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Koninklijke Akademie van Wetenschappen

PROCEEDINGS

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AMSTERDAM,
JOHANNES MULLER.

July 1904.

(Translated from: Verslagen van de Gewone Vergaderingen der Wis- en Natuurkundige
Afdeeling van 30 Mei 1903 tot 23 April 1904. Dl. XII.)

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Koninklijke Akademie van Wetenschappen
te Amsterdam.

PROCEEDINGS

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AMSTERDAM,
JOHANNES MULLER.
December 1903.

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CONTENTS.

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KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING

of Saturday May 30, 1903.

——~—)) { $Co—_______—_—_

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 30 Mei 1903, DI. XII).

CONTENTS.

J. W. Dito: “The action of phosphorus on hydrazine”. (Communicated by Prof. C. A. Lopry
DE Bruyn), p. 1.

J. W. Coumenty and Erxsr Conen: “The electromotive force of the Dayirii-cells”. (Com-
municated by Prof. W. H. Junius), p. 4.

Jax pe Vries: “On complexes of rays in relation tu a rational skew curve”, p. 12.

W. A. Versrvys: “The singularities of the fucal curve of a curve in space’. (Communicated
by Prof. P. H. Scnovurr), p. 17.

P. Zeeman and J. Gersr: “On the double refraction in a magnetic field near the components
of a quadruplet”, p. 19.

J. J. vax Laan: “The course of the melting-point-line of alloys (3.d communication). (Com-
municated by Prof. H. W. Bakuuis RoozeBsoom), p. 21.

M. C. Dekuvuyzen and P. Vermaar: “On the epithelium of the surface of the stomach”.
(Communicated by Prof. C. A. PEKELIARING), p. 30.

E. Wexwa: “On the liberation of trypsin from trypsin-zymogen”. (Communicated by Prof.
H. J. Hamecrcer), p. 34.

A. Paxnekork: “Some remarks on the reversibility of molecular motions”. (Communicated
by Prof. H. A. Lorentz), p. 42.

C. A. J. A. Oupemans and C. J. Koxrse: “On a Sclerotinia hitherto unknown and injurious
to the cultivation of Tobacco (Sclerotinia Nicutianae Ovp. et Konine), p. 48 (with one plate).

J. E. Verscuarrerr: “Contributions to the knowledze of vay pen Waats’ ¢-surface. VI!.
(part 3), The equations of state and the /-surface in the immediate neighbourhood of the critical
state fur binary mixtures with a small proportion of one of the components”. (Communicated
by Prof. H. Kameriincu ONNES), p. 59.

The following papers were read:

Chemistry. — “Vhe action of phosphorus on hydrazine.” By
Mr. J. W. Diro. (Communicated by Prof. C. A. Lopry pr Bruyn).

(Communicated in the meeting of April 24, 1903.)

The last number of the Berichte!) contains a research on phos-
phorus by R. Scuenck. Several of his observations quite corroborate
those which have been announced some time ago’) and which were made

1) Ber. 36. 979.
2) Recueil 18. 297. (1899).

Proceedings Royal Acad. Amsterdam. Vol. VI.

(2)

in 1900—1901, but the publication of which was postponed owing
to other studies which are not yet complete.

In 1895') and also afterwards *) Lopry bE Bruyn, in his studies
on hydrazine, observed that yellow phosphorus in contact with aqueous
hydrazine turns the solution first yellow, then dark brown and finally
black. After some time brownish black amorphous flakes are deposited.
As already stated, I submitted this reaction some years ago to a
closer examination and studied it, both with aqueous and with anhydrous
hydrazine.

I. If we introduce into vacuum tubes 16 gr.(=6 at.) yellow phosphorus
and 5 ¢.e. of a concentrated 90°/,(—1 mol.) aqueous solution of
hydrazine and allow these to be in contact for 1 or 2 months at
the ordinary temperature the whole solidifies to a black amorphous
mass in which a white well-crystallised substanee is distributed. On
opening the tubes a large quantity of hydrogen phosphide appears to be
present. As preliminary experiments had shown that the white substance
was soluble in absolute alcohol but not the black substances, the
tubes were filled with absolute alcohol out of contact with the «air,
the black substance was freed from the white crystals by repeated
washing with absolute alcohol and then dried over sulphuric acid
in vacuum.

The crystalline product obtained on evaporating the alcohol, was
particularly hygroscopic. The analysis agreed best with the assumption
that it consisted of hydrazine phosphite. Found 30.4°/, P and
12.3°/, N (this was determined in a nitrometer by means of vanadic
acid) *). If however notwithstanding the necessary precautions, the
substance has attracted a good deal of moisture in the course of the
different manipulations, there is a possibility of its being hydrazine
hypophosphite *).

The black mass is insoluble in alcohol, ether and carbon disulphide
and free from excess of yellow phosphorus. It has an odour of
hydrogen phosphide; in contact with the air it becomes moist and the
black colour changes to yellow. It contains chemically combined
hydrazine which, in company with a little hydrogen phosphide, is
obtained on distilling with dilute sodium hydroxide and which could
he identified by means of its dibenzaldehyde-derivative which melts
at 93".

1) Recueil 14. 87.

*) Recueil 15. 183.

5) Horrmann and Kisperr Ber. 31. 64.

4) Sapaneverr, Z. anorg. Ch, 20, 21. (1899).

(3)

The black substance is strongly attacked by dilute nitric acid and also
by bromine water. On heating at 100° in a current of dry hydrogen
it loses weight continuously and the black colour changes to red.

On treatment with dilute acids it behaves exactly like the product
isolated by Scuunck from red phosphorus and ammonia’). It is then
converted into a light red amorphous powder whilst the solution
appears to contain a salt of hydrazine. The red powder has the
external appearance of red phosphorus but is distinguished from this
by a more orange tinge and its behaviour towards alkalis. Ammonia
and dilute soda or potash yield black products, which however on
prolonged washing with water lose their feebly combined alkali and
assume their original red color. The substance, therefore, behaves as
a weak acid which forms black alkali salts which readily undergo
hydrolysis.

Strong alkalis act energetically on the red substance with formation
of hydrogen phosphide and a salt of hypophosphorous acid.

In the analysis of the black and the red substance the phosphorus
was determined by means of dilute nitric acid (in sealed tubes) and
with bromine water. The nitrogen determination was done volume-
trically with bromine water in a current of carbon dioxide and the
hydrogen by an elementary analysis. |

The average result was 45.9°/, P, 19.8 N and 5.5°/, H; total
71.2; the balance may be taken as representing oxygen.

The red eompound was free from nitrogen so that the black product
appears to be the hydrazine derivative of the red substance.

The product dried in a desiccator in vacuo contained 91.7 °/, 2
sms. ds ?/,s He).

2. If we place in a vacuum tube an excess of yellow phosphorus
with free hydrazine N, H,, we also notice (although sooner than in
the ease of the aqueous solution) the formation of a black amorphous
substance which in appearance quite resembles the product obtained
from hydrated hydrazine. No white substance is of course formed,
hardly any pressure is noticed and also little or no formation of
hydrogen phosphide takes place. This gas, like the hydrazine phos-
phite, therefore owed its origin to the well-known reaction between
phosphorus and a base.

1) That black compounds are also formed from liquefied ammonia and white
phosphorus is shown by the experiments of Gore, Proc. Roy. Soc. 21. 140. (1872),
Franxun and Kraus, Amer. Ch. J. 20, 820. (1898), and Hueor, Ann. Chim. Phys.
21. 28. (1900).

2) This figure is almost sure to be too high owing to the nature of the process
(elementary analysis).

(4)

The black substance was washed with carbon disulphide and alkohol
and dried in a desiccator in vacuo. Apparently it has absorbed oxygen
during this operation for the analysis showed a deficit of about 13 °/,.
We found: 78.5°/, P, 1.9°/, H and 6.5°/, N.

When treated with dilute acids a red substance was again formed
which in appearance and properties corresponded exactly with the
one already described and contained the same amount of phosphorus
|found, average 92°/,|. The hydrazine has passed into the acid.

3. From the foregoing it follows that substances quite analogous
to those formed by Scuenck’s (impure) red phosphorus and ammonia are
generated directly from hydrazine and vellow phosphorus. Evidently,
the black compounds which are formed from aqueous and anhydrous
hydrazine are of a different nature ; their investigation remains however
very unsatisfactory, owing to their amorphous conditions and want of
tests for purity, in addition to their unstability towards washing-
liquids. But it is pretty certain that the orange red product which
hoth yield, when treated with acids, is a weak acid composed of
phosphorus, hydrogen (and oxygen ?)

Hydrazine is therefore capable of directly giving up hydrogen, not
only to sulphur but also to phosphorus.

Organic chem. Lab. University. Amsterdam, April 1903.

Chemistry. — “The electromotive force of the Danwut-cells.” By
Mr. J. W. Commenin and Prof. Ernst Conrex. (Communicated
by Prof. W. H. Junius).

(Communicated in the meeting of April 24, 1903).

1. In the present state of our electro-chemical knowledge an
exhaustive study of the electromotive force of the Danie.i-cell would
have but littke importance if it related to the use of this cell as a
standard-cell, as we are now in possession of standard-cells which,
if properly constructed, satisfy all requirements.

We have, nevertheless undertaken an exhaustive investigation of
such a cell because J. Cuavpier has published in the ‘Comptes
Rendus”*) certain views which are entirely opposed to our modern
theories on the origin of the electromotive force in cells of this kind.

1) 134, 277 (1902).

(5)

2. CuHavpier gives the following form to the well-known formula
of Nerxst for the electromotive force:

Teens Wh (1 ee log =) -L en
+, Cae ar

This is evidently a mistake as the second term after the sign of
equality does not belong to this formula but forms part of the well-
known equation of Grpps and von Hr_mnontrz').

This mistake we may pass over. The following table contains
Cuavpier’s results which have been obtained by means of Boury’s
method for the measurement of electromotive forces. His cells were
constructed according to the scheme:

Copper sulphate solution Dilute solution of Zine |

Copper |
saturated at 15° C. | sulphate.

Zinc.

3. The paper contains but few details of the manner in which the
experiments were conducted: “lélément Dante. est constitué par
deux vases en verre, contenant Pun la solution de sulfate de zine,
Vautre Ja solution de sulfate de cuivre; ces deux vases sont réunis
par un siphon formé Wun tube de verre rempli de coton imbibe de
la solution de sulfate de zine dans Vune des branches, de la solution

FABLE I.

ZoSO,.7H,0 in 100 parts Elektromot. force (15°C.) Coefficient of temperature.
of water.

0) 1.0590 Volt —U.0024
Wa 1.4138 —0.00015
1/, | £14154 —0) 00013
Vy 1.1368 40 .00005

1 | 1.1331] -L0 00005

2 1.1263 40 00003

4 1.1249 -+0).0003

6 | 1.1208 0.00016
10 | 1.1188 —f). QO0038
3U | 1.1054 / —0 0002
60 | 4.41003 —0. 0002
900 (saturated) | 4.0902 — 00026

1) Cuavupier wrongly calls this equation, the equation of Lord Ketvry.

(46

de sulfate de euivre dans l'autre. Ce dispositif m’a paru donner des
resultats plus constants que les autres.”

It seems to us strange that the E.M.F. should be given to '/,,
millivolt. All authors who up to the present have made a study
of the Daniei-cell have pointed out how difficult it is to obtain
constant values with such cells. For instance, the E. M.F. is in a
high degree dependent on the nature of the copper or zine electrode.
For particulars in this direction we refer to the researches of ALDER
Wricut').

In connection with the measurements under consideration the
following table of Fiemine’s will be found interesting:

ELM. F. of a certain Daxve..-cell.

Copper, perfectly pure, uoxidised 1.072 Volt
” slightly oxidised, brown spots 1.076
” more oxidised 1.082 »
" covered with dark brown oxide film 1.089
iY cleaned, replated with fresh pinkish electro-surface 1.072»

4. In repeating CHacpinr’s measurements it is of the greatest
importance to have the determinations mutually comparable; errors
eaused by an unlike nature of the electrodes had to be carefully
excluded.

As negative electrodes we used pure zine amalgam (1 part. of zine
to 9 parts of mercury) as used in the Ciark standard-cell. The zine
Was a very pure specimen from Merck of Darmstadt in which iron
was not even detectable. The mercury was first shaken with nitric
aid and then distilled twice in’ vacuum according to HtLerr’s *)
method. As we know, the potential difference between this amalgam
and pure zine is very small. Previous experiments by one of us *)
have shown that this difference is) only 0.00048) volt. at O° and
0.000570. volt. at 25°.

As positive electrode we used at first a thick wire of pure copper.

The copper sulphate solution in the different cells was prepared

!) Philosophical magazine (5), 18, 265 (1882); Fiemine, ibid. (5), 20, 126 (1885).
Sr. Linpeck, Zeitschr. fiir Instrumentenkunde 12, 17 (1892). Comp. also Carnart,
Primary Batteries (Boston 1899). Litterature up to 1893 in: Wiepemans, die Lehre
von der Elektricitit. (Braunschweig 1893), pag. 798.

*) Zeitschr. fur phys. Chemie 88, 611 (1900).

*) Conen, Zeitschr. fiir phys, Chemie 84, 619 (1900),

(7)

by first making a saturated solution at 15°. Pure, Merck’s copper
sulphate (free from iron) was dissolved in water and boiled with
copper hydroxide to remove traces of free acid. After filtration the
liquid was cooled and after introducing a crystal of CuSO,. 5 H,O
set aside to erystallise. The salt was then shaken for a long time
(3 to 5 hours) with water at 15° in a thermostat, use being made
of Noyes’) shaking apparatus. All the thermometers used in this
investigation were tested by means of a standard thermometer from
the “Physikalisch-technische Reichsanstalt’” at Charlottenburg.

To make sure that complete saturation had indeed been attained
we took after 38. and 5 hours small samples from the solution in
the shaking bottles and analysed these liquid by means of NeuMANn’s
electrolytic process *).

In this way we found:

(9 hours) 100 parts of water dissolve 19.22 parts of anhydrous
Cuso,.

(3 hours) 100 parts of water dissolve 19.28 parts of anhydrous
CuSOQ,.

The zine sulphate solutions were prepared from a solution which
was saturated at 15° in the same thermostat as the copper sulphate
solutions. The different dilutions were done by weighing.

The zine sulphate gave no reaction with congored; moreover the
same preparation had served in the construction of Crark-cells which
appeared to be perfectly correct. By way of a check we also
determined the quantity of ZnSO, which at 15° is present in the
saturated solution. A weighed quantity of the solution was evaporated
in a platinum dish and the residue (ZnSO, .1H,O) was weighed *).
In 100 erams of water we found 50.94 erams of ZnSO, (as anhy-
dride) whereas previous determinations had given 50.88. If we
accept the figure 50.94, the saturated solution then contains at 15°,
150.56 grams of ZnSO,.7H,O to 100 grams of water. We fail to
see how Cuavpier has arrived at the figure 200 (see table 1).

6. Measurements with Danieni-cells are rather diffieult, for if the
smallest amount of copper sulphate solution comes in contact with

1) Zeitschr. fur phys. Chemie 9, 603 (1892).

2) Neumann, Analytische Elektrolyse der Metalle, (Halle 1897). Pag. 106.

We may casually remark that the figures given in the literature for the solubi-
lity of copper sulphate are incorrect. Compare: Eryst Conen, Vortriige fiir Aerzte
liber physikalische Chemie (Leipzig 1901) pag. 70.

3) See CaLLenDAR en Barnes, Proc. Royal Society 62, 147 (1897); Exnst Couen,
Zeitschrift fiir phys. Chemie 34, 181 (1900).

the zine electrode by diffusion, the E. M. F. of the system is dimi-
nished considerably.

FLEMING for instance states, “the smallest deposit of copper upon
the zinc, due to diffusion of the coppersalt into the zinc is indicated
by a marked depression amounting to 2 or 3 percent”, whilst Wricut
afier prolonged diffusion) noticed depressions up to 6 percent.

After a few preliminary experiments which convinced us of the
accuracy of these remarks we constructed for the definitive measure-
ments the little apparatus shown in fig. 1.

PC )

Fig. 1,

—-
—
—

It consists of three tubes A, B, C, (Sem. high, internal diameter
1.8 em.) which communicate by means of connecting tubes. To the
tube f, 7; a glass tap with a very wide bore (5 or 6 m.m.) is
attached. The zinc amalgam is introduced into A and the platinum
wire /% is then fused into it. A and B also 7, are now filled with
the zine sulphate solution after the bore of the tap has been plugged
with fat-free cottonwool previously sucked in the same zine sulphate
solution. While the tap is still closed, the saturated copper sulphate

solution is poured into C' and also into 7,: The cell is now closed

;
with the india-rubber corks A, A, and A,. Through A, is introduced
a thin glass tube reaching just below the cork. Through this tube the
copper electrode AK may be introduced into the solution when the
measurements take place. The whole apparatus is now plunged as
deep as possible in a thermostat (15°). If required the tap may be
opened or closed by means of the wooden rod GH.

By the introduction of the tube £6 the possibility of contact of the
zine electrode with the copper sulphate solution is quite excluded.
Even if a trace of copper sulphate has diffused into the lower part
of 6 (af the copper solution is lighter than the zinc solution, the
former will float in 5 on the latter) we never find a trace of copper
in the tube A. In the final experiments, the measurements lasted so
short a time that as a rule no copper diffused even into B.

7. After preliminary experiments had shown that the cells cannot
be reproduced when we make use of copper electrodes which have
been cleared with nitrie acid, we afterwards followed the direction
of Wriegnt and Fiemme who electrolytically cover the copper electrode
with a layer of copper immediately before the measurement. For
this purpose we used the bath deseribed by Orrrer ') for the copper
coulometer. After being copperplated the electrode was rinsed with
distilled water and dried with cottonwool. It was then at once put
through the tube into the cell. We always take care that only the
electrolytically copper plated part of the electrode gets into contact
with the liquid.

8. The EK. M. F. of the cells was determined by the compen-
sation method of PoGGEnporrr. As working cell we used a storage

1) Electrochemische Uebungsaufgaben (Halle 1897) pag. 5. All copper electrodes
were always copperplated during 10 minutes with the same current-strength (0.15
ampere) (or density) and at the same temperature. We have also tried, but unsue-
cessfully, to work with copper amalgam. As to copper amalgam, compare PEeTTEN-
KOFER, DinaLerR Polytechnisches Journal 109, 444 (1848) and v. Gersueim. Ibid. 147,
462 (1858).

( 10 )

cell (Deutsches Telegraphenelement), as normal cell a Weston-cell
which was always kept in a thermostat at 25°.

In this thermostat was also placed a Ciark normal cell to allow
comparison between the normal elements.

The rheostats used (2 rheostats of 11111.11 ohms each Hartmann
and Brawn) were carefully compared with a third rheostat standar-
dised by the “Physikalisch-Technische Reichsanstalt.”

filled with the required solutions it was (without the copper electrode)
placed in the thermostat at 15°. After having reached that temperature
the copper electrode was taken from the copperplating bath and after
having been treated as directed it was introduced through the tube

9 The measurements: took place as follows: after a cell had been

into the solution. The tap was now opened and the measurement
carried out; this lasted 1 or 2 minutes. When the tap had been
closed, the cell was taken from the thermostat. The solution in A
was then tested for copper, but as already stated not the slightest
trace of copper was found in this part of the apparatus.

10. As the measurements of ALDER Wrieut, FLeminG and Lorp
RAYLEIGH 2), which were done with fairly concentrated solutions of
zine sulphate bad proved that the reproduction of these cells to less
than 1 millivolt is almost impossible and as our own experiences had
shown us that with more dilute zine sulphate solutions we get. still
vreater deviations, we only give our measurements in millivolts
although the method of measuring employed rendered the determina-
tion of tenths of millivolts (and less) quite possible.

As CHAvpIER only gives one series of measurements We can say
nothing as to the reproduceableness of his cells. According to our
experience no importance need be attached to statements of tenths
of millivolts. Whether it would be possible to attain a greater accuracy
when working with solutions quite free from air is a matter which
we cannot go into any further as our results are quite accurate
enough to completely answer the question in dispute’),

11. Before proceeding to communicate our figures we would
point out that a cell constructed according to the scheme:
| .
copper sulphate solution |
Zine | water DI ae ps | copper
| saturated at 15 |
cannot practically be classed among the reversible cells.
1) Transactions of the Royal Society of London. Vol. 76, 800 (1886),
*) See Epetine, Wiep. Annalen, 30, 530 (1887) and G,. Meyen, ibid, 83, 265 (1888).

CEA.)

We have, therefore, not repeated Cravpirr’s experiment with this

cell. When we consider that cells with very dilute solutions show
deviations amounting to 6 millivolt, we cannot expect much from
measurements with an element of the kind described.

12. The subjoined table contains the results of Our measurements.
Below I and It are placed the values of the E. M.F. which we
found for the same cell in independent experiments. From these
figures it may at the same time be seen in how far the said cells
may be reproduced.

TABLE UE

oe a ~ —_—

Klectromotive force

irams of Zn SO,.7 HO flectre ive force ; Se Hi Ge fs : :
Grams of Zn SO,.7 Hy Electromotive force at 15 at 15°0 in. Volt.

to 100 gram water. in Volt. (COMMELIN and COHEN). (CHAUDIER).
I | II | average,
Vio 1.4143 | 4.4149 1.4146 1.1138
1, 1.444. | 14.446 1.144 oat lg
Yo 1435 | 4.434 oes 1.4368
14st | 4.a3n | 4,431 1.1331
2 Ee Be i Wa F255 1.1263
4 res US ey bee La FC Satay, 1.4249
6 1.416 1.416 1.416 1.4208
10 ps iy i I 2) ip be 1.1188
30 1.104 1 104 1.104 4.i054
150.65 (saturated). AOSts e084 1.081] 1.0902 (200 saturated ?)

15. From this table it will be seen at once that a maximum
value of the E.M.F. at about '/, gram of ZnSO, . 7 H,O to 100 grams
of water, as CuHacpirr claims te have found, does not exist. The
progressive change of the values is on the contrary, quite in harmony
with the equation given by Nernst, which shows a decrease of the
E.M.F. for an increase of the concentration of the zine sulphate.
It would be superfluous to criticise the other conclusions of CHAUDIER
as these are based on the figures discussed.

Utrecht, April 1908.

( 12 )

Mathematics. — “On compleces of rays in relation to a rational
skew curve.’ By Prof. J. DE Vrtks.

(Communicated in the meeting of April 24, 1903).

1. Supposing the tangents of a rational skew curve /?” of degree
n to be arranged in groups of an involution /’ of degree p, let us
consider the complex of rays formed by the common transversals of
each pair of tangents belonging to a group. So this complex contains
each linear congruence the directrices of which belong to a group of
Iv. If these directrices coincide to a double ray a of J? the con-
eruence evidently degenerates into two systems of rays, viz. the sheaf
of rays with the point of contact A of a as vertex and the field of
rays in the corresponding osculating plane «a.

To tind the degree of the complex let us consider the involution
Iv of the intersections of the tangents with an arbitrary plane g.
The surface of the tangents intersects g according to a curve C™ of
degree im = 2 (n—1) and the complex curve of g envelopes the lines
connecting the pairs PP’ of ?. This involution having (m—1) (p—l)
pairs in common with the involution forming the intersection with
an arbitrary pencil of rays, the complex is of degree (2 n—8) (p—1).

2. We then consider the correspondence between two points
Q,Q of C™ situated on a right line PP’. As Q lies on the lines
connecting any of (m—2) (p—1) pairs, there are (m—2) (p—1) (m—3s)
points Q. The correspondence (Q, Q’) has (im—2) (m—8) (p—1)* pairs
in common with /?, so the complexcurve has

1 (m—2) (m

3) (p—1)? = (n—2) (2 n—S) (p—1)?
double tangents, the complercone as many double edges.

Evidently these double rays form a congruence comprised in the
complex, of which order and class are equal to (n—2)(2n—S)(p—l)’.

The complexcurve also possesses a number of threefold tangents,
each containing three points of /?’ belonging to one and the same
vroup. To find this number we make each point of intersection S of
Cm with the right line PP" to correspond to each point P” of the
group indicated by P. To each point P" belong 4 (y—1) (p—2) pairs
P, P', so 4 (p—1) (p—2) (m—2) points S; each point S lies on
(m—2) (p—]) connecting lines P/, and therefore it is conjugate to
Gn—2) (p—1) (p—2) points P". Every time P?" coincides with S, three
points 7 lie in a right line and each of those points is a coincidence
of the correspondence (P",S); so we find 4 (m—2) (p—1) (p—2)
threefold tangents. From this appears at the same time that the

(13 )

right lines of which each euts three tangents of R" belonging to a
same group of /?, form a congruence of which order and class are

equal to (n—2) (p—i) (p—2).

3. Let us consider more closely the group where @ is a double
element and a’ one of the other elements. To the just-mentioned
congruence evidently belongs the pencil of rays in the plane (A,a’) — a,,
with vertex A and the pencil of rays in the osculating plane «
with vertex (a@,a@,)—=A,. So the congruence contains at the least
4 (p—1) (p—2) pencils of rays; each of the 2(p—1) singular points
A is the vertex of (j—2) pencils placed in different planes; each of
the 2 (p—1) singular planes @ bears (p—2\ pencils with different
vertices; on the other hand the 2 (p—1) (p—2) singular points A,
and the 2 (p—1) (p—2) singular planes a, each bear a pencil.

The complex curve is as appears from the above of genus
+ [(2n—3) (p—1)—1 | [(2 n—3) (p—1)—2] — (n—2) (2 n—5) (p—1)*—
3(n—2) (p—I) (p—2). For p=3 this becomes equal to zero which
could be foreseen; for, to each point ? of the curve C™ the connect-
ing line P’P’’ can be made to correspond, by which the tangents
of the complexcurve coincide one by one with the points of a
‘ational curve.

In a plane g through a tangent a’ the complexcurve degenerates, a
pencil of rays the vertex of which lies on the tangent a separating
itself from the whole.

In a plane e@ evidently (p—2) pencils of rays separate themselves.

4. We shall consider more closely the simplest case, where the
complex is determined by a quadratic involution of the tangents of
a skew cubic; n=3, p=2.

If A and & are the points of contact of the tangents a and /
forming the double rays of the involution, and if @ and P are the
corresponding osculating planes, we assume as planes of coordinates
2, = 0, z,=0, x7, = 0, 2, =O successively the osculating plane a,
the tangent plane (a, 5), the tangent plane (4, A), the osculating plane
B. The curve F#* is then represented by

AS SE ee ng aie gad el
and for its tangents we have the relation
Dee aie ee Pee = C8 A SP 2 TL —28 e.

The points A and # being indicated by the parameters ‘=O and
to, the parameters ¢ and ?¢’ of the points of contact of two
conjugate tangenis satisfy the relation ¢-+ ¢’ = 0.

( 14 )

The coordinates of a common transversal of the tangents (f) and
(—1t) evidently satisfy the conditions
i 2 9,2 043 256
Piz P,; + UDPy, 4 3t P23 == t'Ds4 = 2t Paz 0,
= ‘ ' 2933 ea
Pir t+ 2tp,, + Pi, | Ob pas 4 t Pa 2t*p,. = Y,
therefore also
Pra + © (Pi, + 3pa3) + Pas = 0 and OP ss = Pais:
By eliminating ¢ we find the equation of the indicated complex:
Pris Pisa 1 Pas Paz (Pras + 3P33) + Psa P13 — Y.

To this cubic complex belongs the linear congruence p,, = 90,
Y,, = 0. Its directrices / and m are represented by .7, = 0, v, = 0
and «,=0, ,=0; the former connects A with the point («, 4),
the latter unites B and (f, a).

Each ray of the congruence rests on two pairs of tangents; the
corresponding parameters are determined by the equation

Psat’ + (Pig + 3p 25) + Piz = 9-

So the complexcone has a double edge, the complexeurve a

double tangent.

5. This is also evident in the following way. With given values

of ¥,, Ys Y3,Y, the equation p,,=4p,, OF ¥,%,.—Yy,7, =4Y.4, ie)
represents a plane intersecting the complexcone twice according to
P=, py,==0. and moreover according to a right line of the plane
a” (Ya — Yi") + i [(y.,—4."4) ae 3 (5%3—Yar"'s) 05 (3 — Ys") = 0.
0 ,,'= 0;'p,, = 0 is.a:-doublevedge.

If the plane y,.,—y,", = 4(y,2,—y,;) is to touch the complex-
cone along the double edge, the three planes

at —— ig Q) ; A 5 og — A ee 0,
(A?y,+4y,)e, + (BAy,—A*y,) e, + (y,—3 ay.) a, — (49, +93) @, = 9
must pass through one right line, so
OS AY Oye ’ dAy, —VYy, = Oy
Ys — SAY, =—.09; 3 44+). =e
must be satisfied.
sy eliminating @ or o we find

PIs + AY ty = Fy) +959, =O.

The roots of this quadratic equation determine the tangent planes
of the complexcone along the double edge, which becomes a cuspidal
edge when
that is when Bee Ua Sa ee

WY Yadn OK =O

.
;
4

(15 )

So these quadratic skew surfaces of which the first evidently
passes through /?* contain the vertices of the complexcones having
a cuspidal edge.

6. For the points P? of the F*® this cone of course degenerates
into the plane connecting /? with the tangent jp’ in the conjugate
point P' and a quadratic cone touching that plane.

For points on the right lines / and i the complexcone must con-
sist of a plane counted double and the single plane «,=0 or.r,—0.
For, each ray in e« and belongs to the complex, whilst all right
lines resting on / and m are double rays of the complex. Indeed the
substitution y, =O, y, =O in the equation of the complex gives
the relation 2, (y, 7,—y, 7,)? = 0..

For points on one of the tangents « and 4 the complexcone breaks
up into the plane e@ or @ and into a quadratic cone touching it.

For a point of the intersection of @ and ¢ we find a degeneration
into three planes.

For the complexcurves analogous considerations hold good ; e. &. the
complexcurve degenerates into three pencils of rays when the plane
passes through AB.

7. The complexcone degenerates into a plane and a quadratic
cone if the vertex lies in @ or in @ or on the surface of the tangents
of FR. In the former case « or 3 belong to it; in the latter the plane
through the vertex P and the conjugate tangent p’.

To investigate whether there are more points for which sueh a
degeneration takes place, we suppose that the equation of the inter-
section of the complexcone with .«,— 0, thus that

YY," =f ye, —Y sift "i, Yu ly Ws sa (Y2Y~— OY sy, ae

+ BY, Y3%q°©,— 24,9 8,2, —3Y Yt, + (YY, + SY 2Ys)® Cyt, = O,
is deducible to the form
(5,127 +0, 404° +0, 03? +26, e206, 270, +26, ugu’s) (Ct + O,7,+6,2;) = O.

Then the following conditions are to be satisfied:

aan | 6,40. —YiYar oF a ae
b, €,+26, ,c ea ae b, ,€,+26, ,c, — a4 Jools +e Des =o Uae)
b,4¢, +20, ,¢,—=3Y,Y55 b,,¢, +20, ,c, == 24 Y30 ties mari SUM as

(61563 + 55 3¢, + 91 3¢,) = Yi¥s + BY Ys:
Let us in the first place put 56,,= 0 and c,=~y,, then 26,, is
equal to —y, and 2h,, equal to y,. Further we find 4,, = —y, and
¢; = —y,. After some deduction we get as only condition

( 16 )

Wd + 4 Ys?— 89 Yo sta BY a Ys + Ys Ys = 9;
or
(9.9:—9.93) = A(y,%3— Ys) 5)

that is the verter of the compleacone belongs to the SUP Face of tangents.

If we put c,=90, we then arrive after excluding y, =O and
y,=9 (for which the indicated degeneration always takes place)
at the double condition

Yo = Ux ANd YY, = Yas:

that is at the points of FR’.

8. Let us suppose that the tangents of /#* are arranged in the
triplets of a -/*. To determine the degree of the complex of the common
transversals of the pairs of tangents we can also set about as fol-
lows. In an arbitrary pencil we consider the correspondence of two
rays s and »’, which are cut by two tangents belonging to J/*.
To the coincidences of this correspondence (8, 8) belong the four
rays resting on the double rays a, bc, d of J*; the others are united
in pairs to six rays, each resting on two tangents of a triplet, so the
complex is of degree 6.

To find the degree of the congruence of the right lines, each resting
on the three tangents of a group, let us consider the rays they have
in common with the analogous congruence belonging to a second /*.
If »,, 7, is one of the four common pairs of the two involutions,
and 7, and +,’ successively the tangent forming with 7, and 7, a
eroup, the common transversals of 7,,7,, 7, and 7,’ belong to the two
congruences *). Evidently they can have no other rays in common
than those eight, which are indicated by these; consequently the con-
eruence is of order two.

The complexcone of an arbitrary point ? has as appears from
the above, two threefold edges; as it has to be rational, it has
moreover four double edyes.

If P lies on the surface of tangents of /’, this cone degenerates
into the system of planes which connect /? with the two tangents
conjugate to p and a biquadratic cone with threefold edge.

9. The quadratic serolls determined by the triplets of tangents,
evidently form a system of surfaces two of which pass through any
point and two of which touch any plane. This system is thus
represented in point- or tangential coordinates by an equation of the
form

‘) This consideration leads to no result if we consider a rational skew curve
of higher order.

CHE)

P+22Q4+4R=0.

From this ensues that all the surfaces of this system have the eight
common points (tangential planes) of P=0, Q=0, R=0 in common.

The degenerations of this system are four figures consisting each
of two planes as locus of points and of two points as locus of
tangential planes. One of those figures is formed by the planes
@ and «, —(Aa’) and the points A and A, = (ea).

The eight common points A,, B,, C,, D,, A;,6;, C,,.D, and the
eight common tangential planes @,, 8,, ¥,, 5), 43. 23,359; Of the scrolls
are singular for the congruence (2,2). The remaining singular points
and planes are evidently A,B,C, D, A,,B,,C,, D, and 4,3,7,64,,.8 7154,
These 16 points and 16 planes form the well known configuration
of KuMMER.

We can choose the notation in such a way, that A, bears the
planes 8, y, d,a, and A, the planes @,,y,,d,,@, etc. Let us bear in
mind that three osculating planes of /* intersect each other in a
point of the plane of their points of contact and let us further mark
the symmetry of the figure, we can then easily deduce from the
preceding, that

i @ ihe poms Ar tA bs... D,;
ny Gy UT] sae Pale Ak. Bs Ce DD;
2 : sh Ose BD

Re AAP i AeA Ay

Tea ame " Ze Aen Ass pis! Co IDs,
are situated, whilst

A bears the planes @, @,, @,, B,, ¥., 4,

A, I TT] 7] Opie, ia Vas Os,
A; Ui " / a, a, a, 8, Y> J,
A 3 / " " a, a, a, 5) B, > v1 5) J, .

It is clear that for each of these 16 points the complexcone is
composed of a plane counted double and a cone of degree four.

Mathematics. — “Vhe singularities of the focal curve of a curve
in space.’ By Dr. W. A. Versiuys. (Communicated by Prof.
P. H. Scnoure.)

In paper N°. 5 of the “K. A. v. W.” at Amsterdam, Vol. XIII,
I have deduced some formulae expressing the singularities of the
focal developable and of the focal curve in function of the singulari-
ties of a plane curve.
In like manner it is possible to deduce the following formulae
which express the singularities of the focal developable and of the
”)

Proceedings Royal Acad. Amsterdam. Vol. VI.

( 18 )

focal curve of a curve in space in function of the singularities of
this curve. |

Let the curve be of degree u, of rank 9, of classy; let its number
of stationary points be ~, that of its stationary tangents @. Suppose
the curve to have no real nodes or double tangents and no particular
position with respect to the plane at infinity or with respect to the
imaginary circle at infinity. .

In that case the singularities of the evolute or of the cuspidal curve
of its focal developable (G. Darsovx: Classe Remarquable ete. p. 13}
are the following:

Tak 9 2 (pu ms 0).

class, m = 2 9

number of stations ary planes, a= aes (py + ae

double osculating planes, G =

stationary tangents, v7 = 0.

nodes, H=2z=3(u—9) + 7+ 4.

double tangents, @ = 0.

degree, n= 2(3u+r+ 6).

degree nodal curve; «= 2 (u-+ 9)? —10u—29—3(+ 6).

number of planes through two lines which pass through a given
point, y=2 (ue)? — 4u — 49 — (r++).

stationary points, 8 = 12 4u—49—6(v-+ 8).

iene

The chief singularities of the focal curve are:
degree, n= 2° +4nu0+ 0?—11lu—o—38(e4+ 9).
rank, 7 =4uo0+ 0°—4u—4e0
number of stationary tangents, v = 0.
class, m= (8u+2vr+26)(2u+o0)+3u09— 36u-+ 12 o— (+ 8).
number of stationary points, ? = 2 (84+ »+ @)(2u+ 0) — 574+
21 9 — 27 (vw + 6).
“ a planes, a= 6(2u+r-+ 0)(Qu+ 0)—4w—
2u0—20°— 107 u+ 47 9 —57 (w+ 8).

When comparing these singularities with the values of the singu-
larities of the evolute and of the focal curve of a plane curve, we
see that they differ only in the rank of the curve in space being
substituted for the class of the plane curve and in the number of
stationary tangents « being replaced by (v-+ 9). From this follows
that the singularities of the evolute and of the focal curve of a curve \
in space c are the same as those of a plane curve d, which is the
projection of ¢ on an arbitrary plane from an arbitrary point.

(19 )

Physics. “On the double refraction in a inagnetic field near the
components of a quadruplet.” By Prof. P. Zxeman and J. Grxsr.

Qn a former occasion the results were communicated to the
Academy, of an investigation on the magnetic rotation of the plane
of polarization in sodium vapour, in the immediate neighbourhood
of the absorption lines. *)

In the case of very thin vapours this rotation appeared to be
positive outside the components of the doublet, in which the original
spectral line is resolved by the influence of the magnetic forces:
between the components, however, it becomes negative and very
large. In these experiments the light of course passed through the
vapour in the direction of the lines of force.

In the same way, if the light is transmitted through sodium vapour
in a direction normal to the lines of force, we may expect from the
examination of the immediate neighbourhood of the components,
in which the spectral line is split up by the magnetic forces, results
which are of theoretical importance.

Voret has deduced from his theory of magneto-optical phenomena
the existence of a double refraction, which must be produced in
isotropic media, as soon as they are placed in a magnetic field, but
which should only be observable in the neighbourhood of an absorp-
tion line.*) Vorer, together with Wircuert, has observed, that plane
polarised light of a period near that of the lines D, and D,, is no
longer plane polarised but has become elliptically polarised when
it has traversed the flame, there being generated a difference of phase
between the components vibrating parallel and those vibrating per-
pendicularly to the field.

This elliptical polarisation was demonstrated by the above mentioned
physicians with the aid of a Basinet compensator, using a flame
with much sodium and a small Row1anp grating.

The object of our investigation of the magnetic double refraction
was to examine the phenomena, which show themselves, if, beginning
with very small vapour densities, the quantity of sodium is gradually
increased. The present communication deals only with the line D,
in the case of very small densities. This line is resolved into a
quadruplet by the action of the magnetic field.

The grating employed for this investigation and its mounting for

1) Zeeman. Proc. Roy. Acad. Amsterdam Vol. V p. 41, 1902, cf. also Hato
Dissertatie. Amsterdam, 1902.
2) Vorer. Géttinger Nachrichten. Heft 4. 1898; Wiepemany’s Annalen. Bd. 67.
p- 399, 1899.
2%

( 20 )

parallel light (which was necessary also now) have been described
already more than once. *)

The light from an are-lamp or from the sun passed successively
through a Nicol’s prism, whose plane of vibration was inclined at
an angle of 45° to the horizon, the magnetic fieid with its lines of
force normal to the beam, a second Nicol at right angles to the
first. Between the Nicols the BaBiner compensator was placed, the
edges of the two prisms being horizontal. An image of the com-
pensator was formed on the slit of the spectral apparatus; in the
middle of this image the central dark interference fringe, surrounded
by the coloured ones, was seen. In the spectrum a pair of dark
interference fringes are observed and with the field off, only the fine
absorption lines of the vapour are seen. Generally the reversed
sodiumline is observed already in the spectrum of the arc-light
itself and then the presence of sodium vapour between the poles
makes of course no difference at all. In order to obtain the degree
of sharpness of the interference fringes, necessary for this part of the
investigation, we tried several compensators. Sufficient results were
obtained with a Basimer compensator of which the prisms had angles
of about 50', obtained from the firm Srenc & Reuter.

The light passed the flame (a gas flame fed with oxygen) over
a length of nearly 1'/, em. If the field had an intensity of about
23000 C.G.5. units, the quantity of sodium in the flame being very
small, the image observed was very similar to
that represented in Fig. 1. The latter is constructed
with the aid of photographie negatives and of eye
observations. The whole phenomenon is of course
very delicate as it only extends to the region of
the magnetically broadened D, line; moreover it
depends very much on the quantity of sodium
present. We did not yet succeed in getting negatives,
which showed the parts which are of very unequal
intensity all equally well.

Fig. 1. Already some time ago Prof. Voigt was so kind
to inform one of us of the result, which according to his theory may

be anticipated in the case of a quadruplet.

This conclusion is easily arrived at, if the calculation be simplified
by applying a certain approximation, the soundness of which cannot
be judged a priori, because constants appear whose numerical value
is not yet known. With this reservation the behaviour predicted

1) Zeeman |.c, and Arch. Néerl. (2) 5. 237. 1900.

( 21 )

Rae a by theory is represented in Fig. 2. The dotted
rat vertical lines are the four components of the qua-

! druplet. :
i: In comparing the figures 1 and 2 one must take
into consideration, that in Fig. 2 is represented the
shape of the fringes, which arise from a single
f horizontal band. In Fig. 1 in the central part of

the field also occur parts, originating from fringes
-- lying above and under the middle. The vertica]
Fig. 2. medium line of Fig. 1 corresponds to the almost
ever present absorption line due to the are light and is thus in no
way connected with the phenomenon which occupies us.

The agreement in the region between the two interior components
of the quadruplet is undoubtedly of great importance. The whole
form of the double curved line may certainly be regarded as a con-
firmation of theory. How far the darker parts between the exterior
components in the middle of Fig. 1 correspond to the U-shaped parts
of Fig. 2 is at present not yet to be decided.

Chemistry. — “Vhe course of the melting-point-lne of alloys.”
(Third communication). By J. J. van Laar. (Communicated

by Prof. H. W. Baknuis Roozesoom).

I. I have shown in two papers (these proceedings Jan. 31 and
March 28, 1903) that the expression (see the second paper) :

(ig eae

ry 7] (i = ra)*
1 isc U8 Se) ee ate eae

1—J log (1—2z)
very accurately represents the solidification temperatures of tin-
amalgams. This equation may be derived from the general expressions
for the molecular thermodynamic potentials of one of the two com-

ponents in solid condition and in the fluid alloy.

I also pointed out (in the first paper), that already the simple

formula

2
at

ere ge ee ek
1--6 log (1— x)

qualitatively represents the course of the melting-point-line perfectly.

This is simply done by not omitting the logarithmic function /og (1—x).

Though it is a matter of course, that — /og (1—x) can only be

replaced by x, or v-+-$.2°-+ ete. in the case that « is very small, it

( 22 )

seems necessary to continually draw attention to this circumstance.
Already in 1893 in his thesis for a doctor’s degree: “De afwijkingen
van de wetten voor verdunde oplossingen” Honprus BoLpinGH used the
function — log (1—a); also the correction term ex’, omitting however
the denominator (1 + 77)?. Le Cuarrrirr *) used the simple equation (2)
in a somewhat modified form for the melting-point-curves of alloys.
The way however in which he derived this equation is totally wrong °*).

II. Many melting-point-curves show the same type as those of
tin-amalgams; it may therefore be important to investigate, whether
they also may be represented by formula (4). It must however be
observed, that this formula is applicable only in the case that the
solid phase does not form any mixed crystals. Tf the formula (1) does
not hold good, this may therefore indicate the occurrence of mixed
crystals in the solid phase, though it is of course also possible that
other influences e.g. dissociating multiple molecules have caused the
deviation.

In 1897 Heycock and Nrvi.LE ji. a. made experiments on a great
many alloys*). They found that the alloy s¢lver-lead shows the type
of tin-mercury very accurately (comp. the figure on p. 59 of their
paper). I have subjecied the data relating to this point (comp. the
tables of p. 87 and 39) to some numerical investigations.

The initial course is again nearly straight — up to about 20 atom
procents of lead and this part yields for @ the value 0,805. If
we now use this value for the calculation of the quantities @ and 7
from the observations at lower temperature, we do not find constant
values, as in the case of tin-mercury, but considerably different
values according as we have calculated these constants at mean tem-
peratures or at low temperatures. If we take the data for #=0,63
and = «=0,80, or «70,63 and #=0,96 (the eutectic point) as basis

for our calculation, then we find in both cases:
a= 0,453": fae a

The following table may show how bad the agreement is, specially
for the mean temperatures:

') See ia, “Rapport etc.” (Paris, Gauthiers-Villars): La constitution des alliages
métalliques par S. W. Roperrs-Ausren et A. Sransriep. (1900), p. 24.

) On different occasions I have pleaded already before for not omitting the
function log (1—). (comp. i.a. Zeitschr. fiir Phys. Ch. 15, p. 457 sequ. 1894).

5) Complete Freezing-Point Curves of Binary Alloys, containing Silver or Copper
together with another metal (Phil. Trans. of the R. S. of Londen, Series A, Vol.
189 (1897), p. 25-—69),

ee ee eee

( 23 )

eA aaa

i)
0.0052
0.0103
0.0154
0.0254
0.0361

0.0504

0.6733
0.1057

0.1360

0.4732
0.2156
0.2537
0.2949
0.3432
0.4038
0.4542
0.4966
0.5330
0.5851
*0.6312
0.6790
0.7042
0.7353
0.7692
*0 8064
0.8333
#0, 9615 |

0 | 1.0000 | an 1.0000 | 1.0000 | 959.1 959.1 0
0.00003 1.0042 | 0 00001, 0.9966 | 4.00001 | 9540) 954.3 | — 0.3
0.00%t) 4.0083 0. 0000*| 0.9934 | 1.0000 | 948.9) 949.0 | — 0.1

0.0002" 1.0125 | 0.00005, 0.9900 | 4.00009 | 944.0 | 944.0 0
0.0006* | 4.0207 | 0.00098) 0.9835 | 1.0002 | 934.5) 934.4] +0.
0.00139) 4.0296 (00048 0.9767 | 1.0005 | 924.3 | 924.4 | = 104
0.0025!| 1.0416 | 0.00099 0.9675 | 1.0009 |} 910.9} 910.4} 4 0.5
0.00537) 1.0613 0.00191, 0.9530 | 1.0020 390.3 | 886.6 eee
0.01117, 41,0900 0.00897 0.9324 | 1.0043 | 8621 | 853.4] + 8.7
0.0185°| 1.4477 | 0.0065"! 0.9136 | 4.0072 | 837.2] 990.0 | 417.9
0.03009) 1.1531 | 0 01065) 0.8906 | 4.0120 | 808.4] 782.7 | 495.7
0.04645) 1.1955 | 0 01659, 0.8647 | 4.0191 72! 14.6 | 135.6
0.0643°| 1.2356 | 0 02985| 0.848 | 4.0971 | 751.4| 710.0 | 444.1 |
0.08697) 4.2813 | 0.0308*| 0.8176 | 1.0378 | 725.0] 684.1 | +40.9
0.1178 | 1.3385 | 0.0418?| 0.7894 | 1.0530 | 6963] 659.5 | +368
0.1631 1 4164 0.05791! 0.7548 | 4.0767 | 663.4! 635.4 | +28.0
0.2063 | 1.4876 0.07324) 0.7266 | 1.1007 | 688.5) 6193) 449.2
0.2466 | 1.5527 ; 0.0875'| 0 7032 | 1.1244 | 619.41 | 606 2 | +412.9
0.2841 | 4.6131 | 0.1029 | 0.6836 |. 1.1476 | 603.4} 596.14 | 47.3 -
0.3493 | 4.7083 | 0.1215 | 0.6558 | 41.4853 | 581.9) 580.8 | + 1.1
0.3984 | 1.8032 | 0.4414 | 0.6319 | 1.2938 | 563.1 | 563.0 | + 0.1%
0.4610 | 4.9149 | 0.1637 | 0.6073 | 1.2696 | 543.9] 548.3) —44
0.4959 | 1.9808 | 0.1761 | 0.5946 | 1.9962 | 533.2| 536.9 | — 3.7
0.5407 | 2.0702 | 0.1920 | 0.5791 | 4.3316 | 519.5) 593.6 | — 44
0.5917 | 2.4816 | 0.2101 | 0.4727 | 4.3735 | $03.0! 505.5 | — 2.5
0.6503 | 2.3921 | 0.2309 | 0.5695 | 4.4944 | 482.5 | 481.6 | + 0.9%
0.6944 | 2.4425 | 0.2465 a4 14.4635 | 465.4 | 460.6 | -+ 4.5
0.9245 | 3.6226 | 0.3982 | 0.5318 | 1.6943 | 303.2 | 303.3 | — 0.4%
|
1) 7%) The values of values of x marked with asterics are those which are used for tne cal-

culation of the constants z and 7.

( 24 5

Jetween «0,10 and «0,53 the agreement is decidedly bad;
at lower temperatures slightly better. It is striking that the value
we find for « is much too large, namely 0,855; for tin-mercury we
found for @ only the value 0.0453.

We will further investigate whether the value of @ which is
calculated from the initial straight part of the melting-point-line,
namely G—O0,805, is in agreement with the latent heat of solidification
of pure silver.

and as Person has found g, = 107,94 X 21,07 = 2274 Gr. kal.,
we should have for @:

2X 1232
G==- x

== ic t34-
9974

We have, however, found the much sma//er value 0,805. This
indicates the oceurrence of mixed crystals already in the initial part
of the melting-point curve, unless we assume, either that the value
of Person is about 1,35 times too small, or that the association of
the lead, contained in the silver, is 1,35.

III. Let us discuss in the second place the melting-point curve
of silrer-tin. We conclude at once from the figure of Hrycock and
NevitLe, that complications, mixed crystals for instance, must occur.
For though the melting-point curve from 30 atom-procents tin
upwards shows the normal typical course, the initial part, instead
of being nearly straight, is strongly concave towards the side of
silver, so that fwo inflection points occur, quite contrary to the course
indicated by formula (4) or (2).

It is accordingly impossible to determine the value of @ from the
initial part of the curve. If we calculate 6, @ and 7 from three
observations, for instance a = 0,43, «=0,61 and «= 0,86, then
we get with:

T, = 961,5*) + 273,2 = 1234,7
the following values (comp. the table of Hrycock and Neviiin, p. 40
and 41):
O=—1491 . he Do : r= — 0,277.

') The value 959°.2 given by Heycock and Nevitte has been augmented to 961°.5
on account of the accurate observations of Horporn and Day (quoted in Z. f. Ph.
Ch, 35, p. 490—491), from which appeared that pure silver, the air being excluded,
so that no oxygen can be absorbed, has a higher melting point (961°.5) than silver
containing oxygen (955°).

( 25 )

We see that the value calculated for J is considerably higher than
the normal value 1,08 and that @ is also again excessively high.
In order to get a survey of the degree of the deviation from the
theoretical course we will perform here the calculation of equation
(1) with these values of 0, @ and 7. (see table p. 26),

This bad agreement does not improve considerably if we determine
(, « and y from other values of x, for instance from #=0,30, 70.61
and «#=0,93. For these values of .« we find:

P1326 - a= 07474 : r = — 0,38,
so @ has come somewhat nearer to 1,08 and @ is also somewhat
lower. It is true that the agreement for values of « below «0,30

has somewhat though not noticeably improved (4 = —70,3 for w=0,13
becomes now A= -— 55,7) but the agreement for values of x higher

than «2=0,30 is in general still worse. So we find for instance for
a—0,47 for A the value A—-+8,5, whilst in the above table we
found A=-+2,6, ete.

1V. For completeness’ sake we shall draw attention to the two
very short melting-point curves of lead-silver and tin-silver. We may
easily calcuiate the quantities G from the data of the two eutectic
points. As namely these lines may be considered to be straight, we
find J immediately from

We have for lead-silver :
oe 10+ 203,02 —= 6008 3 2==3038)3-+273,2—576,5 ; #=0,03885 4,
therefore
24,3

ie eee sts _— 1,095,
576,5 X0,0385

hence
RT, 2X 600,8
ea Oke 1005
Person found g, =5,369 K 206,9 1111 Gr. cal. The agreement
appears to be nearly perfect. From this follows that siver, solved
in /ead, occurs in it as atom, at least for small concentrations.
As to the melting-point curve é-silver we have for it:
T, = 232,14273,2—505,3 ; 7=221,7+273,2—494,9 ; «—0,0385+.
We find therefore :

— 1097 Gr. eal.

10,4 ye
~ 494.9 0,0885

0,546,

and

( 26 )

SILVER-TIN.
| eT eS Sarak.
| eae: | = Boe te lee ES
ete eS ae

0 | 0 | 4.0000 0 | 4.0000 | 4.0000 | 961.5} 959.2] -+ 2.3
0.00459 0.00002, 4.0068 | 0.00002, 0.9975 | 1.00002 | 953.2 | 936.4 | — 2.9
0.01299, 0.00017, 4.0195 | 0.00012) 0.9928 | 1.0001 | 938.0} 950.0 | —12.0
0.03058, 0.0009" 1.0463 0.00067, 0.9831 4 0007 | 907.9 | 936.8 | —28.4
0.04842, 0 0023'| 4.0739 | 0.0016°| 0.9734 | 1.0017 | 878.4| 921.8 | —43.4
aw 0.00686! 1.1960 | 0.00473] 0.9555 | 1.0049 | s98.7| so1.o | —62.3
0.1324 | 0.01758, 1.2114 '0.0195"| 0.9979 | 1.0136 | 759.9 | 830.2 | —70.3
0.1813 | 0.03947| 1.2978 | 0.02360] 0.9091 | 1.0262 | 703.2| 755.9 | 52.7
0 2953 | 0.05078| 4.3801 | 0.0364) 0.8791 | 1.045 | 658.5) 691.7 | —93.2
0.2633 | 0.06933] 1.4549 | 0.04978) 0 8595 | 1.0579 | 624.6 | 648.2 | —23.6
0.3095 | 0.09579| 1.5514 | 0.06878] 0.8359 | 1.0823 | 588.1 | 603.4 | —15.0
0.3516 | 0.1936 | 1.6450 | 0.08874, 0.8147 | 1.1089 | 559.0 | 567.5 | — 8.5
0 3917 | 0.1534 | 1.7400 | 0.1101 | 0.7948 | 1.4385 | 534.8] 538.7 | — 3.9
#0.4371 | 0.4914 | 1.8555 | 0.1372 | 0.7725 | 4.1776 | 510.4] 510.2 | + 0.9"
0.4764 | 0.9970 | 1.9633 | 0 1630 | 0.7534 | 41.2164 | 49:.8| 489.2] + 2.6
0 5107 | 0.2608 | 2.0644 | 0.4873 | 0.7370 | 1.9541 | 476.9| 474.0 | 4 2.9
0.5426 | 0.9944 | 2.4643 | 0 2144 | 0.7290 | 1.2998 | 464.3] 463.6 | 40.7
0.5731 | 0.3984 | 2.9672 | 0.2958 | 0.7076 | 1.3332 | 452.8] 453.3] - 0.5
0.6148 | 0.3780 | 2.4203 | 0.9714 | 0.6884 | 1.3943 | 438.9 | 487.9 | + 0.3#
0.6510 | 0.4937 | 2.5670 | 0.2042 | 0.6719 | 1.4597 | 4956] 494.9| 40.7
0.6812 | 0.4640 | 2.7019 | 0.3332 | 0.6582 | 4.5062 | 415.1 | 413.0] + 2.4
0.7173 | 0.5145 | 2.8808 | 0.3694 | 0.6421 | 1.5753 | 402.0] 399.2] + 2.8
0.7547 0.5696 | 3.0921 | 0.4090 | 0.6255 | 1.0539 | 387.2) 381.4] + 5.8
0.7687 | 0.5909 | 3.1796 | 0.4243 0.6195 | 4.6849 | 381.0] 380.8 | 4+ 0.2
0.8192 | 0.6711 | 3.5463 | 0.4819 | 0.5977 | 4.8063 | 55.7 | 355.2 | + 0.5
#0.8692 | 0.7555 | 4.0283 | 0.5495 | 0.5764 | 4.9442 | 391.8] 392.6] —0.8*
0.9006 | 0.8114 | 4.4369 | 0.5824 | 0.5633 | 2.0330 | 299.8 9296.9 | — 4.4
0.9344 | 0.8731 | 5.0557 | 0.6269 | 0.5494 | 2.4411 | 999.9 | 959.5 | 29.6
0.9615 | 0.9945 | 5.8490 | 0.6638 | 0.5383 | 2.9399 | 198.2 | 291.7 | —93.5

( 27 )
_ 2X 505,38
Sth BAG
Prrson found for the latent heat of solidification for tin
14,252 118,5 — 1689 Gr. eal.

The difference is so small, that we may assume also here that the

sloatetgr. cal.

silver is present as atom also in tin. This conclusion is the more
justified as Hrycock and NeviLie give for «: “somewhat smaller than
0,0385”, from which follows that @ will be somewhat greater and
Gy somewhat smaller, so that g, approaches still more to 1690.

I draw attention to the fact, that the good agreement of the value
for tim tound by Pkrrson justifies the conclusion that this value is
really rather accurate, so that we must assume that the mercury
(see my previous communication), solved in tin, is present in par-
tially associated condition, the association amounting to about 1,5.

It appeared namely that — when mercury did not occur in the solid
phase, which consisted therefore exclusively of tin — the value

of O was such, that it yielded g, = 2550. In order to make this
value 14 times smaller, G must be augmented, i.e. « must be dimi-
nished, and this can only be done by assuming association to the
same amount.

V. Let is now return to the question of the point of injlection
on the melting-point curve. From:

ax
a ae ay
1—d log (1 —.t)
follows
ar: fe =O an a 2 ata:
ape a ee AT2. 1 2 == > ° au
du N* |—a (1+ 72) N (1+ 72)
therefore
0 ig be igs 0 20 aa?
= — — i, 1+ ———_— | —
da == N* (f— 2)? i Nv (1+ re)?
He 7) Zan i lhe 2a(1—2rx)
=a Sle a a
N?1—w#(1+re)? N (14+7re)‘
or

‘ad lated 8 0 29 ata? Aaax(1—.) ]
= SoS see eel ae
At Gy cal \( =) (1+ rx)’

=o)
12 ee re ae Wes

If a=0, this equation may be written:

( 28 )

Gat vey Et 20 1
dz? =N*(1—2)\ N

as we have also found before (see p. 481 of my first communication).
Whereas for ¢=0O a point of inflection at e=0O (N=1) was
determined with the aid of the simple equation 20=1, or 6=‘/,,
this condition becomes, in the case we are treating now, somewhat
more intricate. If we equate namely the second number of equation
(5) to zero, and further put z=0, N=—1, then we find:

0 (2 @—1) + 2 a=0,

SO
GP—t16t1a=0.
We find therefore that a point of inflection occurs beyond «=0,
always when

O20. aU, a ey al oe ee

In the case of tn-mercury (see the second communication) we had

J=0,396, and a=0,0453; therefore:

0,1568 — 0,1980 + 0,0453 = 0,0041.
This value being positive, a point of inflection was to be expected
between #=O0 and «=1. In fact a point of inflection was found at
4=0.(5.

The equation (4) may also be derived in the following way with-
out making use of equation (3). If we resolve equation (1) into a
series according to x, we get for small values of «:

L=T, (A— 62 + (6? —10 4+ a) x’...

The melting-point curve turns therefore at =O the concave side
towards the ordinate =O in the case that 0? —160+a< 0; and
as the curve approaches the ordinate #=1 asymptotically, a point
of inflection cannot occur. If on the other hand 6? —40+a>0,
then the conver side is turned towards the ordinate «=O and there-
fore a point of inflection must necessarily occur between #=0
and 21.

As @ can be +2 at the utmost, there must exist a value, which the
abscissa of the point of inflection cannot exceed. This maximum value
is found by equating the second member of equation (3) to zero,
and 0 to © [N being equal to —@ log (1-—a)], so we find:

aaa |(Space t+ ax* 4 aaz(1—zwz) if
(1—xz)?’ | — lag (1 -- av) (1 a al tre)? |
— 2alog (1 —w) (1—2 re) =

(1+,r2)* 3 a

Only if a=0, this may simply be written:

2
— log (1—«)
from which we find: 20,865. If however ea is not zero, then the
equation — log (1-—r) = 2 transforms the above equation into the
following one:

—1=0, or —log(1—wx) = 2,

i! | 4aa(l—xz)) | 4a(1—2re)

a — Sees 2
(l—e#)*{ .(i4ra)? } (1+ra)'
or
av
1—2re = ——— (1+ re),
ra OES: (1-4)

which is only true, if

wet

a 1,156—2 :

p= —— = == - = 0,744.
2—w 2-—0,865
We happened to find exactly = — 0,74 for tin-mercury, so -

if O had been equal to «2 — the point of inflection would have been

found at 2=—0;865.

Negative values of @ (or qg,) ave required in order to find a point
of inflection between that value of 7, for which we find the point
of inflection with @—=o , and w—1. These negative values will occur
very seldom, if at all. The principle result of the above investigation

is therefore that the melting-point curve — the case of mixed crystals
being excluded — will show a point of inflection if

FTO E> 0,

ee
sealants oer oga re were i
Jo Vo

or, O being equal to

ere i225 :
——4RT, +4, >,
Jo
He. 11
2RT,
ie
i
RT.

As &, expressed in Gr. Cal., amounts to 2, the condition may
finally be written:

(re te ee eae (3)

1 a,
Jie
where ¢, represents the latent heat (in Gr. Cal.) of the metal, which

is deposited in solid condition, 7, the absolute melting temperature
a, b,? — 2a,,6,b,+ a, b,? ;

ee ep ay -__=*__ also expressed in Gr. Cal.

)

( 30 )

1 i ae
ra? represents in general the heat, which is given
+ ra)?

As the quantity (i

out pro molecule when an infinitely small quantity of the pure
molten metal is mixed with the fluid metal mixture, the quantity
a, 2? will represent that same quantity of heat for «= 0.

We must here notice that the accurate values of @ and q, must

be used, as well in equation (4) as in (5). So in the case of tin-
mercury for instance d6—0,396 is accurate only if the mercury is
solved into the tin as atom. If this is not the case and in the
example mentioned we have every reason to suppose that the mercury
is associated to an amonnt of 1,5 — then @ must undergo a propor-

tional increase. O was namely calculated from 7 ae If we apply

= .
wv

the condition in the form (5), then we must substitute the experi _
mentally determined value of the latent heat for q.

So in the case of tin-mercury @ will not be equal to 0,4 but in
reality to 0,6, and therefore @? — $0 + «= 0,36 — 0,30 + 0,04—0,10,
from which the existence of a point of inflection appears still clearer
than in the supposition 6 = 0,4.

If we apply condition (5), ¢, being equal to 0,0453>1690=77
Gr. Cal., we have certainly 3

AS 503

L100 << ahs -=
1— | <a oh 4

DVD

If a, is positive, as is the general case, then the simple condition
Jo <— 4 Z 0
will include condition (5). This latter form therefore will provide us
in nearly all cases with a reliable criterion whether or not a point
of inflection occurs in the melting-point curve.

Physiology. — “On the epithelium of the surface of the stomach.”
By Dr. M. C. Drexnuyzen and Mr. P. Vermaat. Veterinary
surgeon. (Communicated by Prof. C. A. PEKELHARING).

We are accustomed to regard the stomach in the very first place as an
organ for the digestion of food, for the preparation of the gastric juice.
About its power of resorption its not so much is known. Glucose,
peptones, strychnin, alcohol, dissolved in or diluted with water, are
resorbed by the gastric mucous membrane. The rapidity of resorption is
different in various kinds of animals. The structure of the cells which

(ot)

line the mucous membrane seem to point to secretion of mucus
more particularly than to resorption. The fact is that their peripheral
portion readily undergoes a radical change, whereby it swells and
is expelled as a lump of gastric mucus. Unless the utmost speed
presides at the fixation of the gastric mucous membrane from an)
animal, the epithelium cells, which are still living but insufficiently
fed, undergo intense changes when coming in contact with the by
no means indifferent gastric juice. Until lately the epithelium cells
of the stomach were thought by many to be open mucus cells, a
kind of cylindrical goblet cells, because the above mentioned peripheral
part, the so called “Lump of BreperMann” ') had disappeared and
only the cell-walls, which were more resistant, were left.

Improved means of fixation and chiefly also the fact that histologists
have gradually been brought to see the necessity of a speedy fixation
of perfectly fresh material, have been the cause that at least the open
epithelium cell of the stomach has been acknowledged to be an artefact
and it has been generally adopted that those cells are closed at
their peripheral extremity by a smooth, convex boundary layer *).

Starting from the supposition that microscopical investigation might
bring to light something about the resorbing qualities, when the
perfectly fresh gastric mucous membrane, is treated very rapidly
with favorabie means of fixation, a few young mammals and also
older ones, which received milk along with their food, were killed
by a single stroke on the head and the stomach was extracted
without delay, turned inside out and immediately immersed into
FLemMine’s well-known mixture of */, pCt. chromic acid, 5 pCt.
acetic acid and ?*/, pCt. osmiumtetroxid. White rats and mice (full
grown), a rabbit of 3, one of 15 days and one rabbit of 24 days
nourished with milk, were taken for the experiments.

It now become evident that a comparatively small number of the
epithelium-cells of the surface of the stomach contained sma/l/ drops
of fat: at least fine globules, which were colored black with OsO,
and agreed perfectly in size and appearance with those, which were
visible in great numbers in the gastric contents, which had stuck
to the mucous membrane in different places of the section. The
surface of such gastric cells was not smooth either, but covered
with a differentiation which resembled the striated border of the
fatresorbing epithelium-cells of the intestine.

1) W. BieperManN. Sitzungsberichte der Wiener Ak d. d. Wiss. Mathem. naturw.
Klasse. 71 Bd. S. 377. 1875. ‘

2K. W. Ziumermany. Beilriige zur Kenntniss einiger Driisen und Epithelien.
Arch. f. mikrosk. Anatomie. Bd. 52. 1898. S$. 552.

( 32 )

In the rabbit and the mouse small differentiations of the mucous
membrane occur between the orifices of the pyleric glands as well
as between those of the fundus glands, to which no better name
could be given than that of villi of the stomach: slightly prominent,
blunt elevations, rich in blood-capillaries and supported by a meshwork
of connective adenoid tissue, but in which nothing of a central
chyle-vessel, nor of smooth muscle-fibres could be detected. They
were clothed with a single layer of cylindric epithelium, of which the
cells, situated on or in the neighbourhood of the upper part of such
a gastric villus carried outside of the above-mentioned boundary
layer of the modern histologists, an outer linb, which seemed to
consist of closely packed fibrils, probably cell-processes.

Each cell has its own apparatus; at the edges of the cells, where
the “Schlussleisten’” lie between the cells, the fibrils are wanting.
Tangential sections of the upper part of those epithelium-cells of the
stomach (sections of 1 mw were studied) showed finely speckled
pentagonal and hexagonal figures, separated by pretty wide furrows.
They were stained violet with diluted Rrspert’s phosphormolybdenous
hematein.

The length of these bundles of cell-filaments is rather different in
the various cells, but for one single cell pretty regular; they form
externally gently convex lines; each cell is, as it were lined with a
dome-shaped rather thick covering. There is not the least doubt that
we have of to deal with adhesive gastric contents. These le on
these dome-shaped elevations and are separated from it by a small
interstice, which was probably originally caused by shrinking during
the process (alcohol, carbondisulphide, paraffine, ete.)

The different “outer limbs” of the cells may be grouped between
two extremes: on the one side the extended cell-processes are seen
to diverge more or less, best to be compared to a short brush with
diverging hairs; on the other side we notice the pseudopodia drawn
in, settled like stiff little hairs on the cell ‘““‘membrane’’, and then such
an outer limb resembles the well-known striated border of the resorb-
ing epithelium-cells, or expressed in a more neutral expression: the
surface-epithelium of the intestine.

These epithelium-cells of the stomach with outer limbs now
show in the preparations a peculiarity at their base which has
been noticed and photographed by Carrer’), but the reality of
which has been doubted amongst others, by Von Epner in KOLLIKER’s
1) E. W. Caruier. On intercellular bridges in columnar epithelium. La Cellule, X1.
p. 263. 1896.

( 33 )

handbook’). Tangential cuttings of 1 a of the basal extremities of
the cells show us a picture, which agrees in high degree with
the intracellular little bridges which may be seen to diverge in thin
sections between the smooth musclecells (also in our preparations of
the gastric wall). In other words the aspect reminds one of that of
the riffeells in the rete malpighi. If it be taken for granted that all
this is preformed, then the opinion of Caruimr could be accepted that
the epithelium-cells of the surface of the stomach are conic with their
points turned towards the stroma of the cellular tissue, that they are
mutually connected through fine cell-filaments, between which an
extensive system of ducts to convey the juices might be supposed to
be present ‘“Saftkanalchen”. On good grounds however histologists
somewhat hesitate to accept the preformation of such structures.
They might be post-mortal strinking phenomena, or perhaps contrac-
tions during agony, or both.

However this may be, it is a fact that we have wot observed them
in the intestinal villi of the duodenum of the same animals; the
epitheliumeells there were cilindrical, they firmly closed together at
their basis and had a distinct low striated border. Never could these
two kinds of cells: the resorbing epitheliumeells of the stomach and
those of the duodentum be mistaken for one another; but they have
some resemblance. The differentiations : the outer limbs and the striated
border are probably nothing else but variations of one and the same
cellorgan, which we meet with to a large extent in the intestine of
invertebrate and vertebrate animals: a lining, which in the case of
Ascaris megalocephala, shows the most striking resemblance to a
ciliated lining, but in which we could wot notice the slightest motion,
though we worked under the most favorable circumstances and_ had
quite fresh animals, which moved about intensely. Also in man Zin-
MERMANN (1. ¢. fig. 37) has represented the striated border of the cells
of the colon, which bore cellprocesses strikingly resembling cilia, but not
considered by him as such either. We are of opinion that the intestinal
cells and at least some cells of the surface of the stomach, possess
the power to send out a great number of cell-filaments, which stand
closely together when the striated border is contracted and when
the cellfilaments have their minimumleneth, but which can also be
extended and are then enabled to diverge. The different heights of the
striated border may also be seen in intestinal epithelium cells.

The outer limbs of the epithelium-cells of the stomach are
evidently vulnerable differentiations. In some parts of our preparations

1) A. Koétuker’s Handbuch der Gewebelehre des Menschen. Ge Aufl. IIL 1. S, 155,
3
Proceedings Royal Acad. Amsterdam. Vol. VI.

( 34 )

some of them have been couverted into a homogenous hyaline mass,
with distinet inward and outward boundary. Not that the external
portions had become hyaline bub/es, their shape seemed little changed,
but they were in a way ‘‘verquollen” as the German histologists say.

We must refrain from expressing an opinion whether these outer
limbs are present in all epitheliumeells or not. It is quite possible that
they are much more widely spread than we suspect and that they are
frequently destroyed by imperfect fixation. Manipulating correctly and
applying the same methods, we were not successful in obtaining a
view of them on the surface of the stomach of a small suckling cat.

In studying the literature of the subject, we have found out that
at the early date of 1856 a man of KO6LLIKER’s importance has seen
globules of fat in the epitheltumeells of fresh gastric mucous mem-
branes of young cats, dogs and mice. K6LLIKER Communicated on the
28th of June 1856 to the Wiirzburyer physihalisch-medicinische Gesell-
schaft (VIL p. 175) in a small paper entitled: “Kinige Bemerkungen
iiber die Resorption des Fettes im Darme, iiber das Vorkommen einer
physiologischen Fettleber bei jungen Séaugethieren und iiber die
Function der Milz” that in his opinion he had seen globules of fat
and also rather distinct indications of pores. With these pores he
meant the openings in the “Porenmembran”, the sieve-shaped, pierced,
thickened wall of the cell, which we now call “striated border.”

As far as we know no attention has been paid to this communi-
cation of KOniikER’s, except by OGxrew (Biologischer Centralblatt XII,
S. 689, 1892) who has also seen the structures of Cartmr. To our
mind it is indisputable that thestomach can resorb fat from the
food, although it be in small quantities and it is also probable that
this excellent naturalist has been able to discern with simple means,
What cannot, with the methods of the present time, be effected without
difficulty: namely to point out the striated border-shaped outer limbs

of the stomach cells.

Physiology. — “On the liberation of trypsin from trypsin-zymogen.”
By Dr. E. Hekma. (Communicated by Prof H. J. HampureEr),

1. On the influence of acids on the liberation of trypsin From trypsinogen.

As is well-known, trypsin, the proteolytic digestive ferment of the
pancreas, does not appear as such in this gland, but in the form of
an inactive precedent stage, which Hrmrnnain, to whom we owe this
discovery ') has named ‘zymogen’:

1) R. Hemennais, Beitriige zur Kenntniss des Pankreas. Penigers Archiv 1875,

pag. 5d7,

( 35 )

As besides trypsin, other enzymes have come to our knowledge
which are also secreted when in a preliminary stage, it is preferable,
as is frequenily done now, not to speak here of “zymogen”, but of
“trypsinogen” or “protrypsin”’.

From the very beginning the question arises whether the liberation
of the ferment takes place in the gland or in the intestine. Accor-
ding to researches made by Canes and Gury ') and Denuzennn *), the
latter is usually the case; according to Poprmeiskt*) always.

Then the second question arises: In what way does the lheration
in the intestine take place =
Until a few years ago this liberating action was solely ascribed to
the acid of the gastric juice.

Influenced by researches made in Pawtow’s laboratory, attention
has of late been drawn to the intestinal juice *).

As there appeared to be two ways that might effect the liberation
of trypsin, it was important to know, what relative value could
be ascribed io each of them. I have therefore made the action of
acids, amongst others also of hydrochloric acid, a subject of close
investigation.

Tracing the communications in literature in respect to the influence
of acids on the liberation of trypsin, one is always being directed to
the publication of R. Hetrnxnaiy, just mentioned. When we examine
these writings we find that scarcely a page has been dedicated to this
problem. Only the method, by means of which Hrmernnaty has
obtained the result, is shortly referred to, positive experiments are not
described however. He only mentions, that, when he had arrived at
the end of lus tmvestigations, he sound that glycerine-extracts from
pancreassubstance operate much more effectively when the gland-
substance is med with acetic acid, before glycerine ts added; an
observation which never failed in any of the cases when he applied
this method.

When a man like Hemennars publishes his observations, we have
to take them into account, even although the experiments are not
published along with them. In different text- and handbooks and
monographs, we find related that acids possess the power to effect

1) Camus and Grey; Detezenne. C. R. Soc. de biol. LIV. (1902).
2) L. Popretski, Ueber die Grundeigenschaften des Pankreassaftes. Centralbl. fiir
Physiol. 9 Mai 1903.
3) N. P. Scuerowatnixow, Diss. Petersburg 1899; Pawtow, Das Experiment.
Wiesbaden 1900, p. 15; Watruer, Archives Ital. de Biol. 1901.
H. J. Haweurcer and I. Hexma, “On intestinal juice of man.” Report Royal
.Academy of Sciences 1902, p. 713.

( 36 )

the transformation of trypsinogen into trypsin, resp. of promoting it *).

I have been perfectly able to confirm HeiweNnat’s investigations, but
systematic researches have shown Ie, that they are only available for
glycerine-extracts from the gland, but in no wise for watery extracts
or for the pressed out juice of the pancreas.

From the great number of experiments which I have made to this
end, and which always led to the same results, I shall state here a
single series.

First a repetition of HripeNnatn’s experiment. The method which
Hmennain indicates is as follows:

To every gram of pancreassubstance, which has been cut into
small pieces and subjected to pressure, is added 1 c¢.c. acetic acid of
I’. The mass is again rubbed for 10 minutes, and the thus obtained
compound then mixed with 10 grams of glycerine. After 3 days this
compound is filtered. | now composed a glycerine-extract according
fo this prescription and, along with this, other glycerine-extracts
whereby instead of 1 cc. acetic acid of 1°/,, L took respectively 1 ¢.c.

acetic acid of 2'/, °/;, 1 ee-acetic acid of 0.5°/, and ec. water

The hereby obtained extracts | allowed to act on white of egg
without water (Col. I1) and also after addition of water (Column IID) ”).

It is seen that where the glycerin-extracts of Col. I are brought
fo act on white of ege no digestion appears after 3 days (Col. ID).
This had to be expected. Even if trypsin had been set free, it could
not have worked actively in the pure glycerine; for it is well-known
that trypsin is not soluble in pure glycerine. Trypsin is liberated
however when the glycerine-extracts are diluted with water (Col. IM)
and more so with those extracts which are composed with acetic
acid (1, 2, 3) than in those rehere ordinary water was used 4). The
acetic acid therefore furthers the liberation of the trypsin in elycerin-
mixtures with water. A proportion between the concentration of
the acetic acid and the extent of its operative power, does not exist
however.

It could now be suggested that the trypsin from Col. IIL in Table T,
which was at first inactive being in an indissoluble condition, now

') f only mention here: Hamaansrex, Lehrbuch der physiol. Chemie, 1899. 4er
Druck, pag. 295.
A. GaAmere, (Deutsche Ausgabe von Asner und Beyer), Die Physiol. Chemie
der Verdauung. 1897, pag. 231.
CG. Orrenieimer, Die Fermente und ihre Wirkungen, 1900. p. 74 and 116.
*) Por the quantitative determination of the proteolytic digestion the method of
Merr was followed. The experiments were only made with pig’s pancreas. The
temperature ot the incubitor varied from 37 to 39° C.

TABLE I.
[. Jie HT.

Millimeters of Millimeters of white of ege
consumed after addition of
3 ce. water on 1 cc. extract,
consumed, after the first 3 days,

| white of ege

After 3 days, | After the following 3 days.

|
|

1). Pancreas substance 1 gram
| 50 - 4.70 |
18.

70 + 4.80)

Acetic acid of 19/, 1 c.c. 3ee. 0 70

Glycerin 10 ce.

4 AN) + 4.60

2). Pancreas substance 1 a)
Acetic acid of 21/,°/,4 c.c. i 0 18.30

4.70 + 4.60

Glycerin 10 c.c.

3). Pancreas substance 1 gram
| 4,80 +- 5

300 0 19.70

.90 ++ |

Acetic acid of 0.5/) 4 c.c.

PSS
(by |

Glycerin 10 c.c.

4), Pancreas substance 1 gram

2.10 + 2.80

2.20 -+- 2.80

Water 1Nec: 3ce

Glycerin 1OnG.c:

became active because of the addition of water. Table IT shows
however that in the original eglycerin-extract, not diluted with water,
no trypsin whatever was present.

In the experiments mentioned in Table II, a Na,CO, sol. of 1.2°/,
has namely been added to the glycerin-extracts. If indeed trypsin
had been set free, we might here have expected digestion of white
of ege. The trypsin operates very effectively in presence of Na, CO,
of 1.2°/,, whereas the latter entirely prevents the transformation of
trypsinogen into trypsin; a fact, already proved by Hrmrxnain and
which I have taken advantage of in all my experiments to prove,
whether in certain cases I had to deal with material containing
trypsin or trypsinogen.

From these figures we notice that 1 ec. acetic acid in concen-
trations of resp. 1, 2'/, and 0.5°/, has not the power, just like I ce.
water, to liberate trypsin from 1 gram of pancreas substance in the

(39)

TABLE IL.

NN ————————————— ee

| . . .
Millimeters of white
of ege consumed.

}
}
}

After 3days AfterGdavs
!

EN Ee ee EE
1). Pancreas substance 1 gram }

Acetic acid of 1%, 1 ce. 7 3ee.-+-12ce.Na,CO, opl. v 4 2), | 0 | 0
Glycerin 10 ce. | | |
|
2). Pancreas substance 1 gram
Acetic acid of 2'/,% 41 ee. 7 3ee,4-12ce. Nay CO, opl. Saar 0 | 0
Glycerin 10 ce, | |
oe
3). Pancreas substance 1 gram |
Acetic acid of 0.541 ce. (3ec.+42cc. Nag CO, opl. v.1.2%p | 0 | 0
Glycerin 40 -cc. | |
4). Pancreas substance 4 gram | |
Water 1 ce. }Sec.-+-42ce,Na,CO,opl. v4.24; 0 | 0
Glycerin 10 ce. | |

time (mentioned by Hermennar), during which these liquids had
come into contact with the pancreas substance, before glycerin was
added’) It is however possible, as has been proved from Table I,
io liberate trypsin Jrom the glycerin-ectracts by iIneans of water,
after having been brought into contact with it for a lengthened
period and this process is aided by acetic acid being present. But
the action of acetic acid is only of indirect nature, 7 on/y seems
to neutralize im some degree the unfavourable action which glycerin
vverts on the liberation of trypsin.

Then | thoueht, if this be the case, the favorable action of the
acetic acid must fail to be effective in watery extracts and pressed
out juice of the pancreas. This proved to be true, as table IIL and
IV will show.

1) Tt should be observed that 1 ee, acetic acid, resp. water and 1 gram pan-
greas substance only vive the relative proportions. In reality 5 ee. liquid on
5 grams pancreas substance was always taken and of course 50 cc. glycerin.

Se eee Pe ek Fae

wert | de

( 39 )

TABLE II.

Ol & &

| | | j
| _ Directly. After 18 hours. After 40 hours.
/ |

Fresh Pane. juice. | Ry ee
‘Reaction Reaction

Te . Reaction a :
ie ae | : Millimeters of |"e2¢ton Millimeters of
wo drops. litmus- | litmus- white of ege | litmus- white of egg
| | > : 7 ns © - "
| | paper. | paper. | consumed, paper consumed,
- - ee ee
|
fresh P.juice +See. acetic acid2!/5"\y acid acid 0 acid 0
} / |
» +5 Ces » 1 dF | » 5) ' 0 ) ()
| | | |
» +See. » 0.5 5/4 | »y | » 0 » 0
} |
» +5 ce. » 04 %, } >» | » 0 » 0
| }
< = : 1.404
» +5 Che » 0.05%, » ! ) 0 weak ae. | Tae ay 40
j H ;
o 1. 40-130).
» Dee, water neutral neutral | 0 weak alk!) ° eae
bh eak Ik. 4 90-441.30)° J
| |
} | } ’
© = ve ; ~ | 5 , DA) A0 -
D +5 ee, Na,CO* sol 0.1%) | alkaline alkaline | 0 alkaline 904 ye. 60
sag sie,
; |
|
= + | | O.10+0O.: 2
> hee. » 0.5°/. » » 0 » : 10), ).90
! fe O+0 )
{ . | |
» +5ee, ») | 0 0 » » 0 ) 0)
» 5 GE. » J sah fi ) ) 0 | » | 0
' ~_ | - j
D +5ee. > » A » cae | 0 > | 0
» +5ee. » 3 Wee » » | 0 » 0
| » + See. Extract from the or 4
) SO years 41-440), 2
1.9041 80). 4 i+-4.1 610

i Sting ycosa | p ie FeaAK ALK | rentcoalls
intestinal mucosa ) ne utral weakalk, LSt-L.so)” 1) wealkalk. Aik)

Table HI shows us, that when a few drops of fresh, pressed out
pancreas juice, which according to fig. 9, 10, 11 and 12 contained
no trypsin, are mixed with acetic acid of 2'/,, 1, 0.5 and 0.1 °/,,
there is no digestion of white of egg. But when the acetic acid is
used more diluted, viz. 0.05, then afier a long time, formation of
trypsin takes place, but not to a greater extent than when water
is taken instead of acetic acid.

It could now be supposed that the trypsin would, under the
influence of the acetic acid be liberated, but could not operate actively
in the present acid reaction. Table TV shows that this is partly the
ease. For when an old panereas is taken, in which according to 9,

1) Extract from the intestinal mucosa may be used for the liberation of trypsin
instead of the natural intestinal juice, In a following communication we expect
to treat this subject more fully.

( 40 )

TABLE IV.

eee

Juice of a pancreas which has been ex-| |

: - | : |
posed for 24 hours to room-temperature. Reaction Reaction yrijjimeters of Re action) vriimeters of

‘Directly. After 18 hours. After 40 hours.

: , litmus- | litmus-| white of egg litmus-' white of egg
wo drops. paper. -heinapers| consumed. | paper. | consumed.
1 | old P juice +5 ce.aceticacid2!/,%y | acid acid 0 acid 0
2 ) oa D ee. ) 4 J 0 | ) | » 1) | » O
3 ) + 5ce. » 05 47 ) oP 0 | » 0
g f | 1.30-H1.30) - me 33 eas
4 » + eC. » O:14257- » | » rae ny 5.40 » ae ' 12
|
= = 1.701-1.70) pon | _, dAO+3.30) yo of
5 » + dce. » 0.05°/, » | » 170-4-1.70 6.80 weak UC. 5 99 19 Of) 13.20
. ) | 0+3 20)
9+-9 10) - 3.70-+-3 70) ,-
6 » + water neutral weakalk. aL 80} 7.90 weakalk. = 4013.80) 15
| | } 5 i | . | 90-L3 /
7} > f5.ee, NasCo,sol.04"% |alkaline | alkaline heey 6.20 alkaline 324 3.00) 12.40
|
} if 5 et fi e lp A 9 (
eee fe ieee eel ee pee eee Rh oe ee 3799 11.20
| Par ig ae |
| 14.2041 .30) - 2.604-2.7 7
9; » Fcc, aap aT ep tale 304-4:30) 210 » 60970) 10:60
| | ] |
z = | '4.90-+1.30) - 2.4042.40
10 » -+ aw iGGe » 1.5 Thy » » 4 301 30) Dd.10 » S019 60} 9.90
| | 4130-4. 2 2
| | | | }
( c ‘4 ¢ 9
| | | » +- ny CC. » BU oh » } » rag 5 3.80 | » 3011.70) 7.40
|
es 4 050-+40.50) . | 4+4.90),.
42 | AF See BS | Ss hye ape ae Hea eae 1101.99 450
| Ip 4 Or 4.4 hs
13 » + 5ee. Extract fromthe neutral weakalk. a 2-69) 10.10 weak alk. i 9044903 17.10
intestinal mucosa hee ) le =a

10, 11 and 12 free trypsin is found and according to Table TI,
acetic acid has been added of 2'/,, 1 and 0.5 ,/°, there is no action
whatever. The acid in these concentrations prevents the trypsin from
acting. When however acetic acid of 0.1 °/, is used, then the action
of the trypsin is not neutralized as is shown in Table 4, fig. 4.
Therefore in fig. 4, Table II, the Mheration of trypsin must have been
precented hy acetic acid of Ne Rea

Moreover Table If teaches us that in no single case digestion of
white of ege was obtained with fresh panereasjuice after 18 hours,
except in fig. 15.

Hereby is clearly shown that water and acetic acid of 0.05 °/, are

(41 }

far behind intestinal mucosa, resp. intestinal juice, with regard to
their influence of liberating trypsin from = trypsinogen.

Equal results as with acetic acid were obtained with hydrochloric
acid, lactic acid and butyric acid. For hydrochloric acid this may
appear from the following summary.

TABLE V.

| Atter having been
allowed to st ind for
41 hours in the ineu-

Millimeters of white of ege |bator, so much of
| \Na,C 0, soleus aiael
Fresh pancreasjuice, two drops. consumed. ito 6 and 7, until the

‘proportion of the Na,

| CO, amounted to

about 4 %/o.

) Digest. of white ege
After 17 hours. , After 41 hours. \after once more 2X24

hours in 6 and 7.

1.80-41.70 ¢-

!
1) panereasjuice+- 3 ce. water | 0 LL70-441.90 | 7.10
2) » + 3 ce. Na, CO, opl. 1°. | 0
sec. extr, from the in-) 4.60-+1.50
2, “ i testinal mucosa. | 1.50-4-1.50 | 1640, — A+. tai0} —
4 1.70-+-1.80 jp
4) » +3 ec. HCl 0.02", %o. | 0 | 170-4770 ey
> ‘ a Wink | 1.704-1.60 j ¢ -
5) ; 4.3 ec, HCL0.05 %o. 0 | (6014 60 (6.50
6) » + 3c. HCLOM %. 0 0 0
7) » + 3 ee. HCI 0.5 "/. LH) | 0 0)

These figures show that hydrochloric acid in exfremely weak con-
centrations (0.02"/, and 0.05 °/,) does not hinder the trypsin from
being set free. The effect is not favourable however. Somewhat
stronger concentrations of hydrochloric acid (0.1 °/,, 0.5 °/,) prevent
the liberation of trypsin entirely. That no trypsin has been set free
in 6 and 7, the action of which may have been prevented by the
hydrochloric acid, has been proved from the fact that no digestion
of white of egg had occurred, even after 2 24 hours, when after
41 hours a solution of Na, CO, had been added to the liquids named
in 6 and 7, until the proportion of Na, CO, amounted to cirea 1 °

From these researches we may with certainty draw the following
conclusions.

1) Hemeynaty’s opinion, which has been current since 1875 and

( 42)

widely accepted, as if acids could have the power. of liberating
trypsin from trypsinogen is not correct; on the contrary, they prevent
this liberation.

2) That Hemennais came to this conclusion must be ascribed to
the accidental occurrence, that instead of using the pressed out juice
or watery extracts of the pancreas, he had taken glycerin-extracts
from the gland. The favorable action caused by the presence of
acetic acid in his experiments and which I have been able to confirm,
is to be aseribed to the fact that acetic acid decreases the injurious
action of the glycerin on the liberation.

3) As it has now been proved that the gastric juice does in no
wise further the liberation of trypsin, but rather opposes it, we may
therefore draw the conclusion, that in this process of liberation all
the work falls to the intestinal juice; a Jact stil LCreASINY in tin-
portance where — the vestigations of Popietski have proved, that no
Sree trypsin whatever (Lppears in the pancreassecrela, hut that it is
only there in the shape of trypsinogen.

Having arrived at the end of my communication, I beg Prof.
Hampercer to accept my warm thanks for the opportunity afforded
to me to make these researches and also for the useful hints kindly
given to me.

Physiological laboratory of the State University at

Gronimgen. May 1903.

Physics. — “Some remarks on the reversibility of molecular motions.”
By Dr. A. Paxxekork. (Communicated by Prof. H. A. Lorentz).

1. The following considerations deal chiefly with the question
Whether a mechanical explanation of nature is possible. Mechanics
treat the motion of diserete particles or of Continuous masses; now
the question may be raised, whether all natural phenomena can be
explained by means of such a motion. In other words, it is the
question, Whether or no we know particular properties of these pheno-
mena, Which exclude the possibility of a mechanical explanation of
general application. A particular property which seems to do so, is
the irreversibility of the natural phenomena, the change ina definite
direction. When investiguling whether this is really the case, we need
only consider the simplest form in) which the irreversibility of natural
phenomena occurs: the second law of the mechanical theory of heat.

( 43° )j

Porxcar¥é says about this in his “Thermodynamique”, that it entirely
excludes the possibility of a mechanical explanation of the universe.

The motions of which mechanics treat, are all reversible: there
occur only forces which depend on place, so relations between the
Ot and the 2"¢ derivative according to time; if the sign of / is reversed.
these equations retain their validity. It is true that in mechanics
also cases are treated in which the first derivative according to /
occurs in the equations (friction); we are, however, justified in calling
these cases not purely mechanic, because in them heat is produced,
so that in a complete explanation we must introduce considerations
(thermodynamic ones), which we are just trying to solve in purely
mechanic ones. It is therefore desirable to call only those cases
purely mechanic which are reversible; these only are conservative.
In the above-mentioned not purely mechanic cases there is dissipation
of energy, so that, the law for the conservation of energy being a
general law of nature, a mechanical description of them is not ecom-
plete. The kinetic theory of gases shows us that this description only
mentions the visible motions im the system, but not the molecular
motion, which is required to make the description compléte. The
word mechanic, occurring in the question raised in the beginning
must therefore be interpreted in such a way that we consider only
cases of conservative systems as purely mechanic.

The question whether the irreversibility of the natural phenomena
decisively excludes a mechanical explanation, must be answered in the
negative, when we succeed in giving a mechanical description of one
typical and simple irreversible process, or in other words, if we ean
point out in a certain case that a process consisting of purely
mechanic, so reversible motions, is irreversible. We rust then at the
same time get an insight into the question, how it is in general
possible, that a process in its general character can be so different
from that of the partial processes of which it consists.

2. BowrzMaxn has shown that we meet with such a case, though
an abstract one, when we have a perfect gas, consisting of perfectly
elastic spheres, between which no other forces aet than those even-
tuating in collisions between two particles. He proved that the fune-
tion H=Sf flog fide, in which fd is the number of the molecules
whose points of velocity lie in the volume element (/w of the velocity
diagram *), can only be made smaller, never greater by the collisions.

}) The “velocity diagram” is obtained by representing the velocity of every
molecule by a vector drawn from a fixed point. This vector ends in the “point of
velocity” of this molecule.

( 44 )

As this function taken with the reversed sign, expresses at the same
time the logarithm of the “probability” of a certain distribution of
the velocities, BottzMaNN expresses his result also under the following
form: the effect of the collisions is that a gas always gets from a
more improbable to a more probable condition.

Here we have therefore a process, consisting of purely mechanic
partial processes, which shows change in one direction only. That
however Bo.rzMaNy’s considerations have not yet led to a perfectly
satisfactory insight, and that this contrast is felt as a contradiction,
is proved by the objections and doubts, which have been adduced
against these considerations without refuting them. Let us assume
a fictitious system in which at the moment ¢, all the places are the same,
but all the velocities exactly the opposite of those of the real system.
The two systems can represent a gas in exactly the same way, there
being no possibility of seeing which is the real and which the ficti-
tious one. Yet the fictitious one will successively pass through all
the conditions through which the natural one has passed before the
time ¢,, in reverse order; all the collisions take place in opposite
direction, and the system gets from a “more probable” to a ‘more
improbable” condition.

BoLTZMANN denies that this involves a contradiction, for the fictitious
system is “molecular-geordnet’. That this remark does not solve the
difficulty (BrinLoury, among others, expressed doubts as to this in a
note in the French translation of Bonrzmann’s Vorlesungen) must
be ascribed to the fact, that the ideas ‘ordened” and ‘‘unordened”
for molecular motions are difficult to define sharply. Sometimes ordened
is interpreted as if if meant that in the fictitious system to every
molecule its future course is accurately prescribed. This however is
hot satisfactory. If we know at the moment ¢, the places and velo-
cities of the natural system, we are enabled to determine beforehand,
so to prescribe, the future course for the natural and for the fictitious
system and for both in exactly the same way.

The fact that the motions in the fictitious system are ordened
can be better pointed out by means of the following consideration.
If we take two groups of molecules with the points of velocity 7, and
P', which come into collision, then after the collision the points of
velocity Q, and Q)', R, and &,' ete., will all lie on a sphere of

which the line P,P,' is a diameter. The places of Q, 2, ....on the
sphere depend on the direction of the planes of coilision A Bove

to every plane of collision belongs a definite place of the points of
velocity and the latter are seattered all over the sphere, because the
former have all kinds of directions. If we now take the reversed,

( 45 )

fictitious system, all these points of velocity come back in P,P,
because definite planes of collision uf, .... belong to every pair of
points of velocity Q,Q,'.... The fictitious system, therefore, is sub-
jected to the condition, that molecules with definite points of velocity
do not collide according to arbitrarily chosen planes or to planes
whose direction is determined by chance, but according to planes
which are entirely determined by the position of these points of velo-
city. This condition may be called an ordening of the motions.

We must, however, add another remark. In the natural system
we had not only points of velocity in 7,7’, but also at the ends
of the other diameters of the sphere P?,7P,', 2,7,’ .... ete. and these
too can reach the same points Q,Q,' as P,P,', if only the planes of
collision have every time the required direction different from A.
Of all the points of velocity and planes of collision we have just
now chosen and considered separately all those which in the natural
system lie before, in the fictitious system after the collisions in ?, 7,’
We might, however, just as well have chosen and considered separately
those which in the natural system lie after, in the fictitious system
before the collision in Q,Q,'; in this case we might have been inclined,
to call the fictitious system unordened, and the natural system ordened.
The difference between the two would of course become clear, when
we paid attention to the number of collisions which cause the points
of velocity to pass from P,P,’ to Q,Q,', R,R,' etc. or vice versa.
In reality the collisions in the natural system have a scattering effect,
through which the distribution of the points of velocity over the sphere
is more regular and arbitrary after impact than before. In this respect
there is a real difference between the natural and the fictitious system,
that in the former the distribution before the collision is more irre-
gular, less accidental. The difference between being ordened and
unordened in the molecular motions in the two systems appears here
as a difference in the degree of the ordening.

It seems to me that though we cannot bring forward conclusive
objections against the denomination used by Bo.rzmany, yet further
considerations which throw some light on these phenomena, might
be of some value.

3. The ordening of the motions, in which the difference between
the natural and the fictitious system consists, can only be clear,
when, as in the kinetic theory of gases, we examine larger masses
and mean values, in which the coordinates and velocities are considered
as fluently varying quantities. When we take the particles separately,
in which the coordinates and velocities are perfectly defined, the

( 46 )

difference between a natural and a fictitious system does not appear,
and the process can only be taken as perfectly reversible.

The result of each of the steps of which the whole process is
built up (free path + collision), is determined 1st by the coordinates
and velocities, 2°¢ by the direction of the normal to the collision
plane. In the statistical method of treatment of the kinetic theory
of gases the latter is considered as an independent datum, which
therefore is thought to be defined by chance; we may then give if
different values, which are distributed according to chance, i. e.
regularly, and in this way the seattering, regulating effect of the
collisions appears, which is the cause of the irreversibility of the
process. In the purely mechanic conception, in which we must take
the condition of every separate particle as rigorously defined, the
direction of the normal is no independent datum; in reality this
direction is accurately defined by the coordinates and the velocities
of the colliding particles. Here the result is therefore determined
by the coordinates and the velocities only and according to this way
of considering the question, the process must be considered to be
reversible.

The question how it is possible that a process may be considered
in two ways, so totally different comes therefore to the same as the
question, how quantities which in reality are rigorously determined
by other quantities, may yet be considered to be independent and
determined by chance.

We shall find the answer to this question in the fact, that very
small variations in the coordinates and velocities bring about consider-
able variations in the direction of the normal. If we determine the
directions by means of the points in which they cut a spherical
surface described with a radius equal to the mean free path, the
velocities being measured by the path covered in the mean time
interval between two collisions, and if we call the ratio between the
radius of a molecule and the mean free path a small quantity of
the first order, then we may formulate this proposition more pre-
cisely as follows: variations of a given order of smallness in the
coordinates and the velocities bring about variations in the direction of
the normal which are of one order lower; variations in the direction
of the normal give rise to variations of the same order in the coor-
dinates and the velocities after impact.

If we aseribe to the coordinates and the velocities of two colliding
molecules values iy yy 2, ly Yo 25 My Vy IP, My Vy we, Which are rigorously
determined, then the direction of the normal 2p is also rigorously

determined. Tf however we mean by these 12 data that these quantities

( 47 )

lie between z, and r, + dx, ete.... w, and w, + dw,, i.e. that the
condition is included in a twelve-dimensional volume element or
the jirst order, then 4, w and vy are left undefined. This way of
proceeding is that of the kinetic theory of gases in which we are
therefore justified in considering the normal to the tangent plane of
two colliding molecules to be determined by chance.

If we wish to know this direction accurate to the first order.
then the 12 coordinates and velocities must be known to the second
order. If within this volume element we determine the place by
means of new coordinates .r,'y,'2,'... 0.) u.', (we might call them
coordinates of the 2"¢ ¢lass) which vary within that element over
a finite region, e.g. from 0 to 1, then the direction 4 ur is a funetion
of these coordinates of the second class, and they determine the 12
coordinates and velocities after impact also to the first order.

Every collision brings about a lowering of the order of determination
of the coordinates and the velocities ; every collision causes a scattering
by which the condition of the system becomes one order less
determined. In order to know the condition (the coordinates and the
velocities) after 7 collisions (at least accurate to quantities of the
first order) we must know the initial values of the coordinates and
the velocities accurate to the (+ 1)" order. The longer the period
is for which we want to predict the motion, the higher is the order
which is required for our knowledge at this instant. The limit is here
the pure mechanic conception, according to which the state is determined
for ever, because the data are determined with absolute accuracy.

BoLTzMANN’s observation, that a system, whose motion is reversed
really proceeds from a more probable condition to a less probable one,
namely to that from which the natural system started, and that
afterwards conditions are reached, which show again an increasing
probability, includes the assumption, that in the initial state the
coordinates and the velocities were determined to the (2, + 1)™ order,
so that the reverse motion brings the system after n collisions back
to the initial volume element of the first order; afterwards the
direction of the normal is no longer determined, and the further
process must be investigated according to the rules of the calculus
of probabilities. The condition whose validity is required for the proof
of the H-theorem, is not satisfied during the whole backward course
of the process; if is here therefore impossible to decide anything as
to the decrease or increase of H. As soon as the initial state is again
reached the direction of the normal cerses to be determined, and
the required condition is satisfied. From the further course we may
therefore predict with certaimty, that /7 must decrease.

( 48 )

The observation may here be inserted, that we speak of chance
in nature, when small variations in the initial data occasion considerable
variations in the final elements, because we cannot observe those small
variations. Cyclic motions for instance will also always give rise to
such cases.

For the special case considered here the result we have found
may be formulated as follows: when in a purely mechanic, reversible
process which occurs a great many times in the same way, events
oecur in which small variations in the initial data occasion considerable
variations in the final state, then the total process gets the properties

of an irreversible process.

Botany. — “On a Sclerotinia hitherto unknown and injurious to the
cultivation of tobacco.” (Sclerotinia Nicotianae Ovp. et Koning).
(By Prof. €. A. J. A. Ovupemans and Mr. C.J. Konine).

The following communication contains five paragraphs.

4. IT gives an account of a visit to the tobaccofields in the
Veluwe and Betuwe, in the autumn of 1902, about the time that
the tobaccoleaves begin to be gathered.

Par. IT contains an investigation of the disease which had attacked
the plants, evidently a fungus, which had long been known as
“Rot?, but the nature of which had not yet been cleared up.

Par. IT gives a summary of the experiments made with the
Selerotia of the fungus.

Par. TV deals with the anatomy of the Sclerotia and the Selero-
fia produced from them.

Par. V contains the result of some biochemical investigations.

“ur. VI gives a few hints, the application of which may prevent
or reduce the damage caused by Selerotinia Nicotianae.

l. A VISIT TO THE TOBACCOFIELDS.

In order to study more closely the origin of the well-known
patches and specks on dried tobaccoleaves, one of us repeatedly visited
the tobaccofields in the Veluwe and Betuwe in September 1902.
These visits repaid the trouble very well indeed, as they gave an
opportunity of becoming acquainted with an evil which caused
much damage, had not yet been clearly defined and so deserved a
closer study.

In these visits one was first of all struck by the fact that the very
extensive fields under cultivation were divided into smaller square

( 49 )

plots by beanhedges and that these hedges consisted partly of scarlet:
runners (Phaseolus coccineus = Ph. multijlorus) and partly of “curved-
beak” (a variety of French beans Phaseolus vulgaris Savi’).

On account of their height these plants were considered effective
as windscreens. Tobacco leaves namely, by their large surface as
well as by their tender structure, cannot very well stand air-currents,
which is proved by the fact that the scouring or rubbing of two
leaves against each other by the wind, may cause discoloured spots,
bruising of the tissues and even loss of substance.

Though the method of protecting the tobaccoplant against wind
had evidently been weil chosen, yet the growers themselves had
noticed that if was wrong to use two different kinds of Phaseolus,
because diseased tobaccoplants are much more frequent within hedges
of scarlet-runners than of French beans. Experts are certainly right
in their opinion that the reason of this is that scarlet-runners retain
their leaves much longer than French beans. The latter begin to
lose their leaves already in September and October, when the season
can already be rather damp, whereas the scarlet-runners show no
sign of it yet then. Hence the soaked soil as well as the damp plants
can much better be dried by the wind within the hedges of French
beans than of scarlet-runners. Accordingly. the ‘rot” is in damp years
always much stronger inside the leafed than inside the leafless hedges.

Another drawback of scarlet-runners is that their flower-clusters
have not yet fallen off in September and October, so that, after
having died, they not unfrequently drop down on the tabaccoplants
and soaked through, remain hanging in the axils and in other places,
where like wet sponges they foster the germination of conidia or spores.

In a visit to the tabaccofields of Mr. N. van Os at Amerongen
on Sept. 27, 1902, many plants were found suffering from “rot’’.
As such the growers considered specimens with limp, slippery leaves
and with stems having discoloured stains. This was supported by
the experience that such leaves and stems possess very infectious
properties and that a single diseased leaf, carried to the drying-shed
under a big heap on a wheelbarrow, can in one night easily infect
some fifty others. Any precise idea of the agent here at work, was
not found however among the experts, so that the only means of

1) The tobacco-growers themselves informed us that hedges of beans, especially
of scarlet-runners and ‘“curved-beaks’” as windscreens, have been in use on
tobacco fields as far back as can be remembered. In accordance with this they
are mentioned by the late Prof. van Hatt on page 60 and 61 of his ‘Landhuis-
houdkundige Flora” dating from 1855.

Proceedings Royal Acad. Amsterdam. Vol. VI.

( 50 )

arriving at a scientific result was to take parts of sick plants to the
laboratory and to study them there.

Meanwhile a continued walk through the tobaccofields had revealed
that this was a case not of a bacterial disease as had originally been
supposed but of a sclerotial disease, since in various places in a
greater or less degree spots were found on leaves and stems consisting
of a white down and besides greater or smaller black grains, embedded
in or lying on that down, so that on account of other observations
made elsewhere, it seemed probable that these black organisms under
favourable conditions might produce an ascigerous generation, from
the morphological properties of which the place of the fungus in the
system and its identity or difference with other known species might
be inferred.

The richest crop of material for experiments was gathered in the
dampest places, i.e. in the corners of hedges of scarlet-runners, while
on the other hand in the vicinity of French beans often not a single
grain was to be found. Where flowers or flower-clusters of scarlet-
runners were held fast in the axils of tobaccoleaves, sclerotia were
rarely sought in vain. It can be understood that the uninitiated —
growers and working-men — imagined that the source of the evil
had entirely to be sought in the blossoms of the scarlet-runners.

Il. INVESTIGATION OF THE DISEASE WHICH HAD ATTACKED THE PLANTS.

On various days of September 1902 sick parts of stems and leaves
were taken home from the tobaccofields as well as from the drying
sheds. In doing so each leaf and each stem were separately put into
a sterilised tube and in the laboratory placed into a sterilised glass-
box over wet filtering paper.

At a temperature of 22° C. a distinet change could already be
observed in all the objects after 24 hours. They had developed a
flimsy, transparent, much-branched mycelium. At a lower temperature
the same phenomenon had occurred though less vigorously.

After 3>< 24 hours small bits of the obtained net of threads were
with the necessary precautions placed on malt-gelatine and kept at
22°. Already after 24 hours these bits had grown much and it was
possible after another 24 hours to take away new bits from the
margin of the circular cultures which had now grown to a diameter
of 3,5 centimeters and to inoculate them on freshly prepared malt-
gelatine. In this way a sufficient quantity of pure cultures were
obtained in a relatively short time.

As healthy tobacco-plants were largely at our disposal, it was

( 54 )

possible to carry the downy substance on them and to place the
oO es

infected parts of leaves and stems in damp glass-boxes at 2:
Again a beginning growth was noticeable after 24 hours.

The pure cultures on the malt-gelatine plates became more and
more extensive, forming circles which after three days had diameters
of 8, after four days of 13 centimeters.

By and by the malt-gelatine was peptonised and in a smaller or
greater number of places, near the margin more than in the middle
of the circles, small, white, glossy points arose, which secreted drops
of a colourless, quite clear liquid, but which required no more than
12 hours to turn into black dots. These also continued the process
of drop-formation for some time, when after some further increase
in size they changed into shorter or longer, round or angular little
bodies, which clearly belonged to the class of sclerotia. Having
erown more and more independent of the hyphae which at first
occluded them, these black bodies could now be removed without
damaging them and they appeared to have reached a maximum
length of 10 millimeters and a thickness of 5

The experiments on infection with parts of living tobaccoplants
were all successful on condition that the place of inoculation was
kept very wet, e.g. by wrapping it up in very wet cottonwool or
some woodshavings steeped in water. The attacked tissues became
discoloured also here.

From what precedes we may infer that the fungus cultivated on
malt-gelatine does not differ from that of the tobaccofields, which
was irrefutably proved later when from the sclerotia of both the
same Sclerotinia was obtained.

It is worth mentioning that the myceliumeultures on the malt-

6 millimeters.

gelatine which had produced the sclerotium, had besides given rise
in several places to dull white, granulated spots, which microscopical
examination revealed to consist of 1st. clusters of flask- or cone-shaped
conidiophores, borne by erect or ascending hyphae and 2"¢. a number
of curious crystals pressed against the thread-shaped cells, partly
loosely spread, partly assembled in clusters.

The colourless conidiophores were high 12—16 uw and_ broad
45m and consisted of a cylindrical body tapering a little towards
the lower end, a thinner short neck and a spherical head, which latter
just slightly exceeded the neck in breadth and produced spherical

colourless conidia of 2.5 diameter, which were at first connected
to short chains, but soon broke up and commenced an individual
existence.
The crystals and other bodies, often striated, not occluded in cells,
+*

( 52 )

of varying shape and size, soluble in diluted hydrochloric acid in
which they left a structureless residue, soon appeared to belong to
the class of “caleospherites”: organic compounds of calcium treated
by the late Professor P. Hartine in 1872 in a quarto Treatise of the
Royal Academy of Sciences, entitled: “Morphologie Synthétique sur
la production artificielle de quelques formations calcaires organiques’’.

There could be no doubt that these calecospherites stood in no
relation to the fungus, but had been produced by the gelatine, while
on the other hand, the presence of conidia proved that the new
Sclerotinia, \ike other species of the same genus, could multiply by
conidia as well as by ascospores.

On the maltgelatine-plates which had been exposed to the air of
the tobaccofields and in the drying-sheds, the same mouldy spots
developed under the most favourable conditions of the laboratory,
which had drawn our attention on the stems and leaves in the fields,
and which had afterwards been artificially multiplied. More important
still is that somewhat later the same sort of Sclerotia developed, the
germination and further development of which gave origin to the
formation of apothecia.

There cannot be the least doubt that the conidia floatmg in the
air, by settling on the gelatine-plates, had produced the infection and
the ensuing phenomena, so that these last experiments throw a clear
light on the possibility of extensive tobaccofields being ruined in a
very short time, as soon as by a prevailing uncommonly damp con-
dition of the atmosphere a small patch of mould has anywhere
found occasion to develop threads. At the same time they show that
the opinion of von Taven (Vergl. Morph. der Pilze, 1892, p. 105):
“Es (die Arten von Sclerotinia) sind parasitische Pilze, deren Sclerotien
im Innern der Pflanzentheile sich bilden ganz nach Art einer Claviceps”
cannot be admitted for Sclerotinia Nicotianae, and that here an
ectogenous formation of the Seclerotium has been substituted for an

endogenous one.

[II]. CULTIVATION-EXPERIMENTS APPLIED TO SCLEROTIUM NICOTIANAR.

The sclerotia whose development it was desired to study were
buried in sand, garden-soil, forest-soil and leaf-earth respectively,
placed in suitable dishes partly in daylight, partly in dark, and after
having been properly watered exposed to various temperatures among
which that of 22° C. Not earlier than 6 weeks later the first sign
of new life was observed in the shape of numerous black-brown

( 53 )

little hills with a lighter-coloured top. The earliest appearance was
in the dishes filled with forest-soil aud placed in daylight at 15° C.,
whereas a temperature of 22° C. seemed to have hindered develop-
ment. The culture in sand always remained backward. The hills
gradually assumed the shape of little rods, but took 3—4 months to
reach the appearance of thin little stems or threads, bent down
over the surface. These latter moved in the direction of light.

The number of threads varied widely for the different grains
(Fig. 2 and 5), but did not exceed 20. The progress of the growth
was at first very small indeed (2 millimeters in 40 days) and was
even insignificant between Nov. 1902 and Febr. 1905. But then the
threads rapidly grew in length and in March measured as much as
6 centimeters.

After the thickness of the sprouts had very long remained unchanged,
at last (in March) a distinct swelling appeared at their top, which
at first club-shaped rounded and closed, soon divided into a somewhat
inflated neck (apophysis) and a broader dise-shaped terminal piece,
which latter could easily be recognised as an open shallow apothecium
with the edge slightly bent inward (Fig. 8). The correctness of
this view appeared when the miscroscopical examination had revealed
the presence of spore-bearing asci and paraphyses in the disc (Fig. 9).

A single sclerotium appeared to be able to bear some six well-
developed apothecia and besides some dwarfish rods.

Unburied Sclerotia do not develop, although they remain resting
on the bed of mycelium-threads which produced them. Cultures in
Petri-dishes were mostly spoiled by bacteria.

Bits of a fruit-stem, grown from a Sclerotium buried in humus,
when placed on malt-gelatine gave origin to the development of
white pads, wiich in their turn sometimes produced new Sclerotia
in a week’s time. Bits of white Sclerotial flesh behaved similarly.

The fungus-generation grows very rapidly on malt-gelatine as
well as on bits of tobaccoplants at 22° C., though its temperature
optimum is at about 24° C. At 37° C. the growth is arrested.
Between 15° and 20° C. the development is still satisfactory.

TV. ANATOMICAL INVESTIGATION.

The mouldy threads which in the field develop on the surface of
green parts of plants and which afterwards produce the Sclevotia,
grow equally in all directions and so gradually form white discs, of
increasing diameter, finally reaching an average breadth of 2 centi-
meters. These threads are colourless, 2 m tick, much ramified, repea-

( 54.)

iedly sepiate, filled with a finely granulated protoplasm and occasionally
accompanied by threads five times thicker, the significance of which
could not be discovered.

From the thinner, creeping fibres others rise up on which either
singly or in small clusters, flask- or cone-shaped organs develop,
whose function is to split off conidia and which hence deserve the
name of conidiophores. They are on an average 15 @ high and
3.5 a broad and consist of a thick body, tapering a little at the
bottom, a short, thick neck and aspherical head, only slightly thicker
than the neck. From the spherical or knob-shaped head colourless,
spherical conidia of 2.5 yw diameter come forth, which are very soon
detached from each other, but the multiplication of which goes on
for a very long time, as may be inferred from their extremely large
number.

The Sclerotia, externally black, internally white, diverge little from
the common type as far as their structure is concerned. They consist
of a pseudoparenchym the cells of which are somewhat bigger in
the middle of the grains, somewhat smaller near the surface, show
various, mostly distorted shapes (fig. 7), have very thick walls and
are not separated by intercellular spaces. The walls of the more
superficial cells are black, of the more central ones colourless. If a
sclerotium rests with part of its surface against the glass of a tube
or box, the black colour does not develop there.

The spore-bearing generation (fig. 8) which under favourable
conditions comes forth from not too old Selerotia and consists of a
long, thread-shaped stem and a miniature apothecium, shows, in the
first-mentioned part short, eylindrical or column-shaped, closely packed
cells, which at the surface bend dorsally, but in doing so assume
the shape of clubs or retorts and turn thew broadest part outside.
They have a light-brown shade and impart to the stems and cups
a peculiar appearance as if they were covered with downy scales.

The hymenium consists of asci and numerous loosely packed
paraphyses, of which some protrude a little above the others (Fig. 10).
The asci are tubular, with rounded tips, insensible to iodine,
160—180 > 6—7 | and contain in their */, upper parts 8 inclined,
colourless, oval spores in a_ single row. The paraphyses are only
slightly swollen at the top and almost colourless. Germinating
spores were not seen.

V. BIOCHEMICAL INVESTIGATION.

In order to study the conditions of life of Sclerotinia Nicotianae,

(25D)

the fungus was cultivated on and in different nutritive materials of
known composition.

It appeared in the first place that the presence of free oxygen is
absolutely necessary for its growth; with anaerobic methods of eul-
tivation according to Bucnner and Liporivs no trace of development
took place. It is not improbable that this is the reason why the
mycelium only grows extremely slowly in nutrient liquids, where the
quantity of oxygen below the surface is necessarily small.

On the other hand the fungus appeared to grow very rapidly
when inoculated on malt-gelatine, malt-agar and also on parts of
leaves and stems of the tobaccoplant, sterilised at a high temperature.
Then a woolly mycelium developed, in some places rising above the
surface. Below the surface of liquids or filtrates, obtained from parts
of stems or leaves, after inoculation with the fungus, only a meagre
cloudy mycelium appeared. As soon however as part of this had
reached the surface of the liquid, its growth became much more
vigorous. In some cases a floating sclerotium was even produced.

Next the influence of the reaction of the nutrient liquid was studied.
In a solution of 0.1°/, of potassium nitrate, 0.5°/, glucose, 0.050°/,
magnesiumsulphate and 0.050°/, potassiummonophosphate, containing
carbon and nitrogen assimilable by the fungus, Sclerotinia Nicotianae
does not easily support free acid or alkali. The acid limit lies with
this solution at about 1 cubic centimetre of '/,, normal sulphuric
acid to 100 cubic centimetres of liquid, and the alkaline limit at
0.5 cM’ of */,, normal potassiumhydrate. Neither limit can be sharply
drawn as the fungus only slowly produces acid in the solution men-
tioned. With 1.5 cM’. of */,, normal sulphuric acid no growth
whatever takes place any longer; with the alkaline solution the
limit could not be sharply defined.

Moreover an elaborate investigation was made as to which com-
pounds were profitable to the fungus as carbonaceous and which as
nitrogenous foods. As a carbonaceous food glycose, as a nitrogenous
one saltpetre in the above-mentioned concentration, proved most
satisfactory. Ammonium nitrate, a very good nitrogenous food, was
not available of course in the presence of alkalies.

In the further experiments the saltpetre was replaced by a similar
quantity (0.1 °/,) of the nitrogen compound to be studied or the
elycose by the carbon compound to be studied in the same con-
centration.

a. Nitrogenous food.

Nitrogen was offered to the fungus in the form of potassium

(S50: %

nitrate, potassium nitrite, chloride, nitrate, phosphate, sulphate,
carbonate of ammonia and ammonia. Ammonium nitrate gave the
best results. The other compounds showed little difference. Of
ammonia which was added in very small quantities, hardly anything
Was assimilated.

Of amido compounds, which are generally known as good sources
of nitrogen for fungi, glycocoll, asparagine, aspartic acid, alanine,
tyrosine and leucine gave good results in the present case also. The
nitrogen of urea, creatine, parabame acid and uric acid has little
nutritive value. From the last mentioned substance also carbon can
be assimilated.

Amone aromatic compounds, only the nitrogen of ammoniumsalts
has any nutritive value; among the derivatives of pyridine only the
nitrogen of the residue, not the carbon. To develop the fungus glycose
has consequently to be added to the nutritive material. Nicotine,
being a free alealoid can serve as a source neither of nitrogen nor
of carbon.

If assimilable carbon is present, the nitrogen is used from the
ammoniumsalts of oxalic, tartarie, citric and benzoic acids, least from
ammonium succinate.

b. Carbonaceous food.

Of fatty acids only very dilute acetic acid (0.050 "/,) has a nutritive
value for carbon.

The polvacid alcohols are bad sources of carbon, as was shown
by an investigation with glycerine, erythrite, mannite, sorbite, adonite
and duleite. Least satisfactory was sorbite and also glycerine, a good
carbon-food for many fungi, gave bad results here. Lactie acid in
very small quantities, was available as a carbon-food.

Very differently behaved the sugars. As was already mentioned,
elycose comes first in nutritive value. Besides were studied: arabinose,
xylose, saccharose, fructose, maltose, lactose, raffinose and melibiose.
Of all these only xylose and arabinose had any value as sources of
carbon. In all other solutions only a trace of growth was observed.
Though not without difficulty the fungus was able to derive carbon
from cellulose. On filtering paper wetted with the above-mentioned
nutrient solution, but without glycose, a snowwhite, woolly mycelium
developed. Also from inuline carbon may be obtained.

c. Nitrogenous and carbonaceous food.

As mixed sources of carbon and nitrogen we must mention aspa-
ragine, aspartic acid and alanine. The addition of potassium nitrate

(57 )

improved the growth more with aspartic acid than with asparagine,
which must probably be ascribed to the two carboxylgroups, active
as sources of carbon.

Finally it must be mentioned that also peptone can furnish carbon
as well as nitrogen, but that the nutritive value for nitrogen is
increased here by adding glycose.

In accordance with the results of Kimps, it was found that a high
nutritive value of the liquid had influence on the formation of
Selerotia with alanine, leucine, aspartic acid and glycose. These
bodies appeared under the mentioned favourable conditions at the
surface of the liquid in about three weeks’ time.

VI. HINTS ABOUT THE PREVENTION OF THE SCLEROTINIA-DISKASE

(‘ROT’) IN TOBACCOFIELDS.

As a damp soil and a damp atmosphere are both absolutely
necessary for the development of the “rot” or Sc/erotinia-disease and
as this disease in wet years appears about the time when the tobacco-
leaves begin to be gathered, it is absolutely necessary, for the reasons
given above, to stop the cultivation of scarlet-runners (Phaseolus
coccineus, also named Phas. maitijlorus) on the tabaccofields and
only to admit and to continue the cultivation of French beans
(Phaseolus pulgaris SAVI).

Besides limp leaves or stems or such as are covered with the
least quantity of a white down must immediately be removed and
burned.

The leaves that have been carried into the drying-sheds must at
once be laid asunder and hung up to be dried. Suspected leaves
must be sorted out and destroyed.

DIAGNOSIS LATINA.

Sclerotinia Nicotianae Oud. et Koning. — Sclerotiis ad super-
ficiem caulium et foliorum primo in compagine densissimo filorum
mycelii niveorum absconditis, celeriter mole augentibus, mox itaque
expositis, tandemque a substratu decidentibus, extus nigris, intus albis,
nune subglobosis, tune iterum oblongis, 10 maxime mill. longis, 5—6
mill. maxime erassis, teretibus vel subangulosis. —- Ascomatibus plu-
rimis (usque ad 20) ab uno eodumque sclerotio protrusis, longe sti-
pitatis, tenerrimis; stipite filiformi, tereti, flexuoso, 4—6 centim. longo,
1/, mill. crasso, deorsum scabro, sursum laevi, summo obesiore, sic
ut ascoma satis longe apophysatum videatur, una cum ascomate

( 58 )

pallide fuscescente, floccoso-squamuloso. Ascomate proprio minimo,
primo coniformi, clauso; dein p.m. expanso, perforato; tandem pa-
telliformi, late aperto, 0.8 mill. in diam., 0.2 mull. alto, margine
incurvato. — Ascis eylindricis, apice rotundatis, iodo haud_ caerules-
centibus, deorsum breve stipitatis, 160—i806—7 uw, paraphysibus
7<3—4yu, in partibus
ascorum ®,, superioribus oblique monostichis, levibus, hyalinis.

obvallatis, octosporis. — Sporidis ellipticis, 5

Paraphysibus filiformibus, summo subclavatis, numerosissimis, dense
congestis, ascos paullo superantibus, 2'/, & erassis, protoplasmate
dilute-fuscescente farctis.

Ex mycelii hyphis repentibus hyalinis, septatis, ramosis, numeros-
simae assurgunt hyphae basidiiferae; basidiis sive conidiophor's lageni-
formibus utplurimum conglobatis, summo conidia sphaerica, hyalina,

Conidia ex aére in patellam gelatina praeparata repletam delapsa,
mox germinare incipiunt, myceliumque proferunt, cujus hyphae,
quum plurimis locis arctius inter se coalescant, sclerotiorum novorum
exordia edunt.

diam. 2.5 uw, in catenas breves coadunata procreantibus.

EXPLANATION OF THE PLATES.

Fig. 1. Four mature sclerotia (4—8 X3—4 mill.), magnified.

Fig. 2. Two Selerotia with a certain number of sprouts (juvenile ascomata)
magnified.

Fig. 3. Mieroscopical representation of erect branches of the mycelium, against
the top ef which free calcospherites (from the gelatine) and also clusters
of them have fastened.

Vig. 4. Microscopical representation of lying and ascending mycelium-threads,
with the conidiophores produced by them and the apical conidia and
chains of conidia originated therefrom.

Fig. 5. <A Sclerotium with partly immature, partly full-grown long-stemmed

Sclerotia, magnified.

Fig. 6. Section of a Sclerotium, magnified.

Fig. 7. Microscopical picture of part of a section of a Sclerotium.

Fig. 8. Nearly full-grown and full-grown ascomata, of which one cut longi-
tudinally, magnified.

Fig. . Microscopical representation of part of a longitudinal section of a
mature ascoma, with spore-bearing asci and paraphiyses.

Fig. 10. Part of Fig. 9. enlarged.

Fig. 11. Top of an ascus and a couple of spores, still more enlarged.

teog )

Physics. — Dr. J. E. Verscuarrent: “Contributions to the knowledy:
of VAN DER WAALS’ Y-sur Face VII... The equations of state and
the y-surface in the immediate neighbourhood of the critical
slate for binary mixtures with a small proportion of one of
the components.” (part 3)*). (Supplement N°. 6 to the Com-

munication from the Physical Laboratory at Leiden by Prof.
IKK AMERLINGH QONNES).

(Communicated in the meeting of Febr. 28, 1903.)
- ~ ryy ’ . . 7? . : . .
15. The y-surface in the immediate neighbourhood of the plaitpoint.

By the application, after Krrsom’), of Korrmwna’s projective trans-
formation *) to the equations of the y-surface, I have expressed the
coefficients of my equation (20) in terms of those used by Korrrwne
to study the plait in the paper mentioned.

The following new coordinates must be introduced

Ow Ou
io) eae OU FR (5°), (e— 27,1 ) Ge) ;
v I Tp @) Ty

a" — (e«—£7,) —m (v—vTpl)s

GOT

wy” = (¥

| where im is determined by the equation

; S | (=)
m = == 0;
| Of 7,1 \ 02 Ov) Ti

to the first approximation and by the use of equation (20) this reduces to

— Ea 4
i a Rees aa Sy ).

Since the equation of the y-surface contains a term with Joy,

1) Proc. Amsterdam. 28 June and 27 Sept. 1902.
‘ 2) Proc. Amsterdam. 27 Sept. 1902, p. 341.
3) Wien. Ber., 98, 1159, 1889.
. 4) In agreement with Keesom’s expression (lc. p. 342). The value of m must
also fulfil the two other equations:

| ee ae
3 a ae a i

and

: dy O°y sae ( Oy )
fs poe + 3, 2 2 pm oie, = = 0:

this is really the case when the above values of Xz»: and Vp: are substituted.
; Conversely we can use these equations to determine xrpz and Vrpi, as KoRTEWEG
has done. (Proc. Amsterdam. 31 Jan. 1903, p. 526).

( 60 )

it can only be identified with Korrrwse’s equation (2), when log w
can be expanded in a series. This can only happen when the diffe-
rence between « and rz, is so small that «—r7,) 18 vanishingly
small with regard to xy,,. We remain thus in the immediate neigh-
bourhood of the plaitpoint*). In this case we find that the equation
of the y-surface can be brought into the form

" . _ff2 1 F M3 at! 2 a af. aay | Ss ,/4
woe. + de * dye 7 ME GA eB a a Teas ese

where, to the first approximation

t AT; : 1-297 oe 1 m,,
¢.= - C= = Se : 3) = ee ’
; 2 £Tpl O &°Typl 2 eTpl
1 LRT LRT, 1) on
d, = — — (m’ tlm Se See a ;
P 2RT, (mon a: : 12 2° TyI 5 3 XT pl
ay 1 rials
eo og = SS ("Coe ee) eS Bee
3 2 RT .x Tpl o 3R?27 2. 01 1 4 0
1
j;=—- ¥ Migs CtG."*).

i ** is always positive hence
2 &Tpl

m,, is always negative; it follows that the plaitpoint on the y-sur-
face is always of the first kind *).

Since d/,—=0O when m?,, + R7T.m,,—0, the second special case
of border curve and connodal line treated by me *) agrees with the

The expression 4 ¢,e,

1) The following expansion can thus be used to determine the coordinates of the
critical point of contact, (cf. Keesom l.c. p. 342).

2) The expressions for d,; and e; agree with those found by Keesom (I. ¢. p. 341).

3) See Korrewec, Wien. Ber., p. 1158.

#) Proc. Amsterdam 27 Sept. 1902 p. 329. The reference to this special case
allows me to correct some mistakes in the formulae which are connecled with
this and the preceding special cases. In Proc. of 28 June 1902 p. 267 line 2,

read :
: L ong Un A a ee
Pp, — Pie =| hy = SS Ee eee

€ F wm
SMe. am

and in Proc. 27 Sept. p. 328, line 12:

2 2
: fg Litt 5s L ota, a ;
P —- PIk = ara Mos —_ = = == : - ; — (v — UTE) »

m*, oC. a WR es

. ° > . « ® ~ mo, Mos

Further in the last Proceeding p. 329 line 9 for the coefficient of RT,
ke

read 4 instead of an

( 61 )

first double-plaitpoint case of KorrewrG'). The second case for a
double-plaitpoint, i. e. 4 ¢,e;—d,* = 0, does not occur on the w-surface.

16. Application to a particular equation.

In a communication published in the Proceedings of the Academy
for 31 Jan. 1903, Korrewre has determined the plaitpoint and critical
point of contact for mixtures with a small proportion of one component,
but on the assumption that these mixtures satisfy VAN pER WaA4ALs’
equation of state

RT ae
he v—b, pee
where
ay = a, (l—«)? + 24,, ¢(1 -2) + a, 2?
and

b, = b, (1—a)? 4 2 b,, # (1—2) + 4, 2’.
The formulae found by Kortrwre can be immediately deduced
from my formulae, when we introduce the special forms which my

coefficients will then assume.
First we may note that, in this case, the critical constants for the

homogeneous mixture are

i ee tier Lo Des
tk 27 b,R Pek Urk k

1) l.e.p. 1166. In using the same method with Korrewea’s equation (2), as I
have used to determine the critical constants, [ have found the following expression:

4c,e,e,+ d*,e,—4d,d,e,—4c,d, f,

+= Sree dod) a ke + #,)s
2 d, yr.
(as 3) pee ot, I Ly),

5
and
Ade” ,—2d,e,e,td*, 7,
LZ, — «= SO (a, 1) (Ys — :
2 1 ; 2e.(«?,—4¢,e,) ( 2 == 7) (y, Y;)
where 2), %, Y; and Yg are the coordinates of the ends of the tangent-chord.
In the special case when d; =O we get

z é 1 2
i= — =~ Cs *,) ’ Dine ae pe i a CUR 2),
5 ; Lk
and
Opie (22 at =), 8)
— = — | — — —— }(«, + 2z,)’.
¥, Y;) 2e. C es 8 e, 32 H 1

- By the introduction of the above values for the coefficients, my expressions
for , 9 and € are again found. The first approximation for dj, ¢ and ¢3 will
then be certainly insufficient in the last expression,

( 62)

so that KAMERLINGH ONNES’ Coefficients @, 8B and y become

a b a b b
OY (te ay Se a er ee ital. 12 yee a CY See ere
¥ (*: 2) ( ay b, ) f €;

Further we find, by comparing my equation (18) with the above

equation of state:

3H hes is bat 2 a, l 3 fa > Ors
7 =| = ee SD {— =
i Ed Ty, ALOE a, b,
eae a9) 2 Vie ed Cees
nee Ov Our, Tk 27 ie a, b,

1 “O*p tage
Rise eee Se et sae Se;
6\ dv® / 7; 486 b,

If these special values are substituted in my general formulae,
KorTEWEG’s special formulae are obtained, and in addition some
which he has not given. These are not given here as they are not
sufficiently simple and they can also be easily reproduced.

KortTEWkG has already given the results obtained from these formulae.
I will here only remark that the special cases 1, 2, 3 and 4 of
Kortewee’s fig. 1 agree with my fig. 15 and the cases 5, 6, 7 and
8 with 14. As fig. 15 is obtained for the case that m?,,+ RT; m,,>0
and fig. 14 when m?,, + R7;,m,,< 0, the boundary between the
two cases is determined by m?,, +- R77,m,, = 0, which in connection
with the special equation of state can. be written

3 dy, 6.22 By Uae
] — ——+2—-}4+ 8 an
a, b, a, b,

This is the equation of the parabolic border curve given by KorTEewee.

(June 24, 1903).

(Sing eal

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING
of Saturday June 27, 1903.

DoS

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 27 Juni 1903, DI. XID).

SS heb aa ES.

If. W. Baxuvis Roozesnoom: “The boiling-point curves of the system sulphur and chlorine”,
p- 63.

A. Smits and L. K, Worrr: “The velocity of transformation of carbon monoxide” (II).
(Communicated by Prof. H. W. Baxuvuis Roozesoom), p. 66. ;

J. K. A. Wertrurerm Satomoyson: “A new law concerning the relation between stimulus and
effect.” (Communicated by Prof. C. WiNkLEr), p. 73. (With one plate).

Extract from the Report made by the Committee of advice for the according of the Buys
Batior-Medal, p. 78.

Cc. A. J. A. Oupemans and C. J. Koxine: “On a Sclerotinia hitherto unknown and injurious
to the cultivation of Tobacco (Sclerotinia Nicotianae Oup. et Konine). Postscript. p. 85. (With
one plate).

A. Gorter: “The cause of sleep.” (Communicated by Prof. C. WinKLER), p. 86.

C. A. Lospry pe Bruyn aud C. L. Junaivs: “The condition of hydrates of nickelsulphate in
methylalcoholic solution”, p. 91.

C. A. Losry pe Bruyn and C. L. Juncivs: “The conductive power of hydrates of nickel-
sulphate dissolved in methylalcohol”, p. 94.

C. A. Losry DE Bruyn: “Do the Ions earry the solvent with them in electrolysis’, p. 97.

C. L. Juxervs: “The mutual transformation of the two stereo-isomeric methyl-d-glucosides.”
(Communicated by Prof. C. A. Losry bE Bruyy), p. 99.

S. Trmsrra Bzy.: “The electrolytic conductivity of solutions of sodium in mixtures of ethyl-
or methylaleohol and water”. (Communicated by Prof. C. A. Losry pe Bruyn), p. 104. (With
one plate).
~ W. Exsrnoven: “The string galvanometer and the human electrocardiogram”, p. 107. (With
two plates).

J. E. Verscuarrett: “Contributions to the knowledge of vay per Waats’ ¢-surface. VII.
(part 4), The equation of state and the ¢-surface in the immediate neighbourhood of the critical
state for binary mixtures with a small proportion of one of the components”. (Communicated
by Prof. H. Kameriincu Onnes), p. 115. (With one plate).

J. D. van DER Waats: “The liquid state and the equation of condition”, p. 123.

J. J. van Laar: “On the possible forms of the melting point-curve for binary mixtures of
isomorphous substances.” (Communicated by Prof. H. W. Baxuvis Roozesoom), p. 151. (With
one plate).

The following papers were read:

Chemistry. — “The boiling-point curves of the system sulphur and
chlorine.” By Prof. H. W. Baxuurs Roozesoom.
(Communicated in the meeting of May 30, 1903).

Binary systems in which the formation of complex molecules may
be assumed to take place in a greater or smaller degree have been
frequently investigated as regards the equilibria between a liquid

Proceedings Royal Acad. Amsterdam. Vol. VL.

( 64 )

phase and solid phases, but hardly ever with regard to the equilibria
between liquid and vapour.

I, therefore, proposed to further investigate this relation in the
case of vapour pressure- and boiling-point curves on a series of

rs) 40 4o go 40 59 60 7° $0 go (00
v + J at To S
S Cty St, SCE

examples in which the nature and the degree of the complex mole-
cules varied, in order to obtain a more definite idea of the changes
which these curves undergo as compared with the simple case in
which the binary system consists only of two kinds of molecules.
Such an example is furnished by the system sulphur-chlorine, the
boiling-point curves of which are given in the accompanying figure,
which is constructed from determinations made by Mr. ATEN.

(%5 )

Liquid sulphur and liquid chlorine are miscible in all proportions.
If in these mixtures no compound molecules were formed, two
regular boiling-point curves might be expected which would diverge
very much in the centre because the boiling points of the two
components lie far apart.

In these mixtures, however, a fairly stable compound §,Cl, is
formed. If this compound were absolutely stable, that is if a liquid
and a vapour of the composition §,Cl, consisted of nothing but
molecules of this formula, then the liquid and vapour would at this
point, have exactly the same composition. The system S+Cl would
then in reality be compounded of the two systems S-+8,Cl, and
§.Cl, + Cl, which could no doubt be represented in one figure, but
then the liquid- and the vapour-pressure curves would not pass con-
tinuously into each other at the composition §,Cl,.

As it is known that the dissociation of the vapour of S,Cl, is
small it may be anticipated that, in the system S—+ Cl, the connec-
tion at the composition SCl might become continuous, but in such
a way that the vapour and liquid curves nearly coincide at this point.

This state of affairs was now confirmed and is indicated in the
figure by the liquid curve 1,3 and by the vapour curve 2,4. It will
be seen that the curves 1 and 2 and 3 and 4 nearly meet in a point
situated near the composition SCl, but in reality we have here
continuity, from which it appears that $,Cl, is not absolutely stable
either in the form of liquid or vapour. The difference however, is
so small that this type really exhibits one of the smallest forms of
deviation.

In the case of binary mixtures where the compound formed is
more strongly dissociated the divergence of the two curves at the point
representing the compound will be much greater. The liquid curve
and the vapour curve of the entire system will then more and more
assume the form which in the figure belongs to both halves.

The investigation however, showed a further peculiarity in the
lower half. The boiling-point curves 1 and 2 for the mixtures whose
composition lies between Cl and SCI only relate to mixtures which
are freshly prepared from liquid 8, Cl, and liquid chlorine.

These mixtures at temperatures below 0” retain for a very long
time their yellow colour and then exhibit the boiling point lines
indicated at 1 and 2. At higher temperatures, and very quickly
above 30°, the colour becomes darker and finally blood red, chiefly
in the case of mixtures approaching the composition SCl,.

The boiling points then rise, sometimes very considerably, to a
maximum amount of about 70° so that the line 5 is found for the

3 3

( 66 )

definite boiling points of liquids which have reached their final
equilibrium, which occurs after some hours at the ordinary temperature.

At the same time we get, in place of the vapour curve 2, the new
vapour curve 6. As the velocity of reaction above 40° becomes very
great, the lines 1 and 2 cannot be accurately determined above this
temperature. For 1 this causes no inconvenience as its further course
must be almost vertical, but the upper part of 2 becomes rather
uncertain.

The final boiling-pomt curves 5 and 6 are situated much closer
together than the first named one and have moreover an exceedingly
irregular shape. It cannot as yet be decided whether this is solely
attributable to the formation of SCl, molecules in the mixtures, or
whether other compound molecules are formed.

The formation of compound molecules may be noticed not only
from the change of colour, but also from a diminution of the volume
and will if possible, be studied quantitatively.

The important question in what manner the melting-point curve
of solid SCI, is modified by the presence of more or less compound
molecules in the liquid phase is still the subject of investigation.

Chemistry: — “The velocity of transformation of carbon monoxide IV’.
By Dr. A. Smits and L. Kk. Worrr. (Communicated by Prof.
H. W. Bakuuis Roozxsoom).

(Communicated in the meeting of May 30, 1903).

In our previous paper on the above subject ') we communicated
results obtained at the temperatures 256°, 310° and 340°, from which
we concluded that at these temperatures the transformation of CO
into CO, and C is unimolecular.

Our present paper contains the results obtained at 445°. This
communication appears to us to be of importance for the following
reasons. Three months after our first paper a communication appeared
from ScHEnck and ZiMeERMANN’) from which it appeared that they
had also studied the transformation of CO into CO, and C and had
arrived at the result that the reaction at temperatures from 310°
and 360° was a unimolecular one, thus confirming our experiments,
but that at 445° the reaction became bimolecular.

On continuing our investigation we found, however, that the

1) Proc. 8 Jan. 1903.

2) Ber, 36. p. 1231.

( 67 )

reaction at 445° is also a unimolecular one and that therefore the
observations of ScHENck and ZimMerRMANN must be faulty as far as
the temperature 445° is concerned.

Experiment.

In order that the reaction might not take place too rapidly the
reaction vessel was now filled one third with the catalyser (pumice-
nickel-carbon) *).

The object of the first experiments was to determine the order of
the reaction according to the method of van ’r Horr.

In the first measurement the initial pressure was 770.7 m.m. He.
After 5 minutes the CO tension amounted to 430.5 m.m. Hg from
which

de,
— = 68,04
dt

and for the average pressure of the carbonic oxide
c, = 600,6

In the second measurement the initial pressure was 442.2 m.m. Hg
and after 5 minutes the CO pressure amounted to 239.0 m.m. He.

de
Here -= — 40,64 and c, = 340,6.

If from this we calculate x according to the formula of van’ Horr

de; de,
He Se
=X db} dt
r= ————__.,
log (¢, } ¢y)
we obtain

= 0,987)

2. After having thus become convinced that the reaction at 445°
is also a unimolecular one we made a series of measurements in
order to calculate the reaction constant from them.

The result was as follows:

1) The quantity of iron present in pumice did not appear to exert any influence
as no alteration in pressure was noticed in a reaction vessel containing pumice
and CO when heated to 445°. This time, however, as in Scuenck’s experiments,
the iron was removed from the pumice by reduction with hydrogen and subsequent
treatment with HCl and boiling in a Soxhlet apparatus.

The Ni(NO3). originally contained much iron, but was completely freed from it
by leaving the solution for some time in contact with NiCO;.

*) Also after a longer time (10—15 minutes) ” was found to be practically 1.

Time Pressure in 1 PR 4 2(P)—PA
k= — log; hi = — ¢ )
in minutes. m.m. Hg. to" 2 PrP t Py (2P:—P,)
Lene eee aaaaaaaaaaaaaaaaas
0 769.5

4 660.4 0.03437 0.000129

6 | 616 6 () 03666 0.000143

8 579.1 0.03707 0 000159

10 548.7 | 0.03704 0.000175

ie | 497.8 | 0.03546 0.000208

20 416.7 0 03108 0.000206

30 456.3 0.02246 0 000164

The measurement was started here half a minute after the
commencement of the filling. The filling lasted */, minute.

The third column contains the values of / calculated on the
supposition that the reaction is wnimolecular whilst the fourth column
contains the values of 4’ assuming the reaction to be bamolecular,
as believed by Scnenck and ZimMERMANN. In concordance with what
has been found above, we see that the figures in the third column
are much more nearly constant than those in the fourth. During
the first 15 minutes the values of / (third column) agree fairly well
with each other; afterwards a slow fall takes place. That the first
constant would be smaller than the next was to be expected, as
during the first 4 minutes a small expansion had still to take place.

Although the starting point could not be fixed with the same
accuracy as before, owing to the greater velocity of the reaction, the
fall of / could not be attributed to experimental errors. It therefore,
made us suspect that the reaction might perhaps prove to be perceptibly
reversible at 445°.

It is true that Boupovarp’) had found that CO when in contact
with our catalyser was completely decomposed at 445° into CO,
and C, but as his method was not very accurate we felt we might
doubt this result *).

In order to obtain certainty we made the following experiment.
We filled the apparatus at 445° with CO, and observed whether an

1) Scuenck and Zimmermann have made a mistake calculating the value of k’.

*) Ann. de Chim. et de Phys. [7] T. 24. Sept. p. 5—85 (1901).

*) SApatier and SenpEReENs noticed a complete transformation between 230° and
400°. Bull. Soc. Chim. t. 29 p. 294 (1903),

( 69 )

increase of pressure took place which would indicate that the reaction
CO, -+- C= 2 CO was proceeding.

The experiment removed all doubt as not only an increase of
pressure be could very plainly demonstrated, amounting after a few
hours to several em. of mercury, but after exhausting the apparatus
a quantity of CO could be detected in the gaseous mixture which
accounted for the observed increase of pressure.

Contrary to Boupovarp’s results we have therefore found that the
reaction 2CO = CO, +C is reversible at 445°.

The reason why fairly concordant constants were obtained during
the first 15 minutes although no notice had been taken in the
calculation of the reversal of the reaction, is simply that the equation

aC et ek oe Se
differs but very little from
da
ee SS Sa aT Oia ies eee)
dt

when & or x or both are very small. /, is very small at 445° and
this is the reason why at first the second equation is satisfied, «
being then not yet large.

By means of the first equation we might be able to calculate /

oes k

if we knew the equilibrium constant K = —.
k,

As analysis seemed to us less accurate we have endeavoured to

determine K in the following manner:

The reaction vessel was filled again with CO, while the time
was noted which elapsed between the filling and the first reading
so as to be able to find the starting pressure by extrapolation. The
heating at 445° was now continued until the pressure after the lapse
of some hours did not undergo any further change.

K could then be calculated from the pressure at the start and at
the finish.

To decide whether the final pressure corresponded with a real
condition of equilibrium, the same experiment was repeated starting
with CO,. If the first final condition had been a real equilibrium,
the same value ought now to be found for 4.

Up to the present we found this by no means to be the case but
we do not at all consider the research finished in this direction. We

1) It is taken for granted lere that the reaction CO, + C= 2 CO is also a
unimolecular one.

(70 )

only mention it to explain why the values for / in our last table
have not been corrected.

3. In criticising the experiments of ScHENcK and ZIMMERMANN, it
must first of all be observed that they did not reduce their NiO with
CO but with H,. This is of course, wrong as during the reaction
carbon is deposited and the catalytic Ni surface is changed. If, as in
our experiments, we start with Ni on which previously a coating of
carbon has deposited, it is evident that a further precipitation of car-
bon during the experiment will be of less consequence.

In our former communication it has moreover been shown that
the activity of the catalyser first diminishes owing to deposition of
earbon, but finally becomes practically constant.

If, therefore, we start with Ni without carbon we may expect that,
on account of the deposition of carbon, # will continuously decrease.
The values for / found by ScuEnck and ZIMMERMANN are not at all
constants and show a decrease with an increase of the time.

To find out what can be the’ cause of the bimolecular course
at 445° as found by ScHeNcK and ZIMMERMANN we have repeated the
experiment with pumice-nickel in which the NiO had been reduced
with very pure hydrogen. *)

Our first work was again the determination of the order of the

reaction.
dst measurement. Initial pressure = 756,0 m.m. He
CO pressure after 3 min. = 528,6 i
de > :
== Voie wr = bane
dt
2od measurement. Initial pressure — 275,1 m.m. Hg
CO pressure after 2 min. = 210,9 y .
de, : ;
= eS Bae ee 4
dt 5
therefore Ric eet:

Having found that, contrary to the statement of ScHenck and
ZIMMERMANN, the reaction with this catalyser is also unimolecular we
made a further series of measurements in order to calculate 4.

The results were as follows:

1) By electrolysis of a NaOH solution, using nickel electrodes.

2) After a longer time (5—10 minutes) 7 was found to be practically 1,

ar)

re |

0 762-4

2 671.7 0.0580
4 606.3 0.05708
6 560.5 0.05451
8 528.8 0.05143
10 508.6 0.C4753

The larger values of / and their regular change are due to the
absence of a layer of carbon at the commencement of the experiment.

If we compare this table with the one given by Scuenck and
ZIMMERMANN for 445°

Time Pressure in 1 Po
f : k = — log ————
in minutes. m.m. Hg. t 2P:—P,
0 759
2 626 0.09369
4 548 0.08815
6 522 0.07090
10 510 0.04636

we notice that the very considerable change of 4 cannot be fully
explained by the absence of a layer of carbon but that there must
have been another disturbing factor.

From Scuenck and ZiIMMERMANN’s description it is evident that it
cannot be the absorbed hydrogen’), for this was introduced into
their apparatus only in the jist series of experiments and the second
series shows a still greater change.

For want of further particulars as to the research of ScHENcK and
ZIMMERMANN we cannot make any further suggestions as to the nature
of this second disturbing factor.

1) We found that H, is very strongly absorbed by finely divided Ni but gradually
expelled in vacuum. According to Sapatier and Senperens [G.r. 134 p. 514—516
(1902)] CO and Hy react with each other above 200°? in contact with finely
divided nickel according the equation; CO + 3H, = CH, + H,0,

( 72 )

We must say a few words about their plausible explanation of
the change from a wnimolecular to a bimolecular course, which
they thought they had discovered.

After having made the same supposition as we did for the uni-
molecular course namely

I. CO= C+ 0
LE CO - Oc= -CO,
they say:

Der Dissociation des Kohlenoxydes in seine Elemente wiirde dann
ein Oxydationsvorgang folgen. Spielt sich der letztere, wie bei dem
Sauerstoff im status nascens zu erwarten ist, mit sehr grosser Ge-
schwindigkeit ab, welche die Dissociationsgeschwindigkeit iibertrifft,
so findet man eine monomolekulare Reaction. Steigt bei hédherer
Temperatur die Geschwindigkeit des Dissociationsvorganges verhalt-
nissmassig mehr an als die des Oxydationsprocesses, so fallen
schliesslich die Vorginge zeitlich zusammen, und wir erhalten den
Eindruck einer bimolecularen ,gekoppelten” Reaction.

Auf diese Weise lasst sich fiir die auffallige Erscheinung eine
plausible Erklarung geben.”

But what has been overlooked here is that in order that the
reactions I and II shall give the impression of a unimolecular
reaction, the second must take place with immeasurabie velocity.
If this is true at a low temperature it is certainly so at higher
temperatures and even if the velocity of the first reaction has in-
creased this will be the only one which will be observed so long
as it proceeds with measurable velocity.

We are, therefore, inclined to contend that it is plausible to assume
that if the reaction is a unimolecular one at a low temperature
it cannot be expected that the order of the reaction will increase
at a higher temperature.

Summary of our conclusions:

1. The transformation of CO into CO, and C is unimolecular
for all the temperatures at which we have experimented: 256°, 310°,
340° and 445°.

2. Contrary to the result obtained by Boupovarp the reaction
is reversible at 445°.

3. The equilibrium constant could not be determined, as up to
the present, we have found that the same condition of equilibrium
is not attained starting from CO and from CO, + C.

Amsterdam, Chem. Lab. University, May 1903.

D a. “7? m -

Physiology. — “A new law concerning the relation between stimulus
and effect.’ By Prof. J. K. A. Werrtarm SaLromonson (6t
Communication). (Communicated by Prof. C. Wriyxurr).

(Communicated in the meeting of May 30, 1903)

The numbers used for testing our law* concerning the relation of
stimulus and effect, were for the greater part derived from lifting-heights
in eases of zsotonical muscle-contractions. During each contraction
the tension of the muscle is not perceptibly altered, likewise the
tension remained the same for all contractions belonging to each
single series.

What is the influence of any change of weight on the magnitude
of the constants? It is known already that the lifting-height changes
whenever the tension is changed in any manner. In the formula,
expressing the law for the relation between stimulus and effect

pe A am OO
the maximum lifting-height is represented by the constant A. As the
lifting-height denotes at the same time the maximum quantity of
external labour, we may state directly that the constant A will
certainly be changed at any alteration in the magnitude of weight.

As a matter of course nothing is known about the constant BZ,
neither could I find any indication about the constant C, representing
the threshold-value of the stimulus. It is thence of some importance
to investigate what will happen to the constants B and C, if we
alter the weight attached to the muscle.

To this purpose I have recorded a series of isotonical contractions
of frog-muscles at increasing stimulus. I generally used a gastroe-
nemius-preparation, which was stimulated by means of the nerve. The
experiments were made indifferently with muscles cut out or with
muscles through which the blood circulated in the normal manner,
these offering not the slightest difference between them.

The stimulus employed, was the current of charge of a condensator
of 0.001 microfarad. This was done by pushing down a morsekey
mounted on ebonite, thus connecting the condensator with two points
between which there existed a known potential difference; in so doing the
current of charge of the condensator was led through the nerve of the
preparation. When letting go the key the condensator was short-circuited
and discharged. The variable difference of tension was obtained by
means of a rheochord with platinum-iridium wire, calibrated with the
utmost care, through which a constant current was sent by a large
accumulator. By means of a variable steadying resistance care was
taken that the P. D. at the ends of the wire, measuring one meter,

amounted to exactly 1 Volt. This P. D. was continually controlled
by a recently calibrated precision-galvanometer of SreMENs and
Hatske. In this way every millimeter of the wire represented
0.001 Volt. By means of a vernier 0.1 millimeter could be read
without difficulty. Ever millimeter represented in this manner at
the same time one millionth part of a microcoulomb. The shocks
of the eurrent followed one another with intervals of 15 seconds.

I have succeeded, not without some trouble, in obtaining two
complete series, one of which I have entirely calculated and
inserted here. It consists of five separate series, each including
from eight to ten contractions, all taken from the same gastrocnemius,
but in each succeeding series the weight was increased.

Series. I. Weight 10 Gr.

a 19.15 = 0.0204 @ — 356.3
R Ecaic. Emeas. P
375 6.073 6.4 + 0.027
400 41.297 11.0 — 0.297
425 14.435 ie tate — 0.035
450 16.318 16.6 + 0.282
475 17.450 17 2 — .250
500 18.129 18.0 — 0.129
595 18.537 18.5 — 0.037
550 18.782 19 0 + 0.218
600 19.017 19.4 + 0.083
650 19.102 19.9 + 0.098
Consequently the mean observation error of each single observation
amounts to: py?
Sey
nu—3
Series II. Weight 30 Gr.
A= 138.91 B= 020213 C = 361.6
R Feate. Eyneas. P

375 4,521 4.4 == 0.424
400 10-473 10.2 + 0.027
425 13 491 13.5 + 0.009
450 15.439 15.4 — 0.039
500 Li c200 3 by (Bi ——= 0). (a
[550 17.883 18.3 + 0.417]
600 48.097 18.2 — 0103

800 18,206 18,2 — 0,006

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Proceedings Royal Acad. Amsterdam. Vol. VI.

( 75 )

The mean observation error amounts to 0,0876, if we neglect the
observation placed in parenthesis, which was not used for the calculation.
Series III. Weight 60 Gr.

A = 16.68 B = 0.0202 C= 317.0
R Ecate. Ene. Pp
400 6.4199 6.3 + 0.101
425 10.359 10.3 — 0.059
450 12.863 13.0 +- 0.137
475 14,376 14.2 — 0.176
300 15.290 15.4 + 0.110
550 16.174 16.3 + 0.126
600 16.496 16.4 — 0.096
800 16.674 16.6 — 0.074

The mean observation error amounts to: 0.1457.
Series IV. Weight 100 Gr.

A = 14.52 B = 0.0209 CU = 391.0
R Petia eds: c

400 2.490 2.4 — 0.060
425 7.386 7.4 +. 0.014
450 40.055 10.3 4. 0.245
AT5 12.011 14.9 — 0.414
500 13.032 13.0 — 0.032
550 13.997 13.9 — 0.097
600 14.336 14.6 + 0.264
800 14.492 14.5 + 0.008

The mean error amounts to: 0.1793.
Series V. Weight 160 Gr.

A = 10.74 B= 0.0198 C = 394.4
R Ecate. Ema:. P
4L0 4S 427 AO — 0.127
425 4.880 wae + 0.220
450 7.168 oD — 0.168
AT5 8.563 8.7 + 0.137
500 9.413 9.2 — 0.213
500 10.247 10.4 + 0.153
600 10.557 10.6 + 0.043
800 10.737 1052 — 0.037

The mean error amounts to: 0.1916.

Cie }

These series may teach us in the first place that no change
whatever in the general course of the curve is effected by the
magnitude of weight. The constants only are altered. The following
table will give an easier survey of the manner in which these
changes are effected. The weight is therein represented by Z, whilst
A, B and (’ stand for the three constants of our formula; in the
third column under AL V is given in gram-millimeters the amount
of work done multiplied by the writing-lever. This enlargement,
which in our case took place in the ratio of 5 : 1 will be denoted by V.

L A ALV B C
10 19.45 491.5 0.0204 396.3
30 18.21 546.3 0.0243 361 .6
60 16.68 1000.8 0.0202 377.0
100 14.52 1452. 0.0209 391.0
160 10.74 1718.4 0.0198 394.4

In this table we may observe:

1st. That at increment of weight the lifting-height diminishes, at
first slowly, afterwards more rapidly, an already well-known fact.

24. That the work done increases at first rapidly, afterwards
more slowly. As we know, the work would, if the weight were still
further increased, attain at last a maximum value and finally diminish.

37, That to all practical purposes the coefficient B remains
constant with imereasing weight. For its mean value amounts to
0.02052, the largest deviation being at the utmost 3.8 °/,, the most
probable value being: 0.02052 + 0.000395. Furthermore the devia-
tions are irregular in both directions, so we may conclude that
under ideal technical conditions the merement-constant would have
remained, to all probability, wholly unaltered by different weights.

4%. That the constant C, i.e. the minimum threshold-value augments
at increment of weight. I did not yet find this fact mentioned in
the literature within my reach. Still it may be easily verified even
without writing the record of a complete series, and it was proved
beyond any doubt within the limits of the experiment.

With regard to the series here communicated, we ought to make
mention of the fact that still another series was written, the weight
therein being 200 Gr.; this last series however showed technical
faults of too much importance, than that it could be employed for
the calculation of the constants.

desides the experiments on isotonical contractions with different
weights, I also investigated isometrical contractions. I believe that the

ee)

communication of two of these series will suffice. The first was
taken from the second gastrocnemius of the same frog that had
supplied us with the preparation of the foregoing series.

Series VI. Isometrical.

Y, MN key Be 00251 C = 384.0
R Ee tc. EB’ cas
400 3.163 3.2 + 0.037
425 6.611 6.4 — 0.211
450 8.449 8.4 — 0.049
415 9.480 9.7 +. 0.290
500 410.059 a9 — 0.159
550 10.567 10.7 + 0.133
600 10.726 10.7 — 0.026
800 410.800 10.8 0.000

o- == O1675:

Series VII. Isometrical.

As AZ B = 0.0096 C = 487.0
R Ecate, Exmeas. P
500 4.433 1.6 40.117
550 5.546 5.5 — 0.046
600 8.091 8.3 +. 0.209
650 9.666 9.9 + 0.234
700 40.639 10.2 — 0.439
750 41.249 44.4 — 0.141
800 41.615 44.6 — 0.015
850 11.846 14.9 4. 0.054
900 41.989 12.0 + 0 014
950 42.077 12.0 — 0.077

The mean observation-error amounts to: 9 = 0.2190.

Here again there is sufficient accordance to leave no room for doubt.

Meanwhile it is of importance to remark that both the coefficient
A and the effect H have in this series quite another signification as
they did in cases of isotonical contractions.

Here the maximum tension attained by a muscle during the
contraction, is measured by Z, whilst the highest tension, attainable

(78 )

for that muscle during any single twitch is indicated by A. And
in this case again it is shown that our law concerning the relation

between stimulus and effect enables us to represent with sufficient
accuracy the increment of effect whenever the stimulus is increased.
At present we only wish to state this fact without entering into
any details about its theoretical significance for our knowledge of
the course of isometrical contractions.

Meteorology. — At the chairman’s proposal it was resolved to
insert in the Proceedings the following Extract from the
Report made in the extraordinary meeting held this day by
the committee for awarding the Buys-Batuot Medal, consisting
of Messrs. Junius, HaGa, ZEEMAN, VAN DER Stok and WInp.

In the meteorological literature of late years one definite line of
development in this science has come to the front in such a degree
that, in the opinion of the committee, it is obvious to award the
Buys-BaLLot Medal for this time to a representative of this peculiar
branch of meteorological investigation.

The branch referred to is one of mainly experimental investigation.

In the opinion of some the material collected by the meteorologists
during a long series of years grows so dangerously extensive that, for
instance, Professor ScuustEer could not help in the last meeting of the
British Association expressing a wish, that the meteorologists might
stop their observations for some five years and during that time
might unanimously try to assimilate the materials in store and to
compose a reasonable programme. SCHUSTER in expressing a wish,
as to stopping the observations, cannot have been in full earnest, as
he will grant too that the series of observations, partly as material
for climatic studies, partly as a basis and a test for future theories
have a permanent value and should not be rashly interrupted.
Nevertheless it is true that, in order to prevent waste of capital
and labour and to avoid the loss of valuable data, it is very
desirable, in continuing former series of observations, to constantly
keep in view their value and not to plan others but on reasonable
grounds.

Yet, rather a short time ago the material referred to above,
however extensive, showed an important deficit. Most obviously it
did so, when considered as the foundation of a theory about the
great problems of meteorology, the general circulation of the atmos-

(79 )

phere and the nature of cyclones. When leaving out of consideration
the mountain-stations, whose importance for the purpose in question
is rather limited, the facts observed referred on the whole to the
lower layers of air. This is the reason, why opinions about the
movement of the air in its higher layers, and therefore about the entire
mechanism of circulation, opinions long ago defended by Dove, Maury,
Ferret, James THomson a.o. on the ground of their more or less
incomplete theories, could hold their own by the side of each other,
though in some respects not in keeping with each other. For the
same cause incorrect ideas about the distribution of temperature in
the atmosphere, closely connected with the circulation, could remain
in existence, and important inferences respecting this distribution,
derived from theoretical considerations — the Committee are in the
first place thinking of the interesting thermodynamic investigations
of von Bruzotp — could not yet be put to the test by direct observations.

As an extremely important step in the right direction, therefore,
may be considered the extension of the meteorological investigations
to higher layers of the atmosphere. And so much the more, with
a view to the remark made in connection with Prof. ScHusrEr’s
opinion, should this step be applauded, because it was taken with
the utmost care and with a sharply outlined purpose. This investiga-
tion, entered upon in a former decennary, has in the last ten years
been systematically set about and organized in an efficient way.

If there were one investigator, who could be considered as the
only proper founder and promoter of this new branch of meteoro-
logical investigation, the Committee would not hesitate to design
him for the Buys-BaLtLot Medal. This, however, being not the case,
but there being many explorers, who in the higher ranks have
contributed to its development, it seems advisable to award the medal
to him among so many, who distinguished himself most by his work.
Here, again, it was not easy to choose, the conditions, under which
the labour was done, showing large differences and a decisive rate
of comparison being wanting.

On one side the attention was inmediately drawn to A. LAWRENCE
Rotcu, the energetic director of Blue-Hil] Observatory, founded and
maintained through private means. He was the first to make use,
on a large scale and systematically, of kites, provided with registering
instruments, to become acquainted with the values of meteorological
elements several kilometers high in the air and to put beyond all
doubt the practical usefulness and appropriateness of this method.
Moreover he set the example of using steamships in the observations
with kites, to overcome the difficulty of too great or too slight a force

Proceedings Royal Acad. Amsterdam. Vol, VI.

( 80 )

of the wind, and finally planned an expedition with a purpose of
trying by experiment with kites on board a steamship to make
sure about the movement of the air above the regions of the
trade-winds.

Another investigator, working under similar conditions with no
less skill and success, is LL. TrtsskrENc DE Bort, the founder and
proprietor of the “Observatoire de Météorologie Dynamique” at
Trappes. Having been already for a long time organising ascents
for meteorological purposes this excellent investigator im later years
started his ‘“ballons-sonde” in France and in foreign countries in
large numbers, to record temperature and moisture of the atmosphere
at a height of 10 to 15 kilometers. In the meanwhile he was inde-
fatigably working at the improvement of the recording-apparatus.
Now, for nearly a year, he is — supported by the Swedish and
Danish Governments — very successfully engaged in a systematic
examination, by means of kites and balloons, of the atmosphere
above Jutland and the Danish Isles.

On the other side much respect and admiration are due to the
perseverance and talent, with which H. H. HipDxEBranpsson since
1873 has been trying by means of a large system of stations to make
simultaneous observations of clouds and to get from these the knowledge
of the movements of the upper air, necessary for a development of
the theory of general circulation. He began with observations in
Sweden, but knew by pointing to first results of obvious importance
how to rouse gradually interest for the labour with the meteorolo-
gists of nearly all nations, especially with the “International Meteoro-
logical Committee.’ This led to the nomination of an international
committee for the observation of clouds and in consequence to the
publication of an international cloud-atlas, in which it was principally
his nomenclature of the different forms of clouds that was adopted
and elucidated by plain illustrations. Finally it led also to the
issuing of simultaneous observations all over the civilised world
during a whole year, the ‘“cloud-year” 1896/97.

Very important are the results which have been derived by
HILDEBRANDSSON from the materials gathered. Some current ideas
about the movements of the upper air seem to be entirely subverted.
They have shown e.g. that in the (northern) temperate zone both
the upper and the lower air on an average perform a whirling
movement in the sense of the earth’s rotation, round the pole as a
centre, but with a centripetal component in the lower, a centrifugal
component in the higher layers, a movement, therefore quite different,
from the southwestern lower current and the northwestern higher

( 81 )

current, almost generally adopted hitherto. Of the Report about the
cloud-year only a first part has yet appeared.

Mention must also be made of Professor H. Hereuse.1, the impulsive
and able chairman of the International aeronautic Committee. In
this quality he has contributed much to promote a_ systematic
examination of the higher air and has taken the initiative for the
simultaneous international ascents of balloons, which since November
1900 are being undertaken on the first Thursday of each month
from some ten stations. Moreover he has by his own investigations
very suecessfully contributed to the common task.

Though it would be easy to mention some more meteorologists,
to whom the new branch of investigation owes nearly equally much,
it seems to be difficult, after all these men of great merits, to
indicate another who should more than one of them have advanced
Meteorology by his labour in the line considered. Accordingly the
Committee do not intend to name one person, but wish to recommend

for the Medal two investigators — who are, however, one in their
work — viz, the editors of “Die Wissenschaftlichen Luftfahrten des

deutschen Vereins zur Foérderung der Luftschiffahrt, in Berlin’,
RicHarD AssMANN and ArruurR Berson.

The reason which has determined the Committee to hold these two
explorers as more than any one else worthy of the distinction, is
especially the high value of the said publication. There the editors
have laid down the foundations, the course and the results of their
highly important series of investigations, at the same time clearly
showing their great perseverance and earnestness in their exertions,
their great scrupulousness and punctuality in the accomplishment of
their task. This publication, in which moreover numerous new
instruments and resources are described and results communicated
which immediately have appeared to be of great value, is undoubtedly
a work of classic importance.

The balloon-expeditions, described in this work, were made from
1888 to 1899 and are divided into 6 preparatory (1888—1891),
40 principal (1893—94) and 29 supplementary expeditions; besides
experiments were made with a registering captive balloon and with
registering free balloons. In reality the scientific aerial voyages,
made at Berlin, have not been finished herewith. Among those
not described in the work we mention the rightly well-known
“Hochfahrt” of Berson and Sérinc, undertaken especially to verify
the instruments of the registering free balloons by comparing their
records with eye-observations made in a manned balloon started at the
same time. The free balloons being meant for the greatest heights

( 82 )

(twenty kilometers and more), the manned balloon, in which the parallel
observations were made, had to rise as high as possible. It was
planned to go as high as ten kilometers and reached even a height of
nearly eleven.

It is easy to see that expeditions to such a height cannot be free
from danger, if we think of the atmospheric pressure of = 200 mM
and of the temperature to below —40°C., which have been observed
at these heights. The homage then, which the committee wish to
be paid to BERSON, applies partly to the courage and the intrepidity,
with which this explorer has frequently risked his life in behalf of
the uncommon task, which he imposed upon himself in the service
of science.

The whole work, published in 1899/1900, consists of three big
quarto volumes. The first of these is partly devoted to an historical
and critical survey of the development of scientific aerial voyages,
partly also it deals with the construction of balloons and instruments
and with the methods of observation and reduction. Moreover it
contains the data as to the tracks covered by the balloons and the
figures got by the observations. The second volume offers an ample
description of the separate aerial voyages. In the third the obser-
vations are sifted and discussed, being treated under different heads
as: temperature of the air, moisture, formation of clouds, velocity
of wind, direction of wind, radiaton, atmospheric electricity. This
volume winds up with a chapter, written by von Brzoxp, and entitled:
“Theoretische Schlussbetrachtungen”.

Here we should not omit mentioning the names of Bascuin, Born-
stern, Gross, Kremser, StapE and Sitrinc, who have all of them
contributed to the composition of the great work and also personally
taken part in the scientific aerial voyages.

A short survey of the provisional results of a more general tenor
must not be left aside here.

1st. Formerly it has sometimes been thought that the temperature
in the higher layers of the atmosphere approached a limit of — 35
to —50°C.; these investigations however do not at all point to the
existence of such a limit. Temperatures also, considerably lower than
the above, have come to light.

2-4 In the lower layers of the atmosphere the temperature, in
rising, diminishes on the whole less rapidly than would answer to
convective equilibrium. Above 4000 M, however, the rate of decrease
grows larger and seems to approach that value of nearly 1° C. per
100 meters as a limit. This is in keeping with a supposition of von
BrezoLbp based on theoretical grounds, whilst the behaviour in lower

( 83 )

layers can be accounted for by the influence of radiation, conden-
sation and evaporation.

The distribution of temperature found in this way, is satisfactorily
in agreement with the one found by Trisserenc pe Bort, but dis-
agrees considerably with that which was formerly determined by
GLAISHER.

3°. The diurnal variation of temperature has at a height of 2500
M. shrunk down to less than ‘/,, of its amplitude at the surface of
the earth.

Of the annual variation of temperature the amplitude decreases
rapidly in the lowest layer of 500 M. Higher on it is rather
a retardation of the maximum and minimum of temperature than
a decrease of amplitude, which is still obvious. At a height of
4000 M the highest and lowest temperatures seem to occur about
the middle of September and March.

The non-periodical changes of temperature in the higher layers
are hardly less intensive than at the surface of the earth.

4th. Frequently low, but also sometimes higher in the atmosphere,
there are layers in which the temperature increases instead of
decreasing with the height. ‘“Inversions’ to an amount of even 16°C.
have been observed.

Not seldom there are also layers, in which the temperature in
rising diminishes more rapidly than would answer to the convective
equilibrium. It is very remarkable that these layers, which obviously
tend to provoke a state of unstability in the atmosphere, are often
of a great thickness, reaching even 2500 meter, for instance.

5't, In accordance with results which Hann came to in the Alps,
it has appeared that above Middle-Europe, both in winter and in
summer, the temperatures at equal heights in anticyclones are in
general higher than in cyclones — this, at least, holding good for heights
up to 8 KM. This result tends to corroborate the conviction of most
meteorologists that the cyclones with their ascending and the anti-cyclones
with their descending currents of air cannot as a rule simply owe
their existence to differences of temperature. by still more recent
investigations it has appeared that the rate of decrease of temperature
above the anticyclones, though at first smaller, is at greater heights
greater than the above cyclones, so that it remains possible that in
the very high layers of the atmosphere the temperature above the
anticyclones is lower than above the cyclones.

6th. In most of the cases several layers of a quite different nature
and origin were clearly indicated in the atmosphere.

7, In rising, the moisture of the atmosphere generally decreases

( 84 )

more than Hann had derived from observations of mountain-stations
and from those made by GLaIsHER.

sth. Important data have been acquired about the formation and
origin of clouds, in connection with the distribution of the meteoro-
logical elements.

gth. The velocity of wind increases with the height, strongly
in the layers below 1000 and above 3000 M, less so between these
two heights. At a height of 5000 M it was on an average
4.5 times as large as at the surface of the earth. Important data
were also acquired about the difference in the direction of the wind
between the lower and higher parts of the atmosphere.

10%, Thermally and electrically the surface of a layer of clouds
has a similar effect upon the region above it as the surface of the earth.

11». The rate of decrease of electrical potential seems to diminish,
when rising, and even to vanish entirely in the. higher regions of
the atmosphere. This result, arrived at from only few observations,
has afterwards been corroborated.

It is not only the initiative in and the organisation, guidance,
partly also execntion of, this interesting investigation, which are
mainly due to Assmann. We also owe to him the construction of the
aspiration-thermometer and -psychrometer, which has first rendered
possible trustworthy observations as to temperature and moisture
under the most different circumstances. It has appeared that in
former balloon-expeditions (of GLAISHER e.g.) errors to the extent of
even 15°, owing to radiation, must have occurred in the indications
of the thermometers.

Finally we ought to mention the introduction by Assmann of the
highly appropriate ‘Platz’-balloons made of caoutchoue, which as
free registering-balloons can reach even a height of 20 to 30 kilo-
meters; there they burst and, provided with a parachute, return to
the earth very slowly with the instrument they convey.

Whrat is said above may be a sufficient reason for awarding the
medal to AssMANN and Brrson; yet the committee cannot omit
referring to the excellent work which is being done in the aero-
nautie observatory at Tegel near Berlin, founded by AssMann in 1899
and being directed by him. Here daily observations are made for the
examination of the upper air with the aid of kites, kite- and Platz-
balloons. The results are published daily and, since the beginning of
this year, as graphic reviews also monthly.

If an examination of the higher layers of air can furnish many
important data more for our insight into the mechanism of atmos-
pherie phenomena — which is hardly to be doubted — such a

( 85 )

systematic train of working as is adopted at Tegel seems above all
things to be conducive to that purpose, especially if the example
given there be followed in a sufficient number of stations elsewhere.

In the Tegel observatory Berson as “stiandiger Mitarbeiter’ is stea-
dily cooperating with its director.

One of the more recent results, arrived at in the Tegel obsery-
atory, may still be mentioned here. In the spring of 1902 registering
balloons recorded between 12 and 16 kilometers an inversion
of temperature to an amount of 9°. This seems to point to an
equatorial current in those parts of the atmosphere which, even
higher than the region of the cirrus-clouds, could not but eseape
HILDEBRANDSSON’S Observations.

Almost simultaneously an inversion was observed above France
by TEISSERENC DE Bort at a height of more than 10 kilometer.

The above will certainly be sufficient to give an idea of the nature
and the importance of the new field and the new methods of invest-
igation and to convince you that the development of these methods
owes very much indeed to the two investigators, to whom we last
drew attention.

Concluding the Committee beg to report that in their unanimous
opinion the Buys-BaLLot Medal should be awarded to RicHarp Assmann,
Director of the Aeronautic Observatory at Tegel, and Arruur Berson,
permanent collaborator to the same institution, as a homage to
the great services they have rendered to the development of Meteo-
rology, not only in their just mentioned qualities, but also and
especially as editors of the work entitled: ‘Die Wissenschaftlichen
Luftfahrten des deutschen Vereins zur Férderung der Luftschiffahrt”’,
and as those who have had the greatest share in the investigations
described in this principal work.

Botany. — “On a Sclerotinia hitherto unknown and injurious to
the Cultwation of Tobacco” (Sclerotinia Nicotianae Ovp. et
Koning). (Postscript). By Prof. C. A. J. A. OupEmans and

C. J. Konine.

With regard to the small dimensions of the cups (apothecia) of
Selerotinia Nicotianae, as sketched in our essay (breadth 0,8, depth
0,2 millimetres) we think it worth while to point out that much
stouter cups were obtained from sclerotia which on the 9" of
March ult. were sown out afresh in the known manner in different

( 86 )

kinds of earth (forest-humus, garden-earth, sand, pounded autumn-
leaves of Quercus and Fagus).

After the experimental dishes, covered with glass, had been placed
on a windowsill outside and for 8 weeks had shown no sign of
life, stemmed cups were found on the sclerotia in ail of them,
differing from those obtained formerly in having greater dimensions.
Instead of 0.8 mill. wide and 0.2 deep, the cups were now 1.4—5
mill. wide and 0.2—0.3 mill. deep; the stems on the other hand
were much shorter, varying between 1.5 and 9 mill. against
4—6 cent. in March.

The new numbers agree more with those of other species of
Sclerotinia and can only, we think, have been produced by the
influence of a milder temperature and corresponding increased

metabolism.

The greatest number of cups, sprung from one sclerotium, was 12,
as may be seen in the illustration.

The special features of cups and stems, among which the swelling
under the cups, resembling an apophysis, and the rough surface of the
stems, were present in the newly gained specimens as in the former
ones. Finally it must be stated that the sclerotia with which the
new experiments were made, originated from pure cultures and
that between the microscopical structure of the former and the new
cups and stems no difference was found.

Physiology. — “The cause of sleep.’ By Dr. A. Gortmr. (Com-
municated by Prof. C. Wink LER).

The different well-known theories about the origin of sleep have
hitherto not furnished us with a satisfactory explanation either for
the want of sleeping or for the sleeping state. By anaemia of the
brain quite other symptoms are often presented than by want of
sleep, and the former has been recognised as a phenomenon of repose
even without sleep. The interruption of continuity in the conduction
from the brain to the remaining part of the nervous system was
considered already by Purkinje as the primal cause of sleep and has
been treated of afterwards by Lovis MaurHner in an essay on ona.
In the latter the hypothesis was put forward that the interruption
of the contact occurred in those places where, in cases of Polio-
encephalitis haemorrhagica, the focusses of disease were found *),
This theory has more recently found a powerful supporter in Duvat,

1) Wien. Med. Wochenschrift 1890 no 23--97,

‘gthss

( 87 )

who in 1895 defended the thesis that the interruption of contact is
caused by retraction of the end-arborisations of the neura.

This retraction of the end-arborisations however has never yet
been observed, and might be, if oceurring, a consequence of sleep,
but the investigations of Apatuy and Betuer (1894), who hold that
the fibrils of different neura pass into one another, have rendered it
probable that the causation of sleep is not to be found in this domain.

By the third theory the origin of sleep is ascribed to the effect of
so-called fatigue-substances, which are presumed to be produced by
different functions during the waking state.

Injections of lacteal acid, the sole known fatigue-substanee, mean-
while offered only a negative result, moreover this theory is not
quite in accordance with the facts:

1st. Because during sleep principally such functions are disturbed
as are dependent on momentaneous stimuli, i.e. the psychical fune-
tions, whilst other functions dependent on stimuli (nutrition ete.)
received during the waking state, e.g. respiration, heart-movement,
secretion of sweat and urine, digestion ete., are influenced in a lesser
degree and may be brought likewise to decreased intensity by repose
without sleep.

2nd. Because the want of sleep and the duration of sleep are
neither of them adequate to the performed psychieai and physical
labour.

3'4, Because sleep may be interrupted at any time by a strong
stimulus, the functions operating immediately afterwards in a perfectly
normal manner.

4th. Because among psychical functions those, originating partly
in preceding stimuli, still remain possible (dreams).

5th, Because in the case of a new-born babe the want of sleep
and the duration of sleep both diminish with increasing functions.

The insufficiency of these different theories about eS origin of
sleep have led the physiologist Leonarp Hitt to the conclusion: the
causation of sleep must still be regarded as metaphysical °),

Meanwhile physiological psychology had taught us that the waking
state is consequent on the conduction of stimuli from the surround-
ings to the central nervous system, and as regards man to the
psychical centra, a fact in perfect accordance with the experience
that the originating of sleep is favoured by darkness, monotonous
sounds and silence. The famous experiment of Stritmpriy *), who

1) The Lancet 1890. I. p. 285.
2) Deutches Archiv. fiir Klin, Medicin, 1878 No. 22.

( 88 )

transported an almost wholly anaesthetical woman into instantaneous
sleep by shutting her one eye and her one ear still capable of
seeing and hearing, and who caught from another similar patient the
expression :

,Wenn ich nicht sehen kann, dann bin ich gar nicht”, furnished
another inducement to seek in cessation of stimuli the causation of sleep.

The well-known manner in which patients are transported into
hypnotical sleep, and the fact that by eliminating all external stimuli,
animals may be brought to a state closely resembling sleep, both
point to the same conclusion.

Ziznen schreibt:') .Wahrscheinlich ist das Wesentliche bei dem
Zustandekommen des Schlafs, der Abschluss ausseren Reize und die
Ermiidung der Rindenzellen.”

Hermann 2) Die naihere Ursache welche die Grosshirnrinde ausser
Thiitigkeit setzt ist unbekannt. Die meisten Angaben itber Verande-
rungen im Gehirn sind unbewiesene und zum Theil héchst unwahr-
scheinliche Vermutungen. Die oben angegeben Thatsachen zeigen dass
Sehlaf und Wachen im engsten Zusammenhang mit den Sinnesein-
driicken ‘stehen und man k6nnte sagen dass zur Erhaltung der gewohn-
lichen Thiitigkeit der Rinde d. h. des wachen Zustandes bestandige
Sinneseindriicke ndthig sind, womit aber das Rathsel keineswegs
gelst ist.”

SprUMPELL concludes his well-known article in the Deutsches Archiv *)
with these words:

Eine Reihe von Erseheinungen wie das mégliche Kinschlafen trotz
stiirkeren dusseren Reize, die Periodicitat u. a. bediirfen zu ihrer Erkla-
rung noch andere Voraussetzungen.”

Sleep by intoxication (narcotics), and sleep in some cases of brain-
disease, may be explained by the interrupting of the conduction of
stimuli towards and within the psychical centra. The almost un-
interrupted sleep of the new-born babe also may find a similar
explanation in the still unfinished cortex.

It becomes moreover difficult to continue searching for the causation
of sleep in a peculiar state of the cortex, since dogs, whose brain
had been taken away, have been found to present a_ relatively
reeular alternating of sleep and waking.

Sleep therefore may be said to be caused cither by disease, by
intoxication, or by cessation or decrease of stimuli from the sur-

roundings.

1) Tu. Zienen. Leitfaden der Physiologischen Psychologie p, 218

2) Hermann, Lehrbuch der Physioiogie, p. 460,
3) D, Archiv f. klin, Medicin, No 22 p, 350,

iia

ee
i‘ .

( 89 )

Normal sleep is not caused by disease, neither, fo our knowledge
at least, by intoxication, consequently it may be caused by cessation
or decrease of stimuli from the surroundings, and in examining these
surroundings, we observe the periodically operating cause of sleep
in all nature, in

The settiny of the sun

with which numerous stimuli either disappear or cease to operate.
The peculiar characteristic of sleep, the disturbed funetions, may be
satisfactorily explained by the decrease of stimuli occasioned by the
setting of the sun.

Many functions of the living organism depend on sunlight, and
when sunlight dissappears, their intensity diminishes or they may
even cease altogether.

The assimilation of plants, the search for nourishment by animals,
the receiving of stimuli by which psychical functions are originated,
all these are dependent on sunlight.

The phenomena of sleep having been once recognised as symptoms
of decreased functions, all researches for the species of animals in
which sleep begins, must necessarily remain fruitless, because most
functions of both plants and animals in general are subject to a
change, corresponding to the alternation of day and night.

These stimuli which still continue, operating during sleep, partially
entertain all functions, the psychical ones included, as we are made
to know by experience when dreaming.

The want of sleep in man is a quality inherited from the animal,
and it does not appear so directly dependent on the setting of the
sun as is the case in vegetal and animal kingdom, only because
man continues his struggle for life with the aid of artificial light.

In my opinion, the setting of the sun suffices to explain the
periodicity of sleep, and going to sleep notwithstanding the excita-
tion of still extant powerful stimuli, must be accounted for by
heredity, and I think the solution of the enigma mentioned by
HERMANN, is found here.

The simplicity of this answer to the question about the causation
of sleep, presenting itself as a matter of course and reminding one
of the egg of Columbus, is only an apparent one, because the results
of years of psychological researches have taught us to seek for this
causation outside the functions, physiology having sought vainly for
an explanation to be furnished by the functions themselves.

The existence of night-animals may be explained in this way that

( 90 )

in the struggle for life the dangers threatening them in the day-time,
have led certain species of animals to shorten the day and adequately
to lengthen the night, in the course of which process qualities were
slowly developed, enabling them to carry on with more surety
that struggle at night, whilst the want of sleep was satisfied during
day-time. |

As regards the phenomena of winter-sleep and summer-sleep, both
may be considered as a state of torpor, being no real sleep, and in
all probability originated again in the struggle for life by certain
animals digging themselves into the earth, after their having been
driven away by stronger species to regions, either too cold or too
hot. Only the strongest individuals survived, and after the lapse of
a long period, their progeny may have gradually attained to the
power of remaining alive, for a definite space of time, almost entirely
without functions, as an hereditary quality, no longer dependent on
the influences of heat and cold.

As impossible as it would be for modern man to be kept from
sleeping for a somewhat longer period by means of artificial light,
as impossible it would be to keep a winter- or summersleeper out
of its state of torpor by means of heat or cold, once the season for
that state having returned.

It is not known to us whether amongst animals living under-
ground or in the deep of the sea, there exist any species capable of
living without sleep.

Until a period not so very long ago, sleep for the greater part
of humanity was wholly determined by the sun. During summer man
slept little, during winter much, and even in our modern times the
peasant does not consult science about the term of duration of his
sleep, as his period of sleeping is determined by the sun. The stimuli
that keep him awake (issuing from his soil, his cattle and his machinery),
all cease to operate with the setting of the sun, consequently he
goes to sleep and is awakened again by the stimulus of the sunlight,
either directly or indirectly by intermediary of animals.

In modern times the way in which by far the greater majority
of men are living, gives rise to the question whether the want
of sleep in man may not perhaps wholly or partially disappear
in the course of the struggle for life, because we know that inherited
qualities tend to disappear, when they are no longer of use in that
struggle.

Parily at least this want of sleep has already been conquered in
many instances: numerous men are night-animals, sleeping only for
a short period in the day-time, others continue to enjoy unimpaired

» be

re.

( 91 )

health, whilst sleeping only for three or four hours out of the
twenty-four. Whether in coming generations sleep may be destined
to vanish altogether, cannot be predicted with any certainty, because
we don’t know the exact significance of sleep in the struggle for
life in its connection with the longer or shorter term of duration
of human life, and because on the other hand we are not sure
whether some physiological process does not perhaps continue to
operate in the human organism, parallel with and dependent on the
alternating of day and night.

The fact may be simply stated that man is the only creature
living upon the surface of the earth, capable of making himself no
longer dependent on the setting of the sun, by means of artificial
light, thus foreing the most intense stimuli to act without interrup-
tion on his nervous system. From the point of view of modern
science therefore the possibility cannot be excluded, that in some
remote future a race may exist, descended from man that will
have conquered the want of sleep, the term of duration for indivi-
dual life, however, having become shortened. In this way the
knowledge of the primal cause of sleep in nature, opens a distant
prospect of the entire disappearance of sleep in man, who nevertheless,
because of reasons mentioned already, will never be able to pass
the first weeks of his life in a state of waking.

Leiden, June 1903.

Chemistry. — “The condition of hydrates of nickelsu’phate in
methylaleoholic solution.” By Prof. C. A. Lopry pr Bruyn and
C. L. Junerus.

1. It is known that the old question of the relation between a
dissolved substance and a solvent has been answered from two points
of view. Whilst particularly of late years, some have defended the
theory that the solvent is, as it were, merely a diluent which keeps
the dissolved molecules apart without entering into a closer relation
with them, others have upheld the view that the molecules of the
dissolved substance are most decidedly more or less strongly united
to those of the solvent. Owing to the development of the ionic theory,
the first assumption is now the more universal one particularly for
solutions of salts and their hydrates. On the other hand it must be
acknowledged that no strong evidence has ever been brought forward
to show the existence of hydrates of salts in an aqueous solution
even though it seems natural to presume that to a certain extent

( 92 )

hydrates are already present as such in solutions from which they
crystallise and which are in equilibrium with them,

2. It might be expected that the study of solutions of hydrates
of salts in a solvent other than water would contribute to the eluei-
dation of the problem. In view of this, one of us *) had already been
engaged some ten years ago with determinations of the elevation of
the boiling point caused by the introduction of hydrates of nickel-
sulphate into absolute methylalechol. The preliminary conclusion
then arrived at, led to the assumption that a definite quantity of the
water (about 3 mols.) remained in combination with the NiSQ,.

In calculating the results of the experiments no notice was taken
of certain jfuctors, the importance of which was unknown or but
little appreciated in 1892, namely the occurrence of electrolytic disso-
ciation, even in alcoholic solution and the influence of a dissolved
volatile substance on the elevation of the boiling point. For this reason
the former experiments were recalculated and partly extended.

3. In view of the last mentioned fact, we started with the deter-
mination of the change in the boiling point caused by the introduction
of small quantities of water into absolute methylalecohol. The fol-
lowing result was obtained (Barometer constant).

Evelation of Elevation
CH,OU. HO: Boiling point for 1 pCt.

5d.16 Grm. 0.5720 Grm. 0.291 0.281

54.89 0.6799 0.353 0.285

54.62 0.7866 0.416 0.289

54.3 0.8877 0.457 0.280 Average
54,08 1.0378 0,528 0.275 0.281
53.81 | OAD 7 0.627 0.278

33.04 1.3831 0.725 0.281

53.27 1.5565 0.819 0.280

These experiments, therefore, confirm the conclusion that water
added to methylalcohol causes an elevation of the boiling point from
the commencement and that no minimum boiling-point occurs
here as in the case of ethylaicohol and water (containing about
96 percent of alcohol) *).

') Lopry pve Bruyn, Handelingen 4e Natuur- en Geneeskundig Congres, Gro-
ningen, 1893, p. 83. >

2) W. A. Noyes and Warre.t. J. Amer. Ch. Soc. 23. 463 (L901). Sypney Youne
and Emity Fortey, J. Ch. Soc. 81. 717 (1902). The addition of 20 milligrs. of water to
50 grms of methylalcohol caused a perceptible elevation of the boiling-point,

( 93 )

4. As regards the extent of the electrolytic dissociation we observe
that although we have not succeeded in determining the amount ‘)
the experiments have shown that it is very small. Its existence,
moreover further strengthens the conclusion to which the experiments
have led, namely that a certain proportion of the water remains in
combination with the nickelsulphate.

5. The experiments have been made as before, in the first place
with the hydrates NiSO,, 6 aq. and NiSO,, 7 aq.; a single experiment
was made with NiSO,, 3 H,O 3 CH, OH.

The manner in which the calculation was conducted will be seen
from the following example: « represents here the number of mols.
of water abstracted from the hydrate ’).

59.9 gr. CH,OH, 0.7723 gr. NiSO, 6 aq.
(mol. elevation of b. p. of meth. alc. 8.8. Mol. weight NiSO, 6 aq. = 262)

observed elevation of boiling point = 0*.165
Calculated elevation of boiling point supposing all the water
0.7723 100

ad remal in combinati - 8.8 — 0°.0438
had remained in combination 269 x< 506 x 8.8 0°.043

elevation of b. p. caused by water delivered by the salt = 0°.122

0,122
With this corresponds a quantity of water in solution of Waal al Pe
The abstraction per mol. of dissolved hydrate is, therefore,
__ 0,122 262 1
0,599 — = 4.9 mol. H,O.
= 987 = as 0,7723 4s 18 .
The results of the following experiments were
Methylale. NiSO,6aq. Elevationofb.p. z.
58.5 gr. 0.608 gr. 0°.143 5.4
60.5 » 0.694 » 0.146 4.9
60.5 » 0.551 » 0.125 ee

Average from four experiments 5.1
NiSO,, 7 aq. gave the following results:

Meth. ale. NiSO,4, 7 aq. Elevation of b. p. 2.
60.7 0.432 0.9102 6.25
60-7 0.463 0.109 6.2
60.3 0.449 0.110 6.45
60.6 0.481 0.105 5.65
61.7 0.341 0.080 6.3
61.7 0.560 0.120 3.7

Average 6.1

1) See next communication.

2) Strictly speaking, the elevation of the boiling point caused by the same
amount of water will be modified in a slight degree by dissolving the salt in
methylaleshol. This influence was not taken into account; the slight amount of
electrolytic dissociation (see next article) was also disregarded.

( 94 )

From both experiments the conclusion may be drawn that the
hydrates of nickelsulphate when dissolved in methylaleohol only .
retain one mol. of water of crystallisation. An experiment made with
NiSO,3 H,O 3 CH,O gave as result # = + 2 and thus confirmed
the above conclusion.

6. If now in a one per cent solution of the hydrates of nickel-
sulphate in methylaleohol the salt still retams one mol. of water
notwithstanding the extreme dilution, it may in our opinion be taken
for granted that such is also the case in aqueous solutions. And
now proceeding to concentrated and saturated solutions of hydrates
we arrive at the notion that the salt-molecule enters into a more
or less fixed combination with the water molecules and that, there-
fore, the hydrates (several simultaneously) are already present as
such to a certain extent in the solutions from which they crystallise.
Probably there exists in such a system a highly complicated condition
of equilibrium.

Some years ago PickERING has proved by determinations of the
freezing points of solutions of sulphurie acid (of different concen-
trations) in glacial acetic acid that a definite amount of water remains
in combination with the sulphuric acid.

Amsterdam, June 1908. Organ. Chem. Lab. University.

Chemistry. — “The conductive power of hydrates of nickelsulphate
dissolved in methylalcohol.” By Prof. C. A. Lopry pe Bruyn

and Mr. C. L. Juneius.

The determination of the conductivity of hydrates of nickelsulphate
dissolved in methylaleohol is important for two reasons. Firstly,
in order to ascertain whether the condition of the dissolved substance
is modified after a shorter or longer period; secondly to ascertain
if possible (in connection with the preceding paper) to what extent

the salt is dissociated electrolytically.

I. As regards the first point we recall the phenomenon that after
dissolving the sulphates (of Cu, Zn, Co, Mg, Ni) in absolute methyl-
ulcohol the solutions (some rapidly, others slowly) deposit ') lower
hydrates or mixed alcoholhydrates ; for instance from a solution of

1) Losry pe Bruyn, Recueil, 14, 112 (1892) and Handelingen, 4c Natuur- en
Geneeskundig Congres, Groningen, 1893, p. 83.

ed a ee i a

( 95 )

NiSO,7 aq. or NiSO,6aq.a@ we obtain after some time crystals
of NiSO,3H,0.3CH,O. It is however not impossible that, after
dissolving, the hydrate loses water with a certain rapidity and com-
bines with the methylalcohol so that a definite stationary condition
is not attained immediately. If such were the case we might expect
that this modifieation in the condition of the solution would become
evident, say, by a change in the conductive power.

