 5. Aus Satz 4 ergibt sich dasz die Substitutionen der
Trägheitsgruppe gebildet werden von den Resten der Potenzen A,/
(mod m) worin y gewisze Zahlenwerte hat; die Substitutionen der
Zerlegungsgruppe werden gebildet von den /, ersten Potenzen der
linken Gliedes obenstehender Congruenz. Die Substitution der Zerle-
gungsgruppe
Ate A** AS APP... (mod m)
wird also dann und nur dann eine Substitution der Gruppe g sein,
wenn für jedes System der b die Congruenz

m me m
£9 a0 bon + 24 (Ge) a, ta +9 (75) ube + 0 (75) en eben + .
= 0 (mod p).
gilt. Wir müszen also die Anzahl der Zahlensysteme «, y bestimmen,
welche diesen Congruenzen geniige leisten.
Es folgt aus der Definition der Zahl f, und der Exponenten a;:

fa, = 0 (mod 2); J, % = 0 (mod 3 p‚); gras C4 mod Gye st 1s

1400

Die Summen

2 m m
ve (: p ao bon + 24 € a, ban + p & hann en A

worin ” alle Zahlenwerte hat für welchen 5, =O ist, sind daher

: Pre ;
teilbar durch y, und da e‚f, = — ist, werden die Summen
fy

m me
5 paobon + 2p (5) a, ben + Pp 6 a2 ban + «.
2

durch e, ~, teilbar sein.
Die Congruenzen nehmen daher die foleende Form an:
m m
$ Pb, +29 (2s, eb sE a) band
eg, | : + frybin=0 (mod fp). (1)

é, fy

Es ist OC af, und OC y<*, und es ist erlaubt die ganze
Zahlen welche durch die gebrochene Form dargestellt werden, durch
ihre Reste (mod f,) zu ersetzen. Der Modul der Congruenzen (1) ist
das Product der Anzahlen der Wertevorrate /, fiir x und g, für
y; die Coefficienten der Unbekannten 2 und y, in diesen Congruenzen,
bilden eine Gruppe im additieven Sinne. Die Congruenzen sind daher
derselben Art wie (3) Seite 337 aber jetzt mit nur zwei Unbekann-
ten. Nach der Bemerkung am Ende des § 3 ist die Anzahl der
Lösungen (2, y) also gleich das Quotient der Zahl f, ~, und der
Zahl der Coefficientensysteme. Wir haben nun diese letzte Zahl zu

bestimmen. Die Anzahl der verschiedenen Werte von bi, ist ee

d,
Zu den Zahlen bi, = 0 gehören ue verschiedenen Werte der Bruch-
1

form von (1) Der Wert 6;,=0 musz daher gleichviel Mal vorkom-

¢ 5 p
men und darum werden die übrige — —1 andere Werte der bi»

d,
q
auch soviel Mal auftreten. Es gibt also a Coefficientensysteme.
i 1
Die Anzahl der Lösungen von (1) ist daher
pf
a fi : re ee d',.

Weiter fiige man Folgendes an dem Beweise des Satzes 10 auf
Seite 396 zu, und lasse die letzten 12 Zeilen dieser Seite fort.
Auszerdem geniigen die gesuchten Stellen der 5 noch den Con-

1401

gruenzen, welche man bekommt wenn man in (8) die Systeme der
a durch ihre Vielfache ersetzt. Man wird aber dann auch Systeme
der a bekommen, die schon unter die Vorigen vorkommen. Der
kleinste Wert von wz für welchen

m m m p
ig aa x ao bon +2 Shae Ih an bin +g > Aus la & agbe,+...=0 mod —
h of, nn p,

ist, ist L Nimmt man also für « die Zahlen 0, 1, 2,.. oe —
d', d,
so sind die Systeme za,, za, aa,,...... alle von den vorigen ver-

schieden, weil diese letzten eben diejenige sind welche den Con-
gruenzen

m m
bp ao bon + 2yp i a, bun + P ra aa ben +... == 0 (mod g)
2

genügen wenn n nur die Zahlenwerte hat fiir welche bj, — 0 ist.
Die Totalanzahl der Systeme der a die man in (8) beriicksichtigen
musz, ist also

grenen
et ER Sk
und daher die Anzahl der gesuchten Systeme der 5:
oe shirt dd,
gy, dd, ER
Weiter folge man den Beweis auf Seite 397 dritte Zeile.

Physics. — “The Propagation of Light in Moving, Transparent,
Solid Substances”. II. Measurements on the Fizeau- Effect
in Flint Glass. By Prof. P. Zerman, W. pr Groot, Miss
A. Sneranace and G. C. Dipperz.

(Communicated at the meeting of April 23, 1920.)

More accurate than the results obtained with quartz, an account
of which was given in communication II’); are those of the Fizeau-
effect in moving flint glass.

Six cylindric rods of a length of 20 em. and a circular cross-
section of a diameter of 25 mm. were made for us by the firm
Zeiss at Jena. The kind of glass is the ordinary silicate flint glass
of the type 0.103 of the firm Scrorr und GeNosseN. The endplanes
are plane-parallel in close approximation. The clearness of the inter-
ference fringes appeared to be excellent with stationary glass column,
while, when the necessary precautions were taken, also when the
column was in rapid motion, the fringes remained still very good.
The photos taken were much better than those that had been obtained
before (Il) with quartz. This is partly owing to the excellent
material °), to the greater cross-sections of the rods (now 25 mm.
as against 15 mm. before for quartz), and to the smaller number
of internal reflections *). It appeared finally possible to observe also
the Fizeau-effect for moving flint glass directly in a telescope, as
clearly as it is possible for moving water, and we had the privilege
to demonstrate the effect before several physicists.

The perfect sureness with which the rather complicated apparatus
worked at last, was not obtained until some improvements had been
made in the arrangement as it had been used for quartz. We will
discuss the principal of them.

2. Through different causes the interference fringes can take an
oblique position during the movement of the column of glass cylin-
ders. It is, however, necessary that the fringes remain parallel to

1) These Proc. Vol. XXII, N°. 6, p. 512.
*) Compare II, 2.

1403

the horizontal or vertical cross-lines. Else no photos are obtained
on which measurements can be made.

Already in the experiments with quartz-a compensator was inserted
in one of the interfering beams of light, consisting of a plane-parallel
circular glass plate of a thickness of 5 mm. and a diameter of 25
mm., to which every desired position could be given. The inclina-
tion of the interference fringes can be modified by rotation round
a horizontal axis; a simple arrangement was, therefore, applied
through which the observer, sitting at the eye-piece of the telescope,
could bring about the desired rotation. Besides a plane-parallel plate
was placed before the object glass of the telescope im such a way
that an image of the interference fringes could be observed in a
small telescope placed on one side, while at the same time after
removal of the eye-glass a photo of the fringes was made with the
large telescope. Thus the observer at the small telescope could at
once observe an error in the position of the fringes, and if neces-
sary, redress it during the photographing. This proved to be but
rarely necessary when an experiment had been properly prepared.

3. As was set forth before (I, 4), it was necessary to superpose
20 to 30 photographs of the interference fringes, each with an
exposure of a hundredth second, because otherwise the photographic
image was too faint. This number could be greatly reduced by
working without filters, hence directly with the white arc-light.

Diminution of the number of exposures increases the sharpness
of the photos, and renders it possible to take more in succession,
before the disturbances through fluctuations of the temperature in
the glass-rods, which inevitably occur in consequence of the move-
ment of the apparatus, become troublesome.

For the interpretation of the photo obtained it is then necessary
to know what is the effective wave-length À of the white arc-light,
with which the fringes have been photographed.

The accuracy in the determination of 4 need not be very great,
as will appear presently (see 5).

4. Determination of the effective wave-length of the light used.

The effective wave-length of the operative light, had to be
measured after it had left the last mirror of the interferometer, and
of course for that kind of plates that was used in the experiments.

The beam from the interferometer was focussed with a cylinder
lens on the slit of the collimator of a Hircer spectroscope with

1404

constant deviation, from which the prism had been removed, and
replaced by a small totally reflecting prism.

By placing a grating replica before the object glass of the photo-
graphic camera, a spectrum of the source of light could be
photographed.

The most active part in this spectrum could be made directly
visible by putting a wedge of smoked glass with the side horizontal
before the slit of the collimator (KeNNern Mers method).

The prismatic action of the wedge was counteracted by a second
wedge of clear glass.

The result for the effective wave-length 4 was 4750 A°, with an
uncertainty of + 25 A°. |

5. This accuracy is, however, sufficient. This can be verified by
numerical calculation, or by the following consideration.
We know (II, 9) that the optical effect is given by the formula:

4 bw du
Ra tE a ;

1 dA
By deriving from this the value of md we can see how great
the influence is of an error in the determination of the effective
wave-length on the calculated effect.
Instead of 2 we introduce the frequency », which brings about a
du

slight simplication, and we put p=w—1-+pv ae Then:
v
1dA 1 dy. 1 ;
Ad” p.v dv anaf 6)

Now:

dp du d'u
zz yv ;
dv dv dy?

for which we may write in approximation :
d d
De
dv dv
because u depends almost linearly on v.
Equation (2) then becomes:

1405

d,
poe :p becomes about % for the ordinary flint glass, so that:

dv
1 dA 1 3)
nem
6 dA
For 4 = 5000 A°, da = 25 A° becomes Te aig

6. Ribbon-shutter. The shutter which acts periodically and is
worked electromagnetically, described in I, 4, repeatedly gave cause
for disappointment, because it was never certain that the light was
transmitted at the very moment that the cradle passes a chosen
point of the path.

This is perfectly certain with the ribbon-shutter, which is dia-
grammatically represented in fig. 1.

Fig. 1.

A band of ribbon Z of lancaster linen is clasped between two
blocks B, which are firmly fastened at a chosen place of the bed
of the apparatus. It is passed round the beam with the glass column.
The beam can execute its usual movement to and fro without being
hindered by the ribbon, for this can easily slide over the copper
pieces K, the length of the ribbon remaining constant. There have
been made two openings in the ribbon of 10 or 15 em., which at
a certain position of the beam, but only then, allow the light to
pass through circular holes in the pieces A, and during the time
that corresponds with the length of the openings in the ribbon. By
displacing BBS along the bed, the moment at which the light is trans-
mitted, may be chosen. The edges of the ribbon are provided with
a hem to obtain greater firmness, and prevent fraying.

The copper pieces A are smoothly polished, and the friction of
the ribbon is therefore very slight. Sometimes it was still diminished
by some tale-powder.

The electric shutter, which was used in the experiments described
in II, was now used after a small modification to admit the light
only in one of the movements to and fro of the beam. For this
purpose the movable arm is placed before the arc-lamp. The phase

1406

is adjusted so that the arm turns when the beam has just passed
the middle of its course.

7. Improvement of the Velocity Measurement. In the experiments
with quartz rods the velocity was measured directly according to a
method which has been described in II, § 11. We have made this
method simpler and more delicate, and also arranged it so that the
velocity could be immediately read in every experiment.

In main lines the arrangement is still the same as represented
in Il § 11. The sereen with two slits S, and S, used formerly was
however, replaced by a screen S (cf. figure of the preceding §), the
construction of which will be further explained by referring to figure 2.

Fig. 2.

Our earlier slit S, is replaced by a glass scale, slit S, by a small
aperture. ° :

The graduated glass scale was obtained by covering a glass plate
with a soot-layer, and by drawing by the aid of a chisel of the
width of exactly 1 mm., five lines in the soot-layer at mutual
distances of exactly 1 mm.

Then the soot-layer was fixed with a drop of varnish, and the
first line was covered with red glass, the others with blue glass.
All this was cemented on the beam. In fig. 2 the alternate long
and short lines are indicated under S; the colours render errors of
front and back in the observation through lenses impossible. In the
figure the lines are partially dotted, as they are half covered by a
screen, which can slide to and fro. During the movement of the
beam in one sense the lower, during the movement in opposite
sense the upper half of the scale is automatically covered through
the inertia of the screen. The blocks B, and B, define the extreme
positions of the screen.

As we said, our former slit S, has been replaced by the scale
with the coloured lines; instead of the slit S, there are two fine

1407

apertures P, and P, on either side of a horizontal line through the
middle of the scale. In the position drawn in the figure the light
can leave through P,, because the opening VU, in the moving screen
allows this. When the screen rests against 6,, P, is covered, and
O, comes in the position, in which it is possible that light is emitted
through P,.

As was explained in II § 11 an image of the slit arrangement is
projected on the rotating disc , which is provided with radial slits.
With a weakly magnifying telescope the image projected on the
rotating dise is observed with intervals of 0,001 sec. In this time
the beam moves about 1 cm. at the velocity used in the neigh-
bourhood of 10 M/,... The observer sees the coloured scale S in the
field of vision, and then the “star” P,, or rather the after-image of
the light emitted by this star at a former transmission. The place
of the star on the scale can be read accurately down to $ mm.,
and the distance from P, to S being about 50 mm., the velocity
can be determined certainly accurately down to 1°/,. All the changes
in the velocity of the beam are immediately visible, and the velocity
corresponding to every photo taken can at once be noted down.

It is necessary that the “star” moves at the same level at which
the axis of the rotating disc has been placed, for else a small cor-
rection must still be applied to the velocity.

Thanks are due to Mr. W. M. Kok, assistant at the Physical
Laboratory, for his valuable help in the execution of the arrange-
meni for the velocity measurement.

8. Results. The extreme values of the velocity which were directly
measured in our experiments, were 918 and 994 cm/sec.

There were made two series of measurements, which were dis-
tinguished by the way in which the velocity was found. In the
first series, A, the method of communication II, in the second, B,
that described above in § 7, was followed. All the results for the
effect were reduced to a velocity of 1000 cm./sec.

Series A.

When the measurements of the 34 separate photos obtained on
11 plates are combined, the effect is found to be 0.247 + 0,006.

When first the observations on each plate are combined, and the
mean is taken of the results of 11 plates, the effect is found to be
0,247 + 0,009.

Series B.

gives for the effect derived from 49 observations divided over
13 plates 0,238 + 0,006, for the effect derived from the mean of
the results of the 13 plates 0,240 + 0,008.

91

Proceedings Royal Acad. Amsterdam. Vol. XXIII.

1408

Finally all the 83 observations may be combined; then 0,242
+ 0,004 is found.

When a result is calculated for each of the 24 plates separately,
and then the mean is taken, the effect is found to be 0,243 + 0,006.

The number after the + sign indicates the mean error, and as
was stated before all the results have been reduced to the velocity
1000 cm./sec.

Theoretical value of the effect for flint-glass.

The firm ScHorr und GenossEN, Jena, gives the following indices
of refraction for the flint-glass 0.103 used :

wa’ = 1.6099 417677 A°
he == 10193 6563
up’ = 1.6202 5893
up = 1.6324 4862

" ugi= 6428 4341

The effect can be calculated according to the formula derived
before (Il, 9)

l
By the aid of the given data, values for u and = are derived

for the effective wave-length 4750. The final result is:

ee 4.120. 1000
~ 4750 x 10-8 x 3.1010

This value is almost in perfect agreement with the value
yielded by our experiments.

It is of interest to note that the dispersion term contributes to
the value of the effect — 0,242 by an amount of 0,028.

If the dispersion had not been taken into account, 0,214 would
have been found for the effect, which is incompatible with the
experiments.

(1, 6834—1 + 0,084) = 0,242,

APPENDIX.

1. The publication of the above communication, which was already
laid before the meeting of the Academy of April 23rd 1920, has
been delayed through particular circumstances.

This affords me an opportunity to add a few remarks to the paper.

Our collaborator, Mr. W. pr Groot, phil. docts. orally informed
me of another derivation of the formula for the optical effect (II, 9),

1409

and independent of this at about the same time Prof. F. ZeRNIKE
at Groningen did the same in a letter dated November 11% 1919.
The short, elementary derivation, which in the two communications
is founded on the same idea, will follow here.

In principle the experiment with the moving glass rod can be
classed under the following scheme (fig. 3). From the source of

Fig. 3.

light L issue two beams of light, one through the glass ad, the other
through the air. With the aid of the necessary devices the phases
1 and 2 are compared in two cases, first when the glass ab is at
rest, secondly when it moves e.g. to the left with the velocity w
According to the principle of relativity the glass may as well beat
rest, and the room with the other parts may be made to move to
the right with the velocity w. Whether 1 and 2 are received with
a moving or a stationary apparatus, makes no difference in the
relative phase of the beams of light. Therefore only Z is made to
move to the right with the relative velocity w, and approaches the
glass rod. This only gives a Doppuer effect equal for the two beams,

; pad cs w
in which the wave-length varies from A to 4A—2—. When every-
:

thing is at rest, the phase-difference between 1 and 2 is CEE
A
when / is the length of the glass rod aé.

Hence the change due to the movement is:

_(—})! mS _ wl du
- dì + —-—di= —_l—À—
a + A rite Den dh

To get the total effect the formula should be multiplied by 4 —
i.e. a factor 2 for the movement to and fro of the rays, and a
factor 2 on account of the reversal of the direction of the move-
ment — so that the formula given before, appears.

Also Fizrau’s experiment with the moving water and stationary
glass end-plates may be treated by the method sketched above, but
then the calculation is not so simple. .

Mr. Zernikk still points out that an actual experiment might be
taken with the two beams of light running in opposite directions
and stationary glass rod, as is supposed in the calculation. It would

91*

1410

then only be required in the experiment described before to make
the glass prism slide to and fro, and keep the glass rod at rest.
For different optical and mechanical reasons the execution seems to
me attended with greater difficulties than the experiment made.

2. In a letter of October 22nd 1919 Prof. M. von Lave had the
kindness to draw my attention to a thesis for the doctorate of
P. Harress of 1912), which he sent me, and in which a subject
is treated closely related to our investigations. In Harrrss’s experiment
the light runs to the right and to the left in a cycle of glass prisms,
which as a whole is in rotatory motion.

The comparison of the observed displacement of the interference-
fringes and the theory elaborated by Harress gave a very unsatis-
factory agreement. This is chiefly owing to the theory, in which
the absolute and the relative velocity of the light are mixed up.
Von Lave has redressed this error, which greatly improves the
agreement between theory and observation. Harrgss’s experiment
closely resembles SaGnac’s experiment of 1913, of which, very
remarkably, von Laur gave the relativistic theory already in 1911 *).

In Sagnac’s and Harruss’s experiments the displacement A of the
interference fringes expressed as fraction of their distances is:

in which / is the length of the path passed over in the rotating
apparatus, 7 the distance of this to the axis of rotation, w the angular
velocity, the sum extended to all the different paths.

Index of refraction and dispersion do not occur in this formula,
which in itself is already a difference with our experiments.

It seems unnecessary to enter into a fuller discussion of HarrEss’s
work, as in an interesting paper by von Laur®) the experiments by
Fizeau, Sacnac, Harress, and those made by us are discussed and
compared, and as with exclusion of the influence of the dispersion
the two last-mentioned experiments have also already been treated
in the fourth edition of von Lauw’s Relativitatstheorie *).

3. I pointed out on an earlier occasion that it might be interesting

d
to examine substances in which “ is great.

1) Re-edited in O. Knorr, Ann. d. Phys. 62, 389, 1920.
2) Miinchener Sitz. Ber. 1911, 404.

5) Von Lave, Ann. d. Phys. 62, 448, 1920.

4) Cf, p. 23, 25, 185—189.

1411

In particular substances with strong absorption-bands or lines
deserve attention, such as didymiwm compounds, which can be
obtained as solid solutions in glass, and the vapour of sodium.

When these substances are chosen to work with, horizontal
interference lines must be thrown on the slit of the spectroscope.
Horizontal lines are observed in the telescope, which diminish in
distance from red to violet. Through the Fizrav-effect the lines
would move up and down in case of rapid motion to and fro of
selectively absorbing substances, and at those places in the spectrum

d,
where = assumes large values the amplitude of the movement might

become considerable.
From preliminary experiments on the dispersion of didymium glass
at the ordinary temperature. and at that of liquid air it appeared

d
that the value of En assumes nowhere great values in the visible

spectrum. Though rods of didymium glass of excellent quality are
to be had, I am yet of opinion that it would not be worth the
trouble to make experiments with them on the Fizrav-effect.

Nor can results on the Fizeav-effect be expected with sodium

i d
vapour. Close to the absorption D-lines = can, indeed, become very

great, but at the most interesting place near the D-lines the absorption
too becomes very great. On continuation of the experiments it might
perhaps have deserved recommendation to work with a stationary
tube with sodium vapour and moving prism (see $ 1 of this appendix).
It appeared however, clearly enough from some experiments that
the observation of the Fizrav-effect with sodium vapour was out of
the question.

Though these experiments did not yield the result for which they
were undertaken, they gave occasion to the observation of an
interesting interference phenomenon in sodium vapour, about which

a separate communication will shortly follow *).
Py oe

1) This communication has been published already. These Proceedings Vol. 24,
p. 206, 1922.

Physics. — “Motion relativated by means of a hypothesis of A. Förrr”.
By H. Zanstra. (Communicated by Prof. P. Enarenrusr).

(Communicated at the meeting of March 26, 1921).

§ 1. The fixation of “inertial systems” in classical mechanics without
applying the principle of absolute motion.

It is well known that in the equations of motion of classical
mechanics for a system of 7 material points:

ey my, = ¥; ee ees EE
WS Lek et n.)
the position of those points is referred to a rectangular system of
co-ordinates being at rest or moving uniformly in absolute space.
But when we refer this position to another system of axes that
does not move uniformly or rotates with respect to the above
mentioned systems, the differential equation of motion assumes a
more complicated form. E.g. if the system of axes has an absolute
rotation, it is well known that we get on the left side of equation
(1) terms of the type of centrifugal and Coriolis forces.

Those systems of co-ordinates in which the equation of motion
assumes the simplest form (1), the so-called ‘‘inertial systems” *),
are consequently defined by means of the idea of absolute space.
This idea, introduced by Newton, was at first retained in the later
elaboration of Newron’s mechanics. Newton’s contemporary BERKELEY
however already gave a criticism of this principle of absolute motion
(motion in “absolute space’). The purport of his demonstration is
that motion of bodies must be referred to other bodies and not to
an absolute space *).

In more recent times (+ 1870) this question was taken up again,
especially by C. Neumann, LANGE and Macu *). While NruMANN still

) The idea of “inertial systems” was introduced by LAnGE he calls them
“Inertialsysteme’’.

*) G. BERKELEY. The Principles of Human Knowledge, section 111. e.v.

3) E. Macn. Die Mechanik in ihrer-Entwickelung. As for LANGE and NEUMANN
see § 5. Literature is mentioned in the Enzyklopedie der Math. Wiss. VI 1,
p. 30. See moreover H. SEELIGER. Ueber die sogenannte absolute Bewegung.
Sitzungsber. der Math. Phys. Klasse der Bayr. Ac. der Wiss. 1906. Bd. 36, p. 85.

1413

supported the idea of absolute motion, later criticism led to the
general conviction that motion is relative. The latter being assumed,
we have the following two problems:

1. How can inertial systems be fixed without the aid of an
“absolute space”.

2. Which are, according to this, the equations of motion of
mechanics, if we require that absolute co-ordinates do no more
occur in them, but exclusively relative co-ordinates (that fix the
place of the material points with respect to each other) and their
derivatives.

FörpL gave a solution of the first problem, which shall be treated
in the next $ *). In connection with this we shall give in § 4 a
solution of the second problem. Here already can be remarked that
this solution is quite different from the one given by the theory of:
EINSTEIN, in § 5 we return to this.

2. The hypothesis of A. Forr.*), by which special inertial
systems are fined.

From here we will deal with motion in plane instead of space,
for the sake of simplicity ®).

With FörpL we assume that the total matter in space consists of
a finite number n of material points. For the co-ordinates 2’, y’ in
an inertial system we then have the equations:

m, w'y = X,. my,=Y EEN IE €)
wle)

We suppose further that for the quantities on the right side
(components of force) the law of reciprocal action holds:

Be Ol es a. as ne). | (Ba)
SED ES et 2)

The sign = includes all x points. This is the case e.g. if the points
apply forces upon each other in the direction of the lines that
join them.

From (2), (8a) and (36) follows:

1) Some short critical remarks on this and some other solutions shall be
given in § 5.

*) A. Förrr. Vorlesungen über technische Mechanik. VI. Erster Abschnitt.
Die relative Bewegung.

