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KONINKLIJKE AKADEMIE
VAN WETENSCHAPPEN
-- TE AMSTERDAM -:-

EROCEEDINGS OF THE
SECTION OF SCIENCES

VOLUME XVII
(C= IND PART =)

JOHANNES MULLER :—: AMSTERDAM
JUNE 1915 | :

p ENT Of AMAR 4
U EENS ae i bent NAG +0
EE ro ee ANNE TNH ATRIAL fs
a aes ane ata ae A NOEL WEA AU PATE Ln |
a ne is t Pee sss NES San teas Ss Pies ; 4 th
‘ ta is ie. we 7 eS
ae LN K: pn oe nj
eben Sieh 8 :
Ka M be, ¥ a = i.
“» é EN
(Translated from: Verslagen van de Gewone Vergaderingen der Wis- en ‘Natuur-
kundige Afdeeling van 30 December 1914 tot 23 April 1915. Dl. XXII.)
I QSHQ Fah.

CON To Ren TS:

——_—__<e ~<

Proceedings of the Meeting of December 30, 1914

» » January 30, 1915

» » February 27, »

> » March 27, »

» » April 28, »

Page

873

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING
of Wednesday December 30, 1914.
Vor. XVII.

IGG

President: Prof. H. A. Lorenz,
Secretary: Prof. P. Zeeman.

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Woensdag 30 December 1914, Dl. XXIII).

CON. & BNN WS:

H. pu Bors: “The universality of the ZeEMAN-eftect with respect to the StArk-effect in canal-
rays”, p. 873.

J. J. van Laar: “The calculation of the molecular dimensions from the supposition of the
electric nature of the quasi-elastic atomic forces,” (Communicated by Prof. H. A. Lorentz),
p- 877.

J. K. A. WERTHEIM SALOMONSON: “Exaggeration of Deep Reflexes.” p. 885.

W. H. Kersom and H. Kameritincu Onnesi “The specifie heat at low temperatures. I.
Measurements on the specific heat of lead between 14° and 80° K. and of copper between
159 and 22° K.” (Communicated by Prof. H. KAMERLINGH ONNES). p. 894.

C. Winxter: “A case of occlusion of the arteria cerebelli posterior inferior.” p. 914.

Ernst COHEN and G. pe Bruin: “The metastability of the Metals in consequence of Allotropy
and its significance for Chemistry, Physics and Technics,” III, p. 926.

JAN DE Vries: “Characteristic numbers for nets of algebraic curves.” p. 935.

Erratum, p. 944.

Physics. — “The universality of the Zeeman-effect with respect to the
Stark-effect wm canal-rays.’ By H. pv Bors. (Communication
from the Bosscua-Laboratory).

(Communicated in the meeting of November 28, 1914).

. Notwithstanding several efforts *) no one had succeeded in demon-
strating the smallest influence of electrostatic fields on spectral lines
until Stark *) observed such a specific effect for lines emitted by the

1) See G. F. Hur, Proc. Roy. Soc. 78 p. 80, 1907. P. Zeeman, These Proc.
19 p. 957, 1911; 20 p. 731, 1911. F. Pascuen & W. Geruacu, Phys. Ztschr. 15
p. 489, 1914.

2) J. Starx and his collaborators, Sitz.ber. Berl. Akad. 47 p. 932, 1913; Ann.

58

Proceedings Royal Acad. Amsterdam. Vol. XVII.

874

canal-rays of hydrogen, helium and lithium. In his experiments
the electric field, €, reached values of more than 150 electrostatic
units, viz. €,, in electromagnetic units was more than 45 kilovolt/em;
the largest separation surpassed 2 uu for H7, (A = 434,1 uw).

Starting from the theoretical equivalence of €, and the vector-
product [BH] W. Wien‘) then presumed an analogous specific
magnetic separation of spectral lines of hydrogen canal-rays
and experimentally verified this. In his experiments the maximum
velocity in the canal-rays, ®, reached a value of 7700 km. per
second; while the magnetic field was about 17 kilogauss. The
separation observed for H, was of the order of 0,5 uu, i.e. very
much larger than that ef the ordinary Zeeman-effect, for which the
normal separation in this field would amount to about 0,03 uu only.

As far as we can now already judge, we have here two separate,
without doubt closely connected, phenomena, which are both propor-
tional with the field and which appear to depend on the velocity of
the charges. With an extremely sensitive method PascHENn and GurLacu
sought for an electric effect (€ = 15 kilovolt/em) in mercury vapour;
but in vain. From this they rightly conclude, that there is no
question here of an electric analogon of the real Zeeman-effect. For
this is generally shown by many lines of emission, absorption
and fluorescence of vapours and selective crystals : the unsensitiveness
of certain lines moreover may be only apparent (dà < 0,002 uu
say).

As early as 1899 this problem was treated theoretically by Voter’);
according to him an electro-optic displacement or separation probably
would occur, though maybe a very small one, proportional with 4° €?.
Therefore it would be favourable for observation to choose these two
factors as large as possible. Recently, before the publication of
Wien’s experiments however, WARBURG and ScHWARZSCHILD *) have
developed formulae, the former starting from the theory of quanta, the
latter by means of purely attractory considerations. SCHWARZSCHILD

d. Phys. 43 p. 965—1045, 1914; Phys. Ztschr. 15 pp. 215, 265, 1914; Verh. D.
Phys. Ges. 16 p, 304, 1914. Elektr. Spektr. anal. chem. Atome, Leipzig 1914. A.
Lo Surpo, Rend. Acc. Lincei (1) 23 p. 143, 1914; Phys. Ztschr. 15 p. 122,
1914. H. .Wisar, Gött. Nachr. 9 p. 20, 1914. H. Lunetunp, Ann d. Phys. 45.
p. 517, 1914.

1), W. Wien, Sitz. Ber. Berl. Akad. 48 p. 70, 1914.

2) W. Vorer, Wied: Ann. 69 p. 297, 1899; Ann. d. Phys. 4 p. J97, 1900;
Arch. Néerl. (2) 5 p. 366, 1901. Magneto- und Elektrooptik pp. 357, 380, Leipzig
1908 ; Gött. Nachr. 9 p. 1, 1914; Ann. d. Phys. 45 p. 461, 1914.

5) EK. Warpure, Verh. D. Phys. Ges. 15 p. 1259, 1913. K. ScHWARZSCHILD,
ibidem 16 p. 20, 1914.

875

finds a separation proportional with 4 %€, WarBere however a
broadening proportional with p?2°€, where p denotes the number of
the series. The formulae of GARBAssO, GEHRCKE and Bonr *) differ
from that of Warsure in so far only as, besides other numerical
factors, they contain p*.€ as a parameter. The simultaneous influence
of a magnetic and an electric field was treated both theoretically and
experimentally by ZEEMAN, Stark, GARBASSO and GEHRCKE °).

Luminescent vapours always more or less cause a migration of
electricity which in the experiments of Stark e.g. amounted to several
milliamperes. It seemed to me interesting to examine the influence
of a purely dielectric displacement. As Zunman already pointed out (loc.
cit.) for this purpose we must consider an insulating, selectively
absorbing crystal. Among the series of substances formerly tested
ruby will be found a very good material for such experiments *).
It is not hygroscopic, it insulates extremely well and has an
ordinary index of refraction n,=—1,769 (for 2 = 589 wy), and
Ns = 3,13. Considering the analogy with quartz we may expect
the dielectric constant to be much larger still. In connection with
this research SELENny1*) already investigated in the Bosscna-laboratory
the influence of an elastic deformation on the absorption lines of
ruby. For a pressure of 150 kg/mm’? however he could not detect
an appreciable effect, at least no more than 0,02 uu.

The electrostatic experiment had to be delayed several years by
the difficulty of obtaining artificial rubies of sufficient size, because
of a monopolistic tendency in their preparation. Only recently I was
kindly furnished with sufficient material. From this two disks
“were cut, about 3 mm thick, one 1 and one || the crystal axis:
By means of sealing wax these were fixed within ebonite plates
of the same thickness. Unsymmetrical contraction by sudden cooling
or high electrostatic tension (during a short time) did not appreciably
injure these slides. To both sides of the dielectric plates small brass
disks were fixed. In the middle of these a slit was made so that
an eventual longitudinal effect might be observed. Extremely thin
tubes of German silver fitted in glass tubes connected the brass

1) A. GarBasso, Phys. Ztschr. 15 pp. 123, 310, 1914, B. Geurcxe, Phys. Ztschr. 15
pp. 123, 198, 344, 839, 1914; Verh. D. Phys. Ges. 16 p. 431, 1914. N. Bour,
Phil. Mag. (6) 27 p. 506, 1914.

*) P. ZEEMAN, These proceedings, 14 p. 2, 1911. J. Stark, Verh. D. Phys. Ges. 16
p. 327, 1914. A. Garsasso, Phys. Ztschr. 15 p. 729, 1914, E. Geurcxs, Phys.
Ztschr. 15 p. 839, 1914.

5) H. pu Bors and G. J. Erras, These proceedings, 10 pp. 578, 734, 839,
1908 ; Ann. d. Phys. 27 p. 233, 1908; 35 p. 617, 1911; 45 p. 1160, 1914.

4). P. SeLÉNyi, Verh. D. Phys. Ges. 15 p. 290, 1913.

58*

876

disks with a Wisuurst electrical machine, giving a tension of more
than 90 kilovalt. A vacuum-glass was half filled with liquid air
and covered with an ebonite stopper, which was perforated for the
glass tubes. Though the moisture in the laboratory hardly ever ex-
ceeded 30 to 40°/,, the whole apparatus was placed under the case
of an exsiccator. In this way the ruby could for some time endure
a tension of about 60 kilovolt, that is of 60/0,3 = 200 kilovolt/em.
= 667 electrostatic units.

The absorption lines, especially the two strongest lines A, and R,
in the red (691,8 and 693,2 uu) were observed in the first order
of a concave grating (radius 181 em., 5684 rulings per em.), which
was mounted in the ordinary way. 1 mm corresponded fairly well
to 1 gu, so that a change of the order of 0,005 uu could not escape
observation. No influence of electrification could however be detected;
in any case the displacement or separation is less than one hundredth
part of the magnetic longitudinal effect in a field of 50 kilogauss.
For the latter we formerly found the values:

ee Fi
Axis Il field; triplets with extreme separation dà: 0,37 0,48 uu
Axis 1 field; quadruplets _,, =. ms dà: 0,62 0,62 uu.

Probably an interferential method might give a sharper criterion
than the rather small dissolving power of the grating. Such experiments
might be made with the corresponding fluorescence spectrum of the
ruby at a very low temperature; they must be delayed however
until a more sunny season of the year. As this subject is of great
importance it seems to me interesting even to determine the mini-
mum limits in negative researches.

I also made experiments with the neodymnitrate-hexahydrate
(Nd(NO,),.6H,O) from the series of the rare earths. A natural
monocline plate about 1 mm thick was cut 1 to one of the axes
and in the manner above mentioned mounted between two very thin
glass plates by means of Canada balsam. Observations were made
at —-190° on the group of bands in the red, numbered from I to
VIII in a former paper (loc. cit. § 32). On account of the smaller
thickness of this slide the electric field was even stronger here than
in the case of the ruby; but again no perceptible influence on the
absorption bands was found. Now in a magnetic field the bands
VII and VIII (676,6 and 677,2 uu) give doublets the separation of
which reaches the largest observed value viz. dà =1,0 and 1,1 uw
for 50 kilogauss.

For the sake of completeness I repeated the experiment with an

877

alcoholic solution of the salt in a trough, which contained platinum
electrodes 2 cm distant from each other. A potential difference of
100 volt was applied. At 18° the current density was 75 milli-
amp./em* and in the viscous solution just above the freezing point
of aethyl-aleohol (— 118°) 30 milliamp./em?. I also worked with a
dilute solution in amyl-aleohol (—134°). With a spectral apparatus
of very great dispersion I observed in this case considerably broadened
and diffuse absorption bands, tiie aspect of which did not change
when the current was made. It must be remarked however that
under these circumstances the velocity of the negative ion is very
small as yet.

Physics. — “The calculation of the molecular dimensions from the
supposition of the electric nature of the quasi-elastic atomic
forces”. By Dr. J. J. van Laar. (Communicated by Prof.
H. A. Lorentz).

(Communicated in the meeting of October 31, 1914).

1. In four papers’), in which some new relations between the
critical quantities were given, | have also tried to determine the
form of the function b= f(v,7). While the dependence of 5 on the

volume appeared to be pretty intricate — that namely the found
relations at the critical point and at the same time the limiting
condition at v=v, be satisfied —- the dependence on the temperature

could be given by a very simple relation, namely (see LI, p. 1053,
formula (36) ):
bg — (Po) 9.041 ea PaaS Gok NM
(6)

in which (4,) represents the value of the limiting volume /, = »,,
extrapolated from the direction of the so-called straight diameter
at 7). This formula was an extension of that which was found at
the eritical point, namely (loc. cit. p. 1051):

by — (6,)
(2)
in which y; is the coefficient of direction of the “straight diameter”
in the neighbourhood of the critical point. The table (p. 1052) cal-
culated to support this relation may be reproduced here.

Ss Biv A = OV or Re ee Ve Cp

1) These Proc. of March 26, April 23, May 29 and Sept. 26, 1914,

878

| Tr Vn iten foun
Helium 5:2 | 228° | 0, 0806.4" 907543 + 0.56
Hydrogen 32.3 5.68 | 0.2158 | 0.608 0.604
Argon 150.65 | 12.27) “Ov4 763" Je DES 0.745
Xenon 289.7 | 17.02 | 0.6468 | 0.823 0.813
Acetylene 308.5 | 17.56 | 0.6673 | 0.834 0.858
Isopentane | 460.9 21.47 0.8159 0.908 0.914
Fluorbenzene) 559.6 | 23.66 0.8991 0.950 0.933

We have already repeatedly pointed out, that both the form of
the function D= fw), and the form of the temperature function
b= f(T) suggest that the change cf 5 chiefly, probably even exclusively,
corresponds to a real volume change of the molecules, and that an
apparent change in consequence of the partial overlapping of the
so-called distance spheres must be rejected. (See among others IV,
p. 464).

That such an apparent change loses all foundation in consequence
of the non-existence of the relation 6=4m, has been conclusively
proved by me in my opinion in a later article (These Proceedings
of Nov. 7, 1914). We found there namely (see p. 611), that in con-
sequence of the influence of the (infinitely slight) quasi-association
at v=o the quantity 5 must be diminished by the finite quantity
R:C. (C= the “constant” of the quasi-association). Considerations
of another nature made it probable that 4 must, indeed, be identified
in all cases with the real molecular volume m, at most increased
by a certain influence sphere.

2. We have already seen that the found temperature relation
agrees perfectly with that given by a formuia drawn up by van
DER Waals already much earlier for the variability of 6, viz.

[p Hofs + ABI 0=),)\=fRE, Nn SOANEN
in which A represents the (spacial) constant of the quasi-elastic
atomic forces, which atomic forces were put proportional to the
increase of volume b—b,. The quantity f is a coefficient which
depends on the number of degrees of freedom.

After substitution of 27’: (Vv — 6) for p+ 4/2, and eliminination
of A and 7, formula (3) appeared, however, not to satisfy the
relation 6= /(v) found by us. (See particularly IL, p. 930 in con-

879

‘nection with II, p. 931 and III, p. 1048, where the probable form
for this relation was given). If, however, we do not enter into a
further consideration of the extra-molecular part (p+¢/,»)(b - b,), and
for the present examine only the intra-molecular part A (b —8,)?,
we can, in connection with some plausible supposition concerning
A, examine what conclusions might be derived from it with regard
to the absolute size of the molecules, and whether the found dimen-
sions agree with the molecular dimensions derived from other data.

The simplest supposition concerning A is, that the quasi-atomic forces
are brought about under the influence of two elementary-charges e,
so that for the (linear) constant of the atomic forces, following
LINDEMANN (see among others Conseil Sonvay, German edition of
1914, p. 286; and also pp. 316—317, as far as the derivation from
Tuomson’s atom model is concerned),

E Nne?
er eo Sepa ee ot (4)

may be written, in which N represents the number of molecules
per gr. mol., the valency of the atoms, sub-atoms or atom groups,
and d the equilibrium distance of the charges. If further the devia-
tion is d, the atomic force for not too great values of d is represented
by
== Fd,
and the term of the energy corresponding to A (/— b), X b—b,) by
TO CS:
According to (4) we can now write for Jd?

Nne?

eee f?;,3)

a
or also when s, is the smallest diameter of the molecules (i.e. with

a deviation of the atoms d= 0):

; Nnat / sis :
dj 0. — : |) of) Fe
Se d

If we assume a Spherical shape for the molecules (if this it not
the case, we can yet assume a mean diameter s,, so that m becomes
== TS) we may write:

Fy? Nue* 6 3,\° 1 cy 16)" Ly Nne® £35 \7-1 : Nr
€ ==, „JUS ) OS = — en Jo sd 3
' 8 d Che 28) rd 904 d Ö% Ue )

0 0

in which 4, is the smallest volume of the molecules. The quantity

1) We may point out here, that in consequence of the dimentions of e, viz.
gr.'/2 eme sec.—1 (in electrostatic units), J 3? properly gets the dimensions of
an energy.

880

6, which differs little from 1, has been written by the side of
(6 — b,)*, because x s,* d represents 6— 6, only when d is very
small. Else we have:
b—b, = 1/,x(s, + 2d)? —1/, w 5,3 = er (65,2 0 + 12s, d? + 80%),
so that evidently 6 represents:
Blad: er (68,70 A 123,0* HSO) = (1 + DAR

sa OS ee ce TRS feos
when 7, represents the smallest radius of the molecule = '/, s,
(for d = 0).

For a substance like Argon, where 6;: 6, = 2y,=1,5, r, +d
would eg. be =7,0°1,5=1,1457,, hence 0,14 an
a (EP jam — 0,75 (for by, = bs

For substances as Fluorbenzene, where bj:b,=1,9, P1,9 be-
comes — 1,239, and thus °/,, — 0,239, @= (1,258) “SS 0,635 Eas
H, and He values will be found nearer 1. Thus for He, where
p20, 112) wes set an — 0/0385, 2 = (1,040) "= 0/92; Kore

we have 0;: 6, =1,2, so © = 0,063, 6 = (1,067)-* = 0,80. All these
0
values refer to the case that (for 7%) the atoms (sub-atoms, atomic
groups) in the molecule have almost the greatest deviation, as bz
does not differ much from 5,. We shall presently have to take this
factor @ into account.
When we compare the found expression for /’,d° with the term
A(b —b,)? in (3), we get for the present :
Imp? 8
eee ge (- = tA eee
56: P's, Nae be
so that the quantity A in (3), in consequence of the introduction
of 5—b,, through @ appears to be dependent on tbe extent of the
deviation in a slight degree — in opposition to the quantity #, in
(4), in which the original deviation d occurs. Hence A is (in a
slight degree) both a function of the volume and of the temperature.
Now for infinite volume, according to (3):
Ay (by — b) =f RT,
while according to (4):
by — (bs)
(6,)
in which, as has been said, (b,) does not represent the real limiting
volume 6,=v,, but the limiting volume extrapolated from the
direction of the straight diameter at 7%. We saw in IV, p. 458—459,
that e.g. for Argon 6, is = 0,305 vz, whereas (b,) = 0,286 vj. From

OON 477,

881

(by — (b,)) : 6, = 0,041 V T follows that for Argon, where V 7,= 12,27,
by : (b,) = 1,508. Hence for b,: 6, would be found 1,508 : 1,066 =
= 1,410, because J, : (6,) = 0,305 : 0,286 = 1,066. Hence the value
of (b, —b,):b, is 0,410, so that for 7%, this value can be represented
by (0,410 : 12,27) WT, = 0,0334 WT); and we can, therefore, write
— at least for Argon — instead of (1):

bb
50,0884 YT. So ee ere) ha)

From Ay, (6, — 6,2? = fRT and (19) now follows:
aie R
es ce cee
I~ (0,0834)7b,? bo?
in which, as appears from the derivation of (5) from (4), the coeffi-
cient 0,0334 will still depend with A, on 7 through 6, in a slight
degree, and is strictly speaking only valid at 7%, i.e. the tempera-
ture at which we calculated just now this coefficient from that of
equation (1).
Combination of (5) and (6) now gives immediately :

d\? Og Net on */¢X 6.108 X (4,825 . 10-10)
a WBD Te 896 83,15. 10°

In this (4,825.10—19)? = 23,28.10—°9, and we find:

d ae 6 n 3.88.10? zel n 5-01. 10-8 7
85 = — Vg f 5 7,45.10" — Wg ra ae o,al. ° . ( )

For MN, Avocapro’s value, we have substituted, the most probable
one, viz. 6,0.10% for NN, as it follows both from Pranck’s theory
of radiation and from the values directly determined by Mi.uikan
and Norpiunp. If we namely put for WreN’s constant of radiation
c, =c(h:h) the middle value of Warsure and CoBLENTz, viz. 1,441,
and for Steran-BoLTzMANN’s constant « the mean value of WrsTPpHAL
and several others, viz. 7,6.10-!%, we find from the wellknown
formulae for Ah and 4%:

Bme 480 EOL = 1,595: 40E io, O0 LIE,

For N we find therefore 83,15.10° :1,393.10-16 = 5,97.107* from
R=N Xk. MiLrikAN’s value is 6,06.10?*; NorpLunp’s is V—5,91.107*
(Z. f. Ph. Ch. 87, p. 62). The mean of these three values is 5,98.10°°,
so that witk some probability we may assume about 6,0.10°* for NV.

For N Xe has been found 107,88 : 0,0011180=96494 Coulomb =
== 9649.4 electromagnetic units = 2,895.10" electrostatic units.
Hence we find for the value of the electric elementary quantum e
after division by MN the value 4,825.10—,

(6)

89

882

3. We may now proceed to compare the value of s,, found in
(7), with the values of s, caleulated by other methods.

If we put -7—1, f=1, so monovalent atoms or atom groups,
resp. subatoms, and three degrees of freedom *) corresponding to the
spacial conception of the molecular vibrators, then:

ay?
S> = Ee Oy ae eet | . 10-8,

So
in which 6, represents the value of 6 at the greatest deviation d
corresponding to 6, (accurate at 7%). And because we have calcu-
lated above the coefficient 0,0334 in (1°) from data concerning Argon,
we shall also now substitute the value, which we have found for
Argon, viz. 0,75 (also at 7%) for @,. Hence
a\*
(=) =. 330. 10 Men ie et EN
EE es Se
in which the found value 3,9 will hold by approximation for all
substances on account of the generality of our considerations — at
least for substances with not too complex molecules, where also the
values of s, appear to differ only little.

Let us now calculate the values for s, for Argon, Hydrogen, and
Helium. The values given before for them are most of them inaccu-
rate, partly in consequence of the value of MN, which was assumed
too high (viz. 6,82 .10°° according to Perrin, instead of 6,0. 107°),
partly in consequence of inaccurate suppositions on 5 (e.g. b= 4m),
or formulae which do not hold without reservation, as e.g. that
of the mean length of way, from which then s, was calculated
(viz. «Ns? —v:ly 2).

For Argon a liquid density = 1,374 is found at — 183°. From this
follows for the molecular volume (39,88 : 1,374) :6.10?* —=48,4.10 **.
As the molecules have not yet approached each other in this state
to the shortest distance, we must assume that s, is smaller than the
longitudinal dimension of the cubes, the volume of which amounts
to the above value. Hence we have s, < 3,64.10~.

We can also calculate s, from 8, =06,:0,=0,305. Asv, = 39,88:
: 0,5308 = 75,18, we get b,—0,305 75,13 = 22,92. The molecular

1) In (3) f was namely the factor of RT. Of course our considerations are only
valid for not too low temperatures, as otherwise the limiting term RZ must be
replaced by the known more intricate form on account of the quanta effect. As,
however, the intra-molecular vibrations will probably have a greater frequency
than those of the molecules themselves, the temperature at which the influence
of the effect in question will already make itself felt, will in general be higher
than the corresponding temperature for the molecular system.

883

volume is therefore 38,2.10°°*. If in this shortest distance we still
assume approximate cubie distribution ') of the molecules, then s,
becomes 5 3,37 .10~*, which agrees very well with the just cal-
culated upper limit ’).

We may therefore assume for argon s, = 3,5 . 10” cm.

PERRIN gives for this (Conseil Solvay, German edition, p. 154), the
somewhat too low value 2,7 .10 *, calculated from the length of path.

For Hydrogen we tind 0,086 (Dewar) for the density at the melting
paints). Hence. s° << (2,0152:: 0,086) .:6.1029) “ors <= S81. . 10-24
Sed. 10%

The value of 5, at H, being only known by approximation, no
lower limit can be given. The value of 6, calculated by me before
(These Proc. of April 24,1903) by means of VAN Der WAALS’ equation
of state of the molecule is not suitable for this purpose. I found
then namely 6, almost independent of the temperature, on the other
hand 5, increasing with 7’, which is not probable. If for 5, the value
0,000917, found before, is assumed, we find about 0,00076 for 0,
with 6,:6,=1,2, hence 5,°S (0,00076 22412): 6.10235 28,3. 10-24,
ors, = 3,00 10-2.

[We once more draw attention to this, that if we had put = 4m
according to the current assumption, and 6,= + 2m according to
the theory of the apparent diminution of 6, we had found a much
too small value for the lower limit}.

For the present we can therefore assume s, = + 3,2.10 8 for H,.

The value 4. 10-8, calculated from unknown data, which I found
given somewhere, is therefore slightly too great.

1) I. e. that even at the greatest density the molecules ‘do not occupy a smaller
volume than S93. Only on the supposition of perfect spherical form, and the entire
lack of impenetrable spheres of influence (see § 1) could it be assumed that a
smaller minimum volume than s,° were possible. This, however, seems a physical
impossibility to me, and — like the assumption of an apparent «iminution of 0
in consequence of the partial overlapping of the distance spheres — only a mathe-
matical fiction. Also the existence of crystal nets seems to plead strongly against
the assumption of a denser accumulation than corresponds with s,% It might
sooner lead us to the opposite conclusion.

2) The sign of inequality > namely refers to the possibility that the molecules
can occupy a somewhat smaller volume than 589°.

3) To my regret I have no tabular works as the latest edition of Lanpotr und
Bornstein, Recueil de constantes physiques, and others at my disposal, so that
I had to be content with this slightly antiquated value of Dewar. I do not know
any clear summary of the constants determined in the Leiden Laboratory for
different substances. Neither in KAMERLINGH Onnes and Keesom’s book on the equation
of state, nor in that of Kuenen did | find, except incidentally, numerical values
of experimentally determined constants.

884

For Helium Kamertincu Onnes (Suppl. 21) has found d= 0,15
for liquid He. Hence s,* < (3,99: 0,15): 6.107%, or s5,° < 44,5 .10-%,
therefore s, << 3,54.107°.

If for 6 in the case of He the value 0,0007, given in Suppl. 21,
is assumed, then 06, is about 0,007 : 1,12 = 0,000625, hence
s, > (0,00062° 22412) : 6.10, ie. 5 23,35 . 10-74, or 5,5 2,86. 10-8.

This value is evidently too small; perhaps the d-value, for which
K. O. first (Comm. 1024) gave 0,00043, and which was later on
raised to 0,0007, must be raised somewhat more.

We therefore assume for He the middle value s,= + 3,2.10®.

PERRIN’s value, viz. 1,7.10-® (loc. cit), is at any rate too low.

It appears from the above examples, that for three substances
which differ so much as Argon (mol. weight = 40), Helium (mol.
weight = 4) and the di-atomie H, (mol. weight 2), the values of
s, differ very little.

Also on calculation of other not too complex substances s, appears
to rise very rarely above 4. 10-#.

The found values are in better harmony than could be expected
with the value + 3,9.10-8, which follows from our theoretical
considerations. Not only is the order of magnitude the same, but even
the numerical value is almost identical.

When we bear in mind thats, .(d:s,)*—3,9.10 5, then (d: s,)> =
—1,11 would follow from eg. s,=—= 8,5. 108 (for Argon), hence
d:s,==1,04. The diameter of the molecule would therefore be a
little smaller than the distance of equilibrium d of the two charges,
which might point to a somewhat elongated form of the molecule,
because then the mean diameter s, would be somewhat smaller than
the distance of the centres, in which the charges may be imagined
fictitiously concentrated. But though this supposition is very plausible,
particularly for di-atomic gases, yet there is by no means certainty
on this head on account of the not absolute accuracy of the calculated
values. The more so as there may also be other influences at work,
of which we only mention that of the degrees of freedom by which
the factor f is influenced; and also the influence of the deviation
from the law of equipartition, through which in (3) the factor /
would apparently become smaller. But even when we leave the
factor (d:s,)* in (7a) out of account, the concordance between the
value of s,, calculated from the assumption of electrical forces and
the values found for different substances, in connection with VAN
per Waats’ equation of state of the molecule and the temperature
coefficient of (,—6,):6, found by me, remains remarkably close.

Fontanivent sur Clarens, October 1914.

885
Physiology. — “Hvagqgeration of Deep Reflexes.’ By Prof. J. K. A.

WERTHEIM SALOMONSON.

(Communicated in the meeting of November 28, 1914).

The graphic method of recording pathologically exaggerated deep
reflexes sometimes offers interesting results.

In the literature we find mentioned that exaggeration may show
itself in different ways. A very slight tap on the tendon pro-
duces an unusually brisk contraction: the threshold-value of the
stimulus is lowered. But we also read that the lateney is shortened,
that the duration, velocity and height of the contraction are increased;
that a simple jerk may be changed into a tonic or clonic contraction.
But even with this knowledge we are not quite prepared for the
multiformity of the curves which may be recorded.

I have tried to record the shortening, or more generaily the
thickening of a muscle, following a tap on its tendon. Of course I
found more or less of the changes mentioned before. But the curves
seemed to be so absolutely different that I could not be content
with the simple statement, that some patients showed one form of
curve, some other patients quite another curve. We should like to
know at least something about the mechanism of these different
forms.

A priori the idea of a change in the form caused simply by
exaggeration of a reflex is rather difficnlt to conceive. We can
readily understand that the reflex irritability is increased when an
extremely slight tap on the tensor produces a very strong contract-
ion. And this is conformed by clinical examination. But it is now
generally understood, — and I think I too have contributed to this
opinion -— that the deep reflexes must be considered from a physio-
logical point of view as simple contractions, preceded by one
double-phased current of action. As physiological variations in simple
muscle-twitches we only know slight changes in height, duration
and slope of the curves, caused by fatigue, by temperature ete., if
we abstract from the changes caused by direct poisoning. But we
do not know of an increased shortening, of a notable change in the
latency or of a highly increased duration as long as we consider
only simple muscle-twitches.

If the simple muscle-twitch of the quadriceps known as knee jerk
be recorded, we find under physiological conditions that the duration
of the twitch is very nearly 0.20 second.

Fig. 1.

In many cases of undoubted exaggeration of the knee-jerk we
also find very nearly 0.20 second. Fig. 1 shows such a curve in
which the time marks, as in all the other curves in this paper
represent 0.1 second. This record mnst be considered as an instance
of the simplest form of an exaggerated deep reflex. I can add that
this simplest form is rather a rare one and that more complicated
forms are more usually met with. All the more complicated forms
are characterised by the occurrence of more than one top in the
graphical record. Amongst these we must consider in the first place
the simple clonic reflex, where the simple twitch is entirely absent
and replaced by a small series of clonic contractions (fig. 2). These

bren Erben Een nn nen

Fig 2.
are generally rather limited in number and we find perhaps only
47 contractions in all. But in a few cases quite a long series of
clonic contractions may be seen (fig. 3). Curves of this kind may be
found in patients where the mechanical and physiological conditions
for permanent clonus are present. This means that the reflex irrita-
bility as well as the muscle tonus are greatly increased; also that
the leg of the patient must be kept in such a position that nothing prevents
the occurrence of clonus. Clinically we can find this in patients
with organic as well as functional diseases of the nervous system.
In functional disorders even the tonic rigidity of the muscles need not
be present as a state of active muscle contraction may provide the
mechanical condition for a clonus as well as a tonic spasm does.

887
But under such conditions the clonus generally is not quite as
regular as in organic disorders, as is well known. The very short
cloni, as in fig. 2, were only seen in organic diseases of the central
nervous system.

The complicated forms of deep reflexes, which are now to be
considered, offer the peculiarity that after an initial simple twitch,
the muscle does not entirely relax, but a state of hardening of the
muscle substance persists for a longer or shorter time. This hardening
may be caused in at least three different ways.

Fig. 4 represents a record obtained in a patient with chorea
minor and shows one of the changes described by Gorpon, Hey a. 0.
as occurring in chorea minor. After the initial simple twitch we
observe a second contraction which may be as high or even higher
than the first. It begins either at the end of the simple twitch
or even a little earlier. In this special case the second contraction
showed the short duration of a single twitch, but I have also seen
more tonic contractions in the same patient as well as in others
with the same disease. The latency of this second contraction is of
the order of 0.15—0.20 second and agrees with the latency for a
central reaction on a stimulus applied to the peripheral organs of
sense. As the probable seat of the lesions in chorea is the cerebrum,
we must at least consider the possibility of a central reaction. It
seems to me that this supposition is not entirely unfounded. I. even
think it rather probable, that the deep reflexes are also, at least
partially represented at a higher nervous level than the spinal cord,
In peculiar circumstances, as in chorea minor, this cerebral part
may sometimes appear. I think that this cerebral part of the reflex
is answerable too for the so-called pseudo-kneejerk of Westranu,
which in rare cases of tabes appears with a latency of about 0.2 second
after tapping the knee-tendon or the skin above it. In more than
a few cases of functional neurosis I have also seen reflexes as in
fig. 4. I have never been able to record those reflexes, which as a
matter of fact occurred only the first time that the knee-jerk was
elicited; if the reflex was obtained a second time or at a later
examination, the cerebral restraining impulse was sufficiently intense
to prevent the action of the higher centrum. In chorea this restraining
influence has entirely disappeared as well as the faculty of suppressing
involuntary choreatic movements.

Records closely resembling those of fig. 4 can be obtained some-
times under totally different circumstances. Fig. 5 was recorded in
a case of multiple sclerosis, the patient being nearly paralysed. He
is just able to make a few slow movements with his extremely rigid

888

lower limbs. The kneejerk shows a simple twitch followed by a
second and even a third short contraction ; immediately afterwards
a second kneejerk showed a contraction of half a second’s duration
following the initial twitch.

In cases like this we scarcely need consider a central origin for the

ry at

5

5

889

second contraction especially as contractions of this kind are some--
times found in completely paralysed patients. In some cases of
myelitis or tumor of the spinal cord with complete paralysis we may
often see involuntary movements in the paralysed limb. These move-
ments set in after a slight peripheral stimulus, such as a simple
touch, or the influence of the lower temperature of the air, or even
without appreciable cause ; they cannot be prevented or modified by
the patient. They may be considered as a spinal automatism. Generally
they appear in the form of an adduction or a flexion of the lower
limbs, more rarely as an extension movement. But a tap in the
neighbourhood of the knee often produces a stretching movement
of the leg.

In some records it is not easy to distinguish between a clonus
strietiori sensu and an automatism. The oserllations in the curve of

fig.6 are rather slow for a true clonus, the rhythm being not quite
5 per second. For an automatism the rhythm is rather fast. Perhaps
we might consider it as an intermediate form: clonus and auto-
matism are sufficiently closely related to render this admissible.
There is still a third possible genesis for the after-contraction. In
a former communication on “shortening reflexes” I pointed out, that
these are always accompanied by a tonus-reflex, by which the muscle
adapts itself to its new condition. As soon as a movement is necessary
the muscle tonus is automatically regulated so as to put the muscle
in the best condition for doing its work. Therefore we may a priori
expect a tonus-reflex at the same time as the deep reflex. As a
matter of faet we find that in records of simple deep reflexes, the
simple twitch is generally followed by a slight elevation of the curve,
indicating that immediately after the real muscle twitch tonus is
increased for somewhat less ihan a second. The beginning of the
tonus reflex is not sharply defined, as it starts before the end of the
simple twitch. In favourable circumstances this after-contraction
59

Proceedings Royal Acad. Amsterdam. Vol. XVII.

890

shows a smooth curve; more often we find a clonical after-con-
traction (fig. 7). Reeords of this kind are obtained in cases where

igs 7:

in ordinary conditions the tonus is not quite high enough to permit
of a elonus. But as soon as a tap on the tendon elicits the muscle
twitch and the tonus reflex, the tonus sufficiently increases to render
a short clonus possible. This last disappears as soon as the tonus
reflex in finished. If we can in some way diminish the tonus before
the reflex is obtained, the increase of tonus caused by the reflex may
be insufficient for a clonus. In such a case we should be able to
provoke either a tonic or a clonic after-contraction, only by lowering
or inereasing the tonus beforehand. Resting the foot, slight active
bending of the knee diminishes the tonus in the quadriceps ; supporting

the knee and slight passive bending increases it.

Fig. 8.

Fie. 8 gives a record on which the first reflex shows a clonic,
the second one a tonic aftercontraction, which were obtained in
this way. With all patients of this kind the tonus is not quite
sufficient to admit of a persisting clonus. Only under the most
favourable circumstances, as after prolonged exposure to a low
temperature, and much care in arranging the most favourable

894

positions of the lower limbs, we may be able to produce a damped
clonus or perhaps even a permanent clonus.

We have now to consider another group of records in which the
after-contraction forms the most important and conspicuous part in
the whole reflex.

Fig. 9 gives an exceedingly protracted after-contraction of nearly
5 second’s duration. Clinical observation shows that this is not a
case of spinal automatism. In testing the knee-jerk we find that the
leg is extended in the ordinary way, or perhaps a trifle longer,
and falls down as in a normal reflex. But we see and feel, that
the tendon remains in a state of maximal tension and that the
muscle itself retains its condition of increased tonus. Then the tonus
disappears slowly and gradually and only after several seconds the
original condition has returned. That we have indeed a tonus
variation of excessive magnitude before us and not a contraction
strictiori sensu, may be seen from fig. 10. This record was obtained
from the same patient suffering from diplegia cerebralis pseudobulbaris
and shows two knee-jerks in succession, the second being elicited
before the first had entirely subsided. The second jerk shows, in
exactly the same way as the first a maximal simple twitch,
whereas afterwards the tonus was still more exaggerated. As the
second jerk gives a record which in this patient must be regarded
as a customary one, a real contraction ought to be considered as
highly improbable. Neither is the hypothesis of an automatism very
alluring, as this patient did not show any other typical spinal auto-
matie movement. Finally the clinical examination showed, that in
the almost paralysed patient all changes of the muscle tonus dis-
appeared very slowly, and agreed absolutely with the after-con-
tractions of the knee-jerk.

In another patient with diplegia cerebralis the knee-jerk produced
quite a series of interesting movements, as will be seen in the
records of fig. 11—13. In fig. 11 we find that the initial twitch
can be followed by a protracted tonic aftercontraction, on which
either clonic movements with a rhythm of 8 per second are super-
posed or not. In other circumstances, principally determined by the
position of the limb, and the way of supporting it during the exa-
mination, I could get a series of automatic movements with a
rhythm of about 2°/, per second. At the same time the cionus of
8 per second remained more or less visible (fig. 12). By a slight
change in the way of supporting the knee it was possible to
obtain much longer duration of the automatic movements (fig. 13);
the more rapid clonus disappeared completely after a few seconds

59*

892

893

SATO OS RO EEE ERD RAD.

‘ST “Oly

594

and only the slow automatic extension and flexion movement with
a rhythm of 2°/, per second remained visible, often during 30
seconds and longer.

All the records shown in this paper are obtained from the patellar
tendon-reflex. Yet their significance is more general, as also other
exaggerated deep reflexes sometimes show changes of a similar
nature.

Physics. — “The specifie heat at low temperatures. 1. Measurements
on the specific heat of lead between 14° and 80° K. and of
copper between 15° and 22° K.” By W. H. Kersom and H.
KAMERLINGH ONNEs. Communication N°. 148 from the Physical
Laboratory at Leiden. (Communicated by Prof. H. KAMERLINGH
ONNEs).

(Communicated in the meeting of October 31, 1914).

§ 1. Introduction. Soon after the methods of obtaining baths
of temperatures which are accurately known and can be kept con-
stant for a long time, in the range between the boiling point and
the melting point of hydrogen, had been worked out *) in the eryo-
genic laboratory at Leiden, a series of investigations on the calori-
metry at very low temperatures was started there. Dewar’s measure-
ments on the mean specific heat of different substances between
the temperature of liquid air and the boiling-point of hydrogen ’)
had particularly drawn attention to the interest of those investigations.
The continuation of his experiments in the still lower region of
temperatures mentioned above seemed very desirable *). As was done
by Dewar the series of investigations in this direction was begun
by determinations of the heat of vaporisation of hydrogen. A report
on the first results of those determinations was given at the Dutch

1) Cf. specially H. Kamertinen Onnes, Leiden Comm. NO. 947 (Proceedings
Sept. '06) and H. Kamertinen Onnes, C. BRAAK and J. Cray, Leiden Comm. NP, 101a
(Proceedings Dec. '07).

2) J. Dewar, Proc. Roy. Inst. March 25, 1904, Proc. Roy. Soc. A 76 (1905)
p. 325, later more extensively between the boiling point of nitrogen and that of
hydrogen: Proc. Roy. Soc. A. 89. (1913) p. 158.

35) This was pointed out at the Ist International Congress of Refrigeration at
Paris 1908. H. Kameruincu Onnes, La liquéfaction etc. Note J. Sur les expériences
a faire aux températures très basses. Leiden Gomm. Suppl. N°, 21a p. 29,

895

Congress of Science and Medicine at Groningen (1911) *). An invest-
igation regarding the specific heat of lead, after which other metals
were to follow, at hydrogen temperatures, an investigation which
had a particular interest with a view to Erstnin’s theory and also
in connection with ?) Nernst’s theorem, was announced on that occasion.

Since then in Nernst’s laboratory a highly important series of
investigations on the specific heat bas been made by himself and
by his collaborators *). In particular the investigations on solids at
low temperatures, which had already been made down to the tem-
peratures of liquid air boiling under reduced pressure, were continued
to the temperatures which can be obtained with liquid hydrogen.
Besides KAMERLINGH ONNES and Horst‘) made preliminary measure-
ments of the specific heat of mercury at helium temperatures. The
investigations menticned have already furnished a great number of
highly valuable data, which in particular have served for a test of
the theories of Desire’) and of Born and v. K ARMAN *). The method
„we followed is mainly that which has been developed by Nernst
and Evcken. Notwitbstanding all that the continuation of our programme
seemed to remain desirable. First, when Nrrnst’s investigations had
followed the specifie heat down to the region of hydrogen temperatures,
because only a few of his observations entered into this region and
the accuracy of the observations left some doubt with Nernst himself,
and later, when between the boiling point and the melting point
of hydrogen also more accurate determinations had been made in
his laboratory 7), because for the investigation of the questions which

1) W. H. Keesom. The heat of vaporisation of hydrogen. Handel. 13de Ned.
Nat. en Geneesk. Congres, April 1911, p. 181. Publishedalso Leiden Gomm. N?.137e.

2) Cf. also H. Kamertincu Onnes. Reports of the IInd International Congress of
Refrigeration. Vienna 1910 (Comm. Leiden Suppl. N°. 210 p. 42).

3) For the literature we refer to Leiden Comm. Suppl. N°. 23 “Die Zustands-
gleichung” Math. Encycl. V. 10 Note 838. Later: A. Euckrn and I. ScHWERsS.
Verh. d. D. phys. Ges. 15 (1913) p. 578, W. Nernst and F. Schwers. Berlin
Akad. Sitz. Ber. 1914 p. 355. R. Ewatp Ann. d. Phys. (4) 44 (1914) p. 1213.

4) H. KAMERLINGH ONNEs and G. Horsr. Comm. NO. 142c (Sept. 14).

5) P. Deprye. Ann. d. Phys. (4) 39 (1912), p. 789. W. Nernst and F. A. LINDEMANN
Berlin Akad. Sitz. Ber. 1912, p. 1160. Cf. also W. Nernst, Vorträge Wolfskehl
Congress Göttingen 1913, p. 61.

6) M. Born and Tu. v. Karman. Physik. ZS. 13 (1912), p. 297 ; 14 (1913), p. 15,
65. H. Tarrrine, Physik. ZS. 14 (1913), p. 867; 15 (1914), p. 127, 180. Cf.
M. Born, Ann. d. Phys. (4) 44 (1914), p. 605.

7) A part of our observations had already been made when the results of
Evcxen and Scuwers were published (see § 5). The completion of even the limited
part of the programme, which is contained in this communication, has been much
retarded, partly by the wish to attain very trustworthy results,

896

have now come to the front a high degree of accuracy is desirable.

In this respect it was an advantage: 1s* that particularly by the
investigation of KAMERLINGH Onnes and Horst *) on the seales of the
hydrogen and the helium constant volume thermometers we could
avail ourselves of a more accurate temperature scale *); 2nd that the
eryostats used at Leiden allowed the measurements to be performed
under more favourable circumstances in other respects also. In fact
in the measurements published in this paper an accuracy of 2 °/,
has been reached at hydrogen temperatures, while there is reason
to expect that in subsequent measurements the accuracy will still
be considerably increased. F

§ 2. Method. Apparatus. We followed with some modifications
the method which has been in particular developed by Nernst and
Eucken, and which has shown itself to be very suitable for low
temperatures. In this method a block of the metal to be investigated,
provided with wires for heating and temperature measurement, is.
suspended in a vacuum which is made as perfect as possible. Within
the block a measured quantity of heat is developed by an electric
current, and the increase of temperature produced is measured.

Fig. 1 represents the cryostat with the calorimeter. To protect
the block against the residual heat radiation which enters the calori-
meter vessel C’ (the vacuum-vessels are silvered a slit being left open),
it is silvered on the outside up to a few mms. below the sealing-
places C, of the platinum wires. Moreover the plate C,, which through
a platinum wire is in heat conducting connection with the bath,
prevents radiation from above.

In the block B of the metal to be investigated a chamber has -
been drilled, into which the core K fits tightly. This core contains
the wires which serve for heating and for measuring the temperature ;
when the temperature wire has once been calibrated and the heat
capacity of the core measured separately, it can serve for the
successive measurements of the specific heat of all the metals of
of which suitable blocks can be made, and of other substances also
when use is made of a suitable vessel. The core consists (Fig. 2)
of a solid cylinder AK, and two cylindrical mantles A, and K,, all

1) H. KAMERLINGH Onvnes and G. Hoist. Comm. No. 141a (May 1914).

2) The temperature scale used by Nernst, and also those of EucKEN and
Scawers and of Nernst and ScHWERS are mainly based upon the older cali-
bration of the thermometer Pfy by KAMERLINGH ONNES, BRAAK and CLAY, which
has to be replaced by the newer one of KAMERLINGH ONNEs and Horst. Cf.
further § 3,

897

of copper, provided above with flat, tightly fitting collars, and of a
copper plate A,, which is in addition connected with A, by means

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of a copper screw. Round K, a gold wire has been wound
doubled on itself; for insulation and at the same time for heat
conduction enamel and thin paper were used; the electrodes ee,
stout platinum wires (1,5 mm.), which are led through tbe collars and
insulated from these, and protrude outside the core, are rolled out below
to flat bands which are a few centimeters longer than the cylinder ;
to the ends of these the gold wire is soldered with gold, after which
the band was bent up (e,,...) and fastened to the core and insulated.

The space which remained within A, was filled up with the
copper-tin-amalgam which is used in dentistry. In the same way a
constantin wire was wound round A, and enclosed between A,
and k,. Then the whole was closed by the plate A, below, and
the different parts were united as much as possible by Wood-metal.
The insulation was tested with an insulation meter and found to be
more than sufficient.

The block B is suspended from two platinum wires (0.6 mim.) with the
aid of two small glass rings. These platinum wires serve at the same
time for conduction of the heating current. They are therefore
connected to the electrodes of the constantin wires by platinum
wires (0,2 mm.). For simplicity the wires, which serve for measuring

898

the potential difference between the electrodes ¢,,, e,, of the constantin
wire, are applied outside the calorimeter vessel near the sealing
places. The resistance between these junctions and the ends of the
constantin wire is inappreciable compared with the resistance of
the latter (140 &). For the gold wire, which serves as a thermo-
meter, potential as well as current wires (within the calorimeter
vessel 0.1 mm. platinum, insulated with silk) lead directly to the
electrodes.

The stopcocks 4, and 4, have wide borings, 4, leads to a GaAupE
mercury pump, which serves for evacuating the charcoal and for a
preliminary evacuation of the calorimeter vessel, and to a Mc.-Leod
gauge, R is a reservoir which is filled with hydrogen; with the
aid of the pipette p a quantity of this hydrogen is admitted into
the calorimeter vessel when it is required to bring about heat
conduction between the block and the bath.

The charcoal tube A, made of glazed opaque quartz, was filled
with cocoa-nut charcoal, and evacuated for a sufficient time at
600° C. before each series of measurements. During the measurements
it is cooled with liquid hydrogen.

To diminish the exchange of heat between the metal block and
the bath through the conducting wires, during the measurements
the bath that surrounds the calorimeter was brought as nearly as
possible to the temperature at which the measurement was to be
made. The time-rate of the temperature before the heating and
after the heating, at least after a few tens of seconds, was as a
rule very small, if not inappreciable. For illustration in Fig. 3 and 4

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the time-curve of the galvanometer, which indicates the temperature,
during two measurements is represented, viz. for a measurement of
the specifie heat of lead (Fig. 3) and for a measurement of the
specific heat of copper (Fig. 4), respectively. The increase of tempe-
rature was in both cases about 1 degree. In the measurement with

899

lead the temperature of the core appears to have risen about '/, degree
above the mean temperature of the lead block during the heating,
in the measurement with copper, for which the heat supply per
second was chosen smaller in accordance with the smaller specific
heat, the corresponding temperature difference is not appreciable.
Where necessary, corrections for the heat exchange with the bath
were applied.

The heat supply. The arrangement for sending a current of mea-
sured intensity and potential difference during a definite time through
the constantin heating wire is represented in Fig. 5 together with
the arrangement ') for measuring the resistance of the gold thermo-

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ee,
Fig. -b.

meter wire. Intensity and potential difference were read on accurate
Weston millivolt- and voltmeters. These were calibrated repeatedly
for the measuring ranges used with the aid of a standard element
of the Weston Cy., standard resistances and a compensation apparatus
free from thermoelectric forces with an auxiliary apparatus according
to DiessenHorst, all calibrated at the Physikalisch Technische Reichs-

Fig, 6.

1) In the figure the regulating. resistance and the milli-ampèremeter between

accumulator and commutator have been omitted.

900

anstalt. The switch S for closing and opening the current served
for measuring off the time. Fig. 6 represents the complete arrangement *)
for measuring off and registering the time. The clock U with
second pendulum, provided with a Honwé registering arrangement H,
closes, respectively opens in passing
its equilibrium position a current
which operates a relais Q. This closes,
respectively opens a current, which
makes the bell £ give a stroke every
two seconds; this is registered by
the telegraphic apparatus 7’ the
Morse-key J/ being in its position
of rest. If, after contact has been
made at 7 by a plug, M is pressed
down at a moment that no current
goes through (to be recognized from
the position of the tongue of the bell),
at the next closing of the current
by the relais the beam j; of the
contact-key S; (see Fig. 7) will be
released, the platinum wire p,, will
fall into the mercury, and the heating
current through the constantin wire
wil be closed *). The switching out
Fig. 7, is operated in the same way by S,
the contact plug having been transferred from 7 to wv. As a control
the moments of switching in and out are registered by 7’ (Fig. 6)
through the corresponding dash on the paper strip being absent.
An accuracy of '/,, of a second is certainly attained with this
arrangement.

Cy

|
|

be >|
e

H
E,
5

f)
r Ha
i

: 00.71)

A

The temperature measurement. The scale of the gold resistance
thermometer is dealt with in § 3. In Fig. 6 the THomson bridge

') This arrangement was already used in the determination of the heat of
vaporisation of hydrogen, cf. Comm. N°. 137e.

2) The distances of the points of pi, and pu, (fig. 7) above, and below the
respective mercury surfaces (covered with paraffin oil partly for suppressing the
opening spark) are small and are made equal to each other by adjusting the
mereury cups, whereas the velocity of fall of the two beams ji and ju was also
made as equal as possible. The two other cups (see pit and u2) may serve to use
the apparatus as a switch-over key (e.g. if the same wire has to be used as a
heating and as athermometer wire, cf. §3 at the end); in the present experiments
they were not filled with mercury.

90)

for the measurement of the resistance is also represented. The galvano-
meter was of the DrmsserHORST type with a period (undamped)
of 4 sec. Before a calorimetric determination the resistance was
measured, and the deflection of the galvanometer for a definite
change in the ratio of the branches in the THomson bridge, the
“sensitivity”, determined. Then with a definite ratio of the branches
the movement of the galvanometer (Fig. 3 and 4) was followed
during the experiment. After this the measurements of the resistance
and of the sensitivity were repeated. The current for measuring the
resistance was 5 milliamperes. The heating current was for the lead
30 tot 50, for the copper 12 to 27 milliamperes. Considering the ratio
between the resistances of the thermometer and the heating wires
the development of heat in the temperature measurement does not
come into account.

We gladly record our cordial thanks to Dr. G. Housr and Mr. P.
G. Carr for the aid they afforded us in undertaking the temperature
measurements.

Account had to be taken cf the circumstance, that the reduction
factor, which gives the ratio between the galvanometer current in
the Thomson bridge and the difference between the measured resist-
ance and the resistance which would give no deflection, depends
on the resistance in the variable branches of the bridge. A correction
for this was always applied.

§ 3. The resistance thermometer. For the resistance thermometer
a gold wire was chosen, as in the range of the measurements
(14—90° K.) gold is more suitable for interpolation than platinum *),
and as on the other hand the indications of the gold thermometer are
constant, if it is suitably treated before use (glowing before winding,
then repeatedly cooling in liquid hydrogen and returning to room
temperature’. Before each series of measurements the constancy of
the resistance of the wire was tested by a measurement at the boiling
point of hydrogen.

In the temperature range of liquid hydrogen the gold thermometer
was calibrated with the aid of a hydrogen vapour pressure appa-
ratus as used in Comm. N°. 137d. The temperatures were deduced from
formula (1) of that paper. In this way the scale of the gold thermo-
meter is reduced to that of Ptr, which has been once more accu-
rately fixed by the research of KAMERLINGH ONNes and Horst (Comm.
N°. 1414). In the range of liquid oxygen this was done with the aid

1) H. KAMERLINGH ONNES and G. Hoist. Comm. N°. 142a@ (June 1914).

Yo?

of auxiliary thermometers of platinum and of gold which had been
compared directly with Pé.

The data for the gold thermometer Av), which was used in the
measurements of May —June 1915 (table IV), were inserted in Comm.
N°. 142a § 4e. Table I contains the data for the gold thermometer
Art. which was used in June—July 1914.

TABLE 1.
Resistance of Au a 2) RSPAS
T ae in £ ~~ constantin
| WR; WR || Const. C3
14.16°K. 0.6148 0.00 | 0.00 | 136.621
| 15.79 gese — te | A | 918
| 17.00 e419 | — 14 | 0 | 137.138
| 17.96 6542 | — 14 | 0 | 312
19.35 6140 | — 8 | 0 | 565
| 20.31 6911 0 0 | 743
20.48 eng | Sh eh Se 716
68.22 2.6093 | | | 143.388
78.28 | 3.0917 | | | 144.000
90.27 | 3.6549 | | | 656 |

We also communicate in table II the calibration data of a gold
thermometer Av, which became defective in some measurements
concerning the specifie heat of aluminium.

In connection with a remark by ZeRNIKE in a paper published
in these Proceedings, viz. that the resistance of Av, (Comm. N°. 142a $ 42)
for the range of hydrogen temperatures can be represented fairly
accurately by a formula

Wan ne a ee
we have inserted under W_— ZR; in the tables I and II the differences
between the observed temperatures and those calculated from the
resistances with the formulae:

W = 0.5912 +- 5.871.107. 7 (Au). 2 Ze
W = 0.07279 + 1.0974 .10~7. T* (Aun) … (26)

In Fig. 8 we have represented besides these deviations (indicated
by squares and triangles respectively), also those of Au, (indicated
by circles), for which 7 was calculated from

1) Wire of 0.05 mm. of HERAEUS.
2) Wire of 0.1 imm. furnished in January 1914 by Heraeus.

903

TABLEME

Resistance of Au 1)

N°. Yi _ Resistance WR;

In liquid hydrogen with
vapour pressure apparatus

9 Dec. 13 II 14.25 0.077315 0.00
I 14.95 | 1831 ag
IV 16.02 aig) "Eg
de Tm ME | Od
HER ede Ow! en Ben | = 11
8Dec. I 18.04 | 8466 2h OS
| 9 » Vila 19.96 a much | ae
b| 19.365 | 88395 | — 55 |itte_ appara
| VIIL | __ 20.36 | 9165 | Oe
in liquid oxygen with Pé, |
16Dec: IV | 59.00 | 0.4392 |
| Il | fis! 6552
15 > | 86.41 | 7511
|
16 > ONE Sf 1519 |
15 » 1 90.20 | 1941
fae» 20.30 7962
— 915
AT
O12

1) Wire of 0.1 mm, of Heraeus.

904

W = 0.26914 543510 7 (Ag Piatt. a ee

These deviations are certainly not large (at most rather more than
0.1 degree); they are, however, appreciably larger than the inaccuracy
of the measurements. They are on the whole larger as the impurity

of the wire (ss estimated by the ratio 7) increases. This increase
of the deviations with increasing impurity seems, however, not to
be strong enough to warrant the conclusion, that for pure gold
proportionality of the resistance with 7'* within the limits of the
accuracy of the measurements would exist in the hydrogen region.
This will find its expression in ZerRNikE’s more general interpolation
formula in the fact, that in this range the coefficients of the polynomial
in the denominator already make their influence felt. GRÜNRISEN’s
relation W-C,7' brings this in connection with the deviation
which the specifie heat of gold shows in this range from the 7’*-law’).

In table I under JV—R,; we have also inserted the deviations
between the observed temperatures and those calculated from the
formula: .

WV = 0.6879—0.01741 7 + 0.000865 7”. (Au) 27 (

Practically this formula represents the resistance of A1, accurately
in this range, so that in the hydrogen range dW/d7 depends
linearly ou 7. Outside this range the formula would lead, however,
to quite incorrect values *).

For the calculation of the results of the calorimetric determinations
dealt with in this paper graphic interpolation was made use of.
For the hydrogen range graphs of W and of 4 W/AT were made
on a sufficiently large scale according to the observed values. For
the higher temperatures 7’ and dIW/d7' were taken from graphs for
the whole range of the calibration; for that purpose the W-curve
was first drawn, from this values of dIW/d7' were taken for a

1) 8"/, at 20° K. if for gold 6 = 166 is assumed according to. Desue.

2) We have also investigated whether the resistances of Auc, and Aue, (of
Which the first mentioned was enclosed in enamel, the second in paraffin) can be reduced
to each other, either with the linear relation, which according to Nernst, or with
the quadratic one, which according to Henning exists between the values of the
resistances of those wires corresponding to the same temperature. We found,
however, that in the range from 14° to 90° K. both relations give deviations of
several tenths of a degree between calculation and observation. The same result
as regards Neryst’s rule was found recently by H Scuimanx, Ann. d. Phys. (4)
45 (1914), p. 706. As regards the exceptional difference between observation and
calculation in the case of Aw -, which was found by this physicist, we refer to
the erratum given in Suppl. NC. 19 (May 1908): in Comm. NO. 99¢ p. 22 table I
column Awy, for 0.16822 is to be read 0.25234.

905
number of points in the range between hydrogen and oxygen tempe-
ratures, and these values were then smoothed graphically in the
dW/dT-tigure.

Together with the gold wire we accurately calibrated each time
the constantin wire which was to serve for the heating, in order
that this wire might serve as thermometer also (cf. p. 904 note 2) in
case the gold wire should become defective. The corresponding data
are given in Comm. N°. 142a § 4d and in this paper table I.

§ 4. Heat capacity of the core. This was measured separately in
TABLE II.

Heat capacity of the core Ky

No. : | Mean | Increase of | _Heat capacity
temperature | temperature in Joules / degree

10 June II (see tc) Ke | 0.763 | 0.727
Ill | 15.28 ee ee 0.785,
IV 16.19 0.992 0.887
Team Ey Be le a aed 1.019

| VI © | 18,285 0.964 | 1.155
Det IG. Tie 0.867 1.288

| EE TED oe |) ~ A 1.530
VIII 20.16 Wee ee 1.406
IX 21.13 0.938 1.565
X*1) | 28.375 0.979 2.99

| XP | 29.00 0.927 3.17

| XIL | 36.40 0.675 5.04

| XIII | 46.32 0.509 8.19

13 June II* | 61.87 0.503 | 12.91 |
Hr | 62.16 0.490 13.22
IV | 70.33 0.429 15.39
rn re ANN ET 15.58

| I* 80.36 | 0.346 18.74

| i4Junel 80.519 0.318 17.87
I | 80.88 | 0.356 18.56

1) For the measurements marked by an * the calculation of the increase of
60
Proceedings Royal Acad. Amsterdam. Vol. XVII.

906

the same way as described in the preceding $$ for the block of

metal and core together. We only communicate the results of the
measurements for the core Azz which served for the measurements
of June/July 1914 (table Tl).

§ 5. Lead. With lead (‘Kanipaum’’) 3 series of measurements
were made. The results of the first two series (1913) have been
united in table IV, that of the last series (1914) in table V. Weight
of the lead block: for the measurements of table IV : 715,6 grammes,
for those of table V (the same block after removal of a layer at
the surface) 709.7 grammes.

The measurements of 1914 must be considered as more accurate

ints oy TABLE Wve at
Atomic heat of lead

Nal | Mean increase of nace | id. | en |
temperature hbm block +ecorein, core C= È |
Joules | |degree | | P Ol

16 May 713 II 14.96° K. | 0.66 23.79 | 0.28 1.62

Ill | 15.86 0.735 27.27 | 0.33 1.86

Iv | 16.625 | 0.67 20.7 1 DN B

v | 17.38 0.81 31.37 | 0.42 2.14

VI | 18.19 | 0.735 33.85 0.49 2.30

vi | 18.98 | 0,845 35.46 0.58 2.41

VIII 19.81 0.805 37.20 0.69 2.52

5 June ’13 I 15.00 0.735 24.73 0.29 | 1.69

HM | 15.71 0.795 | 27.11 0.32 | 1.85

III | 16.43 0.71 30.37 0.36 2.07

| LV) \i 1%. 22 0.84 31.58 0.41 | 2.15

| wo eae 0.78 34.73 | 0.49 | 2.36
| VI 219 {10 0.95 36.68 0.59 | 2.49 |
VII 20.105 0.95 | 3678 | 0.4 2.49 |

temperature was not based on the determinations of the sensitivity (§ 2) immedi.
ately before and after those measurements, as in this case irregularities appeared
to have occurred which have not yet been explained, but on an average value of
the sensitivity, which was deduced for a number of successive measurements to
which these belong. Apart from these irregularities the individual values for the
sensitivity im one series of measurements did not differ as a rule by more than
2 to 4°/) (occasionally by 6 °/,).

ll

90

{han those of 1913. Nevertheless the latter are also communicated,
as they confirm the conclusions to be drawn from the others.
~-(, was derived from C, with the aid of the relation given by
Nernst’) for lead:
C, Ur 1 on ee
In fig. 9 C, is represented according to the observations of 1914;
fig. 10 gives a representation for the range of the hydrogen tem_

TABLE V.

| Atomic heat of lead. |

= 2 tee, Atomigheat |
= aci : |
se iene : : lead block + — 6
= 5 |Joules/ degree Cp | C,
23 June 14 XIV) 14.19° K, | 1.106 23.08 1.56 | 1.56 | 85.7
I | 15.315 0.927 26.83 | 1.818 | 1.815 | 85.9
IV | 16.275 0.9805 20.42 1.99 | 1.99 | 86.6
v | 17.24 1.001 32.18 | 217 | 2.17 | 86,9
VI | 18.255 | 1.008 35.12 | 2.41 | 2,41 | 86.3
vi} 19.27 | 1.054 |- 37.56 | 2.53 | 2.53 | 98.2 |
VIII} 20.305 1.073 39.57 |' 2.66 |: 2.66 |: 89,5 |
H | 22.31 0.962 44.58 2.98 | 2.97 | 89.9
IX | 27.51 1.019 54.41 3.60 | 3.59 | 92.4
X | 28.50 0.993 55.52 3.66 | 3.65 | 94.05
XI | 36.495 1.061 69.33 4.47 | 4.45 | 90.5
XII | 45.615 0.469 71.53 | 4.85 | 4.81
XII, 46.25 0.907 80.50 5.04 | 5.00 | 87.9 |
24 June 1 57.20 0.476 89.47 5.43 | 5.38
IL | 58.00 0.804 88.93 5.31 | 5.32 | 88.5
Ill | 69.28 0.676 92.19 5.37 | 5.31
IV | 69.97 0.723 92.82 5.40 | 5.34
V*1) | 80.365 0.661 101.07 5.71 | 5.70
8 VIX | 80.865 0.671 99.82 5.61 | 5.60 | 90.1

1) W. Nernst. Ann. d, Phys. (4) 36 (1914), p. 426.
60*

908

peratures separately, the observations of 1913 (AA and 77) being
also included.

In these figures the curve, which according to Depije represents
the atomie heat, calculated with @—= 88, which value was derived
by Becker and Scuwers from their measurements on lead, is also
represented. In agreement with Evucken and Scnwers we find that
the observations show a good concordance with Dersur’s formula
over the whole range. This concordance is, however, not complete ;
deviations show themselves which exceed the uncertainty of the results

909

of the observations '). This appears to be the case in the first place
in the range of hydrogen temperatures: the curve which unites the
experimental results crosses the curve calculated according to
Desue (Fig. 10), in such a way that at 14° K. the specifie heat is
greater, at 20° K. it is smaller than the value calculated with 6 = 88.
These deviations continue in the lower part of the range between
hydrogen and oxygen temperatures, and decrease again in the higher part.
It is true that the drawing of a conclusion is made uneertain in
this region by the interpolation, which the gold thermometer requires
there. We do not, however, consider it probable, that the deviations in
this region are to be ascribed to the inaccuracy of the interpolation:
1. as they are a regular continuation of the deviations in the hydrogen
region which are established with certainty, 2. as there are no indi-
cations that the deviations have a different sign in one part of the
region of interpolation than in the other, as would have been the
consequence of an inaccurate interpolation with the method of inter-
polation used ($ 3).

We are therefore led to the conclusion that the specific heat of
lead shows deviations from the curve calenlated according to Desun,
which unites the determinations at oxygen and at hydrogen tempe-
ratures in the best possible way (6 = 88), in the intermediate range
of the temperatures, to the extent of about 4°/, at 30° K. (ef. also
table VI).

These deviations may presumably find their explanation in one
or more of the following circumstances: a. that we did not observe
with a homogeneous substance crystallized in the regular system,
but with a micro-crystalline aggregate consisting of different phases,
such as the two different states of crystallisation assumed in supra-
conductors for the explanation of the micro-residual resistance (Comm.
N*. 133 § 11), which perhaps also come into play in the experi-
ments of Conen and HELDERMAN ®), who on the ground of their inves-
tigations assume, that with lead we are dealing with a metastable
complex of two or more modifications, 6. that the approximate sup-
positions. concerning the elastic spectrum made in Depie’s theory

1) At the points 7’=57.20, 6928 and 69.97 the irregularities mentioned in
note 1 p. 905 in the determination of the sensitivity have presumably also occurred,
though in a less degree. The first point has probably been calculated with too
large. the last two with too small a value for the sensitivity.

2, E. Cowen, These Proc. June 1914, p. 200; E. Conen and HeLpeRMAN, These
Proc. Noy. ’14, p. 822. CoHeN |. c. quotes measurements of LE VERRIER according
to which at 220 to 250°C. lead would pass into another modification with appreci-
ably larger specific heat (al constant pressure). The measurements by P. Scniisen,
Zs. f. anorg. Chem. &7 (1914), p. 81, do not, however, confirm this result.

910

are not strictly valid, c. in a change with the temperature of the
quantity @ which occurs in that theory, in other words of the elastic
properties of the material *).

Concerning } it may be remarked that for a substance which should
crystallize in the simplest cubical space-lattice Trurring has derived
an expression for the specific heat from the theory of Born and
v. K&rmsn which in consequence of the more rigorous consideration
of the molecular structure followed in this theory might give a nearer
approximation to the actual conditions. It is true that for a thorough
discussion in connection witb Txrrrine’s deductions the data about
the elastic constants in the temperature region considered are as yet
wanting. Without these we can, however, establish the following facts.

In table VI are given besides the deviations (W-Rp) between the

TABLE VI.
: Cy gs 6 à 615) Ee me |
ee ME Ë iz os —_ ek
facto | 1.56 4 0.085 |
15.315 1.815 + gs
16.275 1.99 Bie ge |
17.24 2.17 EPD + 0.26 7
18.255 2.41 dort + 28 |
19.27 2.53 0 TG |
20.305 2.66 ER aen
22.31 2.97 EN, Ed
27.51 | 3.59 eae: Lied
28.50 3.65 ae nee 6 — 0.20
36.495 4.45 aD: See one
se ihe whee 0 0 4 aid
58.00 5.32 Ee ee oi ENG

observed values of C, and those calculated according to DrBuu
with @ = 88, also the deviations W-Rz7,,, between the observations
and the values calculated from a series given by THrRRING :

1) In determining this influence it should be borne in mind that, as is specially
pointed out by Everen, Verh. d. D. physik. Ges. 15 (1913), p. 571, the elastic
properties must have been measured on homogeneous crystalline material.

=

=

911

B, fOr) 5 Bf Ore Orn |
eee 5 NS SY tan) | in EE Re Pea
ies | Sl r) Be 7) oak ol 4°)

in which 5,,5,... are the Bernouillian coefficients and Oy, is a
constant. Apparently the agreement of the observations with DrBun’s
formula is closer than that with this series of Tuirrine.

It deserves further to be noticed, that this series can only be
derived from the theory of Born and v. KArman by the introduction
of imaginary values for the elastic constants (assuming that they are
independent of the temperature). From the series which Turrrine
derives from the theory a aaa above :

h B IN
Gie: — Re ere
| 2 yo Ba tae a Ee ' ©)

where /,, /,...-/, represent definite functions *) of the elastic constants
Cry) Eys Coo introduced by Vorer, the following series may be derived
as the one which at the higher temperatures approaches nearest to
series (4)”):

Orn Or, Bf OT%\'
1— Sa 1 == = == 1825: — 5 ee "
= a “5 mal “a ae a

B, On $ | ;
+ 163987 (on el Pd

Under W—Rm, in table VI are given fe deviations between the
observations and the values calculated from (6) with 47, = 68. It
appears that Tuirrine’s formula (5) with the special assumptions
concerning the elastic constants for which it passes into (6), in the
region for which the coefficients have been developed by him,
practically coincides with Desise’s formula. Whereas, when the
elastic constants do not agree with those assumptions, THIRRING’s
formula deviates from Dersisr’s formula in a direction opposite to
the observations.

Hence we come to the conclusion that a closer consideration of
the molecular structure in the sense in which it is done in the
theories of Born and v. Kirmin and of Tuirrine, at least on the
assumption of the arrangement in the simplest cubic space-lattice,
does not account for the deviations indicated above.

It remains either to consider an arrangement in one of the other
space-lattices of the regular system *), or to assume that one or both of the
_D H. Turrrine, Physik. Z.S. 14 (1913), p.870 and 15 (1914), p. 181 note 1.

2) This would require cj = 4 C44, G12 = O-

5) A comparison with the deduction by Born, Ann. d. Phys. (4) 44 (1914), p. 607
of Cy for the space-lattice as deduced. by Brace for diamond (also a regular
crystal) leads, however, to quite analogous results as are given above for the simplest
cubic space-lattice.

912

circumstances mentioned above under a and ¢ also play a part}).
The latter of these, viz. a change of the elastic properties with the
temperature, would be connected with deviations from the linear
relation between the forces between the molecules and their relative
displacements, which deviations DeBiJr*®) also makes responsible for
the thermal expansion.

In table V are given the values of 7, which are obtained by
applying Depisn’s formula for C, to the individual observations. They
are united in Fig. 11 *) ‘).

1h 24 36 48 60 72 84

Fig. 11

$ 6. Copper. With copper we were as yet only able to make a
series of measurements between 15 and 22° K. The copper was
electrolytic copper of FerLTEN and GurLLauMe, 596,0 grammes.

U, in table VII represents the mean atomic heat between the
initial and final temperatures; for correction to the “true” atomic

1) Regarding a it may still be remarked that the presence of a second modifi-
cation of appreciably different properties in a considerable quantity would lead us to
expect much larger deviations from DepBie's formula than appear actually to
exist. If the circumstance mentioned under a plays a part, we therefore have to
assume a small quantity of a second modification, or a second modification
whose elastic properties are only little different from those of the first.

2) P. Depise, Vorträge Wolfskehlcongres Göttingen 1913.

3) The slow change, which EuckEN and ScHwers le. observed in the values
of § for lead as derived from their measurements, and which does not coincide
with that found by us, is considered by them as probably due to the uncertainty
of the temperature coefficient of their resistance thermometer.

4) Fig. 11 gives a special illustration of the character of the deviations from
Desise’s formula over the whole range, and can also serve to calculate a smoothed
value of C, by reading the value of 6 corresponding to a definite 7 from the
smoothed curve. At the same time it should be remarked, that the values of 4
represented in Fig. 11 do not coincide with hymaz/k, if ymax, the maximum frequency
according to Desi, changes with 7.

913

heat C, = C, corresponding to the mean temperature of the measure-
ment use was made of the proportionality C, — 7°, which appears
to be valid in this region.

Table VIIi contains the comparison of the experimental values

TABLE VIL

Atomic heat of copper.

ne | fen erge Male |
| in Joules/degree. | Cp Cp in
3 July ’14 | |
ll 15.249 K.| 4,222 | 2.748 | 0.0500 0.0491
HI ti Sp 0.920. | 3,805 | > Bep za,
Iv 18.03 0.842 | __ 4.222 | 792 | m2 |
Yves 18,80 0.726 | 4.884 930 930
VI 19.58 0.606 | 5.305 1010 1010
VII | 20.88 1.355 | 6.417 | 1248 | 1241 |
| I 21.505 2.156 | 7.159 | 1414 | 1410
TABLE VIII
| Atomic heat of copper.
Ra Pg | Obs —Cate.
ae Cy : | 023035) | in 9
| | :
15.24 | 0.0491 | 322.3 | 0.0486 | + 0.0008 | + 1.0
17.50 726 304.9 | 735 | — a Sid
18.03 792 | 325.2 304 | — eg Recetas We
18.89 | 930 | 322.9 925 | + ie ae! at
19.58 | 1010 325.6 | 1030 | — Bois) saayh 20
20.88 1247 ET Ne a re EEE
21.505 1410 320.0 | 138 | + 45 | +33
‚mean 323.5 | |

914
with the relation given by DeBue for sufficiently low temperatures :
a 3
Co = 1794. 3B (5) Se Ueki Das 42 Sie

The column headed 4 contains the values of 9 calculated accord-
ing to formula (7) from the individual measurements.

From these measurements the conclusion can be drawn, that in
the temperature range from 15 to 22° K. the specific heat of copper
follows Drsue’s 71° law within 2 °/, 5.

Anatomy. — “A case of occlusion of the arteria cerebelli posterior
inferior.” By Prof.:C. WINKLER.

(Communicated in the meeting of November 28, 1914).

J. P., aged 58, artisan-painter, has never before shown any other irregularities
but palpitations after physical exertion before the beginning of his illness on
October 20% 1912.

At the age of twelve he became an apprentice-painter, and always afterwards
kept to this handicraft. As a young man he used to smoke much, and also drank
much beer, but he firmly denies any sort of veneric infection, though he under-
went a treatment for strictura urethrae at the age of 45 His father died of con-
sumption, his mother of jaundice. The eldest sister died of apoplexy. The patient
is the sixth among nine children. He married young and has five healthy children.

At eight o'clock in the morning of the 20™ October he suddenly complained
of dizziness and was obliged to sit down on a chair. He did not lose consci-
ousness, but could no longer walk because his right leg had become lax. He
could neither speak nor swallow, and suffered of double vision.

Before the beginning of this attack he had walked for a quarter of an hour
over hilly ground, and for the rest had even kept himself unusually quiet.

For this attack of vertigo he was treated in the hospital at Pretoria. After a
fortnight he was again able to speak in so far as to make himself intel-
ligible, although he never completely recovered his voice; swallowing too was
performed normally again at this time.

After two months he began to walk about again wilh the aid of a stick. Since
the attack however lis sense of taste had suffered much After three months the
double vision had disappeared too.

He did not suffer from headache either before or during the attack of vertigo.
Neither had there been any vomiting, nor singultus.

it left however some lasting symptoms, to wit:

1. formications (needle-prickings) in the right half of the body and in the left
half of the face.

2, his right eye seemed to him to be covered by a film.

3. he (is) was unable to distinguish between cold and heat with his right hand.

1) Later, more accurate measurements, which however have not yet been com-
pletely finished, seem to show that in this region a small deviation from the
T3-law exists which slightly surpasses the amount mentioned above. [Added in
the translation |.

915

4. he is unable to walk without a stick, because he often feels suddenly dizzy.

5. he cannot look quickly sideways, without losing his equilibrium.

6. when looking suddenly sideways (especially to the right), he cannot recog:
nize the objects standing beside him, at least not immediately.
_ For the rest the patient declares that his hearing was bad since long. Eating,
drinking and sleeping are all right. No disturbances in the deposition of the urine
or in defecation.

Status praesens. A strongly built man, average height, good nutrition, well-fed.
Colouring of the skin and mucous membranes healthy.

The left arteria temporalis is visibly crumpled, its wall has surely doubly
the thickness of that on the right. To the touch it seems to be tense,

The tongue is moist, not coated. Nowhere any swelling of glands.

Pulse 90 per minute, regular and equal.

Breathing abdominal, 24 per minute, regular.

Heart under percussion normal, under auscultation a slightly accentuated dia-
stolic sound in the aorta. Lungs normal both under percussion and auscultation.
No irregularities are to be stated in the abdomen. Urine: acid reaction — no
albumen, no glucose.

The local sense of J. P. is good, he knows that he is in the Binnengasthuis,
is aware too of the right date. His surroundings do not however interest him much.

His memory is good. A number of six figures is correctly reproduced after a
lapse of five minutes. Simple and even somewhat more complicated arithmetical
questions are correctly solved mentally, e.g. 13 14 = 182.

The internal speech is unimpaired.

The external speech is rather monotonous, lacking articulation.

‘The voice is hoarse.

Reading presents no difficulties, neither does writing, which is done in a very
neat hand.

The hair-covering of the head is normal, as are likewise the boundaries of the*
hair-growth. The head is ever kept turned somewhat to the right. The face is
asymmetrical. The left cheek is thicker than the right one, it feels hotter to the
touch and is injected. The left regio temperalis is salient. The left orbital fissure
is nurrower than that to the right. The left bulb is slightly directed upward.

The circumference of the head is 59 cm.

Not unfrequently an involuntary movement may be observed, by which the
head is thrown to the right. The eyes then are turning first to the left and
afterwards follow slowly the movement of the head to the right.

The nerves of the brain:

I. Olfactorius. The patient states that his sense of smelling was enfeebled long
before his illness. To the left he recognizes neither Eau de cologne nor anisseed-oil.
Il. Opticus. Visus (after correction of the hypermetropy + 3D) on both sides I.

The fundus is normal on both sides, as is likewise the field of vision.

lll, IV, V. Movements of the eye. The pupil on the left side is somewhut
narrower than that on the right, the latter is of normal width. On both sides
the pupils are reacting on light and on convergency. The orbital fissure to the
left is narrower than that to the right. The left bulbus is slightly protruding.

The position of the bulbi is somewhat diverging. When in rest, sometimes
nystagmoid movements appear, usually to- the left and in horizontal direction.

916

They disappear when the patient regards fixedly. In darkness nystagmus to
the left.

The convergency is normal, the right bulbus however deviates soon towards
the left. No double vision.

The moving of the two bulbi is normal to the right, to the left it is accom-
panied by nystagmus, which however soon ceases afterwards, the moving of the
two bulbi upward and downward is likewise complicated by nystagmus.

Besides this there is no paralysis of the muscles of the eye.

When the patient is looking straight forward, and is summoned to regard fixedly
anybody standing on the right of him, he does so in the following manner:
He turns his head to the right; both eyes remain behind in this movement,
they are even drawn towards the left for one moment, it is only after this that
they are following slowly the movement of the head, and that the patient looks
fixedly into the desired direction.

V. The N. trigeminus. All motor functions of mastication etc. are undisturbed.

Sensibility on the contrary has suffered.

The tactile sense is unimpaired on both sides. Every contact, however slight,
with a hair-pencil or a small plug of cottonwool, is instantly perceived.

On the other hand the perception of pain is destroyed over the whole of the
trigeminus-area on the left side. The difference between the head and the point
of a pin is not distinguished. Nowhere at any point within this area is a painful
contact perceived. To the right the sensibility to pain is intact.

The perception of temperature, intact to the right, is likewise disturbed to the
left. On this side melting ice is still recognized to be cold, but as being less
cold than to the right. With regard to the perception of heat, there is always a
difference disfavourable to the left side. The boundary-line of the left analgesy
(conf. the scheme) is distinctly defined against the median line, it then passes over
the top of the head and returns behind the ear (which is included in the analgesia)
_ along, the chin to the median line, where it meets the analgetic right half of the
body (conf. later on).

The left half of the mucous membrane of the cavity of the mouth is likewise
analgetic, the boundary-line passing over the median line of the tongue and +
over the middle of the palatum. The latter is swollen (conf. later on).

A deep impression is correctly perceived both to the right and to the left within
the trigeminus-area. The two points of the compass of WEBER are well distinguished
on both sides at a distance of + 20 em. (vertically). The sense of localisation
is intact on both sides.

The cornea is normally sensible to the right. To the left both the pain-sensi-
bility and the tactile sense have completely disappeared in it, and a piece of
melting ice on the left cornea is not felt to be cold. The cornea-reflex is failing.

The left facial half is hyperaemic and swollen, it feels hotter to the touch, but
there is no trophical abnormality.

Vil. The N. facialis is intact on both sides. All mimical and voluntary inner-
vation of the face is performed on both sides in the same manner.

Villa. The Nervus cochlearis. The tympanic membrane (observation of Dr.
VAN GILSE) is normal to the right, and to the left it becomes normal too after
the removal of a plug of cerumen.

The patient has not heard well to the right since long (before the attack of
vertigo).

917

To the right upper limit of hearing by bone-conduction (monochord STRUYCKEN)
15!/, (norm. 13—14).

Upper limit of hearing by air-conduction idem 31 (norm. 14).
To the left , ef 2 ,», bone-conduction idem 15/3.
5 yet ve De „ air-conduction idem 31.
Whispering voice. To the right + 8 cm.
To the left low zone + 3 cm.

high zone + 5 cm.

To the right the patient does hear:

SCHWABACH shortened. WEBER not lateralized. RINNE to the left +, to the right —.

VIIIb. The nervus vestibularis. Injection of cold water.

On the right side it distinctly produces nystagmus to the left. Afterwards
there is + no deviation to be found in both arms in pointing at a fixed object.

On the left side there is as distinctly produced nystagmus to the right. The
pointing experiment made after this shows no deviation for the right arm, but it
does so for the left arm that is deviating to the right.

IX, X, XI. The taste has not suffered either to the left or to the right.
Subjectively the patient declares that his sense of taste has diminished on the tip
of the tongue.

The uvula is swollen clubshaped at its end, on its right upperside there is a
sear. It is deviating towards the right.

The arcus palatini to the right are placed lower than those to the left. On
innervation both arches are lifted slightly (a result of the swollen uvula). Insigni-
ficant Rhinolalia aperta.

Laryngoscopically (Dr. van Gitse). Epiglottis abnormally small. During phona-
tion the right vocal cord is passing far over the median line. Of the left
vocal cord only a small margin is visible, half concealed under the swollen false
vocal cord. The left vocal cord is entirely motionless, there are neither abductor
nor adductor motions.

The motions of the right vocal cord are normal.

To the left there is tumefaction in the region of the arythenoid-cartilage and
in the sinus piriformis.

A complete paralysis of the left N. accessorius of the oblongata is assumed
to exist.

The shoulders are lifted without any difficulty. M. trapezoides and M. sterno-cleido-
mastoidens are not atrophic.

Swallowing presents difficulties, because according to patient, there is an impe-
diment io the left.

XIL The N. hypoglossus. When in repose the tongue is normal, when put
out it is stretched straightforward. Strong tremor, especially at the tip. Movements
can be made in all directions. The innervation of the bottom of the month is
equal on both sides.

Neck and trunk. The attitude of the head is always turned to the right. For
the rest no irregularities in the movements of neck and trunk. The vertebral
column is nowhere painful. The patient is able to raise himself from a declining
posture to a sitting one without the aid of his arms.

Sensibility. The tactile sense is undisturbed both to the right and to the left,
even the slightest contact with a plug of cottonwool or a hair-pencil is instantly
perceived.

918

On the contrary the pain-sensibility is entirely destroyed on the right side
with distinct boundary-lines at the mid-ventral and mid-doisal lines. Diminished in
the region of the neck and at the right side of the occiput (see the dotted lines
in the scheme), this incomplete disiurbance is distinctly separate both from the
complete analgesia of the trunk and from the normally sensible region of the
trigeminus to the left.

The sense for temperature has likewise completely disappeared on the right
side. No difference is felt between melting ice and hot water. A tube containing
cold or hot water is called alternately cold and hot.

J. P. Aged 59. ///// Complete Thermo-anaesthesia and Analgesia.
_ Incomplete Thermo-anaesthesia and Hypalgesia.
November 1914,

As soon however as the patient is touched on the right side with a hot object,
he feels a peculiar pricking sensation at the left exterior corner of the eye and
at the left nostril.

Further the reflex-actions of the abdomen and the -cremaster exist on both sides.

Arms. On inspection no abnormality, well developed muscular system, normal
tonus on both sides. All movements are performed powerfully with strength. The
dynamometre points 85 on the Right, 65 on the Left. No ataxy when pointing
with the index to the tip of the nose, or when the two indices are brought
together. Normal diadokynesis. The reflex-actions are high on both sides.

JIJ

The tactile sense is undisturbed on both sides.

The perceptions of pain and of temperature are completely destroyed to the
right (conf. the schema), to the right they are undisturbed.

The nerve-trunks remain painless under pressure.

The perception of active and passive movements is particularly good. On hoth
sides localisation is normal. The two points of the compass of WEBER are recog-
nized and distinguished within the appointed scale. On both sides stereognosia is
perfectly normal.

Legs. On inspection no irregularities, powerful muscular development with normal
tenus. Neither tremor nor accessory movements.

All movements are executed on both sides powerfully and with equal strength.
No ataxy of movement when the kneé-heel experiment is made or when describing
a small circle.

During repose however there is a slight static ataxy. When standing with both
feet closely joined, the. patient totters and threatens to fall, usually to the left.
This becomes rather worse when his eyes are closed. The patient walks with
legs wide apart, and generally deviates towards the left of his course. It is impossible
for him to stand on one leg either on the left or on the right, and likewise to halt.

When walking, the trunk is borne somewhat stiffly.

The reflex-actions of the knee and of the tendo Achillis are normal on both sides.

Reflex-action of the plant of the foot to the right: plantar-flexion of all toes
with averting movement.

To the left plantar-flexion of the little toes after irritation of the planta pedis.
and when the tibia is stroked.

The tactile sense is undisturbed on both sides. Even the slightest contact is perceived,

Pain-sensibility. Normal to the left. On this side a frightened reaction,
accompanied by a deep inhalation, repeatedly follows on a pin-prick, as if there
existed a strong hyperaesthesia.

Nowhere on the right is pain-perceived. Although sometimes by an effort the
patient is able to distinguish between the contact with the head or with the point
of a pin, still this distinction is not founded on any perception of the sensation
of pain.

The exterior genitals are analgetic to the right, though the boundarylines do
not follow strictly the median line, but deviates somewhat towards the right.

The perception of heat and cold is intact on the left, it has disappeared
on the right.

On both sides passive and active movements are perceived with absolute
correctness. The sense of space is undisturbed on both sides. Localisation, though
with a rather large declination, is good on both sides.

The state of the patient remained unchanged during the months of October and
November. The reaction of WASSERMANN was found to be negative in the blood.
Lumbar punction was not performed.

-

Summing up, we may state the case as follows:

On the 20% of October 1912, at eight o’clock in the morning,
accompanied by violent vertigo, but without loss of consciousness,
a complex of symptoms presented itself, fitting into the general view
of the so-called per-acute bulbar paralysis. Part of these symptoms

920

— the disturbances of speech, the difficulty in swallowing, the laxity
of the right leg — have been soon meliorated or cured. Another
part of them however have become lasting.

The most important of these residue symptoms are:

a. Complete analgesia and thermanaesthesia in those regions of
skin and mucous membrane that are controlled by the left N. trigeminus,
— the tactile sense, localisation and motor-power having been
preserved in the trigeminus-muscles.

The reflex-action of the cornea no longer exists.

This analgesia alternates with:

4. Complete analgesia and thermanaesthesia in the right half of
the body. Within the region of the upper cervical roots on the right
this disturbance is incomplete. The tactile sense, the deep sensibility,
tbe sense of space, localisation and stereognosy are undisturbed and
have not suffered in the right half of the body. There is not one
single symptom of hemiplegia. |

c. Complete paralysis of the larynx to the left. Incomplete paralysis

of the swallowing-muscles on that side.

d. A peculiar involuntary attitude of the head, turned towards the
right, together with a dissociation of the conjugate movement of the
eyes and the head turning to that side. When this movement is
made, the eyes cannot follow it. They first turn towards the left,
afterwards slowly following the movement of the head towards the
right, the patient being consequently unable to recognize instantly
the objects placed beside him, on account of the defective stand of
the eyes.

e. A slight degree of static ataxy.

Without any doubt this disturbance is caused by an occlusion in
the arteria cerebelli posterior inferior and a softening (eventually a
eyst) in the latero-dorsal portion of the left half of the medulla
oblongata.

This morbid affection has been tirst described and appreciated
by Senator’), subsequently it has been carefully analysed by
WALLENBERG*) and Marpure*), who have done most meritorious

1) H. Senator. Zur Diagnostik der Nervenkrankungen in der Brücke und in dem
verlängerten Mark. Arch. f. Phych. Bd. 14. 1883. p. 643 ff.

2) ApoLF WALLENBERG. Acute Bulbir-affection (Embolie der arteria Cerebel-
laris posterior inferior sinistra). Arch. f. Phych. Bd. 27. 1895 p. 504 ff. and:

WALLENBERG. Anatomischer Befund in einem als Embolie der art. cerebellaris
posterior inf. sinislra beschriebenen Falle. Arch. f. Ps. Bd. 34. 1901. S. 923

3) R. BREUER und Orro MARBURG. Zur Klinik und Pathologie der apoplecti-
formen Bulbärparalyse. Arbeiten aus dem neurologischen Instituten der Wiener
Universität (OBERSTEINER) Bd. IX. 1902. p. 181.

oe

921

work for the pathology of the medulla oblongata. Rupour Brun?)
has given a nearly complete summary of the literature on this
subject, into which I will not enter here.

The foregoing case has been communicated, because in a clinical
sense it is a peculiarly well-defined case.

A few remarks I may be allowed to add still about it. Before
the arteria vertebralis has united with the contra-lateral one to
form the arteria basilaris, it supplies the medulla oblongata with
several small branches. Among these branches the art. spinalis dorsalis

Scheme of the Nutrient bloodvessels of the medulla oblongata after Durer.

(Archives de Physiologie. 1873. Tome V. Planche VIII).
Fig. I. A. Art. cerebellaris posterior
(inferior).
B. Art. cerebellaris media
(inferior anterior).
C, Art. cerebellaris superior.
D. Art. cerebellaris posterior.
1. Art. radicularis (N. acces-
soril spinalis).
. Art. spinalis anterior.
3. Art. radicularis (N. X et
NS EX):
4. Art. auditiva spinalis (N.
VII et N. VIII).
5. Art. radicularis N. VI,
6—7. Arteriae fossae supra:

bo

olivaris,

8. Arteria auditiva interna
(from B).

9. Art. Ny Ve

10. Art, radicularis N. XII.
Fig. Il. A. Plexus chorioideus.

B. Tela chorioidea.

C. Foramen Morgagni.

D. Clavus.

!. Arteria cerebelli posterior
inferior.

2—4, Small branches of this
artery.

5. Arteria spinalis posterior.

6—8. Small branches of this
artery.

1) Ruporr Brun. Ein Fall von doppelseitigen symmetrischen Erweichungssystem
im verlängerten Mark.
Arbeiten aus dem hirnanatomischen Institute der Universität in Zürich. Bd. VI.
1912. S. 270—400.
61
Proceedings Royal Acad. Amsterdam. Vol. XVII.

922

and the art. cerebelli posterior inferior are of especial interest to us.
They originate on both sides from a joint small branch of the art.
vertebralis on the anterior side of the oblongata. The art. spinalis
dorsalis then descends along the lateral surface of the oblongata and
provides for the caudal portion of the medulla oblongata. The art.
cerebelli ascends between’ the corp. restiformis and the oliva inferior,
it provides for the laterodorsal portion of the m. oblongata in its
proximal part by means of small branches originating from it in
perpendicular direction, and then leaves the corpus restiforme to
supply further with blood the distal half of the basal cerebellum-
laminae.

The area of irrigation of the art. cerebelli inferior posterior is
accordingly situated within the latero-dorsal portion of the med.
oblongata proximally to that of the art. spinalis dorsalis.

The N. octavus is lying proximal to this irrigation-zone.

The boundary line between pons and oblongata forms the proximal
demarcation of this region, about there where the distal part of the
nucleus N. VI is to be found. Caudally it is confined by the N.
ambiguus, the caudal extremity of which is provided for by the
art. spinalis dorsalis. The ventral boundary is indicated approximatively
by the Oliva-nucleus; the dorsal one by the basal nuclei that have
their own suppiy of arteries, the medial boundary by the nucleus
and the roots of the N. XII.

Surveying a topographical map of the meduila oblongata, we may
see that within the irrigation zone of the art. cerebelli posterior inferior
are found:

Fig. Ill. Scheme of the area of irrigation of the
art. cerebelli inferior hit by a frontal section.

Trans por FHF

<

a. That part of the tractus spinalis N. V, that is going in a caudal

923
direction opposite to the upper half of the oliva inferior. The sensible
nucleus of this nerve and its motor nucleus are not included.

6. The so-called “aberrirendes Seitenstrangfeld’’, in which are found
the spino-thalamie (EpINGER’s) tract, the rubro-spinal (Monaxow’s)
tract, and the ventral spino-cerebellar (Gownr’s) tract.

c. The proximal part of the N. ambiguus, i.e. the ventral nucleus
of the N. IX, X, and partly too of the N. XI, besides the forth-coming
roots of these nerves.

d. The interior portion of the Corpus restiforme (Monakow’s I. A.
K.) with the descending root of the N. VIII that is found within it.

Besides, in the immediate vicinity of this region is lying the
Nucleus dorsalis N. X, especially the tractus solitarias with it nuclei,
and if medialward this region extends really so far as the radices
N. XII demarcate the formatio reticularis grisea, then the tractus
vestibulo-spinalis belongs likewise to it.

Moreover the caudal basal portion of the cerebellum must be also
reckoned to belong to this irrigation zone.

According to the symptoms this dorso-lateral portion of the oblongata
is destroyed on the left side.

As the most prominent disturbance there was found:

I. Alternating paralysis of the sensibility for pain and for thermal
stimuli, to the left in the region controlled by the N.V, to the right
over the whole half of the body, with the exception of the Trigeminus-area.

The tactile sense, localisalition and the sense of space, perception
of passive and active movements, stereognosia, are all preserved in
the normal way.

The dissociation in these perceptions — aiid the literature proves
that it has been observed more than once — is most remarkable. It
shows that the conduction of pain- and heat-sensation within the
entire region of the trigeminus ought necessarily to be sought for
in the tractus spinalis of this nerve, which has been interrupted in the
proximal oblongata. The tactile impressions may still find their way
along the nucleus sensibilis N.V, which remains unimpaired (as are
likewise the N. motorius and its radix mesencephalicus). It is interesting
that the reflex-action of the cornea has disappeared and that the
cornea no longer perceives anything. Probably the cornea — without
tactile corpuscles and without hairs — does not possess any contriv-
ance for the tactile sense.

The interruption of the spino-thalamie tract on the left side is
assumed to be responsible for the defective conduction of the thermal
and pain-stimuli in the right half of the body.

The lemniscus medialis, is not attained by the lesion — the long
61*

924

posterior root-fibres end in the nuclei of Gor and Burpacn, and
the fibres originating in these nuclei have continued their course
therein through the decussatio lemnisci — from this is determined
the intactness of deep sensibility (stereognosia, sense of space, per-
ception of passive and active motion of the right half of the body).

It is generally taken for granted that the thin fibres in the marginal
zone of Lissaugr conduct their impulses into the fibres of the spongiosa
of the formatio RorLaNpo, and after passing through the substantia
gelatinosa and the cells of Gierkr are absorbed by the terminal cells,
adjacent to the substantia gelatinosa.

The axones of the cells are then thought to cross one another in
the anterior (and posterior) commissure, and to continue their course
as tractus spino-thalamicus in the lateral column of the medulla.

It is just because of experiences similar to the case here described
that the tractus spinothalamicus has been assumed to be invested
with the function of conducting the thermal and pain-impulses.

It is different for the tactile sense. Tactile impulses enter likewise
into the thin fibres of the zone of Lissaver, but they may pass
thence immediately into the marginal cells of the spongiosa of the
formatio RoraNpo, — the zonal cells. Their axones may ascend as
well through the posterior as through the lateral cords of the uni-
lateral and the controlateral side, it is even most probable that these
prolongations are so diffused in the tegmentum of the spinal cord,
that the conduct of these impulses remains possible as long as even
a small part of it has been preserved. In the left half of the

Fig. IV. Scheme of the LissAvER marginal zone and of the substantia RoLanpo
with the origin of the tractus spino-thalamicus.

oblongata there is a sufficient number of fibres, both in the lemniscus
medialis and in the median portions of the formatio reticularis grisea

to bring about the conduct of the tactile impressions from the right
half of the body. The tactile sense of the right side remains therefore
undisturbed.

II. The paralysis of the swallowing muscles to the left (that has
been much meliorated) and the lasting paralysis of the muscles of
the larynx on that side are symptoms following almost necessarily
from the former. The ventral (motor) nucleus of the IXth, Xt and
XItt nerve has been destroyed by the lesion.

Whether the dorsal vagus nucleus has been injured, forms an
independent question. For the moment the sense of taste to the left
has suffered only very slightly. Those who believe the tractus solitarius
to be a continuation of centripetal glosso-pharyngeus-fibres as it
doubtlessly is in part and who consider it as a tract conducting
taste-impulses, will be rather inclined to think it has not been injured.

On the other hand the analgesia trangresses into the zone of the
N. trigeminus in the region of the ear, whilst pain- and heat-sensation
are disturbed in the dermal branch dependent on the N. X, a fact
easily: to be understood, considering the destroying of the forthcoming
roots of this nerve.

ill. The dissociation of the conjugate movement of the eyes and
the head towards the right.

I believe this symptom to be a consequence of the portio interna
corporis restiformis to the left. Within this portion is contained the
radix descendens N. VIII. It contains the descending root-tibres of
of the N. vestibularis, which enter into it on a higher plane than
that where is situated the focus of disease. The N. vestibularis here-
fore bas been destroyed partially, not completely — the coldwater-
reaction of Barany proves that vestibularis-impulses still act upon
the double-eye.

The influence of the one-sided destruction of the vestibular tonus
on the double-eye is well-known. Both in man and in animals the
uni-lateral eye is turned downward and inward, the contro-lateral
one upward and outward. They deviate therefore in a direction
opposite to the lesion.

In the present case however that involuntary stand of the eyes
has found compensations, amongst others the oblique attitude of the
head. The motor mechanism for the double eye is consequently
brought into another state of equilibrium than the normal one. It
undergoes an innervation tendency to direct both eyes more than
is usual towards the left side. | 8

This mechanism has been disposed in that way by means of reflex-
actions through the exercise that has led to compensation.

926 /

As soon as a voluntary act does make use of the motor mechanism
of the double eye which is connected indissolubly with the turning of
the head towards the right, there will necessarily be made an
endeavour to employ another mechanism than that existing in the
norma.

The prevailing innervation-tendency for turning the eyes towards
the left is now in conflict with the impulse of turning towards the
right. As a result of it, first the turning of both eyes towards the
left may be observed, whilst it is only after this that the position
of extreme turning towards the right is attained.

As a consequence of this the fixation of the eyes on objects
standing to the right is not synchrone with the turning of the head.
Therefore these objects are not instantly recognized, as long as the
settling of the eyes remains defective.

The same case does present itself if the head is turned towards
the left, with this difference that no turning of the double eye
towards the left then precedes. In this latter case the voluntary and
the reflective movements are added up together, the eyes are moving
too quickly, with the result that objects standing on the right are
again not instantly well-recognized, though the irregularity is redressed
much sooner than when looking towards the right. As fourth and
last symptom we find the static ataxy shown by the patient, a
symptom that may depend either on an interruption of rubro-spinal
or vestibulo-spinal tracts, or on the softening that probably exists at
the base of the cerebellum, or on both.

All symptoms taken together however indicate a sudden inefficacy
of the nerve-area, irrigated by the arteria cerebelli posterior inferior.

Chemistry. — “The metastability of the Metals in consequence
of Allotropy and its significance for Chemistry, Physics and
Technics. IIT?’ By Prof. Ernst ConeN and G. pr BRUIN.

The specific Heat of the Metals 2.

1. In the first paper on this subject *) it was pointed out that
the existing data on the physical and mechanical constants of metals
known up to the present are to be considered as entirely fortuitous
values, since they refer to the indefinite metastable systems which
are produced when metals pass from the molten to the solid state.
In other words: all physical and mechanical constants of the metals
are functions of the previous thermal history of the specimen expe-
rimented with.

1) Proc. 16, 632 (1913).

a taat Pe ie le td os

927
In the second paper') we called attention to the fact that this
result was corroborated by Le Vwrrigr’s experiments, who found as
long as twenty two years ago, that the specific heat of Pb, Zn, Al,
Ag, and Cu is a function of the previous thermal treatment of
these metals.

2. Although the values given by Lr Verrier are mentioned in
different physico-chemical tables, only small attention has been given
to them. In those cases where this has been done, they have generally
been considered as less accurate. Such is for example the.case with
SCHÜBEL *), who says in a paper published recently :

“Nicht mit aufgenommen sind die Beobachtungen von Lr VeRRIER,
Al, Cu, Ag, Zn; Le Verrter findet Unstetigkeiten in seinen Kurven
der mittleren spezifischen Wärme als Funktion der Temperatur,
welche nicht wieder beobachtet wurden, so dass die von ihm
gefundenen Werte für die mittlere spezifische Wärme héchst unwahr-
scheinlich geworden sind.”

3. However, it may be pointed out that others would have been
able to find the same results as Le Verrimr only if they had inves-
tigated specimina of the same metal possessing different thermal histo-
ries, as Lr Verrier did.

We shall see below what discrepancies occur if this precaution
is omitted. It will be proved then also that Le Verrier has been
up to the present the only investigator who has paid sufficient
attention to this point.

4. The fact that different authors have found (at the same tem-
perature) for a certain metal very different values of the specific
heat, must partly be attributed to their omitting to take into account
the previous heat treatment of the metal experimented with. From
the enormous material found in the literature, we only quote here
the values for bismuth found at 18° by L. Lorenz *) to be 0,0308,
whilst JAEGER and DriessrLHORST *) give 0,0292. The difference is
3 percent. But also differences as high as 13 percent occur, as might
be seen from the paper of ScHüBEL, mentioned above.

5. That these facts recently have attracted notice on the part of

1) Proc. 17, 200 (1914).

2) Zeitschr. f. anorg. Chemie 87, 81 °(1914).

3) Wied. Ann. 13, 437 (1881).

4) Abhandl. der Physik, Techn, Reichsanstalt 3, 269 (1900).

928

physicists, is evident from a paper published by E. H. Grirriras
and Ezer Grirritus'), who say: “a further possible source of uncer-
tainty is the effect of sudden chilling of a metal when rapidly cooled
from a high temperature. However they do not mention the reasons
which led them to this conclusion.

As these investigations as well as those of Ezer Grirritus ?) on
“The variation with temperature of the specific Heat of Sodium in
the Solid and Liquid State’, play an important rôle in our subsequent
arguments, we must dwell upon them.

Using a special calorimeter in which the metal was electrically
heated, they determined the true specific heat of different metals (Cu,
Ag, Zn, Sn, Pb, Al and Cd®) at different temperatures. As the
substances were raised from a given temperature through very small
ranges of temperature (about 1.4° C.) their previous thermal history
was not changed by the experiment itself. Evidently this is of high
importance, as in the methods in use up to the present (method of
mixtures, ice-calorimeter) the substances are heated to considerably
higher temperatures by which procedure changes may occur which
are uncontrollable.

6. The metals experimented with were of high purity. In this
way Messrs. GrirritHs succeeded in determining for a certain piece
of metal at a definite temperature values of the specific heat which
were quite reproducible while the conditions of the experiments were
changed within wide limits. For a certain piece of copper, the
previous thermal history of which was however indefinite, they
found. at-0> 6:

Mean of 5 independent determinations 0.09094 (probable experi-
mental error of the group 0.01 percent).

Mean of 5 independent determinations 0.09079 (probable experi-
mental error of the group 0.03 percent).

Mean of 4 independent determinations 0.09098 (probable experi.
mental error of the group 0.05 percent). |

Mean of 4 independent determinations 0.09088 (probable experi-
mental error of the group 0.08 percent).

7. The metals used by the authors were cast. Evidently they
were of opinion that the condition of their material was definite.
This is most surprising, as they themselves called attention to the

1) Phil. Trans. Roy. Soc. London 213 (A), 119 (1914),
2?) Proc. Roy. Soc. London 89, (A) 561 (1914),
8) And Iron.

929

fact that previous thermal treatment must be taken into account.
It will be proved below that the metals experimented with by
Messrs. Grirritas did not correspond to definite states: the values they
found for the specific heat must therefore be considered as fortuitous
values. This is the more to be regretted as their measurements were
carried out with the greatest care.

8. We shall now consider the experiments concerning sodium.

The high importance of this research with respect to the question
which occupies us, may be characterized by the following four points:

a. The previous thermal history of the pure metal was strictly
defined.

b. Each value given for the ¢rwe specific heat is the mean ot
4 or 6 independent determinations which were carried out under
varying conditions (change of the quantity of electric energy supplied).
As the tables (I and II) show, the agreement of the measurements
is perfect.

c. The determinations have been carried out with the solid metal
from 0° up to the melting point.

d. The authors have exclusively taken the standpoint of ex-
perimental physicists, giving their quantitative results without any
commentary.

9. Concerning the item a the following may be pointed out. The
authors had found that the true specifie heat of molten sodium can
be reproduced with great accuracy, even if the previous heat treat-
ment of the molten metal is changed within wide limits. The contrary
occurs with the solid metal: discrepancies of 2 per cent at the same
temperature were found in their early experiments. Referring to this
result they say: “The importance of this point was not sufficiently
realised in the early determinations and a large number of otherwise
excellent experiments have been rendered worthless through lack of
attention to the precise nature of the previous heat treatment.”

The metal used in the final experiments was prepared as follows:

«“ Annealed’. (Table I): The rate of cooling from the liquid state
was less than 4° per hour, which was the rate of fall of the bath
from 100° to 86°.

“Quenched”’ (Table II): The metal was heated in an oil bath to
130° and then rapidly transferred to a vessel of ice-cold water.

The metal was enclosed in a case of copper of special form. The
determinations with the quenched metal were made starting from
the lowest temperature (0° C.) and progressing in steps up to 95°.

930

TABLE 4.
Na — slowly cooled (Annealed)

Temperature Data Spec. Heat | Mean

0° Aug. 28 0.2835

0.2836
0.2820 0.2829

0.2826

28° .82 | Aug. 19 0.2911

0.2910
0.2929 0.2910

0.2893

49°. 38 Aug. 8 0.2954
0.2952

0.2951 |

0.2055 0.2953

0.2951

0.2955

49°.21 | Aug. 16 0.2946
| 0.2949 0.2953
| | 0.2064

499.07 | Aug. 17 0.2963 |
Aug. 20 | 0.2945 0.2950
0.2942

67°.79 Aug. 21 0.3014
0.3037
0.3018 0.3019
0.3010
0.3018

79°.15 Aug. 22 0.3083

0.3085
0.3086 0.3083

0.3079

85° .65 Aug. 15 | 0.3168
0.3181 |
0.3165 0.3171
0.3178
0.3159 |

90°.03 | Aug. 23 0.3209

0.3208
0.3208 | €-3209

0.3210

PS) Aug. 24 0.3260
| 0.3254 0.3258
0.3260

|
|

If the cooling had taken place very slowly, the values found at
each temperature were definite and reproducible. This proves that
the values given in table I refer to the state of equilibrium at the

931

FABLE: IE
Na — “quenched”.

Temperature Data Spec. Heat Mean

Br: Aug. 29 0.2892

0.2874
0.2864 0.2870

0.2852

40°. 16 Aug. 30 0.2973
0.3002 |
0.2953 | 0.2981
0.2992 |
0.2983

68° .60 Aug. 31 0.3024
0.3049
0.3073

-- 0.3040

68° .60 sept. 2 0.3034
0.3020
0.3038

822.15 Sept 0.3087

0.3094
0.3095 0.3089

0.3079

94° .02 Sept. 4 0.3195

0.3213
0.3192 0.3200

0.3200

corresponding temperature. The measurements of 8 Aug. giving the
value 0.2953 (at 49°.38) having been completed, the metal was taken
out of the calorimeter, heated up to 100° (melted) and allowed to cool
rapidly in air. The value then obtained for the specific heat (at
49°.38) was 0.8014. Again heating to 100° (melting) and allowing
to cool very slowly, gave the value 0.2953 (at 49°.38), identical
with the value previously obtained for the ‘‘annealed” metal.
Evidently the process is a reversible one.

10. We shall now consider the diagram (fig. 1 See next p. 932)
which represents the results graphically. The broken line apd
represents the results of the determinations after the sodium had
had been quenched whilst the curve cpd represents those concerning
the solid metal. This diagram is also given by Ezer Grirritus with-
out any commentary.

True specific heat —

Temperature —
Fig. 1.

Considering the figure more closely it is evident that sodium has
a transition point between O° and 90°: this was not known up to
the present *).

11. We have here for the first time a case where it is possible
to obtain at will, and in nearly quantitative yield, either the stable
or the metastable solid modification from a metallic melt. Until now
Ernst COHEN, HRELDERMAN, Morsverp and VAN DEN Boscn have not been
able to get this result in their investigations on bismuth *), copper’),
zine *), antimony®) and lead’). In these cases the different modi-

1) Scräprer [Lieb. Ann. 20, 2 (1836)], thinks it probable that sodium crystallizes
in the regular system, whilst Lone [Journ. Chem. Soc. 13, 122 (1860)] found
that it is also able to crystallize in the quadratic system.

2) Zeitschr. f. physik. Chemie 85, 419 (1913).

8) Proc. 16, 628 (1913); 17, 60 (1914).

4) Proc. 16, 565 (1913); 17, 59, 641 (1914).

5) Proc. 17, 645 (1914).

6) Proc. 17, 822 (1914),

033

fications were always simultaneously present in the material ex-
perimented with.

Only with cadmium") did they succeed in preparing the pure a, 3
and y-modifications by preparing electrolytically the y-form, which
was transformed afterwards into the B- or- e-modification.

12. From the work of ConeN and his collaborators it follows
that a piece of sodium, chosen at random, is at ordinary tempera-
tures in a metastable condition, as there are simultaneously present
both the «- and g-sodium. This conclusion is proved in a quantitative
way by the very exact measurements of Ezer Grirritus. It is to be
expected that sodium which has received heat treatment of an inter-
mediate character (between chilling and annealing) will have at a
given temperature a specific heat between the values found at the
same temperature for the “chilled” and “annealed” material respectively.

The following experiment proves that this is really the case.
The metal was melted and allowed to cool freely in air. (Samples
A and 2, table III). Whilst the specific heat of the “annealed”
metal was found to be 0.2829 at O° C. and that of the chilled 0.2870,
the experiment gave now (at 0’ C.) the values of table III.

The specific heat values are found now between 0.2829 and 0.2870.

GRIFFITHS says: “Several determinations were made at tempera-
tures between 88° and 94° after a somewhat similar heat-treatment,
and the same feature is common to all, the values falling between
the extremes corresponding to the “annealed” and the “quenched”
states”’.

TABLE UL

Preparation | Date | maa oe Mean

A April 7 0.2861
0.2868
0.2866 0.2864
0.2864
0.2858

B June 4 0.2864
| 0.2871
5 0.2862
: 0.2855 0.2863
6 0.2864 u
0.2863

1) Proc. 16, 485 (1913); 17, 54, 122, 638 (1914).

934

13. These experiments consequently prove in a quantitative way
that sodium as it has been known up to the present, is also a
metastable system in consequence of allotropy and that the physical
and mechanical constants of this metal which have been determined
hitherto (except the values of the specific heat, mentioned in the
tables I and II) are entirely fortuitous values.

14. Some preliminary experiments carried out by Ezer GRIFFITHS
proved that there exists a measurable difference between the densities
of a- and g-sodium at the same temperature. We hope to report
shortly on some dilatometric measurements in this direction.

Summary of Results.

Relying on the investigations of Ernst COHEN, HELDERMAN, MOESVELD
and vAN DEN Boscu and those of E. H. and Ezer Grirrirus on the
true specific heat of metals at different temperatures we find that:

1. The true specific heat of sodium is a function of its previous
thermal history.

2. Both with the slowly cooled and the chilled metal, at a definite
temperature detinite and reproducible values of this physical con-
stant are found.

3. An intermediate previous thermal history gives values of the
specific heat between the extremes mentioned under 2.

4. The experiments of Le Verrier (1892) on the specific heat of
metals which had not been understood up to the present are cor-
roborated by the investigations recently carried out with high preci-
sion by E. H. and Ezer Grirritus.

5. Sodium is enantiotropic; there exists a transition temperature
between O° and 90° C. *)

6. Sodium, as it is known hitherto, is a metastable system as
might be expected on account of the investigations on bismuth,
cadmium, copper, zinc, antimony and lead, described some time ago.

7. All physical and mechanical ‘constants’ known up to the
present of the metals are entirely fortuitous values; they must be

redetermined with the pure a-,@-,y-,.... modifications of these
substances.
Utrecht, December 1914. yan ’r Horr-Labordatory.

*) The exact position of this point will be determined by dilatometric measurements.

935

Mathematics. — ‘Characteristic numbers for nets of algebraic
curves.” By Professor JAN pr VRIES.

(Communicated in the mecting of November 28, 1914).

1. The curves of order n, c”, which belong to a net N, cut a
straight line / in the groups of an involution of the second rank,
I,,°. The latter has 3 (n—2) groups each with a triple element); /
is therefore stationary tangent for 3 (n—2) curves of XV.

Any point P is base-point of a pencil belonging to .V, hence
inflectional point for three curves’) of NV.

The locus of the inflectional points of MN which send their tangent
i through P, is therefore a curve (Ip of order 3 (n—1) with triple
point P.

If the net has a base-point in B any straight line through 5 is
stationary tangent with point of inflection in B. Consequently (D)p
passes through all the base-points of the net.

We shall suppose that MN has only single base-points.

On PB WN determines an /?_,; the latter has -3 (n—3) triple
elements; from which it ensues that B is an inflectional point of
(/)p having PB as tangent 7.

Through P pass 3 (n—1) (2n—38) straight lines, each of which
touch a singular curve in its node‘); all these nodes D lie apparently
on (/)p.

2. Every c”, which osculates / in a point /, cuts it moreover in
(n—3) points S. We consider the locus of the points S, which belong
in this way to (/)p. Since P, as base-point of a pencil, lies on
3(n—3) (n+-1) tangents of inflexion‘), the curve (S) has in Pa
3 (n—8) (n+1)-fold point. Apart from P each ray of the pencil (/)
contains 3 (n—2)(n—3) points S; hence (S) is a curve of order
3 (n—3d) (2n—1).

Let us now consider the correspondence between the rays s and
s, which connect a point Jf with two points S and Z belonging to

1) If the J,? is transported to a rational curve c* and determined by the field
of rays, these groups lie on the stationary tangents.

2) For the characteristic numbers of a pencil my paper “Faisceaux de courbes
planes” may be referred to (Archives Teyler, sér. II, t. XI, 99—113), For the
sake of brevity it will be quoted by 7.

8) Cf. for instance my paper “On nets of algebraic plane curves”. (Proceedings
volume VII, p. 631).

4) T. p. 100.

936

the same cr. Any ray s contains 3 (n—3) (2n—1) points S, determines
therefore as many rays s'; any ray s contains 3 (n—1) points E
determines therefore 8 (n—1)(n—8) points S and consequently as
many rays s. The number of rays of coincidence s — s amounts
therefore to 3 (n—3) (2n—1) + 3 (n—3) (n—1) = 3 (n—3) (Bn—2). The
ray MP contains 3 (n—2) points /, which are each associated to (n— 3)
points S; consequently MP represents 3 (n—2) (n—3) coincidences.
The remaining 6n (n — 3) coincidences arise from coincidences [= $,
consequently from points of undulation U. Through P pass conse-
quently 6n(n—8) four-point tangents t,; the tangents t, envelop there-
fore a curve of class 6n (n—3).

3. We further consider the correspondence between the rays
SS, Which connect M with two points S belonging to the same
point /. This symmetrical correspondence has apparently as charac-
teristic number 38 (2—8) (2n—1) (n—4). The ray MP contains 3 (n—2)
points of inflection, hence 3 (n—2) (n—3) (n—4) pairs S,, S, ; as many
coincidences s,—s, coincide with MP. The remaining coincidences
pass through points of contact of tangents 42,3 (straight lines, which
touch a c* in a point R and osculate it in a point /). The tangents
log envelop therefore a curve of class 9 n(n—8s) (n—A).

4. Let a be an arbitrary straight line; each of its points is, as
base-point of a pencil, point of inflection for three c”. The curves
cr coupled by this to a form a system {c"] with index 6 (n—l);
for the inflectional points of the curves c”‚ which pass through a
point P, lie on a curve of order 6 (n —1)*), and the latter cuts a
in 6(n—1) points 4. The stationary tangents 2, which have their
point of contact J on a, form a system [4] with index 3 (m — 1),
for through a point P pass the straight lines 2, which connect P
with the intersections of a and (/)p.

The systems [c”| and [4] are projective; on a straight line / they
determine between two series of points a correspondence which has
as characteristic numbers 6(n—1) and 38(n—1)n. The coincidences
of this correspondence lie in the points, in which / is cut by the
loci of the points 7 and S, which every z determines on the associated
cn. As any point of a is point of inflection for three c", a belongs
nine times to the locus in question. Hence the points S lie on a
curve (S)q of order 3 (n?-+-n—5).

For n=8 the number 21 is found; this is in keeping with the

1) T. p. 104.