In carrying out the experiments the conductive power was first
determined as quickly as possible after preparing the solution (after
about 7 minutes). A portion of the solution (which contained about
5°/, of the salt) was set aside at the ordinary temperature or boiled
for 15 minutes. In the Jatter case the solution was made up again
to its original weight. In no cases was a change of the conductivity
observed. The same applies to the methylaicoholic solutions of the
sulphates of copper and magnesium. The latter exhibits the peculi-
arity of becoming turbid on heating to 60° and of clearing again
on cooling; it was again proved that after heating at 60° for 7
minutes and subsequent cooling the conductive power remained
unchanged.

From these experiments we may therefore draw the conclusion
that a stationary condition has very probably set in immediately
after the sulphates have dissolved in the methylaleohol and that
the crystallisation of lower hydrates or of alcoholhydrates, which
sometimes occurs after a long time, must be looked upon as a
phenomenon of retardation.

2. Secondly, the conductive power was determined of NiSO, 7 aq.,
NiSO, 6 aq., NiSO, 3aq, 3CH,O and NiSO, 1 aq. dissolved in absolute
methylaleohol and at decreasing concentrations. As observed, these
determinations were made with the object of studying the extent of
the electrolytic dissociation of nickelsulphate in methylalcohol (in
connection with the contents of the preceding article). Previous re-
searches, particularly those of Carrara, had led to the result that, at
least with salts composed of univalent ions, the electrolytic dissociation
is very considerable, in many cases about */, to */, of that in aqueous
solution. In the case of salts with a bivalent ion the conductive
power in methylaleohol is considerably smaller *); that of salts
composed of two bivalent atoms has, as far as we are aware, not
yet been investigated in methylalcohol solution.

The experiments were made at 18° according to the usual method
of KonLrauscH—OstwaLp; the methylalcohol (sp. gr. 0.7397 at 18°)

1) Correrti, Gazz. Chim. 33, 56.

Proceedings Royal Acad. Amsterdam. Vol. VI.

Was again fractionated after addition of some sulphurie acid; the
ws have been corrected for the small remaining conduetivity of the
alcohol.

With NiSO,6aq. pure methylaleohol was used as diluting agent
in one series; in a second series an alcohol was used containing the
same amount of water as that generated by the hydrate on dissolving.
The methylaleohol used for the experiment with NiSO, 1 aq. had
been purposely rectified over anhydrous coppersulphate.

The following table contains the results of the measurements.

NiSO,3 M. | Ni SO, 7 aq. Nif£O, 1 aq.

Ni SO, 6 aq. | Ni SO, 6aq.

Anhydrous C Ha on tea Anhydrous Anhydrous
CH; OH 0/9 He O. CH; OH CH; OH. CH OH.
b BH | Ap] p | Ap | #& | Au] # | Au fe Au
|
ee ee ee Se eee
8. 13.92 3.01 | a Se) ao
— 0.66 | — 0.58 = — 0.66 =
fae 2 56.| 263%) 2.54 2.56 —
— 0.63 | — 0.55 — 0.60 | —0.65 -
32 1.93 2.08 | 4.94 1 354 2.14
== (037) | — 0.30 — 0.32 — 9.38 —- 0,32
64 164° | 1.78 1.62 1D Delo
| — 0.13 — 0.06 —0A3 —0.15 — 0.09
128 1.48 | dale 149 1.38 1.70
'+0.02 | + 0.15 + 0.02 + 0.05 + 0.06
956 | 1.50 4.87 454 1.43 4116
+ 0.21 | 10.43 +017 SI). 10.95
AD, del 771 2.30 | 1.68 1.63 2.01
+04 | +- 0.75 + 0.20 +0 64 + 0.55
1024 | 2.42 3.05 1.88 O07 2.56
+ 0.52 |-- 443 + 0,24 +0.42 + 0.80
2048 | 2.64 4.18 | 240 | 2.69 3.36
0.97 2.44 } — — a
4096 | 8.01 st | 6.02 5 | = | — | ~-

From the figures given it will be seen that the object of the inves-
tigation, that is to say the determination of the extent of the elec-
troiytie dissociation, has not been attained because we meet with the
peculiar phenomenon that the conductive power at first decreases and
that for »=128 a minimum for uw occurs; on further dilution the
conductivity again increases but a uo cannot be determined. We
cannot, at present, account for this occurrence of a minimum which
appears in the case of all the hydrates at the same concentration
(vy = 128) and is consequently a definite property of nickelsulphate.

We further notice also that the conductivity of nickelsulphate
in methylalcohol (also when this contains a few per cent of water)

is very small, many times smaller than that of salts with univalent
ions, and at least 20 times smaller than in water. It is for this reason
that we have thought proper to disregard the influence of the ionie
dissociation on the results given in the preceding communication.
Moreover, this influence would only strengthen the conclusion arrived
at in that paper.

Amsterdam, June 1903. Organ. Chem. Lab. University.

Chemistry. — “Do the lons carry the solvent with them in electro-
lysis?” By Prof. C. A. Lopry pr Bruyn.

It is generally known that the behaviour of electrolytes in solu-
tion has in many respects not yet been elucidated. We know, for
instance, that strongly dissociated electrolytes do not conform to
OstwaLp’s law of dilution. In view of this, H. JAHN ') some time
ago developed a theory in which he attributes this ‘‘deviation” to a
mutual interaction of the ions, whilst Nernst?) also assumes interac-
tion between the ions and the non-dissociated molecules.

A priori it did not appear to be impossible that the ions might exert an
action on the molecules of the solvent which would cause them to
earry the solvent with them during the electrolysis. If this were found
to be the case, it would have to be taken into account in the study
of the phenomena of electrolysis.

The question whether the ions carry with them during electro-
lysis one or more molecules of the solvent cannot as a matter of
fact be studied by using purely aqueous solutions, but it can be done
by means of solutions of an electrolyte, say, in mixtures of water
and methylaleohol. Then if one of the ions carried with it one of
the solvents, this would be found out by the difference in the pro-
portion of the two solvents at the cathode and the anode both by
comparing them with each other and with the original solution *).

In the research an apparatus of the usual kind was employed
such as is used for the determination of the transport numbers of

1) Z. ph. Ch. 36. 458, 37. 490, 38. 125. 2) Ibid. 38. 487.

2) When the experiments were already in progress Prof. Aspraa told me that
Prof. Nernst had already made similar experiments using water -+ mannitol as sol-
vent. These experiments, which only appeared in the Géttinger Nachrichten [1900. 68]
had not led to a definite conclusion; Prof. Nernsr confirmed this statement. J.
Trause (Chem. Zt. 1902, 90) also thinks it probable that each ion is in unstable

combination with one molecule of the solvent.
7%

( 98 )

ions (capacity 150 ec.); a few experiments were made with a larger
pattern (capacity 450 cc.) As solvent a mixture of methylalcohol and
water was used of three different concentrations.

As electrolyte, cuprichloride was first used; when this substance
appeared to be unsuitable for the purpose (owing to formation of
cuprouschloride) silvernitrate was taken. This salt was sufficiently
soluble in the diluted methylalcohol and did not seem to affect it
during the electrolysis. The electrodes were made of silver, the cathode
was placed in the uppermost limb of the apparatus and the anode,
around which the increase of concentration of the silvernitrate takes
place, in the other. After placing the apparatus in the waterbath a
eurrent of 70 volts was passed for 3 to 4 hours; the strength of
the current was determined by means of a milli-ampere-meter.

Separate experiments had shown that the methylaleohol could
be very accurately determined by distillation. The liquid to be ana-
lysed (25 ec. of the cathode- and anode solutions) was mixed with
25 ec. of water and of this mixture 25 cc. were very carefully
redistilled into a weighed measuring flask. The amount of silver-
nitrate was found by titration and the silver deposited on the cathode
was weighed. From the following particulars of the experiments, we
may draw the conclusion that under the circumstances of the expe-
riments there is no question of a transference of the solvent along
with one of the ions.

It was found previously that on dissolving AgNO, in dilute
methylaleohol the volume of the liquid is scarcely affected.
Methylalcohol of 25 pCt. by weight.

Weight of measuring flask after distillation from solvent 36.838
36.872
, solution n. AgNO )
Sete
I. Meth. ale. of 25 pCt. by weight. Small apparat. Curr. 0.386 ampéres.

Time: 3'/, hours. Silver on the cathode: 4.50 grams.

Cone. Ag NO, before the experiment: normal.

; anode 1.30 normal
Cone. Ag NO, after \
eit j i ! cathode 0.54

| solution at anode 386.876

Weight of measuring flask after the distill. » qeathodle. 36.875

II. Meth. ale. 85pCt. by weight. Large apparatus. Current 0.32 ampere.
Time: 4 hours. Silver at cathode: 4.1 grams.

Ber

( 99 )

Cone. of AgNO, before the experiment: normal.

{ anode 1.37 normal

! cathode 0.94
original solution 36.498
Weight of measuring flask after the distill. ; solution at anode 36.508

| i" , cathode36.503

i " " after !

Ill. Meth. ale. of 64 °/, by weight. Small apparatus. Current 0.15
ampere. Time: 3'/, hours, Silver on the cathode: 1.80 gr.
Cone. of silver before the experim. : normal.

( anode: Ag NO, crystal. out

after
ae, ae a: " "1 cathode: 0.73 normal.

original solution 35.100
Weight of measuring flask after the distil. ; solution at anode 35.100
y at cathode 35.094

By an easy calculation we now find that if for instance, the
Ag- or NO,-ion had carried with it one molecule of the solvent, for every
4 grams of silver an increase or decrease of 0,6 to 0,7 gr. of water
or of about 1.2 grams of methylalcohol at the anode or cathode would
have been stated. This would have been plainly detected by the
analysis even though the amount had been largely diminished by
diffusion *).

I have to thank my assistants Messrs. C. L. Junaius and §. Tymstra
for their assistance rendered in these experiments.

Chemistry. — Prof. C. A. Lopry pe Bruyn presents communication
N°. 5 on Intramolecular Migrations: C. L. Juneis. “The
mutual transformation of the two stereo-isomeric methyl-d-
glucosides.”

1. When in 1893 Emm Fiscusr *) discovered the glucosides of the
alcohols and proposed for these substances a formula deduced by
him from the glucose-formula of ToLLENs, namely

CH,O —CH—CHOH—CHOH—CH—CHOH—CH,OH,
Peace. "Sui Ge sake 2 oo

he suggested that on account of the appearance of a new asymmetric

1) It is possible of course that the two ions act in the same manner and carry
with them equal quantities of one of the solvents or of both.
2) Ber. 26. 2409.

carbon-atom two stereo-isomeric glucosides ought to be capable of
existence. These two isomers would then be comparable to the two
penta-acetates then known.

About a year afterwards, ALBERDA VAN EKernsTgIN ') sueceeded in
obtaining this second isomer 3-methylglucoside. He found that if
the reaction between glucose and methylalcohol (with hydrochloric
acid as catalyser) was stopped the moment that all the glucose as
such had disappeared, the two isomers were both present, the
e-form being predominant. They could be separated by fractional
eystallisation. He further noticed that the 3-form passes into the «-form
in presence of a solution of hydrochloric acid in methylaleohol; if,
therefore, the reaction is continued for a long time, we observe
that the rotation increases [the [¢]p of the a«-isomer is +- 158°, that
of the j-isomer—32°| whilst the 3-methylglucoside disappears more
and more.

The p-isomer therefore appeared to be the metastable and the
a-isomer the stable form..

The observations of ALBERDA lead to the conclusion that, as in so
many analogous cases, the so-called metastable form is here the first
product of the reaction and that the isomer is produced from this
afterwards.

It now became important to further investigate the transformation
of the one isomer into the other with a view both to its velocity
and to the influencing factors. The view propounded by Emi. FiscHEer*)
that glucosedimethylacetal CH, OH- (CHOH), CH (OCH,)? may be
the intermediate product in the formation of the two glucosides might
be tested by an investigation of this kind. This acetal is a syrupy
liquid which occurs as the first product of the action of methyl-
alcoholic hydrochloric acid on glucose ; it does not react with phe-
nylhydrazine or Frxiine’s solution and is very readily reconverted
into glucose by the aqueous acids; it was however not obtained pure
and not analysed. As this substance, supposed to be the dimethyl-
acetal, was converted into the two glucosides on warming with methyl-
alcoholic hydrochloric acid, the transformation being however not
complete and as moreover the two other substances were obtained
when starting from one of the two glucosides, Fiscuer concluded:
ydass der Vorgang welcher vom Acetal zum Glucosid fiihrt, umkehr-
bar ist, dass ferner die Verwandlung der Glucoside in einander iiber
das Acetal fiihrt and dass mithin die drei Verbindungen als Factoren

1) Recueil 18. 183.
2) Ber. 28, 1146.

a a
an
a
».¥j ;
4

( 101 )

eines Gleichgewichtzustandes resultiren’’; a-methylglucoside is then
always present in the largest quantity.

2. My research has now led to the following results.

If we start on the one hand from pure e- and on the other hand
from pure §-methylglucoside’) the methylalcoholic solution of HCl
arrives in both cases at the same condition of equilibrium in which
the a-and f8-compounds are both present. After removing the HCl.
with PbCO, and evaporating the solvent a crystalline mass was left
which was extracted with acetic ether. This on evaporation yielded
an extremely small quantity of a non-crystallisable product [at most
10 milligr. from 2.5 gram of e-glucoside] which may possibly be
FisHer’s dimethylacetal. Its concentration is, therefore at any rate
exceedingly small in comparison with those of the two glucosides.

3. From the rotation of the solution, after equilibrium is attained,
it may be found by calculation that 77 °/, of the glucoside is present
in the a- and 23°/, in the 3-form.

From the change in rotation with the time the velocity, with
which the transformation takes place, may be calculated. It appears
that the formula for a non-complete unimolecular reaction is appli-
cable here;

ee =)

[a anda’ are the concentrations of the two glucosides at the moment
the measurement begins, z is the quantity converted after the time f}.

By integration this formula gives

ae ag, ae
t Lv

x, is the total quantity converted from t=O to f=o.

k+k’ remained satisfactorily constant during the reaction both
when the «- and when the #-glucoside was used, and led in both
eases to the same figure. With a 1.34 normal solution of HCl in
methylaleohol £-+ k’ at 25° was found to be 0.0051 ; (the time
expressed in hours); the transformation at that HCl-concentration
therefore proceeds tolerably slowly; the equilibrium is practically
attained after about 20 days.

4. The result of the velocity determinations is most simply expressed
by supposing that the reciprocal transformation of the two isomers
represents an intramolecular migration, in this way: «<>. The in-

1) I have to thank Mr. Atserpa van Exenstew for kindly supplying me with a
certain quantity of these two substances.
2) This formula has been first applied by Kistiakowsky to esterification.

( 102 )

termediate occurrence of acetal is improbable; we should then have
the reaction: a acetal > 2. The quantities measured being the velo-
cities with which e or p disappears and 8 or @ appears. It would
satisfy the formula for the reversible unimolecular transformations only
if the acetal was converted with an immeasurably great velocity into
8 or a. An attempt was made to elucidate this question by means of
a separate experiment. Supposing the mechanism of the transformation
to be really:
a-glucoside = acetal = @-glucoside

we should then have two equilibrium reactions for which there would
exist four velocity constants.

k:, for e-gluc. acetal, 4’, for acetal = a-glue.

!
boty “ER een oy aay ps pa
As it had, however, been ascertained that in the condition of equili-

brium, acetal is practically absent, the limit for the two equilibrium
reactions is situated close to the two glucosides; from this follows

a cae
that the ratios Band must be very large. This is only possible if

1 Le)
k, and k, are very small or in other words if the transformation,
setting out from either of the glucosides, proceeds very slowly, or
if &', and #', are very large, that is to say if the acetal is converted
with extraordinary rapidity into the two glucosides. From the results
of the velocity determinations already given, it follows that the first
possibility does not exist; to test the second supposition, the non-
crystallisable substance, which Fiscurr reservedly considered to be
the possible dimethylacetal of glucose was prepared according to his
directions. The syrup obtained by extraction with acetic ether was
laevorotatory [it however still reduced Frntine’s solution slightly | ;
it was dissolved in 2 7. methyl alcoholic hydrochloric acid (about
2,5 er. in 25 ¢.c.m.) and the change at the ordinary temperature
was observed. This took place by no means rapidly.

totation: t= 0 —1°.0 t#=19 hours + 17°.5
—p Ricci + 0°.7 26.5 4 19°
=2 hours +5°.5 43 ” 22°.9

67 r 26°.0

Everything considered it must be assumed to be very improbable that
the syrupy substance {perhaps the acetal] occurs as an intermediate
product in the reaction 8- = a-glucoside. The traces of a syrup which

oes

( 103 )

were found are then due to a secondary reaction which does not
interfere with the study of the main reaction.

The conclusion should therefore rather be that the two glucosides
are directly converted into each other.

5. The point in question would be solved with complete
certainty if the reciprocal transformation of @ into B were observed
in another solvent than methylalcohol. Except in water these
elucosides are also slightly soluble in ethylalcohol. As aqueous
hydrochloric acid causes a resolution into sugar and methylalcohol
the behaviour of ethylalcoholic hydrochloric acid was investigated.
In this solvent the transformation also proceeded according to the
formula for reversible reactions, the same limit being reached as
when methylalcohol was used as solvent '*).

6. The concentration of hydrochloric acid necessary to cause the
mutual transformation of the two isomers to take place with mea-
surable velocity, is tolerably large; much larger than is usually the
case in catalytic reactions. The possibility is therefore not exclu-
ded that HCl takes part in some unknown way in the reaction. This
theory is supported by the strongly retarding influence of water on
the mutual transformation.

For a HCl-conecentration of L.O7 norm. & +4" is about 0.0040. In the
presence of 1 mol. of H,O to 1 mol. of HCl. [about 2 vol. °/, water]
in the solution £+4' was found to be reduced to 0.0012. If to 1 HCl,
5 H,O was added [about 10 vol. °/, of water], the transformation
took place exceedingly slowly, & + &' = 0.0001; in this case a little
glucose was also formed.

Finally, the constants which have been calculated by means of the

il az : ;
formula —1——*—\ for different HCl-concentrations, point to a more

v ie av

rapid increase of £-+ %' with the HCl-concentration than that required
by simple proportionality :

ran ee
Concentration HCl | k++ | 7 Hoe
n. 1.34 (inCH,OH) | 0.005: | 0.0038
» 2.06 ( » ) 0.0091 0.0044
» 2.98 (in CoH,OH) | 0.0130 0.0057
»4A€ > oy |: 0.0384 0.0082

1) The product obtained was syrupy and crystallised very slowly. Apparently,
a little ethylacetal or ethylglucoside must have been formed.

( 104 )

7. With a view of ascertaining whether a transformation was
also possible without HCl, the 3-glucoside was kept for a long time
in a fused condition. After cooling the ap appeared to be quite
unchanged.

Zinechloride in methylaleoholic solution is also incapable of causing
the transformation.

8. In conclusion it may be mentioned that the rotatory power of

a solution of methylmannoside [of which glucoside only one form

is known as yet] in a solution of hydrochloric acid in methylalcohol
gradually decreases without formation of mannose.

It seems natural to assume that this is caused by a partial change
into a B-isomer which may, perhaps, also be isolated.

These investigations are being continued.

Org. Chem. Lab. University. Amsterdam, Jane 1908.

Chemistry. “Vhe electrolytic conductivity of solutions of Sodium m
mixtures of ethyl- or methylaleohol and water.’ By Mr.
S. Tumstra Bz. (Communicated by Prof. C. A. Lopry pr Bruyn).

In his study of the velocity of substitution of one nitro-group in
o- and p-dinitrobenzene by an oxyalkyl*) Srecer arrives at the result
that the reaction constants of o-dinitrobenzene and the two alcoholates
Na OC,H, and Na OCH, are not changed by dilution or by addition
of a sodium salt. On the other hand, in the formation of ethers,
these constants are increased by dilution, as shown by Hrecut, Conrap
and Brickner, and decreased by addition of a sodium salt as demon-
strated by STEGER.

Lopry DE Bruyn pointed out that it would be necessary to inves-
tigate the conductivity of Na OC,H, in alcoholic solution.

In a further investigation of the influence of water on the substi-
tution of the NO,-group in o-dinitrobenzene by an oxyalkyl*) and on
the formation of ethers *) it appeared; 1st. that the velocity coefficients
of these reactions remained constant when water was added up to
an amount of 50 per cent by weight; 2°¢. that the addition of water
decreased the velocity of reaction of Na OC,H, but increased that of
Na OCH, (at least at the commencement, afterwards the velocity

1) Dissertation, Amsterdam, 1898. Receuil 18, 13. (1899).

*) Lopry pe Bruyn and Apu. Stecer, Receuil 18, 41.

’) Lopry pE Bruyn and Aupx. Srecer, Receuil 18, 311.

—

( 105 )

diminishes again); 8'¢. that in mixtures of water and alcohol in which
Na is ‘dissolved, the sodium alcoholates are still present.

This last conclusion seems at first sight strange. But previous
observations had been made which justified the belief that Na OC,H,
is present in an aqueous-alcoholic solution of sodium. HENRIQUES ') for
instance showed that in the saponification of fats with aqueous-aleo-
holic soda the fats are not directly decomposed by the NaOH (the
alcohol would then only play the part of a solvent) but that at first
the ethyl esters of the fatty acids are formed. The well-known reaction
of BauMANN—ScuHOTTEN leads to a similar conclusion.

Some three years after the above mentioned memoirs appeared,
Lunors *) studied the action of sodium alcoholate on chloro- (bromo-
or iodo-) dinitrobenzene (1, 2, 4), and observed the influence of
dilution with both absolute and dilute alcohol. It was then shown
that the reaction constants are really affected by the concentration
which was not the case in STEGER’s experiments; decrease of the
concentration increases the constant, addition of a salt with a common
ion, such-as Nabr, decreases the constant both in absolute and
dilute ethylaleohol. Here again the water seemed to exert an in-
fluence, for in the case of ethyl alcohol a fali in the reaction constants
took place whilst with methyl alcohol first a rise and then a fall
was noticed. Why all this occurred could not be explained.

From the above facts it was evident (and it was repeatedly pointed
out in the papers in question) that it was necessary to study the
conductivity of sodiumethylate and -methylate in mixtures of water
and alcohol. For this reason I decided to undertake this investigation.

A short review of the results is given in the following tables and
the graphical representations connected therewith. A fuller description
of the experiments will be given elsewhere.

As starting pomt I always used solutions which were about
‘7, normal, determined their resistance and from the diluted solutions
prepared therefrom, I calculated the w’s for those dilutions and deter-
mined by interpolation the w’s for the dilutions of 1 molecule in
1,-2, 4, 8,.,.. 512 Litres. The experiments were all done ata
temperature of 18°.

In the following tables, the figures are represented graphically in
Fig. I, I, HI and IV, where the w’s are taken as ordinates and
the logarithms of the dilutions as abscissae. by using the logarithms
the seale of the drawing is reduced. The alcoholic percentages are

1) Z. f. angew. Ch., 1898, 338, 697.
) Dissertatie, Amsterdam, 1901. Recueil 20, 292. (1901).

( 106 )

by weight and have been determined by means of the specific
gravity bottle.

, [It is to be noticed that Fig. HI is not reproduced on the same
scale as Fig. I; since the methyl alcohol curves wouid intersect and
the. figure would therefore become confused, the scale of the abscissae
has been taken four times larger].

Sodium in Ethyl Alcohol + Water.

‘of ieoner 99.44 96.54 88.85 86.50 78.83 70.40" 48-18 ~ oes
by weight. pCt. pCt. pCt. pCt. pCt. pCt. pCt. pCt.
Po — 5.32 6.866 7.737 ¢11459 - MGSe > iordo 70.05
pak 7.602 8.916 44.43 ° 42.44 » 47220 293 289 2) Ato aoe
Boma AO aO th 99 ret. 7 16.87 22.44" 29.70 49272." Semas
[So 1 PO am 2) aaeaiae W a 20.77 26.38 3454 5446 94:62
Be, =, 15.79 47.95. 22.04 24.29 30.10 = 38.67 58.07 99.80
Petes Sede, £21 24 25 .27 27.66. 33.48. 4QA9 “161,34 Alaa
Pye 22.148 24.53 28.59 30.86 36.60 4.22 63.68 10792
P93 20-4 Zig VW SteDSs 3.10 8923 27368) 64°89 0S
956 28.54 DOpS2.) ated 36.54 44.52 49.67 65.40 141.2
P—sjg 31.30 33.62 37.04 38.97 43.00 50.81 64.54 442.0
Sodium in Methylalcohol + Water.
Percentage 400 93.09 87.72 81.40 74.70 69.99 HORo7
of alcohol. pCt. pCt. pCt. pCt. pCt. pCt. pCt.
yy 21.49 22.77 23.89 25.72 27.85 30.24 33.48
Ay 9 31.18 32.66 33.59 35.02 36 92 38.80 42,75
er 40.38 40.97 AA 21 4A 97 43.43 45.26 49.01
Pg 48.13 47.90 47.03 47,24 48 36 49.93 53.60
P16 54.78 53.63 52.07 51. Ad bao! 54 O4 57.30
ae 60.77 58.65 5645 55,08 © 55.73 | 57.307 .s ame
#84 65.97 63.08 59.64 58.43 58.68 59.79 62.87
Bale 70.42 66.98 69.62 60.98 61.00 62.07 64.99
ees 74.50 70.09 64.73 62.12 62.60 63.57 66.40
Py 519 77.92 72.44 66.49 62.99 63.72 64.55 67.01

From these figures we obtain the important result that methyl-
alcohol differs from ethylalcohol in its behaviour. This is seen at
once from the graphical representation in Fig. [IV (showing the
changes of the ws, namely of the f.—1, we ete. with the amount
of water). At the gas concentration (v = 22) a minimum occurs

. Laie

( 107 )

with methylaleohol. This minimum is not present in the higher
concentrations but at the larger dilutions it becomes more and more
evident. This minimum is found precisely in the neighbourhood of
those dilutions (v= 22 and higher) at which Losry pr Breyn and
Steger and Lunors have worked in the experiments referred to
above and the amount of water in the alcohol is also the same as
that for which these investigators have found the maximum of
reaction velocity, namely in 60 to 80 per cent alcohol. There is
therefore parallelism between the two phenomena; for methyl] alcohol
+ water + sodium a maximum of the reaction velocity corresponds
with a minimum of conductivity.

The experiments are being continued up to pure H,O and also
extended to mixtures of ethyl- and methylalcohol.

Amsterdam, June 1903. Org. Chem. Lab. University.
Physiology. — The string galvanometer and the human electro-

cardiogram. By Professor W. Einrnoven. (Physiological labo-
ratory at Leyden.)

In the Bosscha-celebration volume of the “Archives Néerlandaises”’ *)
the principle of a new galvanometer was mentioned and the theory
of the instrument dealt with. The practical usefulness of the instrument
especially for electrophysiological measurements may be judged from
what follows.

It may be remembered that the instrument consists principally of
a silvered quartz thread which is stretched like a string in a strong
magnetic field. When an electric current is passed through the thread,
this latter deflects perpendicularly to the direction of the magnetic
lines of force and the amount of the deflection can directly be meas-
ured by means of a microscope with an eye-piece micrometer.

What is the sensitiveness that can be obtained in this manner?

Since the above-mentioned publication a number of material impro-
vements have been made in the instrument by which it is possible,
for instance, to give a very feeble tension to the string, now a quartz
thread 2.4 uw thick, with a resistance of 10000 Ohms. If the tension
is so regulated that a deflection takes place in from 10 to 15 seconds
depending on its amount, every millimetre of the displacement of
the image of the string corresponds to a current of 1O—'! Amp. when
a 660-fold magnification is used. As under these circumstances a

1) W. Erntuoven. Un nouveau galvanométre. Archives Néerlandaises des sciences
exactes et naturelles. Sér. Il. Tome VI. p. 625. 1901.

( 108 )

displacement of 0,1 mm. is still noticeable, as will appear from the
discussion of the plates, currents of 10—'!? Amp. can consequently be
detected.

As far as is known to the writer, no other galvanometer is capable
of demonstrating with certainty such feeble currents. In practical
work the string galvanometer must consequently be placed on a line
with the most sensitive galvanometers of other construction and must
be distinguished from so-called oscillographs which only react on much
stronger currents.

The force which deflects the string in a field of 20000 C.G.5.
with a current of 10~—!? Amp. is very small and works out for a
length of 12.5em. at 2.510—'! grammes i.e. four times less than
one ten millionth part of a milligramme.

By giving the string a greater tension its movements become quicker
but its deflections for equal currents less. It is easy to give the string
exactly such a tension that a current of given intensity causes a
predetermined deflection, as may appear from the photograms of the
two accompanying plates. These pbotograms were obtained in the
same way as the formerly described capillary-electrometric curves *).

The 660-fold enlarged image of the middle part of the string is
projected on a_ slit, perpendicular to the image. Before the slit a
cylindrical lens is placed, the axis of which is parallel to it; behind
it a sensitive plate is moved in the direction of the image of the
string. While the movements of the string are thus registered, at the
same time a system of coordinates is projected on the sensitive plate
by the excellent method of Garren *). Of these coordinates the hori-
zontal lines are obtained by mounting a glass millimetre-scale close
before the sensitive plate so that the sharp shadows of the scale-
divisions fall on the plate, while the vertical lines owe their origin
to a uniformly rotating spoked disc which intermittently intercepts
the light falling on the slit. The distance of the vertical as well as
of the horizontal lines has in our photograms been taken about one
millimetre, every fifth line being somewhat thicker. This latter pecu-
liarity can easily be introduced into the coordinate system by drawing
every fifth line in the glass millimetre-scale before the sensitive plate
slightly thicker and by also making every fifth spoke of the rotating
dise somewhat broader.

1) See various essays in ‘Pruiticer’s Arch. f. d. gesammte Physiol.” and in
“Onderzoekingen physiol. laborat. Leyden.” 2nd series.

*) Dr. Stearriep Garten. Ueber rhythmische elektrische Vorgiinge im querge-
streiften Skeletmuskel. Abhandl. der Kénigl. Sachs. Gesellsch. der Wissensch. zu
Leipzig. Mathem. phys. Classe, Bd. 26, No, 5. S. 331. 1901.

_—"

( 109 )

The first photogram, fig. 1 plate I represents the deflections of the
string when currents of 1,2 and 3><10 -? Amp. are successively passed
through the galvanometer. In the coordinate system a length of 1 mm.
of the abscissae has a value of 0.1 second, an ordinate of 1 mm.
representing 10-'© Amp. Although the image of the string has
considerable breadth and has no perfectly sharp outlines — as must
be expected with a magnification of 660 times — yet its displacement
in the coordinate system can easily be determined with an accuracy
of 0.1 mm. For if one of the margins of the image before and after
the deflection is observed, observation with the unaided eye or with
a magnifying-glass will show that the deflection differs from the
tabulated amount by less than 0.1 mm. Hence the currents are
measured in the photogram with an accuracy of 10—!! Amp.

One notices that the deflections are accurately proportional to the
intensity of the eurrent, that they are dead-beat and that they are
accomplished in 1 to 2 seconds according to their magnitude. The
strong damping must be ascribed to the resistance of the air, for
during the registering of the curves a resistance of one Megohm was
put into the galvanometer circuit by which the ordinary electromag-
netic damping was almost entirely suppressed.

If the tension of the string is made ten times less, the galvano-
‘meter becomes ten times more sensitive and, as stated above, currents
of 10—'? Amp. may still be observed. But with this greater sensi-
tiveness the deflections are no longer proportional to the current and
the movements of the string are difficult to record, as the quartz
thread no longer moves exactly in a plane. Yet the instrument can
still be used then for direct observation with the microscope.

Figure 2 plate I shows that the deflections to the right and to
the left — in the tigure corresponding to upward and downward
deflections, are equal. The velocity of the sensitive plate has
remained the same so that again an abscissa of one millimetre
corresponds to a time of 0.1 second. But the tension of the string
is 200 times stronger so that one millimetre of the ordinates repre-
sents 210-8 Amp. A current of 4<10—7 Amp. is alternately sent in
opposite directions through the galvanometer and hence causes
deviations of 20 mm. to the right and also to the left. It is easy to
ascertain that these deviations are equal to each other up to 0.1 millimetre.

The movement of the string is very quick so that during the
deflection the string can only cast a feeble shadow on the sensitive
plate. The ascending and descending nearly vertical lines which in
the original negative are still visible as very thin streaks have become
invisible in the reproduced photogram.

( 110 )

In fig. 3. plate I a movement of the string is represented when
a current of 3><10-8 Amp. is suddenly made and broken. The
sensitive plate has been moved along with a tenfold velocity and the
string has ten times more tension than in fig. 1, consequently one
mm. abse. = 0.01 second and one mm. ord. = 10-9 Amp. The gal-
vanometer circuit contains again one Megohm so that the same causes
of damping exist as in fig. 1. The movement is still dead-beat, but
on account of the 10 times greater force on the string it is 10 times
quicker, as can easily be ascertained by comparing the great descending
curve of fig. 1 with one of the curves of fig. 3 or better still by
superposing diapositives of the curves of both figures. They will
then be seen to cover each other exactly and since in one figure
the velocity of the moving plate is ten times greater than in the
other, the deflection of the string must in one case take place ten
times more quickly than in the other. At the same time the resistance
of the air is proved in our case to increase proportionally to the
velocity of the string itself.

In recording the curves of fig. 4 and 5 of plate I the velocity of
the moving plate has been increased to 250 mm. per sec. so that
1 mm. of the abscissae is 0.004 sec. The plate at first moves slowly
and reaches the mentioned velocity only when it has travelled through
a distance of 4 or 5 centimetres, whereas the spokes of the rotating
dise always cast their shadows on the plate accurately every 0.004
second. Hence the coordinate system is in the first sixth part of the
photogram compressed in the direction of the abscissae.

In fig. 4 one mm. ord. = 210-SAmp., while in fig.5 one mm.
ord. = 310-8 Amp. These two figures together show us the limit-
value of the sensitiveness for which the movement of the string is
still dead-beat. In fig. 4 a current of 4<10—7 Amp., in fig. 5 a current
of 610-7 Amp. has been transmitted through the galvanometer and
interrupted. One sees that the deflection in fig. 4 is still dead-beat
and is completed in about 0.009 sec., whereas in fig. 5 the motion
begins to become oscillatory and for a single oscillation takes 0.006
sec. The sensitiveness with which the motion of the string is on the
border between aperiodic and oscillatory motion is consequently such
that a deflection of one millimetre corresponds to a current between
2 and 3 10-5 Amp.

In the tracing of fig. 4 and 5 only an insignificant resistance is
put into the galvanometer circuit so that here besides the viscosity
of the air also the ordinary electromagnetic damping checks the motion.

Now some particulars may be mentioned referring to the 5 photo-
grams of plate 1 in common.

em BE os

In order to obtain the image of the string equally sharp in all
parts of the visual field, the string must move in a plane perpen-
dicular to the optical axis of the projecting microscope. A displace-
ment of the string of 0.5m in the direction of the optical axis suffices
to cause a noticeable indistinctness of the image with the magnifica-
tion used. The photograms show that such a displacement does not
take place.

The great constancy of the zero point and the equality of the
deflections deserve notice and also — which is especially important
for practical work with the instrument in electro-physiological
measurements — the possibility of accurately fixing beforehand the
sensitiveness of the instrument. The unaided eye can already observe
in nearly all the figures of plate I that this can be done successfully
with an error of less than 0.1 mm. for deflections of 30 or 40 mm.,
i.e. with an error of less than 2.5 or 3 per thousand. Only fig. 5
shows a real deficiency of about 0.1 mm. which some greater care
might have avoided.

It is hardly necessary to point out that the galvanometer is
not affected by variations in the surrounding magnetic field. Moreover
it is not to any extent affected by tremors of the floor. It stands
on the same stone pillar on which a large tin dise with spokes is
rapidly rotated by an electromotor. This electromotor is only at a
few centimetres’ distance from the galvanometer, while another
motor, coupled with a heavy fly-wheel, for moving the sensitive
plate, is clamped to the same pillar at a somewhat greater distance.
Yet no trace of mechanical vibrations appears in the photograms.

The first electro-physiological investigation made with the string
galvanometer was one concerning the shape of the human electro-
cardiogram discovered by Ave. D. Water’). Until now this could
only be obtained by means of the capillary electrometer. But the
curve traced by that instrument gives, when superficially observed,
a quite erroneous idea of the changes of potential differences actually
occurring during the registering. In order to know these they have
to be calculated from the shape of the recorded curve and the pro-
perties of the capillary used. This leads to the construction of a new
eurve, the form of which is the correct expression of the actual
variations of potential.

1) Avevstus D. Watter. On the electromotive changes, connected with the beat
of the mammalian heart and of the human heart in particular. Philosoph. Trans-
actions of the Royal Society of London, vol. 180 (1899), B, pp. 169—194.

Proceedings Royal Acad, Amsterdam. Vol. VI.

An example may explain this *).
The following fig. 1 represents the curve traced for the electro-
cardiogram of Mr. vy. bp. W. when the current was derived from

the right and left hands, whereas fig. 2 is the constructed curve.
The differences are obvious. Especially the tops C’ and JP in the
registered curve should be compared with the corresponding tops
Rand T in the secondary curve which latter alone truly represents
the ratio of the heights of the tops.

We shall now try to compare the string galvanometer as a research
instrument with the capillary electrometer and must first of all bear
in mind that the deflections of the string galvanometer measure a
current, that of the capillary electrometer an electromotive force.
But it must be remarked that whenever variations in current or
tension are measured, the mercury meniscus as well as the string
moves. And during this movement the capillary must be charged or
discharged by an electric current, whereas the string in the magnetic
field develops an opposed electromotive force. Moreover, when there
is a constant considerable resistance with negligeable self-induction,

such as commonly occurs in electro-physiological investigations, the -

l) See Priiicer’s Arch. Bd, 60. 1895 and *Onderzoekingen”. Physiol. Laborat.
Leyden. 2nd series, vol. 2.

(113)

intensity of the current will at any moment be proportional to the
active electromotive force, so that the fundamental difference between

the electrometer and the galvanometer is no obstacle to a comparison

of both instruments.

The string galvanometer has several advantages over the capillary
electrometer. First the deflection of the string galvanometer will in
many cases and especially in the case of tracing a human cardiogram
be greater and quicker than the deflection of the capillary electro-
meter. Then the capillary electrometer is less accurate in the constancy
of its indications, their proportionality to the potential differences and
their equality in opposed directions.

A highly magnified image of the mercury meniscus cannot be so
sharply projected as that of a fine thread and one cannot regulate the
sensitiveness of the capillary electrometer to a predetermined amount.
The electrical insulation of the string galvanometer is much easier
than of the capillary electrometer and a phenomenon like “creeping”’
does not occur with the galvanometer.

In the capillary electrometer the movement of the meniscus is
damped by the friction of the mereury and sulphuric acid when
streaming through a narrow tube. Invisibly small traces of impu-
rities may hinder or even entirely stop the movement of the mer-
cury meniscus. Many a capillary had after a relatively short time to
be replaced by a new one because there was a “hitch” in the
movement of the meniscus. In the string galvanometer, on the
other hand, we have air-damping as well as electromagnetic damping,
both of which work with perfect regularity. The electromagnetic
damping can moreover be varied at will by changing the intensity
of the field and the resistance in the galvanometer circuit.

Plate II] contains the electrocardiograms of some six persons, traced
by means of the string galvanometer. In the coordinate system an
absciss of one millimetre has a value of 0.04 see., while an ordinate
of one mm. represents a P.D. of 10-4 Volts. By choosing these round
numbers the curves satisfy generally the requirements of the inter-
national committee for the unification of physiological methods.

The movement of the quartz thread, as may be seen from the
normal curves at the end of each photogram, was dead-beat and very
quick, so that the traced electrocardiogram is a fair representation of
the oscillations in the potential difference existing between the right
and left hands of the experimental person. As a rule this may be
admitted for the lower tops P, Q, S and 7 without any noticeable
error. But for the high and sharp top # a correction should be
applied especially in photograms 8 and 9, a correction by which

Q¥*

( 114 )

the extremity of the top would be shifted a little to the left and
upwards. The necessary correction is small however and its amount
may be approximately estimated at less than 0.2 mm. for the shiftmg
to the left and less than one mm. for the shifting upwards.

Photogram 8 represents the electrocardiogram of the same person
whose capillary-electrometric curve is shown in the text. When the
registered curve of fig. 8 plate Il is compared with the formerly
plotted curve of fig. 2 in the text, it is evident that. both curves
have great similarity. The tops P, Q, R, S, and T are not only
present in both curves, but have also the same relative height in both.

In the plotted curve 1 millivolt of ordmate has been made equal
to 0.1 sec. of absciss, while in the galvanometer curve 1 millivolt
of ordinate corresponds to 0.4 sec. of absciss. Hence the galvano-
meter curve is compressed in the direction of the abscissae, as a
superficial inspection will reveal. besides the galvanometer curve,
on account of the gradual transitions of ome top to another, gives
the impression of being in its minor details a more faithful represent-
ation of nature than the plotted curve. It is obvious that of this
latter curve only a limited number of points could be accurately
calculated, while for the rest the calculated points had to be joined
by the curve that fitted them best. But these small differences are
immaterial.

It may give some satisfaction that the results formerly obtained
hy means of the eapillary electrometer and more or less laborious
caleulation and plotting have been fully confirmed in a different and
simple manner by means of the new instrument. For this affords usa
twofold proof, first of the validity of the theory and of the practical
usefulness of the formerly followed methods and secondly of the
accuracy of the new instrument itself.

The six electrocardiograms of plate Il were selected among a
ereater number and arranged after the dimensions of the downward
top S (see the figure in the text). In 6 and 7 the curve remains,
at the spot where S ought to be, above the zero-line of the diastole,
in 8 and 9 S is only small, in 10 and 11 great. The numbers
6 and 11 mark in this respect the extremes which occur in our
collection of electrocardiograms, whereas N°. 8, that of Mr. v.p. W.
represents a sort of norm with which the other numbers may
all be easily compared.

The constancy of shape of the curve for a certain person is
remarkable. This shape seems even to change so little in course of
time, that with some practice one may recognize many an individual
by his eleetrocardiogram. We conclude this essay with a remark on the

(115 )

small irregular vibrations occurring in most electrocardiograms, where
they sometimes reach a height of 0,1 to 0.5 mm. and more, but
are sometimes entirely absent, as e.g. in N*®. 6 of Mr. Ap.

These vibrations are not caused by tremors of the floor or other
irregularities which should be ascribed to an insufficient technique
as is easily shown by the vibrationless normal curves at the end
of almost every series of electrocardiograms. Hence they must be
caused by electromotive agents in the human body itself and the
question arises whether they find their origin in the action of the
heart or of other organs. We may expect that an investigation
undertaken with this object will give a definite answer to this question.

Physics. — Dr. J. E. Verscuarret. “Contributions to the knowledye
of VAN DER WAALS’ w-surface. VII. The equation of state and
the w-surface im the immediate neighbourhood of the critical
state for binary mixtures with a small proportion of one of
the components.” (part 4). Supplement N°. 6 (continued) to
the Communications from the Physical Laboratory at Leyden
by Prof. KAMERLINGH ONNEs.

(Communicated in the meeting of May 30, 1903).
g y )

17. The a, B-diagram.

In the previous communications the different phenomena in the
neighbourhood of the eritieal point in substances with small propor-
tions of one component have, according to our plan set forth at the
beginning, entirely been expressed by means of the @ and # and
the co-efficients that can be derived from the general empirical reduced

equation of state. For shortness, and to avoid the constant repetition

of the same factors (comp. §1) I have used till now, instead of the
differential quotients of the general empirical reduced equation of
state, the co-efficients 4, where the m’s (comp. form. 19) have been
expressed by means of a@ and f, but henceforth, as the numerical
values are more important I shall make use again of the differential
quotients of the reduced equation of state itself, used in equation (1).
It seemed important to me to completely determine by means of
the numerical values of @ and 8 the different cases which, according
to the formulae found by Krrsom (Comm. N°. 75) and by me (loc.
cit.), may present themselves in the relative situation of the different
critical points. To illustrate this I intend to divide an a, (?-diagram
into fields in which there is a definite relative situation, by means

( 116 )

of lines, as Kortewsc has done in another diagram (the x, y-diagram)’).

This investigation showed that the last of the eight cases distin-
guished by KortewrG of which the inconsistency was demonstrated
by him for one special case only, did not exist in general, at least
for all the equations of state which satisfy the law of corresponding
states. Not to make the investigation too elaborate I have compared
the situation of the plaitpoint only with that of the critical state of
the pure substance, that is to say I have considered the fields within
which 77: > or < Tk, pri > or < pe and Uzpi > or <x. I have
also determined in which area the retrograde condensation is of the
first or the second kind; and lastly I have indicated in the diagram
what had been observed experimentally.

The plaitpoint temperature. According to form. (59) the plaitpoint
temperature of the mixture is higher or lower than the critical
temperature of the pure substance as the expression

m*,,+RkTym,, ia m?,,+hkTim,,
Ripa oe
is positive or negative; and, 4,, being negative, 7; — T;, has the
same sign as the numerator.

If for shortness we put

Op 07y 0°) 0*» 04)

Fer ag io cae dude at dpt0c es Pso = vc = a

and for convenience we leave out an index which refers to the
critical state, because only those values are used which refer to
the critical state,

eg, A RL EM, = PEO a), en el
so that the area, where 7',..; > 7), is separated from that where
Tiel <. T;. by a line of which the equation is:

(8: =p; a) to oe — 0:
This line, a parabola, represented on the annexed plate *) by
1) Proc. Royal Acad., Jan. 31, 1903. The » and y are connected in a simple

linear way with 2 and 6 (comp. the previous communication p. 666).
2) For we have (comp. form. (19):

Pk 1 Pk
m,, = p(B — },, a), m,, = ——)p,, a, m,, = — Bis [y., ¢+Y,, (a—A)],---
Ui; UE
1 py hp
m are Bigs bet? Mg = 5A a Peay elé:s

For the definition of Cy comp. Kamertinau Onnes (Arch. Néerl. (2), 5, 670, 1901;
Comm. no. 66).

3) The figure is drawn by using the values of p,), p)) ete. which will be calculated
in the next section. For clearness | have represented the «’s in a 5 times larger
scale than the #’s.

( 147)

bAODb’ corresponds to Kortewsa’s first boundary *). Outside the parabola
T»1 > Ty, inside Tait < Pe.

The plaitpointpressure. From form. (60) we derive that p,,) > or
< peas Po, (2 — Py, a)? > or << C,Y,, B®. The equation of the boundary
Por (3 — Po a)? Ti C, Pia B = 0,
is that of a parabola represented in the figure by cOLc’. Outside

the parabola py, > pe; inside < pr.

The plaitpointvolume. The manner in which v,,; depends on a and
may be derived from form. (61); it is expressed by KgxEsom’s formula
(2c), which I borrow from him in my notations:

(F—Po @)rne
C*ParPao

Hence the boundary is here:
O=— P11 (BP ©)? + CaP 31 (BP @)? + 36,071 a(B- rae) +e, * PrP ao (4-8).

This is a curve of the third degree, like Korrewse’s third boundary,
with which it corresponds in this diagram.

In order to investigate this curve I introduce, following the example
of KorTEwrG, a parameter z, by putting

Vapl == Vk - vpe(a-B)ax ae Ly, i(3-, 1a)’ a CY, i(3-¥, 1a) — 3C “P* n@].

Fas Bae a

and I find that @ and 8, by means of that parameter are expressed thus:

a= lott t Chane — CP Pol

oo >) ae Po Pua 2° =e C, auPn Por <2 ee iz ra Cr Pua mee
where
a C* Pia Bao (Poi Fane 1) ee C, Po e-

As a and @ are single valued functions of z, all lines which are
parallel to the straight line P=vy,, @ (Oa of the figure) intersect
the curve at one single point at a finite distance.

If we put:

CP s0(Por— 1) 2)
ae
the straight line 8 = p,, a + z,, being a dotted line in the figure (CD),

~ ——

1) To avoid mistakes I use here the word boundary, instead of the expression
border curve used by Kortewee; for in our demonstrations the word border curve
has a very special meaning, viz. that of a boundary between stable and unstable states.

2) As y is also equal to the direction-cosine (F) of the tangent to the re-
adi Jk

duced vapour tension curve at the critical point, and as it follows from the form

dp i
of that line that (3) > 1, % must necessarily be positive.
Pal =

( 118 )

is an asymptote of the cubic curve. It has two branches, of which
the one (dGEu') situated above the asymptote, is given by values
of z, which are larger than 2,, the other (d'’OHFd"), below the
asymptote for z< Z,.

a becomes equal to zero not only for z=0O, but also for two
other real values of z, of which the one is positive, the other negative;
I shall call the positive root z,, the negative one z,. In the same manner
8 vanishes for z= 0 and also for two other real values of z, of which
again one (z,) is positive, the other (¢,) negative. We can prove
that always z,>z,; for z, and z,, three cases are possible: both.
are larger than z,, and then z, >z,, or both are equal to z,, or
both are smaller than z, and then z,< z,. With the values of the
derivatives, to be introduced presently, the order of the roots is:

‘ 2, Deg Se ee
and hence follows the form of the cubic curve as it is drawn in the
figure ').

One can easily see that v,,; >v,~ above the branch z >z,, and
within the branch z<z,, while vz)1<( vg im the area which lies
partly between those two branches and which extends further to the
right of both.

Retrograde condensation is of the first kind when v7 v7,; and
of the second when vy, >>vz,. According to form. (41) and (26)
UT > UTr When m,, and m,, + RT,m,, have the same sign ;
m',, + RT; m,, is positive outside the parabola bAOb' and negative
inside, while im,, is positive above the straight line Oa and negative
below it. Hence we have v7, > v7, and retrograde condensation
of the second kind: 1st. inside the parabola )AO#' and below the
straight line Oa, 24. outside the parabola and above the straight line;
at all other points v7,,< vz,and the retrograde condensation is of
the first kind.

Here follow the physical characteristics of the fields into which the
figure is divided by the boundaries under consideration :

Field 1: Trpl = Ty, 9 Papl > Pk > Vxpl = Uk 9 UTpl = UTr ce.

Hie

2: Pet > Tr » Papl SPE a Gat <EDe 4 OT > Ua eee II
3: Top) > Tk + Papi > Pk Orpl So UE se CRpl < 7, toe I
As Top > Te, Papl > PR's Mal > Me eT — OTe, ee
5S. Lap > Te Punt <P veoh Uke Tr I
O- Trp csi A Pxpl < DE ic tml SU OT > Tr, tT Il
he T'zpl <u ey > Pxpl << Pk » Vapl im Ve y UTpl ae UTr 5 Y. C. I
Ss Pryl < hk: y Paral < Pk » Vzpl <UL s Vel < UT, WF. Ge I

gis

926 Toot << Tes Pepl > ks Val — Ye ep ee

1) It will be seen that this form agrees entirely with that derived by KORTEWEG
in the x, y-diagram from a special equation of state,

€ 149-5

It will be seen that the figures 1 and 2 of the plate belonging to
the first paper (Comm. 81) refer to points situated in the part on the
right of the B-axis of the fields 1 and 2: figs. 3 and 4 to the same
fields on the left of the B-axis; figs. 5 and 6 to the fields 7, 8 and
9; figs. 7 and 8 to the part of the fields 3, 4 and 5 lying on the
right of the p-axis; figs. 9 and 10 to the same fields on the left of
the p-axis; and lastly figs. 11 and 12 to field 6.

In the figure I have marked three points P, Q and R, of which
the first relates to carbon dioxide with a small quantity of hydrogen
(a= —1,17, B=—1.62), the second to carbon dioxide with a
small quantity of methyl chloride («= 0,378, 8 = 0,088) and
the third to methylchloride with a small quantity of carbon dioxide
(a = — 0,221, B= 0,281). From the situation of P, viz. in field 2,
it should follow’ that ie T;., whereas the observations showed
that 7,.< 7%; this deviation has been pointed out before. ') More-
over the situation of P in field 2 points to a system of isothermals
of the mixtures as represented in figs. 1 and 2 of the first paper,
while in reality this system of isothermals corresponds to figs. 5 and 6,
that is to say to one of the fields 7, 8 or 9. The point P lies very
near the limit of field 9, and hence it is possible that a more accurate
determination of @ and 8 would remove the point P into field 9 where
indeed it should lie according to the plaitpoint constants observed
and the character of this field, if at least the law of corresponding
states can be applied. The points Q and R, so far as we know with
certainty, are situated in the right field. *)

The straight line B= ),, @ agrees with Korrrwsxe’s second boun-
dary. It is determined by the circumstance that along the conno-

la:
dal line () —0; we find from the formulae (37), (41) and (26) that:
pl

dv
da 2M, 1d i Mo,

ey | ier 7 OT = CIT) Aa Sala
dv J yl m*,,+hTpm,, , : 1 Cod Rs

dat tie
so. that (3) becomes zero with m,,. Thus above the straight line Oa
av l
p

(=) is positive, below it, negative, hence in connection with tae
dv} 1

1) Comp. 2nd paper, p. 334.

#) It must be remarked that the deviation of the point Q in consequence of our
insufficient knowledge of 2 and 6 would be much less striking than in the case of
point P; e.g. whether Q ought to be placed in the neighbouring field 4 or not,
couid be only concluded from the sign of vx)! — vk, but we do not know with certainty
what this sign should be for mixtures of carbon dioxide and methylchloride,

( 120 )

preceding it follows that Korrrwse’s eighth case:
es . dx
Tpit Ty. ’ Urpl< Vk en <a 0
dv pl
is in general not possible.
A direct proof of this circumstance may easily be given. Because
must be negative, I put 3=7,.4¢—7; Topi 7), requires that

: rit s?

(6 — p,, 2)? =Cy,,@a—s*. Hence we may put: «= and

Pia

rt + s? POPE «
Gi pee = Uk a =, 0ai? Pane +2r‘)],

aT ae
4 Pua C aP11P 30

Crpl = tk —Vk (Por)

so that all the terms of 2, ; are positive. Hence we see that, if
dx

Pept < Ty, and (5

<0, Vip! <C vg is an impossibility.
pl

18. The numerical value of the reduced differential quotients.
j q

To find this numerical value I have first tried to derive it directly
from the observations by means of graphical representations; but as
I did not succeed in finding more or less reliable values for the
higher differential quotients (¥,,, P,5, P4> etc.) | was obliged to use
formulae which satisfactorily represented the observations. Undoubtedly
KAMERLINGH QOnNzEs’*) developments in series are best fitted for this
purpose, although just in the neighbourhood of the critical point,
where in our case they have to be applied, they deviate rather much
from the observations *). Therefore the values of the derivatives obtained
in that way, especially those of the higher orders, can only be con-
sidered as approximate.

By means of the temperature co-efficients of reduced virial co-
efficients marked by V.s.1?) derived from AmacGart’s observations,
I find for those virial co-efficients (U,, 3,, ete.) and their first deriv-
atives according to the temperature (,, ¥’, etc.) at the critical
pont. (¢ = 1),

1) Proc. Royal Acad. 29 June 1901, Comm. N’. 71, and Arch. Néerl. (2), 6, 874,
1901, Comm. N’. 74.

2) Comp. Arch. Néerl. loc. cit. p. 887. Previously I have given parabolic for-
mulae (Proc. Royal Acad., 31 March 1900, Comm. N°. 55 and Arch. Néerl. (2), 6,
650, 1901) which very well represent the observations just in the neighbourhood
of the critical point. These formulae, however, do not harmonize with our consi-
derations, because they do not yield finite values for higher derivatives.

8) Comm. N°. 74, p. 12.

a, = + 366,25 x 10° Ww, = + 366,25 10-3
er — 4 861A SK h0—* BS’, = + 662,387 10-8
©, = + 233,300 x 10- 9, = — 355,774 & 10

D, = — 360,485 « 10-'S sy, = + 789,380 « 10-8
eee 685,01, Suk? Sp is a en a

$, = — 90,14 x 10-* §, = — 698,82 x 10-*
If further we put 2A=0,00102 (calculated from 7%—=304,45, p,—=72,9
and v,==0,00424, we find at the critical point:
Poo 0.98833, y,,—0,10305, »,,—=—0,16831, p,,—=— 5,30648,
P49 75,79292, p,,=7,34410, p,,=—9,99986, »,,—= 27,76382, ete.

The values of »,,, ¥,, and »,, ought to be equal to 1, O and O
respectively ; the tolerably large deviation of the two last derivatives
proves that the series used do not represent the shape of the iso-
thermals in the neighbourhood of the critical point so accurately as
we might wish’). Hence it follows that the values of the other
derivatives calculated here cannot be very precise, and probably this
uncertainty increases with the order of the derivative.

I take as approximate values of the reduced differential quotients
at the critical point:

Pa — 0, 163.92. Ds 10, p,, = 28, while C =3,627)
According to YAN pER WAALS’ original (reduced) equation of state:
8t 3
yp = —————
3y—1 te
we should have
a a oO 7 8 wd
ee 4 pS Op — 18, C0, = 5 = 2,75}
vo
and according to this modified equation:
St del-t
i= — :
22 y?
a9 eae fo hs — =. 2s, — oe: C= af

Finally I substitute the numerical values of the derivatives obtained

1) On the cause of that inaccuracy and the possibility of improving upon it
“a new communication by KameruncH OnnEs is to be expected. (Comp. Comm.
n°, 74, p. 15).

2) Keesom gives (Comm. n°. 75, p. 9 and 10) Cy=3,45, p) =7, py =— 9.3.

3) It will be seen that these values agree tolerably well with the former ; it is
thus not remarkable that so close a resemblance exists between the forms of
the boundaries found by Kortewea and by me, which indeed is based on VAN DER
Waats’ original equation.

( 199 )

above in formulae (9) and (10) and compare the result with the
observations.
Equation (9) yields:

1
t(o,—»)=|/% 6 a—y=3 ame Ts
oer Pao

and equation (10):

Bese oh 2a |. s sete (1 — 1) = 10,9 (1 — 9.

2 ; P30 0 Pao

In order to compare these results with the parabolic formulae of
Maruias'), formulae must be derived for the reduced densities of the
co-existing phases; representing these reduced densities by », and 9, |
find, according to a transformation employed formerly : *)

1 MIA
rs (0, —d,) = 3,37 Y1—t

(>, +->,) -1= (37 —10,9) (1—t) =0,5 (1—2).

In the last formula, however, the co-efficient 0,5 is somewhat uncertain.
Maruias gives for the liquid branch, according to the observations
of CaimnLetet and MArTHtas *),
ee AT (1 he 2 ol
and for the vapour branch
a Or (1 2 th = Sa a
f From these formulae it would follow that the two branches of the
border curve belong to different parabolae. The co-efficient of V1—r
or the vapour branch perfectly agrees with the one found, and the
fact that Maruias has found a greater value for the same co-efficient
in the liquid branch, may clearly be ascribed to the uncertainty of
the then existing data on this subject. If we neglect this difference,
the formulae of MATHIAS give:

b, + >.) —1= 0,25 0 —9,

a sufficient agreement with the co-efficient 0,858 later derived by
him from AMAGAT’s Observations. The value 0,5 found above is in
good harmony with this.

) Journ. d. Pliys., (3), 1, 53, 1892. Ann. d. Toulouse, V.
*) Proc. Royal Acad., 27 June 1896; Comm. no. 28, p. 12. Mere acurately we have

1 ey ~ UV Nani :
= ———_ = (pri —
VE + Pic + icon V Ie > v4" i vy? y )

%) Journ. d, Phys., (3), 2, 5, 1893, Ann. d, Toulouse, VL.

verre ee es F

hiv ss)

Physics. — “The liquid state and the equation of condition.” By
Prof. J. D. van DER WAALS.

(Communicated in the meeting of May 30th and June 27th 1903),

It has been repeatedly pointed out that if we keep the values of
the quantities a and 4 of the equation of state constant, this equation
indicates the course of the phenomena only qualitatively, but in
many cases does not yield numerically accurate results. In par-
ticular Daniet BERTHELOT testing the equation of state at the expe-
rimental investigations of AMaGAT, has shown that there occur some
curves in the net of isothermals, e. g. those indicating the points for
which the value of the product pv is a minimum, and other curves
of the same kind, whose general course is correctly predicted by the
equation of state, but whose actual shape and _ position as determined
by the experiments of AmMAGAT, shows considerable deviations from
the course of those curves as it may be derived from the equation
of state.

In consequence of this circumstance the quantities @ and / have
been considered as functions of the temperature and volume. Already
Chausius proposed such a modification for the quantity a; for car-
bonie acid he does not put @= constant, but he multiplies it with
273 ae we
og Such a modification seems to be required principally with a
view to the course of the saturated vapour tension.

From the beginning I myself have clearly pointed out that, though
a may probably be constant, this cannot be the case with the quantity
}. One of the circumstances which I was convinced that I had shown
with the highest degree of certainty as well in the theoretic way as
by means of the comparison of the experiments of ANDREWS, was
that the quantity 4 must decrease when the volume decreases. So
for carbonic acid I calculated for 4 in the gaseous state at 15° the
value 0,00242 and in the liquid state a value decreasing to 0,001565.
But the law of the variability of 4 not being known, I have been
often obliged to proceed as if / were constant. In the following
pages I will keep to the suppositions assumed by me from the begin-
ning, namely that a is constant and that 4 varies with the volume;
and I will show that if we do so, the considerable deviations dis-
appear for the greater part and that it is possible to assume already now
a law for the variability of ) with the volume, from which we may
ealeulate in many cases numerically accurate data even for the liquid
state at low temperatures.

( dea)

To that purpose we shall begin with the discussion of the tension
of the saturated vapour over liquids at low temperature. From the
conditions for coexisting phases of a simple substance, that namely
p, T and the thermodynamic potential are the same in both phases,

follows
(pe = for, = (pv — {ty
a < dv a du
(>» —< —ar f- = (ve —*— rr {- }
v —b/, v v—b

If we put 6=constant i.e. 6 independent of the volume, then the
latter equation assumes the well known form:

E See log 0 | = E eee Ie log (0 }
v 1 Uv 2

Properly speaking this equation is not suitable for the direct calculation
of the coexistence pressure; it must be considered to give a relation
between the specific volumes and so also between the densities of the
coexisting phases. At lower temperatures, however, for which the
vapour phase, which we have indicated by means of the index 2, is rare
and may be estimated not to deviate noticeably from the gas-laws,
the equation becomes suitable for the calculation of the pressure of
the saturated vapour. In this case it assumes the following form:

=
Ov, BS T log (v,—b) — RT = RT log oP
We find after successive deductions which are too aan to require

special discussion :

a a(v,—b) p (v,—8)
Pope 2 Ane Rey pee a oe —b) = RT lox
eas say (+. es =) Crd ae
B a fait ; “2 P
a = RT log
b v," a
Po —
1
a v,—b as a4
pb — i + - a [RT — p (v,—b)] = RT log
h a
| Za
1
(a 2b) a
ae b . 7 b v,—b ] Y
= SS a : Ene 00
RT ¥% Porras

( 125 )

, . » a ~ ‘p
Undoubtedly p may be neglected by the side of —. Even if p
=
1
amounts to one Atmosphere, its value is certainly still smaller than
a v(v— 2b
0.0001 part of —. In the same way Pas
Vv, D

may undoubtedly

be neglected by the side of — or pv, (v,—2h) by the side of a —

)

. . a . . .
and this for the same reason, for — is a quantity of the same
v,(2b—v,) ;
F a
erier as. —.
wis
So the equation may be simplified to:
a
Pp b v,—b
log — = — = Oe re eas
v,?
For the limiting case, when v, may be equated to 6, we get:
a
p b
log — = — —.
* RE
Be
If we introduce the critical data, namely :
la ae:
pv = — —and RT,p=—— -,
27 b? 276
then we get the following equation for the calculation of p:
aed EN ad 5
— log fs FS pg 27
Pk we |

or, as logy 27 is equal to 3,3 and may therefore be nearly equated

27 et
to ewe get with a high degree of approximation:

This last equation is nearly equal to that derived by prof.
KAMERLINGH ONNES by means of a graphical method from the equation
of state with a and & constant, namely:

Pk
KaAMERLINGH OnNzES found this equation to hold in approximation up
to the critical temperature, here we could only derive it for low

1) Arch. Neérl. Livre Jub. dédié & H. A. Lorentz. p. 676.

( 126 )

temperatures.

If in equation (1) we do not immediately introduce
v, = 6, we may write it as follows:

a
P b v,—b
l Ss See
“9 HCD AN: RT z b
ie D,
Oe
a
log = é ——— Wie yor 2 log Be
a Ge RE L 2p

For values of »v

1
v,—b

only slightly greater than & we may write
. vy a
for log re So we get:

)

Pie ca! Die ee

— log — - e ognads
Dis Bel b ;

v,—b

; varies with the temperature and starts with
)
the value zero for 7 = 0°.

The value of

It may be calculated from:
a wm

=e O70) i gd i

This last equation may be written as follows:
Vv
8 T Ls ')
OF 1 ee eae
CG)
na

With = tiaaes we find for jae the value * and with ee — (0,54
DM RIS 3 b 5 Py :
l : fis 1 Ai
the value T With hie

)
the value of eee is equal to 0,2125.
k a ) 5
v,—b

pa et
The quantity varying with the temperature, the term —

Ma ap
does not represent the total variation of 8 with the temperature,
but the difference is small.

)

$ , he dp
We might calculate the value of — —

p dl
from the above equation, but it is simpler to calculate this quantity
from the following equation :

TT Op FS 0&
Roe he »=(5),

( 127 )

For coexisting phases this equation becomes :

wn op mess ah |
Te aa % ‘
( v,—?,
or
a a
Peek gale aan (2
-— == == ay a 2)
dil V.—?, U,V,

For low temperatures this yields:

a a a(v,—b)
T dp . v, b v,b
ie sare ae, RT
or
a
LT dp b v,
pdr iad
or

T dp Pit al hg v,—b
ey apie ey ce ae

For 7 = 7; equation (2) yields:

T dp
——]|]z=4
p aT Ji.

For the highest temperature, therefore, at which the pressure curve

ae : : k Praxis - :
occurs, the coefficient with which — must be multiplied in order to yield

ryy

T dt
the value of ieee
Pp di

temperature at which the liquid may exist without solidification.
Here we have one of the striking instances, how the equation of
state with constant a and 4 may represent the general course of a
quantity just as it is found in reality, though the numerical value
differs considerably. For the real course of the vapour tension is at
least in approximation represented by the formula:
a ee

— log —- =
oe J .

does not differ much from that for the lowest

but the value of f is not 4 or somewhat less — but for a great many
substances a value is found which does not differ much from 7.
Before discussing this point further, we shall calculate some other
quantities whose values for the liquid state for low temperatures
follow from the equation of state when we keep @ and ¢/ constant.
9
Proceedings Royal Acad. Amsterdam. Vol. VI.

( 128 )
Let us take again p to be so small that we may write
a is
—(v—b)= RT.
”
From this we may deduce:

TOO Sc v
av vo aT p=0 v—b :

’

wT
For = 0,585 (Ether at 0°)

i v—b

Eon i
Sg Tg oe

Pte A Po
b

—4,7 we find:

T f{ dv rs uf
PETS pants

So we find for the coefficient of dilatation under low pressure
and at this temperature which is so low that we may neglect the
pressure, the value:

1 (dv 0,00367 cee
= = eS 7) 0010.
v Gel 2,7

Comparing this value with that which the experiment has yielded
and which we may put at 0,001513, we see that it may be used
at least as an approximated value.

is equal to 4,7 as appears from :

With this value

U0,

Z : 1 dv P
The above equation (8) yields for —( ) With 2 = —20nen
p—v0

pn» Node
. . wl a . . . .
infinite value and so i 35° This quite agrees with the circumstance
k va ;
, Land ee
that the isothermal for fF, a5 touches the )-axis and it warns us
k 94

that equation (8) cannot yield any but approximated values for much
lower values of 7’.
dv
For the coefficient of compressibility @ namely —(=) in that
vdp/T
same liquid state we find

pe Se | a a ee 2)
j B,J POO a DO /

(129 >)

With the aid of the above data and putting »yz=957,5 atmospheres
we find:

8 = 0.0006 (nearly).

The experiment has yielded no more than about 0,00016 for this
value. So we have found it so many times too large, that for this
quantity the equation of state with constant @ and / cannot be con-
sidered to hold good even in approximation.

From the well known equation:

dv (OT) (Op\ _ hove
(or) (op) oe)
T (dv Op ) : (3
—| — 22 ew
a vp sm),

follows

and therefore

With the values mentioned above and yielded by the experiment
we should therefore have for ether at 0°:
Mes HOTS We, ee BN?
2 == 2 SC 31,5
0,00016

b 2
a= ss

According to this equation v should be smaller than 6 which would
be absurd, if 4 does not vary with the volume.
a bP

then we find for ether

If we calculate the value of 6 from ‘
Pk
6 = 0,0057 circa; in reality the liquid volume appears to be smal-
ler than 4. Dividing namely the molecular liquid volume by the nor-
mal molecular gas volume we find about 0,6047 *). From this appears
convineibly that the variability of 6 exists in reality and that there-
fore an equation of state in which this variability is not taken into
account, cannot possibly yield the data of the liquid state.
Let us return to the equation:
Pk aie
— log— = f ——.,
ye 7
which holds good at least approximately, as is confirmed by the
experiments, if we take for 7 a value which is about twice as great
as would follow from the equation of state if we keep a and 6 con-

1) Continuitét 2nd Edition, p. 171.
2) Continuitit 2nd Edition, p. 172.

( 130 )

stant. What modification must the equation of state be subjected to
in order to account for this twice greater value? C1Lausius answered
this question by supposing a to be a function of the temperature

Bre tints

Bil 10% “Vt
When we consider the question superficially, the difficulty seems
to be solved. But it is only seemingly so. At 7’= 7, this modifica-
tion really causes f to assume the value 7 — but this supposition
has consequences which for lower temperatures are contrary to the

experiment. If we calculate the value of

e.g. by substituting a

dp t.-—=
tH hy pie ee
am ee ey
; : a 273
as on page 4 and if we take into account that ¢= — 2 — oa
)
find
a 273
Tdp pret bac: fi
padT 2) ee
For lower temperatures we will put v, = 6 and we deduce
approximately :
Tdp 74% a 273
pare ie rer
or 3)
Pidp hae Oe (Ey
pads teat OWN,
Jk 1 T dp i 3 :
For ——=— we find then for —— a value which is not twice
Ty 2 p dl

as great as that which follows from a constant value of a, but a
value which is four times as great.

The equation :
|» == pie | == E = free
y 1 2

yields for this value of a:
Pp 2 Le we Ty
—log—=2XK — —/ 27 — Lt.

(Tk oh ;
In order to agree with 7 (G1) the positive term of the right-

ryyY

9
’ ; al Lk
hand member of this equation should have the form 2 x 37: and
the negative term should not be log 2 X& 27, but log 27°,

1) Continuitat, p. 171.

( 131 )

The imperfect agreement between the real course of the Vapour
tension and that derived from the equation of state with a and / con-
stant, has induced us to assume that @ is a function of the tem-
perature. It appears however that this agreement is not satisfactorily
established by the modification proposed by Cuavsivus. It will there-
fore be of no use to proceed further in this way — specially be-
cause this modification in itself is certainly insufficient to account for
the fact that liquid volumes occur which are even smaller than /.

If we had not supposed a@ to increase so quickly with decreasing

Pe; my 5
temperature as agrees with a ap if we had chosen ae 7 for in-

stance, then the greater part of the above difficulties would have
vanished.
We should then have found:

B
LLC EM Seiad Sense
p di Ty) RT»,
T

T\ \-=
The expression (1+ Tp \e T, is equal to 2 at 7 — Tz and at
k

T= 0 it would have increased to ¢=2,728 etc.; so the increase is
relatively small. But the term which should be found equal to
log 27°, would also have remained far below the required value. For
this reason it seems desirable to me to inquire, in how far the
variability of 4 alone can account for the course of the vapour
tension.

As I dared not expect that the variability of 6 could explain the
course of the vapour tension as it is found experimentally, and in any
case not being able to calculate this variability, I have often looked
for other causes, which might increase the value of the factor / from

27 a
— to about twice that value. The quantity — representing the amount
;

with which the energy of the substance in rare gaseous condition
surpasses that of the same substance in liquid condition, and this

Td
pd
it should be, I have thought that the transformation of liquid into
vapour ought perhaps to be regarded as to consist of two transforma-
tions. These two transformations would be: that of liquid into
vapour and that of complex molecules into simple gasmolecules.
If this really happened then the liquid state would essentially differ
from the gaseous state even for substances which we consider to be

quantity seeming — from the value of to be only half of what

( 152 )

normal. We should then have reason to speak of “molécules liquidogenes”’
and “molecules gazogenes”. It would then, however, be required that
the following equalities happened to be satisfied. In the first place
the two transformations would require the same amount of energy;
and in the second place the number of ‘‘molecules liquidogenes”’ in the
liquid state *) at every temperature would have to be proportional with

P(’, ares )

the value of The following equation would then hold:

a
Goa E
Tdp v, v, tes a

Ace (v7,—w,)é
v,) V,U,P p(v,—?,)

Not succeeding in deducing this course of the amount of the
liquidogene molecules from the thermodynamic rules and in aeceoun-
ting for the above mentioned accidental equalities I have relinquished
this idea, the more so as this supposition is unable to explain the
fact that the liquid volume ean decrease below /.

If we ask what kind of modification is required in the equation
of state with constant a and 4 in order to obtain a smaller vapour
tension, we may answer that question as follows. Every modification
which lowers the pression with an amount which is larger according
as the volume is smaller, satisfies the requirement mentioned. In
the following figure the traced curve represents the isothermal for
constant a and 6; the straight line AZ, which has been constructed
according to the well known rule indicates the coexisting phases,
and the points C and PD represent the phases with minimum pressure
and maximum pressure. The dotted curve has been constructed in
such a way that for very large volumes it coincides sensibly with
the traced curve, but for smaller volumes it lies lower, and the
distance is the greater according as the volume is smaller. Then
the point D' has shifted towards the right and the point C" towards
the left. For in the point exactly below PD as well as in the point

pdT a y pr,

dp
exactly below C' the value of - for the dotted curve is positive;
av

these points lie therefore on the unstable part of the modified iso-
thermal and the limits of the unstable region are farther apart.
But it is also evident — and this is of primary interest — that
if for the modified isothermal we trace again the straight line of
the coexisting phases according to the well know rule, this line
will lie lower than the line AZ. The area of the figure above AB

1) Diminished with that number in the gaseous state,

( 133 )

has decreased, that of the figure below A# has increased in conse-
quence of the modification. The line A'S’ must therefore be traced
noticeably lower in order to get again equal areas. /’ will of course
lie on the right of 4, and we may also expect that A’ will lie on
the left of A.

We have, however, put the question in too general terms; for
our purpose it should have been put as follows: what modification
in the quantities @ and 4 makes the vapour pressure at a temperature
which is an equal fraction of 7), decrease below the amount which
we find for it, keeping a and ¢ constant and it would even be
still more accurate not to speak of the absolute value of the pres-

: ; : P Sp : :
sure, but of the fraction —. The modifications in a@ and #+ should

Pk
then be such, — if we base our considerations on the preceding
figure — that in consequence of the modifications themselves the

values of 7), and p, either do not change at all or very slightly.
If we make @ a function of the temperature we have to compare
the following two equations:

Tie a
—= —— ——
: v—b wv
and
Bele Oly
a —
v—b Tv?
Botl fer pte 22 na et
: ations yie = —— anc —— 1.e. the same
oth equations yield fi /;, 27 b and Dk = 57 53 ne sa

values for 7; and p, if a and ¢& have the same values in both

( 134 )

equations. The value of » — the values of 7 and wv being the
same for both curves — for the modified isothermal is smaller than
that for the isothermal with constant a@ and 4, and the difference is
greater according as the volume is smaller. According to the figure

discussed e — the value of = being the same for both curves —
Dk ie
will therefore have a smaller value for the modified isothermal than
for the unmodified one. A value of @ increasing with decreasing
value of v would have the same effect. But I have not discussed a
modification of this kind, at least not elaborately, because I had con-
cluded already before (see ‘Livre Jub. dédié a LorEnrz” p. 407) that
the value of the coefficient of compressibility in liquid state can only

The

be explained by assuming a molecular pressure of the form
v

supposition of complex molecules in the liquid state would involve

a modification of the kinetic pressure to g(vT), where g (v, T)

CEQ

must increase with decreasing value of v. Also this supposition would lead

Op b.. ee batt
to a smaller value of — for the same value of ae This is namely
Pk k

certainly true, if the greater complexity has disappeared in the critical
state, and if therefore the values of 7), and p; are unmodified; pro-
bably it will also be the case if still some complex molecules occur
even in the critical state. But whether this is so or not can only be
settled by a direct closer investigation, and for this case the property
of the drawn figure alone is not decisive. I have, however, already
shown above, that we cannot regard this circumstance as_ the
probable cause of the considerable difference between the real value
of the vapour pressure and that calculated from the equation
of state with constant a and 6. So we have no choice but to
return to my original point of view of 30 years ago and to suppose
6 to be variable, so that the value of 6 decreases with decreasing
volume. It is clear that a variability of this kind causes the kinetic

,7]

pressure to be smaller than we should find it with constant 4,

v—b

and the more so according as / is smaller. Moreover it is possible
in this way to account for the fact, that liquid volumes occur smal-
ler than the value which 4 has for very large volumes and which
I shall henceforth denote by 6,. Or I may more accurately say that
I do not return to that point of view, for properly speaking I have
never left it. As the law of the variability was not known, I could

( 135 )

not develop the consequences of this decreasing value of 4 — but
it appears already in my paper on ‘The equation of state and the
theory of cyclic motions” and in the paper in the “Livre Jub. dédié
a Lorentz” quoted above that I still regarded the question from the
same point of view.

My first supposition concerning the cause of the decrease of 4
with the volume was not that the smaller value of ) corresponded
to smaller volume of the molecules. 6, being equal to four times
the molecular volume, I supposed smaller values of 4 to be lower
multiples of this volume. In this way of considering the question
the decrease of 6 does not indicate, a real decrease of the volume
of the molecules. We will therefore call it a quasi-decrease.

It can scarcely be doubted that such a quasi-decrease of the
volume of the molecules exists. In his ‘“Vorlesungen” BorrzmMann
started from the fundamental supposition that the state of equilibrium
ie. the state of maximum-entropy is at the same time the “most
probable state”; in doing which he was obliged to take into account
the chance that two distance spheres partially coincide. And comparing
the expression which he found in this way for the maximiun-entropy

°° =

with the expression Rf (i.e. the entropy in the state of equi-

v—l
librium according to the equation of state) it was possible for him
to determine the values of some of the coefficients of the expression:

b=ty}t—o( 2) 4a(“) baa .

This method is indirect. I myself had tried to find these coeffi-
cients by investigating directly the influence of the coincidence of
the distance spheres on the value of the pressure. According to
these two different methods different values for the coefficients were
found. My son has afterwards pointed out (see these Proceedings
1902) that also according to the direct method a value of a equal
to that calculated by Bonrzmann is found, if we form another
conception of the influence on the pressure than I had formed and
since then I am inclined to adopt the coefficients calculated according to
the method of BontzMANN as accurate.

But these values apply only to spherical molecules and only in
the case of mofiatomic gases we may suppose molecules with such
a shape. It is not impossible that for complex molecules these coef-
ficients will be found to be much smaller. Moreover for the determina-
tion of a knowledge of all the coefficients is required — and

( 136 )

we cannot expect that the calculations required for this purpose will
soon be performed. Even the determination of 3 required an enormous
amount of work — compare the calculations of van Laar.

For complex molecules another reason is possible for decrease of
6 with decreasing volume. The molecules might really become
smaller under high kinetic pressure i.e. in- the case of high density.
If the atoms move within the molecule and we can hardly doubt
that they do so — they require free space. And it is highly probable,
we may even say it is certain, that this space will diminish when
the pressure which they exercise on one another, is increased. The
mechanism of the molecules however being totally unknown it is
impossible to decide apriori whether this decrease of the volume
of the molecules will have a noticeable effect on the course of
the isothermal. In my application of the theory of cyclic motions
on the equation of state I have tried to give the formula which
would represent such a real decrease of the volume of the molecules
with diminishing volume. vAN LaAar has tested this formula to AMAGAT’S
observations on hydrogen, — and though new difficulties have
arisen, the agreement is such that we may use the given formula
at any rate as an approximated formula for the dependency of 6
on v. IL will apply the formula, which may have a different form
in different cases, in the following form:

b—l b—b, \?

feel (ae)
vo—b bg—b,
The symbols 4, and 4, in this formula denote the limiting values

for 6, the first for infinitely large volume, the second for the
smallest volume in which the substance can be contained. For

more particulars I refer to my paper on ‘‘The equation of state and
the theory of cyclic motions.” Van Laar concluded from his inves-
tigation that agreement is only to be obtained if, decreases with 7,
a result which I myself had already obtained applying the formula
for carbonic acid (Arch. Néerl. Serie I, Tome IV, pag. 267). If this
is really the case and if it appears to be also true after we have
modified the formula in some way or other compatible with the
manner in which it is derived, then the following difference exists
between the course of 4 with v» when ascribed to a quasi-diminishing
and when ascribed to a real diminishing of the volume of the
molecules: in the first case 6 is independent of 7’, in the second

pr Lirica dp\ .
case however it does depend on 7”. The fact that i) is not per-
at /y

fectly constant seems to plead for the latter supposition.

( 137 )

For the present, however, I leave these questions and difficulties
out of consideration, and I confine myself to showing that a for-
mula of the form (4) can really make the considerable differences
disappear which we have met with till now. The more so as this
formula appears to be adapted for the derivation of general conse-
quences, which follow from the decrease of 4 with v. I leave there-
fore a possible dependency of 4, on 7’ out of consideration. Moreover
in applying the formula I will suppose ),—20,. I choose one —
in some respect arbitrarily — from all the forms which | have found
to be possible (compare also my paper in the Arch. Néerl. “Livre
Jub. dédié a Bosscha). The numerous calculations required in order
to investigate in how far modifications are necessary and possible
in order to make the agreement with the experiments more perfect,
may perhaps be performed later.

A. The tension of the saturated vapour.
: /

Let us begin with the caiculation of the pressure of the saturated
vapour at low temperatures and let us to that purpose write the
equation expressing that. the thermo-dynamic potential has the same
value in coexisting phases, in the following form:

a d (v-b) Sf 300
pe-—- kT —-RTj—_| = Wnty 28 hoe tal nd rae
v v-b v-b |, x

a (db
| we = - RT log(v-b) — RI ( | = | ee oro ene |
v J vb), 2

In my paper “De kinetische beteekenis der thermodynamische
yotentiaal” I have already pointed out the signification of the term
I : 8

a
re. 5° it represents namely the amount of work performed by
p— ;

the kinetic pressure on the molecule when this passes ina reversible
way from the condition of the first phase into that of the second
phase and when its volume is therefore enlarged either fictitiously or
as we now take it to be, really. We may calculate this term if we
assume the chosen form for / and this is one of the reasons why
I adhere to the idea of a real increase of the molecular volume.
But though its value may depend upon the particular form which
we have assumed for 4, it will certainly have a positive value for
every law of variability of 6 with v which we may choose.

: . (de b—b,
Let us for the ealeulation of fe denote

v—b b,—b,

by z, then we

( 138 )

have db= (bh, rye and according to the form of formula (4)
chosen for 4:
bo
v—b z
SS? db 1—2z? 1
in consequence of which | sp Passes into J dz — logz — an

Substituting into the expression for the thermodynamic potential

we get:

—b 1 b—b, \?
pe — — — RT log (v—b) — RT log. Sek !
v b,—b, 2 bg—b,

If we suppose the temperature to be low, the second phase is a
rare gas phase and we have:

b—b
pv = RT, log (v —b) = — log a and > my ey ay! |

In consequence of this we get:

b-b, ped. \? “<a
Pr, =, RT og ( -b,)-RTlog Ree) =RT4. RT bg = =e

tbc: ate oA Gee, RT 2
or
b,-b, 1 b, -b, p(e,- b,)
; -—-RT- RTlo« * RT log
8 a5. 2h, “15 Rey! RT
or
-b, | -b b,- 5
pb, Fees eres POY | RT gg 4 = RT = RP log —
eS fe ae aes ss
Pie
VY

As yet we have not applied any approximation for the liquid
condition.

If in the first member we collect the terms containing p, we may
write them as follows:
v,>—2b,2,

The value of v, in the liquid condition being only slightly larger
than 24,, the value of this expression remains below pé, and it may
certainly be neglected; if in the second member we neglect also

p compared with —, then we may write the equation for the caleu-
Vv;

lation of the vapour pressure at low temperatures as follows:

p b, v,—b, b,—), b,—4,
log + = — eet olay 7 5
a RT 6, SE Gt aL IOe SF (9)

wise. 4

In order to draw attention to the principle circumstances, we
shall assume for the present that the following equations also hold
in the case that 4 is variable :

and

Equation (5) may then be written in this form :

P 2d Tibg Vv, - b, b,—b, b,- b
log = — — a —— — log ——— ——
aa a b, b,—b, v,—b

He apt
27n(~*)
VY,

A comparison of this equation with :

Ty,
— log & =i(F —1
Pk

shows that it is possible to satisfy the condition that the coefficient of

Fy = Sagal) pe
ca approaches to 7 by equating 7" to 2, ie. by assuming that the
1
molecules in volumes equal to the volume of liquids at low tempe-
‘atures are only half as large as those in the gaseous condition. But

; Lk
the agreement in the value of the coefficient of Z does not suffice for

establishing agreement between the calculated value and_ that of
the formula which at low temperatures is followed by the vapour
tension, though it be only in large features. For this purpose it is

required that
log 27 Ga?) paren 2 ie Ux nee ae Cites
Oy b,—6, v,—b, b,

differs only slightly from 7.

We must return to the equation of state in order to be able to
determine the value of this expression, and we must investigate its
consequences for the case that p may be neglected compared with

= So we must return to:
a ry?
tO ee ee ae
Vv,

If we express }, and v, in the quantity z, we get:
b, —b, + z(b,—2,)

and

—~ (by —b,)

7 oe

( 140 )

2.
», =b, + (« - Jr)

iA
~

Substituting these values and putting b,=76, we get the equation:

n(n—1 é
8 T gear
oF 7 ee z 2
1+ hike es (n—1)
If t 2; th t f 0,8
we put n=2, then we get z=— or at)
it f.
4 = _ 33 Dy
5 She
1 qr"
2 y ——(0),65
6 Ty
I SH ae
z= be —_=0 655;
‘ Ty,
For very small values of ¢ we may neglect z* compared to unity
and we may calculate the value of z from the approximated equation:
BALE 22
OT pe ol oe
; Ses See!
which equation yields the value of acre for es ae For such
b,—b v,—b z v 1422
pirealiewaluecal cowe have ..————— — and — ieee
v,—)b, b, l+z b, l+z

We will assume that for all temperatures below 0,6 7), the vapour
phase may be considered to have a sufficient degree of rarefaction
for following the gaslaws; therefore we may assume z to have a

1 il On he
value below 7 If we choose. z = 7 then we find for ( “) the
v,
By \2 ih 4><16 ae ;
value 4 | — ] =4| ——— Jor = 2,56. With this value
we have:

by *ba—b, 1 b,—b, v,—)b, £ ten i ecw <"
log 27 | — | — - + ——— = log 27 20,5 + — + 0,11.
; b,—b 2 v,—b, b, ; 2
It is true that this value is smaller than /og 27, but it approaches
sufficiently to that value. The fact that it is smaller than /og 27? is in

perfect agreement with the circumstance that for the quantity / in
Pp ee 18

the formula — log —~ =/ Tp according to. the experiments at low
Pk

( 141 )

temperatures a higher value must be chosen in order to establish
agreement. For a higher value of 7 yields the same result as a not

ee ees B8
higher value of / in bars from which a smaller quantity is subtracted.

It might appear that the dependency of pon 7’is strongly increased

by the difference between the values of z for different temperatures.

The following relation however always holds good if / is indepen-
dent of 7’:

a
T dp ee
pat Pag

= and therefore (see p. 127)

Tdp _27Tyby v,—b
pdT 8 Tb, b
In the supposition made here, this is equal to:

LPdp AT, z

pdt 4T1+2 I1+2

which expression does not vary much with z, if z remains small.

T dp
Yet we find the value of ——— at low temperatures for most sub-

eS p aT
_ stances to be somewhat higher than is indicated by this formula.
a We should in fact have found a higher value if we had assumed

b, >2b,. If therefore we had only to deal with the formula for the
vapour tension, then it would be rational to investigate the conse-

4 quences of the suppositions: m = _ or n= 2 = Other experi-
mental quantities however follow less perfectly the formula chosen
for 6, if we give m these values. Therefore I will confine myself
to the investigation of the consequences of the equation chosen for
mo with 2 — 2.

I think the following theoretical observation to be of some impor-
tance, even if we disregard the question whether we have established
a perfect, numerically accurate agreement with the experiments, by
assuming the quantity 4 only to be variable, and even this varia-
bility to be independent of 7. The pressures in two coexisting phases
which lie at a great distance from the critical conditions satisfy, if

( 142 )

we suppose the volume of the molecules to be invariable, the follo-
wing approximated equation

a
p b
6g :
< M AT
In this formula J/ denotes the pressure of the liquid phase i. e.

a
the molecular pressure, and 3 the heat required for the transfor-

)

mation.
The following approximated equation holds for molecules of

variable volume:

a
Pp b,
log = —
“ Mk Jag be

a . . . . .
where again i, denotes the heat required for the transformation, which
)

1
is greater if the molecules in the liquid phase are smaller, as well in the
case that this diminishing of the volume is real, as in the case that it
is only fictitious. Again the molecular pressure is also higher. But
the molecular pressure is now provided with the factor A. If
it is a real diminishing then the signification of this factor can be
sharply defined. The factor is in this case at least approximately

b,—b ; Sere : : :
z a its signification can be derived from the following

0
equations, (comp. my paper: “The equation of state and the Theory

of cyclic Motions’) :

OP,
J ——— 1 (i) ——= M
| £+(F), 1@ i Nicsemre a

one 4, pees
Ob , b, (bg— = v

OP;
M + | —
b,—b, Ob b=b,

b,—b, + A '
OG)5, = b,
)

; OP, : : ;
The quantity (5 in this equation represents the atomic forces,

equal to

)
which keep the molecule intact or at least contribute to the causes
which keep the molecule intact. Making use of this value of A we
find :

log - 7 coal Ee Se ae

The first member of this equation contains the logarithm of the
product of two ratios, namely the ratio of the inwardly directed forces
which keep the molecules — considered as separate systems —
inside the vapour and the liquid phase, and the ratio of the inwardly
directed forces which keep these systems in both phases intact. In
the case that it is a quasi-decrease it is impossible to indicate the
db
v—b
differing also in this case from zero, the above considerations show
with certainty that the quantity A’ exists also in this case, The
question whether it will be larger or smaller can only be decided
by a comparison of the course of 6 with v in the supposition of a
quasi decrease with that in the supposition of a real diminishing,

=) . . > UJ
= has been neglected in equation (6), This equa-

signification of K in such a precise manner; but the qwantity

b
The term oe

ae U0
tion applies only for low temperatures, and for those temperatures

1
the term in question is equal to-> according to the formula given

for 6. It is remarkable that also many other suppositions concerning the
nature of the forces which keep the molecules intact, different from
those suppositions which have led to the form chosen for 6, yield
the same equation (6), every time however only after neglection of
a relatively small quantity in whose kinetic interpretation I have
not yet succeeded. We obtain equation (6) when we assume, 1* that
the molecule may be regarded to be a binary system consisting of
two atoms or of two closely connected groups of atoms, which we shall
eall radicals, 2"¢ that these parts move relatively to each other, and
3'¢ that the amplitudes of these motions are of the same order
as the dimensions of the atoms. If the parts are radicals, other
motions take place inside those radicals, but the amplitudes of these
motions are so small that they have no noticeable effect on the
volume of the radicals. We have represented the forces which the
atoms or radicals exercise on one another by « (/—4,), so in the
gaseous state by a@ (b,—0,). So, as we have derived the equation:
hyo) eile
and as 6,—#, is constant, ¢@ must be proportional with the temperature,
and I must acknowledge that it is difficult to image a mechanism
10

Proceedings Royal Acad. Amsterdam. Vol. VI.

( 144 )

for the molecule in which the forces between the two parts of which
it is thought to consist, satisfy the conditions, that they are propor-
tional with the distance, and at the same time increase proportionally
with 7. Perhaps we get a more comprehensive conception of a molecule,
if we ascribe the forces which keep the atoms together in the molecule
not to a mutual attraction of the atoms, but to the action of the
general medium by which the atoms are surrounded. The molecules of
a gas are free to move inside the space in which they are included
and they are kept inside that space only by the action of the walls;
in the same way it might be that the atoms of a molecule were
free to move inside a certain space — the volume of the molecuie —
and that they are only prevented from separating by an enclosure
of ether. Still assuming that 6,—é, has for all temperatures the
same value, we should be again obliged to conclude that the forces
which keep the molecule intact are proportional with the temperature,
but this conclusion would now be much less incomprehensible.
According to these suppositions it is also rational to assume that the
force required to split up the molecule into two atoms is the same
for all temperatures. So we should obtain the formula:
Peale ; b—-b,

v—b b,—b
With this equation we have:

b b
J
lb 1 i b,— 6 b—b
2 = fa Ne aye fs
—b b—b, b,—b, b—b v—b
:

Ss |
b
ves

b, ‘
— has now twice
I—O

0
the value it had before, but the chief term has remained unchanged.
In my further investigation, however, I will continue with the dis-
cussion of equation (4), because my chief aim is only to investigate
the principle consequences of the nearly certainly existing diminution
of 6, independent of the question whether this diminution is real or
only fictitious; and in doing so I will confine myself to a certain

conception of the molecule — that which leads to equation (4) —

The term which must be subtracted from log

as an instance.

B. The coefficient of dilatation and the coefficient of compres-
ae of “we t /
sibility of liquids.

Let us again assume the temperature to be so low that » may be

. a .
neglected compared with — and that we therefore have:
7B)

(145 )

~ (v—b) = RT.
v

The value for za (=) which we may calculate from this equa-
v \dT/,

tion applies only to the pressure p= 0, and is therefore not the
same as would be found for another constant pressure; neither
is it that which corresponds to the points of the border curve.
For very low temperatures the difference will probably be small
For higher temperatures the differences might be considerable; and
for the temperature which is so high that the isothermal in its lowest
dv
dT
be absurd to suppose the two values to be mutually equal

point touches the v-axis, in which case — = © , it would even
v
4

1 (/ dv
An accurate calculation of the value of — yields aceor-

Vv d tf p=0

ding to the relations chosen above :
1 22"
ar ay eee

T/dv ok l—<z
v Oe z
1—(n—1) ae — 4 (n— 1) -a_ 2)

We will put #1 and the following approximated relation :

T (dv ee
OWT eg hae

(»—1)2] 14

ety i

1
With Lae (see p. 140) this yields 0,4 for the value of Tay ox
a = on (for ether) = 0,00146. Our assumptions therefore appear to

lead to a value for the coefficient of dilatation which does not deviate
much from the experimental value.
fal
If we had taken the form ae 7% for a, then the corresponding

value of z would have been and we should have had:

T ( dv oh 22
Se ee :
v\dT)}, Ped (fa On eee

which is only about *,, of the true value. From this we conclude
that the assumption that oni relations are satisfied and that at the
B

same time a has the form ae 7* leads to inaccurate results..
10*

( 146 )

vd 1
We might also write a value for (- ) or 7 , but we will
5

culate the coefficient only indirectly from:
T ( dv dp a
v\dT}, dvr v

ie Pa
0,413 X 6000 = 27 p, (=)
v

or with approximation :

oo
>

1,6 —— ,
1+2¢

1
which agrees with z= ee

The value of calculated according to our relations may there-
fore be considered to be at any rate approximately accurate.

Yet it remains strange that for the liquid volume itself a calculation
according to our suppositions yields a value which is much too small.

According to a table in Cont. I 224 p. 172 the liquid volume for

1
temperatures which do not differ much from - 77, is equal to 0,8 4,.

—

Even if we take into account that 49 <6, we cannot diminish the
factor 0,8 to less than 0,7.
We have then the equation
0,7 bg = 6, (L + 22)
or 077 oth De.

1
With n= 2, this yields z= —, which does not agree with the
oO

1
value 7 which we must assume for z, as we saw above. I have

not yet been able to investigate, what modification must be made
in the relation assumed for 4; e.g. to put 21,8 or to suppose 4,
really to be smaller at low temperatures. If we suppose }, to be
a function of the temperature, then the calculations become very
intricate and difficulties of another kind arise. Therefore I prefer to
regard the above considerations as conducing to point out that
everything shows that 4 must really increase with v.

Let us investigate what consequences of general nature follow from
this variability of 6. In the first place we observe that the three
real values of v for given temperature and given pressure cannot
be calculated any more by means of an equation of the third degree.
The equation of state namely may assume a very intricate form if

( 147 )

we substitute in it the expression for 6 which we get by solving
the equation which expresses the variability of 6 with » and 7 —
the possibility of a dependency of 6 on 7 being admitted. We shall
represent the solution of this equation by

Bailey! |).

But the general course has remained the same; e.g. the fact that
for temperatures below the critical temperature a maximum and a
minimum pressure occurs. The critical temperature is that for which
this maximum and this minimum pressure coincide and the critical
point may again be calculated from the three equations:

p= Fe, T),

dp
and (3? — 0
dv? } T

If therefore we could exclude all disturbing influences, if we
could neglect phenomena of capillarity and adsorption, if we could
neutralize gravity, if we could keep the temperature absolutely
constant throughout the space occupied by the substance, if we
could perform the experiments with perfectly pure substances without
the slightest trace of admixtures and if we could suppose that the equi-
librium is established instantaneously, then we should have coexistence
of two homogeneous phases of well defined properties for all tempera-
tures below the critical one, and exactly at the critical temperature
only one homogeneous phase of well defined properties would exist.

But the requirements enumerated here can never be fulfilled.
Already below the critical temperature deviations occur. The straight
line representing the evaporation parallel with the v-axis has probably
never been realised as yet in connection with the circumstance
that nobody has as yet experimented with a perfectly pure substance.
The boiling point always varies when the distillation is continued,
chiefly if we observe near the critical temperature. If in a closed
vessel we heat a substance which is separated into a liquid and a
vapour phase, then the properties of the liquid phase may be varied
by shaking the vessel (Eversnem. Phys. Zeitschr. 15t June 1903),
probably in connection with the circumstance that the liquid expanding
during the heating is internally cooled in consequence of the expansion
and the evaporation and reaches the surrounding temperature only
very slowly by conduction; and also in connection with the always
occurring impurities. If further the substance is subjected to gravity,
then neither vapour phase nor liquid phase is homogeneous. To

( 148 )

every horizontal layer corresponds another density according to the
formula of hydrostatics:

dp = — oadh.

For temperatures far below the critical one this circumstance is
of little importance; for the critical temperature itself, however, the
influence of gravity is considerable. If we write namely the formula
of hydrostatics in the following form:

1 dp dh
—— = — g—,
o do do
dp dh : ‘
then we see that — = Oor— =o at that point of the height of the
-” 2

do
vessel where the critical phase really occurs, i. e. where = ==
u

If therefore we construct a graphical representation of the successive
densities, laying out the height as abscissa and the density as the
ordinate, then we get a continually descending curve. In the beginning
its concave side is turned downwards; at a certain point the tangent
is vertical and the curve has a point of inflexion; farther the convex
side is turned downwards. In the neighbourhood of the critical
phase we find therefore a rapid change in the density.

The equation of state can only account for the state of equilibrium
described above as it deals only with states of equilibrium. Another
question is how that equilibrium is established and whether it is
established in a longer or shorter time according to the method of
investigation.

It has been observed several times in these latter years that the
state of equilibrium of a quantity of a substance which is contained
in a closed vessel slowly heated to the critical temperature, requires
so long a time before it has been reached that some investigators have
concluded that the liquid consists of other molecules than the vapour.
De Heen, Gauirzinzg, TRavse and others speak therefore of “molecules
liquidogenes” and ‘molecules gasogenes’. Some of them suppose the
“molécules liquidogénes” to be more complex, others suppose them
to be only smaller. This latter supposition agrees with the ideas
I have expressed in my ‘The equation of state and the theory of
cycle motions.” And for an explanation of the fact that the equi-
librium is so slowly established, these investigators refer to the slow
diffusion of the heterogeneous molecules.

To this fact they refer however wrongly. The kinetic theory
accounts satisfactorily for the slowness of the diffusion and has even
enabled us to calculate the coefficient of diffusion for mixtures of

( 149 )

heterogeneous molecules which cannot pass into one another. Here
however we are dealing with molecules which can pass into each
other. And if in such a case the establishing of the equilibrium
requires a long time, then we must account for the fact that in this
case more-atomic molecules only slowly conform their size to the
varied circumstances, though in other cases they can bring their
internal motions so quickly into harmony with, for instance, a variation
of the temperature.

I therefore think it not to be proved, that the increase of } being
either a real or a quasi increase, requires a noticeable time to be
brought about, till the real constancy of the temperature throughout
the closed vessel and the perfect purity of the substance has been
proved, which as yet is not the case.

It must be granted that the summit of the boundary curve is
broadened and flattened by the variability of 6 and that the critical
isothermal may be estimated to have a larger part which is nearly
parallel with the v-axis. And this causes considerable differences
of density to follow from small differences of pressure. But if no
causes even for small differences of pressure can be pointed out,
then the occurrence of differences of density larger than those that
follow from the action of gravity cannot even be called phenomena of
retardation, these latter being also a kind of phenomena of equilibrium.

Another observation of general nature before I conclude at least
for the present these considerations on the influence of the variability
of 6. This variability accounts for the possibility of deviations
from the law of corresponding states. If the way in which 6 varies
with tue volume is different for different substances i.a. in couse-
quence of a different ratio of 4, and 4,, then the general course
remains the same, but the isothermals become different in details. I
have even begun to doubt whether the behaviour of substances
containing the radical OH in the molecule acids, alcohols, water
ete., which in gaseous state present no association to double molecules
and which are often indicated by the name of abnormal substances
— which behaviour deviates so markedly from that of other sub-
stances, must really be aseribed to association of the molecules in
the liquid state.

In connection with equation (6) (see p. 143) the question arises: Is the

Ty
Ob
small? Is the easy substitution of one of the components perhaps an
indication of a feeble connection of the parts of the compound which
involves a strong variability of the size of the molecule. The so called

quantity which I have denoted by for these substances perhaps

( 150 )

abnormal substances would then be those whose molecules can undergo
large variations in size. More suchlike questions arise — but I will
no further discuss them without a closer investigation.

POSTSCRIPT UM:

When the above paper was printed I received a kind letter from
Dr. Gustav TrIcHNER, who informs me that he has sent me one of
his tubes filled with CCl, in which he has succeeded in strikingly
showing the large differences in density at the critical temperature
by means of floating glass spheres whose specific gravity has been
determined accurately. He himself however acknowledges emphatically :
“dass diese Erscheinungen insofern keine Gleichgewichtszustande vor-
stellen, als die Phasen in Beriihrung mit eimander sich aiisserst lang-
sam (beim Riihren sofort) zu einer homogenen Mischung vereinigen.”

The equation of state deals only with states of equilibrium as I
have observed already before. Discussing these anomalies as I have
done in this paper, I treated questions which properly speaking lie
outside my subject. I have mentioned them, because I also expected
for a moment that the variability of 4 assumed by me, might account
for the slowly establishing of the state of equilibrium. But this is
only the case if we assume, that the molecule does not immediately
assume the size which agrees with the value of 7 and v — and this
seems after all to be improbable to me, though I acknowledge that
molecular transformations occur which proceed slowly. The expectation
of Dr. Tricuner, that the theory would lead to two really homo-
geneous phases is inaccurate in consequence of the action of gravity —
as has been shown already before i. a. by Govy. Not the phenomenon
itself as it is seen, is anomalous, only the differences of the density
are anomalously large. It is true that Dr. TkICHNER writes to me
that he has ascertained that the temperature was constant but even a

1
difference of temperature of 100 degree yields a very considerable

difference in density. For densities which are larger than the critical
one we have:

S a being comparable to unity. If therefore in a point the tempe-

1
rature is 7 degree too low, a diminishing of ihe pressure with

( 151 )

: 1 .
an amount of about 00 atmosphere will keep such a phase in equi-
librinm, at least as far as the pressure is concerned. And a cause
; ; 1
which accounts for a difference of pressure of about 00 atmosphere

accounts also for considerable differences in density as the critical
isothermal runs nearly horizontally in the neighbourhood of the
critical point.

A return to the time when we thought to explain a thing by
speaking of solubility and insolubility, seems not to be desirable to me.

Chemistry. — “On the possible forms of the melting point-curve
for binary mixtures of tsomorphous substances.” By J. J.
vAN Laar. (Communicated by Prof. H. W. Baknurs RoozEBoom).

I. The occurrence of so called “eutectic points” in meltingpoint-
curves does not seem to agree with the supposition of perfect tsomorphy
of the two solid components and of their mixtures. This fact has
been repeatedly pointed out. It has been assumed that an inter-
ruption in the curve representing the solid mixtures (as in fig. 1 of
the plate) can only occur for tsodimorphous substances, and that the
series of mixtures in the case of isomorphous substances was necessarily
to be uninterrupted (as in fig. 2).

Lately STORTENBEKER *) expressed again the same idea and this induced
me to subject the question to a closer investigation. In the following
paper I hope to show that an interruption in the series of the
mixtures can very well occur even for perfectly isomorphous sub-
stances. In order to do this we must keep in view that — especially
in the solid condition — wnstable phases may occur, and that in all
occurring cases it is possible to trace the meltingpoint-curve conti-
nuously through the eutectic point. Only the stable conditions which
generally lie above the eutectic point are liable to be realized, so the
series of the mixtures is interrupted only practically.

Prof. Bakuuis RoozeBoom has expressed the idea of prolonging
the meltingpoint-curve beyond the eutectic point already before;
the way however in which we must think this to be performed is
indicated inaccurately in the figure of an earlier paper of SrORTENBEKER”).

1) Ueber Liicken in der Mischungsreihe bei isomorphen Substanzen, Zeitschrift
fiir Ph. Ch. 48, 629 (1903).

2) Ueber die Léslichkeit von fydratierten Mischkrystallen, Z. f. Ph. Ch. 17,
645 (1895).

( 152 )

The following considerations are an abbreviated survey of a more
elaborate paper which will be published elsewhere *).

II. I have shown in a previous communication’), that we may
express the molecular thermodynamic potentials of the two compo-
if we assume the equation of state of
as follows:

nents of a Liquid mixture
VAN DER WAALS

a,x?
ul, — e, — C, Al — (x, --- h) fi log i —- Gara? — RT log (1—2)
a (il—ezy
pe, —¢, T'— (kh, +B) T log T ae + RT log «

The different quantities occurring in these equations have the well
known signification, indicated in the paper quoted above.
In order to simplify the calculation we shall always assume in

: —b,-+6, ‘
the following, that r| = 5 = 0, and therefore that the equa-
1
A A
ons f¢, = a eLL 0h—— Apo ote identically satisfied, A representing
yy 2 ai

a, 6,2 —2a,, 6,6, +a, 6,?. This assumption comes to the same as
the supposition that the molecular volumes of the two components
differ only slightly, which supposition may be considered to be

«0° a,(1—a)?
———— and ———
(1+re)y (1+ re)?
influence of the two components in the mixture only approaimately.

In the second place I shall assume that the above expressions also
apply to the solid state, an assumption which we may expect to be
satisfied in first approximation, as the case we are dealing with,
namely that of mixed crystals or solid solutions*), shows in many
respects the greatest analogy with liquid solutions.

If we also suppose 7 in the solid phase to differ little from zero, and if
we indicate all quantities in that phase with accents, then we may write:

For the liquid phase:

uw, me, —¢, T— (hk, + R) Tlog T+ ax? + RT log 1—2)

justified, as the terms represent the mutual

u, =e, —¢, T— (k, + KR) Tlog T+- a —2) + RT log x
For the solid phase: eek,
wae, —¢, T— (kh, + BR) Tlog T+ a! &? + RT log (1—2’)
we ae,—¢, T—(k, + RT log T+ a (1-2!) + RT loge

1) In the Archives Teyler.

2) These proceedings April 24, 1903.

3) Mixed crystal will always be treated here as solid solutions, though in these
latter years difficulties have sometimes arisen against this view. See 1a. Storven-
BEKER, l.c., p. 633,

ali Ah ae he

( 153 )

The components are in equilibrium in both phases if
HSH, FW Hy,
so that we get (the terms with 7Z’/oy 7’ cancel each other):
e,—¢, T4+a274-RT log (1—2x) = e7»,—e'", T4-a' 2" + RT log (1— 22’)
e,—¢e, T+a(l—a)?+RT log « = ¢',—e', T+ a! (1—2')? + RT log a
or with
a a a . = .
€:,— O71 1» Og Og Fg OO 11 OO Y;,:

i = _/
RT log i : = 9q,—7, T+ (a 2*—a' x’)

—— ae
'

RT log

: —= 751s T+ [a(1—a)?—a'(1 —w')?]

If we pay attention to the circumstance that for 7~=0, «’=0 the
quantity 7’ must be equal to 7, and in the same way 7= 7’, for
w=1, w=1 (7, and 7, are the meltingtemperatures of the pure
components), then we may write:

LG renee
ee ? er
We have therefore
7 Zp 2, 2 ! fo
T | —+ Rlog i = q,+(a 2’—a' 2’)
sare
Wg ge z air,
T | — + Rlog = q,+[a(1—az)?—a(1—z')?]
oi x :
or with
C= Ge. e = 4. 8:
qi !
1+ © (ea—2)—s(0—2'y"
1 t a?§— p': “ts
tT ji a pe ee 8
re f= RY, a’
1+ — log 1+ log —
qd: 1—z Is z

These are the two fundamental equations from which we may cal-
culate the values of « and 7’ corresponding to each given value of
z, and which represent a course of the meltingpoint-curve which is
perfectly continuous, at least theoretically.

It is easy to see that in the case that no mixed crystals occur, 2
is continuously equal to zero, and the equation is reduced to

14-82
T —T. BEF

ds ’
1— log (1—«)
a

1
an equation which I have already deduced in a previous paper.
But in the present paper we will assume that the mixing-proportion

( 154 )

in which one of the components occurs in the solid phase, though in
the extreme case it can be exceedingly small (i. e. practically
equal to zero), yet in general can never be rigorously equal to zero.
In this way the continuity remains preserved, and we may give all
possible values to the quantities @ and #' as to # from 0 to o.

We shall observe here at once that the quantity which dominates
the whole phenomenon is the quantity p' of the sold phase. When
this quantity has a high value, the solid phase will contain only a
very small trace of one of the two components, and only when the value
of this quantity becomes comparable with the corresponding quantity
8 in the liquid phase, the case of fig. 2 can occur. It is therefore
of the highest importance to know the exact signification of these
quantities 8 and ’, or rather of the quantities a=q,Pand a’ =4q, #.

From the above deductions appears namely that the quantity ea
does not represent anything else but the absorbed latent heat required
for the mizing per Gr. Mol. for the case that an infinitely small
quantity of one or the components is mixed with the solution in
which the mixing-proportion for this component is 1—a. In
the same way the quantity a@(1—~z)*? represents the latent heat
for the other component in this solution. The quantity a@ itself is
therefore the latent heat for the first component for «1; i.e. for
the case that the first component is mixed with a solution which
consists exclusively of the second component — or we may
also say that a is the latent heat for the second component for
«=O; i.e. for the case that this component is mixed with a solu-
tion consisting exclusively of the first. The fact that these two
quantities of latent heat are the same is a consequence of our

supposition 4, = 06,, from which follows that «, = a is equal to
)
1

er In reality these two quantities will not always be equal.

2 2°

That the signification we have ascribed to the quantities av? and
a(1—,7)? is the true one, may be shown from the numerators of
equation (2), which being respectively multiplied with g, and q,,
represent the ¢ota/ latent heats of liquefaction a, and w,, namely
w, = q, A + Ba? — Pe”) = 4, + aa? — aa” |

q (3)

0, ==, (: “fp = [8 (1-2)? - B' (1-1) = q, + a (1-«)? - a (l-«)
2
The total latent heat required for the liquefaction is therefore equal

to the pure latent heat of liquefaction, augmented with the latent heat
required for the mixing of the liquid phase, diminished with that
required for the mixing of the solid phase.

Foal
—

(155 )

A high value for a@ (or ®) means therefore a high value of the
latent heat of mixing, and when we shall presently see that a high value
of #8’ leads to very small values of x’ or of 1—v’, this circumstance
may be interpreted as follows:

If a large amount of energy is required in order to make one
of the solid components enter into the solid solution (or the mixed
erystal) then this solid solution will contain only a slight trace of
one of these two components.

ll. We now proceed to the discussion of the fundamental equa-
tions (2).

; ; ae okie dT
Let us in the first place determine the quantities a and — by
av az -

totally differentiating the conditions of equilibrium — w’, + a, = 0 and
— mw, +4, =9 according to T. After several transformations we get:

. 05 a
ee. ar OO ae ;
de (1—2')w,+e'w, ’ da! (l—z)w,taw, — (4)

These well known equations have been deduced several times '),
i.a. by Prof. van per Waats for the analogous equilibrium of liquid
and gaseous phases.

dT Atte eS
From (4) we may deduce the quantity (=) , i. e. the initial direc-
dz /, ‘

tion of the meltingpoint-curve.

Ou RT
Baer + 2 ax, we have
Ox 1l—«z
07g 1 ou, RT .
— = — — 2a,
Our? z Ov x(1—2) if
therefore, for z=—0, T= T,
07g RE,
we have: —,}]/= :
oe £,
if we write z, for c=0O. For r—0O we havealsoxz’ — 0. The

denominator of appears therefore to be equal to (#,), = 4,, hence

?
‘

' 1
=) (x, v 4 a, ba lia (2 ae <n)
rea ae ; q1 q1 ty J
1) See ia. my Lehrbuch der math. Uhemie, p. 118 and 123—124. (Leipzig,
J. A. Barty, 1901).

|
NS
|

(156 )

from which follows that — g, being supposed to be positive —
dT ee
the value of (=) can only be positive if — should be greater than
av 0 L,
et
unity. Let us therefore determine the limiting value of —. With
zy
T=, z=; 2 = 0 we may ‘derive from ‘the equations (2):
1 eae ‘@—8)
T = T, ————___
: ae (Oe
1+ log —
By
and we have:
ce “(-8)

PLE if
eee ot = 1B

wv
Therefore the value of — remains smaller than unity, and the

L 0

meltingpoint-curve continues to descend, as long as we have:

ey te
g—a<(P-1). Re ey
Lees

. lg
In the following we will always assume 7, >T, or a —I1
2

positive. The above condition will then the sooner be satisfied, accor-
ding as ~’ in the solid phase has a higher positive value. Now
probably 8 will nearly always have a very small positive value and £’
a rather large positive value. The condition will therefore probably
be nearly always satisfied. If we put 8=O, then we get simply:

! ! fh
—d=—n8<9,(F-1).
2

If 8’ (or a’) is positive, i.e. if heat is absorbed in mixing the solid
oD
SU

& “ie
phase, then we shall always have — <1 and therefore the melting-
&

0
point curve will aheays descend on the side of the highest temperature.

An initially ascending part and in connection with this the occurrence
of a maximum-meltingtemperature is therefore almost totally ea-
cluded. The possibility of a maximum exists only in the exceptional
and nearly inconcewable case, that B’ has a much smaller positive
value than 8, or even a negative value.

If we determine (S =) at the side of the /owest temperature quite
Vt — a)

in the same way, then we find, denoting 1—.# by 1

.¢

(=) _* RE? (2 2)
da Cs | = Va Yo

where:
leq 22 = vag (=) )
BE SS Se z
Yo Rk ?, PT,
The quantity Jo. is therefore always smaller than unity if
Yo
Y ied

== ee ee, Se: | Bes
Eos (5bis)

The second member being negative, this condition can only be
satisfied if 8’ has a high positive value. Two cases may therefore
oceur, according to p’ being larger or smaller. In the first ease the
initial part of the curve near 7’, descends again and a minimuin
will therefore occur (fig. 2). In the second case the curve ascends
near 7,; it will therefore descend continuously from 7’, to 7’, without
presenting a minimum. |

For the case 7, = 7, the conditions (5) and (5%) pass into

8 nim B <A 0,
and a minimum will always in this case oceur if §’ > 8, and
probably this will always be the case.
: dT
The same considerations apply of course for (S) ;
dx’),

In the above considerations we have tacitly assumed that wnoma-
fous components occur in neither of the phases; formation of complex
molecules or dissociation are therefore always excluded in the cases
which we consider. When one or both of the components of the
solid phase for instance consist totally or partially of double molecules,
then the occurrence of a maximum is not excluded at all.

We now proceed to the discussion of the equations (2) for different
values of 8’, starting with very high values.

IV. In the following we shall always put ?—O (in the liquid
phase). This simplifies the calculations in a high degree and it does
not alter the results qualitatively. The equations (2) then take the
following form:

qi, '
: ae gis (: —2ya-2y)
L, (=f a *) hee VE ae
* log ; 1+ 2 log —

Let us further assume the following values, in order to be able

to execute the calculations numerically :

1 = (6)

me RT | ae ae AT a
vB reel Ts

T= 1200 q, = 2400 Gr. cal.,
7 500 | 1 000 sae
Then we get (h = 2):

2 or = 500 Gat 2 te
eS 00 A—86' a =e ( ,2 B' ( ee See

1—a' 1
1 + log Ba ages

S25 &
if a av wv

We will begin with assuming #’ to be very large, e.g. p' = 5.
As we have a’ = 4g, 2’ this means that the latent heat of mixing for
the first component when z=—1 or of the second when «= 0)
is five times as great as the latent heat of solidification of the first
component. From the above equation:

pp —_ 1200(—5a"*) _ 500(1—601—2"/)

* 1— a 1
1+log 1+ — log
4 iz, 2 .

ul
&
wv

we may calculate the temperature 7’ corresponding to an arbitrarily
chosen value of x, the value of «' being exceedingly small. So we get
jor:
1200
ar 1—log(1—ay’
and for a’:
1 a 20
1+ oy log a = 15 (1 —- log (1—~)).

The following table I (p. 159) gives a survey of the corresponding
values of x, 2 and T’. ;

This represents the branch AA’ of the meltingpoint-curves which
starts from 1200° (see fig. 3). AB’ is the curve 7 = f(a’).

If we put 1—x=—y and 1—z' =’ then we have the equations
500(1—6y") — 1200(1—5(1 —y’)?)

1 1—z/' y!
1+ — log : 1+log —
7 Na a sai ieee

from which we may calculate a new series of corresponding values
of x, w and 7. So we get the branch BB’ starting from 500° (BA' is
again the curve 7’= f(w')). The value of y' being in this case very
small, 7’ may again be calculated from
500
— 1—0,5/og(1—y)

‘yy

and 7 from

( 159 )
TABLE I. TABLE IL.
aoa
a | = >< 108 | 2! >< 108 ee | x10" | X10
| ' / 4
0 | 4900 | 24 0 0 300 | 25 lo
0.4 | 4086 | 14 14 0.4 | 475 | 15 | 15
0.2 | 981) 83 | 47 0.2 150 8.6 17
0.3 | 884 4.8 14 0.3 a“ hd 14
0.4 | 794| 2.6 | 40 04 | 398 | 2.0 8
0.5 | 709 | 1.2 | 6 0.5 | 374] 0.89 4
0.6 | 69%] 0.46 | 3 0-6.) .253-| 0.31
0.7 | 545 | 0.44 | 4 0.7 | 312| 0.078 | 0.5
08 | 460 | 0.026} 0.2 0.8 | 97) OAL | 0.09
o.9 | 363| 0.0014 0.01 0.9 | 939 0.00040 | 0.006
0.95 300 | 0, 6. 0.95 | 200 | 0, 0,
097 266 | 0, Oe 0.97 | 485 | 0, 0,
0.99 | 214] 0, 0... 0.99 | 151} 0, 0,.
\ ef a 0 1 0 | 0 0
1+ bg =— =C 0,5 log (1—y)).

The values calculated in this way are found in table II (see above).

The values found for 7 are even smaller than those for the first
branch. In both branches we clearly see the occurrence of a maximum
in the curves 7’= 7 (2’), from which point the value «' (or 7’) does
not increase any more, but falls again to zero.

The position of that maximum may be easily found from the

: dT ; :

general equation (4) for rac The tangent running vertically, the

denominator (1—.) w,+-.2w,=O0 must be zero and therefore we have,
as we have assumed @ to be equal to zero:

Ig q ' '\2
(1—a) g, (1—B 2”) + 2g, A— ae (1—2’')’) = 0.
3
Neglecting w' we get:
(l—a) 9, + 29s ( = 2 9) = 0,
11

Proceedings Royal Acad. Amsterdam. Vol. VI.

( 160 )

and therefore

a ee = = = Mess Crate
( ‘ Gt (
Fey (2:0~1) Nato
vE
Introducing our values for g, and g, and p'=5, we get x,—='*/,,—=0,19.
1200

= 991°. Further we have

ame ko

With this value corresponds 7

a ¥ a ee : 4
( i 0,00087, and therefore «',, = 0,00017, which agrees with the

value found in the first table for the first branch.
For the second branch we have exactly in the same way:

Yn — a = a yea! 2, au eee (7bis)
qa-1-9,(8.— 1) 9a —- G+ GP

With 2 ==; gus: yields;4— 5. — Oe

500 Sam e
T., is there ~=- 457°, |~} = 0,000010, and_ therefore
1,093 ¥y me

-Yy'm=9,0000017, which value again agrees with that found in the

second table.

If 2’, and 2’, represent the proportions in which the second com-
ponent oceurs in the two solid phases which coexist in the eztectic
point C with the liquid phase w«, then the point C may be
found by solving a double set of equations (6), namely those with
x, and those with «’,. From these equations the quantities 7) 7, 2’,
and wz’, may be solved.

If x, and 1—w', may be neglected, then we get simply:

ieee » oe ;
Cue Lie 2/57 a
1 - log (1—«) 1— = log x
hh vE

from which follows after introduction of our values for 7’, ete.
20809). J==4527,

The corresponding values of « and y' (2, and 1—u',) may be
calculated as has been done above. (Compare also the tables for
OO), |

A closer consideration of the equations (6) shows (comp. fig. 3),
that besides the branches mentioned above a third branch exists,
which may to some extent be regarded as the connecting curve of
the two former ones. This branch, however, lies wholly within the
region of the negative absolute temperatures and has therefore only
mathematical importance for the continuity of the meltingpoint-curve.
The curve 7’=/ (wx), namely A’'DA' forms the connection between

( 161 )

AA and BB. EDF is the corresponding curve 7=/ (v’), which
touches A’'DB in the common minimum JD, where «= u’.
The point D is therefore determined by the equations
‘yy rm fg 7 qi ’ @
T=, (1—@0) =T,0—“ea—ay),. . . - (9)
Ys
or with our values:

T = 1200 (1—5a?) = 500 (1—6(1—2)’),

which gives «=a = 0,494, 7 = — 264°.
The point / indicates another value of 2’, corresponding to the
point A’ of the curve 7’=/ (a), where c=1, but now T= — 0°.

This peint is obviously determined by the equation (comp. (6))
poke B(t—2) =O (therefore w= 0),. - = (10)
q

which yields «' = 0.592.
The point F indicates a value of wx’ corresponding to the point
B’ of the curve T—/ («), where z= 0, T=—0°. Now we have:
1—Pa? = (therefore w,— 0), . .. . (10bis)
from which foilows: « = 0,447.

The curve 7=/ (x) has therefore obtained a continuous course
through the points A’ and 45’, the curve 7’=/(a') however changes
abruptly at 5’ from B' to /, and at A’ from A’ to F; further its
course is continuous from / through D to F.

The question might be put: in what case does the point / come -
in A’ and the point / in J’ and has the discontinuity in the curve
T= / (2) therefore reached its highest possible value? Obviously
this is the case for p’ =o. For then w, =O can vanish for z'=1

and w, for wv’ =O. In this case the lines A'D and LD coincide
over their whole length with the axis «—41, and the lines b'D
and FD with the axis «— 0.

At all temperatures above the absolute zero the values of «' and
y' vanish in this case continuously; this represents therefore the
ease, that the solid phase contains only one component.

The lines A'DB and EDF lie, as we have seen, wholly in the
region of negative absolute temperatures; besides this they lie with
their whole course in the region of the wnstable phases, as is
shown by a closer examination of the relations

Poa Rh wee RT
dz? a(l1—a)’ de? 2'(1—2’)

V. The value of #, for which the point D, where =~’, is
found exactly at 7’=0O, may be calculated by solving the equations

ae a

( 162 )

which yield:

0S es) = oa 2 (1 —2')’),
qs

f ! —s q:

p=(1+V

: 2 g —l
;) ae ae ( —- V2) ; force Ge ees
11 vB

i.e. with our values of 9, and g,,; B'= 3,659 and «' — 0,523.

The whole curve EDF or T=/ («’) of fig. 3 has here contracted
to the single point D (see fig. 4), and the curve A'DB' or T= f (2)
is degenerated into a straight line, all whose values coexist with
that one value of «’.

This line A'DS' and the point P still represent wnstable phases.

If for this case we calculate the maxima for «’ and 7’ of the two
principle branches as we have done above, then we find:

ti, = 026 aa, ar, = 000088;
Gini Vay eg 290 a OOD 0G 2:

The maximum value for 2 appears to have increased to about 5
times the value it had with 3’—5, and that for y' to about 36 times
its former value. The maximum value for y' now lies below the
eutectic point. A simple calculation may show that in our case this

already happens as soon as becomes smaller than 4,55. The

maximum on the other side will require a much smaller value of 3’
before it descends below the eutectic point.

q2 \*
As soon as ? becomes smaller than (2 +y=) or with our
V1

assumptions < 3,66, the curve A’'DA' begins to turn upwards and
we get the course indicated in fig. 5 for e.g. p’ = 2,5.

The line A'DB' lies now wholly in the stable region for T= f (x),
2

=, being henceforth always positive. The line HDF on the other
Ah

hand lies wholly in the unstable region for T= f(a’), as easily

Fal

appears from the expression for wr This latter circumstance how-
aL

ever is not permanently fulfilled; by continually diminishing #', a

point of LDF may be reached for which sis is equal to zero and

this is a condition for a further change of the shape of the melting-
point curve. But this will be treated in another chapter.
The maximum values for z and 7’ are now the following (namely
for fp = 2,59):
Og 0,375, T ge B1b° 4:2, — 09,0044;
Ym — 0,357; “2ise= 410° > Yn = 0,0016.

(163 )

- Gradually z' and 7 assume practically measurable values.
We find from (9) for the maximum J):

ee eh == 223°,

We find for £, «' = 0,423; for F, « — 0,633 (see (10) and (10°)).

VI. We now proceed to the description of the further develop-
ment of the parts of the meltingpoint-curve lying below (.

According as ~’ decreases, the curve A’ DA mounts higher and
higher and finally it will touch the line LB’, e.g. in P (Comp. fig. 6).
But the values of z and 7’ of both curves 7’= f(x) coinciding in
P, the values of 2x’ also will necessarily coincide — or in other
words the curves BA’ and HDF will meet at the same time, namely

ar!

in the point Q. In this point however —— must vanish, as ? may be

Oa"?
regarded as a cusp in the continuous curve AA’ DPS. If therefore we

trace in the figure the curve. ,—0, —i.e. T=a' «' (1—a') = 49, p'2' 1—2’),
v

which will be a parabolic curve, whose axis of symmetry is the
ordinate «—='/,, and whose summit lies lower according as ?’
decreases — then the curves BA’ and EDF meet this curve at
the same time in Q.

The direction of the two curves BA’ and HDF will there not be
horizontal, as appears immediately from the direction of the curve
07g)
0'x?

=O in the point Q. Therefore not only the numerators in the

dT
expressions for a of those two curves must vanish in consequence
&
2"!

of the factor Er —, but also the denominators (1-«)w, +«w,. In other words:

the two curves will meet each other at the place of their maxima
for x’ and 1—2”’, exactly at a point where both curves had a vertical

dT i
tangent a moment before. So the expressions for — are undetermined
a Lv

in Q and the real direction of the pieces BQ and A’Q, DQ and FQ
must be determined in another way.

Fig. 7 represents the position of the different lines a moment
later. 8’ is here somewhat smaller than in fig. 6. It may be clearly
seen that the lower branches 6’ 2?’ 4’ and A’Q’F have got detached;
henceforth they are isolated and disappear more and more downwards
according as p’ decreases. They may be regarded as rudiments of the
original meltingpoint-curve. The upper parts form henceforth the proper

( 164 )

meltingpoint-curve, namely AA’ DPB, constituting the line 7 = f(),
and AB’ EDQB, constituting the corresponding line 7—/(z’). The
curves 7=/(x’) now run horizontally in Q and Q’, in consequence

earl

of the relation ert for the denominator (1—) wv, + «w, no longer

v
vanishes for both curves at the same time. The places in the two
curves where this occurred before (we may imagine them to he
between Q and Q’) have henceforth disappeared. These points Q
and Q’ of the curves 7—/(«x’) correspond to the two cusps P and
P’ of the curves T= / (a).

The process of detaching, described above, took place on the side of
& — i.e. on the side of the highest temperature — but we shall
see that the same process is repeated on the side of A, when §’ still
further decreases, which is represented in the figures 8 and 9.

The second detaching takes place at #& and S and gives rise to
two new rudimentary parts of the original meltingpoint curve on the
lower side. The proper meltingpoint-curve is now ARDPB for
T= f(a), and ASDQB for T= f(z’). The two points S and S’,

where the curves 7’= f(x’) run horizontally in consequence of the

27!

relation —-—O correspond with the new cusps #& and #’ in the

Oa:'
Imes 2°== 7 (@)-
It is of course important to know at what values of p’ the two
processes of detaching described above, take place.

as
In the point Q (fig. 6) we have in the first place as ee 0 or

T=q,-p'«' (1—2z’'); but we have there also (l—z)w,+aw,—0, from

which follows:

mare

gp ee Se ee

w,— W, Ww, agli

In connection with the equations (6) and taking into account the
equations (3) for w, and w,, we may deduce from these relations
a set of transcendental equations from which the quantities 7 2’ and 3’
may be solved by successive approximations. So we find for the
first detaching with the values assumed by us for 7’, ete.:

Bisa 400) @ = 0,9108(Q)" 5 a= VU 2500(P). *, "SS ae

For the second we find as second solution:
b= 1,10207.,.. #2 = 0,11 49(08))—,) Sa Or OaGh). 6 wel 268°,9.

The case of fig. 9, i.e. just after the second detaching, has been
calculated by me point for point throughout its course, putting ?

i» a

equal to I.
ARDPB (T=

i ae
(4) 1200
0.47 an 0.05 | 749
0.882 | 0.4 | 301
(R) 0.958 | 0.197 (S)| 292
0.929 | 0.2 | 335
0.886 | 03 | 384
0.846 | 0.4 9
0.810 | 0.5 _
0.780 | 0.6 | 456
0.756 | 0.7 | 4583
(D) 0.749 | 0.749 | 88
(P) 0.748 | 0.776 (@)| 458%
0.749 | 0.8 461
0.795 | 0.9 465
0 867 | 0.95 | 476
0.911 | 0.97 | 484
0.967 | 0.99 | 494
(2) 4 | 4 | 500

( 165 )

The following

f (2)), corresponding with ASDQS (T= 7 («')), and
also the four ee a ee ey parts.

tables

represent

the

chief branch

z 2! | T
(4) 4 | O (a o

0.995 0.05 | 193
(R’) 0.981 | 0.104 (S')) 245

0.995 | 0.120 | 193
(4') 4 | 0.130 (B)| 0

£ | z! T

yon 0 1 (4) 0

e—7-7 | 0.9997 | 168
(P)) e—* =| 0,990 (@)) 25°

e—7-6 | 0.970 | 168
(B’) 0 0.954

(F)| 0

For the exact calculations, of which these tables give the results,
we refer to the more elaborate paper which will appear later. Also
the figures relating to them are to be found there.

The maximum JD has been calculated from the equation (9), which
yields «= w' —0,7494, T= 458°,62.

The points P and Q, ete. are calculated from (6) in connection with

Ee or
Da"? ,

Rte

yD is ae

IV | «

=@¢b2 (i—2).

0.7762
0.1268
0.9901
==, P2b03o

(Q)

(S) |
(Q)
(S') |

We find the following jouw; solutions:

0.7484 (P)
0.9579 (R) |
octet ec)

0.9808 (R’)

—]

ae aaa

( 166 )

The points /# and F' are again determined by (10) and (10a).
For Ewe have {2=——1,.7 = 0) a’ = 01296; tor (2 =e
x’ = 0,9535.

Combining equation (6) for 2,’ and «,', we find finally for the
eutectic point C:

¢== 030673 ; 2.’ = 008893 ; 2,’ = 0;911075, T= 466441.

Formerly, when 2’ could be neglected, we have found from (8),
20,809, T= 452° (see IV).

It is remarkable that the value found for 2,’ is exactly equal to
i—v,’. It is easy to show that this is an immediate consequence of
ihe equations (6) (compare our previous paper).

In cases however in which our assumption @,’ = e@,’ (which fol-
lows from 4,’ = 4,’) is not satisfied, the value of x,’ for the eutectic
pomt will also not be equal to 1 —2,’.

When the amount of heat required for the mixing of the first compo-
nent for v=1 ts equal to that of the second component for «=O,
then the compositions of the two solid phases at the eutectic pomt will
be complementary.

Vil. We shall now discuss the question, how the two parts
ending in the cusps ? and FR will gradually disappear. We may
follow this process step by step in the following figures.

a) In fig. 10 we see that the cusp P of the line 7 = / (@), which

; - . . be)
till now was situated mside the curve ae O, has reached that curve,

in consequence of which the point Q of the line 7 = f(z’) coincides
with P, and also with the maximum point D, which lies between
P and Q. The curves /= f(x) and T= f(a’) run therefore both
horizontally in P, and henceforth the curve 7’= f(a’) will no longer
touch the branch RP in JD, but the branch PB (in a minimum).
After the horizontal position in fig. 10 the cusp at P will be turned
upwards instead of downwards.

This transformation is apparently determined by the relations

T=T.(l—p'e

—
NW
-

fh » 2 2! ‘
z (: —- i p (1—z) ) =9, Pp «(l—2z) » eee

This yields with the values assumed for 7) ete. :
f= 10610 : © = 457606 ; T = 4637-5a.

4. The figures 11 and 12 show a second peculiarity of the tran-

ah eae OL ol be lees tied

eet OAS
¢

or a

Tern ee See ke ee

ary

( 167 )

sition. Here the cusp P lies at the same height as C; we find
therefore at the temperature of the eutectic point for the first time
four values of x’: x,’ and 2,’ corresponding to Cand the coinciding
points x,’ and x,’ corresponding to P. These latter two points still
represent wistable conditions. A moment later P has risen above
C' and the two coinciding points x,’ and «,’ have separated (fig. 12).
The values 2," and 2,’ always correspond to C, x,’ and «,’ to two
other points of the line 7’=/ (x). The phase to which «
unstable, that to which x,’ relates metastable.

The transition of fig. 11 is determined in combination of (6)
ne and 2. (with 2,), for «,’ (with “,), IN connection with
the relation 7 = g, B xz,’ (1—.2,’). By means of these relations we
may determine 77 7, 7, 7,’, 7,’, v;’, 8’, if we moreover take into account
‘—1W—z,’ (compare VI above).

/ .
; relates, is

£.

ce. The figures 13 and 14 represent a new and very important
case of transition. Formerly the branch AW intersected the branch
BP always on the left of the maximum (or minimum) J in the
eutectic point C; in fig. 13 it passes exactly through the point D.
From this follows, that the point «,’ coincides in C’ with x, (both
= ww), which point represents a stable phase from this moment.
Afterwards the minimum J lies on the left of the eutectic point
C (see fig. 44) in consequence of which the realizable part of the
meltingpoint curve begins to show a totally dijferent shape, namely
with a minimum (see fig. 14a). The point «,' which till now lay
on the left of C, lies in future on the right of that point. On the other
hand wx, has got on the left of C and it corresponds to a point of
the line 7’= f(x) between B and D.

It will not escape our notice that the case drawn in fig. 14a
occurs to some extent in the mixtures of Ag NO, and Na NO,, inves-
tigated by Mr. Hissin (see fig. 144). The difference is only that the
minimum JD in the line 7’=// (x) in the case of fig. 146 appears
beyond «—1 and has therefore already disappeared. In our case
we have supposed this to occur in a later stage.

The case of transition of fig. 13 is calculated from the equations
(6) for x,’ and 2,', taking into account «=2z,', and moreover
v,' (= x,) = 1—2z,'. The numerical solution of these equations yields

the following values :

fe (47); = 0,1940.; 2 2) = ce = 0,8060 5 T= 479",1.
We may then calculate x,’ and 7, from equation (6).

d. Finally the figures 15 and 16 represent the most important
case of transition.

( 168 )

Here Q and S coincide with the summit of the curve Ee O, and
Cc

so also, P and FR with. C. The parts with the cusps have now
disappeared once for all through the eutectic point.
The points .,’, 7,’ and «,’ coincide with the horizontal tangent in
the point of injlevion Q,S. This point Q,S lies apparently at.’ = 3,
25/

Ss ry ’ n ote . io
as the curve ae O or 7 =q,'2' (1—z’) is perfectly symmetrical
at”

on either side of the summit at z = 4 according to our supposition

a,’ =a,’ (in consequence of 5,’ = 6,’).

Not before this instant we may say that the meltingpoint curve
has obtained a perfec‘ly normal course, running continuously without
any cusp from A to B with a minimum in D where x = «’ (fig. 16). The
point of inflexion with a horizontal tangent has passed into an ordinary
point of inflexion with an oblique tangent. This point of inflexion also
will gradually disappear when ~’ continues to diminish, and for still
smaller values the minimum also will disappear from the melting-
point line which will then show a continuously ascending course from
B to A. It is of course possible that the minimum has disappeared
already before, of which fig. 144 gives an example.

The transition of fig. 15 is determined by the equations (6) for

os
; : 1
ote =a — 7,') =}, 1m connection with 573 =) ore A q B.
v a
We find:
Bie 0,8226..05 2 = 0,8030 > FT = 402°,0—.. (2, = er

The points «,’ and v, may further be calculated from equation (6).

e). The minimum disappears apparently (see III] equation (5/z),

when
vies eta 14
i <i Tari : . . . . . . . ( )
: Dede . Te
For with 8 =O formula (5 bis) passes into — p’ < eee
1

T,—T,
or p’ > — walks This formula expresses the condition for the oceur-

1
rence of a minimum. Formula (14) expresses consequently that 70

minimum will oceur.
The minimum disappears therefore in our case as soon as p’

7 ye
becomes equal to ig OF 0,5823.

f. In the above considerations we have lost sight of the rudi-
mentary pieces which have been detached (compare VI).

Repent

( 169 )

We shall now investigate when they also disappear. Apparently
this is the case, when the summits P’ and Q’, R’ and S’ lie at
T=—O0; i.e. when these points coincide with B’ and A’. These summits
ave determined by the equations (6), in connection with 7—=,, 3.’ (1—vr
Now 2” coincides with 6 and Q’ with A, if these equations are satis-
fied by 7=—0, r—0, wv’ =1. It is clear that this requires 3’/—=1.
Further ’ coincides with A’ and S’ with 3B’, if the equations are
Sanne: py 2 — 0, «—1, «’—0. And this can only be the

| ox

q =! ! “ne
case when 6’ = —., in our case #' = — = 0,8333.

VIII. It is easy to see that the results of the above investigation
would remain unchanged qualitatively, if we had not neglected the
quantity 7 in the term ar’, and if we had not omitted the quantity 3 for
the liquid phase by the side of the corresponding quantity 3’ (3 being
nearly always very small compared with 3’). Then all the values given
for 3’, z, « and 7’ would be slightly changed nwmerically, but the
transformations and transitions which we have discussed, would have
occurred in the same order and exactly in the same way as we have
described above.

We conclude from the above considerations, that the occurrence
of a eutectic point and the apparent interruption in the series of
the solid mixtures caused by it, necessarily follow from the theory
represented by the equations (2) or (6), which teaches that high values
of p’ (or a’), i.e. of the heat required for the mixing of the solid
phase, cause the occurrence of wnstable conditions. In reality the
curve is continuous, as is shown in the different figures, but in
general only a part of the continuous meltingpoint-curve is liable
to be realized. And only tis part of course is found by means of
the experiments.

Finally I regard it as an agreeable duty to express my thanks to
Prof. Bakuuis RoozkEBoom, who has encouraged me to undertake this
investigation, and who has given me many a useful hint also for
my former papers on the meltingpoint-curves of amalgams and
alloys. —

(August 27, 1903).

>
2

- k
on AOS WN
4£

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,

PROCEEDINGS OF THE MEETING

of Saturday September 26, 1903.

Ce—_—_—_—_——

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 26 September 1903, DI. XID).

CoS eek LS.

A. Sours: “The course of the solubility curve in the region of critical temperatures of binary
mixtures”. (Communicated by Prof. H. W. Bakuvis Roozesoom), p. 171,

Pu. van Harreverp: “On the penetration into mercury of the roots of freely floating germi-
nating seeds”. (Communicated by Prof. J. W. Mott), p. 182. (With one plate).

JAN DE Vrigs: “The harmonic curves belonging to a given plane cubic curve”, p. 197.

A. F. Hotreman: “Preparation of cyclohexanol”, p. 201.

Tu. Weevers and Mrs. C. J. WrEEvERS—DE Graarr: “Investigations of some xanthine deri-
vatives in connection with the internal mutation of plants’. (Communicated by Prof. C. A.
Losry DE Bruyn), p. 203.

J. VAN DE GRIEND Jr.: “Rectifying curves”. (Communicated by Prof. J. Carpinaav), p. 208.
(With one plate).

J. Borxe: “On the development of the myocard in Teleosts”. (Communicated by Prof.
T. Prace), p. 218. (With one plate).

Extract from a letter of Mr. V. Wittior to the Academy, p. 226.

The following papers were read:

Chemistry. — “The course of the solubility curve in the region of
critical temperatures of binary mixtures"). By Dr. A. Smuts.
(Communicated by Prof. H. W. Bakuvuts Roozesoom).

The results of the experiments on critical temperatures of binary
mixtures, which have been suggested by the theory of vAN per WAALS,
and the completion of the pressure-temperature-concentration-diagram
for the equilibrium of so/fid phases with liquid and vapour lately
given by Baxkuuis Roozesoom *), made it probable that the pending

1) My first communication on this subject appeared in Zeitschr. f. Elektroch.
33, 6635 (1903).
*) Proc. Royal Academy Amsterdam 1902, 276.
12
Proceedings Royal Acad. Amsterdam. Vol. VI.

(172 a

problem of the course of the solubility curve of a solid in the region
of critical temperatures was now capable of solution.

It follows namely from the combination of the two conceptions
mentioned above, that the course of the solubility curve cannot show
anything remarkable, unless the least volatile substance (B) occurs
as a solid phase and its melting point lies higher than the critical
temperature of the more volatile substance (A), which for the sake
of brevity we shall call solvent.

We will now consider only the case when the two substances in
the liquid state are miscible in all proportions. Then there is in the
p, t, v-diagram a continued critical curve, connecting the critical points
of the two components. Three different cases may now occur.

Fig. 1.

4 = Gas. A= Gas

7} = Unsaturated solutions. B= Unsaturated solutions.

( =Supersaturated solutions or } = Supersaturated solutions or
solid £-+ vapour. solid B-+ vapour.

Fig 1 and 2 are p,¢-projections of the representation in space,
a is the critical point of A, 4 of 6, while d represents the melting
point of solid 5. The line ad is the critical curve and cd the p, f-line
for the three-phases equilibrium: solid 5-+-solution+vapour. Further
ea is the vapour-tension line of liquid A, 7d that of liquid SD.

Now the case of fig. 1 will occur when the solubility of solid 5
in A is comparatively great. In this case the vapour-tensions of the
saturated solutions are rather small and so the curve cd lies totally
below the critical curve.

The line cd runs on uninterruptedly as far as the melting point
of £L; the series of the saturated solutions of 2B is not interrupted
by the critical phenomena of the solution; the solubility curve shows
nothing remarkable. On the other hand the critical curve also goes
on uninterruptedly, the critical phenomena being only those of
solutions which are unsaturated of solid B,

In the second case, fig. 2, I supposed the solubility of 2B in A,
even at the critical temperature of A, to be still so small, that just
a little above it the line cd intersects the critical curve. Then such
an intersection takes place in two points p and ¢.

Now the critical temperatures and pressures between @ and p and
between g and # refer to unsaturated solutions. At p and q, however
where the p, é-line of the solutions and vapours saturated of solid B
and the critical curve meet, the case occurs, when the saturated
solution is found at its critical temperature; for here the vapour-
tension of the saturated solution is quite equal to the critical pres-
sure and so saturation temperature and critical temperature must
coincide.

If we were to prolong the critical curve from p to g, we should
pass through the region of solutions and vapours supersaturated of
solid 5. Hence critical phenomena will be possible here only provided
that the solid phase 6 does not occur. So this part of the critical
curve is metastable.

To prolong the three-phases-line between p and q, on the other
hand, is impossible, as will soon be evident.

A third case forming a transition between fig. 1 and 2 would be
the following: the curve cd would touch the inside of the critical
curve in one point. The points p and q would coincide at this point.
Hence the chance that such a case should occur is extremely small.

A better insight than by the p, éprojections of the representation
ii space is, however, given by the p, «projections, especially when
these are combined for different temperatures as in fig. 3 and 4,
which has already been indicated by Prof. Baxnurs Roozesoom °*).
That is why I here add p, «-projections both for case 1 and for
case 2 and in order to be able to construct from these projections
the entire #,7-diagrams also, I have given the projections starting
from the critical temperature of A up to the melting point of B.

The preceding px-diagrams 3 and 4 correspond with the p, é-dia-
grams 1 and 2. Let us first confine ourselves to fig. 3. At the
critical temperature ¢ of the substance A, ae and ac are the p, e-
curves for coexisting vapours and liquids (unsaturated solutions).
The points ¢ and ¢ indicate the saturated solution and the vapour
in equilibrium with it. Further for the same temperature g ¢ is the
p, v-eurve for the vapours and cf the p, «-curve for the solutions
coexisting with solid 4. According to the theory of vAN per Waats
ge and cf are at bottom two portions of a continuous curve, which

1) Zeitschr. f. Elektroch. 33, 665, (1903).
ges

(174)

Fig- 4,

ts th fe- 22 =< ~fy PSSST

A x ee
A = Gas. A = Gas.
B= Unsaturated solutions. B= Unsaturated solutions.
C =Supersaturated solutions or C = Supersaturated solutions or
solid B+ vapour. solid B+ vapour.

has between ¢ and e a part only partly to be realized with a
maximum and a minimum.

For a somewhat higher temperature the diagram is a little different,
because now the vapour- and liquid curve continuously pass into
each other with a critical point in @,, the vapour-line g,e, being
shorter than at the former temperature. At rise of temperature this
vapour-line continually decreases in length, until at the me]ting point
of B in the point d it has disappeared altogether. Above the melting
point a saturated solution is no longer possible and so there we
get only a liquid- and a vapour-line with a critical point in a,. If
we draw a line through the points a, a,, a@,, a, and 6, a second
through the points c, ¢,, c, and d and a third through the points

( 175 )

é, €,, e, and d, these lines indicate the said ¢,.7-projections; a) is
the critical curve, cd the curve of the saturated solutions and ed
that of the vapours saturated with 5. In accordance with fig. 1
the whole of the eritical curve lies above the solubility curve; above
the critical curve lies the gas-region and below the solubility curve
the region of solid 4+ vapour or of the supersaturated solutions.

After what precedes the connection between the fig. 2 and 4 is
easy to see.

The solubility of 46 in A at the temperature ¢, being small, the
vapour and liquid-lines ae and ae are short. Above ¢, ae and ae
again fluently pass into each other and have already approached
nearer to each other, because the saturated solution c¢, and the
coexisting vapour ¢, differ less from each other; a consequence
of this is that the lines g,¢, and ¢, 7, have also approached to each
other. At ¢,, the first critical temperature of the saturated solution,
the solubility curve ce, p, the vapour-line ee, p and the critical curve
aa, p coneur. This implies that at this temperature the curve Js P)
for the vapour coexisting with solid 5 is the prolongation of the
curve pf, for the solution coexisting with solid 6. The same occurs
at a great many higher temperatures.

That a continuation of the lines cp and ep is imaginary, Clearly
appears from this diagram, as the vapour- and the liquid-line, if
both were prolonged, would change places, which is impossible. *)

Whereas from ¢, to ¢, saturated solutions are absolutely impossible,
at ¢, the same phenomenon occurs as at ¢,; here also the solubility
eurve de,qg, the vapour-line de,g and the critical curve ba, a, q con-
verge and the critical phenomenon is observed with a saturated
solution.

At higher temperatures a convergence of the three curves ean
no longer oceur and in consequence all critical temperatures
between 7¢, and /,, just as between 7, and ¢,, are critical temperatures
of unsaturated solutions. If between p and q solution + vapour +
solid £6 be impossible, it is conceivable, as suggested before, that
we may succeed in getting spersaturated solutiors and observing
their critical phenomena. In such a case the dotted critical curve
if prolonged might be realized between p and gq, so this dotted line
is metastable.

For a thorough knowledge of the phenomenon a p, «, ¢diagram
is most desirable and a », x, f-diagram indispensable. Both space-

1) In the first communication, Zeitschr. f. Elektr, 33, 663, this point was not
sufficiently cleared up.

( 176°)

representation I hope to communicate after some time and now I want
to point out only the fact, that the point p, which is bound to a
certain concentration can be reached at only one very definite volume,
which holds true for g also.

By means of the v, x, diagram it can also be made clear, that no line
can be drawn of a definite limitation between the region for solid B+
vapour and the region of unsaturated vapours. In the region for
solid £-+ vapour we have namely a system consisting of two com-
ponents in two phases, therefore a bivariant system wherein there
are numberless ways in which with rise of temperature the pressure
can be changed. Consequently it depends altogether on the volume
what course we follow at increase of temperature.

In order to test the discussed phenomena by an example I chose
for the substances A and B ether and anthrachinon. The eritieal
temperature of ether is 190°, hence it is rather low, nor is the
critical pressure high, namely + 36 atmospheres. It is obvious that
these two circumstances make the experiment much easier. Anthra-
chinon was chosen because this substance is very little soluble in
ether, its melting point lies 283° above the critical temperature of
ether and it is still very stable at its melting point.

The experiments were carried out in thick-walled tubes of 5 ¢.m.
length filled with weighed quantities of ether and anthrachinon. The
ether was free from alcohol and water; the anthrachinon was crystallized
from icevinegar. The tubes filled with ether and anthrachinon were
closed by melting while in a bath of — 80° (solid CO, + alcohol)
and then hanged up in an air-bath with little mica windows. This
air-bath had been supplied with an apparatus, driven by a motor,
for keeping the tubes constantly swinging. The temperature of the
bath could be kept constant within 1°.

In order to determine the solubility curve the temperature was
observed at which all the anthrachinon had been dissolved. In order
to determine the eritical curve at very slow decrease or increase of
temperature this was noted down when formation of nebula occurred,
resp. the liquid phase disappeared. The average of the two tempe-
ratures was noted down in the graphical representation. If possible
the volume of the liquid was chosen in such a way, that on reaching
the critical temperature the tube was nearly filled with liquid. Only
saturation- and critical temperatures for mixtures of definite concen-
tration being determined by these experiments, only a ¢, «-diagram
can of course be constructed from them, which is given in fig. 5,

From a comparison with fig. 4 it is easy to see that the direction
of the two pieces of the critical line and that of the line for the

A
vO 6s laa

See
0 10 2

Oy ah) GO USO 8 60n a G0. G00 100
Ether 2 .
Yb Anthrachinon

solutions saturated with solid £4 is quite conformable with the 4,
a-projection in fig. 4. The point p lies at 195°, 95°/, ether and
5°/, anthrachinon. The point g has, as regards the concentration,
not yet exactly been determined; I estimate it at 70°/, ether and
30°/, anthrachinon, the temperature lies at 241°.

In order to elucidate the very remarkable phenomena we found,
I shall more closely consider the case that we start from a mixture
of ether and anthrachinon composed of 45°/, ether and 55°/, anthra-
ehinon (A fig. 5) and slowly heat this mixture. The quantity of
anthrachinon being so great and the volume rather small, we always
have below 195° excess of solid anthrachinon together with a saturated
solution and vapour. The concentration of the saturated solution
at rise of temperature moves along ihe line cp. At about 195° we
reach the first critical temperature of the saturated solution, when
more heat is added the solution disappears and we get solid anthra-
chinon -+ vapour. Apart from the continually increasing evaporation
of anthrachinon all remains unchanged up to about 241°. At this
temperature the critical phenomenon occurs again; whereas at p the
liquidphase disappeared, here it is formed again *). On further rise of
temperature more anthrachinon is continually dissolving and along

1) The points p and q can never be accurately reached in one experiment, a
yery definite volume being required for every concentration.

(1785

qd we go to the point A, where at 247° all anthrachinon has
exactly been dissolved. If we now increase the temperature still
more we come into the region of wrsaturated solutions; from A
therefore, we go parallel to the Z-axis upwards to the temperature
350°, where the wnsaturated solution has reached its eritical tem-
perature and all passes into the gaseous state.

The influence, which greatly diminishes the accuracy of the results,
is the dependency of the volume; the error created by it, is small
for the critical curve ap and for the solubility curve bg, because
these curves have a rather slight curvature. For the critical curve bq
and especially for the lower part the possivle error in the concentra-
tion is rather great, so that the point q is pretty uncertain.

It seemed very interesting to me to investigate, whether or not it
would be possible to determine points of the metastable part of the
critical curve. I indeed succeeded to get between the temperatures
f, and ¢, a solution, which, as discussed before, was supersaturated.
A tube filled with 6°/, anthrachinon and 94°/, ether was heated in
the air-bath. The solution saturated at the first critical temperature
containing only 5°/, anthrachinon, some solid anthrachinon was still
left above the critical temperature of 195°. At increase of temperature
always more anthrachinon passed into vapour and at last all had
become gas. Now, if I made the temperature fall rather quickly, no
solid anthrachinon was deposited, which would have been normal,
but at 211° a nebula appeared and a supersaturated solution was
formed. Then, when I made the temperature fall slowly, the solution
remained over a range of temperature of 9°. At 202° suddenly
a transformation appeared by which the solution passed into solid
anthrachinon and vapour and the metastable phase disappeared.
On subtracting more heat the formation of nebula once more appeared
at +195°, the first critical temperature of the saturated solution, and
for the second time a liquid was formed, but now this liquid was
a stable phase. This phenomenon shows, that vapours are also possible,
which are supersaturated of solid and for their transition into the
stable phase choose a round-about way by another metastable phase,
Viz. a supersaturated solution.

I repeated the same experiment with a greater anthrachinon-con-
centration; now the formation of nebula appeared at 216°, it is true,
but before a visible quantity of liquid had been formed, solid anthra-
chinon already was deposited. These two temperatures could not serve
to determine the metastable part of the critical curve, because the
vapour-space in the tube happened to be too large. So the tempera-
tures under observation were not critical temperatures,

Yohd.¥

_The results obtained enable me to somewhat elucidate a few dark
points oceurring in literature. From the experiments of Wappen and
CENTNERSZWER*) on the solubility of KJ in liquid S¢ ), up to 96°, it
is obvious that after one of the two liquid layers, which are coexis-
tent between 77°.3 and 88°, have disappeared, the solubility decreases
and at 96° amounts to no more than 0,58 mol. °/, KJ.

On account of this in their diagram they make the solubility
curve below 100° terminate into the axis, as indicated in fig. 6.
It is obvious, that this is not compatible with the theory given above,
the prolonging of the solubility curve as far as the “axis is certainly
wrong. Most probably the same phenomenon appears with SO, and
KJ as with ether and anthrachinon; the diagram may be somewhat
different, the type, however, will be the same’). Hence it is not
improbable, that on prolonging the solubility curve up to higher tem-
peratures we should again observe an increase of the solubility, so
that the direction up to the first critical temperature of the saturated

solution will be somewhat like that indicated in fig. 7.

Fig. 6.

¥00

oe Fig. 7.
go°
Car
Y
85°
iy

re] 10 20
AI

Since 1880 many more experiments have been made which point
to the fact, that gases above their critical state are able to dissolve

1) Zeilschr. f. physik. Chem. 42, 456 (1903)
*) For the systems SO,-+RbJ and SO,+NaJ the same holds true. Zeitschr f.
physik. Chem. 39, 552 (1902).

( 180 )

liquids and solids’). Vituarp e.g. found, that when he compressed
oxygen at the usual temperature (17°) to + 200 atmospheres in a
tube with bromine, this evaporated in a much higher degree than
corresponded with the vapour-tension at the temperature of observation.
This could be observed because, while the oxygen was being com-
pressed, the colour of the vapour grew darker and darker and beeause
bromine on decrease of pressure was deposited against the wall in
the form of little drops. |

Fig 8. Prof. Bakuvts Roozrsoom’) has already given
an explanation of this phenomenon by means of
the p-r-loop, which applies to the said system of
orygen—bromine at 17°, because this temperature
lies far above the critical temperature of oxygen
(— 111°) and also above the melting point of
bromine (— 7,3°).

According to Hartmann *) this p-a-loop has the
& form, given in fig. 8. It follows from the great
ieee B vise and running back of the vapour-line LRP,
that the partial pressure of the vapour of B between FR and P must
be much greater than the pressure in /7. Though increase of pressure
alone is sufficient to increase the vapour-tension, the influence of
compressed gases is much greater in consequence of the solution of

the gas in the lquid.

It is clear that by increase of the oxygen-tension ¢ota/ evaporation
can be reached here, the region liquid + vapour having for a certain
concentration of A given place to the gas-region.

With the systems CH,—C,H,Cl, CH,—CS,, CH,—C,H,OH Vitiarp
found the same phenomenon in an even more striking way. Also
with solids Viriarp could observe an increase of the partial pressure.
The partial pressure of iodine was perceptibly increased by an
oxygen-pressure of - 100 atmospheres, whereas with hydrogen a
perceptible increase did not occur until at 200 a 300 atmospheres
At + 300 atmospheres methane dissolves very perceptible quantities
of camphor and paraffine, even so much that on decrease of pressure
the dissolved substances crystallize in visible quantities against the
walls of the tube.

At 300 atmospheres aethylene dissolves rather much J, which on

1) Hannay and Hocarru. Proc. Roy. Soc. 30, 178, (L880).
Vittarp. Journ. de Phys (3) 5, 453 (1896).
Woop. Phyl. Mag. 41, 423, (1896).

2) Die Heterogene Gleichgewichte 2, 99.

5) Journ, phys. Chem. 5 425 (1901).

fae ht ti i i ty iia

ae er

( 181 )

decrease of pressure is deposited in crystals. Parafline strongly dissolves
in aethylene; so much so that under a pressure of 150 atmospheres
we can make it evaporate altogether. Stearine acid also easily dis-
solves in aethylene, but not to such a high degree as paraffine.

As yet we have not been able to explain the total evaporation of
a solid by a gas above its critical state, without an intermediate
liquid phase; this is owing to the fact, that there was no suspicion
of the behaviour shown by the system ether and anthrachinon. If
we compare the figures 3 and 4 with each other, it is obvious that
if in fig. 3 we start from solid 5 and by compression of A at a
constant temperature we follow a course parallel to the .v-axis from
right to left, a liquid phase will always appear first before we
come into the gas-region. This phenomenon observed by VinLarp
in the system camphor-aethylene will also occur in fig. 4 between
the temperatures f, and ¢, and between ¢, and ¢,, so that this be-
haviour does not decide the type to which the system belongs.
Investigations at different temperatures only would enable us to do so.

It is, however, quite different, when the solid evaporates altogether
without giving a liquid first. Lf this be the case we can directly
point out the type; then it belongs namely to type fig. 4, for there
only it is possible when coming from the region for solid B+-vapour
to pass ito the gas-region without an intermediate liquid-phase, as
long as we work between the temperatures t, and ty.

Probably the systems alcohol + KI, KBr, CaCl, and Cs, + I, ot
Hannay and Hoegartn, ether+Hel, of Woop and CO,-+-1, of Virtarp
belong for the greater part to the type fig. 4.

That, as would follow from Vinnarp’s experiments, also the partial
vapour tension of solids would be considerably increased by relat-
ively slight pressures (100 a 200 atmospheres) of an additional gas,
seems, however, possible to me only when the vapour-line of the
system solid-vapour can get a course similar to that of liquid-vapour,
which will probably be the case only when the added gas A dissolves
in the solid phase 6. This point wili soon be investigated by me.

Chemical laboratory of the University.

Amsterdam, September 1903.

( 182 )

Botany. — “On the penetration into mercury of the roots of freely
B

floating germinating seeds.” By Pu. vax Harreverp. (Com-
municated by Prof. J. W. Mo11).

The first who mentioned that growing germroots can penetrate
into mercury was JuLes Pinot in 1829. He placed various seeds in
a thin layer of water on mercury and observed that on germination
a number of roots pushed themselves into the mercury.

His experiments were important in two respects. Firstly from a
physiological point of view: the penetration of the germroots into a
liquid of so high a specific gravity as mercury proved that during
growth considerable forces are developed. And secondly from a
physical point of view: the seeds lay loose and yet the germroots
were not lifted out of ithe mercury by the upward pressure.

These two results of Prnor’s experiments must be clearly distin-
enished. On the first much work has later been done; Sacus and
other investigators used mercury repeatedly in order to give a
great and uniform resistance to a downward growing root. On the
second point, the physical paradox of the root which penetrates into
mercury without a hold, no publication has appeared after that
of Wieanp in 1854. Pivot himself was only struck by the second
result of his experiment, the penetration of loose lying seeds. As this
phenomenon could not be explained by physical laws, he called in
the aid of vital force, as was still very common in his days.

The vitalistie doctrine however had found a fierce opponent in
Durrocuet’). The latter declared the experiments to be untrust-
worthy. Several investigators, on the other hand, confirmed Prvot’s
observation. Thereupon Dtraxp and Dvrrocurr gave, in 1845, an
explanation of the curious fact which was generally accepted. Although
Wicanpd in 1854 assured once more that Pinot’s observation was
correct and still awaited an explanation, no further attention was
paid to it. Pivot was often quoted for his first result; for the
phenomena of freely floating seeds at best reference was made to the
refutation by Duranp and Dvurrocuer.

Reading the astonishment of Wicanp, when he was obliged to
state the correctness of Pinot’s observations, I repeated the experi-
ments. I found that Pinor was right indeed. The explanation of the
seeming physical paradox can nowadays be easily given; a “vital
force” is not needed for it.

In the older literature on geotropic phenomena one meets with
such contradictory opinions about the penetration of freely floating

1) J. Sacus, Geschichte der Botanik 1875. pag. 550,

( 183 )

seeds, that it may be useful to give a short synopsis of the literature
on the subject. I shall afterwards compare the various opinions with
the true explanation.

Historical SYNOPSts.

On February 23, 1829, Jutes Pinor sent to the Paris Academy
of Sciences a paper on the penetration of germroots into mereury.
The Academy appointed a committee of three members to examine
this paper.

Pinot repeated his experiments in the ,jardin du Roi’ in the
presence of two of the members of this committee. He also showed
one member a new experiment, in order to guard his conclusions
against possible objections. In a letter to the Academy, dated July
27, 1829, he gave a description of it. Neither the paper nor the
letter seem to have been printed. But Pixor published a short account
of his first paper, together with an extract of his letter about the
new experiment, in the Revue Bibliographique of July 1829 °*).

According to this account he arranged his experiments in the fol-
lowing manner: a little trough, 18 mm. deep and 10 mm. broad
was filled with mercury and a thin layer of water poured out on
the mereury. The trough stood in a small dish with water over
which a little bell-jar was placed. Seeds of Lathyrus odoratus, soaked
in water, were placed on the mercury with the hilum turned towards
the mercury surface.

The layer of water was sufficient to maintain germination, but
was on the other hand, as thin as possible in order not to favour
rotting of the seeds. Now on germination the roots of the freely
floating Lathyrus seeds penetrated to a fairly considerable depth into
the mercury without lifting the seed. Also with other seeds the
experiment was successful; the penetration sometimes exceeded 8 or
10 mm. When however the growing little stem was killed by a
drop of sulphuric acid, the root came to the surface.

1) Revue Bibliographique pour servir de complément aux Annales des sciences
naturelles; par M. M. Audouin, Ad. Brongniart et Dumas. Année 1829 page 94—906.

This Revue Bibliographique only appeared in the years 1829, 1830 and 1831.
With many specimens each of the three yearly volumes is bound with one of the
three volumes which appeared annually of the Annales des sciences naturelles. As
they have a separate pagination however, it is not sufficient to quote the number
of the page and the volume of the Ann. d. sc. nat., as Hormersrer (1860), Cresienkt
(1872) and others do. A. P. De Cannotte in his Physiologie végétale Il. p. 828,
note (1) calls this Revue Bibl. wrongly: Ann. sc. nat., Bull. which may cause
confusion with the ‘Bulletin des sciences naturelles et de géologie’, which appeared
from 1824 (T. 1) till 1831 (T. XXVID.

( 184 )

In order to discover to what extent the weight of the seed and
its adhesion to the moist mercury-surface could be the cause of this
penetration, Pinot devised the following experiment, described in the
extract of his letter. A silver needle rested in the middle very movably
on an axis. On one end a germinating Lathyrus seed was stuck,
on the other end a movable pellet of wax, just balancing the seed.
The seed hung about two millimetres above a moist mercury-surface ;
a bell-jar again kept the air moist. The germination now proceeded
somewhat more slowly, but the root still reached the mercury-surface;
next it forced itself into the mercury, as in the case of the unsup-
ported seeds, without pushing the balance-arm upwards. For this
experiment Lathyrus was chosen because with it the cotyledons
remain within the coats of the seed. Neither could the weight cause
the penetration as it was balanced by the wax-pellet and also adhesion
between the cotyledons and the mercury was excluded as they did
not touch each other.

Pinot gave the facts as he observed them but he did not venture
an explanation. That he would not have been averse to using the
vital force for it, however, appears from the mention he makes of
the sulphuric acid: as soon as he kiiled the germinating plant by
it, the root came to the surface of the mercury.

Pixor also communicated his discovery to the ‘Société de Phar-
macie de Paris’, which gave an extract of his letter in the Bulletin
of the transactions of its meeting of August 15, 1829.*) The same
article is found in Flora of that year *), in the Edinburgh New
Philos. Journal *) and in the Annalen der Gewachskunde ‘).

These publications drew general attention, firstly because it appeared
from them that roots grow downwards with great force and secondly
because it remained unexplained how the seeds found a point of
resistance against the upward pressure of the mercury. This latter
point occupied more particularly Pixor’s countrymen, whereas some
foreign workers were especially struck by the former. Among these
Crass Munper of Franeker repeated the experiments and gave a
translation of Prnor’s article in the Revue bibliographique together
with the description of his own experiments in the autumn of 1829. *)

1) Journal de Pharmacie et des sciences accessoires, T. XV 1829 pag, 490—491.

2) Flora oder Botanische Zeitung, XIL'et Jahrgang Zweiter Band 1829 pag.
687—B6ds.

3) The Edinburgh New Philosophical Journal, July—October 1829 pag. 376—377.

4) Annalen der Gewiichskunde, Bd. IV pag. 407—408.

5) Bijdragen tot de natuurkundige Wetenschappen, verzameld door H. C, van
Haut, W. Vrouix en G. J. Mutper. Vierde deel 1829 pag. 428—437.

( 185 )

Fede ie “small beer-glasses” of a little more than 5 em. diameter

- (Mvzper speaks of N. inches, i.e. new inches or centimetres) and
them with mercury 4 cm. deep, on which lay a layer of
; water with pigeon-beans (Vicia faba minima) and buckwheat. The
=e roots of buckwheat did not penetrate into the mercury and went on
‘ “creeping over the surface for a month. When the beans had frOW)
ems of two centimetres, five of them had their roots in the mere ury ;

the rest lay on the surface but had evidently been submerged.

In order to prevent capsizing, a few of the seedlings of Vicia

—

ere eet out aoe had straight roots and these were stuck

oreury. iispecially between the wall of the glass and Ke mercury
now observed the penetration of the secondary roots.

‘His conclusion is that these experiments afford a new proof that
innate tendency of the root to grow downwards, must be con-
red as a vital action dependent upon internal foree which external
cur umstances can hinder, modify and even render almost irrecog-
nisable, but by no means destroy. *)

ILDER thinks only of the force with which the roots 2row
nwards. The physical paradox escapes his attention, although

the silver needle. By bis using big seeds, seedlings in an
cet ag and cork, his ee — sic ene oe

Baicnett to eliminate the ole of the seeds ve lee them
to the holes of a wooden cross which above the mercury was
held fast in a conically shaped glass) No more than Mctper he
noticed Pinot’s physical paradox, for the friction of the seed in the

. » lic. pag. 436.

2), Revue Bibliographique. Dec. 1830, pag. 129—130.

3) Linnaea Bd. 5, pag. 191 of the ,Literatur-Bericht”.

4) Verhandlungen des Vereins zur Beférderung des Gartenbaues, VIfter Band
1831, pag. 204-206,

( 186 )

holes of the wooden cross now counteracted the upward pressure
of the mercury. GorPPERT worked even with the bulb ofa hyacinth!

It has been remarked above that in France it was exactly the unsup-
ported condition of the seeds which drew attention because it seemed
to plead for “vital force’. Dutrrocner had commenced the great fight
against this latter and consequently he was prompt to stave off the
danger. He repeated Pinot’s experiments and obtained a negative result.
Thereupon, on Nov. 16, 1829, he made the following communication
to the Académie des sciences, of which he was a corresponding
member. ’) “Par les journaux et particulierement par les Annales
d’expériences présentées a |’ Academie” *) he had learnt that the roots
of plants would penetrate into mercury to a greater depth than
corresponded to their weight, consequently by a physiological action.
He had repeated these experiments carefully but had by no means
obtained the result of the author. The root never went deeper than
it ought to by its weight and when after a few days it turned black
and died, it did not come to the surface either. The author must
be entirely mistaken; there was nothing that could be ascribed to
physiological or vital action.

In this meeting of the Academie Mirpen communicated that the
committee of enquiry had also repeated the experiments, but had
obtained the same result as Durrocurr*). This statement is contrary
to what Pinot had said of the committee in his letter to the Academie
of July 27, 1829. The committee has given no written report *).

Durrocuet evidently was no unprejudiced observer when he
repeated Prnor’s experiments. They were troublesome to the new
conceptions of which he was a champion.

A considerable part of Durrocuer’s observations on various subjects

1) Revue Bibliographique. Dec. 1829, pag. 146—147.

2) A periodical of tais name is not known to me. Only in 1835 the Académie
began to publish a printed account of its meetings viz. the: Comptes Rendus
hebdomadaires des séances de |’Académie des Sciences. Of its transactions, entitled:
“Mémoires de !’Académie des Sciences de I’Jnstitut de France”, the new series was
commenced as early as 1818, but not all the Mémoires that came in, are found
in it. [t contains an account of the proceedings of the Académie of some years;
vol. XI 1832, has the account of 1828, vol. XVI 1838, that of 1830 and 1831,
but exactly an account of 1829 is wanting in the intermediate volumes. Yet one
reads in the *Analyse des travaux de l’Académie pendant l'année 1831” in Tome
XVI 1838, page CCL: ‘Dans Vanalyse des travaux de 1829, on a déja donné une
description...”, from which would follow that the account for 1829 had been
published.

3) Revue Bibl. Dec. 1829 p. 147.

') Comtes rendus T. XX 1845 p. 1258.

187 )

has later been proved to be false. And in spite of all the praise
which Sacus justly bestows on him, he adds that Durrocner “sich
oft durch seine eigenen Vorurtheile beirren liesz” ').

Meanwhile the question remained unsettled, for Durrocner gave
only a negation and no explanation. On Dec. 9, 1829, he also read
his article to the Société de Pharmacie de Paris *).

In 1832 appeared the Physiologie végétale by A. P. pr CANDOLLE
who gave a short description of the experiments of Pinot and Mutprr *).
He wrongly was of opinion that Privor fixed the seeds, for his silver
needle was a movable balance. From Munprr’s experiments he drew
the conclusion that the roots penetrated into the mercury on account
of their ‘stiffness’; the tender roots of the buckwheat were not stiff
enough then to force themselves in. To the penetration of freely
floating seeds he opposed DutTrocuet’s negation.

Several handbooks of those days, as those of Biscnorr, LINDLEY,
Treviranus and Mryren, make no mention of the experiments with
mercury. Durrocuer himself omits them entirely from his “Mémoires
pour servir & histoire anatomique et physiologique des végétaux et
des animaux”, 1837.

On May 27,1844, however, Payrr sent a paper to the Académie,
entitled “Mémoire sur la tendence des racines a s’enfoncer dans la
terre et sur leur force de pénétration.” In this paper he described
his experiments which seemed to confirm Prot’s observations. The
paper itself does not seem to have been printed; an extract of it
however was given by Payrr in the Comptes Rendus *), while an
elaborate report of it occurs in the Comptes Rendus of 1845 °).

Payer devised an apparatus in order to determine the depth to
which a germroot could penetrate into the mercury. For this purpose
he used layers of mercury of varying thickness, heing at the bottom
in contact with a layer of water. In a glass trough namely, one or

1) Sacus, Geschichte der Botanik 1875 p. 555.

*) Journai de Pharmacie Tome XVI 1830 p. 28.

3) A. P. pe Canpoie, Physiologie végétale Tome II 1832 p. 827—828.

4) Comptes rendus Tome XVIII. 1844 pag. 993—995. HormeisteR gives p. 933
instead of p. 993; this mistake is found in the following papers:

Hormetster, Ber. der kén. Sachs. Ges. d. Wiss. zu Leipzig XIL 1860 p. 203.

Hormeister, Pringsh. Jahrb. IL 1863 p. 105.

Hormetster, Die Lehre von der Pflanzenzelle 1867 p. 284.

A. B. Frank, Beitriige zur Pflanzenp!iysiologie, 1868 p. 22.

Tu. Ctestetxt, in Cohn’s Beitriige zur Biologie der Pflanzen I, 2 1872 p. 11.

A. Scuoser, Die Anschauungen tiber den Geotropismus der Pflanzen seit Knight,
1899 pag. 9. ‘

5) Comptes rendus Tome XX 1845 p. 1257—1268.

15
Proceedings Royal Acad. Amsterdam. Vol. VI.

( 188 )

more pieces of platinum gauze were fixed horizontally, on which a
patch of muslin or cotton was placed. The trough was filled with
water as high as the patch, in some experiments it contained oil or
only air; then the mercury was poured on the patch. The tension
of the lower mercury-surface was great enough to prevent the mercury
from being forced through the meshes.

Now Payer made various seeds germinate in the layer of water
on the mercury. It will be presently seen that he fixed the seeds to
some extent. Of some he saw the roots penetrate through a layer of
mereury of as much as two centimetres and appear in the water
under it. Of other seeds the roots remained creeping on the mercury,
of others still they only penetrated a few millimetres. Hence Payer
concludes that the roots have a different penetrative power, not
depending on differences of weight, stiffness or size. Weight alone
cannot be the cause, for if the roots are taken from the mercury
they do not sink in it again. They remain floating and only the
growing part can penetrate again. Differences in stiffness cannot cause
the varying behaviour, any more than differences in size. For roots
of garden-cress (Lepidium sativum) do penetrate, those of buckwheat
do not, although the latter are bigger, stiffer and heavier than the
former.

Of the committee which had to report on this paper by Payrr,
Dvurrocuer (since 188! an ordinary member of the Académie) was
the reporter. The report was late in appearing and meanwhile on
March 24,1845, Duranp sent a paper to the Académie in which he
thought to be able to reconcile the conflicting opinions.

Dvuranp says in the extract of his “Mémoire sur un fait singulier
de la physiologie des racines’’*) about the experiments of Prvor,
Mciper and Payer: ‘J’avais toujours vu la, au contratre, une de ces
expériences trop légerement faites et illégitimement imposées a la science,
dont elles faussent ou paralysent les inductions: un fait a rayer des
catalogues physiologiques.” Therefore he wants to repeat these experi-
ments and to give their normal explanation. He makes a clear
distinction between loose and fixed seeds. He gives the following
synopsis of the cases which can oceur.

1. The seed is fixed above the mercury ; the root then penetrates
into the mercury perpendicularly to a depth of more than 4
centimetres.

2. The seed is loose. Here we have two Cases :

A. It reaches the margin of the mercury-surface. Then the root

1) Comptes rendus Tome XX 1845 pag. 861—862,

__——— *

( 189 )

forces itself between glass and mercury and is held fast by the
lateral pressure of the mercury.

£. It stays in the middle. Here again two cases:

a. The mercurial surface remains pure. Then the root does not
sink deeper than it should do on account of its weight.

bh. A resistent, flexible layer is formed on the mercury, consisting
of soluble matter of the seed which on evaporation of the water
remains on the mercury. The root can then penetrate as this layer
sticks the seed to the surface.

Case a. occurred in Durrocurt’s experiments and in those of the
committee for Pinot’s paper; case / is that of Pinor and Muuper.
With Mvuntper buckwheat did not penetrate because it gave off little
or no soluble matter to the water. So Duranp reduces all the cases
of a penetration, greater than the weight, to the first-mentioned
ease, fixation of the seeds.

It appears from Dvurrocuet’s report that Duranp also speaks of
“une adhérence capillaire entre la graine et la surface du mercure”, ')
which gives the seed some support for the penetration of the germroot
when the layer of water has almost evaporated. It is not clear
whether he means the evaporating layer of water or the resistent
layer which he later uses for the explanation of the case under /.

On April 28, 1845, i.e. a month later, a combined report appeared
on the papers by Payer and Duranp. Dutrocuet was the reporter. *)

In the meantime it had become clear that Paynr had not distinctly
felt the difference between experiments on germination upon mercury
with loose and with partly fixed seeds. He had not mentioned
namely in his Mémoire that his germroots were put through holes
in a slice of cork or lay in cottonwool; not till later, on April 15,
1845, he had declared this to the committee. Payer moreover
declared that he had used the word ‘“penetrative power only in
a superficial meaning, not involving a special vital force.

So Payer’s experiments were no longer alarming, especially now
that Duranp had given an explanation of those of Pivor. For in
these latter the seedling was stated to have stuck to the surface of
the mereury, because on evaporation of the water a sticking-plaster
was formed of soluble substances of the seed with mercury. In his
report Durrocner says*): ‘La couche dont il est ici question est une
mixtion avec le mercure des substances organiques qui ont été
dissoutes dans leau.” <‘Telle est selon M. Duranp, la cause de la
1263.

1) Comptes rendus Tome XX {845 p.
AS p. 1257—1268.

*) Comptes rendus Tome XX 18
5) Idem p. 1264,

13%

(190 )

pénétration de la radicule -dans le merecure lorsque la graine est
déposée sur la surface de ce métal couvert dun peu deau ; il faut
que la graine soit agglutinée a la surface de ce métal par le moyen
@un enduit qui s’y forme pour que cette peénétration ait lieu.
Lorsque le mercure conserve son poli, les radicules ne s’y enfoncent
jamais au dela de ce qui est déterminé par la pesanteur des graines.”

So the paradox had been subjected to known physical laws.

The matter seemed to be settled for good and all, when in 1854
once more an investigator confirmed Pinor’s observations.

Aubert Wicanp at Marburg wrote in his “Botanische Untersu-
chungen” a chapter, entitled ‘“Versuche iiber das Richtungsgesetz
der Pflanze beim Keimen’’). He mentioned in it the experiments
of Pivot, Munprer and Dutrrocuet, without quoting the literature on
the subject. He said that Prvor and Mutprr fixed the seeds but that
Dvutrrocuet let them free and hence obtained a negative result. *)
Evidently he derived this erroneous idea about Pixor from Répxr’s
translation of Dr Canpouin’s Physiologie végetale.

Wicanpd dared scarcely confess that he also had made seeds
germinate when they floated on the mercury, so firmly was he
convinced of the impossibility of success in this case. *).

But the result was undeniable, and so he nevertheless deseribed
his experiments.

The seedlings grew in a very thin layer of water on the mercury
or on dry mercury in an atmosphere saturated with water-vapour.
Some roots penetrated perpendicularly into the mercury as far as
4 «Zoll”.*) Others grew in a slanting direction into the mercury
or at first perpendicularly and then more horizontally or the apex
came out of the mercury again or it grew horizontally at first and
then perpendicularly downwards. A great number of roots remained
creeping over the surface. Seedlings that had been taken out of the
mercury could be replaced to the same depth. Along the glass wall
many roots penetrated.

For seeds of smaller size than beans, weight was hardly a factor
for the penetration; a seed of garden-cress made scarcely any de-
pression in the mereury and yet the root penetrated fairly deep.
Nor could the reason be found in a greater adhesion of seeds and
mercury by the secretion of certain substances. For often mercury .

1) Botanische Untersuchungen von Dr. Atpert Wieanp, Braunschweig 1854
pp. 1381—166.

2) Idem p. 136.

3) Idem p. 137.

4) 12 Linien = | Zoll = 27,075 mm.

(191 )

‘stuck to the radicles, to be sure, but only to old, dying, not to
fresh and growing roots.

WicAND gave no explanation. To him it seemed to be “ein bis
jetzt ungeléstes mechanisches Paradoxon, nicht minder als Miinchhausen,
der sich und sein Pferd an seinem eigenen Zopfe aus dem Sumpfe
zieht’’ *).

But he entirely confused the force with which the root penetrated
and the cause which prevents the seedling from capsizing in the
mercury. For he thought: the penetration of germroots in a solid
soil quite as mysterious, although here there was no question of
upward pressure.

No attention has later been paid to these observations; not even
by those who quoted various other points from this chapter of WiGanp.
It was considered sufficient to refer to the refutation by Duranp
and Durrocurr in 1845.

So Hormeister wrote in 18607): “Prxor und Payer sind bereits
1845 dureh Durand und Dvrrocuer so griindlich widerlegt, die
Ursachen der Téiuschungen jener sind so vollstandig aufgedeckt worden,
dass die ausfiihrliche Mittheilung von mir selbst iiber diesen Gegen-
stand angestellter Beobachtungen kaum noch noéthig ist” *). HormEistER
obtained the same result as Duranp and Dutrocuer: penetration
by weight or because the seedling stuck to the mercury by dissolved
matter.

Sacus wrote in 1865: “Die an sich schon unglaublich klingenden
Angaben Pinot’s und Payrr’s iiber das tiefe Eindringen der Wurzeln
in Quecksilber, wurden schon von Duranp und Dutrocuet widerlegt” *).

In 1867 Hormerister wrote tnat the penetration of growing roots
into mercury was caused by stretching of the hypocotyl, “wie
bereits Duranp und Dutrocuet erschépfend gezeigt haben” °).

Experiments on germination upon mercury now became very
frequent in the following years in order to combat Hormnrister’s
theory of positive geotropism. This latter namely, like Kyigut’s
theory, was based on the supposition that the apex of the root was
of a plastic nature and therefore the penetration of the roots into

1) le. p. 140.

2) W. Hormetster, Ueber die durch die Schwerkraft bestimmten Richtungen
von Pflanzentheilen, in Berichte tiber die Verhandlungen der kén. Siichs. Ges. der
Wiss. zu Leipzig, Mathematisch-Physische Classe, XIlter Band 1860, pag. 175—213.
The same article in Prinesueim’s Jahrbiicher fiir wiss. Botanik IIL 1863 pag. 77—114.
4) 1. c..p- 203 resp: p. 105:
4) J. Sacus. Handbuch der Experimental-Physiologie der Pflanzen, 1865, pag. 104.
5) W. Hormetsrer. Die Lehre von der Pflanzenzelle, 1867, pag. 283 Anm. 4,

( 199 }

mereury was no welcome fact to these theories. In this way arose the
fierce controversy between Hormeister and FRANK *), concerning which
we also mention the papers by N. J. C. Mtnier*), N. Spescunerr *),
Tu. Crestetki*), Sacus*), SaposHnikow °), and WacusrTe.‘). FRANK,
like Wicanp, derived from Dr Canpo.iE *) the erroneous idea that
Pivot fixed his seeds *), and for the rest entirely embraced the views
of Duranp and Dvrrocuet’’). To the loose lying seeds none of
them paid attention nor is anything found about them in later
text- or handbooks.

In 1899 Dr. A. Schober gave a historical synopsis of the various
hypotheses on geotropism in which he also deals with the experi-
ments on germination upon mercury *'). He does not deal with
loose seeds in it however.

Explanation of the phenomenon.
1 : L

The penetration of the roots of entirely freely floating seeds into
mercury has been stated by few investigators only. From the
preceding historical synopsis it would appear that this was done
only by Pivot and Wicanp. .

Muiprer, Gorppert and Payer gave support to the seed, by putting
the roots through holes in a slice of cork (Munprr and Payer), in
a wooden cross (GOEPPERT), or by placing the seeds in or on a
plug of cottonwool (Payer). Hereby the frictional resistance against
upward movements was increased and also the circumstances at the
surface of mercury and water were modified, so that the seeds were
less easily lifted out by upward pressure.

So I repeated the experiments as Pinot and Wicanp had made
them. Although Wieanp gives no dimensions, yet one can see from
his description that he did not use such small troughs of mereury

1) Bot. Ztg. 1868 and 1869.
2) Bot. Ztg. i869, 1870 and 1871.
3) Bot. Ztg. 1870.

4) Cony’s Beitriige zur Biologie der Pflanzen I, 2 1872.

5) Arb. des bot. Inst. in Wiirzburg I, 3 1873.

6) Report in Bot. Jahresbericht XV, 1 1887; less extensive in Bot. Centralblatt
Band 33, 1888.

7) Bot. Centra'blatt Band 63, 1895.

8) Physiologie végétale II, 1832, pag. 82.

%) Beitriige zur Pflanzenphysiologie, Leipzig 1868, pag. 5.

1) Idem pag. 22.

11) Die Anschauungen tiber den Geotropismus der Pflanzen seit Kyieur. Ham-
burg 1899. pp. 9 and 18,

- er ee
Mm =

“*

as Pivor who used them only about one centimetre broad. So I
took first rectangular glass troughs of 4 em. breadth and crystallising
dishes of 10 em. diameter which were filled with mereury about
two centimetres deep.

On the dry mereury I had to pour a fairly large quantity of
water before this would spread over the whole surface; by means
of a pipette so much was drawn off that only a very thin layer
remained. In this water the soaked or dry seeds were put. The
seeds had to emerge for a great part above the layer of water; if
this latter was too thick they rotted and grew mouldy, especially
if the temperature was somewhat high, as in a hothouse. The dishes
were covered with glass or placed under a_bell-jar in order to
prevent strong evaporation. Distilled water was used by preference.

The seeds used were: pea (Pisum sativum), garden-cress (Lepidium
sativum), wheat (Triticum vulgare), buckwheat (Polygonum Fago-
pyrum) and Lathyrus odoratus. The garden-cress grew quickest, so
that I could make a number of experiments in succession in a short
time with it.

Most roots crept over the surface of the mercury or only pene-
trated into it with their extreme tip. Sometimes however a radicle
had advanced to a fairly considerable depth. Thus on February 19,
1900, the radicle of a seed of garden-cress of two days was 7 min.
long, of which 38 mm. were in the mercury. On March 17, 1900,
several radicles of garden-cress had, after three days, advanced 4 to
6 mm. perpendicularly into the mereury, of a pea the radicle was
5 mm. in the mereury. On March 28, 1900, after three days, again
a few radicles of garden-cress were 5 mm. in the mercury. The
radicles that had found their way into it had for the greater part
had a downward direction immediately at their germination, so that
only a short piece protruded above the mercury. Sometimes however

- roots of garden-cress, after having grown laterally about one centi-

metre, had still pierced the mercury 4 mm. with their apex.

With wheat the three secondary roots crept over the mercury, an
apex seldom penetrated any length. Radicles of buckwheat I did
not see penetrating. Lathyrus sometimes 5 to 7 mm.

On further growth the plantlets that had pierced the mercury
were upset and were lifted out of the liquid as was the case with
the great majority of seedlings at the very beginning. Hence the
experiments were soon finished. So the circumstance that the roots
turned black and died later and that the seeds rotted and grew
mouldy, gave little trouble. The mercury however had to be per-
fectly pure, since otherwise the radicles stopped growing too soon

( 194 )

and turned brown. The purification took place with dilute nitric acid,

In these experiments some roots had so far grown down that
weight alone could not explain this. My radicles did not go down
so deep as those of Wicanp however. Now it soon became clear
in what respect the plantlets that had grown into the mercury were
distinguished from those which had not. They were not quite
free, namely, but lay against another seed; round and between both
seeds the water had risen through ecapillarity and gave some support
to the seed by the tension of its concave surface. The molecular
forces of the water thus opposed the upward pressure of the mercury.

Duranp calculated the force with which the mercury forces seedlings
of Lathyrus odoratus upwards. For a cylindrical radicle of */, mm.

9
0

2
diameter this force amounted per mm. length to 2 6 <x 13,6
milligrammes; for a length of 20 mm. this is 120 milliigrammes.

The volume of the radicles can be approximately determined from
the length and the thickness in various places; or by weighing the
cut off radicles. (The specific gravity is about one).

The tapering of the roots towards the top makes the determination
of the volume from measurements of thicknesses rather inaccurate.
For approximate values the two methods supplement each other
sufficiently, however.

For radicles of Lathyrus of 5 to 7 mm. length I found volumes
of 5 to 8 mm*.; the upward pressure of the mereury is then 68 to
109 mg. The Lathyrus plantlets weighed about 200 me.

Roots of garden-cress of 5 to 9 mm. had volumes of J to 2 mm*.;
the upward pressure is then 14 to 27 mg. The cress plantlets weighed,
before the seedeoat had fallen off, about 17 me., after the falling
Of, -O me. *).

The weights of the plantlets are considerably diminished, however,
by their lying in the water with parts that are much more voluminous
than the radicle. When the upward pressure of the layer of water
has been subtracted, the weight that must be compared to the upward
pressure of the mercury remains. In the case of Lathyrus this
weight will still be in excess, but with garden-cress there is a greater
or smaller deficiency. For the greater depths of Pinor and WiGAnp
this deficiency becomes greater still, but its amount remains small
and can easily be compensated by the molecular forces of the water.
If the seedling be raised through a very small distance, the surface
of the water that has been raised against the seed by capillarity,

1) The cast off seedcoat alone weighs about 16 mg., evidently because it is
filled with water, retained by capillarity.

_- pa

(195 )

must be extended along the whole margin. The capillary constant
of water is 8,8, henee for each mm. of the circumference of the
raised water a force of 8,8 mg. is necessary.

This circumference measures with the swollen seed of garden-cress
14 mm., with Lathyrus about 29 mm., so that a force of more than
100 mg. is available for compensating differences of upward pres-
sure and weight.

Therefore it is necessary however that the seed or plantlet cannot
capsize too easily. The capsizing is a rotation round a horizontal
axis by which the water-surface need not be increased. The vertical
component of the surface-tension is consequently of no effect to prevent
the plantlet from being upset and hence being lifted out. This rotation
is rendered more difficult by water, rising by capillarity between
two seedlings that lie close together, or between the glass and the
seedling, because this water has a greater horizontal surface which
must be increased during the capsizing. Hence it is against the glass
wall that the roots penetrate most frequently, in which case also the
friction between wall and root facilitates the penetration by the
unilateral horizontal pressure of the mercury.

The thinner the layer of water, the closer the centres of surface-
tension and upward pressure lie together and the shorter is also the
lever-arm with which a lateral component of the hydrostatic pressure
acts on a somewhat slanting radicle in order to upset the plantlet.
With a seed in an entirely free position, penetration will be possible
but in the most favourable case only an unstable equilibrium will exist.
The penetration of freely placed seeds will consequently be generally
absent, not because the upward pressure soon exceeds the weight of
the little plant, but because the plant is overturned by rotation.

Pinot immediately obtained such a good result because his mercury-
troughs were so small, only one centimetre broad. So I also repeated
the experiments in this way. Of a glass tube of one cm. diameter
bits were cut off and closed at the bottom with a cork. These troughs
were filled with mercury and in each a soaked seed of Lathyrus or
garden-cress was put with as little water as possible. The water that
was raised by eapillarity now stuck the seed against the glass wall
and the root penetrated more easily because it was less easily
upset. When I placed the seeds with the radicle turned towards the
centre of the trough, it grew down into the mercury itself, not between
the glass wall and the mercury.

Pivot used still another and effective means to prevent capsizing
and at the same time to eliminate the weight of the seed, viz. by
the experiment with the silver needle, described above. I repeated

( 196 )

this experiment in the following manner, see fig. 1. Of thin sheet-
aluminium a flat balance-ceam was made, 6'/, em. long, resting
with a brass cap on a steel point. On one end a Lathyrus seed was
stuck, to the other a small bit of paraffin was melted, balancing
the seed. Exactly under the seed a small trough of mercury was
placed with very little water on the mercury. By another small
vessel, filied with water, and by a little bell-jar over the whole
arrangement, the air was kept moist. The root after a few days grew
down 7 mm. into the mercury, without the balance being lifted. By
adding to it and by melting away from it, the small bit of paraffin
was occasionally brought into equilibrium with the growing seedling,
after the latter had been dried with filtering paper. The upward
pressure of the mercury which amounted to more than 100 me.,
was now balanced by the surface-tension of the water, raised by
capillarity. It might even have been a great deal more, for on the
other arm of the balance I could still place about 100 mg. in addition
to the bit of paraffin before the plantlet was lifted out of the mercury.

We can now explain why various investigators could give such
totally contradictory reports.

In the first place we may trust Prnor’s results (1829). The
description of his experiments gives the impression that he observed
accurately.

DutrrocuetT (1829) did not repeat the experiments with the perse-
verance which is necessary to obtain a good result.