3) For space we have a quite analogic reasoning. Then the use of vectors
can be recommended, :

1414

Eme=0 Smy=0 5 do)

Em (ey — y' al) =0 HOLWOHOL dav gn (4D)
and after integration:

Eme'=1, Smy=T, . Pi BIT Da)
Emile er dd Rise verde mets al GB

the 3 constants 7’, 7, and AR still being quite arbitrary. In analogie
way we get in space 6 constants 7, 7, 7, R,, R‚‚ R,. Itis always
possible to choose an inertial system in this way that 3 of these 6
quantities vanish, more of them cannot vanish without a special
hypothesis.

The hypothesis of Förer is:

There are inertial systems, for which all six constants T,, T,, T,,
RR, R, vanish together.

Consequently for the plane:

Dea) Ae a END ae ee ERN
or also, after (Sa) and (56):

Sme'=—0 Emy =0. Ste rn enden Me Ale

ES mey — ya!) =0 zE Krin vpieh et ee alb)

To these special inertial systems belong also those for which
moreover = mx’ =O and: 2 my’ =O, the origin thus coinciding
permanently with the centre of gravity of the system of points,
such a system is called by Förer a principal system of reference
(Hauptbezugssystem) ’).

Such a principal system Xs VY, can be constructed as follows:
Take a system of axes NX, Y, of which the origin coincides perma-
nently with the centre of gravity of the system of points, the axis
of X passing permanently through one of the material points.

Calculate > mr°8 in X, Vz. Take a second system of co-ordinates

NXg Yp with its origin also permanently in the centre of gravity

, i ; = mr" 6 :

and give it in X, Y, a velocity of rotation w = —— =. In this
= mr

way a principal system, consequently an inertial system, has been

fixed without the aid of an ‘absolute space”.

1) The hypothesis of FörPL in its original form is: for an inertial system
with origin in the centre of gravity the total moment of momentum vanishes
permanently. F

1415

3. Motion relativated without the aid of the hypothesis of Förrr..

First we will give a solution of the second problem of $ 1,
without applying the hypothesis of Förer.

We assume the same as in § 2, so we start from the differential
equation (2), for which hold the relations (4a) and (46), we assume
moreover that the forces, of which X, and Y, are the components
only depend on the relative position of the points (e.g. Newton force).

Take now a new system of axes XY with its origin permanently
in an arbitrary material. point, which we will call point 1, and
with its axis of X permanently through a second arbitrary-point 2
of the system of points. The new co-ordinates w and y are now
relative co-ordinates as meant in § 1. After transformation of the
former co-ordinates to the new system of axes’), the equations of
motion (2) pass, considering (4a) and (45), into:

oe 8 NE jn
BW WE — 2wy ==
my m,
(8a)
oe ¢ C Ys, V2
nw wy, | 2we, = —
My m

1

in which w is given by:
au Abn os Os Nine fap NSD)
a, 6 and c are functions of the a, y, x, y and a, y of the n points
a= Emmet + y?) —(S me)? — (Z my).
b= EmEm(ee + yy) — Sma Eme — Emy = my. (8c)
e= Sm > m (ey — yx) — (E me E my — TS my Sma).

The sign = includes all points.

There are 2n—3 co-ordinates 2,,y, and according to this 2n—3
equations (8a) of the second order, the auxiliary quantity w occurs
in one equation (85) of the first order in w. So (8a) and (86) form
together a system of order 2 (2n—3) + 1 = 4n—5. After elimination
of w there remain 2n—38 co-ordinates, so that e.g. the system can
be reduced to 2n—4 equations of the second and one of the third
order: In these equations only the relative co-ordinates, their deri-
vatives and the quantities X, Y, occur. As we supposed the com-
ponents X,Y, dependent on the relative position of the material
points only, the problem is solved.

) See § 5.6.

1416
4. Motion relatwated with the aid of the hypothesis of Forpu.

In this § we shall give a much simpler solution of the second
problem of $ 1 by making the same suppositions as in the preceding
§, moreover making use of the hypothesis of Forru. Instead of (4a)
and (46) we take the equations (7a) and (76), but further we proceed
in exactly the same way.

After transformation to the new, relative co-ordinates’), the
equations of motion (2) pass, considering (7a) and (76), into:

Nia Ahk,

by — wy, — wa, — 2 wi) = ae
my, mM,

‚ (94)
E ; : Prion:
yy + wa, — w*y, + 2 wae, = — ——.
my m,

in which

Ër _ mJ m (ny — yx) — (Eme SE my — EmyEme) 0%
NDR — SmZm (2? + y?) — (= mz)? — (= my)? ie
The sign = includes all n points.

The equations (9a) are the desired equations of motion in relative
co-ordinates, if for w we substitute the value (96). After this sub-
stitution we get 2n—3 independent differential equations of the second
order.

Without introducing Förer’s hypothesis we came in $ 3 to 2n—4
equations of the second and one of the third order. Owing to the
hypothesis of Förp, we have found in this § 2n—3 equations of
the second order. For this reason the equations (9a) and (90), we
found here, are preferable to the equations (8a), (85) and (8c).

5. Remarks.

a. Lanen’s method of trial bodies”) gives an experimental way of
finding inertial systems. He does not discuss however their connection
with the total of matter in space.

b. Neumann*) and afterwards BorTZMANN!) try to do this by
referring the place of the material points to the principal axes of
inertia of the total system. They do not give differential equations.
A further consideration of this question will bring the conviction,

4) See § 5, &.

*) L. LANGE. Geschichtliche Entwickelung des Bewegungsbegriffs.

) C. NEUMANN. Ueber die Prinzipien der Galilei-Newtonschen Mechanik.
*) BOLTZMANN. Vorlesungen über die Prinzipien der Mechanik. Leipzig 1904.
IL paas.

va

1417

that the differential equations holding in such a system must be of
a different form from Newron’s. On the other hand the system of
Föprer does not require any alteration of Newron’s differential equations,
but only a definite value of some integration constants (§ 2).

c. The problems studied by Konkmuier') are in many respects
more extensive. So he eliminates also absolute time. In this connection
it is sufficient to state, that he does not find equations of the type
of § 4, because he does not make use of Förrr’s hypothesis.

d. Einsrei gives in his theory of relativity a way of relativating,
founded on quite different principles from those held in this essay.
This is connected with the fact that he wants to relativate not only
mechanical but also electromagnetical and optical phenomena.

e. In connection with an experiment, made by Förrr*) and a
remark by Freunpuicu’), the following thought-experiment may be
discussed: At the north-pole of the earth the pendulum-experiment
of Fovcaurr is made. Under the pendulum a heavy flywheel with
vertical axis of rotation has been mounted. Problem: Does the
pendulum’s motion alter, when we revolve the flywheel? Förrr’s
hypothesis and our equations give us the following answers: With
respect to the principal system remains: 1°. the rotation of the
pendulum’s plane permanently =0; 2°. the sum of moments of
momentum of flywheel and earth = a constant, also this sum for
the rest of the bodies of the universe, because the total sum has to
remain —0Q. Consequently the rotation of the pendulum’s plane
with respect to the rest of the bodies (the fixed stars) does not alter
(it does alter with respect to the earth, the rotation of the latter
having undergone some change).

f. From the point of view of Newron’s mechanics can be said:
1°. If only two celestial bodies were in universe, it were possible
that they moved round each other at a constant distance. 2°. A
liquid mass, supposed to be the only body in space, can be flattened
by centrifugal forces, though no relative motion of its particles is
observed. With the view taken here, which is based on Förrr’s
hypothesis, this is impossible.

g. For the transformations of $ 4 we can start from a principal

') N. H. KorkMEYER. Eliminatie van de begrippen assenstelsel, lengte en
tijd uit de vergelijkingen voor de planetenbewegingen. Dissertation Amster-
dam 1915.

*) A. Förrpr. Sitzungsber. der math.-phys. Klasse der Bayr. Ac. der Wiss.
1904. Bd. 34, p. 3.

5) ERWIN FREUNDLICH. Die Grundlagen der EiNsreiNschen Gravitations-
theorie. Berlin 1916, p. 27,

1418

system, the origin of which is consequently situated in the centre
of gravity of the system of points, while the total moment of
momentum continuously vanishes (§ 2).

mal, = X, fi Conor B Lai er)
Zina == 0 9S mya 0 ail OS Aeleniiye 10a)

Sn (tay a a er ee

First we pass to a second system of axes, with its origin perma-

nently in point 1 of the system of points and which is continuously
parallel to the principal system, for this second system holds:

Pg tA al esd el IGN se! (6
my m
=m J m (ay — ye) — (Eme Emy — Emy Emo)=0. (12)

(106), becomes (12) because according to (10a) 2’, Sm = — Ema,
y' =m = — J my.

If we take a third system of axes with its origin also in point 1
and its axis of X permanently through point 2, and indicate the
velocity of rotation of the third system of axes with respect to the
second by one w, the equations (11) and (12) pass after transform-
ation into the final equations (9a) and (6). Now w can be con-
sidered as an auxiliary quantity, that can be substituted from (96)
into (9a). .

For the transformations of § 3 the first system of axes can also
be chosen with its origin in the centre of gravity of the system of
points, the calculations are quite analogous, however more complicated.

Physics. — ‘Space-time symmetry. I. General Considerations’. By
N. H. Ko.kmever. Communication N°. 7a from the Laboratory
of Physics and Physical Chemistry of the Veterinary College
at Utrecht. (Communicated on behalf of Prof. W.H. Kensom,
Director of the Laboratory, by Prof. H. KAMERLINGH ONNES).

(Communicated at the meeting of December 18, 1920).

§ 1. Introduction. In the literature of later years some propositions
are found for changes in the original atom-model of RurHERFoRD-Bonr.
These propositions are founded on different considerations. So Lewis *)
and Lanemuir*) were led by considerations on the chemical structure.
SOMMERFELD *) was brought to his combinations of ellipses by investi-
gations of the cause of the fact that the defect of charge of the
nucleus is not a whole number for the Z-series. Born, LANpÉ and
MApDELUNG *) again studied the absolute dimensions of the elementary
cells of crystals, the transformations of energy, and especially the
compressibility. By these considerations they were led (partly in
cooperation) to the invention and nearer inspection of cubical
models analogous to those of Lewis and LANGMUIR.

Evidently Born, LANDÉ and Maprerune especially felt the necessity
of a change in the considerations on symmetry that were valid until
now, because they considered moving systems. On the same ground
I felt necessitated to introduce some new symmetry-elements, in
which time also plays a role *). It now seemed desirable to consider
the space-time-symmetry more systematically than could be done in
Communication N°. 4. In this paper the way to attack this problem
will be indicated.

$ 2. Restriction to a definite kind of operations. A symmetry
operation will further on be denoted by A, a complex symmetry

1) G. N. Lewis, Journ. of the Amer. Chem. Soc. 38 (1916) p. 762.
2) J. Lanemurr, Journ. of the Amer. Chem. Soc. 41 (1919) p. 868.
3) A. Sommerretp, Physik. ZS. 19 (1918) p. 297.
4) M. Born and A. Lanpé, Verh. d. D. Phys. Ges. 20 (1918) p. 210.
M. Born, Verh. d. D. Phys. Ges. 20 (1918) p. 230.
A. Lanpé, Sitz.-Ber. d. Berl. Akad. 1919 p. 101.
Verh. d. D. Phys. Ges. 21 (1919) p. 2, 644, 653.
ZS. f. Phys. 2 (1920) p. 83.
E. Mapetune and A. Lanpé, ZS. f. Phys. 2 (1920) p. 230.
5) N. H. Kotxmener, Comm. N°. 4, These Proceedings 23 (1920) p. 120.

1420

operation ') by AA. ScrHornruies*) and his predecessors only consider
such A’s that an application of them to a point A produces a point
B, the coordinates of which are found from those of A by a linear
orthogonal substitution. By these operations the distance between
two points therefore does not change.

It seems natural to introduce for space-time symmetry-operations
too the restriction that an application of them to two four-dimensio-
nal xyz-ict-points (or rather 2'x?2*x*-points) A and B does not change
the four-dimensional distance A B.

In the first place we thus limit our considerations to those A’s
the algebraic representation of which is a linear orthogonal four
dimensional substitution and to corresponding symmetry-elements.

Secondly, (as was also done by ScHorNFrims and his predecessors
in an analogous sense) we exclude those A’s, the repeated applica-
tion of which to a point A gives an infinite number of points at
the same time within a finite space or within a finite time-interval
at the same place.

Thirdly it will prove desirable to introduce still one restriction,
which has not its analogue in the three-dimensional problem.
From the algebraic substitution mentioned we see, that 2", 2’, v° of
the new point B depend on z of the original point A. Thus, applica-
tion of the A’s in question to A gives a point B that is displaced
in the course of time to an infinite distance even when A remains
on the spot. This fact is an objection against the consideration of
such a A; an objection however that may be avoided by considering
only the final result of subsequent applications of more than one 4
of the kind mentioned to a point A, of a AA therefore.

So we limit ourselves to the consideration of such A’s, the appli-
cation of which to a point A gives a point B with a world-line
parallel with the «*-axis, when the world-line of A has that direction.

In the next §§ we shall see to which kind of A’s we are led by
this restriction.

§ 3. Geometrical meaning and analytical indication of one of the
kinds of operations considered. In a R, with coordinates 2, 2, 2°
and at=vict, R, be an arbitrary linear space of three dimensions.
We shall call R, a symmetry-space’) (symbol r) when the

corresponding operation (symbol X, name space-time-reflection) changes

1) In the same sense as f.i. a rotatory-reflection is a AA.

2) A. Scuoenriies. Krystallsysteme und Krystallstructur, Leipzig 1891.

5) This name has already been used by P. H. Scuoute, Verh. Kon. Ak. Amst.
Eerste Sectie Il 7 (1894) p. 16.

1421

& point’ A(c,', 7,7, 2", 2,‘) into a point “B(a,', 2,7, 7,", v,‘) that is
geometrically to be found in the following way.

Draw through A a perpendicular to t and measure the length of
that perpendicular on the other side of its point of intersection
with r. The end-point of this stretch is the point 5.

When X is given by the length /, of the perpendicular from the
origin of R, on t and its direction cosines ~,', p,°, p‚° and p‚*, where

Pt PET Oy eee oy! Sy

then we find by substitution of one of the four indices 1, 2,3 and 4
for n

tr == + 2 Pi" (,—9,' DP BP, EP, x, ") GP ee (2)

When in a three-dimensional w'2’2?-system we consider a plane
V through the origin, the direction cosines of its normal being
in the ratio p‚*, m,? and g,*, then the points A’ and 5’, corres-
ponding in this system to A and B in the four-dimensional system,
are lying on the same perpendicular to V, «,»—.,” being proportional
to gy," for the values n = 1, 2,3.

When the distances from A’ and B’ to V are denoted by —y»
with m==1 and 2 resp., then we have

9," an A y,* Em + y,° Bin”
Vlet

Im = (3)

and therefore
Ys Fad waa: 2 V1—g? (;-—- V1—o?? YP a,*) (4)
a," = a," + 2 Pr" Lt Me Y:—Pr a, *)

Thus the distance from B’ to V and the new value of ict are
evidently found from the values of these quantities for the point-
incident A by drawing in a two-dimensional ya*-system a line in
such a way, that the perpendicular to it from the origin has a
length 7, and forms with the z2* axis an angle with a cosine= 9,‘
and by reflecting the point A" with the coordinates x,‘ and y, in that
line. The coordinates of the point B" thus found give the new value
of the time and the new distance to V in the three-dimensional figure.

§ 4. Hach space-time-symmetry-operation of the constdered kind
may be regarded as a complex symmetry-operation of space-time-
reflections.

The A’s treated by ScHoENFLIEsS and predecessors, reflection in
a plane, inversion about a centre, translation, rotation through
Ln tag a and thd 2-, 3-, 4- and 6-al screws, 2-, 3-, 4- and 6-al
ee a ee 6
rotatory-reflections and gliding reflection may all be regarded as

1422

complex reflections in one or more planes). This is a consequence
of the linear-orthogonal character of the substitution by which only
congruent and symmetrical figures are possible.

For the same reason we must also assume that each imaginable
space-time-A of the considered kind may be considered as a complex
reflection in one or more symmetry-spaces. This shows at once the
way in which each space-time-symmetry-element can be found.

§ 5. General formula for the coordinates of the point B, found
from the point A by application of an arbitrary complex space-time-
symmetry-operation. of the above considered kind.

k=m
on =d 2 Bea! UPE EPR U Ok DoY Bo) [PE +

l=m

+ ERG (Q, k) + = (1, p)(p, 4) + & (Lp) (p, 9) | 4) +) Viart)

where (p,q) has been written for
— Zp! Pq + Pp Pa? + Pp Pq? + Fp* Pa‘)
while we must take 1 >p >q > ete.

§ 6. We can derive all space-time-symmetry-operations by simply
combining, all space-symmetry-operations that have been mentioned
without the limiting to 2-, 3-, 4- or 6-al axes with time-symmetry-
operations. The linear orthogonal substitution, expressed by formula
(5) will have a scheme of coefficients :

1% 145 1%3 1% 1

2%) 2% 27 24 ot

si zl, 323 314 3%

Gh Gig gla? 4G, Gas
while these coefficients are connected by the following relations:
14,7+ ,4,7+,4,°+,a7%=1) 14, 14, +44, 243 +,4, ,4,+,4, 4,0:
a + ,a,7+ ,4,°-+ 0,7 =1 pi ay 1%, 143 12% 9% 13% 9%, 1,4, 2, — 9
A Hea Hide +44 =l | 12, 144 Ha 24, +,4, ,a,+,0,,¢,—09 |
a Hea Hira Ha =l VAE +48, 7%, + 40, A + 2,40, =0
1% 14e Hr aq al ty Fe staat 1% = LO
1%; ,4,+,4, a, +,4, ,4,+,2, ,a, =O

1) (Note added during translation). See f.i. G. Viota N. Jahrb. f. Miner., Geol.

und Pal. Beil. Bd. 10 p. 495 1896. G. Wurrr Zs f. Kryst. u. Miner. 27 p. 556
1896.

1423

Because of the third restriction introduced in § 2 we must suppose
ls 24, and „a, to equal zero. Substituting this in (6) and (7) we find:

4224
Bee eee OO Ee t(D)

while (6) and (7) are then reduced to:

ie + 3) sai’ elli 1% 1% 3%, ada Hdi an — 0 |

nt a sas — | am (9) and 14, 14, + 9%, 44, + 44, 2, = a tie (10)
rde 1.0,” â Saul | ETE UE FH gy pg. 0 |

Equations (8) say, that the transformed time depends on the time
only, and that the transformed space-coordinates are dependent of
the original ones only. Equations (9) and (10) show, that this last
transformation is linear orthogonal. By this we have proved the
proposition stated at the beginning of this §. We need therefore
only apply equation (5) for values of p‚‚* =O viz. for a pure space-
transformation and of ¢,*=1 viz. for a pure time-transformation.

§ 7. Meaning of the cases y,'=0 and yi =1. A RN with
(mi = 90 is nothing else than a reflection. (Symbol S, symbol of the
symmetry-plane 8). .

It might seem interesting to derive all imaginable space-A’s by
investigating which combinations of G’s when considered as complex
A, are compatible with the restrictions 1 and 2 of $ 2'). A point
of consideration could be whether the order of application of the
reflections in the AA should be chosen arbitrarily or not. In the
first case’), we find, that each AA may be regarded as a combination
of those already used by SCHoeNrFLies and predecessors, but we might
say just as well, that the A’s used by ScroeNrries are but combi-
nations of ©’s and that there exist combinations, which were not
treated by him. Proceeding in the indicated way, we find some
A's that are aequivalent with point- and space-groups of SCHOENELIES.
After this we might investigate which space-groups can be formed
from those A’s.

As however the result of such an investigation has already been
obtained by ScHoerrLies we shall do better to combine each of his

1) (Note added during translation). CG. Viota and G. Wurrr partly executed
such a plan (l.c).

*) This seems natural by analogy with A's that were known before and is also
demanded by the principle that around each particle the configuration of the other
particles is the same. An exception to this last demand is formed by the definition
of the sense of rotation and translation resp. dilation for a screw resp. time-
rotation (see further on).

92

Proceedings Royal Acad. Amsterdam. Vol. XXIII.

1424

A’s without restrietion to 2-, 3-, 4- or 6-al axes with the possible
time-A’s*). Which are these?

One single X with g*=1 will be called a “retroduction”’ *),
the corresponding symmetry-element a ‘“‘symmetry-moment”. In a
moving system of particles there exists a ®M (symbol for a retro-
duction), when each point P, where at the moment ¢ a particle A
is present, is also occupied by a particle B at the moment 2m—d,
where m is the symbol for a symmetry-moment and so the value
of its ¢ too. When then at the moment t+ At A is at Q, there
must also be present a particle at Q at the moment 2m —t—Ât.
Because of the second restriction of § 2 we conclude that this last
particle must be particle B. The velocities of A and B at P are
therefore equal and opposite. At the moment m there would thus
be at the same place two particles with opposite velocities. This
would be in conflict with the impermeability of matter (which we
shall assume to hold for the electrons too), unless the two particles
are identical *). Let us therefore suppose this to be the case. Then
each particle must have come to rest at the moment m and hence
describe its path in the opposite direction.

When we have however a AA of a ® and a © we must change
the above “at tbe same place” into “at the image of the place in 8”.
Then the difficulty of two particles with different velocities being
at the same moment (at the moment m) at the same place, would
be avoided, unless at the moment m the particles were lying in the 8.
In this case the velocity at that moment would not necessarily be
0, when only the two particles were supposed to be identical.
Having passed the 8 the particle then describes the symmetrical
path and when moreover the § was intersected perpendicularly by
the path there would not be any discontinuity in the motion. In
Comm. n°. 4 le. the symmetry-element of such a A (symbol MS)
has been called ‘‘reversal-symmetry-plane”’. Further on we shall call
it reversal-plane and the operation reversal-reflexion.

Other AA’s of time- and space-A’s may be investigated in the
indicated way.

1) After this we have still to form groups with the A's used by ScroenrLres
and with the newly introduced ones.

2) This name (from retro =back and duco=I lead) and the name dilation
(from differo =I postpone) introduced later on have been chosen in consultation
with Prof. DamsrtÉ of Utrecht.

8) We exclude therefore cases as imaginéd by Lanpé l.c, in which after a
collision two electrons suddenly get each others velocities in direction and mag-
nitude. Lanpé himself designs these cases as improbable.

1425

§ 8. The AA’s of two and more W's. Regarding time-A’s as special
cases of As, we see from the end of § 4, that we can find all
kinds of time-A’s by only studying AA’s of M's.

The applicability of the complex symmetry-operation of IN, and
M, (symbol P, name ‘dilation’, symbol and name of the sy mmetry-
element p and “period”) to a system of particles, means that when
at a moment ¢ a particle A is at the point / there are also particles
B resp. C at P at the moments 2m,—2m,-+ ¢ and 2m,—2m, + ¢
respectively. In this case P is every time occupied by a particle
after a lapse of time, 2(m,—m,). When the number of particles at
our disposition is not infinite, the same particle A must necessarily
at the end arrive at P again. Moreover, each particle, when arriving
at P must have the same velocity and the same direction of motion,
which will become evident, when we consider the state at moments
2(m,—m,) +¢-+ At. All particles are thus distributed in unequal
numbers over differently shaped closed paths in which they circulate
with phase-differences, that are the same for the different paths and
also for the different particles in one and the same path. The times
of revolution in two paths are proportional to the numbers of the
circulating particles.

: an
A AA of a 9 and a rotation through — about a n-al symme-
n

try-axis was already used in Comm. n°. 4 Le. We shall call its
symmetry-element „-al time-axis, the symmetry-operation time-rota-
tion ') (symbol WW).

The complex operation of %,, M, and M, (symbol H, name reversal-
dilation) is a symmetry-operation of a system of particles, when it
fulfills this condition: When at the moment ¢ the point Pis occupied
by a particle A, we shall find there particles B, C ete. at the
moments: j
— Jm, 2m, 2m —t, 2m,— 2m,+2m,—?¢ and 2m,+2m,—2m,— 1.

In the first place we have therefore three symmetry moments.
At those moments all particles must therefore return in their paths.
As this must happen at more than one moment each particle oscil-
lates in a different path of arbitrary form, while the moments of
returning are the same for all paths. It is evident that in each
path one particle only can circulate now. Secondly there evidently
exists a period. To find it the following considerations will be of
use: When to a moment ¢ we apply the order MMM, and to the

1) The distinction we must make here between the two possible combinations
of sense of rotation and sense of dilation is analogous to that which Scroenrues
and his predecessors made between left- and right-handed screws.