937
‘well-known theorem, according to which a net of eubies contains
21 figures, composed of a conic and a straight line.

5. To the intersections of a with the curve (5), belong the 38(—2)
groups of (n — 3) points S, arising from the curves c”, which
osculate a. In each of the remaining 3(n?-+-n—5) — 3(n—2)(n—3)
intersections a point / coincides with a point S of one of the three
cr, which have / as point of inflection. The corresponding tangent
{then has in common with c* four points coinciding in J, so that
I is point of undulation. Zhe points of undulation of the net he
therefore on a curve (U) of order 3 (6n — 11).

For n= 3 we find the 21 straight lines belonging to the degenerate
eubies of the net.

As a base-point B of a net is point of inflection of oo! curves
cr, there will have to be a finite number of curves, for which 5
is point of undulation. In order to find this number we consider
the locus of the points Z’ which any ray ¢ passing through B has
still in common with the c", which osculates it in 5. As Bis point
of inflection on three c* of the pencil which has an arbitrary point
P as base-point, the curves of N falling under consideration here
form a system [c”| with index three, which is projective with the
pencil of rays (¢).

The two systems produce a curve of order (2 + 3), which is cut
by a ray ¢ in (n— 3) points 7. Consequently it has in 6a sextuple
point, and there are six curves c”, on which JZ is point of undulation.

If the net has base-points they are sixfold points on the curve (U).

For n= 3 the curve degenerates into a sixray, which consists of
parts of compound curves.

6. To each c”, which possesses a point of undulation U we shall
associate its fourpoint tangent w; the latter cuts it moreover in
(n—4) points V. The locus of the points forms with the curve (U)
counted four times the product of the projective systems |c"| and
(u). In the pencil which a point P sets apart from MN occur
6(n—-3)(8n—2) curves, which possess a point U*); this number is
therefore the index of {c"|. The system [u] has, as appears from
§2, the index 6n(n—3). In a similar way as above ($ 4) we find
now for the order of (V) 6(n—3)(8n—2)+6n?(n—-3) —12(6n—11) =
=6(n— 4)(n? +4n—7).

We now associate on each straight line w the point U to each

1) T. p. 105.

62

Proceedings Royal Acad. Amsterdam. Vol. XVII.

938

of the (n—4) points V. By this the rays of a pencil (J/) are arranged
into a correspondence with characteristic numbers 3(62—11)(n—4)
and 6(2—4)(7?+4n—7). Observing that the 6rn(n—3) fourpoint
tangents, which meet in J/, represent (n—4) coincidences each, we
find for the coincidences U — V the number
(n—A) [38(6n—11) + 6(n?+-4n—7) —6n(n—8) ] =15(n—4)(4n—5). This
is therefore the number of curves c* with a jivepoint tangent t,.

Let us now consider the correspondence between two points
V,,V., which lie on the same tangent wu. Using the correspondence
arising between the rays MV, MV, we find in a similar way for
the number of coincidences V, = V, 12(n?+4n—7)(n—4)(n—5)—6n(n—9)
(n—4)(n—5) = 6(n—4)(n—5)(n? +11n—14). With this the number of
curves of N has been found, which are in possession of a tangent
tys, consequently of a point of undulation, the tangent of which
touches the curve moreover.

7. The involution of the second rank, which .V determines on a
straight line /, has 2(n—2)(n—3) groups, each of which possesses
two double elements; / is therefore bitangent for as many curves
of the net. If / rotates round a point P, the points of contact
R,R’ will describe a curve, which passes (2 —3)(n-+-4) times through
P; for P as base-point of a net lies on (m—3)(n-+4) curves, which
are each touched in / by one of their bitangents. From this follows
that the locus of the pairs R,R’, which we shall indicate by (f)p
is a curve of order (n—3)(5n—4).

If we consider the correspondence (AR) on the rays of the
pencil (P), and, in connection with this, the correspondence between
the rays MR, MR’, we arrive at the number of coincidences A = R’
and we find once more that the fourpoint tangents envelop a curve
of class 6n(n—8).

Let us now determine the order of the locus of the groups of
(n—4) points S, which / has in common with the 2(n—2)(n—3)
curves cr, for which / is bitangent. The pencil determined by P
contains 2(n—8)(n—4)(n+1) curves which are cut*) in P by one
of their bitangents. This number indicates at the same time the
number of branches of the curve (S)p passing through P; for its
order we find therefore 2(n—8)(n—4)(n+1)+2(n—2)(n—8)(n—4), or
2(n—3)(n—4)(2n—1).

If we associate each point PR to each of the points S belonging
to the same c”, a correspondence is determined in the pencil of rays

1) T. p. 102.

939

with vertex J/, which correspondence has (m—8) (5n—4) (n—-+) and
4 (n—3) (n—4) (2n—1) as characteristic numbers.

Since the ray MP contains 4 (n—2) (n— 3) points R, which are
each associated to (n—4) points S, so that MP is to be considered
as 4 (n—2) (n—3) (n—4)-fold coincidence, we find for the number of
coincidences In (n—-3) (n—-4). By this we again find the class of
the curve enveloped by the tangents fo3 (cf. $ 3).

A new result is arrived at from the correspondence between two
points SS, belonging to the same pair R, Rk’. The symmetrical
correspondence between the rays J/S,, MS, has as characteristic
number 2 (2n—1) (n—3) (n— 4) (n—5). Any of the groups of (n-—4)
points S lying on MP produces (n-—4)n—5) pairs S,,S,, so that
MP represents 2 (n— 3) (n—A4) (n—5) coincidences. The remaining
[4 (2n—1) — 2 (n—2)] (n—3) (n—4) (n—5) coincidences are, taken
three by three, points of contact of triple tangents f222. Through
an arbitrary point P pass consequently 2n (n-—3) (n—4) (n—5) triple
tangents.

8. Let a again be an arbitrary straight line; each of its points
is, as base-point of a pencil belonging to MN, point of contact R of
nd) (n— 3) bitangents d'). We determine the order of the locus
of the second point of contact A’. The latter has in common with
a the pairs of points R, Rk’, in which a is touched by c”, and also
the ae of undulation (R’== fF), lying on a, consequently
4 (n—2) (n—3) + 3 (6n—11) or (4n?—2n—9Y) in all. This number is
apparently A order of the curve (A), in question.

In order to determine the locus of the points W, which each
bitangent d of the system in question has moreover in common
with the c”, twice touched by it, we associate to each of those
curves c”, the bitangent d, for which the point of contact 7 lies on a.

To the pencil, which a point P sets apart from NV, a curve of
order (n—8) (2n?-+-d5n—6) is associated, which contains the points
of contact of the bitangents to the curves of that pencil’). By this
the number of straight lines d becomes known, of which a point
of contact lies on a; the system [c*| has therefore as index (n—8)
(2n? + 5n —6). The index of the system |d | is (n—3) (5n—4); for this
is (§ 7) the ae of intersections of @ with the curve (&)p. The
systems |c"| and |{d] rendered projective, produce a locus of order
(n—3) (2n*? + 5n—6) + n (n—8) (5n—4). To it belongs the straight
1) T. p. 102.

3) Bitangential curve; cf. T. p. 107.

940

line a 2(n-+4) (n——3)-times, because each of its points is point of
contact of (n--4) (n—8) bitangents. The curve (/’)a belongs moreover
twice to it. For the order of the curve (W), we find consequently
(n —8)(7n? +-n-—6) — Un — 8)(n4+4) —2(4n?—2n—9) = (n —4)(7n?—2n — 15).

We now consider the correspondence between the rays7’ = Mh’
and w= MW. A ray r’ contains (4n?—2n—9) points /’, consequently
determines (4n?—2n—9) (n—4) rays w; to a ray w (n—4)(7n?—2n—15)

rays 7’ are associated. Each of the (n—3)(5n—4) lines d, which

connect J/ with the intersections of a and (f)j;, is apparently an
(n—-4)-fold coincidence. The number of coincidences R’= W amounts
therefore to (n—4) [ (4n? —2n—9) + (7n?—2n—-15) — (n—8) (5n—4) |=
(n—4) (6n?+15n—36). This number is the order of the locus (R)23

of the points of contact R of the tangents to.

9. In order to find also the order of the locus (/)23 of the
inflectional points 1 of the tangents f23, we return to the system [e"|
considered in §4, of which all the curves have an inflectional point
I on a given line a. The points S, which the corresponding stationary
tangent has moreover in common with ec”, lie on a curve (Sao
order 3(n?+n—5). We consider now the correspondence between
two points S,,S, of the same curve. It determines in a pencil of
rays (M) a symmetrical correspondence with characteristic number
3 (n?-+n—5) (n—4). The rays connecting M with the intersections
of a and (/)y, are (n—8) (n—4)-fold coincidences ; as their number
amounts to 3(m—1) ($1), we find for the number of coincidences
S,=S, [2 (nv? + n—5) — (n—1) (n—-3)] or 3 (n—A4) (n° + 6n—13).
This, however, is also the number of tangents f23, the point of
inflection of which lies on a, consequentiy the order of the locus
In3 of the points of inflection of the tangents te3.

By means of the curves (L)23 and (/)23, belonging to the system
[ts], we can again determine the number of /ivepount-tangents t,.
For this purpose we associate the lines MR and MJ, on account
of which a correspondence with characteristic numbers 5 (2—4)
(2n? +5n—12) and 3 (n—A4) (n’?+6n—13) arises. The In (n—8) (n— 4)
tangents f 3 converging in J/ are coincidences. On the remaining
ones A coincides with /. So we find for the number of the t,
3 (n—A) (3n?+1412n—25) — In (n—3) (n—A4) or 15 (n—4, (4n—5S).

10. We return to the system [c”] of the curves, which (§ 8) are
each touched by one of their bitangents d in a point / of a straight
line @.

If on a line d two of the points W coincide d-becomes a triple

941

tangent. The correspondence between two points W,, W, of asame
c” determines in the pencil of rays 7 asymmetrical correspondence
with characteristic number (7n? — 2n — 15) (n — 4) (n — 5). As each
bitangent through J/ having one of its poinis of contact on a,
represents (n— 4)(n— 5) coincidences, the number of coincidences
W,= W, amounts to 2 (n—A4) (n—5) (7n?—2n—15) — (n—4) (n—S)
(n—8) (5n—4) =(n—4) (n —-5) (An? + 15n—42). As they lie two by
two on tangents to22, the locus of the points of contact of the triple

2,2
tangents is a curve Roos of order } (n—4) (n—5) (8n* + 5n—14).
We consider now the system [c”] of the curves possessing a
tangent too, and determine the order of the loeus of the points Q,
which each cr has moreover in common with its 4,2. The system
[c*] has as index (n — 3) (n — 4) (n — 5) (n° + 3n — 2); for this is
the number of c* of the pencil determined by a point P possessing
a toes ©). The index of the system [f292]| is (§7) 2n (n — 3) (n — 4)
(n—-5). To the figure produced by |[c”] and [f22| the curve (R)oo°

23454

belongs twice. For the order of (Q) we find consequently (2 — 3)
(n— 4) (n— 5) (n° + Bn — 2) + 2n? (n— 3) (n — 4) (n— 5) —
3 (n — 4) (n — 5) (Bn? + 5n— 14) or (n — 4) (n — 5) (n — 6) (8n? +
+ 3n — 8).

11. On each 4292 we associate each of the points of contact. R
to each of the intersections Q, and consider the correspondence
(WR, MQ). Its characteristic numbers are $ (Bn? + 5n — 14) (n— 4)
(n — 5) (n — 6) and 3 (n — 4) (n— 5) (n — 6) (Bn? +3n—8). Each of the
2n (n—3) (n—4) (n— 5) tangents f222 converging in JZ, represents
apparently 3 (2 — 6) coincidences. Taking this into consideration we
find for the number of coincidences R= Q, consequently for the
number of tangents toa, $(n — 4) (n — 5) (n — 6) (5n? + 23n — 30).

The correspondence between two points Q belonging to the same
ct determines in the pencil of rays (J/) asymmetrical correspondence
with characteristic number (3n°+3n—8) (n—A4) (n—5) (n—6) (n—7).
To this each of the 2n(n—3) (n—4) (n—5) tangents converging in J/
belongs (n —6) (n—7)-times. Paying attention to this we find for the
number of coincidences Q,=Q, 4(n—4) (n—5) (n—-6) (n—7) (n—1)
(n+-4). There are consequently (2—4) w—5) (n—6) (n—7) (n-—1) nd)
quadruple tangents.

12. We shall now consider the system of the curves ct possessing
a tangent f3, which touches it in a point #, and osculates it in a
point J. In order to find the locus of the points S, which ec” has

Dy Pe pe AG,

942

moreover in common with f23, we determine the order of the figure
produced by the projective systems [c”| and [f23|. The former has
as index 3 (n—8) (n—A4) (n’?+6n—4) i.e. the number of c” with a f23
appearing in a pencil’) of N. The index of. [t3] is (§ 3) On (n—3)
(n—4). The figure produced contains the curve (A) twice, the curve
(/) three times. For the order of S we find therefore

3(n—3)n—4)(n? + 6n—A4)-+ In? (n—3)(n—4)—6(n—4)(2n? + 5n —12)—

—-9(n—4)(n? + 6n—13)=3(n —4)(n—5)(4n? + 7n—15).

By means of this result we can determine the number of twice
osculating lines ¢33. For this purpose we consider the correspondence
(MR, MS). Its characteristic numbers are

3 (2n?+5n— 12) (n—A4) (n—5) and 3 (4n?+7n—15) n—A4) (n—5S).

Each of the 9n (n—®8) (n—4) f23 belonging to the pencil (M/) is
(n—5)-fold coincidence, hence the number of coincidences RS is
(n—4)(n—5) [(6n?-+-15n— 36)4-(12n?+-21n—45)—9n (n—3) | = (n—4)
(n—5) (9n?-+63n—81). But then the number of twice osculating
tangents t33 amounts to 2(n—4) (n—5) (n° +7n—9).

By means of the correspondence between the points / and S of
the tangents f23 we can find back the number of tangents to, found
already in § 6. Analogously we obtain by means of the correspond-
ence between two points S of the same f3 again the number of
tangents f293 found in $ 11.

18. If the net has a base-point B, the curves er, having an
inflection in B are cut by their stationary tangents ¢ in groups of
(n—3) points 7, lying on a curve (7’)"+% with sextuple point B
(§ 5). This curve is of class (n+3)(n+2) —30; through L pass
(n?-+5n—36) of its tangents. In the point of contact A of such a
tangent the latter is touched by a c”, which it osculates in B;
consequently B is a (n—4)(n-+9)-fold point on the curve (Das.

The curves cr, which touch in B at a ray d, form a pencil, con-
sequently determine on d an involution of order (n—2). As it possesses
2‘n—3) coineidences there are 2(n—8) c’, which have d as bitangent,
of which B is one of the points of contact. The second point of
contact, R, coincides with B if d becomes fourpoint tangent, con-
sequently B point of undulation. This occurs six times; hence the
locus (Rs of the points R is a curve of order 2n, with sextuple
point B.

Every straight line d cuts the cv, which it touches in B and in
R, moreover in (n—4) points S. In order to determine the locus

“nT. p. 106.

943

(S)p of these points, we associate each ray d to the 2(n—8) curves
ce, to whieh it belongs, and consider the figure produced by the
projective systems [c*} and (d) thus determined.

Through a point P passes a pencil of ec"; the base-point B is point
of contact of (n—3)(n+4) bitangents ; this number is the index of
[er]. The order of the figure produced now amounts to (72 — 3)(n--4) +
+ 2n(n—3) = (n—3)(8n-+4). To this the curve (Ld) apparently belongs
twice; for the order of (S)g we find therefore (n—3)3n-4)—4n or
3(2+- 1 )(n—-4).

As every d, outside B, contains 2 (n—3)(n—4) points S, (S)g will
have in B a multiple point of order 3(n-++-1)(n—4)—2(n—3)(n—4)
or (n-+9)(n—A4).

14. Let us now consider the correspondence (MR, MS), if R
and S lie on the same ray d through B. To each ray MAR belong
2n(n—4) rays MS, each ray MS determines 3(n-+1)(n—4) rays MR.
The ray MB eontains 2(n—3) points A, consequently represents
2n—3)(n—4) coincidences. The remaining ones, to the number of
(n—4)(2n+3n+3—2n-+6), pass through points R=. So there are
3(n—-4)(n-+3) rays d, which each touch a cr in B and osculate it
in a point J; the curve (Rog has consequently a 3(n—4)(n+3)-fold
point in B,

Now we pay attention to the symmetrical correspondence of the
rays, which connect JZ with two points S belonging to the same c”.
The characteristic number is here 3(n—-+1)(n—4)(n—5), while MB
represents 2(n—3)(n— 4)(n—5) coincidences. The remaining (n—4)(n —9)
[6(n+1)—2(n-—3)] lie in pairs on a triple tangent, which bas one
of its points of contact in B. From this we conclude that the curve
(R)z22 possesses in B a Un-3) (n—4) (n—5)-fold point.

15. Let D be node of an c”, ¢ one of the tangents in D, S one
of the intersections of ¢ with ct. In order to find the locus of S,
we associate to each nodal c* its two tangents ¢ and determine the
order of the figure produced by it. The tangents ¢ envelop the curve
of ZrUTHEN; they form consequently a system with index 38(7—1)’;
for a pencil contains 3(7—1)? nodal curves. By means of the corre-
spondence of the series of points, which the two systems determine
on a line, we now find again the order of the figure produced.
Considering that the locus of J) belongs six times to it, we obtain
as order of the curve (S) 3n(n—1)(2n—3) + 6(n—1)?—18(n—1) =
= 3(n-—1)(2n?—n—8). For n=83 we find 42 for it; the 21 straight
lines of the degenerate curves must indeed be counted twice.

944

We now consider the correspondence (MD, MS). Its characteristic
numbers are 3(n—1).2(n—38) and 3(n—1)(2n’—n—8), while each
of the tangents ¢ converging in J/, apparently produces 1— 8) coinci-
dences. The remaining ones arise from coincidences D = S, conse-
quently from nodal curves, for which D has an inflection on one
of its branches. It now ensues from 6(n—J)(n—3)+3(n—1)(2n’—n —8)
—3 (n—1) (n—-3) (2n—3) = 3(n—1) (10n—23), that the net contains
3(n—1)(10n—23) curves with a fleenodal point.

ERR AcE DM
In the Proceedings of the meeting of November 28, 1914.

p. 870 line 15 from the bottom: Add: Supplement N°. 37 to the
Communications from the Physical Laboratory at Leiden.
Communicated by Prof. H. KAMERLINGH ONNES.

January 28, 1915.

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.
PROCEEDINGS OF THE MEETING
of Saturday January 30, 1915.
Vor. XVII.

De

President: Prof. H. A. Lorentz.

Secretary: Prof. P. Zeman.

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 30 Januari 1915, Dl. XXIII.

EUT LE ENT EE

J. P. Kurnen: “On the measurement of the capillary pressure in a soap-bubble”, p. 946.

H. KAMERLINGE ONNES, C. DORSMAN, and G. Horst: “Isothermals of di-atomic substances
and their binary mixtures. XV. Vapour-pressures of oxygen and critical point of oxygen
and nitrogen’. p. 950.

E. Marrras, H. KAMERLINGH Onnes, and C. A. CROMMEDIN: “The rectilinear diameter of
nitrogen”, p. 953.

C. A. CROMMELIN: “Isothermals of di-atomie substances’and their binary mixtures, XVI
Vapour-pressures of nitrogen between the critical point and the boiling point”. (Commu-
nicated by Prof. H. KAmMERLINGH ONNES), p. 959.

A. Sits and S. C. Boxnorsr: “On the vapour pressure lines of the system phosphorus.” III.
(Communicated by Prof. J. D. van DER WAALS). p. 962.

A. Smits and S. C. Boxuorsr: “Further particulars concerning the system phosphorus,’
(Communicated by Prof. J. D. van DER Waars), p. 973.

J. Boeke: “On the termination of the efferent nerves in plain muscle=cells, and its bearing
on the sympathetic (accessory) innervation of the striated muscle-fibre”, p. 982. (With
one plate).

J. Boeke: “On the mode of attachment of the muscular fibre to its tendonfibres in the strid*
ted muscles of the vertebrates”, p. 989.

J. Droste: “On the field of a single centre in Erysrer’s theory of gravitation’. (Communi-
cated by Prof. H. A. Lorentz), p. 998.

F. E. C. Scuerrer: “On gas equilibria, and a test of Prof. J. D. van per Waars JR.’s
formula”. If. (Communicated by Prof. J. D. van per Waats), p. 1011. .

A. F. Horreman: “The replacement of substituents in benzene derivatives”, p. 1027.

P. van Rompuren and Miss. D. W. WensiNK: “On the interaction of ammonia and methyl«
amine on 2.3.4-trinitrodimethylaniline”’, p. 1034.

C. H. Sturrer: “The influence of the hydration and of the deviations from the ideal gas-
laws in aqueous solutions of salts on the solidifying and the boiling points”. (Communi-
cated by Prof. A. F. HorreMaN), p. 1036.

W. pr Sirrer: “On the figure of the planet Jupiter”, p. 1047.

Ernst Conen and W. D. Hetperman: “The Allotropy of Cadmium.” V, p. 1050.

Ernst Conen and W. D. Hetprerman: “Note on our paper: The Allotropy of Lead”. I, p. 1055.

JAN DE Vries: “Characteristic numbers for a triply infinite system of algebraic plane curves”,
p- 1055.

J. P. Kurenen: “The diffusion-coefficient of gases and the viscosity of gas-mixtures.” p. 1068.

Errata, p. 1073.

$

63
Proceedings Royal Acad. Amsterdam. Vol. XVII.

946

Physics. — “On the measurement of the capillary pressure in a
soap-bubble.” By Prof. J. P. KurreN. (Communication N°. 145a
from the Physical Laboratory at Leiden).

(Communicated in the meeting of December 30, 1914).

In the measurement of the pressure in a soap-bubble by means of
an open liquid gauge the peculiar case may present itself, that the
measurement becomes impossible owing to the condition becoming
unstable. This fact accidentally came under my notice, when an
attempt was being made to increase the accuracy of the measure-
ment of the comparatively small pressure by the use of a micro-
manometer; in this instrument the construction of which is otherwise
of no importance for the present purpose the pressure to be measured
acts on a large liquid surface (about 427 em?) which on a change
of pressure is displaced over the same distance, as if the instrument
were a simple open water-gauge with two tubes of the same width.
When this manometer was used, it appeared impossible to work
with soap-bubbles of less than about 1 em. diameter, as smaller
bubbles always contracted of their own accord, though no-leakage
could be discovered in the apparatus, whereas with a gauge with
narrow tubes a similar difficulty had never presented itself.

A consideration of the equilibrium-relations had to lead to the
explanation of the phenomenon and it soon appeared, that it was
connected with the change of volume in the gauge which accompa-
nies the displacement of the liquid surface on a change of pressure.
Starting from a condition of equilibrium between the surface-tension
o and the excess of pressure p— p, (Pp, = atmospheric pressure),
in which therefore p— p, =" (r = radius of bubble), and applying
to the bubble a virtual change, say a diminution of the radius, the
capillary pressure will increase and this will cause the liquid-surface
in the gauge to descend, which in its turn involves an increase of
the volume. Now the condition will certainly be unstable, if this
increase of volume exceeds the diminution of volume given to the
soap-bubble; because in the enlarged volume the pressure of the
gas will be smaller and this* decrease will cause a further contraction
of the soap-bubble. It now also becomes clear, why the phenomenon
was observed for the first time in using the wide gauge: the increase
of volume which goes with an increase of pressure is much more
prominent in this case.

One might be inclined to draw the conclusion, that the limit

a

947

between stable and unstable must be found in that condition, whére
the two changes of volume referred to are equal to each
other. This conclusion appears to be incorrect, however, when the
condition for stability or non-stability is accurately established. The
nature of the equilibrium depends upon, whether in a virtual con-
traction of the soap-bubble the pressure caused by the surface-tension
increases less or more than the pressure of the gas, and the latter.
is given by Boytn’s law, if the temperature is supposed to remain
constant. In the former case the gas-pressure prevails, when the
bubble contracts, and the condition is stable, in the latter case the
condition is unstable.

Calling the volume of the space from the orifice of the tube, on
which the bubble is blown, to the liquid surface, when the pressures
inside and outside are equal, v,, the displacement of the liquid /
and the cross-section of the manometer-tube O, and treating the
bubble as a complete sphere, the total volume is

4
v=v,+ anit r? + hO,

whereas, d being the density of the liquid in the gauge,

46

2hdg =p—p,. Es

5

so that
‘ ae oe i 260
ZEN ea ee CN .
3 y 3 rdg
The change of the capillary pressure is given by the relation
_ dp-—p,) _ 46
dnt ie

whereas for the gas-pressure pu =c, so that
dp dw 200 260
ea (4 4 nr? oe me Hens LOE
dr dv dr 5

and the condition will be stable or unstable, according to whether:

46 260
de Pp 4n oo 2 EE iT er .
Po ty r dq

The same result is obtained from the condition, that in stable,
respectively unstable equilibrium the free energy w of a closed
system at constant temperature is a minimum, respectively a maxi-
mum. In our case w may be written in the form:

w= 8ar' 6 —clogv + Oh? dg + py»,
63*

948

whence :
dy 16 e dv 1 20hd dh 4 dy
— ZZ CC ON nen 3 ig@— +p, —,
dr 4 v dr iid dr Po dr
or after reduction
dw
—= 16 aro— (p—p,)427r".
dr
a bas 6 kern dw
rhe condition of equilibrium — —0 gives the relation p— p, =
ar
46 ;
= —, made use of above.
JR
We have further:
Ip dp dv
eat xo —(p—p,) 8ar— eas be del
dy? dv dr
k p . 260 >
=— l6mo+ —[ 427? — — ]427°— 0,
== 5 ( 1 dg 1 <<

which leads to the same unequality as arrived at above.

This relation reveals the remarkable fact, that even without the

manometer the condition may be unstable, viz. when
45 p Ov
pits en Mn
r v Xp

The value of 7 is limited by the circumstance, that it cannot be
smaller than the radius of the tube to which the soap-bubble is
blown, and, as p is of the order 10°, 5 for a soap-solution being
about 25, the unstable condition cannot be realized unless with a
large volume v. In order to test the above result a carboy of 30
liters (v = 30000) was attached to the apparatus without gauge: in
this case the condition becomes 7 < 0.7 cm. That the condition was
unstable, was manifested in blowing the bulb in the fact, that, as
soon as the bubble exceeded the half-sphere, it blew itself up quickly
to a considerable size. In diminishing the bulb below the given limit
by letting out air the unstable nature of the equilibrium showed
itself less clearly. The bubble sometimes remained for a considerable
time without appreciable change in size; this must be due to a
retardation the nature of which was not fully explained: as a rule
by tapping the tube the bubble could be made to contract in accord-
ance with expectation.

As shown by the above complete relation, the addition of the
gauge on which the second term on the right-hand side depends
will make it possible to realize the unstable condition with a much
smaller volume, the more easily ‚the larger the section O of the

949

manometer is. Calculation shows, that even with v= 1000 cc. the
left hand side of the relation is much too small to have an effect,
and the condition thus becomes with near approximation

„> 260 OE oO

<7? dg S2ndg

In this case the condition for the transition to the unstable con-
dition agrees, as is at once seen, with that mentioned in the
beginning, that the change of volume of the bubble becomes smaller
than that of the gauge.

In order to make the phenomenon even more prominent than
with the open gauge, the latter was replaced by a large funnel
which was connected to the apparatus and placed upside down in
a large trough of water with its rim just below the water level.
The area O was now 642 cm’ and moreover the displacement A
was almost completely confined to the water-surface inside the
funnel (as the level in the large trough does not change appreciably)
and thus twice as large as with the open gauge with tubes of the
same width. In this case hdg = p—p, and the condition becomes

ee
Sady’
which with the numerical values given above leads to r< 1.1 em.
as the transition to the unstable condition. In agreement with this
result the experiment showed, that the bubble could not be made
smaller than 2 em. in diameter without the bubble gradually be-
ginning to contract.

The contraction continues, as long as the bubble is larger than
a half-sphere; beyond this state 7 begins to increase; the capillary
pressure thus begins to diminish and the contraction will cease,
when the capillary pressure has become equal to the pressure
exerted by the gas present. The condition can now but be stable,
as a further contraction involves a diminution of the capillary
pressure and therefore a diminution of the volume in the gauge
and an increase of the gas-pressure.

By means of the above relations the further question may be
solved whether an increase of c in the formula pv =e, Le. an
increase of temperature or of the quantity of gas, will make the
bubble larger or smaller. The relation :

4m

shows, that in the stable condition the bubble will increase and
conversely in the unstable condition.

950

Physics. — “Jsothermals of di-atomic substances and their binary
mixtures. XV. Vapour-pressures of oxygen and critical point
of oxygen and nitrogen.” By H. KAMBRLINGH Onnes, C. DORSMAN,
and G. Horst. (Communication N°. 1455 from the Physical
Laboratory at Leiden). (Communicated by Prof. H KAMERLINGH
ONNES,)

(Communicated in the meeting of December 50, 1914).

1. Apparatus and method.

The vapour-pressures of oxygen at twelve different temperatures
and the eritical points of oxygen and nitrogen were determined by
means of the apparatus which was first used by KAMERLINGH ONNES
and HYNDMAN for unpublished investigations of oxygen, of which
those published on this occasion form a repetition, and later on by
CROMMELIN for a determination of vapour-pressures of argon. A
detailed description was given in Comm. Phys. Lab. N°. 115 (Meeting
of April 1910). In the piezometer is an electromagnetic stirrer
according to KUENEN.

In order to make a study of the critical phenomena possible two
narrow slits of the vacuum-vessel of the cryostat were left unsilvered.
(Compare Comm. N°. 83. Meetings of Dec. 1902 and Febr. 1903. As
mentioned in an erratum to Plate IV $ 6, the vessel 4’, is drawn
18 cms longer than it was). Besides the piezometer there were two Pt-
resistance thermometers in the cryostat which had both been directly
compared with the hydrogen-thermometer. One of them (the other
one Pt, broke afterwards) was Pt; of Comm. N’. 14la $6, the same
which was also used in the measurements concerning the diameter.
The pressures above 20 atm. were measured with the closed hydrogen-
manometer described in Comm. N°. 97a § 3. At lower pressures the
open gauge of KAMERLINGH ONNES (Comm. N°. 44) was used.

In order, to determine the critical constants small portions of
isothermals were studied in the neighbourhood of the critical point.
At temperatures below the critical temperature starting from a
suitably chosen volume and compressing by small amounts a con-
dition can be found by sufficient compression in which the next
compression produces condensation; at temperatures above the critical
temperature condensation cannot occur. .

The critical point having been approximately determined in this
way, the observations were repeated within narrower limits of
pressure, at temperatures ascending by about '/,,° C. Beginning with
a pressure below the critical pressure and proceeding along an

951

isothermal still smaller portions than before were taken by applying
very small compressions. This process was continued until the critical
pressure had been passed. After each compression some minutes
were allowed to elapse, the substance being meanwhile thoroughly
stirred with the electromagnetic stirrer, so that all traces of the heat
developed by the adiabatic compression must have disappeared by
the time it was ascertained whether condensation had taken place.
After this the process was repeated in the reverse direction, gradually
going down to lower pressures and ascertaining, what at each sub-
sequent stage the effect was of a very small expansion, say of '/,,
of an atmosphere. As before after each expansion some time was
allowed to pass, until it could be assumed, that the gas had returned
to the original temperature. If we proceed in this way along an
isothermal immediately above 7% it is found that in the neighbourhood
of the eritical condition ata small sudden, and therefore approximately
adiabatic, expansion a liquid surface appears which disappears again
with thorough stirring. If the isothermal lies below 7%, the meniscus
produced by a very small expansion does not disappear on stirring.

As the critical point we ultimately took the point at which on a
small expansion the meniscus appeared half way up the tube and
where conversely as the temperature re-established itself it disappeared
again at the same level. By this procedure the critical temperature
could easily be determined to about '/,,° C. On a future occasion
this method will be published in greater detail with the addition of
numerical results.

It is worth mentioning that we did not succeed in observing the
critical opalescence '), although in the experiments temperature and
pressure were completely under control and the distinctness of
observation of the phenomena in the piezometer-vessel left nothing
to be desired as regards the permanent transparency of the walls.
Our result, that the opalescence if existing must be very slight,
derives its weight from the fact, that we looked for it with special
attention, because on a former occasion one of us (H. K. O.) had
been struck by its absence.

§ 2. Preparation of the substances. The oxygen was prepared from

1) These experiments were made in 1911. Looking through the literature of the
subject, while writing this communication, we find the absence of the critical
opalescence mentioned for the first time in a preliminary uote by E. Carposo,
Eléments critiques et phases coéxisiantes des gaz permanents (II). Arch. d. Sc.
phys. et nat. 15 Aout 1914 p. 137.

CARDOSO adds a partial explanation based upon SMOLUCHOWSKI's theory in
connection with the law of corresponding states. '

pure, recrystallized potassium permanganate, by heating in an apparatus
which was completely of glass, and leading the gas over heated plati-
nized asbestos. The apparatus which had served the same purpose
in Comm. N°. 78 § 44, had been improved by Dr. C. A. CROMMELIN
when reconstructed, in that the tubes for drying and for absorbing
the carbon dioxide had been replaced by an arrangement which
allowed the gas to be condensed by cooling with liquid air and the
liquid obtained to be re-evaporated (comp. Comm. N°. 117). A deserip-
tion of the apparatus will be given on a future occasion.

The nitrogen was prepared in the Pharmaceutical Laboratory
under the supervision of Professor van ITaLti, to whom we hereby
express our hearty thanks. The method of preparation was by boiling
a solution of sodiumnitrite and sodiumsulphate with ammonia; the
nitrogen was then led over sulphuric acid in order to keep back
ammonia that might be carried over.

The purity of both substances was checked by condensation expe-
riments (comp. Comm. N°.145d), when it appeared that the vapour-
pressure between the beginning and the end of the condensation
did not rise by more than a few hundredths of an atmosphere,

§ 3. Results. The results are contained in the following tables.

TABLE 1.
Vapour pressure of oxygen.
gtje) PERE pin dn
|
—154.91 C. 118.18 K. 9.096
149.29 123.80 12.506
138.98 134.11 21.328
138.95 134.14 21.342
135.99 137.10 24.528
130.67 142.42 30.914
125.31 147.78 38.571
121.36 151.73 45.138
121.35 151.74 45.142
| 121.33 151.16 45.217
120.04 153.05 47.258
118.70 154.19 49.640
Eren TOER Pikes iid a!

953
TABLE Ik

Critical point of oxygen.

= ke ae pee ay
Op cia tid Ty, =o Lhe? Zake Pe = 49.713 atm. |

Critical point of nitrogen.

irda) Set i We
0, ——147°.13C.| Ty, = 125°.96K. | p, = 33.490 atm. |

In the mean time we confine ourselves to communicating the
numerical results and we will only add, that using the critical values
obtained for oxygen the critical coefficient

k
Koe
PkVkd

where vg is the critical volume derived from the diameter, is now
found to be 3.419 instead of the previous value 3.346 deduced by
Marmras and KAMERLINGH Onnus using incorrect data found elsewhere
in the literature on the subject. (Comm. N°. 117).

The new value is no longer abnormally small when compared
with that of normal substances of higher critical temperature and
very nearly the same as that of argon 3.424 (Comm. N°. 1814).

Physics. — “The rectilinear diameter of nitrogen” By E. MATHIAS,
H. Kamertincu Onnes, and C. A. CROMMELIN. (Communication
N°. 145c from the Physical Laboratory at Leiden.)

- (Communicated in the meeting of December 30, 1914).

§ 1. Introduction. This communication is a continuation of the
investigation undertaken in the Leiden Laboratory on the diameter
for substances of low critical temperature and simple molecular
structure, which was begun with oxygen’) and continued with
argon”). The object and the importance of these investigations were
fully gone into in the paper on the diameter of oxygen and we
need not recur to this here. For the further continuation of this
research helium, hydrogen, and neon did not seem very suitable
at present in view of the greater experimental difficulties, which

1) E‚ Marutas and H. KAMERLINGH ONNES, Proc. Febr. 1911, Comm. N°. 117.
2) E. Marnras, H. KAMERLINGH Onnes, and C. A. GROMMELIN, Proc. Oct. and
Dec. 1911 and Jan. 1912, Comm. N°. 18la.

954

have been partly, but not entirely surmounted. The obvious
choice lay between nitrogen and carbon monoxide and it fell on
nitrogen partly because for this substance more thermodynamical
data are available than for carbon monoxide, whereby the import-
ance of the investigation is much enhanced and partly because we
could use the very pure nitrogen, with which determinations of
the critical constants") had been made. A separate experiment’)
showed that the nitrogen was indeed of very high purity.

a
a a
2 le
9, ©,
Q SD
QT

ED |

BEEBE EEn eeen

H tb
ag ral
4
on N H om
sp ica
& :
2 ET
[aay
= H
4
i L
9 $40452025cTIL.
lef
Fig. 1.

§ 2. Apparatus. The apparatus were practically the same as
used for the determination of the diameter for argon; we, therefore,

') This number of the Proc., H. KAMERLINGH ONNES, C. DORSMAN, and G. Horst,
Comm. NO, 1455.
2) Comp. this number of the Proc. CG. A. GROMMELIN, Comm. N°. 145d.

955

refer to the communication quoted above. For the sake of comple-
teness we will mention two small improvements *) :

1. The tube of the glass compression vessel a, was made much
longer in order to preclude all danger of the mercury when it rises
quickly penetrating into the metal capillaries.

2. In the connection between the small high-pressure reservoir a
and the compression vessel a,, (by the taps c,,, ¢,,, &,, and k,,) a
glass pipette of about one litre was introduced by means of a
T-piece, so as to make it possible to transfer the nitrogen to the
compression vessel in measured quantities.

These two improvements have added considerably to the certainty
and convenience with which the apparatus could be manipulated.

§ 3. As regards the method of conducting the experiments we
may also in the main refer to the previous paper.

The vapour-pressure measurements, which are needed for the
calculation of the corrections, were not made during the diameter-
determinations this time, but in a separate series of experiments,
which will form the subject of a separate communication by one
of us. *)

The temperature was again measured and at the same time kept
constant by means of two platinum-thermometers /P¢,, and Pt,
which had been compared shortly before the measurements with
the standard platinum-resistance-thermometer /%';. The latter had
not long ago been once more very carefully compared with the
hydrogen-thermometer*), so that the temperature-measurement in
our determinations must have satistied very high requirements. The
agreement of the two resistance-thermometers used left indeed nothing
to be desired. In these measurements we were assisted by Mr. P. G.
Carn, phil. nat. cand., whom we gladly hereby express our thanks
for his coöperation.

4. Calculations. As regards these we may again refer to the
previous communication. The reductions for tie dead spaces at low
temperature could not be made with the same certainty as in the
case of argon; for the latter substance extensive series of observations
of isotherms for low temperatures‘) were available, whereas for
nitrogen the same data are at present entirely lacking. We were

1) Comp. fig. 1 which is the improved form of the right-hand part of fig. 1 in
Comm. NO. 1314.

2) CG. A. CROMMELIN, This number of the Proc, Comm. N°. 145d.

3) KAMERLINGH ONNES and G. Horst, Proc. Sept. 1914, Comm. NO. 141a.

4) H. KAMERLINGH ORNEs and C. A. CROMMELIN, Proc. Dec. 1910, Comm.
N'. 1185, and C. A. CROMMELIN, Dissertation, Leiden. 1910.

956

thus compelled to make use of the general reduced equation of
state VII. 1.*) which in the region in question does not yet appre-
ciably deviate from the special equation of state for argon VILA. 3. *)
which might otherwise have been preferable. This comes to the same
as assuming, that nitrogen at the reduced temperatures under con-
sideration corresponds to ether and isopentane.

For the calculation of the capillary corrections for the liquid
nitrogen the observations by Baty and Donnan ®) were again utilized.

As the normal specifie mass of nitrogen we have adopted the
value 1.2514 germs. per Liter, as found in complete agreement by
Rayweied *) and by Lepvc ®).

Finally it should be mentioned, that the vapour-densities at the
lowest 5 temperatures were not measured, but were calculated from
the equation VII. 1.

5. Results. The results are represented graphically in fig. 2 and

put together in the following table.
YIP = nn —- — = —- ee 7

4) 5
lee ot t i |e | =I.
Ee a = 5 or = +40 z La 7 Q 4R a0
= 240° ) 205° «PP A 5 aR SO ig Sb sho TDI = Tan? fe
— §
Fig. 2.

1) Comm. Leiden. Suppl. N°. 19, May 1908.
2) H. KAMERLINGH ONNES and C A. CromMELIN, Proc. June 1912, Comm. 128.

5) E. GC. CG. Baty and F. G. Donnan, Journ. of the Chem. Soc. (Trans.) 81
(1902) p. 907.

*) Lord RayLeigH, Proc. R. S. 62 (1897) p. 204.
5) A. Lepuc, CG, R. 126, (1898), p. 413.

a lo Centigrade! | |
| Bath scale in Kel, Migr = @vap.r Dor obs. Drcatc. obs.—calc. |
vin degrees | |

alee | bei |

O, | — 208.36 | 0.8622 0.00089 0.4316 | 0.4308 | + 0.0008
O, | — 205.45 0.8499 | 0.00136 | 0.4256 | 0.4251 |+ 5 |
O2 | — 200.03 | 0.8265 | 0.00218 | 0.4146 | 0.4145 | + 1 |
0, | — 195.09 | 0.8043 | 0.00490 | 0.4046 | 0.4048 He 2 |
O, | — 182.51 | 0.7433 0.01558 0.3794 | 0.3802 |) eel
CH, | — 173.73 | 0.6922 | 0.02962 | 0.3609 | 0.3630 | — 21 |
CH, — 161.20 0.6071 | 0.06987 0.3385 0.3385 0
CH, | — 153.65 | 0.5332 | 0.1177 \ 0.3255 | 0.3237 | + 18 |
CoH, | — 149.75 | 0.4799 | 0.1638 0.3219 0.3161 bale 58 |
CH, | — 148.61 | 0.4504 | 0.1862 | 0.3183 | 0.3138 ee 45 |
CoH; —- 148.08 | 0.4314 0.2000 | 0.3157 | 0.3128 + 29 |

In the table og is the density and D the ordinate of the diameter ;
liq. and vap. refer to the liquid and the saturated vapour, and the
index T indicates that the density is given in grammes per cc). *)

The ordinates of the diameter are calculated from the formula:

Dor = 9.022904 — 0.0019577 6.

The coefficients in this formula were calculated by the method of
least squares from all the observations with the exception of those
at — 149°.75, — 148°.61 and —1448°.08. The reason, why these
three observations were not used in the calculation of the coefficients,

will appear later on.

§ 6. Discussion. As appears from the table and even more plainly
from figure 2 the deviations from the calculated rectilinear diameter *)
are (1) systematic (2) near the critical point fairly considerable. It
would be possible to distribute the deviations more evenly over the
entire diameter by taking up the three observations which we have
just referred to in the calculation of the coefficients; we have,
however, preferred the method of calculation as given above, because

1) For the notations see also H. KAMERLINGH ONNES and W. H. Kersom, Enc.
math. W-cs. V. 10. Comm. Suppl. N°. 23.

2) In a preliminary note ‘“Eléments critiques et phases coéxistantes des gaz
permanents’ (Arch. d. Sz. phys. et nat. Genève, 15 Aug. 1914, pg. 187) without
numerical data E. Garposo mentions, that the diameters of oxygen and nitrogen
are rectilinear up to the critical point.

958

in that manner the very approximately rectilinear character of a
large part of the diameter shows better and also because by
that method the critical density ozq is obtained in the most rational
way. Leaving out the deviations in the neighbourhood of the critical
temperature and confining ourselves to those which refer to the
direction of the diameter from (3) below the critical temperature
downwards, it may be remarked, that these deviations although
somewhat larger than those found with many other substances still
in their general character do not differ from those shown by say
carbon-dioxide and argon; the latter substances also possess at the
lower temperatures a diameter which is convex on the side of the
temperature-axis.

As regards the deviations near the critical point, although appa-
rently they increase systematically, we cannot help being surprised
at the exceptionally high amount of them (nearly 2°/,). A syste-
matie fault of the apparatus or the method of working, although in
the region of the higher temperatures our apparatus does not gua-
rantee the same degree of accuracy which we may consider as
assured in the region of the lower temperatures, may be considered
as excluded by the results obtained with oxygen and argon. Again
although the manner in which in the absence of all experimental
material concerning the isotherms of nitrogen at low temperatures
we were obliged to apply the corrections for the dead spaces in the
glass capillary in the cryostat (and therefore at the low temperature)
is open to some objection *), still deviations of the said magnitude
cannot thereby be explained.

In fact these corrections need not be known with more than a
very small relative accuracy. It would be less improbable to look
for the explanation in the presence of some admixture whose influence
was too small to make itself felt in the test referred to by means
of evaporation under constant pressure. Taking everything into account
we consider it probable, that the large deviations do not find their
explanation in the uncertainties of observation or calculation, but
are connected with the deviation of the critical point from the extra-
polated vapour-pressure curve. In order to find a conclusive answer
to the questions raised here, a special investigation will be needed
of the diameter of nitrogen in the immediate neighbourhood of the
critical point with apparatus specially constructed for the purpose,
us also in general a thermodynamical investigation in that region in
which amongst other things the mixing of the phases by stirring
will have to be provided for.

a) Comp. above § 4.

959

The coefficient of inclination of the diameter is:
bar = — 0.0019577,

and thus a good deal smaller than the coefficients of argon (—-0.0026235)
and of oxygen (— 0.002265).

The “undisturbed” critical density derived from the diameter using
as the eritieal temperature —147°.13') is found to be:

ord = 0.31096.

A comparison with the value for the “undisturbed” critical density

: 5 3 > n Op dp
which might be derived by the aid of the equation ( ,) = (ar)

7 hf OI A Pe
from the vapour-pressure curve and the isotherms near the critical
point (as this was carried out for argon) is impossible for nitrogen,
as isotherms are not available in the mean time.

The critical coefficient is

Kad = da,

a comparatively small value, as was to be expected in connection
with the simple molecular structure of nitrogen, its deviation from
the theoretical value } is in the same direction and to much the
same degree as that of argon (3.424) and that of oxygen (3.419) ’).

The liquid densities at the lower temperatures are in fairly
good agreement with those found bv Baty and Donnan *), the diffe-
rences being of the order of 1°/,.

Physics. — J/sothermals of di-atomic substances and their binary
mixtures. XVI. Vapour-pressures of nitrogen between the
critical point and the boiling point” By Dr. C. A. CROMMELIN.
(Communication N°. 145d from the Physical Laboratory at
Leiden). (Communicated by Prof. H. KAMERLINGH ONNss).

(Communicated in the meeting of December 30, 1914).

The determination of the density-curves and the diameter of
nitrogen *) offered a welcome opportunity for determining the vapour-
pressures of nitrogen between the critical point and the boiling
point, therefore in the region of the higher pressures, and thus
making a contribution towards the knowledge of the equation of

1, H. KAMERLINGH ONNES, C. DoORSMAN and G. Horsr, This number of the
Proc. Comm. 1455.

2) Calculated with the critical constants of Comm. 1455.

8-1. €.

4) E. Maruias, H. KAMERLINGH ONNES and G. A. CROMMELIN, This number
of the Proc., Comm. N°. 145c.

960

state of nitrogen at low temperatures. Moreover several of these
data were required for the computation of the corrections of the
diameter-measurements.

In the region here dealt with so far all experimental data were
lacking, at least if we leave out of account two old determinations
by v. Wrostewski’), which differ considerably from mine. Vapour-
pressures have been measured by Baty’) between — 196° and
— 182°, by FiscHer and Aur®) between —195° and — 210° and
by von SIEMENS“) between —.192° and — 205°, but, as will be seen,
they all refer to regions of low temperatures and pressures.

The nitrogen was liquefied in the same dilatometer and by the
same compression-cylinder, which had been used in the diameter-
measurements of argon and nitrogen. It should be mentioned, that
this dilatometer was not provided with a stirring-arrangement, so
that the determinations were made without stirring. It is possibly
due to this circumstance, that the vapour-pressures of nitrogen seem
to be a trifle less accurate than those of oxygen. ’)

As in the previous measurements the temperature was determined
by means of two platinum-thermometers which had been compared
with the standard resistance-thermometer Pf). As regards all this
we may therefore refer to previous communications"). The pressures
above 20 atm. were determined by means of the closed hydrogen-
manometer’), those below 20 atm. with the open standard-mano-
meter °).

The calculations do not call for special remarks. The atmosphere
at Leiden was taken equivalent to 75.9488 cms. mercury. ,

The nitrogen with which the experiments were made was, as
mentioned in connection with the diameter-measurements, the same
as was used for the determinations of the critical constants. By these
determinations the purity of the substance had been submitted to a

1) S. v. WroBLEwsKI, C. R. 102. (1886) p. 1010.
2) E. C. C. Baty, Phil. Mag. (5) 49 (1900) p. 517.
)

wo

K. T. FrscHer and H. Aur, Ann. d. Phys. (4) 9 (1902) p. 1149.

4) H. von Stemens, Ann. d. Phys. 42. (1913) p. 871.

5) H. KAMERLINGH Onyes, C. DoRsMAN and G. Horst, This number of the
Proc. Comm. No. 1450.

6) E. Marrias, H. KAMERLINGH Onnes and C. A. CROMMELIN, Proc. Oct. and
Dec. 1912 and Jan. 1913. Comm. No. 13la (argon) and these Proc. above Comm.
No. 145c (nitrogen).

7) H. KAMERLINGE ONNEs and H. H. F. Hynpman, Proc. April 1902, Comm.
No. 78 (§ 17) and ,H. KAMERLINGH ONNES and C. BRAAK, Proc. March 1907,
Comm. No. 97a (§ 3).

5) H. KAMERLINGH ONNes, Proc. Nov. 1898, Comm. No. 44.

961
severe test. The nitrogen was moreover once more tested for its
purity in the apparatus itself. For this purpose the vapour-pressure
was measured at a temperature which was kept constant (about
— 158°), first when only a drop of liquid was present in the appendix
of the dilatometer and immediately afterwards with the dilatometer
completely filled with liquid. The vapour-pressure was found in the
two cases to be
25.38 and 25.41 atm.

This difference of about one thousandth of the total value is not
far removed from the limits of accuracy of the observations and
proves (1) that the nitrogen was very pure and (2) that the tempe-
rature-difference near the top and near the bottom in the cryostat
must have been inappreciable.

In the further observations the liquid-surface was always brought
to about the middle of the dilatometerbulb.

==: - rr 5 = = = = en

Te

La 8 a ae obs. Peale. Obs.-calc. (abs.) Rests ens
1914 eens, tm. int. (lo)
21 Febr. |X | — 148.85 30.364 | 30.631 =<" 0961 yaaa bee

: IX | — 152.11 | 25.889 | 26.087 | — 0.18 | — 0.8

REM =. 155.47-| 21.620 | 21.945) | = 00188 zele
20 Febr. | VII | — 161.31 | 15.949 | 15.949 | 0.000 0.0
17 Febr. |V | — 173.58 | 7.3705| 7.3705 | 0.0000 0.0

: IV. | — 170.18 | 4.8278| 4.8632 | — 0.0354 |. = 07
16 Febr. |1 | — 182.47 | 3.7248| 3.7117 | + 0.0131 +04

f IL | — 186.88| 2.5067| 2.4863 + 0.0204 + 0.8

; Im |— 191.88| 1.4727] 1.4721 0.0000 | 0.0

In the above table are given the results of the measurements and
a comparison with a formula of the form
b c d
logp=a+ at aa t
where 7’ represents the absolute temperature, the coefficients having
the values

a = + 5.76881
b = — 858.522
¢ = + 54872.3
d = — 1783500

Proceedings Royal Acad. Amsterdam. Vol. XVII.

962

which satisfy the following values of the critical constants
pr == 33.49 atm, and 7, = 125.°96 K 3)
(Or= Ti —Tfoc=— 147.°13 C. in Kelvin-degrees)

The circumstance, that the observations do not agree very well with
the formula, finds its explanation, at least partly, in the fact, that
the critical point falls a little outside the extrapolated vapour-pressure
curve. The same fact occurs with the vapour-pressure curves of
argon (CROMMELIN) *), ether (Ramsay and Yocng) *), isopentane (Youn) *)
normal octane (Youne) *), carbon disulphide (BaTTELLt) ®) in contrast
with what is found with the great majority of vapour-pressure curves
of other substances, with regard to the critical point.

A systematic inquiry into the cause of these deviations would be
very desirable.

In conclusion I wish to thank Prof. H. KAMERLINGH ONNES most
heartily for the continued interest shown in my work.

Chemistry. — “On the vapour pressure lines of the system phos-
phorus.’ TI. By Prof. A. Smits and S. C. BokHorst. (Com-
municated by Prof. J. D. vaN DER Waats).

(Communicated in the meeting of December 30, 1914).
I. Determinations of the vapour pressure of the violet phosphorus.
In the preliminary investigation about the vapour tension of the
violet phosphorus we found a vapour pressure line with a discontinuity

at about 450°, which result seemed to confirm the existence of a

transition point found by Jormors ®) at + 460. |

To get further certainty about the existence or non-existence of
this transition point, it had to be examined whether really two
branches intersecting each other, could be realized here. For this
purpose it would be necessary to determine also a part of the
metastable prolongations on either side of the transition point, and
keeping this end in view we undertook the definitive investigation.

The preliminary experiments were made with a preparation N°. 1,
which was obtained by heating pure white phosphorus with 0,1 °/,

Iodium at + 300° for 24 hours. This preparation was hard and

1) Comm. 1450.
2) C. A. CROMMELIN,' Proc. May 1910 and Oct. 1913, Comm. 115 and 138c

and Dissertation Leiden 1910.

8) W. Ramsay and S. Youne, Phil. Trans A 178, (1887) p. 57.
4) S. Youne, Proc. phys. Soc. 1894/1895 p. 602.
5) S. Youne, Journ. Chem. Soc. 77 (1900) p. 1145.

)
) A. Barrett, Mem. d. Ac. di Torino, (2) 41 I (1890) and 42 I (1891).
) GC. r 149, 287 (1909); 151, 382 (1910).

a

~

963

brittle, possessed a violet colour, and did not emit light in the dark:

We started again from the same preparation; it was heated in a
tube of not readily fusible glass in vacuo for twelve hours at 510°,
so above the supposed transition point, and then it was suddenly
cooled. Then half of the tube was heated in a bath at 200°, to
condense the white phosphorus that had deposited from the vapour
in the colder upper end of the tube. After careful cooling the tube
was cut in the middle, and the glass spring (pressure indicator) was
filled with the red phosphorus obtained in this way. Then the glass
spring was evacuated by means of the pump and heated in an
asbestus jacket at +150 for an hour to be sure that all the air
was expelled, and then fused to at the bottom. The heating should
not be carried up higher than 150°, because else, as appeared later,
a great disturbance of the internal equilibrium takes place in conse-
quence of the pumping off of the most volatile molecule kind from
the phosphorus, which disturbance is only gradually prevented at
higher temperature.

That in this way we really succeeded in removing all the air from
the glass spring appears from this that at the end of the determinations
no appreciable zero point change of the glass spring could be
demonstrated.

The vapour tensions determined with this phosphorus were much
too high, higher than before, and presented a close resemblance with
that of the white phosphorus for the lower temperatures. It followed
from this that the white phosphorus had not been sufficiently removed
from the preparation, and that a subsequent treatment had to follow
to remove it completely.

In future the violet phosphorus was therefore extracted in a Sohxlet=
apparatus with CS, for 6 hours, and then treated with ammonia to
remove the possibly formed phosphoric acid. Then the preparation
was washed with absolute ether, and dried in a vacuum exsiccator
over P,O, ').

Now three preparations were made, which were all subjected to
the same after-treatment, which we shall designate by :

Preparation N°. 2 made from preparation N°. 1 by heating it
once more with 0.1 °/, Iodium at 375° for six days, and then sub:
jecting it to the said after-treatment.

Preparation No. 3 prepared from white phosphorus by first heating
it without Iodium at 300° for some hours, and then once more

\) In this after-treatment part of the pseudo-component soluble in the CS, will
of course be ejected from the mass, which is in internal equilibrium. This, however,
is of no importance, as this is restricted to the surface-layer only.

64*

964

heating the formed red phosphorus, after addition of 0.4 °/, I at
400° for 3 days, after which the said after-treatment was of course
applied again.

Preparation No. 4 prepared from white phosphorus by heating
it at 550°, for 5 hours, without the addition of Todium, followed by
the known after-treatment.

These preparations, of which we thought ourselves justified in
expecting that they had assumed internal equilibrium resp. at 375°,
400°, 550° gave the following vapour pressures.

TABLE UE

Preparation No. 2 Preparation No. 3 | Preparation No. 4

Temp. of preparat. 375° Temp. of preparat.410° Temp. of preparat. 550°
Manometer No. 69 Manometer No. 72 Manometer No. 74
Temp. Pressure Temp. Pressure | Temp. Pressure
290° 0.05 atm. 308 .5° 0.08 atm. | 308.5° 0.07 atm.
308.5 0.09. „ 346 Dev 346 | WAS 5
328 | 0:15 315:5 0.40 , 379.5 035 -5
346 Oras 394.5 Oba 408.5 061996
365 Res EE ee 418 Ay Vd 433:5 >| “1-49,
384.5 | 0.60 , 448.5 | 2.23 , 450.5 | 230 7%
AAO |: (4:02 5 457.5 | 2.89 , 463.5 er
429 rel cry 461.5 317 > Ol? eee 3:88",
444.5 | 2.16 , 474.5 A190) 486.5 5.46,
456 RB

In these determinations we took care that when it seemed that
at constant temperature also the pressure had become constant, the
vapour pressure was observed at the same temperature for 10 or
20 minutes more, to examine if it really did not change any more.

When considering the result found here, which is represented
graphically in Fig. 1, we observe that the mentioned preparations
do not give the same vapour pressure line, but that the curve lies
lower as the preparation is prepared at higher temperature. This
imperfect coincidence of the three vapour pressure lines suggests
that the establishment of the internal equilibrium in the range of
temperature passed through here, proceeds so slowly, that no internal

965

8
rg
6
5
P
4
3 Wi,
Chea
vA
- |e vi
a.
300 me 400 7" 450

equilibrium can set in during the determination of the vapour
pressure. That the preparation that has been prepared at the highest
temperature, showed the lowest vapour tension, was further an
indication that the establishment of the internal equilibrium was com-
pletest at the highest temperature of preparation. On closer examina-
tion of the observed vapour tensions it appeared later (see the
following “communication’”’) that this view was really the correct one.

It was now the question in how far the now found vapour
pressure line was in harmony with the determinations of the vapour
pressure, of higher temperature.

For the vapour pressure at temperatures of 505° up to the triple
point temperature the following values were found: (see page 966).

If we now represent this result together with that of Table I,
preparation 4 in the same Figure, we get the following P7-diagram
Fig. 2, from which it appears that the different determinations yield

966

TABLE, i

_ Preparation i |
EED _|Giass spring

Temperature Vapour ténsion |
505° | 8.67 atm. No, 11
515 | “A039 Ly go 3
52239 i ae Bai ee |
578 34.35 „ | vn
581 36.49 „ ES
BIRK ol MRI 12
588 42.10 , ak
589 dB 2 Le a
Triple point 589.5 ADT) = | Pressure
| found by
| interpolation

WEES AE
MME VAN
EEE ZE
et |

967

a curve with a perfectly regular course, so that there is no question
of the occurrence of the discontinuity found before at 450°, which
rendered the existence of a transition point, stating it mildly, very
doubtful.

First of all it had to be examined what was the cause of the
discrepant result of the earlier, preliminary determinations, and
whether a preparation prepared in the same way again yielded such
a line with a break at + 450°.

To decide this question a new preparation N°. 5 was made, chiefly
prepared in the same way as N°. 1; white phosphorus with 0,2°/, 1
was heated at 400° for 6 hours, then cooled very slowly to give the
white phosphorus depositing from the vapour every possible oppor-
tunity to be converted to violet phosphorus.

This cooling lasted 14 hours, and when the tube was opened in
the dark no emission of light could be observed. The obtained phos-
phorus was not extracted with CS,, but only treated with water to
remove oxidation products which might possibly be present, then
washed with ether, and dried in a vacuum exsiccator over P,O,

The vapour pressure line determined with this preparation in glass
spring N°. 78, is represented in Fig. 1. We see from it that first
four points were found which were much too high. In the determi-
nation of the fifth point a remarkable phenomenon was observed,
which threw light on the vapour pressure line determined earlier.
After the pressure had risen to 2,99 atm. at 442°, and had remained
constant for five minutes, the pressure began to descend at first
slowly, then more rapidly, and at last again more slowly.

When the phosphorus had been kept at the same temperature of
442° for two hours, the pressure had fallen to 2,21 atm., a value
which agrees pretty well with that obtained with the preparations
NE DENS and. 4

On continned investigation towards higher temperatures this agree-
ment continued to exist, which follows from the subjoined table. (p. 968).

The result of this experiment is of great importance, for in the first
place it follows from this that violet phosphorus prepared in the same
way as for preparation N°. 5, so by tbe heating of white phosphorus
with a trace of iodium, consists without after treatment of violet
phosphorus, which was very nearly in internal equilibrium at the
temperature of preparation, and that by the side of it a little white
phosphorus is found, which has deposited on cooling from the vapour
phase after the preparation of the violet phosphorus. It must now
be attributed to the presence of this quantity of white phosphorus
that in our preliminary investigation, just as in this last-mentioned

968

experiment, too high vapour tensions were found at the lower tem-:
peratures, and a discontinuity occurred in the neighbourhood of 450°.

Vapour pressure

Temp. in atmospheres
309° 4 .OA2s,
346 | 0.23
| too high
305’:
424 | 1.90
442 2.21 (at first 2.99, then
falling to 2.21)

459.5 3.15
411.5) 4.10
488 | 6.00
424 1.55

Above 360° the white phosphorus is already converted with great
velocity, but the concentration of the violet phosphorus in internal
equilibrium differs so greatly from that of the liquid white and the
gaseous phosphorus that a great internal chemical transformation of
the volatile pseudo-component « into the little volatile 3 must take
place before the violet modification is formed. As long as this is
not the case, the product of conversion will contain too much of
the violet pseudo-component @, hence the vapour tension will be
too high.

Below 450° the complete transformation in the stable state of
internal equilibrium of the solid substance (the violet phosphorus)
requires much more time than we at first supposed, so that the
vapour tension of a preparation which contained a little white
phosphorus at first, was found too high below that temperature. It
is true that we never proceeded to a following determination before
the pressure had practically not changed for 15 minutes, but this
time appeared to have been much too short. At higher temperature,
however, this lapse of time was long enough to enable us to find
out that the mass had not yet assumed internal equilibrium, for as
was already mentioned above, the pressure began to descend already
appreciably at 442°, and not until two hours later had it practically
become constant, at which the pressure had reached a value which
is in good harmony with the continuous vapour pressure line, which

969

was found with the preparations from which the white phosphorus
had beforehand been quite removed by extraction with CS,

This result gave the solution of the difficulty, for it was now
clear that the discontinuity found before at zE 450° was to be
ascribed to this that only in the neighbourhood of this temperature
the internal equilibrium begins to set in with such velocity that
the internal transformation betrays itself by the setting in of a
decrease of pressure within a few minutes.

At about the same temperature Jortors found a discontinuity in
the curve of heating, and it is now perfectly certain that this
irregularity must be accounted for in the same way as that found
by us at first.

At 500° the velocity of the establishment of the internal
equilibrium bas become sufficiently great to render a reliable deter-
mination of the vapour tension of the violet phosphorus possible
within one hour; and this is therefore the reason that the vapour
tension with different preparations at temperatures above 490° are
in good harmony with those of the preliminary investigation. Thus
the vapour tension was once more determined with the same pre-
paration N°. 5 at the temperature 561°, in which a pressure of
24,3 atm. was found. *)

As for the triple point pressure, it was determined in the following
way. One of the pure preparations of violet phosphorus was heated
very slowly in a perfectly evacuated tube of sparingly fusible glass
placed in a glass beaker with molten potassium-sodium nitrate,
the temperature being at the same time observed by means of a
resistance thermometer and a thermo-element. Thus on repetition
589°.5 was found for the triple point temperature. As now the
molten violet phosphorus yields a straight line for 7'/n P as function
of 7, it could be read with great accuracy from this line to what
value of ZY’/n P the temperature of 589,5° corresponded; in this
way the value 3246.6 was found for 7'/n P at 589.5°, from which
the value of the triple point pressure = 43.1 followed immediately,
a value which is probably accurate within 0.5 atm.

With regard to the accuracy of the vapour pressure line we will
here emphatically point out that the vapour tensions at temperatures
below 500° will not agree perfectly with states of internal equilibrium,
as at those temperatures the establishment of the internal equilibrium
still proceeds too slowly. In consequence of this the equilibrium
solid 2 vapour could, below 400°, only be approximated coming

1) This point has also been given in Fig. 2.

from lower temperatures, because passing from higher to lower
temperature, the establishment of the equilibrium required far too
much time. Owing to this we are unfortunately uncertain about the
degree of the accuracy, but the error cannot be very great, as the
preparations of different temperatures of preparation yield vapour
pressure lines which, below 500°, differ comparatively little from
each other in situation, with the exception of the very lowest points.

2. Corroborations of the theory of allotropy.
bese PY

The theory of allotropy says that every phase of an allotropous
substance exhibits the phenomenon of molecular allotropy, hence the
violet phosphorus had also to be a state of internal equilibrium,
which equilibrium is in general dependent on temperature and pressure.

To test this view the following experiment was made. By sub-
lination in vacuo it was tried to expel the more volatile pseudo
component at a temperature at which the internal equilibrium sets
in only very slowly, and the formation of the more volatile from
the less volatile pseudo component takes, therefore, place with very
slight velocity. If this succeeded, a substance would be obtained
with a considerably smaller vapour tension than the preparation
from which we had started.

Keeping this purpose in view part of the preparation N°. 4, with
which the vapour pressure line with manometer N°. 74 had been
determined was heated in a glass tube for two hours in the bigh
vacuum of the Gaede-pump at somewhat more than 360°, during
which small drops of liquid white phoshorus condensed against the
colder part of the tube. After the tube had been cut in the middle,
so that the violet phosphorus was separated from the white, a new
glass spring N°. 75 was filled with the thus obtained violet P N°. 4a
without any further treatment, and then we proceeded to the deter-
mination of the vapour tension.

It now really appeared that the vapour tension of this preparation
was much too low, which is clearly indicated by the vapour pressure
line N°. 75 in our PT-figure.

As this figure shows, this vapour tension line is not continued
beyond 473°, because at this temperature a reading of the pressure
was no longer possible on account of the continual slow rise of the
vapour tension. Also this result was in perfect agreement with our
expectations, because the internal equilibrium sets in already notice-
ably at 473°.

Now we might have continued the determination of the vapour

pressure at 473°, till the vapour pressure line which had been found
before with preparation N°. 4, had been reached, but then the expe-
riment would certainly have been continued for several hours, which
gave rise to difficulties. To reach our purpose more quickly, the
experiment was finished, and part of the same preparation N°. 4a,
with which now a too low vapour pressure had been found, was
heated with 0,15°/, Iodium at 410° for five hours, and then again
subjected to the known after-treatment with CS,. Finally the vapour
tension of this preparation N°. 45 was once more determined with
the glass spring N°. 77 and then a vapour tension line was found
which up to 450° perfectly coincided with the curve N°. 74, which
had been found with the same material before the internal equili-
brium had been disturbed. *)

This experiment has, therefore, shown in the most convincing way
that for violet phosphorus we have to do here with an internal equi-
hbrium between at least two pseudo components, which greatly differ
in volatility.

3. Designation of the unary stable solid state of the phosphorus,

and the nature of red phosphorus.

Our investigation has taught us that there is only one stable solid
modification, and it is now the question by what name this modifi-
cation will be denoted. In not very finely crystallized condition the
colour of this stable solid state of the phosphorus is violet. If this
substance is rubbed fine, however, the colour becomes dark red,
and the greater the fineness, the lighter the colour. In the same
way of preparing preparations of different colour are often obtained,
which, however, had entirely to be ascribed to a difference in
fineness, for it always appeared that though the colour was different,
the preparations had the same vapour tension.

In virtue of this the name of violet phosphorus naturally suggests

1) It should be noticed that when iodium is added to the solid red phosphorus,
only a superficial internal equilibrium is obtained. If the vapour tension of the
obtained solid substance is determined, the case can therefore occur that the vapour
tension begins to deviate from the accurate curve at a definite temperature, in
consequence of this that the quantity of the most volatile pseudo-component present
has become insufficient, and the velocity of the internal conversion is not great
enough to supply the quantity that is lacking. This case was temporarily met with
in the above-mentioned experiment above 450°. Above this temperature somewhat
too low pressures were namely found, but if the temperature was kept constant
for half an hour, a rise of the pressure occurred again.

972

itself as a designation of the stable solid modification of the
phosphorus ’).

Messrs. Conen and Ormw *) thought that the violet phosphorus was
a simple substance, and that the red phosphorus had to be taken
as a solid solution of white phosphorus in violet phosphorus, the
concentration of which would be a temperature function, or in
other words that the red phosphorus would be a state of internal
equilibrium.

It has now, however, appeared most convincingly that this view
is erroneous, and that the violet modification of the phosphorus,
ie. the wnary stable form of the phosphorus, just as the unary
metastable form, the white phosphorus, is a state of internal equi-
librium, and that what is understood by red phosphorus is an in-
termediate metastable state, which is not im internal equilibrium.

This intermediate state, which, therefore, does not occur in the
unary system, is a state of the pseudo system, and consists of one
or more mixed crystals. |

That the phosphorus with which Messrs. ConeN and Orme worked,
was no state of internal equilibrium, one of us (Smits) *) demonstrated
already before by pointing out that it follows from their experiments
that when red phosphorus was brought from higher to lower tem-
perature, the specific gravity was not reduced, though the state of
equilibrium at a lower temperature would have to correspond to a
smaller specifie gravity.

4. Transition point of the white phosphorus.

While thus the red phosphorus has disappeared from the unary
system of this element, this vacancy has again been filled by
BRIDGMAN *), who found lately that the white phosphorus exhibits a
transition point at — 80°, where the regular white phosphorus as-
sumes a hexagonal form. It follows therefore from this that the
phosphorus possesses a metastable transition point.

5. Brineman’s black phosphorus.

BRIDGMAN speaks further of black phosphorus, which he has obtained
by subjecting white phosphorus at 200° to a pressure of from 12000

1) In our previous communication we thouglit we had to retain the denomina-
tion of red phosphorus, but it appeared that this might give rise to all kinds of
mistaken ideas.

4) Zeef. Phys. Chem. 71, 4 (1900):

5) Z. f. phys. Chem. 76, 421 (1911).

4) Journ. Amer. Chem. Soc. 36, 1344 (1914).

973

to 13000 ke. per em?. When red phosphorus was started from, this
black phosphorus did not form, however, under the same circum-
stances of temperature and pressure. Undoubtedly this difference is
owing to the circumstance that the chemical transformation required
to obtain the black phosphorus makes its appearance more easily in
the strongly metastable liquid than in the much less strongly meta-
stable intermediate state, the red phosphorus. At higher temperature
also red phosphorus, and also the violet modification, will have to
become black.

Whether this black modification is really a new modification is
still to be decided.

After Bripeman’s publication had come under our notice, we asked
him to supply us with a small quantity of his black phosphorus
in order to investigate this state further by means of vapour pressure
determinations etc. Mr. BrIDGMAN has very kindly complied with this
request, and we gladly avail ourselves of this opportunity to render
him our best thanks for his kindness.

Amsterdam, 24% Dec. 1914. Anorg. Chem. Laboratory
of the University.

Chemistry. — “Murther particulars concerning the system phosphorus.”
By Prof. A. Smits and 8. C. Boxnorst. (Communicated by
Prof. J. D. van DER WAALS).

(Communicated in the meeting of December 30, 1914).

1. The vapour tension formula for the violet phosphorus.

When calculating the values for 7'/n P from the observed vapour
tensions of the solid violet phosphorus (see preceding communication),
we find what follows. ;

When just as we have done for liquid violet phosphorus, we
represent 7'/n P graphically as function of 7’, we come to the result
that as Fig. 1 shows the values for 7’/n P obtained for the prepa-
rations + and 1 with the exception of the two lowest points, are
without any doubt situated practically on a straight line.

That this is not the case with the two lowest points, is of course
to be ascribed to an inaccuracy in the experiment. This inaccuracy
may be owing to this that during the heating of the phosphorus in
the glass spring, when the latter was being evacuated with the
GAEDE pump, a small quantity of white phosphorus was condensed
from the vapour on the wall of the glass spring, which of course

TABLE i.
Preparation 2.

t fr P TinP
290° 563° 0.05 atm. | — 1686.6
308.5 | 581.5 | 0.09 , — 1400.2
328 GN) = ak Gade ude
346 61910525 — 858.1
365 638 0.39 160027
384.5 | 657.5 | 0.60 , — 335.8
410 683 ine ee 105
429 702 1.54, sl aps
re eam Ti 12e 4. 552.5
456 729 zE 4+ 755.7

TABLE IL.

Preparation 3.

t ; & | P TinP
|

308.5 | 581-5 | 0.08 atm. | — 1468.7
346 619 sia — 1096.8
315.5 | 648.5 | 0.40 , — 594.2
304.5 | 667.5 | 0.65 , SS) WES
a18 | 691 Kie + 18.3
48.5 | 721.5 | 2.23 , + 578.6
457.5 | 730.5 | 2.89 , er Td
461.5 | 734.5 aay + 9847.4
TAS | Se ea) + 1070.9
re TABLE IIL.

Preparation 4.
308% | s81°% | 0.07 atm. | — 1543.1
346 bio | 043, — 1263.1
379.5 | A messes — 685.13
408.5 | 681:5 | 0.79 , — 160.67
433.5. 17065 | 149 , + 281.79
450.5 | A25 Den. + 587.64
463.5 | 136.5 | 318 , + 852.20
412.5 | 745.5 | 3.88, 4+ 1011.0
4505 59.5 ses + 1289.5

975

TABLE IV.
Preparation 1. !)

t | 7 P TinP
505° 778? | 8.67 atm. 1680.4
515 | 788 10.43 „ 1847.6
522.5 | 795.5 11,61 =, 1950.4
561 | 834 AIS 2661.3
578 | 851 BY ess eee 3009.6
581 | 854 36.49 , 3071.8
587.5 869.5 Ale Tar, 3211.5

588 861 8240, 3220. 1
589 ‚ 862 ea 3232.1
580.5 | 8625 | 431 , 3246.6

350 jij no 300
r Fig. 1
1) Only the most reliable determinations have been used here. The determination
at 561° refers to preparation 5,

976
gives rise to a'too high pressure at the lower temperatures, where
the establishment of the internal equilibrium takes place so exceed-
ingly slowly.

Besides it is possible, and this is probably the chief reason, that
preparation 4 has not yet entirely assumed internal equilibrium at
the temperature of preparation, and that therefore the preparation
still contained somewhat too much of the volatile pseudo-component.

This somewhat too much caused at those temperatures at which
the internal equilibrium sets in most slowly, the greatest error and
this will probably be the reason why the deviations are greatest at
the lowest temperatures. Considered from this point of view also the
much greater discrepancies which the preparations 2 and 3 exhibit
at lower temperatures, can be accounted for in a plausible way.

Hence it follows from our investigation about the vapour tension
of the solid violet phosphorus that just as for the liquid violet phos-
phorus 7'/n P represented as function of 7, yields a straight line,
from which it therefore appears that the quantity Q in the equation:

dnp __ Q
dT RT

ERE

may be considered as a constant, so that we get through integration:

Q
DI GE et >. (2
np RT + (2)
or
cages
AD ecg ON (el

As we have also done for the liquid violet phosphorus, we can
again find the constant C graphically also here, as it is equal to the
tangent of the angle a, which the line PnP as function of 7’ forms
with the temperature axis, for:

T lnp,—T,lnp,

Ln

We have T‚lnP,—=—1400 for 7,=343,5°4+-273°; T,nP,=3246,6
for 7’, = 589,5° + 273°, from which follows C—= 18,889, a value
which is about twice the value of the constant for the diguid violet
phosphorus.

C= = iga.

When with this value for C we now calculate the quantity :

for different temperatures, making use of the tables II and IV, we
get what follows:

977

a ery en en neen

Temperature 7
308°.5 12527
346 12958
379.5 13010
408.5 13034
433.5 13065
450.5 13079
463.5 13060
472.5 13071
486.4 13057
505 13006
515 13037
522.5 13076
(561) (13092)
578 13065
581 13060
587.5 13043
588 13044
589 13051
589.5 13046

Mean 13050

When we now disregard the two first values, because as the
graphical representation shows, they certainly refer to determinations
which contain a much greater error than the others, and if we also
exclude the determination at 561°, because certainly no internal
equilibrium had set in here yet, we get as mean value 13050.

Q
Now that C and Fi are known, we can calculate the pressures

for the temperatures at which the preparations 1 and 4 have been
investigated. Doing this, we get what follows:
| 65
Proceedings Royal Acad. Amsterdam. Vol. XVII.

978

Temperature Observed pressure Calculated pressure

308.5 0.07 atm. 0.03 atm.
346 gas | Oni.
379.5 0.35 , 0.33 ,
408.5 ord, Ds,
433.5 a 1.52 ,
450.5 2.30. 5 2.34: ,
463.5 3.18 , 3.22 ,
472.5 3.88 , 3.99 ,
486.5 5.46, 5.51 ,
505 8.61 , 8.29 ,
515 10.43, 10.26 ,
522.5 11.61 , 11.98 ,
561 (24.2) 5.5»
578 34.35 , 34.95 ,
581 36.49 , 36.90 ,
587.5 ATT , 41.38 „
588 42.10 , Aas
589 42.6 , 45
589.5 43.1 , Eda

2. Heat of sublimation, heat of evaporation and heat of melting
of the violet phosphorus in connection with the theory of allotropy.

From the foregoing calculations exceedingly remarkable conclusions
may be drawn.

)
From the value for © = 13050 follows for the mol. heat of subli-

mation the extraordinarily high value 25.839 K. Cal., while we
have found 9.962 K. Cal. for the mol. heat of evaporation of liquid
violet phosphorus, so that 15.877 K. Cal. follows from these two
quantities for the mol. heat of melting.

According to the theory of allotropy evaporation and melting is
accompanied with a chemical reaction between the pseudo components
of the substance, and the more the coexisting phases differ in con-

979

centration, the greater will be the chemical transformation of one
phase into another. It follows from this that the sublimation heat,
the evaporation heat of the liquid and the melting heat will consist
for a greater part of a chemical heat as the coexisting phases differ
more in concentration. The quantities of heat found above are of
importance in this respect, because they confirm this view in the
most convincing way.

According to the theory of allotropy the difference in concentra:
tion between the solid violet phosphorus and the vapour is greatest,
and that between the liquid phosphorus and the vapour smallest.
This tallies perfectly with the colour of the phases; the vapour
phase is always colourless, just as the liquid phase.

The evaporation of the solid phosphorus and the melting of the
solid phosphorus will therefore be processes which are accompanied
with a strong chemical conversion, whereas this reaction is probably
only slight during the evaporation of the liquid.

The found values for the three mentioned quantities of heat
confirm this perfectly, and the exceedingly high values for the mol.
sublimation heat and the mol. melting heat prove that the heat
effect is for the greater part a chemical heat. The sublimation heat
of the violet phosphorus is even so great that it is of the order of
magnitude of the sublimation heat of NH,Cl, which amounts to
37.9 K. Cal., and in which the dissociation heat is included.

For the difference of energy between white and violet phosphorus
per gram-atom the following has been found:

Pie eg Roter + 44 cal. a

If we now assume for a moment, what certainly is not far from
the truth, that this heat effect is entirely a chemical heat, and if
we. further assume that these two phases differ almost as much
from each other in concentration as the violet phosphorus and its
vapour, then a chemical heat of about 4 x 4,4 K. Cal. will be in-
cluded in the mol. sublimation heat. If we subtract this heat effect
from the molecular sublimation heat, we keep for the physical heat
25,8 —-17,6 = 8.2 K. Cal.; this is a heat effect that lies already
much nearer the sublimation heats of other comparable substances
in which a chemical heat is also included, but a much smaller one
than for the violet phosphorus. The mol. sublimation heat of SO,
e.g. amounts to 11,79 K. Cal.’).

The difference in concentration between violet phosphorus and

1) GrRAN, Ann. Chim. phys. (7) 30, 203 (1903).
2) C. R. 90, 1511 (1880).
65*

980

the coexisting colourless liquid phase is certainly considerably smaller
than that between violet phosphorus and its vapour, which also
follows from the molecular heat of melting, for which we found,
as was stated above, 15,877 K. Cal. from the mol. sublimation heat

and evaporation heat.

B. Size of the phosphorus molecule.

As we published some time ago’) we succeeded in determining
the vapour tension line of liquid phosphorus between 504° and 634?.
On that occasion we showed at the same time that when 7’ ln P
is represented as function of 7, a perfectly straight line is formed
as a proof that here too the Q from the equation:

= Aes
Tin P= — R + C1
is no appreciable function of the temperature.

Now lately Want *) determined the critical temperature of liquid
violet phosphorus in a quartz tube, and found for it the temperature
695°. As now the line for 7’ P as function of 7, appeared to
be a straight line from 504° to 634°, it was perfectly justifiable to
prolong this line to 695°, hence to read the value of 7'/nP at
T = 695° + 273° = 968° by extrapolation, and derive from this the
value of P, hence of the critical pressure. In this way 4284 was
found for 7'/n P, from which follows P, = 83.56 atm.

Now that we know the critical data for the liquid violet phosphorus
it is of importance to inquire what can be derived from these data
about the size of the phosphorus molecule.

For this purpose we calculate the 4 value by the aid of VAN DER
Waats’ relation :

“5, sll aaa GE
78218 Bp 2828.85.6

or
b = 0,005304.

When we now assume the 5 to be an additive quantity we can

find the 4 of a phosphorus atom e.g. from the h-value of e.g. PH,,

and when we then divide the 4 value of the phosphorus molecule

by this value, we find the number of atoms of phosphorus present

in the molecule.

1) These Proc. Vol XVI. p. 1174.
2) Meddelanden Fran Finska Kemistsamfundet 1913, 3.

98 |

For the critical quantities of PH, Lrpuc and SACERDOTE *) found
what follows:
. i; = 52,5" and Pi = 64 atm.

If the 6 is calculated from this, we find:

bh = 0,002330.

According to vaN peR Waars’ new views “The volume of the
molecules and the volume of the component atoms” *) hydrogen presents
the peculiarity that the 6 of a hydrogen atom in a compound is
much smaller than in the hydrogen molecule; it amounts viz. to
0.000362 instead of 0.000825, from which follows that for the
3 hydrogen atoms in PH,, 0,001086 must be taken. We then get:

0.002330—0.001086 = 0.001244
for the h-value of the phosphorus atom, from which follows:
0,005304
0,001244 —
for the size of the phosphorus molecule at the critical temperature
and pressure of the liquid violet phosphorus.

This result already points to a small association, for on an average

the phosphorus molecule is greater than 1.

4,26

4. Caleulation of the factor f of Vax per Waars’ vapour tension
formula.

Finally we have also calculated the value of the factor f from
the empirical vapour tension equation of VAN DER WAALS.

Ts,
— AE geen (5 — 1)
DE ~. JR

When we consider the pressures at two different temperatures,
then it follows from this relation that
0,4348 (T,InP,—T,InP,)
See ROE
1 rd 2

. from which it-appears that f is graphically to be derived from the

line that represents 7'/n P as function of 7. Over a range of tem-

perature of 200°, viz. from 500° to 700°, 7'{p P increases from
2388 to 4332, so by 1944.
From this follows that:

_ 0,4848 X 1944 __

An Ee

4,221.

1) C.R. 125, 397 1897).
2) These Proc. Vol. XVI. p. 880.

982

For substances for which the size of the molecules in the vapour
and the liquid phase is equal or about equal f is about 3, so that
the value 4,221 indicates that for the violet phosphorus the average
size of the molecules in the coexisting vapour and liquid phases is
different.

A discussion of the vapour tension line of the white phosphorus
will be reserved for another paper.

Anorg. Chem. Laboratory of the University.

Amsterdam, Dec. 24, 1914.

Anatomy. — “On the termination of the efferent nerves in plain
muscle-cells, and its bearing on the sympathetic (accessory)
innervation of the striated muscle-fibre. By Prof. J. Boek.

(Communicated in the meeting of December 30, 1914).

In recent years it has been demonstrated for a large number of
different types of striated muscle-fibres of vertebrates, that the motor
nerve-endings, which carry the nervous impulses towards the muscular
libres, are hypolemmal in position, i.e. are not lying outside the
sarcolemma of the muscle-fibres as maintained by most of the earlier
observers, but pass through the sarcolemma, which becomes conti-
nuous with the neurilemma, penetrate into the sarcoplasm of the
muscle-fibre, which is considerably thickened as the site of formation
of the end-organs, and it was further assumed, that here the neuro-
fibrillar expansion of the motor nerve-ending is directly continuous
with a reticulum in the sarcoplasm, the so-called ‘periterminal
network” *). |

At the same time it was shown, that beside the common motor
nerve-ending there must be distinguished another afferent nerve-
ending on the striated muscle-fibres of vertebrates, which may either
be found imbedded in the same granular bed of sarcoplasm or “sole”
of the motor endorgan of KiiHNE, or reaching the muscle-fibre inde-
pendent of this, but always having a hypolemmal position in the
muscle-fibre®). This “accessory” nerve-ending is always found at
the end of a non-medullated nerve-fibre. As it could be shown, that
these accessory nerve-endings did not degenerate after the cutting
of the efferent muscle-nerve near the place of exit from the central
nervous system, before the entering of the sympathetic nerve-fibres

1) J. Boeke. Beiträge zur Kenntuiss der motorischen Nervenendigungen. I. II.
Internat. Monatschr. f. Anatomie und Physiotogie Bd. 28. 1911.

2) J. Boeke. Die doppelte (motorische und sympathetisch) efferente Innervation
der quergestreiften Muskelfasern. Anat. Anzeiger. 44. Band. 1913,

983

(for example the accessory nerve-endings of the eye-muscle after
the cutting of the nervus trochlearis near the mid-brain) which
causes the motor nerve-endings of Kürnrr to degenerate, there was
room for the conclusion, that the accessory nerve-fibres and their
endorgans were of sympathetic origin, and perhaps had something
to do with the tonie innervation of the striated muscle’), In my
first paper, which dealt with these nerve-fibres (Congress Utrecht,
April 1909), this conclusion was already drawn by me’). In the years
1913 and 1914 strong supporting evidence has been given to it by
the admirable physiological experiments of px Boxr*).

In Fig. 1 is shown a degenerated motor nerve-ending (m) in a

Fig. 1.

Nerve-endings in muscle-fibres of the musc. obl, sup.
oculi of the cat, 3!/, days after section of the nervus
trochlearis.
af = accessory (sympathetic) fibre with end-organ, not

degenerated.

m = degenerated motor nerve-fibre with degenerated
end organ.

muscle-fibre of the superior oblique muscle of the eye-ball of a cat
some days after section of the nervus trochlearis near the mid-brain.
The accessory non-medullated nerve-fibre (af) is not degenerated,

«

1) See note 2, p. 982.

*) Proceedings of the 9th phys. and medical Congress. Utrecht, April 1909. See
also the more detailed description in the Anat. Anzeiger 44, Band, 1913.

5) S. DE Boer. Folia Neuro-biologica 1913 and 1914,

984

and shows a normal hypolemmal nerve-ending in a muscle-fibre at
the end of one of the non-medullated nerve-fibres.

If thus we may assume this so called accessory innervating appa-
ratus of the striated muscle-fibres to be of a sympathetic (parasym-
pathetic) nature, then the following question arises immediately :
both the motor nerve-ending and the accessory nerve-endings are
hypolemmal in position, i.e. the nerve-fibre passes through the sarco-
lemma and enters the muscle-fibre, being imbedded in the granular
substance of the sarcoplasma, aud directly continuous with the
intraprotoplasmatie reticulum of the periterminal network. Now itis
generally assumed, that the efferent sympathetic nerve-endings do not
enter the plain muscle-cells, but terminate by tapered or bulbous extre-
mities which are applied to the outer surface of the cells. Why should
there exist such a curious contradiction between equivalent elements ?
Why should the accessory nerve-ending in the voluntary muscle-fibres
(when of sympathetic origin) be hypolemmal, and the sympathetic
nerve-ending in plain muscle-cells remain on the outside of the inner-
vated elements? We will try to show, that there is no such contra-
diction, and that the efferent nerve-endings in plain muscle-cells have
exactly the same position as the accessory nerve-endings, which give
the striated muscle-fibres their tonic impulses.

In general the modes of termination of the efferent nerves in
involuntary muscles are rather difficult to study. The Golgi-method
and staining with methylene blue often procure splendid results,
but these methods do not allow to give a definite answer as to the
exact relations between the nerve-endings and the plain muscle-cells.
Apart from earlier aberrant accounts, that localised the terminations
of the nerve-fibres inside the cell, even inside the nucleus and the
nucleolus (THANHOFER, lastly Osrecia in 1890), all the observers
agree (I need only mention the names of Köruker, Lowit, Eric
Mürrer, Huser and pe Wirt, S. Rerzius), that the efferent nerves
of the plain muscle-cells form complicated plexuses between the
elements of the involuntary muscular tissue, in which the nerve-
fibres bifurcate and give off branches at frequent intervals, and then,
either united with those from adjoining nerve-fibres or not, come
into close relation with the plain muscle-cells themselves, either
terminating by tapered or bulbous extremities which are applied
to the surfaces of the cells, or ending in networks and loops, without
having free extremities.

Thus even the last observer in this field, AGABABOW *), who studied

1) A. AcaBaBow. Ueber die Nerven der Augenhäuten, v. Graefe's Archiv für
Ophthalmologie, 83. Bnd, 2. Heft. 1912,

J. BOEKE: “On the termination of the afferent nerves in plain muscle-cells, and
its bearing on the sympathetic (accessory) innervation of the striated

muscle-fibre.”’

en im

Fig; 2.
Terminations of the different nerves of the Musculus Ciliaris
of the human eye.
ab = sensory terminal buds.
c = neurofibrillar network between the musclecells.
d—h = efferent motor intracellular endings.

Proceedings Royal Acad. Amsterdam. Vol. XVII.

985

the distribution and mode of termination of the nerve-fibres in the
corpus ciliare and the adjacent membranes of the human eyeball,
states, that “in keinem einzigen seiner Praeparate je etwas zu
sehen war, was als ein unmittelbarer Zusammenhang des Nerven-
fadchens mit dem Protoplasma, dem Kern oder gar dem Nucleolus
der Muskelzellen zu deuten wäre”.

AGABABOW, as I mentioned before, studied the innervation of the
corpus ciliare. This led him chiefly to a confirmation of his earlier
observations on the same subject in the year 1897. In the corpus
ciliare of human eyes and of the eyeballs of albinotie cats AGABABOW
demonstrated the presence of the following nerve-terminations :
1. endorgans of the motor nerves in the plain muscle-cells of the
musculus ciliaris, 2. vasomotor nerves for the ciliary bloodvessels,
3. terminations of afferent sensory nerves in the corpus ciliare,
4. terminations of afferent nerves in the lamina suprachorioidea,
which covers the corpus ciliare as a loose soft membrane of areolar
connective tissue at the outside. As for the motor nerves of the
musculus ciliaris, they appeared in his preparations of cats’ and
mens’ eyes (Golgi- and methylene blue-preparations) as numerous
fine varicose threads running between the muscle-cells; at different
points, always outside the cell-boundary, the nerve-fibres terminate
and the ends are applied to the cell-surface. This however is after
the observations of AGABABow not yet the real ending of the nerve-
fibres, for sometimes he could see one of these delicate fibres bifur-
cate again and the two exceedingly delicate terminal branches could
be followed around the muscle-cell, encircling it on both sides. From
these observations AGABABOW draws the conclusion”): ‘dass eine
jede Muskelzelle von einem Netze sehr feiner Nervenfaden umflochten
wird; hierbei stehen die Nervennetze der Nachbarzellen noch durch
2—3 Fadchen unter einander in Verbinding. Diese Endigungsart der
motorischen Nerven in Gestalt eines perizellulären Netzes, welches
eine jede Muskelzelle umspinnt (ohne terminale Anschwellungen)
ist mit grosser Wahrscheinlichkeit eine fiir die motorischen Nerven
der glatten Muskulatur (Sphincter iridis, Gefässe, Darm) allgemeine
Erscheinung”’.

AGABABOW studied the innervation of the corpus ciliare by means
of the Golgi-method and intra-vitam staining with methylene blue.
Now this account of AGABABow coincides entirely with what I have
seen in a number of Golgi- and methylene blue preparations of the

1) le. p. 355.
2) lie, p. 358. cf. Tmtoresew 1896.

986

muscular coat of the intestine and of bloodvessels. The pictures only
vary on account of the presence or of the distribution and number
of the so-called terminal buds. Preparations after these methods are
not sufficient however to study the intrinsic relations between nerve-
endings and miuscle-cells. For this we need thin (5—10 u) serial
sections of material sharply stained after the neurofibrillar staining-
methods of Casati or Birnscnowsky and counterstained by Haema-
toxylin and Eosin or Orange G. Unfortunately these staining-methods
generally give only mediocre results, when applied to involuntary
muscle-cells, and even in the best preparations the nervous plexuses
between the muscular elements may be stained very sharply, but
generally the final terminations are either not stained at all or take
such a light stain, that it is impossible to draw any conclusions
about the real relations between the nervous and muscular elements
from them.

Some time ago however I got at my disposal, thanks to the
kindness of Prof. P. Ta. Kan, the director of the oto-laryngological
section of the academic Hospital of our University, a freshly-enucleated
normal human eye, which immediately after having been enucleated,
had been put into a large quantity of neutral formaline-solution
pres

Parts of the corpus ciliare and iris of this object were treated by
the method of BrerscHowskKy, and these preparations turned out to
have taken such a splendid stain as I had never yet met with in
any of my neurofibrillar preparations of plain muscle-cells. Beside a
very good preservation of the different histological elements the
sections showed a _ perfect and strong colouring of the nervous
elements, of which even the finest ‘terminal fibrils and endings
were visible as extremely delicate black lines, the thinnest of which
were scarcely visible except under the highest power, but still stained
a dark brown.

In this object I studied the relations between the nervous elements
and the muscle-cells of the corpus ciliare. Serial sections (4—20 u)
were made through the corpus ciliare and iris in a transverse or a
tangential direction. As a counterstain for the nuclei and the proto-
plasm were used haematoxylin and eosin or orange G. Especially
the tangential sections through the musculus ciliaris were very
instructive.

Letting alone for the moment the sensory innervation of the sur-
rounding tissues, which need not be described here, we find, on turn-
ing our attention to the musculus ciliaris, two different systems of
nervous terminations between the muscle cells. In the first place a

987

loose plexus (at places perhaps a network) with wide meshes of
nervous non-medullated or partly medullated fibres, that end in
distinct sheathed bulbous or coiled-up terminations; some of these
are shown in fig. 2 (a and 6). Since these nerve-fibres and their
terminations lie in the connective-tissue around bundles of the
plain muscle-cells and remain entirely independent of the muscle-
cells, they must be regarded as the free nerve-endings of sensory
nerves, which are already described by AGaBaBow as being distri-
buted in large numbers throughout the whole of the corpus ciliare.

In the second place we see in the musculus ciliaris a very fine
plexus and network of very fine non-medullated nerve-fibres, with
small meshes, lying between the muscle-cells, which at first sight
seems to be of a bewildering complexity. Only gradually one learns
to find one's way in the mass of extremely delicate black-stained threads
running to and fro between the muscle-cells, and then it becomes
clear, that this plexus contains in the first place the network described
by AGaBaBow, consisting of fine varicose nerve-threads, running
between the muscle-cells, surrounding these cells, encircling them
with smaller and longer meshes of extremely delicate fibrils and
more or less thickened points of junction. At these points, visible
in methylene blue-preparations as knots of a homogeneous blue colour,
the neurofibrillar apparatus appears, when studied under the highest
power, to be broken up into an extremely fine network of fibrillae.
In fig. 2 at c a mesh of this network, magnified 2100 diameters
is drawn. This network is the terminal network of AGABaBow. But
now a close study of the sections soon reveals the fact, that this
network, which encircles the muscle-cells, is not the terminal nervous
apparatus. From the nerve-threads composing the meshes of this
network, lying between the muscular elements and encircling them,
are branched off at all points extremely delicate neurofibrillae, fine
filaments having only a diameter of several millimicra, but appearing,
thanks to the splendid impregnation of the sections, as distinctly
visible black-stained threads of the greatest tenuity. Only these threads,
that form a second network or plexus, exhibit the ring-shaped
varicosities, the end-rings and small terminal nets, which must be
regarded as the real terminations of the nervous apparatus. Some
of these end-rings are drawn from the sections in fig. 2, d—/. But
the fact, which interests us chiefly here, is that these end-rings (the
termination of these final nervous branches is chiefly in the form
of small rings or loops) are found lying @traprotoplasmatically inside
the muscle-cells, and the fine fibrillae, composing this second network,
form a reticulum in the protoplasm of the muscle-cells, encircling

988

the nucleus, running between the myofibrillae of the cell, and thus
showing their intracellular position, finally giving off branches, that
are so exceedingly fine and form such small mehses, that they cannot
be distinguished from the protoplasmatic reticulum of the cytoplasm
of the muscle-cells itself. Indeed, one gets the impression, that these
finest terminal branches, given off by the delicate threads of the
intraprotoplasmatic neurofibrillar reticulum, described above, are in
the end nothing else but the protoplasmatic reticulum.

That this intraprotoplasmatie neurofibrillar reticulum with its ring-
shaped varicosities and end-rings or terminal nets at the end of
short twigs in reality lies inside the cell in the cytoplasm and
not applied to the surface at the outside of the cell, may be demon-
strated in the first place by the following fact. The muscle-cells of
the musculus ciliaris are not always compact, but especially in the
inner part more loosely arranged, so that in tangential sections
through the inner parts of the corpus ciliare one often sees muscle-
cells lying entirely isolated in the connective tissue. In these cases
it is easy to determine whether the second neurofibrillar reticulum,
mentioned above, lies inside the cytoplasm of the muscle-cell or
simply surrounds the cell at the outside, and the intraprotoplasmatic
position of this second reticulum with its ringshaped varicosities and
end-rings, together with the very delicate threads passing from this
netwerk into the protoplasmatie reticulum could be established with
accuracy. Still, there is room for doubt, for a bundle of two muscle-
cells might be cut lengthwise and it might be possible, that what
was thought to lie in the cytoplasm, in reality was lying just
between the two muscle-cells.

But the conclusion that the terminal branches of the neurofibrillar
apparatus together with the terminal rings are intraprotoplasmatic
in position is placed on a perfectly sure basis, when cases are found
as are figured in fig. 2 g and /. Here we see the small terminal rings
and nets of the second neurofibrillar network lying so close to the
nucleus of the muscle-cell, that they even make an indentation into
the nucleus, and thus are found lying in a shallow hole in the side
or on the top of the elongated nucleus (fig. 2 g and h). Such cases
are not rare in my preparations, indeed in nearly every section
through the musculus ciliaris were found one or two of them; they
can only be explained by adopting an intraprotopiasmatic position
for the neurofibrillar rings. In many of these cases the connection
of the rings, lying in the indentation of the nucleus, with the neuro-
fibrillar network could be observed with perfect accuracy, and in
several cases the direct connection of this intraprotoplasmatic neuro-

989

fibrillar network with the network lying between the muscle-cells
on one side, with an exceedingly fine protoplasmatie reticulum on the
other side, losing itself in the cytoplasm, could be seen with ereat
clearness.

Thus the apparent controversy between the relations of the accessory
nerve-terminations and the striated muscle-fibres on the one hand,
of the sympathetic nerve-terminations and the plain muscle-cells on the
other hand, is seen to disappear. In the plain muscle-cells we find
the same identical relations of nerve-endings and sarcoplasm as in
the striated musele-fibres. In both elements the neurofibrillar appa-
‘atus penetrates into the protoplasmatic (sarcoplasmatic) cell-body,
forms the terminal nerve-endings inside the cell-body as small
end-rings and loose netlike extremities or varicosities, and is in con-
tinuous connection with a very delicate protoplasmatie (or intra-
protoplasmatic) reticulum, the periterminal network.

Leiden, December 1914.

Anatomy. — “On the mode of attachment of the muscular fibre to
its tendonfibres in the striated muscles of the vertebrates.”
By Prof. J. Borkr.

(Communicated in the meeting of December 30, 1914).

Where the cross-striated musclefibres end in a tendon, the tendon
“becomes subdivided into as many small bundles as there are fibres
in the end of the muscle, and each separate musclefibre has its
separate small bundle of tendonfibrillae, to which it is attached. It
often seems at first sight as if the tendon-fibres are directly continued
into the muscular substance, but until recently it was generally
admitted, that the fibres of each tendon-bundle ended abruptly on
reaching the rounded or obliquely truncated often somewhat swollen
extremity of a muscular fibre, and are only so intimately united to
the prolongation of sarcolemma which covers the rounded extremity
of the muscular fibre entirely, as to render the separation of the two
diffieuit if not impossible, while the muscular substance, on the other
hand, may readily be caused to retract from the sarcolemma at this
point as at other points of its course.

While thus it was until recently generally admitted, that the
extremity of a muscle fibre was covered entirely by the uninterrupted
sarcolemmal membrane, in the year 1912 O. Scnurtze *) and after
him several of his pupils published the results of observations of a

1, O. ScHuLttze. Ueber den direkten Zusammenhang von Muskelfibrillen und
Sehnenfibrillen. Arch. f. Mikrosk. Anatomie, Bd. 79. 1912. pag. 307 —351.

990

different nature, viz. that at the supposed end of the muscle fibres,
where the fibres are attached to the tendon, the myofibrillae are
directly continued into the tendon-fibres and the sarcolemma is not
closed at the extremity of the muscle fibres, but perforated by the
myoftibrillae, these being directly continuous with the fibrillae of the
tendon. According to these statements we should find in the striated
muscles the curious disposition, that protoplasmatic, strongly diffe-
rentiated, intracellular fibrillae, the myofibrillae, would be directly
continuous with collagenous connective tissue-fibrillae, which are formed
eatracellularly by special connective-tissue cells, the fibroblasts.

It is easily understood, that such an opinion would not remain
uncontradicted, and thus the publication of the paper by ScHULTZE
mentioned above has called into life already a pretty large number
of papers on the same subject; and indeed, one should think twice
before joining in a strife about such a difficult problem, and which
is not always conducted with the impartiality and courtesy held so
high in scientific discussions. And the writer of the present paper
surely would not have entered the arena, if it were not, that
his observations, which are recorded in the present paper, according
to his opinion, are apt to show, that in both statements there is an
element of truth, as far as the observations go, made by ScHULTZE
and his opponents in their preparations of adult muscle fibres —
though the line must be drawn here, and in reality the truth seems
to lie not in the middle, but on the side of the opponents of ScHuULTzE,
the interpretation of his observations being wrong.

Undoubtedly longitudinal sections of adult musclefibres often seem
to show a mode of attachment to the tendon-fibres corresponding
exactly with the drawings and statements made by ScnuLrtze and
his followers, and when studying a great number of well-preserved
and well-stained sections of muscle- and tendonfibres, as I did in the
course of the last ten years’), one is often tempted to doubt the
truth of the theory of the discontinuity of the muscle- and tendon-
fibres and the closed appearance of the sarcolemma ai the extremity
of the muscle-fibres.

Again and again one tries to find the boundary line of the sarco-
lemma without getting definite results, and surely the paper by
SCHULTZE would have been hailed as containing the long sought-
for solution of this histological problem, were it not that the study

1) Even as long ago as 1901 I made a series of sections through the musculature
of small salmonidae, which seemed to show with exquisite clearness the direct
continuity of muscle- and tendon-fibrillae.

991

of the ontogenetic development of the musele-fibres always brought
me back to the old, time-honoured theory.

But I must add immediately that even for the adult muscle-fibres
the study of the admirable preparations made by Miss Dr. M. van Hrr-
WERDEN, Which she had the kindness to show me in my laboratory,
left no doubt as to the truth of her observations against the state-
ments made by Scuuttze and his pupils. Both the sharply-stained
extremely thin sections and the preparations in which the muscular
fiber was digested by means of a trypsine-solution '), the sarcolemma
and the tendonfibres however left intact, demonstrated very clearly
the discontinuity of the elements in question.

It seems to me, that the solution of this problem is given by the
ontogenie development of the musecle-fibres, and even here the
minute details are not always sufficiently clear to give a definite
account of the development of the muscle-cells in relation to their
mode of attachment to the tendon-fibrillae.

Splendid material to work with in this direction is given by the
developing myomeres, the trunkmyotomes of several teleostians,
and especially in meraenotds the details of the developmental processes
are shown with the utmost clearness. Of muraenoid eggs and larvae,
preserved after the best methods, and cut into thin (4—6 «) longitudinal
and transverse sections, stained with iron-haematoxylin and counter-
stained by eosine, our laboratory possesses a large collection of
more than a hundred specimens, and at the hand of this series -of
preparations I will give here an account of the development of
the* muscle-fibres of the trunk-myotomes.

The general development of the trunkmyotomes, the changes in
form and size, the differentiation of the musele-cells, have been
described very fully and illustrated by a large number of drawings
in the inaugural dissertation of Dr. A. Sunier’), so I need not
enter into these details here. The first evidences of muscular different-
iation consist of the lengthening of the cells of the myotome, until
they reach from one end of the myotome, the cranial end, well into
the mass of cells toward the other end. The nuclei of these cells
alter their staining reaction and begin to divide amitotically,

h The opposite results, obtained by SecHuurze in his digesting experiments, are,
as Dr. vAN HERWERDEN tells me, due to his having used an alkaline solution of
trypsine and not tlie neutral one, he should have used to leave the collagenous
fibres intact. ,

2) A. J. L. Sunter. Les premiers stades de Ja différentiation interne du myotome
et la formation des éléments sclérotomatiques chez les acraniens, les sélaciens, et
les téléostéens. Inaug. Dis. Groningen. Brill, Leiden 1911. Has been published
also in the Tijdschrift der Nederl. Dierkundige Vereeniging Jaarg. 1911.

992

at a rate which greatly increases the number of nuclei without
dividing the cell body. This latter grows longer until it reaches
from the anterior to the posterior boundary of the myotome, while
its numerous nuclei are stretched in a single row (in a sagittal
section through the body of the larva) from one end to the other.
The cells have changed from mononucleated embryonic cells into
the elongated and multinucleated sarcoblasts.

In these sarcoblasts the muscle fibrillae, the myofibrillae, now
begin to appear in the protoplasm. At this stage each sarcoblast
appears as a flat, multinucleated, plate-like cel!body, surrounded on
all sides by a very delicate but clearly defined thin membrane, the
sarcolemma. In each myotome these flat, plate-like sarcoblasts are
arranged very regularly in a row as the leaves of a book, so that
their broad sides are lying in the frontal plane of the body. They
all reach from one end of the myotome through its whole length to
the other boundary of the myotome. At the end of the myotome
the rows of the thin rounded edges of the muscleplates nearly
touch the homologous extremities of the sarcoblasts of the foregoing
or following myotome.

When we now study these boundary-surfaces between the myotomes,
where the corineetive-tissue myoseptum is found in older forms and
in the full-grown leptocephali, in thin sagittal sections through the
larval body, in which sections therefore the sarcoblasts are cut
longitudinally and at right angles to the broad surface of the plate-
like cellbody, it is always the same sort of picture we get to view.
The protoplasmatic’) cellbodies of the sarcoblasts, appearing, when
cut in the direction mentioned above, as long regular rod-shaped
elements, are separated from each other by very thin but clearly
defined boundary-lines, running exactly parallel to each other,
and at the extremity of the myotome these boundary-lines follow
the rounded ends of the sarcoblast in an extremely regular curve,
which runs very clearly and distinctly around the entire end of the
sarcoblast. There is no interruption of this boundary-line whatever
to be seen. Thus all the sarcoblasts of the two myotomes in question are
standing with their rounded and perfectly isolated endings in two
opposite rows, and they are generally arranged in such a manner,
that the ends of the sarcoblasts of one row alternate with those of
the sarcoblasts of the other row, belonging to the second myotome,
and thus the space between the two rows of sarcoblasts is reduced
to a minimum; in this space in a later period of development the

1) Before the appearance of the myofibrillae.

993
myoseptum is formed. In the developmental stage, which we are
studying now, this myoseptum is already to be seen as an extremely
thin (0,5—1 w) layer of a homogeneous gelatinous substance (not
an effect of shrinkage of the elements in the sections), that fills up
entirely the room between the two opposite rows of sarcoblastendings.

This homogeneous layer or film of gelatinous substance remains
in the same form and conditions throughout the whole of the
forelarval period. It is only at the end of this first period of
development, when the yolk is nearly absorbed and the small
forelarvae begin to migrate towards the bottom of the sea and to
grow out to leptocephali, that the formation of tendon fibrillae sets in.

The next step in the differentiation of the sarcoblasts consists of
the formation of the striated myofibrillae in the cytoplasm.

I will not enter here into details about the relations between the
mitochondria ‘and the myofibrillae and about the first signs of
eytoplasmatie differentiation, and only mention here, that we find
the first traces of myofibrillar differentiation in the cytoplasm of the
sarcoblasts near the extremity of the cell-bodies. And here we meet
with an important phenomenon, which in the end, as we shall see
later on, gives us the clue to the understanding of the most important
facts of the myofibrillar differentiation and the solution of the
problem of the union of the tendon- and muscle-fibrillae, which was
the starting-point of the present paper, viz. that, as the first traces
of the myofibrillae appear as small dots er rods, stained black by
the iron-haematoxylin, in the two rows of sarcoblast-ends of two
different myotomes, separated by the thin layer of gelatinous substance
of the primitive myoseptum, these dots or rods are lying exactly
opposite to each other in the protoplasm of the two sets of sarcoblasts,

In the developmental stages following the one described here, we
find the myotibrillae as long delicate threads, showing the typical
cross striation, and running parallel to each other straight from one
end of the sarcoblast to the other, congregated into two distinct
bundles, thin and flat, leaving a narrow median band of cytoplasm
between, in which the nuclei lie imbedded in the protoplasm. By
a longitudinal splitting of the myofibrillae and later on of the small
bundles, new systems of fibrils are formed *), and this accumulation
of fibrils is continued until each sarcoblast seems to be a mass of
fibrils with a central median thin layer of sarcoplasm containing
the nuclei. In the course of this accumulation-process the extremities
of the sarcoblast lining the myoseptum get broader and flatten

1) This process is described very fuily in the paper by Dr. SuNteR mentioned above.
66
Proceedings Royal Acad. Amsterdam, Vol. XVII.

994

against the latter, but they still show the same regular outlines.
The closer study of these extremities of the muscle-plates lining the
myoseptum, always in thin sagittal or frontal sections through the
larval body, brings out the following facts. In the first place, as
mentioned above, the outline of the extremity of the sarcoblast
remains as clearly defined as before, although now the sarcoblast
has lost its regular curved outline, but is flattened and broader. The
extremely delicate boundary-line of the sarcoblast (we may speak
here already of the sarcolemma) is everywhere to be followed
with great precision around the entire extremity of the musclefibre.

In the second place, even when a large number of myofibrillae
has been accumulated inside the cellbodies of the sarcoblasts, the
extremities of these myofibrillae where they touch the sarcolemma,
stand in the two rows of muscle-plates lining the thin layer of the
primitive myoseptum, always individually exactly opposite each
other, in this way, that if we follow the line of a fibril of one of
the muscle-plates through the septum into the opposite muscle-plate,
we are certain to touch a fibril there with, | should say, mathema-
tical certainty. |

As was mentioned above, the myofibrillae arrange themselves
inside the cell-body of the muscle plates into two flat bundles, leaving
a median layer of undifferentiated sarcoplasm between them con-
taining the nuclei. But at the extremities of the muscleplates lining
the myoseptum the ends of the myofibrillae touching the sarcolemma
are distributed very regularly over the whole extent of the rounded
endline of the muscleplates. To attain this regular distribution the
myofibrillae of the two plate-like bundles have to curve round a
little at their ends before reaching the sarcolemma, and it is even
by this fact, that is shown the accuracy with which nature strives
to place the ends of two opposite fibrils exactly in one line. When
we prolong the line of such a fibrilla, softly curving round to reach
the middle of the extremity of the muscleplate, in the same direction
we are certain to touch with the selfsame curve a myofibrilla of
the opposite muscle-plate. It is easily understood, that only in this
manner a regular distribution of the contracting forces and a correct
cooperation of the contracting forces of the contiguous muscle-plates
of two myotomes is attained.

From a histogenetic point of view I would explain it in the fol
lowing manner, without venturing too far out upon the unfamiliar
ground of physical theories; we must assume that through the
dividing layers of sarcolemma and myoseptum (in this stage of
development only an exceedingly thin layer of gelatinous substance,

995

less than 1 yw thick) the protoplasts of two opposite muscle-plates
exert an influence on each other, in this way that the differentiation
of the contractile elements sets in at corresponding points at the
surface (the inside of the sarcolemma) or near it, and so the myo-
fibrillae of one muscle-plate have corresponding fibrils in the opposite
cells, lying exactly in the same line. But what is the nature of this
influence cannot be discussed here.

Thus we see that the myofibrillae can be traced to the sarco-
lemma, but not beyond it, and that every fibril of a given muscle-
plate has a fibril corresponding to it and lying in the same line in
the adjacent myotome.

In the stage of development following on the one just described,
the larva greatly increases in length, and with this the myotomes
lengthen considerably. The myofibrillae inside the muscle plates still
extend from one extremity of the cell to the other, and so follow
the extension of the myotomes. *) Now this longitudinal growth of
the myofibrillae does not take place along the whole fibre, but only
at two points near the ends. There where the cross striation of the
musele fibre has been fully developed, a further Jengthening of the
fibril is not possible any more; we never see any signs of a division
of the anisotropic or isotropic portions of the striated sarcous seg-
ments, the pattern of striation is always the same in all the muscle
fibres of the different myotomes, and the breadth of the sarcous seg-
ments is always of the same order. But when we study the muscle
fibre closely along its whole course, we see that in this larval stage
the striation of the myofibrillae does not extend to the extremity of
the muscle fibre, but ends abruptly (for all the myofibrillae of a
given muscle fibre at the same point) at some distance from the
end, Here the myofibrillae of the same bundle are more or less
fused together, thickened and so a’ sort of intercalated knot is
formed, which takes a strong black stain when stained with iron-
haematoxylin; at this point of the myofibrillae we must locate the
lengthening, the longitudinal growth of the entire fibril. From this
point onwards to the place of attachment of the fibrillae to the
sarcolemma, a distance of about 10—4 u, there is no trace of a
striation visible; the individual myofibrillae are again separated,
attach themselves at different points to the sarcolemma, and here
the fibrillae take a somewhat lighter stain than in the striated part
of the fibre, and a stain which more or less resembles the colour
of the collagenous connective tissue fibrils of a later period of develop-

1) In his paper mentioned above, Dr. SunseR gives many drawings, which show
several details of the process of differentiation of the myofibrillae.

66*

996

ment. Probably it has a slightly altered chemical constitution, and
may be regarded as having not a contractile but only a mechanical
function and therefore representing to a certain extent a sort of
intracellular tendon-fibril. This noncontractile part of the myofibril
is formed as a differentiation of the extremity of the myofibrilla, is
therefore entirely continuous with the striated part of it, is lying
completely intracellular, inside the sarcolemma and attached to it at
its end. It is this relation between apparently different sorts of fibrils
which is visible in many of the figures of the paper by ScHuLTzE
mentioned above. According to the mode of development described
here, one is not entitled to draw from it the conclusions SCHULTZE
and his followers draw from their preparations.

Until now we had to do only with the intracellular fibrillar
differentiations. But at this point begins the second phase of the
development of the muscle-fibres, the forming of the tendon-fibrillae.

The thin layer of homogeneous gelatinous substance of the primitive
myoseptum between the myotomes begins to thicken, connective-
tissue cells lying between the epithelium and the myotome begin to
migrate slowly in between the myotomes and so step by step the
connective-tissue septum of the leptocephali is built up. Afterwards
these cells of the secondary myoseptum send cells down between the
muscle plates into the myotome, tater on blood capillaries follow,
and so gradually the features of the adult myotomes are laid down.
Even at the first thickening of the primitive myoseptum the differen-
tiation sets in which interests us here most of all, viz. the forming
of the tendonfibrillae, a fibrillisation of the substance of the myoseptum ,
whether under the influence of immigrating connective tissue-cells
or directly under the influence of the growing and expanding myotomes
is not to be determined. The fact that interests us chiefly here is
that in the process of formation of these primary tendon-fibrillae
essentially the same features are shown as in the formation
of the myofibrillae in the adjacent myotomes. Here likewise we see
the fibrillae, the homologa of the collagenous fibrillae of the connection-
tissue myoseptum of older forms, differentiated in direct connection
with the ends of the myofibrillae of the muscle-plates of the adjacent
myotomes. Exactly at the point, where inside the sarcolemma (which
is still visible with the same clearness around the extremity of the
muscle fibre as before) a myofibrilla is attached to it, a tendon-
fibrilla appears attached to the outside of the sarcolemma. And at
whatever point we study the differentiation of the tendon-fibrillae,
whether in the regular clearly defined myoseptum between the two
rows of parallel and close standing muscle-cells of the adjacent

997

myotomes, or at those points of the larval body, where (as is the
case with the muscular differentiations in the head and neck region
of the larvae) the muscular elements are arranged more loosely and
less regularly, and, instead of being closely packed together as is
the case in the myotomes, often end separately or in small bundles
in the connective tissue, everywhere we see the formation of the
connective tissue fibrils, the tendonfibrils, established in such a manner
{hat the tendon-fibrils are formed in direct connection with the
myofibrillae, but outside the sarcolemma.

Thus the investigation of the phenomena of muscular differentiation
in the muraenoid larva shows us the following picture of the connection
between muscle fibre and tendonfibrils: inside the muscle fibre striated
myofibrillae running through the entire length of the fibre, but losing
their striation at a small distance of the end, and being attached to
the inside of the sarcolemma at the end of the muscle fibre as a
homogeneous fibril bearing some resemblance to a tendon fibril. Then
follows the delicate line of the sarcolemma running around the
extremity of the muscle fibre, to which are inserted the homogeneous
ends of the myofibrillae; outside the sarcolemma, attached to it at
exactly the same points where the myofibrillae are inserted, appear
the tendonfibrillae, running at first in exactly the same direction as
the myofibril with which they are connected. Thus there is established
a continuity, but not in the sense of SCHULTZE.

But it is easy to understand, that as soon as the myofibrillae
accumulate to such numbers as to fill up nearly the entire cell body,
it will become extremely difficult to follow the delicate line of the
sarcolemma between those bundles of fibrils lying as close together.
And then it is we get the pictures drawn by Scrurrze in his figures
and known to us from many a preparation, in which the sarco-
lemma is clearly defined where there are no myofibrils and only
sarcoplasm is present, but in which at those points, where close
bundles of myofibrillae attain the end of the muscle fibre, no dividing
boundary-line of sarcolemma is to be seen between those bundles
and the tendonfibrils lying in the same plane and running in the
same direction. This is the continuity which in the figures of SCAULTZE
is so conspicuous and seems to be so conclusive. 1 hope | have
been able to demonstrate that at least in the case I have studied,
it is only an apparent, not a real continuity.