The experiments of Munper (1829) were too coarse and valueless
for Pixot’s problem. Of Gorppert (1831) the same may be said.

Payer (1844) used a slice of cork or a plug of cottonwool on a
thick layer of water, so that later writers wrongly always mention
Pryor and Payer together. His experiment, described above, with a
layer of mercury above a layer of water, is ingenious. I repeated
it, using lacquered iron-gauze instead of platinum-gauze. The roots
of seeds of Lathyrus and Phaseolus, stuek on pins in corks, grew
very finely through the mercury into the water; see fig. 2. The
mereury is indistinct in the figure because of the patch of muslin
which lies on the gauze. It was namely pushed downwards in the
glass trough in order to show the seeds stuck on the pins.

Payer stated that the roots did not penetrate again into the mer-
eury once they had been taken out of it. Pinor and WiGAnp asserted
the contrary. This can easily be explained. The latter left the seeds
free indeed and the surface-tension acted as before when the plant
was replaced in the mercury in its former position. Payrr’s seedlings,
on the other hand, were fixed; they penetrated into the mercury

Pu. van HARREVELD. ,On the penetration into mercury of the roots

of freely floating germinating seeds.”

Proceedings Royal Acad. Amsterdam. Vol VI.

en
is bs

(197 )

to a far greater depth and when they had been taken out of it, they
did not so easily regain their former support.

Duranp (1845) gave the explanation which a large, old seedling
on mercury suggested to him. It had stayed so long on it, that
an adhesive layer had been formed on the mercury of sufficient
thickness to fasten the plant to some extent. That therefore all
seedlings whose roots penetrate into mercury, should stick to it by
such a layer is not true. The penetration takes places after a short
time when the mercury is still bright.

Dutrocuet (1845) accepted Duranp’s explanation and made expe-
riments on the formation of the sticky layer. But he did not put to
himself the question whether in all the observed cases such a
“plaster” had been present.

Wicganpd (1854) has undoubtedly obtained Pinort’s results. In his
discussion however he confused and complicated the question as
Mcrprr had done. For this reason later investigators did not bestow
much attention to the paradox which he had so clearly pronounced.
Where he speaks of penetration into dry mercury, this must cer-
tainly not be taken literally; the soaked seeds retain a layer of water.

Hormeister (1860) studied the penetration of roots in relation with
his theory of the plastic apex. He di’ not obtain the result of Pryor
and Wicanp and accepted Durann’s explanation which also Durrocnnt
had aecepted.

Later investigators all followed Hormuisrrr’s opinion,

Mathematics. — “The harmonic curves belonging to a given plane

cubic curve.” By Prof. JAN pE VRizs.

1. The “harmonic” curve of a given point P with respect to a
given plane cubie curve f° is the locus of the point H separated
harmonically from P by two of the points of intersection A,,A,, A,
of 4° and PH"). We shall determine the equation of the harmonic
curve /* when 4* is indicated by the equation

a*,— b*, = (a, «, + a, a, + a, «,)@) = 0,
and P by the coordinates (y,, y,, 7s).

1) This curve appears in Sreter’s treatise: ‘Ueber solche algebraische Curven,
welche einen Mittelpunkt haben,..... * (J. of Crelle, XLVID, and is there more
generally specified as a curve of order 7. Stereometrically it has been determined
by Dr. H. pe Vries in his dissertation: “Over de restdoorsnede van twee volgens
eene vlakke kromme perspeclivische kegels, en over satellietkrommen”’, Amsterdam
1901, p. © and 88.

( 198.)

To the points of intersection of 4° and h*® belong the points of
contact of the six tangents from P to %*. If A, is one of the remaining
three points of intersection, then A, and A, are harmonically separated
by A, and P, that is P lies on the polar conic of A,; from this
follows however that A, lies on the polar line of ?. So the curve
h® passes through the points of intersection of 4° with both the polar
conic p? and the polar line p* of P. Its equation is therefore of
the form wa*,+a,a?,b?,b,=0. If point X belongs to the harmonic
curve of point Y, it is evident that J” lies on the harmonic curve
of X; so our equation must be symmetric with regard to the
variables x; and y;; that is, it has the form

9p Oy Eh Og Gy Dp O yg == 0S ee

To determine 2 we suppose P to be lying on a,—0O and we then
consider the points of 4° which are lying on «,=0. If we represent
the linear factors of the binary form a*,—6*,—(a, #,+-a, «,)%) by
Px, Gz and 1r;,. then the points H,, H,, H, are indicated by the
equation

he. (Px Vy == Py qu) (px y == Py rx) (qx Vy => dy ry) ==) F
or by
h?, — = Px qx Vy ry =— 2 Paz Py Tx Vy Tx Ty = Ox. Sn Bk eee (2)
6

We now have
3 a?¢ dy — Pr Ye Py + Px Vy Me + Py Ye Vas
3 by b%y = Pe Vy Ty + Py Yo Py 4 Py Vy Pes
and as we moreover have
Py Vy %y = Oy
we find out of (2)
h*, = 9 a*x dy by b?y — a*y baa 0. One oti
This equation also represents the harmonic curve, if we but again
regard a*, as the symbol for (a,,+ 4,7, + a,a,)©.

2. The polar conic of P with regard to the curve 4°; repre=

sented by (1) has as equation
3 Wy dy by +4 (2 aya’, by b’, + a*y dy b,) = Or
or, if we put
— K and Ay ay — L,
we find
@ +a), Kp oS". fe

It is evident from this that the polar conies of P with respect to

the curves of ihe pencil determined by 4° and /* touch each other

( 199 )

in their points of intersection with the polar line p', therefore the
polar line of P with respect to all the curves 4°; of this pencil.
For the curve 4°, passing through P ensues from this that it
must have a node in P.
Evidently the equation of this curve is
a7 Oy — Ga dy by b?, = 0, .. . te er OO)
whilst its polar conic is indicated by
ay Ay b* — a, a’y b, b*, — 0,
or by
bs, K—L?=0,
from which is evident that it is composed of the tangents through
P to the polar conic P? with respect to 4°.
For 4=—93 we find a 4* with the polar conic L7=0. So it
possesses three inflectional tangents meeting in 7.

3. The satellite conie of P with respect to £’ (that is the conic
through the points where 4° is intersected by the tangents drawn
out of P) has for equation *)

4 a?, ay by — o ar ay b., b°, eS Saw Han hei (6)
or
eee Ns ee a) a a)
To determine the satellite conic for the curve /*, we put
Py, = a*z by + 2a, dy by b*y.
Then we find
Sie ly == (A-S}-43) a7 chy by + 22a, ay by by 3
6 i, Py = 2 (4+ 8) az a’, 6°, 4 22 (a, by 67 az a7, by),
or
Ll, Py = (2-51) a, ay bey 3
FG. 1).a8, 0",

So according to (6) the equation of the satellite of 4°) is
4[(A-+-3) a 70° y + 22a;,0° yb,b* | (A-- 1) ¢*,d*,— 9 (4+ 1)? a,07,b*,c,07d*, = 0,
or as.a, 6, ¢ and d are equivalent symbols,

(4 } -. 12) aes ly bey — (2 a 9) Ay a*y b, b* =)
or
(eae ee OPE? 0.2 4 72 /(8)

From this ensues that the satellite conics and the polar conics of
P with respect to the curves /?; belong to the same pencil. If we
represent this by the equation

1) The deduction of this equation is found in Satmon “Higher plane curves”
A stereometrical treatment of the satellite curves is found in the above-mentioned
dissertation of Dr. H. pe Vries, p. 18, 19 ete.

( 200 )
BK peo ae oe ee ee
then
a = 24:(4 +3) furnishes the polar conic,
ui = — (a + 9): (44-4 12) the satellite’ conic of 4%.

Between the parameters # and #' exists the bilinear relation

u—4y=—3.

So for 1 ——1 and n= we find two curves 4°, for which
polar conic and satellite coincide.
In the first case we have 2=—1; so we have the curve s*)

possessing in P a node.

In the second case we find 2= 3, so a curve for which the

polar conic is a double right line.

For 2— — 9 the satellite is indicated by K —0O: We then have

the harmonic curve for which the satellite coincides with the polar
conic of 4°; this well-known property indeed, ensues immediately
from the definition of 1°.

4. Let us now consider the system of the satellite conics of a

given point /? with respect to the cubic curves of any pencil
AAS BO:

By means of a selfevident notation the just mentioned system is

represented by the equation
A{A, 2B) (KG 7K) 3b a ay = 0:

So through each point of the plane pass two satellites; the imdex
u is here two.

The satellite consists of two right lines when / is situated on
the Husstan. Now the Hesstans of the pencil evidently form a system
with index three; the number of pairs of lines d is therefore three.

A double line is found only when P lies on the cubie curve;
consequently for our system 9 is equal to 1.

Between the characteristic numbers of a system of conies exist
the wellknown relations

2u—rvty and 2y—u+d.

We find from the first »—3, « being equal to 2 and to 1.
The second then gives d=4. From this ensues that the just men-
tioned satellite formed of two coinciding right lines must at the
same time be regarded as a pair of lines, thus as a figure in which
the centres of the two pencils of tangents have coincided.

From the equation

9 (Kat4Ks) (La+4 L;)—(4,+4 B,) (A+a B)=0

a ee en ea

SS ee Oe

(

O1 )

it is evident that the harmonic curves of P with respect to the
curves of the cubic pencil also form a system with index fwo.

For &° passing through P the curve /’ breaks up into the system
of the polar conic and the polar line of P with respect to that
curve which touch each other in P.

As k* and h® have in common the tangents out of P?, being thus
of the same class, the harmonic curve has only then a node when
this is the case with the original curve.

5. If with respect to a given &* we determine on each right
line through P the points 5,, B,, 6, in such a way that B; is
harmonically separated by <A; from A; and Az, we get as locus of
the pomts 6 a curve of order sur, 4°, with a threefold point in LP.
For, if 5, coincides with P, then A, is one of the points of inter-
section of 4° with the polar line of ? and the reverse (see § 1).

As the points 5 correspond one by one to the points A, the curve
h® is of the same genus as 4°, so it has still 6 double points or
cusps. This last is excluded because in that case not a single tangent
could be drawn from P to /°, whilst it is clear that the tangents
out of P to &* also touch 1’.

From the. definition of 4° follows immediately that this curve can
meet the curve 4° only in the points of contact R of the above
mentioned six tangents: so in each point & they have three points
in common. The right line PR having in FL two points in common
with 4°, but three points with 4°, 2 must be one of the six nodes
of A° and PR one of the tangents in that node.

Chemistry. SS “Preparation of cyclohexanol.” By Prof. A. F.
HOLLEMAN.

The preparation of ketohexamethylene in somewhat large quantities
is one of the most lengthy operations, whatever known process
may be used.

Since, by means of the addition of hydrogen to benzene, by the
process of SABATIER and SuNDERENS, hexa-hydrobenzene has become
a readily accessible substance, it was thought advisable to use this
as a starting point for the preparation of the said ketone by first
converting it into monochlorohexamethylene, converting this in the
usual manner into the corresponding alcohol and then oxidising this
to ketone by the process indicated by Banynr. Mr. van per Laan
has tried, in my laboratory to realise this.

( 202 )

The method, however, appeared impracticable as the chlorocyclo-
hexane was not readily converted into the alcohol. MarkownNikorr
has tried to attain this by using alcoholic potash ; we have tried it
by shaking the said chloro-compound for several days and at different
temperatures with silver oxide and water + alcohol, but a trans-
formation worthy of the name was not controlled.

The chlorination of cyclohexane in quantities of 80—100 grams
to the monochloroeompound was moreover a disagreeable and slow
operation. The most satisfactory results were obtained by MARKOWNIKOFF'S
first method (A. 801, 184) by pouring the hydrocarbon on to water
in a Drechsel flask and then passing chlorine into the water at 30—40°.
The influence of light is very pronounced in this case. Direct sunlight
causes explosion. If chlorine 1s passed through the hydrocarbon
exposed to faint light it dissolves with a yellow colour. If now this
solution is exposed to sunlight a violent evolution of hydrogen chloride
takes place; in strong light this is accompanied by luminous phenomena.

Mr. van per Laan, however, succeeded in readily preparing
ketohexamethylene by another process. It appeared that phenol and
hydrogen combine to hexahydrophenol by the method of SaBatier
and SenpERENS and that the cyclohexanol obtaimed could then be
oxidised to the corresponding ketone:

C,H,OH + 3H, —C,H,,OH ; C,H,,OH + 0=C,H,,0 + H,0.

For the preparation of cyclohexanol C,H,,OH a combustion tube
was quite filled with nickeloxide which was then reduced by means
of pure hydrogen. By means of an asbestos stopper, one end of the
tube was connected with a wash-bottle containing phenol; this was
placed in an airbath heated to 160—170°. The tube was placed in
a combustion furnace in an iron gutter lined with asbestos. The bulbs
of two thermometers were also placed in the gutter and the flames
were so regulated that they showed 140—160°. By means of another
asbestos stopper, the other end of the tube was connected with an
adapter leading into a flask closed with a doubly-perforated cork.
Through the second hole was passed a gas exit tube by means of
which the absorption could be controlled.

The current of pure and dry hydrogen which was passed into the
wash-bottle containing the phenol charged itself with vapour which
in the presence of an excess of hydrogen was exposed to the catalytic
action of the nickel. .

In the receiver a liquid consisting of two layers collected, the bottom
layer being water.

The top layer was submitted to distillation, From 85°—110° a liquid

( 203 )

distilled, which separated into two layers one of which consisted of
water whilst the other had a bitter peppermint-like odour. From 110°
the temperature rapidly rose to 160° and from 160—180° a consi-
derable fraction passed over. What distilled above 180° was mainly
unchanged phenol, which was again subjected to treatment with
hydrogen. To remove any phenol, the fraction 160—180° was washed
a few times with dilute soda-lye, the alkaline washings were shaken
with ether to recover any dissolved cyclohexanol, the ether was
evaporated and the residue united with the main liquid. After a few
more distillations a liquid was obtained, perfectly clear and of a
thick consistency, boiling at 160—161°, the b.p. of cyclohexanol
being recorded as 160°.3. A combustion gave the following result.
0.1740 erm. gave 0.4610 grm. CO, and 0.2017erm. H,O; found:
C 72.2 H12.8
calculated for C,H,,0: C 72.0 H 12.0

By oxidation with BeckMANy’s chromic acid mixture (1 mol. K,Cr,O,
+ 2'/, mol H,SO, in 300 germs. of water) of which 135 grams were
used for 10 grams of hexanol and operating at a low temperature,
hexanol gives a fair yield of ketohexamethylene.

Mr. vAN DER Laan has not determined the exact amount of cyclo-
hexanol obtainable from phenol but this is certain that the yield is
quite satisfactory. If four tubes with nickelpowder are heated at the
same time 1 kilo of hexanol may be easily prepared within 7 or
10 days.

As a result of this investigation some substances which were only
accessible with the greatest difficultly, have now become easy of
preparation. First of all cyclohexanol and ketohexamethylene. The

latter may be nearly quantitatively oxidised to adipic acid and as

its calcium salt gives a fair yield of ketopentamethylene when sub-
mitted to dry distillation, these two latter substances are no longer
to be regarded as chemical curiosities.

Groningen, Lab. Univs. September 1903.

Vegetable Physiology. — “Jnvestiyations of some «xanthine deriva-

twes im connection with the internal mutation of plants’. By

Dr. TH. Werevers and Mrs. C. J. Wervers —pr Graarr. (Com-
municated by Prof. C. A. Lospry pr Bruty).

The investigations of CLauTriau*) and of SuzvuKi*) as to the function

of caffeine have shown that this substance must probably be regarded
as a decomposition (‘‘Abbau’’) product of albumenoids.

1) G. Craurriau. Nature et Signification des Alcaloides végétaux, Bruxelles 1900.
2) Svuzuxi. Bull. Coll. Agric. Tokyo Imp. Univ. Vol. 4. 1901. pag. 289.

14
Proceedings Royal Acad. Amsterdam. Vol. VI.

( 204 )

These investigations, however, did not clearly show that the caffeine
when once formed again took part in the internal mutation processes ;
they rather pointed to a preservation of this substance as such and
in such cases where it was shown that the quantity of caffeine had
decreased, this might have, possibly, been due to migration.

We, therefore thought it desirable to subject plants containing
xanthine derivatives to a renewed investigation, to examine as many
species as possible and particularly to study the question whether
these xanthine derivatives are an intermediary or a final product of
the internal mutation. Coffea and Thea species were the only plants
investigated up to the present so we also included in our research
Kola ‘acuminata Horsf. et Benn. and Theobroma Cacao both of which
contain caffeine as well as theobromine. A stay at the Botanical
Gardens at Buitenzorg (Java) afforded us ample opportunity °).

At Buitenzorg many physiological experiments were made and
material collected for quantitative determinations, the results of which
wili be published later on; qualitative and microchemical tests were
also made and of these a short description will be given below.

First of all a few words as to the methods employed for the
detection of the xanthine derivatives in the various parts.

Brnrens’s method was used for plants containing caffeine only.
The parts were triturated in a mortar with quick lime and extracted
with 96°/, alcohol. A few drops of the alcoholic solution were then
evaporated to dryness and the residue sublimed. The sublimate after
breathing on it then showed crystals of hydrated caffeine.

In the case of plants containing both caffeme and theobromine
the parts were boiled with water slightly acidified with acetic acid.
The aqueous extract was filtered and precipitated with lead acetate ;
the filtrate after being neutralised with sodium carbonate was then
evaporated to dryness. Up to this stage the method proposed by
BewreNS had been again used but the dry mass was not now heated
in order to sublime the xanthine derivatives but was extracted with
a little chloroform. Both xanthine derivatives passed into this solvent
and on evaporating the same they were left behind as well defined
crystals; sometimes the residue had to be first sublimed.

Both methods are very delicate; traces of either caffeine or
theobromine may be detected.

The investigation extended over the following plants: Coffea
arabica L., C. liberica Bull., C. stenophylla G. Don., Thea assamica

1) Paullinia sorbilis Mart. and Ilex paraguariensis St. Hilaire could not be

investigated but we hope to do so on some future occasion.

( 205 )

Griff., T. sinensis Sims., Kola acuminata Horsf. et Benn. and Theobroma
Cacao L.’).

a. Loots:

In Thea sp. ?) Coffea sp. and Theobroma neither the roots of the
full grown plants, nor those of the seedlings showed traces of caffeine
or theobromine. In Kola acuminata the roots of the full grown
specimens did not show any either; those of the seedlings, however,
contained theobromine but no caffeine.

b. Stems:

1. Extending young shoots contained :

caffeme in Thea sp. and Coffea sp.

caffeine and theobromine in Kola acuminata.

theobromine no caffeine in Theobroma Cacao.

2. One year old branches contained :

caffeine in T. assamica, T. sinensis, Coffea liberica, C. arabica ;
no caffeine or theobromine in Coffea stenophylla, Theobroma Cacao,
Kola acuminata.

3. Two years old branches contained :

caffeine in T. assamica, T. sinensis, Coffea arabica, none in any
of the others °*).

In branches, these xanthine derivatives are always found in the
bark and not in the wood, at least if the branches are old enough
to render possible a neat separation of the two.

ec. Leaves:

1. young leaves of Thea sp. and Coffea sp. contained caffeine,
those of Theobroma Cacao and Kola acuminata theobromine and
caffeine.

2. Full grown leaves of Thea sp., Coffea arabica and Coffea
liberica contained caffeine; those of Theobroma Cacao traces of
theobromine. Those of Coffea stenophylla contained no caffeine, those
of Kola acuminata neitaer theobrumine nor caffeine.

d. Flowers:

Thea assamica: caffeme in all parts of the flowers, calyx, petals,
stamens and _ pistil.

Coffea liberica: caffeine in the pistil only.

Theobroma Cacao: theobromine (no caffeine) in the pistil only.

1) Coffea bengalensis Roxb. Camellea japonica L., C. Sasangua Thb. and
C. minahassae Koorders were also tested but in neither of them any caffeine was
found.

*) These species are only those mentioned above and not those in note 1.

3) The bark of very thick old branches of Thea assamica contains caffeine ;
none is found in that of Thea sinensis.

14*

( 206 )

Kola acuminata: caffeine and theobromine both in the petals and
stamens of the ¢ and in the corolla and pistil of the ? flowers ’).

e. Fruits:

Thea sp.: both young and ripe seeds (in husk) contained caffeime
(but only in very small quantities).

Coffea sp.: much caffeine in the cotyllae and also in the testa
and husk.

Theobroma Cacao: When the fruit is ripening, theobromine first
makes its appearance in the external fruit wall; afterwards a xanthine
derivative (caffeine) occurs in the fruit pulp; finally the seeds them-
selves show the presence of theobromine and caffeine while the
theobromine is disappearing from the external fruit wall.

Kola acuminata: The fruit wall, fruit pulp and also the seeds
contain both xanthine derivatives during the maturation process.

On looking at these facts we first of all observe that the said
xanthine derivatives are present in all the young parts of these plants
which grow above ground even when they spring from old_ parts
utterly devoid of these substances. For instance, the flowers of Coffea
liberica sometimes result from old branches, the bark of which is
devoid of caffeine and still they contain this substance. In the ease
of Theobroma Cacao the flower branches (and sometimes the young
shoots) always spring from old branches utterly devoid of theobro-
mine and with Kola acuminata this is still more pronounced ; the
flowers and young shoots always result from branches in which no
theobromine or caffeme can be detected either before or after the.
budding.

From this it is evident that during the period of development and
growth of the young parts of the said plants, caffeine or theobromine
is always formed and remains localized in those parts for a longer or
shorter period. This fact may be very well reconciled with the theory
that these substances may be decomposition products of albumenoids *)
although, perhaps another explanation may be possible.

At the same time, however, it appears from the above that these
xanthine derivatives very often diminish in quantity during the growth
of the young parts and that they disappear from the full grown ones.

They are found to disappear from the leaves of Coffea stenophylLla,
Theobroma Cacao and Kola acuminata, from the branches of these
species and from those of Thea sinensis, Coffea liberica and C. ara-

') Flowers of 'T. sinensis and Coffea arabica were not at our disposal.
*) How the facts observed with roots may be reconciled with this theory
remains as yet unexplained,

= :
' 3
i.

le
*

( 207 )

bica; one would, therefore, be inclined to think that caffeine and
theobromine may again take part in the internal mutation.

Let us, therefore, take the case of a fairly young non-blossoming
specimen of Kola acuminata. .

During the unfolding of the young buds the plant is very rich in
caffeine and theobromine; the young leaves and branches, however,
retain these substances for a short time only, so that after two months
they have completely disappeared. There is then not a single part,
young or old which contains any caffeine or theobromine and as no
parts have become detached, this fact can only be explained by
assuming that these xanthine derivatives have again entered into the
internal mutation.

With the Thea species the matter appears quite different; the
young leaves and also the full grown ones are rich in caffeine and
the quantity found in the bark is a mere nothing as compared with
that contained in the leaves. Here it would appear as if, with the
falling of the leaves, the caffeine as such would be lost; this view,
however, is not correct.

On testing tea leaves which had turned yellow and would fall
at the merest touch, it appeared that they were quite cajeine-free
both in the case of Thea assamica and T. sinensis. The same was
noticed with Coffea liberica and Theobroma Cacao (also in regard
to theobromine) that is to say in the case of all species whose full
grown leaves still contained xanthine derivatives, with the exception
of Coffea arabica. During our stay at Buitenzorg it was, however,
not possible to obtain leaves which had fallen after having turned
yellow in the normal manner. All the leaves had been attacked by
Hemileia vastatrix which causes a premature turning yellow and
falling. It is probably due to this fact that no caffeine-free yellow
leaves were met with.

We, therefore, see that these xanthine derivatives disappear from
the leaves shortly before they fall, whilst the bark of the older
branches bearing these leaves is either free from these substances
(and remains so as in the case of Theobroma Cacao and Coffea
liberica) or contains such a trifling quantity thereof that it is as
nothing compared with the quantity disappeared from the leaves, as
in the case of Thea sp.

If we now take into consideration that the leaves of the branches
which are quite devoid of young shoots or flowers also show the
same behaviour, we can state with certainty that the xanthine deri-

-vatives again enter into the internal mutation and are, therefore, at

least in this case, an intermediary and not a jinal product. This

( 208 )

conclusion may be supported by quantitative determinations, but these
are not necessary in order to prove its correctness.

The shrubs of Thea assamica of the Agricultural Garden at
Tjikeumeuh bear a number of variegated leaves often so discoloured
that one side of the midrib is yellow whilst the other side is green.

These two sections which are of course, equally old and exactly
similar and which differ only by the absence or presence of chorophyH,
were compared as to their amount of caffeine. The operation was
conducted in the manner previously described *) for catechol.

Of a small number of leaves a yellow and an equally large green
piece was taken, both were triturated separately with quick lime,
extracted with the same amount of alcohol and the deposits obtained
by sublimation were then compared.

Each time the sublimates obtained from the yellow part of the
leaves were found to be much denser; the part free from chlorophyll
consequently contains decidedly more caffeine than the one containsng
chlorophyll; a very significant fact which may enable us to get a
better insight into the chemical processes of this plant.

At the end of this preliminary communication we desire to thank
Prof. vax Romwpvuren acting director of the Botanical Gardens at
Buitenzorg, for his kind assistance.

Mathematics. — “Rectifying curves.’ By My. J. van pu Grimnp Jr.
communicated by Prof. J. CARDINAAL.

It is known that every motion of an invariable piane system can
be regarded as the rolling of a definite curve of the moving system
(the “movable polar curve’) over another definite curve of the
immovable plane (the “fixed polar curve’). In the following paper the
special case will be treated of this general motion, where the movable
polar curve is a right line and the motion therefore consists in the
rolling of one of the tangents of the fixed polar curve over that curve.

Here, however, the constant polar curve itself will not be given;
according to a stated law (see N°. 1) this will have to be deduced
from another curve given in the moving plane (its rectifying curve)
Which takes its place and determines it by means of the rectilinear
movable polar curve. The replacement of the fixed polar curve by its
rectifying curve will give rise to the advantage that in some cases
the rectifying curve will be a much simpler one than the rectified

1) Investigations of glucosides in connection with the internal mutation of plants,
September 1902,

( 209 )

polar curve itself, which will cause its properties to be easily studied
and caleulations of surface and leneth of are to be executed in an
easier way. And it will»be possible to trace in what way the consi-
dered fixed polar curve can be deseribed by other curves, the recti-
fying ones of which are likewise given (N°. 3,4). Moreover the
investigation of these rectifying curves in a certain case (N°. 42)
leads back to two kinds of spirals, found already by Puisrux in
consequence of their tautochronism for forces proportional to the
distance (Journal de Liouville, T. IX), but of which by this theory
more could be found about their geometrical properties.

Summing up in the following the chief points of my investigations
very concisely I intend, if possible, to revert to them more in detail.

§ 1. Notion of the rectifying curve; simplest case.

1. Given in a movable plane an invariable system () consisting
of a right line AB (the azs fig. 1a) and a curve (/’). The system
moves with the axis A as movable polar curve. Let point Q of
this axis be the momentary pole, Q’ the following, QP and Q’P’
1 As. Let the elementary rotation de round Q’ be taken of such
a dimension that the right line Q’P’ coincides after the rotation
with Q’P regarded as a right line of the immovable plane; let then
the rotation around Q’’ be taken in sucha way that Q’’P’’ coineides
with Q’’1” ete. Then point Q describes a curve (/)(fig. 1) the locus
of the poles in the immovable plane, so the fixed polar curve
or the envelope of the axis AZ in the immovable plane.

We call (/) the rectifying curve of (7); then (/) itself is the
rectified curve with respect to (fF),

The lines QP and Q’P’ being two successive normals of the
curve (/) cutting each other in P, the point P is the centre of
curvature of (/).

If we assume in the system (+) the axis ABas v-axis anda right
line OY perpendicular to it as y-axis, we then immediately see on
account of the nature of the generation of the curve:

a. that the abscissae « of (/’) are the lengths of are and the
ordinates y are the radii of curvature of (/), so that the reetifying
curve is at the same time the curve representing the radius of
curvature 9g as a function of the are s;

6. that the elementary rotation of the system (&) or the angle
di
y?

c. that the trajectory of point P moving along (/’) in the immo-

of contingency of (f/f) is de =

( 210 )
vable plane is the evolute of (f) of which the length of are is
found on the ordinate of (F);

d. that the trajectory of an arbitrary fixed point C of AB
is one of the evolvents of (7) starting from that point of (/),
which becomes the pole in the immovable plane when Q is in C;

e. that the area of the figure, comprised between the rectified
curve (/), its evolute (7?) and two of its radii of curvature, is half
of the area of the figure between (/’), the axis AB and the corre-
sponding ordinates.

2. Light line as rectifying curve. Let the rectifying curve be the
right line AB (tig. 2) and let the motion have advanced as far as
the pole Q, centre of curvature of (7) P. The following motion is
an elementary rotation de= / P°QO'P or 7 QPQ’ round Q’. If
we let fall out of Q and Q’ perpendiculars QV and Q’V’ on AB,
then at the limit the points V’ and Q’ lie on the circle, described
on PQ as a diameter. So / QVQY’ = / QPQ, consequently also
LV V'=7 POP’, the elementary rotation. Farthermore / Q’ V’A
being a right angle the system rotation round Q’ causes point V’’ to
arrive in JV represented as a point of the immovable plane. The
same holds good for the following rotations. So the (variable) pro-
jection V of Q on AB in the immovable plane is a fixed point.
As moreover the angle |’QA (angle of the tangent of the rectified
curve with the radius vector out of J”) remains constant, the
rectified curve is a logarithmic spiral with V for pole.

The trajectory of the pole of the logarithmic spiral in the movable
system is the right line A. So when a logarithmic spiral rolls over
one of its tangents, its pole describes a right line.

The place of the pole in the movable system is found for every
moment by projecting the corresponding momentary centre Q of
the motion on the right line (#’). The part QA of the z-axis
corresponds to the are of the logarithmic spiral, which approaching
the pole, winds round it in an infinite number of revolutions; the point
A of the w-axis is unattainable by this are; QA is the limit of the
length of are of @ measured towards the pole. The shape of the
logarithmic spiral depends exclusively upon one datum: the angle
of the right line (/*) with the 2-axis.

As a special case there is the right line parallel to the «z-axis as
rectifying curve: the rectified one becomes a circle (logarithmic
spiral where the angle between radius vector and tangent is aright
one; the pole of the spiral becomes the centre of the circle.)

ee ee ee ee ea ae ee ee

( 241 )
§ 2. Movable and variable rectifying curves.

3. If two curves (7) and (/") osculate each other ina point Q and
if the evolute (p') of the latter is allowed to roll over the evolute
(p) of the former, the curve (f) which does not move, will be the
envelope of the moving curve (/') described osculatingly by it in
all points ; the point of contact Q displacing itself along the moving
curve (/’) describes the fixed curve (/).

Let us take of (f) and (7’) the rectifying curves (/’) and (F’)
(Fig. 3), then for the first condition (osculating each other in Q) the
x-axes Of these rectifying curves must coincide and the two rectifying
curves must intersect each other in P perpendicularly over Q. The
following ordinate (radius of curvature of (7”)) P’,Q’, of (F”) is
equal to the ordinate (radius of curvature of (7)) P,Q, of (F). To
make these rays of curvature coincide a displacement of the system
of the rectifying curves (/”) is necessary over a distance Q’,Q,

So the above-mentioned osculating description of a curve (f) by
another curve (/’) corresponds te the description of its rectifying
curve (/’) by the rectifying curve (/”) by means ofa parallel displa-
cement of (/”) parallel to the z-axis; the variable point of intersection
P on (£”) describes the curve (/). The amount of the elementary
displacement Q’,Q,—=dx— dz’ is determined by the difference of
the abscis-elements dv and dz’ which correspond in both curves to

‘the increase of the coinciding ordinate y to the following ordinate

y + dy.

4. When the rectifying curve (/”) does not intersect the rectifying
curve (/°) but touches it, the rectified curve (/’) has the following

radius of curvature in common with (7) which it touches by a

contact of the third order (four consecutive points in common). If
we allow (/) to be described envelopingly by the rectifying curve
(/”) which then not only changes its position but also its shape
according to a definite law, then this corresponds to the description
in fourpoint contact of the rectified curve (7) by the variable and
moving rectified curve (7’).

The evolute of (7) is described osculatingly by the variable and
moving evolute of (7”); the evolute of the evolute of (7) is enveloped
by that of (7’. in twopoint contact.

5. In particular an arbitrary rectifying curve can be described
intersectingly by a right line of constant direction or tangentially
by a right line of variable direction; this is (2) every curve in
threepoint contact by a constant logarithmic spiral or in fowrpoint contact

f AV? )

by a variable logarithmic spiral. If the right line of the constant
direction is parallel to the z-axis, then the osculating spiral becomes
circle of curvature (however not remaining of constant size during
the motion). So the osculating description of a curve (7) by a variable
circle of which the centre generates its evolute, becomes a special case
of the osculating description by a constant logarithmic spiral, of
which the pole JW (determined according to 2) generates a definite
eurve to be ealled an obique evolute of (f) (because it is formed
by the intersection of the successive right lines forming with the
successive tangents of (7) a constant oblique angle). By changing the
oblique angle we obtain for one and the same curve (/) an infinite
number of these oblique evolutes. In contrast to this there is only
one single trajectory of the pole of the variable logarithmie spiral in four-
point contact ; the pole V of this spiral is found in every position of
the system by projecting the deseribing point Qof(/) on the tangent
of the rectifying curve in P. We wish to determine the tangent and
the radius of curvature (7, 8) of the oblique evolutes or trajectories
of the poles of the logarithmic spirals in threepoint contact and of
that of the spiral in fourpoint contact. Some investigations must
however precede concerning the motion of the line connecting Q
and V (6).

6. To determine the point of contact ') of the right line Q V
(fig. 4) we notice that the motion of this right line as invariable
system is determined by the motion of the point Q following the
describing point of (/) and having thus a displacement equal to de
along SQ, and the condition QV 4 SP, must remain tangent to (7).
For the latter it is necessary that the rotation of QV is equal to
that of SP: so we have first to determine the motion of SP (inva-
riable system determined by the motion of P as the describing point
of the evolute of (7) do) and the contact of (/’)). The motion of
SP results from two rotations: the system rotation de aut round

y
Q and the rotation de of the radius of curvature J/P round the
eentre of curvature J/ of the rectifying curve (/’), which gives the
tangent SP its following position. So the momentary centre oi the
resulting motion of SP lies on J/Q; moreover P having in conse-
quence of this resulting motion to cover the element of are of the
evolute of (/), that is having to undergo a displacement dy L AQ,
the momentary centre must also lie on P/ 1 PQ and is thus the

1) Point of intersection of the right line QV with its following position.

—-S ee ee

( 2433)
point of intersection U of MQ with P/. The rotation of SP round

saa if de.

[

This same rotation must be performed by the invariable system
QV round its unknown momentary centre XY, whilst (@ is displaced
along AQ covering a distance = dx =y de. From the latter ensues
that the unknown momentary centre AX must lie on QP, where

bi OM
ne XX

oS : 2 ;
this pomt is 8 times the rotation round Q, that is

< de = y de. From this we find

XQ UM PM
y QM. DM”
Therefore the point of contact 2 of QV is found by drawing YR yQ
and as also PV L QV, the above mentioned equation becomes
KO -- PM
VQ DM’
So this is the equation which determines the position of the point
of contact R on QV.

7. Trajectory (V) of the pole of the logarithmic spiral in four-
powt contact.

a). Tangent. Let us describe a circle (.V) through P, V and Q
(fig. 4), we can then regard this circle as a similar varying system
of which point P has a motion dy 1 SQ and point Q a motion dr
along SQ. The centre of the velocities of this motion is J’, because
Z. VPP = 7 VQQ and VP: VQ=dy: dz. This centre of the velo-
cities being situated on circle (.V) itself, it is at the same time one
of the points of contact of circle (VY). Pomt V has in general dis-
placed itself along the circle in its second position; the tangents of
the two positions in JV differ infinitesimally, so the tangent to the
trajectory (V) is the tangent VV’ to the circle (V} in V.

b). Radius of curvature. To find the centre of curvature of
the trajectory (J) let us search for the point of intersection of
two consecutive normals NV of this trajectory. For that purpose
we shall consider A VNQ. The vertex Q@ is displaced in the
direction QQ’, the vertex V according to the tangent J’ J’’, the vertex
NV, as a point of the similar system CV), in the direction NN’, if
ZVNN'=7VQQ’. We ean easily convince ourselves that these
three directions concur in ove point. So the triangle moves perspec-
tively; so the points of contact of the sides lie in one right line.
The point of contact of NQ (normal of the curve (7)) is P (centre
of curvature of (/)); the point of contact of QV is & (6). We then

( 244 )

find the point of VN, in other words the required centre of curva-
ture MM, of (V) as the point of intersection of NV with PR.

8. Trajectory (W) of the pole of the constant logarithmic spiral
in threepomnt contact.

a). Tangent. Let the rectifying curve of the logarithmic spiral be
Sw P (fig. 5), pole W.

Angle PS, Q remaining constant the triangle PIWQ forms during
the whole motion a similar varying system. Of this system V, the
pole of the spiral in fourpoint contact (7), is the centre of the velocities,
because “VPP’ = 4 VQQ' and VP: VQ= dy: dz. So the vertex
W of A PWQ moves in such a way that ~VWW' = / VPP.
As P, W, V, Q are concyclic it is easy to see that WIV’ lies in the
production of QI. So QI is the tangent to the trajectory (JV).

b). Radius of curvature. To find the centre of curvature of the
trajectory (JV) we must find the point of contact of the normal
PW of this trajectory, that is that point of PW of which the
motion is directed according to PIV itself, if we regard this right
line again as a right line of the similar varying system QW P.
This point is found by letting down VJ/, out of the centre of velo-
cities V in such a way that ~ VM,S,= ~VPP’, oc 7 VM ye =
supplement of ~VPP’ = / VIP. So I, My, V, P lie on a circle
and “/VP being a right angle “/Mw/P is a right one too. So the
desired centre of curvature J/, is found by producing QV L S,P
till it intersects P/ in / and by letting down a perpendicular JM,
Guta 1 On: 102 Se

§ 3. Contes on thew axes as rectifying curves.

9. As a means for the treatment of the conics as rectifying curves
let us first regard the right line PW (fig. 6), where P in the system
motion of (X) deseribes the evolute of (7) whilst WV is a fixed point
of the «z-axis and let us then determine its point of contact. The
right line PN of which the motion is determined by the motion
of P and NV (P describes the evolute, NV one of the evolvents of (/) (4),
can be regarded as a similar system; point P has a motion = dy 4 AN;

point iV, as a consequence of the system rotation = ds about Q, a
motion = QN de likewise y AN. So the point of contact 7’ in
question lies on /°N in such a way that

d MRS ie dy

sr" we. = Co

( 215.)

; dt LP y dy dy rs
Now dé is equal to iF (1), so TN ON aa! Time if we produce
QV. tangent SP as far as the intersection J with PJ // x-axis. So
YL) ey mal
TN QN

That is: the point of contact 7 in question is the point where
?N is intersected by QV.

10. Ellipse on one of ius axes as rectifying curve. If we take

‘for the constant point N of the a-axis (9) the centre O of

the ellipse (fig. 7), then the displacements of ( and Pare respectively
Sh dx ‘

and dy; the quotient ——— is according to
y dy

Q 0). Qe ds — 7 mts o

ry 2

pees
the central equation of the ellipse constant = —. So the point of

contact of the right line OP remains during the whole mot’oa a
fixed point; this point of contact is the point & where OP is inter-
sected by QV (9); so this point of intersection remains a fixed point
during the whole of the motion. The quotient of the displacements
meee and 1s 20> RP. so Ox BP —a’ : b?.

In order to find the nature of the rectified curve, making use of
this fixed point A, we determine‘) of ?Q, considered as similar
system, the points moving perpendicularly on their radius vector
out of ; these points 7 prove to be real for the ellipse and lie in

b ;
such a way that r TQ” + —; their distance to R remains constant
a

during the whole of the motion; they describe a circle with centre 2.
If we produce 7’ till it intersects the z-axis in U and the y-axis in Y,
then ZU and UY also remain constant during the entire motion.
From all this ensues that the rectified curve is an epi- or hypocycloid
with R as centre; 7’ describes the circle of the basis.

11. To find the length of the radii RZ and 4 TU (fig. 7) expressed
in the half axes a and ¢/ of the ellipse, we presuppose the figure in
such a position where # has arrived in the production of the small axis ;

tens Riera RES BR APT yb
we make use here of the above given relations => = a lrg = i
Without any difficulty we find for the radius of the rolling circle
ab
ri ToC =—@—,
- 2(a + b)

1) We give here for shortness’sake the results only.

and for the radius of the tixed one

ab? ab?

Moreover
R b R b

= = en ——

27 a R + 2r a

For a= (circle) # becomes equal too, the rectified curve
equal to a cycloid.

12. Hyperbola on one of its axes as rectifying curve. Let us
first take the real axis as the axis of the ares (fig. 8). As in 10 it
is evident, that the point of intersection R of OP and QV is a

" : : : RO we

fixed point during the whole of the motion, where — >= W— —

Diy b?

(2a and 20 real and imaginary axis of the hyperbola). The point 7 (10)

is imaginary here; instead of this we consider the constant three-

point logarithmic spiral whose rectifying curve WP is parallel to
one of the asymptotes of the hyperbola.

Let us project both FR and JW (pole of the logarithmic spiral)
on PQ, it then follows from the equation PR: RO= 0? : a’, that

the quotient of the projections of PR and RO is equal to —, and
a

from the rectangular triangle PQ, where PW: WQ=6b:a, that

the quotient of the projections of PW and JIWQ is likewise equal
io 4? : a7. So the projections of FR and J coincide in L. So the
tangent JQ of the trajectory (JV) (8) forms a constant angle
W’WR= 7 WQO with the radius vector RI; so the trajectory
(W) is a logarithmic spiral of the same shape as the constant
describing logarithmic spiral (IVP), that is the curve (/) is described
by a constant logarithmic spiral which moves in threepoint contact
with itself in such a way that its pole describes the same logarithmic
spiral with opposite curvature.

Allowing for the modification of the figure we find that these
considerations are literally the same for the hyperbola on the
imaginary axis as the axis of the ares. Of the additional geometric
considerations to which the two kinds of spirals whose rectifying
curves are hyperbolae give rise, we shall mention only that the
two kinds of spirals are each other’s evolutes and that both of them
approach asymptotically logarithmic spirals of a definite position,
with which they have a fourfold contact at infinity (the rectifying
curves being the asymptotes of the hyperbola).

13. Parabola on the axis as rectifying curve. For the parabola

(fig. 9) the centre O is at infinity; the considerations about the point

R based on this centre do not hold good here. If we determine the
radius of curvature of the evolute as a special case of a polar trajectory
of a threepoint logarithmic spiral (8) by drawing QV L tangent PV,
it is evident according to the properties of the parabola that this
radius of curvature remains constant, equal to p, parameter of the
parabola, because PJ represents the length of the subnormal. So the
evolute is a circle and the rectified curve (7) an evolvent of the
circle. Point R (point of contact of QV) coincides here with /, because
T is a fixed point of V. So it is situated here too on the right line
(PJ) connecting 7 with the centre of the parabola. |

14. Yautochronism. The condition that a motion along a given
curve be tautochronous is: the tangential component of the force must
be proportional to the length of the are between the moving point
to a point of the curve; in that case the motion takes place as a
single oscillatory motion. For the curves whose rectifying curves are
central conics (10, 12) where the force is supposed to act from the
fixed point Rk, RL (fig. 7, 8) is proportional to QO as b° to c (10).
In order that the motion along those curves be tautochronous with O as
centre, the tangential component of the force must be proportional
to RL, so the force itself (directed along RQ) proportional to RQ, that
is to the distance. So for a force acting from the centre 2 in pro-
portion to the distance both curves are tautochronous. But the centre
of tautochronism © is to be reached along the curve only in the
eases of circle, ellipse or hyperbola (z-axis imaginary) as rectifying
curves, so only cycloid, epi- and hypocycloid and the spiral of the
second kind (rectifying curve a hyperbola on the imaginary axis)
are in reality tautochrone; for the spiral of the first kind the centre
of tautochronism does not lie on the curve, for the evolvent of the
circle it lies at infinite distance. For the epicycloid the force must
repel; for the hypocycloid and the spiral of the second kind it must
attract.

For the cycloid point # lies at infinite distance ; the foree becomes
constant and is directed according to the tangent in a cusp,

( 218 )

Physiology. — “On the development of the myocard in Teleosts.”
By Dr. J. Borxe. (Communicated by Prof. T. Pracn.)

During the last few years much attention has been given to the
structure of the heart muscle, and several investigators have stated
the opinion, that the heart muscle of the vertebrate heart is not
composed of definite cells, separated by clearly defined limits, but
that the heart muscle forms a syneytium, in which no cell bound-
aries can be recognised. For the embryonic heart this is shown
most completely by Gopiuwski, independently from Goprewsk1, but
less fully by Hoyrr and Hemenway, confirmed and worked out
by Marcerav.

For the adult heart (homo, mammalia) it has been M. Hrmennain’),
who has done most in this direction, and who has most strongly
urged the conception of the heart muscle as asyneytium. According
to him the septa, the “Treppen’’, the delicate lines standing at right
angles to the course of the myofibrillae, which are regarded by other
investigators as cell-limits, have nothing to do with real intercellular
structures (except perhaps from a phylogenetic point of view); they
are “Schaltstiicke”’, portions of the musclefibre which remained as it
were in an indifferent state, and play a part in the process of longi-
tudinal growth of the fibres. For the still growing heart HEmENHAIN
draws the following conclusion: ‘dass die Schaltstiicke ihrem urspriing-
lichen Verhalten nach wachsende Teile sind, Teile, welche das
Langenwachstum besorgen und nach beiden Segmentenden hin das
Material fiir die Angliederung neuer Muskelfacher liefern” (I. ¢.
1901 Pag. 69).

Hocun?) on the other hand takes these ‘“Schaltstiicke’, for real
cellular limits, though incomplete. He maintains that the Schaltstiicke,
the cement substance between the cells of the heart muscle, which
according to Epurti*) are homogeneous and after Browicz*) are in
some cases homogeneous, in other cases composed of small rods
arranged parallel to each other, separate the cells of the myocard,
but only in the course of the myofibrillae. Between these ‘“batonnets”
“le sarcoplasme qui remplit les interstices des fibrilles se continue
sans interruption apparente dune cellule dans Vantre.’ The small
rods are lying just between the ends of the myofibrillae of the

1) Anat. Anzeiger Bd. XVI 1899. Anat. Anzeiger Bd. XX 1901.
2) Bibliogr. Anatomique 1897.

3) Arch. fiir path. Anat. und Physiologie, Bd. 37,

4) Virchow’s Archiy. Bd. 139,

fy,

adjoining cells, which they bring in connection with each other.
“Cette zone des batonnets constituerait done....une réelle limite
intercellulaire, mais une limite incomplete.”

Von Epner’) regards the cementlines, the “Schaltstiicke’”’, as broken-
off perimysiummembranes, ‘‘abgerissene Perimysiumhéutchen”.

SzymMonowicz reproduces in his textbook of histology, which appeared
two years ago, a drawing of a section through the heart muscle of
a hydropie cor, in which the myofibrillae of one cell are seen clearly
to be in connection each with a fibrilla of the adjoining cell.

For the embryonic heart the disappearance of the cell boundaries
has been described by several authors in different animals.

H#IDENHAIN *?) reproduces a section through the heart of a duck
embryo three days old, in which no traces of cellular limits are to
be seen and the myofibrillae may be followed with great distinctness
without interruption over a great area and the same fibrilla passing
different nuclei.

According to Hoyer *) in the cells of Purkinje the fibrillae (found
only im the peripheral region of the cell body) may be followed
without break through many cells. In young larvae of Triton Hoyrr
found a complete absence of cell boundaries. According to this
author the heart muscle is originally composed of isolated cells,
but these cells fuse during the later stages of development, and the
result is a syncytium.

That this is really the case is shown by GopLEwski. A preliminary
communication ‘) appeared simultaneously with the paper by Hoyrr.
In the elaborate study *) which appeared somewhat later, this process
of fusion of the cells of the heart muscle in young rabbit and cavia
embryos is described very fully. Here the cells of the myocard
form at first a network composed of loosely arranged cells. By
division and growth these cells get nearer to each other, and the
intercellular protoplasmic bridges thicken, the intercellular spaces
narrow; ‘“dadurech verschmelzen die Zellen allmahlig in eine einheit-
liche Masse, in welcher die Kerne zerstreut gelegen sind... Schiliess-
lich stellt die Anlage des Herzmuskels eine vol/Aommen einheitliche
Protoplasmamasse dar.’ In the protoplasm of this syncytium there
appear small granules, staining deeply with iron-haematoxylin ; during
the next stages of development these granules arrange tiiemselves in

1) Sitzungsber. Wiener Akademie. Math. naturw. Classe. Bd. 109 1900. Abth. Ii.

elec. 1899 en 1901.

5) Bull. internat. de l’Acad. des Sciences de Cracovie 1899 Noy., 1901 Mars.

4) Bull. internat. de l’Ac. des Se. de Cracovie Mars 1901.

®) Arch. f. mikrosk. Anat. Bd. 60, 1902.

Proceedings Royal Acad. Amsterdam. Vol. VI.

( 220 )

rows (the same process was described by GopLewskr for the striped
muscle fibres of the body muscles) and in this manner the delicate
primitive histological myofibrillae are formed. In these originally
homogeneous fibrillae during the course of development two elements
appear, Staining differently with iron-haematoxylin and eosin, the
first sien of cross-striation, of the anisotropous and isotropous dises.
The later stages of development and the appearance of the “Schalt-
stiicke’ were not studied by GopDLEWskI,

An essentially similar view has since been advocated by Marcrat *)
1902). In a series of brief papers this author described the continuity
of the heart muscle fibres in mammals, birds and lower vertebrates,
and accepted in the main HetpENnnain’s suggestion of the function of
the “Schaltstiiecke” in the adult and the still growing heart.

In teleosts — I refer especially to the eggs of the Muraenoidae,
which provided me chiefly with the materials for the study of the
processes 1 am about to describe here — the heart muscle cells
are derived from the cells of the median portion of the walls of
the pericardial cavity, which, as is the case in all anamnia, grow
from either side underneath the entodermal tube and fuse with each
other in the median line, so that a tube is formed between them,
which opens at one end into the yolk-sac, at the other end into the
arterial vessels, formed at the same time (ostium venosum and ostium
arteriosum). Inside of this tube the endothelium of the heart is formed
out of cells of the ‘masses intermediaires” of the mesoderm of the
head and partly out of cells which migrate from the region of the
tail-knob towards the heart, and lay themselves against the myocard
there where the heart tube opens into the yolk-sae.

In fig. 1 is reproduced a longitudinal section through the region
of the heart of an embryo of Muraena N°. 1 with 38 pairs of
muscle segments, which illustrates these features clearly. On the left
side of the drawine the vostral end of the chorda is seen, and
beneath the chorda the entoderm, which shows the widening of
the oesophagus corresponding with the preopercular apertures, the
primary gill-clefts. Between the entoderm and the periblast the
heart is seen, and at the venous end of the heart tabe lies a
cluster of loose separate cells, which by their peculiar form and
by the protoplasmic processes with which they (the @reater part in
the following sections), unite with the endothelium of the heart, appear
as cells which aid to build up the endocard. The history of the genesis
of the endocard however we will drop for the present, the repro-

1) CG. R. de la Soc. de Biologie, T. 54, pag. 714—716, 981—984, 1485—1487; 1902.

oat)

duced drawing serving only to show the topographic relations. It is
only the myocard that interests us here. The cells of those parts of
the walls of the pericardial cavity that form the myocard, are di-
stinctly separated at this stage of development, are of a cubical or
cylindrical shape and very regular, as is shown in the figure. They
possess a rather large round nucleus and have a granular looking
protoplasm which shows no definite structure organisation. At both
ends of the heart tube they gradually diminish in height until the
flat shape of the cells of the other parts of the pericardial plates
is reached.

The cell boundaries between the heart muscle cells are every where
sharply defined; in preparations stained with iron-haematoxylin, at
both sides of the heart tube (that turned towards the endocard and
that turned towards the pericardial cavity) a delicate black line,
following the cellular limits, is to be seen — the “Schlussleiste’’.

The first signs of differentiation, which showed themselves in the
heart muscle cells, tend already to give rise to a fibrillar structure.
A granular stage, as described by GopLEwsk1, during which the proto-
plasm of the cells is full of deeply staining granules, which arrange
themselves in rows and fuse to give rise to the myofibrillae, I have
not been able to find. On the stage of the granular looking mesh-
work with small meshes, the usual appearance of protoplasm, there
followed in my preparations immediately a stage, in which at the
basal end of the cell (viz. that turned towards the endocard), extremely
delicate fibrillae are to be made out, which in most cases run at
right angles to the longitudinal axis of the heart tube.

These fibrillae, as far as could be made out, are homogeneous
from the beginning, and do not give the impression of being composed
of or derived from granules arranged in rows. However, this need
not lead us to doubt the formation of the fibrillae in this way
even here; the beautiful figures and clear descriptions of GoDLEWsKi
are too convincing on this point. Perhaps this stage lasts only a short
time and is not represented in my preparations which are stained
with iron-haematoxylin. Be this as it may, we only find the extre-
mely delicate fibrillae*), which thicken and become more distinct during
the following stage. To this stage belong the sections drawn in fig.
2 and fig. 3 (longitudinal sections) and fig. 4 (cross section through
the heart tube).

In order to understand these drawings rightly, the following may
be of use. The heart is during this stage still lying as a straight

1) A regular network consisting of large protoplasmic discs as described by Mc
Cattum, I have never been able to find.

15%

( 222 )

cylindrical tube in the direction of the embryonic axis, but always
the heart tube deviates in its course somewhat to the right (or to the
left). In longitudinal sections through the embryo the heart therefore
is cut obliquely, and in the same section of 4 or 5 mw we are able
io study the external half of the heart muscle cells (thatis to say the
side of the cells turned towards the pericardial cavity) at the venous
end of the tube, the basal half of the adjoining cells, and then the
endocardium and the median cross section of the heart muscle cells
at both sides of the heart.

In fig. 3 are shown the two parts of the heart muscle cells as
seen in one and the same section. The two parts of the figure are
in the section continuous, but are lying in different optical planes.
It was not possible however to reproduce the two parts in the same
drawing, because in the section (thickness 4 ) different optical planes
presented a different aspect of the same point. So I separated the
two halves by a line, to indicate the point, where the drawing is
made after a different optical section.

On the right side the cells of the myocard are seen from the side
turned towards the pericardial cavity. They appear to be separated
by distinct boundaries, are very regular, and show between the cells
the black lines and meshes of the “Schlussleiste’. Ou the left side
of the figure the basal side of the heart muscle cells is to be seen.
Because of the curved surface of the heart tube, at both sides the
cells are seen in cross section, in the median part of the figure the
basal part of the cells comes into view. In this part of the heart
muscle cells the cell membranes have completely disappeared. There
is only a mass of protoplasm to be seen, which has taken a faint
stain with eosin; imbedded in it lie thin fibrillae stained black with
iron-haematoxylin; these fibrillae run for the greater part at right
angles to the heart axis round the heart-tube; some of them run
more or less obliquely (fig. 3). The same fibrilla may be followed
through more than one cell. At both sides the fibrillae curve round
and run at right angles to the surface of the section. They present
there a small point of a darker colour. The fibrillae are entirely
homogeneous.

That these fibrillae are lying in reality only at the basal end of
the cell is shown in fig. 2, in which a part of the myocardium is
drawn as it appears in a median longitudinal section through the
heart tube; as the fibrillae are running here at right angles to the
optical plane, they appear as dots and where their course is more or
less oblique, as short lines. In the corners of the cells we see (at
the side of the cells turned towards the pericardial cavity) the black

a | a ee

_a. To. -

a—owe,

ale Pil ae en

Pe ee Tee ee eee

( 223 )

_ dots of the “Schlussleisten”. The cell boundaries cannot be followed

now from one side of the wall to the other; at the basal side of the
cells, there where the fibrillae are formed, the cell membranes have
disappeared and the protoplasm of the cells is continuous. It seemed
to me that the disappearance of the cell limits preceded the ditferen-
tiation of the myofibrillae, on the other hand the question arises,
whether the differentiation of the fibrillae does not give the impulse
for the disappearance of the cell membranes. For in studying these
cells closer, we sometimes find in cells, where only at the basal side
of the cell the cellular membranes have disappeared, fibrillae lying
there where the cells are still distinctly separated. These fibrillae do
not pass from one cell to another, but end close to the cell-membrane
with a small thickened point (fig. 3), and sometimes in two adjoining
cells a pair of such fibrillae are seen just opposite to each other.
In following stages of development in this part of the cells a greater
number of fibrillae is to be found; these fibrillae then are seen to
pass through different cells and the membranes of the cells have
disappeared here too. These facts remind us of the appearance of the
fibrillae on the boundaries of the myotomes (in longitudinal sections),
and this being the beginning of the fusion of the fibrillae of the
adjoining myotomes, the question arises, whether a similar process
is going on in the heart muscle cells. Be this as it may, the fact
remains, that only at that side of the cell in which the myofibrillae
are formed, the membranes disappear and the protoplasma fuses.

We may call attention here to the fact, that the black meshes and
lines of the “Schlussleiste” have disappeared at the basal side of the
cells, there where the cell limits ceased to exist; at the other side
of the cells, there where the cells are still sharply separated, they
remain as clear and distinct as before.

In fig. 4 one half of a cross section through the heart tube is
drawn, to demonstrate once more the course of the fibrillae and the
structure of the myocard cells.

In the figure we see the endocardium (end.) composed of flattened
cells, and around it the myocard'). The fibrillae are here cut length-
wise, and may be followed without break through different cells.
The cellular limits, seen in the outer half of the cell-body and absent
in the inner half, we need not deseribe at length any niore.

In preparations in which the centrosomes are stained in the other
embryonic cells, in some cells of the myocard too they were visible

1) A pericardial membrane as a covering of the myocard, as it shows itself in
salmons during the later stages of development, is not yet developed here. The
heart lies entirely free inside the pericardial cavity.

( 224 )

as minute black granules (diplosomes) in the centre of an ovalshaped
“heller Hof”.

They were lying on the side of the nucleus in a rather indifferent
position now on this side of the cell, than on that.

In the course of development the cells of the myocardium flatten
more and more. The cell membranes disappear from between the
cell bodies throughout the entire thickness of the myocard. In_ this
stage the fibrillae are not so exclusively confined to the basal side
of the cells, but are found more or less seattered throughout the
cells. The greater part of the fibrillae, however, 1s still visible in the
basal half of the heart muscle syneytium.

In fig. 5 a surface view (of the atrium) of such a myocard is
drawn. Beneath the fibrillae we see three nuclei, no trace whatever
of cell boundaries is visible. The course of the fibrillae is not so
regular as it was before. They seem to be running now in different
directions, although there is still one predominant course. This facet
is due to the rae of growth of the heart tube being not the same
in different directions. The heart has no more the shape of a simple
cylindrical tube, but is differentiated already in sinus venosus, atrium
and ventricle. With the growth of the different parts of the heart
tube the displacing of the bundles of fibrillae goes hand in hand.

As shown in the figure, the myofibrillae of the heart now present
a beautiful cross striation. But it must be noticed that the commen-
cement of the functions of the heart muscle, of rhythmical peristaltic
contractions coincides with the differentiation of the homogeneous
fibrillae mentioned above. The differentiation of the fibrillae in
isotropous and anisotropous dises takes place after the heart having
contracted quite regularly for a long time already, and has nothing
to do with the contractility of the fibrillae.

In this stage of development (the last stage which can be studied
here, the muraenoid larvae invariably dying after having reached
the critical period) the wall of the heart is still a simple membrane.
The bundles of muscle fibres so characteristic for the adult vertebrate
heart are not yet developed. For this reason I have reproduced in
fic, 6 a part of a longitudinal section of the myoeard of a larva
of Salmo fario of 22 m.M., where the sponge-like structure of the
myocard was established already. The myofibrillae, for the greater
part arranged in bundles, may be followed over a great area past
different nuclei of the myocard-syneytium. There is no trace of
cellular limits, nor of “Schaltstiicke” te be found.

So we must draw the conclusion, that in the case of teleosts too
the myocard forms a syneytium, as maintained by GobDLEWSKI,

—— a

Se ae | SN Pe Ue

VAAN

( 22a

Hemennais, Hover and Marcerav; that the myocard originally is formed
of distinct cells, but that during the differentiation of the my ofibrillae
the cell limits of the myocard cells get lost, the cell bodies fuse and
in this manner a syncytium is formed; that this disappearance of
the cell membranes can be stated at first only there where the
myofibrillae are formed, and that chronologically the formation of
the fibrillae and the disappearance of the membranes coincide.

Where now the formation of this syncytium by a fusion of
originally separated cells can be demonstrated in lower vertebrates
and in the higher vertebrates, and the continuity of the fibrillae over
a great area can be stated, there the hypothesis of Heipenuatn, that
in the adult mammalian heart the ‘Schaltstiicke’’ (cement lines) of
the myocard which are not to be found in lower vertebrates and
which appear in mammals in a relatively late stage of development,
have nothing to do with cell limits, seems to have some truth in
it. That this is’ of great importance for the physiology of the
heart muscle, for the problem of the conduction of the impulse
by the heart muscle fibres, I need only mention here.

As to the functions of the ‘Schaltstiicke” we are, I think, still
entirely in the dark, but for the hypothesis of Hrmernnary. This
must be tested by further study. The study of the later stages of
development of the mammalian heart with the use of the modern
histological methods will throw more light upon this, as was pointed
out already by Gopiewski. Perhaps the study of the structure of
the muscular bridges, connecting the different parts of the mammalian
myocard, too will throw some light upon this question.

DESCRIPTION OF THE FIGURES ON THE PLATE.

Fig. 1. Longitudinal section through the heart of an embryo of Mur. N°. 1
with 38 pairs of muscle segments. ph = pericardial cavity, m = myocard, e = endo-
card, per = periblast, ent = entoderm, ch = chorda, oes = oesophagus. Enl. = 240.

Fig. 2. Two cells of the myocard of an embryo of the same species of Mur.
N°. 1 with 44 muscle segments. Longitudinal section, sublim.-formol, iron-haema-
toxylin and eosin. Enlarg. = 800.

Fig. 3. The same, cut tangentially. Enlarg = 800.

Fig. 4. Cross section through the heart of a slightly older embryo.

Fig. 5. Surface section of the wall of the atrium of a larva of Mur. N° 1,
five days old.

Fig. 6. Section through the wall of the ventricle of a larva of salmo fario of
22 mM. Enlarge. = 800.

Mathematics. Extract of a letter of Mr. V. Witiiot, to the Academy.

In his splendid work entitled: “Théorie, propriétés, formules de
transformation et méthodes d’évaluation des integrales définies”
Mr. Brerens pr Haan takes as basis to determine the general formulae
(143, 144, 145, 146) of page 154 a definite discontinuous integral
the value of which has been established farther on in the work
(Partie III, Méthode 9, N°. 16) at page 333 as

IU 7
a forp >
= : du Tt.
sim ( pe) cos (gv) == re JOT QO ek ak oe phn oe (1)

v
0 0 forp<q
the value with respect to the discontinuity p= q being the mean

of the extreme values.
But he gives this result on page 135 in the form:

oye CF Fe ee)
sin rz cos ge — =— forg<_r
Lv 2 =
0 0 for ga

so that in the continuation of his deduction we find that the term
corresponding to g=7 amounts to double the value of the real
value and that the general formulae of page 154 are to be rectified
in this way as well as the applications.

Particularly on page 639 formula 1900 we find

io 2)

. SIN & COS At? jt om Ey 4 pe
et Gt es <
= di > pr — — ——_,,
. 9 t ?
J 1—2peosatp? « 2D a 2 l—p

whilst the exact value of this integral is

ei pel x lip
2 a pa-1 | pa? = — pri :
es + ptt poh + pt tee] Pe pe
And really writing after multiplication by p:
a psinea COS Ut x I1+p
| a eer ree ae
. —2pcosx-+p x =p

0
it is sufficient to develop the first factor of the function of which
the integral is to be found

psn a D ;
z je 3 = pk sin ka:

1—2 p cos w+ p* k=l
to refind by means of the integral (1) the development of the second

term of the equation:

¢225 3

vs pe ease al pot at pir? +... | ;
ee 2. ‘

It was in looking for a way to place in a form of a definite
integral the general term of the series of Lambert modified by
CLAUSEN :

lta? , a acos(n+1)a@ da

1—2w” cos a+-av*" a

1+ a ha d
0

that I found this error.

It is easily seen that the rectification has to be extended to the
whole N°. 12 of the method 41 of which the above mentioned
integral forms a part and to any other application of the general
formulae of page 134.

This paper was given to Dr. J.C. Kiuyver, who made the follow-
ing communication about it:

The remarks of Mr. Wittiort are on the whole correct. In the
of Brerens Dr Haan we really find on

“Exposé de la Théorie ete.’
page 639
ie 6)

SIM & COS Mit ; kj as aes
. Ch Sa
1—2p cos «+ p? i 2 I1|—p

and this is incorrect whether @ is an entire number or not.
Mr. WiLLIoT now gives as an answer

By 1+p

—s prt ed ee

and that will do for @ as an entire number.

Vea p

In the meanwhile he might have observed that this result neither
holds good for @ (not an entire number) and that we find for any
possible positive a:

g pla—e] + » [a+]
p<: * poten Wee.

1l—p
3 —[a—2] 1 »—(a+?]
pees ee cP
4 p (p—1)

(Here [a] means the greatest entire number smaller than @).

(October 27, 1903).

a) Bc Py

See ai heat 4

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING

of Saturday October 31, 1903.

DO Co_______——_

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 31 October 1903, Dl. XID).

GoW TaN TS

J. D. vAN DER Waars: “The equilibrium between a solid body and a fluid phase, especially
in the neighbourhood of the critical state”, p. 230.

J. J. van Laar: “The possible forms of the meltingpoint-curve for binary mixtures of isomorphous
substances.” (2nd Communication). (Communicated by Prof. H. W. Bakuuis Roozrnoom
p. 244. (With one plate). 4

H. W. Baxuvis Roozesoom: “The phenomena of solidification and transformation in the
systems NH,NO3, AgNO; and KNO;, AgNOs”, p. 259.

A. F. Horreman and J. Porrer van Loon: “The transformation of benzidine.” p. 262.

H. Raxen: “The transformation of diphenylnitrosamine into p-nitrosodiphenylamine and its
velocity.”” (Communicated by Prof. C. A. Losry Dr Bruyn), p. 267.

W. H. Junius: “The periodicity of solar phenemena and the corresponding periodicity in the
variations of meteorological and earthmagnetic elements, explained by the dispersion of light”, p. 270.

Hans Srranui: “The process of involution of the mucous membrane of the uterus of Tarsius
spectrum after parturition.” (Communicated by Prof. A. A. W. Husrecir), p, 302.

J. C. Kiruyver: “Series derived from the series a %, p. 305.

G. Griwxys: “The Ascusform of Aspergillus fumigatus Fresenius.” (Communicated by Prof.
hepAS Es ©. WiENT), p- 312.

W. van Bemne cen: “The daily field of magnetic disturbance.” (Communicated by Dr. J.P.
VAN DER SrToK), p. 313.

J. Il. Bonnema: “A piece of Lime-stone of the Ceratopyge-zone from the Dutch Diluvium.”
(Communicated by Prof. K. Marry), p. 319.

S. Hoocewrerrr and W. A. van Dore: “On the compounds of unsaturated ketones and
acids”, p. 325. :

Tu. H. Benrens: “The conduct of vegetal and animal fibers towards coal-tar-colours”, p. 325.

The following papers were read:

Proceedings Royal Acad. Amsterdam. Vol. VI.

( 230 )

Physics. — “The equilibrium between a solid body and a fluid
phase, especially in the neighbourhood of the critical state.”
By Prof. J. D. vAN DER Waats.

After the publication of the experiments of Dr. A. Sits in the
proceedings of the September meeting, communicated by Prof. Baknuts
Roozrsoom, I had a discussion with the latter chiefly on the question
if and in what way the liquid equilibriums and the gas equilibriums
which may exist by the side of a solid phase, must be thought to
be connected by a theoretic curve at given temperature, in conse-
quence of the continuity between liquid and gas. It is in agreement
with the wish of Prof. Baxuurs Roozrsoom, that I communicate the
following observations.

Let us imagine the y-surface of a binary mixture, anthraquinone
and ether, in which we will eall ether the second substance, at a
temperature slightly above 77 for ether. Then there is a lquid-
vapour plait, closed on the side for ether.

Let us add the y-curve or the w-surface for the solid state,
the y-curve when the solid state has an invariable concentration.
If only pure anthraquinone should be possible in the solid’ state,
this y-curve would lie in the surface for which =O. For the sake
of perspicuity we shall start from this hypothesis in our first deserip-
tion. Then we find the phases which coexist with the solid anthra-
quinone, by rolling a plane over the y-surface and the conjugate
y-curve.

On account of the slight compressibility of the solid body, we
ean describe a cone, unless the pressure be excessively high. This
surface enables us to find the coexisting phases; its vertex lies viz.
in the point r—0, v=v, and y:=y,, if v, represents the molecular
volume of the solid anthrayuinone and y, the value of the free
energy, both at the temperature considered. The curve of contact
of this cone and the y-surface represents then the coexisting phases.
For shortness’ sake we will use for it the name of contact-curve,
though it is properly speaking also a connodal curve on the y-surface
of the binary mixture having its second or conjugate branch on the
y-surface of the solid state.

Now we ean have three cases for the course of this contact-curve.
Ist. If may remain wholly outside the liquid-vapour-plait, and will
form then a perfectly continuous curve. 24. It may pass through
that plait, in which case one part of this curve will represent gas
phases and another liquid phases, which two parts will be connected
by a third part lying between the two branches of the connodal

( 234 )

curve and representing metastable and unstable phases. 3. It may
touch as intermediate case the connodal curve of the transverse plait
in a point which will be the plaitpoint, as will appear presently.

As to the course of the liquid part of the contact-curve we may
at once conclude, though this will be shown afterwards in a more
striking way, that two cases may occur. From the point on the
connodal curve where it enters the liquid part of the w-surface with
increasing pressure, the curve will namely move more and more
towards decreasing values of x, and finally terminate at «= 0
or it can move towards increasing values of wv.

If we trace the y-curve for «=O, and add a portion of the

fig. 1 (a)

y-curve for the solid body to the figure, then if this portion has
position (a), so if the volume of the solid body is smaller than
that of the liquid, only one bi-tangent can be drawn, and this
wil represent a coexisting gas phase. If on the other hand the
added portion of the w-curve for the solid phase has position (4),

(5)

fig. 1 (b)

so if the volume of the solid phase is larger than that of the liquid,
two hbi-tangents may be drawn. At low pressure, a coexisting gas
oO * | © rs)
phase will exist, and at high pressure a coexisting liquid. In the
latter case the liquid part of the contact-curve will move towards
points for which « decreases when the pressure increases.
$6*

( 232 )

For a contact-curve which passes through the plait of the y-sur-
face, the property holds of course good that the pressure is the
same for the two points, in which it meets the connodal curve of
the transverse plait. If namely a bi-tangent plane is made to roll
simultaneously over the y-curve (or the y-surface) of the solid
substance, and over the gas part of the y-surface of the binary
mixture, then if this tangent plane meets a point of the binodal curve
of the transverse plait, this tangent plane will also touch the w-surface
in a point of the other branch of the binodal curve, and this point
will represent a liquid phase. Three phases are then in equilibrium.
The pressure that then prevails, is therefore the three-phase-pressure
at given temperature. If the temperature should be such that the
contact-curve no longer passes through the plait, then no three-
phase pressure, exists any longer for that value of 7. For the
intermediate case the solid body is in equilibrium with two phases,
which have become equal and the two points of the connodal curve
which the contact-curve has in common with it, have coincided in
the plaitpoint.

Particulars as to the course of the contact curve are found from
the differential equation of p, when wv and 7’ varies. If we represent
the concentration and the molecular volume of the solid body by
xv, and v, and that of the coexisting phase, whether it be a gas phase
or a liquid phase, by wr and v,, this equation may be brought under
the following form, which is perfectly analogous to that which holds
for the coexisting phases of a binary mixture :

- BS Woe
Of dp = (ws—) de? a + as di
Le p

For the signification of ve and W,, I refer to Cont. I, p. 107 ete.
If 7 is kept constant, we have for the course of p the differential

equation :
dp aS
v sf 5 === (ws-—#/) 25
aie dif? /yT

As long as the contact-curve does not pass through the plait,
ae ne
—— is always positive.
Ge f is

If in the solid state only the pure first substance (in the case under
consideration anthraquinone) should occur, then «, = 0.

But the same differential equation holds also, if wz, should be
variable. For the case of anthraquinone and ether the value of «
in the gas phase is higher than that of the liquid phase for coexisting

liquid and gas phases, or w, >4,. It is therefore to be expected,

¢ 9335

that the value of x, in the solid state will a fortiori be smaller than
that of the phase coexisting with it, whether the latter is a gas or
a liquid phase. We do not wish to state positively that there are
no exceptions to this rule. But for the case ether and anthraquinone
we may safely assume that «,—.1, is negative.
Now it remains only to know the sign of 7.7, to be able to derive
the sign of LS
aX f
: F ; : dV +)
The expression vf stands in the place of (v,—vy)—(“,— vy) (ee)
ge A) hs

and represents the decrease of volume per molecular quantity when
an infinitely small quantity of the solid phase passes into the coexist-
ing phase at constant pressure and constant temperature. If this
coexisting phase should be a vapour phase, this decrease of volume
is undoubtedly negative. But this quantity may also be positive, and
if we make the series of pressures include all kinds of values, so
if we make the pressure ascend from very low values up to very
high ones, there is undoubtedly at least once reversal of sign,
and for the case that the contact-curve under high pressure moves
towards increasing values of « there is even twice reversal of sign.

To demonstrate this, we inquire first into the geometrical meaning
of ve. Let the point P be the representation of the solid phase,
with 7, and ws, as coordinates — and the point Q the representation
of the coexisting fluid phase with 7, and wy as coordinates. Let us
draw through @Q the isobar and let us determine the point 2”, in
which the tangent to this isobar of Q cuts the line which has
been drawn through P parallel to the volume-axis, then —vr~=P)”’.
If the point /” lies on the positive side of P, then v,¢ is negative.
For the special case that the tangent to the isobar of Q passes
through P, v= 0. In the same way v,¢ wouid be positive, if P’
should lie on the negative side of P.

In order to know the sign of 7,7, the course of the curves of
equal pressure must therefore be known. In my “Ternary systems”
I (These proceedings Febr. 22:4 1902, p. 455) I have represented
for the analogous case of a binary system, for which the second
component has the lowest 7), the course of the isobars by the line
BEDD'E’B’ in Fig. 2. 1 have added another isobar to the repro-
duction of this figure — and I have represented the solid phase
by the point P,. The added isobar passes through the plaitpoint.
This isobar has an inflection point somewhat to the right of the
plaitpoint. Each of these lines of equal pressure having an inflection
point, there is a locus for these points, which I have left out in the

figure. It extends all over the width of the figure. Always when 7’, lies
on the side of the small volumes of an isobar, two tangents may
be drawn to such a line from ?P,. These tangents touch the isobar
at points, lying on either side of the inflection point; and for these
points of contact ry = 0. Another isobar will furnish two other
points of contact, if we leave the point ?, unchanged. We have
therefore for every point P?, a locus, consisting of two branches,
for which r+. =O. If the point 2; lay at greater volume, i. e, on

the other side of the isobars, it would no longer be possible to draw
two tangents, and the locus for which, with regard to /,, the value
of ve is O, would have but one branch.

Now, however, the point P, is variable, first because the volume
of the solid body depends on the pressure, and secondly when the
concentration should change. This enhances of course the difficulty,
if we wished to determine this locus. But this will not detract from
the thesis that for the contact-curve, when it ascends from low
pressure to high pressure, twice 7.¢ is 0, when the solid body has
a smaller volume than it would have in fluid form at the same
temperature and under the same pressure — and that only once
vsy 1S O in the opposite case. When 7, is variable, the locus for
which vs¢ = 0, is construed by drawing from every special position
of Ps the tangents to the isobar of the pressure of Ps, and by joining
the points of contact obtained in this way.

If the contact-curve does not pass through the plait, the value of
Vg IS negative for the points outside the two branches of the locus
Vsf =O, and positive for the points inside.

If however the contact-curve passes through the plait, the value
of vy is more complicated. In the figure the two tangents have been
drawn io the isobar BE DD'L' hb’, P, being supposed to be in the
position that corresponds to the pressure of this line. In this case
too the value of vy is negative for the points lying outside the two
points of contact. For the points between the points of contact we
cannot assume vy to be positive, however. This holds only till
the points D and D’ are reached. Between D and D’, ry is again
negative, and the transition from positive to negative takes place
in the points D and /’ through infinitely great.

LS
dxf”

In the same way the value of ( ) is complicated for the
pr

points of a contact-curve, passing through the plait. I have stated this

already in ‘Ternary systems’ I, Proceedings February 22»¢ 1902

footnote p. 456. For the points between the connodal and the spinodal

curve this quantity is still positive; for the points between the
o?w

spmodal and the curve for which aT is O, it is negative ; whereas
v

for the points inside this last curve it is again positive. This last
transition from negative to positive takes place through infini-
tely great.

at f

Let us write the equation for the determination of in the fol-

lowing form:

O7us dp d?y 07
= 1 sf — (#5 el /) > 2 2
Ofer da; Ove? Ou?
or
op dp _, , (Op O*yp Aras
— ref = = (a,—29 \—, — —( —— ] |.
Ove? dnp | dx, ; Our? On Ov¢

In this way we simplify the discussion. The factor of 2,— vx, never
becomes infinitely great in this case. This factor is then positive
outside the spinodal curve and negative inside it. On the spinodal
curve itself it is zero. As «,—r, is always negative in the case of
anthraquinone and ether, the second member of the last equation is
negative outside the spinodal curve and positive inside it. From this
last equation follows: 1 that if we follow the contact-curve throughout
its course, there exists a maximum and a minimum value for the
pressure for the points lving inside the plait, that is when the spinodal

apo AES
curve is passed. 2°¢ that when v7, = 0, the value of — is either

av
: sae Ae i dw
twice or only once infinitely great. In the points where ;=9%;
avy
dp . (9P : =
—— has the value of |——], as follows from the equation given if
das Ons J -
d*y :
we put there aaa =(, but which also follows directly from :
os
Op Op
bp == ase —.dvy,
emery Aad: 3 eee
ap
putting ey
~ Ove

For contact-curves which pass through the plait not far from the
plaitpoint, it appears clearly from the figure, that the points for
dp d p

which —- is infinitely ereat, lie outside those for which
at ; av f

moth |B

That is to say, that the locus for which v7.7 = 0, lies outside the
spinodal curve. In the neighbourhood of the top of the plait they
lie even outside the connodal eurve. Also for the isobar bE DDL’ hb’
I have drawn them in the figure given in such a way that the
points of contact of tangents from P, lie outside the spinodal curve.
| have not yet been able to decide whether there are any exceptions.
In the following figure (3) I have represented the relation between
p and wy for a contact-curve, assuming that the points of contact
lie as I have drawn them in fig. 2, and as they are sure to lie,
when we are in the neighbourhood of the plaitpoint. The gas pliases
which are in equilibrium with the solid body lie below B.

fig. 3

The liquid equilibriums lie above C. The position of the line BC
indicates the three-phase-pressure. The curve HCPA denotes the
liquid-vapour equilibriums, of which the part lying below CA may
only be realized by retardation of the appearance of the solid state.

Let us now examine what happens at higher temperature as well
to the curve of the liquid-vapour equilibriums as to that of the
equilibriums between the solid state and the fluid state. From the
theory of the binary mixtures (Cont. II, p. 107 ete.) we know, that
the first mentioned curve LCPAE contracts and moves upwards. If
we assume d7’ to be infinitely small, all the points of this curve
will be subjected to an infinitely small displacement, with the exception
of one point, i.e. that for which JI’,,—= 0. This point can lie on
the right or on the left of the plaitpoint 7, according as the plait-
poit eurve descends or ascends. Also the curve of the solid and
fluid equilibriums is transformed and = displaced. The modification
Which this curve undergoes with increase of temperature has been
denoted by the dotted curve in fig. 4 and fig. 5. We shall presently
explain this further. Now two cases may take place, which both
occur for mixtures of anthraquinone and ether. Either the three-
phase-pressure rises with 7, or it fails. But in both cases such a
temperature may occur that the straight line, which joins the two
fluid phases coexisting with the solid body, has contracted to
a point.

To the former of these two cases applies fig. 4. In this case the
curve AB moves towards smaller values of « with increasing tem-
perature. Not indefinitely, however. Near the highest value of 7,

( 238 )

Fig. 4

the branches AA’ and BB’ have met, and so there is a minimum
value for the value of w4.

To the second case ayplies fig. 5. Then the curve AB will move
to the right with decreasing temperature. With decreasing value of

ryy - . .
7 the branches A’A and BBR’ will approach each other; and this

Pp T+oT:

'
‘
\
\
'
t
\

Fig. 5.

leads to the conclusion that there will be a maximum value ofp.
In fig. 6 the value of « for the two fluid phases of the thiree-phase-

Fig. 6.

pressure as function of 7’ is graphically represented. The highest
temperature (the triple point of anthraquinone) applies to. = 0. The
lowest point of the part of the «, 7’ figure lying on the left is one
plaitpoint and the highest point of the part of the ., 7’ figure lying
on the right is the second plaitpoint.

If we represented the relation between p and. for the fluid phases
of the three-phase-equilibrium, we should also get two separate parts.
It is easy to see that for smaller values of 1 an ascending closed
branch is obtained, not unlike the closed p,v curve for a binary
mixture at constant temperature — and that for higher values of”,
a similar but descending curve is found.

The p,7 projection for the three-pbase-pressure, so of the curve
according to which the two p,., 7’ surfaces intersect, consists of
two separate curves, that for the higher temperatures being a
descending curve, terminating in the p and 7’ of the triple point of
anthraquinone. The part for the lower temperatures is an ascending
curve, beginning in the triple point of ether, if namely, we assume

( 240 )

perfect mixture also for the solid state. The two p, 7 7 surfaces meant
in the preceding statement, are that for the coexistence of the two
fluid phases with each other and that for the solid state and the
fluid phases.

I shall proceed to give a few mathematical observations, which
may serve to gain a better understanding of the whole phenomenon,
and which are also required for the proof of some properties, which
have been given above.

First the assumed deformation in the shape of the p, x curve (solid
and fluid phase) for increase of temperature.

From the equation :

ae 0°S sf am
if ‘- dp = (7,— ys) a day +) dl
dxp? ) pT fi

follows that for constant a, the equation holds:

Op =
l Weave "2
T gu Re SR Vy
dT Be Vos iat v
= sf
Oe
Wy being negative, the numerator of this expression is negative
, “yw a reeeare. a :
outside the curve for which ee = 0, and positive inside this curve.
7

The numerator is the same quantity as has been discussed before
(p. 235). From this follows that for constant wy the curve p,7’ has
a tangent normal to the Z-axis in two points, and between them
two points, in which a maximum and a minimum value of p occurs
— just as was the case with the p,. curve at constant temperature.
One curve might be substituted for the other, but still, there is a
difference. The p,« curve has its maximum and minimum coinciding
in the plaitpoint. The p, 7’ curve has it, when it runs through the

she y af Tat ae ;
point for which ape has two coinciding values equal to zero; so in
Us

the point which would be the critical point, when the binary mixture
behaved as a simple substance.) The consequence of this is, that if
we trace the two p,7’ curves, (that for liquid and vapour and that
for solid and fluid), these two curves intersect in the plaitpoint for
the value of wv of a plaitpoint, and that they do not touch as is the
case with the p,v curves. Only for another value of.v (the maximum

1) It has appeared to me that the course of the p,7’ curve requires further
elucidation. | intend therefore to soon add some remarks on this subject to this
communication.

( 244 )

and minimum discussed above) the two p,7 curves touch. This point
of contact yields of course an element for the three-phase-pressure.

The differential equation for the section of the two p, 7’. surfaces,
is found from the two reiations which hold both at the same time -

0°% ee
Vox dp == (w,--@,) a du, + — dl
map

1
and
lp = ( 7 ae ee or
Vo ( i — Vo— U Ae ae AW = 5 c .
a eee) iiss Z
We find then:
ao) dT
at a
dp dz,” pT : 7
(ws—w,)w,,—(#,—2#,)ws, Vs, Wey V 91s, (ws—w,)e,,— (w,-—#, Us,

We shall shortly mention some obvious consequences. (1) If

07g
(5 =} =O, the p, « and the 7, 2 figure show a minimum or a
eS i

1 vp

maximum. So they exist for a plaitpoint. (2). For a maximum or

Wes Ws

. . . “S1
minimum of x, — must be —.
Vo1 Vai
Now :
; 0&,
Wo, = PVs, Ste é,—€, (w, 07 a
Ow, Jp
and :
dg,
Ws, = Pus, ot. &:—&, (5 —<0)) Sey
Ou,

v,—?, ( =) Us— 0, (5: ) v,—0;, Us—v,
L,—@, Ow, pT ls—v, 02, ) pT 2,—2, &—z,

dp, dps A pros : :
ar a) = (4) ae or in words, the direc-
: 4 c z ¢

tion of the (p,7), curve for liquid and vapour, and that of the
(p,l), curve for solid and fluid state are the same in the point of
maximum and minimum value of « and the same as that of the
p,f curve for the three-phase-pressure. The p,7’ curve of the three-
phase-pressure descending with the temperature in the case of minimum
«x and vice versa, we conclude concerning the point of contact that
in the first case it lies between critical point of contact and maximum
pressure of the liquid vapour curve, in the second case on the vapour
branch of the curve.

( 242 )

If we suppose that the two critical phases with which the solid
body can coexist, and which differ considerably in concentration for
anthraquinone and ether, approach each other, the two separate
parts of the 7’, figure and also that of the p, x figure and that of
the p, 7 figure will approach each other. At the point of contact the
two parts of the 7, figure, and that of the p, x figure will intersect
at an acute angle. If we continue this modification further, the
two upper branches of these figures have joimed, forming one con-
tinuous curve; in the same way the two lower branches. Then the
ji Teurve shows a maximum. The existence of this maximum three-
phase-pressure has already been demonstrated and discussed by me
on the occasion of former investigations by prof. BakHuts RoozEBooM °).
We find again the result obtained before, now under the following form:
ep @s=%,) Fis 2y,, RO a pean

P(e, as v) + oa ec

2 .
’

ae 4 Us— we, Us —wv,
which means, that if we write for that special point of the three-

phase-pressure :

the value of 4w would be 0.

If we now examine the course of the 7,7’ curve for the three-
phase-pressure more closely, making use of the formula on p. 241,
or what comes to the same thing according to the formula of
Verslag 1897, Deel 5, p. 491, it appears, that other complications
may occur; and that it is not perfectly accurate to say that the
pl curve on the side of the anthraquinone is an ascending curve,
till the triple point of this substance has been reached. Then we can
also account for the asymmetric behaviour of the p, 7’ curve. It ascends
from the triple pomt of ether and descends on the other side.

In this consideration we shall denote by wa, a and ws the concen-
tration of the vapour, of the liquid and of the solid body. In the
same way we shall use ég, é1 and €,; then we get for avery small
quantity of the admixture :

1 wa &q + pra
] vl &] + pry

, dp ees ] pes &s +. Pes = ; AMwd— es) (a) ra) “
dT l wa va (wa-- as) (vi— v9) — (#1 ars) (Va 0)
] vl Vi
Ll ws Us

1) Verslag Kon. Akad. Amsterdam, 1885, 3e reeks, Deel I, pag. 380.

2) The more accurate value of the numerator of the last fraction is:
(vq — 4%) 4A 1—ay) 4+ AB a — (ei—as) fra (1 — ea) + rp ed

In this we have, however, disregarded the heat of rarefaction,

( 243 )

We denote then the latent heat of liquefaction by 4 and the
heat of evaporation by +.

Let the principal component be anthraquinone at its triple point. If
we add a very small quantity of ether, v, and 2; and «, will be
small but wg >. > as. We may even assume by approximation
for this case, that no ether passes into the solid phase; hardly
any will be found in the liquid, but most of it in the vapour. So

Ld. ‘ i) beh
“, = Oand —is very great. For the limiting case which may be
LI ‘ ;
supposed, in which «, would be zero, we have:
dp 2
Geese es
im gy,

The initial direction of the p,7Z’ curve is that of the melting curve,
and when 7 > vs, this curve begins as an ascending curve with
increasing temperature. but as soon as after further addition of

v(—#s al : :
—has become equal to —, in which still a
LE aay | *s Ci Us

ether the value of

very small value of x; is supposed, the numerator of the expression
: dp
for 7’ —
di
numerator is reversed and the p,7 curve is no longer ascending,
but descending with increase of 7”.

is infinitely large and on further addition the sign of the

Now let ether be the principal component. In this case we have
to distinguish two different cases. 1st. Ether and anthraquinone are
in solid state miscible in all proportions; then the solid substance
which we must think present, is so/id ether and we start from the
triple point of ether. 2°. For all equilibriums anthraquinone remains
unmixed with ether. Then the temperature must be thought slightly
above the triple point of ether.

In the first case, if at the triple point of ether a little of the
so much less volatile substance, anthraquinone is added, if is to
be expected neither in the vapour, nor in the solid body, but only
in the liquid; then we find:

_, op rt.
- = :
dT va—vs

So an increase of p with 7 as occurs in the case of equilibrium

between vapour and solid, in concordance with the rule, that if
two phases of a mixture in which more phases are present, are of
the same concentration, the equilibrium conforms to these two phases.

In the second ease, in which we think ether present in liquid
and vapour state at slightly higher temperature than that of the

( 244 )

triple point, added anthraquinone in solid condition will not pass
into the vapour state. Then r,= 1 and «=O. We get:
i. dp r—xj (r + 4)
Lee vj— vr] —2](vqa—Us)

The quantity 4 is now the latent heat of liquefaction of anthra-
quinone.

For vanishing value of «, we find increase of p with T, as°8
found in case of equilibrium between liquid and vapour. In neither
of these cases the numerator can become equal to zero when a
small quantity of the second substance is added to the principal
substance.

But I shall not enter into more particulars, nor discuss the treat-
ment of special circumstances. If they are brought to light by the
experiment, they can necessarily be derived from the above formulae.
Nor shall I discuss the v,., 7’ curves, which would lead to greater
digressions. For this discussion we should have to make use of
two equations, of which that for the coexistence of liquid and vapour
occurs in Cont. II, p. 104. For the v,# projection of the three-
phase-equilibrium we get for anthraquinone and ether two separate
branches, lying outside the limits of the maximum and the minimum
value of « mentioned above. When these two values of x coincide,
these branches meet, intersecting at an acute angle; at further
modification the two v,e curves, viz. those for liquid and vapour,
will yield a highest and a lowest value for the volume; at any
case the v,v curve for the vapour phase. As appeared in an oral
communication, Dr. Smrrs had already arrived at this result.

I shall conclude with pointing out, that cases of retrograde
solidification must repeatedly occur, both when the temperature is
kept constant with change of pressure and when the pressure is
kept constant with change of temperature.

Chemistry. — “Ve possible forms of the meltingpoint-curve for binary
mictures of isomorphous substances.” By J, J. VAN LAAR.
(294 ¢Ommunication). (Communicated by Prof. H. W. Bakuurs

RoozEBOOM).

1. My investigations concerning the possible forms of the melting-
point-curve for binary mixtures of isomorphous substances, commu-
nicated in the Proceedings of the meeting of the 27% of June 1908,
have, apart from the different theoretical considerations, led to the

following practical results.

x
.
'
B.
J

i
7
,
4

( 245 )

a. When the latent heat of mixing in the solid phase a’ = q, ?'
is great, the solid phase contains but very little of the second com-
ponent. The portion of the meltingpoint-curve which may be realized,
has a course as in fig. 1 (see the plate). The curves 7’=— /f(e'), viz.
Aa and Bh show maxima at m and n, which maxima descend
eradually for smaller values of 2’ till they are below a and 4, the
maximum at 7 sooner than that at m. (fig. 2). [We leave for the moment
out of consideration what happens below the horizontal line through
the point C, the eutectic point : for this see my preceding communication |.

6. For smaller values of f’ we get the case of fig. 3, where the
branch BC shows a minimum, no longer below the temperature of
C, but exactly at C. Immediately after (i. e. when ' is still somewhat
smaller), the meltingpoint-curve assumes a shape as in fig. 4. C
remains the eutectic point, where the two branches of the melting-
point-curve meet with a break. As appears from the figure, we
have now got parts of the meltingpoint-curve, which may be realized,
also below the point C' (see also fig. 14 and 14a of the communi-
cation referred to).

It is however very well possible, that in the meantime the minimum
at D has already disappeared, and then we get a course as is
represented in fig. 5 (observed i. a. by Hissink for mixtures of
AgNO, and’ NaNQ,. (see also fig. 146 1.c.).

ce. For still smaller values of #' the curve 7 = («’) becomes
continuously realizable. The points > and a coincide in a point of
inflection 6, a with horizontal tangent (fig. 6), which point of inflection
soon passes into one with an oblique tangent L (fig. 7), while in most
cases it disappears afterwards altogether for still smaller values of
(hie. 8).

The break at C has disappeared in the case of fig. 6 and from
this moment there is no longer question of a eutectic point, and

the meltingpoint-curve assumes the perfectly continuous shape of
fig. 7 and 8.

d. As has already been observed in 4, also the minimum at D
will sooner or later disappear. For very small values of §' we get
then always a course as in fig. 9.

Observation. As has been elaborately demonstrated in the preceding
paper, a maximum at A for normal components can never occur
with positive values of the different absorbed latent heats of lique-
faction and mixing (see p. 156 l.c.). When such a maximum is
observed, as was done e. g. by F. M. Jancrr’) for two isomeric

1) Akademisch Proefschrift (1903), p. 173—174.
17
Proceedings Royal Acad. Amsterdam. Vol VI.

( 246 )

tribroomtoluols, this always points to difference in size of the molecules
in the liquid and solid phase’). In fact Jarcer, found that his
isomers are very likely bi-molecular in the solid phase ’).

2. We may now put the question: When will the minimum at
D, which will disappear in any case for values of 3 smaller than
those for which fig. 3 holds, disappear before the case of fig. 6, so
that a course as in fig. 5 becomes possible ; and when will it disappear
after the case of fig. 6, as has been assumed in our figures 6 to 8.

To answer this question, we shall first state for what values of p’

the case of fig. 6 occurs.

a7!
The point 4,a lying then on the top of the curve = 0 at
L
x’ —'/,*), we have, besides the equations (2) for 2’="/, (see p. 153.1. €.),
03) : Bd bi 2 ;
also the relation —- =O or ———— — 2’ =0, i. e. with R=2
Ow"? u(1—«')

the relation 7’=— a’x’(1—w’).
The condition sought is accordingly :
to} O-.

vi l—«# vB "a
for which with regard to the fundamental equations, some simplifying
hypotheses permissible for our purpose have been made, which may
be found on page 152 of the paper mentioned.

Now we can solve (Rk = 2):

9 fo ss pe ee 9 pot Bg ie
0,5 tie + 4 T , 0.5 4 q. ree

f 1 1 1 } VT
fi] peas, oA Lage

'!) See p. 208 and 209 of the *Proefschrift’, where Jagecer gives the proof of

a : eo tet oo 3 =
B' 4 | Tie
eC. Fi +e

this thesis, which | had communicated to him in a letter.
2) See p. 208 and 194 of the *Proefschrift”.
%) Only if we assume z') =’) (so b,; = by), this parabolic curve will be sym-

1r—l1

metric and its top will be exactly at w'= 1/9,

Pas ee

iam

mrt

( 247 )

and this is the equation, from which 3’ can be solved. Unfortunately
however 8’ cannot be solved from this in an explicit form.
Now the minimum disappears, when (see p. 168, 1. c.):
pete
fy.’ - of i

(2)

That this takes place exactly at the same moment as that at whieh
the case of fig. 6 occurs, is expressed by the relation:

Blase a(t) eee (+)
oe [ek eee Cee tT, 4 T,

zal (5).
If we write for shortness :
rah pao ; 7 =i v0 ts 2)
the equation (5) becomes:
£ 1 1 it | Pe }. 1 ag

= F=ore +9)| —2| 2 7 +9) |
e a e — 2, (Sa)
where 4 will always be < 1 (7, is assumed < 7').

It is now easy to see that there are always corresponding values
oa 2. £; ‘and y, to be found, which satisfy (38), so that the minimum
may just as well disappear before as after the case of fig. 6. In
order to define the limits of 7,, 7,, q, and qg,, in which either the
one or the other will occur, we shall express e.g. y, in function
of g, and 2. We get then successively :

i ia 2 1 ek 63 9 Ps 2
coe + G,) {a 9 r Fs) ag
e +e == i,
1 2 1 @y4
i fa ere me
: .e 1—} — Get ee af :
2
ee —
a —g, —2 Fs : = log (2 e /s e Is Ps =1)
_ ee
so finally :
a 2
ant 1/
a. oi : see 1 ;) .
i. ec t 2 J (+)
2 gates

’s _ This will be equal to 0 (first limiting-value, as # cannot become
y :

-_ ,' ~
f=<0), when
ny

sl
\*2 ,

2
eee. eee
2 SE Mara
ay ey 1-24.
or
5) pSuail
af = = = log (2 € ~— 1) = — 1,546,
r i ae 3
so when
4
Q;, = SS 3,092
: th -

Ad
Pips Gang + 0,908 (~, =

The quantity g, will be » (second limiting-value, as p may

have all values up to 2), when

OWA
we
2 g, l—2 .
i. e. when
4} ; »
Pa ate (Psa coc oS

It is evident that the difference between the two limits of g,
is exactly 0,91.
We have now the following survey for different values of 2.

70 7 , pee | A=?/, a=l1

| |
f= 0) ge, =U ee eg | py = 12,91) » pare

~,= | 7, =' Q = 19838) 9,=—=4 |g= 12 Pf, =
ry * Vs *
From this we see, that , — Fr may have all values from 0 to

; qd ba Ad: ‘ 3
but that the values of gy, = aR are limited to an interval, which

1
ry.

varies with the value of 4= —

7, approches to 7’, the smaller this interval comparatively becomes;
» the value of g, required must then become larger and larger.
All this applies to the case that the minimum disappears at the

same moment as in the case of fig. 6. It is easy to see that when

The greater 2 becomes, i. e. the more

the minimum disappears before the case of fig. 6 the value of g,
will have to be /wrger than that which is determined by (4) for

ee a ie ii

( 249 )

given values of g, and 4 The opposite case, i. e. that the minimum
disappears after the case of fig. 6, will take place when g, is
smaller than that value.

For, when the minimum has already disappeared, the value of

Sra
6 in fig. (6) will be smaller than i —. We must accordingly
z 1
substitute a smaller value of 8’ in (1), or what comes to the same
thing, give a higher value to 7, i. e. increase the value of /. But
it is obvious from the above table that when 2 increases, a highei
value of g, will correspond to the same value of g,.

Let us take as first example 7, = 1000, 7, = 500, ¢, = 4500
Gr. cal., g, = 250 Gr. cal. 2 is therefore — '/,, y, = 4,5 and gy, = 0,5.
The value of g, ranges therefore within the interval 4 to 4,91, which
helds for-2.== */,,
in the neighbourhood of (or exactly in) the case of fig. 6. The condition
for its disappearance for the value of »' corresponding to that case,
would be that there corresponded to A=?

so that it is possible, that the minimum disappears

y, = 4,5, according

2?
to (4), a value of y,, given by :
: — 1,73 Lee
log (1,2151 — e log 1,0322 ae
. Se = = == 5 0B.
0,9-— 9 /18

So to g, = 0,50 corresponds a greater value of g, than the one
given, viz. 4,5. This value is therefore too /ow, and the minimum
will disappear after the case of fig. 6.

Second example. Let 7, be again 1000, 7’, be 500, but now
q, = 3000, ¢, = 1000.

We shail not have to execute any calculation now, as this value falls
beyond the interval 4 to 4,91, g, being 3 with A='/,; g, is much
too low to be able to correspond with any value of g, whatever,
and again the minimum will have to disappear when the case of
fig. 6 occurs.

If on the other hand 7, had been 1000, 7, = 500, g, = 5000,
G2 = 2000, then it would be clear without any calculation, that now

the minimum fas already disappeared when the case of fig. 6

occurs, g, = 5 now lying beyond the interval on the high side.
A course as in fig. 5 therefore becomes now possible, when the
value of p' lies between that of fig. 3 and fig. 6.

The case of fig. 5, observed among others by HissinkK in mixtures
of AgNO, and NaNQ,, belongs therefore to the possibilities, and can
occur for given 7, 7, and ¢q,, as soon as qg, has a sufficiently
high value, or what comes to the same thing, as soon as for given
7,, 7, and g, the quantity g, has a sufficiently /ow value. The

\? 2

value of ae or g, must then be smaller than that calculated from
2

(4). If we then find a negative value for g,, the case of fig. 5 is

entirely excluded for the given values of 7, 7, and q,. In the

equation (4) we have therefore at any rate a criterion to determine

whether or no the case of fig. 5 can occur, when the value of

lies between those to which the figures 3 and 6 apply.

3. Another important question will be, when the point of inflection
L with oblique tangent (fig. 7) will disappear, and whether it can
still be present e.g. with p' =O.

: dT CT
Let us for this purpose determine the values — and —.
Putt da! da!”
We found before (l.c. p. 155):
i eae
ee ee v wv
dT = ) Ow? rfl bi aa Ox'?
da (l—a') w, +-2'w, dz' (l—a)w,+ aw,
where
07g BP 076) RF >t
= Das — — 2a,

dx? a«(1—z) On? 2! (i—z')
heat (ie al aa W,—=4, + a(1—a)?—a (l—a)’.

Hence we get:

la ee : a ge alg ah
L—ae —— 2 uv—a')| ————_ — 2
dT T ha oh wv (t—z2) i = v'(1—2') ‘ }

= — [ —____——_ a , (6)

da: (1 —2')w, +a, du (1—2) w,+aw,

, dT dT

from which we see i.a., that when e.g. — has been calculated, ——
Av Av

can be found by substituting 2’ for «, — T for 7, —a’ for a’ and

—a for a and by then reversing the sign of the second member.

rm J OL eT : s x >

The same holds for a? when ae determined. From (6) follows

Av ~ av

forethepomt) A> where 7==7), c= ==05 7,"

ty hal sks” a! dT 1d ila a
) ee | 1) — | ale a — «\ <= eile)
at /, q; a), da}, dy Ly ae
The initial direction depends therefore on the limit of the value of

—. We found for this expression (l.c. p. 156):

a i Ds + a-—a' J
ib, ve (2 2 fila’). ak eee
4g (: ; RL T. 7 (8)

iam ate

( 254 )
from which appears, i.a. that for « = x, ~ approaches toe”, hence
it approaches rapidly to 0.

SNCme &)
Let us now differentiate the expression (6) for a with respect
ak

to v. We tind then, logarithmically differentiated :

da'
Pr ar elas) (a-a')\(1-27) R(«- ~w') dT -26(1-")

n(1—a) d. x
dx yee dar 23?(1—zx)? +a °( —a) da v da
dT “Fa —T as RT A =
du: (e—a’) Be <3) — 2a
die! dw, _dw,
(w,—w,)— + (=a!) 53 +
dx: da
ie w, + a'w, :
We find therefore for T= T7,, c=7’=0, where therefore pe aes
u(l—a

’

R1
at = a)

dir!
ery aT) 1 (aT “91 ae “oe eos)
Berge et
2az (2- =) (w,—w Ne!
Lae: da. ; “da
Sr) ee a)

dw
may be replaced by , and where = is evidently 0:

T \de (c—x)RT, w

da!
Now we must ealculate the value of (=) ;
av

From (6) follows immediately :

BRL
——— — 2a
dx’ «x(1—2) wi te (w,—v,) (
dn OT wa! (w,—w,) 2)
ee P
w' (1—z2’)
or
2aux (1—z) wi—wv,
ia ee
da’ «(1—«’) RI wy
dz x(1—z) 2a'a'(1—2') w,—w,
—_— >. Sa 1 pases =
Et Be wu

henee for 7’ — T,:

dz 2a'a'—2 a — ae —w,
Bact (+ Uise sgk

org( Fe ==):

! ' ! '
da au ae — ae
€ Lv 0 L 1

. & .
So this approaches to —, but as will appear presently,
&

determination of the term

da
a(1—e) (1) —@= ) 1— 22)

we must also retain the terms of lower order, as those of higher

order disappear. We have further :

da' ax’ —aa
av { l—— | = («#—- 2’) — a
( a) bee Ts

+@—s) |=

ee ji» - a'«e' — az ee
ge |(e—2')T,

The term mentioned becomes therefore :

(v—2') (a “<n (Ay =

Hence we get:

~2n)) = («—a') (x— AQ).
!
1H
aa & =
a & wWs—w,

for the

ra heal alr ee An A AB ee aN
i \=(a nba ae at “

(w—w)T, “

{| =(@—#) aa)

k , : Sef bale pie haa a!
or introducing the value of A, and of Seas (a
5 a“

!
av W,

—W,

iad dT Wie ww Ft, OP ea
aks ee ees = Ty +1 + a
den). dv a a e|(e-a)T, w, OP

bo
|

! Pea ete
v ve at —ae

(5 a aw,
Rr E) fs RATES 4. he coe
dx Ne 2 x vw,

d7 a : £ |i.
“aCe es
No ee Aiea

(ae) = (ae)
Ae Os '
Ai

a
where , ’ has the value given in (8%.
aL ;

j ; 7
a“ a (a— £) i hs

Ww,

i ai]
9 va a& — ae

a "D, 2 (w—a')T,
so that we finally

cet :

ale ad eis ) +47, — 2 (4,4 e—a) =

(9)

+ mae
co c™

MAE InE Ae. es yO Se
~_ a “7. ‘

("2538-3

This expression for (| =) is still very complicated, even after the
ee ae

great simplifications, which attend the introduction of «= «’ = 0.

: af Goer
Besides by a direct calculation, the corresponding value for (Fz)
ai” 0

may also be found by changing letters and signs’ as mentioned
above, and the latter method is even the easier. Then we get:

aT ! f

(2) HB) afi Joon (Yona
a)
2 ee 15.4 | Ce
aT |
Os
Uv) 4

Be er eT
In the discussion of the two quantities Wire and qa}? two
ar 0 Av 0

limiting cases are chiefly worthy of consideration, viz. a’ = and
«@’ =0. Let us further always put @ (latent heat required for the
mixing of the liquid phase) — 0.

(Ya)

'
”

Lv
a. For a =a — becomes exponentially — 0, hence
—— L

"\ 4
Lim. (« =“) will be 0. The two expressions are then transformed
& 0

; 2T 1 (dT ro 4 \ ,
% eh aes wt

2 = eG dee) nh atv i ig

mf 27 r al

ae ae = at ae = = a’ + i a {2 -- 2 it

an 4 dc epee dee’ 0 Js a! 0 15 oP

feet, €. into:

ra fad bd di 3 \
ae ; ae | al 3)
: (cs -60) Soin Fa ge)
dT eae
a GG

‘These expressions teach us, that in case the solid phase contains
‘ +8; 4

€
very little or nothing of the second component, (

into:

277

dae
ie when g, =4 7,. In this case therefore the point of inflection appears
fem the curve 7, f(z) exactly. at «— 0.

) becomes QO,
0

dT , le bg it ao :
& being negative, i will also be negative if 9, >4T.
ee OD a 0
The meltingpoint curve will then turn its concave side to the v-axis
at A, and no point of inflection will occur. This is in perfect agree-
ment with what we found in our former paper. *)
‘aid ie ; : dT
As to |—~—], we see that this expression, just as {—, } will
= :) &
always be negatively large. For great a’ the concave side of the
curve 7'=/(a'), running almost vertically downward, is turned
towards the z-axis, but the curve 7’'= /f(q’) finally touching the
ordinate «=O asymptotically at 77 =O, a point of inflection must
at any rate be present beyond the maximum of the curve 7 = f(z’)
(see fic. 1; at L).

This point of inflection £ will occur immediately after the maxi-
mum at m for large values of a’, and these two points gradually
approach the point A, where 7’= 7), 2’ = 0.

As to the maximum m, this is of course represented by

> 1 'e

(1—2)w,-+-aw,—0 (see (6)) or « = ———. Now w,==-q,—a'x"=9,, and
105—— 2p
1 ay |

w,=4¢,—¢ (1—2’)?=— a’, when a’ is large and 2’ very small;

henee the maximum occurs at
hh Pele
= —t—_, Pt oat Oe

Qi eae he, A,
If therefore p’ approaches to a, then x, (so also x’) approaches to 0.
As to the point of inflection at Z, the following remarks hold

eood for it.

From the expression for a (see (a) follows, when @ =O and
a’ is large:
al aT a{l=2) w, G2 a(l=2) 4; dT «xl-«) 1
dit! ee w'(1 -«')w, +a(wi-wv,) ao ee q,-we! if dea! 1-p'a

At small 2’ we get:

. (b)

T fa
ye RT, ;
1 — log (1—«)
qi
hence :
dT “hi LY Fol ee si fi Ge 1
du N? Bl l—z alee I, (1-.) (1 <= 2 Gx)’

as N? = (i—@ log (1—v))?> = 14+ 6r4+..)? = A + 2 62).

1) These proceedings, Febr. 25th 1902, p. 427; June 24th 1903, p. 29—30,

ee ae. ee Se eee Oe ee

We have therefore :

dT RT? « 1 RT a!" 1
ae ge Sees, 2 1S a
when #' is great with respect to 6, and hence :
Rae ; we tet:
eT BES ae (1-1 he ot
da? oe. qr “x (1—B'z)? 5. 2 ‘

Consequently this is 0, when

' ! da ! or ! dius
x (1—p'x) oe B: —P «—Pa - |.
da: da

da
Now we may write for oe (see (0) ):
Awe

da «a (1—=2) 1

€
so that —— = 0, when

du
82 (1—ax
ote) (1-8 pel iss \ =)
1—pe
ue pea
i aaah wv ( + 1—p'x ;

hee gece =e (1+ :
=e( eae along f

From this we find:

' p'
a,
1—
so finally :
2,
el = ° . : A“ ° ° e ° . (12)
p

being the value of x, at which for large values of 8’ the point of
1
inflection will be situated after the maximum at v= 3 (see (11)).

So this value of 7 too approaches to 0, when ?’ approaches to x.

It is now evident that according to (10) for large values of ' the

; hea

quantity ce

neighbourhood of A the direction of the curve 7’= / (2’), which was

initially almost vertical, changes into a perfectly vertical direction at
the maximum.

) approaches to —o. For already in the ammediate
0

( 256 )

b) The other limiting case is a’ = 0. The expressions (9) and (9a)
take then the form

(= (efor (2) enna
(5) = f(a) vere (S)fo-en-n]

(2) =. a2) 3 ae

We see from these expressions, that even with 3’ =O a point of
inflection at «=O (and so also before it) is possible for the two
curves 7’ = (x) and T=/ a’). For this it is required for the
curve 7’ = f(a), that

i oe gq,—4T as f
& Mit [ea ae ES 2 hs = Gq) 2 129 eal’

q—47,
or
1 1 ee
ce | ia ae == Og jo ee é
Y CA See’ ioe ; q, -4T7,
If 2 a sre is not large, we may write for it by approximation :
Oi ee
= (i Sr yes das 7 cla i c= 2
pee ATs=39 4
elie ast

We see that in any case must be positive.

27 ae
The condition may now be ere as follows:

W-g, | AE 9 ae ve q,
—<—_ = =| 1l— - —l1},
Ys cv Ae Aa 47, hs

hence

ae See ee oe LA. —> =
os ’ *

C25)
Yoh
i oe 9; ,
= th . . . . . . . (15)
SPp ss
ae

eee a= f1OO ieee DOU, Gg, == 2200, g, = 1980, the first

11 10 / Fe
/9 / ah
member is ‘/,, the second member pinata so also '/,. | he term
hare

r= 0s ats 440
under the /og-sign is here ——— — !/. |.
n—4T, ee 2200

Even with @'=0O a point of inflection can very well occur
somewhere in the curve 7’= f(x). The corresponding condition for
the occurrence of a point of inflection at «=O in the curve
T = f (#’) becomes:

(5) eo Gi te, oe 1
#7, t4T,—2¢,-9.) , 9 aoa
qa,
or
1 1
Is ae ee gee log | == thea ee OS ;
Tp. Pee:
for which we may write for small values of g,—4q,: .
ve Bierce
T,-T ee”
rr oi (4, J= a aT

This is only possible when ¢, >g,. Again we may write:

Cb a iat san ar Y) a (: at hh \G a 1),
Ts aT 4T i lp

vB si 1 é )
or — = — + —— | —— 1],
q2 fi BAS dj
Gee Sh
my 2 2 a (15a)
aT D
— 1
a8
ges. te == FIO =e q¢ == 2200; gq, == 1650; the’ first
4/ 11/
member is again */,, and also the second member Carey = he
ce
hata a AOR 1
| The term 2 aE is now sane ea

Also in the curve 7 = f(a’) a point of inflection may occur even
win, B' = 0:
And now we have given a complete answer to the question

( 258 }

raised in the beginning of § 3. The point of inflection at L (fig. 7)
need not have disappeared in either of the two meltingpoint-curves,
when ~’ has reached the extreme value 0.

In a following paper we shall give a fuller discussion of the
important limiting case p' = 0.

4. Finally we wish to discuss more at length an important property
of the eutectic point C, which was only shortly mentioned in the
preceding communication. (I.c., p. 166).

A rule was namely given there of very general application, i.e. :

When a, =a, (i.e. latent heat required for the mixing of the first
component with «= 1 is equal to that of the second component with

= 0) the compositions of the two solid phases will be complementary.

We shall proceed to give the proof of this thesis.

Evidently the system of equations holds for the eutectic point (the
compositions w,’ and w,’ of the solid phase are there in equilibrium
with that of the liquid 2):

‘a mts n(1— 3 =n") sf af
T= f| iC —pP eH, 5) gh kt qT i a az id —Be, ‘) nite
a Jar & 1 ae devil Be ae de 1 == Se
ipa fy se ee (222
TN Le Ts bi n mee lb-—.
7 qT, ! 2
di aes (eave
vB
as : Ee ss 16
Ra. ’ x ( )
1+ - log =
( 2 7H
If we solve from this /og (A—.) and i a, we get:
log (1—z2) = log (1—2',) 4 a fi es ee \
e Py, aa: Ri ys 1
log #& = loge’, + ts : 4 ce 3’ (1—e',)’
: ; 0 arpa eA ip feet :
! q i I. qs ! !
log (A—: on eee + cy Fi ae
og (1—a) = log (1—#’,) + R Ges ca, t rp?”
] / ! Je DV 1 1 ae qi, 3 1 '\9
og = 09g dl 2 R Ts T RT ( aa )
from which follows by equalization :
1—w q ! Ie 19 v q au Ye No
log pee = ra re) (ie 7— 2, Bf log a = a p | (1 —t, y—( — wv, val
which is evidently satisfied by
#," =1I—n, = (17)

diend:

J J. VAN LAAR. “On possible forms of the meltingpoint-curve for binary mixtures

of isomorphous substances.” (2nd communication).

ics, 1. Fig. 8.

Proceedings Royal Acad. Amsterdam. Vol. VI.

ad inl” ale iad ial

al» il

( 259 )

The two above equations pass now into one :
1—w,!

q
loc PE i 18
Pa x," ath. Pt 1) i

In this complementary composition we have a distinct criterion,
whether or no it is allowed to put a’, =a’, (i.e. r=0). Further
the equation (18) furnishes a simple means, when 7 may really be
put. ==0;. for caleulating the quantity p from the composition 0 OF
the solid phase at the eutectic point.

If we find e.g. x, —0,1, we may find by means of 7,

ea LO
ie 2400 :

Pa 2400 mecite
qu = —_ fp. < or
“J 1600
hence :
Bs)
A’ === tog 9 = 1,14.
48

If x’ had been 0,01, we should have found with the same values
oi 7, andig;-
12

, »

3’ xX 0,98,

hence :
e135 .
B SS SS log 9o°== 1,95.
294
It is seen, that a slight increase of £$’ is able to depress the
composition 2,’ of the solid phase at the eutectic point very strongly.
This is of course in connection which the enormously strong decrease
!

d . . . . . . ) a ryy
of the relation — with increasing 3’. This relation was e.g. for 7= 7,

a
Q/ a! RT, / .”)) :
and great §’ represented by { —]}] =e (see § 3), which con-
vo
verges very quickly to 0.
Chemistry. — “Vhe phenomena of solidification and transformation

im the systems NH, NO,, AgNO, and KNO,, AgNO,.” By
Professor H. W. Baxnuts Roozrpoom.

(Communicated in the meeting of September 26, 1903.)

Of the nitrates of univalent metals, those of Li, Na, Ag, NH,, K, Tl
have been studied more in detail as to their mutual relations. It
has already been shown that the nitrates of the first three are very
prone to yield mixed crystals and the same takes place with the
last three, Li NO, and also Na NO, do not seem to form with the

( 260 )

nitrates of the last group any mixed crystals at all or else only to
a small extent and in any case they do not enter into chemical |
combination.

As regards the relation of AgNO, to the nitrates of the second
group, the only system examined up to the present (by van Eyk)
was that consisting of AgNO, + TINO, in which a compound in the
proportion 1:1, was formed. To complete our knowledge in this
direction, the systems NH, NO, + AgNO, and KNO, + AgNO, have
been investigated by Zawrpzki and Ussow and the results are com-
prised in the Figures 1 and 2.

O- O2 GY Of OF aD al nag 0% Nowe
AinNos fig N bs i

Fig. 1 and 2.

The first system is interesting on account of the fact that with
NH, NO, four and with AgNO, two solid phases succeed each other
which, starting from the melting-point, we will designate by Am
1—4 and Ag 1—2.

It now appears that in the case of mixtures of the two salts the

( 261 )

transition point of AgNO, and the first transition point of NH, NO,
falls in the region where these mixtures are still partially liquid; the
two lower transition points of NH, NO,, however, are situated in the
region where everything has already become solidified.

Owing to this, the deposition of AgNO, from melted mixtures rich
in silver takes place according to two lines which meet each other
at 160°; the solidification of NH, NO, from mixtures rich in this
salt, also takes place along two lines which meet each other at 125°.
Neither transition point is modified by the mixing process, from
which we may conclude that the salts are deposited in a pure con-
dition and do not yield mixed crystals.

From the intermediate concentrations, however, a compound
D = NH, NO,. AgNO, is deposited with a pure melting point at 109.6°.
Its melting-point-line extends towards the Ag-side only up to 52
Mol. °/,, towards the NH,-side up to 30°/, Ag. Consequently, all
mixtures of 50—100°/, Ag solidify at 109°.6 to conglomerates of
D + Ag, and all mixtures of O—50"/, A
of Am, + D.

The latter, on further cooling, undergo a new transformation at
85° and 35° owing to the reversion of Am, into Am, and then into
Am,. As both take place in the different mixtures at the same tem-
perature at which reversion of the pure AmNO, takes place, this
proves that no mixed crystals occur between this salt and the
double salt.

If now we express the liquid mixtures by L we have in Fig. 1
the following regions.

1 Am, +L 7 Am, + D 3 L- Ag,
2 Am,+L 8 Am,+D 4 L++ Ag,
5 D +L 9 Am,+D 6 D- Ag,

The system AgNO, + KNQ, is simpler in so far that KNO, has
only got one transition temperature at 126°.

The transition point of AgNO, again falls within the partially
liquid region and the solidification of the mixtures rich in Ag therefore,
again takes place according to two lines which meet each other at
160°. Under normal conditions, the transition point of KNO, falls
within the solid region, consequently there is only one melting point
line for the first form of the KNO,:K,; in the figure this line
is represented only from 210° to lower temperatures; it must be
imagined to extend to the KNO, axis at its melting point of 338°.

From the intermediate concentrations there is also deposited a
double salt D—KNO, . AgNO, but its melting-point-line only
extends from

2 at LOL’.5 to conglomerates

18
Proceedings Royal Acad. Amsterdam. Vol. VI.

( 262 )

131° and 38°/, KNO, to 184°.5 and 45 °/, KNO,

Consequently, there exists no pure melting point but D is trans-
formed on heating to 134°.5 into KNO, solid ++ solution of 45 °/,.

All mixtures of O0O—50KNO, solidify at 131° to Ag, + D, all
mixtures of 50—100 KNO, at 134°.5 to conglomerates of D-+ K,.
The first named remain unchanged on furtiier cooling. The last
named ought to change at 126° into D+ Kk, but this takes place
with great difficulty.

The double salt is also not readily formed. If it does not make
its appearance, the melting-point-line for K, runs through to 126°,
and below this K, is converted into K, much more readily than in
the solid conglomerates. The melting-line of K, runs through to
120° at 42°/, KNO, where it meets the prolongation of the melting
line of Ag,. If D does not appear, a// liquid mixtures solidify at
120° to a conglomerate of Ag, + k,.

The following zones comprised between the full lines represent

stable conditions

1: Wee 4 ak:
2. Nar sg ee
3 Ag, + D 6 DasK

eg pe.e

All metastable boundaries are indicated by dotted lines. The regions
concerned may be easily deduced from the figure.

From the above it follows that at the ordinary temperature, only
the simple salts in the forms which are stable at that temperature
and also the double salts 1:1 can occur as stable conditions; this
agrees with what Rwreers has previously found for the products of
crystallisation from aqueous solutions at 15°. |

Chemistry. — “The transformation of benzdine”. By Prof. A. F.
HoLLEMAN and J. Porter van Loon.

(Communicated in the meeting of September 26, 1903).

In the report of the meeting of this section of Nov. 29, °02 there
will be found a preliminary communication as to the experiments
conducted in my laboratory by Dr. J. Potter van Loon, who has
since brought his research to a close. His results are briefly described
below.

The method by which he succeeded in obtaining benzidine and
hydrazobenzene in a perfectly pure condition has already been given
in the preliminary communication. In connection with this it may
be mentioned that hydrazobenzene was separated as a snow-white

( 263 )

substance, but after a few days exposure to the air it again turns
faint yellow.

An improvement was also desirable in the quantitative determina-
tion of benzidine. At first van Loon collected the precipitated benzi-
dine sulphate on a weighed filter, which was then dried at 100° in
a steam oven and reweighed. Here we met with the unpleasant
fact that the filter often turned blackish probably owing to a decom-
position of the sulphate, which may unfavourably affect the deter-
minations. The improved process now consisted in removing the
washed sulphate from the filter and boiling it with excess.of standard
alkali. If now the excess of alkali is titrated at the boiling heat
with standard acid, the benzidine sulphate behaves like free sulphuric
acid when litmus is used as indicator. In this way the determination
becomes more rapid and accurate. The usual correction for the
solubility of benzidine sulphate had, of course, to be made.

The determinations made by Dr. van Loon of the ratio between
the quantities of benzidine and diphenyline formed during the
transformation of hydrazobenzene by acids have demonstrated the
influence of various circumstances on that relation and may be best
represented in a tabular and graphical form.

I. INFLUENCE OF THE CONCENTRATION OF THE ACID (ILYDROCHLORIC ACID).

a) Solvent: Water. Temp. 18°—25°.
. J j j —_
Bvenntention Amount of Mer. mol. Weight of dipheny
°/, benzidine. line on 100

of the acid. |

acid in
mer. mol, |

hydrazobenzol. Bes
) parts of benzidine.

259/, = 7.8 n. hs.< 1 — 84.5 18.3
Zig. == 128 D- 77.8 2.011 80 0 25
3.90 n. 77.8 2.— 90.0 1 ee
|
non. 50 2.— | 90.5—89.5 10.5—12.4
b) Solvent: Alcohol of 50°/)1). Temp. 25°.
Concentration a Mer. mol. | hea ph ach Soe
acid in | 0), benzidine. | line on 100
’ the acid. ara i er
pee aond | mer. mol. ieee oiat | parts of benzidine.
oA DR: 77.8 2.— 89.0 25
1), n. 50.— 2.— 84.8 a7 9
0.6 n. | 30 — | 1.440 83.6 19.6
|
0.1 n, | Be _ 83.0 90.5

1) Always percents of weight are meant.

18*

( 264 )

Il. INFLUENCE OF THE SOLVENT. Temp. 18°—25°. HYDROCHLORIC ACID.

rau ts te. ;
Nature of the | Concentr. | Amounto!) vor mol} % Wee
acid in | | line on 100
solvent. oftheacid| hydrazo. | benzidine. oe aes
/mer. mol | | parts of benzidine.
| |
Alcohol of 97%,| O42n. | 12 | 1.533 | 805 4.9
» » 50% | O1n. | 10and5 /4 6304and2 | 84.Jand83.1 18.9—20.3
» » 50%, | Y, n. 50 24 2 |} 848 17.9
| }
» See ioe ny.’ i Bs) 2 87.5 14.3
Water 1/, n. 50 F .63804and2 |90.5and89.0 10,5—12.4
Methyl alcohol i Pais a) 2 T4 % | do.1

Aleohol and methy! alcohol alter the relation of the transformation
to the disadvantage of the benzidine and the effect becomes greater
when the amount of water becomes less. This may be caused by
the circumstance that in another medium the reaction may take a
different course (for instance, the velocity of the formation of diphe-
nyline may increase) but it is also possible that the deviation must
simply be attributed to the increased solvent action which dilute
alcohol exerts on hydrazobenzene or an intermediary product of the
reaction. It is nof due to an increased solubility of benzidine sulphate
in dilute aleohol as has been proved by a purposely made direct
experiment.

II. INFLUENCE OF THE KIND OF ACID.

a) Temp. 100°. Water.

; | | nuigenin of ad | Mgr. mol. | =

Acid. Concentration. | 9/, benzidine,

| in mgr. mol. | bydrazobenzene

|. =. he eee laa
HCl 0.03 n. 4 1.6304 66.4—70.6
HNO, 0.05 n. 6.4 1.6304 67,.3—71.7
HS0, | 0.03 n. 4A | 1.6304 | 634

|
HBr | 0.03-n. 4 1.6304 | 65.8

As at 100° a small quantity of azobenzene or aniline may be
formed (the formation of the latter has not been investigated for
the weak hydrochloric acid concentration) the figures for the forma-
tion of diphenyline would be valueless and they have, therefore, been
omitted in table III. Those for benzidine are probably a little too
Jow as the formation of azobenzene could not be entirely avoided.

( 265 )

b) Temp. 25°. 50 %, Alcohol. Columns as under I and IL.

HCL. BaMrh es ne aa 50 2 84.8 17.9
HNO,. 1 50 2 82.2 4.7
H.SO,. Ih n. 50 9 | 29.8 11.4

CHCl.COOH. Wyn. 50 | 9 |. 885 | 19.8

|
Except for sulphuric acid which yields a higher value, the relation
of the transformation does not differ much in the case of the other
acids.
IV. INFLUENCE OF THE TEMPERATURE.
a) Alcohol of 50°. Hydrochloric acid.

z, ; [ Voi bof deat a ey
| one Amount of Mer. mol. Weight of GSpneBY
Temp. acid in ("/o benzidine. line on 100
| ofthe ae mgr. mol. | Pe | parts of benzidine,
|
0° | Od a 5 hid | 87.8 13.9
95° 1, De a0 2 84.8 17.9
50° | 1) n. 50 2 79.0 26.6
75° 1) n. 50 bee 67.4 48 4
|
4) Water. Hydrochloric acid.
4° Mon. | 50 1.6304 | 90.5 10.5
po Y/, n. | D0 y 89.0 12.4
/ | | i
ait nn. | 50 Pr! oh 86.6 15.3
| | | aes
75° Lae | 50 peas | 80.8 23.8
des = OY? a. ob 9 74.9 33.54
| { | |
400° | O203 ne.) 4. 1.6304 | 66.4—70.6 50.6—41 .6
| i

The figures given in the tables are in most cases the average of
several fairly concordant determinations.

The influence of the temperature as shown by this table is again
the same for both solvents and is shown by a fall in the ratio of
the transformation with a rise in the temperature.

The following observation should be made as to the last column
contained in these tables; the substance which was not precipitated
as benzidine sulphate is supposed to have been converted into
diphenyline. This, however, has only been once isolated as such, so
that it is not impossible that other bases besides diphenyline may
have been formed, the sulphates of which are soluble in water. As
other investigators have already taken up this subject, Dr. van Loon
has not extended his research in that direction.

The graphic vepesentations, following here, are those of the above
mentioned tables,

Fig. I.

i=]
=]
—

Influence of the concentration of the acid on the ratio of transformation.
Temp. 25°.

Standard of the hydrochloric acid.

Pe) i=) oO
an ~ uw

w Oo w
oO N wo o P)

Formed benzidine in procents.

Figuur II. Influence of the amount of alcohol on the ratio of transformation.

0.1 n. hydrochloric acid, ¢ = 25%,
Ee ee 2 eee fo)
; a
. =
=
iS)
<=
9
ite
3
_—
cm
a
~
fo} o
See
i)
_—
=
: &
=
5
=
é =
N n
~~
S
o
2
~
wu wo ro) 3) =) wo S} 2 a
x = Es) 8 N R 3S o To) a my

100

Formed benzidine in procents.

Figuur ILI. Influence of the temperature on the ratio of transformation.

100 ,

1.— n. hydrochloric acid

100°

ra)

& ©
be

7 5
os
oS
>

° 2

oO a

Tt =
®
onl

°o

[~) 0 o [o)
fe = 3 3 u R 8 8 iB 0

Foymed benzidine in procents,

( 267 )

Dr. van Loon has also been engaged in determining the velocity
of the transformation. An excess of finely powdered lydrazobenzene
was introduced into dilute alcohol, to which had been added acid of
a definite coneentration, the mixture being vigorously stirred. At
stated times certain quantities of liquid were withdrawn from the
mixture and the amount of benzidine was quantitatively determined.

If C, is called the concentration of the benzidine formed, Cyc
that of the hydrochloric acid at any moinent, the equation

d Cy KC
ag =e C* AO!
was found to represent the transformation; in this ¢ is the time (in
minutes) and AC the reaction constant. No special figure is given for
the concentration of the hydrazobenzene as this may be taken as
constant in the modus operandi followed.

The transformation is due to the hydrogen ions of the acid, for
on comparing the action of hydrochloric acid and dichloroacetic acid
the reaction constant was shown to be proportional to the degree of
ionisation of the acids employed. This caused Dr. van Loon to sug-
gest that during the transformation two H-ions are first linked to
hydrazobenzene forming

Or BN NH CE
H+ H+
and that then the repulsion of the two positive charges causes the

molecule to break up between the two nitrogen atoms, whereupon
the two portions again unite in such a manner that the positive
charges are at a greater distance from each other. This representation
accounts for the presence of C*yo in the equation of velocity, as
according to this equation one mol. of hydrazobenzene reacts with
two H-ions.

Chem. Lab. Univ. Groningen, July 1903.

Chemistry. — “The transformation of diphenylnitrosamine into p.-
nitroso-diphenylamine and its velocity.” By H. Raxen. (Com-
municated by Prof. C. A. Lopry pr Bruyn as communication
N°. 6 on intramolecular rearrangements).

(Communicated in the meeting of September 26, 1903).

In 1886 Orro Fiscunr discovered the interesting fact that under
the influence of alcoholie hydrochloric acid the nitrogen-combined
nitrosogroup of methylphenylnitrosamine changes place with the
para-hydrogen atom of the benzene nucleus and is thus converted
into the isomeric nitrosobase.

( 268 )

7 CBs : ZNSE
Ne 80 —> ON Nhe Bes .

FiscHer and Ep. Hepp have made a closer study of this reaction
and found it to be a general one’); it also takes place with
diphenyInitrosamine.

It was deemed of importance to study the exact conditions under
which this transformation takes place and particularly to learn its
order by means of a determination of the reaction velocity. A method
which permitted the quantitative estimation of the two isomers in
presence of each other with sufficient accuracy, was not at hand.
The chemical behaviour of the two isomers does not differ greatly
and the nitrosobase (at least in this case) is far too weak to be
titrated. It was therefore attempted to utilise the difference in colour
of the two isomers; diphenylnitrosamine has a faint yellow colour,
which in dilute solutions may be neglected. The nitrosobase however,
in combination with hydrochloric acid forms a brown powder whose
dilute alcoholic solution is deep yellow, whilst more concentrated
solutions are dark brown or red.

It was therefore decided to carry out the measurements by means
of a colorimetric process using the polarisation-colorimeter of Kriss.
An unexpected difficulty arose, however, owing to the fact that
different preparations of the hydrochloride gave greatly different results
when examined in the colorimeter, although they had been prepared
in exactly the same manner. As it was, of course, necessary to
prepare the standard liquids with the perfectly pure salt, I have
taken a great deal of trouble to obtain this. It appeared that a
solution of this salt is slightly decomposed and darkened by the
oxygen of the air and by prolonged contact with excess of hydro-
chloric acid; the salt was therefore prepared in an atmosphere of
carbonic acid and under specified conditions. The compound was
taken as pure when different preparations gave the same result in
the colorimeter; an analysis was of no service. And after it had
been found that the free base (which in the solid state forms steel-
blue needles) exhibits the same colour as the hydrochloride in dilute
alcoholic solutions, the basis of the measurements was obtained.

From the colorimetric identity of the free base and the hydro-
chloride it follows that the latter, in very dilute solutions, must be
completely alcoholytically dissociated and also that only solutions of
a certain degree of dilution are comparable with each other.

1) Ber. 19. 2991. 20. 1247. 2471, 21, 861. Ann. 255. 144, (1886—1889) etc.

— ae ee a ee

( 269 )

The concordant and very definite results obtained during the
measurements may in turn be taken as a proof that the standard-
comparison solutions were trustworthy.

Experiments were made in alcoholic solution with hydrochloric
acid as catalyzer.

The results are briefly as follows:

1. The reaction is one of the first order.

2. The reaction constant is proportional to the concentration of
the hydrochloric acid causing the transformation. In absolute ethy|
alcohol at 85° (time in hours) was found for

1 mol. HCl 2 mols. HCl 3 mols. HCl
k = 0.0081 0.018 0.026

3. Addition of water causes a serious fall in the reaction con-
stant; for instance, for ¢—= 35° and 3 mols. HCl in abs. alcohol:
k = 0.026; in 92:5°/, alcohol: £ — 0.0026.

The water apparently withdraws a portion of the hydrochloric acid
or renders it less active.

4. The temperature coefficient is very great; about 5 for each 10°.

We may therefore draw the general conclusion that the trans-
formation of the nitrosamines into the mitrosobases is a real intra-
molecular displacement of atoms. This is all the more likely if we
consider that in this case the velocity with which the transformation
product was formed, was measured. This result remains the same if
we suppose that at first (with unmeasurably large velocity) an
intermediate additive product was formed from the nitrosamine and
the hydrochloric acid acting as catalyzer. We then have, practically,
measured the transformation of the latter into the isomer; that trans-
formation however requires also an intramolecular rearrangement.

We shall later on return to the possibility of the occurrence of
an intermediate product. Further particulars will then be communi-
cated as to the action of other catalyzers and on the influence of
other solvents on the migration; experiments in this direction are
already in progress.

( 270 )

Physics. — “The periodicity of solar phenomena and the corre-
sponding periodicity in the variations of meteorological and
earth-magnetic elements, explained by the dispersion of light.”

By Prof. W. HH. Junwws.

(Communicated in the meeting of September 26, 1903).

Table of contents.
Introduction.
I. The path of the projection of the Earth on the Sun. The probable origin of the
11-year period.
Il. The variability of the solar radiation.
Ill. The periodical variations in the appearance of the Sun.
1. Sun-spots and faculae.
2. Prominences.
IV. The periodicity in the variations of meteorological and earth-magnetic elements.
1. Do these phenomena require the hypothesis that the Sun exhibits a varying
activity ?
2. Effects of the movement of the Earth through the irregular field of the
Sun’s radiation.
A. The semi-annual and annual periods in the position of the Earth in
the irregular field of radiation.
B. The periodicity of the fluctuations of illumination which coincides with
the periodicity of solar phenomena.
3. Polar lights.
4. The annual variation in the diurnal inequality of terrestrial magnetism.
5. Magnetic disturbances.
G. The annual variation in the daily oscillations of atmospheric pressure.
7. ‘the annual and secular variations of atmospheric pressure.
8. Cosmic influence on other terrestrial phenomena.
Summary of results.

INTRODUCTION.

The whole science of astrophysics rests on the hypothesis that
the same laws, which we have recognized by observation and
experimental research, hold good for other celestial bodies as well
as for the Earth, and that we are justified in applying to the Sun
and the comets, to nebulae and double stars, the results of thermo-
dynamics, of spectrum-analysis, of the theory of electrons. It would
therefore be illogical to make an exception with regard to our
knowledge of the refraction and dispersion of light in masses of
variable optical density ; and by adhering to the supposition, that in the
Sun and its nearest vicinity the light travels in straight lines, we
should take an untenable standpoint.

=. .

i te

—

( 2a)

The results of some recent investigations ‘) all tend to confirm the
hypothesis that the causation of anomalous dispersion is a general
property of matter. Thence, even highly rarefied gases, whose density
is unequally distributed, cause some kinds of rays to be considerably
deflected. All the conclusions arrived at by Youne, Lockyrr and
others, as to the thickness of the various concentric layers in the
solar atmosphere, the velocities of the prominences, the displacement
of matter in the sun-spots, the dissociation of elements in the Sun
ete., must be sacrificed in so far as they are based on the erroneous
notion that the objects are situated in the exact direction where they
are seen by us.

A. Scummpt?) has gone so far as to demonstrate that the sharply
defined circular outline of the Sun’s dise is no proof of the Sun being
a spherical body. Owing to the curvilinear propagation of the rays,
a gradually fading luminous mass of gas might appear to us as a
sharply outlined dise.

We may therefore be allowed to consider the Sun an unconfined
gaseous mass.

By taking also into account the laws of the anomalous dispersion
of light, we sueeeeded in finding explanations for almost all the
phenomena observed on the surface of the Sun and on its edge *).
We felt justified in starting from the simple supposition that in the
gaseous, unlimited body of the Sun, the several elements are not
locally separated but intrinsically mixed. Perhaps future investigations
may lead us to admit that in the solar body some elements are
locally separated, but I think that the present state of our knowledge
regarding the properties of sun-spots, faculae and prominences does not
warrant such an assumption. |

Our new conception of the Sun leaving no longer any room for
the hypothesis of a periodical activity manifesting itself in violent
eruptions, we are naturally led to inquire whether all the phenomena
attributed to this cause, may equally well — perhaps better — be
explained as effects of the dispersion of light.

The following data may assist in the elucidation of this question.

1) O. Lumwer und E. Prinesnem, Zur anomalen Dispersion der Gase, Physik.
Zeitschr. 4, S. 430—431. 1903.

H. Fert, Die anomale Dispersion der Metalldiimpfe. Phys. Zeilschr. 4, $. 473— 476.

H. Eserr, Die anomale Dispersion und die Sonnenphiinomene, Astr. Nachir. 162,
S. 194—195.

2) A. Scummpr, Die Strahlenbrechung auf der Sonne. Stuttgart, 189°.

3) W. H. Juuus, Proc. Roy. Acad. Amst. II, p. 575—588; Ill, p. 195—203;
IV, p. 162—171; 589—602; 662—666.

I. THE PATH OF THE KARTH’S PROJECTION ON THE SUN.
THE PROBABLE ORIGIN OF THE 11-YRAR PERIOD.

If it be true that sun-spots, faculae and prominences are effects of
‘ay-curving, if stands to reason that their form and situation will
depend in a far greater measure on the position occupied by the observer,
than would be the case, if they were themselves light-emitting bodies.

A correct idea of the movement of the Earth with respect to the
revolving body of the Sun must therefore be the basis of our invest-
igations. Unfortunately it is impossible to give an absolutely exact
idea of this relative motion, for not only are we in ignorance of the
exact period of the Sun’s rotation, but it is extremely difficult to
define the meaning of that term, because we take the Sun to be a
mobile gaseous mass. On the other hand it is quite evident that we
are dealing with a periodical phenomenon ; the only question therefore
is, Whether we shall succeed in selecting from the various values
on record, the one which has the greatest significance from our
point of view on Earth.

As a matter of course we select a synodical period of revolution.
It is a known fact that different values for the period are obtained
from the movement of spots and faculae, varying from 26 to 30 days
according to their heliographie latitude. By the application of DoprLEr’s
principle, Dunér found that near the equator, the period of rotation
of the photosphere was 25,46 days and at 75° latitude up to 38,55
days. In 1871 Hornstein observed in the deviations of the magnetie¢
declination at Prague a period of about 26 days, which other invest-
igators have found also in various meteorological phenomena. The
results obtained led to the conclusion, that the rotation of the equa-
torial regions of the Sun exercises a greater influence on the Earth
than that of the other zones.

From the following table it will appear how indefinite as yet is
our knowledge of the period of the Sun’s rotation :

Srratonorr (faculae near the equator) 26,06 5
CARRINGTON (sun-spots near the equator) 26,82 ')
Dvnér (photosphere near the equator) 25,46 *)
Hornstem (magnetic observations at Prague) 26509. 7)

Ap. Scumipt (most probable value deduced from the mag-
1) Arrnuentus, Lehrb. d. kosmischen Physik, p. 148.

2) This value is communicated by Duner as being the sider eal period of rotation,
and appears to have been generally accepted as such. Prof. J. C. Kapreyy, however,
kindly informed me that in Dunér’s interpretation an error has slipped, and that
he result must be taken as the synodical period.

( 273 )
netic observations of Broun, Hornstein, MULLER and Liznar,
until 1886) 25,92 *)
Ap. Scumipr (magnetic observations at Batavia) 25,87 %)

VAN DER Srok (barometrical observations at Batavia and
St. Petersburg and magnetic observations at Prague and

St. Petersburg) 25,80
von Brzoup (thunderstorms in 5. Germany) 25,84
Exnotm and Arruentus (polar lights) 25,929*)
BiceLow (meteorological and magnetic observations in the

United States of America) 26,68 *)

The justification of the choice we make between these different
numbers must for the greater part be found in the value of the con-
sequences we derive from it. However, there are some good reasons
why we should prefer a priori the value obtained from investigations
on the frequency of polar lights by Exknotm and Arruenius. For
although the results of others (especially those of Ab. Scuurpr and
of VAN DER StTOK), from a point of view of careful and critical reaso-
ning, are of no less value than those of Eknoum and Arruenivs,
the variations of the barometer and the oscillations of terrestrial
magnetism are phenomena of a more complicated nature than polar
lights. They are influenced by local conditions, the distribution of
land and water, ete.; because they partly depend on the circulation
in the lower layers of the atmosphere. On the other hand it would
appear that the polar lights take their origin principally in the higher
layers and thus, by revealing to us more directly the action of the
Sun’s radiation, they will propably lead to a sharper determination
of the period. |

Whilst the periods of rotation necessarily differ in the various
parts of the Sun’s mass, there must be somewhere in the plane of
the equator a series of points, where the synodical period of rotation
is 25,929 days. Through these points we imagine a sphere £, the
centre of which is laid in the centre of the Sun, and we make
the sphere rotate around the Sun’s axis with a constant angular
velocity, so as to bring its synodical period of rotation at circa
25,929 days. This sphere represents to us “the rotating Sun’, but
we must keep in mind that with respect to 6 the various parts
of the gaseous mass may alter their position.

1) Ap. Scummr, Sitz. Ber. Kais. Akad. d. W. Wien, Bd. 96, p. 990 and 1005.

2) VAN peR Stox, Verh. Kon. Akad. v. W. Amsterdam, 1890.

3) Arruentus, Lehrb. d. kosmischen Physik, p. 148.

*) Bigetow, Un. States Weather Bureau Bulletin No. 21, Washington, 1898. See
also Scuuster’s criticism, Terrestrial Magnetism III, p. 179.

( 274%)

The line AZ, which connects the centre A of the Earth with
the centre Z of the Sun, intersects B at the point P. We call this
point “the projection of the Earth on the Sun” and will determine
its track on B.

The inclination of the Sun’s equator on the ecliptic is 7°15’. About
the 4 of June and the 6 of December the Earth passes through
the nodal line.

Fig. 1 represents part of the sphere B; HE" is the intersection

Bigs A.

with the ecliptic, QQ’ that with the Sun’s equator. On the 4* of
June the Earth’s projection is in P?,. Through this pomt we draw
the first meridian J/. In the space of about 25,929 days J/ has
made a synodical revolution and is intersected for the second time
by the line AZ (not marked in the diagram) but this time at the
point P,, a little to the north of the equator. In the interval P has
been describing one convolution P?, P' P" P, of it helical course.

The next points of intersection ?, and P, of the path of P with
the first meridian again lhe somewhat more to the north, but about
the 4% of September the path has reached its utmost latitude 7°45!
and then gradually descends towards the equator, which on the 6" of
December it intersects a little beyond P..

All the points of intersection for one year are marked on the
meridian J/ in its first position. P, to P,, lie in the southern
is reached after 14 25,929 — 363,006 days; the
sideral year has 365,256 days, consequently P,, does not coincide
with P,; the track of P intersects the Sun’s equator 2,25 days later.

hemisphere. P,,

During the second year, /P, in its helical course, passes through
entirely different points of our spherical surface than in the first year,
and so do the suecessive annual spirals; they each time skip an angle

a ee ee a ee ee ee vee.

= “et

( 275 )

2,25

of 2 a. The spirals of the twelfth and thirteenth year

25,929 7%
come again very close to that of the first year and lie on each side
of it. It is therefore reasonable to expect that after a period of
a little more than 141 years a very similar succession of incidents
will take place. *)

It now remains for us to consider which conditions and phenomena
may be governed by the position of ? on the sphere.

The Sun is an immense mass of matter, and considering its age
we may take it for granted, that within the memory of man it has
remained in an almost stationary condition. We know that the
violent eruptions which have been thought to take place on its sur-
face, have led to a quite different conception, but at present we can
realise *) that relatively small local variations in density, such as
necessarily must occur in vortices along the surfaces of discontinuity
between stationarily streaming layers of gas, are quite sufficient to
produce strongly marked variable optical effects, such as promi-
nences etc.

The large currents of the general solar circulation must be
cyclic movements, which do not perceptibly alter the configuration
of the entire mass, only causing along the surfaces of discontinuity
a somewhat varying distribution of matter, due to undulations and
whirling. We admit that on account of the Sun not being perfectly
symmetrical around its axis, the movability of the parts involves a
gradual change of form, but this change we will leave for the
present out of consideration.

The rays emanating from the intensily bright core of the Sun
reach us, whatever be the position of the Earth, through a space in
which matter is unequally distributed. P therefore determines the
principal characteristics of what might be called the ‘‘optical system”
through which we see the Sun. When / shifts its position, this
system changes with it; when P for the second time traverses the
same path on the rotating sphere, to the eye of the observer on Earth
all the phenomena which are produced by the refraction of light in
the gases of the Sun, will repeat themselves in the same order.

1) Had we for the Hornstein period taken 25,924 days, instead of 25,929,
25,924
then the mean value of the spot period would have been —> 39
therefore we wished to supplement the table on p. 272—273 with a value derived
by theoretical considerations from the I1-year period, the number 25,924 would
commend itself.

2) W. H. Juuus, Proc. Roy. Acad. Amst. IV, p. 162—171.

= 11.17 years. If

Il. THE VARIABILITY OF THE SOLAR RADIATION.

It is well known that the composition as well as the intensity of
the Sun’s radiation is incoustant. As to the variation of the total
intensity, this could not be ascertained by actinometrical measure-
ment, owing to the capricious disturbances caused by the clouds;
it has therefore been determined in an indirect way, from the values
of the mean temperature all over the Earth. But the variability in
the composition of the light has been revealed by a careful study of
the Fravnnorrr lines which has shown that several lines are at one
time more enhanced than at others (JrweLn') Hawn’), Laneney *)).
In the spectrum of sun-spots also, in which several lines are com-
paratively very wide, N. Lockyrr ‘) noticed that the mean type of
the spot-spectrum undergoes a periodical modification, the period of
which coincides with that of sun-spot frequency.

As yet we have no certain indications that this periodicity also
exists in the varying aspects of the Fraunnormr lines of the average
photosphere spectrum. The abnormal spectrum photographed by
Haun‘) in 1894 (i.e. at a sun-spot maximum) presented, as has been
shown elsewhere "), this peculiarity that the lines, which in the chromo-
sphere spectrum are generally strongly marked (principally belonging
to Fe, H, Ca, Sr, Al, Ti), were very faint, whilst the strong lines
(belonging to Zr, Mn, Y, V and some of unknown origin) did
not correspond to any of the chromospheric lines.

The periodical variability observed by Lockyer in the spot spectrum
consisted’ herein, that when at spot maximum the most enhanced
lines were selected, they proved for the greater part to be “unknown
lines” i.e. lines which in the normal solar spectrum are extremely
weak, and that the strong lines of Fe, Nz, 7%, which during minima
of spot periods often appear very wide, were then searcely visible.

1) Jewett, Astroph. Journ. 3, 89—118, 1896; 11, 234—240, 1900.

2) Hate, Astroph. Journ. 3, 156—161, 1896; 16, 220—233, 1902.

3) Lanatey, Annals of the Astroph. Observatory of the Smiths. Instit., Vol. I,
1900. On p. 208, 209 and 216 mention is made of irregular changes in the heat
spectrum (especially in ¢, ¥ and ©), which do not seem to be occasioned hy
absorption in our atmosphere and are therefore the effect of cosmic influences.
Lanatry’s excellent method of investigation may prove of the utmost value in the
study of the variability of the Sun’s radiation, as il gives directly comparable
values for the energy of the various kinds of rays in this important part of the
spectrum.

4) Lockyer, Proc. Roy. Soc. 40, p. 347; 42, p. 37; 46, p. 385; 57, p. 199;
67, p. 409, (1886—1900).

5) Hate, Astroph. Journ. 16, 220—233.

6) W. H. Junius, Proc. Roy. Acad. Amst., IV, 589—602.

( 277)

The analegy between these abnormal appearances and those of the
spectrum of HaLe is obvious. Unfortunately the part of the spectrum
investigated by Lockyer (extending from 24868 to 25893) lies entirely
outside the part photographed by Hane (4 3812—4 4132) which
renders direct comparison impossible, but the parallelism to which
we pointed, makes us anticipate that also in the aspect of the average
photosphere spectrum, as well as in the spot spectrum, the I1-year
period will be found.

LockyEr holds that in years of spot maximum the Sun’s activity is
greatly increased; that the more violent eruptions then cause a
considerable rise in its temperature. To this fact he ascribes the
appearance of “unknown lines” and the weakening of the known
lines, on the same principle as that which governs the variations
produced in the emission spectra when passing from the are to the
induction spark *).

On the other hand Cr. NorpMann *) has published the results of
an exhaustive inquiry into the variations of the temperature all over
the Earth, between the years 1870 and 1900. From his statements
it appears that the mean temperature undergoes indeed a_ periodical
variation comeiding with the sun-spot period, but in this manner,
that the maxima of the curve of spot frequency correspond to the
minima of the temperature curve. This result seems to us a serious
objection to the views of Lockyrr.

We will now see if by applying our theory, based on the disper-
sion of light, it is possible to find a consistent explanation for the

To us the peculiarities of Lockymr’s spot spectrum are phenomena
of the same nature as those observed in the abnormal spectrum
described by Hann. We have found an explanation for the latter by
supposing that just at the time when the photograph was taken,
a long corona streamer was directed to the Earth, so that the line
of sight almost coincided with the tangent af a surface of discon-
tinuity. The visible structure of the corona with its long, almost
straight lines, is to us an indication that the light of the Sun, accor-
ding to the position occupied by the Earth, must at one time reach
us along sharply defined surfaces of discontinuity and at others not.
Provisionally neglecting possible variations in the distribution of
matter which might fake place in the Sun itself, the condition for
each successive moment will be accurately defined by the place

1) Lockyer, Proc. Roy. Soc. 67, p. 411—416, (1900).

*) Cu, Norpmany, C. R. 136, p. 1047—1050, (1903).

Proceediigs Royal Acad. Amsterdam. Vol. V1,

Gores

occupied by P in its helical course on the sphere, and we need only
admit that at sun-spot macinum the separate rays of the total beam
of light reaching the Harth, and from which PA ts the central line,
more often pass for a considerable distance closely along surfaces
of discontinuity, than in times of minimum. If we admit this view,
then our explanation of the spectral peculiarities reads thus:

A monochromatic beam of light, passing on its way closely along
a surface of discontinuity, will undergo a marked change of diver-
gency, When, for those particular waves, the medium has a great
(positive or negative) refraction constant. We may rather expect an
increase than a decrease of the divergency, because the medium
becomes more rarefied with the increasing distance from the Sun’s
centre. As a rule such a beam will reach the Earth with a lesser
intensity than the beams of rays which undergo less refraction. The
consequence is that, through the scattering of neighbouring rays, all
Fractnnorer lines which cause anomalous dispersion will have a
somewhat darkened background. With some lines this background
is broad (H, K, the lines of hydrogen, iron, in a word, all the
well known widened lines of the solar spectrum); with others it is
narrow; it depends on the proportion of these elements contained
in the solar atmosphere and on the shape of the dispersion curve ;
but at all events, the mean intensity over the entire spectrum must
have become less, by the light passing along the surfaces of discon-
tinuity. In years of sun-spot maxima this happens more often
than at minima, and this gives us the explanation of the results
obtained by NORDMANN. *)

It now remains for us to prove that the same cause, which in
the period of spot maximum makes weak lines in the spot spectrum
fo appear strengthened, makes also strong lines to appear weakened.

We again refer to our explanation of the abnormal spectrum of
Hate. At that time we supposed the structure of the corona to be
“tubular”. Later considerations have induced us to define the structure
of the exterior parts of the Sun as rather ‘lamellar’, a correction
1) The kinds of rays which by dispersion have disappeared from the sunlight
visible to us, travel to other parts of the universe, far from the orbits of the
planets, where they would be seen as faculae, chromosphere light and corona
light. If it were possible, by means of the spectroscope there to study the mean
radiation, we should find in the continuous spectrum some bright lines, fying on
both sides of the real absorption lines and in close proximity to them. Some slars
present this phenomenon. It may, therefore, be explained by the assumption that
they are bodies resembling the Sun, but that our line of sight forms a rather
large angle with their equator.

( 279)

which does not affeet the arguments of our former conclusions.
When the light travels through this stucture almost parallel to the
surfaces of discontinuity, the most strongly refracted rays follow
undulating paths (vide Proce. Roy. Acad. Amst. IV, p. 596—597).
They are kept together, are so to speak guided along the lamellar
structure, and their intensity when reaching the Earth is greater than
that of rays which undergo a lesser refraction. Consequently in the
Fracyuorer lines which show a broad background (being produced
by elements which are rather strongly represented in the coronal gases
and which therefore, even during the minima of spot periods, give rise to
marked anomalous dispersion) the parts nearest to the true absorption
line will at periods of spot maxima appear brighter. In fact, the
ereater ray-curving, which marks these periods, enhances the shadowy
background, but at the same time it restores the light to the central
parts of the band. Thence the impression that the absorption line
has been weakened.

On the other hand, lines with a faint, narrow background will
at times of maxima appear considerably strengthened, because their
brighter central parts, if present, are too narrow to be visible.

The explanations here given are supported by the results of an
experimental investigation. a detailed account of which will appear
elsewhere. Our object was to ascertain the action of a system of
artificial surfaces of discontinuity on the absorption spectrum of sodium
vapour. In principle the apparatus is similar to that described in my
paper: “On maxima and minima of intensity sometimes observed
within the shading of strongly widened spectral lines’). A beam of
electric light, which had first been passed through a long sodium
flame was directed on the slit of a big grating spectroscope. But a
great improvement had been since made in the burner. The aperture
is 75 ¢M. long and O15 ¢.M. wide; the supply of an adjustable
mixture of gas and air is so regulated that the flame burns evenly
over its whole length. A special contrivance within the burner
allows of the feeding of the flame with sodium vapour during the
experiment and regulating the quantity as required.

By means of this instrument we tested the effect on the absorp-
tion spectrum of the variations in the angle of inclination between
the planes of discontinuity and the beam of light; of modifica-
tions in the quantity of sodium vapour; of diaphragms on_ the
path of the rays, etc. All the phenomena observed may be explained

1) W. H. Jutrus, Proc. Roy. Acad. Amst. V, p. 665,
19%

( 280 )

from the different measure in which the anomalously dispersed rays
are curved; and the varying peculiarities of the sun-spot spectrum are
easily reproduced in this experiment. We make particular mention
of the fact that, when the flame is parallel to the beam of light, a
small quantity of sodium vapour produced very dark enhanced D
lines, e. g. 0.5 or 1 Angstr. units wide; by adding more of this
vapour the lines extended into very wide bands in which the central
portions became gradually brighter, leaving only a narrow, well-
defined central absorption line.

Ill. Tue pPeriopICAL VARIATIONS IN THE APPEARANCE OF THE SUN.
1. Sunspots and faculae.

In a communication dated Febr. 19007) I started the hypothesis
that sun-spots are the results of refraction, more especially of ano-
malous dispersicn. Since then Esrrr*) has published an experiment
in which, through the dispersion of the light of an are lamp in a
flame of burning sodium, effects were produced, closely resembling
the phenomena observed in sun-spots, such as their spectral peculiar-
ities, reversals, displacements, ranification of the lines, ete.

I have recently repeated this experiment, but instead of using
pieces of burning sodium, I employed the long flame, which afforded
ereater facility for controlling the operation and noting the phenomena.
They were substantially the same as those observed by Eprrr.

Moreover, the use of the long flame enabled us to make some
observations with respect to the optical effects of almost flat surfaces
of discontinuity. Similar surfaces being important factors in our
theory, a short description of ow experiment may be found useful.

The light of an are lamp was concentrated on a diaphragm 15
m.M. in diameter, which was placed almost in the focus of a second
lens. The emergent rays were slightly divergent; within this beam,
at a distance of 20 M., a telescope was placed and focussed on the lens.
By pushing out the eye-piece an enlarged image of the lens was
projected on a screen; this represented the Sun. Between the lens
and telescope, but close to the former, was placed the long flame.
When the mouth of the burner was so adjusted as to lie exactly
parallel to the axis of the beam, so that the prolongations of the
surfaces of discontinuity intersected the objective of the telescope,

1) Proc. Roy. Acad. Amst. I, p. 585—587.

2) H. Evert, Die anomale Dispersion gliithender Metalldiimpfe und ihr Einfluss
auf Phiinomene der Sonnenoberfliiche. Astron. Nachr, 155, S. 179—182.

( 281 )

there appeared on the screen a system of two very dark spots,
corresponding to the two sheets of the tlame, in which the combustion
principally takes place. Even a slight change in the position of
the burner had a marked effect on the form of the spots. By
turning it a few degrees round a vertical axis the distinct spots rapidly
disappeared ; but then, of course, over a larger space of the illu-
minated surface quivering shadows of varying intensity remained visible.

Let us now more fully consider, what, in the present state of
our knowledge, we may take the structure of the gaseous Sun to
be. We find there the surfaces of revolution, first described by
Emprn '), surfaces of discontinuity, where according to v. HELMHoLrz
undulation and formation of whirls take place. It is not unreasonable
to suppose that the striped appearance of the corona presents to us,
in some way, the generatrices of these surfaces, although at present
we cannot enter into the question of how this takes place.

As a rule it will be found that the density varies most rapidly
in the direction perpendicular to the planes of discontinuity ; and
wherever the whirling process is going on, the density will be least
in the axes of the whirls.

In broad terms, therefore, the structure of the Sun may _ be called
lamellar and at the places where whirls are formed, we would
rather call it tubufar. The position of the whirls in the surfaces of
discontinuity is varying, but the average direction of the axes of
the whirls coincides with the generatrices of the surfaces of revolution.

The prolongations of some of the surfaces of discontinuity intersect
the Earth; whenever this happens, our line of sight, when directed
on the Sun, very nearly touches a sheet of such a surface. These
sheets are projected on the Sun’s dise in the form of bands of greater
or lesser width, stretching parallel to its equator. The narrower these
bands are, the nearer our line of sight really touches the surfaces
of discontinuity and the greater will therefore be the effect of
refraction, i.e. the dispersion especially of the anomalously refracted
light. The width of these projections on the various parts of the
Sun’s dise will of course vary with the position occupied by P on
the sphere A.

If the axis of a whirl falls exactly in the line of sight, we see a
dark speck. In parts where the whirling process is very active, the
separate axes of the vortices need not be parallel to each other,
but it is essential that they should all lie in the surfaces of discon-
tinuity. This explains why a spot, i.e. an accumulation of a great

*) R. Empey, Beitriige zur Sonnentheorie. Ann. d. Phys. [4], 7, p. 176—197.

( 282 )

many whirls, notwithstanding the Sun’s rotation, may remain visible
for a lone time, although continually changing its form, for we
really look along a succession of other axes of whirls. The experiment
described above, may serve to illustrate the fact that whirls, situated
in surfaces of discontinuity which are not projected in very narrow
bands, will not be seen as distinet spots. This is e.g. the case with
whirls, formed at more than 30° heliographic latitude. Near the
equator also spots are rarely seen; but this follows, according to
Eupen’s theory, from the circumstance that in those regions there
is less cause for the formation of whirls.

To resume, spots will be seen in those parts where the distri-
bution of matter is such as to cause an abnormal merease in the
divergency of the beams of light on their way to the Earth. As a
matter of course, there must also be parts where the distribution of
density causes a decrease in divergency and these are the places
where faciulae are seen, On a smaller scale we find the same con-
trast in the so-called “pores and granulations” of the photosphere.
All these solar phenonema are subject to rapid changes, because the
complicated optical system through which the rays of light reach us,
continually alters its position with respect to the Earth.

The periodicity of the sun-spots. We will now endeavour to prove
that in order to explain the 11-year period in the frequency, the
total spotted area and the mean heliographic latitude of the sun-spots,
we need not admit the hypothesis of a periodical change in the Sun's
‘aetivity .

Let us for a moment suppose that all actual changes in the form
of the Sun suddenly came to a stand-still, but that its rotation con-
tinned; even then an w-year period would be observable in the
Sun's appearance, the position of spots and faculae ete., because each
time, after w years have elapsed, the point / follows again nearly
the same path.

However, the real configuration of the Sun is wot perfectly con-
stant (although probably its change is very slow and gradual)
and so we may consider the 11-year period to be the result of the
jot action of a continuous (perhaps somewhat irregular but not
necessarily periodical) change in the Suis surfaces of discontinuity,
together with the periodical variation in the position of the bLarth
with respect to the “average rotating sun.

We define the meaning of this latter expression by our sphere ,
whose synodieal period of revolution coincides with the period of

eirea 26 days, which has been noted in terrestrial phenomena.

€. 233")

It seems expedient here to enter somewhat further into the question
as to how the periodical change of position of our point of view
mImay cause the number of spots seen in the course of a year gra-
dually to decrease for a period of 6 or 7 years, then to go on
increasing, till after 11 years the maximum is reached again.

With that object we again refer to our spiral and start from the
14 convolutions of the year of spot maximum.

The second year’s spiral is slightly shifted with respect to that of
the first, but it runs still very close to it and therefore its position
with regard to the system of surfaces of discontinuity will resemble
that of the first, which was the most favourable for the observation
of spots; thence we may conclude that the difference between the
number of spots seen in the first and second year will be but small.

The spiral of the third year diverges again from that of the second
and is consequently somewhat farther removed from the spiral, which
traversed the series of optical combinations most favourable to the
observation of spots, and so on.

We must not lose sight of the fact that the track of P has but
a slight inclination with respect to the surfaces of discontinuity, so
that at one time the Earth may remain for a rather long while
under the influence of such surfaces, at other times, during much
longer periods still, may pass between them.

There is no reason to expect that the decrease in the number of
spots seen will proceed in a perfectly regular manner, but at all events
there must be a vear-spiral in which the circumstances are most
unfavourable for their observation; for in proportion as the twelfth
spiral is approached, which nearly coincides with the first, the con-
ditions must necessarily again improve.

The length of the spot period is irregular and the height of the
maxima varying. This would already be the case, were the Sun
totally stationary, tor the twelfth spiral of P does not exactly coincide
with the first; besides it is evident that modifications in the distri-
bution of matter may cause even greater irregularities in the successive
fluctuations.

2. Prominences.

On a former occasion ') we have already given an explanation of
the appearance of prominences and their spectral peculiarities, based
on our hypothesis that they are due to the anomalous dispersion of
the photosphere light in the whirling parts of the surfaces of discon-

1) Proce. Roy. Acad. Amst. IV, p. 162.

( 284 )

tinuity, which are seen projected on the edge of the Sun’s dise. It will
now be easy to determine in how far they are connected with spots
and faculae and to understand, that, like the spots and for the same
reasons, they may be expected to show a certain periodicity in their
frequency and place of appearance.

The so-called metallic or eruptive prominences are only seen in
the vicinity, at least in the zones, of the sun-spots, never in the polar
regions. Nebulous prominences, on the contrary, are found in all
latitudes. In accordance with owr theory this fact may be thus explained.
The anomalous dispersion of the kinds of light found m the spectrum
of the metallic prominences near the lines of Va. My, Ba, Fe, Ti, Cr,
Mn, is less intense than that of the light close to the lines of H, He,
(a; and therefore greater differences in density will be necessary to
produce eruptive than nebulous prominences (in which asa rule only
the lines of H, He and (i are seen). The results of EMpEN’s inves-
tigation in fact prove, that a more active formation of vortices May
be expected in medial latitudes than in the equatorial or polar regions.

The zones where prominences appear must extend farther than
those where spots are seen; for as soon as we have gained a clear
conception of the direction of the surfaces of discontinuity and of the
axes of the whirls in them, it becomes plain that to see spots, the
position of the Earth with respect to the structural elements of the
Sun is subordinate to preciser conditions than in the case of promi-
nences. For prominences are visible as soon as the line of sight,
directed on the apparent edge of the Sun, passes closely along a
series of whirls; more particularly so, when the line of sight touches
the surface of discontinuity near the whirling area. In order to see
spots it is not only essential for the line of sight to touch the surface
of discontinuity in the area of the whirls, it must at the same time
coincide with the direction of their axes.

The periodicity of promimences. The parts of the Sun’s edge where
at a given moment the prominences appear, will not only be determined
by the condition of the Sun itself, but at the same time by the position
of P. Consequently the periodicity in the frequency and position of
the prominences must agree with the periodicity of the motion of P.

A graphic survey of the periodicity of spots and prominences in
connexion with their heliographie latitude has been given by Sir
N. Lockyer and W. J. Lockyrr*') in a paper on “Solar prominences
and spot circulation from 1872—1901." In some of their former
communications?) the same observers had already alluded to the facet

l) Sir N. Lockver and W. J. 8, Lockyer, Nature 67, p. 569—9571, (1903).
2) The same authors, Nature 66, p. 249; 67, p, 377.

285.)

“that the epochs of maximum prominence disturbance in the higher
latitudes are widely different from those near the equator. The latter
are closely associated with the epochs of maxima spotted area, the
former occur both N. and S. at intervening times.”

Now it follows from our theory, thaf prominences are seen in
places where the line of sight touches whirling parts of surfaces of
discontinuity near the Sun’s edge; so it is evident that at spot maxima
this will happen most often in the spot zones, and that the most
favourable occasions for seeing them in other latitudes fal! at other times.

Therefore, although in the curve of prominence frequency the 11-
year spot period is easily recognized, vet in several points it deviates
from the spot curve. Smaller maxima and minima of frequency are
superposed upon the head curve and point to a three-year period.
We find a rational explanation for these minor fluctuations too in
the successive positions assumed by the Sun with respect to the Earth.

IV. THe PrRIODICITY IN THE VARIATIONS OF METEOROLOGICAL AND

BARTH-MAGNETIC ELEMENTS.

1. Do these phenomena require the hypothesis that the Sun
/ ff YI

exhibits a varying activity ?

In the preceding pages we ascribed the inconstaney of the solar
phenomena principally to the continuous change of the point of sight
from which we look at the Sun. We supposed the modifications,
produced in the general condition of the body of the Sun itself by
radiation and by the relative motion of the gaseous layers, to be
comparatively slight and regular. Our theory had no need of the
interference of violent eruptions, commotions, periods of increased or
decreased solar “activity”; it allowed us to consider the quantity of
energy emitted by the Sun in a unit of time, to be almost constant.

For this reason it would now at first sight seem more difficult
yet to account for the periodical variations of several terrestrial
phenomena which closely follow in their course the frequency of
spots and prominences. But even with the hypothesis of a variable
solar output as a starting point, as far as [I know, nota single theory
has been advanced in explanation of the connexion between sun-spots
and terrestrial phenomena, so convincing, that it would be a pity
to abandon it.

Let us briefly consider what has been attempted in that direction.

Periods of maximum spot frequency are marked by certain commo-
tions on Earth and by increased circulation; the rainfall is greater,

( 286 )

cyclones, polar lights, magnetic deflections are more frequent. But
because at those times the mean temperature over the entire Earth
is somewhat lower than in the minima periods') we come to the
conclusion that the total energy which reaches the Earth in maxima
of spot cycles must actually be less. This is our first objection to
any explanation based on a periodical variation in the total output
of the Sun’s energy.

Now it might happen that, although in years of spot maxima the
average output of solar energy be lessened, the emission exhibits at
those times a greater variability than at minima. Various and numerous
observations have been undertaken with the object of ascertaining
whether the appearance of spots and faculae, or their crossing the
central meridian of the Sun, was generally accompanied by excessive
manifestations of terrestrial phenomena, and the results proved that
this was not invariably the case. An exhaustive inquiry into this
question has been recently made by A. L. Corrin’). The investigations
of Farner SrmpGreaves, extending over the years 1881—1896, had
already clearly shown that periods of increased solar activity were
indeed marked by violent magnetic storms, but that many spots were
not accompanied by magnetic disturbances and that such disturbances
often took place when the Sun was spot-free. ‘These results’, says
Cortin, “are adverse to any theory which would place the cause of
inagnetic storms, and by the cause we mean the efficient cause, any where
on or in the vicinity of the Sun.” He himself for three years (1899—
1901) studied the appearances of the Sun’s face in connexion with
the magnetic curves registered at Stonyhurst. He found that the
aimual means of spotted area and of the variations in declination
fairly agreed; but his table on p. 207 shows that this is not the case
when the average results for each single solar rotation are studied ;
and the immediate comparison of the daily solar observations with
the diurnal magnetic curves shows more clearly still, that spots and
disturbances do not necessarily always go together. For example,
during a great magnetic storm on Febr. 12 1899, the Sun was
almost entirely free from spots, and the very large spot observed
in May L901, which persisted during two solar rotations, was not
accompanied by any unusual magnetic disturbance. Cortin comes to
the conclusion that sun-spots and magnetic storms probably are
correlated as “two connected, though sometimes independent effects
of one common cause.”

1) Cu, Norpmann, CG. R. 136, p. 1047—1050, 1903.

*) A. L. Corti, 5. J., Astrophysical Journal 16, p. 203—210, 1902,

If, therefore, spots and faculae ave not in themselves the factors
Which by their peculiar radiation of light and heat cause the supposed
fluctuations in the output of solar energy, it might be expected that
entirely different agencies play the most conspicuous part in the
production of the phenomena under consideration.

In this sense ArruHENIUS') has started an hypothesis in which the
latest discoveries in connexion with the kathodic rays, the ionisation
of gases, the properties of ions and electrons and the pressure of
radiation have been introduced. He attributes the said periodical
phenomena on Earth to solar matter, charged with negative electricity
and being propelled from the Sun’s surface by certain centres of
activity there present (thus accounting for the period of 25,929 days).
The amount of electricity thus generated varies with the Sun’s
activity, it being greatest at maxima of spot frequency. This solar
matter is scattered through space by the pressure of radiation and
causes the higher layers of the terrestrial atmosphere to be charged
with negative electricity. By the discharges kathodic rays and
polar lights are produced; the electrified particles, carried along by
the wind, form electrical currents which disturb the magnetism of
the Earth.

Several points of this theory have been criticised by Cu. NORDMANN *),
who offers an entirely different explanation for the variable influence
of the Sun on meteorological phenomena. He aseribes it to /ong
electrical waves, sent out by the Sun, more particularly in the regions
of spots and faculae, and at times of maximum spot frequency.
Whenever these Hertzian waves penetrate into the higher layers of the
atmosphere, they increase their conductivity and render them luminous.
In this manner he accounts for the fact that during spot maxima
stronger electrical currents are present in the atmosphere, magnetic
variations are more marked and polar lights more frequent and intense.

But we have seen before that neither important magnetic
disturbances nor intense polar lights invariably accompany very
conspicuous solar phenomena. NORDMANN’s theory therefore requires
the admission of the existence on the solar surface of separate
emission centres of long electric waves, independent of spots and
faculae. This hypothesis does not simplify our conception of the
constitution of the Sun.

bierLtow’) aseribes the influence of the Sun on the magnetism of

1) Arruenius, Rev. gén. d. Se. 13, p. 65—76; Lehrb. d. kosm. Physik, S$. 149—155.

2) Cu. Norpmann, Rev. gén. d. Sc. p. 379—388.

3) Bicetow, Solar and Terrestrial Magnetism, U. 8. Weath. Bur. Bulletin No. 21,
1898; Eclipse Meteorology and Allied Problems. Washington 1902. p, 104,

( 288 )
the Earth for the main part to direct magnetic action of the Sun;
he supposes the magnetic condition of the Sun to be very variable.
3ut as Lord Kenvix') has demonstrated that the solar magnetism
and its variability ought to be enormous to produce, by direct induction,
these disturbances of the terrestrial magnetism, BiGkELow also admits
a variable generation of electricity in the higher layers of the at-
mosphere, through the ionising action of the Sun’s inconstant radiation.
These views of BiggELow have been analysed and criticised by ScHUsTER?).

All these theories fail in one important point. Indeed, the meteoro-
logical and earth-magnetic disturbances generally manifest themselves
in such a manner that they cannot be considered simply an increase
or decrease of normal activity. For instance in the case of magnetic
storms, the disturbance-vector is entirely out of keeping with the
normal daily variations. The capricious origination and course of the
barometric depressions, which play so prominent a part in deter-
mining the weather conditions in many parts of the globe, cannot be
explained as merely resulting from increased ordinary atmospheric
cireulation; and many more examples might be added to these.

We must therefore consider the nature of the cosmic influence to
be such, that, although emanating from the Sun and striking the
Earth within cones whose opening is only 17,6" wide, it notwith-
standing acts very differently in the various regions of the globe.
Moreover, this influence distinetly shows a semi-annual periodicity.
As yet no theory, based on the conception of a variable solar output,
has been found to account for these striking characteristics of the
cosmic influence.

If then, in order to explain the periodicity of se/ar phenomena, it
has not been necessary to admit a varying activity of the Sun, we need
not be deterred from accepting this conclusion by the consideration
that it implies the abandoning of all prevailing ideas as to the
influence of the Sun’s activity on meteorological disturbances.

2. Eyjects of the movement of the Earth through the

irregular field of the Sun's radiation.

When the rays of the Sun fall through a piece of ordinary window-
glass on a distant sereen, we notice an irregular distribution of
light. In the same manner we imagine the rays proceeding from the
inner parts of the Sun, after traversing the outer and thinner layers,

1) Lorp Ketvin, Nature 47, p. 107-110. (1892).

*) Scuuster, Terrestrial Magnetism 3, p. 179—183, (1898).

= 4

( 289 )

to spread with unequal intensity through space. Consequently the
Earth moves through an irregular field of radiation. And although
we know the refractive power of the coronal gases to be but small,
still we may assume that those kinds of rays, which undergo anomal-
ous dispersion, will be liable to a rather strong incurvation and
their beams to variation in divergency, especially in those places
where they travel closely along the surfaces of discontinuity.

On this principle we base our explanation of the periodically
varying influence, which an almost unchanging Sun exercises on
terrestrial phenomena.

A. The semi-annual and annual periods in the position of the
Earth in the wregqular field of radiation.

At great distances from the centre of the Sun the surfaces of
discontinuity become nearly flat. Those which are near the plane of
the equator will be almost parallel to it. This assumption is in har-
mony with the appearance of the structural lines of the outer corona
as well as with theoretical considerations.

If now we suppose the surfaces of discontinuity to be (geometric-
ally) prolonged to the orbit of the Earth, it is evident that they will
intersect its surface in a series of parallel circles, but the position of
these circles with regard to the parallels of the Earth, will change
with the position of the Earth in its orbit. Let us consider some
particular positions.

Fig. 2, @ represents the position of the Earth on the 21st of
March, as seen from the Sun. In the spring the Sun’s south pole is

( 290 )

turned towards the Earth: on the 5 of March the Earth moves
through that point of its orbit which lies farthest from the plane of
the Sun’s equator. In our diagram the latter might therefore be
represented by a line running almost parallel to the ecliptie 4, ata
little over 7° heliographic latitude to the north of it. (The radius of
the Earth is only 8",8). The prolongations of the planes of disconti-
nuity at 7° south of the Sun’s equator being still almost parallel to it,
their position may be indicated by the dotted lines ¢ which, on the
21st of March, are only slightly inclined to £.

In Fig. 2, 4 we see the illuminated hemisphere of the Earth on
the 24st of June. A short time before, on the 4 of June, the Earth
passed through the nodal line of the Sun’s equator and the ecliptic,
so that, on the 21st of June, the planes of discontinuity @ may still
be represented by lines with an inclination of about 7° to the ecliptic.

Fig. 2, ¢ shows the position on the 22¢ of September; at that date
the Sun’s equator lies south of the Earth.

Fig. 2, d represents the position of the Earth on the 21% of
December.

From these diagrams it is plain that about the time of the equi-
noxes any point on the strongly illuminated parts of the Earth (we
except those places where the Sun stands low) in its diurnal rotation
always moves in the same sense with regard to the planes of dis-
continuity, making with them rather large angles (about 23°).
But soon after the solstices, in the beginning of July and January,
at midday the said point will move about parallel to the planes of
discontinuity; in the morning and in the afternoon its movement with
regard to these planes is in contrary directions.

Now, as in the system of the surfaces of discontinuity the most
rapid changes of density occur in a direction perpendicular to the
surfaces, it follows that any point on the Earth, in its diurnal move-
ment, will pass through a greater variety of conditions in spring
and autumn than in winter and summer.

Besides it is evident that the variations in the said conditions will
be less marked in the winter than in the summer solstice, because
in the former season the days are so much shorter.

We may therefore expect an annual variation in the amplitude of
certain daily inequalities showing the following periodicity :

maximum end of March
minimum beginning of July
maximum end of September

minimum beginning of January

( 291 )

whilst, especially in the temperate zones, the winter minimum will
be lower than that of the summer.

Let us here once more call to mind the optical significance of the
surfaces of discontinuity. As a rule they impart a greater divergence to
the beams of light which travel closely along them; consequently at
their intersection with the surface of the Earth they determine zones
where the illumination will be weakened, whilst in the intermediate
regions it will be strengthened. This does not apply in the same
measure to every kind of light in the spectrum, but especially to the
waves which undergo anomalous dispersion.

All terrestrial phenomena which are governed by the conditions
of illumination will therefore, to a greater or lesser extent, be sub-
ordinate to the above-mentioned periodical variations.

There is probably still another reason for the greater variability
of the effects of radiation in spring and autumn than in summer
and winter. It is namely not improbable that in regions 6° or 7°
distant from the Sun’s equator greater differences of density will be
found along the surfaces of discontinuity, than in the equatorial zones.

B. The perwdicity of the fluctuations of umination which
coincides with the periodicity of solar phenomena.

In the course of a certain number of vears the Earth describes
through the system of the surfaces of discontinuity a somewhat
complicated path, which we have represented by the track of P? on
the sphere 4. The Earth therefore continually comes under the
influence of another portion of the system; and the phenomena
appearing on the Sun inform us whether, in a certain space of time,
the light on its way to the Earth passes more or less often closely
along surfaces of discontinuity. For this circumstance is intimately
connected with the frequency of prominences and sun-spots and with
the aspect of many of the FravNnuorer lines (especially in the spot
spectrum). A so-called “maximum of solar activity’ means, that the
Earth during that period has been many times intersected by the
prolongations of sharply defined surfaces of discontinuity, and all
the terrestrial phenomena resulting from the variations of illumination
will then also be at a maximum.

As to the nature of the connection between sun-spots and promi-
nences on the one hand and the values of meteorological and mag-
netic variations on the other, it has been universally conceded that
no other definition was possible but this: ‘that they were the effects
of one and the same common cause.”

We believe to have found this common cause in the va rying

292. )

position of the Earth with respect to the surfaces of
discontinuity and in the fluctuations inthe conditions
of illumination resulting from it.

Not only the fluctuations in the total intensity of illumination, but
the changes in the composition of the solar light also, will have

their significance in this respect.
3. Polar lights.

Polar lights belong to that class of phenomena which seem but
little influenced by the local conditions on the surface of the Earth.
The altitude at which they originate has been variously estimated ;
it is generally supposed to be very high, several kilometers. No one
doubts but that this phenomenon is closely connected with the solar
radiation, an opinion supported by the existence of a daily period
with its maximum at 2540™ p.m. and its minimum at 7'40™ a.m.
(CARLHEIM-GYLLENSKIOLD). Most probably polar lights owe their origin
to the discharges of electricity generated during the day in the
higher layers of the atmosphere through the ionising action of the
Sun’s irradiation.

If this be so, local differences in the Sun’s irradiation must favour
the appearance of polar lights and consequently we may expect in
their frequency the semi-annual and annual periods described under
A as well as the less regular variations spoken of under J.

The following table, taken from the Lehrbuch der kosmischen
Physik by ArrueEnius, p. 913, gives a survey of the frequency of
polar lights from the enumerations made by EkHoLm and ARRHENIUS
for various parts of the globe.

Sweden. Norway. Iceland and U.States of Southern
Greenland, N. America. Polar lights.
I883—1896. 1861—1895. 1872—1892. 1871—1893. 1856—1894.

January 1056 251 804 1005 D6
February 1173 331 734 1455 126
March 1312 530 613 1396 1838
April aG8 90 128 1724 148
May 170 tj 1 1270 54
June 10 ) 0 1061 AO
July D4 0 0 1293 Bo
August 191 18 0) 1210 7)
September 1053 209 ADd9 1735 120
October 1114 Bits) 716 16380 192
November 1077 326 S11 1240 142

December OO) 260 863 492 81

( 293 )

The last two columns distinctly show the expected periodicity :
maxima in Mareh or April and in September or October, minima
in June or July and December or January, whilst in each case the
winter minimum is lowest, although the long winter nights favour
the observation of polar lights. In the other three columns, dealing
with higher latitudes, the summer maximum, as ARRHENIUS Observes,
is only apparently so low, because in these regions no time is left
for the observation of polar lights owing to the length of the days.

The data collected by Frrrz and Arruenius (Lehrb. d. kosm. Phys.
p. 915), moreover afford sufficient evidence that the sun-spot period
too is reflected in the frequency of polar lights.

4.) The annual variation in the diurnal inequality of

terrestrial magnetism.

It is an acknowledged fact that the magnetism of the Earth is
under the influence of the Sun’s irradiation. In recent years this view
has been strengthened by the appearance of magnetic disturbances
within the belt of totality during total eclipses of the Sun.

Let us suppose the mean magnetic foree at every point of the Earth
to be represented by a vector. If we now represent the daily varia-
tion by an additional, variable vector, the whole of all these additional
vectors will form the ‘“‘variation field”. ScuustEr and v. BrzoLp have
computed and constructed this field and shown that by its move-
ment from east to west with a velocity of 15° an hour, a fairly
accurate idea may be obtained of the diurnal deflections of the mag-
netic needle on all parts of the Earth.

This ‘variation field”, according to ScuustEr, is formed for about
*/, parts by electrical currents in the atmosphere and for */, part by
Earth currents. By the electrical current in the atmosphere we under-
stand a convection current formed by electrified particles, which are
carried along by the cyclonic and anticyclonic movements of the
general circulation.

This theory of Scuustrr and vy. Brzonp therefore implies that the
diurnal magnetic variations will increase both with the intensity of
the general circulation and with the amount of ionisation in the
higher layers of the atmosphere. If one or both of these processes
are in a great measure influenced by the variability of solar irradia-
tion (which is not improbable, vide Arruentus, Lehrbuch p. 886,
888, 890, 898), then all the periods which according to our theory
occur in the variability of the Sun’s irradiation must find their counter-
part in the diurnal inequality of the elements of terrestrial magnetism,

Proceedings Royal Acad. Amsterdam, Vol. VI,

( 294 )

A clear and concise exposition of the variations of terrestrial
magnetism has been recently published by Cure). The “mean
monthly range” of a magnetic quantity is according to his definition:
“the difference between the greatest and least of the twenty-four
hourly values in the mean diurnal inequality for the month in
question, based on the five quiet days selected for the month by the
Astronomer Royal”. If this range be represented by # and if S
means the number by which Wo.rer expresses the sun-spot frequency,
we have, according to Cure, the following relation :

R=a+bs.

His investigation extends over the 11-year period 1890—1900.
He divides the twelve months into three seasons: November to
February: winter; March, April, September and October: spring
and autumn; May to August: summer, and finds the following

values for a and Ob.

Declination. Inclination. Horiz: int. | Vert. int.

a b a b a b a b

Winter 323. 10.0325 0/.63 0.0105 10.5 O61 7.0 0.032

Spring and | 739 69,0478 | 1.96 0.047 | 235 0.221 | 172 0.096
autumn |

Summer $OF 0.0498*>| 1.61... 0.01ST aes OMS) 27 0.035

Mean | 649 0.0H0 | 147 0.0130 | 215 0491 15.6 0,034

a marks the variability according to the seasons, irrespective of
the spot-period.

/ shows in how far the influence of the spot-period depends on
the seasons. S in the period under consideration oscillated between
0.3 and 129,2, its mean value being 41,7.

From the point of view of our theory these figures prove that:

a in each element shows a minimum in winter and a maximum in
summer; this we explain by the greater intensity of the Sun’s irradi-
ation in summer increasing both the general circulation and the
generation of electricity. But the table shows also that the values of
a in spring and autumn are invariably greater than the mean value
for the whole year; this points to superposed maxima during the
vquinowes, and this we ascribe to the way in which the variability
of illumination is dependent on the position of the Earth’s axis with
respect to the surfaces of discontinuity, (periodicity A p. 289).

1!) Caner, Preliminary Note on the Relationships between Sun-spots and Ter-
restrial Magnetism, Proc. Roy. Soc. 71, p. 221—224, 1903,

( 295 )

In the values of 4 the periodicity A plays a far greater part than
in those of a. That stands to reason; for the term 4S less concerns
the amount of the general atmospheric circulation, than it does the
peculiarities of the surfaces of discontinuity in respect to the Earth.

In the values of the vertical intensity, 4, as compared to a, has a far
lesser significance than in those of the other three elements. Curer
makes the mean value of 4 over a whole year 100 and then arrives
at the following values of 4 for the seasons.

Declination Inclination Horiz. int.
Winter 79 Sl 85
Spring and autumn 117 115 116
Summer 104 106 99

Thus it appears that the amplitude of the diurnal inequality, taken
absolutely, depends in a far greater measure on sun-spot frequency
at the times of the equinoxes than at other times. The reason of this
we find in the faet that the greater variety of sharply defined planes
of discontinuity which at spot maxima intersect the Earth, causes
greater diversity in its illumination when the projection of the diurnal
motion on the normals to the planes is large, than when it is small.
(Compare Fig. 2 p. 289).

Now, if we consider the influence of the spot frequency notabso-
lutely, but in comparison with the influence of the annual variation
taken for average spot frequency, a relative value which Cree

oe ATED ;
expresses by the quotient ——, then we obtain:
a
Declination Inclination Horiz. int.
Winter 0.42. . 0.69 0.60
Spring and autumn 0.27 0.49 0.39
Summer 0.20 0.35 0.26

which shows that the influence of the spot frequency on the ampli-
tude of the daily inequality is comparatively strongest in winter. This
must be attributed to the fact that during a winter day the changes of
position of a point on the globe with respect to the Sun and to the
surfaces of discontinuity are proportionally small, and consequently
the variations in illumination are then principally caused by irregular-
ities, occurring in the system of the planes of discontinuity itself.
The investigations of Curne were confined to the observations at
Kew, A synopsis of the annual variations in the daily inequality of
20%

( 296 )

the horizontal mtensity, collected from the various readings in different
parts of the globe between 1841 and 1899, will be found in Prof.
Frank Bice.ow’s “Studies on the Statics and Kinematics of the atmos-

phere in the U. S. of America’, p. 56—57.

The figures tally in every respect with the above results.
S: Magnetic disturbances.

If now we apply the preceding arguments to the irregular disturb-
ances or magnetic storms, their explanation will offer no difficulties.

We attribute these phenomena to extraordinary differences in
density, which may at times be found on each side of the planes
of discontinuity in the line connecting the Earth with the Sun. The
system of the surfaces of discontinuity moves so rapidly with respect
to the Earth, that almost all parts of the illuminated hemisphere are
influenced simultaneously by the extraordinary local condition of the
radiation field: whereas it is evident that the abnormal illumination
at the same time may be more intense in some regions of the
Earth than in others!). Consequently magnetic storms will be noticed
everywhere almost simultaneously, and their effects will be almost
identical in places lying rather close together, whilst, in regions
farther distant from each other, they may be entirely different,
perhaps quite opposite.

Enis has made a study of the annual variation in the frequency
of magnetic disturbances and classed them into certain groups.
“Strong disturbances’, (over 1° in declination and 300 units of the
fifth decimal in horizontal force) have two maxima, one in April and
one in September; ‘weak disturbances” (10" and 50 units) show a
maximum in summer and a minimum in winter. The characteristics
of periodicity A (p. 289) at once strike us here, and it seems to us
also to afford a satisfactory explanation in this case. Besides we find
especially in the curve of the disturbance frequency an argument in
favour of the opinion expressed on p. 291 viz. that along planes of
discontinuity at 6° or 7° from the Sun’s equator, greater irregularities
in the distribution of density will be met with than in the equatorial
zones. And in the diurnal period of the disturbances, which im the
tropics shows a maximum at midday, we see another argument in
support of this assumption.

After the explanations given under 4, it will cause no surprise
fo recognize in the magnetic disturbances the periodicity of solar
phenomena. There is but an indirect connexion between magnetic

1!) The rapid changes noticed in Hare's abnormal spectra support this view.

( 297 )

storms and sun-spots, faculae, prominences. Both kinds of pheno-
mena depend on the presence of sharply defined surfaces of disecon-
tinuity, but the appearance of the solar phenomena is more particularly
determined by the direction and divergency of the rays of light in
the vicinity of the Swn, whereas the terrestrial disturbances rather
depend upon the divergency of these rays nearer the Larth. Theretore
it may often happen that magnetic storms coincide with the
appearance of large sun-spots, or faculae, or prominences, but this
is not an indispensable condition.

According to Lockyer “great” magnetic storms are synchronous
with maxima of prominence frequency near the poles of the Sun,
whilst the curve for the mean variability of terrestrial magnetism
is almost an exact reproduction of the curve for the prominence
frequency in equatorial regions *).

This fact may be explained as follows. The appearance of promin-
ences near the poles is the result of the optical effects of parts of
surfaces of discontinuity which are strongly inclined on the plane
of the equator. We may assume that similar parts will also produce
irregularities in the radiation field, at the site where the Earth is situated,
and that the structure of these irregularities will not be parallel to the
principal structure, i. e. to the solar equator. In moving along the
Earth they must give rise to stronger and more evanescent distur-
bances in the terrestrial magnetism than the irregularities corre-
sponding to the normal lamellar structure, which makes but very
small angles with the ecliptic.

6. The annual variation in the daily oscillations

of atmospheric pressure.

The polar lights and the variations of terrestrial magnetism are
principally governed by conditions in the higher layers of the atmos-
phere and but little by those on the surface of the Earth. The
barometric pressure, the temperature, the rainfall, the direction of
the wind and all meteorological phenomena which accompany them, are
to a considerable extent influenced by the distribution of land and
water. Among local influences, cosmic action therefore, will not be
prominent in these latter phenomena.

In the higher layers of the atmosphere the matter becomes much
simpler. A short time ago BicrLow *) has called attention to the fact that

") Lockyer, G. R. 135, p. 361—365, (1902); Proc. Roy. Soc. 71, (1903).
*) Bigetow, Studies on the Meteorological Effects in the Un. States of the Solar
and Terrestrial Physical Processes. Wheather Bureau No. 290, Washington 1903.

298 )

the well-known semi-diurnal period in the pressure, the atmospheric
electricity, the vapour tension and the absolute humidity, disappears
in proportion as higher layers of the air are examined and resolves
itself into a simple diurnal period, having its minimum about 3" a.m.
and its maximum at 3" p. m.

However it is only in recent years that a systematic investigation
of the higher layers of the atmosphere has been undertaken, prin-
cipally in N. America and in Germany, and the results published
until now are insufficient to deduce from them the cosmie periods.
Anyhow, the same annual variation as that which marks the polar
lichts and the terrestrial magnetism has been observed in the diurnal
oscillation of barometric pressure near the surface, notwithstanding the
complexity of the influences there at work.