JA

1426

result of this operation the order M, M, W,, the influences of Mt,
neutralize each other, so that in fact we have only applied the
double dilation M,M,M,M, *). Besides the intervals of time 4 (m,—m,)
between the passages of particles by P, we find the intervals
4(m,—m,) and 4(m,—m,) too. Now we come into conflict with the
second restriction of § 2, unless the quantities m,—m, and m,—m,
have a greatest common measure. This is the time of oscillation.
We can easily prove that then all demands of § 2 are satisfied.

By the investigation of AA’s of 9’s and space-A’s we shall find
ia. that the paths may be closed in the same way as has been
found for }, but that then half of the paths (chosen in a definite
way) is described in the opposite direction.

§ 9. There are no other time A's than ®, YP and A. For all
AA’s of even numbers of M's the same considerations hold as the
following for four W's. When at a moment ¢ the particle A is at
P, and when we have to do with a AA of four Ds we must find at
P also particles B, Cete. at the moments +2m,+2m,+2m,+ 2m,-++7,
where the sign + has to be chosen for half of the +-signs, the
sign — for the other half. This gives therefore more than one dila-
tion, which together yield however (comp. the considerations on 9)
only a dilation equal to their greatest common measure, which case
is already comprised in .

For all AA’s of uneven numbers of M's we can follow the
reasoning on the case of 9. Thus this neither gives something new.

Combinations of time-A’s yield nothing that has not yet been treated.

§ 10. Symbols for the new symmetry-operations and symmetry
elements. For shortness sake we shall give names and symbols to
the s.-t.-A’s and symmetry-elements. As a preliminary system we
propose the following:

With a small change now and then we retain the names and
symbols ot ScHosnriiss. When now a A of ScHornriizs is combined
with a retroduction the name of the first A might be changed by
joining to it the prefix reversal. The same may be done with the
names of the symmetry-elements. Before the symbols of A’s and
symmetry-elements we add M and m resp. When the change relates
to a dilation the prefix is “time”, for the symbols this becomes

1) In the here indicated way the treatment of AA’s of R's (and therefore of
M's and E's) is much simplified. By applying one of the A's thus found to the
symmetry-elements of another one we can see whether this brings us into conflict
with the restrictions of § 2. A AA found in this way evidently forms a group
of A's.

Without time A With M

Identity IN | Retroduction (symm.-moment). . .
Inversion (centre). mel i Reversal-inversion,... << Gan «Dey
Reflection (symmetry-plane) . sG 8 Reversal- reflection (reversal-plane) . MS
Rotation (n-al axis) . RE a Reversal-rotation . . . .....MU
Rotatory-reflection (n-al reflect.-axis) 2% Reversal-rotatory reflection. . . . MU
Translation (place-period). Ak t Reversal-translation . . . . . . . ME
Gliding-reflection (gliding plane). . 5 Reversal-gliding-reflection . ... MT
Screw (n-al screw axis) „% Reversal screw .………. .…... ME
With W With D

Dilation (period). 0... p Reversal-dilation . . ......60O
imiesinversion. …… ……. « c's S pi Reversal-time-inversion . . .. . D5
Time-reflection (time-plane). . . . PS ps Reversal-time-reflection . . . . . D6
Time-rotation . . .... . . . P% | pa | Reversal-time-rotation. . . . . . OU
Time-rotatory-reflection. . . .. . PA Reversal-time-rotatory-reflection . . Hy
Time-translation . .......WE Pt | Reversal-time-translation. . . . . OF
Time-gliding-reflection. . .... ps Reversal-time-gliding-reflection. . . DF
RE serewarn. Va rione hte vaya) Pee Reversal-time screw. . . .. . . Q&

1427

P and p. When an operation is combined with a reversal-dilation
we add the prefix reversal-time and for the symbols 9 and q.
Sometimes the name obtained in this way is still somewhat shortened.
In the following table we find these provisionally fixed names
together with the symbols.

§ 11. The way in which s.-t.-symmetry-operations may be combined
into groups. When the point groups of ScHoENriuEs are completed
by those, which contain other than 2-, 3-, 4- and 6-al rotations ete.
we can form from each of the thus found groups, s.-¢.-groups by

combining each of the non-aequivalent operations of a group with

either no time-operation or with a ® or witha, or witha 2. Each
of the thus found groups must then still be examined to find out
whether the time-operations added are perhaps in conflict with each
other. Several of the groups obtained will also be found to be the same.

The same might be done with the translation-groups.*), which are
formed by ScHOENFLIES as a means to change point-groups into
space-groups. After this, all obtained s.-é.-point-groups are multiplied
by each of the s.-¢.-translation-groups found. Examples of such groups
will be given in a following paper (N°. 76).

1) In the case of translation-groups we have no longer a ground for the assump-
tion that a and a © cause the paths to be closed. The only thing we should
have won by omitting this hypothesis however would be the allowance of a conti-
Ruous translatory motion of the whole system of particles. It would not be desirable
to include this motion in our considerations.

m
mi

ms
ma

mt

qt
qs
qa

qt

Physics. — Space-time-symmetry. Il. Discussion of a special case.
The tetrahedrical atom-models of Lanpé”. By N. H. Kork-
MEIJKR. Communicaton N°. 76 from the Laboratory of Physics
and Physical Chemistry of the Veterinary College at Utrecht.
(Communicated on behalf of Prof. W. H. Kegsom, Director of

the Laboratory, by Prof. H. KAMERLINGH ONNrs).

(Communicated at the meeting of January 29, 1921).

§ 1. Introduction. Recently, Born, Lanpé and Mape.une *) (parti-
ally in cooperation) have studied atom models in which the Beton
circulating about the nucleus are distributed over a number of shells
over each of which they are spread symmetrically.

LANDÉ treats?) the problem of finding ‘orbits with polyhedrical
symmetry” with the intention of reducing the p-bodies-problem of
the p electrons (the nucleus is thought at rest) to a one-body-problem.

A survey of the possibilities arising in this problem and an
insight in the symmetry-character of the models in question can
easily be obtained by considering the latter from the point of view
of space-time-symmetry (denoted further on by s-t-symmetry) treated
in a former communication ®). At the same time we may test in
this way the usefulness of the considerations in question. We shall
only consider the tetrahedrical models of LANDÉ.

§ 2. 4 ie space group of SCHOENELIKS, on which the tetrahedrical |
atom models of luANDÉ are based. In fig. 1
the 24 points are indicated, that arise from
the symmetry of the tetrahedrical group of the
second kind Jy (hemimorphous hemihedry of
the cubic system) of ScHOENFLIEs, when one
of them is chosen arbitrarily *). SCHOENFLIES
gives a summary of the non-aequivalent sy mme-
try-operations of this group in the following way:

1) See the papers cited in note 4 p. 1419.

8) A. LANpÉ Verh. d. D. Phys. Ges. 21 (1919) p. 2, 644, 653, Zs. f. Physik 2
(1920) p. 83.

3) N. H. Kotkmever Comm. NO. 7a. These Proceedings p. 1419.

4) The points at the other side of the sphere are denoted by thinner small circles.

1429

1 u B WW Sr Use VS: Weg
eee bn nn: bi TP Ae AS USz-- AU"Sz
U: U: 9" gyi’ WE, UE WS HNE q

ie : 2% :
where U, B and 28 denote rotations through —- about the binary

; 2a
axes, U, UW, U" and U” rotations through a about the ternary axes
and Gz a reflection by one of the planes of symmetry.

§ 3. The model with 24 electrons. When we think the nucleus
coinciding with the centre of the sphere on which the points have
been drawn, then an electron will collide with another one when
in its motion it reaches the sides or the edges of the solid angle
within which its motion takes place. As has been remarked in
Comm. N°. 7a Lanpé sometimes supposes such a collision to take
place; but he thinks it rather improbable. Here we shall consider
such collisions as impossible. Each electron must therefore describe
a path that remains inside the solid angle (elementary domain).

Now a s.-t.-symmetrical atom is continually changing its aspect
and at the same time perhaps not all its properties but at least
those depending on the aspect. It would be difficult, if not imposs-
ible to recognize such an atom by its properties when not approxi-
mately the same configuration of the electrons came back from time
to time. This would be an indication of time-symmetry when at
least the intervals between the moments of two equal configurations
are approximately equal te each other.

Perhaps the returning configuration might take another position
in space than the original one. As long however as we have not
to do with the relation of an atom to a neighbouring one, it is
allowed to choose a system of coordinates the origin of which moves
with the nucleus, and which may rotate about its origin in such a
way that the recurring configuration takes the same position with
respect to the system as the original one.

In Communication Nr. 7a we have seen that an electron returning
to the same place (in the system of coordinates) after the lapse of
a certain time while the same relation holds for all electrons, is an
indication of the existence ofa “dilation” } or a “reversal dilation” .

In the same way as in a space lattice an infinite group is formed
by the translations, an infinite group 1, P, W* ete.*) is formed by

1) According to Scnoenrmes each symmetry operation of a group transforms a
particle into another one (at the same moment) but for the identity. Therefore the

1430

the dilations. Let us denote this group by MZ. ScnornriiEes denotes
some space groups by placing between broken
brackets the symbol of the translation group
used for the formation of the group and sepa-
rated from it by a comma, the symbol of the
isomorphous point group. Now the group of
symmetry operations of the above mentioned
atom model with 24 electrons will evidently
aN et be represented by { 7’, 1}. The group contains
Fig. 2. therefore the symmetry operations I and Il and
moreover the same symmetry-operations, each multiplied by Pm,
where for m must be taken each positive or negative whole number.
Fig. 2 shows possible paths of 12 ‘of the 24 electrons.

§ 4. The model with 12 electrons. Let us suppose now that only
12 electrons are circulating with as much tetrahedrical symmetry
as is possible. Of the above 24 electrons each pair must then coin-
cide. In this case an electron must be able to cross the boundary
of its domain, but for the trivial case that it is always moving in
a &. When only space symmetry existed this crossing would be
impossible. At the moment of the crossing of a 8 the two electrons
coincide, but the velocity of one of them is symmetrical to that of
the other one with respect to the plane. The collision caused by
such velocities might be avoided when one electron reverted in its
path. From comm. Nr. 7a this evidently happens, when the reflection
in the 8 is accompanied by a retroduction 9 or a reversal dilation
D viz. a retroduction M multiplied by a dilation Y.

For causing each two electrons to coincide we have only to choose
for the symmetry moment of the retroduction that of the crossing
of one of the six s’s. We may form the group of the symmetry
operations for this case in the following way. Replace II from

§ 2 by:
MEg MUE | MBE MWE
HIT < MAS = MA'Sy MA"Ey MUN ay

MU Ez 2) Melee coe Sd MA" Eq

number of symmetry operations of a group equals that of the particles. In the
group in question however each operation transforms a particle into the same
particle at a different moment. By this the number of particles is no longer equal
to that of the operations in the group. This last number is equal now to that of
the positions of all the particles required for the definition of the model.

1431

I and III then form a group which we shall call F,. This group

multiplied by MZ gives the demanded group. Thus 1’ =D, IT}.
Here we may make the following remark.
In the deduction of the above model we have
quite followed LanpÉ’s considerations spoken
of in the introduction. According to these p
electrons describe 2 = pg paths in such a way,
that they continually show the symmetry of
a sub group, while each of the p electrons
describes q definite paths successively, where
Fig. 3. pq denotes the number of operations in a group.
The above model is therefore also a ““tetra-
hedrical atom model”. Lanpé however does not consider this model
with 12 electrons. In the model discussed above each of the 12
electrons describes a path (see fig. 3 where the projection of the
paths of 3 electrons on a plane perpendicular to a ternary axis has
been represented) symmetrical with respect to a g, while the two
electrons that may be derived from a third one by application of
u and Y°, describe paths that may be derived from that of the
third one in the same way. (The period p of P is just-equal to the
time of revolution in such an orbit). Without pointing expressively
to the necessity of this, LANDÉ considers the case that the three
paths in question coincide and form one path, symmetrical with
respect to the three s’s, while the three elec-
trons are circulating in it with difference in

phase of */, (see fig. 4).

We may find the group of the symmetry
operations of the model of Lanpé by multi-
plying the whole group found above by M’Ga’,
where Gq’ means a second S while 5’ refers
to the moment when it is passed. IMGq and
M'S being at the same time symmetry ope-
rations, MM/E1S,/ is also a symmetry operation viz. a time-rotation

Fig. 4.

an nen .
with a rotation through = and a period */, of the time of revolu-

tion = twice the time between the moments in which the two
g’s are crossed. When the group of the powers of dilations with
period equal to '/, of time of revolution is called ZH’, then the new
group is 1,’’ = $1), M’;. The group ML discussed above is a sub-group
of group I’.

§ 5. The model with 4 electrons. LanpÉ also discusses the case of

1432

4 electrons. This case is found from the foregoing model of Lanp£
when the two electrons that are derived from a third one by a

i Qn : ;
single and a double rotation through 3 about a ternary axis, coin-

cide with this third one and when this is the case for each of the
ternary axes. Thereto we have only to’change the ternary axes
into ternary timeaxes, to choose the period equal to '/, of the time
of revolution of the electrons in their orbits and to take care to
combine positive dilations with rotations about the axes in senses
corresponding with the direction of revolution of the electrons. In
that case however [ and III, both changed in the indicated way,
do not longer form a group. Let us consider however the group.

te oe an ITS ME MUS, MVS, MBS

which forms namely a group differing in the same sense from the
group Vq of ScroeNrries as the group 1, from 77. When we
multiply this group which we shall call 4’, by the infinite group
IT” of the time-rotations 1, WA, PU etc., where Pp has a »=7/,
time of revolution, then we obtain the required group PT, = {T1,, 77"; ').
II is a sub-group of JZ" too. This case too is represented in fig. 4
when two of the three indicated particles are cancelled.

§ 6. The model of MapeLuNe and LANDÉ. MADELUNG and LANDÉ
have treated still a model (le), in which four electrons are moving
in the lastly mentioned way. They are circulating with a uniform
velocity in circles, while each electron is followed by another one
in the same orbit at an angular distance of 75°, so that totally eight
electrons are circulating. This model may easilv be derived from the
preceding one by choosing the moment of M not equal to that of
the crossing of one of the 8’s. Then two electrons are namely cir-
culating in each orbit, with a constant phase-difference when the
orbits are circular and when the velocity is uniform. This last con-
dition cannot be expressed by the used operations. The model in

1) Though it is not here our purpose to find out all possible cases, we may
point at another way in which the electrons may be brought to coincide, viz.
when the binary axes are replaced by time-axes. We then obtain six electrons
each of which could move f.i. over a face of a cube. Perhaps LANDÉ did not
consider this model because it has no binary axes. Still we must also consider
this model as a case of “tetrahedrical” s-t…-symmetry. Moreover it may also be
treated as a special case of the model of LANDÉ of six electrons in rhombohedrical
symmetry connection.

1433

question thus belongs as a special case to the group 7, = {JI,, 7",
where I, is:

Mel WB as IT{~ MSa MuSa MBEa M' WE

§ 7. Final remarks. In the same way we can also study the
cubic model with 48, 24 and 8 electrons respectively, and also the
models with other numbers of electrons. We may still draw the
attention to the problem of the s-t-symmetrical relation between the
different shells of an atom with respect to the above said on the
periodicity of the configurations of the electrons.

Finally the following may be remarked:

When a certain number of electrons is moving in such a way
that s-t-symmetry exists, it is evident from the preceding that
perhaps no pure space symmetry element exists. In the equations
of motion given by LANDÉ for one of four electrons the remaining
space symmetry of the four electrons was taken into consideration.
These equations proved to possess the symmetry of the group 7 of
SCHOENFLIES, so that the four-bodies-problem of the four electrons
was reduced to a one-body-problem. From the preceding we now
see, that this reduction could only be the consequence of the existence
of the s-t-symmetry of the electron configuration in the equations;
and that this symmetry would not suffice when the time-symmetry
parts are omitted. It may be verified easily though that, in the cases
discussed above no change is brought into the conclusion by this
remark. We have seen moreover, that the appearance of s.-t.-sym-
metry instead of space-symmetry was always connected with the
coincidence of two or more orbits; and algebraically this is expressed
by boundary conditions, not by a property of the equations of
motion..

Physics. — “Space-time-symmetry. Ill. Remarks on the deduction
of groups of space-time symmetry-operations.” By N. H. Kork-
MEIJER. Communication N°. 7c from the Laboratory of Physics
and Physical Chemistry of the Veterinary College at Utrecht.
(Communicated on behalf of Prof. W. H. Krersom, Director of
the Laboratory, by Prof. H. KAMERLINGH ONNES.)

(Communicated at the meeting of January 29, 1921).

§ 1. Zntroduction. In Comm. N°. 7a’) the s.-t.-symmetry opera-
tions have been derived, Comm. N°. 75%) gave examples of the
application of these on a couple of models. With the purpose to
start the study of the s.-t.-symmetrical atom models I have spent
some time with finding out all groups of s.-t.-symmetry operations
that are connected with point groups. The results of this investiga-
tion would take too much space here. Therefore only a few remarks
follow on the way of deduction of the groups in question.

As moving particles we shall choose one atom nucleus and a
finite number of electrons, all without dimensions.

§ 2. Possibility of the existence of the s.-t.-symmetrical atom models.
In the first place we may prove in a way analogous to that followed
by Lanpé®) in the discussion of the possibility of his models, that the
s.-t.-symmetrical atom models are consistent with the action of the
forces. |

In the second place: Among the models found in the way here
indicated there will be some that do not satisfy the demand, (Comm.
N°. 76%), for an atom model, that the configuration of nucleus and
electrons returns periodically. This is f.i. the case with all models in
which we have to do with one retroduction only. We might call
them quasi atom models. For the sake of a systematic treatment
we shall have to consider these too.

In the next § we shall see, that it is impossible that to the ope-

1) These Proceedings, p. 1419.

3) These Proceedings, p. 1428.

5) A. LANDÉ, Verh. d. D. Physik. Ges. 21, p. 2, 1919.
“yale:

1435

rations in question there belong those that are combined with trans-
lations. Thus we have only to consider rotations, rotatory reflections
(including reflections and inversions) and combinations of these two
with retroductions, dilations and reversal dilations.

§ 3. We need not consider other configurations of space symmetry
elements than those considered in the theory of space-symmetry.
Evidently the configuration of the space symmetry elements (including
the geometrical parts of the s.-t.-A) is a figure at rest, so that when
one of the s.-t.-A, composed of a s.- and a t.-A, is applied to it, it
will give a congruent or symmetrical configuration, though at a
different moment, but also at the same moment. The s.-A alone
being then a A of the configuration '), this latter must correspond
with one of those obtained in the theory of space-symmetry ’).

§ 4. Introduction of the generative operations of a group. That
the method indicated in communication N°. 7a Le. for the searching
of all groups of s.-t.-symmetry-operations is valid has been proved in
the preceding. This method however may be much simplified by
making use of the generative operations of the point-groups *) viz. of
operations chosen in such a way, that each operation of the group
can be considered as a product of some of those generative opera-
tions (the order in which the factors are taken having influence).
We shall indicate each group by placing the symbols of the gene-
rative operations, separated by comma’s, between broken brackets.

When to each of the generative operations of the group G=
(U, D,E, we add a time operation (including the identity) we obtain
the group T= {O, HB, KE. When moreover pure time operations
are added as generative operations, so that we obtain lr, =;... ,
M, GA, HB, KC}, we need only vary the operations G, , KX, ¥, M...
in all possible ways to find all groups of s.-t.-symmetry operations,
that can be derived from G. Now though it is possible that in
a group IT, which has been found in some other way and which

1) This holds also for translations. As we have confined the number of nuclei
to 1, no A’s composed by means of translations can occur in the groups sought for.
*) It might seem doubtful, whether for time rotations the restriction to those

through rae radians, remains valid. In fact in these considerations there is no

objection to time rotations with infinitesimal rotation. This has a meaning only

when besides the time period is infinitesimal. Then this symmetry element indicates,

a uniform circular motion. But for the rest this does not change the followin

considerations.
5) A. ScHOENFLIES, Krystallsysteme und Krystallstructur, Leipzig 1891.

1436

necessarily must have 6%, HE and KE in common with one of the
varied groups I (fi. I’), we find another one of the non-aequiva-
lent operations of G multiplied by the time operation 2%, while in
T this added operation is 9; we can however add to T' as a gene-
rative operation a time operation Q in such a way that 2) = ®, and
then we obtain a group I”, which does no longer show the indi-
cated difference with ZP, and which doubtlessly belongs to the
groups found by the variation of the group If.

§ 5. The time operations added cannot be in contradiction. From
the preceding it is evident that in some one of the groups obtained
in this way, one of the non-aequivalent operations of G could occur
more than once, each time multiplied by another time operation.
When these should be in conflict with each other, this would only
mean, that all electrons are at rest. For a point at rest has each
conceivable time operation as a symmetry-operation. Then the group
is the same as G@ itself with the special condition that the particles
do not move.

§ 6. Restriction of the time operations that are to be added.
Never need reversal-dilations to be added to the generative opera-
tions of a group as G. A reversal dilation 2 namely means nothing
else but a group of time operations among which f.i. IN, MPM, and
MM M,. It is evident that the same effect is obtained by adding to
U the order M, Mm, M, only. For, when later on time operations are
added as generative operations to the groups that have been formed
already we necessarily add f.i. also the operation M,M, MM, which
multiplied by M,N, M, A gives again MMM, A. As further MMM,
is a retroduction and as in the derivation of the groups we neces-
sarily add each retroduction it has no sense to consider the form
MIM, WM, especially. Similar considerations show, that of the orders
MM, and MM, that are included in a dilation we need only to
add one. Thus the generative operations of group G are multiplied
by M or MM, only; for the same reason we add later on as.
generative operations only either ®, or M,M,, or M, and M,.

§ 7. Choice of the generative operations. Proceeding in the indicated
way we are sure to omit none of the groups of s.-t.-symmetry
operations. It will however very well be possible that we thus obtain
the same group more than once, each time in a different form and
thus that those different forms do not always show their aequivalence
directly. We shall see how that aequivalence of two such forms can

be found out. For this purpose it will prove to be desirable to
choose the generative operations for each group G in such a way,
that a possibly low power of each of these operations is aequivalent
to the identity. Thereto we shall even sacrifice sometimes the ad-

1437

vantage of a possibly small number of generative operations.

nj")
rl, Us

Els W's}

U, Gri
Ss Sl Sal
2, Sa}
Al, Sp
A, Sa}
a, S}

el, S}

On the other

1) Analogous to ScHOENFLIES' distinction between “point groups of the first kind”
(the first 5) and “point groups of the second kind” (the rest), we might discern

n
(8 3') =-
n
; : pe
Vn = —
(A, 81) 5
Be Wo Bi Bases
(8» Pi v h) = (8 v Dz
Jt
(SD

Jt
(a, a’) ee

n
(a, a',) = 2arctg V2 . Al, Ur

Jl ! mn
(a, a!) — 9 Le ate 2}

1 4- yd 5 ES) LL
aif ald EUA. U}

(a, a'‚) = 2are tg — =

2n

1
(a, $n) Rake V3

1
(a, 8a) Ge V3

GD = 1, WS}
—1 5
(a) == art Palet le hr hr O1

2

hand it will be practical to choose as generative
operations when possible aequivalent operations of the group, as is
evident from the following. The octahedral group of SCHOENFLIES f.1.

between “finite nuclear groups of the first and of the second kind”.

1438

may be represented as well by {%,, W,}*) as by {%,, U, }. Adding
to the operations M, and M,M, in every combination, we find for
the second notation 9, for the first one 6 groups, as evidently
Er, AU, U} and {A,, MW}, and also {MM A, Wy} and (U, MM, AW}
and also {Mt,W,, Wt, MW’, } and {MM A,, MW} are aequivalent groups.
Therefore the first notation is preferable.

Generally both desiderata on the choice of the generative opera-

tions cannot be fulfilled at the same time. Then it is desirable to
satisfy both separately and to consider the two notations compara-
tively. :
All point groups (between which therefore the 32 classes in ques-
tion of ScHorneiirs) are then included in the preceding scheme of
14 kinds of groups for some of which two notations have been
given (see table p. 1437).