The observations of Scuunrzr are right, his deductions from these
must be regarded with true scepticism, and the conclusions drawn
by Dr. van HeRWERDEN from her trypsine-digestion-preparations, and
declared by Scnuurze to be wrong, are, when viewed in the light

998

of the ontogenetic development of these structures laid down here,
entirely right and founded on facts.

A direct continuity between myofibrillae and tendon fibrillae in the
sense of Scuvrrzm does not exist.

Leiden, December 1914.

Physics. — “On the field of a single centre in Kinsruiy’s theory of
gravitation” By J. Droste. (Communicated by Prof. H. A.
LORENTZ).

(Communicated in the meeting of December 30, 1914).

1. The equations which determine the field of gravitation in
EINSTEIN and GrossmMann’s theory *), are not linear, hence the field
: ol (2) oo
corresponding to the tensor ee eg (o‚v = 1, 2, 3, 4) is not the sum

3 > : (1 (2 .
of the fields corresponding to the tensors 20) and 25). The equations,
indeed, present a certain homogeneity ; when all the g’s are multiplied

by the constant factor 2 and the 2’s also, then the equations
y |

Eme in Oe oe
= Dr a 5 Ee Yes p gr 12 ar) A
bd Ce HIP wg

and

0 04 ay ~
Py Gn (v= Yada. 5e) == % (22 + to») (op = 1, 2, 3, 4) 7 (2)

„an Ox ap

remain valid, if they were so before the multiplication. But yet it
follows by no means from this that a field would be possible, whose
gs and Vs would be the 4-foild of a given field. Rather the contrary
may be said to be the case, and this finds its cause in the accessory
condition that for infinitely increasing distance to the places where
SE, differs from zero, g,,, Jas, and g,, must converge towards —1,
g,, towards c’.

These remarks suffice to make us see that the calculation of fields
of gravitation is incomparably more difficult in the new theory than in
the old. (Newron’s theory). In the latter the field may be found by
an integration; in the former theory this is impossible as appears
from the above. Now equations (2) are, however, intended to pass

1) [. Entwurf einer verallgemeinerten Relativitätstheorie und einer Theorie der
Gravitation, Leipzig bij B. G. Teusner. This treatise has been reprinted in ‘Zeit-
schrift fiir Mathematik und Physik’, Vol. 62.

Il. Kovarianzeigenschaften der Feldgleichungen der auf die verallgemeinerte
Relativitätstheorie gegründeter Gravitationstheorie. Zeitschr, fiir Math. u. Phys., Vol. 63,

399

into Poisson equations for infinitely weak fields, and so the solution
of these equations may be reduced to the solution of Potsson equa-
tions, if we content ourselves with successive approximations. We
start namely with supposing that the g’sand y’s differ little from the
values that they must have at infinity ; which comes to this that
the squares and the products of the differences with those ‘values at
infinity’ are neglected. Then we have to solve ten Poisson equations,
and we find the differences multiplied by the factor x. Then anew
correction is introduced, multiplied by the factor x’; this new cor-
rection is likewise the solution of a Poisson equation, the second
member of which has now, however, been calculated by the aid of
the first correction. Going on thus indefinitely, the whole solution is
obtained in the form of a power series in x. For the case of a spherical
body, that can be considered as an incompressible fluid, H. A. Lorentz
has calculated the field, neglecting terms which are multiplied by
x° and higher powers of x. I have tried to follow the method
used in this calculation, as I have understood it from oral commu-
nications of Prof. Lorentz, in calculating the field of two spherical
bodies at rest with respect to each other, which I hope to publish
in a later communication.

2. The calculation of the field of a single centre requires only
that of three functions of the distance to the centre, which may be
seen in the following way, given by Prof. Lorentz.

Let the origin be chosen in the centre of the attracting sphere.
It is clear that the g’s and y’s can only be functions of the distance
nm toythée centre. Let: g,, = U, 91s = 9s, ==) and;.g,, ==20. in, a point
P, lying on the a-axis. The field being supposed stationary, g,, =
=o — 4 — =O — Fi — 9, and ds reversion. Of one, of the
three coordinate axes can have no influence on ds’, also g,,, Gis;
Jas» Jai» Js; and g;, are zero. Hence

ds? = ude? + v (dy’+ dz’) + wdt?
= v (dx? + dy’? +-dz’?) + (u—v) da? + wit’.

In this expression dx? + dy?-+ dz*=dl represents the square of
an element of length in the space (a, y, 2); dz’ is nothing but dr”.
We can, therefore, also write

de = vd? Se (u—v) dr? pir ate Po Se. ND)
and this does not contain anything that refers to the particular
situation of the point P. If we had, therefore, taken P on an auxi-
liary axis ve’, ie. if we had taken P arbitrary, ds* still would have
been given by (3). If x,y,z are the coordinates of P, then

1000

av

at aye Me a gy A ny a
ip ,

oP

hence we get
‚ > 2
ds? = v (da? + dy? 4-dz”) + (u—v) & de + ce dy + — a: ) + wdt?,
r r r

in which w, v,and w are functions of 7. From the form of ds? we find
immediately for the values of the g’s the scheme

ve vy uz
v + —(u—v) | (2) —(u—v) 0
7 r 7
“! (u—v) v + a (u—v) ad (u—v) 0
rT (le
vz ye Ke
ed) eN Aan Ld 0
r r 7
0 0 0 w
A similar scheme holds for the ¥’s, viz.
0 vy ne
ga AP) 2 (P—9) pg U
(id Ue r
Ly y? yz
pal) ot alae ne) hal de Ua
UZ yz Zi
— (p—9) me ty 4 (Py) 0
r r r
0 0 0 s
In this p, g, and s are functions of 7 satisfying the relations
pega WES rs So eee

which is seen in the simplest way by choosing P on one of
the axes of coordinates.

3. In order to find the differential equations, which w, v, and w
or, what comes to the same thing, p, g, and s satisfy, we make use
of the thesis of the calculus of variations, which occurs in the second
paper of EiNsreiN and Grossmann cited above, and which states that

the first variation of [Hd is equal to

nf (2 ys fr) de.

x ey
afsp Ot x Ow,
the integration is to be performed over a region of the manifold
(v,y, 2,0), dr is an element of that region, and the variations must

In this

1001

be taken starting from the real (sought) values of the g’s and the y’s,
and so that they are zero at the boundary of the region.

Let us first calculate H. We must then differentiate the g’s and
the y’s with respect to the coordinates; then we can take all the
quantities as they are in a point of the z-axis at a distance r= x
from the origin, and thus we find

In = 5 Jaa Jas UV 9 Jaa FW 0 Yn =P sv Van = Yan SI > Yaa — 8

09,4 =) 0959 Beas: a) 0944 ae 091, = Os; Hae 0915 _ 9951 es
Oe — 9 de Ow ” Ox Open Oye de os ken
OF; et Dis bd Os = ire per ee ae. Oy; fd Oi eae a BEG
we | OR Ox Ow " Oy Oye da OE be nee

FS WO.
In this the accents denote differentiations with respect to 7; the
values that have not been given are zero.
Let us call V—g r for brevity. Then on account of (4)

Bong Sia ar nL Sd oe A ek)
We find for H

Fo}
HS Ar

pup! + ed + ws) + Aedo:

as in virtue of (4)

jee 3
gep — 4) — 9 É ener =H
pr ej p

this becomes

H=—tFp

p q 3! 4 q> 2

TE GR BRED pat EE PA

ette

We now apply the thesis of the calculus of variations to the region
Oy ETS ota ye ees

bi ’

then the first variation of [Adr becomes

tg 72 rz
óf Hat = re Aard. H = — Aa (tt) d [ Lar,
1

ry ri

Prater afl. ©
P q 8 P

re | de = PES Tav Oy pv

py

if we put

L=—H?r =} Fp

For

1002

we find
x (t,—t,) - leat (Td Te, 6a Tea Li)»
so that we get z
[ar [0 (—L) — arr (T,,dp + T,,69 + T,,4q + Tod) = 9.
Now
T= DV —g Yen Tu

and therefore in our case

cae — Vi=9 Vas Tib ’
from which follows

4, 1 Pst =)
ET en ER Faes Elis Sen and, sT „==
P q q 8
By substituting this and replacing
[6 (—L) dr by
(d (ÒL\ IL wp LU ae a (aL) PL),
sf Ps oe Pp dr 0q' oq haa Fe Os! nde 5e a

we get, as the coefticients of dp, dq, and ds must be separately zero,

* (55) — 5p OL r z d (5) OL r° 5 5)
ee a poe — x —(s - $
vr, dr 0 ' Ay ae ~ 32 mee PAU
Ee, q ’ q q (7)

In this # must be looked upon as a known function of p, q, and s,
given by (9).

The tensor 2,,:/—g possesses the same symmetry properties as gs.
Of the equations (1) only the first does not pass into an identity,
but into

Pet egia(Er+ete+csj=o. .. ©
fe q 5
if we put Eu A Sne S.

Then this equation with the three equations (7) form a system
of four differential equations for the determination of p, q, and s,
and say P, if, in connection with the nature of the substance,
we know two more relations between P, Q, and S. If eg. Q=P
and S=const., we have the case of an incompressible fluid;
Q= P, S=f(P) represents the case of a compressible liquid or gas.

1003

4. In some cases it is possible to derive another relation from
(7) and (8), in which only first derivatives occur, a socalled
first integral. For this purpose we multiply the equations (7)
successively by p’, q’, and s’, and we then add them. The result
may be written in the form

OL OL OL ÒL aL SH q ae

Al trae S aot alter e a (Zp+2te+"s).

From (6) we find that

OL OL OL cay
cage Sea ds’ ==} FD

OL p? q” s!?
so that we get in connection with (8)

d 12 13 '2 / 2 \
GIN
dr p De ne p
p ‘4 q? 3? = 5 ; dP
Ee a eet rame Q)
Pp de

For the equations (7), written in full, we find, after having
multiplied them successively by p, $q, and s,

d p! (
— (ern!) —4L—4Fp (1 — 1) a5 xn PE
dr p p/p
d !
(ero) ae apt — 1) 2 wg Dat ey, EN
r q P/P

d !
= (vr) +340 = x's.
dr 8

We now add twice the second equation to the first, and get in
this way

and

(9)

S|

ala (2 42 al NL ar EE OE = 5 GAD
dr p q

When we subtract twice (11) from 7 times (9) we find

a 12 s/2 2
(5 ae +). —!) | |-
Pp q s p
/ p' el q'? s? a \2
= Hae + 22) 4 bep iG TE. ‚) a s(1- L) | =
dr p q Pp gnd p

or

dP
—= — 2x {r° a + r° eP+Q)| 5
ar
Bor a fluid Q= £ and -
‚2 12 12 2 eT) !
ee (5 zat +5 )e— (1-2) (err? + 2) rar
Pre p Eng (12)
+ 2xr* P = const. |

In this case therefore we have a first integral. If S is only
different from zero, when 7 < #, the same thing is the case with
P and Q, whether P be equal to Q or not. For r > R (42) then
becomes always a first integral, if we put P=0O. In this case
we can get another first integral for 7 > &, by subtracting the third
equation (10) from (11), viz.:

rep(E +27 — =) = come oN, van ol ore
Ee Le

5. I have not succeeded in finding other first integrals of the
system (10); in what follows we shall therefore content ourselves
with the calculation of the approximation already found by Lorentz ;
but we shall for this purpose start from the equations (10), and
besides we shall not suppose ®,, to be constant. However intricate the
way may be in which the different quantities £,, depend on each
other and on the field, £,, can only depend on 7; hence we put

Ess = O(r).

We suppose the values of the other %’s only different from zero in
consequence of the gravitation and therefore we may suppose these
values to be zero in first approximation. We now think p,q, and s
expanded in a series of powers of x, and the expansion broken off
after the term of the first degree in x. We then find from (10),
neglecting terms with x° etc,

x

A GRE LANS Po
rd: re Ue en

From the first two equations it follows, that
rp? (p'+2q') =econst. and r? (v'—q') = const.
As p’ and q’ must be infinite for = 0, the two constants appear
to be zero, hence p’ = q’ =0 and p=q=-—1. No terms of the
first order will occur, therefore, in p and q. Further

1005

r

rs == — "fora ee a (7)
Sod Tee Ay Sa ETE
0
if we put

lor’ dr = a(r).

-

0

oo
1 te ser Gi: d
s= r.
c? er

:
Let this approximation of s be called s,. We now go a step
further, by retaining the terms with x? in p, q, s, and in the equations

(10). We may put

Hence

we
Wehe Beer
cr
We now put
fas, SG, |
which makes the third equation (10) pass into
- d 3 gi 4 Ae 7a? :

——|rr-—ter nee
dr Se ; 4 cr? °

Now, up to the terms of the first order,

Ë 3 x “a ee 3x Ca
SS et he cl 1 a ee aie En fe tee ie
ad ¢ 2c.) r?

r

so that we find
Ly Acer eT ah Ea we, fa forint.
— —(er’s) — — — —|r%c*s, |—dr | — = x70,
dr Cc a dr GT 2e dr ay A4cr? al

which in consequence of

passes into

1006
and therefore

90 00 oo oa r
a2 »
1 dd s- Kk a dr (a?
== + di 3 dr dr +1 4— | —dr).
2 3 „2 2 „2 „2 4 „2 2
c c 7 7 1 JJ r
r F a5 r 0

At a great distance from the attracting centre we may put
a=a,, (constant) and 9 = 0. In this way we get

If we now put

1 pee ree
zate f5 n= |,
u

we may write 4k°/c'a, for x? in the last term of s, and so we find

1 i 2k ok? a
5s — rs + ee + Zer? . . . . . . ( )

We further put

p=—1+5,¢=—-—1+7.
The first and second of the equations (10) then become
be 4 “a AGN:
= (6) = AED
Aer” c
EN xa? * Ont
— (r°n 2 (En) — ——- = — Qr",
dr an) 5) ed ae:
from which it follows that
nae
<I Ek m= A (P+ 29475
» (15)
dare z was
=i Ee = 7) =e == 1 (P—Q —
Ip 2074 5,2,2°

in this P and Q must be calculated up to the terms of the
first order, which can take place by the aid of an equation, that
follows from (8) viz.

if one more relation is given between Pand Q If e.g. P=, then

AL

eo}
5 ene xr ("ao
= + 2n Ts 5 Sas + === aodr = a dr,

4c?

£ r

,

oo
a wip? “a? yx? ad
§ — y= —— | — dr + — fa’dr.
el r° dl

r 0

But whatever may be the particular properties of the central
body, we can put P= Q=o=0 and a=a, at a large distance,
in consequence of which we find from (15)

xa. a 3B
5 — 2 is ——
ers en 3 : Sy hae os pee

8c? 7?

in which B is a constant of the second order.
From this it follows that
x a 2B B
p=—l + — + OSS a eee:

8 c? r? r? r

6. We shall now examine how a particle moves in the field of

a single centre.
The motion is determined by a principle corresponding to that

of HAMILTON, viz.

to to
sf Lam deM ge tel verver gnd.
ty t
In the case under consideration, we have
ds? = v (da? + dy? + de?) + (u—v) dr? + wdt’.
If we introduce polar coordinates r, 3, p, we get
ds* = wdt? + udr* + vr? dIJ* + vr’ sin? H dy’,

hence

L=Vw es ur? + or? B? +L cr? sin? 9 p°.
One of the three equations of motion is

a(aL\_,
ase

which shows that if ¢ once is zero, it remains so; we see from this
that the motion takes place in a plane, and, knowing this, we can

~

choose the coordinates so that this plane becomes the plane 9 ==.

md

Accordingly

L=Vw a ur? + or g?

and the equations of motion become:

d
dt Or Or dt Òp 5

The equation of energy

1008

- OL 0
L — r — — Pp — = constant
Or Op
and the equation |
OL
— = constant
og

are first integrals, which together can replace the equations of
motion. If we call the first constant / and the second Ah, then

w

oh (17)
Vw + ur? + vr? p'

and

—v

ep =A:
w

<4 (RR)
By these two equations p and 7 are given as functions of ¢;
(18) presents close resemblance to KerPrer’s second law.

Eliminating y from (17) and (18), we find

apy rn Ar
ul — | — w* | — —_—- ]—w
dt h?

vr” ;
by which r

is defined as a function of ¢; (18) then gives p as a
function of f.

In the case that the orbit just extends into infinity, r dr p*,
and also ur? + vr? g* must be zero for r=—= ce, hence h—c accord-
ing to (17). If h<ec, then 7 remains finite, and if h >c, the
velocity is different from zero also for infinitely increasing 7.

The orbit may also be circular; as in virtue of (18) y is constant

in this case, dL/or will be constant, and the first equation (16)
shows that

OL ‘
‘an 1
RENE:
dw = d 2 0
— gp? — (vr?) =
dr Sa dr (or)

by which the angular velocity is determined as a function of 7.
fe

In order to examine closer the motion of a particle we
make use of the approximations for wu, v, and w, found above. If
we put in (17)

== Ts

2k
w——c?{ 1 — —}],
er
we get, expanding the root,

k r? +. 7? op? h
— Sted ey ae
or 20” c EE,
and from (18) we find, by putting v=—1 and w=c?,
r? 7 Ane ana ke oe et (LOO

The formulae (17a) and (18a) lead to the ordinary planetary
motion as described by Keruer’s laws. We now sball go a step further
with the approximation. Equation (17a) shows that %/cr? and
7? + 7? g?/c? are of the same order of magnitude; both quantities
are small, as the second represents the square of the ratio of the
planetary velocity to the velocity of light. We shall call these
quantities (also 1—h/c) of the first order of magnitude, and we
wish to retain in (17) also the quantities of the second order of
magnitude. For this purpose we still need not go further in wand v
7, and are
of the second order of magnitude, but would give terms of the third
order of magnitude in (17), because they occur there multiplied by

than to terms without x, as £ and y contain the factor x

r? and 242. The motion of the material point will, accordingly,
not depend on the special properties of the substance of the
attracting body.
Let us now put for brevity
h
1——-=l/, w= c*(1--d+8),
C
in which / and d are of the first order, ¢ of the second order in z.
We now expand the root in (17), and omit terms of higher order
than the second; this implies that in the terms of the second order we
may apply equation (172), ie.:
r? ay 2
See ey ae
C
in order to eliminate 7” + rg? from the terms of the second order.
The result is

rit pg? = — 2c (1+3l) + ed(1 44) — et(etd"). . (17%)
To proceed a step further with the approximation in (18), we
need only put v=—1 and w= c?(1—4); this gives
pip = Ace a OL Nee ay
In connection with this we may write for (17°)
(5) + aoe ee
r\dp) | r At At? | Ate?

As ws=1 we get
1
heit {1+d-+(d?—e)}.

67
Proceedings Royal Acad. Amsterdam. Vol. XVII.

1010

If we compare this with (14), and moreover put r3;=1, then
BE NEE =
B HS) = Tr gags Ot Ea ot opaae

The function
S= a + Beos y(y+C)
solves this differential equation by suitable choice of the values
a, B, and 7; we can take the integration constant C'to be zero, as this
choice only determines from where we measure g. The function
S= a + Beos y¢
satisfies the differential equation, if
- (14-2) = 2 _ 2) 4,2 aoe Ba Dh A
en ee y (raat
Instead of the integration constants 7 and A, which we introduced
before, we can now consider « and 3 as such. y differs from 1
only in terms of the second order, and therefore the equation
k
Die wre
is accurate up to terms of the second order.
We may, therefore, use the value of A’c*, which follows from
this, for the caleulation of y, and so we find

2

bk
y=l— 2 a,
and from this
] dk
—_—1=>—a.
Y 4e?
If we now put yp ==, then
ok

aia
and

1
SBER oe 8. aa
E

This is the equation of a conic section in polar coordinates.

The angle 5 hkay/4c?, between the major axis and the fixed
line gy =O, is proportional to the angle wy, between the radius
vector and the major axis. For one revolution the ‘motion of the
perihelium’ is 450 ke/c* degrees; it depends only on the parameter
l/a of the orbit. As Prof. pr Srrrer has calculated from equations
of motion determined by Prof. Lorentz, it amounts for Mercurius
to 18" per century, the observed motion being 44”. It is
worthy of note that the motion of the perihelium does not depend

1011

on the particular properties of the substance of which the centre of
‘attraction consists.

The time of revolution 7’ (the time in which g increases by 22)
can easily be calculated. It follows namely from (18) and (19) that

; 2k
dp = Ac*y (a+8 cos w)? {1 — — (4+ eos wi,
Cc.

and from this, accurate up to quantities of the second order of
magnitude,

dy 2k dw
Ac*ydt = —_—_—_—— + — ————_.
(a+B cosy)? cc a+Pcos wp
From this it easily follows, that

Wer 2n a 4 k
if Verg? a? — B? ce)

Let us call a half the major axis of the ellipse, then

and we get

k En rn k
a Kr : Sata

T depends therefore still exclusively on the major axis of the orbit;
this is, however, not the case with the time of revolution in the
ellipse. In the first member we may substitute 42°a*/c’ Tl tor hea

and thus we get
her ara le 7 k
a = |: : en
AET An?

instead of the third law of KEPLER.

Chemistry. — “On gas equilibria, and a test of Prof. J. D. vas
DER Waats Jr.’s formula’. I. By Dr. F. B. C. SCHEFFER,
(Communicated by Prof. J. D. van per WaaLs).

(Communicated in the meeting of Dec. 30, 1914.)

7. The equilibrium I, = 21. (Continued).

In my preceding paper') I have shown that from the determi-
nations of the iodine equilibrium the value 0.41 10-° em. follows
for the radius of inertia of the iodine molecule; the iodine disso-
ciation can therefore be represented by equation 8, when 2= 15u
and log M = — 38.20 are there substituted. That this equation
sufficiently represents the experimentally found values, appears from

. 1) These Proc. 17, 695 (1914/15).
Gi*

1012

table V, in which the value 34690 cal. has been chosen for Yn Ero
so that in my opinion the most probable expression for the disso-
ciation constant is as follows:

972

7589

1 Bik
log K = — 5 + > log T + log (1 T ) + 1.887 . (13)

TABLE ME

= ia oe l
f(Cels) | „Tor K (found). log K (calc.) difference

|

800 | 1073 | 0.111—4 | 0.104—4 | — 0.007
|

900 |. 4173 | -0,692-A4 | .0.708=4 | 40-00
1000 1273 | 0.199—3 | 0.206—3 | + 0.007
1100 | 1373 | 0.639-3 | 0.634-3 | — 0.005

1200 1413 | 0.009—2
| |

0.003 —2 | — 0.006

The diserepancies between the found and the calculated values
are smaller than the errors of observation.

8. Before proceeding with the calculation of chemical equilibria
by the aid of the expressions for the gas entropy mentioned in § 2
and Prof. vaN per Waats Jr.’s expression mentioned in § 4, I will
discuss the results at which Stern has arrived in his paper, which
I mentioned in the “Postscript” of my latest communication.

The expressions for the gas entropy used by Srern, deviate in a
very essential point from those mentioned in $ 2. The entropy of
a gas is determined by Srern with respect to the solid state at
T—O as zero condition. The expression for monatomic gases
agrees with equation 1 of my first paper, when there the value

3 5
7 ln 2 + R-+S solid at T=0
js substituted for C,. In the same way the value of a di-atomic
Roy 2
gas is indicated by equation 2, if En R + Ssotid at T=0-') is taken for

C,. It is clear that in contrast with the application of the entropy
values of § 2, therefore according to Stern the algebraic sum of the
entropies of the solid substances at 7’=0 occurs in the expressions

1) Besides Stern takes the vibration in the diatomic molecule into account,
which in equation 2 necessitates the addition of an expression with v. Also the
variability of the specific heats is therefore taken into account with this expression,

1013

for the equilibrium constant of the gas equilibrium. Hence whereas
the expressions of § 2, which were exclusively derived from gas
properties, leave the value for the entropy of solid out of account,
and the calculations of the gas equilibria have nothing to do with
the solid state either, so that the determination of the entropy of
solid according to S=k log W remains a separate problem, the test
of STeRN’s expressions can give a decision of the validity of Nurnst’s
theorem of heat. If we assume Srern’s derivations for the gas
entropy to be correct, then on application to the iodine equilibrium
it appears that the algebraic sum of the entropies of the solid sub-
stances at 7’=0O is not zero, which it ought to be according to
the heat theorem, but about — 7. In this test it is assumed that
the moment of inertia of the iodine molecules has the value that
would follow from the mean molecule radius for iodine (from the
index of refraction). We have here, however, two quantities at our
disposal: the moment of inertia and ='S,.ia. It is clear that reversely
the assumption that the sum of the entropies of the solid substances
at T=0 is zero (through which this algebraic sum disappears from
the constant of equilibrium and the expression deviates from that
of Prof. van per Waars Jr. only in this that it is assumed in the
former that the specific heat of the vibration has already reached
its amount of equipartition) changes the value of the moment of
inertia. On this assumption it gets about the value which was
indicated in my first paper.

9. The objection advanced by STERN against a small moment of
inertia, is founded on the value of the chemical constant of /,, which
was calculated by Sackur on the assumption of the mean molecule
radius (from the index of refraction) for the moment of inertia, and
with which the vapour pressure values of solid iodine can very
well be represented as appears from Sackur’s test. *) In virtue of
this, however, I do not think myself justified in rejecting the moment
of inertia calculated by me.

The said test of the vapour pressure line has been carried out
by Sackur on simultaneous assumption of the expression 2 of § 2
and of Scolid ar T=0 = 0. We are then led to the question whether
these two assumptions are identical or in conflict with each other.
Discussions with Prof. van per Waats Jr. concerning this question
have led us to the following opinion. If the entropy of a gas is determined
by means of log W, the expressions 1 and 2 of § 2 are found for

1) Sackur, Ann. der Physik (4) 40 87 (1913).

1014

it; these values are entirely independent of the entropy of the solid
substance. The gas entropy is namely found then by examining the
probability of the gas state; if this is done at temperatures where
solid substance is impossible, so far above the melting-point, the
chance to a solid configuration must be entirely excluded. When the
iodine equilibrium is tested, where the temperatures amount to
1000° K. and more, the chance to solid substance (melting point
387° K.) may certainly be put zero. And therefore the expressions of
Sackur, TeTRODE, and vaN DER Waars will in my opinion yield the
correct values for the moment of inertia, and the test remains entirely
outside the theorem of heat, in whatever form it be.

If, however, for the entropy of gas i log W has been chosen —
I will call these values the gas scale for the entropy — it is the
question what will be the entropy of solid. This value might

d
either be determined by means of Sa or by applying the

expression k log W also to the solid state. The latter, however, is
only feasible on the assumption of one or more hypotheses concern-
ing the constitution of the solid substance; these derivations must,
therefore, certainly remain arbitrary in a high degree. For a mon-
atomic solid substance a comparatively simple mechanism may be
devised corresponding to the properties of solid *), but for multi-atomie
solid substances the model becomes necessarily more intricate, hence
more arbitrary. ”)

If it is, however, assumed, as is often done, that the entropy of
solid at 7’=0 is zero, then starting from this the entropy of other

eee Oh
states can be determined with the aid of dS=—, - This scale of

entropy, which I will eall the scale for solid, need not coincide,
however, with the gas scale in my opinion. And if it does so for
one substance, this need not necessarily be the case for all. At any
rate this coinciding of the two scaies requires experimental verification.
The only data from the literature which can furnish such a test,
are in my opinion:
1. the theoretical derivations of SrerN's gas entropy.

2. the vapour pressure line of mercury.

! gas dQ En
3. the calculation of > — for iodine.
solid T=0

1) Stern, Physik. Zeitschr. 14 629 (1913).
*) Srern, Ann. der Physik. (4) 44 520 (1914).

1015

1. Srern’s derivations rest on the above mentioned assumptions
concerning the mechanism of solid substance. Srrrn’s expressions
and those of § 2 agree in a high degree, but that in his expressions
the constant part has been accurately represented holds only for
the definite conception which Stern forms for the solid substance ').
A rigorous proof for the coincidence of the two scales is in my
opinion not furnished by this derivation.

2. The testing of the mercury line seems to plead for the coin-
cidence of the two scales. In a recent paper in these Proceedings
Prof. Lorentz carries out a similar test*). In connection with the
above I think i can state the result as follows: If coincidence of
the above mentioned scales is assumed, the dimension of the “elementary
regions” appears to be about 4%, but as the coincidence of the scales
is not proved, little weight is to be attached to the conclusion con-
cerning the extent of the “elementary regions”. This is probably a
too rigorous statement of the conclusion of the mentioned paper;
for the other difficulties which attend this testing, I must refer to
the cited paper. Let us now consider that the entropies of § 2 (of
my preceding paper) rest on the assumption that the area of the
regions is really 4’; then at least if the expressions are correct and
may therefore be applied to the evaporation, the coincidence of the
two scales would become probable for this case.

3. From the caloric data on iodine SrerN has calculated the
difference of entropy between solid iodine (/,) at 7’= 0 and gaseous
iodine (in atomic state) at 7 — 323%). Stern now uses for the
entropy of the gaseous atomic iodine the expression which was
derived by him for monatomic gases, and in which (see $ 8) the
entropy of solid atomic iodine at 7’=0O is taken as zero. It is
clear that in this way the algebraic sum of the entropies of the
solid substances at 7’—=O can be calculated.

If, however, the values of § 2 are introduced for the entropy of
atomic gaseous iodine, we do not find in this way the algebraic
sum of the entropies of the solid substances, but only the entropy
of solid iodine (/,) at 7=—0O. If, therefore, the entropies of § 2
are assumed as the correct ones, it follows from this calculation
that the entropy of solid iodine (/,) at Z’=O does not become
zero, but — 7.6. Thus interpreted, this would plead against the
coinciding of the two entropy scales for iodine.

10. With this interpretation I think I can also get agreement with
1) Stern, |. c.

2) Verslagen Kon. Ak. Amsterdam, 28. 515. (1914/15), (still to be translated).
5) Stern, Ann. der Physik. (4) 44 513 et seq. (1914).

1016

the determinations of the vapour tension of solid iodine. The “chemical
S gas —Cp + Rink — Solid T= 0

2.3 R
in which S',„s represents the entropy constant according to the gas
scale, and in which Sg r—=o is generally also put zero (which in
my opinion need not therefore be the case in the gas scale), is
3,27 according to Sacktr'). The entropy constant of the gas is
calculated by Sackur on the assumption that the moment of inertia
calculated from the mean molecule radius (index of refraction) is

the correct one. As the radius of inertia calculated by me in my
2

first paper, is at or 5.5 times smaller, and the moment of inertia

therefore about 30 times smaller, the value of S'j;, in which the
moment of inertia M occurs as RlnM*), would become Aln 30 or
6,75 times smaller when the value found by me is used. Hence if
we want to retain the value 3,27 for the “chemical constant’,
Ssolid T=o must not be taken zero, but — 6,75, which is in satis-
factory agreement with the result at the end of § 9. I think therefore
I am justified in taking this as a confirmation of the validity of my
former calculation.

constant” of iodine, which is given by C=

11. I would therefore summarize the above as follows:

1. from the vapour pressure line of mercury the entropy of solid
mercury appears to be about zero at the absolute zero point in the
gas scale.

2. it follows from the caloric data of iodine that the entropy of
solid iodine (/,) at 7 =O is about — 7.

3. it appears from the calculation of my preceding communication
that the radius of inertia of /, is about five times smaller than the
mean molecule radius determined from the index of refraction.

4. when this radius of inertia is used the test of the vapour
pressure line of iodine yields for the entropy of solid iodine a
value of about — 7 in agreement with the second conclusion.

5. the cited data do not allow of a test of the theorem of heat.

6. In agreement with the third conclusion Manprrstoot’s calcu-
lations lead to moments of inertia which are smaller than would
agree with the mean molecule radii (index of refraction, internal
friction, and b-values of the equation of state) ®).

1) Sackur, |. c.

*) These Proceedings, Vol. XVII p. 697, (equation 2).

5) ManpersLoor, Thesis for the Doctorate. Utrecht. 1914. See also: These Proc.
Vol. XVII, p. 702. (1914/15).

1017

12. Other equilibria of the type ABZ A+ B.

None of the data which are to be found in the literature on
other equilibria of the above type, allow of a sufficiently accurate
calculation of the moments of inertia.

There exists a very interesting investigation on hydrogen dissocia-
tion by Lanemurr, who coneludes to dissociation of the hydrogen
molecules from the abnormally high energy required to keep the
tungsten wires in a hydrogen atmosphere at high temperature, and
who tries to calculate the degree of dissociation from these energy
measurements. *) On account of the insufficient accuracy of the
required quantities these calculations cannot yield any but rough
values. From the values of the degree of dissociation, which LANGMUIR
considers the most probable, I have calculated the moment of inertia
by the aid of equation 4 and 4a, resp. 6 and 6a of my preceding
communication ; the limits for the values for log M found thus amount
to — 44.3 (Terrope and vaN pER Waats at À =0), and — 45.3
(vAN DER Waars at A=20u). From this moment of inertia the
value 8.10! resp. 2.5.10-" em. would follow for the atom distance.
The moment of inertia of hydrogen, however, is in my opinion suffi-
ciently accurately known to justify us in rejecting these values, and
in concluding that the values given by Langmuir, are not accurate.

Reversely it would certainly be of importance to seek an inter-
pretation of the phenomena found by Lanemuir, by the aid of equa-
tions 4 and 6 and of the value of the moment of inertia of hydrogen,
as it is found according to other methods. *).

The chlorine dissociation has been examined at temperatures
between 1760 and 2000 K. by Pier; owing to the great experi-
mental difficulties accompanying this investigation, these values are
not accurate either. °) If we calculate for this case the value of the
moment of inertia, we find values for log M varying between about
— 54 and — 37. Now we can certainly disregard the smallest values,
because they are found from the determinations at the lowest tem-
peratures, where the degree of dissociation is very small, and a
small absolute error manifests itself greatly enlarged in the equili-
brium constant. But also at the higher temoeratures the value of
log M varies too much to allow us to draw satisfactory conclusions.

The case of the bromine dissociation is somewhat more favourable.
If we apply the equations 4 and 6 to the values found by Prrman

1) LANeMuIR, Journ. Amer. Chem. Soc. 34. 860. (1912).

2) Cf. for the moment of inertia of hydrogen among others Einstein and Stern,
Ann. der. Physik. (4) 40. 551. (1913).

5) Pier, Zeitschr. f. physik, Chemie. 62. 417, (1908).

1018

and ATKINSON ') we find further that the determinations at the lowest
temperatures, where the degree of dissociation is very small, are
useless for the calculation. If the term with v is omitted from
equation 6, it can be brought into the following form for the bromine
dissociation :

3
. + — log T — 88802, % (14)

in which w represents the degree of dissociation at atmospheric
pressure. Application of this expression to the experimental deter-
minations yields the following table :

TABLE VI.
| 2nd member ATCy
t x of (14) (TC)—9 | (AT Jo
900 0.0148 | —30.039 35236
—40.75
950 | 0.0253 a ab lead tee ge
| —39.85
1000 | 0.0398 — 30.845 39266
| — 40.75
1050 | 0.0630 | —31.220 | 41304
| mean — 40.45

The thus found value of — 40.45 yields 4.10—!° em. for the radius
of inertia. If the experimental determinations do not contain great
errors, a very small radius of inertia follows from this calculation.
And this radius would be found still smaller, if the term with » was
taken into account. I think, however, that no great importance is
to be attached to this value, because the values of the fifth column
differ too much from each other, and the determinations are less
numerous and less accurate than for the iodine dissociation. The
accuracy is here again smaller, because the equilibrium lies strongly
on one side in these determinations.

13. The equilibrium 2ABZ A, + B

When Prof. van Der Waats Jr.’s considerations are applied in a
perfectly analogous way to the equilibrium 2 AB A, Bb,, we
find for the dissociation constant:

SnET—0

2
ih
Se a he = en
NA. NB: > myg.mp, M,M ee 4) 4
eee R1 a ee en (15)

2 3 U2 :
NAB map Ma al je
le KT) \l—e KT

1) PERMAN and Arkinson, Z. phys. Chem. 38. 215. 577 (1900) Cf. also: Arzoo.
Handbuch 4. 2. 233 (1913),

1019

in which J/,, M,, and J/, represent the moments of inertia, r,, r
and r, the vibrations. of the molecules AB, A,, and B,

If by the aid of the entropy values of §2 the value of K is
determined we get, disregarding the term with the r-values, an
identical expression. Hence the expressions of SACKUR, TETRODE, VAN
DER Waats Jr., and also those of Stern, when at least with regard
to the latter it is assumed that Nernst’s heat theorem is valid, yield
the same result here.

With regard to the test of this expression we must remark that
there occur three moments of inertia in equation 15, and that the
ratio of the moments of inertia can only be determined from the
equilibrium values.

The value of Sn/yp=., which naturally cannot be directly deter-
mined with the equilibrium /, 2 2/, can generally be calculated
here from the calorie data of BerramLor, THomsen, and others.

From equation 15 follows for the transformation energy :

Thay Ths
anh = SnE T= + ae Ek ie —2 aus ngs yb)

RT —_\ kT A ekT __]

2

If we, therefore, know the r-values from the specifie heats, the
value of 2n Hypo can be determined from the thermo-chemical
determination of nf. The r-terms are generally so small that they
do not cause appreciable deviations between these quantities.

At low temperatures in equation 15 the term with the frequencies
has about the value 1. The material that admits of testing, now
consists for a great part of determinations of electromotive forces of
gas cells, in winch the term of vibration may therefore be left out.
Then, however, the agreement with Sacktr’s expressions becomes
perfect, and | can therefore refer to his paper for the testing of
these determinations.') Sackur finds good agreement between the
experimental determinations and his expressions, which are founded
on the moment of inertia, which follows from the mean molecule
radii (6 of the equation of state, index of refraction and internal
friction). At higher temperatures, however, the term with vp asserts
its influence, and we shall, therefore, have to examine it; for the
sake of completeness | have inserted the values of the gas cells
also in the subjoined tables.

14. The equilibrium UHCI H, + CI.
The heat of formation of 2HCl from H, and Cl, is given by

1) Sackur, Ann. der Physik. (4) 40 101 (1913),

1020

TromseN and BERTHELOT in good agreement at 44000 cal. The specific
heats of H, and HCI differ little from 5 at room temperatnre; the
energy of vibration is, therefore, still imperceptible here. Hence the
corresponding terms with rp can be omitted in 16. The specific heat
of chlorine amounts to 8.130—1.985 —= 6.145 at 7==616.4 according
to STRECKER (for constant volume)'). This value corresponds to
2=9.5u (see eqnation 12). If this is substituted in equation 16,
the term with », appears to have no appreciable value at room
temperature either; we may, therefore, take nH and Yn Lp
equal, and for the hydrochloric acid equation 15 may be transformed

into:
SEN

: 44000 & —e “| MM,

log K= — 18717 + log ———— 5 oa — + log - Meee (17)
& aN, |
or
adonke”

MM, es 4) 9626

log —— + log —- - = log K + a + 1,458 (18)

M, % x Yoh ee vgh
Leg ELAN a EE

The experimental determinations which admit of a test of 18,
are the determinations of the gas cells of DorrzaLeK®) and Mürrur®)
and the direct determination of the dissociation of LOWENSTEIN *).

If the values found by them are filled in in 18, we find:

E ABLE Vi

" T | ER Second mem- / MM;

ber of 18 | 08 ye Observer
| | |
25 298 — 33.18 0.58 | 0.58 MiiLLER
30 °-| 303.) 3/32, 80y le OLED a RIEN DOLEZALEK
1556 | 1829 | — 5.772 0.95 0.70 | LOWENSTEIN
| |
mean 0.71

1) Srrecker Wied. Ann. 17. 102 (1882). Cf. also Pier. Zeitschr. f. physik. chem.
62 416 (1908).

2) DorezareK. Zeitschr. f. physik. Chem. 26 321 (1898). Bopensrein and Geieen.
ibid. 49 72 (1904).

3) Mürren. Zeitschr. f. physik. Chem. 40 158 (1902). Nernst. Sitz. Ber. Preuss.
Akad. 1909. 263.

4) Lowenstein. Zeitschr. f. physik. Chem. 54. 715 (1906). The value given in
the table VI has been corrected for the dissociation of chlorine into atoms. See
Nernst. Zeitschr, f. Elektroch. 15 689 (1909).

1021

In the first two determinations the v-term has no perceptible in-
fluence; in the last it has. The value of the term for chlorine will
certainly predominate here. If this is taken into account (A= 9.5 w),
MM,

Mu?

calculated from the mean molecule radii, as they are given by
Sackur, we find 0.82, which is therefore in satisfactory agreement
with the mean value 0,71. We must therefore ¢onclude, that if the
centres in Cl, and H, are closer together than corresponds with the
mean molecule radius, the same thing is the case in about the same

degree with HCl.

1S

we tind the value of column 5. When the value of log

15. The equilibrium 2 HBr 2 H, + Br,.

When for =n we substitute in 15 the value 24200 cal, which
was calculated by Osrwarp from THOMSEN’s measurements’), this
equation may be transformed into:

yh 3
MV, en iT) 5294

= log K +

IM? HART, ak : T
Deg eI =. eP

Application to the determinations of BoDENsTRIN and GeicER*) and
VocEL von FaLcKenstHIN *) here yields:

DAB EE VIJE

Ait 968. 449)

t | T | logK Second eae

| | ber of 19 Observer
30 303 | —18.43 | £01 BODENSTEIN and GEIGER
1024 | 1207 — 5.20 0.85 | VOGEL VON FALCKENSTEIN
1108 1381 | — 4.87 | 0.93 a
1222 1495 | — 4.53 | 0.98 5
|

| |
At T=303 the influence of the r-term is still imperceptible ;

M,M ; é SRA.
log 5 =, therefore, amounts to 1,01 according to this determination.
iM,

MM,

From the mean molecule radii we find log = 1,11 in good
1

harmony with it.

1) OsrwaLD. Allgem. Chem. II. 1, 110.

2) BoDENSTEIN and GEIGER. Zeitschr. f. physik. Chem. 49, 70 (1904).

$) VOGEL VON FALCKENSTEIN. Zeitschr. f. physik. Chem. 68, 279 (1909) and 72,
i15 (1910).

1022

With regard to the observations at high temperatures it should be
borne in mind that the term with rv is positive, because the influence
of the bromine vibration will be the greatest. Hence the value of
M‚M
log —

Sa
the above table. But moreover the value for log X has been calcu-
lated on the assumption that at the test temperatures bromine is not
dissociated into atoms. From the expression of the bromine dissociation
of § 12 (equation 14) it would, however, follow, that under the
circumstances of these experiments the bromine is split up for a
great part, and that thence a large correction is to be applied for
log K. This correction, however, makes log K smaller, hence the
value in the fourth column also becomes smaller, which would

3

becomes smaller than the values of the fourth column of

render the agreement with the first value of log TEN still worse. I
1
have not succeeded in bringing these determinations in satisfactory
concordance with the electromotive ones. If the correction which is
to be applied in Voce von FALCKENSTEIN's observations for the disso-
ciation of bromine into atoms, was sufficiently accurately known,
an attempt would be justified to get agreement between the values
MA

aí

Mr

1 :
a smaller value for the heat of reaction; the energy term in 19

MM,
at the lowest

Jf 2

Cal
temperature than at the higher temperatures. The consequence of
MM,
this would then be that the value of ——
My
corresponds to the mean molecule radii. But then the value which can
be derived from BertTHEeLot’s observations, and which is not smaller,

but greater than that of THomsrn, would plead against this attempt.

* by a change in Sn. We should then have to choose

of log

then yields a greater decrease of the value of log

became smaller than

16. The equilibrium 2 HIZH, + J,.

The value for the reaction energy having a very great influence
on the value of the moments of inertia also at this equilibrium, I
will try to derive this value directly from the observations them-
selves in an analogous way as in the iodine dissociation. This is
possible here because the number of observations of the iodine
hydrogen dissociation equilibrium is much greater than the bromine
hydrogen equilibrium.

When in 15 we fill in the values for the masses of the reacting

1023

molecules, and bear in mind that in HI and H, the vibration of
the atoms at ordinary temperature does not yet manifest itself in
the amount of the specific heats, but that this 7s the case for iodine,
(see § 6), so that the term of vibration of the iodine molecule will
be the predominating one, then with neglect of the r-terms for
HI and H,, equation 15 may be transformed into: .

MM, ZnEro ; ie |
En ann -==log K + log\ 1—e FT) + 2.263 . (20)

ABTT
If we now fill in the value 15u for 4, (see § 6), the observations
of STRGMÜLLER (gas cells)') and of Bopenstri (direct dissociation
determinations) *) yield the following table: (p. 1024)
If equation 20 is written in the form:

M,M Sn Tro
aen EN Te d
°F 4.571

log

(21)

in which C represents the value of the second member of 20, every
time multiplied by the corresponding absolute temperature, then ina
graphical representation, in which C is laid out as function of 77,
the observations must forma straight line. Then it appears graphically
that a straight line can be drawn through the observations with the
MM, nr :

— = 1,184 and ED 529; the observed points

4

are then spread on both sides of this line. Then follows for the
expression of the iodine hydrogen equilibrium:

parameters /og

972
529 OT
ieee dee le MRE

It will certainly be possible to make a slight modification in the
parameters without appreciably impairing the agreement between
calculated and found values; it appears from the subjoined table
that the errors in the observations at the lowest temperatures are
pretty large, but that the expression 22 satisfactorily represents the
other observations.

Dissociation determinations at high temperatures have been made
by Voer, von FaArCKENSTEIN®). They have been carried out by
measurement of the partial pressure of the hydrogen, use being
made of the permeability of platinum to this gas, and of its imper-
meability to the other gases. The equilibrium constants, which have

1) SrEGMÜLLER. Zeitschr. f. Elektrochem. 16. 85 (1910).
2) BoDeNsTEIN. Zeitschr. f. physik. Chem. 29, 295 (1899).
8) loc. cit.

Second mem-

t 7 | LOEK + term ber of 20 Observer
31.6 | 304.6 —— 21925 fe — 20,018 — 0.680 | STEGMÜLLER
55.2 328.2 — 2.692 | — 0.023 | — 0.452 i
81.6 354.6 | — 2.416 | — 0.029 | — 0.182 | '

280 553 — 1.931 0.082 | -+ 0.250 | BODENSTEIN
300 573 | — 1.905 | — 0.088 0.270 | ;
320 | 593 | — 1.878 | — 0.094 | 0.291 | 4
340 613 St Beal 20 re 0.312 | 5
360 633 | — 1.823 | — 0.105 0.335 | 3
380 653 — 1.794 —0O.111 0.358 | k
400 673 =— 1.765 | — 0,117 0.381 à
420 693 = ES |= be) 0.405 — 5
440 713 — 1.705 | — 0.128 | 0.430 ;
460 | 133 == N67 {| == 00184 el 0.454 3
480 | 753 A ene 0.479 | ‘
500 «|, 5.773 RD ht a HV 0.506 | :
520 793 5 1.580" |? —" 0151 0.532 | 5
TABLE X

T log K(found) log K (calc.) if

log K (found) log K (calc.)

304.6 |
328.2
354.6
553
573
593
613
633

— 2.925
— 2.692
— 2.416
— 1.931
— 1.905
— 1.878
— 1.851
— 1.823

| — 2.798
— 2.668
-— 2.542
— 1.954
— 1.914
— 1.877
1.842
— 1.810

|

653
673
693
113
133
153
713
7193

— 1.794
— 1.765
— 1.735
— 1.705
— 1.675
— 1.644
— 1.612
— 1.580

— 1.778
— 1.748
— 1.719
— 1.693
= oom
— 1.642
— 1.618
— 1.595

1025

been inserted in the above table in the fourth column, were caleu-
lated from the values of this pressure.

PAS Bs. By, ol
EIEREN Ei log K log K (corr.) ee aby
| | 4
1022 | 1295 | 0.329 1.221 — 1.368 — 1.210
| |
1217 1490 0.3755 | — 1.044 | — 1.384 — 1.115
| |

The values of the fourth column have been caleulated on the
assumption that all the iodine is present as /,; this now is certainly
not the case according to the determinations of the iodine dissocia-
tion (see § 5). At these temperatures the iodine has already percep-
tibly been split up into atoms, and specially at the low iodine
tension of these experiments the splitting up will be great. Through
the correction which is to be applied for this, log K of column 4
becomes smaller.

Let us suppose the iodine to be partially split up into atoms
(degree of splitting y), then the total iodine pressure is not equal
to the hydrogen pressure, but 1+ y times greater. Let us call the
hydrogen pressure Py,, the total pressure /, then we have for the
partial tensions of hydrogen, iodine atoms, iodine molecules and
iodine hydrogen :

Pro on dem vel gh Pa, ande, Bo oe.

Hence the equilibrium constant for iodine hydrogen becomes :
ects (uaa
__ [P—Pa,(2+y)

and that for the iodine dissociation expressed in partial pressures :

2

K mi

‚ (23)

Pu, . 5 ‘ è ‘ . ‘ e (24)

AR —: np

Now from the equation for the iodine dissociation (equation 18)
follows for the equilibrium constant (in partial pressures ; pressure
unity the atmosphere) :

Pa l295 log K}, = — 0.668

(25)
T = 1490 log Kj, = + 0.148

If we now introduce the values of 25 and the found values of
Py, into 24, y may be calculated from it. This value of y sub-
stituted in 28, yields the values log & (corr.) of table XI. When

68

Proceedings Royal Acad. Amsterdam. Vol. XVII .

1026

the value of log K is calculated from 22, we get the values of the
sixth column of table XI, which appreciably differ from those of
the fifth column. This deviation can, however, be accounted for by
this that the terms with » of HJ, and possibly also those of H,
play a part at these high temperatures; the term with HZ will
render the value of log K according to 22 smaller. The iodine
vibration which prevails at low temperatures, will also continue to
do so at high temperatures. The value of the iodine term amounts
to — 0.277 at 7 = 1295; and ‘to. — 0.319 at 774490 - \the. term,
therefore, which occurs in expression 22 through the vibration of
the atoms in H/, remains below this value; and in this way an
agreement may be probably arrived at, as the discrepancies between
the values of the fifth and the sixth columns are smaller than the
mentioned ones. Moreover some variation is still possible in the
choice of the parameters of the straight line (equation 21).

The equation 22, which is accordingly in satisfactory agreement
with all the determinations of the iodine hydrogen equilibrium,
MM,
TER
radii, as they are given by Sackur, the value of the expression
mentioned is calculated, we find 1,21 which is therefore in good
agreement with the preceding one.

From formula 22 the value 2530 cal. follows for Zn lr—300,
this value differs but little from that used by Nernst in his calcula-
tions?); most of the data which can be derived from direct caloric
determinations, are useless.

yields the value 1,184 for log lf from the mean molecule

17. From the ealeulations of the dissociation equilibria of the
three halogen hydrogens we come therefore to the conclusion that
the quotient of the moments of inertia agrees with that calculated
from the mean molecule radit.

This conclusion, at which Sackur by the aid of his expressions
had arrived already before, but which was only meant to be roughly
valid, appears also to be in good harmony with Prof. vaN DER
Waars Jr.’s expression, in which the vibrations of the atoms are
taken into account.

Amsterdam, Dec. 1914. Anorg. Chem. Lab. of the University.

1) Zeitschr. f, Elektrochem. 15, 687 (1909).

1027

Chemistry. — “The replacement of substituents in benzene deriva-
tives.” By Prof. Honteman.

(Communicated in the meeting of December 30, 1914).

In close connexion with the problem of the introduction of sub-
stituents in aromatic compounds exists another: that of the replace-
ment of substituents already present, for after all the introduction
is really also a substitution, namely of hydrogen. It, therefore,
appeared to me desirable to also take in hand the study of the
replacement, in addition to my researches on the introduction of
substituents.

Some generalities on this subject are to be found in every text-
book on organie chemistry. We know that the substituent in mono-
substituted benzene derivatives is very difficult of substitution ; that
in the disubstituted derivatives it is the combination of halogen and
the mitro-group in which halogen is replaceable if the groups are o
or p in regard to each other; that in compounds C,H,ABC replace-
ment also occurs if the substituents consist of halogen, nitro, car-
boxyl, cyanogen or the sulpho-group (with this understanding, how-
ever, that except in a very few cases, there is no such thing as
A=bB=O); finally that also in the higher substituted benzene deri-
vatives instances of replacement occur. As interacting substances
have been employed almost exclusively alcoholates, ammonia and
amines. In order to obtain a better insight in this problem the com-
pounds C,H,X could be passed over; on the other hand the literature
on the compounds C,H,AB and C,H,ABC had to be studied more
closely.

Statistically, this yielded the following results: If we consider the
compounds C,H,AB and C,H,ABC, in which also A, B, and C may
be equal, and if for these substituents we take the following 14:
F, Cl, Br, J, NO,, SO,H, Alkyl (Aryl), CO,H, NH, (amine), OH (O Alk),
. - eet m(n+1) 1415
CN, NO, CHO, COR, we can derive from C,H,AB- Ae —~—105
repeated combinations all of which can form three isomerides ; hence
a total of 315 cases (included A = 5).

Of C,H,A, are possible > 14 combinations; 3 isomerides of each
= 42 cases.

Of C,H,A,B are possible n(n—1) = 14X18 = 182 combinations ;
each can occur in 6 isomerides, thus representing 1092 cases.

NL / 2,

Of C,H,ABC are possible se ee coms

binations ; 10 isomerides of each = 3640 cases.

68*

1028

For all compounds C,H,ARC with repetitions this gives a total of
42 + 1092 + 3640 = 4774 cases. *) ,

If now we inquire how many of these theoretically possible iso-
merides have been tested as to the replacement of their substituents
we get the following information :

Of the 315 possible isomerides C,H, AB (incl. A= B) 130 have
been tested as to substitution and the results are distributed over
214 papers.

For the 4774 possible isomerides C,H,ABC (incl. A,B and A,) these
figures are: of 232 compounds the substitution has been described
in 360 papers.

This shows that only a very small portion of the possible com-
pounds C,H,AB and C,H,ABC has been tested as to the replacement
of their substituents ; it only amounts to fully 7 °/,.

Hence, it is hardly to be expected that from this general conclu-
sions might be drawn even if all published cases of substitution were
suitable for the object in view. But this is by no means the case.
After a careful study of the above named 214 + 360 — 574 articles
we even arrive at the disappointing result that this vast material is
almost valueless for a closer study of the substitution. For in such
a study we not only want to know in what particular combinations
substitution ean occur, but also how this takes place under the same
conditions. For only then will it be possible to compare mutually
the substitution in the different groups and thus obtain a better
insight by investigating this problem. And exactly in this regard,
the material at disposal almost entirely forsakes us.

The reason is obvious. The experiments on substitution carried
out up to the present have always been executed with quite a
different purpose and were not intended for a systematic study of
this problem. Hence, the work was conducted hardly ever under
comparable conditions. The only results obtained up to the present
is that we know that in a comparatively limited number of cases
substitution is possible. From this we may predict with great pro-
bability that there is a possibility of substitution in a number of
other cases. If, for instance we know that in chloronitrobenzenes
with one or several chlorine atoms or nitro-groups the chlorine is
mobile, it is to be considered as very probable that this will also
be the case with the other halogen-nitrobenzenes of the same
structure.

1) Our fellow member Hk. Dr Vries was kind enough to furnish me with the
formulae used here.

1029

The first thing to do here must be an orientating investigation to
see which combinations of substituents give rise to the mobility of
one or more of the same when they are examined under exactly
the same conditions. It is, of course, impossible to include all the
5089 compounds C,H,AB and C,H,ABC, of which 4727 have never
as yet been tested in any way as to substitution, and of which a
good many are sure to be still unknown, in such an orientating
investigation. A choice had to be made. It appeared to me desirable
to start with a gauging of the intricateness of this problem by (1)
measuring in a complete set of isomerides the velocity of the trans-
formation; (2) to do this for two different substances acting thereon;
(3) to execute this at different temperatures. From this would then
be shown in the tirst place the influence of the position of the
substituents. In the second place it would show whether there exists
a definite ratio between the constants when working with different
reagents and in the third place whether that ratio also remains
permanent at various temperatures. If this really were so this would
cause a considerable simplification of the problem. We then would
only have to work at a well chosen temperature and with a ditto
reagent to generally obtain comparable velocity constants.

The subjomed investigation of Dr. pr Moois briefly described here
has taught, however, that the said ratio does not exist either for
temperature or for difference in reagent. This shows that the sub-
stitution problem possesses such a degree of complicateness that an
accurate insight therein is still a matter of the distant future.

As objects for the research of Dr. pre Moois were chosen the six
isomeric nitrodichlorobenzenes. All these are comparatively readily
Cl
Orel
prepared in quite a pure condition; only for the isomeride | |
NOANDE
an easier process of preparation had to be discovered and was
successfully worked out.

He brought these six isomerides in contact with absolute-methyl-
alcoholic solutions of sodium methoxide and of diethylamine, isolated
all the products of transformation and determined the velocity con-
stants at three different temperatures. The symmetric isomeride gave
with methoxide a complicated reaction product consisting presumably
of azoxycompounds ; diethylamine did not act on it on heating for
seven days at 110°, so that with this isomeride no velocity measure-
ments could be carried out.

1030

The three chloronitrobenzenes, likewise the three dichlorobenzenes
were also treated in the same manner when it appeared, however,
that the last named did not react with diethylamine even at 180°,
but they reacted with NaOCH,. The disubstituted products were
tested to ascertain whether from the velocity constants of their
transformations, those of the compounds C,H,Cl,NO, could be
deduced. Also this did not appear to be so.

From the results obtained by Dr. pe Moor the following will be
communicated. In all the cases investigated only chlorine was
replaced, not the nitro-group.

1. Chloronitrobenzenes. Of these was measured the reaction velocity
with sodium methoxide and with diethylamine both in absolute
methylaleoholie solution. Whereas with the first named compound
the velocity constant for the p-compound was found greater than
that of the o-compound, this was just the reverse with diethylamine.
The reaction with diethylamine proceeds here as well as in all
other cases much more slowly than with methoxide. (see table III).

2. Dichlorobenzenes. These were heated with sodium methoxide
at 175—176° when one Cl-atom was replaced by OH, as the solution
was not quite anhydrous. For the constants (time in hours) was
found, when 1 mol. of dichlorobenzene was made to react with 5
mols. of methoxide :

TABLE 1.
EN AT ht
|
ortho | 0.0382 | 3.35
meta 0.0506 | 4.44
para | 0.014 | 1

from which is shown the very remarkable result that the 7-com-
pound is the one most rapidly converted, a fact that was quite
unexpected.

3. Nitrodichlorobenzenes. The most successful measurements obtained
here are those with sodium methoxide as the values of K at different
reaction periods were found to be pretty constant. In the measure-
ments with diethylamine this was only the case with the isomerides
1,2,4 and 1,2,5 (NO, on 1); with the others the value K diminished
as time proceeded, Particularly interesting was the behaviour of the

1031

isomerides 1,2,4 and 1,2,6. In the first compound, at the interaction
of NaOCH,, both chlorine atoms appeared to be already mobile at
85°, but contrary to what takes place with monochloronitrobenzenes,
the chlorine atom on 2 is being replaced first. The consequence was
that at this temperature the constant became greater as time proceeded.
At 25° and 50°, however, the reaction with the p-Cl-atom in regard
to that of the o-Cl-atom was so retarded that very concordant values
were now found for K. With diethylamine, only the o-Cl-atom was
mobile.

In the isomeride 1,2,6 the two Cl-atoms were situated in o-positions
in regard to the nitro-group. Nevertheless only one Cl-atom could
be made to react with NaOCH, at 85°; and the same likewise with
diethylamine at 150°.

The subjoined table IT gives a survey of the measured velocity

TABLE: It
Isomeride 25° 50? 85° 110°
1,28 == — | 74 | 143
1,2,4 | 0.030 | 0.628 | 19.41 —
|
See BOOR OEL +}, IOS : 5450
1, 2,6 = = 0.135 | 1.34
153, 4} 0,033 0.601 17.42 —
1,2 va = 0.369 | 3.09
1, 4 me == 1.39 | 11.45
|

constants with Na-methoxide. The figures in heavy type indicate the
Cl-atom that is being replaced. NO, on 1. Time in hours. On 1 mol.
of nitrodichlorobenzene one mol. of methoxide was employed. Both
were in about gas-concentration. From this we notice that the
position of the groups in regard to each other exerts a very great
influence on the velocity of the reaction. If we put the reaction
velocity of 1,2,4 at 85° = 100, that of 1,2,6 will then be only 0.7.
also in the case of the other vicinal isomeride the reaction constant
is very small, namely only 8.9 for 1, 2, 4 — 100.

If we compare the reaction constant of o-chloronitrobenzene with
that of the nitrodichlorobenzenes in which also one of the Cl-atoms
is situated in the o-position in regard to NO,, the introduction of a
second chlorine atom then appears to considerably increase that
constant, except in the case where the second Cl-atom occupied the

1032

position 6. Likewise the reaction constant of 1,3,4 is considerably
greater than that of 1,4. |

The reaction constants with diethvlamine were determined with
the proportion of 1 mol. of nitro-dichlorobenzene to 2 and to 10
mols. of diethylamine, which did not yield quite the same values
for those constants. In table III the values found are united. The
time has again been recorded in hours. NO, = 1.

TABLE Ill.
85° | 110°
Isomeride
aa Wie ae Bete Beg | ise 4) Bi
| |
1,2,3 | 0.0023 | 0.0016 | 0.0094 | 0.0073
1,2,4 | 0.025 | 0.027 0.12 | 0.095
1, 2,5 | 0.0068 0.0067 0.032 0.023
1,26 | = 0.00024 — | 0.0011
1,3,4 | 0.0052 0.0044 | 0.020 | 0.017
1,2 a 0.0014 a 0.0053
1,4 |

— 0.00065 | — | 0.0024

The impression made by this table is in the main the same as
that of table I]. Also here the reaction constants of the two vicinal
isomerides are considerably smaller than those of the other nitro-
dichlorobenzenes and that for the isomeride 1,2,6 is also the smallest.
The isomeride 1,2,4 has also here the greatest reaction constant but
now this is not followed up by that of 1, 3,4 as in the case of the
methoxide reaction; presumably this is connected with the fact that
the reaction constant for 1,4 with diethylamine is smaller than that
of 1,2, whereas with methoxide this is just the reverse. That, however,
also in the other cases which run parallel, there can be no question
of a constant relation between the reaction constants with methoxide
and with diethylamine may be seen at once from table IV. p. 1033.

Not only are the figures in a same column very divergent, but
the corresponding figures of the two columns differ very much;
those at 110° are all about twice greater than those at 85°, which
indicates that the reaction velocity for methoxide increases much
more rapidly with the temperature than that for diethylamine.

Table V gives the figures as to the influence of the temperature
on the reaction constant. Whereas the ratios for methoxide on the

10338

TABLE "IV.

|

K NaOH Kamine.

Isomeride __
| = 85° T= Ti’

_————_—_— nn

123 | 892 1744
1, 2,4 Sane ME
1,2,5 | se2 | 1200
£26 | se |.) i28
i*3-4@ |. 3629 ay

„2 | 26 | 583

1, 4 2138 | 4771

one side and for diethylamine on the other side agree fairly well,
this is by no means the case for the two reagents mutually.

TABLE V. Na-methoxide.

Diethylamine (1 : 10)
Isomeride | Kos : Kso : Kgs : Krio Kas : Kino
Kgs : Kuro
ee
Pay — ¥ 822 1: 4.4
1p 2 ae | boy 208902 G47 = 1:3.5
ff 2,0 1 : 19.2 : 624 : 5238 1: 8.4 {> 3.4
(enter! - 1: 10 1: 4.6
1, 3, 4 12182: 528 — 133,329
ie = 1: 8.4 1: 3.8
14 — 1 :-8.2 ers |

Summarising we arrive at the following conclusions :

1. The number of cases of replacement of substituents in the
compounds C,H,AB and C,H,ABC quoted in the literature is small
in comparison = the mance of possible cases.

2. The data of the literature are of little value for a systematic
research as to the substitution problem as they have rarely been
obtained under comparable conditions.

3. From the study of the replacement of chlorine in the three
dichlorobenzenes, the three chloronitrobenzenes and the six nitro-
dichlorobenzenes by OCH, and N(C,H,), it is shown:

1034

a. that the replacement of the halogen is largely dependeut on
the position of the substituents:

b. that it is dependent on the reacting agent.

c. that the influence of the temperature on the extent of the
velocity constants is different for the two reactions, although fairly
equal for the different isomerides in each reaction.

A more detailed communication of the above will appear in the
Recueil.

Amsterdam, Deec.1914. Org. Chem. Lab. University.
Chemistry. “On the interaction of ammonia and methylamine

on 2.3.4-trinitrodimethylaniline.” By Prof. van RompurGH and
Miss D. W. WeEnsINK.
(Communicated in the meeting of December 30, 1914).

3.4.6.- as well as 2.3.4.-trinitrodimethylaniline, contains a mobile
nitro-group (in the position 8) which is readily substituted in the
interaction of ammonia and amines’). The mobility of that group
in the second mentioned product is, however, considerably greater,
as was to be expected. If, for instance we pour strong alcoholic
ammonia on the 2.3.4.-trinitrodimethylaniline melting at 154°, the
nitro-group gets substituted by the amino-group already at the ordi-
nary temperature, whereas the other product melting at 196° does
not exhibit any reaction whatever in these circumstances and requires
heating to enable the reaction to take place.

If, however, we heat the compound melting at 154°, or the 2.4.-
dinitro-3-aminodimetbylaniline generated thereof by ammonia, in a
sealed tube at 125° with alcoholic ammonia, the dimethylaminogroup
appears to become substituted in a remarkable manner by amino,
with formation of 2.4.-dinitro-1.3.-phenylenediamine. ’)

In a perfectly analogous manner reacts methylamine in which,

case 2.4.-dinitrodimethylphenylenediamine is formed ;
N(CH), NH,
: / NNO: H,N 7 RG:

+7 | ahd)

+ C,
~~ ee Os a 4
NO, %

N(CH3)2

JNNO:
|

/NSHLCH,

NO,

N(CHs)p a N/A \ NE,
HE \N0, Yo, So,

NI.CH;
CH,-NH, Ve \No:

|
\ nom

No,

1) Van Romsvren, Verslagen Kon. Akademie Amsterdam Febr. 1895.

2) In the said paper it is stated that indeed derivatives of m-phenylenediamine

are formed.

1035

If, for instance, we dissolve 0.5 gram of 2.3.4.-trinitrodimethyl-
aniline in aleohol and add to the solution a few c.c. of strong aleo-
holie ammonia a beautiful pale yellow product crystallizes after a
short time, which when recrystallised from acetone melts at 162°.

The nitrogen determination gave 24.70 and 24.52°/, N.
calculated for C,H,(NO,), N(CH,), NH, 24.6°/, N.

If, however, we heat this product (or the original substance melting
at 154°) for some hours with alcoholic ammonia in a sealed tube
at 125°, we find in the tube after cooling an abundant quantity of
a substance crystallizing in brownish needles, which dissolves with
great difficulty in the ordinary solvents. By recrystallisation from
boiling methyl salicylate it could be obtained in beautiful pale brown
or orange needles, which get decomposed at about 250°’).

The elementary analysis gave the following result:

C 36,22°/,, H3,55°/,, N 28,18°/,; calculated for C,H,(NO,),.(NH,)
pooae),, da,0t },, N 28,28") -

In the original mother-liquor of the brown needles in the tube,
the presence of dimethylamine could be demonstrated. To ascertain
this, it was acidified with hydrochloric acid and evaporated to dryness.

0°? 2

The residue — mixture of ammonium chloride and dimethylamine
hydroebloride — was extracted with absolute alcohol. After distilling

off the alcohol, there remained a little of a salt which, after being
washed with absolute alcohol to remove traces of nitro-compound,
was decomposed by boiling with aleoholie potassium hydroxide.
The distillate gave with 1-bromo 2.4-dinitrobenzene, yellow crystals
of 2.4.-dinitrodimethylaniline m.p. 87°, thus demonstrating the presence
of dimethylaniline.

The 2.3.4.-trinitrodimethylaniline yields with methylamine in alco-
holie solution after a while yellow crystals of 2.4.-dinitro 3-methyl-
aminodimethylaniline m.p. 125°.

Nitrogen determination: Found 23.32°/, N.

Calculated for C,H,(NO,), NHCH,N(CH,), 23.35°/, N.

From this is formed on heating with methylamine at 125° in a
sealed tube, a substance melting at 169°.

Nitrogen determination: Found 25.0°/,; calculated for C,H, (NO),
(NHCH,), 24.8°/, N.

This compound already prepared by BrANKsMaA *) has the structural
formula:

1) Barr, B. 21, 1545 (1888).
2) Rec. 27, 54 (1908),

1036

NH.CHs

mi se
\ NUCH

NO,

This could further be proved by. carefully oxydising the trinitro-
compound (m.p. 154°) with chromic acid in acetic acid solution,
which yields the monomethyl compound melting at 147°. This gives
with alcoholic methylamine-solution the m-phenylene-derivative melting
at 169°.

A continued oxidation with chromic acid yields from the trinitro-
compound m.p. 154°, a 2.3.4.-trinitroaniline (m.p. 190°), which on
treatment with ammonia gives the above cited 2.4.-dinitrophenylene-
diamine.

N(CH), NHCH; NH CH;
ANNO: co NN neem / \NO
| 154° | —— >| 147° | > | 169° |
\ 50s \ JNO: \ J NECH:
NOs NO, NO,
NILCH; NH, NH,
ZONA, CrOz Ve NO; H.N AN
| 147° | —— | i ——> | 250°
\ 4 N02 \ N02 \ A Nie
NO, NO, NO,
Utrecht. Org. Chem. Lab. Univ.
Chemistry. — “The injluence of the hydration and of the deviations

from the ideal gas-laws in aqueous solutions of salts on the
solidifying and the boiling points” By Dr. C. H. Sturrer.
(Communicated by Prof. A. F. HOLLEMAN.)

(Communicated in the meeting of December 30, 1914).

When, according to van ’r Horr, we determine the irrationality
coefficient (factor ¢) of good electrolytes in the well-known manner
with the telephone bridge of Konrravscu, for different solutions
from the formula 7=1-+ (n—1)e, in which » represents the number
of ions that can be yielded by one molecule, and « the dissociation
degree a (A = equivalent conductivity power), this appears to

00

fairly increase with the growing dilution until almost the theoretical
limit has been attained,

1037

If by other means, namely by measuring the depression of the
solidifying point, or the rise in the boiling point of the solutions,
we try to determine, approximately the value of ¢ according to the
formula :

Observed depression S.p. or rise in B.p.
‘= Moleeular depression S.p. or rise in B.p. x ¢’
in which c’ represents the number of gram-mols per 1000 grams
of water, the values thus found, particularly in the case of concen-
trated solutions appear to agree very badly with the first named ones.

Two different causes can be adduced for these divergencies. First,
the hydrations of the salt molecules and of their ions, owing to
which a part of the water has been rendered inactive as a solvent.
Hence, in the last formula a smaller value will be found for c’
than it would have been if the salt had been really caleulated on
1000 grams of solvent. The caleulated value of 7 will thus be greater
than it would have been without hydration. At high concentrations
the amount of solvent withdrawn as water of hydration will be
larger than at low concentrations, so that the influence on 7 will
be most pronounced in the first case. Also, strongly hydrated salts
such as MgCl, and CaCl, will exhibit greater differences of 7 than
the but little hydrated ones such as NaCl and KCl.

The second cause of the divergencies lies in the relative appli-
cability of the so-called “ideal gas-laws”. When, according to VAN DER
Waats, the influence of the factors « and 5 on the gas pressure
also applies to the osmotic pressure of the solutions, their solidifying and
boiling points will also be affected thereby. We may compare solutions
of salts to gases of high molecular weight beeause the mass of
hydrated particles will be comparatively larger. With concentrations
of about one gram-mol. per litre we may then expect that the
factor 4 (volume of the particles) will exert a stronger influence
than the factor a (proportional to the mutual attraction of the par-
ticles). The osmotic pressure, therefore also ¢ will then be greater
than one would expect it to be without those factors. At these large
concentrations the hydration and the last named circumstance thus
act on z in the same direction.

When at smaller concentrations, a becomes predominant, the
osmotic pressure, hence also 7, will become smaller than would be
the case according to the ideal gas-laws. Now, as a rule, the question
is whether « can overcome not only the influence of 5 but also
that of the hydration of some kind of salt, so that # really
becomes smaller than would be the case without one of these per-
turbing factors.

1038

In the determination of 4 we are only concerned with the number
of ions present in a certain volume of the solution so that the said
perturbing factors exert no influence on the calculation of 7. The
relation ill therefore indicates the actual value of 7 when V repre-

Ax
sents the reciprocal value of the number of gram-mols per 1000 ce.
of solution.

I have endeavoured to ascertain, by the measurement of A the
depression of the solidifying point and the rise in the boiling point at
equal concentrations and temperatures, in how far these considerations
are in agreement with the result of 7 in the case of NaCl, KCl, MgCl,
and CaCl,. The arrangement of the experiments did not admit of
making direct experiments at equal concentrations. I have, therefore
approximated the values of 7 as accurately as possible by graphic
interpolation. Properly speaking I ought to have determined 4 at
the solidifying and boiling points of the solution instead of at O° and
100°. As, however, the change of 7 with the temperature is very
slow, this correction would not counterbalance the inaccuracies which
would then be introduced owing to the great experimental difficulties.

I have also occupied myself with the calculation of 7 from satur-
ated vapour determinations of saline solutions, were we can expect
the same divergencies as in the dynamic determinations. Notwith-
standing detailed and laborious experiments I have not succeeded in
obtaining, in this manner, results sufficiently accurate for controlling
the above mentioned values of 7. I will only mention that 7, when
accurately determined within one decimal, gave the same results
with the statical and the dynamical method.

In the “Chemisch Weekblad” (1915) will appear a more elaborate
description of the apparatus employed by me and the corrections
applied for the calculation of 7, whilst the agreement and the dif-
ferences of my results with those of other observers will also be
discussed.

The following points of a more general importance, I wish to
mention here.

The manner in which the conductivity power of the water, used
in the 4 determinations, is computed is generally carried out by
multiplying the specific conductivity power of the water with the
dilution of the solution expressed in cc.

This empirical method, however, keeps no account with the position
of the sliding contact on the measuring bridge. The following
deduction may demonstrate, however, that this position exerts a strong
influence on the correction to be applied. Suppose :

1039

Wo = resistance of the solution.
Wz = comparison resistance on the bridge.

W y= resistance of the “conductivity water”.
W corrected resistance of the solution in case the water

possessed an infinitely great resistance.
If we assume that the conductivity power of the water is inde-
pendent of the nature of the solution (as will be certainly the case
with neutral salts) we have:

1 1 1 1 1 if

ie We We

If we call the parts of the bridge wire, when the solution is
shunted in « and 5 and those when the water only is shunted in

c and d we have:

Ee PS read
W Wo W el

Wo b 1 a 1
=- OP —=>-x*= (2)
Wp a Wo b W
and
Ww ad 1 ty 1

—— = or = ——,
Wp c Ww a x Wr
Substitution of (2) and (3) in (1) gives:

1 EE 4 x6
== == BEN nr old ee
Ww Wert d

If we put 2 the correction to the left, hence the diminution of
a, Which must be applied in the case when the water had an infi-
nitely great resistance, we find in a similar manner:

1 a—x 1 4
iin ee SNORT er Or ed
Substitution of (4) in (5) gives:
at a ¢ a—a ad—be bec
bte db d me btw DRR: en a d(a+-b)—be
if L=a+b=c-+d= length of the bridge wire and if we
neglect be in regard to dL we have: EK KEE
If, herein we again neglect Le in regard to £* we get:

Re
z=ex (5) .

Consequently the further the sliding contact is situated towards
the right, the smaller will be the corrections to be applied. In my
measurements MW, was always chosen in such a manner that 5
was as small as possible without the telephone minima becoming
less sharp. Not a single other observer appears to have applied this

1040

correction in this manner, which, with great dilutions, can cause a
difference in the value of A of several percentages. When now we
represent their results of 4, graphically asa function of the logarithm
of the dilution, the curved lines in the vicinity of WV = 2000 and
higher often exhibit very peculiar bends so that sometimes the
graphical approximation of 4, becomes impossible. ‘The curved lines
deduced from my results all appear to run asymptotically with a
line parallel to the dilution axis, as required by theory.

The approximation of 4,, particularly at 100°, is rather uncertain,
because with very great dilutions the above described correction
method for the conductivity water also fails. In order to get com-
parable results, [ have applied the empirical method of BrEDIG ')
and of Norrs®) taking A= Aco + 2,5 N at 25° (NV = product
of the valencies of anion and eation). I have chosen the coefficient
of VN at O° so much smaller and at 100° so many times larger as
the proportional decrease and increase of 4,,,, amounts to at those
temperatures.

In the measurements at 100° which were carried out in a steam-
bath, the solution being kept under a pressure of 5 atm. to prevent
evolution of vapour at the electrodes, a correction had to be applied
for the influence of the barometer indication on the steam-temperature.
For this purpose the temperature coefficient of 4 of the different
salts as determined by Jones’) between O° and 65°, was used with
a proportional reduction to 100°.

Here follow the thus corrected results of 7 at different dilutions
(V) at O° and 100°. For each measurement the concentration at
15° was determined separately and in this way eventual errors
caused by pipetting off and delivering into the measuring vessel
were avoided.

The depression of the solidifying points was determined according
to the method of Ronertson and Wanker *) in which corrections for
the influence of the radiation and for the slowness with which the
temperature exchange takes place, are done away with. The liquid
siphoned off from the ice-saltsolvent mixture was rapidly brought to
the temperature of the room and titrated. The thermometer in the
Dewar vessel remained constant for a considerable time when this
vessel was properly surrounded by ice.

The concentrations all relate to a temperature of 15°.

1) Zs. phys. Chem. 18. 191. (1894).
2) Technol. Quart. 17. 293 (1904).

3) Carnegie Inst. of Washington, publ. 170 (1912).
4) Proc. Royal Soc. 24, 363 (1902).

1041

V5} NOP je 20° | A100° i1009 Ao? | #0 A100" £100°
|
Sodium chloride Potassium chloride.
1 | 48.41 | 1.7191 | 219.3 | 1.6094 63.83 | 1.7773 | 267.1 | 1.6704
2 | 51.53 1.7656 | 242.4 | 1.6736 66.41 1.8089 | 286.9 “1.7201
4 | 54.28 | 1.8063 | 260.7 | 1.7244 68.69 1.8366 306.4 1.7686
10 | 57.72 | 1.8576 | 283.1 | 1.7868 71.50 | 1.8709 | 329.2 1.8262
20 | 60.04 | 1.8921 | 298.8 | 1.8305 73.52 | 1.8954 | 343.8 1.8628
40 | 61.81 | 1.9183 315.2 1.8760 75.44 1.9187 | 361.3 | 1.9067
100 | 63.47 | 1.9430 | 331.5 | 1.9210 11.46 | 1.9432 | 374.1 _ 1.9389
400 | 65.32 | 1.9703 346,3 | 1.9625 79.63 1.9699 | 385.9 1.9685
1000 | 65.82 | 1.9777 | 351.8 | 1.9777 80.61 1.9817 | 391.0 "1.9813
2000 | 66.04 1.9811 355.0 1.9865 . 81.00 | 1.9865 | 392.7 | 1.9856
oo | 67.32 | 2 359.8 2 82.11 | 2 398.5 | 2
Magnesium chloride. Calcium chloride.
ei a eas aid Ae Nh
1 | 68.02) 2.0552 | 306.2 | 1.8860 76.33) 2.1128 | 326.2 | 1.9356
2) 77.03) 2.1950 | 373.8 | 2.0816 85.02) 2.2392 | 394.3 | 2.1308
4 85.71 2.326 430.3 | 2.2452 93.10 2.3570 445.7 | 2.2786
10 | 96.50 2.4970 491.9 | 2.4234 103.2 | 2.5042 506.1 2.4518
20 | 104.4 | 2.6196 534.4 2.5462 110.5 | 2.6108 | 546.2 | 2.5668
40 | 110.6 | 2.7156 | 567.2 2.6416 116.8 | 2.7030 | 587.8 | 2.6838
100 117.0 2.8152 | 611.8 | 2.7702 123.8 | 2.8048 | 621.9 | 2.7838
400 | 123.3 | 2.9126 | 657.1 2.9016 131.3 2.9144 ‚664,5 "2.9060
1000 | 125.9 | 2.9532 | 675.0 2.9532 134.2 © 2.9562. 682.1 2.9566
2000 | 127.1 | 2.9716 | 680.5 | 2.9690 135.0 2.9680 | 686.2 | 2.9680
o | 128.9| 3 691.1 | 3 137.2 | 3 | 697.4 | 3
| |

For the calculation of the number of gram-mols per 1000 grams
1000 ¢
1000d-cM
the directly-titrated concentration, d the sp. gr. of the solution and

M the molecular weight of the salt.

of water the formula c’ = was used, in which c represents

69
Proceedings Royal Acad. Amsterdam. Vol. XVII.

1042

For. the calculation of 7 the theoretical value 1,855° was chosen
for the molecular depression in 1000 ce of water.
t

We then have 2=—— 5
1,855 .c'

when ¢ is the depression of the
solidifying point.

The graphic representation, in which ¢ is represented as function
a IK EE OS ES

| Depres- | — t ; | Depres- t
c ie al i = Te c sion i Ei
Sodium chloride. Potassium chloride.
0.9539 3.180° | 1.797 0.9486 3.201° 1.819
0.6224 2.095 i} tae 0.7964 2.696 1.821
0.4011 1.361 1.829 0.6120 2.078 1.830
0.3772 1.283 | 1.833 0.5016 1.710 1.838
0.1702 0.586 | 1.857 0.3047 | 1.051 1.859
0.1501 | 0.518 | i.861 0.1571 | 0.549 1.884
0.04014 | 0.142 | 1.91 0.07565 | 0.269 1.918
0.03042 | 0.109 | 1.93 0.02283 | 0.082 1.94
0.01161 | 0.042 1.95 0.01301 0.047 1.95
Magnesium chloride. Calcium chloride.
0.9583 6.063° 3.410 1.0092 5.966° | 3.188
0.9795 | 4.726 3.185 0.8156 4.494 — 2.970
0.7078 | 4.033 3.072 0.6285 3.243 | 2.782
0.5322 2.847 2.883 0.4840 2.401 | 2.674
0.4889 Jol Tl 2.841 0.3422 | 1.645 | 2.590
0.3852 | 1.972 2.759 0.2992 | 1.424 2.565
0.2280 1.146 | 2.710 1) 0.1968 | 0.933 2.556 ')
0.1917 | 0.964 2.711 0.1384 | 0.664 2.586
0.08023 | 0.408 2.741 0.07150 | 0.354 | 2.669
0.03135 | 0.163 2.80 0.03555 | 0.181 2.74
0.01352 | 0.074 2.95 0.01297 | 0.070 2.91
| 0.00611 | 0.034 3.0

1) Minimum value of 2.

1045

of the concentration, yields for NaCl and KCl almost straight lines
whereas those for MgCl, and CaCl, exhibit a slight bending upwards
at the greater concentrations.

The values of 7 exhibit with MeCl, and CaCl, a minimum for
c= + 0,2,. whilst also here, contrary to the calculation from A,
those of MgCl, are larger than those of CaCl,. Also the difference
between NaCl and KCl is here smaller than followed from the A
determinations.

The most trustworthy observations of other investigators mostly
agree well with those of mine for KCl and NaCl, whereas those
for MeCl, and CaCl, exhibit at both sides deviations of at most
2°/, of the value of ¢ according to the graphic representation.

The determinations of the boiling points were carried out in metal
vessels internaliy silver plated and surrounded by a steam jacket.
In order to avoid corrections for the barometric pressure, a second
vessel with pure water was always boiled under exactly the same
conditions as the one containing the saline solution. An exchange
of the thermometers in the two vessels could always take place without
any danger of escape of vapour by placing these thermometers ina
thin-walled tube containing mercury. These tubes were placed in
the two vessels at an equal depth so that no correction for the hydro-
statie pressure was required. By lengthening the refrigerating tube
until it penetrates lower into the boiling vessel it was avoided that
the colder reflux water had an influence on the thermometer bulb.

A retardation of boiling was counteracted by placing in each
vessel 200 grams of clear glass beads and 10 silver tetrahedrons.
A correction of the concentration for the water withdrawn from the
solution by evaporation was applied. By experimenting this was
determined as 0.2 °/, of the concentration when the vessel contained
250 ec. of liquid. The concentration was determined before as well
as after the boiling and then yielded no measurable differences. The
necessary scale corrections were introduced on the thermometer. The
calculation of c’ from c was executed as directed above. Here also, these
quantities relate to a temperature of 15°.

The graphic representation in which ¢ was again plotted as
function of ec shows that the faintly bent curved lines for NaCl and
KCl almost coincide, NaCl now being situated a little higher than
KCl. Just as with the solidifying points, MgCl, is again higher than CaCl,,.

In the caleulation of z¢ the theoretical value 0,52° was again chosen
for the molecular increase of the boiling point in 1000 ce. of water.
The values of # now exhibit with all salts a minimum, with NaC!
and KCl for c’ =+0,3 and with MgCl, and CaCl, for c’ = + 0,2.

69*

1044

The results of other investigators exhibit in a graphic represen-
tation, also mutually, much stronger differences than with the depres-
sions of the solidifying point. As a rule the values found by meare
situated lower, probably in consequence of a retardation of boiling
during measurements in glass apparatus according to Beckmann. My
observations show a good relative agreement with those of Smits ’),
although this observer, notwithstanding metal vessels, always found
somewhat higher values. In part, these small differences are probably
due to the correction of c’ for the water evaporated, which Sirs
does not seem to have applied. Here follow my results.

For the purpose of comparison of the results here obtained I have

\

c’ | ies pura al c pater | ps es
| Increase £ 0.52 ¢ increase ¢ 0.52 ¢’
pelt: |
Sodium chloride. Potassium chloride.
1.0342 0.950° | 1.767 1.0263 09320 «| 1.748
0.7729 | 0.694 | 1.726 0.7751 | 0.686 1.703
0.5147 | 0.454 | 1.697 0.5106 | 0.445 1.675
0.3532 ó 0.310 | 1.688 0.3482 | 0.301 1.663 2)
0.2601 | 0.228 | 1.686 1) 0.2622 | 0.227 1.664
0.1721 | 0.153 | 1.710 0.1703 0.148 1.670
0.0962 | 0.089 | 1.78 0.1053 | 0.04 | 1.72
0.05128 | 0.049 | 1.84 0.05619 | 0.052 - 1.78
Magnesium chloride. Calcium chloride.
(OLC 1156330 | 3.094 1.0052 1.5629 2.988
0.7698 1416.75) 2.785 0.7499 1.054 2.704
0.5146 0.672 | 2.510 0.5101 0.657 2.471
0.3551 0.435 2.356 0.3482 0.421 2.326
0.2558 0.304 2.282 1) 0.2528 0.298 2.264
0.1671 0.199 2.286 0.1712 0.202 2.270
0.0946 0.115 2.34 0.0972 0.117 232

0.04832 0.060 | 2.39 0.05183 , 0.064 ZS

Zs. phys. Chem. 39, 385 (1901).
Minimum value of 7.

3)
*)

1045

= hal |
C ifrom A Wake | i'—1 lifrom A | # from | =
Gram mol. p.. S25 | boiling |
L. solution | 20° | “Za | at oe || at 100°) point | at 100°
| D | |

Sodium chloride

1.000 | 1.719 | 1.795 | 0.0764 | 1.600 | 1.764 | 0.155 4
| 1.742 | 1.807 | 0.065] || 1.642 | 1.725 |

0.500 | 1.766 | 1.821 | 0.055 1.674 | 1.697 | 0.023
0.250 | 1.806 | 1.846 | 0.040 1.724 | 1.687 |—0.037

0.100 | 1.858 | 1.884 | 0.026] || 1.787 | 1.776 |—0.011

0.0507 th:382— |, 11-905 0.013 | || 1.831 1.840 . 0.009

Potassium chloride

1.000 | 1.777 | 1.816 | 0.0394 | 1.670 | 1.748 | 0.078
0.750 | 1.793 \ 1.823 | 0.030] | 1.695 | 1.702 | 0.007 |.
0.500 | 1.809 \ 1.837 | 0.028, | 1.720 | 1.674 |—0.046
0.250 | 1.837 | 1.869 | 0.032] || 1.769 | 1.665 |—0.104
0.100 | 1.871 | 1.906 | 0.035! || 1.826 | 1.723 |—0.103
0.050 1.895 1.928 | 0 003 | 1.968 | 1.784 ate

||
1]

Magnesium chloride

1.000 | 2.055 | 3.48 1.4304 | 1.886 | 3.004 | 1.208
0.150 | 2.126 | 3.140 | 1.015] || 1.984 | 2.773 | 0.789
0.500 | 2.195 | 2.858 | 0.663] | 2.082 | 2.498 | 0.416

0.250 2.330 | 2.718 | 0.388) || 2.245 | 2.282 | 0.037
0.100 2.497 | 2.736 | 0.230] || 2.423 | 2.338 —0.085

0.050 2.020 | 2.780 |, 0.160 | 2.546 | 2.390 —0.156

Calcium chloride

1.000 | 2.113 | 3.195 | 1.082 1.936 | 3.006 | 1.070

| | 2.913 | 0.737] || 2.033 | 2.719 | 0.686
0.500 | 2.239 | 2.684 | 0.445| | 2.131 | 2.470 | 0.339
0.250 | 2.359 | 2.562 | 0.205 2.279 | 2.264 —0.015

0.100 2.504 | 2.632 | 0.128 | 2.452 Als. 10134

|
0.0500. 1 2-61) -\ 2.710. 0.090 2.567 2.313 |—0.194
| | | |

1046

represented 7 graphically from the solidifying and the boiling points
as a function of c.

From this I have interpolated the values of 7 at the same concen-
trations as used in the determination of A. The third decimal of 2’
is, however, very vague on account of the powerful bends in the
vicinity of the minima, which the thus obtained lines exhibit. From
the differences of the dynamically obtained values of 2’ and those of
i from A at corresponding temperatures we can control the previously
mentioned views with a sufficient accuracy. From this appears the
following.

At O° 7’ is always greater than z and the difference increases
regularly with the concentration (with KCl we found small oscillations
in the third decimal, so within experimental errors). With the most
hydrated salt, namely MgCl,, the increase of 2’—z is the strongest,
then follows CaCl,, then NaCl, whilst the feeblest hydrated salt KCl
shows the least increase of 7’—7. With MgCl, and CaCl, the factor
6 seems to predominate in the large concentrations for there the
decrease of 2’—7 with the dilution is much stronger than it is in the
case of NaCl. Not in the case of a single salt does the factor a
become so predominant that the influence of the hydration becomes
also subdued. At 100°, on the other hand, 2’—, in the case of all
salts, occasionally becomes negative, so that the influence of a is
there stronger than that of 4 and the hydration together. With NaCl
and KCl 7’—z even exhibits a minimum, so that with these salts in
the smallest concentrations the hydration seems to gain the best of a.

With MgCl, and CaCl, the differences at 100° are smaller than
at O° owing to the lesser hydration of these salts at a higher tem-
perature. At the smallest concentrations the predominance of a
steadily increases so that finally 7’—z becomes fairly strongly negative.

As in the calculation of 7 the choice of A, had to be rather
arbitrary, whereas the molecular depression of the solidifying points
and the rise of the boiling points could not be determined in a
direct manner in consequence of the same perturbing influences that
occurred in the solutions investigated, | cannot credit the results of
i—i with possessing absolute values. The direction in which 2’—<
changes with the concentration will, however, remain the same
when another choice is made from the said constants. This direction
and the velocity with which the change takes place can, however,
just give us some insight into the strength of the influence of the
perturbing causes, each separately. For a more detailed discussion
on this point, I must again refer to the more elaborate article in
the Chemisch Weekblad (1915).

Dec. 1914. Chem. Laboratory of the H.B.S. Bois le Duc.

1047
Astronomy. — “On the figure of the planet Jupiter.” By Prof.
W. DE SITTER.

The potential function of a body possessing axial symmetry is *)

= 1 Nd B; 3
Sune a -{- = GE Pi (swt ORT.

EN je C
Bi OE} be) dm.
m fa)

S

where

In these formulas the axis of symmetry is chosen as axis of §,
The coordinates of the element of mass dm are §, 4,5; 9? =§ +
+ 7° + 6’, and the integrals must be extended over the whole body.
Further d is the planetocentric latitude, and P; are the zonal har-
monies of order 2. If the origin of coordinates is taken in the centre
of gravity, we have

Be).
If the plane of §, 4 is a plane of symmetry, then also
Be bss = Oar aes, EL
I adopt from the theory of the four large satellites
rr, = — 0.01462.
The motion of the perijove of satellite V then gives

15
24 000058.

bt
By anaiogy we can conclude
B,
pe = — 0.00002.

The effect of the term in B, can thus never amount to more
than a few units in the fifth decimal place, even at the surface of
the planet. Since the values of B, and B, are uncertain to a larger
amount than this, we neglect 4, altogether.

If now the body rotates about the axis of & with the velocity w,
we must, at the surface, have

| Ti Soh EEE NT:

VP, = fm E + en P, (sind) + en) P, (sin | + $ wr? cos? d= const.

If we put

jm

where b is the equatorial semidiameter, and

1) TisseranD, Méc. cél. Il p. 319—822.

then we find
3

-
pd zi -ompeley

r B B,
en 1 + DE P,(sin d) + Pi P,(sin d) + to
The value of w is different for different latitudes. At the equator
the period of rotation is nearly
T= 9502.
In higher latitudes in the northern hemisphere it is about
P= 905506
while in the southern hemisphere the average is
7 == BoP.

In the northern hemisphere 7, appears to increase somewhat from
the equator to the pole, while in the southern hemisphere there seems
to be a slight decrease '). These results are, however, still rather
uncertain and it seems better to adopt a mean value.

For 7, = 9507.5 we have 0, = 0.09017
and. tor 7 == A09 Ie i, = yy AEL

If now we write the equation (1) first for a point on the equator
[r=6], and then for the pole |r=6(1—e,)|, taking both times g = 9,,
we find the following condition determining «,

1 B, 9473 3 B 53
gek Reden NT [124] + $ De as].
where

L
,=

= (ener

I thus find
e, = 0.06494 —1/,..,,
From the eclipses of the satellites observed at Harvard College |
derived ?):
From satellite I e= 0.0604 + .00380

3 vs II (0764-29715
ys eed 0544 + 30
7 sf [V ‚0649 + 10

It is well known that also the values of ¢ derived by different
observers from micrometrical measures of the diameters are very
discordant. They range from about 0.055 to 0.075. The value derived

1) Srantey Wittiams, Observatory 1913, page 465.
*) Monthly Notices LXXI. page 96.

1049

here from the equation (1) is probably more exact than any of these.

This value of «, has been used for the computation of the values
of the radiusvector given in the second, third and fourth columns of
the following table. The third and fourth columns were computed
by the equation (1), using for g the values g, and g, respectively.

The table gives ed.

D
Equipotential surface | Difference
d | Ellipsord |—.——— en [2 wrd! | api
Qo | Q, | Qo / 0, |
0e 0.00000 | + 0.00042 | + 0.00042 bles 30
5 | — .00055 — .00014 — 0.00056 | 4 40 | — 0.00001 — 28
10 — .00216 — .00181 — .00222 | + 35 | — 6 | 0 |
15 | — .00478 | — .00452 — 00490 ze 2% | — sand
20 | — .00830 | | — .00850 |= 20; — 14
30 | — .01750 | | — .01786 | ae A ee
40 | — .02843 | — .02890 | z= 47| — 34
50 | — .03968 | — .04014 | ee 46.) — 33 |
60 | — .04990 — .05026 | =, on HER AE
70 | — .05799 | — .05819 | \— iN ee:
80 | — .06317 | — .06322_ _ Gaon
90 | — .06494 | — .06494 | | 0

The deviation from the ellipsoid thus consists of a protuberance
along the equator, produced by the increase of the velocity of rotation,
and a depression in mean latitudes’). The transition probably takes
place rather suddenly somewhere near the latitude Tes

We have up to now taken no account of the variability of in

1) If quantities of the order of e° are neglected, the deviation from the ellipsoid
is easily shown to be (for constant w) of the form

— x sin’? 2d ,
where
hs 1 2 4 2274 — 9.00088
a eg T 39 pA zy. .

The actual depression is only about #/; of this.
For the earth the value of « is of the order of 0.0000005 = 3 meters.

1050

the higher latitudes. A difference of Om4 in 7’ corresponds to a
difference of 0.00006 in 4 o. Therefore, if we had used for each
latitude its own value of w or o, only the last decimal of ”/, would
have been affected. In that case, however, we must also dismiss the
assumption 5, = 0. Of the true value of B, we know nothing, but
we can assert with considerable certainty that it will be of the same
order of magnitude as the difference between the northern and
southern rotations, i.e. that it will, like the other causes of uncer-
tainty discussed above, not exceed the fifth decimal place.

The deviations from the ellipsoid are, of course, far beyond the
reach of direct micrometrical measures. In fact they are always
below O".01. The effect on the times of the phenomena of the satel-
lites is, at latitude 60°, O8.034 for satellite L and 05.070 for satellite
IV, which also is beyond the accuracy of the observations. Thus
for all practical purposes we can treat the surface of Jupiter as a
true ellipsoid.

Chemistry. — “The Allotropy of Cadmium V”. By Prof. Ernst
Coner and W. D. HELDERMAN.

The heat of Transformation in the reaction Cd(a) 2 Cd(y).

1. As we pointed out some time ago in our sixth communication
on the thermodynamics of standard cells,*) in calculating the chemical
energy of the Weston cell we have to take into account that cad-
mium is able to exist in different allotropic moditications.. While
this problem will be treated later in full, it may be pointed cut
here that it is very important to know the quantity of heat which
is involved in the reaction

Cd(a) = Cd(y).

The investigations to be described here have reference to this

problem.

2. Up to the present such a heat of transformation of a metal
has only been determined in one single case. Some months ago
BRONSTED °) carried out some measurements on the heat of the trans-
formation

grey tin — white tin.

1) Chem. Weekblad 11, 740 (1914).
2) Zeitschr. f. physik. Chemie 88, 479 (1914),

1051
He found it to be 532 gram calories per gram atom of tin at 0° C.

3. For several reasons the calorimetric method used by Brénstep
cannot be applied to our case. We therefore carried out our expe-
riments with a Transition Cell of the sixth kind, which has been
deseribed by Ernst COHEN. *)

This cell is constructed according to the scheme:

Electrode of a metal M Solution of a salt of M | Electrode of the metal
in its stable modi- of an arbitrary M in its metastable
fication. concentration. | modification.

4. Hitherto it was impossible to make a quantitative application
of this cell, as no metal, having a transition point, was known
which exists in an electrically sharply defined condition.

Our measurements will prove that the transformation a-cadmium
= y-cadmium is especially suitable for such an investigation.

As we have in view the carrying out of some other measurements
with our a- and y-cadmium, we have not brought them together in
one single transition cell, but used them as the negative electrodes
in cells which were constructed according to the scheme given by
Hurerr. These cells were studied separately. Consequently our cells
were made up as follows:

Unsaturated solution |

Cd-a of CdSO, of an Cadmium amalgam... .(a-cell).
arbitrary concentration | 8 percent by weight
and
Unsaturated solution
Cd-y of CdSO, of an | Cadmium amalgam .. . (y-cell).
arbitrary concentration 8 percent by weight.

5. On applying the equation of Gipps—von HELMHOLTz:
«

pw pee
RT

to the a- and y-cell separately, we find:

den ne |
(En). = oe tl; Ant eee

ne dT
and :
4 (£. )y 7 dh,
EN =—— nend 7 aig at na a COLL)
dT 7

1) Zeitschr. f. physik. Chemie 30, 623 (1899)

1052

(K)« represents the electric energy of the a-cell at 7°; (Ha the
quantity of heat which is generated if at 7° one gram atom of
a-Cadmium is dissolved in an unlimited quantity of cadmium amal-
gam (8 percent by weight).

The signification of (/.), and (£,), is quite analogous.

6. From our equations we get:

dE, dE,
(£.), ey (B) = NE | 29, irr (Ee) nn (Gz) - EM k (1)

The expression on the left represents the heat of transformation
which accompanies the change of J gram atom y-cadmium into
a-cadmium, i. e. the value to be determined.

Therefore we have only to measure the E.M.F. as well as the
temperature coefficients of the a- and y-cell at 7°.

7. As we pointed out some time ago the cells which have been studied
by Hererr *) are our y-cells. From his determinations between 0°
and 40° ©. it follows that

(H,)® = 0.05047 —0.0002437 (t —25) Vole. . . . (2)

8. We constructed our a-cells starting from y-cells, in which the
y-cadmium was transformed into «-cadmium.

The way in which these y-cells were prepared and in which their
E. M. F. was determined has been described in full in our third
paper on the allotropy of cadmium. *) As standard cells we used
two Weston-cells and two CLARK-eells which were standing in a
thermostat at 25.°O. The E. M. F. of the Wesror-cell was assumed
to be 1.0181 Volt at 25°.0.

E. M. F. Crark
E. M. F. Weston

Oct. 31. 1914 1.3948
Dec. 17. 1914 1.3947 .
Jan. 19. 1915 1.3947
We prepared 11 ytells. At 25°.0 their E.M. F. was 0.0504 Volt.
After standing for a fortnight at 25°.0 the y-cadmium was trans-
formed into the /°-modification as was shown by the fact that the
E. M. F. had decreased to 0.048 Volt at 25°.0. In order to trans-
form the g-modification into a-cadmium we put the cells for a
fortnight into a thermostat which was kept at 47°.5 C. We now

The ratio ( ) was found to be:
25°.0

1) Trans. Americ. electrochem. Soc. 15, 435 (1909). Hurerr used a 10 percent
amalgam (by weight). This is a two-phase system between 0° and 40°.
2) These Proc. Vol. XVII. p. 122.

1053

put a fresh amalgam into the cells, while a fresh solution of ead-
mium sulphate was also introduced. We found that in 4 cells (out
of eleven) the 6-cadmium had been transformed into the a-modifi-
cation. The E. M. F. of these cells was 0.0474 Volt at 25°.0.
(See our third paper on the allotropy of cadmium).

9. These a-cells were systematically investigated at 25°.0, 20°.0 and
15°.0 respectively, in order to determine their temperature coefti-
cients. Table I contains the results.

Tl ;
ie measurements may be represented by the equation:

LH) = 0,04742 — 0,000200 (¢ —25) Volt... . (3)

TABLE}
E. M. F. of «-Cells (Volt).

Date {TEMPE} Cen, | CellH, | CellH; | CellH, | Mean
Jan. 14 25.0 | 0.04751 | 0.04740 | 0.04763 | 0.04758
15am. | 25.0 | 0.04725 | 0.04797 | 0.04710 | 0.04714
0.04742
15 p.m. | 25.0 | 0.04721 | 0.04790 | 0.04710 | 0.04710
16 25.0 | 0.04728 | 0.04794 | 0.04731 | 0.04731
Jan. 18 20.0 | 0.04848 | 0.04837 ES ra
19 a.m. | 20.0 | 0.04843 | 0.04833 ES a
19 p.m. | 20.0 \ 0.04849 | 0.04841 = ie
19 night | 20.0 | 0.04832 | 0.04836 — | == 0.04841
20 20.0 | 0.04849 | — | BE
21 | 20.0 | 0.04843 | — | 0.04850 | 0.04860
22 20.0 | 0.04893 | — 0.04833 0.04843
Jan. 23 am. 15.0 | 0.04908 - = — | 0.04944 | 0.04047
23 pm. 15.0 | 0.04925 | — | 0.04966 | 0.04968
| | | | | _0.04943
24 15.0 0.04959 = — _ 0.04948 0.04950

| |
25 15.0 | 0.04924 | or | 0.04928 | 0.04937

oS oN I EN ee!
| |
Jans 25 | 25-0 0.04752 | — 0.04759 | 0.04761 |

|
|

1054

10. The reproducibility of these cells is not less good than that
of the y-cells. Calculating from (3) the E.M.F. of an a-cell at 0° C.
the value (E,)°° = 0.05245 Volt is found, while a cell which had
formerly been measured at 0° C. (see our third paper on the allotropy
of cadmium) gave the value 0,05225 Volt. This cell had been prepared
at a different time using different materiais.

11. In order to calculate the heat of transformation of e-cadmium
into y-cadmium at 18°.0 C. we have to introduce the numerical
values into our equation (1).

From (2) we find:

(E.)'" = 0,05217 Volt.

EE), — — 0,0002437 SL,

1 0 Pr degree
From (3) we get:

(£)18° = 0,04885 Volt.

dE. \18° Volt
= — 0,000200 —
al J. degree

(E,)18° — (£,)18° = [0,05217 — 0,04885 — 291 (—0,0002437 +
7 x
+ 0,000200)] 46105 = 739 gram calories.
If one gram atom of e-cadmium is transformed into y-cadmium,
the change is accompanied at 18°.0 C. by an absorption of 739
gram calories.

12. It may be pointed out that the temperature at which (£,),—(/),
represents the metastable transition point of the reaction ¢-cadmium
= y-cadmium.

If we put (2) = (3), we find:

0.00305 == 0.0000437 (¢ — 25)
j= 348

Utrecht, January 1915. van ’T Horr- Laboratory.

1055

Chemistry. — Note on our paper: “The Allotropy of Lead 1”
by Prof. Ernst Corner and W. D. HerDERMAN.

In our first communication on the Allotropy of Lead *) we stated
that we resumed our investigations on this subject after having
received a letter from Mr. Hans Herrer in Leipsie which showed us
the way in which fresh experiments had to be directed. In this
letter Mr. Herrer kindly invited us to continue these investigations.

As Mr. Herrer writes in a letter dated Jan. 21st 1915: “Gewünscht
hätte ich freilich, dass der Ort, an dem ich meine Versuche machte,
das hiesige Chemische Laboratorium, in der Veröffentliehung genannt
worden ware’, we comply with pleasure with his request by publishing
the above statement.

Utrecht, January 1915. VAN ’T Horr- Laboratory.

Mathematics. — “Characteristic numbers for a triply infinite system
of algebraic plane curves” By Prof. Jan pe Veris.

(Communicated in the meeting of Dec. 30, 1914).

1. The curves of order n, c”‚ of a triply infinite system I (complex)
cut a straight line / in the groups of an involution /,° of the third
rank. The latter possesses 4 (n — 3) groups with a quadruple element ;
/ is consequently four-point tangent, ¢,, for 4 (n—3) curves c”. Any
point P is base-point of a net N belonging to I, hence point of
undulation, #,, for si curves c”".*) If ¢ rotates round P, the points
Rk, describe a curve (R,)p of order (4n—6), with sixfold point P.

The tangent ¢, cuts er moreover in (n—4) points 5; the locus
GS)p has apart from P, 4 (n—3)(n—-4) points in common with /.
The tangents ¢, of a net envelop a curve of class 6n (n—3) *);-as
P is sixfold point on the curve (#,) belonging to the net determined
by P, P will lie on 6n (n—38) — 24 or 6 (n—4) (n-+1) tangents t,
of which the point of contact FR, lies outside P. So P is a 6 (n—4)(n-++1)-
fold point on (S)p, and the order of this curve is 4 (n —3) (n—4)
+ 6 (n-+1)(n—4) or 2 (n—4) (5n-—3).

Let us now consider the correspondence which is determined in

1) Proceedings 17, 822 (1914).

2) Cf. p. 937 of my paper: “Characteristic numbers for nets of algebraic
curves”. (Proceedings Vol. XVII, p. 935). For the sake of brevity this paper will
be quoted by N.

3) N. p. 936.

1056

a pencil of rays with vertex J/ by the pairs of associated points Zi,
and S. Any ray MR, contains (4n—6) points A, consequently
determines (dn— 6)(n— 4) points S; any ray MS contains (n—4)10n—6)
points S, produces therefore as many rays MA. To the (n—4)(142—1 2)
coincidences, the ray MP belongs 4 (n —3) (n—4) times; for on MP
lie 4 (n— 8) points R,, hence 4 (n—3) (n—A4) points S. The remaining
coincidences arise from the coinciding of a point A, with one of
the corresponding points S. This takes place in the point of contact
R, of a er with a five-point tangent ¢,. From this it ensues that the
five-point tangents of T envelop a curve of class 10n (n—4).

We further consider the symmetrical correspondence between the
rays of (J/), containing two intersections S,S’ belonging to the same
point of contact #,. Its characteristic number is apparently (10n—6)
(n—4) (n—5). On MP lie 4 (n—8) (n—4) (n—S) pairs S, S’; as many
coincidences are represented by MP. The remaining coincidences arise
from the coinciding of a point S’ with a point S, hence arise from
lines #42, which have with a c* ina point R, a four-point contact, and
in a point R, a two-point contact. The tangents ts, envelop therefore
a curve of class 16n (n—4) (n—S).

2. Any point of the arbitrary straight line a is, as basepoint of
a net belonging to J, point of contact A, for six curves c”. The
sextuples in this way coupled to a form a system |{e”|, of which
the index is equal to the order of the locus of the points of undu-
lation Rk, on the curves of the net set apart out of by an arbitrary
point P, consequently equal to 3(6n— 11) *). The tangents ¢,, of which
the points of contact &, lie on a, form a system [é,| with index
(4n—6) for through P pass (4n—6) straight lines ¢,, having their
point of contact R, on a ($ 1). Two projective systems [cr | and [cs |
with indices @ and o produce a curve of order (ro + gs). If to each
cr of the above system the line ¢, is associated, which touches it on
a, a figure arises of order 3(62n—11) + n(4n—6). The latter consists
of the straight line « counted 24 times, and the locus of the points
S, which each ¢, has moreover in common with the corresponding
cr. This curve (S)a is therefore of order (4n?-+-12n—57).

For n= 4, (S), is therefore of order 55. In a complex of curves
ct occur therefore 55 figures consisting of a c’ and a straight line c’.
If all cf pass through 11 fixed points the straight lines c* are appa-
rently the sides of the complete polygon determined by the base-points.

To the intersections of (S)a with a belong the 4(n-—3) groups of

1) N bl. 937,

105%

(n—A4) points S arising from the er having a as tangent ¢,. In each
of the remaining intersections a point R, has coincided with a point
S into a point R;. The points, where a c* possesses a five-point tangent,
lie therefore on a curve (R‚) es order (40n—105).

For n= 4, the number 55 is duly found.

3. To each cr possessing a tangent ¢,, we associate that tangent ;
the latter cuts it moreover in (n—5) points |. The locus of the
points |’, together with the curve (/?,) to be counted five times, is
produced by the He eae systems [c"] and [¢,]. The system [¢,|
has (§ 1) as index 10n(n —4). The curves c” passing through a point
P form a net; in this net occur 15(-—4)(4n—5) curves with a ¢, ');
this number is the index of [c"|. For the order of the curve (V) is
found 15 (n — 4) (dn —- 5) + 10n 2(n — 4) — 5(40n — 105) = 5(n — 35)
(21° + l4n — 33).

In the pencil of rays (JM) the pairs of points &,,V determine
a correspondence with characteristic numbers (n—5) (40n—105) and
(n—5) (10n?+70n—165). The 10n(n—4) tangents ¢, passing through
M produce each (n—5) coincidences. As the remaining ones arise
from the coinciding of R, with V, it appears that I contains
3O(n—5) (5n—9) curves with a sia-point tangent ty.

The symmetrical correspondence (MV, MV") has as characteristic
number (102?+70n—165) (n—5) (n—6), while the 10n(72—4) tangents
t, passing through Jf represent each (n—5)(n—6) coincidences.
From this ensues that I possesses 10 (n—5) (n—6) (n?+18n-— 33)
curves with a tangent t5,2.

4. The Z?, which I determines on /, possesses 6(n—3) (n—4)
groups in which a triple element occurs beside a twofold one;
consequently is / for 6 (n—98)(n—4) curves a tangent f23. If / rotates
round P, the points of contact AR, and R, describe two curves
(Re)o3 and (Ra)o3. P is as base-point of a net, point of contact Ff,
for 3 (n— 4) (n+3)’), point of contact Rk, for (n—4) (n-+-9)*) curves.
So (Ro)o2 is of order (n—4)(8n-++-9)+-6(n—3)(n—4) or (n—4)(9n—-9)
and (Rs)23 of order (n—4) (n-+-9)-+-6 (n—3) (n—4) or (n—A) (7n—9).

From the correspondence (MR, Wf,) may be deduced again that
t, envelops a curve of class 10n (n—4). (See $ 1).

Each tangent fez passing through P cuts the corresponding c* in
(n—5) points W; on a ray passing through P lie therefore 6 (n—3)

70
Proceedings Royal Acad. Amsterdam. Vol. XVII.

1058

(n—4) (n--5) points of the curve (W)p. The ec” passing through P
form a net, of which the tangents f23 envelop a curve of class
In (n—3) (n—A4). *)

As P is point of contact A, for (n—4)(8n-+-9) and point of
contact R, for (n — 4) (n + 9) curves of the net, P lies, as point
W, on Ins (n — 4) (Bn + 9) — 3 (n — 4) (n + 9)
— 9 (n— 4) (n—S) (n+1) tangents ‘23. The order of (W)p amounts
therefore to 6 (n—3) (n—A4) (n—5) + 9 (n—A4) (n—5)(n +1) or
3 (n—A) (n—5S) (Sn—3).

Starting from the correspondence (f,, IV) we arrive again at the
class of the curve enveloped by 442 ($ 1).

A new result is produced by the correspondence of the rays
MR,, MW. Its characteristic numbers are (f (72-4) (n—ò) and
(15n—9) (n—4)(n—5). The ray MP adr 6 (n—3) (n—4) (n—5)
coincidences. The remaining 187 (n— 4) (n—5) arise from coincidences
R,= W. consequently from tangents f5,5. As each /33 determines
two coincidences, the twice osculating tangents ts,5 envelop a curve
of class In (n—4) (n—S). come

The symmetrical correspondence between the rays connecting J/
with the pairs of points IV, W’, belonging to the same c”, has as
characteristic number (n—4) (2—5) (n—6) (15n—9). As MP represents
6 (n—-3) (n—4) (n—5) (n—6) coincidences, and the remaining ones
arise in pairs from tangents fo23, the tangents 1253 envelop a curve

of class 12n (n—A) (n

5) (n—6).

5. The /,°, which IP determines on /, contains 4(n—3)(n— 4)\(n—5)
groups with three double elements; as many curves c” have / as
triple tangent f22. In the net determined by P occur 2 (n + 3) :
(n—4) (n—5) Cc”, on which P is point of contact of a triple tangent”)
If / rotates round P, the points of contact describe therefore a curve
of order 4 (n—38) (n—4) (n—5) + 2 (nr + 3) (n—4) (n—5) or 6 (n—4)
(n—-5) (n—1).

We further determine the order of the locus of the groups of
(n—6) points Q, which / has moreover in common with the cr,
which it touches three times. The 422 belonging to the net with
base-point P envelop a curve of class 2n (n—3) (n—A4) (n—5).*) As
P is point of contact for 2 (n+3) (n—4) (n—5) c”, the number of c*
intersecting their f22 in P amounts to 2n (n—3) (n—4) (n—5) —
— + (n+3) (n—4) (n—5) or 2 (nd) (n—-+) (n—5) (n —6). The order

1

ES oF p. 936.
2) N. p. 943.
en BN. p. 280.

1059

of (Q) is therefore equal to 2 (n+-1) (n—4) (n—5) (n-—6) + 4 (n—3)
(nd) (n—5) (n—6) or } (5n—3) (n—4) (n—5) (n—6).

The correspondence (MR, MQ) produces again the class of the
envelop of 4223 ($ 4).

From the symmetrical correspondence (MQ, MQ), which has as
characteristic number 3 (5n—8) (n— 4) (n—5) (n—6) (n— 7) and has in
MP + (n—3) (n—4) (n—5) (n—6) (n—7) coincidences, we find that the
quadiuple tangents tsooa envelop a curve of class 4 n(n—A4) (n— 5)

(n—6) (n—7).

6. Any point of the arbitrary straight line a, is, as base-point
of a net, point of contact A, of (n—-4) (n+9) tangents f25.1) The
locus (,), of the corresponding points of contact PR, has two groups
of points in common with a; the first group contains the (407 — 105)
intersections with the curve (#,), the second contains the 6 (n—3)
(n—4) points A, where a is touched by the curves c”, osculating
it in a point A, From this ensues that (2,), is of order (62?—2n—33).

In order to find the order of the locus of the points JV’, which
each fo3 has in common with its c”, we consider the figure produced
by projective association of the corresponding systems [c”] and [to |.
The curves c”, of the*net determined by P, which possess a fos,
have their points of contact R, on a curve of order 3 (n—4)
(n?+6n—13)*); the latter intersects a in the points /, of the curves
of [c"] passing through P. The index of [f3] is, see § 4, (n—4)
(7n—9). Considering that the figure produced is composed of 3 (n—4)
(n+9) times the straight line a, twice the curve (R,)a and the
locus (W),, we find for the order of tbe last-mentioned curve

(n—A4) (Bn* + 18n—39) + n (n—4) (7n—9) — 3 (n—A) (n + 9) —

— 2 (6n?—2n—33) = (n— 5) (10n? + 4n—-66).

The curve (W), cuts a in 6 (n—3) (n—4) groups of (n—5) points
W; in each of the remaining intersections a c” has a four-point
contact with a line 449. Consequently the points of contact R, of the
tangents ty. lie on a curve of order (n—5) (4n?+46n—138).

The pairs of points R,,W determine in a pencil of rays (M)
a correspondence with characteristic numbers (n—5) (10n’?+-4n—66)
and (n—®5) (6n?—2n—33). The (n—4) (7n—9) rays to passing through
M, which have their point of contact AR, on a, represent each
(n—5) coincidences. From this ensues that the points of contact
(inflectional points) of the twice osculating lines are situated on a
curve of order (n—5) (9n?+39n—135).

1) N. p. 942.

8) N. p. 940.

10*

1060

The symmetrical correspondence (MW, MW’) has as characteristic
number (2—5) (n—6) (10n°+4n—66) and possesses (n—5) (n-—6)
coincidences in each of the (n—-4) (7n—9) rays WR, . The remaining
ones arise in pairs from tangents 422,3. So we find that the inflectional
points R, of the tangents tao3 lie on a curve of order } (n—5) (n—6)
(13n?++457—168).

7. Let us now consider the system {c”| of the curves which
have the point of contact /, of their tangent t,3 on the straight
line a. The curve (R,), cuts a in (40n—105) points R, and in
6 (n—3)(n—4) points R,, where a osculates a c”, for which it is
tangent t3. Consequently (R,), is of order (6n*— 2n— 33).

The system |c"] has as index (n—4)(6n?+-15n—36)'); for (toa
the index is, see § 4, (”—4j (9n—9). The figure produced by these
projective systems consists of 2(n—d)(3n9) times the straight
line a, three times the curve (R,), and the locus of the points W*,
which each fs; has moreover in common with its c”. For the order
of (W*), we find (7—A4) (6n?-+-15n—36) + n (n—4) (9n—9) — 2 (n—4)
(Bn4-9) — 3 (6n?—2n—33) or (n—3) (L5n?—3n—68).

The number of the intersections of (MW) with a again produces
the order of the curve (/?3)33.