The table here subjoined, taken from the handbook of ARRHENIUS
p. 603, gives the mean amplitude of the semi-diurnal oscillations of
the barometer, expressed in m.m., for the following places:

1) Upsala 59°52’ n. lat, 2) Leipzig 51°20’ n. lat.,- 3) Munieh
48°9’ n. lat.. 4) Klagenfurt 46°37’ n. lat., 5) Milan 45 28’ n. lat.,
6) Rome 41°52’ n. lat., 7) 22°30 s. lat., 9) HOS an. dae
Jan. Febr. Mrch’ Apr. | May.) June. July. | Aug. | Sept.) Oct. | Nov. | Dec. | Year

|
1) 0.43 0.14 0.15 0.160.441 0.13/0.13 0.44] 0.17, 0.15) 0.41 0.40; 0.18
2) 0.46) 0.20) 0.24 0.27| 0.22 0.20) 0.21 | 0.23 | 0.2% 0.22) 0.21) 0.16 0.22
3) 10.21 | 0.23} 0.28 0.£9| 0.98 | 0.26 | 0.25 | 0 250.28 0.97 0.21 0.21 0.95
1) 10.93 0 29/085) 0.26 | 0,96 | 0.25 | 0.84) 0.97 | 0.97 | 0.24] 0.21 | 0.9% 0.97

5) 10.30 0.35/0.38) 0.36 | 0.30 | 0.29} 0.2910 31 | 9.32 | @.33

SY)
=
=
e
—_—
=~
as)
ae)
lm

6) 10.30) 0.33! 0.35) 0.32| 0.29 | 0.26} 0.96 | 0 30} 0.35 | 0.36] 0.33 | 0.99 | 0.31

7) | 0.65! 0.68} 0.70) 0.68 | 0.64; 0 64 0.63 | 0.66 | 0 72/0 72) 0 69) 0.66 | 0.67

8) 10.79! 0.20! 0.83! 0.82} 0.73} 0.65 | 0.65 | 0.69 | 0.75 | 0.78 9 82/0.79|0.76
| | |

li will be seen that the maxima again coincide with the equinoxes;
that the winter minimum for places above 45° lat. is lower than the
suinmer minimum, thus agreeing in every respect with the perio-
dicity described under «1. Tt is indeed easy to understand that ihe
amplitude of the fluctuations in’ the atmospheric pressure will increase
or decrease according as the variability of the illumination increases
or decreases. The circumstance that in lesser latitudes, north as well
as south of the equator, the July minimum seems lowest, is ascribed
by Arrienivs to the faet that the Earth is at that time farther away
from the Sun than in January.

CCU,
: .

( 299 )
(. The annual and secular variations of atmospheric pressure.

When we compare the system of isobars obtained for each separate
month, it becomes at once apparent that the annual variation of the
barometric pressure is very different in the various regions of the
Karth. In the tropics the fluctuations are generally insignificant ; in the
central parts of the continents of the temperate zones the atmospheric
pressure is low in summer and high in winter; in mid-ocean this is
the reverse; beyond 45° lat. south the pressure is uniformly low ;
on the other parts of the globe the greatest diversity exists in its
annual course.

Nevertheless most of the annual curves (especially those of the
temperate zones) display, next to local peculiarities, a common charac-
teristic. They exhibit, more or less distinctly, two minima at the times
of the equinoxes and maxima in winter and summer. The regions
near the North Pole seem to make an exception to this rule (perhaps
also those at the South Pole); there the maxima occur in spring and
autumn and the minima in winter and summer.

Some important statisties in connexion with the atmospheric pres-
sure in N. America have been published in the Report of the Chief
of the Weather Bureau 1900—1901. Vol. I. Chapter X treats of
the annual and secular variations; there we find the monthly
deviations from the mean barometri¢ pressure over a certain number
of years (1873—1899) arranged by Prof. BiceLow into 10 groups,
according to the geographical position of the observation stations,
and the mean annual course of these deviations charted for each group.

The ten curves thus obtained show great differences, due to the
more continental or more maritime ¢haracter of the region to which
they refer, but all reveal a cosmic influence in showing minima at
the times of the equinoxes and maxima during the solstices.

From our point of view this cosmic influence may be thus defined.

The greater variability in the Sun’s irradiation during the spring
and autumn increases the atmospheric circulation, and this augments
the average horizontal velocity component of the air as well as the
evaporation, and both processes cause the atmospheric pressure to
decrease. In the polar regions the solar radiation exercises a lesser
influence; in those parts compensation can take place and conse-
quently the maxima occur in spring and autumn.

BigeLow has also tabulated the same data in another manner.
He has calculated for each station the successive yearly means and
subtracted from them the check mean of the whole period (1873—

300

1899) thus obtaining 27 residuals. The stations were then again
gathered into the same groups, this time only eight in number
(because the observations for the West Indies were considered too
incomplete) and for each group the 27 mean values of the residuals
were computed.

The curves representing these mean residuals show for each
of the eight districts the secular variations of atmospheric pressure
in that region. ;

The eight curves certainly exhibit many differences when compared
to each other; nevertheless in the number of thei maxima and
minima we observe such an unmistakable similarity, that it is
evident they are acted upon by a common influence, the cosmic
nature of which is not doubtful.

Similar charts have been framed by Lockyrr and by Biernow for
other parts of the globe and compared with the curve of prominence
frequency. They resulted in the conclusion that an undeniable relation
exists between these phenomena.

However, to find this relation is not such a simple matter. In
some regions of the Earth the maxima of prominence frequency
coincide with the maxima of atmospheric pressure (Bombay, Batavia,
Perth, Adelaide, Sidney), in others on the contrary with the minima
(Cordoba, Mobile, Jacksonville, Pensacola, San Diego), whilst else-
where again the maxima are shifted, although the general character
of the curves persists.

As yet the barometrical observations undertaken in elucidation
of this question are confined to too small a number of places to
allow of general conclusions being drawn from the data collected.
Ii is therefore under reservation that we emit the following hypo-
thesis as a guide for further investigation.

At periods of maximum prominence frequency the
atmospheric circulation is intensified owing to the
Irregularities of the solar radiation freld This ¢amees
adecrease of the mean barometric pressure at all those
places, where the enhanced circulation causes an excess
of humidity, whilst at places where this is not the
case, the mean atmospheric pressure will be above
the normal.

8. Cosmic influence on other terrestrial phenomena.
If the Earth moved through a perfectly regular radiation field,
there would be a certain normal atmospheric circulation, and in
connexion with this circulation there would be at each place a fixed

hal

( 301 )

and regular state of the weather, varying of course with its geograph-
ical position and the actual seasons, but otherwise recurring from
year to year with only small accidental variations.

As things are, meteorological conditions are the reverse from reliable.
We attribute their variability to the irregularity of the radiation field,

The peculiarities of the surfaces of discontinuity add their quota
in determining the localities, where minima of atmospheric pressure
will occur; they influence the depth and movement of the depressions,
the course of the cyclones, the direction of the wind, the formation
of clouds and the rainfall.

Metprem found that between the equator and 25° southern latitude,
cyclones are more violent and.more frequent at spot maxima than
at minima. Pony established the same fact for the cyclones in the
Antilles; and to this again it is attributed that in years of spot maxima
during the spring, south winds are predominant in Western Europe ;
that less frosty days occur at that season, the ice melts at an earlier
date than usual, the water-mark stands higher for the great rivers,
plants are more forward, ete. (ARRHENIUS Lehrbuch d. kosm. Phys.
p. 141—146).

Neither does it seem out of place to attribute the periodical alter-
nations of years with much rain and years of drought in British
India *), which react in so conspicuous a manner on the economical
condition of that country, to the periodicity in the varying position
of the Earth with respect to the surfaces of discontinuity. An excess
of rainfall seems there a regular occurrence within a three year
period around the maximum and a three year period around the
minimum of sun-spots. The intervening years are marked by drought,
the cause of famine. The regular course of these meteorological
phenomena was interrupted in 1899, when great drought and excessive
famine coincided with a spot minimum; but at the same time the
widened lines of the spot spectrum presented an abnormal appearance.
Here again we find a circumstance in support of our assumption,
that the irregularities of the mean atmospheric circulation are caused
by the surfaces of discontinuity. However, similar local meteorological
phenomena depend on so many conditions, that we dare not look
forward to a speedy solution of the problems they present.

SUMMARY OF RESULTS.

Overlooking the results of this investigation we see that the prin-

1) Sir N. Lock.er and W. J. 8S. Lockyer, *On Solar Changes of Temperature
and Variations in Rainfall in the Region surrounding the Indian Ocean’. Proe.

Roy. Soc. London 67, p. 409—431 (1901).

( 302 -)

ciple of anomalous dispersion opens a way to account for the con-
nection between solar phenomena and terrestrial disturbances.

There is a striking feature in the manifestations of solar influence
on meteorological and earth-magnetic elements, which it is especially
difficult to explain by other principles, namely the circumstance that
this cosmieal influence does not affect the illuminated hemisphere
uniformly, but often appears to act variously on different regions of
the Earth, although the solar parallax is only 8.8"

This peculiarity of the solar influence, as well as the divers perio-
dicities observed in the variations of meteorological and magnetic
elements, may be readily explained as consequences of the irregulari-
ties of the solar radiation field, which in their turn are caused by
surfaces of discontinuity.

Our aim has been also to show, that even when supposing the
solar output to be constant, periodical alterations in the frequency
of spots, faculae and prominences and in the appearance of widened
spectral lines must result from the mere change of the Earth’s position
relative to our rotating luminary. The 11-year period, especially,
seems to follow as a natural consequence from these considerations.

It may be that we have touched here the only efficient cause of
the periodicities noticed and that there really remains no ground
for the admission of a variable solar activity. This latter inference we
have, however, not proved, but for the sake of argument taken
for granted.

Zoology. — “The process of involution of the mucous membrane of
the uterus of Tarsius spectrum after parturition.” By Prof.
Hans Srrann of Giessen. (Communicated by Prof. J. D. van
pbER WaaAts, on behalf of Prof. A. A. W. Huprecnt).

| am indebted to Professor Husrecut for some exceedingly interesting
specimens of uteri of Tarsius spectrum, which enable me to throw
some further light on the different phases of the process of involution
gone through by the uterus during this animal’s puerperal period.

This material was especially valuable as I had an opportunity, on
previous occasions, Of examining the same process in a series of
other mammalia, and I am now enabled to determine how far Tarsius
agrees with the forms hitherto under observation, and where it differs
from them.

I had a considerable number of uteri at my disposal, some from the

( 303 )

latest period of pregnancy; a great many dating shortly after
delivery, others again of later date, and some showing the condition
of the uteri in a non-puerperal or non-pregnant: state.

Before summing up briefly, in this paper, the results of my expe-
riments, | must at once point out that the involution process in the
ease of Tarsius, throughout iis development, takes its own peculiar
course and is unlike any of the other forms of mammals that have
had the uterus carefully examined up to now.

As far as we know up to the present, we can divide the mam-
malia with so-called full-placenta, (all classified under the heading
of deciduata in the old-fashioned terminology), into three groups
according to the process of involution. In the species of the first
vroup, to which man and the monkeys belong, the placenta is spread out
flatly on the inside of the uterus while in the mucous membrane,
which has turned into decidua vera, the epithelium is entirely absent.

In the second group the placenta is also spread out over the
entire inside of the uterus, but in addition to this the womb is
covered throughout with uterus epithelium. Such uteri are found
in carnivores. In the rodents we often meet with the third
form; here, towards the end of gestation, not only is the womb
covered with cell-tissue, but this epithelium also runs from the
fimbriae right underneath the placenta, undermining it till it is
finally only adhering to the walls of the uterus by a slender cord,
carrying the vessels.

It is evident that, — taken as a whole class, — the uteri of the
3 group will resume relatively quickly their non-puerperal
appearance, while those of the first-named have to go through a

complicated process of involution.

We may add at once that Tarsius belongs to the third group.
The lumen of the uterus gravidus just before parturition was found
to be entirely covered with epithelium which ran underneath the
rim of the placenta towards the centre of it, up to the connecting
tissue-string, carrying the vessels of the placenta.

As already described by Htsrecut in his excellent work on the
placenta of Tarsius, we find in this placenta-cord conglomerations
of uterus-glands, the cell-tissue of which present every possible
phase of involution, while others are covered with well-preserved
cells. These remains of glands in the placenta play a prominent
part in the puerperal involution.

In two of the puerperal uteri I find the placenta still existent ;
I think it possible that here it is so far a question of physiological
and not of pathological circumstances, as perhaps the placenta,

B04 )

instead of being at once thrust out after the parturition, has remained
for a little while in the mother’s genital duets.

Once the placenta gone, the seat of the placenta in the mucous
membrane of the uterus can be traced microscopically or by means
of a magnifying glass for some considerable time. It is found to
protrude above the surrounding mucous membrane like a round or
oval-shaped body which I will call the placenta-bed.

This bed, as we learn from the microscopic preparations, is limited
by the accumulation of the remains of the glands lying along the
vessels situated in the placenta-cord, which I will give the name
of “paravascular epithelial tubes’” and in the centre of which the
remains of the vessels of the placenta in a state of thrombosis, form
a ‘“placenta-plug”’.

sy the side of the placenta-hbed the mucous membrane forms little
folds which often protude into the lumen of the uterus in the shape
of vesicle-shaped cavities.

Among the changes that now set in during the process of invo-
lution we have to distinguish between those which take place inde-
pendently, in the material at our disposal, and those which are
noticeable from a topographical point of view.

As regards the first, even during pregnancy so much material
has been accumulated for the formation of the new mucous mem-
brane — the changes in which will only be described here — that
it has now really become a question of elimination of the super-
fluous. It is especially epithileam which is got rid of, as far as
dispensable, by its being shed.

Topographically two things are happening. At what used to be
the seat of the placenta we find as paravascular epithelial tubes
remains of uterus-glands, in considerable number, while in the other
sections of the womb there is a small number only of these uterus-
elands.

In both the uterus-horns of the non-puerperal uterus the glands
which in this condition of the womb are of a narrow and elongated
shape, run close together and are equally distributed, but this condition
can only be arrived at by means of two simultaneous events: At
the recent seat of the placenta the material of the large and wide
paravascular vessels is almost entirely got rid of by its dying
off. A litthe of it survives, to form the nucleus of fresh uterus
elands.

In the other parts of the womb a large number of new glands
are developing at the surface of the epithelium in the same way
as the glands are vrowing during the time of pregnancy, namely

———E—————

( 305 )

through the forming of small epithelium plugs, growing downwards
from the surface.

And while the whole uterus is trying to regain ifs normal shape
by means of contraction of all its muscles throughout, the mucous
membrane must of course shrink considerably; this process follows
new lines, different from those which I have so far met with in any
of the puerperal uteri of mammalia, hitherto examined.

How this involution process progresses will be described in details
by Dr. W. Kurz in an exhaustive work, freely enriched with illu-
strations, and in which due attention is paid to the works of reference
written on the subject.

ay xt : yp L@),,
Mathematics. “Series derived from the series + ——.” By Prof.
WL
J. C. Kivyver.

By «in) we denote an arithmetical function of the integer im,
which equals O if i be divisible by a square, and otherwise equals
+1 or —1, according as m is a product of an even or of an odd
number of prime numbers.

The series

M— wR

mm) 1 1 1 i! 1 1 1
a enh roa kG T 9639 30
m=|

was considered by Evirr, who concluded that it converged towards
0, a theorem only recently proved by von Manconipr (1897) and
by Lanpavu (1899).

In this paper it will be shewn that in innumerable ways we may
select from Evnrr’s series infinite groups of terms, each of these
groups again Constituting a convergent series.

In fact we may assume a linear congruence

te Pas... (mod. ~b)
and from Ever’s series retain only those terms the denominators
of which are solutions of the congruence.

From
]] eto 0)
= —~ LL 771
i N (mn)
7
m=1
we get thus the new series
; m=e
u(mb +h)

T) — a
ey om mb +h

m—O0

Sopel! We ER So RR Oe a ek ee et on ee ee
- oer oa. ~—d us 2 ? mah) oe aS
- ee + ? *

( 306 )

and it will be found that this series has a definite sum, whatever
may be the integers 4 and / (h<b).

Firstly consider the case / = 0 and suppose 4 to be prime. As
it is necessary to start with finite series we write, g being any
positive number,

mb<g mb--h <q
79 u(mb) 7 u(mb-+h)
b,0 a mb : LN eed nh +h
m=l m=0
Then, since p(m) is either 0 or —y(m) according as m is
divisible by 4 or not, we have
h=b—1 q q q
iF aes if ri Sr
[0 TSS ee ;
5,0 hb bh b 1,0 b,0
it
or
1 a 1 I
WJ = cee b —- a b
6,0, 5 pt ee. oe
and in the same way
a 1 I 1 Lik
ae 70 _ b2
7 = ot :
b,0 h 1,0 b b.0
g 1 I ff.
rp , 63 3
ot ee
b,0 b= 18 Far bo

Supposing yg to lie between 4% and 4+! we infer from these
equations

k=z q
1 ue
a Ape ee a
Ts ‘ FE ae eee ‘<-
i
Now it follows from the identity
m<g
(
I) Bi
m
m=1
that
m<q
A)
ba m
ml
is always finite and less than 2; hence equation (5) gives
5)

| v9 | -
| 10| S51

( 307 )

however large the number g may be, and taking this ineq:ality into
account it is seen from equation (A) that we have necessarily

50! ak
The proof given here is easily extended to the case in whieh 4
is not prime but a product of unequal prime factors. Square factors
are excluded, for then 7% is identically zero.
Let ¢ be a prime number not dividing 4, then instead of equation
(4) we can establish the relation

7 g

| Aa 1
cf WJ ae ee, ee ih c = ae, Ci c
4 be,0 ae rp b,0 as c bc,0 ‘

q
and it will appear that 7%.» tends to zero, if we can show that
g : ;
Lim 1T,6=90. Now the latter theorem is proved for any prime
He
number 4, hence it must remain true if repeatedly we multiply /
by other prime factors c.
In order to investigate the series 7%), we consider the series of
functions

m= n
um)"
Le 2m ;
m=1

Evidently it converges for z<1, and expanding each term into
a power series, we find

M—B m=

(mm) 2”
eg PMO 4

m1 m=1 d/m

for the sum 2 «a(d), in which the summation is extended over all
djm

divisors d¢ of m, unity and i itself included, is zero except form == 1.
Similarly we have by changing m into im

m=e m—BD

u(mb)zm

foal: = ©: emb¥ (bd).

mn! m=} d/im

Let 6 be the product of the prime factors p,, p,,.--. pe, then

Su(bd) is zero but for those integers im that are of the peculiar form
djm

hy Ly. 3 : ~
: pe , and in that case we have SY y (bd) = u (6).

d/m

p' P

Hence we may write

( 308 )

m—e

~~ pa(mb) 2m
N oe == a (>) ) ond.
_- — eg a)

= hy Eig ao EE
m1 1,72; Ie

Fy Fy ZL.
i ZB 5.2 a )

(a relation still holding for any / having square factors).
Integrating from the above equations we deduce

MD
tn)
‘ ia log (A— 2") == ==",

ya m

mn :
ahO

as uu(mb) loa (1—<m’) —— (db) be St

a) ; dam! «=o ND

m=l1 Fy 5 Ayn Zp.

and subtracting

h=)5—1 m=
= u(mb +h) —~ 2
Ss Yt) ee
Foal aot mo —T/t
1) == | m=O ZANE 0025p

Denoting by / a number less than 4 and prime to 4 I substitute

2zi —

oe
s

and afterwards make < tend to unity.
The righthand side ultimately takes the value of

k .
Qz ) Xe pu) Y d 277 D u(b)

h ome n 1 1 1 =
STE 2o WOO Fs b = ———— ne =
; Pi Ps Pk

where g(/) indicates the number of integers less than 4 and prime
to 4 and the equation itself may be written

= ( a *) ani gb)
a ed - =f (4 Sear rary) L ;

N re. h > loy i asp b —— Pip b 4. N i : (C)
pb)

It implies / prime to 4, but for other integers /: less than 4 and
not prime to / a similar equation can be established.

( 309 )

Suppose
Fh hd
ay
where i’ and }’ are now prime to each other, then we have
h'=b'—1 pale, Per f (b')
aaa 7 p< lo 1 e b' —s e b! at
a Or == a ——-.
ae es ie: g(')
i!

But denoting by / all integers less than 6 that satisfy the con-
gruence
h=h’... (mod. b')
we have evidently
Mee hp tte a Mts aioe GD)
aco
h
and also

ont ol
/ 1" b 1 ‘ lo i| x Lig | 2%
Ava if} b, h ~ log 1 —eé —— i b’, h’ DS og e ;

hence in case -/: is not prime to 4 we are led to the equation

h=b= hk Bs ta w(b')

y* ee) loc 1l—e Y nC, ot, dja E)
2 b, h X log g nee
—r

if only we omit at the lefthand side the terms corresponding to those
integers / that are multiples of 6’. With this limitation the equation
(/) applies to all values of /, for if & be prime to 6, from it we
get back the equation (C).

In this way we obtain by putting successively 4 = 1,2,...6—1
a set of /—1 equations, from which we find in the shape of deter-
minants finite values for the 4 — 1 quantities DL ih

Actually we have got more equations than were wanted, for we
may separate real and imaginary parts.

We put

1
LZ [a] oe 72 (a);

so that P(x) stands for the fractional part of the number « minus

ee Now we have generally

1
log (1 — e2ttx) — = log 4 sin? ra + ia P (2),
hence instead of (#) we get the two equations

21
Proceedings Royal Acad. Amsterdam. Vol. VI.

( 310 )

h=b—1

hk k u(b')

dha log 4 sin? % — = — 2 cos 2 x — 2 A
a bh X log nx ; cos2 x b + gy’ (F’)
h=1
and
k=b—1
hk 1 k
pall Meee) at eer SS
i=l
Again the equation (/’) supposes that if we have
k ~ k!
ieee

no multiples of 4’ should be substituted for 4 in the summation at
the lefthand side. As for the equation ((@) this limitation is super-
fluous since the discontinuous function P(z) vanishes for integer
values of w.

As the solutions of the equation (/’) and (G) seem in general to
present neither regularity nor symmetry, we will proceed to consider
some particular cases.

In the case 4 = 2, we have at once

Liye ee eee eee ==)
os WA eases
1 if 1 1
Bee 1 a ks
5) 5) 7 11
Putting = 3 and substituting /=1 in (G) we find
145 1a 3
—— 713, + T32=— —;
25
and since
34 --432—=0,
we have
“ doar thet eke | 3/3
13.1 = 1——+—-—-— 6s A
7 10. 43. 19 2a
a ‘eae eee er 3/3
fe me — — — —— —+—...=>— ys .
2 5) 1S seas Be! 2n

In the case = 6 we may apply (D). Thus we obtain relations

yy ry’ ry) ryy ry rm 3 3
o3 Te5—2o1—0,, Te s=Ts0=—0, Tei14+T.a=e ee atid
2x
T) yyy ryy 3 3
T6,2 + 16,4 = 12,0=0, To2+ Tos Tog
x

Joining to these the equation resulting by substituting b= 6,

== 361)

i i i

Tees el
2 + y > ,
>

( 314 )
if - a
(16,1 — T6,5)P| — )}+ (%o,2— 76,4) P| —~ |) =— sin —,
6 ax 3
there follows

ad ee es 3 1 3
en pik enable Be) Bua s 2h a gee ee aha
ie 7 13 19 31 a Be sitestae: on
era 3 1 1 V3
5 Fg ame I ee Me i hee yo I ae
st 5 11 17 23 oes Te =+istotate on

If we take = 4, we have by applying (J)
T's,9 = To, = 0,
Wa sie a hoy 0,
and by the substitution == 4, £=1 in (@)

ryy 1 ry. a B) 1
Te ees | haa Ef)
4 4 Ey 4

hence we find

a3 1 1 1 1 2
Gara oe alas a oy ar
se 1 1 1 1
a — sear ee oe RAC Te, ae
And by subtraction we obtain
ae, u(4m+1) p(4m-+3) 4
> |- a ee
m=0

a result which may be compared with Lerpnirz’s theorem

ys 1 1 __ 2%
wt | Am+1 4m4+3{ 4-
m—0

Lastly the series 75% can be evaluated if we substitute J=5,
k=1 in (Ff) and 6=5, k=1, k—=2 in (G). Thus we obtain

: 23 27 1
ee Te. \ log Aeain® (Fes 755) log 4 sin? — bie ee os
3) 5 5
1 23
(Ts) sy) P(S ) + (15,2— Toa) P(= ) a pi ed
5 a 5
: 2 j a a
(Ps: Ten) (=) + (ap Ta) PS 3) — — _— gin? =
r3) : 5 = 5

moreover we have
Vsi + T52+ 153+ T54= —Ts5o=— 0:
Solving the four equations, the result is as follows
21*

oi 1 : Sas : ! si 72° in 36°
5,1 == aera eon ta a ee + sin 36°) —
1 4 cos 12"
— = 1.128,
8 log 2 sin 18° 2
i! 1 1 1 1 i
ig a ory >= hi * = ey YORE Ba Ro
T'59 5 7 77 Sea eae eee t 3 sin 30°) +
1 + 4 cos 72°
= — 0,710
8 log 2 sin 18° :
1 1 1 t i 1
— ae Py aeoed ew ee De \ 2)
T5,3—= — Se | Seer Soha ee sin 72° + 3 sin 36°) +
1 + 4 cos 72° oaEe
8 log 2.sin 18°.
x 1 1 re eee | eg 3 sin 72° : .
P54=— Nee ey ig bad 36°" > og eee a sin 36°) —
1 + 4 cos 72°
1 OS eee

8 log 2 sin 18°
100
As a numerical test I have directly calculated 75, . The results

were respectively: +1.123, —0.685, —0.449, +-0.08

From these few particular cases it will be evident that the equations
(F) and (G) always permit to evaluate 7); and the fact that such
a series has in all cases a finite sum may with more or less justice be
interpreted thus: Among the integers without quadratic factors less
than a given large number g, that are solutions of a given congruence

P= hb. seo Os)

the integers made up by an odd number of prime factors are
sensibly equal in number to the integers made up by an even number

of prime factors.

Botany. — “The Ascus-form of Aspergillus fumigatus Fresenius”.
By Dr. G. Grins. (Communicated by Prof. F. A. F. C. Went.)

While during the last course I was occupied with determining
fungi in the botanical laboratory under the superintendence of Prof. WENT,
I noticed that in a pure culture of Aspergillus fumigatus, a couple
of months old, sporefruits had formed; on inoculation from this
culture these same bodies were always produced in the new cultures.

As nutrient substance [ used Konrna’s malt-canesugar-agar-agar.

The ascus-form of Aspergillus fumigatus has not yet been deseribed,
for the statements of Brnrens and SmBeNMANN are justly doubted by
Weumer, nor do they agree with my result.

( 343 )

The conidiophores agree so well with Wernmerr’s description’) and
with his picture, also with regard to dimensions, that the diagnosis
need not be doubted.

The fruit-bodies appear as small globules having the colour of
fresh hazelnuts; their size is only about */, mm. With feeble mag-
nification they appear to be enclosed by an envelope of small, round,
highly refractive, greenish globules, enclosing a dark body. The
elobules on stronger magnification turn out to be mycelium cells
with a greatly thickened wall, which remain joined by a few thin
threads. The body within is little transparent, deep red and irregularly
egg-shaped. It has a thin fragile wall, consisting of two layers of
flat cells in which a red pigment is found.

The space within is filled up with a dense web of colourless
hyphae, the contents of which are homogeneous and between which
the asci are found.

These are egg-shaped and have a very thin wall, which in mature
asci is difficult to observe, but which can easily be recognised in
immature ones still containing colourless spores.

The mature spores, of which eight are found in each ascus, have
a deep red colour, which is turned blue by alkali (ammonia). They
have the shape of convex lenses, the thickness of which differs only
little from the diameter. Round the aequator a hyaline seam is found,
showing fine radial striae or folds.

The perithecia consequently resemble those of Aspergillus nidulans
which differs, however, by wanting the ramified sterigmata. Also the
ascospores with their radially striated seam are different from those
of nidulans which show a groove.

Terrestrial magnetism. — “The daily jield of magnetic disturbance.”
By W. van Brmmeven. (Communicated by Dr. J. P. van per
STOR).

In 1895 I published *) the results of a research on the change in
magnetic force on days following large magnetic disturbances.

By comparing the mean daily force on a day directly following
a disturbance with the force some days after, a differential vector
was obtained directed chiefly South with a deflection to West or
East of rather constant azimuth for each station.

) C. Wenmer. Die Pilzgattung Aspergillus, Genéve 1901. p. 71.
*) Meteorologische Zeitschr. 1895, pg. 321,

( 314 )

Later considerations *) brought me to the result that the regular
part of the disturbance phenomenon might be ascribed to the existence
of a circular system of electric currents chiefly in the higher layers
of the atmosphere, compassing the earth, and parallel to the lines of
equal frequency of aurora borealis.

Considering with Scummt*) magnetic disturbances to be caused by
movement of smaller current-rings over the surface of the earth, the
whole exhibits a strong analogy to the great cyclonic movement of
atmospheric air around the poles and the wandering depressions
within it, so as it has recently been described by H. HmprBranpsson.
It seemed evident that such a system of circular currents must
undergo a daily fluctuation caused by the rotation of the earth
and I tried to separate this influence by taking the difference of
corresponding hourly values on days following a magnetic disturbance.

Though the results pointed to an influence indeed, they were too
vague to lead to definite conclusions; the minuteness of this daily
fluctuation as compared with the irregular changes accompanying
magnetic disturbance being no doubt the cause of it.

Now in 1899 Dr. Lipetine *) showed that sharp results were to be
obtained, when comparing the hourly values of the horizontal com-
ponents on quiet days (Normaltage) with those for all days. In his
interesting paper he gives the hourly values of the horizontal com-
ponents (7, and ys) of disturbing force for the aretic stations for the
months June and July 1883.

The vectordiagrams drawn by him show the remarkable fact that
the vector for all stations moves anticlockwise, with the only excep-
lion of that for the station Kingua Fjord where the vector moves
decidedly in a clockwise direction. Also at Godthaab during part of
the day the same occurs.

In order to study these diagrams for other parts of the earth I
computed them for Greenwich, Washington, Tiflis, Zi-Ka-Wei, Batavia,
South Georgia and Cape Hoorn for the same months (June, July);
also deriving on the same principles the vertical component for
these latter stations and the arctic ones, I found this component to
exhibit chiefly a single daily fluctuation of an amount of the same
order as that found for the horizontal component.

It was easy to classify the stations in the following groups:

') Terrestrial Magnetism V, pg. 123.

*) Meteorologische Zeitschrift 1899, pg. 385.

5) Terrestrial Magnetism IV, pg. 245.

( 315 )
Station Hor. vector moves in diagram : Vertical component shows:
Max. Min.
Kingua Fjord clockwise Evening Morning
Godthaab anticlockwise, but
clockwise in the
evening.
Cape Thordsen \ Evening Morning
Jan Mayen At Ssagastyr ¢ unthrusty.
Ssagastyr At Nova Zembla two maxima and
F ae Rae anticlock- two minima, Z; tends to disappear.
apie wise. At Point Barrow and Bossekop the
Point Barrow fluctuation is the contrary and shows
Nova Zembla a max. in the morning and a
Bossekop / min. in the evening.
Sodankyli anticlockwise, but
clockwise in the
morning. TheE/W Evening Morning
compon. tends to
disappear.
Pawlowsk ee tee
Greenwich ane Morning Evening
Tiflis ; clockwise, but
Washington anticlockwise in Morning Evening.
the evening.
Zi-Ka-Wei No change Morning Evening
in direction,
which stays
WSW-ENE.
Batavia anticlockwise, but Noon Morning
clockwise in the
evening
South Georgia | Oe
clockwise ;
Cape Hoorn 3 Morning Evening

The change in the sense of rotation of the horizontal vector and
in the times of occurrence of maximum and minimum of the vertical
component proceeds quite regularly, when classifying the stations,
as has been done here, by their distance from a pole, which may
be called pole of aurora borealis and is located in + 80°.5 N and
fe GO) WV.

Now it is remarkable that in my paper on the “Erdmagnetische
Nachstérung”’, quoted above, I came to the result, that the disturbing
force acts in planes, which cut the surface of the earth along curves
converging into this pole.

In order to study the behaviour of the horizontal component the

( 316 )

simultaneous horizontal vectors for the arctic stations (after the data
given by LipeLine) have been plotted in a series of 12 maps cor-
responding to the hours of 0%, 2%, 44"..... 22" mean Géttingen time.
These maps revealed the fact that one part of these vectors pointed
to one focus and the rest emanated from another.

The successive places of these foci have been determined as unbiased
as possible. Rectangular coérdinates have been made use of with the
origin in the north pole and taking for « and y axis the meridians
180° and 90° E from Greenwich. The unity for the values of the
coordinates as given underneath is 2 4g 0°.5; accordingly the value of
Vu?+y? represents nearly the polar distance in degrees, because
the maps have been drawn in stereographic projection. The focus
to which the vectors point has been called a positive focus, that
from which they emanate a negative focus.

Mean Gottingen Positive focus Negative focus
hour x. y- un Yy-

Ok 7.4 —22.2 — 8.2 1.6

2 9.6 —17.0 —13.2 — 54

4 11.2 —11.0 —13.2 — 88

6 11.2 — 6.2 —16.0 —11.6

8 8.8 2.2 —12.6 —21.2

10 0.0 2.2 — 8.8 -—28.0
Noon — 44 2.2 2.2 —23.6
14 — 8.8 — 0.6 8.8 —23.6

16 —11.8 — 6.6 13.8 —10.4

18 —14.0 —15.4 9.4 — 6.0

20 —13.2 —26.2 2.8 8.2

22 — 8.8 30.2 — 6.2 6.2
Mean — 11 —10.7 3.4 —10.2

Harmonie formulae caleulated for these four series :

(a= —1.1 + 13.5 sin (¢ + 15°) + 2.1 sin 2 (¢ + 19°)
+ focus ; i
ly — —10.7 + 14.3 sin (¢ + 14°—90°) + 2.4 sin 2 (¢—2°)
f va —3.4 at. 13.6 sin (t + 24° + 180°) + 3.2 sin 2 (t—15°)
ons fy = —10.2 + 15.7 sin (t + 24°+ 90°) + 3.0 sin 2 (¢—50°)

From the constants of these formulae it follows evidently, that both
foci move in nearly the same circular path with almost constant
velocity and with a mutual distance of 180°.

This being granted and calling «, the mean of the «’s for positive

('S17-}
| pana Bray (eae 9 ee
and negative focus: #, = —,——_ = _ —2.3, and y, the mean
oy a7 = 10:2 aa |
for the y's for the foci: 4, = = = —10.5, the values of

(@h—2y)9 —(@y.h—&y)s (Ygh—Yo) and (—Y,,2—yY,) and so on,
must represent the same quantity, from which we may compute a
set of 12 means. The harmonic formulae representing this set is :
v4. = —2.3 + 14.5 sin (x + 22°) + 1.3 sin 2 (« + 28°).

The term of the second order, already small in comparison with that
of the first order, having been still more diminished by this operation,
it may be safely neglected. So we may adopt (for Greenwich time):

4—= — 2.3 4+ 14.5 sin (w + 12°)
y4. = —10.5 4+ 14.5 sin (@ + 12°—90°).
The centre of the circular path, which is best called ‘pole of dis-
turbance” lies accordingly in
bo Nee amd CS" iW
For the pole of aurora borealis I accepted
80°.5 N. and 80° W.
and according to Scumipt the magnetic axis for 1885 cuts the surface in
78°.5 N. and 68°.5 W.

So we have arrived at the remarkable result, that the daily move-
ment of the arctic foci of disturbing force takes place in a circular
path of 14°.5 radius around a pole practically coinciding with the
pole of aurora borealis and lying very near to the north end of’ the
magnetic ais. ;

When now supposing this fluctuation of disturbing force to be
caused by a field, which slides around the earth from East to West
(as has already been remarked by Lipnnine in his paper quoted
above) and this in analogy with our actual views regarding the field
of the ordinary daily variation, we are obliged to assume the field
of disturbance to revolve around the axis just found, viz.

fSPNR Toe IW t0 8 -O. 201° “Ei.

In order to represent the daily field, we have to study the vector-
diagrams themselves. Of coarse the vector-diagrams of one group
show mutual differences caused partly by insufficient material (for
the arctic stations 2 or 3 months only) and partly by local influences,
as has already been indicated by Scummr (Met. Z. 1899).

In order to avoid irregularities bringing confusion in the result,
which may prevent interpretation of this phenomenon (this being of

course the principal aim), I have chosen as representative for each
group one station with an obviously regular diagram.

They are: Kingua Fjord, Jan Mayen, Sodankyla, Greenwich,
Tiflis, Zi-Ka-Wei, Batavia, Cape Hoorn, (Godthaab has been left out,
it being rather superfluous for the horizontal component, and the
vertical component not being available).

The values of the components have been graphically smoothed.
Now to obtain a representation of the daily field the method at
present common of distributing the successive hourly values for each
station along the parallel of that station, has been applied, and thus
I have constructed a map in Mercaror’s projection but according to the
avis of disturbance with the lines of equal vertical component and
horizontal vectors on it.

The lines of equal vertical component compass chiefly eight foci
of maximum and minimum vertical force (of which two are double),
tabulated hereafter. (It should be kept in mind, that latitudes and
longitudes are according to the axis of disturbance). The longitude
of the sun for its position on June 21st has been taken zero.

Latitude Longitude Amount Latitude Longitude Amount
ae eens ce pols 6E Hees
il 161° W 47 y i 74° S1E 456 »
52 156 W Se 4
52 Q ee
ome siya Oe eenuas e
-—10 41 W + 3 22 129K — 15
South of —60 ot W- — ? South of —60 2 + ?

The horizontal vectors drawn in the same map are pointing almost
without exception towards the positive foci and AWay from the
negative Ones.

Supposing the disturbing force to originate from existing electric
currents, the fact that these currents must follow nearly the course
of the lines of equal vertical foree conducts to the hypothesis of
systems of circular currents with eight foci revolving daily around
the axis of disturbance.

The horizontal vector being directed to the point where the vertical
component is upwards, the application of Amprre’s rule teaches that
these currents must flow for the greater part above the surface of
the earth.

temarkable is the rapid diminution of the foree with the polar
distance, almost parallel to the equally rapid diminution in the
occurrence of auroral display. I must emphasize an important
divergence between the fields of ordinary daily variation and that

i +

of disturbance: viz. the former has its foci near the meridians
of noon and midnight, the latter near the line of separation of day
and night.

The axis around which the field of disturbance revolves is so
nearly coincident with the magnetic axis of the earth, that it seems
the field is caused by any emanation from the sun, deflected by the
earth-magnet acting as a whole, and not by the surface distribution
of terrestrial magnetic force.

Full account on this research will be soon given in the Natuur-
kundig Tijdschrift voor Nederlandsch-Indié.

Geology. — “A piece of Lime-stone of the ceratopyge-zone from
the Dutch Diluvium.’ By J. H. Bornema (Communicated
by Prof. Marry).

In a few papers which a short time ago appeared in these reports,
I communicated some particulars of the Cambrian erratic blocks
from the loam-pit near Hemelum; this time I intend to treat of the
Under-silurian ones.

First of all, however, I wish to add something to my information
coneerning the way in which Under-cambrian sandstone with Disci-
nella Holsti Mopera is spread. I then*) said that I had not been
able to find anything certain, in German literature, about erratic-
blocks of this stone. This was a consequence of my sources of
information on sedimentary erratic-blocks being incomplete. After my
paper had appeared, Prof. Sroniny*?) was so kind as to send me
an essay that had seen the light already a few years before, in which
the occurrence of this kind of erratic-blocks in the German diluvium
is made mention of.

No more did I find, here in the Hemelum loam-pit, the opinion
confirmed expressed i. a. by Srarine *), Martin *) and SCHROEDER VAN
per Korx*), that Under-silurian erratic-blocks were almost entirely

1) Bonnema, Some new Under-cambrian erratic- blocks from the Dutch Diluvium.
Proc. Royal Acad. Amsterdam. Vol. V (1903) p. 561.

2) Srottey, Einige neue Sedimentirgeschiebe ans Schleswig-Holstein und benach-
barten Gebieten. Schriften des Naturwissenschaftlichen Vereins fiir Schleswig-
Holstein. 1898. Bd. XI. p. 133.

3) Srarine, De bodem van Nederland. 1860. II. p. 99.

4) Martin, Niederliindische und Nordwestdeutsche Sedimentiirgeschiebe. 1878.
p. 14.

5) ScHRoEDER vAN DER Kork, Bijdrage tot de kennis der verspreiding onzer
kristalliine zwervelingen. Dissertatie. 1891, p. 51. Stelling VIL.

( 320 )

absent in our diluvium. With regard to Groningen this was already
told us by Van Catker'). Afterwards I pointed out the same thing
for Kloosterholt*), and it will appear, too, that boulder-clay of
Hemelum contains as many Under-silurian erratic-blocks as the loam
of the places mentioned.

That the above-named writers are of different opinions may be
easily explained by the way in which stones used to be gathered.
Formerly the hammer was hardly ever used and there is no doubt
that only those stones were gathered whose outward appearance
drew the attention. Now, this very rarely happens with Under-
Silurian erratics. The polyparia of syringophyllum organum L.,
which are probably without any exception Under-silurian, are con-
spicuous for their form, and we really see that old collections contain
these fossils in large numbers. The Upper-silurian erratics, however,
on the outside of which it is sometimes already visible that they
are rich in fossils (which is i.a. the case with limestones with
chonetes striatella Dalm), much sooner draw the attention. This is
especially the case with petrified corals, which mostly bave an
Upper-silurian age. They form, indeed, the greater part of the old
collections.

Even if one uses a hammer while gathering stones, one is sure to
find, in proportion, more Upper-Silurian erratics with determinable
fossils than Under-Silurian ones, because as a rule the former are
much richer in fossils than the latter.

Moreover, in Upper-Silurian erratics Leperditia-valves are frequently
found. As, in consequence of their comparatively small size and their
smooth surface, these valves are easily exposed to view and the
different kinds of Leperditia are easily distinguished and are charae-
teristic of different strata, one may, by means of these remains, deter-
mine the age of many Upper-Silurian erraties.

A great part of our Under-Silurian erraties, however, consist of
pieces of tough, greyish lime-stone, which does not possess many
petrifactions, so that these pieces seldom give a determinable fossil.
Very often an Asaphus, an Illaenus or an Endoceras, found in them,
proves their Under-Silurian age, whereas these remains are too
incomplete to allow of their being ranged under a definite division
of Under-Silurian erratics.

This is even more the case with that kind of limestone of frequent

1) Van Catker, Ueber das Vorkommen cambrischer und untersilurischer Geschiebe
bei Groningen. Zeitschr. d. deutsch. geol. Gesellschaft. Bd. XLIIL pag. 792.

2) Bonnema, De sedimentaire zwerfblokken yan Kioosrernotr. Versl, y. d. Koninkl,
Akad. vy. Wetenschappen. 1898. pag. 448.

( 324 )

occurrence, which petrographically resembles the lithographical one
and probably is of the same age as the Wesenbergen stratum. In
this stone a petrifaction is hardly ever found.

Consequently it takes a long time to gather a collection in which
the different divisions of Under-Silurian stone are clearly represented.
I did not succeed in composing such a collection from the Hemelum
loam-pit. This is partly owing to the fact that this opportunity to
gather erratics existed only a short time. The boulder clay proving
unfit for use in brick-works, digging has been left off.

The principal cause is, however, that boulder clay used to be dug
there in the beginning of winter, and that in the latter part of that
season the erratics found were broken to pieces for macadamizing
roads, whilst in this very part of the year neither my occupations
nor the weather allow of my making excursions.

The erratic I am going to treat of, was found by me in the
Hemelum loampit a few years ago; it may undoubtedly be ranged
under the Ceratopyge-zone, the eldest of the Under-Silurian kinds.

It contained a kernel of compact, splintery limestone, of a light-
grey, more or less greenish colour. This kernel was surrounded by
a yellow-brown, softer crust, caused by corrosion, which was coloured
greyish at the surface. Occasionally I distinguished small glauconite-

and pyrite-grains.

When I broke it to pieces, the kernel naturally did not give me
any fossils; I succeeded, however, in exposing to view, from the
corrosion-crust, the following fossils:

1. Ceratopyge forficula Sars’). Of this species I found a head-
midshell, a free cheek and three fragments of pygidium. These
remains come from the variety acicularis Sars et Boeck, the axis of
the pygidium consisting of 6 segments. The head-midshell, too, bears
more resemblance to fig. 15 than to fig. 17.

2. Symphysurus angustatus Sars et Boeck *). One glabella and
three small pygidia were found. In the latter it becomes quite
clear that as a rule the axis may be clearly distinguished only in
stone-kernels.

3. Holometopus (?) elatifrons Ang*). Numerous more or less unin-
jured head-midshells presented themselves. Only in one specimen,
one side of which is still in the stone, the prick in which the glabella
ends towards the back is visible.

1) Broéecer, Die silurischen Etagen 2 und 3. p. 123. Tab. IIL. fig. 15—22.

*) Bréecer loc. cit. p. 60. Tab. IIL. fig. 9, 10, 11.
3) Broeeer loc. cit. p. 128. Tab. IIL. fig. 13,

—— ee ee

( 322 )

4. Euloma ornatum Ang’). A piece of a head-midshell and of a
pygidium were exposed to view.

5. Agnostus Sidenbladhi Linrs.*). This species is represented by
a head-shell.

6. Shumardia pusilla Savs*)? 1 am inclined to range under this
head a very small pygidium, which doubtless comes from a Shu-
mardia-species. That I am not quite certain here, is owing to the
fact that it shows a lateral compression and consequently is not so
broad as the pygidium pictured by Mosere *). The latter, which has
been produced from slate, may be somewhat flattened, whereas the
pygidium out of my erratic-block has probably retained its original
shape. It is also possible, however, that it comes from a new Shu-
mardia-species. According to Hennig *) such a new species is met
with in the Ceratopyge-zone of Figels’ng. Unfortunately the essay in
which this species was to be described — which essay was shortly
to be published, according to that writer —, still keeps us waiting.

7. Orthis Christianiae Kjerulf*). Several valves of this little
Brachiopode were found.

The three first species of Trilobites are, according to TULLBERG ‘)
also met with in the lowest strata of Oeland Orthocere-lime, but as
this does not appear to be the case with the other fossils, I do not
hesitate to call this erratic-block a piece of Ceratopyge-lime.

Erratic-blocks from the Ceratopyge-zone with remains of Trilobites
seem to be very rare in the German and the Dutch diluvium. As
far as I can see, only two have been made mention of by REmMELs *)
and one by Srouiey’), as most certainly belonging to this zone.

1) Bréacer loc. cit. p. 97. Tab. Ill. fig. 5, 6.

2) Linnarsson, Om Vesiergotlands cambriska och siluriska aflagringa. Svenska
Vetenskaps-Akademiens handlingar. 1869. Bd. 8 No, 2. p. 74. Tab, Il. fig 38, 34.

3) Broacer, loc. cit. p. 125. Tab. XII. fig. 9.

*) Mosere, Om en afdelning inom Oelands Dictyonema-skiffer s*som motsvarighet
till Geratopygeskiffern i Norge. Sveriges geologiska undersdkning. Ser. GC. No. 109.
p. 4.

5) Hennic, Geologischer Fiihrer durch Schonen. 1900. p. 33.

6) Gacet, Die Brachiopoden der Cambrischen und Silurischen Geschiebe im Diluvium
der Provinzen Ost- und Westpreussen. Beitriige zur Naturkunde Preussens, heraus-
gegeben von der Physikalisch-Oeconomischen Gesellschaft zu K6nigsberg. No. 6.
1890. p. 34. Taf. II. fig. 22.

7) TutteerG, Férelépande redogérelse for geologiska resor pa Oeland. Geologiska
Féreningens i Stockholm Férhandlingar. 1882. Bd. VI. p. 231.

5) Remett, Ueber das Vorkommen des Schwedischen Ceratopyge-kalks unter den
Norddeutschen Diluvialgeschieben. Zeitschr. d. deutschen geol. Gesellschaft 1881.
Bd. 33. p. 696.

%) Srouey, loc, cit. p. 135.

( 323 )

They are, however, not like the Hemelum piece, those of Remenx
being many-coloured and that of Srontny being a piece of yellow
iron-ochre, which aceording to him probably originates, through the
influence of corrosion, from a Cclayish kind of stone, which is rich
in iron.

Formerly Reme.t *) declared that the erratic-block found near
Neustrelitz, from which Bryricu described his Harpides rugosus, most
probably was Ceratopyge-lime. He came to this conclusion especially
beeause in the Swedish and Norwegian Ceratopyge-zones is found
the species that is the nearest relation to Harpides rugosus Sars. et
Boeck, and that at the time no specimen of this species had been
found in higher strata.

Now that Tuniperc*) has informed us, however, that in the
lowest, grey Orthoceratite-lime of Oeland a new species of Harpides
is found, this erratie-block is much less likely to be Ceratopyge-lime.
The less so, as according to Remeré this erratic greatly resembles
glauconite Vaginaten-lime (= lowest grey Orthoceratite-lime).

If attention is paid only to the petrographical nature and the
presence of Orthis Christiniae, most probably more erratics of the
same kind have been found in the German diluvium. GorrscHe *)
at least makes mention of a light-grey, splintery lime-stone, green-
and yellow-tinted, which Lunperrn took for Ceratopyge-lime. He
also tells us, however, that this stone perfectly resembles pieces
of Ceratopyge-lime that were gathered by Damns near Aeleklinta,
whereas Horm *) informs us that this Under-silurian zone is entirely
absent there.

It is possible, too, that to this kind belongs the Ceratopyge-lime
which Sreusstorr*) under 4 described as light-grey lime with a
greenish tint and a little Orthis.

Corresponding erratics seem also to have been found by Stouiey °).

1) Reme eg, loc. cit. p. 500, 695.

2) Tuttpere, loc. cit. p. 232.

5) Gorrscue, Die Sedimentiir-Geschiebe der Provinz Schleswig-Holstein. 1883.
p. 14.

4) Horm, Om de vigtigaste resultaten frin en sommaren 1882 utférd geologisk-
palaeontologisk resa pi Oeland. Oefversigt of Kongl. Vetenskaps Akademiens
Forhandlingar. 1883. p. 67.

5) SreussLorr, Sedimentiirgeschiebe von Neubrandenburg. Archiv des Vereins der
Freunde der Naturgeschichte in Mecklenburg. 1892. p. 163.

6) Srottey, Die cambrischen und silurischen Geschiebe Schleswig-Holsteins und

ihre Brachiopodenfauna. Archiv fiir Anthropologie und Geologie Schleswig-Holsteins
und der benachbarten Gebiete. 1895. Bd. I. p. 43.

( 324:)

Only those pieces are considered which, as he says, are so compact
as to resemble serpentine.

An erratic-block of the same kind has perhaps also been found
in the eastern part of the German diluvium. GaceEL’) at least speaks
of a greenish, hard piece of limestone, with yellow spots here and
there in consequence of corrosion, in which little glauconite-grains
occur rather scattered. He does not tell us whether it is compact.

Though in all these pieces, except that of SreussLorr, Orthis
Christianiae is declared to be present, and though petrographically
they seem more or less to resemble my erratic-block, — I dare not
take it for granted that they are closely related to it.

It must further be traced where corresponding limestone is still
found as firm rock. This is certainly the case at Ottenby on the
western coast of the southernmost part of Oeland. Last summer I
could convince myself of this. Ceratopyge-lime is there not only of
ihe same petrographical nature (in most cases at least), but is also
rich in fossils. Hotm informs us that towards the midst of the island
this stratum is less developed; its colour is more reddish here, and
it is less rich in fossils, so that as a rule only Orthis Christianiae
is met with. In the northern part of Oeland it is altogether absent,
according to Hom.

In Schonen, Ceratopyge-lime has been found only near Figelsgng,
as far as one knows for certain. This kind, however, is more bluish-
coloured, which I can observe in a piece I received from Prof. Moperre.
Corresponding limestone may also occur in West-Gotland, on Kinne-
kulle and Hunneberg. According to Linnarsson *) the Kinnekulle-stone
is a hard, light-grey, mostly bluish and greenish limestone, often
with numerous small, blackish-green glauconite-grains. He says that
the Hunneberge limestone is little or not at all bituminous, now com-
pact, now crystalline, either black or grey, and frequently containing
pyrite. So there is a possibility, to be sure, that such-like limestone
is found there; but without any material for comparison nothing
can be said with certainty.

Ceratopyge-lime, which, as is generally known, is not met with
in the Russian Baltic-seaprovinces, moreover still occurs as firm rock
in the south of Norway and in the environs of Christiania and
Mjésen. Horm *) declares it to be occasionally so much like that of
Ottenby in Oeland, that he is unable to distinguish one kind from

1) GaceL, loc. cit. p. 9. 10.
2) Linnarsson, loc. cit. p. 30, 56,

8) Hom, loc. cit.

( 325 )

the other. Bréeerr'), however, tells us again and again that it is
blue-coloured, so that I suppose that in colour it more resembles
that of Fagelsing. A piece of Ceratopyge-lime which I saw at the
Groningen Geological Institute, seems to confirm this opinion.

Finally it remains to be examined where we must look for the
origin of this erratic-block. I suppose it to come from a place not
far from Ottenby. The in every respect perfect resemblance between
our erratic and Ceratopyge-lime that is found there, may first of all
be said to speak in favour of this opinion. The circumstance, secondly,
that in the Hemelum loampit I found many kinds of erratic-blocks
that are also found in Oeland, makes this highly probable. I need
only remind of those pieces which I formerly described, pieces of
Scolithus-sandstone, sandstone with intersecting layers and Discinella
Holsti-sandstone; whilst there are many more, as I hope I shall
point out within a short time. This resemblance in- erratic-blocks
makes it more probable, first that the ice came down to us via
those regions, and at the same time that a piece of Ceratopyge-lime
was brought from there to here.

Chemistry. — In the meeting of Saturday May 30, 1903 Prof.
S. Hoogrwerrr and Dr. W. A. van Dore communicated a paper:
“On the compounds of unsaturated ketones with acids” and in the
meeting of Saturday September 26, 1903 Prof. Tu. H. Brnrens com-
municated a paper: “The conduct of vegetal and animal jibers towards
coal-tar-colours’’.

(Both communications will not be published in these Proceedings).

1) Bréager, loc. cit. p. 14.

(November 25, 1903).

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,

PROCEEDINGS OF THE MEETING

of Saturday November 28, 1903.

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige

Afdeeling van Zaterdag 28 November 1903, DI. XID.

Ce ain aay TES.

A. F. Hotiteman and J. W. Beexman: “Benzene fluoride and some of its derivations”, p. 327.

H. W. Bakuvis Roozresoom: “The system Bromine + Iodine”, p. 331.

R. O. Herzoce : “On the action of emulsin”. (Communicated by Prof. C. A. PEKELUARING), p. 332.

Eve. Drnois: “Deep boulder-clay beds of a iatter glacial period in North-Holland”. (Com-
municated by Prof. K. Marry), p. 340.

G. vay Risyperk: “On the fact of sensible skin-areas Gying away in a centripetal direction”
(Communicated by Prof. C. WiykLEr), p. 346.

C. Wrsker and G. vax Ruwxeerk: “Structure and function of the trunk-dermatoma”, IV, p. 347.

J. D. vax per Waats: “On the equilibrium between a solid body and a fluid phase, especially
in the neighbourhood of the critical state”, (II part), p. 357.

P. H. Scnovre: “Centric decomposition uf polytopes” p. 366.

J. M. van Bemuecen: “Absorption-compounds which may change into chemical compounds
or solutions’, p. 368.

The following papers were read :

Chemistry. — “Benzene fluoride and some of its derivations.” By
Prof. A. F. HoLteman and Dr. J. W. Brevxman.

(Communicated in the meeting of September 26, 1903).

Benzene fluoride has, up to the present, been a not at all readily
accessible substance. The best known method of preparation is
that of Watnnacnh and Hevster (A. 245, 255) which consists in
first preparing benzenediazopiperidide and decomposing this with

oy,

Proceedings Royal Acad. Amsterdam. Vol. VI.

( 328 )

hydrogen fluoride. These chemists are even of opinion that benzene
fluoride may thus be readily prepared by the kilo. As regards the
course of the reaction our experiences are quite in harmony with
those of Wannacn and Hevsier, but we differ in the appreciation of
the convenience of the method. Apart from the fact that in our
pumerous experiments we have never succeeded in obtaming the
yield of 50°/, (on an average we only got 30°/, from the aniline
employed) which they claim to obtain, the recovery of the piperidine
proved to be very tedious. Notwithstanding its price is considerably
lower than it used to be, as it is now prepared by electrolytic
reduction of pyridine, it is still such that this recovery could not be
avoided. The base must be again isolated in a state of perfect purity,
because the yield of diazopiperidide becomes very small if the smallest
impurity should be present. The method is also very tedious as
not more than 10 grams of diazopiperidide at a time should be
treated with hydrofluoric acid, otherwise the reaction becoming too
violent. After having prepared about 150 grams of benzene fluoride in
this way we, therefore, decided to abandon this method and to endea-
vour to obtain benzene fluoride by the direct diazotation of aniline.

For this purpose VALENTINER and Scuwarrz have taken out a
patent (Centralblatt 1898 1, 1224) consisting in heating a solution of
benzenediazonium chloride with hydrogen fluoride. We may surmise
that the product will be a benzene fluoride contaminated with benzene
chloride; on following their directions this proved to be the case to
such an extent that after repeated fractionation of the product 100
erams of aniline yielded) only two grams of fairly pure benzene
fluoride. This showed that in the diazotation of aniline, intended for
the preparation of benzene fluoride hydrochloric acid should be avoided.

| do not wish to enter into particulars as to the various ways
in which we _ have ~-tried to prepare benzene fluoride directly
from aniline. Dr. Brekman has stated something about this in his
dissertation. It will be sufficient to mention here that the yield
of the desired) product increased with the amount of hydrofluoric
acid employed. This is the method which we finally adopted: 93
erams of aniline are dissolved in sulphuric acid and diazotated in
the usual manner, care being taken that the volume of liquid does
not exceed 1.25 litre. The ice-cold solution is then poured slowly
with vigorous stirring info a copper vessel containing 500 ce. of 55°/,
hydrofluoric acid heated nearly to the boiling point and kept at that
temperature. The benzene fhioride distills over and is condensed ina
leaden worm-condenser surrounded by ice and salt. The distillate
consists of a colorless liquid, which is freed from traces of phenol

iat

by washing with a little alkali. After drying over calcium chloride
it at once distilled over at a constant temperature of 85°. From 93 grams
of aniline 37 erams of benzene fluoride are thus obtained in a_per-
fectly pure condition, that is to say 40°), of that required by theory.
The deficiency in the yield is caused by the formation of phenol.
Probably this may be reduced to a minimum if instead of hydro-
fluorie acid a mixture of sulphuric acid and calcium, fluoride is used
in such a manner that the concentration of the hydrogen fluoride
remains about constant. As this plan involves vigorous stirring and
as our mechanical appliances were inadequate to stir the resulting
paste of g@ypsum, we have not been able to practically confirm
this obvious conclusion.

In quite an analogous manner the para- and metanitrobenzene
fluoride may be prepared from the corresponding nitranilines and
the three toluene fluorides from the toluidenes. Anthranilic acid,
however, only yielded small quantities of o-fluorobenzoic acid and
was nearly all converted into salicylic acid. It was very interesting
to notice that, when treated by this process, orthonitraniline did not
yield a trace of ortho-nitrobenzene fluoride but only resinous masses.
Watiacn has also been unable to prepare this substance by his own
method as he did not succeed in purifying the piperidide required.
We have made two further attempts to prepare this substance.
Firstly by isolating it from the nitration product of benzene fluoride,
but as this coutains but little of it we did not succeed either by
freezing or by fractional distillation. Secondly from parafluoronitro-
benzene; the p-aniline fluoride obtained by its reduction yields when
nitrated in sulphuric acid solution

C,H; ELNH, NO. 74-2)
so that by eliminating the amido-group, o-nitrobenzene fluoride must
be formed. But only resinous masses were again produced here.

The determination of carbon, hydrogen and nitrogen in the fluorine
compounds could be done in the usual manner. For that of the
fluorine we used a platinum tube 35 cm. in length and 1.8 cm. in
diameter in) which the substance was introduced mixed with CaO.
After heating the mass contains the fluorine as calcium fluoride,
which is then freed from the excess of lime by treatment with
dilute acetic acid, collected on a filter and weighed. As we never
found lime to be perfectly soluble in dilute acetic acid, it was
purified by dissolving it in dilute acetic acid, precipitating with
ammonium carbonate and igniting the carbonate so obtained.

The physical constants of some of the compounds prepared by us,
were accurately determined and the following values were found:

22%

m. p b. p sp. gr. at 84°.48
m-initrobenzene fluoride {oy IOS 1.2532
P- 9 = 26°.5 205° 12583
p-aniline fluoride — 187° Se
nitraniline fluoride(1:2:4) 98° = am.
benzene fluoride —41°.2 85° 1.0256 (at 20°/4)

It is a well known fact that the halogen in the halogen benzenes
is very inert but that on further substitution in the benzene nucleus its
displacement may be much facilitated. In how far this is the case with
benzene fluoride and its derivatives has received but insufficient notice up
to the present. Wantacu and Hrusner (A. 248, 242) state that sodium
acting at a gentle heat on an ethereal solution of benzene fluoride
abstracts all the fluorine with formation of diphenyl. We repeated
this experiment, but noticed but little formation of diphenyl! although
considerable quantities of resin were formed. Moreover, the sodium
was but litthe attacked. Another process for studying the decomposition
of halogen benzenes is that of LOWENHERZ consisting in dissolving the
compound in a large excess of alcohol and then adding sodium. If
we call (Va) the number of gram-atoms of sodium which is present
at a given moment in a kilo of solvent, @ the original halogen
compound and .« the portion then converted we have according to
him the relation

du:

—= Ke a,
d(.Na) : \

in which A’ is a constant which he gives the name of ‘useful effect”
(Nutzeffect).

We repeated one of LOWrENHERZ’s experimental series with benzene
chloride and found the useful effect to be O.261 whereas he had
found 0.254 and 0.268.

On applying the process to benzene fluoride if was found that
sodiuin when acting on its alcoholic solution does not abstract a
trace of fluorine, so that the useful effect =O. This result is sur-
prising, because according to the investigations of LOwrnnErz the
useful effect is about equally great for the other halogen benzenes.
It shows that the fluorine in the nucleus is more firmly combined
than the other halogens; some data of Wannacn and Hruster agree
With this view, for instance, that by the action of sodium on an
ethereal solution of p-benzene fhiorobromide for 8 days a large amount
of sodium bromide had separated but not a trace of Na FL.

Qn the other hand we notice the great facility with which the
fluorine of the benzene nitrofluorides reacts with sodium methylate ;

( Sa)

the m- and p-compounds, when heated for a short time with this
reagent in a methyl alcoholic solution, ave quantitatively converted
into the corresponding nitro-anisols. In the case of benzene dinitro-
fluoride (Fl. NO, : NO, = 1:2:4) the progressive action of the sodium
methylate was studied by the method eniployed by Lenors for the
corresponding Cl-compound and it appeared that the reaction was
quite completed within a few minutes. Owing to this great celerity,
accurate quantitative measurements were very difficult; but it was
found that the reaction constant im round numbers is 600 times
larger than with the chlorine compound.
Groningen, Sept. 19038. Chem. Lab. University.

Chemistry. — ‘Vie system Bromine + Todine.” By Prof. H.W,
Bakuvls RoozkBoom.

(Communicated in the meeting of September 26, 1903.)

The elements chlorine and
iodine vield two chemical com-
J00

160

pounds which have been aceu-
rately investigated by SrTorTEN-
BEKER. Up to the present the
relations of the other halogens
S40 remaimed in’ obscurity. The
system Bromine and Todine
investigated by Mr. Mrrrum Trr-
Wwoer gave, provisionally, the
ais results represented in our tem-
perature-concentration figure.
Kirst of all the two boiling

da
lines ADB and ACB, which
es were both determined at 1 Atm.
pressure. The first line represents
yo the boiling points of the series
of liquid mixtures from 100°/,
2% Br. to 100°/, I; the second line
represents the vapours yielded by
a these mixtures. The correspond-

ing points are situated on hori-
zontal joining lines.
The figure shows that these

curves are continuous, but

approach each other between 50 and 60°/, I. This case, therefore, is
similar to the behaviour of the mixtures of Cl and 5 studied some
time ago’), with this difference that for the composition 5,Cl, the lines
nearly came into contact, whilst in this case the distance remains
much greater.

The peculiar form of the boiling lines points, however, to the
existence of combined molecules of the two elements. Whether these
answer to the formula Br I cannot be decided from the form of this line,
but perhaps better from the p,x-lines which will be studied afterwards.

Below the line ADB the region of the liquids is situated. These
on further cooling deposit solid phases. These phenomena are represented
by the two lines EFG and EHG. The second line shows the
initial and the first line the final solidifying points. They form
two continuous lines which however come into contact at 50 atom
percent I.

A similar type of solidification points as a rule to mixed crystals.

The equality of the composition of liquid and solid at the con-

centration Brl — without this point being a maximum or a mini-
mum — could, however, only be explained by assuming that Br I

is a chemical compound.

Possibly this is the case, which has never as yet been satisfactorily
proved, where a compound is mixable with both its components.
We will endeavour to elucidate this matter by a determination of
the density ete.

Chemistry. — ‘On the action of emulsin.” by Dr. R. O. Herzog.
(Communicated by Prof. C. A. P&rkeLHARINe).

(Communicated in the meeting of October 31, 1903).

Il. If we mix a solution of canesugar with invertin and determine
the quantity inverted in definite times at a constant temperature, it
appears that the inversion does not proceed as a reaction of the first

pee
order ( & — yi -} the “constants” calculated from this equation
increasing continuously during the period of the inversion. This
might be explained by the increasing activity of the enzyme or by
the inthuence exerted by the invert sugar formed.

V. Henri?) has shown in an exhaustive paper that the latter

is the cause and that the reaction proceeds according to the law

1) These Proc. June 1903.
*) Zeitschr. fiir physikalische Chemie 39, 194 (1901),

( 333 )

regulating the unimolecular reaction where the products of reaction
act (positively) autocatalytically.
For a similar case, OstwaLp') has given the equation of reaction:
da
— tee eeoay(a—z). . . . . » «= Gl)
dt
If we integrate this equation and take «=O, ¢=0O we find:
Lake th)
ktka | k(a—a)
In this equation @ is the concentration at the beginning, « the
amount of sugar inverted at the period ¢, k, and k, are the velocity
constants. If we call

ak,
252 3), lS ee eee ©)
k,
we obtain the expression
1 atewv
oe ay (4)
t(1 +e) a— wv
which is more- convenient for purposes of calculation.
In this particular case +1, therefore for ~=1 k, = &,.
Equation (4) now becomes:
1 ate
ey Boe bee pes. 2s (hy

t a-—-2x

2. If we measure the velocity of the emulsin action if appears
that the “constants” of the logarithmic expression keep on decreasing
as has already been stated by Ta wMany °*).

As it appears from Hknri’s experiments *) that the enzyme suffers
no change, at least when the time of reaction is a short one, it was
evident that the cause of the phenomenon was to be sought in a
negative autocatalysis namely, i the retardating miluence of the
products of Nversion.

In a similar case the equation of the reaction assumes, according
to Ostwanp *) this form:

ioe ee ee) se Oe sw) e 2 = (6)

After integration and calling «=O t=O, we find:

1) Lehrbuch der allgemeinen Chemie. II, 2. 1 Teil. S. 264, 265.
2) Zeitschr. fiir physikalische Chemie 18. p. 426 (1895).

5) Théses P. 106, 107. (Paris 1903).

4) ].c. 271,

334 )

<2 /. GEN ecsaes sfo (7)
k.—ak, | k,(ak,—k,)
If again we take :
ak
—=8 8
; (8)
we find :
1 ] a—EéEe 9
=o a (9)
or
Lv
1—e-—
1 a .
I, —) =
Lv
, eee
a

in which @ is the concentration at the beginning, 7 the amount of
sugar inverted in the period f, i, the velocity constant of the reac-
tion if taking place without autocatalysis and 4, the constant of the

autocatalysis.

3. This formula was investigated in a number of cases and it
appeared that the reaction may indeed, be represented by that
expression.

As in the ease of invertin it has appeared that the quantity ¢,
whieh, according to the assumption made, need only remain constant
during the same series of experiments, as a rule suffers but little
change (from 0.6 to 0.8). Probably, the value of ¢ depends on the
previous history of the enzyme, but it should be remembered that
emulsin is much more sensitive than invertin.

In the following tables

a stands for the concentration at the start

wv the quantity inverted, therefore

= the relative quantity inverted

¢ the corresponding time in minutes.

The third column contains the value of 4, (1—s) caleulated accor-
ding to (LO).

In the fourth column we find 9 = —2.

Jon

Experiments by V. Hexri') on October 80, 1902
bs
0.14 N. Salicin solution == 0.6,
2 ——-
ee) da =< 10° 2
a t [( ) zy] ~
0.132 25 [64 | AG
0.209 aD SO ASD
0.306 87 SI 182
0.534 D4 78 DSi
0.603 | 274 76 148
O.GS86 375 73 135
0.950 1325 Apa LOO
I]
0.07 N. Salicin} solution -= 0.6.
= a =
= t [(i—=) #,j70' | -><105
0.174 D4 15 345
0.351 D4 16 34S
0.450 86 14 302
0.691 210 13 IAS
0.775 270 14 AG)
0.847 | 14 220
Experiments by V. Henri on October 8, 1902.

0.14 N. Salicin solution

Sea ja
L -

t=) 10

a : “i
0.110 Ol [G68]
0.305 125 a3
0). 447 211 58
0.516 276 aD
0.583 343 a6

) Theses P, 108—109.
*) Calculated by Henri le. p. 103.

Il.

O.07 N. Saliemn solution :—= 0.6.
r 7 BAe

fy } =) )7' )

a [(A— =) A, ] A

0.476 122 It
0.654 20) 12
0.691 275 10
0.767 42 1}

336 )

IIT.

0 O35 N. Salicin solution <«

0.6,

-- t ((A—=) Ay] 104

0.182 | 9®& | 13
0.564 191 | 15
0685 | 208 | 43
O.818 975 | 16
0.879 341 17

Experiments by V. Henri on October 10, 1902.

lf Il.

0.14 N. Salicin solution =: =0.&. 0.105 N. Salicin solution -—0O.8,
i t ((A— 2) &,] 10° : t ((1—s) &,] 40°
ee ee ee
0.479 60 31 0.216 6) 39
0.374 177 97 0.462 176 37
etot oie IO4. DS 0.606 | Wy 9) vAg)
0.550 355 27 0.636 357 36
0 579 415 25

III. IVs

().075 N. Salicin solution + 0.035 N. 0.105 N. Salicin solution + 0.035 N.
(Saligenin + glucose) == 4, (Saligenin + glucose) :=0°8.

I] 108 cs | 4. a
a t [ 1-2) 4] rs t ((1 =) &,} A

().457 i 28 0.128 59 »
0.400 172 32 0.344 176 9
0.539 9) | By 0. 59 293 23

0.597 300 32 Ose 357 24

iS VI.

0.07 N. Salicin solution + 0.07 N.

(Saligenin + glucose :=0.8.) 0.7 N. Saliein solution :— 0.8.
0 eae eee aes fit eA |
ie | t | ((A—2) #,]10 - t [(1—=) £,] 10°
0.146 a 25 0.291 58 (a
Asean 173. - | De 0). 524. 172 50
O376) }..2802° | [17] 0.688 | 291 ays)
|
0.536 | 335 25 () 712°) 355 49
VI. VIII.
0.035 N. Salicin solution + 0.035 N. Heh
(Saligenin + glucose) :=0.8. 0.035 N. Salicin solution -=—0.8&,
i uae Ne es aa ms = wv r= | 2 ; -
3 t | [( 1—:) ky] 10° oT | t {(1— 2) hy | 10%
0.194 Sie 36 Q) 394 | D6 Q5
|
0.469 110s 42 0.695 170 gy»
0.618 989 | 49, 0.880 IRS [136}

Experiment communicated by TAMMANN.

Zeitschr. fiir physikalische Chemie. 18. 436

3.007 gram Salicin in 180 cc. water :=0.6.
SS SS SS SS - —
=f (>) [A—z) &] 108 | 2108 8)

sar S71 geet D4 61
0.32 | 3 | I5 D7
(ONS aie ems | [38] [75]
0 65 8 30) ts)
0.76 12 29 52
(OT ite 26 ath AO
0 98 | 59 | IR | 35

| | ;

By way of comparison I cite an experiment with amyedalin which

I have made in the course of another investigation.

1) In the original paper it says 0.612, but this is probably a mistake.

2) In hours.
3) Calculated by Tammany,

The hydrocyanic acid was titrated by Linsic’s method; in the first
period of the reaction, values are found corresponding with those

of the sugar determination *).

0.4 N. Amyegdalin solution.

t [(1—=) Ay] 10*

a |
0 507 | 60, 25
0.619 80 26
0.732 12) 27

4. These tables show that the immutability of the expression in
the third column is satisfactory. In Hrxris experiments those values
differ but little more than those of the invertin action. To some
extent the experimental errors may certainly be attributed to the
sensitiveness of the emulsin and partly also to the method followed.
The table with TAmMANN’s experiments proves this. The constants
vary within rather large limits but agree reasonably with an average
valtie.
>. If we now accept the hypothesis of the negative *) autocata-
lysis, and after What has been stated this seems to me quite per-
mnissible, there will be found to exist an evident parallelism between
the action of emulsin *) and invertin.

The ferment-reactions which up to the present have been accurately
studied proceed therefore according to the scheme :

da:
a == (hee Saat) LO) ork
in which 4, may also be zero *).

This, however, only means that 4 is constant for the same series
of experiments or for a definite concentration of material *) and enzyme.

We may say that there exists a function of the form:

k, a (a, h) oe erg tate a sae eee (12)
in which a is the concentration of the inve:tat.le matter and 4 that
of the ferment.

1) Compare Tammany, Zeilschr. fiir physikalische Chemie. 3, 27 (1889).

2) This may be one of the causes that the synthetical experiments with emulsin
(Tammany, Eamerting) have given a negative result

3) This is probably also the case with other ferment-reactions.

‘) It is not inconceivable that cases may occur where if ¢ is small, 2 would at
first act positively and afterwards negatively.

5) Up to the present it is only haemase for which Srnrer (Zeitschr. fiir physi-
kalische Chemie 44. p. 257, (1903)), has obtained diferent results within a small
concentration limit.

( 339 )

In any case we may conclude that the differential equation (11)
is incomplete and that it would be better to give it the form for
a reaction of a higher order’).

= (A, =" ka) (¢—w') (Ji, ach See ea G5 3
dt F

which corresponds within certain limits with experience *
Generally this relation is expressed by the equation:

a) ky
— eet SERENE SS ae 14
6 k

/ 2

From TAMMANN’s*) experiments with emulsin if appears that in
any case
i ieee — oo tee eo, a (19)
It is also important to observe that /;, is apparently only changeable
within the limits of the experimental errors, whether we start from
the concentration a, of the substances to be inverted or whether we
choose as the starting point the concentration a, -+ 7, in which a, << a,
and w corresponds with an amount of inverted product corresponding

with @,—a«a,; Henrt has already pointed this out for invertin.
< ak, E
From —— = constant we obtain the somewhat unexpected result :
k,
em
a Pe k,
Ce a
V2

in which @ and @ represent the concentrations of the substances
undergoing inversion, 4, and /,, y, and y, the corresponding velocity
constants. [ hope shortly to revert to this matter.
The matter communicated here has no connection with the later
formulation of Henri’) which I cannot vet accept as conclusive.
Utrecht, ab. gen. and inorg. Chemistry University.

du: ar
1) The formula 7 == (ee ee a (Goat) = he ee — r) («@ —- w) represents
( "3

indeed an expression for a bimolecular reaction.

2) Compare, Zeitschr. fiir physiologische Chemie, 37, 159. (1902).

There is an evident connection with Horrsema’s experiments (Zeitsclir. fiir physi-
kalische Chemie) 17, 1 (1895) but it seems to me that we must not think with
Héper (Physikalische Chemie der Zellen und Gewebe, 1902 p. 312), ef any diss >-
ciation of the ferment, but rather of that of the substances dissolved therein. Like
Ho6ser however, | attach no particular importance to an explanation of this kind
based on analogy,

%) Zeitschr. fiir plysikalische Chemie. 18. 426, (1895),

4) Lois générales. p. 107.

( 340 )

Geology. — “Deep houlder-clay heds of ad latter ylacial period iN
North-Holland’. By Prof. Eve. Desots.

(Communicated by Prof. Marry in the meeting of May 30, 1903).

In the dunes near Castricum, borings have been done lately, a
provincial lunatic asylum being planned on the spot. With the kind
permission of Mr. J. Scronren, chief-engineer of the ‘‘Provinciale
Waterstaat” in North-Holland, 1 was allowed to make some hydro-
logical observations and to inspect the specimens of the sediments
met with in the borings.

When examining them a remarkable peculiarity came to light,
which I subsequently learned to have been found also in a former
boring at Uitgeest.

While, namely, in the dunes at Castricum, down to the lowest depth
of the borings, no geological facts were observed not known to me
from elsewhere, in two boring-holes, at a distance of about half
a kilometer from each other, frem north to south, at a depth of
32.5 > A.P., a very tough clay was found which possesses
al the qualities of boulder-clay. Immediately on it rests a bed,
about 12 M. thick, of coarse-grained sand and gravel, which, near
to its basis, together with Rhinish pebbles, contains also Scandinavian
ones. Very probable =—_ several circumstances point in that
direction — many, at least of the latter, had been imbedded in
the clay.

As already said, the clay was very tough, mixed however with
very angular, finer and coarser grit. Washed, it proves to consist
for a large proportion of real clay (hydrous aluminous silicate).
Dried it is hard as bricks. In short it is a real, glacial boulder-clay.
The colour is bluish-grey ; yellow or reddish clay could indeed not
he expected at such a depth.

The pebbles from the gravel-bed, and partly no doubt from the
clay, are remarkable for their petrographical character.

Besides quartzite of different colours and fine-grained sandstone
largely intermixed with mica, white quartz, lydite, flint, there are
granite and some other stones of eruptive rock species; amongst
others also alndite, altogether 30 pebbles, all of them evidently of
Seandinavian origin, but [also picked up from the gravel, overlying
the elay-bed, (part of it apparently had got washed out from the
clay-bed by the boring process) some thirty pebbles of Silurian
limestone, mostly beyrichian-limestone, of the same kind as those,

~ well known to me, from the bottom-moraine of the Mirdum = Klif in
Gaasterland, which fact places their origin beyond any doubt.

The biggest of those limestone pebbles, consisting of coral-lime-
stone, is of 32, the smallest of 8 mM., maximal dimension. <A
dark slate stone of 3838 mM. greatest dimension, shows a polished
surface as by ice-action.

The fact that we meet here with a formation of the same kind
as the one found on the south coast of Friesland, grew perfectly
clear when examining specimens of deposits from borings, done by
Mr. A. J. Storn:, near the station of Uitgeest, at 5 or 6 K. M. south-
east of those near Castricum. Mr. Srorn who made also the borings
in the dunes near Castricum, had not only kept the specimens of
those at Uitgeest, but of many others done by him, which speci-
mens he allowed me to study.

Also at Uitgeest, at a depth equal to that at Castricum, i.e. from
31 M. down to 38 M. > A.P., a large number of stones have been
found imbedded in clay, mixed with grit of rocks, perfectly similar
in their petrographical character to those at Castricum; those stones
were even of considerable dimensions and for more than the half
undoubtedly of Scandinavian origin. Under the clay again gravelly
sand, to a depth of 45 M., where it rests on a bed of rather stuf clay.

According to communications from Mr. Srorn, the stones, for the
greater part, come from the clay-bed, 7 M. thick.

Indeed some of the stones show some still adhering clay. Amongst
the rocks are prominent, besides quartzite — of which the biggest
stone is 85 m.M., maximal dimension —, white quartz, an odd lydite
and sandstone, some pieces of crystalline arkose, from the Bunter
on the Rhine, of the size of a walnut, further different eruptive rocks
of Scandinavian origin, namely granite, compact porphyry, lestivarite,
orndite, especially flint nodules, some of these being 60 mM. But
also here, the Silurian limestone-pebbles are the most important; 5
of them have been kept, consisting mostly of beyrichian-limestone,
strikingly resembling those which occur in the boulder-clay of the
Mirdum Kkilif.

Those pebbles are of the following dimensions.

Lao S33 > 24 aN WereEte <3 5e< 5 mW
Il. 33 & 25

5 ey Lee as Vacs SS SCAT.
Neo eed FS IO

IT and Il show unmistakabie signs of having been polished and
characteristically striated by glacial action, whereas the three others,
although not very hard stones, have at least the angular appea-
rance of glacial pebbles.

( 342 )

We may further mention that here, as in the till of the Mirdum
Klif, flints and Silurian lime-stones, occur most frequently.

Lately Mr. Srorn gave me a number of Scandinavian stones from
a boring at Koog near Zaandam. Amongst these, met with at about
40 M. > A.P., are an alnodite of 120 m.M. largest dimension, a
eranite, not much smaller, different Silurian limestones, one of which
is 65 m.M.

The facts stated prove, that in the mentioned part of North-
Holland, beneath 31 + A.P. there is a bed of boulder-clay, a
real bottom-moraine. On it rests at Uitgeest and at Castricum,
coarse-grained sand and gravel from the lowest part of which,
no doubt, some of the deseribed erratica come and which contains
shells, marking it to belong to the so called Kem-bed, the equi-
valent of the /landiien of Rutot.

Of importance, for the comparison of the geological structure with
other localities in our North-Sea provinces, is the fact that boulder-
clay was lacking at a corresponding depth in two other borings,
fabout mid-way between the two described| in the dunes at Castri-

cum, one of which went as deep as 45 M.— A.P. There, at
40 M.— A.P., was a thin layer of 0.30 to 0.40 M., and between
30 to 35 M. — A.P. coarse-grained sand and eravel, contaming

similar small pebbles of beyrichian-limestone. On account of the
absence, in the two last mentioned borings, of distinctly marked
houlder-clay, the existence of a bottom-moraine, immediately under
the Kem-bed, would have been presumed as little here as in
most other cases elsewhere. Still proofs of its existence; also in
other spots in and near the dunes of the North-Holland mainland
are not wanting.

For instance, at borings done, some years ago, in behalf of the
Harlem waterworks, at 3 K.M. west of Santpoort and 12.5 K.M.
South-west of the boring-hole at Uitgeest, at a depth from 38.75 to
43.75 — A.P., a bank of sandy clay or rather till was found, 5 M.
thick, towards its base changing into sand mixed with clay, which
now appeared being only another part of the same bottom-
moraine as the one at Castricum and at Uitgeest. Shells of the
fem-bed occur in it, down to 35 — A.P., although the clay or the
till seems to be rather pure, washing shows it for quite */, to
consist of angular grains of sand, containing some = small stones
of a peculiar nature. From about 100 cM*. of that clay 9 angular
pebbles, of beyrichian-limestone were obtained, of which the biggest
is 10 mM., and 12 fragments of eruptive rocks of different kinds, of

—

| 348

which two are of felsite-porphyry. An about equal quantity of sharp
sand, mixed with clay, taken at the basis, 43.55 M. — A. P. deep,
produced ten pebbles of the same Seandinavian limestone species,
the biggest having 12 mM. maximal dimension, besides 15 pieces of
various eruptive rocks, amongst which two of compact porphyry.
For the rest the specimens contain only a few red and grey quart-
zites and an odd flint-nodule; the typical Rhinish rocks are at any
rate by far in the minority. No doubt this clay of the northern
extremity of the prise d’eau of the Harlem waterworks is a boulder-
clay of Seandinavian origin, the bottom-moraine of an_ ice-sheet
preceding the deposition of Eem-bed, which is considered to be the
youngest stratum of the Diluvium in our country ; so the basis of the
mentioned bed with sea-shells, indeed corresponds with the end of
the last advance of the northern ice. In a recent, much larger boring,
in close proximity of the just mentioned one, the uppermost occurrence
of Scandinavian stones, measuring 4 ¢.M. ad marimium, side by side
with a large majority of stones of Rhinish origin, is found to be at
32 M.>A.P. The boring did not go deep enough to reach the
boulder-clay bed, but at 33.5 — A.P. it met witha thin layer of black
loam, containing some remains of freshwater-plants. The basis of the
Pleistocene shell-bed clearly is at 32 M. > A.P.

At Harlem Lorm found that basis at 35.6 M. + A.P. and
I found it at a similar depth myself, in a number of borings
done at Harlem, of which Mr. Storr had kept the specimens. At
Velsen, shells characteristic for the Eem-bed are found down to
oo M.—A.P.; at Castricum to -31.5 M.,- at Uiteeest to 31 M.: at
Purmerend to 32 M.; at Alkmaar to 54 M.; (a similar figure is given
by Lori¥), at Vogelenzang (according to Lorif) to 36.6 M.; in the
dunes between Katwijk and Scheveningen, in borings for the Leyden and
the Hague waterworks, the shells were found, down to 28 M. ~ A.P.;
and at Monster, in borings for the Delft waterworks, down to at least
pews AP.

A little higher, at about 30 M. — A. P. average depth, or a few
meters less deep, lies in the western chief part of North- and South-
Holland, the upper side of a zone of coarse-grained, often gravelly
sand, even of real fine gravel, whieh often contains bigger or
smaller stones. It corresponds with a last increase of the geological
transport in the Pleistocene, which was connected with a last period
of glaciation. Fourteen vears ago, ifs existence was thought not
altogether impossible by Dr. Lorié, though, (considering the knowledge
we then had of the Dutch soil), he did not venture to draw a

Proceedings Royal Acad. Amsterdam. Vol. VI.

( 344 )

more definite conclusion’); the fact that in the F/andrien Seandi-
navian erratic stones occur, was stated by Ruror’) in 1899.

That here indeed we have before us evidence of a glacial period
is proved not only by the above stated facts, but also by the other
fact that, in the mentioned zone of coarse-grained sand and eravel,
often big stones occur, in the very midst of less coarse material,
which stones ino some cases are of Scandinavian origin. So in the
mentioned deep-borings for the Harlem waterworks, at 386 > A. P.,
a very big pebble of calcareous sandstone was found of which a frag-
ment LL cM. long has been preserved, and in other deep-borings
near the Harlem water-tower, at 33.5— A. P., a flint of 12 and
a quartzite of 7 cM. largest dimension. At Hillegom, where the
eravel on the whole is rather coarse, I saw fragments of a
reddish sandstone (from the German Bunter), found there at a
depth of 32 M.>A.P., which must have been bigger than a fist,
and from Heemstede a violet (Bunter) quartzite stone, of 9 ¢M.,
largest dimension, raised from a depth of 25.5 -- A. P., among small
gravel, with many shells. Mr. D. KE. L. van per ARrgEND, showed me
from borings, done at Adolfshoeve in the Harlemmermeer polder, a
number of pebbles, raised among coarse-grained sand and fine gravel,
amonest which was a grey quartzite of 10 eM. In borings done in
behalf of the Leyden waterworks, in the Katwijk dunes, where, just
as at Hillegom, the gravel is coarser-grained than mostly elsewhere,
at a corresponding depth, pebbles of the size of a walnut, up to
that of an egg, were repeatedly met with. Nearly all these stones
are of Rhinish origin, giving evidence of transport by floating ice.
Mr. J. LANkenMa of Purmerend, told me, that in the many borings
he yearly does, he had generally found in North-Holland, at about
30 M. > A.P., stones, sometimes in such a large number and of
such a considerable size, that they considerably hindered the borings;
even to such an extent, in the Oostschermer polder (Polder Ix), on
the Blokker road and at 1 K.M. south of the church, that they had to
throw up the work, any further progress being rendered impossible
by the bore striking on an impenetrable stone-bed, immediately
under the shell-bed. At Enkhuizen, Mr. Laxketma found, at an equal
depth polished) and serateched Scandinavian stones, which he had
frequently come across (according to his opinion: granites). From

borings done at Alkmaar, Mr. Srorn gave me a fragment almost as

') Bulletin de la Société helge de Geologie, de Paléontologie et d’ Hydrologie.
Tome 3, (1889), Mémoires, p. 440.

)

*) Ibid. Tome 4, (1899), Proces-Verbaux, p. 321.

( 345 )

big as a fist, of a smooth, but angular stone, consisting of felsite-

porphyry, raised from a depth of 46 M.— A. P.')

Those instances may suffice to show the very frequent occurrence,
in North- and South-Holland, of evidence of an increased transporting
power, in the latter part of the Pleistocene or Diluvitm Period, not
only of the water, but also of an other means of transport, i.e. by
the ice.

The facts known at present, no longer leave any doubt as to the
real existence of a younger “gravel-diluvium’, here and there alter-
nating with boulder-clay. This younger formation is less powerful
than the older “eraveldiluvium’, for it rarely considerably exceeds
ten meters, but it has an equal right as the already long known
older and more powerful one to be considered as partially produced
by an advance of the Scandinavian land-ice, partially by an increased
and modificated transporting power of the Rhine, which river then
carried much floating ice.

Before concluding I may be permitted to add a thing observed,
a year ago, in the boulder-clay of the Mirdum Klif. Amongst other
beautifully scratched, glaciated stones, I collected there four, of which
three consist of beyrichian-limestone, which are not less typically
faceted as those described from the e@lacial Permian in the Salt
Range of the Punjab, from which circumstance it is evident that
there is no necessity to suppose for the Palaeozoic glacial period,
circumstances entirely different from those of the Pleistocene Ice Age.

1) Towards the east of the Harlemmermeer polder stones occur at a much
higher level. This was frequently stated in borings done on the grounds of the
military waterworks near Sloten; amongst more other pebbles, | saw a fragment
of greenish grey sand-stone, 14 c¢.M., largest dimension, which fragment had been
raised near the Ringvaart of the Harlemmermeer polder, from a depth not greater
than 16,5 M.+ A.P. <A similar fact is known from Aalsmeer. The undisturbed
horizontality of the deep peat-layers m this region (the one, more continuous,
having its base at 11 or 13 M. — A.P., the other, fragmentary, at about 18
M.~ A. P. and nearly continuous to the north and north west, from Purmerend
to Heorn and Enkbuizen and from Wormerveer, Velsen and Beyverwiyk to LJmuiden,
its base being, indifferently, at 17 to 20 M. > A. P.) shows ihat we have not before
us at Sloten and Aalsmeer, the result of a general sloping of the strata, but
only a locally higher situation of the upper part of the Diluvium, the coarse
sediments having here been locally upheaped.

23%

( 346 >

Physiology. — “On the fact of sensible skin-areas dying away
in a centripetal direction.” By Dr. G. vax Risyperk. (Com-

municated by Prof. C. WINKLER).

(Communicated in the meeting of October 31, 1905.)

The manner in which, in our experiments on dogs,*) the isolated
root-area of the skin (dermatoma), dies away, if the root to which
it corresponds, is killed by compression, gives rise to the supposition
that this peculiar series of gradually narrowing and shrinking areas,
proceeding from ventral to dorsal part, from the lateral parts towards
the centrum, may be caused by very simple reasons. This point
was demonstrated in our last Communication.

In the case of a root being slowly destroyed, its sensibility in
the sensible skin-area dies away first in its most peripherical part,
continually diminishing further in a centripetal direction. In orden
to test this conclusion still in another way, I have chosen the old
experiment of compressing the nervus ulnaris in the human body.
Having taken the necessary precautions for securing a precise loca-
lisation of the trauma, I tried this experiment twice on myself. The
results, as far as I can judge, were in perfect accordance with the
rule, established in our former essays. They may be described as
follows: shortly after the compression has begun (by means of a
pencil put into the fossa wlnaris), paraesthesia’s are observed, princi-
pally in the tops of the fourth and fifth finger, descending slowly
from thence to extend over the whole of the ulnar side of the
hand, and finally ending in perfect insensibility. If the skin of the
ulnaris-area is pricked with a sharp pin in the first period of the
paraesthesias, it is experienced beyond any doubt that the pain-
sensation is much less acute in the little finger than in the lateral
part of the hand. Somewhat later a new symptom may be observed :
the sensation is becoming distinctly dissociated. At every renewed
pricking, at first only a slight touch is felt, and only a little after-
wards a sensation of pain sets in, continuing for a rather long
period. This symptom of dissociation too has its beginning in the
little finger. After some lapse of time it also reaches the lateral
side of the hand, whilst in the little finger it has already undergone
a change, the interval between the sensation of touch and that of
pain having become longer, and this latter sensation greatly diminished,

l) Prof. GQ. Wixkter and Dr. G. van Ruyperk. On function and structure of
the trunkdermatoma I, Ul, Tl, Royal Aead, of Sciences, Amsterdam 1901—’02
and IV ibid. 1903.

ee, =,
, et

At last the sensation of pain is wholly lost, and only that of touch
remains, till finally the latter too has disappeared, and_ first the little
finger, afterwards also the external lateral part of the hand have
become absolutely insensible.

As I said before, these results appear to me to be in perfect
accordance — for the pain-stimuli at least with the rule we
have iried to establish: putting to work nearly equal causes, (i.e.
both slowly destroying the conduction in a nervepath) the consequences,
as well for the sensible ulnaris-area as for the dermatoma, will be
equal too. In both skin-areas the pain-sensibility begins dying away
in that part, situated at the greatest distance from the centrum,
the most peripherical part therefore, this process continuing slowly
in a centripetal direction. As to the dissociation, our experiments
on dogs have taught us likewise that it may not so very rarely be
observed, how the reaction on the pain-sensation, when pinching
the sensible area, is retarded. Principally in cases where this area
was a small one, or only the remnant of the central area after
a very considerable reduction of if. In such cases moreover the
pain-reaction was generally very protracted. The results of the
experiments taken on dogs and of those tried on myself, are there-
fore in perfect accordance with.one another.

As to the sensation of touch, the experiments on dogs could not
teach us anything about this, because it was impossible to make use
of any other but pain-sensations for our definitions. The ulnaris-
experiment however has shown us, that paralysis of the sense of
touch does begin in a later stadium than that of the pain-sensation ;
whilst its dying away in a centripetal direction cannot be demon-
strated with the same evidence as for this latter sensation.

At any rate the first fact is very significant, the more so, if considered
in connexion with SHeERRINGTON’s Communication ') on dissociative
anaesthesia, as has been explained more fully in our fourth com-
munication 7?) on funetion and structure of the trunk-dermatoma.

Physiology. — “Structure and function of the trunk-dermatoma” IV.
By Prof. C. Winkier and Dr. G. van RiJNBERK.
(Communicated in the meeling of October 31, 1903).
In the course of three preceding communications *), a few observations
concerning the structure and the functions of the trunkdermatomata,
have been treated. of.

!) Journal of Physiology. Vol. 27. i1901—02.

)
) Royal Acad. of Sciences, Amsterdam, Oct. 51, 1905.
3) See: Proc. of the Royal Academy Nov. 30', Dec 28th 1901, Febr. 22th 1902,

At present, guided by some new experiments in this matter, we
intend to make an endeavour towards constructing our former results
provisorily into a whole, in order to bring the facts, found by means
of physiological researches, into accordance with the anatomical records
of the peripherical skin-innervation of the trunk.

We know but little with cettainty about the topography and the
exact form of the different trunkdermatomata in man. Our knowledge
of both, such as it is, is due for the greater part to a more just
evaluation of the skin-innervation of the nervi intercostales *).

It is evident however, that in the physiological experiment the
anatomical proportions — will have to find their expression on the
periphery, and to all probability our dermatomata, determined by
physiologic methods, will be proved to be wholly identical with the
extension-areas of the skinbranches of the nervi intercostales.

According to our belief, on dogs this supposition has been even
proved already by our experiments. For by means of a careful
examination of a series of central areas, it has been made clear
that the differences in shape, manifesting themselves by shortenings
or interruptions, may all be retraced to anatomical proportions.

The division of the interrupted central area into a dorsal and
a ventral part, follows almost directly from the anatomy of the
intercostal nerve, whose skinbranches consist in a posterior and an
anterior, respectively a dorsal and a latero-ventrai branch. The place
where the central area generally suffers interruption, or where in
favorable cases on the contrary it is found to be broadest (the lateral
part therefore of our trunk-dermatoma) corresponds to the skin-area
of the rami cutanei laterales of this nerve.

In this way, for the physiologist too, the central area is divided
into three individually different parts, form and function of each of
which ought to be treated separately. For a knowledge of both is
necessary in order to understand the significance of the dermatomata
on the extremities.

The dorsal part of the central area is shaped like a truncated
triangle, whose basis is situated against the mid-dorsal line. Its apex
approaches the lateral line. Between the latter and the mid-dorsal
line a line may be traced from the dorsal border of the axilla to
the fossa ing@uinatlis.

li has become evident already from our former communications that
in favorable cases the dorsal central area towards the mid-dorsal
line possesses almost the same breadth as the whole dermatoma.

1) Bork. Hen en ander over segmentaal-anatomie etc. N. T. vy. Geneeskunde
1897, Vol. Il, N® 10.

ees

849 )

In less favorable cases it is narrowed, in very unfavorable ones it
has shrunken away to the sensible area situated at a small distance
from the mid-dorsal line (fig. 1, 2, 3, 4, @). It is there (see fie. 1 @)
that is situated a maximum of the dorsal part of the central area,

at the same time the ultimum moriens of the whole dermatoma.

Fig. 4. The different parts of the dermatoma.
d =yid-dorsal line.
» == mid-ventral line.
¢ =lateral line.
(dd = dorso-lateral limitline (from dorsal border of axilla to fossa ineuinalis).

i = ventro-lateral limitline (from ventral border of axilla to fossa inguinalis).

1 = Boundaries of the theoretical dermatoma.

2 = Boundaries of the dermatoma (central area) as it may be observed in very
favorable cases.

3 = Boundaries of the central area in less favorable cases.

4 = Boundaries of the dorsal part of the central area and 6 = Boundaries of the
ventral part of the central area as they are observed in very unfavorable cases
with interrupted central areas.

®) a= dorsal, QD l= lateral, eRe c— ventral maximum.

ro)

The lateral part of the central area, more difficult to be rendered

because of its great variability of form, may be represented, in cases .
very favorable to isolation, by a nearly hexagonal figure (see fig.
1, 5). In very unfavorable cases it cannot be shown at all. In such
cases the central area appears to be interrupted. Between both /

extremes other cases may be observed. in which the lateral central
area has been only partly preserved.

An instance may be forwarded by the following observation:

I. On a strong male dog the 16% dermatoma is isolated in the usual manner.
The day after the operation a central area is determined, the extension of which
is represented in fig. 2. Possessing a broad basis at the mid-dorsal line, it ends
in a point towards the mid-ventral line.

Fig. 2. A continuous central area, extending itself from the
m. 4.1. to the m. v. 1.
After two days, this area has fallen asunder into three parts, viz. a triangular
area towards the mid-dorsal line, a rhomboidal area towards the mid-ventral line
(see fig. 7), and a circular area situated between the former two (see fig. 3).

Fig. 3. After two days, this area has fallen asunder
into three parts.

Evidently in this case the three separate paris, into which the
originally continuous central area of the dermatoma has divided
itself as it were under our very eves, may be considered as the
three unities which we believed ourselves justified in distinguishing in
the dermatoma ‘'), their considerable shrinking having made it possible
to demonstrate each of them individually.

For these same reasons the small circular area between the dorsal
and ventral parts, signifies here a maximum (see fig. 1 4) in the
lateral part of the central area, similar to the one shown already in
the dorsal part.

Though it may not be found very often, the foregoing observation
stands in no wise alone. In the experiment also, from which the
annexed fig. 4 was taken, the central area, having fallen asunder
into three pieces, might be observed for more than a week.

The proportional rarity of this last maximum may be easily
accounted for. In the first place it is relatively a feeble maximum.
If therefore the traumatic lesion of the central area is too important,
the maximum is destroyed, together with the whole lateral part. If on
the contrary it is: not important enough, in such a manner that, all-
though there has been an interruption of the central area, still a larger
part of the lateral piece remains unimpaired, the sensible remnant
of the lateral piece will confound itself with the ventral piece. In
order therefore to demonstrate an isolated maximum, we need a
certain degree of exhaustion of the lateral piece, not strictly definable,
not strong enough to render this part quite insensible, yet sufficiently
strong to destroy its eventual connexion with the ventral piece. 7)

Finally the ventral part of the central area. This may be represented
as an oblonely stretched oval along the mid-ventral line (see fig. 1,6.).

Very rarely this may be observed as an isolated whole, because it
easily unites itself with a part of the lateral piece of the central area,
situated roundabout the lateral maximum. Still the case does present
itself sometimes, whether or no the maximum of the lateral part
has been preserved. Fig. 5 and 6 offer instances of this case, whilst
in fig. 7 the same dog, represented already by fig. 2 and fig. 3, is
designed in another attitude, in order to show the ventral part.

1) See the Proc. of the Royal Acad. of Sciences, mentioned before.
2) See: Proc. of the Royal Acad. Noy. 30% 1901,- fig. 4 and also: C. Winker.
Ueber die Rumpfdermatome. Monatschrift fiir Psychiatrie und Neurologie. Bd. XII.

Heft 3.

‘pody jvayuad oyy JO syand oot} Ot} Buimoys ‘sop goyjouy “y ‘tA

Fig. 6.

Fig. 5 and 6, Dorsal and ventral central area, defined two days after the operation.

Nie. 7. The same dog from Fig, 2 and 3, photographed in another attitude in order
to show the whole of the ventral piece of the central area,

SrA

The ventral part of the central area foo possesses its maximum,
still to be demonstrated in cases, where the maximum of the lateral
central area (see fig. 6) has already descended under the threshold
of sensibility, and is therefore lost.

It is of a somewhat rhomboidal form (see fig. 1 ©).

in resuming the total of our observations, we obtain for the
trunkdermatomata the following results:

Ist. The central area is composed of three parts of distinct signifi-
cance, their individual difference showing itself already in the manner
in which they overlap one another. ‘)

Qed. They may be demonstrated independently of one another.

3rd. Each of them suffers in a different way the reducing influence
of the operative trauma.

4%) Each of them individually possesses a maximum, centre or
ulfimum moriens; in this manner that the ultimum moriens of the
dorsal piece must be understood at the same time to be that of
the whole dermatoma.

5%. Each of them corresponds to the extension-area of a different
branch of the intercostal nerve.

Starting from these facts, an endeavour may be made to explain
the singular reduction of the sensible area, because of which it
becomes only possible to demonstrate that part of the dermatoma
we have ealled its central area. Though its cause certainly ought to
be sought in the operative trauma, yet this accounts in no wise for
the different manner, in which the reduction may be observed in
the dorsal, lateral and ventral parts of this central area.

The pointed narrowing of the cental area towards the ventral
side, hitherto has been accounted for by the greater stretching of
ihe ventral part of the trunkskin as compared with its dorsal part.
If was supposed that an originally equal number of nerve-arborisa-
tions existed on the dorsal as on the ventral side. This number

being extended over a larger surface — as is the case for the
ventral side the result will be a higher threshold of sensibility

on this side. In our nomenclature this was called: enlarging of the
marginal area at the expense of the central area.

Partly too, the perhaps still larger extension, caused by the
erowth of the extremities, may be called in aid to explain the fact,
that ihe lateral piece is at onee the broadest as well as the feeblest
part of the dermatoma. But yet there must needs be found another
collaborating factor, if we intend clearing the apparent contradie-

1!) See: Proc. of the Royal Acad, Febr. 12%h 1902,

( 355 )

tion, that it has been proved impossible to isolate a ventral piece,
the breadth of which is in any way comparable to that of the
dorsal, much less to, that of the lateral part. For though the streteh-
ing of the lateral piece caused by the growth of the cone of the
extremities, must be very considerable, yet it does not become
sufficiently clear at first sight why it should be precisely the ventral
parts of the dermatomata that remain the narrowest portions of the
central area, even in the most favorable cases.

We believe it is in the peripherical relations of the skin-inner-
vation, that the factor will be found, accounting for the fact that.
uw. favorable cases, the lateral part of the dermatomata has been
observed to be so much broader than the ventral part.

Experience has taught us that each single part of the central area
is slowly becoming imsensthle from its periphery towards its maciinium
or centrum, and that the central area as a whole does the same
from ventral towards dorsal side, and as these maxima or centra
correspond with tolerable accuracy to the entrance-place of the
peripherical sensible nerves, some explanation is already afforded.

The maxima thence would be those places situated nearest to the
centrum (ganglion or medulla). If now by means ofa trauma hitting
the nerve-root, the free conduction of stimuli is hindered, the stimuli,
retaining their activity longest, will be those that are enabled to reach
the centrum along the shortest path from the root-region. This rule
prevails for the whole dermatoma as well as for each single part
of the central area. In the case of dogs, where the medulla is
situated very close to the back, the distance from ventral skin to
medulla is at least twice as large as the distance from back to
medulla. For this reason alone already, the ventral part, indepen-
dently of its greater extension, will be the first to be reduced,
and the ultimum moriens of the whole dermatoma will be found
opposite the entrance-place of the dorsal skin-branch into the dorsal
piece of the central area. The lateral piece of the central area, being
put by ts tension into unfavorable conditions, probably even more
unfavorable than those of the ventral piece, still remains less ill-
conditioned than the ventral piece of the central area, because of
the shorter path followed by the stimuli in order to reach the
medulla. In cases favorable to isolation, it is to this latter factor that
we have to look for discovering the final cause, why the lateral
piece remains very broad, and why the ventral piece, its nerve-
path being so much jonger, becomes narrowed. In cases unfavorable
to isolation on the contrary, it is the other factor that prevails, and

the greater tension causes the lateral part to become insensible
earlier than the ventral part.

This opinion is supported by the facts which we may observe, when
compressing a peripherical nerve, e. g. the nervus wharis. In that
case too, the sensibility for pain-stimuli slowly dies away from the
periphery of the innervation-area on the skin towards its centrum,
i.e. the entrance place of this nerve into the innervation-area.

The recent communications of SHERRINGTON *) too, apparently point
to this same fact: the central areas dying away slowly m a
centripetal direction.

His third conclusion especially may be said to be of importance
in this matter: ‘In the skin of macacus the ‘pain-field” and the
“heat-field’” of a single sensory spinal root, at least in the case of
certain spinal nerves, are each less extensive than is the ‘touch-field”
of the same root.”

As in our experiments the stimuli employed were exclusively
maximum pain-stimuli, a doubt may arise, whether our central-areas
ought not to be considered simply as those areas of the dermatoma
that are sensible to pain. The peculiar way, in which the intensity
of the operative trauma exerts its influence on the form of the
central avea, renders this supposition highly improbable. Much more
probable it is, that the before-mentioned conclusion Of SHERRINGTON
expresses in a different manner that the pain-sensibility in sensible
skin-areas is dying away in a centripetal direction. The sensibility
for pain however — and the ulnaris-experiment also points this
Way is lost much sooner than the sense of touch. Experiments
made by one of us on sharks, that will be communicated afterwards,
are in accordance with this observation.

Both the peculiar proportions of the peripherical skin-innervation
(entrance-places, extension-areas of the skin-branches in the root-area),
and the general rules for the nerve-conduction, are therefore of
equal importance for determining experimentally the form of the
dermatomata.

Because three afferent nerves of different significance innerve three
pieces of the trunkdermatoma, possessing each of them a different
degree of extension, the sensibility for pain, decreasing (in cases of
progressive lesions) in a centripetal direction, will be the cause of the
apparently capriciously-shaped central areas, deseribed in the course
of our observations.

1) Suerrineton, On dissociative anaesthesia (Journal of Physiology. vol. 27,
1901 —’O2).

( 357 )

Physics. ite “()y) the equilibrium hetiveen al solid hody and if fluid
phase, especially mm the neighbourhood of the critical state.”
@l part). By Prof.-J. D. vAN DER WaAAts.

In my former communication the curve of the three-phase-equili-
briums was considered as the section of two (p, 7.) surfaces, viz.
that of the two fluid) equilibriums, and that of the equilibriums
between solid and fluid phases. For anthraquinone and ether this
section consists of two separate parts, one on the side of the ether, and
the other on the side of the anthraquinone. For values of wv ranging
between two definite values, the two mentioned surfaces do not
intersect. These values of are nearer to each other than those of
the critical phases coexisting with the solid body. 1 have indicated
them in my preceding communication as a maximiun value or a
minimum value of w We might also distinguish them by writing
ve and w«, for them. Then «, is the smallest value of « for which
the two (py, 7\.7) surfaces have still a point in common on the side
of the ether. In the same way z, is the largest value of « for the
corresponding pomt on the side of the anthraquinone.

In order to examine closer the particularities which take place in
the points in which the two (), 7.) surfaces separate, it is useful,
to draw besides the p,. sections of the preceding communication,
also the sections of the two (jp, 7, .c) surfaces for constant value
of w. As the particularities in the points, at which the two surfaces
separate, differ on the side of the ether from those on the side of
the anthraquinone, [| have drawn the two following figures, fig. 7
representing the particularities on the ether side, and fig. 8 those
on the other side.

In fig. 7 we see first traced the well-known loop for the fluid
equilibriums, (Cont. II, p. 138). It is taken for the value of «
of the critical phase on the side of the ether, which coexists with
the solid body. Let ? represent that critical phase and so be the
plaitpoint. This plaitpoint has been chosen left of the maximum
pressure, in accordance with the circumstance that the plaitpoit
pressure will most likely increase with the temperature. In this
point the two (p, 7.) surfaces would have a common tangent,
which would be normal to the plane of the figure, and so does
not appear in the figure given. This common tangent is of course
a tangent to the section of the two surfaces, which section is projected
on the plane of the figure as the (p, 7’) curve for the three-phase-
equilibriums. As in this (jp, 77) curve the value of p increases with
T, it may be traced in two ways; either as has been done in the

( 358 )
ar
,
ae
B tii ne
ie .
: Ye ‘
Hs, i
ALi G
Zo! '
We .
=“ y y
of
Tike
° Af
re
D
y 2s Eee
Fig. 7.

figure, passing through a point of the upper branch, or through
a point which has not been indicated and which would lie on the
lower branch. This projection of the three-phase-pressure is denoted
by a curve, which consists of alternate dots and dashes. So besides
P, also the point A is a point of the section of the two (p, 7).x)
surfaces for the value of . chosen; the point 1, however, at lower
temperature. The two curves A and PCD indicate further points
of the section for constant value of . of the solidfluid surface,
in so far as this section does not lie within the region, in which
one fluid phase splits up into two fluid phases (liquid and vapour).
lustead of the theoretical course of the section between the point

A and 7?. we vet the three-phase-pressure.
| |

There is one circumstance, which decides whether the course of

the curve of the three-phase-pressure is as it has been traced, so
running to a point of of the liquid sheet, or whether it ought to
rin fo a point of the vapour sheet. For a value of « lying nearer

Fig. 8.

to the side of anthraquinone, the theoretical part, in whose stead
we get the three-phase-curve, must become smaller, and it will
finally contract to a point of contact lying somewhere on the curve
AP. If therefore for a certain smaller value of, the above mentioned
curves are drawn as has been done by the dotted curves, the defor-
mation and displacement of the other curves must be such, that
a point of contact can occur on the line AP. So the question is,
to what modification must the (p,7") curve of the fluid equilibriums
be subjected, when it is traced for smaller value of .. The answer

Bre ahs ; ._( op ; oe
to this question is given by the sign of (2). Both for the equili-
briums between two fluid phases and for those between a fluid and
a solid phase, this quantity is positive as a rule. Only in a limited
region reversal of sign may take place. But this does not prevent
us from seeing immediately, that in fig. 7 for smaller values of x
the main position of the liquid-vapour curve will have to be lower
— and in order to be able to touch the curve A? the position
of this latter curve must be as it is drawn. If it had the other

24
Proceedings Royal Acad, Amsterdam, Vol, VI,

360 )

position which has been stated as possible, the contact could only
be brought about by drawing the dotted lines higher. In the first
place this proves that the last point which the two (p, 7,.) surfaces
have in common, lies on the upper sheet of the equilibriums
between the fluid phases and secondly, that the section of the
surface of the equilibriums of the solid phase for the value of wv of
the point of contact must have besides two vertical tangents, also
two horizontal tangents. This is in so far in concordance with what
has been observed on p. 240 of the preceding communication, that
a similar course for such a curve has been given there. But in so
fav different, that on account of an incomplete investigation the
opinion was expressed there, that the two horizontal tangents are

subjected to the condition = — 0. For, if they were subjected to
this condition, they would exist theoretically, but they could not be
realized. I shall continue and complete the investigation of p. 240
presently, when it will appear, that the shape derived in fig. 7 for
a section can occur at constant « and that it can really show a
maximum and a minimum in the realizable part.

But let us now proceed to examine fig. 8. There the particulari-
ties of the contact of the curves are drawn in the neighbourhood
of the « of the second critical phase which can coexist with the solid
body, viz. that which is richer in anthraquinone. Again for the « of
the critical phase the (p,7’) curve has been drawn of the equilibriums
between the fluid phases, and the plaitpomt ? on this curve has
heen chosen left of the maximum pressure. If the course of this

ae dp . Sekar? sale
plaitpoint curve should be such that sre negative for this plaitpoint,
we ought to have chosen it right of the maximum pressure. But
for owr purpose the place where P is chosen, whether right or left
of the maximum pressure, is of no account. Only P must not be
chosen on the lower sheet, as would be the case for ?. C. /7. Also
the projection of the three-phase-pressure has been drawn this time,
in concordance with the fact, that p decreases with increasing value
of 7. Now that P is chosen on the left, the three-phase-pressure
need not decrease so rapidly, as would be the case, when P was
chosen on the right. The points P and Q of this figure are now two
points of the section of the two (p, 7’..v) surfaces for the value of
w, Which we may denote by (rp)a. For the point of contact of the
two surfaces we must know the circumstances at aq, which value
is larger than (c,), Now we shall be able to bring about the contact,
which is assumed to take place in the figure in point 7, by raising

( 364 )

the curve of the equilibriums between the fluid phases, which is
necessarily attended by contraction. In this position the (p, 7’) curve
of the equilibriums between solid and fluid phases need not show
the maximum and the minimum of p, and only the necessity of the
two vertical tangents remains. For still larger values of « and so
for « > wg, the two curves, which are dotted in fig. 8 and touch
in #&, and which also touch the curve of the three-phase-equilibriums
in the same point, are separated, and the (p, 7’) curve of the equili-
briums between solid and fluid phases surrounds the equilibriums
between the fluid phases altogether, so that the latter could only
appear in consequence of retardation of the appearance of the
solid phase.

What precedes fully explains in a graphical manner the way in
which the two (p, 7, x) surfaces get detached, and it remains only

: ; : dp *
to complete the discussion of p. 240 on the course of (+) , which
: y, a

has not been fully carried out there. For the determination of this
quantity we have the equation:

d W,
(B=
¢ rp s/

The course of the denominator in the second member, viz. Vy,
has been discussed p. 233. It has been proved there that a locus
exists in the (J’,) diagram, generally consisting of two branches,
outside which this quantity is negative. These two branches are
further apart than the points D and D’ (fig. 2 of the preceding com-
munication), and at least in the neighbourhood of the plaitpoint, also
further apart than the points of the spinodal curve and even the
connodal curve. It is possible and even probable that the two
branches of this locus meet. If namely the direction of the tangent
in the inflection point of an isobar points just to the point P,
of the figure 2, the two branches coincide. And whereas in
the point A the direction of the tangent is parallel to the y-axis in
the inflection point, in inflection points more to the right of the
isobars the tangent mentioned assumes more and more a_ position,
directed to Ps. This locus, for which v.y = 0, is therefore a curve .
closed on the right, just as is the case with the connodal curve
and the spinodal curve and the curve of the points D, for which
O?w
Ov?

that part of the region, however, that lies outside the locus of the

= 0. Outside this region vy << 0, and inside ry > O — only in

2 b]
points D. If however we take the product of =f and ry, we need
not make a difference for the points inside v.¢ = 0, and we may
assuine that outside the locus, for which vg =O, this product is
negative and inside it, positive. | need hardly mention, that just as
0? yp
the connodal curve, the spinodal curve and the curve — = O are

Ov?

modified and displaced according to the temperature, also the curve

vey =O depends on the value of 7. On the whole it will contract
and move towards the side of the anthraquinone with increase
of temperature, and so follow the same course as the other loci
mentioned.

The course of the value of the denominator, viz. of I. has not
yet been discussed. In the preceding communication I had thought
that I could leave out this discussion, first because I did not think
t necessary at all, but also because I thought that the result of this
discussion could not be brought under a simple form, and finally,
because I did not wish to add another to the number of loci.

The particularity in the course of the (py, 7’) curve, for the equilibrium
between solid and fluid, however, to which we have had to eonelude
in fig. 7, has proved, that the discussion is not to be evaded, at
least if we wish to explain fully by theoretical means, the way in
which the two (p, 7,.) surfaces get detached. And the result of the
discussion of the quantity IV.- has proved to be very simple —
and almost exactly the same as the result of the discussion concerning
the quantity Vz Just as there is a locus for which V.=0, so
there is one for which JV’.,= 0. Just as the curve for which Vy = 0
consists of two branches further from each other than the points
D and D’ of fig. 2, which two branches meet outside the top of
the plait, in the same way the curve W.-=0 consists of two
branches, further from each other than the points D and D’, and
these two branches meet also, either outside the top of the plait, or
inside it. And finally the locus, for which W,-= 0, lies entirely
within that for which V.¢ = 0. The resemblance goes further. Outside
Vsy=O0 this quantity is negative, and outside W,-=0O the value
of Wy is negative. Inside V,r¢=0 the quantity Vy is positive and
increases to infinite when we reach the points D and D’, being
again negative inside these limits. The same applies to the quantity
Wer, Inside the curve for which JV,¢ = 0, this quantity is positive.
In the curve of the points D and D’ the value has increased to
infinite, being again negative inside the points D and D’, If we

( 363 )

dap

examine the product Sa Ws, we see that this product is negative
Ove
outside IW.~,—=0, and positive inside it.
There is therefore only a small region, in which the quantities
Wy and Vy have different signs, namely that region inclosed
between the loci, for which these quantities are zero. In this case

dp Siew :
(4) is negative. In fig. 7 this is the case for some points on the
Lh ax

eurve BA’ RC” on the left of A’, so for the points lying between
the point for which the tangent is vertical, and the point A’, for
Which the tangent is horizontal. In the same way for some points
on the right of the maximum, up to the point where the tangent is
vertical.

In order to arrive at this result as to the course of the quantity
Wsr, I had first brought this quantity under the form which has
been given Cont. I, p.110, for the analogous case of the equilibrium
between two fluid phases, viz:

; 5 dé ¢
Wsp = DV sp + &s — tf — (ws — «/) ( f)
Se

We may write then (I refer to the page cited of Cont. II and the
following page for the signification of the notation) ;

ryy dp (Es plp
1 = = p = = :
dT Jy, Vy

If we represent in a figure the value of ef for a curve of equal
pressure, passing through the unstable region, e.g. BEDD’'L’ B’ of
fig. 2, we obtain a curve as is represented in fig. 9. The points of
this curve, for which ¢ is small, represent the energy of the liquid
states correspoiding to this pressure. The points lying between the
two vertical tangents represent the value of é¢¢ for the unstable
phases, and the remaining points represent the energy for what we
may call gas states. The absolute height of the curve is not deter-
mined by anything, as it represents energy. Only if we also represent
the energy of the solid body, the latter energy, being smaller than
that of the liquid phase of the same concentration and of the same
pressure and temperature, will be indicated by a point lying below
the curve traced. I have represented it by «

. Whenever the tangent

to this curve cuts the axis above E> (&s)p is negative and vice versa.
aA :

The same circumstances which occur for the sign of )’.7, are also

found here.

¢
4s

fig. 9.

™
-

But though I have concluded to the course of this value of Woy <= '

above mentioned from considerations derived from this figure, have
understood afterwards, that we may acquire a survey of thiscourse — —

in a simpler way. We may give JI’.y a somewhat different shape,

which occurs on p. 1 Cont. HU, viz. : ee

7 de/ ed “J

About the quantity (e,;), we know, that it is negative, save for
the exceptional case of water below 4°.') Of Vy¢ we know, that
inside the locus for which this quantity is equal to zero, itis positive
and increases rapidly, till it is infinitely large on the curve of the 4
points D and D’. And as the factor of Vy is necessarily positive, a

it follows, that IH, is equal to zero on a curve, which lies between _

i
=

that for which J’.¢ is equal to zero, in which case Wer = (€ep)o and =a re
negative, and the curve, on which JI’sy is positive and has risen to
infinitely large. The latter curve is that of the points D and D).
We have come to the conclusion that the curve J.y~= 0 in the

1) See for the value of (&&)» also “Ternary systems III.” These Proc. IV p. 632.

( 365 )

neighbourhood of its tops passes round the top of the plait in a
fairly wide circle, so that it also encompasses the plaitpoint. We
know about the curve of the points Dand VD’, or the points for which
Gane
Ov?
Wy= 0, which lies between them, we do not know a priori how
its top is situated with regard to the top of the plait. We may only
expect, that when there is a great distance between the tops of the
plait and those of the points |’,,= 0, there is a greater chance that
also the locus JW,¢—=0O will pass round the plait. For the plaitpoint
of fiz, 7 the latter ease has then be realized. For the plaitpoint of
fig. 8 probably the opposite case.
For the points, for which V,-=0, we get:

In
T ap
dT
dp a
dT
We might immediately tae come to this conclusion. For from :

0 Op
p= (sr) dT +(3),. w+ (Ze a

iP Ow
follows the above relation, keeping .“ constant, hae — or ~— being zero.

i ys?
“dp ca a EsA)y

r(B) = 7(®) 4 eo
aT wp 07 Sos t J sf

and now take into consideration that (e¢), is negative, we derive:

dp js Op E
ce ZF ie a x,

when Ver is negative and vice versa.

that its top les inside the plait. As to the new locus

Tf we write:

If we compare the value of we ae for the three-phase-pressure in

(

the immediate neighbourhood of a plaitpoint, with the value of
dp
7 ($5) for the equilibrium of solid and fluid phases in the next

point, it may be demonstrated in several ways, that these quantities
have the same value. In fig. 7 it has been really represented like
this, but in fig. 8 we see in the neighbourhood of P a sudden break
in the direction of the pressure, which does not exist in reality.

( 366 )

The curve extending upwards from /? should therefore be bent in

such a way, that its initial direction was the same as that of the
curve of the three-phase-pressure.

The tangent plane to the (p, 7, «/) surface being normal to the
plane of the figure, because it contains a line which in P is
normal to the figure, every curve on that surface, passing through
P, will have its projection in the section of the tangent plane with
the plane of the figure; and so both the curves extending upwards
from P and those extending downwards, will have their projections
in this same section. This follows also from the values of p. 241
(preceding communication). We have for the three-phase-pressure:

Ws, 20.5
7 P _ sm, Hi,
ae Us, os a
igh eo a
To v
In the immediate neighbourhood of a plaitpoint : eaten and re
so Te 27:9 anal

| | f vero, (Cont Uap ciate eam see fii ye
is. equal to zero, (wont: Lip: 2); and we fing ar \ar).

One more remark to conclude with. Now that we have concluded
to the existence of the tops of the curves V.-=0O and Wy=0,
we shall also have to accept the conclusion, that the complications
in the course of the (p,.) and the (p, 7’) sections of the surface of
fluid phases coexisting with solid ones, remain restricted to the
neighbourhood of the critical phases. It is therefore uncertain, whether
in a section for given ., if the latter is e.g. chosen halfway between
e and tq, the two vertical tangents still occur. As soon as they
have coimeided, the section has no longer any special point, and so
the retrograde solidification has also disappeared.

Mathematics. — ‘“Cventric decomposition of polytopes.” By. Prof.
P. H: ScHouts.

In the following lines it will be shown how a regular polytope
can be decomposed according to its vertices or to its limiting spaces
of the greatest number of dimensions into a system of congruent

regular polytopes with a common centre. For this ee shall re-
present a regular polytope, limited by m spaces S,—; in Sp, with a
length 7 of the edges; and moreover we shall omit as much as
possible the number a of the dimensions and always each of the
predicates “regular’, “congruent” and “concentric”,

In our space the theorems hold good: —

se : . ‘ 1)
I. “The eight vertices of a cube Py can be arranged into two
quadruples of vertices not connected by edges, or of non-adjacent

: (V2)
vertices, the vertices of two tetraeders 1,

~ : ; Tl) 3

IY. “The eight faces of an octaeder Ps can be arranged into two
quadruples of planes of which no two planes pass through one
and the same edge, i.e. of quadruples of non-adjacent planes, the

(CaaS
faces of two tetraeders Py.

at U9 ee
II¢. “The twenty vertices of a Pio form taken fiice the vertices

KI4-VY5)]

of five Pe and taken once in two different ways the vertices
PSC(I4+5)V2]
of five P,
} mn . . (1) . . 5 e
ii; “The twenty faces ot a Px) form taken fieice the faces of
aH 5) V2

five 3 and taken once in two ways the faces of five
JBGH/5)1/2)
i

The length of the edges indicated for the components follows
immediately from the observation that for the decomposition according
to the vertices the radius of the circumscribed sphere, for the
decomposition according to the faces the radius of the inseribed

sphere remains unchanged.

For Sy we have the followime theorems :

Ill. «The sixteen vertices of a oy can be arranged into two
octuples of non-adjacent vertices, the vertices of two sixteen-cells
(V2) 1)
Pig . In like way Pig gives according to the limiting spaces two
AVY2

Pe ae
IV. “The twenty-four vertices of a /’s4 form the three octuples
(/2
of vertices of three Pig . In like way Ps, gives according to the

; (42
limiting spaces three /?s

V. «The one hundred and twenty vertices of a 99 form in five
=e : [3 (I-15) yes

different ways the vertices of five 24 . In like way P29 gives

; cae ; f : aE 7+31/5,172] ¢.
according to the limiting spaces in five ways five /’24

365. )

q)
VI. “The six hundred vertices of a P;o9 form in two. different
: 4045) V2 CB) aera
ways the vertices of five oo . In like way goo gives in two

Nide \ [3Vs—DV2)
ways the limiting spaces of five P20
With the aid of these theorems it is easy to arrive at the remaiming
possible centric decompositions of the four-dimensional polytopes.

In spaces with a greater number of dimensions it is known that

but three regular polytopes are to be-found, 1 e. in S, the simplex
2
Qt

Pat; the polytope of measure Ps, and ‘the polytope P., reciprocally

related to the preceding. With respect. to these there is an extension
: 4 pete
for theorem [ and theorem II] only, namely I for 72 —1 and

Ill tor » — 2’. These extensions run as follows:

q = oP __ (15 :
Mile. “ant space Sp, the 2 vertices of a Po ; form the

2(2/’_]

d yp ole pe ("| ; (1) :
vertices of 2°‘ simplexes Pe ’, In like way a P|“ gives
2 |
, et) Sn fae ; eg SS
according to the limiting spaces of 2°—2 dimensions 2 sinmplexes
pv 2b
al
: : wP : 7 XG! ; :
Vill. “In space Sj), the: 2--vertices’ of at om from the vertices
z out}
ee eer aes ree Dane
G6 eee Fiphs i, In like way a P|, gives according to the
2° 2-
f
oe ; Hep =) el Virol Pigs
limiting spaces of 2’—1 dimensions 2°‘ pa :
p+

In the meeting of June 27, 1908 Prof. J. M. vax BemMeELEN com-
municated a paper: “On absorptioncompounds which may change

into chemical compounds or solution.”

(This paper will not be published in these Proceedings.)

(December 23, 1903).

Koninklijke Akademie van Wetenschappen
te Amsterdam.

PROCEEDINGS

ee Ch Oey ORs CLE NCES.

WOE CE My ee VE.

(2nd PART)

AMSTERDAM,
JOHANNES MULLER.
July 1904.

3 7 ~ ‘ in = ’ ; # “ary ih . i ; a ~ 7
X ox 7 ty % <a ; 7 - va . ‘. i, bal rt: ic a 1
. =

. a a .* —_*. 7 - = > > » ti “
— iS a =, * Ay é eas = ; 7 s ad Yih i PN ce! ny
¥ ¢ i Ae Oa! \ ey , 'e *
7 tame char) Pix Thee ‘alt Pee
: af . ie 7 =’
Z . Rs ihe)
| 1
y —- I,
» = a ° .
:
65
wal

(Translated from: Verslagen van de Gewone Vergaderingen der Wis- en Natt
Afdeeling van 19 December 1903 tot 23 April 1904. DI XII.)

,
.
, =
™ ~
4

oe, a

: -
; : ~
Sa ae gy ra
é 7 3 he ve** om
f e* me an’ to. ~ ;
% } = ie = 5 *
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Proceedings of the Meeting of Decca tage 1908". s,s. 2 809
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KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING

of Saturday December 19, 1903.

DES

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 19 December 1903, DI. XII).

OE EE eS ase ES

E. F. van pe Sanpe Bakuvyzen: “Investigation of the errors of the tables of the moon of
ILanseEN—NeEwcome for the years 1895—1902”, p. 370.

J. P. Kurenen: “On the critical mixing-point of the two liquids”. (Communicated by Prof.
J. D. vAN DER WAALS), p. 387.

C. Winkirer and G. van Risnperx: “Something concerning the growth of the lateral areas of
the trunkdermatomata on the caudal portion of the upper extremity”, p. 392.

A. P. N. Franxcuimmont presents the disseitation of Dr. F. M. Jarcrr: “Crystallographic and
molecular symmetry of position isomeric benzene derivatives’, p. 406.

H. W. Baxuvis Roozrsoom: “The sublimation lines of binary mixtures”, p. 408.

A. F. Hotteman and G, L. Vorrman: “A quantitative research concerning Baryer’s tension
theory”, p. 410.

E. F. vay pe Sanprk Bakuvyzen: “Investigation of the errors of the tables of the moon of
Hansen— NEwComB in the years 1895—1902” (2nd Paper), p. 412. —(2nd Paper, part IT), p. 422.

C. Sanpers: “Contributions to the determination of geographical positions on the West-coast
of Africa” (11), (Communicated by Dr. E. F. van pe SanpE BakuuyZzey), p. 426.

G. van Disk and J. Kunst: “A determination of the electrochemical equivalent of silver”,
(Communicated by Prof. H. Haca), p. 441.

The following papers were read:
| 25
Proceedings Royal Acad. Amsterdam. Vol. VI.

( 370 )

Astronomy. — “Jnvestigation of the errors of the tables of the moon
of Hansen—Newcoms for the years 1895—1902”. By Dr. E. F.
VAN DE SANDE BaKkHUIJZEN.

(Communicated in the meeting of June 27, 1903).

1. Introduction.

1. In the years 1901—1902 Mr. C. Sanpers has made a longitude
determination on the West-coast of Africa by means of the moon.
The investigation described in the following pages was undertaken in
order to furnish him with accurate data for the moon’s places.

Especially with regard to the systematic errors which affect all
the observations of the moon’s limbs, it is desirable to use for this
purpose not only a few observations made in the neighbourhood of
the days for which the places of the moon are required, but to
make a more extensive investigation of the errors of the tables.
There was still another reason for doimg so. For when I first
undertook the work, for which the observations at Greenwich had to
form the basis, I could dispose only of those up to the year 1899,
so that a direct determination of the required corrections was entirely
impossible.

So at first I employed only the observations of the years 1895—
1899, but later I was able to extend my investigation also over the
3 following years. For this I am indebted to the courtesy of Mr, Curistin,
who sent me a complete copy of the observations of the moon made
at Greenwich during the vears 1900—1902 and who thus enabled me
to render my results much more reliable. In the same letter, however,
Mr. Curistiz told me that a similar investigation for a similar pur-
pose had been undertaken at Greenwich’) and at first this made
me doubt whether in this circumstance it would not be better to
stop my work. But as my calculations for the period 1895—1899
were rather far advanced, I ultimately resolved to continue them.
I considered that perhaps in this case it might be useful when two
independent investigations should confirm each other.

2. It is well-known that the motion of the moon offers many
unsolved problems. Quite recently NewcomB in a paper read at the
March-meeting of the English Royal Astronomical Society *), (when |
had already begun my work), once more clearly pointed out the
deficiencies of the theory which chiefly his investigations had brought
to light. Let us shortly recapitulate those investigations.

1) Comp. Report of the Astronomer Royal.... read 1903 June 6, p. 9.
2) Monthl. Not. R. Astr. Soc. Vol. 63, p. 316.

a a -

eee

ee ee ee

— =

( 371 )

In 1876 Newcoms published a comparison of the observations of
the moon from 1862—1874 with the tables of Hansen ') and showed
the existence of slowly increasing errors in the tabular mean longitude.
On the other hand, after having applied theoretical corrections to
the coefficients of some of Hansen’s inequalities of short period, he
found a hitherto unsuspected inequality in the true longitude of the
form «sin(y+ N), where g represents the mean anomaly and N
an angle increasing by about 20° per annum. The long period errors
were further investigated by Newcoms in his Researches *), which
appeared in 1878. After an elaborate investigation of all the obser-
vations before 1750, he embodied the errors found in an empirical
formula, which apparently satisfied all the available observations.

In the same year he published his “Corrections to Hansen’s tables
of the moon’, where tables were given for the application of the
long period corrections according to the empirical formula alluded to
above and for the correction of a term of the true longitude accidentally
introduced into the tables with a wrong sign. For the time being he
did not consider it advisable to apply other corrections. These
“Corrections” have since been introduced into all the lunar ephemerides.

For the empirical term of long period no theoretical basis has
been found until now. As for the term depending on g + WN,
Neison’s and Hit’s investigations have shown that it may be the
“Jovian Evection’’.

IT. Investigation of the errors of longitude.

3. In my investigation I followed the same method as Newcomp
in his paper of 1876, that is to say, instead of the errors of longitude
and latitude I used those of right ascension and declination. Although
in this way the caleulations become somewhat more intricate, it offers
the great advantage that the errors of observation, the systematic
and the chance errors, in the two coordinates do not become intermixed.

Thus in investigating the errors of longitude, I started from the
differences Aa, which, in accordance with Newcoms I take in the
sense : Computation—Observation.

4. In the first place I had to investigate the systematic errors
in the observed transits of the two limbs, but, as it is well-known,
the values found for them depend to a high degree on the value
adopted for the parallactic inequality. This renders an independent
determination of the two very difficult, as, for instance, it may be
1) 5. Newcoms, Investigation of corrections to Haysen’s tables of the moon with
tables for their application. Washington 1876.

*) S. Newcomp, Researches on the motion of the moon. Washington 1878.
25*

($725

seen from an examinination of Newcoms’s elaborate investigation,
laid down in his “Astronomical constants” p. 148—151.

Therefore I thought it best to leave out an independent determination
of the coefficient of the parallactic inequality. For in the first place
the investigations of the last years have yielded a value of the solar
parallax that must be pretty accurate and in the second place the
direct determinations of the parallactic inequality that are entirely
or partly free from the disadvantage mentioned, namely those of
BaTTERMANN ') from occultations observed at Berlin and those of
Franz’) from transit observations of the crater Méstinc A made at
Konigsberg, give results which agree satisfactorily with the most
probable value of the solar parallax.

Whilst as this most probable value we may consider 2 = 8".796,
the investigations of BarrermMann and Franz yield:

BaTTERMANN 1864—85 2 = 8".794
rT 1894—96 8. 775
FRANZ 1892 8. 770")

On the other hand Newcoms derived from the transit observations

of the limbs by eliminating as far as possible the systematic errors:
Newcoms 1862—94 a= 8."802.

I have adopted «= 8".796, hence as the correction of the value
used ultimately by Hansen in the Tables dela Lune: 6 « = — 0".120,
whence as correction of the coefficient of the principal term of
the parallactic inequality in the mean longitude:

dé P=— 1410 % dx=—+ 1".69
and P= —124".01

The correction of the value adopted by Nrwcoms becomes:
EP == 08-738.

5. I now proceeded as follows. The residuals 4 @ for each year
were arranged according to the observed limb and the true age
of the moon expressed in days. In this way each year yielded
25 groups of residuals and for each of them’ the mean value was
derived.

1) H. Batrermany, Beobachtungs-Ergebnisse der Sternwarte zu Berlin No. 5,
Berlin 1891.

H. Barrermann, Beobachtungs-Ergebnisse der Sternwarte zu Berlin No. 11.
Berlin 1902.

*) Astron. Nachr. Bd. 136. p. 354.

8) I had overlooked the discussion by Franz of the observations of Mésrine
A made at Gérrincen 1891—93 (Astron. Nachr. Vol. 144 p. 177). The com-
bined result from K6niespere and Gértincen is: +=8".805. (Added 1903 Dec.)

== ee ee ee eee

( 373 )

These annual means for each day of the moon’s age had then to
be corrected 1st for the correction of the parallactic inequality, 2"¢ for
the small theoretical corrections derived by Newcomp on p. 10 of
his “/nvestigation”. However, for these annual means some of the
latter might be neglected and besides I might identify annual means
of Ae with those of the residuals in mean longitude and also
annual means of the true age with those of the mean age, the
argument D.*)

For the years 1895—97 I had at my disposal not only the results
of the transit observations, but also those obtained with the altazimuth.
As however in this case the advantage of also using observations
made at small elongations is more than balanced by the difliculty
of determining their systematic errors, I have ultimately only used
the transit observations *).

From these corrected means, which are not given here, I further
derived mean vaiues for each year for each of the two limbs. They
were obtained by combining with equal weights the results for each
day of the age of the moon. However, for reasons to be given
hereafter, the values for the ages of 4 and 26 days were ultimately
rejected altogether.

In this way I found:

SS Ra cay og ee

1895 — 08062 — 0s072 — 0s010 — 0067
1896 — 0.131 — 0.044 | + 0.087 — 0.088
1897 — 0.134 | — 0.126 | + 0.008 — 0.130
1898 — 0.177 — 0.104 | + 0 073 — 0.140
4899 — 0.125 | — 0.070 | + 0.055 — 0.098
4900 — 0.151 — 0.104 + 0.047 — 0.128
1901 — 0.144 | — 0.091 + 0.053 | — 0.118
1902 — 0.189 | — 0.123 | + 0.066 | — 0.156
Mean + 03047

1) The corrections actually applied were the annual means for each value of D
of the values of Newcomp’s Table VII, after they had been corrected for the adopted
value of the principal term of the parallactic inequality.

2) At first 1 had also used the altazimuth observations and from results obtained
on the same day with both instruments I had derived for Az Akar for obser-

vations of the ist limb + 0:.126, and for those of the 2nd limb —0s,122,

( 374 )

By subtracting these annual means for each limb as they are
given in the second and third columns of the table above from the
means for the same limb for each day of the moon’s age I obtained
for each year a_ set of about 25 residuals and finally I combined
the corresponding residuals of the 8 years with their respective
weights. |

These mean residuals follow here:

Limb I | Limb IT.

Age >A 2 |Weight| Age Ree | Weight
i) ge oe 14h | — 0:097 14
5 — .069 39 15 eae 5 33
6 > 4028 36 16 she 028 61
7 — .036 MA 17 + .030 49
8 + 022 50 18 = ONS 53
9 = 5007 46 19 a” S088 45
10 + 002 43 20 + 008 34
MI a OA 50 24 + 003 31
42 2» 1014 Bd 29 a O18 37
43 + 029 49 93 O17 38
14 3 (007) |= 29 oy ——" 1015 34
15 | 000 | 97 Oe + .008 49
| | % | + 196 | 8

If we assume the adopted values for the inequalities depending
on D to be correct, the two preceding tables show us the effect
of the systematic errors of the observations. At a first glance at the
second table we perceive that the right ascensions observed at the
age of 4 and 26 days show abnormally great discordances, which
both agree in sign with those which would result if the observers
estimated the moon’s diameter to be smaller when observed at
daylight.

If we except these two groups, the observations of the 2°4 limb
no longer show any regular increase, whilst the results for the
1st limb between the ages of 5 and 8 days stillseem to vary somewhat
regularly. However, after due consideration of the case, I have ulti-
mately assumed the personal error to be constant for the first limb

( 375 )

between the age of 5 and 15 days and for the second limb between
those of 14 and 25 days and I simply rejected the observations at
the age of 4 and 26 days which are few in number. Perhaps it
would have been better to apply a special correction at least to the
resulis at the age of 5 days.

As stated above, the values in the 2"¢ and 3'¢ columns of the first
table are those found after the rejection of the two extreme groups,
and from them I derived further the differences I1—I and the values
of '/, (I + Il). The IJ—I represent the differences between the personal
errors for the two limbs. In the first three years these differences show
considerable variations, but for the last five years there is a good
agreement. However, as at first I only discussed the period 1895—1899
1 adopted a mean value of I[—I for these years and another for the
following three, and for the corrections to be applied to the obser-
vations of the first and the second limbs to reduce them to the mean
of the two I assumed for 1895—1899 + 03.02, for 1900—1903
+ 0.03.

For a closer investigation of the personal errors it would be
necessary to discuss separately the results of the different observers.

6. After having applied the corrections for personal error we
must now compute for the separate observations the corrections to be
applied to the mean longitude: in the first place those resulting from
the corrections of the parallactic inequality of the annual equation,
of the variation and of the evection — the last three as derived
by Newcoms — and secondly the long period corrections. From the
corrections of the mean longitude we must then derive those of
the right ascensions.

The corrections of the first kind (comp. Newcoms Jnvest. p. 10 and
37 and Barrermann N°. 5 p. 21) are, using Hansrn’s notations:

nd z= + 1."69 sin D + 0."16 sin (D — g) — 0."24 sin (D 4+ 9’)
+ 0."09 sin g' — 0."33 sin 2. D — 0."21 sin (2 D — g).

For the application of these corrections I have calculated 2 tables,
partly arranged as Nuwcomp’s Table VIL and VIII.

For the long period corrections I first tried to derive accurate
values from the whole available material.

For although the empirical correction derived by Newcoms in his
Researches, has reduced the differences from the observations to a
much smaller amount, there still remain unaccounted for discre-
pancies. This has been shown by Tisserand in his very lucid
account of the questions involved here “Sur l'état actuel de Ja théorie
de la lune” in the 3'4 volume of his Mécanique Céleste. He also
showed there that we cannot improve the agreement by altering the

( 376 )
period of the empirical term which Newcoms fixed on 273 years.

Hoping to find some indication about the empirical law which would
represent the outstanding differences, I put together for the whole
period 1847-1902 the values of the mean annual errors in longitude
or in R. A. according to the observations at Greenwich. Those as
far as 1882') were borrowed from Stonz’s papers in the Mordthl.
Not., applying to his results Newcoms’s corrections, while those
. for the subsequent years were taken from the Annual Reports of
the Astronomical Society. To all these results the small corrections
were applied for the reduction of the observations to the same standard
time-star catalogue. As such I adopted the 2"¢ 10 year Catalogue.

I added to the Greenwich results: for the years 1862—1874
Newcoms’s results which partly depend on the Washington observa-
tions, for the years 1880—1892 the results of the observations at
Oxford as given by Stonz, applying to both Nrwcomps’s corrections
and for the years 1895—1902 the results derived from the Green-
wich observations by myself ($ (1+ I) in the first table of section
5). From a comparison of the results of different observatories for
the same year we may infer that they are tolerably accurate. The
differences between my results and those computed at Greenwich
range from 0."00 to 0."36.

I do not, however, give these annual mean errors here, as I did
not sueceed in deriving anything from them with certainty. By
assuming the existence of a new inequality with a period of about
50 years with maxima about 1862 and 1887 and a coefficient of
about 3” we should attain a somewhat better, but even then not
an absolute agreement.

So the only thing | could do to obtain the mean corrections
required for my purpose, was to represent the annual mean errors
from 1886—1902 by a smooth curve. The following values were
derived from it.

1895.0 da=-+ 053

1896.0 1.06
1897.0 1.44
1898.0 1.72
1899.0 1.93
1900.0 2.09
1901.0 2.21
1902.0 2.28
1903.0 2.30

1) For the years 1847—1861 the new reduction of the Greenwich observations
of the moon (Month/. Not. Vol. 50) was used.

ees

ae eee Te

~~ =——— -

. ain

Obviously the last values cannot be very certain.

After thus having formed the total corrections to be applied to
the mean longitude, they have been reduced to corrections of the
right ascensions. For this reduction I could use the values / and
(v. a) given by Nuwcome in his Table 1X and XI. The very small
reduction from orbit longitude to ecliptic longitude could be neglected.
(Comp. also /nvestigation p. 12 and 14).

7. The 4 e« corrected in this way were now used to derive from
them the corrections of the true longitude, which depend on the
sine and cosine of the mean anomaly. In his J/nvestigation p. 16
Newcomsp has shown that for this purpose we may use instead of
the residuals of true longitude those of right ascension and although
the error of the longitude of the node which is assumed to be
small has increased since 1868, his conclusion still holds.

For each year the 4 a were arranged in 18 groups according to
the values of the mean anomaly, the first group containing those
between g = O° and 20°, the second those between g = 20° and
40° ete. Then the sums and the means for each group were formed
and were regarded as corresponding to g = 10°, g = 30° ete. just
as had been done by Nrwcoms.

If we represent the corrections which are to be applied to the
true longitude of Hansen by

JSl—=—hsng — keosg
we obtain for each year 18 equations of the form
ecthsng+kesg=r
where c¢ is the outstanding mean error of longitude, whilst for /
and & the signs are in accordance with NEwcome.

The equations were solved for each year by least squares with
due regard to the weights of 7, which were assumed to be pro-
portional to the number of observations used.

So I obtained the following values of 4 and /:

h k

1895.5 + 0"29 + 044
1896.5 + 0.66 + 1.16
1897.5 +0.57 41.77
1898.5 + 0.51 4 2.10
1899.5 — 0.938 4 2.83
1900.5 —1.66 41.12

5 —1.46 + 0.52
1902.5 —1.18 + 0.01

It is obvious that these coefficients cannot result from errors in the

( 378 )

excentricity and the longitude of the perigee only, and their periodic
character fully confirms the existence of the inequality discovered
by Newcoms.

At a closer inspection, however, it appears that Newcoms’s formula
does not represent satisfactorily my / and 4, and this need not
astonish us if we consider the great extrapolation involved in the
application of Nrwcoms’s formula to my results.

8. To correct Newcomp’s formula by successive approximations
I have proceeded in the following way :

By comparing the / and / now obtained with those in the table in
Investigation p. 28, it may be easily seen that the period of the argu-

ment V, on which / and / depend through the formulae 4 = h,—a sin N’

and k =k, -+ acos VN, must be greater than 16?/, years — the period
assumed by Nrwcomp — and cannot differ much from 18 years.
This corresponds to an annual variation of 20° and it will be con-
venient to adopt this value as a first approximation.

The special aim of my first operation was to find reliable values for
the constant parts of the coefficients, 4. and f,. I tried to attain this
by calculating values of 4 and / for each year of the 18 year-cycle
by means of the results of Newcoms’s two series and of those found
for 1895—1902.

Assuming the argument for 1862.0 = n> 18 to be O, I derived
normal values for the arguments 0.5, 1.5 etc. to 17.5, assigning
the weights 1, 3 and 2 to the results of the 3 series. I had no
value for the argument 14.5 and therefore had to form it by
interpolation.

In this way I found:

Arg | h k Arg h k
i ; a

0.5 | +073 | + 1158 95 | +451 | -— Ov74
15° | 0076+ 2] Ree Teale ede o7 a | snes
a5 | —1.9 |°-440 Sas | ee; | lone
3.5 | = 1,90. | Odes Pe | Sp aeron |e aes
45° | — 0.69 | — 0.06 13.5 | + 0.80 + 1.24
5,0 — 0.79 — 0.68 14.5 |° + 0.80 | + 0.84
6:5 | + 0.90 7) -e2 tem 15.5 | +029 | 40.44
75 | $4.94 |! =1.68 §] 465 | 4068 | + 446
8.5. fd diQOr> | 18 are enone eeenrias

From these values formulae were derived, which after a trans-

formation in order to bring the zero-epoch on 1868.5 become:
h = + 0".45 — 1".30 sim [167°.1 + 20° (¢—1868.5)|
k = + 0".26 + 1".46 cos [149°.3 + 20° (¢—1868.5)].

If we assume that the amplitude and the argument of the two
periodic terms must be equal, the formulae become :

h = + 0".45 — 1".37 sin [157°.7 +- 20° (t—1868.5)]
k= + 0".26 +- 1".37 cos [157°.7 + 20° (¢—1868.5)].

The object of the second operation was to derive from the obser-
vations 1895—1902 the most reliable value of NV for the middle-
epoch, assuming its annual variation to be 20°. Starting from the
8 < 18 values of 7 and assuming as known only the values of ¢,
(as found from the solution of the equations for each year) and those
of h. and hk, (as found above), I first subtracted the c from the 7
and then freed the latter from the influence of fh. and ..

The residuals must then be of the form:

r’ =—asin N sing + acos N cos g = acos(g + No+t X 20°)
and now it is clear that the 8 >< 18 residuals correspond with only
18 different values of the argument V,-+ 9-+7>x 20’. Consequently
these residuals could be combined in 18 values, for instance the
7’ for g==10° in 1895 could be combined with that for g= 350° in
1896, with that for g = 330° in 1897 ete.

Having due regard to the weights, the following mean values of
r’ were derived. The arguments g hold for 1898 i.e. for 1898.5.

! !

J 7 g " g r

t0°n-e 161 $509 == 1°39 250° + 013
S001 1,68 50S == 1209 270 + 0.04
50 + 0.65 [70—- = 431 290 + 0.62
70 -+- 0.28 P90. > = =1.05 B10 = 1.27
Sinise CA eae ne 330 -L 1.66
ROSES C2 A= = 0077 350 + 1.48

These values are represented by the formula:
— 0".42 sin g ++ 1".51 cos g = + 1".57 cos (g + 15°.5).
and 15°.5 will be a pretty accurate normal value of NV for 1898.5.
For the derivation of a similar normal value from each of the two
series of Newcoms I chose a less direct but simpler method. In each
series I reduced the WV derived from each year to a mean epoch by
means of the annual variation 20° and then combined them with the
weights as given by Nrwcomp’). I did not however use the N of

1) Applying the same method to the observations 1895—1902 I should have
found for N, 16°.9 instead of 15°.5.

( 380 )

Newcoms, but the slightly modified values, which were obtained by
taking 4, —-+ 0".45 and k, = + 0".26.
The three normal values obtained thus were:
1692.6 NV = 2007 Weight1 0. — C. — 9°0
1868.5 1G6%.9 *) 3 + 4.6
1898.5 15.5 2 — 2.3
and from them I derived a corrected formula for .V; I found:
N = 157°.3 + 19°.35 (¢ — 1868.5)
or taking the mean year as zero-epoch
N = 302°.4 + 19°.35 (¢ — 1876.0).

The outstanding differences Obs.—Comp. are given above.

If I had assigned equal weights to the three normal values, I
should have found for the annual motion 19°.45, while by excluding
the first I should have found 19°.12, both differing only slightly from
ihe most probable value.

At first when Nerwcoms’s value for the annual variation of
appeared to be too large I had thought tbat the true value might
be equal to the theoretical annual variation of the argument of the
Jovian Evection, i.e. 20°.65. It appears, however, that even the latter
is too large to satisfy the observations.

To judge in how far this is the case a comparison is given below
of the values of .V for each year as directly derived from obser-
vations, first with my formula, secondly with the formula we obtain
if we assume the same value of NN for 1876.0, but take as annual
variation 20°.65. The two sets of differences are given under the
headings No—Ne and No—N,.

E poch }] eight No—Nec No—N.,

1847.8 1 SIE aRGS aaa eg?
48.9 3 aheea + 46
50.4 3 cay” sieges?
51.2 3 =F 9 ce dis
52.4 4 <= a) J Ae |
53.5 3 Ee) ee
54.6 3 rae Vi yO
55.8 0.5 ae, Jere
56.9 3 cae rt vey
58.1 1 + 101 + 124

1) With Newcoms’s values of V we should have found 200.°5 and 161.°7,

( d8t )
Epoch Weight No—Ne No—N,z
1862.5 3 aes At 0)
63.5 5 =) ao — )
64.5 5 = ae — 4
65.5 4 fe ty Laas ont
66.5 2 — 19 — 7
67.5 4 a) i = 13
68.5 4 + 19 4+ 29
69.5 5 ea 47 4. 45
70.5 5 4+ 20 497
71.5 3 4 28 ery 34
72.5 4 4 22 4 97
73.5 4 Ee. 42 ite
74.5 4 4+ 10 aes
1895.5 0.5 4+ 82 ay,
96.5 2 oe: — 419
OFS 4 ae Eg. ee
98.5 4 =e) =— 49
99.5 6 === 9 el
1900.5 4 4 49 ca 50
OLS 4 SEG ee,
02.5 4 Pips ma 30

That the differences, even those with the formula that is made to
represent the observations as well as possible, are not altogether
accidental, may be seen from the great number of permanencies of
sign. Yet I hold that we are entitled to the conclusion that an annual
variation of .V of 19°.35 better represents reality than one of 20°.65.

Having thus derived a formula for .V representing as well as
possible the results at my disposal, I had still to correct the adopted
values of the coefficient @ and of A, and é,.

To this end I compared the observed values of 4 and & with the
formulae

h= + 0".45 — 1".50 sin (302°.4 + 19°.35 (¢ — 1876.0)|

k = -+ 0.26 + 1.50 cos [302°.4 + 19°.35 (¢ — 1876.0)]
and formed the outstanding residuals Obs.—Comp. These residuals
which for shortness are not given here, were divided into 4 groups
according to the 4 quadrants of NV, and for each of these groups
mean values were formed which follow here:

(3827)
Sh dk
I ==. 0"0S + O"41
Il + 0.26 —=(hO2
oul eNO A soe
IV =e elias
Hence :
dan = 2 = O14
Ga) ea

da) =) -— 0"36 “according to the
<= a O25 - Abies hk:

Mean value of Jd a == (3:05

The two values for a@ obtained in this way do not agree satis-
factorily. The mean value «= 1".45, however, differs little from that
deduced above by assuming the annual variation of .V to be 20°.

The values of 4- and fc remain also more or less uncertain. The
dh and dk show a systematic character even to a higher degree than
the dV, but I did not succeed in finding the real law of the discor-
dances. If, for instance, we assume that 4, and 4, vary proportion-
ally with the time, the agreement does not improve.

As the most probable results of my investigation I adopt:

h = + 0".31 — 1".45 sin [302°.4 + 19°.35 ¢ — 1876.0)|
k= + 0".24 + 1".45 cos [3027.4 + 19°.35 (t — 1876.0) |

Thence follow as corrections of the eccentricity and of the longitude
of the perigee :

dé == 0746
edx—=+0"12
J = oo 2.2
while an eventual correction of the motion of the perigee remains
entirely uncertain.
The correction of the true longitude of the moon thus becomes:
J 1 = — 0".31 sin gy — 0".24 cos g +
+ 1".45 sin [g + 212°.4 + 19°.35 (¢ — 1876.0)].

With this formula we may compare the two fesults, which
BaTTERMANN derived from his occultations and which hold for about
1885.0 and 1896.0.

BarrerMANN found for the total corrections depending on g (comp.
ni. p.44, n".-11 p. 52).

1885.0 d/—=— 1".14 sin g + 2".67 cos g
1896.0 =, = — 0".90 sin g — 1".35 cos q

( 383 )

while from my formula would follow:
1885.0 d/=-+ 0".99 sing + O" AL cos 4
1896.0 . , =—1".05 sm g —1".49 cos g

Thus we find a very good agreement for 1896.0, but the results
for 1885.0 cannot at all be brought to harmonize. It would be very
interesting to investigate also the meridian observations of the years
about 1885.

The annual variation found for NM agrees in absolute value almost
exactly with that of the longitude of the node and we might put
for the argument of the inequality: g—@-+ 216°. It is probable,
however, that we have only to do here with a casual agreement.

The theoretical value of the “Jovian Evection” is according to
the most accurate calculation by Hin :

JS 1 = + 0".90 sin [g + 238° + 20°.65 (¢ — 1876.0)].

For 1856 the theoretical argument and that of the empirical term
are in good agreement, but in the following years they are more
and more discordant.

9. It only remains now to put together the final results for the
mean corrections of the longitude, as they were derived from the
solution of the equations for each year.

In the following table the column headed Jd 2 contains the residual
corrections found after the corrections derived from my curve had
been applied, while the column headed d4y contains the total cor-
rections to be applied to the longitude of Hansun-Newcoms.

dA JAN
1895.5 — 0"07 + 0"73
96.5 — 0.05 + 1.21
97.5 + 0.56 + 1.95
98.5 + 0.22 + 2.05
99.5 —0.48 + 1.55
1900.5 —0.27 + 1.85
01.5 —0.46 + 1.79
02.5 + 0.16 + 2.46

The mean value of the 64 amounts to — 0."07, which might be
applied as a constant correction to the results according to my curve.

These resuits of the transit observations, which contain the unknown
personal errors in observing the moon’s limbs may be compared with
those of Barrermann and also with those derived by Frayz from the
observations of the crater Mésting A. We then find that the results
found by them for the mean longitude for 1885.0, 1896.0 and

( 384 )

1892.5 after being reduced on the system of the 2.4 10 year cata-
logue are greater by + 0.6, + 0."1 and + 0."5 respectively than
those of the transit observations at Greenwich *).

As to the occultations, it is proved by H. G. v. p. SanpE Bak-
HUYZEN *) that values for the moon’s longitude derived from them will
generally be too small and therefore it is probable that the moon's
longitude according to the observations at Greenwich is still in need

of a positive correction.
Il. Lnvestigation of the errors of the latitude.

10. My investigation of the errors of the moon’s latitude was
based on that of the errors in declination.

First I tried to determine the constant errors in the observations of the
moon’s declination and to this end I utilized the observations from
1895 to 1899. From the differences A d = Comp.—Obs. I derived
mean values for each of the two limbs for each month of the year
and from them annual means were derived by taking the mean of
the monthly means without regard to their weights.

In this way I obtained the results given in the following table.
The 2°¢ and 3°¢ columns contain the annual means for the north
limb and the south limb, the 4% the means of the two, the 5" their
differences i.e. the errors of the moon’s diameter, while the 6% con-
tains this same error derived only from simultaneous observations
of the two limbs near full moon.

— ein

| ees
North South hee — N—S (V — 8);
1895 — O15 + 055 + 0'20 — 0"70 — 0'65
1896 — 0.15 | —649 — 0.32 + 0.34 + 0.19
4897 —0.55 | + 0.29 = Onis — 0 &4 = a ee
ig98 | + 0.05 — 0.08 + 0.01 + 0.08 + 0.78

i899 | + 0.35 + 0.08 + 0.29 Soy + 0.46

Mean | — O09 | + 0°08 o'00 =| — ONT — 0"22

1) If we combine Franz’s result from his Kénigsberg observations with that
which he derived from those at Gétlingen, which had been overlooked by me, the
last difference, instead of + 0."5, becomes + 0."3 (Added 1903 Dec.)

2) H. G. v. pb. Sanne Baxuvyzen: The relation between the brightness of a
luminous point and the moments at which we observe its sudden appearance or
disappearance. Proc. Acad. Amst. 4. 465.

a a.

( 385 )

Although the differences between the results of the separate years
seem to be real, 1 have applied only to the 4d derived from obser-
vations of the north and the south limb the constant corrections
+ 0".1 and —O"1.

For the observations of 1900—1902 I did not know which
limb was observed. While, however, in the preceding years the
constant errors appeared to be small and in the mean for the two
limbs were found to be 0.0, I thought myself justified in neglecting
them altogether for 1900—1902.

11. In the second place the 4 d had to be corrected for the errors
of longitude.

We find to a sufficient degree of approximation (comp. also /nvesti-
gation p. 31—82")) that the derivative of the declination relatively
to the mean longitude is:

l
pe ( + ¢ — € cos 2d) cos 4 + b cos (A — A)
«

+ 2 ae cos (24 — x) + 2 becos (24 — 1 — A)

where By: a= sme | = 0.398
b =="cosesnay = 0.083
6 = bem se = 0.040

For our purpose we may neglect the 3¢ and the 4 terms; their
short periods permit of their influence being regarded as fortuitous.
Also the 2° term has provisionally been neglected, as its influence *),
may easily be accounted for afterwards.

So there only remains the 1s* term, which has been tabulated by
Newcoms in his Table XI, and I multiplied it by the total errors
of the mean longitude. The errors of the true longitude depending
on g, give rise in dd only to terms of very short and of very long
period which could be neglected as being without influence on the
results to be derived.

12. The Ad corrected in this way were arranged for each year
into 18 groups according to the values of the argument of the
latitude w, in the same way as it was done for the Ae according
to the values of gy, and then the sums and the means for each group
were formed.

I do not give here these annual means, but only the general means
derived from the total sums.

1) In the formula on p.32 3% K and 3e¢// ought to be 2e K and 2e H.

2) This term is the influence of the error in longitude on the latitude and
consequently directly influences the determination of the longitude of the node,
but not that of the inclination.

26
» Proceedings Royal Acad. Amsterdam. Vol. V1.

( 386 )

u Ad u

10° + 0"67 190° — 0"93

30 + 0.70 210 — 0.57

50 + 1.11 230 — 0.42

70 + 0.75 250 — 0.06

90 + 0.81 | 2a 0.00
110 —- 041 290 + 0.39
130 — 0.01 LO + 0.58
150 — 0.54 300 + 1.05
170 — 1.11 30 + 0.51

Each of the mean residuals gives an equation of condition:
Ld = — 0.96 sin (A— 6) Si 4- 0.96 cos (2A-O) i dO

where dz and d@ represent the corrections to the inclination and
the longitude of the node. As the Ad may still contain an outstanding
constant error, the equations were actually put in the form:

Ld =a + bsin(4—O) + ec cos (A—6).

These equations were solved substituting in them, 1s* the mean
results of the years 1895—1898, 24 those of 1899—1902, 34 those
of the 8 years combined (in all cases the mean results as derived
from the total sums).

In this way we obtained :

h c c corrected
1895—1898 — 0"25 + 1"11 + 1°28
1899—1902 + 0.62 + 0.63 + 0.79

18951902, + 0"18 - :0"86 4700

The last column contains the values of ¢c corrected for the influence
dd
of the 2¢ term of ore The corrections actually applied are its
ah ;

products with the mean corrections of the longitude.

The two partial results do not agree very well, especially those
for 6, or for the correction of the inclination, and if we compare the
corresponding values of 4d from the two four-yeargroups, systematic
differences between the two sets are clearly shown. Considering
however my results in connection with those of Nrwcoms there
seems to be as yet no sufficient ground to assume a periodic part
in the coefficients 4 and ec.

From the 8 years combined we derive :

ig Na 19
dA = + 1".04

$6 = +11"5

( 387 )

13. Finally we may combine our results with those of Newcoms
and also with those derived by FRavz. *)
For the correction of the inclination we find :

Newcoms 1868 di—=—O"15 weight 3

FRANZ 1892 + 0.37 1

BAKH. 1899 — 0.19 3
Mean result J 1 — — 0"09

The correction of the inclination is thus found to be small.
For the correction of the longitude of the node we find :

Newcoms 1868 d646—-+ 4"5 weight 3

FRANZ 1892 + 7.4 1
Bako. 1899 Ss aS 3
Mean result 1885 d6=—-+ 7'9.
As Newcomp found for 1710 d6 = —16" (Researches p. 273),

we obtain :
Correction of the centennial motion = + 14’.

Physics. — “On the critical mixing-point of two liquids’. By
J. P. Kvenen. (Communicated by Professor VAN DER WAALS
in the meeting of October 31, 1903).

A critical mixing-point of two liquids is in general a point where
two coexisting liquids become identical in every respect: it corresponds
to a plaitpoint or critical point of the two-liquid plait on VAN DER
Waats’s w-surface or of its projection in the volume-composition
diagram, the socalled saturationcurve for the two liquid phases ; the
term is used more especially to denote the condition, where the
liquids are at the same time in equilibrium with their saturated
vapour. In the v—r diagram this condition corresponds to the point
of contact between the two-liquid curve in its critical point with the
vapour-liquid curve: in this condition a change of temperature will
either make the critical point appear outside or disappear inside the
vapour-liquid curve. The contact sometimes takes place on the inside
of the latter curve and the two-liquid curve then lies entirely in the
metastable and unstable parts of the diagram, or it lies outside in
the stable part of the figure. In other cases it is the vapour curve
the critical point of which comes into contact with a two-liquid curve,
but whatever the case may be, the geometrical conditions are the

1) The combined results of Franz from the observations at Kénigsberg and at
Géttingen have been considered in my second paper. (Added Dec. 1903).

26*

( 388 )

same and the conclusions to be derived from these must hold good
in general.

For the sake of clearness we will consider a special case, viz.
that in which the liquid curve falls outside the vapour curve and
the contact takes place in the critical point of the former. As the
saturation curves contract on heating, the two curves will in this
case separate when the temperature is raised above the critical
temperature ; on the other hand the liquid curve begins to intersect
the vapour curve when the temperature is lowered. The relative
position of the curves here assumed is very common: it was discovered
for the first time by van per Lee for mixtures of phenol and water’).

When the liquid curve intersects the vapour-liquid curve an equili-
brium between a vapour phase and two liquid phases is possible,
but vAN per Waats*) shas shown how this equilibrium may be
ignored and a continuous vapour-liquid curve traced out through
the metastable and unstable parts of the diagram: along this curve
the liquid phase passes twice through the spinodal curve of the
two-liquid curve and at the same moments the vapour branch of
the curve forms cusps; the vapour pressure considered as a function
of the composition of the liquid passes at the same time through a
maximum or minimum; the thermodynamical condition in these

2
points is @E 0, where § is the thermodynamical potential.

In many cases the further complication arises that there is a
condition, where the compositions of the liquid and the vapour,
x, and «#,, are the same and where therefore the pressure is again

a& maximum or minimum: if this point falls, as it often does, between
2

the two points where ae 0, it can only be a minimum and both
Co

the other points are then maxima; the composition of the vapour
in the three-phase equilibrium then lies between the compositions
of the liquids and the three-phase pressure is higher than the pressure
of neighbouring mixtures on both sides. This is the case which was
assumed by van ber Lee in drawing his diagrams for phenol and
water, but from subsequent measurements by SCHREINEMAKERS”*) it
appears that for these mixtures the maximum where v, =, lies
outside the three-phase triangle in the »—« diagram.

As the temperature approaches the critical point, where the two

)

1) Van ver Ler, Dissertatie, Amsterdam 1898. Zeitschr. Physik. Chemie 33 p. 622.
2) Van per Waats, Continuitit I, p. 18, fig. 3.
5) Scurememakers, Zeitschr. Physik. Chemie, 35, p. 461.

——

saturation curves separate, the two liquid phases approach each other
and finally coincide in the critical point: what becomes of the
minimum (7, =.) during this change, if we suppose such a point
to lie inside the three-phase triangle? The simplest supposition which

( 389 )

we can make is that up to the last moment the minimum remains
between the two maxima and thus a fortiori between the coexisting
liquids; on that supposition the various points would all coincide
in the critical point and unite into one maximum; in the critical
point we should then have the condition 7, = ,, i.e. the liquid in
the critical point would have the same composition as the vapour
with which it is in equilibrium. This assumption was made as almost
self-evident by myself*) as well as by van per Ler’), but on fuller
consideration it now appears to me to be incorrect; VAN DER LEE*)
tried to prove its correctness by the aid of the thermodynamical
relations for binary mixtures, but we shall show that the proof was
not valid.
The equation to be used is the following :

dp _«,—4, 0°g,
ae ee ae.)
0?

~ = 0, which defines the spino-

introducing into this the condition ,
ay

dal curve and thus holds a fortiori in the critical point, we obtain

the equation = = 0: but it does not follow from this that the vapour
vy

pressure has a maximum value; for it may be proved that not only

d d
the first differential coefficient ae but also the second Zs disappears.
zy Ly

d? dp
Calculating the value of — from — we find:
zy Ly

ioe aaa fo: \ 1 (de, 0°¢, Bo dos: 07g,
= ea Fie Na age Or SS
dx, %, Gt \0F,"Jy ¥,,\ Ge, O%;" Jn U4, dm, 0x,7 ]p

but in the poimt of contact of the two curves we have not only

076, d 075
; }=— 0, but at the same time — = 0, because the spinodal
dx, Pp dx dz?

curve of the two-liquid. curve touches the connodal curve of the
: vapour-liquid curve in the critical point of contact ; thus as none of

1) Kuenen en Rosson, Phil. Mag. (5) 48 p. 184, fig. 2.
*) Van ver Leg, 1. c. p. 69.
3) Van per Leg, |. c. p. 74.

( 390 1

the coefficients in the above expression become infinite, all the terms
:

vanish and —— = 0. In the eritical point the pressure is in general

he
not a maximum, but the vapour branch of the saturation curve in
the p—zx diagram (t= constant) has a point of inflexion with a
tangent parallel to the z-axis.
In a special case vAN DER Ler’s conclusion drawn from the equa-
tion becomes valid, viz. when in the critical point the condition
@,—= 2, is fulfilled; for in that case the next differential. coefficient

d® dp *P ; ;
becomes 0, as well as — and ig After substitution ‘of the

ae* C vy vs”
076 a7 O75 ‘
general conditions {—, } =0 and ~( - |} =O the expression for
dz,7/, dz \ 02,7),
d*p

is reduced to:
dz,

d*p (Sey ee 075,
dz? a ae da? a
and this expression is equal to O, if z,= w«,, but not otherwise.

Without using the equations the same conclusions may be drawn
geometrically from the properties of the saturation curve in the
p—x diagram; if there are only one minimum and one maximum
in the p—a, curve, three points of intersection coincide in the critical
point and consequently there is a point of inflexion, if on the other
hand there is a minimum as well as two maxima, four points of
intersection coincide in the critical point and there will be a maximum
of the second order.

The whole argument thus turns on the question, whether it is
legitimate to assume as self-evident, that the point, where wz, = a,,

sy\o

Gre
remains between the two points, where & = 0; that thisse
Ly Jy

not the case follows from the fact that the condition 2, =, is
totally independent of the condition of critical contact between the
two saturation curves: in fact there are cases, such as those referred
to above, where the point 7, =, lies at a far distance from the
critical point, and others where there is no maximum or minimum
at all, either outside or inside the three-phase triangle, such as for
mixtures of ethane with the lower alcohol’). The question therefore
arises and has to be answered: how does the point where v, = a,,
which is known in many cases to be inside the two other maximum

1) Kuenen en Ropson, Phil. Mag. (5) 48, p. 192, foll.

( 39T )

points at some distance from the critical temperature, appear outside
in the realisable part of the diagram before the critical point is
reached ? The answer to this question is the following: the minimum

*S,
(v7, = ,) approaches one of the maxima ( -) + 0) and at a
; 02,7 p
ee 5 oe __ ap
given temperature coincides with it; from the expressions for and
3 As
1

d*p e ees .
at or by geometry, it follows that both coefficients vanish in this
re a %
1
point and that the p—r, curve has a point of inflexion with a tangent
parallel to the z-axis. Immediately afterwards the two points in
question have passed each other and have exchanged their character,
2
1

av,”
other point, where 2,—2«,, is a maximum: the latter point lies
at first in the metastable part of the diagram between the minimum
and one of the liquids of the three-phase equilibrium ; a further
change of temperature makes it coincide with this liquid and ultimately
brings it outside into the stable part of the figure. The maximum
and minimum in the non-stable part approach each other and finally
coincide, as explained before.

For the sake of clearness we will once more go through the
various changes as deduced above in the opposite order, i.e. while
the temperature falls towards and passes through the eritical point.
Above the critical mixing-point there is a separate two-liquid curve

i. e. the point, where ( ) = 0, is now a minimum’) and the

_ turning its critical point towards the vapour-liquid curve: in the

latter we assume a well defined maximum (v,—~-,). When the
temperature falls the two curves approach and at a given moment
come into contact; this contact takes place in the critical point of
the liquid curve, but in general at a smaller or larger distance
from the maximum on the vapour-liquid curve : doubtless the distance
may in some cases be small, but that does not affect the general
argument; on further lowering of the temperature the maximum
is in many cases taken up inside the three-phase equilibrium and
so disappears from the realisable portion of the diagram; it passes
successively the connodal and the spinodal curves and lies then
ultimately in the non-stable region, where it is found at low temperatures.

It was mentioned in the beginning that similar changes occur in
other cases, e.g. when the two-liquid curve lies inside the vapour-

2) Compare the figure for sulphurous acid and water, van p—ER Waats, Conti-
nuitat II, p. 18, fig. 3.

liquid curve at first and then appears outside, either on the tempe-
rature being raised, as is the case with mixtures of triethylamine
and water’), or on lowering the temperature, as with propane and
methylaleohol*); if in those cases a maximum vapour pressure exists,
this maximum may disappear in a manner similar to the one
sketched above. 7

The above conclusions may be summarised as follows:

The critical mixing-point of two liquids does not coincide with a
point of maximum vapour pressure, if such a point exists; but the
latter point may sooner or later at some distance from the critical
point be enclosed inside the three-phase equilibrium; in the critical
point the liquid branch of the saturation curve in the p—a diagram
has a point of inflexion with a tangent parallel to the z-axis.

University College, Dundee.

Physiology. — “Sumething concerning the growth of the lateral
areas of the trunkdermatomata on the caudal portion of the
upper extremity.” By Prof. C. Winkisr from researches made
in connection with Dr. G. van RiJNBERK.

(Communicated in the meeting of November 28, 1903).

A methodical treatment of the dermatomata of the upper extremity
offers very considerable difficulties, which have been confronted for
the first time by the eminent labour of SuErrineton, though to our
belief he has not wholly succeeded in conquering them.

The first difficulty we encounter, when essaying their physiological
elaboration, is a technical one. The upper extremity transforms by
its growth the dermatomata (of neck and trunk) situated above
and beneath it. Owing to this transformation their extension-areas
overlap one another mutually in a very peculiar manner, and only
by means of cutting through numerous — sometimes from 7 to 9—
adjacent posterior roots, it becomes possible to isolate them completely.
The operation therefore presents greater difficulties, its duration is
prolonged, its dangers are increased, partly because of the near
vicinity of the medulla oblongata, partly because of the presence of the
large perimedullar venous blood-reservoirs (air-embolus, hemorrhage).

The experimental definition of the extension of a root-area on the
extremity, already more complicated than it is on the trunk, because

1) Kuenen, Phil. Mag. (6) 6, p. 687—653.

( 393 )

of the mutual removal of the neighbouring dermatomata, will be
exposed moreover, in consequence of the more important operation,
to a greater variability of shape, and we must be prepared to obtain
only caricatures of its real shape.

In order however to undertake a just evaluation of these carica-
tures, it is necessary to know beforehand the variations in shape,
suffered for the same reasons by the trunkdermatomata. A knowledge
of the significance of the dorsal, lateral and ventral portions of the
dermatoma, of their maxima and of their different reactions on a
more or less serious trauma, is needed to enable us to understand
the caricatures, obtained on the extremities. Even the technical
mastership of SHERRINGTON has not wholly succeeded, we believe,
in interpretating them truly.

The second difficulty, the perfect control of which we owe to
SHERRINGTON, is found in the individual variations, presented by the
animals experimented upon. On all dogs it is not always the same
dermatomata that participate in the covering of the extremity. In
most cases it will be the 5—11 posterior roots that participate
in the innervation of this extremity, yet it may sometimes occur
that the 4%—10" (in cases of so-called pre-fixion), or also the
6th__12th (in cases of post-fixion) take their place. For this reason
we cannot always be sure of the equivalence of two roots situated
at the same height. The 9" root e.g. may (in cases of pre-fixion)
take up the part generally performed by the 10%, or (in cases of
post-fixion) that generally performed by the 8" ete.

Even if one is prepared by a previous knowledge of the trunk-
dermatomata for > true interpretation of the caricatures, and knows
the dangers arising from pre- and post-fixion, it will still be necessary,
as it has been done by SHERRINGTON, to describe the consequences
of every separate isolation in the same manner, in order to retain
one identical point of view for all of them.

In order to find this point of view, we have thought it convenient
to adopt for the extremities mid-dorsal and mid-ventral lines, in the
same way as had been done already by BoLk and SHERRINGTON;
moreover we made use of a simple artifice.

As soon as a dermatoma has been isolated on an animal, employed for
our experiments, and the boundaries of the insensible zones have been
defined on the skin, the animal is photographed in different attitudes.
When by these preliminaries we have obtained the photos necessary
for controlling the experiment, the animal is killed, and the skin
with the designs upon it, after having been prepared further in a
defimte methodical manner, is tanned and stretched, in order that it

( 394 )

may be compared with other similar skins, on which are designed
likewise the boundaries of the isolated dermatomata.

This is done in the following manner. On the skin of the corpse
the mid-ventral line of the trunk is drawn, and upon this line is
designed on the sternum a point C, situated between the affixture of
the 24 and 3° rib.

Seginning from this point, we next design, on the ventral side of
the maximum abducted foreleg turned towards us, a line in the longi-
tudinal axis, passing through the plica cubiti cranially of the epicon-
dylus medialis humeri straight through the plant of the hand, towards
the middle of the plant of the third finger.

This having been done on both sides, the stripping off of the skin
may begin.

In the first place a circular incision, beginning above the third
neck-vertebra is made around the neck, perpendicularly upon the
longitudinal axis of the animal.

Next a similar circular incision is made around the trunk over
the 17™ vertebra.

Thirdly these two circular incisions are united by a skin-incision
in the mid-ventral line.

Fourthly olecranon and epicondylus humeri medialis are marked
on the skin by means of a striking colour.

Fifthly an incision is made on the extremity along the ventral line,
continued through the plant of the third finger. That half of this
latter situated next to the thumb, is stripped off, the web between
the 3¢ and the 2¢ finger is split open between fore- and back-side;
next the plant of the 2¢ finger is stripped off, the web between the
2" finger and the thumb is split, and the plant of the thumb is loosened.

The same operation is then performed for the finger-plants and
webs of the ulnar fingers.

Finally the skin on the back-side of the fingers is loosened, the
end-phalanges of each finger being cut one by one, in such a Waye
that the nails remain affixed to the skin of the back-side. Both hands
being thus stripped off, the animal is flayed further.

The piece of skin, obtained in this manner, with the boundary-
lines designed upon it, is nexi stretched, tanned and dried. After-
wards the insensible areas are coloured white by means of oil-paint
and then varnished, and under control of the originally obtained
photos such a piece of skin may be compared with other similar ones.

These skins are read in the following manner (fig. 1.5): AA’ is the
cranial boundary (the incision around the neck), 65’ the caudal boundary
(the incision around the trunk). Of course the point C recurs four

( 395 )

times on the boundary-line, as C, C’, C", C'". To the left and to
the right C"A and CA’ are the mid-ventral lines of the neck,
CB and C’B those of the trunk. COED corresponds to the line
drawn on the extremity, whilst the skin of the fingers, beginning to
count from cranial to caudal part, is placed as follows: half of the
plant of the 34 finger, the plant of the 2¢ finger, that of the thumb,
the back-(nail)side of thumb, 2¢, 34, 4t™ and 5 finger, the plant of
the 5t and 4h finger and the other half of the plant of the 34
finger. Two white spots indicate the position of the olecranon and that
of the epicondylus humeri medialis.

The 11th dermatoma.

On October 3rd 1902, on a strong foxdog, designed as dog VI, by means
of an incision in the skin to the left of the mid-dorsal line (in order to
spare the dorsal nerve-branches of the neck to the right), the spinal column
is discovered from the 4th—14th processus spinosus, and the arches of the
6th —14th vertebra are opened. Autopsy on October 8th confirms afterwards
that to the right the 7, 8th, Oth, 10th, 12%, 13% and 14¢» pair of spinal roots
have been cut tarough, and that to the left the 11™ root is cut through.

Reproductions on a reduced scale (fig. I) of the outlines of the photos
and skin, represent the results of the determination of sensibility for maxi-
mum stimuli, performed on the 5, 6 and 7'> of October. On the right
part of the body a sensible area is found, bounded cranially by an insensible
zone, interrupted in its ventral, caudally by an insensible zone, interrupted
in its lateral part (see fig. I, 1 and 2 and the right side of 5).

a. The dorsal portion of the cranial insensible zone is bounded cranially
by a boundary-line, starting perpendicularly from the mid-dorsal line atthe
7h vertebra, reaching after 10 c.m. the spina scapulae 3 ¢.m. below the
acromion, then turning first in a cranial, afterwards again in a caudal
direction, and continuing on the upper-arm towards the epicondylus humeri
lateralis (the leg being stretched) (see fig. I, 1). Nearly 5c.m. before reaching
this latter, it takes a bend, slowly continuing in a caudal direction towards
the epicondylus humeri medialis, which it does not reach either (see fig. I, 2).
It then turns towards the mid-ventral line, approaching it to a distance
of 6 cm., enters profoundly into the axilla, and bends, continually deviating
in a caudal direction, into the caudal boundary line of the insensible dorsal
part. This caudal boundary line, directed towards the olecranon, parallel
with the plica axillaris posterior (see fig. I, 2), forms an angle of 90° with
itself before reaching the olecranon, continues in caudal direction, reaches
the dorsal side of the upperarm, turns again rectangularly, and continues,
with the exception of a caudally directed curve, straight unto the mid-
dorsal line, which is reached at the 9 vertebra (see fig. I, 1 and 5).

6. The ventral part of the cranial insensible zone is found as a triangularly
shaped area, commencing at the third rib, 5 cm. below the manubrium
sterni.

¢. The dorsal part of the caudal insensible zone is shaped like a sugar-
loaf (see fig. I, 1 and 5). The cranial boundary-line has its origin between

( 396 )

the 10 and 11t) vertebrae, the caudal one at the 13 vertebra against the
mid-dorsal line (fig. I, 1 and 5).

d The ventral part of the caudal zone is shaped like a rectangular
triangle, having its hypothenuse along the plica axillaris posterior, and
forming an outward curve in the direction of this latter (see fig. I, 2, 1 and 5).

To the left are found two insensible spots. One of these, opposite the
sensible ventral portion to the right, is elliptic and advances obliquely
towards the axilla (see fig. I, 2 and 3). The other, likewise elliptic, has its
longitudinal axis almost perpendicular to that of the first, this latter
being confluent with the plica axillaris posterior (see fig. I, 3, 4 and 5 to
the left).

Fig. I. 11 root.

Dog VI. 11‘ root isolated to the right by
cutting through the 7‘, 8th, Oth, 10th, 12%, 13% and 14th
roots, and cut through to the left.

The 10th dermatoma.

On September 19t® 1902 on a strong male dog, designed as dog IV, by a
similar operation as on dog VI, the 6th, 7th, 8th, gth, 11th, 19th and 138% pair
of roots to the right is cut through. 7o the left the 10 is cut through.

Autopsy on September 24 confirms this having been performed. A repro-
duction of the results found on Sept. 22t is given in fig. Il.

—

ae = tage Val
~—

( 397 )

To the right is found an interrupted sensible area, encompassed between
two insensible zones.

a. The cranial insensible zone is bounded cranially by a line, leaving the
mid-dorsal line at the 6 vertebra (see fig. IJ, 1), continuing in the direction
of the acromion, and then, avoiding this and the caput humeri, taking a
bend towards the mid-ventral line. It approaches this latter until a distance
of 1!/, cm. (see fig. II, 2), continues parallel] to it for 4 cm. in a caudal
direction, leaves it again at the third rib, borders cranially the sensible
ventral triangle of the 10 dermatoma, thus becoming itself the caudal
boundary line of the cranial insensible zone. As such it recedes to a distance
of 8 c.m. from the mid-ventral line, circumscribing next caudally the sensible
triangle, it returns as the cranial boundary line of the caudal (interrupted)
insensible zone to the mid-ventral line, approaching this to a distance of 1
c.m., taking again a caudal bend and accompanying it for 3 cm. Next
starting perpendicularly from the mid-ventral line, it continues along the
plica axillaris posterior towards the upper-arm, in a cranial direction and
turns with a sharp curve to the epicondylus medialis. Passing between
olecranon and epicondylus, it circumscribes the first (see fig. Il, 2 and 4),
turns on the dorsal side of the arm towards the epicondylus lateralis, and

Fig. II. 10% root.

Dog IV. The 10 root isolated to the right by cutting through
the 6th, 7th, 8th, gt, 11%, 12th and 13t roots,
cut through to the left.

( 33g |

returns, taking a rectangular bend, as the caudal boundary-line of the anterior
insensible zone, after having made a caudal outward curve at the spina
scapulae (8 c.m. from the acromion) to the mid-dorsal line between the
8th and 9t® vertebra.

The caudal insensible zone is interrupted. The dorsal part forms a triangle,
whose basis begins between the 9t? and 10™ vertebra and ends above the
13%, (see fig. II, 1).

To the left are found two insensible spots. One of these, elliptic, opposite
the sensible area at the mid-ventral line (see fig. Il, 2 and 4). The other,
likewise elliptic, having its longitudinal axis perpendicular to the mid-
ventral line, and including olecranon and epicondylus humeri.

The 9th dermatoma.

On December 5 1902, by a similar operation as before, on a strong grey
foxdog, designed as dog IX, ¢o the right the 5th, 6th, 7th, 8th 10th, 11% and
12th pair of roots are cut through. To the left the 9 is cut through. Autopsy
on Dec. 9" confirms this having been performed. On September 5 1902
on a strong brown female dog, designed as dog I, to the right the 8 and
9th root, to the left the 9 root are cut through. Autopsy again confirms this.

Fig. Ill 9th root.

Dog IX. 9'» root isolated to the right by cutting through
the 5th, 6th, 7th, sth, 10th, 11th, 19t and 13% root,
cut through to the left.

( 399 )

A reduced reproduction of the photos and of the results of both experiments,
in as much as they concern the 9 dermatoma, put together on one sheet,
is given by fig. III (1, 2 and 5 to the right belonging to dog IX; 3, 4 and
5 to the left belonging to dog i).

Dog IX: To the right the sensible area is encompassed by a large insen-
sible zone, extending dorsally from the 4 to the 12» vertebra, ventrally
from 5 c.m. below the manubrium sterni unto the middle of the neck. Its
caudal boundary-line bends towards the mid veniral line in a forward convex
arch, crossing first the scapular angle, and then following the plica axillaris
posterior.

The description of the boundary-line of the sensible area may begin on
the m. triceps (see fig. III, 2). From thence it bends on the ventral side of
the extremity towards the sulcus bicipitalis medialis unto the commencement
of the axilla, where it takes a turn in opposite direction, continuing caudally
of the epicondylus medialis humeri, passing on the forearm over the thickest
part of the flexores and reaching along the ulnar margin of the plant, the
back of the hand between the 24 and 34 finger. Then it returns between the
plant and the back of the fingers (the plant of the 34 and 4 finger having
retained its sensibility, the back of both not), passing between the 4th and

Fig. IV. 7 and 8 root.

Dog VIII. The 7 and 8 root isolated to the right
by cutting through the 4*2, 5th, 6th, 9th, 10th, 11th,
12 and 13', to the left root 8 has been cut through.

( 400 )

5th finger on the back of the hand, and rising straight over the extensors
of hand .and fingers, between olecranon and epicondylus humeri lateralis,
to the tricepstendon, which is crossed by it. On the foreside of the m. triceps
it meets again its point of starting (see fic. HE xh):

Dog I: to the left are found two insensible spots. One of these is a very
small one against the mid-ventral line at the affixion of the second rib.

The other, elliptic, having its longitudinal axis in that of the arm, is
bounded by a line beginning high up in the axilla, continuing in the direction
of the olecranon and avoiding this, passing on the dorsal surface of the
extremity. It continues over the sinews of the extensors of hand and fingers
until 1 ¢.m. before the plant, returns then on the ventral surface, crossing
there the flexores, and passing beyond the plica cubiti cranially from the
epicondylus humeri medialis, it takes a bend over the m.biceps. Crossing
this muscle it reaches again, deviating in a caudal direction, its starting-
point high up in the axilla.

The 8th + the 7th dermatoma.

On October 10‘ 1902 on a small black female dog, designed as dog VIII,
are cut through to the right the 4%, 5%, 6th, 9th, 10%, 11 and 12 pair of
roots. To the left thé 8» pair of roots is cut through. Autopsy on Oct. 13"
verifies this. A reproduction of the result is found in fig. IV. To the right
is a sensible area, encompassed by a large, continuous insensible zone,
extending dorsally from the 3% to the 13 vertebra. Ventrally it extends
from 5 c.m. above the manubrium unto 1 c.m. below it. Somewhere between
the 24 and 34 rib its ventral boundary-line passes beyond the mid-ventral
line to the left. The boundary-line of the sensible area begins at 1 ¢.m.
caudally of the acromion, goes straight to the epicondylus humeri lateralis,
and accompanies the ulna unto the fore-plant (see fig. IV, 1 and 3), then
taking a sudden turn, it makes for the ventral surface of the extremity,
that is reached halfway the fore-arm, crosses it obliquely through the elbow,
regains the dorsal side on the upper-arm, and rejoins its starting-point below
the acromion.

To the left no insensibility is found on the extremity, with the exception
of a small insensible spot at the mid-ventral line of the trunk.

The 9th + the 10th dermatoma.

On Sept. 22t 1902 on a dark male dog, designed as dog V, are cut through,
to the right the 4th, 5th, 6th, 7th, Sth, 11th, 12th, 13th and 14 pair of roots.
To the left the 10 is cut through.

Autopsy on Sept. 28" confirms this having been performed. A reproduction
of the results is given by fig. V.

To the right two insensible zones encompass a sensible area. The cranial
boundary-line of the cranial zone extends from the 3™ vertebra to the mid-
ventral line 4 ¢.m. above the sternum. The caudal boundary-line of the
caudal zone extends from the 13" vertebra to the mid-ventral line, nearly
perpendicular to the longitudinal axis of the animal.

The cranial boundary-line of the sensible area starts from the mid-dorsal
line at the 8 vertebra and continues straight towards the epicondylus

‘
f

( 401 )

lateralis humeri, crossing the spina scapulae 3 c.m. below the acromion,
following on the dorsal surface of the fore-arm the furrow between radius
and ulna, and passing over the metacarpus of the little finger, between this
and the 4 finger to the plant. Next it crosses the latter in a cranial
direction, in such a manner that the plants of the fingers are insensible
with the exception of the 4% and the 5, circumscribes the plant of the
hand and crosses again the hand towards the radial side, goes upward
again, at first in the direction of the epicondylus humeri medialis, then taking
a bend in the direction of the plica axillaris ventralis, approaching this
very closely, and reaching the mid-ventral line, towards which it is directed
perpendicularly, at the second rib.

The caudal boundary-line starts from the back at the 10% vertebra, con-
tinuing perpendicularly on the longitudinal axis, crosses the spina scapulae
and continues parallel with the plica axillaris in a cranial direction until
very close to the cranial border. Between the two a very narrow sensible
area remains. It then takes a bend in caudal direction, reaching the mid-
ventral line at the third rib.

To the left are two insensible spots. One of these is found opposite the
2ed and 3™ rib at the mid-ventral line. The other, elliptic, is almost identical
with that found on dog IV.

Fig. V. 9th and 10 root.

Dog. V. 9" and 10 root isolated to the right
by cutting through 4, 5, 6, 7, 8, 11, 12, 13 and 14,
to the left 10 has been cut through.

Proceedings Royal Acad. Amsterdam. Vol VI.

Rode Ce ae Oe eS OK 8 ig Ce To
= r a rye pe Sy oe eae ; se wad 4 , eo Pp
3 ae v es = et *

( 402 )
The 9th + the 6th dermatoma.

On April 24 1902 on a dog, designed as dog XII the 4th, 5th, 7th, gth,
10%, 11% and 12t pair of roots are cut through. Autopsy on April 8 con-
firms that such has been the case. A reproduction of the results is found
in fig. VI.

To the right begins at the 3° vertebra the cranial boundary-line of an
insensible zone, at first perpendicular to the mid-dorsal line, then suddenly
taking a bend in cranial direction (see fig. VI, 1 and 3), and approaching
the mid-ventral line 4 c.m. above the manubrium. It then turns to continue
parallel with the mid-ventral line until beyond the manubrium, rising next
with a steep curve in the direction of the epicondylus humerus medialis,
and bending back to reach again the sternum caudally of the second rib.

Fig. VI. 6h and 9 root.

Dog XII. 6'» and 9" root isolated by cutting
through 4, 5, 7, 8, 10, 11 and 12.

(The skin is here not quite in accordance with photo 2, the latter having
been taken on April 5'8, On April 7 a narrow sensible band had appeared,
establishing a connection between the sensible ventral triangle and the sen-

( 403 )

sible zone on the extremity). The line then continues downward along the
sternum until beyond the 4t, rib, takes again a turn upward, and bending
cranially it ends in a point near the extremity of the spina scapulae.
Caudally there is found no insensible dorsal portion.

Near to the angulus scapulae, the line turns back again on the dorsal
surface of the upper-arm, straight in the direction of the olecranon, 2 c.m.
before reaching this, it takes a bend towards the ventral surface of the upper-
arm, and crossing this, returns to the ventral portion. It is separated by
a narrow zone from the sensible ventral triangle. (On the skin it passes
here into the caudal boundary-line of the sensible ventral triangle). Above
the latter it takes a turn in dorsal direction, and having reached again the
dorsal surface on the middle of the upper-arm, it makes straight for the
back, reaching this at the 6 vertebra.

Moreover there is found an insensible spot on the lower part of the extremity.

This has its beginning a little under the epicondylus humeri lateralis,
it crosses longitudinally, the backside of the fore-arm likewise the hand and
passes along the ulnar margin on to the plant, crosses along side the plants of
the fingers which are insensible, and continues, taking a rectangular bend before
the plant of the 4 finger, straight upward towards the epicondylus lateralis.

It is allowed to draw a few conclusions from these experiments.

1st. The caudal portions of those dermatomata, bounding the
extremity caudally, especially of the 10% and the 11, are pushed
over the lower situated dermatomata.

We have observed already previously that, cranially of the 15%
dermatoma, the cutting through of at least three adjoining roots is
necessary, in order to obtain insensible dorsal spots. Only when 4
adjoining roots are cut through, a continuous insensible zone is found
in that region. This presents a marked difference with the conditions
existing on the trunk, where for the same purpose, the cutting through
of two, resp. three roots, suffices.