§ 8. Investigation of the aequivalence of groups that are found.
Here we ean only give some indications, which together with the
drawing of a figure or the writing out of the non- aequivalent opera-
tions of the group (the two last ways of proceeding are most times
superfluous) are at all events sufficient.

Ry way of illustration we shall directly apply, these indications
to one of the groups G for which we shall choose {%,, U}.

We must try to reduce to one all notations, by which a
group can appear. When therefore a M,M, that is added to one
of the generative operations, can be reduced to ® or even to the
identity, we shall do it. Example: {¥t,2,, M,M,W'}.. In the first
place we may replace MM, by M,M, de loss of zh
(let this proceeding never De omitted). Further, (MN, U,)? = M, is
an operation of the group. When therefore we consider M, As U,
separately as generative operations of the group we have already
followed the precept partly. We can however follow it still more
completely. As namely ®, has now become a generative operation,
we may substitute Dt, U, for M,M,U',. As then however (MW, W',)* = M,
is also an operation of the group, we must take as generative ope-
rations again M', and U, instead of MA. The group {M,A,,
MMA} is thanefere aequivalent with ie group SM, My, A, Wf.
When the newly found generative (pure time-) operations had not
happened to appear in one of the above given forms MW, MM, or
MM, we should have reduced them to one of those forms or,

; ul vate 4
1) In the following Y, means a rotation through En 360°, S a reflection in a

plane, %, a rotatory reflection.

1439

if impossible, we should be already in the above mentioned case
that all electrons are at rest, so that we had to omit all added time
operations.

From this example it is evident, that we must try to find out all
pure time operations that are included in the adding of time opera-
tions to generative operations of a group G. Evidenty we find them
all by considering all products, of the generative operations of G
that are aequivalent to the identity. In most cases these are seen
on first sight in a sufficient number. In the above example f. 1.
(U)? = 1 suffices. When however we meet with difficulties we make
use of the second notation that has been given for each group. In
this way are obtain the following scheme:

U Ws} =p, = A, (U), U,} NM, U, Ws}

Eer Ut = Pe, U, U OPERA Pi LD EO

RUE IR ME Arse MM, We, Wy, WW} — HM, Me, AU, U}

SN We WA, Ut = MM, U, U} DM, We, MU, WJM, M,, U, W,}

ER US A MWE — (DE, Wess UU MM. MU, , We, We, U} IDE, We, Us AU}

ENH, DOME At == (IDE )?, MM, WE, Me, UW, We, We, U} = (ML, Me)’,

zel ny > ame ' 5 a1; We NM I, Y

(MM), (WD APN (De, ME AU (MN, ME y’,} He

{My Wy, UJ Pt, Wey AU, Ws}

EN, ML, Ws = EN, Wey, Wy, Ws} De, , WM, MU, Wy} =D, Ms, U, 33

ED, MA, MUF = (NN, Wy, U} LED, Mes ML, DEU} — DN, MA, Wy
EN, MMU, U} (MMA, UF | EN, De, MMU, Uj= DN, Me, U, U}
EN, MA, MM, UJ, We, A, U} | $Me, DM, ADD, U} — (ND, WW}
FM, DL, ML, ADL, MUD DAA} | $e, Me, We, MA , We, MWe, U LD MAU}
so that the following 5 groups only remain:
Ps U} ED, U, U} {OEM A, WL; NM, Wy, A}
and fi i
EEM), ORDE A, NM)! Wy
First we derive all groups, in which no pure time operations are
added yet to G as generative operations; this simplifies very much
the derivation of the other groups. Above we saw that everywhere
MA, must be replaced directly by M and Y%,. As to (NM, M,U,, U}
we must attend to two things: firstly that (,M,A, == (M, W,)*;
secondly that (MIM, WU, U', 4)? —= (MMU)? — (M,M,)?, and therefore
also M M,, are operations of the group, so that the generative operation
M, M,4, has to be replaced by thegenerative operations M, M, and Y,.
93
Proceedings Royal Acad. Amsterdam. Vol. XXIII.

1440

In the case of {M,M, A, MM, A’,} the operations (MN, M,A,)? = (M,M,)*,
and in the same way (2,,)*, but also (MMA, (MN,m,W',)—)? =
= (MM, MMU jr AN, ws, MM) = MM)? belong to the
group. Now these three dilations must give together a G.C.M. of
their periods, by which the new dilation WM, is determined. Then
we must have (IN, M,)? = (MWE, (MM)? — (MM) and (MM) —
= (MN, M,)", (4, Ll and m integers). This involves Mt, IM, = (MW,)4/3,
MM, = (MM, )!/F and MM, (DM)? so that MMM, MN, =
= (MM, )//F+-m/2 — MD, = (MMS or 1/3 + m/2— k/3 and l=k+3n
(n an integer). Taking the newly found dilation as a generative opera-
tion the group becomes therefore {DM M,, MN, M,) 4/3 AU, (MIM, )" +43 A’.
In the factors of A, and U, we may of course omit powers of
M,M, with integer exponents, so that ” vanishes and we can choose
for k 1 and 2 only. Here (IN,M,)?/5 A, means nothing but AN W,)—/3 A,
the time rotation with period opposite to that of QN,I",)1/3U,. When
besides in order to avoid fractions we substitute (M, M,) for M,M,,
we obtain {M, M,)*, (MN, Me, )LtA,, WI, WM, ji W441, where +--+ means
that in the exponents only the + signs or only the — signs may
be combined.

Other time operations that must be attended to will not easily
be found beside those above mentioned. Here we have a case, that
we consider the figure using at the same time the new form for
the symbol of the group. Then it is evident, that a simple dilation .
is allowed.

In the investigation of the following groups the new symbols for the
groups obtained until now can be used. (Example: SON, M,, MM, W,, W’,}).
Not only we attend then to the groups that have been discussed
already and to which a generative time operation is joined, but
also to the groups treated before that are obtained by joining that
time operation to each of the generative operations of the first group.

Finally we may draw the attention to a way of proceeding, which
gives us easily a new generative time operation when we are joining
a generative time operation. When f.i. M, is joined to {M,2,, M, U},
so that we obtain {M,,Dt,%,, 7, W',}, then according to the above we
consider also {M,, M, Mt, A,, Wt, A}. However not only M,W,A,, but
also MMU, and therefore (MMA) — UMM, is an opera-
tion of the group, and so M,M,U, AM, M, — (MM)? too. In the
same way of course (9, M,). Further we then proceed in a similar
way as has been indicated above for {,M,U, Me, Me, W’,}.

$ 9. Final remarks. With the aid of the preceding we can find
in a rather simple way the 167 kinds of groups of space-time

1441

symmetry operations. Each kind of groups as f.i. {2} contains one
group for each value given to ”. In another paper a list of these
kinds of groups will be given. ')

Finally still the remark that not in all cases that may be found,
the nucleus must remain at rest. *)

1) Physik. ZS. 22, p. 457, 1921.

4) In contrast with the theory of space symmetry, which has a mathematical
character the theory of space time symmetry must be regarded as having a
mechanical nature. Born, Lanpé and Mape.une (see for the literature Comm.
N°. 7a) have already started with the subdivision of this theory called by them
dynamics of atoms; then the preceding might be regarded as an introduction to
the kinematics of atoms.

93*

Physiology. — “On Smelling during complete Exhaustion (resp.
adaptation) for a given odour.” By K. Komuro (Nagasaki).
(Communicated by Prof. H. ZWAARDEMAKER.)

(Communicated at the meeting of March 26, 1921).

A rather considerable number of qualities (so-called specific ener-
gies) is to be distinguished in the sense of smell. This is borne out
by exhaustion-experiments performed long ago by FROHLICH, ARON-
SOHN, ZWAARDEMAKER, HERMANIDES.

FrOuHLIcH') first fatigued his olfactory organ by a given odorous
substance and then tried to find out whether this organ was still
sensitive to other smells. In his discourse he wrote: “Wenn z. B.
Valeriana Celtica gerochen wurde, so wurde darauf der so nahe
stehende Geruch von Patchouli nicht wahrgenommen; wohl aber
erregte Valeriana nach Patchouli noch einen sehr lebhaften EKindruck.”’

ARONSOHN’) has made a more careful study of the subject. He
used some phials filled with different odorous substances. He kept
smelling at them until his sense-organ had absolutely been blunted
for the scent. Then he took another phial and tried to smell its
odour, if possible, and he determined its intensity.

By their intensity he groups the odorous substances into three
classes, viz. 1°. those of insistent intensity; 2°. those of decreased
intensity, and 3°. those that become inodorous. When e.g. his sense-
organ was exhausted for the tincture of iodine, it was still fully
sensitive to the stimulus of ethereal oils and also ether; only faintly
so to that of oil of citron, of sage, of nutmeg-blossom, of turpentine,
of bergamot and of cloves. Nothing was smelled, however, of balsam
of copaiba and of spiritus. Some more exhaustion-experiments were
made for sulphammonium, camhpor and oleum juniperi. He describes
his result as follows: ‘‘Verschiedene Geruchsqualitäten afficiren ver-
schiedene Bezirke der Geruchsnerven derart, dass eine Classe von
Riechstoffen einen Bezirk maximal erregt, einen zweiten Bezirk in
niederen Grade, einen dritten gar nicht erregt.”

Similar experiments have been performed by ZwAsaRDEMAKER*) in

1) FROHLICH, E. Sitzungsber. d. Kaiserl. Akad. d. Wissensch. Wien. Bd.
Vins. 2322.
*) ARONSOHN, E. Archiv. f. Anat. u. Physiol. 1886. S. 361.

3) ZWAARDEMAKER, H. Die Physiologie des Geruchs. Leipzig. Engelmann.
S. 255. 1895.

1443

cases of toxic anosmia evolved by cocain and in a case of post-
diphterial anosmia. His results were distributed over two tables. In
toxic anosmia evolved by cocain the smell of oil of camphor, of
nutmeg, of Roman chamomile, of lavender and of laurel was un-
impaired, whereas oil of thyme, tinctura nucis toncae, oil of euca-
lyptus, of peppermint, oleum spicae, and oil of valerian was more
or less obtused. Complete obtusion was attained with oil of cloves,
of anise, of hyssop, of rosemary and with asafoetida.

HERMANIDES’) examined exhaustion by taking for an index the
lengthening of the reaction-time it causes and tabulated his results
as follows:

Lengthening of

Reaction-time Constant Reaction-time

After Exhaustion with

Isoamylacetate } le Nitrobenzol
Nitrobenzol ree Valerianic acid
Valerianic acid deel Nitrobenzol
Scatol Scatol Isoamylacetate
Nitrobenzol

Valerianic acid

E. L. Backman’) objects to the idea of “exhaustion” and prefers
the word “adaptation”, which, however, he also wishes to avoid,
because he bases the whole phenomenon upon his differential-
hypothesis. He assumes namely that a smell-sensation can be aroused
only when a scent can penetrate as far as the olfactory cells in an
increasing or decreasing quantity, but not when the accession
of the odorous molecules (Hryninx’s odorivectors)*) occurs equably
through invariable supplies per diffusion. The olfactory stimulus
arises only when a certain procentic increase of the number of
intruding molecules has taken place. From this hypothesis it follows
that, with complete exhaustion (adaptation), only with a certain procentic
increase of the concentration of the odorous matter in the air that
reaches the olfactory region, a just noticeable sensation must be
obtained. Backman’s hypothesis on this point has entirely been
confirmed by my experiments conducted in ZWAARDEMAKER’s camera

') HERMANIDES, J. Onderz. Physiol. Lab. Utrecht.. (5) Deel 10, p. 1.

?) BACKMAN, E. L. Exp. Undersökningar öfter Luktsinnets Fysiologi. Upsala.
Läkare förendings Föfhandlingar. N. T. Bd. 22, p. 319, 1917.

°) Heyninx, A. Essai d’olfactique physiologique. These Bruxelles, 1919, p. 2.

1444

odorata, in which first exhaustion (adaptation) for a given odour
was obtained, and directly after a measurement of smelling was
taken. These experiments will be published in another paper.

For terpineol, guajacol, caproic acid, I made tests in which, after
complete exhaustion (adaptation), the smell-measurement was made
in perfumed air, which of itself did not set up a smell-sensation
any longer.

In order to make a comparative estimate of the quantity of smell
in the camera of 400 liters, I have determined, at the termination
of my experiments, the minimum perceptibile in ZWAARDEMAKER’S
smelling-box for the odour for which I had exhausted my sense-organ.

I then found that for terpineol the just noticeable concentration
was 3.9.10-10 erms. per c.c. of air. It is called. olfactie, so this
definite small quantity of odourous matter per cc. represents the value
of one olfactie of my individual unexhausted olfactory sense. At the
commencement of the experiment the absolute quantity of odorivector —
per ce. corresponding with the minimum perceptibile, was presumably
smaller, seeing that my smelling capacity for the odours used had
certainly decreased a little during my experiments. On this account
the term “exhaustion” is perhaps more correct than “adaptation”. I
will, therefore, use it for the present series of experiments *), although
it should on the other hand be acknowledged that for the lower
values the term is quite appropriate in connection with the constancy
of the liminal values of differentiation and with the analogy to the
sensation of light. (BACKMAN).

After evaporation of one drop of terpineol the camera of 400 liters
in which the head of the observer is enclosed, contains per cc. of
air 5.10-® grms of odorous substance. This concentration represents
125 of my olfacties as could be established at the termination of
my experiments. [| remained in the perfumed air for 6 minutes.
At the end of this period my olfactory sense had quite adapted
itself to the condition, so that I was not aware of any sensation of
smell. I did not perceive anything of the kind either when breathing
deeply or when sniffing.

1) Olfactometrical determinations showed that the obtusion for terpineol
and guajacol was rather considerable at the end of my experiments, when
compared with the beginning; for caproic acid, however, there was none.
This may be inferred from the length to which the cylinder had to be moved
out for the minimum perceptibile. It was:

at the outset at the end
tor terpineol 0.200 c.m. 0.300 c.m.
for Suajacol 0.145 c.m. 0.300 c.m.

for caproic acid 0.110 c.m. 0.110 c.m.

1445

In subsequent experiments this was repeated for guajacol.

The minimum perceptibile in ZWAARDEMAKER’S camera amounted
for my olfactory organ with guajacol to 6.4.10—'° grms per ce. of
air. This concentration corresponds with the value of 1 olfactie.

After one drop of guajacol was evaporated the camera of 400 liters
contained 8.2.10-§ grms per cc. of air, in other words 128 of my
olfacties. [ remained for 7 minutes in the perfumed air.

The same was repeated with caproic acid in a third series of
experiments.

The minimum perceptibile for caproic acid in ZWAARDEMAKER’S
camera per cc. of air was 3.3.10—!° germs, corresponding with one
olfactie. |

After evaporation of 0.5 drop of caproic acid the camera which
encloses the observer’s head, contains per c.c. of air: 3.35.10—§ grms
of this odorous substance. This concentration represents 118 of my
olfacties. I remained for 6 minutes in the perfumed air before
making measurements.

In these 6 minutes my organ got completely exhausted, so that
no observations could be made either when breathing deeply or
when sniffing.

When making a measurement in an inodorous surrounding with
the olfactometrical cylinders that I used, the min. pere. for my
organ corresponded with

airy lacetale.: samen wedt Ue eeu:
NUTOURNZO! ne OSR
(erpimeol sn ae eh
Artif. MOSChUB: A Sn EO
allvialeoha! … torn Tanen OREN
gaapacol:” nr irt OLS Eee
CABEDICSAEId, ha ah Urata:
AOL REESE DEE
BERDE rs Re eee

However, performing the same determination in the perfumed air
of the camera, the results are quite different.

With a view to making these determinations in the camera an
olfactometer is attached to the bottom, through which an inspiration-
tube of the olfactometer projects. This inside tube of the olfactometer
can be freed from adhering odour by means of a current of air
passing through the long movable glass-tube, which can be inserted
or disconnected at will. During the measurement the turned up part

1446

of the inspiration tube is passed into the forward half of the nostril,
while the back part and the other nostril are left open. So the

Into this chamber, mounted on high
legs, the observers head is thrust
through an opening below, which can
further be closed by a sliding lid. Under
this lid an olfactometer is applied.
Through the camera runs a movable
glass tube for a current of air to pass
through. This current serves to clean
the inside tube of the olfactometer in
the intervals of the experiments. To the
left is a rotating fan. (When the space
is used as a camera inodorata a
uviol-mercury lamp is burning to destroy
the adsorbed odours through ultra-
violet light.)

Smelling Chamber of a capacity of
400 liters arranged for exhaustion-
experiments.

observer inspires the air from the olfactometer with the one nostril,
and with the contralateral nostril he inhales the perfumed air of
the camera. In order to perfume the air that passes through the
olfactometer in the same degree as the air in the large camera a
flexible tube is led from the camera to the olfactometer. This tube
is taken up by an obturator applied to the outer cylinder of the
olfactometer.

As the flexible tube consists of metallic rings held together by
caoutchoue, it is necessary first to wash the tube out with tapwater
without drying it in order to deodorize the caoutchouc.

These precautions enable us to make the measurements at the
olfactometer while being assured that they take place in the perfumed
air for which the sense-organ has been fatigued and which does
not per se impart a smell sensation to the observer.

It is interesting now to determine the sensitiveness of the olfactory
organ for guajacol with complete terpineol-exhaustion, for terpineol
and guajacol with complete caproic acid-exhaustion.

This is shown in the subjoined tables:

1447

eT

Complete ter pineol-exhaustion !).

Min. perc. in
olfacties.
EEE el nn A Cee EN ene
Amylacetate kad
Nitrobenzol 1.4
Terpineol ao
Art. Moschus 5.0
Allylalcohol 4.5
Guajacol 4.3
Caproic acid 4.2
Pyridin 1.5
Scatol 5.0

1) Time in which complete exhaustion was attained:

with terpineol 1 drop 6 min.,
with guajacol badrop 7 min.,
with caproic acid 0.5 drop 8 min.

It appears then that exhaustion is attained sooner for terpineol, then follows
caproic acid, while guajacol comes last.

gnd

Complete guajacol-exhaustion.

Min. perc. in
olfacties.
et eee ES
Amylacetate Weel
Nitrobenzol 1:3
Terpineol 4.9
Art. Moschus . One
Allylalcohol 8.5
Guajacol ee)
Caproic acid IS)
Pyridin Ne
Scatol 5.5

1448

Complete caproic acid exhaustion.

| Min. perc. in

olfacties.
Amylacetate 1.6
Nitrobenzol 1.3
Terpineol 3.3
Art. Moschus Bad
Allylalcohol 5:5
Guajacol 5.3
Caproic acid oo
Pyridin 1.5
Scatol 4.5

GENERAL CONCLUSION.

Amylacetate, nitrobenzol and pyridin are odours for which an
olfactory organ that has been exhausted by the smell of terpineol,
guajacol or caproic acid is blunted only very slightly. The liminal
value is about 1'/, times higher than is normally the case. So the
anosmia evolved is about 7/,.

For other qualities of the series of 9 standard-odours (except
that for which complete exhaustion exists) the organ is blunted to

hs or be

Chemistry. — “On the Acceleration of Solubility of Metals in
Acids by Reducible Compounds.” By H. J. Prins. (Communi-
cated by Prof. J. BöesEKEN.)

(Communicated at the meeting of March 26, 1921).

It is a well-known fact that though there are a great many means
available for the reduction of organic compounds, the choice of the
reducer greatly contributes to the success of the reduction, so that
it is not sufficient to bring hydrogen in status nascens in the presence
of the substance that is to be reduced. It ensues from this that there
must be a relation between the reducer and the compound that is
to be reduced; if this relation were known it would be possible to
make a choice with certainty from the available reducers for a
definite purpose, or to find new reducers.

Some years ago it was pointed out') that in case of reductions
the velocity of solubility of the metal in the acid is enhanced by
the reducible substance, and that evidently a cooperation, a coaction
must take place between metal, acid, and reducible compound in
order to bring about the reduction; which is then accompanied by
a more rapid dissolving of the metal.

Definite examples of this have not been recorded, except in the
literature *) of patents.

Such coactions, which are reckoned among the mutual inductions,
are however, known in all kinds of other reactions, especially oxi-
dation reactions. Besides it is known that metals dissolve more
rapidly in the presence of oxidizers,*) in such cases it is, however,
difficult to decide, whether one bas to do with a mutual induction
or a subsequent reaction, while the formation of primary oxides
assumed by some scientists to take place in such reactions as inter-

1) Prins, Chem. Weekbl. 14, 72 (also note) and id. 1004 (1917).
Ibid 11, 476, 477 (1914).
Ibid 12, 38 et seq. (1915).
Journ. f. prakt. Chem. N. F. 89. 448 et seq. (1914).
7) LASSAR Coun, Arbeitsmeth. d. org. Chem.
3) Van Name, Chem. Gentr.bl. (1914). I 20; (1918). 1 257, 907.
Satkowski, Chem. Ztg. 40. 448 (1916).

1450

mediate product, cannot serve as an explanation in the reduction of
nitro compounds, aldehydes, and similar substances. *)

Besides for the knowledge of the phenomena of reduction and
undoubtedly also for the knowledge of the phenomena of oxidation,
more in particular in organic chemistry, this phenomenon of co-
action is of importance in that it is in close relation with catalysis,
and can easily pass into it.

The possibility that three substances which in couples do not
react on each other or in a very small degree, when brought together,
react all three on each other follows from the theory of the mutual
activation; the catalysis can then be considered as a special case of
the coaction, viz. in which two of the three possible reactions
between the three components do not take place or only in a very
small degree. At the same time this theory explains how such
coactions can be realized, and can be changed into a catalytic
action in some cases. If two compounds A and B are placed over
against a third one, C, and C is built up of two parts in such a
way that one part can be attacked by A, the other by B, a coaction
may be expected between A, B and C.

It was now the intention to examine a number of systems, con-
sisting of metal, acid or alkali and reducible compound, first of all
qualitatively with regard to the influence that the reducible compound
has on the velocity of solution of the metal, either with generation
of hydrogen or without.

It now appeared that not only nitrobenzene, but also an aldehyde
as benzaldehyde exert a surprisingly accelerating influence on the
velocity of solution. It is often, especially in the case of nitrobenzene,
so great that the metal dissolves from five hundred to a thousand
times more rapidly when nitrobenzene is present. Besides it appears,
what was also to be expected, that though nitrobenzene has almost
always an accelerating action, benzaldehyde is more selective.
(See table).

It is further remarkable that the greatest acceleration was observed
in those cases in which in the presence of the reducible compound
solution of the metal took place, but no generation of hydrogen,
which is probably related to the fact that the contact between
metal and reducible compound is prevented by the forming hydrogen,
which would also point to the probability that the reduction does

1) SKRABAL, Die induzierten Reaktionen. Samm. Chem. und chem. techn. Vorträge.
XIII. Bnd. 10. Heft. 1908.

No.

Co oH Oo On +, WO YP —

— et
oo) SS

ie)

14

26

Metal

Iron wire (%)

Zinc wire (e)

”

”

Zinc leaf (A)
Lead leaf (£)

Copper gauze (h)
”

Nickel wool (A)

Aluminium (A) leaf

id. shiny amalg.

27 Silver wire (2)
(e) = electric conduction, is nearly pure.
(A) = commercial quality.

(£) = so-called tea lead.

6,

1451

Acid

alcoh. HCI

”

acetic acid
formic acid
acetic acid

”

alcoh. acetic acid
alcoh. HCI
acetic acid

acetic acid in acetic
acid anhydr.

alcoh. acetic acid

formic acid

”

oleic acid in tur-

pentine

lauric acid in para-
fin oil

alcoh. HCI
acetic acid
formic acid

sol. potassium in
90 0/9 alcohol

HCl
KCN
HCI
HCI

alcoh.
alcoh.
alcoh.
alcoh.
alcoh. acetic acid

alcoh. NaCN

Decrease |
blank
| < 1000

280

in 40 min.

0

in 40 min.

13

| in 180 min.

in 20 min.

0

in 20 min.

230

50
250

50

4

(f)
(3)

Decrease
nitrob.

790
720
200
180
135
120
470
920
490
50
1800

in 3 min.

1150

in 10 min.

3080
in 4 min.

460

| 1070
in 10 min.
690

in 3 min.

470

in 10 min.

560

1910
1330
144
125
1450

132

pure.