The correspondence (MR,, MW) has as characteristic numbers
(n—D5) (15n? —38n—63) and (n —5) (6n?—2n—3833), while each of the
rays f23 passing through J/ represents (n—5) coincidences. From
(n—5) [(15n?-—3n—63) + (6n?—2n—33) — (n—A4) (Yn—9)] we find
now that the points of contact R, of the tangents to, are situated
on a curve of order (n—5) (12n?+40n—132).

The symmetrical correspondence (MW, MW,*) furnishes in the
same way from (n—5) (n—6) | (80n?-—6n—1 26) — (n — 4) (9n—9)] the
result, that the points of contact R, of the tangents t93 lie on a
curve of order (n—5) n—6) (21n?+39n—162).

8. Let us now consider the system [c”| of the curves with triple
tangent of which one of the points of contact, #,, lies on the
straight line a. The other two points of contact 7,, lie on a curve
(7.)., which has two groups of points in common with a. The
former contains the (n—5) (4n?+46n—138) points ft, of tangents
tio (§ 6), the latter the groups of three points of contact 7, lying
on the curves c”, for which a is triple tangent; these points are
apparently to be counted twice. Consequently (7), is of order (n—5)
(4n?+-46n— 138) + 8 (n—5S) (n—A4) (n-—3) or (n—5 (12n?—10n—42).

IN. p. 940.

1061

We now consider again the figure produced by the projective
systems [c"] and [422]. The former has as index $(n—4)(n—-5)(3n?-+-
+5n—14) '), the latter, see § 5, 6(n—4)(n—5)(n—1). As the figure
produced consists of 4(2-+3)(n—4)(n—5) times the line a ®, twice
the curve (7), and the locus of the points Q, which each c” has
moreover in common with its 4292, we find for the order of (Q),

ty (n—d) (Bn? + 5n—14) + 6(n —4) (n—5) (n—1) n—4 (n-- 4)
(n—5) (n-+3) — 2 (n—5) (12n?—10n—42) or + (n—5)(n—6) (210? —
Lin --72). :

The curve (Ca is cut by a in 4(n—3)(n—4)(n—5) groups of
(n—6) points Q, which are each to be counted thrice, and in a
number of points (7), where a c”is osculated by a tangent ts.
From 4 (n—5)(n-—6)(21n?—11n—72) — 4 (n—8) (n—A4) (n—5)(n —6)
ensues again (§ 6), that the points of contact T, of the tangents
i322 are situated on a curve of order 4 (n—5)(n—6)(138n?+45n—168).

The correspondence between the points 7, outside a, and the
corresponding points Q, produces again the order of the curve (2,)
belonging to the tangents f293 ($ 7).

The symmetrical correspondence (MQ, MQ) has as characteristic
number 4(2— 5)(n—6)(n—7)(21n?—11n—72) and in each be passing
through J/ (n—6)(n—7) coincidences. From (2—5)(n—6)(n—7)| (210? —
14n—72)—6(n—1)(n —4)| ensues that the locus of the points of
contact of the quadruple tangents is a curve of order 5 (n——5)(n—6)
(n—7) (15n?+19n—96).

9. Let us now consider the figure determined by the projectivity
between the curves c”, which possess a f2222 and those quadruple
tangents. The system [c”] has as index (n—1)(n-+-4) (n—4) (n—5)
(n—6)(n—7) *), the tangents f.222 form ($ 5) a system with index
$n(n—4)(n—5)(n—6)(n—7). The figure produced consists of twice
the locus of the points of contact ($8) and the curve (S) of the
intersections of the ct with its quadruple tangents. For the order
of (S) we now find £(n—4)(n—5)(n—6)(n—7)( Tn? +-9n—12)—4 (n—5)
(n—6) (n—7) (80n? + 38n—192) or 4 (n—5)(n—6)(n—7)(n—8)(7n? +
in—30).

The correspondence (7, S) determines in the pencil of rays (J/)
a correspondence with characteristic numbers }(2—95)(7-—6)(n—7)
(n--8\(157?+19n—96 and 4(n—5\(n—6)(n—7)(n—8)(7n? + 7n—380).
As the tangents f022 passing through J/ each represent 4(n—8)

1062

coincidences, we find that the complex contains (n—5)(n—6)(n—‘7)
(n—8)(9n?+37n—72) curves with a tangent te2,2,.

The correspondence (MS, MS’) has as characteristic number
HN --5)(n—6)(n—7)(n—8)(n—9)(7n? +-7n — 30); each tangent f2202

Tt |
passing through J/ represents (2—8)(n

9) coincidences. From
2 (n—5)(n—6)(n—-7)(n—8(n—9)| (Tn? +- 72—30)— 2n(n—4)] ensues that
49(7—5)(n—6)(n—:7)(n—8(n—9)(n?4-38n—6) curves of IT possess a
quintuple tangent t99,29.

10. The curves c” with a twice osculating tangent 433 form a
system with index $(—4)(n—5)(n?+-7n—9) *), their tangents 433
(§ 4) a system with index 9n(n—4)(n—5). The figure produced by
these projective systems consists of three times the curve (Js)s,3,
containing the points of contact ($ 6) and the locus of the points 0,
which each c” has moreover in common with its é 3. For the order
of (O) we find 3(n—4)n—5)(n?+7n—9)+ In (n —4)(n-—5)— 3(n— 5)
(9n?+39n+135) = $(n —5)(n—6)(3n?+-7n— 21).

The correspondence (MR, MO) has as characteristic numbers
n—5)(n—6(Ou*439In—135) and 9(n—5)(n— 6)(38n? H7n—21); each
tas passing through JM/ represents 2(n—6) coincidences. From this
we find, that the complex contains 6(n— 5)(n — 6)Bn° J-29n—54)
curves with a tangent tss.

The correspondence (MO, MO’) has as characteristic number
$(n—5) n—6)(n—7)(3n? + 7n—21) and possesses in each f3,3 passing
through Jf an (n—6)(n—7)-fold coincidence. From this ensues that 1
possesses 9(72—5)(n —6)(n—7)(2n? +11 n—21) curves with a tangent taz.

11. The curves c” with a tangent ty» form a system with index
6(n —4)(n——5)(n?-+-11n—14) *), their tangents t2 (§ 1) a system with
index 16n(n—4)(n—5). These projective systems produce a figure,
composed of four times the curve (/t4)42, see § 6, twice the curve
(Re), see § 7, and the locus of the points S, which each c” has
moreover in common with its ty».

For the order of (S) we find 6 (2 —4)(n—5)(n?+11n—14) + 16n?
(n — 4) (n — 5) — 4 (n—5) (4n?+ 46n—138) — 2(n—5)(12n* + 40n—
132) = (n — 5) (n — 6) (22n? + 70n — 192).

From (MR,, MS) we find again the number of the fa {§ 3),
from (MR, MS) the number of the #34 ($ 10).

The symmetrical correspondence (MS, MS’) produces one new.
characteristic number. Its characteristic number is apparently (2—5)
(n—6)(n—7) (22n?=-70n—192), while the 16n (n—4) (n— 5) lines #42

1) N p. 942.

3) N p. 938.

1068

passing through M represent each (n—6) (v-—7) coincidences. From
the remaining ones we find, that I possesses (n—5) (n—6) (n-—7)
dn? + 102n —192) curves with a tangent tips.

12. Any point is, in general, node of one er belonging to T.
We consider the system of the ct having their node D on a straight
line a. The straight line connecting D with the arbitrary point P,
intersects cr moreover in (n—2) points /7. The nodal curves of which
a point / lies in P belong to the net with base-point P. Now the
locus J of the nodes of the net (JAacosi’s curve) is a curve of order
3 (n—1), with node in P. The locus (/) has therefore a 3 (n-—1)-fold
point in P; so it is of order (4m —5). In each intersection of (/)
with a, ac” has a node D, of which one of the tangents d passes
through P. Consequently the locus (D)p of the nodes of which one
of the tangents passes through P is a curve of order (42—5) having
a node in P. Hence a straight line passing through P contains
moreover (4n—7) points D; any straight line is therefore tangent in
the node for (4n—T7) nodal curves.

On a straight line / the tangents d of the nodal curves of which
the node lies on a, determine a symmetrical correspondence (ZL, L’):
its characteristic number is apparently (42—5). The intersection of
a and / represents two coincidences, for the ¢”, which has a node
there, determines two points Z each coinciding with the correspond-
ing point LZ’. The remaining coincidences are produced by coinciding
tangents d,d’. So the locus (C) of the cusps (cusp-locus) of Tis a
curve of order 4(2n—3).

18. The curves (D)p and (D)q see § 12, have the (4n—7)
points D in common, for which PQ is one of the tangents. The
remaining (42—5)? — (4n—7) = 16n? — 44n + 32 intersections are
nodes of curves ce", of which the lines d and d’ pass through P
and Q.

We now consider the system of the nodal c”, of which a tangent
d passes through 2. The pairs of tangents d,d’ determine on a
straight line / a correspondence (L, 1’). Any ray d is tangent for
(4n—7) curves; to its intersection L correspond therefore (4/—7)
points ZL’. Through L’ pass (167°—44n 4-32) tangents d’; as many
points £ have been associated to L’. The coincidences of (L, L’)
form two groups; the first contains the (42—5) points D situated
on /, for which d passes through P. The remaining ones arise in
consequence of d’ coinciding with d; the tangents in the cusps of
the complex envelop therefore a curve of class (16n? —44n+30).

1064

14. To each nodal c*‚ of which the node D lies on a we
associate its tangents dd’, and consider the figure produced by those
projective systems. As the ct passing through a point P form a net,
3(n--1) nodal curves of the system in question pass through P.
The index of the system [d‚d’] is, as appeared above, (4n—5). To
the produced figure the straight line a belongs six times. So the
order of the locus of the points /, which c” has moreover in
common with d,d’, is a curve of order 7 (4n—5) + 6(n—1) — 6 =
= 4n?-+n-—12.

For n=3 we find 27; in this case (É) consists apparently
of 27 straight lines. If I has six base-points, this result is confirmed
as follows. Each c* passing through 5 base-points intersects a in
two points D; the lines connecting these points with the 6'h base-
point form each with c? a c* of T, and belong to (/); in this way
12 straight lines are found. The connecting line 4 of two base-points
cuts a in a point D, which determines with the remaining four
base-points a c°; the 15 lines 4 belong apparently also to (/).

The curve (B) euts a in (42—7) groups of (n—3) points / arising
from the nodal curves which have a for tangent in their nodes. In
each of the remaining intersections a nodal c” has a three-point
contact with one of its tangents d. From this ensues that the locus
(I) of the jlecnodes is a curve of order (20n—883).

In the above case n=3 this figure consists of six conics and
fifteen straight lines.

15. The tangents d‚d’ in the nodes of the nodal curves of a
net envelop a curve of class 3(2—1)(2n—3)"). If the net has a base-
point B there is a c* having a node in 5. Through B pass then
3(n—1) (2n—8)—6 tangents d of nodal curves of which the node
does not lie in B. In order to understand this we consider a net
of cubics with seven base-points. Through the base-point B pass no
tangents of proper nodal curves. But the straight line connecting B
with another base-point 5’, forms with the c° passing through the
remaining base-points a binodal c*; the straight line 55” represents
therefore two tangents d. For n= 3 we have 3(n—1)(2n—3) = 18;
as the 6 straight lines BB’ represent 12 tangents d, the tangents d
of the nodal c* having its node in B are each to be counted thrice.

We now consider the system of the nodal curves ec”, which send
one of their tangents d through P. Any ray passing through P is
tangent d for (4m—7) curves (§ 12) and is moreover cut by those

1) Cf. for instance my paper “On nets of algebraic plane curves.” (These
Proceedings VII, 631—633).

1065

curves in (4n—7) (n—3) points G. As base-point of a net belonging
to I P lies on (6n?—15n-+3) tangents d of nodal curves passing
through P; so the locus (G) has in P a (6n? 15n-+-3)-fold point
and is therefore of order (6n?—15n-+3) + (4n—7) (n—3) = 10n? —
— 34n + 24.

The correspondence (MD, MG) has as characteristic numbers
(4n— 5)(n—3) and (10n’—34n+24); the ray MP represents (42 —7)
(n—8) coincidences. As the remaining ones arise from coincidences

D=G, it ensues that the inflectional tangents of the flecnodes envelop
a curve of class (10n?—82n+18),

16. Let the complex be given by the equation

aA + pB+ yC + dD=0.

If the derivative of A with regard to ep is indicated by Aj it
ensues from the equations

aA, + BB, + yCe+ dD, =0 (k=1,2,3)
that an arbitrary point is node of one c”, unless
ede
|
| A, B,
be Bern de
be satisfied.

The exceptional points in question K (critical points) are conse-
quently common points of the four curves of Jacost belonging to
the=weis a = 07.6 =O = 0, ¢ = 0:

To the intersections of |A;,5;,C, —=0 with BeCy Dy =0 belong
the points, for which we have

lie! ZA ot Smee 2 on j
| =e)
| C, C, oF |
and they are not situated on the two other curves /. The last
mentioned relation is apparently satisfied by 2?(m—1)?— (n—1)?=
3(n—1)’ points; consequently the number of critical points amounts
to 3° (n—1)*? — 3 (n—1)’ or 6 (n—1)’.

17. If Fr has a base-point B this is as base-point of any net of
FP, node of the curves J, consequently represents four points K.
The number of critical points of a complex with b base-points
amounts therefore to 6 (n—1)*—4b.

Any point K is node of o' curves forming a pencil, hence cusp
of two curves; the cuspidal tangents are the double rays of the

1066

involution formed by the pairs d,d’. So K is node of the locus (C)
of the cusps.

All er passing through an arbitrary point P form a net, N. The
curve J of N has a node in B and passes through all the points
K; for through B passes one c* of the pencil of nodal curves deter-
mined by A. The curves (C) and J have two points in common
in each point A; they further intersect in the 12 (n—1) (n— 2) cusps
of N; the remaining intersections are found in B. From 4 (2r—3)
(8n—8) —- 2 [6(n—1)* —4] —12 (n—1) (n—2) = 8 it appears that the
curve (C) has a quadruple point in B.

B is node for all c* of a pencil, consequently cusp of two c*;
from this follows that each of the two cusptangents is touched by
two branches of (C).

Any point K is fleenode for jive cv. In order to understand this
we consider the curve which arises if to each nodal c” of the pencil
(K) its tangents d,d’ are associated. The crt? thus produced has
with a line d only (n—8) points outside A in common.

The locus (EF) of the jlecnodes passes therefore five times through
each of the critical points.

The locus J of the nodes in the net MN, which is set apart from
r by an arbitrary point P, has with (/’) five intersections in each
point K. They further have the 3 (m—1)(10n—23) fleenodes *) of
N in common; the remaining intersections lie in the 5 base-points.
From 3 (n—1 ) (20n—383)—5| 6(n—1)*—46 |—-3 (n—1) (10n—23) = 206
it appears that the curve I passes ten times through each of the
base-points.

Each of the inflectional tangents f of the five c”, having a flecnode
in B, touches two of the branches.

18. The curves (C) and (/’) have in the critical points AK and
the base-points B of FP 10[6(n—1) — 46] + 406, or 60 (n—1)’
points in common. Each of the remaining (202 —383) (82—12)—60
(n—1)* intersections is a cusp with a four-point tangent and at the
same time to be counted twice as fleenode. /n V occur therefore
(50n?—192n-+168) cusps with four-point tangent.

If we have n=3, b==6, these particular curves are easy to
determine. Any line BB’ is tangent of two conies passing through
the remaining four base-points; through each point 6 pass two
tangents to the conic of the remaining five base-points. All in all

IN p. 944.

1067

we find therefore 15x 2+6x2= 42 figures (c’, c’), satisfying
the condition.

The tangents in a fleenode we shall indicate by f and d; f indi-
cates the inflectional tangent. We shall determine the index of the
system [d |.

The curve (D)p, containing the nodes which send one of their
tangents through YP (§ 12), passes through the points A’ and twice
through the points 6. With (/’) it has, apart from those points,
(4n—-5)(20n— 33)—30(n—1)?_ or 50n?—172n+135 intersections. As
many tangents f and d pass through ?. The number of lines /
amounts according to $15 to (10n’—32n+-18), hence [d | has as
index (40?—140n--117). f

In order to find the locus of the points G, which any flecnodal
en has in common with its tangent d we consider the product of
the projective systems [c” | and [d |. Their indices are 3(n—1)(10n—23),
i.e. the number of fleenodal c” in a net, and (40n? — 140n + 117).
Since the curve (/’) belongs three times to the figure produced, we
find for the order of (G) 3(¢n—1) (10n —23) + n(40n?—140n+-117)—
—3(20n—33) or (40n°?—110n?—42n+168).

Let us now consider the correspondence (MF, MG). The straight
lines d passing through MZ produce each (n—3) coincidences; the
number of the remaining ones amounts to (202—33)(n—3)+(40n?—
110n’—42n+-168)—(40n?—140n-+-117)(2 —3)—=170n? —672n+ 618.

To the coincidences “= G determined by this belong in the first
place the cusps with tangent ¢,; the remaining ones arise in pairs
from nodal curves with two inflectional tangents f. Their number
amounts therefore to 4 [(170n°—672n4618) — (50n?—192n+-168)] ;
the complex contains (6On? — 240n + 225) curves with a flejlecnode.

In the case n=3, b=6 we find 45 for it. Each of the trilaterals
belonging to I’ is apparently to be considered as a figure with three
flefleenodes.

19. In a similar way as in N$5, 15, 14 it may be determined
how many times a base-point 4 of the complex is point of contact
of a particular tangent. We find then in the first place that B is
point of contact A, of ten tangents ¢,. It is further consecutively
found that B is point of contact ft, of (n—5) (n-+-16) tangents 44,9,
point of contact 2, of 3 (n—5) (n+6) tangen:s ¢s3 and of 2 —5)
(n—6) (n+6) tangents 4322, point of contact A, of 2(m—5) (8-8)
tangents fas, of 3(n—5) (n—6) (3n+8) tangents fo39, and } (n—5)
(n—6)(n—7)\(3n-+-8) tangents f2209.

ge

1068

Physics. -— “The diffusion-coeffictent of gases and the viscosity of
gas-miatures.” By Prof. J. P. Kurnen. (Communications from
the Physical Laboratory at Leiden. Suppl. 38).

In two previous communications’) on the same subject it was
shown to what cause the difference between the results of the two
current theories of gas-diffusion is to be ascribed. Whereas MaxweLr’s
theory (STRFAN, LANGEVIN, CHAPMAN ®)) leads to the result, that the
coefficient of diffusion is independent of the proportion in which two
gases are mixed, O. E. Meyer’s theory which uses the method of
the molecular free path gives a coefficient which changes with the
composition of the mixture. For two gases whose molecules have
, the coefficient of diffusion lies between two
limiting values which are to each other in the proportion m,:m,.
The coefficient of diffusion for carbon-dioxide (J/,—44) with a
trace of hydrogen (J/, = 2) would be 22 times larger than that of
hydrogen with a trace of carbon-dioxide; between those limiting
values D would diminish regularly with the composition.

The cause of this difference between the two results is due to
the circumstance, that in O. EK. Mnygr’s theory no account is taken
of the ‘persistence’ of molecular motion which was introduced into

masses 7, and m

the kinetic theory by Jrars®). The persistence consists in that a
molecule, when colliding with another, retains on the average a
component of velocity in the direction of its motion before the
collision, so that after a collision all directions are not, as used to
be generally assumed, equally probable. The manner in which
Juans corrects O. E. Mryrr’s formula for the persistence is incorrect,
however, and does not lead to a better result, because he takes for
the persistence the value derived by him for a single gas, whereas
the persistence in a mixture should have been introduced. In the
previous papers cited above it was shown, that by doing the latter,
the formula is modified in such a way, that the strong contradiction
with the result of the other theory disappears.

Qualitatively the matter may be put as follows. Let us first
consider earbon-dioxide with a trace of hydrogen; the theory shows
that in this mixture D is determined by the mobility and by the
free path of the hydrogen-molecules which are both relatively large,

1) J, P. Kuenen. These Proc. 15. p. 1152. 1913. 16. p. 1162. 1914. Comm.
Leiden, Suppl. 28, 36.

2) S. CraPuaN, Phil. Trans. 211 A p. 483. 1912; this article which was not
mentioned in the previous papers may be specially referred to on this occasion.

5) J. H. Jeans Dyn. Theory of gases. 1904. p. 236. seq.

1069

viz. the former inversely proportional to W/m, and the latter propor-

. . . . m 1 . .

tional to VWm,, so that D is proportional to | 7™. Similarly for
m, ;

(en $ Á : m,
a trace of carbon-dioxide in hydrogen YD is proportional to Sat

Mm,
so that the ratio of the two coefficients is as mm, : m, = 44: 2. When
the persistence is taken into account the ratio becomes quite different :
the persistence is much smaller for the light hydrogen-molecules
than for the heavy carbon-dioxide molecules, the consequence being,
that the diffusion-coefficient is much less increased by the correction
in the former than in the latter case. With the value given for the
persistence in the papers mentioned the compensation was even
complete, so that D for n,=0O became equal to D for n, =0,
whereas for intermediate mixtures D obtained other values.

Quite recently Miss A. SNEeTHLAGE, student of physics at Amsterdam,
who is engaged on an investigation of various applications of the
persistence-theory, has drawn my attention to the fact, that the
expression given by me for the persistence cannot be correct. For,
whereas for the case, that the masses m, and m, of the molecules
are equal, it gives correctly the expression found by Juans, on the
other hand for m, infinite it gives a negative value, although a
simple calculation shows that its value must be nought in this case.

In repeating the calculation it was found that on the former
occasion an error had crept in which would have been noticed
before, if the agreement with Jmans’s value for m, =m, had not
erroneously been taken as a proof of its being correct. The present
caleulation yielded the following expression for the mean persistence
of a molecule m, colliding with a molecule m, :

m, 1 m,” V(m, + m,) + Vm,
NE Gm, +m) |E mgle(m, $m,” Vm, Hm) — Vn,
which is identical with that found by miss Syeranace. The calcula-
tion may be shortly reproduced; with a view to an easy com-
parison with JrANs his notation and also, as far as possible, his
method of calculation will be used.

We take two molecules with definite velocities a and 6, which
collide in all possible ways, and calculate for molecule a the mean
velocity after the collision taken in the original direction of its
motion. Maxwerr has proved, that this velocity is equal to that of
the centre of mass projected on the same direction. Calling the
angle between a and 4 &, this projection p is given by

am, + bm, cos 3

ee 7
m, + ™,

1070

This projection has now to be averaged for all angies 9, taking
into account, that the chance of a collision for each direction is
proportional to the relative velocity + and to 4 sin 0dd. The mean
is therefore given by

| prsin ddd

0

Tt

Ir sin d dd

: 0
As r?>=a’?-+ 6? —2abcos%, it follows, that rdr = ab sin dS.
After substitution of si 9d9 and of p and integration we obtain
2m, +m,) a° + m,b? mM, 3 da'4-10a7b?+40* |
NE : for’ >b

EE TOR

2(m,-+-m,) a =

and
(2m, Am) a +-m,b° m, 3 a'+10a7b? +564
EN ze “for a <b;

m,+m, 10a a’? t- 3b?

2(m,+m,)a
these expressions have to replace those given by Jrans (l.c. p. 239).
With Jrans we may put a= xb.
ry . mn = .
The chance per second, that a molecule with velocity a collides
with a molecule with velocity 5, the relative velocity being 7, is

aa oe b
2n, 0 x h® m,* kml? — db r? dr,
a

where 7, is the number of molecules im, per unit volume, and as

2

the number of molecules per unit volume with velocity a is equal to

h'm,® .
An, ehm? qa? da
nr

(n, = total number of molecules m, per unit volume), the total
number of collisions of the kind considered will be

Sn. n, 62h? Vm? m,? e— hOma?Hmsb?) ab da db r? dr.
1 8 1

2
Integrated with respect to r for a >> b, when the limits of 7 are
a+ and a—b, this becomes

16 Ars,

mt oh Vm'm, ehm atmabì) ab? (Pa? + 5”) da db
and similarly for a <b

16 ee STEN
ie ot h®? Vm? mt eh ma*-+mad?) ab (a° +. 3b?) da db.

e

In both expressions we may again put a =x.

1071

To find the mean persistence the above expressions for the number
of collisions have to be multiplied each by the corresponding mean
persistence, separately for a> and a< bd, then to be integrated
with respect to 6 between O and oo, further with respect to x,
in the former case between 1 and oo and in the latter between O
and 1, and finally to be divided by the total number of collisions :

A x (m, Jm, )
2n,n, O° é
3 hm. im,

The result of this somewhat lengthy calculation which need not
be detailed any further was given above. A corresponding expression
is found for the 77,-molecules viz.

ma, 1 m,” V(m, +m. 1) a Vim,

v, ze Ee + en log EE
2 (m, — m,) 4 m,'l2 (m,+m, )*/2 Vm, Gi Adel Vin,

The formulae given before for the coefficient of diffusion are now
somewhat modified. Qualitatively there is no change, but the com-
pensation at the limits referred to above is not so complete as
before.

For D the same expression holds as before viz. :

I ,
= ae (as ulder de nu, lbf),

where /, and /, keep their oe viz

== . ;: pee m, +m, ia
W2n, ze, 1 Bie 57 rn + 1,16 ee 1 + =

Ave 5
i Sa Me Wan (1 ps 7 ae naal eA mm,

; nt C . ; oen mm, Ex
ed BS | Vn (1) 1.x0.406-n,20°| ea Sime ‚|

and
, — 5 C k ; m ETR GC
besl ë | 1-Wen,ns, (14.55 )x0.400—1 20 ye = EE DAAR
For n,=0O and n, =O we now obtain:
5 0) g (ea om, ; ie Gs; 1
Bee 3nzo' hm, (m, 4m.) re 273 16)

and

1072

2 m, Gn 1
a : 14 —* le,
Suaro® ahm,(m,+-m,) 273] 1—#d

the ratio of which is:

Din,=9) _ m, 1—d3,
D(n,=9) m, 1—9,

Caleulation gives for the persistence of carbon-dioxide in relation
to hydrogen 0.942, for that of hydrogen in earbon-dioxide 0.239, so
that for these two gases the above ratio becomes 0.77. According
to the theory as corrected the ratio is therefore still much nearer
unity than according to the uncorrected theory of O. E. Meyer
which gives @; = 0.045 in this case. As a complete agreement with
Maxwerr’s theory is in any case lacking, the remaining difference
between the two limiting values is not of any special consequence
and no useful purpose would be served by communicating further |
numerical results. With combinations of gases which differ less in
molecular weight the difference between the limiting values is smaller.

The formula for the viscosity of a gas-miature undergoes a cor-
responding modification. As before the relatiod holds:

i n
et ~ 1 a or 2 at
= 0.385 dnl fy’ + 035 duly

n

where /’, and /’, now have the values:

= C
eae ie Wa nxs | 1 -+- En lL. x< 0.406 —
ì 273

The ete ide which are now found for mixtures of carbon-
dioxide and hydrogen, and of argon and helium respectively are
somewhat lower than before, but the maxima which had to be
explained by the theory remain. For the former pair of gases cal-
culation for n, =n, —=+4n gives 74 == 0.0001470 (observed 144), for
the latter pair 4 = 0.0002306 for n, =n, = $n and xj = 0.0002281
for n,=2n, n,=2n, which results differ even a little less from
the observed maximum 0.0002207 than according to the former
calculation. |

ERRATA.
In the Proceedings of the Meeting of September 26, 1914:

p. 528 line 9 and 10 from the top: For: “On plate IA of Comm.
N°. 107a may be seen that part of the apparatus” read: “Part of
the apparatus of Plate IA of Comm. N°. 107a is similar to that
of our apparatus”;

p. 532 line 6 from the bottom: for “the radius of molecular
action is larger” read: “the sphere of molecular action reaches in
the liquid to further layers of surrounding molecules”.

In the Proceedings of the Meeting of December 30, 1914: p. 905
line 6 from the top: for 904 read 900.

February 27, 1915.

«
Li
4 Je Vy Ei # . Ee
ds in 7
ak,
Ed 5
ri fia =
pj k Eh : .
ive a) - \ ; ri
— jn 1 5 . ‘
pi bi
+ Vb Me \ nl
if En _
5 =»
wi miss a + « \
a a rj ú ® 5
\ Een
n ‘
Ss d i 8. Ed 7 de _
ie en 1S :
r §
a So ie
J ; -
y ng we . i ra
ap om - '
h ’ i “a ‘ *
7 i N
N > a i
ane u =
Ep gs ” \ ;
5, Oe ee en ee aus j
a Wi 3 5 ‘J

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING
of Saturday February 27, 1915.
Vor. XVII.

3G
President: Prof. D. J. Korrrwee.

Secretary: Prof. P. ZERMAN.

Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 27 Februari 1915, Dl, XXIII).

NED: IT EE EENES:

S. pr Boer: “On the heart-rhythm”. (Communicated by Prof. J. K. A. WerrnHeim
SALOMONSON), p. 1075.

K. Kuieer Jr.: “The physiology of the air-bladder of fishes”. (Communicated by Prof. Max
WeBER), p. 1088.

Miss Apa Prins: “On critical end-points and the system ethane-naphtalene”. (Communicated
by Prof. A. F. HOLLEMAN), p. 1095.

JAN DE Vriks: “Systems of circles determined by a pencil of conics”, p. 1107, ;

F. A. H. ScHRRINEMAKERS and Miss W. C. pr Baar: “Compounds of the arsenious oxide” I,
js akiats

Ernst Conen and S. Worrr: “The allotropy of potassium” I, p. 1115.

H. A. VERMEULEN: “The vagus area in camelidae”. (Communicated by Prof. L. Bork), p. 1119.

Physiology. — “On the heart-rhythm”. By Dr. S. pr Boer. (Com-
municated by Prof. Dr. WeRTHEIM SALOMONSON).

(Communicated in the meeting of Jan. 30, 1915).

1. The a-v-interval and the refractory period. *)

The normal heart-rhythm is caused by a system of different fac-
tors, among which the irritability and the transmission of stimulation
of the different parts of the heart are of great significance. I have
now made a series of experiments on frogs, in which | have modi-
fied these two principal properties of the heart by means of veratrine.
I followed in my experiments this method: the heart was suspended
on the point, after I had removed the sternum, cut open the peri-
cardium and cut the frenulum in two. The single suspension was
used, because I intended to note down, after the poisoning, during

1) The experiments mentioned here were communicated by me in a lecture,
held in the meeting of the biological section of the Genootschap ter bevordering
der Natuur-, Genees- en Heelkunde at Amsterdam of November 19th 1914,

71
Proceedings Royal Acad. Amsterdam. Vol. XVIL.

1076

a. couple of hours and longer, all systoles; this aim can be better
reached with one lever than with two. By doing so I had to watch
only one friction on the smoked paper, when noting down the
systoles of the auricles and ventricles, so that their succession, with
regard to time, can be better estimated and we obtain a better
survey of the whole reproduction. The curves were noted down by
the lever on an endless smoked paper which was wound round
three kymographia; the motion was obtained in the usual way by
making one of these apparatuses turn, whilst the two others with
unserewed axes followed the revolution. In this way I could note
down during two hours and a half after the poisoning all the curves
and obtained the entire reproduction of the poisoning; in order to
make a comparison first about one hundred systoles of the unpoi-
soned heart were reproduced. To a maximum of ten drops of 1 °/,
acetas veratrini were then injected into the abdominal cavity. About
10 minutes after the injection the systoles became larger and wider,
the a-v-interval increased, the electric irritability of the ventricle
diminished. When I fixed before the poisoning the weakest stimu-
lation with which I could obtain an extra-systole after the beginning
of the diastole, I had, after the poisoning, either to strengthen it or
to apply it later, in order to obtain the same effect. This continued
till in the end, during the whole diastole, I did not obtain any
effect on the ventricle not even with the strongest stimulation.

In this stage of the poisoning I observed quite a new phenomenon :
at the end of the diastole no extrasystole was obtained after irri-
tation, but a pause of the ventricle. The duration of this pause
was always of such a nature that, added to the duration of the
preceding heartperiod, they amounted together to two heart-periods.
The pause began with an extrasystole of the auricle. The auricle
was now irritable indeed, which was promoted by lengthening the
a-v-interval. This extrasystole of the auricle was caused by retro-
gressive transmission of stimulation or with strong stimulation by
current-loops.

The next-following irritation coming from the sinus venosus finds
then the auricle refractory. The result is that one auricle- but likewise
one ventricle-systole falls out of the normal rhythm, and so an
extra pause takes place. Now it is remarkable to see, how strongly
widened the postcompensatory systoles are after these extra-pauses
without extra-systoles. This fact is indeed entirely in accordance
with the law on the conservation of the energy of the heart
(LANGENDORFF). In my case indeed pause of the ventricle 1. e. rest
of the ventricle appears without preceding extra-systole. The condi-

1O77

tions for the formation of a postcompensatory systole as wide as
possible (according to LANGENDORFF) are then most favourable.

The irritability of the heart-muscle during the diastole has much
improved again during the pause. This appears from the fact, that
the next-following systole, after the posteompensatory one, occurs in
the diastole of this posteompensatory systole. The ventricle conse-
quently is now susceptible of the weak physiological irritation
coming from the auricle, whilst, two heart-periods before during the
diastole, it was still insusceptible of a much stronger, artificial
stimulation. By artificial irritation in the diastole of the post-com-
pensatory curve I could again bring about extra-systoles, which did
not occur when, with the same strength of stimulation, I irritated
at the same moment of the diastole in the normal rhythm. The
refractory period however can be enlarged during this great systole
without extending to the diastole. Experiments, in which I noted
likewise the action-currents, taught me, that during the extra-pause
the ventricle neither produced action-current.

[ repeated this experiment more than a hundred times. An

extra-stimulation occurring somewhat later caused again an extra-

systole (vide Fig. 1 the 7 systole of the second curveseries).

In a later period of the poisoning the rhythm of the ventricle is
halved, after the extent of the systoles has first diminished. The
cause of this phenomenon lies in the prolongation of the refractory
period and of the a—vy-interval. An auricle systole falls consequently
at last in the refractory period of the preceding ventricle-systole, so
that then every 2" auricle-systole remains unanswered by the ventricle.

[Ne

1078

Soth of auricle and ventricle the halving of the rhythm can also
suddenly oceur (i.e. with regard to the sinus-contractions).

After this rhythm-halving the a-v-interval is shortened again, the
irritability of the ventricle has improved: an extra-stimulation during
the diastole causes again an extra-systole, but now without compen-
satory pause; the row of the ventricle-curves has only been removed
by one auricle-systole. Tbe duration of this extré-period + the duration
of the preceding period is now equal to the duration of 1*/, heart-
periods. :

When now this halved rhythm of the ventricle has existed for ¢
short time, I can, with one induction-stroke during the diastole,
reduce this rhythm to the original one, which can continue again
for some time: consequently an artificial return to the original
rhythm. This experiment can be explained as follows: Im the first
place it is irrefutable, that the metabolic condition of the heartmuscle
was such as to allow the heart to pulsate in the normal rhythm;
nor were the physiological irritations proceeding from the auricle
wanting, for only the ‘ventricle pulsated in the halved rhythm; and
yet this halved rhythm would have continued, if I had not intervened
by an extra-stimulation. The cause of this phenomenon is, that the
systoles of the halved type are much larger and wider than those
of the not halved one. Each systole in itself of the halved type has
consequently a larger refractory period, so that each second auricle-
systole cannot be answered by the ventricle. The ventricle is conse-
quently, as it were imprisoned in its own rhythm; if there were
enly one narrower systole with a smaller refractory period between,
then the normal rhythm would have been restored with the smaller
systoles. Now I obtain this little systole as an answer to the extra-
stimulation, and because the latter took place directly after an auricle-
systole, the extra-systole is not followed by a compensatory pause,
but after the extra-stimulation I detect a continual recovery of the
original rhythm. If the extra-systole was foliowed by a compensatory
pause, this recovery of the rhythm could not take place, for the
postcompensatory systole would have been enlarged (= widened)
again, and would thus restore again the halved rhythm. At the same
time we have here consequently before us an example of an extra-
systole without a compensatory pause. The ventricle can thus again
pulsate e. g. about 5 minutes in the original rhythm and then pass
again in the ordinary way into the halved rhythm. During the first
time of halving the metabolic condition of the heartmuscle had
certainly much improved, but every large systole of this type has
in itself a larger refractory period than every little systole of the

: 1079

normal rhythm. The pauses in the latter rhythm, however, are much
shorter, so that after some time the refractory period, at a given
moment, after a systole of the ventricle, no longer depends only
upon the preceding systole; for on account of the insufficient restor-
ation between the quick heart-periods the preceding systoles have
also had influence upon it; the refractory period increases again in such
a way, that once more a halving of the ventricle-rhythm takes place.
T could also bring about this change artificially, by intervening exactly
in the same manner, by which I could alter the balved rhythm.
By an extra-stimulation during or a short time after the diastole I
made an extra-systole; this was followed by a compensatory pause,
after which the post-compensatory systole, as always, is enlarged
and widened. The enlarged refractory period is the cause that the
halved rhythm returns again, because the first-following auricle-systole
takes now again place in this refractory period. I could consequently
these variations of rhythm bring about discretionally when the
ventricle-rhythm had been halved for some time.

I practised a second method of variation of rbythm according to
a quite different principle and with as certain a result. When the
ventricle pulsated after the veratrine-poisoning in the halved rhythm,
1 eould by refrigeration of the sinus venosus make the impulses,
originating in the latter, reach the ventricle in a slower tempo.
Thus every second auricle-systole moved over.the refractory period
of the preceeding ventricle systole, and restoration of the original
ventricle-rhythm was the result. As a transition I obtained then
heart-bigeminy and trigeminy. Consequently we obtained here by
refrigeration of the sinus venosis an increase of the frequency of
the ventricle. this is an exception to GaskELI’s experiment which
teaches us, that refrigeration causes a decrease of the rhythm. Cale-
faction of the sinus venosus causes, after the preceding experiment,
a return of the rhythm to the halved one.

Another method of bringing about variations of rhythm is cale-
faction and refrigeration of the ventricle. Calefaction of the ventricle
shortens the refractory period, and changes consequently the halved
rhythm into the normal one; refrigeration of the ventricle causes
then again a restoration of the halved rhythm. I could most quickly
change the halved rhythm of the ventricle into the normal one by
refrigerating the sinus venosis, and at the same time calefying the
ventricle. Especially by this latter method the variation of the rhythm
sueceeds always. The variation by an induction-stroke succeeds only,
when the halved rythm has not yet existed a long time, or when
at the reaction of the poisoning, the halved rhythm was to change

1080

again after the lapse of not too long a time into the not halved one.

I saw also repeatedly variations of rhythm occur spontaneously.
When the poisoning-process increased these variations of rhythm
resulted in the halved rhythm, which by further halvings applied to
1 ventricle-systole caused 4, 8 or sometimes 5, 6, or 7 auricle-systoles.
At the reaction of the poisoning during the halving period these
variations of rhythm are accompanied with varying lengthening and
shortening of the a-v-interval. The lengthening occurs during the
quick rhythm, the shortening by restoration during the slowly
halved rhythm.

When the poisoning continues, no restoration takes place, but
through lengthening of the a-v-interval and the refractory period
further halving is the necessary result.

2. The transmission of stimulation in the ventricle.

We have seen that by poisoning with veratrine the transmission
of stimulation between auricle and ventricle slackens. The mechano-
grams do not tell us anything about the transmission of the stimula-
tion in the ventricle-muscle itself. In order to obtain more information
about this subject I reproduced the action-currents before and at
fixed times after the poisoning.

In Fig. 2 we have the suspension-curve and the electrogram of
a not poisoned frog’s heart. Time in '/, sec. Electrodes auricle-
ventrical.

Whilst leaving for the rest all the circumstances the same, I
make 12 minutes after the injection of 5 drops 1°/, acet. veratrine
(vide Fig. 3) another reproduction.

The R-top is raised and widened, it is somewhat split.

The T-top has become positive, the line of connection between
R and the T is lowered. The heartrhythm has slackened. The pauses
between the mechanograms have lengthened, but those between the
electrograms have shortened. The electrograms before the poisoning
lasted till the beginning, after the poisoning till the end of the diastole ;
the duration of the electrograms runs parallel with the duration of
the refractory period.

Both are indications of the metabolic processes of the heart-muscle.
After the poisoning the beginning of the R-oscillation goes much
more in advance of the suspension-curve than before the poisoning.
The period of the latent irritation has consequently considerably
lengthened after the poisoning.

Directly after the halving of the ventricle-rhythm, 1 hour 20 min.
after the injection I obtain the representation of Fig. 4.

1081

“(pagauaop Áppuonbasuoo ‘aun, oy] Jo UOIejDsO UR SJAAND

JIM AAAND UOIsUIdsns a} sAvOpop Ua] ses *, ur doy ayy yw st ou ayy Of Pur “Gy 7

Oe Ge

otf) [LE ul SMOTS

0

sised OU} JO APANRF0U or) Baris ayy JO Suo|RpOso auy wWoyOg ayy Ie tau ayy spaeasroy, payoap doz am

1082

1083

1084 .

We see that with the restoration of the metabolic condition of
the heartmuscle the variations indicated above have for the greater
part regressed again. I call only the attention to the shorter duration
of the R-oscillation. The a-v-interval is even again shorter than before’
the poisoning. Slackening of rhythm promotes shortening, poisoning
lengthening of this interval.

Directly after the halving shortening prevails.

35 minutes after the reproduction of Fig. 4 I obtain representation
Fig. 5. The R-branch has widened and split again, the a-v-interval
has increased, and likewise the period of the latent irritation.

If now, in analogy with the duration of the action-currents for
the striped muscles, we see in the duration of the R-oscillation a
measure for the speed of the transmission of stimulation in the heart
musele. then the variation of the duration of the R-oscillation becomes
immediately intelligible. Through the poisoning the speed of the
transmission of stimulation decreases, after the halving it improves
again in the beginning, when the poisoning continues, the transmission
falls afterwards off again into this halved rhythm.

We saw before, that the irritability of the heart muscle sustains
the same oscillations during the poisoning and the halving-process.
This canvot be otherwise, for transmission of stimulation means, that
a level that is in irritation influences an adjacent level. The
speed with which this influence can take place depends upon the
irritability. .

In a following period of the poisoning the basis and the point
of the ventricle palpitate alternatively stronger (Vide Fig. 6). The
a-v-time has increased again.

If now 25 minutes later I make another reproduction (vide Fig. 7)
every 3'¢ systole has fallen out. In Fig. 7 we see consequently a
bigeminusgroup, the point and the basis of which pulsate alternatively.
With the naked eye this could be distinetly observed. We see after
the long pause a short a-v-interval, after a short pause a long
a-v-interval. On my suspension-curves of heart-bigeminy and -trigeminy,
after veratrine-poisoning, of which I possess a great number, the
increase of the a-v-interval in the bi- and trigeminus- groups can be
observed. As an example I give Fig. 8.

I have asked myself if we have here a strict, legal proportion.
Is the transmission of stimulation after a long pause always better
than after a short one?

With a quite different intention I have now made an extensive
investigation concerning the potential differences occurring in the
heart at extra-systoles. In a series of experiments I irritated the

LO85

auricle for this purpose. [ could consequently make use of these
curves for the measurements, and now I find the a-v-interval

Fig. 8.

increased for the extra-systoles, decreased for the postcompensatory
systoles, in comparison with the undisturbed rhythm. The duration
of the R-oscillation behaved in the same manner’).

Herewith I suppose, that I have established a law of the conser-
vation of the power of transmission, both for the connecting systems
of the separate partitions of the heart and for the heart-muscle itself.
In this way LANGENDORFF has established, that the extra-systole is
smaller, the posteompensatory systole larger than the normal systoles,
and saw in ita law for the conservation of energy for the heart-muscle.

When now, 20 minutes after the reproduction of Fig. 7, I make
another reproduction, the basispulsations have ceased and with this
again halving of rhythm has taken place, but now with systoles of
the point-type. Between every two point-systoles there is now one
auricle-systole that is not answered by the ventricle. This second
way of halving of rhythm I saw also often in my suspension-curves.
As a transition-stage heartpoly-, tri- and bigeminy were formed then.

The slackening of the transmission of stimulation by poisoning
with veratrine caused the formation of a split R-top. As an
example I give here Fig. 9.

L shall shortly indicate in what mannet this electrogram was made.

1) The height of the R-top during the extra-systole was enlarged, during the
postcompensatory systole diminished. In this manner it was, if the circulation of
the blood was undistyrbed. That was caused by the bloodfilling of the heart. This
was small during the extra-systole, through which the potential differences are
less exchanged and stronger during the postcompensatory systole, through which
the potential differences are more exchanged. When the bloodcirculation was
disturbed all the R-tops had the same height.

1086

Fig. 10

1087

At half past 2 o'clock L injected the frog 8 drops 1 °/, veratrine
into the abdominal cavity; at LO minutes to three there was halving
of rhythm, the electrogram shows a very quick R-top. In the fol-
lowing reproductions at 3 o'clock, 10 min. past, half past 3 and a
quarter to four, the R-top remains unsplit, but at every reproduction
it becomes wider. The duration of the R-top is in the last repro-
duction 1*/, time-unity of */, second. In the following three repro-
ductions at 5 minutes, 20 minutes, and half past 4 o’eloek the duration
is L*/,, 2 and almost 3 time-unities.

With the increase of the duration of the R the splitting becomes
more conspicuous after every reproduction. The reproduction of half
past four o’clock is represented here in fig. 9. By this the formation
of the splitting of the R-branch becomes obvious. By the slackening
of the transmission of stimulation the influence of the apexnegativity
comes constantly somewhat later (this influence is after all the cause
of the decline of R). At last this influence comes so late, that the
basisnegativity after the quick original oscillation increases again
before the tonical slow oscillation of T.

By the next reproduction, which I made at 4.40, this connection
becomes still more conspicuous. For this purpose I had amply
cauterized the point of the heart with a red-hot probe. With a, for
the rest equal, deduction (auricle-heartpoint) I obtained now the
reproduction Fig. 10.

Here I see indeed again the same initial top. This explains the
splitting of the top. The cause of it is to be found in the slackening
of the transmission of stimulation and the manner in which the
heart-muscle contracts.

At the same time we can see in these experiments an experi-
mental proof that the two components, in the interference of
which the detinitive electrogram originates (at diphasical deduction)
consist of a quick initial oscillation and a subsequent slow one. Accord-
ing to SAMOJLOFF, who saw likewise in his monophasical ventricle-
curves the initial top, this would originate, beeause the deduction
could never be obtained purely monophasically; he supposed the
curves still to be partially diphasieal, which would be the origin
of the sharp initiai top. In my curves, however, the initial top is
detected before the influence of the apex-negativity is felt. The
part of the ventricle-curve into which the sharp initial top falls is
consequenily purely monophasical. In the hearts of my frogs that
were poiscned with veratrine, I always found this split R-top; it is
however no special consequence of the effect of the veratrine, but
wheresoever slackening of the transmission of stimulation takes place

1088

the split R-top appears, as likewise with the extra-systoles of
mammals.

The latter experiments indicate likewise, how, also with other
methods, the splitting of the R-branch can be brought about. For
the genesis of the electrocardiagram this fact is of great significance.
There is, in my opinion, likewise great probability that the purely
diphasical electrogram of the ventricle consists of a quick diphasical
R-oscillation, and a T-branch that is either positive or negative. This
conception would then at the same time afford an explanation of the
formation of the S-branch.

Zoology. — “The physiology of the air-bladder of fishes”. By
Dr. K. Kurerr Jr. of the Physiological Laboratory at Amsterdam.
(Communicated by Prof. Max Weerg).

(Communicated in the meeting of November 28, 1914).
I. The air-bladder as a hydrostatic organ.

For a long time it has been held that fishes possessing an air-
bladder could modify its contents by muscular action, which would
enable them to regulate, within certain limits their own specifie gravity.

If the fish wanted to go down to lower strata a decrease in the
contents of its air-bladder would enable it to increase its specific
gravity. To rise to the surface it needed only to relax the tension
of the muscles of the air-bladder; the gases in the air-bladder
expanded and this increased volume carried the fish upward.

In the latter half of the 19 century, this view, which was
established more especially by Borgiii, and which prevailed during
some centuries without being sufficiently tested by experiment, was
declared erroneous by A. Morrav. Some simple but ingenious experi-
ments convinced him that a modification in the S.G. by an active
muscular action was out of the question.

A fish which, placed in a cage of thin wire, is submitted to
modifications in the pressure on the water in which it is, behaves
exactly like the cartesian diver.

He caused a fish to swim round in a glass vessel which was
closed hermetically, and which was entirely filled with water. The
stopper was pierced by a bent glass tube in which the water-meniscus,
when the fish was at the bottom, was found at a certain point, A
for instance. When the fish swam upward, the meniscus moved
slowly forward, that is to say a decrease of the water column

1089

resting upon the fish, increased its volume. When the fish sank to
the bottom again the meniscus returned to 4. Such meniscus-
fluctuations did not take place if fishes without air-bladders were
put into the vessel. These volume-changes being always synehronal
with the vertical movements, Mornav was led to conclude that they
were passive.

According to Mornav’s view, therefore, the fish could not avail
itself of its air-bladder to change its S.G. in accordance with the
needs of its locomotion. Morpav, discovered however, in the course
of his further experiments that fishes can indeed modify the gas-
pressure in the air-bladder. And this happens in such a manner that
the fish adapts its S.G. to the water-stratum in which it is. It tries
to remain floating in this stratum. If it is placed in deeper water
where it is subjected to a greater pressure, the tension of the gases
in the bladder increases. The volume which had decreased, owing
to the greater pressure from outside, increases again till the S.G.
is 1 again in the stratum in which the fish now finds itself.

If the fish is suddenly placed at the surface of the water two things
may happen; if the fish is a physostomus, then it lets escape through
the ductus pneumaticus, which connects the air-bladder with the
esophagus, as much gas as is necessary to bring it in a state of
equilibrium in the upper stratum; if the fish is a-physoclistus,
missing the above-mentioned safetyvalve, then it can get into equili-
brium with its new.stratum by a slow resorption of the surplus gas.
In a natural state, therefore, every fish will, according to Morgauv,
have one certain depth where it lives by preference. This plane is
called by him “plan des moindres efforts.”

Subsequent investigations by CHARBONNEL-SALLE, BAGLIONL and
Guréror strengthened Morntav’s theory. Only JarGer thinks that
BoreLii’s view has not been conclusively disproved.

Baauiont, who sides with Moreau, draws the attention to the
swimming-movements of a fish when it is exposed to a higher or
lower pressure than that to which it is adapted. Besides being a
hydrostatic organ the air-bladder is, according to him, an organ of
sense which enables the fish to perceive modifications in the pressure.

Jancrr declares himself unconvinced by the experiments of
Mornav and CHARBONNEL-SALLE, and demands that the meniscus-
changes of the water in Morrau’s experiment shall correspond
exactly with the physical volume-moditications of the air-bladder
during the removal to another plane. It is not such a simple thing
of course to demonstrate this. JAEGER tries to prove, by the following
experiment, that the fish modifies its volume by active muscular

1090

contractions. He repeated Morrav’s second experiment, but took a
fish whick bad ‘been narcotized with ether, and hence sank side-
ways to the bottom of the glass basin. When the animal came to,
it gradually raised itself without any motion of the fins and at the
same time the meniscus in the capillary tube moved forward.

GurÉror opposes this view of JAEGER, and tries to prove that both
facts and interpretations in JAEGER’s study are incorrect.

As it seemed to me that the investigations of both authors showed
methodical defects, [ resolved to verify them.

It was not difficult to confirm the general phenomena relating to
fishes living under modified pressures, as described by Morrav,
BAGLIONI, and others. I could establish that different fishes were
sensible to a decreased pressure of from 1—2 centimeters of mercury.
Already before this decrease became such as to drive upward a
fish resting on the bottom of the basin, it showed by the restless
motion of its fins that it responded to this decreased pressure.

I found that in the experiments as carried out by Jancrr and
GuyÉnNor, inaccuracies might slip in, which rendered the results
absolutely unreliable, inaccuracies which seemed to have been noticed
or taken into account by neither of these authors.

The principal mistake was certainly the absence of any means
of verifying temperature-changes in the water during the experiment.
A large glass bottle into which a bent capillary-tube has been
fastened hermetically must needs act as a water-thermometer. If the
water in the bottle has not exactly the same temperature as the
surroundings, considerable meniscus-movements will be the result,
which are by no means due to the presence of the fish in the
bottle.

In the preliminary experiments, carried out without a fish, it
became obvious that such meniscus-movements resulted indeed from
temperature-changes. This rendered the results both of JAEGER and
of Guyénor worthless as soon as the experiments of which they
were the outcome were of a somewhat longer duration (e.g. a quarter
of an hour or longer.)

Hence it was necessary to find a means of eliminating the effect
of the temperature.

Therefore the bottle which served as a volumeter was placed in
a large water-reservoir, from which the bottle itself was filled. ‘This,
however, was found to be no decisive improvement. Changes in the
temperature of the room where the experiments were carried out,
always brought about a slight change in the temperature of the
water. Therefore I placed a second bottle, identical with that used

1091

for the experiment, by the side of the latter. No fish was placed
in it. It only served to verify. Before and after the experiment the
temperature of the water was taken with a sensitive BECKMANN-
thermometer. Thus it could be established whether the changes o1
the two menisci were due to temperature-fluctuations or not.

My experiments showed that active volume-changes of fishes occur
indeed, though in quite another manner than it was supposed by
Borerrt and others. Slow meniscus-movements, namely, manifested
themselves, which did not run parallel to movements of the fish in
the horizontal plane. The meniscus-movements in the bottle could
not be explained by expansion of the water as a result of heat-
production by the fish, for in all experiments the temperature in
the two bottles was the same. What may be the cause of these
volume-changes of the fish, which, it must be admitted, are never
very great; viz. up to +0.3°/, of its body-volume? Satisfactory
explanations might be found in: 1. change of the tonus of the
muscles in the surface of the body, 2. changes of pressure in the
air-bladder. It seems unlikely that the latter should be the cause.
The changes in the gas-pressure found by Morrav and others, took
place very slowly, whilst the volume-changes in my experiments
occurred in a rather short time.

A calculation showed that the maximum volume changes, ascer-
tained by me for a fish whose static plane lay at a depth of one
metre, caused this plane to move 16 centimetres.

On the ground of the facts mentioned 1 do not wish to declare
myself an adherent of the theory of BoreLrt; I only wish to point
out that Morwau’s classical experiments do not sufficiently refute
Boreui’s theory.

We saw already that the fish responds to slight changes in the
pressure to which it is subjected namely by well-coordinated swimming-
motions. BAGLIONr asked himself where the stimuli arise that awaken
these movements, which he looks upon as averting-reflexes. He
supposes this to take place in the surface of the air-bladder. The
numerous nerve-endiugs described by DerNeka would, according to
him, be stimulated when the tension in the bladder-surface was
modified. In those fishes which possess the well-known organ of
WeBer (the 4 pair of bones connecting the surface of the air-bladder
with the perilymphatic space of the vestibular apparatus) this organ
might be an important factor in the perception of pressure-modi-
fications.

Evidently it is difficult to give direct proofs for the tempting
theory of BAGLIONT. It cannot be proved that the upward or down-

72

Proceedings Royal Acad. Amsterdam. Vol. XVII.

1092

ward pressure acting upon the fish, does not cause the swimming-
reactions by the stimulation of some other organ such as eye, laby-
rinth or lateral line.

Some of my experiments lead me indeed to suspect that the
pressure modification to which a fish is subjected, is not exclusively
perceived by means of the bladder and the organ of Wesrr.

Morrav pointed out that the fish by modifying the gas-density in
the bladder can adapt itself slowly to a modification in the pressure.
I therefore caused a perch to adapt itself to a decrease of 10 cen-
timetres of mercury. If such a fish is exposed again to normal cir-
cumstances, it responds to this pressure, which is now too high for
it, by swimming upward. After some time it sinks to the bottom
and remains there panting. To the back of the animal a cork was
now fastened by means of thin copper-wire, which drew the animal
to the surface. On the bladder now presses 1 atmosphere i.e. 10
centimetres of mercury — 25 centimetres of water more than that
to which the fish adapted itself. Yet the animal continually tries to
swim downward. Being pulled up by the cork, it remains lying at
the surface at last.

This swimming-reaction takes place, therefore, in a direction
exactly opposite to that which was caused by the pressure-modification.

That in the ostariophysi the transmission of stimuli is not
exclusively due to the organ of WrBerR becomes evident from the
following fact.

The sensitiveness of tenches to pressure-changes is not affected if,
on one or on both sides, the nervus octavus between vestibular-
apparatus and brain, is cut through. Since, after the nerve has been
eut on both sides, there was no longer any connection between the
brain and the statie organ, the stimulus must have awakened the
swimming-reflex by another route.

Summarized in a few words my conclusions, drawn from the
above disquisition, are the following:

1. Active volume-changes can under careful exclusion of disturbing
influences, be demonstrated in fishes. Not, however, in the sense in
which it is understood by Borerrrs theory. The facts observed by
me have been overlooked by Morrav owing to the short duration
of his experiments, by his adherents and opponents owing to tech-
nical defects in their experiments.

Cause and significance of the changes have not been discovered yet.

2. In agreement with BaGriont we must look upon the air-bladder
as a hydrostatic organ of sense.

1093

The stimuli awakened by a modified pressure are certainly per-
ceived via other channels besides that suggested by BaGLiont.

Il. The air in the air-bladder.

Since Priester we have known already that the gases, found in the
air-bladder, are the same as those of the air. The proportion between
oxygen, nitrogen, and carbonic acid varies, however, to a considerable
extent. As a rule fishes living in deep water have a high percentage
of oxygen; sometimes it rises to + 90°/,.

It was established experimentally that the fish is able to gather
gases in the interior of its bladder, for example when the gases,
present in the first instance, are removed by means of a trocar or
air-pump (physostomi).

Moreau proved that the newly-formed gas is oxygen, at least that
after the gas-regeneration the percentage of oxygen is considerably
higher than before.

The fish can regulate the gas-pressure in the air-bladder in accord-
ance with the outward pressure to which the fish is subjected.
Deep-sea fisbes have extremely high tensions in the air-bladder whilst
in animals kept under an artificially increased or decreased pressure,
an increase or a decrease in the tension of the air-bladder can be
demonstrated.

This gas-production cannot be a simple osmotic phenomenon,
especially on account of the enormous tension met with in deep-sea
fishes; it is a secretion. It is easiest to prove the secretion of oxygen ;
according to Hürner’s investigations, however, we must also assume
nitrogen-secretion.

This secretion has especially drawn the attention of Bonr in con-
nection with his researches and hypotheses on the gas-changes in
the lungs, which, as we know, are likewise reduced by him to a
secretory phenomenon.

Bonr determined which nerves influence the secretion. Moreau
had suggested already that cutting the sympathie fibres occasioned
an increase in the oxygen-percentage. These nerves would, therefore,
impede the oxygen-secretion. BoHr cut on both sides the vagus-
branches innerving air-bladder and intestines and found that the
secretion ceased entirely.

By a series of experiments I tried to fill up to some extent some
gaps in our knowledge relating to the secretion-phenomena de-
scribed above.

Fishes kept under a continually variable pressure adapt themselves

72*

1094

to it by an increased or decreased gas tension. The increase is
‘effected by secretion; the physostomi, which possess a channel from
the air-bladder to the esophagus, bring about a decrease by letting
one or more gas-bubbles escape, the physoclisti, which lack this
safety-valve, by a slow resorption of gases into the blood.

The first question | wanted answered was the following: is it
possible to bring about by means of an artificial decrease of the
specific gravity of a physoclistus, the same reaction, in the form of
gas-resorption from the bladder, as that caused by a decreased out-
ward pressure? For this purpose the time was determined, necessary
for perches to adapt themselves to a pressure-decrease of 25 centi-
metres of mercury. It was found that within 18 hours they had
adapted themselves to more than 15 centimetres. Now when by
means of corks, fastened to their body, the 5. G. of perches was
lessened, the same downward swimming-reactions were observed as
those occurring at a decreased pressure. The gas-tension in the air-
bladder decreased much more slowly. The condition reached in the
former experiment within 24 hours manifested itself in the latter
category only after about 5 > 24 hours.

Another question that suggested itself was the following: If a fish
whose bladder has been emptied, is by means of a cork brought
into artificial equilibrium with the surrounding water, will the
regeneration of gases no longer take place?

This turns out still to be the case. To a carp the air-bladder of
which has been sucked empty, a cork is fastened on the back, ofa
size to keep the animal in equilibrium in the water. After some
days it floats on the surface. The gases have been regenerated again
to such an extent that the fish emits air-bubbles when the air pressure
is reduced to less than */, atmosphere. It follows from this that the
secretion, viewed by Morrav and others as a reaction on an increased
pressure from outside, is independent of the specific gravity of the
fish as a whole, but is probably governed by the degree of tension
of the bladder.

This tension is but slightly modified by a vertical movement of
the fish in the experimental basin (40 centimetres deep), if we compare
it with the tension-change in the air-bladder caused by the bladder
being sucked empty.

Probably the stimulus causing gas-regeneration finds indeed its
origin in the nervous terminal apparatus described by DeINEKA.

As regards the influence of the gas-secretion on the nervous system
I may mention that the experiences of Bour, with reference to the
Gadus callarias were confirmed by me in the case of Cyprinus carpio,

1095

Tinca vulgaris, Perca fluviatilis. An emptied air-bladder was never
filled again after the Rami intestinales Vagi had been cut through on
both sides.

Finally I have tried to ascertain if, for some time after the air-
bladder has been emptied, an increased absorption of oxygen could
be observed. Theoretically there is of course every reason to expect
this, and the strong almost asphyxial respiratory movements of the
fish after the bladder has been emptied, render it very probable.

The experimental proof is difficult to give. I omit here the tech-
nical details relating to the oxygen determinations. On comparing the
oxygen consumed by a fish in rest, before the bladder has been
emptied and after it, it is found that in the latter case an increase
may be observed. It is a remarkable fact, which is difficult to
explain, that often immediately after the gas-extraction the oxygen-
consumption fell below the average.

Chemistry. — “On critical end-points and the system ethane-naph-
talene’. By Dr. Apa Prins. (Communicated by Prof. A. F.
HOLLEMAN).

(Communicated in the meeting of Jan. 30, 1915).

After Smits’ investigation of the system ether-anthraquinone *) no
other binary system has been found which shows in a similar way
the critical end-points. It was, therefore, my intention to search for
such a case. Should [ succeed in finding end-points p and g.
which might be easily realized, it would be possible by an appro-
priate choice of the components to obtain one of the types of ternary
systems theoretically developed by Sirs *) by combination of two
binary ones. As the following shows, I have not been successful
in finding a system analogous to ether-anthraquinone; so I had to
give up the research of a ternary system.

Obviously either ether or anthraquinone recommended itself as
one of the components. As the melting-point of the less volatile
component must be above the critical temperature of the more vola-
tile one, and the solubility of the former substance must be slight
even at the critical temperature of the latter, and moreover no
decomposition may occur, the number of substances suitable for
investigation, is not large.

The preliminary experiments, showing whether critical end-points
occurred or not, were made in small sealed tubes, which were heated

1) Z. Phys. Chem. 51, page 193.
2) Proc. R. Acad. Amsterdam June 1912.

1096

in an air-bath. If the first critical end-point was observed, the pres-
sure and temperature of p were determined oy the Cam.Lerer-method
and g was also sought for.

The binary systems which | examined are the following:

Ether-alizarine.

A preliminary investigation by Smirs ') had already shown that
the three-phase line intersects the plaitpoint line. The meltingpoint
of alizarine (290°) is about as high as that of anthraquinone (284.6°)
and much above the critical point of ether (77, 193.9°, P;, 36.1 atm.).
I observed the first critical end-point p at 196.4° and 37.5 atm.
So the solubility of alizarine in ether proves to be so small, that
the critical temperature of ether is only increased by 2.5°. This in-
crement is much smaller than in the case of the ether-anthraquinone
system, where p lies at 203° and 43 atm.

For the determination of g a mixture of higher concentration of
alizarine was required. The large quantity of alizarine caused however
the observation to be extremely difficult; the vapour-phase and the
liquid-phase were both dark black-red, so that the meniscus was no
more to be distinguished. On this account it could only approxi-
mately be established, that qg lies about 258°; the system was im-
proper for an exact investigation.

Ether-hexachlorobenzene.

The melting-point of hexachlorobenzene lies at 224°; the difference
with the critical temperature of ether being much smaller than in
the former case. The solubility appeared to be so great, that the
three-phase curve does not meet the plaitpoint line.

Ether-isophtalic acid.

Isophtalic acid having a high melting-point (880°) dissolves so
slightly in ether, that the critical line starting from ether is already
intersected at 196.1° and 36.8 atm. Since the isophtalic acid is decom-
posed by heating a long time at high temperatures, q could not be
determined.

Hexane-anthraquinone.

This system does not show critical end-points.
As the combination of either ether or anthraquinone with another

) Z. Phys. Chem. 51. p. 214.

20

1097

substance did not give satisfactory results, | resolved to investigate
systems one of the components of which is a gas at ordinary
temperature. : }

According to bicuner’s research *) CO, gives critical end-points
with several other substances. It was however not closely examined
whether these systems belonged to the simple case ether-anthraquinone
or to the type diphenylamine-carbonic acid, discovered by BücHNer.

The systems naphtalene-carbonic acid and diphenyl-carbonic acid,
which 1 studied, showed both the first critical end-point. The fact.
that in both systems the three-phase curve starting from the triple
point of the solid substance had a steep rise (fig. 1), led to the con-
clusion, that the systems were analogous to the system diphenylamine-
carbonic acid.

K = Critic. point CO,

p = Critic. endpoint
diphenyl.

p, = Critic. endpoint
naphtalene.

Biest.

This made me suppose that other systems with carbonie acid would
also show a steep three-phase curve and accordingly q at a high
pressure or no gq at all. So 1 resolved to try systems with ethane.

Ethane-naphtalene.

Preliminary experiments showed also this system to have the
above mentioned property. Because it had proved very difficult to
find another example of the type ether-anthraquinone and as moreover
the phenomena suggested that in this system points might be realized
which had not yet been observed, I still commenced a closer study.

1) ‚Thesis for the doctorate, Amsterdam 1905.

oa

1098

The type, to which this system belongs has been theoretically
developed by Bicuner') in his study on systems with limited
miscibility, in which together with the equilibrium of fluid phases
a solid phase occurs. It has in common with the system ether-
anthraquinone, that the melting-point of the less volatile component
B lies above the critical point of the more volatile A and that the
solubility of solid B in liquid A is small. The three-phase curve,
on which solid B coexists with its solution in liquid A and with
a vapour-phase, intersects the critical curve starting from the critical
point 1 = G of the first component, giving rise to the first critical
end-point p. As however the component B has not only in the
solid state a small solubility in liquid A, but’ also molten B is only
partially miscible with A, the second critical end-point may arise in
a way different from that in the system ether-anthraquinone.

From the triple point of B a second three-phase curve starts,
giving the equilibrium of-solid B with the solution of A in liquid B and
with a vapour phase. As the melting-point of B lies above the critical
point of A the vapour of this three-phase line at high pressures will have
densities corresponding to a liquid; therefore the line will rise steeply.
The point of intersection of this curve and the critical line L, = G
or L, = L, is the second critical end-point. Here two liquid phases

Fig. 2

become identical in presence of a solid phase. Figure 2 represents
the P-7 projection of the space figure of this case. BicHNner has
found the first experimental instance of this type in the system
diphenylamine-carbonic acid. The critical end-point q could not be
determined because the critical pressure was not attainable or did
not exist.

1) loc, cit.

1099

In the system ethane-naphtalene I succeeded not only in finding the
point p, but also g.

The ethane was prepared by electrolyzing sodiumacetate. The
anode gas was purified by bromine water and a strong solution of
potassium hydroxide, dried over sodalime and condensed in a receiver
by liquid air. Subsequently it was again dried over phosphorus
pentoxide and separated from the more volatile part by fractionating
by the use of liquid air. The disappearance of the discharge in a
GrIsLER tube attached to the apparatus served as criterion of purity.
I determined the critical point from three fractions of the so purified
ethane. The following well agreeing values were found:

Ist fraction) 31.8° | 48.23 atm.
2nd fraction! 32.3° mean | 48.09 atm. ean
| le)
3rd fraction) 32.350 | 32-32° | 48.18 atm, | 48-13 atm.

The further investigations were made with the second and third
fraction.

The naphtalene was purified by sublimation; the melting-point
was 80.8°. .

The apparatus represented in fig. 3 was used for the preparation
of the mixtures.

A is the storing-vessel with purified ethane. B is calibrated. In C
ethane may be condensed by liquid air, whereas D is filled with
cocoanut charcoal to absorb the last traces of air after the evacua-
tion of the apparatus. The Cailletet tube / was connected with the
rest of the apparatus by rubber tubing protected by mercury. A
weighed quantity of naphtalene and an electromagnetic stirrer were
placed beforehand in the Cailletet tube and fused on to the top by
carefully heating. After exhausting the whole apparatus, the naphtalene
being cooled by solid carbonic acid and alcohol, ethane of definite
pressure, to be read on the manometer G, was pressed over
into the Cailletet tube by the aid of air-free mercury contained
in the vessel /’; in this way the required quantity of gas was
mixed with the naphtalene. The tube was then placed in the pressure
cylinder filled with pure mercury freed from air by boiling. The
tube was heated and the pressure regulated in the same way as

1100

Fig. 3

was already used before in this laboratory.*) Fig. 4 shows the P7-
projection of the space figure, whilst table I gives a survey of the
observations.

The three-phase line BSQ, on which solid naphtalene coexists
with a solution of ethane in liquid naphtalene and vapour, was
determined by slowly heating at a definite pressure till the mass
began to fuse. As the equilibria established themselves extraordinarily
slowly, the experiments required much time, and it was very difficult
to fix the moment that the liquid appeared and increased.

The second critical end-point g could not directly be observed.
lt was almost impossible to determine the point, where two phases
became identical in the presence of the third, because the tem-
perature varies only extremely slightly at considerable changes of

3) SCHEFFER, Proc. Royal Acad, Amsterdam 1912.

1101

TABLE CLE

128.68
127.07
125549
123.76
120.56

130.26
21.07
126.59
125.75
124.C6
123.06
122591
(22:21

126.64
123.81
124.8

Critical point ethane.

Critical point unsaturated solution

P
Curve BSQ

SplsG of SplaL

” ”

End-condensation line EF, mixture 25 a 26 mol. % 9 napht.

LAGE

”

„

»

‘ (metastable)
End-condensation line GH, mixture 24.75 mol. °/9 napht.
LGL
y

”

+ (metastable)

” ”

Point max. pressure mixture + 24%) napht.

Point upperbranch P7-loop same mixture,

q

1108

the pressure and moreover the appearing and disappearing of the
solid is much liable to retardation.

To determine the point ¢ still as exactly as possible I used the
method described below, which offers values, deviating only slightly
from the real ones. The following figures will illustrate it.

Fig. 5 gives the P-\ projection of the three-phase line. When we

Fig. 5. Fig. 6.

consider a mixture of the composition 2,, which contains more
naphtalene than is necessary for realizing g, we see that the P7
projection of this mixture must be as is drawn in fig. 6, in which
the points a, 6, and c(==q) correspond with the homonymous in
fig. 5. This section gives the part of the three-phase line between
hb and c(=q). If a direct determination had been possible, g might
have been found with this mixture. Although I failed to find g,
I could study in this section the line of end-condensations, and the
point of intersection @ of this curve with the three-phase line (see
table I and fig. 4).

This point a will slightly differ from q, when z, lies near «,.
From the distance of dr(Z—=G) from a we can judge whether
this is actually the case, because in the P7 section #, kr and a
coincide. The smaller the distance the nearer we are to g. It is
however possible that the composition along the critical line varies
only slightly with the temperature, so that in a mixture the com-
position of which differs slightly from «, dv is nevertheless far from
a. This proved to be actually the case on studying a second mixture.
If the concentration of this mixture had been exactly that of g,
then the PZ’ projection of fig. 7 would have been found. Here the
point q lies just on the line of the end-condensations. By studying
the upper branch of the loop-line LG, on which the meniscus dis-

1104

appears at the bottom and determining graphically the point of
intersection with the three-phase line, g might be found.

Fig. 7.

Fig. 8 gives the P-7' projection for a mixture z,, which has a
concentration smaller than «,. The point Ar has entered the meta-
stable region, so that the upper limit of the Z-G region here also

Fig. 8.

is indicated by the disappearance of the meniscus at the bottom.
Here the point #r can only be realized, when the solid phase does
not appear. The stable part of the L-G loop must offer everywhere
retrograde phenomena. If the composition on the critical line varies
only slightly when the temperature rises, the point kr in fig. 8 also
will move rapidly from a to lower temperatures, when 2, differs
slightly from z,. The point g is never to be realized with a mixture
©, ey, though here as well a will deviate slightly from q when
the difference between «x, and z, is small.

1105

Fig. 9.

The combination of the fig. 6,7, and
8 gives fig. 9. When we draw the
P-X section for 7, we obtain fig. 10,
where the points corresponding with
those in fig. 9 are denoted by the same
numbers.

The point of maximum pressure lies
on the eritical curve. The composition
of 1 will deviate a little from x, when

Fig. 10. _T, lies slightly higher than 7,, and
this is still more exactly the case when the composition of the critical
line varies little with variation of the temperature. To find the com-
position of 1 experimentally we must start from a mixture z,, which
contains more solid substance than is required for g. With this
mixture we determine at 7, the point of end-condensation 3. Then
after cooling some of the solid substance is pushed under the mercury
meniscus, whereby the composition of the mixture is changed a
little to the left in fig. 10. Again with the composition so obtained
e.g. v, we determine the upper limit of the loop LG at 7. When
we isolate successively different quantities of the solid, points of the
line 3, 1, 2 and 4+ in the P-X section may be found. Evidently the
maximum pressure, point 1, corresponds to the mixture 2,. If there-
fore the maximum pressure is realized, we have the mixture z,,
deviating a little from z,, at least if 7’, deviates slightly from 7%.

1106

So when with this mixture the upper limit of the P-7' loop is
determined, the intersection of this curve with the three-phase line
will give approximately the point q.

The first mixture, that I studied, corresponds to 2, in fig. 9.
Determining the upper limit of the P-7’ loop, I saw the meniscus
always disappear in the top of the tube, so that 4r must lie at a
temperature higher than 71.4°. (see fig. 6, fig. 2 line ZF and table 1).
The composition of this mixture was between 25 and 26 mol. °/,
naphthalene. As I did not succeed in observing q directly with this
mixture, although I sometimes saw a fluid phase in contact with
solid, I resolved to proceed along the previously described way.

The second mixture contained 24.75 mol. °/, naphtalene; it might
therefore lie on the left or on the right of g, or it might happen
to have exactly the composition of x, itself.

On determining the P-7' loop the meniscus also here always disap-
peared in the top of the tube, indicating, that the mixture contained
more napbtalene than «a, (see table 1 and fig. 2 line GH). Three
points could be found on the metastable part of the curve. The
pressure of the point at 52.4° and 122.27 atm. is high, which can
be explained by assuming that perhaps some solid has got under
the mercury.

With this mixture the composition of point 1 from fig. 10 was
experimentally sought. From the intersection of the two end-conden-
sation lines with the three-phase curve I might conclude, that g lay
at about 57°. I chose 59.9° as temperature of the experiment, also
2.9° higher than the assumed 7. The above mentioned method
gave at 59.9° a pressure maximum of 126.64 atm.

With this mixture, showing Ar at 59.9° and 126.64 atm. another
point of the P7' loop was determined at a temperature lower than
kr. The meniscus disappeared a little below the middle of the tube
at 55.5° and 123.81 atm. (metastable point). The intersection of the
curve, which joins those two points, with the three-phase curve
offers a value for g, which is very near the true one. This shows
the second critical end-point to lie at 57.4° and 124.8 atm. and the
composition to be between 20 and 25 mol. °/,.

Finally I wish to express my thanks to Dr. F. E. C. SCHEFFER
for his help and advice.

Amsterdam, January 1915. Inorg. Chem. Laboratory
of the University.

1107

Mathematics. — “Systems of circles determined by a pencil of
conics’. By Professor JAN pr Vrins.
(Communicated in the meeting ef Jan. 30, 1915.)

The osculating circles and the bitangent circles of the comics of
a pencil form two doubly infinite systems: of these I shall consider
some properties in this paper.

1. Any straight line # passing through a base-point B of a
pencil of conies (67), is a normal line of one 3°. To » l associate the
diameter 1 of 8’ passing through 5. As each line passing through
B bears the centra of two 8’, a correspondence (2,1) exists between
m and n. Each coincidence is an axis; each base-point ts therefore
verten of three conics: the axes envelop a curve of class three, *a.

As the line at infinity /, is axis for the two parabolae of the
pencil, consequently ditangent of *e, only one axis belongs to a
pencil of parallel rays.

The axes a form on the rational curve *e@ a quadratic involution,
of which each pair consists of the axes a,,a, of a definite conic.
The central conic of the pencil (locus of the centra) is the curve of
involution and at the same time part of the orthoptic line of °a;
the missing part’) is apparently the line /,.

The locus of the vertices 7’ of the conics 8? has a triple point
in each base-point. As an arbitrary p° has four vertices, it will have
16 points in common with (7); the curve in question is therefore
of order 8. It has apparently nodes in the nodes D of the degenerated
conics. The vertices of the conics le therefore on a (T)* with four
triple points and three nodes.

A. Hach g° possesses two systems of bitangent circles, 72,2. For the
parabolae one system exists of the pairs of lines formed by a tangent
and the line /,.

As each point P bears three axes, P is the centre of three circles
yoo. A perpendicular to the plane + of (8) contains therefore six
poles of circles yap, in other words the system [2,2 | is the cyclographic
representation of a surface of order six, w’.

The intersection of wm’ with rt is apparently the locus of the foci
(focal curve of the pencil); the latter is consequently a bicircular
curve of order six, having the nodes of the three pairs of lines as nodes.

The tangents p of the two parabolae are the images of the points
at infinity on the cones of revolution mw’, the generatrices of which

1) On a straight line 7, the pairs of orthogonal tangents of %x determine a (3,3).
Any intersection of two orthogonal tangents is a double coincidence; the orthoptic
line is therefore a figure of order 5.
. me
(3
Proceedings Royal Acad. Amsterdam, Vol. XVII.

1108

intersect the plane r at angles of 45°. As two tangents p may be

drawn in any direction, the curve at infinity d? of those cones is
nodal curve of @’.

The circles passing through two points ?.Q are the images of
an orthogonal hyperbola wu’, situated in the normal plane in the
middle of PQ. with the middle of PQ as centre, while its asymp-
totes intersect + at angles of 45°.

As it has four points in common with d*, it intersects @* in eight
finite points, whieh will be the poles of four circles yo. passing
through PQ. Through two arbitrary points pass therefore four
hitangent circles.

If one of these points is a point at infinity, each of the four
circles is formed by /, with one of the tangents going from the
other point to the two parabolae *).

3. The circles y22 passing through a point P form the image of
the intersection of w° with the cone of revolution w’, having P as
vertex, while its edges intersect t at angles of 45°. The latter has

in common with w°,

besides the nodal curve d*_ , also a 0°, containing
the poles of the circles yo9 passing through Z. Hence: the locus of
the centres of the bitangent circles passing through a fired point ts
a curve of order four, pr

The tangents from to the two parabolae determine the points
at infinity of this curve. It is intersected by the perpendicular at
the middle point of PC in the centres of the yo. passing through
Pand: 6

Let us consider the corresponding loeus for the case that P is
replaced by a base-point B. Any ray n passing through B is normal
line of one 6°, consequently contains the centres of two yo. touching
this 8? in B; B cannot be centre of such a circle; so the locus in
question is a conic. This was to be expected, for the four tangents
of the parabolae determining the centres at infinity coincide here in
pairs. The central curve p* will have the perpendicular in the middle
of PB as bitangent.

4. The circles having the axes of g? as diameters belong to the
system [yo]. These principal circles are represented on w° by a
twisted curve o°, having the central conic of (3°) as projection. For
any point of the centre is centre of two principal circles so that

1) Similar considerations concerning the system of the orthoptic circles of (6?)

may be found in my paper ‘On the orthoptic circles belonging to linear systems
of conics” (These Proceedings I, 305—310).

1109

any plane perpendicular on « contains eight poles. o° is four times
intersected on d°, by the cone of revolution w? (§ 3); the remaining
intersections are poles of six principal circles. The principal circles
form therefore a system with index six.

As a base-point B is vertex of three 8’, consequently lies on three
principal circles, these circles are to be counted twice.

5. We shall now consider the system formed by the osculating
circles, y,, of the conics of the pencil. For a point R‚ of as
consists of /_ and the asymptote touching in R,. To the osculating
circles of the two parabolae belong the figures consisting of /, and
a diameter.

The asymptotes envelop a curve of class three,*8, which has 1, as
bitangent. The tangents of °3 passing through a base-point B are
apparently the lines connecting 4 with the other three base-points.

The circles y, passing through a point P and a point Q) consist
of 7, combined with an asymptote or a diameter of a parabola;
their number amounts therefore to jive.

From this it may be deduced that through any two points P,Q,
five osculating circles may be laid.

First it may be observed that the locus of the centres of the circles
y, passing through P must be a curve c°, for five of those circles
have their centre on /,.

If the system [y,| is considered as the cyclographic representation
of a surface 2, c° is the orthogonal projection of a curve o'° lying
on 2. The latter has 20 points in common with the orthogonal
hyperbola uw? ($ 2) determined by P and Q. Of these 10 lie on the
curve d°, (§ 2) representing the asymptotes; the remaining 10 form
5 pairs of poles of circles passing through 7? and Q. Consequently
Jive circles 3 pass through two given points.

The cone of revolution w’? ($ 3) with vertex P has in common
with @ the curves Jd’, and o'°; so @ is a surface of order six,
Hence, any point of the plane vr is centre of three osculating circles.

6. Let S be the intersection of a 8? with the osculating circle
which has B as point of contact, w a ray passing through & parallel
to one of the axes of 3’. In order to investigate how often a straight
line & drawn through 4 becomes chord of osculation, we associate
the reflected image s of & with regard to « to the straight line f,
touching §? in 5. To a line ¢ belong two lines u, but only one
line s; a ray s determines with / two lines wu, but only one p’,
consequently one ray ¢. The two coincidences s—t belong to two

73*

1110

conies having & as chord of oseulation BS. As Bis vertex of
three 8? consequently coincides thrice with JS, the locus of S will
be a curve o°, having a triple point in 4 and nodes in the remaining
base-points. It passes moreover through the cyclic points /, 7, on
/,, for on the @? laid through / that point S belongs to all circles
of osculation.

We can now easily point out the five cireles y, passing through
two base-points B, 2,: two osculate in 4, and intersect in D,,
two osculate in B, and intersect in B,, the fifth consists of BB,
and: We:

That any line / is chord of osculation for five circles y, may be
proved as follows.

If in each point L of / the tangent ¢ is drawn at the 98° passing
through ZL, a system of rays with index 3 is obtained; for / is
touched by two 98°, is consequently bitangent of the curve enveloped
by ¢. Through £ we draw the lines w and w’ parallel to the axes
of B? and the lines » and v’, bisecting the angles between / and t.
If the pair of lines v,v’ coincides with w,u’, Lis chord of oscu-
lation of £?.

If t,u,u’,v,v’, retaining their directions, are transferred to a point
O of /, a correspondence (4,6) arises in the pencil of rays (U).
For a ray u determines ($ 1) one 6’, so two points £ and four
rays v; a ray v determines three tangents f, therefore six rays u.
The ten coincidences wv form five orthogonal pairs; so there are
Jive conics for which Lis chord of osculation.

If the point of contact L of a y, describes the straight line /, the
end S of the chord of osculation will describe a curve of order
thirteen, for on / lie eight vertices of conics.

7. On each conic @ arises a cubic involution, if the three points
R, of which the osculating circles meet in a point S of 9’, are
joined into a group.

If 6’ is an hyperbola, this /, has the points of contact of the
asymptotes as triple elements; these two replace the four groups
with a two-fold element, which an /, possesses in general.

For the ellipse these triple elements become imaginary ; for if it
is considered as the orthogonal projection of a circle, the /, appears
to be the projection of the /, formed by the angular points of the
regular triangles described in that circle.

For a parabola each group of the /, consists of a point of the
parabola and the point at infinity of that curve counted twice.

Let us now consider the triple involution T,, in the plane r,

dip |

formed by the involutions (2,, Zit, 2,) belonging to the conics of
the pencil (8%).

The curves 6° belonging to two base-points B, B, ($ 6) have in
those points 12 intersections and 8 in 46,, 4,; they further pass

through the eyelie points on /, and through the point at infinity

"
of B,B,. The two points S, which they lave moreover in common
are each the end of two chords of osculation BS, b,S. Any two
base-points belong therefore to two groups of 7;.

Let us now consider the locus of the points 2,, R, belonging to
R, =8,. This singular curve, @,, has nodes in B,, B,,.6,, but does
not pass through B,, 7, possessing no coincidences outside /,. As
an arbitrary conic of (8°) contains one pair R,, &,, consequently has
eight points in common with 8,, each base-point determines a rational
singular curve of order four.

The parabolae too are singular curves and as such associated to
their points at infinity.

Any straight line Bj B, corresponds to itself in the transformation
(R,, R,); for each of its points may be considered as point of
contact of a y,, intersecting 6, 6, on /.

If AR, describes a A’, B? is described twice by &, (A). So Bp’ is
transformed by (/?,, R,) into the figure composed of the four singular
curves 8. and the conic 8? counted twice, consequently into a
figure of order 20. From this it ensues that the transformation im
question transforms a straight line into a curve of order ten.

This c'° has in each base-point a quadruple point.

Prof.

—
Cit

Chemistry. — “Compounds of the arsenious owide”. 1. H
F. A. H. SCHREINEMAKERS and Miss W. C. pi Baar.

The system: H,O—As,0,—NH, at 30°.

Of the different ammonium arsenites which may be imagined to
be deduced of the H,AsO,, H,As,O, and. HAsO,, (NH,),As,O, and
NH,AsO, are described as crystals and (NH,),AsO, as a thick-fluid
yellow mass.

Now we have examined the system H,O—As,O,—NH, at 30°;
from this it is apparent that the salt NH,AsO, oceurs at 30°, while
the possibility that also still a sait of the composition NH,H,AsO,
exists, is not excluded.

In fig. 1 we find a schematical representation of the equilibria
occurring in this system at 30°; with the aid of table L we can
accurately draw the different curves.

1112

The point Dei, represents the NH,AsO,; in order tô find the
position of this point in the triangle, we must consider that:
2 NH, AsO; ==(NE.) EO Ag SD

the salt NH,AsO, contains consequently 13,6°/, NH,; 7,2°/, H,O
and 79.2°/, As,O, so that the position of the point Do, is known.

The point Dos; represents the NH,H,AsO,; as

2 NH, AsO, =] (NH) 0), ASD Se
this salt contains,.11.9.°/, NHS 43:0°/, BO and 69.24/ As 0

When we draw in the figure the points Do;,; and Ds3,, then it
is apparent that they are situated on a straight line with the angle-
point IV. That this must really be the case, follows also from the
equation

NH,AsO, + H,O = NH,H, AsO,
from which it is apparent that the NH,H,AsO, may be considered
as consisting of NH,AsO, and H,O.

Curve ab represents the solutions saturated with solid As,O,;
these complexes have been shaken during about a month at 30°.
The As,O, which we have used was an extremely fine flour-like
powder; in each of the small bottles we brought a little sublimated
As,O, and a little As,O, which was recrystallized from a strong,
heat solution of chlorie acid.

Point @ represents the solubility of As,O, in pure water; as it is
apparent from table 1 we find for this 2.26°/,; Bruner and TorLoczkKo
found that at 25° and 39,8° in 100 Gr. water 2.03 and 2.93 Gr.
As,O, are dissolved. It appears from the analysis of the rests that
the solid phase is not a hydrate, but that it is the anhydric
As,Q,.

Fig. 1.
Curve bed represents the solutions with Dei, —= NH,AsO,. As the

1113

line WD», intersects this curve 6d in the point c, the salt NH,AsO,
is soluble in water at 30° without decomposition. The saturated
aqueous solution of this salt is represented by point e; it is apparent
from the position of the points JV, ¢ and Mo, with respect to one
another that this solution contains = 19.2 "/, NH,AsO,.

We have deduced with the aid of the rest-method the composition
of the solid phase, which is in equilibrium with the solutions of
branch bed. The conjugationlines liquid-rest are going viz. all through
the point Dyii. As the point Do 31, however, is situated close to
Dai, the conjugationlines for the solutions of branch be go within
the errors of analysis, also through the point Ds3;. Although
it is, therefore, sure that the solutions of cd which are situated at
some distance of c, are saturated with Di, = NH,AsO,, yet the
possibility exists that the other solutions are saturated with Do 3) =
NH,H,AsO,.

It is apparent from the table that branch bcd is determined no
further than to a solution d, which contains 14,28°/, NH,. In order
to examine if with higher content of NH, in the solution perhaps
still a compound should occur with more NH, than in the compound
NH,AsO,, we have still examined a solution at 0°, which contained
36,05°/, NH,. It was apparent that also in this case the solid phase
was still the NH,AsQ,.

From the course of curve ab and from table 1 it is apparent
that the solubility of the As,O, increases strongly with increasing
content of ammonia of the solution. The terminating point 5, viz. the
solution which is saturated with As,O, + NH,AsO,, is not determined.
The solution of branch ab which is experimentally determined and
which is situated the nearest to the point 6 contains (compare table)
21.17°/, As,O, and 2,86°/, NH,. It is apparent from the course of
the branches a/ and dcd that the solution 4 will contain + 22°/, AsO,
and + 2,87°/,NH,. From this it appears, therefore, that small
quantities of NH, strongly increase the solubility of the As,O,.

We imagine in tig. 1 the line NH,—¢ to be drawn; its point of
intersection with the side JV—As,O, is represented in the figure
by /; this point f indicates a complex which contains + 22,5 °/,
As,O, and consequently + 77,5 °/, water. Now we take a complex
e, situated between a and /; this contains, therefore, more than
2,26 °/ and less than 22,5°/, As,O, and consequently it consists
of solution « + solid As,O,. When we bring NH,-gas into this

complex, then it follows the line e—NH, ; this line intersects, starting
from e, firstly the region ab As,O,, afterwards the region Wabed

and further the region bed D211. Hence it follows that by adding

1114

gaseous NH, first the As,O, is dissolved and an unsaturated
solution occurs and that on further addition of NH,, the solid
NH, AsO, is separated; the solution follows the curve bed in this case,
starting from 6 and gets, therefore, gradually poorer in As,O,, which
is deposited as NH,AsO,. We imagine also in fig. 1 the line NH, —
Ds, to be drawn; its point of intersection with W—As,O, is
represented by /. The point 4 indicates a complex which contains
+91.5°/, As,O, and consequently + 8,5 °/, water. Now we take
a complex g between h and f; this contains, therefore, more than
22,5°/, and less than 91,5°/, As,O, and it consists of solution
a + solid As,O,. When we bring NH,-gas into this complex, it follows
the line g—-NH,; this line intersects, starting from g, first the
region ab As,O,, after that the threephasetriangle 6. Do1,. As,O,
and afterwards the region bcd. As,O,. Hence it follows that on
addition of gaseous NH, first As,O, is dissolved until solution b

T-ABE BE: L

Compositions in percentages by weight at 309,

of the solution | of the rest |
| | ‚solid phase
Oo NH3 Io As203/ fo NH3_%o As203,

—————— en

o | 2.26 | — EAF ND
1.41 | 10.98 | 0.37 | 59.79 | „
2.78 | 20.49 | 1.24 | 63.10 ;
2.86 | 21.17 | 1,21 | 64.26 | :

5 ie at cag de Nn
3.13 | 12.30 | 7.25 | 38.59 3
3.18 | 11.13 | 7.51 | 38.39 .
3.91 1265 | 8.24 | 35.80 | .
5.82 5.61 | 9.08 | 36.44 ile, Gas
6.08 Hp eaten ie,
9.25 | 3.44 | 11.42 | 41.79 P
9.93 | 3.20 | 11.74 | 42.44 ;
10.06 | 3.14 | 12.22 | 49.14 é
13198.’ aan olsa eten
14.28 | 2.16 13.77 | 44.78 eae

1415

is formed; the liquid contains then 22 °/, As,O, and 2.87 °/, NH,. On
further addition of NH, the solution keeps the composition 6 as long
as the complex remains within the threephasetriangle 6. Da, . As,0,,
and we have the complex: As,O, + NH,AsO, + solution 6. The
only thing that happens on addition of NH, is the conversion of
As,O, into NH,AsO,. When all the As,O, has disappeared and has
been converted into NH,AsO,, then on further addition of NH, the
solution follows curve bed, in which ease its content of As,O,
decreases continuously.

Leiden, Anorg. Chem. Lab.

Chemistry. — “The allotropy of potassium.” I. By Prof. Ernst
Conen and Dr. 5. Worrr.

1. We have in view to investigate here whether potassium as
it has been known hitherto is a metastable system in consequence
of the simultaneous presence of two or more allotropic forms of
this metal.

It will become evident from the following lines that the literature
already contains very accurate data for solving this problem.

2. As long as thirty years ago Ernst HAGEN') published his
very careful experiments on the determination of the coefficient of
expansion of potassium, which were carried out with the dilatometer.

Contrarily to many other physicists he bestowed much care on
the purity of the material used. The specimen of potassium experi-
mented with contained only a trace of sodium (in 6 or 7 grams).

3. For a description of the details of the measurements the
reader is referred to the original paper, but it may be pointed out
here that the agreement between the determinations made with two
different dilatometers (containing + 40 grams of potassium each)
was exceedingly satisfactory.

The measurements are summarized in the Tables I and II, where
¢ indicates the temperatures at which the experiments were made,
while v indicates the volume (in ccm.) of 1 gram of the metal.

1) Wied, Ann. 19, 436 (1883),

1116

TABLE 1. T.ABLBWIL
Dilatometer 1. Dilatometer 2.
ft | |
t Vv t Vv t Vv t | u
| |
le} fe) fe} ©
0 1.15665 | 59.8 1.19170 0 1.15692 | 59.8 1.19348
17.3 | 1.16148 || 59.8 1.19457 17.35 | 1.16168 || 50.8 1.19693
40.5 | 1.16823 | 60 1.19643 40.7 1.16843 60 1.19877
|
tot 49.9 | 1.17125 || 60.1 | 1.19949
50.1 | 1.17108 || 60.1 1.19719 |
| 50.2 | 1.17137 || 60 1. 19976
50.2 | 1.17110 || 60 1.19734 |
| 50.1 | 1.17134 || 59.7 1.19918
19.6 | 1.16238 | 59.7 | 1.19593
18.2 | 1.16211 || 59.6 1.19575
31.2 | 1.16542 || 59.6 | 1.19353 | |
| 31.3 | 1.16587 | 64.6 1.20495
41.1 | 1.16829 || 64.6 | 1.20480 (liquid)
| (liquid) |
| | 41.1 | 1.16863 || 54.25 | 1.17611
49.7 | 1.17097 || 54.25 | 1.17452 | | (solid)
| (solid) |
49.7 | 1.17129
55.1 | 1.17607
| 55. | 1.17712 ||
58.2 | 1.18611 ||
| 58.2 | 1.18755
19.7 | 1.16199
| 19,7 | 1.16223
0) ibe 15650 | |
| 0 1.15680 ||
52.0) 1 ATT | |
| 5-7. | 1.07841
52.8 | 1.17258 | |
| 52.8 | 1.17312 ||
52.85 | 1.17259 | |
| 52.85 | 1.17317

4. In order to calculate the coefficients of expansion, HAGEN
only used the observations between O° and 50° C. He found that
the coefficient increases rapidly above 50° C.; there is between this
temperature and the melting point an increase of volume of 0.5 per
cent which is followed by a sudden increase of 2.5 per cent at
the melting point (62°,1).

5. In order to get a clear survey of the phenomena the results
of those determinations which ,were carried out with both dilato-
meters at the same temperatures are summarized in Table III. The
fourth column contains the differences of volume (in hundredths of
amm*) of 1 gram of potassium which is found with the two
instruments at the same temperature.

1117

TABLE Ill.

Volume of | gr. Volume of 1 gr. « Difference
Temperature | of potassium of potassium (hundredths
| in Dilatometer 1 in Dilatometer 2 of mm.3)
Age RS ea Ea a aes

0° | 1. 15665 1. 15692 21
50.2 | 1.17110 ree) Det 7
50.1 | BOBs ae 1.17134 26
41.1 | 1.16829 1.16863 | 34
49.7 | 1.17097 | 1.17129 | 30
B51 | 1.17607 Ut) 4; eA
58.2 | 1.18611 1.18755 | 144
19.7 1.16199 1.16223 | 24

0 | 1.15650 | 1.15680 30
52.7 | ecg ee 42 41SAT eatin Hy Nid
52.8 | 1.17258 | 1.17312 «| 54
ee oh tose REA PR AN
59.8 | 1.19170 | 1.19348 | 178
59.8 | 1.19457 | 1.19693. | 236
60 1.19643 {2108770 hak

60 | 1.19734 1.19976 | 242
59.7 | 1.19593 1.19918 | 32
59.6 | 1.19353 | 1.19575 322
ee 1.20480 1.20495 | 15
(liquid) (liquid)
54.25 1.17452. | 1.17611 | 159
(solid) | (solid)

6. As long as the dilatometers have not been exposed to tempe-
ratures higher than 53°, the differences remain small and nearly
constant (24—24 units). At higher temperatures they become large
(up to 325 units). However, if we go back to O° C., the difference
has become the same (30 units) as it was before at the same
temperature. From these data it follows that there has occurred in
one dilatometer or in both a reversible transformation. That it has
taken place in the solid metal, is evident from the fact that the

difference is again very small (15 units) after the metal has been
melted (at 64°.6 C.). If the metal is now cooled to 54°.25 (at which

1115

temperature it is solid), the large differences (159 units) are observed
again *).

7. If we consider the phenomena with one of the dilatometers
(for example with N°. 1) it is evident that at the constant temperature
of 59°.8 C. there occurs an increase of volume (287 units). Some
time later the volume at 59°.6 C. is 183 units greater than before
at 59°.8 C. although the temperature is lower (0°.2).

8. Considering that in the second dilatometer also the same
phenomena occurred at 59°.8 C. [the volume increases at constant
temperature (345 units) and is afterwards at 59°.6 C. greater (227
units) than before at a temperature which is 0°.2 lower| we may
conclude that the transformation has taken place in both dilatometers.

(Comp. $ 6).

9. These experiments consequently prove that potassium can
undergo transformation into a second modification (3-Potassium) and
that the metal as it has hitherto been known is at ordinary tempe-
ratures a metastable system in consequence of the presence of both
forms at the same time.

10. The indications found in the earlier literature that this metal
is able to crystallize as well in the regular as in the tetragonal
systems *), gains more importance in the light of these results.

141. R. W. and R. C. Duncan *) found that there existed a large
difference between the indices of refraction of two mirrors which
had been formed from molten potassium. Fresh experiments are
wanted in order to decide whether these discrepancies are to be
attributed to the presence of different quantities of the two modifi-
cations in the mirrors experimented with.

12. As the change of volume which accompanies the trans-
formation mentioned, is considerable, it will be possible to investigate
these phenomena by dilatometric measurements more closely than
can be done at present from the data given by HaarN. We hope
to report shortly on this point.

Utrecht, January 1915. van ’r Horr-Laboratory.

1) If the phenomena were to be ascribed to the melting process, the difference
at 54°.25 C. at which temperature the metal is solid, would have been small (30
units), which is really not the case.

2) Apece’s Handbuch der anorg. Chemie 2, (1) 338—839 (Leipzig 1908) ; Lone.
Journ. Chem. Soc. 18, 122 (1860).

3) Phys. Rev. (2) 1, 294 (1918).

1119

Anatomy. — “The vagus area in camelidae”. By Dr. H. A. VerMEcien.
(Communicated by Prof. L. Bork).

(Communicated in the meeting of December 30, 1914),

In a previous paper’) | demonstrated the relation between the
development of the dorsal motor vagus nucleus of some domestic
animals with the size and structure of the stomach, as well as with
the development of the stomach musculature. In that article I pointed
out that the shape of its cell-column differs among our ruminating
domestic animals; in the ox, for instance, it reaches its full size
midway in its length, whereas in the goat not until past the frontal
third part, which circumstance | connected with the fact that the
omasus, a strongly developed and highly muscular division of the
stomach in the ox, is very poorly developed in the goat. Later 1
examined the dorsal motor vagus-nucleus of the sheep, which animal
has also a small omasus, and found similar proportions as in the
goat as regards its form and size. [In one respect only did the two
cell-columns differ, viz. in the goat, */, of the nucleus lie spinally
and */, of it frontally of the calamus; in the sheep the reverse is
found; here, as in the horse and ox, */, of the nucleus lie in the
closed, and */, of it in the open portion of the oblongata. (Series of
921 sections, of which 135 spinal and 186 frontal of the calamus,
fig. 1).

Calamus Calamus
| |
| |
frontal CO caudal frontal za caudal
; |
1 i
Ovis aries Capra hircus
Calamus Calamus

frontal Ce caudal frontal = caudal

MR commissure nucleus

‘
Auchenia lama Camelus bactrianus
Fig. 1. Dorsal motor vagus nucleus.

1) The size of the dorsal motor vagus-nucleus and its relation to the development
of the stomach. These Proceedings Vol. XVI p. 305.

44129

I fortunately happened to get hold of the brain-stem of a camel.
This ruminating animal is also in the possession of a huge
stomach (245 liters capacity) which, however, differs from those of
our ruminating domestic animals in many respects. It must be
remarked here, however, that the largest of the proventriculi, the
rumen, has at both poles a great many (about 50) distinctly separate
bulges, each of which can be shut off from the rest of the rumen
by a sfincter, and has a capacity of 200 to 300 ¢.c. These bulges
were described by Printus and by many after him as water-
reservoirs. Even if this be so, which to an animal of the desert may
be considered of great use, it cannot be the only function, for the
mucous membrane in these peculiar stomach appendices is richly
provided with glands (LesBrr), which points to a digestive function,
and at the same time forms a great difference with the inner coating
of the rumen in other ruminantia, which have all over a very
horny cutaneous mucous membrane. Another remarkable point is
that Cameliden have no omasus at all.

The Central Institute for Brain Research at Amsterdam, enabled me
to further prosecute my researches. From the above-mentioned
Institute I obtained the brainstem of another Camelide, a lama, for
which 1 offer my thanks.

The research was not limited to the dorsal motor vagus-nucleus ;
other nuclei have also been examined, in particular the nucleus
accessorii and the nucleus ambiguus. Special attention was paid to
the two last nuclei, in the first place because, according to LEsBrn’s
researches, the nervus accessorius spinalis does not occur in Came-
lidae, and in the second place because in these animals the nervus
laryngeus inferior has no obvious recurrent course.

In his “Recherches anatomiques sur les Camélidés (Archives du
Museum d'Histoire naturelle de Lyon, Vol. VIII 1903) he says on
p. 191: “Thespinal nerve (the accessory of Wiilis) is completely wanting ;
the sterno-mastoideus, mastoido-humeral, omo-trachelian and trapezius
muscles receive their double innervation, sensory and motor, from
the cervical pair. The absence of the spinal accessory nerve in
Camelidae is an anatomical fact of great importance bithertho un-
known.” A number of root-fibres issuing behind the nervus vagus
unite into a declining stem of 3 to + em. in length. This little stem,
running to the jugular ganglion, is considered by LesBRrE as being the
only part present of the nervus accessorius, the nervus accessorius vagi.

From his description of the innervation of the pharynx and the
larynx it will be seen that in Camelidae the ramus pharyngeus vagi
and the three laryngeal nerves, the nervus laryngeus externus for

1121

pharynx musculature and the musculus cricothyroideus, the nervus
laryngeus superior and the nervus laryngeus inferior (recurrens)
rise from one stem, in such a way that this stem soon divides into
two branches, one of which splits into the two first-named nerves,
and a third descending branch, which gives off a ramus oesophagaeus,
besides the nervus laryngeus inferior. This last describes a slight
curve before reaching the larynx, is thus also recurrent, though not
in the ordinary sense of the word.

This unusual course of the nervus recurrens is quite contrary to
what has been hitherto assumed in favour of the phylogenetic and
ontogenetic development of this portion of the periferal nervous system.
In amphibians, which possess only one cervical vertebra, the heart
is situated caudo-ventrally from the larynx. The nervi laryngei
inferiores reach the larynx behind the large blood-vessels which come
from the heart. With the development of the neck, the heart changes
its place in a caudal direction and causes the above-mentioned nerves
to descend with it ana to reach their territory of innervation by a
long recurrent course. Lespre, who in his detailed treatise, gives a
very clear illustration of the devious course of these nerves in
Camelidae, is of opinion that the ordinary recurrent course of the
nervi laryngei inferiores has been sacrificed to the unusual length of
neck in these animals, and expresses the desirability of investigations
as to whether similar differences are to be seen in the giraffe.

This fact, meanwhile, implies that the nervus laryngeus inferior
in Camelidae has much less to do than in other animals which
possess a genuine recurrens in which also more elements are joined.

Of both Camelidae the vagus area was cut serially into sections
of 18 microns; that of the camel was coloured with eresyl-violet
and that of the lama with toluidineblue.

Camelus bactrianus. The region of the dorsal motor vagus nucleus
is cut into a series of 571 sections, of which 365 are spinal and
206 frontal from the calamus, so that, as in the goat about */, of
the nucleus lie in the closed portion and ?/, in the open part of
the oblongata (fig. 1). The nucleus begins caudally as a narrow
horizontal row of cells, dorso-lateral from the canalis centr. in a
region where the anterior horns of the eervical cord are still in
full development. The nucleus increases slowly, and principally at
its lateral side; 70 sections more frontally, before any distinet cells
of nucleus XII are present, we see also the medial side becoming
slightly thicker, and in the bridge which connects the nuclei right
and left, dorsally from the central canal, a few cells oceur, of the

4199

same type as those of the vagus nuclei. More frontally the cells in
the connecting bridge increase in number and soon both vagus
nuclei form with the motor commissural nucleus, dorsally from the
central canal, an elongated transverse nucleus column which thickens
at both sides. In several sections this transverse cell-column is of
uniform thickness, with the exception of the extremities, where the
connection with the lateral nuclei occurs. (fig. 2). Ninety sections
caudally from the calamus the connecting nucleus ceases, the lateral
side of the dorsal motor vagus nucleus is then noticeably thicker and
towards the calamus this side dips in a ventro-lateral direction
(fig. 3). Here too, as in other animals, it may be noted that in the
ventro-lateral portion of the nucleus, numerous cells occur of a larger
type than in the rest of it.

X Dorsal motor vagus nuclei and commissural motor X nucleus
in the camel; b = bloodvessels, c = canalis centralis.

Fig. 3. a = aberraut bundles, 5 = bloodvessels.

A nucleus motorius commissuralis vagi has never yet been met
with in any other animal: as we shall presently see it also occurs
in the lama. The connecting nucleus lies principally in the region
of the commissura infima, the decussation of the tractus solitarn,
the sensory glossopharyngeo-vagus tracts.

1123

In the calamus the dorsal motor vagus nucleus has grown thicker:
it then contains about 70 cells of the mixed type, the larger of
which lie for tbe most part ventro-laterally. Frontally from the
calamus the dorso-medial portion broadens out so that the nucleus
becomes triangular in form with the base of the triangle turned
towards the ependyma (fig. 4). In the frontal third part of the
nucleus 170 cells can be counted in many of the sections, frequently
we see the large-celled type in groups together in the ventro-lateral

(the figure is reversed ; it represents the left side)
Fig. 4. a = aberrant bundles, b = bloodvessels. Fig. 5. b = bloodvessels.

portion. As usually the nueleus decreases here first in its dors6-
medial portion, a thin column, which creeps up the ependyma, is
preserved longest and, as the ventral portion is well developed
there, the nucleus in this region shows the form of a pyramid,
with the apex pointing upwards. (fig. 5).

The dorsal motor vagus nucleus of the camel does not reach to
the level of the facialis nucleus, as is the case in several other
mammals.

At the spinal extremity of the dorsal motor vagus nucleus in the
camel, the nucleus accessorius is still clearly visible rather more ventral
and’ decidedly lateral, in the substantia reticularis. It can even be
seen on a level near the caudal extremity of the nucleus XII. (fig.6).

Here the accessorins nucleus is very unequally developed, fre-
quently but few cells are found; but we may see a more or less
round group of the familiar large cells, at the most 20—24, very

74

Proceedings Royal Acad. Amsterdam. Vol. XVII.

1124

strongly developed. Im several preparations intermediate cells are
to be seen between the nucleus accessorius and the dorsal motor vagus

PZ LLL Lkeph hades

ee A ITZIILILD

ze at + it.
- +
Ar 4 zitt +5455 +3+1+5s>

Fig. 6. Camelus bactrianus. ')
EXP a AN ARTON:

ee Cahn Gti Ole rf Ee = we  IX

DIN = He 2X N= = He ae 8 mm =/ LZ lerne:T
nucleus (fig. 7). Here, too, in several sections ventro-lateral outgrowths
of the accessorius nucleus are present, which might give the impression

as if this nucleus in the camel continues directly into the nucleus
ambiguus. This, however, can be proved not to be the case, since the
ambiguus shows itself much more ventro-laterally. In a few sections
both the accessorius nucleus and ambiguus are present’) (fig. 8) and
their separate character is then easily seen. As the remainder
of nucleus XI we frontally see a small cluster of cells medial
from the ventral border of the radix descendens nervi V. The fact
that the ambiguus in a more frontal plain is also found near this
border, explains the old theory that the ambiguus is a continuas

1) In this diagram (Fig. 6) the caudal extremity of the nucl. ambiguus is a
little shortened for clearness sake.

1125

tion of the accessorius nucleus. The rad. descend. V is, however,
more developed in the oblongata, and its ventral border comes to
lie in a much lower region. Ambiguus and accessorius nucleus are
both derivatives of the dorsal motory vagus nucleus. This has been
proved phylogenetically and ontogenetically by Karpers, and is again
confirmed in the camel by the intermediate cells between the dorsal
motor X nucleus and the nucleus XI and the simultaneous but
distinctly separate presence of the latter and the nucleus ambiguus
on the same transverse level.

The nucleus ambiguus of the camel is, with the exception of its
frontal pole, but slightly developed. In the closed part of the oblon-
gata it shows no more than 10 to J2 cells in one section and very
frequently none at all are to be found. This holds good also for
the rest, with the exception, as said above, of the frontal pole. On
a transverse level corresponding with the frontal end of nucleus XII,
we still find clusters of 4—6 large ambiguus cells, while on the other
hand, on the level corresponding with the frontal pole of the dorsal!
motor vagus nucleus, the nucleus ambiguus enlarges very rapidly to
an immense compiex of cells in which a maximum of 80—85 cells

5 - os eral = es ~ .
A tre Ch af r ” v
é = mr Sit Sw er 5 ¥
+ - De =
rn. Wes CK B von
: *t . ed En v Pid
“ Pi , - a
fees Laus Fie g
Racy darBdymmnd: o° ~
ages Frontal enlargement
; a of the nucleus ambi-
x guus in the camel.

Fig. 8.
Showing the separate character of the nucleus
accessorius and nucleus ambiguus.

may be counted. Frontally the enlarged nucleus ambiguus can be
divided into a medial portion with smaller and a lateral portion with
larger cells. While the frontal enlargement of the ambiguus (where
it occurs) is generally described as a mass of closely crowded cells
of smaller type than the ordinary ambiguus cells, it is here remark-
able that the cell group is not so crowded together and contains,
especially in the lateral portion, typically large ambiguus cells (fig. 9).

Its frontal extremity has clearly shifted ventrally. Lt is 54 sections
long and extends 30 sections frontally from the dorsal motor vagus
nucleus (fig. 6). Twelve sections further the nueleus VII begins.

Coneerning the Aypoglossus nucleus it may be mentioned that its

1126

caudal extremity is not easily determined, efferent hypoglossus roots
can be observed very far caudad and it is frequently seen that,
frontally from sections in which XII cells are present, ventral horn
cells again appear; a sharp boundary between ventral horn and
hypoglossus nucleus is not present (fig. 6). Also, it can be seen in
several of the sections that cells have shifted from the vagus column
ventrally to near the hypoglossus region (fig. 7), a position which
strongly resembles that in birds. The first constant XII cells appear
dorsally, close to the dorsal motor vagus nucleus, then the medial
group of XII cells appears and finally its ventro-lateral group.
Spinally from the calamus, the three groups of XII cells are not
clearly defined and one or two groups of it are rather poorly
developed. Frontally from the calamus the grouping is clearer and
also central cells occur. The- dorso-lateral group is most strongly
represented and is the most constant, the other groups are in several
sections less strongly developed. Frontally the dorso-lateral group
disappears first, and the ventral remains longest.

The hypoglossus column extends 134 sections frontal from the calamus. —

The vliva inferior of the camel is poorly developed. It appears
with a ventral lamella, rather ventro-lateral. on the transverse
level of the spinal pole of the nucleus XII. This ventral lamella
spreads medially and then creeps up the raphe. The second lamella
lying dorsally and representing the olivary nucleus sense strictiori
does not appear before in the neighbourhood of the calamus. At the
frontal pole of nucleus XII, it becomes thicker; it ends rather
frontally from the ambiguus swelling (fig. 6). Its cell type is small,
the cells being thinly sown in some places.

The exceedingly poor development of the nucleus reticularis inferior
is striking. Very few cells occur in the raphe, most of them front-
ally in the ventral portion,

In the series of this camel, through the whole vagus region, at
the left side, an aberrating descending bundle is seen. In the acoustic
region we see cross-sections of a few small sharply outlined bundles,
under the lateral ependyma, of the IV ventricle. At the right side
we find at that place one little bundle. Caudally the bundles on the
left side increase greatly in number and their diameter varies greatly.
At the frontal pole of nucleus X dorsalis the bundles are crowded into a
wedgeshape between the cells of this nucleus: fig. 4 (This figure is rever-
sed, it represents the left side). An ascending bundle of fibres, beneath the
ependyma runs in a dorsal direction along the top of the vagus nucleus;
more caudally a ventral branch also appears, which runs medially from

the XII nucleus in the direction of the raphe. Near the calamus
40 bundles can be counted on the left side; at the right, where a
few more are added, only 3 or + are to be found. The dorsal
branch of the bundles has disappeared; caudally from the calamus
the complex runs ventrally from the dorsal motor vagus nucleus
and medially from the central canal (fig. 3). The complex gradually
decreases, its outline finally fades away and 170 sections spinally from
the calamus the last bundle disappears in the raphe. Regarding the
exact connections of the latter I do not venture to make any
Statement.

Auchenia lama. Series of 365 sections; the calamus falls in section

3/
/ 5

of the
dorsal motor vagus nucleus lie in the closed part of the oblongata
(fig. 1). The nucleus begins caudally as a small, round group of
cells, dorso-lateral from the canalis centralis; it increases slowly in

219, so that here too, as in the goat and the camel,

size chiefly at its lateral side, so that it becomes egg-shaped, not
before the middle of the spinal portion does it become more oblong in
shape and the first commissure cells appear, frequently lying more
dorsally than in the camel, so that the whole cell-column, dorsally
from the central canal takes a more or less curved course. (fig. 10).

Fig. 10. Dorsal motor vagus nuclei and motor commissural

X nucleus in the lama.

The motor commissural vagus nucleus of the lama (Fig. 10) is in
general not so well developed as that of the camel. Although it
stretches further frontally than in the camel (ending 20 sections
spinally from the calamus) it is smaller in comparison (tig. 1). Its size
is not constant, in some places it is more or less poorly developed.

In the lama too, the dorsal motor vagus nucleus lies obliquely
near the calamus, and it has a much thicker ventro-lateral pole,
containing many cells of the large type; in front of the calamus
the dorsomedial part also bulges distinctly, and the nucleus thereby
beeomes triangular in shape, with the base directed towards the

1128

bottom of the ventricle; more frontally it loses this form because
the ventro-lateral pole also enlarges, after which the structure of
the nucleus becomes looser and the number of cells grows less. Here
too, the ventro-lateral portion remains longest, and the dorsal motor
vagus nucleus does not reach into the region of the nucleus facialis.

The nucleus accessorii lies more medially into the lamat han in the
camel, just on the border of the anterior and posterior horns. Near
the spinal pole of the dorsal motor vagus nucleus it is well developed ;
in some sections + 90 large XI cells, and medially from this, in
the same level, 5—8 dorsal vagus cells can be counted (fig. 11). Very
soon a tendency can be observed in the XI nucleus to extend medially ;
in one section it contains as many as 35 large cells and it is clearly
prolonged in the direction of the dorsal motor vagus-nucleus ;

wr
NN A BRL,
A fay ae
re eee \Ww 4
SIG) a N
Sk er NLS
ey 5 Xf KP N
YS. re : N \
Vide Loe BEA
yer eee AA mG Fae See ee
SIN ¢ . y, ee ten ae
Dx Odie, ;
BS st Aa A 6
ee. Er on A
wD) ff J ‘ Ge

iy Sas eee, a.
a Day my £ DN % a a
15 LO, rend ie = okey: 44
/ Wy fie Foes x AIM IN
„1 UA: \\ WY) Grane. > K'
Fig. 11. A posterior horn, B anterior horn. _ Fig. 12. A posterior horn, B anterior horn,

C canalis centralis.
immediately after the two nuclei join to one large group containing
55 cells, of which the most medial ones have kept the smaller type of
the dorsal vagus cells, whereas the lateral cells exhibit the large acces-
sorius-nucleus type (fig. 12 and 14). This constellation soon decreases
in size and is only to be seen in 4 consecutive sections after which
the vagus nucleus remains in its usual extent at that place; it con-
tains then about 30 cells of mixed type; the large cell-type remains
principally lateral. After this on more frontal levels with a very
few exceptions nothing more of the nucleus accessorii is to be seen.
Near the spinal extremity of nucleus XII, however, the process
repeats itself to a slight extent, and we see a few XI cells rise and
shift in a medial direction’). As far as the material at our disposal
extended, i.e. 165 sections spinally from the beginning of the dorsal

1) Not indicated in the diagram of fig. 14,

1129

motor vagus nucleus, the XI nucleus did ‘seem to be constantly
present and was very unequally developed. [n the very first sections,
however, it could be seen; on an average it contains here 8— 20 cells.

Concerning the nucleus ambiguus it may be said that in general
this is better developed in the lama than in the camel. It begins
caudally from the place where the nucleus XII is clearly present
and where the anterior horns of the cervical cord are still visible.
More frontally it soon enlarges, but soon decreases again, and occurs
but very slightly in the calamus region. In the open part of the
oblongata its appearance is very different; as far as the frontal pole
of nucleus XII its ventro-lateral part is generally the most strongly
developed; occasionally the nucleus then contains 20—25 cells. As
far as the frontal pole of the dorsal motor vagus nucleus, the
development is again very poor, after which we see a round group
of 8—10 cells arise that enlarges greatly on a level frontal from the
dorsal vagus nucleus. Originally two cell groups can be distinguished
in the frontal enlargement, but very soon these join to form one
large complex, containing at the most 75 cells, mostly of the large
type; the majority of the large cells are here also found in the
lateral part (fig. 13). Also this enlargement of the nucleus ambiguus
distinctly lies in a more ventral plane than the rest of the nucleus;

Frontal enlarge-
ment of the nu-
cleus ambiguus in

the lama. Fig. 14. Auchenia lama !).
(Explanation as in figure 6.)
as is usually the case in lower mammals. It projects 56 sections
in front of the frontal extremity of the dorsal motor vagus nucleus
(fig. 14) and it is in this region that the first cells of the nucleus
facialis appear.