This fact is confirmed here. By cutting through the 12%, 13%
and 14 root (fig. I) or the 11, 12 and 13 root (fig: ID), anal-
getic areas are called into existence both dorsally and ventrally,
but no continuous zones; when cutting through the 10%, 11 and
12 root (fig. VI), the analgetic dorsal area fails even, though the
10", 11% and 12 dermatoma possess each of them a dorsal
portion, which it is possible to isolate.

The significance of this fact is evident. The growth of the extre-
mity in caudal direction, removes the caudal boundaries of the 10
and 11 dermatoma towards the caudal side. In the lateral part the
10" dermatoma overlaps the 14%, the 11% the 15. The dorsal pieces
of the 10, 11% and 12% dermatoma are lying so near to one
another or even covering one another, that the unimpaired 6, QYth
and 13 are able to provide together for the sensory innervation

27%

( 404 )

along the back. The ventral pieces are pressed on one another against
the sternum about the second rib.

9nd. The ventral and dorsal pieces, pressed on one another, are
becoming gradually smaller and of less importance. It is only the
lateral pieces that are pushing on the extremity.

In isolating the 11% dermatoma (fig. I. 5) it has been shown that
the cranial portion of the lateral part of it is stretched on the extremity.
At the same time its cranio-caudal axis is displaced. On the trunk
it was parallel to that of the ventral and dorsal pieces, here it
forms with them an acute resp. an obtuse angle. On the boundaries
between lateral and ventral part the dermatoma suffers a rather
deep indentation.

In isolating the 10% dermatoma (fig. IT, 4) the stretching of the
eranial lateral portion is even more important, and the difference in
direction between the cranio-caudal axis of the lateral and that of
the ventral part has become so great, that here they are already
placed nearly perpendicularly to one another.

The indentation here has become so deep, that apparently the
dermatoma has been split into two parts, the lateral piece being
torn from the ventral. Apparently only, for most probably this result
of isolating the 10% dermatoma is but a caricature. For in cases
where it is isolated together with the 9 (fig. V) or with the 6%
(fig. VI 3) dermatoma, a narrow sensible zone unites the ventral
to the lateral area.

Thus much however is sure: only the lateral part, not the ventral
part of the 10% dermatoma passes on the extremity.

Something similar happens for the dorsal pieces of the 10™ and
of the 11% dermatoma. Here we find likewise an _ indentation,
though a less profound one, on the boundary of the lateral pieces
towards their cranial side.

Yet there exists a great difference between the ventral and the
dorsal indentations. Because of the fan-shaped extension of the
displaced cranio-caudal axes of the lateral pieces, there must of
necessity remain towards the ventral side, between two axes, close
to the indentation, on the caudal portion of the extremity, a skin-area
that owes its sensibility to one dermatoma only. Close to the dorsal
indentation such is not the case.

This is shown if the 11 or 10 voot are cut through. There are
always produced two insensible areas, a small ventral area, such as
we found much larger on the trunk and an area on the caudal
portion of the extremity, where the lateral pieces of the 12 and
10% dermatoma no longer overlap the 11, or those of the 11%

— sh lS

and 9t no longer the 10 dermatoma (see fig. I and II, left side).

After cutting through the 9 root (see fig. III to the left) we like-
wise may observe these two areas; by cutting through the 8 root
no lateral insensible area is produced, at the utmost a very small
one at the mid-ventral line.

The isolation of the 9 dermatoma (see fig. UI to the right)
shows, that the stretching has had a very strong effect on it. Neither
ventrally nor dorsally it has retained any longer any connection with
the mid-ventral and mid-dorsal lines, and only by projections shaped
pointwise the direction of this lost connection is indicated.

But this does not prove that this sensible area is the whole of the
dermatoma. Only its lateral portion is isolated there. Dorsal and
ventral portion have dwindled away to insignificant pieces with
a minimum sensory value, rapidly falling beneath the threshold.
Isolation of the 9 dermatoma together with the 10" (see fig. Y)
produces however a very large dorsal area, and by cutting through
the 9t8 root a very small ventral spot is still produced.

Much more probable than that it should pass as a whole on the
extremity, it is therefore that the 9'* dermatoma, like the 10, sends
only its lateral part on the caudal half of the extremity, whilst it
still possesses a very small ventral spot (as may be shown by
cutting through the root), perhaps even a still less important dorsal
spot (that may be found by isolating the root together with one of
the neighbouring ones, the 10 or the 6%).

But the 7 and eight dermatoma too, that have wholly lost the
dorsal piece (see fig. 1V to the right), send only their lateral pieces
on the extremity. In cases where one ventral side has been made
wholly insensible, if the 8" root on the other side is cut through,
the consequence will even be a small outward curve passing beyond
the mid-ventral line. But the 7" and the 8" dermatoma overlap
one another completely. If the 8 root is cut through, there is found
no lateral insensible area on the hand.

In short, the innervation of the extremity is provided for exclu-
sively by the lateral parts of the dermatomata. Their ventral and
dorsal parts become gradually smaller, and are at last (in as much
as concerns the 7 and 8") wholly or almost wholly lost.

Thus it has become possible to survey in a simple form the man-
ner in which the extremity makes use of the lateral parts of the
dermatoma.

A cone of the extremity growing in caudal direction, a lateral
growth, meets on its way the lateral parts of the dermatomata (at

( 406 )

the very least 4) thickly pressed on one another, and pushes them
forward in its course. It shoves before it the 7 and 8%, which
remain situated on its top, overlapping one another for the greater
part (c.f. fig. IM and fig. VI). This however cannot be done without
a considerable stretching, especially of the 9% and in a somewhat
less degree of the 6. Like the first floral leaves of an opening
bud, on whose top are lying the 7 and 8, the 9% dermatoma
remains situated on the caudal, the 6 on the cranial side (see
fig. VI) to the right. Caudally the 10% and eranially the 5 derma-
toma are staying behind like the basal floral leaves of this bud.

The altogether different influence, exerted on the cranial derma-
tomata by the growth of the extremity in caudal direction, will be
treated separately afterwards, but only the lateral portions pass on
the extremity. Neither the conception of SHERRINGTON, representing
the dermatomata passing as an unbroken whole on the extremity, nor
that of BoLk, representing their latero-ventral parts (the 7 and 8™
as a whole) moving roundabout an axis like the links of a chain,
are capable of satisfying us completely, albeit our fundamental thoughts
are the same, and borrowed from theirs.

Keeping provisorily to a mechanical conception, we regard the
ranging of the dermatomata on the extremity as a consequence of
the stretching of the lateral parts, caused by an impulsive force,
beginning to act on the middle of the seventh and eight dermatoma,
and operating from centrum towards periphery in a caudal direction.

We hold it therefore not impossible that anatomy, in admitting
or rejecting a homology between the skin-branches of the lateral
intercostal nerves and those of the plexus bracchialis, may either
confirm or refute our conclusions.

Chemistry. — Professor Francumont presents to the Library the
dissertation of Dr. F. M. Janeer on: “Crystallographic and
molecular symmetry of position isomeric benzene derwatives”

and gives a brief explanation of the same.
(Communicated in the meeting of November 28, 1903).

After Mirscuerticn at the beginning of last century had discovered
isomorphism and Lavrunr some years later had pointed out certain
form-analogies in the aromatic substitution-products, there appeared
in 1870 the masterly researches of Grorn on morphotropy. From
all this it might be surmised that, as all chemical and physical
properties of organic compounds depend not only on their compo-

( 407. )

sition, but also on their chemical structure in the broadest sense
this would also be the case with tbe crystalline form. Dr. Janecrr
has, however, perceived that the relation between form and struc-
ture cannot be quite so simple and only stands a chance of being
discovered by a very delicate investigation of properly chosen series
of objects and he justifies the choice of the six isomeric tribromo-
toluenes used in his research: by their high molecular weight and
the slight difference in chemical properties, so that practically, only
the relative position of the groups of atoms in the molecule causes
a difference and because the number of isomers is not too small.

Dr. JanGur has prepared these substances, which were only known
as fine needles, in a form suited to measurement and an accurate
examination of them showed that four of them belong to the mono-
clinic, one to the rhombic and one to the tetragonal system. The
last two are those with the vicinal position of the three bromine
atoms. Of the first four there are two which exhibit an isomorphism
bordering on identity and which can form mixed crystals in all
proportions.

The densities of the four monoclinic forms do not differ greatly,
that of the rhombic isomer, however, is smaller and that of the
tetragonal form still smaller so that a higher symmetry of form is
accompanied by a lesser density.

He further determined the fifteen possible melting point lines of
the binary mixtures of the six isomers and obtained very notable
results, some of which have already been mentioned by Dr. Van Laar
at the last meeting.

From the isomorphism bordering on identity of the two monoclinic
forms we may certainly conclude that there is great similarity in
the structure of their chemical molecules although these are not
expressed in our chemical formulae; they are the compounds 1. 2.
3.5. and 1.2.4.6. if CH, stands on 1. This similarity appears,
however, if we keep in view the analogy which exists, -in a certain
sense, between the group CH, and a bromine atom, which has
been noticed in a number of cases and which may be referred to
a similarity in space relationships, volume perhaps. A conformity
already pointed out by Grora in 1870 and which has been since
observed by many chemists, for instance in cases of so-called sterical
obstacle.

The relations found by Dr. Jarerr between chemical and cerystal-
lographie symmetry have given rise to a number of problems, which
he is now engaged in solving, for instance whether the isomorphism
of the two monoclinic tribromotoluenes remains intact when substi-

' 408 )

tuting the other H-atoms by feeble morphotropic groups such as VO,.

In regard to this, he recently informed me that both form a
dinitroderivative, but with a different melting point and that not
only the isomorphism is completely preserved, but that even the
typical twin formation in certain solvents takes place with both in
exactly the same manner, so that it looks as if one were dealing
with the same material.

Chemistry. — “The sublimation lines of binary mixtures’. By Prof.
H. W. Baxututs Roozepoom.

(Communicated in the meeting of November 28, 1903).

From the consideration of the p, ¢, z-representation of the equi-
libria for solid, liquid and gaseous phases of binary mixtures given
by me a short time ago’) it may be deduced in what manner the
evaporation of the mixtures of two solid substances, or inversely
their condensation on cooling a mixture of vapours, takes place at
a constant pressure by a change of temperature.

It is only necessary to take a ¢, «-section at constant pressure
ihrough the figure at such a height, that no other equilibria occur
than those between solid and vapour or between solid and solid.
This is possible as long as we keep below the pressure of the qua-
druple-point where solid A, solid 46, liquid and vapour coexist.

The adjoined figure then indicates
the general character of the section,
in which the vertical axis represents

rs G the temperature and the horizontal
axis the concentrations of the mixtures.
F f° is then the sublimation tempera-

ture of the pure substance A, G, that
of pure £. These temperatures are
depressed along the lines #'# and
GL until, below the point #, total

C D condensation of the vapour mixture to
solid A+ solid B oceurs.

,. cone B Conversely the sublimation com-
mences at the temperature given by
the line CED and one of the two solid substances then disappears

according to the concentration, unless the composition corresponds

with /, in which case they both sublime simultaneously.

1) These Proc. V, p. 279.

~~ ee eee

( 409 )

If one of them has remained, the further sublimation takes place
at a constantly increasing temperature until the pomt of the line
EE ovr GH is reached, which corresponds with the original con-
centration of the mixture.

The whole figure is quite analogous with that representing the
solidification or fusion of binary mixtures in which only the two
components occur as solid phases, 7 #’ and G / resemble the mel-
ting point lines, /’ the eutectic point.

The analogy also holds good for the initial parts of the sublimation
lines, for whose direction a formula similar to that for the lowering
of the melting point may be deduced.

For the equilibrium of a single solid substance with its vapour
we have the relation

dlp Q
dt 2T?

which is true for the increase of the sublimation pressure, when
@ represents the molecular heat of evaporation of the solid substance.

If we now assume that a small part of this line is straight and
that Q is constant, then if the pressure p is diminished by ho O01 p
the sublimation temperature will diminish by 47’, for which we find:

( A
Apes BE pon
a We p
nee CORE

If we now add to the vapour of the solid substance, which has
at T7— A Ta pressure p—0.01 p, 1 mol. °/, of the vapour of a
second substance, the total pressure again becomes p and 7 — A 7’
is therefore, at that pressure, the sublimation temperature of the
solid substance with 1 mol. °/, of admixture. Consequently A 7’ is
also the lowering of that sublimation temperature by 1 mol. °/, of
admixture.

The formula for the decrease therefore corresponds perfectly with
that for the molecular lowering of the freezing point, provided that
we take for Q the molecular heat of sublimation.

The formula, however, only applies in the case of exceedingly
small quantities of admixture, as the supposition that the p,t-line for
the equilibrium of a single solid substance with its vapour is a
straight one, is incorrect. |

If we take into consideration its curvature, it follows that the
sublimation lines of each solid substance of the mixture are concave
to the z-axis.

( 410 )

The lower the sublimation temperature of the added substance,
the further downward the course of the sublimation line of a solid
substance will extend. If, therefore, gases are used as admixtures
and in sufficient excess, any solid substanee ought, theoretically, to
volatilise at a very low temperature.

Of this circumstance advantage has often been taken in the artifi-
cial preparation of minerals by sublimation-methods in whieh gases
or vapours (.VH, C/) have been used as second substance.

If, however, they exercise a chemical action on the others, the
sublimation phenomena belong to systems of three or more components.

The sublimation phenomena may also be accompanied by pheno-
mena of fusion, as may be deduced from an examination of other
sections through my three dimensional figure.

Chemistry. — “A quantitative research concerning Banyer’s Tension

Theory.” By Prof. A. F. Hotteman and Dr. G. L. Vorrmay.

(Communicated in the meeting of November 28, 1905).

Baryer’s tension theory gives an explanation of numerous pheno-
mena in organic chemistry, but it is, however, almost exclusively
of a qualitative nature. The preference for ithe formation of cyclic
compounds with 5 and the instability of eyele systems with a larger
or smaller number of atoms required by the theory are con-
firmed in many instances. Meanwhile as far as I am aware, that
“preference” and that ‘instability’? has never been expressed in
figures. And so long as this is not the case such expressions remain
vague, as we do not possess any measure with which we can gauge
the ‘preference’ for the cycle formation with 5 over one with a
different number of atoms, and also are not in a position to compare
the stability of one compound with that of another.

I, therefore, suggested to Dr. VorrMAN to investigate quantitatively
the relative stability of the members of a special class of cyclic sys-
tems, namely the anhydrides of the dibasic acids of the normal satu-
rated series. They are again converted by the action of water into
the dibasic acids. The ease with which they re-absorb water must
depend on the degree of tension in the ring contained in these
anhydrides, as the ring opens and the bonds then can retake their
normal position. The velocity with which these anhydrides are
converted into the corresponding acids may therefore, be taken as
the measure of the tension in the ring.

———. , ee ea eo

1
.
2
j

( 411 )

Dr. VorrMan has first of all prepared these anhydrides, then dis-
solved them in a large amount of water and determined the velocity
of their transformation into acids.

The anhydrides investigated were those of succinic acid (C,), glutaric
acid (C,), adipinic acid (C,), pimelic acid (C,), suberic acid (C,),
azelaic acid (C,) and sebacie acid (C,,). Many of these acids are dif-
ficult to procure, but Dr. Vorrman has succeeded in greatly impro-
ving their mode of preparation, for the particulars of which we refer
to a communication shortly to appear in the Recueil.

In order to determine the velocity with which these anhydrides
pass into acids when introduced into water, it was necessary to be
able to determine at any given moment the quantity of acid which
had already been formed. This is done by measuring the electric
conductivity of the solution, taking it for granted that the solution
of the anhydride does not conduct the current.

This supposition is first of all justified by the observation that
the conductive power of the anhydride solution is smaller the sooner
it is measured after it has been prepared and secondly because the
acid anhydrides do not belong to the class of electrolytes. In order
to obtain the concentration of the acid in the solution from its con-
ductivity it is only necessary to measure the conductivities of solutions
of the acids at the temperature employed over the range of con-
centrations which is considered in the experiments. These measure-
ments were conducted by Dr. Vorrman, who generally used the
acids which were recovered from the anhydrides by the action of
water in order to work under quite the same conditions as existed
in his velocity determinations. As might, however, have been expected
the same values were obtained for the conductivity of the acids
themselves and those recovered from their anhydrides.

As the concentration of the acid, after the complete conversion
of the anhydride, in the velocity measurements did not exceed */,,
normal, the quantity of water may be taken as constant, so that the
conversion may be represented by the equation for unimolecular
reactions. This indeed, gave satisfactory values for the constant
occurring therein.

It is, however, only in the case of the anhydrides of succinic and
glutaric acids that Dr. Vorrman has obtained satisfactory determi-

nations, at 25°, of the values of A = (¢ in minutes, C=

t.—t, ae
erm. mol. per Litre).

He obtained the values 0.1683, and 0.1708 showing that the

5-ring is somewhat more stable than the 6-ring. In the case of the

( 419 5

higher anhydrides we met with an obstacle which prevented accurate
measurements. This was their small solubility in water. He always
noticed in their solutions a gradual increase in the electric conductive
power showing that they first dissolve as such before being con-
verted into acids, but this increase was too small to allow the velocity
constant to be calculated. It is worthy of note that although when
boiled with water they form only globules which are but slowly
converted into acids, they are so hygroscopic that they keep but a
short time unchanged when exposed to the air. This may, perhaps
be attributed to the fact that water in the liquid condition consists
mainly of polymeric molecules, whereas in the state of vapour they
are normal. The anhydrides of glutaric and sucecinie acid do not
show this peculiarity.

But the higher anhydrides also differ in another respect from the
two first mentioned namely in their molecular complexity. Deter-
minations of the boiling points of their solutions in acetone show
that they are much polymerised whilst the anhydrides of succinic
and glutaric acids behave normally. This, perhaps, explains their
difficult solubility in water.

Groningen, Lab. Univers. Nov. ’03.

Astronomy. — ‘J/nvestigation of the errors of the tables of the
1902.” By

moon of Hansen—Nuwcoms in the years 1895
Dr. KE. F. van pe Sanne Baknuyzen. (2"¢ Paper).

(Communicated in the meeting of September 26 1903).

14. After my previous paper under this title was read at the
meeting of the Academy of June 27, 1903, a preliminary communi-
cation on the investigation undertaken at Greenwich on similar lines
has also been published. Mr. P. H. Cowrnn who was occupied with

this work gave a summary of his results in “Zhe Observatory” of

September 1903 in a paper under the title “Analysis of the errors
of the moon”, which he kindly sent to me in advance of publication.

Mr. Cowr.t utilized for his investigation the observations of right
ascension Of the period 1883—1898. His method in the main agrees
with that used by Newcoms in his ‘“/nvestigation”’, whieh I had also
followed and our results for the years 1895—98 are substantially
in accordance. In the second place he compared his empirical results
with those derived from theory.

This last part of Cowg.’s paper has drawn my attention to the

ee, a

id Jive wt

( 418 )

fact that the theoretical formulae which I had used for the same
comparison were incomplete. For I had not noticed that Rapav in
his valuable “Recherches concernant les incgalités planctaires du
mouvement de la line’ *), had found that besides the “Jovian Evection”
there exist some other inequalities of a nearly monthly period with
appreciable coeflicients. Nor had I paid attention to the fact that
according to Huiu’s researches on the inequalities resulting from
the figure of the earth’), made following Detaunay’s method, an
appreciable term of monthly period must be added to those inserted
into the tables of HANSEN.

It is this gap of my preceding investigation which I shall here
try to fill up. But I shall go no farther, for from the beginning
the aim of my work was limited and there would be still less
reason to continue it, now that Mr. Cowen intends to continue his
work and to extend it also to other periods.

15. The principal terms of a nearly monthly period which, according
to Rapau and Hm, are still to be added to the true longitude from
Hansen’s tables are:

== 068 dn (o-- ea -aavy— ds)... . fl)
= OSG ase. (Ge ae en ee ED)
Be 38 cs (Gee tees ee ye EY)
Si Lov einai) CORN Gan wen cess a, eo ae eh TMD

where V7, # and / represent the mean longitude of Venus, the
Earth and Jupiter. The first three are terms found by Rapav as
arising from the planets, while the fourth expresses the difference
between the inequalities arising from the figure of the earth after
Hint and after HansEn’).

1) Annales de 1 Observatoire de Paris. Mémoires TY. XXI.

2) G. W. Hut Determination of the inequalities of the moon’s motion which are
produced by the figure of the earth. Astron. papers American Ephemeris and
Naut. Alm. Vol Il. Part. IL.

3) Comp. also Cowext |.c. Cowet introduces still two other terms, numbered
by him 2 and 6 (Observ. p. 350). It seems doubtful to me whether their intro-
duction is sufficiently justified.

As to 2, we must, if we consider Newcoms’s empirical term of long period as
an inequality of the mean longitude, like the first Venus-inequality of Hansen, and

this seems the most plausible, also accept the inequality of short period in the
true longitude connected with it.

Cowet.’s correction 6 results from the rejection of Hansen’s constant term in
the latitude — 1".00. It seems however that the correction of the tabular latitude
or declination with + 1'.00 is @ posteriori not justified. From a comparison of
the declinations determined at Greenwich in the years 1895—1902 I found as the
mean difference Obs.—Comp. — 90'.17, and after the reduction to Newcoms’s

( 414 )

The second term — the Jovian evection, whose coefficient given
here according to Rapav agrees almost exactly with Hini’s value —
and the 4 term give rise in the coefficients of sim gq and cos q to
terms of a period of about 18 years (the exact periods are 17.41
and 18.61 years respectively), while the periods of 2% +3 V—5#
and of 2~%—3/+7° amount to 9.74 and 37.25 years respectively,
i.e. about half and double the length of the former.

The combined influence of the theoretical terms II and IV therefore
must be represented approximately by Nrwcoms’s and my empirical
term, for which I found a period of 18.6 years, and the other terms
ean have but little influence on its determination. In one respect,
however, the method followed in our computations will be erroneous:
we have wrongly assumed that /’ and 4” have the same argument
as well as the same coefficient.

To investigate in how far the different theoretical terms were
confirmed by the observations I have proceeded as follows. On the
one hand | have tried to find whether the formulae determined
originally for / and k, where the equality of argument and coefficient
was not yet assumed, point to the existence of the term IV. On the
other hand I have investigated whether the differences found before
between the observed and the computed / and /: point to the existence
of the terms | and III. For their influence must be exhibited in
those differences.

If we take 1876.0 as zero epoch and assume for the annual
variation of the argument the value finally found + 19°.35, the
first formulae derived on p. 379 of my first paper are.

h= + 0".45 — 1.30 sin [317°.1 + 19°.35 (¢ — 1876.0)]
k= + 0.26 + 1".46 cos [299°.3 + 19°.35 (¢ — 1876.0)]
If we assume that the variable part of 4 must consist in: Is’. a

term which agrees in argument and coefficient with the variable
part of 4, and 2.4. a term of the form IV, we find for the latter:

Fundamental Catalogue this becomes -+-0".13. Newcoms found (Jnvest. p. 33) for
1862—73 as mean difference: Declination observed at Greenwich — Tabular Deeli-
nation + 0".36. Constant corrections had already been applied to the observations
by Newcoms and, if accounting for them I now reduce the results to Newcoms’s
F. C., 1 find Obs.—Comp. = — 0.08. So the constant correction to be applied
to the tabular declinations is found to be small for the two periods. (Comp. also
below section 18 last part).

If the observations were reduced with Newcoms’s value of the moon’s parallax,
the differences Obs.—Comp. would be about + O'.44 and + 0.23 (/ast part
added 1903 Dec. )

ee ee ee Se

( 415 )

kiy = + 1".46 cos [299°.3 + 19°.35 (t — 1876.0)]
— 1.30 cos [317°.1 + 19°.35 (¢ — 1876.0)]
= + 0".46 sin [328° + 19°.35 (¢ — 1876.0)]
while, according to theory, this ought to be:
kyy = + 0".45 sin [857° + 19°.35 (¢ — 1876.0)]

which, considering the great uncertainty in the difference between
the two empirical terms, is a satisfactory agreement‘).

In the second place we shall try to find whether the differences
between the observed /% and / and those derived from the formulae
in the 1st paper, p. 382 reveal the influence of the terms I and
III. Therefore I shall give here those differences, which formerly
were omitted. They are found in the following table (p. 416) under
the headings Obs.—Comp. I. The contents of the columns Obs.—
Comp. Il will be explained later.

The differences Obs.—Comp. I will serve in the first place to find
what the observations teach us about the term I. I have therefore
arranged them according to the values of the argument 2 2+3 V—5 E,
and by mutually combining the results of the 3 series, of which
the means had first been reduced to zero, with the weights 1, 3
and 2, we obtained the following 10 normal values for 4h and Lk.

Arg. | Lh

aoe
319° | —0"'5 | Lor
356 | —0.34 | 10.08
33 | +0.29 | —0.29
70 | Gres | -=0(48
107 | 40.08 | +0 32
143 —0.4" | +1041
180 | 40.04 1 —0.18
247 | —0.092 | +0 03
4 | —028 | +0.40
BG ab ak: 6 45

) The results of p. 382 of the first paper would seem to point to a greater
difference between the coefficients of the variable parts of # and k&; this would
improve the agreement between the empirical and the theoretical argument of kyr.

( 416 )

Ah Ak

0—CI = ae Oy: | C=C

4847.8.| to" | +08 | +0"97- | +4798

4848.9 | +0.11 —0.24 0155: of Oars
4850 4 ~ 0.03 6.99 -|_.—0-78 4 oes
ig.2 | —o.1 | —0.g3 | om | —0.43
1952.4 | —0.69 | —0.68 | —4.38 | —0.78
163.5..|-—097 |-045 | =a aeons
1954.6 | —0.90.| -10.08 | =4.10 “) 0756
1855.8 | —0.99 | —0.66 | +0.02 | 40.43
1856.9 “44 | -F029 4) Sina 44,99
49584 | ==1.40 | —44a | eoegoeeee
|
4869.5. | -10.68 | -10.79 | =<Os0 0m

18635 | +0.32 | 40.33 | +0.83 | +0.45
1864.5 | +0.05 | —0.03 | +0.60 | +0.92

1905.5 |.+0.09 | —0.07 | —047° | =0.52
1966.5 |.4049 | +0.99 | 4057 | +0.97
1867.5 | 0.27 | —0.52 | 40.47 | --0 26
1868.5 | 0.60 | 0.33 | —0.37 | —0.49
4969.5 | 14.44 | +1.16 | —0.95 | —0.m4
1870.5 | +0.77 | +0.50 | +0.01 | +0.01
is71.5 | 440.51 | 40.26 | 40.59 | 40.64
1972.5 | 4065 | 40.42 | 40.47 | 10.56
i973.5 | 40.01 | —0.01 | +0.99 | +-0.44
1974.5 | +0.16 | —0.05 | 40.98 | +0.35
1995.5 | —0.96 | —0.55 |.—0.91 | —0.84
1296.5 | =0.47 | 4049°|- 0.49) ome
1997.5 | 40.91 | +0.51 | +0.08 | —0.09
1898.5 | 40.64 | +0.88 | 40.48 | +0.91
1899.5 | —0.37 | 0.92 | 41.43 | 41.10
1900.5 | —077-| —0.78 | +0.07 | —0.98
1901.5 | 0:36 | —0.41 | =<0.07,4) "ome
1902.5 | —0.05 | —0.19 | —0.40 | —0.45

( 417 )

Hence, by solving the 10 equations by least squares, we derive:
Ah = -+ 0".02 cos (2 w 4-3 V—S EL)
Ak = 0".00 sin (2.7 + 3 V—5 EF)

While according to theory the two coefficients ought to be + 0.68.

Thus it seems that the term I is not confirmed by the observa-
tions used here. | shall show later that a somewhat modified com-
putation leads to the same result. It may be that in the years
considered here another inequality has neutralized its effect.

In the second place we shal! try to find what may be derived from
the O.—C. I about the term III. I have therefore arranged the
Lh and 4k according to the values of 22—3 J+ 7° and found the
following normal values which, however, do not eovera full revolu-
tion of the argument.

225° 0"34 | +0136
55 | 10.82 |. —0.03
O85 40.10 | +0.99
315 - | = 0-09, | > 10.90
BAD 40.46 | -10:67

15 » —0.63 —0).24
45 —0).48 —0 74
75 —0.48 —().96

105 40.51 +0.91

I have represented these values by the eXPressions :
Ah=a + 6 cos(22%- 3J-+ 7°)
Ak = a' + 5' sin (22—3J+ 7°)
and by solving the equations by least squares I found:
b= —'0".55
b' — — 0".40
or trom the 4h and 4/: combined:
0 = A6
while the theoretical value is — 0".32.
The empirical determination of these coefficients is still very un-
certain. In so far as the observations have a conclusive force, we
may say that they confirm the inequality II.

28
Proceedings Royal Acad. Amsterdam. Vol. VI.

( 418 )

The final result of the foregoing investigation is therefore that
the observations confirm the existence of the inequalities IIT and IV,
but that they seem to contradict the existence of the term I.

16. I then made a new determination of the principal term -of
the empirical inequality, after first having corrected the h and &
for the inequalities III] and IV, for which I accepted the theoretical
values.

From the /’ and £& for each year corrected thus, from which
moreover the constants 4, = —+ 0".55 and &,—= + 0".26 were sub-

tracted '), I have first derived the values af .V. They follow here:
. Sea ce
A O08) } ow 0-20
|
1847.8 Ho | —66 | 1868.5 1730 | 49°
|
1848.9 137 —5 || 1869.5 211 +30
|
1850.4 155 = | 4870.5 | yxIey. a) +13
1851.2 152 | - 35 || 1874.5 5 | +96
1852.4 175 | —35 || 1872.5 262 | 93
| j
1853.5 207 —24 || 1873.5 273 Hi5
:
1854.6 297 | —95 Il 4974.5 290 | -H3
1855.8 314 | +4138 | |
| | 1895 5 333 | +8
1856.9 | 320 +23 | .
tat a4 é | 1895.5 Sel fee
ASD&. i] | 47 } ++ i /
| | | 1897.5 | 343 | —920
1862.5 | 35 | —40 || 1898.5 | 349 | —34
1863.5 47 | —18 || 1899.5°| 31 | —41
1864.5 | 80 | — 4 |] 1900.5 83. | 199
1865.5 129 4419 |] 1901.5 400 | +4419
| |
1866.5 | 449 | —4 |i 1902.5 116 | +46
1867.5 | 190 | —99

If to these values we assign the same weights as before, we obtain
the following normal values:

') These values of the constants were found as a first approximation after the
inequality If had been accounted for. The differences between them and those
which were finally found, + 0'.43 and +0".17 are unimportant in comparison
with the great systematic discordances which still remain.

ivy A
as

eee ae | ee ee

( 419 )
1853.6 W=290073 - Waeht 1 -0—C— — 13°.7
1868.5 168.7 5B) + 7 0
1898.5 18.9 2 — 3.6

whence
N = 306°.9 + 19°.36 (¢ — 1876.0)

The annual variation of iV according to the new formula is
practically equal to the value found before. The values of O—(
whieh are joined to those of NV in the table above show, however,
that the systematic discordances are still great and the outstanding
errors of the three normal values are even somewhat greater than
before.

In the second place I have determined anew the coefficient of
the inequality. I have not done this by deriving directly values for
each year from the corrected / and & and then taking the mean
of the separate values, as by doimg so [ should have obtained a too
large coefficient. But I have represented the corrected 4 and & by the
formulae :

h'=—asinN
ki = + acos N
assuming for V the computed values.
In this way I derived
from the h’ a= + 1".23
from the f’ =-+1 34
from the two combined a=+1 .28.
Hence the formulae for /’ and 4%’ become
h! — 1".28 sin [307° + 19°.4 (¢ — 1876.0)]
ki = + 1".28 cos [307° + 19°.4 (f — 1876.0)]
while from the theoretical term II, the Jovian Evection, there would
follow :

ll ||

hy = — 0".88 sin [329° 4 a .68 (¢ — 1876.0)]
ky = + 0".88 cos [329° + 20°.68 (¢ — 1876.0)].

There still remains a considerable ean between the empirical
and the theoretical values; for 1902 the difference between the
arguments amounts to as much as 57°. Therefore we cannot but
conclude that still other inequalities join their influence to that of
the Jovian Evection.

17. The expressions obtained for 4 and / according to the two
preceding sections are therefore:
h=h +h + Aq
k= ke +k + kin + kiv

For f/,. and fs, we find from the mean of all the observations
used here:
he = + 0".43
p Sepcceesie seat Beebe
so that the complete formulae become :
h=+0".43—1".28 sin [307°+19°.4(t— 1876.0)]—0".32 cos (2a—3J+7°)
k= + 0".17-+1".28 cos [307° 19°.4(t—1876.0)]- 0.32 sin (2a—3J+T7)
—0".45 sin 6
or putting for 2a —3./+ 7° and for @ their values and combining
the terms /’ and /yy which have the same period :
h = + 0".43—1".28 sin [307° + 19°.4 (¢—1876.0)]
—(0".32 cos [198° — 9°.67 (t— 1876.0)]
k= + 0".17 + 1”.65 cos [297° + 19°.4 (¢—1876.0)]
_— (".32 sin [198° — 9°.67 (€—1876.0)]

The values derived from these formulae I call Comp. I and the
differences between these and the / and / derived directly from the
observations are shownin the table of page 416 under the headings
O—C TT.

Also the O—C'/TJ still show a distinct systematic character. The
number of permanencies of sign has but little diminished, yet the
mean discordance has become somewhat smaller.

We find:

Mean discordance from C. | in A+ 0".62 in & = 0".638
from C, I in a= 053 In & ee

while using only the second and third series we should have found:
Mean discordance from C. 1 + in A 0.57 in’ & = "ae
from C. I m Ase OU in & + 0".49

Finally | have employed the differences O—C' // to investigate
once more whether the observations reveal an inequality with a
period of 9.74 years. Disregarding the less accurate first series, and
using directly the annual results, | found :

for the term in / + 0".04 cos (2 ~ + 3 V—5 £)
for the term in & -+- 0".08 sin (2 a + 3 V—5 E)

As we see the coefficients are again found to be small, while their

theoretical value amounts to -- O'.68.

[8. After the Communication of my first paper to the Academy,
| have still made some new calculations about the errors of latitude,
of which the results follow here.

The coniputation given on p. 886 of my first paper had shown
that especially the values of 4 from the equation

( 421 )

Ad=a + hsinu + ¢ cos u

as derived separately from the years 1895—98, and from 1899— 1902
were not in good agreement, and that between the A d for the same
value of w from both periods there exist distinct systematic differences.

Therefore 1 have also solved rigorously the equations for the
separate years. As the 4d for the period investigated bij Nrwcoms
are less accurate (therefore Nrwcoms himself used only the mean
values for the whole period) I have solved for this period not the
equations for the separate years but those for groups of 2 or 3 years.

In this way I obtained the following values of a, 4 and ¢. To
the ec of 1895—1902 the corrections mentioned before have been
applied. The values of a@ derived from the two series are not directly
comparable inter se, as the declinations were not reduced to the

same system ').

a b c

| ie
1862—64 | —0"6 | --0"G2 | +0"61
1se5—66 | 40.97 |. 40.97 | -b0.57
1867-68 | —0.38 | +0.02 | +0.95
1369-70 | —0 38 | +050 | +0.60
1874-72 | —0.44 | -0.43 | —0.08
i873—72 | 20/32) = 0.65 +0 39
1895 +06 |= 0.76.) +10 81
1896 —0) 29 O47 | +4.19
1897 0/2 eee ty a eee Be

1898 +0 08 +0 15 1.89
1899 0.35 | +0.79 +1 .02
1900 +055 +0. 45 +40. 89
1901 +-0.54 +050 +0 40
1902 | +0. ).78 +0.79

cb
Ww

To these results we may add those for 1892 derived by Franz.
I had at first overlooked the fact that Fraxz had not only discussed
his own observations of the crater Mésting A, but also the results
of a similar series of observations made in the same years at

1) Comp. also the remark at the end of this section.

as *. 1’
2 “meal wa
( 422 ) =
Géttingen*). As the most probable results from the two series he —
found: *) :
‘ di = + 0'.46
eb — 20 ag
dO = +. 8".7
These values correspond to
b= —0"44°- ¢ SP ee

Considering these results it seems possible that we must assume
the existence of a periodic term in 4. But for the present we
cannot go farther and we must await the results of other series of
observations before we can formulate more definite conclusions.

I will now only add the following remark. As within each year
the observations are fairly regularly distributed over the anomalistie
revolution, the fact that in the present investigation we have disre-
garded the corrections of the longitude depending on g cannot have
had an appreciable intlnence on the determination of the 4 and e
from the separate years. On the other hand an apparent periodicity
in the @ may have arisen from it.

The corrections of the longitude alluded to are of the form:

d/—ssin (9 +4)
where g is a slowly varying angle. The corresponding corrections
that ought to be applied to the declimations are:
dS — 0.40 cos 1X s sin (a + YX)
= 0.20 ssin(2 a }- a + 7) — 0.205 sin (a — x)
i. e. partly nearly half-monthly terms, partly terms of long period
which modify the values found for a.
From the largest term in the correction of the longitude:
Sl— + 1.28 sin (gq + N — 90°)
arises a term :
5 od = — 0".26 sin (x — N+ 90°)
which term has a period of 17 years.

Astronomy. — ‘“Jiivestiyaton of the errors of the tables of the
moon of Hansexn—Newcomp wi the years 1895—1902.” By
Dr. E. F. vax be Sanpe Bakavizex. (Second paper, part II).

(Cominunicated in the meeting of November 28, 1903.)

19. In the preceding considerations I had not taken into account
the correction which Hansey’s value for the obliquity of the ecliptie
may need. Nor had I paid heed to the errors in the observed deeli-
nations which vary with the declination itself.

1) Astron. Nachr. Bd. 144, S. 177.
7) | adopt the mean of the results found by Franz in two different ways.

( 423 )

The latter would have required a special investigation of those
observations, which I did not intend. As to the former point too
little certainty seemed to exist. For although the obliquity of the
ecliptic adopted finally by Newcomp has for the 2d part of the
19% century values. which are larger by 0'.2—0".3° than those
from Hansen, yet the value derived directly by Newcomp from the
observations of the sun only agrees well with Hansry for this period.

We have:

L860 1900

BAA. Barat’

HANSEN 26'"74 8$'03
NEWCOMB 27.00 8.26
Nrwcomsp Sun 26.81 eae

On closer consideration, however, we see that we ought not to use
the absolutely most probable value of the obliquity, but that it is
best to adopt for each series of observations of the moon the value
which is derived from the observations of the sun which have been
made at the same time and with the same instrument and have been
reduced in the same way. For it may be easily seen that in this
way we eliminate for the greater part the errors in the refraction,
the flexure of the instrument etc. Some systematic errors, namely
those depending on the conditions of the observations which are
different for the sun and for the moon will be retained undiminished
in the results, yet I hold the course proposed here for the best,
unless elaborate researches on the errors of the observations have been
made. In this way, at any rate we may get some insight into the
influence which the values adopted for the reduction elements of the
observations have on the elements derived for the plane of the
moon's orbit.

20. For the periods discussed by Nrwcomp and by myself we
must therefore find the values of the obliquity of the ecliptic which
follow directly from the observations as they are given in the Annals
of Greenwich and of Washington.

For Greenwich [ could use the resulting values given for each
year in the Greenwich observations and derive from them the correc-
tions of Hansen’s obliquity. For 1895—1902 these corrections were
combined into one mean, but the period 1862—1874 was divided
into two parts: 1862—67 and 1868—74, because in the year 1568
Sronr’s refraction constant had come into use, which is smaller by
about 0.5°/, than that of Brsset. There are also differences between

( 424)

the values adopted for the flexure of the instrument in the different
vears, particularly between those betore and after the piercing of
the eube in the autumn of 1865, but these differences are neutralized
for the greater part by the different values which are adopted for
the so-called R—D correction, and therefore I thought best not to

make more subdivisions. In this way I found :

Greenwich J ¢ HANSEN
1862—1867 4+ 0" 41
1S68—1874 =e (he
1895—1902 + 0.31

For Washington I could only use the values given by Newcome in
his Astronomical Constants p. 38 ate! supposed that the values given
there for d’s, if again I subtracted from them the reduction to the
“Pulkowa refraction’, would agree with those which follow imme-
diately from the results in the Washington observations’). In this

way | found :

Washington J ¢ HANSEN
1862—1874 ee

Hence the corrections which must be applied to the obliquity of
the ecliptic according to HANSEN become:

1862—1867 J&— + 0".20
[868— 1874 a | A
1895—1 902 +0 .31

The results of Fraxz cannot be corrected in this way. T assumed
for them, according to Newcoms’s final formula d¢ = + 0".24,
We now can determine directly the influence of these corrections
on the coefficients of sv ma and cos w derived from the observations.
For we have as a sufficient approximation :
d Sd = cos € sec d snl de = 0.96 snl de

= 0.96 (cos 6 sin u + sin G cos u) dé

and the corrections that must be applied to the coefficients 4 and ¢
are therefore a O96 Cos 4 (l & and + O96 sin A d & respectively.
Hence we find as the corrected values of 4 and ec:
') | could not make out this with certainty from the snecinct discussi n in the

Asir. Const, and, as it is well-known, a more detailed publication of these impor-
lant researches was frustrated by circumstances,

yaa

A ’
[Xk62—b4 -LO"4 +0"44
{S65—66 +0 Os | +).51
[867—68 —(). 04. +0 .25
1869—70 054 +0 .52
1o7— 12 =e 15 —().18
1873—T4 Aye? +0 .33
{892 =) By +0 90
{895 a) ere] +0.74

1896 +0 .08 0.96
1897 +0.42 | -10.87
1898 40.24 ) +41.60
1899 +0.78 | 40.72
1900 | -+0.35 | +0.61
1901 10.34 |. 0.47
1902 +052 +0.63

If we examine the values of 4, it appears that the periodic
character which before they seemed to reveal, has become much
less distinct, while the preceding remarks point to the possibility
that also the corrected values of 6 and ¢ may still be affected by sensible
systematic errors, for instance by an error of HANsrn’s parallax of
the moon. For the time being there is therefore no sufficient reason
fo assume the existence of unknown inequalities in the inclination
and the longitude of the node.

The mean results for the two elements then become:

i y Weight
1868 —0"08 +37 3
1892 +, 28 +10.5 | |
1899) —0,95 + 9.2 3

Mean 1885 —0".10 +7".0

( 426 )
Hence :
Correction of the centennial motion of the node + 13"
ome) re

If for the constant of the moon’s parallax we accept, instead of
Hansen’s value, that of Newcomp which is larger by O41, the cor-
responding variation in the 4d becomes —O".41 sin 2 or about:
— 0'.31 + 0°10 sin /, hence that in the 4 and c respectively:
+ 0°10 cos 6 and + 0".10 sin. @.

We then obtain:

oF ob | Weight
1868 —0"05 + 40 3
ig92 | 10.01 | 144.3 109
1999.10.96 | 4 See
Mean (885 —O"l0 +69

Hence:
dG 19005 = 12> SS Seok
The influence on the final results therefore is immaterial.

Astronomy. — “Contributions to the determination of geographical
positions on the West-coast of ATTIC (il): -By-G. SANDERS.
(Communicated by Dr. E. F. van be Sande BakHUYZEN).

: (Communicated in the meeting of October 31, 1903),

I. Determination of the longitude of Chiloango made
in the years 19OL and 1902.

I. In a preceding paper ‘Contributions to the determination of
geographical positions on the West-coast of Africa’ *) | have given
some preliminary results obtained for the longitude of Chiloango ’).
After that time until my temporary return to Europe in the autumn
of 1902 1 have, as far as possible, continued my observations and
extended them to the 2¢ limb of the moon. Lately I have been
able to reduce the whole set of observations with all possible accuracy

') Proceedings Acad. Amst. IV, 1901, p. 274.
*) Owing to an error in the sign, the results given there for March 3 and May I

were wrong.

( 42%)

2. Arrangement of the observations. On this subject [ have said
a few words in the paper mentioned. Here I shall consider some
points more in detail.

All my observations were made by the method of equal altitudes
of the moon and a star. Because of the small latitude of my station
(9 = . such |
the parallel was at small angles with the vertical circle, i.e. that

5°12’) I could make the observations in such positions that

the parallactic angle differed little from 90° or 270°. Hence the angles
of the moon’s orbit with the vertical circle were not great either
and therefore the accuracy that can be reached by means of obser-
vations of the moon was actually attained very nearly, in so far as
it depends on the geometrical conditions.

| used my universal instrument described before, and the obser-
vations consisted in noting down the moments at which the
visible limb of the moon and the comparison star attained the same
altitude. The instants of transit over the horizontal threads were
determined, first for the one, then for the other object, either com-
bined with readings of the alidade-level. In this way I have obtained
24 observations of the 1st limb scattered over 10 nights and 12
observations of the 2! limb over 3 nights. I regret that it has not
been possible to add to the last mumber.

The instrument has always been used in the same position, telescope
right. In order to prepare myself for the observations 1 beforehand
computed for given moments the azimuth and the zenith-distanee of
the moon and the star, while the azimuth of the instrument was
known by means of the harbour-light*). Each time the level was
read just before the transit observations. The reticule has remained
in the same position since February 19017), so that each time the
transits could be observed over 7 threads.

The distances between these threads were about 7s, 6s, 45, 4s, 7s,
6 and owing to the rapid succession of the transits and the rather
small power of the telescope, I did not sueceed in estimating further
than the full beats of the chronometer. In future observations itmay
perhaps be better to sacrifice some transits in order to try to reach
a higher degree of accuracy in the others.

Another result of the rapid succession of the separate transits was
that I was unable to follow the observed object in azimuth during
its transit over the reticule. Hence in some cases it passed in
a somewhat oblique direction and while | always took care that the

1) Comp. Contributions to the determination of geographical positions ete. I.
p. 3 (276).
*) Ibid. p. 16 (289).

( 428 )

transit over the middle thread should take place very near the middle,
the transits over the other threads were observed on either side of
it. It may be easily shown, however, that in the present case no
appreciable errors can arise from ils.

In the first place we shall show that even the errors in the abso-
lute zenith distances generally will be small. By the symmetrical
arrangement of the observations, the influence of an inclination of the
reticnle as a whole will be eliminated from the mean result and
the influence of the curvature of the parallel of altitude will always
be small for my observations. At a horizontal distance c¢ from the
middle of the field the influence of the curvature of the parallel on
the zenith distance Is:

]
A z= —¢’ cot. z sin ‘i
») e

Now the proportion of the horizontal to the vertical motion, putting
for the parallactic angle p, is coly. p, and for a transit over a thread
at a distance 7 from the middle thread the correction of the zenith
distance will be

2= = 7? cota’ p cota z sin 1
while the extreme threads are at distances of about 175 or 250" from
the middle thread. In one observation, that of 1901 Febr. 25, which
owing to the unfavourable relative positions of the moon and the
star perhaps had best be excluded, the value of cotg. p was 0.68,
while for the rest its greatest value amounted to 0.84 and it was
generally much smaller. In the most unfavourable case, therefore, we
have for the extreme threads «= 170" and Az = O".08. In all the
other observations we have always Az < 0".02.

The influence on the difference between the zenith distances of
the moon and the star, however, is much smaller still, as the moon
and the star always differed little in declination and hence at the
moments of the observations were at about the same parallactic
angle. The difference between the parallactic angles was, excluding
the observation of 1901 Febr. 25. for. which p p=T7 In maximo
3°. So the influence of the curvature of the parallel is almost entirely
eliminated in the results of the observations. The same is the case
with the influence of the inclination of the individual threads.

That | did not follow the star in azimuth has therefore had no
injurious consequences and no corrections are required. On the other
hand the consequence may have been that the stability of the instrument
during each transit was greater.

( 429 )

After the first object had been observed, the instrument was
carefully brought into the azimuth of the second. The difference
between the level readings in the two positions was always smaller
than | division —95".4 and for 33 of the 36 observations smaller
than 02.5. The interval between two corresponding transits of the
moon and the star was always less than 25 minutes and generally
much less.

Finally | remark that, excluding 1901 Febr. 25, the value of the

parallactic angle during the observations was always enclosed between
80° and 110° or between 250° and 280°.
3. Determinations of time. Rates of the chronometer. Except on 2
nights (L901 Oct. 6 and 13), when I observed transits of stars over
the meridian, the corrections of my chronometer to the mean time
of Chiloango were always determined by observations of altitude.
For this I refer to my previous paper (Contributions I p. (276) 3),
where I have also given the corrections of the chronometer and the
daily rates for the period 1900 Oct.—1901 July. As, however, |
have since been able to correct the observed altitudes for the rather
large division errors and the flexure of my instrument (Comp. I. ¢.
p. (285) 12), I once more give in the following table the corrections
and the rates for the whole period 1901 Jan.—1902 May. The rates
hold for the interval between the date on the line above and _ that
on the same line. In the next column are given the mean tempera-
tures; those for L902 Jan. 6—Febr. 5 are interpolated values because
thermometer readings were wanting. (See table p. 430).

From these data I have derived a formula for the imfluence of
the temperature on the rate. As the differences in temperature are
small I could only determine a linear influence. I found:

1901 Jan. 18—Apr. 28 + 05.91 + 26°.0

1902 Febr. 5—May 17 + 1.07 + 25.8

Mean + 0.99 + 25.9
api 10-2 0: 19 -4 964

1901 June 17
hence :
Influence of 1° + 08.178 *).

By means of this temperature coefficient | have reduced all the
observed rates to + 24° and these reduced rates are given in the

1) For this computation too the rate in the interval 1902 April 30—May 12, during
which the chronometer was transported to Mayili and back, was used erroneously.
If we exclude it, we find for the second summer-rate +- 18.05 at 26°.0 and for the
temperature coefficient + 05.171, which differs little from the value found above.

Dec.
1902 Jan.
”
Febr.
March
”

”

April

— wo NM ~& =1 ©

=) GO) GO) OO 300) “OO 1 CO—n'OO™= CO I) (1 ST) +S! 4G: OOO’ GO “oO 60

CcCcmowomwHoco 2 ~4 “I

co coconZx x

bo oC

m s
+5 1 oo:
39.

2)
SA /
Hd

5 OFT

00) 35

ho
for)
bo

bo
On
Sen aT es

no no
es ou
coonmoruo

to
=
to

22,
23.

23
23.

i) bo
ou ive)
eal (COR Sie ec tbs

to
RSS
lor)

[24.9]

( 481 )

last column of the preceding table. There seems to be a slight
gradual retardation, but for the rest the reduced rates in the main
agree satisfactorily, while some of the most discordant values belong
to short intervals. As the lengths of these intervals are very different,
it would have little sense to derive a value for the mean dis-

cordance.

4. The reduction of the observations for longitude. For the
reduction of my observations I followed the method given by Prof.
QUDEMANS ').

I also followed his advice not to reduce the transits to the middle
thread, but simply to take the mean of the observed times of transit.
A slight disadvantage of the course followed by me is that, when
either for the moon or for the star the transit over a thread has
not been observed, we must also exclude the corresponding transit
of the other object. This was only the case with the two observa-
tions of 1901 May 217).

Having found in this way the times of the passage over the mean
of the threads we had now first to determine the differences § between
the observed differences in zenith distance of the moon and the star
as shown by the level-readings and the values computed for them
with adopted reduction elements, among which an assumed longitude
of the station. Secondly the equations of condition were formed, by
means of which the values of § are connected with the variations of
the adopted elements. These equations were transformed so as to
express 4/, the variation of the adopted longitude, as a function
of §, and of the variations of the adopted latitude, of the adopted
correction of the chronometer, of the times of transit of the moon
and the star, of the adopted right ascension and declination of the
two objects and of the adopted values for the parallax and the
semidiameter of the moon.

On the one hand this course enabled me to correct the results
found provisionally as soon as corrected values of the reduction
elements had been derived; on the other hand the equations showed
the influence of residual errors in the observed quantities and in the
reduction elements.

In the first place I shall consider the values adopted finally for
the elements of reduction. | accepted as the latitude of the station
5? 12'4".0 (Contributions Ge: (284) 11). The corrections of the

1) Versl. en Med. Kon. Akad. Amsterdam 6, 1857, p. 25—40.
*) By using only corresponding transits we also eliminate the influence of the
refraction.

( 432 )

chronometer were found by direct interpolation between the observed
values as given in the table above. As the temperature varied only
slowly I deemed it unnecessary to account especially for its influence.
The right ascension and declination of the Comparison stars were taken
from the ephemerides of the nautical almanac which for these years
are based on Nrwcomp’s Fundamental Catalogue and for my purpose
could be considered as absolutely correct. This is not the case with
the right ascension and declination of the moon, as the errors in
the values computed by means of the tables of Hansex-NEwcomB
may still be quite sensible.

Especially with a view to my observations, E. F. van pr SANDE
Bakuvyzen has undertaken an investigation of the errors of those
tables *) and I could avail myself of his results. For the derivation of
the corrections that must be applied to the moon’s places I, on his
advice, proceeded as follows.

Let us first consider the errors of the iongitude. For the constant part
of the correction of the mean longitude I adopted + 2”.20 (Baku. I p.
376 and 3838) and to this I added the corrections for the parallactic
inequality ete. computed from the formula of Baku. | p. 3875. The
sums of these two corrections were transformed into corrections of
the true longitude, and I again added to these the corrections for
the inequality in the true longitude which Nrwcoms had been the
first to. find and which Baknvyzen had determined anew from the
observations. [| used therefor the values of the coefficients 4 and /
as given by the formulae in Baka. IL p. 420, but added to either
of them the constant correction — 0".30, in order better to represent
the observations (comp. Le. p. 416). These corrections should be
applied to the orbit longitude, but with sufficient approximation might
be considered as corrections of the ecliptic longitude.

As correction of the moon’s latitude [adopted (comp. Baku. I] 421),

A p= — 0".58 sin wu + 0.086 (A J — 12" 1) cos u

Where represents the argument of the latitude and 4/ the total
correction of the longitude, while I assumed for the correction of
the longitude of the node for 1902 + 42" 1.

From the corrections of the longitude and the latitude formed in this
way, I derived those of the right ascensions and the deelinations by
means Of the tables in Newcomp’s “/nrestigation”. Another correction,
however, had still to be applied to the right ascensions, the reduction

') K.P. vay pe Sanne Baknvuyzey, Investigation of the errors of the tables of the
moon of Hansex-Newcoms in the years 1895—1902. | and IL. Proc. Acad. Amster-
dam Dee. 19th 1903. These two papers [ shall quote as Baku. | and Baku. II.

—— wt owe

from the equinox of the LO Year Catalogue, for which the errors of
the moon had been determined, to that of Newcoms’s Fundamental
Catalogue from which the positions of the stars were taken. |
adopted for this reduction -+ 08.054.

The adopted corrections in 2 and @ and those in @ and J are
given in the following table together with the Comparison stars used.

Al AB Ax A3 Star

" " "
1901 Jan. 22.2 1.27 —0.52 10.146 — 0.03 9 Aquarii
23.3 +4.72 —().27 167 +0. 42 « Aquarii
» 25.3 +2.80 0.46 293 +1.24 2 Piscium
Febr. 25.3 $4.27 +0.72 40) +1 56 z Tauri
Warch) S23 +4.75 +0 .65 Bord —0 90 z Leonis
May 1.2 +3 .88 0,22 .290 — 1.69 z Virginis
) 21.3 +-4.410 -++0.89 347 4-0.53 2? Geminorum
23.3 +4 85 +0.71 387 —0_ 56 z Cancri
July 22.3 44.47 —0.26 327 —1.94 % Vireinis
Nova! . 7-3 2.38 —O.57 224 +0.12 3 Capricorni
1902 Jan. 24.4 +3.54 0.57 2011 —(.42 z Cancri
March 25.3 +3. 12 —0.59 234 —1.73 z Virginis
April 23.3 +2.8%4 —O.87 | 294 —1.70 z Librae

For the moon’s parallax | have provisionally adopted Hansun’s
consiant, while for the computation of the corrections for parallax
BrsseL’s elements of the figure of the earth were used. The correction
of Hansen's constant is still uncertain and at any rate not large.
It will appear moreover that its influence is eliminated to a great
extent in the final result because observations have been made
as well before as after the meridian passage.

The value for the moon’s diameter corresponding to my mode of
observation must naturally be derived from my observations them-
selves by comparing the results for the first and the second limb.

In the following table IT shall give a summary of the results
obtained. The 27% and 34 columns contain the values of § and of

4 = correction of the assumed longitude — 48"32s.0 each computed

by means of the moon’s places of the Nautical Almanac, but, with

the values finally adopted for the other reduction elements. The
29

Proceedings Royal Acad. Amsterdam. Vol. VI.

4th and 5% columns contain the corrections of 4 Z resulting from
the adopted corrections of the right ascension and the declination of the
moon, the 6 contains the corrected values of 2 Zand the 7™ the mean
results for 4 from the observations of each day. The last column
shows the derivatives of the longitude relatively to the corrections
of the chronometer. The derivatives relatively to the other elements
are omitted to save room. I shall only give hereafter their mean
values for the observations of each limb. (See table p. 435).

Now the question arises what weights must be assigned to these
results and how they will be best combined.

First it must be borne in mind that in L9OL January the transits
were observed over 2 threads only and in all the following obser-
vations over 7, except in two cases over 6 threads. Therefore w2
have assigned the weight */, to the first mentioned observations.
Secondly we must pay attention to special unfavourable cireum-
stances during the observations. and then we find that for that
of 1902 Jan. 24 the star was only faintly visible through the
hazy atmosphere, and that for the first observation of 1902 March 25
an uncertainty prevails about one of the level-readings. To these
observations also the weight ’/, was assigned *).

Finally we had to pay heed to unfavourable geometrical conditions
for some observations, which might highly increase the influence of
some reduction elements, and also to special cases of uncertainty
in one of those elements. I have already mentioned that on 1901
Febr. 25 the observation had been made with very unfavourable
relative positions of the moon and the star. The values of the
parallactic angle were for the moon and the star 124° and 117°
respectively, while in the other cases the most unfavourable value
was 1O8S’? and the ereatest difference between the values for the
moon and the star amounted to 3’. We now see that owing to this
the derivative relatively to the chronometer-correction is exceptionally
large, while also those relatively to the latitude of the station and
to the moon's declination have the largest value here.

A special uncertainty. on certain days can only be expected
in the chronometer-correction. A measure for this uncertainty is
given by the interval between the observation of the moon and
the nearest time-determination, and it appears that this interval
for almost ail the observations lies between O and 3 days, but
for TOL Febr. 25 amounts to 6 and for 1901 March 3 to 12
days. Another time-determination had still been made on Febr. 28

1) This has been taken into account in the derivation of the mean result for

March 25 in the table above.

( 435 )

RESULTS.
—eeeeeeeeeeEeoEoEoEoEEEEEEEE—EEEEEE—————eeeeEeEEE————— —
Corr for Corr. for yey Mean | dL

Date. e WL :
zx Moon 2 Moon corr. | AL | db

LIMB I,

1901 yr . < .
Jan, 22 —7 18 —I348 — 3.99 0.00 —17.17 . —().74
» » 45.45 + Gao — 3.99 0.00 + 2.36 iy ees 77
» 23 +455 | + 853°! — 4.67 | +0.07 + 393 | +3.93 | —0.78
‘ OF, +382 + 7.59 = Gas 10.52 ATs bas 1.02
» » +-3.46 + UND — 6°39 | +0.50 = 70596 —1.02
» +4.02 + 7 91 — 638 +0.48 + 2.01 4.2
» se2 Lar a =.6.35 | 40.47 =s15e23 | —O ALT 4 08
Febr. 25 +2.05 + 4.60 SS Gon fea 19 ee = 2 2644 5 49
March 3 —) 37 +141.94 42-03 +0 95 + 0 26 et te
» » —) 06 +414 =123::19' | 40.42 Sat PT. +0 .02
» ) —6 92 +16 Ol — 2 37 | +0 50 + 441% 41 36 0 29
May 1 —4.58 | 19386} — 9.22} 40.05 | + 0.69 | +0.69 | —0.72
» 21 +4.69 + 8.20 — 8.86 | 40.24 + 0.08 40.03
» » —1.06 ASG {75.00 | E0522 —10.03 | —4.98 | —0.02
D 23 +1.4 a> 265 == G9 | = rae —— 7.76 = 0'56
» » +2 .90 454 AQ? O29 Ce eh 4, =). 59
duly 22 | +7 83°) £46 99° | — "0-44 |"-00.25'|- +1. 6.80 —0.61
» ) Oo AE 756") OAR] 220 | ++ 7.86 —0.64
» » +6.42 443.14 —10.36 40.15 + 2.93 ) +4+5.70 | —0.67
PON thee feat. foe OR. 19 0:03° |» <=. 198 —0.43
» » ora = Gta aha) O02], 19-58 0.46
» » +4.36 + 8.48 == (p25! yy Se IY | —0.64
» » See Oe yea PG) 98} = 0-01 Je. — 0.47 —0.59
D +4.00 | + 7.84 — 631 —0.01 -- 152. | —2.07 | —0.55
LIMB II.
1902 "
s s s s s
Jan. 24 0.00 0 00 — 8 43°) +0 20 — 8.23 | —8.23 | —0.67
March 25 +0 86 == Ae EAD 40.11 = eo e0278
» » —8.06 +4651 | — 7.08 +0.07 + 9.50 ==). 76
» » —3 47 + 7.08 — 706 +0.04 + 0.06 =f.
> » —2.03 + AAG ety sa eh ON = 20 72
» ) —4 64 4+ 94! eS 75@) (i- —4p04 +236 44.03 | —0 69
Apr. 93 ae FHT +10 0) =. j, 49 =O 44 = s.S7 TS:
» » —1 .86 = ith Bits — 6/47 20349 | =~ 9:88 = hi72
» » == 5) at 4413.17 == §-45-) —0-9% + 6.48 ==O370
» » —3 7d 4.7.57 mani Zee a4) 0) ++ 0.54 = 20u
» » —4 62 19.32 — 6.40 —0.36 + 2.56 —().68
» » — 1.52 +7 O2U0 — 6.38 —0.42 — 3.74 | 41.19 | —0.66

( 436 )

but the resulting chronometer-correction: Febr. 28 8'.4 + 56™ 15s.53
is somewhat uncertain.

After due consideration of all these circumstances, I have entirely
rejected the observation of Febr. 25: to the 3 observations of
March 3, however, I have ultimately assigned full weight. For the
derivatives relatively to the chronometer-correction for March 3 are
very small and their mean value is only ++ 0.04, while on the other
hand the chronometer-correction for March 3 changes only 0526, if the
time-determination of Febr. 28 is taken into account.

This being established, we had still to find in what way the
separate results had to be combined. We had first to investigate
whether constant errors had to be feared for the results of the same
night. On the one hand | therefore derived mean results for each
limb by combining the separate observations with the accepted weights
and from the discordances found I computed the mean error of a
result with weight 1. On the other hand I determined the mean
error free from the influence of the constant error’ of the night by
comparing the separate results with the mean result of the night
for those nights in which more than 3 observations had been made.

In this way I found for weight 1, i.e. for the result of one obser-
vation without special uncertainty :

Total mean error Limb I + 5:s.65
4 ne fs oe i ee
Partial ., % eR er ie a Sh

Althongh the last value is very uncertain, there seems to be no
reason to assume in the results of the final reduction errors that
remain constant during the same night. Hence in deducing the final
results we need not ask in which night the observations have been made.

In this way we shall now derive for each limb the mean value of
Z£/, and also those of the derivatives of the longitude respec-
lively to the other variable quantities. Let us put for the varia-
tions of the latitude of the station, of the chronometer-correction, of
the chronometer-time of transit of the moon, of its right ascension, of
its declination, of its parallax and of its semidiameter: Ag, 46,
At, 4a, &d6, Ka and AR and let A?, Aa’, and Ad’ be the cor
responding quantities for the star. Then we obtain:

ly tw se— 1s.08 — 0.03 Ag 0.48 46+ 28.05 4t
28.03 A ft 29.05 A a + 28.53 A a + 0.0248
0.00 4 d' + 0.86 4 a 4- 2.0004 R.... Weight 19.5

PAL + 0:.70 + 0.01 Xe —0.71 A 6 28S ee
29.22 A ¢ — 29.51 Aa + 29.22 Aad + 00GAG
0.06 4 0d 1.72 Aa—2.03 4 h.... Weight 11

os CTE” ae ee oil”

a oe

_— 'ee--~.
i» 3 ‘i

( 437 )

The variations A 1, 26, 4t, Of, Qa and Le’ are expressed in
seconds of time, the. other ones in seconds of are, and the deri-
vatives are formed accordingly. Naturally the terms in 26, 4f,
At’, La, La, &d and 4d now ean only relate to constant errors
in these elements. The 42 and 4F of the separate equations rigo-
rously express the variations of the parallax values and semidiameters
for the actual distances, but might approximately be considered as
those of a, and #,, the parallax-constant and the semidiameter, for
distance 1 ').

We now perceive that the influence of an error in the latitude
is very slight and that this is also the case with constant errors in
the declination of the moon or the stars. An equinox-error common
to the moon and the stars is not entirely eliminated, but its influence
is immaterial and my personal error in transit observations, which
influences 4, ¢ and ?#, is eliminated in so far as the error is the
same for the moon and the stars. The only terms which we have
to consider further are therefore those depending on 4.2 and 4 /.

If we accept for the two limbs as mean error for weight 1 = 5°.65

and + 45.84 respectively, as it may be that indeed the observations

of the second limb are a litthe more accurate, then we have:
DAE — O60 A xt 200k fe — 12.08. + 15.28
WLALEVM2A x 203 A Ry —- 0:70 + 15.46

The mean of the two results without regard to their weights is:
KE + 043A a: 43-0024 Ky — 08.19 + 0°.97

and the resulting longitude found in this way, apart from the fact
that it is not wholly free from personal error, is affected only by
the uncertainty in the constant of the parallax. If instead of HANsEN’s
constant we adopt that of Newcoms (Astronomical Constants p. 198
Which is larger by 0."4, our result becomes:

Ai A oe == ()?. 94
Hence we see that the influence of the uncertainty in the constant
of the parallax is probably not great.

As my final result I accept 4 2 = — 0°.3, and hence :
LONGITUDE OF THE OBSERVATIONPIER
EL — 48™ 323 = 18.0

1) If the coefficients of Az, and AR, are delermined rigorously we find:
for limb I ++ 0.83 and +1.93, for limb Il — 1.66 and — 1.95, or practically
the same values as formerly (added 1904 Jan).

438. )

Besides we find by subtracting the two equations:

4.958 A 2,+ 4.03 A BR, = + 1.78 +4".94

or
AR, -+ 0.64 A 2, = + 0".44 + 0.48
and |
forom DANSEN .-.. . 2 > A= POs
Nawcome 9.4. .. 578 ==- eats

or the semidiameter corresponding to my observations does not differ
much from that of HANsEN.

As to the accuracy reached in my observations we find as mean
error of an observation over 7 threads without special uncertainty,
as it is derived from the observations of the two limbs:

|) RSS ee SS!)

With this mean error we may compare the one found by Prof.
OvpreMaNs for the analogous observations made by 5. H. and G. H. pr
Langer at Batavia?) and that derived by Auwrrs from several longitude
determinations made by Frecriis by means of moon-culninations?)

pe Langer 1851—54 M.: EK. of obs: == DS Ze
Frevriais 1867—70 M. E. of average obs. + 35.14

The value for FLevriats is the mean of the results from the obser-
vations at 9 stations. In comparing these results it should be borne
in mind that the two instruments and especially that of FLEURIAIS were
more powerful than mine. On the other hand it was more difficult
D4.

Finally [ shall reduce my result to the harbourlight and to the

to derive accurate places of the moon for the years 1851
flagstail of the residence at Landana. By means of the triangulation
mentioned before *) [T found as differences of longitude :
Harbourlight — Observationpier = -+ 08.22
lagstall = *F a= a AG:
Hence the longitudes from Greenwich become:
LoncitupE Harpournient — 48™32s.1 + 1°.0
LONGITUDE FLAGSTAPE —48 33.8 +1.0
The English Admiralty-chart gives for the longitude of the harbour-
heht 12’ 8’ Kast = 48" 32s.

IH. Determination of the geographical position of Mayili.

». Mayili, a factory of the firm Harrox and Cookson is situated

') J. A.C Ovnemans. Verslag van den geographischen dienst in Nederlandsch-Indié.
1858- 1859, Batavia LS8G6O.

4) Astron. Nachr. Bd. 108, p. 313.

$) Contributions Tp. (287) 14.

( 439 )

on the left bank of the Chiloango river a little below the confluence
of the Luali and Loango rivers.

In May 1902 1 had an opportunity for making here a latitude
determination and for determining the difference of longitude with
Chiloango.

My instrument was mounted on a heavy wooden tripod, made
especially for the purpose, which secured sufficient stability. The
observations, however, were very difficult, owing to myriads of
insects which made it almost impossible for me to hear the beats
of the chronometer.

On May 3 1 made the first time-determination, on May 4 I
observed the cireummeridian altitudes of @ Ursae Majoris and 4
Centauri for the determination of the latitude and lastly on May 7
I made a second time-determination.

6. Determination of the latitude. The two stars used for the deter-
mination of the latitude culminated at zenith distances of 62°.0 North
and 57°.4 South. At each of them 8 pointings have been made, 4
in either position, and so that the last pomting was made in the
suine position as the first and that they were made on either side
of the meridian.

As run-correction for the mean of the two microscopes L applied
per 10'+ 2”.0. The value of a level-division was put at 5”4 as
before and the refraction was computed from Bussen’s tables.

Here follow the results obiained. For each star 4 results have
been formed from the 4 pairs of pointings. To the means of those
4 results corrections for division error and flexure have been applied,
derived from the formulae computed before. The circle was at
zenith-point O°,

RESULTS FOR THE LATITUDE.
5°4’ 39"46
48.20

44.23

46.59

Mean == a CAAL GD

Corrected

3 Ursae majors

go 4’ 40".2

5°4’ 36"08
Daou
aoclO
BOOZ
Mean Sa. ae a as
imbecedtiny =i eS te fh bh AY AOS

2 Centauri

( 440 )

The two corrected results agree nearly exactly, while also the
_5°4’ 40" 1 differs only very little

mean of the uncorrected results
from them.
I therefore accept :

Latitude of Mayiu1 g = — dS 4’ 40".

7. Determination of the longitude. The time-determination of

May 3 was made by the observation of Sirius in the West, that of.

May 7 by the observation of Sirius in the West and of @ Virginis
in the East. Unifortunately in the observation of May 38 one of the
level readings is uncertain.

The reduction by means of the final value for the latitude,
correcting the circle readings for division error and flexure, gave
the following corrections of the chronometer to the mean time of

Mayili:

Chronom. corr. DRS
May 3 84 1 {ieee
ie ae RS + 1228.22 + 45,22
28.00
Mean 1. dod, Veale

For the correction to the mean tine of Chiloango 1 obtained
before and after the travel to Mayili: ;
Chronos :cOrt: eee
April 80° 8'3 + 1'0™ 58-72

+ 41°16

May 12.8.4 (odeess

If from these resulis we interpolate the corrections for the instants
of the time-determinations at Mayili and compare them with those
determined there we find:

Mayih Kast of Chiloango May 3 A 5
= pod 21 Oo:

The time-determination of May 8 is, as said before, somewhat
uncertain, yet on the other hand it seems better not to rejeet it
allogether, as owing to the two travels and to the fact that the
temperature at) Mayili was higher by 1 or 2 degrees than that at
Chiloango we may not a priori Count on the constaney of the rate
between April 30 and May 12,

The two results do not differ much and | adopt:

Mayit East or CHiLoanco 1™215.3
LONGITUDE, PROM GREENWICH — 49m 53:.6.

( 444 )

Physics. — A determination of the elvetrochemical equivalent of
silver.” By G. vax Duk and J. Kunst. (Communicated by

Prof, H.. HaGa:

The principal determinations of the electrochemical equivalent of
silver have yielded the following values: *)

MASCART O.O11L156 1884
F. and W. Konbrauscn O.OLL185 [S84
Lord Ray.erign and Mrs. Sipawick O,OL1179 L884
Priiat and Portier 0.011192 1590
I AHLE O.OLT185 1898
Parrerson and GUTHE 0.011192 1898
Preiiat and Lepuc LOTTI». 1903

The difference in these numbers is due, partly to the method of
the determination of the strength of the current, partly to the way
of constructing and using the voltameter.

In most of the investigations the strength of the current was
measured by means of an electrodynamometer in some form or other,
either directly or indirectly with the aid of a standard cell (cell of
Ciark). F. and W. Konnravscn used a tangent galvanometer.

For the voltameter the circumstances differed as to the composi-
tion and the concentration of the electrolyte, the shape, the dimensions
and the composition of the cathode, the way of washing and drying
the silver deposit.

The “Bedingungen unter denen bei der Darstellung des AMPERE
die Abscheidung des Silbers. statizufinden hat” are inserted in the
“Reichsgesetzblatt’ of May 6, 1901, p.127°) among the regulations
of the law concerning the electric umits sub § 50.

In connection with the rather considerable difference between the
values found for the electrochemical equivalent of silver, a new
investigation as to the value of this quantity in which the above
mentioned conditions are followed, did not seem to be supertluous
to us. The tangent galvanometer has been chosen for the measure-
ment of the strength of the current. Owing to the Iigh degree of
accuracy with which the constant of this instrument, and the hori-

1) Mascart. Journ. de Phys. (2) 3, p. 283, [884 F.and W. Kontravsca. Wied.
Ann. 27, p. 1, 1886. Lord Rayreréa and Mrs. Siwwewicr. Phil. Trans. 2, p. 411, 1884.
Petitar and Portier. Journ. de Phys. (2) 9, p. 381, 1890. Kante. Wied. Ann. 67,
p. 1, 1899. Patrerson and Gutue. The Phys. Review 7, p.251, 1898. Petar and
Lepuc. Compt. Rend. 136, p. 1649, 1905.

2) Also Zeitschr. f. Instrumentenk. 6 Heft. 1901, p. 180,

(dao

zontal intensity of the terrestrial magnetism and its space- and
fime-variations may be determined, this method is very well adapted
for a laboratory, which has been built without iron and in a place,
where no vibrations or stray currents in the earth are to be feared.

Determination of the horizontal intensity of the terrestrial
magnetism : FH.

To this purpose we have followed the bifilarmagnetic method of
F. Kontravscn (Wied. Ann. 17, p 737, 1882). The absolute bifilar
magnetometer was fastened at the top of a high wooden tripod. 90
em. to the north and to the south of it the tangent galvanometers.
were erected on pillars of freestone cemented on the bottom with plaster.
The dimensions of the magnetometers of these galvanometers are
about the same as those of the ‘Elfenbeinmagnetometer” of KoHL-
rauscH, but they differ from it in an important detail. The needle
with the mirror of the ‘“Elfenbeimmagnetometer” oscillates within a
sinall cylindric space, whose sides are only a few millimeters apart
and parallel to the plane of the mirror. In this way the damping
has been obtained. The local influence of the instrument is nearly
exclusively determined by the magnetic or diamagnetic properties of
the material of which the front and back sides consist, which is
usually glass. In consequence of the small distance between the needle
and the @lass walls this influence is variable with their relative
position. This renders the magnetometer in this form unsuitable for
observations which require a somewhat longer time, as we are not
sure of a constant position of the needie. It is therefore that we
have modified the instrument in such a way that the distance of the
needle from the fixed parts of the apparatus is large enough, the
damping being obtained in another manner. The space in which needle
and mirror oscillate is a vertical, thinwalled turned cylinder of wood
with an internal diameter of 4¢.m. The frontwall has been pierced and
round the hole a rim has been cemented in which the glass front
fits. A vane of mica is suspended on the cross, which supports the
mirror and to which the needle is riveted. This wine can move in
a narrow space which is found in the base of the instrument and whose
width amounts to a few m.m. In this way a strong air-damping
has been obtained.

In order to determine the local influence the magnetometer was
turned round the needle, sometimes in positive and sometimes in
negative direction; cach time over an angle of 5°. Before the mirror
a telescope with a scale was placed, and the distance had been

( 443 5

regulated such, that turning an angle of 5° corresponded to 50 em,
of the seale. From different series of observations, in which the

variations of the declination were read from another magnetometer,

it appeared that turning an angle of -- 5” or ) from the position
of equilibrium caused a deviation of the mirror from —-- 0,003 > cm.
10 0,002 cm. for one of the magnetometers and from —- 0,003 can.
{0 0,007 em. for the other. (The sign +- indicates that the tur
ning of the mirror and of the magnetometer are in the same direc-
tion.) These numbers are the mean values of a series of usually JO
observations. The needle had a different position in different obser-
vations, either more foreward or more backward; no fixed relation
between the deviation and the place of the needle could be observed.
We have equated the local influence to zero; the error ensuing from
this will not amount to more than to some hundredthousandths.

A rectangular turned copper ring 8,4 mum. large and 3,6 mom.
thick, supported by a wooden frame formed the cireuit of the tangent
galvanometer, which was placed south of the bifilar magnetometer.
It resembles the apparatus described by Kontravscn Wied. Ann. 15,
p. 952, 1882.

The circuit of the tangent galvanometer placed to the north was
formed by a copper wire of 0,059 cm. diameter, tightly strained
round a marble dise; the magnetometer can be placed ina triangular
opening, which is cut out of the cise.

In order to determine the local influence, the magnetometer was
supported free from the other part of the tangent galvanometer and
this was turned over an angle of 80° round it to either side. We

found that turning the marble: galvanometer from —- 30° to — 30°
caused a deviation of the mirror in’ one series of — 0,002 ¢m.,

another time of 0,000 cm. For the other galvanometer this deviation
amounted to +- 0.004 em. This difference may be ascribed to expe-
rimental errors, and therefore no influence of the instrument exists
here either.

The ratio of the values of Hat the place where the bifilar magnet,
and at those where the needles of the magnetometers were suspended,
was determined with the local-variometer of Kou.racuscn: a bifilar
variometer indicated the time-variations of “7.

Krom the observations with the local-variometer — the corrections for
the time-variations being applied — the ratio of the values of the inten-
sity of the magnetic field was derived as the average value of a

1
10000 /
The ratio of H at the places of the bifilar magnet and of the

series of numbers, whose extreme values differed less than

( 444 )

needles inside the magnetometers may be deduced from these data.

The distance between the suspension-wires above and below, the
length of the wires and the weight which they support, are of
primary importance for an accurate determination of the value of
HS M for the bifilar magnetometer (.J/ = magnetic moment of the
magnet). The wires run above and below closely along two small
scales divided in */, mm. The distance between the wire. and the
two adjacent divisions of the scale is determined by a microscope
with ocular seale. (1 m.m. corresponds to about 25 divisions of
the ocular scale) and the distance between the divisions of the two
scales is determined with a comparator. The distance is about
12.4 em. These measurements have been performed before and
after the observations (August 1903): the difference of the distance
of the wires found in the two determinations amounted to:

above 0,004 m.m. below 0.002. m.m.

The mean value of the two determinations has been taken as the
distance during the observations. It does not differ more from tbose
values than ———.
bO000

The length of the wires has been determined before, after, and a
few times between the observations with the aid of a glass scale.
The extreme values of the lengths reduced to the same temperature
differed O13 m.m.; the length of the wires being about 232 em.
An error of O,1 m.m. causes an error in the result of 46000"

The pieces, suspended on the wires are: the horizontal cross-bar with
its vertical rod and the bearer of the magnet which are made of
uuminium, the magnet, and a vane of mica in diluted glycerin for
the damping. These different pieces (with the exception of the mica-
vane) have been weighed separately and together; the difference
was [1 mgr., the total weight about 160 er. The weight of the
Inica-vane with its suspension-wire, immerged in the liquid so far
as during the observations, was determined at: before the obser-
vations, 1444 er. afierwards 1,457 er, average value 1,450 er.
The error which may ensue from this difference is not ereat: a

difference of 7 mer. gives an error of ——— in the result.
46000
In order to determine the value of a Wwe must measure the polar

distance of the magnet and the distance of the centers of the needles.
The polar distance of the magnet, 16,06 em. long, was derived

a ee Pe ee ee oe en eres

(soa.

7. Ses

_ OS = | Te ee

a a ae ee

( 445 )

from the deviations of the magnetometer-needles caused by the magnet
when placed normal to the magnetic meridian in two different
positions symmetrical with respect to these needies. Two deter-
minations in which the distances were chosen: SO and LOO em., and
75 and 105 cm. vielded the values 13,40 and 138,28 em. The diffe-
| es, 1
rence may be due to experimental errors. A variation of 4p Mem.
of one of the distances, causes — ceteris paribus — a variation in the
value of the polar distance larger than the difference between the
two values found. We have taken for the polar distance the mean
value 13,31 cm. This agrees fairly well with */, of the length.
(°/, < length — 13,38).

In order to ascertain the distance between the centers of the
needles, we first determined the difference of their distance from
the cocoon silk suspension-fibres. This difference was derived from the
deviations of the needles caused by the magnet, as well in one of the
positions of the magnetometers as when they had changed place, care
being taken that the silk fibres had the same positions both times. In two
observations this difference amounted to 0,007 em. and 0,009 ¢.m.:
average value 0,008 cm. A difference of distance of 0,001 cm. has
an influence on the result of —————.

120000

The distance of the silk fibres was measured by projecting the
fibres from two telescopes, 180 cm. apart and at a distance of about
> m. from the magnetometers, on a horizontal scale placed behind
them.

It appeared that the walls of the tube of the magnetometer had
no influence on the course of the rays.

We determined the value of H before and after the time of the pas-
sage of the current, in order to arrive at the mean value of H during
that time. During all this time the indications of the local-vario-
meter of KoHLRAuscH, erected in a room with nearly constant tempe-
rature, were read, during the determinations of HW every 2 minutes,
in the time between those determinations every 5 minutes.

The value of H during the passage of the current was derived
from the constants of the variometer, the mean reading during the
first determination of /7 and during the passing of the current and
the value of H found in the first determination of H. The same
calculation was performed with the second determination of H. The
two values found in this way for AH during the passage of the

current differed in most cases only ———— or not even so much. Only
* 9000

( 446 )

1
—— or ——.
GOO0 4500
of the two values of /7 found in this way, was taken as value of H.

The mean

a few times the difference amounted to

The tangent galvanometers.

Five diameters of the tangent galvanometer “north” were measured
by comparing them with a standard meter by means of a katheto-
meter; they differed less than 0,1 m.m. Before the observations we
found for the mean value of the external diameter: 41.3833 ¢.m,
t{—14°5, after the observations we found 41.3842 ¢.m., f=17°.5.
Reduction of the former value to the temperature ¢= 17°.5 yields
41.3843 ¢m. So the agreement is perfect. ;

The ring of the tangent galvanometer “‘south’” was not so per-
fectly circular; moreover its shape was not quite constant. Yet the
different determinations yielded mean values for the diameter which
agreed very well. Ten diameters have been measured, five on each
side, the distances of which were as nearly equal as could be
obtained. The values found are:

after the observations 2 /? = 40,445 cin. pases PES
before the observations — 40,443 em. ete
a still earlier determination yielded 40,446 e.m. at ¢—= 19°.8. When
reduced to equal temperature these values differ much less than
]

40.000"

For the determination of the intensity of the current sometimes
one, sometimes the other tangent galvanometer was used. The current
was supplied by a battery of 3 or 5 accumulators ; resistances of
about 20 olims, two voltameters, a commutator and one of the
galvanometers were inserted in the circuit. The intensity of the
current varied between 0.380 and 0.45 amperes, the quantity of
silver deposited was about 1 gram; the current passed therefore during
48 or 32 minutes. Half a minute after the current was closed the
deflection of the tangent galvanometer was observed for the first
time, and further every minute. While the current passed through
one of the galvanometers, the variations of the declination were

observed on the other. At '/, and at */, of the interval during the

4 +
passage of the current, the current was reversed ; during the short time
required for the reversal, a short circuit was formed, so that the current
did not) pass through the galvanometer; the error arising from this
circumstance is however so small, that it cannot have any influence
on the result. The influence of the reversal of the current in one

( 447 )

of the galvanometers on the reading on the other may be calculated
with a sufficient degree of accuracy from the dimensions of the
ealvanometer, their mutual distance, and the approximated know-
ledge of the intensity of the current. Before, after and between the
different determinations the two galvanometers were read at the
same time in order to ascertain their course. The time was deter-
mined with a chronometer, which ticked 120 times a minute, every
day it was compared with an astronomical clock of great accuracy.

The voltameters.

The cathodes consisted of platinum, two of them were cup-shaped,
the third was a cylinder ending in a hemisphere; a silver rod served
as anode. In order to intercept particles, which might fall from the
‘anode a SoXHLer? filtering-paper finger was placed round it, manufactured
by ScHLEicuER and Scxatin. A 20°/, neutral solution of Ag NO, formed
the electrolyte. This was partly obtained from KE. Murex, Darmstadt,
partly from the firm J. W. Gittay, formerly P. J. Kipp and Sons,
at Delft.

Two voltameters were placed in the circuit in order to ascertain
that no irregularities occurred in the deposition of the silver. In
most cases the weight of the deposit at the cathode agreed to within
O,1 m.egr., once it amounted to more than 0,2 m.gr. The mean value
of the two weights was assumed for the weight of the deposited silver.

The weights used for the weighing had been corrected by testing
them to a standard kilogram.

In the same way all scales used for the measurements have been
compared with a standard meter, whose divisions are again compared
with a standard leneth of 2 d.m. whose corrections were accura-
tely known.

The distance from the scales to the bifilar magnetometer and the
galvanometers was measured with a wooden scale of 3 meters. Marks
were made at distances of 1 meter and brass scales divided into
m.m. could slide along the ends; these scales ended in points of
ivory. For the galvanometers the distance from the scale to the glass
front was measured, for the bifilar magnetometer the distance to the
uurror. For each observation these distances were measured and also
the distance of the sitk fibres of the magnetometers. The different
corrections for the imelination of the murror, the thickness of the
glass front, the distance from the front to the mirror, etc. were
applied to the distance.

The length of the scale of 3 meters proved not to be perfectly

PS a a )
| 2 . North | South

= “a : P galvano-— galvano-

ve meter meter

). 18186 0 039083 2169.05 0.94417 0.011184 |

—
_
~—

2 0.418187 0.043462 2160.05 1.05014 O O11186

3 0.18156 0.044659 2160.05 1 .COG647 0.014185

4 0.48150 | 0.04171 2160.05 1.00759 0.011183
5 0.48157 0.045081 1920.05 0.96799 0.011184 |
6 0.48160 O 045481 1920.05 0.97657 | 0.01483 | |
7 0 18159 6.039307 9400 06 | 1 OD477 | | 0.01118] |
8 0.18202 0.088134 2400 06 4.09354 | 0.011184
9 0.18191 0 O38)D88 D4 OG 4 03565 0 0114183 | |
10 0.18160 0) O88770 2400 06 1.04007 0.011178
a 0.18164 0.031629 2880 .O7 1.01895 0.011188
12 0.148157 0.036271 2640 06 4.07048 0.014179 |
13 0.48162 0.036644 2400.06 0 98335 | 0.011181
14 0.18189 0.030924 288007 0.99574 0.011182 |
i) 0.18170 0 030813 2880 .07 0.99248 0.014184 :
16 0.18198 030284 2880 O7 0.97501 | 0.014179
17 0.18164 0). 040637 2160.05 0.98136 0.011180
Is 0.18123 0.043140 2160.05 1.04181 _ 0.011180
19 0.18155 0.033 ‘°82 2640 .06 0.98849 O_O11183
2) 0.48192 0.037478 2400 OG 1.00565 0.011480
2| O.A8163 0.039023 2400.06 1 04695 O2011479
22 O.18140 0.035231 2640 06 1.03997 O O11184 |
93 O.A8163 0.037327 2400 06 1.00162 QO. |
4, O.18191 0.037678 2400.06 1.01106 0.011181

Mean value O.01118i6 O.O0111821

+0. 00000066 +-0 .COO00060

(mean error).

H denotes the horizontal intensity, 7 the intensity of the current, ¢ the time, p the
weight of the silver-deposit, a the electrochemical equivalent. All these quantities
are measured in c. g. c. units.

( 449

constant; it had imereased about 0,2 m.m. during the time from
before till after the observations. A determination of a part of the
leneth, which was performed between the observations, convinced us
that the change had taken place gradually. The mean value of the
length before and after the observations is used as the length of the
scale for all observations.

This will have but a very small influence on the result; it will
cause the first of the values found for the equivalent to be somewhat
too large, the last to be somewhat too small. The difference however

1
does not amount to more than 16000- The distance from the scales
to the galvanometers was about 314,2 cm., that to the bifilar mag-
netometer about 317.5 em.

We have made 24 determinations of the electrochemical equivalent
of silver. The annexed table (p. 448) shows the results.

The values for the electrochemical equivalent @ deduced from the

; 1
observations with the different galvanometers differ less than 50000.
As the mean value of all determinations we find :

a= 0.0111818 = 0.0000004. Gnean error).

In connection with the agreement between the different obser-

vations, we are of opimion that this number is accurate to ———.
10000
The observations will be published later in extenso.

Physical Laboratory, University Groningen.

(January 21, 1904).

*
»

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING

of Saturday January 30, 1904.

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 30 Januari 1904, DI. XII).

eS Wy aes.

W. Avperpa van Exensters:” “Dibenzal- and benzalmethylglucosides.” (Communicated by
Prof. C. A. Lopry DE Bruyn), p. 452.

C. H. Siurrer: “The transfurmation of isonitrosoacetophenonsodium into sodium benzoate and
hydrogen cyanide.” (Communicated by Prof. C. A. Lospry pe Bruyn), p. 453.

H. W. Bakuvis Roozesoom and A. H. W. Aren: “Abnormal solubility lines in binary
mixtures owing to the existence of compounds in the solution”, p. 456.

M. W. Beiertcx and A. van Decpen: “On the bacteria which are active in flax-rotting”,
p. 462. (With one plate).

J. K. A. Wertaem Satomonson: “On tactual after-images.” (Communicated by Prof. C.

WINKLER), p. 481.

A. Smits: “The course of the solubility curve in the region of critical temperatures of binary
mixtures.” (Communicated by Prof. H. W. Bakuuis Roozesoom), p. 484.

C. A. J. A. OtpEemans: “Exosporina Laricis Ocp. — A new microscopic fungas occurring on
the Larch and very injurious to this tree”, p. 498. (With one plate).

P. H. Scnovure: “Piucker’s numbers of a curve in Sn”, p. 501.

Jan DE Vrirs: “On systems of conics belonging to involutions on rational curves’, p.. 505.

Jan DE Vries: “Fundamental involutions on rational curves of order five”, p. 508.

C. H. Briskuan: “The determination of the pressure with a closed air-manometer.” (Commu-
nicated by Prof. J. D. van DER WaAats), p. 510.

J. J. van Laar: “On the shape of meltingpoint-curves fur binary mixtures, when the latent
heat required fur the mixing is very small or =O in the two phases”, (3rd communication).
(Communicated by Prof. H. W. Bakuuis Roozenoom), p. 518 (With one plate).

W. H. Keresom: “Isothermals of mixtures of oxygen and carbon dioxide. I. The calibration
of manometer and piezometer tubes”, p. 532. Il. “The preparation of the mixtures and the cum-
pressibility at small densities’, p. 541. ILI. “The deteimination of isothermals between 60 and
140 atmospheres, and between — 15° C. and + 60° C.”, p. 554. IV. “Isothermals of pure carbon
dioxide between 25° C. and 60° C. and between 60 and 140 atmospheres”, p. 565. V. “Isother-
mals of mixtures of the molecular compositions 0. 1047 and 0.1994 of oxygen, and the compa-
rison of them with those of pure carbon dioxide”, p. 577 and 588. (With 2 plates). V1I.“Influence
of gravitation on the phenomena in the neighbourhood of the plaitpoint with binary mixtures”,
p- 593. ‘Communicated by Prof. H. Kameriincu Onnes).

H. E. J. G. pv Bois: “Hysteretic orientatic-phenomena.” (Communicated by Prof. J. D. van

DER WAALS), p, 597.

The following papers were read:
30

Proceedings Royal Acad. Amsierdam. Vol. VI.

( 452 )

Chemistry. — Professor Losry pr Brey presents a communication
from Mr. W. Atperpa vAN Exenstetn on: ‘“Dibenzal- and

benzalmethylglucosules.”

(Communicated in the meeting of December 19, 1903).

While derivatives of formaldehyde may be obtained from sugars
by using sulphuric or phosphoric acid as condensing agent *) it is
also possible to effect the condensation of aromatic aldehydes and
ketones with these substances by using phosphoruspentoxide.

In the case of benzaldehyde the desired substances are obtained
by mixing two paris of the sugar in a mortar with three parts of
the freshly distilled aldehyde and then adding with continuous
stirring three parts of P,V,. The clear mass is left for half an hour,
then diluted with iced-water and the precipitate is dissolved in
methylalcohol.

From this solution the pentosederivatives are obtained as well-
crystallised products while the aldohexoses (also fructose and sorbose)
yield thick syrups which as yet have not been made to crystallise.

The pentosederivatives contain two benzal-groups and no hydroxyl-~
group. For this reason their constitution is probably analogous to
that of the formal derivatives, for instance.

HC_O The hexosederivatives are also formed
sm Nc.H, from two mol. of benzaldehyde; judging
f C— A from their behaviour towards aceticanhy-
QO aa dride they still contain a hydroxylgroup.
Snes It is not improbable that the substances
4 Sun obtained from the hexoses are mixtures of

i Di isomers.
H,C—0”% When these aldehydederivatives are

formed, the carbonylgroups have disappeared as in the case of the
compounds derived from formaldehyde; consequently they do not
reduce Frnuine’s solution. The number of benzalgroups may be
readily determined by boiling with phenylbydrazine dissolved in
dilute acid and weighing the benzalphenylhydrazone which has been
formed.

Dibenzalarabinose, melting point 154°, [a]p = + 27° (in methyl-
alcohol). Found C 69.8, H 5.6. Caleulated from C,,H,,O,: C 69.9, H 5.5.
Completely hydrolysed by boiling with dilute sulphuric acid ; emulsin
has no action.

1) Lopry pe Bruyn and Atserpa van Exenstein, Proc. June 28. 1902.

( 453 )

Dibenzalrylose, m.p. 130°, [¢]p = + 37°.5 (in M. alc.).
Dibenzalrhamnose, m.p. 128°, [«]p = + 56 ae

Of the oily dibenzalhexoses, those derived from mannose, glucose
and galactose show a faint right-handed polarisation, but the products
obtained from fructose and sorbose are somewhat laevo-rotatory.
It has already been noticed that they still retain a hydroxylgroup ;
these acetylderivatives also have not as yet been obtained in a
crystalline state.

The glucosides react much more readily with benzaldehyde than
the sugars. On dissolving the substances in benzaldehyde and boiling
for some hours with addition of a little anhydrous sodiumsulphate,
benzalderivatives are formed which are all readily crystallisable
substances.

Monobenzal a- methylglucoside, m.p. 158°, [a]p = + 85°.

s Ao 7M oO
” ” p. » 3? » 194 > [e|p — 05) P
Ee. methylmannoside, ,, 110°, faint laevo-rotatory
IEE vir, x * ae I ts a a bP

The last two are formed simultaneously and may be separated
by means of hot water.

It must also be observed that other aromatic aldehydes, such as
p-totuylaldehyde and cuminol, also enter into combination with sugars;
salicylaldehyde cannot react with sugars because it is two readily
converted by P,O,; into disalicylaldehyde, but its derivatives with
glucosides have however already been obtained.

Further particulars of this research will be published more fully
later on in the Recueil.

Lab. of the Fin. Dep. Nov. 1903.

Chemistry. — Professor Lospry pr Bruyn presents a communication
from Mr. C. H. Siurrer on: “The transformation of isonitro-
soacetophenonsodium into sodium benzoate and hydrogen cyanide?’ .

(Communicated in the meeting of Dec. 19, 1903).

When Craisen bad discovered his well-known condensation process
and had demonstrated for ketones that the hydrogen of the methyl
group adjacent to the carbonyl group is readily replaceable, he also
found that the isonitrosoketones could be obtained with the aid of
amylnitrite and sodium alcoholate'). With Manassg?) he investigated

1) Ber. 20. 656.
2) Ber. 20. 2194.
30%

( 454 )

the properties of isonitrosoacetophenon: C,H,COCH : NOH. This sub-
stance appeared to be a fairly strong acid. The sodium salt suffers
a remarkable decomposition into sodium benzoate and hydrogen
cyanide when touched with a hot substance, when moistened with
a drop of strong acid or when warmed with ecess of aqueous soda.

C,H,COCH: NjONa = C,H,COONa + CNH.

The HCN-molecule is therefore, so to speak removed from the
molecule of the sodium salt whilst ONa migrates to the carbonylgroup.
Cratsen further states that after being heated for two days with two
mols. of n-soda, the sodium salt had been completely converted into
sodium cyanide and benzoate.

It was of importance to subject this reaction to a further dyna-
mieal research to determine its order and to investigate the influence
of the addition of alkali and of a salt and also that of the solvent.

The sodium salt was made according to CLaisEn’s directions. As’

a perfectly pure salt was required, it was prepared by recrystallising
the free isonitrosoderivative from chloroform and neutralising this
with the equivalent quantity of sodium alcoholate.

If the salt is dissolved in 70°/, alcohol, it may be precipitated
by addition of ether as a yellowish coloured hydrate containing four
mols. of water of crystallisation.

Found: 29.5 °/, H,O, ecaleul.: 29.6 °/,. The salt obtained on drying
contained 13.5 °/, of sodium, theory 13.45 °/,. When gently heated
the yellow salt loses water and turns orange-red, which is the colour
of the anhydrous salt.

After some fruitless efforts to trace the progress of the transformation
by titration it was found that this may be accurately done by
the aid of the colorimeter, for the aqueous solution of the sodium
salt is yellow whilst the decomposition products are colourless.

In the preliminary experiments required for ascertaining the pro-
porties of the colorimetric standard liquid, it was found that the
colour of the dissolved salt is modified by dilution. The concentrated
solutions of the sodium salt have an orange tinge, which turns
yellow on dilution; the experiment further showed that, if we work
with solutions not exceeding 1 °/,, the diminution in colour may be
taken as proportionate to the dilution. This does not hold good for
more concentrated solutions; 100 ¢.c. of a 1°/, solution is colori-
metrically equal to 47 ¢.c. of a 2°/, solution and not to 50 e.e.

These phenomena are probably connected with the increasing
electrolytic dissociation of the salt on dilution. As the aqueous
solution has an alkaline reaction, a perceptible hydrolytic decompo-

*
vil

= se

{ 455 )

sition takes place, the extent of which I will try to determine.

Some preliminary experiments had also shown that temperatures
from 50° to 70° lend themselves very well to the determination of
the reaction velocity. In carrying out the experiments, a weighed
quantity of the salt was dissolved in previously heated water, so
that on introducing the solution into the thermostat, the temperature
equilibrium was soon reached. At definite times an aliquot part of
the liquid was taken from the bottle by means of a pipette, at once
strongly cooled and after diluting if necessary to about 1°/,, it was
compared colorimetrically. with the standard liquid. As such the
liquid which was taken from the bottle the first time, namely on
commensing the measurement, was used. Special experiments had
shown that at the ordinary temperature the transformation proceeds
so slowly that it is not measurable within 24 hours.

The experiment was generally continued until 30 to 40 °/, of the
salt had been converted; at 60° this was the case after 1’/, to 2
hours.

It has now appeared that the velocity of decomposition of isonitroso-
acetophenonsodium is represented by the equation of the first order ;
it is unimolecular, since the reaction constant is independent of the
concentration. In the case of a 1°/, solution at 53.°6 & was found
to be 0.00062, for a 5°/, solution 4 = 0.00059 (time in minutes). *)
The increase of the reaction velocity with the temperature was shown
by the following figures: 1°/, solution at 60°41 & = 0.0023; at 70°
k = 0.00487)

The influence of a salt with a common ion and that of free alkali
is peculiar. That addition of NaCl diminishes the electrolytic disso-
ciation of the sodium salt, was to be expected and may be readily
proved colorimetrically, the addition of 1 mol. of NaCl and 1 mol.
of NaOH (or 1 mol. KCN) increases the colour of a 1°/, solution
in the proportion of 93 to 100, that of 10 mols. of NaOH in the
proportion of 81 to 100.

NaCl and NaOH exert, however, also a retarding influence on
the reaction velocity. For a 1°/, solution and 1 mol. of NaCl
&= 0.0015; *'/,, mol. NaOH, 4 = 0.0014; 1 mol. NaOH £4 = 0.0015
whilst for pure water 4 = 0.0023. In another experiment, when the
transformation had to some extent taken place in pure water, */, mol.
of NaOH was added to the liquid and & then fell from 0.0022 to

1) With solutions of a greater concentration the colour after some time gets
more pronounced evidently by polymerisation of the HCN formed.

®) 0.89/9 sol. at 69°, k =0.0045. The temperature coeff. seems to decrease with
increasing temp.; this requires further investigation.

0.0013 (temp. 60:.1). If a large excess of NaOH is added from the
commencement, the transformation velocity again reaches the same
figure as for pure water; for 10 mols. of NaOH, £ = 0.0022.

We are dealing here with a special unknown influence of the
added substances; these certainly will modify the concentration of
the molecules undergoing change, [either the salt mol. or the acid
ion} by the diminution of the electrolytic dissociation, but as the
reaction constant is independent of the concentration, this cannot
explain the fall of that constant.

In the dry state the salt is more permanent than in solution, for
after heating for about 2'/, hours at 60° it was not perceptibly
decomposed and gave no odour of HCN. At 70° it turns darker
after some time and evolves HCN; the decomposition is then evidently
more complicated.

Finally, the decomposition velocity was also determined in methyl
and ethylaleohol; that in ethylalecohol is the smallest whilst methyl-
alcohol stands between water and ethylaleohol. I found at 60°
for 1°/, solution in water 0.0023, in absolute methylaleohol 0.0017,
in 97°/, methylaleohol 0.0018, for a */,°/, solution in 97°/, ethyl-
alcohol 0.001°, for 50°/, ethylaleohol 0.0013. Addition of water
consequently accelerates the transformation.

The intensity of the colour ofa solution containing the same amount
of sodium salt is largest for ethylalcohol, smaller for methylaleohol
and smallest for water‘); this phenomenon is undoubtedly connected
with the fact that the electrolytic dissociation of salts in the said
solvents increases in the order indicated.

Amsterdam, Dec. 1903. Org. Chem. Lab. Univ.

Chemistry. — Prof. H. W. Bakuvis Roozmsoom presents a communi-
cation from himself and Mr. A. H. W. Atrn on: “Abnormal
solubility lines in binary mixtures owing to the existence of
compounds in the solution.”

(Communicated in the meeting of December 19, 1903),

Last year’) when engaged in a research on acetaldehyde and its
polymer paraldehyde, I investigated the connection between the equi-
libria of phases of substances which in the liquid and gaseous con-
dition consist of mixtures of two kinds of molecules in equilibrium,
and the equilibria of phases in binary mixtures.

1) The solubility of the salt in ethylalcohol is also the smallest.
2) Proc. Oct. 1903, p. 283.

This investigation is capable of further extension and so we can
examine the equilibria of phases in binary mixtures in which the
two components form one or more compounds.

Let us limit ourselves to the first case. If an equilibrium exists
the quantity of the compound in the liquid or vapour will be depen-
dent on the proportion of the two mixed components and on the
temperature and pressure.

We now consider only the equilibria between liquid and_ solid
and this at constant pressure. If the compound is wholly undissociated,
the phenomena of melting and solidifying may be represented in space
by means of an equilateral triangular prism in which the height
represents the temperature and points in the equilateral triangle
represent the relative proportions of the components a, and 4, and
of the compound.

For convenience we suppose the latter to be ab. It now behaves
as an independent component, as it is supposed that there is no
equilibrium between ab, a, and b,. We then obtain, in space, for
each of the three solid substances a melting-surface which takes a
downward course from the melting point.

Should, however, the compound be in equilibrium with its com-
ponents, it ceases to be an independent component and at each tem-
perature only those relative proportions can exist in a liquid condition,
which are in internal equilibrium.

a, tt be So a pie
adjoining figure represents such
W an equilibrium line, which there-
Pp fore indicates the only proportions
capable of existing at a given
temperature. We call this line

the dissociation-isotherm.
If the compound did not form
an equilibrium with its compo-
ak nents and if the chosen tempera-
ture was situated below the melting
fig. 1. point of a, a line pq would then
be the solubility-isotherm for the solid substance a, and in the case
of an ideal ,course of the melting-surface of this component a, p
would be equal to a,qg and the line pg would be straight. The
points of the line pg then indicate the solutions which can be in

equilibrium with solid a, at the temperature in question.

If, however, a,76, is the equilibrium line of the liquid phase,
the point s will be the only point of the line pq which can exist

The curved line a,7 4, in the

( 458 )

simultaneously with solid @, and be also in internal equilibrium.

But if that internal condition of equilibrium is not known we can
only determine the gross composition of the liquid as a mixture
of a, and b, and in this way we find the point ¢ which is the
projection of s.

Acting in the same manner we should obtain for all temperatures
the actual composition of the solutions which at various tempera-
tures are in equilibrium with solid a, and also their gross composition
if we look upon them as binary mixtures built up from a, and 4,.

The same might be determined in regard to the liquids in equili-
brium with solid 4, or solid ab. This shows that the equilibria of
binary mixtures in which a dissociating compound may be formed
from the components, must really be looked upon as ternary mixtures
with a limiting clause, implied in the dissociation equilibrium in
the liquid.

For this reason the form of the solubility-lines which we obtain
in the system, considered as a binary mixture, is totally dependent on
the manner in which the dissociation in the liquid phase and the
melting-surfaces of the components change with a change of temperature.

Guided by these ideas, Mr. Arrn has worked out different theore-
tically-possible cases which can partly explain abnormal solubility-
lines and which point, in addition, to phenomena as yet undiscovered.

Let us first suppose that the compound aé in the liquid condition
is exothermic.

In such a case the dissociation of the compound at first imereases
but little as the temperature rises, then very much and afterwards
again but little. If we draw, in the triangle, a series of dissociation
isotherms for equal temperature intervals, these will at elevated
temperatures lie close to the side a,b, and will differ but little.
Afterwards they will diverge greatly and finally come close together
and approach the sides 0,ab and 6,ab. In Fig 2, nine such isotherms
are shown.

Let us now draw for the same series of temperature the solubility-
isotherms of a, and assume as the most normal case that they come
closer together as the temperature falls (from 9 to 1).

The locus of the intersections of the dissociation- and solubility-
isotherms is the projection of the spacial melting-point-curve for a,.

By projection on the side a,/, we get the gross composition expressed
in a, and 4, and by now plotting temperatures as ordinates we
obtain the solubility line ABCDEF commencing at the melting
point A. The line thus drawn exhibits three portions HF, FC and
CBA which, particularly in the case of many salts, have been

( 459 )

repeatedly met with in different combinations and of which the
middle part is particularly interesting because here the solubility of
the component a, decreases with an increase of temperature.
|
A|

ee ee ee ee eee eee

CEs
ae

460. )

The heat of solution is here thermochemically positive; and zero
in F and C. The explanation is now as follows:

The dissolution of the solid substance a considered by itself will
be accompanied by absorption -of heat; the formation of the compound,
this being exothermic, with development of heat. In that region of
temperature in which the formation of the compound chiefly takes
place, it may, therefore, happen that the heat of formation of the
compound exceeds that which is absorbed during the dissolution. This
is the case from F/ to C between which temperatures, as seen in
the triangle, the dissociation isotherms are the most divergent and
the quantity of the compound formed, therefore, increases most
rapidly with a decreasing temperature.

The solubility-isotherms for a, will, at a sufficiently low tempe-
rature, approach to the side 6, ab. If at a lower temperature the
combination is complete, the intersection of the dissociation- and melting-
isotherm will finally come very close to the angular point of the
compound and the projected melting point line will, therefore, become
an asymptote to the straight line ?Q which indicates the composition
of the compound. It is also possible that the melting point curve
does not intersect the straight line PQ for the second time but
‘yemains to the right of PQ.

When a larger quantity of the compound is already present at
a higher temperature, the bend is shifted further to the left, so
that it may happen that the melting point line is not intersected
by PQ.

If the formation of the compound takes place over a larger tempe-
rature interval, the bend BCU DF may disappear from the line and
there may only remain a more strongly inclined part.

In a similar manner the solubility line for the compound ad or
for the component 6, may be determined. The different forms which
these lines assume either wholly or in those parts which, owing to
their mutual interference, are alone capable of existence, are again
entirely dependent on the manner in which the solution-isotherms
shift in regard to the dissociation-isotherms.

In this way all the known cases of the meeting of the lines of
the components with those of the compound may be deduced. It
also is shown how it is possible that the compound which exists
partly in the liquid eannot separate in the solid condition and must,
therefore, again be decomposed when the components solidify.

Another case, as yet unknown, may also be possible namely that
after the solidification of the two components by cooling a liquid is
again formed from which on further cooling the compound is depo-

( 461 )

sited (Fig. 3). This ease is possible when the lines of the components
‘ g. 3). :

have the shape of Fig.

Fig. 3.

2 and meet above (.

In the space indicated by L
there exist again unsaturated solu-
tions all situated below the eutectie
point C' of a+ b.

When the compound is endo-
thermic the order of the dissoci-
ation isotherms is the reverse of
that indicated in Fig. 2. Without
entering into all the peculiarities
Which the solubility-lines may
must be
called to two as yet quite unknown
types of melting point lines which
may occur (Figs. 4 and 5),

then exhibit, attention

In the first figure we have the
remarkable fact that the compound
forms with the component a a
eutectic point C' as well as a
transition point D. In the second
figure, the melting point line of

the compound occurs as a closed

curve with two vertical lines in points where the heat of solution

is zero, and two melting points.

462»

In the upper point P the compound passes into the liquid state,
heat being absorbed. This absorption consists of two parts, the ordinary
heat of fusion and the heat evolved when a part of the liquid (endo-
thermic) compound decomposes until the equilibrium in the liquid is
reached. As at higher temperatures the quantity of the compound in
the liquid is large, the second quantity of heat will be small in
comparison with the first and the melting will cause absorption
of heat.

At Q it is, however, just the reverse because at a low tempera-
ture there exists but litthe compound in the liquid and the dissocia-
tion of a large proportion of the liquid compound may evolute so
much heat that this exceeds the actual heat of fusion of the
solid compound. The total fusion therefore produces heat and con-
sequently the liquid field is situated below Q.

Up to the present, however, no endothermic compounds are known
in the liquid state.

Microbiology. — Professor Brtyerinck presents a paper from himself
and Mr. A. van Deipen: ‘On the bacteria which are active in
flax-rotting’’.

(Communicated in the meeting of December 19, 1903).
1. How jar flax-rotting should qo.

The object of flax-rotting is the partly solving and softening of the
rind of the flax-stalk to remove the pectose, in consequence of which
the bast-bundles are freed so that later, after drying, the fibres may
easily be separated from the wood by breaking and _ scutching.
Pectose (pt Fig. 1) is the substance of which the young cell-walls
consist, as also the outer layers of the old cell-walls; these walls are
further built up from ce/luwlose, which in a good rotting does not
undergo any change’).

By the rotting also the middle-lamellae, by which the fibres in the
bast-bundles stick together, may go into solution and consequently
the bast-bundles would be decomposed into the fibres proper. This is
not desirable as in this case no large coherent ‘“‘lints’” would be got
in seutching, but only loose fibres, of about 2 em. in length.

The fibres of the bast-bundles, however, separate with much greater

') For the microbes which affect the cellulose proper see Ometsansky, Centralb.
f. Bacteriol. 2 Abt. Bd. 8 p. 193, 1901, and G. van Irerson. These Proceedings
24 April 1903.

( 463 )

difficulty than the cells of the rind, because, in the middle-lamellae
between the flax-fibres, besides pectose, also lignose is found *), which
is not affected by the rotting (/g Fig. 1).

It is just by the absence of lignose that the rind is so much more
easily affected by the rotting process than the bast-bundles, that the
latter, in a well-conducted rotting keep together and may be obtained
after the scutching as a whole.

Hence, the art of rotting consists in pushing the process on to a
determined point and no further.

It is not easy to indicate where this point is situated, chiefly
because the flax-stalks, which at the pulling from the field are united
into sheaves for the rotting, are not all equally ripe. As now the
unripe stalks are more easily rotted than the riper and tougher
ones, a very unequal product is obtained by submitting all to a
like process. Therefore great pains are taken at the Leie, near
Courtray, as much as possible to sort the flax before the rotting, in
order to form lots of the same quality. Moreover, they rot the flax
there twice, which renders it possible partly to redress the irregularities
originated in the first rotting.

From a theoretical point of view we assume that rotting should
proceed just so far (“strong rotting’) as is necessary for the easy
removing of the wood (ry Fig. 1) from the bast-bundles (7 Fig. 1), but
not so far (‘‘feeble rotting’) as to decompose them into the elementary
fibres. Therefor it is necessary that the secondary bark (cs Fig. 1)
of the flax-stalks be quite dissolved and that the primary rind
(cp Fig. 1) be decomposed into cells’).

2. Pectose and Pectine.

Pectose is sa lime compound whose composition is not yet clear.
Non-reckoning its rate of lime, this substance, though chemically
related to, is not identic with cellulose. According to ToLLEns and
Tromp DE Haas*) we find for it, after removing the lime, the

1) J. Bexnrens, Natiirliche Réstmethoden. Das Wesen des Réstprocesses vom
chemischen Standpunkte. Centralbl. f. Bacteriologie, 2te Abt. Bd. 8, pag. 161, 1902.

2) Whether this standpoint is right in all cases (or rather will prove to be so
when the flax industry will have ceased to bea very primitive agricultural industry)
is doubtfui. As in a good rotting process the flax-fibre itself is not injured, it is
an open question whether the spimner might not be able to spin threads of greater
equality from the wholly isolated fibres, then when they are still united in bast-
bundles of very unequal properties.

3) Untersuchungen iiber die Pectinstoffe, Liesie’s Annalen der Chemie. Bd. 286
p- 278, 1895 and Tottens, Ueber die Constitution des Pectins. Ibid. p. 292.
As in hydrolysis the peciinic substances, besides glucose and galactose, also yield
pentose, ToLtens gives as probable composition (CG° H* O41. C> H5 O°.

( 464 )

formula n(C* H?°O*) or n(C?? H? QO), but not exactly, a small
excess of O pointing to the presence of a COOH-group, which
should be substituted in the pectose (the said authors use the
word pectine). Toitens takes the here concerned acid for gluconic
acid (C° H* 0°), or an acid related to it, and this would occur in
the pectose as lakton or ester, that is in neutral condition. He calls
pectose an oxy-plantslime, but does not mention the lime.

By treating with acids the various pectose-forms are more or less

ay ™,

ee me cange
—~
. = — ~~.
Ir,

: a eee ae Ce
ThA SRST
CLUES SS :
BWORE Za
gees arse <eY

Fig. | (550). Transverse section of the bark and wood ofa flax-stalk. Pectose pt dotted,
cellulose ce left white, lignose Iq hatched lines; ep epidermis, cp primary rind-
cells with outer wall of pectose, f bast-fibres with outer wall of pectose + lignose,
es secondary rind cells, and ca cambiumcells whose walls quite consist of pectose,
xy wood, with large punctations,

’ * .

( 465 )

easily hydrolised, the pectose of the flax not so easily. Hereby first
result pectine or metapectine, which have an acid character and are
therefore also called pectinic acid and metapectinic acid. The pectine
gelatinises in presence of lime, through the enzyme pectase, moreover
through alkalies and ammonia, likewise in presence of a lime. salt.

In absence of lime the compounds of alkalies with the pectine
are soluble in water. Gelatinisation proper is unknown with meta-
pectinie acid.

With continued hydrolysis, pectine and metapectine, hence, also
pectose, produce galactose and pentose, and according to ToL.ens,
with certain pectine kinds, dextrose and arabinose too, which sugars
are easily fermented by Granulobacter.

By boiling with nitric acid pectose and pectine yield mucous acid.

Pectose is insoluble in coid and boiling water and in cupri-
oxyde-ammonia. The pectose of the flax-sialk is moreover not easily
affected by dilute acids and alkalies, and remains unchanged after
a short heating in water-vapour at 120° C.

Pectose can be softened by the successive influence first of an
acid then of an alkali. If the flax-stalk is first extracted with
dilute hydrochloric acid, by which the pectose changes into pectine,
which however, as an insoluble lamella, still holds the cells together,
washed out to remove the lime, salts become soluble by the hydro-
chloric acid, then treated with ammonia or natriumecarbonate, a conside-
rable softening takes place. On this method, first suggested by Manein 3),
reposes the so-called chemical rotting after the patent of Bauer, which
has, however, produced nothing of practical use, and only shows that
the “inventor’’ did not know the requirements to which well-rotted
flax should answer.

A better way of dissolving the pectose of the flax-stalks we found
by placing them in a strong solution of ammonium-oxalate, but only
after 3 weeks the rotting process was completely finished, so that
this means has not any practical value either.

Whereas the preparation of pure pectose is troublesome in conse-
quence of its insolubility, it is easy to make pectine.

Herefor*) one takes the rootstocks of Gentiana lutea of the
chemists, grounds them finely, first extracts with H?O and _ places

1) Although it may be read everywhere that pectose after Manern’s method
goes “into solution”, it is my experience that this is exaggeration, and that, of the
decomposition of parts of plants into free cells as in rotting, there is no question
in this case.

*) To compare Bovurquetor and Herissey, Journal de Pharmacie et de Chimie,
sér. 6, T. 8 p. 145, 1898,

( 466 )

the washed material under a large quantity of 3°/, HCl, filtrates,
and precipitates with alcohol. The precipitate is dissolved in boiling
water, precipitated again with alcohol and this is repeated until the
chlorine reaction disappears. The thus obtained pectine reacts feebly
acid and solidifies with pectase + a lime salt, or with alkali + a lime
salt, into a consistent transparent jelly.

3. The rotting is caused by microbes and may be called
pectose- fermentation.

Dissolving and removing of the pectose from the rind of the flax
is completely effected, without any injury of the cellulose wall of
the jfibres*), by some microbe species belonging to the moulds and
bacteria, and hereupon the usual rotting methods are based.

; ep

Fig. 2 (350). Rotting observed in a microscopic preparation lying in a drop of
good rottingwater and consisting of a longitudinal section of the rind and the
wood of a flax-stalk. Signification of the letters see Fig. 1, further: se cell of a
stoma, 0” air chamber in the primary rind, Gp Granulobacter pectinovorum, the
pectose bacterium proper, Gu Granulobacter urocephalum. The primary rind cp is
seen to decompose into cells by solution of the pectose, and thereby the secondary
rind cs and the cambium ca completely liquefy.

Moulds are the active agents in the very primitive so-called dew-
rotting on the field; bacteria on the other hand, in the rotting after

1) But not of the cellwalls of the rind-cells from which the cellulose itself is
also partly dissolved,

—— oS. wo

A oy

ive

( 467 )

steeping of the flax in water, that is in the white- and the blue-
rotting.

In the dew-rotting a most unequal product is obtained; this
process shall not further be discussed here.

In the blue-rotting in ditches and ponds, as also in the white-rotting, a
so-called anaerobic bacterium is the active agent. This highly interesting
organism belongs to the genus Granulobacter and shall be called G. pec-
tinovorum *) ((rp fig. 2). At the present moment the whole rotting indus-
try is nothing else but a more or less rational culture-method of
this bacterium.

From a theoretical point of view it is interesting that there are
also some aerobic bacteria with which rotting is possible with free
access of air. These are the various kinds of the so-called hay-
bacteria group, also known by the name of potato-bacteria, the chief
species of which are Bacillus mesentericus vulgatus, B. subtilis, and
Granulobacter (Bacillus) polymyxa (= B. solaniperda Kramer).

4. Arrangement of the rotting experiments in the laboratory for the
examination of microbes im pure culture on their power of rotting.

_In order to ascertain if any microbe can be used for rotting it is
necessary to dispose of perfectly sterile flax. This is obtained by
heating the flax for some time at 125—130° C. in the steam sterilis-
ator, whereby it is seen that it is not rotted at all by this overheating.

For the laboratory experiments with the ‘anaerobes’, thick walled
test-tubes were so closely filled with flax, washed out or not, that
the pressure against the glass-wall prevents it from mounting up
when the tube is further filled with water. After cotton-plugging
the filled tubes are sterilised in the sterilisator.

It is true that in these tubes air can penetrate from above, but
if the pieces of the flax-stalks are not too short, say 20 em., the entrance
of air is not noxious to the anaerobes, provided some ordinary aerobic
microbe be added, which lives at the surface and there absorbs the
oxygen. We always used to this end a Jorula yeast.

For testing the aerobic microbes the flax is spread in a thin layer
at the bottom of a wide Ertenmeier-flask, and after immersing in
a little water the whole is sterilised, after cooling infected with the
Species concerned and cultivated at 35°, or lower, in accordance with
the microbes to be examined. After 2 or 3 days the rotting is finished.

*) First discovered by Winocrapsky (Comptes rendus T. 121, pag. 742, 1895).

StérMer (Mittheil. der deutschen Landwirthschafts Gesellschaft Bd. 32, pag. 193
1903) used for it the name of Plectridium pectinovorum.

jl
Proceedings Royal Acad. Amsterdam. Vol. VI.

( 468 )

At the examination of the numerous microbes which may be obtained
from flax in rotting condition, the result was negative for by far the
greater part of the species. No rotting was to be observed with the
various kinds of yeast, of Mycoderma, of Torula, of Oidium and of
red yeast, nor with the lactic-acid ferments, the vinegar bacteria and
the different forms of the Aerobacter-group, such as A. coh and
A. aerogenes, which organisms are all universally found in the rotting
water of natural rottings.

The aerobic bacteria of the hay-bacteriagroup (B. mesentericus and
B. subtilis), which, at sufficient supply of air are on the contrary
strong rotting-organisms, are rare in good rotting water. For rotting
they should be kept at least at 30°.

5. The rotting reposes on the action of the enzyme pectosinase
which is secreted by the pectose-bacteria.

The action on the flax, as well of the anaerobic Granzlobacter
pectinovorum as of the aerobic hay-bacteria and the moulds, is caused
by a specific enzyme pectosinase *). This enzyme, like the acids, exerts
an hydrolytic influence, first converts the pectose into pectine, and
subsequently the pectine into sugars, which are fermented by G.
pectinovorum (Gp fig. 2) under production of hydrogen, carbonic
acid and a little butyric acid, and assimilated in case the hay-bacteria
are used for the experiment.

These sugars are most probably galactose and xylose, and (perhaps
in some cases) also glucose and arabinose, which as we saw before,
have been found by To.iens as products of the hydrolysis of the
pectinie substances with acids.

Pectosinase is not easily soluble in water and can be precipitated
with alcohol. In presence of chloroform and in absence of the
microbes, we succeeded thereby to decompose into cells thin slices
of potato, and further to liquefy with it solid plates of pectine,
made by solidifying pectine from Gentiana lutea (see § 2) with
pectase + CaCl’. The action of the isolated enzyme is feeble, much
feebler than when also the seereting bacteria themselves are present
in living condition. This is evident from the facility with which the
hay-bacteria at 387° C. decompose slices of living potatoes, whilst this
gives much more trouble when effected by the enzyme prepared
separately.

') Not identic with the “pektinase’” of Bourguetot and Heérissey (Comptes
rendus T. 127 pg. 191 1898) from green malt (which is identic with the *cytase”
of Brown and Morris (Journ. Chem. Soc. Trans. 1890, p. 458)) for with malt
flax cannot be rotted.

q
.

;

( 469 )

The insolubility of pectosinase in water and, much more the fact
that all the pectose bacteria examined by us lose suddenly in
certain not well defined circumstances the power to secrete it render
the study of this enzyme very troublesome. Particularly important is
its following property.

Whilst the action of the pectosinase is favoured by a little acid,
the growth of the pectose bacterium is retarded by acid.

As to the rotting-process, for which the production of the enzyme
is clearly the essential point, one has, if not exclusively, at least
chiefly to reckon with the properties of the microbes themselves,
more especially with the conditions for their production. Hence,
from this point of view only a slight production of acid will be
favorable for the rotting.

From the above it follows that the chief question of flax-rotting
is: what are the conditions of life of the bacteria concerned and
how can their multiplication and accumulation in the flax-stalks
be attained so profusely as to expel the other microbes, and, by a
sufficient formation of pectosinase cause the rotting-process to go on
regularly *

Winoerapsky has, it is true, partly answered this question by the
discovery of the pectose-bacterium. But the essential point in the
arrangement of a rotting experiment has quite escaped him, for he
has not recognised the necessity of the water refreshing. Hence, hitherto
there exists no clear method which may give rise to a natural
accumulation of the bacteria specifically concerned in the rotting and
accordingly neither for the really rational arrangement of the rotting-
process.

This gap will be filled-up here.

6. Fundamental experiment for the explanation
of the rotting-process.

A cylindrical glass vessel A, Fig. 3 is quite filled with flax V,
so that the stalks by their pressure mutually and against the
glass-wall, are prevented from floating up as the vessel is further
filled with water. Thereby is obtained 5 to 10°/, of weight in flax
to 100 of water.

To the bottom of the vessel A, a glass tube B reaches, through
which pure water can flow down from the higher placed reservoir C.
This water flows upward through the flax-stalks, according as the
washing-water flows off by the tube , and thereby extracts most
of the soluble subStanees from the flax, whilst the insoluble

31*

Fig. 3. Apparatus for rotting-experiment with water-current. A cylindrical glass
jar with flax V, B tube supplying water from the reservoir C to the bottom of A,
D tube to draw off the water. 7 thermostat.

pectose remains behind in the stalks. What is drawn off by D may
be called “rotting-water’, but this water is widely different, at the
starting of the experiment, when it contains much dissolved matter
and few bacteria, from that, obtained in a later period, when many
bacteria and few dissolved substances occur in it.

The jar A is kept at a temperature of 28 to 35°C. by placing
it in the thermostat 7’ .

If after 2 or 3 days the flax is removed from A it proves to
be more or less sufficiently rotted, if the water supply has been
great enough to refresh the rotting-water from 5 to 10 times. Through
our apparatus of 3800 ce., 1.5 to 3 1. of water had thus to pass.
Whilst in the Laboratory experiment the water is introduced at the
bottom of the jar and drawn off at the top in order to prevent
stopping of the tubes by the gases formed by the fermentation, this
would be faulty with experiments on a larger scale, — in this latter
ease the heavier rotting-water should be drained off at the bottom,

If the rotted bark of the flax, or the pith, or the juice, contained in
the rotted stalk, is microscopically examined, we find there accumulated
the above mentioned very characteristic Granulobacter pectinovorum
(Plate Fig. 1), which has supplanted nearly all other microbes and
which literally fills up the intercellular spaces (Gp Fig. 2), in many
places quite covers the surface of the fibres and has, moreover, com-
pletely dissolved the thin-walled cells of the secondary rind, and
thereby freed the bast-bundles from the wood. In an iodine solution
this bacterium turns deep blue over nearly its whole length in con-
sequence of its amount of granulose.

This is a so-called anaerobe. From the experiment described, where
an aerated water-current incessantly flows around the flax, it follows,
however, that a fair amount of air is of no prejudice to its develop-
ment; and a more minute observation shows that here, too, as
with all other anaerobes, a limited aeration is not only harmless,
but beneficent, and even necessary to make the growth go on in
the long run.

Our observation that the water of the Leie, near and at Courtray,
is strongly polluted by sulphuretied hydrogen, induced us to add
c.a. 50 mgrs. of H’S per |. to the water for our rotting-experiment,
by which even in the rotting-water flowing off a little H?S might be
detected. The rotting was decidedly retarded by this addition and
was less complete than in absence of sulphuretted hydrogen; yet,
Gr. pectinovorum had strongly accumulated, though less profusely
than commonly.

Quite otherwise was the effect of KNO’. If 0.2 gers. of it were
added per 1. of the water-current, then a trace of KNO* might
still be demonstrated in the rotting-water. Accumulation of G. pec-
tinovorum and rotting proved complete in this case, so that, when
Mr. Puatsier, flax-merchant at Hendrik Ido Ambacht, came to judge
of our rotted flax-samples, he classified our saltpeter-flax as “first
rate’. But it is clear that the presence of saltpeter is not necessary.

In fact, the accumulation of bacteria in the said experiment reposes,
besides on the slight but necessary aeration, on the circumstance that
by the water-current in the first 24 hours, such a complete extraction
of the flax is attained, that all soluble nitrogen compounds are
nearly completely expelled from it, and only the not easily soluble
protoplasmatic proteid remains in the flax-cells, which substance,
together with the still present carbohydrates and the pectose, prove
to be the very nutriment for G. pectinovorum and, moreover, the
food required to give rise to the secretion of pectosinase, hence, to
the rotting-process. If the extraction has not taken place and the

( 472 )

experiment is made without the water-current going through the
flax, a rich growth of all kinds of other bacteria will arise, but a
real accumulation of G. pectinovorum and a good rotting-process is
not obtained in the first two or three days.

The cause of this striking phenomenon reposes exclusively on
the competition of the different microbe species. This is evident
from the fact that with pure cultures of G. pectinovorum, even without
refreshing the water, a very good rotting is possible. The substances
removed from the flax by the water-current are not in themselves
prejudicial to G. pectinovorum, but they favour the growth of the
other species, in particular of the lactic-acid micrococci, so much more
strongly, that G. pectinovorum can develop only later and with very
great difficulty. It is also certain that the secretion of pectosinase in
the dilute liquid is more profuse than in the more concentrated
nutrient solutions. Thus we did not succeed in rotting flax by placing
it in dilute sterilised malt-extraect with chalk, of about 2° on the saccharo-
meter of Banune, which was in a vigorous fermentation by a
pure culture of G. pectinovorum. Evidently no pectosinase secretion
takes place under so favourable nutrient conditions.

Hence, there is a double reason why extraction so much promotes
the rotting: the pectose bacterium gets the ascendeney, and its faculty
of secreting pectosinase becomes active.

If we compare the microscopic image of the bacteria (Pl. Fig. 1)
of the flax, rotted after the current ‘experiment’, with that, treated in
the usual way, after the white or blue rotting methods, one is struck
by the enormous difference. In the latter case hardly anything is seen
but the foreign species and G. pectinovorum is scarcely detected ;
whilst in the product, obtained by the current-experiment (7. pectino-
vorum is seemingly in pure culture’).

7. Simplification of the current-eaperiment.

When the great importance for the rotting-process of extraction
of the flax-stalks and of aeration had been recognised, it was natural
to try whether the current-method could be replaced by a more
rational way of water-refreshing for the practice.

This was effected in the following simple manner.

After standing 24 hours on the flax, the water was completely
decanted off, so that all spaces between the stalks were drained and
could fill with air. Subsequently anew supply of water was provided,
either of fresh water of about 30° C. or of good rotting-water of

1) Compare further § 12.

Ee eo

1M a

a previous rotting. When using fresh water it proved desirable
after every 24 hours to repeat the refreshing, but when good rotting-
water could be had a second renewing was not required, good
rotting-water containing already a sufficient accumulation of G. pec-
tinovorum.

By this treatment, too, which may be called the ‘‘decanting method”,
excellent rotted samples were produced in 2'/, or 3 days. It even
seems that it should be preferred to the ‘“‘current method’, because
by decanting the concentrated rotting-water will be enabled more
completely to flow off from the narrow interspaces of the flax-stalks
than will be possible when replacing it by slowly streaming pure
water. For the same reason the aeration must needs be more com-
plete anywhere in the sheaves by “decanting” than by “streaming.”

On account of these experiences there is no doubt but any other
method of water supply which can give rise to a sufficient extraction
and aeration, can replace the ‘‘streaming” and the ‘‘decanting method”,
if only care be taken during the rotting not to injure the delicate
and easily bruised flax-stalks.

Here once more it may be observed, that although G. pectinovorum
belongs to the so-called obligative anaerobic bacteria, the strong
aeration, described above, should be pronounced decidedly favorable
to this bacterium. This is, however, quite in accordance with the
experience acquired for all other well-observed anaerobes. Hence,
it may be considered as a truth, confirmed by each subsequent
research, that anaerobes, in the strict sense of the word, do not
exist, and that the term ‘‘microaerophily” more precisely denotes
the relation between such organisms and free oxygen, than the term
“anaerobes ’.

8. Application of the current experiment for practical rotting *).

Practical rotting has until now been managed in a very primitive
way. Even at the Leie, near Courtray, from whence the best flax-fibre
comes to the market, even the superficial observer is struck by the
numerous and great deficiencies existing there.

1) By “vat-rotting”, the bleaching of the flax on the field through light, so
essential in “white rotting’, is excluded. In the flax-rotting establishments to come,
it will therefore be necessary to make the rotting be followed by a chemical
bleaching process. Experiments have shown that ozon or hydrogen-superoxide may
be used to this end Whether hypochlorites (‘electrical bleaching’’) will also prove
applicable without weakening the fibres, will have to be made out by dynamometrical
estimations. Vat-rotting will also call attention to good drying-apparatus and, no
doubt, to other troublesome problems, which, completely to solve, will require
surely much time and many an industrial effort.

474 )

The first step towards improvement was taken in our country
already in 1892 by the Society for the Promotion of Flax-Indrustry,
which tried to replace the roiting in open water by rotting in vats.

Afier this method the flax-sheaves are placed vertically and close
to one another in a large wooden trough, in which, at some distance
from the bottom, a second, perforated bottom is fitted. This false
bottom supports the flax and underneath the heavier rotting-water is
collected, which flows down from the flax after the vat has been
quite filled with water.

Baron Reneers at Oenkerk, too, has tried to improve the rotting
of flax, by treating it after the so-called hot-waterprocess, by which
he seems to have obtained very satisfactory results.

Vat-rotting and hot-waterrotting can, however, only succeed with
sufficient certainty, when care is taken to provide a due refreshing
of water; this may be done in various ways, but has not hitherto
been sufficiently attended to.

By ‘‘vat-rotting” the following advantages may be obtained.

First. The vats can be placed in a manufactory, where the other
manipulations which the flax has to undergo, can also be effected.

Second. The temperature of the rotting-water may be modified
at will, by which the difference between vat-rotting and hot-water
rotting disappears. Rotting will be possible throughout the year.

Third. The extraction and aeration of the flax can easily be
regulated, so that the accumulation and multiplication of the pectose
bacterium is made sure, and the lactic-acid micrococci, the great
enemies in the rotting process, are expelled.

The theoretical requirements for vat-rotting are im general to be
seen from what precedes, but it is still necessary to call attention to
the following points on which the success of that process depends.

In the first place, care should be taken that the heavier water,
produced by the extraction of the flax, can easily be removed. By
the use of a false bottom the water collects underneath the flax, so ©
that it is possible first quite to fill the vat, allow it to stand for 24
hours, and then to drain off all the water. The flax thereby comes
quite equally into contact with the air, so that even the densest
places of the sheaves are duly aerated (‘‘decanting method”’).

It will be sufficient only once to refresh the water °).

1) The experiments with pure cultures of the pectose bacterium prove that
theoretically the refreshing of the water is not even once fully required, but pro-
bably the competition, particularly of the lactic-acid and butyric-acid ferments,
struggling to displace the pectose bacterium, will render this ideal condition unat-
tainable for vat-rotting on a large scale.

( 475 )

It is a mistake to draw off the rotting-water from the vats at the
top and introduce the fresh water at the bottom. Hereby the heavier
washing-water is driven back among the flax-stalks and renders a
complete extraction impossible, because the rising water will always
seek those places, where there is the least resistance, i.e. the open-
spaces of the sheaves, and will not enter the close places, where
it is most wanted. Thus the growth of the pectosebacterium is
hindered and that of the lactic-acid ferments promoted. Moreover the
aeration, which, when the washing water is completely drained off,
takes place of itself, and quite equally and everywhere throughout
the flax, would become most irregular and imperfect.

In the second place, the vat should after the first draining not be
filled with fresh water only, but this water should be mixed with
a fair quantity of good rotting-water, taken from a previous rotting.
By this means the pectose bacteria are at every point introduced into
the flax, which of itself harbours only a small number of these
microbes, which are not at all generally distributed, neither on the
flax nor in the waters.

Before commanding of good rotting-water it will be necessary
once more after 24 hours, so two days after the first filling, to
draw off all the water and replace it by fresh water. The pectose,
bacteria have then already so strongly accumulated in the flax-stalk,
that they can only for a small portion be washed away.

How easily good rotting-water is to be obtained follows from the
description of the current-experiment.

In the third place the rotting-temperature will have to be exactly
regulated. Our laboratory experiments make it evident that the most
favorable temperature lies between 28° and 35°C. After 2*/, to 3
days the flax may then be removed from the vats in an excellent
rotted condition (see note 1 § 8). Perhaps with a longer rotting-
time the temperature might be lowered and reduced to from 25° to
27° C. Practice will have to decide whether this is desirable.

9. Pure culture of the pectose bacterium.

The pure culture of G. pectinovorum, which like all other species
of Granulobacter, produces spores, is successfully effected as follows.

On a culture medium in a glass box, consisting of dilute malt
extract of c.a. 2°/, BaLLinc, with 2°/, agar and 2°/, chalk, some
material taken from the rind of a well-rotted flax-stalk, pasteurised
at 90° C., is put, in order to obtain colonies of G. pectinovorum
in streak-culture. The pasteurisation serves to kill the foreign

( £76)

bacteria of which the majority produce no spores, in particular the
lactic-acid ferments, but it should not be done at too high a tempe-
rature, as also most spores of the pectose-bacterium itself die already
at the boiling point.

The glass-box is now placed in a well-closing exsiccator, with a
three way stop-cock, in which a small dish with hydrosulphite
of sodium is put. The exsiceator is evacuated by a K6rtING pump,
filled with hydrogen (or carbonic acid), and again evacuated ;
and this is repeated until it may be assumed that the oxygen,
which can never be completely removed, is reduced to the minimum
pressure tolerated by the anaerobes, wherein the hydrosulphite is
also useful. The exsiccator is placed in a thermostat at about 35°C.
and after 2 to 3 days the anaerobic colonies are seen to develop.
They chiefly belong to the four following species of Granulobacter :

1. G. peetinovorum.

2. G. urocephalum.

3. G. saccharobutyricum.

4. (7. butylicum.

The third of which was alluded to and the fourth described by
me in a former research '). The two first species only, viz. G. pec-
tinovorum and G. urocephalum, are real rotting-bacteria, the former
acts strongly, the latter feebly rotting. The two last mentioned, viz.
the butyric acid ferment (G. saccharobutyricum) and the butylie fer-
ment (G. butylicum) cause no rotting at all.

The colonies of all the four kinds colour deep blue when treated
with iodine solution, in consequence of their contents of granulose in
thin, elongated elostridria. Besides, rodlets are found in all colonies,
which do not stain blue with iodine, and which, in a former paper,
have been described as “oxygen forms” of Granulobacter*). Some
colonies consist of the oxygen form only, hence do not stain with
iodine at all, and only contain rodlets, in which spores are seldom found.

If the material taken from the flax-stalks has not been sterilised
previously to the sowing, various colonies of lactie-acid micrococei
will develop on the plates, surpassing the Granulobacter colonies
many times in dimensions and thereby easily recognisable.

10. Description of Granulobacter pectinovorum.

The colonies of this bacterium are recognised by the ‘moire-
phenomenon”, figured on Plate Fig. 3. It consists in the appearance

1) Sur Ja fermentation et le ferment butyliques. Archives Néerl, T. 29, pg. 1. 1896
*) Fermentation butylique. pag. 35.

of characteristic, nearly rectangular dark and light fields to be observed
in the colonies when obliquely illumined, which fields can interchange
of tint and originate by the reflexion of light on groups of mutually
parallel bacteria; of the different groups the longitudinal axes meet
at nearly right angles.

As to the bacterium itself, its description by WrvoGrapsky') is
in good accordance with our results. It is a rather long species,
producing spores at a terminal swelling (a little beneath the end) of
the very long and very thin clostridia, resembling common staves,
which then look like frog-spawn (Plate Fig. 4). The rodlets are 10
to 15 uw long by 0.8 w wide but eventually much longer. The older
ones become thicker and swell at the end, to 3 ym in width; the oval
spore, formed in this swelling, measures 1.8 w by 1.2 uw.

In dilute malt-extract, with exclusion of air, a vigorous fermentation
takes rise, without formation of butyric acid.

With starch*), inulin, mannite, erythrite, glycerin, fermentation
could not be produced under any circumstances.

With peptone and with dilute broth, or albumine as sources of
nitrogen, our bacterium causes fermentation in glucose, laevulose,
galactose, milksugar, and maltose, with a slight production of butyric
acid. Proteids and gelatin are peptonised.

With ammonium salts as source of nitrogen, fermentation cannot be
produced with any of these sugars. Nitrates are not assimilated and
not changed at all.

Sex

Fig. 4 (650). Culture of Granulobacter pectinovorum in pectin-ammonium-sulphate
solution. The thick ends contain oval spores; the dark spots in the rodlets
indicate granulose.

1) Comptes rendus T. 121, p. 744, 1895.
2) Winoerapsky asserts that starch does ferment.

( 478 )

- Pectine, prepared as indicated § 2, is decomposed, as well with.

albumine, peptone, or broth, as with ammoniumsalts for source
of nitrogen, by which this bacterium stands by itself and is sharply
distinguished, especially from the butyric-acid and the butylic fer-
ments, which do not attack pectine at all. When the pectose is
attacked, pectosinase secretion occurs.

Cellulose as filter-paper, is not in the least affected by G. pec-
tinovorum. Hence, the flax-fibre as such remains quite unchanged in
the rotting, but the less resistant forms of cellulose are solved quite
as the pectose itself. Gum arabic remains intact. As is seen from the
photogram (Plate Fig. 2), the image of the pure culture on malt-
extract agar is quite different from that of the butyric-acid ferment,
which latter forms thick clostridia.

This difference is not less clear in the culture liquids. Thus, in fig. 4
we see the form of the bacterium in a pectine fermentation at 35° C. in:
Tap-water 100, Pectine 2, (NH*)? SO* 0,05, K?HPO‘ 0,05, Chalk 2.

The dark portions represent the places where granulose is accu-
mulated. Clostridia of the common form are completely absent. The
shape of our bacterium in this or such like culture liquids is charac-
teristic, and is not found in any other species except G. wrocephalum.

11. Description of Granulobacter urocephalum.

The difference between G. pectinovorum (Gp F. 2, Plate Fig. 3)
and G. urocephalum (Gu Fig. 2 Plate Fig. 4) which likewise, albeit
in smaller number, accumulates in the rotting flax, consists first in
the shape, which for the latter more approaches the “drumstick
form’, although the spores are not round, but oval, as Fig. 2 § 3
shows with great distinctness. Further, in the former secreting a
much larger quantity of the rotting-enzyme pectosinase, which is the
very reason why G. pectinovorum is more common in rotting flax
than G. wrocephalum.

Both species produce much mucus, which consists of the thickened
and liquetied cell-walls of the bacteria themselves, and is found back
in the so-called rotting-gum, obtained by evaporation to dryness of
the rotting-water. That this species also stains deep blue with iodine
is suggested by the generic name.

A characteristic difference between the two species is the following.

The colonies of G. pectinovorum (Pl. Fig. 3), when kept on plates
of dilute malt extract agar with chalk, will relatively promptly be
decomposed into a detritus, wherein only the spores can clearly
be recognised, whereas the colonies of G. wrocephalum (Pl. Fig. 4)

|
|
;
|
|
|

EE ——————

————

( 479 )

remain much longer unchanged and continue distinctly to show the
shape of the bacteria. This phenomenon of bacteriolysis is perhaps
associated with the pectosinase secretion and is also observed in the
hay-bacteria.

The essential difference between G. wrocephalum and G. pectino-
vorum is that the former with ammonium-salts as source of nitrogen,
can ferment all kinds of carbohydrates, such as glucose, milk-sugar,
cane-sugar and dextrine, for which G. pectinovorum requires peptone
or broth. On the other hand, pectose is so little attacked by G. wroce-
phalum that fermentation cannot be observed with this substance,
even not when broth is present as source of nitrogen. Trypsine-
formation is with G. uw. about as vigorous as with G. p. and much
more abundant than with G. saccharobutyricum. The secretion of
diastase, on the other hand, is extremely feeble in both species and
much less vigorous than in the butyric-acid ferment.

12. Accumulation experiment for G. urocephalum. Why the butyric
acid- und the lactic-acid ferments disappear from good jlax-rottings.

That G. pectinovorum so strongly accumulates in our ‘“current-”
and ‘decanting experiments’, reposes on the double adaptation of
this ferment, on the one hand to the insoluble albuminoids of the
flax-stalk by a strongly peptonising enzyme, on the other hand to the
insoluble pectose by the secretion of pectosinase.

Why G. wrocephalum also accumulates in the flax, but much less
strongly, and why the common and vigorous butyric-acid ferment
disappears nearly completely, was made clear by the following accu-
mulation-experiment for G. wrocephalum, devised by Mr. G. van
Irmrson, at the occasion ofa researeh on the butyric-acid fermentation.

If to any carbohydrate, for example insoluble starch, glucose,
cane-sugar, or milk-sugar, a slight quantity of egg-albumine or peptone,
or very little broth, is added as nitrogen source, in the proportion:

Tapwater 100, Glucose 5, Albumine 0.1, K*HPO*005, Chalk 5,

infected with garden-soil and cultivated in a_ stoppered bottle at
35° C., there will first, that is so long as soluble carbon compounds
are still present, originate a butyric fermentation, but this is soon
replaced by a Uvocephalum-fermentation.

If from the thus obtained first fermentation a small drop is
transported into the same mixture, the butyric-acid ferment, indeed,
does not completely disappear, but the intensity of the Urocephalum-
fermentation becomes thereby much enhanced. If at the end of the

( 480 )

fermentation a new quantity of sugar (and chalk) is added, a further
purification of the ferment is observed.

When using a smaller dose of sugar, the soluble nitrogen com-
pounds which occur in the albuminous matter, become more trouble-
some as they make the butyric fermentation more prominent.

If the same experiment is made, the albumine being replaced by
an ammonium salt, G. wrocephalum is quite expelled and the butyric
ferment, G. saccharobutyricum, gains the victory.

That this experiment reposes only on competition, is proved by
the fact that G. urocephalum in pure culture, can grow excellently
and ferment with the said sugars and an ammoniumsalt as source
of nitrogen. Further, the pure culture on dilute malt-extract gelatin
proves that G. urocephalum, like G. pectinovorum, liquefies the gelatin
much more strongly than the butyricferment, and thus secretes more
trypsine.

The reason why these three bacteria accumulate so unequally in
the flax in the ‘current-experiment”’, and why G. urocephalum
takes the middle between the pectose-bacterium and the butyric
ferment, is thus evidently as follows.

During the extraction the insoluble nitrogen compounds are removed,
so that, as source of nitrogen there remains nothing else but the in-
soluble vegetal proteids. This assures the victory to the strongly pep-
tonising G. pectinovorum and G'. urocephalum over the not or feebly
peptonising butyric ferment.

This latter yields much more diastase than G. pectinovorum and
G. urocephalum, so that its presence is a source of sugar formation,
starch being never completely absent.

Hence, as soon as the butyric-ferment disappears, the insoluble
varbohydrates, too, will promptly be removed by the extraction
and the fermentation. The insoluble pectose only is now left behind,
by which G. pectinovorum, which secretes much pectosinase, finally
also subdues G. urocephalum, which produces little or no pectosinase
at all.

The lactic-acid micrococei produce no enzymes which attack
proteids, pectose, or carbohydrates. So, from the moment, that only
insoluble proteids and insoluble carbohydrates are present, they
‘an no more multiply and are carried off by the water-current.

EXPLANATION OF THE PLATE.
Fig. 1 (600).

Drop pressed from flax-stalk at the maximum point of a rotting during the
“current experiment’, stained with iodine, and showing the natural accumulation

OO Oe Oe ve

M. W. BEIJERINCK and A. VAN DELDEN: ,,Bacteria active in flax-rotting.”

Fig. 4. Fig. 3.

: ( 481 )

of G. pectinovorum, which is more, and of Gr. urocephalum which is less
common. Here and there oxygen forms, which do not stain with iodine.
Fig. 2 (900).

Granulobacter pectinovorum, as pure culture, on dilute malt extract agar with
chalk. Granulose stained blue with iodine, among the bacteria much detritus
formed by bacteriolysis.

Fig. 3 (15).

Colonies of G. pectinovorum on the same culture medium to demonstrate the
“moiré-phenomenon.”

Vig. 4 (900).

Granulobacter urocephalum, as pure culture, on dilute malt-extract agar. No
detritus is found among the bacteria.

Physiology. — “On tactual after-images”. By Prot. J. K. A. Werte
Satomonson. (Communicated by Prof. C. Wuiykuer).

(Communicated in the meeting of December 19, 1903).

In 1881 the following fact was mentioned by GoLpscuerper in his
thesis on “die Lehre von den specifischen Energien der Sinnesorgane’”’ :

“Wenn man mit einer Messerspitze schnell, am besten die Hohlhand
beriihrt, so tritt momentan nur die Tastempfindung auf, welcher
dann erst der stechende Schmerz folgt. Dasselbe kann man bei einem
leichten Schlag mit der flachen Messerklinge wahrnehmen.”

In the Zeitschrift f. Klin. Mediz. 1891 20. 4—6, he again
takes up this subject in an article, signed likewise by Prof. Gap.
This article has been republished afterwards in his Gesammelte
Abhandlungen Bd. 2, pag. 876 under the title: ‘Ueber die Summation
von Hautreizen”.

In this article the conditions under which the phenomenon may
be observed, are defined with greater accuracy. According to GoLp-
SCHEIDER the best result is obtained by exerting by means of the
point of a pin a short and feeble pression on the skin of the back
ar of the palm of the hand: “so hat man ausser der ersten sofort
eintretenden stechenden Empfindung nach emem empfindungslosen
Intervall eine ziweite, gleichfalls stechende Emptindung, welche sich
in ihrem Character dadurch von der ersten unterscheidet, dass ihr
nichts von Tastempfindung beigemischt ist, sie vielmehr gleichsam
wie von innen zu kommen scheint. Bei missiger, noch nicht schmerz-
hatter Intensitét der primaren Empfindung kann die secundare schmerz-
haft sein ..... Das Phanomen der seecundiiren Emptindung tritt schon
bei sehr schwachen, vom Schwellenwerth nicht weit entfernten
Reizen auf.”

( 482 )

Gap and GoOLDscHEIDER have made methodical experiments con-
cerning the phenomenon, causing them to consider it as a sensation
brought about by summation of stimuli.

They also have pointed out already the analogy with the after-
images, of the retina, produced by optic stimuli of snort duration.

An exact analysis however of the subjective phenomena, following
ihe experiment indicated by GoLpscnEIDER shows, that the anology
between what happens for the skin and for the eye, is a far greater
one than we might think at first sight.

For by this analysis it becomes evident that something may be
added still to GoLpscuerper’s description. The subjective impression
does not stop at the secondary sensation, but constantly a tertiary
sensation may be observed.

As soon as I am trying the experiment of GOLDscCHEIDER upon
myself, applying on the skin with the point of a blunt pin a prick
of very short duration, but very feeble, the skin being depressed
hardly more than */, millimeter, the first, primary sensation arises
almost simultaneously with the contact. After an interval of from
0.8 — 0.96 second the secondary sensation commences in accordance
with the description of GOLDSCHEIDER.

About from one to three seconds after this, a tertiary sensation
follows, consisting in a pecular feeling of irritation and itching,
compelling us involuntarily to rub the irritated portion of the skin
with the hand. This last sensation rises very slowly, reaching
its maximum in little more than one second, and disappearing again
with far greater slowness. The duration of the first sensation amounts
io a very small part of 1 second, the second sensation is like-
wise a short one, though generally somewhat longer than the first;
the duration of the tertiary sensation is still longer, amounting to
from 2—10 seconds, and even more if the intensity of the prick
was somewhat stronger. The curve of the three sensations may be
represented graphically by a figure.

2 | “

Figure 1.
The analogy with the visual after-images, such as these have been
described recently by rims, Huss, Hamaker and others, is most

( 483 )

striking. There too we find a primary image followed by the “satellite,”
and this followed in its turn by the fertiary positive image. The
latter is ever followed by a negative after-image. In the opinion
of Hess, the primary image and the satellite are also followed by
negative after-images. A scheme of the total of the sensation is
given by him as a sinusoide with a rapidly decreasing amplitude
and an increasing period; see fig. 2, in which the direct image

Fig. 2.
is represented by 1, the satellite by 38, the positive after-image
by 5, and by 6 the final, easily visible after-image. Hrss pretends
to perceive likewise the negative after-images 2 and 4, which I have
never been able to see; for several reasons, not to be given here, I
seriously doubt whether these after-images 2 and 4 really exist.

Leaving this question, I only wish to point out the close resemblance,
offered by the tactual sensation, following a single feeble touch of
a pin-point, with the series of positive after-images of the eye,
represented by the combination 1, 3 and 5. The course of the
phenomena is the same in both cases: the relative duration of
each subdivision is perfectly equal for both senses, only the absolute
duration is somewhat longer for the skin.

Still another analogy is shown by the quality of the three separate
images being different, as well for the eve as for the skin. [wish
to lay great stress on the statement of this last fact, because it
opens the possibility of a new conception, equally different from that
of Gotpscumiprr as from that of Huss. Even the experiments of
GoLpscHEpER, alleged by him in favour of his hypothesis of summatio
are subject to another explanation.

GOLDSCHEIDER observed that one single induction-shock, however
strong it may be, applied as a cutaneous stimulus, is never able to
rouse the secondary sensation, whilst this was effected easily and
constantly by 3 or 4 shocks of the induced current, even rather feeble
ones, following each other in rapid succession.

Proceedings Royal Acad. Amsterdam. Vol. VL.

( 484 )

Now let us consider only what happens for the vasomotor nerves.
If these are excited by frequent shocks of the induced current, they
react by a vasoconstriction followed by vasodilatation. If the shocks
of the current are following one another very slowly, only dilatation
is obtained. And finally, if a peripherical motor nerve iner-
vating both striped muscle-fibres and vascular muscles, is stimulated,
it may occur sometimes, that after one single shock of the current
only contraction of the voluntary fibres follows. Ifseveral elementary
stimuli, following one another in an appropriate rhythm, are apphed,
first a contraction of the striped muscles, may be observed, next of
the vasoconstrictor, and finally of the vasodilatator fibres.

As soon as we suppose in the retina or in the skin the presence
of more than one species of end-organs the possibility may be
assumed that only one of these species reacts on stimuli of short
duration, whilst other organs react on stimuli of longer duration.
If stimuli of definite duration and intensity are made use of, both
organs will react, each after its own -latent period, in the same
way as happens for muscles, vasoconstrictors and vasodilatators, so
that we will obtain two sensations subsequent to each other. In
eases, where three excitable organs coexist, even three separate
sensations may be felt, as in the case of stimulation of the skin
and of the retina.

Chemistry. — “The course of the solubility curve in the region of
critical temperatures of binary mivtures. (Second communica-
tion). By Dr. A. Sars. (Communicated by Prof. H. W. Bakutis
ROOZEBOOM.

(Communicated in the meeting of December 19, 1903).

In my preceding communication!) on this subject I have repre-
sented in the figures 3 and 4 the p-v-sections for different temperatures,
starting with the critical temperature of 1 and finishing at the melting
point of 4. Fig. 3) holds for the case that the three-phase-curve
lies entirely below the plaitpoint-curve, and Fig. 4 applied to the
ease that the three-phase-curve cuts the plaitpoint-curve. In order
to obtain the 7*2- projection from the combination of the different
p-w-sections, the variations of pressure were left out of account.

To complete what precedes the actual succession of the p-«-sections
for different temperatures will be represented here.

1) These Proc. Oct. 27th 1903, p. 171.

—”

A H =

Fig 1 holds for the case that the whole of the three-phase-
curve lies under the plaitpoint-curve. cc, ¢,¢,d is the curve of the
solutions saturated with solid B; ee,e,e,d is the curve of the
vapours coexisting with these saturated solutions. Both these curves
terminate in the point d, the melting point of 4. The hatched streak
@ €, €, e, dc, C,¢,¢ first ascends coming from lower temperatures; if
reaches a maximum, and then descends again.

The curve aa,a,a,a,a,6 is the apparent outline of the p-a-t-
surface on the p-x-plane, or the J/-curve, aa,a, a, was the apparent
outline of the p-z-t-surface on the 7-x-plane or the /-curve.

As has been proved by van per Waats the curves ge and c/
are two parts of one continuous curve with an intervening piece
which is partly not realisable, and with two vertical tangents.

Fig. 2 represents the case, that the three-phase-curve cuts the
plaitpoint-curve.

32*

;
1 /
eU

At p the curve of the saturated solutions cc, passes here without
a break into the curve of the saturated vapours ¢ ¢,.

The curve ma, touches the curve ¢¢, pc, ¢ ina point on the left side
of p and becomes there metastable, becoming stable again at a point on
the right side of g. At y we observe the same thing as at Pp, Vib. a
breakless meeting of the curves e, and de,. The curves rpr, and vg ey,
Which represent the “fluid? phases, coexisting with solid 2B, have
the course given here, as has been shown by VAN prr Waans'). The
possibility of drawing two vertical tangents to these curves, imples
the phenomenon of retrograde solidification. In the immediate neigh-
bourhood of p and gq we do not see any change in this, but at
greater distances, e.g. halfway between p and g it is possible that

the two tangents coincide, which causes the retrograde solidifieation

1) These Proc. VI 230 Oct. 31st 1903 and VI 357 Nov. 23rd 1903.

( 487 j

to vanish '); the inflection point, however, continues to exist *). In
my first paper I was led by the experiments of VinLarp to accept
the possibility of a retrogression of the p-r-curve, which for a system
of the type ether-anthraquinone represents the ‘fliid” phases coexisting
with solid 4 and now we see that this is necessarily so for the
immediate neighbourhood of jy and gy. So it has been ascertained
theoretically, that we can make solid 4 evaporate somewhat in the
immediate neighbourhood of p and q. If for a system of the type
ether-anthraquinone an entire volatili- sation of arbitrary quantities
of 4 were observed, this would point to a p-r-loop as is found for
the system oxygen-bromine at 17°, or in other words to continuity
hetween the so/i/ and the ‘fluid’ phases.

As | said before if is necessary to examine the 7-.-sections for
different temperatures in order to gain a better understanding of
the question.

Let us first consider the usual case, that the three-phase-curve
lies entirely below the plaitpoint-curve.

For a temperature below the eritical temperature of A, we get
the following v-7-section. (Fig. 3).

Aa represents the mol. vol. of the saturated vapour of A, Ad that
of liquid A. Be is the mol. vol. of the saturated vapour of Band B7
the mol. vol. of solid A.

ah denotes the mol. vols. of the vapour mixtures A+ 4, coexisting

Fig. 3,

1) loc. cit.

*) This is the case when the curve has originally only one inflection point. If
it has two inflection points, which is most likely also possible, they can both
disappear.

488 )

with the liquid mixtures, for which the line de represents the
molecular volumes.

The point 4 indicates the mol. vol. of the vapour saturated with
B and e the mol. vol. of the liquid saturated with . abed is the
region of the phase-complexes / + G, the nodal lines drawn in it
connect coexisting phases.

The mol. vols. of the vapours coexisting with solid 6 lie on the
curve bc, and the triangle /cf is the region for the phase-complexes
Spt+ G.

The coexisting phases le in this case on lines traced from / to
the curve tc. The triangle }fe is the three-phase-triangle and there-
fore the region for Sg+ L-+ G.

The line eh, which divides the space under def into two parts,
represents the mol. vols. of the liquids coexisting with solid 4. For
smaller volumes this line runs to the left, because in normal cases
the solubility of 4 in A diminishes with decrease of volume.

The quadrangle effi is the region of the phase-complexes Sz + L,
the coexisting phases are indicated by the small lines drawn in the
figure. Inside dehy we have only one phase, viz. liquid, and above
abe only gas.

The lines ch and eh are two portions of a continuous curve with
an intermediate portion, which will have two vertical tangents in
normal cases. It is easy to prove this with the aid of the theory
of vaAN DER WaAats, and this can be done in a way analogous to
that, in which van per Waats') has proved the existence of two
vertical tangents to the pw-curve for solid-liquid.

We start then from the differential equation of v when 2 and 7
vary. (Cont., If pag. 104).

Let us denote the concentration and the mol. vol. of the solid
phase by zs, and vy, and that of the coexisting gas phase and liquid
phase by wy and vy, the equation is then:

07 yp 0? yp Oey aS :
irony eur aes (reins dy r ede dT=0.

. rar 2 . .
If 7’ is kept constant, the last term of the first member becomes

zero and we get after an unimportant transposition :

j 0? uw 0? uw ; O° wp O*xp 5
nop) a al avis: | bon veri emesis i a ia

07 Ov > H 0°y 07yp
: (vz -U ) (#5 wv ) ( - ) | Se | UV = + (#,-27/A) —— Ider.
AL : : One) pT oe Ov Ow F eeray) Ou? ne

( 489 )

We have :
Ove
(v,<—vs) — (ts—~7r) >, == Vef's
tp) pT

vsr denotes the decrease of volume per molecular quantity, when
an infinitely small quantity of the solid phase passes into the eo-
existing phase at constant pressure and constant temperature.

By substitution we get:

Van pveR Waats has lately demonstrated that v¢,, can twice
become zero when vr, is smaller than vy, in consequence of which

dv ere as
—— becomes twice infinitely large.

AL ¢
Zap
Further ae can also twice become zero, but this does not give
Ve =
| cae dep Op
rise to an infinitely large value for ee or being zero, and
LU Uf 5

we being therefore in D or D’ (Fig. 2 vax per WAAtzs), Ver =
Cc aK ‘ as

and ie has therefore a finite value.
uD ¢

If 7, is larger than 7, which may also occur, then only one vertical
tangent is possible. This is attended by a change also in the course
of the lower part of the line chek. In the above figure eA runs to
the left for smaller volumes, but then this curve must directly run
to the right, which means that the solubility of 4 in A increases
for smaller volumes (larger pressures), a behaviour which may also
be expected theoretically for smaller volumes when initially v¢ > x,
whereas the reverse, so the usual course is found for larger volumes.
If, however, v, > vy the course must be the abnormal one from the
beginning.

For the better understanding of fig. 3 I shall add a few words
about each of the different regions.

Let us assume that we have a mixture of the concentration .v,
for a volume 2, v,; we are then in the region of 1+ G. If we
draw the nodal line nv, n, through v,, n denotes the mol. vols. and

490

the concentration of the liquid and , those for the vapour coexisting
with this liquid. In addition the relation between the volumes of
liquid and vapour may be read from the pieces, into which the

liquid nv

. a . . ° . ‘pote |
point v, divides the nodal line; it is viz. ==
VAPOUr 2 Vv

1
With a concentration «, and volume 7,7, we are in the region
Sp + G; the mol. vols. and the concentration of the vapour coexisting

with solid B, are denoted by ¢,; the relation of the volumes by
solid NV,
vapour 7 e: UV.

If we now take a concentration «, with a volume «,v,, we are
in the three-phase-triangle. The mol. vols. of the three phases are
indicated by the three angles; the relative volumes are found by
drawing a line from / through v,, till it intersects the line be. The

solid NU, liquid ‘bn .

relation —— —=-—— and the relation ———_ =—. If finally
liquid+-vapour fs vapour en,

we have a concentration v, with a volume x, 7,, we are in the region

L+ Sp; the mol. vols. of the coexisting phases are now expressed
: Ep : ee liquid uN’,
by », and v’,, the relative quantities being indicated by ——~ =
j ¥ ‘ solidB v,n,

When the temperature rises, this “v-section suffers a change; in the
first place the curves ab and be are moved lower and the curves
de and ef are moved upward. The displacement of the point /
however is very small compared with the other displacements. The
points 4 and ¢ are also moved to the right, because the solubility
of 4 in A is supposed to increase with rise of temperature.

These are the changes for the case that we are still below the
critical temperature of 4; when we have reached this temperature,
the curves ba and ed pass without a break into each other and
with rise of temperature up to the melting point of 5 we get a
series of conditions represented in Fig. 4. (p. 491).

The binodal curves 67?e with the plaitpomts in 7? lie all inside
each other; they cannot be prolonged to the 4 side below the
melting temperature of 4, because the substances “4 and 4 become
miscible in all proportions only at the melting point of 4. Just above
the critical temperature of “1 the nodal lines for the saturated vapours
and liquids have a strongly slanting position; at higher temperatures,
however, they slant less, because the difference in concentration
between 4 and ¢ becomes smaller.

The curve G4,6,4, is the v-t-curve for the saturated vapours, the

Fig. 4
ee
Pa
“
i
a
Fo
Yi
x
a
A ;
c
6 oe

A z Se %, 7

curve ¢¢,e,f, 18 the +-fcurve for the saturated liquids. The former
curve has a minimum, the second a maximum ‘).

That the r--curve of the saturated vapour must have a minimum
can be easily proved for the system AgNO,—H,O%*). In this case
the matter is so simple, first because the vapour consists only of
water and secondly because the maximum of the pressure is. still
below 1*/, atmosphere and therefore the law of BoyiE-Gay-Lvssac
may be applied for an approximation.

The vapour tensions of the saturated AgNO,-solutions are not yet
accurately known, but this is of no importance here. We may
assume here for the moment, that the values are perfectly accurate
and then see what the position of the ¢-fcurve for the vapour
must be.

We get the following result :

') Probably this need not always be the case.
2) These Proc. IV, 371. Dec. 28, 1901.

( 492 )

——$—<—<—$—<—$—<————————————
= Ti ae |

Vapour tension | Mol. vols. of the

ee: | in m.m. Hg. | vapour in liters
133 | 760 | 33.35
135 | 800 24.29
150 960 27.49
160 1000 27 .02
170 4910 27.37
185 900 31.75
191 760 38.09

/o00

P ae

$00

ty ”” 30 (4g (90 (60 I~g 180 190 Joo
T

maximum at 170°

The figures 5 and 6 are graphical representations of the pé- and
the vé-curves.

We see, that the maximum in the pé-curve lies at about 170°,
and that the minimum in the 7/-curve lies at 161°. The maximum
in fig. 5 is therefore not found at the same temperature as the
minimum in fig. 6. (p. 493).

That this must be the case can be easily proved by applying the
equation P= R77. If we differentiate this equation, we get :

dp ar dp
or
dv Uv 1 tt dp
dT at pat

2 ote dv :
For the minimum in the vf-curve ‘yi is therefore :

oe i

( 493 )
Fig. 6,
50

74%
$0 Iya re seu, yo 100 490 goo
7
minimum at 161°.
Tap
a oe = GY
p aT
or
dp P
ar ¥
: dv dp Te :
So when — — 0, — has a positive value. In the maximum of
dT dl
the vapour tension curve we have :
dp ; dv v
ah hence —~=—_.

Wh dT out

( 494 )

So for the temperature, at which the vapour tension curve has
reached its maximum, the 7--curve is ascending.

dp pie
ae fhe BO
|

Finally I shall briefly poimt out that the value for
: ) Z

calculated from the vapour tension curve harmonizes well with the
: Pim ae ; ote nine
theoretical vaiue rid For the range of temperature between 150°—

170°, p may be found from the following interpolation formula
P = Prien + 9,9 (100) — 0,15 ¢—150);
For 161° follows from this
we = 22
aT .
and
Pp 1001
= = aS 2,0
71 434

It follows from the construction that the 7-+curve for the satu-
rated solutions can have a maximum, but if is not easy to deduce
this theoretically.

We shall now continue the discussion of fig. 4.

If we take a concentration .7, with a volume «jr, and at the
temperature for which the first 7-r1-section holds, we are in the
three-phase-triangle fe, and so we have side by side Sg + L + G.
At the temperature for which the second ¢-7-section is drawn, the
point v, is no longer in the three-phase-triangle, but in the region
for Sp-+ G@; the liquid has therefore disappeared, and only solid
2B + vapour is left.

At the temperature corresponding to the third v-r-section the point
v, has returned to the three-phase-triangle and solid 4 -- vapour
has therefore been partly converted into a liquid. At the tempera-
ture corresponding to the fourth 7-r-section the point 7, is found in
the region of the unsaturated liquids with their vapours and at the
melting point of the substance 5, 7, lies in the region of the
vapour and so everything has evaporated.

If on the other hand we had started from the concentration «,
with a volume .r,7,, we should have left the three-phase-triangle
with increase of temperature and we should have reached the region
for Sp+G, and have passed from there straight into the gas-
region. As v, is situated above the 7--curve b4,, there is here nothing
retrograde as in the case discussed above. It is obvious that the
retrograde phenomenon will occur for conditions lying above the
tangent drawn to the v--curve 44, from a certain point 7 (between

——_.'

( 495 )

fj, and f,), and below that part of the curve 4, that lies between
the point of contact and the point 4, ’

If we further consider the case that the composition is ., and the
volume v,, we have the case that with rise of temperature we get
from the three-phase-triangle into the region for + Sp, and so
that the vapour disappears. With further increase of temperature
we pass directly from the region 4+ Sp, into the gas-region, just
as for the condition «,v, we passed from the region Sy + G into
the gas-region. In the remaining cases nothing noteworthy takes
place; we must only point out, that for systems of the type of
fig. 4 the critical phenomenon can only be observed for wnsaturated
solutions.

Fig. 7 applies to systems of the type of ether-anthraquinone. The
difference between this figure and the preceding one lies in the faet

A. 3 DL, = B

1) Centyerszwer (Zeitschr. f. Elektrochem. N°. 40 S. 799 (1903) has lately drawn
attention to this retrograde phenomenon.

( 496 )

that if we come from low temperatures the v-t-curve for the saturated
vapour and that for the saturated liquid approach each other more
and more, and finally pass without a break into each other. At ¢
we get a repetition of what precedes in reversed order. On the
left of p and on the right of q we have the same thing as in
fig.
here the critical phenomenon can be observed for a just saturated

4; at p and q however, we see something special, viz. that

solution.

We have further seen in fig. 4 that the suecession of conditions
L+Sp+ G>Sp+ GG could occur there for conditions lying
above the curve 44,. In fig. 7 this takes place, besides above the
curves bp and qh, also between the concentrations «, and w,, corre-
sponding with the points p and q, for any arbitrary chosen volume,
hecause the region for Sz-+ G between p and gq passes continuously
into the region for Sz-+ “4. Hence this phenomenon will occur much
more frequently for the type of fig. 7 than for the type of fig. 4.

The usual succession L+ Sp+G—>L+4 G—G is here only
possible for conditions lying within the v-tcurve ee, e, pb, b, 6.

The retrograde phenomenon discussed above will here be observed
for all conditions lying below the branch 6, 6, q of the second
v-t-curve and above the tangent drawn to the branch qe, 7, from a
point f (between /f, and /,). A very essential point of difference with
the case of fig. 4 is further to be found, first in the circumstance
that with a concentration z, and a volume w,v, we pass here sud-
denly from the region 1 + Spg-+ G@ into the gas region and secondly
that for a composition slightly richer in B than 2, and with a volume
vr, U, just at the moment at which all the solid 6B would evaporate,
a saturated solution is formed, which reaches its critical temperature
immediately after its formation.

From fig. 7 follows that if we started from a concentration 7, with
a volume x,v,, with which therefore the point q can be reached,
the transition L+S;+ G—>S,+ G takes place at a temperature
lower than that corresponding to the point p, so that the points p
and gq can never be determined by one experiment, which it is
practically superfluous to mention.

The curves p, pp, 77,, ¢é, and q,qq,, which denote the mol.
vols. and the concentrations of the “fluide”’ phases coexisting with solid
Lb, have still two vertical tangents, as they are in the immediate neigh-
bourhood of p and qy, from which the retrograde soliditication follows.
For the curve SS,, drawn halfway between p and q, the two
vertical tangents coincide in accordance with the pa-curve in Fig. 2,
which means, that there retrograde solidification is no longer possible.

( 497-)

We shall conclude with some remarks on the determination of
the plaitpoint- or critical temperature.

As is known, the eritical phenomenon for binary mixtures can
only be observed, when before the region 1+ is left, there is
exactly the same quantity of liquid as of vapour, or in other words,
when the volume is exactly the same as the plaitpoint volume (see
fig. 4). In this case we enter the gas region at the plaitpoint ?. In
general every concentration requires then another volume. If the volume
is greater or smaller than the plaitpoint volume, we do not observe
a critical phenomenon. In the first case we come to the gas branch
of the binodal curve, and consequently total evaporation of the liquid
takes place when the temperature rises slowly; the liquid mass
decreases more and more and disappears in the lower part of the
tube. In the second case we reach the liquid branch of the binodal
curve and the whole tube is finally filled with liquid.

A sudden transition from the region J+ into the gas region,
in consequence of the fact that the liquid and the gas phase become
wlentical is only observed for a volume equal to the plaitpoint volume,
also when the temperature rises very slowly. Yet for other volumes
phenomena may be observed, closely resembling the critical ones,
but this is only to be attributed to the fact that the temperature rises
too quickly for the equilibrium to be established.

For a simple substance the plaitpoimt temperature is the highest,
but this is not the case for binary mixtures. The highest temperature
for a binary system will be observed for the volume of the critical
tangent fF, so for a volume larger than the plaitpoint volume (see
fig. 4). For still larger volumes the liquid will again disappear at
lower temperatures, so that from the plaitpoint volume to larger
volumes the temperature, at which all the liquid has disappeared,
and which we might also call condensation temperature, passes
through a maximum value. If the volume is smaller than the plait-
point volume, the tube is completely filled with liquid, but the tem-
perature at which this takes place, is always lower than the plait-
point temperature.

Amsterdam, Dec. 1908.

Chemical Laboratory of the University.

( 498 )

Botany. — “Exosporina Laricis Ovp. — A new microscopic
fungus occurring on the Larch and very UP LOUS to this tree.”
3y Prof. C. A. J. A. OupEMans.

On June 11, 1903, Mr. C. A. G. Beins collected on the estate
“de Groote Bunte’’ at Nunspeet and sent to me a number of needles
and twigs of the common Larch (Larce decidua = Lari europaea),
the former of which, although they belonged to recently grown
dwarfshoots, had for the greater part a sickly appearance, and had
exchanged their light-green colour for a light-brown one.

The question naturally arose: what could be the cause of this
phenomenon, and whether a fungus might be at the root of it.

An investigation concerning this matter soon showed me that the
twigs were normal, and consequently had not been visited by the
to the Larch very injurious Peziza (Dasyscypha) Willkommi, but
that the needles were spotted on both sides, but especially on the
lower side, with very small black specks (Fig. 1).

These specks, spread at random, sometimes more, sometimes less
numerous, mostly circular, had a diameter of LOO—150 w at the
utmost, and most resembled Leptostroma- or Leptothyraun-specks,
although a closer examination showed that they shared no property
of any importance with these genera. They cohered firmly with the
epiderm, and it soon appeared that they had not been hidden under
if and gradually found an exit, but that they had existed from the
beginning on the surface of the needles.

This result was not obtained by examining cross-sections, which
the very minute specks did not allow to make, but by heating the
needles for a few minutes in a ten percent solution of caustic potash,
washing them, making them transparent with chloral-hydrate, and
gently pressing them with a cover-slip. Under the microscope light-
brown, wavy, occasionally bifurcated threads or ribbons of varying
breadth were seen on the leaf, which in various places produced
little disks, from whieh new threads were sent out in some other
direction (Fig. 2).

The threads consisted of articulate hyphae and the disks of a
small-celled parenchym. By pressing the latter more strongly and so
dividing them into smaller fragments, it appeared that they were not
flat but globular, and that they protruded like little cupolas above
the epiderm to which they were firmly attached.

These fragments also gave an opportunity of gaining an idea about
the internal structure, of the disks. From their small-celled_ tissue,
namely, certain favoured hyphae had grown up in a elose buneh, in

— -- ©. 7 | - —_— oe

+ 499 )

such a way that their height increased regularly from the edge to
the middle. These hyphae, by forming numerous partitions, had got
an articulate appearance. On closer inspection the multicellular rods
appeared, in a more mature state, to consist in the lower parts of
cubical, in the higher ones of more rounded cells, and finally to
become disintegrated, so that, on account of similar cases, there
could be no doubt that the cast-off cells were the means of
multiplication and had consequently to be considered as conidia.

These conidia, from which new infections may be expected, are
mostly 5—6 pg high and 5g broad, have a light-brown colour and
are perfectly smooth. By far the greater part of them are undivided:
only a few show perpendicular or inclined partitions.

If we now ask what harm is done to Larie decidua by the above
described fungus, the answer can only be that the stomata are blocke«
up and rendered useless by it; that the function of the leaves is
interfered with, and that the chlorophyll is changed in such a manner,
that its assimilative power is reduced, and that evaporation is in no
small measure prevented. This is proved by the brownish colour of
the leaves replacing the green one. In one and the same spiral of
needles, such as are found with Larix, the morbid process proceeds
from the outside to the interior, so that for a considerable period
needles of two colours are observed on the rosettes.

As the needles fall off pretty soon, and lodge no mycelium threads
which might have gone on to the twigs, it follows that, in order to
prevent future damage to the trees, the fallen needles should be
removed and burnt. Spraying might perhaps save attacked trees
from further decay. For trees that are visited by the fungus, begin
to languish, their growth is impeded, their resistance diminishes, and
so they soon fall a victim to all sorts of Dematiaceae which give
them a dirty blackish appearance.

The next question is: what place in the system the fungus ought
to occupy, and what name has to be assigned to it.

To begin with, it undoubtedly belongs to the “Fungi imperfecti”,
lately entitled ‘“Deuteromycetae” by Saccarpo (Syll. XIV, p. 4).
Secondly we must exclude the Sphacropsideae, which possess a perithe-
cium, as well as the MJelanconieac, the conidia of which, without being
occluded in a perithecium, develop within parts of plants and rest
on a stroma. Our fungus rather belongs to the third and last, at the
same time the largest class of the Deuteromycetae, which have no
perithecium and the conidia of which, produced on threads or hyphae,

live either independent of each other, which is the general case, or

are gathered in bundles, forming a so called “Coremium’”.
P 33
Proceedings Royal Acad. Amsterdam. Vol VI.

eR) -)

For the sake of brevity we shall state at once that our fungus
belongs to the Tubereulariaceae, with coloured hyphae and conidia
linked like a rosary, and that first Corpa (Ieones Fung. I, p. 9 and
fiz. 148), and later Saccarpo (Syll. IV, 757) assigned the generic
name Trinmatostroma to a similar fungus.

The species, described and represented by the former, he cailed
Trimmatostroma Salicis, after its host. Now it deserves notice that
Saccarpo found a fungus on rose hips and first called it Exosportum
fructicola (Fungi Mtalici, pl. 40), which he later transplaced to Trimma-
tostroma and called Tr. fructicola: firstly because in the genus
Exosporinm, introduced by Lixk and exemplitied by L. Tihae (plate 1,
fie. 8 of his Observationes mycologicae), the conidia are not linked
together, but adjacent, and secondly because in his opinion the structure
of Exosporium fracticola did not agree with that of Erosporium
Tiliae, Wut with that of Trimmatostroma Salicts.

Now our plate shows Zrimmatostroma. Salicis Corda (tig. E) as
well as Vrimmatostroma fructicola (fig. F), reproduced from the
original drawings, in order to elucidate our conviction that between
these two, points of difference are to be found rather than points
of resemblance, and this to such an extent, that it seemed to us that
Trimmatostroma had to be shifted again, this time to the genus
Evosporina, introduced by us for /. Laricis, with which Saccarpo's
fungus has the greatest resemblance.

The characteristics of the three repeatedly mentioned genera can
now be summarised as follows:

Exosporina. — Conidia in strings, undivided, falling off singly.
Stroma not or only slightly developed.

Exosporiuin. — Conidia consisting of two or more cells, not
united to strings, forming a close assemblage on a stroma.

Trimmatostroma. — Multicellwlar conidia, loosely cohering,
forming a dense aggregate on a well developed stroma.

Of the genus 7rimmutostroma, in Corpa’s sense, only two species
are known besides 7. salicis, viz. Tr. americana Thiim. Mycol.
Univ. N°. 793 (Sace. Syl. TV, 757) on twigs of Sali discolor, and
Tr. amentornm Bresad. et Sace., on female catkins of Alnus meana.
A species described by Donrrry under the name of Tr. abietina (am?)
Botanical Gazette 1900, p. 401, and Sace. Syl XVI, 1107) agrees
more with a Sporodesmium according to the description, and is
considered as such by Saccarpo. All these three fungi need not be
considered here. We would only remark that 7iimmatostroma abietina,
which like our Evosporina Laricis occurs on the leaves of Conifera,

( 501 )

causes great damage to plantations of Abies balsamea in the environs
of Guelph in Ontario. Though it may be very probable that the
fungus mentioned does not belong to the genus 7riminatostrom«a, yet
it appears from Donerry’s article that it greatly impedes the growth
of the trees by choosing their needles as substrate. About the checking
of the evil nothing is mentioned by Dounerrry, so that we cannot
profit by advice from Ontario. No suffering trees were found at
Nunspeet except at “de Groote Bunte”.

EXOSPORINA Ovp. n. g.

Fungi expositi vel endogeni, stromate nullo vel parum evoluto,
conidiis in catenas stipatas digestis, singulatim secedentibus, homo-
morphis, continuis, coloratis.

K. Laricis Ovup. — Stromatibus amphigenis, expositis, puncti-
formibus, nigris, catenas conidiorum longiusculas, in placentam con-
vexam arcte condensatas, gerentibus; conidiis primo angulatis, denique
6X 5 u, singulatim secedentibus, ferrugineis.

globulosis, continuis, 5

EXPLANATION OF THE PLATE.

Vig. A. Needle of Larix decidua ; magnification 10 times; with the black spots
of Exosporina Laricis Ovp.

Vig. B. Hyphae or ribbons, extending over the leaf and in various places grown
out to small-celled little disks, from which later the conidia, connected to strings,

200
will arise Magn. :

Fig. G. Ripe cushion of strings of conidia, as they would appear on a cross-

E DVO

section. Magn. re

a : 1000 }

Fig. D. Part of such a cushion, enlarged ree Each separate string shows a
spherical top-cell.

Fig. E. Corpa’s picture of Trimmatostroma Salicis.

Fig. F. Saccarpo’s picture of Exosporium fructicola.

I am much indebted to Mr. C. J. Koyxinc at Bussum, who has
been kind enough to draw the plate for me.

Mathematics. — “Pritcker’s numbers of a curve in S,” by Prof.
P. H. Scnoure.

The Piicker’s numbers of a curve in the space S, with 7 dimen-
sions have been given for the first time by Veronese (Math. Annalen,
vol. 19, page 195), yet they have been seldom applied although dating
from 1882. This is probably due to the more or less awkward

33%

( 502 )

notation which is made use of and whieh has been adopted i. a
in Pascan’s Repertorium der hiheren Mathematnk (Leipzig, Teubner,
1902). In the following lines I intend to give a more concise notation,
making it possible to write down the 3 (#—1) relations between the
32 PLECKER’s quantities in three formulae with an index, which must
take the values 1,2,...,n—1 successively. In order to make the
deduction clear to those, who are not so familiar with polydimen-
sional theories [ shall begin by indicating them for the case 7=3

of our space.

2. As is known the six relations between the nine PLitcKEr’s
quantities of a skew curve are derived in two triplets from the
consideration of two plane curves, the first of which is the central
projection of the given skew curve C from any point O on any
plane «, whilst the second is the section of any plane @ with the
developable of the tangents to the curve C. Let us indicate suecces-
sively order, rank, class of the curve C’by 1, 7, m and Jet us represent
as is customary by (a, 6), (y.4),(7,y) the three’ pairs of dualisti-
cally related numbers, of which 4 is the number of stationary points,
AW the number of apparent nodes, « the order of the nodal curve of
the developable; then the sextupies

Geek

WEE RUe AO nile, Wey 05) . (m5, m,4-d

bss Key b,)

3° 2

of the quantities (order, class and numbers of nodes, double tangents,
cusps and intlexions) characterizing the two plane curves are
expressed by the equations

oF eo
Mey SS m, SSS
OR ba 2 ery
t, =) ty ; ; i : (1)
Kee 0 Mey
b, SS} b, i

in the nie characterizing values of C: so in conneetion with the
well known Pricker’s formulae for a plane curve the two triplets
of relations hold @ood :

r—n(n—1l)— 2h-3 6 m—=r(r—l) —22—3n
n= r (r—1) — 2 y—3m : r—=m(m—1) — 2g—3a | . (2)
m—h = 3 (r—n) | a—n == 53 (m—?r) )

If we substitute 7,,7,,7,.7,,7, for the row of quantities 4, 72, 7, 1m, a

( 90s )

and if we put d,,¢, and d,,¢, for A, y and w,y the equations (1)

pass lito

i
eee Ge tyay, SS
og Sr)
Se)
and identities, Whilst the two triplets of equations (2) are united to
Pe r(r; —1)— 2d4;-—-3 7;_) |\
‘ Se ne Tee ee —1)— 2%;—83 Vite | cea Ge) ee mr O's |
Tie — 7) = 8 (741 — ri) |

And now these equations pass into those for the general case as
s00n as the addition (21, 2) is exchanged for (2 = 1, 2,...,—1).

3. We shall now pass to the general ease of a curve C, of order
nv, lying in an S, but not in an S,—; and we remind the readers
how here we determine the 5(z—1) relations between the 52 charac-
terizing quantities. If we take in S, two non-intersecting spaces S,,
ey 1, anid iW we project-C, out Of 5,1 on 5,, the projection
is a curve €,. If we imagine this process to be performed for

PB
p=2,3,...,n—1, we arrive at — the curve C, included — a
: (Pp)
series of n—1 curves (5, Cs,..., Gr—i, Cp. If farthermore Cs — once
more for p= d2,3,...,n—1 — is_the section of the locus of the
spaces S_; through p successive points of the curve C,4) with any
plane lying in the space S,11 of that curve, we arrive at, — if the
(1)
plane curve (2 already found above is represented by C, —, n—1
‘aie (n-=1)
pine. curves’ Gs 5 -Ca jy. Co and these furnish m1 triplets of

relations. If the sextuples (7, 7; d; t;, k;, 6); .@ == 1, 2; 1eey M—1)
represent the characterizing numbers of these plane curves the 3@:—1)
equations hold good :

m, = nj (uj—1) — 2d;—8h;

nj = mj (mj—1) — 2 ti—3b;

(, @=1,2,...,n—1),

\
bj—k; = 3 (m;—ni)
By representing the series of 7 —-—+ 2 quantities

! C1) ‘)) (qneeale
b n TOD. 982), rh? m a

number of numbers number of
stavionary . order, eo a a
tee is of rank,

class, stationary
points

spaces S,—

( 304 )

of C, bY ry,ii,.--> lo Tntt we find the equations (1’) extended from
(¢=1,2) to ¢—1,2,...,n—1), which equations cause the above-

mentioned 3(7—1) equations to pass into the equations (2”), in the
same way extended from (¢= 1, 2) to (.=1,2,:..,m—4).

4. According to this notation the system of the 32 PLtcker’s
numbers of (,, consists of three groups: a group of n+ 2 quantities
~ (numbers of rank), a group of 2—1 quantities d (numbers of double
points), a group of 7—1 quantities ¢ (numbers of double tangents).
We shall now indicate what is the exact signification of those quantities.

Numbers of rank. We consider 7, T,, ?a—1 separately.

By 7 we understand the number of stationary points of C), 1.e.
the number of the points through which + 1 successive spaces
S, 1 through n successive points of the curve pass.

Por p=—1,2;...,% Wwe find that 7,
through p successive points of (, cut any space oie of these

indicates how many spaces
pt ;
numbers 7, is the order and 7, the class of C.

The number of stationary spaces S,—; of C,, i.e. the number of
spaces S,-; through 2-1 successive points of (', is indicated
by Myti-

Numbers of double poimts. The quantity d, is the number of

double points of the section (, of the locus of the spaces S,—1

through p successive points of ( with a plane situated in the

e+
space S,41 of that curve. So by returning from the: projection C,41
io the given curve (, we find the following: If we project the
single infinite number of spaces S,—1 through p successive points of
CG, out of any space S,-»22 we find a single infinite number of
spaces S, 2 and therefore a twofold infinite number of intersections
S,—4 of two non-successive spaces S,-2. The locus of those spaces
S,-4 is a curved space with m—2 dimensions, cut in a certain
number of points by any plane. This number of points, at the same
time the order of this curved space, is d,.

Numbers of double tangents. The quantity ¢, is the number of

(p)

double tangents of C,. By ascending from C,4; to C, we arrive
at the following: By projecting the single infinite number of spaces
S, through p--l successive points of C, out of any space Se
we find a single infinite number of spaces S,—; enveloping a curved
space of #—1 dimensions. The number of double tangents of any
plane section of this envelope is ¢.

For the rest it is easy to see that the numbers d¢, and ¢,—, refer
to quantities dualistically opposite in the space S

’
—i*

ee ae

~
be
'*

( 505 )

5. By means of the simple form of the PLicker’s formulae we

p)
are now enabled to show more clearly that really all curves (5

belong as they should to the same genus. For this we prove the

(i (+1

equality of the genera g; and gi41 of C2 and Cy

According to the relations (1’) extended to C, we have

2 gi = (m—1) (nj—2) — 2 (d; +k) = (ri—1) (ri — 2) — 2 (di +71)
and therefore

2 (9;-+-:1—91) — Aree a 2 (dj) —d;j) —3 ("14-1—7i) --2 (7% ri—1) . (5).

Moreover the first of the three equations (2’) for 7and /—+ 1 gives
by means of subtraction

2
a aa Pee 2 (dj —d;) a (F441 = ri) Tia 3(7; = TI ) . (4)

rit2—r 41 = (7
Thus by subtraction of (4) from (3) we get
2 (91-+1— 91) = (ri-2—Ti41) — 2 (ri4-1—7%) + (7I— 1)
= (Fai i OAR eo)

and from this equation the second member disappears in consequence
of the third of the equations (2’).

Let us observe by the way that the numbers of rank 7, 71. 72. -- 741
of (C, form the first terms of a recurrent series with the third of

the equations (2) as equation of condition and thus — for « as
the variable — with (1—.)* as denominator of the generating fraction.

In order to cause the representation to remain as simple as possible
we have supposed the curve C, to lack all higher singularities. For
the influence of the latter we refer to the above-mentioned essay of
VERONESE.

The Pxrtcxer’s formulae given here shall be applied elsewhere to
the ease of the curve C, of order 27—! forming in S, the section of

Ete
n—1 quadratic spaces &, .

Mathematics. — ‘“‘( SYSteiis of CONICS belonging to involitions On
rational curves.” By Prof. Jax pr Vrirs.

1. We suppose the points of a rational plane curve C” to be
arranged in the groups of an involution /*,s>>5, and bring a conic
(* through each quintuple of points belonging to a_ selfsame
group. The system |(*| formed in this way has evidently no double
right lines, so that 70. So between the characterizing numbers
u,v, d exist the relations 2r=a+d and 2u=r: so we have

=2y and d= 3p.

( 506 )

The numbers of pairs of lines can be determined in the following
way. Let P,P’, P" be three points of the same group of the J*;
we make P to correspond to each of the points S which the right
line P'P" determines on €”; as to P belong 4 (s—1) (s—2) pairs
P',P" each point P in the correspondence (/, S) is conjugate to
(s— 1),.(n—2) points S. The pencil of rays having S as. vertex
determines on C® an /”—! having (n—2)(s—1) pairs P',P" in com-

mon with /%; so to each point S correspond (7—2)(s—1)\(s—2) points P.
When now two conjugate points 7, 8 coincide, three points P, P', P"
lie in the same right line and each of those points is to be regarded
as a coincidence of the correspondence (PS). So the number of these
collinear triplets is (#—2)(s—1),. The bearer of such a triplet forms
with the connecting line of two points belonging to the same group
a pair of lines of | C*|; consequently '

dS = (n—2)(s—1),(s— 3), = 6 (n— 2)(s —1),.

From this ensues again

wu = 2 (n—2)(s—1), and r = 4 (n—2)(s—1),.

2. On each conic of the system |[C?] five points P are lying and
(2n—5) points Y more. Each point of C” can be regarded as a
point ? and as a point XY. Of the « conics through that point there
are (s—1),, connecting ? with four points P? belonging to the same
5\(s—1), contain besides a quintuple
of points of the /* and (2n—6) points X’ more, which we shall adjoin

eroup; the remaining (27

to X. The points ,.X' evidently form a symmetric correspondence
5)(s—1),. Each coincidence
of (V,N') furnishes a conie of RGF touching C”, |

Besides these 2(2n—6)(2n

with the characterizing number (27—6)(27

D)(s—1), conies there is a group of
touching conies each of which connects a coincidence of /*s with
three points belonging to the same group of /*; their number amounts
to 2(s—1)(s—2), = 8(s—1),.

But there is still a third group of tangential conics. When a point
P coincides with one of the points Y, the conie touching C™ in
PX represents two curves; so in that point C” touches likewise
the envelope of [C*|. Now to each point P belong (2n—-5)(s—4),
points .Y, whilst each point VY is conjugate to 5(2n

D)(s—1), points
-5)(s—1), conics. By

P. Therefore the third group contains 6(2n
counting these double we arrive at

[2(2n —6)(2n—5) +- 8 + 12 (2n—5)|(s—1), or 4(n —2)(2n—1)(s—1),
conies touching €”. This number ean be easily controlled; for, a
curve C" of class 4, is touched by (4 -+ mr) curves of a system

( 507 )

(u,v). If for 7% we substitute here 2(.—1) and for p.r the above-

‘

mentioned numbers, the number 4(—2)(2n—1)\(s—1), appears again.

3. Let us still consider the correspondence between a point Y
and a point P, belonging to the group of /*, five points of which
lie with VY ona C?. Each point NX is conjugate to (2—5)(s—1), . (s—5
points P,; reversely (s—1), .(2n—5) points NX correspond to P,.
If two conjugate points coincide we have evidently a conic bearing
six points belonging to a selfsame group of /*. As each of those six
points can be regarded as a point \ the number of those conics is
equal to the sixth part of the number of coincidences of the corres-
pondence (/,, \), thus equal to (2n—5)(s—1)..