> 1000 |

|
Decrease | Original

Benzald. | weight
>< 1000 | in gr.
90 1.98
90 1.98
100 1.98
10 1.97
0 1.68
40 1.86
640 | We (7e
50 Wel
— 1.39
50 1252
50 1.80
in 40 min.
40 bats
in 40 min.
13 3.08
in 180 min.
0 1.39
10 | 2.13
320 tS
0 2.07
170 1.07
in 50 min.
6 0.69
in 20 min.
0 0.47
in 20 min.
— 0.67
== 3.04
480 ZOET
— 0.441
110 0.985
— 1.45
— 0.152

To 50 cc. of acid was added 10 cc. of nitrobenzene, resp. benzaldehyde.

Time in
min.

240

120

20
120

tin foil contains a trace of lead.

1452

not take. place through hydrogen in status nascens, but that a
coaction between the three components is required.

These preliminary experiments were so executed that only character-
istic differences could be expressed; this was desirable in view
of the fact that through impurities, presence of different modi-
fications, structure in connection with the treatment, change of the
surface in consequence of the solution etc. the metals in themselves
can already give differences in the velocity of solution, which might
vitiate the conclusions to be drawn.

Use was made of metal in the form of gauze, leaf, or wire, of
which a roll or spiral was made, so that the surface that was in
contact with the liquid was as much as possible the same. Three rolls
of the same weight and surface were now placed in three Erlen-
meyer flasks, to each of which the acid was added, and after they had
assumed the temperature of the waterbath benzaldehyde was added
to the one, nitrobenzene to the second, the third containing only an
acid by the side of the metal. As soon as a perceptible action had
been exerted on one of the three, or as soon as in one of them the
metal was quite dissolved, the metal was taken out of them, washed
with water, alcohol, and ether, dried and weighed.

The original weight of the metal, the time, and the decrease are
recorded in the following table for a number of the principal
experiments.

Unless expressly stated 10 c.c. of nitrobenzene or benzaldehyde
was added to 50 ee. of acid (Cf. the table on the next page).

It appears very clearly from the table that the influence of reduc-
ible compounds on the velocity of solution of a metal can be very
great, in some cases even so great that most probably there is no
longer question of an acceleration of an existing reaction, but of a
new one.

Though in almost all cases nitrobenzene shows a very great
acceleration, also a compound as benzaldehyde appears to be able
to exert a strong positive influence (see N°. 7, 11, 12, 18, 23, 25).

It is clear that guided by the theory of these reactions shortly
mentioned in the beginning, the number of combinations can be
extended, which renders it possible greatly to increase the number
of reducers, and to define the conditions which a reducer has to
satisfy in a definite case.

Thus metal, a salt of hydrochloric acid, a feeble acid (acetic acid),
and nitrobenzene may be taken instead of metal, hydrochloric
acid, and nitrobenzene, in this way a coaction is realized in a
system of four components.

1453

When nitrobenzene is present in great concentration no hydrogen
generation is observed; the solution of the metal and the generation
of hydrogen is, however, accelerated by a smaller concentration of
the nitrobenzene.

Two strips of zinc-leaf, weighing 10.18 gr., surface 38.6 cm’,
etched with 2 norm. HCI, were placed in 190 cc. of 80°/, acetic
acid, while to one besides 2 cc. of nitrobenzene was added. After
having been kept at 73° for 40 min., the zine was weighed and the
generated hydrogen measured. The zine in the nitrobenzene experi-
ment weighed 7,45 gr, the quantity of hydrogen was 17 ce. (11°
and 772 mm.). The zine in the blank experiment weighed 10.15 gr.
and the quantity of hydrogen was 6 cc.

In this experiment there is, however, an unfairness towards the
zine in the blank experiment, because though the two experiments
start with the same surface, the nitrobenzene very soon considerably
enlarges the surfaces through its strongly corrosive action, which
gives il a permanent advantage. Therefore an experiment was made
in which the zine was etched first with diluted hydrochloric acid,
then one of the strips of zinc besides with nitrobenzene in 80°/,
acetic acid, and after purification this latter was used for the blank
experiment. The result was now as follows:

Weight of the zinc 16.32 gr. Surface 59.2 cm’. The cone. of the
nitrobenzene was taken still smaller, viz. 2,4 gr. to 170 ce. of 80°/,
acetic acid. A third experiment was made with benzophenone, viz.
3.6 gr. to 170 ee. of 80°/, acetic acid. In connection with the benzo-
phenone experiment the temperature was chosen 20° higher, i.e. 93°.

After 30 min. the condition was as follows: Weight zine in blank
experiment 16,04 gr., generated hydrogen 50 cc. (temp. 11°, baro-
meter 767 mm.). Weight zinc nitrobenzene experiment: 12.50 gr,
generated hydrogen 115 cc. Weight zinc benzophenone experiment:
16,09 gr., generated hydrogen 10 cc.

It appears from this, just as from the table that a reducible
compound can exert both an accelerating and a retarding influence as
well on the dissolving of the metal and on the hydrogen generation.

Finally a similar experiment was made with zine that had been
etched in boiling 30°/, acetic acid, to which nitrobenzene was added,
so that the nature of the zine surface was the same as in the
presence of nitrobenzene for all experiments. The quantity of benzo-
phenone was doubled, so that the quantity of reducible oxygen was
equal to that of nitrobenzene.

Weight zinc: 14,32 gr., surface 60 cm’. Blank experiment con-
tained 170 cc. of 80°/, acetic acid; the two others resp. 2,4 gr.

1454

of nitrobenzene and 7,2 gr. of benzophenone. The temperature was
kept at 65—66°.

After an hour the condition was as follows:

Weight zinc blank experiment: 14,08 gr. Generated hydrogen :
45 ec. (temp. 14°. Barometer 770 mm.).

Weight zine nitrobenzene experiment: 10,47 gr., generated hy-
drogen: 142 ce.

Weight zine benzophenone experiment: 14,19 gr., generated hy-
drogen 8 ec.

Here too benzophenone gives a retardation, it appearing at the
same time from the comparison with the hydrogen generated in the
blank experiment that part of the hydrogen has been used for the
reduction of the benzophenone. It seems, therefore, that the nature
of the surface has no influence on the qualitative result

According to the way indicated sabove it is further possible to
take in these experiments more intricate systems, in which through
coaction reactions are brought about or accelerated. Thus in the mixture
of metal, hydrochloric acid, and nitrobenzene, the hydrochloric acid
can be replaced by a feeble acid, as acetic acid, and a salt of
bydrochlorie acid.

Then a coaction takes place between four compounds:

1. Copper with 50 ec. 80°/, acetic acid and 5 gr. CaCl,.

Decrease 0.180 gr.

2. Copper with as above, and 5cc. nitrobenzene. Decrease 0.065 gr.

3. Copper with 50 ee. 70°/, aleoholand 5 gr. CaCl,. Decrease 0.015 gr.

4. Copper witb alcoh. as above and CaCl, as

above, and 5 ce. nitrobenzene. Decrease 0.005 gr.
5. Copper with 50 ce. 80°/, acetic acid and 5 gr.
CaCl, and 5 ce. nitrobenzene Decrease 0.245 gr.

Similar coactions, the explanation of which rests likewise on the
considerations given above are met with in the oxidation of organic
compounds, and can be most clearly shown by the study of the
velocity of dissolving of metal-peroxides in acids whether in presence
of oxidyzible compounds or not. Experiments on this subject are
still in progress.

It appears from the above preliminary experiments that there is
a cooperation, a coaction between metal, acid and reducible com-
pound, which is to be explained by this that a certain mutual
activation of the components must take place if the reduction is to
appear in a considerable degree. This appears to be the case both
in alcoholic and aqueous acetic acid solution, and in anhydrous
acetic or paraffin.

CONTENTS.

ABSORPTION- and extinction measurements (Photographic). Contributions to
the study of liquid crystals. V. Extinction-measurements. 807.

ACCELERATION OF SOLUBILITY (On the) of metals in acids by reducible
compounds. 1449.

Acip (On the crystalforms of some substituted amides of para-toluene-
sulphonic). 347.

Acips (The solubility of some organic) in fatty oils. 783.

— (On the acceleration of solubility of metals in) by reducible
compounds. 1449.

ADAPTATION (On smelling during complete exhaustion, resp.) for a given
odour. 1442.

ADIABATIC INVARIANTS (On the determination of quanta-conditions by means
of). 826.

ADRENAL CORTEX (Concerning the influence of the) upon the growth and
the reproduction of lower organisms and its presumable antitoxis
action. 1339.

ApsoRPTION (On) of poisons by constituents of the animal body. II. The
adsorbent power of rabbit's serum for atropin. 486.

— (On the) of odorous molecules to the surface of solids. 654.

ALKALI (The influence of different substances on the decomposition of
monoses by an) and on the inversion of cane sugar by hydro-chloric
acid. 149,

ALKALIROCKS (On the) of the Serra do Gericino to the northwest of Rio
de Janeiro and the resemblance between the eruptive-rocks of Brazil
and those of South-Africa. 1241.

ALUMINATES (The) of sodium. Equilibriums in the system Na, O-Al, Os-H,O. 129.

ALUMINIUM (The electromotive behaviour of). Il. 966.

AMIDEs (On the crystalforms of some substituted) of para-toluenesulphonic
acid. 347.

AMINES (On some condensation-products of aromatic aldehydes and). 74.

Analyse mathématique. ARNAUD DENJoy: “Sur une propriété de séries
trigonométriques.’ 220.

Anatomy. L. Bork: “On the index cephalicus and the absolute dimensions
of the head of the population of Holland.” 103.

— M. W. WOERDEMAN: “On a human ovary with a large number of
abnormal follicles and the genetic significance of this deviation.” 448.

94
Proceedings Royal Acad. Amsterdam. XXIII.

II CO NIE NTS

Anatomy. D. van Vuar: “On the homology of the M. marsupialis and
the M. pyramidalis in mammals.” 1119.

— G. C. HERINGA: “OMBREDANNE’S theory of the” lames vasculaires”
and the anatomy of the canalis cruralis.” 1209.

— L. Bork: “On the character of morphological modifications in conse-
quence of affections of the endocrine organs.” 1328.

ANIMAL BODY (On adsorption of poisons by constituents of the). II. The
adsorbent power of rabbit's serum for atropin. 486.

ANIMALS (On the serological specificity of haemoglobin in different species
of). LGE

— (Concerning the sensitivity to poisons in) suffering from avita-
minosis. 1170.
— (On the influence of the season on laboratory). 1192.

ANTIGEN (On heterogenetic). 1166.

ANTITOXIS ACTION (Concerning the influence of the adrenal cortex upon
the growth and the reproduction of lower organisms and its presum-
able). 1339.

ANTONIUS (H. O.). Bemerkungen über einige Säugetierschädel von
Sardinien. 37.

AQUEOUS SOLUTIONS (The existence of hydrates in). 969.

ARACHNIDA (Die Verwandtschaft der Merostomata mit den) und den anderen
Abteilungen der Arthropoda. 739.

ARENDSEN HEIN (S. A). v. HEIN (S. A. ARENDSEN).

AROMATIC ALDEHYDES and amines (On some condensation-products of). 74.

ARTHROPODA (Die Verwandtschaft der Merostomata mit den Arachnida und
den anderen Abteilungen der). 739.

ASSOCIATION (On the critical quantities in the case of) when the molecular
attraction is considerably increased on dissociation of the molecules
to the isolated atoms, also in connection with the critical quantities of

mercury. II. 282.

Astronomy. A. PANNEKOEK: “The distance of the dark Nebulae in Taurus.”
707. Further remarks. 720.

— W. DE Sitter: “On the possibility of statistical equilibrium of the
universe.” 866.

ATOM-MODELS of LANDE (The tetrahedrical). 1428.

Atoms (On the determination of the configuration of cyclic cis and trans
diols and the rearrangements of) and groups of atoms during chemical
reactions. 69.

— (On the critical quantities in the case of association, when the molecular
attraction is considerably increased on dissociation of the molecules to the

isolated) also in connection with the critical quantities of mercury. II. 282.

CEOANATSENN (TS HI

ATROPIN (The adsorbent power of rabbit's serum for). 486.
— (A quantitative inquiry into the antogonism pilocarpin-) on the surviving

cat-gut. 628.

AVENA SATIVA (Ueber die tropistische Wirkung von rotem Licht auf
Dunkelpflanzen von). 577.

AVITAMINOSIS (Concerning the sensitivity to poisons in animals suffering
from). 1170.

BACTERIAL ACTIONS (Identity of the blood-digestive and gelatine-liquefying). 115.

BEAM (Graphical determination of the moments of transition of an elastically
supported, statically indeterminate). II. 60.

BEAUFORT (L. F. DE). Fossils of cretaceous age in mesozoic deep-
sea deposits. 997.

Beck (R. Pu.) and A. Smits. The electromotive behaviour of magnesium.
i O75.

BEEGER (N. G. W. H.). Bestimmung der Klassenzahl aller Unterkörper
des Kreiskörpers der m-ten Einheitswurzeln. (Verbesserung). 1399.

BEMMELEN (J. F. vAN) presents a paper of Dr. H. O. Antonius:
“Bemerkungen über einige Säugetierschädel von Sardinien.” 37.
— The colour-markings on the body of Lepidoptera, compared to those
of theire larvae and pupae, and to those of their wings. 363.
— The wing-design of mimetic butterflies. 877.
BENZENE NUCLEUS (The velocity of the diazotisation reaction as a contri-
bution to the problem of substitution in the). 249.
BERGER (G.) and F. M. JAEGER. The photochemical decomposition of
potassium-cobaltioxalate and its catalysis by neutral salts. 84.
BERGH (A. A: “HirmMa Nis vy An DEN) and P. MuLLER. On serum-
lipochrome. Part II. 766.
— Concerning sulphaemoglobinaemia. 1392.
BERNSTEIN (F.). Die Integralgleichung der elliptischen Thetanullfunktion.
2e Note: Allgemeine Lésung. 817.
BHATTACHARYA (D. N.), A. K. Darra and Nit RATAN Duar. Catalysis.
VIII. 299,
BiEZENO (C. B). Graphical determination of the moments of transition
of an elastically supported, statically indeterminate beam. II. 60.
BINDING RINGS (Remark on the possible existence of) in diamond. 120.
Birps (Factors which are of importance for the habitformation of). I. Visual
sensations. 338.
BLAAUW (A. H.) presents a paper of Dr. W. E. pe Mor: “On ‘the
influence of circumstances of culture on the habitus and partial sterility
of the pollengrains of hyacinthus orientalis.” 1289.
BLED frog’s heart (On artificial and spontaneous changes of rhythm in the). 552.

94*

IV COW T ENS

BLOODCORPUSCLES (A direct proof of the impermeability of the) of man and
of the rabbit to glucose. 1256.

BLOOD-DIGESTIVE (Identity of the) and gelatine-liquefying bacterial actions. 115.

BLoop-PLASM (The interchange between) on one hand and humor aqueus
and cerebro-spinal fluid on the other hand, studied from their sugar-

percentages and in connection with the problem of combined sugar. 1343.

BoEKE (J.) presents a paper of Dr. G. Stiasny: “Ueber westindische
Tornarien nebst einer Uebersicht über die bisher bekannten tentaculaten
Tornarien.” 2.

— presents a paper of Dr. M. W. WOERDEMAN: “On a human ovary
with a large number of abnormal follicles and the genetic significance
of this deviation.” 448.

— presents a paper of Dr. G. C. HERINGA: “OMBREDANNE's theory of
the” lames vasculaires “and the anatomy of the canalis cruralis.” 1209.

Boer (J. H. pe) and F. M. JAEGER. Colloidal sulphurcompounds of
ruthenium. 95.

Boer (S. DE). On fibrillation of the heart. I. 319. Hl. On the relation
between fibrillation of the heart and “Gehdufte” extra-systoles. 329.
Ill. Ventricular fibrillation and “Gehäufte” extra-systoles of the ventricle
excited by the “Erregung” consequent on an artificial auricular systole. 533.

— On the artificial extra-pause of the ventricle of the frog’s heart. 542.

— On artificial and spontaneous changes of rhythm in the bled frog’s
heart. 552.

BOESEKEN (J.) and Cur. vAN Loon. On the determination of the con-
figuration of cyclic cis and trans diols and the rearrangements of atoms
and groups of atoms during chemical reactions. 69.

— presents a paper of Dr. F. GOUDRIAAN: “The aluminates of sodium.
Equilibriums in the system Na,O—Al, O,—H,O.” 129.

— presents a paper of Prof. H. I. WATERMAN and J. Groot: “The
influence of different substances on the decomposition of monoses by
an alkali and on the inversion of cane sugar by hydrochloric acid.” 149.

— W. F. BRANDSMA and H. A. J. SCHOUTISSEN. The velocity of the
diazotisation reaction as a contribution to the problem of substitution
in the benzene nucleus. 249.

— presents a paper of Dr. P. E. VERKADE: “On the action of micro-
organisms on organic compounds. II. The solubility of some organic
acids in fatty oils.” 783. ;

— presents a paper of Mr. H. J. Prins: “On the acceleration of solubility
of metals in acids by reducible compounds.” 1449. 5

Bork (L.). On the index cephalicus and the absolute dimensions of the
head of the population of Helland. 103.

GON TIEN TS Vv

Bork (L.) presents a paper of Mr. D. vaN Vuar: “On the homology of
the M. marsupialis and the M. pyramidalis in mammals.” 1119.

— On the character of morphological modifications in consequence of
affections of the endocrine organs. 1328.

Botany. TH. WeEEvERS: “On the calcifuge plants of the inland dunes of
the island of Goeree.” 475.

— Miss CLARA ZOLLIKOFER: “Ueber die tropistische Wirkung von rotem
Licht auf Dunkelpflanzen von Avena sativa.’ 577.

— W. E. pe Mor: “On the influence of circumstances of culture on
the habitus and partial sterility of the pollengrains of hyacinthus
orientalis.” 1289.

— M. PiNkHor: “A new method of recording the modifications in aperture
of stomata.” (first comm.). 1303.

BOUMAN (P.), A. Smits and L. v. p. LANDE. The existence of hydrates
in aqueous solutions. 969.

BRANDSMA (W. F.), J. BOESEKEN and H. A.J. SCHOUTISSEN. The velocity
of the diazotisation reaction as a contribution to the problem of

substitution in the benzene nucleus. 249.

BRAMSON (J.). Experimental proof for the active dilatation of cross-striated
muscle-tissue. 111.

BREEDING of tenebrio molitor (Technical experiences in the). 193.
BRINKMAN (R.) and S. vAN CREVELD. A direct proof of the impermeability
of the bloodcorpuscles of man and of the rabbit to glucose. 1256.

— and Miss E. van Dam. The significance of the concentration of
calciumions for the movements of the stomach caused by stimulation
of the N. vagus. 1262.

BROEKE (Miss C. VAN DEN) and W. STORM VAN LEEUWEN. A quantita-
tive inquiry into the antogonism pilocarpin-atropin on the surviving
cat-gut. 628.

BROUWER (H. A). Crystallization and resorption in the magma of the
volcano Ruang. (Sangi Islands). 561.

— Fractures and faults near the surface of moving geanticlines. I. 570.

— On the composition and the xenoliths of the lavadome of the Galunggung
(West-Java). 1234.

— On the alkalirocks of the Serra de Gericino to the northwest of Rio
de Janeiro and the resemblance between the eruptive-rocks of Brazil
and those of South-Africa. 1241.

BROUWER (L. E. J.). Ueber eineindeutige, stetige Transformationen von
Flächen in sich. (7e Mitteilung). 232.

— presents a paper of Prof. J. Worrr: “On the theorem of Picarp.” 585.

VI GON T EN fs

BROUWER (L. E. J.) presents a paper of Prof. F. BERNSTEIN: “Die Inte-
gralgleichung der elliptischen Thetanullfunktion. 2e Note: Allgemeine
Lösung’. 817.

— Intuitionistische Mengenlehre. 949.

— Besitzt jede reelle Zahl eine Dezimalbruchentwickelung ? 955.

BuRGER (H. C.). The process of solidification as a problem of conduction
of heat. 616.

— Observations of the temperature during solidification. 691.

— and P. H. van Citrert. Measurements on the intensity of spectrum
lines by the aid of the echelon. 790.

BuRGERS (J. M.). On the resistance of fluids and vortex motion. 774.

— Stationary streaming caused by a body in a fluid with friction. 1082.

BUTTERFLIES (The wing-design of mimetic). 877.

BisLSMA (M. G.) and R. MAGNus. On the pharmacological action of
isoamyl-hydrocuprein (eukupin) and isoctyl hydrocuprein (vuzin). 481.

BisvoET (J. M.), A. KARSSEN and N. H. KOLKMEIJER. Investigation by
means of x-rays of the crystalstructure of sodium-chlorate and sodium-
bromate. 644.

— and A. KARSSEN. Research by means of Röntgenrays on the structure
of the crystals of lithium and some of its compounds with light
elements. I. 1365.

CALCIFUGE PLANTS (On the) of the inland dunes of the island of Goeree. 475.

CALCIUMIONS (The significance of the concentration of) for the movements
of the stomach caused by stimulation of the N. vagus 1262.

CANALIS CRURALIS (OMBREDANNE’S theory of the “lames vasculaires” and
the anatomy of the). 1209.

CANE suGAR (The influence of different substances on the decomposition
of monoses by an alkali and on the inversion of) by hydrochloric
acid. 149.

CAPILLARY PHENOMENON. (The osmotic pressure, regarded as a). 184.

CARDINAAL (J.) presents a paper of Prof. C. B. Biezeno: “Graphical
determination of the moments of transition of an elastically supported,
statically indeterminate beam.” II. 60.

— presents a paper of Prof. W. vAN DER WOUDE: “On the motion of
a fixed system’. 589.
— presents a paper of Prof. H. J. vAN VEEN: “Properties of congruen-
ces of “rays”. 1206?
CaraLysis. Part. VU. Temperature coefficient of physiological processes. 44.
— Part. VIII. 299. Part. IX. Thermal and photochemical reactions. 308.
X. Explanation of some abnormally large and small temperature
coefficients. 313. XII. Some induced reactions and their mechanism. 1074.

GSO NTE NLS VII

CAT-GUT (A quantitative inquiry into the antogonism pilocarpin-atropin on
the surviving). 628.

CEREBRO-SPINAL FLUID (The interchange between blood-plasm on one hand
and humor aqueus and) on the other hand, studied from their sugar-

percentages and in connection with the problem of combined sugar. 1343.

CERVICAL REFLEXES (On the effect of tonic labyrinthine and) upon the
eye-muscles. 509.

CHEMICAL CONSTANT (Deduction of the dissociation-equilibrium from the

theory of quanta and a calculation of the) based on this. 162.

CHEMICAL REACTIONS (On the determination of the configuration of cyclic
cis and trans diols and the rearrangements of atoms and groups of
atoms during). 69.

Chemistry. Nit Ratan Duar: “Catalysis. Part VII. Temperature coefficient
of physiological processes”. 44.
— ARNAUD DENJoy: “Sur une classe de fonctions admettant une dérivée

seconde généralisée”. 50.

— J. BÖESEKEN and Cur. vAN Loon: “On the determination of the confi-
guration of cyclic cis and trans diols and the rearrangements of atoms

and groups of atoms during chemical reactions”. 69.

— F. M. JAEGER: “On some condensation-products of aromatic aldehydes

and amines”. 74.

— F. M. JAEGER and G. BERGER: “The photochemical decomposition of
potassium-cobaltioxalate and its catalysis by neutral salts”. 84.

— F. M. JAEGER and J. H. DE Boer: “Colloidal sulphurcompounds of
ruthenium”. 95.

— F. GOUDRIAAN: “The aluminates of sodium. Equilibriums in the system
NazO— AkOs— H2O”. 129.

— H. I. WATERMAN and J. Groot: “The influence of different substances
on the decomposition of monoses by an alkali and on the inversion
of cane sugar by hydrochloric acid”. 149.

— J. BöESEKEN, W. F. BRANDSMA and H. A. J. SCHOUTISSEN: “The
velocity of the diazotisation reaction as a contribution to the problem
of substitution in the benzene nucleus”. 249.

— Nit Ratan Duar, A. K. Datta and D. N. BHATTACHARYA: “Catalysis”.
VIII. 299.

— Nix Ratan Duar: “Catalysis”. IX. Thermal and photochemical reactions”.
308. X. “Explanation of some abnormally large and small temperature
coefficients”. 313. XII. “Some induced reactions and their mechanism”.
1074.