Also in the lama the connection of the nucleus hypoglosst with
the anterior horn of the cervical cord be observed (fig. 14). Behind
the calamus, the XII nucleus is poorly developed in this animal,
and a division into groups can hardly be observed here. Frontally from
the calamus the medial group appears, and soon after also the

1) In this diagram (Fig. 14) the caudal extremity of the nucl. ambiguus is a
little: shortened for clearness’ sake.

1130

ventro-lateral group. The nucleus is now well developed; the dorso-
lateral part lies more ventrally than in the camel, so that we better
speak of a dorsal group and a ventro-lateral group in this animal.
More frontally the medial group becomes thicker and then contains
cells of a larger type than those behind. The dorso-lateral group first
disappears, and then the medial, so that the large cells of the ventro-
lateral group remain longest visible. . .
The nucleus extends 116 sections in front of the calamus.

The oliva inferior is much better developed in the lama than in
the camel. Also here it occurs latero-ventrally in the region of the spinal
part of nucleus XII. It contains more cells than that of the camel,
and the cell type in general is larger. On the level of the frontal pole
of nucleus X dorsalis it is still clearly present; it decreases rapidly
and ceases at the frontal extremity of the nucleus ambiguus (fig. 14).

The nucleus reticularis inferior is extremely well developed in the
lama. It grows dorsally over the olive and spreads medially from
the raphe into the substantia reticularis. A clearly defined cell group
lies under the efferent vagus root. This disappears first, and the rest
near the region of the nue. facialis.

The dorsal motor vagus nucleus of Camelides lies, as in all
other animals, in a region, that is rich in blood-vessels. All the
illustrations of it, which occur in this article and which have been
made after microphotographs, show cross-sections of large blood-vessels.

The form of the nucleus differs in Camelidae as well as in the
sheep and goat, from that in the cow in so far as in the last-named
animal it attains its greatest extent on the half of its extent, while
in the first-named animals it does so not before the frontal third
part. Since in the cow ?7/, of the nucleus lies spinally from the
calamus, the most developed part of the nucleus, which at this place
is clearly less in size in other ruminantia, begins just frontally from
the calamus and we must therefore look for the centre of the
mnnervation of the omasus in the most caudal portion of the fossa
rhomboidea, at least in the ov and sheep. In the goat and in Camelidae,
where a larger part of the nucleus stretches into the closed portion
of the oblongata than in the first-named animals, that centrum may
stretch, or at least partially, somewhat spinally from the calamus.

LesBki has shown that a nervus accessorius spinalis, such as we
know in all other mammals hitherto examined, as a nerve which
arises from a nucleus of its own in the cervical cord and runs

1131

upwards united between the roots of cervical nerves, does not occur in
Camelidae, and says of this that it is “un fait anatomique de haute
importance’. I have, however, proved that a spinal nucleus acces-
sorius does really occur in these animals. It must a priori be con-
sidered as extremely doubtful that an anatomical centre which
occurs so constantly in mammals should be absent in these animals.
Undoubtedly it is highly remarkable that the spinal accessorius fibres
are not united in these animals to one stem but physiologically this
cannot be regarded as a fact of “haute importance”, since also in
these animals spinal accessorius fibres reach their destination, though
more directly with cervical nerves, and not by a detour.

In all anatomical text-books the nervus accessorii Willisii will be
found described as consisting of two parts, a spinal and a bulbar
part, the latter (because it unites wholly or partly with the nervus
vagus) being called also the nervus accessorius vagi. The distinction
is based on the fact that in man the accessorius spinalis and
accessorius vagi unite into one stem, viz. the nervus accessorius
communis, after which the bulbar part separates again to join the
vagus after this nerve has passed the jugular ganglion. Ramon Y
CasAL says meanwhile in his “Histologie du systeme nerveux de
Phomme et des vertebrés” (Vol. I, p. 719) that he shares the
opinion of Kosaka that this division into an accessorius spinalis and
bulbaris has no significance, since they are convinced that a bulbar
accessorius does not exist, but that the latter originates in the dorsal
motory vagus nucleus and thus contains ordinary vagus fibres.

Ido not agree with CayaL and Kosaka, though their view seems
to be proved by the fact that in domestic animals the two parts of
the nervus accessorius do not unite into one stem, e.g. in the horse
the front part of the pars bulbaris enters the ganglion jugulare,
while only the hindmost part joins the accessorius spinalis; in
ruminants and carnivora, on the other hand, the entire accessorius
bulbaris enters the ganglion jugulare, while in the pig this part
reaches the nervus vagus late, viz. at the place where the ramus
pharyngeus is given off. On account of my observations, however,
in the camel and in the Jama, I have come to the conclusion that
accessorius cells really do occur in the oblongata. In these animals
the accessorius nucleus is very distinct in the region of the dorsal
motor vagus nucleus; in the lama it immediately joins the aforesaid
vagus nucleus, in the camel there are only traces of such a connection.
In any case, in both animals the accessorius nucleus extends into
the oblongata. I am willing to assume that in the so called ramus
internus n. accessorii, i.e. in such part of it as joins the nervus

1132

vagus,” genuine vagus fibres run, but there is no doubt whatever
that a part of the nervus accessorius originates in the oblongata.
Even the fact that fibres originate in the dorsal motor vagus nucl.
does not in my opinion prove that they are necessarily vagus fibres.
I consider it remarkable that in all the animals | have examined as
yet the dorsal motor vagus nucleus shortly after its caudal appear-
ance exhibits in the lateral part a type of cell which is larger
than its original cell-type, a type which is maintained over a part
of the nucleus, chiefly at its ventro-lateral and ventral sides.’) I
venture to express the supposition that these large cells, although
they pass over into the dorsal motor vagus nucleus, are accessorius
elements. The accessorius nucleus, which has originated ontogenetic-
ally and phylogenetically from the caudal part of the dorsal motor X
nucleus (Kappers’)), thus exhibits this relationship in Camelus and
Lama still in the full-grown animal. |

The enlargement of the dorsal motor vagus nucleus in Camelide
with the motor commissural nucleus may be explained by the striking
differences which the oesophagus and stomach of these animals
exhibit from other ruminants. Not only is the oesophagus in these
animals remarkably long in proportion (in Camelus + 2 meters !)
but this organ is likewise in every respect particularly rich in glands
(Lessee), and, as has already been stated, the rumen contains many
glands in some of its divisions. In this connection | may mention
that, after I had shown the motor commissural vagus nucleus in
Camelus and Lama, I car efully examined my series of the sheep and the
the goat in respect to this, and only found in some sections indications
of this connecting nucleus, a remarkable symptom, since in these
animals glands are but rarely met with in the oesophagus and in
a part of the omasus. The position of the nucleus motorius com-
missuralis vagi in the eommissura inferior visceralis which contains
descending sensory fibres of oesophagus and stomach must be ascribed
to neuro-biotactic influences.

The short course of the nervus laryngeus inferior seems to
be correlated with a smaller development of the caudal third
part of the nucleus ambiguus. The pronounced development of
the frontal enlargement of the nucleus ambiguus, the centre of
the motor glossopharyngeus, may be explained by the exceptional

1) SruurmAN has also pointed out the occurrence of two celllypes in the dorsal
motor vagus nucleus. F. J. Stuurman, “Over den oorsprong van den nervus vagus
by het konijn.” Acad. Proefschrift, Amsterdam. 1913

2) Weitere Mitteilungen über Neurobiotaxis, VII. Folia Neurobiologica. Bnd. VL.
Sommerergänzungs Heft, p. 94.

1133

length of the pharynx in Camelides (Lesser). The unusual wealth
of glands in the digestive tract of these animals is a result of their
mode of living. Numerous plants on which they feed in a wild
state are abundantly covered with large strong thorns, so that an
extra development of glands in the mucous membranes is really not
superfluous for them.

CONCLUSIONS.

The centre of the innervation of the omasus of the Ruminantia
must be looked for in the most caudal part of the fossa rbomboidea
or, for a part directly caudally from the Calamus.

In Camelidae an extension of the dorsal motor vagus nucleus
occurs in the region of the sensory commissura infima visceralis,
so that the motor dorsal X nuclei from the two sides are united
(nucleus motorius commissuralis vagi). In the sheep and the goat only
slight indications of this connecting nucleus are present.

The nervus recurrens is given of in Camelidae in conjunetion with
the ramus pharyngeus n. vagi and the nervus laryngeus superior
(LesBre); in accordance with this unusually short course the nucleus
ambiguus, especially in the spinal third part, seems to be less
developed than in other animals.

The frontal enlargement of the nucleus ambiguus in these animals
is particularly strong, and possesses numerous cells of a larger type
than are usually met with at that place.

A nervus accessorius spinalis is not present in Camelidae (Lussre);
since a nucleus accessorii is present in the cervical cord, however,
the accessorius fibres must run with the cervical nerves.

An accessorius nucleus is also very clearly seen in the region of
the dorsal motor vagus nucleus; since the region of this vagus nucleus
is considered to belong to the bulbus, a really bulbar part of the
nucleus accessorii has to be accepted, the presence of which has
been denied by Casa and Kosaka.

In those sections where in Lama and Camel the nuel. ambiguus
and the nucleus accessorius are both present, they remain clearly
separated. The nucleus accessorius is not continuous in these animals
with the nucl. ambiguus. |

1134

In the lama a direct connection of the nucleus XI with the nucleus
motorius dorsalis X, as has been observed embryologically (KappERs),
can be distinctly demonstrated, The accessorius nucleus thus enlarges
the vagus nucleus in question at its lateral side with cells of a

larger type.

The nucleus XII in Camelidae exhibits very primitive features
and has preserved its connection with grey matter of the anterior
horn as in lower vertebrates.

In the camel the oliva inferior and the nucleus reticularis inferior
are only slightly, in the lama on the contrary rather strongly, developed.

Utrecht, December 1914.

March 26, 1915.

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING
of Saturday March 27, 1915.
Vor. XVII.
President: Prof. H. A. Lorentz.
Secretary: Prof. P. ZreMaN.

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 27 Maart 1915, Dl. XXIII.

OEE ER Ne ES

S. pr Borr: “On the heart-rhythm”. II, (Communicated by, Prof. J. K. A. Weerritrim
SALOMONSON), p. 1135.

P, H. GarrÉ: “On the relation between departures from the normal in the strength of the
trade-winds of the Atlantic Ocean and those in the waterlevel and temperature in the
northern European seas”, (Communicated by Dr. J. P. vaN DER STOK), p. 1447.

H. R. Krurr and Jac. van per Seek: “The connexion between the limit value and the
concentration of Arsenic 'Trisulphide sols”. (Communicated by Prof. E. Conen, p. 1158.

R. A. WeEERMAN: “Action of sodium hypochlorite on amides of #-oxyacids. A new method
for the degradation of sugars.” (Communicated by Prof. A. P. N. FRANCHIMONT), p. 1164.

H, Trrropr: “Theoretical determination of the entropy constant of gases and liquids”. (Com-
municated by Prof. H‚ A. Lorentz), p. 1167.

P, Enrenrest: “On interference phenomena to be expected when Röntgen rays pass through
a di-atomic gas”. (Communicated by Prof. H. A, Lorenrz), p. 1184.

H. A. Brouwer: “On the granitic area of Rokan (Middle Sumatra) and on contact-pheno:
mena in the surrounding schists.” (Communicated by Prof. G. A. F, Motenaraarr), p. 1190.

Errata, p. 1202.

Physiology. — “On the heart-rhythm.” ‘) U. By Dr. S. pr Boer.
(Communicated by Prof. J. K. A. WeRrHEIM SALOMONSON).

(Communicated in the meeting of February 27, 1915).

Pulsus bi-, tri- and polygeminus.

In my former communication I incidentally called the attention
to the fact that pulsus bigeminus occurs as a transition-period from
the normal heart-rhythm to the halved one. In the following pages
I intend to communicate, in what way the normal heart-rhythm can
through different intermediate periods pass into the halved one. As
an example of this manner of halving the following experiment
may serve:

1) According to investigations made in the physiological laboratory of the
University of Amsterdam.
75
Proceedings Royal Acad. Amsterdam. Vol. XVII.

1156

After about one hundred systoles of a frog’s heart had been
transferred to the smoked paper, according to the suspension-method,
10 drops of a 1°/, solution of acetas veratrini are injected into the
abdominal cavity. The rhythm slackens, the a-v interval increases,
till half an hour after the injection one auricle- and one ventricle-
systole fall out (Vide Fig. I upper-row). Afterwards the 10%

Suspensioncurves of a frog’s heart poisoned with veratrine ; in the upper-row
of curves twice on systole of ventricle and auricle fall out.

The lower row of curves shows bigeminus-groups and is reproduced 20 minutes
later. Time | sec. (just as in all further figures).

Both rows of curves are continuations of those of Fig. 1, but 27 systoles afterwards.

auricle- and ventricle-systoles fall out again (still to be seen in the
figure). Thereupon again and again but a little earlier one auricle-
and one ventricle-systole fall out. Fig. 2 is reproduced 27 systoles
after the former. In the upper row we see here p quadri- and trigeminus.
Then for a short time larger groups occur again. So Fie. 3 is
represented twenty systoles after the former. In this figure (upper row

tt antr en am am Caen ee a oe Py on

Fig. 3.
Continuation of Fig. 2 but 20 systoles afterwards.
of curves) a special peculiarity can be seen, which I observed on
this curve-page only there, and then twice. After the first and also
the second falling out of an auricle- and a ventricle-systole (fig. 3
there comes a little later a new auricle- and ventricle-systole. The
latter falls entirely beyond the normal heart-period, it is perhaps an
extra-systole, originating in the auricle. which has then not caused
an irritation of the sinus venosus by retrograde conduction (for the
normal heartperiod is not disturbed, whilst the process continues),
Another possibility is, that for this curve the conduction in the
si—a-systems of connection is very slow, and consequently the fol-
lowing auricle is so much retarded.

In this figure again one systole falls out, but now such an ab-
normally retarded systole does not occur. (3'¢ hiatus in the upper
row). If now we measure here the duration from the beginning of
the ventricle-systole before the pause to the beginning of the ventricle-
systole after it, we find a duration that is much shorter than that
of 2 heart-periods.

This difference is caused by the abbreviation of the s/-a-interval
and the a-v-interval after the longer pause. Moreover the last
ventricle-systole before the pause begins very late, because the con-

PT ewe
{27

duction along these two systems of connection is much retarded.
The widening and enlargement of the systoles after the longer pauses
is here, as likewise in the other figures, very conspicuous. Fig. 4

bee)

is reproduced 150 systoles after the former.

Fig. 4.

Continuation of Fig. 5, 150 systoles afterwards.

In the mean time the groups have become smaller and they now
form here trigeminus-groups. In all 4 figures the bigeminus-groups
have been reproduced 20 minutes later than the first row.

The second systole of each bigeminus- and the third of each
(rigeminus-group is always least high and wide. In each group there
is consequently a diminution of the dimension of the systoles. From
my former communication it is known, that in bigeminus-groups
the point and the basis can pulsate alternately. In this case every
systole was not a systole of the whole ventricle musculature, but
for each of the two systoles every time another part of the ventricle-
muscle was in contraction. Consequently there can be no doubt but
partial asystole is possible. And so I saw here with every bigeminus-
group during the first systole the whole ventricle contract, and during
the second the point of the ventricle continued inactive. We must
explain this by the fact, that the irritability of the heart-point
diminishes here during the groups, so that after every first systole
the conducted irritation cannot make it contract. This is likewise
true for the trigeminus-groups.

In order to make a more accurate investigation into the cause
of the falling out of the first systole (vide Fig. 1) I have measured

1139

the a-v-interval of the last 6 systoles before the hiatus, and of
8 after it. The numbers

before the hiatus are: after the hiatus are:
09 sec. 0,7 sec.
dn OER =.
| 0:95
del 5, 095,
ci Waa 0,95,
© ees
0,95 ,,
0:95-,,

Consequently we see that the «-v-interval increases in duration,
whenever a ventricle- and an auricle-systole fall out. After the hiatus
the a-v-interval is smaller, and afterwards increases again in
duration.

Further I fixed the duration of the beginning of each ventricle-
systole to the beginning of the next following auricle-systole. As
variable quantities in these measurements must be taken into con-
sideration in the first place the retardation or anticipation (by
increase or decrease of the intervals s/-a and a-v) of the ventricle
systole with which I began the measurement, and then the retard-
ation or anticipation of the beginning of the following auricle-systole
(through modification caused in the velocity of conduct between s7
and «)*). Beginning with the 6 systole before the first hiatus this
duration for this systole and the following one amounted to:

1,8

1,8

de,

18

1,8

3,4 (at the first hiatus)

2,1

1,9

1,8

1,8

1

3,7 (at the second hiatus)

2,1
1) Where I speak of the time of conduction between si and @ and between a
and v. I understand by it the time required for the stimulation to transmit itself
along the systems of conduct + the lime, that the stimulation requires to influence
the atrium resp. the ventricle.

1140

If now we examine more closely the number 3,4 ie. the distance
from the beginning of the last ventricle-systole before the hiatus to
the beginning of the first auricle-systole after this, we must take
into consideration that this includes the duration of one entire
ventricle-period + the duration of the beginning of one ventricle-
systole to the beginning of the following auricle-systole. The duration
of a heart-period is 2,75 see. This subtracted from the duration of
3,4 sec. which we found, gives 0.65 sec. If now we compare this
number with the others of the above list we see that it is about
'/, part of it. The cause of this short duration is in the first place
the retardation in the conduct systems (st-a and a-v) which made
the last ventricle-systole before the hiatus begin very late; after the
hiatus the conduct si—a has much improved, by which the begin-
ning of the first auricle-systole after the hiatus is anticipated. The
co-operation of these two factors has consequently reduced the
number we found to one third.

The following number of the list, on the contrary, is again much
greater; the anticipation of the first ventricle-systole after the hiatus
is the cause of it. The number we found for the second hiatus is
0.3 second greater than the equivalent number for the first hiatus.
This means that now less repair of conduct takes place in the con-
nection-systems s- than at the first falling out of a heart-period.
After this the next following number is also again greater than
usually. At first it seems astonishing, that this number is again as
great (2,1 sec.) as after the first falling out. If the increase of this
number is caused by the anticipation of the preceding systole, this
number ought to be inferior here, for the preceding systole is here
less anticipated than after the first hiatus. We must however not
forget that, on account of the better conduct in the connection-systems
the second ventricle-systole has also been a little anticipated, and
that this anticipation is now less important than after the first hiatus.

It appears with certainty from the measurements I made also for
the following hiatuses, that the repair of conduct in the connection-
systems becomes constantly worse. This is the cause that a heart-
period must constantly sooner fall out. The fact that the repair of
the irritability of the heart-musele constantly diminishes, and con-
sequently the duration of the refractory period, directly after an
hiatus, decreases less, will certainly have its influence in this respect.
In the further progress of the curves we see indeed that the heart-
periods fall out sooner. In this respect I made still a great number
of measurements, for the sake of brevity L do not mention these
here. From all these measurements the repair of conduct after the

1141

falling out of a heart-period appeared distinetly. I will just fix the
attention to one deviation that 1 detected. When I fixed in the
bigeminusgroups the a-v-interval, calculated from the beginning of
the auricle-systole to the beginning of the ventricle-systole, 1 con-
stantly obtained for the large ventricle-systole, occurring after the
hiatus, a greater value than for the next little second systole.

This would consequently be entirely in contradiction with the
irrefutable fact, that after longer pauses this interval decreases. |
think, | am able to indicate the cause of this phenomenon, it is of
a pure technical nature, and depends upon the manner of registering.
The first ventricle-systole of each bigeminus-group begins in the
beginning of the diastole of the preceding auricle-systole. Conse-
quently the entire heart is lengthened at the beginning of this ventricle-
systole by the then allongating auricle, and shortened by the ventricle
which at the same time passes into systole. The beginning of the
systole is consequentiy only expressed in the curve, as soon as the
shortening of the ventricle prevails; this causes the retardation. This
is not the case with the second ventricle-systole of every bigeminus-
group, because the ventricle-systole begins later, and moreover the
preceding auricle-systole during this process is very little. I did not

“a

In the curve-row 3 the reproduction of the curves of the auricle-systoles
changes, as soon as these occur in the beginning of the ventricle-systole.

1142

discover this deviation of the «-v-interval directly after the larger
pauses for the poly- and trigeminusgroups. The reason of this pheno-
menon is. that here the ventricle-systole begins during the systole of
the preceding auricle (vide Figs. 1, 2, 3, and 4). Consequently these
two shortenings sum up and the systole of the ventricle is not
retarded in the curves. From this it appears again, that the repair
of conduct in the connection-systems becomes constantly worse after
the falling out of one systole. Till the trigeminus-groups (these included)
the first ventricle-curve after a hiatus begins during the systole of
the preceding auricle; with the bigeminus-groups the first ventricle-
systole begins during the diastole of the preceding auricle-curve.
(I can explain with another example the fact, that the curve of the
systole of one partition of the heart changes entirely, when at the
same time another partition of the heart is in diastole (vide Fig. 5).

The third row of curves is here represented 45 min. after the
injection of 5 drops of 1°/, acetas veratrini. Here the auricle-systole
begins at the 3°¢ and 5" curves in the beginning of the diastole of
the ventricle, and then, as it were, it sinks entirely away; if, on
the contrary, the auricle-systele begins at the top, then it is much
larger. This piece has been photographed from a row of 2'/, m. in
length, in which, whenever the auricle occurs in the BE of
the ventricle-diastole, the latter decreases. In the following row of
curves the rhythm is halved, and an everywhere equal auricle-
svstole is represented on the ventricle-curve. )

| have thus noted for 1°/, hour bigeminus-groups of this heart;

Fig. 6.

Transition from pbigeminus into the normal rhythm, then again
p. bigeminus and afterwards halving of rhythm.

1145

when these groups had existed 45 minutes, extra-systoles intervened
between the groups. It is well-known, that these occur by preference
in greater pauses.

Halving of the rhythm has not been attained with this heart;
most likely it would have occurred, if the poisoning had made
greater progress. So | often saw p-bigeminus as a transition from
the normal rhythm into the halved one and in transitions of rhythms
(vide Fig. 6).

Here we see in the upper-row of curves (20 min. after the injection
of 4 drops of 1°/, veratrine) bigeminus-groups pass into the normal
rhythm; 5 minutes before the bieeminus-groups the rhythm was
halved: in the next row (5 min. later) we have again bigeminus-
groups, and 15 min. after this (Br row) the rhythm is: halved

int os

First row: Suspension-curves of the unpoisoned frog’s heart; 2nd 10 min. after

the injection of 10 drops of 1/0 acel. veratrini; 3rd row: 5 min. later halving
of the rhythm; 4th row: 10 min. after row 3, the systoles of the halved rhythm
grow smaller: 5th row: 9 min. after row 4, bigeminus-groups. These groups
develop „themselves because each 3rd and each 2nd systole of the normal rhythm
are represented; in the latter part of this row every 3rd systole can twice be
observed. The bigeminus groups form here a transition between the halved rhythm
and the rhythm, of which every 3rd systole of the rhythm shows itself.

1144

again. The duration of 3 periods of this halved stage is equal to
the duration of 2 bigeminus-groups. The distance between 2 auricles
in one group is 2 sec., the duration from the 2rd to the first of the
following group is 2'/, sec. This teaches us how great the retardation
can be in the connection-systems between the sinus venosus and the
auricle.

P-bigeminus does not only occur as transition with halving of
rhythm, but likewise as transition between the halved rhythm and
a still slower rhythm.

Fig. 7 is an example of this phenomenon.-The upper-row gives
the curves before the injection. The 2™¢ row of curves is represented
10 min. after the injection of 10 drops of veratrine into the abdo-
minal cavity. In the 8° row (represented 5 min. after the 2rd) the
rhythm is halved. The same stage exists still in the 4 row, but
the systoles have become smaller, the «-v-interval has increased a
second time (in the halved rhythm of row 3 the lengthened a-v-
interval was reduced again). In the 5th row the systoles are ranged
in bigeminus-groups. Measurement shows us that from the normal
rhythm after the first systole of each group one systole, after the
Jud systole 2 systoles, are missing.

Here we have consequently a bigeminus of which alternately
every 3° and every 2"¢ systole are expressed. This bigeminus also
is again a transition into a slower rhythm. The last 2 systoles of tiis
row indicate this rhythm. Here every 3 systole is every time
expressed.

With unpoisoned frog’s hearts heart-bigeminy occurs also frequently
as transition with halving and variation of rhythm. Thus T have a
series of curves of a suspended normal frog’s heart, on which first
groups of 8, 10, 4, and 3 were formed; afterwards bigeminy took
place, which was converted into the halved rhythm.

Fig. 8.

Bigeminus-groups — halved rhythm — bigeminus-groups.

This halved rhythm was afterwards converted again into heart-
bigeminy. These last 2 transitions are represented in Fig. 8. Two
of the bigeminus-groups answer to 3 systoles of the halved rhythm.

1145

By measurement we can easily discover the important retardation in
the conducting-systems between the partitions of the heart for every
2d systole of the groups.

In all the cases of heart-bigeminy mentioned here we have before
us a heart, pulsating in 2 rhythms. The first systole of each group,
which is preceded by a longer pause, is of the type of a slower rhythm,
the Zed systole is of a quicker rhythm. Each group has one systole
out of each of the 2 rhythms, between which the bigeminy occurs
as a transition.

In every bigeminus-group the first systole is wider than the 2";
what is wanting in the 2ed systole after the shorter pause, is added
again to the first systole after the longer pause (law of the conser-
vation of energy of the heart), The same relation we found in the
velocity of the conduct in the connection-systems between the parti-
tions of the heart for the two systoles of the bigeminusgroups. In
my former communication I called already the attention to this fact.

Likewise in another way I saw heart-bigeminy occur after poisoning
with veratrine. In the still normal rhythm the conduct in the connestion-
systems of the partitions of the heart can be alternately retarded.
This is the origin of bigeminus-groups. Fig. 9 represents an example.

AEANAAAAARAA A

Fig. 9.
The lower row of curves shows bigeminus-groups caused by alternating
lengthening of the «-r-interval.

In the 2"' row of curves we see every second «-v-interval retarded ;
the auricle-systoles for these heart-periods have diminished. | found
still a third cause for the occurrence of heart-bigeminy in the hearts
of my frogs that were poisoned with veratrine. Up till now | found
this sort of heart-bigeminy only once. In fig. 10 in the upper row
we find them represented. I represented this row about 15 min. after
the injection of 8 drops of 1°/, veratrine. Each curve of this row

L146

is an extra-systole of both ventricle and auricle at the same time
(the irritation originated thus evidently in the connection-systems of
these two partitions of the heart). The pauses between the first 5
curves are equal in length. Then we obtain alternately longer pauses,
whilst between these longer pauses again normal ones occur (normal
at least for this row of extra-systoles). So bigeminus-groups develop
themselves, the two curves of which consist of extra-systoles of
ventricle and auricle at the same time. It is evident that here the
connection-systems between the sinus venosis and the auricle are

Fig. 10.

Upper row: Extrasystoles of ventricle and auricle in frog’s heart poisoned with
veratrine after blockading of the si-a connecting systems. The curves range
themselves from the sixth curve in bigeminus-groups.

2nd row: Cessation of the heart-blockade, the ventricle pulsates in the halved
rhythm.

3rd row: Increase of the u-r-interval of curve 1—4; after the falling out of 1
ventricle-systole shortening of the w-v-interval, which is lengthened again already
in the following curve.

blockaded. It is difficult to explain the cause why the extra-systoles
range themselves here in bigeminus-groups. In the 2"¢ row we see
still 2 extra-systoles, after which suddenly the separate auricle- and
ventricle-systoles appear again. The ventricle pulsates in the halved
rhythm. The auricle-rhythm is much quicker than that of the extra-
systoles. This is an affirmation of the well known fact that the
peculiar rhythm for auricle and ventricle is much less frequent than
the rhythm that originates in the sinus venosis (2"¢ Srannivs ligature).
The lower row of curves shows again a lengthening a-v-interval,
till the 5'® ventricle-systole falls out; for the next-following heart-

1147

period the a-v-interval is again much shortened, in the then following
period it lengthens again.

We found thus, that heart-bigeminy after poisoning with veratrine
can develop itself in 3 ways.

1. as transition-stage between the normal rhythm and the halved one ;

2. by alternating retardation in the conduct-systems between the
different heart-partitions.

3. with accumulations of extra-systoles after blockading of the
connection-systems between sinus venosus and atrium. I found the
manner of development as it is indicated by Hering only in dis-
connected groups. I never found a row of bigeminus-groups of which
every 2nd systole was an extra-systole.

Geophysics. — On the relation between departures from the normal
in the strength of the trade-winds of the Atlantic Ocean and
those in the waterlevel and temperature in the northern European
seas. By P. H. Gaus. (Communicated by Dr. J. P. vAN DER STOK).

(Communicated in the meeting cf February 27, 1915).

1. From hydrodynamical and oceanographical investigations in
the North-Sea, the Baltic, the Norwegian and the Barents-Sea, the
existence of the following phenomena is evident.

a. Mean values from Dutch’), Norwegian’), German*) and
Finnish *) tide-gauges show an annual periodicity in the waterlevel
of the North-Sea and the Baltic, displaying a minimum in spring,
a maximum and secondary-maximum — separated by a rather clearly
indicated secondary-minimum — in autumn.

6. Temperature and salinity observations of the underlayers in the
North-Sea’*), the Norwegian’) and the Barents-Sea"), show a periodicity

1) Koninklijk Nederlandse Meteorologisch Instituut N° 90.

J. P. VAN DER Stok. Etudes des phénomenes de marée sur les côtes néerlandaises.

1. Analyse des mouvements périodiques et apériodiques du niveau de la mer, 1904.

2) H. GEELMUYDEN. Resultater af Vandstands Observationer paa den Norske Kyst.
Hefte VI, 1904.

8) Orro Perrpersson. Ueber die Wahrscheinlichkeit von periodischen und unperio-
dischen Schwankungen in dem Atlantischen Strome und ihren Beziehungen zu
meteorologischen und biologischen Phaenomenen. Rapports et Procés Verbaux du
Conseil Permanent pour |’Exploration de la mer. Vol. HI, 1905.

4) Rour Wirtina. Finländische Hydrographische-Biologische Untersuchungen N°. 7,
Helsingfors 1912. |

5) Report on Norwegian Fishery and Marine-Investigations Vol. IL, 1909, NO, 2,
The Norwegian Sea, its physical oceanography, based upon the Norwegian Researches
1900—1904 by BjörN HeLLAND—HANSEN and FRipTJor NANSEN.

6) L. Brerrrusz. Oceanographische Studiën über das Barentsmeer. Petermanns
Geogr. Mitth. 1904 Heft IL.

1145 &

of the same kind; a minimum in spring, a corresponding maximum
in autumn.

To explain the phenomenon, whose generality has become known
only of late years, different ways have been tried.

In the supposition that it was limited to the southern part of the
North-Sea and the Baltic and thinking the wind responsible for the
periodical fluctuations VAN DER STOK comes to the following conclusion. *)

“A comparison of these (wind) results with those, indicating the
periodical and non-periodical fluctuation of the sealevel shows, that
— though some correspondency as the distinet November-minima
cannot be denied — a real connection fails. Neither the April-minimum,
nor the Oetober-maximum can be explained as a result of the wind
on our coast.

A more accurate investigation of the fluctuations in the waterlevel
as well as of those in the windsystem both on the Duteh coast and
the whole North-Sea is desirable.”

GEELMUYDEN says:

“The yearly fluctuation is very marked along the whole Norwegian
coast; 1 think an explanation must be looked for in periodical
changes of pressure and wind.” |

In Prrrerson’s work the following quotation is to be found:

“Tf on the other hand, only Dutch observations had been acces-
sible, the inferences drawn from them would certainly have pointed
to the wind as the originator of the fluctuations. Now, since a
comparison of facts has shown the analogy of the fluctuations in
the North-sea, the Baltic and the Kattegat, such inferior explanations
are excluded, and we must acknowledge the fluctuations to be the
outcome of a general pulsation of the ocean from the tropics to the
Polar Sea. The pulsation of the northern seas is analogous with that
of the Atlantic.”

Speaking about the North-Atlantic Current it is evident he considers
that stream not to be a direct offshoot of the Gulfstream, an opinion
hot generally shared.

Wirrtnc after having pointed out the correspondency of phenomena
in North-Sea and Baltic, tries to find an explanation in fluctuations
in the quantity of water in these seas. In his opinion these fluctuations
are caused by the wind, however not by the wind in the North-Sea
or in the Baltic, but so far as the Baltic is concerned by the wind
near its gates; the Skager Rak, the Belts and the Kattegat.

Breitrusz found from serial-observations in latitude 71° N. and

dte pe 20.

1149

longitude 33°.5 E. that from June till November the temperature
as well as the salinity of the whole watermass increased and
especially in the deeper layers. The velocity of the current also
increased in this period; we have to do here with the Northeape-
current, one of the outer ramifications of the Gulfstream. After
discussing this increase Brerrrusz continues:

“Not in local conditions we should look for the origin of these
fluctuations, but in the Gulfstream and in the many causes that
modify the stream on its way, thousands of miles long, from its
cradle under the Equator, through the Caribbean Sea and the
Atlantic to the Polar regions.

2. In our opinion fluctuations in the intensity of the Gulfstream
are the cause of the fluctuations in the waterlevel and we were
strengthened in this opinion, when we learned from Breirrusz’s
investigations the general nature of this phenomenon.

But if fluctuations in the Gulfstream are responsible, then it must
be possible to detect a similar periodicity in the North- and South-
Equatorial current and in the North- and South-East trades.

We calculated the monthly mean values and departures from

TABLE 1.
| pad ed Current 1855-1900 Wind 1855 —1914

with Ee A EN | aa SS Fee TE oe

En | Direction ee | Departure Direction en Departure
| January | 1393 | N281°E.) 4.95 —1.27 | N64°E.\ 5.46 | 40.26
February | 1161 | 285 4.41 —1.81 62 5.17 | —0.03
March 1398 | 282 | 5.05 | 1.17 | 63 mist 20,56
April (138: | 282 | 5.34 |-—0:88 |’ 02 4.69 | —0.51
May 1425 285 5.89 | —0.33 | 60 5.16 | +0.56
| June 1250 ‘278 6.97. | 40,15") «50 6.25 | +105
July Mi1-| 272 8.90 +268 56 | 6.12 40.92
August 1265 | 267 1.50 \ +128 | 56 5.28 | 40.08
September 1114 268 7.84 [71.62 jet” fe S86 ate. 08
‚October 1098 270 6.71 +0.49 67 - | 4,54 0,66
| November | 1096 | 269 611: b Zo: vont |) abe Ede

| December | 1411 | 273 4.00 laa os PAAP ED |

1150

yearly mean values for the region 15°—25° N. and 25°—40° W.,
as given in the preceding table *).

For the South-Atlantie monthly data are not at our disposition,
below we give the three-monthly mean values and departures from
the normal for the region 5°—10° S. and 15°—35° W.?).

TABLE 11.

Direction «_m. p. sec. | Departure

Dec.—Febr. N123° E, 4.58 — 0.56
March—May iB Wy 4.29 — 0.85
June—Aug. 132 6-12 ‚ + 0.98

| + 0.44

Sept.—Nov. | 137 5.58

Maxima and minima of the North-East and South-East trades
appear to coincide fairly well, table [ shows a real correspondency
between the North-East trade and the North-Equatorial current ; the
positive and negative departures in the strength of the trade wind
correspond with one exception with those in the velocity of the
Equatorial current and show a difference in phase of one month.
We should keep in mind, that winds with great stability as the
trades and monsoons are generally considered to be the prime cur-
rent-generators : furtheron in this study we will try to explain depart-
ures from normal-level in the North-Sea or from the normal-surface
of open water in the Barents-Sea, with the aid of fluctuations in
the strength of the North-East trade.

It would be better for this purpose to make use of fluctuations
in the North-Equatorial current, but as a matter of fact current-
observations are always less in number than windobservations and
therefore we have to rely on the wind.

In the following table we give the monthly departures from the
yearly mean level, as they have been calculated from long tide-gauge-
observations at 7 Baltic and 3 North-Sea stations; Fig. 1 shows the
departures in velocity of the stream and in the waterlevel.

1) Kon. Ned. Met. Instituut.

N°, 95. Observations océanographiques et météorologiques dans la region du
courant de Guinée 1855—19G0. Utrecht 1904.

N°. 107. Monthly Meteorological Data for ten-degree squares in the Atlantic and
Indian Oceans 1900—1914.

*) Pilot Chart of the South Atlantic Ocean. Dec.—Jan.—Febr. etc. Hydrographic
Office and Weather Bureau Washington D. C.

1451

The correspondeney is considerable, in spring we have a phase:
difference of two months, in autumn of three, it stands to reason
that either phasedifference can be 2'/, months.

KABEE, UI

Monthly departures in waterlevel in cm.

|

I La ay vv | vr fv) ex) xt |

|
|
| |
| | | | | |

dl ae
2.5 4.0/8.8 | —9.0]—6.7 ae 48445 +6.7| +8.6
fe EN Pee a) A Ss LA EN AE

|
}

1.7 | 15.6

a. Waterlevel North-Sea and Baltic. 0. Raising-power North-Sea-wind.
c. Equatorial Current.

It is evident from the above:
1st. Monthly fluctuations in the velocity of the North-Kquatorial
current (or in the strength of the North-East trade) are responsible
for monthly fluctuations of the waterlevel in the North-Sea and the
Baltic.
76
Proceedings Royal Acad. Amsterdam. Vol. XVII.

1152

2.1. The two groups of fluctuations show a phasedifference of 2
or 3 months.

34. The origin of the Gulfstream lies under the Equator, the
North-Atlantie current is a direct offshoot of the Gulfstream and
is the connection between the Gulfstream proper and the North-Sea,
the Baltic, the Norwegian and the Barents-Sea.

4th. Breireusz was in 1904 the first to point out the direction in
which we had to look for the solution of this problem.

3. We mentioned before that VAN per Stok and Wirrine thought
the water-raising power of the local wind or of that near the entrances
of the North-Sea and the Baltic responsible for the fluctuations in
the waterlevel.

We do not know how Wirtine proceeded; from mean monthly
windresultants, as calculated but not published by Van DER STOK
for Swambister, Bergen, Skudeness, Helder and Flushing, we derived
a mean monthly “North-Sea-wind” (Table IV).

TABLE IV,

Fe Me vi v | vi | vir | vi 1x xox |x
1
|

F
i
|

199 /

| Direction| 206° | 207 | 220 | 278 | 314 | 321 | 282 | 256 | 235 | 216 | 196 |

| Fost

ee p.s. 2.69/2.15/1.88 0.58 1.80 1.90 2.05 2.03, 2.06 Loo 2.42 2.85,
| | | | |

The first thing necessary to cause a rise of the waterlevel on a’
coast is a motion of the water or a current perpendicular to that
coast. The direction of the Dutch, Danish, and Norwegian coast is
about SSW—NNE; a maximum rise of the water will be caused
by an ESE-ly current. Wirtinc has shown that between wind and
winddrift in inland seas as the Baltic, a difference in direction exists
of 25° to the right (southern latitude to the left); the most favour-
able winddirection to cause a rise of the water, is in our case
N 268°0O E.

In order to judge of the waterraising-power of the different monthly
windresultants of table IV we project them on the direction N 268° E.
and consider the squares of the projections; we get the following
monthly values and departures from the mean {Table V 4 Fig. 1).

The minima in spring and autumn in waterlevel and raising-power
coincide; the maximum raising-power between July and August is

1153
TABLE V.

| | |
| xt | xt

Shite ome) Ave MVL 2E VID Be VIER eed pes |
ed EO | | RE baton A | |

4.03 3.56 2.43 | 1.81 2.93

+-0.72\—0.38 0.26 —2.29--0.37|— 0.45/41 45 41.41 +0.04 0 19 —0.81 40.31
oe = | | a | gues Ws xs | :

followed by a maximum in level in October, the December-level-
maximum nearly coincides with the maximum in raising-power of
the wind between December and January.

We also calculated the raising-power of the monthly windresultants
and their departures from the normal (5) alone for the Dutch coast
(Table VI); Fig. 2 shows them with the departures in waterlevel
(a) on the Dutch coast and those in the Equatorial eurrent (c).

TABLE VI.

jn itt wey | ow) va | vm IN Ee 0

cM. 16.0

sy —7.0|—5.8|—9.7| 6.1 412.1) +2.6| 41.1)
| =.

| EE IE ae
Fh nn lenen neder eee aad
Kie GN NE ea | Ph AL |

The correspondency between the different curves has become
clearer and we cannot doubt any longer that besides fluctuations in
the velocity of the Equatorial current, monthly fluctuations in the
waterraising-power of the wind are responsible for periodical fluctuat-
ions in the waterlevel of the North-Sea and adjoining seas.

The question is raised :

“Is it possible to express numerically the relation between fluctuat-
ions in waterlevel in the North-Sea and in the Baltic and fluctuat-
ions in the trade-winds and waterraising-power of the wind on our
coast 2”

We have already pointed to the fact that for the solution of this
question we had to consider the Equatorial current or trade-wind
for an earlier period as that relative to the waterlevel.

In our opinion the waterlevel of 1914 is governed by the Equa-
torial current November 1913—October 1914. The correlationfactor
between fluctuations in waterlevel and trade-wind is 0.66.

76*

a. Waterlevel Dutch coast. b. Raising-power wind Dutch coast.

c. Equatorial Current.

The correlation between waterlevel, trade-wind and water-raising
power is 0.82.

If it were possible to make a trustworthy prognostication about
the ‘North-Sea wind’, we should be able to forecast with a fair
certainty the level to be expected, for during two years we have
known fairly well the behaviour of the trade winds from month
to month,’) a progress made by international coöperation on VAN DER
Srok’s instigation.

The correlation between fluctuations in the Equatorial current and
the waterlevel is far greater viz. 0.85. It will be tried to secure
current observations in time in sufficient quantity, for in our opinion

1) Kon. Ned. Meteor. Instituut 1074 and 107. Monthly Meteorological Data for
ten-degree squares in the Atlantic and Indian Oceans.

1074 Computed by the Royal Netherlands Meteorological Institute from Swedish
and Dutch Observations 1900—1912 and from international observations January—
June 1913.

107 Computed by the Royal Netherlands Meteorological Institute from inter-
national logs and observations I’! January—June 1913, 1? July—December 1913,
Utrecht 1914.

Vids

the solution of some meteorological and biological problems is closely
connected with a more accurate knowledge of the watertransport
through the ocean to our shores.

GEELMUYDEN found that along the Norwegian coast the behaviour
of the waterlevel was the same as along the more southern shores
in question; from the constants he gave for the partial tide Sa, it
was however not possible to conclude anything about the existence
of a November-secondary-minimum.

In the North of Norway the maximum falls later than in the South ;
the reason why. may perhaps be found, by comparison of table VI
with the following table, where we calculated the departures from
the average (1893—1913) of the water-raising power of the wind
for Bodo.

TABLE EV.

I II ip Re aah li AM IG as
| Er | i

a
DE ORD EKE

| = | 4] Tj = = a TE TRE) PE = lad
+0.24,—1.99 Piety anne .41 42. ahaa ‚59 +1 „880.57 F0. 4750. IL
| Aen 24, SB | 2 |

4. In the preceding pages we think we have demonstrated that
— at least for a rather great number of years — monthly fluctuat-
ions in the waterlevel in the North-Sea and the Baltic and halfyearly
fluctuations in temperature and salinity in the Barents-Sea are origin-
ated by monthly fluctuations in the velocity of the Equatorial current
or strength of the North-Hast trade in the North-Atlantic in connect-
ion with the water-raising power of the wind in the neighbourhood.

The question arises — and with this we come to the direct appli-
cation of the preceding theory — is it possible now, to say something

definite about future fluctuations in meteorological or oceanographieal
elements in one of the Northern Seas.

We told already, why we had — by way of introduction at least —
to make use of fluctuations in the North-East trade and that the
effect of these fluctuations was felt after about two or three months
in the northern European Seas.

We give the following examples.

Purrersson has found that between Thorshavn and Iceland from
August 1902—August 1903 the water of Atlantic origin lost 131
Kilogram-calories daily, from August 1908—August 1904 the daily
gain was 230 calories.

_ We have to calculate the mean strength of the trade from June
1902— 1903 and 1903—1904 and find N 78° E., 2.07 and N 69° E.

J

1156

3.26 Bravurort-units; the average annual strength is N 70° EK. 2.85.
These values agree with the above-mentioned figures of loss and
gain of heat.

A second series of data to justify our theory we find in HerLLAND-
HANsEN’s and Nansen’s wellknown work’), where the following
figures for the open water in the Barents-Sea for May are given in
thousands of square kilometers.

TABLE Vir

BEES | Sone meat
May 1900 | 1901 | 1902 1903 1904 | 1905 | 1906 | 1907 ‚ 1908 |

645

THoneands a | tE | | |
| albers 440 | 398 | 249 | 469 | 696 | 639 | 576

568 |

In Nansen’s opinion, the surface of open water depends in a great
measure upon the watertemperature of the preceding winter. According
to this we have only to compare the strength of the trade with
these figures, keeping in mind that departures from the mean surface
of open water in May 1900 should be in accordance with departures
from the mean strength of the trade-wind for the period Sept. or
Oct. 1898—Sept. or Oct. 1899.

In table IX we give the corresponding departures, the correlation
is 0.55.

TABEL IX,

| 1900 | 1901 | 1902 | 1903 | 1904 | 1905 | 1906 1907 | 1908
=

ae = nn : ste NEK =

_9.28 | - 0.43 | —0.12 | —0.13 | —0.10 | 40.53 | +0.22 | +-0.03 | +-0.28

| | |

| —80 | —122 | -271 | —S1 | +176 | +119 | +56 | +125 | +48

Lastly we will consider the relation between the departures from
the mean value of the annual North-sea level on the Dutch coast ®)
and those in the mean average strength of the trade, in such a way
that the windyear ends consecutively 31% August, 30% September
ete.; the wateryear always on 31st December. In table X it is
evident that « difference in time of two months gives the best

1) The Norwegian Sea. Its physical oceanography based upon the Norwegian
researches 1900—1904 by Björ: HELLAND HANSEN and Fripryor NANSEN. Report
on Norwegian Fishery and Marine Investigations. Vol. Il 1909. NO, 2.

2) The data required for this purpose we owe to the service of the “Rijks-
Waterstaat”.

1157

correlation; in Fig. 3 the curves representing. the departures in
water level (6) and strength of the trade (a) are given.

1902 3903 1904 1905 1906 1907 =. 1908 1909 1910 199) 1912

Fig. 3.
FABEE OX.

+ | ee EE CTI sae 5 1 an Ex “7
1902 | 1903 | 1904 | 1905 | 1906 | 1907 | 1908 | 1909 | 1910 1911 1912 Corr.

| | |

—92mM.| H15 | +1 | —23 | 44

—0.18 a Sat oy 4alC0.09|<b: rakis0! tal - ovaal wo. adlko tale. het Aug. | 0.24
|

| —18 | —23 | +27 | +37| +9 | +65 |

Tt
}
|

|

—0.38 |—0.16|+0.35/-+0.05/—0. 120. 13/—0.07 +0.07/-+0.11/—0.30'-+0.25| Sept. | 0.55

Pi

—0.42 |_0.02-40.26 40.12 0.20 +0.19)—0.20}-+0.14-+0.08)—0.24 +0.34 Oct. | 0.65
| | | | |
|

—0.45 |—0.16|+-0.28'-+-0.22,—0.25/+-0.38 ue MRR rd hd +0.02

|

40.21 Nov. | 0.46 |

—0.42 —0.04'-40.19-+0.18 —0. 1840.32 — 0.46 —0.02-+0.17—0.08/-40.34 Dec. | 0.59

The answer to the question put in the beginning of this chapter,
is therefore, that when we have to do with somewhat important

1158

departures from the average in the strength of the North-East trade,
it seems possible to us, to make a forecast about the sign of the
departure from the normal of some phenomena in the Northern
European seas.

Whether the correlation will prove to be greater or smaller if
longer series are at our disposition, cannot be said with any certainty
beforehand.

Chemistry. — “The connexion between the limit value and the
concentration of Arsenic Trisulphide sols’. By Dr. H. R. Krurr
and JAC. vAN DER SPEK. (Communicated by Prof. E. Conen).

(Communicated in the meeting of February 27, 1915).

1. When one of us‘) carried out experiments with the As,S, sol
conjointly with C. F. van Duin, it once struck us that a sol, which
we had diluted to half its concentration, had retained nearly the
same limit value. The object of the investigation communicated here
was to endeavour to get some more knowledge as to the connexion
between the As,S, concentration and the limit value of the sol.

2. One may preconceive an idea as to this connexion. We assume
for the moment that the sols differ only in concentration but not in
the size of their particles. Now the limit value y is the concentration
at which so much of the coagulating cation is withdrawn by
adsorption that the charge of the particles is diminished to a definite
value differing but little from 0. Hence, the adsorbed quantity of
cation («) per particle is characteristic of the limit value. This again
is connected with the concentration y in cation in the solution after
the congulation’) according to this equation:

i
am kyr
so that y is, therefore, also characteristic of the limit value but
independent of the concentration of the sol. As for the limit value y
we simply take into account the bruto-added electrolyte quantity, y
is as a rule not independent of the concentration.

In -the Fig. 1 and 2 are represented schematically two sols in
which the second has the double concentration of the first. When
properly choosing the units we have in Fig. 1: y,=xz--4, in
Fie. 2: y,=x-+ 2a.

1) Kruyr and van Duin, Koll. Beih. 5, 269 (1914).
2) For fuller details compare Kruyt, Proc. 17, 623 (1914).

Fig. 1. Fig. 2. :

It will now be evident without any further comment that the
limit value is not (or but very faintly so) a function of the
concentration when a is small in regard to y and when consequently
vy =y. In the case of monovalent cations with their relatively high
limit value this will have to be the case. In the di-, and still in a
higher degree in the trivalent cations, the limit value will have to
increase with the concentration.

8. Concentrated sols of As,S, were made according to a method

devised by ScHurze *). After in a nearly saturated solution of As,O,
this had been converted into As,S,, a fresh quantity of As,O, was
dissolved and H,S again passed through. This treatment was then
repeated a few times’). The determination of the limit value for
such concentrated sols must be modified somewhat. A mere shaking
of the glasses is not sufficient as after the congulation, they may be
placed upside down without anything running out. Hence, before
and after the two hours required, stirring rods were used. In the
case of monovalent cations the precipitate obstinately adheres to the
glass walls thus rendering the observation much more difficult.

In the first five columns of the subjoined table 1 are communicated
the results of a series of measurements. The determinations have
been carried out with the same measuring instruments, standard
solutions, working arrangements, in fact as much as possible under
the same conditions. For each concentration a separate sol was prepared.

The concentration was determined by precipitating the As,S, with
HCI, drying on a Gooca filter at 50° and weighing.

In Table 1 all concentrations are end concentrations, that is they
relate to the volume after addition of the electrolyte solution.

In Fig. 3 these results are represented in such a manner that the
limit value of experiment 1 is put for each electrolyte each time as

1) Journ. f. prakt, Chem. N. F. 25, 431 (1882).
2) Full experimental details will be published elsewhere.

1160

TABIE IS
me B Limit value Number of particles
HU | : = Ze
Be Pe as | Dilution | 20 times ‚Number calcul- |
| 5 x KCI BaCl, AIK[SOy), | |

used the number | ated for 1 : 2000

1)| 5 56 | 0.99 | 0.183 | ze | = = |

2 | 18.0 | 69| 1.20 | 0.291 210 wrs 19
3 | 42.8 | 50| 1.92 0.540 ee NE 55
| | |

4 1454) 4 58: 1 2287 470. 648 “a | | 37 | 185 |

eer

1) No. 1 is borrowed from the investigation of KRuyT and van Duin, |

loc.cit. Table X,

Ratio limit value

5 18,0 42.8 74.7

concentration As2S3
Fig. 3.

1.00. From this we notice how the resulls completely confirm the
correctness of the train of thoughts of the previous paragraph. To
the less regular course with the monovalent cation we will refer
presently.

4. We desired to get some insight whether our premise that the
dispersity “degree of our sols was still the same, had proved satis-
factory. Direct determinations of the dispersity degree have been
carried out by Zsigmonpy') with gold sols, by Wiener *) with oil

1) Ann. de Phys. [4] 10 16 (1903).
2) Koll. Beih. 2 213 (1911).

[IGI

emulsions. For that purpose are counted in the ultramicroscope the
number of particles in a detinite volume-element. We have also
done this with the ultra microscope (source of light self-regulating
arc lamp according to Weurw, width of aperture 5, objective Zriss
D*, compensation ocular 18, length of cylinder 16, Enrticn’s screen
17). Dilutions were made in such a manner that never more than
five particles were simultaneously present in the field of vision. In
consequence of the Brownian movement the mean from a number
of observations had to be taken. Generally a series of 20 observations
was made four times. Below in Table 2 the list of the observations
of one sol (N°. 2) is given; for the other sols the end results are
given in Table 1.

TABLE 2.

Bie hy Bo aloe SED rl 2 Ale ie ba dee eed
PERES Ro Dis Bik Be a. eee A aan
NI Bh onl a by Bea |), 2a En aa 4
fe aS, Rel dr Bk IA = Se Oil gee A eal
oe EER 2 NEN A Oe BA Abe Soho ae ae Me
| ni en Ee |
| total 38 total 35 total 39 total 39 |
| general average of 20 measurements 38

These results cannot be interpreted in the same manner as those
relating to gold sols. For there we see the luminous particles against
a completely dark background. Here on the other hand we notice
besides the partieles an undistinguishable pale blue illumination of
the field. We therefore have particles of unequal size in the sol and
we only count the large particles. If now at the different concentrations
all was equal, we ought, on recalculating our results to one standard
solution, to find figures which increase proportionally with the con-
centration. Such figures are found in the last column of Table 1; they
are so chosen that the concentration and standard figure in experiment
2 are about equal. We now see at once that the number of large
particles increases more rapidly than the concentration, therefore,
the concentrated sols possess probably a smaller average dispersity
degree than the diluted ones. This can be readily understood because
the repeated boiling, in order to dissolve fresh As,O,, probably leads
to enlargement of the particles.

Nevertheless this result does not diminish the value of our con-

1162

firmatory experiment. Just the reverse; with a lesser dispersity cor-
responds a lower limit value. Hence, if the dispersity had been the
same in all these experiments the difference between the K-, Ba:
and Al-:-ion would have been still more pronounced.

5. In order to completely exclude meanwhile the complication
of the difference in dispersity degree we have still made another
series of experiments. We have prepared a large quantity of a
concentrated sol and from this made by dilution with water three
sols of different concentration. Of these four sols which thus were
derived from the same original liquid and exhibit undoubtedly *) the
same average size of particles, we have again determined the value
limits with KCl, BaCl, and AIK (SO,),. To eliminate all differences
which might occur owing to the duration of the experiment all deter-
minations have been made within 38 hours. Table 3 shows the result:

TABLE 3.

| ya Limit vande
| . AsyS
No. | gr 293

‚G. sol | |
RT cl | mac | Anso, I
ne 5 | mn 4
(te 5 81 1.35 | 0.106
| 2 25 61 1570 | 3 30.286 05 |
|
3 36 56 2.11 | 0.350
4 50 53 2 hers: 10402
a
4
ui
vo
es 3
£ k Ba’
io)
Ko.
AT Os, SR
5 25 36 50
Concentration As,53
Fig. 4.

1) It cannot be denied with absolute certainty that the dilution may exert an
influence on the size of the particles, but even if such an influence does exist it is
certainly of a lower order.

1168

In Fig. 4 the results are again represented graphically with the
limit value of the sol N°. 1 as unit. The result agrees well with
what was expected, only the limit values for K. exhibit an unmis-
takable depression with increasing sulphide concentration. We must
for the present refrain from trying to explain this remarkable
anomaly.

6. The experience gained during the above described research
has given rise to a number of questions; fresh experimental series
started with the intention of answering those had to be postponed
on account of the present circumstances. Hence, we can only point
to some provisional results.

We feel convinced that on boiling an As,S, sol an enlargement of
the particles really takes place (light absorption, ultramicroscopic
image, depression of the limit value of the Al--ion). At the same
time it appeared that, on boiling, the particles do not become
enlarged equally, but that the boiled sol contains particles of all
sizes and that a fractional precipitation seems possible. This fact
has, up to the present, only been recorded in the case of colloidal
sulphur *), but does not seem to be a specific property of that colloid.

The frequently recorded dependence of the value limit on the
previous history becomes more comprehensible by these experiences.
Further researches concerning all the above cited questions, as to
the density of the sols (on which we already carried out a few
series of measurements) and other correlated problems must be
postponed till more peaceful times.

Utrecht. van ’r Horr-Laboratory.

Chemistry. — “Action of sodium hypochlorite on amides of a-oxy-
acids. A new method for the degradation of sugars. By
R. A. Wuherman. (Communicated by Prof. FrANcHrMONr).

‘(Communicated in the meeting of February 27, 1915).
g y )

In a previous communication *) a method was described by me
for the degradation of amides of «-} unsaturated acids to the alde-
hydes containing one atom of carbon less.

It now seemed possible to degrade in the same manner the amides
of a-oxyacids. The experiment has confirmed this supposition.

1) Sven Open, Der kolloide Schwefel, Upsala 1913.
2) Proc. 1909; more fully in Liepia’s Annalen 401, 1 [1913].

4164

By way of a simple example first of all the action of sodium
hypochlorite on the amide of mandelic acid was investigated. This
readily gives benzaldehyde. As the amide is insoluble in water a
methylaleoholic solution was employed. That in this reaction an
intramolecular atom-rearrangement analogous to that in Hormann’s
reaction takes place, was shown by the fact that on adding hydrazine-
sulfate to the reaction liquid and neutralizing it there was formed
benzalazine, benzalsemicarbazone and also a little azodicarbonamide,
which could be readily separated with ether and alcohol.

From the appearance of the two last named compounds it necessarily
follows that in the reaction sodium isocyanate is formed.

The course of the reaction may, therefore, be represented as follows:

CH, Cr — CQ, + NaOCl->C,H,Cou—C° Nna—> CU, H,Con—N=C=0
CHC — N= C= 0 + NaOH => C,H,C5 + NaNCO
NH,
Jl | Zl
NaNCO + NH, .NH,. H,SO, CO

NH — NH,
NH — NH,

Tl
NaNCO +2. NH, .NH,. H,S0, CO

A
NH — NH,

In the ease of these a-oxyacids the halogen amide cannot be
isolated beeause the reaction takes place momentarily. The reaction
is further distinguished from that in the saturated and unsaturated
acid amides in so far that in the latter are formed from the isocyanic.
esters carbaminic salts or urethanes, whereas here with the a-oxy-
acids the isocyanate group is split off as such.

After the course of the reaction had been ascertained for mandel-
amide, it was applied to amides of acids formed on oxidation of
sugars and in this manner was obtained a new method for the
degradation of sugars.

Degradation of d-glucose.

The course of the reaction was represented by the following scheme:

1165

cho ORE CONH, Cr
H| OH HIOH \ H OH HOH
HO H BREE LO + NaOC]+NaQH> HOH +NaNCO
EDE EL er H OH H OH
H OH H OH H OH |
‘oi Coin Coin Coin
d-glucose *) lactone d-oluconamide d-arabinose

d-gluconate

The d-gluconamide is prepared by passing ammonia into the
absolute-aleoholie solution of the lactone. It erystallises in needles
m.p. 142148" [a]? = + 33,8°. The rotation in aqueous solution
slowly retrogrades, probably due to saponification. In an impure
condition the amide has already been prepared by Irvine, THomson
and GARRETT. *)

The d-arabinose obtained from the amide with alkaline hypochlorite
solution was isolated as diphenylhydrazone*). It melted at 202°—203°
(corr. 206°—207°). ToLLeNs and MAURENBRECHER*) give as the melting
point 204°—205°.

0,1348 gr. gave 10,4c¢.c.N at 14°C and 755 mm.
Found: 8,97 °/, N
Calculated for C,,H,,0,N,: 8,86 °/, N

The melting point of a specimen of diphenylbydrazone, prepared
from d-arabinose, which I received from the laboratory of the
Department of Finances at Amsterdam through the agency of Prof.
BLANKSMA, and which had been prepared according to Rurr’s method, was
likewise found to melt at 202°—203°; a mixture of the two melted
at the same temperature.

The yield of hydrazone amounted to 50°/, of the theoretical
amount calculated on amide.

From the diphenylhydrazone the d-arabinose was liberated with
formaldehyde. M.p. 156°—157° [a] 1° = — 105,7° (24 hours after
dissolving.)

0,1018 gram gave 0,1488 gram CO, and 0,0633 gram H,O.
Found: 39,86.°/,. 0; °.6,90°/, H

Calculated for C,H,,O,: 40 °/, C; 6,67°/, H

1) For the sake of convenience the aldehyde formula is used here for the sugars.

2) J. Ch. Soc. 103, 245 [1913].

3) NeuserG, Zeitschr. i. physiologische Ch. 35, 34 [1902].

*) Ber. 38, 500 [1905]. Neupera’s statement as to the melting point being 218°
is incorrect (see TOLLENS).

1166

The fact that in the oxidation of d-gluconamide with sodium
hypochlorite sodium isocyanate is also formed was demonstrated by
addition of hydrazine sulphate, neutralisation and subsequent addition
of benzaldebyde.

The precipitate formed contained beside benzalazine, benzalse-
miearbazone, which were separated by means of ether.

Degradation of d-galactose.

d-galactose was degraded in exactly the same way to d-lyxose.

NH,
Cu CO CH
HOH H | OH HO | H
HO | H HOH HO |H
— —
HO H HO H HOH
HOH H OH
Hs I, Ha
Cor Con Cor
d-galactose d-galactonamide d-lyxose

The d-lyxose was isolated as parabromophenylhydrazone, *) Melting
puint 156°—157°.

0,1488 gram gave 11,3 c.c. N at 16° C. and 762 m.m.
Found: 8,83 °/, N.
Calculated for C,,H,,0O,N, Br.: 8,78 °/, N.

On mixing it with a specimen of p-bromophenylhydrazone from
d-lyxose, prepared according to Rurr’s method, and which I likewise
received from the laboratory at Amsterdam, the melting point remained
unchanged.

I want to point out that the preparation of the amides of the
pentonie and the hexonic acids is easy of execution, as the lactones
need not be isolated in a crystallised condition. For instance, from
the calcium salt of d-galactonie acid I obtained a yield of 95°/, of
d-galactonamide. Mannonamide and arabonamide are also readily
formed in this manner. With gluconamide the yield is less favourable
because the formation of the lactone does not take place normally *).

1) ALBERDA VAN EKENSTEIN and BLANKSMA, Chem. Weekbl. 11, 191 [1914].
Levene and La Fores, Journ. of Biol. Ch. 18, 325 [1914].
2) Ner, Liepie’s Annalen 403, 322 [1914].

1167

I am occupied with the application of the above described degra-
dation method to other sugars such as pentoses.

The more fully detailed communication will be given elsewhere.

I have to tender my thanks to Prof. BrANKsMA for kindly giving
me the opportunity to work in the organic-chemical laboratory of
the University.

Leiden, February 1915. Organic-Chemical

Laboratory of the University.

Physics. — “Theoretical determination of the entropy constant of
gases and liquids.” By H. Trrropr. (Communicated by Prof.
H. A. Lorentz).

(Communicated in the meeting of Febr, 27, 1915),

§ 1. Introduction and survey.

If the entropy of an ideal gas per gramme molecule for the
temperature 7’ and the pressure p is given by:

S= Cplog T — Rlogp Jahn «+. « ve (1)
in which f is the gas constant and GC, denotes the heat capacity
under constant pressure assumed as invariable for the range of
temperature considered, then « is a constant remaining undetermined
in classical thermodynamics. This value has, however, a definite
value according to NerNst's heat theorem, when namely the entropy
is defined so that it becomes zero for 7’ = 0 for the condensed gas,
i.e. for a chemically homogeneous solid or liquid substance, which
we shall always tacitly supposed to be done in what follows. Ther
we can determine a from measurements of the vapour tension, when
we also know the course of the specific heat of the solid (or liquid)
substance also at the lowest temperatures '),

On the ground of a general definition of the thermodynamic
probability in connection with the hypothesis of quanta I have
derived the value of ~ for different cases in a previous paper*®), in
which, however, at first undetermined universal values z, z,, and z,
still occurred, which I supposed to be =1, while others thought
they had to assign a different value at least to z*).

u Me
1) The quantity C= R logy) é is generally called the chemical constant of the gas.
v

2) H. Terrope, Ann. d. Phys. 38, 434 and 39, 255 (1912).
5) O. SACKUR, Ann. d. Phys. 40, 67 (1913).
77

Proceedings Royal Acad. Amsterdam. Vol. XVII.

1168

‘Tn what follows we shall now determine the entropy constant a
through the direct calculation of the vapour tension according to
classical statistieal mechanics, hence for higher temperatures, while
we shall of course have to know again the thermodynamic behaviour
of the condensed phase for very low temperatures; the latter is,
however, the case at present for solid substances on certain simpli-
fying suppositions. In this way we shall not only get a direct
confirmation of the formulae given before (with z=2z,=z,—1),
but shall also be able to establish the general *) definition of probability
(of course for higher temperatures) for gases and liquids, which
must be applied for the entropy determination.

As a further elucidation of the results found for multi-atomic
molecules we shall also insert a few hypothetical considerations on
the forces acting in the chemical binding between the atoms.

The main point in our considerations is the discussion of the
exchangeability of similar atoms and molecules and of the influence
of this on the thermodynamic probability and the entropy.

§ 2. Suppositions on the properties of the solid substance.

As we shall have to know the entropy of the solid substance,
and as we can only give this at present theoretically when the
motions of the molecules and atoms consist of sine vibrations,
hence when the potential energy is a quadratic function of their
eoordinates, we shall have to suppose this of our solid substance.
We may do this when the amplitude of the molecular motion is
slight on the whole, when the molecules therefore depart little from
their position of equilibrium. This. however, does not exclude that
some rare molecules possessing an exceptionally great energy pass
over larger distances, for which the general assumption does not
hold, that they even now and then slip through between the
surrounding molecules, or can detach themselves from the molecule
complex, and pass into the vapour state, provided their number be
so small at the considered temperature that it may be neglected for
the calculation of averages.

Our assumption implies that the volume of the solid substance is
independent of pressure*) and temperature. The specific heat at
“constant pressure then becomes equal to that at constant volume,
whereas in reality it is as much as from + to 12°/, greater at the
temperatures that are to be considered. Though our theoretical

1) Cf. however, the conclusion of § 3.
®) Large pressures do not occur in our problem.

1169

substance in this respect differs more or less from a real substance,
yet. this will not cause a very great error in the final result, seeing
that the difference is comparatively small. It seems even probable
to me that when we consider a system approaching reality still more
closely whose vibrations are not purely sine shaped, an accurate
knowledge of the thermodynamic behaviour of it at low temperatures
would lead us to no other final result for the entropy constant of
the gas, that therefore the expressions to be found possess universal
validity.

The thermal energy of a solid substance as assumed by us according
to a formula which has been accepted and confirmed of late years,
is given by:

hy;
-—— + const.,

Io,
kT — J]
in which A and / are the constants of PLAaNck, while the summation
is to be extended over all the degrees of freedom of the system,
each of a frequency »;. The entropy is then given by :

1 dU hy; 1 ane
sl en ( ed . a L > log 1 bm kT (2

T AT aD; ; B

which for the higher temperatures, with which we shall be exclu.
sively occupied in what follows, passes into :

hy; hv
Sia ks Jom ob en Oe rn ee
(trg) = & (1 = toy (3

in which 2 is the number of degrees of freedom, and the line
expresses the mean value.

§ 3. Calculation of the vapour pressure of a monatomic solid
substance and of the entropy constant of the gas *).

Let us now consider a gramme molecule of a monatomic substance
consisting of NV molecules, inclosed within the invariable volume V
and in temperature equilibrium with its surroundings. This system
may then be considered as part of a much larger one of the same
temperature. If qi,....gsn are the coordinates of the molecules,

1) A similar calculation with the correct final result has already been published
by O. Srern (Phys. Zeitschr. 14, 629 (1913)), however with an imaginary solid
substance, which perhaps departs somewhat too much from reality. Nor is in this
way the occurrence of N! in the general formula (see below), caused by the
exchangeability of the molecules, made clear.

wry
bj

i,-.., psn the corresponding quantities of motion, then the proba-
bility that at an arbitrarily chosen moment the system will be in
a state for which the coordinates will suecessively have values lying
between g, and g, + dg, q, and q, + dq, ete., and the quantities
of motion between p, and p, + dp,, etc, will be given by:

w dG = w (p,,-+ + 93N) dp, ---dqsn = Ie kT dp,..:dq3n;, .@ 4)
in which Z is the energy of the system, and

1 me
= fe «dp... dg

the integration being extended over all the values of the q’s within
the volume V and all the p's from —o tot + 0!)

If we now assume that 7’ and V have. been chosen so that part
of the system is gaseous, the other solid, we may write for the
probability that the molecules 1 up to # (w inclusive) are in the
gaseous state, 7 +1 up to N (N inelusive) on the other hand in
the solid state, as follows :

,

(frre) = rfe « _k1 dp, ++ ~dd3n je kT dpd +»: dqaN, (B)

in which the 6n-fold integral must be taken with respeet to the
gaseous part of the system, the 6(N—n)-fold one with respect to
the solid part. The volumes of both are determined by JV" and the
volume of the solid part that is only dependent on V—v.*) Further :

il > 2
Ee ee (p, 4. eee Pp, )
is the energy of the gas,
é=epte,tre= LaF ” + k ) +
et d et Ln Ps nt se Psy
3N 3N 3N

+2 aij giqy+ hath, + ne,
Bal 8n--1 3n-+-1

in which N—n=n' is put, the energy of the solid body, s
e+:'=F. ce and the a’s and /’s are constants; —c is the work
which is to be applied to detach a molecule resting in its position

) Wee may Et say that the system, as it is at a definite moment, forms part
of a canonical ensemble, with modulus kT’.

2) In principle also other arrangements of the molecules than those of solid
substance or gas are of course conceivable, at least for a short time; they will,
however, be so improbable, that they may be disregarded. Nor is it necessary to
consider a solid phase of variable density.

1171

id

of equilibrium from its connection with the solid body, and to bring
it in the gas space, hence c is negative.

We can immediately integrate with respect to the gas, through
which we get:

/

(| wd |) = 1 (2 m kT)" hn vr fe be psn Esse AIEN ne wor (6)
n LE
in which v is the volume of the gas.
Now we can replace the values gs: to sv (inclusive) by
variables @',,....,@3/ Which are in linear connection with them,

Bn’ Bn’
so that &, = 4 > fig:” with all positive /’s, while &)= 5— =p’,
1 : am 4

; OBS ts
when p'; is the value corresponding to q';, hence Dn The quantities
qi
qi are evidently a criterion for the deviations of the molecules from
their positions of equilibrium.

As according to a known thesis dpi... d's; = dpsn4i---dgsn,
we get:
Le Os nl
E = fg? Ep
z ne ‘ ey Leet 2m 2
kT WET SER are La
e dpgnti +++ dq3N = ¢ +e dpy' es dan . (7)

When we however should simply integrate on the right with
respect to all the values of —o to + oe, and substitute the result
in (6), as being equal to the integral with respect to the leftside
member of (7), we should commit a serious error and arrive at an
absurd final result.

We had namely originally to integrate with respect to all the
values of the q’s inside the volume occupied by the solid body. In
this those values are naturally left out of account for which the
energy is very great, for which a molecule is therefore pretty far
from its position of equilibrium, as this according to the formula
for the probability very rarely occurs. The proportionality of the
energy with g’, however, only holds for slight departures out of
the position of equilibrium, and no longer when a molecule has got
so far that it can pass between the neighbouring ones. This must
actually occasionally occur, though very seldom, and in this way
two molecules can interchange their original positions, and each
molecule can successively be found at all possible points of the
solid body, and have a position of equilibrium which was before

1172

peculiar to another.) This new position is a priori as probable as
the preceding one.

As it is now tacitly assumed by simply integrating the righthand
side of (7) over the range from —o to + that a molecule cannot
leave its place, the thus obtained integral must still be multiplied
by v'/, this being the number of the interchanges possible between
the molecules of the solid body.

When this is taken into account, we find:

nic

@ wd “) —= Ie FT (2ZamkTyle ni (kT) IF, … (B)

3\ Ve
in which ZZ denotes the product of the 37 values Gas
Ji

This is therefore the probability that the molecules from | to n
inclusive form a gas with the volume v, the nm’ remaining ones a
solid body with the volume v' = V — v.’)

It is. however, of no importance whatever for thermodynamies
whether it is just the molecules numbered 1 up to ” that are in
the gas state. What we want to know is rather the probability that
n arbitrary molecules are in the gas state, the remaining ones in
the solid state. This probability, which we shall call W(), is obtained

N!

by multiplying the expression (8) by
. : nin’!

being the number of

different ways in which the MN molecules can be divided between
gas and solid body on the condition that always remain in the gas.
We get:
= ne

Win} =F = e kT (AamkTy lan orks Hs tdk
n

Mr 1 ft. ; /
Bearing in mind that — — is the frequency r; for the vari-
‘ mL

me

able g;', we may also write:

ne
log W(ny==log [+ Nlog N — N—nlogu + n — — + $nlog (2am) + |
a | kT, (10)
+ $n log (k T) +n loy v — u log p+ a log (RT), |

in which loy rv is the mean value of loy v;.

1) In this it is assumed that the energy required for a molecule to slip through
the surrounding ones, is not infinite; at any rate it is, however, possible to imagine
the interchange of the molecules to be brought about by evaporation and renewed
condensation, which must really continually take place at the surface.

2) As we have assumed the density of the solid substance to be pee ©

» = V—v’' is determined by wn’, and therefore by x.

In order to find the most probable distribution of the molecules
between gas and solid substance for given values of 7’ and V,
which is the only one that need be considered for the thermo-
dynamical equilibrium, we must see for what value of 7 the function
Wn) is a maximum, so that JW ==0, or what comes to the same
thing dlogW=0.

As dn’ = — dn, x Eg dhe 4 = ==!) — cd : ib sl hj . ee, and / is

u v v v Nn v n

independent of n, we get the equation :

: + 8 logy — log (kT) (11)
=

, C 4 poet
0 = — logn + iT + $log (2am) + log v +
7

L

We know from the ordinary kinetic gas theory that the pressure

nkT
p of the gas is ——, on account of which we may write for (11):
ss
| Reser ae En 3 Low (2m) —logp + ne —- 3 log p — + lor (/7’) (12)
GEERT 2 YY Tr Y | nkT ‘ 2 iW = :

The entropy S’ of a gramme molecule of solid substance is now

(see § 2) = 3u (1 — log =)
kT
Equation (12) then becomes:
Ob ets POS ee 4 Oe gee
== iT +. 3 log (2am) — loy p + ET EN + log (kT) — dlogh +5 (15)
It is further clear that the increase of the internal energy at the
evaporation amounts to *):
U=— Ne +&kNT — SINT =— Ne —4kNT. . . (14)
If S is now the entropy of a gramme molecule of gas, the increase
of entropy at the evaporation is:

[ Bs N N pi

| al a Ne N pv
Ei eee ee (15)
n

Pr EAI
We finally find for S from (18) and (15):
S= kN |E log (kT) — loy p + $ log (2am) — 8 logh + 3} ~. (16)

Konner and Wintrernirz*) have calculated the chemical constant
of hydrogen for low temperatures, in which this behaves as a mona-

!
Dd

1!) On account of the constant density mt
[À
2) A possible zero point energy had to be simply taken into account in c here
and in the following 38.
3) vy. KoHNER und P. WiINTERNITZ, Phys. 4.5. 15, 393 and 645 (1914).

1174

tomic gas‘), from thermochemicat data; they have found with the
atmosphere as pressure unity:

C= — 1,308
with an uncertainty which they estimate at most at + 0,15. They
calculate from (16):

C= — 1,17,
which may be considered as a very satisfactory agreement.

On the other hand QO. Srern*) has also derived the entropy of
monatomic gaseous iodine from thermochemical data, and found a
value which very greatly deviates from that following from (16).
He infers from this that either the heat theorem is not valid for
the reaction 2I,oia@ 2 Isola, that therefore the difference of entropy
remains finite for 7’=0, or that the vapour tension of monatomic
iodine cannot be accurately calculated with the aid of (16). He
seems to think the former rather probable. It seems to me that they
come to the same thing. It may namely be very well the case
that the heat theorem only holds for substances that really exist,
and this eannot be said of monatomic solid iodine. Then the calcu-
lation of the vapour tension as we have carried it out in this 9,
has no longer any meaning: monatomic gaseous iodine cannot exist
at low temperatures either. The formulae of this and the following
§§ for the entropy constant can lay claim to validity only for such
substances as also occur in the same molecular form at low tempe-
ratures, as the gases of the He group, the metal vapours, further
also gases as H,,O,,CO, 1, ete.; but not gases as I, Br or such like
ones. Of course the possibility continues to exist that an unexpeetedly
great error occurs in the data used by STERN.

§ 4. On the vapour pressure of a diatomic solid substance and
the entropy constant of the gas.

In a corresponding way the vapour pressure of a diatomic sub-
stance and the entropy of the vapour can be caleulated, when it is
assumed that here too the atom motions censist of sine vibrations,
while moreover the two atoms of one molecule are always at a
definite distance from each other*) as they also are in the gas for

1) A. Eucken, Sitz. Ber. Berl. Akad., 1 Febr. 1912.

2) O. Stern, Ann. d. Phys. 44, 497 (1914).

8) When the possibility of existence of the solid substance falls below the region
within which classical mechanics may still be applied to the rotation of the mole-
cules, the calculation has of course no direct meaning, and it will be preferred
to follow another method; see § 5.

A possible mutual vibration of the aloms with a zero point energy ghy would

1175

an extensive temperature region, so that the molecule has tive degrees
of freedom. It is then still necessary to assume that at a definite
point of the solid body which is to be thought as a crystal, the molecule
axis passing through the centres of gravity of the atoms can only have
one definite direction, from which it will of course deviate periodi-
cally by small angles on account of the heat motion. If the two
atoms are then still supposed to be different, so that the opposite
direction does not mean the same thing, and is therefore not possible,
we find for the entropy of the gas’):

S=kN log (kT) — logp + $log(2am) + log(2aJ/)— dloyh+ log(4ar)+ ¥} ‚ (17)
and for the constant a

a 2am

5 2rJ
ine 5 + log —— :

Tr + log(4m),. . . (18)

in which J is the principal moment of inertia of a molecule, of
course for an axis which is normal to that passing through the
centres of gravity of the atoms.

If on the other hand we assume the two atoms in the molecule
as perfectly equal and indistinguishable, so that at any point in the
crystal the axis of the molecule might as well be rotated by 180°,
we find for S, resp. a a kNlog2 smaller value. In the formula
analogous with (8) we get then namely 2” 7’! instead of 7'/.

In reality we shall have to assume at Jeast in most cases, that
also 2 similar atoms in a molecule perform a different function, e.g.
that one is positive, the other electrically negative, or else that the
molecule possesses a magnetic moment, that they are therefore indeed
to be distinguished and the molecule can only have one direction at
any place in the erystal. Then the formulae (17) and (18) will be
universally valid.

§ 5. On the dissociation of di-atomic gas molecules.

We can come to the same conclusion when we investigate the
dissociation of a di-atomie gas statistically-mechanically, and assume
the formula (16) for the entropy of the mon-atomie components to
be correct.

We must then assume that the atoms in the molecule vibrate
against each other with a frequency rv, so that the energy of the

render the distance variable by only a practically insignificant amount for mole-

cules consisting of heavier atoms; for hydrogen this would, however, be consi-

derable. (The value of » may be calculated from the specilic heat at high tempe-

ralures, the moment of inertia from EUCKEN’s experiments and formulae (16) and (17)).
4) For the calculation cf. SS 6 and 7.

1176
fn Oe hy ;
vibration becomes = ————— + const. according to the formula of
7
|

PraNCK-EINsreIN. It could be neglected for the temperatures that are
to be taken into account for the evaporation’). For very high values
of the energy of vibration, which, however, will be so rare at not
too high temperatures that they may be left out of account in the
caleulation of the mean value, the mutual motion of the atoms is
no longer a simple sine vibration; and at still greater value of the
energy the attractive force between the atoms becomes very small,
they get detached from each other, and the molecule is dissociated.’)

We may imagine that each of the (spherical) atoms has a pole,
and that in the molecule the two poles coincide or are removed
from each other a small distance through the heat motion, however
in such a way that the axes of the two atoms passing through pole
and centre are always in the production of each other.

When the atoms are of different kinds, say A and B, we find
for the constant of equilibrium of the reaction AB 2 A + BB’):

hy
dl

eae uaa ge A ak fee EF LT
be eT gay ele teas Fe haan ALOE en hoen
ny mA +MB J h 2 an

in which #, resp. m, is the number of split resp. unsplit molecules
per volume unity, m4 and mg the masses of the atoms, and / the
moment of inertia of the molecule. c is the heat of dissociation, as
it would be for the absolute zero.

For lower temperatures this reduces to:

Berge Meee ty bh CER NE
u, m4+mpB 2Ih\ 29

On the other hand according to thermodynamics:

2 Ss 1 \2-1
=de Pils) Secs Tere Cal ae ep ee

1

aa Has d-dAB
; ;

in which log A=
3 R

c has the same meaning as in (20)

1) If namely a possible zero point energy is not so great that the moment of
inertia becomes variable in consequence.

*) In reality it may of course occur that the vibrations are already no longer
sine-shaped for small values of the energy; it is, however, not possible for the
present to take this into account theoretically.

5) J. D. vAN DER Waars Jr., these Proceedings XVI, p. 1082.

ib bey,

gases at constant pressure, divided by A, i.e. =} -+$— $= #

and c is the algebraic sum of the heat capacities of the reacting

a4, «B and arg are the entropy constants of the gases defined in (1)
By equating (20) and (21) we find:

Zlogma + Hlogmpg log mag — log (2S) —logh + Hlog (kT) — 4 log (2a)y=

= = = — a + 4 log T—log k,

in which mag == mtd mg is the mass of a molecule AD.
When in this we substitute for a4 and ay the values following

from (16) and (1), we find :

aAB a

Erk =log J + Hlogk — 5louh + Hlogmag +43 log 2 + log,

corresponding to (18).
When, however, we assume the two atoms to be of the same

kind, we shall find a value of half the amount for the dissociation
AY

n - . . . . .
constant = in the kinetic calculation : the probability that two atoms
ny

meet that can unite is now namely twice as great as before, all the
rest remaining the same.
Thermodynamically we find, however, a four times smaller value :

; Led 3 De B ;
in (21) En)’ must then be substituted for > *, the righthand side
ny n

1
remaining unchanged. In this case, just as in the preceding §, we
should, therefore, find an & log 2 smaller value for a,z.

As, however, as was said above, it must be generally assumed
that two similar atoms do not perform the same function in chemical
combination, we shall have to give a somewhat more general form
to the suppositions made by van ber Waars Jr. about the chemical
forces. We suppose every atom to possess two poles, a positive and
a negative one, and that in a certain combination of two dissimilar
atoms A and B always e.g. the positive pole of A gets in contact
with the negative pole of 4. In a combination of two similar atoms
the positive pole of the one will always be connected with the
negative pole of the other; in this case it is of no consequence,
however, which atom is connected through its positive, which through
its negative pole. This makes the number of possibilities of binding
still 2 X greater than for dissimilar atoms, and the change of coming
together becoming already 2 > greater through the mere fact of
the atoms being equal (see above), it now becomes 4 x greater,
which is in harmony with the thermodynamic formula, so that also
in this case we have to assign the value (18) to aap.

1178

It should, however, be kept in view that the suppositions on the
chemical forces used in this $, possibly do not sufficiently agree with
reality; nor do they any longer appertain to pure classical mechanics:
we have, namely, assumed that in case of a chemical binding the atoms
must have a definite relative orientation, though we have not spoken
at all of a rotation of the atoms. We might imagine other repre-
sentations of the acting forces, but the one used seems to me the
simplest and the most obvious. After what has been said at the
conclusion of § 3, it will be clear that the application of (16) is
probably not permissible for the entropy of the monatomic compo-
nents, viz. in the case of one kind of atoms.

The contents of this $ is then only interesting from a theoretical
point of view, viz. to show how the same result as in $ 4 can be
found in another way too. A third derivation of the entropy constant
of the rotation for di-atomie molecules has been given by O. Stern’)
by the aid of LANGEVIN's theory of paramagnetism. From this
we see that this derivation only holds for the case that the two
atoms do not perform the same function. The result agrees with
ours.

© § 6. General formula for the vapour pressure of a multi-atomic
solid substance and the entropy of the vapour.

We will now calculate the vapour pressure of arbitrary multi-
atomic solid substances in an analogous way as we did in § 3 for
monatomic ones. We then only assume (for simplicity’s sake) ?*) that
the vapour is an ideal gas, i.e. a gas with independent molecules,
whose energy, therefore, does not depend on the volume; the specific
heat, however, may indeed vary with the temperature, if only
classical mechanics remain of application. Hence the internal mole-
cule movements need not exclusively consist of rotations and sine
vibrations. For the solid substance we continue, of course, to con-
sider the suppositions of $2 as valid, to which we may add, as in
$ 4 that at every place in the erystal the molecule present there
can only have one definite orientation. *)

Thus we find for the probability that » of the .V-molecules belong
to the vapour, the formula which is analogous with (10):

1) O. Stern, Ann. d. Phys. 44, 497 (1914).

*) It is shown in § 8 that the formula to be found for the entropy holds just
as well for non-ideal gases and for liquids.
5) The impossibility of another orientation must of course be understood so that
a very great energy would be required for this.

1179

és i + N log N—N

log Win) = log / -}- loa Ds HI

—nlogn +- n H- jn! log (kT) — jn' log r, |

in which j is the number of degrees of freedom per molecule,

p= | EN f. kT dp; +..dqjn

and the other quantities have a meaning corresponding to that which
they had before. ¢ is now of course the whole energy of the n gas

1 ; :
molecules, = the jN-fold integral

sl vrl,
| NE f- kT dp, 20+ dqjn

As 3n of the jn coordinates of the gas molecules denote the
positions of the molecular centres of gravity, they do not oceur in £;
in consequence of this and on account of what was said above # is
of the form:

B (En woe. os. tate lia ot HERO)
in which the function f is a (2j—8)-fold integral referring only to
one molecule, which therefore besides on 7’, depends only on the
mechanical constants of the molecules. It follows from this that:

OD n 0 log D

EN — DP, or

Ov v 0 log v ee Rs ae

The equation for the most probable value of 7, hence for the
thermodynamic equilibrium becomes:
A dlagb c

sa + TE logn — jlog (kT) + jlogv. . . . (25)

Now:

d log ® 0 log P Oloq D\ do 1 ape nv de ov
—____ = | |l | —=-— log ® Te ==
dn On ot Ov Jo dn n s vn \dn vn

just as in $ 3).
Hence we get:

ii n C ‘ Yr
0 == log DH —.—+ — — log n + jlog —. « « + (26)
AEN mens. RI u SP AE

The entropy of the solid substance is:

Further :

1180

sS—_ = —

when 4 is the energy of N molecules of gas

glee de Se et

u

When it is borne in mind that pr == kn?’ it follows from (26),
(27), (28), that:

: IN E
S—= — kN logn + — log B — kj Nlogh + 7 + kN,
u _
or when for the sake of simplicity we put n= JN:

~y
1
4

d yi
S=klog 6 — kN log N+ kN + pe kj N log hos. Je SO)
Hence the free energy is:

FEES TE rr. 31
eN ae be) > JINN! oh ae eis akte (51)

We find for the free energy, either by substituting the value (29)
for E in (30, or by differentiating (81) with respect to 7’:

S= — era fae — kloq (HIN) — klog(N!),. . ; (32)

in which:

e kT if On ds OENE dG

$ 7. Caleulation of the entropy of gases with arbitrary rigid
molecules.

We will now apply the formulae (31), resp. (82) found in the
preceding § to two simple cases of general oecurrence.

We can of course first find back the formula (16) of § 3. We
further find for a gas, the molecules of which possess two rotation
degrees of freedom with the moment of inertia J, and will be rigid
for the rest:

.

2amkT r QatkT

Sk {3 Nlog Ep + log N? +. N log —_—— +N log (4) + £ Nj (33)
Lx .

2
2

which formula we already meet in $$ + and 5.
For rigid molecules with three rotation degrees of freedom and
the chief moments of inertia J,, J,, and /,, we find:

2

1181

NEN 2amkT / v ar 2d kT
ae eee f cr apes! NI +. 5 IV log — iq
(34)
: 27d kT x. 225 kT 5 ,
de i N log — ———— | , N a eee — + N log (S2r*) +3 A |
IE 1

Without entering further into the caleulation it is yet easy to see
the analogy of the formulae (35), (54), and (16). If we write the
last in the form:

oper vias: anh T os aha
Pal dN LOG OG ar eat ,
= h? Wile a
we see that in each of the three expressions per degree of freedom
2amkT 2aJkT

first of all a term + N log Mags EED 4 N log occurs, ac-
2 ¢

le
cording as it is one of rectilinear or of rotatory motion. For the
three degrees of freedom of rectilinear motion moreover a term
log ae is everywhere found. In this » is the three-dimensional ex-
tension of the coordinates denoting the place of the centre of gravity
of a molecule, while the division by N/ is caused by the inter-
changeability of the molecules, as has been fully set forth in § 3.

We find in (33) 4 instead of v and in (34) 82? for the rotatory
motion. In (33) 4a is the two-dimensional extension of the angular
coordinates, which indicate the direction of that axis of the molecule
round which it does not revolve, while in (84) another factor 22
is added, being the extension of the third angular coordinate, which
denotes the revolution round the said axis, which now, indeed, does
take place. Finally there is everywhere still a term 4 N per degree
of freedom,

§ 8. On the general definition of the thermodynamic probability
for gases and liquids.

We know from ordinary statistical mechanics that the changes
of the expressions (32) and (81) denote generally the change of the
entropy, resp. free energy. for changed values of v and 7. As they,
as we have seen, indicate for a system in one definite condition
(ideal gas), the absolute values of S and # (i.e. those with the
accurate additive constant), they will have to do this for all eondi-
tions. In this it should of course be taken into account that ¢ for
smaller values of v can also depend on the mutual distances (and
possibly orientations) of the molecules.

The formulae (31) and (32) are therefore of general validity on
the suppositions made, also for non-ideal gases and for liquids,

1182

which latter can namely be formed from gases in a continuous way.
They would also have to hold for solid substances, when these were
considered in the same way; as it is however customary to consider
the molecules in this case as not interchangeable, N/ resp. the term
with log (N/) must be omitted. This is namely the case when the
solid substance is imagined as a system of fixed ‘‘oscillators”’.

Though properly speaking we have only generally proved the
formulae on the assumption that the system can pass into an ideal
solid body without loss of degrees of freedom, it yet seems plausible
that a general validity may be ascribed to it.

We have, namely, seen in § 5 that it may also be derived in
another way for a definite case, and the conclusion suggests itself
that this will also be possible in other cases. We have, however,
at the same time learnt to know the probable limits of the validity.

If we want to drop the supposition that no indistinguishable
atoms occur in a molecule, we shall have to add still a term
kN log p to (32), when p is the number of different ways, in
which a molecule can be made to cover itself.

We can finally give still another form to (32). When the integra-
tion is replaced by a summation, and when in this dG = h/* is

always put, we get:
S=—k > f dG; log (f; d Gi) — klog (N!) —klog(pN). . (35)
When a canonical ensemble consists of so great a number M of
systems that the number W;= Mfid(r; lying in an elementary
region dG; is a large number, we can write:
MS = — kM fi dGjlog (Mf, dG;) 4+- kM log M—kM log (N!) — kM log (p\)=
; M! |
0 SUN (MOMMY, ae
This being the entropy of a system of J/N molecules, the ex-
pression must only depend on the product MN, independent of the
way in which this has been separated into factors. This may be
seen still better as follows.
When in (85) N is replaced by MN, we get according to (23):

MN cr ; | ae 4 Pee
PynN = Vv uN [7(7)] MN — (Mvy) MN [/(T)] MN — MMN PMN,
Hence
BEE M
e kT 7 iN

JiMN = 5 ari —. Mn

because when corresponding elementary regions are compared, NV = N.
Further dGimn = hiMN = (dGin).

1183

Then © fd; taken over an arbitrary group of elementary regions,
is the probability that the system lies in one of them; when this
group is now chosen so that the interval syn corresponding to it
becomes equal to the M-fold of that of the group of a system of V
molecules compared with the group, evidently :

(SA IG) un = (ZVidGi)n
Le

As the interval Ae of & may be chosen so small that ae it
may be put, the argument of the logarithm in (35) may be put
constant in the summation extended over a group.

In this way we get:

Sun = — kE fiuNdG arn log (fiun €Giun ) —klog (MN)! — klog (p UN) =
iM

—k& fid: log ae [dG] i)

—kMNlog M—kMN log N + kMN—kMN log p= — KM fd; log (f;dG;)
+ (MN log MM). (Efi dG) + ete. =
(as 2fidGi= 1)
— AME f; dG; log (f,dG;) — kMN log N + kMN — kMN log p = MSy,
which we have now derived from an expression depending only on

the product MN, which expression we had, of course, to treat
differently, as far as M/ and N are concerned.

Prof. Lorentz, whose communication ““Opmerkingen over de theorie
der eenatomige gassen”*) induced me to take up the treated problems,
points ont to me, among different valuable remarks, for which I
am greatly indebted to him, that [ have now indeed demonstrated
that my formulae may be considered as convenient precepts for the
caleulations for the thermodynamic probability of the gas, but that
I have not yet explained how through the consideration of the gas
alone they could be derived, in particular why after all it is in this
case necessary to divide by N/. This is a difficult question. In some
connection with it is what follows:

We have seen that a di-atomic gas, the molecules of which consist
of perfectly equal atoms, at higher temperatures must have a &: log (2)
smaller entropy than when the atoms are different. Must not the
specific heat of the gas then have a different course in the two
cases at low temperatures, and how could this be accounted for?

1) H. A. Lorentz, Zittingsversl. Akad. Amsterdam, 23, 515 (1914). Not yet
translated.
78
Proceedings Royal Acad. Amsterdam. Vol. XVII.

1184

Or will the entropy of the gas, which is monatomic from a thermo-
dynamic point of view at very low temperatures, perhaps not be
represented by (16), but have a value £AN log 2 smaller? This seems
improbable, at least at first sight. A perfectly satisfactory answer to
this question is probably to be expected only from a general theory
of quanta.

However, something can be said about the division by MN/ also
without having recourse to the solid phase. Suppose we have the
general theory of quanta. We come to the conclusion that for the
determination of the thermodynamic probability we have not to
reckon with infinitely small regions, but with such of a definite
finite extent. This, however, holds only without reservation for
systems the molecules of which are all different. Of a gas for which
this is the case, we could not say that the entropy was proportional
to the mass; it would much sooner contain a term k log N!. Now,

N!

however, the entropy of a mixture of different gases is / log —
5 Ee Pen

1 2
greater than when the gases are equal, which can be thermody-
namically derived for large values 7, etc, while it seems natural
to consider it also as valid for small n’s, (7, ete. are of course the
numbers of molecules for the different kinds, N is == Xu;). If now
all n’s are =1, in other words, if the gas consists of nothing but
different molecules, the entropy will be & log (N/) greater than for
a gas consisting of nothing but equal molecules. For the latter we
shall then have to subtract %/og(N/) from the original entropy
expression. Such considerations have originally led me to the division
by N/ and to the formula (46).

Physics. — “On interference phenomena to be expected when Röntgen
rays pass through a di-atomic gas.” By Prof. P. EnreENresr.
(Communicated by Prof. H. A. Lorentz.)

(Communicated in the meeting of February 27, 1915).

As is known W. Friepricn ®) has ascertained that a beam of
Röntgen rays passing through yellow wax and other amorphous solid
substances gives interference rings on a photographic plate placed
behind it. Liquid paraffin also gives a ring, which, however, does
not represent a maximum of darkness, but an inflection point of

1) W, Ertepricu, Kine neue Interferenzerscheining bei Röntgenstralen : Phys.
@schir. 14, (1913), p. 317.

1185

the decrease of darkness. Frmepricu shortly discusses two possible
explanations of the observed phenomenon.

a. The solid amorphous bodies may be imagined as built up of
small erystals. The interference spots of the different individual
bodies uniformly turned in all directions unite on the photographic
plate to rings.

6. For the solid amorphous substances and particularly of the
liquids is “die Anordnung der Teilehen eine vollkommen regellose”’.
In the case of the passage of Röntgen rays through such an amorph-
ous medium we should meet with a phenomenon analogous to that
of the passage of rays of light through a glass plate strewn with
lyeopodium powder. ')

Friepricn sites the circumstance that also for liquid paraffin an
interference ring occurs, in favour of the second explanation, and
he therefore expresses the supposition that here we should have to
do “mit Beugung am Molekiii resp. Atom”.

E. Hupka’*) tries, if I have understood him correctly, to give
another explanation, in which the mean distance of the molecules
is decisive as “grating constant”.

A trustworthy introduction of statistical considerations on which
the calculation of the dark rings must rest, does not seem easy to
me even for ‘liquids on account of the compact arrangement of the
molecules and particularly on account of the unknown complexes
(association) of adjacent molecules.

I may be therefore allowed to point out briefly that the problem
is considerably simpler in case of transition of Röntgen rays through
a di-atomic gas. Whether the experimental difficulties can be sur-
mounted, I cannot judge; in case this should be so, some new data
might be obtained in this way on the situation of the atoms in the
gas molecule.

$ 1. Let homogeneous plane Röntgen rays fall on an isolated di-
àtomie gas molecule. Both atoms emit secondary waves which inter-
fere in the whole space. We consider the interference in an arbi-
trary point P of a plane / (photographic plate), which lies normal
to the direction of incidence of the Röntgen ray at the distance D
behind the molecule. ) may be considered as infinitely great with
- 1) Drupe, Optik I, Afd. Kap. IV; M. Lave, Beugungserscheinungen an vielen un-
regelmässig verteilten Teilchen. Sitzber. d. preuss. Akad. 1915.

*) E. Hurka, Die Interferenz der Röntgenstrahlen Samml. Vieweg, Heft 18
1914), p. 62.

78*

1186

respect to the central distance a of the two atoms of the molecule,
which are supposed to be equal for the sake of simplicity.

If consecutively the molecule axis is given all possible directions
by the molecule being turned round one of the two atoms A,, the
phase difference with which the secondary waves of A, and A,
interfere in the point P changes. hence the intensity of the radia-
tion there. ,

We calculate the mean intensity in the point P and inquire: am
what way does this mean intensity vary with the situation of P on
the plate b?

For reasons of symmetry the mean intensity is of course the
same for all those points ? for which the direction molecule —
point P forms the same angle y with the direction of incidence of
the Röntgen rays. With increase of gy the mean density however
changes oscillatorily namely as:

sin 220

Pe En dk: ie aE

92
2210

AG ey sl
= SUN — . . . .
9

¢ - (2)

[2 is the wavelength of the Röntgen rays; @ the distance of the two
atoms (supposed as points *)) from each other}.
The consecutive maxima and minima of (1) are in the following
ratio to each other’):
Fe OTS del OE el OF
and lie at:
2n0o=—=0; 4,49; 7,72; 10,90; 14,07.

Iz || oo | 90° | — | —
Pe HE 06 ra 1 AHA ane

1) See appendix.

2) It is convenient to confine ourselves for the present to this schematisation,
till experiment shall give an indication for possibly necessary refinement of the
scheme. _

sin X

— in Jaunve u. Empe. Functionentafeln.

X

35) Comp. the tables for

1187

The preceding table gives the corresponding values of 7 for different

a
values of a

§ 2. Instead of a single di-atomic gas molecule now a whole gas
mass is irradiated; the dimensions of the irradiated quantity, however,
will be comparatively small compared with the distance between the
gas and the photographic plate Z (e.g. 1 mm. to 5 em.)

We state '):

The dark rings on the photographic plate will then — except for
a slight diminution in sharpness — continue to be represented by
equation (1).

The decrease of sharpness corresponds with the slight changes in
situation and size, which the rings (1) undergo when the centre of
the molecule discussed in §1 is made to pass consecutively through
all the points of the small irradiated region.

§ 3. In the experimental realisation of these rings we are confronted
with difficulties which are indeed very great, but yet possibly not
insurmountable.

1. The probably very slight intensity of the whole secondary
radiation. In any case we shall choose vapours the atoms of which
will be as heavy as possible’).

2. The incident radiation must be as homogeneous as possible or
anyway possess such a distribution of intensity in the spectrum that
at least the first ring does not fade away entirely. In order to be
still able to calculate a in the latter case from the distribution of
light and dark, the spectrum distribution must be known from
interference figures for crystals.

3. If the first ring is to fall on favourable values of ¢, « : 4 must
certainly be greater than one (see the table in § 1).

4. Possibly the dark rings that originate from the amorphous
glass vessel in which the vapour is contained, might be troublesome *).
Then we should have to replace the amorphous glass e.g. by mica.

APPENDIX.

The secondary waves which two atoms A, B send to a definite

1) See appendix.

*) Or perhaps solutions; but here the phenomena are theoretically more com-
plicated.

5) They have not occurred in FRIEDRICH’s experiments with yellow wax.

1188

point P of the photographic plate, give at that place conjointly the
disturbance of equilibrium
Msin p(t —t4) + Msinp(t—te) .- ve». « » (a)
The time average of the square of (a4), — taken over a period, is:
Af 2
mat + 2oosp (ta —tB) +1] = M [1 + cosp(t4 — tp)] . (B)

If the two atoms A, B belong to different molecules of the gas,
the quantity cos p(t1—tzB) assumes equally often equally large positive
and negative values during the time of exposure in consequence of
the independent movement of the molecules, so that here the time
average of cos p(ta—tp) becomes zero.

It is different with two atoms belonging to the same molecule.
We split up here the taking of the time average into two phases:
J. All possible orientations of the axis of the di-atomic molecule,
one atom being fixed. //. Repetition of this average value deter-
mination for all possible situations of that atom inside the (irradiated)
gas space.

Mean value determination I.

Let CA be an incident Röntgen ray, „AD the secondary ray that
travels from atom 1 to the point P of the photographie plate. What
is the locus of all the situations of the atom B, for which the
difference of path

CDA —EBF=BL4
has one and the same value? ’) Answer: Deseribe round A a sphere
with radius equal to the fixed distance of the atoms AL= a.
Intersect this sphere with the plane 5’ YA, which is normal to the
plane of drawing C’AD, and parallel to the straight line AU”).
The circle BB’ along which this plane intersects the sphere is the
required loeus; for all its points:
BBE = EBS.
Hence all of them give one and the same difference of path with
respect to CAD, which can also be represented by
NEENFZ SEA
finally also by
(
NZ VA We OAT edn LE als

=

1) AB is so small compared with AP and BP that AP and BP may be con-
sidered as parallel, hence A as the difference of path with which the secondary
waves from A and B arrive in P.

?) A mirror parallel to the plane Bb’ YL would just reflect the rays Lb’, YX, KB
in the direction BF’, YZ, BE.

1189

In connection with this

cos p (TA Te == cag = olie Gaat ete
C
and the mean value determination I consists in this that (d) is integrated
with respect to all the zones of the sphere parallel to BB’, and
divided by the surface of the sphere.
If we put

A SSA
this yields
+a th
1 AN OE 2p q
EEND AID. iat ave dh cos Î h sin £ =
47a’ c de c 2
—=<¢ 0

sin 200
COS he
(f
> ij
Jap sin —
a } 9 0
sed

210

In this

1190

is put for shortness.
Thus we get the dark rings:

w(t ‚sn 2720
220

which were mentioned in § 1°).

Determination of the mean value 11.

The distances from Röntgen tube to molecule, and from molecule
to photographic plate being enormously large in comparison with
the distance AL=u, we could act up to now as if we had to deal
with an interference problem of FRAUENHOFER. If for the determination
of the mean value II the molecule is made to cecupy all situations
in the irradiated space, these molecule displacements are practically
still infinitesimal compared with the distance from Röntgen tube,
but not compared with the distance from molecule to plate.
In connection with this in the slight displacements of the molecule
parallel to the photographie plate the dark rings move over an
equally large distance. In displacement normal to the plate a slight
enlargement or diminution of the rings occurs. We see that this
brings about a slight fading of the rings.

Geology. — “On the granitic area of Rokan (Middle-Sumatra)
and on contact-phenomena in the surrounding schists. By Dr.

H. A. Brouwer. (Communicated by Prof. G. A. F. MOLENGRAAFE).
(Communicated in the meeting of June 27, 1914).

Between Rokan and Loeboek Bandhara the Rokan Kiri cuts a
granitic mass of about 4°/, km. in width, which on its northwestern
and southeastern sides is adjoined by tertiary sandstones and conglo-
merates, which however, along a portion of the south west limit, are
separated from the granite by a narrow strip of schists.

During the exploration of this area some facts were collected
concerning the various facies of the granites and the contactphenomena
in the surrounding schists. The schists dip towards the granitic mass

1) The factor M? varies of course also with 9; perhaps in the same way as
cos? g. In § 1 we have however disregarded this variation for the present to get
a first survey.

1191
the strike chiefly being W.N.W. to N.N.W., and the dip alternating
between north east and south west; the sandstones and conglo-
merates which unconformably overlie the schists and the granite,
and are far younger, dip away from the granite-mass on both sides.
In his description of a portion of the Western Coast of Sumatr:

Fig. 1. Map of the granitic mass of the Rokan-county (after the map in the
“Jaarboek van het Mijuwezen in Nederlandsch Indië” for 1902, made under the
supervision of the engineer E. A. NeeEB). Scale 1 to 100.000.

Fig. 2. Intersection over the middle of fig. 1.

XXX

granites, diorites etc. schists etc. tertiary.

1192

VerBeeEK *) describes numerous quartz diorites, which probably form
irregular patches in the granites and some veins of quartz diorite
in granitite. In the granitic area of the Rokan county granitic veins
occur in quartz-dioritic rocks and thus a part of tne granites must
be younger than the quartz diorites.

FACIES OF THE GRANITES.

The rocks of the granitic area which were examined contain
two-mica granites, biotite granites and their transitions into quartz-
diorites. The quartz-diorites examined are rich in biotite and contain
a green amphibole in small quantities.

Porphyritic vocks with very large feldsparphenocrists are very
numerous, just as in the Malakka granites. Often the phenocrists
show a more or less distinct parallel arrangement, and the porphyritie
rocks sometimes occur in alternating layers with the normal ones.
Rocks with gneissoid structure also occur.

Pegmatitic facies are very numerous. Along both borders of the
Rokan Kiri and in the numerous side-rivers of the Rokan Kiri
running through the granitic area, their outcrops are repeatedly
visible as more or less irregularly defined masses or as veins running
regularly for some distance; as a rule, these rocks are rich in
tourmaline. In the rocks Batoe Kandik projecting on the right side
of the Rokan Kiri pegmatites are found containing very much
biotite, their crystals measuring sometimes several cm’, and for the
rest consisting chiefly of feldspar, quartz and tourmaline. Dykes of
quartz tourmaline rocks free from feldspar also occur here; the
rock which intersects these pegmatites is a medium grained granite
without phenocrists. The rock which protudes at the mouth of
the St Mahang in the middle of the Rokan Kiri shows a great
variety of rocks. Along with medium-grained granites one finds
here very many pegmatitic segregations which for the greater part
consist of feldspar, quartz, tourmaline with dark or light-coloured
mica, Whereas patches with the structure of graphic granite protrude
as knobs from the surrounding rock.

Dykes which are more acid and contain fewer dark minerals than
the rocks they intersect were found in several places. To quote one
instance dykes of light-coloured biotite granite on various points cut
through quartzdiorites on both borders of the Rokan Kiri.

1) R. D. M. VerseeK, Topographische en geologische beschrijving van een ge-
deelte van Sumatra’s Westkust, 1883, p. 220.

1198

Biotitic granites.

A biotitic granite of the right border of the Rokan Kiri near
Tanah Dingin contains besides orthoclase some microcline and very
little acid plagioclase. Quartz is found in large quantities and shows
the aggregate polarisation or undular extinction commonly occurring
in the granite quartzes of strongly folded regions. Muscovite only
occurs in very small quantity in this rock; ore and apatite are both
present. The two last mentioned minerals are often intergrown with
biotite.

Similar biotite granites have been collected on the left border or
the Rokan Kiri, in the sharp bend downstream from Tandjong
Medan. Granophyric intergrowths of quartz and feldspar were found
here in small quantities.

According to ABENDANON, green augite occurs in granites rich
in biotite from the upper part of the Se Pemandang. (Cf. “Jaarboek
van het Mijnwezen” for 1902, p. 138.)

Two-mica-granites.

The medium-grained rocks in which the numerous pegmatites of
the Batoe Kandik occur, belong to this group. They are poor in
dark constituents and consist chiefly of orthoclase, some microcline
and acid plagioclase and quartz. Brown as well as green biotite
occur, often intergrown in one crystal and in alternating layers.
Small quartz crystals are sometimes poikilitically enclosed by the
feldspars; the feldspars are slightly sericitized. In these rocks again,
the quartz shows aggregate polarisation and undular extinction.
Ore and apatite occur in very small quantities only.

In the medium-grained rocks with the numerous pegmatites from
the cliffs near the mouth of the 5% Mahang the percentage of plagio-
clase has increased, whereas muscovite is found in smaller quantities
than biotite. Besides orthoclase some microcline is found. The plagio-
clase has almost the constitution of oligoclase-albite, the quartz
shows aggregate polarisation, small rounded crystals of quartz are
sometimes poikilitically enclosed by the feldspars. Some of the feld-
spars are feebly sericitized, whereas larger muscovite crystals more
or less in parallel position one to the other are sometimes enclosed.

Mediuin-grained granites very poor in mica minerals protrude as
rocks in the bed of the Rokan Kiri near Tandjong Medan.

Quartzdiorites.
These rocks contain less quartz and generally more biotite than
the granites deseribed above.

1194

From the first rocks in situ on the left bank of the Rokan Kiri,
in the sharp bend downstream of Tandjong Medan, and from the
rocks projecting there from the right bank specimens of dioritic
rocks were collected consistmg chiefly of plagioclase with quartz
and biotite, the further constituents being amphibole, titanite, apatite,
some chlorite and very little ore. .

The plagioclase has -almost the same composition as andesine,
some more acidic mixtures (oligoclase-andesine) also occurring, and
a feebly zonar structure with repeated alternations of zones more
acidic and more basic being rather common. Exceptionally the
plagioclase was found to be partly surrounded by a narrow margin
of granophyric texture in which the feldspar is not polysynthetically
twinned. In slides of the symmetrical zone of the plagioclase this
last feldspar shows a straight extinction, this fact pointing to ortho-
clase. The quartz shows aggregate polarisation, the lamellae of the
plagioclases being bent. The biotite with very small axial angle is
as a rule fresh, exceptionally some alteration into chlorite occurs.
Green amphibole is found in small quantity, titanite occurs in grains
and in more or less rounded crystals, and, as well as the apatite, is
often enclosed by biotite. On the other hand small biotite crystals
in places are enclosed by a large crystal of titanite.

Granitic dykes in the diorites.

At a distance of about 2 m. from each other on the left bank
of the Rokan Kiri in the sharp bend down Tandjong Medan two
dykes were found cutting the quartz diorites. These medium to fine-
grained rocks, light coloured, consist largely of orthoclase (and micro-
cline) and quartz. Acid plagioclases are found in small quantity,
the further constituents being: biotite, apatite, and some green
chlorite. Ore is almost totally absent. The chlorite is sometimes
found alternating in layers with biotite in the flakes of the latter
mineral. An intergrowth of kalifeldspar with quartz is remarkable
in which numerous small rounded or almost idiomorphie crystals
of quartz enclosed by the feldspar extinguish at the same time.

Granophyrie intergrowths, in which the quartz is irregularly shaped,
also oceur in small quantities.

One of the granitic dykes in the quartz diorites on the other bank
of the Rokan Kiri consists entirely of a mixture of quartz and feld-
spar, some traces only of biotite and chlorite occurring.

(rneissoid granites.
In a left branch of the Pakis river, near the kampong Pakis,

a

1195

porphyritic rocks were found showing a distinet parallel structure
and containing only few dark constituents. They are poor in plagio-
clase, microcline occurring in varying quantity with orthoelase. The
feldspars only occur as phenocrists, as a rule rounded and showing
more or less irregular contours; they show traces of sericitization and
sometimes enclose rather large crystals of colourless mica. The biotite
sometimes contains ore in numerous disseminated minute crystals
and often it is partly chloritized.

Pyrite occurs in rather numerous small crystals in some of these
rocks. Feldspar and quartz are sometimes granophyrically intergrown.
The crystals of the groundmass are often found enclosed by the
phenocrists of feldspar and the matrix sometimes penetrates into the
phenocrisis. The often occurring irregular extinctions of the quartzes
point to pressure after the crystallization of the rocks.

Pegmatites.

Some provisional facts will be given here on the constitution of
the very numerous pegmatites. The pegmatites rich in biotite, from
the Batoe Kandik, consist chiefly of plagioclase, orthoclase, quartz
with undular extinction and biotite, tourmaline and colourless
mica also occurring. The plagioclase has almost the constitution of
oligoclase, whereas more acid mixtures approaching to oligoclase-
albite, also occur. As a rule, the tourmaline shows absorption colours
of brownish hue, more bluish colours sometimes being found round
the brown colours as a bordering zone of varying breadth and
occasionally missing; no sharp distinction exists between these varieties.

A dyke of a width of about 2 metres with N. N. W. strike, consisting
of pegmatite containing tourmaline and occasionally much biotite,
in which numerous small erystals of reddish brown garnet are
macroscopically visible, over a short distance appears outcropping
in small rocks, which, the level of the water being low, are visible
on the left bank of the Rokan Kiri near Tandjong Medan. They
are rich in acid plagioclase, orthoclase and quartz. Several of
the plagioclases proved on examination to be acid oligoclase-albite,
more basic mixtures, however, also occurring. The feldspars some-
times are to some extent sericitized. The crystals of the garnet are
idiomorphous and microscopically colourless. The tourmaline is usually
not idiomorphous in the prismatic zone, the brown colour of the crystals
is often less deep in the central parties than in the bordering zone,
more blue colours moreover occurring in the central parts. Finally,
the occurrence of zircon in small idiomorphous crystals with pyramidal
limit outlines must be mentioned.

1196

In the small rocky isle near the mouth of the S* Mahang, peg-
matites with much dark ov light coloured mica are almost similarly
constituted as the surrounding granites; the feldspar crystals measuring
up to ten decimeters, found at the same place, which are beautifully
graphic-eranitically intérgrown with quartz, have been mentioned above.

A kind of pegmatitic inter-
growth of quartz and black
tourmaline in equal propor-
tion appears to be a wide-
spread rock in the granitic
area,numerous boulders of this
type being found in the 5"
Pemandang, a left branch of
the Rokan Kiri.

Under the microscope large
quartz erystals are seen with
undular extinction or aggre-
gate polarisation intergrown
with isolated irregularly sha-

Fig. 3. Goncretion of one quartz and one ped fragments of tourmaline

tourmaline crystal. of which a great many extin-
T =tourmaline. Qu. = quartz. guish at the same time and

consequently belong to the same crystal. The tourmaline chiefly shows
brown absorption colours, more bluish colours sometimes occurring
in the bordering zones; a blue tourmaline is occasionally crystallized
in small erystals at the periphery of the brown crystals. In these
pegmatites as yet no tin-ore was found; about the same thing is
reported by Tosier*) from the granites of the mountains of Doeablas
in Djambi, which as well as the granite of the Rokan-county are
closely related to the tin-granites of Banka and Malakka. Numerous
pneumatolytic veins consisting of quartz and tourmaline are found there.

THE SURROUNDING SCHISTS.

The schists which separate the granites along a portion of their
southwestern limit from the tertiary sandstones and conglomerates,
we laid bare by denudation in several places on both borders of the
Rokan Kiri, and they can be excellently observed on the banks of
the Sei Pakis, which crosses the whole length of the strip of schists
northwest of the Rokan Kiri.

1) A. Toren. Voorloopige mededeeling over de geologie der Residentie Djambi.
Jaarb. v. h. Mijnwezen in Ned. Oost-Indië, 1910; Verhandelingen, p. 20.

1197

So far as they do not show any traces — or to a slight degree
only — of contactmetamorphism, they are of small mineralogical

importance ; the contact-rocks only will be mentioned underneath.

Many of the rocks contain calcite in varying quantity, and the
series of rocks examined includes various gradations between
limestone, sericite schist, and chert or quartzitie schist free from calcite
and sericite. Limestones are e.g. exposed for a great distance in the
St Mangis, a small right branch of the Sei Pakis, about halfway
between the kampong Pakis and the Rokan Kiri. Those are partly
White semi-crystalline limestones, partly they are very dark coloured
or rich in strongly pigmented veins. Farther upstream in the river
Mangis these rocks are covered by the tertiary sandstones and
conglomerates.

Transitions of these rocks into phyllites rich in calcite by intermediance
of rocks with little quartz and sericite in a calcitic matrix are found ;
whereas by an increase of the percentage of quartz and mica,
transitions into the calcium-phyllites are formed. Calcium-plhyllites
with sericite schists are e.g. exposed in the banks of the S* Pakis
near its mouth, and higher upstream in the river similar rocks
alternating with rocks richer in calcite and with. limestones are
repeatedly exposed. The sericite schists are sometimes macrosco-
pically dense rocks, sometimes they are crystalline and strongly
schistose. The latter often contain tourmaline, whereas also varieties
rich in pyrite are found. |

The tourmaline is often more or less idiomorphous in the prismatic
zone, sometimes the crystals being divided into various irregular,
simultaneously extinguishing parts, separated by the quartz-sericite-
mixture.

The quartz shows aggregate polarisation and undular extinction,
kataklastic structures often occurring.

Fine-granular and strongly schistose two-mica-schists containing
much mica which are found in the left bank of the Sei Pakis,
contain some tourmaline and pyrite, and moreover in lenticular portions
which are poor in mica or free from mica some feldspar was found
in small quantity between the quartz crystals. This fact in connection
with the high percentage of biotite and with the facts to be mentioned
underneath, renders it probable that these rocks have already to a
certain degree been affected by contact-metamorphism,

- Finally the occurrence of brecciated rocks may be mentioned con-
taining fragments of sericite schists cemented by a fine aggregate of
quartz grains. In these sericite schists black layers strongly pigmented
alternate with those containing little pigment.

1198
CONTACT-PHENOMENA.

Although in consequence of the fact that little roek in situ is exposed,
not a continuous section is found from the granite area into not
contact-metamorphie rocks, the character of the metamorphism may
sufficiently be determined from the facts collected.

Between the kampong Pakis and the northwestern side of the
strip of schists, in the middle of the river, two little rocks arise,
consisting partly of granite, partly of contact-metamorphic rocks. At
the same place, in the right bank of the river, granitic rocks of dis-
tinctly parallel structure are exposed.

N

Fig. 4. Contact of granite and schists a short distance upstream from
kampong Pakis.
(g = granite. S = hornfels etc. cut by apophyses of granite.