4. If every group of an /* contains less than 5 points, there is
no indicated system [(C*]|. In that case we can take (5
points A,, f£=1 to (5—s), and join these by a C” with the
s points of a group of the /*. To find the characterizing number u
for the system | C*} obtained in this way, we consider the conics passing

s) arbitrary

through the points A; and moreover through the arbitrary point «1,.
2n

They intersect C” in the groups of an involution /,—; of order

» ts
2n and rank (s—1). Now two involutions es and fe. have according
to a theorem of Lr Paice’), (n,—/,):,(n,—h,)., groups of (4, + /,)
2n s
points in common. Applying this to the involutions /;_,; and /;, we
find that through A, pass (27—s+1) conics containing each a group
of the 7s. So w= (2n—s +1), vp = 2 (Qn—s-+1) and d = 3 (Qn—s+1).

». For s=2 three fixed: points A,, A,, A, are wanted. The
pairs of lines of [C?] form two groups. A figure of the first group
consists of a right line A; A; and the line connecting A, with
the point which forms with one of the » points of intersection of
(™ and A, A; a pair of the /*. In a figure of the second group the
line containing a point A, bears a pair of the /*. The number of
pairs situated on rays through A,, amounts to (7— 1). So we find
JS=3n + 3(n— 1) =3(2n—1), in correspondence with the general
result given above. -

For s=3 we have to take two fixed points A,, A,. The pairs of
lines form three groups. In the first place there are (z— 3) col-
linear triplets (see § 1), of which the bearers through A, A, are
completed to a pair of lines; secondly each point of intersection of

1) Sur le nombre des groupes communs 4 des involutions supérieures, marquées
sur un méme support (Bull. de l’Acad. Royale de Belgique, 3e série, t. XI, p. 121).

( 508 }

A, A, with €" determines a group of the 7* of which the remaining
two points furnish the second right line of the degenerated C? ;
thirdly each of the points A,, 4, is collinear with 2 (#— 1) pairs of
the /*. So we have d=n—24+n+4(n — 1)=—6(n —1).

For s = 4 we want but one fixed poimt A,. There are 3 (7 — 2)
collinear triplets and 38 (7 —1) pairs of lines, where each of the
right lines bears two points of a group of /*:; so here we find
Ye nw—2)+3 = 4) =n 5).

6. The correspondence X. iX’)> has’ for s< 5 the characterizing

number (27— s) (27 —sx— 1): in the correspondence (P?, X) each
point P is conjugate to (27 —s) points Y, each point V to s (2m — s)
points 72. As /* contains 2 (s—1) coimeidences the number of conics
of [C*] touching (” is now represented by 2 (22 —s)(2n—s—1j3+
+ 2(2n —s)(s +1)+ 2(s— 1) = 2(2n —1)(2n— +1), which corres-
ponds to the value the namber (/;4 + iv) possesses here.

The correspondence (.V,.\’) for an /° is of order (22—?*) (2n
it has (2n —.2) (Qn

3):

3) pais in common with Z*.
So the system |C*| contains (i — 1) ‘22 — 3) conics bearing each

two pairs of the quadratic involution.

Mathematics. — ‘Fundamental involutions on rational curves of

order jive” by Prof. Jax pr Vrixs.

1. If the points of a rational curve of order five, C%, with six
double points Dz (= 1, 2,3, 4,5, 6), are arranged in the pairs P’,
P" of an involution 7’, the line P?' P" envelopes a directing curve
of class four. For, the indicated involution has four pairs in common
with the central involution of order five, which is determined by the
rays of a pencil. If a pair of the /* is formed by the points J’,
and )", |ving in DY, on the two branches of the C*, the directing
curve breaks up into a curve of class three and the pencil of rays
having its vertex in D,. If a second pair consists of the points D’,
and )",, the real directing curve will be a conic. Then we evidently
get an /* given with C*®; we shall therefore call it a Jundamental
involution. It is determined by the pencil of conics with the base-points

BD. DD. Dy.

2. The bearer of a pair of points of the fundamental involution

I’,, meets €* in three points more 7", 7", 7" forming a group
of a cubic involution. For, of the tangents out of a point 7” = P'

i
ian

( 509 )

of the C* one goes to point 7", whilst the second contains a pair

of the #,, besides the points 7", 7" conjugate to 7, so that 7"
appears in but one group of the correspondence (7, 7"). So the

directing conic g,, is at the same time the directing curve for the
BY

fundamental involution /’,, composed of linear triplets 7', 7", 7".
The tangents out of a pont P?' of the C® to g,, will coincide only
in the case that /?” is situated on the tangent in 7” to CC®. From
this follows that @,, touches the curve C® in five points; it is easy
to see that these pomts are the coincidences of the correspondence

(2, 3) in which a point 7? corresponds to a point 7”. Besides the

tangents in these points to be counted double C°® and ¢,, have six
tangents more in common, which are determined by the coincidences

2 3
ie sand: Be

3. The cubic curves connecting three triplets of the /, with

the six points YD, determine a pencil! of curves determining the

3
groups of this involution. A pair of the /, consisting of the points
D',, D',, the eubie pencil (C*) will contain a curve having in D,
a node; but from this follows that the remaining curves must touch

each other in D,, so also in D,. The triplet of the /’,,, of which

the bearer ¢, passes through MY, determines in the pencil (€") a

degenerated curve consisting of f, and the conic /,,,,, through the
points D, (k= 1, 2,3,4,5). A second degenerated curve consists
through D,. From this ensues that

DS]

of the conic £,,;,, and a ray tf,

the ninth base-point of (C*) lies in the point of intersection of ¢, and

> ”

(whilst “%,..,, 18 touched in’D; by ¢, and &,,,,, in D, by €,; 4

6 6
goes without saying that in VD, and VP, all curves of (C*) have the
lines ¢, and f, as tangenis.

4. We consider the two fundamental involutions /, and F,,,

3 3
besides the involutions /,, and /,, determined by them and we

inquire after the meaning of the common tangents of the directing
conics ¢,, and g,,.

2 3
The involutions /’,, and /’;, have besides the pair of points D’,,

( 510 )

also by re

& pair in common which we shall indicate by P',,, P",, and
Py oe:

also the points 7”,,, 7,,, 7°",,. which can just as well be indicated

Qn the connecting line + of these points are

by the symbols 7'",,, 2',,, P";,:; consequently ¢ bears also the pair

a6
9

2
which /’,, and /’,, have in common (besides D',, D",).

3 3
The involutions /’,, and /,, have four pairs in common among

which the pair /)',, D",; the remaining three lie on three common

tangents of g,, and g,,; the fourth common tangent is evidently the
above mentioned right line +.

5. Let Sp, be the point of intersection of C® with the right line
D, i. From the preceding ensues that the lines S,,.S,,,S,,S,, and
S,,S,, determine with the lines ¢,, ¢, touching the conies /,,.,;,

kies1¢ Nn D., D, a conie ¢,, touching C* five times.

Besides the fifteen pairs of fandamental involutions Fu, Fa we
still notice the 6 central fundamental cubic involutions intersected
by the pencils of rays with vertices D,;. For these the directing
curve (being for a general /* of class 8) breaks up into the vertex
to be counted three times and the remaining five points D.

Physics. — “Vhe determination of the pressure with a Closed air-
manometer. By C. H. Brixkwan. (Communicated by Prof. J. D.
VAN DER WAALS).

For the determination of the pressure with the aid of closed
urmanometers we may avail ourselves of AMAGat’s wellknown deter-
minations of isotherms’). In table 5 and 10 (1.c.) four air isotherms
are given for pressures ranging between LOO a 3000 ats. For pres-
sures, smaller than 100 ats. we have to extrapolate. I have thought
that I could justly avail myself for this extrapolation of the equation
of state of VAN DER WAALS:

i) (1 + a) (1—4,) (1 + at) a

if me} wa

if / is taken here as a function of the volume.
The variability of 4 with the volume has been interpreted in two
Ways: I. as a quasi change in consequence of the partial coinci-

) Mémoires sur |’élasticité et Ja dilatabilité des fluides jusqu’aux trés hautes
pressions. Ann. Ch. Phys. Ge s. 1893.

(514 )

dence of the distance spheres, 2"¢ as a real change causel by
compression *). !

At first I thought that I had to make use of the formula, derived
by Prof. van pbeR Waatrs on the second supposition with the aid
of the theory of cyclic motion; when testing this formula to the
hydrogen isotherms of Amacar, Van Laar?’), found it to harmonize
well with _the observations. In the calculation we are, however.
confronted with the difficulty that for the accurate determination
of the constants 6, and 4, a preliminary accurate knowledge of
the a is required. It not having been ascertained to which of the
two causes the variability of the 4 is due, and it being improbable, that
the first mentioned cause can be left out of consideration, | have used
the formula derived on the first supposition for the variability of the 4:

; 2 3
b = by Rie "8 4 a“ = yt Wetan yh
u t U \

Of the eleven correction terms which will occur for spherical
molecules*), only the first two have been calculated. I have confined
myself here to three terms. By a comparison with the values of
p and v observed by Amacat at 15,°7 C. we shall have to deter-
mine the values of «a, 4,, ¢, 3 and y which agree closest with the
observations between 100 and 3000 ats. In order to avoid when
applying the method of least squares, the elaborate calculation of
five normal equations with twenty coefficients, | have determined
the most probable values of « and 6, with the aid of assumed

»)

. vo .
values of a, B and y. For this purpose I put @ = --, which value was
5

found according to two different methods by BonrzMaxn *) and by Van
pER WAALS Jun.*); further G=0,0958, which value has been calewlated
by van Laar’*) and adopted") by Botrzmaxn; quite arbitrarily I put
y == 0,01 and I assumed as approximated values of a and b, a = 0,002
hy = 0,0020"). So if Aa and 44, are the differences between the

1) See Van per Waats, These Proc. V. June 27 1903, p. 123.
= 4 » » Botrzmann Festschrift p. 305.
#) These Proce. V. March 28, 1903 p.- 573.
5) Van Laan, Evaluation de la deuxiéme correction sur la grandeur }, Arch.
Teyler, série II, t. VI 1899 p. 48.
4) Gastheorié If p. 152.
5) These Proc. V. February 28 1903 p. 487.
6) These Proc. | March 25, 1899, p. 398. Adopted namely for the calculation
of his second correction term, which has the value
323 957
3 = — — —_.,
2 8960
Here @ has the value 0,0958 calculated by van Laar so @! = 0,0369. (Febr. 24, 1904).
7) In Cont. I a = 0,0037, 6 = 0.0026 is derived from the observations of Reqnavtr.
When multiplied with 0,76 with change of the unity of pressure, the above values
are obtained.

( 512 )

most probable and the assumed values of a and 4,, 4 p the difference
between the observed pressure and that calculated with the aid of
the five assumed constants, the normal equations become:

(0p)? Op Op Op
sae | gos (OP, Ol es gee
ial? oe ee

Op 0 >} ri) ee 0 )
( SS {Op 2 = oy Ss, SS | I re es iat
kes | da 0b, | erty | 0b, ae ae Ob,

By solving them for seven observations between 100 and 400 ats.

fehiere the influence of the arbitrary values y, 3 and @ is not yet
very great), we find: @ = 2410 ; b, = 1906 *).

In the third column of table I the difference between the observed
values of p and those calculated with these new values of @ and 6,
have been given in per cents of p: the agreement is satisfactory up
to 1000 ats. In order to find values of @, 3 and y, which give a
better agreement for higher pressures, I have calculated the 4 for
volumes 3209, 2060, 1648 and 1466 (with corresponding pressures
of 400, 1000, 2000 and 8000 ats. *) from the equation of state with
the aid of the just found a. Let us now write the correction formula
of the 4 in this form:

1 1 1 1
Bo IS @ bb = .B. 6,7. + —.y¥ 6° =A
b, r vn? ; ve

Then with the aid of those four sets of values of 4 and v we may
calculate from four linear equations with four unknown quantities
ah, a, andy, which with a= 2410 for volumes 3209, 2060, 16438
and 1466 yield values for p, which agree perfectly with the observed
values. We find 4, = 1863, a4 = 0,3616, 8 = 0,1330, y = 0,05176 ;
with the aid of these values of e, Bandy we find now the values
of a and 4, which give the best agreement with the observation, by
applying the two normal equations to ten observations between LOO
and 1000 ats. The values found in this way and the deviations of p
ealeulated by means of them are given in the fourth column of
‘table I; now the agreement is satisfactory up to 2000 ats. Only by
changing 3 and y we can obtain a better agreement for the highest
pressures. New values of 3 and y are now found from the correction
formula for the 4 with the aid of the just found values ofa, b, and
«, and these new values make the agreement at 2000 and 3000 ats.
satisfactory.

1) The values given for a, 4 and v must be multiplied with in

2) The values of p, given by Amacar for different values of 7, have heen borrowed
up to 1000 ats. from his “‘methode des regards’, those from 1000 to 3000 ats,
from his “methode des contracts électriques”’.

SS Oa

(3t3 )
TABLE I
a | -240 | 2358.6 | 2358.6
}
b, | 41906 | 1852.0 | 1852.0
2 | 0375 | 0.3616 | 0.3616

z | 0.0958 | 0.1330 | 0.41325

7 O01 0.05176 | 0.05083 |

gl oie ioay ee a eA 1 OA |
MnO 200A | Ped Pevoaiay 0.8
sit | 6900 |. — 0.4 | oo | oo
3913 | 300 | 04 0.2 0.2

S00) 0D =e”) gh [es Oey |
9999 | 500 | O4 | O28 | 0.2
2060 | 1 — S| OF of 52.0.0
ry eg ae aes ee ey a
1643 | 9000 | fig i 0.8 | 0.3
1542 | 00 | —125 1-09 | 02
1466 | 3000 —4 O57 bi 06

These values and the deviations of p calculated with them are
given in the fifth column of table I. The deviations are of the same
order as those which Prof. KameriincH OnnNegs *) obtains when repre-
senting AmaGat’s observations by an equation of state with six
constants in the form of a series.

A reliable extrapolation for pressures below 100 ats. has now
become possible; at a temperature of 15°,7 C. the pressure correspon-
ding to every volume can be determined with the aid of the five
constants.

If the air-manometer is placed in a water bath, the temperature
of which is kept constant by a thermo-regulator, a temperature of
20° or 25° will be preferred to 15°,7 C. It is therefore of importance
to ascertain, whether also at those higher temperatures the equation
of state with the same five constants yields values which sufficiently
harmonize with Amagar’s observations. It is to be expected that
this will only be possible within a limited range of temperatures ;

1) These Proc. IV June 29, 1901. p. 128.

( 514 )

1 De ee 7 -
for the quantity — derived by Amacar from the isotherm is not

Ot,
constant, which points to the fact that by assuming the constants
independent of the temperature, no perfect agreement with the
observations will be obtained.
By means of the formula:

Op (1. +a) (1—d,). a

Ot, a
which is derived from the equation of state, when the constants are

Op
put independent of the temperature, I have determined the -— for

Ot
different volumes, and compared these values with those found by

AMAGAT.')
A Dray eee

7 (0°) & (o°—100°) ~ ee
(observed) (abseeutcd)y Sal Cores
9730 100 | "0/2695 SO ciass a rene
5050 200 | 1.105 | 1.073 | 2.9
|
3658 300 1.800 | Jct 750 a) Pees
3036 400 | 2.470 eee 2.5
2680 509 | 3.085 ie a, Ue
2450 £00 | 3.718 Li) OAS 2 ais cig
dp 1 é
In the third column of table II the values of ap, we given derived
p

by Amacar from his determination of isotherms at 0° and at 100°, in

the fourth column the calculated values, and in the fifth the devia-

) | Op

tions expressed In per cents ot sae
Ot,

_ Op
If by means of the formula for 5, we calculate from the pressure
(

.
at 15°,7 the» pressure at 25°, then the deviation of 0,9°/, in the
Op .

5, passes into one of 0,04°/, in the pressure for the volume 9730.
(

The deviation of the p introduced in this way, is smaller than

l) |. c. Table 26.

( 515 )

those which are mentioned at 15°,7 in table 1; from which follows
that the accuracy of the values of p at 25° derived from the equa-
tion of state is still of the same order as those which are calculated
pt ae bce

In table HI the values of p are given at temperatures of 15°,7,
20° and 25° C. for different volumes calculated from the equation of
state with the constants mentioned in the fifth column of table I. In
order to render the calculation of pressures possible also for other tempe-

Op
ratures, the calculated values of — are mentioned in the fifth column

Ot,
of table III. (p. 516).

As unit of volume we have taken the normal volume, i. e. the
volume which the air would oceupy at 0° C. and 1 atm. (0°, 45° N. B.).

So it is possible to represent an isotherm for a large range of
densities, with the aid of the equation of state and values for the
constants @ and £, differing little from the theoretical values.

These differences will be chiefly determined, besides by syste-
matic errors of the observations, by 1st- the non-spherical shape of
bi-atomic molecules, 2°¢4 the possibility of a simultaneous real
diminution, which could then explain at the same time the slight

Oat Op
variability of —.

In table V the influence for different densities of the three
terms of the correction formula for the 6 is rendered. In the fourth,
fifth and sixth column the values are given, with which the 6, is
diminished in consequence of the correction terms with «@, 8 and y,
expressed in per cents of 6,; in the seventh column the decrease
of b, in consequence of the three terms together is given in percents
of 6,. In the eighth column the influence of the decrease of 6, on
the pressure is represented ; if we calculate the p from the equation
of state keeping 6 constant and equal to 4,, then this p will be
greater than that calculated by means of the decreasing 0.

The difference between them is given in percents of p. With a
volume of 0,02 already the decrease of 6 will manifest itself in a
decrease of p.

It appears that the application of several correction terms would
be desirable for the smallest of the volumes observed by Amagat.
For larger volumes, however, they have no influence, and their
theoretical values still being unknown, I have thought that in this
case three terms would be sufficient.

Several observers (i. a. Kunnen, Quinr) have made use of the air-
isotherm, determined by AmaGaT as early as 1864, for pressures

34
Proceedings Royal Acad. Amsterdam. Vol. VI.

( 516 )

PAB LB: SEIT 4).

eS Geen) | 20%) | peor) Ls
| 9 | dtr
ae a eee -5.45 | 0.018
10 40.54 | 40.70° | 1089 0.037
| 45 15.79 16.03 16.32 0.057
20 21 02 HS! |) OAs 0.076
| 25 | 26.24 96.66 | 9744 0.096
| 30 | 31.4 | 31.95 | 9258 | 0.446
fen eo 21 63 G5 | 3793 | 37.92 0 137
40 | Me | 42.52 | 13.31 0.158
| 45 | 47.02 47.79 48.69 | 0.179
50 9291 | 58.07 54.08 0.201
esis sy tess ee 8.36 | 59.48 | 0.994
60 62.58 | 63.64 34.87 0.246
65 67.78 | 68.94 70.28 0.269
| co | 97 | 74.98 75.69 0.293
75 | 7848 79.54 81.13 | 0.317
80 | 83.39 | 84.86 | 86.57 | 0.344
| 9 | 98.63 | 90.20 | 92.03 | 0.366 |
90 | 93.88 95.56 97.52 0.291
95 | 99.15 | 40095 | 410303 | 0.447
100 | 104.44 | 106.34 | 108.56 | 0.443
105 | 109.76 | 14.78 | 114.43 0.470
110 | 115.40 | 4117.94 | 119.73 0.497
45 | 190:47 | 199.73. | 195.36 0.525
| 420 | 195.8) | 198.97 | 431.04 0.554
| 196 | 131.33 i 133.84 | 136.75 | 0.583
| 430 | 436,82 | 139.46 | 449,52 | 0.619 |
135 | 449.36 | 415.42 | 448.33 0.642
| 440 | 447.91 | 450.80 | 454.47 0.672
| 145 | 453.53 | 456.55 |. 160.07 0.703
| 150 159 91 162.38 166.05 0.735

1) The error of calculation, made in the p by Mer US HOe linearly for inter-
mediate volumes, is smaller than 0.01 atm.

( 517 )

ere) ae’ TV.

a hier he a il |

» — | p (45° 7 — | = | ee | = | Ig — 2 | Ap
100000 | 10.54) 0.02 | 0.67 0.00 | 0.00 | 0.67 | 0.0 |
20000 | 52.21 | 0.09 | 3.35 atl O00 | 3.4 04
10000 | 104.4 | 0.49 | 6.70 “18 0.03 | 628 | 9 |
| 4504 | 249.5 | 0.44 | 1487 | 9.941 0.95 | 12.98 | 16 |
| 9899 eer | 0.66 93 73 eer 1.44 | 19.46 | 59 |

9060 | 999.9 | 0.90 | 32.51 |—10.71 | 3.69 | 25.49 | 353

1643 1994 1.13 | 40.76 |—16.84 |“ 7.98 | 31.90

1466 | 3000 | 4.26 | 45.68 | 21.15 10.25 | 34.78 |

between 25 and 85 ats., and a temperature of 16° C. As unit of volume
the volume at 16° C. and 1 atm. has been used; so in order to be
able to compare these results with those found later, all the observed
volumes must be multiplied with 1,05875, and we can also calculate
the pressure at 15°,7 from the pressure at 16° with the aid of the

Op
= calculated before.

It appears in the graphical representation of pv as function of
a that the last series of observations, starting with 100 ats., can
v
by no means be considered as a continuation of the former series
which ends at 85 ats, so that it is impossible to use the two
series together.

In the second column of table V the results of the measurements
in 1864") are given, reduced to 15°,7 C. and to the normal volume as
unit of volume; in the third column those which have been extra-
polated in the way described above from the observations of 1893:
in the fourth column the differences have been given in percents.

For the following reasons the later measurements seem more
accurate to me. 1 The differences between two series of determina-
tions found in the later measurements (‘‘méthode des regards” and
“méthode des contacts”) amount to at the utmost 0,1°/, at 15°,7. 224
The manometers of DrscorrE used in these determinations have been
compared and the deviations are not great, specially for high pres-

Al. c. Table IL.
34%

( 518 )
PAD Loh sv.

|
p (15°.7) | p (45°.7)

eit 1864 1893 | ts |
ye boss a ! |
| 39820 | 26.29 | 26.36 | 0.97 |
31790 | 39.85 | 32.96 | 0.33 |
| 26440 | 39.43 | 39.58 | 0.37 |
| 99610 | 46.00 | 46.92 | 0.48 |
| 49760 |~ 50.57 | 59.84 | 0.54
| 47550 | 50.14 | 59.45 | 0.53
15790 | 65.714 | 66.04 | 0.50. |
1300 | 72.98 | 72.69 | 0.56 |
13140 | 78.85 | 79.38 | 0.64
| 12140 | 85.42 | 85.88 | 0.53

sures, whereas the determination of the pressure in 1864 with
an open manometer 65 meters high has been very difficuit. 3°* Com-
parison of the accurate hydrogen isotherm of ScuaLkwiJk (Diss. 1902)
with the values extrapolated from AmaGat’s determinations gives
differences of about 0,1 °/,.

Chemistry. — “On the shape of meltingpoint-curves for binary
mirtures, when the latent heat required for the mixing ts very
small or =0 in the tivo phases.” (3° communication). By
J. J. van Laar. Communicated by Prof. H. W. Baknuis
RoozEBOOM.

I. By the side of the dea/ case, that the latent heat of imieing in the
liquid phase = 0, whereas it is « in the solid phase (a = 0, a! = @) —

so that the so/// phase consists only of one component — there is
another case, also idea/, viz. that the latent heat of mixing = 0 in

both phases, or may be neglected. (e=0,¢=0). The solid phase
consists then of the two components in a proportion which is ¢com-
parable to that in the liquid phase.

The former ideal case is that of the processes of solidification,
in which no solid solutions (or mixed erystals) are found, the latter
may be appropriately called the ideal case of the mixed crystals.

To consider such ideal cases has always this use — apart from

( 519 )

the simplifications in the considerations and calculations — that these
cases may be adopted as the norma/ ones, from which all the other
cases are to be considered as deviations in greater or smaller degree.

In our ease the consideration of the limiting case «—0, «a —0
offers another advantage, viz. that much of what will be deduced
in what follows, may be transferred with some restrictions to the
boilingpomnt-lines for ideal liquid and gaseous phases. For the thermo-
dynamie relations of equilibrium agree perfectly, when the distinguish-
ing feature between the two kinds of equilibrium, viz. the degree of
the mutual influence of the two components in each of the phases has
vanished. The difference consists only in this, that for the processes
of melting the pure latent heat of melting may be assumed to be inde-
pendent of the temperature, whereas for the processes of boiling the
latent heat of evaporation will decrease with increasing temperature.
Only in those cases, therefore, in which the boiling points of the two
components do not differ much, the following considerations may be
transferred to boilingpoint-curves of liquids, where @ may be put
= 0. When the difference between the boiling points is larger, this
cannot be done any more.

Il. The fundamental equations (2) of my jirst paper') become

(3 = “=0, f=5= 0) simply:

qi qi
a i T
SS ee
Bd 1l—e# AT: a
1+ log 1 + —— log ——
1 er, qs wv

It is now possible to eliminate «', and to express « explicitly in
7, and in the same way to express the quantity «' explicitly in 7’
after eliminating x.

In the first place we find:

a oF gee) eS
| ee ENE 7) z Pay ay x
== @ 7 —== 6

js. aL

dee Sed)

so that, when for shortness we put:

Cy a 1 9. (1 1
es ey} ’ a ea ear a Ne ele
y tan Oi ) ike Ge of is (3)

we get, in consequence of (1—za') + 7 =1, the relation:

Gye 14s OSE.

1) These Proc. VI, June 27, 1903, p. 151.

In the same way:

(l—a')e ~+ een —— wale

From this we solve:

y a
pt pe ae

Al 28 eae 1) | 49g

ae é <= (4

or, in a form convenient for the calculation:
i;
Yn | a
a ae er iS ae (4)
A al 2 1
é —
From these equations, and also from equation (4) of the first com-
munication (in which w, —4q, and w,=4q,) we find easily:
dT fit a—a' ale ~ ote lie a—x'

ea i (1-2')q, +2'9, , wv (1-2) ete ae (1-«) 9, +24, a’ (1-2')
For the initial course of the meltingpoint-curve follows from this

ee — rye
ei ( ar Rl’? x
--"(.-()): (0) =)
< U/) 9 dex 0 q1 a 0

e) RT,
dx /, q,
or, in connection with (2):

AT RT? pe 1T 1 iMag
(-) =- = (0-9 (B) =e
dx 0 1 dic 0 "1

when we put:
ft. -4
a G = 7 ) = 6, . . . . . . . (6)

3
The jinal course (for the lowest temperature 7,) is found by
changing the letters, so, by putting further 1—a=y and 1—2’=y’:

ao at Ee) =
dy }, 15 yJod > Mi, gee ae

i.e. taking (2) into account:

dT RT,? dT Te eS a
GJ= i Gla
dy 0 qs dy 0 qs

Paw 1 a.
4 Coa alte ..g Sa

6, and @, being both positive quantities (7, is always smaller

when putting :

6 i oe 4 =
than 7,), e' ande’* will always be >1, e ‘' and e * always <1.

. gab okt a dT dT
From this follows, that the quantities 7 and aa will always
AL
0 0

) GE Ales Ge
er 3 +

:
h
:

; : dT dl ea
be negative, the quantities (|) and & always positive. For the
Y 7. Y So

latent heat of mixing g, and g, can never become negative.

So in the ideal case a =O, a =O the meltingpoint-curve always
begins to descend at the highest temperature, and to ascend at the
lowest temperature, so that in this case a minimum is excluded.
This eS also from the fact that the condition for a minimum

is >=

occur, a ihe meltingpoint-curve will therefore gradually descend
from 7, to T,. ,

That a maximum cannot occur in any case for normal components,
whatever value @ or @ may have, — provided @’ be larger than a —
has been proved already in my first communication (loc. cit. p. 156).

The equations (5) and (5a) give rise to the following discussion.

‘7?

—T,
— (loc. cit. p. 168), so that for 8’ —O this can never

, ate dil
In_ the limiting case g, =0 (, finite) we have 2 ie — wn,

dT dT™
== = =a so that the two meltingpoint-
dx dy dy!

curves > will Saiecicn to the = A (fig.1)

|
'
'
'
'
'
U
!
'

—~
\ ee

dT d dT ;
For 9g, = ®, Pe ae oF i ill approach to 0, (= ) to w (on

RE -

5 dT Viale
account of the term e’), but a) to a limit, viz. {7 a8 é
dy q:
e 0 2

converges to 0. This gives the limiting-type 6 (fig.1).

‘dl dd 1
When q. = 9 = 0 (4, finite), we have = A) and = eae a)
LYE y .

1T :
and ag, —g. The meltingpoint-curves approach to the type C
0

dy
(fig.2).
dT RE aD
If, however, g, = ©, then & a : -|=—o, and
oo Ee qi de: :

dT dT r dT
—— ) and { — } approach both to 0. Now {——] approaches to a
dy /, dy}, du),

limit, as e ° converges to 0. This gives rise to the limiting-type
D (fig.2).

We shall see presently, that according to g, being greater or
smaller, the final course for 7’= 7 (’) in the case (’, and the initial
course for 7=/ (x) in the case D may vary as to their curvature.

All the other cases lie between these extremes, but we shall see
that there can yet be a great difference in course as to concavity
and convevity. In order to form an opinion on this, however, we
must write down the second differential-quotients.

Ill. We found for them in our second communication ') for 7 = 7,,
when « and a’ = 0:

as w
Cole ae a o ees, (") Koch ae ||
od Lat
(ce) = 1 (2) G 47} ae 1 | (,+4T,) — 2 Q.- @) ||
O27 oo 9. NG

; ; & —4 é : ;
in which (=), is e * according to (2) and (6). For the corresponding
v

dT
expressions for 7, we find by the same changes as for °F
> x

(see above) :

tg 1 Mech ae bb
(2) (em () oven]
OJ a ols Yo (Ta)
21 d1 y
m=-(5 ;) (4, Poa (qa, +47,) +2 (4-4)
dy 0 Y)

in which (£) — ¢" according to (2) and (6a).
es fe

That these equations can give rise to a point of inflection in the

g } L
meltingpoint-curve, so even at @’ = 0, | have already proved in my
second communication (loc. cit. p. 256—257).

1) These Proc. VI, Oct. 31, 1903, p. 256.

E eT
For a concave beginning (i.e. turned towards the A-axis) oc
‘ . ‘ ax

La dz? dz

positive. On the other hand this quotient will be negative for a conver

Cah AE . 2T dT
is alwavs negative { for ; becomes larger negative }. Hence ;
: = ik

heginning. In the same way for De sF ek

gry dT
With a concave end —~— will again be negative | —— becomes
dy? dy
oe aT a eran
- — negative. For a convex end this
dy? dy
quantity will be positive. We have therefore the following transition

conditions.

smaller positive ) so

concave | ae 2 3
{ hecinning 2(9,-q.)+(9,-47)) (= 8) 20

ts or f=)
i convex | <A

: coneave | | ren — A

1 Kor 2 = fa 1 —2(9,-9,)—(9,-4T,) -e ARO
J) convex oe (2:-9.)—@ ) WS

2 concave Tene —§, >
» TF lax’ £2(q.-9,).—(9,+4T7,)(1-e

Pile For: P= f(a bees beginning2(9,-9,,—(¢.+ 47) -e 329
3 s concave Fay <i,

ee Por. — F(z nda. *“-—2z(9g— +47) (e*-1 0
I or =F @ lg enc (9:-9a) HQ. +47;) (e ) S

or in another form :

Cn ek Tess} 2(q,44T
I I; = 47, = (7. = a Ill qs — (q.+ : )
trate a ie
(8)
VEE 2(q, +42
a ay gg arp ol a
a as | > ra

The different regions with their limits, which occur in these
conditions, are represented in fig. 3 (Plate). The figure holds for
T,='/, T,, the values of g, and q, are expressed in multiples of 7;.

Let us subject the limiting-curves to a closer examination (see fig. 3).

a. Curve I, viz.
2(q,—417,,) (81)
1té:

According to (8) all the curves 7’7= f (2) with a concave beginning
will lie above this curve, with a conver beginning below it. For q,
must then be respectively larger or smaller than the values given
by the second member.

1p See Se

( 524 )

The curve will also yield g, = 0 for g, = 9, for which e? —1.
The initial direction is given by 9, = 4. (45°). Further for q, = 47,

ts 6,
is evidently also g,=47,, and for q,=%, e becoming = ©,»

g, will again be 47,. The curve I will therefore run pretty rapidly
asymtotically to the straight line g, = 47, for higher values of 4,

and will show a mazximum somewhere past g, = 47,. (JM, in fig. 3).

, ‘de
This maximum is represented by te =)
C

oe age 2 ee ee

J Yo 1 1 . a) 7
as: 02 = — wan according to (6). We have then:

2 1/

—fo . a :
(i+e ) Os OE Toe aa

3
= 6,
or Ge '’= 14 4T,—,
JT
(R= 2) Bie eae
or —- \ § — = 4 :
or Ch : -

From this we may find @, by approximation, so also q,,

is found from (84). As 9g, — 47, ae + Bw we have:

q = 4t $ate Par, 422 (4 —1-47,),

LAU a
2 6, ; vB
- —— 6) y 9 Vo
hence g, = 2q, — 47, —2—,
6,
” : 4 te
| ig gd. = 2a. — eth ees
71 “4, Te i
Now fig.3 holds for 7,—='/, T,, so (8a) becomes:
=e
GO, 4 FF

yielding #0, — 3,05. Consequently 9, = 26,7, = 6,10 7;.
according to (8b) 9, = 29, — 87, = 4,20 T,.

(8a)

and 4,

(80)

Further

Of the curve I (comp. 84) I have determined the following points

F 4 q:
With phe at gs 80. haat 0, == =o

Qo 1 Pile? 1.65 bg, = 1,78 2, |\9,=7T, | 7 = 88,1'lg, — 4,17 7,
gre | 2,72 292° || a 54,6, 114
3 A 4,48 Ge a 20 te ee oe
bf ae Falko | Pipes} 15 ,,( 1810 | 401
Ge FZ 20,1 | 4,19 ,, | A | en 22000 4.00

Really the maximum lies just past ¢,—=67,. (We saw already
above, that for g, = 47, also 9g, = 47;,).
6. The curve II, viz
2(9,—47,)
Bake

This curve separates the curves 7 = (/ (7) with concave end (left
of this curve, because g, is then smaller than the second member)
from that with a convex end (right of the curve, where q, is larger).

For ¢,=0 also g,=0, as 6,=0; (imitial direction again
q, = 9, (45°)); for ¢,=4T, also g,=4T,, and for ¢,=—, g, will

(841)

approach to 29, —47,, because ¢ ‘ approaches to 0. The mating

direction of the curve II is therefore given by 7, =24,, or q,='/2 4:
(26°,5). met

It will necessarily cut I. When 7,='/,7,, this point of inter-
section S, lies somewhat on the left of the maximum J/,. It is
found by combining

2 (q¢,—4T. 2 (q,—2T.
qs — AT. =f CP 2 CA )

and ee :
92/97, = rE 5 oF —h/97,

lte lte

By approximation we find g, = 5,907,, q, = 4,197, .

The further calculation leads to the following summary.

9, = 1T,\e '=0,61 |g, — 0,76 T,|\\q =8 Te - * — 0,02 (9, = 13,8 7,
as 0,22 3,64 ,, Le bad 0,011 rege
sae 0,135 Behe aa | sia Ba | 0,00 28,0 ,,
aa 0,08 7,56 4 {|| 20 4 0,00' 38,0 ,,
oer 0,05 > | |

Borg = 2h (=-47 } ee q. == 27 (see abov e).
c. The curve III, i.e
2(q, + 47,)
n=—47, +B...

( 926-)

For values of g, larger than the second member the beginning of
T=f (2) is concave; these curves lie therefore above the curve. In
the same way all the lines 7=//(2’) with convex beginning lie
below this curve.

Again q,=90, when ¢,=0 (initial direction 9,=4, (45°). When 4,
approaches to a, g, approaches to 29, + 47,, so the limiting direc-
tion becomes g, = 2 q, (63°.5). This curve lies entirely outside the
two first, more to the left.

Some points of the curve III follow.

9, =17,\e *=0,61 |g, = 2,207, |'q,=8 T,|e 7 = 0,02 |9, = 19,6 T,
aes 0,37 ae 10 0,01. PE ue
eS 0,13° (ea NN Aes 0,00. 34,0 ,,
pe 0,05 15,000] 1-0 S| 0,00. 44,0 ,,

d. The curve IV, i.e.
2(q, + 47,)

: (8/V)
eee

Te —— = ale alt

If g, is smaller than the second member, the end of T= f(2’)

will be concave; these lines lie accordingly eft of the curve; on
the right the lines 77= 7 (2') with convex end are found.

For 9, = 0 again g, = 0 (initial direction 9, = @, (45°)). fg, =o,
q, evidently approaches asymptotically to q,=—4T,, just as the
curve I approached asymptotically to ¢, =47,, when ¢g, =o. The
curve IV lies therefore only for a small part within the region of
the positive g,, and will therefore necessarily cut the g,-axis some-
where in S,, and yield a maximum value M, for g, before that time.
This curve too lies therefore entirely outside the preceding curves,
and again more to the left.

The g,-axis is cut, when (7, =—'/, T,)

je OF
qi | = 1 sn
Woe te — fps
/24
Rees pwc
or when
1 27; Se nh =e
; Oe

iin 7

( 527 )

The maximum is found in exactly the same way as in I, and is
determined by

ee eT:
6,—e i ile Jo a ait a LSS)
to which belongs :
hele
ae 8
qs q1 T.—T, ( d)
If 7,='/, T,, then (8c) yields:
6,— e” ae! F

from which 6, = 0,567, or g, = 1,137,. According to (8d) we have:
g, = 29, — 27. = 0,26T,.

Further we have the following values for g, for increasing values

of 4q,.
9, =2T, le! =2,72|\q,— 0,16 7, ||g, = 10 7, |e! = 148|g, = — 1,847,
| :
4a | 7,39 = 0,575, || 15, 1810) Bg
| ||
6,,| 20,1 | 0,84 5; || |
Already at g,—=157, the limiting direction g,=—4/7’, (here
= —2T,) has been all but reached... 5

IV. So we have seen, that the four limiting curves (see fig.5),
which divide the g,,9,-space into different fields, radiate from the
origin (7, = 49, =) in the space. All of them touch in the origin
the straight line g, = g,, the former two on the right, the latter two
on the left. Only I is intersected by Il; IV falls for the greater part
outside the positive region; I and IV show maxima.

Below I and on the right of II lies the field A of the convex
shaped meltingpoint-curves.

Between I and II on the left of the poimt of intersection jS, lies
a small region B,, where the end of 7’= f(x) has become concave ;
on its right is the region B,, where the beginning of T= 7 (x) has
become concave.

Between II and III (on the left of S,, between I and III) lies
the field C, where 7’ = / (x) is concave throughout its course, 7’ = 7 (.c’)
convex.

Between IIL and the g,-axis (below S, between II] and IV) lies
the field D, where only the end of 77= 7 (x’) is still convex.

Finally there is still a very small region between IV and the
g,-axis, where the meltingpoint curve — both 7 = /(~) and 7’= f(’)—
is concave throughout its course.

If we assume a fixed value for 9,, e.g. ¢, = 937), and vary 7, from

( 528 )

O tot o, we pass successively through the four regions A, B,, C
and D. For g,=10 7, e.g. we should pass through the region B,
instead of through B,.

If g, is assumed to be constant, e.g. = 17), we pass successively
through the fields A, 5,, C, D and #, when gq, decreases from @ tot 0.

Fig.4 gives a representation of the first mentioned transition, viz.
10P-g a ols.

Between the meltingpoint-curves, marked 2,4 and 2,8 (so holding
for g,—= 2,4. and 2,877,), the transition from A to 4, (hatched) is
situated. Between 3,4 and 3,8 (see the hatched parts) is the transition
from B, to C. Between 7 and 8 (in this case for 7 = f(w’)) that
from C to D. Further the cases ¢, =1, 9g, = 2 (A), g, =5(C) and

q.= 3 T,

(Ss yCre ai Ly . 7 EX x ile ; | H | | |

Ae APE | OR lo.47, 2.87; |3.47,|3.87, |) 57, | He | oY GR RAIL
i | | | {
:
| z’=0.008| 0.015} 0.019 0.022! 0.626} 0.029
T0995 7.) |

0.038 | 0.051 | 0.057 | 0.069

0.08 Q.068| 0.079} 0.091; 0.41 | 0.12 | 0.16 b 0.21 | 0.24 | 0.28

| 2’ = 0.019! 0.038! 0.043! 0.052} 0.058 0.066| 0.080} 0.10 |

| | |

- |x=0.07| 0.14 | 0.16 | 0.185| 0.22 | 0.25 | 0.30 | 0.39 | 0.43 | 0.50
| | | | | /

|
|
|

|
| 0.13

~
=
—

0.13 | 0.16 | 0.17 | 0.19
0.67

| 2’ =0.039| 0.022| 0.072} 0.082| 0.03%} 0.10

0.36

20.114] 0.21 | 0.25 | 0.28 | 0.33 0.44 a 0.55 | 0.59
ie alee

| 2’ —0.053| 0.095] 0.11 | 0.12 | 0.14 | 0.15 | 0.18 | 0.22
0.80 ,, | | |

0.23 | 0.255
«=0.16 | 0.29 | 0.34 | 0.38 0.44 | 0.47 | 0.56 | 0.67

0.72 | 0.785

x’ =0.08?| 0.14 | 0.16 | 0.18 | 0.20 | 0.215] 0.25 |} 0.29 | 0.30 | 0.32

ST ier | |
|x =0,22 | 0 39 | 0.44 | 0.48 | 0.55 | 0.58 | 0.67 | 0.78 | 0.815] 0:87
nis ——___—_- 5 ba
| a’ =0.125| 0.20 | 0.23 | 0.25 | 0.28 | 0.29 | 0.33 | 0.36 | 0.38 | 0.39
O70. 244 |
a = 0.295! 0.48 | 0.54 | 0.59 | 0.65 | 0.69 | 0.77 | 0.86 | 0.89 | 0.928

| | }
=0.19 | 0.29 | 0.32 | 0.33 | 0.37} 0.89 | 0.43 |°0.46 | 0.47
Octo s . |
x =0.38 | 0.59 | 0.65 | 0.69 | 0.75 | 0.98 | 0.85 | 0.918} 0.928) 0.964

c' = 0.305! 0.43 | 0.46 | 0.48 | 0:51 | 0.525] 0.555) 0.58 |} 0.59 | 0:60

x =0.50 | 0.71 | 0.76 | 0.80 | 0.84 | 0.87 | 0.915) 0.969) 0.971) 0.986

/ | | <
rc’ =0.52 | 0.64 | 0.665! 0.695! OF.) OSes | Orie 0.755} 0.76
| | |

r =0.68 | 0.84 | 0.87-| 0.913} 0.927 | a 0.965 il 0.991) 0.997

, Li. ts" ghy them "Teta face | |

£4

( 529 )

qd: =10(D) have been traced. The curves 2,8 and 3,4 represent
therefore the type #, with convex beginning and concave end for
T= f(x). The calculations (according to formulae (4)) are summarized
in the annexed table, i.e. for 7,—= 4 7,, to which fig.3 applies.

With this change of 7, we do not enter the region /’; therefore
g, would have to be smaller than 0,26 7) (see above).

V. It remains to answer the question, to what modifications the
fields and their limits drawn in fig. 3 are subjected, when 7’,
not 4 7,, but eg. 0,9 T, or 0.1 T,.

The initial directions of the curves I to IV remain quite the same,
also the final directions, but between them there are some modifi-
cations; specially the place of the points of intersection and of the
maxima is changed.

a. If T, is no longer 0,5 7,, but e.g. 0,9 7,, so that 7, and T,

are very near to each other, we find for the maximum J/, from

(8a) and (80):

—4
Ge), = Bi 5 ag, = 2g, = 407,,

yielding 6, = 1,45°, hence, as 49, =4(5 — =) is now iar
i 20,2 7, Por g, we find then ¢, = '2,4 7.
The maximum has now got quite outside the limits of the values
of g which occur practically, so that the curve I now gradually rises
within these limits. (fig.5).
The point of intersection of I with II has not been displaced much.
We find now for itg, = 5,85 T, , g, = 5,55 T,, so that the value of

gq, has remained nearly constant.

The consequence of the modified course of the curves I and II
is, that the region 6, has all but disappeared; on the left of S,
I and II nearly coincide; the region 6, has strongly diminished.

But also C and D have considerably diminished, so that the greater
part of the space is left for A and ZL.

The considerable increase of the region / is due to the fact, that
the point of intersection of the curve IV with the g,-axis lies much
higher than in fig. 3, and that the maximum has moved considerably
to the right. In fact. we find for the point of intersection mentioned :

Ls 3,67 n/
ELIE SN et ahaa me (ee eae
"1/187, 187,
l+e
q

from which

( 530 )
The maximum is given by (8c) and (8d), viz.

6, — ess 0.8 5 9, = 2¢,— 32423;
giving 0, — 1,125, so q, = 203 T°, 9, == Spee

In the following table some more data are given, which have been
used for the construction of fig.5.
Curve I alp=1 8 5 8 10 15 2 2% 30 40 50 100 150
1/7, =1,09 3,09 456 7,13 837 10,7 11,9 12,85 12,26 110 9,89 4,74 pe
Curve _ IT afp=1 2 4 6 8 W 1 0 30 40 60 100
92/7, =0,93 1,91 4,04 640 8,96 11,7 195 283 48,0 69,3 1125 196
Curve TIT m/p=1 2 4 6 8 10 1 20 30 40 60 100 |
n/7, =1,14 233 4,88 7,65 106 138 22,5 32,1 532 5A 120 203 \
Curve IV %/p=1 3 5 8 10 1 WO B 30 40 50 100 150,
92/7, =087 245 381 546 6,32 7,67 8,09 7,82 7,08 4,93 268 28 353)

b. Let us now take 7,—0,1 7,, so that the two temperatures

of melting lie very far apart. This case (see fig.6) agrees more closely
with that for which 7, —0,5 7; only the maximum of the curve
II has got nearer to g,=4 7,, and the point of intersection of II
with I has moved much farther to the right. This has made the field
B, considerably larger than in the case 7/7, = 0,5, which field had

nearly vanished for 72/7, = 0,9.

But nearly the whole of curve IV lies now outside the positive
region, so that the appearance of bi-concave meltingpoint-curves 1s
almost excluded.

The maximum of I| is determined by

G,--e _— 19 : IN —= 29,—2' |. 1Gt

yielding: 0, = 19. As 0, == ——s so. 9g, = 4"), 2g, Dene ee

: vi ; ; 0; Re
For the point of intersection of I] with I we find, as e~ is very
UF
large and e very small,
a AO i ee ee Oe 0,42 = Tae

The curve IV cuts the g,-axis, when

0,2 i. a See 3
Bil
2), fhe
be”?
i
7 q; :
so when 0,2e° = + 0,2,

("S01 >)

n 10
3) T, q)
or ee? *— — —_ —— ]
Susy
This give 71 __ 9. 903, hence g, = 0,0457
Dy fives 2) 7 ee IU ence Vy —_—_— 9» 0 ye
ou
The maximum is found from
=6j * of)
A, —e ae ee oy 0.0444 7 z.

This is satisfied by 6, = 0,1025, hence 7, = 09,0228 T,, 7, = 0,0012 T,.

We can further caleulate the following points of the four curves.

Curve I /7,= 2, 4/, 6), 8), 10/, 20,
hig 106" 197 93,15 368 9389 - 3,96._- 4,00
Curve Il n wis —— I/y 2/5 4/5 ¢/, 8/, 10/, 20/, 3 4
2/T,= 0040 014 048 O91 136 181 4,04 560 7,60
Curve TT 2/7 = % 2/y 4/5 6), 5), 10/, -20/, 3
i/p = IJ 211 383 489 (560 615 844 100
Curve IV 1/7.= “'b 2/, 7 aie ch tae 1), aH,
93/7, =— — 0,014 — 0,066 — 0,20 — 0,30 —035 —0,38 —0,49

c. Hence when we draw near to the limiting case 7, = 7), all
four eurves will evidently approach to the straight line 7, = 4,.
which euts the angle of the coordinates in two equal parts. Fig.5 is
to a certain extent already a representation of this case.

If, however, 7, is very small, so that 72/7, approaches to 0, then ]
passes evidently into the straight line 9, = 47, ; If into q, = 2g, ;

Hil into g,==0, so into the g,-axis; IV into g,= — 4T,=—0, so

again into the q,-axis. Of this fig.6 gives already an idea.
As to the two maxima and the two points of intersection, we
have finally the following summary.

My, M,
Ts/p =0 01 0,5 09 1140 O1 OO
a/r,—=4 42 6,1 262 © | 0 0,0012 026 82 o

n/T, — 4 4,0 4,2 12,4 we 0 0,0228 1,13 20,3 oa

S, S,

7/7, =0 0,1 0,5 0,9 1/0 0,1 ie oe %
fp = 7,6 5,9 3,85 4 = 0 0 0 0
n/7 =4 4,0 4,2 5,55 4 | 0 0,045 2,51 64,4 o

And in this way I think that the ideal case a= 0, a = 0 has
been sufficiently elucidated.

Proceedings Royal Acad. Amsterdam. Vol. VI.

( 532 )

Physics. — *Tsothermals of murtures of orygen and carbon dioxide.
I. The calibration of manometer and piezometer tubes”. By
W. H. Kersom. Communication N° 88 from the Physical

Laboratory at Leiden, by Prof. H. KameriincH Onnks.

(Communicated in the meeting of September 26, 1903).

§ 1. With a view to the investigations of isothermals, critical
and condensation phenomena, of which | hope to give the results in
a following paper, I have carefully calibrated a manometer and a
piezometer tube. The results of these calibrations have been reduced
according to a method to which Prof. Kameriincu Onnes has drawn
my attention, According to that method the bore of the tube is repre-
sented by some terms of a series of Fourtsr, the coefficients of which
are derived from the observations. Thus we start from a continuous
representation of that bore im opposition to the discontinuous variations
which we must adopt when we derive mean bores from the length
of the mercury column at different places, and regard them as bores
at the middle of the column. From the following may be judged
what can be reached by means of this method. *)

§ 2. The manometertube was constructed after the model described
in Comm. N* 50 of the Phys. Lab. at Leiden, ?) differing herein that
with a view to the higher pressures a ring was blown on to the
part 4,°%), thus preventing the tube from moving along the cement
in consequence of which the thinwalled part a, would be pressed
against the steel of the flanged tube, while the tube A, is bent
parallel to the length of the tube with the same purpose and in the
manner as has been described in Comm. N° 69 (These Proe. I] Mareh
30, 1901, p. 625). The stem (c, of fig. 4 Comm. N° 50), graduated in mm.,
had a leneth of 50 em., the innerbore was 0.83 mm., the outer bore
6 mm., the capacity of the reservoir a, was about 25 ce., the widened
part ¢/, above had an immer bore of 2.6 mm., an outer bore of 9 mm. and
had been taken so long that the manometer, filled with hydrogen, could
indicate pressures from about 60 to about 190 atmospheres. The upper
cylindrical part of the experimental tube for the investigation of the

') In consideration of the cireumstance that with these tubes observations have
been made which will form the subject of following papers, we shall give already
here for the sake of simplicity some data on stem calibration, together with some
remarks on the way in which the further data about these tubes are obtained.

2) These Proe. Il June 24, 1899, p. 29.

*) See plate I, fig. 4 of that Comm.

( 533 )

mixtures was originally long 50 em. and divided in mm.’s, had an
inner bore of about 2.6 mm., an outer bore of about 7 mm.

The relation of the bores of the graduated parts of the manometer
tube and the experimental tube at different places was determined
by repeatedly moving a mereury column of about 10 em. length
over 5em. and then measuring its length. To effect this the manometer
tube was placed in a horizontal position and the places of the ends
of the merenry column were read with an eye-glass. We avoided
parallax by taking care that the nearest graduation on the g@lass
should be seen to cover its image on the mercury. For the wider
experimental tube this method could not be used owing to the
change of form of the mercury meniscus at the ends of the column
in consequence of gravitation. Therefore the experimental tube was
provided with a glass cock to which a narrow glass capillary had
been connected. From tlis the air escaped only slowly under the
excess of pressure of LO em. mercury. Then the tube was placed
vertically after a mercury column of the length mentioned had
been admitted. The latter could each time easily be moved over 5
em. and the position of the ends read.

Then a longer mereury column was admitted into the tube in order
to derive the mean bore from its weight. The bore of the above
mentioned tube under the great reservoir (/,), and also the volume of
the reservoir were then determined by weighing the mercury.

§ 3. As an instance of the process of the calibrations and the

(EA sth HE.
= ne |
MM j L hy
ee | 4
+ 6.90 1.40 | 10.11

9.96 | 41.33 | 0.04
14.989 | 44.31 | 10.09

198 | 11.30 | 40.01 |
4.76 | 11.30 | 0.01 |

1121S —0.11

|
t {

30.08 | 44.31 | +0.02
35.028 | 14.25 —0.04
39.90 | 11.20 —0.09
4h 29

mean: 11.29

( 534 )

ealeulations the data about the manometer will be given. The gia-
duated tube has been calibrated twice, in 1901 (1) and in 1902 (B).
I shall give here the data and the caleulations concerning cali-
bration B. Calibration A has been made in entirely the same way ;
the results of it will be given at the end of this paper and compared with
those of £B. Table I shows the results of the calibrations with the
mercury column; column .J/ contains the means, / the length of
the mereury thread, 4 the difference from the mean length. The
temperature could be considered as having remained constant.

T A Bia i aie

Ends of the mercury column:

Ist position: 3.795 49.98° temp. 20.7 |
2d » 30.35 in the graduated stem,... 9.25 mm. above

the division of the

thin capillary e, ; » 20.65
3d » 2.80 49.00 »- 20:0

Weight of the mercury (in vacuo): 3.3777 gr.
Caleulation :
Let » be the bore of the tube at an arbitrary place, indicated by
the coordinate xv (from O to 50). We may put:
=s, +d

where s, is a particular, normal, bore.

The volume between the 2 divisions p and gq will be:

q q q
Ve oa [ de =) (s, + d) dx = s, (q — p) + fa ds ./-.e
> P p

The length of the mercury column :
q—p=m+A4
if = the mean length (comp. table I). If 1, represents the volume
of the mereury column then :

q
Ve 38,m+ 5,4 +f the
P

We may choose s, so that :

Mk, == HA
then :
4 q
] .
A= ——fd.de= — { d’. da
ne e
p p
: d ;
| ia men If we knew the form of the function ¢', we might derive

( 535 )

a number of equations from table 1 to determine the coefficients
occurring there. Although the form of that function is unknown, yet
d' for wv between 0 and / must be representable by a series of Fourrer.
It may now be asked whether it is possible within the limits of the
accuracy given by the observations, to represent « by some terms
of a series of Fourmr. Therefore | have put :

Er din Pe Sax

d' = a’, cos + a', cos ee + a’, cos 7

where / is the length of the tube:

The term «@, is omitted, because, in connection with the cireum-

stance that 4 represents the difference between the length of the
mereury column and the mean length, we could expect beforehand
that it would become small.

For —A4—{f{d.dev we then find, if we bear in mind that

P
q¢—p=m-+A, where A may be put small:

eet ee EL 4 x q+t+p
Ne ay | “a sim oT m + ZL eos ry, m) cos or
l bs 4 2m ¢ )
+ a’, = sin cs m + A cos ae m | COs : a (2)
A 3m 3a q+p
fa 5 f= sin Py m + A cos 3 sie COS 73 tion .
For the case under. consideration /= 50, m— 11.29, so that if
as in table I we put: — = ee
ae ol | iad Oy ea de
= A — tt, 11.05 + U.94 A | COS ie M
‘tee are eee
es }Lo.3i SE OREO AA | COS 7 M i + AS (lem

3
cere | 9.28 + 0.48 A cos =

The data of table 1 now lead to the equations combined in table
Il: first I have derived from table I the values of L for M—= 10,
15 etc., as this offers some advantage in the calculations (the value
L with 176.90 is kept, as it did not seem advisable to me to
extrapolate as far as J/ — 5).

Giapic
TABLE IIL. TABLE II),
ede = 10.13 a 6.76 a’, + 2.49 a, SAAB
— 0.04 = 8.97 a, + 3.07 a', — 2.744, + 0.00 B',
en 6.510', == 03.07 ai, 2 8.esey — 6.248,
eae 3.264. 8.40 a, ee ae + 0.00 8,
— 0.01 — 0.00 a, — 10.38 a’, + 0.00 a, + 6.24 0’,
— 0.02 = — 3.19a',— 8.41 a’, + 7.9240, + 0.00 8,
Age GAT, — “805 a, eee — 6.25 8,
4909 = —" 8.88 o', + -3.04e, oa.) 4 ee
0.115 — — 10.420', + 8.330, — 5 42a, ee oe

By means of the method of least squares '), we find the normal
equations combined in table IV.

TABLE IV. TABLE IVé.
475.8 a, 17.920’, — 180.65 a', 4+ 3.8284—0 | = iegee
— 17.92a',+ 401.4 a',— 28.31¢,—0.6606=—0 | —60.338,

— 130.650’, — 28.31a', + 319.0 a’, + 0.0882=—0 | — 21.028,

[= 13.310',— 60330, —21.020'. ae0.69 00s. oe

These equations yield:
{ 4

a’, = — 0.00908 , |
a, == <-0,000964, 0) Be eae ee
a’, = — 0.00391 . j

sy means of the equation (8) we can now calculate the values of
£ for the different values of J/ in order to judge whether they
agree sufficiently with the values given by the experiment. Then in
the second number we may assign to 4 the values of table I, and
so use the coefficients given in table III, as these terms have little
influence on the result. It now appeared that it was advantageous

') Although each of the equations (3) contains 2 quantities deduced from obser-
vation, I have not applied here the method described in Supplement N° 4 to the
Communications from the Phys. Lab. of Leiden, These Proc. V Sept. 27, 1902 p.
236 on the reduction of equations of observations containing more than one measured
quantity, because M in comparison with /, may he supposed to be accurately known,

< pia

to add a fourth term to the equation (3), viz. one that contained the
72 OSE : - :
factor sin irr M. Independent of this, I had arrived at the same

conclusion in the ealeulation of the calibration A. Therefore | put :

27x Be a7 5a

d' =a’, cos = +a’, cox = + a’, cos + Be sin =... (5)
so that we had to add to the second member of (2) :
+ U', = sin > m + QJ cos = m | sin aa — (2b)
and to the second member of (3):
+ h', {6.24 — 0.20 A| sin = Pee oe ty a as (30)

To the equations of table III] we had to add the terms combined
in table III/, to those of table IV to the first members the terms
given in table 1V/, and also the fourth equation given there. These

equations gave :

a’, = — 9.00915
a,—= 9.000796 |
(0)
a’, = — 0.00402 |
b', = — 0.001048

By means of these we have derived from the equation (3) with
the supplementary term (3/) the values for 4 for the different values
of J/. The results are given in table V under the heading 4,, while
column 4, shows the observed values, and the last column contains

ee bo ia.

i :

vf en Pea.

| | ———

6.90 | +0403 | + 0.11 | — 0.007 |
10 + 0.069 | + 0.04 | + 0.029

15 40.0200 40.02 | 0.000 |
20 aa 0 O06 os 0.04 — (). 004
25 -O0S | +001 | + 0.005
30 | + 0.007 | +0.02 |. — 0.018

3 | — 0.0988 | —0.04 | 40.012 |

| 40 Be e073 | 0.09 + 0 017 |
| 45 — 0.117 — 0.445 — 0.002

Assis®)

the differences. From this we derive for the probable error: 0.009,
which with regard to the accuracy is permissible, so that the
equation (5) with the coefficients (6) well represents our observations.

From equation (1) follows for the volume between the divisions
O and Q:

ay
Vow, Jo fe an x
0

where Q’—Q+¢q and
Q
hs Os Oa QO 1a Oa da Q
=) d' da —| a'.sinan— 4+ —sinQ@n— + 38x on
=| {f Ls 2 es yee pee
0

Table VI gives for the values for @ from O to 50 the values
computed in this way for Q', the reduced readings. By means of
this table we may inter alia judge of the irregularity of the tube.

T A.B deck ae :
| oe eee 2, | Qo '\ g | Q | qa |
|
| 0 | 0.000 |} 47 | 16.878 || 34 | 33.864 |
| 1 | 0987 |) 48 | 47.978 || 35. | 34.866 —
| 2) 1.975 | 49 | 18.878 || 36 | 35.869
| |
| 3 | 9.968 | 20 | 49.878 |] 37 | 36.879
| |
# | 3.950 || 21 | 20.877 || 38 | 97.877
| |
5 4.938 || 22 |} 24.877 || 39 | 38.882
93 | 99 975° || 40 | 30.888 |
93.874 || 44 | 40.895

8 | 7.908

|
95 | 94.872 || 42 | 44.903

7] & 900 26. -| 2b 870e 43 42,911

10 | 9893 |] 97 | 96.868 |] 44 | 43.9905 |

—
_
_
—
—

0.888 || 28 | 27.867 || 45 | 44.931

|
| |
884 || 29 | 98.865 |] 46

—=
bo
—=

AS .9A2Q

|
13 | 42.881 || 30 | 99.864 || 47 | 46.954

14 | 43.879 || 31 | 30.863 || 48 | 47.966

15 | 14.878 S24 Bisab3 49

46 | 15.878 33 32.863 50

|
48 980
AY. 9938

The data of table I] enable us now to determine the normal bore s,.
By means of table VI we find for the reduced length of the mercury
column at 20°.6 C. the values :

46.232 cm.
46.215 em.

mean: 46.223° cm.
Hence at 20° C.: s, = 0.0053948 em’.
From the data of table Il we may also derive the volume of the
widened part (, (lig. 4 of Comm. N° 50). The bore of the capillary
e, Was measured with a microscope by comparison with a fine

graduation on glass by means of a micrometer eyepiece. The bore is :
0.000301 cm’*. We then find for the volume of the part d, between
the division 50 on the graduated stem and the mark on the capillary
at 20° C.: 0.14239 ce.

Using the value found for s,, we may derive from table VI the
volumes J’,& between the division 0 and the division Q, and then,
using the volume found for the widened upper part, the volumes
from division @ to the mark on the narrow capillary.

The calibration A has been made and reduced in entirely the
same way. The results of either are combined in a table which
indicates the volume for each centimeter division Q from O to 50.
Table VII is an extract from that table.

1p Ae ER — Vil.

« | a ee ee of, diff.
0 0.44161 04209 | O11
5 0.38487 G5) 8.45
10 | 0.35800 | 0.35872 | 0.20
15 | 0.33195 0.33183 | 0.47

| 20. 0.30441 0.30485 | 0.14
2 | 0.97731 0.27791 0.2
30 0.25028 0.25098 0.28
35 | 0.99357 0). 22400 0.19
40 0.19673 0.196905 | 0.09
45 | 0.46988 | 0.16970 | 0.19 |
50 0.44189 0.14939 | 0.35 |

Column V4 contains the volumes from the mark on the narrow
capillary to the division Q at 20°C., as resulting from the calibration
A, Vp as resulting from the calibration 4. The last column shows
the percentage differences. The mean percentage difference between
V4 and Vz in the complete table amounts to 0.19 °/,, for the part
from 0 to 41 inclusive, which only was used in the following

observations: 0.17°/,. For our purpose this agreement is sufficient.

From the fact that ]'z
accuracy might be iunproved by more determinations of s, and of

}"4 is always positive it follows that the

the volume in the widened upper part. I hope to revert again to
this subject in a following paper.

§ 4. To determine the capacity of the reservoir a, with 4, (see
fig. 4 l.c.) and also the bore of the part /,, the manometertube,
which at the end e, was provided with a cock with a fine point,
was exhausted by the mercury vacuumpump and then filled with
mercury in a reversed position until the mereury stood above at
7, (in the drawing below). A quantity of mercury was drawn
off twice and weighed so that we could determine the bore of /,
at different places. The level of the mercury in the tube was read
by means of a cathetometer. Then so much mereury was drawn off
that the mercury still stood in the graduated stem ¢,, and this was
weighed. This served) to determine the capacity of a, -+ 6,. The
following results were obtained: the portion 7, is divided into milli-
meters, the centimeterdivisions are marked from 0 to 6, O being
nearest to a,. It appeared that the bore could not be put constant;

I have put:

a7 1 aa a
and found :
a== 0.00585 7 %s;.== O3504 (emer
so. that

V,2— 0.3564 i + 0.0029 Q | Q.

Table VIIL (p. 541) contains the volumes from the division O to
the division Q at 20°C.

For the caleulation of the volumes of the menisci I have used
SCHALKWIJk’s table occurring in Comm. N°. 67°). For the volume
between the division O on 7, and the division O on ec, I found at
20° ©. : 25.024 ce. |

In the calibration of an experimental tube it will in general be

1) These Proc. III Jan. 27, 1901, p. 488.

( 544 )

TABLE VIII.

| Q V9

| 4 | 0 3574 |
5

| 9 0O 7 169

4 | 1.440 |

| ’
5 {8078 |
G6 | 2.4756 |

necessary to take into account an electromagnetic stirrer, consisting
of a soft iron rod in glass. in my case it consisted of a cylindrical
portion with two bulbs at either end. The bores were measured
with a micrometer screw, the length with a pair of sliding compasses.
Each time when the experimental tube had to be refilled with a new
quantity of gas, it had to be opened at the top in order to be
cleaned. Because the stirrer had to be brought in, it was not possible
to seal on a thin capillary as had been done for the manometer
tube. Nor could the stirrer be placed into it beforehand, as this would
be a hindrance in the cleaning and especially in the calibration with
mercury. The volume of the top portion was determined each time
after the measurements by cutting off so much from the top that on
that piece one division at least was well visible (the upper divisions
over a length of about 5 mm. were lost in the sealing). The fracture
was ground flat, the piece after being cleaned and dried was entirely
filled with mereury and the superfluous mercury was removed by
sliding a properly cleaned flat piece of glass over the ground off
end. The mercury was weighed, the position of the ground end
was observed with regard to the divisions of the tube with a cathe-
tometer and from this the volume of the top portion was derived.

Physics. — ‘‘J/sothermals of mixtures of oxygen and carbon diovide.
Il. The preparation of the mictures and the compressibility
at small densities.” By W. H. Kersom. Communication N°. 88,
continued, from the Physical Laboratory at Leiden, by Prof.
H. KAMERLINGH ONNEs.

(Communicated in the meeting of September 26, 1903).

§ 1. In this paper I shall deseribe the preparation of the mix-
tures of accurately known Composition in the mixing apparatus

( 542 )

deseribed by Kamertincu OnNneS and HynpMman, the determination
of the compressibility of carbon dioxide and some mixtures of earbon
dioxide and oxygen at ordinary pressures, together with the results.

§ 2. The substances. To obtain the carbon dioxide I used the
method followed in the Physical Laboratory at Leiden‘), which
together with the improvements made in the last years will be
described in a paper on the apparatus and methods used in the
Cryogenic Laboratory.

The purity of the carbon dioxide thus obtained appears from the
increase of the pressure at the condensation at 25°.5 C. which amounts
to only 0.07 atm.

The oxygen was prepared from potassium permanganate in the
way described in Comm. N°. 78, These Proc. IV, April 1902, p. 768.

§ 3. The preparation of the mirtures, the determination of the com-
position and the compressibility of the mirtures at ordinary pressures.
For the preparation of the mixtures I had at my disposal the appa-
ratus described in Comm. N°. 84, These Proc. V, March 19038, § 21. As
the operations required for the preparation of a mixture of accurately
known composition are deseribed there, I need not enlarge here on
the details of this subject. [ shall only mention that the apparatus was
connected by means of the cock 7, (see plate Il of that paper) to
the apparatus for the preparation of oxygen, by means of cock 7,
to the carbon dioxide reservoir, before which there was a drying
tube filled with phosphorous pentoxide, and also to the experimental
tube that had to be filled. After the mixture had been prepared, I
have investigated in the volumenometer /’ the deviation from the law
of Boye, in order to be able to express the volumes of my mixture
at high pressures in terms of the theoretical normal volume. Although

cae 1
for my investigation an accuracy of TI would have been sufficient,
| have gone a little further because in itself the knowledge of the
deviations from the law of BoyLr at ordinary pressures is important and
the apparatus without difficulty admits of a higher degree of accu-

racy. Taking all possible precautions an accuracy of ——— might
Y © T0000

. . 1
be reached. Yet I was satisfied with an accuracy of ———. To judge
“ , 5000 te

of this the following may serve :

') Comp. among others Kurnen, Arch. Néerl. t. XXVI, p. 3 and VerscHarreLt
Aittingsversl. Juni ‘95, Comm. N°, 18, Leiden.

( 543 )

Measurement of the volume :
In order to judge of the accuracy we shall proceed as if we
had to consider a quantity of gas measured in the first large bulb
kh,, above (see |. e. plate IH fig. 1). There the relative error is
largest as the small bulb 4, above is only used for auxiliary
measurements. The cathetometer used certainly reads well at 0.04 mm. ;
let the error be 0.02 mm. With a bore of 44, of about 200 mm,
F ae anes . We 95 Reese, ees
this gives an error of 4 mm’; on 250 ce. : 60000°
The height of the mercury meniscus read in the volumenometer was on
an average 0.140 em. I have supposed that the volume of the mercury

3
meniscus is found by multiplying the bore by 7 of the height. The

mean height undoubtedly lies between the half and the whole height (ef.
ScHALKWUK Comm. N°. 67, These Proe. IIT Jan. 1901 p. 488), so that the

; i aon : 1
error is certainly smaller than LT of the height, say ae Hence this
; 1
gives qg X10 mm.=—018 mm., on the volume an error of

36 mm* or ———. In order to reach an accuracy of
10000

more detailed investigation of the volumes of the mercury menisci
at this radius (7.8 mm.) would be required, in the way as SCHALKWIJK
le. has done for radii from 0.5 to 4 mm.

The variation of the volume due to temperature can accurately
be accounted for.

Variation of volume owing to difference of pressure in and outside
the volumenometer: ;

If we avail ourselves of the circumstance that the thickness of the
wall is small as compared with the radius, a calculation applied to
each bulb individually gives:

SV 31—u(pi—pe) Kk
Vi abe des ihe -

1
or for our case, putting: # = 6500 K.G./mm.’, uw = GT? with | ieee

mm., d=.0.5 mm.::

dV
SSeS 0.00000177 (p;i—pe)

if pi and p, are expressed in centimeters of mercury; so that for
JV 1 3 ; ; ; j
——=--———. For this a correction is applied

= =— ot. €M.: = 7
ae Be “= = 79000

( 544 )

hence the error of the correction owing to the coefficient not being
precisely known, may be neglected.
The volume in Lb above Lh,,,

by means of mercury, may be determined with sufficient accuracy

which could not be determined

volumenometrically, as we have to do with proportions of much
larger volumes.

Measurement of the pressure:

In most cases if will be possible to follow the rule of making
the adjustment of the mercury in the volumenometer at a mark so
that the pressure of the gas above if is not less than 0.5 atm. For
a measurement of the pressure 4 cathetometer readings are required;
let us put for the probable error of the result: 2><0.02—0.04 mm.;
this is on 40 em. : wate Only at the volumenometrical determina-
tion of the relation of //, and what is above it to 44, the pressure
was smaller, but this relation, being, as it has been said, only used
as an auxiliary quantity, need not be so accurately known. The
same may be said of the measurement of the remainder of the first
gas in /, after as much gas as possible has been transferred to
the mixing vessel /.

Although / had been accurately vertically mounted, so that the
mereury menisci of both “4,, and “£4, could be seen sharply without
altering the focusing of the cathetometer telescope, it yet appeared
that the windows “Lh, were not exactly vertical, but that they all
deviated from this position in the same direction at an angle estimated
at 0.2° by means of a level fastened at right angles to a flat piece
of steel. Therefore as the windows are not placed perpendicularly
to the line of vision of the cathetometer telescope, refraction occurs,

which causes an apparent displacement of the mercury meniscus of

n—l

ast:

cm., @d being the distance from the meniscus to the window,
n f

7 the angle of the normal on the window and the horizon, n the
refractive index of water. In our case (d= 8.6 em., n = 1.33) this

: ote 1
displacement amounts to: 0.0075 cm. This gives on > atmosphere an
eo ; te
error of aaa As we have to do with relations of quantities to each
0

of which a correction in the same sense would have to be applied,
the error in the result is smaller. If a higher degree of accuracy
is wanted, the angle formed by the windows and the vertical will
have to be determined more accurately, so that the correction may
be applied. For our purpose this was not necessary.

( 545 )

Correction for the temperature of the mercury :

[f the pressure amounts to say 0.5 atm., measured as the difference of
two mercury columns of 76 and 38 cm. respectively, the temperature of
the long column must be known precisely to within 0°.5, ifan accuracy

1
of .>=——
5000
mereury columns together with the thermometers are packed in wool.
The difference between the indications of the thermometer at the
lower end and at the upper end of the barometer Sar. did not as

is required. We must assume that this is possible if the

a rule amount to more than 0°.5 C., hence we may accept that the
uncertainty caused by this in the knowledge of the temperature did
not exceed by much 07.25 C. For the difference of the temperature
of the mercury in J/ and # a correction is applied.

The capillary depressions are largest in the volumenometer, and
of the order of say 0.07 mm. The uncertainty here is surely much
smaller than the errors resulting from the windows not being vertical.

Corrections for the difference in level between the meniscus in
Bar below, and in-J/, and also those for the reduction of the pres-
sure immediately above the mercury in / to the mean pressure of
the gas above it, may be applied with sufficient accuracy.

Measurement of the temperature :

During the time of one measurement (25 minutes) the temperature
by means of a thermostat of ScHALKWIJK*) can certainly be kept
constant at O0°.03 C., while if the water at constant temperature
flows rapidly enough through /, the temperatures at the lower and
at the upper end did not differ more. The temperature was read on
a thermometer 7/ connected with the stirrer Hr, which therefore
could be placed in different positions.. The thermometer was
graduated in 0°.05, so that O°.01 could be easily read; it has
heen repeatedly compared with a standardthermometer tested at
the Reichsanstalt. As therefore the error in the measurement of
temperature does not amount to 0°.038 C., the accuracy is certainly
0.03 : i
OY 300 = 10000

A portion of the volume (in the tubes Hbg, and Hby,, which
have an inner bore of 1.2 mm.) is not enclosed in the jacket. This
volume is a little less than 1 ce. For its temperature which is put
equal to the temperature of J/ a correction is applied. If in a
measurement in the first bulb £4, we assume that in the temperature
of that portion there is an error of 5°, the error in the mean

1) Comp. Comm. N°. 70, These Proc. IV May 25, 1901, p. 29.

. Date: 7 Feb. 703.
Time : 12.56. Nee |
Temp. bath ; 20.07. | |
69.500
69.373.

Mercury level in //,: Top 2-5

Mark 4 on fy,...... | 2.8 | 69. 405
OES sey a, RE: | 2.8 69.504

88586 ‘A

2.0 88 426

Manometer J: Top.....

ap peas
bo

_ Temp. J: 15.6.
Barometer Bar, :
Upper men.: Top... 3.2 78.372
Basis... 3.0 78 266
Lower men.: Top.... 2.2 — 0.5 + 0.052 —

ihe BasiSins ioe 2.2 | — 0.6 + 0.04
- Temp. Bar. below: 14.4 3
—_ above : 15.3
z can Lower men.: Basis. . | 9. ip ple les + 0.042
i Hope iw 1.5 | —0:5 + 0.0%
i Upper men. : Basis... V7 78.262

te ; thy SERB) eae ores 2.2 78.370

Manometer WV:

Temp.: 15.4.

Basin +. eae aewine 1.0 88. 420
POD tise cease ites 0.8 88.577
Mercury level in 2, : . ‘.
Mage-d tice eee or we ye
de em ee 22 69.400
Basis is ve fc hes 2.3 69.368 |
Le Re ae? | 2.3 69.494

Temp. bath: 20,08,
Time: 1.22.

a's ere

( 547 )

temperature of the whole becomes 0°.02 and may be disregarded,
especially in consideration of the fact that the difference in tempe-
rature between the jacket and the surrounding atmosphere as a
rile is less than 5° and therefore the error made will certainly be
smaller.

Hence only in very unfavourable cases the error in the result
5000” and we may expect that in most cases

the error will not exceed this amount.

will be larger than

To judge of the course of a measurement | have given in table [X
(p. 446) the experimental figures of an adjustement for the determi-
nation of the deviation from the law of Boyne of the mixture of
0.2 oxygen with O.8 carbon dioxide. Column Af contains the readings
of the level (see Comm. N°.60 These Proc. HI Sept. 29, 1900 p. 312),
/ the readings of the cathetometer.

The volumenometer had beforehand been calibrated with mereury
by Dr. C. Zakrzewski. Hence we knew at the same temperature the
volumes of the bulbs /,, measured between the middle marks on
the glass screens £y, and also the bores £b,, /b,, Eb,, Eb, Eb,
In the apparatus used the mercury could not be read while it stood
in £h,, because owing to a former manipulation in the blow-pipe the
hore at that place was not perfectly cylindrical. There the sum of
the volumes of the two neighbouring bulbs had been measured.

To test this and also to determine the volume of 44, with what
lies above it I have determined volumenometrically the relation of
the different volumes with dry air free from carbon dioxide. To
account for the deviation from the law of BoyLe I could make use
of coefficients of KAMERLINGH ONNES’') series:

Ba y
pra = oF es a ss a a == F =* es.
A A A A A
put kindly at my disposal, which accurately represent to within
0.2°/, the conduct of air as indicated by Amacar’s experiments. The
three first coefficients are for 20° C:

. 7 — 1.0738
Bsa = — 0.40495 x 10-3
C4. = o> OR(oox re":

We find for the relation of the volumes J’, and J, which are
filled with the same quantity of gas at the same temperature to
pressures p, and p, to the first approximation:

1) Gomm. N°. 71. These Proc. If June 29, 1901, p. 125.

: 36

Proceedings Royal Acad. Amsterdam. Vol, VL.

( 548 )

B.
Plt Epa, . eos ees

Ke Pi a

if p, and p, are expressed in atmospheres (0° C, 45° northern latitude).

A second approximation where the coefficient Cy would occur is

not necessary with a view to the accuracy required.

TABLE Xa. TABLE XA.

A Bel C BE |
A eS | ; 5 |
V, 5.01 El, | 0.00A085 |
| is
€. 18913 | 1.8910 _ 0.016 ib, 0.000675 |
: eae 0.000314
Vi 20e Os yee)
pe 1.9396 1.9400 | + 0.622 Bb, 0.000165 |
rs | I De |
Ys |4,9499 | 4.94205 | -— 0.072 ee ee
7, |
Table X shows the results of the calibration. There we have
called: V, the volume above /b,,, V, the one above b,, V, the

lib, «ete.
the volumes according to the mercury calibration, 5 according to
the
Column

one above Column A of table Xw gives the relations of

volumenometrical determination, C' the percentage differences.
I} of table X4 eives the relation of the volume of 1 mim.
of the indicated bore to the entire volume above it. It may be seen
that

following caleulations the mercury calibration has been adopted as

the agreement between the two calibrations is sufficient. In
being the more accurate.

For the calculation of the composition we derive from the meas-
the

(oxygen in carbon dioxide) are combined in table XL. A contains the

urements in volumenometerdata, as those for the mixture 0.2
data of the oxygen in the volumenometer, 5 refers to the oxygen

which has remained in /’ after the transference of the greater part

into FF’, C' veters to the carbon dioxide.

T2A=B G3.

A B C

Volume ..

Pressure..

‘Temperature

0.99979 /,
4) 396

19.81

0.98905 Vy

0.380

0.99994 V,
66.961 |

19.83

( 549 )

First of all we may derive from / the pressure which the remainder
of the oxygen would have exerted in the volume 0.99979 J, and
at a temperature of 19°.81 C. In this calculation the law of Borie
may be applied with sufficient accuracy. We then find: 0.022 em.
The pressure which the quantity of oxygen transferred to the mixture
would exert in the volume 0.99979 V7,, at 19°.81 C. is then represented
with sufficient accuracy by :

40.396 — 0.022 — 40.374 em.

The pressures of the oxygen and the carbon dioxide may be reduced
to the same temperature 19°.82 C., by deriving coefficients of pressure
variation from the series gives in Comm. N°. 71, or by means of
the value for oxygen 0.005674 found directly by Jonny, and the
value 0.003711 which follows from Crapruis’ data (Trav. et Mém.
du Bureau International des Poids et Mesures. t. I] p. 124) for the
“real” coefficient of pressure variation of carbon dioxide at 20° ©.
and an initial pressure of 1 atmosphere ‘).

We find for the oxygen: 40.575, for the carbon dioxide ; 66.959 em.
If p,, VV are the pressure and the volume of the first gas, p,, V,
of the second, it may be easily found that the number of molecules
of the first gas is proportional to:

pi V
By,
ae

Sas Py

that of the seeond to:

1 =f: arte Lh 4
ye
Where, at least with regard to the denominators, p, and p, are
expressed in atmospheres. We find from the data of Comm. N°. 71,
These Proc. Lil June 29, 1901 p. 130 and 132:
for oxygen :
V9) oe 1.074237
Bye ae io: 10-2.

1) We shall not consider here the variation of the coefficient of pressure-variation
with the initial pressure: this variation would be for a difference of 50 em. in
the initial pressure according to Cuapputs, | c¢., 0.000034, which with a reduction
of the pressure for 1° difference of temperature would give an error of only
sana: Keeping in view the fact that such large differences in the temperature
30000
do not occur, this may be neglected.

For earbon dioxide we may use the value derived directly from
observation which will be given later :

B Avg

These values may also be taken with sufficient accuracy for the

== =—— 0.00507n:

iemperature used (19°.82 C.). The composition of the mixtiure considered
is easily found to be: 0.19942 (oxygen in carbon dioxide).

§ 4. In the volumenometer | have determined the compressibility
at ordinary pressures as indicated in Comm. N’. 84, These Proc. V
March 28, 1903, p. 641, for the mixtures with molecular proportions
of 0.1994 and 0.3072 (oxygen in carbon dioxide), and also that for
the pure carbon dioxide. Although this has already been done by
Reenactt?), AMmaAGat?), Fucus*), Lepuc*) and lately by CHapptis’*) it
seemed to me important to make that determination with the same
earbon dioxide and in the same apparatus as for the mixtures, so
as to have the most favourable circumstances for the comparison of
the conduet of the mixtures with that of pure carbon dioxide.

Table XII gives the values directly derived from the observations
for volume, pressure and temperature belonging to each other. The
columns A. B and C refer to different adjustments with the same
quantity of gas. .

Tk Bo a heen
a. Carbon dioxide.

A B | C

Volume .:... 0.99969 V, | 0.99995 V, | 0.99958 VY,
Pressure... .. 47 264 Dx. 662 | 443.397 cm.
Temperature | 19.99 20.02 |. 49.97

4. Mixture with molecular proportion : ie = 0.1994.

dA B

| = ea SR a |

Volume..... | 1.00088 ¥, | 0.99934 7,

Pressure .... 97.708 |} 51.8178 cm.
|
|
‘Temperature 20.08 19.96

1) Mém. de Inst. de France. t. XXL, p. 329.

2) Ann, de Chim. et de phys. (4) t. 29, p. 246, 1873.

%) Wied. Ann. Bd. 35, p. 430, 1888.

4) Recherches sur les Gaz, p. S6.

5) Tray. eb Mem. du Bureau Internat, des Poids et Mesures, t. XII, 1908,

ce. Mixture with moleeular proportion : a = 0.5072.

} : A B oy
Volume..... 0.99975 ¥, | 0.99983 1, | 0.99972 F,
|
Pressure... .. 48 188 a9. 839 | 445.752 em.
| Temperature | 20.410 20.414 20.44

As an instance for the calculation we shall consider the last
mixture more in detail. First the pressures were reduced to. the
mean temperature 20°.15 C., by means of the “veal” coefficient of

poe ke Op oe .
pressure variation = (5) at 20°: 0.0034.7). This gave for A, B,
Pp O7
C, 48.193, 59.837 and 115.748 cm. respectively. If p,. V, and p,,
I", respectively represent a corresponding pressure and volume,
we have to the first approximation, which for our case is sufficient :

1 Ps. E, ro Bs

ae 7 ea ee ee Wee hk sy ay
A
Where p, and p, are expressed in atmospheres. From this we may
derive se In the cease considered we found:
ay
from A with C: aes = — 0.0035795
A,
pee et ln — 0.003407
mean: — 0.003493 at 20.13 C.
In the same way for carbon dioxide at 20°.00 C. :
from A with DB: es a
A’
Or: are ke Se — 0.005536
mean y = 0.005675,
and for the mixture 0.2 at 20°.00 C.:
Ba .
— = = — 0.003847.
AY

If the coefficient of pressure variation were known (mean coetti-
cient between O and 20°) we could easily derive 4, for the
different cases. For if for the mixture 0.3 at ¢= 20.13 in the equation:

1) Comp. p. 553.

B
PvaA = Ay + ar a . . . . . . . . (3)

we put v4 = 1, we obtain:
1+a,. 20,138 = A, + Ba,
if «, is the corresponding coefficient of pressure variation,
From the two relations between A4 and by, 44 may be derived
and then Ay, may be found from the relation’):
Ae AA. lea 0.0036625t) . «it 4 Tet, Seen

A difficulty arises from the uncertainty of @, for the mixtures :
an error in @, passes over into Ay, 20 times magnified. This may
be avoided in the following manner:

As normal temperature we shall temporarily adopt 20° C., and
then we write KAMERLINGH ONNES’ equation for the area of the
pressures considered here:

pV = Vins (ne a 2 oi af

V is the volume really occupied by the gas, V.y,, the normal
volume at 20° C., viz. the volume occupied by the quantity of gas
considered at 20° C. and 1 atmosphere

Now:
F ee 0.0086625 ; |
Ax = Axky ae eS ff
; eat 1B 1 + 20 X 0.0036625 |
AK,, }! + 0.004125 (20) i. +, a
A comparison with
Ba Vn
Ma Fi remetee| A VAG ae a
/ 4 | « ' V ( )
where J’y is the normal volume at O° C., gives the relations:
Ad» Vi == Age clas 8
Ba V3, = Bie are eee (©)
whence:
By BK
{2 == rE e ° . * e e . (9)
ne! : K
Hence it is given that for the mixture 0.3 at 20°.13C.:
Br
r — — 0:003498.
G K
From (5) follows, putting ¢— 20°.13 and V= Vy,:

1) Comp. Comm. N'. 71, These Proc. III June 29, 1901, p. 180.

1 +018 apx = Ax + Bx.

«kK represents the coefficient of pressure-variation of the mixture

)

he mean coefficient between 20° and 7), if the original pressure (at

20° C.) is 1 atm. From these two relations A, may be derived; it

must be remarked that now an error in @q passes over diminished

into the result. By means of (6) Ax, may be derived from Ax.
So 1 found for the mixture under consideration :

fore20". 15.0.2: AR 1.003969 , Ber = —.0.009521:

Further | accepted for a,x: 0.005445, found by linear interpolation
according to wv between the value 0.008454 for carbon dioxide derived
from Craprcis’ data, and the value 0.005423 for oxygen derived
from Joniy’s data. It then follows that Ax,, = 1.008524.

The different values thus found are combined in Table XIII.

T A Bol, BRUT

| ee ON Se | Weight. |
are rs |
Carbon dioxide | 1.00574 | 0 1 |
| 9
Mixture 0.2 | 4.00388 | 0.1994 | =
» 0.3 | 4.00352} 0.3072 ei

Oxygen | 4.00064 | 14

—

For oxygen Ax,, is derived from the data for Ay,, and L4,, given
on p. 549.
I have put:
sAg,, = 1+ a, (1—a)? + 24,, a 1—a) + @, 2’,
and have calculated the coefficients by means of the method of least
squares. There «ras compared with »lq,, —- 1 may be considered as

perfectly accurately known. I found:

i 0.00570
a, == 9.00142
a == 0:00065:

In table XIV (p. 554) the values (' derived from them are com-
pared with the values derived directly from observation 0.

In order to derive the coefficients A4, from the coefficients <1 x,,
an accurate knowledge of the coefficient of pressure-variation is
required, In a following paper, however, will be deseribed how the
coelficients A,,, may be used to derive from the volume of a gas

Carbon dioxide) 1.00574 | 1.00570 | 4- 0.00004 |

Mixture 0.2 | 4.00388 | 1.00413 | at 95 |
|
» 0.3 | 4.00852 | 1.00340 | + 12
Oxygen 1.00064 | 4.00065 | — 4

measured at about 20° CC the theoretical normal volume of that
quantity of gas (at O° ©).

Physics. — ‘“/sothermals of imictures of ovyygen and carbon dioxide.
ITl. The determination of tsothermatls between 60 and 140
atmospheres, aud hetiseen. —15 ‘Es and +60" ede By WE.
Kresom. Communication N°. 88 (8° part) from the Physical
Laboratory at Leiden, by Prof. H. KamErnincn Ones.

(Communicated in the meeting of October 31, 1903).

§ 14. During my measurements of the isothermals of mixtures of

oxygen and carbon dioxide it appeared desirable to take several
precantions and to make some modifications in the usual methods.

They will be described here in connection with and in behalf of

following papers on the results obtained.

§ 2. The arrangement. The manometertube and the experimental
tube which beforehand had been cemented into a steel flanged tube
(comp. Comm. N°. 70 V, These Proc. IV June 29, ’01 p: 107) were
placed into steel pressure eylinders. For the shapes of these see also
Comm. N°. 43, These Proc. 1 June 25, 1898, p. Se, fie. 2a ie
arrangement as drawn there has been modified, viz. the two pressure
eylinders into whieh the aforementioned tubes were placed were
entirely filled with mercury. They communicated at their lower ends
by means of a steel tube and of a steel T-piece with each other and
with a third pressure cylinder. This was filled partly with mercury
partly with glycerine. To obtain pressure, glycerine was forced into
it by means of a ScuArrer-BepeNBerG pump. This arrangement offers
the advantage that the tubes filled with gas do not come into contact
with the glycerine, and the mercury which is forced into the tubes
only slightly with the glycerine. In this way it was very easy to
redetermine the normal volume after lifting out the experimental tube

from the pressure cylinder, while the mercury menisci in the tubes

Eee

( 555

kept good during a very long time and no or very little soil was
deposited in the tubes.

The pressure cylinders and the connecting tubes had been well
‘cleaned beforehand with benzene, which was removed by heating
while air was sucked through. The connections were tightened by
leather washers soaked in paraffin. The packing which had to prevent
leakage of mercury along the pivot of the high pressure cocks through
which the mercury passed which was to be forced into the observation
tubes, consisted of rings cut from selected Spanish corks. During the
observations the two observation cylinders were disconnected from
that. where the pressure of the glycerine was transferred to the
mercury in order to be independent of leakage that might occur in
the pump or in the glycerine lead’). A perfectly tight fit of this
enclosed portion even at the highest pressures was secured.

§ =p The measurement of the rolumes. The determination of the
normal volume was made in the same way as has been described
in Comm. N°. 70 V. These Proc. 1V June 29, 1901, p. 107 and in
Comm. N°. 78, These Proc. VI April 19, 1902, p. 761, especially the
same precautions for the constant temperature and pressure were taken.

The normal volume was determined at least twice before and
twice after the measurements. It must be recorded, however, that
this was not done with the first quantity of carbon dioxide of which
the isothermals from 25°.55 C. to 37°.09 C. were investigated, because
the experimental tube had broken, while in the case of the manometer
we may profitably substitute a direct comparison with a standard
manometer, {0 which Comparison [ shall refer later.

I found for the normal volume of the hydrogen manometer :

22 Sept. ’O2: Dsed b= Ce:
23.494
55 rs Ma HS
12’ Nov. 23.220

As the first 3 measurements are not made in the bath of constant

temperature TI have in the calculation of the mean assigned the
weight 3 to ihe last determination and have adopted J7y = 23.210% ce.

From the following the advantage of a hydrogen manometer may
appear *). Most of the determinations with the first mixture (0.1
oxygen in carbon dioxide) were made with an air manometer. During
the experiments phenomena occurred which pointed to variations of

') Small variations of pressure could then be applied by screwing slightly in
or out the pivot of one of the fine high pressure cocks in the enelosed portion.
*) Comp. Comm. N°. 50, These Proc. II June 24, 1899, p 29.

the normal volume of this manometer. The manometer was removed
from the pressure cylinder and the normal volume redetermined, and
it appeared that from 22.114 ce. (May 9 1901) it had fallen to
22.056 ce. (Aug. 23 ’02). After this the manometer has been cali-
brated for the second time (calibration /) *) and filled with hydrogen;
of each of the isothermals determined some points have been tested
by means of the hydrogen manometer. Column (€' of table XV gives
the mean relation of the pressure measured with the hydrogen mano-
meter and that measured with the air manometer, where for the
normal volume of the latter we have taken the mean between
those before and after the experiments. Column A gives the date,
B the temperature relating to the isothermal.

TABLE XV.

A B. | C

20 June ’02 17.60 4.0020
20» » 90.29 | 4.0017
aS » » 94.99 1.0016"
D4 » » 99) 68 4S 42 O23
Ua Se 23.99 \. A 0013
Yb » » 95.290 |i 1.0019

mean : 1.0018

i
|

From column C we cannot derive a regular course in this short
period, so that for these isothermals [ have multiplied all the pres-
sures measured with the air manometer by the coefficient 1.0018.
On June 5, 6 and Aug. 21 points of the border curve have
been determined. These could only be brought to harmonize with
those determined later with the hydrogen manometer by multiplying
the pressures by coefficients which are combined in the following
fable together with that afore-mentioned. Hence this shows the course
of the variation during that period.

If we compare these figures with the values for the normal volume
before and after the measurements, it appears that almost the entire
variation has taken place during this last period. From May ’O1 to

') Comp. this Comm. |. p. 534.

TABLE XVI.

5/6 June ’02 1.0021%
90/26 » 5 et OOIS8

|
|
21Aug. > | 0.9997

June °02 the manometer was but seldom used, and the pressure
during that time was low, while the pressure in the months June
Augustus “O02 was often and during a long time from 60 to 125
atmospheres. Hence it seems that this variation is much greater at a
high than at a low pressure.

A similar variation of an air manometer with the time, probably
owing to the absorption of oxygen in the mercury, has also been
noted by Kurnen and Rosson (Phil. Mag. Jan. ’02 p. 150).

In the mixtures of the molecular proportions O.1 and 0.2 of

oxygen the variations of the normal volume were less than

1000 In

those cases we have accepted for the normal volume the mean
of the values before and after the measurements.

On the other hand, in a mixture with a molecular proportion of
0.3072, which for some weeks had uninterruptedly been exposed to
high pressure, the normal volume of 72.878° cc. before the expe-
riments (15 June °03) had fallen to 70.980 cc. after the experiments
(13 Aug.). It being highly probable that the variation of the normal
volume involves a considerable variation in composition, the results
of the measurements with this mixture which with regard to the end
condensation pressures and volumes extended to —14°.7 C., will
not be given here.

This also shows how very important it is that we should be
able to determine the normal volume after the measurements *),

From the observation of the volume oceupied by the gas at a
temperature of about 20° C. and a pressure of about 1 atmosphere
we derived the volume which the gas would occuppy at 20°C. and
Tatm. (75.9467¢m. mereury at Leiden, comp. Comm. N°.70, These Proce.
IV June 29, 1901. p. 111). Use was made of the coefficient of pressure
variation given in this Comm. II, p. 553, and the law of Boyne
was applied. By multiplication by the values of the coefficients
Ax, given in table XIV p. 554 under ( we find from this the
volume which the gas would have occupied if from an infinitely

1) Comp. Comm. N®. 50. These Proc. Il June 1899, p. 29, and N°. 70. V.
‘These Proc. IV, June 29, 1901, p. 107.

(995. )

large volume at 20° C. it were reduced to a pressure of 1 atm.,
and it had followed the laws of the ideal gases. We then find the
theoretical normal volume (at 0° C.) by means of the coefficient of
pressure variation (= coefficient of dilatation) for the ideal gaseous
state. As the calculations of the correction that according to Comm.
N’. 71 (These Proc. IV June 29, 1901, p. 125) must be applied to
the coefficient of pressure variation of pure hydrogen in order to find
that coefficient for the ideal gaseous state were not finished when I
began my calculations, | have adopted for this the value 0.0036625,
which in Comm. N°. 71 was given as a first approximation. The
corrections, however, which accordingly must be applied to the
results, will certainly lie far below the degree of aceuracy which I
could attain in my experiments of the isothermals at high pressures.

After what has been said on the calibrations’), the measurement of
the normal volume and the reduction to the theoretical normal volume
[ can confine myself to a short note on the measurement of the
volumes. The top and the base of the mercury were read with an
eye-glass, parallax was avoided in the way described before (Comp.
this Comm, [ p. 553). In this manner 0.1 mm. could be read. We
assumed that the mereury meniscus in the graduated stem of the
experimental tube has the form of a spherical segment, hence by
multiplication of the bore by half the height the volume may be
found with a sufficient degree of accuracy, our method of reading
considered. When the mixtures split into two phases, the position
of the liquid meniscus was also read. Corrections were applied for
the expansion of glass due to heat and to the inner pressure.

§ 4. The measurement of the pressures. The pressures were
measured with a hydrogen manometer, ranging from 62 to 196
atmospheres *).

In the first part of this Comm. (p. 932 ff.) | have discussed the
calibration, in § 8 of this paper the determination of the normal
volume. We need only add that the hydrogen was prepared as
deseribed in Comm. N°. 27 Zittingsversl. V, Mei 1896 p. 42.

From the means of the values of J74 and Vy of the table
from which table VIL forms an extract and from the normal volume

!) Comp. this Comm. [, p. 532. :

*) It appeared that the manipulations of the stems of the manometer- and the
piezometer tubes in the blow-pipe, as for instance the sealing of the top of the
latter, lad to be made with special care and the tube had to be cooled very care-
fully and slowly, else tensions will rise in the glass and consequently when high
pressure is applied (in these experiments 140 atm. was reached, the manometer
has stood 195 atms. several times) the tube will burst.

given in § 3, while the volume of the narrow capillary above
between the mark and the place where if is sealed was accounted
for, a table was derived. This new table gives for each division Q the
density d4 of the hydrogen when the mercury reaches that division
at a temperature of 20° C., expressed in terms of the normal density
(O° C., 1 atm. 45° N.L.) as unity. For the values of Q between
25 and 50 the table increases by 0.5; hence also for the higher
values of the pressure (as far as Q@ = 40) the error made by
interpolating linearly is less than 1 atin.

To derive from these densities the corresponding pressures we must

know the isothermal of hydrogen at 20° C. Measurements of this
have been made by ScHALKWUK; they do not, however, exceed the
density 54. An extrapolation from these observations for the densities
wanted is not allowed with a view to the mean error of his determination
of the (' of the series of KAMERLINGH ONNES (cf. SCHALKWIJkK’s Thesis
for the doctorate, p. 115). Observations at higher densities have been
made by Amacar (from LOO to 3000 aims.) The isothermal for hydrogen
at 20° C. derived from AmaGart’s data:
PUA gy) = 1.07252 + 0.0007194 14 + O.000000672 4?

(cf. ScHatkwik’s Thesis for the doctorate p. 121) does not agree,
however, with that from ScHALKWIk’s) observations. From these”
for instance, follows at d4=55: pv4,, = 1.11194 (cf. 1c. p. 124),
hence p= 61.157, whereas from the isothermal given by Amacar
we derive at p= 61.157: d4 = 54.897. ScHALKWiJk’s observations

have been made very carefully especially uis determination of the
normal volume (see Comm. N°. 70, V, These Proce. 1V June 29, 1901, p.
107). If with this we compare the way in which AmaGar has determined
his normal volume (Ann. de Chimie et de Physique, t. 39, 1893, p. 83)
it seems not entirely without reason if, while waiting for more
accurate determinations of the isothermals of hydrogen at higher
densities, we make those of AMAGar agree with those of ScHALKWIJK

“Ore ‘ D4.897
by multiplying all the volumes of the former by the factor ———
v0

So we obtain:
PUAgo = 1.0705 + 0.000717 4 + 0.00000067 (1.47.
To test this we compare the value of pry,, at d4 = 1, viz. : 1.0712
resulting from it, with the value of pe4,, which follows from
the value of the coefficient of expansion according to CHaApputs :

]
«, = 0.0036606 *), Via: 1.0732. The difference is — , so that the

1) See Scuatkwisk, Thesis for the doctorate p. 116.

( 560 )

equation found, which deviates from AmMaAGat’s observations at higher

ee 1 ;
densities ae does not deviate from the observations at smaller
D900

densities by more than =—
i 500

The following term in the series of KAMERLINGH ONNES would be
Da : Lats E
—. If we derive a value of )4 from the data given in Comm. N°.71,
vA
These Proc. IV June 29, 1901, p. 132, for hydrogen at O°C., 15°.4C.,
99°.25 C. and 200°.25 C., we find that this term for d4—=150
would yield in pra,,: 0.0009, so that if we omit this term at the

is made. As there exists

highest pressures an error of less than 7000
already some uncertainty about the exact shape of the isothermal,
I have omitted this term.

The values prg,, calculated thus for the different values of d4 of
the table mentioned at the beginning of this section, have been added
to this table together with the values for p derived from them‘),

When the isothermal of hydrogen at the densities occurring here
will be known more accurately, the pressures given here will require
a correction for which the afore mentioned table may be useful.

The temperature of the manometer differed at most a few tenths
of a degree from 20° C. The temperature coefficients for hydrogen
at 20° C. are found from the value of Aa, (given in Comm. N°. 71)
of the series of KameruincH Onnxes and AmaGat’s values of Ba and
(4 (given in ScHALKWik’s Thesis for the doctorate, p. 120), for the
femperatures O° C., 15°.4 C. and 47°.8 C., observing the reduction
mentioned to obtain the agreement with ScHaLkwisk’s isothermal.

TABLE XVII.

“Tiere
males:

200 0.714 | 150 | 0.531 100 | 0.349 |
19) 0.677 ! 140 -| 0.494 90 "| ~0.344
|

{RO 0.640 130 0.458

170 0.608 20 | 0.499

|
160 | 0.567 |} 410 | 0.385 G0
| |

!) This table has been given in my thesis for the doctorate,

|
.

( 561 )

0
Column Ge) of table XVII gives the temperature coefficients thus
ar J,

found for the different pressures p.

Also a correction was applied for the difference in level of the
mercury columns in the manometer and the experimental tube, for
the expansion of the volume of the manometer tube cansed by the
inner pressure, and for the difference in capillary depression in the
two tubes. For the latter a separate experiment has been made to
determine the depression in a tube of the same inner bore as thie
manometer tube. This correction was 0.01 atmosphere.

The manometer was read in the same way as the piezometer

- (see p. 558). The level of the mercury in the manometer tube and
the temperature of this were read before and after the reading of
the meniscus and the temperature of the experimental tube. The
temperature of the manometer could be read to within 0°.05.

After the isothermal determinations the hydrogen manometer was
compared with the standard manometers (Comm. N°.50, Proce. June 1899)
which have been very accurately compared with the open manometer
by ScwatkwukK (Comm. N°. 67, Proc. Dec. 1900 and Jan. 1901,
Comm. N°. 70, Proc. May and June 1901). To render this possible
the hydrogen manometer had been constructed so that the lowest
pressure which could be read on it could still be measured with
the standard manometer IV‘). Table XVIII gives under the heading
A the pressure as measured with the hydrogen manometer used by
me, under the heading B the same pressure measured with the
standard manometer.

TABLE XVIII.

aw | B
|
| 64.04 | 64.040
| 64.02 | 64.024

Obviously the agreement is quite satisfactory. This comparison
comes in the place of the determination of the normal volume after
the measurements, and also of more determinations of the normal
bore of the graduated stem. (Comp. p. 540). As the there mentioned
mean percentage difference 0.19 °/, is principally due to the difference

') For the way in which this comparison has been made comp. VeRscHAFFELT.
Thesis for the doctorate p. 17,

between the two determinations of the normal bore, this comparison
highly improves the accuracy of the manometer.

The thermodynamical equilibrium in the experimental tube was
reached by means of an electromagnetic stirring apparatus; to
secure the equilibrium of pressure between the experimental tube
and the manometer [| waited 5 minutes after each adjustment before
reading. Of each isothermal two series of observations were usually
made, one beginning with the lowest and ending with the highest pres-
sure, the other in reversed order. Only rarely the results of these two
differed as much as = To judge of this see table XTX, which relates

”
to the isothermal for 22°.68 C. of a mixture of O.1047 oxygen in
earbon dioxide. Here 7 represents the volume, p, and py the corre-
sponding pressures in the two series, with a constantly rising and
a constantly falling pressure respectively, 4p the difference, rji,, and
Vig. the volumes of the liquid also in the two series, 4orj,, the
difference between them.

The agreement of the pressures is satisfactory, that of the volumes
of the liquid leaves to be desired. Although this is partly explained
by the circumstance that the volume of the liquid cannot be read
so accurately because the form of the meniscus is not so sharply
determined as is the case with mercury, and parallax could not
so easily be avoided as with the mercury menisci, if yet appears
that, if we desire to investigate this subject more fully, more care should
he taken to procure equilibrium by stirrmg and waiting.

§5. The constancy and the measurement of the temperatures. The
manometer was surrounded by a jacket with flowing water kept at
constant temperature by a thermostat, as described by ScHALKWIIK
Comm. N°. 70, Proc. May ’O1) with the modification in the thermo-
regulator described in Comm. N°. 78 (Proc. April 1902 p. 762).

In jhe same way the experimental tube was kept at constant
femperature by means of a second thermostat. This differed from
the former in the following respects:

The connection between the heating bath and the mixing bath,
the mixing bath and the connection between the mixing bath and
the observation bath have been insulated more carefully by means
of wool, paper and felt; this was necessary because greater differences
of temperature with the surrounding atmosphere occur here.

To the glass portion of the thermoregulator a side-tube with a

cock is sealed on, which facilitates the admission of a quantity of

mercury from a mercury reservoir, which by means of an india
rubber tube is connected with that side-tube, into the thermoregulator

——

(563 )
TABLE XIX.

“s fr Pf Ap Tl4r rig. f Arig

0.012159 | 58.66 58.60 | +0.06

41384 60.88 60.92 —0.04

|
|

40605 | 63.27 63.31 —0.04
0.009826 | 65.7% | 65.775 | —0.03
9047 | 68.26 68.31 —0.05

|
! :
| 8269 7090 | 70.9% | —0.04
/
|
|
|
)

7489°| 73.47 73.51 —C.04

67125 76.07 76.44 —.0%

59085 78.725 de. difference in saturationvolume:
5917? 78 .75° —Q.03 bec. —0. 000009
| 546 79.95° |-79.985 | —0.03 | 0.000217 0.000180 9.000037
| 5157 | 81.26 | 81.395 | —0.43 397 ete) \h eee 6
| 708 82..88° 82.895 = O12 583 ~ 29
4379 84. 70° 84.765 —=() 0G 746 672 oo 47

4309 | 85.05 | 591

4978 | 85.22 | | | 625

4258 85.35 | 288

4243 | 85.40 95

4A9| 85.54 | | | 125

reve 85.54 | | | @ce. difference in saturationvolume :
| 420° 85.52 | 10.02) ee. —0. 000005

194.64 1124.36 | 40.98

‘and hence the adjustment for different temperatures*). The narrow

part of the glass tube where the supply of gas is regulated, has

') A similar arrangement has been described by Friepuinper, Zeitschrift
fiir physikalische Chemie, Bd. 38 p. 401, 1901.
oT
Proceedings Royal Acad. Amsterdam. Vol. VI.

fenos: *)

been eraduated in mm. over a length of 4 em., which facilitates a
finer adjustment by moving up and down the supply tube.

For temperatures higher than 85° the water streamed succes-
sively through two heating baths, each provided with a thermo-
revulator; the first brought the water to 35° C., the second to the
desired temperature. To avoid exchange of heat with the surrounding
atmosphere the last bath was coated with asbestos, except where
it came into contact with the flames.

One thermoregulator had been constructed for higher temperatures,
filled with xylene and goes as far as + 90° C., the other for lower
temperatures was filled with benzole, of which the coefficient of
expansion was determined at 0.0011 and goes from —40 to+ 40°C.

For temperatures below that of the water supply, the water
streamed between the overflow and the heating bath through a zine
vessel insulated with felt, where small pieces of ice were continually
brought in.

By leading the water back to the overtlow after it has flown
through the observation jacket by means of a membrane pump *)
through tubes enclosed in wool, we could make measurements to
about 1°.9 C. For the experiments with the mixture 0.3, mentioned
in § 3, we used the current of solution of calciumehloride at constant
temperature, described in Comin. N°. 87, Zittingsversl Deel XI
Juni 1903 (see Pl. IL of that Comm., which shows the whole arran-
gement with the thermostat and the observation bath).

For temperatures above 380°, and also for temperatures as much
again below the temperature of the room, it appeared necessary
to replace the observation bath, which first consisted of a simple
vlass tube, by a vacuum jacket *). After this the difference in tem-
perature at 84°C. over a height of 33 em. without stirring amounted
to O'.02 C. Moreover we have always stirred before each observa-
tion. The water was insulated from the copper piece with which
the jacket was fastened to the steel flanged tube of the experimental
tube by a laver of sulphur. This prevented the cement from softening.

In order to prevent variations of temperature of the gas Compressed
in the experimental tube owing to conduction of heat along the
merenry column to the mercury in the compression tubes, we took
care that in the observations, where the mercury meniscus was lowest
the mereury column still stood over a length of 40 ems. in the jacket.

l) Comp. pe Haas, Thesis for the doctorate fig. I.

2) Comp. Comm. N°. 85, Versi. Deel XIE Juni 1903, p. 214. The case acting as
a spring was placed as low as possible to leave room for the coil which moves
the electro-magnetic stirrer.

'( 565 )

The temperature of the experimental tube was read with an eye-
glass to within O°.OL on an “‘Einschlussthermometer”’, divided into
O°.1, with a seale on milkglass. From time to time this was
compared at different temperatures with a similar thermometer tested
at the Reichsanstalt with the air thermometer, while the variation
of the zero of the latter in the mean time was accounted for and
also the temporary depression of the zero, which, after the thermo-
meter had for a long time been heated at 48° C., amounted to
0°.02* C.

6. Reduction of the observations. In cases where, in contrast
to the determination of the plaitpoint and the point of contact of
the mixtures and the critical point of carbon dioxide, the greatest
possible constancy of the temperature was not absolutely necessary,
the temperature during the determination of an isothermal which
lasted on an average from 3 to 4 hours was allowed to vary a few
hundredths of a degree. For the reduction to one temperature,
temperature coefficients for the different volumes were derived from
the observations.

In the two series, one at an always increasing, the other at an
always decreasing pressure, pressures were measured, corresponding
to different volumes, which in the two series differed but little.
Pressures were derived from them for the same volume and then
the mean was. found. When it appeared that these pressures agreed
sufficiently (comp. § 4) we have afterwards simply taken for two
corresponding points the mean of the volume and the pressure.

Physics. — “Lsothermals of mivtures of orygen and carbon diovide.
LV. Isothermals of pure carbon dioxide between 25° C. and
60° C. and between 60 and 140 atmospheres.” By W.H. Krrsom.
Communication N°. 88 (4 part) from the Physical Laboratory
at Leiden, by Prof. H. KammEruincH ONNEs.

§ 1. Reason for the investigation of carbon dioxide. Although the
isothermals of carbon dioxide have been extensively investigated by
Amacat, [| have yet determined a number of isothermals together
with its critical point. I was led to it by the following considerations :

Ist. it was desirable that I should be able to judge of the purity
of the carbon dioxide which I used for the preparation of the mix-
tures, and it seems that this judgment may best be derived from the
increase of the vapour pressure with condensation at a stationary
temperature *) ;

4) Comp. Comm. N°. 79, Proc. April 1902.

( 566 >

2nd_ difficulties had arisen about some quantities at the critical point
of carbon dioxide, which are important for the theory of the mix-
tures. Amacat, for instance, had determined the critical pressure at
72.9 atm., while Verscuarre.r from AmMAGat’s isothermals derived
73.6 atm."). Obviously this may give rise to an error in the deter-
mination of the data of the critical point of the mixtures, if as in
Comm. N°. 592) the logarithmical systems of isothermais are shifted
over each other. Moreover in Comm. N°. 75, Proc. Dec. 1901 p. 299,

for (=) at the critical point from AmaGart’s isothermals: 7.3
Or
had been derived: from his determinations of the saturated vapour
pressures: 6.5. This points to an uncertainty in the determination
of the critical volume. AmaGcar has determined the critical point
and the vapour pressures in different apparatus and hence probably
also with other carbon dioxide than the isothermals; by determining
the two in the same tube with the same carbon dioxide I hoped to
arrive at more certainty on these points.
3°. By comparing the isothermals of the mixtures after Raveau’s
method with isothermals of carbon dioxide observed in the same
experimental tube some systematical errors which might oceur in the
observations are eliminated from the determination of the critical
data of the mixtures. In this way an error in the determination
of the diameter of the graduated stem of the experimental tube
would have no influence on the critical pressure and temperature of
the mixture.

§ 2. In the following tables ¢ is the volume expressed in terms of
the theoretical normal volume, p the pressure in atmospheres (0° C.,
45° Northern latitude), vy, the volume of the liquid. The points of
the beginning and the end of the condensation are marked by the
letters be and ec. For the point 4¢ we adopted the point where
after having decreased the volume there appeared for the first time
With proper stirring a liquid ‘Schlier” on the wall, or after having
increased the volume with proper. stirring only such ‘“Seblier”
remained. These two points agreed sufficiently. The point ec could
be observed sharply, as with a small variation of the volume the
last part of the phase disappeared or reappeared. Especially here,
however, phenomena of retardation had to be avoided by forcible
stirring. J"), stands for the theoretical normal volume, the meaning
of Ag, is explained in the 2%4 part of this Comm., p. 552.

) Comp. Comm. N® 55. Proc. April L900,
*) Proc. Sept. 1900.

(O67 9
First carbon dioxide.

Before the measurements : My. = 71.020° c.c.
Ax,, = 1.00570

a. Isothermal of 25°.55 C.

No v | Pp pe tig
| 4 | 0.008573 | 63.12 | 0.54115 |
| 9} 7812 | 64.36 5028 | be
| 3 | T0AG | 64.42 4539 | 0.000420 |
| 4] al 64.44 AOL | 859
| 5 | 504 | 64 A 3545 | 0.001276 |
| 6| 4837| 64.40 | 315 | 1664
a 4068 | 61.39 | 2619! 9088
g| 3205 | 64.49 | 2065 | 9507
| 9| 3085 | 64.37 | » 1986 | £652
140} 2869 | ost | 1848 2)
4278 | 64.433) | 1025) ¢ |
12 | 2645 | zo. | 1876 |
13| - 2520 | 80.658 | 2033 |
| 44 | 2438 | 99.97 | 2967
45 | 9366 | 105.79 | 2503
16 |

2309 | 122.555 | 2830 |
| :

2970

1) We shall later revert again to the purity of the carbon dioxide, as it appears
from the increase of pressure at the condensation.

2) Here the liquid meniscus reached the part of the tube where through the
sealing in the blow-pipe the marks no longer were visible.

( 568 )

h. Isothermal of 28°.15 C.

ive 4 |p | BE | "liq
| 1 | 0.009238 — 63.4 0.5924
| 2 8565 | 65.19 5583
| 3 | 7807s| 66.755) 5212 | |
| 4 | 7030 | 67.995| 4780
| 5 | 6950 | 68.49 | 47395
6 | 6673 | 68.39 | 4564 | be
7 6300 | og.41 | 4310 | 0.(00290
8 | 5502 | 68.41 | 3764 oj
9 A712 | 68.438| 32248 0.001625
10 3974 | 68.48 | 9724 2189
11; 349] 68.45 | 2135 1)
4a! 3011 | 68 48. | 9060 | ec
43 og13 | 72.408; 2037 |
| 9670 | 78.55 | 2097 |
15 | 9546 | 89.54 | 9279 |
16 | 2446 | 103.47 | 2534 |
17 936) | 449.61 | 2834 |
18 9315 '| 136.58 3161 |
| | |

e. Bordereurve in the neighbourhood of the critical point.

Beginning condensation End condensation
aera oe [eae Bae
| Temp. | v 1 ae Temp. | v p
| a i
30.05 | 0.005594 | 71.47 } 30.41 | 0.003398 | 71.53
30.82 4833 | 72.725| | 30.81 3725 | 72.74
a |

, ad. Critical point:
Temp.: 80.98 Pressure: 72.93 Volume: 0.00443 *).

‘) Comp. footnote to the preceding table.
2) For the determination of this comp. § 5.

1 0,0L0068

2 0.009314

63.36

65,39

ee ee)

3 | 8582 | 67.22 |
4 | 7809 | 6.085
5 | 7034 70.73
6 | 6975 | 74.95
7 5483 | 72.746
, 8 5102 | 72.87
9 KI77 | 72.93
10 4403 | 72.94
i Wh | 72.48
12 3959 72.96
430 3656 72.£95
(| 3906 | 73.53
it 3230 73.89
46 | 3051 | 75.43 |
147 | 2862} 79.48
| 18 | 2724 | 86.40 |
149} 2593 | 95.70 |
120) 9509 | 106.18
2| 2435 | 419.35
| 29 | 2362 | 138.65

0.
QO.
0.
0.
0.
0.
ho.

6379 |
6090.
5769 |
D099 |
ANT

ADD

3988 |

3718

3214

3104

28885
2669 |

2423

26645 |

.2906%

0.010086 | 638

Isothermal of

31.89

0.009214 | 65.99?
9570 | 67.945
Tile ee, LOL OS
7017 | 71.68
6267 | 73.038
5598 | 73.94
B17 | 74.24
NT495| Th, 4A
43045! 74.56
2942 | 74.69 |
3610 | 75.00
3998 | 76.90 |
9883 | 82.02
DAT 89.90

9593 | £9.77
2503 | 114.45
2439 | 122.79
9377 | 136.71

iO).

CU,

~2365
2443
2587

.2790

fore -) .
g. Isothermal of 34°.02 C. h. Isothermal of 37°.09 C.
| No. | D RAE J | pe | | No. | v | p | pp
4 | 0.010067 | 65.48 | 0.6562 1 0.010863 64 56 | 0.7013
| 2 | 0.009337 | 67.295) 0.6283 | 2} 10093 | 66.£0 | 0.6752
| 3] 8560 | 69.49 | 0.5048 | 3 | 0.009339 | 69.99 | 0.6471
\ 4 | 7791 | 71.64 | 0.55845) | 4 | S54 | 74.73 0.61359, /
| 5 | 70238) 73.65 | 0.5173 | bs | 7810 7411 | 0.5788 | |
6| 6255.} 75.24 | 0.4712 | | 6 | | 7059 | 76.40 | 0.5394 |
| 7] 558€5) 76.605) 0.4926 | | 7 | 6987 | 78.585} 0.4940 | |
| 8 AG72 | 77.57%) 0.3624 back 55255| 80.47 | 0.4446 |
psa 20744) 78.385] 0.3148 | tO) AUTO) 82.40 | 0 aati
| 40 | 3243 | 81.41 | 0.26305 10 4011 | 83.89 | 0.3365
11 9955 | 86.16 | 0.2546 | |41 | 3930 | 88.89 | 0.2871
| 412 2746 | 95.02 | 0.2809 | 42 9799 | 103.08 | 0.2885
13| 9614 | 105.95 | 0.270 | 13) 9609 | 419.97 | 0.3112
14 2540 | 119.53 | 0.3000 | 144] 2495 136.01 0.3893)

15. | 2426 | 136.66 | 0.3316 = zt

Second carbon diovide *).
sefore the experiments: Vi,;7~ = 69.647 ¢.c., weight 2
Aiter: Ws z 62.629) 2 ayer

Mean bog be
2. Isothermal of 41°.95 C. k. Isothermal of 48°.40 C.

No | v Le ee | pe | No. | v | p | pe
1 | 0.011546 | 64.85 | 0.7487 | | 4 | 0.012311 | 65.20 | 0.8027
2 | 407945| 67.28 | 0 7262% | | 44572 1. 67°69) | Osveae
| 3} 40047 | 69.84 | 0.7014 | 3} 407875) 70.52 | 9.7607 |
4 | 0 C0911 | 72.78 | 0.6704 - 0.009970 | 73.61 | 0.7339 |
5-|. - 9486 | 75.48 | 0.6405 5 | 9932 | 76.61 | 0.7073
G61 7640 | 78.57 | 0.6003 6 | 8442 | 80.07 | 0.6769
7; 6915 | 81.34 | 0.5699 | 7 | . 7678 | 83.38 | 0.6402
8 G81 | 84.04 | 0.51945 8 | 6899 87.07 | 0.6007
9 5320 | 87.18 | 0.4638 | 9} 6118 | 90.90 | 0.5561
10 4530 | 90.13 | 0.40825 | 40 | D380 | 94.78 | 0.5099 |
i 3778 | 94.40 | 0.3555 414| 4570 | 99.62 | 0.4552 |
12 3087 | 105.01 | 0.3242 12} 3898 | 405.50 | 0.4033
143 | 9817 | 117.96 | 0.3393 13 31995 | 449.38 | 0.3736
114 9642 | 134.85 | 0.3563 | 144] 9864 | 185.56 | 0.3883

') Because the experimental tube has broken, the first quantity was lost. As,
however, the fracture occurred below the graduated portion of the stem, the
advantage mentioned in § 1, sub 3 remained.

/.. Isothermal of 57°.75

1 | 0.013174 66.27 | 0.8730

me 49356 69.20 | 0.8559
3 1586 FAAS 0.8363
4 AC807°| 75.42 | 0 8154
5 400095} 78 99 | 0.7506
6 0.009271 | 82:49 | 0.7648
q 8489 | 86.62 | 0.7347
8 | 7668 | 91.16 | 0.6990
SN 6930 95.73 | 0.6638
10 6113 | 101.32 | 0.6194
| 11 y | 4107.06" |20: 5754 |
| 42 4596 | 114.45 | 0.5960 |
| 13 3795 | 196.10 | 0.4786
| |
14 34915] 435.81 |-0.4647 |

|
|

§ 38. To simplify later calculations I have caleulated for the
isothermals e, 7, g, h, i, h, ¢ the values of pr for regularly increasing

1
densities E . Therefor each value has been interpolated from 4 points
v

derived directly from observation; only for the extreme values we
have interpolated between 38 points’). So we find the values given

1) For this we used the formula of Lagrange, which may be easily written in
the following form:
d—d, | , (d—d,) (d—d,) (d—d,)
— TF +), hes Pp. Jy +(P, ro ae )\—

d,—d, a) (b= dad)
—d,) (d—d,) (d—d,)
Po petroea EAU ss a Lhe
“te E De (d. ee ee ae
where
call gy a tte
at 7 ea
d,—d,
(Any ea 2 2 a
Coad

P represents pr, while — is represented by d. Supposing that @ lies between
i ; :

d, and ds, the two last terms of P become relatively small and they may be
easily calculated with a sliding-rule.

in table XN; the first column gives the different densities (expressed
in terms of the theoretical normal density), the following columns
pe each time for the temperature
mentioned at the head of the column.

the values of delonging to it,

Y ASB

Isothermals of carbon dioxide.

XX.

30. 982-3189? 4, 02 miUGe Al .$5° 48 10° Die
:
od is oa
80 0.8583
400 | 0.6355 | 0.6411 | 0.6528 | 0.6749 0.6997) | 0273497) 087203
420 | 0.5653 0.5745 | 0.5844 0.6036 0.6335 | 0.6742 | 0.7285
140 0.5037 0.5094 0.5240 | 0.54405 0.5746 | 0.6135 | 0.6743
160 0.4499 | 0.4566 | 0.4708 | 0.4918 | 0.5937 | 0.5640 | 0.6273
{80 | 0.4039 0.41065 0.4254 | 0.4466 | 6.4796 | 0.5212 | 0.5864
200 | 0.3646 | 0.3746 | 0.3863 | 0.4081 | 0.446°! 0.4847 | 0.5521
220 | 0.3314 | 0.3387 | 0.349% | 0.3754 | 0.4094 | 0.4536 | 0.52965:
940 | 0.3041 . 0.3109 0.3996 | 0.3477 | 0.38195| 0.4964 | 0.4991
960 | 0.2806 | 0.29875 | 0.3021 | 0.2243°| 0.354575| 0.4048 | 0 4812
980 0.2611 0.29680 | 0.£895>) 0.3052 | 0.3423" 0.3872 | 0.4692
200 | 0.2448 0.9521 | 0.2677 | 0.29155! 0.3302 | 0.3763 |
330 0.2333. 0.2410 0.2590 0.9835 0.32455) 0.3737 |
340 | 0.2273 0.2221 0.25549 | 0.9863 0.3255 | 0.8817 + |
360 0.2305 | 0.2401 | 0.9588 0.2900 | 0.3362
380 0.2497 «0: 9530.--0.2742 | 0 3073
400 0.2690 0.2800 0.30381 0.3376
420 | 0.24695! 0.3230

§ 4.

a and 4 in the following way: From the height of the liquid meniscus

ry, Was reduced to the same temperature for the isothermals

we directly derived the volume of the vapour phase: 7,9). If 7, is
the specific volume of the existent liquid phase, 7, the specific volume
of the vapour (as unity we always have here the theoretical normal

volume), we find:
LV yap. Vira: ( v, dr, vio de,
eg, A Vs— 0, \ Ca AT V—U, pw

After the vapour volumes have thus been reduced to one tempe-
rature, the liquid volumes are derived from this. We have assumed

in this that 7, and v, are functions of the temperature 7 only and

not also of v, as De Hern and others think. On this supposition

we can derive v, and v, from each pair of observations of ri, at

different + and at the same temperature. The values calculated thus

liq

have been combined in table XXI together with those derived directly
from observation.

TABLE XXI.

wo ee (3

Isothermal of 2: Isothermal of 28°.15 C.

| Nrs vi Vo Nrs. vy "9
2 0.CO07812 6 0.006673
3and7 0.002799 7736 7and9 0 003043 6680 |
4ands 9819 77122, Sand 10° 9998 6709 |
Dand9 9809 TAT 19 3011
44 2798 ae = =
te + = 1 ake oS Ae mean 0.003016 0. O06684 |
mean 0. 0028039 0 .007773° = == seis 3 i!

We see that no regular variation in the values of 7, and 7, can
be remarked, so that this justifies with regard to these experiments
our assumption of the dependence of v, and v, on the temperature
only.

In the calculation of the mean values of 7, and rv, in table XXI
we have accorded the same weight to the value borrowed directly
from mean of the values derived from the
other observations.

observation as to the

§ 5. For the determination of the critical point the following may
serve: The thermostat was adjusted at a few hundredths of a degree
below the critical temperature (the temperature above which no
stationary meniscus is observed). By letting a small quantity of water
of higher temperature into the mixing bath, the experimental tube
was brought to a few hundredths of a degree above the critical
and the substance was well stirred. Then the tempe-
If the volume lies between certain linits,

temperature,
rature falls. very slowly.
the following phenomena may be seen: A blue mist is formed which

( 574 )

at a definite place becomes denser and denser’). At a given moment
“strive” appear, the substance boils and rains, a meniscus is formed.
From the very first, the latter is perfectly sharp and flat, it remains
at the same place also. after stirring. The temperature was observed
immediately after the appearance of the striae, then the pressure and
the volume and then the temperature was determined again. So we
obtain the pressure for one or a few hundredths of a degree below
the critical temperature. For this a correction has been applied.

If we allow the temperature to rise, we still see a meniscus
during a considerable length of time after the temperature in the
bath has risen to a few hundredths of a degree above the critical
temperature. It disappears immediately, however, when we stir.
Hence this is no phenomenon of equilibrium.

So we could derive the temperature and the pressure directly
from observation. For the volume this was not possible, as owing
to the effect of gravitation the phenomena described above occur
at different volumes, so for instance in my observations with a
volume: 0.003924 (stirrer below), where the meniscus appeared
in the immediate neighbourhood of the top of the tube, and with a
volume 0.004281 (stirrer above) where the meniscus appeared 1 mm.
above the mercury.

The method generally used for the determination of the critical
volume consists in determining some liquid and vapour densities
at temperatures below the critical, and then using the rule of the
rectilinear diameter of CaiLnetet and Marnias. To this end we
have drawn on a diagram the densities resulting from the data of
§ 4, table XXT and § 2, ¢ as a function of the temperature, and
the diameter has been drawn on it. A deviation from the rectilinearity
could not be stated with certainty. For the critical density, expressed
in terms of the theoretical normal density we derive from this diagram
239, hence for the critical volume 0.00418.

dp Oy
Another method is this: At the eritieal point ) == aay
dd CoeL. 01 v

“y

(for the proof see for instance Comm. N°. 75).
a “dp rat
Mo determine (<= we have combined in table XXIT under O
( 5 :
\ 4 COCL

the vapour pressures resulting from § 2; for the temperatures 25°.55 C
and 28°.15 C we have taken the means from the different values
for the pressure.

') If the temperature is kept constant, the mist during a considerable length

of time (say 10 minutes) does not change to the eye.

( 575 )
TABLE XXII.

Temp. QO. C. O0=C:

D5) 64.40 64.41 + 0.01

28.45 OS .43 68.43 0.00
30.05 Taleras 71.44 == (hes
BOS Foe 720 = (()) (O:
30.98 72.93 |

If we calculate for the different values the coefficient 7 for van
pER Waats’s formula’):
p T—T,
log = wp ae
Pk i
we find with imereasing temperature regularly decreasing values of

jy. If in the development in powers of Ps take one term more,

so that we arrive at the formula:
ie Ce PRESET
log == ——— {| /+ 9 ——— |],
Pk | i i aay
and we calculate the values of 7 and g which give the best agree-
ment, we find very nearly g=//. Then I have put:
re i es grata ae
log —= f ———— +
eo) ee y ig
and found / = 2.914°. By means of this we obtain the values for
p given in column €. The agreement is quite satisfactory, only for
the temperature 30°.82 C. there is a considerable deviation : the same
is also found in the comparison of the saturation volumes so that
here we have probably to do with an error of observation.
From this we find at the critical point:

dp
d oil:
dT coer.

From the determinations of the isothermals we cannot with cer-
et ae (f Op
tainty derive a definite variation of | ~~] at the same volume with

. OE Ts
NS 7 U
the temperature, as may be best derived from table XX. Therefore |

ae |
have derived cad for the different densities from the isothermals
jie

of 30°.98 C. and 48°.10 C. and found the following values:

1) Continuitiit | p. 158.

100 0.581 200 1.403 300 9 304
120 0.742 990) Ae oT 320 2 G24
140 0.898 240 11s 340 3.066
160 1.066 260 1.886
180 {233 £80 2.062

If from this we interpolate in the same way as in § 9 we find that

0 2

ae — 1.610 for the density 225.50, to which belongs the volume:
rt ae
0.00445.

This value does not agree with that derived above from the densities.
The difference is larger than can be ascribed to the errors in the
observation. The deviation is in the same sense as follows from
AmaGat’s experiments. The following might serve as an explanation
of this difference :

According to a remark of Prof. KAMERLINGH ONNEsS from whom a
new paper on the cause of the deviations near the critical point may
be expected (comp. Comm. N°. 74, Arch. Neerl. serie IT, t. VI, p. 887)
the appearance of the mist in the neighbourhood of the critical
point seems to indieate that a part of the substance condenses round
numerous centra equally distributed over the whole space. That only
in this area this appears so distinetly, might be ascribed to the cir-
cumstance that here small forces are sufficient to cause great variations
of density. These condensations might have a perceptible influence
for instance on the saturation volume although the variation of the
pressure would not become perceptible in consequence of It.

In a comparison of mixtures with pure substances according to
the Jaw ef corresponding states we must disregard those conden-
salions, as they do not occur at corresponding points (in mixtures
near the plaitpoint). Hence our purpose will probably be served best
if we adopt for the critical volume: 0.00443, as this value according
to a thermodynamical relation results from determinations not so near
to the critical point, and where therefore particular phenomena which

occur i its immediate neighbourhood have played no part.

The following quantities are further fennd at the critical point,
which are necessary for the comparison of the observations with the
theoretical results of Comms. N°. 75 and N°. 81:

a) ) Ul: i 0 P :
ret Rede) Co )=— 269
(san), Bence (, Di (sie é ata

Here, in agreement with the value of the coefficient of expansion
for the ideal gaseous state accepted in this Comm. II, p. 558 we
have put: 7\= 273.04.

Physics. — ‘fsothermals of miLetures of oLrygen and carbon dioaide.
V. Lsothermals of mictures of the molecular compositions 0.1047
and OAI9IA of oxygen, and the comparison of them with those
of pure carbon diode”. By W. H. Kersom. Communication
N°. 88 (5% part) from the Physical Laboratory at Leiden by

Prof. KAMERLINGH ONNES.

(Communicated in the meeting of October 31, 1905.)

§ 1. The following sections contain the tables about two mixtures
of carbon dioxide and oxygen. For the meaning of r. p, Viiy, and
the determination of the 6.c.- and the ¢.c-points I refer to this Comm.
IV § 2. Of the end condensation point it should be remarked that over
a definite area below and above the plaitpoint temperature the meniscus,
in consequence of the effect of gravitation, disappeared in the tube.

The data about the plaitpoint were derived directly from the
experiment. On the phenomena near the plaitpoint I find the following
remarks among my notes of the observations: When the volume
increases from the homogeneous (liquid) state a blac mist gradually
forms itself. As the volume increases (small variations at a time)
this becomes denser. If the volume increases still more, layers of
different degrees of vefrangibility suddenly appear, which quickly
move among themselves. When we stir, however, they still dissolve
into the thickening blue mist. At a given moment, after the volume
has been increased again a little, these layers begin to concentrate
towards the middle of the tube, at the top and at the bottom it

( 578 )

becomes clear, small bubbles or drops are seen to move from below
and from above towards a certain point in the tube. At last-a
ineniscus appears there. This remains at that place. The temperature
at which these phenomena were observed was adopted as the plaitpoint-
temperature of the mixture considered, the volume and the pressure
as plaitpoint volume and pressure.

If the temperature is alittle higher, the meniscus appears lower
in the tube. The exact point where it appears cannot be observed
with certainty: drops are seen to move from above to below, and
bubbles from below to above more and more regularly towards one
place; at this place the meniscus will appear, but this place is rising
already before the meniscus has properly formed itself. When it is
formed, it generally still rises. If the temperature is still higher the
meniscus is distinctly seen to rise from the bottom of the tube. At
the lower end a quantity of liquid is gathered by the drops which
fall from the top to the meniscus. The same holds, mutatis mutandis,
for temperatures below the plaitpomt temperature.

Of the data about the point of contact only the temperature could
accurately be (to within O°.O1) derived from the experiment. To
determine the pressure some points at the beginning and at the
end of the condensation to within O°.1 of the point of contact
were observed; they were drawn and the point where the tangent
is at right angles with the axis of temperature was found. This
gave the pressure of the point of contact with sufficient accuracy.
Then the point of contact volume was deduced from the isothermal.

The molecular proportion of oxygen will be represented by w,
Vix is the theoretical normal volume, for the meaning of Ax
comp. this Comm. IL p. 552.

§ 2. first mirture of carbon dioxide and ovygen.

7 —— Onna y
Before the measurements: Viz" = 69.743. ce.
»

After A * COLT:

a. Border curve.
Beginning condensation. End condensation.
Temp. D p Temp. | D p |
17.53° | 0.008552 | 66.08 | 44.68 | 0.002597 | 85.52
17.63 8483 | 66.40 14.78 9757 | 87.09
19.48 7708 | 69.48 17.525 9949 | 88.95
20.19 7362 | 71.59 17.68 9986 | 88.29
90.98 | 7988 | 71.94 19.38 3195 | 88.465
21 48 | 6709 | 74.85 | 90.19 3292 | 88.35
22.06 | 6456 | 76.24 | 90.28 3323 | 88.35
92.38 6098 | 77.85 48 3664 | 87.35
22 83 | 5860 | 79.44 92.09 3880 | 86.58
99.87 | 5822 | 7996 | 99.43 4069 | 86.03
92.98 | 5697 | 79.95 | 22.80 | 4301 | 85.34
93.93 | 5366 | 81.46 | 92. 883 4394 | 85.42
99.98 4441 | 84.90
93.18 4663 | 84.16
b. Isothermal of 17°.60 C.
| No. v | p pe | Diig. |
| 1 | 0.011384 | 58.35 | 0.6642
| 2} 40605 | 60.46 | 0.642
3 | 0.009826 | 62.62 | 0.6153 |
4 9047 | 64.84 | 0.5866
5 9503 | 66.24 | 0.56395] de |
6 7489°| 67.85 | 0.5'82 | 0.000338
7 67125| 69.54 | 0.4668 | 574
8 6108 | 71.42 | 0.4344 826
f <9.) 5935 | 74.65 | 0.49595 879
40 5385 | 73.39 | 0.3952 | 0.001105
| 41 5157 | 74.26 | 0.3830 1194
19 | 44865 | 77.42 | 0.3460 4502
13 | 43795 | 77.68 | 0.3402 1556
14| 3482 | 83.35 | 0.9902 2189
45 | 9954 | 88.30 | 0.2608 | ec
16 9848 | 91.715) 0.2612
17 | 97195| 97.38 | 0.2648 | |
18 9572 | 109.13 | 0.2807
19 | WEG |

193.34 | 0.3042 |
!

Proceedings Royal Acad. Amsterdam. Vol. VI.

: SS Se ee ee ee ae
es ee eae oe ee ee oe ee
| a > pe toate
4 ~
4 ( 580 )
: c. Isothermal of 20°.29 C.
No. | v | p | pe | Viig.
3 4 | 0.011699 | 58.86 | 0.6886
oS 2| 414384 | 59 72 | 0.6798
E 3 40605 | 61 94 | 0.6569
gi | 4 | 0.009826 | 64.31 | 0.6319
x 5 9047 | 66.62 | 0.6097
6 8900 | 67.15 | 0.5976
. 7 8269 | 69.04 | 0.5709
7 8 7490 | 74.44 | 0.5348
E | 9 7291 | 71.98 | 0.5248 | be |
10 6713 | 73.07 | 0.4905 | 0.000267
q 44 | 59358 | 72.32 | 0.4470 5965
Za | 12 5157 77.9% | 0.40195 968 |
4 | 43 4468 | 89.88 | 0.3614 | 0.001360
| 44 4379 | 81.39 | 0.3564 4445
15 9640 | 85.85 | 0.3195 |. 2930
1G 3501 | 86.91 | 0 3043 / 540
4 | 47 9335 | 88.98 | 0.2944 | ec
| 48 3132 | 91.50 | @.2866
49 9959 | 95.64 | 0.2830
20 9897 | 97.76 | 0.2832
a 9759 | 104.46 | 0.28895
29 9613 | 114.89 | @.3002
im | 93 | 9597 | 125.128| 0.3162
d. ee! isothermal (21°.99 C.).
No. | D | p Se Brine a oS pe | Din
1 0. 019159 | 58.36 | 0.7096
: 2 41384 | 60 52 0.6889
3 | 0.009826 | 65.32 | 0 6419
2 4 8269 | 70.37 | 0.5819
5 6743 | 75.37 | 0 50595
6 6400 | 76.49 | 0.4891 | be
| 7| 5935 | 77.64 | 0.4608 | 0.000210
| 8 5157 | 80.34 | 0.4143 638
9 | 4379 | 83.76 | 0.3668 | 0.001169
) 10 3878 | &6.60 | 0.3358 | pp
. 1 3613 88.74 | 0 3206
; 42 3004 | 97.418) 0.2966 |
13 9769 | 109,96 | 0.3025
44 | 9598 | 14] 9808. | $288) Oe 98.75°) Osdats |

( 581 )

e. Isothermal of 22°.68 C.

| No. v | p | p | Lig
i —
4 | 0.012159 | 58.63 | 0.7129 | |
2 41384 | 60.99 | 0.6933
3 10605 | 63.29 | 0.6742 |
4 | 0.009826 | 65.76 0.6461" |
5 | 9047 | 68.285 | 0.6178
| 6 | 8269 | 70.92 | 0.5865
7 | 7489° | 73.49 | 0.5504
| 8 | 6712° | 76.09 | 0.5108 |
9 5913 | 78.74 | 0.4656 | dc
| 40 5546 | 79.97 | 0.4435 | 0.000198°
M4 | 5157 | 81.33 | 0.4194 400
42 | 4768 | 82.89 | 0.3952 5975
43 | 4379 | 84.735} 0.3744 709
14 | 4309 | 85.05 | 0.36645 591 |
15 4278 | 85.22 | 0.2646 625
16 4958 | 85.35 | 0.3634 288
17 4243 | 85.40 | 0.36235 951) |
18 4219 | 85.54 | 0.3609 425
49 4218 | 85.53 | 0.3608 | ec
20 30918 | 87.03 | 0.3474
24 3604 | 90.23 | 0.3252
99 3049 | 99.49 | 0.2025
93 9752 | 412.67 | 0.3401 |
24 9612 | 124.50 |
|

1) To explain the irregular course of vj, here, we refer to this Comm. III, p. 562,
while we remark that the variations of %, with the temperature and with the
volume become very large in this area, so that a small error in the latter may
‘give rise to a large error in the value of 7i;.

38*

( 582 )

J. Point of contact isothermal (23°.29 C.). g. Isothermal of 25°.20 C.

No. v p | pe | No. v | Pp | pp |

1 | 0.019150 | 58.95 | 0.7168) | 4 | 0.012159 | 59.81 | 0.7279
9 411785 | 60.04 | 0.70755| 2 41384 | 62.44 | 0.7074
3 11384 | 61 21 | 0.6968 | 3 10605 | 64.59 | 0.6850
4 40605 | 63.59 | 0.6744 4 | 0.009826 | 67.23 | 6.6606
5 | 0.009825 | 66.09 | 0.6404 | 5 9047 | 69.97 | 0.6330
6 9047 | 68.70 | 0.6215 | 6 8°69 | 72.78 | 0.6018

2 8269 | 71.34 | 0.5890 | 7 7490 | 75.69 | 0.5669

| s| —-74¢0 | 74.04 | 0.5545 | 8 67125| 78.59 | 0.5976

9 | 67125} 76.71 | 0.5149 | 9} 5935 | 81.69 | 0 4848

| 10} 5935 | 79.48 | 0.4717 | 10 5156°| 84.85 | 0.4376

au 5546 | 80.80 | 0 4481 | 1 4768 | 86.61 | 0.4430

| 12 5157 | 82.93 0.4241 12) 4379 | 88.70 0.3885

43 4768 | 83.78 | 0.3995 | 13 3 91°| 91 40 | 0.3648

| 14 4379 85.88 | 0.3761 | 14 3609 | 9497 | 0 3427

| 15 3991 | 87.97 | 0.4541 | 15 3229 | 101.13 | 0 3266

46 3605 | 91 26 | 0.3290 16 9846 | 114.98 | 0.3273
17 3046 | 101.03 | 0 2077 17 2710 | 124.35 | 0.3370

| 18 27915 | 112.40 | 0.3138 | :

“49 2646 | 124.08 | 0.3283 |

Point of contact:

0.005005

82.83 |

eee

This mixture has been prepared in a simpler mixing apparatus
than that referred to in this Comm. II § 3, and the pressures are
measured with an air manometer and then reduced to the indications
of the hydrogen manometer used later, as said in IIT § 38.

Of the border curve it may be remarked that below 19°.38 C.
the end condensation pressure decreases at a falling temperature,
which has not been observed by Verscuarre.t in mixtures of earbon
dioxide and hydrogen at the temperatures at which he observed.

Between the plaitpoint- and the point-of-contact-temperature there -
was retrograde condensation of the first kind (temporary liquid phase), -, Ke

me
i)

( 583 )
§ 3. Second inieture of carbon dioxide and oxygen.
g = 0.1994
Ax,, = 1.00413.
Before the experiments: Vi;~ = 69.608 cc’.
After __,, 69.555":,,

mean: 69.581° ,,

a. Border curve.

Beginning condensation. End condensation.

No. |’ Temp. = p | No. | Temp. v | p
| 4 | 10.06 | 0 .0092336| 66.35 Tt 10:09 | 0.003205 | 102.485
Zap- 12,456 81905) 71.57 2} 412.20 3633 | 100.055
3 | 14.425 Tb" hleas 3 | 14.44 39945 | 97.375
4} 16.01 5803 | 86.02 4} 16.00 A784 | 92.57
5

a 16.23 5530 | 87.84 | | | 16.22 5156 | 90.55 |

6. Isothermal of 9°.62 C.

No. D | p | pv | Vig
4 | 0.009795 | 64.05 | 0.6274
9 9M12 | 65.36 | 0.6152 | bc
3 8742 | 66.89 | 0.5881 | 0.000124
4 7918 | 69.46 | 0.5497 308
5 147 | 74.79 | 0.5131 470
6 6404 | 7%.92 | 0.4798 | | 672
7 5500 | 79.65 | 0.4381 909
8 AS. | 84.23 | 0.4052 | 0.001122
9 4022 | 91.55 | 0.3682 1464
10 3338 | 100.07 | 0.3340 2991
i 316% | 102.67 | 0.3248 | ec.
12 9874 | 412.50 | 0.3233
13 2742 | 121.35 | 0.3397
14 2699 | 125.18 | 0 3379 :
45 £632 | 129.33 | 0.3404 |

16 2581 | 135 67 | 0.3502 |

a NE

( 584 )

ec. Isothermal of 11°.35 C.

| Ne. | D | p | pe | Pig.
| 4 | 0.010341 | 63.46 | 0.6562
| 2} 0.009505 | 66.25 | 0.6298 |
3 8763 | 68.905| 0.6038
4 8629 | 69.37 | 0.5986 | dc
5 7950 | 70.95 | 0.56405| 0.000217
6 7203 | 73.535| 0.5997 384
7 6396 | 77 C2 | 0.4926 573 -
8 5608 | 81.14 | 0.4550 781 |
9 | 4829 | 86 40 | 0.4172 | 0.001097
10 | 4097 | 92.84 | 0.2804 4376
AA | 3712 | 96.79 | 0.3593 4707
42 3446 | 100.08 | 0.3449 2336
13 3397 | 100 89 | 0.3497 | e
14 3980 | 703.21 | 0.3385
45 3028 | 110.48 | 0.3345
16 9853 | 119.41 | 0.3398
47 9718 | 198.44 | 0.3491
18 96-1 | 137.56 | 0.3605

d. Plaitpoint isothermal (12°.51 C.).

No. | v | p | pe | Pig.
1 | 0.010259 | 64.42 | 0.6609
2 | 0.009570 | 66.77 | 0.6390
3 874 | 69.74 | 0.6096
4 8040 | 72.27 | 0.5814 | ac

Fé 7197 | 75.46 | 0.5409 | 0.000201

6 6378 | 78.56 | 0.50105 439
7 5597 | 82.66 | 0.4627 674
8 4772 | 88.24 | 0.4214 | 0.001044 |
9 3981 | 95.61 | 0.3806 1360
10 3606 | 99.65 | 0.3593 | pp

rw 3299 | 105.38 | 0.3476"

42 3057 | 112.34 | 0 3434

13 2870 | 121.71 | 0.3493

( 585 )
e. Isothermal of 14°.04 C.
No. | v | P | pr | "re. |
1 | 0.010318 | 65.06 | 0.6713

9 | 0.009504 | 67.91 | 0.6454
3 8726 | 70.87 | 0.6184

4 7926 | 74.06 | 0.5870
5 7272 | 7679 | 0.5584 | bc
6 7095 77.46 | 0.5496 | 0.000043
7 6337 80.59 | 0.5107 | 0.000265
8 56904 | 84.05 | 0.4786 457
9 4701 90.15 | 0.4292 786
40 4402 | 93.16 | 0.4101 888
44 4066 | 96.35 | 0.3918 933
42 3947 97.55 | 0.3850 | ec 1)
13 3700 | 100.97 | 0.3736
14 3987 | 109 15 | 0.3588
45 3002 | 118.66 | 0.3562
16. 9893 | 128.20 | 0.3619

Ibe Si ea le ee

f. Isothermal of 15°.41 C.

No. | v | P | pe | rig.

4 | 0.010276 | 66.02 | 0.6784

2 | 0.009515 | 68.77 | 0.6543°

3 8763 | 71.71 | 0.6284

4 7991 74.91 | 0 5986

a) 7159 | 78.62 | 0.5628

6 6435 | 82.05 | 0.5280 | be

! 5971 84.325 | 0.5035 | 0.000139
8
9

5604 | 86.34 | 0.4838 998
5099 | 88.71 | 0.4639 397

40 4997 | 90.31 | 0.4515 367

AA ugh | 91.44 | 0.4429 387

42 4667 | 92.81 | 0.4334 361

43. 4538 | 93.84 | 0.4258 973

44 4460 | 94.43 | 0.42415 164

45 4A | 94.87 | 0.4192 | ec

46 4045 | 98.88 | 0 4000

47 3692 | 103.36 | 0.3816

18 3953 | 413.06 | 0.3678

49 3908 | 122 03 | 0.3671

20 9821 | 133.47 | 0.3757

a" 9732 | 144.72 | 0.3872

ae oe Ee ee ee

1) Here we also had retrograde condensation of the first kind, although this
does not appear from the values given.

( 586 )

g. Point of contact isothermal (16°.27 C.). 1. Isothermal of 17°.66 C.

| No. p | p pe |
1 | 0.010312 | 66.345) 0.68415
2 | 0.009519 | 69.28 | 0 6595
3 | 8701 | 72.58 | 0.6315
4 7955 | 75 77 | 0.6028
5 | 7163 | 79.27 | 0 5685
6 | 6389 | 83.90 | 0.5316
7 | 5934 | 85.31 | 0.5105
8 5592 | 87.57 | 0.4897
9 | 5228 | 89.80 | 0.4695
10 | 4824 | 92.72 | 0.4473
11 | 4434 | 96.05 | 0.4959
12} 4031 | 100.54 | 0.1053
13 3647 | 106.62 | 0.3888
14 3284 | 14 98 | 0.3753
| 15 3053 | 122.99 | 0.3734
16 9857 | 133.275! 0.3808
va 2759 | 140.71 | 0.3832
‘Point of contact:
0.005322 | 89.20

| 7) P Pp v

4 | 0.010273 | 67.26 | 0.6910
2 | 0.009510 | 70.17 | 0.6673
3 | 8683. | 73.60 | 0.6391

| 4} 7920 | 76.98 0.6097
5 | 7161 ‘| 80.58°| 0.5774
6 6359 | 84.77 | 0.52905
7 5610 | 89.45 | 0.5001
8 4843 | 94.59 | 0.4584
9 4087 | 102.08 | 0.4472
10 3688 | 108.02 | 0.3984
rr 3280 | 417.36 | 0.3849
12 973 | 129.44 | 0.3848
3 9816 | 144.48 | 0.3976

§ 4. Coinparison of the mixtures according to the law of corre-

sponding states with carbon dioxide.

In Comm. N°. 59, Proc. Sept.

1900 methods are discussed for a graphical comparison of isothermals
of mixtures with those of a simple substance. Here as well for

er : . pv
carbon dioxide as for the two mixtures log’) was drawn as

a function of /ogv for the different temperatures. (For the absolute
zero we accepted — 273°.04 C.). If the law of corresponding states
also holds for mixtures of normal substances it must be possible to

live pressures occur, the drawing of /og

!) As the temperatures are so high that in the theoretical isothermals no nega-

wm
a offers no difficulty.

( 587 )

make the corresponding isothermals of the different diagrams coincide
by shifting them only in the direction of the /og v-axis.

I found that it was not possible to place the diagrams in such
a way over each other that the isothermals of the whole system
coincided ; I, however, sueceeded for the large volumes. According to
KAMERLINGH ONNES this signifies that in the mixture the coefficients
A,B,C,D,E,F of his series do not hang together with the coefficients of
the pure substance at corresponding temperatures in such a manner as
would follow from the law of corresponding states, but that for the
volumes where the terms with D, /, / in comparison with the others
are still so small that we may neglect the differences between these
terms and those given by coefficients which would obey the law
of corresponding states, the diagrams will coincide over such a large
range of temperature that 6 and C’ may still be regarded as corre-
sponding functions of temperature, hence a critical temperature and
a critical pressure holding for this range of volume and temperature
may be deduced from the law of corresponding states.

On the plate the diagrams are placed over each other so as
to give the best agreement for the larger volumes. In the hori-

i : 3 pv
zontal direction /ogv is drawn, in the vertical /og a The complete

lines refer to carbon dioxide, the dash lines to the first mixture,
the dash-dots lines refer to the second mixture. The points for
carbon dioxide are enclosed in circles, those for the first mixture in
triangles, for the second in squares. The different isothermals are
indicated by the letters a, 6, ete., with which they are communicated
in IV § 2 and V §§ 2 and 3. The pomts at the beginning and the
end of the condensation are marked by 6.c. and e¢.c.; they are con-
nected by curves which thus separate the homogeneous area from
the area where separation occurs. Finally the plaitpoints and the
points of contact are indicated by P and Ff, 4 is the point adopted
according to IV § 5 for the critical point of carbon dioxide.

It appears that the agreement for volumes larger than the critical
is_very satisfactory. In the smaller volumes, however, considerable
systematic deviations from the law of corresponding states occur.
We have already used these diagrams to determine the critical
temperature, pressure and volume in the sense as explained above
for the different mixtures. Although these results are satisfactory
they will not be given here, as more accurate results may be expected
from the same operations with diagrams projected on double the
scale for the part concerned.

If on a pT-diagram we draw the point of contact- and the plait-

( 388 )
point curves, they are seen to touch each other at the end .(critical
point of pure carbon dioxide) in agreement with Comm. N’. 81
§§ 9 and 14 (Proc. Oct. 1902). In the investigated part the curves
do not show the point of inflection found by VerscHarreLr with
mixtures of hydrogen and carbon dioxide (Comm. N°. 47 Proc. Feb.
1899); they are always concave towards the Z-axis.

Physics. — ‘‘/sothermals of mixtures of oxygen and carbon dioxide.
V. Lsothermals of mixtures of the molecular compositions 0.1047
and 0.1994 of oxygen, and the comparison of them with those of
pure carbon dioxide.” By W.H. Kezsom. Communication N°. 88
(6 part) from the Physical Laboratory at Leiden, by Prof.
IKAMERLINGH ONNES.

(Communicated in the meeting of November 28. 1903).

§ 5. According to § 4 (p. 586) the observations allowed of a
more accurate determination of the data for the critical point of
the mixtures for the range of the larger volumes and the range of
temperatures over which the observations have been made, in the
sense as it has been explained there, than it was possible from the
drawing given there. To this end diagrams were projected on
double the scale for the points in the homogeneous area for which the
volume is larger than 0.005; in these diagrams 0.0005 is represented
Ve

‘yy

by 1 mm. both for doy — and for logv. To determine the relation

of the critical pressures independently and to test the relation of the
critical temperatures of mixtures to that of pure carbon dioxide,

: : pr.
diagrams were constructed for the same area, where log Fis drawn

as a function of log p: here 1 mm. represents: on the Jog p-axis
v

0.00025, on the log Gaxis 0.0005.

§ 6. The diagram for the mixture which had been transferred on
tracing paper and in the middle of which a cross of axes was drawn
in order to permit an accurate judgment of the agreement of the
systems of axes for the two diagrams, was placed over the diagram
for carbon dioxide, so that the Jogv-, and log p-axes respectively
coincided, and then they were shifted until to the eye the isother-
mals of the mixture coincided with the system for carbon dioxide.

"~~ - =

W. H. KEESOM. Isothermals of mixtures of oxygen and carbon

dioxide. V. Isothermals of mixtures of the molecular com-

positions 0.1047 and 0.1994 of oxygen, and the comparison
of them with those of pure carbon dioxide.

400 -

Proceedings Royal Acad. Amsterdam. Vol. VI.

( 589 )

Then we measured off for the isothermals of carbon dioxide which
-lay between those of the mixtures, the situation of the former with
regard to the two neighbouring isothermals of the latter; this was
done for a number of points distributed at regular distances. Let
T, and 7, be the temperatures of the two neighbouring isothermals
of the mixture, and 7” the temperature which for the mixture cor-
responds to that of the isothermal of carbon dioxide considered, then
ep.
jeer Be
We assumed that the isothermals coincided best when the mean
square of the differences of gw and the mean g were as small as
possible.

Table XXIV, which refers to the comparison of the Jog j-diagram
of the mixture 0.1 with that of carbon dioxide shows in the 3¢ column
the afore-mentioned mean square of the differences, viz. for the
isothermals of 41.95° C. and 37.09° C. of carbon dioxide (after reduction
to the same temperature interval 7’,—7',) combined, for the different
superimposings of the coinciding systems indicated in the 1st column,
while 1.85 of the mixture coincided with the values of log p for
carbon dioxide given in the 2¢ column.

we obtain a great number of values for the relation g =

PBN BE i XING

It | 4.8850 | 0.012165
feniIte hy 48840) = 0.040535
lll | 4.8829 | 0.004783
Iv | 4.9821 | 0.004440 |
Vv | 4.8810° | 0.006221

Accepted; 4.88235

In table XXV we find the data for the critical points of the mixtures
thus found, combined with the data about the plaitpoints and the
points of contact, and also the critical points of carbon dioxide and
oxygen (the latter according to O1szEwskl). *)

1) It here appears that in the diagram given in § 4 (p. 587) in order to
obtain the best agreement for the area of the larger volumes, the isothermals of
the mixture 0.1 must be moved 5 mm. to the left, those of the second mixture
6 mm. to the right. The conclusions about the non-correspondence at the smaller
yolumes, however, still hold, the deviations even increase.

( 590 )

PAA Ee ioe B Se

Se | estaiceihs eel bie ee eneic (ne.

ait Pryi | Lor | Tk | Prpl | Par | Pork | Pzpl | Yar | Yak
| | | | :
0 304 .02/30%.02/304 02)72.93 72.93 72.93 | 0.00443
0.41047 | 295 .03/296 .33/ 285.68 | 86. 60/82.83 67.70 0.003878 |0.005005 450
| } | |
| | | | |
| 0.1994/2985 .55/989 31) 272.92|99.65/89.20) 67.30 3606 | D322 | 431

| 154.2 |154.2 (154 2 [50.7 |50.7 |50.7 | | |
esa | ea

The values of 7, derived from different diagrams and belonging
to different coinciding isothermals, did not differ more than 0.5 deg.

: ie ; 5
We-obtan~ for. ¢, = Wee for the mixtures 0.1 and 0.2 re-
oPrkUxk

spectively: 3.485 and 3.446, in sufficient harmony with the value
3.45, derived on p.577 of this Comm. IV for carbon dioxide.
About the critical data the following may be remarked: v,; shows
a maximum in the range investigated; for « between 0.1 and 0.2
por descends much slower than between 0 and 0.1; the same holds
in a less degree for 7%.
§ 7. To calculate the quantities introduced in Comm. No. 75, (Proce.

Dec. 1901):
il , De int Ip rck
—— one we rd , ete.
Ty \ de /r=0 Eee U6 45

I have represented several quantities of Table XXV as functions of «.
Observations for more values of « would'be required to determine
with some certainty how say v,, depends on w. As it appeared
that in consideration of the critical volume of oxygen, the data of
table XXV, could not be satisfactorily represented by a quadia-
tic funetion, I have added a term with «* and have derived the
coefficients from the data for carbon dioxide and oxygen (putting
herefor C’, equal to the value for carbon dioxide) and the two
mixtures. In this way I found:

Trt == Ty{1 — 0.6563 w + 0.8350 2? — 0.6715 2°}.
Pek = pe }l— 1.0871 «w 4 4.1885 2? — 3.40638 2°}.

Vek = ve {1 + 0.54225 w — 4.0310 a? + 3.2183° vt.
Papt = Ty {1 — 0.25792 & — 0.2349 a7}.

Pupl = pe {1 + 1.6639 @& + 1.5775 a? — 3.5462 2°}.
Trr = Ty. {1 — 0.2474 & + 0.0898 x? — 0.3352 2°}.
Poy == pe (fF 1.4963 2° — 1911S a 0 ee,

( 591 )

The data about 7°; could be represented very accurately by a
quadratic function.

We may expect that for values of x outside the range of obser-
vation these formulae will show important deviations from the
experiment, because errors in the observations for «=0O.1 and

x = 0.2 pass over increased into the values for the other range. This
holds especially for 77, pre and v,, which are exposed to so much
more sources of errors than the other quantities.

§ 8. From the formulae given above we find:

Oe — 4 0871;

1 (dog 3
= al “) ) _ 0.54295,
Uk dx ]x—0

while « — 3 — 0.4808. That this value does not agree better with
the value of y found directly, while in § 6 we found that for the

Pxk Vek : F
—““ was properly satisfied, is due to

May (3
the representation by the above-mentioned functions, which may be
expected to show just at the limits the largest deviations with regard
to the differential quotients.

two mixtures the relation

, : : 1 dT’ zy
With a view to this the agreements between —— and
—"

eX. ae
ee Le fdn- 1 /dp;,
=) ) and between — (2% ) and ~( Sk ) must be
Ty \ de Jxr=0 pe\ dae Jx=0 pe\ dx Jr=0

considered as satisfactory.

; : jae a i Le
The values of @ and ? derived from the values of — :
DM re

1 (dpxp
and — (=) by means of the formulae (2a) and (24) of
Gee edt fe aan

Comm. No. 75 and the values found in this Comm. IV (p. 577)

Ox O'2
for the coefficients C,, |] and C, | —— ] occurring there, and
Or Owdr
PP t (ae; ‘ der
the values of «@ and ~p derived from — = and —
ys ‘ dx 0 da 70

(as according to Comm. No. 81, Proc. Oct. 1902, p. a the same
formulae hold for these quantities) have been combined with the
values derived from the critical points A in Table XXVI, where the
first column indicates from which point the data have been derived.

1) Comp. VerscHAFFELT, Comm. N°. 81, Proc. Oct. 1902, p. 325.

( 592 )

PAB. Br ACEVe.

Z }

| x | —0.6563 | —4.0874 |
P —0.6864 —1.2190 |

R | —0.6174 | —0.9892 |

For this application of the formulae of Comm. N°. 75 it should
be borne in mind that in the derivation of them we have used the law
of corresponding states, while in §4 (p. 587) it appeared that already
at the critical volumes deviations could be detected. As long as z,
however, is very small, the points 7? for the different mixtures will
lie in an area where according to KAMERLINGH ONNES (comp. § 4)
the law of corresponding states may be considered to hold at least
to the first approximation, so that then we find an ae and a @# for
the critical points for that area. The same may be said of the points
R. From the numbers given it appears that the values of @ and p>
with relation to those points, at least to the first approximation, agree
with those relating to the critical point of the mixtures for the area
of the larger volumes.

For the slopes on the p7-diagram for the plaitpoint- and the point
of contact curve with small «2, we find:

T;. ( dp Lye f di
= (4) apes yi, Mee 2 () = 6.0445
pke\di pl pie \ dT],

values which agree sufficiently.
For the slopes of the curves which in the same diagram connect
the points A and P we find:

For the mixture 0.1: ne cae == 2102)
Pypl = Tk

For the mixture 0.2: 2.561.

For the curves which connect A and R:
For the mixture 0.1; 2“? — 1.491
Day — Tk
For the mixture 0.2: 1.336.
From either side, therefore, there is an approach towards the value
1.610, which both quotients must have for very small 2.
§ 9. From the formulae given in § 7 it would follow that the
largest plaitpoint pressure to be expected in mixtures of carbon
dioxide and oxygen would be 132 atms. (with «—= 0.57), while the

largest value for 7',—T,; would be expected to be 15°.7 C. (with

( 593 )

z= 0.63). The last value will probably be too large, as the curves
which, according to the afore-mentioned formulae, represent 7’, and
al as a function of «, and which for =O almost touch each
other, do not do so for «1 and hence for larger x yield too
large values for T7,—Toy1-

§ 10. Purity of the carbon dioxide. The values of a and 8 found
and the increase of vapour pressure found at 25°.55 C. with the
condensation: 0.07 atm. (comp. this Comm. IV, p. 567) allow us
to judge of the purity of the carbon dioxide used. By means of
formula (9) of Comm. N°. 79, Proce. April ’02, which for the unities
used in this paper may be written

(0,—v,) (Py— Ps) = Ar (e+ e-k—2)
if

A, = 14+ 0.0036625 ¢
and .
Eo -—p oY Cis!)
| pd? A;
we find, on the supposition that the admixture were oxygen, and
using for @ and the values derived from the point A:
x2 = 0.00027 .

§ 11. Retrograde condensation. In the annexed plate we give
for the two mixtures investigated curves which represent vj, as
function of v according to the tables given in sections 2 and 3
(p. 579 ff.). The curves for the different temperatures are marked by the
letters, by which the corresponding isothermals have been indicated.

~The numbers on the plate hold for the unity 0.00001.

Physics. — ‘‘J/sothermals of mixtures of oxygen and carbon dioxide.
VI. Injluence of gravitation on the phenomena in the neigh-
bourhood of the plaitpoint for binary miatures. By W. H.
KrEsom. Communication N°. 88 (7 part) from the Physical
Laboratory at Leiden, by Prof. KamertincH Onngs.

(Communicated in the meeting of November 28, 1903).

§ 1. In this Communication V, § 1 (p. 577) it was remarked
that the liquid meniscus at the end of the condensation over a certain
range of temperatures appeared or disappeared in the tube. Kturnen
(Comm. N°. 17, Zittingsversl. May 1895) was the first who explained
these phenomena by the theory of van per Waats on the influence
of gravitation on the thermodynamic equilibrium in mixtures. (Contin. JI

( 594 )

p. 30). The following pages may show that there is also a quanti-
tative agreement between the phenomena and that theory.

§ 2. In the mixture with the molecular proportion 0.1047 of
oxygen the meniscus by increasing the volume at 21°.86 C. appeared
at the top of the tube, at 21°.94 C. it was formed at the mark
44.99 (stirrer below, mercury meniscus at 41.66); at 22°17 C. the
meniscus appeared at the bottom of the tube, at 22°.09° C. it was
formed at the mark 43.93 (stirrer below, mercury meniscus at 41.57).
The top of the tube was at the mark 47.40 (em).

In the mixture of the molecular proportion 0.1994 the meniscus
appeared at 13°.12 C. at the bottom of the tube, at 13°.07 C. it
appeared at the mark 38.5 (stirrer above, mercury meniscus at 37.4);
at 11°.89 C. the meniscus appeared at the top of the tube, at11°.92 C.
it appeared at 42.3 (stirrer below, mercury meniscus at 37.7). The
top of the tube was at the mark 42.97. We may assume that for this
mixture the limits between which the meniscus appears in the tube
are: 13°.10 C. and 11°.90 C.

In these observations the volume from the homogeneous state was
increased by small variations; in this case the meniscus even without
stirring appears quickly at its definite place, which is not altered
by stirring. If on the contrary we start from the state where separation
into two phases occurs and the volume is decreased, the meniscus
only disappears after stirring and then suddenly; hence it seems
that in the former case the equilibrium is established much sooner *).

§ 3. In order to be able to compare the observations discussed
above with theory, I have found what may be deduced for it if
x is supposed very small. It may be easily derived from conside-
rations of vAN pER Waats (Contin. II, p. 30 ff.) that the phases
which are in equilibrium are determined by the following pair of
equations :

M(1—2)+M,o(/Oypy Oy |
T : : M,——-M,) | —— }} odi
i Lv °F (5 ta ( 2 Fy AYE Ox ey u

M (1—2)+M,a/f 07» 0?
Fde= a : aye ras + (M,—M,) alld gdh
v Ov 0a: Ova:

Here y is the free energy for the molecular quantity of the mixture,
vy the molecular volume in ce., J, the molecular weight of the
substance of which the quantity in the mixture is indicated by «

1) Compare with this what has been remarked in this Comm IV p. 574 about
the circumstance that the equilibrium was not immediately reached after the
heating of carbon dioxide at the critical point. Comp, also Gouy, C. R. t. 116,
p. 1291 and Maruias, Le Point critique des corps purs, p. 89.

‘

Se. <= |

iii

(aun)

(admixture), /, that of the other substance, while

= (Gr) (=) Gear)

The equations (1) determine on the w-surface a curve which
according to Kurnen (1. ¢. p. 6) I call the gravitation-curve’).
From (1) we derive:

M,A—«)+ Mx

dae (5) F v
dit gy On)» ($2) M,A—«)+ Mae & O7Y + (Mt, — re +)

Ov v Ow0r

ao a ee, dv On
From this equation it follows that at the plaitpoint —|{—}],
ditgr 1
: P
hence the gravitation-curve touches the isobar, and accordingly also
the spinodal curve, for which /=0O. Then also at the following
point of the gravitation-curve which passes through the plaitpoint,

mae dv
to the first approximation —-— = | — }, or at the plaitpoint
div gy Ow pT

d?v 07x 2)
ligt Ou? ee :

By means of this we have for a point of the gravitation curve
which passes through the plaitpoint, in the neighbourhood of the

latter: 7
pod ecwn, gh (Oh) (BE) a (BEVOY go BEV) (BF
=3 010 \ (5) (Sas a aoe as) tara) de) ta)

in which equation the differential quotients of /’ and v must be
taken at the plaitpoint. If here we put w7,; small, we may reduce
this form using reductions as in Comm. N°. 75, § 7 (Proc. Dee.
1901), to the first approximation to:

0 PS \

1 MM Tele Ger
Le a ae \ ae Jr

2 wT pl (op)?
; Ow vT

in which relation the differential quotients of p must be taken at
the critical point of the simple substance.

1) Comp. also Kuenen, |. c. Fig. 2.
2) This has been demonstrated for the gravitation-curve on the y-surface for a
constant mass in a different manner by Kuenen, |. c. p. 8

og
Proceedings Royal Acad. Amsterdam. Vol. VI.

( 596 )

If also in the second member of the equations (1) we put.” small
Wwe may integrate the latter to

(3). 3
M,
1 5 9 Tol = ~ gh | constant

‘Sai ap . 2
ait & Tl) (MRT, nH Eat (2)

From this equation we may easily derive the value of x7,; if the
mean composition Y, the height of the tube /7 and the place where
the meniscus appears are given, and hence also «7,;—_X, if this
takes place just at the top or at the bottom of the tube. Let 7’y,;
be the plaitpoint temperature belonging to the composition X, 7%; the
temperature at which the meniscus appears just at the top of the
tube, 7’,.,, the same for the bottom of the tube, then we obtain :

at oe Pin eo Sop Bi ge 2 ae, AT pt
| pl — Try f : 3 = ’
4A MRT, \0a)or (; ) dar
Vie
Te

Ov"

and for 7%; the same formula with the other sign.
If as in Comm. N°. 75, § 2 we introduce the law of corre-
sponding states this formula becomes :

2 pa = ee On AT xpi 4 3 MoH
via 7T X \p—ea ars = a ae (3)
PRL» C, ( )

Ow?
dd

upl

where for we still could substitute the form given in Comm.

N°. 75 equation 2a.

§ 4. In the comparison of formula (8) with the observations
mentioned in § 2 1 have assumed that for the area of the plait-
points the law of corresponding states holds to the first approximation,

and I have taken for @ and 3 the values derived from the observations
of the plaitpoints (comp. this Comm. V, § 8).

On
For (53) I have taken the value —5.3 calculated by VerscHarrent
ae

(Comm. Suppl. N°. 6, Proc. June 1903, p. 121) from the series of KamEr-

s (0°n
LINGH ONNEs, which value with C,—3.45 *) gives ( C, (; ) = — 216%),
e

With the value 7 = 5.8 cm., and the critical density for carbon dioxide

1) Comp. this Comm. IV, p. 577.
“) Gomp. Gomm. N°. 75,, Proc. Dec. 1901, p. 307.

p ae Oo

Ta ens

M
— = 0.448, derived from the data of this Comm. IV, we find,
UE
supposing that formula (3) were to hold as far as the value 7 = 0.1047:
T spi — Poyl a Lt ae

The agreement with the value found in §2 (between 0°.15 C.
and 0°.31 C.) is better than might be reasonably expected with the
suppositions made. The circumstance that for the second mixture
1°.20 C. was found for this shows that for this value of « terms
with * etc. have already a preponderating influence.

Physics. — ‘“Hysteretic orientatic-phenoment.” By Prof. H. E. J. G.

pu Bors. (Communicated by Prof J. D. van per WaAats).

(This paper will not be published in these Proceedings).

(February 25, 1904).

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,

PROCEEDINGS OF THE MEETING

of Saturday February 27, 1904.

QOS —s

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 27 Februari 1904, Dl. XII).

Gi © BEE aro Abs:

H. W. Baxkuvis Roozesoom and A. H. W. Aren: “The melting point lines of the system
sulphur + chlorine”, p. 599.

A. W. Visser: “Enzymactions considered as equilibria in a homogenous system”. (Commu-
nicated by Prof. C. A. Lopry be Bruyn), p. 605.

A. J. P. vax pen Broek: “The foetal membranes and the placenta of Phoca vitulina.”
(Communicated by Prof. L. Bork), p. 610.

W. Karremn: “On the differential equation of MonGr’, p. 629.

W. A. Verstuys: “The singularities of the focal curve of a plane general curve touching
the line eat infinity > times and passing « times through each of the imaginary circle points at
infinity.” (Communicated by Prof. P. H. Scmours), p. 621.

W. A. Verstuys: “On the position of the three puints which a twisted curve has in common
with its osculating plane.” (Communicated by Prof. P. H. Scuourr), p. 622.

A. Smits: “A contribution to the knowledge of the course of the decrease of the vapour
tension for aqueous solutions.” (Communicated by Prof. H. W. Bakuuis Roozesoom), p, 628.
(With one plate).

H. Kameriincu Onnes and C. A. CromMerin: “On the measurement of very low temperatures.
VI. Improvements of the protected thermoelements; a battery of standard-thermoelements and ~
its use for thermoelectric determinations of temperature’, p. 642. (With 2 plates).

J. E. Verscusrrett: “Contributions to the knowledge of van per Waats’ /-surface. VIII.
The ¥-surface in the neighbourhood of a binary mixture which behaves as a pure substance.”
(Communicated by Prof. H. Kameriincu Onngs), p. 649. (With one plate).

The following papers were read:

Chemistry. — “The melting point lines of the system sulphur
+ chlorine.” By Prof. H. W. Baknvis Roozesoom and
fe He WwW Aran.

(Communicated in the meeting of January 30, 1904).

The boiling point lines of this system have already been described
at the meeting in May 1903. These led to the view that the com-
pound §,Cl, in the liquid and vaporous condition is but very little
dissociated and also that further compounds occur at a not too low
temperature in liquids with a higher proportion of chlorine.

Proceedings Royal Acad. Amsterdam. Vol. VI.

( 600 )

A closer study of the changes in volume which take place in these
liquids and of the velocity with which this happens has rendered
it probable that SCI, is chiefly formed and in addition also SCl,.

The equilibrium between $,Cl,, SCl,, 5Cl, and Cl, which takes
place in the liquids is not modified to any extent by cooling below
O° and remains totally unchanged at those low temperatures at
which these mixtures may deposit solid substances. This gives rise,
during the solidification, to very peculiar phenomena which, up to
the present, have not been noticed with other systems but which
may be explained by the views of the phase doctrine.

/o0

Bf)

ot iat

On the other hand nothing noteworthy occurs with mixtures con-
taining 50—100 atomic per cent of 5S. These behave entirely like
mixtures S.C], +8. The melting point of 5,Cl, (—80°) is lowered
by sulphur to F; the melting point of sulphur is also lowered by
5,Cl, from B (120°) to F.

At a low temperature the solubility of 5 in S,Cl, is very small.
The solubility or melting point line of 5 consists of two curved lines

( 601 )

FC and CB, which at C=96° join at an angle. The top line relates
to monoclinic, the lower one to rhombic sulphur.

Mixtures of O—50 atomic °/, sulphur may on cooling, give as
solid phases Cl,, S,Cl, and SCI,.

The manner in which they are successively deposited may be

best explained by first observing in what manner the solidification
of a mixture of these three substances would take place when the
SC], could be considered as an independent third component.

This would be the case if this compound did not dissociate in the
liquid condition and also was not formed from liquid $,Cl, and Cl,.
The system would then behave as a ternary system, the solidification
phenomena of which could only be completely represented by a
spacial figure.

We may also, however, disregard the constitution of the liquid
and express its gross composition only in Cl, and $,Cl, which is
all the more justifiable as there is no means of determining the
amount of SCI, in the presence of Cl, and $,Cl,.

We then obtain a representation in a plane (see fig. 2) which is
the projection of the spacial figure *).

In this figure EH and HA
are the solidification lines of
the binary mixtures SCI, and
Cl,, EK and KD those: of SCI,
and §,Cl,, AG and DG those
of Cl, and §,Cl,.

The ternary mixtures whose
compositions lie within the
region IHAG first deposit solid
chlorine, those in IKDG solid
S,Cl, and those in HEKI solid
SCl,. For each gross composi-
tion there exists a greater or
smaller series of molecular

_ arrangements which cannot be
ICL, Scly pee represented in the plane, but on
which the temperature at which
the one or other solid phase
commences to be deposited depends. (Some mixtures may even sepa-
rate more than one phase according to their molecular composition).

1)'We must then accept as components: 3 Cl, and S,Cl, in order that the
middle of the abscissa axis represents the composition SCI.

40*

( 602 )

This difference is further shown by the different crystallisation paths
which on further cooling are traversed by mixtures of the same
eross composition.

These crystallisation paths start in each of the regions mentioned
from the point representing the melting point of the solid phase,
that is from A, D and E respectively, and indieate the series of
mother liquors which remain, during a continued cooling, at each
temperature. The crystallisation paths in the first region end in HI
or IG, those for the second in KI or IG, for the third in HI or KI.
The lines I and I] schematically indicate two similar paths in the
last region, the vertical line EE’ is a third one which applies to a
liquid of the gross composition SCl,.

As soon as the crystallisation paths arrive at HI, KI or GI, the
subsequent solidification takes place along these lines, each time
with deposition of two solid phases: Cl, -- SCI, on HI, 5,Cl, + SCI,
on KI and Cl, +.5,Cl, on GI.

Finally the last liquid solidifies in 1 to a ternary eutecticum of
the three phases.

This would be the state of affairs if — as has been said — SCl,,
S,Cl, and Cl, were miscible in all proportions without transformation.

If, however, SCI, were a dissociable compound whose formation
and decomposition led to complete equilibria at all solidification
temperatures, then instead of the solidification deseribed another
would occur along the lines AH’, H’E’K’, K’D causing the system
fo appear as a binary one in) which occurs a compound which
enters into equilibrium with its Components in the liquid condition.
The position of these lines within the figure of the ternary system
is determined by the degree of dissociation of the liquid compound.
If this is extremely small, these lines approach to AH, HEK and
KD, if very large they approximate to AG and GD and the com-
pound does not appear as a solid phase. Solid Cl, is deposited along
AH’, solid SCl, along H’EH’K’, solid S,Cl,-alone K’D; HH” andake
are two eutectic points where complete solidification takes place.
These three lines are not only the first series of solidifying points of
the different mixtures, but at the same time the crystallisation paths
of all mixtures.

Now with mixtures of S,Cl, and Cl, neither the first nor the second
case is quite realised. At the low temperatures at which the soli-
difications take place, Cl,, S,Cl, and SCl, behave as independent
components ; for instance Cl, and $,Cl, may be mixed in the liquid
condition without entering into combination and in this way the
two solidifying lines AG and GD (fig. 1 and 2) of these mixtures

( 603 )
have been determined. Neither does SCI, undergo decomposition at
those low temperatures. If, therefore, it were possible to isolate pure
SCI,, all imaginable mixtures thereof with Cl, and $,Cl, or with
both might be obtained and the further portions of fig. 2 could then
be constructed. This, however, is not the case.

On account of the extreme minuteness of its crystals and the low
temperature at which crystallisation takes place, the compound SCI,
cannot be isolated in a pure condition and cannot, therefore, be
added in definite proportions to Cl, or 5,Cl,. By exposing various
mixtures of these compounds to temperatures of O° and higher it is
possible to cause the voluntary formation of those quantities of SCI,
which are in equilibrium with Cl, and 5,Cl, at the temperature
chosen. As these do not change much with the temperature, the
same series of mixtures is fairly well retained on cooling to the
crystallisation temperatures. The number of ternary mixtures whose
crystallisation may be investigated is, therefore, restricted to one for
each gross composition.

We, therefore, always obtain for the first solidifying points a series
such as AH’E’K’D in fig. 2, just as if we were dealing with a
binary mixture in which a dissociable compound occurred. If, however,
the equilibrium in the liquid does not change when Cl,, SCI, or
5,Cl, crystallises out, the system on solidification must behave as a
ternary one.

This should have appeared in practice by the fact that the curve
of the first solidifying points did not also represent the path of
crystallisation, and, therefore, the mother liquor left after cooling
each mixture to a lower temperature differed in composition from
that given by the point on the curve corresponding with the
temperature in question. Owing to the nature of the crystals,
however, it was impossible to remove the mother-liquor with a
pipette.

It was, however, possible to prove in the case of a liquid of the
gross composition SCI, that this does not completely solidify to SCI,
at EK’, but only commences to deposit SCI, at that temperature
(—30°), which quantity increases on further cooling, but in such a
manner that no complete solidification takes place below —80°. In
the points on both sides of E’ the continuity is still more pronounced
and this makes the accurate determination of even the first solidifying
points very difficult.

In the second place the solidification of the different mixtures
ought not to be complete in H’ or in K’, but only in I after traversing
the crystallisation paths H’'l and Kk’.

( 604 )

This is confirmed qualitatively but the exact determination of the
lines HT and K'l and consequently also of the ternary eutecticum
proved to be impossible. .

In this way no more was obtained than is indicated in Fig, 1,
namely the solidification lines AG and GD for the mixtures of Cl,
and S,Cl, in which no compound had formed and besides these the
series of the first solidifying points AH, HEK and KD for the par-
tially combined liquids formed at O°.

These lines therefore correspond with the accentuated lines in
Fig. 2. The true melting point of SCl,, without decomposition ot
the liquid (E Fig. 2) is therefore not yet known. If SCI, could have
been prepared in pure crystals, this might have probably been
determined as it would presumably be situated below the tempera-
ture where the liquid compound shows perceptible decomposition.

This is rendered more probable by the observation that notwith-
standing their minuteness the crystals of SCI, when rapidly heated,
are quite permanent up to — 20°.

Fig. 1 does not agree with fig. 2 in an important point. In
the latter DK is placed above DG, in the first DK is found below
DG. DG_ represents the lowering of the melting point of 5,Cl, by
added Cl, when this remains unchanged: Dk when a portion of it
combines with a part of the S,Cl, to SCI, according to the equation

§.Cl, + 3 Cl, = 2 SCI,.

If we now compare the total amount of the foreign molecules
which oceur along with the 5,Cl,, for the same total amount of
Cl,, these numbers are smaller in the case of a partial formation
of SCL, than when this is not the case. According to this supposition
DK ought to be situated higher than DG.

As in practice, the reverse position was found we must look for
a cause whieh may explain this fact. We find this by supposing
that besides SCI, there is also formed in the liquid a considerable
proportion of SCL, according to the equation

S.Ck Ch aes

By taking this view the number of foreign molecules mixed
with the S,Cl, becomes greater owing to the formation of SCI, than
without this.

The formation in the liquid of an amount of SCI, exceeding that
of SCL, which had already become probable by the dilatometric
experiments has, therefore, been confirmed. The slow: crystallisation
of SCL, will now be better understood; but the liquids between Cl,
and §,Cl, should now be considered not as ternary but as quater-

( 605 )

nary mixtures. If during the crystallisation SCI, in the solution does
not vield SCL, according to the equation

3 SCI, = SCI, + 8,Cl,

solid SCl, ought to be found somewhere on the way to complete
solidification. This point could not be decided.

Chemistry. — ‘“nzymactions considered as equilibria in a homo-
genous system.” By A. W. Visser. (Communicated by Prot.
C. A. Lopry pr Brtyy).

(Communicated in the meeting of January 30, 1904.)

1. A number of facts exist which indicate that the reactions
created by enzymes are reversible. Crort-Hin1') succeeded in partly
converting a concentrated solution of glucose into a disaccharide with
the aid of maltase and reversibly the disaccharide into glucose. He
supposed it to be maltose but afterwards EmMMERLING *) proved it to
be isomaltose; the fact however remains that maltase may cause
a reversible formation of polysaccharides. Recently, Crort-HiLu *)
has further proved that there is formed from glucose by means of
maltase a new crystallised biglucose called revertose, he thinks
it probable that also maltose may be formed ‘). KaAs?TLE and
LOEWENHART *) and afterwards Hayriot *) found that the fat-splitting
enzyme lipase is capable of resolving butyricester into butyric
acid and aleohol and on the other hand of forming the ester from the
decomposition products. EMMERLING’) noticed the regeneration of amygd-
alin from nitrilglucoside-amygdalate and glucose under the influence of
maltase. E. Fiscuer and FRANKLAND ARMSTRONG *) prepared with the
aid of Kefir-lactase a disaccharide from a mixture of galactose and
glucose called isolactose, which up to the present could not be
isolated in a state of purity. The same authors also found that
kefir-lactase forms a disaccharide from glucose alone and_ that
emulsin does the same from a mixture of glucose and galactose.

1) J. C. S. 78, 634 (1898).

2) Ber. 34, 600, 2206 (1901).

8) J. C. S. 83, 578 (1903).

4) All these experiments show that the substance supposed to be maltase still
contains other ferments.

®) Am. Ch. J, 26, 533 (1901).

6) GC. R. 182, 212 (1901).

7) Ber. 34, 3810 (1901).

8) Ber. 35, 3151 (1902).

( 606 )

From several experiments I have made, I think the conclusion
may be drawn that it is probable that saccharose may be rege-
nerated to a slight extent from glucose and fructose by means
of invertase, whilst it may be taken as proved with tolerable
certainty that salicin may be regenerated from saligenin and glucose
by means of emulsin.

If, with the usual precautions, a N/, solution of saccharose *) is
exposed to the action of invertase, the former is resolved into
glucose ++ fructose and the liquid shows a final polarisation
of — 3°.26°).

If a similar solution is inverted by N/, HCl the final polarisation
becomes — 3°.42.

A solution containing the same amount of glucose and fructose *)
as is formed after total inversion of a N/, solution of saecharose

also gives a final polarisation of — 3°.42.

A solution containing equal quantities of glucose + fructose and
which showed at the start a polarisation of — 12°.46 gave after
two. months action of invertase a polarisation of — 12°.29. These

experiments have been repeated a few times.

A N/,, solution of salicin, resolved by emulsin into saligenin and
glucose, gave a final polarisation of 1°.03 whilst a solution containing
as much saligenin and glucose as ought to be formed by the
complete decomposition of a N/,, solution of salicin shows a polari-
sation of 1°.18. Such a solution which contains the same amount
of emulsin as the N/,, solution of salicin gave after a month
a polarisation of 1°.03.

The formation of saliein, which shows that the reaction is
reversible, may be proved qualitatively in the following manner.
The glucose was got rid of as much as possible by fermentation
and after filterimg, the saligenin was completely removed by agitating
the solution with ether. The liquid was now concentrated to about
5 ¢c¢. on the waterbath. To one half of it was added a drop of
ferricchloride solution (1:10); this gave no coloration showing the
absence of saligenin, a mere trace of which would give a blue
coloration. The remainder was evaporated to dryness and gave
with H, SO, a red coloration (formation of rutilin). 0.5 ¢.e. of al °/,

bacterial action: all apparatus and utensils were also previously sterilised.

?) A Lippich-polarimeter was used. The readings were accurate up to 0°.02
and all observations were made at 25°.

°) I have to thank Mr, Atperpa van Exenstein for supplying me with these
perfectly pure sugars.

( 607 )

salicin solution and 1 gram of glucose was diluted with a 1 °/,
saligeninsolution up to 50 ¢.c.; the 0.005 gram of salicin present
could be detected in the manner described. Great care must be taken
to ensure the complete removal of the saligenin, as this also gives
a red coloration with strong H, SO,.

[ think these experiments warrant the conclusion that the
resolution of saccharose by invertase may be probably considered
as an equilibrium reaction and that this is tolerably certain in
the case of the action of emulsin on salicin.

As regards the last reaction, TAmMMann had come to the conclusion
that, although incomplete, it is not however a limited reaction, as
the limit did not undergo retrogression on adding the products of
decomposition. TamMann however has not worked with sterile
solutions so that, as others have already observed, his experiments
are not conclusive. Moreover, the figures found by TamMann for
the concentration in the condition of equilibrium at 0°? and 25°
differ not inconsiderably from my own.

2.. Dynamical researches as to the action of enzymes have soon
shown that certain decompositions do not proceed in such a simple
manner as in the case where acids are employed. Although
O’Suntiivan and Tompson first believed that the hydrolytic resolution
of saccharose by invertase is represented by the same simple
formula (for reactions of the first order) as that for the same
reaction by H-ions, TammMann and Dvuciavx have demonstrated that
such is by no means the case. This has been confirmed by subsequent
researches particularly by those of Henri. The reactioncoefticient of the
system saccharose + invertase calculated according to the logarithmic
formula appeared to increase; for the system salicin + emulsin it
appeared to decrease with the time. So TamMann comes to the
conclusion that the enzymes do not conform to the same laws as
the inorganic catalyzers and that these laws will not readily be
traced, and Ducnavx is of opinion that the laws of physical chemistry
do not apply at all to enzym actions.

As the dynamic investigation of the action of ferments had only
just commenced, these conclusions could hardly be accepted as final.
The exhaustive researches published in 1901 by Vicror Henri *)
and afterwards continued *) have indeed proved that the course of
ferment actions may decidedly be expressed by a formula. It has
already been observed that the resolution of saecharose by invertase
proceeds more rapidly than is expressed by the formula for reactions

1) Z. phys. ch. 39. 194 (1901).
2) Lois générales de l’action des diasases. Théses, Paris, Février 1903.

( 608 )

of the first order; it was therefore obvious to assume here an acce-
lerating autocatalysis, a reaction for which Ostwap *) had worked
out a formula. Henri has now followed this course indicated by
OstwaLp and deduced an empirical formula which, when applied to
his experiments led to coefficients which may be taken as practi-
cally constant for N/100 to N solutions. Henrt accepted a theory
of the mechanism of the action of invertase according to which the
ferment should enter into combination with saccharose as well as with
fructose (according to an equilibrium-reaction). By now trying diffe-
rent values for the equilibrium constants of these two reactions, he
arrives at two figures, the introduction of which into the formula
leads to the said constants. I believe to have succeeded in proving
that Henri’s views are not correct judging from his own experi-
mental data and from my own observations.

Recently Herzoc *), for the resolution of salicin by emulsin, (where
on applying the formula for reactions of the first order the coeffi-
cients regularly decrease) has applied Ostwatp’s formula for reactions
with negative autocatalysis *) to Henris and TAMMANN’s experiments
on the said reaction; he has found that this formula leads to
reaction coefficients which may be considered as constants. These
constants Change with the iitial concentration of the salicin solutions.

Hrrzoc however observes that Ostwawp’s differential equation for
negative autocatalytic transformations is incomplete ‘and that it
would be better to give it the form of a _ reaction of a higher
order’. This was already done by me some time ago.

3. Given the fact (now toleradly well substantiated) that enzym-
actions are equilibrium reactions, I have taken a view of the theory
of these decompositions different from that hitherto accepted and first
deduced formulae giving the relation between velocity of reaction
and chemical equilibrium. These formulae differ from those at present
applicated to this ease *); I have deduced them for mono-, bi- and
trimolecular equilibrium reactions *), first tested them in well-kwown
cases (ester formation; the transformation studied by KisvEr *) ete)
also by ScHoori’s observations on the action of sugars on urea *)
which I have myself extended and subsequently applied them to the
observations of Henri as well as to my own series of determinations
relating to the saccharose and salicin resolutions. The results of this

1) Lehrbuch, II, 2, 262.

2) These Proc. VI November 28 1903, p. 332.
’) Lehrbuch Il. 2. 270.

4) Osrwaup’s Lehrbuch Il, 2, 251, e.v.

6) Z. phys. ch. 18, 161 (1895).

6) Rec, 22. 31, Dissertation, 1902.

( 609 )

application are very satisfactory. I have further been able to develop
for the activity of the enzymes an intensityformula wherein, besides
the concentrations of the solutions, the constants found experimen-
tally occur and which I believe, gives a fair representation of the
quantitative progress of the enzym actions as studied by previous
observers and myself.

4+. These mathematical deductions and the details of the other
results obtained by me will be published fully elsewhere. [ may
only remark further, that my results show that, starting with a N/,
saccharosesolution (171 grams per litre) we arrive at a final con-
dition where fully 1 gram of saccharose still remains present. The
inversion therefore proceeds to an amount greater than 99°/,. This
seems also the case in the resolution of salicin.

My experiments further show :

1st. that the two ferments invertase and emulsin retain their
quantitative activity for some weeks in properly sterilised solutions.

2ed. that the average factor for the change of the velocity of the
saccharose decomposition with the temperature equals 2 for 10°
between O° and 25°,

3°. that by a change of temperature from O° to 25° the equili-
brium is displaced very little or not at all, which quite agrees with
theory as the caloric effect of the reaction is very small.

4th that at a definite temperature the change in concentration of
the enzymes has no influence on the equilibrium but only on the
velocity; the latter, as in other catalytic actions, is directly propor-
tional to the enzyme concentration.

5th. that as already observed by Henri, the intensity of the
invertase is smaller in proportion as the quantity of invertsugar,
present with the same amount of saccharose, is greater.

6. that the intensity not only depends on the quantity of invert-
sugar but also on the quantity of saccharose present in the solution ;
it is smaller when this quantity is greater.

This last conclusion does not agree with that of Henri (Theses,
p. 72) where he states that the addition of saccharose at the
commencement of a reaction has no influence on the velocity of the
inversion, but accelerates it when the addition takes place in the
middle of a reaction.

7, that, as duly required by theory, the reversal of the reactions
between glucose and fructose and between glucose and saligenin
proceeds very slowly and requires several weeks.