— F. M. JAEGER: “Two isomeric chloro-tetracetyl-d-fructoses”’. 342,

VII GON. T ESN, TS

Chemistry. F. M. JAEGER: “On the crystalforms of some substituted
amides of para-toluenesulphonic acid”. 347.

— F. M. JAEGER: “Some remarks concerning the Röntgenograms obtained
by means of micapiles composed by crossed lamellae’. 676.

— A. Smits: “On the validity of the law of partition for the equilibrium
between a mixed-crystal phase and a coexisting liquid’. I. 679.

— A. Smits and J. SPUYMAN: “The thermo-electric determination of
transition points”. I. 687.

— P. E. VERKADE: “On the action of micro-organisms on organic
compounds. II. The solubility of some organic acids in fatty oils”. 783.

— A. Smits. and G. J. pe GrulTER: “The electromotive behaviour of
aluminium”. II. 966.

— A. Smits, L. v. D. LANDE and P. Bouman: “The existence of hydrates
in aqueous solutions”. 969

— A. Smits and R. Pu. Beck: “The electromotive behaviour of mag-
nesium”’. I. 975.

— A. Smits and J. SPUIJMAN: “A thermo-electrical differential method
for the determination of transition points of metals at comparatively
low temperatures’. 977.

— F. A. H. ScHREINEMAKERS: “In-, mono- and divariant equilibria.”
ROSAS.

— H. J. Prins: “On the acceleration of solubility of metals in acids by
reducible compounds.” 1449.

CHLORO-TETRACETYL-d-fructoses (Two isomeric). 342.
CittTeERT (P. H. vAN) and W. H. Jurrius. The general relativity theory
and the solar spectrum. 522.

— and H. C. BurGer. Measurements on the intensity of spectrum lines
by the aid of the echelon. 790.

CLASSE DE FONCTIONS. (Sur une) admettant une dérivée seconde généralisée. 50.

COASTREEFS (On the occurrence of Halimeda in old-miocene) of East-
Borneo. 506.

COEFFICIENT (Temperature) of physiological processes. 44.

COEXISTING LIQUID (On the validity of the law of partition for the equilibrium
between a mixed crystal phase and a). I. 679.

COHEN (ERNST) presents a paper of Dr. Nit Ratan Duar: “Catalysis.
Part. VII. Temperature coefficient of physiological processes.” 44.

— presents a paper of Messrs. Nir Ratan Duar, A. K. Datta and D.
N. BHATTACHARYA: “Catalysis.” VIII. 299.

— presents papers of Dr. Nit Ratan Duar: “Catalysis IX. Thermal and
photochemical reactions.” 308. “Catalysis X. Explanation of some
abnormally large and small temperature coefficients.” 313. “Catalysis

XII. Some induced reactions and their mechanism.” 1074.

COINS TEEN: TS IX

COHESION FORCES (The) in the theory of VAN DER Waars. 943.
COLLOIDAL sulphurcompounds of ruthenium. 95.
COLOUR-MARKINGS (The) on the body of Lepidoptera, compared to those of
their larvae and pupae, and to those of their wings. 363.
Compounps (On the action of micro-organisms on organic) II. The solubility
of some organic acids in fatty oils. 783.
— (On the acceleration of solubility of metals in acids by reducible). 1449.
CONCENTRATION of calciumions (The significance of the) for the movements
of the stomach caused by stimulation of the N. vagus. 1262.
CONDENSATION-PRODUCTS (On some) of aromatic aldehydes and amines. 74.
CONDUCTION OF HEAT (The process of solidification as a problem of). 616.
CONGRUENCE of REYE (An involution of rays defined by a) and an involutory
homology. 466.

CONGRUENCES OF RAYS (Properties of). 1206.

CORALREEFS (On the relation between the pleistocene glacial period and
the origin of the Sunda-sea (Java- and South China-sea), and its influence
on the distribution of) and on the land- and freshwater fauna. 395.

CRANIAL CAPACITY (On the significance of the large) of homo neander-
talensis. 1271.

CRETACEOUS AGE (Fossils of) in mesozoic deep-sea deposits. 997.
CREVELD (S. VAN) and R. BRINKMAN. A direct proof of the impermeability
of the bloodcorpuscles of man and of the rabbit to glucose. 1256.

— and J. DE Haan. The interchange between blood-plasm on one hand
and humor aqueus and cerebro-spinal fluid on the other hand, studied
from their sugar-percentages and in connection with the problem of
combined sugar. 1343. é

CRITICAL QUANTITIES (On the) of mercury in connection with the increase
of the molecular attraction on dissociation of the double molecules.
E267, 1 2 282.

CROMMELIN (C. A.), H. KAMERLINGH ONNES and E. Matuias. The
rectilinear diameter of hydrogen. 1175.

— and H. KAMERLINGH ONNES. Methods and apparatus used in the
cryogenic laboratory. XVIII. Improved form of a hydrogen vapour
cryostat for temperatures between —217 C. and —253°C. 1185.

CRYOGENIC LABORATORY (methods and apparatus used in the). XVIII.
Improved form of a hydrogen vapour cryostat for temperatures between
EST GC. and —253° Cri kI85:

CRYSTALFORMS (On the) of some substituted amides of para- toluenesulphonic
acid. 347.

CRYSTALLIZATION and resorption in the magma of the volcano Ruang.
(Sangi Islands). 561.

X COIN TE NCT S

CRYSTAL PHASE (On the validity of the law of partition for the equilibrium
between a mixed) and a coexisting liquid. I. 679.
CRYSTAL-STRUCTURE (Investigation by means of x-rays of the) of sodium-

chlorate and sodium-bromate. 644.

CrysTALs (Contributions to the study of liquid). V. Extinction-measure-
ments. 807.
— (Explanation of some interference curves of uniaxial and biaxial) by
superposition of elliptic pencils. 1223.
— (Research by means of Röntgen-rays on the structure of the) of lithium
and some of its compounds with light elements. I. 1365.
Curie (On the deviations of liquid oxygen from the law of). 1127.
CYANOGEN-BANDS (The so-called). 727.
DAM (Miss E. vAN) and R. BRINKMAN. The significance of the concentration
of calciumions for the movements of the stomach caused by stimulation
of the N. vagus. 1262.
DARK NEBULAE (The distance of the) in Taurus. 707. Further remarks. 720.

DaTTA (A. K.), D. N. BHATTACHARYA and Nit RaTAN Duar. Catalysis.
VIII. 299.

DEMOLE (R.) and J. VERSLUYs. Die Verwandtschaft der Merostomata mit den
Arachnida und den anderen Abteilungen der Arthropoda. 739.

DENJOY (ARNAUD). Sur une classe de fonctions admettant une dérivée
seconde généralisée. 50.

— Sur une propriété de séries trigonométriques. 220.

DERIVEE SECONDE généralisée (Sur une classe de fonctions admettant une). 50.

DEUMENS (ALPH.). Extinction by a blackened photographic plate as
function of wavelength, quantity of silver, and size of the grains. 848.

DEZIMALBRUCHENTWICKELUNG (Besitzt jede reelle Zahl eine)? 955.

DIAMETER (The rectilinear) of hydrogen. 1175.

DIAMOND (Remark on the possible existence of binding rings in). 120.

DIAZOTISATION REACTION (The velocity of the) as a contribution to the
problem of substitution in the benzene nucleus. 249.

DiBBETzZ (G. C.), P. ZEEMAN, W. DE GROOT and Miss A. SNETHLAGE.
The propagation of light in moving, transparent, solid substances. III.
Measurements on the Fizeau-effect in flint glass. 1402.

DIFFERENTIAL METHOD (A thermo-electrical) for the determination of transition
points of metals at comparatively low temperatures. 977.

DILATATION (Experimental proof for the active) of cross-striated muscle-
tissue. 111.

Diors (On the determination of the configuration of cyclic sis and trans)

and the rearrangements of atoms and groups of atoms during chemical
reactions. 69.

GCONTEN TS XI

DissociATION (On the critical quantities of mercury in connection with the
increase of the molecular attraction on) of the double molecules. I.
267. 1b; 282.

DISSOCIATION-EQUILIBRIUM (Deduction of the) from the theory of quanta
and a calculation of the chemical constant based on this. 162.

DOUBLE MOLECULES (On the critical quantities of mercury in connection
with the increase of the molecular attraction on dissociation of the).
L267; 11. 282,

Dusois (Eug.). The proto-Australian fossil man of Wadjak, Java. 1013.

— On the significance of the large cranial capacity of homo neander-
talensis. 1271.
— On the motion of ground water in frost and thawing weather. 1321.

DUNKELFLANZEN (Ueber die tropistische Wirkung von rotem Licht auf)

von Avena sativa. 577.

EasT-BORNEO (On the occurrence of Halimeda in old-miocene coastreefs
of). 506.

ECHELON (Measurements on the intensity of spectrum lines by the aid of
the). 790.

EHRENFEST (P.) and V. TrraL. Deduction of the dissociation-equilibrium

from the theory of quanta and a calculation of the chemical constant
based on this. 162.

— presents a paper of Prof. J. M. Burgers: “On the resistance of
fluids and vortex motion”. 774.

— presents a paper of Dr. G. KrutkKow: “On the determination of
quanta-conditions by means of adiabatic invariants”. 826.

— Note on the paramagnetism of solids. 989.

— presents a paper of Prof. J. M. Burgers: “Stationary streaming caused
by a body in a fluid with friction”. 1082.

— presents a paper of Dr. P. S. Epstein: “On the principles of the
theory of quanta”. 1193.

— presents a paper of Mr. H. Zanstra: “Motion relativated by means
of a hypothesis of A. Förrpr”. 1412.

EINHEITSWURZELN (Bestimmung der Klassenzahl aller Unterkörper des
Kreiskörpers der mm-ten). (Verbesserung). 1399.
EINSTEIN’S THEORY of gravitation (The geodesic precession: a conse-
quence of). 729.
— (On the application of) to a stationary field of gravitation. 1052.
EINTHOVEN (W.) presents a paper of Dr. S. pe Boer: “On the artifi-
cial extra-pause of the ventricle of the frog’s heart’. 542.

XII GiOUN UTE Ne rs

EINTHOVEN (W.) presents a paper of Dr. S. DE Boer: “On artificial
and spontaneous changes of rhythm in the bled frog’s heart”. 552.
— On the observation and representation of thin threads. 705.
ELECTRIC ORGAN (An inquiry into the distribution of potassium compounds
in the) of the Thorn-back (Raja clavata). 842.
ELECTROLYTES (On Spray-electricity of solutions of). 658.
ELECTROMOTIVE BEHAVIOUR (The) of aluminium. II. 966.
— of magnesium. [. 975.
ELLIPTIC PENCILS (Explanation of some interference curves of uniaxial and
biaxial crystals by superposition of). 1223.
ENDOCRINE organs (On the character of morphological modifications in
consequence of affections of the). 1328.
EPsTEIN (P. S.). On the principles of the theory of quanta. 1193.
EQUATION OF STATE (On the) for arbitrary temperatures and volumes.
Analogy with PLANCK's formula. II. 887.
EQUILIBRIA (In-, mono- and divariant). XXI. 1151.
EQUILIBRIUMS in the system Na,O-Al, Os-H,O. The aluminates of sodium. 129.
— (On the validity of the law of partition for the) between a mixed-
crystal phase and a coexisting liquid. I. 679.
— (On the possibility of statistical) of the universe. 866.
ERUPTIVE-ROCKS (On the alkalirocks of the Serra do Gericino to the northwest
of Rio de Janeiro and the resemblance between the) of Brazil and
those of South-Africa. 1241.
EXHAUSTION (On smelling during complete) (resp. adaptation) for a given
odour. 1442. :
EXTINCTION-measurements (Photographic absorption- and). Contributions to
the study of liquid crystals. V. Extinction-measurements. 807.
— by a blackened photographic plate as function of wavelength, quantity
of silver, and size of the grains. 848.
EXTRA-PAUSE (On the artificial) of the ventricle of the frog’s heart. 542.

EYE-MUSCLES (On the effect of tonic labyrinthine and cervical reflexes
upon the). 509.

EyYKMAN (C.) presents a paper of Prof. J. J. van LOGHEM: “Identity of
the blood-digestive and gelatine-liquefying bacterial actions.” 115.
FELDBRUGGE (J.) and F. Rorrs. On the development of attention from

the 8th until and including the 12 year of life. 1371.

FrBriLLATION (On) of the heart. I. 319. IL. On the relation between fibrilla-
tion of the heart and “Gehäufte” extra-systoles. 329. III. Ventricular
fibrillation and “Gehäufte” extrasystoles of the ventricle excited by the
“Erregung’ consequent on an artificial auricular systole. 533.

FIELD OF CIRCLES (Two representations of the) on point-space. 1323.

CO NSTBEN:T /S XIII

FIXED SYSTEM (On the motion of a). 589.
FIZEAU EFFECT (measurements on the) in flint glass. 1402.

FLacHEN (Ueber eineindeutige, stetige Transformationen von) in sich.
(7e Mitteilung). 232.

FLINT GLASS (Measurements on the Fizeau-effect in). 1402.

FoKKER (A. D.). The geodesic precession: a consequence of EINSTEIN’s
theory of gravitation. 729.

FoLLICLEs (On a human ovary with a large number of abnormal) and the
genetic significance of this deviation. 448.

FöprrPr (A.) (Motion relativated by means of a hypothesis of). 1412.

FossiL-MAN (The proto-Australian) of Wadjak, Java. 1013.

FossiLs of cretaceous age in mesozoic deep-sea deposits. 997.

FRAUNHOFER LINES (Mutual influence of neighbouring). 1113.

FRICTION (Stationary streaming caused by a body in a fluid with). 1082.

FroG’s HEART (On the artificial extra-pause of the ventricle of the). 542.

— (On artificial and spontaneous changes of rhythm in the bled). 552.

Frost (On the motion of ground-water in) and thawing weather. 1321.

Frucroses (Two isomeric chloro-tetracetyl-d-). 342.

Functions (On analytic) defined by certain LAMBERT series. 1226.

GALUNGGUNG (West-Java) (On the composition and the xenoliths of the
lavadome of the). 1234.

GAS PRESSURE (On centres of luminescence and variations of the) in spectrum
tubes at electrical discharges. 379.

GAS REACTIONS (Derivation of a formula for the temperature dependence
of the velocity constants in) from a special image of the process. 143.

GEANTICLINES (Fractures and faults near the surface of moving). I. 570.

GEODESIC PRECESSION (The): a consequence of EINSTEIN’s theory of gravi-
tation. 729.

— (On). 1108.

Geology. G. A. F. MOLENGRAAFF and MAx WEBER: “On the relation between
the pleistocene glacial period and the origin of the Sunda sea (Java-
and South China-sea), and its influence on the distribution of coralreefs
and on the land- and freshwater fauna.” 395.

— G. A. F. MOLENGRAAFF: “On the geological position of the oil-fields
of the Dutch East-Indies.” 440.

— H. A. Brouwer: “Crystallization and resorption in the magma of the
volcano Ruang. (Sangi Islands).” 561.

— H. A. Brouwer: “Fractures and faults near the surface of moving
geanticlines. I.” 570.

— G. A. F. MOLENGRAAFF: “On manganese nodules in mesozoic deep-sea
deposits of Dutch Timor,’ with a preliminary note of Dr. L. F. DE
BEAUFORT: “Fossils of cretaceous age in those deposits.” 997.

XIV CON TE ENN TS

Geology. L. RurreN: “Quaternary and tertiary limestones of North-New
Guinea between the Tami-, and the Biri-river basins.” 1137.

— L. Rutren: “On the age of the tertiary oil-bearing deposits of the
peninsula of Klias and Pulu Labuan (N. W. Borneo).” 1142.

— H. A. BROUWER: “On the composition and the xenoliths of the
lavadome of the Galunggung.” (West-Java). 1234.

— H. A. Brouwer: “On the alkalirocks of the Serra do Gericino to the
northwest of Rio de Janeiro and the resemblance between the eruptive-
rocks of Brazil and those of South-Africa.” 1241.

Grucose (A direct proof of the impermeability of the bloodcorpuscles of
man and of the rabbit to). 1256.
GOEREE (On the calcifuge plants of the inland dunes of the island of). 475.

GOUDRIAAN (F.). The aluminates of sodium. Equilibriums in the system
Na,O-Al,O3-H,O. 129.

GRAINS (Extinction by a blackened photographic plate as tunction of wave-
length, quantity of silver, and size of the). 848.

GRAVITATION (The geodesic precession: a consequence of EINSTEIN's
theory of). 729.

— (On the application of EINsTEIN’s theory of) to a stationary field of
gravitation. 1052.

Groot (J.) and H. I. WATERMAN. The influence of different substances
on the decomposition of monoses by an alkali and on the inversion
of cane sugar by hydrochloric acid. 149.

Groot (W. DE), Miss A. SNETHLAGE, G. C. DiBBETz and P. ZEEMAN.
The propagation of light in moving, transparent, solid substances. III.
Measurements on the Fizeau-effect in flint-glass. 1402.

GROUND-WATER (On the motion of) in frost and thawing weather. 1321.

GruyTER (G. J. DE) and A. Smits. The electromotive behaviour of alumi-
nium. II. 966.

HAALMEYER (B. P.). On elementary surfaces of the third order.
(5th comm). 920.

HAAN (J. DE) and S. vaN CREVELD. The interchange between blood-plasm
on one hand and humor aqueus and cerebro-spinal fluid on the other
hand, studied from their sugar-percentages and in connection with the
problem of combined sugar. 1343. ‘

HABITFORMATION (Factors which are of importance for the) of birds. I.
Visual sensations. 338.

HAEMOGLOBIN (On the serological specificity of) in different species of
animals. 1161.

HALIMEDA (On the occurrence of) in oldmiocene coastreefs of East-
Borneo. 506.

CO ONT EON LTS XV

HAMBURGER (H. J.) presents a paper of Mrs. S. VAN CREVELD and R.
BRINKMAN: “A direct proof of the impermeability of the bloodcorpuscles
of man and of the rabbit to glucose.” 1256.
— presents a paper of Mr. R. BRINKMAN and Miss E. van Dam: “The
significance of the concentration of calciumions for the movements of
the stomach caused by stimulation of the N. vagus.” 1262.

— presents a paper of Mrs. J. DE HAAN and S. vaN CREVELD: “The
interchange between bloodplasm on one hand and humor aqueus and
cerebro-spinal fluid on the other hand, studied from their sugar-
percentages and in connection with the problem of combined
sugar.” 1343.

HAMBURGER (L.). On centres of luminescence and variations of the gas
pressure in spectrum tubes at electrical discharges. 379.

Heap of the population (On the index cephalicus and the absolute dimensions
of the) of Holland. 103.

Heart (On fibrillation of the). I. 319. II. On the relation between fibrillation
of the heart and “Gehäufte” extra-systoles. 329. II. 533.

Hein (S. A. ARENDSEN). Technical experiences in the breeding of
tenebrio molitor. 193.

HERINGA (G. C.). OMBREDANNE’s theory of the “lames vasculaires” and
the anatomy of the canalis cruralis. 1209.

HERWERDEN (Miss M. A. vaN). Concerning the influence of the adrenal
cortex upon the growth and the reproduction of lower organisms and
its presumable antitoxis action. 1339.

Heux (J. W. N. Le). Explanation of some interference curves of uniaxial

and biaxial crystals by superposition of elliptic pencils. 1223.

Histology. M. W. WOERDEMAN: “An inquiry into the distribution of
potassium-compounds in the electric organ of the Thorn-back (Raja-
clavata)” 842.

HOLLAND (On the index cephalicus and the absolute dimensions of the
head of the population of). 103.

Ho.tst (G.) and E. OosrerHuis. The so-called cyanogen-bands. 727.

Homo .oaies (An involutory transformation of the rays of space which is
defined by two involutory). 462.

Homotocy (On the) of the M. marsupialis and the M. pyramidalis in
mammals. 1119.

HOMO NEANDERTALENSIS (On the significance of the large cranial capacity
of). 1271.

Hormones (On sensibilization to radioactivity by the action of). 838.

HursHor (H.). The osmotic pressure, regarded as a capillary pheno-

menon. 184.

XVI CON TENS

HUMOR AQUEUS FLUID (The interchange between blood-plasm on one hand
and) and cerebro-spinal fluid on the other hand, studied from their
sugar-percentages and in connection with the problem of combined
sugar. 1343.

HyYACINTHUS ORIENTALIS (On the influence of circumstances of culture on
the habitus and partial sterility of the pollengrains of). 1289.

HyprRaTEs (The existence of) in aqueous solutions. 969.

HypROCHLORIC ACID (The influence of different substances on the decom-
position of monoses by an alkali and on the inversion of cane sugar by). 149.

HYDROGEN (The rectilinear diameter of). 1175.

HYDROGEN VAPOUR CRYOSTAT (Improved form of a) for temperatures between
al Cand <= 253° CISS;

Hydrology. Euc. Dusois: “On the motion of ground water in frost and
thawing weather.” 1321.
HIJMANS VAN DEN BERGH (A. A.) v. BERGH (A. A. HIJMANS VAN DEN).
HypoTHEsis of A. F6ppL (Motion relativated by means of a). 1412.
HysTEREsSIS (On the theory of) according to VOLTERRA. 663.
IHLE (J. E. W.) and G. J. vAN Oorpr. On the larval development of
oxyuris equi (Schrank). 603.
IMPERMEABILITY (A direct proof of the) of the bloodcorpuscles of man and
of the rabbit to glucose. 1256.
INDEX CEPHALICUS (On the) and the absolute dimensions of the head of
the population of Holland. 103.
INTEGRALGLEICHUNG (Die) der elliptischen Thetanullfunktion. 2e Note:
Allgemeine Lösung. 817.
INTENSITY (Measurements on the) of spectrum lines by the aid of the echelon. 790.
INTERFERENCE CURVES (Explanation of some) of uniaxial and biaxial crystals
by superposition of elliptic pencils. 1223.
INTERRUPTER (The mechanism of the automatic current). 869.
INVOLUTION of rays (An) defined by a congruence of REYE and an involutory
homology. 466.
ISOAMYLHYDROCUPREIN (eukupin) and isoctyl hydrocuprein (vuzin). (On the
pharmacological action of). 481.
JAEGER (F. M.). On some condensation-products of aromatic aldehydes
and amines. 74.
— and G. BERGER. The photochemical decomposition of potassium-
cobaltioxalate and its catalysis by neutral salts. 84.
— and J. H. pr Boer. Colloidal sulphurcompounds of ruthenium. 95.
— Two isomeric chloro-tetracetyl-d-fructoses. 342.

— On the crystalforms of some substituted amides of para-toluenesulphonic
acid. 347.

GONTEN TS XVII

JAEGER (F. M.). Some remarks concerning the Röntgenograms obtained
by means of mica-piles composed by crossed lamellae. 676.

Jurrius (W. H.) and P. H. van Crrrerr. The general relativity theory
and the solar spectrum. 522.

— presents a paper of Dr. H. C. Burger: “The process of solidification
as a problem of conduction of heat.” 616.

— presents a paper of Dr. W. Koster Dz.: “On the theory of hysteresis
according to VOLTERRA. 663.

— presents a paper of Dr. H. C. BurGer and P. H. vaN CITTERT:
“Measurements on the intensity of spectrum lines by the aid of the
echelon.” 790.

— presents a paper of Miss Rassa RIWLIN: “Photographic absorption-
and extinction-measurements. Contributions to the study of liquid
crystals. V. Extinction-measurements.” 807.

— presents a paper of Mr. ALpH. DEUMENS: “Extinction by a blackened
photographic plate as function of wavelength, quantity of silver, and
size of the grains.” 848.

— Mutual influence of neighbouring Fraunhofer lines. 1113.

KAMERLINGH ONNEsS (H.) v. ONNEs (H. KAMERLINGH).

KAPTEYN (J. C.) presents a paper of Dr. A. PANNEKOEK: “The distance
of the dark Nebulae a Taurus.” 707. Further remarks. 720.

KAPTEYN (W.) presents a paper of Dr. N. G. W. H. Beecer: “Bestimmung
der Klassenzahl aller Unterkörper des Kreiskörpers der m-ten Einheits-
wurzeln.” (Verbesserung). 1399.

KARSSEN (A), N. H. KorkMEYER and J. M. Bisvoet. Investigation by
means of x-rays of the crystalstructure of sodium-chlorate and sodium-
bromate. 644.