The northern portion of the small rock I is composed of granitic
rocks, the southern portion as well as the rock II consisting chiefly
of hornfels with intercalated apophyses of igneous origin. The granites
ave dark coloured; they contain much biotite and show distinctly
parallel structure. The rocks are altered into a hard, fine crystalline
erayish-black hornfels, showing the original schistosity of the un-
altered sediments. Very thin layers of granitic material can be
distinguished even macroscopically.

Microscopically the hornfels and the intercalated granitic bands
do not show sharp lines of demarcation.

The granite from the northern portion of rock I consists of ortho
clase, plagioclase, quartz, biotite, some ore, zircon and apatite. The
feldspars form larger crystals, enclosed by a finer quartzose crystal-
line mixture containing feldspar and other minerals. The rocks
therefore show a more or less distinct porphyritic structure with
a subordinate groundmass. The plagioclases belong to the andesine

L195

group; in some slides, a.o. from the extreme northern end of rock |
they show a zonar structure with a bordering zone of great acidity.
Sometimes the crystals have been broken and the different fragments
have been shifted with respect to each other, and later a greenish
mica substance has been deposited in the cracks. The flakes of
biotite also are often bent and show strongly undular extinctions ;
the quartz, found in great quantity in the groundmass, shows a
strong aggregate polarisation. The cliff on the right bank of the
St Pakis near the rocky islands, contains rather large plagioclase
and orthoclase erystals in the quartzose mixture of quartz, feldspar
and biotite. Various plagioelases were determined to be andesine,
they often show a zonar structure with more acidic bordering zone.
Along the circumference of the feldspar crystals a granophyric
texture is found in places. The rock contains rather much calcite,
and also some crystals of zircon.

The contact-metamorphic sediments alternate with numerous

layers of granitic rocks, several similar layers — sometimes
macroscopically, sometimes only microscopically observable, — also

occurring in the hornfels. Thus it is a case of injection of granite
in the schists, whereas between the stratified granitic apophyses
the schist moreover has been feldspathised independently of the
development of the feldspars in the granite.

Granitie apophyses in the island II principally consist of ortho-
clase and of, sometimes zonar, plagioclase, quartz and biotite. The
feldspars occur as crystals of good size, more or less rounded and some-
times strongly sericitized, enclosed by a fine-grained granular mixture
of quartz and biotite with well marked strongly schistose structure.

The quartz shows a strong aggregate-polarisation. Further these
apophyses contain rather much brown or greenish brown tourmaline,
some pyrite and a few small erystals of zircon '), which sometimes
show rounded forms, sometimes are idiomorph, with pyramidal limita-
tion. The hornfels differs from the granite of the apophyses with regard
to the size of grains and the mutual relation of constituting minerals.
They are very schistose, rich in biotite, often contain tourmaline too,
and show a more or less distinct porphyritic structure caused by
the large size of several of the feldspar crystals. The feldspars are
free from inclusions, or they include a few quartzcrystals and flakes
of biotite only. In some metamorphic rocks apatite is found in
numerous crystals.

1) These crystals are colourless and often show pyramidal limitation. In basal
intersections we somelimes meet with distinct cleavage lines according to (110).
As yel no cassiterite has been demonstrated to be present in these rocks.

79

Proceedings Royal Acad. Amsterdam. Vol, XVII.

1200

Very schistose hornfels in the same island the layers of which
dip away beneath the rocks mentioned above consist almost
entirely of feldspathised schists with intercalated layers of granitic
material which are very thin and partly can only be observed
under the microscope. In this hornfels too, larger feldspars contrast
with the fine crystalline quartz-biotite-mixture surrounding the feld-
spars. Here also, inclusions of quartz and biotite occur in small
number in some feldspars, sometimes being arranged in the direction
of schistosity. Exceptionally and in a small number, these inclusions
also occur in a hornfels near the contact with the granites in the
little island I, and here too a more or less distinct arrangement parallel
to the schistplanes of the rock can be observed ; however, for far
the greater part the feldspars are totally free from inclusions. More-
over, this rock is much coarser crystalline than those mentioned
above. Some larger feldsparerystals occur in the finer crystalline
mixture. The structure of the hornfels is very much like that of
the adjoining granite rocks and no sharp line of demarcation exists
between the two kinds of rocks.

Further away from the contact, metamorphic rocks were collected
in which much muscovite is present along with biotite.

In the southern part of the island II, similar granitic rocks as in
the northern part of the island I occur; here the feldspars are very
strongly. sericitized and the rock contains much secondary calcite ;
numerous pyritecrystals also occur. Adjoining these granites, but
dipping away from the granite with strike W. 20 N. and dip 40°
N,E. dense cherts and sericite-schists occur, which on microscopical
examination prove to consist of a very fine-grained mixture of quartz-
crystals and aggregates of small quartz-grains. In the quartz-mixture
sericite occurs in varying quantity; along with sericite, chlorite,
iron-ore and some apatite occur. These rocks show no traces of
contactmeta morphism.

Rather well crystallized muscovite schists in the banks-of the
St Pakis have been mentioned above.

Not far downstream from the kampong Pakis rocks resembling
hornfels are found, in which much muscovite occurs along with
biotite; in some of them traces of feldspathisation were observed.
However, many of the rocks examined are free from feldspar; they
contain a few larger quartz crystals, with undular, extincuon, or
aggregates of quartz-grains in a finer-crystalline mass chiefly, con-
sisting of quartz with biotite and muscovite.

Tourmaline crystals of idiomorphie or almost idiomorphie limitation
are sometimes rather numerous, a blue core is sometimes rather

1201

sharply separated from a brown bordering zone. Finally, small
crystals of apatite and fine ore-particles occur in these rocks. In the
left branch of the S% Pakis near the kampong Pakis, the first solid
rocks found in situ are granites with a parallel-structure often apparent.
It is highly probable that in the part not exposed between the
granites and the Sei Pakis, the zone of the feldspar hornfels. and
granite apophyses occurs, which ‘farther up the river is exposed.
The granites at the contact contain much biotite, the increase of the
percentage of biotite being a common phenomenon of endomorph
contact-metamorphism. This fact may here account for the high per-
centage of mica, although elsewhere in the granitic area, rocks
containing much biotite also occur.

VerBEKK *) describes dark gray, sometimes black hornfels containing
feldspar, from Pamoesian near the river Sinamar in the Ngalau-
Sariboe mountains. The percentage of feldspar (chiefly plagioclase)
is only contained in the contact-rocks just touching the granite, as
soon as we get away from the granite more than. 2 or 3 m., the
percentage of feldspar diminishes and ‘soon. totally disappears. Appa-
rently we have to do here with contact-phenomena equivalent to
those mentioned above.

Putting together the data obtained in several localities, the following
statement may be given on the nature of the contact-metamorphism.

1. At the contact of the granites a narrow zone of the surrounding
schists has heen feldspathised. The contact rocks almost graduate
into gneisses, and the sharp contrast between igneous rock and
sediment has disappeared. Granite apophyses occur in alternating
layers with the schists. Farther away from the contact this feld-
spathisation is entirely missing.

2. In the hornfels the original stratification of the rocks has
been conserved.

3. biotite is the mica found in the feldspathised hornfells near
the contact with the granite, muscovite appearing in the contact
metamorphosed ‘rocks farther away from the contact.

4. The zone of the contact rocks with Al-silicates (andalusite ete.)
is missing, the zone of the mica schists succeeding the feldspathised
zone *).

5. Tourmaline is a common mineral in the contact-metamorphie
rocks.

1) R. D. M. VeRBEEK, loc. cil. p. 179.
2) “Knolenglimmerschieler”’ and ‘“Kuotenthouschiefer’ were not met with, but
the author considers undecided whether they are entirely missing or not,

1202

6. The often appearing porphyritie structure with rounded edges,
of the apparent feldspar phenoerists of the granites, and the highly
undular extinctions and aggregate-polarisations of the quartz in the
granites and hornrocks point to strong pressure in the rocks after
they had been solidified.

This metamorphism thus shows an entirely different character from
that of the classic contact-zones of the type Steiger Schiefer (RoseN-
puscH), where the sediments furnish the mineral constituents, the eruptive
rocks heat and pressure, molecular interchanging only taking place
in the contact-zone. It is much like the metamorphism described
by Micner Lévy for the Plateau Central, by Barrots for Brittany,
and by Lacrorx for the Pyrenees. The feldspathisation of the schists
without connection with the stratified granite apophyses, and the
manifold occurrence of tourmaline, point to the influence of mine-
ralisators and to a supply of constituents of the granitic magma in
the contact-zone.

The numerous pegmatites mentioned above tend to prove that
mineralisators have been present in the granitic magma in large
quantities. The presence of feldspars and tourmaline as well in
the pegmatites as in the contactmetamorphie rocks, illustrates the
pneumatolytie character of the contact-metamorpbism.

BRR A “TAA,

In the Proceedings of the Meeting of September 26, 1914.

p. 507 in the table: in the column headed 10°£/ for 237 read 244.
the numbers of the column headed R—1 are to be provided

with the sign —.

April 23. 1915.

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN

PROCEEDINGS OF THE MEETING
of Friday April 23, 1915.
Vor. XVII.

DOG

President: Prof. H. A. Lorentz.

Secretary: Prof. P. Zeeman.

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Vrijdag 23 April 1915, Dl. XXIII).

CON TEN ES:

F. M. Jarcer: “On a New Phenomenon Accompanying the Diffraction of Röntgenrays in
Birefiingent Crystals.” (Communicated by Prof. H. Haca), p. 1204. (With 4 plates).

F. M. Jarcer: “Researches on Pasreur’s Principle of the Connection between Molecular
and Physical Dissymmetry.” I. (Communicated by Prof. P. vay RompBurGH), p. 1217.

Ernst Conen: “The Allotropy of Bismuth” LI, p. 1236.

Erxst Conen and W. D. HELDERMAN: “The Metastability of the Metals in consequence of
Allotropy and its Significance for Chemistry, Physics and Technics” IV, p. 1238.

P. Eurenrest: “On the Kinetic Interpretation of the Osmotic Pressure.” (Communicated by
Prof. H. A. Lorentz), p. 1241.

W. van per Woupr: “On Nöruer’s theorem.” (Communicated by Prof. JAN DE VRIES),
p- 1245.

Jan Dr Vries: “A bilinear congruence of rational twisted quinties”, p. 1250,

JAN DE Vries: “Some particular bilinear congruences of twisted cubics”, p. 1256.

F. A. H. Scurememaxkers: “Equilibria in Ternary Systems”. X VILL, p. 1260.

A. W. K. pr Jose: “Action of Sunlight on the Cinnamic Acids’. (Communicated by Prof.
P. van RompureGn). p. 1274.

C. E. B. Bremexamur: “On the mutual influence of phototropie and geotropic reactions in
plants”. (Communicated by Prof. F. A. F. C. Went), p. 1278.

W. ve Sirrer: “On the mean radius of the earth, the intensity of gravity, and the moon’s
patallax”’, p. 1291.

W. pvr Sitter: “On Isostasy, the moments of inertia, and the compression of the earth,”
p- 1295.

W. pe Sivrer: “The motions of the lunar perigee and node, and the figure of the moon”,
p. 1309.

A. B. Droocirever Fortuyn: “The decoloration of fuchsin-solutions by amorphous carbon.”
(Communicated by Prof. J. Borke), p. 1322.

H. J. Hameurcer: “Phagocytes and respiratory centre. Their behaviour when acted upon

by oxygen, carbonic acid, and fat-dissolving substances. Explanation of the excitement
Stage in narcosis”, p. 1325.

80
Proceedings Royal Acad. Amsterdam. Vol. XVII.

1204

Physics. — “On a New Phenomenon Accompanying the Diffraction
of Röntgenrays in Birefringent Crystals.’ By Prof. Dr. F. M.
JAEGER. (Communicated by Prof. H. Haca.)

(Communicated in the meeting of March 27, 1915).

§ 1. A short time ago Haca and JARGER') made some observa-
tions on the diffraction of RÖNTGEN-rays in crystals of cordierite,
from very beautiful, perfectly transparent and homogeneous examples
of which suitable plates were cut parallel to the three pinacoidal
faces 100}, SOLO} and SOOÏf. On this occasion the RÖNTGENOgram
of the plate parallel to {0014 of this mineral hitherto considered
rhombie-bipyramidal, appeared in fact to possess two symmetry-
planes perpendicular to each other, as well as a binary axis; the
patterns however, obtained by the transmission of RÖNTGEN-rays
through the plates parallel to {100} and {010}, appeared to possess
only one single symmetry-plane. This combination of symmetry-
elements is just the essential of rhombic-hemimorphic crystals.

It must be remarked however, that this fact is contrary to the
consequences which follow from the theory of these phenomena, as
far as it regards the expected symmetry of the ROnTGEN-patterns.

The question, what will eventually be the symmetry of the
RONTGENOgrams of crystals of a certain symmetry-class, can be
answered comparatively easily. Deductions of this kind were made
for the first time in 1913 by G. Frieper®), who concladed, that
under no circumstances such symmetry of crystals, as were character-
ized by the absence of a centre of symmetry, could be revealed in
their RÖNTGEN-patterns.

The reasoning of FrirpEL is principally as follows. He deduces
the complex of symmetry-properties which is characteristic of hemi-
hedrical and tetartohedrical crystals, from those belonging to the
holohedrical forms, by the suppression of certain symmetry-elements
in the latter groups, thereby making use of the wellknown fact,
that in the holohedrical crystals every plane of symmetry corresponds
to a binary axis perpendicular to it. This results from the fact, that
all holohedrical crystals possess a centre of symmetry, and that such
a centre, if combined with either a plane of symmetry or with an
axis of pair period, necessarily wiil cause the presence of the other

lb) H. Haca and F.M. Jaeger, Proc. of the R. Acad. Amsterdam, 17. 430. (1914).

*) G. Frreper, Compt, rend. de I’\cad. des Sciences, Paris 157, 1533, (1913).

1205

of any of those three symmetry-elements; thus the combination of
a symmetry-centre with a symmetry-plane having always the presence
of a binary axis perpendicular to that plane as a consequence; and
a centre combined with an axis of pair period always involving
the existence of a symmetry-plane perpendicular to that axis. If
now all hemibedrical and tetartohedrical crystals are considered as
polyhedra, whose symmetry-groups correspond to complete secondary
groups of the symmetry-complex of the holohedrical forms of the
same system, then those secondary groups can be mathematically
deduced from the primary groups, by suppression of definite sym-
metry-properties from the primary groups; from a mathematical stand-
point nothing can be objected to such a way of reasoning; only it
is necessary to keep always in mind, that from a cristallogenetical
standpoint the hemi- and tetartohedrical erystalforms have of course
nothing to do with the holohedrical ones.

Just because the centre, the plane of symmetry and the binary
axis perpendicular to it, are always connected two and two in the
way described before, it follows,: that the deduction of the hemi-
hedrical and tetartohedrical secondary groups from the holohedrical
ones, can occur only by simultaneous suppression of two of them,
in the symmetrygroups of the holohedrical forms. This suppression
‘an be made in three ways:

a) So that one or more symmetry-planes + symmetry-centre are
eliminated.

6) So that one symmetry-plane + a binary axis perpendicular to
it are eliminated.

c) So that a binary axis + the symmetry-centre disappear.

If now in a holohedrical crystal of any system, S, and S, are
two secondary RONTGEN-rays, which will be equivalent by symmetry
to a certain plane |, they will also be symmetrically situated with
respect to the binary axis perpendicular to the plane J”; S, and 8,
will moreover always be centrically symmetrical to themselves,
because every particle of the space-lattice, if reached by the ether-
motion, will start as a centre of a secondary radiation in all
directions.

If now in the holohedrical form of the system we imagine the
centre of symmetry suppressed, then:

in the case of a) S, and S, will still remain symmetrically arranged
to the binary axis, perpendicular to the simultaneously disappearing
plane; and:

in the case of c), they will remain symmetrical with respect to

BU

1206

the plane, perpendicular to the binary axis, which disappears at the
same time as the symmetry-centre.

Thus in both these cases the symmetry of the RÖNTGRN-patterns
will evidently remain unchanged ; they will show the same symmetry
as the R6nreEN-patterns of the holohedrical forms of the system
would possess. From this results that all merohedrical crystals whose
symmetry can be derived in the ways described sub a) and ©), will
give RönrerNograms of the same symmetry as in the case of the
corresponding holohedrical crystals.

Only for the merohedrical crystals of the type mentioned sub 5),
the RörreeNogram will possibly manifest a different symmetry, than
may be expected in the case of the holohedrical forms.

The sub a) mentioned symmetry-groups are characteristic of all
erystals, which only possess avia/ symmetry ; that is to say : for all
crystals of those eleven classes, whose forms are different from their
mirror-images, and which can exist therefore as enantiomorphous
polyhedra. Thus all dextro- and laevogyratory antipodes will neces-
sarily manifest identical RONTGEN-patterns.

Furthermore to the groups derived sub a) and ec) will belong all
those crystals whose symmetry is that of hemzmorphic crystals ; in
the latter therefore the absence of the symmetry-centre will not be
shown by the RörrceNograms in any other way than in the case
of crystals of other symmetry-classes.

On more detailed consideration it appears that the cause, why
the absence of a symmetry-centre in the crystals can never be
revealed in the RÖNrGeN-patterns, is to be ascribed to tbe fact, that the
venerated secondary radiation is in itself of a centrically symme-
trical nature, just as in the case of ordinary light-waves. If tbis were
not the ease, then the symmetry of the RörrGeNograms could be
discerned in the same 32 symmetry-classes, just as with the poly-
hedrical erystalforms themselves, which are generated under the
influence of the one-sided forces of erystallisation. However it will
appear that even such a supposition would not be sufficient to give
an explanation of the new phenomena to be recorded here.

$ 2. The problem we have had before us for a long time, and
which evidently could only be answered by means of numerous
experiments, was just this: what symmetry will ev entually be revealed
in the RöNreeN-patterns of all kinds of merohedrical crystals.

Originally it seemed as if the experience hitherto obtained fully
supported the correctness of the above mentioned theoretical de-
ductions.

1207

In the RöÖNrGreNogram *) of the sphalerite: ZnS, which crystallizes
in the hexacistetrahedrical class, no other symmetry could be stated
than that which corresponds to the hexacis-octahedrical crystals.

On the other hand there is certainly another symmetry present
in the case of pyrite’): FeS, which belongs to the dyacisdodeca-
hedrical class, and which possesses thus a centre of symmetry.

The right-handed and left-handed rotating crystals of sodiumchlorate :
NaClO, gave, on transmission of a pencil of R6nreuNrays, identical
patterns (Table I, fig. 1 and 2), which, if the plates were parallel
to the faces of the cube, were of the same apparent symmetry, as
the images of the pyrite, — just as Ewarp and Friepricn’) have
also stated. It can be easily shown, that the same erystal (dextro-
gyratory), if radiated through perpendicularly to each of the cube-
faces, always gave the same image, absolutely corresponding with
that of a laevogyratory crystal, under the same conditions of expe-
riment. Thus the absence of a symmetry-centre in this case could
not be stated; both the symmetry-planes, perpendicular to each other,
which in the case of the pyrite can be attributed to the crystals
themselves, appear here in the RONTGENogram, because the symmetry-
centrum of the radiation is superimposed on the symmetry of the
chlorate-crystals, which symmetry is characterised by the presence
of only three perpendicular binary axes and the four ternary ones *).

According to Frieper, plates of dextro- and laevogyratory quartz,
if cut parallel to {OOO1}, will give ¢dentical ROnreEN-patterns. Just
in the same way, the crystals of dextro- and laevogyratory /uteo-tiiaethy-
lenediamine-kobaltibromide *) : {Co(Aein),}Br,-+-2H,O, which erystallizes
in the tetragonal system, gave identical R6OnTGEN-patterns, showing
the presence of four vertical planes of symmetry.

1) Laur, Frieprica und Knippine, Bayr. Ak. der Wiss. München, 303, (1912).

2) It is remarkable, that the spots have not an oval, but a rectangular shape here;
this fact cannot be explained in the way suggested by Brace, by the incomplete
parallellism of the incident rays of the pencil. Such phenomena were observed
likewise with some other crystals, so eg. with sylvine (KCl), perpendicular to
the ternary axis. With sy/vine also perpendicular to a quaternary axis the rectan-
gular spots were observed ; moreover the central spot here shows a radiation in
eight directions, parallel to the faces of the rhombusdodecahedron, a phenomenon
quite unexplicable at this moment. As to the rectangular shape of the spots, we
are persuaded now that it is principally connected with the thickness of the
crystalplates: the phenomenon manifests itself only in the case of thick plates,
being more prominent, if the plate is thicker,

3) Ewatp und Friepricu, Ann. der Phys. (4), 44, 1183 (1914); vide also; Friepricu,
Deutsche Naturforscher und Arztetag, Wien, (1913); Brace, Proc. R. Soc. London,
89 A, 477, (1914).

4) F. M. Jaecer, Verslagen Kon. Ak. Amst. April, (1915). (Still to be translated
in these Proceedings). .

1208

On the other hand, in the ease of the neutral ethylsulfates of the
rare earth-metals *), which possess hexagonal-bipyramidal symmetry,
the hemihedrical structure was found to be expressed quite clearly
in the RörteeNogram, which is also in full accordance with the
consequences of the theory, as this represents the case above mentioned
sub 5).

Further control of the exactness of these conclusions by experiment
was finally only possible to me with the aid of the beautiful RÖNTGEN-
ograms obtained at the Physical Laboratory of this University by
my friend and colleague H. Haca with the erystallographieal material
especially selected by me for this purpose. Without his aid and
kindness this investigation would have been quite impossible, and I
therefore wish to express to him here my sincere thanks once more.

In fig. 1 the corresponding photo of the apatite: Ca,Cl(PO,), is
reproduced in stereographical projection *).

The plate used here was cut perpendicularly to the c-axis; it
gave a very beautiful photographic image (Table I, fig. 3). The
presence of a senary axis, but the absence of all vertical symmetry-
planes is immediately recognisable here.

§ 3. For the purpose of obtaining further data of this kind,
plane-parallel plates were cut from crystals of ferric-ammonia-alum :
Fe (SO), . NH), SO, . 24H,O, and of potassium-chromic-alum :
K,SO,. Cr,SO,), .24H,O, — in both cases perpendicularly to a
ternary axis. ;

In fig. 2 and 3 the patterns obtained are reproduced in stereo-
graphic projection. It is immediately evident that these images only
show a ternary axis, but no planes of symmetry whatever. This is
in full agreement with the theory: for the alums, just like pyrite,
are dyacisdodecahedrical, and from the theoretical considerations
mentioned above it follows, that they may eventually manifest their
hemihedrical character in their RONTGENograms. But because these
crystals do not possess any other planes of symmetry than those
which are parallel to the faces of the cube, the image perpendicular
to the ternary axis will in fact manifest no other symmetry-properties
than those which follow from the mere presence of the ternary
axis itself.

1) F. M. Jaeger, these Proceed. 16. 1095. (1914); Receuil des Trav. des Chim.
des Pays Bas et de la Belgique, T. 33, 343. (1914).

2) In all these projections, d signifies the thickness of the crystalplate, A the
distance between the frontal face of the crystal plate and the sensitive film of the
photographic plate,

1209

Thus as far as experience goes, the phenomena observed in crystals
of the regular system seem to be in all cases in full agreement
with the postulations of the theory. In this connection it may here
be definitely stated, that the conclusions made by Haca and JarGer!)
some time ago, from their experiments with boracite above and
below 400° C., are now seen to be completely justified. For boracite
at room-temperature, — if it were really regular, — would be of
hexacis-tetrahedrical symmetry; and thus its ROnraunogram would
possess just the same symmetry as that of the sphalerite; i.e. that
the image would be identical with the pattern of boracite, which
was obtained above 400° C., — because this corresponds to the
holohedrical symmetry of the regular system. But the image obtained
by the authors at room-temperature, now only shows the presence
of two perpendicular planes of symmetry and a binary axis: there-
fore it van only correspond either to a rhombic structure, or to a
dyacisdodecahedrical, or to a tetrahedrical-pentagonedodecahedrical
crystal. The last mentioned two symmetry-groups however must be
excluded definitely because of the characteristic development of the
boundary forms of the boracite; thus the symmetry of the RÖNTGEN-
pattern at room-temperature can only correspond to a rhombic arran-
gement of the molecules, the optical behaviour (biaxial) of the
composing lamellae being in full agreement with this supposition.
The internal change of symmetry of the boracite, if heated above
400° C., seems therefore to be incontestably proved by the authors
in this experiment.

§ 4. If now we leave for the present out of consideration the
cases of the composite pseudo-symmetrical (mimetic) crystals hitherto
studied, it seems really, as if in a// cases, where regular or uniaxial
crystals were studied, the results of the experiments were in full
agreement with the conclusions which necessarily follow from the
uow adopted theory of the said phenomena.

However, the case of the rhombic curdierite is in flagrant contra-
diction with it: for from the theory it follows immediately, that
crystals of all three classes of the rhombic system must give Röntgen-
ograms whose symmetry corresponds to that of the holohedrical forms.

Thus plates parallel to the three pinacoidal faces: {LOO}, {O10}
and {001}, must always give patterns which are symmetrical with
respect to two perpendicular planes of symmetry; their intersection,
i.e. the line perpendicular to the photographic plate, must therefore
in all cases be a binary axis.

: 1) H. Haca and I, M. Jaeger, These Proceed. 16. 792. (1914).

1210

If the cordierite therefore were really hemimorphic, even then its
hemimorphy could under no circumstances be revealed in ifs
RöxteeNpatterns in the way formerly observed by us! Notwith-
standing that however, nobody can doubt the fact, that the RöNTGEN-
ograms of plates parallel to {100} and {OLO}{, only manifest one
single vertical symmetry-plane. There must be some unknown cause
therefore, why the other planes of symmetry in the images have
vanished.

As long as this case was the only one known, it was allowable
to regard it as quite accidental.

The following experiments however carry the conviction, that the
theoretical views demonstrated in the beginning of this paper, are
quite insufficient to explain the phenomena, as soon as they are
studied in biaxial crystals, instead of in optically isotropous or uni-
axial crystals, radiated through parallel to their optical axis.

The nature of these deviations may be seen from the facts described

further-on; it will however be adviceable first to say something
more in connection with the RÖNTGENOgrams of some uniaxial crystals,
from which plates cut perpendicularly to the optical axis were studied.

Turmaline is ditrigonal-pyramidal; according to the above mentioned
theory the RÖNTGEN-pattern must show the same symmetry as calcite,
which is of ditrigonal-scalenohedrical symmetry. Just in the same
way the pattern of the strongly dextrogyratory cinnabar: HgS,
which crystallizes in the trigonal-trapezohedrical class, should manifest
„the same symmetry.

Indeed, it can be seen from fig. 4 and 5, — which represent in
stereographical projection the RÖNTGEN-patterns, obtained with plates
perpendicular to the optical axis, —- that these images do not only

possess a ternary principal axis, but moreover three vertical planes
of symmetry; and they thus really show the same symmetry in
their RÖNTGENograms, as the calcite.

From this it follows immediately, that e.g. the images for dextro-
and laevogyratory cinnabar, if radiated through perpendicularly to
the basal face {0001}, must be quite identical.

In Plate I fig. 4 the original photograph for turmaline is repro-
duced. Whether crystalplates of these minerals, when parallel to {12104
will now really show the presence of a binary axis in their
RonreeNograms as follows from the theory, we have yet to find
out by more numerous experiments’). But in any case we can say,

1) Really we have found now this conclusion confirmed by experiment, as will
be published in a short time,

1211

7

that if these crystals are radiated through in a direction, in which
they are optically-isotropous, hitherto nothing could be found which
indicated a divergence between the theory and he experiments.

§ 5. Quite different however are the phenomena observed in the
cases of biaxial erystals, i.e. of such crystals, which are birefringent
in all directions, and in which therefore the anisotropy of the ether
will manifest itself in a// directions.

In order to study the simpler cases first, we started with crystals
of rhombic symmetry. Plates were cut from them going exactly
parallel to the three pinacoidal faces: {100}, {010} and {OOI}. It
might be expected therefore, that every image would appear sym-
metrical with respect to a pair of perpendicular symmetry-planes,
while the normal on the photographie plate would be a binary axis.

The experiments were first of all made with plates ofa beautiful,
perfectly transparent crystal of dextrogyratory sodium-ammontum-
tartrate: Na(NH,)C,H,O, +4H,0. The crystallographic measurements
were in perfect agreement with those of RAMMELSBERG : the salt is
rhombie-bisphenoidical, and thus possesses as symmetry-elements
only three perpendicular binary axes, but neither a plane nor a
centre of symmetry.

In fig. 6, 7, and 8 the stereographical projections of the obtained
RoyreENograms are given; on Plate IL, in fig. 5 and 6, the original
photographs of plates parallel to {010} and {100} are further repro-
duced; they were, as in all following cases, obtained with the use
of a screen “Eresco” behind the photographic plate.

Although the time of exposure was fully three hours, the im-
pressions on the photographic plate in the case of a plate parallel
to {001} were extremely feeble; this fact could perhaps be partially
caused by the rather great distance of the spots from the centre of
the plate. The characteristic symmetry towards both perpendicular
planes (vid. projection fig. 8) is however immediately recognisable.

The same fact, that the transmission of the RÖNTGEN-rays is so
much less effective in one direction of the crystal than that in the
others, will be found in other cases also, e.g. in that of the hambergite
which will be described afterwards.

It is immediately evident, that these results are in total disharmony
with the postulations of the theory.

The stereographical projection (fig. 7) of the image obtained by
transmission of the RÖNtTGEN-rays in the direction of the b-axis (plate
parallel to {O10}), only possesses one single plane of symmetry :
there is neither a binary axis nor a symmetry-centre present. The

1212 °
plane of symmetry i.e. is parallel to {001}. The plane of the optical
axes of the erystal being parallel to {100}, while the c-axis coincides
with the first bisectrix of negative character, it is evident, that the
homologous spots are missing in the photograph which lie in the
directions parallel to the a-axis, i.e. parallel to the direction of the
smaller optical elasticity of the crystal plate.

The figure corresponding to the image of a plate parallel to {100}
(vid. fig. 6), also possesses only one single plane of symmetry; but
it is now just the plane {001}, which has disappeared as such, while
{010} remains. Here we therefore miss the spots which would
correspond to directions parallel to the c-axis; thus on the photo-
graph the spots have vanished, completely or partially, which would
lie in the direction of the greater optical-elasticity of the crystal-plate.

On the other hand the image of a plate perpendicular to the c-axis
(fig. 8) shows two perpendicular planes of symmetry, as well as a
binary axis; the intensity of the spots is however very feeble indeed.

It must here be remarked, that the combination of symmetry-
properties observed in these three ROnTGEN-patterns is geometrically
quite impossible for the crystals themselves. The case considered is
therefore again more convincing than that of the cordierite. Hence
the cause of the newly discovered phenomenon can „ot be sought
in the special symmetry-character of the crystals; there must be
still some unknown factor, which determines the phenomenon of
the unexpected disappearance of the planes of symmetry.

§ 6. As a second case of this kind we have reproduced here
the RÖNrTGENograms which were obtained in the same way with
plates of hambergite.

The choice of this very rare mineral, got at Helyarden, Lange-
sundford, Norway, was made with a view to its chemical composi-
tion: Be, (OH) BO,; the compound’ being composed of the lighter
elements in the periodical system, whose atomic weights are all
smaller than 20. Hambergite is rhombic; its parameter-ratio is:
a:b:¢ =0.7988:1:0.7267. The crystals were glassy and splendidly
homogeneous; they showed the forms {110}, {100}, {O10} and {011},
and had a prismatic aspect. A perfect cleavage is present parallel
to {010}, a good one parallel to {100}. The crystals are very strongly
birefringent; the birefringency is about: 0.072. The plane of the
optical axes is parallel to {010}; the first bisectrix, which has
positive character, coincides with the vertical axis. The dispersion
round the first bisectrix is only feeble, with o < v.

In fig. 9, LO and 11 the stereographical projections of the RÖNTGEN-

1213
patterns obtained are reproduced. When perpendieular to the c-axis,
the photograph, remained very feeble even after 34 hours’ exposure ;
in both the other principal directions however, even after much
shorter exposure, the photographs were very sharp.

The plate perpendicular to the c-axis, in fact shows two normal
planes of sy LoS ONE as well as the binary axis: in the direction of

i 1 5 a — LANAANNN Nonnen Je |) Wein inten dn

ERRATA.

In the paper of F. M. Jarcrr: A new Phenomenon accompanying
the Diffraction of R6nrGEn-rays, ete. the following errors must be
corrected :

On Table IV Fig. 10. Plate parallel (010). Read: Plate parallel (001).

Fig. 11. Plate perpendicular to the c-axis. Read: Plate
parallel to the 6-axis.

A comparison with the photo’s 8 on Table II and 9 on Table III
will also immediately make this evident.

In connection herewith, on p. 1213, in the 19" line from the
top, in stead cf Fig. 11 should be read: Fig. 10.

a- and b-axis 15 only sligttly different in it.

Both pinacoides {100} and {010} have thus in an optical sense
about the same relation to the direction of the c-axis, and therefore
we observe that the plane of symmetry parallel to (001) disappears
on the corresponding photos. In both plates the spots which lie
in directions parallel to the greater elasticity have thus disappeared
completely, just as in the case of hambergite.

$ 7. Finally we point out the peculiarities found in the study

1212 °
plane of symmetry i.e. is parallel to ,OOL. The plane of the optical
axes of the crystal being parallel to {100}, while the c-axis coincides
with the first biseetrix of negative character, it is evident, that the
homologous spots are missing in the photograph which lie in the
directions parallel to the a-axis, i.e. parallel to the direction of the
smaller ontieal elasticity of the crystal plate.

SiS ri a os OEE Oe are ae ee
a:b:c=0.7988:1:0.7267. The crystals were glassy and splendidly
homogeneous; they showed the forms {110}, {100}, {O10} and {011},
and had a prismatic aspect. A perfect cleavage is present parallel
to $010%, a good one parallel to {100}. The crystals are very strongly
birefringent; the birefringency is about: 0.072. The plane of the
optical axes is parallel to {O10}; the first bisectrix, which has
positive character, coincides with the vertical axis. The dispersion
round the first bisectrix is only feeble, with 9 < wv.

In fig. 9, LOand 11 the stereographical projections of the RÖNTGEN-

1213

patterns obtained are reproduced. When perpendicular to the c-axis,
the photograph, remained very feeble even after 34 hours’ exposure;
in both the other principal directions however, even after much
shorter exposure, the photographs were very sharp.

The plate perpendicular to the c-axis, in fact shows two normal
planes of symmetry, as well as the binary axis: in the direction of
the a-axis (parallel to the plane (010), the density of the spots
seems to be greatest, but this is only slight in comparison with that
of the very numerous and intense spots on both the other patterns.

When the RöNreeNogram is perpendicular to the a-axis (fig. 9),
the expected symmetry is also unmistakably present; the circles con-
taining most spots here lie in the direction of the c-axis (parallel to
the plane (010).

The photograph however, obtained with a plate perpendicular to
the J-axis manifests only one single plane of symmetry, namely that
parallel to {001}. It is evident, that this combination of symmetry-
properties would be also erystallographieally quite impossible, and
the only suitable explanation in this case is, that the plane of sym-
metry (parallel to {100)) has disappeared for some reason. Fig. 11
proves, that the above mentioned symmetry-plane is really expressed
in that photo; but if the RöNrGeN-rays are transmitted parallel to
the direction of the optical normal (i.e. perpendicularly to the direct-
ions of maximum and minimum optical elasticity) evidently the spots
which would be expected in the direction of maximuin elasticity
either come out in the photo not at all or only partially.

In table IL moreover two of the original photographs in figs. 7
and 8 are also reproduced; they show the said phenomenon very
clearly.

In the case of cordierite only the two vertical planes of symmetry
were found, for plates cut parallel to {100} and {O10}. In cordierite
{100} is the optical axial plane, and the c-axis is the first bisectrix,
and of negative character. However cordierite is a but feebly birefringent
mineral (about: 0.010) and the optical elasticity in the directions of
a- and b-axis is only slightly different in it.

Both pinacoides {100} and {010} have thus in an optical sense
about the same relation to the direction of the c-axis, and therefore
we observe that the plane of symmetry parallel to {001} disappears
on the corresponding photos. lm both plates the spots which lie
in directions parallel to the greater elasticity have thus disappeared
completely, just as in the case of hambergite.

§ 7. Finally we point out the peculiarities found in the study

1214

of benitoite. This very beautiful mineral, which is used as a gem,
and whose chemical composition is: BaTiSi,O,, has some importance
from the mineralogical standpoint, because it has been considered
by mineralogists as the only representative of the trigonal-bipyramidal,
or, — with greater probability, — of the ditrigonal-bipyramidal class.

The first opinion was expressed by Rogers *), the last by PaLacne’),
who as a proof of the correctness of his view emphasized the presence
of a form {2241} in many crystals. Later on however JEZEK") made
it probable that the ternary axis was of a polar nature, and that
benitoite-erystals were twins with respect to the basal face (0001; ;
by this author benitoite is considered to be a ditrigonal-pyramidal
mineral.

Evidently the question about the real symmetry of this remarkable,
enormously diehroitie mineral, is not yet settled; for that reason
this object was chosen for the study of the diffraction phenomena
of RÖNTGEN-rays. .

We had at our disposition very beautiful pink erystals from San
Benito County in California, where benitoite is accompanied by
natrolithe and neptunite. They were flattened parallel to {0001}, and
showed a combination of the forms: {0001}, {1011}, {0111}, {1010}
and {0110}. From a beautiful, homogeneous crystal three plates were
prepared exactly parallel to {OO01{, to 1010} and to {1210}. The
optical investigations of the plate perpendicular to the c-axis, very
soon proved that the crystals show only pseudo-trigonal symmetry,
and that they are in reality not uniaxial, but biaxial, with a very
small axial angle, and with positive character of their tirst bisectrix
which coincides with the direction of the c-axis. In no position was
the plate completely dark when between crossed nicols. On rotating
the microscope-table the interference-image often showed a deform-
ation of the central part and distinct lemniscate-shaped inner rings,
as well as the transformation of the dark cross into two branches
of a black hyperbola; the plane of the optical axes is evidently
perpendicular to {L010}, with the c-axis as the direction of the first
bisectrix, which has a positive character. The birefringence of the
mineral is strong; in basal sections local disturbances of the image
are also observed, suggesting at once the memetic character of the

1) Rogers, Science, 28, 676, (1908).

2) Patacue, Amer. Journ. of Science, 27, 398, (1909).

8) Jezek, Bull. intern. de Acad. des Sciences de Bohème, Prague (1909). Vide
also on benitoite: LouperBack. Publ. of Calif. Univ. 5, 9, 149, (1907); Kraus,
Science 27, 696, 710, (1908).

—

Pror. DR. F. M. JAEGER. PLATE I.
A NEW PHENOMENON, ACCOMPANYING THE DIFFRACTION OF RONTGEN-RAYS
IN BIREFRINGENT CRYSTALS.

i a Ra,
4 Ps .
é
f
£ % - hd oi ek
IE wensen
ns a
én
ots
eo - ” het *
a ® 3
Fig. 1. Fig. 2.
Dextrogyratory Sodiumchlorate. Plate parallel to (100). Laevogyratory Sodiumchlorate, Plate parellel to (100).
d = 2,95 m.M.; A = 45.8 mM. = 2.25 mM.; A = 45.7 m.M.
*
¥
a,
5
Fig. 3. Fig. 4.
Apatite; plate perpendicular to the c-axis. Turmaline ; plate perpendicular to the c- axis.
d= 15 m.M.; A = 43 m.M. d = 1.1 m.M.; A = 44 m.M.

Proceedings Royal Academy Amsterdam Vol. XVII. HELIOTYPIE, VAN LEER, AMSTERDAM

PROF. DR. F. M. JAEGER. Epe!
A NEW PHENOMENON, ACCOMPANYING THE DIFFRACTION OF RÖNTGEN-RAYS
IN BIREFRINGENT CRYSTALS.

+
a“
Fig. 6.
Fig. 5. Dextrogyratory Sodium-Ammonium Tartrate (4 H30).
Dextrogyratory Sodium-Ammonium Tartrate (4 H90). Plate perpendicular to the 6 - axis.

Plate perpendicular to the a - axis.

, Ld
;
; ‘ae
:
; x
6 *f ; 'e
1 Ld , ®
® ’ . A
é
- En 7
we
| - ad «
d
A tie cab "
EE" ‘
Fig. 7. Fig. &
Hambergite ; plate perpendicular to the a-axis Hambergite ; plate perpendicular to the b-axis.
d = 1.56 m.M.; A = 50 m.M. d = 1.54 m.M.; A = 50 m.M.

roceedings Royal Academy Amsterdam Vol. XVII. HELIOTYPIE, VAN LEER, AMSTERDAM

‘
N
dt sl Vake B

a) B be der ntm oP maton BE ing ee
*

j PROF. DR. F. M. JAEGER. PLATE III.
NEW PHENOMENON, ACCOMPANYING THE DIFFRACTION OF RÖNTGEN-RAYS
IN BIREFRINGENT CRYSTALS,

Fig. 10.
4 Benitoite; plate parallel to Loro
Fig. 9. d = 152 m.M.; A = 50 m.

| Hambergite; plate perpendicular to the c- axis.
d = 152 m.M.; A = 50 m.M.

Fig. 11. Fig. 12.
Benitoite; plate parallel to {aio} gig plate parellel to {0001
d = 1.50 m.M.; A = 50 m.M = 1.50 m.M.; A = 50 m

Proceedings Royal Academy Amsterdam Vol. XVII. HELIOTYPIE, VAN LEER, AMSTERDAM.

6. Stereographical P
gen-pattern of dextrog
onium-Tartrate. Plate

A
a

AN

Ly)

eet,
WLI]

8. Stereographical P
a of dextrog
onium-Tartrate. Plate

Fig. 13. Stereographical Projection of the Röntgen-
pattern of Benitoite. Plate parallel to (1210).

Fig. 14. Stereographical Projection of the Röntgen-
pattern of Benitoite. Plate perpendicular to the c-axis.

Prof. Dr. F. M. JAEGER: „On a New Phenomenon accompanying the Diffraction of Röntgen-rays in birefringent Crystals.” Plate IV.

i i i jecti i i i he Fig. 9. Stereographical Projection of the Röntgen- Fig. 10. Stereographical Projection of the Rontgen- Fig. 13
3 e Fig. 2. Stereographical Projection of the Fig. 5, Stereographical Projectian of the Fig. 6, Stereographical Projection of t 1
Re ie Benet ike Rontgen-paltern of ieee Minnariand Rontgen-pattern of dextrogyratory Cinnabar. 2 Rontgen-pattern of dextrogyratory Sodium pattern of Hambergite. Plate parallel to (100). pattern of Hambergite. Plate parallel to (010).
intgen-patte A 3
si CEpeHOteHar to the c-axis, Alum. Crystalplate parallel to (111). Plate parallel to (0001).) ee yi | Ammonium-Tartrate. Plate parallel to (100)

Stereographical Projection of the Rontgen-
pattern of Benitoite. Plate parallel to (TTO).

/
/
| /
\
Fig. 3. Stereographical Projection of the Fig. 4. Stereographical Projection of the Fig. 7. Stereographical Projection of the Fig. 8 Stereographical Projection of the Fig. Il. Stereographical Projection of the Rontgen- Fig. 12. Stereographical Projection of the Rontgen- Fig. 14. Stereographical Projection of the Röntgen-
Rontgen-pattern of Potassium-Chromic= Rontgen-pattern of Turmatine. Plate per- Röntgen-pattern of dextrogyratory Sodium- Rontgen-pattern of dextrogyratory Sodium rattern of Hambergite. Plate perpendicular to the c axis. pattern of Henitoite. Plate parallel to (1010), pattern of Benitoite, Plate perpendicular to the c-axis.
Alum. Plate parallel to (111), pendicular to the c-axis. Ammonium-Tartrate, Plate parallel to (010), Ammonium-Tartrate, Plate parallel to (001).

1215

henitoite ; it appears to be composed of lamellae, which with respect
to each other are turned through an angle of 120°, and seem to
possess rhombic-hemimorphic or monoclinic symmetry. |

The plates parallel to {1010} and {1210} also betrayed this lamellar
structure in a more or less convincing way: the plate parallel to {1210}
showed this lamellar character very clearly, and was composed of
two sets of nearly perpendicular crossing lamellae, which made
about 53° with the c-axis, while an irregular partition in fields of
different colour and dichroism could be observed in some cases
besides.

The crystals are very strongly dichroitie: for vibrations parallel
to the c-axis the crystals have a deep blue colour, for such perpen-
dicular to the c-axis, they are almost colourless, with a very faint
lilac hue.

The cleavage is very imperfect, and parallel to {1014}; from the
goniometrical measurements it follows, that the psendo-trigonal
complex has an axial ratio of: a:¢ =1: 0.73819.

In figures 12, 15, 14, are reproduced the stereographical projections
of the very fine RÖNrGeNograms which were obtained in our expe-
riments. Figures 9,10, and 11 on plate III are reproductions of the
original photographs.

The plate perpendicular to the c-axis (fig. 14) gave a R6NTGEN-
pattern, which possessed no more than one single plane of symmetry,
parallel to 11010} notwithstanding its undeniable trigonal design.

In agreement with this, the image in fig. 13, obtained with a
plate perpendicular to {1210%, shows a vertical symmetry-plane. Lt
may appear doubtful whether this image also possesses a horizontal
plane of symmetry: a very slight but noticeable difference in the
intensity of the spots at the ends of the vertical axis seems to be
present.

The question is however, whether this would indicate a real, and
in that case very feeble polarity of the c-axis, or if it should be
considered as a photographic effect, caused perhaps by a slight
deviation of the plate from its normal position. In fig. 12, obtained
by transmission of the pencil of R6ONTGENrays in a direction perpen-
dicular to {1010}, the polarity of the c-axis is however very much
more easily recognisable, — not only in the differences in intensity,
but also in the different arrangement of the spots.

However, whether one considers the c-axis a polar one or not,
the combination of the symmetry-properties observed is here geome-
trically quite impossible also; for if the c-axis is of a polar nature,

1216

then fic. 14 must be symmetrical with respect to both perpendicular
planes; and if the c-axis is not of that kind, fig. 14 should neces-
sarily possess the same symmetry.

In every case therefore, one plane of symmetry must have dis-
appeared in fig. 14; here also no other supposition is possible than
that there must be some reason why the expected spots in directions
parallel to the intersection (OOOL) : (1010) are completely or partially
suppressed. The real symmetry of the pseudotrigonal complex of
lamellae can thus be regarded after this as a matter of secondary
importance; for it is very well possible, that in tg. 12 also a
second symmetry-plane, parallel to {OOL{ has disappeared, and in
that case the resulting combination of symmetry-properties would
be geometrically impossible too, just as in all preceding cases.

§ 8. We here thus meet the extremely remarkable phenomenon, that
in biavial crystals, in striking contradiction to the experience hitherto
gathered from optical isotropous or uniaaial crystals if studied
perpendicular to their optical axis, certain symmetry-elements of the
RÖNrGENograms which were to be expected according to the Liaur-BraGg-
theory absolutely vanish. Thereby a complex of symmetry-properties
is revealed in the complete set of RoOnrexNpatterns of the same
erystal, which is geometrically impossible, and which theretore cannot
be a representation of the special symmetry of the crystal itself.

As far as experience now goes, and provided that the more com-
plicated case of the mimetic benitoite is for the present left out of
consideration, the suppression of the spots occurred in two of the
cases studied, in those images which are obtained by the trans-
mission of the RÖNTGeN-rays parallel to the optical normal; te. the
spots disappeared there in the plane in which the differences of the
optical elasticity. of the erystal are as great as possible. In the case
of the sodiumammoniumtartrate the suppression occurred for crystal-
plates either parallel to the optical axial plane, or perpendicular to
the second bisectrix; i.e. in the directions of the greatest and smallest
elasticity, not however in the direction of the optical normal.

One would be inclined to explain these phenomena, — just because
they are observable exclusively in those crystals whose optical
anisotropy is manifested in all directions, — by supposing some
condition of polarisation of the generated secondary waves. which
polarisation would finally find its expression, — somewhat in the
same way as in the case of ordinary light-waves, — in an unequi-
valence of perpendicular directions. Or one again would be inclined
to suppose an anisotropy in the mode of motion of the particles

121%

affected by the impulse of the incident rays, in three perpendicular
directions, and to investigate the consequences of such a supposition
for the process of the generating of the spots on the photographic plate *).

In connection with this last supposition, the question could then
be considered once more, whether the unequal deviations of the law
of Frantz and WikpeMANN in the principal directions of crystallised
bismuth and hematite formerly observed,*) were not perhaps to
be explained in some analogous way?

Jut let be it as it may, a final explanation of the phenomona
observed here cannot be given at this moment. In any case it has
become quite evident, that in the temporarily adopted theory for
the diffraction-phenomena of RöNtGeN-rays in crystals, a certain factor
is yet missing, which has the result that the consequences of the
theory are in agreement with the experimental results only if it is
applied to isotropous crystals or to those in which the transmission
of the RÖNTGEN-rays takes place in a direction, in which the erystal
behaves like an optically isotropous one.

Only in the last-mentioned cases do the facts appear as full
illustrations of the theoretical deductions.

But as long as that theory is unable to explain why the facts
observed with biaxial crystals do „of coincide with those expected
by it, the theory can hardly be said to give a final explanation of
the diffraction-phenomena in crystals at all.

Systematical experiments with the purpose to elucidate these
phenomena as well as possible, are momentaneously going on.

Groningen, Laboratories for Physics and for Inorganic
March 15, 1915. Chemistry of the University.
Chemistry. — ‘Researches on Pasteur’s Principle of the Connection

between Molecular and Physical Dissymmetry.” 1. By Prof.
Dr. F. M. JarGer. (Communicated by Prof. van RoMBURGH).

(Communicated in the meeting of March 27, 1915).

§ 1. It is now matter of common knowledge among scientists

R\

how the classic investigations *) of L. Pasteur, regarding the con-
nection between the so-called “molecular dissymmetry” of organic
compounds and their optical behaviour, and especially those investi-

1) The case of the tartrate has in so far some analogy with that of cordierite,
that in this case also the optical elasticities in the directions of both the a- and
h-axes, do not differ very appreciably, in comparison with that in the c-axis.

2) F. M. Jaeger, These Proc. 15. 27, 89. (1907).

8) L. Pasteur, Récherches sur ta Dissymmetrie Moléculaire; Legons professées
devant la Société Chimique de Paris, (1860).

1218

vations which bear upon the properties of the racemic and tartric
acids and their salts, — have led to that more detailed conception
of the spacial arrangement of the atoms in the molecules, which
has finally obtained expression in the stereochemical views of modern
times. The conclusion to which Pastrur was led can be shortly
expressed in this way: in all cases where a substance is characterised
by a dissymmetrical arrangement of the composing atoms in its
molecules, the possibility can be foreseen of the existence of two
modifications of that substance, whose physical properties can be
described by spacial systems of vectors, which are in the relation
to each other of right- and lefthand-systems.

This statement has proved to be satisfactorily general and so
indefinite as to have led to numerous remarks and even to misunder-
standing. With respect to the second part of the above-mentioned
conclusion, there can hardly be any divergence of opinion: it is of
course quite apparent, that here only can be question about vectorial,
never about sca/ar quantities. Thermical, caloric, and volumetrical
constants, e.g., will thus be identical with the two modifications in all
cases; and from those properties which are expressed by means of
vectors, only such can be taken into account, whose descriptive
-vector-systems will not coincide with its mirror-images; the pyro-
and piezo-electrical phenomena, etc, which cannot be described by
centrically-symmetrical, but only by “polar” vectors.

The first part of Pasrrur’s conclusion however will immediately
lead to the question: what is the proper meaning of the expression
“molecular dissymmetry’, and under which circumstances will it
manifest itself? It becomes clear on fuller examination, that the
introduction of the word ‘“dissymmetry’’ in these cases, has often
caused misconceptions, and that it has led to erroneous or at least
incomplete statements, even with well-known authors; and what is
more, it seems continually to lead to unintelligibility about the
conditions which will determine the isomerism indicated, notwith-
standing the evident feeling of incertitude, which can occasionally
be stated *).

The doctrine of the so-called ‘“unsymmetric atoms” of Le Bet and
vAN “tT Horr brought, as is well-known, a first rational explanation
of that “molecular dissymmetry”. Since then the presence of an
n-valent atom, saturated by 2 unequal substitutes, has begun to be
considered as the necessary condition which must be fulfilled, if the
case of a possible isomerism as foreseen by Pasteur, is to be realized;

1) Conf. Ga, M. van DEventER, Chem. Weekblad 10. 1046, (1913).

1219

and as Guynr’s suggestive ideas prove, they even tried to point out
an immediate connection between the more or less considerable
degree of such molecular dissymmetry, and the more or less palpable
differences, e. g. in mass, which can be stated between those 7 un-
equal atoms or radicals"). In that case the idea is evidently always
present, that a chemical molecule possessing such ‘‘unsymmetric
atoms’, will necessarily be characterized by a complete lack of
symmetry, and thus can be defined in the full sense of the word,
as an “unsymmetric’ molecule.

As long as one is of opinion, that in this question the ordinary
chemical differences of the radieals-which are linked to the multivalent
atom, will really be the predominant factor, it perhaps is allowable
to consider such a molecule as a spacial complex which does not
possess any more symmetry-properties. But it must immediately be
pointed out here, that this conclusion is by no means an inevitable
one: it must be considered to be quite precipitate, to suppose the
molecules of this kind as necessarily unsymmetrical ones for all
kinds of physical properties, just because we do not know the
undoubtedly very complicated structure of the atoms themselves.
The more, as the “absence of symmetry-planes”’, commonly brought
to the fore on this oceasion, will by no means involve the absence
of any symmetry in such a spacial system, nor will this single
condition be sufficient to make the presence of two modifications,
which relate to each other as mirror-images, a necessary consequence.’)

In connection with these erroneous conceptions about the conditions
which will imvolve the mirror-image-isomerism in the case of such
spacial systems, it must be esteemed of the highest importance that we
have begun to understand that the presence of an ‘“unsymmetric”
multivalent atom, as defined by the conception of LeBeL and vaAN

1) PH. A. Guye. Compt. rend. 110. 744 (1890); Thèse Paris, (1891).

4) If for instance one accepts the idea that the atoms of the chemical elements,
notwithstanding their different nature, contain some structure-elements which are
common to all of them, and that it will principally depend just on the spacial
arrangement of those common constituents (e.g. systems of electrons), which will
determine the symmetry of the physical properties or at least of some of them
in the resulting substances, — then it does by no means follow from the chemical
inequality of the substitutes in the molecule, that the spacial system of those
determining structure-elements of the atoms, necessarily represents a non-sym-
metrical complex. As long as we do not know, on what particular circum-
stances the physical dissymmetry of the molecules properly depends, it is not
allowable in my opinion to consider the chemical inequality of the substitutes as
the necessary condition of the physical dissymmetry of the substance; it can at
pest be esteemed a very favourable moment for it.

S1

Proceedings Royal Acad. Amsterdam. Vol. XVII.

1220

‘t Horr, must really be considered only as a very favourable factor
with respect to the mentioned possibility of such isomerism; but
that the chemical difference of the substitutes in this ease may not
absolutely be regarded as the predominant factor therein.

Finally the right- and left-hand isomerism must appear possible wi
all those cases, where, — it matters not whether the substitutes are
equal or unequal, — the spacial arrangement in the molecule and
the distribution of the intramolecular forces, will fulfil the special
conditions of symmetry which can be generally deduced and formu-
lated for all kinds of spacial systems differing from their mirror-
images.

$ 2. The investigations of the last few years have completely
justified the conclusion, that in the first instance it depends in this
question upon the spacial arrangement alone. That e.g. the differences
of mass of the substitutes, are no measure for the lower or higher
degree of “molecular dissymmetry”, has inter alia resulted from
FiscHeRr’s experiments’) relating to the propyl-isopropyl-cyano-acetic
acid, whose optically active components show a fairly high specific
rotation (about 11°), notwithstanding the equal masses of both the
hydrocarbon-radicals in their molecules. Furthermore Swarts tried
to prove firstly that no other carbon-atoms need to be linked directly
to the unsymmetric atom in such active molecules; but it was only
recently proved in a final way by Pops, in the case of the Ammoniwm-
salt of Chloro-jodo-methane-sulfonic acid’).

And that also the above-mentioned isomerism can occur in cases
where no symmetrical atoms, surrounded by unequal substituents, are
present, was proved some years ago by the experiments of Porw,
Perkin and Warracn *), with respect to the 1-methyl-cycloherylidene-
4-acetic acid:

Cc COOH
Ne “(J Me
a eee

However the solubility *) of these and related substances in almost

1) E. FrscHer and E. Frarau. Ber. d. d. Chem. Ges. 42. 981 (1909).

*) W. J. Pope and J. Reap. Proceed. Cambridge Phil. Soc. 17 (1914); Trans.
Chem. Soc. 105. 811 (1914).

5) Pope, PERKIN and WaArLACH. Trans. Chem. Soc. 95, 1789. (1909): Pope and
PERKIN, ibid. 99. 1510 (1910).

+) According to a private communication given by Prof. PoPr to me.

1221

all solvents is so great, that it was hitherto impossible to prove
the correctness of Pasrrur’s principle in these cases, just with respect
to the erystalforms of the antipodes.

The strongest evidence however in favour of the views previously
explained about the necessary conditions for the occurrence of
mirror-image-isomerism, can be deduced from the theoretically com-
paratively simple cases which for the first time became known asa
result of A. WerNer’s masterly investigations on the complex-salts,
and more especially of the /wteo-triaethylenediamine-cobaltic salts *).

Later on he found analogous phenomena with a number of other
salts with complex ions, e.g. with the analogous derivatives of oxalic
acid. Not only did these facts prove the correctness of WeRNER’s
views considering the spacial arrangement of the six coordinated
substitutes round the polyvalent central-atom, but they have also
brought direct proof of the correctness of the other idea, that in the
question of ‘molecular dissymmetry’, as commonly understood, it
is not primarily the inequality of the substituents, but exclusively
their spacial arrangement, which is of importance.

A new problem is thereby brought to the fore: to find the cireum-
stances and conditions, which will cause a spacial configuration of
the atoms in the molecules, which will be different from its mirror-
image even in those cases where no chemical differences between
those substitutes are present *).

1) A. WERNER. Ber. d.d. Chem. Ges. 45. 121. (1912); 47. 1960, 3093. (1914).
2) In this connection it may be well, shortly to remind of the conditions for the
occurrence of spacial configurations, which will not be congruent with their mirror-
images, and to mention the significance there-with of the commonly emphasized
“Jack of symmetry-planes” in this phenomenon. If one chooses as the descriptive
“symmetry-elements’ for such spacial arrangements: the symmetry-axes

2
(period = =) of the first and of the second class (“axes of alternating symmetry’’),
: L

— then one can say that all configurations which do not possess such axes of the
second class, will be different from their mirror-images. All such configurations,
which differ from their mirror-images, can possess only axial symmetry. As an
axis of the second class, for which n = 2, corresponds to a “centre of symmetry”,
and one for which m= 1, corresponds to a mere mirror-plane, it becomes clear
that such “enantiomorphic”” arrangements neither possess a centre of symmetry,
nor a plane of symmetry. But the reverse statement is not true: among the
32 possible symmetrical groups of crystallography e.g. there are already (ree which
do not possess any plane of symmetry, and whose configurations, notwithstanding
that, do not differ from their mirror-images (in the cases apparently, where there
is only one axis of the second class present, with m= 2, 4 or 6 ). And there
are several groups, which have no centre of symmetry, and are however identical
with their mirror images. It can moreover be remarked here, that axes of the

» $1*

1222

$ 3. Evidently it must be considered of the highest importance

to bring in this theoretically simplest case, — that namely where
by the equality of the substitutes the “molecular dissymmetry” mani-
fests itself only by the spacial arrangement of equal things, — the

complete proof, that Pastrur’s principle is really right. It is
therefore necessary to prove not only the optical activity of the
antipodes obtained, but at the same time the ecrystallographical enan-
tiomorphism of them. It was with this purpose, that the following
investigations were made, and especially, because there are known
cases, in which notwithstanding the clearly stated optical activity,
an enantiomorpbism of the antipodes could not be proved with
certainty, as e.g. in the case of lupeol’).

According to Werner the enantiomorphism of these isomerides has
been hitherto proved only in one single case: i.e with the potassiwm-
salt of the rhodiumoralic acid: {Rho (C,O,),} K,; +1 H,O. These
crystals however being, according to that author, triclinic, they must
then evidently belong to the pedia/ class of that system, where „0
symmetry at all is present. It is moreover well-known, that a number
of substances in this class without any trace of optical activity, also
crystallise ; [ myself described a very convincing instance of this kind
some time ago with the (active diethylenediamine-diisorhodanato-
(Ae), |
(NCS), §
its stereochemical configuration must undoubtedly be considered as
a racemic compound of two enantiomorphic modifications. The occur-
rence of this triclinic-pedial symmetry is therefore no a very favour-
able circumstance for the convincing proof of the here discussed
connection ; and it thus seemed necessary to give the desired erystal-
lonomical proof in less doubtful cases and with substances showing
a higher crystallographical symmetry. In what follows it will become
clear, what has been the result of it.

chromichloride: *) {Cr C7, a substance which on account of

It may be again mentioned here, — before giving the detailed
description of our objects in the next publication, — that Werner

moreover succeeded recently in proving, that for the occurrence of
the mirror-image-isomerism, the presence of carbon-atoms .in the
molecule evidently is as little a necessary condition, as that of unsym-
metric atoms in general. He was able to obtain the antipodes of the

second class, whose number m is divisible by 4, can never be replaced by any
combination of axes of the first class with a centre of symmetry, or with a
plane of symmetry.

') EF. M. JAEGER. Zeits. f. Kryst. 44. 568. (1908).

*) EF. M. JAEGER. Zeits. f. Kryst. 89. 579. (1904).

1223

dodecamine-hewol-tetra-cobaltibromide*), whieh salt has the same type
as the triethylenediamine-cobalti-salts, but no longer possesses one
single carbon-atom.

$ 4. As suitable objects for this investigation 1 have chosen the
luteo-triethylenediamine-cobalti-salts of the type: {Co (Aein),} X,, in
which X was varied in several ways, for the purpose of elucidating
as well as possible the mere influence of the complex cation. |
prepared these salts, starting from the already obtained optically
active components of the corresponding bromide, and by making
them react in aqueous solution with the silversalts of nitric acid,
chloric acid, perchloric acid, ete., or by double decomposition with
the potassium-, or sodiumsalts of hydrojodie or rhodanie acid. The
optically active bromides themselves were obtained from the racemic
salt by means of the corresponding bromotartrates, whose dextro-
gyratory form is also described in the next paper. The great stability
of the active components, even when heated in aqueous solution,
was of preponderant importance in these experiments; an autorace-
misation does not occur in any appreciable degree.

The racemic salt was prepared by two different methods: 1.
bv starting from praseo-diethylenediamine-dichloro-cobalti-chloride :
Co (Aein),

Cl,
and 2. by starting from purpureo-pentamine-chloro-cobaltichloride :
Co oe Cl, and transforming it by boiling it, for a longer
time with ethylenediamine. This last method of preparation, described
by Prremrer’), was also followed, because the description of the
obtained salt by this author differs in some particulars from that,
given with respect to the salt obtained in the first mentioned method.
However by a more detailed comparison of the two products it was
clearly pointed out, that notwithstanding slight differences in the
external habitus of the racemic salt in the two cases, the optically active
products were perfectly identical; and that tie preparations obtained
by the two methods, must undoubtedly be considered as quite the
same. (Vid. publication II).

With respect to the isomerism ie, this can in all cases be illu-
strated for the complex cation by means of the following perspective
drawings, (fig. 1), which can be constructed immediately, starting

| Cl, and heating with a 10 °/,-solution of ethylenediamine ;

1) A. WERNER. loco cit., 3093 (1914).
2) Preirer, Ann. der Chem. 346, 59, (1906).

1224

from Werner’s well-known octahedrical arrangement of the six
equivalent coordination-places round the central cobalt-atom.

\
\

Fig. 1.

A more detailed study of the real symmetry of these spacial
arrangements, in connection with the perfectly symmetrical atomistic
configuration of the ethylenediamine-molecule itself, shows how these
complex cations are rather highly “symmetrical”; they possess the
following symmetry-elements: one bipolar ternary principal axis,
and three polar binary axes in a plane perpendicular to the ternary
axis, intersecting each other at angles of 60° (or 120°). In fig. 1
the plane of these three polar axes is drawn parallel to the face
of the octahedron, lying in the octant right- and left-above. There
is no symmetry-centre nor any symmetry-plane present in the
configuration. The symmetry deduced is the same as in erystallo-
eraphy is described as characteristic of the forms of the ¢rigonal-
trapezohedrical class, which symmetry is shown also e.g. by the
erystals of cinnabar, quartz and some camphora-species, etc. Just as
in the case of these substances, both the cations here schematically
drawn are not identical with their mirror-images, and it is for this
reason, that the salts derived occasionally occur in two modifications,
which are to each other in the relation of right- and left-handed
forms. It may be remarked that a slight indication of the trigonal
symmetry of these cations may be observed in the fact, that under
the racemic compounds the chloride and bromide, erystallising with
three water-molecules, and also the racemic nitrite, possess an appar-
ent or real trigonal symmetry (vid. paper IH). However the corre-
sponding antipodes of the bromide unhappily erystallise with two
molecules of water, while the tetragonal or rhombic symmetry of
these optically active salts, which occurs in several cases, can more-

over not be easily brought into immediate connection with the
supposition of the presence of a ternary axis in the molecules. The
trigonal symmetry of the racemic bromide moreover will appear to
be only an apparent one: these crystals are really only lamellar
intergrowths of probably monoclinic symmetry.
Furthermore it may be remarked here, that if the three equal

substitutes were not highly symmetrical, — as e.g. in the case of
NH,

a-propylenediamine: CH (CH,), — the three polar binary axes would
CH,—NH,

in fact disappear in the cations, even if the three molecules of the
base were placed in an analogous way, but that the ternary axis,
— these being of a polar nature, — would be preserved in salts
of the type: {Co (Propin),} X,. However it is by no means impossible
in this case, that one of the three substitutes was present in an
antilogous (reversed) position with respect to the other two; in that
case the cation would no longer possess any symmetry-element
whatever, and the possibility could then be foreseen, that two more
mirror-image-isomerides might on occasion occur again. Thus, if one
excludes for the present the possibility of a separation of the «-
propylenediamine itself into two antipodes, even then for salts of
the type {Co (Propin),} X, a greater number of isomerides might be
expected. It is not at all impossible, that the difficulties, which
always in our experience present themselves, if one tries to get the
salts of this type in well developed crystals, must be connected with
the fact that really here a mucture of isomeric salts is always
operated with, which of course will not erystallise as well as in
the case of a single, chemically homogeneous compound. We hope
in the future to have an opportunity, of again drawing attention
to the properties of these salts.

§ 5. The crystallographical material, collected during these investiga-
tions will be published in the next paper (IJ). The data however
with regard to the rotation of the salts studied in solution, and of
their remarkable rotation-dispersvon, may find their place here, as
they can give the right impression about the fact, that one has in
these cases in reality to deal with ““dissymmetric” compounds, as
understood in Pasrsur’s principle and to what high degree.

These experiments were made with a large Lippicu-polarimeter
from Scumipt and HAENrTsCH; it possessed a telescope-field with three

divisions, and it was combined with a spectral monochromator. By
comparison with the spectra of hydrogen and of the metals: sodium
lithium, ecaleium and thallium, the micrometerscrew of the mono-
chromator was calibrated beforehand. As luminous source a NERNST-
lamp was used; the tubes had in all experiments a length of 20 cm.

The wave-lengths are expressed in Anastrom-units (A. U.); the
molar rotation {m| was caleulated from the expression:

|mj| =a 7
in which « is the observed rotation, / the length of the tube in
em., and V is the volume of the solution in cm”, containing just
one grammolecule of the anhydrous salt. With the purpose of
avoiding too big numbers especially in the graphical representation
(fig. 2), [m|.10—!'-is everywhere given.

~The exact determination of the rotation-dispersion was in all cases
limited by the strong absorption of the redbrown or yellow solutions;
for the same reason too concentrated solutions could not be studied.

The exactness of these determinations is of course not unappreciably
less than in the case of colourless solutions; however a schematic
and fairly true expression of the dispersion was beyond doubt
obtained in this way.

It was observed moreover, how in the immediate neighbourhood
of an absorptionline, the rotation reaches a maximum value, and
then decreases very vapidly, in some cases the algebraic sign of
the rotation being even reversed. Probably the remarkable pheno-
mena of abnormal rotation-dispersion, observed by WeRNER in some
cases, among others with the trioxalo-derivatives, etc, will prove
to be in an analogous connection with the absorption-lines present
in the spectra of the solutions of these salts.

The molecular rotation-dispersion of the luteo-triethylenediamine-
cobalti-cation has an enormous value: for the sake of comparison
the corresponding curve for saccharose is reproduced in fig. 2 on
the same scale.

The temperature of the studied solutions varied from 15°—20° C.;
special experiments at 10°, 18°, 54° and 98° showed us that the
rotation does not change very appreciably with the temperature.

The results of the measurements are reproduced in the following
tables; all rotations. are calculated with respect to one gram-molecwe
of the anhydrous salts.

1227
I. Dextrogyratory Triethylenediamine-Cobalti-Bromide.

Solution A contained 0.5720 gram of the hydrated salt to 29.89
grams of water; the specific gravity at 15° C. was: 1.010.

Solution B contained 2.3669 grams of the hydrated salt in
32,56 grams of water; at 15° C the specifie gravity of the solution
was : 1.035. |

Solution Cecontained 2.0126 grams of crystallised salt to 31,49 grams
of water; the specifie weight at 15° C was : 1.026.

With solution A the limits of exact determination were given for
the wave-lengths: 6900 A.U. and 5420 A.U. respectively; with
B and C observation could only satisfactorily take place for wave-
lengths smaller than 5600 A.U.

| Observed Rotation | Molar Rotation [7] >< 10—!
Wave-lengthin es We ike AN eed Nd x
iat eae ba | BS EN NEE
| | | | | |
6750 LOT ENNE eee | 4+ 145.0 br es 4+ 164.7
6600 aaa ee oe 5.46 185.7 | + 212-4} 2217
6425 1.95 | 7.84 1.34 264.3 288.6} 306.1
6265 2.67 | 10.02| 9.44 361.9 | 368.9} 393.7
6100 3.29 | 12.97| 12.29] 445.9 | 477.5| 512.6
soio. |= 4.a7 | 16.47 | > 15:30) es | 606.4 | 638.1
5160 | 559 | 20.77 | 19.85 | 757.7 | 164.7, 827,9
5595 | 7.89 — | | 1069.4 _ |

Il. Laevogyratory Triethylenediamine-Cobalti-Bromide.

Solution A contained 0.5651 gram of crystallised salt in 25,85 grams
of water; the specific gravity at 15° C. was: 1.011.

Solution B contained 0.1239 gram of the hydrated salt in 26.08
grams of water.

Solution C contained 2.1759 grams of erystallised salt in 30.11
grams of water; the specific gravity of the solution was 1.0338 at 15° C.

Solution A allowed the passage of the light between ca. 6900 A.U.
and 5400 A.U.

Solution B between 7000 A.U. and 4850 A.U.; solution C between
6900 A.U. and 5700 A.U.

swaveclensthl

Observed Rotation

Molar Rotation [zz] > 10-1!

in AU. | i à 2 : i i
6750 er — 443 | — 126.2 Say 16s
0 i es Ie 6.36 | 216.8 — | 234.6
6425 2.37 at 8.51 | 282.3 et 313.9
6265 3.16 ae 10.23 316.4 a 311.4
UN mal ee 12.91 | 472.8 = 477.0
sory | 8.06.1) A 16.62 602.6 | — 571.0 | 613.1
5760 6.60 | 1.43 21.20 786.1 771.7 | 782.1
5505 | BBL a ee 2 1049.3 913.6 =
5420 11.95 | 2.32 ee 1423.3 1261.7 ~.
5260 ee Ehle e en 1767.4 =
5085 = en = es 2284. | en

Evidently a rational connection between the deviations of these
numbers and the degree of dilution of the aqueous solutions, can
values, used in the construction of the
owing numbers:

not be

Wave-length _

deduced.
dispersion-curve, we have thus the foll

As

Mean

Molar Rotation [zz] > 10-1!

Mean value:

in A. U.
‚ Dextrogyratory salt Laevogyratory salt |
6750 | + 1672 en Hod + 165.3
6600 206.2 | 225.7 215.9
6425 282.8 298 . 1 290.4
6265 374.0 376.9 375.4
6100 400.6 | 474.9 411.8
5910 603.1 595.6 599.3
5760 797.0 782.0 790
5595 1080 981.5 931
5420 1456 1342 1399
5260 2038 1767 1903
5085 2469 2284 2371
4920 2705 = 2705

4229

In the third column the mean values of the numbers of the second
column are mentioned; with these numbers the dispersion-curve was
drawn.

III and IV. Dewtro- and Laevogyratory Triethylenediamine-
Cobalti- Nitrate.

In an analogous way to that of both bromides, the dispersion-
curves for the other salts were drawn.

Of the dextrogyratory nitrate a solution was used, containing
0.2085 gram of the salt in 30.21 grams of water; the numbers of
the laevogyratory nitrate relate to a solution, containing 0.2534
gram of the salt in 30.52 grams of water. The specific gravity did
not differ appreciably from that of pure water.

The determinations were too uncertain for values of 2 smaller
than 5085 A.U.

| Observed Rotation ‚_ Molar Rotation: 10—1 |
Wavelengths | |
se. f= Ant en ne ] | Mean value

in A. U. | Dextrogyra- | Laevogyra- Dextrogyra- | Laevogyra- |

| tory salt | tory salt tory salt tory salt |
6600 | + 0°44 — 0°62 + 136%. | — 158% | + 147°7
Bi) 0.66 | One. WENGE Tee etnies 211.2
6265 002 [OS eae ra ee mie 279
2 a es u ended | 362.9 366.2 | 364.5
5910 1:56 0 22.80. aaa amen Ten 4105
GE OE VAS (OE ERE en 651.3 596.8 624.0
5595 2.98 dire ba Dod sms ata 121 sotd
Bao. >) ezel JON ara 1203.0 | 10830 | 1143.0
sono ets 1663.0 1447.0 | 1555.0

V and VI. Dewtro- and Laevogyratory Triethylenediamine-
Cobalti-lodide.

The numbers relate in the case of the dextrogyratory salt to a
solution, which contained 0.1775 gram of the crystallised salt
(with 1 H,O) in 30.01 grams of water ; in the case of the laevogyratory
salt, the concentration was : 0.1679 gram of salt to 30.20 grams of water.

For wave-lengths greater than 6600 A.U. and smaller than 4920
A.U., almost no light comes through the liquid.

1230

Observed Rotation | Molar Rotation: > 10—!
Wave-length, _

7 | ~ Mean value:
in A. U. Dextrogyra- | Laevogyra- Dextrogyra- Laevogyra- |

tory salt tory salt tory salt tory salt
6600 + 0°39 — | + 2114 = 21194
6425 0.50 — 0°83 271.1 216°1 | 213.6
6265 0.67 0.61 363.2 352.1 | 357.1
6100 0.86 0.82 466.2 473.3 469.7
5910 1.08 1.06 585.5 611.9 598.7
5760 1.45 1.32 786.1 762.0 | 774.0
5595 1.93 1.90 1046.0 1097.0 | 1072.0
5420 2.60 2:58 1409.0 1460.0 1435.0
5260 | SNE — | 1843.0 = 1843.0

BOBS np wle RO Fd = [> 2158.05] — 2158.0

VIE and VIII. Dewvtro- and Laevogyratory Triethylenediamine-
Cobalti- Rhodanide.

The dextrogyratory solution contained 0.2065 gram of the salt
in 30.20 grams of water; the laevogyratory in the same way : 0.2455
gram in 30.15 grams of water. For wave-lengths greater than 6600
A.U. and smaller than 5260 A.U., the measurements with the polari-
meter were no more reliable.

| Observed Rotation ' Molar Rotation: 10-1!
Wave-length | |
| a EDE Ca ate ; Mean value:
in A. U. Dextrogyra- | Laevogyra- | Dextrogyra- | Laevogyra-

| tory salt tory salt | tory salt tory salt
6425 +054 | —o76 | 41643 | — 19494 | + 1793
6265 0.81 12 246.5 286.6 266.6
6100 1.40 1.47 | 426.0 | 376.1 401.1
5910 1.56 1.98 474.7 506.6 490.7
5760 1.80 2.60 541.1 | 665.2 616.5
5595 2.18 Sade 663.4 908.3 | 781.3

5420 = 5.20 = | 1330.0 1330.0

TX and X.

The

tration; 0.1748

1650"

450"

4900

dextro-

SO 52

1231

Deatrvo- and Laevogyratory. Triethylenediamme-
Cobalti- Perchlorate.
and laevogyratory solutions had the equal concen-
oram of salt in 30.37 grams of water. They allowed

Wave-length Observed Molar
in A.U. Rotation | Rotation > 10!
ik ed ee EE RA LS
6600 — 0:24 — 21253
6425 | 0.37 327.3
6265 0.46 | 406.9
6100 0.50 | 444.1
5910 0.58 | 513.1
5760 0.84 | | 743.1
5595 1.13 | 999
5420 | 1.59 | 1407
5260 2.04 | 1804
5085 2.98, 4 Oa Wzn

© ® %
4 4
pe ES
N selves, Mars con La)

7
oa OM, i
Da Ek Arelsrintir ~
bran :

a
100 0 gam ss «eC ew om 0 MO soo 660 O1 Cf pa
a a : Angelina his Men

Fig. 2. Rotation-dispersion of the Luteo-triethylenediamine-Cobalti-salts,

1232

the passage of light between the wave-lengths 6600 A.U. and 4920
A.U. The numbers for the two components were almost the same within
the limits of experimental errors. The foregoing data are those
obtained with the laevogyratory salt: (see p. 1231)

For the sake of comparison the mean values of the molar rota-
tions of the different salts are once more reviewed in the following
table:

Molar Rotation > 10—!
Wave-length| el IEN EEN =
in A. U. |
| Bromides lodides = Nitrates Perchlorates, Rhodanides
— | !
6750 a faethe | = =
6000 Sides Aiba we ed? jage-7 |. Hersen fyi =
6425 | 290 274 211 327 179°
6265 | B75. il 357 2105 401 | 267
6100 478 | 470 shied © 444 | 401
5910 599 | 509 | Ae 515. 4 491
5760 190 | EE 624 | 743 616
5595 | 34 OTN ER SEP ae 810 | 999 781
5420 | 1399 | 1435 ho AAS bp 1207 1330
5260 | 1903 1843 | 1555 1804 wy
BOBS.) 14) BTR, 2185 = {eat ORs a =
4920 | 2705: «| — — | — | 2

From this table, and from fig. 2, one can see immediately, that
in the first place the enormous magnitude of the dispersion and the
mean shape of the dispersion-curves manifest themselves in all cases
in a quite analogous way; the predominant influence of the complex
cation being thus placed beyond doubt. This predominant influence
of the. spacial configuration of the complex ion in compounds of this
kind, was, as L have previously had an opportunity (Zeits. f. Kryst.
39, 575 (1904)) of showing, to a certainty brought to the fore by
the fact that all these complex cobalti-salts reveal close crystallo-
uomical family-relations: The probability for the assumption of an
octahedral or pseudo-octahedral arrangement of the six coordination-

1233

places round the central metal-atom, is well illustrated by the fact
that not only do most of these salts possess a high crystallographic
symmetry (vid. p.574 of the mentioned paper), but also, that in the
case of the optically active components of the triethylenediamine-
salts studied here, a rhombic or tetragonal symmetry is everywhere
found, with a mean parameter-ratio oscillating between 0,82 and
0,86.

It is however evident at the same time, that the influence of the
cation is undoubtedly varied by the presence of different anions :
Br’, J’, NO’, CLO,’ and CNS’ in the solutions; and in particular
it becomes evident, that the influence of halogen-, or halogen-con-
taining anions, will differ appreciably from that of the ions NO,’
and CNS’. This difference manifests itself very plainly in the greater
values of [mm] for the same wave-lengths, with salts of the first
group, in comparison with those of the second group.

This can most evidently be seen for those wave-lengths, for which
the measurements can be made most accurately :

ae yeti pial aes Differences Idem, for the rhodanides Differences
AD sen) for the bromides, | rid: aat: |
iodides and perchlorates: | L | &
| | |
6265 380° | 273°
| 84 | 109
6100 464 | 382 |
106 100
5910 570 | | 482
| } 189 138
5160 159 620
242 | 211
5595 1001 | 831

The question, in how far this different influence is possibly linked
directly with a not yet complete electrolytic dissociation in the
solutions, could perhaps be answered by the determination of [7 |
for infinite great dilutions; however, because of the embarrassing
absorption in the coloured solutions, the measurements are not suffi-
ciently accurate to elucidate this matter quite finally.

§ 7. Whilé now by the foregoing investigations the positive and
negative optical activity of these complex salts appears to occur
beyond all doubt, if must now be our task to investigate the
correctness of the second part of Pasteur’s conclusion also: in how
far the results of the crystallographical research is able to demon-

4934.

strate an existent connection between this optical activity of these
antipodes and their enantiomorphism ?

As will be seen in the following, it must now be considered as
a very remarkable fact, that the occurrence of enantiomorphie forms
with these antipodes, can be stated in a few cases only, while in
most of the cases studied not only could no argument be given to
make the existence of such enantiomorphism probable, but it could
be even demonstrated to be absent, as follows from the certain
occurrence of holohedrical forms in these crystals.

We are thus compelled to suppose, — in contradiction to the now
still universally accepted doctrine about the necessary connection
between the optical activity of crystals and the mere “‘axial’’-sym-
metrical molecular arrangement of their crystal-structure, — that
erystalforms can correspond to such optically active substances,
whose symmetry appears to be holohedrical; just as the reverse is
‚the case e.g. with crystals of dextro- and laevogyratory sodium-
chlorate, where the enantiomorphic molecular structures are built
up by optically active molecules.

Properly speaking, — of all the salts of this series, only in the
vases of the nitrates and of the perchlorates could it be demonstrated
beyond doubt, that a “hémiédrie non superposable” really occurred.
In all other cases it was not present, or possibly, notwithstanding
the enormous optical activity, — so feebly revealed itself, that no
rational proof of its existence could be given: on the contrary, in
the cases of the /odides and rhodanides all evidence was certainly
present in favour of a true holohedrical symmetry.

Also all experiments, made with the purpose of varying the crystal-
habitus by the admixture of other salts in the solutions, in such a
way that mere “axial’’-symmetrical crystalforms would appear, were
without any positive result as far as this problem is concerned.

The crystals of the dextro-, and laevogyratory bromides e.g.,
remained identical under the most varied circumstances : in solutions,
containing sodiumbromide for instance, more needle-shaped crystals
were obtained, which were however again the same for the two anti-
podes and evidently represented no other than holohedrical forms.

As far as our experience now goes, it would be only dogmatical,
to persevere in the doctrine of the necessary axial-symmetrical nature
of the dextro-, and laevogyratory crystals in cases like these, where no
argument could be brought in favour of that supposition, while there
are many indications just against the occurrence of enantiomorphic
forms.

1235

§ 8. If we thus review the facts here mentioned and later-on to
be demonstrated in detail, we can consider it as proved that in all
the Zuteo-triethylenediamine-cobalti-salts, — just as is foreseen by
Pastrur’s principle, — the spacial configuration in the molecules,
different from its mirror-image, is always without exception combined
with an enormous optical activity of their solutions ; that the enantio-
morphism of their erystalforms however may sometimes be revealed,
but evidently does not necessarily appear. From this fact, one may
furthermore conclude, that the optical activity of the molecules prin-
cipally seems to be determined by the “unsymmetrical” arrangement
of the substitutes, as understood by Pasreur, and that it may reach
enormous values even in those cases where such “unsymmetrically”
arranged substitutes are all chemically identical. But it appears, that
for the occurrence of the crystal-enantiomorphism, the chemical mequa-
lity of these substitutes is a very predominant factor: and from this
fact the significance of Le Ber's and van ’r Horr’s “unsymmetrical
atoms’ for the whole problem has now become somewhat more
comprehensible. |

For in the question considered evidently ‘wo influences must
properly be distinguished: «) that of the spacial configuration, which
differs from its mirror-image, independently of whether the sub-
stitutes are equal or unequal, and whether the molecule possesses
any other symmetry-elements (only axes of the first class); and
4) the greater or smaller chemical differences of the substitutes,
which are arranged in the manner, indicated sub a). The influence
sub a) appears principally to cause the phenomenon of optical
activity; that sub 6) the more or less evident enantiomorphism of
the crystalline structure, and the resulting polarity of homologous
directions in it. Evidently the case of the “unsymmetric atoms’ has
thus to be considered only as an extremely favourable opportunity
for the occurrence of the complete phenomenon, which is formulated
in Pasrgevr’s principle: here these influences are superposed, the one
upon the other, because in most cases where the circumstances
mentioned sub 6) are present, those indicated sub a) will also be
present. If the influence mentioned sub 6) is not present, but only

that sub a), — and this occurs precisely in the simple case of the
complex cobalti-salts here studied, — then the enantiomorphous

structure can be revealed eventually in the solid state, but it can
evidently also be totally absent under the simultaneous influence of
other factors. In our case the special nature of the electronegative
part (anion) of the molecule seems to belong to these special circum-
stances: for the enantiomorpbism of the crystalline structure seems
82
Proceedings Royal Acad. Amsterdam. Vol. XVII.

1236

clearly to reveal itself only in the case of those cobalti-salts whose
anions contain several ovygen-atoms. *)

It must be proved by future investigations, in how far this influence
of the oxygen-containing radicals may be considered as a general
and essential one; and if general, of what nature it actually is.

In any case it has now become clear that in the phenomenon
discovered by Pasteur, the optical activity of the molecules at the
one side, and the enantiomorphism of the crystalforms, as well as
the phenomena connected therewith regarding the pyro- and piezo-
electric properties, — do not play an equivalent role. More detailed
and more extensive investigations in this same direction will perhaps
be able to teach us more exactly than now, what share the special
configuration of the molecules really possesses for the occurrence
of each of these categories of physical phenomena.

Groningen, March 1915. Laboratory for Inorganic Chemistry

of the University.

Chemistry. — “The Allotropy of Bismuth.” 11. By Prof. Ernst COHEN.

(Communicated in the meeting of March 27, 1915).

1. In my first paper?) on this matter (published in collaboration
with Mr. A. L. Ta. Morsverp) we pointed out that bismuth can
be transformed into a second allotropic modification at 75° C., and
that this metal as it has been known up to the present is a
metastable system at ordinary temperatures, in consequence of the
marked retardation which accompanies that transformation.

2. However, the results obtained with cadmium, copper, antimony
ete. gave rise to the supposition that in this case also the previous
thermal history of the metal might have an influence on the transition
temperature, which would prove that there exist more than two
forms of bismuth.

3. Our dilatometrie measurements carried out in order to clear
up this point more fully were made in the same way as in the
experiments with cadmium *).

1) In this connection it may be remarked that such enantiomorphism as the
nitrates and perchlorates possess, could also be stated in the case of the rhombic
dithionates ((S,0,)’-ions). However the crystals of this salt contain much water
of crystallisation, and effloresce so rapidly, that no exact measurements could be
made. It is for that reason, that the salts are not described in paper IL.

2) Zeitschr. f. physik. Ghemie 85, 419 (1913).

8) Proc. 16, 485 (1913),

1237

4. After having reduced the metal (500 grms. “Wismuth Kanipaum’”)
to a fine powder, we studied its behaviour in a dilatometer. The
metal had „of undergone any previous treatment with an electrolyte.
At 70°C. there did not occur any transformation.

5. After this the bismuth was kept in contact with a solution
of potassiuin chloride (10 per cent) during 12 hours, and put again
into a dilatometer. The results are given in Table I. The values
indicated with A represent the duration of the observations (minutes),
those indicated with B the level on the millimeter scale.

TABLE I.
70°.0 || 812.0 || 909.0 || _ 96.0
wien i | 4 | PiReb li) <
PY Se at er i: arr cy: eee ea
| U
o- |.382 || o | 275 || o | t92 || 90 | 207
15 | 190 || 45 | 160} 20 | 187 || 40 | 155
32 | 64 || 65 | 120 |} 80 | 176 || 210 | 161
45 Ohe-O0 «loden hone Vos 164

|| 290

6. Comparing these measurements with those carried out formerly *)
with a preparation of different previous thermal history (see table !1)
it is evident that there exist more than two forms of bismuth.

TABLE Il.

Temperature

99-7
93.7
87.7
71.7
15.1
14.1
15

‚Duration of the ob-

Rise of the level

| servations in hours | in mm.
20 + 450
2 + 16
13 + 12
30 + 16
24 | + 10
14 | — 10
36 — 95

Whilst we found formerly (Table IT) at 81° and 90° an increase
of volume, we now find a decrease (Table I) at these temperatures.

1) Zeitschr. f. physik. Chemie 85, 419 (1915).

82

1238

7. These results are corroborated by the observations made at
96°.0 ©. (Table I); there occurs a change in the direction of motion
of the meniscus at a constant temperature.

8. I hope to report shortly on the limits of stability of the
different modifications.
Utrecht, March 1915. vAN “tT Horr-Laboratory.

Chemistry. — “The Metastability of the Metals in consequence of
Allotropy and its Significance for Chemistry, Physics, and
Technics.” IV. By Prof. Ernst Conen and Mr. W. D. Her.DERMAN.

(Communicated in the meeting of March 27, 1915).

On the necessity of redetermining the data of
Thermochemistry. 1.

1. Since our investigations as well as those of our collaborators
have proved that the metals are metastable systems in consequence
of the fact that different allotropie modifications of these substances
may be simultaneously present, we wish to consider here some
conclusions which may have an important bearing on thermochemistry.

a. Heats of Reaction.

2. The heat developed when a definite quantity of a metal reacts
with any other substance, will be a function of the previous thermal
treatment of the metal, as the relative quantities of the a-, B-, y-,....
modifications present in the metal are dependent on that treatment.

For instance, a definite quantity of cadmium (chemically pure)
formed from the molten metal and which we shall indicate by the
~ symbol M,, will develop a different quantity of heat when it combines
with any other substance than the same quantity of cadmium (M,)
will do which has been formed at ordinary temperatures by electro-
lysis of the solution of a cadmium salt.

While M, contains unknown quantities of a-, 8-, y-cadmium, M,
consists of pure y-cadmium; moreover we know to-day that the
heat of transformation (per gram atom) of y-cadmium — «-cadmium
is 739 gram calories at 18° C.’).

If, for instance, equal quantities of M, and M, are dissolved at
18° C. in equal quantities of HCl. 200H,O, the evolution of heat
which accompanies this reaction will be in maximo 739 gram calories

1) Proc. 17, 1050 (1915).

1239

higher in the case of M, than in that of M,. Such will be the ease
if M, consists entirely of a-cadmium. If B- and y-cadmium are
simultaneously present (this represents the general case) the difference
will be less than 739 gram calories per gram atom.

4. Tu. W. RicHarps and Buraess') found that the heat of reaction
between HCl. 200 H,O and cadmium which has been electrolytically
deposited, (y-cadmium) is 17200 gram calories (at 20° C) per gram
atom of the metal. In this case the error would be 4.3°/, in maximo.
But even if it should reach only a small fraction of this value it
would surpass the experimental errors, as thermochemical measurements
can be carried out to-day with a precision of some tenths of one
per cent. From this we may conclude that the presence of the
different modifications must be taken into account.

Up to the present this could not be done, so that all the heats
of reaction of the metals determined hitherto are to be considered
as fortuitous values.

5. This is also true of the figures found by Junius TuomsenN®) for
the heat of reaction ‘of cadmium with different solutions of HCI, as
he used the metal in the form of plates. The metal had been melted
and consequently contained unknown quantities of a-, ?-, y-cadmium *).

6. What has been said here concerning cadmium evidently holds
also for the other metals.

7. All thermochemical values which have been ealculated on the
basis of these erroneous values, evidently include the same errors:
they are fortuitous values.

8. The measurements of TH. W. RicHarps and Burarss, cited
above, which have been partly redetermined by E. E. SOMERMEIER ®),
indicate that the previous thermal treatment of the metal experimented
with plays a role.

As these results are not strictly comparable amongst themselves,
we shall not discuss them here.

9. The true heats of reaction of the metals, which represent

1) Journ. Americ. Chem. Soc. 32, 431, 1176 (1910).

*) Thermochemische Untersuchungen 3, 277 Leipzig (1883). Comp. Tu, W. Rrenarps
and Burgess, Journ. Americ. Chem. Soc. 32, 431 (1910).

3) Comp. our paper Zeitschr. f, physik, Chemie 89, 287 (1915),

4) Phys. Rev. (2) 1, 141 (1913).

1240

strictly defined and reproducible values are not known up to the
present; they must be determined using the pure a-, f-, y,....
modifications of the metals.

b. Latent heat of fusion.

10. If a molten metal solidifies at temperatures more or less
below its melting point, there may be formed different modifications
which remain simultaneously present after solidification. From this
we may conclude a priori that different observers will find different
values for the latent heat of fusion of that metal. These values will
be a function of the thermal history of the specimen experimented
with, this history depending on the special conditions of the experiment.

14. In other words if a definite quantity of a molten metal
solidifies. the heat effect will be a function of the quantities of the
a-, B-, y-,... modifications, which are formed during solidification.

As the heats of transformation are of the same order as the latent
heats of fusion, we may expect large differences in the case of different
observers, owing to the varying circumstances of the experiments.

For instance the latent heat of fusion of cadmium is said to be
13,7 gram calories per gram’), whilst we found’) the heat of
transformation of y-cadmium into @-cadmium to be 6.6 gram calories
per gram at 18° C.

12. Reviewing the literature, we have found indeed (comp.’
Table I p. 1241) that there exist very marked differences.

While they reach 20 per cent in the case of lead, they are as
high as 80 per cent in the case of sodium.

13. Without doubt these deviations are partly to be attributed
to the presence of impurities in the metals experimented with, while
the influence of errors of thermometry is also to be taken into
account. These errors cannot however give rise to the differences
shown in the table. We hope to report shortly on this question in
detail.

14. From what has been said above it is evident, that the latent
heats of fusion of the metals known hitherto as well as their heats
of reacton and other data calculated from these values must be
redetermined with the pure a-, 8-, y-,... modifications of the metals.

1) Ann. de chim. et de phys. (3) 24, 274 (1848).
2) Proc. 17, 1050 (1915).

1241

TABLE KE
Latent heat of Fusion in gram calories per | gram of metal.

| 8 IN AN Á a

Metal | Latent heat of fusion | Author | gr
Potassium | 15 cf JOANNIS ') |
| 13.61 BERNINI ?) | a
Lead | 5.86 RUDBERG 8) |
| 5.37 PERSON 4) | |
Dal | MAzzoTTO 5) | 20
Sie | SPRING 6) |
6.45 ROBERTSON 7) /
Sodium * | a | | JOANNIS !) .
17.75 BERNINI °) | | 80
| 21,5 | EZER GRIFFITHS 8) |
Tin 13-3 | RUDBERG 3) | \
(white) | |
| 14.25 | PERSON 4) | |
14.65 | SPRING §) |) 10
13.6 | MAzzoTTo 5) | |
| 14.05 | ROBERTSON 7) | /
| | |
Utrecht, March 1915. vAN “Tt Horr-Laboratory.
Physics. — “On the Kinetic Interpretation of the Osmotic Pressure.”

By Prof. P. Eurenrest. (Communicated by Prof. H. A. Lorentz).
(Communicated in the meeting of March 27, 1915).

The fact that the dissolved molecules of a diluted solution exert
on a semi-permeable membrane in spite of the presence of the solvent
exactly the same pressure as if they alone were present and that
in the ideal gas state — this fact is so startling that attempts have

1) Ann. de chim. et de phys. (6) 12, 381 (1887).

2) Nuov. Cim. (5) 10, 1 (1905); Physik. Zeitschr. 7, 168 (1906).
3) Pogg. Ann. 19, 133 (1830).

4) Ann. de chim. et de phys. (3) 24, 129 (1848).

5) Mem. Ist. Lombardo 16, 1 (1891).

6) Bulletin Acad, Roy. de Belg. (3) 11, 400 (1886).

7) Journ. chem. Soc. 81, 1233 (1902).

5) Proc. Roy. Soc. London 89, (A) 119, (1914).

1242

been repeatedly made to get a kinetie interpretation that was as
lucid as possible. With regard to its contents the following discussion
is closely connected with the well-known work of lL. Bo.rzmann’),
H. A. Lorentz?), O. Stern*), G. Jäcer *), and particularly that of
P: Lancevin*)*). By making use of the virial thesis and of the
remarkable property which is further on formulated by equation
(1), it is, however, possible to simplify the derivation.

Let in an infinitely extended mass of water through a closed
surface 2 a region G of the volume V be distinguished by the
following definition: let inside 2 besides the water molecules (IV )
also n sugar molecules (S,....S,...-.S,) be present, outside it
only watermolecules. The surface 2 may possess the following
properties (of a “semi-permeable membrane’): whenever the centre
of gravity of a molecule S is about to pass through &, the molecule
is perfectly elastically reflected by 2; 2 does not exert any forces
on the molecules HW’, bowever. We want to know the pressure
(osmotic pressure), which @ experiences per cm* through the collisions
of the sugar molecules.

Crausius’ virial thesis, applied only to the sugar molecules, requires
that:

OD + Srl Kmer Yay eee =O ee ee

Here

Ths Yhy 2h are the coordinates of the centre of gravity of the th
sugar molecule at an arbitrary moment 4;

X,, Yr, Zn are the resultants*) of all forces acting at the moment
ton the At sugar molecule;

L the kinetic energy of the translation of all the molecules S
added together at the moment 7.

The horizontal line expresses: taking a mean of a very long time @.

Let us now follow the A‘ molecule S during the time 4. The
force Ny, Yr. Z, on the Ath molecule is owing to three causes:

1. to the collisions on the surface 2— N;’, YM’, Zi’:

2. to the attraction and repulsion by all the other molecules
> Mae yt als

1) L. Botrzmann, Z. f. ph. Ch. 6 (1890) 474 ; 7 (1891) SS. [Wiss. Abh. N°. 93, 94].

2) H. A. Lorentz, Z, f. ph. Ch. 7 (1891) 36. |Abbandl. I, p. 175].

3) O. Stern, Z. f. ph. Ch. 81 (1912) 441.

4) G. Jäcer, Ann. de Phys. 41 (1913) 854.

5) P. Langevin, Journ. Ch. phys. 10 (1912) 524; 527.

6) Cf. also Pu. Konnsramm, These Proc. 7, 729.

7) We suppose for the sake of simplicity that the molecules are centres of force
of one dimension,

1245

5. to the attraction and repulsion by all the molecules V—_NX;",
Mn.

During the greater part of 4 the Ath molecule S is found in
volume elements far inside the region G, and only during a very
small part of 6 in the periferie volume elements of G close to the
surface 2. Let us now first direct our attention to a volume element
de dy dz far in the interior of the region (G, far from &. Repeatedly
the molecule .S; is found for a short time in this element.

In this we find that:

An Xp, Vn Va", Ze + Zi
assumes now positive, now negative values of rapidly varying
amount, and — because we are far from @, in the midst of the
homogeneous solution — equally frequently equally large positive as
negative values. Because besides X7’, Yn’, Zi’ are always zero,
it is clear that the mean contribution to the virial yielded by the
ht molecule S, i.e. S;, during its residence in an “internal” volume
element dx dy dz of the region G, is:

de dy dz{e#X,+yY,i2AJ—=0..... (1)
and likewise for every “internal” volume-element. This is no longer
the case for ““peripheric” volume elements close to the surface @.
Here in the direction of the normal to 2 the symmetry is disturbed:

1. The force exerted at the impact by 2 on the molecule Sj is
always directed inward ;

2. The joint molecules S, which act on S, all lie on one side
of 2 (the inside);

3. On account of the presence of the molecules S the concen.
tration of the water on the inside of @ is different from that on
the other side.

Let us now add the contributions yielded by all the mole-
cules S during their presence in all the ‘‘peripheric” volume elements
to the second term of the equation (A): Thus we get corresponding
to the above mentioned three kinds of forces an expression with
three terms:

yi (A7 Uh, a. % Yh + Lh Zh) = W' + w" ao Vi Aenea. (2)

If the concentration C, of the molecules decreases to zero, W'
becomes small of the same order of magnitude as Cy, on the other
hand W" and W" of higher order.

1) We draw attention to the fact, that this holds as well for repulsive as- for
attractive forces.

1244 .

It should be namely borne in mind that:
First of all all the three W’s become smaller already on account

of this that in (2) the Ni must be taken over a number of molecules

S, which decreases in direct ratio with cs.

Secondly, however, IV" decreases besides on account of this that
the forces Xa, Y;", Z|’ which a certain molecule S experiences
from all the other molecules S, decreases at the same time with the
number of the latter to zero, likewise WW", because the dijerence

of the concentrations of the molecules W on the two sides of &,

——
MI

which determines vw X", y Y", zZ", decreases to zero at the same
time with c,. For W', which arises from the collisions of the molecules
S with &, there does not exist an analogous second reason to approach
zero.
If therefore in the case of diluted solutions we contine ourselves
in equation (A) to terms of the first order in cs, we have:
AE WILOO. ien ede cp
One can now easily convince oneself that this expresses that the
dissolved molecules S exert on 2 the same pressure as when they
were only enclosed in £2 and that as an ideal gas. W' can namely
be calculated from the pressure P exerted by 2 on the sugar mole-
cules, and becomes:
pa EB IO a
Further :
RLS BRT Ae he Ge ee
when «7 is the mean kinetic energy per degree of freedom.
If we take particularly one gramme molecule of sugar, i.e. 7
equal to the Avogadro value N, and put
ND aed Be deel BAe, egies eee
(A’) passes into:
PY = nia ce ette en
Van ’r Horr’s equation for the osmotic pressure of a dilute solution.
The deviations from equation .(6) for solutions which are no
longer exceedingly diluted, have been repeatedly treated thermodyna-
mically.*) O. Sturn has tried to give a purely kinetic treatment in
analogy with the kinetic theory of non-ideal gases. *) Compare also

1) Comp. the perfectly analogous calculation for ideal gases L. Botrzmann.
Gastheorie Il, p. 143, § 50.

2) Van Laar: Z. f. phys. Ch. 15 (1894) 457; “6 Vorträge" (1906); vaN DER
Waats and Kouystamm, Lehrbuch d. Thermodynamik.
5) loc.cit.

1245

the indications given by LANGrvIN. ©) For the experimental investi-
J |

gation we may refer to Finpray ‘Der osmotische Druck” (Dres-

den 1914).

Remarks.

For the pressure on a semi-permeable membrane in the case of
very dilute solutions it is, as we see immaterial whether or no
there is interaction between the molecules S and the molecules JW.
Certain other effects of the osmotic pressure, can, however, only
be brought about in consequence of such interaction: e.g. the dif-
ference of level that comes about between the solution and the pure
water, when they are in tubes open at the top, and are in com-
munication through a semi-permeable membrane. Let us consider
the following imaginary case: The “sugar” molecules have no in-
teraction at all with the water molecules. It is clear that there
cannot ensue a difference of level -— the sugar simply evaporates
from the solution. When a glass bell-jar is put over the two commu-
nicating tubes, the following state of equilibrium is obtained: two
solutions of the same concentration on either side with an equally
high level. If the two tubes are placed each under a bell-jar of its
own, sugar-vapour is formed over the solution with a pressure of
the same value as the osmotic pressure of the solution and no diffe-
rence of level appears then either.

If the difference in level in question is to make its appearance,
none of the three following factors can, indeed, be omitted : first
the tendency of the sugar to spread (its kinetic pressure), secondly
the cohesion of the water, thirdly the interaction of the molecules
S and W, without which it would not be possible for the sugar
to lift up the water.

Mathematics. — “On Nörner’s theorem’. By Dr. W. van DER
Woupe. (Communicated by Prof. JAN bE Vries).

(Communicated in the meeting of March 27, 1915).

$ 1. Britt and Nörner’s well-known paper on algebraic functions *)
has as starting-point a theorem*) shortly before pronounced by
Nörner. Its meaning may principally be indicated as follows:
“A curve I, may be represented by the form
F,=AF, + BF,

2?) Mata. Annalen, 7 (p. 271.)
5) Math. Annalen, 6 (p. 351): “Ueber einen Satz aus der Theorie der algebrai-
schen Funktionen.”

1246

if it has a (p+q—l)-fold point in each point of intersection in which
F, possesses a p- fold and F, a q-fold-point, and if no tangents at
F, and F, coincide in the points of intersection”

After the simplest case‘), in which #, and F, have only |
points of intersection, had been treated by Nörnrer before, he gives
in the above mentioned article a proof of the general case. Further
proofs have appeared from the hands of HaArPHeN*) and Voss*). Yet
the importance of the theorem may justify the attempt made here
to deduce it once more in a most simple way.

$ 2. We understand by #, and F,, curves respectively of order
m and n, which may also be degenerate, however, not in such
a way that /, and #, possess a common divisor. We suppose that
zm oeeurs in /,, 2 in #,; further that no intersections of the two
curves are at infinity and no points of intersection are connected by
a line parallel to one of the axes of coordinates. By these suppo-
sitions which are always to be arrived at by a linear transformation
and a fit supposition of the axes, nothing is done to diminish
the universality.

The curves are represented by

Fey.) ay Sea Eef 2%), Ji ae ee
F(a, y)=b,a° +b, 4....+5=0... 2
From these two equations we find by elimination of w the resultant
DNO rn at a nd oh ee
in which
a, a, 4,--0 Cte a ds ode ea
|
Oa zere Oa ADE ENE ST
0 0 0 Gin BAO Gi Ax F,
9 (y) — =
bbs 0 OR MERK Pe
Dh bre OBD eer a
os ged Se ° Re ass S = |
000 De | 000 Ee |

1) The proof for this case occurs in J. BacuaracH’s dissertation: “Ueber Schnitt-
punktsysteme algebraischer Curven” (Erlangen 1881) and in a paper of the same
author in the Math. Annalen, 26 (p. 275).

*) Bulletin de la Société Math. de France, V (p. 160): ‘Sur un theorème
d’Algebre.”

5) Math. Annalen, 27 (p.527): ‘Ueber einen Fundamentalsatz aus der Theorie
der algebraischen Funktionen.”

The second determinant is deduced from the first by multiplying
the terms of the first column by mdr! , those of the second by

omm? and by adding them afterwards to those of the last
column. At the same time appears from this the well-known identity:
OSE ENE BA On, SY aD)

in which P and Q are of no higher order than (n—l) and (m—1) in «.

Let now /’; be an arbitrary integral function of « and y of degree
r in & (r2m, r2n); we arrange F,, #, and F, according to the
descending powers of « and divide /’, by FF, let us call ‘the
quotient q and the rest /,', then

ENDE AI MERANER)

The function /', is in 2 of no higher order than (m + n—1).

From (4) follows

EERE PB A QR 0e 8)

The terms in the second member whose degrees in « are higher
than vm +- 72 — 1) must disappear.

If we therefore divide PF, and Qs", by F,F,, after arrangement
according to the descending powers of a, the quotients will be each
other's opposites.

Hence:

Pe Re RE
QF F, =—qF.F, + SF,
By this (6) is reduced to
es sm DA en ata lay OR
in which #& and S are of no higher degree than (n—1) and (7—1) in w.

From this identity Nörner’s theorem is simply and generally to

‘be deduced.

§ 3. We suppose now provisionally that all the points of inter-
section of /’, and /’, are simple ones. Is /, =O the equation of a
curve passing through all the points of intersection of /, and /,,
the same is true according to (5) for the curve represented by /,’ = 0.
We will prove that now in the identity

Gh SS, GO Shige ea ed
the functions # and S are divisible by v.

We take for convenience sake one of the points of intersection 0
as origin of our system of coordinates, y is then a factor of g. As
falso passes through 0, off, has a node in 0; while #, and /,
possess only simple points there with different tangents. This is only
possible if # and S also pass through 0.

han |
—

1248

Further has /, apart from 0 moreover (m— 1) points of intersection
with the X-axis, which intersections do not lie on #,, so they do
on SS; in the same way the points of intersection of /, with the
X-axis lie to the number of (n—1) on R.

Now the X-axis has already n points of intersection with FR, and
m points of intersection with S all situated in the finite while R
and S are respectively of degree (n—1) and (m—1) in 2. So Rand
S are both divisible by y. We may, however, prove in the same
way that Zand S are divisible by all the other factors of #, so
that we find :

Fl 2 RR SFY fen ee

From (5) it further ensues

PSS Ag BR SS ee

§ 4. The preceding proof undergoes only a slight change if #,
and /, show contact in one or more of their points of intersection, or
possess multiple points there. We suppose in the first place that 4,
and /*, touch each other in a point 0, which we again take as
origin of the system of coordinates ; moreover that /’, too bas in
that point the same tangent / as /’, and #5,

Let us now again consider the identity

PFU RE BRK Yn) Ate eeN

If we suppose that the curves # and S do not both pass through
0, we might determine by RF, and SF, which have in 0a tangent
/ in common,- a pencil of which one of the curves A has a node
in 0; AK would however not be touched by / in that case.

For in that case A would have one point of intersection more
there with RF, or SF, than these two possess there between them.
Now ef, is a curve, however, from the pencil determined by AF, and
SF, and one of its tangents in O coincides with the common tangent
of F, and F,. Consequently R and S must pass through 0.

As in $ 3 it appears further that R and S are divisible by 4
and by all the other factors of vg. Consequently the identities (8)
and (9) remain in force.

In the same way it appears that (9) remains in force if #, and
F, have in any point contact of higher order, provided that they
show there contact of the same order with #, as well.

Let us finally suppose that in a point 0, which we again take as
origin of the system of coordinates, the curve /, possesses a p-fold,
#, a g-fold point; we provisionally suppose that /’, and F, have

1249

no common tangent in 0. /’, is supposed to pass through all the
points of intersection of /’, and /’, and to possess in Oa (p-+-g—1)-
fold point; it is to be seen at once that the curve /’,’ determined
by (5) satisfies the same requirements.

Let us again consider the identity

OF = ee eros BE NEN) ie he
The’ resultant g contains the factor y’7; PF, has no terms of a

lower degree than (p + q — 1).
Let us write the equations of #, and #, thus:

PF, =(y — ae) (y — aya)... (y — apt) + uti + ute +... + un = 0
fF, =(y — Be) y — 82)... (y — Bot) + Vga + rgpet+.--ttr=0,

in which a; = Br,

then it appears from (7) that the terms of the lowest degree in R,
must at least be of degree , those in S at least of degree p. For
if R or S were of a lower degree the terms of the lowest degree
in RI, and SF, could not neutralize eaeh other and in RF, + SF,
terms of a lower degree than (pg) must consequently occur. So
R has a q-fold, S a p-fold point in 0. R passes moreover through
all the points which /’, — to the number of (n—g) — has in
common with the X-axis apart from 0; the function R contains
therefore the factor y. At the same time y is a factor of S and so
we may divide both members of (7) by y. After that we may
however, follow the same reasoning once more and going on in
that way, prove that both members of (7) are divisible by 777.
Consequently all the factors of @ are again divisible on R and S
and in this case too we find again
i ith A AN EV UR A eR ed ae ee)

To wind up with we may suppose that /’, possesses in 0 a p-
fold point, /, a q-fold, that they have moreover in 0 at one of
the branches contact of an arbitrary order. Reasoning in the same
Way as above, we find, that even now the identity (9) remains in
force, if only #, has a (p+-q—1)-fold point in O and moreover in
0 contact with /’, and /’, of the same order as they have between
them.

Observation. We have supposed that in the points of intersection
of /, and /, neither curve has a multiple point with coinciding
tangents. Nörner has already shown how that case may be reduced
to one of those treated here.

§ 5. If F, is a curve of degree », we can observe that the

1250

curves A and B need at most be of degree (r—m) and (r—n). If
this is not the case, however, the terms of the highest degree of
AF, and BF, will cancel each other; as the terms of the highest
degree in F, and F, have no common factor, those of AF, and
BF, will be divisible by those of MM.
Let us therefore suppose
AF, =A'F,F, + A'F.
BF, =BF UF, + BIE,
in which we extend the division by /',/, only so far that the
terms of the highest degree in Af, and ALI’, have disappeared,
we have
AZS B
So we find
P =A" F,. BF,
in which A" and B" are of a lower degree than A and 5. So we
may go on till we find
F,=AOF, + BOF,
in which A© and B are at most of degree “r—m) and (r—n).

Mathematics. — “A bilinear congruence of rational twisted quintics’’.
By Professor JAN pr Vrins.

(Communicated in the meeting of March 27, 1915).

1. The base-curves of the pencils belonging to a net | &*| of cubic
surfaces form a bilinear congruence. For through an arbitrary point
passes only one curve, and an arbitrary straight line is chord of
one curve; for the involution /,*, which the net determines on that
line, has one neutral pair of points.

We shall consider the particular net, the base of which consists
of the twisted cubic o*, the straight line s and the points F,, F,, F. *)
The surfaces ®*, which connect this basis with a point P have
moreover a twisted quintic g° in common. A bilinear congruence
|9°| is therefore determined by | #*]. A plane passing through s
intersects two arbitrary surfaces of the net in two conics; of their
intersections three lie on o’, the fourth belongs to @° ; consequently
this curve has four points in common with s, is therefore rational.

The straight line s is apparently a singular quadrisecant.

The figure consisting of s, 6° and o° is, as complete intersection

') Two other particular nets | have considered in two communications placed
in volume XVI (p. 733 and p. 1186) of these ‘ Proceedings”. They determine
bilinear congruences of twisted quartics (1st and 2nd species).

1251

of two &*, of rank 36. As 6? is of rank four and 0° as rational
curve of rank eight, while s has four points in common with @?,
gv and o° will have eight points in common. We can therefore
determine the congruence [v°| as the system of rational curves 9°
passing through three fundamental points FF, F,, cutting the singular
curve 0° eight times and having s as singular quadrisecant.

It incidentally follows from this, that g° may satisfy 20 simple
conditions.

2. Let b be a bisecant of 6°, resting on s; all ® passing through
a point of 4 have this line in common, theretore determine a pencil
the base of which consists of s, 6, o* and a rational 0*, which has
three points with s six points with 0°, consequently one point in
common with 6.

There are also figures of [g°| consisting of a conic g° and a
cubic 9’. The plane ®, passing through /’, and s forms with the
ruled surface ®,’, determined by 6%, #, and /,, a ®,*. Any other
figure of [®°] intersects ®, along a conic ge,’ in the plane ®,,
passing through #, and the intersections S,“ of 60°, and a twisted
curve uv," intersecting 6* in five points C,, C,’, which are determined
by ®,°; it passes of course through #, and 4.

To the curves 0,* belong two degenerate figures each formed by
the bisecant of 6° out of one of the points C, and the conic ,*, in
which ®,° is intersected by the plane that connects the points /’,
and /’, with the other point C. Apparently p‚* and the corresponding

a

9, form a degenerate curve g°.

N

The three degenerate conics g,* as well determine degenerate
curves o*. For the straight line S,'S," is a bisecant 6; hence the

line FS," forms with the corresponding o,* a degenerate figure ¢*.

3. To the net [®*] belongs the surface >*, which has a node
in a point S of o’. This nodal surface determines with any other
surface of the net a 9°, intersecting o* in S, is therefore the locus
of the g° passing through the singular point S.

The surfaces ,* and =,* have s, o* and a 9° in common, conse-
quently one @° passes through two points S,, S, of o°. The groups
of eight points, which the curves of the congruence determine on
6° form therefore an involution of the second rank. From this ensues
that o*® is osculated by 18 curves 0°, and contains 21 pairs S,, 5,
through which oe curves g° pass. So there are 21 surfaces ®*° each
possessing fwo nodes lying on 6°,

A straight line passing through the vertex S of the monotd =* inter-

83

Proceedings Royal Acad. Amsterdam. Vol, XVII.

1252

sects the latter moreover in a point P and the plane ¢ passing
through F,, /,,/, in a point P’, which we shall consider as an
image of P. As one 9° passes through any point P, the curves of
the congruence lying on 2? are represented by a pencil of rational
curves g*. Every g* has in common with the intersection gy* of 2°
the five points, in which the corresponding 9° intersects the plane ¢ ;
the remaining seven intersections of g* with pf are base-points of
the pencil (y‘). To them belong the points /, /,, F,; the remaining
four are intersections of four straight lines lying on &*. One of them
is intersected by every 9° in S and in a point P, is therefore a
singular bisecant p of the congruence ; the involution which the oo!
curves 0° determine on it, is parabolic; so we might call p a
parabolic bisecant. The remaining three straight lines d,, d,, d, passing
through S are common trisevants of the curves 9°; on these singular
trisecants as well the involution of the points of support is special,
for each group contains the point S.

The monoid * contains moreover two straight lines passing
through S viz. the two bisecants of 65° cutting s, being consequently
component parts of two o° degenerated into a straight line 4 and a 9’.

The pencil (v*) has three double base-points D,, D,, D, and four
single base-points ZF, F,, /,; it contains six compound figures :
three figures consisting of a nodal ¢* and a straight line and three
pairs of conics.

Let us now first consider the figure formed by the straight line
D,D, and the g?, which has a nodal point in D, and passes
through the remaining six base-points. It is the image of a figure
consisting of a bisecant 4 and a rational curve 9‘; for the plane
passing through d, and d, has only one straight line in common
with 2? so that D, D, cannot be the image of a conic passing
through S. Consequently there lie on X° three straight lines 6 not
passing through S, and therefore three curves ¢* passing through S.

The conic passing through D,, D,, D,, ZE, F, is the image of the
conic 9? which the plane (fs) kas in common with 2’: the conic
to be associated to her passing through D,, D,, D,, /,, /; is the
image of the ©? forming with g? a curve of the congruence [9°].
There are apparently there figures (o°, 09°) on =’,

4. The curves 0°, meeting s in a point S* lie on the nodal
surface °, which has S* as node. The monoids =** belonging to
two points of s, have one g° in common; so the groups of four
points which the 9° have in common with s form a /,*. There are conse-
quently six e*® which osculate s, and three binodal surfaces ®* which

1253

have their nodes on xs, consequently contain oo! curves 0°, inter-
secting s in the same two points.

The 0° of the monoid }** are represented on the plane y — F’, F, FP,
by a pencil of g*, which have the intersection D of s as triple
point and pass through /,, /,, /,. The remaining base-points /,,
EK, E, of that pencil lie in the intersections of straight lines py
of the monoid, which lines meet in S* and apparently are parabolic
singular bisecants. The sixth straight line of the monoid passing
through S* is the bisecant 6 of 6°, consequently part of a de-
generate 0°.

The straight line D/’, is the image of the conic @,*, in which
the monoid is moreover intersected by the plane (s/’,); the nodal
y* completing it into a y* represents the cubic 9°, belonging to @,’.
So three figures (o’, 9’) lie on 2*.

The straight line DE, forms with the nodal cubic passing through
KE, E,, F,, F,, F, and twice through D, the image of a degenerate
0°, consisting of the straight line h in the plane (sp,) and a rational
o* passing through S*. The monoid 2* too contains therefore five

figures (Db, 9%).

5. We can now determine the order of the locus of the rational
curves of. It has s as quadruple straight line and passes thrice
through 6° ($ 3). Its intersection with a 2* consists apart from
these multiple lines of five curves 9‘, is therefore of order 33. The
rational curves 9* lie therefore on a surface of order eleven.