The results of Henri’s experiments are in accordance with the
intensity formula, which I have deduced.

( 610 )

Anatomy. — “Vhe foetal membranes and the placenta of Phoca
vitulina.’ By A. J. P. van pen Brork. (Communicated by
Prof. I. Bork).

(Communicated in the meeting of January 30, 1904).

Some time ago a seal in an advanced state of gestation was sent to
the anatomical Laboratory of the Amsterdam University. As neither
the foetal envelopes nor the placenta of the pinnepedal carnivores have
been described in detail, I was very gratified to be entrusted by the
Director of the Laboratory with the task of carefully examining these
organs. The preparation turned out to be in very good condition and
well enough preserved for microscopic examination.

Whereas a more detailed description wiil be published in another
place, the following may be given here as the principal results of
my investigations.

The gravid uterus was U-shaped, the convexity being on the eranial
side. The organ, which was somewhat flattened dorso-ventrally was
lying in transverse direction, so that the fundus uteri was situated
in the righthand part of the body. This U-shaped curve was ac-
companied by a twisting of the organ, so that the left ovarium,
entirely enveloped by an ovarial bag, was medially situated.

The greater part of the ligamentum latum had become absorbed ;
the ligamentum rotundum, a very powerful cord, ran from the front-,
respectively hind-wall of the uterus, that is: from the spot where
the ovarium was lying against the uterine wall, running down in a
slanting direction across the latter, towards the abdominal wall. The
ostium uteri, filled with a mucous clot, showed an aperture of +3 em.

Close to the top of this ostium, which formed an oval foramen in
the middle of the portio vaginalis, the foetal sac, rather strained,
could be felt. All this seemed to indicate that the animal, being in
labour, had gone ashore, when it was caught.

On opening the uterus by means of a longitudinal incision in the
organ, along the convexity, the following was noticed: The wall of
the uterus is extremely thin in proportion to the voluminous organ,
a little more than 1 mm., but increases in thickness towards the
vagina. The muscularis of the wall of the latter, however, is rather
thick (1 em.).

The chorion, as well as the placenta, is only loosely attached to
the walls of the uterus all over. It appears that the foetal sac reaches
down to the ostium uteri. On detaching the placenta I found septa
of cellular tissue adhering to the inner surface of the wall of the
uterus, which, just there, is somewhat thicker.

( 611 )

The placenta forms a perfectly closed girdle, situated about the
middle of the foetal sac, or, with regard to the uterus, in the
curve of that organ.

The uterine surface presents a lobated structure, the various irre-
gular lobes being separated by pretty wide fissures, and as moreover,
the placenta is comparatively thin, it is not very compact.

The circumference, measured at the surface of the uterus, is 66
em., the width, which is the same all over, 32 cm. The edges are
not stumpy and thick; rather thin. Several thick bloodvessels emerge
from the sides of the placenta, branching off into the chorion so
abundantly as to leave not a single part of it without a supply of
vessels. On splitting the chorion and the placenta along the convex
curve of the foetal sac, the amnion becomes visible. This is quite
disconnected. There was no direct contact between the two tissues
anywhere, nor with the placenta, the amnion not covering the foetal
surface of the placenta, but branching off at the placentary end of
the umbilical cord. The amnion, like a bag with thin walls, invests
the foetus pretty closely, especially along the back. Only behind
the tail-end of the foetus, which is turned towards the fundus uteri,
we find another part of the amnion that is not taken up by the
foetus, but filled with a substance that is soft to the touch. The
amnion is partly vascularized, partly devoid of any vessels ; especi-
ally in the immediate vicinity of the umbilical cord a vascular part
is noticeable. Here the amnion membrane seems also to be somewhat
thicker and to consist of two layers, which are moveable one over
the other. Here we find the umbilical sac, in the shape of an
elongated organ, connected with the amnion right along, lying against
this membrane.

As the amnion has not coalesced with the foetal surface of the
placenta, the latter can be at once examined after opening the
chorion. Of an insertion proper of the umbilical cord into the
placenta there can hardly be any question, the vessels dividing and
branching off long before they reach the placenta.

These ramifications enter the placenta at a rather considerable
distance from each other. Slips of the allantois, which lines the
placenta, cover these vessels, which therefore are found in dupli-
‘atures in this membrane as soon as they leave the cord. The
main canals of each of the two umbilical arteries branch off
into a girdle-shaped half of the placenta, and with fairly large
ramifications spread further into the chorion. When the convex
surface of the amnion is slit open very little foetal fluid runs out.
The foetus is found to be lying with its muzzle towards the ostium

( 612 )

uteri, its back turned upwards. It also appears that the available
space behind the tail-end of the foetus is filled up with about 3 liter
of lanugo, some of which was also adhering in places to the body
of the foetus. In the skin itself there were no remains of the lanugo-
covering, which consisted of short, straight hairs, all of the same
pearl grey colour. Speckled or black hairs were not found.

The umbilical cord has a length of only 12 em. so that the animal,
at the time of birth, is bound to pull out the placenta along with
the membranes. The skin is continued for about 1 cm. along the
umbilical cord, which is compressed sideways along its whole length.
Taking into consideration the thickness of the umbilical cord there
is only a small quantity of connective tissue. The three umbilical
vessels are not twisted around each other. The outer surface of the
umbilical cord is yellowish, shining, and feels hard.

A microscopical examination gave the following results:

The umbilical cord is covered with an epithelium forming a pave-
ment of several layers, which forcibly reminds one of the epithelium
of the epidermis. The lower layer of cells consists of high cells of
a somewhat cylindrical shape, lying close together, with large round
nuclei. Towards the surface the cells grow flatter, their limits being
well defined in the layers immediately following the basal one. As
the cells flatten down, the nuclei grow less prominent. Finally,
forming the outside layer, there is a horny surface with lamelliform
structure, in which, (by means of staining with haematoxyline) the
remains of nuclei can be traced in places. This horny layer is sharply
marked off from the epithelium-layer.

Where the amnion leaves the umbilical cord, this epithelium of
many layers changes into a simple epithelium.

In the cord itself there are in section five channels of unequal
width and with a wall of uneven thickness.

The two umbilical arteries and the vena umbilicalis have a very
thick muscular coating of circular muscle-fibres. The muscle-cells
show a lamelliform arrangement, the lamelli being separated by
connective tissue.

Elastic filaments cannot be traced, Towards their lumen the blood-
vessels are covered with an intima, which is not clearly defined
towards the periphery.

In the walls of the blood-vessels we find, almost right up to the
intima, the lumina of vasa vasorum, belonging to the system of the
vessels proper of the umbilical cord, to be mentioned presently.

A fourth lumen is that of the second vena umbilicalis. The wall
of it clearly shows an intima, round this there is a circular muscular

( 613 )

coating, and then, right round this, a coating of bundles of muscles
running lengthways, but not adhering close together. In the walls of
this vena I have not noticed any bloodvessels. In the lumen I found
here and there some blood-corpuscles. In following up this partly
obliterated vena towards the foetus, it is found to divide itself into
two branches shortly before the foetal insertion of the umbilical
cord; the two branches run together a little way down, then one of
them splits up again and three branches can be traced right up to
the front abdominal wall, where they lose themselves. Towards the
placenta this vena also splits up into ramifications, which grow finer
and finer and finally branch off into the tissue of the umbilical cord,

The fifth lumen in the umbilical cord is situated in the foetal half
between the two umbilical arteries ; towards the placenta these approach
each other and the vessel runs alongside of them. This lumen is
of an irregular shape, somewhat compressed and provided with an
epithelium composed of cells that are flattened and arranged in several
layers, the respective limits not being distinctly defined.

This lumen runs right through the cord till close to the placenta
where it suddenly stops. There is no communication between this
lumen and the yolksac. That we have here a continuation of the
allantois-channel is proved by its original position between the two
umbilical arteries, which position I also noticed inside the abdominal
wall. I did not notice any remains of a yolk duct with certainty.

The stroma of the umbilical cord consists of cellular tissue with
exceedingly fine fibrils pursuing a circular course. Underneath the
epithelial coating this circular direction is deviated from and the
curve becomes irregular. Round the vessels there is no distinct system
of circular fibres. Between the two arteries the character of the
stroma changes somewhat, it is of a looser construction and contains
a few longitudinal bundles of smooth muscular tissue. These can
best be seen by staining with polychrome methylen-blue (Unna) and
ean be traced right through the whole cord. By the side of this the
profusion of the bloodvessels belonging to stroma funiculi proper
seems remarkable.

These vasa propria funiculi umbilicalis ave met with right along
the funiculus, most of all in the foetal part. They appear to be con-
nected with the vasa of the subcutaneous cellular tissue of the abdo-
minal wall. Arteries as well as large veins filled with blood are
noticeable. The distribution is somewhat irregular. Especially round
the umbilical vessels they are heaped up together, entering the walls
close up to the intima. I have not been able to ascertain the existence
of a connection between the vasa propria funiculi and the vasa

( 614)

umbilicalia. As far as I know, a case of the presence of vasa propria
funiculi in any animal was not on record.

This isolated case suggests the general peculiarity of the vascular
system of seals, to which attention has already been drawn by
Hyer’). I may add that the immediately surrounding parts of the
allantois were also very rich in vasa propria, which, however, were
generally of smaller size.

A microscopic examination of the chorion, or rather of the wall of
the outermost and widest embryo-sac, shows us that there are two
layers, an outer one and an inner one, connected by extremely
loosely woven cellular tissues; between the two layers the blood-
vessels are situated. The outer, or uterine layer, the chorion proper,
is lined with a simple cylindrical epithelium about 20 uw igh. The
nuclei are oval-shaped and in the basal half of the cell; the proto-
plasm is finely granulated. Cell limits are distinctly visible. The inner
lining consists of one layer of flat cells with much-flattened nuclei.
The inner coat is nothing but the outer surface of the allantois.
(This connection will be referred to bye and bye). We cannot, there-
fore, call this membrane the chorion, strictly speaking, the name of
outer foetal envelope is more to the point. The bloodvessels in the
wall of this sae are of unequal caliber, in the centre, between the
two layers, larger vessels are met with, the arteries have a thick
muscular coating, smaller vessels are found partly in the stroma of
the allantois, in greater quantity however right under the chorion-
ectoderm.

Even with the naked eye an accumulation of small villi, conspi-
cuous by their velvety aspect, could be seen in some places on the
uterine surface of the outer foetal sac. A microscopic examination
confirmed that these were rudimentary villi. The epithelium did not
differ from the other parts, but the stroma was a much more com-
pact tissue and the interior was filled with very numerous capillaries
the central ones of which had a fairly large lumen.

The amnion, too, or rather the inner foetal sac, is found to consist
of two layers, lying against each other along the whole surface; only
where the wmbilical vesicle is situated they separate to envelop this.
The inner layer is covered with a cubic epithelium of 10 u., the outer
one is identical with the inner layer of the outer foetal sae and
must be considered to be a layer of the allantois. On comparing
foetal sacs of Phoca vitulina with those of other carnivores, Phoea

1) Hyrti. Ueber einige Kigentiimlichkeiten der arteriellen Gefissveriistelungen bei
den Seehunden.

Sitz. Ber. d. mata. naturw. Classe d. Akad. d. Wissensch. Vienna. Bi, XI, 1854,

( 615 )

is found to exhibit somewhat different conditions. In dogs, for
instance, according to the investigations of biscHorr*), SrRanL?) and
others, the allantois-sac forces its way between the chorion and the
amnion. While the allantois is thus making its way further and
further between the two membranes, gradually separating them
almost entirely, the edges of the allantois are coming closer together.
But these edges, according to the drawings of Biscnorr (l.c. Plate XV,
fig. 8) remain separated; according to STRAHL"), they establish contact
by means of cellular tissue, chorion and amnion being thus connected
at this point of contact. In Phoca I found neither the edges of the
allantois-sac, nor a connection like Srraun noticed in dogs; I must
therefore assume that in Phoca the development has gone a little
further and that through the elimination of the partition between
the two edges of the allantois-sac, mentioned by Srrant, the outer
and inner sac have become entirely isolated. The whole of the
original extra-embryonal coelom-cavity has in this way disappeared;
the space between the inner and outer foetal sac is the allantois-cavity.

I have already pointed out that the umbilical cord was connected
with the placenta by means of a so-called insertio velamentosa. The
vessels running towards the placenta or in the inverse direction, are
enclosed by the membrane covering the foetal side of the placenta,
viz. the outer layer of the allantois-sac, which continues on the
chorion along the edge of the placenta.

As far as the inner foetal membrane is vascularised, the vessels
show the same proportions as in the outer foetal sac.

The umbilical sac is situated in the inner wall of the foetal sac,
between the amnion and the allantois, connected by thin cords of
cellular tissue with both. It is a much-elongated, narrow bag, with
folded walls.

The walls consist of strongly vascularized connective tissue, its
limits are not sharply separated from the stroma of the amnion-
and allantois membranes. Only here and there we find the remains
of an original coating of epithelium. The bloodvessels, some of which
have a fairly large lumen, run almost entirely lengthways through the
organ. The majority of these vessels have a thick muscular wall and
were filled with blood. These vessels and the umbilical ones are
connected with one another.

With ‘regard to the placenta the following may here be stated.

1) Biscuorr, Die Entwickelungsgeschichte des Hundeéies.

2) Straut, Untersuchungen tiber den Bau des Placenta. III. Archiv fiir Anatomie

und Entwickelungsgeschichte. 1890.
S)l.G= pee oo:

41
Proceedings Royal Acad. Amsterdam. Vol. VI.

( 616 )

As already mentioned, the seal has a placenta zonaria, which, com-
pared with that of the dog or the cat, is of much looser construction.
The uterine side shows many more or less deep grooves, which
divide the organ into a number of lobes. The deeper grooves, as a
rule, run through the placenta in a longitudinal direction.

In the seal a green border-zone, such as we find described
in the placenta of several carnivores, does not exist. Yet there is
something like it. On detaching the placenta from the wall of the
uterus, one could see, even with the naked eye, that both edges
of the placenta were freely dotted with small, light-orange coloured
particles, some as large as a pin’s head; found, on examination, to
consist of bilirubine. This pigment was found in enormous quantities
and a microscopical investigation showed that the whole edge was
saturated with these orange coloured bits. Owing to them, the narrow
border-seam, instead of being a dark red, like the other parts of
the placenta, was of a dirty brown colour.

As far as the blood-pigment penetrates in the placentary tissue
— for these corpuscles may safely be taken to be transformed blood —
the whole tissue, when seen under the microscope, is tinged a light
yellow.

On following up this tinged zone under the microscope, we shall
see that along the outer edge the amorphous pigment is found in
ereat quantities, but no newly ejected blood is. found. Only at some
distance from the edge the clots of pigment become smaller, but at
the same time they are found to be lying in ejected blood that can
still be easily recognised as such, until finally, at the placental end
of the brown zone, the blood predominates and here and there a
elittering orange-coloured pigment clot is met with.

From this we may infer that the hemorrhage, during the devel-
opment of the foetus, first occius on the outer limits of the placenta
and gradually more towards the centre.

The bleedings at the edge are not the only ones I noticed in the
placenta.

In dogs, for instance, Srrani describes some so-called green islets
in the placenta, spots corresponding to the green edge-zone. These
islets do not occur in seals either, at least they are not visible
macroscopically. Under the microscope, however, we can see in
many places, under the foetal coating of the placenta, some uniformly
coloured light yellow spots. On close inspection if is seen that in
such places, situated immediately below the foetal surface, hemor-
rhage has taken place, and that round this seat of bleeding the
placental tissue is of a light yellow hue all over, Blood-pigment in

t Olt: )

amorphous condition I have not been able to trace in such spots.
The discoloration of the tissue may be explained in this way that
the blood-corpuscles give off their haemoglobine to the surrounding
parts and that this is absorbed gradually by the surrounding placenta-
tissue. This latter point is the most significant part of the process,
for, why should this surrounding tissue, which, unlike the corpuscles,
can hardly be regarded as having died off, absorb the altered blood-
pigment so uniformly? That we have here no post-mortem pheno-
menon appears clearly on examination of the blood-vessels at the
edge of the placenta. As already stated, this is of a more intense
yellow hue than that of the spots under the foetal surface, partly
through the more considerable amount of pigment. Now, we find in the
tissue of the border of the placenta, several vessels, the lumen of
which, in addition to blood-corpuscles, is filled with pigment. These
are foetal vessels. In the vasa umbilicalia I only found some blood,
but no pigment.

The presence of this pigment in the vessels proves, that this yellow
hue of the placenta-tissues is a vital reabsorption-process, and not
one of post-mortem diffusion. There is another fact in favour of
this view: it is my discovering (in the border-zone, where the
villi are not very much elongated and the villous epithelium, or
chorion ectoderm, is still intact), some distinct pigment-particles in
these cells, which had been absorbed from the pigment situated close
against this epithelium.

And on further comparing the structure of the placenta of Phoca
with that of fissipede carnivores (e.g. the dog), it is found that the
spongy layer is entirely missing; all along the thickness of the
placenta the same uniform structure is maintained.

The foetal surface of the placenta is covered with a layer of
the allantois, coated with a single layer of flat endothelium, as
already described. Underneath this, there is a thin layer of fairly
firm connective tissue, in which the larger ramifications of the umbilical
vessels are found.

From this tissue coarse septa of connective tissue find their way
into the placenta, which gradually diminish as they run towards
the foetal surface, although they usually succeed in reaching it. In
these septa the ramifications of the foetal vessels are found. Coarse
septa send out finer compartments in every direction. The coarser
ones divide the very compact mass of placenta into smaller sections.

From the maternal side too, some septa of connective tissue filling
up the aforesaid grooves on the foetal side of the placenta, enter
the latter; they are however less voluminous than those coming

41%

( 618 )

from the foetal side. The compact cellular tissue of the placenta
reaches right up to the wall; between the latter's coating of
muscles and the compact placenta tissue a very narrow, loosely
woven layer of connective tissue runs. In this layer, lying against
the muscular coat, we find the diameters of the very wide
uterine vessels and also in several places some uterus-glands. These
glands, in the shape of elongated tubes with short ramifications and
parallel with the surface of the uterus, are squeezed in between the
muscular coat and the placenta. They have a distinct lumen, the
epithelium is highly cylindrical. They are glands that have obviously
fully developed, but have not been invaded by villi. On the foetal
surface of the placenta moreover, distinct extremities of glands are
met with, which, like those just described, have bent round and
which run parallel with the muscular coat, in which a foetal villus
is plainly visible. These villi are not lying close to the inner surface
of the follicle, but are somewhat retracted from it. I did not succeed
in observing a distinct epithelium on these villi.

Some of these uterus glands appear in another form: the cells
have very much increased in volume, have swollen and are bulging
out in several places in the lumen. The protoplasm of these cells is
of a well defined reticular structure, the cell nuclei are in the basal
part of the cells. In the lumen of such glands we find some inde-
pendent cells, or combinations of only a few, some with nuclei,
the larger ones without any; moreover some conglomerations of
deeply stained fine particles may be observed here and there.

The compact mass of the placenta, when magnified, turns out to
contain a great number of bloodvessel-lumina, adhering close together,
each one of them surrounded by a distinct endothelium-wall. The
ramifications of the foetal vessels, together with some connective tissue,
run between these branches of the placental vessels. Forming a separating
laver between these two systems of blood-vessels, we find in the
greater part of the placenta one single layer of nuclei, situated in
a mass of protoplasm, in which, however, no cell limits could be
traced. This layer of nuclei, is to be regarded as belonging to a
syncytium. In some places I counted two, sometimes even more,
rows of nuclei between the branches of the placental- and those
of the foetal vessels, without my being able to say with certainty
which part of it should be taken to be of a syneytial character.

In the cases of suballantoidal hemorrhage and in the surrounding
parts, the nuclei of cells, lining the endothelium-walls of placental
vessels and the foetal villi adhering to the blood-mass, are of a
much darker hue than those of other parts of the placenta, As a

coating of these foetal villi I often observed a double layer of
nuclei, viz. a layer of flattened nuclei, lying close together, coating
the villus and, round this, a layer of round, large nuclei. Against
the latter layer the extravasated blood is found. Between the nuclei of
the inner series, cell-limits are sometimes noticeable (chorionectoderm).

Finally I want to offer a few remarks about the villi in the
border-seam.

The mass of coagulated blood found near the edge of the placenta,
and the bulk of which has the shape of amorphous, orange coloured
lumps, is mainly situated between two very long villi, running in
a slanting direction from the foetal surface of the placenta to the
wall of the uterus. From these villi and from the part of the
chorion that is lying between the bases of the two, a number of
shorter villi, with ramifications, find their way into the above
mentioned mass.

These villi are generally somewhat swollen and rounded off at
their extremities. They are all conspicuous by their profuse vascularity.

The chorion between the bases of the two villi just described is
covered with a layer of very darkly-stained nuclei, lying very close
together. It remains doubtful whether this was a syncytium.

The secondary villi, passing into the above mass also have such
a coating. In some cases two rows of nuclei could be seen on
the surface, while it seemed to me that the row of nuclei turned
towards the villus was not of such a dark hue as the outer one
turned towards the blood-mass. At the extremities of the villi the
nuclei are found to lie very closely together and to be more numerous.

Both in the protoplasm of the latter layer, covering the chorion,
and in that of the villi one observes accumulations of orange-
coloured particles.

Reabsorption of these corpuscles from the mass found in the border-
seam of the placenta is therefore effected by means of the coating
of the said layer of the chorion as well as that of the villi.

In one or two instances I found a coloured particle in the stroma
of a villus or in the capillaries running into it.

( 620 )

Mathematics. — “On the dijjerential equation of Monee” by Prof.
W. KaApreyn.

(Communicated in the meeting of January 30, 1904).

If we suppose that in the differential equation
Hr 4: OKs 3 1 es ee ee
H, K, L depend only on p and 4q, the necessary and sufficient condi-
tions for the existence of two intermediate integrals are the following.
In the first place H, A and ZL must be proportional to the second
differential coefficients of a function 6; thus
eS ee L

dT iT ea i piage iat ag a
O55) Sa eee, Ee

13 22

In the second place the function 6 must satisfy the differential
equation of the fourth order

2D(6 0? D 4 o?7D 4 ue 0S Oe
= 22 Op? 12 Op age ifs Og aa

=sle D\ 4, DW, 4 (oD :
=e fae = 2 Op Og Ge) | See (3)

eS VO Oia 4...
The general integral of this differential equation can be represented
by the following formulae :

where

Fea \
| dea Re Tare
14“—1

! !

Via ae
u— UV

) i \ Sn
a 24 g' du — 2 fu ys” dv — (g' — fh’) (g' + wy’) —

e e

9 = 5
ae : |v —h)(g' —w) — (g—w) Y — M) |
where w and v indicate arbitrary parameters and
g=9) , h=h@& , G=H— » P= Hl)
four arbitrary functions, and
dy deg
/ Tait oe ae ta
If the conditions (2) and (3) are. satisfied the equation (1) will
possess the two intermediate integrals
ze—c gy" — Ww g' —= iy (1),

e—yy'—ah! =3(0)

Where 5 denotes an arbitrary function and w and + the functions
of p and q, derived from the equations (4).

In the particular case that the function @ satisfies the two members
of the equation (8) separately, we have to distinguish two cases
according to the double sign im

dD 6 2 os ahha — 6, Ove 0D

sR ae ES —=—= (0,
Og fs Op
The general integral can be written in both cases respectively
ES.
pj [ute = 9-)) HF (yu)
VW |
q= ys + (9)

A6=(2wy"'—4ugdt4o zw ryp— 2f( gq" = v)jupdu |

where g=g(w) has the same meaning as betore, whilst 7 and +
represent two new arbitrary functions of the arguments placed after
these symbols.
In these cases the two intermediate integrals are
epy(ug"’—a')— alu r" + 7") = & (u),
yt af (uve eo H=Slee +7),
the values of w and v being expressed in p and y with the aid of
the formulae (5).
The condition (8) appears, although in a different shape, already
in the excellent dissertation of J. VAnyi (hKlausenburg 1880).

Mathematics. — * 7% singularities of the focal CUTIVE of a plane
general curve touching the line at injinity 6 times and passing &
times through each of the imaginary circle points at injinity.”

By Dr. W. A. Versicys. (Communicated by Prof. P. H. Scnovurs).
(Communicated in the meeting of January 30, 1904).

In “Verhandeling’” 5 of the “Kon. Ak. v. W.” at Amsterdam Vol.
VIII, I have deduced some formulae expressing the singularities of
the focal developable and of the focal curve in function of the sin-
gularities of a plane curve having no particular position.

In a similar way it is possible to deduce the following formulae
expressing the singularities of the focal developable and of the focal
curve of a plane curve touching the line at infinity o times and

passing ¢ times through each of the imaginary circle points at infinity.
Let the plane curve be of order pg, of class v and let ¢ represent
the number of its inflectionai points. Then the singularities of the
evolute or of the cuspidal curve of its focal developable are the following :
rank, r= 2(u+ »v — 2e — 9)
class, m = 2p
number of stationary planes, 4 — 2¢
double osculating planes, G = v* — » — uw — 384 = 30° 4+ 28 — 6
stationary tangents, v = 0
double points, = 3(u—r)+-¢
double tangents, w = 0
order, n= 2 (3 u + 4 — 6e — 306)
stationary points 8 = 2 (64 — 2v 4+ 3 — 12e — 60)
stationary points not at infinity and not in the plane of the curve
B' = 2 (Su — 38y + 31 — 8e — 30)
order of the nodal curve « = 2 (uw -+ rv)? — 10u — 2v — 3t — Bue
— 4uo — 8re — 4ro + 8? + 80-1 26?
+ 20s + 106.
The chief singularities of the focal curve are:

order, n= 2m? + 4uy + vr? — Llu — vp — dt — 8ue — 40 — Bre — 2rd

+82? + 86 + o° +20 4+ 9o
rank, 7 = 4ur + r* — 4u — 4v — 8re — 2r0 — 30° + 8e + 50 :
number of stationary tangents, 7 =O
class, m = 6°? + buy + 4ute 4- 2re — 36u — 12y — 181 — 24ue

— buco — l2re — 4ro — 81e — 20 + 246? + 1286 — 86?
+ 60e + 280
number of stationary points 8B = 2 (84 + 4) (2u + vr) — 57a + 21y
— 2/0 — 48pe — louo — 12ve — Aba
— Sue — 26 + 4828? + 368s6 + 40?
+ 3686 + 9b6e + 400.

Mathematics. — “On the position of the three points which a
tivisted curve has in common with its ose ulating plane.” by
Dr. W. A. Verstuys. (Communicated by Prof. P. H. ScnovuTe.)

(Communicated in the meeling of January 30, 1904).

§ 1. Let d be the section of the osculating plane V in a point
P of the twisted curve C’ with the developable O of which C is the
cuspidal curve; then the twisted curve C and the section d have in
the point / only two points in common, that is they have in
P a contact of the first order.

( 623 )

The curve C has in P three successive points in common with
the plane V. The curve C’ is situated on the surface V, so the three
common points must lie on the section of VY with VV. This section
consists of the curve d and of the common tangent / in P of (C
and d, counting double. In the following way can be proved that
of the three common points only two lie on d.

Let us first take instead of a general curve a twisted cubic C,.
Let P be the origin; the property being projective the plane at
infinity can be chosen in such a way, that the curve is represented
by the equations

=o PSO —= eh

If now in point ¢=—O the curves (, and d, had three common
points then in the origin also the radii of curvature of the two
curves would be the same. Let # be the radii of curvature of
C, in P and ¢ the radius of curvature of d, in P, we then easily
find:

ans: ds* it (l+4+ 9¢*)*2
VEAP BRE CH Vk 868 + 8604

So for ¢=0 we find K=-—

The surface OU, is enveloped by the plane
e—3yt+32P —#=—0.

So the curve d, is enveloped by the line

—syt+3s2t—P—0

Consequently the equation of d, is

so the radius of curvature 7 = The curves C, and d, have in
the origin not the same radius of curvature, so they have not three
or more points in common.

Let p be the orthogonal projection of C, on V7 (7 = 0), then C,
has with p three successive points in common in P, for all points
which (, has in common with JV’ must le on the section p of V
-with the projecting cylinder of C,. The projection p has for equation

, nee 1
-and so also the radius of curvature in the origin R= z showing

-
again that the curves p and C, have in the origin three points in
common.

( 624 )

Out of the two values R=~— and »—=-— ensues that the section

d, lies near P on the convex side of the projection p.

§ 3. The latter can also be proved as follows tor any curve
with the aid of Descriptive Geometry.

If we take the osculating plane J’, in any point of the curve C,
to be the vertical plane of projection and the normal plane of the
curve to be the horizontal one (plane of projection), then the vertical
projection p” is a curve cutting the axis perpendicularly in a common
point P and the horizontal projection p' is a curve having in P a
cusp with the axis for cuspidal tangent. Let us now construct
the vertical trace d" of OU. The vertical traces of the generating
lines of O lie on the tangents to p", thus all on the convex side
of p", whilst those traces are also situated on the same side of the
perpendicular on the axis in /?, where also p” and p’ are lying. So
the curves d" and p" turn the concave side to the same side, whilst
d" near P lies outside p". So the curves d" and p" have an even
number of points in common.

Thus if @ and d" had the three points of C) lying in J’, in common,
then also p" and ¢/ would have three points near ? in common,
So according to what was proved above p" and d” had four points
in common. That fourth common point of p” and dd” would, lying
on d", also lie on OV and would be the projection of a point Q of
the curve ( lying as near to it as one desires. So at the limit the
projecting line of Q would be a tangent of O. Thus near Pa tangent
of O might be perpendicular to the osculating plane JV’, which is
impossible. So C and (" have no three points in common.

§ 4. We can prove moreover as follows synthetically that the

twisted cubic C, has not three points in common with the trace ¢/,.

If (, and d, had three points in common at ? then ¢, and the
projection p, of C, on Vo out of any arbitrary point A would have
three successive points in common. This projection p, is a eubic
curve of class four. The three inflexional tangents of p, ave the traces
of the three osculating planes through A, thus they are also tangents
to d,. As the contact of the second order in ? must count for three
common tangents and each of the three inflectional tangents of p,
for two common tangents, two curves respectively of class two and
class four would have nine common tangents, which is impossible,
So the curves C', and d, lave at P no three points In common,

( 625 )

§ 5. It follows from what was proved above for a twisted cubic
that also a general twisted curve ( has not more than two points in
common with the section d¢ of its developable ( and the osculating
plane WV. If C and d had three points in common, then (/ and
the projection p of C out of any arbitrary point A on the plane V’

of ¢ would have three points in common. Let (, be a twisted cubic

;
having in 7 six successive points in common with (. Now |” is
also the osculating plane of C, in P?; let d’ be the trace of the
developable O, belonging to C, and let p’ be the projection of C, on
V out of A. As the developables VU and OV, have five successive
generating lines in common, so ¢ and d have at least three succes-
sive points in common, whilst » and p' have six successive points
in common. Now, if d and p had three successive points 'n common
at P, this would also be the case with d’ and p'. According to the
preceding § the latter is not true, so C and d have neither three
points in common.

§ 6. The theorem can also be proved by searching for the points
of intersection of the cuspidal curve v or of the nodal curve § with
a second polar surface 4?0, just as Cremona did (CremMoNA—CURTZE;
p. 87—90). To simplify the matter I shall first apply this proof to
a twisted cubic, after which the proof for the general case can be
more easily followed.

Let us take for developable O' the surface consisting of a develop-
able OU, and of a quadratic cone A with vertex 7) passing through
the conic d, situated in the osculating plane*)” of P and on (,,.
The cuspidal curve of this surface of order six is tne cuspidal curve
C, of O,, so » = 3. The nodal curve & consists of d, and of a
curve of order six s. This curve s intersects the plane V of the
conic d, six times, three times of which in the points where d,
meets a generating line of V,, for which the tangent plane passes
through 7’, these three points being points of contact of double
tangent planes of ©’. Consequently s has in /P three successive
points im common with d,. Let A?V' be the second polar surface
for a point A lying in V. The order of A?’ is four.

In the formula of Cremona for §(@— 2) | have only to keep the
first and the third term, none of the singularities appearing on the
surface under consideration which are furnishing the other terms;
but a term P must be added for the particular point ? where
another third sheet of the surface O” passes through a plane curve
d, lying on O,. This singularity has not been considered by Cremona ;

( 626 )

it appears on the foeal surface of a plane or twisted curve touching
the plane at infinity.

So the formula of Cremona becomes :

s(o—- 2) = number of times that s meets the curve
of contact of A+ 324+ P.

The curve of contact of A consists of the generating lines of O”
of which the tangent plane passes through A. Of these generating
lines two are situated on the cone A, each of these meeting the
curve ys three times and two are situated on Q, as A lies on the
osculating plane J”; the latter meet s each one time. This number
of points of intersection of s with 4? Q’ is thus eight. According
to Cremona they must each be counted one time, so the first term is 8.

The section of QO” with JV" consists of ¢, and of the tangent in P
to d,, both counted double. So the second polar curve of A for this
curve or the section of |” with 4* 0’ consists of a curve of order
four, touching d, twice in /P, having thus with d, and with s
too only four points in common. The formula of CREMONA gives:

6S See ee

Consequently : 4 = 4.

The points 4 are the poimts outside ? where the cuspidal curve
meets another sheet. As (’, meets the cone A in all six times, C,
can meet the cone A in P only twice, so C, has also with the

curve d, lying on A but two points in common.

§ 7. If we had taken A outside the plane V" this change would
have had no influence on the number of points 2, but the term
issuing from the lines of contact would have been one more, so P
would in that case have counted for 3.

By applying the above used method to the nodal curve d,, we
find that 4* O’ of an arbitrary point A lying outside J” also meets
/, in three points. The singularity 2? counts for six points of inter-
section of the total nodal curve § with A* 0’, thus for as many
points of intersection as two points 4.

Out of the formula of Cremona for » (9 — 2) it is evident that P
counts for two points of intersection of the cuspidal curve C, with
ZL? 0’, thus also for two points 2. From what precedes ensues that
the cone A’ passing through d@, is an ordinary touching cone and
that the point of contact P counts in both formulae of Cremona for
two points A.

§ 8. Let the curve C’ be a general twisted curve of order vy. Let

‘

VY be its developable, the class u, the rank @ and let the order of

( 627 )

the nodal curve on ( be §. Let the number of stationary tangents
be @ and that of the double tangents w. Let P be an ordinary point
on C, / the tangent in P to C, V the osculatine plane in ?
and d the curve of intersection of |}” with the surface O. Let ce.
be a conic having at ?P five suecessive points in common with d.
Let 7’ be the vertex of a quadratic cone A’ passing through c, where
7 is arbitrary but taken in such a way that A’ cuts the curve Cin
none of its singular points. Let s be the curve of intersection of O
with A. This curve, of order 2, shows singular points: 1st in P;
2"' where C or a line 6 cuts the cone A’ (point P excepted), these
are cusps 42 on s; 3° where A meets the curve & or a line w:; these
pomts are on the surface Q’ consisting of OU and A’ triple points
t and nodal points on ys.

If we now determine the points of intersection of s with the
second polar surface 4° V' of a point A lying in V" then according
to Cremona the cusps 2 must count three times and the triple
points t, through which only two branches of s pass, must count
twice. in order to find out for how many points of intersection the
point ? must count, we consider the first polar curve of the section
of Y with V. This section consists of the right line / counted twice,
of the curve d and of the conic c,. So the first polar curve consists
of the right line / and of a curve of which one branch has five
points in common at ? with c, or with ¢ and of a branch touching
/ also in P and lying at ? between / and d. So the second polar
curve shows at / two branches touching c,. The two branches
of s passing through P touch / in P, and JV’ being also of both
branches the plane of osculation, they have both with |” or with
c, three points in common. Each branch of s through /? has thus
with 4? 0° in LP but four pomts in common, so that the point P
counts for eight points of intersection.

Besides meeting the curve s in these singular points of s the polar
surface 4? V’ meets it moreover in the ordinary points where s meets
the curve of contact of tangent planes through 1. These points
count according to Cremona each one time. The curve of contact
consists of two generating lines of A’ each meeting the curve s
o times and of (u—1) generating lines of V, as A is situated in the
osculating plane J’. These generating lines each meet s two times,
so that to determine 4 we arrive at the formula:

207=—344+45--4w+8+20+4+2(u—])),

« SG ee ee 25 cae Eee. oc 6) ae
a= Bio o—p—25—2H— 3}.

As according to one of the formulae of CayLry-PLUcKER

( 628 )
o? —-o—n—2§—20—3(74 A),

then
A=2rv+ 20—2.

So the curve (' meets the cone A’ outside P still 2 r— 2 ‘times,
and P counts for two points of intersection. So the curve C' also
ineets the conic c, lying on A’ only two times and consequently
the curve d, having with c, five points in common at /?, meets it
also only two times.

Chemistry. — “A contribution to the knowledge of the course of
the decrease of the papour tension for Aqueous solutions.”
By Dr. A. Smits. (Communicated by Prof. H. W. Baxatis
RoOZEBOOM.)

1. In 1788 BiacpEN') discovered the relation between the lowering
of the freezing pomt and the quantity of the solved substance.
Among the substances which he examined, were however also some,
which showed deviations, either in this sense that the lowering of
the freezing point increased more rapidly or in that sense that it
increased more slowly than the concentration.

Réporrr*), who quite ignorant of BLAGpEN’s work, made the
same discovery in 1861, and Copprt*), who ten vears later (1871),
continued RiporRerr’s investigations, came both to the result, that
deviations from the rule first discovered by BrLaGprEN, occurred both
in one sense and in the other. A disproportionately rapid inerease
of the lowering of the freezing point with the concentration was
found among others for Nabr, NaJ, CaCl, H,SO, and also for NaCl,
whereas for the nitrates of Na, NH,, Ba, Ca, Sr, Pb, Ag and for
Na,SO,, Na,CO,, NH,CNS the reverse was observed.

As an illustration of the course, as for Nabr etc. Réporrr had
already adopted the formation of hydrates. Copper assumed for the
deviations for -the nitrates, which are mostly anhydrous, that they
are modified by the action of water or by the fall of the tempera-
ture in a certain, not further defined way.

Results analogous to those of BLaGprn, RtpoRFE and Copprt were
obtained by ‘TAmMANN*) in 1887 when determining the decrease of
the vapour tension. TAMMANN found namely, that for most of the salt

1) Wied. Ann. 39, 1. (1890).

*) Pogg. 114, 63. (1861); ib. 116, 55 (1862); ib. 145, 599 (1871).

*) Ann. Chim. Phys. (4) 23, 366. (1871); ib. 25, 502. (1872); ib. 26, 98 (1872).
') Wied. Ann. 24, 523. (1885).

— =a

( 629 )

solutions the diminution of the vapour tension with increase of con-
centration increased more than the concentration, whereas for the
nitrates of K, Na and for KCIO, the reverse was observed. The
later investigations of Bremer'), HetMHonrz*), WALKER*) and Dirererict*)
gave the same result as those of their predecessors viz. this that in
general the diminution of the vapour tension increases more rapidly
than the concentration, and that the salts which form an exception
to this rule are chiefly the anhydrous nitrates.

Up to 1905 the determinations of the freezing point of salt
solutions of smaller concentrations than those which had been earlier
investigated, yielded the result, that the molecular lowering of the
freezing point decreases with increase of the concentration. As these
measurements were continued to the concentration of + 1 gr. mol. per
1000 er. H,O, it followed necessarily, that where the reverse course
had been ascertained by the earlier observers, a minimum value had
to occur in the molecular decrease of the freezing point, but for a
concentration which lay above that where the investigators of later
time had stopped. |

In 1896, however, I had come to the conelusion in the determi-
nations of the vapour tension by means of the micromanometer °),
that for dilute solutions, i.e. for solutions below the concentration
of 1 gr. mol. per 1000 gr. H,O, the molecuiar diminution of the
vapour tension creased with the concentration. This was found
inter alia for solutions of NaCl, KOH, H,SO, and CuSO,, whereas
for KNQ,-solutions the reversed course was found. This result was
therefore in perfect accordance with what had been found by my
predecessors for more concentrated solutions, but was directly opposed
(except KNO,) to the results of the determinations of the freezing
point.

The question was now: “Which results are the correct ones ?”

In the determination of the boiling point 1 hoped to find a means
to answer this question. After having applied some improvements
to the method and after having rendered myself independent of the
fluctuations of the atmospheric pressure by using a imanostat, | began
the investigations and the result was published in April 1900 °).

1) Rec. tr. Chim. 6, 122. (1887).

2) Wied. Ann. 27, 568. (1886).

3) Zeitschr. f. phys. Chem. 2, 602. (1888).

4) Wied. Ann. 42, 513. (1893); ib. 62. 616. (1897). Ann. phys. Chem. 27, 4. (1898).

8) Archiv. Néerl. (2) 1 (1897).

6) These Proceedings II April 21 1900 p. 635, April 20 1901, Jil p. 717. In the
same year (1900) Jones, Cuampers and FRazer eryoscopically found minima for
MgCl, and BaCl, lying at 0.1—0.2 gr. mol.

( 630 )

I arrived at the following result :

The molecular rise of the boiling point increased for solutions of
NaCl and KCI from the concentratien + 0.3 gr. mol. per 1000 er.
H,O, both towards higher and towards lower concentrations, or in
other words, the molecular rise of the boiling point proved to have
a minimum value lying at + 0.38 gr. mol. For the anhydrous
nitrates of K, Na, Ba, Ag and Pb, however, the molecular rise of
the boiling point proved, quite in concordance with the determi-
nations of the vapour tension, to continually decrease with increase
of the concentration.

The method which was the least accurate in appearance, proved
to be able to point out a mistake both in the method of the freezing
pomt and in that of the vapour tension. The first work was then
to force the micromanometer to greater accuracy by applying some
improvements, and then to repeat the experiments. In 1901") anew
series of experiments yielded really a result which qualitatively
harmonized perfectly with that obtained by means of the boiling
point method. For NaCl as well as for H,SO, a minimum occurred
in the molecular decrease of the vapour tension, lying at + 0.5 er.
mol. As before KNQO,-solutions gave a strong decrease of ¢ with
increase of the concentration.

In the same year KAHLENBERG?) found for solutions of NaCl,
KCl, KBr, KJ and MegCl,, that the molecular rise of the boiling
point increased continually with the concentration for the first and
the last salt from the concentration + 0.2 gr. mol. to = 5 gr. mol.,
whereas for KCl, KBr and KJ a more or less clearly marked
minimum was found.

Bitz *) was the first to confirm my results with certainty in 1902.
He found a minimum in the molecular rise of the boiling point,
not only for KCl and NaCl, but also for RbCl and LiCl. His deter-
minations of the freezing point of alkali chlorides showed only for
LiCl a continual increase of the molecular lowering of the freezing
point with the concentration; a minimum was not found, however,
for the chlorides of the alkali metals by this method. For LiNO,
and Libr Binrtz found a faint minimum, whereas for the chlorides
of the bivalent metals by the cryoscopie way very strongly pro-
nounced minima were found, mostly lying between 0.1 and 0.2 ger.

1) These Proc. IV September 28 1901 p. 163.
*) Journ. Phys. Chem. 5, 339 (1901).
3) Zeitsch. f. Phys. chem. 40 s. 185 (1902).

( 631 )

mol., which is in accordance with the observations of Jonrs, CHAMBERS
and FRAZER‘).

The first who by the cryoscopic way discovered minima in the
molecular lowering of the freezing point for chlorides of the alkali
metals below the concentration 1 gr. mol., were JonES and GrTMAN *),
who published their results in the newly published Jubelhand fiir
Ostwald. It is remarkable that working with the common apparatus
of BECKMANN these observers obtained more accurate results than Raovu
with his apparently ideal apparatus. For Raovuitr found for NaCl-solutions
up to the concentration 1 gr. mol. a regular decrease of the molecular
lowering of the freezing point with increase of the concentration.

2. After having thus shortly pointed out what the boiling point
method, the vapour tension method and the freezing point method
have brought to light for the study of the non-diluted solutions, [|
proceed to give the results of the determinations of the diminution
of the vapour tension of NaCl and NaNO,-solutions, made by means
of the méicromanometer, in which the aniline-water-manometer was
replaced by the manometer of Lord Rayixien *). It seemed namely
very desirable for the greater certainty of the results, to repeat
some measurements with another apparatus, the accuracy of which
did not differ too much from that of my manometer. Lord Rayirieu’s
invention was therefore very welcome to me, because his manometer
was stated to reach an accuracy of + 0.00045 m.m. Hg, and mine
had an accuracy of 0.00025 m.m. Hg.

Lord RayiricH’s manometer and the arrangement of this apparatus
has been represented in fig. 1 and 2. A is a barometer tube, which
branches into two parts at the top; the two branches are blown out
to two bulbs of + 25 mm. diameterat LA. In these bulbs extend
two finely drawn out glass points, which are ground off to a sharp
point at the lower end. On the tubes LL, of which the one more
to the left is split up into two branches, as is seen in the horizontal
projection, and which thus furnish three points of support, a glass
plate .V is laid which bears a mirror J/, whose front is silvered.
The glass plate .V is fastened to the three points of support and
the mirror J/ to the glass plate by means of water glass.

Lord Rayieien had connected the tubes CC with his apparatus by
means of straight glass tubes 3 meters long, but here some glass
spirals = 35 c.m. long have been added between them in order to
prevent any wrenching.

1) Amer. chem. Journ. 23, 89 (1900); ib. 23, 512 (1900).

2) Zeitschr. f. Physik chem. 46, 244 (1903).

3) Zeitschr. f. Physik chem. 37, 713 (1901).

Proceedings Royal Acad. Amsterdam. Vol. VL.

( 632 )

The manometer / with baro-

meter tube A is (see fig. 2) fastened
M. | Scie
in a groove of asolid board P by
means of Cailletet cement. This
board is part of an adjusting table

S, which can rotate round an
horizontal axis by means of the

screw 2. This axis passes through
the poimts of support of two sets
of screws Z, only one of which
is to be seen in the figure 2. The
mirror of the manometer has

the axis mentioned is parallel
to its front and coincides with
its middle. The air trap V, in
which the barometer tube ends,
is by means of an India rubber
tube provided with two clamps
(F and Hf and connected with a
mercury reservoir J. |
The principle, on which this
manometer rests, is as follows:
If the barometer tube is filled
with Hg as far as in the bulbs BB
and if the pressure is the same
in the two legs of the manometer,
we can cause the two glass points

io just touch the mercury mirrors,
which are now iw one horizontal

Pigiah:

plane, by using simultaneously the
clamp Hf‘) and the screw 2. This point can be very accurately
determined, as we can observe the reflected images at the same time
with the points and so it is as if we saw twice two points approach
each other. If the light of an incandescent lamp g, concentrated by
a lens, was thrown on the manometer through a mirror im, a great
accuracy of adjustment could be reached after some practice, when

1) The clamp G serves for the rough adjustment.

2) As it proved necessary to prevent heating of the manometer as much as
possible, a thick plate of asbesios 7 was adjusted between the incandescent lamp

and the manometer; in this plate a glass vessel # was fastened with a solution
of alum for the absorption of the rays of heat.

been placed in such a way, that.

—

( 633 )

the points were simultaneously observed through two magnifying
vlasses.

The position which the mirror J/ occupies in this adjustment,
so the zero position, could be accurately determined by means of a
scale and a reading telescope with a cross wire. If now a difference
in pressure was brought about e.g. such that the mercury mirror
in the left lee fell somewhat and that jn the right leg rose somewhat,
the adjustment of the two points on the mercury mirrors could be
again reached by turning the adjusting table, to which the manometer
is fastened, over a small angle to the left by means of the screw P,
for which at the same time the screw // was to be used, as the
bulbs LL are no perfect spheres, and have not perfectly the same
diameter either.

When the glass points are again placed in the required way and
the reading glass is again read, it is clear, that
we can calculate the difference in level of the
mereury mirrors in a simple way from the
angle of rotation, when we know the distance

é.1, between the glass points. If this distance is /,
ea the angle of rotation @, the difference in height
Fig. 3. between the two mercury mirrors is:

k=l sin a.
If we represent the deviation observed with the telescope expressed
in m.m. @ and the distance from the scale to the mirror J, then
a

a (
tg. ¢.= 3 for which we may write ty t= >, provided @ be very
: ) ‘ e , ‘

small.
As further for small angles sim @ = ty a, we may write in this case:
la
Be a a oie Ne oeeatiese ieee Mer
If the angles are too large for this assumption, we get the following
form for /:
la x a7
b= (1-+ 55) Se, wore Seem rae eee
The distance between the glass points was determined by means
of a comparator and amounted to 24.66 m.m. = /. The distance
from the scale to the mirror amounted to 2735 m.m. = 6.

It now proved that when the deviation @ was smaller than 100
m.m., formula (1) could be applied, whereas for larger deviations
formula (2) appeared to be required.

The accuracy of adjustment, obtained in this arrangement with

42%

( 6354 )

Lord Ray.eiGn’s manometer, appeared to amount to 0.1 scale division
or to 0.00045 m.m. Hg, whereas with my manometer it amounted
to 0.00025 m.m. He, as has been said before.

Fig. 4 represents the whole arrangement. A is the micromanometer,
B the antomatic mercury air-pump, C'’ the manometer of Lord
taYLEIGH and PD the reading glass with scale and mirror, a is a strip
of mirror, cut from a sphere. In the focus an incandescent lamp 6
is placed, over which a glass cup has been placed enveloped with
filtering paper. A parallel pencil of rays falls through the glass seale
e and is reflected by the mirror J/ from the manometer into the
reading glass /.

From this figure the connection of C with A through the long
glass tubes ¢ and 7 is also clearly visible. The results obtained by
this arrangement are summarized in the following tables.

T Asis 15 SB eee

Na Cl.

ea rides y ees) (SE P, *) | Po—P, N Dn
in er. mol, p. in mem. He inmm. He | t= Pe n 008316 ”
1000 er. HO of 0°. of 0°,

0.0441 0 00720 0.163 | 1.96

0.41073 O O1619 Of151 | 1.81

0.3823 0 05535 0.1447 1 740

0.6299 0 O9125 0.1449 1.742

Q OQSST 0.14564 0.1473 | lena

2 O476 Q.31017 0.1515 4 822

3.3524 0.53442 0.41594 4.947

With the aniline-water manometer the following results had been
before obtained.

We see from this that the tables I and Il harmonize very well
qualitatively ; both give a minimum vaiue of ¢ for the concentration
+ 0):5. of. mG.

That there are differences in many cases in the absolute values of
ris probably due to the uncertainty which exists in applying the
temperature correction when working with my manometer. In future

1) Pm = molecular diminution of vapour tension.
2) 0,08316 = theoretical mol, dimmution of vap. tens. at 0°,

Na Cl.

ee je aes Pn | p—p, W Pi
in gr. mol. p. in mm. Hg in m.m. Hg ‘= “Dp. nh U,URBIG
1000 gr. HO | of 0°. of 0°.

0.0591 0.00879 0.149 4.79

0 0643 0.00039 0.146 1.76

0 1077 0.01541 0 143 1,72

0 4597 0.06400 0.441 eof (8.

0.4976 0 OGIR7 0.4144 4.70

4 OS0S 0.45484 0 143 1 723

1, 2521 0.48014 0.4144 1.730

1 8298 0.26757 (). 147 1.765

2.1927 0.33406 0.153 1.832

4 6362 0.78345 0.169 2 032

it will therefore be advisable to place the manometer in a thermostat.
Up to this time the manometer was placed in a glass vessel, through
which the water of the aqueduct flowed. If a correction is rendered
unnecessary by keeping the manometer at constant temperature, the
greater sensitiveness of the aniline-water-manometer will be still more
apparent *).

For the comparison of the results of the determinations of the
vapour pressure with those obtained in a cryoscopic way, the results
of Raovir?), Jones and Grtrman and mine for NaCl-solutions are
placed side by side in the following table.

So Raovir did not find a minimum in the factor 7 in spite of his

1) After having read my publication in the Archives Néerlandaises, BareLit made
some measurements with a manometer which differed from mine only in so far,
that it was erected in reversed position, in order to make the closure with mercury
instead of with oil possible. This change was sufficient, as Prof. Cassuro,
under whose superintendence Bareitt seems to have worked, wrote to me, to omit
my name altogether in the publication in the Ann. de Chim. et de Phys. T. XXV
1902, though they used the most essential part of my work viz. a dilute solution of
Na OH, Naz CO. or glass, which causes the aniline to run in a tube of the aqueous
solution, and to which the great accuracy is actually due.

*) Zeitschr. {. Physik. Ghem. 27, 638 (1898).

( 636 )

2A i
Na Cl.

SEE

|
ig- JONES and

ip — SMITS.
GETMAN. |

Concentration ,?g— RAOULT. |
|
| |

Cen ee a Per cA

04 | 1-865 —- > eee | 1.81

05 | 41.86 | 1.804 | 4.74

1.0 | 4.838 | 1.906 | 1.77

2.0 | 2.007 1.82

3.0 | 2.490 1.92
|

ig = ‘ caleulated from the lowering of the freezing point
in > » » » diminution of the vapour tension.

method which seemed so very accurate, though he continued the
experiments up to the coneentration 1 gr. mol.; JONES and GETMAN,
however, found a strongly pronounced minimum lying at the con-
centration + 0.1 gr. mol., whereas the determinations of the vapour
tension give a minimum at + 0.5 gr. mol.

[ have already pointed out in a previous paper’), that only for
ihe case that we have to deal with exceedingly diluted solutions the
value of 7 calculated from the lowering of the freezing point must
be in harmony with that calculated from the diminution of the vapour
tension.

For the calculation of 7 from the lowering of the freezing point
the following equation is used:

ead.
fs ae ee
RL* mn

and for the calculation of ¢ from the diminution of the vapour tension,

ic AF

we applied the equation

Ap N
bp a he IS, Weal eC ae
Po
For exceedingly diluted solutions 7g = 7p or
Ap N Le ae
— Bs of i: ae =e . . . (3)
Po di 5) 7]
or
Lp mh eee
a Al 6. oars . . . . (4)
Po KT,”

1) These Proc. Ill, Febr. 23 1901, p. 507.

=— so Se

( 637 )

For not very dilute solutions this is however no longer the case
and as VAN Laar!) found, for them the following relation holds:

Pega Regen ° 5
oO” i 2 RT? : iy : x 7 % 4 - f ())
or
Ap. 1 (Ap! nae 5
sess ( Sar Se ae 8)
Po 2 [ Po Ri o. /

If therefore we wish to compare the results of non-diluted solutions,
we can e.g. calculate instead of 7¢—=/p according to (1) and (2) the
following values:

S {RANG
Bre To. x

Lp EfApy N
an i ot.
Po 2 Po 4 M
which theoretically must have exactly the same value.
I have already shown before *), that the error committed by putting

ig=tp instead of /g= /p for not very dilute solutions, is not
sensible before we reach the concentration + 1

lf a

or,
If we now compare the results obtained by Raovrt, Jones, Gur an
and myself by means of the factor /, we get the following table:

At Bey Boo,

It is obvious that the second column is now qualitatively in
concordance with the two following; also the factor / derived from
the observations of Raovit, gives a minimum, but it is very faint,
so faint, that it did not appear in the calculation of 7g (table IL) *).

1) Zeitschr. f. physik. Chem. 15, 457 (1894).

2) These Proceedings II, Febr. 23 1901 p. 512.

3) This has already been shown by van Laan in a somewhat different way.
(Archives Teijler 8 (1903) ).

( 638 )

We see further that the differences between the third and the
fourth column in this table are about as great as in table IV, so
that it is sufficient to calculate 7g and zp for a first investigation of
the concordance of the results obtained by different methods.

The investigation of NaNO,-solutions yielded the following result.

T 2A 1B as ae
Na NO,.

Concentration | Pa es Pin ‘
‘és es aa H H eer cree =
] or. mol. p. i ls of SS SS SS SS oer
rg nol. p in mm. Hg no m.m g Po 3 0.08316
1000 gr. 11,0 of O°. of O°.
0.0515 0.00718 0.143 i bea
0.0901 0.01257 0.139 1.68
0.3385 0.04578 Oneae 1.626
0.8328 0.11042 6.1326 4 594
2.8168 0.33126 0.1176 1.41%
4.0544 0 46119 0.11375 1.268
7.3151 0 79056 0.10807 1.300

It follows from this table, that the factor ¢ decreases continually
with NaNQO,-solutions.

Also Jones and German have observed the same course in their
determinations of the freezing point, which follows from the following
table.

flee Rial oa Dp Ship
Na NO,,.

Molecular
Concentration. freezing point t
depression

0 05 3440 | 1.85

0.10 3498 | 4 843
0.20 | 3.345 1.798
1.00 | 3.198 1.719
2.00 | 3.074 | 4.65:
3.00 2 969 1.596

( 639 )

3. The minimum in 7 may be brought about by the formation
of hydrates in solution. I showed already before‘), how great the
influence can be, which the formation of hydrates in solution can
exert on the course of the factor 7, specially with regard to not
very dilute solutions.

For very small concentrations, however, the number of water
molecules is so predominant, that the number of molecules withdrawn
from the solution, practically does not bring about any change in
the molecular concentration. Towards higher concentrations the in-
crease of the molecular concentration in consequence of the forma-
tion of hydrates augments continually, and so it may be assumed,
that for a certain concentration it has increased so much, that it has
become equal to the diminution of the molecular concentration in
consequence of the retrogression of the electrolytic dissociation. If this
is the case, 7 has reached its smallest value, and will increase
towards higher concentration, because the influence of the formation
of hydrates prevails more and more over the retrogression of the
electrolytic dissociation.

Besides the above mentioned formation of hydrates, we may gene-
rally assume auto-complex-formation and hydrolysis, so that probably
many electrolytes form a system so intricate, that some time will
probably elapse before the desired insight into it will be acquired.
Referring here to salts of strong bases and acids I could leave hydrolysis
out of account. The auto-complex-formation has not been discussed,
because it brings about a diminution of the molecular concentration,
and was therefore of no use for the explanation of the phenomenon.

4. Finally I will call attention to the very remarkable fact, that
solutions of NaNO,, which qualitatively behave in a very normal
way, do not follow the dilution law of OstwaLp, whereas solutions
of KNO, follow this law according to my measurements, and as the
deviations for NaNO, solutions lie in this direction that A’ increases
with the concentration as is seen in the following table, this points
to an influence as e.g. occurs for NaCl solutions, but in a much
smaller degree *).

1) Archiv. Néerl. (2) 1 (1897).

2) That KNOs,-solutions harmonize better with the theory than NaNO,-solutions
is in accordance with the results of experiments made by ABeaa and BopLanpeR
(Zeitschr. f. anorg. Chem. 20, 453 (1899)), from which could be derived, that the
tendency to complex-formation depends on the degree of the tendency to ionisation,
which latter tendency is indicated by the tendency of dissociation. The greater
the tendency to ionisation the smaller the tendency to complex-formation. According
to Witsmore (Zeitschr. f. physik. Chem. 35, 318 (1900)) the tension of disso-
ciation is for K =3.20 and for Na =2.82, from which would follow, that kalium
salts have a slighter tendency to complex-formation than natrium salts.

{ 640 )

Die Bs ea:
Na NOQ,.

From the determinations of the vapour tension at U°
with Lord RAYLEIGH’s manometer.

Degree of | 2
Concentration. Dissociation | cK —¢ coe
| : | Mi
0.0515 | 0.72 0.09
0.0901 0.68 0.16
0 3585 0.63 0.35
0.8328 0.59 0.72

From the determinations of the boiling point at + 100°.

0.0469

0.83 0.49
0.0852 0.81 0.28
0.4448 0.72 0.76
0.8630 Osa 4.50

TA Bie Ver
KNO,.

From the determinations of the vapour tension at 0° with the
aniline-water-manometer.

Degree of a2
Concentration dissociation K=¢,-—
az

GS 2

0.0400 0.81 | 0.441)
0.4450 0.58 0.42
0).5997 0.39 0.15
0), 9288 0 804 O42

From the determinations of the boiling point at + 100°,

0.4000 0.91 0.$22)
0.4994 0 74 A065
0.7486 0 67 4.02
0.9921 0.651 | 1.21

average 1.05

!) We must not attach too much importance to the absolute value of K, as a
slight error in the sensibility of the manometer appears in K greatly magnified.

2) By this method we cannot make use of more diluted solutions to test the
dilution-law, as the error of the observation has too much influence then. For the
concentration 0.1 gr. mol. per 1000 gr. H3O this influence is already fairly strong.
If e.g. for this concentration we had found a rise of the boiling point of 0.1°
instead. of 0.099°, we should have had z=0.93 and K = 1.98..

( 641 )

It is remarkable that the law of dilution proves to apply here
up to fairly high concentrations. It would therefore be interesting
to carry on the series towards higher concentrations to see where
the deviations begin to appear.

That the freezing point method is inferior to the vapour tension
method and the boiling point method with a view to accuracy
follows also from the fact, that no constant values for K can be
caleulated from the observations of Loomis, Jones and GETMAN, as
appears from the following table.

A Ra Be LX:
KNO,,.

From the determinations of the freezing point.

Dapres of | w2
Concentration. dissociation | K=€ <P
a

0.05 0.83 | 0.21

0.40 0.78 | 0.28 > Loomts !).

0.20 era 0.35

0.40 0.69 | 0.78

0.50 0.65 | 0.61 | JoNES and GETMAN.

1.00 | Oa | 0.44 |

The fact, however, that Brmrz?) obtained concordant results for
solutions of caesium nitrate by means of the freezing point method
justifies the hope, that when the experiments are made very carefully,
also by this method the law of dilution will prove to hold for
KNO,-solutions.

I have agreed with Dr. Binrz that he will examine the behaviour
of chlorates, perchlorates and permanganates with regard to the law
of dilution and I shall investigate the nitrates.

The above salts manifest little tendency. for complex formation and
are therefore the most suitable material for the above mentioned
purpose.

Febr. 1904, Amsterdam.
Chemical Laboratory of the University.

1) Phys. Rey. 3, 279 (1896).
2) loc. cit.

( 642 )

Physics. — *n the measurement of very low fem peratures. VI.
[improvements of the protected thermoelements : a hattery of
standard-thermoelements and its use for thermoelectric deter-
minations of temperature”. By HH. KaMertincH ONNkES and :
C. A. CROMMELIN.

(Communicated in the meeting of November 28, 1903).

§ 1. Lmprovements of the protected thermoelements. Comm, N°. 27
II (June °96) contains a description of the apparatus with which at
that time the thermoelectric determinations of temperature were
made. The measurements for the sake of which these determinations ‘

were made are not yet closed, because they have been repeated with 4

: : : ¥
constantly improved arrangements. In the mean time the thermo- |
electric determination of temperature itself has been improved. The .

experiments of Mr. HoniMann') have offered an opportunity for
remarks about some of these improvements. Yet up to now a com-
plete description of the modifications made since the appearance of
Comm. N°. 27 has been deferred. It is now given in the following
paper.

Zesides the “protected” (comp. Comm. N°. 27) observation-elements
we still use protected comparison- or standard-elements. We have also
retained the construction of both the observation-elements and the
comparison- or standard-elements, so that the two “limbs” (the
junctures with their protecting-tubes) can be immersed into steam,
ice or into some liquefied gas or other to test whether the element
is free of current with equal temperatures of the junctures.

For the observation-element we avail ourselves of a combination of
coustantin and steel to obtain a considerable electromotive force. We
found for it with constantin wire furnished by Harrmann and Braun
46 microvolts per degree (O°C.— + 100°C.) Kirmencic and CzErMak*)
give for constantin-iron 51, Crova*) 63, van AvBeL and Paiior*) 47,
H. Rupexs*) 53, Honpory and Wien*) 56, Keer *) 58, Fucus *) 54.
1) Bakxuvis Roozepoom. Proc. Vol. 5, p. 283, 1902.

Houumann. Zeitschr. f. Phys. Ghem. Bd. 43. 2. p. 129. 1903.

2) Kiementic and Czermax, Wied. Ann. Bd. 50, p. 174. 1893.

3) A. Crova, C. R. 125, p. 804. 1897.

') Van Avper and Pamtot, Arch. d. Sc. phys. et nat. Genéve Per. 3. T.. de.
p. 148. 185.

5) H. Rupens, Zeitschr. f. Instrk. Bd. 18 p. 65. 1898.

6) Hotsorn and Wien, Wied. Ann. Bd. 59, p. 213. 1896.

7) Kueiver, Arch. d. Se. phys. et nat. Geneve. Per. 3, T. 32, p. 280.

s) Fucus, Ueber das thermo-electrische Verhalten einiger Nickel-Kupfer-Legier-

ungen, Graz, LSS.

CC ——

( 645 )

Constantin and steel appeared to satisfy the requirements for thermo-
elements laid down in Comm. N°. 27. We succeeded in tinding
wires of which, after they had been treated as described in Comm.
N°. 27, the potential-differences at a temperature difference of 100° C.
amount to no more than 0.5 microvolt along the whole wire and at
the extremities over a length from 50 to 60 em. no more than
0.05 microvolt *).

In order to be able to test whether the element is free of current
a steel wire has been soldered on to each of the ends of the wire.
The junctures of the two steel wires with the copper leads are kept
at an equal constant temperature viz. 0° C. Each of these protected
junctures constantly kept at 0° C. has its own ice-pot which is mounted
insulated from the others (See fig. 1 Pl. | and compare with this
figs. 1 and 2 of Pl. I Comm. N°. 27).

As to the principal features the arrangement of the limbs like
that of the whole element has remained the same as in Comm. N°. 27.
The constantin wire, which like the German-silver wire might easily
be bent in sharp curves and then show disturbing electromotive forces,
is again protected by a thickwalled indiarubber tube connected
hermetically with the glass protecting-tubes of the limbs. Owing to
its elasticity the steel wire did not require this protection; a layer
of shellac protects it from rust (for a better protection of this layer
it may also be coated with a thinwalled indiarubber tube).

In the limb constantin-steel the constantin-wire (1 mm. thick, 0.25
2 resistance per m.) is enclosed in the inner glass tube (see fig. 2
Pl. | and comp. fig. 4 Pl. HI Comm. N°. 27), the steel wire goes
straight between the inner and the outer tube (see fig. 2 Pl. I and
comp. fig. 4 Pl. Ill of Comm. N°. 27). Owing to the small condue-
tivity it was not necessary to wind the steel wire round the inner
tube (see fig. 4 Pl. II] of Comm. N°. 27). For the limbs which are
always immersed in ice, a firm outer protecting-tube is very desirable
with a view to the circumstance that the ice must repeatedly be
packed together. Each ice-pot is enclosed in a protecting cone-shaped
piece of paste-board soaked in oil of which the lower rim stands in
in the water on its dish, thus forming an air-jacket round the ice-pot
which is closed at the bottom; yet in warm weather it is advisable
to pack the ice every five minutes.

Although to simplify the construction of the elements we have

1) The defects which were avoided in the treatment described in Comm. N°. 27,
have later been detected in thermoelements of the Phys. Techn. Reichsanstalt.
There the treatment considered has also been applied in following cases. (Cf.
Zeitschr. f. Instrk. Bd. 19. p. 249, 1899).

( 644 )

used tubes with two openings (see fig. 6 Pl. I) through which the
two wires of the element are drawn, yet in many of these tubes
tensions appeared, which proved an impediment to their being
operated upon.

Formerly it was very difficult to make a connection between the
copperblock (for the meaning of this ef. Comm. N’.27) and the protecting-
tube, which connection should not only be airtight, but which also
must allow of being placed into steam and at low temperatures into
different kinds of liquids. This difficulty has been entirely overcome.
In N°. 27 we have spoken of our intention to try, following the method
‘of Caitieter, and solder the copper block on to glass which to this
end had been platinized. In this we succeeded to perfection. The
glass tube is platinized at the end with platinum-chloride in the blow-
pipe while care must be taken that if remains perfectly cylindrical,
then it is coppered galvanically and tinned over an alcohol flame.
Then the thin upright rim turned on to the block, which is also
tinned and carefully cleaned, is pushed round the end after which
they are soldered together by means of resin asa flux. Then the -
cap, the juncture seam and the tinned glass together are galva-
nically platinized and gilt. In this manner an important improvement
has been obtained. The indiarubber protecting-ring which made the
limb much thicker is removed, the fit is perfectly tight and permanent,
the limb may be fastened into almost any apparatus and be immersed
into any liquid without the least fear of action on the wires or of
shunt-circuits anywhere between the two wires.

Platinizing and gilding are not always necessary. The thermo-
element used in the experiments of HoLuMann I|.c. was only tinned,
as acetaldehyd does not attack tin. If for one reason or other we
do not wish to bring the protected thermoelements into direct contact
with a liquid with strong chemical action in which it is immersed,
they are enclosed in a separate protecting-tube (see figs. 3 and 4,
Pl. I) terminating in a thinwalled copper cap soldered on to it in
the way as described above, into which the block of the thermo-
element fits exactly, and which cap is covered galvanically with a
suitable metal. This auxiliary means was for instance used here
in determinations of melting-points of mixtures of chloride and
sulphur by Mr. Arr. Between the limb of the thermoelement and
the protecting-tube provided with a platinized and gilt cap, a little
pentane was poured to fill up the space.

In addition to the description of Comm. N°. 27 we remark that
the airtight connection of the outer glass protecting-tubes with the
indiarubber protecting-tube has been made by means of indiarubber

(645 )

foil and indiarubber solution in one of the ways represented in
figs. 2, 3 and 5.

For the filling of the tubes we can recommend in general dry
hydrogen.

§ 2. Battery of standard-thermoelements. At the end of Comm, N°. 27
it was remarked that the comparison-thermoelement itself with
junctures placed in ice and steam, the electromotive force of the obser-
vation-element being expressed in terms of that of the comparison-
thermoelement, could be used as a standard. One of the junctures
is easily kept at 0° C. when the precautions are taken described in
Comm. N°. 27 and in this paper §1. As to the other which is placed
in steam we must make sure that in the boiling-apparatus described
in Comm. N°. 27 the water vapour flows out at a steady rate and we
must apply the small correction for the variation of the boiling-point
with the barometric height in order to easily reduce the electromotive
force to that which would be obtained if this juncture were kept
precisely at 100° C. If the metals do not undergo a secular variation,
we always have at our disposal a constant electromotive force
(although it cannot be reproduced with certainty independent of the
special apparatus) which is very appropriate for the calibration of
sensitive galvanometers in general, and has moreover the advantage
in thermoelectric determinations of temperature that it belongs to the
same size as the electromotive force to be measured.

It seems “that this idea has later been developed by the Phys.
Techn. Reichsanstalt ’).

At the time of Comm. N°. 27 (June °96) the comparison thermo-
element was compared at intervals with a standard-element (then
Ciark’s). On the whole it satisfied the requirements better than the
Crark-cell, which had to be replaced repeatedly, while owing to the
improvements of the protection of thermoelements we had obtained
comparison-thermoelements which could serve unaltered for indefinite
time. The favourable experiences made with the German-silver-
copper-element in Comm. N°. 27 led us to replace the single comparison-
or standard-thermoelement by a battery of 3 standard-thermoelements
each with its own boiling-apparatus and its own ice-pot, which are
mounted insulated. Two of those elements ?, and /?, are made of con-
stantin-steel, the third Q, is the afore-mentioned German silver-copper-
element with a3 times smaller electromotive force than that of ?, or P,.

1) Vgl. Zeitschr. f. Instrk. Bd. 17, p. 174, 1897.

Idem Bd. 18, p. 183, 1898.
Idem Bd. 22, p. 149, 1902.
Idem Bd. 23, p. 174, 1903.

( 646 )

By means of an elements-switch of which the arrangement may be
seen without further description from Pl. I fig. 7 and PI. II, we
can switch the single elements or combinations of them in series or
in opposition and obtain electromotive forces in the ratios of
1, 2, 3, 4, 5, 6, 7 which by the central commutator of the elements-
switch are connected to the galvanometer wires (@ in a positive or
negative sense. The elements-switch has been made of galvanoplastic
copper (mounted on ebonite) and packed in a case with cottonwool
so that there electromotive forces are excluded.

The electromotive forces mentioned cover at intervals of about
30 degs more than the whole range of temperatures below 0° C.
Therefore in the measurement of a temperature we can each time
use a very near combination of standard-thermoelements for comparison.

§ 3. Determinations of the electromotive forces of the observation-
element. In Comm. N°. 27 the observation- and the comparison-
element were compared by means of the deflections which they
produced successively on the same galvanometer. This deflection-
method must always be applied whenever the determinations must
he made quickly. For these determinations of the deflection the
string-galvanometer of ErtHoven') which owing to its sensibility
and independence of magnetic disturbances would for the rest be
probably also very suitable for thermoelectric determinations, would
have the advantage above other galvanometers that the indications
are instantaneous. An opportunity to test this instrument has not
yet presented itself.

In determinations, however, where we especially want to observe
fluctuations of the electromotive force about an almost constant value
a compensation-method offers large advantages. Jn order to avail
ourselves of the advantages offered by the circumstance that the
electromotive forces to be compared are approximately equal, the
switching in opposition of the observation- and the comparison-
element was rendered possible in Comm. N°. 27, where the battery
of the standard-elements of the nearest electromotive force would
then be used. To the arrangement of Comm. N°. 27 for measure-
ments of deflections an arrangement has been added which allows
of a determination of the electromotive force of the observation-
element at perfect compensation by means of a zero-method. Thus
the comparison of the standard-element with the Criark-cell of the
arrangements of Comm. N°. 27 by means of the deflection-method
is left out. In this case the element must give a very small but

1) Proc. 1903—1904 p. 107.

( 647)

perceptible current while its resistance, owing to the variations
which it undergoes, must always be determined separately. The
connections which instead of this are added to that of Comm. N°. 27
are in principle the potentiometer-arrangement and have been drawn
diagrammatically in the annexed figure *).

3 eT Weston batt

UU |

A | |B | Mest

NG, es ve.

ae ( fs)

Soi 1 a te
— UNAISINA I Ass nn WAV yp a
/ a, A; i NK
| ace |
ES a were ————_______._.._

In the circuit of an accumulator (with a negligible resistance)
three resistance-boxes R,, R,, R-. and a fixed resistance FP’ are
introduced, of which the first serves to regulate the resistance in
the whole cireuit, the second and third serve as shunts for two.
circuits A and B in which the observation-element and the battery
of comparison-elements are inserted, while the third, a resistance
of 8000 2 tested at the Phys. Techn. Reichsanstalt serves as a
shunt for the circuit C, in which is inserted a battery of Weston-
elements. These side circuits may be connected to the galvanometer,
each by means of its own commutator with mercury contacts (as
described in Comm. N°. 27 see pl. V) and be commutated in order to
read in how far we have attained the desired zero-adjustment by
regulation of the different resistances and to. apply a correction for
the deflection which might have remained.

The principal resistance-boxes are adjusted by means of plugs like
the auxiliary boxes arranged in parallel for the finer adjustment.
This is preferable to an adjustment with a slide-wire where also
small differences remain’). As the F,, 2, and &, are known approxi-
mately beforehand, (with an adjustment at — 116°C. about 7290 2,
40 2 and 40 2 respectively) the current given by the Weston-
elements will always be very small. In order to make it still less

1) Cf. for instance JAzcer, Die Normaleleménte, p. 100.
Dewar and Femina, Phil. Mag. (5), 40, 95. 1895.
*) Cf. Lesretpt, Phil. Mag. Ser. 6 Vol. 5. p. 668. 1903.
45
Proceedings Royal Acad. Amsterdam. Vol. VI.

( 648 )

disadvantageous five of those elements, in order to obtain an
equal distribution of the current each with a series-resistance of
5000 2, are connected parallel to each other. Finally, when the
adjustment is obtained, the battery which has served in the regulation
is replaced by altering a plug in the commutator, by a battery
arranged in the same way, which serves for the measurements.

The peculiarity of this arrangement is that we can make imme-
diately after each other all the readings required for the measurements
by handling the commutator-boards (comp. successively Pl. V Comm.
N°. 27) and without making other contacts than those of mercury ; this
would be impossible without the commutators and the current-rever-
sers with mercury-contacts. This again reveals the great advantages
which these apparatus offer for similar measurements. It seems,
however, that little attention has been paid to them.

The whole arrangement with 6 current-reversers 1, 2, 3, 4, 5, 6
and 4 commutators A, B, C, D for both deflection- and zero-method
as it has become now may be easily seen on Pl. Il. The current-
reversers and commutators with mercury-contacts have been indicated
by three and four parallel lines respectively.

1 serves to connect one of the two galvanometers, that of Harr-
MANN and Braun, described in Comm. N°. 27 or a magnetically
protected galvanometer of Du Bors and Rusens.

2 and 4 to switch the galvanometer on to one of the three
branches A, B, C,

3 to switch the battery of comparison-elements on to the branch
A or on to B,

5 to introduce the observation-element and the comparison-battery
separately or in series or in opposition (cf. 3),

6 to introduce either the observation-element or the comparison-
elements.

A, B and C make and reverse the connection of the three circuits
with the galvanometer, JD reverses the accumulator. The commutators
and the current-reversers, like the Werston-battery have been packed
in cottonwool, placed together in large cases. Only the tubes where
the contact of the mereury is made by handling the commutator-
board (see Pl. V Comm. N°. 27) project beyond it.

( 649 )

Physics. — “Contributions to the knowledge of vax pur Waats’
w-surface. VUI. The w-surface in the neighbourhood of a
binary mixture which behaves as a pure substance.” By Dr. J. B.
VERSCHAFFELT. Supplement n°. 7 to the Communications from

the Physical Laboratory at Leiden by Prof. H. Kamerninen

ONNES.

(Communicated in the meeting of October 31, 1903).

General part.

Distillation of a mixture without its composition being altered,
and reversely also condensation of a mixture by decrease of volume,
without variation of pressure, quite as a pure substance, can only
occur at one special temperature. Experiments of KugNEN') have
shown for the first time that this phenomenon may be observed in
the neighbourhood of the plaitpoint of the mixture; this circumstance
has been theoretically investigated and explained by van DER WaatLs?).

If a mixture behaves as a pure substance just at the plaitpoint
temperature the critical point of the homogeneous mixture, the critical
point of contact and the plaitpoint coincide at a same point which
may therefore properly be called the critical point of the special
mixture and of which I shall represent the elements, as for a simple
substance, by 7%, pz and vy.

Then according to VAN DER Waais*) we have at the plaitpoint
(=), = 0. Hence the isothermals of two neighbouring mixtures
at the same temperature must intersect in pairs, so that the system
of isothermals of the mixtures at the critical temperature of the
special mixture must agree with fig. 16 of my paper in these Proce.
Oct. 25 1902 p. 345. In the annexed figure a similar system of
isothermals is drawn according to observations of Quin? ‘) with
mixtures of hydrochloric acid and ethane.

Although the special mixture behaves as a simple substance at the
critical point, yet it does not follow from this that its border curve
on the p, v, ¢ diagram may be found in the same way as for a
simple substance, i. e. by making use of the theorem of Maxwet.-
Ciavusius. For just below the critical temperature the pressure no
longer remains unchanged during the condensation and the expe-
rimental isothermal is no longer perfectly parallel with the v-axis,

1) Phil. Mag., 40, 173—194, 1895. Comm. phys. lab. Leiden, n°. 16.

2) Arch. Neéerl., 30, 266, 1896.

3) Contin. II p. 116.
4) Thesis for the doctorate, Amsterdam 1900.

( 650 )

though the variation of pressure is vanishingly small. Consequently
the system of isothermals satisfies the law of corresponding states,
but the border curve does not necessarily do so. Hence we shall
see that for the border curve this is only the case to a first and
a second approximation.

The w-surface. 1 shall represent by a, the composition of the
mixture which behaves as a simple substance. In the neighbourhood
of the critical point the system of isothermals of this mixture may be
represented by the equations (2) and (2’) of my paper in these proc.
Oct. 25 1902 p. 321; for the rest all the considerations of sections 2 and
3 of the same paper are directly applicable, except that z—a, must
everywhere be substituted for «7, and hence also 274.—k for x7. Thus
we find back, for the system of isothermals of the mixtures at a
temperature which differs little from 77, the equations (18) and (18’),
where x—azvy, is vanishingly small, but not z and «7, separately ;

f)
from the circumstance that at the critical point @ = 0, it also
Uv

Ov
follows that m,, = 0; and because m,, = px@—k,, 7,4 we must have:
3 my 0
ee Sa Ss << Sea
a Pk: Or k

Finally we may remark that whereas in fig. 16 (1. c.) the dotted line
which, agreeing with «<0, had no physical meaning, this line can
really exist here, since «<2, may as well be imagined as x > ax.

The equation of the y-surface may now be written in this case:

1 1
w= — m, (v—v7k) — an (v—v7,.)?— a Ms (v—vTr)* — z m® (v—v7z)*. -
: 1 “z—xzyz)* 2ap—--1 (x—az)’
1.2 a,?(1—az)? 2.3 «,°(1—axz)*

day —daz.+1 («—az;z)'
T 3.4 ai(1— a)! arc | (2)
where again a linear function of z is omitted, while m,, = pre, and
further m,,, m,, and m,, may be put equal to zero.

The border curve at a temperature T. In the same way as before ')
I find, putting
$(%,+%)—°m =P , 3(%,—-r71)=9
b(e,+2,)—omn = , $(,—#)=&
v, v, 2, @, representing the molecular volumes and the molecular
compositions of the coexisting phases, that

1) These Proc. V, Oct. 25 1902, p. 330.

2 mi, = 3
gas . (3)
30
: 1 oer ft 2
1 my, 2M, Ms o- gi Ma sy aes 3 ar" 30— ph ipwe
pf —-— ==. 4 Si! em (4
Ms sp 2kTm,, (4)
"ep (1-ax)
¥ 1 m,,m,, 2 i"; M:,
= ‘02 aie Al eases = ae
eed ie 3 Ms, a me, . 6)
ran See BT Ge a
m, Na
xy. (1-2xz)
1 m,,m,, 1 em yee :
Pe Pte en a - + —m2,,—— ] +). - - (6)
Meso 0 m 30

The relations (2) and (5) are the same as I have found before *)
for the special case m,, = 90, on the edge of the w-surface, while
the expression for ® becomes the same when we put 2, =O or
z= 1. 1 also find again for the border curve on the p,v diagram
of the mixtures at the temperature 7’ to the first approximation the
same parabola of the fourth degree: }

2 2 4
aise m7. im ms, Sm", %,, nes *
Pie = = (ois +. =a v—vUTE}-- (4)
ied, o> WM, a Ns

The plaitpoint, i.e. the apex of this parabola, coincides to the
first approximation with the point prz, VTL, v7Tk- According as the
factor between brackets is positive or negative this parabola is turned
upwards or downwards; in the first case the special mixture has a
minimum vapour tension, in the second a maximum vapour tension.

The isobars. If in equation (18) l.c. p. 327 we consider 2 and v
as two variable quantities depending on each other and p as a
parameter, this equation represents the projection of the system
of isobars on the wz, v-surface. If m,, were not zero this system
would resemble a system of isothermals with the point 77%, U7Tz

1) Of all the coefficients m which occur here I have formerly given the expres-
sions in the k’s and 2 and 6, except of mg, for which the expression follows here:
m,,— 8 pk + ky, @ (a—8) Ti + &, @” T;? + k,, a (a—8) v% Tr—k,, a Ty

or reduced:

1
——e [3 + a (a—p) Por == 2 a’ Pos == a (a—p) ae Pail:

2) These Proc. V, Oct. 25, 1902, p. 329.

( 652 )

as critical point’). Here it consists, in the neighbourhood of that

same point, in a double system of curves of hyperbolical shape,

as may be seen in the annexed figure, separated by two curves,
of which the equation is obtained by putting p—=pz,. To the first
approximation the system of isobars is represented by the equation

m,,(t—xTk)? + m,, (t—xTE) (v—vTKE) = p—pre, - - (8)

which represents hyperbolae, of which the one asymptote is:

mM,4

L—LT, —= — —(v—vTe) - . .. .
” 02
while the second, z—a7, — 0, may be written to the second (9)
approximation |
Ms 4
£—2£T;, = — — (v—v7z)* -
M4 J

_ The connodal line. In order to find the projection of the connodal
line on the «z, v-surface we eliminate p—pz7; between the equation
of the isobar and that of the border curve; we then find to the
first approximation

Mg «

(e«—z7,.) = — (UOTE) 6 ein oe

mM,

The critical point of contact, the apex of this hyperbola, coin-
cides, like the plaitpoint, to the first approximation with the point
UTk: UTk> PTk-

The border curve for a mixture x. If in the equation (8) we con-

sider « as constant and 7, hence x7, and v7; as variable, and if

finally we make use of the equation of state of the mixture
(equation (13) le. p. 825) to express 7’ in p and v, we obtain the
‘

1) The systems of isobars may then be written in the form:
z—=n, — n, (v—vz7z) + 2, (v—v7z)? +....
where the 7’s are stil] fictions of p, for instance:
t= Mog Noy (P—pTk) 5 Nos (p—prk)’ = ote piace
If the v's are expresscd in the m’s, we find:

meee Ag 1 ees } ads. Moo 0 as 51
Noo — Tk; tot — — . Noo ———— > ; 4 Nig — VU, Ns = “ei:
Mo m 01 m 01
2
, s Mos slg 4 M5 As 0 —_ m ll Mey
ty, — ne —— Si ; 5 Noo = 5 Ney = = = ; 9° ls. =e ee
01 M1 m 01 m 01
m m m
> F 30 11 30 40
RG I EE orc FW Tica , etc.
Yon m 01 Mo,

( 653 )

border curve of the mixture # in the p, v, 7’ diagram. To the first
approximation its equation is:

k 1 Ko (

Z eWeek ee 2 “EER

P—Pxk = —
11

as for a simple substance’). Hence to the first approximation the
border curve satisfies the law of cor responding states.

That the border curve, apart from the deviations existing already
in pure substances does not altogether satisfy the law of correspon-
ding states, has a double cause. It is not only for mixtures which
differ little from the special mixture 2, that the experimental isother-
mal shows a slight slope, but this is even the case for the mixture
a, itself; only at the plaitpoint temperature it is perfectly horizontal
so that already for the mixture wz the border curve must deviate
from the law of corresponding states. If as before!) we develop the
equation of the experimental isothermal :

Ee ie ho
we find:
1 m,,m,, k in" ,, m7, :
ie —— | ee 3 ——+-— ; (a x TI.) a
Ms, i) are,
Ems ae Ln m,.\"
neat pees MeL
, 3 M,, Diss Waa 2
—8m “Fi (v—v7p) (c—2«7Trx) + . (12)

gen ole’ Mm.
m*,, + —
Se ieee er)

and hence, for «= xz,

2 2
Lan m;; ae 1 a Pe
Mya Ye 2

ah
30 (v-v;,)

(L-T;)’

ar,

p=prth,, (te T;)—-8m’,,

+ (13
2 RT m,, Bo Are

ees

only for z,—=O or 1, that is to say for the pure su tances, the
third term is left out — and in the same way all the crms which
contain v—vk.

If now by elmination of 7—7;, between the eq: ation of state
of the mixture z;, (equation (2), l.c. p. 325) and the experimental
isothermal (10), we search for the border curve for that special
mixture, we see that the slope of the experimental isothermal only
influences the third term — viz. with (v—v;)* — in the development
(11) of the border curve, so that this border curve only to a third
approximation shows a deviation from the law of corresponding

1) These Proc. V, Oct. 25, 1902, p. 336.

( 654 )

states. Also for a neighbouring mixture this deviation is only percep-
tible in third approximation, while for mixtures with a small com-
position, i.e. on the edge of the y-surface, it exists already in second
approximation.

The cause of this smaller deviation in mixtures near the special
mixture must be looked for in the circumstance that those mixtures
in all their qualities deviate only in second approximation from a
single substance; thus we deduce from equation (11) that the critical
points: plaitpoint, critical point of contact, critical point of the homo-
geneous mixture and point of maximum coexistence pressure, differ
only in second approximation, so that the four curves (in the space
with p, v and 7’ as coordinates), which connect these critical points
of all mixtures touch each other at the critical point of the special
mixture, which in general is not the case at the two critical points
of the pure components.

Application to mixtures of hydrochloric acid and ethane.

The experiments of KuENEN with mixtures of ethane and nitrous
oxide, the first where the existence was shown of a mixture that
in its critical phenomena agrees with a simple substance, does not
allow us to form a complete image of the conduct of neighbouring
mixtures. Besides, his investigations were only aimed at the discovery
of the second kind of retrograde condensation, and the existence of
that special mixture was a new discovery, and not the object of the
investigation. Suitable data for our purpose are given by the measure-
ments of Quint on mixtures of hydrochloric acid and ethane; accord-
ing to Qurr the composition of the mixture which behaves as a
simple substance is «7, = 0.44, 1.e. 0.44 gram molecules ethane and
0.56 gram molecules hydrogen chloride. Mixtures behaving as a
pure substance have also been observed bij Causper*) in his experi-
ments with CH,Cl and SO,; as Cavsnr however investigated only
two mixtures of this binary system, his data are insufficient for
our purpose.

In order to proceed with the mixtures investigated by Quint in
the way indicated by KamErRLINGH ONNES, we must determine in the
first place the critical elements of the homogeneous mixture 7, por, Vok-

pv é
7 log p diagrams
it was sufficient, as in the case of my former investigations?) of the

Instead, however of drawing, the /og pv, logv or

1) Liquéfaction des mélanges gazeux, Paris, 1900.
2) Arch. Néerl., (2), 5, 644, 1900.

fe
abe ‘

( 655.)

mixtures of carbon dioxide and hydrogen to use the log p, log v
diagrams, as | found that not only the logarithmical diagrams of
the pure substances but also those of the four mixtures investigated
could be made to coincide with the iogarithmical diagram of carbon
dioxide by shifting them parallel to each other.

Unfortunately Quint made only few observations in the neigh-
bourhood of the critical point, a circumstance which rendered this
investigation rather difficult. For it is by means of those very parts
situated in the neighbourhood of the point of inflection that the
superimposing of the diagrams may be obtained in the most accurate
way, While in the area of the larger volumes a shifting within rather
wide limits does not cause a perceptible deviation of the superim-
posed diagrams.
bourhood of the critical point in the case of hydrochloric acid is to
be regretted because the difference between the critical point given
by Quint and that found by shifting is much larger than we should
expect, the diagrams covering each other in a satisfactory way. The
more so because, when for ethane and carbon dioxide the diagrams
are made covering each other in the observed area the critical points
too coincide.

Here follow the values found, for the different mixtures, as ele-
ments of the critical point of the homogeneous mixture:

Especially the want of observations in the neigh-

= = (pure HCl) 0 1318 0 4035 0 ,6167 0,714. (4 pure C,H,)
—— 42°.5 30°,0 26°,4 os

pek = 7} Svat. 05'.5 58 6 or ak

Urk = 0 00429 =0 00190 =§=0 00543 ~—— 0 —,00570

tpi== ss 51°33 43° 1 309,53 *27°,25 27°,37 319,88
pri 84,13 atm. 77 ,51 65 42 54 30 56 84 48 ,94
Drpl = 0 ,00380 0 00420 =O. 00471 0 00540 =—5_ 00576 0 00652
C.- 3 48 3 46 3 45 0 45 3,50

In order to make a comparison I have written in this table the
plaitpoint elements of the mixtures as observed by Quint, and in

RT) ee
which here
Prk Vrk

are about the same for all the mixtures, especially in the neigh-
bourhood of the special mixture. By means of Quinv’s data we find
however, for HCl, the much larger number C, = 3,71; this deviation
evidently must be brought in connection with the other one I mentioned
before.

the last line the values of the expression C’,—=

( 656 )

If we draw the ¢,, and ¢,,; as ordinates and 2 as abscis we obtain
two curves which obviously touch each other at one point; it is
difficult, however, to define this point of contact precisely. If the
same is done with p,¢ and py), the determination of the point of
contact of the two curves is even less certain, owing to the cireum-
stance that, according to the table above, for z = 0,4035 = piz > papi,
which surely follows from the inaccuracy of the method. And the
deduction of this point of contact from a graphical representation
of the 7, and v,,; is quite impossible because these volumes are
known by no means with sufficient accuracy.

Therefore it seems to me that the best method is that of Quint
who deduced the composition of the special mixture from the shape
of the plaitpoint curve by searching on this curve the point where
the bordercurve, which terminates at that point, touches the plaitpoint
curve. That point may be determined fairly accurately: we find
for its coordinates 7; —= 29°,0 and vo; = 63,8 atms., whence again
x, — 0,44 and vz = 0,00500.

By means of the graphical representations of the fx, Pre and Ox,

aL 1p »1-
I find in the neighbourhood of x; = 0,44, si 20, ih a
dx dx
Ivy, 5
and Baro 0,0020; hence «a = — 0,07 8B = + 0,50 and y=0,40, so
at

that the relations y= a—fin—- 7,3 are confirmed: in a satisfac-
a

tory way.

By means of Quint’s observations, by inter- or extrapolation, partly
also by using the law of corresponding states and the values of
teks Dek» Urk found above, I have drawn the isothermals for the 6
z-values considered, at the critical temperature 29°.0 C. of the special
mixture « — 0.44. Those isothermals are represented in the annexed
figure, which thus shows the p-v-diagram of the mixtures at the
temperature 29°.0 C. The dot-dash line is the critical «= 0.44 with
the critical point in C. The isothermal «= 0.40 is a dash line in
the unstable part; owing to their small curvature the experimental
isothermals are represented by straight lines. The border curve is
a complete line like the observable parts of the isothermals.

Under the p,v-diagram I have represented the projection on the
p, e-surface. The critical isobar (63.8 atms.) is represented by a dot-
dash line; some other isobars are drawn, like the projection of the
connodal line (also projection of the afore-mentioned border curve),
while the isobars in the unstable part, i.e. within the projection, are
dotted. The temperature 29° being lower than the critical temperature

of pure ethane (31°.88), the connodal line consists of another part,
which I have not drawn, however, in order not to make the figure
uselessly intricate. This second piece should have its apex, the critical
point of contact, at about v7, —= 0.92, and v7, = 0063, and would
intersect the axis r=1 at v= 0.00472 and v = 0.01081.

To this second piece of the connodal a second border curve cor-
responds which would begin at a height p = 46.1 (maximum tension
of ethane at 29°.0 C.) and terminate at the plaitpoint p7,; = 51.2,
vtpi = 9.0063. But this border curve too I have omitted like the
isothermal of pure ethane.

At the lower part of the figure it may be seen that the isobars
in the neighbourhood of the critical point C, indeed to the first
approximation, are hyperbolae of which one of the asymptotes, which
agree with the critical pressure, is parallel to the v-axis, the other
cuts this axis at a given angle. To the second approximation the
first asymptote is a parabola which coincides with the projection of
the connodal line.

It were useless to investigate whether indeed the border curve is
of the fourth degree and the connodol of the second degree; for this
the data are not numerous enough and the drawing not sufficiently
accurate. But it is obvious why the border curve should be of a
higher order than the connodal. The p, v, z-surface, of which the
projections on the surfaces p,v and 2,v are shown in the fig., is in
the neighbourhood of the critical point a saddle-shaped surface, which
at the upper part of the figure is seen parallel to the tangent surface
at the point C. The isothermals of the mixtures «= 0, «— 014
and «= 0.40 are situated on the slope turned towards us; the latter
over a fairly extensive range (of large volumes to about 2 = 0.006)
forms nearly the border of the surface; the critical isothermal lies
just beyond that border, but becomes visible at Cand remains visible
for small volumes. The isothermals «= 0.62, 7=0.71 and x=1
occur on the back of the p, v, z-surface, yet for small volumes they
become visible. The parabola:

2 2 — re

which envelops the isothermals in the neighbourhood of the point C
(l.c. p. 344 and fig. 16) is the apparent outline of the surface in
that neighbourhood.

The lower part of the figure represent the surface seen from above;
the isobars are there level-curves. The critical isobar forms a loop
which agrees with the described shape of the surface. A section of
a horizontal surface situated a little higher consists of two pieces,

( 658 )

of which one, lying within the loop is closed. Within the loop
therefore, the surface shows an elevation of which the top almost
agrees with «= 040, v= 0.06, p= 63.9. For higher horizontal
surfaces the section consists of one branch only. For horizontal
surfaces corresponding to p < 63.8 atm.. the sections also consist in
one branch which surrounds the critical loop.

From «=O the bordercurve occurs on the front of the p, v, a-
surface, but reaches the border almost at the volume 0.008, then
occurs on the back where it remains until the point C, and returns
to the front. At the point C’ the osculation plane to the border
curve, at the same time the tangent plane to the surface, is horizontal;
the projection on the «,v-plane shows the border curve more and
more in its true shape the more we approach the point C; whereas
in the upper projection that border curve is seen more and more in
an oblique direction and finally in a tangent one, so that it must
appear flattened, which accounts for the higher order of the border
curve in that projection.

(March 23, 1904).

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,

PROCEEDINGS OF THE MEETING

of Saturday March 19, 1904.

_—— SOG

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 19 Maart 1904, Dl. XII).

= = a

CON PEN P's.

A. F. Hotieman: “The nitration of Benzene Fluoride”, p. 659.

Jax Rurren: “Description of an apparatus for regulating the pressure when distilling under
reduced pressure.” (Communicated by Prof. S. HooGrwerrr), p. 665.

H. Kaweruincu Onnes: “Methods and apparatus in the cryogenic laboratory. VI. The methyl-
chloride circulation”, p. 668. (With 2 plates).

H. Kameriiscu Oyyes and H. Harrer: “The representation of the continuity of the liquid
and gaseous conditions on the one hand and the various solid aggregations on the other by
the entropy-volume-energy surface of Gipss”, p. 678. (With 4 plates).

P. vay Romevren: “On Ocimene.” (Communicated by Prof. C. A. Lopry pe Bruyy), p. 700.

P. van Rompveren: “Additive compounds of s. trinitrobenzene.” (Communicated by Prof.
C. A. Lopry bE Bruyn), p. 702.

E. Verscnarrett: “Determination of the action of poisons on plants.” (Communicated by
Prof. C. A. Lospry pe Brryn and Prof. HvGo pr Vrirs), p. 703.

W. Emstioven: “On some applications of the string-galvanometer”, p. 707.

A. F. Hotieman: “Action of hydrogen peroxyde on diketones 1,2 and on z-ketonic acids”, p. 715

L. E. J. Brovwer: “On a decomposition of a continuous motion about a fixed point O of S;
into two continuous motions about O of S,’s.’? (Communicated by Prot. D.J. Korrewee), p. 716

C. A. Losry pe Bruyn and L. K. Worrr: “Can the presence of the molecules in solutions
be proved by application of the optical method of TynpaLi?’ p. 735.

J. J. Buayxsma: “On the substitution of the core of Benzeng.” (Communicated by Prof
C. A. Lopry pe Bruyn and A. F. HoLtremay), p. 735.

The following papers were read:

Chemistry. — “Vhe Nitration of Benzene Fluoride.” By Prof.
A. F. HoLieman.

(Communicated in the meeting of February 27, 1904).

Dr. Brekman who made some communications in his dissertation
as to the above nitration came, although his experiments remained
unfinished, to the conclusion that in this case the isomeric mono-
nitrocompounds are formed in quite a different proportion as in the
nitration of the other halogen benzenes. As it appeared fo me very

Proceedings Royal Acad. Amsterdam. Vol. VI.

( 660 )

important to further confirm this statement and as Dr. BEEKMAN could
not undertake this himself, I have studied this subject once more
and now communicate the results obtained.

The difficulty which presented itself was that we were unable to
obtain benzene orthonitrofluoride so that it was impossible to apply
the methods which, in the case of the products of nitration of the
other halogen benzenes, lead to the knowledge of the proportion in
which the isomers are formed. Two observations by Dr. BEEKMAN
furnished us, however, with a key to find the said proportion. These
were: 1. the very ready transformation of benzene p-nitrofluoride
with sodium methoxide into the corresponding anisol; 2. the further
nitration of the benzene orthonitrofluoride present in the nitrating
mixture to benzene dinitrofluoride (Fl: NO, : NO, =1:2:4) which
compound has been obtained by Dr. BEEKMAN in a pure condition.

I convinced myself in the first place of the quantitative course of
the transformation of benzene p-nitrofluoride with NaOCH,.

1.8347 grams of p-NO, C, Hy. Fl = 13.01 millimols. were dissolved in a very
little pure methy!] alcohol, an equivalent quantity of sodium metoxide dis-
solved in methyl alcohol to the concentration of 0.75 normal was added
and the mixture was heated in a reflux apparatus for fully one hour in
the boiling waterbath. The liquid still possessed a faint alkaline reaction
but became neutral on our adding a trace of dilute acetic acid. On pouring it
into water a very beautiful white mass was precipitated which was drained
and then air-dried. Without being recrystallised it exhibited a melting
point of 52—53°, showing it to be pure p-nitranisol.

On the other hand in this dilution benzene metanitrofluoride is
but very little affected by treatment with sodium methoxide for one
hour in the boiling waterbath :

1.0842 grams m-NO, C, H,Fl=7.7 millimols. were mixed with 10c.c. of
Njj.09, NaOCH, this being the equivalent quantity, After being diluted with
water, the liquid was titrated back with 7.50 cc, of acid, theory requiring
7.7cc. Only 0.2 millimols of the compound had therefore, been decomposed,
or 2.6°/) of the total amount,

This renders it possible to quantitatively determine the amount of
benzene p- and m-nitrofluoride in a mixture of the two compounds
as shown by the following experiments :

a. 1.1040 grams = 7.83 millimols. of a mixture of 89°/, of the para and
11°/, of the meta compound were mixed with 10.1 cc. of 7/).09; sodium
methoxide and heated in a reflux apparatus for one hour in the boiling water-
bath, After being poured into water the liquid was titrated back with 0,8 cc,

( 661 )

of m acid corresponding with 0.82 millimols of meta if we apply the correc-
tion of 2.69, for the meta compound attacked. 0.82 millimols = 10.5°/,
of the meta compound.

b. 1.1250 grams = 7.98 millimols. of the said mixture were treated in
an analogouS manner with the equivalent quantity (16.9 cc.) of m/9.:
sodium methoxide. The liquid was then titrated back with 0.85 cc. of 7 acid,
corresponding, after applying the correction, with 0.87 millimols. of the meta
compound, or 10.9°/,. Taking the mean of these two experiments we find
10.7 °/, of the meta-compound.

Dr. Berkman had observed that benzene dinitrofluoride (Fl: NO, :
NO, = 1:2:4) is converted at 15° in a few minutes into the corre-
sponding anisol by the action of sodium methoxide. This e¢ircum-
stance might be taken advantage of for the quantitative determ'nation
of this dinitro compound in the presence of benzene p-nitrofluoride
if the latter should suffer no change. This was, indeed, the case:

1.0035 grams of the para compound were treated at 15° for 5 minutes
with 9.53 cc. of /).9, = 5 cc. n sodium methoxide. After being poured into
water the liquid was titrated back with 5 ce. of n acid.

A mixture of the two gave the following result:

1.1680 grams of a mixture containing 10.9°/, of the dinitro compound were
digested at 15° for 5 minutes with 17.6 c.c. of m/24. Na OCHs. The liquid
was then titrated back with 7.6 cc. of m acid; there was, therefore, present

17.6
a quantity of dinitro compound of mo — 7.6 = 0.7 millimols , or 0.1302 gram

corresponding with 11.1 °/, of the dinitro compound.

The above observations rendered it possible to quantitatively deter-
mine any benzene di- or metanitrofluoride eventually present in a
nitration product of benzene fluoride. In order to determine the
benzene orthonitrofluoride contained therein, | converted this into the
dinitrocompound by renewed treatment of the nitration product with
concentrated nitric acid. Dr. Berkman had found that a further nitra-
tion took place (as shown by the increased sp. gr.) when the said
product was treated for half an hour at O° with five times its weight
of nitric acid of 1.52 sp. gr., but that even after this treatment,
traces of benzene orthonitrofluoride may still be detected by boiling
the compound with aqueous sodium hydroxide which yields o-nitro-
phenol. On the other hand Dr. Berkman showed that pure benzene
p- and m-nitrofiuoride are quite unaffected by this renewed treatment.
In order to get a further and complete nitration of the ortho
compound, | prolonged the time of the renewed treatment with
nitric acid to one hour after first ascertaining whether benzene

44*

( 662 )

p-nitrofluoride is unaffected thereby. This did not seem to be quite
the case, so a small correction has to be applied:

a. 2.95 grams of pure p-NO;.C,.Hy.Fl were treated at 0° with five times
the weight of fuming nitric acid of 1.52 sp. gr. The compound rapidly dis-
solved without elevation of temperature. After one hour the liquid was
poured into ice water and the fluorine derivative was instantly precipitated
in a solid condition. When the liquid had become clear it was carefully
filtered and the mass was repeatedly triturated in ice water until] the
acid reaction had completely disappeared. It was then treated with 9.65 ce.
Of 7/}.; NaOCH; for 5 minutes at 15°. The liquid was then titrated

Q GEA
back with 4.77 cc. of m acid. This gives — 4.77 = 0.23 cc. of nalkali
consumed, corresponding with 0.428 gram of dinitro compouud, or 1.4 °/).

b. 1.732 grams ofthe para compound were treated in the same manner.
But after the acid had been removed by washing, the residue was melted
to a clear liquid by applying a gentle heat. It was then cooledin ice water
and again triturated and washed in ice water until the last traces of acid
had disappeared: it was then treated as in a. 10.48 ce. of 1/1.93 Na OCH,
were used and the liquid was titrated back with 5.3 cc. m acid; 0.1 cc. of
n alkali had therefore been absorbed corresponding. with 0.186 gram of
dinitro compound or 1.0°/,¢ The mean of the two determinations is there-
fore 1.2°/.

Being in possession of these data, I have now subjected the nitra-
tion product of benzene fluoride to the same test. Dr. Brrxman had
previously found that the nitration at O° with a mixture of 25 ce.
of nitric acid of 1.48 sp.gr., 5 ce. acid of 1.51 sp. gr. and 10 grams
of benzene fluoride yields a compound consisting solely of mononitro
compound (to judge from its percentage of nitrogen; found 9.95
calculated 9.93). 1, therefore, nitrated in the same manner and purified
the product, which in ice water is semi--solid, by first washing it
in ice water, being careful not to lose any oily globules, and then
with water at 20°, which caused the whole mass to melt to a homo-
genous liquid. After all acid reaction had disappeared the bulk of
the water was removed by means of a separatory funnel, the clear
pale yellow oil was freed from a few drops of adhering water by
means of a strip of filterpaper and then finally heated in a testtube
at 9O°—100° until it no longer became hazy on cooling. We may
assume that all the moisture has then been removed, likewise small
quantities of any unchanged benzene fluoride. The product so obtained
solidified after inoculation at 15°.7; a second preparation at 187.6.

It does not contain benzene dinitrofluoride :

1.4115 grams were treated for 5 minutes with 9.45 cc. of ”1/,.9, sodium
methoxide. The liquid was titrated back with 4.9 cc, 7 acid, or 9.46 72/;.9g acid,

( 663 )
But on the other hand it contains benzene metanitrofluoride :

a. 5.208 gram of the nitration product = 36.9 millimols. were heated
with the equivalent quantity, namely 78.5 c.c., of 7/3... sodium methoxide
for one hour in the boiling waterbath. After being poured into water, the liquid
was titrated back with 1.5 cc. n acid; this after correction corresponds
with 0.2170 gram of meta compound or 42 "9.

b. 5.817 gram of the nitration product — 41.3 millimols were treated in
the same manner with the equivalent quantity, namely 79.7 cc. of 7/;.9s
sodium methoxide. The liquid was titrated back with 1.55 c.c. n acid;
which after correction for tne attacked meta compound (2.6 °/,) corresponds
with 0.2243 gram, or 3.9%) meta compound. The mean of the two determi-
nations is, therefore, 4.1 °/.

In this determination of the quantity of meta compound it has
been assumed (and such is very probably the case) that the benzene
orthonitrofluoride present in the nitration product also reacts quanti-
tatively with sodium methoxide.

By renewed treatment of the nitration product with concentrated
nitric acid in the manner described, its solidifying point does not
perceptibly alter, for it was found to be at 18°.8. This had already
been noticed by Dr. Berkman. Still, the twice nitrated product now
contains benzene dinitrofluoride:

a. 1.0015 gram of twice nitrated product was left in contact for 5 minutes
at 15° with 8.45 cc. of /;.9,; sodium methoxide. The liquid was titrated

back with 3.9 cc. m acid. Therefore, alkali absorbed = — 3.9 =0.5 cc.

nm alkali = 0.093 gram dinitro compound, or 9.3 °/5.
b. 2.264 grams were treated in an analogous manner with 10.15 cc. of
n/j.9, sodium methocide. The liquid was titrated back with 4.25 cc. nacid.

10.1
Alkali consumed, therefore — — 4,25 = 1.06 cc. corresponding with 0.197

gram, or 8-7 °/) dinitro compound. The mean of the two determinations is,
therefore, 9.0 °/.

Now we have seen that by treating pure benzene p-nitrofluoride
with strong nitric acid for one hour 1.2°/, undergo further nitration.
In the twice nitrated mixture there is present 9°/, of dinitro- and
4°/, of meta compound '), therefore 87°/, of para; 1.2°/, of this
represents 1°/, of the whole. This quantity of 1°/, must, therefore,
be deducted from the amount of benzene dinitrofluoride found, in
order to obtain the quantity which owes its existence solely to the

1) 9.0°/9 dinitro = 6.4°/, mononitro. By subsequent nitration, 100 parts of the
once-nitrated product increase to 100 + (9.0—6.4) or 102.6 parts which contain
4.1 parts of meta, or 4°.

( 664 )

subsequent nitration of the benzene o-nitrofluoride. This, therefore,
amounts to 8°/,, corresponding with 6.1°/, of ortho compound. Accor-

ding to the above the composition of the nitration product is therefore :

6.1°/, benzene ortho nitro- Pages) Being formed by nitration of ben-
4.1° / » meta a zene fluoride at 0° with the concen-
69.8", 5 +para 5 | tration of the acid stated on p. 662.

The composition of the twice nitrated product was found to be
9°/ of benzene dinitrofluoride, 4°/, of meta- and 87°/, of para com-
pound. This was easily controlled by making an artificial mixture
having this composition as all the three components were at disposal.
Its properties must then be identical with that of the twice nitrated
product. And indeed, the solidifying point of such a mixture was
found to be 18°.7 and 18°.9 whilst that of the said product was at
18°.8. According to BrEKMAN’s data’), the sp. gr. of the artificial
mixture should amount to 1.27738, whereas 1.2791 was found for the
twice nitrated product. This higher figure is, probably, to be attri-
buted to the fact that the corrections to be applied are somewhat
uncertain so that the results could only be accurate to within about
1°/,. If this should cause a little excess of dinitro and a little defi-
ciency of meta compound, the sp. gr. will be at once seriously
affected, whilst the solidifying point does not perceptibly alter. In

fact, an excess of 0.8°/, of dinitro compound is sufficient to explain
ihe difference in the sp. gr.

I have also endeavoured to nitrate benzene fluoride at —30°,
using the same acid mixture employed in the nitration at 0°. On
-adding the fluoride drop by drop to the acid cooled to that temperature
it dissolves with a dark brown colour causing but little rise in
temperature, just as had been observed in the nitration of benzene
bromide. After all the benzene fluoride had been added, the colour
gradually began to fade and when the nitration vessel was removed
from the refrigerating mixture and its contents reached a temperature
of about —20°, the liquid soon became pale yellow and the temperature
rose to about + 10°. It, therefore, appears that the velocity of
nitration at —30° is already considerably retarded, as the intro-
duction of each drop of benzene fluoride at O° is accompanied by
a very perceptible caloric effect. The solidifying point of the product
which was collected in the way described, was situated at 19.°1,
from which it may be concluded that it differs but little from the
product obtained by nitration O° This can only contain about 1°/,
less of by: “products.

1) Sp. gr. meta 1.2532; para 1.2583; dinitro 1.4718, all at 840.48.

( 665 )

' >
Let us now see what the quantitative determinations of the nitration
products of the halogen benzenes have taught us:

iC, Bo Rhe| CoH! Or |. C,H, Br. | C,.H, J

OUGNG: Seer | 6.41 99.8 3 Ye: 34.2

) |
meta. =... | £4) | O.3(2)|)" 0139(2)} | = platen
temp. O°.
HALAS see <a, 89.8 69 9 62.4 } 65.8 |
| { -
ortho , as | 9.6 | 34.4 35.3
| nitration
ews ist oP — D3 (?)| 0.3 -- :
ed pee “) | temp. -30°.
Saray, < wi. : — ae ee 63.3 | 64.7

From this nitration of benzene fluoride it is also shown in the plainest
manner that the influence of the fluorine atom on the position of
the nitro group is quite different from that of other halogens
which in this respect behave very similarly.

Groningen, Dee. 1908. Lab. Univers.

; ‘ : ' ‘ i ‘
Chemistry. — ‘ Description of an apparatus for vequlating the
pressure when distilling under reduced pressure.” By Jax

Rorren. (Communicated by Prof. 8. Hoogrwrrrr).

(Communicated in the meeting of February 27, 1904).

When distilling under reduced pressure it is always of importance
to keep this constant during the distillation: moreover, the pressure
during the operation must frequently be a definite one. This is, for
instance, the case in the testing of mineral oils, where it is generally
required that a definite quantity shall distill over at a definite pressure,
which is in general considerably less than that of the atmosphere,
and at a definite temperature.

As it is not possible to keep the pressure sufficiently constant by
the admission of air, the quantity of which is regulated by a screw-

( 666)

clamp, many apparatus have been recommended by various investi-
gators in order to effect this purpose automatically *).

As, however, these apparatus are either somewhat complicated or
else do not always effect a satisfactory regulation of the pressure,
and as I had very often to carry out distillations under reduced
pressure, [I have tried to construct an apparatus which would suit
my purpose. I have used this apparatus for a year and a half
and it quite satisfies my requirements.

The apparatus may be used for any pressure situated between that
of a column of mercury of a few m.m. and one of about 600 m.m.
in height; the required pressure is kept fairly accurately constant.

For the sake of clearness, the lower half of the annexed drawing
represents a section of the apparatus and the upper half gives a
view of the latter.

A is a glass tube with an internal diameter of about 19 mim. and
to which is sealed a tube 4 2 mm. wide; // is a trap-bulb; Ca
manometer tube which stands in the same mercury vessel as the
barometer J. A is attached to the wooden piece C which may be
moved in a vertical direction between the pieces /. The tube A
may be moved upwards and downwards by means of a wheel. A is
placed in a vessel partly filled with mercury; the lower opening of
A is closed with an indiarubber stopper having a vertical hole of
about 5mm. diameter. To the extremity of the thin tube 4 a piece
EL is connected: /F is made of wood, cork or rubber and has a
vertical perforation by means of which it may be pulled over the
tube 4. It has in addition a side /\ (triangular) crevice running as
far as the vertical perforation. The proper action of the instrument
depends on the piece L.

Between the tube C' and the barometer PD is situated a calibrated
scale movable in a vertical direction by means of £, which renders
an accurate reading of the pressure possible. From the drawing
it is further shown, that A and C' are connected by means of glass
T pieces and of thick indiarubber tubes, not only mutually, but also
with the airpump and the space to be evacuated. (So as not to

1) Kamertincu Onnes, These Proc. June 1903
SraepeL & Haun, Liebigs Ann. 195 p. 218.

Goperroy. Ann. Chem. Phys. [6] 1884 — I — p. 138.

Avcer. Bull. Soc. Chem. [3] 1898 — 19 — p. 731.

Hausser. Bull. Soc. Chem. [3] 1899 — 21 — p. 253.

Bertrand. Bull. Soc. Chem. [3] 1903 — 29/30 — p. 776,
Chem. Centr. 1903 — 2 — p. 611.

aA. Smits. These Proc. 27-11-1897.

nn eee aad
PO Sidaacieaet

p—==t LLL

A001 Rana ASE A NRRErY NR

Nd alr tk 9

spoil the drawing, the tube has been cut near S; one must linagine
between the two S’s a piece of tubing, about 50 ¢.m. long). Neither
the lower nor the upper side of A has been narrowed, so as to
facilitate the cleaning of the tube.

After the mercury vessels have been properly filled and the
apparatus connected, the air is rarefied by means of a powerfully
acting removable water-pump. In consequence the mercury rises in
AS ant 0.

When the requisite pressure is attained, A is raised by means of

( 668 )

the wheel until the point of the triangular opening of the piece E
just reaches above the mercury. This will be observed at once as a
current of air and mercury then passes from 4 towards 7. If for
some reason the division of air and mercury does not take place at
once, a tapping of B is sufficient to effect this. The mereury which
is carried over, is thrown forcibly against the side of 7, but this
being constructed as a trap, no mercury can be carried over with
the escaping air through / or A.

If the desired pressure is not yet attained, A is turned lower or
higher, should the pressure be still too great or too small. But once
the required pressure attained, it will remain constant as air is
being continuously admitted through A.

Suppose, for instance, that, owing to incipient decomposition, badly
condensable gases are formed during the distillation, the mereury
falls in A; the additional mercury now arriving in the mercury
vessel venders the part of the /\ shaped opening, which projected
above the mercury, smaller and in consequence less air can proceed
from 2 to H; unless the power of the waterpump is exceeded the
original pressure will be maintained. If such is not the case the
original pressure must be again restored by moving 4.

Instead of the barometer and the manometer tube a shortened
pressure gauge with movable scale (like the gauge of an airpump)
may be employed *).

Physics. — “Jethods and apparatus used in the cryogenic labora-
tory VI. The methylehloride circulation.” By Prof. H. Kammr-
rInGH Onngs. (Comm. N°. 87 from the physical Laboratory at
Leiden).

(Communicated in the meeting of June 27, 1903),

§ 1. The methylchloride boiling vessel. In Comm. N° 14 Dee.
‘94 in the description of the cascade of circulations which produces
the permanent bath of liquid oxygen for different measurements, I
have mentioned that the methylehloride refrigerator used there left
much to be desired. At the time when I arranged the cryogenic
laboratory at Leiden, the use of liquefied ethylene in a circulation
to obtain an efficient circulation of liquid oxygen was an untouched
scientific problem, As a result my attention was principally concen-
trated — besides on the question of obtaining a permanent bath of liquid

1) The apparatus may be obtained from the Ned. Instrumenten Fabriek. Utrecht.
Holland.

( 669 )

oxygen — on the ethylene circulation, so that this might be made a type
of a low temperature circulation with a small quantity of working
gas. The removal of the principal deficiencies of Picrer’s first cycle
in place of which my methylchloride cyele is used, was thus, as
far as possible, deferred until an ethylene condensation was required
quicker than the one then necessary.

One important improvement in the cascade method could not be
dispensed with even then in the methylchloride circulation, if I wished to
work with success. It was the introduction of a regenerator with the
methylchloride refrigerator. Regenerators had been already, as I found
later, used or patented by Siemens and So.yvay for freezing-machines.
Still it appears that they were first used by me for the systematic
production of liquefied gases, and that the combination of regenerators
with the cascade method, in addition to my other auxiliary apparatus,
first made this method practical.

The regenerator, where the vapour rising from the methylchloride
cools the ethylene which proceeds to the condenser immersed in
methylchloride, has been very curtly mentioned inComm.N? 14(Dec.’94).
It is shown on Pl. IV of Comm. N° 51, Sept. °99 and on Pl. ILof
the present communication, where further under D the same letters
will be found as employed in Comm. N° 51. In the following the
details are always indicated by suffixes to the Gothic letters which
are used as distinctive for the various kinds of apparatus. Dy is the well
known Picter refrigerator (first designed tor sulphur dioxide), Oz
the regenerator. The liquid methylchloride flows into the condenser
through 2) (J ef. Comm. N° 51), and is pumped away through Dx.
The spiral within the regenerator contains N,O in the case repre-
sented in the plate (represented by doubly marked lines).

This refrigerator and regenerator is now almost exclusively used
for the production of liquid N,O (¢.f. Comm. N° 51 Sept. °99). A
refrigerator and regenerator with a much larger working surface and
a better construction is combined with the condenser and its pump
for use with liquid ethylene. These were constructed with great care
by the mechanist of the cryogenic laboratory Mr. G. J. Fro. Their
description has now become necessary, since the increased rapidity
with which this quantity of ethylene can be circulated by their
means has rendered many recent measurements possible.

The ethylene boiling vessel’) of § 5 Comm. N° 14 Dec. ’94 served
as a model for the new arrangement. In that model the regenerator
and refrigerator have been combined to a single piece of apparatus.

1) Represented in the account by Marrtutas, Rev. Gen. des Sciences 30 April
1895, p. 385.

( 670 )

In the same way the regenerator and refrigerator for methyl-
chloride are combined (see © Pl. if for the elevation and Pl. I for
the section) in one apparatus which we will call the methylehloride
boiling vessel. The experience with the ethylene boiling vessel has
been put to use, so that in its turn also the methylehloride apparatus
will serve as a model for an improved ethylene boiling vessel. The
increase of the ratio between the surfaces of regenerator and _ refri-
gerator allows the methylehloride to leave the apparatus at nearly
ordinary temperature, even when the BurckHarpT pump as described
Comm. N° 83 Apr. 03 sucks with its full foree, which could not
be obtained before with the ethylene boiling vessel. The condensing
surface measured in the tube is about 0.9 M*., and the regenerator
surface, similarly measured, nearly the same.

The walls of the boiling vessel are soldered to form one whole ;
those of the refrigerator Cu,, and Da (see Pl. I) are of copper 1mm.
thick, that of the refrigerator #a of thin brass 0.5 mm. thick. The
neck / of the refrigerator is soldered to the regenerator and _ this
again to the mouthpiece Ga. Owing to the length of the regenerator
and the thinness of the walls it is possible to make the latter of brass.
Even with this material the heat conduction is of no importance.
Since the vessel must be evacuated it must show a considerable
resistance to external pressure. The resistance of the walls themselves
is in the first place increased by the addition of small ridges which
are shown as Ca, in the main drawing with the detail of the wall
to the right and the section to the left. In the conical space D six
triangular copper plates ,, (cf principal figure and the section at
bottom right of Pl. TI) give the necessary stiffness. These have flanges
Dy,
side they carry the conical wall of the vessel through three rings
D,,, D-, ad D,,. Resistance to outward pressure, which becomes
necessary when leaks have to be sought, is provided by pressing the
bottom of the refrigerator against the plates 1,,, by means of four
wooden balks Ca, which also protect C4,, pressing on crossed laths

D,,,. which rest on one side on the bottom, on the other

(), which are screwed up to rest on the round upper surface by
means of steel rods C,, and a ring Ci, -

In contrast with the scheme of the ethylene boiling vessel, it was
not considered necessary that the height of the liquid should remain
very little above the windings of the condensation spiral. To condense
oxygen in the ethylene boiling vessel it was of all importance that
the temperature of the condensation spiral should fall as far as pos-
sible and thus that the ethylene should boil under a very low pressure.
Now in that case there would be no advantage in the vacuum pump

( 671 )

removing the vapour under very low pressure, which implies a
rather considerable loss of work by friction, if boiling nevertheless
occurred at a higher pressure. And this must occur when to the
suction pressure was to be added a noticeable hydrostatic pressure
due to the turns of the condensationspiral, where the vapour forms,
being much beneath the surface of the evaporating liquid. In the case
of the methylehloride circulation it seemed to me that the obtaining
of the lowest possible temperature was not of utmost importance and
that there was no objection to simplify the construction by allowing
liquid to be introduced to a height of 20 em. in the refrigerator,
though not all profit is taken in this way of the low pressure (at most
20 mm. of mercury) under which the BorckHarpr—Welss vacuum
pump, which is introduced into the methylehloride circulation, sucks
at full speed (usually about 8 mm. is employed).

The spiral where the ethylene is liquefied (length 53 m., inner
diameter 6.4 mm., thickness of wall 0.8 mm.) lies in two windings
in the hollow eylindrieal mantel C" in which the conical refrigerating
vessel J) terminates beiow. There is just room between the two
windings of the spiral (see section bottom left below and the elevation
of the section through D bottom right on the plate) for the ascending
tube Ad by which the lower end of the inner spiral Ac Ad is jomed
to the upper end of the outer. These two cylindrically wound spirals
are joined to a flat spiral Ac which lies on the bottom of the boiling
vessel. When the latter is well filled this spiral lies just under the
surface of the liquefied gas introduced through the cock .V. The spirals
are coupled so that the liquid is driven out by the pressure of the
gas. If the boiling vessel is always kept so full that the flat spiral is
immersed, it is advantageous to let out the condensed gas from the
last spiral. Should it be desirable to work with a smaller quantity,
it is better to first run the gas to be condensed through the flat
spiral ; this case is shown in the drawing. If the flat spiral is immersed
the temperature (usually —87°C.) of the liquid can be read on the
thermometer ©, the stem of which is bent for convenience and is
immersed in the tube Dg, filled with aleohol and protected from
interchange of temperature with the air by means of an ebonite
tube Dy, joined to it with fish glue. The capacity for liquefied gas
when the cylinder- and flat spirals are covered is 6 liters, the volume
of the spiral 1 liter.

The conical space of the refrigerator is sufficient even for. an
excessive boiling up of the liquid, which is always large at low
temperatures as can be seen from the movements of the float.

The regenerator spiral consists of two long tubes 4), and 4,, 39 m.

( 672 )

and 2B. and Ba 19 m. respectively, which are wound in the space
between the outer wall /,, of the regenerator and the very thin
walled inner cylinder #, divided into three parts by two wooden
rings. The inner diameter of the tubes is 7.5 mm., the walls are 1 mm.
thick. The two spirals can be joined otherwise than in the manner
shown in the figure, but further description is unnecessary. A safety
cap <A, (c.f. the ethylene boiling vessel Comm. N°. 14 § 5) is also
joined to the spiral, so that the bursting of the spirals within the
boiling vessel is not possible. The figure shows clearly how, without
a complicated construction, an intimate contact between the rising
vapour with the regenerator spiral is produced and also a constant
intermixture of the vapour partially warmed by contact with the
metal and of the still unheated portions, convection currents which
extend to some distance being avoided.

The interchange of heat between the vapour, which rises in the
regenerator, and the gas which is put into the spiral is furthered
without appreciable loss of pressure by friction, by laying a perforated
copper plate 4,,,, through which the spiral find its way, horizontally
above each lattice spiral 4,,, (see detail right section and plan). This
plate is soldered to the spiral where it turns downwards. In the detail
figure to the right, section and view above a plate, the soldering
place can be seen to the right of 4,,, at the vertical section of the
spiral. In this figure the perforations are only drawn over a small
portion of the plate for simplicity. The perforated plate is insulated
by wooden blocks 4;,, from the adjacent lattice, against which these
blocks press. Further cotton and parchment paper are wrapped round
the column of plates and thus the spiral with the plates is made to
a whole that just fits into the regenerator space. In this way the
gas, finding the way through the inner cylinder shut, can only
escape through the perforated plates. The inner cylinder is insulated
by paper from the perforated plates, and is usually closed above by
H,. Should it have to sustain pressure owing to perhaps a sudden
violent development of vapour, or owing to the closure of a sieve
plate by the freezing of moisture the vapour can immediately eseape
through the safety valve /,, the construction of which is shown
sufficiently in the drawing.

The whole boiling vessel hangs on the solid neck (,, dong which
the vapour escapes, in the same manner as the ethylene boiling
vessel (7, rests with a collar G. on a bracket (see P]. 11). The main
outlet tube G, gives off a branch through a large but light cock
/ — the construction of which is sufficiently shown on the drawing

( 673 )

— to the wide feeding tube of the BurcHHarpt—Wreilss vacuum
pump (% Pl. I), arranged as deseribed in Comm. N°. 83.

A second narrower branch with ordinary cock Z runs to one of the
combined pumps of the Société Génevoise, mentioned in Comm. N°. 14.

On commencing to work with the methylchloride circulation ¥&
is used alone, afterwards 2% and % in series. Naturally when no
more liquid ethylene is required than was formerly used (Comm.
No. 14 Dec. °94) the pump % can be used alone and %,7 (PI. II)
remains closed.

A third branch G7 goes to the safety cap A, the construction of
which is sufficiently shown in the diagram, and as soon as the
pressure reaches above the atmospheric the vapour is conveyed into
large rubber sacks of 500 liters capacity each which are them-
selves connected with a safety tube ,.

If a sudden violent development of vapour occurs or the outlet
becomes closed unexpectedly, the vapour can escape through the
safetyeap JZ Pl. I. The arrangement of this can be seen from the
detailed drawing near J/. The caoutchoue sheet J7,, covered on its
lower surface by a tin plate nearly up to the sides, and fixed to
the rim JZ, (on which a rim is turned to prevent lateral motion),
rests on the perforated plate J/, and is thus protected from the effect
of exhausting the vessel. It is also not blown out by pressure as it is
pressed by the cap JZ7. As soon as the pressure rises above that at
which the spring is set (0,15 Ats above the atmospheric) the catch on
which the spring presses flies open, the cap is driven upwards and
the caoutchoue bursts.

The soldered connection between the main outlet tube and the
regenerator is not exposed to strain since above and below tie latter,
stout wooden rings /y / are laid and strengthened with iron bands
F,, £,. The upper is fastened to the cover by three rings &,, the
lower is drawn against the upper by steel wires F7,,, at constant
tension temperature, changes being allowed for by springs #7... The
tension is adjusted to the mean of the weight of the whole apparatus
and that of the regenerator. The lower ring /,, just mentioned is
fixed sideways by bands S, and Sj (see chief figure and detailed figure
to left), it carries further another iron band S, onto which various
cocks are fixed (see also Pl. II, €).

The cock .V to admit methylchloride is also fixed on an extension
S. of this ring. The most advantageous cock would be one constructed
in the manner of that on the ethylene boiling vessel (see Maruivs
description l.¢. p. 385). It is however sufficient that it should have
the construction of that at D (Pl. Il. of this and Pl. IV of Comm.

( 674 )

Nr. 51, and shown in detail in the above mentioned description Le. p,
aoe Nr): -

The long pin (see Pl. 1). .V, runs first through the inlet tube
Nig» Continued by .V,, for the methylchloride and is pressed against
the opening in the bottom .V;,, of the tube .V;,, by means of a
screw in V2, above the side inlet tube N, for methylchloride. The
tube with cock .N) rests loosely in the special tube D,,. The joint
is closed by caoutchoue D,, on the enlargement .V;,, and allowance
is made in this manner for the relative shifting of the tubes owing
to change of temperature.

This arrangement is used when methylchloride at the ordinary
temperature is admitted to the apparatus. The cock NV insulated from
the tube DY, is kept at the ordinary temperature by the thick iron
ring S. and the caoutchoue at the upper end thus remains soft
while otherwise having become brittle by cooling it would break
owing to the unequal displacement of .V and J. It is always neees-
sary to introduce the methylehloride at the ordinary temperature
when it is not quite pure and dry, otherwise the cock will be
frozen fast. A cock of the model .V is very appropriated for the
adinission of methylehloride at the ordinary temperature.

A good method for purifying the necessary quantity of methylchloride
consists in drawing off the methylehloride in the boiling vessel by means
of the cock .V and causing it to evaporate by condensing ethylene in
the spiral. If the cock freezes, the pressure is made equal to that of
the atmosphere by shutting 4 off, or if necessary bringing the apparatus
in connection with the sacks 9 (Pl. IL.) through Z. .V can then be
taken out of D,. Before using the flask after a process of purification
it is first dried by the aid of the tube and cock Tu.

If the methylehloride is first cooled by contact with a cold gas,
as is shown at ©’ on Pl. I] next to the principal drawing, the inlet
tube passes through an ordinary cock N,.

The cock 7, serves to introduce the ethylene to be condensed, the
cock 7, which is placed on wood and packed in wool, to draw it off.

The cock 7’, is inserted in the tube A,, which runs to the bottom
of the cylindrical space C’ and is used for cleaning and drying.

The position of the liquid) methylehloride can be seen from the
float ?,, which moves up and down in the central tube (C,, itself
in connection with the space round the spiral through the tube
(,,. By means of an aluminium wire, a silk cord and a platinum
wire, P?, is joined to a silk cord P,, Which passes over the pulley
(), into the glass tube @Q

<a>

where it is attached to a weight 7,
which runs along a seale fixed to the tube Qa.

—-

The flask is packed in the same way as the ethylene boiling vessel
(Comm. N° 14) first with nickel paper and then with several layers
of wool, the number of layers increasing at the colder parts, as can
be seen from the drawing PI. I. They are contained between varnished
and nickelled paper as is seen in Cj, C;, C., C, Fi, Fi, Fy, while
horizontal strips of felt, dotted in the drawing, prevent convection
currents. These various layers form airtight compartments, which
are connected together by means of small tubes C,, C,, while the
whole airtight space is connected with the atmosphere through a
drying tube F/. The outer surface is painted white.

§ 2. The methylchloride cycle. A short description of this is
desirable. The liquid methylchloride is preserved in the tubulated
condensor ©, which is cooled by running water. Its pressure is
measured by the manometer and its level can be seen in the level
glass ©,, with blow-off cocks as used with water boilers (to make
a reading the connecting tube for liquid methylchloride ©,, must be
cooled with ice as shown diagrammatically on PI. II (for farther par-
ticulars the quoted description of Martutas p. 383 N° 2)). A large
cock ©,, protected by a filter (shown l.c. as N° 9) makes it possible
to shut the condenser off immediately by a small movement, even when
a strong stream of methylchloride is sent through the condenser. This
cock is followed by a regulating cock ©,, to which the tubes for
liquid methylehloride are connected. The latter run to:

1s. the refrigerator D, which is used to obtain liquid nitrous oxide,
either in the manner given in Comm. N° 51 Sept. ’99, or by drawing
it off into a vacuum vessel U from which the nitrous oxide can
be siphoned over into other vacuum vessels and thus be brought to
apparatus arranged in other rooms.

As far as the nitrous oxide circulation according to Comm. N° 51
is concerned the mercury and auxiliary compressors (Comm. N° 54)
can be used as & in place of the BrotnerHoop of Comm. N°. 51.

The various pieces of apparatus, for which the nitrous oxide in %
is used, are generally connected to the tube App and the sack &
from which the gas can be repumped into B. Plate II shows the
use of a small 2°K.G. cylinder 8 of the kind usually used in this
laboratory for this purpose.

2d. other apparatus formerly described e.g. one of the cryostats
(Comms. N° 51 and 83),

3d. the boiling vessel for the preparation of liquid ethylene €
Pl. II as described in § 1, either directly or through the regenerator
€’ where the methylchloride is cooled by cold vapour coming from
another vessel and passing from Jn to Ex,

45
Proceedings Royal Acad. Amsterdam. Vol, VI.

( 676 )

4th. an apparatus gy which will be described in detail in the following
section and intended to deliver a stream of calciumchloride solution
at a low but very constant temperature.

We may consider the methylchloride vapour which streams out
of these refrigerators and regenerators. In the case 3 above (some-
times also in case 2 for which the connection %; serves) it would
be sucked by a BurckHarpDT—WEIss vacuum pump %, installed in
the manner given in Comm. No. 83. From here it would travel to
one of the conjugated pumps of the Société Génevoise 3, mentioned
in Comm. No. 14, which receive the vapour from the BurcKHARDT
or from all other apparatus (D Pl. II and further indicated under 2).
This pump % may for another example take the vapour directly from
the boiling vessel © (see Pl, IJ and Z Pl. I) as well as between the
high and low pressure cylinder from the branch tube , which too
allows gas to be pumped from one of the four above mentioned
sacks , in which the methylchloride can be preserved for a short
time and of which only one is represented on Pl. I, while other
sacks can be connected to apparatus from which methylchloride
escapes under constant pressure. The pump is provided with an
indicator on the low pressure cylinder, a vacuummeter between
the high and low pressure cylinders and a manometer on the high
pressure cylinder, besides several cocks which are required for
pumping, drying and filling with methylehloride. The vacuum meter
¥my indicates the pressure of the gas which enters the high pressure
cylinder. From the cylinder volume and the number of strokes one
ean derive the volume of gas and reduce it to that under normal
conditions moved in the cycle, so that the velocity with which the
liquid in the refrigerator evaporates can be followed.

In addition a safety valve Sw is added to the high pressure cylinder
principally to protect the condensor &.

The methylehloride which can escape from this safety valve is
passed into the above mentioned sacks §. Usually, all the methyl-
chloride passes into the condenser, where it is cooled by running
water from the main. In between, an oil trap § is placed which
is slightly warmed by steam (see ©,c,), so that the transported oil
shall give up the dissolved methylchloride. The oil thus separated
by the change of direction is run into a flask 8. The last portion
of the methylchloride, freed here, is carried to the sack . At the
top of the oil trap, the gas is freed from the last traces of oil by
layers of felt and wadding contained between sheets of metal gauze.
(C.f. the oil trap of the ethylene circulation shown by Maratas l,c,
p. 383 fig. 1).

is
——

( 677 )

§ 3. Circulation of calcium chloride solution at constant tempera-
ture below zero C. The thermostat is similar to that described in
Comm. No. 70 III May ’01, but with the difference that at P, a
side tube with cock and mercury resevoir is introduced, so that the
regulator can be set for high temperatures (very well to 60° C.)
and also for a low one by the choice of a suitable fluid. The spiral is
filled with benzene and, instead of water from the main (as in No. 70),
a cooled stream of calcium chloride solution is run into the heating
vessel. The solution is contained in a vessel ® with filter and
float Na and is driven through the refrigerator €, and regenerator ©,
in which the methylchloride evaporates and thus cools the circulating
calcium chloride solution. This is caused to move by a force pump =
with valves €, connected to one of the conjugated compressors %
while a bent tube prevents the cooled solution from falling.

In the refrigerator the liquid methylchloride runs through the
tube €7, and regulating cock €,, to the inner space, while the
calcium chloride solution runs spirally in the outer. The liquid
methylehioride running into the refrigerator is cooled by the vapour
evolved, which escapes by a wider tube ©, to the regenerator, from
which projected liquid returns by a narrow tube &;. Finally the
danger which might arise when the cooled methylchloride, left
between the cocks d and the shut off cock of the tubing G, returned
to the ordinary temperature, is avoided by connecting a safety cap
with a closed tube ©; added above. At 12 Atm. the thin plate breaks
and sufficient space is produced without communication with the air.
The walls are all calculated to stand the ordinary pressure of the
methy|lchloride.

The pressure under which methylchloride

‘ evaporates must not fall below a certain value,
=, as the calcium chloride might then freeze out.
br It is kept constant by the pressure regulator &

Pl. II. When the pressure falls the mercury
rises in 6, see accompanying figure, and forces
the float a, upwards, so that the lever / rotates
about g and thus closes the suction channel by
the double valve h,h,. A safety tube & Pl. II
“ and a tube to receive spilt mercury complete
the apparatus. The properly cooled calcium
chloride solution runs from the refrigerator ©, to the thermostat XY,
where it is rewarmed to the required low temperature and conducted
to the apparatus which must be held at constant temperature.
On Pl. IL a piezometer surrounded by a vacuumglass is shown,
45*

where the outer surfaces are connected by the copper box used
for the vacuum jacket of Comm. N°. 85. This jacket remains
free from dew deposit, so that the divisions on the tube can be
clearly read. Above the liquid surface the vacuum tube is lengthened
by an ordinary tube of about 50 cm, so that the solution is protected
from the atmosphere by a layer of cold air.

The apparatus was e.g. placed once at about 25 meters distance
from the refrigerator, in another room. It would be less suitable
to convey the methylchloride itself over this long distance owing to
the increased danger from fire.

The calcium chloride solution had a specific density of 1.28, the
vacuum under which the combined pumps worked was set so as to
produce a temperature of — 45° C. in the refrigerator and remained
satisfactorily constant. The small pump moves about 2 liters of
solution per minute.

In order to keep temperatures below — 20°C. constant at long
distances by a methylchloride circulation, it will be necessary to
have a refrigerator with a greater cooling surface.

Physics. — Communication N° 86 from te Physical Laboratory
at Leiden. “The representation of the continuity of the liquid
and gaseous conditions on the one hand and the various solid
aggregations on the other by the entropy-volume-energy surface
of Gisps” (By Prof. H. KameriineH Onnzs and Dr. H. Harper).

(Communicated in the meeting of June 27, 1903).

§ 1. The meaning of the following research will be best made
clear by showing its relation to the former communications (66, 71,
74) from one of us (H. K. O.). Like these it: arises from the cer-
tainty that it is increasingly necessary to represent the experimental
values for an equation of state from a general point of view.

In the first place this research is connected with that of N°. 66 *)
on the reduced 4, €, v (y = entropy, € = energy, v = volume) Gipss’
surface formed after vAN DER WaAALtLs’ original equation of state.

The drawings of N°. 66 show that a ridge appears on the side
of small volumes on the Gipps’ surface given there, by shifting the
constant isotherm (fig. 1) of simple form (l.c. Pl. I and II), derived
from the above mentioned equation of state, along a vertical directrix.

1) KamertincH Onnes, Die reducirten Greps’schen Flachen. Vol. jub. Lorentz,
Archiv. Néerl. Sér. Il, T. V. p. 665—678. Leiden, Comm. n°. 66.

Fig. 1. Fig. 2.

This ridge — the liquid ridge — carries the liquid branch of the
connodal of the liquid vapour plait; the isotherms run over the
ridge from the vapour to the liquid side and from higher to lower
entropy (l.c. Pl. I, fig.1.). In the vicinity of the critical temperature
the ridge becomes broader and smoothes down into the double
convex surface (I. c. Pl. I, fig. 3) which further forward is everywhere
double convex. For lower reduced temperatures the ridge passes
nearly into an yeplane. The projection of the ridge on this plane
is a curve along which the inclination (tang—! = absolute temperature
T) decreases towards negative values of the entropy (see fig. 2). The
projection of a cross section of the ridge shows the rapid change
of the inclination in the v «plane (tang—! = pressure p) for a small
change of volume. The correspondence of the properties expansion,
compressibility and specific heat, for liquid and solid shows imme-
diately that the representation in the 4, ¢,v coordinatesystem of the
experimentally determined conditions, belonging to one of the solid
averegations of a material, can be supposed to belong to a ridge
corresponding to the liquid ridge. Also that other solid varieties
require further ridges. So long as we exclusively keep to the
experimentally determined values only narrow strips of these sup-
posed ridges are given for a short distance to the side of the tops
and thus form themselves isolated parts, not connected with the
vapour and liquid regions, of the whole Gres’ surface for the
special substance.

Tbe various ridges, if we for a moment admit their existence,
will be more or less shifted, according to the density, towards zero
volume (v) and according to the fusion and transformation heats
more or less to zero entropy (7). The difference in specific heat of
the modifications, will be given by a variation in curvature. Looking

( 680 )

from the side of large v, we
oe should see a succession of ridges,
= and where we for simplicity con-
sider the case of a single solid
bas state of aggregation, we should
, see the resulting ridge rising at
lower temperatures above the

Fig. 3. liquid ridge (ef. fig. 3).

To find the coexisting phases from the region a’ a" or from the
region 6’ with the vapour phase from the region c, one must lay
the common tangent plane on the curved surface in ¢ and the given
ridge. In the case that a rarefied gas phase occurs in c, the ridges
would be represented approximately by curved lines. This is then
also to be permitted in the search for the corners a and 6 of the funda-
mental triangle of the triple point. The general thermodynamical
character of a solid state occurring together with the VAN DER WAALS
state (liquid, gas and labile intermediate states) would be thus obtained
by representing it on a Gisss’ surface by a ridge of a somewhat
other position and form but generally analagous to the liquid ridge.

There is thus every reason to suppose that outside the region
of observations and towards the large volumes the first continuations
of the isotherms obey an analogous law as to form and change
of form with temperature as the liquid isotherms, and thus by
a slight extension really produce a ridge. This appears to be more
probable when one notices that there is also a ridge on the Gisss’
surface which does not correspond to the original equation of
VAN DER Waats where a and #6 are taken as unchangeable but
which belongs to the equation into which this changes when a and
4 are taken as functions of temperature and volume. Thus when
shifting the variable or corrected isotherms (cf. N°. 66 § 3 end) in
place of the original constant one a similar ridge as that which
we have considered would also be always formed, though the suc-
cessive isotherms are no longer equal and similar, but show a small
continuous change with temperature. In this way one cannot escape
the conclusion that metastable states occur at the side of the solid
state between solid and gas.

The observed part of the isotherm on the vapour side for tempe-
ratures far below the furthest limit of the observed undercooling of
liquid does not extend beyond the sublimation line. Still from ana-
logy with what is known for vapour at higher temperatures, it must
be assumed until the contrary is proved, that the Grsss’ surface extends
inside the sublimation line to metastable and even to labile equili-

ae
|
|
|
|

( 681 )

bria, not in principle different from those given by van per Waats’
theory. And very clear and special evidence must be brought forward
(which is not the case (cf. § 2)) to show that the two above men-
tioned parts of an isotherm must not be united.

Now, (cf. fig. 4) for a
substance which exists in
the liquid and solid states,
call cd and ef the portions
of the connodal of the liquid
and solid ridges, gh and ih:
portions of isotherms on the
liquid and solid ridges. It is
clear that ¢ and h may be
joined by a continuous line.

For the formation of two
ridges it is clearly only neces-
sary, that two isotherms g’h’, i’k’, should incline to the v-axis very
strongly, but still not differ much from the two preceding isotherms
gh, ik, and also that A’v’, hi should not differ much. With such
small variations resulting from the above mentioned controlled changes
of the isotherms with the temperature on the Gisss’ surface, we are very
familiar since the a and 6 of van per Waats are taken as temperature
functions. The difference between 7k and. the isotherm g/ is analogous
to the difference between the true empirical isotherm g/ and the simplest
form of isotherm given by van per Waats who has long shown
that 6 must necessarily be a volume function. The portion /z alone
appears tou have received a somewhat greater change which we may
ascribe to a further change of 6*) with the volume.

With this explanation of the cause for the displacement of the
isotherm on the Gisss’ surface we do not come into collision with
the assumptions of vAN DER WaAAaLs, who assumes that ) undergoes
a change in the fluid state owing to the compression of the molecule.
We thus only specify the possibility of a yet further change of the
same sort, which finally produces a new equilibrium between 4
and v in the solid state. Beforehand there can be no question of
explaining the solid state by referring it to the same processes as
those which exist in the liquid state. This can only be done when
the relation of the elasticity for instantaneous changes of volume and
the time of relaxation for the liquid and solid states are worked out

1) We use the a and 2 of van per Waats in the most general manner given
by this physicist.

( 682 )

and the great change of the time of relaxation with the above men-
tioned further change of 6 at the transformation from solid to liquid
is explained on the same grounds. Still keeping this in view we may
say that by prolonging the line /z till it reaches the solid state we
have given what van per Waats calls the equation of state of the
molecule.

Now it follows immediately from this representation that the form
of the connecting line 4z must be taken as dependent upon the tem-
perature and the inflection as decreasing and finally vanishing with
rising temperature. Thus the above consideration of the form of the
liquid ridge on the Grsss’ surface necessitates the assumption that the -
solid can be joined to the liquid ridge by a plait. This will be gene-
rally perpendicular to the v-axis and will end in a plaitpoint i.e. this
indicates the continuity of the gaseous and solid states of aggregation.

With these considerations we have not treated the question whether
the conditions in the plait which we assume to exist in the gap
between the two states of aggregation (c.f. § 2 for outside the plait)
are also conditions of equilibrium, labile or otherwise. We have
advanced no reason for this. This is as far as we know not done
by others either who have assumed the existence of similar condi-
tions *). In considering the vapour, we stated that there have not
been observed metastable states connecting the solid with the gaseous
and liquid states. However these appear very clearly and markedly
between the gaseous and liquid states, and have an important bearing
in the theory of vaN pur WAALS.

Also it is not unlikely that van per Waats has never in his
writings treated the continuity of the gaseous and solid states, and
has expressly kept it in the background, because the use of such
intermediate states as those above considered is only allowed theo-
retically when it is shown as VAN DER Waats did for the inter-
mediate vapour-liquid states — that these intermediate states may be
treated as conditions of equilibrium. However we do not propose to
determine “the molecular equation of state’ from a given mechanism,
but to seek for an empirical form for this from the known facts by
induction. In this case we must use the most obvious analogies as
indications and it is not allowed to deviate from the most simple
suppositions without proving each step. With variable molecules it
is probable that relations between entropy and volume can exist
other than those which van per Waats has already treated in
his equation of state based on the theory of cyclic motion. In order

1) See especially Ostwatp, Textbook of general chemistry.

te.)

( 683 )

to be able to fix a meaning for some of the conditions which according
to this possibility are suggested by us, we must suppose that the material
can suffer stresses with imponderable as well as with ponderable
mechanism. Thus we may obtain actual values for 9 as well as for v
at which we can keep the material homogeneous which in reality
would be impossible. No difficulty should arise if we in addition to
general assumptions suppose that the entropy can be kept constant.
We only extend to the imponderable mechanism what is generally
allowed for the ponderable, when one supposes the substance kept
homogeneous with constant volume in VAN DER WAALS labile conditions.

We have thus in the following set ourselves to model the parts
of the Grsps’ surface which are experimentally known, for substances
which exist in the solid state, to add to these portions the vapour
and liquid regions following vAN per Waats, and to combine the
region thus obtained with the solid ridge in such a manner that the
isotherms on the Gusss’ surface shall differ as little as possible from
the wnchanged isotherm of van per Waats, and the course of the
isotherm in the y v projection shall be as simple as possible. We have
e.g. excluded states on the surface where 7'’= 0 except at 7 = —
and have supposed that for every value of 7 and v only one value
of ¢ belongs.

It is clear that the problem formulated thus does not extend further
than the search for a continuous function, which for a known range
coincides with the Grsps’ surface and satisfies a given — but phy-
sically we hope happily chosen — criterion of simplicity. The solution
obtained from this determination has a certain value and forms a
continuation of the investigation of Comm. Nos. 71 and 74°), the
development of the equation of state in series.

There also the principal object was to produce a numerically correct
combination of the experiments independent of the thermodynamic
peculiarities of the substances treated. The solid state was at first not
considered in order to avoid a too large field. With this limitation
it appeared that the whole range of experiment for normal substances
could be expressed by a series condensed to a polynomial in powers of

1
e so that we could find exact valnes for p, for 4 = =|z —dv, for

= ef Te — r) (and other quantities e.g. w= — | pdv) for all

states within the region considered, without tedious calculations.

1) KameruineH Onnes. Ueber die Reihenentwickelung fiir die Zustandsgleichung
der Gase und Fliissigkeiten, Livre jubil. Bosscua Archives Néerl. (II) T, VI p. 874—
888, ‘01. Leiden Comm. n°. 74.

( 684 )

The extension of this idea to associated substances was necessarily
excluded since the law of corresponding states was taken as the
basis of the development. The existence of a maximum density for
water need then bring no difficulty for the representation of the

qo —Teenittd state in the consideration that in general p, and thus 7 also,

é 1
is given along an isotherm by powers of —. The question, if the
v

connection between 7 and v, which follows from the mechanism of
the liquid or gaseous states, can in general be given by expressing

1
7 in powers of —, could be left out of account. Now that we wish
Vv

to introduce the solid state into the polynomial — until now not used,
but after some change perhaps applicable for this purpose — we meet
the difficulty that with many substances solidification is accompanied
with increase of volume. For water, which falls in this case, the
question is treated more fully in §§3 and 4. Still if this case could not,
as we have supposed, be explained by association, and if in general
the complete knowledge of the mechanism of the solid state for the
isotherms of gas, liquid and solid leads to an implicit relation between
7 and v, still for one part of the range of it will be possible to
express this directly by one value in terms of v. It appears to us
to be quite possible that with certain normal substances p can be

1
empirically expressed in powers of — over the whole range under
v

consideration.

The Gippss’ surface, which we have constructed for this first class
of substances, will serve to give not improbable corresponding values
of p and v for an isotherm in the liquid-solid plait, and to permit

computation of useful values for the virial coefficients — the coeffi-
cients in a polynomial
BS oe,
les se Reape ete Perc a, tw, 6 Pia.) We

If we seek for the values which these coefficients can have, we
find a second connection between this investigation and Comms
Nos. 71 and 74. In both of these it is shown that values will be
found for the reduced virial coefficients of different substances, which
are sufficiently, but still not quite, equal. These differences in B @
ete. will just give the deviations of the various substances from the
law of corresponding states. They express parts of the molecular
interaction which cannot be explained or represented by the actions
of homologous points which last actions are those whose mechanical

( 685 )

similarity results in the law of corresponding states. The various
substances certainly differ widely in the solid state when they are
expressed with reduced coefficients. Thus the mechanical dissimilarity
of the actions of unhomologous points appears at once. When the
same isotherm passes through the gaseous liquid and solid states,
the higher coefficients of the polynomium must without doubt differ
considerably. It is thus to be expected that the lower coefficients,
will also exhibit certain but smaller differences, which are connected
with those in the higher coefficients. In this manner, in the compa-
rison of two substances, the deviations from the law of corresponding
states would be clearly connected with the solid properties of the
two given substances.

Further, as the virial coefficients give the deviations from the
BoyrLe Gay-Lussac law we may say that these deviatious do not only
express the properties of the liquid state as given by VAN DER WAALS
but also those of the solid state. Really a connection between the
deviations and the properties of the solid state is also implied in
VAN DER Waats’ last development of the equation of state after the
method of cyclic motion.

§ 2. The best possible connection of the known part of the solid
with the liquid ridge by a continuous surface has some similarity with
the use of the continuous line by which J. THomson connected the
liquid and gaseous states found by Anprews. Still there remains a
marked difference. THomson could start from the existence of a cri-
tical point. A continuous change from the solid to the liquid state
is not experimentally proved, it is doubted by some and as to the
crystalline modification it is directly contradicted by Tammany. If
TamMann’s theoretical considerations were correct, then it would already
be clear that we had produced only a simple empirical interpolation
when we intended to have constructed a group of intermediate states
which beforehand would be at least probable on physical grounds.

TamMMANN’s objections are certainly not conclusive. They rest in
the same way as our assumptions on extrapolations outside the
experimental region, and it appears that our extrapolation is more
probable than his. Also Tammann’s combination of the fusionline of
water, an associating substance, with that of other substances as if
they were two cases which could pass one into the other by change
of temperature and pressure, presents some important difficulties. We
have not to consider these conclusions so long as we exclude asso-
ciated substances and substances of perhaps very complicated character.
Instead of giving immediately a general treatment of cases so

( 686 )

different in principle, we confine ourselves to the simplest group
of substances.

For these we have constructed the representation which we shall
further develop in the following.

In agreement with TamMMANN, we also assume, although under-
cooling only occurs to a limited extent, that the liquid ridge
continues to very low temperatures (at first we may assume to the
absolute zero) states with increasing times of relaxation up to the
glass condition being encountered in passing over the ridge towards
decreasing temperature. Thus we do not come into collision with the
observations. Still we do not mean that it is quite impossible for
crystalline properties to be found on the glassy ridge e.g. at very low
temperatures. Further we do not suppose that the existence of one
such a ridge would exclude the possibility of other amorphous condi-
tions where other equilibrium relations between entropy and volume
could equally be found. Moreover it is highly doubtful if the term
amorphous does not include very various structures in the solid state,
so that it is certainly not necessary that an amorphous condition
should be present on the ridge where liquid would be found at a
higher temperature. As to the crystalline ridge, our whole represen-
tation makes it appear more probable to us, that the crystalline
ridge in the simplest case should run next to the liquid ridge down
to very low temperatures, than that it should follow Tammann’s ring
shaped form (c. f. § 4).

The process of transformation from the crystalline to the gaseous
(below the liquid-gas critical temperature, liquid) state does not at all
disagree with the usual assumptions concerning the molecular forces,
but is immediately to. be deduced from them. A very satisfactory
agreement with the suppositions would be obtained when the charac-
teristic difference between two ridges appeared to result from the
differences of density and entropy (specitic heat) of the modifications,
the crystalline or amorphous form taken by each of these modifications
being thermodynamically of secondary importance, so that for a first
investigation they would not come into account in comparison with
the change of properties of the solid phase due to differences of
density and entropy.

However it may be, we must certainly assume that the crystalline
form will result from the molecules being by choice oriented and
arranged in a given manner owing to the forces from the not
corresponding points. The directing and arranging forces will then
be different for different densities and entropies, whence the most
probably occurring orientation and arrangement will be different

hb! death

( 687 )

for different densities and entropies and the crystal form will be
different for various modifications.

The increase of the vibration energy will gradually efface the
mean predominant most probable distribution and orientation as the
crystal is raised in temperature and although the whole continually
approaches a uniform mean distribution and orientation still some
different groups will remain in arrangements of most probable predo-
minant distribution and orientation. In particular if this hypothesis
is applied to the case of a gaseous and a solid phase in equili-
brium which are brought together to a higher temperature, fresh
hypotheses must be made to render it clear that no identity of the
two phases can become possible and therefore no continuity of solid
and gaseous states will be found. Of course it does not matter if
the temperature under consideration is above the liquid-gas critical
point. Further there is no reason known why it should not be
allowed to extend the double convex part of the Gisss’ surface, —
containing essentially states of equilibrium, to higher temperatures and
pressures, so that it surrounds the critical point at the end of the plait.

Is is quite in harmony with our assumptions of § 1 that, in the
gaseous phase of a substance occurring also as solid, molecular groups
will at all times be found (produced always from different indivi-
duals) in which the particular attraction between not equivalent
points '), predominating in the solid state, will also be manifest.
Below a certain temperature it will then be necessary to momenta-
rily consider certain portions of the gas as crystalline. We are here
only following the method employed by Bottzmann for the deter-
mination of the equilibrium distribution, which is the most probable.
We apply it to a given density and velocity distribution but also
extend it to orientation and arrangement.

We have mentioned above the existence of more ridges which
appear successively on the Gusps’ surface towards the side of
diminishing volume. This case appears to us to be the normal one.
It is probable that the various solid modifications are not known for
most substances. If we further consider that a small change in the
course of the isotherms can cause one ridge to rise above another and
thus to represent more stable phases or not, it is not at all probable that
just those modifications of the various substances are known, which
belong to corresponding ridges. It is therefore, possible that in the solid
state the various substances would differ less than now appears to be
the case if one were acquainted with all their modifications; finally the

1) Comp. Retneanum, Drudes Annalen. 1903. 10 p. 334,

( 688 )

possibility remains that more liquid ridges could exist along which with
falling temperature the time of relaxation would not increase to the
value required for the solid state, while states of equilibrium between
the two are to be expected, so that the same substance could exist
in two liquid modifications.

The reasons why such a case is not known and why the various
solid modifications are usually crystalline, must be further explained
by a theory of the solid state.

§ 3. Following the lines developed we have constructed three
models of Gipss’ surfaces.

We have first considered an imaginary substance, which partially
‘corresponds with carbon dioxide, in the liquid state is in harmony
with vAN DER WAALS’ original equation, and which further can exist
in one solid (crystalline) modification. For the Gress’ surface of this
substance constructed according to our ideas, we have only considered
that portion where the fusion line of the substance is to be found.
This model serves principaliy to present clearly the views on the
solid state advanced in this communication.

Having assumed that we can express the character of the
peculiarities in the transition from solid to liquid by this model,
we have further constructed two others, which refer to the actual
CO, and on which all known thermodynamical properties are
expressed as numerically exact as possible.

One of the models represents the whole surface for CO, with the
exception of the portions for the ideal gas state and for very low
temperatures.

The second gives, on a necessarily larger scale, the region where the
transition occurs between the various modifcations with small volumes.

Finally another model has been formed which demonstrates
sufficiently, that taking it in general, a substance like water can be
represented in the manner followed by us. We mean that the
deviations which this substance exhibits can be brought into line

with the association. In general a liquid ridge which

: corresponded sufficiently with the vAN prR WAALS
, i equation of state, would be pressed upwards and

i towards decreasing volume by the association. This

7
1% i transformation is represented schematically in the y v
aaa projection by fig. 5. To the right lies the undisturbed
Pay a VAN pDrER Waats ridge, given by the portion where
nent

the connodal liquid-vapour, the curve drawn, runs
Fig. 9. to the left, the twisted ridge is again given by the

tl tt ae eS re Ns

( 689 )

altered portion, the two portions of the connodal solid-vapour are
again drawn (unfortunately the altered connection is omitted in the
figure). At m lies the maximum density of water under its own
vapour pressure. The preliminary model made by us serves to show,
that the most notable properties of H, O will be correctly given if
we consider the ice ridge as an ordinary solid ridge on the surface, and
the liquid ridge as changed by the last mentioned process owing to the
association.

We hope shortly to obtain models which will exhibit the trans-
formation of the different modifications or allotropic states as well as
the peculiarities of the expansion phenomena. In this way we hope
to contribute to a somewhat better insight, at least to a_ better
survey, of the thermodynamical character of the different substances.
However in addition to the questions relating to association there
are others, which have reference to mixtures, saturated solutions
etc., and which would necessitate a long investigation. We hence
think that the results now obtained from a sufficiently independent
whole to be published.

We have thus in the above made the meaning of our work
clear and can now proceed to describe the models somewhat more
fully and to show that the experimental data can really be obtained
on these surfaces.

I. THE SOLID-LIQUID PLAIT ON THE GIBBS’ SURFACE.
(Representation of the continuity of the solid and gaseous states).

The specific heat of the imaginary substance in the gaseous state
has been assumed to be equal to half that of liquid carbon dioxide:
the specific heat in the solid state as equal to that which is found
by employing Nreumann’s law. Also the substance obeys the VAN DER
Waals equation of state for carbon dioxide in the liquid and gaseous
States. It appeared useful to give for this model (pl. Il, fig. 1) front
and side elevations and plan (pl. III fig. 1, 2, 3, 4) with the lines
7 = const., v = const., 7’= const. (dashed lines) p = const. (dotted
lines), for which the drawings are sufficiently explanatory. The con-
nodal fluid (gas)-solid is drawn on this model and the coexisting
states joined by steel wires.

The principal difference between our representation and TAMMANN’s
is very clearly seen on comparing the plan (pl. II fig. 2) with his
figure (Drupe’s Ann. 3 p. 190).

This model is also useful for a comparison of our idea with the
well known scheme given by Maxwext (Theory of Heat, p. 207)

( 690 )

our plan is easily compared with the latter for the small volume
part. To find how our vapour plait will be connected with this
portion, it is only necessary to use pl. III fig. 2. The chief difference
is seen in the different forms of the spinodal line. Ours is given
by the dot-dash line of fig.6 and Maxwsrt1’s in fig. 7. Ours consists
of two portions which remain apart to the lowest temperature

WY Z
2, Z
Z Z
LYb- Z BZ
Z
Zz
Fig. 6. ied.

(T=0), while Maxwet.’s shows only a secondary loop. Quite
improbable are MAxweEtt’s isotherms. They show in the vapour plait
a point of inflection in the isotherms. Thereby they differ entirely
from the equation of state of vAN DER WaAatLs, which is certainly
qualitatively correct for vapour and liquid.
II. Tur Gipps’ suRFACE FOR CQ,.
(The general model).
This model was constructed by the help of the empirical equation

of state given in Comms. Nos. 71 and 74 with the assistance of the
thermody namical i mulae ore in No. 66.

E&yT — €K =f ars flag sa) (cz -*) dv
: dp
wr w= fee fi) ft)

whence
oats 6,+26,+ 46, peo c, +2¢,+ 4c
e=c¢,,(l — Ty) — pe s a == 5 ae ae

b, ie = 4—
perv % +2b,+ 40D, Pk t i
et v a

2 v? 2° )

,
|

( 691 )
yf Vics UE: A amv Ik UE {s —t,—3 "h
| ae epl— Sin ta ——. |- at a - — a =) ee
Ty; Dy th, OE iy 2?
os Pk Vk c, —¢, —3¢, a Pk Uk Pape d, — 32,
2 Tp he 4T;, 25
& c ac
Pk Uk ti —k, an es Pk Uk hae 3 - LiF ae
ae Fe aN Ce oor eS Q)

As specific heat ¢, in the ideal gas state we have taken
0,17.419.10° — 71,2 * 10°"), and it is considered constant. For the
critical constants we have used

qr
== -304,5") pp — 13 1014 10F = T40.10° ———

em sec? .

from the experiments of AmaGcaT and

1, = 2.20 —— from the experiments of Kurnen and Rosson ’)
yk a7

cm
deduced by the law of the rectilinear diameter.
The assumed critical values give:
2 = 0,001044.
With (1) and (2) have been calculated
a) five points belonging to the ideal gas state, where v, is taken
as 180:
fy for £:==.0:40 By is 200
y = 43,1><105
s== sOU 10"
2. for ‘ = 0.60 aj == 180
mec te8 C10

= == 46 « 10°
en lor f= O68 vy = 180

ap a See OE

& =645610!
AD (os ee i — 180

yn == 108 >< 10°
Re Be ei

oe sort == 118 vy — 180
a == 1205
heey Wy pore | 91,

b) two points on the gaseous branch of the connodal line for which
KvurENEN and Rosson (loc cit) have given the values of 7 and v

1) Sufficiently near the value given by REGNAULT.
2) Kuenen and Rosson, Phil. Mag. 6 p. 149, 1902.

46
Proceedings Royal Acad. Amsterdam. Vol. VI.

o>) for w= O24 i 74
a) $= ba Sa .
E> = 61a 1"
1 dor == 4008 v= 119
Ber 10 Sot
Be =e, KE:

The first of these belong to the triple-point gas-liquid-solid.

c.) The points of the liquid state belonging to 6 and 7 are ealeu-
lated with the help of Kurnen and Rosson’s numbers for the heat of
vaporisation. We have found

6 1or £0 (14 Up = 0,85

4 —=— 10210:

€ = — 262 x«10'
9. for t = 0.68 vy == 0583

y =—122 «10:

é =— 304 x10!

In the same way taking into account the heat of fusion at the
triple point we find for a point belonging to the solid state.
1.0: forl t= OTIS “ar 3.068

S187 520
& —— 446 <10'
The model (see Pl. I! fig. 2) is constructed with
the values of v in ems —'/, of the above numerical values
1
” ” » WY, ”? —— sarge aersy Os ” ” 9
10°
1
” ” » & 5; » ==, 9108” 9 ” ” ”

According to TamMann two solid modifications of CO, exist so that
we must add two solid ridges (see Pl. II fig. 2) in addition to the
liquid ridge. We have assumed that Tammann’s 2"¢ modification lies
between the fluid state and the first modification, and we call TAMMANN’S
2>¢ modification A and his first £. The reason why we have assumed
this arrangement between the two solid modifications is the following :
TamMANN ') has determined the fusion line for the modification A as
well as for &, and also the transition line for the second modification.

dp
He found (see PI. I fig. 1) that the values of are greatest for the points
a

on the equilibrium line c, smallest for the fusion line a@ of the modi-
fication A and found between the two another locus for the fusion
line of the modification £. The same is also to be obtained from our

1) Tammany, Ann. Phys. u. Chemie 1899 Bd. 68 pg. 553.

( 693 )

model with the position of the ridges chosen, while it is at the same
time easy to see that by another arrangement the “3 for the three
lines will not agree so well either with TamMann’s values or with
our desire to make the course of the temperature line the simplest
possible. We hence consider that the arrangement of the ridges which
we have chosen agrees with the experiments and that thus the specific
volume of the modification A is larger than that of JB.

On this model the binodal for the liquid and gaseous condition
(line GL) is shown and also the gas branch of the binodal for the
gaseous state and the modification 6 (line GLz). The three points
belonging to the triple-point gas-liquid-solid 6 are joined two and
two by steel wires. The dashed line which passes through these
points is the isotherm of the triple-point, and close to this runs the
critical isotherm. The dotted line is the pressure line of the triple-
point. According to TAmMann’s values the solid phase of this triple-
point belongs to the modification 6, while the ridge of the A modi-
fication (see Pl. II fig. 5) lies below the fundamental plane of the
triple-point determined by Kurnen and Rosson. A tangent plane that
touches at more than three points, cannot be placed on our model
which is in agreement with the phase rule. In addition to the just
mentioned triple-point the existence of two others on our model, the
triple-point gas-liquid-solid A and the triple-point liquid with the two
solid modifications A and £ is rendered probable by TamMann’s
experiments.

On comparing our model with one constructed after the equation
of vAN DER WAALS, one sees that on ours the liquid ridge rises
more steeply from the critical temperature to the lower temperatures.
It hence follows that the specific heat of the liquid is too small on
the model after van pier Waats. The slow rise of the liquid ridge
in the latter has also the result that the heat of vaporisation is
too small.

Ill. THe Gress’ surFace ror CO, AT GREATER DENSITIES.

(Detail model of the liquid and solid states).

For the general model the specific heat at constant volume was
assumed to be constant in the ideal gas state. But for the construction
of the detail model, to be now described, we have been obliged to
consider the variability of c,. RecNautt and E. Wiepremann have
measured c, for CO, at one atmosphere pressure and various tempe-
ratures, and have expressed the change with 7’ by empirical formulae.

46*

( 694 )

The results of the two investigators agree well. If one seeks from
the empirical equation of state for 0°0 C. the correction which must
be made on c at one atmosphere to reduce it to the ideal state,
one finds 0.003 cal., which quantity lies within the limit of experi-
mental error. The correction is still smaller for higher temperatures.
We also find that the correction, which is necessary to reduce the
specific heat c, of aether found by E. WiepEemann to the ideal state,
is too small to come into account. The formulae given by Reenacit
and E. Wirprmann for the specific heat of gases and vapours are
thus applicable to the ideal state at least with close approximation.
Hence Lepvc’s contention’) is refuted that for substances which obey
to the law of corresponding states both c, and c, are constant in the ideal
gas state. From the experimental values of c, and the well known

R
relation c,—c, —=—, we can calculate the value of c, and its variation
m7

with the temperature.

Having found c, in this manner we calculated the corrections
which must be made to the equations (1) and (2) due to the variation
of c,. We find the following new values for the points on the liquid
branch at t=0.714 and t=—0.68 and for the solid phase at the
triple-point

points of the liquid state
Pion f= "O08 wear O88

4 == — 117><10°
——_ 286 10'
lh fort) "6714-0 0,85
y—=— 96105
& — — 245><10"

point of the solid state
If. for’ t'== @ 714-4 =— 0.676
4 = — 18010*
é = — 42010"

Now we must investigate the liquid range for higher pressures
more exactly and in the first place determine c,. This follows from
the formula

1) Lepuc, Recherches sur les gaz. Paris 1898 and 99.

( 695 )

by introducing the value of p from the empirical equation of state,
this gives

_ Lepe( PD mw LPR (mu) LPO (rx
it a Ray a geo ay dt? \ Fp rays ee

ede fo \' ay (eX? |
rag ae c) 3 ae (eb
for £ = 0.897 or’ 2 = 273 and v = 1,020 we find
6. ep = 0.0432
or, since at T —273' cyp— 0.1431 is
€3, = 01863
The point corresponding to v=1.02 and t=1 in the liquid
region is now found. This was obtained by the aid of the equations 1)
and 2) where the term ® must be certainly taken into account;

we find
lV. fort=1 yy = 1.020
y= 717T,,=— 42.10 *& 10°
e= 87, = — bia S16?

If we now assume that at the same temperature the difference
between the specific heats at constant volume in the ideal gas state
and for the volume 1.020, is constant and equal to £, we have

R
é—éT, = | ep dT — (= a t) (2-1: J,
rh
c k L
ol ey EAR (Biel: gees a | ee
ko T m Ty,
Tk

with which the following points for v= 1.020 are calculated:
V. for t=0.864 v, = 1.020

7 = jae ctor

e ——145x<10'
Nig sor e== bate oy, — 1-020

4 —— 28X<10*

€ ——33X10'

According to the numbers of KuENEN and Rosson the first of these
two points lies on the liquid branch of the binodal line.
The model Pl. II fig. 3 is constructed from the values for these

points.
The values of v used are 100 times the calculated
a Le tate dee i eee MOT wheal 652 4
Ere etn she! BO" ie ee is

( 696 )

Further, care has been taken to give the tangent plane the proper

inclination at these points in agreement with
"|

dg 0g
ome as ge ime yaw that temperature and pressure shall

have their real value.
On the given drawings (scale ‘/, of model) for plan and elevation

Pl. Ill, fig. 5 and 6 — one side elevation has been rejected as it
does not clearly show the course of the pressure and temperature
line — the behaviour of the line 7’ = const, p= const, v = const,

4 =—const and the position of the triple point can be seen without
further explanation. We draw attention to the intersection of the connodal
line S4 Sp by the connodal line S; Sg and further to the passage
of the isotherms over the connodal line and the crossing of the
isotherms with their corresponding isopiestics. In order to read from
the isotherms, given on the model, the corresponding values of p
and v, the diagram of the isotherms (see PI. I, fig. 2) was constructed,
which reminds one of the course of the isotherms derived from the
VAN DER Waats’ equation. The point 7, in this figure corresponds
to the triple point for liquid and the two solid modifications of
earbon dioxide. According to Tammann the pressure is 2800 K.G.
The point ALS, is the critical point of the modification A in the fusion
line. According to the model the critical pressure would be 6500 K.G.
and the reduced temperature 1.7,

The critical point GZ occurs so far to the right on this scale
(the unit of volume is equal to that of Pl. HI fig. 5 and 6) that it
cannot be represented in the drawing.

No critical pomt exists for the transition of Sg to LZ owing to
the interposition of the ridge S4. The binodal line on Sg and Z,
loses its physical meaning at a given position of the rolling tangent
plane. A continuous passage from Sz to S7z, is only possible through
the gaseous as an intermediate state.

An important result can be obtained from the foregoing. Whenever
substances exist whose molecules undergo changes in the transition
to the solid state, which are mechanically similar to those which
determine the condition of the two phases, these said substances
will also agree with the law of corresponding states in the solid
condition. An experimental investigation for the continuity of the

solid and gaseous states would be best made on the substance with —

the lowest critical pressure. If, for the moment, we assume that AH, and
CO, are sufficiently comparable from this point of view — at present
no better example is at hand —- the eritical point solid-gas should
be sought at about 1800 atm. and —210°C., and thus in possible

( 697 )

experimental pressure and temperature ranges. For many years a
similar investigation has stood on the program of the Leiden Labo-
ratory.

IV. Tae Gipss’ surrack FoR H,O vor GREAT DENSITIES.
(Model for the equilibrium of TamMann’s ice varieties and water).

The Greps’ surface suffers a deformation from association in the
case of water, and the general character of the change has been
already given in § 3 according to our views. Having once arrived
at a given idea about the general form, we can more exactly deter-
mine the form to be ascribed to the ridges according to this idea
by the help of the experimental numbers. The model that we have
obtained by our method is shown on Pl. I fig. 4. As Tammann has
already indicated, two other ice varieties (ice II and ice III) are
found, in addition to ordinary ice (ice 1). The general position of
the ridges belonging to these values follows from TAMMANN’s measu-
rements concerning the volume change and heat of transformation
for the transition of one ice variety into another or into water. If
we give the value O to the last and 1, 2 and 3 to the three ice
varieties, TAMMANN finds at 7’ = 251 (triplepoint water — ice J — ice LI)

Ay t= O44

Av,,; = — 0.05

Av,, = + 0.193
’,, = — 73 cal.
P= 10K 5
m=t+ 3

Also TamMANN finds that Av,, is very nearly equal to Av,,. We
have assumed that Av,, 1s somewhat greater than Av,,. We then
find the general arrangement given in Pl. IV fig. 1 for the water
and three ice varieties. The dashed line gives the isotherm through
the triple point water — ice | — ice III, the dotted line the isopiestic.

We have not taken these from pl. II, fig. 4, where no isotherms

or isopiestics are drawn, because this figure is not sufficiently worked
out for this purpose. We have drawn on Pl. IV. schematic figures
in order that they may be used in continual comparison with the
surface, whenever we wish to further explain the properties of the

-surface. From these we can show easily that they agree with the

model of Pl. II, fig. 4.
We now further specify our ideas for the modification O and 1.

Here = is negative for points on the binodal line, and this also

( 698 )

follows from the modei. In fig. 2 Pl. IV, let AA’ and BB' be a
pair of coexisting phases. A higher temperature belongs to AA’ than
to BB', while the pressure at AA’ is greater than that at BB’. If
we extend the fusion line of ice in the direction of falling pressure,

Ree . é. 4p
it is probable that for a given negative value of p, would change

dt
; , a ., op
its sign and become positive. Those phases for which ao 0 would

be determined by DD', LE’ and FF". The critical point water-ice I
would be found at G and would therefore present a negative value.
Poyntinc ') came to the same conclusion in a different way. A second
critical point at positive pressure, which is deduced by Poyntine
and also by Pranck’*) by linear extrapolation of the variation of
the latent heat of fusion, which is also given by us, becomes
impossible by the appearing of the other ice varieties, which we will
describe now. If we assume, returning to AA’, that by rolling the
common tangent plane to ('C’ in the direction towards 55’ on the
water and ice J ridge, we should also touch the ridge ice J//

dp ue
at '. Then = would be positive for water and ice ///, in agreement
dt

with TAmMann’s measurements. If now we suppose that ice //J is
non-existent, we may prolong the binodal line AC’ A’ C" to a little
over CC' which gives us continually lower temperatures and higher
pressures. For a given position the tangent plane will now also touch the
ice II ridge. Hence we obtain a lower temperature 7’, for this triple
point than for the triple point water —ice I— ice HI, while the pressure

is higher for 7, than for 7. This is also in agreement with TAMMANN’s

_ dp
results. In the same way for water — ice III and water — ice II is —- >.
t

According to our model the fusion curve of ice II has a termination
at higher pressures and temperatures and therefore we have assumed
that a critical point water — ice II exists.

Now we consider further the transformation line ice I to ice IL.
According to TamMann the heat of transformation from ice I to ice LL
is positive in the neighbourhood of the critical point 7’= 251° and
at lower temperatures negative. In order to be in agreement with
this, the ice I ridge has been given a strong curvature and the ice Il
ridge a weak (see fig. 3 Pl. IV where the elevation of the ridges
from the side of the ye plane is shown). Hence the course of the

1) Poyntine Phil. Mag. (5). 12. 1881.

2) Puancx. Wied. Ann. Bd. 15 p. 460, 1882.

H HAPPEL The representation of
d and gaseous conditions on the one

tions on the other by the
1g am

H. KAMERLINGH ONNES and
the continuity of the liqui
hand and the various solid aggrega

entropy-volume-energy surface of Gibbs.

? Co
fe ¢

fig. 2

Proceedings Royal Acad. Amsterdam. Vol. VI.

( 699 )
binodal curve is given by the line drawn in fig. 4 Pl. LV. It is easy
Ip : Ip
to see that now . < 0 at the triple point 251° and > O at lower
€ C

temperatures. The transformation line has thus the course drawn in
fig. 5 Pl. IV, which qualitatively is in complete agreement with
TamMANn’s determinations for this line.

The transformation line from ice I to ice Il is very similar to
that from ice I to ice III. Since the ice II ridge distinctly rises more
steeply than the ice Ill ridge the line of transformation from ice |]
to ice II is more curved than that for ice I to ice LI. The result
is that the line of transformation from ice I to ice II cuts, above
the absolute zero, the vapour pressure line of ice I, which runs very
close to the Z-axis (see fig. 6 Pl. IV). A triple point vapour
— ice I — ice II corresponds with this common point, this has not
been observed, but TamMann holds its existence as probable. Also the
transformation curve from ice I to ice Hl (Pl IV fig. 5) when
produced cuts the Z-axis. The common point then corresponds to a
negative temperature, and thus this triple point cannot be realised.

The curve of transformation from ice II to ice III was not deter-
mined by Tammany, but its course can be seen on our model.

From the model it follows that Tammann could obtain ice II by
cooling to — 80° C., while less cooling would be sufficient for ice III.

Owing to the form which we have chosen for the liquid ridge,
the expansion coefficient of water near 0° C. would be negative and
water would show a maximum density, while the expansion coeffi-
cient of ice would be positive, all in agreement with experiment.
The pressure lines for water (see fig. 7 Pl. IV) run in accordance
with this (at least near 0°) from larger to smaller value of v, and
simultaneously from lower to higher temperatures. The maximum
density of water, on our model, is shifted by increase of pressure
towards decreasing temperature, while at the same time it becomes
less marked and finally vanishes; also in agreement with experiment. *)

1) Amacat. Recherches sur les gaz.
v. p. Waats. Arch. Néerl. Vol. XII. p. 457.
Grassi. Ann. d. chim. 3. 31, p. 437. 1851.

( 700.)

Chemistry. — “On ocimene”. By Prof. P. van Rompurcu. (Com-
municated by Prof. C. A. Lopry pre Broyy).

(Communicated in the meeting of February 27, 1904).

At the December meeting 1900, I had the honour to submit to
the Academy a communication on the essential oil from an Ocimum
Basilicum L. which contains besides a large quantity of eugenol, a
hydrocarbon of the formula C,,H,, to which I gave the name of
Ocimene. The peculiar behaviour of that hydrocarbon reminded me
of the olefinic terpenes, discovered by Semmirr, of which myrcene,
isolated by Powrr and Kirper, was the best known. Ocimene,
however, did not appear to be identical with myrcene.

CHapman') has shown some time ago that the essential oil of hops
contains 40—50 °/, of an olefinic terpene which he considers to be
identical with myrcene. In his paper, CHapmMan disagrees with my
observation that myrcene is noi so changeable as stated by Powsrr
and Kisser. According to these investigators this substance becomes
polymerised after standing for a week, whereas I could preserve it
for months, of course in a properly sealed bottle. Cuapman refers to
a paper of Harries”) to show the unstability of myrcene. There we
read, however, only that the polymerisation “sehr leicht zu bewirken
ist durch langeres Stehen oder durch mehrstiindiges Erhitzen auf
300°”, whilst SemmieR*), in accordance with my observations, says
that he found it to be ‘‘iiberhaupt nicht so leicht veranderlich”.

The olefine terpene from hops has the power of absorbing oxygen,
like ocimene. In one of CHaApMAN’s experiments 16 cc. of oxygen
were absorbed in three days by 1 ce. of the terpene. I had already
found previously that myrcene does not absorb in the same time any
notable quantity (only fractions of a ce.) and, recently, on repeating
my experiments I found my previous observation confirmed. If,
however, myrcene was left in contact with oxygen for a long time
(in tubes 1.5 cm. in diameter) the volume of the gas began to de-
crease gradually, but with increasing velocity, so that after 16 days
30 ec. had been absorbed. Of a sample of ocimene which had been
kept in a properly sealed bottle for three years and had twice made
the journey to and from Java, 1 ec. absorbed 17.8 cc. of oxygen in
11 hours; in the case of this terpene I again noticed that after

1) Journ. of the Chem. Soc. Trans 1903. 83 p. 505.
2) Berl. Ber. 35 (1902). S. 3259.
5) Berl. Ber. 34 (1901). S, 3126.

( 701 )

oxidation had set in, the absorption proceeded more rapidly so that
on the second day, for instance, oxygen was being absorbed at the
rate of 2 cc. per hour.

Still, I should not feel justified in saying that hops-terpene and
myrcene are not identical, merely on account of the difference in
oxygen absorption, because further experiments have taught me that
under certain undefined conditions even this hydrocarbon may some-
times be left in contact with oxygen for a day without absorbing a
notable quantity’). But as soon as the absorption has commenced
it proceeds at a fairly rapid rate.

By the action of oxygen a colorless viscous substance is obtained.

I hope to refer to these experiments more fully later on.

In the same paper CHAPMAN expresses some doubts as to the
“chemical individuality” of ocimene. Although I have already pointed
out in my previous communication that the boiling point at 20 mm.,
the behaviour on distilling at the ordinary atmospheric pressure and
the index of refraction of ocimene and myrcene differ considerably,
I will now adduce additional facts which undoubtedly prove that
ocimene and myrcene are different compounds.

Mr. C. J. Enxnaar, who has taken up the study of ocimene in the
Utrecht laboratory, repeated in the first place the determination of
the index of refraction of this hydrocarbon and for a product care-
fully fractioned over metallic sodium he found np—1.4872 and
np = 1.4867, which values satisfactorily agree with 1.4861 previously
found by myself by means of another apparatus. For myrcene, Power
and Kreper have found np—1.4674 whilst I had, previously, found
1.4685.

SEMMLER (loc. cit.) has shown that myrcene is reduced by sodium
and aleohol to dihydro-myrcene. On applying this reaction to ocimene,
Mr. Enkiaar obtained a dihydro-ocimene, which not only differs
from dihydro-myrcene *) as regards boiling point, specific gravity
and index of refraction, but also by the fact that it yields with
bromine a crystallised additive compound. These investigations are
being continued.

1) Not improbably, traces of moisture or of products of oxidation exercise a
catalytic influence. A retardation was noticed when ocimene freshly distilled over
metallic sodium was placed in dry oxygen.

*) Dihydro-ocimene boils at 168° at 763 mm. At 21 mm. the boiling point is
65°. Sp. gr. at 15° 0.775. The boiling point of dihydro-myrcene is 171°.5—173°.5

at the ordinary pressure and its sp. gr. 0.7802,

( 702 )

Chemistry. — ‘Additive compounds of s. trinitrobenzene.” By Prof.
P. van RompurcH. (Communicated by Prof. C. A. Losry pr
BRUYN).

(Communicated in the meeting of February 27, 1904.)

A communication from Jackson and CLARKE') on additive com-
pounds of substituted nitrobenzenes and dimethylaniline and another
from Hissert and SupporouGH*) on. additive compounds of s. trini-
trobenzene and alkylated arylamines induces me to call attention to
the fact that I have been engaged for a long time with the study
of the additive compounds of m. dinitro- and s. trinitrobenzene. In
addition to those which I have described in former papers *) I have
prepared a large number of compounds with different aromatic amines
(such as toluidines, phenylendiamines, benzidine and their alkyl
derivatives) which will be fully described elsewhere as soon as the
crystallographic investigation of many of these products, kindly
undertaken by Dr. F. M. Jancur, has been concluded.

Besides with benzene and naphthalene‘), s. trinitrobenzene combines,
like picrie acid, with different aromatic hydrocarbons. It forms with
anthracene fine orange-red needles (m.p. 161°), with a methylanthracene
reddish colored needles (m.p. 138°), with phenanthrene an orange-
yellow compound (m.p. 168°)*) with jlworene a yellow compound.

In all these compounds we find that 1 mol. of s. trinitrobenzene
is combined with one mol. of the hydrocarbon.

s. Trinitrobenzene forms with a-bromonaphthalene a fine lemon-
yellow compound (m.p. 189°) and a similar one with dibenzylidene-
acetone.

Substituted aromatic amino-compounds such as anthranilic acid,
and its methylester, p. aminoacetophenone, ethyl m. and p. amino-
benzoate brought together with s. trinitrobenzene in alcoholic solution
readily form colored well-crystallised compounds, the first two of
which are colored orange and the others red. p. Aminobenzoie acid
combines less readily and I have not sueceeded in obtaining an
additive compound with m. aminobenzoie acid, which is a stronger
acid than its isomers.

Among the above compounds are some which will, presumably,
prove of importance in the hands of the micro-chemist for the
detection of certain substances.

1) Berl. Ber. 37, (1904), S. 177.

4) Journ. Chem. Soc. 83 p. 1334.

3) Rec. d. Trav. chim. d. Pays-Bas 6, 366; 7, 3, 228; 8, 274; 14, 69.

4) Hepp, Ann. d, Chemie 215, S. 376.

6) In the Dutch publication of this article, the melting point has been stated
incorrectly.

E703?)

Botany. — ‘Determination of the action of poisons on plants.” By
Prof. E. Verscuarrett. (Communicated by Profs. C. A. Losry
pE Bruyn and Hveo pe Vriszs.)

When a part of a living organ of a land-plant is placed in water
it usually absorbs water on account of the well-known osmotic
properties of the protoplasm and this absorption goes on until the
cell-walls allow of no further extension. The accompanying increase
in volume and the phenomena of tension in the tissue which may
result therefrom, have, since Huco pr Vriss laid the foundations of
the subject, given rise to many an investigation which it will be
superfluous to mention here again. Evidently this absorption of
water will also cause the weight of the fragment of tissue to increase
and it is easily understood that fairly considerable differences in
weight will arise as soon as the organ is somewhat rich in parenchym.

All this only happens however as long as the part of the plant
is alive. When a part of an organ that has been previously killed
is placed in water, no more water is absorbed; on the contrary,
since the semipermeability of the protoplasm has been destroyed,
the dissolved substances of the cell-sap diffuse out; with them part
of the water that stretches the cell-wall leaves the fragment of tissue,
and this latter diminishes in weight as well as in volume.

Hence it seems possible, by determining the changes in weight,
subsequent upon placing a plant-organ in water, to decide whether
this latter is alive or dead. If it turns out that no other cireum-
stances have a disturbing influence, we should have a new criterion
for determining the lethal limit of measurable external circumstances,
besides the diffusion of colouring matter at the death of plant-cells’),
used by Hugo pr Vrizs, and the non-appearance of the plasmolytic
phenomenon, recently applied by A. J. J. van pg Vexps?). In order
to test the practicableness of the method I tried to determine in
this way the toxic limit of a few substances and it seems to me
that this has been successful. Not every arbitrarily chosen plant-organ
can be expected to lend itself equally well for these experiments;
most of them proved serviceable, however, and as very fit for this
purpose I mention the potato-tuber, beetroot, fleshy leaves of Aloe,
juicy leaf-stalks like those of Begonia, Rheum and other plants.

One example may illustrate the proceeding and give an idea about
the observed differences in weight.

1) Arch. Néerl. VI, 1871.
*) Transactions of the four first Flemish Physical and Medical Congresses
(Dutch).

( 704 )

After a preliminary experiment had proved that the toxic limit
of CuSO, for potato lay below a concentration of 0,005 grammol.
per litre, four fragments of potato were dried with filtering-paper,
weighed, and placed in solutions of CuSO, containing:

a 0,001; 6 0,002; ¢ 0,003 and d 0,004 gr. mol.

The bits of potato weighed respectively :

a 3,715: 6'3,225- ¢ 2,860 and’ d°3,195"er.;

After having stayed in the solutions for 24 hours, they were
dried and weighed again, the results being:

a 4,620; 6 3,310; ¢ 2,895 and d 3,260 gr.

So they all had absorbed water; the toxic effect of the cupric
sulphate penetrating at the same time would now soon become
apparent, however. The bits were washed and placed in water from
the supply (water from the dunes); after 24 hours they weighed:

a. 4,670; 6. 3,350; c. 2,825 and d. 3,150 gr.

This time c. and d. had lost weight and this loss increased steadily
during the following day, whereas a and 6 went on absorbing water.
The toxic limit of CuSO, for bits of potato weighing 3—5 grammes
consequently lies, after 24 hours, between 0,002 and 0,003 grammol.
per litre, i.e. between 0,03 and 0,05 per cent (molecular weight of
Cu SO, = 159).

Henceforth a piece of tissue was considered undamaged if, after
having stayed in the poisonous solution for 24 hours and then for
another 48 hours in water (once or twice renewed), it had, at all
events, not lost weight, if it had not gained. It is obvious that in
these experiments only such organs can be used as will remain alive
for a fairly long time, when immersed in water. I can state concerning
potatoes, that normal fragments, placed in water which was daily
renewed, even after 18—20 days did not lose weight but absorbed
small quantities of water. It made no difference, at least within this
period of time, whether water from the supply or distilled water
was used. In all similar experiments the results obtained by weighing
are confirmed in a striking manner by the circumstance that bits of
potato, when they die off, turn dark-grey (conversion of tyrosine
into homogentisinic acid by enzyme-action). Also various other parts
of plants show some similar phenomenon which may serve as a
check, in tbe first place the diffusion of colouring matter, as with
red beetroot, Begonia and others.

In the manner described above, also the harmful limit of con-
centration may be determined of neutral mineral salts which in a
certain dilution are innocuous for a long time, but in more concen-

|
:
‘
3

( 705 )

trated solutions must necessarily become harmful if it were only on
account of their strong osmotic action on plant-cells; in other words,
it is possible to determine the toxic limit of plasmolysing substances.
In these cases the results of weighing are different in that the tissues
in the salt-solution obviously lose weight but recover weight again
when placed in water, if they have remained undamaged. If during
the deplasmolysis death might occur, this can afterwards be recognised
by a diminution of weight.

By this method I have been able to ascertain that the potato-
tuber is rather sensitive for plasmolysing agents. Pieces of this organ
appear to be damaged when they have stayed for 24 hours in
0.4 grammol. NaCl (2.34°/,), and are then placed in water. We
will not decide whether death took place already in the salt-solution
or on entering the water; sometimes, however, the grey discoloration
already began to appear in the solution. A solution of 0.3 grammol.
NaCl (1.75°/,) is perfectly harmless when acting for a day. Now
other parts of plants offer a much greater resistance to neutral salts.
The limiting concentration of NaCl for pieces of beetroot, e.g., lies,
when acting for a day, at between 1 and 1.5 grammol.; I did not
determine this limit more accurately. Similar values are furnished
by various other parts of plants, such as the tuber of Colchicum
autumnale, the leaf of Aloe dichotoma and Aloe succotrina.

For KBr, KNO,, the molecular concentration at which pieces of
potato begin to be injured is pretty much the same as that given
above for NaCl. For the present, however, it was not my intention
to extend this investigation to a greater number of salts, although
this would undoubtedly lead to many interesting results, also perhaps
concerning the action of ions on the living cell. It only must be
mentioned here that with glucose and saccharose, injurious effects
on pieces of potato began to be noticeable at a concentration of
0.5 or 0.6 grammol. which is only slightly higher than with NaCl.

Interesting observations on the action of sait-solutions on plant-
cells have been formerly made by J. C. Cosrerus'); although they
have not been repeated by the weighing-method, I must not omit
drawing attention to them, since they seem to point to a different
behaviour of the cells in the salt-solution, depending on the presence
or absence of oxygen, which may be of importance with regard to
what follows.

The determination of the lowest limit of concentration for which
substances are poisonous, led us to investigate whether this limit can

1) Arch. Néerland. t. 15. 1880.

( 706 )

be shifted by adding other compounds to the solution. This is indeed
often the ease, and so the weighing-method lends itself to a repeti-
tion of the experiments of KaHLENBERG and TrurE*) and those of
True and Gtks*) in which by a different method the toxicity of
metallic compounds was proved to be diminished by the addition of
certain salts. The case which I have examined a little more closely
does not concern a metaliic poison, however, but an alkaloid.