— and J. M. Biuvoer. Research by means of Röntgen-rays on the
structure of the crystals of lithium and some of its compounds with
light elements. I. 1365.

KeEESOM (W. H.). The quadrupole moments of the oxygen and nitrogen
molecules. 939.

— The cohesion forces in the theory of vAN DER WAALS. 943.

— On the deviations of liquid oxygen from the law of Curis. 1127.

KLEYN (A. DE). On the effect of tonic labyrinthine and cervical reflexes
upon the eye-muscles. 509.

— and R. Maanus. The function of the otolithes. 907.

— Experiments on the quick component phase of vestibular nystagmus
in the rabbit. 1357.

Krras and Pulu Labuan (N. W. Borneo) (On the age of the tertiary oil-
bearing deposits of the peninsula of). 1142.

tee aes 95

Proceedings Royal Acad, Amsterdam. Vol. XXIII,

XVIII CAC NM TeE NURS

KLOEDENELLA (The identity of the genera Poloniella and). 993.

Kruyver (J. GC). On analytic functions defined by certain LAMBERT
series. 1226.

KoLKMEYER (N. H.). Remark on the possible existence of binding rings
in diamond. 120.

— J. M. Bijvoet and A. KARSSEN. Investigation by means of x-rays of
the crystalstructure of sodium-chlorate and sodium-bromate. 644.

— Space-time symmetry. I. General considerations. 1419. Il. Discussion
of a special case. The tetrahedrical atom-models of LANpÉ. 1428. IIL.
Remarks on the deduction of groups of space-time symmetry-
operations. 1434.

Komuro (K.). On smelling during complete exhaustion (resp. adaptation)
for a given odour. 1442.
Koster Dz. (W.). Onthe theory of hysteresis according to VOLTERRA. 663.

KRAMERS (H. A.). On the application of EINSTEIN’s theory of gravitation
to a Stationary field of gravitation. 1052.

KREISKORPERS (Bestimmung der Klassenzahl aller Unterkörper des) der m-ten
Einheitswurzeln. (Verbesserung). 1399.

KrutKkow (G.). On the determination of quanta-conditions by means of

adiabatic invariants. 826.

Kryo-Biology. P. GirBERT Raum: “Einwirkung sehr niederer Temperaturen
auf die Moosfauna.” 235. .

LAAR (J. J. van). On the critical quantities of mercury in connection
with the increase of the molecular attraction on dissociation of the
double molecules. I. 267. II. 282.

— On the equation of state for arbitrary temperatures and volumes.
Analogy with PLANCK's formula. II. 887.

LABORATORY ANIMALS (On the influence of the season on). 1192.

LAMBERT SERIES (On analytic function defined by certain). 1226.

LAMELLAE (Some remarks concerning the Röntgenograms obtained by means
of mica-piles composed by crossed). 676. ;

LAMES VASCULAIRES (OMBREDANNE’S theory of the) and the anatomy of the
canalis cruralis. 1209.

LAND- AND FRESHWATER FAUNA (On the relation between the pleistocene
glacial period and the origin of the Sunda sea (Java- and South China-
sea), and its influence on the distribution of coralreefs and on the). 395.

LANDE (The tetrahedrical atom-models of). 1428.

LANDE (L. v. D.), P. Bouman and A. Smits. The existence of hydrates
in aqueous solutions. 969.

LANDSTEINER (K.). On the serological specificity of haemoglobin in

different species of animals. 1161.

CG O'N T BINT SS XIX

LANDSTEINER (K.). On heterogenetic antigen. 1166.

LARVAL DEVELOPMENT (On the) of oxyuris equi (Schrank). 603.

LAVADOME (On the composition and the xenoliths of the) of the Galunggung
(West-Java). 1234. y

Law of Curie (On the deviations of liquid oxygen from the). 1127.

LAW OF PARTITION (On the validity of the) for the equilibrium between a
mixed-crystal phase and a coexisting liquid. I. 679.

LEEUWEN (W. STORM VAN) and J. ZEYDNER. On adsorption of
poisons by constituents of the animal body. II. The adsorbent power
of rabbit’s serum of atropin. 486.

— and Miss C. VAN DEN BROEKE. A quantitative inquiry into the anto-
gonism pilocarpin-atropin on the surviving cat-gut. 628.
— and F. Verzar. Concerning the sensitivity to poisons in animals

suffering from avitaminosis. 1170.

LEPIDOPTERA (The colour-markings of the body of) compared to those of
their larvae and pupae, and to those of their wings. 363.

Licut (Ueber, die tropistische. Wirkung von rotem) auf Dunkelpflanzen
von Avena sativa. 577.

Licht (The propagation of) in moving, transparent, solid substances. III.
Measurements on the Fizeau-effect in flint glass. 1402.

LIMESTONES (Quaternary and tertiary) of North-New Guinea between the
Tami-, and the Biri-river basins. 1137.

LINEAR SYSTEMS (Degenerations in) of plane cubics. 797.

LirHium (Research by means of Röntgen-rays on the structure of the
crystals of) and some of its compounds with light elements. I. 1365.

LOGHEM (J. J. van). Identity of the blood-digestive and gelatine-liquefying
bacterial actions. 115.

LOON (CHR. VAN) and J. BöESEKEN. On the determination of the
configuration of cyclic cis and trans diols and the rearrangements of

atoms and groups of atoms during chemical reactions. 69.

LoRENTZ (H. A.) presents a paper of Dr. J. TrEsLING: “Derivation of
a formula for the temperature dependence of the velocity constants in
gas reactions from a special image of the process.” 143.

— presents a paper of Dr. H. Hutsuor: “The osmotic pressure, regarded
as a capillary phenomenon.” 184.

— presents a paper of Dr. J. J. vaN LAAR: “On the critical quantities
of mercury in connection with the increase of the molecular attraction
on dissociation of the double molecules.” I. 267. Il. 282.

— presents a paper of Dr. L. HAMBURGER: “On centres of luminescence
and variations of the gas pressure in spectrum tubes at electrical
discharges.” 379. ‘

XX CONTEBRES

LoRENTz (H. A.) presents a paper of Dr. B. VAN DER Pot Jr.: “Disconti-
nuities in the magnetisation.” 637. II. 980.

— presents a paper of Dr. H.C. Burcer: “Observations of the temperature
during solidification.” 691.

— presents a paper of Dr. A. D. Fokker: “The geodesic precession: a
consequence of EINSTEIN’s theory of gravitation.” 729.

— presents a paper of Dr. J. J. van LAAR: “On the equation of state
for arbitrary temperatures and volumes. Analogy with PLANCK's for-
mula.” II. 887.

— presents a paper of Dr. H. A. Kramers: “On the application of
EInsTEIN’s theory of gravitation to a stationary field of gravitation.” 1052.

— presents a paper of Prof. J. A. ScHouTEN: “On geodesic precession.”
1108.

LUMINESCENCE (On centres of) and variations of the gas pressure in spectrum
tubes at electrical discharges. 379.

MAGMA (Crystallization and resorption in the) of the volcano Ruang. (Sangi
Islands). 561.

MAGNEsIUM (The electromotive behaviour of). [. 975.

MAGNETISATION (Discontinuities in the). 637. II. 980.

MaGNus (R.) and U. G. Butsma. On the pharmacological action of
isoamylhydrocuprein (eukupin) and isoctyl hydrocuprein (vuzin). 481.

— presents a paper of Prof. W. STORM VAN LEEUWEN and J. ZEYDNER:
On adsorption of poisons by constituents of the animal body. Il. The
adsorbent power of rabbit's serum for atropin.” 486.

— presents a paper of Dr. A. DE KLEYN: “On the effect of tonic labyrinthine
and cervical reflexes upon the eye-muscles.” 509.

— presents a paper of Prof. W. STORM VAN LEEUWEN and Miss C. vaN
DEN BROEKE: “A quantitative inquiry into the antogonism pilocarpin-
atropin on the surviving cat-gut.” 628.

— and A. pe KreyN. The function of the otolithes. 907.

— presents a paper of Prof. W. STORM VAN LEEUWEN and F. VERzaR:
“Concerning the sensitivity to poisons in animals suffering from avita-
minosis.” 1170.

— presents a paper of Dr. A. pe KreEyN: “Experiments on the quick
component phase of vestibular nystagmus in the rabbit.” 1357.

MAMMALS (On the homology of the M. marsupialis and the M. pyramidalis
in). 1119;
MANGANESE NODULES (On) in mesozoic deepsea deposits of Dutch Timor. 997.

Mathematics. C. B. BiEzENO: “Graphical determination of the moments
of transition of an elastically supported, statically indeterminate
beam”. II. 60.

CONTENTS XXI

Mathematics. ARN. DenNsoy: “Sur une propriété de séries trigonométri-

ques”’. 220.

— L. E. J. Brouwer: “Ueber eineindeutige, stetige Transformationen
von Flachen in sich.” (siebente Mitteilung). 232.

~ JAN DE Vries: “An involutory transformation of the rays of space
which is defined by two involutory homologies.” 462.

— JAN DE Vries: “An involution of rays defined by a congruence of
REYE and an involutory homology.” 466.

— J. Worrr: “On the theorem of Picarp.’ 585.

— W. VAN DER WoubeE: “On the motion of a fixed system.” 589.

— K. W. Rotacers: “Degenerations in linear systems of plane cubics.” 797.

— F. BERNSTEIN: “Die Integralgleichung der elliptischen Thetanullfunktion.
2e Note: Allgemeine Lösung.” 817.

— B. P. HAALMEYER: “On elementary surfaces of the third order.” (fifth
comm.). 920.

— L. E. J. Brouwer: “Intuitionistische Mengenlehre.” 949.

— L. E. J. Brouwer: “Besitzt jede reelle Zahl eine Dezimalbruch-
entwickelung ?” 955.

— H. J. vaN VEEN: “Properties of congruences of rays.” 1206.

— J. W. N. re Heux: “Explanation of some interference curves of

uniaxial and biaxial crystals by superposition of elliptic pencils.’ 1223.

— J. GC. Kruyver: “On analytic functions defined by certain LAMBERT
series.” 1226.

— JAN DE Vries: “Two representations of the field of circles on point-
space.” 1323.

— N. G. W. H. Beecer: “Bestimmung der Klassenzahl aller Unterkörper
des Kreiskörpers der m- ten Einheitswurzeln.” (Verbesserung). 1399.

MATHIAS (E.), C. A. CROMMELIN and H. KAMERLINGH ONNES. The recti-
linear diameter of hydrogen. 1175.

MENGENLEHRE (Intuitionistische). 949.

Mercury (On the critical quantities of) in connection with the increase of
the molecular attraction on dissociation of the double molecules. I.
267. 115 282.

MerostomaTa (Die Verwandtschaft der) mit den Arachnida und den
anderen Abteilungen der Arthropoda. 739.

MESOZOIC DEEPSEA DEPOSITS (On manganese nodules in) of Dutch
Timor. 997.

Merars (A thermo-electrical differential method for the determination of
transition points of) at comparatively low temperatures. 977.

— (On the acceleration of solubility of) in acids by reducible

compounds. 1449.

XXII CONTENTS

MerHops and apparatus used in the cryogenic laboratory. XVII. Improved
form of a hydrogen vapour cryostat for temperatures between —217° C.
and 253°, Cioll&5,

Mica-pites (Some remarks concerning the Röntgenograms obtained by
means of) composed by crossed lamellae. 676.

MICRO-ORGANISMS (On the action of) on organic compounds. II. The solubility

of some organic acids in fatty oils. 783.

M. MARSUPIALIS and the M. pyramidalis (On the homology of the) in

mammals. 1119.

MOLECULAR ATTRACTION (On the critical quantities of mercury in connection
with the increase of the) on dissociation of the double molecules. I.
260282:

Morrcures (On the critical quantities in the case of association, when the
molecular attraction is considerably increased on dissociation of the)
to the isolated atoms, also in connection with the critical quantities of
mercury. II. 282.

— (The quadrupole moments of the oxygen and nitrogen). 939.

MOLENGRAAFF (G. A. F.) and Max Weber. On the relation between
the pleistocene glacial period and the origin of the Sunda sea (Java-
and South China-sea), and its influence on the distribution of coralreefs
and on the land- and freshwater fauna. 395.

— On the geological position of the oil-fields of the Dutch East-
Indies. 440.

— presents a paper of Prof. H. A. BROUWER: “Crystallization and resorption
in the magma of the volcano Ruang. (Sangi Islands)” 561.

— presents a paper of Prof. H. A. BROUWER: “Fractures and faults near
the surface of moving geanticlines.” I. 570.

— On manganese nodules in mesozoic deep-sea deposits of Dutch Timor;
with a preliminary note on “Fossils of cretaceous age in those
deposits.” 997.

— presents a paper of Prof. H. A. BROUWER: “On the composition and
the xenoliths of the lavadome of the Galunggung (West-Java).” 1234.

— presents a paper of Prof. H. A. Brouwer: “On the alkalirocks of
the Serra do Goricino to the northwest of Rio de Janeiro and the
resemblance between the eruptive-rocks of Brazil and those of South-
Africa.” 1241.

Mor (W. E. pe). On the influence of circumstances of culture on the
habitus and partial ‘sterility of the pollengrains of hyacinthus orien-
talis. 1289.

Morr (J. W.) presents a paper of Mr. S. A. ARENDSEN HEIN: “Technical

experiences in the breeding of tenebrio molitor.” 193.

CON TiE'N T S XXII

Morr (J. W.) presents a paper of Miss J. E. vaN VEEN: “The identity
of the genera Poloniella and Kloedenella.” 993.

MOMENTS OF TRANSITION (Graphical determination of the) of an elastically
supported, statically indeterminate beam. II. 60.

Monoses (The influence of different substances on the decomposition of)

by an alkali and on the inversion of cane sugar by hydrochloric acid. 149.
Moosrauna (Einwirkung sehr niederer Temperaturen auf die). 235.

MORPHOLOGICAL modifications (On the character of) in consequence of
affections of the endocrine organs. 1328.

Morion (On the) of a fixed system. 589.

MULLER (P.) and A. A. HIJMANS. VAN DEN BERGH. On serum-lipochrome.
Part. Il. 766.

Muscre-rissuE (Experimental proof for the active dilatation of cross-
striated). 111.

New GUINEA (Quaternary and tertiary limestones of North) between the
Tami-, and the Biri-river basins. 1137.

Nit RATAN DHARr. Catalysis. Part VI]. Temperature coefficient of phy-
siological processes. 44.

— A. K. Datta and D. N. BHATTACHARYA. Catalysis VIII. 299.

— Catalysis. IX. Thermal and photochemical reactions. 308. X. Explana-
tion of some abnormally large and small temperature coefficients. 313.
XII. Some induced reactions and their mechanism. 1074.

NITROGEN molecules (On the quadrupole moments of the oxygen and). 939.

N. vacus (The significance of the concentration of calciumions for the
movements of the stomach caused by stimulation of the). 1262.

NysTAGMUS (Experiments on the quick component phase of vestibular) in
the rabbit. 1357.

Oporous MOLECULES (On the adsorption of) to the surface of solids. 654.

Opour (On smelling during complete exhaustion (resp. adaptation) for a

; given). 1442.

OIL-BEARING deposits (On the age of the tertiary) of the peninsula of Klias
and Pulu Labuan (N. W. Borneo). 1142.

OIL-FIELDs (On the geological position of the) of the Dutch East-Indies. 440.

Oirs (The solubility of some organic acids in fatty). 783.

OMBREDANNES THEORY of the “lames vasculaires” and the anatomy
of the canalis cruralis. 1209.

ONNEs (H. KAMERLINGH) presents a paper of Dr. N. H. KOLKMEYER:
“Remark on the possible existence of binding rings in diamond.”. 120.

— presents a paper of Mr. P. GirBerT Raum: “Einwirkung sehr niederer

Temperaturen auf die Moosfauna.” 235.

XXIV CG WO UN TENTS

ONNES (H. KAMERLING H)presents a paper of Messrs N. H. KOLKMEYER,
J. M. Bisvoer and A. KARSSEN: “Investigation by means of x-rays of
the crystalstructure of sodium-chlorate and sodium-bromate.” 644.

— presents a paper of Messrs G. Horsr and E. OosrerHuis: “The so-
called cyanogen-bands.” 727.

— presents a paper of Prof. W. H. Kreesom: “The quadrupole moments
of the oxygen and nitrogen molecules.” 939.

— presents a paper of Prof. W. H. Kegsom: “The cohesion forces in
the theory of VAN DER WAALs.” 943.

— presents a paper of Prof. W. H. Keresom: “On the deviations of
liquid oxygen from the law of Curt.” 1127.

— E. Marnuias and ©. A. CROMMELIN. The rectilinear diameter of hy-
drogen. 1175.

— and C. A. CROMMELIN. Methods and apparatus used in the cryogenic
laboratory. XVIII. Improved form of a hydrogen vapour cryostat for
temperatures between —217° C. and —253° C. 1185.

— presents a papers of Dr. N. H. KoLkmeyer: “Space-time symmetry.
I. General considerations.” 1419. II. Discussion of a special case. The
tetrahedrical atom-models of LANDÉ. 1428. II]. Remarks on the deduc-
tion of groups of space-time symmetry-operations. 1434.

OorptT (G. J. vAN) and J. E. W. Inve. On the larval development of
oxyuris equi (Schrank). 603.

OosTERHUIS (E.) and G. Horst. The so-called cyanogen-bands. 727.

OSMOTIC PRESSURE (The) regarded as a capillary phenomenon. 184.

OTOLITHES (The function of the) 907.

Ovary (On a human) with a large number of abnormal follicles and the
genetic significance of this deviation. 448.

OXYGEN and nitrogen molecules (The quadrupole moments of the). 939.

— (On the deviations of liquid) from the law of Curie. 1127.

Oxyuris EQui (Schrank) (On the larval development of). 603.
Palaeontology. L. RUTTEN: “On the occurrence of Halimeda in old-miocene
coastreefs of East-Borneo.” 506.

— Miss J. E. van VEEN: “The identity of the genera Poloniella and
Kloedenella.” 993.

— Eve. Dusots: “The proto-Australian fossil-man of Wadjak, Java.” 1013.

— Eus. Dusois: “On the significance of the large cranial capacity of
homo neandertalensis.” 1271.

PANNEKOEK (A). The distance of the dark Nebulae in Taurus. 707.
Further remarks. 720.
PARAMAGNETISM (Note on the) of solids. 989.

PARA-TOLUENESULPHONIC acid (On the crystalforms of some substituted
amides of). 347.

COON “PE NSE S XXV

PEKELHARING (C. A.) presents a paper of Miss M. A. VAN HERWERDEN:
_ “Concerning the influence of the adrenal cortex upon the growth and
the reproduction of lower organisms and its presumable antitoxis
action.” 1339.
PHOTOCHEMICAL decomposition (The) of potassium-cobaltioxalate and its

catalysis by neutral salts. 84.

PHOTOGRAPHIC PLATE (Extinction by a blackened) as function of wavelength,
quantity of silver and size of the grains. 848.

Physics N. H. KOLKMEYER: “Remark on the possible existence of binding
rings in diamond.” 120.

— J. Tresuinc: “Derivation of a formula for the temperature dependence
of the velocity constants in gas reactions from a special image of the
process.” 143.

— P. EHRENFEST and V. TRKAL: “Deduction of the dissociation-equilibrium
from the theory of quanta and a calculation of the chemical constant
based on this.” 162.

— H. HursHor: “The osmotic pressure, regarded as a capillary pheno-
menon. 184.

— J. J. vAN LAAR: “On the critical quantities of mercury in connection
with the increase of the molecular attraction on dissociation of the
double molecules.” I. 267. II. 282.

— L. HAMBURGER: “On centres of luminescence and variations of the
gas pressure in spectrum tubes at electrical discharges.” 379.

— W. H. Jurrius and P. H. van Citrert: “The general relativity theory
and the solar spectrum.” 522.

— |. K. A. WERTHEIM SALOMONSON: “The limit of sensitiveness of the
String-galvanometer.” (2d communication). 613.

— H. C. Burcer: “The process of solidification as a problem of
conduction of heat.” 616.

— B. VAN DER Pou Jr.: “Discontinuities in the magnetisation.” 637. II. 980.

— N. H. KorkMEYER, J. M. BiyvoET and A. KARSSEN: “Investigation by
means of x-rays of the crystalstructure of sodium-chlorate and sodium-
bromate.” 644.

— W. Koster Dz.: “On the theory of hysteresis according to
VOLTERRA. 663. .

— H. C. Burcer: “Observations of the temperature during solidifi-
cation.” 691.

— G. Horsr and E. OosreErHuis: “The so-called cyanogen-bands.” 727.

— A. D. Fokker: “The geodesic precession: a consequence of EINSTEIN’S
theory of gravitation.” 729.

— J. M. BurGcers: “On the resistance of fluids and vortex motion.” 774,

XXVI GOoNTEN &S5

Physics. H. C. BurGer and P. H. van Cittert: “Measurements on the

intensity of spectrum lines by the aid of the echelon.” 790.

— Miss Rassa RriwriN: “Photographic absorption- and extinction-
measurements. Contributions to the study of liquid crystals. V.
Extinction-measurements.” 807.

— G. KrurKow: “On the determination of quanta-conditions by means
of adiabatic invariants.” 826.

— Arpa. DEUMENS: “Extinction by a blackened photographic plate as
function of wavelength, quantity of silver, and size of the grains.” 848.

— 1. K. A. WERTHEIM SALOMONSON: “The mechanism of the automatic
current interrupter.” 869.

— J.J. VAN LAAR: “On the equation of state for arbitrary temperatures
and volumes. Analogy with PLANCK’s formula.” II. 887.

— W. H. Keesom: “The quadrupole moments of the oxygen and nitrogen
molecules.” 939. |

— W. H. Keesom: “The cohesion forces in the theory of VAN DER
Waats.” 943.

— P. EHRENFEST: “Note on the paramagnetism of solids.” 989.

— H. A. Kramers: “On the application of EINSTEIN’s theory of gravi-
tation to a stationary field of gravitation.” 1052.

— J. M. BurcGers: “Stationary streaming caused by a body in a fluid
with friction.” 1082.

— J. A. SCHOUTEN: “On geodesic precession.” 1108.

— W. H. Jurrius: “Mutual influence of neighbouring Fraunhofer lines.” 1113.

— W. H. Kessom: “On the deviations of liquid oxygen from the law of
Curie.” 1127.

— E. Martuias, C. A. CROMMELIN and H. KAMERLINGH ONNEs: “The
rectilinear diameter of hydrogen.” 1175. |

— H. KAMERLINGH ONNEs and C. A. CROMMELIN : “Methods and appa-
ratus used in the cryogenic laboratory. XVIII. Improved form of a
hydrogen vapour cryostat for temperatures between —217° C. and
—253° C. 1185.

— P. S. Epstein: “On the principles of the theory of quanta.” 1193.

— J. M. BiyvorT 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.” I. 1365.

— P. ZEEMAN, W. DE Groot, Miss A. SNETHLAGE and G. C. DIBBETz:
“The propagation of light in moving, transparent, solid substances. III.
Measurements on the Fizeau-effect in flint glass.” 1402.

— H. Zanstra: “Motion relativated by means of a hypothesis of A.
FörrL.” 1412.

CONTENTS XXVII

Physics. N. H. KoLKMEYER: “Space-time symmetry. I. General considerations.”
1419. Il. Discussion of a special case. The tetrahedrical atom-models
of LANDÉ. 1428. III. Remarks on the deduction of groups of space-time
symmetry-operations. 1434.

Physiology. J. BRAMSON: “Experimental proof for the active dilatation of

cross-striated muscle-tissue.” 111.

— Jj. J. VAN LOGHEM: “Identity of the blood-digestive and gelatine-
liquefying bacterial actions.” 115.

— S. pe Boer: “On fibrillation of the heart.” I. 319. II. “On the rela-
tion between fibrillation of the heart and “Gehäufte” extra-systoles.”
329. III. “Ventricular fibrillation and “Gehäufte” extrasystoles of the
ventricle excited by the “Erregung’ consequent on an artificial auri-
cular systole.” 533.

— Lucire W. Scuut: “Factors which are of importance for the habit-
formation of birds. I. Visual sensations.” 338.

— R. Macnus and U. G. BijrsMaA: “On the pharmacological action of
isoamyl hydrocuprein (eukuprin) and isoctyl hydrocuprein (vuzin).” 481.