The section of this surface ®'' with the plane (F's) consists of
the quadruple straight line s, and parts of degenerate figures of.
To it belong in the first place the three straight lines joining /’, to
the intersections S,® of o* (§ 2); the remaining section is formed
by the two @,’ belonging to the bisecants 6 out of the points

\',C,' (§ 2). A straight line passing through /’, intersects ®'* four

times on s and has with each of the two conies 0,’ a point of
intersection not lying in /,; so five intersections lie in F. The
three fundamental points F are therefore quintuple points of DP",

In order to determine the locus of the intersection 5 of a o'
with the bisecant coupled to it, we consider on s the correspond-
ence between its intersections with 4 and eo“. Through any point
P passes one 6; to it are associated the three points Q, which of
has in common with s. In each point Q, s is intersected by four

4

curves v‘; hence four points P are associated to Q. From this it
appears that s contains seven points 4. A plane passing through s
contains three straight lines 4, consequently three points B; so the

83%

1254

points B lie on a curve B'° with septuple secant s. In the same way
it appears that 8'° meets 6? in 15 points. The surfaces *' and (b)'
have in s and o* a section of order 4+ 3 X 2X3; moreover they
have B'° in common. The remaining section of order 12 must consist
of straight lines belonging to degenerate figures 9°, each composed
of a o° and fwo straight lines 6 intersecting it. From this it ensues
that [9°] contains sie figures consisting of a twisted cubic and two
of its secants.

This result may also be formulated in this way: through three
points /;, pass 6 curves y* which intersect a given o* four times
and a straight line s twice. Such a g° intersects the ruled surface
(Dt in two points B lying outside s and o*; through these points

pass the two straight lines >, completing 9’ into a 9’.

N

6. Any straight line d having three points in common with a 0°
is a singular trisecant of the congruence. For through it passes one
®* and the remaining surfaces of the net intersect it in the triplets
of an involution. From this it ensues that the trisecants of the o°
form a congruence of order three, as a 9° is intersected in each of
its points by three trisecants. In § 3 it has been proved that any
point S of 6° also sends out three straight lines d; on these singular
trisecants, however, all the groups of the /, have the point S in
common.

Let 4 be a bisecant of a o° intersecting o*. Through it passes one
p*; the net therefore determines on 6 an involution /?, so that 6
is a singular bisecant.

Through a point P? pass four straight lines b. For the curve @%,,

which can be laid through P is projected out of # by a cone &*;
the latter has in common with o* the eight points in which 9%,

3

rests on o®. The remaining four intersections lie on edges of £*,
which have in common with o> two points not lying on o*, conse-

quently are singular bisecants.

These four straight lines 6 lie on the surface ZI, which is the
loeus of the pairs of points, which the curves of [o°] have in common
with their chords passing through the point ?. JM is apparently a
surface of order six with quadruple point P, the tangent cone of
which coincides with £*.

I’ contains s and o*, therefore has with an aroditrary o° four
points of s and eight points of o* in common; of the remaining 18
points of intersection 12 lie on the 6 chords, which 9° sends through
P, and 6 in the points /. Hence H* has three nodes Fr.

1255

With the cone £* ZH has the curve gp?’ in common; the remaining
section can only consist of straight lines. To it belong the three
parabolic bisecants Pf), and the four singular bisecants 5. From
this it ensues that the three trisecants d which ep? sends through
P are nodal lines of HI’.

For a point S of the singular curve o° the surface /7° degenerates
into the monoid +* and a cubic cone &*, formed by singular bi-
secants 6. The straight lines 5 form therefore a congruence of order
four, with singular curve o*, consequently of class nine.

7. The surface A formed by the 9%, intersecting a straight line
l, has the 9° intersecting / twice as nodal curve.

As 7 intersects every monoid ** thrice, s and 6? are triple lines
on A. The section of 4 with the plane (/'s) consists of the triple
straight line s and three conics @,’; of these, one passes through
the intersection of /, the other two are determined by the two
curves 9,° resting on /. So A is a surface of order nine, with triple
points in FF, F;.

On A’ lie 15 straight lines, 9 conies, 9 curves @* and 15 rational
curves of. For / intersects 4 bisecants b, 11 curves 9’; 3 conics
and 6 curves 9’.

A plane À passing through / intersects //" along a curve 4°; the
latter has in common with / the points, in which / is intersected by the
0°, which has / as bisecant. In each of the remaining six points À
is touched by a 9° of the congruence.

The locus of the points in which a plane p is touched by curves
0’ is therefore a curve p°. It is the curve of coincidence of the
quintuple involution, which determines |9°| on g. The intersections
S*,S,,.S,,S, of the singular lines s,o* are apparently nodes of g°.

With the surface 4’ belonging to an arbitrary straight line /, ¢"
has in those intersections 4 X 3 > 2 points in common; in each of
the remaining intersections p is touched by a @° resting on /.

The curves 9° touching p form therefore a surface D°.

A monoid 2? has in the points S*, 5, 4 >< 2 points in common
with °; on g° lie therefore the points of contact of 10 curves 9°
of the monoid. From this it ensues that s and 6° are decuple lines of d°°.

With the curve wy‘, belonging to the plane yw, #*° has, in the
four nodes of w’, 4 > 2 X 10 points in common; in each of the
remaining intersections y is touched by a 9’, which at the same
time touches the plane gy. There are consequently 100 curves o°,
touching two given planes.

The plane p bas with °°, besides the curve of contact p° to be

1256

counted twice, a curve g'* in common possessing four sextuple points
in S*, Sy. Apart from the multiple points, g° and g'* have moreover
6 x 18—4xX2%* 6 points in common; from this it ensues that
each plane is osculated by thirty curves @’.

Mathematics. — “Some particular bilinear congruences of twisted
cubics.” By Prof. JAN DE VRIES.
(Communicated in the meeting of March 27, 1915).

The bilinear congruences of twisted eubies o° may principally be
brought to two groups.') The congruences of the first group may
be produced by two pencils of ruled quadries, the bases of which
have a straight line in common; the congruences of the second
group consist of the base-curves of the pencils belonging to a net
of cubic surfaces, which have in common a fixed point and a
twisted curve of order six and genus three. Reryn’s congruence
formed by the 9° passing through five given points /;, belongs to
both groups; it may be produced by two pencils of quadratic cones;
the straight lines, connecting each of two points /,, /, with each
of the remaining four, are base-edges. We shall now consider some
other particular cases of congruences of the first group, which may
also be produced by two pencils of quadratic cones.

1. We consider the curves 9* passing through the fundamental
points F,, F,, F,, #, and having the lines s, (passing through /’)
and s, (passing through #’,) as chords. Each y* is the partial inter-
section of a quadratic cone passing through the lines (s,,/, 4,4, 7,,/,/,);
(s,, EF, FF, FF); the congruence is consequently bilinear.
Apparently s, and s, are singular bisecants. Any point S, of s, is
singular; the y* passing through S, lie on the cone of the second
pencil passing through .S,. Consequently s,, as well as s,, is a
singular straight line of order tivo.

The figures of the congruence consisting of a straight line d and
a conic d*, may be brought to four groups.

A. The straight line d,, = FF, may be combined with any d?
of the system of conies passing through /’, and F, and resting on

\) Vereroni, Rendiconti del Circolo matematico di Palermo, tomo XVI, 209—
229. In a short communication in vol. XXXVII, 259, of the Rendiconti del Ist.
Lombardo, Veneront has added to these two main types a third which by the
way may be considered as a limit case of the first type. This congruence may be
produced by a pencil of quadrics and a pencil of quartic surfaces, one surface of
which is composed of two quadrics of the first pencil. The bases of the pencils
have a straight line in common, which is nodal line for the second pencil,

1257

the three straight lines d,,,s,,s,- These curves lie on the hyper-
boloid H?, which contains the three straight lines mentioned and
the points F,,/’,').

B. The straight line /',/’,=d,, may be coupled to any d?* of
the pencil in the plane (/,s,), which has the points /,, /, and the
intersections of s, and d,, as base-points. Similar systems of degenerate
o* are determined by the straight lines d,,,d,,,d,, with pencils
lving in the planes (Ps), #5), (/35,)-

C. The transversal g, of s, and s, passing through /, may be
coupled to any d? of a pencil in the plane £, #, #F,; the base
consists of £,, #,, /, and the intersection of gs.

Analogously with this is the system determined by the transversal
g, of s,, s, through #,; the pencil lies in that case in the plane
PF,

D. In the plane F, F, Ff, a pencil (d°) is determined, the base
of which consists of the intersection S, of s, and the points /,, /,,
F,. To each d? belongs a ray d of the pencil which has #, as
vertex and is situated in the plane (/’, s,). In this system both com-
ponent parts of (d, d*) are variable.

A system analogous with this is formed by the pencil of rays in
the plane (Fs,), with vertex F,, and a (d*) in the plane #, HB

Summarising we observe that the figures d* form a locus of
degree ten. In the general congruence of the first principal group
the figures Jd? form also a surface of order ten; it does, however,
not consist, as in this case, of different figures.

2. We can now easily determine the order of the surface d
formed by the gy’, intersecting a given straight line / For that
purpose we observe that the intersection of 4 with the plane /, £, /,
must consist of figures d and d*. To this belongs in the first place
the J? of the pencil lying in this plane, which meets /; further
twice the straight line d,,, for / rests in its points of intersection
with the hyperboloid H? on two 4’; finally the two straight lines
dd, each belonging to a figure the d* of which rests on /. The
intersection with FFF, is therefore a figure of order six, passing
four times through #, and F,, thrice through #,.

The curves 9’ intersecting / consequently form a surface A", having
d,, as nodal line, passing through dd, d,,,d,, and possessing

1) The conics passing through two points and resting on three arbitrary straight
lines form a quartic surface. Here the planes #3 F, F, and #3 F, Fj contain each
a pencil of conics which cannot be taken into consideration so that their planes
fall away.

1258

quadruple points in F,, F,, triple points in F’,, F,. 4° further contains
the straight lines g,,y, and the nodal lines s,,s,; the latter arises
from the observation that / intersects two curves g° meeting >, ors,
in a point S, or S, lying on them.

The intersection of the surfaces A belonging to two straight lines
ll’ consists of: 6 curves 9%, resting on / and /’, the nodal lines
Si Ss dj, and ‘the straight: lines! dip. d, ‚does deer Gas Oe

The cubic transformation, which, in tetrahedrical coordinates is
determined by

Oi, es — 4 — Cf
transforms this congruence into the bilinear congruence of rays,
which has the images s,*,s,*, of s,,s, as directrices’). The surface
A passes in consequence of this into the ruled surface formed by
the straight lines r, which rest on _ s,*,s,* and on the curve 2°
passing through the four points # into which / is transformed. The
image of A is apparently a ruled surface of order four with nodal
lines s,*,s,*. As this, apart from the points / has six points in
common with an arbitrary curve 9° laid through those points, it is
found onee more that A must be of order six.

Now that the surface A is completely known, the characteristic
numbers of the congruence may be found in the usual way’).

In an arbritary plane ® this congruence determines a cubic
involution possessing three singular points of order two (the inter-
sections of d,,, s,, s,) and six singular points of order one (the
intersections of d,,, dy, dass dass Js, g.)- It has been more fully
described in my paper on “Cubic involutions in the plane”. *)

3. Let us now consider the congruence [g°|, which possesses
three fundamental pots F,, F,, F, and four singular bisecants
Si Sis Sos 52, Of which the first two pass through F, the other two
through /. Here too two pencils of quadratic cones that can pro-
duce it are easily pointed out, while the four straight lines s are
again singular straight lines of order two.

The degenerate figures (d, J?) now form the following groups:

A. The conic d* passes through #, and rests on the five straight
lines d,,= FF, FE, s,, 8, 53, 8, ; the locus of d? is the ruled cubie
surface L*, of which d,, is the nodal line, the second transversal ¢

') This transformation may effectively be used in the investigation of Rreys’s
congruence (see my paper in volume XI of these Proceedings, p. 84),

*) Cf. my paper in vol. XIV (p. 255) of these Proceedings,

8) These Proc, XVI, p 974 (8 6),

of the lines s being the second directrix. It is quite determined by the
lines s and the transversal out of #, via d,, and ¢.

B. In the plane (s,,s,') lies a pencil (d®), having /’, and the
intersections of s,, s, and d,, as base-points. Each of these J? forms
with d,, a figure 9’.

In the same way d,, is to be combined with a d* of a pencil
lying in the plane (s,, s,')

C. The straight line ¢ may be coupled to any conic J? passing
through 4, F,, F,, which meets ¢.

D. In the plane (/’,s,) lies a (d*), having as base-points /’,, F,
and the intersections of s,,s,'. The corresponding straight line d
passes through /’, and rests on s,'. Both component parts of (d, d®)
are variable.

In the same way each of the planes (/',s,'), (/;s,), (/,s,') contains
a pencil (d*); the corresponding pencils of rays lie in the planes
Hs,), A75), GAP

Here too the figures d° form a locus of order ten.

The intersection of the plane /’, FF, with the surface 4 now
consists of a conic (resting on /), the straight lines /’,/’, and F,/,
(belonging to figures Jd’, .intersecting / elsewhere) and the straight
line /,/',, which is a triple one, because 4* contains three d* resting
on /. The straight line / consequently determines a surface /’,
which has d,, as triple ae line, passes through d,,, d,,,/ and
possesses four nodal lines s,, 5,', 53,51; Fo, f, are quintuple points,
FP, is a triple point.

In an arbitrary plane ® this congruence determines a cubic in-
volution with one singular point of order three, four singular points
of order two, and three singular points of order one. *)

4. ie shall finally consider the Le” |, which has /’,, /’, as fun-
damental points, the straight lines s,,s,',5," and s,,s,',5," as singular
bisecants; the first three meet in F. the other three in /’,.

The straight line d,, = /',/’, is triple directrix of a ruled quartic
surface A*, which has the six straight lines s as generators. Any
plane passing through two generators intersecting on d,, intersects
4* moreover along a conic d* resting on d,, and on the straight
lines s, consequently forms a degenerate figure 9’.

In the plane (s,s,') lies a pencil (d*) having as base-points /’, and
the intersections of s,,s,',s,"; each of these curves forms a figure 9°
with a definite ray d of the plane pencil which has #, as vertex

1) It has been treated more fully in my paper quoted above (Proc. XVI, S 13).

1260

and lies in the plane (/’,s,"). Both component parts are variable.

There are apparently five more systems equivalent to this, each
determined by a pencil (d*) and a pencil (d).

The locus of the conics d° is therefore also here of order ten.

The surface A appears to be of order eight; it has d,, as quadruple
straight line, each of the six straight lines s as nodal lines. For if
the complete intersection of two surfaces A is considered, it appears
that the order w is to be found from the equation 2? — 3u — 40 =0;
hence «= 8.

In a plane ® a cubic involution possessing one singular point of
order four and six singular points of order two is determined by
this [o*|. It has been described in $ 14 of my paper quoted above.

\

Chemistry. — ‘“Hquilibria in Ternary Systems” XVIII. By Prof.
SCHREINEMAKERS.

In the previgus communications here and there some equilibria
between solid substances and vapour have been brought in discussion
already ; now we will consider some of these equilibria more in
detail. We may distinguish several cases according as /’ and G are
unary, binary or ternary phases.

I. The equilibrium /+G; F is a ternary compound, G a
ternary vapour.

The equilibrium /#’+ G is monovariant (P and 7’ constant), this
means that the vapours, which can be in equilibrium with solid F,
are represented by a curve. In order to find this curve we construct
a cone, which touches the vapourleaf of the S-surface and which
has its top in the point, representing the & of the solid substance /.
The projection of the tangent curve is the curve sought for, viz.
the saturationcurve (P and 7’ constant) of the substance £. From
this deduction it is apparent also, that this curve is circumphased
and that we cannot construct from / a tangent to it.

The equilibrium + G is determined by:

Wy

0Z, OZ,
Z, +-,(a—«,) ane + (B) Oy, = Gai ne Si (1)

When we keep P and 7’ constant in (1), it determines the vapour-
saturationcurve (P, 7’) of #. When we assume that in the vapour
the compound # is completely decomposed into its components and
that the gas-laws are true, (1) passes into:

aloga, + Blog y, + (l—a—8) log (lL—#,—y,)=C - - (8)

1261
or:
we Oo (VE Ot) Bees A ee ey
wherein C and C, are independent of P and 7. When we intro-
duce the partial vapour-tension :
Psa, Pa=y,P and Po=(1l—«,—y,) P
then (2) passes into:

alog Pa + Blog PB + (1—a—p)log Pp = C . . . . (3)
Or:
4 B plas :
Bas ai 8 fe a= (yt leus CO)

_ When we keep the temperature constant, it follows from (1)

(we) 7, -F (y¥,—8)s,] da, + [le ee, + (WB dy, =
OV, OV, .
me |" Ph (aw) Ov, + (8—y,) | dP
We call / the distance from / to a point (x, y,) of the vapour-

saturationeurve; we take d/ positive in sueh a direction that /
becomes larger. Then we have:
dl dz, dy,

l ea vof

When we substitute these values of dw, and dy, in (4) and when
we represent the coefficient of dP by AV,, we find:

Poe 1. AV,.dP
(or, + 2 (@,—@) (y,—B) 8, + (B),

Herein AV, is the increase of volume when 1 mol. solid /
sublimates into such a large quantity of vapour that the composition
does not change. It follows from (5): each point of the vapoursatu-
rationeurve moves on increase of pressure (dP>>0) away from
F (dl > 0) and on decrease of pressure (dP <0) towards F
(dl< 0). We may express this also in the following way: on
increase of pressure the vapoursaturationcurve extends itself, on
decrease of pressure it contracts.

In a similar way we find: on increase of pressure the vapour:
saturationeurve contracts, on decrease of pressure it extends.

When we keep the temperature constant and when we lower the
pressure, then the vapoursaturationcurve shall, as it contracts, reduce
itself under a definite pressure to the point #. The solid substance /’is
then in equilibrium with a vapour of the composition /’ or in other
words: the solid substance / sublimates. To every temperature 7’
consequently a definite pressure P belongs, under which /’ subli-
mates. When we draw in a P, 7-diagram the temperatures and the

(4)

(5)

corresponding sublimation-pressures, we obtain the sublimationcurve
of the substance F. [Confer for instance curve aX in fig. 3 (LID).
Previously we saw that this curve ends in the uppermost sublima-
tionpoint A; at higher temperatures viz. is formed solid #” + liquid
+ vapour. When the formation of liquid fails to make its appear-
ance, this curve may be extended of course.

Ul. The equilibrium #4 G; F is a binary compound, G is a
ternary vapour.

With the aid of the vapourleaf of the ¢-surface we find that the
vapours, which can be in equilibrium with solid #, form again a
curve. When # is a binary compound of B and C, this vapour-
saturationcurve has two terminatingpoints on side BC; the point /
is always situated between these two terminatingpoints. Therefore
we call this curve circumphased again. Consequently the binary
compound can be in equilibrium with a series of ternary vapours and
with two binary vapours, consisting of B and C. The equilibrium
is determined by (1) when we put herein a=0O. We find from
this for the vapoursaturationcurve :

Le, 7, + (y,—8) sl dz, + [7, 5, + (y,—A) 4) dy, =O . - (6)

(We find this also from (4) by putting herein a = Oand dP = 0}.
For a terminatingpoint of this curve on the side BC is #,=0 and
Lim «,7,= RT; the tangent in this terminatingpoint is conse-
quently fixed by :

(2) Ct BT + GSB og aad) + gif E
kn ae ne a

The first expression is generally applicable ; the second only when
the gas-laws hold good.

The rules mentioned sub I apply to the movement of this curve
on change of P or of 7’.

In a similar way as we have acted in I, we find also here, that at
each temperature a definite pressure exists, under which the vapour-
saturationcurve reduces itself to the point /’; this pressure is the
sublimation-pressure of the binary compound /”. Therefore we may
draw in a P,7-diagram a sublimationcurve of #.

IU. The equilibrium “+ G; F is one of the components, G is
a ternary vapour,

We find that the vapours, being in equilibrium with solid #, form
again a curve. When F is the component B, this vapoursaturation-
curve has two terminatingpoints, the one on side BA, the other on
side BC, The component B can, therefore, be in equilibrium with

du,

1268

a series of ternary and with two binary vapours. The one binary
vapour contains B and C, the other B and A. The equilibrium is
determined by (1) when we put herein «e= 0 and @='0.. The
rules mentioned above, apply again to the movement of this curve
on change of P or of 7. The same as in the case I applies to the
disappearance of the vapoursaturationcurve in point B, to the subli-
mation-pressure and to the sublimationcurve of B.

IV. The equilibrium #4 /” HG; G is a ternary vapour.
We distinguish herewith two cases, according as the solid sub-
stances together contain the three components or not.

1. F and F” contain together the three components.

The line FF’ consequently is situated within the triangle; of
course this is always the case, when one of the substances or both
are ternary compounds. It may however be also the case when both
substances are binary compounds and even when one of those is
one of the components.

The equilibrium /’-+ /” + G@ is, under a constant P and at a
constant 7. invariant; this means that at a given temperature and
under a given pressure the vapour has a fixed composition. We may
understand this also in the following way. We imagine under the
given P and at the given 7 the vapour saturationcurves of I’ and
F’ to be drawn. These: may either intersect one another or not;
they can touch one another as transition-case. When they do not
intersect one another, no vapours exist; when they intersect one
another, two vapours G, and G, exist, which may be in equilibrium
with F4 F’, both these vapours are situated on the two sides of
the line FF’. The points #,F’ and r may be situated with respect
to one another in three ways.

A. The point r is situated between / and /”; consequently the
two curves touch one another outwardly in r. Consequently the
reaction + F’ ZG may occur. When we bring / and /” into,
a space, a part of each of these substances evaporates in order to
form the vapour G. We eall this a congruent sublimation of / + 47.

B. The point /” is situated between /’ and 7; both the curves
touch one another in 7, consequently externally ; the vapoursatu-
rationcurve of / surrounds that of /#”. Consequently the reaction
Ff’ 2FAG may occur. When we bring / and £” into a space,
then, in order to form the vapour G, only a part of /” shall eva-
porate, while at the same time solid /’ is separated. In order to
obtain the equilibrium 4 + /” + G, consequently we have only to

41264

bring a sufficient quantity of / into a space. We cull this an in:
congruent sublimation of £ + 1”.

C. The point / is situated between /” and r. This case is exactly
analogous with the previous.

D. As transitioncase between A and 5 (or C) point 7 coincides
with /” (or £). We shall refer to this later.

When we lower the pressure below P,, the points of inter-
section disappear. In the case, mentioned sub A, then the two curves
are situated outside one another; the equilibria /’) + G and #” + G
then both occur in stable condition. On further decrease of P these
curves disappear; that of # under the sublimationpressure of /,
that of F’ at the sublimationpressure of 2”.

In the case B the two curves touch one another internally in 7;
further the curve of /” is surrounded by that of /. On decrease of
P both the curves contract and then two cases are imaginable.
When in the vicinity of r curve F contracts more rapidly than curve #7,
two points of intersection arise; when, however, curve /” contracts
more rapidly than curve F, curve /” happens to fall completely
within curve #. In order to show that only this latter is the case,
we apply (5) to the point of contact r of the two curves. When
we represent / by /, formula (5) is true for curve F. When we
represent /’r by /, then for curve #” a formula (5) is true, in
which /, @ and 2 are replaced by /’, @ and 6’. As the value of AV,
is very approximately the same in both the formulae, the relation
di: dl’ =U :1. follows. This means: on change of P the velocities
of the two curves in the vicinity of their point of contact are in
inverse ratio to one another, as the distances from 7 to F and Ff”.
In the case, now under consideration, (/ > //) curve /” consequently
moves in the vicinity of the point 7 more rapidly than curve /.
On increase of P consequently two points of intersection arise; on
decrease of P these points of intersection disappear and curve /”
is completely surrounded by curve /. The equilibrium # + G occurs,
therefore, in stable” condition; the equilibrium /” + G can occur
only in metastable condition.

When we lower the pressure still further, firstly curve 4” disappears
and afterwards curve /’; consequently the sublimation-point of the
substance /” is metastable. In the case A, / and /’ may both
sublimate without decomposition ; in the case B only / sublimates
without decomposition, while /” converts itself into /’+ G. |

As to the case B analogous considerations apply to the case C.

From the previous considerations among others the following can
be deduced: To each temperature 7’ belongs a definite congruent or

1265
incongruent sublimationpressure of + F’. This sublimationpressure
is higher than that of each of the substances / and 4’ separately,
independent of whether both or only one of them has a stable
sublimationpressure.

When we draw in « P,7-diagram the temperatures and the cor-
responding sublimationpressures of 4, /” and # + #”, we obtain
three curves. In fig. 1 (VII) aA is the sublimationeurve of #, a’ A’
that of ZF’ and a"D that of [+ F”. According to the previous
curve a“ must of course be situated higher than the curves aA
and a’K’. Formerly we saw that these curves terminate in A, A’
and D; when the formation of liquid fails to come, we can pursue
them further.

In the case A the curves ak, a’K’ and aD can be realised in
stable condition; for this we must bring into a space solid F, or
I” or F+ F” and we must take care that the solid substances are
not evaporated completely. In fig. 1 (VID a’A’ is situated above
ak, the reverse can of course be the case also.

In the ease 5 only the curves aA and a"D may be realised in
stable condition, for this purpose we must bring into a vacuum
F or F+ #’. When, however, we bring /” into a space, then
solid #” + vapour /” is not formed, but in more stable condition
F+ F’+ vapour. Consequently we do not determine the sublima-
tioncurve a’K’ of HF’, but that of “+ F”, therefore, curve a'D.
We would be able to determine the curve a’A’, only when the
reaction /#” > /+G failed to come. Further it is apparent that
curve a’K’ must be situated higher than aX.

Analogous considerations apply to the case Cas in the preceding
case 5.

In the transition case D we assume that 7 coincides with /.
While the cases A, B, and C may occur at a series of temperatures,
D occurs at a definite temperature only. In order to understand
this, we imagine the vapoursaturationcurves of / and ZF’, which
touch one another in a point # on the line FF’. When we change
the temperature, we must also change the pressure, in order to let
the two curves touch one another again; their point of contact 7
however, shall also get another place on the line #’/”. Consequently
on change of 7’ not only the sublimation-pressure of # + #’, but
also thé composition of the vapour r changes. As, therefore, the
point 7 shifts on change of temperature along the line FF’, it may
coincide at a definite temperature with /”. The vapoursaturation-
curve of /” is reduced in this case to the point /” and that of #
goes through the point /”. The pressure corresponding with this

1266

temperature is consequently the sublimationpressure of #7. Therefore
we find: r can coincide with /”; the equilibrium /-+ #”+G
passes then into /’+ /”-+ vapour /”. This can only be the case at
a definite temperature and under a corresponding pressure; this
pressure is the sublimation-pressure of /”.

In the P,T-diagram the sublimation-curves of / + F” and of F”
have, therefore, a point in common with one another, as the first
curve is situated generally above the second, the two curves touch
consequently one another in this point. We may express this also
in the following way: when in the concentrationdiagram the com-
mon point of contact of two vapoursaturationcurves goes through
F’, then in the P,7-diagram the sublimationcurves of /’-+- F’ and 4’
touch one another.

This point of contact divides both the curves into two parts. At
the one side of this point on the curve of + #’ congruent subli-
mation takes place and the curve of /” is stable; at the other
side of this point on the curve of /’+ #” incongruent sublimation
takes place and the curve of /” is metastable.

2. # and F” contain together two components only.

The line FF’ coincides, therefore, with one side of the triangle.
This is always the case when both the substances are components ;
it may yet also be the case when one of them or both substances
are binary compounds. The previous considerations sub IV. 1. apply
still also now, with slight changes however, which- we shall indicate
briefly. Firstly we take (at 7’ constant) a pressure, under which
the two vapoursaturationcurves intersect one another. The two curves
have, however, one point of intersection now, so that only one
equilibrium /’+ /” + G occurs. When we assume, for fixing the
ideas, that # and /” contain together the components B and C,
this point of intersection moves on decrease of pressure towards the
side BC, in order to fall on the side BC under a definite pressure
P,. As r is now a binary vapour, the equilibrium +4 FF’ + G, is
binary; P, is the sublimationpressure of #° + /”.

Although 4, /” and r are situated on a straight line, yet the
two curves do not touch one another in this point 7 in this case;
this is, as we have seen above, indeed the case when 7 is situated
within the triangle. The cases 4, B and C of IV.1. apply to the
position of the points /, ZF’ and r with respect to one another.

On further decrease of pressure the two curves contract, the
same as is described in [V.1 applies to their position with respect
to one another, the considerations given there about the sublimation-
curves remain also valid here. |

1267

It follows immediately from the direction of the tangent which
is determined by (7) that, as has been said above, the two curves do
not touch one another in the point 7 on side BC. As this direction
depends not only on y,, but also on 8, and as @ is different for
fF and #”’, the two tangents do not coincide.

V. The equilibrium /#’-+ /” + #"-+ G; G is a ternary vapour.

We may also distinguish “here two cases, according as the solid
substances contain together the three components or not.

1. F, #’ and F" are not situated on a straight line.

As the three components occur in four phases, the equilibrium is
monovariant, consequently at each temperature it exists under a
definite P only and also the vapour has a definite composition. We
ean understand this also in the following way. We imagine the
vapour saturationcurves of /, /” and #” to be drawn for any 7’ and
P; it is evident that as a maximum six points of intersection
can occur. “Now we change the pressure, while the temperature
remains constant; a definite pressure 2, will occur, under which the
three curves go through one and the same point w. Consequently
the equilibrium /+/”+/"+G occurs under a definite pressure
P, and the vapour G has then the composition uv. As each curve
intersects each of the two other curves in two points, P, is higher
than the sublimationpressure of the three pairs of liquids: MH, F4"
and /” + F'". Consequently we find: the sublimationpressure of
FHI + F" is larger than that of “+ #',F + F" and F'+ #”
and, therefore, also larger than that of /’, #’, and 2".

Now we can distinguish three cases, according to the position of
u with respect to the solid substances.

A. The reaction / + #’ + F”’ 2G occurs. When we bring;
therefore, the three substances into a space, a part of each of these
substances evaporates in order to form the vapour G. Consequently
we have a congruent sublimation of #! + /#” + F'’,

B. The reaction # + #” 2 F+ G occurs. When we bring 2°, /”
and /”’ into a space, consequently, in order to form G, only a part
of / and /” will evaporate, while at the same time solid +” is
deposited. In order to obtain the equilibrium + /” + #”’ + G,
we have, therefore, only to bring a sufficient quantity of #4 +”
into a space. Consequently we have an incongruent sublimation of
Fh 4h".

C. The reaction FV Fk’ + F’’ + G occurs. When we bring the
three solid substances into a space, then, in order to form the
vapour (, only a part of # will evaporate, while at the same

84

Proceedings Royal Acad. Amsterdam. Vol. XVII.

1268

time solid /” + F”’ is deposited. In order to obtain the equilibrium
FAP A4 FH G, consequently we have only to bring a sufficient
quantity of / into a space. We have, therefore, again a congruent
sublimation.

D. The vapour G@ is represented by a point, which is situated
with two of the solid substances on a straight line. We shall refer
to this later.

When we change the temperature, then also the sublimation-
pressure of F+ F’ + F’’ changes, consequently in a P,T-diagram
a sublimationcurve of + F’ + [’’ may be drawn. Herein the
sublimationeurve of #4 /” + F”’’ is situated higher than that of
FF, F+F” and F+ FH", that of F+ FH” higher than that
of F and F’, that of F4 /’’ higher than that of # and /”’ and
that of #” + F’ higher than that of /” and #7’. Of these seven
curves, several may represent metastable conditions. To each of
these sublimationeurves applies:

„raw
dT NN (8)

Herein AW is the heat, which must be added, AJ” the change
of volume, when a reaction occurs under a constant P and at a
constant 7’ between the phases, which are in equilibrium. When
the gas-laws are valid (8) can also be written in another form.

We can represent the sublimationcurve of £+ 4” + F”’ also in
the concentration-diagram. At change of 7’ we change viz. not only
the sublimationpressure, but also the composition of the vapour G
(point w). The point w consequently traces a curve in the concentra-
tion diagram, the sublimationcurve of /’-+ /” + F’’. With each
point of this curve a definite 7’ and P correspond.

When this curye intersects one of the sides (or its prolongation)
of the threephase-triangle FF’, the transitioncase mentioned sub D
occurs. We assume that this point of intersection w is situated on the
line FF’. Consequently a definite temperature 7’, and a definite pressnre
P, belong to this point w. When we imagine the vapoursaturation-
curves of F, F’ and F’’ to be drawn, it is apparent that those of /
and /” touch one another in the point w. Consequently the pressure
P. is the congruent or incongruent sublimation-pressure of / + #”
belonging to the temperature 7. In the P,7-diagram the sublimation-
curves of F4 PF’ + F” and F4 F’ will therefore, touch one _
another at the temperature 7. Consequently we find: when in the
concentration-diagram the sublimationcurve of F+ 4” + f’” inter-
sects the line /’/’, then in the P,7-diagram the sublimationcurves
of Ftd’ + F'' and F4 F” touch one another in the P,7-diagram,

1269

We may ‘also imagine the case that the sublimationeurve of

rth’ +r’ goes casually through the point /. We see easily
that then in the P?, 7-diagram the sublimationeurves of FHH’ //,
F+ ik’, F+ F" and F touch one another.
_ The sublimationeurve of /’-+ /” + F'' ends when a new phase
X occurs; Y can be « solid substance or a liquid. This equilibrium
IH IH FH X-+G is invariant; it exists, therefore, only at
a definite Z’ and under a definite P. In the P, 7-diagram it is con-
sequently represented by a point, the quintuple point. Five quadruple-
curves proceed from this quintuplepoint, the position of these curves
and of the threephase regions with respect to one another is fixed
by definite rules and is dependent on the position of the five phases
in the concentration-diagram. *)

2. I, F’ and F" are situated in a straight line.

We distinguish, with respect to the position of this line /’/’ /"

two cases.
_ A. The substances together contain the three components, the line
FIFE" is, therefore, situated within the components-triangle. In order
to find the vapour, which is in equilibrium with “+ 4” + F", we
may act in the following way. We represent the &s of the solid
snlistances. Jy 4E and, 2 by aly, Fi and 2) As 20k and £"
are situated on a straight line, /,, #,' and /’," are situated in a
vertical plane, but generally not on a straight line. Consequently
the equilibrium /’+ /” + F" cannot occur and of the equilibria
EKA FF’, F+ F" and #” + F" two (one) are stable and, therefore,
one (two) are metastable. Now we take a definite P and 7’; we
keep the temperature constant and we change the pressure; under
a definite pressure the points /’,, #' and #,” fall then ina straight
line, so that the equilibrium / + #” + F" occurs.

When this line is situated below the vapourleaf of the ¢-surface,
then the equilibrium /’+ /” + F" is stable; we can construct then
through this line two tangentialplanes to the vapourleaf; we call
w and v the projections of the two points of contact. These points
u and v are situated on either side of the line “’/” /'". At the assumed
temperature consequently a pressure P. = P, exists, under which
occur the equilibria: A+ HP, FHH! HG, and
RAR +R" + G,.

Generally the vapoursaturationcurves of /’, /” and /'" intersect
one another in six points; it is apparent from the previous that

IF. A. H. Scureinemakers, Die heterogenen Gleichgewichte von Baxuuis Roo-
ZEBOOM, III!, 218—248,

84°

1270

they intersect one another under the pressure P,, = P, only in two
points, viz. w and v. It follows from the intersection of these curves
that the pressure P,, = P, is greater than the sublimationpressure of
FF, EHF" and fF’ + fF".

We have seen above that at each temperature a pressure P, = P,
exists, under which the points /,, /' and /’,", fall in a straight
line. When this line is situated below the vapourleaf of the S-surface,
the equilibria: P+ F4 FPF", F+ + "+ G, and #-+ # +
+" +, oeeur in stable condition. When this line is situated
above the vapourleaf or when it intersects the vapourleaf, then the
equilibrium /’+ /’ + PF" is metastable and the equilibria “+--+ #” +
+ fF" +) are impossible. As transition-case this line touches the
vapourleaf at a definite temperature 7} and under a corresponding
pressure P,; the projection 7 of the point of contact is situated on
the line FF’ EF". The vapoursaturationeurves of F, /” and /" touch
one another at this temperature and under this pressure consequently
in the point 7. In this transitioncase the vapourpressure is P,, there-
fore, not larger but equal to the sublimationpressure of #’-+ 1”,
FA HF" and fF’ + F".

When we bring the three substances at a given temperature into
a space, then vapour is formed, the composition of which is repre-
sented by a point of the line //”F". It is apparent from this that
the equilibrium “+ /” + F"+ G, (or G,) cannot arise in this
way, unless casually the temperature 7} was chosen. Therefore, we
shall not call the pressure P?,, = P, the sublimationpressure, but the
equilibriumpressure of /’+- /’ + /'". When we bring together the
three solid phases into a space, generally, therefore, one of them
will disappear; then one of the equilibria #4 /” + G, F+F"+G
or 4’ + FF" HG is formed. Then the pressure becomes also not
the equilibrium-pressure P, = P,, but one of the lower sublimation
pressures.

We may draw the equilibrium “+ /’ + F" + G as well in
the P, 7, as in the concentrationdiagram. When we draw the com-
positions of the vapours G, and G, in the concentrationdiagram,
the points « and v trace a curve on change of 7. Definite Tand P
correspond with each point of this curve. At the temperature 7
the points « and wv coincide in the point r of the line FFF". This
point 7 divides the curve into two parts; with each point w of the
one branch viz. a point v of the other branch corresponds and
in this way, that a same 7’ and P belong to these points. Hence
it follows that along this curve in the point7, Tand P (consequently
7. and P,) are maximum or minimum.

127)
In order to examine this more in detail, we take the conditions
of equilibrium for FH FH F"-+G; they are:
rj ÒZ, ,
Fete w,) Di “Ap y
sc |

Z
iy a ee (9)

Ja
and still two of such equations wherein the magnitudes, which
relate to the solid substance /, have been replaced by those of
F’ and F". With the aid of (9) we may write them also in this
way:

„0Z, A
ER wissers (10)
vy U.

and

r

"

(c tE ead Reese 1a)

The conditions (9), one and ae are generally valid, when F,
F’ and Ff" are situated on a straight line, we have
(BB): (e— ea) = (@— 8B"): (a— a") =p. . . (12)
It follows from (10) and (11) with the aid of (12) that:
(a — e/)$+ (a —a")$4 (e’—a)f’=0. . . . (13)
This equation (18) is at the same time the condition for the
occurrence of the equilibrium #4 HF’ + HF", It is apparent from
this, therefore, as has already been found above, that the equilibria
EE HF" and F+ W+ F"+ 6 occur at the same 7 and
under the same P. From (13) follows:
dH. (o'—a)n+(e—a')y'+ (a'-—a)y" AH AW
dT — (a"—a')v + (a—a''\u'4-(a'—a)o" AV TAV
which is true as well for the equilibrium /+ /” + F" as for
P+’ HF HG. The meaning of AH, AW and AV is easily
seen. When we choose the reaction in such a way that AW is
positive, then AV may be 20. The equilibrium AH WL PL G
is fixed by (9), (10) and (14). Now we shall consider it in the
point 7: the point of intersection of the equilibrium-curve with the
line FFF". In this point:
B —B):(a a) =P): (e —e)=u. ... (14)

when we develop (9) into a series, we find:

Ky H,—y
(7, + 4s, )da, + (8, +t, dy, + (Zaar ( Se art
A

(14)

at,

+4 (- 0 Jan HED Jae, dy, + » (15)
É, R

+3 (- | Jar = 0.

ad; ad,

1272

It follows from (10) that:

aor a—a

r, tus,)de,+(s,-+ut,)dy,+ gr: +A )dP— ne Bey? dT+-
( 1 Kad 1 1 waak Jil !
- (26)

+4Cdw,°*+ Dde,dy, +3 Edy, + 0 |

We may easily calculate what is represented in (15) and (16) by

A, B, C, D and Z. R and R’ contain only terms which are in-

finitely small with respect to those, which have been written down

already. When we subtract (15) from (16) and when we put for
the sake of abbreviation:

$ r,dx,? + s,dxv,dy, +

Kh

Edit KK . 68 ye
then we find:
Vi—e vv H,—y -4.,,. K
(es =e = dP — En — ‘an ———=f" (18)
ad, gd Gr bmm’ uit,

Herein A contains only terms which are infinitely small with
respect to dP, dT, dx,*, dx, dy, and dy,”. Now between the phases
FF, F’ and G we imagine a reaction to take place, at which the
unity of quantity of vapour is generated. Let AV, be the increase
of volume, 4H, the increase of entropy at this reaction. When we
put as first approximation in (18) Rk" = 0, then follows:

AV,.dP—AH,.dT=K . RC
Hence follows with the aid of (14):
AH
Ae. == 2 AY MP AS eee

AV, is a thousand times larger than AV; consequently the
coefficient of dP is generally positive; it is apparent from (17) that
K is also positive. Therefore we find dP >O or: the pressure is

a minimum in 7, As d7’= AW dT is ze consequently the

temperature is in 7 maximum or minimum.

Now we consider the P,7-diagram. The equilibrium AHF’
is represented by a curve; as on this curve the conversion of one of
the solid substances takes place into the two others, or reversally,
we call this curve the conversion-curve. It follows from (14) that
on increase of 7’ the pressure can as well increase as decrease.
The equilibrium-curve /’-+ FH "+ G coincides with the conversion-
curve; it covers this curve, however, only partly. As the pressure
is a minimum in its terminatingpoint 7, it proceeds starting from r
towards higher pressures. Through this point r moreover go the

1273

sublimation-curves of + #”, F+ #" and #’+ 4”’. It is apparent
from (8) that these three curves do not touch one another in 7, but
they intersect one another. According to our previous considerations,
these curves, except in the point 7, are always situated below the
equilibrium-curve PH #” + #’’ HG. Further it appears that at
the one side of the point 7 two of these curves represent stable
conditions, on the other side one of these curves.

Consequently we find: in the point 7 five curves come together,
the conversion-curve (/° + #” +. F”’’)- and the equilibrium-curve
(P+ fb’ + #’’ + G) of which coincide. This last curve ends in 7;
the four other curves go through this point; the point 7 divides
these curves into two parts, the one of which represents stable con-
ditions and the other metastable conditions.

We find these results also in the following way. We may consider
the equilibrium /’-+ /” + FH G, when G is represented by a
point of FFF’, consequently it is invariant and it can be represented
in the P, 7-diagram by a point 7. Therefore, through r four triple-
curves must go, viz. the conversion-curve (/’+ PF’ + F”’) and the
sublimation-curves of /’-+ #”,F+ #" and FF’ + F’’. When we
consider stable conditions only, we may say that these curves start
all from 7 or that they end in #. The situation of these four curves
with respect to one another is fixed by a definite rule.) We may
determine the direction of these curves with the aid of the iso-
volumetric and the isentropic reaction, which can occur between
these 4 phases.*) Let the isentropical reaction be:

ON LES) Jes We rad PUN Me er (AE)
wherein one or two of the coefficients 7, m’ and n" can be negative;
in the ordinary manner we must write the phases relating to that
in the right part of the equation. As the volume of the vapour (@
is very large with respect to that of the solid substances, the reaction
will take place from the right to the left with decrease of volume.
The equilibria, which are formed at this reaction (from the right to
the left) occur consequently under higher pressures. As we, in order
to get tbe equilibrium /’+ /” + #”’, must cause the reaction to
take place from the right to the left, the conversion-curve (AH 4” 4/7’)
will go consequently always starting from * towards higher pressures.
This is in accordance with our previous considerations,

1) F. A. H. SCHREINEMAKERS, Z. f. Phys. Chem. 82 59 (1913).
F. E. CG. ScHEFFER, These Procéedings 21 446 (1912).
2) F. A. H. ScHREINEMAKERS, Die heterogenen Gleichg. von BAKHuis Roozr-
Boom, lll’, 219—220.

We may also represent the isovolumetric reaction by (21), then
the coefficients will have another value. As at the reaction from
right to left heat can as well be given out as absorbed, the equili-
brium F4 F’ +4 F”’ can, therefore, starting from r go as well towards
higher as towards lower temperatures.

Leyden, Anorg. Chem. Lab. ; (To be continued).
Chemistry. — “Action of Sunlight on the Cinnamic Acids”. By
Dr. A. W: K. pe Jone. (Communicated by Prof. P. van
ROMBURGH).

(Communicated in the meeting of March 27, 1915).

Some time ago *) | communicated that «l/o-cinnamie acid is converted
in sunlight into @-, B-truxillie acid and normal cinnamic acid.

In a communication as to this photo-action in the Recueil’) I
drew, in connexion with the progressive change of the transformation
and also because the addition of normal cinnamic to the a//o-acid
increased the quantity of g-truxillie acid, the conclusion that B-truxillie
acid was formed by the combination of one molecule of «/lo-acid
with one molecule of normal acid.

For a further study of @-truxillic acid it was of great importance
to possess larger quantities of the same.

The preparation may take place from the split off coca acids, or
from the «/lo-cinnamie acid that has been affected by sunlight.

The first process is tedious and, from a comparatively large
quantity of split off acids, it yields but a small amount of g-truxillie
acid.

In connexion herewith, attention may be called to the fact that.
commercial cinnamic acid may often contain not unappreciable
quantities of g-truxillie acid which very likely has got into it in the
preparation of the cinnamic acid from the above coca acids (both
acids possess calcium salts sparingly soluble in water). For instance,
a product called Ac. cinnamylicum puriss. D. Ap. V. contained 1.8°/,
and another labelled Ac. cinnamylicum synth. puriss 3°/, of 9-truxillie
acid, whilst in the Ae. cinnamylicum purum of the same works
occurred a trace. The g-truxillie acid, being the stronger acid, may
be readily separated from the cinnamic acid by dilute aqueous
sodium hydroxide.

*) Proc. 14, 100 (1911),

2) R. 31, 258 (1912).

1275

The second way of preparing g-truxillie acid did, however, not
seem difficult, if only a sufficient quantity of a//ocinnamic acid were
at disposal.

Owing to the researches of STOERMER*) to whom belongs the credit
-of having found an easy method for the preparation of the a//o-form
of cinnamic acid and its derivatives, it was possible to prepare the
allo-acid from cinnamic acid with the aid of sunlight. A solution
of sodium cinnamate was exposed daily in large bottles to sunlight
and after a few months the alloeinnamic acid was isolated in the
usual manner as the aniline salt. In this manner, I came, in a short
time, in possession of a fairly large quantity of a//ocinnamic acid.

As the conditions, in which the most advantageous formation of
B-truxillie acid takes place, were not yet known, it was first of all
ascertained what influence can be exerted by different factors.

For these experiments I used porcelain dishes. The a//ocinnamic
acid was dissolved and by evaporating the liquid and moving the
dish thus allowing it to spread all over the sides of the dish, the
distribution of the acid over the surface was made as even as possible.
The exposure to light took place simultaneously and for the same
length of time.

After the end of the exposure the product was treated as follows.

The acids were dissolved in dilute ammonia and this solution was
precipitated with barium chloride. After 24 hours the precipitate
was collected, washed and the g-truxillic acid liberated by means of
hydrochloric acid. The filtrate from the barium salt was acidified
with hydrochloric acid, the precipitate collected, washed and dried.
By heating with benzine the cinnamic acid was separated from the
a-truxillic acid.

It was found that the fusion of the qa//ocinnamic acid (which
readily takes place in sunlight) was prejudicial to the formation
of B-truxillie acid as it causes the acid to collect in droplets. Hence,
in the other experiments the dishes were kept cold by allowing
them to float upon water.

The size of the surface over which the acid was distributed also
exerted an influence, which will be readily understood, as a small
surface receives in the same time less light than a large one.

Also in sunlight, iu the same time, more g-truxillie acid was
formed than in diffused daylight.

The covering with a glass plate impeded the formation of 3-truxil-
lic acid.

1) Ber. 42, 4865 (1909) 44, 637 (1911).

The transformation was very much favoured by repeatedly inter-
rupting the illumination and redissolving and recrystallising the mass.

The addition of benzoic acid, a- or g-truxillie acid to the allo-
cinnamic acid (?/, gram alloacid +1 gram of the other acids) was
found to be injurious, whereas the admixture with cinnamic acid
was very advantageous. From half a gram of alloeinnamie acid
alone, 0.264. gram of g-truxillie acid was formed, whilst this quantity
of alloacid when mixed with one gram of 7-cinnamic acid had yielded
0.707 gram of 3-truxillie acid.

This result is, therefore, quite in harmony with what was found
previously.

This increased yield of 3-truxillie acid on adding normal cinnamic
acid to the alloacid was formerly explained by me by assuming that
B-truxillie acid might be formed from one molecule of ad/oacid and
one molecule of normal cinnamic acid. It is, however, obvious that
we should observe the same thing when „-einnamic acid itself was
transformed into g-truxillie acid and when the alloacid formed
B-truxillie acid indirectly over the n-cinnamic acid.

Up to the present, however, the transformation of n-cinnamic acid
into g-truxillie acid has not been observed. Riper *), CrAMICIAN and
Si.Ber ?) and also myself when following Ruser’s plan of illumination,
could not demonstrate a formation of 3-truxillie acid from 2-cinnamic
acid.

In order, however, to be able to make a choice of these two expla-
nations, the following experiment was made.

On three dishes (diameter 18 cm.) of equal size and shape were
distributed in the manner directed 1 gram of «lloacid, 1 gram of
n-cinnamie acid and '/, gram of «lloacid + '/, gram of n-cinnamic
acid, respectively. The illumination took place for two hours in sun-
light; after each half hour, however, the acids were redissolved and
recrystallised. The following quantities of «- and g-truxillie acid were
found to have formed.

a 8
1 gr. of allocinnamic acid trace 0.073
1) ers, cinnamie, acid 0.417)0, 495

er. ,, allo- +1 gr. normal cinnamic acid 0.013 _ 0193
) Ber. 35, 2908 (1902).
) Ber. 35, 4128 (1902), 46, 1564 (1913).
) The transformation of #-cinnamic acid into z-truxillie acid was first noticed
by’ J. Berrram and KürsteN [Journ. f. prakt. Chemie 51, 324 (1896) and Ber.
28 IV, 387 (1896)].

]
2

>

A second experiment similarly conducted gave a concordant result.
Hence, it appears that

a. normal cinnamic acid can yield a- as well as d-truxillie acid,

bh. the formation of g-truxillie acid takes place not primarily but
secondarily over the normal acid,

c. B-truxillie acid is not formed by the union of 1 molecule of
normal and one molecule of allocinnamic acid as was supposed
formerly. ».

It was still required to ascertain the reason why the modus
operandi applied by Rurer did not give g-truxillie acid.

According to this method the powdered cinnamic acid is spread
out in a thin layer on a sheet of paper and placed in a photogra-
phic frame.

From the results of the following experiment it will be seen that
the finely divided state of the cinnamic acid obstructs the for-
mation of 3-truxillie acid.

On sheets of paper were plotted surfaces of equal size. These
sheets were placed on enfleurage frames and on each marked space
were spread out 1 gram of cinnamic acid powdered or crystallised.
After about an hour’s exposure to light, both the powders and the
crystals were treated as stated in the following survey. In all, the
exposure occupied 5 hours.

With Without
glass covering glass covering
a B a p
Powdered 0.364 nihil 0.650 nihil
i mixing 0.260 ne 0.705 i
Crystallised in porcelain dish and
removed by scraping 0.120 0.044 0.321 0.150
Same, after being recrystallised in
the same manner each hour 0.061 0.088 0.221 0.176

The glass used as covering and derived from photographic plates
was not of uniform quality, hence the results obtained with glass
covering are not mutuaily comparable.

The powdered cinnamic acid, both with and without glass covering,
has always yielded e-truxillie acid only. From the crystals @- and p-
truxillie acid have formed in both cases.

I hope, shortly, to revert to this remarkable transformation.

1278

Botany. — “On the mutual influence of phototropic and geotropic
reactions in plants.” By Dr. C. E. B. BREMEKAMP. (Communi-
cated by Prof. F. A. F. C. Went).

(Communicated in the meeting of March 27, 1915).
§ 1. Zntroduction.

It is conceivable that part of the quantity of unilaterally incident
light which is just sufficient to cause a naked eye curvature in
etiolated Avena coleoptiles, might be replaceable by a geotropic
induction of shorter duration than the presentation time. Starting
from this supposition Mrs. C. J. Rorren— PEKELHARING ') has carried
out a number of experiments in which the seedling received both a
light- and a gravitational stimulus, either simultaneously or in rapid
succession and both lasting about two-thirds of what had been found
to be the phototropic and the geotropic presentation time. These
experiments gave uniformly negative results. Macroscopic curvatures
were never observed.

Experiments of Mad. PoLowzow’*) and of Matnunrer*) on geotropic
curvatures and of Arisz*) on phototropic ones, have shown that
after a stimulus which had no macroscopic effect, deviations from
the original position could nevertheless be demonstrated with suitable
apparatus. In this connection the results of Mrs. Rurren’s experiments
are somewhat puzzling. An obvious deduction from them would be
that light exercises an unfavourable influence on the gravitational
reaction or, alternatively, gravity on the phototropic curvature. Before
abiding by this conelusion, however, it is necessary to take another
possibility into consideration.

Statements in the literature show, that in many cases a marked
difference may be observed between the rates at which the phototropic
and the geotropie reaction processes proceed. The gravitational cur-
vature is generally visible sooner and reaches its maximum more
quickly. When therefore the two stimuli are applied simultaneously
or immediately after one another, there is every chance that the
phototropic curvature will only have reached a very small value when
the geotropic one has already passed its maximum and that, when

1) GC. J. RurreN—PeKELHARING. Untersuchungen über die Perzeption des Schwer-
kraftreizes. Recueil des Trav. Botan. Néerl. Vol. VIL 1910.

2) W. Porowzow. Untersuchungen über Reizerscheinungen bei den Pflanzen.
Jena 1909.

3) A. Mattterer. Etude sur la réaction géotropique. Bull. Soc. Vaud. Se. Nat.
XLVI. 1910. Nouvelle étude experimentale sur le géotropisme. ibidem XLVIIL. 1912.

4) W.H. Arisz. Proceedings K. Akad. v. Wet. Amsterdam. 1911.

1279

thereupon the light curvature begins to approach its maximum,
there remain only traces of the other. There can in this case be
no question of a clear reinforcement of the first reaction by the
second. On the other hand, this reinforcement may be expected to
be very pronounced, when so much time elapses between the stimuli
that both curvatures reach their maxima at the same time.

It is convincingly proved by experiments which are described
in the following section, that a complete summation does indeed
take place in this last case. Moreover the surmise was confirmed
that, when -a small light-stimulus and a geotropic induction are
applied simultaneously or in rapid succession, the geotropie
curvature reaches its maximum before the phototropic one is clearly
visible and has more or less disappeared again, when the latter has
attained its greatest value. Mrs. RurreN’s results thus find a simple
explanation.

We must, however, guard against concluding from these data
that there is no modification of the phototropic reaction, due to
gravity, or of the geotropic curvature under the influence of light.

Prerrer ') has already pointed out the possibility of such changes.
Excepting, however, certain special cases relating to plagiotropic
organs (e.g. rhizomes of Adoxa, in which case Stan. first showed
a change in the geotropic reaction under the influence of light) this
phenomenon has not been completely demonstrated. (Compare Gurrex-
BPRG*)). I have succeeded in finding several’ examples of this in
Avena seedlings. The reversal of the geotropie reaction after omni-
lateral illumination of certain duration may be put forward as a
striking case. Details and discussion relating to these phenomena are
embodied in sections 3 and 4.

§ 2. Summation of phototropic and geotropic curvatures.

After it had been found, in a number of preliminary experitnents
of which details may here be omitted, in what time light- and
gravitational curvatures, as reactions to stimuli of definite strength,
reached their maxima, I arranged the experiments in the following way.

I used for illumination a 10 candle-power Osram-lamp fed by an
storage battery, which I kept constant at 10 volts. Since this had
however drawbacks, the battery was strengthened later and the
current was kept at the desired strength by the use of an adjustable

') W. Prerrer. Planzenphysiologie. 1 Aufl. 1881, Bd. 2, p. 338.
*) H. Rrrrer von Gurrenperc. Ueber das Zusaramenwirken von Geotropismus
und Heliotropismus in parallelotropen Pflanzenteilen. Pringsheim’s Jhrb. XLY. 1908,

‘

4280

resistance. At a certain distance from the lamp were placed boxes
of Avena seedlings which were always put in such a position that
their longitudinal axis made a small angle with the direction of the
rays of light, so that the seedlings which to the number of 17 to
20 stood in each box in one row, did not shade each other. For
the geotropic stimulation the boxes were put upright on one of the
narrow sides. For further details reference must be made to the
fuller communication, which will appear later.

The apparatus was placed in a part of the laboratory greenhouse
at Utrecht fitted up as dark room, where arrangements for ventilation
and warming make it possible to carry out experiments at constant
temperature and in pure air. In this case the temperature was kept
ata? °C.

A series of experiments was generally carried out with six boxes.
Nos. 1, 2, 3, and 4 were stimulated phototropically for six or ten
seconds; No. 1 at a distance of 70 em. from the lamp, the other ones
at one metre. The geotropic stimulation of boxes 3, 4, and 5 began
50 minutes after the illumination and lasted 20 minutes (in some
series 15 min.). Box 3 was placed upright in such a way that the
side which during illumination had been in front, was now under-
neath, whilst with box 4 the front of the illumination came upper-
most; 6 had already been placed upright 20 (in other cases 15)
minutes earlier and remained 40 (or 30) in this position. Two hours
after illumination, i.e; 50 minutes after the end of the geotropic
stimulation, the light as well as the gravitational curvature had
reached its maximum; at that moment their magnitude was noted.
For this I used a method recommended by LINDNER®, in which a
lamp, placed at a sufficient distance, throws a shadow of the box
on a strip of bromide paper, stretched immediately behind. This was
later developed and preserved as protocol of the experiment. The
horizontal deviation from the apex in mm. served as a measure of
the curvature.

In order to ascertain how far the average deviation of the
17—20 seedlings in one box furnished a sufficiently reliable value,
five boxes were stimulated in the same way phototropically and
geotropically: first illuminated unilaterally for six seconds with an
intensity of 10 M.C. and then 50 minutes afterwards placed upright
and left for 20 minutes in this position. After 2*/, hours the devia-
tions in m.m. amounted to:

3.2, 3.2, 3.2, 3.3 and 3.3.

1) P. Linpner, Ber. d.d. Bot. Ges. XXXII, 4. 1914.

1281

The values found in the experiments are collected in the following
table. Each horizontal line represents a separate series. The figures
in brackets indicate the magnitude of the light stimulus in metre
candle seconds (MCS) and the duration of the gravitational stimulus
in minutes.

ARE BE er 3 Pe bellighe te aR ane

I | 2.8 (200) | 2.6 (100) | Re. 3.6 (100 +15 min) 0.8 (15 min.) 1.3 (30 min.)
IL 2.5 (120) 1.9 (60) | 1.0(60—15 min) 2.2 (60415 , ) 0.4 (15 „ }1.6(30 „)
III | 2.3(120) | 2.1 (60) * 13.2 (60415 , ) 1.0 (15 , {1.6.30 ,, )
IV | 2.7(120) | 2.5 (60) | 0.5 (60-20 , ) 3.1 (60-20 , ) 1.7(20,, )2.9(40, )
V | 2.2 (120) | 1.6 (60) —0.2 (60—20 , 12.5 (60-20 „)|1.4(20 , )2.1 (40 ,)
VI | 2.4(120) | 2.1 (60) | 1.2(60—20 , ) 3.4 (60420, ) 1.2(20, ) 2.6 (40 0)

|
2.0 (120) | 1.4 (60) |—0.2 (60—20 , ) 2.6 (60420 ,, ) 1.2 (20, )2.0(40 , )
| | | |

5

The fairly considerable divergence which sometimes occurs between
the series, is explained by the difference in length of the seedlings
used; thus those of IV were very tall, those of VIT very short; in
connection with this comparison should be made with Artsz’ data’)
for photetropie curvatures and with MaiLunrer’s detailed tables for
geotropic ones (1912 Lc.)

When the ‘experiments were taking place it could be noted that
the phototropic curvatures were often already visible before the end
of the gravitational stimulation. In those seedlings in which light-
and. gravitational curvatures acted in opposite direction, the photo-
tropic one extended already lower down, at the moment when the
geotropic one became visible at the apex, so that the coleoptile
temporarily acquired a weak S-shaped bend.

As the figures show, the curvature which arises when light and
gravity bring about deviations in the same direction, more or less
equals the sum of the curvatures which each stimulus calls forth,
when acting separately. When they act in opposition to one another,
then the resulting deviation is approximately the same as the difference
of the separate deviations. In the following table the relative figures
are once more placed side by side with the sums and differences
calculated from 2 and 5 placed between brackets after those found,

1) W‚ H. Arisz, Onderzoekingen over fototropie, Diss. Utrecht, 1914,

ae 5 4 3
yt nen Pe aha ESES
I |] 2.6 | 0.8 | 3663.4) =
Bal 10 Manet le pie 1.0 (1.5)
io) Bier Laren MA oe
v | 25 | 1.7 | 3.142) 0.5 (0.8)
Vel 5D) LIN DLD
vi | 21 | 1.2 | 3.433) 1.2 (0.9)
vit | 1.4 | 1.2 | 2.6(@.6) | —0.2 (0.2)

|

This complete ‘summation is all the more remarkable when the
figures are compared with those of the illumination with the double
amount of energy. These remain everywhere behind the summation
curvatures. We find here a confirmation of the surmise that the
phototropie curvature does not remain below a certain maximum
in consequence of increased mechanical resistance, but that in reality
under the influence of the illumination there occurs a change of
condition in the plant, whereby the phototropic curvature with increase
of the stimulus finally again diminishes and may even attain negative
values, as Crark') and Arisz*) have shown for Avena.

If the gravitational stimulus is applied immediately after illumi-
nation, then the geotropic curvature has almost completely dis-
appeared when the phototropic one reaches its maximum. A single
example will suffice to show this.

Deviations in mm. 2'/, hours after the beginning of the experiment:

1.6 (40) 1.3(40 -20min.) 1.9(40-++20 min.) ae: min.)

The maximal geotropie curvature 50 minutes after the cessation
of stimulation amounted in this case to about 1.5 mm. The small
deviation which still remains after 2'/, hours, shows itself clearly
however in the figures of 3 and 4.

In some experimental series the boxes were placed on the clinostat
before and after stimulation in order to eliminate the opposing

1) O. L. Crark. Uber negativen Phototropismus bei Avena sativa. Zeitschr. f.
Bot. V. 1913.
2) W. H. Arisz. Proceedings K. Akad. v. Wet. Amsterdam. October 1913.

1283

effect of gravity.') It is of little importance in this case whether the
stimuli are applied immediately after one another or with a certain
interval between them. The speedy falling off of the curvature as
soon as it has reached its maximum, is not observable in plants
which turn on a horizontal axis. On the other hand the phototropic
reaction goes on for so much longer than the geotropic one (a
difference of hours) that it is experimentally impossible to make the
maxima coincide. We must in this case therefore limit ourselves to
establishing that the curvature of seedlings to which both stimuli
have been applied, according as they have acted to reinforce or
counteract each other, equals the sum or the difference of the
curvatures which are shown by two groups of controls of which one
is only illuminated and the other only stimulated geotropically. This
is found to be possible at any moment, chosen arbitrarily. In the
following example the geotropic stimulation was administered 50
minutes after the phototropic and the record was made 5 hours
after the commencement of the experiment.

2 | 3 | 4 5

7.7 (100) °8.5(100 -20min)

11.1 (100--20 min.) | 3.3 (20 min.)

Since it might be considered objectionable when dealing with
such marked curvatures to take the horizontal deviation of the apex
as a measure, I have in addition determined the angle of the
curvature. For the sake of simplicity I considered the curvature as
a circular arc, to which the lines bisecting the base and the
apex — which latter at this moment has become straight again, — are
tangents. The supplement of this arc gives an idea of the distance
travelled. This amounts to:

There is here therefore also a complete summation.
The experiments which are described in this section, lead to the
following conclusion :

1) In very small curvatures, it is principally the longitudinal component which
opposes the reaction. Cf. § 4.
85
Proceedings Royal Acad. Amsterdam. Vol. XVII.

1284

The reactions to small light and gravitational stimuli do not
noticeably influence each other.

§ 3. Changes in the phototropic and geotropic reactions under the
influence of light.

Up to this point we only used unilateral illumination of fairly
slight intensity. The question now is whether other results are
obtained by the application of greater quantities of light. By changing
the duration of illumination as well as its intensity it is possible to
bring about modifications in the phototropic reaction which for our
purpose we may arrange in two different categories: 1. reversal of
the direction of the curvature and 2. change in the rate of reaction.
If we wish to know how a definite phototropic curve at its maxi-
mum extent is combined with a maximal geotropic deviation, we
have only to determine the length of time after which the maximal
light-eurve is reached and then to administer the two stimuli with such
an interval that the curvature maxima coincide.

In carrying out these experiments it is found to be quite imma-
terial whether we are concerned with a positive phototropic curvature
or one in the opposite direction and whether the maximum is reached
after a shorter or longer time. Summation always takes place.

This is, however, not the end of the process. If, after stimulation,
the seedlings are placed on the clinostat and observation is continued
for a considerable time, then one begins to note deviations, at least
when there has not been too great an interval of time between the
two stimulations. By summation of curvatures of the same direction
apex curvatures finally occur in opposite direction and seedlings in
which opposite curvatures have been induced, sometimes show
stronger curvatures.

The same phenomenon was to be observed when unilateral was
replaced by omnilateral illumination.

During illumination which in different experiments was varied in
strength as well as in duration, the seedlings were rotated at constant
velocity round their axis. When illumination ceased, they were imme-
diately placed in a horizontal position and stimulated geotropically
for some time.

Already in the first series of experiments differences were obvious.
The distance from the Osram lamp of 10 candle power amounted in
this case to 2 metres. The times of illumination are in the following table
placed in the top line, with the product of intensity and duration
in metre-candle-seconds (M.C.S.) placed between brackets. The last
box was not illuminated beforehand. The geotropic induction lasted

1285

20 minutes. Examination took place 55 minutes after its end. As
in the former section the horizontal deviation of the apex in mm.
is given as a measure of the curvature.

rn

| | |
| ! min. (150) 30sec. 5), =
EE Sey ee eee ee ee ae

20 min. (3000) ,10 min. (1500) 5 min. (750) 2.5 min. (375)
| |

0.5 yy EA | dere LD Bd SLA 1.4
| |

These figures were contirmed in different series of experiments.
In these it was further noticed that the curvatures arose every where
at the same time and at first also increased at the same rate.

Thus further observations were suggested with the object of seeing
to what these differences arising in the course of the curvature-
process might lead.

In the following table the magnitude of curvature after 40 minutes
and after 2 bours are placed side by side.

Curvature

Duration of Strength of

illumination | illumination ent On After 40/ Aster 2 Ben
Boden Me ishet 750 | os | —0.9 (0.1)
150 eran ME 375 RE en ACN
180 ,„ ijs LMG | 22.5 20e | =
0, nen MIE Sel 11.25 Shits Ed

Not illuminated | | anda 0 OLA)

The duration of the geotropic stimulation amounted to 380 min.
Seedlings which were illuminated beforehand. with 750 and 375
M.C.S., showed a clear S-shape after 2 hours. The apex of those
that were not illuminated, was quite straight. The figures given are
the apex-curvatures. Placed after in brackets are the figures which
indicate the amount of the remainder of the original curvature,
calculated on the assumption that the apex was straight. The anta-
gonistic geotropic curvature was not yet measurable as is shown
by the last line. The curvatures of the previously illuminated seed-
lings cannot therefore be ascribed to this cause. Experiments in
which, after the cessation of geotropic stimulations, plants were
placed on the ¢linostat, have indeed convincingly proved that without

. 8

1286

the unilateral opposition of gravity, curvatures arise in a contrary
direction in plants previously illuminated omnilaterally.

These experiments can be simplified by illuminating the seedlings
from above instead of making them perform a certain number of
revolutions during illumination. This has been done in all subsequent
experiments. The quantity of light is again given in M.C.S. ; in con-
nection with this it should be remembered that it of course makes
a difference to the plant whether the uppermost part of the apex
only is constantly exposed to the light or whether successively the
whole surface. Further, another sort of incandescent lamp was used
in these experiments.

Geotropic stimulation lasted 380 minutes. After this removal to
the clinostat. Examination 3’/, hours after the completion of stimulation.

Duration of Strength of Product MCS

illumination illumination | Curvature
16 min. SME: wl 4000 ke
4 „ 8 MC 1000 ek
ier 8 MC 250 + 0.7
15 sec. 8 MC 60 | Eel 3
= — — EEK:

In other experiments the duration of the geotropic stimulation was _
changed, e. g.:

Time of illumination 20 min., strength 8 M.C., product 5000 M.C.S.

Horizontal during

40 min. 20 min. 10 min 5 min.

_

|

|
—09 —25 — 2,0 | — 1.8 (3 hoars on the cli«

nostat).

As is seen, the result is only slightly dependent on the duration
of the geotropic stimulation.

The fact that in 40 min. a great deviation is observed, is undoubt-
edly connected with the fairly rapid cessation of the influence of
preliminary illumination. When half-an-hour is allowed to elapse
between illumination and geotropic stimulation, the influence of the
first factor can no longer be demonstrated with certainty. This
result is in remarkable agreement with the rapid disappearance of the

1287

phototropic change of sensitiveness after preliminary illumination
(Arisz 1914 le. “fading of the excitation’).

CrarK |. ¢. has described experiments in which a unilateral geo-
tropic stimulation was followed by omnilateral illumination. Under
these conditions also there occurs a curvature in contrary direction.
With regard to the nature of the curvature which arises, it is difficult
to form a definite judgment by this method of experimentation,
because the geotropic stimulation induces a dorsiventrality (as vet
not outwardly visible). A dorsiventral organ can, however, quite
easily react to an omnilaterally symmetrical stimulus with a curva-
ture of definite direction. In connection with the experiments
described above it is however indeed probable that the curvatures
mentioned by Crark correspond to those observed in the present
investigation.

May we now regard these curvatures as positively geotropic? Before
answering this question, we may briefly examine the curvatures of
opposite direction which arise in other cases and consider whether
it is possible to form a simple conception of the way in which they
arise. I have chosen Avena coleoptiles for a further analysis, because
in their case inverse phototropic curvatures are very easily obtainable.

In Arisz’ experiments (I. e. 1914), in which the seedlings were
given an omnilateral preliminary illumination of varying duration,
it was found that the sensitiveness rapidly diminished at the beginning,
and after more prolonged illumination increased again somewhat.

If the intensity of illumination was also varied, then the initial
decrease in sensitiveness was seen to take place more rapidly accord-
ing as the seedlings were exposed to stronger light, whilst the
return of sensitiveness was thereby slightly delayed. Since when
illumination is unilateral the front absorbs part of the light, the
back receives less light. The consequence of this is that there the sen-
sitiveness during illumination declines less markedly than in the front.
When therefore after some time the sensitiveness of the front has
more or less disappeared, the reaction of the posterior side can pre-
dominate. The result must then be a curvature away from the
source of light.

In order to find out whether the here postulated differences in
sensitiveness of the anterior and posterior sides can actually be
observed, I have made a series of experiments in which three groups
of boxes were always compared. The first group consisted of one
box, the other two of from four to eight. The experiment began
with an equally long and equally strong unilateral illumination of
all the boxes. Afterwards the box of the first group was placed in

1288

the dark and those of the other two groups stimulated again with
different quantities of light, one group from the same side as before,
the other from the opposite side. Finally, the curvatures obtained
were compared. In this way I succeeded in showing that after a
unilateral illumination sometimes important differences in sensitiveness
of the posterior and the anterior sides occur. These are greatest in the
neighbourhood in which the negative curvature begins to arise.
Further data on this point will be published later.

We arrive therefore at the conclusion that the curvature away
from the source of light arises, because the sensitiveness of the
anterior side diminishes more quickly than that of the posterior and
consequently the reaction predominates at the back.

This leads us further to deny the possibility of any direct com-
parison of this curvature with the negative phototropic reaction of roots
which is not preceded by a positive one’) and remains on continued
illumination. We ought therefore henceforth to distinguish the cur-
vatures of contrary direction which occur in Avena coleoptiles by
another name. They may be called antiphototropic.

Is it now possible to explain in the same way the contrary
curvatures which arise when coleoptiles of Avena are stimulated
geotropically after preliminary -omnilateral illumination and the negative
geotropic curvatures which Josr and Miss Srorrper *) were able to
observe in roots of Lupinus albus which were exposed to high
centrifugal forces? Evidently not. The difference of pressure must
always be the same in the cells of the upper and lower side. A

1) K. Linspaver and V. Vouk. (Zur Kenntnis des Heliotropismus der Wurzeln.
Vorl. Mitteilung. Ber. d. d. bot. Ges. Bd. 27. 1909) have stated that in roots
of Sinapis alba and Raphanus sativa small iatensities of light cause positive
curvatures and greater intensities negative ones. Vouk has described these experi-
ments somewhat more fully (Zur Kenntnis des Phototropismus der Wurzeln.
Sitzungsber. d. K. K. Akad. d. Wiss. zu Wien Bd. 121. Abt. J. 1912). It results
from this that the positive phototropic curvatures which these investigators observed
in Sinapis alba, arose when there was illumination for 15 hours with an intensity
of 0.64M.C.; therefore by a quantity of light of 34.560 M.C.S. Vouk on page 503
gives a table, in which are found different examples of illumination with 128 M.G.
during 5 minutes, by which means a quantity of light amounting to 38.400 M.G.S.
was applied. The occurrence of a positive curvature is nowhere mentioned. Moreover
with illumination lasting 2 minutes no positive curvature arose either. This discre-
pancy permits us to doubt the phototropie nature of the curvatures found. It is
moreover quite unintelligible why even in the most favourable case not more than
119/, of the roots reacted in this manner.

*) L. Jost und R. Stopper. Studien über Geotropismus Il, Zeitschr. für Bot. Bd,
IV. 1912.

1289

direct reversal of the reaction would only be possible through a
reversal of the polarity of the cells, a hypothesis far from simple and
hitherto not susceptible of experimental verification. For this reason
I may direct attention to another possibility.

In the cells which are given preliminary illumination, phototropic
reactions are in progress which cannot lead to curvatures, because
they keep each other in equilibrium. In consequence of the geotropic
stimulation this equilibrium is now upset. It might be imagined, for
example, that the geotropic stimulation displaces or destroys a
substance necessary for the pbototropie reaction. The resulting cur-
vature would in reality therefore be phototropie. It is not impossible
that also in the experiments of Jost and Miss Stopper an omnilateral
stimulation (perhaps hydrotropic) thus expresses itself as a curvature.

§ 4. Changes of the geotropie and phototropic reactions

under the influence of gravity.

‘According to Martr-MarrHe Risz *) an omnilateral gravitational
stimulus has no effect on the sensitiveness with respect to a subse-
quent unilateral one. From the data in the second part of her paper,
however, one may deduce that this is not correct. For Miss Risz
there proves, that the component of gravity in the direction of the
organ?) weakens the reaction. After an omnilateral gravitational
stimulus acting at an angle of 90° and having therefore a longitudinal
component equal to 0, the reaction must be stronger than when the
plant is placed vertically for the stimulation (longitudinal compo-
nent + me.). This was indeed the case in my own experiments.

Some boxes rotated for a certain time round the horizontal axis
of the clinostat and were subsequently subjected to a unilateral
gravitational stimulus simultaneously with a control box. I examined
the curvatures forty minutes after the end of stimulation.

Differences such as those found here, are also observable when
the boxes are placed for some time in the reverse position (longi-
tudinal component — mg.)

Duration of unilateral geotropic stimulus 30 minutes.

Previously placed on the clinostat during.

1) Marie-Martue Risz. Uber den Einflusz allseitig und in der Längsrichtung
wirkender Schwerkraft auf Wurzeln. Jhrb. f. wiss. Bot. LI. 1913.

2) | already pointed out in 1912 the importance of this component. Die
rotierende Nutation und der Geotropismus der Windepflanzen. Rec. d. Tray. Bot.

Néerl. IX. p. 298—301.

2 hours 1 hour ', hour | Control
— 25 22 Bl
1.7 LY 1.8 15
7 Aa | — — 2.3

Much more distinct differences oecur when transverse and longi-
tudinal gravitational stimuli are applied simultaneously. A slight
modification of Miss Risz’ procedure enables us to demonstrate also
the influence of the longitudinal component, when the latter has a
negative value. With this object two boxes are placed parallel to
the vertical axis of the centrifuge so that the seedlings in one box
have their apices turned towards the axis, in the other away from
it. If now such a revolution-velocity is given to the axis as to apply
to the seedlings a force mg. then the longitudinal component for
the first box is + mg. and for the second — mg. Furthermore gravity
acts on the seedlings at the same time. After centrifuging the boxes
were again placed in their original position. A box which for the
same length of time had been horizontal, served as control, since
in this ease the longitudinal component is 0.

With a stimulation of 30 minutes the curvatures were 40 minutes
after its cessation :

2.9 1.6 0.2
3.4 1.5 0.3
ST La ie ep 0.9

If a unilateral light-stimulus is applied after an omnilateral gravi-
tational stimulus, then similar differences can be observed.

For this the boxes are again placed on the centrifuge, whose axis
After 30 minutes centrifuging the seedlings
are illuminated during 6 seconds with an intensity of 10 M.C. The

this time is horizontal.

control box, which remained in its ordinary position, was naturally
subjected to the same conditions as the seedlings on the centrifuge,
which had their apices pointing towards the axis. In both eases the
longitudinal component was + mg.

1291

After 2 hours the curvatures amounted to:

User C | 4 mg
|
|

|

2.5 | 1.5 1.5

The influence of the longitudinal component is therefore once more
evident.

The term longitudinal component of gravity is of course only a
phrase. No way of explaining it physiologically has so far beer found.

The phototropic curvatures of the coleoptiles of Avena when
illuminated at different angles, showed a very marked deviation from
the expected sine relation. As Arisz (l.c. 1914) has justly argued,
the paraboloid shape of the apex must be a very important factor
in this connection. SN

In geotropie reactions another factor must also be taken into
account, namely, the polarisation of separate cells.

It is generally assumed that a difference exists in the sensitiveness
to pressure of the protoplasm lining the inner and the outer walls
of the cells. The idea that there may be a similar difference of
sensitiveness between the apical and basal part of each cell, may
therefore not be summarily rejected. In this way the longitudinal!
component can also be explained. In the rotating apices of climbing
plants where I could establish its influence on growth as well as on
the nature of geotropie curvature, this is probably the right conception.
The paraboloid vegetation point of a stem which bents at its end
like a hook, may here take up any sort of position and hardly
deserves consideration in connection with gravitational stimuli.

Utrecht, March 1915. Botanical Laboratory.

Astronomy. — “On the mean radius of the earth, the intensity
of gravity, and the moon’s parallax. By Prof. W. De Sirrer.

1. Newcoms has more than once‘) pointed out that the mean
radius of the earth is more appropriate for use as a standard of
reference, than the equatorial radius, which is always used in

astronomical practice. The mean radius in fact, which — if we
neglect quantities of the second order in the compression — is also

the mean radius of curvature, is more nearly the quantity actually

1) Researches on the motion of the moon, second paper, page 41
Tables of the sun, page 12, footnote.

1292

determined by geodetic measures, which are practically all made in
mean latitudes.

The several definitions of the mean radius’) are identical to the
first order of the compression ¢. I adopt as mean radius the radius
at the geographical latitude whose sine is V/1/,, and which is given
by the formula

7, bl 4 ee eS EREN gee

Hetmert has recently *) collected the following determinations of
b, from which I derive the value of 7, by means of the corresponding
value of «.

1. From four European ares, all reduced with Besser’s €! = 299.15.

h = 6378150 f= Garvie
2. From ares in India and South-Africa, reduced with e—! = 298.3.
b = 6378332 r, == 6371237

3. From the geodetic measures in the United States, reduced with
el A06 00:
h = 6378388 r, = 6371268
It will be seen that the agreement of the several values of 7, is
much better than of 5.

Combining these values of +, with the weights assigned by HELMERT
to the corresponding values of 4, we find

r=6871287 +49... U

N
The mean error has been derived from the residuals. If the values
of h are combined in the same way we find from the residuals the
mean error + 66.

2. A similar reasoning applies to the acceleration of gravity.
HELMERT *) finds
g = 9.78080 {1 + 0.005302 sin? p — 0.000007 sin? 2g}.

1) Hetmert, Höhere Geodäsie, 1, pages 64—68.

2) Geoid und Erdellipsoid. Zeitschr. der Ges. für Erdkunde, 1913, page 17.

5) Eneyelopädie der Math. Wiss.; Band VI. 1 B, Heft 2, page 95. The alternative
formula given there, viz.:

g = 9.78028 $1 + 0.005800 sin? g — 0.000002 sin? 2 gy}

must be dismissed, since for theoretical reasons the coefficient of sin? 29 must be
included between the limits —0 0000955 and —0.0000088. The theoretical expres-
sion of the coefficient is + pe? — Jep — 432 By, where B, is necessarily positive,
and smaller than = J. Taking « = 0.00338, « = 0.00345, J= 0.00165, we find
the stated limits. The value of the coefficient in the formula of the text corresponds
to DARWIN's value of B4 viz; 0.0000029,

For sin? p‚ = 1/,; this gives
Oe:
Hayrorp and Bowie!) have
g = 9.78038 {1 + 0.005304 sin? p — 0.000007 sin? 2},
from which

~J
de)
an
he

(3)

9, 9.79762.

The fundamental determination at Potsdam by Ktunen and Furr-
WANGLER, V1Z: gp= 9.81274, combined with the value of ¢, which
will be derived in the following paper, viz: e—! = 296.0, gives

Gp ahd WO ie Cara, a ny cay Le OD
I adopt*) this last value (3’).
We then find the attraction of the earth by the formula

= 2 122 145 Br
JT ar ha le = aga. OT pe Lure (4)
where
Se 8 20,
0, = = =" = 0.0034496),
M og,
e — 0.00338, B, = 0.0000029,
which gives
0 SBO: Eran red eS ALE)
sin ” :
3. Now let »a'=-——W be the constant of the lunar parallax.
Sin

By Brown’s theory we have
b
x’ = [0.0003940] — ,
a

where the number in square brackets is a logarithm, and by Kerrer’s
third law
a’n? = fi (1+) *)
We find thus
1) Effect of Topography and Isostatie compensation upon the intensity of gravity
(second paper) U. S. Goast and Geod. Survey, speciai publ. No. 12, page 25.
*) In the original Dutch communication the value (3) was adopted. The difference
is negligible.
35) The quantity which is commonly used is
os
D= — , + $0,’ = 0.0031676.
Jo
+) Strictly speaking this value of M is not exactly the same as that used in
(4), since the latter is exclusive of the atmosphere. The mass of the almosphere
is 0.000000865 M. The effect on 7’ is 0”.001.

1294

[0.0011820] — n? Bs, {
Re en - rea eee oe
sin 1 Le or," A
Using now the value (1) of 6, or
b
— = (1 4-58) (1 — je),
r;
and the values (2) and (5) of 7, and g,', and taking
u-! = 81.50 + 0.07

we find
n= BATS GOS (P= Pele io 2: 7. EAN
The uncertainty of the numerical factor may be estimated as
follows :

dice. tar, +2, 171 44 a Bes
EE) atis ee Peep + 0 „006
ne ak ne ee

In the following paper we will derive the value
e—l => 296.0. 0.2.
This gives
x’ = 3422"544 + 0".015 Tr eee
The mean error includes the effects of r,, g, and u as given
above, to which has been added:

dus tes waste E00
From the recent determination of the lunar parallax by the obser-

vatories at Greenwich and the Cape!) — assuming the corrections
given to be applicable to Hansrn’s parallax 5422".07 — we find the
following comparison :

sl Cape-Greenwich Formula (7)

293 3422".60 3422".58

294 4 ‚57

295 ‚48 Oo

296 42 54°

297 36 59,

This would give:

e—! — 293.4, z' = 3422".58.

With e=! = 296.0 would correspond the observed value 2'=3422".42,
which is O'.12 smaller than (8). It does not appear impossible to
ascribe this quantity to errors of observation, especially to a constant
error of pointing on the Crater Mösting A by the observers at
Greenwich and the Cape.

1) Monthly Notices, Vol. LXXI, page 526.

1295

The equation (6) has in the course of time been used for the
determination of u, of 7, and of ¢. It is, however, doubtful whether
the accuracy, needed to derive a real correction to our present know-
ledge of any of these constants, could be attained even by a series of
observations such as is proposed by E. W. Brown in his address to
the British Association in Australia. It certainly should determine the
parallax within a fraction of + 0”.Ol to be of real value. To make
this possible the selenocentric coordinates, especially the radius-vector
of the Crater Mésting A, or any other feature of the lunar surface
which is used for the determination, must be accurately known.
The determinations of the height of Mösting A over the mean
radius are:

HAYN *) + °2".2 = '0".6 effect on &’ . . . 0".087
STRATTON’) + 3.00.7 a Sel pe Sic EE

The difference between the two determinations makes a difference
in the parallax larger than the uncertainty due to any of the con-
stants 7,,:°9,, u Or €.

Our eonelusion is thus that the value (8) of the lunar parallax
is more accurate than any that can at present be derived by direct
observations.

Geodesy. — “On 1sostasy, the Moments of Inertia, and the Com-
pression of the Earth’. By Prof. W. pr Srrrer.

1. The hypothesis of isostasy is strictly speaking a compound ot
two hypotheses, -viz. :

A. Up to a certain distance from the centre the constitution of
the earth is in agreement with the theory of Crarraur; i, e. the
equipotential surfaces are surfaces of equal density, and the density
never increases*) from the centre outwards. | Apart from this con-
dition it may vary in any manner, even discontinuously.| The last

1) Selenographische Koordinaten. ILI. (1907). Abh. der K. Siichs. Ges. der Wiss.
Band XXX. page 74.
2) Memoirs of the R. A. S. Vol. LIX, Part IV, page 276.

dL

8) Strictly speaking it is not necessary that always Tb <0. It is sufficient if, for
)

b b

dà . d&
all valaesvof b, §8* —— d3< 0, ands} 8° « —_dp<0.
dp d3

0 0

1296

équipotential surface which satisfies these postulates is called the
isostatic surface, and will be denoted by S,.

B. In the crust outside S, the distribution of mass is such that
over sufficiently large areas of S, there is the same mass as there
would be with a certain normal distribution. How exactly this nor-
mal distribution is supposed to be, is generally not explicitly stated.
In any case with the normal distribution the whole mass of the
erust would be inclosed between S, and a certain normal surface S.

The actual surface of the earth is neither an equipotential surface,
nor a surface of equal density. The actual surfaces of the oceans
may be supposed to be parts of one and the same equipotential
surface, which is called the geoid. The figure of this geoid is derived
from geodetic measures made on the continents or from determinations
of the intensity of gravity made on the continents and on the sea.
It has been found that the geoid differs very little from an ellipsoid
of revolution. This “ellipsoid of reference’ may be taken to be
identical with the normal surface, or more precisely the several
‘ellipsoids of reference found from each separate investigation are
considered to be approximations to the normal surface. The latter
is thus determined as the ellipsoid best fitting the several partial
ellipsoids of reference.

2. On the basis of the theory of isostasy we must consider the
isostatic surface S, as primarily given, though of course its figure
is unknown, and must be determined from that of S. Now the
relation between S, and S is not very explicitly stated by the different
authors on the subject.

The most natural assumption evidently is that S would be a equi-
potential surface and a surface of equal density. The normal surface
satisfying these conditions, which are those of the theory of CLAIRAUT,
will be called the deal surface of the earth, and will be denoted by S,.

When Hermert originally introduced the method of condensation,
he supposed the radius-vector of the surface of condensation to be
proportional to that of the normal surface: r, =r (1—e). In the
reductions according to the theory of isostasy the isostatic surface S,
corresponds to Hermert’s surface of condensation. The normal surface
would then be given by 7==r, (1—a)—. This surface may be called
the proportional surface, and will be denoted by $,.

Some authors also state as a definition that the depth of the
isostatic surface below the normal surface is constant. We should
thus have r=r, + Z. The surface so defined may be called the
equidistant surface, and will be denoted by 5;.

1297

Let
b==the aequatorial radius 8
: of any surface,
e = the compression ;
Further
b dé
en
NEE
then we have approximately

18
€, = 75 (rbi:

. b a
For the earth we have 1, == 0.561. Taking — = = 0.0179, and

)

s = 0.00338, we find

&,— & = + 0.000084
The difference of the numerators is

== eN
ë‚ le, == sl) 5

1) A better approximation is obtained by also taking into account the variation
of ,. Let
A = the density at ‘ B
5 ae: any equipotential surface,
D = the mean density within

b dD
Dap.

then the theory of Crarraur gives, neglecting the second order in «

A
c= (d>)

pO KLI)
= == | Y)—Iy—7.
db Ì he!

If the crust were constituted in accordance with the theory of Cuarravt, it
would consist of a solid crust entirely covered by an ocean of a depth of about
2.4 km. The bottom of this ocean would be an equipotential surface, say Ss. For
Sj we have now

Cres

4, == 1.08 D, seni
from which we find

Then, with .; = 0.561, we find

dn
ig eet EES ae
dh),

Therefore, since 6,—bs = 0.00038 b,, we have

d
no = 4, — (6,—b1) (7) = 0.550,
1

}

For the surface Sy we then have

1298

For the proportional surface we have, of course,
ES er
The equidistant surface is not an exact ellipsoid, but it differs
only in quantities of the second order in ¢ from the ellipsoid whose
compression is,

dt
where k = a Fherefore
)

&, — &, = — 0.000070
Pe Rate ey

The depth of the isostatic surface below the normal surface is in

the three cases

r — 7, =kb[1 + € (14+) (5 -— sn’ g)],
r, — 7, =kb[1 + e(t — sin’ pp),

Nr, = kb.

or, expressed in kilometers
— r, = 114 + 0.59 (4 — sin’ g),
—r, — 114 + 0.388 (4 — sin’ p)
—r, = 114. ;

The difference between the three definitions of the relation of the
isostatic and the normal surfaces is thus considerable, especially in
its effect on the compression. If the undisturbed surface of the
different oceans are parts of one and the same equipotential surface,
which is the geoid, and if at the same time the geoid does not
differ more than a few tens of meters *) from an ellipsoid of revolution,

as

A

Lge

rs

db
Further if we put b= %(d, + bo), we have bs—d) = 0.0177 b, and consequently
HN =H — 9.0177 X 1.63 = 0.530. .

u id 2 dy
Ley Riddell eee
b

Taking now
n == Hq, +9) = 0.546, e=te,+¢,), 6,—b, = 0.0181 8,
We find
#,—&, =.0.0181 7. = 0.0099 &.
Taking = = 0.00336, we have
&,—&, = 0.000038.
é, iej == 2.9.
1) HetmMert, Geoid und Erdellipsoid, Zeitschr. der Ges. für Erdkunde, 1913,
p.r17 sai

1299

Wwe cannot but take this latter as the normal surface. In that case
the normal surface is very nearly an equipotential surface. The
deviations of the geoid from the ellipsoid, or, which is the same
thing, of the normal surface from the equipotential surface, are
caused by the irregularities in the crust. They would be very much
larger — in fact of the order of 1000 meters *) — if there were
no isostatic compensation. If this point of view is adopted, then the
normal surface can differ only very little from the “ideal” surface
S, as detined above. This will be assumed in what follows and no
further reference will be made to the surfaces S, and S,. They were
only discussed here to point out the necessity of precision in the
‚definition of the relation between the isostatie and the normal surfaces.

3. Let A< B<C be the moments of inertia of a body about
the axes of a, y, 2. If the body rotates about the axis of z with the
velocity w, then the outer surface, if it is an equipotential surface,
is very nearly *) an ellipsoid whose principal axes are

b, b(1—v), &6(1—4pr) (1—e).

If C—A and C—B are of the first order of smallness, and B—A

of the second order, and if

26 A-~ B BA
fa ee a
el 2 Mb? Mb?
then to the second order inclusive we have
sd koke hen, AB, 2. ed)

aen ne kend a (EN
The radius of the equator in longitude 2 is b[1—v sin? (A—2,)],
if A, be the longitude of the axis of z. The compression of the
meridian in longitude 2 is thus &, = € + 5 r cos 2 (à —2,). Consequently
e is the average compression of the meridians.
The value of o, in (4), viz.

N 1

* = 0.0034496,

g 1
‘an be assumed to be exactly known. Further
, = 0.0000029.
The equation (1) can thus be written
Bh OOP TOS EEN fP)

1) Hetmert, Höhere Geodäsie, Il, p. 356.
*) The deviation from the ellipsoid is — xb sin? 2c, where
%=eo-- fe? + 8 B, — 0.0000051,
or bs = 3.26 meters. DARWIN, Scientific Papers, Vol. Ill, p. 102.
86
Proceedings Royal Acad. Amsterdam. Vol. XVII.

1300

and the uncertainty in the numerical part is no more than a few
units in the last decimal place given.
We also need the ratio
2C—A—B
= one
For the ideal surface we have A, = B, and consequently
‘ C ET A, H CA,

1
4 f == — Ee EE — -

PN C,

The true moments of inertia A and B may however be unequal.
The ratio H can be determined with great accuracy from the
constant of precession. The best modern determinations of this
constant are (for 1850):
NewcomB (with corrections by Hoven and Harm) *) p,=50".2486
Boss *) 50°.2511
Dyson and THACKERAY“) 50 .2503
We can thus take
p, = 50".2500 + 0".0010.
The lunisolar precession then becomes
p= 90.378.
If now we take for the mass of the moon
p= Slot 6.07,
we find
H = 0.0032775 + 0.0000022.

The uncertainty is almost entirely due to w and not to p.

So far no assumptions have been made regarding the constitution
of the earth. The theory of Crarraur now leads to a determination
of the ratio of J and H. We are thus able from H to compute
J, and then ¢ from (1). Rapav’s transformation of CLAIRAUT’s
differential equation gives, to the first order of « *),

i= ae = hee de ee . Vai

J
where, also to the first order, 1 = 3 — 5 —, and /\, is a certain
&

1) Monthly Notices, Vol. LXX, p. 587. See also: The Observatory, July 1913,
p. 299.

2) Astronomical Journal, Vol. XXVI. p. 118.

3) Monthly Notices, Vol. LXV, p. 443.

4) This and other formulas of the theory of GrLATRAUT will be collected in the
following paper.

1301

mean value of a function / of 4 which differs very little from
unity for values of 4 between O and 4,.

If the formula (3) is extended to the second order, it becomes
very complicated. The range of #, becomes wider, and therefore
also of g and «. The formula has been elaborated by Darwin!) and
Vironnet*). The formulae given by these two authors are very
different. Darwin starts from a definite assumption regarding the
constitution of the earth, and thus finds a definite value of «.
VÉRONNET introduces no assumptions, and consequently only gives
limits for e. Introducing the above value of MH we find:

Darwin . …. . &-! = 296.03.
VÉRONNET . . . 295.84 < e—! < 296.68.

The lower limit of et corresponds to the case of homogeneity,
the upper limit to concentration of the whole mass in the centre.
There can be no doubt, but that the actual distribution is nearer
the first limit. The agreement of the results of Darwin and VÉRONNET
is thus complete, and we can adopt the value derived from Darwin’s
formula. The m. e. of e-! due to the uncertainty of H is + 0.16.
From the agreement of the results of Darwin and VÉRONNET we may
conclude that any probable hypothesis regarding the constitution of
the earth differing from that of Darwin would not cause in st a
difference exceeding say + 0.10. le thus estimate the total uncer-
tainty of es! at + 0.19.

4. However, the value of H used above is the ratio of the true
moments of inertia. The equation (3) on the other hand is only
applicable to the 7deal: surface. We must thus try to derive the .
values of /, and MH, for the ideal surface from the true values J
and H, and at the same time determine the difference e—e, of the
compressions of the normal and the ideal surfaces. This will be
done on the basis of the hypothesis of isostasy.

Tbe normal surface is the ellipsoid best fitting the geoid. The
potential on the geoid depends on the true momeuts of inertia. The
compressions pv and ¢ of the normal surface are therefore derived
by the equations (1) or (1) and (2) by using the true values of ./
and A. The equation (1) or (1') also applies to the ideal surface.
Consequently

1) The theory of the figure of the earth to the second order of small quantities.
Scientific Papers, Vol. Ill, p. 78-118.
2) Rotation de lellipsoide hétérogène et figure exacte de la Terre. Journal des
Math. 1912, 4me fascicule.
86*

1502

E—E, = J — = (A
The change in H due to the change in C in the denominator is
very small (of the order of */;,,) compared with the effect of the
change in the numerator. Consequently
J —J,=9(H — H)).
and
se (H =H) 0.5902 (f B eee
The part contributed towards the moments of inertia by an element
of mass m at latitude gy, longitude 4, and distance from the centre 7 is
dC = mr" cos? p‚

2

dA —= mr° {1 — cos* gf cos" (2

il,
dB = mr? [1 — cos’ p sin* (A — A)|, 7
from which
d[C — 4(A+ B)| = mr° (1 — 3 sin’ g)
d|B — A] = mr* cos° pp cos 2 (A — A,).

If now over a surface element w of the ideal surface the height
of the continent is /, and the mean density A, then the mass is
m—=oh, WW Z, is the depth of the isostatic surface below the
ideal surface, the defect of density needed to compensate this mass,
if equally distributed over the whole depth, isd = 4 Ih . The change
in 2mr* produced by the continent and its isostatic en
then is, if 7, be the radius vector of the ideal surface :

Tj + hy r)
d (Smr*) =| Aw «dx ==] dwx?da = Awh, (Z + h,) (7, —42, +AA), - (5)
Ty nl

Similarly for an oceanic element, let d, be the depth of the bottom
of the ocean below the ideal surface and 4’ the difference of density

between the water and the mean density of the crust. The com-

d
1 ange
Ye

yensating excess of density below the sea then becomes d' =
le) A

and the change in Zn” is
d (Emr?)= A'od, [(—Z, +2d)r, +AA: +4Z,d].- . (6)
It has been found sufficiently exact for our purpose instead of
(5) and (6) to use the approximate formulas
d (Sar) 9 el nr Dee
d (mr) = — 0Stgvds - 2 ce ee
The height A, above the ideal surface is the sum of the height
h above the normal surface and the height 4’ of the normal above
the ideal surface. This latter is

1303

h = (&—e,) b, 4 — sin’ p).
Taking Z, == 0.0179 r,, and A, = 2.70, and integrating over the
whole surface we find for this part of H—H,, using also (4):
dB = 0.023 (e—e,) — 0.012(H—H,) . . . . (%)
The principal part of H—H, is due to the deviation of the actual
surface from the normal surface. This has been computed by (5’)
and (6), replacing 4, and d, by 4 and d respectively. The value
of the constant g depends on Z and on the units used. | have
adopted. A:== 2.70, 2! = 1.70"), Z= 114-km.
The surface of the earth was divided into compartments of about
100 square degrees. For each compartment the value of
Q = qu (a,h — 0.57 ed).
was computed, where a, and «, are the fractions of the compart-
ment covered by land and by sea respectively (so that «¢, + «, = 1).
Further
P= Q(1—8 sin? p)
R= Q cos? p cos 2A
S= Q cos* op, sin 22.

The units had been so chosen that

20-—A—B Beit
dl EP
2C
ae is SS ain |
J G = 10-7 (2K. cos 2a, + 2S. sm 2A,},
The longitude 2, is determined by
=S cos 24, — {RK sin 24, — 0.

1 found the following results. (See table p. 1304).
We ‘find thus
2C0—A—B
Se ae
2C

BoA |
8 = + 0.00000205,

and the axis of minimum moment of inertia (4) is situated in the
longitude

4, = 86.°5 West of Greenwich.

This computation, of course, is rather rough. It would perhaps
be worth while to repeat it with greater care. The small influence
of the continents, especially of Asia, is somewhat surprising. This
1) The normal density of the crust in the upper few kilometers be/ow the
normal surface was thus taken to be 2.73, and the density of the land projecting
above that surface 2.70.

1304

Parts of the world. | 2 P | fien =S
1. North Polar Area | + 2.44 — 0.02 =- 0,03
2. Europe | — 0.83 | + 0.39 — 0.47
| 3. Asia = del, |e ale see
| 4, North-America == S04) == 1036 — 1.28
5. Northern Atlantic Ocean — 5.00 | — 0.23 | — 11.36
6. South-America + 3.21 | — 216...) F oe.
7 Southern Atlantic Ocean ee ee re rere
8. Africa Kn ae er de KI
9. Indian Ocean — 2.58 + 15.11 + 7.09
10. Indian Archipelago and Australia — 2.14 | ate ely bce) been MA a
11. Pacific Ocean — 29.97 — 17.96 + 17.97
| 12. South Polar Area AT = WOE aoe

is due to the remarkable fact that the great mountainous regions
of the earth (Himalaya, the Alps, Rocky Montains, the higher part
of South Africa) are situated on or near the neutral latitude of which
the sine is V1/, [p = 85°.3].

The value of dH found here is not yet exact, for if the crust
were built according to the theory of Crairaur it would consist of
a solid erust covered by an ocean of a mean depth of about 2.4 km
In the above computation this ecean has been taken of the density
2.73 instead of 1.03. To remedy this we must apply a correction,
which by the theory of CrarRAUT is

by

l
d, (C—A) = # a {a pe dp = $, a. 2.4 (5 Jm) be.
di
[sa
This gives
; dH = + 0.00000213. *)
The bottom and the surface of this ocean would be ellipsoids of
revolution, the neglect has therefore no effect on the value of B— A.

There now remains
JH = — 0.00000299,

1) There is an error of computation in this number. It should be +0.00000260.
The final value then becomes e—! = 295.98. The difference from the value in the
text in negligible. (Added in the English translation.)

1505

Adding this to d’H as given by (7) we have altogether

H — H, = — 0.00000299 + 0,012 (H—H,)
:
’ H — H,—=— 0.0000081,
Then we find by (4)
& — &, = — 0.0000016
ele 4 0.14.
From

H = 0.0032775
we find thus.
HH, = 0.0032806.

Darwin’s equation then gives

el 295.82,
and from the equation of VÉRONNET we find
295.62 < ¢,—1 < 296.46,

It has already been mentioned that Darwin’s value may be assumed
to be very near the truth. Adopting this and adding the value of
é Lel, which has been found above, we have)

el =,295.96.

It is very difficult to estimate the uncertainty of the correction
H—H,, since it depends not only on the correctness of the data
used, but also, and probably for the greater part, on the exactness
of the hypothesis that the compensating defect or excess of density
is distributed equally over the whole depth Z The whole correction
to el however only amounts to 0.07, and its uncertainty is almost
certainly overestimated if we take it equal to the whole amount,
+ 0.07. Combining this with the m.e. + 0.19 due to the uncertainty
of H, and of Darwtn’s hypothesis, the total uncertainty of se! is
found to be + 0.20.

The greater part of this is due to the uncertainty of H, and this
is wholly due to that of the adopted value of the moon’s mass.
Consequently, in order to improve our knowledge of « we must
determine wu, which is found from the lunar inequality of
the sun’s longitude and the solar parallax. A correction of + 0.05
to the adopted value of u! would give —0.10 in e!.

For ‚the ideal surface 6, = A,, or K,=0. Therefore for the
normal surface

ra Se a : ne = 0.00000105.
Mo? C
The longest radius of the equator, in the longitude 86°.5 is thus

en

1) See note on p. 1304.

1306

6.4 meters longer than the shortest radius. The compression of the
meridian €, varies between e + $v and «— Sr. For central Europe,
i 00 ae santa

(e) 1 = 295.98
and for North-America, 2 = 100°

(ej) 1 == 295.92.

5. The methods mostly used for the determination of the com-
pression of the earth are: .
I. From geodetic measures,
Il. From the intensity of gravity,
II]. From the moon’s parallax,
IV. From the lunar theory.
By the first method the geodetic measures made in the United
States of America give |
EVOL 2°12 lo Soh 4 AO ee
This agrees within the limits of the mean error with the value
296.0 found above.
From a great number of determinations of the intensity of gravity
HeLMERT derived
el B08 8 ds lers et eee
This result agrees with the final result from the American deter-
minations, viz.:
LEAD a (ee

In judging the value of these results it must be remembered that
both the direction (method I) and the intensity (method IT) of gravity,
before they are used for the determination of the figure of the
geoid, or of an ellipsoid of reference, need certain corrections, which
have been applied by different investigators more or less in agreement
with the hypothesis of isostasy. All investigators however use
approximate formulas, and it is not clear which of the definitions,
treated in art. 2 above, has been adopted. The American investigators
take a constant depth below the actual surface of the earth (under
the sea even below the bottom). HeLMERT uses the reduction as in
free air‘), thus assuming that the isostatic compensation is complete.

Now it is of course impossible from the observations to decide
between the three cases of art. 2, and also the corrections computed
under the three assumptions will be very nearly equal. But small

1) The American observations reduced by the free air method give instead of
(II’) e~! = 202.1 + 1.7. See Bowie, Effect of topography and isostatic compensation
upon the intensity of Gravity, second paper, p. 26.

1307

differences in the radius of curvature, or in the values ofy, have a
large influence on the compression, and it seems not impossible that
the resulting value of ¢ has been influenced by inaccuracies in the
reductions. Discussing the large difference between the compressions
found by Bresse, (et = 299.15) and Crarke (293.47) partly from
the same observations, HerMerr *) asserts that this difference can be
fully explained by a difference of a few meters in the adopted
height of the geoid over the normal surface. If this is so, we can
expect that considerably larger differences of the isostatic reduction
will lead to similar effects *).

For these reasons it appears to me that the agreement of the
three values (I), (II) and (II) ean only be accidental. It is not at
all certain a priori whether they refer to the same normal surface,
and their uncertainty undoubtedly is considerably larger than would
be inferred from the mean errors. *)

From the lunar parallax we found in the preceding paper

er OOB Be see ee od ol et 7 QLD

We also showed that the value 296.0 cannot be said fo be
excluded by the observations.

The lunar theory gives J, from which e is found by the equation
(1). The principal term, which is commonly used for the deter-

1) Geoid und Erdellipsoid, Le. p. 18.

2) The values of « derived from the American determinations by different methods
of reduction (and different combinations of stations) are widely divergent. Thus
e.g. from the observations in the United States and in Alaska by the isostatic
method 300.4 +0.7 and by the free air method 291.2 + 0.7. See Bowie, lc. p. 26.
The former of these should properly be quoted instead of (II’) as the final result
from the American determinations.

5) Hetmert’s formula of 1901, from which (IL) is derived, reduced to the Pots-
dam system, is

g = 9.78030 [1 + 0.005302 sin® p — 0.000007 sin? 2 p]. . (a)

With the compression ¢—!= 296.0, and a constant correction of + 0.00011

this becomes
g = 9.78041 [ 1 + 0.0052764 sin? p — 0.0000074 sin? 2g]. (B)

The residuals of these two formulas for different zones of latitude are as follows,
expressed in units of 0.00001 :

Zone 5° dae 25° 35° 45° 55° 65° 75°
(a) a 0 — 20 +6 + 6 i —7 — 3
(A) ie In Si eee eee) Te "| ede haa

The m.e. of each of these residuals is +11. The residuals # naturally are
somewhat systematic, but they are not larger than (z\, and can very well be due
to errors of observation or inaccuracies in the reductions. A new discussion on
the basis of the theory of isostasy, and including the valuable material, which has
become available since 1900, is very desirable. [Note added in the English translation).

1308

mination of J, is a periodic term in the latitude, whose period is
one month and whose coefficient is, by Brown’s theory : *)

B = — [3.7046] J — 0".017.
From the observations Brown finds’)
B=— 8",19-+.0".06,— [0.40 + .0".20] . 7,

where 7’ is the time expressed in centuries and counted from 1850.0.
If we take the mean epoch of the observations, i.e. about 1875,
we find’) J =0.001633, and consequently

ea). == 207 SE Bette a ee

It appears to me that this determination is not very reliable,
chiefly on account of the large and uncertain coefficient of 7’ in
the observed value. Brown proposes to use it not to determine «,
but the inclination of the ecliptic and its secular variation. It seems
very doubtful whether a correction to these elements thus determined
would be a real improvement to our knowledge of them derived
from other sources.

A great weight is attributed by Brown to the determination of /
from the motion of the perigee and the node. He finds

et = 296.5 TE Oni ee el eae NN

In deriving the m.e. no account has been taken of the uncertainty
of the theoretically determined part of these motions due to other
causes. Among these other causes, however, is the figure of the moon,
which is very imperfectly known. It will be shown in the following
paper that it is very well possible to adopt such values for the
quantities defining this figure, that the motions of the perigee and
the node are in agreement with the value et = 296.0. Smaller
values of « however lead to very improbable conclusions regarding
the constitution of the moon.

All our discussions thus lead to the conclusion that none of the
other determinations is equal in accuracy to, or can throw a doubt
on the determination from the constant of precession. We must
therefore adopt as final value of the compression the result of this
determination, viz:

Ee = 295.96 + 0.20.

&

1) Part V, Chapter XIII. (Memoirs of the R.A.S, Vol. LIX, Part I). On p. 80
the inequality is given as — 8”.355 sin (w,-+ #). This should be — 8”.553.

2) Monthly Notices, Vol. LX XIV, p. 564. Brown gives probable errors, which
I have changed to mean errors.

3) The theoretical value for 1875, corresponding to <—! = 297.0 is — 8”.312,
the observed value is — 8/28, The difference is therefore 0 —C=-++0".03 and
not —0”,03 as stated by Brown, l.c. p. 565,

1309

Astronomy. — “The Motions of the Lunar Perigee and Node,
and the Figure of the Moon.’ By Prof. W. pr Srrrer.

1. The motions of the perigee and node of the moon have been
derived from the observations by different investigators.
For the perigee the resulting sideral motions are :

E. W. Brown’) 146435".35
P. H. CoweLr?®) ot
E. J. pr Vos VAN STEENWIJK *) 29
Newcoms *) ‚30

All these values have been reduced to the value 50”.2500 of the
constant of precession (see the preceding paper). The first three
depend on meridian observations. The agreement between Cowerr.
and Brown is excellent, but the result of pr Vos deviates rather
more than can be explained by the mean errors (which are about
+ 0".02 for each result). It is, however, in perfect agreement with
the value derived by Nerwcoms from the discussion of occultations.

The theoretical motion due to other causes than the figures of
the earth and moon is by Brown’s theory:

146428".77.
There thus remains for these two causes
I. Brown —COWELL dw = + 6".59
I]. Newcomp—be Vos dw = + 6 .53.

For the node the results derived by Newcoms*‘) and Brown’) are

in perfect agreement. They both find

— 69679" .44°
The theoretical value, as above, is
— 69673".22,
The part due to the figures of the earth and moon is thus
d), = — 6".22°.

The mean errors of both values of do and of dS), so far as it
is due to the observations, is + 0".02. The theoretical value, how-
ever, in both cases is the sum of a large number of terms, each

1) Monthly Notices, Vol. LXXIV, p. 419.

2) Monthly Notices, Vol. LXV, p. 275.

5) These Proceedings, Vol. XVI, p. 891.

4) Researches on the motion of the Moon. (Second paper), p. 224. The cor-
rections indicated by Brown, M.N. Vol. LXXIV, pp. 420 and 562 have been applied,

5) Monthly Notices, Vol. LXXIV, p. 563,

1310 .

of which was computed to two decimals only, and may thus be
(0.005 in error. The mean error of the sum can be assumed on
this account to be about + 0".02. The mean error of the differences
dé and dQ thus becomes + 0".03.

2. The terms due to the figure of the earth are, by Brown’s
theory, the factors being given as logarithms :
dis — [3.5907] J,
dj), = — [8.5620] J,
With e—! = 295.96 + 0.20 (see the preceding paper), we have
J = 0.0016502, from which
dw = 6".430 + 0".008,
dQ, = — 6.019 + 0:007.

There thus remains for the figure of the moon
IF do= + 0".16 + 0".03,

IQ, = — 020° + 0.03 … (1
II dj = + 0.10 + 0.03, 18 Se

The values used in Brown’s theory are
do = +. 0".03, dQ) = — 0".14.

The contradiction is apparently very great. It will be shown,
however, that the values (1) can very well be ascribed to the figure
of the moon. Brown’s values depend only partially on actually
determined constants, from which they are derived by means of

En
)

G
the hypothesis that the ratio g==} —— has the same value for the

Mb?
moon as for the earth. It will be seen below that the values (1)
lead to a different value g’.

Let A’, B’,C’ be the moments of inertia, J/’ the mass, and 6’
the largest radius of the moon. Further, in analogy with the notation
used for the earth

2C'—A'-- B' B'-A’
ale — 5 vie — . Vb?

2M'b"
Then the theoretical expressions for the motions of the perigee and
the node are

daw = + 390" J'—1027"K’,

gnl IE TN

A= ATO EK (2)

The coefficients are easily derived from Brown’s theory, Chapter
V, §378 5), where however db, = 6'.57, db, = —6".15, must be

1) Memoirs R. Astr. Soc, Vol. LEX, Part I, p- 81,

Lda

substituted for + 6”.41 and — 6".00 respectively. The numerical
coefficients in the next line of formulas then become
8".62, — 45".4 and — 8”.07.
Then, discarding the assumption regarding “/j,: /p, and intro-
ducing J’ and A’, the formulas (2) are easily derived.
Comparing (1) and (2) we find
1 i (TELE) mae.
J' = 0.000435 0.000410 0.000422 zE 0.000055 |
K' =0,000009 0.000057 0.000033) & 0.000082 | -
3. The ratios
C'—B' C'—A' B—A'

Ce AN re tS

(3)

GN
are. in the case of the moon, so small that we may neglect the
difference of the numerators, and take B= a + y.
These ratios appear in the theory of the libration of the moon"),
C—A
where they are analogous to H = aie in the theory of precession

5 B a .
and nutation. Generally 3 and ots are introduced as unknown
(

quantities to be determined from the observations. The constant @ is
derived with great accuracy from the mean inclination of the moon’s
equator on the ecliptic. The equation determining this mean inclina-
tion U, as a function of 3 is given by TissERAND, Vol lly p42;
and also, more exactly, by Hayy, Selenographische Koördinaten, I”),
p. 900, with a further addition on p. 909. The values of 9, derived
by different investigators are:

Franz, from observations by Scuniter 7, = 1°31'22"1 + 7.3

STRATTON, 5, Ms a ss Oot: a
ait cs ANR RAe eed BETE Ae er 1.597 6 22005
1 adopt

6, = 1931/40" + 20".
Introducing this into Hayy’s equation, I find
B(1 +. 0.0047 f) = 0.0006286 + .0900022.
For f=0 this gives @ = 0.0006286,
pnd, tok fa NEN 8 = 0.0006257.
Now we have from (3)
J' 4 4 K' = 0.000439 + .000066

1) See e.g. TISSERAND, Mécanique céleste, Tome II, Chapter XXVIII.
2) Abh. der K. Sächs. Ges. der Wiss. Band XXVII, Nr. IX, 1902.

1312

Referring to the definitions given above we havé
JL PK =9 ig
Taking now
B = 0.000626 + .000002,
we find
g' = 0.70 + 0.11,
which differs considerably from the value for the earth (g = 0.502).
If f is brought into evidence in the expressions for do and df
we have,
da = {| — 832" + 1222" f] (J’ + EK),
ag = — A470" (F' + 4 Ry:
From ds, we find, of course, the value of /' + 4 K' stated above,
and then from do: ;

uf LE (1+ II) m.e. 5
fz DE 0.87 0.92° a= 0-06" 6)

Generally f is determined from the coefticients of certain terms
in the libration in longitude, which depend on y*), and of which
the largest are, for f= 4, — 156" sin S and + 22" sin M, where
S and M/ are the mean anomalies of the sun and moon respectively.
The geocentric amplitudes of these oscillations are 1".4 and 0".2
respectively. It is hardly surprising that the determinations of such
small quantities by different observers are not very accordant. The
results are

FRANZ F = 048717 2 0027S
STRATTON 0.50 + 0.03
HAYN 0.75 + 0.04,

The results of Franz and Srrarron are both derived from the
observations by Scurürer. The results of the different observers are
very discordant amongst themselves as well as with the value (5).
It seems certain that the mean errors of the values derived from
the observations of the libration are no true measure of the real
accuracy. The true value of f is certainly much nearer to unity
than to 4. The value found by Scurürer and others for the coefficient
of the principal term of the libration in longitude must then be due
to systematic errors in the observations with a period of a year’).

1) [t would thus be more natural to take as unknown 5 1—f. All writers

have however expressed their results in terms of f.

2) See also Hayn, Selenographische Koordinaten II, p. 135—136. He there finds
f = 0,85 + 0.07 and explains how the smaller values found by FRANz and Harr-
wia (0.47) can be due to errors in the adopted radius-vector of MösrinG A which,
through optical libration, give rise to a spurious oscillation of yearly period, if the
observations are made near the time of full moon.

1313

We may remark that’ / cannot exceed unity. A value of f larget
than 1 would mean that the moment “of inertia about the axis
pointing to the earth was larger than about the axis which is tangent
to the orbit, and this would be an unstable state:

4. The theory of Crarraur would lead to values of J', 8, fand qe
which are absolutely in contradiction with those found above from
the observations.

Although the development of the theory is well known, and also
its application to an ellipsoid with three unequal axes introduces no
new principles, it is perhaps not devoid of interest to collect the
different formulas into a concise summary.

The forces acting on the moon are: its own gravitational attract-
ion, the attraction of the earth, and the centrifugal force. Take a
system of coordinate axes, with its origin in the centre of gravity
of the moon and the axis of Z along the axis of rotation. We can
with sufficient approximation suppose the earth to be situated on the
axis of Y at a constant distance A from the origin.

The equipotential surfaces are approximately ellipsoids of which
the principal axes are situated along the coordinate axes, and have
the lengths

Br NE (i)? MEEO)
Further the equipotential surfaces are also surfaces of equal den-
sity. The density at any point is denoted by A and the mean density
within any equipotential surface by D. We have thus

1 ted
D= | A —[p* (1 —o) (1 — v)] dp.
: 0

As we will only develop the theory to the first order of r ando
inclusive, we require D only to the order zero, thus

5

Ê
3 7.
D=; farde
pe
Further we introduce the ‘integrals
Ê b
1 d lo
S= [AZ ermee, T= [a de,
8) dp reeds
0 2
£ b

1314

If then 7, p‚ 4 are the polar coordinates of any point, the poten-
tial V, at that point due to the attraction of the moon is given by *)

3 D3° meu
Zy T= evin jer
Aan f r i 7

nig
HEB cos? gp sin® À Ë PR rol.
Tr .

If w be the velocity of rotation, and if we put

Bro
ST AafD
then the potential of the centrifugal force is
i IV = Dor COR ip
Aaf
Further if J/ be the mass of the earth, and
OM
~ dae RED’

the potential of the attraction of the earth is

=e

»)
— V, = Dz{l — 4 sin” p — 3 cos® p sin® dik:
4arf |

Along an equipotential surface the sum V = DV, + V,+ V,
must be constant. If we are content with the first order of o and
» we can also take == — in the factors of S, 7, P, Q;.0 and x

The equation to the equipotential surface then becomes, if a is a
constant :

TDL + 49) + — Saint DES + 1) + 4 De + Del
+ (} Boost y sin® 2) [FP + Q) + De].
The equation of the ellipsoid is
r= 6 (1 — osin? p — v cos’ p sin? 2},
Comparing the coefficients of sin* p and cos’ sin’ 4, we find
Do=2(S+ T) +4 Do +3 Dx, (6)
Do=3(P + IE De debt

The quantities referring to the outer surface will be distinguished
by the suffix 1. We then have

M'=taD,b*,
ES, bs B — Al = 3. x P, bY,
T= 0, Q,=0.