— W. STORM VAN LEEUWEN and J. ZEYDNER: “On adsorption of poisons
by constituents of the animal body. II. The adsorbent power of rabbit's
serum for atropin.” 486.

— A. DE KLEYN: “On the effect of tonic labyrinthine and cervical
reflexes upon the eye-muscles.” 509.

— S. pre Boer: “On the artificial extrapause of the ventricle of the
frog’s heart.” 542.

— S. pe Boer: “On artificial and spontaneous changes of rhythm in the
bled frog’s heart.” 552.

— W. STORM VAN LEEUWEN and Miss C. VAN DEN BROEKE: “A quantitative
inquiry into the antogonism pilocarpin-atropin on the surviving cat-gut.” 628.

— H. ZwAARDEMAKER: “On the adsorption of odorous molecules to the
surface of solids.” 654.

— H. ZWAARDEMAKER and H. ZEEHUISEN: “On Spray-electricity of
solutions of electrolytes.” 658.

— W. EINTHOVEN: “On the observation and representation of thin
threads.” 705.

— A. A. HIJMANS VAN DEN BERGH and P. MULLER: “On serum-lipo-
chrome.” II. 766.

— H. ZWAARDEMAKER: “On sensibilization to radioactivity by the action
of hormones.” 838.

— R. Maanus and A. DE KreEyN: “The function of the otolithes.” 907.

— K. LANDSTEINER: “On the serological specificity of haemoglobin in

different species of animals.” 1161.

XXVIII GC OANAT HINTS

Physiology. K. LANDSTEINER: “On heterogenetic antigen.” 1166.
— W. STORM VAN LEEUWEN and F. VERrzáR: “Concerning the sensitivity

to poisons in animals suffering from avitaminosis.” 1170.

— H. ZWAARDEMAKER: “On the influence of the season on laboratory
animals.” 1192.

— S. vAN CREVELD and R. BRINKMAN: “A direct proof of the impermeability
of the bloodcorpuscles of man and of the rabbit to glucose.” 1256.

— R. BRINKMAN and Miss E. van Dam: “The significance of the con-
centration of calciumions for the movements of the stomach caused
by stimulation of the N. vagus.” 1262.

— Miss M. A. vAN HERWERDEN: “Concerning the influence of the adrenal
cortex upon the growth and the reproduction of lower organisms and
its presumable antitoxis action.” 1339.

— J. pe HAAN and S. vaN CREVELD: “The interchange between blood-
plasm on one hand and humor aqueus and cerebro-spinal fluid on the
other hand, studied from their sugar-percentages and in connection
with the problem of combined sugar.” 1343.

— A. DE KrEYN: “Experiments on the quick component phase of vestibular
nystagmus in the rabbit.” 1357.

— A. A. HIJMANS VAN DEN BERGH: “Concerning sulphaemoglobinaemia.”
1392.

— K. Komuro: “On smelling during complete exhaustion (resp. adaptation)
for a given odour.” 1442.

P1caRD (On the theory of). 585.

PILOCARPIN-ATROPIN (A quantitative inquiry into the antogonism) on the
surviving cat-gut. 628.

PiNnKkKHor (M.). A new method of recording the modifications in aperture
of stomata. (first comm.). 1303.

PLANCK’s formula (Analogy with). II. 887.

PLANE CUBICS (Degenerations in linear systems of). 797.

PLEISTOCENE GLACIAL PERIOD (On the relation between the) and the origin
of the Sunda sea (Java- and South China-sea), and its influence on the
distribution of coralreefs and on the land- and freshwater fauna. 395.

POINT-SPACE (Two representations of the field of circles on). 1323.

Poisons (On adsorption of) by constituents of the animal body. II. The
adsorbent power of rabbit's serum for atropin. 486.

— (Concerning the sensitivity to) in animals suffering from avitaminosis. 1170.
Por Jr. (B. VAN DER). Discontinuities in the magnetisation. 637. II. 980.
POLLENGRAINS (On the influence of circumstances of culture on the habitus

and partial sterility of the) of hyacinthus orientalis. 1289.

POLONIELLA and Kloedenella (The identity of the genera). 993.

C’'O'N T°E!N:‘T'S XXIX

POTASSIUM-COBALTIOXALATE (The photochemical decomposition of) and its
catalysis by neutral salts. 84. a

PoTASSIUM COMPOUNDS (An inquiry into the distribution of) in the electric
organ of the Thorn-back (Raja clavata). 842.

Prins (H. J.). On the acceleration of solubility of metals in acids by
reducible compounds. 1449.

Psychology (Experimental). F. Rorers and J. FELDBRUGGE: “On the
development of attention from the 8" until and including the 12th year
of life.” 1371. |

QUADRUPOLE MOMENTS (The) of the oxygen and nitrogen molecules. 939.

QUANTA (Deduction of the dissociation-equilibrium from the theory of) and

a calculation of the chemical constant based on this. 162.
— (On the principles of the theory of). 1193.

QUANTA-CONDITIONS (On the determination of) by means of adiabatic
invariants. 826.

QUATERNARY and tertiary limestones of North-New Guinea between the

Tami-, and the Biri-river basins. 1137.

RassiT (A direct proof of the impermeability of the bloodcorpuscles of man
and of the) to glucose. 1256.

— (Experiments on the quick component phase of vestibular nystagmus

in the). 1357.

RABBIT’S SERUM (The adsorbent power of) for atropin. 486.

Rapioactivity (On sensibilization to) by the action of hormones. 838.

Raum (P. GirBERT). Einwirkung sehr niederer Temperaturen auf die
Moosfauna. 235.

Rays OF SPACE (An involutory transformation of the) which is defined by
two involutory homologies. 462.

RELATIVITY THEORY (The general) and the solar spectrum. 522.

RESISTANCE of fluids (On the) and vortex motion. 774.

RESORPTION (Crystallization and) in the magma of the volcano Ruang.
(Sangi Islands). 561.

REYE (An involution of rays defined by a congruence of) and an involutory
homology. 466.

RHYTHM (On artificial and spontaneous changes of) in the bled frog’s heart. 552.

,

RrwriN (Miss Rassa). Photographic absorption- and extinction-measure-
ments. Contributions to the study of liquid crystals. V. Extinction-
measurements. 807.

Roets (F.) and J. FELDBRUGGE. On the development of attention from
the 8th until and including the 12% year of life. 1371.

RONTGENOGRAMS (Some remarks concerning the) obtained by means of

mica-piles composed by crossed lamellae. 676.

XXX CON TEN: TS

RONTGENRAYS (Research by means of) on the structure of the crystals of

lithium and some of its compounds with light elements. I. 1365.
RuTGERs (K. W.). Degenerations in linear systems of plane cubics. 797.
RUTHENIUM (Colloidal sulphurcompounds of). 95.

RuTTEN (L.). On the occurrence of Halimeda in old-miocene coastreefs
of East-Borneo. 506.

— Quaternary and tertiary limestones of North-New Guinea between the
Tami-, and the Biri-river basins. 1137.

— On the age of the tertiary oil-bearing deposits of the peninsula of
Klias and Pulu Labuan (N.W. Borneo). 1142.

RIJNBERK (G. VAN) presents a paper of Mr. J. BRAMSON: “Experimental
proof for the active dilatation of cross-striated muscle-tissue.” 111.
— presents a paper of Miss Lucie W. ScnuT: “Factors which are of
importance for the habitformation of birds. I. Visual sensations.” 338.
SALOMONSON (I. K. A. WERTHEIM) presents a paper of Dr. S. DE
Boer: “On fibrillation of the heart.” I. 319. II. “On the relation between
fibrillation of the heart and “Gehäufte” extra-systoles.” 329. III:
“Ventricular fibrillation and “Gehäufte” extra-systoles of the ventricle
excited by the ‘“Erregung’” consequent on an artificial auricular
systole.” 533.
— The limit of sensitiveness of the String-galvanometer. (2d communi-
cation). 613.
— The mechanism of the automatic current interrupter. 869.
SaLts (The photochemical decomposition of potassium-cobaltioxalate and
its catalysis by neutral). 84.
SARDINIEN (Bemerkungen über einige Säugetierschädel von). 37.

SäUGETIERSCHÄDEL (Bemerkungen über einige) von Sardinien. 37.
SCHOUTEN (J. A). On geodesic precession. 1108.

SCHOUTISSEN (H. A. J.), J. BOESEKEN and W. F. BRANDSMA. The velocity
of the diazotisation reaction as a contribution to the problem of
substitution in the benzene nucleus. 249.

SCHREINEMAKERS (F. A. H.). In-, mono- and divariant equilibria.
NK altal.

SCHUT (Miss Lucie W.). Factors which are of importance for the

habitformation of birds. I. Visual sensations. 338.

SENSIBILIZATION (On) to radioactivity by the action of hormones. 838.
SENSITIVENESS (The limit of) of the String-galvanometer. 613.

SERIES triSonométriques (Sur une propriété de). 220.

SEROLOGICAL specificity (On the) of haemoglobin in different species of

animals. 1161.

GON TSE N “FSS XXXI

SERRA DO GERICINO (On the alkalirocks of the) to the northwest of Rio de
Janeiro and the resemblance between the eruptive-rocks of Brazil and
those of South Africa. 1241.

SERUM-LIPOCHROME (On). Part II. 766.

SILVER (Extinction by a blackened photographic plate as function of
wavelength, quantity of) and size of the grains. 848.

SITTER (W. pe). On the possibility of statistical equilibrium of the
universe. 866.

SLUITER (C. PH.) presents a paper of Prof. J. E. W. InrE and Dr. G.
J. vAN Oorptr: “On the larval development of oxyuris equi (Schrank).” 603.

SMITS (A). On the validity of the law of partition for the equilibrium
between a mixed-crystal phase and a coexisting liquid. I. 679.

— and J. SPUYMAN. The thermo-electric determination of transition
points. I. 687.

— and G. J. De Gruyter. The electromotive behaviour of aluminium.
II. 966.

— L. v. p. LANDE and P. Bouman. The existence of hydrates in aqueous
solutions. 969.

— and R. Pu. Beck. The electromotive behaviour of magnesium. I. 975.

— and J. SPUYMAN. A thermo-electrical differential method for the
determination of transition points of metals at comparatively low
temperatures. 977.

SNETHLAGE (Miss A.), G. C. Dippetz, P. ZEEMAN and W. DE GROOT.
The propagation of light in moving, transparent, solid substances. III.
Measurements on the Fizeau-effect in flint glass. 1402.

Sopium (The aluminates of). Equilibriums in the system Na; O—Al, O;,—H,0O.
129.
SODIUM-CHLORATE and sodium-bromate (Investigation by means of x-rays
of the crystalstructure of). 644.
SOLAR SPECTRUM (The general relativity theory and the). 522.
SOLIDIFICATION (The process of), as a problem of conduction of heat. 616.
— (Observations of the temperature during). 691.
Souips (On the adsorption of odorous molecules to the surface of). 654.
— (Note on the paramagnetism of). 989.
SPACE TIME SYMMETRY. I. General considerations. 1419. II. Discussion of a
special case. The tetrahedrical atom-models of Landé. 1428. III. Remarks
on the deduction of groups of space-time symmetry-operations. 1434.
SPECTRUM-LINES (Measurements on the intensity of) by the aid of the
echelon. 790.
SPECTRUM TUBES (On centres of luminescence and variations of the gas

pressure in) at electrical discharges. 379.

XXXII CONTENTS

SPRAY-ELECTRICITY (On) of solutions of electrolytes. 658.
SPRONCK (C. H. H.) presents a paper of Mr. K. LANDSTEINER: “On the
serological specificity of haemoglobin in different species of animals.” 1161.
— presents a paper of Mr. K. LANDSTEINER: “On heterogenetic antigen.”
1166.
SpuYMAN (J.) and A. Smits. The thermo-electric determination of trans-
ition points I. 687.
— and A. Smits. A thermo-electrial differential method for the determination

of transition points of metals at comparatively low temperatures. 977.

STATISTICAL EQUILIBRIUM (On the possibility of) of the universe. 866.

STIASNY (GUSTAV). Ueber westindische Tornarien nebst einer Ueber-
sicht tiber die bisher bekannten tentaculaten Tornarien. 2.

STtoMACcH (The significance of the concentration of calciumions for the
movements of the) caused by stimulation of the N. vagus. 1262.

STOMATA (A new method of recording the modifications in aperture of)
(first comm.). 1303.

STORM VAN LEEUWEN (W.) v. LEEUWEN (W. STORM VAN).

STREAMING (Stationary) caused by a body in a fluid with friction. 1082.

STRING-GALVANOMETER (The limit of sensitiveness of the). 613.

SUBSTANCES (The propagation of light in moving, transparent, solid). III.
Measurements on the Fizeau-effect in flint glass. 1402.

SUBSTITUTION (The velocity of the diazotisation reaction as a contribution
of the problem of) in the benzene nucleus. 249.

SUGAR-PERCENTAGES (The interchange between bloodplasm on one hand
and humor aqueus and cerebro-spinal fluid on the other hand, studied
from their) and in connection with the problem of combined sugar. 1343.

SULPHAEMOGLOBINAEMIA (Concerning). 1392.

SULPHURCOMPOUNDS of ruthenium (Colloidal). 95.

SUNDA-SEA (On the relation between the pleistocene glacial period and the
origin of the) (Java- and South China-sea), and its influence on the
distribution of coralreefs and on the land- and freshwater fauna. 395.

SUPERPOSITION of elliptic pencils (Explanation of some interference curves
of uniaxial and biaxial crystals by). 1223.

SURFACES (On elementary) of the third order. (Stb comm.). 920.

Taurus (The distance of the dark Nebulae in). 707. Further remarks. 720.

TEMPERATURE (Observations of the) during solidification. 691.

TEMPERATURE DEPENDENCE (Derivation of a formula for the) of the velocity
constants in gas reactions from a special image of the process. 143.

TEMPERATUREN (Einwirkung sehr niederer) auf die Moosfauna. 235.

TEMPERATURES and volumes (On the equation of state for arbitrary).

Analogy with PLANCK's formula. II. 887.

GlOUNST BSN (TS XXXIII

TEMPERATURES (A thermo-electrical differential method for the determination
of transition points of metals at comparatively low). 977.
— (Improved form of a hydrogen vapour cryostat for) between —217° C.
and —253°C. 1185.
TENEBRIO MOLITOR (Technical experiences in the breeding of). 193.
THAWING WEATHER (On the motion of ground water in frost and). 1321.
THEORY of PicarD (On the). 585.
— of quanta (On the principles of the). 1193.
THERMO-ELECTRIC determination (The) of transition points. I. 687.
THETANULLFUNCTION (Die Integralgleichung der elliptischen). 2e Note: All-
gemeine Lösung. 817.
THIN THREADS (On the observation and representation of). 705.
THORN-BACK (Raja clavata) (An inquiry into the distribution of potassium-
compounds in the electric organ of the). 842.
Timor (On manganese nodules in mesozoic deep-sea deposits of Dutch). 997.
TONIC LABYRINTHINE (On the effect of) and cervical-reflexes upon the eye-
muscles. 509.
TORNARIEN (Ueber westindische) nebst einer Uebersicht über die bisher
bekannten tentaculaten Tornarien. 2.
TRANSFORMATION (An involutory) of the rays of space which is defined by
two involutory homologies. 462.
TRANSFORMATIONEN (Ueber eineindeutige, stetige) von Flächen in sich. (7e
Mitteilung). 232.
TRANSITION-POINTS (The thermo-electric determination of) I. 687.
— A thermo-electrical differential method for the determination of) of
metals at comparatively low temperatures. 977.
TRESLING (J.). Derivation of a formula for the temperature dependence of the
velocity constants in gas reactions from a special image of the process. 143.
TRKAL (V.) and P. EHRENFEsT. Deduction of the dissociation-eavilintiam
from the theory of quanta and a calculation of the chemical constant
based on this. 162.

UNIVERSE (On the possibility of statistical equilibrium of the). 866.
UNTERKÖRPER (Bestimmung der Klassenzahl aller) des Kreiskörpers der

m-ten Einheitswurzeln. (Verbesserung). 1399.

VEEN (H. J. van). Properties of congruences of rays. 1206.

VEEN (Miss J. E. vaN). The identity of the genera Poloniella and Kloe-
denella. 993.

VeLocity (The) of the diazotisation reaction as a contribution to the
problem of substitution in the benzene nucleus. 249.

VELOCITY CONSTANTS (Derivation of a formula for the temperature depend-

ence of the) in gas reactions from a special image of the process. 143.

XXXIV CON TENDS

VENTRICLE (Ventricular fibrillation and ,,Gehdufte’” extrasystoles of the)

excited by the ,,Erregung” consequent on an artificial auricular systole. 533.
— (On the artificial extra-pause of the) of the frog’s heart. 542.

VERKADE (P. E). On the action of micro-organisms on organic com-
pounds. II. The solubility of some organic acids in fatty oils. 783.

Verstuys (J.) and R. DeMorr. Die Verwandtschaft der Merostomata
mit den Arachnida und den anderen Abteilungen der Arthropoda. 739.

VerzarR (F.) and W. STORM VAN LEEUWEN. Concerning the sensitivity
to poisons in animals suffering from avitaminosis. 1170.

VISUAL sensations. 338.

VOLCANO RuANG (Sangi Islands) (Crystallization and resorption in the
magma of the). 561.

VOLTERRA (On the theory of hysteresis according to). 663.

VoruMes (On the equation of state for arbitrary temperatures and). Analogy
with PLANCK's formula. II. 887.

VORTEX MOTION (On the resistance of fluids and). 774.

Vries (HENDRIK DE) presents a paper of Dr. B. P. HAALMEYER: “On
elementary surfaces of the third order.” (Stk comm.). 920.

— presents a paper of Dr. J. W. N. Le Heux: “Explanation of some
interference curves of uniaxial and biaxial crystals by superposition of
elliptic pencils.” 1223.

VRIES (JAN DE). An involutory transformation of the rays of space
which is defined by two involutory homologies. 462.

— An involution of rays defined by a congruence of REYE and an
involutory homology. 466.

— presents a paper of Prof. K. W. Rutgers: “Degenerations in linear
systems of plane cubics.” 797.

— Two representations of the field of circles on point-space. 1323.

VucT (D. vAN). On the homology of the M. marsupialis and the M.
pyramidalis in mammals. 1119.

W AALS (VAN DER) (The cohesion forces in the theory of). 943.

Wapiak, Java (The proto Australian fossil man of). 1013.

WATERMAN (H. I.) and J. Groot. The influence of different substances
on the decomposition of monoses by an alkali and on the inversion
of cane sugar by hydrochloric acid. 149.

WAVELENGTH (Extinction by a blackened photographic plate as function of)
quantity of silver and size of the grains. 848.

WEBER (MAX) and G. A. F. MOLENGRAAFF. On the relation between
the pleistocene glacial period and the origin of the Sunda sea (Java-
and South China-sea), and its influence on the distribution of coralreefs

and on the land- and freshwater fauna. 395.

GO NTE NL Ss XXXV

WEBER (MAx) presents a paper of Prof. J. VERSLUYS and R. DEMOLL:
“Die Verwandtschaft der Merostomata mit den Arachnida und den
anderen Abteilungen der Arthropoda.” 739.

WeEEVERS (TH.). On the calcifuge plants of the inland dunes of the
island of Goeree. 475.
Went (F. A. F. C.) presents a paper of Dr. TH. WeEeEveErRs: “On the
calcifuge plants: of the inland dunes of the island of Goeree.” 475.
— presents a paper of Miss Dr. CLARA ZOLLIKOFER: “Ueber die tropis-
tische Wirkung von rotem Licht auf Dunkelpflanzen von Avena sativa.” 577.
— presents a paper of Mr. M. PiNKkHor: “A new method of recording

the modifications in aperture of stomata.” (first comm.). 1303.

WERTHEIM SALOMONSON (I. K. A). v. SALOMONSON (I. K. A.
WERTHEIM). |

WING-DESIGN (The) of mimetic butterflies. 877.

Wincs (The colour-markings on the body of Lepidoptera, compared to
those of their larvae and pupae, and to those of their). 363.

WINKLER (C.) presents a paper of Mrs. F. Roers and J. FELDBRUGGE:
“On the development of attention from the 8 until and including the
12th year of life.” 1371.

WOERDEMAN (M. W.). On a human ovary with a large number of ab-
normal follicles and the genetic significance of this deviation. 448.

— An inquiry into the distribution of potassium-compounds in the electric
organ of the Thorn-back (Raja clavata). 842.

Worrr (J.). On the theorem of PicARD. 585.

W oUDE (W. VAN DER). On the motion of a fixed system. 589.

X-rays (Investigation by means of) of the crystalstructure of sodium-chlorate
and sodium-bromate. 644. :

YEAR OF LIFE (On the development of attention from the 8t» until and
including the 12th), 1371.

ZAHL (Besitzt jede reelle) eine Decimalbruchentwickelung? 955.

ZANSTRA (H.). Motion relativated by means of a hypothesis of A.
Förrer. 1412.

ZEEHUISEN (H.) and H. ZWAARDEMAKER. On Spray-electricity of solutions
of electrolytes. 658.

ZEEMAN (P.) presents a paper of Prof. A. Smits: “On the validity of the
law of partition for the equilibrium between a mixed-crystal phase
and a coexisting liquid.” I. 679.

— presents a paper of Prof. A. Smits and J. SPUYMAN: “The thermo-
electric determination of transition points.” I. 687.
— presents a paper of Prof. A. Smits and G. J. DE GRUYTER: “The

electromotive behaviour of aluminium.” II. 966.

XXXVI GON TEN GDS

ZEEMAN (P.) presents a paper of Prof. A. Smits, L. v. p. LANDE and P.
BouMAN: “The existence of hydrates in aqueous solutions.” 969.

— presents a paper of Prof. A. Smits and R. Pu. Beck: “The electro-
motive behaviour of magnesium.” 1. 975.

— presents a paper of Prof. A. Smits and J.'SPUYMAN: “A thermo-
electrical differential method for the determination of transition points
of metals at comparatively low temperatures.” 977.

— presents a paper of Mrs J. M. Bivoer 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.” [. 1365.

—, W. pe Groot, Miss A. SNETHLAGE and G. C. DrBBeTz. The propagation
of light in moving transparent, solid substances. III]. Measurements
on the Fizeau-effect in flint glass. 1402.

ZEYDNER (J.) and W. STORM VAN LEEUWEN. On adsorption of poisons
by constituents of the animal body. II. The adsorbent power of rabbit's
serum for atropin. 486.

ZOLLIKOFER (Miss CLARA). Ueber die tropistische Wirkung von rotem
Licht auf Dunkelpflanzen von Avena sativa. 577.

Zoology. G. Sriasny: “Ueber westindische Tornarien nebst einer Ueber-
sicht iiber die bisher bekannten tentaculaten Tornarien.” 2.

— H. O. ANTOoNius: “Bemerkungen über einige Säugetierschädel von
Sardinien.” 37.

— S. A. ARENDSEN HEIN: “Technical experiences in the breeding of
tenebrio molitor.” 193.

— J. F. van BEMMELEN: “The colour-markings of the body of Lepidop-
tera, compared to those of their larvae and pupae, and to those of
their wings.” 363.

— J. E. W. Inve and G. J. van Oorptr: “On the larval development of
oxyuris equi (Schrank). 603.

— J. VERSLUYS and R. DEMOLL: “Die Verwandtschaft der Merostomata
mit den Arachnida und den anderen Abteilungen der Arthropoda.” 739.

— J. F. vaN BEMMELEN: “The wing-design of mimetic butterflies.” 877.

ZWAARDEMAKER (H.). On the adsorption of odorous molecules to the
surface of solids. 654.

— and H. ZEEHUISEN. On Spray-electricity of solutions of electrolytes. 658.
— On sensibilization to radioactivity by the action of hormones. 838.

— presents a paper of Mr. M. W. WOERDEMAN: “An inquiry into the
distribution of potassium-compounds in the electric organ of the Thorn-
back (Raja clavata)” 842.

— On the influence of the season on laboratory animals. 1192.

— presents a paper of Mr. K. Komuro: “On smelling during complete
exhaustion (resp. adaptation) for a given odour.” 1442.

KONINKLIJKE AKADEMIE
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VOLUME XXIII
— (2° PART) —
— (Nos. 6—9) —

PUBLISHED BY
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JUNE 1922

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