1) The constant of the gravitation f in this formula of course is a different thing
from the ratio f, which has been defined above.

1315
Consequently for the outer surface we have
C'—A'

5, =} M'd?” = 2Q, Pi de)
hue BA 4 nk (7)
ce rye oe

Putting now
— 1
&, = 6,—72?,;

so that ¢, is the mean ee a of the meridians, we find

a es Gy;
4 be, (5)
5. We now put
B do B dp g dD
N=. ee ees, GR ee
oO dp yv dp D dp

From the definition of D we find easily

A
¢=—3,1——}.
D
If now the assumption is made that the density never increases
A
from the centre outwards '), we have always 1 ee 0, or

Gs

We now differentiate the equations (6). If the whole mass rotates
as one solid body, then Do is constant. Also Dx is a constant. We

1 +- 5 et Eee ')

er en ky REG
P
64 a(S, 1)=0.

8° oD (6—1) = 3 (8° S—p* Ao).

We have thus

te ee eee .
If for B'S we write [4 1p (3°95) dB, and integrate by parts, we find
; A
Li)

dh

1) It is not necessary to suppose that, for all values of B, es” If is suffi-
Pp ie
; Mey B 8" ki
cient if fr — dB <0 and |B aa, d3< 0.
i. dp zg dp
0 0

87
Proceedings Royal Acad. Amsterdam. Vol. XVII.

1316
Ê
GES
8 oD (S—1) = — 3 [Bo —dfp.
dp
0

5 dh . Mi
Since PT is supposed never to be positive, the integral also cannot
;

be positive, and we conclude
age
Similarly we find
$2 6.

Now differentiating (9) again, we find

: dy “ s ;
B 4759 dB 10;
dp
10
| aes (0)
A 7E L 50 + 4 — (1 + 0) =0.
di

For 8=0 we have 1j=—= 60 =0. For small values of @, 4 and
dy ; 8 3 :
on therefore necessarily of the same sign. It follows from (10)
Bil

ee . a dy
that this is only possible when 4 is positive ; 7 and EE thus begin
dj
by being both positive, and * cannot become negative without
passing through zero. But, for values of 2 larger than zero, we find
Aga: jee om
from (10) that, for 7 = 0, a is positive. It follows that 1 can never
dj

become negative. The same reasoning holds for 6. Collecting
the different inequalities, which have been found we can write

Cis GS 3;
= | Ee
0<A<5<3.
From (10) we find

d A
BPF CO) ee ier ar)
eh
Putting now
=e
oa

we find
dy v
B dp aa [6 + 1 + fed —— 26] y == 0 e ° e . . (12)

The factor in square brackets is necessarily positive, and is equal
to-6 for B=0O. Putting thus

4317

[6 4-0 —25}=6 pi + q8 +...
ya-+ b8 He? +...
and substituting in (12), we can successively determine the constants
a,b,c... We find that all these coefficients are zero. Consequently
YOE
eo.

This being 50 for small values of 3, it remains true for all 9,
since 4 and @ satisfy the same differential equation.

Referring now to the various definitions given above, we conclude

ew AE OOP Bet bx,

TR AT oe == be. oe (lS
o | 8 1 8, CA $x +40, ess a

Now, since the velocity of rotation equals the mean motion in
the orbit, we have by KerPrer’s third law, for the average value of £&,
Ro? = AfM (1+),

where the factor A is taken from the lunar theory. Therefore

© = Alu) = 1.0095
x

We have thus from (13):
1 7 = 0.7482, f= 0.2518.
We found above that for the actual moon the true value of / is
probably very near unity. We must thus conclude that the distribution

of mass within the moon is „ot approximately in accordance with
the theory of CrAIRAUT,

6. Continuing however to trace the consequences of this theory,
we now apply Rapav’s transformation of the differential equation
(10) of Crairaur. Since On, it is sufficient to treat the equation
for 4.

Put

D= DB’ VIA.

Differentiating, and comparing with (10), we find

ESS yg rg pa ae
dg V1 4m
Os ae i Boma vou

Now the function “= -

is nearly constant for small

BE ke 1]
values of 4, as will be seen from the following little table
87*

1318

y= 0 „FEL

= 1.00074 (maximum)
0.6 0.99928

1 0.98995

3 0.8

Therefore, /, being a certain mean value of /, which will
never differ much from unity, we have

DB V1+4 = &=5F, [DBtds, . … . . . (1A)

Now the moment of inertia C’ is given by

zi
: =e
C=iAn ae [3° (1—o) (1—v)*] dB

0
b
=$ ar [Aptdp — (C'—A') — 2(B—A').
0
If in C’ we neglect small quantities of the first order, we can take

1D
A= D(1i—15= D+ 36 a , and consequently
ä

; dD
af A ptdp = | DB'd8 + 4 Je 6° = dp.
7.

Integrating the second integral in the right hand member by parts,
and substituting in the value for C’, we find
b'
C’=8aD,b"* — 1S x | D3'dp.
0
The integral is determined by (14). Introducing the mass
M'= 426" D, we find

Pre en (15)
EE Fo ic EST.
Since OS 4, < 3, we have
B>g>0.

The upper limit corresponds to homogeneity, the lower limit to
condensation of the whole mass in the centre.
We have found above
pO 70 ste 0 Wilt 2 ee cote eee EE
The most probable value of gq’ is therefore outside the limits
of Crarravr, thongh the mean error does not entirely exclude
a value near the upper limit. An excess of g’ over the value for

1319

homogeneity indicates that in the moon the density wcreases from
the centre outwards. A small excess could of course be due to
irregularities in the distribution of the mass. But, unless we are
prepared to admit a considerable excess of density of the outer
layers of the moon over the mean density, we are led to the con-
clusion that the true value of y’ is certainly not larger and probably
smaller than the value (16). Now this value was determined from
the observed motion of the node combined with the adopted com-
pression of the earth e—! = 296.0. For e—! = 297.0 we should have
found g’ = 0.85, and Hrtmert’s value 298.3 gives y”= 1.02. Thus,
if the observed motion of the node is accepted, any value of ¢
appreciably smaller than '/,,, becomes very improbable.

7. From (7) and (9), combined with (11), we find easily
70, + 3%, 506,540, + PL,
The numerical value is approximately
0, = *, = 0.0000078.

Therefore
0.0000156 < 6, < 0.0000390
0.0000117 < », < 0.0000292.
Take e.g.
6, = 0.0000300, rv, = 0.0000225.
We then have from (6)
tgn 0.0000144 EE eh: 0000108
2 M'b" : 2 M'b* ;
and consequently
J 9000028... K' = 0.000081.
For the limiting case of homogeneity, these values would become
S= 0.000082 ‚°° K' = 0.000018.
The values derived from the motions of the perigee and the
node were
J' = 0.000422 + .000055 , K'=— 0.000033 + „000032.

Further we have from (9), with the above value of 0, :

5 C a 1 4
7, = 3| 1 — — — | = 9.60.
2 MO B,

Then from (15) taking #,=1, we find 7 =0.494 and conse-
quently :

1320

C'— A’
ft fee or = 0.000029.

For the case of homogeneity this would become
B= 0 000059.
The value derived from the mean inclination of the moon’s
equator was
B = 0.000626 + .000002.
Here again we find an enormous difference between the true
values and the theory of CrLAIRAUT.

8. The conclusion that the distribution of mass in the body of
the moon is not in agreement with the theory of hydrostatic equi-
librium, has already been reached by LaAPLAcg’).

The mass constituting the crust of the earth is not in equilibrium
either. But below the isostatie surface there is equilibrium. We
are naturally led to assume that the depth of the isostatic surface
is the depth at which the pressure of the outer layers becomes so
large that tiie material of the earth behaves as a fluid and there-
fore necessarily is in equilibrium’). To form an estimate of the
pressure at the isostatic depth we can compute the pressure as it
would be if the whole earth, including the crust, were in hydro-
statie equilibrium. Then, treating the earth as a sphere, we have

b
Pp =| Lg dr,
b—Z

where y is the acceleration of gravity. Now
__ fim ZT
I= ee, i eA:

Theretore

b—Z
For the earth the interval of integration is relatively small, and
we can take A and D constant. Then D= D, and very approximately
A=4D,. Further if Z= kb; we find
pta Di ike et

1) Mécanique Céleste, Livre V, Chapitre Il, § 18.

2) So far as constant, or slowly varying forces and stresses are concerned. The
behaviour of the material with respect to sudden forces is of no importance for
our argument.

1321

The material out of which the meon is built up is probably not
very different from that of the outer layers of the earth. We will
therefore assume that it requires the same pressure to be fluid
enough for the state of permanent equilibrium. If now on the moon
the depth of the isostatic surface, if there be one, is Z” = k/b’, we have

vo

Now we can put A’. D’ = aD,’?. If the moon were homogeneous,
we should have «= 1. If the density increases towards the centre,
then at the outer surface a <1, and at the centre a > 1. If «, be
a certain mean value of « over the interval of integration, we have

p = tra Db [Eh]

Now
b=0272b , D,'= 0.610 D,.
Taking further 4—= 0.018, we find from the condition p’ = p
0.32
Ft,
a,
If we take a, = 1, we find
k= 0.40.

Most probably the true value of @, does not differ much from
unity. The isostatic surface in the moon would thus be situated at
a depth of about two fifths of the radius, and little more than one
fifth of the total volume would be inclosed within it. Of course
there can be no question of an isostatic compensation as there is
in the earth. The differences of the moments of inertia are almost
entirely determined by the irregularities in the “crust”, which here
contains by far the largest part of the mass, and the small central
part has only very little influence.

This reasoning, of course, is not entirely rigorous, but it undoubt-
edly points out the true reason why the theory of Crairavur, which
in the case of the earth agrees so well with the actual facts, is not
at all applicable to the moon.

1322

Physiology. — “The decoloration of fuchsin-solutions by amor-
phous carbon.” By Dr. A. B. Droocieever Fortorn. (Commu-
nicated by Prof. Dr. J. Boeke).

Pulverized amorphous carbon has the faculty of decoloring solu-
tions in water of several dyes, and the general explanation of
this phenomenon is to be found in the fact that these pigments are
absorbed by the carbon.

Freunpiicu and Losmv (Zeitschrift für physikalische Chemie, Bd. 59,
1907) discovered, that for Crystallviolett and Neufuchsin of the
Höchster Farbwerke another explanation must be given. These two
dyes are chlorides. If their solution in water is brought into
contact with carbon, then the solution decolors. The dyes are how-
ever not absorbed as such, but they are decomposed into hydrochloric
acid and color-base. The color-base is absorbed by the carbon,
presumably in the form of a polymerisation product, which by means
of aleohol can again be removed from the carbon. The hydrochloric
acid remains behind in the fluid, and can be shown in the filtrate
of the solution that has been decolored by carbon by the opacity
that occurs in it with silver-nitrate, and its acid reaction upon
litmus.

In 1909 (Zeitschr. £. Physik. Chemie, Bd. 67) Freunpiicn and NEUMANN
wrote again about the absorption of Neufuchsin by carbon and
corrected some inaccuracies in their former paper a.o. by remarking
that the decolored filtrate of Neufuchsin does not react acidly
upon litmus. They proved that over 33°/, of the chlorine occur-
ring in the Neufuchsin remains behind in the filtrate decolored by
carbon. They could not indicate with certainty the kation belonging
to this anion Cl, but they are of opinion that these are partly H-ions,
partly other ions resulting from inevitable contaminations of the carbon.
According to them the thing absorbed by carbon from the Neufuchsin-
solution may still be the color-base, but more probably it is a color-
salt formed with contaminations of the carbon.

When repeating these experiments with “Crystallviolett”” no devia-
tions were found, but with ““Neufuchsin” I observed a phenomenon
being not in accordance with the view entertained by FREUNDLICH
and his cooperators about the decoloration of solutions of this dye
by carbon. This phenomenon consists in the fact, that a watery
solution of */,,,°/, Neufuchsin decolored by carbon and filtrated from
the carbon resumes its color for a great deal when it has been
standing for a considerable time.

Not only Neufuchsin, but likewise the “fuchsine” of Kirp, Fuchsin

of GRrÜBLER and Magentaroth of Grisirr, all very similar if not
identical dyes, behave in the same manner.

This phenomenon is most easily, and in the shortest time observed,
when so little carbon is added to the fuchsin-solution, that the color
does not totally disappear, but a light-pink tinge remains. To control
the change of the color a fuchsin-solution can be used that has been
so far diluted, that, to the eye, it corresponds with the nearly deco-
lored solution, It will be seen that after the filtrage of the carbon,
for which operation I used filters of ScnrricHeR and ScnüLr, the
color of the fluid becomes very distinctly deeper. That, after all,
the carbon had really acted absorbingly, is proved by the deeply
staining of aethylaleohol 96°/,, if the filtrated carbon is thrown into
it. If we take carbon to an excess, it may easily occur, that the
color is not seen returning in the decolored solution, presumably
because the concentration of the newly formed dye is insufficient.

The carbon originally used by me was gross-grained char-coal,
which had not been carefully purified. Consequently the phenomenon
could be attributed also to contaminations of the carbon. Therefore
1 purified the carbon according to the method likewise applied
by FreUNDprICH and Losrv by boiling it three times with 25°/, HCI
and washing it with distilled water. Even after very long washing
all the hydrochloric acid bad not yet been removed, and carbon used
in this condition prevented the return of the color of the decolored
fuchsin. But by adding ammonia to the carbon to which hydrochloric
acid had been applied, and after washing it again, I could obtain
carbon, the extract of which with distilled water contained no longer
a vestige of chlorine. Only this carbon could be considered applic-
able to my purpose and with this carbon purified by me the pheno-
menon was regularly observed.

The fact that no heterogeneous substances could be the cause of the
return of the color, was further confirmed by what follows. I obtai-
ned some samples of carbon from the ,,Kkon. Pharmaceutische Handels-
vereeniging” Amsterdam. If one washes one of these Carbo animal.
depur. humida with distilled water, the filtrate reacts strongly acidly
and it contains much chlorine. When this carbon was applied the pheno-
menon did not occur. Neither when Carbo sanguinis was used, the
watery extract of which contained likewise chlorine but was alkaline.
On the contrary the extract with water of Carbo ligni tiliae pulvis
B. 50 as preseribed in the Dutch Pharmacopy Ed. IV was neutral, and
no precipitation with silver-nitrate could be obtained. This carbon,
which consequently can be regarded as sufficiently pure for my
purpose admits the return of the color in an almost decolored

1324

fuchsin-solution. It is only not so handsome in its application as
oross-grained carbon, because it is inclined to pass through the
filter, and easily too much of it is added to the fuchsin-solution.
If one adds carefully so little carbon, that the decoloration takes
place slowly, e.g. in the course of a day, then one obtains here
also easily a light-pink filtrate, which after: some time becomes
dark-red again.

Now the question rises how the return of the color in the
almost wholly decolored fuchsin-solution can be explained. It is
not for me to answer this question. This will have to be done by
chemico-physical methods by a person who is sufficiently conversant
with the theory of carbon-absorption. As an histologist 1 can do no
more than publish the fact I have discovered, hoping that somebody
else will further investigate its nature. Yet I have tried to find
for myself an explanation of the case, and have come to a working
hypothesis, which after all proved to be untenable, but made me
discover some other facts that may have importance for the expla-
nation | tried to find.

It was supposed, that in the almost decolored fuchsin-solution
besides chlorine-ions or hydrochloric acid also uncolored dye kations
or color-base would oceur and this even in so great a quantity, that
they must partly reconstruct the dye, causing likewise the color
partly to return. This cannot be a pure ion-reaction for ion-reactions
have a quick process, and the color returns only slowly, but in the
color-base an alteration of structure may have taken place, a
phenomenon of which examples are known.

Is it now possible to ascertain, that in an almost decolored
fuchsin-solution more hydrochlorid acid and color-base occur than
in an equally stained diluted fuchsin-solution which has never been
in contact with carbon? Apparently it is.

Silver-nitrate occasions in the almost decolored fuchsin-solution a
distinct opacity, but does not do so in the as deeply stained diluted
solution. Consequently there are in the former case more Cl-ions
than in the latter. In fact this is in conformity with what FREUNDLICH
and Loskv discovered.

Adding a few drops of acetic acid causes the color to return
quickly and intensely in the almost decolored fuchsin-solution,
whereas an as deeply stained diluted solution does not change its
color by it. So, perhaps the acetic acid enables the color-base in
the decolored solution to form very quickly a colored salt, for which
there is of course no opportunity in the diluted solution.

| did not meet the phenomenon offered by fuchsin again in “Crystall-

1325

violett”” nor in any other dye experimented upon in this respect.
Only „Säure-fuchsin”, a dye which is no chloride and deviates con-
siderably in composition from fuchsin showed something like it. It does
not make any difference whether Säurefuchsin or Rubin S of GRÜBLER or
Säurefuchsin S.M.P. of the Actien-Gesellschaft fiir Anilinfabrikation of
Berlin is used for this purpose. I have never been able to state with
certainty whether in a '/,,°/, Säure-fuchsin-solution being almost
entirely decolored the color partly returns after the filtration of the
carbon, But | have experienced, that in the almost decolored solu-
tion after the filtration and even after the lapse of some weeks the
color can suddenly and very intensely be reproduced by acetic acid.
It must be taken in consideration in this case, that acetic acid
stains likewise a diluted Säure-fuchsin-solution which has never been
in contact with carbon, somewhat more deeply, but by far not so
much as the solution almost decolored by carbon.

1 desist from suggesting an hypothesis for the explanation of the
last mentioned phenomenon, and only hope, that the nature of what
1 have communicated here may, at some time or other, be explained
and increase our knowledge of the theory of histological staining
methods.

Physiology. — “Phagocytes and respiratory centre.”
Their behaviour when acted upon by oxygen, carbonic acid,
and fat-dissolving substances. Explanation of the excitement-
stage in narcosis.” *) By Prof. H. J. HAMBURGER.
(Communicated in the meeting of March 27, 1915).
Introduction.

In a former paper it was shown that Iodoform, even in extremely
slight quantities can accelerate phagocytosis, to a considerable extent’).
We explained this action by assuming that this substance, after being
dissolved in the lipoid surface, softens the cells, thus facilitating the
amoeboid motion.

If this view were correct, it might be expected that other substances
which are soluble in lipoids, would act in the same way. This was
indeed the case, without a single exception, with all the substances
investigated, only not, as we found afterwards, with carbon sulphide.
But in chloroform, chloralhydrate, ethylalcohol *), butyric acid, propionic
acid*), benzole, turpentine, camphor, Peruvian balsam‘) (cinnamic

1) A detailed account will appear in the Internationale Zeitschrift für physikalisch-
-chemische Biologie. (ENGELMANN, Leipzig).

2) H. J. HAmpureer, J. pe Haan and F. Busanovic, These Proceedings, March 25, 1911.

5) H. J, HAMBURGER and J. pe Haan, Ibid, October 28, 1911.

1326

acid) the same property became manifest, even when they were
taken in very weak concentrations e.g. propionic acid 1 : 10.000.000,
chloroform 1 : 5.000.000, chloralhydrate 1 : 20.000, alcohol 1 : 10.000,
concentrations answering to the division-coefficients of these substances
between oil and water.

In order to penetrate more deeply into the nature of this pheno-
menon, we asked ourselves if the entrance of these substances into
the phagocytes resulted in a decreased viscosity or in a decreased
surface-tension. But experiments in this direction made by BuBaNnovic
in our laboratory’), and after another and better method in that of
Prof. ARRHENIUS’) at Stockholm, gave negative results; so did other
experiments taken by myself later on. The object of these experiments
was to investigate if the surface-tension of oil decreased under the
influence of small quantities of chloroform and similar substances.

It must, however, be remembered that the lipoids of the cell-
surface may not be considered identical with oil, so that it is
not impossible that after all we have to deal with a decreased
surface-tension. In order to ascertain if this is really the case the
experiments of BuBanovic would have to be repeated with the lipoids
of the white blood-corpuscles, but it is very difficult to obtain these
substances in sufficient quantities. Perhaps in the future, methods
may be available enabling us to determine these values with slighter
quantities than are required at present.

But however this may be, as yet the experiments which aimed
at establishing a modification in the viscosity or surface-tension under
the influence of traces of fat-dissolving substances, have led to
negative results. *)

Whilst looking forward to these researches with the lipoids of
the blood-corpuscles or, better still, with naked protoplasm, we asked
ourselves whether perhaps the acceleration of phago-
cytosis would not be accompanied by an increased
oxygen-consumption, would perhaps even be caused
by it.

This possibility had already been suggested by us before *), and

IE. BuBanovic, Zeitschr. f. Chemie und Jndustrie der Kolloide. 10 (1912), 178.

2) F. Busanovic, Middelanden f. K. Vetenskaps-Akademiens, Nobelinstitut N°. 17
(EIA):

5) Later experiments however have shown, that small amounts of chloroform
diminish the viscosity of York. [Note added to the translation). :

4) H. J. Hampurcer: Physikalisch-chemische Untersuchungen über Phagozyten.

Ihre Bedeutung von allgemein biologischem und pathologischem Gesichtspunkt.
Wiesbaden, J. F. BERGMANN, 1912, S. 167.

432%

had led Hrerr and BaArven to investigate the absorptive power of
red blood-corpuscles for chloroform in chloroform-narcosis. These
investigators found indeed that during the chloroform-narcosis the
oxygen-percentage of the red blood-corpuscles is modified *). It was
found to have increased. Because less oxygen is used?

We began now by investigating, to what extent in an ordinary
leneocyte-suspension i.e. without chloroform the phagocytosis depended
on the oxygen-percentage of the medium.

For these investigations no carbon was used, because, as we
know, this substance possesses the property of absorbing gases to a
considerable extent. Instead of it we made use of amylum of rice-
flour. The technical part had been worked out by Dr. J. pr Haan,
who, in consequence of the European war was prevented from
completing his investigation. A detailed description of the technical
part will, therefore, be published later on.

The principle for determining the degree of phagocytosis was the
same as that for the taking up of carbon. It was namely determined
which percentage of the leucocytes counted, had taken up amylum
after a certain time.

I. Comparison of the extent of the phagocytosis in a NaCt-
solution which had been treuted with nitrogen, with
atmospheric aw and with oaygen.

As regards the way in which the experiments were carried out
the following may be observed.

A thick suspension of horse-leucocytes in NaCl 0.9°/, is prepared
in the manner we described before. *)

Further a considerable volume of NaCl-sol. 0.9" , is boiled out,
an increase in the concentration being obviated.

a. part is treated with nitrogen.
| att Re eee ,, atmospheric air.
eae Cag ML Ls » Oxygen.

Thus NaCl-solutions with increasing oxygen-percentages were ob-
tained. We satisfied ourselves of this by oxygen-determinations accord-
ing to the method of Winkier with manganous chloride, natrium-
thiosulphate, hydrochloric acid and I in Kl. 1 cubic centimetre of
the thiosulphate-solution corresponds with 0.0782 mmg. of oxygen.

1) Hecer et Barucu. Instit. Solvay 13 Fasc. 1; Bulletin de Acad. Royale de
Médecine de Belgique Séance du 26 Juillet 1915.

2) Cf. inter alia. Physik. chem. Untersuchungen über Phagozyten. Wiesbaden, J. F.
BERGMANN 1912,

‘

1525

A description of the method is given a.o. by Hans Fini, Zeitschrift
f. allgem. Physiol. 8, (1908) 496.

To 4 ec. of the solutions a, 6 and c 0,1 cc. of serum is added
and to these mixtures 0.3 cc. of the thick leucocyte-suspension.

After they have been exposed to room-temperature for half an hour,
during which time they were repeatedly stirred gently, 0.3 cc. of
an amylum-suspension in NaCl 0.9°/, is added to the suspensions,
after which they are kept at 37° in an incubator. After 20 or
30 minutes they are simultaneously taken out and the phagocytosis
is stopped by placing them in icewater and adding formol. Then
preparations are made which are examined after.

The reader will have noticed that in these experiments serum is
added. Unlike carbon, amylum is only taken up if the fluid contains
some serum. The most desirable quantity amounts according to
pE Haan’s researches to 2'/, vol. percent. This was confirmed by
OUWELEEN, who will soon publish further particulars in a dissertation.

Further - particulars relating to the technicalities of the amylum-
phagocytosis are omitted here. We can now proceed to summarize
the results of one series of experiments in a table.

TABLE £

Comparison of the extent of the phagocytosis in NaCl-solution, which had
been treated with nitrogen, with oxygen and with atmospheric air.
Phagocytes and amylum had been in contact for 20 minutes !).

Number of leuco- Percentage of leu-

Number of leuco- cytes having taken cocytes containing

The leucocytes are in cytes counted

up amylum amylum

NaCl-solution ,
treated with nitrogen 571 159 28.5 0/0
NaCl-solution
treated with air 672 130 19.3%,
NaCl-solution 835 AE 13.1%

treated with oxygen

1) If the leucocyte-Suspension remains at 37° in contact with amylum for a
longer time, the values denoting the extent of phagocytosis will be greater. But
the differences in the degree of phagocytosis become smaller and smaller. At
length a time will come when in all three fluids the phagocytosis is the same.
This is the case mostly after about 11/, hour. The reason is that we have to do
with a difference in velocity. Evidently the phagocytosis went slowest in the
solution treated with oxygen, fastest in the one treated with nitrogen. If the
phagocytes in the oxygen solution are left sufficient time, they will finally have
taken up amylum in as ample a degree as the phagocytes in the nitrogen-medium
in a shorter time.

1329

This table brings the unexpected result, the phagoeytosis is greatest
where the slightest! amount of oxygen was present.
We see namely that in the NaCl-solution treated with nitrogen

rae 28-—19
the phagocytosis is about ES > 100 = 47°/, greater than in the

e

one treated with air; and in the latter again EE Cae < 100 == 46°/,

greater than in the one treated with oxygen.

A repetition of the experiment when only the NaCl solutions
were compared which had been treated with nitrogen and with
oxygen gave a similar result.

TABEE RN

Effect of nitrogen and of oxygen on phagocytosis.

In the fluid treated with nitrogen 22.2 0/,
” ” ” ” ” oxygen 1 7 = 6 »
” ” ” ” ” nitrogen 29 4 4 ”
” „ ” ” ” oxygen 23 ee 4 ”

In the following series of experiments NaCl-solutions which had
not been boiled out have been compared ; some had been treated
with nitrogen, others had not. This treatment consisted in N-gas
(from ‘a metal cylinder) being led for '/, hour into the bottle with
NaCl-solution of 0.9°/, whilst the fluid was shaken every 5 minutes
with the gas on the top of it.

It goes without saying that just as in the experiments of Tables
I and IL a complete expulsion of oxygen could not be expected,
but this was not desired. If this had been aimed at, the suspension
which was added afterwards, should also have been treated with N.

TABLE IL

Effect of nitrogen on phagocytosis.

The fluid is not It is treated with

treated nitrogen
20 0/, 27.9 0/,
Mt | ede He
kras | zene

16.6 , | gn

1330

Here again the phagocytosis is increased everywhere by nitrogen.
A new confirmation is supplied by the following series of expe-
riments.

FABLE IV.

Effect of a treatment with nitrogen on phagocytosis.
Degree of phagocytosis.

The fluid is not | It is treated with

treated | nitrogen
|

22.9 %p | 26.1 0/0

23:8, | B

a3 3. | 978

20.5 , | 31.2 ,

Here again a higher degree of phagocytosis showed itself unmis-
takablu, where only a slighter amount of oxygen was met with.

It must be noted that in two instances the results were different.
It appeared namely that in one of the experiments the result was
as follows :

in the NaCl-solution treated with air... . . . phagocytosis 34.7°/,
LE iw = go OBYGER oss. 5 86. +3
and in the other case:
NaCl-solution treated with air... . . . phagocytosis 40.6°/,
ms es 3. ORDEN et py ELT

It is obvious, that am increased O-percentage has caused no decrease
of the phagocytosis here, rather a slight increase. But these two
results will have to be attributed either to mistakes in the experi-
ment, or to individual differences, often met with in the phagocytes
of different horses. The considerable amount of material which we
have experimented with for many years, leaves no doubt about
such differences. It has even occurred that the same horse which
had been used 6 times at long intervals, and which had always
supplied jieucocytes that gave satisfactory results, gave cells the 7‘
time with which hardly any phagocytosis could be obtained.

This could not be attributed to the nature of the fluids, for with
the same fluids another horse gave irreproachable results.

Yet in the results obtained with nitrogen, the possibility remained
that this gas contained substances which had accelerated the phago-
eytosis. This was not very probable since the N, supplied by the

1331

Company “Oxygenium” at Schiedam had been prepared by fractio-
nated distillation of liquid air. Tt still contains about 1°/, of oxygen,
further gases of the helium group, and a bit of oil-products due to
the pumps. At any rate it seemed desirable to carry out experi-
ments with hydrogen likewise.

Il. Lifect of hydrogen phagocytosis.

These experiments were carried out lke those with nitrogen.
Here too compressed gas was used which had been purified in the
usual way. The results, however, were different from what we had
expected, the phagocytosis was found to have decreased instead of
increased.

The phagocytosis was compared in fluids of which the NaCl-
solution had not been treated, and which contained therefore compa-
ratively much oxygen, with the phagocytosis in fluids of which the
NaCl-solution had lost the greater part of its oxygen by being treated
with H.

TABLE-V:

Effect of hydrogen on phagocytosis.
Degree of phagocytosis.

The fluid is not It is treated with
treated | hydrogen
24.5 A 14.7 0/0
ZEI 5 ; 14.9";
10 5, OE 5
219 EE

The average of the first column comes to 21.5°/,, that of the
second to 17.1°/,. There can be no doubt, therefore, but the hydrogen
has impaired the phagocytosis.

The most obvious explanation was, that some noxious impurity
had not been removed altogether. Therefore we used in the follo-
wing experiments hydrogen which we had prepared ourselves from
chemically pure zine, which had been provided with a thin layer
of copper by means of a copper-sulphate-solution of 5°/,.

Now the results were entirely different ; ¢variably the phagocytosis
wus promoted by the treatment with hydrogen.

88
Proceedings Royal Acad. Amslerdam. Vol. XVII.

1332

TABLE ME

Effect of Hydrogen on the phagocytosis
Degree of Phagocytosis.

The fluid is not It is treated with
treated hydrogen -
20.1 Oo | 25.7 %
20.5 „ | 28,
18:9- 253»
Eee | 24.9 ,

This table shows that if the salt-solution is not treated with hydrogen,
the phagocytosis averages 19.4°/,, if it is treated with hydrogen
24.9°/,. -

Besides these experiments several others were carried out, which
all resulted invariably in phagocytosis being promoted by the action
of hydrogen.

Only a few series of experiments must be more particularly drawn
attention to. Their purpose was to investigate to what extent an
intense hydrogen-treatment would produce another degree of phago-
cytosis than a less intense one.

It appeared then that a less intense treatment raised the phago-
eytosis from 41.2°/, to 47.1°/,, whilst an intense treatment only
raised it to 45.4 °/,.

It seemed to us that this must be due to the fact that an extensive
removal of oxygen causes incipient paralysis, which will make itself
the more felt as the oxygen is more completely removed.

If this view was correct, then it must be possible to lower the
phagocytosis still more by a still more energetic removal of oxygen,
nay to make it fall below that observed in the fluids not treated
with hydrogen. It was indeed found possible to do so. We shall
give an account of a few experiments taken with nitrogen.

Ill. Eject of an extensive removal of oxygen.

A NaCl-solution of 0,9°/, is thoroughly treated with nitrogen ;
this is also done with the bloodserum, which we did not do as yet;
of this serum 2'/, vol. pere. is added to the NaCl-solution. Of this
we take 4cem., add 0,3 eem. of a thick leucocyte-suspension (in
NaCl 0,9°/,) and leave the mixture exposed to roomtemperature for
half an hour. Thus the leucocytes lose oxygen. Now 0,3 ccm. of a

1333

suspension of amylum in NaCl-solution are added, which had likewise
been treated with N, and the mixture thus obtained is exposed to
the effect of body-temperature for 25 minutes.

If, however, the same experiment was carried out in exactly the
same manner, but only with this difference that the fluid treated
with nitrogen could act at room-temperature for 5 hours instead of
half an hour on the phagocytes, then the phagocytosis was found
to be much less than in the original fluid, which had not been
treated with nitrogen. Hence after a longer exposure of the phago-
eytes to a medium which contains little oxygen, paralysis will set
in, the available amount of oxygen being consumed to a great extent.

This may appear from the following experiments.

PA BLE, ME

Effect of an extensive withdrawal of O on phagocytosis by a
long exposure of the phagocytes to the normal medium
and to the medium treated with N.

| Phagocytosis

After a 5 hours’ exposure of the 681
phagocytes to the serous NaCl-sol. | — * 100 = 50.71°/,
which had not been treated with N. | 1941

After a 5 hours’ exposure of the 521
phagocytes to the serous NaCl-sol. | 4-4 > 100 = 44.380/,
which had been treated with N. 1174

Whilst formerly after an exposure of one hour an increased
phagocytosis was invariably observed, this increase has changed
into a decrease after a 5 hours’ exposure.

We shall add another experiment, showing the effect on the
same leucocytes of an exposure of '/, hour and 4'/, hours.

FABLE Vill.

Effect of a short and of a long exposure of the phagocytes to
a solution containing only traces of oxygen.

Exposure of 1/2 hour | Exposure of 41/9 hours
|
In the ee serous In the normal serous
44

NaCl-sol.: 44 < 100 = 25.90, NaCl-sol. : os > 100=39.49/

941
In the serous NaCl-sol. contain.|In the serous NaCl-sol. contain.

2
atrace of O: =! 100 = 34.59/o'a trace of O: ne X< 1003255

930

1334

Hence we see that the same phagocytes which, after being exposed
to nitrogen for half an hour, give a considerable increase viz.

34 5—25.9

OEE xx 100 = 33.2°/,, show a decreased phagocytosis of
25.9

39.4 — 325 ne |
OL > 100 =17.5°/, after. an jacuon of 4°/, hours, the loss

of O having become greater in that time. A longer exposure to the
medium containing little O would probably have lowered the phago-
cytosis still more. The phagocytes will consume more and more
their own oxygen.

IV. Respiratory centre and phagocytosis. Eject of carbonic acid
and of potassium cyanide. Discussion of the results obtained.

If we submit the results obtained to a close examination, we
are struck by the agreement between the effect whieh a withdrawal
of oxygen has on the respiratory centre on the one hand, and on
the phagocytes on the other.

After the many researches on the respiratory centre we may take
it for granted that, besides by the action of carbonie acid, the respi-
ratory centre is also stimulated by a withdrawal of oxygen.

If in an animal the O-pereentage of the blood is increased by
frequent deep respiration, then this respiration may be stopped for
some time without the animal showing any need of it (apnoea).
Under these circumstances the stimulus passing from the respiratory
centre on to the nerve centres of the respiratory muscles is evidently
too weak to act upon it successfully. Likewise with the phagocytes
we observe that a considerable increase of the O-supply leads to a
decreased activity, a decreased phagocytosis. Af the O-percentage
decreases, the phagocytes are stimulated into a higher activity, the
phagocytosis increases, while it decreases more anil more, subsequently,
as more O is lost, in accordance with the fact that all cells of the
animal organism need oxygen, if they are to continue their functions.

The respiratory centre too increases its activity when O is very
scarce (dyspnoea), and is paralyzed when O continues to be withdrawn.

Hitherto we have made no quantitative comparisons between the O-percentage
of the fluid in which the phagocytes are paralyzed, and that in which the nervous
centre refuses to act. These comparisons, however, can only relate. to the medium,
hardly to the cells themselves. In view of these considerations and also owing to
the fact that a quantitative determination of phagocytosis is very liresome, no
experiments have been made in this direction. It may be expected that the respira-
tory centre will be more sensitive to a withdrawal of oxygen than the phagocytes.
The higher nervous centres are certainly still more sensitive than the respiratory centre.

1335

In view of this agreement between phagocytes
and respiratory centre the question suggests
itself whether other substances have likewise
the same effect on both.

Therefore we have in the first place investigated the effect of
carbonic acid on phagocytosis. Some years ago already we published
investigations on the effect of CO, on phagocytes, and arrived at
the conclusion that the use of somewhat large amounts of CO, had
an injurious effect on phagocytosis’). The effect of slight quantities
was not investigated then.

Now that we had a more accurate methode at our disposal, it became
desirable to repeat the experiments with slighter quantities of CO,

NaCl-solutions were made with different CO,-percentages by
mixing different quantities of a boiled out NaCl-solution with the
same NaCl-solution which had been saturated with CO,

We prepared the following mixtures: containing

4 Vol. NaCl-sol. + 1 Vol. of the NaCl-sol. saturated with CO... 85 Vol. pet CO,

ons": F Sparkle VOL Ns - 7 jd EIN oet ers

19 ” ” = 1 Vol. ” ” ” ” ” ” 8.75 ” „ El

KO 5 ioe Wy Olas! 45 8 2 3 5 Set ven

99 2 ” oe 1 Vol. ” 9. ” ” ” ” 1 75 „ 9 „
TABLE IX

Effect of CO, on phagocytosis.

Boiled out NaCl-sol. | Phagocytosis

containing : |
no CO, 46.3 %
go Vols” Perc, “CO, 0
ae ' pe 0.7 %
8.15, 5 ABe
3, ; 7 A
V's; 8 ” 4215

This table shows that carbonic acid has effected an entire or
entire paralysis of the phagocytosis, except in the concentrations
3.5 °/, and 1.75 °/,.

1) Hampurger. Virscnow's Archiv 156 (1899), 329.

1336

Now the question was whether perhaps below, or in the neigh-
bourhood of the concentration of 1,75°/,, there would not be one,
in which the phagocytosis was increased. Therefore the experiment
was repeated also with weaker concentrations.

TABLE &%

Effect of CO, on phagocytosis.

Boiled out NaCl-sol.

containing Phagocytosis
no CO, ax 100 = 27.99,
17.5 Vol. percent CO, 0
ie a mead Fog X 100 = 26.7%
tie. AN or X 100 = 31.9%
0.35 , aaa tap X 100 = 30 0
0.175 , ait aan X 100 = 27.6%

From this series of experiments it appears, just as from the
preceding table, that in the NaCl-solution containing 17.5 °/, CO,
the phagocytosis is O, in that containing 3.5°/, about the same as
if there had been no CO, in it. At 1.75 vol. pere. the phagocytosis
has risen 14.2°/, and at 0.35 vol. pere. CO,, 7°/,. At 3.5 vol. perc.
the promotive action is therefore compensated by the noxious effect
peculiar to CO,

Consequently this series of experiments plainly demonstrates that
in weak concentrations carbonic acid increases the phagocytosis, and
that in higher concentrations it has a paralyzing effect.

We shall adduce no more experiments in this short article. Let
the statement suffice that the result was repeatedly and invariably
confirmed.

It should, however, be pointed out that the amount of CO,, re-
quired to effect an increase (or also a paralysis) will have to be
greater when the phagocytes are surrounded by serum, than in our
experiments where the medium was a NaCl-solution containing only
24 vol. pere. of serum. On another occasion we shall, for a different

1337

purpose, (the effect of artificial venous congestion on the phago-
cytosis of bacteria) determine the amount of CO, which accelerates
phagocytosis when only serum is used.

At any rate it may now be looked upon as an established fact
that, as regards carbonic acid, the phagocytes behave exactly like the
respiratory centre. For the respiratory centre is also stimulated by
slight quantities and paralyzed by greater ones.

As we know, potassiumeyanide has a highly stimulating effect on
the respiratory centre before paralysis sets in. A violent dyspnoea
manifests itself.

It is all but certain that this symptom must be connected with
the property this substance has of obstructing the oxygen-consump-
tion of the cells. This becomes manifest, for instance, when we
note the effect of KCN on muscular contraction. Even if to the
blood with which the muscle is supplied, oxygen is added in an
ample degree, traces of potassiumcyanide lower the oxygen-consump-
tion considerably.

What may be the effect of potassiumeyanide on phagocytosis ?

The following tables will supply an answer.

TABLE XL

Effect of KCN on phagocytosis.

Serous ee Phagocytosis

0 | 12.1 9,

1 : 1000 0

{> 2000 | 0

1: 5000 | 6.6 0/,

1: 10.C00 dn

1: 50.000 23.9

1 : 100.000 18:25,

From this table it appears that in a concentration of 1 to 1000
and also of 1 :10000, KCN has had a noxious, but on the other
hand in weaker concentrations, a favourable effect on phagocytosis.

The following table contains experiments also with weaker con-
centrations.

1338

TABLE AIL
Effect of KCN on phagocytosis.

Serous NaCl-sol.

Phagocytosis
+ KCN |

| 187
de — 0
0 599 X 100 = 30%

204

289
1: 50.000 | 2 X<100=42.8 ,

231

1: 100.000 624% 100 = 36.8 5

1: 1000.000 A X 100 = 29.9 :

Hence we see that in slight quantities potassiumcyanide has a highly
stimulating effect on phagocytosis, which is checked by greater quan-
tities. Here again a perfect agreement in the behaviour of respiratory
centre and phagocytes.

V. Explanation of the stimulating effect of traces of chloroform
on phagocytosis, and of the excitement-stage in narcosis.

Let us now return to our startingpoint, viz. to the question what
may be the reason why traces of chloroform and similar substances
cause an acceleration of phagocytosis.

By Verworn and his school it has been demonstrated that in the
chloroform-narcosis the cells have lost the power of using the oxygen
offered to them, for oxydation purposes. There is asphyxia. The
supposition suggests itself that the application of small amounts of
chloroform brings about this blockade of oxygen imperfectly, and
that the phagocytes are thus reduced to a condition similar to that
which is met with when a short treatment with nitrogen and
hydrogen has caused them to lose part of their oxygen, which loss
has brought them into a state of increased sensitiveness.

The action of greater amounts of chloroform will cause the
potential oxygen percentage, if we may call it thus, to fall still
lower, the phagocytosis will begin to decrease: a decrease which
likewise sets in at a long action of a medium containing little
oxygen, as we obtained it by treatment with nitrogen or hydrogen.
(Comp. § III).

We have tested this view experimentally, for instance by allowing

1559

chloroform and nitrogen to act together under various conditions as
regards time and concentration. But we shall omit giving an account
of these experiments to restrict the size of this paper. Moreover a
detailed report will, as we said before, be published elsewhere.

And now the excitement-stage in narcosis.

If we let the various narcosis-theories pass in review, then it
appears that not a single one has even attempted to give an expla-
nation of the excitement-stage. Our researches on phagocytosis, and
the agreement in the conduct of respiratory centre and phagocytes
enable us to do so.

When Max Verworn in his article “Narkose” in the “Handbuch
der Naturwissenschaften” B. VI, 1912, has explained that. in his
opinion, narcosis is nothing but a consequence of acute asphyxia,
and adds a few words on the attendant symptoms in narcosis, he
expresses himself as follows :

“Es ist nicht wahrscheinlich, dass diese Neben wirkung (Excitations-
stadium) ebenfalls aus dem einem Punkte der Oxydationslähmung in
der Zelle entspringt, doch fehlt für die Genese dieser Nebemwirkung
bisher noch gede Analyse”.

Our investigations of the origin of an increased phagocytosis by
oxygen-withdrawal, have shown that also the excitement-stage in
narcosis is in perfect agreement with the fact stated by Verworn
in his narcosis theory.

We need only conceive that at the beginning of the narcosis, owing
to a decrease in the amount of available oxygen, the sensibility of
the higher nervecentres is heightened.

If the chloroform-inhalation is continued, this sensibility will
decrease, owing to a further decrease of the potential O-percentage,
and finally narcosis will set in. Whether the state of complete
narcosis is partly due to other factors, for instance to a semi-
coagulation of the protoplasm in the sense of CLaupr BERNARD, or
to a decrease of dispersity of enzymes ete. need not be considered
here. First the higher centres which are, as we know, very sensitive
to oxygen withdrawal, are paralyzed, then the spinal centres and
after that the respiratory centre.

We may add that in the first stage of narcosis not only the
higher cortical centres and the spinal centr s pass through an
excitement-stage, but according to researches of KNouL and of ARLOING
the respiratory centre is also in a state of heightened irritability.

The question which first suggests itself, is the following: how is
it that a decrease of the available oxygen-percentage heightens the
irritability of the phagocytes (and ganglion cells).

1540

We might suppose that — as regards the phagocytes — the
withdrawal of oxygen affects in the first place the surface of the cells;
owing to this fact the surface layer will plunge into their inner part
which contains more oxygen; thus the amoeboid motion would be
accentuated. The phenomenon would remind of the chemotactical
motion of bacteria to an airbubble. In the case of phagocytes we
might speak of an “entochemotaxis’, if | may be allowed to call it so.

But it might also be assumed that a withdrawal of oxygen causes
a decreased viscosity in the cells.

[L have indeed found that if yolk is treated with oxygen, the viscosity increases,
whence il follows that the viscosity is indeed affected by the oxygen percentage.
Albuminous solutions were not so affected; we must, therefore, think of lipoid
substances, and in this we are strengthened by observations of THUNBERG, which
were amply confirmed by WARBURG, viz. that lecithin in the presence of iron can
bind oxygen in relatively great quantities. They think that an oxydative decomposition
of lecithin takes place, but could find no oxydation-products In my opinion we
have to deal here with a compound of lecithin iron, which, like haemoglobin, can
bind oxygen in a dissociable form.

In this way oxygen might be supplied in a concentrated form to the oxydable
substances in the cell. It is the task of the red blood-corpuscles to supply on
their way through the capillaries, and by means of plasma and lymph, the oxygen
required for the tissue-cells|. 4)

In this direction my investigations are continued. More problems

suggest themselves which will not be discussed now.

SUMMARY.

lL. Lf phagocytes are exposed during half an hour to a medium
from which O has been almost entirely removed, they display a
considerable acceleration of phagocytosis.

If the cells are left for a longer time, e.g. 5 hours, in this
solution, then the acceleration of the phagocytosis will give way to
a retardation.

2. For this acceleration of the phagocytosis by lack of O, which
may seem strange at a first glance, and which was indeed unex-
pected, an analogy may be found in the respiratory centre. Here too
lack of O heightens the irritability (dyspnoea), the respiration
ceasing entirely when the amount of O is further decreased.

3. This view is confirmed by the corresponding behaviour of both
cellspecies when exposed to KON.

1) || Note added to the translation.

1341

It is well-known that this substance cheeks the O-consumption.
When applied in traces, which renders the check imperfect, KCN
was found to acceierate phagocytosis considerably. On the respiratory
centre the effect of slight quantities of KCN is the same: Violent
respiratory movements set in. Greater quantities cause paralysis in
both cases.

4. Also as regards carbonic acid an analogy is found between
_ phagocytes and respiratory centre. Traces of CO, were discovered to
promote phagocytosis, whilst greater quantities decreased it. As we
know the irritability of the respiratory centre is likewise increased
by CO,, but the centre is paralyzed by an excess of CO, in the
blood.

5. The facts and views set forth here, supply an obvious answer
to the question which formed the starting-point of the present in-
vestigation: why do traces of chloroform and other fat-dissolving
substances cause an acceleration of phagocytosis ?

The numerous researches of VeERWORN and his pupils on narcosis
have established the fact that narcotics such as chloroform have the
property of impeding the O-consumption by the cells (spinal centres,
nerve-fibres, amoebae etc.). Now it is obvious that as long as mere
traces of chloroform are acting, only part of the available oxygen
will be rendered useless, in other terms, the blockade of the oxygen
will be incomplete. And then the phagocytes are in the case of the
experiments mentioned sub 1, where partial removal of oxygen by
nitrogen or hydrogen causes an acceleration of the phagocytosis.
This acceleration gradually passes into a retardation in proportion
as the store of oxygen of the cell becomes more exbausted; an
exhaustion which sets in quickly when, for instance by the admini-
stration of larger amounts of chloroform, the oxygen-consumption
has fallen to a minimum or has ceased altogether.

hb. The explanation given sub 5 of the acceleration of phago-
eytosis by traces of chloroform is in perfect agreement with the
fact that in the first stage of chloroform-narcosis the irritability of the
respiratory-centre is increased. Likewise the excitement-stage is ea
plained, which manifests itself at the beginning of the narcosis, and
which hitherto none of the narcosis theories have so much as attempted
to explain. (Cf. note 3 p. 1326).

Here too, with the higher nerve-centres, the explanation must be
sought in a heightened sensitiveness in consequence of an incipient

1342
lack of oxygen, which increases if the chloroform inhalation is
continued, and finally leads to a paralysis of consciousness. When
this sets in, the respiratory centre has not been paralyzed yet. It
is indeed a well-known fact that the higher brain-centres are more
sensitive to oxygen-wathdrawal than all other cells of the body.

Probably the increased sensitiveness, as a result of a partial oxygen-
withdrawal, must be looked upon as a general phenomenon. The
sensitiveness of the vomit-centre for instance decreases, just like
that of respiratory centre and phagocytes, if more oxygen is supplied.
Hence the inclination to vomit may be subdued to some extent Dy
frequent and deep breathing, whilst if is stimulated by lack of
oxygen.

Groningen, March 1915. Physiological Laboratory.

(June 3, 1915).

CONTENTS.

ABEL’s polynomia (On Hermire’s and). 192.
ABSORPTION LINES D, and D, (On the structure of the). 720.
AIR-BLADDER (The physiology of the) of fishes. 1088.
ALBUMINOUS FLUIDS (The identification of traces of bilirubin in). 807.
ALKALIES (The coloration of some derivatives of Picrylmethylamide with). 647.
ALLOTROPY (The) of cadmium. II. 54. LIL, 122. IV, 638. V. 1050.
— of zine. II. 59. IIL. 641.
— of copper. II. 60.
— of antimony. I. 645.
— of lead. 1. 822. Note. 1055.
— of potassium. I. 1115.
— of bismuth. Il, 1256,
— (The application of the theory of) to electromotive equilibria. II. 37. III. 680.
— (The metastability of metals in consequence of) and its significance for Chemistry,
Phyies and Technics. 200. III. 926. LV. 1238.
— (The metastable continuation of the mixed erystal series of pseudo-components
in connection of the phenomenon). II. 672.
ALMOND (Gummosis in the fruit of the) and the Peachalmorid as a process of normal
life. 810.
AMIDES of z-oxyacids (Action of sodium-hypochlorite on). 1163.
AMMONIA (On the interaction of) and methylamine on 2.3.4-trinitrodimethylaniline.
1034.
amMonta-water (The system). 182,
AMORPHOUS CARBON (The decoloration of fuchsin-solutions by). 1322,
Anatomy. P. Réraic and C. U. Artins Kapprers: “Further contributions to our
knowledge of the brain of Myxine glutinosa”. 2.
— C, WINKLER: “A case of occlusion of the arteria cerebelli posterior inferior”. 914.
— J. Boeker: “On the termination of the efferent nerves in plain muscle-cells,
and its bearing on the sympathetic (accessory) innervation of the striated muscle-
fibre”. 982.

— J. Boeke: “On the mode of attachment of the muscular fibre to its tendonfibres
in the striated muscles of the vertebrates’, 989.

— H. A. VERMEULEN: “The vagus area in Camelidae”, 1119.
ANOMALIES (On SEELIGER’s hypothesis about the) in the motion of the inner planets, 23,
ANTIBODIES (On the formation of) after injection of sensitized antigens, II, 818,

89
Proceedings Royal Acad, Amsterdam, Vol, XVII.

JI CON TEAN EIB,

ANTIGENS (On the formation of antibodies after injection of sensitized). II. 318.

antimony (The allotropy of). I. 645.

APOPHYLLITE (On the real symmetry of cordierite and). 430.

ARIËNS KAPPERS (C. U.). v. Kappers (C. U. ARIENs).

ARSENIC TRISULPHIDE soLs (The connection between the limit value and the concen-
tration of). 1158.

ARSENIOUS OXIDE (Compounds of). I, 1111.

ARTERIA cerebelli posterior inferior (A case of occlusion of the). 914.

Astronomy. J. Wouter Jr: “On SEELIGER’s hypothesis about the anomalies in the
motion of the inner planets”. 23.

— W. pr Sirrer: “Remarks on Mr. WorrtJer’s paper concerning SEELIGER’s
hypothesis”. 33.

— W. pre Sitrer: “The figure of the planet Jupiter”. 1047,

— W. pr Sirrer: “On the mean radius of the earth, the intensity of gravity and
the moon’s parallax”. L291.

— W. pe Sirrer: “On isostasy, the moments of inertia and the compression of
the earth”. 1295.

— W. pe Srrrer: “The motions of the lunar perigee and node and the figure of
the moon’. 1309.

ATEN (A. H. w.) and A. Smits. The application of the theory of allotropy to electro-
motive equilibria. If. 37. III. 680. ;

ATLANTIC OCEAN (On the relation between departures from the normal in the strength
of the trade-winds of the) and those in the waterlevel and temperature in the
Northern European seas. 1147.

ATOMIC FORCES (The calculation of the molecular dimensions from the supposition of
the electric nature of the quasi-elastic). 877.

BAAT (W.C. DE) and F, A. H. ScHREINEMAKERS. The system : copper sulphate, copper

| chlorid, potassium sulphate, potassium chlorid and water at 30° C. 533.

— On the quaternary system KC]l—CuCl,—BaClon—H,O. 781.
— Compounds of the arsenious oxide. I. 1111.

BACKER (H. J.) and A. P. N. FRANCHIMONT. The coloration of some derivatives of
picrylmethylamide with alkalies. 647.

— z-Sulpho-propionic acid and its resolution into optically active isomerides. 653.

BAKHUYZEN (H.G. VAN DE SANDE). Comparison of the Dutch platinum-
iridium Metre NO, 27 with the international Metre M as derived from the
measurements by the Duth Metre Commission in 1879 and 1880, and a prelimi-
nary determination of the length of the measuring-bar of the French base
apparatus in international metres. 311.

—- N. Winprsorr and J. W. DrreerINK: “Comparison of the measuring bar
used in the base measurement at Stroe with the Dutch Metre N® 27. 300.
BASE MEASUREMENT (Comparison of the measuring bar used in the) at Stroe with the

Dutch Metre No. 27. 300.
BEEGER (N. G. W. H.). On Hermrre’s and ABEL’s polynomia. 192.
BENZENE DERIVATIVES (The replacement of substituents in). 1027,

GUNT BNR SE Tit

BENZENES (The nitration of the mixed dihalogen). 846.

BEIJERINCK (M. W.). Gummosis in the fruit of the Almond and the Peachalmond
as a process of normal life, 810.

BILIRUBIN (The identification of traces of) in albuminous fluids. 807.

BINARY MIXTURES (Isothermals of monatomic substances and their). XVI. 275.
— (lsothermals of di-atomic substances and their). XV. 950, XVI. 959.

BINARY SYSTEM (On unmixing in a) for which the three-phase pressure is greater than
the sum of the vapour tensions of the two components. 834,
BismuTH (The allotropy of). IL. 1236.
BOEKE (J.). On the termination of the efferent nerves in plain muscle-cells and its
bearing on the sympathetic (accessory) innervation of the striated muscle-fibre. 982.
— On the mode of attachment of the muscular fibre to its tendonfibres in the
striated muscles of the vertebrates. 989.
—- presents a paper of Dr, A. B, DROOGLEEVER Fortuyn: “The decoloration of
fuchsin-solutions by amorphous carbon”. 1322.
BOER (s. DE). On the heart-rhythm. 1075 IL. 1135.
BOESEKEN (J.). On catalyse. 546.
— and W. D. Conen. The reduction of aromatic ketones. ILL. Contribution to the
knowledge of the photochemical phenomena. 849.
BOILING POINTS (The influence of the hydration and of the deviations from the ideal
gas-laws in aqueous solutions of salts on the solidifying and the). 1036,
BOIs (H. DU). Modern electromagnets, especially for surgical and metallurgic
practice. 468. |
— The universality of the ZEEMAN-eftect with respect to the Stark-effect in canal-
rays. 873.
BOKHORST (s. C.) and A. Smits. On the vapour pressure lines in the system phos-
phorus. IL, 678. IIL. 962.
— Further particulars concerning the system phosphorus. 973,
BOLK (L) presents a paper of Dr. P. Rörmra and Dr. C. U. Artiins Kappes:
«Further contributions to our knowledge of the brain of Myxine glutinosa”. 2,
— presents a paper of Dr. H. A. VERMEULEN : “The vagus area in Camelidae”. 1119,
BOSCH (J. C, VAN DEN) and ErNsr Conen. The allotropy of antimony, I. 645.
Botany. Miss Lucie C. Doyer: “Energy transformations during the germination of
wheat-grains”’. 62. id
— M. W. Bewertnck: “Gummosis in the fruit of the Almond and the Peachal-
mond as a process of normal life”. $10.
— C. FE. B. Bremexame: “The mutual iufluence of phototropic and geotropic
reactions in plants”. 1278.
BRAIN of Myxine glutinosa (Further contributions to our knowledge of the). 2.
BRAVAIS (The theory of) (on errors in space) for polydimensional space with
applications to correlation (Continuation). 150.
BREMEKAMP (C. BE. B) On the mutual influence of phototropic and geotropic
reactions in plants. 1278,

89*

IV CONTENTS.

BROUWER (u. A). On the granitic area of Rokan (Middle-Sumatra) and on contact

phenomena in the surrounding schists. 1190,
BRUIN (G. DE). A crystallized compound of isoprene with sulphur dioxide. 585.
— and Ernst Couen. The metastability of the metals in consequence of allotropy,
and its significance for Chemistry, Physics and Technics. IIL. 926.
BiicH NER (E. u.) and L. K. Worrr. On the behaviour of gels towards liquids and
the vapours thereof. Il. 92.
CADMIUM (The allotropy of). IL. 54. IIT. 122. IV. 638. V. 1050.
CAMELIDAE (The vagus area in). 1119.
cANAL-RAYS (The universality of the ZrrMaN-eftect with respect to the Srark-effect
in). 873.
CAPILLARY PRESSURE (On the measurement of the) in a soap-bubble. 946.
CAPILLARITY (Measurements on the) of liquid hydrogen. 528.
CATALYSE (On). 546.
CHEMICAL constant (The) and the application of the quantumtheory by the method
of the natural vibrations to the equation of state of an ideal monatomic gas, 20.
Chemistry. A. Smrrs and A. H. W. Aten: “The application of the theory of allotropy
to electromotive equilibria”. IL. 37. ILI. 680.
— E. Conen and W. D. HELDERMAN : “The allotropy of cadmium. IL. 54, [IT 122.
IV. 638. V. 1050.
— E. Corner and W. D. Hetperman: “The allotropy of zinc.” IL. 59. IIL. 641.
— E. Conen and W. D. Hetperman: “The allotropy of copper”. II. 60.
— F. A. H. SCHREINEMAKERS: “Equilibria in ternary systems”. XV. 70. XV1. 169.
XVII. 767. XVIII. 1260.
— L. K. Worrr and E. H. Biiconer: “On the behaviour of gels towards liquids,
and the vapours thereof’. IL. 92.
— A. Smrrs and 8. Postma: “The system ammonia-water’’. 182.
— Ernst Couen: “The metastability of the metals in consequence of allotropy and
its significance for Chemistry, Physics and Technics”. 200.
— F. M. JARGER and Ant. SIMEK: “Studies in the field of Silicate-chemistry”.
11. 239. III. 251.
— F. M. Jarcer: “The temperature-coefticients of the free surface-energy of liquids
at temperatures from —80° to 16509 C. I. 329. F. M. JArGER and M. Smit.
II. 365. III. 386. F. M. JaeGer and J. Kann. IV, 395. F. M. Jarcer. V. 405.
VI. 416. VII. 555, VIUI.9571:.
— F. A. H. ScHREINEMAKERS and Miss W. C. pe Baar: “The system: copper

sulphate, copper chlorid, potassium sulphate, potassium chlorid and water at
80° C.” 533.

— J. Borsnken: “On catalyse”. 546.

— G. pr Bruin: “A crystallized compound of isoprene with sulphur dioxide”, 585.
— H. KR. Krouyr: “Current potentials of electrolyte solutions”. 615.

— H. R. Krurr: “Electric charge and limit value of colloids”. 623.

— Ernst ConeN and J. C vaN DEN BoscH: “The allotropy of antimony”. I, 645,

GONTENTS. Vv

Chemistry. A. P. N. FRANCHIMONT and H. J. Backer: “The coloration of some deri-
vatives of Picrylmethylamide with alkalies”. 647.

— A. P. N. FRANCHIMONT and H. J. Backer: “a Sulpho-propionic acid and its
resolution into optically active isomerides’”. 653.

— A. Smits: “The metastable continuation of the mixed crystal series of pseudo-
components in connection with the phenomenon allotropy”. [L. 672.

— A. Smits and S. C. Bokuorst: “On the vapour pressure lines of the system
phosphorus”. [L, 678.

— F. E. C. Scuzrrer: “On gas equilibria and a test of Prof. v. p. Waars Jr.s
formula”, I. 695. If. 1011.

— W. Rerypers; “Equilibria in the system Pb-S-O, the roasting reaction
process”. 703.

— F. A. H. ScHREINEMAKERS and Miss W. C. pr Baar: “On the quaternary
system KCl-CuClo-BaClp-H,0”. 781

— Ernst Conen and W. D. Heiperman: “The allotropy of lead”. 822. Note. 1055.

— A. F. HOLLEMAN: “The nitration of the mixed dihalogenbenzenes”. 846,

— J. BÖEsSEKEN and W. D. Conen: “The reduction of aromatic ketones. III. Contri-
bution to the knowledge of the photo-chemical phenomena’’. 849.

— Ernst COHEN and G. bE Bruin: “The metastability of the metals in cons>-
quence of allotropy and its significance for Chemistry, Physics and Technics’.
Il]. 926.

— A. Smits and 8. ©. Bokuorst: “On the vapour pressure lines of the system
phosphorus”. IL. 678. ILL. 962.

— A. Smits and 8. C. Boxnorst: “Further particulars concerning the system
phosphorus”. 973.

— A. F. HorLEMAN : “The replacement of substituents in benzene derivatives’’. 1027.

— P. van RomBureu and Miss D. W. Wensinx: “On the interaction of ammonia
and methylamine on 2.3.4.-trinitrodimethylaniline”. 1034.

— C, H. Suuirer: “The influence of the hydration and of the deviations from the
ideal gas-laws in aqueous solutions of salts on the solidifying and the boiling
points”. 1036.

— Miss Apa Prins: “On critical end-points and the system ethanenaphtalene” 1095.

— F. A. H. Scutreinemakers and Miss W.C. pe Baat: “Compounds of the
arsenious oxyde”. 1111.

— Ernst Conen and S. Worrr: “The allotropy of potassium”. I. 1115.

— H. R. Kruyt and Jac. van DER SPEK: ‘“‘The connection between the limit
value and the concentration of arsenic trisulphide sols”. 1158.

— R. A. WEERMAN: “Action of sodium hypochlorite on amides of g-oxyacids’’. 1163,

— F. M. Jagcer: “Researches on Pasreur’s principle of the connection between
molecular and physical dissymmetry”’. 1. 1217.

— Ernst Conen: “The allotropy of bismuth”. [L. 1236.

— Erwst COHEN and W. D. HELDERMAN: “The metastability of the metals in
consequence of allotropy and its significance for Chemistry, Physics and Tech-
nics”, IV. 1238.

VI CONTENTS.

Ghemistry. A. W. K. pr Jone: “Action of sunlight on the einnamie acids”. 1274.
CINNAMIC AcIps (Action of sunlight on the). 1274.
crncLEs (Systems of) determined by a pencil of conics. 1107,
COHEN (ERNST). The metastability of the metals in consequence of allotropy, and
its significance for Chemistry, Physics and Technics, IT. 200.
— presents a paper of Dr. H. R. Kruyr: “Current potentials of electrolyte
solutions”. 615.
— presents a paper of Dr. H. R. Krurr: “Electric charge and limit value of
colloids”. 623.
— presents a paper of Dr. H. R. Kruyt and Jac. van DER Spek: “The connection
between the limit value and the concentration of arsenic trisulphide sols”. 1158.
— The allotropy of bismuth. IL. 1236.
— and J. C. van pen Boscu. The allotropy of antimony. I. 645.
— and G. pe Bruin. The metastability of the metals in consequence of allotropy
and its significance for Chemistry, Physics and Technics. III. 926.
— and W. D. Hentperman. The allotropy of Cadmium. IL. 54. LIL. 122, IV. 638.
V. 1050.
— The allotropy of zinc. IL, 59. II. 541.
— The allotropy of copper. IL. 60.
— The allotropy of lead. I. 522. Note 1055.
— The metastability of the metals in consequence of allotropy and its significance
for Chemistry, Physics and Technics. IV. 1238.
— and S. Worrr. The allotropy of potassium. L. 1115.
COHEN (w. p.) and J, Bérsexen. The reduction of aromatic ketones. IIT. Contri-
bution to the knowledge of the photochemical phenomena. 849.
coLLorps (Electric charge and limit value of). 623.
COLORATION (The) of some derivatives of Picrylmethylamide with alkalies. 647.
coLours (On FresNEr’s coeflicient for light of different). Ist part. 415.
COMPOUND (A crystallized) of isoprene with sulphar dioxide. 585.
COMPOUNDS of arsenious oxide. I, 1111.
CONCENTRATION (The connection between the limit value and the) of arsenic trisulphide
sols. 1158.
CONGRUENCE (A bilinear) of rational twisted quinties. 1250.
CONGRUENCES (Some particular bilinear) of twisted cubies. 1256.
conics (Systems of circles determined by a pencil of). 1107.
CONTACT=PHENOMENA (On the granitic area of Rokan (Middle-Sumatra) and on) in
the surrounding schists. 1190.
cOPPER (The allotropy of). II. 60.
— (Measurements on the specific heat of lead between 14° and 80° K. and of)
between 15° and 22° K. 894.
COPPER SULPHATE, Copper chlorid (The system :), potassium sulphate, potassium chlorid
and water at 30°. 533.
CORDIERITE and Apophyllite (On the real symmetry of). 430,

CONTENTS. ; Vil

CORRELATION (The theory of Bravars (on errors in space) for polydimensional space,
with applications to) (Continuation), 150.

CORRESPONDING sTATEs (Contribution to the theory of), 840.

CRITICAL POINT (Vapour pressures of oxygen and) of oxygen and nitrogen, 950.

CRITICAL QUANTITIES (A new relation between the) and on the unity of all substances
in their thermic behaviour, 451.

— (Some remarks on the values of the) in case of association. 598.

CROMMELIN (c. A). Isothermals of monatomic substances and their binary mix-
tures. XVI. 275.

— Isothermals of di-atomic substances and their binary mixtures. XVI. Vapour
pressures of nitrogen between the critical point and the boiling point. 959.
— E. Marutas and H. KaMERLINGH ONNes. The rectilinear diameter of nitrogen. 953.

CRYSTAL SERIES (The metastable continuation of the mixed) of pseudo-components in
connection with the phenomenon allotropy. LI. 672,

CRYSTALS (On a new phenomenon accompanying the diffraction of RÖNTGEN rays in
birefringent). 1204.

cuBe (The different ways of floating of an homogeneous). 224,

cusrcs (Some particular bilinear congruences of twisted). 1256.

curves (Characteristic numbers for nets of algebraic). 935.

— (Characteristic numbers for a triply infinite system of algebraic plane). 1055.

DECOLORATION (The) of fuchsin-solutions by amorphous carbon. 1322.

DEEP reflexes (Exaggeration of). 885.

DENSITY (On the manner in which the susceptibility of paramagnetic substances depends
on the). 110.

— (Accidental deviations of) and opalescence at the critical point of a single
substance. 793.

DIAMETER (The rectilinear) of nitrogen. 953. /

DIEPERINK (J. G.), N. WirpeBoemr and H. G. VAN DE SANDE BAKHUYZEN. Com-
parison of the measuring bar used in the base measurement at Stroe with the
Dutch Metre NO, 27. 300.

DIFFRACTION (On a new phenomenon accompanying the) of Röntgen rays in bire-
fringent crystals. 1204,

DIFFUSION COEFFICIENT (The) of gases and the viscosity of gas-mixtures. 1068.

DISCONTINUITIES (On apparent thermodynamic) in connection with the value of the
quantity 4 for infinitely large volume. 606.

DISSYMMETRY (Researches on PasTEvR’s principle of the connection between molecular
and physical). I. 1217.

DORSMAN (C.), H. KAMERLINGE Onnes and G. Horst. Isothermals of di-atomic
substances and their binary mixtures. XV. Vapour pressures of oxygen and critical
point of oxygen and nitrogen, 950.

DOYER (LUCIE c.). Energy transformations during the germination of wheat-grains. 62.

DROOGLEEVER FORTUYN (A. B). v. Fortuyn (A, B. DROOGLEEVER).

DROSTE (J.). On the field of a single centre in EINSTEIN'S theory of gravi-
tation. 998,

VIII GSOSNE DENS TES,

awe (The mean radius of the), the intensity of gravity and the moon’s parallax. 1291.
— (On isostasy, the moments of inertia and the compression of the). 1295.

EURENPEST (P.) and H. KAMERLINGH ONNEsS. Simplified deduction of the formula
from the theory of combinations which PrANcK uses as the basis of his radiation-
theory. 870.

— On interference phenomena to be expected when RÖNTGEN rays pass through a
di-atomic gas. 1184.
— On the kinetic interpretation of the osmotic pressure. 1241.

EHRENFEST (T.)—APFANASSJEWA. Contribution to the theory of corresponding
states. 840.

EINSTEINS theory of gravitation (On the field of a single centre in). 998.

EINTHOVEN (On the theory of the string-galvanometer of). 784.

ELASTIC DEFORMATION (On the lowering of the freezing point in consequence
of an). 782.

ELECTRIC CHARGE and limit value of colloids, 623.

pLecrropes (The effect of magnetisation of the) on the electromotive force. 745.

ELECTROLYTE SOLUTIONS (Current potentials of) 615.

ELECTROMAGNETS (Modern), especially for surgical and metallurgie practice. 468.

ELECTROMETER (A new) specially arranged for radio-active investigations. 659.

ELECTROMOTIVE FORCE (The eflect of magnetisation of the electrodes on the). 745.

ELIAS (G. J.). On the structure of the absorption lines D, and D,. 720.

— On the lowering of the freezing point in consequence of an elastic deforma-
tion. 732.
— The eftect of magnetisation of the electrodes on the electromotive force. 745.

END-POINTS (On critical) and the system ethane-naphtalene. 1095.

ENERGY- SURFACE (The temperature-coeflicients of the free) of liquids at temperatures
from —80° C. to 1650° C. 1. 329. If. 365. Hl. 386. IV. 395. V. 405. VI. 416,
VII. 555. VITL. 571.

ENERGY-TRANSFORMATIONS during the germination of wheat-grains. 62.

ENTROPY CONSTANT (Theoretical determination of the) of gases and liquids. 1167,

EQUATION or sTaTE (The chemical constant and the application of the quantum theory
by the method of the natural vibrations to the) of an ideal monatomic gas. 20.

EQUILIBRIA (The application of the theory of allotropy to electromotive). IL. 37. IIL. 680.

— in the system Pb—SO, the roasting reaction process. 703.
-- in ternary systems. XV. 70. XVI. 169. XVIL 767. XVIII, 1260.

ERRATUM. 944. 1073. 1202.

ERRORS IN space (The theory of Bravats, on) for polydimensional space with appli-
cations to correlation. (Continuation). 150.

ETHANE-naphtalene (On critical end-points and the system). 1095.

EUROPEAN sEAs (On the relation between departures from the normal in the strength
of the trade-winds in the Atlantic Ocean and those in the waterlevel and tem-
perature in the Northern). 1147.

EYKMAN (c.) presents a paper of Dr. L. K. Worrr : “On the formation of antibodies
after injection of sensitized antigens”. IL 318,

6 ON ft EBON TS IX

FISHES (The physiology of the air-bladder of). 1088,

FLOATING (The different ways of) of an homogeneous cube, 224.

FLORES (On the tin of the island of). 474.

FOLMER (MISS H.). A new electrometer, specially arrauged for radio-active
investigations. 659.

FONTAINE SCHLUITER (J. J. DE LA). v. SCHLUITER (J. J. DE LA FoNTAINE).

FORTUYN (A. B. DROOGLEEVER). The decoloration of fuchsin-solutions by
amorphous carbon, 1322.

FRANCHIMONT (A. P. N.) presents a paper of Dr. R. A. Weerman: “Action
of sodium hypochlorite on amides of g-oxyacids”, 1163.

— and H. J. Backer. The coloration of some derivatives of Picrylmethylamide with
alkalies, 647.

— a-sulpho-propionic acid and its resolution into optically active isomerides. 653.
FREEZING POINT (On the lowering of the) in connection of an elastic deformation. 732.
FREQUENCIES (The treatment of) of directed quantities. 586.

FRESNEL’s coefficient (On) for light of different colours. 445.

FUCHSIN-SOLUTIONS (The decoloration of) by amorphous carbon. 1322.

FUNCTIONS of HERMITE (On the). 1st part. 139.

GALLE (P. H.). On the relation between departures from the normal in the strength
of the trade-winds of the Atlantic Ocean and those in the waterlevel and tem-
perature in the Northern European seas. 1147.

GAs (The chemical constant and the application of the quantum theory by the method
of the natural vibrations to the equation of state of an ideal monatomic). 20.

— (On interference phenomena to be expected when Röntgen rays pass through a
di-atomic). 1184.

GAsES (The diffusion-coefticient of) and the viscosity of gas-mixtures. 1068.

— (Theoretical determination of the entropy constant of) and liquids. 1167.

GAS EQUILIBRIA (On) and a test of Prof. v. p. Waars Jr.’s theorema. 1. 695. IL. 1011.

Gas-Laws (The influence of the hydration and of the deviations from the ideal) in
aqueous solutions of salts on the solidifying and the boiling points. 1036.

GAS-MIXTURES (The diffusion-coefficient of gases and the viscosity of). 1068.

GELs (On the behaviour of) towards liquids and the vapours thereof. IL. 92.

Geodesy. H. G. VAN DE SANDE BAKHUYZEN, N. WiLpeBoEr and J. W. Dieperink :
“Comparison of the measuring bar used in the base-measurement at Stroe, with
the Dutch Metre NO. 27”. 300.

— H. G. van DE SANDE BAKHUYZEN: “Comparison of the platinum-iridium Metre
No. 27 with the international Metre M as derived from the measurements by
the Metre-Commission in 1879 and 1880, and a preliminary determination of
the length of the measuring-bar of the French base-apparatus in international
metres”. 311.

Geology. H. A. Brouwer: “On the granitic area of Rokan (Middle-Sumatra) and on
contact-phenomena in the surrounding schists”. 1190.

Geophysics. J. P. van DER Stok: “The treatment of frequencies of directed quanti-
ties”. 586,

X C1OENET TEEN] DIS.

Geophysics. P. H. GarrÉ: “On the relation between departures from the normal in the
strength of the trade-winds of the Atlantic Ocean and those in the waterlevel
and temperature in the Northern European seas”, 1147.

GEOTROPIC REACTIONS (On the mutual influence of phototropic and) in plants. 1278.
GERMINATION (Energy transformations during the) of wheat-grains. 62.

GRANITIC AREA (On the) of Rokan (Middle-Sumatra) and on contact-phenomena in
the surrounding schists. 1190.

GRAVITATION (On the field of a single centre in ErnstTeIn’s theory of). 998.
Gravity (The mean radius of the earth, the intensity of) and the moon’s parallax. 1291.

GuMMosis in the fruit (of the Almond and the Peachalmond as a process of normal
life. 810.

HAGA (H.) presents a paper of Miss H. J. Former: “A new electrometer, especi-
ally arranged for radio-active investigations”. 659.

— presents a paper of Prof. Ff. M. Jarcer: “On a new phenomenon accompanying
the diffraction of Röntgenrays in birefringent crystals”. 1204.

— and F. M, JAEGER. On the real symmetry of cordierite and apophyllite. 430.

HAMBURGER (i, J.) presents a paper of Dr. E, Laquevr: ‘On the survival of
isolated mammalian organs ‘with automatic function”. 270.

— presents a paper of Prof. A. A. HYMANs van DEN BERGH and J. J. DE La
Fontatne SCHLUITER: “The identification of traces of bilirubin in albuminous
fluids”. 807.

— Phagocytes and respiratory centre, 1325.

HEART-RHYTHM (On the). 1075. II. 1185.
HELDERMAN (W. D.) and Ernst Conen. The allotropy of cadmium. LL, 54. III.
122. IV. 638. V. 1050.

— The allotropy of zinc. IL. 59.

— The allotropy of copper. IL. 60.

— The allotropy of lead. 1. 822. Note. 1055.

— The metastability of the metals in consequence of allotropy and its significance
for Chemistry, Physics and Technics. LV. 1238.

HELIUM (Further experiments with liquid), [. 12. 278. K. 283. L. 514. N. 520. M. 769.
HERMITE (On the functions of). 1st part. 139.

— and aBEL’s polynomia (On). 192.

HoF (Kk) and H. KaMERLINGH Onnes. Further experiments with liquid helium. N. 520.
HOLLEMAN (A. F.) presents a paper of Dr. L. K. Worrr and Dr. E. H, Bicaner:
“On the behaviour of gels towards liquids and the vapours thereof. II. 92.

— presents a paper of Prof. J. BöESEKEN : “On catalyse”. 546.

— The nitration of the mixed dihalogen benzenes. 846.

— presents a paper of Prof. J. BöesEKEN and W. D. Conen: “The reduction of
aromatic ketones. III. Contribution to the knowledge of the photochemical
phenomena”. 849.

— The replacement of substituents in benzene derivatives. 1027.

— presents a paper of Dr. C, H. Sturrer: “The influence of the hydration and

OCOPN LE NEES: xl

of the deviations from the ideal gaslaws in aqueous solutions of salts on the
solidifying and the boiling points”. 1036.

HOLLEMAN (A. F.) presents a paper of Miss ADA Prins: „On critical end-points
and the system ethane-naphtalene”. 1095.

HOLST (G.) and H. KAMERLINGH Onnes. The measurement of very low temperatures.
XXIV. The hydrogen and helium thermometers of constant volume down to the
freezing point of hydrogen compared with each other and with the platinum-
resistance thermometer, 501.

— On the electrical resistance of pure metals. IX. 508.

— Further experiments with liquid helium. M. 760.

— H. KAMERLINGH Onnes and C. Dorsman. Isothermals of di-atomie substances
and their binary mixtures. XV. Vapour pressures of oxygen and critical point
of oxygen and nitrogen. 950.

HOOGEWERFF (s.) presents a paper of Prof, W. Reipens: “Equilibria in the system
Pb-S-O, the roasting reactionprocess. 703.

HULSHOF (H.). On the thermodynamic potential as a kinetic quantity. Ist part. 85.

HYDRATION (The influence of the) and of the deviations from the ideal gas-laws in
aqueous solutions of salts on the solidifying and the boiling points. 1036.

HYDROGEN (Measurements of isotherms of) at 20° C. and 13.95 C. 203.

— (Measurements on the capillarity of liquid). 528,

HYDROGEN ISOTHERMS (lhe) of 20° C. and of 15°.5 C. between 1 and 2200 atms. 217.

Hydrostatics. D. J. Korrewrec: “The different ways of floating of an homogeneous
cube”. 224.

HYMANS VAN DEN BERGH (A. A.) and J. J. DE La FONTAINE Scu.urrer. The
identification of traces of bilirubin in albuminous fluids. 807.

INERTIA (On isostasy, the moments of) and the compression of the earth. 1295,
INNERVATION (On the termination of the elilerent nerves in plain muscle-cells and
its bearing on the sympathetic (accessory) ) of the striated muscle-fibre, 982.

INTEGRAL EQUATIONS (On some). 286, .
INTEGRAL-FORMULA (On an) of STIELTJEs. 829.
INTERFERENCE-PHENOMENA (On) to be expected when Röntgen-rays pass through a
di-atomic gas. 1184.
INVOLUTION (A cubic) of the second class. 105.
— (A triple) of the third class. 134.
ISOMERIDES (4-Sulpho-propionie acid and its resolution into optically active). 653.
ISOPRENE (A crystallized compound of) with sulphur dioxide. 585.
tsostasy (On), the moments of inertia and the compression of the earth. 1295.
ISOTHERMALS of di-atomic substances and their binary mixtures. XV. Vapour pressures
of oxygen and critical point of oxygen and nitrogen. 950. XVI. Vapour-pressures
of nitrogen between the critical point and the boiling point. 959.
— of monatomic substances and their binary mixtures. XVI. 275.
ISOTHERMS (The hydrogen) of 20° C. and of 15% C. between 1 and 2200 atms. 217.
— of hydrogen (Measurements of) at 20° C, and 1595 C, 203.

XII - CO ANAESERNATSS.

JAEGER (fF. M.). The temperature-coeflicients of the free surface-energy of liquids at
temperatures from —80° ©. to 1650° C. 1, 329. V. 405. VI. 416. VII. 555.
WIil. ‘671:

— On-a new phenomenon accompanying the diffraction of Röntgenrays in birefrin-
gent crystals. 1204.

— Researches on Pasreur’s principle of the connection between molecular and
physical dissymmetry. [. 1217.

— and H Haga. On the real symmetry of cordierite and apophyllite. 430.

— and Jur, Kaun. The temperature coefficients of the free surface-energy of
liquids at temperatures from —80° C. to 1650° C. LV. 395.

— and ANT. SrMEK. Studies in the field of silicate-chemistry. IL. 239. ILL. 251.

— and M. J. Smir. The temperature-ccefticients of the free surface energy of liquids
at temperatures from —80° C. to 1650° C. LI. 365. IIL. 386.

JONG (A. W. K. DE). Action of sunlight on the cinnamic acids. 1274.
Juprrer (The figure of the planet). 1047.

KAHN (JUL) and F. M. Jaren. The temperature-coefficients of the free surface—
energy of liquids at temperatures from —80° C. to 1650° C. LV. 395.

KAMERLINGH ONNES (H.). v. Onnes (H. KAMERLINGH).

KAPPERS (C. U. ARIENS) and Pr Röruro. Further contributions to our know-
ledge of the brain of Myxine glutinosa. 2.

KAPTEYN (J. c.) presents a paper of Prof. M, J. van Uven: “The theory of
Bravats (on errors in space) for polydimensional space, with applications to
correlation”, Continuation. 150.

KAPTEYN (w.). On the functions of Hermite. Lst part. 139.

— presents a paper of Dr. N. G. W. H. Beecer: “On Hermire’s and ABEL’s
polynomia”’. 192.

— On some integral equations. 286.

— presents a paper of Prof. M. J. van Uven: “The theory of the combination
of observations and the determination of the precision, illustrated by means of
vectors”. 49.

KEESOM (w. u.). The chemical constant and the application of the quantum theory
by the method of the natural vibrations to the equation of state of an ideal
monatomic gas, 20.

— On the matter in which the susceptibility of paramagnetic: substances depends
on the density. 110.

— and H. KAMERLINGH Onnes. The specific heat at low temperatures. I. Measure-
ments on the specific heat of lead between 14° and 80° K. and of copper
between 15° and 22° K. 894.

KETONES (The reduction of aromatic). III. Contribution to the knowledge of the photo-
chemical phenomena. 849,

KINETIC INTERPRETATION (On the) of the osmotic pressure. 1241.

KINETIC QUANTITY (On the thermodynamic potential as a). Ist part. 85.

KLUYVER (J. c.). On an integral formula of STIELTJES. 829.

CONTENTS XIII

KOHNSTAMM (PH.) and K. W, Warsrra. Measurements of isotherms of hydrogen
at 20° C. and 150,5 C. 203.
KORTEWEG (pb. J.). The different ways of floating of an homogeneous cube. 224,
KRUYT (H. R.). Current potentials of electrolyte solutions, 615.
— Electric charge and limit value of colloids. 623.
— and Jac. van DER Spek. The connection between the limit value and the
concentration of arsenic trisulphide sols. 1158.
KUENEN (J. e.). On the measurement of the capillary pressure in a soap-bubble. 946,
— The diffusion-coefficient of gases and the viscosity of gas-mixtures. 1068.

KUIPER JR. (K.). The physiology of the air-bladder of fishes. 1088.

KUYPERS (H. A.) and H. KAMERLINGH ONNEs. Measurements on the capillarity of
liquid hydrogen. 528.

LAAR (J. J. VAN). A new relation between the critical quantities and on the unity
of all substances in their thermic behaviour. 451.

— Some remarks on the values of the critical quantities in case of association. 598.

— On apparent thermodynamic discontinuities in connection with the value of the
quantity 4 for infinitely large volume. 606.

— The calculation of the molecular dimensions from the supposition of the electric
nature of the quasi-elastic atomic forces. 877.

LAQUEUR (E.). On the survival of isolated mammalhan organs with automatic
function. 270.

LEAD (The allotropy of). I. 822, Note. 1055.

— (Measurements on the specific heat of) between 14° and 80° Kk. and of copper
between 15° and 22° K, 894.

LIGHT (On FRESNEL’s coefficient for) of different colours, 445.

LIMIT VALUE (Electric charge and) of colloids. 623.

— (The connection between the) and the concentration of arsenic trisulphide
sols. 1158.

LiQuips (On the behaviour of gels towards) and the vapours thereof. IL, 92.

— (Theoretical determination of the entropy constant of gases and). 1167.

— (The temperature-coefficients of the free energy-surface of) at temperatures from
—80° C. to 1650° C. I. 329. IL. 365. IIL. 389. IV. 395. V. 405. VI. 416. VIL.
555. VIIL 571.

LORENTZ (H. A.) presents a paper of Dr. J. J. van LAAR: “A new relation between
the critical quantities and on the unity of all substances in their thermic
behaviour”. 451.

— presents a paper of Dr. J. J. van LAAR: “Some remarks on the values of the
critical quantities in case of association’. 598.

— presents a paper of Dr. J. J. van Laar: “On apparent thermodynamie discon=
tinuities in connection with the value of the quantity 4 for infinitely large
volume”. 606.

— presents a paper of Dr. G, J, Erras: “On the structure of the absorption lines
D, and D,”, 720,

XIV CONTENTS.

LORENTZ (H. A.) presents a paper of Dr. G. J. Exias; “On the lowering of the
freezing point in consequence of an elastic deformation”. 732.

—- presents a paper of Dr. G. J. Eras: “The effect of magnetisation of the elec-
trodes on the electromotive force”. 745.

— presents a paper of Dr. L. S. ORNSTEIN: “On the theory of the string galvano-
meter of EINTHOVEN”. 784.

— presents a paper of Dr. L. S, OrNsteiN and Dr. F. Zeentke: “Accidental
deviations of density and opalescence at the critical point of a single sub-
stance”. 793.

— presents a paper of Mrs. T, Enrenrest—AranassjEwa: “Contribution to the
theory of corresponding states”. 840.

— presents a paper of Dr, J. J. van Laar: “The calculation jof the molecular
dimensions from the supposition of the electric nature of the quasi-elastic atomic
forces”. 877.

— presents a paper of Mr, J. Drosre: “On the field of a single centre in
ErxsTEIn’s theory of gravitation”. 998.

— presents of paper of Mr. H. Terropg: “Theoretical determination of the entropy
constant of gases and liquids”. 1167.

— presents a paper of Prof, P. Enrenrest: “On interference-phenomena to be
expected when RÖNrGeN rays pass through a di-atomic gas”. 1184.

— presents a paper of Prof. P, Eurenrest: “On the kinetic interpretation of the
osmotic pressure”. 1241.
LUNAR PERIGEE (The motions of the) and node and the figure of the moon. 1309.
MAGNETISATION (The effect of) of the electrodes on the electromotive force. 745.
MAMMALIAN ORGANS (On the survival of isolated) with automatic function. 270.
Mathematics. Jan pe Vries: “A cubic involution of the second class”. 105.

— JAN pvp Vries: “A triple involution of the third class”. 134,

— W. Kaprreyn: “On the functions of HERMITE”. 3th part. 139.

— M. J. van Uven: “Ihe theory of Bravats (on errors in space) for polydi-
mensional space with applications to correlation”. (Continuation). 150.

— M. J. van Uven: “Combination of observations with and without conditions
and determination of the weights of the unknown quantities, derived from me-
chanical principles”. 157.

— N. G. W. H. Bereer: “On Hermire’s and ABer’s polymonia”. 192,

— W. Kapreyn: “On some integral equations”. 286.

— M. J. van Uven: “The theory of the combination of observations and the
determination of the precision, illustrated by means of vectors”. 490.

— J.C. Kuvyver: “On an integral formula of SrieutJes”’. 829.

— Jan DE Vries: “Characteristic numbers for nets of algebraic curves”, 935.

— Jan pp Veres: “Characteristic numbers for a triple infinite system of algebraic
plane curves”, 1055.

— Jan pr Veres: “Systems of circles determined by a pencil of conics”. 1107.

— W. van DER Woupe: “On Nörnem’s theorem”, 1245.
— JAN pe Vries: “A bilinear congruence of rational twisted quintics”. 1250,

CON TLE NT ss XV

Mathematics. JAN pr Vries: “Some particular bilinear congruences of twisted cubics”.
1256.

MATHIAS (B), H. KAMERLINGH ONNEs and C. A, CROMMELIN. The rectilinear
diameter of nitrogen. 953.

MEASUREMENT (The) of very low temperatures. XXIV, The hydrogen and helium.
thermometers of constant volume, down to the freezing point of hydrogen compared
with each other and with the platinum-resistance thermometer. 501.

MEASUREMENTS on the-capillarity of liquid hydrogen. 528.

— of isotherms of hydrogen at 29 C. and 15°95 C. 203.

— on the specific heat of lead between 14° and 80° K. and of copper between
15° and 22° K. 894,

MEASURING BAR (Comparison of the) used in the base measurement at Stroe with the
Dutch Metre NO, 27. 500.

— (Comparison of the Dutch platinum-iridium Metre NO, 27 with the international
Metre M as derived from the measurements by the Dutch Metre-Commission in
1879 and 1880, and: a preliminary determination of the length of the) of the
French base-apparatus in international metres. 311.

MECHANICAL PRINCIPLES (Combination of observations with and without conditions and
„determination of the weights of the unknown quantities derived from). 157.
METALS (The metastability of) in consequence of allotropy, and its significance for

Chemistry, Physics and Technics. 200. III. 926. 1V. 1238.

— (On the electrical resistance of pure). IX. 508.

METASTABILITY (The) of metals in consequence of allotropy and its significance for
Chemistry, Physics and Technics. 200. LIL. 926. IV. 1238.

METHYLAMINE (On the interaction of ammonia and) on 2. 3. 4.-trinitrodimethylaniline.
1034,

METRE No. 27 (Comparison of the Dutch platinum-iridium) with the international
metre M as derived from the measurements by the Dutch Metre-Commission in
1879 and 1880, and a preliminary determination of the length of the measu:
ring bar of the French baseapparatus in international metres. 311.

Mineralogy. H. Haga and HF. M, Jarcer: “On the real symmetry of cordierite and
apophyllite””. 450.

— C. E. A. WicHMaNN : “On the tin of the island of llores”. 474.

MOLECULAR DIMENSIONS (The calculation of the) from the supposition of the electric
nature of the quasi-elastic atomic forces. 877.

MOLENGRAAFF (G, A. F.) presents a paper of Dr. H. A, Brouwer: “On the
granitic area of Rokan (Middle-Sumatra) and on contact-phenomena in the sur-
rounding schists’. L190.

moon (The motions of the lunar perigee and node and the figure of the). 1309.

MOON’S PARALLAX (The mean radius of the earth, the intensity of gravity and the), 1291.

MUSCLE-CELLS (On the termination of the efferent nerves in plain) and its bearing
on the sympathetic (accessory) innervation of the striated muscle-fibre. 982.

MUSCULAR FIBRE (On the mode of attachment of the) to its tendonfibres in the
striated muscles of the vertebrates, 989,

XVI CONTENTS.

MYXINE GLUTINOSA (Further contributions to our knowledge of the brain of). 2.
NERVE-DISTRIBUTION (On the) in the trunk-dermatoma. 632.
nerves (On the termination of the efferent) in plain muscle cells and its bearing on
the sympathetic (accessory) innervation of the striated muscle-fibre. 982.
nets (Characteristic numbers for) of aigebraic curves. 935,
NITRATION (The) of the mixed dihalogen benzenes. 846.
NITROGEN (Vapour pressures of oxygen and critical point of oxygen and). 950.
— (The rectilinear diameter of). 953.
— (Vapour pressures of) between the critical point and the boiling point. 959.
NÖTHER’s theorem (On). 1245.
OCCLUSION (A case of) of the arteria cerebelli posterior inferior. 914.
ONNES (H. KAMERLINGH). Further experiments with liquid helium. J. 12.
278. K. 283. L. 514.

— presents a paper of Dr. W. H, Kegsom: “The chemical constant and the appli-
cation of the quantum-theory by the method of the natural vibrations to the
equation of state of an ideal monatomic gas’. 20.

— presents a paper of Dr. W. H. Krersom: “On the matter in which the suscep-
tibility of paramagnetic substances deperds on the density”. 110,

— presents a paper of Dr. C. A. Crommetin: “Isothermals of monatomic sub-
stances and their binary mixtures”. XVI. 275.

— presents a paper of Dr. C. A. CROMMELIN: “Tsothermals of di-atomic substances
and their binary mixtures”, XVI. 959.

— C. Dorsman and G. Horst. Isothermals of di-atomic substances and their binary
mixtures. XV. Vapour pressures of oxygen and critical point of oxygen and
nitrogen, 950.

— and P. Exrenrest. Simplified deduction of the formula from the theory of
combinations which PLANOK uses as the basis of his radiation theory. 870.

— and K. Hor. Further experiments with liquid helium. N. 520.

— and G. Hotst. The measurement of very low temperatures. XXIV. The hydrogen
and helium thermometers of constant volume down to the freezing point of
hydrogen compared with each other and with the platinum-resistance thermo-
meter. 501.

— On the electrical resistance of pure metals. IX. 508.

— Further experiments with liquid helium. M. 760.

— and W. H. Krrsom. The specific heat at low temperatures. I. Measurements
on the specific heat of lead between 14° and 80° k. and of copper between
15° and 22° K, 894.

— and H. A. Kuypers. Measurements on the capillarity of liquid hydrogen. 528.

— E. Marutas and C. A. CROMMELIN. The rectilinear diameter of nitrogen. 953.

OPALESCENCR (Accidental deviations of density and) at the critical point of a single
substance. 793.
ORNSTEIN (L. 8.). On the theory of the stringgalvanometer of KINTHOVEN. 784.

— and F. ZeRNIKE. Accidental deviations of density and opalescence at the critical
point of a single substance. 798.

GONE HEN TS XVII

OSMOTIC PRESSURE (On the kinetic interpretation of the). 1241. °
OXYGEN (Vapour pressures of) and critical point of oxygen and nitrogen. 950.

PARAMAGNETIC SUBSTANCES (On the matter in which the susceptibility of) depends on
the density. 110.

PASTEUR’s principle (Researches on) of the connection between molecular and
physical dissymmetry. I. 1217.

PEACHALMOND (Gummosis in the fruit of the Almond and the) as a process of normal
life. 810.

Petrography. A. WicuMann: “On some rocks of the island of Taliabu (Sula islands), 226.

PHAGOCYTES and respiratory centre. 1325.

PHOSPHORUS (On the vapour pressure lines of the system). IL. 678. IIL. 962.

— (Further particulars concerning the system). 973.

PHOTOCHEMICAL phenomena (Contribution to the knowledge of the). 849.

PHOTOTROPIC and geotropic reactions (On the mutual influence of) in plants. 1278.

Physics. H. KAMERLINGH Onnes: “Further experiments with liquid helium”. J. 12.
278. K. 283. L. 514. N. 520. M. 760.

— W. H. Kegsom: “The chemical constant and the application of the quantum-
theory by the method of the natural vibrations to the equation of state of an
ideal monatomic gas”. 20.

— H. Huisuor: “On the thermodynamic potential as a kinetic quantity”. 1st part. 85.

-- W. H. Kersom: “On the manner in which the susceptibility of paramagnetic
substances depends on the density”. 110.

— Pu, Kounstamm and Kk, W. Warsrra: ‘Measurement of isotherms of hydrogen
at 20° C. and 15% C,” 203.

— K. W. Warsrra: “The hydrogen isotherms of 20° C, and of 1595 C. between
1 and 2200 atm.” 217.

— C. A. CROMMELIN: “‘[sothermals of monatomic substances and their binary
mixtures”, XVI. 275.

— P. ZEEMAN: ‘FResNEL’s coefficient for light for difterent colours’. 1‘tpart. 445,

— J. J. van Laar: “A new relation between the critical quantities and on the
unity of all substances in their thermic behaviour”, 451.

— H. vu Bois: “Modern electromagnets, especially tor surgical and metallurgic
practice”. 468,

— H. KAMERLING ONNEs and G. Horst: “On the measurement of very low
temperatures, XXIV, The hydrogen and helium thermometers of constant volume,
down to the freezing-point of hydrogen compared with each other and with the
platinum resistance thermometer”, 501,

= H, KAMERLINGH Onnus and G, Horst; “On the electrical resistance of pure
metals etc.”, IX. 508,

— H, KAMERLINGH ONNEs and H, A, Kuypers: “Measurements on the capillarity
of liquid hydrogen”. 528;

= J. J. van LAAR: “Some remarks on the values of the critical quantities in case
of association”. 598.

90

Proceedings Royal Acad. Amsterdam. Vol. XVII.

XVIII CONTENTS

Physics. J. J. van LAAR: “On apparent thermodynamic discontinuities in connection
with the value of the quantity 4 for infinitely large volume’’. 606.
— Miss H. J. Former: “A new electrometer, especially arranged for radio-active
investigations”. 659.
- — G.J. Erras: “On the structure of the absorptionlines D, and JD”, 720.
— G. J, Erras: “The lowering of the freezing point in consequence of an elastic
deformation’’. 732.

— G.J. Extras: “The effect of maguetisation of the electrodes on the electromotive
force”. 745.

— L. 8. ORNSTEIN: “On the theory of the string-galvanometer of ErntHoven”’. 784.

— L. S. Ornstein and F. ZERNIKE: “Accidental deviations of density and opales-
cense at the critical point of a single substance”. 793.

— F. E. C. Scuerrer: “On unmixing in a binary system for which the three
phase pressure is greater than the sum of the vapour tensions of the two compo-
nents”. 834,

— Mrs. T. EHRENFEST—AFANASSJEWA: “Contribution to the theory of corresponding
states”. 840.

— P. Exrenrest and H. KAMERLINGH ONNEs: “Simplified deduction of the
formula from the theory of combinations which PLANcK uses as the basis of his
radiationtheory”. 870.

— H. vu Bors: “The universality of the Zeeman-effect witk respect to the STARK-
effect in canal-rays”. 873.

— J. J. van Laar: “The calculation of the molecular dimensions from the suppo-
sition of the electric nature of the quasi-elastic atomic forces”. 877.

— W. H. Kersom and H. KAMERLINGH Onnes: “The specific heat at low tempe-
ratures. I. Measurements on the specific heat of lead between 14° and 80° K.
and of copper between 159 and 22° k.” 894.

— J. P. Kuenen: “On the measurement of the capillary pressure in a soap-bubble”.
946.

— H. KAMERLINGH ONNEs, C. Dorsman and G. Horst: “Isothermals of di-atomic
substances and their binary mixtures. XV. Vapour pressures of oxygen and critical
point of oxygen and nitrogen”. 950.

— E. Maratas, H. KAMERLINGH ONNEs and U, A. CROMMELIN : “The rectilinear
diameter of nitrogen”. 953,

— ©, A. CROMMELIN: “Isothermals of di-atomic substances and their binary mixe-
tures. XVI. Vapour pressures of nitrogen between the critical point and the
boiling point”. 959,

= J. Droste: “On the field of a single centre in E1nsTEtn’s theory of gravitation”,
998,

— J. P. Kuenen: “The diffusion coefficient of gases and the viscosity of gase
mixtures”. 1068,

— H, Terrope: “Theoretical determination of the enttopy constant of gases and
liquids”. 1167.

CONTENTS XIX

Physics. P. PrreNrest: “On interference phenomena to be expected when Röntgen
rays pass through a di-atomic gas”, 1184.
— F. M. JarGer: “On a new phenomenon accompanying the diffraction of
Röntgen rays in birefringent crystals”. 1204,
— P, Enrenrest: “On the kinetic interpretation of the osmotic pressure”. 1241,
Physiology. B, Laqueur: “On the survival of isolated mammalian organs with auto-
matic function”. 270,
— L. K. Wotrr: “On the formation of antibodies after injection of sentizised
antigens”. II. 318.
— G. van RijNBERK: “On the nerve-distribution in the trunk-dermatoma”. 632,
— A. A. HYMANs VAN DEN BERGH and J. J. DE LA Fonrarne ScaLuIrEr: “The
identification of traces of bilirubin in albuminous fluids”. 807.

— I. K. A. WERTHEIM SALOMONSON: “Exaggeration of deep reflexes”. 885.

— 8S. DE Boer: “On the heart-rhythm”. 1075. IL. 1135,

— A. B, DrooarLEBVER Fortuyn: “The decoloration of fuchsin-solutions by amor-

phous carbon”. 1322.
— H. J. HAMBURGER: “Phagocytes and respiratory centre”. 1825,
PICRYLMETHYLAMIDE (The coloration of some derivatives of) with alkalies. 647.
PLANCK (Simplified deduction of the formula from the theory of combinations which)
uses as the basis for his radiation theory. 870.

PLANET Jupiter (The figure of the). 1047.

PLANETS (On SEELIGER’s hypothesis about the anomalies in the motion of the
inner). 23.

PLANTS (On the mutual influence of the phototropic and geotropic reactions in). 1278

POLYNOMIA (On HeErmite’s and ABEL’s). 192.

POSTMA (s.) and A. Smits. The system Ammonia-water. 182.

POTASSIUM (The allotropy of). 1. 1115.

POTASSIUM SULPHATE, potassium chlorid (The system: copper sulphate, copper chlorid)
and water at 30°. 538.

POTENTIAL (On the thermodynamic) as a kinetic quantity. lst part. 85.

POTENTIALS (Current) of electrolyte solutions. 615.

PRECISION (The theory of the combination of observations and the determination of
the), illustrated by means of vectors. 490.

PRINS (Miss aDA). On critical end-points and the system ethane-naphtalene. 1095.

PSEUDO-COMPONENTS (The metastable continuation of the mixed crystal series of) in
connection with the phenomenon allotropy. IL. 672.

quantity 4 (On apparent thermodynamic discontinuities in connection with the value
of the) for infinitely large volume. 606.

QUANTUM-THEORY (The chemical constant and the application of the) by the method
of the natural vibrations to the equation of state of an ideal monatomic gas). 20,

QUATERNARY SYSTEM KCl—CuClg—BaClo-—H,20 (On the). 781.

auintics (A bilinear congruence of rational twisted). 1250.

RADIATION THEORY (Simplified deduction of the formula from the theory of combina-
tions which PLANCK uses as the basis for his), 870.

xXx CONTENTS

RADIO-ACTIVE investigations (A new electrometer, specially arranged for). 659.
REFLEXES (Exaggeration of deep). 885.
REINDERS (w.). Equilibria in the system Pb-S-O, the roasting reaction process. 703.
RESISTANCE (On the electrical) of pure metals. IX. 508.
RESPIRATORY CENTRE (Phagocytes and). 1325. Ee
ROASTING REACTION PROCESS (Equilibria in the system Pb-S-O, the). 703.
rocks (On some) of the island of Taliabu (Sula islands). 226.
ROKAN (Middle-Sumatra) (On the granitic area of) and on contact phenomena in the
surrounding schists. 1190.
ROMBURGH (P. VAN) presents a paper of Prof. F. M. JAEGER and Dr. Anr. SIMEK:
“Studies in the field of silicate-chemistry”. Il. 239, ILL, 251.
— presents a paper of Prof. F. M. Jaraer: “The temperature-coefficients of the
free surface-energy of liquids at temperatures from —80° to 1650° C.” I. 329.
Il. 365. III. 386. IV. 395. V. 405. VI. 416. VII. 555, VIIL 571.
— presents a paper of Mr. G. pr Bruin: “A crystallized component of isoprene
with sulphur dioxide”. 585.
— presents a paper of Prof. F. M. Jarcer: ‘Researches on PasrEUR's principle of
the connection between molecular and physical dissymmetry”. I. 1217.
— presents a paper of Dr. A. W. K. pr Jona: “Action of sunlight on the cin-
namic acids’. 1274.
— and Miss D. W. Wenstnx. On the interaction of ammonia and methylamine
on 2.3.4,-trinitrodimethylaniline. 1034,
RÖNTGEN RAYS (On interference phenomena to be expected when) pass through a
di-atomic gas. 1184.
— (On a new phenomenon accompanying the diffraction of) in birefringent
crystals. 1204.
ROTHIG (p.) and C. U. Artins Kappers. Further contributions to our knowledge
of the brain of Myxine glutinosa. 2.
RIJNBERK (G. VAN). On the nerve-distribution of the trunk-dermatoma. 632.
SALOMONSON (J. K. A. WERTHEIM). LExaggeration of deep reflexes, 885.
— presents a paper of Dr. S. pe Boer: “On the heart-rhythm”. 1075. LL. 1135.
saurs (The influence of the hydration and of the deviations from the ideal gas-laws
in aqueous solutions of) on the solidifying and the boiling point. 1036.
SANDE BAKHUYZEN (H.G. VAN DE). v. BAKHUYZEN (H. G. VAN DE SANDE).
SCHEFFER (F. E. C.). On gas equilibria and a test of Prof. v. p. Waars Jr's
theorema, I. 695. IL. 1011.
— On unmixing in a binary system for which the three-phase pressure is greater
than the sum of the vapour tensions of the two components. 834, :
SCHLUITER (J. J. DE LA FONTAINE) and A. A. HyMans VAN DEN BERGH.
The identification of traces of bilirubin in albuminous fluids, 807.
SCHREINEMAKERS (F. A. H.). Equilibria in ternary systems. XV. 70. XVI.
169. XVII. 767. XVIII. 1260. el
— and Miss W. C. pe Baar. The system: copper sulphate, copper chlorid, potas-
sium sulphate, potassium chlorid and water at 30° C, 533,

O7O Nel EEN) Ds; XXI

SCHREINEMAKERS (¥. A. H.) and Miss W. C. pr Baar, On the quaternary
system KCl-CuClg-BaClo-H,C. 781.
— Compounds of the arsenious oxide, I. 1111.
SEEL1GER’s hypothesis (On) about the anomalies in the motion of the inner planets, 23.
— (Remarks on Mr. WoLtseR’s paper concerning). 33.
SILICATE-CHEMISTRY (Studies in the field of). IL. 239, III. 251.
SIMEK (ANT) and F. M. Jarcer. Studies in the field of silicate-chemistry. II,
239. IIT. 251.
SITTER (W. DE) presents a paper of Mr. J. WortJer gr.: “On SEELIGER’s hypo-
thesis about the anomalies in the motion of the inner planets”. 23.
— Remarks on Mr. Woutynr’s paper concerning Srenicer’s hypothesis. 33.
— The figure of the planet Jupiter. 1047.
— On the mean radius of the earth, the intensity of gravity and the moon’s parallax. 1291,
— On isostasy, the moment of inertia and the compression of the earth. 1295.
— The motions of the lunar perigee and node and the figure of the moon, 1309
SLUITER (Cc. H.). The influence. of the hydration and of the deviations from the ideal
gas-laws in aqueous solutions of salts on the solidifying and the boiling-point. 1036,
SMIT (M.) and I, M. Jarcer. The temperature-coefticients of the free-surface-energy
of liquids at temperatures from —$0° C. to 1650° C. IL. 365. III, 381.
SMITS (a). The metastable continuation of the mixed crystal series of pseudo-
components in connection with the phenomenon allotropy. II, 672.
— and Aven (A. H. W.). The application cf tle theory of allotropy to electro-
motive equilibria. II. 37. IIL. 680.
— and S. C. Boxuorsr. On the vapour pressure lines in the system phosphorus. II.
678. III. 962.
— Further particulars concerning the system phosphorus, 973.
— and 8. Postma. The system ammoniawater. 182.
SOAP-BUBBLE (On the measurement of the capillary pressure in a). 946,
SODIUM-HYPOCHLORITE (Action of) on amides of z-oxyacids. 1163.
SPECIFIC HEAT (The) at low temperatures. I. Measurements on the specific heat of lead
between 14° and 80° K. and of copper between 15° and 22° Kk, 894.
SPEK (JAC. VAN DER) and H. R. Kruyr. The connection between the limit
value and the concentration of arsenie trisulphide sols. 1158,
staRK-eflect (The universality of the Zeeman-eflect with respect to the) in canal-rays. 878
STIELTJES (On an integral-formula of). 829.
STOK (J. P. VAN DER). The treatment of frequencies of directed quantities. 586.
— presents a paper of Mr. P, H. GarrÉ: “On the relation between departures
from the normal in the strength of the trade-winds in the Atlantic Ocean and
those in the waterlevel and temperature in the Northern European seas.’ 1147.
STRING-GALVANOMETER (On the the theory of the) of EintHoven. 784.
STROE (Comparison of the measuring bar used in the base measurement at) with the
Dutch Metre n° 27. 300.
SUBSTANCES ([sothermals of monatomic) and their binary mixtures. XVI, 275.
— (Isothermals of di-atomic) and their binary mixtures. XV. 950, XVI. 959.

XXII CONTENTS.

SUBSTANCES (A new relation between the critical quantities and on the unity of all)

in their thermic behaviour. 451.
SUBSTITUENTS (The replacement of) in benzene derivatives. 1027.

2-SULPIIO-PROPIONIC AcrD and its resolution into optically active isomerides. 653.

SULPHUR DIOXIDE (A crystallized compound of isoprene with). 585.

SUNLIGHT (Action of) on the cinnamic acids. 1274.

system P/-S-O (Equilibria in the), the roasting reaction process. 703.

— (The) copper sulphate, copper chlorid, potassium sulphate, potassium chlorid and
water at 30° C. 533.

— (Characteristic numbers for a triply infinite) of algebraic plane curves. 1055.

— ammonia—water (The). 182.

— ethane—naphthalene (On critical endpoints and the), 1095.

— phosphorus (On the vapour pressure lines in the). I. 678. [IL, 962.

— phosphorus (further particulars concerning the). 973.

TALIABU (Sula islands) (On some rocks of the island of). 226.

TEMPERATURE (On the relation between departures from the normal in the strength
of the trade-winds of the Atlantic Ocean and those in the waterlevel and) in
the Northern European seas. 1147.

TEMPERATURE-COEFFICIENTS (The) of the free energy surface of liquids at tempera-
tures from —80° C. to 16509 C. I. 329. IL. 365. ILL. 386. LV. 395. V. 405,
VE. 416. VEL +655; VET 571.

TEMPERATURES (The measurement of very low). XXIV. The hydrogen and helium
thermometers of constant volume down to the freezing point of hydrogen com.
pared with each other and with the platinum-resistance thermometer. 501.

— (The specific heat at low). I. Measurements on the specific heat of lead between
14° and 80° K. and of copper between 15° and 22° K. 894.

TENDONFIBRES (On the mode of attachment of the muscular fibre to its) in the striated
muscles of the vertebrates. 989.

TERNARY SYSTEMS (Equilibria in). XV. 70. XVL. 169. XVIL 767. XVIII. 1260.

TETRODE (u.). Theoretical determination of the entropy constant of gases and liquids, 1167.

THEORY of allotropy (The application of the) to electromotive equilibria. II. 37. III. 680.

— of Bravars (The) (on errors in space) for polydimensional space with applica-
tions to correlation. (Continuation). 150.

— (The) of the combination of observations and the determination of the precision,
illustrated by means of vectors. 490.

— of combinations (Simplified deduction of the formula from the) which PLanck
uses as the basis of his radiation theory. 870.

— of corresponding states (Contribution to the). $40.

— of gravitation (On the field of a single centre in ErNsTEIN's). 993.

THERMOMETERS (The hydrogen and helium) of constant volume, down to the freezing
point of hydrogen compared with each other, and with the platinum-resistan ce
thermometer, 501.

TURDE-PHASE PRESSURE (On unmixing in a binary system for which the) is greater
than the sum of the vapour tensions of the two components, 834,

OVOEN TEN ES, XXIII

TIN (On the) of the island of Flores. 474,

TRADE-WINDs (On the relation between departures from the normal in the strength
of the) in the Atlantic Ocean and those in the waterlevel and temperature in
the Northern European seas. 1147.

TRINITRODIMETHYLANILINE (On the interaction of ammonia and methylamine on
2.3.4.-). 1034.

-TRUNK-DERMATOMA (On the nerve-distribution in the). 632.

UNMIXING (On) in a binary system for which the three-phase pressure is greater than
the sum of the vapour tensions of the two components. 834.

UVEN (M. J. VAN). The theory of Bravars (on errors in space) for polydimensional
space with applications to correlation. (Continuation). 150.

— Combination of observations with and without conditions and determination of
the weights of the unknown quantities, derived from mechanical principles. 157.

— The theory of the combination of observations and the determination of the
precision, illustrated by means of vectors. 490.

VAGUS AREA (The) in Camelidae. 1119.
VAPOUR PRESSURE LINES (On the) in the system phosphorus. IL. 678. IIL. 962,
VAPOUR PRESSURES of oxygen and critical point of-oxygen and nitrogen. 950.

— of nitrogen between the critical point and the boiling point. 959.

VAPOUR TENSIONS (On unmixing in a binary system for which the three-phase pressure
is greater than the sum of the) of the two components. 834.

vectors (The theory of the combination of observations and the determination of the
precision, illustrated by means of). 490,

VERMEULEN (H. A.). The vagus area in Camelidae. 1119.

VERTEBRATES (On the mode of attachment of the muscular fibre to its tendonfibres
in the striated muscles of the). 989. _

viscosity of gas-mixtures (The diftusion-coefticient of gases and the). 1068.

VRIES (JAN DE). A cubic involution of the second class. 105.

— A triple involution of the third class. 134.

— presents a paper of Prof. M. J. van Uven: “Combination of observations with
and without conditions and determination of the weights of the unknown quantities,
derived from mechanical principles”, 157.

— Characteristic numbers for nets of algebraic curves. 935.

— Characteristic numbers for a triple infinite system of algebraic plane curves. 1055.

— Systems of circles determined by a pencil of conics, 1107.

— presents a paper of Dr. W. van per Woupve: “On Nöruer’s theorem”. 1245.

— A bilinear congruence of rational twisted quinties. 1250.

— Some particular biliaear congruences of twisted cubics. 1256.

WAALS (J. D. VAN DER) presents a paper of Prof. A. Smrrs and Dr. A. H. W,
ATEN: “The application of the theory of allotropy to electromotive equilibria”
Ii, 37. ILL. 680,
— presents a paper of Dr, H. Hursnor: “On the thermodynamic potential as a
kinetic quantity”, Ist. part. 85.
— presents a paper of Prof. A, Smits and S. Posrma: “The system ammonia-water.”’ 182,

SNIV CTO ND TEENS TES:

WAALS (J. D. VAN DER) presents a paper of Prof. Pu. KounstamM and Kk. W.

Watstra: “Measurements of isotherms of hydrogen at 20° C. and 15° C.” 203.

— presents a paper of Mr. K. W. Waustra: “The hydrogen isotherms of 20° C,
and of 15°.5 C. between 1 and 2200 atm.”, 217.

— presents a paper of Prof. A. Suits: “The metastable continuation of the

mixed crystal series of pseudo-components in connection with the phenomenon

allotropy”. II. 672.
— presents a paper of Prof. A. Smits and S. C. Boxuorst: “The vapour pressure

lines of the system phosphorus”. tI. 678. III. 962.

— presents a paper of Dr. F. E. ©. Screrrer: “On gas equilibria and a test of.
Prof. vaN DER Waats Jr.’s formula”. I. 695. II, 1011.

— presents a paper of Dr. F. E. C. Scnrrrer: “On unmixing in a binary system
for which the three-phase pressure is greater than the sum of the vapour tensions
of the components”. 834.

— presents a paper of Prof. A, Surrs and 8. C. Boknomrst: “Further particulars

concerning the system phosphorus”. 973.

WAALS Jr's theorema (On gas equilibria and a test of Prof.). 1. 695. [Ls 10 Ek

WALsTRA (Kk. W.). The hydrogen isotherms of 20° C. and of 15% C. between i

and 2200 atm. 217.

_— and Pu. KounstamM. Measurements of isotherms of hydrogen at 20° C, and
15°.5 C. 203.

WATER (The system ammonia—). 182.

— (The system: copper sulphate, copper chlorid, potassium sulphate, potassium
chlorid and) at 30°, 533.

WATERLEVEL (On the relation between departures from the normal in the strength of
the trade-winds in the Atlantic ocean and those in the) and temperature in the
Northern European seas. 1147.

WEBER (MAX) presents a paper of Dr. K. Kuiper Jr.: “The physiology of the
air-bladder of fishes”, 1088.

WEERMAN (R. A). Action of sodium hypochlorite on amides of g-oxyacids. 1163.
weients (Combination of observations with and without conditions and determination
of the) of the unknown quantities, derived from mechanical principles. 157.
WENSINK (Miss p. w.) and P. van Rompurcu. On the interaction of ammonia

and methylamine on 2.3.4.-trinitrodimethylaniline, 1034.

WENT (F. A. F. ©.) presents a paper of Miss Lucie C. Doyer: “Energy transfor-
mations during the germination of wheat-grains”. 62.

— presents a paper of Dr. C. E. B, BREMEKAMP: “On the mutual influence of
phototropic and geotropic reactions in plants”. 1278.

WERTHEIM SALOMONSON (I. K. A.). v. SALOMONSON (I. K. A. WERTHEIM).
WHBAT-GRAINS (Energy transformations during the germination of). 62.
WICHMANN (A). On some rocks of the island of Taliabu (Sula islands), 226.

— On the tin of the island of Flores. 474.

WILDEBOER (N.), J. G. Dieperink and H. G. VAN DE SANDE BakHUYZEN. Com-
parison of the measuring bar used in the base measurement at Stroe with the
Dutch Metre No. 27. 300,

GON TENT 8, XXV

WINKLER (c.) presents a paper of Prof. G. van RIJNBERK : “On the nerve-distri-
bution of the trunkdermatoma.” 632.
— A case of occlusion of the arteria cerebelli posterior inferior. 914.
WOLFF (L. K.). On the formation of antibodies after injection of sensitized antigens,
II. 318.
— and E‚ H. Bicnner. On the behaviour of gels towards liquids and the vapours
thereof. II. 92.
WOLFF (s.) and Ernst Conen. The allotropy of potassium. L. 1115.
WOLTJER JR. (3.). On SEELIGER’s hypothesis about the anomalies in the motion
of the inner planets. 23.
WOUDE (W. VAN DER). On Nöruer’s theorem. 1245.
ZEEMAN (P.). On FRESNEL’s coefficient for light of different colours, 445.
ZEEMAN-eflect (The universality of the) with respect to the Srark-eftect in canal-
rays. 873.
ZERNIKE (r.) and L. S, Ornstern. Accidental deviations of density and opalescence
at the critical point of a single substance. 793.
zinc (The allotropy of). IL. 59. ILI. 641.
Zoology. K. Kuiper Jr: “The physiology of the air-bladder of fishes.” 1088.

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