The lowest poisonous concentration of chinine hydrochloride for
potato is a very low one, namely 0.001 grammol. per litre *), the
action lasting 24 hours. All parts of plants which I examined, proved
to be about equally sensitive to this poison. The result of adding
NaCl in a certain concentration to the chinine solution, is that after
the same time, death occurs at a considerably higher concentration

of the chinine, this concentration

depending again on the amount

of NaCl in the solution. The figure

represents graphically this shifting

of the toxic limit. One sees from

it that by 0.2 grammol. NaCl per

litre the harmful concentration of

the chinine hydrochloride is raised

from 0.001 to 0.005 grammol.,

a further addition of salt acting

less favourably again. At 0.4 gram-

Paes eee eae es mol., as was pointed out before,
2 i “ yaci pure NaCl is injurious to the potato.

As far as I have been able to gather, the toxic action of chinine
hydrochloride on plants generally is modified in the same sense by
NaCl. At any rate I obtained the same results with pieces of sugar-
beetroot, the leaf-stalk of Begonia, fragments of the leaves of Aloe.
As the cells of the sugar-beetroot resist much higher concentrations
of common salt than those of the potato, it is not surprising that
also in the presence of more than 1 grammol. NaCl per liter the
antagonistic action towards chinine can be observed with this plant.

The diminution of toxicity, observed by the above-mentioned
authors when certain salts, harmless in themselves, are added to
metallic compounds, has been ascribed in most cases to the concentration
of toxic ions being decreased; their results agree with the connection

0,005

0,004

‘TyooapAy “UTUTT,)

0,003
0,002

0,001

1) Botan. Gazette. vol. 22, 1896.
*) Bulletin Torrey Botan. Club. vol. 30. 1903.
3) or 0,03965 °/); mol. weight of Cy9 Ha, N2 O23. HCl -+ 2 H,O = 396,5.

f-.

ste el | te:

( 707 )

between disinfecting power and degree of dissociation '), formerly
studied by Patni and Kronicg. Antitoxic actions of metal on metal
with animal cells as reagent, studied by Lors, proved however that
the explanation cannot always be sought in this direction’). So a
deeper interpretation of the case here mentioned must be put off for
the present, the more as, very likely, it will appear not to belong
to the domain of physiology but of chemistry.

The observations may be completed with the results of some ex-
periments with other compounds.

The toxicity of chinine hydrochloride for potato and for sugar-
beetroot is as clearly as by NaCl diminished by KBr, Li Br, Ca(NQ,),,
which are rather different salts. Glucose and saccharose, on the
other hand, have no influence whatever.

Also of another organic poison, namely oxalic acid, the action
proved to be partially neutralised by NaCl being also present in
the solution. Especially the sugar-beetroot gave very distinct results
here, although also with the potato the antitoxie influence of the
salt was clear. In a less degree, but yet in an unmistakable manner,
the toxicity ef oxalic acid is counteracted by saccharose.

Some experiments with a metallic poison (cupric salts) gave results
which were in general concordant with those of KaHLENBERG and

his collaborators.

Physiology. — “On some applications of the string galvanometer’’.
By Prof. W. Einrnoven. Communication from the Physiological
laboratory at Leyden.

In a former paper*) the amount of sensitiveness of the string
galvanometer and the time in which the deflections of the quartz-
thread are accomplished were mentioned and illustrated by a few
photograms. We = stated that with a feeble tension of the wire a
current of 10-!2 Amp. could still be observed and that with a
stronger tension, so that the movement of the wire is still dead-beat
and the sensitiveness is reduced to a deflection of 1 mm. for
210-8 Amp., a deflection of 20mm. requires about 0.009 seconds.

1) Zeitschr. fiir physikal. Chemie. Bd. 12. 1896. Zeitschr. fiir Hygiene. Bd. 25. 1897.

2) Prricer’s Archiv. Bd. 88. 1901. Americ. Journ. of physiol. vol. 6. 1902

Other observations belonging to the same category of animal physiology, were
recently made by E. Lesyé and Cu. Ricner rics, (Arch. internat. de Pharmacody-
namie. XII. 1903).

3) These Proc. June 27. 1903. p. 107.

Proceedings Royal Acad. Amsterdam. Vol. VI.

( 708 )

These data may be sufficient to form an opinion about the mstru-
ment in theory and to give an idea of its fitness for practical work;
yet on this latter point the applications alone can give full and
convincing evidence.

In what follows we intend to mention some of these applications.

Where the object is to measure very feeble currents no other
ealvanometer seems to equal the instrument we are considering. It
is obvious that theoretically there is no limit to the sensitiveness of
any arbitrary galvanometer for constant currents. One can indefinitely
increase the period of oscillation of the magnets as well as the
distance of the scale and so obtain any desired sensitiveness in theory.
sut practical difficulties soon draw a limit. One among other diffi-
culties is the inconstancy of the zero-point, which is influenced by
many circumstances and which causes the more trouble the more
the period of oscillation increases.

This is probably the reason why an electrometer is preferred toa
galvanometer when very feeble currents have to be measured, e. g.
when great insulating resistances have to be examined or the ionising
power of radio-active substances.

In the celebrated investigation by Mr. and Mrs. Crrte *), which led
to the discovery of radium, the radio-activity of various materials
was judged by their power to render air conductive; and the conduc-
tivity of the air was measured by means of an electrometer. The
electrometer had to be charged by a current, which passed through
a conducting layer of air, the rate at which the electrometer was
charged being a measure for the current.

Evidently if was not an easy matter tO measure currents in this
way; so Mr. and Mrs. Curm preferred a method of compensation
by means of a rod of piezo-electric quartz. The charge received by
the electrometer through the layer of conductive air was compensated
by a contrary charge derived from the quartz-rod. To effect this the
rod was subjected to a steadily increasing pull by continuously adding
weight to a scale suspended on the quartz-rod. In this way the
image of the mirror of the electrometer had to be kept at zero, the
increase of the pull during the time being the measure for the current
and in this case also for the conductivity of the air.

It is much easier to make these measurements with the string
valvanometer.

| connected the instrument with two brass plates A, and A,, fig. 1.

1) See eg. Mme Skiopowska Curae, Recherches sur les substances radioactives,
Annales de Chimie et de Physique 7, T. 30, p. 99, 1903,

( 709 )

Both plates were round, had a diameter of about 25 cm., were
insulated and mounted at a distance of about 2 cm. from each other ;
the laboratory-battery of about 60 Volts and a resistance of 1 Megohm
were inserted in the circuit from the galvanometer @ to the plates.

1 Megohin.

The sensitiveness of the galvanometer was adjusted at 1 mm.
deflection for 210-1! Amp., the time required for a deflection
being about 5 to 7 seconds. Now a round plate, covered over a
diameter of about 20 em. with powdered uraniun-trioxide (containing
water) was shoved in between <A, and A, and laid on A,. The
galvanometer » now showed a deflection of 2.5 mm. As soon as the
uranium-preparation was removed it pointed exactly zero again.

The uranium-preparation was in this way repeatedly brought between
the plates of the condenser and taken away again and each time
the galvanometer showed the same deflection of exactly 2.5 mm.
Each measurement was made in from 5 to 7 seconds; since, as has
been shown before, a deviation of 0.1 mm. can still be noticed, the
probable error of the observations may be put at 4 per cent.

The current measured amounted to 5 10—!! Amp., a value of
the same order as that calculated by Mis. Curm for other uranium-
compounds which had been examined under similar circumstances
by means of the piezo-electrometer.

We will briefly mention some experiments with a few milligrams
of a radium-salt. When the radium was placed between the condenser
plates, a P.D. of 2 Volts proved sufficient to deflect the image of
the wire a few centimetres. With a P. D. of 40 Volts in the circuit
the same effect could be obtained by holding the radium-preparation
at a distance of 1 metre from the plates. A definite distance of the
radium from the plates corresponded to a definite indication of the
galvanometer and it was obviously easy to drive the image from the
scale by approaching the radium. It was remarkable in all these
experiments that when the preparation of uranium or radium was

47*

( 710 )

not moved, the deflection of the galvanometer also remained steady.

These observations also show how easy it is to measure an insu-
lating resistance with the string galvanometer. The experiment with
the uranium-trioxide showed that the resistance of the layer of air

60 Volts
between the two plates of the condenser amounted to -——_-, —— =
3 >CLO>)! Amp:
= 1.2 10'? Ohms or rather more than a million Megohms. An
insulating resistance of 6 >< 10'% Ohms ean be demonstrated with
the 60 Volts laboratory-battery by a lasting deflection.

We finally mention another application of the string galvanometer
for measuring very feeble currents, namely those which are caused
by atmospheric electricity. A spirit-lamp is held up on a long pole
in the open air. An insulated wire connects the flame with one ter-
minal of the galvanometer-wire, the other terminal being earthed.
Under these conditions one sees a lasting deviation of the galvano-
meter which diminishes and disappears as soon as the pole is lowered
and carried indoors, but which returns as soon as it is taken out
and held up again.

The deflection of the galvanometer in these experiments was
generally more or less oscillating on account of the wind causing
fluctuations in the contact of the flame and the end of the wire.

Besides for measuring feeble currents, the wire-galvanometer is
suitable in practical work for detecting small quantities of electricity
and especially for accurately measuring rapid variations of electric
tension or of feeble electric current. As the instrument for feeble
currents which is quickest in its indications, it will undoubtedly prove
useful for transoceanic telegraphy.

The smallest quantity of electricity that can be detected by it, can
easily be calculated. Let us imagine that a great resistance has been
inserted in the circuit so that the electromagnetic damping of the
moving wire may be neglected and that now suddenly a current of
constant intensity is sent through the wire.

The movement of the wire under these circumstances is accurately
represented in the formerly published photograms *). Theoretically the
wire will, at the moment the current starts, experience an electro-
magnetic force by which an acceleration will be imparted to it. Its
motion will be an accelerated one until a speed is attained such that
the resultant of the electromagnetic force and the tension of the wire
will make equilibrium with the resistance of the air,

) These Proc. June aly 1903. p. 107,

eit }

If however the tension of the wire is feeble enough, the duration
of this accelerated motion is very small compared with the total
duration of the deflection so that it may be neglected. We are then
allowed to speak of an initial velocity of the wire and may disregard
its mass. The initial velocity is proportional to the current and may
be estimated at about 20 mm. per second fora current of 10—-% Amp.
with an image as is obtained with our magnification ‘).

A current then of 10-% Amp. only needs to last for LS sec. to
cause a deviation of 0.1 mm. and as the photograms prove such a
deviation to be still visible, a quantity of electricity of 5 >< 10—!2
Ampere-seconds can consequently be detected. This quantity is equal
to the charge of a condenser of 1 microfarad at a potential of
510-6 Volts or to the charge of a sphere of 4.5 em. radius at
a potential of 1 Volt.

Since, as was pointed out above, the initial velocity is proportional
to the current, the deflection for a small quantity of electricity, will
entirely depend on that quantity itself, and it will make no difference
whether a strong current passes during a short time or a feeble cur-
rent during a longer time, if only the time of passage be small enough.

The properties of the wire-galvanometer lead us to expect another
very remarkable consequence. If the tension of the wire is increased,
the velocity with which a deflection is accomplished, will increase,
but at the same time the amount of the deflection for a given cur-
rent will diminish. Now it has already appeared from the photograms
that, provided the tension of the wire is not too great, the change
in sensitiveness is exactly inversely proportional to the change in
deflectional velocity, so that the initial velocity for a given current
is independent of the tension of the wire. From this we derive the
seemingly paradoxical result that under the condition mentioned the
deviation for a quickly passed, small quantity of electricity is the
same for any tension of the wire.

The facts are in complete accordance with this argument and for
an observer who is not accustomed to the instrument, it is very
curious to see, how with a relatively much greater tension of the
wire and a consequent great diminution in sensitiveness for constant

1) This amount of 20 mm. is only approximately true. I hope soon to be able
to deal more extensively with the movement of the wire under various conditions.
The influence of the viscosity of the air will then be compared with that of the
electromagnetic damping. It would be a decided advantage if the wire could be
placed in an air-tight space, which would enable us to observe its deflections either
in a vacuum or under increased pressure.

(712 )

currents, the sensitiveness for a quickly passed small quantity of
electricity remains nearly unaltered.

And the practical application lies at hand. Whenever rapid varia-
tions in electric tension have to be discovered and the disturbance
by slowly varying currents has to be avoided, a requirement which
frequently imposes itself in electro-physiological investigations, the wire
must be relatively strongly stretched.

The described sensitiveness for small and quickly passing quan-
tities of electricity, more even than its sensitiveness for constant
currents, makes the wire-galvanometer a suitable research-instrument
for a number of phenomena which are usually observed by means of
an electrometer.

If one end of the wire is earthed, the other joined to an insulated
conductor, e.g. a resistance-box, a rubbed ebonite rod, brought near
the resistance-box, will act by influence and easily drive the image
from the scale. A single advancing or receding movement of the rod
must obviously result in a double movement of the wire, since this
latter always returns to zero when the rod stops moving. At a distance
of a few metres, rubbing the rod with a silk cloth will still cause
deviations of the galvanometer, each single stroke of the hand ocea-
sioning ato and fro movement of the wire.

When I had laid aside the ebonite rod and the silk cloth and
came near the resistance-box with the hand only, a small deflection
of a few millimetres could still be observed. When quickly approach-
ing the hand, the wire showed a momentary deviation im one
direction, when quickly withdrawing it, in the opposite sense. Even
moving the fingers round one of the plugs of the resistance-box
caused the wire to move. It must be emphasised that the resistance-
box was not touched by the hand so that ordinary conduction
from the body through the galyanometer to the earth was out of
the question. .

I could not at once explain the phenomenon. My first thought was
that the body or at any rate the hand was charged to a certain
potential and like the ebonite rod drove electricity by influence
through the resistance-box and the galvanometer. But the potential
of one of the hands of an uninsulated person is too small to explain
the movement of the wire.

Also clothing, e.g. a woollen sleeve, appeared to play no part.
If a round metal disk connected to the earth by a conducting wire
and hence having presumably the same potential as the galvanometer
and the resistance-box, was suddenly brought near or removed from

(713 )

the latter, the same deviations were noticed as when moving the
human hand.

Also these deflections changed only litthke when the metal disk was
moved, after having been charged by a storage-cell to a potential of
+ 2 or —2.

The idea that the strange phenomenon had to be ascribed to
currents in the air which would ‘generate electricity by friction, had
to be rejected at once, as soon as, by means of a pair of bellows,
a powerful air-current had been directed against the resistance-box
without the wire showing the least motion. But in the end the
explanation appeared to be very simple. The ebonite plate of the
resistance-box has a certain charge and the lines of electric force
bend from the ebonite to the metal plugs. As soon as a conductor
now approaches, the lines of force are displaced and thus electricity
is moved from the metal through the galvanometer to the earth.

That this is the real explanation could be easily shown by rubbing
the ebonite of the resistance-box and so charging it to a higher
potential. When this was done the deviations became many times
larger.

An interesting proof of the usefulness of the wire-galvanometer
as a sensitive instrument which at the same time is quick in its
indieations, is afforded by the ease and accuracy with which it
registers sounds.

When a Stemens’ telephone is connected with the galvanometer,
the sound-vibrations falling on the plate of the telephone will send
induced currents through the wire, by which this latter will be moved,

As soon as a tone of arbitrary pitch is made to sound against
the telephone with constant intensity, the image of the wire broadens
in a curious way. In the bright field the narrow, black image is
broadened to a band of several centimetres breadth, which has a
light grey tint and whose appearance in the field is feebler as it is
broader. The middle of the grey band always corresponds to the
image of the quartz-thread in rest. The margins have a somewhat
darker delineation than the rest of the band.

This appearance is entirely explained by the circumstance that the
wire executes regular, rapid vibrations of the same rhythm as the
sound-vibrations striking the telephone.

One peculiarity has still to be mentioned. If a sound like @ or 0
is sung against the telephone-piate, one sees the grey band divided
into parts. Symmetrically with respect to the middle of the image,
within its real margins something like secondary and tertiary margins

( 714 )

are visible which admit of no other explanation than that the motion
of the wire, representing the sound in its fundamental and _ partial
tones, consists of a number of vibrations of different frequencies
and amplitudes.

We hope soon to analyse this phenomenon photographically. When
the intensity of the sound is changed, the breadth of the grey band
also changes immediately. And at the moment the sound stops, one
sees the narrow, black image of the wire standing perfectly still
again in the bright field.

When the telephone is replaced by a microphone and a suitable
induction-coil, tie same phenomena are observed; with these contriv-
ances however the arrangement has become much more sensitive.
Feeble sounds now give rise to considerable broadening and it is
surprising to see, how, when one speaks softly at a distance of one
or more metres from the microphone, the image of the wire reacts
powerfully on each word that is spoken or rather on each syllable
that is pronounced, but always immediately occupies its position of
rest as soon as the sound stops for a moment.

Feeble sounds, as e.g. the cardiac sounds of a rabbit are excel-
lently rendered by the galvanometer.

desides for the study of phonetics and of cardiac sounds, the wire-
galvanometer will find fruitful applications over an extensive range
of physiological research. We already communicated some results of
an investigation concerning the human electrocardiogram '). Besides,
an investigation of the nerve-currents is now in course of progress,
about which we will only mention in this place that the action-
currents of a nerve, resulting upon simple stimulation, can be shown
and registered in an excellent manner. As far as I know action-
currents of the ischiadic of a frog, arising by the stimulus at the make
and break of an ascending and of a descending constant current, have
never been observed hitherto. The string galvanometer shows them in
all their details as they must be expected according to PrLtGEr’s law
of contractions and the existence of which could until now only be
surmised from the observed muscular contractions. One also sees the
superposition of the phenomena of electrotonus on those of the action-
current, which need be no impediment to the interpretation of the
obtained curves. We seem to be justified in supposing that perhaps
new points of view will be opened about the manner in which the
nerve is capable of reacting on various stimuli.

Oe Bue

a i i

( 745 )

Chemistry. — “Action of hydrogen peroryde on diketones 1,2 and

on a-ketonic acids. By Prof. A. F. HoLLeman.

Some aromatic acids may be obtained by first thtroducing the
acetyl group by means of the reaction of Frirpen and Crarts and
oxidising this to the carboxyl group. In many cases, however, this
oxidation does not take place readily; the group CO.CH, yields with
comparative ease the group CO.CO,H but the further transformation
of the latter into the carboxyl group is often attended with great
loss. Even the method of HooGrwerrr and van Dorp, consisting in
heating the a-ketonic acid with concentrated sulphuric acid does not
yield the theoretical quantity. I have tried whether this transforma-
tion might perhaps be attained quantitatively by means of hydrogen
peroxide, according to the equation :

R.CO. CO,H R.COOH.

+ HOOH — + HOCO,H (= H,O+C0,)

This was indeed the case. Aqueous solutions of pyruvic acid,
benzoylformic acid, thienylglyoxylic acid when heated with the
calculated amount of 30 °/, hydrogen peroxyde (Merck) at once
eliminated CO and yielded almost quantitative amounts of acetic
acid, benzoic acid and thiophenic acid. From Prof. EyKman, | received
small specimens of four a@-ketonic acids which he is investigating
and these, when heated in aqueous or acetic acid solution with a
slight excess of H,O, also eliminated CO. On titrating the acids
obtained from them it was found that their group CO .CO,H had
passed into CO,H.

This result led us to suppose that «-diketones might also be readily
resolved by the action of H, O,,

R.CO. CQ.R'
+ HO OH

Some of the diketones, such as benzil, camphorquinone and

= R. CO, H+ R'. CO, d,

phenarthrenequinone were dissolved in glacial acetic acid and warmed
for some days with a small excess of 30 °/, H, O,. The expected
reaction took place almost quantitatively: it was remarkable that
campherquinone did not at once yield camphoric acid but first the
anhydrde, which was converted by boiling with dilute alkali into
camphoric acid.

Messis. J. Huisrnca and J. W. Berkman have carried out the
experiments.

Groningen, March 1904. Lab. Univers.

( 716 )

Mathematics. — “On a decomposition of a continuous motion
about a fived point O of S, mto two continuous motions
about O of SJs’ by Mr. L. E. J. Brouwer, communicated
by Prof. Korrewse.

(Communicated in the meeting of February 27, 1904).

Two planes in NS, making two equal angles of position are called
mutually “equiangular to the right” if one is (with its normal plane)
plane of rotation for an equiangular double rotation to the right
about the other one and its normal plane.

We will call the sides of one and the same acute angle of position
“corresponding vectors” through the point of intersection of twe
equiangular intersecting planes.

As is known a system of planes equiangular to the right or to
the left is infinite of order two. Of course a determined equiangular
system of planes to the right can have with a determined equian-
gular system of planes to the Jeft not more than one pair of planes
in common (two pairs of planes cannot intersect each other at che
same time equiangularly to the right and to the left); but one
pair of planes they always have in common. We will show how
that common pair of planes can be found.

A pair of intersecting pairs of planes of both svstems is of coirse
easy to find. We lay through any vector OC’ the planes belonging
to the two systems; their normal planes intersect each other in a
second vector OD. Thus OCD is one plane of position of those
two pairs of planes. In the second plane of position the four planes
furnish four lines of intersection, let us say OH, OF, OK, OG,
in such a way, that the considered pairs of planes must be OCH;
ODK and OCT; ODG. The following figures are supposed to be
situated in those two planes of position.

' D :
5

‘,

Fig. 1.

Let the pair of planes OCH; ODK belong to the giver system
equiangular to the right, and OCF; ODG to the giver system
equiangular to the left,

e717 )

The vectors in the second plane of position are drawn in such a
Way that either
\ OH > OC
, (1)
}OK > OD
is an equiangular double rotation to the right, or that such is the
case with
\ OH SOC
,OK > OD
We shall suppose the first to be true (the reasoning is the same
for the second case). Then
OF > OC
1OG = OD
is also an equiangular double rotation to the right; for, the planes
OFC and OGD ean be brought to coincide with these directions
of rotation with the planes OHC and OAD, having the directions
of rotation
OL > OC

|OK > OD

\ OF =F OC

| OG' + OD
is an equiangular double rotation to the left.
If farthermore OA and OF are bisectors of the angles HOF and

KOG, and 4 we have-made “COA! => 7 DOB > FYaA0A =
== POL = VARs == "7G 0B, then: the, pair of planes

{ AOA!

BOB

is a pair of planes of rotation as well for the equiangular double
rotation to the right (1) as for the equiangular double rotation to
the left (2). So it is the pair of common planes which was looked
for of the two systems of planes.

We shall think now that through two
arbitrary vectors OA and UF two planes
intersecting each other equiangularly to the
left have been laid; we shall now consider
more closely the position which two such
planes have with respect to the plane
OAL and its normal plane. We shall call
the indicated equiangular planes. to the left
a and 3; and indicate UAB by y and its

Fig. 2. normal plane by J. In fig. 2 the lines
drawn upwards lie in d and those drawn downwards in y.

(ito)

The plane OCC” is the plane of position of y and @, intersected
by y in OF, by a4 in OC. Fig. 3 is supposed to lie in that plane
of position. We have made fartheron in fig. 1 the angles A’OD’,
C’OD’, COD equal to 7 AOB =g, and the directions of rotation
indicated in those planes belong to a double rotation to the right.
Fig. 4 is supposed to lie in the plane ODD’, and the lines OG and
OG’ are drawn in it in such a way, that ODGD'G’ = OCFC EF’.

F.= ce! G D’
oe ee
¥ rs
0 0 D

Fig. 3. Fig. 4.

We shall consider the plane BOG more closely. Let us project
Ob and OG both on a, then it is not difficult to see that the
execution of those two operations, each of which is threedimensional,
gives as a result two lines OH and OA, mutually perpendicular
(see fig. 5, supposed to lie in a).

The projecting planes are successively: OF” (tig. 6) and OGA’
(fig. 7).

0 5 F A
=
H K
Ns H 0 A 8) E

Fig. 5. Fig. 6. Fig. 7

We shall directly see that OA and O/” are situated on diffe-
rent sides of OH, and OG and OA’ on different sides of OX,
and that ~HOB = /WOG, if we suppose ourselves to be successively
in the threedimensional spaces, in which the projecting takes place.

So we see that the plane BOG has two mutually perpendicular
vectors, making equal angles with @ and projecting itself on «
according to two perpendicular vectors namely OF and OG, projecting
themselves according to O/T and OX: the characteristic of equiangular
intersection.

Let us still examine of which kind that equiangular intersection
is; we shall then perceive that on account of OB being transferred
into OG by the equiangular double rotation

( 719 )

OF' — OA'
OH => OK
and this being of the same kind as
OF —» OA'
OA— OF
which in its turn can be made to coimeide with
OC' = OA'
OA = OC
by a single rotation about the plane OAA', the kind of equiangular
intersection is the same as the kind of the double rotation
OC' = OA'
OA = OC
which is to the left according to the data.
So the plane OBG is identical with the plane 2, for through OB
only one plane equiangular to the left with @ can pass.

If we now introduce the notation Eq ) equiangular to the right”

ce
indicating if abcd denote four vectors through QO, that the planes
(ab) and (cd) are equiangular to the right and that the same double
equangular rotation to the right transferring @ into 4, also transfers

c into d, then
OA, OB
OF, OG

is equiangular to the right and the corresponding equiangular double
rotation to the right transfers @ into Bp. In other words we have
proved the

Theorem 1. If (

s) is equiangular to the right, then = is equian-
gular to the left; or in other words though less significant :

By an equiangular double rotation to the right any plane passes
into one equiangular to it to the left.

If we suppose three vectors ac (whose position of course determines
the position of S,) to have come after some equiangular double rotations

ab\ . :
to the right into the position de/, then Ce is equiangular to the left
ade

ac ; : ad ! ;
and equiangular to the left; so é ) equiangular to the right
. :

ad 555)
and ( -) equiangular to the right, so finally

ad
ef

( 720 )

equiangular to the right; in other words the final position would
have been obtainable out of the initial posiuion by a single equiangular
double rotation to the right; with which is proved:

Theorem 2. Equiangular double rotations of the same kind form a
eroup.

Let us suppose given two equiangular systems to the right and two
vectors OA and OF through each of which we bring the planes
belonging to both systems; then the’ equiangular double rotation to
the left, transferring OA into U4, will transfer at the same time
the angle of position formed in OA into the one formed in OB, thus:

Theorem 3. Two equiangular systems to the right form in each
vector the same angle, which can be called the angle of the two
systems.

The obtained results we shall verify by deducing analytically

theorems I and 8, which deduction will also throw some more light.
Suppose a rectangular system of coordinates to be given in such

( OX be
Oe 0x

a way that

is equiangular to the right. The same then holds good for
( OX,, pi ee bee net
ORG ay: OX,; OX,

A vector @ through O we can determine by its four cosines of
direction @,, @,, G5, @,.

A plane passing through the vectors @ and 3 with direction
of rotation from «@ to ~p, is determined by its six coefficients of
position (i. e. projections of a vector unity) 2y55 2515 412+ Aras Aeas Aaa,
which are detined by the following relations, if we represent ¢,3,—a,(),

by 5:

a ene rere ne eevee oer ———————., ete.
a tame Be oe pee el a == ae 5 3 5 2
a 4 333° 7! S31 “hp Sre + Sis 2 ik 334

We must take the positive sign in the denominator, for A,, must
he positive, when the projection of @on OX, NX, to that of 8 on OX, NX,
rotates through an angle less than a in the same way as (LX, to
ON,; and in that same case §,, gives us a positive value. If we
how represent that positive root of the denominator by AY, then

S
, 32 “ 3;
a = 743, — sah etc.
; A K

An equiangular double rotation to the right can be given by the

(721)

system of equiangular planes of rotation to the right with direction
and the angle of rotation.
For all those planes of rotation

Past Avg

have the same values. These three values «,,@,,,, besides the
cosinus of the angle of rotation a@,, we can take as determining
quantities of the equiangular double rotation to the right. A rotation
<_2a is unequivocally determined by that (for, whether the angle

of rotation is a, which is left undecided by the value of the cosinus,

follows from the sign of the a,, a, d,).
Saat an arbitrary vector @ to be transferred by the rotation
into 3, then it holds good for each pair of vectors aj that:
a,@, —a, 8, + a,8,—a,8,=— K.a
a, 3, —a, 8, + a, 8,—a,8, = K.a,
a, Bp, — a, B, + 4,8,—a,8, = K.a

a, B, + a, 8, + 4; 8 + 4,6, = 4,.

If however we consider that A = + Vsin? 9, if & is the angle of
rotation, then A’ proves to be a constant for all pairs of vectors so
that we may regard A.a,, K.a,, A.a, and a, as determining quan-
tities of the double rotation which we shall call 2,, 2,, a,.,; and
we shall write the relations:

2 ets
— a, Pp, — a, B, + a, 8, + «,8,=—2, '
a, 2, Toy 3, mses Ps of as By = Es ]
(ZT)
ae ae
og Suen er By a, Bs + a; 8, — *; |

a Pr @, Bye, fp, + @, p, =
in which we have at the same time arranged the first members
according to 3,;3,.3;,3,. We now se as

B+ afta ft aVHK740,,7 +4,,.7° +4,.7+24,744,7% +4, +
+r Stas pe os a oer aes
WGN | ot See |) oe
= sin? } + cos? &
ail B
So we can regard 27,, %,, 7,7, as cosines of direction of a vector
through QO in S, and we can represent an equiangular double rotation
to the right by a vector through O in S,, which determines it

( 722 )

unequivocally. (A vector without length; lateron we shall determine
it, likewise unequivocally, by a vector with length, in JS;).

If we farthermore consider the determinant on the coefficients of
8,.3,,3,.3, in (/7) it proves to. satisfy all the conditions of an
orthogonal transformation.

We call that transformation with that determinant

—a, —a, +a, +a,
+a, —a, —a, +a,
6, = @, eee
+a, +a, +a, +4,

the (+7) a-transformation; it appears in the relations (//), if the
first members are arranged according to the cosines of direction of
the final position of the rotating vector. If they are arranged according
to the cosines of direction of the initial position the determinant of
the coefficients becomes

B, Bs a Bs ig B,

7 B; B, B, Parak B,

B, = B, B, B,

B, b, B, By
which we shall eall the (— 7) 8-transformation.

(Juite analogous to this we have for equiangular double rotations
to the left (9, 9, @,9,) bilinear homogeneous equations between the
cosines of direction of initial and final position of a vector, let us say
e and 3, which arranged according to the 8's, give as determinant
of the coefficients

a. ss a, — a,

a, =e, =-.e.
— a, a, a, —@,

a, a, a, ans

the (+ /) «transformation and arranged according to the a’s
Ps By 3,
= Bs vid B, PB, B.
By oe eB
2, By Bs By.
the (—/) 3-transformation.
We can now state the following:
If the equiangular double rotation to the right (2, a, 2, 7,) transfers
the vector (@, a, @, 4,) into (3, 8, 3, 8,) then the (+ 7) a-transformation
transfers the vector (7, 2, #, %,) into (8, 8, 8, B,)

aE eee

( 723 )

and the (—v,) §-transformation transfers the vector (7, 27, 7, 7,)
into (a@, a, @, @,).

Analogous to this:

If the equiangular double rotation to the left (g, 9, @; @,) transfers
the vector (a, a, a, @,) into (3, 3, 2, %,), then the (+ /) a-transformation
transfers the vector (9, @, @, @,) into (, 8, B, B,)

and the (—/) #-transformation transfers the vector (e, 9, 9, @,) into
(a, a, as at,).

Let us now suppose that S, has first an equiangular double rotation
to the right (x) transferring an arbitrary vector @ into #'; then an
equiangular double rotation to the left (@), transferring #’ into y, then
we can write:

x = [(+ re]? e=((—)rl?

(+ ye] - [(—Ar}e

where the form between {} denotes the determinant of transformation
having as first row the sum of the products of the terms of the
first row of [(+ 7) a] with the corresponding ones of respectively the
first, second, third and fourth of [(— 2) y], whilst the second etc. row
in a corresponding manner is deduced out of the second etc. row
of [(+,r) a] (all this in the way of forming a product of determinants).

If S, has first an equiangular double rotation to the left (g) transferring
a into @" and then an equiangular double rotation to the right (2’),
transferring 8” into y, we have:

e=[((+)a] RX F=[((—nNxe
x ={{(—r7] - (+ 9elhe.

—

But now
(+ ye] -(—)y=l-— 7] - (4 De)
which can be at once verified, so:
a = 2.

Thus:

If S, is allowed successively an equiangular double rotation to the
right (x) and one to the left (g) the order of the two rotations may
be interchanged. For, in both cases an initial position of a vector e
gives the same final position y.

And if we regard the quadruple a, #’, 6",y, then os is
yf

equiangular to the right, according to the rotation (a) and € 7
(3

equiangular to the left according to the rotation (eg); by which we
assuredly once more have proved theorem 1.
48
Proceedings Royal Acad. Amsterdam. Vol. VI.

( 724 )

Let us farthermore suppose (6) and (tr) to be two equiangular
double rotations to the right, transferring a given vector ¢ the for-
mer into &, the latter into 4. Then

o={G-H8s- =i ele

The same orthogonal transformation transferring o into §, transfers
zt into 7, so that the angle between $ and 1 is the angle between the
vectors o and t independent of the initial position «. As a special
case theorem 3 is included in this, for the case that the twe double
rotations take place about an angle $2; for then the angle between
$ and 7 is the angle of the two planes of rotation through ¢, proving
to be independent of «.

We have still to mention that theorem 1 in the second form is
entirely included in the applications of the biquaternions on S, as
given by Dr. W. A. Wurtnorr in his dissertation: “De Biquaternion
als bewerking in de ruimte van vier afmetingen” (the biquaternion
as an operation in fourdimensional space). For an equiangular double
rotation to the right is represented by Q.¢, +, (p. 127) where
Q represents a certain quaternion with norm unity.

This applied to an arbitrary double vector

@,&, + 4,8,,
changes it into
Qa,é, ar AE os
so it leaves the isosceles part of that double vector to the left
unchanged and so also the equiangular system of planes to the left to
which it belongs. This holds good for an arbitrary double vector,
so particularly for a plane.

Finally theorem 3 can be proved as follows:

If g and w are the acute angles of position of two planes, then
if we represent the coefficients of position respectively by 2’s and w’s:

cos ~P cos W = 4,, Usa ta Marrs rat Arg Mig tag Maa tes Hae =
= = (A,,+4,,) (u,; +44) aes = (4,; TAS oi My).
For intersecting planes with angle of position g:
cos p= & (45,4, 4) (Us Urs) = & (Ags 414) (Has Yaa):

So for two intersecting planes, belonging to two definite equiangular

systems to the right or two to the left
Vig ee age a oe and Bei iE as +i x

resp. BF a a and fetal an and cos gy —— 008 gy.

We shall now resume our geometrical reasoning dropped after
theorem 3. Let us take through O a definite vector OW in S, but
not movable with S, and let us represent each system of planes equi-

Pores)

angular to the right by the line of intersection of the plane through
OW belonging to it with S,1 OW. That S, is thus, entirely filled
with these representing lines which are in (1,1)-correspondence with
the represented systems of planes.

We shall call that S,;1 OW regarded as a complex of the rays
representing the equiangular to the right systems of planes, “‘the repre-
senting S, to the right of S,” or shorter “the S, of S,’. In the same
way we form the ‘“S, of S,’. Each pair of planes in S, is then
unequivocally determined by its representants in S, and S,and rever-
sely the pair of planes determines unequivocally its representants.

Theorem 4. An equiangular double rotation to the right of the S,
about a certain equiangular system to the right which double rotation
leaves according to theorem 1 the position of S; unchanged, givesa
rotation of S, about the representant of the system of the planes of
rotation over an angle equal to double the angle, over which the
equiangular double rotation to the right of S, takes place.

Proof. In the first place ensues from theorem

Th a 3 that the representants in S, keep making mutu-
ally the same angles; so S, has a ‘motion as a
nF solid”. We suppose through OW to be laid its
plane of rotation a in S, and its normal plane ~.

In fig. 8 we suppose the lines tending downward
¢ to lie in @ and those tending upward to lie in@

those of the equiangular double rotation to the

Ww’ right which we consider. Angle WOC'is made equal
Fig. 8. to } x. Then the S, is the S, through OC and

B. Let OP be an arbitrary vector in 8 and @ the angle, over which

the equiangular double rotation to the right takes place. The double

rotation leaves OC unchanged as representant of the equiangular

system to the right on (a8). Moreover it transfers OW into OW’ and

OP into OP’. If we then still make “ P’’OP’ equal to “” P’OP
we have:

OP, OP'

( ow. ee equiangular to the right, thus :

OB OP

OW, ey equiangular to the left, or also:

ORY, OP
ow' equiangular to the left, so at last

ieee.»

The plane POW giving OP as representant of its equiangular
system to the right before its double rotation, gives after that rotation
(transferred to P’OW") as representant OP’’ making an angle 29
with OP; so an arbitrary vector OP in S,1OC (the invariable
vector) rotates about OC over an angle 2¢, with which the theorem
is proved.

We can now say: For an S, moving as a solid about a fixed
point the position is at every moment determined by its “position
to the right” (the position of the S, moving as a solid about a
fixed point) and its “position to the left” (the position of S,). For,
if of two positions the pairs of planes through O coincide, then this
is the case too for all planes, thus for all rays too.

N.B. We can remark by the way, that in this way we have
proved quite synthetically that two positions of S, have a common
pair of planes, namely that pair, which has as representants the
axis of rotation of the two positions to the right and that of the two
positions to the left; so, taking into consideration that also the
common fixed point is always there (having as projections on the
positions of planes remained invariable the centres of rotation of
the projections of S, on it), that the double rotation is the most
general displacement of S,. However, until now we have occupied
ourselves only and wish to keep doing so with the motions of S,,
where always the same point ( is in rest.

For a continuous motion of S, the position and the condition of
motion are at every moment determined by S,and_S;; so the motion
of S, is quite determined by the motions of S, and S;; and at every
moment the resulting displacement of S, is quite determined by
that of S, and of S;, independent of the order of succession or
combining of the two latter; they have no influence upon each
other. We can regard a motion of S, as a sum of two entirely
heterogeneous things, i. e. which cannot influence each other in any
way or be transformed into each other.

We can proceed another step by indicating not only by a line in
S, a system of equiangular planes of rotation to the right, but
also by a line vector along it an equiangular velocity of rotation
to the right, that line vector being equal in size to the double
velocity of rotation of the double rotation and directed along the
vector moving with jS, in the direction of OW. Then equal and
opposite velocities of rotations to the right of S, are indicated
by equal and opposite vectors in 5S,.

Let OP. be such an indicating vector and OQ, and OS, two
mutually perpendicular vectors in the plane erected perpendicularly

727.)

to OP, in S, in such a way that

OP,, OW
A OS, )
is equiangular to the right, then to the equiangular double rotation
to the right of S,, indicated by OP, corresponds the rotation of S,
about OP. equal to the length of OP, in the direction of OQ, ~ OS,.
Let OP’. be another indicating vector and let us determine in an
analogous way OQ’, and OS',, then the orthogonal systems of vectors

OW P, Q, S, and
OWP', Q,S',

are congruent, can thus be made to coincide by a rotation of S,,

with OW, thus SS, too, remaining in its place, so that the indicating
vector OP, by a motion of S, in itself can be made to coincide
with the indicating vector OP’. in such a way, that at the same
time the directions of rotation of S, belonging to it coincide in the
normal planes. But then an indicating vector in S, represents that
velocity of rotation entirely in the way usual in space of three
dimensions, as also by its length it indicates the size of the velocity
of rotation of S, belonging to it; if namely we endeavour to regard
the definition of that usual mode of representation entirely apart
from the notion ‘‘motion with or against the hands” which is lacking
in S,; and say simply after having taken in that space a system
of coordinates OXNYZ: the vector of rotation will be erected to
that side of the plane of rotation, that for the plane of rotation
being by motion inside the space made to coincide with the plane
of YY in such a way, that the direction of rotation runs from OX
to OY, the vector of rotation is directed along the positive axis of Z.

For us that system of -coordinates in S,: OX,, OY,, OZ, has
been chosen in such a way that with OW it forms a system of
coordinates in S,, for which

OF.» O4; O2,, OX, OX OF;
on ony oe on fon a)
are equiangular to the right.

A vector along Q(X, then indicates a rotation of S, in the sense
a OY, = 02,

Entirely analogous reasonings hold good for S). It being however
more profitable to be able to say also for S;: a vector along OX;
represents a velocity of rotation of S; in the sense of OY;—~ OZ,
we must modify the preceding either by choosing the system
OX: Y;Z, W in such a way that

( 728 )

OF), OF
es en
is no more equiangular to the right, but to the left, or if we suppose
OY), OZ,
a)
to be also equiangular to the right, we must take as indicating vector
in S; that vector in the direction of which OW would move together
with |S,, not the one moving together with S, in the direction of OW.
We shall do the latter. The advantage of this choice will be evident
from what follows. |

We have still to remark, that if only the position of S, and S;is
determined, the position of S, ensues from it not in one, but in
two ways; for, a position of S, gives no other positions of S, and
S; as its “opposite position” for which all vectors are reversed ; that
opposite position can be obtained by an arbitrary equiangular double
rotation over an angle a; S, and S; then rotate 2 a and are again
in their former position.

But a continuous motion of S, out of a given initial position is
unequivocally determined by the given continuous movements of
S, and S; out of the corresponding initial positions. So we shall
have completely answered the question how a solid S, moves under
the action of determined forces if we can point out how S, and 5;
move under those actions; in other words if we can point out “the
cones of rotation in the solid and in space”.

APPLICATION. The Euler motion in S,.

The equations of motion for this have been given for the first
time by Franm in the ‘“Mathematische Annalen” Band 8, 1874 p. 35.
The system of coordinates OX, X, X, X, in the solid we shall
choose in such a way that the products of inertia disappear. We

shall suppose
OXF Ox,
OX,, "OX,

to be equiangular to the right.
And we choose OX, Y,Z, and OX; Yi Z in such a way that:
OX;, OR Okan 05.
ee ee
is equiangular to the right and
OX OR. Re
Cee

( 729 )

equiangular to the left, (from which ensues as a matter of fact

that also
OX, OF), (OX, oe)
Sie ae i a Ow
are equiangular to the right).

The systems OX, Y, Z and OX; Y; Z execute the motions of
S, and S; which are to be considered.

Let us farther call ,@,, ,@,,,@,,,@,,,.@,,,@, the components of
the velocities of rotation according to the system OY, X, X, X,;
and §,, Y,; P, the components of the velocities of rotation of S,
according to OX,, OY,, OZ, likewise w,,w,,w, the components
of the velocities of rotation of S; according to OX), OY), OZ. Then
we know the components of velocity of rotation to the right
OX 0X. OY,— OZ,
OX, —> OX, or according to OX.>0W
and analogues, and likewise the components of velocity of rotation

4 (,w, + ,,) according to

OX, > OX,
to the left 4(,@, — ,w,) according to OX,» OX, or according to
OY; — OZ,
OW > 0X; and analogues.
Therefore :

P, = 2; + 1, P, = 0; — 10,

C= O35 Oo, wy, = ,W, — ,o,.-

The Euler equations of motion “in the solid” (giving the opposite
of the apparent motion of the surrounding space) follow more simply
than according to FrAHM out of the vector formula

fluxion of moment of motion = moment of force — rota-
tion X moment of motion ;

which is easy to understand for a three dimensional space as well
as for a four dimensional one,

(and where the sign X indicates the vector product)

For, “in the space” the fluxion of the moment of motion = moment
of force; but of this for the position in solid has already been
marked the fluxion wanted to keep the position constant in the solid,
i.e. the fluxion which corresponds to the rotation of the moment-
vector about the rotationvector and this is — rotation & moment
of motion.

Let us call the squares of inertia 2m,’ etc. P, etc. and let us put

( 730 )

P,+P,4+P,+P,=R
—P,+P,+ P,—-—P,=A,
PBS Pr 2 Sek
Pye says Sipe ay.
Then we can write the rotationvector in the form:
29,7 + ,0,j + 0,4 + h(,@,7-+ 0,7 + ,, 4)
or in the form
€(P.¢+ Pej t Ps*) + & (Wit + UI + Ys &)-

The notations 2 and « are taken from the above-named dissertation
of Dr. W. A. Wurtnorr; / is defined on page 67; €, and ¢, on page 78.

The moment of motion becomes

: nil P,) 05 0 BE ich, Fi A eee ee
+ AP, + P,) 10,4 +A, + Pd) 9.9 + Ce Py) 0.8
or in an other form
be, (Rp, + 4, w,)i+ (Rp, + A,w,)j + (Re, + Ay.) B+
4 he, (Rw, + A, 7,)i+ (Ry, + 4,9,)5 + (Ry, + 4,75) B-
If ¢ and w represent the rotation vectors in #, and R;, we can
write the rotation: .
é, p+ & wy,
and the moment
tR(e,p +e, v) + 4 &,- (Aw + 2, (A) g),
where the notation (A)p means: A, y,71-++ A, ¢,j + As &, &.

The first and strongest of these terms falls along the rotationvector ;
for a body with equal squares of inertia it is the only one; the
second, which, together with the A’s, becomes stronger as the body is
more asymmetric, we might call the “crossed moment” because its
right part is caused by the left part of the rotation and inversely.

Let us put finally the moment of force in the form ¢, "+ &, »,
where gw and py are threedimensional vectors ; then the above given
formula of the vector can be broken up into the six following
components, given successively by the coefficients of & 7, € 7, & J,
£, 9,6, kb, &, k.

Ry, + A.W, = 4, Gs — As Wa Ys + 2m,
Rp, + Ay 9: = A, 9. Vs — Aa Ps W + 20,
Ro, + A, y, = 4,9, 9: — 4. Gs + 2H,
Ry, + A, GP, = As Fs Wi — A, 9, Ws + 20,
Ry, + Ay, = A, p, gy, — AY, 9, + 2H,
Ry, + 4,9, = 4,9, ¥: — 4,9, W, + 20,

( 731 )

If we put R?—A,?=a, and RA, + A, A,=—45,, and if we
represent the vector a4, 9,7 + 4, ,j + 4; 9; *%, by (a) yg, we can write
the six equations of motion:

(a) p = V.(b)w.g + 2Ru — 2Av
(a) p= V.(b)p.w + 2Rv — 2Ap.

For absence of external forces:

(a) p=V.(K)y.g

’ (h)
(b= V.Og-y

In this form we can directly read:

1st. If in the initial position g =, then g remains equal to y,
i.e. if the initial rotation of S, is a rotation // to a principal space
of inertia, then the motion remains a rotation // to that space. The
equations of motion for that case can be reduced to a system to be
treated as the well known Euler motion in 8, when the forces are
missing.

29d, For unequal A’s “invariable rotating’? is only possible under
the following two conditions which are each in itself sufficient:

a. for g and w both directed along one and the same axis of
coordinate (X-, Y- or Z-axis of the representing spaces) i.e. for a
double rotation of 8, about a pair of principal planes of inertia;

6. for g=O or p=—O, i.e. for an equiangular double rotation
of Sy

It has been pointed out by K6rtrer (see ‘Berliner Berichte”
1891, p. 47), how a system of equations analogous with what was
given, can be integrated. (The problem treated there is the motion of
a solid in a liquid). According to the method followed by him the
six components of rotation can be expressed explicitly by hyper-
elliptic functions in the time. If however we have ¢,, Gs; Fs, Wy; Was Wy
expressed in the time, we have the “cones in the solid” for S, and
S; To deduce from these the “cones in space’ we set about as
follows. We notice that the moment of motion to the right Rg + (A) w
in S, remains invariable “in space’’ (in S; that vector changes of
course its direction, but there Ry + (A), remains invariable); calling
the two spheric coordinates (“polar distance” and ‘‘length’’) of y with
respect to Rp + (A) w during the motion of in space & and x and

remarking that each element of the “cone in space” at the moment

of contact coincides with the corresponding element of the “cone in
the solid”, we can express #, # and x in the time, with which the

fol}

“cone in space’ for S, is found. Analogously the “cone in space”
is determined for S,; with respect to Ry + (A)g.

We shall just show that as soon as two of the squares of inertia
P become equal, which means the same as two A’s becoming equal
we can do with usual elliptic functions only.

For instance let. A, = A,) thus also \as— a, =<a,5°0,'— 0)
Let us call ,g, and ,w, the value of the decomponents of g and w in
the YZ-plane, r, and Fy the anomalies of those decomponents (counted
from Y to Z), and f the difference of anomaly of ,w, and ,7,; then
the equations (2) become for this case:

a, DP, = — 45, oP, , SIN F apy ==" 38 Pee si
243 Ps = 35 P, oP, sim F a%3 gW, = — 2s oPs Wy SiN F
gene A. 203 - 2W; Se mat b, 2s 23
Fo = — W, —— G, 608 F Fy = —— pcos, F
gts Phar of s 2s 2-3 273
. 6b b w p
ae} TEES ar3 253
P= (y,—w,) + 2008 6 (p= yy
ats ats of) 2s

from which we deduce four integral relations between
Pi sf, 5%, » ,, and F, namely

Cy :
CLR ks ieee
2% Ps ri a, YP," == Cr ois (7), os ow,” - a, w,? == ec,” oa (1)
243 20s 2fs 2; cos F =e a, b, f W, — C4 is Z s < (iV)
If we put in these

2 Cy ‘
-f, == cos 1, 7 ea sin 1,
Phar a,
C3
abe cos §, ay = sin §,
243 a,
we have the differential eqations
2°3 . : 2s .
y= — ——¢, cos $sinF, $= — C, COS Y Sin F
2% Va, 2X3 Ya,

with the two integrals:
c, siny + ¢,sin$=—c,,
: : ¢
20, cos 4 cos § cos F + B, sin y sin 5 : :
2 "3

so that after elimination we obtain the following differential equation in 7:

5@;° 0,6, - cos *4 . n? = (,b,?—),”) ¢,* sin *y
— 2c, (,0,?—6,?) ¢,° sin *4
“Ig Cy" (,0;°—6,7) ar (6,7 ¢;”) SP - Ore b, } C5” sim *"
+ 2c, (c,?.,5,? + ¢,.6,)¢, sin y
is Cy” (c,*—¢,*) 305° —C,"

( 733 )

or c, siny(=/Y a,.%,) put equal to wu:
3a," a, uw? = F,(u), in which we can easily verify that 7’, (w) has two
real roots between —c, and +c, (the two other roots are real

outside those limits or imaginary according to ,0,’—0,* being z than Q);

those two roots indicate the limits between which 4 swings to and
fro according to a course indicated by elliptic functions. For the
case ,),? > b,? for instance, thus for four real roots uw, << u, << u, << U,,
that course becomes:

a | =
Oh, eh EVD tps Sw (2b 2b:
u— U, -- 37, where sn = sn rf i ate 8 ( 3 1 )
ply— gl, 87 a,? a,
and pig Ug — Ups
Farthermore :
oe. b, 20; oP; > gw, Cos F
eg aL Oe a ea a
a%s ats 2fs

where the second member is a rational function of ¢, (w, can be
rationally expressed in ¢, according to (I), ,¢,’ according to (II),
2fs 2W; cos F according to (IV)), so that -, too can be expressed in ¢
by elliptic functions and by that the entire ‘cone in the solid” ;.and
further according to the above method also “the cone in space’.

The following special cases can very easily be traced to the end.
1st. The four squares of inertia are equal two by two. This case
is obtained by putting A, = A, — 0.
Then
aé.= hh — A,* b= KA,
24 Tt? tb 0!

And the equations of motion pass into:

a, 9, —0 a,y,—9
03.P5—0 5,0, —0
b, b,
> — tp _——
} a%3 ; : 43

from which we directly read, ¢,, ,g;, w, and ,y, remaining constant,
that the “cone in the solid’ for S, and for S; is a cone of revolution
with the X axis as axis of revolution. Farthermore the moment

( 734 )

Rg+A,y, to the right lying in
the meridian plane of g remains in
S, invariable. Thus ‘“‘in space” that
meridian plane rotates about the
vector Ry+ A,w,, by which the
“cone in space’ is known, and
likewise proves to be a cone of
revolution. Analogous for S;. Fig. 9
shows the two cones of rotation
in S, The outer cone is the
moving one.

2d, Three of the squares of inertia are equal and unequal to the
fourth. We take the axis of the unequal one as X, axis in S,. Then
Abe Als A= A; 6. > 62S Sa, = 6, = eee
equations (/) pass into

E vee
g—— V Ww. @
a
: b
w——Vg.yp
a

therefore g and yw are both perpendicular to y and to y, whilst pt+w=0,
so y+ w is constant and ¢ and yw are each for itself constant in absolute
value, so that they both rotate about their sum (‘in space’ that
vector of the sum has in general quite a different position for S,
than for S,) by which the two “cones in the solid” are determined.
“Invariable rotating’ of S, we have here wherever » and y,

y regardless of their value, coincide. To find
aT aaa the ‘cone in space” for |S,, we notice the

invariability in S, of Ry + Ay. ‘In space”

p rotates about Rp + Aw, for the angle
‘’ between those two vectors remains constant.

In S, rotates analogously “in space’’ w about

7 Rw + Ay. Fig. 10 represents the two cones
Fig. 10. of rotations in S,. (Here too the outer cone
is the moving one).

We remind the readers once more, that where we bring g and y,
as far as their positions in the solid are concerned, into relationship
with each other, we must of course in our mind make the positions
to the right and the left that is of the systems of coordinates OX,
Y, Z, and OX, Y, Z, to coincide with each other, so that but one
system of coordinates OX YZ is left (for instance for the equations

sa. Ss es Te ae 2 i

( 735 )

(h) this must be noticed); but in space (i. e. the S, 1 OW)
those systems of coordinates OX, Y, Z. and OX; Y; Z have at
each moment very definite positions differing from one another.

Chemistry. — Prof. C. A. Lospry pr Broyn read also in the name
of Mr. L. K. Wourr a paper entitled: “Can the presence of
the molecules in solutions be proved by application of the
optical method of Tyxpau.?”

(This paper will not be published in these Proceedings).
Chemistry. — Prof. C. A. Lopry pg Bruyn presents also in the

name of Prof. A. F. HoLLeEMAN a paper by Dr. J. J. BLANKsMa,
entitled: “On the substitution of the core of Benzene.”

(This paper will not be published in the Proceedings).

(April 19, 1904).

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,

PROCEEDINGS OF THE MEETING

of Saturday April 23, 1904.

——_—— =00ce—-

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 23 April 1904, Dl. XII).

Eve. Dvsors: “Facts leading to trace out the motion and _ the origin of the underground
water in our sea-provinees.” (Communicated by Prof. H. W. Baxuvuis KhoozEBoom), p. 738.

L. H. Sierrsema: “Investigation of a source of errors in measurements of magnetic rotations
of the plane of polarisation in absorbing solutions.” (Communicated by Prof. H. Kameruincu
ONNES), p. 760.

Frep. Scuvu: “An equation of reality for real and imaginary plane curves with higher
singularities.’ (Communicated by Prof. D. J. Korrewrec and P. H. Scnoure), p. 764,

C. A. Losry pE Bruyn and C. H. Sivrrer: “The BeckMAny-rearrangement: transformation
of acetophenoxime into acetanilide and its velocity”, p. 773.

C. L. Jenerus: “The mutual transformation of the two stereoisomeric pentacetates of d-glucose.”
(Communicated by Prof. C. A. Lorry pr Bruyn), p. 779.

Pp. H. Scuoure: “Regular projections of regular polytopes”, p. 783.

L. E. J. Brouwer: “On symmetric transformation of S, in connection with S, and §)”.
(Communicated by Prof. D. J. Korrewee). p. 785.

Pu. Konxstamm: “On the equations of Ciavstus and van DER Waats for the mean length
of path and the number of collisions.” (Communicated by Prof. J. D. van per Waats), p. 787.

Pr. Konxstamm: “On van DER WAAaLs’ equation of state.” (Communicated by Prof. J. D.
VAN DER WAALS), p. 794.

J. Revpter: Note on Sypnrey Youna’s law of distillation.” (Communicated by Prof. J. D.
VAN DER WAALS), p. 807.

H. A. Lorentz: “Electromagnetic phenomena in a system moving with any velocity smaller
than that of light’, p. S09.

E. Janyxe: “Observation on the paper communicated on Febr. 27 1904 by Mr. Brouwer:
“On a decomposition of the continuous motion about a point O of S, into two continuous
motions about O of §3’s.” (Communicated by Prof. D. J. Korrewxe), p. 831.

L. E. J. Brouwer: “Algebraic deduction of the decomposability of the continuous motion
about a fixed point of S, into those of two S,’s.” (Communicated by Prof. D. J. Korrewes),
p- 832.

A. A. W. Husrecut: “On the relationship of various invertebrate-phyla”, p. 839.

Max. Weser: “On some of the results of the Siboga-expedition”, p. 846.

L. Bork: “The dispersion of the blondine and brunette type in our country”, p. 846,

R. P. vay Carcar and C. A. Losry bE Bruyn: “Changes of concentration in and crystallisation
from solutions by centrifugal power”, p. 846.

C. L. Juncivus: “Theoretical consideration concerning boundary reactions, which decline in
two or more successive phases.” (Communicated by Prof. C. A. Lopry pe Bruyn p. 846.

The following papers were read:
49
Proceedings Royal Acad. Amsterdam. Vol. VI.

( 738 )

Geology. — “Facts leading to trace out the motion and the origin of
the underground water in our sea-provinces”. By Prof. Eve.

Dvnors. (Communicated by Prof. H. W. Bakauis RoozEsoom).
(Communicated in the meeting of June 27th, 1903).

As to the origin and the condition of the underground water in
our low-lands, we are, as vet, almost entirely in the dark; facts,
that might throw light on the subject, are almost entirely lacking.

The hazardous suppositions made on the subject by some, and
the extraordinary caution, which others thought necessary in practice,
prove this. Only lately Darapsky, in a dictatorially written article,
held forth that even now rivers of former geological periods
follow theit very same channels, but now as underground streams.
The underground water he considered as almost exclusively river-
water ').

Others have admitted powerful artesian currents from the eastern
high-land, without any decided facts supporting that opinion. Again
others fancied to have found the explanation in VoueeEr’s hypothesis,
on the condensation of vapour in the ground; a hypothesis, refuted
already a long time ago by no less an authority than Hann *). A single
phenomenon observed in one of the East-Frisian Islands, already
years ago observed in our own country, and explained, but now
forgotten, led some to imagine possibilities, as to the sea threatening
us also from below, a thing which filled them with anxiety. Not to
mention altogether absurd and physically impossible suppositions.

However it appeared to me that an earnest searching for facts,
could not but bring to light something that would give us a elue,
further to find our way in this important question, important both in a
scientific and a practical respect. Indeed, thanks to the kindness
I met from different sides, I was enabled, during these latter months,
to make a large number of observations and to collect facts which
show forth, in outline, the direction, the origin and the general
condition of the underground water in the main part of our
low-lands.

Since it will take some time fully to work out the results obtained,
the present circumstances make it desirable I think, already now, in
this short communication, to make known the most important of

!) L. Danapsky, Die Trinkwasserfrage in Amsterdam. Journal fiir Gasbeleuchtung
und Wasserversorgung. 46 Jahrgang, p. 468, sqq. (1903).
*) J. Hany, Zeitschrift fiir Meteorologie, 1886, p. 482—486,

( 739 .)

them. My researches were principally limited to the southern part
of the North-Holland low-lands, including the dunes, and the adjacent
parts of the provinces of Utrecht and of South-Holland. It is a
matter of course that also here | had to limit myself to the chief
points of the question.

In the last decennia, hundreds of borings have been done in the
polders, in the dunes and in the area between them by the corps
of military engineers and by others, with the object of making
fortifications or of obtaining fresh water. Down to a certain depth,
the constitution of the soil is consequently pretty well known, and some
deeper borings have tolerably well acquainted us also with the
constitution of the soil at greater depth. Sand is the chief substance,
alternating with beds of always very impure clay. Close to the
surface, pretty generally, a zone is found of clayey substances, (the
well-known ‘old sea-clay” of Svrarine), over considerable areas,
covered with a layer of peat, which clay, in the dunes, where that
peat is generally lacking, is covered with blown sand. Under the
finer sand of the upper-soil, often mixed with clay, in which occur,
in large areas, deeper layers of peat, there is a zone of coarse-grained,
often gravelly sand, not unfrequently containing pebbles. In the
west of the mentioned region, the top of that zone lies about 30 M.
+~AP. deep, or a few metres higher; in the east, near Aalsmeer,
Sloten, Amstelveen, Mijdrecht, Wilnis, Oudhuizen, it rises to 16 or
14 M.- A.P.; near Muiden and Nigtevecht as high as 10 or 8 M.
-~ A.P. and its reaches the surface further east. Under Amsterdam and
both south-east and north-east of it, the soil, on the whole, is much
richer in clay.

Also at greater depths, clay-beds occur, but never as unbroken
layers, extending over great distances; the most regular zone is
after all that of the so-called old sea-clay, near the surface. It is
besides of importance, that near our eastern frontiers much older
formations come to the surface, than have been found, some hundreds
of metres deep, under the lowlying lands in the west. This in itself
is a reason not to expect artesian water, from Germany, in our
western sea-provinces, to some hundreds of metres below the surface,
at least.

Of great significance for the problem is also the fact that more or
less pure clay rarely occurs. What is considered as such, on further
examination, (washing of a number of samples of different origin,
and especially chemical analysis, which analysis Dr. N. Scnoor.
was kind enough to do at my request) proved to consist for only
one third of clay at the most, generally for much less, even for only

49%

( 740 )

one seventeenth. The investigations by Prof. Sprixe?) have proved
the fact that, and the reason why, even very thick layers of im-
pure clay, e.g. the limon supérieur de la Hesbaye, let through water.
What then must we think of our clay, which, though technicians
will call it impermeable or “rich clay’’, likewise, for the greater part,
consists of sand !

The chemical analysis of specimens of the fattest clay-sorts selected
from their outward look, (a large number of such specimens being
at my disposal from a variety of borings) showed the real clay
percentage to consist of less than @ third: at Sloten (boring IV. 2,
at +M.—A.P.) and at Uitgeest (Station, at 43 M.— A.P.). Of about
a fourth: at Hoofddorp, Haarlemmermeer (at 6 M. and also at
34 M.—A.P.); at Amsterdam (Dairy at the Prinsengracht, at 9
M. -A.P.) and in the dunes, 3 K.M. west of Santpoort (at 40 M. ~A.P ).
Of about « jifth: at Amsterdam, (Dairy in the Second Spaarndammer
Dwarsstraat, at 3.5 M. — A.P.); at Harlem (Hagestraat, at 14 M. —A.P.);
at Hillegom (Treslong, at 14 M.~+ A.P.); at Beverwijk (Middle of
Breestraat, at 19 M.—A.P.); at Alkmaar (Station, at 22 M. ~ A.P);
in the northern part of the Watergraafsmeer polder (near the Ooster-
railroad, at 35 M.—+ A.P.); at Katwijk (875 M. South-West of the
water-tower of the Leyden waterworks, at 1.6 M. > A.P.). Of about
a siath: at Sloten (boring III. 1, at 5.50 M.-—> A.P.) and at Eertden-
koning, in the west of the Haarlemmermeer polder (at 19.5 M. —A.P.).
Of about a seventh: at Velsen (near Rosenstein, at 2.50 M. — A.P.); at
Katwijk (in the same borings, at 3.8 M.—~ A.P.). An eighth to a ninth:
at Beverwijk in the same borings at 5 M.—A.P.); at Amsterdam
(Prinsengracht, at 6 M.—+ A.P.) and in the Koningsduin near Castri-
cum (at 32 M.+A.P.). Of less than @ tenth: at Driehuis (Nunnery,
at 18 M.—A.P.). Of about a jifteenth: at Amsterdam (Second
Spaarndammer Dwarsstraat, at 62 M-> A.P.); at Hillegom (Treslong,
at 4M. A.P.). Of about a seventeenth: in the Watergraafsmeer polder
(at 8 M.+ A.P.). No clay at all, at Amsterdam (Second Spaarndam-
mer Dwarsstraat, at 48 M.->A.P.). The last specimen, looking like
fine-sandy clay, proved to consist of sandy caleareous tufa with
td Wg AeaoG,.

As to peat, experiments have shown to me that its impermeableness

1) W. Sprine, Quelques expériences sur la perméabilité de l’argile. Annales de
la Société géologique de Belgique. Tome 28, p. 117—127 (1901), and : Recherches
expérimentales sur la filtration et la pénétration de l'eau dans le sable et le limon.
Ibid, Tome 29, p. 17—48, 1892). Compare also the report of H. Rasozéer on those
investigations in: Bulletin de la Société belge de Géologie, de Paléontologie et
d'Hydrologie. Tome 16, p. 269—295, (1902),

( 741)

is equal to that of sandy clay, but that in another respect, it is
very different from clay, i.e. in its water-containing capacity. Whereas
clay, like sand, can contain water for scarcely more than a third
of the volume of the dry substance, non-cgmpressed peat can do so
many times over. Peat of the Rieker polder, near Sloten, on the
territory of the military water-works, was found to have a capacity
of holding water, nine times the volume of the dry peat; and the
water in it can, although slowly, yet freely move.

On the whole we have to deal with an upper-soil of finer, often
clayey sand water, and on which or in which, in most places,
enormous water-reservoirs occur: the peat beds, for even the com-
pressed peat contains still a large quantity of water. In the colder
(rainy) seasons the upper peat layers are not only always kept filled
with fresh water, but they can, though slowly, provide lower regions
from their water-store ; and along with the water, no doubt with carbonic
acid, which deep below will dissolve iron and chalk ; and methane
which, in the same way as carbonic acid, the more easily dissolves,
the higher the pressure is. Deep down the latter product of decaying
organic matter, cannot be formed, on account of the absence of
bacteria.

Those upper-layers, little permeable, more or less shut off the
zone of gravelly coarse-grained sand which at the bottom, in a
similar way but much more imperfectly, in its turn is shut off by the
irregular beds of impure clay and fine-grained sand, occurring there.
Under those conditions the vertica/ motion of the water, must on
the whole be difficult; at one place more and at the other less,
according to clay or sand locally prevailing and in proportion to
the latter being finer- or coarser-grained, whereas in the coarse-
grained medium zone or zones, horizontal motion is comparatively
easy ; that medium zone is therefore the great channel, and in
extracting underground water this “‘water-vein’” is generally found
at about 80 M.— A.P. or a little deeper still.

That indeed below that depth the underground water has an easy
horizontal passage, appears from the fact, that the height to which
the water ascends in tube-wells, driven below the upper-edge of the
coarse-grained bed, falls but little; whereas higher up in the fine-
grained sand, it nearly always is considerably higher, (i.e. excepting
the deep polders, where the deep water will naturally rise above
the surface of the soil).

As to fixing the direction in which the deep underground water
moves, a thing that will enable us to inquire after the existence of those
currents, supposed by some, and also the origin of the underground

( 742 )

water, the means to do so, although hardly ever applied, are evident.
Just as on the surface, it is the law of gravitation that also deep
below, gives to the water its horizontal course. The direction of that
motion, as caused by gravitation, can be demonstrated from the
inclination of the pression-line of the water, deep below, for that
motion can happen only from spots under greater, to those of smaller
pression. The vertical motion, under any given constitution of the
soil, can, as a rule, be inferred from the positive or negative character
of the pression below, with respect to the level of the water on
the surface.

When the water from the underground, freely rismg in a tube-
well, remains below the level of that in the upper soil, that vertical
motion can take place only in a downward direction — if at
any rate, then and there, a motion in a vertical direction on the
whole is possible, which is mostly the case. When, on the other
hand, the level of the water, in the tube-well rises higher than that
of the surface-water, as is the case in the deep polders, vertical
motion in a somewhat permeable soil, can take place only in an
upward direction. The quantity of chlorides in the water, determined
as chlorine, furnishes us with an other indication of the direction
of that vertical motion.

So the observation of the height to which the water ascends in
the tube-wells and the mutual comparison of the same, can teach
us much as to the direction in which the water moves. A great number
of those observations have enabled me to ascertain, that also deep
below, the motion of the underground water (uninfluenced though it
remains by small irregularities), depends on the shape of the surface.
In short, the direction is from the dunes to the lower regions ;
from the higher to the deeper polders, and any great unevenness of
the surface, makes its influence felt, already at a considerable distance.
In the dunes the deep underground water is under the highest
pressure ; in the deepest polders it ascends in the tube-wells to a
level some metres lower, although there it wells up above the
ground. Near a low-lying polder the water falls also in very deep
wells. So not only near the surface, but also deep below, there is
a motion from the dunes to those polders and also from the higher
to the lower polders.

Before communicating the observations, on which those results are
founded, 1 must specially state, that there are influences, which for a
time may more or less change the pression of the water in the
underground, as it appears from the rise or fall in the wells. In the
first place must be mentioned: rains, which make their influence felt

A hema

{ 743: )

almost immediately, which influence is far more powerful, than any
other. After the heavy rains in the fourth week of April 1908,
a number of deep wells on being sounded (Aprii 27%") showed a
higher level of 0.18 to 0.20 M. A week later it had sunk about
0.06 M., and only after the dry latter half of May, towards the
end of that month, it was again what it had been towards the end
of April, before the heavy rains. The rising of ihe deep well-water,
immediately after much rain, may be in part the result of the
greater ‘pressure of the upper-soil. In the same way, a train passing
over the railway-dike in the Watergraafsmeer polder, for a moment
raised the water 7 m.m. in a deep well, at a distance of 18 M.,
which well was 34.5 M. beneath the surface of the polder. Principally
ihe rain will increase the hydrostatic pression. In the second place,
changes in the pression of the atmosphere have a passing influence
on the level of the water in deep wells. Those changes make them-
selves felt at once, but that natural barometer is an imperfect one;
the effect of the changes in the atmospheric pression soon disappears.
For some hours however millimeters rising or falling of the quick-
silver have their equivalent in centimeters on the watergauge.

In the third place the low and the high tide of the sea, exercise
i negative or a positive pression on the deep underground water, i. e.
on those spots, which are not too far from the sea (3 or 4 K.M.
seems to be the utmost limit here). I have always taken those
circumstances in te account. For the rest, as far as necessary, the dates
of the observations are stated here. With a few exceptions, I myself
ascertained the ievel of the water (with respect to N.A.P., the new
water-mark of Amsterdam, as a standard) or it was done under my
control; some other results I hold from reliable sources.

In the dunes now, the pression of the deep underground water ascends
to about 38 M. above A.P. So on Maréh 30% 1903, in a well of the
Harlem waterworks sunk down to 53 M.A. P., situated in the
midst of the dunes, at 3 Kk. M. west of Sandpoort, and a little further
from the polderland, the level of the water was observed to be at
2.91 M. +-A.P.; in another well in the dunes, deep 45.5 M. = A. P.,
almost 2 K.M. further south, and at a distance of 2?/, K. M. from
the polderland, the water ascended to 2.19 M.-+- A. P. In a third
well, close to the water-tower near Overveen and 1 Kk. M. from the
low-lying lands, as deep as 54 M. ~ A. P., it rose only to 1.20 + A.P.
Those three wells are at a distance of 2'/, to 3 K.M. from the sea,
In another well, near to the Brouwerskolkje, sunk down to 70 M.~ A.P.,
(in 1890), at */, K.M. from the one near Overveen and less than '/, K.M,
from the low-lying land, the water had been seen to ascend to

( 744 )

0.30 M.-+ A.P. The boring-hole, although still in the dunes, being
comparatively low, the water rose here above the ground. The fact
that those four wells are situated in the dunes, together with their
comparative distances from the lower regions, distinctly make their
influence felt here.

Nearer to the inland dunes, the level of the water is every-
where lower than in the middle. On the 11% of April 19038, in
the Koningsduin near Castricum, the level of the water in two
wells, sunk down to 32 M.= A.P., was°1.195 and 1:23 M.+ AP.
They were at a distance of about */, K.M. from each other and
they were */, K.M. from the low-lying land; the distance from
the sea being 2°/, kK.M. On the same day the level of the water
was 0.29 M.-- A-P., in a well, deep 33 M.— A.P., near Sant-
poort, at the inland of the dunes and 2200 M. from the Zuid-
Spaarndam polder (the level of the superficial water or the Summer
Level here being 2.60 M.->A.P.), whereas it reached no higher
level than 0.055 M.-+ A.P. at Rosenstein, separated from the dunes
by the plain of Driehuis, and only 13800 M. from the Noord-Spaarn-
dam polder, (of the same depth as the polder of Zuid-Spaarndam).

Just as in the Brouwerskolkje near Overveen, the water rises
above the boring-hole also near Bergen, on the grounds of the
Alkmaar waterworks, in wells, only about 20 M. — A. P. deep,
for the reason of the dunes having purposely been lowered. Here
however, in the midst of high dunes and at */, kK. M. from rather
shallow polders (summer-level + 1.33M.), it rose to a level of 1.385 M.
+ A.P., on March dst 1903.

Ina well, deep 40 M.> A.P., on the grounds of the paper-manufactory
of the firm van GELDER & Sons, at Velsen, which well is situated at
1300 M. from the Noord- en Zuidwijkermeer poiders (having 2.40 M.
— A. P. Summer-Level) the water on April 14% 1903, had a level
of 0.26 M.+ A.P. without, for 53 hours, there having been any
pumping, neither there nor at any of the other wells. Under meteor-
ological conditions which admit of comparison, a well, deep 44 M.
— A.P., near the small steam-mill, in the Meerweiden, on the North-

Sea Canal, had a level of 0.485 M. — A.P., it being situated
only 3870 M. from those polders and between two shallower ones
(— 0.50 and + 1.40 M. Summer-Level). In the Zuidwijkermeer-

fort, situated in the polder of the same name, a well, 45 M.—> A.P.
deep, had on March 8 1902 a level of about 0.80 M. — A.P.
Here we distinctly see the lowering of the level of the water in
deep wells, from the dunes to the polders, which shows a horizontal
motion in that direction.

The same appeared, still more distinctly, south of Harlem, through the
influence, which the extensive Haarlemmermeer polder, with its outlying
polders, eastward, has on it; the summer level of those polders,
which together cover 42000 H. A., being about 5 M. or more under A.P.

At Aerdenhout a well, 82 M. > A.P. deep, showed a level of
0.52 M. + A.P. on May 5 1903. We may admit that at the time
the level of the other wells was being ascertained, it must have
been here about 0.40 M. + A.P. This well is 3600 M. from the
Haarlemmermeer poider and only 350 M. from the Veenpolder
(Summer-Level ~- 0.75 M.). A well at Heemstede, on Kennemeroord,
deep only 26.8 M.—> A.P.; but sunk down into the gravelly sand,
had on June 2°¢ 1903 a level of 0.575 M.—A.P. That well,
although in the inner-dunes, lies only 2200 M. from the Haarlem-
meer polder. Another well, some 100 M. north of the Common-Hall
at Heemstede, at about 13800 M. from that polder and. still in the
inner dunes, had on May 29%, a level of 0.78 M.-> A.P. In a third
one, nearly 30 M.-> A.P. deep, situated within the precincts of the
community of Heemstede, but at only 440 M. from the Haarlemmer
polder, on Bosbeek, at the border of the inner dunes, and under
meteorologic conditions admittting of comparison, the level of the water
was 1.29 M.— A.P. A well on the Leyden Canal, deep 32 M. — A.P.,
near the remise of the Harlem Electric Tram, on April 9% 1908,
had a level of 0.225 M. > A.P. This well, within the Veenpolder
(Suminer-Level ~ 0.75 M.), lies one side at 3700 M. from the encircling
canal of the Haarlemmermeer polder, but also at only 1400 M. from
the Noordschalkwijk polder, (Summer-Level~} 1.25 M.) and the other
side about 1 K.M. from the dunes. A well near the Harlem Gas
Works, in the Veenpolder (+ 1.40 M. Summer-Level), 1700 M. from
the encircling canal of the H.M.P., had, on March 51st 1903, a level
of about 1.00 M.— A.P., and in a well on the grounds, reserved
for the Harlem Abattoir, the level on April 4! was 1.08 M.—> A.P.
This well lies in the Roomolen polder (Summer-Level ~ 1.25 M.), at
1300 M. from the encircling canal of the H. M. P.

On the other hand in a well at Hillegom (behind the building of
the Hillegom Bankvereeniging), sunk down to 389 M. > A.P.,
1200 from the Haarlemmermeer polder, the level of the water on
April 8 1903 was only 1.20 M.~> A.P. Although equally far from
that polder as the well near the Common-Hall at Heemstede, the
distance that separates this well at Hillegom from the central range
of dunes, being 2900 M.; that at Heemstede only 1650 M. The
upper-soil moreover at Hillegom is much richer in clay than that
at Heemstede, the deep underground water consequently on the first

( 746 )

mentioned spot, being much more under the influence of the pression
which makes itself felt in the H. M. polder.

At only 1125 M. north-east of the well at Hillegom, but BOO M.
within the Haarlemmermeerpolder, at “‘Eert-den-Koning”, a well

has been sunk down to 26.3 M. + A.P., in which on April 21%,
(before the heavy rains of the last weeks of that month), the level
of the water was 2.57 M. + A.P. The cause of such a difference

is some 1500 M. greater proximity of the centre of the Haarlem-
mermeer polder. In the midst of that polder, at Adolfshoeve, on
the east Hoofdweg, 890 M. southwest of the Vijfhuizer Dwarsweg,
I saw the water ascend only to 4.70 M.+A.P. in a well, deep
34 M.—A.P., sunk down below a bank of clay. slightly less deep.
Probably the rains of a few days before, had raised the water a
decimeter above its dry weather level. At Hoofddorp I found on
May 8 1903 a level of 5.038 M.—-A.P., in a well only 18.5 M.>
A.P. deep. Although less deep than the other wells, also this was
sunk into the less fine sand, and near the top of the coarse-grained
sand, beneath the less permeable upper-soil of fine sand and clay.
If the well had been sunk below the clay-bank and 34 M.-> A.P.
deep, the water no doubt would have risen a little higher. So the
result is, that in the midst of the Haarlemmermeer polder, the under-
ground water, from under the deeper lying clay, can ascend half a
metre above Summer Level (this being 5.20 M.— A.P.), on the other
hand, from under the clayey top-layer. it can rise but little above
it. The pression it acquired in the dunes and in the surrounding,
shallower polders, on its way to the H.M. polder, is in the middle
of it, at 18.5 M.— A.P., almost entirely lost; and at 34 M. — A-P.
reduced to about half a metre. so it can rise but little above
the surface underground water, whereas at ~Eert-den-Koning’, the
ascending capacity of the water rising from 26 M. — A.P. is 2.63 M.
above Summer Level, or about 1.50 M. above the grass-land of
the polder. The upper-soil, we must bear in mind is half permeable,
and on its way to the middle of the polder, the water gradually
loses more or less its ascending-capacity. Consequently also, the water
cannot horizontally move further east, for then it would have to
move to parts, where there is more pression.

That indeed the difference in pression between the surrounding
higher parts and this deep polder, is the cause of the motion,
appeared from observations taken on other spots round the Haarlem-
mermeer polder, and in the deep polders more east, adjacent to it,
including the large Mijdrecht-polder.

North-east of the Haarlemmermeer polder, in the Rieker-polder,

( 747 )

a great many wells have been sunk for military purposes, most of
which wells are about 50M. > A.P. deep. The levels in them were
repeatedly sounded by me, which, considering their large number,
led to important results. Specially of great significance is what those
soundings teach us, as to the direction in which the deep underground
water moves. Subjomed table, in which, as much as possible, only
wells of corresponding depths have been put down, entirely confirms
what I found elsewhere.

Those soundings were done on June 5 1903. The distances of
the wells to the H.M.polder itself, one will get by adding 80 M. to
the figure that expresses the distance between them and the encircling
canal. |

Distance in M., to Level of the water

Number Depth, the encircling canal in the well,
of the well. in-M.— A.P. from the H. M. P. m Mo — A.P:
ie, 8 56.5 25 3.00
reals 47.0 50 2.99
20 49.8 ae 2.985
| 45.6 100 2.995
| NO a 47.2 367 2.94
10 ad 525 2:91
21 51:5 750 2.835
23 52.3 795 2.83
25 52.9 840 2.82
35 55.0 1090 2.81
36 54.0 1120 2.80
od 50.6 1145 2.80
40 52.8 1225 2.78

Here clearly comes out a motion of the deep underground waiter,
from the higher polders, north of the Haarlemmermeer polder,
towards this deep polder. On 1200 M. of distance there is an
inclination of 0.22 M., or 1,8: 10000, whereas in other directions,
there is no regular inclination. That indeed no general motion from
east to west or vice versa is to be thought of, naturally follows
from the comparison between the level of the water in wells thus
situated. For instance from the following row of wells, all at 25 M.
trom the encircling canal of the H. M. polder.

( 748 )
Number Depth Distance in M. Level,
of well. in M.—A.P. from well II. 5. m Ma Ale
if a 56.3 0 3.025
6 39.0 50 2.98
7 40.1 100 2.98
8 56.5 150 3.00
10 46.5 250 2.99
12 30.0 318 3.005
14 44.0 380 3.025
nis 38.0 595 3.01

At the same time the fact stands forth that, once a level reached
under the fine-grained and clayey upper-strata, further differences in
depths are of little consequence.

Comparison of the other soundings will show forth the same for
either statement.

The average level of last mentioned 8 soundings, in wells at
25 M. distance from the encircling canal, is ~ 3.00 M., so equal
to that in well Il 8 which we used as starting-point in the first table.

Though there is no great current in the one or the other direction,
vertical on the one towards the H. M. polder, (so from east or west,)
there seems to exist a slight local motion from the Nieuwe Meer
(level about — 0.60 M.) to the west (Summer Level of Rieker polder
~ 1.80 M.), as may be seen from the comparison between wells,
situated at increasing distances from that small lake, but pretty well
at an equal distance from the H. M. polder.

Number Depth, Distance in M., Level,
of well. in M.— A.P. from the N. Meer. in Mi. SAE
Ls 48.5 60 2.935
2 48.7 90 2.9939
3 50.5 110 2.925
4 51.0 135 2.932
7 52.8 220 2.955
8 5 ies 235 2.95
i) 50.0 235 2.955
LO 49.5 235 2.96
12 41.3 300 2.98

Il 14 44.0 690 3.025

——— ar ie ile

( 749 )

The real existence of the above indicated motion, from the
shallow polders, north of the H. M. polder, towards the latter, is
confirmed by observing the level in a well, sunk down to 32.5 M.
—A.P. under the direction of Dr. ALEXANDER KLEIN, near the
“Huis de Vraag’’, between the Rieker polder and the Sloter binnen-
and Middelveldsche combined Polders (Summer Level — 2.15 M.),
not far behind the Vondel Park. On June 16% 1903, I found the
level to be 2.46 M. + A.P. The well lies 5100 M. from the H. M.
polder, or about 1800 M. further than well [Hk 40, in the Rieker
polder. So also here there is an inclination of about 1.8 : 10000.

Also towards the polders which le eastward, adjacent to the
H. M. poider, and hydrologically one with it, the motion of the
water, deep down, is from the higher to the lower ones. This was
shown by soundings, done on June 24% 1903, in wells, all sunk
down to about 30 M. — A.P. and belonging to fortifications south-
east of Amsterdam. There appeared to be an impelling force in that
deep water towards the Groot-Mijdrecht polder (where they keep the
water to a Summer Level of — 6.60 M.).

The following small table, concerning observed levels on August
26" 1903, shows this :

Distance to the Level,
Groot-Mijdrecht Polder in M. > A.P.
Fort near Nigtevecht 7 KM. 1.775
Mil. Post near Oostzijdschen Watermill 5.5 _,, 2.01
Fort near Abcoude aa a
a De Winkel Dakss, 2.29
3. 3 ~betshol i ee 4.43

The fact that the inclination of the pression-line is specially great
here, near the deep polder, and also from Nigtevecht to the Oost-
zijdschen Watermill, must, I think, be attributed to the greater height
to which the gravel-diluvium rises in this part, a thing to which
attention has been called, already at the beginning of this paper.
The influence of surface-water can therefore make itself felt comp-
aratively strongly, when locally rapid changes occur; at Botshol,
on account of the neighbourhood of the deeper polder, and at
Nigtevecht on account of the rising of the upper-part of the deposit
of coarse grained sand, which at a comparative small distance, east
of Nigtevecht, at certain spots, even reaches the surface. The reason
being that the artesian regularity of pression, to which the deep

( 750 )

underground water is submitted, is broken by those local irregularities
of the geological structure.

That we have not to think of strong currents of the deep under-
eround water, in a general direction for all, but of currents, dependent
on the local form of the surface, may finally be confirmed by
soundings in two wells, sunk also under the direction of Dr. KLEIN,
in the Watergraafsmeer polder (Summer Level ~ 5.50 M.). One of those
wells, in the north of that polder, near the Ooster-railway, at 250
M. north-west of the so called Poort, deep about 39.5 M. = A.P.,
had on June 18 1903 a level of 3.215 M.—A.P. In another,
presumingly 385 M.-> A.P. deep, in the south of that polder, near
the Omval, the level was 3.125 M.— A.P., on June 23¢ 1903. The
latter lies 5 K.M. almost straight east, from that near the “Huis de
Vraag,” which in its turn hes 2.8 K.M. east, but a little towards
the north, from well III. 40, in the Rieker polder.

Another well, about 25 M.-—- A.P. deep lies, in the south-west
corner of the Bijlmermeer polder (Summer Level > 4.80), at 4 K.M.
north-west of the well near the Oostzijdsehen Water-mill, 4.8 K.M.
south-east of that near the Omval and 11 K.M. from the Bullen-
wijker and Holendrechter polder (Summer Level +3.35 M.). This
well had, under the same meteorological conditions, a level of 3.075
M.~+ A.P. At the well-known boring done by the corps of military
engineers, at Diemerbrug, near the Weesp turnpike, beyond the
northern extremity of the bBijlmermeer polder, the level of the water
in the well, then 73 M.— A.P. deep, was 2.51 + A.P. on Oct. 18%
[888. That well was 2 k.M. from the eastern border of the Water-
graafsmeer polder.

Consequently the result of the different observations is, that there
is not a general, so called ‘‘artesian’ current from east to west
or vice versa, in the region between Amsterdam and the H. M.
polder, neither south-east of Amsterdam; those found, are but special
currents originating in local differences of height of the surface and
directed towards the Haarlemmermeer- and adjacent other deep polders
and towards the Watergraafsmeer-, the Bijlmermeer- and the Holen-
drechter polders.

Another result is the conclusion we may draw, as to the direction
of the vertical motion of the underground water, by comparing the
different levels of the water in the deep wells with that of the
varying levels of the underground water rising from smaller depths
and with the highest level this reaches. In short in the shallow
polders, in the dunes and in the area between them, the direetion
appears to be downward; in the deep polders, on the other hand,

(751)

such as the Haarlemmermeer polder and the adjacent deep ones,
upward. It is a wellknown fact that the water in deep wells rises
above the surface of the underground water and above the grass-
land of the deep polders. In polders of smaller depth, the deep
wellwater remains below the surface. Likewise the ascending
power of the water, as a rule, gradually diminishes towards the
middle of the deep poiders. In higher parts, such as in the dunes
and in the flat sandy adjacent area, the surface of the wunder-
ground water is considerably higher than the level of the water
in the deep wells. So here we find increase of pression from
below upward, and descending movement of the water. In the
dunes near Castricum the level of the surface of the underground
water is about 1.30 M. higher than that reached in the deep
wells; at Santpoort, at the inland side of the dunes, the difference
even being 1.80 M.

In connection with the above indicated conditions, especially in
the colder seasons, when the underground water is generally fed
with the water penetrating the soil from the rainfall, the dunes,
the shallow polders and the intermediate area will get a fresh
supply of water, whereas there is always a loss by the pumping in
the deep polders, to which, certainly in no less degree than to the
sea, there is a constant affluence. The underground water not being
of distant origin, it can as a matter of course be derived only from
rains on the spot itself, or at a small distance.

Just a passing remark in connection with the results arrived at,
to call the attention to the drying out of the dunes and especially
of the lower stretches of land west of the H. M. polder. This drying
out, i.e. considerable lowering of the surface-level of the underground
water, actually noticed for already halfia century, has repeatedly been
attributed to the waterworks in the dunes for the water-provision
of Amsterdam; to my opinion however it is in the first place
due to the draming of the Haarlemmermeer, just half a century
ago, from which event dates the powerful subterranean current
from the dunes to the deep extensive Haarlemmermeer — polder.
Especially in the lower tracts from Ziuidschalkwiyk to Bennebroek,
up to a few kilometers from that polder, the drying out process
has made itself felt, on account of clay above the coarse-grained
sand being almost entirely lacking. In those parts the water in the
ditches, when there is no fresh artificial in-flow, will soon sink down,
actually making its way under the encircling canal of the H. M.
polder, as is proved by the considerably lower level in part of

that region’). Ever since, a few years ago, the level of the H. M.
polder was lowered 0.30 M., the level of the water in a pond, 4 M.
higher, at Meer-en-Berg, and 400 M. outside the polder, was observed
to be lowered as much. From this we can imagine how powerful
the influence of a lower level of 5 M. must have been at the
time when the Lake of Harlem was being drained dry.

As to the motion of the deep underground water, at the side of
the dunes, facing the sea, I have been able to make only a few
observations. The great uniformity with which the dunes border on
the sea however, in connection with the other results of my investiga-
tion, permit drawing pretty safe conclusions from them, as to the
general condition.

A well known fact is that the superficial water flows from the
dunes towards the sea, just as it does inland from the dunes to
ihe adjacent flat area and the polders. A remarkable proof of the
water flowing from the dunes to the sea, is the welling up, at
ebb-tide, of fresh water on the beach, north of Noordwijk-aan-
Zee. Puddles and furrows form themselves, from which, as long
as if is ebb, not unlike rills, fed from sources, large quantities
of water, only partly consisting of salt-water, flow. towards the sea.
Particles of clay brought up with the water and found in the ripple-
marks on the beach, suggest the presence of a clay-bed, close to
the surface, through interruptions of which the welling up of the
water takes place. On March 27% 1903, at 11 a.m., it being low-
tide, about 9 hours after high-tide, (the wind 8.S.E.), I scooped
opposite strand-pole N°. 78, from such a rill, about 200 M. long,
(the debit of which might be calculated to be in the least 7 M*® an
hour), a sample of water, which proved to contain 11550 mG. of
chlorine the Liter. So for '/, it was fresh- and for ?/, sea-water,
and hourly more than 2.3 M* fresh water found its way into the
sea, through that litthe ebb-rill. The great uniformity now with which
the dunes slope down to become beach permit us to accept as
a general though in most cases invisible fact what here, through
local circumstances, happens visibly.

Another proof for the considerable flowing down of fresh surface-
water towards the sea, furnished to me a stone-well at the foot of the
dunes, on the beach at Zandvoort, from which the fishing-smacks
take their water-store. The bottom of that well is 0.72 M. ~ A.P.,

1) That also from the encircling canal itself, which is about 3 M.— A.P. deep,
the water is sinking down, is proved by the fact, that near the Cruquius, the
level is always some centimeters lower than in the Spaarne and in the canals
of Harlem.

( 753 )

i. e. 0.04 M. above average low-tide mark, and’ 4.0 M. below
high-tide mark. On Febr. 18% 1903, at 4.20 p.m., it being low-tide,
the quantity of chlorme of the water in that well, was 291 m.G.
the Liter. On Mareh 6 1903, at 10.380 a.m., about three hours after
high-tide, the level of the water in that well was 0.95 M. + A.P.
or 0.76 M. above the sea, at that moment.

Also in the deeper, coarse-grained sand-layers, there is a main
current of fresh water towards the sea. In a well in the dunes,
350 M. from the sea (low-water line), on the Kerkplein at Zandvoort,
sunk down to 28.38 M.— A.P., the level of the water on the 14‘ of
April 1903 was as follows :

At 430 pm. 1445 M.-+ AP.
d gi) MAF
1.520

Os) =
So a distinct influence of the high-tide, which at IJmuiden rea che
its highest level, 1.43 M.--A.P., at 4.55 p.m.; at Zandvoort presum-
ably 8 minutes earlier, is evident.
The next day, in the same well — the deeper one of the two —
the level of the water was found to be:

At 12 o'clock 1.28 M.+A.P.
3, 42:85 pm. 1.24
penta ee Th 22
we ‘Gout thew
esteem Bangs ys, Lee
1.193
: 1.205
ree age mee 1 20

Comparing the above figures with those of the self-registering
tide-gauge at IJmuiden, it appeared that the influence of the tide
makes itself felt 40 minutes later in that well, situated 350 M. from
the sea. The sudden way in which the gradual rising of the water
stopped at 3.5 p.m. was found to correspond with the somewhat earlier,
change in the level of the sea, the difference in time corresponding.

At IWJmuiden, 1.30 p.an., the low-tide level was observed to be
0.76 M.= A.P.. So the water in the well was 1.95 M. higher. At
high-tide however, it was at that time, but about 0.10 M. above the
level of the sea. So the amplitude of the tide influence in the well,

Proceediags Royal Acad. Amsterdam. Vol. VI.

( 752 )

was then about 0.34 M. But the tide rose then unusually high
(0.55 M. above the average high-tide mark) the low-tide mark being
then just the average one. I think I may estimate the average vertical
amplitude in the well to be, at the most, 0.30 M., and believe pretty
near to hit it, when accepting 1.30 M.-+ A.P. as the average level
in that well, or 1.50 M. above the average sea-level.

When considering the motion of the deep ground-water, in the
direction of the sea, caused by the hydraulic pression in the dunes, we
must not overlook the much greater specific weight of sea-water. A
column of sea- water 30 M. deep, (with a specific weight of 1.0244, on the
average, as that of the North-sea-water), will be kept in balance by a
column of fresh water, about 0.75 M. higher. No doubt however the
depth of the fresh water, in the coarse-grained sand below it, is much
greater than 30 M.— A.P., without any considerable decrease in the
ascending power. A direct proof of this is the small percentage of
chlorine of the water in the deep well in the Kerkplem, amounting
only to 45 m.G. p. Liter, and that in the well on the beach,
30 M. deep, about 250 M. more south, was 52 m.G. the Liter. In
statistic equilibrium, 1.50 M. above the average-level of the fresh under-
ground water would correspond with a depth of 61.5 M. But on
account of the motion of the fresh water we have here to deal with
a condition of dynamic equilibrium; the pressure at great depths
consequently is not ‘simply settled by the height, to which the
water ascends higher up, in the ground, However below 30 M. (in
the coarse-grained sand) there will be little difference, so we cannot
but accept, that an extra-pression of 1.50 M. of the sweet ground-
water, apparent from the level the water reached in the tube, will
correspond with a depth of about 60 M. > A.P.; taking in con-
sideration the decrease of pression downward, we may safely state
the depth to be 50 a 60 M..— A.P. One thing is sure, the water
which rises from about 30 M. > A.P., has still ascending power
above the level of the sea. This may be distinctly observed in the
well, sunk on the beach, although being 300 M. nearer to the
low-tide line, a considerable decrease can be noticed. At that small
distance, the deep underground water in the dunes has already, for
the greater part, lost its ascending power and we may accept that
not far out into the sea, if is entirely gone. That strong pression-fall
must be principally attributed to tide-fluctuation, which every time
renews a fourth of the water in the sand, as far as that fluctuation
makes itself felt; apparently (the well in the Kerkplein shows it) at
a rather considerable distance, from the sea. But also the fact that
the beach slopes down at Zandvoort the depth of the sea, 400 M,

( 755

)
from the low-tide line, being 2.5 M.; 1200 M. beyond that line,
5 M. below A.P. and that the fine-grained sand intermixed with
clay of the original upperlayers for a great part will have been
replaced by coarser sea-sand, must considerably have contributed
towards greatly increasing the pression-fall of the deep underground

water, at the sea-side. At high-tide the flowing off however is very
small, and all things considered, the flowing off of the water from
the dunes, at the polderland side, certainly will not be less considerable
than that towards the sea.

But let us drop this subject, too few facts being at our disposal
to judge of that complicated process, and watch the influence of the sea-
water at a greater distance from the coast. There can exist no doubt
as to the underground of our low-lands being soaked with sea-water. In
none of the borings executed in the last scores of years, if only deep
enough earried through, the proof of it was lacking; more or less deep,
according to circumstances, but the underground water showing an ever
increasing quantity of salt, highly exceeding that ofall polders ditches
or canals, exceeding even that of the Zuiderzee. In or near the dunes,
one must go much deeper to find sea-water, than in the polders;
and in the polders, on higher ground, as a rule, deeper than in those
lower situated. In the Brouwerskolkje, at a depth of 72 M. > A.P.,
the percentage of chlorine did not exceed that of surface dune-water,
neither was this the case in wells of the Harlem water-works, deep
54 M. — A.P.; nor in the one, in the dunes at Elswout, 80 M. ~ A.P.
deep; nor in the Rieker polder at more than 50 M.—+A.P. Near
the Huis-de-Vraag, in the north-east corner of the Rieker polder,
down to 32.5 M.— A.P. only 34 m.G. chlorine a Liter was found;
at 46.5 M.—A.P. not more than 81 m.G.; and near “Het Kalfje’,
on the Amstel, south of Amsterdam, at 351 M.-—> A.P., only 47 m.G.
a Liter. At Purmerend, situated in shallow polders, with Summer
Levels of 1.25 to 1.60 M.—A.P., but surrounded by the deep
Purmer- (Summer-Level —- 4.47 M.), the Beemster- (S.L. + 4.00 M.)
and the Wijdewormer polder (S.L.-> 4.50 M.), the water rising from
50 M. — A.P., has a quantity of only 45 m.G. of chlorine a Liter. The
well-water at Schermerhorn, in shallow polders, between the deep
Beemster- and Schermer polders, at 76 M.— A.P. deep, contains 170
m.G. chlorine a Liter. Although the underground water in those
deep polders, on the whole is brackish, the quantity of chlorine
was only 192 m.G. a L. in the Purmer polder, at about 1 K.M.
from the encircling dike, in the direction of Purmerend on the Wester-
weg, and 600 M. north the church. Similar fresh deep underground

a0*

( 756 )

water is also found in the south-east corner of the Beemster polder,
opposite Purmerend.

On the whole west of the Haarlemmermeer polder, in wells not
greatly exceeding 30 M. in depth, the underground water is equally
fresh as dune-water, also at Heemstede and at Hillegom and in some
of the shallow polders near Haarlem. At great depth, there is in
those parts a considerable increase in the quantity of chlorme. Near
ihe railwaystation of Vogelenzang, between the Leidsche vaart and the
rail-road, at 1600 M. from the Haarlemmermeer polder, at a depth of
88M. A.P., it amounted to 184.6 m.G. a Liter, it being only 35.5 m.G.
a Liter at 25 M.~> A.P. Near the villa Bennebroek, 650 M. from the
Haarlemmermeer polder, 47 M.~> A.P. deep, it contained 99.4 m.G.,
and at a depth of 89 M., 245 m.G. chlorine a Liter; on Bosbeek,
in the parish of Heemstede, being only 440 M. from that polder, at
about 380 M.+A.P., 58 m.G. a L. Numerous instances may be
brought forward of the quantity of salt in the underground water
growing with its greater depth, and at a higher level, as one draws
nearer to the deep polders. A well-known fact is, that in consequence
of the flowing down of the underground water from off the dunes,
the water of the neighbouring low-lands, up to quite a few kilo-
meters’ distance, may be fresh. More considerable and noticeable at
greater distance however, is that down-flow deep in the ground.
Close to the steam-nill for the draining of the land, in the Meer-
weiden near Velsen, at: full '/, K.M. from the dunes, the under-
ground water, 28 M. below A.P., contained 30.5 m.G. chlorine and
at 44 M. below A.P., 65.4 m.G.; and even 1 K.M. more east,
within the precincts of the fort, in the western corner of the Zuid-
wijkermeer polder (S.L.-—- 2.40 M.), at 34 M. > A.P., only 60 m.G.; at
45 M.—+ A.P., on the other hand, 603 m.G. chlorine a Liter. In
the midst of the dunes themselves the ground-water seems to get
brackish only at about 150 M. below A.P.

Of special significance is the fact, already stated above, that the
underground water in the deep polders is growing salter at a much
higher level. So at Eert-den-Koning, only 300 M. within the Haarlem-
mermeer polder, at 26 M.> A.P., the underground water had 367m.G.
chlorine a Liter. Similar conditions are generally prevailing there. That,
generally speaking, the higher percentage of salt cannot be attributed to
water from the canals (‘““‘boezemwater’’), so cannot have got in from the
surface, may in the first place, be proved from the fact, that the
water in shallow polders, in many places, down to considerable
depths is as perfectly sweet as that in the dunes, although one can
prove that there is no communication with the dunes; in the second

( 757 )

place, that within those polders, just as outside them, but already
at a higher level, the water deeper down will be found to have a
higher salt standard. At Hoofddorp the quantity of chlorine, at
18.5 M.—A.P., was 202 m.G. a Liter; at 28 M.— A.P., 260 mG.
and at 38 M. > A.P., 993 m.G. With such a rapid increase as in
the last 10 M., unmixed sea-water may be expected, at little greater
depth.

No doubt can be entertained as to underground sea-water and
fresh water in our sea-provinces balancing each other in a way, as
indicated by Bapoy Guysex and HerzperG'), very much however
modified, in general and in special cases, by the general geological
structure with its local modifications. There is no ground for fear
of the sea-water coming up from below, in part of the dunes, in
which the underground water has been lowered down to the sea-
level; the very fact that there are polders, which already for
centuries lie below it, and still have fresh water, down to great
depths, and that even of the deepest polders the upper-soil, several
scores of metres deep, is much more soaked with fresh than with
salt water, refutes that fear.

Remarkable however is that at Hoofddorp, although situated in
the midst of the Haarlemmermeer polder, the deep underground water is
less salt than at Eert-den-Koning, near the edge of the polder, and
less still so than some kilometres north-west of Hoofddorp, e.g. on
the farm Mentz, where a deep well, presumably equally deep, has
water containing 6535 m.G. chlorine a Liter, i.e. 24 times the
quantity of that at Hoofddorp. Differences in the condition of the
sub-soil are evidently the cause of those differences in the salt quantity.

In the shallow polders, on account of the direction downward of
the vertical motion, also the water from the canals (“‘boezemwater’’)
may be the cause of rendering the deep underground water salt,
when locally the structure of the soil does not prevent it.

Bearing in mind, for the motion of the underground water, the
significance of the different heights of the polders, and not forgetting
the irregularities in the extent, the thickness and the comparative
pureness of the clayey beds, also irregularities in the vertical distri-
bution of the water and in the composition of it may be explained.

1) W. Bapon Guypen in: Tydschrift van het Kon. Instituut van Ingenieurs L889,
p. 21; Herzeernc in: Journal fiir Gasbeleuchtung und Wasseryersorgung. 1901,
p. 815 s.q.q. I count myself happy to have pointed out in lectures, conversations
and letters this forgotten merit of one of our engineering-officers, in consequence
of which remembrance Mr. GC. E. P. Rissis and Mr. R. p’AnpRimontr have, in
their publications given due uonours to our compatriot.

Intermixing with water, richer in salt, both from above and from
below, may consequently be hindered or furthered by it, also the
oozing in of fresh water; the different mixtures, as an other conse-
quence, being able to move horizontally in the one or the other
direction, or be prevented to move at all, which explains the different
levels they reach.

The hypothetic currents can be dispensed with to explain the
existence of fresh water, between 385 and 50 M. — A.P., in the old
boring at Sloten, so often urged in proot of powerful subterranean
water-currents of distant origin. Of the above mentioned wells in
the Rieker polder, those, most west, are only 800 M. east of the
boring of 1887. The different levels observed in the wells at Sloten
can in reality be due only to local motion, in the direction of the
shallower polders (with their higher upper-pression) to the deeper
polders, where the pression from above is less powertul. The fresh
water, everywhere found there at great depths, down to 50 M. > A.P.,
can find its origin only in those shallow polders themselves. The very
position of the old boring at Sloten, at a corner of the shallow
Rieker polder, between two deep polders (the H. M. polder and the
Middelveldschen Akerpolder (S. L. — 4.20 M.)), explains the irregu-
larities of composition observed there in the vertical distribution of
water, and thus it is, with the boring near Diemerbrug, outside the
north corner of the deep bijJmermeer polder (S.L.—> 4.20 M.). At about
250 M. + A.P. water of a somewhat lower standard of salt (mini-
mum 1192 m.G. a Liter) was found; no fresh water, as DaARapsky
lately held forth. Considering what influences are at work in the
distribution of the water in our soil, one can but see natural
phenomena in all those deviations.

Considering the geological condition of the place itself and of its
surroundings, the occurrence at Wijk-aan-Zee, both of fresh water down
to 31 M. ~ A.P. (47.8 m.G. chlorine) and of its getting brackish, already
at 50 M. > A.P. (851 m.G. chlorine) may be easily explained; also
the presence of a layer of fresh water, between the sea-water, in
the sub-soil of [Jmuiden.

In this discourse on some general features of the movement of
the underground water in our lowlands the question ‘remains to be
settled, how it is that some shallow polders, of which the canals
and the ditches like those of other, deeper polders, are mostly filled
with brackish water, can furnish fresh underground water.

In the first place the answer will be that, by no means, all
surface waters of the polders are brackish. Even in the H. M. polder,
I found, also at dry seasons, in some places fresh surface water

755 )

containing only 78, 60, 35.5 mG. of chlorine a Liter. Holes made
in the midst of deep-polder meadows often fill with fresh water,
even when a long period of absolute dry weather precedes the
digging of them; so in the Purmer-polder, near the above mentioned
deep well, on May 13 1903, the water in such a hole, dug about
1.80 M. deep, contained only 72.6 m.G. chlorine a Liter, the
adjacent ditch water having 407 m.G. Near Hoofddorp, in the
H. M. polder, in the midst of the Slaperdijk, 250 M. southwest of
the Hoofdvaart, after weeks of dry weather, in a hole, the Corps
of military engineers had dug, down to 0.40 M. below polder-level,
water oozed in, which contained not more than 102 m.G. chlorine
a Liter, still that dike (the summit of which is about = A.P.)
over all its length stretches between two canals 10 a 15 M. wide,
only 40 M. apart and always filled with brackish water, 1 or 41.5 M.
deep. The water of those canals at that moment contained 5141 m.G.
of chlorine a Liter. The level of the water that had gathered in
the hole, was O.11 M. Iigher than that in the canals and at that
time they were even considerably higher than they had been the
last month. But those are deep polders, in which the vertical motion
of the underground water is from below upward. What to think
now of the water that penetrates the soil of the shallow polders ?
The extent of the land, in the polders, generally exceeding that -of
the water at least 25 times, and the level of the underground water
in rainy seasons, being considerably higher than the neighbouring
ditch water, consequently the fresh water will filter down, in a far
greater proportion than the brackish, the surface of which forming
but an insignificant portion of that of the fresh water fallen in the
meadows. The water of the canals (‘‘boezemwater’’) consequently can
but little add, in those rainy seasons, to the salt-standard of the
underground water. In the dry season, on the other hand, the land
drying out, water must be let in; the soil is then absorbing brackish
water from the canals. In fact, however, even such shallow polders,
as the Rieker polder and those of Purmerend, which possess fresh
underground water below the recent more or less impermeable strata,
have brackish underground water near the surface, all the year round,
Nevertheless, to my opinion, a great number of phenomena point to
the supposition of the deep fresh underground water, found in some
of our shallow polders, which have brackish underground water
near the surface, being due to rainfall on the spot itself, or at a
comparative short distance. This question will be the subject of a
further communication.

Considering the facts communicated here, in connection with others,

€ 760 )

concerning the quantities of water which from the rainfall penetrates
the soil, it need not be further demonstrated that in the sub-soil under
the dunes, under the adjacent flat elevated area and under some
shallow polders, drinkable water is and will not be lacking, in the
main land of the provinces North- and South-Holland, superficially
judging so little favoured in this respect, and with two fifths of the
population of our country. That the velocity with whieh the deep
underground water can move through the coarse-grained sand, is quite
sufficient to make it possible to procure it from the sand in large
quantities, a great number of facts prove it. I will mention but one,
that of the paper-manufactory at Velsen, of which the six wells,
encompassing an area of 0.85 H.A., every 24 hours, on the average,
furnish at least 2200 M* of fresh water or nearly as much as the
town of Harlem wants and about a tenth of what Amsterdam
consumed during these latter years. And those wells furnish water,
which shows no. signs as yet of a too slow horizontal motion ere
long being likely, by disturbing the natural equilibrium of the under-
eround fresh and salt-water, to convert the pumped fresh into salt-
water. On the contrary the water of the oldest well, full six years
in use, has grown a little sweeter still.

Physics.
of magnetic rotations of the plane of polarisation in absorbing
solutions.’ By Dr. L. H. Siertsema. (Communication N°. 91
from the Physieal Laboratory of Leiden by Prof. H. Kammriinen
ONNES.)

“Tnvestigation of a source of errors in measurements

(Communicated in the meeting of January 30, 1904),

In a great number of measurements of the magnetic rotation of
the plane of polarisation it was found, that this rotation assumes very
large values in the neighbourhood of an absorption-band. Similar large
values were found by me in an investigation on the negative mag-
netic rotation of potassium ferricyanide ') in dilute solutions. These
results agree with the new optical theories which yield for the
magnetic rotation the dispersion formula: ’)

e Aa dn

; : dn
since the quantity Pa also assumes a large value near a band.
Oh

tl) Arch. Néerl. (2) 5 p. 447; These Proc. 1901/02 p. 339; Comm. Phys. Lab.
Leiden N°, 62, 76,
*) These Proc, 1902/03 p. 413; Comm. Phys. Lab, N° 82.

( 761 )

Much attention should therefore be paid to the fact that Bares *)
has made measurements with solutions of cyanine, fuchsine, litmus
and aniline blue, from which it would follow that these large
rotations did not exist, whereas ScHuMAuss*) with these very sub-
stances has found very large rotations. According to Bares these
large differences are caused by a source of error which arises from
the circumstance that for these measurements we make use of light
of which the intensity varies with the wave length"). He shows
that both with the half-shadow method, and with that where we
adjust on a dark or a bright band in the spectrum, great errors may
be made as soon as we arrive at a region where the intensity-curve
of the light used shows a considerable decrease, and that this may
produce apparently large rotations.

As this source of errors might also occur in my measurements
with potassium ferricyanide, it seemed important to me to investigate
in how far this may have had a disturbing influence, and thus in
how far the large rotations then found would have to be ascribed
to it.

With the method involving the use of a dark band in the spectrum,
the source of above errors comes to this, that as soon as the intensity
of the light on the two sides of the band is not the same, we are
inclined to wrongly adjust the middle of the band, and to displace
it too much towards the dark side. For we may suppose that for
an adjustment we, as a rule, search for two points on the borders
of the band which are of equal intensity and then adjust between
them. It must be noted that attention has been repeatedly drawn to
this source of error *) although, as far as I know, an experimental
investigation of the errors which may so arise was first made by
Batrs*). A theoretical solution would be possible in the manner
indicated by Bares, but this requires a knowledge of the intensity-
curve of the spectrum which is seen by the observer in the absence
of the magnetic rotation. Moreover we ought to know which of
the intensities on the edges is used by the observer to determine
the middle of the band, and this especially will partly depend on
the observer. An experimental determination may easily be made.
We need only produce a spectrum with a movable dark band and

1) Bares. Ann. d. Phys. (4) 12 p. 1091.
2) Scumavss, Ann. d. Phys. (4) 2 p. 280; 8 p. 842; 10 p. 853.
3) Bares. Ann. de Phys. (4) 12 p. 1080,
4) Gernez. Ann. éc. norm. | p. 12 (1864).
Van Scuatk. Thesis for the doctorate. Utrecht 1882 p. 30,
*) Bates |. c. p. 1086,

( 762 )

examine it while the light passes or does not pass through an
absorbent substance. The apparent displacement of the band near
the limit of abserption must then immediately appear.

For my measurements with potassium ferricyanide I have made
use of rotations of 11° and higher. A quartz plate 0.4 m.m. thick,
cut at right angles to the optical axis was now used and with it a
similar rotation is obtained near the limit of absorption. This plate
preceded and followed by a nicol was placed between the collimator
and the experimental tubes, which moreover were mounted in precisely
the same way as they were for measurements of the rotation in
potassium ferricyanide. A large number of adjustments have been
made by rotating one of the nicols, one set where the experimental
tube was filled with a ‘/,°/, solution of potassium ferricyanide, and
one with water instead of the salt-solution. The calibration of the
spectrum was made as before with a mercury arc lamp. The following
values have thus been obtained, as means of pairs of adjustments:

band with

nicol water solution
din py

83°O" 629° 650
82°30’ 611 612
82°0’ 593° 5935
81°30’ 577 O77
81°O’ 5625 565
80-30’ 549 549°
SO°O’ 538 538
12-30’ 525 526°
79°O’ 515° 516
78°50’ 5125
18°45’ 510°
78°40’ 509
78°35’ 508°
78°30’ 505 905°
78°25’ 504
78°20’ 502°
78°15’ dOL
78°10’ S00
78°5’ 498
78°O" 495°

77°30" 486°

7450! v7

(limit of absorption, about 481)

The annexed figure represents
graphically a part of these read-
ings for both sets. The irregular
differences, may apparently be
ascribed to errors of observation,
which near the limit of absorp-
tion will be somewhat larger

than at other places, owing to
the smaller intensity of the light.
They do not amount to much
more than dau. A deviation
of the kind whieh we might
expect from the source of errors

supposed by Barrs, would reveal

itself, near the limit of absorp-

tion, in a displacement of the
band towards this limit. Such

+ series, with, water a displacement is not at all
o J . solution ; : "

‘ indicated by these observations.
= Umit ontahenoption Let us consider what apparent
'

displacement must have taken
place, to account for the anomalous rotations which are found in
the measurements. This may be found by supposing for a moment
that the rotation of the sait is normal, and by putting it equal to
that of water. If for instance we start from the value g,,=7.1 for
2, = 606") and we call 2, the wave-length, where the band ought
to have appeared with the solution, if it appeared with water at
4, = 519, then we find by a simple calculation 4, = 509, while we
have observed 2, = 500. According to what has been said before a
displacement of the band of 9 wu cannot be apparent. Hence the
validity of the results obtained before is not affected by the error
supposed by Barns.

1) Comm. N°, 76 p. 4; Proc. Royal Acad, 1901/02 p. 340,

( 764 )

Mathematics. — ‘An equation of reality for real and Lnypinary
plane curves with lugher singularities”. By Myr. Frep. Scuvn.

(Communicated by Prof. D. J. KortEwne.)
(Communicated in the meeting of March 19, 1904).

For a plane algebraic curve having an equation with real coeffi-
cients only and possessing no higher singularities than the four of
Prickrr, Kir ') has deduced (as an extension of relations of reality
found by ZevTHEN in a C) the equation

nt Pe 2s" bag og" 2A 2) eee
where

n is the order, / the class of the curve,

3 the number of real inflexions,

# the number of real cusps,

vr’ the number of real isolated bitangents and

dé" the number of real isolated double points.

This equation of Kiem can be extended to curves with higher
smgularites and it then becomes most remarkably simpler and
merariably holds good also for curves in whose equation imaginary
coefficients appear, Which is not the ease with the equation of KLEIN.

The equation found by me runs as follows :

fil ES ocak 1 eshte. adi VL teste eee

Here ='7, denotes the sum of the orders of the singularities with
real point, X'v, the sum of the classes of the singularities with rea/
tangent. By an element of the curve I understand in the following a
pomt of the curve together with the tangent belonging to it, exclu-
sively as forming a part of one branch of the curve, which can
be represented by one single Puisrvx-development (with exponents
fractional or not). The element I call a singularity: 1st if point or
tangent or both are singular, or 2°¢ if point or tangent or both
belong to several elements of the curve, or 3'¢ if the point is real
and the tangent imaginary or reyersely,

If through the same point more branches pass, we call the point
a manifold singular point; this is to be regarded so many times as
a singularity as there are branches passing through it. Correlative
to this is a manifold singular tangent.

}) F. Kets, Eme neue Relation zwischen den Singularitiiten emer algebraischen
Curve. Math. Ann., Bd. 10 (1876), p. 199.

( 765 )

With Priicker') we understand by the order ¢ of a single sin-
gularity the number of the points of intersection coinciding in the
(singular) point with an arbitrary line of intersection through that
point. If eventually more branches pass through the singular point,
we must of course count those points of intersection only, which by
a slight displacement of the intersecting line are found on_ the
branch belonging to the singularity in question. Correlative to the
order is the class v of the singularity. This class is at the same
time equal to the number of points of intersection approaching the
(singular) point along the branch in question with an intersecting
line passing through that poimt and about to coincide with the (sin-
gular) tangent.

If we regard this last quality as the definition of the class of
a singularity, then the development in point coordinates with the
(singular) point as origin and the (singular) tangent as axis of «

itv
becomes y= au ; + ...., after having given all exponents an
equal denominator though as small as possible (for a small value
of « gives ¢ small roots y, on the contrary a small value of y
gives ¢-+-v small roots ~). If farthermore Y and Y are the line
coordinates of the straight line 7 + Y.«—+ Y = 0, then the development

the correlativeness of ¢ and +. At the same time it is evident from
this that order and class of a singularity can be read immediately
from the corresponding development, from those in point coordinates
as well as from those in line coordinates.

In (2) X't, denotes a summation with respect to the singularities
with real point, Xv, to the singularities with real tangent, where
a manifold singularity must be taken into consideration as many times
as it possesses single singularities. Here not only the higher and
PitckeEr-singularities must be counted, but also those elements of
the curve, the counting of which has an influence on the equation
(2); thus also those elements (¢= v= 1) of which the point is real
and the tangent imaginary or reversely. It is clearly indifferent

1) J. Pricer. Theorie der algebraischen Curven. Bonn, A. Marcus, 1839, p. 205.

2) O. Srouz. Ueber die singuliren Punkte der algebraischen Functionen und
Curven. Math. Ann., Bd. 8 (1875), p. 415 (spec. p. 441—442),

H. G. Zeutuen. Note sur les singularités des courbes planes. Math. Ann. Bd.
10, p. 210 (spec. p. 211—212).

H. J. SrepHen Swirg. On the Higher Singularities of Plane Curves. Proc. London
Math, Soc,, Vol. 6 (1874—75), p. 103 (spec. p. 163—164),

( 766 )

whether we do or do not include entirely real or entirely imaginary
non-singular elements among the +’-signs.
The equation (2) holds good for curves with inagmary equation

as well as for curves with veal equation.

Now follow the chief poimts of the deduction of the equation
discussed. This will be given more minutely in my dissertation ’)
still to appear.

To this end we shall treat in $1, 2 and 3 the relation (2) for
curves with real equation, taking that of KLEIN as our starting
point. In § 4 we shall indicate it for curves with imaginary equation
too, and in § 5 we shall transform it to other forms.

§ 1. Curves with real equation and with no other manifold
singularities than double points and bitangents.

For the present we shall take a one-sided point of view where a
curve is regarded as a locus of points.

If the curve has higher unifold singularities we dissolve them.
This means that we bring about such a small vea/ modification in
the equation in point coordinates with preservation of the order,
that the higher singularities disappear without PLOcKER-point-singu-
larities (cusps and double pomts) taking their place (but of course
inflexions and bitangents). After this dissolution, where we assumed
the Précker-singularities already present to be remaming, we apply
the equation of KLEIN.

To this end we must consider how many isolated bitangents and
how many real inflexions appear in the dissolution of a higher
singularity. In two ways isolated bitangents can be formed, namely
Ist in the dissolution of a real singularity, i. e. a singularity
whose corresponding singular branch is real, 24 in the dissolution
of two conjugate imaginary singularities; here point as well as
fangent must be imaginary, as otherwise we should be treating a
manifold singularity, which we exclude from this paragraph. Of
course real inflexions can arise only from the dissolution of real
singularities.

By dissolving the singularity the class of the curve undergoes
an increase 7. Here d represents the reduction of class of the singu-
larity (called by Swira, Le., p. 155 the diserimimantal index) i.e. the

1) Over den invloed van hoogere singulariteiten op aanrakingsproblemen van
vlakke algebraische krommen. (On the influence of higher singularities on problems
of contact of plane algebraic curves.)

( 767 )

multiplicity of the singular point as point of intersection of the curve
with the first polar of an arbitrary point.

INFLUENCE OF A REAL SINGULARITY. Suppose when dissolving a
real higher singularity with a reduction of class d,, we arrive at 3,
real inflexions and 1, isolated bitangents. The class then becomes
kk +d so that ensues from the equation of Kier, if for simplicity’s
sake we think the curve to possess but ove higher singularity :

n in p oF at" = By oe 2 =k so d, ar x sal 20".

What the value is of 3, and of t’, separately, depends upon the
manner of dissolution. If however we apply the above equation to
curves formed in different manners of dissolution, we find that
B42", has always the same value, called by me the reduction of
reality of the singularity. In my dissertation I shall deduce out ofa
definite) manner of dissolution for that reduction of reality the
value d, + v,—t#,, which causes the latter equation to become

n+p 4 2r°+%,=k+x 4 26"+4,*'). . . . (3)

INFLUENCE OF TWO CONJUGATE IMAGINARY SINGULARITIES. As we exeluded

_ —

1) This equation agrees with the index of reality given by A. Bratt (Ueber
Singularitiiten ebener algebraischer Curven und eine neue Curvenspecies. Math.
Ann., Bd. 16 (1880), p. 348, spec. p. 391) based upon the decomposition of the
higher singularity in Piicxer-singularities. A. Gavitey (On the Higher Singularities
of a Plane Curve. Quart. Journ. of Math., Vol.7 (1866), p. 212, Collected Math.
papers, Vol. 5, p.520) has namely shown, although in a not entirely satisfactory
way, that the Pricker-equations as well as the equation of deficiency keep holding
good for curves with higher singularities, if we regard such a singularity as equi-
valent to %* cusps, 6* inflexions, 3* double points and +* bitangents. For «* and 6*
CAYLEY gives

x*=t —1 , Pr=v—1 Se Ws so oo
and he indicates how 3* and r* can be deduced from the Puiseux-developments
in point and line coordinates.

Later on fuller proofs for the results of Caytey have been furnished, among which
that of StepHey Sairn excels for its simplicity and rigorousness (I. ¢., p. 153— 162),
based upon the line of thoughts of Caytey. For the CayLey-numbers of equivalence
Smita introduces (l.c, p. 161) the names cuspidal index, inflexional index, nodal
index and bitangential index and among them he finds a simple relation (1. ¢., p. 166).

Britt has shown that this Caytey-equivalence does not only completely satisfy the
Pritcker-equations and the equation of deficiency, but that it is possible to deform
the curve retaining order, class and deficiency in such a way that the higher singu-
larities are decomposed into the equivalent ones of Pricker. Bruty calls this opera-
tion a deformation of the singularity (I. c. p. 361). Already Caytey (On the Cusp
of the second kind or Nodecusp. Quart. Journ. of Math., Vol. 6 (1864), p. 74,
Collected Math. papers, Vol. 5, p. 265) gives for the case of a ramphoid cusp an example
of a such like deformation although he does not emphatically draw the attention
to the fact that class and deficiency remain unaltered.

In an elegant way Britt indicates further algebraically, that for every real defor-

( 768 )

from this paragraph the manifold higher singularities, point and
tangent of conjugate imaginary singularities must both be imaginary.
If we decompose those singularities into the equivalent ones of
Picker in the manner indicated by Britt (see note), thus without
changing order and class of the curve, then of those PLickER-singu-
larities point as well as tangent are imaginary, as was also the case
with the original singularities. So no PL¢cKER-singularities are formed,
which appear in the equation of Kien, so that that equation inva-
riably holds good for a curve, possessing only higher singularities
of which point and tangent are both imaginary.

Comprising the results of this paragraph, we thus find fora curve
without manifold higher singularities the equation
n+ p+ 2c" + Dv, => k+ x'+ 2d" 4 Dt, . . «. (8)
where the summations must be extended only to the real higher singu-
larities.

§ 2. Curves with real equation and with
\ /

manifold higher singularities.

If the curve has manifold higher singularities, we can imagine
that these are driven asunder in the separate singularities in such
a way by a slight vea/ modification in the equation of the curve
retaining order and class of the curve, that its singular points and
tangents all differ, but without the nature of the separate singularities
having undergone a change. This operation which I shall explain
more minutely in my dissertation for the case of one manifold
singularity only, I eall the despersion of the manifold singularity ?).
mation of a higher singularity «*! — 6*! + 2 (3*" — c*") retains the same value,
which he calls the index of reality of that singularity. Here «*’, B*', 3*”, <*!
represent the numbers of the real cusps and inflexions and of the isolated double
points and bitangents, generated at the deformation. How large those numbers are
separately depends on the manner of deformation.

This however is not a new result, but an immediate consequence of the equation of
Kieiw if after various deformations we apply it to a curve possessing at first but
one higher singularity.

Britt (l.c. p. 391) says he intends to point out elsewhere that the index of
reality of a singularity (however, this must run: of a vea/ singularity) amounts
to x*—f*, so according to (4) to ¢— v. In connection with

n+ B+ Qe" + BY + De™ = Kh + xe! + 23" 4+ 4! 4 D5"
the equation (3) follows immediately from it. However | am not aware where
Britt gives the promised proof.
*) So here we leave the one-sided point of view of the beginning of § 1.

( 769 )

By this dispersion however new isolated double points and isolated
bitangents are formed, but the higher manifold singularities disappear,
so that the equation (5) is applicable, provided among J” and rt" the
newly generated isolated double points and bitangents are counted
These however can be formed only as points of intersection and
common tangents of two conjugate imaginary branches.

Here are three cases to be distinguished with respect to the reality
of the two pomts and tangents of the manifold singularity consisting
of two conjugate imaginary branches. The case already discussed, that
the points and the tangents are both imaginary, does not give rise
to a manifold singularity, so it does not come into consideration now.

Ponts OF CONTACT REAL, TANGENTS IMAGINARY. From both branches
being conjugate imaginary ensues that the points of contact coincide,
but that the tangents differ. If the order of each of the singularities
is ¢, then both branches intersect each other in ? coinciding points,
which after the dispersion of the singular points cause # double points
to be generated. If that dispersion takes place, as we keep assuming,
in such a way that the equation of the curve remains real, then the
singular points become conjugate imaginary, whilst the singular
tangents remain imaginary. So after the dispersion we get singula-
rities which have no influence on the equation of Kier. However
we have got another ¢ double points of which ¢(¢—1) are imaginary
and ¢ are isolated. The latter is easy to understand by causing the
¢ coinciding tangents of each of the singularities to diverge a little
before the dispersion, by which each of the two singularities changes
into a common f¢-fold point with separated but slightly differing imagi-
nary tangents. The ¢ tangents originating from the one singularity
are conjugate to those of the other. With the dispersion the ¢ pair
of conjugate imaginary tangents give ¢ isolated points, whilst the
remaining double points become imaginary.

After the dispersion of the singular points by which the number
of isolated points has become Jd” +¢ and the number of isolated
bitangents has remained invariable, we find by applying the equation (5)

me So = bE x + 2d" +2) + Se.
For this again we may write :
rarer se Sg ae Ue get Ot. Sate | I aay
if we but extend ='t, to those higher singularities of which the point
is real but the tangent imaginary.
POINTS OF CONTACT IMAGINARY, TANGENTS REAL. This case is quite
correlative to the preceding. Now the points of contact are different,
whilst the tangents coincide. Out of this common tangent is formed

ot
Proceedings Royal Acad. Amsterdam. Vol. VI.

(770 )

by the dispersion of the singular tangents v* new bitangents, of which
v are isolated. So for this case too the equation (5) holds good if
we but extend +'r, to those higher singularities of which the point
is imaginary but the tangent is real.

POINTS OF CONTACT AND TANGENTS BOTH REAL. Now point and tangent
of both imaginary singularities coincide. So the two branches touch each
other. This may be an ordinary contact or a higher one, as the
Puisrux-developments of both singularities correspond in the first terms
(which are then real); the unequal terms are conjugate imaginary.

If ¢ and v denote order and class of each of the singularities and
e a number which need not be known more closely, the numbers
D and 7’ respectively of the coinciding points of intersection and
of the coinciding common tangents of both branches amount to

D=F se, ;
(ie ee Ee “pl

This ensues from a relation which always exists for two singular

branches touching each other between the numbers D and 7, namely

T— D=(8,* + 1) (6,* + 1) — («,* + 1) («,* + 1),
where 3,* and 3,* denote the inflectional indices, z,* and z,* the
cuspidal indices of both singularities *). This relation was first deduced
by STEPHEN SwitH (l.c., p. 167). If according to (4)') we express
the indices in order and class of the singularities, we find

T — D= 0,0, =t ts
or, “as:an- our ‘case 7, == i, = 1 and 0, 2=0;=;
T—DPD = v*.—’,;

from which ensue the two equations (6).

If therefore we disperse both singularities in such a way that the
singular points and tangents begin to differ, this causes point and
tangent to become imaginary, whilst D new double points and 7
new bitangents appear. If among these are D" isolated double points
and 7” isolated bitangents, then

Pot es

By es
which [ shall prove more minutely in my dissertation.
sy the dispersion of the singularities the numbers of the isolated
double points and bitangents have become dé"+t-+c' resp. t’+r+e'
So the equation (5) gives .

m+ P+ 2(e"4v+e)4 By =k x4 2(e"+t+e)4+ 2 ‘3
So before that dispersion

Ree

1) See note p. 767—76s,

( aii)

nt+Pt2e"+ Do, Sk4+2 +204 Vt... . (5)
where the two summations must also be extended to the imaginary
singularities with real points and tangents.

§ 3. Proof of equation (2) for a curve with real equation.

The considerations of the two preceding paragraphs all lead up to
the equation (5) thus holding good for every curve with real equation
and with higher singularities. The summations must be extended
only to the Aigher singularities, namely %’/, to those with real points,
y’v, to those with real tangents.

The equation (5) can be considerably simplified by including also
the PLitckrr-singularities among the ’-signs.

InrLtexion. For an inflexion we have t=1, v=2. If we omit
Bp’ but extend ’t, and Y’v, to the real inflexions then in (5) due
consideration is taken of the presence of those inflexions.

Cuse. For this ¢= 2, v=1, so that for the cusps the same holds
good as tor the inflexions.

IsoLATED PpoINT. An _ isolated point is formed by two conjugate
imaginary elements, of which the points are real, thus coinciding,
the tangents imaginary, thus differing. For each of those elements
¢—v=1. If we extend the summations to the isolated points, this
has no influence on S"v, (the tangents being imaginary), whilst on
the contrary '/, increases with 2d". If now in (5) we omit the
term 20", but extend 7, to the isolated points, the equation remains
frue.

ISOLATED BITANGENT. This is formed by two elements (f= v= 1)
with real tangents and imaginary points of contact. For this holds
good the correlative of what was observed for an isolated point.

So if the summations are extended also to the PLiéckrr-singularities
the equation (5) becomes

Rl ees JF ! é
Ye ee oe he gh ncn ge ee
where, if one pleases, every other element of the curve may be

included among the +'-signs.

§ 4. Proof of equation (2) for a curve with imaginary equation.

To prove the relation (2) for a curve with imaginary equation,
we write it in the form :
J =k—n+t+ art: ad PAC =p
So we must show, that also for a curve with imaginary equation
J has the value zero. Let g+7y—O0 be the equation of that
51*

( 772 )

curve, were g and y possess but real coefficients. For that curve J
has of course the same value as for the curve p—iyw=—0O, e.g.
the value -/,.

For the curve g? + w? = 0, consisting of the two first-mentioned
curves, J has thus the value 2./,, as J consists only of terms, which
are formed additively for a degenerated curve out of the corresponding
terms of the partial curves. The equation of that curve is however
real, so that the relation (2) is applicable to it. From this ensues
a 2S, ==! 50 J =):

This proves, that / has the value zero for the curve g+7y~=0
too, and that for this the equation (2) also holds good.

For this deduction we have tacitly made the supposition that @
and w have no common divisor, as otherwise the curve g?+y?=—0
would possess a part counting double and thus an infinite number
of singularities. If g and yw have such a common divisor, that is if
the curve degenerates into a curve with real equation and into one
with an imaginary one, the relation (2) still holds good. For, as we
have seen, this is the case for the two partial curves, from which
ensues by addition the corresponding equation for the total curve.

Kuen (l.¢., p. 207) finds by applying his equation to the curve
gy? + uy? =—0, for a curve with imaginary equation, of which the p
real points and the + real tangents are not singular, the relation

t-Pr Sk pl lL

This equation can be immediately deduced from (2).

Farthermore ensues from (2):

The equation (8) of KLE for imaginary curves holds good also
if that curve possesses real singular points or real singular tangents
if only they count for as many real points or tangents as is indicated
hy the order resp. the class.

§ 5. Other forms for the equation (2).

The equation (2) can be reduced to still other forms. The PLicker-
equation 3 (4 —n) =~ — x becomes namely for a curve with higher
singularities 3 (k — n) = p—x-+ J (3,*—=,*), or according -to (4)')
3(k —n) = B—x+ D(vr,—4), where the Y-sign must-be extended
to the /igher singularities, the real ones as well as the imaginary
ones. By including the PLtcker-singularities, and if one likes also
the ordinary points of the curve, under the +-sign the equation
becomes

!) See note p. 767—76s8.

(773)

a Re Pe we et OB)
The equation of reality (2), ean thus be written in the following
form:

SS \ ~ sels » 7 Sl fe 7
= t, — &v, = 3(2 t, — = »,). Bera (os Os a ee
If farthermore 2” ¢, indicates a summation over the ¢maginary

points, "vr, over the tnaginary tangents, then Yt,=+'t, + >"t,, ete.

so that (10) becomes
ier kee Ce ee ee)

The equations (2), (9) and (10) are of course but different forms

for the same relation of reality.

Sneek, March 1904.

Chemistry. — Professor Lospry pr Bruyn presents communication
N° 7 on intramolecular rearrangements: C. A. Lospry pe BruyN
and ©. H. Sivirmr. “The BrecokMany-rearrangement ; trans for-

mation of acetophenoxime mto acetanilide and its velocity.”

(Communicated in the meeting of Febuary 27, 1904).

Among the many intramolecular rearrangements known in organic
chemistry, the one associated with the name of Brckmayn belongs
to one of the most important series on account of the extent of its
region and its scientific significance. As is well known, it consists
in the transformation of the oximes, under the influence ofa certain
number of reagents, into the isomeric acid amides, for instance :
R,CNOH — RCONHR. Its extent is obvious if we remember that all
ketones and aldehydes are capable of yielding oximes and that a
large number of these, particularly of the ketoximes, can undergo
the rearrangement. Its scientific importance is chiefly due to the fact
that its application to the stereoisomeric ketoximes has been the means
of determining the configuration of those stereoisomers, in this manner :

RCR’ RCR’
| — RCNHR’ and || — RHNCR’
NOH Q) HON 0

The rearrangement generally takes place under the influence of
different reagents such as sulphuric acid, hydrochloric acid, phos-
phorus pentachloride and -oxide, aecylehlorides, acetic acid with its
anhydride and HCl, zinechloride, alkalis. As these substances are
always applied in relatively large quantities, it is thought most pro-
bable, that the actual rearrangement nearly always relates to inter-

(wire)

mediate products, additive compounds or derivatives of the oximes,
which occasionally have been separated '). These intermediate products
then contain a negative group’ (or the group OK) attached to the
nitrogen which changes place with the C-combined alkyl- or aryl-
group. On subsequent treatment with water the amide is generated.
We then have ;

RCR’ RCR’ RCX+H,O RC=O
Le tee TL Goal eee ea ee el ee
NOH NX NR’ NHR’

That hydroxyl] itself can assume the function of the group X which
changes place with R’ is shown by the interesting observations of
WerRNER and buss’), Werner and Skipa*), Posner‘) and Auwsrs
and Czerny °), who have noticed some cases of the BECKMANN-rearran-
gement in the absence of any reagent. Dibenzhydroximic acid
CC HC0L0 Can:

obtained from chlorobenzhydroximie acid

Nou
Werner and Buss it changes after some days spontaneously into its
isomer C,H,CO.NHOCOC,H, m.p. 161°; on heating this takes
place more rapidly. Possner observed that o-cyanobenzaldoxime
changes into ifs isomer when simply heated above its melting point ;
it first melts at 175°, then solidifies and finally melts again at 203°,
Here we consequently have the direct conversion :
JANG HC SH ACH NC .C, H, COH
pases eet r eS NC. G, H, CO Nil)
NOH NH
Finally, Avuwers and Czerxy have found that 0-oxy-m-methyl-

benzophenonoxime: HO.H, CC, H, C-C, H, partly undergoes the

a
BECKMANN-rearrangement when submitted to distillation.
These observations from Werxer and his pupils, of Posner and
of Avwers and Czerxy are of fundamental importance for the under-

!) Beckmann for instance (Ber. 19. 988) obtained C,H; CCl: NCgH, from (CgH;)2 C:NOH
and PCI;. It is very probable that (CQH,); G@: NCI is formed first as an intermediate
product.

*) Ber. 27, 2198 (1894).

3) Ber, 32, 1654 (1899).

4) Ber. 30, 1693 (1897).

5) Ber. 31, 2692 (1898).

bo it3s)

standing of the mechanism of the Brckmany-rearrangement. They
prove that this important transformation is most decidedly a real
intramolecular rearrangement, which may oceur in some cases with
the oxime, but in the majority of eases with derivatives in which,
instead of the OH-group, another negative group or a halogen has
been attached to the nitrogen. In that case the change from IL into
III represents the actual rearrangement.

Avuwers and Czerxy have already pointed out that the above rearran-
gement caused by distillation deserves the closest attention. They are
of opinion that this observation leads to the view that the BrckMANN-
rearrangement is a catalytical process which is in accord with
BECKMANN’s own ideas. But is it permissible to speak of a catalytic
process when the catalyzer is wanting? And do not Auwers and
CzeRNY withdraw their own statement when they say that “es sich
vielmehr handelt um die directe Ueberfiihrung eines weniger stabilen
System in ein stabileres?”’

The BrckMANN-rearrangement has not, up to the present, been
subjected to a dynamical investigation. Such a study is not rendered
less desirable or less important by the fact that, as a rule, the
rearrangement of the intermediate product and not that of the oximes
themselves will be investigated.

The oxime which has been studied in the first place is aceto-
phenonoxime of which only one form is known and whieh quantita-
tively passes into acetanilide. Its configuration is therefore :

C.H,—C—CH, — C,H,. HN. COCH,.

|
HON

The rearrangement, which Beckmann found to take place under
the influence of concentrated sulphuric acid was studied in the first
place. Before starting it was necessary to work out an analytical
method allowing the quantitative determination of the resulting anilid
in the presence of the unchanged oxime. After several preliminary
experiments it was found that the anilide formed on adding water
was completely hydrolyzed by boiling for a few hours and that the
acetic acid could then be distilled off and titrated; the excess of
oxime did not interfere. We have in consequence determined the
velocity with which the anilide was formed. In carrying out the
experiments 2.5 grams of the oxime were dissolved in 50 or 100 ce.
of sulphuric acid, previously heated to the temperature at which the
experiment was made (60° or 65°) and at detinite periods a certain
quantity was pipetted off from the bottle (which was placed in a
thermostat) and analysed.

( 776 )

The reaction proved to be one of the first order, the velocity constant
did not change with the concentration; so it is a monomolecular
one. At 65°, for instance 4; = 0.0019 for a solution of 2.5 grams of
the oxime in 50 as well as in 100 ce. of 93.6°/, sulphuric acid (time
in minutes; transformation of */, of the oxime after 160 minutes).

The transformation velocity increases with the concentration of the

acid as shown from the following table:

Temp. 60°. Velocity- Time of 7/,
Concentration H,SO,. constant. transformation.
93.6 0.0011 275 min.
94.6 13 232
97.2 38 75
Lo 70 45
At 65°, a 86.5°/, sulphuric acid gave a constant of 0.0006 (time
of '/, transformation = 501 minutes). When using 99.2°/, acid at 60°,

practically all the oxime had been converted after 15 minutes.

The influence of the temperature is apparent from the following
figures :

at 60°, 93.6°/, HSO, £=0,0011; 946°), H,S50,,. 4==000ms

65°, $3 = 3 = 10,0089 ~ x = 0,00

The temperature-coefficient for 10° is therefore about 3.

A solution of SO, in chloroform did not appear to cause any trans-
formation of the oxime.

The results of this research therefore confirm the view that im the
3ECKMANN-transformation we are dealing with a real intramolecular
rearrangement. Even if the application of sulphuric acid should cause
the formation of an intermediate compound (which has not yet been
positively proved, but which is very probable’) ) our experiments
show that this formation (or the conversion T into II) takes place
With immeasurably great velocity. The very perceptible development
of heat which occurs on mixing the oxime with the concentrated
sulphuric acids also points to this facet.

Addendum. Of late years, Srimauirz and his coworkers (Amer.
Chem. J. 1896-19038) have been engaged in the study of the
BeckKMANN-rearrangement. In my opinion Stinenitz’s ideas cannot be
accepted in their entirety. Recently this chemist has given a summary
of his conclusions in a separate article “on the BeckMANN-rearrange-

1) If to an ethereal solution of the oxime is added a solution of sulphurie acid
in ether, a precipitate is obtained the nature of which will. be investigated,

(CCC)

ment” (Amer. Chem. J. 7, 29.49 (1903)). He then arrives at the fol-
lowing views.

The analogy of the LlorMaNN-transformation of the amides into
amines with the BrCKMANN-rearrangement (an analogy first pointed
out by Hoogrwerrr and van Dorr (Rec. 6.373, 8.173 ete.) ) and
the fact that the acid azides of Curtivus are converted with elimina-
tion of nitrogen into the same isocyanates which occur as inter-
mediate products in the Hormann-transformation, induces STimeGLirz
to attempt to explain these reactions from a same point of view.
He believes that in the three above transformations there must be
formed intermediate molecule-residues containing univalent nitrogen;
with the azides for instance CH,CO.N.N, > CH,CO.N + N,; with
the bromoamides for instance, CH,CONHBrSCH,CO.N + HBr. These
molecule-residues are then supposed to be converted straight into
the isocyanate: CH,—CO .N—=sCONCH,. In order to arrive, in the
transformation of oximes into amides, at such molecules with univalent
N-atoms, Srimeuitz assumes that first of all HCI is attached to the
oxime Owing for instance to the action of PCI,. R,C = NOH+ HCl
> R,CCI—NHOH,; this additive compound under the influence of
PCI, then loses one mol., of water and gives R,CCI—N which
molecule-residue is then supposed to be converted into RCCI=NR,
which on treatment with water yields the amide.

Now, first of all it is difficult to see where the HCl, which gets
attached to the oxime, is to come from; if is of course known. that
some oximes yield with PCl, compounds such as R,C CIN with
formation of HCl, but this is not the formation which Srinenirz had
in mind. We also fail to see how sulphuric acid, acting as dehydra-
ting reagent will, in the rearrangement, cause a mol. of water to

be first attached and then to be again eliminated; neither do we
understand how the transformation under the influence of, say, P,O,
or ZnCl, can be reconciled with the ideas of Stimenitz. Finally,
Stinciitz himself admits of his own theory that “it does not agree
so well with the more obscure relations of the theory of stereo-
isomerism of ketoximes and their influence on the rearrangement
of these isomers. It

s hoped that future work will remove this
difficulty’. (Am. Ch. J. 7, 29, 67). The difficulty is this, that Stmenitz
theory utterly ignores a fact of fundamental importance, namely the
formation of two different amides from the stereoisomeric ketoximes;
these according to StTincnitz ought to lead to the same intermediate
product from which the same amide only could be formed. And
finally the transformations of an oxime into the isomeric amide
Without any reagent whatever, gs observed by Werner and _ his

(778)

coworkers, by Possyer and by Avwers and Czerny are directly
opposed to his representations.

In his last theoretical paper, Srieciirz attributes the transformation
of some more hydroxylamino-derivates to the intermediary formation
of molecule-residues with wunivalent. nitrogen; he ineludes all these
under the name of ‘BECKMANN-arrangement”.

I think, IT have shown that this classification is not permissible.
If it were so, the HorMann-transformation might claim priority over
the “BrckMANN-arrangement’, which is of more recent date.

In order to avoid confusion I think it absolutely necessary to let
each of the said transformations retain its Own name and to treat
them as separate reactions. In the Curtics-transformation CH,CON .N,
—= CONCH, + N,, the assumption of the intermediary occurrence of
a molecule residue CH,CO.N is permissible; in the Hormany-reaction
CH,CONHBr — CONCH, + HB, such is possible but not necessary,
Br . C—OK
inay also have been formed as an intermediate product

NCH,
(Hanrzscn); finally we may admit in the BrckMANN rearrangement.
R.C.R’ ~ R.C— X — RCOH (= RCO. NHR’ .)
NX NR’ NR’
a same mechanism as in the HorMany-transformation, but according
to my Opinion, not the presence of a moleculeresidue with univalent
nitrogen.
The physico-chemical investigation of the BrokMANN-rearrangement
is being continued.
Lopry DE Breyy.

Amsterdam, February 1904. Oigan. chem. lab. of the Univ.

!) X =Cl, Br, OH or SO,H [respectively H,SO,], OCOCH,.

(7799)

Chemistry. — Prof. C. A. Lopry pe Brvyy presents communication
N°. 8 on intramolecular rearrangements: C. LL. Junaies. “The
mutual transformation of the tivo) stereoisomerie pentacetates

of d-glucose.”

(Communicated in the meeting of March 19, 1904),

1. It is well known that the esterification of alcohols by means
of acetic anhydride is accelerated in a high degree by the presence
of catalyzers and this of course also applies to the sugars. But if
is a remarkable fact that in the case of these polyhydrie alcohols
We arrive at various isomeric pentacetates according to the nature
of the eatalyzer. The investigations of FRaxcHimont *) and of HrrzrE.p *)
have shown that, when dry sodiumacetate is used as catalyzer, we
obtain a product melting at 154° (3), whilst according to Erwie and
KGnia@s *) treatment with ZnCl, yields a product melting at 112° («).
After Francuimont had proved that these two compounds were in
reality isomeric’) {the first was formerly thought to be a diglucose-
octacetate} this chemist supported the view that they may be best
represented as derived from the so-called oxide-form of glucose *).
The two pentacetates will then be stereoisomers as the oxide-form
of glucose, which contains one asymmetric carbon atom more than
the aldehyde-form, must give rise to two isomers.

As in the case of the two methylglucosides*) we arrive, on applying
ToLLENs’ glucose formula, at the following constitution of the
pentacetates :

AcO — CH — CHOAc
—0O-

The existence of two isomers is explained by the fact that the

CHOAe — CH — CHOAe — CH,OAc®)

terminal C-atom on the left appears as a new asymmetric atom.
2. It was known that the p-isomer formed by sodiumacetate is

1) A few years ago, Tayrer described a third isomeric glucosepentacetate
m.p. 86) (Bull. 18. 261 (1895). My investigation has led me to the conclusion
that this isomer does not exist but is a mixture of the other two,

*) Ber. 12. 1940.

3) Ber. 13. 265.

4) Ber. 22. 1464.

5) Recueil. 11. 106 (1892) Recueil. 12. 310.

6) These Proc. June 24 1893.

7) E. Fiscner B. 26. 2400 (1893).

8) Ac = CH; — CO.

( 780 )

converted into the other compound by boiling its solution in acetic
anhydride for a short time with a little ZnCl,.

I have made a closer study of this transformation; it is caused by
an intramolecular migration at the terminal asymmetric carbon atom.
One might feel disposed to explain the transformation in an acetic
anhydride solution by an addition and subsequent elimination of
a molecule of the solvent, sach as FiscHeER supposed to happen in

the mutual transformation of the two isomeric methylglucosides +).

This view, however, becomes untenable as the transformation can
also take place without the presence of acetic anhydride. Then
Lopry p& Broynx, by simply melting the p-isomer m.p. 134° with dry
ZuCl,, at once obtained the other compound m.p. 112°. T also succeeded
in causing the same transformation ina chloroform solution contaming
SO,. On shaking chloroform with fuming sulphuric acid, a portion
of the SO, passes into the chloroform. This solution has been found
to aeeelerate many reactions by catalytical action. A solution of
the B-pentacetate in CHCL, which contained 18.8 milligrs. of SO, per
ce. at first rotated but slightly towards the right; after a short time
its rotatory power had increased. The SO, was now removed by
means of dilute alkali and the chloroform distilled off. The residue
was recrystallised from alcohol and in this way the pure a-isomer
m.p. 112° was obtained.

3. As in the case of the two methylglucosides, the final con-
dition in the transformation between the two stereoisomers is here
also an equilibrium; the limit however is— situated close to the
form melting at 112°. A’ solution prepared by dissolving 5 grams
of B-pentacetate in 100° ce. acetic anhydride (containing 2 grams
of zinechloride) showed an initial rotation of + 1° (polariscope
Scumipr and Harxscu; JO em. tube). On keeping this solution at
35°, the rotation increased with measurable velocity and finally arrived
au + 14°.5. In the case of a quite similar solution of the a@-isomer,
having an initial rotation of -+- 16°.3) the final rotation was also
+ 14°.5. From this we calculate that in the condition of equilibrium
there exists 88°/, of the @ and 12°/, of the p-compound. The former

could in facet be isolated in a pure condition: in addition also some
erystals which melted at 95——-98° and eontained both isomers.

4. By determining at definite times the said changes in the rotation
the velocity of the mutual transformation could be measured.
It conformed with the formula for the unimolecular reversible

1) Compare my communication, these Proc, June 27, 1903,

€ 7an*)
d oP. a. Ory !
transformation ; for ; la. ——') was found a constant value whieh
a a Oe
a

was the same in the case of either isomer.

This average value representing the sum of the velocity constants
of the two contrary reactions is 0.0095 (the time expressed in hours
and using ordinary logarithms) at 35° and a concentration of 2°/, zine-
chloride. At 45° and 2°/, ZnCl,, the average constant was 0.028. The
temperature coefficient of the transformation for every 10° is, there-
fore, 3.01. Further determinations were also made with 1"/, solutions
of zincchloride at 45° and the constant was found to be 0.0135.
This seems therefore to be proportionate to the concentration of
the catalyzer.

d. Besides these two isomers, Tanrer (Bull. 1895, 18, 261) ima-
gined to have found a third glucose-pentacetate.

On treating glucose with acetic anhydride and a little zinechloride
and recrystallising the product from alcohol, he obtained from the
mother-liquor crystals with [a], = + 59° at 62°. This substance had
no sharply defined melting point situated below the melting points
of the above isomers. As he could not effect a further sepa-
ration of these crystals by recrystallisation, he took it to be a third
modification with a melting point of about 86°, but still occluding
a small quantity of the other two, which it was difficult to get rid
off. It is however obvious that this so-called third modification is
only a mixture of the other two, which is deposited from an alco-
holic solution saturated with both compounds. The following facts
are im favour of this view.

Ist. If it were a third isomer, it might be got perfectly free from
the others by recrystallisation and present a definite melting point.

Qed. Tf we make a mixture of the isomers melting at 134° and
112° so that [@|p = 60° the product will show the same melting-
traject as that of Tanrer*), namely 91—94".

34, A solution saturated with both isomers, and a saturated
solution of Tanrer’s product appear to contain the same amount of
pentacetate. | have used 50°/, alcohol as solvent. On shaking at 25°
with an excess of the two pure isomers a solution was obtained
containing 3.08—3.10°/, of pentacetate; Tanrer’s product similarly
treated gave a solution containing 3.13—3.14 °/).

1) a2» is the rotation in the condition of equilibrium, z) the initial rotation, z
the same at a stated period.

*) Mr. Tayret had the kindness to forward a specimen of his preparation to
Prof. Lopry pe Bruyn. With this sample the experiments have been made.

It is therefore not a matter of doubt that a third isomer does
not exist but that it is a mixture of the other two *).

The two stereoisomeric methylglucosides may be converted into the
corresponding pentacetates and conversely, the latter into the former *).
The «-glucoside corresponds with the pentacetate m.p. 112°, the
p-elucoside with the pentacetate m.p. 134°. It is therefore as well
to indicate the two pentacetates, respectively, with @ and ~, as has
in fact been done in the said article of BeHrenp and Roru.

6. The mutual transformation of the methylglucosides and pent-
acetates throws a new light on the phenomenon of the multirotation
of sugars. We may accept as the most probable explanation of this
phenomenon a mutual direct transformation of the two stereoisomeric
modifications which must exist according to ToLLENs’ glucose formula.
The recently published investigations of Fraykuanp ArMsTRoNG*) and
of Brnrenpd and Rorn*) have furnished strong arguments in favour
of this view.

But it must be remembered that ToLLeNns’ formula does not express
the aldehydic properties of glucose; one is therefore inclined to
assume that in a glucose solution there must occur also molecules
in the aldehyde-form, or molecules which contain 1 more H,O with
the group HC(OH),. One may then also come to the conclusion
that this hydrated aldehyde-form does not act as an intermediate
product in the transformation between the two stereoisomeric oxide
modifications *), but that we have here a complete analogy of what
takes place with the glucosides, namely that, although a direct trans-
formation takes place between the stereoisomers, there also occurs
a quantitatively imsignificant, secondary reaction involving addition
and elimination of the solvent. These reactions will then all be in
equilibrium with each other. This poimt, I will also try to’ elucidate
experimentally °).

1) This view is also held in a quite recently published article of BeEHREND
and Rorn Ann. 331, 359.

?) E. Fiscuer and E. Franxitanp Amsrronea. Ber. 34, 2885.

3) Journ, Chem. Soc. 838, 1305. 1903.

4) Ann. 331, 359.

5) Compare Marrix Lowry, Journ. Chem. Soc. 75, 212, (1899). 83, 1314. (1903).

6) Several chemists (v. Lippmann, Chemie d. Zuckerarten II, 130, 990. Ber. 29,
203, Trev, Z. f. phys. Ch. 18, 193, Soon, C.R. 182, 487), and myself (Ber. 28,
3081 (1895) ) have expressed the opinion that with the three [z|p’s of -- 106°,
+ 53° and --22°,5 known for glucose, correspond three modifications, namely
two oxide forms and one aldehyde form, After the research of Mr. Juxerus on
the methylglucosides and the pentacetates it is practically certain that the [e]p of

( 783 )
The particulars of this research will be published later on elsewhere.

Amsterdam, March 1904. Organ. Chem. Lab. of the Univ.

Mathematics. — ‘“Reyular projections of regular polytopes.” By
Prof. P. H. ScHoure.

We consider for this end the three regular polytopes u1,, Br, C;,
of the space S, with dimensions, which correspond respectively
to the tetrahedron, the hexahedron and the octahedron of our
space and setting aside the polytope 4, with its exceedingly simple
properties we treat some special cases of the following two. general
theorems relating to A, and C,, of which the proof will be given
elsewhere.

Eheore m ;I.

“Let mm represent $n or 4(n--1) according to the number of
dimensions 7 of JS, being even or odd.”

“Construe in m planes «@,,@, . . @ congruent regular polygons
with n+l [or 27] sides; let g be the circumradius of those polygons.”

“Let us take in each of those planes a vertex of the polygon as
the origin O and a definite sense, in which distance is counted from
this origin to any other vertex along the circuit.”

“Let us place at the remaining vertices the numbers 1, 2
in such a way that the number jp is put in a, near the vertex which
is distant from the vertex O in the sense assumed in «@ a number
pk jor p (2k—1)| sides. In other words: let us place in «eg, moving
round from O in the indicated sense the numbers 1, 2 in such a
way that when continuing to a following number we skip 4—1
[or 2(4—1)| vertices. Here the polygon in «em can be reduced as far

. _ ntl at Bie
as the numbering goes to a regular polygon with or — | sides,
| . 1 Y
each vertex of which bears g numbers, as soon as / and w+1

53° belongs to a condition of equilibrium between the two oxide forms. The
question put to me by Messrs. Benrenp and Rors in their recent paper (Ann.
331, 309) has therefore now been answered. My former contention that glucose
with [@|o+ 106° might crystallise from a solution in which it was not present
(namely, from glucose with a [z|p+ 53°) is, of course, no longer tenable. It is,
as Bb. and KR observe, a question of the relative solubility of the two or three
isomers able to be converted into each other. | had already shared this view for
a considerable time. Lowry and Ir. Arnmsrronce have also expressed the opinion
that it is a question of equilibrium. As stated above, Mr. Junaivs will try to determine
the precise nature of this equilibrium. Lo ps8:

( 784 )

[or 2h:
odd n the polygon is reduced in @, in this respect to a linesegment
long 29 bearing at one end the even numbers 0, 2, 4, .. . and at

1 and 2n| have the greatest common divisor g. And for

the other the odd numbers 1, 3, 5

“Let us replace for odd # the just mentioned linesegment 20 by
a linesegment eo) 2 bearing at its ends the same groups of numbers.”

“Let us place for even # the mm planes and for odd n the m—1
planes and the linesegment g¥ 2 in such a way in the space S, that
in a common point they are rectangular to one another.”

“Then the n+1 {or 2n| points 7; of that space the projections of
which on these mm elements coincide with the vertices numbered
with 7, are the vertices of a regular polytope A, with length of
edges oVn+1 [or C, with length of edges @Vn].”

This double theorem where with respect to the continuous bifur-
eation “this [or that\”’ we must either always read this placed
before the brackets or always that placed inside the brackets,
reminds one of the decomposition of the general motion in |S, into
m components for even 7 in 7 rotations, for odd 7 in m—1 rotations
and a translation. This remark is important with respect to the
decomposition of the groups of anallagmatic motions belonging to
Aj. and.e,,.

Theorem II.

“Let S,-1 and S, be two spaces rectangular to each other in a
point and let Sop represent the space determined by them.”

(1)
“Let us, take in Sp) @ regular polytope Aes in Sp a regular
ar
poly tope c, having both as the index (1) indicates unity as length
of edges.”

“Let us number the p vertices of A, 4 with the pairs of numbers
(O, p), G,p +1), (2, p + 2),.-- (p—1, 2p—1) and let us assign to
each of the 2p vertices of C, one of the numbers 0, 1, 2,... 2p—14
under the condition that the p diagonals bear at the ends again the
pairs of numbers (0, »), (14,p + 1), 2(p + 2),- . -(p—t, 2p—1).”

“Then the 2p points P; of Ss, 1, whose projections en S,p—1and S)
coincide with the vertices of Apt and G, bearing the equal numbers,

(V2)
form the vertices of a regular polytope As, —; with length of edges
(1)
V2 which projects itself on S,—1 according to two comeiding Ages
(1)

and on ip according 10 a Cp

By this simple theorem we are enabled to deduce the proof of

]
;

‘2

we weet aig

( 785 )
theorem I for the polytope C;,, out of the one for the polytope An.
By repeated application we arrive at:
oh we of the space Sa) can project itself on a definite
system of mutually rectangular spaces S,y—1, S,g-2,..-5,,5,,5,

gil ~ 3) 274)
respectively according to a Cri , two coincided C 4-2 pre

V2) (1) e's
27-3 coincided Cy, 27-2 coincided squares Cy, and 27—! conicided
. (1) ”
linesegments C) ”
Mathematics. — “On symmetric transformation of S, in connection

with S, and S).? By Mr. L. E. J. Brouwer. (Communicated

by Prof. D. J. Korrrwne).

Let us for the present occupy ourselves with a particular case of
symmetric transformation — the reflection, and let us investigate its
influence on S, and S;. As WS, and .S are independent of the choice
of a system of axes, we make a suitable choice by selecting the
XxX,
cosines of direction of a vector before the reflection ; 8,, 8, 8,, 3,

axis along the axis of reflection. Let us call a,, @,, a,, a, the
those after it; let us moreover represent a,' a," —a@,'a," etc. by
6, etc, and p, 8,’ —8,' 8B," ete. by x, etc: and let us call 2,, ete.
the coefficients of position of a plane with sense of rotation included
before the reflection and u,, etc. those after it. Then:

CS B,

a= 3B,

CC ae B,
Gai = %,, Si, = Kis
S31 —— han S43 Sn Maa
5, Aaa Ss, ——T om hed

V 5703 +8751: +8715 4871448704483 Has tH’: ik Hag Se as. era Oe

So also:

as = F2; 14—— — Pia
As, = Us: Ay, — esd
7 le 7! Ae y Pp ee (s4

Proceedings Royal Acad, Amsterdam. Vol. VI.

( 786 )

OF:
“par 4.4 = ths fy Az = Ars = {454
As, = = As —= (43, — [hg, As, =a das —= Hs T Lag (a)
ee a His Hs, Ax = As = Uy, 34 |

Now however

are the eosmes of direction of the representant of the system of
planes equangular to the right with 4 with respect to a system
of coordinates OX, Y,Z, taken in S,, as that was defined (These
Proceedings Febr. 1904, page 729).

And likewise

Ae. <a ais
7 <a Aey
Za <7 A,

are the cosines of direction of the representant of the system of
planes equiangular to the left with 4 with respect to a system of
coordinates OX, Y)Z taken in an analogous manner in‘).

So from the formulae («) ensues that the effect of a reflection is
what we might call a reciprocal interchange of S, and Sj, Le. a
suchlike interchange that every vector of Sy takes the place of that
vector of S. which has substituted itself for it.

But now an arbitrary symmetric transformation of S, can be
replaced by a reflection preceded or followed by a double rotation ;
which is represented by a reciprocal interchange of S, and 5S;
preceded or followed by a rotation of S, and one of Sj; therefore:

The arbitrary symmetric transformation of |S, is represented by
an interchange of S, and S in arbitrary positions.

Let us now consider that for such an arbitrary interchange of

S. and SS; a system of coordinates @ of S, is placed on a system of

et
coordinates 3 of S; whilst that system of coordinates 3 of S; itselfis
placed on a system y of S,; then we can replace the interchange
by a “reciprocal interchange” placing @ on 3 and 3 on a, followed
by a rotation of S,, placing @ on y, or also by a rotation of 4,,
placing «@ on y, followed by a reciprocal interchange, placing 7 on p
and 8 on y.

Consequently we have proved :

“An arbitrary symmetric transformation of S, can be replaced by
a reflection preceded or followed by a double rotation equiangular

to. the right and likewise of course by a reflection preceded or
followed by a double rotation equiangular to the left.”

The plane of rotation of the equiangular double rotation passing
through the axis of reflection remains for both parts of the trans-
formation in an unaltered position; it undergoes by the double rotation
& congruent transformation and by the reflection a symmetric one.

The plane of rotation of the equiangular double rotation situated
in the space perpendicular to the axis of reflection remains also for
both parts of the transformation in an unaltered position; it is not
transformed at the reflection and undergoes by the double rotation
a congruent transformation.

Those two planes of rotation are perpendicular to each other, so
that geometrically the wellknown property is proved:

“For symmetric transformation of S, about a fixed point one pair
of planes remains at its place; and one plane of it is transformed
congruently, the other symmetrically.”

Physics. — “On the equations of Ciavsivs and vax per WAALS for
the mean length of path and the number of collisions.” By
Dr. Pu. Kounstamm. (Communicated by Prof. van per WAALS).

Several of the methods proposed for the derivation of the equation
of state, make use of formulae for the mean length of path. It is
therefore not to be expected that we shall arrive at undoubted results
as to the former, so long as the results as to the latter quantity are
not concordant. Now it is generally known that van per WaAaAts has
found for the length of path and the number of collisions in a gas
with perfectly hard, perfectly elastic spherical molecules:

v—b u xrns? _—

————— } Spee ab NR Pi ee Mt 5

zens" $F v—b

It does not seem to be so generally known, that Chavsius') and
in accordance with him JAGER?) and Bontzmann*), have obtained
another result, viz:

b 11 b
Sei Pes pa SegG
c= 2 i i — his st ; 3 (2)
ns? 7 jae 4 v Pan)
8 V =

1) Kinetische Theorie der Gase, p. 60.
2) Wien. Sitzungsber. 105, p. 97.
3, Bottzmann Gastheorie, p. 164.

( 788 )

It is clear that at least one of these formulae must be wrong and
it does not seem doubtful to me that (1) is so. As is known, formula
(1) has been found by vay DER Waa.s by applying a correction to
Chausius’ original formula *)

{= ——__ Se ae te (3)
wns? 7 a

Now it is easy to show that fs correction has been wrongly
applied to (3). We can do this without much difficulty either by
making the original proof of Chausius for (3) applicable, taking into
account the reasons which lead to the correction in question, or by
making use of vAN DER WaAaLs’ reasoning for (1), which leads really
to (3). For shortness I shall confine myself here to pointing out the
mistake in the train of thought, which led van per Waats*) and
after him Korrewse*) to the application of this correction. This
reasoning is chiefly this. First it is demonstrated that formula (3)
holds for a gas, the molecules of which are dises of the same diameter
and nature as the spheres in question, which discs have further the
property to take a position normal to the direction of their relative
motion with regard to a molecule, with which they are going to
collide. Then it is thus demonstrated that formula (3) must hold for
spheres. (I derive this passage from the proof of KorTrEwse*), with
which that of VAN DER WaAaLs agrees perfectly).

“Now, however, the moment has come, to remove the incorrect
hypothesis — introduced in § 38 — and replace the dises again by
spheres. The consequence of this will not be that the nature of the
collisions is changed, for any molecule J/, which pursuing its way
would have reached any disc, will infallibly first reach the surface
of the sphere, which we now put in its place. All the molecules
will therefore strike against the same molecules, whose discs we have
supposed to be cut by their centres; but all these collisions will take
place somewhat earlier, in other words, the paths will be shortened.”
From this shortening of the mean path follows the increase of the
number of collisions, as this number is in inverse ratio to the length
of path.

That this reasoning has been able to deceive not only its inven-
tors, but so many after them, is exclusively due to the ambiguous

*) Verslagen Kon. Ak. Afd. Natuurk. Tweede reeks, X. 321. Continuitat 1899.
p. 40 et seq.

°) Verslagen Kon. Ak, Afd. Natuurk. Tweede reeks, X. p. 349,

+) 1. Cp. 3a.

( 789 )

use of the word length of path. If we avoid this, every one will
see through the mistake; for really the reasoning comes to this: In
au certain time a number of particles reach a certain surface A: now
every particle reaches a surface 4 somewhat sooner, so more particles
reach 4 than A in the same time. In essentially the same way we
might show that more vertical falling raindrops would strike a pointed
roof than a flat one of a section of equal area. Nobody will make
this mistake, because it is clear that the number of raindrops falling
on the roof depends solely on the quantities, which govern the
stream of those drops and on the area of the section of the roof.
The same holds for the molecules; and the quantities which determine
the strength of the stream of molecules are only the velocity of
the molecules, the law of the distribution of velocity which is the
same, Whatever the form be of the molecules, and the number of
molecules per unit of volume.

I said already, that the opposed opinion derives its foree from the
ambiguous use of the word “length of path.” We might also justly
say of the raindrops that the path which they describe to get from
a certain poimt to the roof, is ‘shortened, when we think the roof
pointed. In the same way we may say of the molecules, that the
path from a certain fixed point to the sphere is shorter than that to
the disc, but this does not hold for the mean path and of course
the latter only is in inverse ratio to the number of collisions. The
validity of this reasoning is easy to see by means of any of the
seemingly different definitions for the length of path. I shall for
shortness, confine myself to that according to which the mean length
of path of molecules moving with the velocity ¢, is found by
examining, how many molecules strike against a certain molecule
Within a certain interval of time, by adding the paths described by
any of those muiecules between this collision and the preceding one,
and by dividing this sum by the number of those molecules. Let us
now determine the mean path of the molecules which strike with a
velocity c from a direction ? 7 either against the disc S, or the
spherical surface 6 (Fig. 1). We shall call these molecules the
molecules of the group in question. The fact that a molecule of the
group in question whose last collision before it reached B or S took
place in a point A‘), will have a shorter path to £B than to S, does
not call for discussion. In so far VAN DER WaAAaALs and Korrewere are

1) We shall call such a poimi henceforth the ‘last point of collision”. This is
therefore the poimt where the collision tukes place, which makes a molecule pass
into the “group in question’. The collision with B or S makes the molecule leave
this group again.

(7390 4

therefore undoubtedly right. But it follows by no means from this
fhat also the mean path is smaller in the first case. For it is clear,

Fig. 1.

that among the molecules of the group in question which in the
period 7’ reach JS, there are some which have their last point of
collision close to S, e.g. in D. These molecules with their very short
path do not count for the group which reach 4. On the other hand
there will be others whose last point of collision lies so far from 4,
eg. in HL, that they can reach 4, but not S in the interval of time
T under consideration; they must therefore be taken into account
for B, but not for S. That the mean path remains unchanged when
we take these circumstances into consideration is best seen by thinking
the space, in which the last points of collision lie, divided by planes
parallel to B or S. It is clear that all molecules which have their
last point of collision in parts marked by the same number, (Fig. 2)
have the same path; also clear that those points of collision are
regularly distributed over the whole volume and that the volume
of the parts with the same numbers is the same, so that also the
mean path must be the same. So
if the reason of correction given by
VAN DER Waats were the only one,
then the formula (3) would. strictly
apply unmodified; this is, however,
not the case, as there is another
reason for correction, Which we have
not taken into account as yet, as this

influence was expressively excluded
by van peR Waats and Korrewee in their calculation, by VAN DER

( 781 )

Waatrs in the following words '): “This formula —- viz. (1) can
only hold for the case that the chance that more than two molecules
come into collision at the same time may be considered as zero
compared to the chance that only two come into collision.” KorTEWKG
has expressed this more pointedly in the following way’): “For a
short time after each collision the possibilities of fresh collisions are
considerably intlueneed by the proximity of the departing molecule.
This influence, certainly of very difficult mathematical treatment, is
disregarded in my caleulations.”” Chausivs was the first to take this
influence into account *), through which he came to formula (2). 1 will
discuss his proof here, as it may lead to a closer approximated value
of the length of path, even in principle to the drawing up of a strictly
accurate equation, which we shall want for the derivation of the
equation of state.

Chavsivs (loc. cit.) considers the general case of a point moving
in a volume JV between several surfaces in rest. He calculates the
chance, that the point will strike against a surface element with the
velocity d/, by considering the point for a moment as stationary,
and by giving the surface element the opposite velocity. If 4 is the
angle of the normal to the element with the direction of motion,
then the chance that the point lies in the cylindre cos 6 ds dl, is

cos @ ds dl

equal to rages If we bring this in connection with the chance
that such an angle 6 occurs, and if we integrate over all the angles,
Die | dS

we find tor the total chance that the element is struck tL ee
for the total surface a d/; if the mean velocity is 7, so d/ =a dt
then :

Su 4W

P = = == a ——- «
4 ih Su

This derivation appears to be strictly accurate, as long as all
surface elements have an equal chance of being struck and all
volume elements have an equal chance of containing the point. If
there should be elements for which this chance is zero, they must
not be included in the integration. If we think the surfaces to be
movable, then it is clear, that we must introduce the mean relative
velocity in the way known.

Hole Gy piaae.
2) Nature 45 p. 152.
®) Pogg. Erghd. 7 p. 244, cf. Kinetische Theorie der Gase 1. c.

( 792 )

From this general formula Cravsicvs could easily determine Pand /
also for our case. He has only to take into account that in a
collision the centre of a molecule must necessarily be on the surface
of the distance sphere of the other. If we, therefore, want to determine
the number of collisions of the former, we need only see how great
the chance is that this molecule will strike against the surface formed
by the distance spheres.

We get then:

v4 a ns* —

— = pS:

ans’? 7 v

Cravusius observes, however, that not all surface elements can be
struck by the moving point, viz. not those which are found within
distance spheres. In the same way we must subtract. from the
volume v the volume lying within the distance spheres. By deter-
mining the area of these surface elements by first approximation,
CLavusius obtains:

b 11d
- l|—2— : 1— ae
7 g Oh a o
Paes = pa ee 2) as
a ns* 7 ils U eee
8 2 r
b
1—2 —
;
It is clear that the fraction ara occurring in these formulae
8a

is only the first approximation of the more general

available volume

free

surface of distance spheres
tota
If we wish to determine this fraction more accurately we must
add to the denominator of this fraction the surface which is found
within two distance spheres at the same time, as this quantity has

)
been twice instead of once subtracted in the term are when deter-
v »

mining this fraction we have namely assumed that all distance spheres
fall outside each other. But this is not the whole term of the order

—, as bontzMann') has shown, for in the determination of the

1) These Proc. I p. 348.

( 793 )

11 4 '
quantity —--- we have made a supposition which only holds when
Cc v

b?
neglecting the terms with
(> Ios
We must further add to the numerator the volume of the distance
spheres, lying within other distance spheres, which quantity has been
twice instead of once subtracted in the term 24. We geet then
the form

ll b : _ bn
1—>—4 Bl+....4N—
1 = ait
Fale A SY 3 eae Ls Wie eae
Ma ooo ee ee > eat
a ane nn o Sri = ae te.

where 7 is a finite number; for a point cannot lie in more than a
finite number of distance spheres at the same time; as van LAar *)
has made probable, in not more than twelve. We must however
keep in view, that the quantity v which occurs in 2, does not
represent the volume v but the available volume and that this quan-
tity would therefore have to be determined from the equation of
the nt degree:

hb? dy, G8 a hn
\

= Fat ge 2
LG. %,, rete est

There is not much to be said about the coefficients, occurring in
the quantity 8. As Bonrzmann*) has shown they need not change
their signs, on account of the circumstance mentioned by him, as
we should expect if we did not take this circumstance into account.
So is eg. as BottzMann has shown, C, not negative, but positive.
For the present there is not much chance that further coefficients
will be determined on account of the exceedingly laborious caleula-
tions, which would have to be carried out. Yet formula (4) may
already in this form be of use for the question of the derivation
of the equation of state.

1) The developments of Botrzmany’s theory of Gas, p. 148 et seq. further con-
tinued, lead to the same form.

2) Arch. Teyter (2) VII last page.
8) These Proc. | p. 390.

( 794 )

Physics. — “On van per WaAaLs’ equation of state,’ by Dr. Pu.
KkouNsTAMM. (Communicated by Prof. vAN DER WAALs).

§ 1. The way, in which we have to take the extension of mole-
cules into account for the derivation of the equation of state, has been
repeatedly a subject of discussion. It is known that, in order to avoid
the introduction of repulsive elastic forces and therefore the apparent
contradiction with the supposition that only attractive forces act,
VAN DER WaAats has, in the first derivation of his equation, not allowed
for this extension by means of the virial, but by quite other means. This
departure from the path first taken was disapproved of by Maxwe..'),
and strongly condemned by Tarr*), who himself from the equation
of the virial had arrived at an equation of state, as also Lorentz

had derived, viz. :
a pt i h
¢ == a — 7 1 _— 3 . : . . F . (1)

More than ten years ago an interesting controversy was carried on
between Tair?), RayLeigH*) and Kortrwere*) on the value of this form
in comparison with the original form :

(ct NC Oe RE a snl -pg ee

Whereas Tait considered an equation of the form (1) as the only
correct one and the derivation of van per Waats as decidedly
wrong, because it could never lead to this form, Korrrwre thought
that he could prove, that on the contrary the final result ought to
have torm (2), a form which he greatly preferred. This preference,
Which is not to be justified from a purely mathematical point of view
as the two formulae are identical when we take only the terms of

the order — into account — and the terms of higher order are
s

neglected in both cases — may be easily understood when we con-

sider that we have here to do with physieal problems. For whereas
from the form (1) neither the existence of a minimum volume, nor

1) Nature 10, p. 477.

*) Nature 44, p. 546, 627; 45, 199.
5) Nature 44, p. 499, 597; 45, 80.
4) Nature 45, p. 152, 277.

(13)

that of a critical pomt can be derived’), it is known that equation
(2) indicates both, thongh not numerically accurate; one of the nume-
rous cases, where the equation of VAN per WaAAts is a safe guide
for the qualitative course of the phenomena, though it is unable to
represent them quantitatively. Korrrwre derives, therefore, from the
equation (1), (2)?) by putting as it was deduced by van pER WaAALs

VV 227s?

and himself ” =-———— for the value for the number of collisions
v—D

: VV 2ans* Ms

instead of P= ————, which value was used by Tart and Lorenvz.
v

This discussion has not led to a perfect agreement, any more than
a later discussion carried on between BoitzMann*) and VAN DER
Waats ‘) about the corrections, which are to be applied to the value
of 4, which is put constant in (1) and (2) and equal to the fourfold
of the volume of the molecules. As is known, JAGER*) and BourzMann *)

ab
found by first approximation 4, = 6, (: Sa -) for the > from (1);
:

17h
VAN DER Waats /, = ips (: *\ ao ) for that from (2): afterwards

SP 2 8

= i : ; ab
VAN DER Waars Jr.‘) has found for the latter b=, (2- )
‘ Sr

in a different way, so that his result, as far as the terms of the order
b Lb?

: ca -, are concerned, agrees with that of JAGeR and BorrzmMann. In
his publications which have appeared since *), his father has pro-
nounced himself ‘inclined to acknowledge */, as the correct value.’
but it is not doubtful for an attentive reader, that this “inclination”

leaves ample room for doubt, both with regard to the value of the

3
s?

coetficient and to the following coefficient p, which was given

on one side as 0.0958, on the other side as 0.0369,

1) Evidently Tarr has not seen this, but he thinks that the peculiarity of form
(2) exists in this, that it is a cubic with respect to 7; evidently on account of
the part which the three sections of the isotherm with a line parallel to the
r-axis, play in the theory of van per Waats. But he overlooked, that every valid
equation of state will have to represent these three volumes.

*) See also van pekR Waats: Continuitiit 1899, p. 60.

3) These Proc. I, p. 598.

*) These Proc. I, p. 468.

5) Wien. Sitzungsber. 105, p. 15.

6) Gastheorie, p. 152.

7) These Proe. 5, p. 487.

on~

3) These Proc. 6, p. 155,

( 796 )

Now it has clearly appeared of late, of how preponderating an
importance the knowledge of these corrections is for an accurate
equation of state. In the first place Brinkman’) has succeeded in
proving, that the behaviour of air at O° between I and 3000 atms.
can be very accurately represented by means of coefficients which
do not differ considerably from the values found by BourzmMann;
then vAN DER Waats?) has proved — as van Laar*) had done

before that with the aid of these corrections the critical coefficient
‘RT 4 Z %

becomes ( ye 3.6 and in this way one of the great discrepancies
pr).

hetween theory and experiment seems to be removed. And this last

result makes it again clear, how great from a physical point of

view, the difference is between an equation of form (1) and (2),

though from a mathematical point of view they may be identical by

first, second and further approximation. Already a long time ago

Dinrerict') proved, as lately Happrn’) has also done, that with an

equation of the form:

: =A ely Faw l \ , bh I? } :
Ge ae “Tr ele le ay ‘; |b eee
ihe critical coefficient can reach at the utmost the value 3 with the
theoretical values of the coefficients, and that this form can therefore
never represent the experimental data. It seems therefore not devoid
of interest to me, to examine the different derivations of the equation
of state, in order to find which form must be taken as the correct
one. This investigation will at the same time enable us to form an
opinion about the difference between BoLTZMANN and VAN DER WAALS.

§ 2. As is well-known, the proof which van per WAALS originally
gave for his equation of state, rests on two theorems, the first of
which is explicitly stated, the other is assumed without argument
as self-evident. The first theorem states, that the number of collisions
in a gas with spherical molecules is represented by the before-

: : VY 22ns*
mentioned formula ? = ——

Now I have already pointed out

in a former paper’), that this formula is inaccurate, and must
!) These Proc. VI, p. 510.

2) Botrzmann-Festschrift, p. 305.

*) Archives Teyler (2) VII.

4) Wied. 69, p. G85.

5) Drude 13, p. 352.

6) These Proc. p. 787.

( 797 )

' 114
: . : /2ans? 8 wv
be changed by first approximation into P = —-—-— Ts aes
v )
1~2

F ate [2a ns? ab
neglecting the terms of higher order ? = -———-—_{ 1 + — — ]}.
;

The other theorem says that the pressure on the wall (or an
imaginary partition) is inversely proportionate to the mean length of
path. Already KorrrwrG') has felt an objection to this theorem, and
has therefore looked for another way of deriving the equation of
state; though convinced of the validity of the theorem, vAN DER WAALS”)
has later on given another proof, because he considered this theorem
as a not to be proved dictum. After the appearance of the already
cited paper by VAN DER Waats Jr., however, it is in my opinion
beyond doubt, that this theorem does not contain an unprovable truth,
but — at least in the terms given here — a provable untruth. For
it says the same thing as the statement, that the pressure exerted
by the collisions on the distance-spheres per plane unity is equal to
that on an imaginary or real wall. It seems to me, however, that
VAN DER Waats Jr. has convincingly proved, that when the terms

b
of the order — are taken into account, the relation between these
i

pressures defined in the usual way, is 1 — : is

If this result is combined with the just mentioned value for the
number of collisions, which determine the pressure on the distance-
spheres, it is seen, that also in this way the fourfold of the volume
of the molecules is found as first correction, but for the present this
does not teach us anything about the final form, because in the
communication of VAN DER Waars Jr. the relation of the pressures
is not given in its true form, but developed to an infinitely extended
series with neglect of the higher powers, which are, however, material
to the determination of the final form.

In order to derive the final form, we may, if we want to avoid
speaking of repulsive forces, make use of the method based on the
increase of the transport of moment brought about by the collisions.
We start in this from the observation, that the quantity of motion,
which, bound to the molecules, generally moves on with the velocity
of them, proceeds in a collision over a certain distance with infinite

1) Verslagen der Kon. Ak. Afd. Natuurk. Tweede reeks, X, p. 362.
*) Continuitéat 1899, p. 60 cf.

( 798 )

velocity which is best seen by imagining a central shock, in whieh
both molecules pursue their way in the direction from which they
came, but adopting each other's motion. It is therefore just as if
they have passed through each other with infinite velocity and as
if further nothing has happened, so also as if the quantity of motion

of whose motion the pressure of the gas is a consequence —
does not move with the velocity of the molecules, but as if with
every mean path which is described, a distance is saved, which is
a mean of the distances of the centres of the molecules in collisions.
If the distance obtained in this way is '/, sV2 for every mean path of

then the increase of the pressure is:

V 2a01s*
a 1 D
| a. : + 3 mY = /
Y ied LPO )
SS EE Se
] v
iY 2 sens?
If the mean path. when we take into consideration that the
; : ss v h
distance spheres cover each other, is ———— , wherep=g| — },
V2 ans* v

b
then the factor which we must take into account is 1 + —~?, and
v

we get the strictly accurate equation :

a RP b-
P aa ” == eS ] at = B ° e . . ; . (4)

The tran of thought which we have sketched here in a few
words, and from which G. JAGER (loc. cit.) arrived for the first time

; 3) ) .
at the correction term =0,(142—) has already been rigorously
:

developed by Korrrwre'), but he seems to have come to another
resulf. This disagreement is, however, only seeming. KorTEWEG

says”): “the sum of all the distances saved by collisions is therefore

4. APr cos «dt*). The sum, however, of all the distances with whieh the
J bd

P molecules approach the plane A in the time dt is evidently

Pv cos € dt.’

Now it is beyond doubt-in my opinion, that if a number of mole-
cules in the time df by their own velocity pass over a way Pu cos & dt,
1) Verslagen der Kon. Ak. Afd. Natuurk. Tweede reeks X p. 362.
=rihaeGs p. 369.

be . |
) A= in our terminology; v represents the velocity of the molecules in

Kir

KORTEWEG’S paper.

( 799 )

and at the same time a way 4.A/’» cos & dt is saved by the collisions,
those molecules seem to move with a velocity Prcosedt(1 + 4A),
and so the number of collisions has increased in the same ratio.
KorrewrG, however, continues: ‘In order to obtain therefore the
same number of collisions with the plane 14, the molecules will
only have to pass over a way Pv cos edt, instead of over a way
Pv cos € (A — 4A) dé, in other words, the number of collisions of this
system increases in the ratio (1 — 44): 1.” Now between the two
results there is only difference of order r and in so far as we wish

to neglect the quantities of this order, Korrmwxa’s result may cer-
tainly be accepted. If, however, we wish to solve the problem
rigorously, the first result alone can be accepted.

For Korrewrka makes it appear, as if — taking into account the part

of the way being saved — an equally Jong way is described in the
time (1—4A)dt, as in the time dt without doing so. Now in the
last case the molecules pass over a way /r cos édt in the time df,
so. Pycos edt (1 —44A) in the time (1 — 4A)d¢. In the time d¢ there
is saved 4APvcosedt, in the time (1 — 4A)(/t therefore (1 — 4.1)
4 APv cos edt; so the distance, passed over in the time (1 — 4A)d¢
by saving way and really moving together is somewhat slighter
wiz. 16 A* Pecos edt) than that passed over by the real motion alone
in the time cf).
1) Perhaps Korrewea was led when drawing up the formula mentioned in the
text by the solution of the problem in one dimension which he has given in
Nature (loc. cit.) later on. He finds there — perfectly accurately — for the time
passing between two collisions against the wall of a row of 7 particles of diameter
A which can move over a total distance LZ with a velocity V:

This formula reminds us more of Korrewea’s result than of ours, really however
it agrees with the latter, not with the former. For, if we determine the ratio of
the number of collisions with and without saving way, it is Q = ae Now Lis the

?
total distance over which the molecules can move, so the path described by their
own motion + the path saved: mA is the path saved. So Z corresponds with
(1+ 4A) Prcosedt, na with 4 A Pv cos: dt; so the ratio of the collisions is here
: p ; ; L—n
again (1+ 4 A): 1. To Korrewea’s result 1 : (1L—4 A) would the formula Q = = =
Li — 4 IA.

- : ' : HA :
correspond, which agrees with the first as to the terms of the order L , but which

is certainly not sérictly accurate.

It is true that with the formula for one dimension, with regard to its physical
meaning, an equation of state agrees, in which a quantity is subtracted from the
volume which is a function of 6 and v, not a formula of form (1); but we shall
see that our formula derived in the text, leads also to such a final form.

( 800 )

§ 3. So we arrive at equation (4) without making use of the
equation of the virial and without speaking of repulsive forees. That
the introduction of these and the determination of the so-called
“repulsive virial” in the same way as has been done by Lorentz,
Tarr and BonitzMann, leads to the same result, is easy to see, if we

V2 ans? V2 ans? | .

put everywhere —— $ instead of -————— for the number of

v v

collisions in the formulae used by them. The expression 8 does not

depend on any of the integrations and the repulsive virial yields
h 4

therefore RZ — 3 instead of RT —. This is easy to understand, even
v v

without following the proofs of Lorentz and BoirzMann, for it is

clear that the term which is introduced into the equation of the

virial through the collisions, must be proportional to the number of

those collisions, as two collisions can never be of a different kind‘).

It seems therefore as if theory really leads to the form expected
by Tarr and Dinrerict, which conforms so little with the experiment.
In reality, however, the result is quite different. For — as I pointed
out in my other communication — 2 has by first approximation not

the form: 1+ a > as JAGER and BoLrzMann generally write, but we
e v

8 v

find in the way first indicated by Crausius —— > for it, and only
)

by carrying out the division and by neglecting the terms of higher
uD ;
order, we get the form 1+ a a As | showed, we get, taking the
fo} yh, ;

terms of higher order into account :

VaAsb b? hn

esas caine AE 2) per Ne
ve o 2 vy” pn 3
jeg b&b 17B? b* rn jn (°)

ey 160 Se ead bess

where # is a finite number.

Now it is true that the other coefficients of this series, C, and B
excepted, are unknown, and we might conclude from this, that it
must therefore be indifferent for the present, whether the equation
of state is written

') Konrewea and van per Waazs have also made use of this property in their
derivation of equation (2) from (1), mentioned on p. 795.

( 801 )

11}? L? ht

b == |- B— }-
a RT | 5 v 0” ve 6
(> r 7 Fg ae CORE eee

| o— Qh } - } C,
16 v v?
or

a RT \ ' 1 h ' 5 5? ' > /? } (7)
13 — le - Sian en eee

P t yy? r | Y 8 »? : v? |

but this conelusion would be unjustifiable. For it is possible, nay
even probable, that the coeflicients of numerator and denominator in
(6) decrease rapidly; it is therefore possible, that the true form is
accurately represented by a quotient of two forms, which have each
only three or four terms; from this follows by no means, that also
in the form (7) we should get a close approximation with three or
four terms, for the coefficients of the higher powers in (7) do not
depend only on the coefficients of the Aigher powers in numerator
and denominator of (6), but they are also functions of the coefficients
of the lower powers 1; *'/,; 2; ‘'/,,; and in such a way that they
do not become zero, when the coefficients of the higher powers in
(6) do so. Now the difference between (6) and (7) vanishes, of course,
for such large values of v, that the series (7) converges strongly,
but for the critical volume and even more so for liquid volumes tlie
difference is very pronounced. This appears already from the simple
fact, that a form as (6) ean easily yield a minimum volume; but
(7) only when an infinite number of terms is taken into account.
And also the before mentioned difference between the results of
Dirrertct on one side, and van Laar and van per Waats on the
other side, prove how careful we must be with the introduction of
simplifications which seem perfectly allowable.

§ 4. Also the other ways proposed for finding the equation of
State, arrive at similar final results.

This is easy to see for the most direct way, indicated by BontzMaNn ‘).
For it is clear, that his formula (4), which leads to the form:

‘ a\v—2b ies
(p+3 ——=RT .......@

requires another correction on account of the fact that the distance
spheres cover each other partially. The numerator of this fraction

1) Gastheorie p. 9.
99
Proceedings Royal Acad. Amsterdam. Vol. VI.

( 802 )

becomes then identical with the denominator of the fraction from (5).
In the denominator we get a correction for the part of the eylindre
y, which falls within more than one distance sphere, or as we may
also say, for the part of a surface -l, which is found within more
than one distance sphere, if we define this surface A by the condi-
tion, that it is found everywhere at a distance s from the outer
surface. We shall call this surface A henceforth ‘surface of impact”,
hecause the foree which in a collision acts on the centres of the
molecules, acts in this surface. The determination of the numerical
value of the further coefficients seems an exceedingly elaborate work,
at least BoLTzM\NN announced already in the Lorentz volume of the
Arch. Neéerl. that he would have this calculation carried out for the
next coefficient, but this caleulation has not yet been published. It
seems, however not doubtful to me, that also the numerical value
must be the same as the value found in other ways. At all events
the final form becomes also by this method

on 17)? 2 hn
AY Gate Cera eS)
ieee aaa ee ere tee
Leo ey ee
rh pit

in which » represents a finite number.

Now it is not difficult to show that the only remaining method
for deriving the equation of state, which led to the correction '7/,,,
must lead to exactly the same equation as (9), when its principles
are consistently applied. As is known, this method assumes, that
the pressure is to be integrated not only over the volume v, but
also over half of that of the distance spheres: 4, because a molecule
whose centre has got on a distance sphere, is subjected to exactly
the same force as when it has got on the surface of impact (the
volume enclosed by the surface of impact may be put =v). The
volume of the distance spheres, however, is really smaller than h,
hecause some distance spheres coincide, and we get therefore *):

u 17 i? ok
p+ | Ct 4 os) aR , i)
yp o2 Uv F ‘

Now van ver Waats Jr. (loc. cit.) has already pointed out, that
it is tacitly assumed here, that the surface of the distance sphere
which is found within another distance sphere experiences a pressure
= 0, and that therefore, for the sake of consequence, also the parts of
the surface of impact falling within distance spheres, must be supposed

1) Continuitaét 1899, p. 65.

( 803 )

to experience a pressure =O. He has, however, not worked out
this thought further; as it seems to me, because he has not fully
appreciated the ideas which led his father to the correction ‘7/,,. He
has, therefore, substituted for this view, another, undoubtedly correet
one, but he has not explained, how the former might be completed in
order to yield also the true result. If, however, we make use of
the observation made by him, then it is clear that the pressure
au

which seems to be P= p ++ “2 per unit of surface when we. think
it as working in the usual way on the total area of the surface
of impact 0, must be really larger in the gas, viz. equal to
ial S

paca 771

, When this pressure p' acts only on the /ree surface O”.

Now it is clear that this quantity is which hereby gets into the
denominator of the first member of the equation of state is identical
with the quantity introduced by BoLtzMaNn in this place. For he,
too, determines this denominator by examining what part of the
surface of impact falls within the distance spheres. This shows us
at the same time another point. In the few words which van DER
Waats') bestows on this derivation of the equation of state, he says,
that the pressure is not to be integrated over the total volume of
the distance spheres, as we might expect, but over half of it. Now
I have been struck with this from the beginning, and I have tried
to find the reason in vain. Jt appears from what precedes that we
have really to integrate over the total volume and that VAN DER
Waats has only introduced the division by two as compensation for

the circumstance overlooked by him, but which we take here into
219

2 av
account. So he got »—#, instead of ———, which evidently does
v0—OD

not make any difference by first approximation. But already the
second approximation cannot properly be found in this way.

It appears now, that we must integrate the pressure p’, determined in the
way above indicated, over the whole outer surface, that of the distance
spheres included in so far as they fall outside each other?), and that

1) Continuitit 1899, p. 62.

*) The iogical inference from this theorem: that the true equation of state is found
by assuming that every surface element, lying either on a plane or a curved wall,
experiences a pressure: p' per unit of surface provided it does not lie within a distance
sphere, in which case the pressure must be put equal to 0, would involve, that
we did not mtegrate the pressure over the available volume (volume diminished
by the free volume of the distance spheres), but that another correction was applied

53*

( 804 )

the axiom from which vAN DER WAALS started, viz. that we must
equate the pressure on the distance spheres and that on the outer
wall, is true, if only we apply it to the pressure p’. This result is
only in apparent contradiction with the result of van per Waats Jr.,
that the pressure ? on a fixed plane wall stands to the pressure P'

,
on the distance spheres in the ratio of 1: 1 — mae For these pressures
»

P and P' have been found by supposing the quantity of moment
furnished by the wall (and the distance spheres) in the collisions to
be distributed over the fota/ surface, so by assuming that every
surface element contributes an equal amount to the impulse; the
pressure p' of which there is question here, and which proved to be
the same for both, is found on the other hand by supposing, that
only the mean /ree surface contributes to the quantity of motion,
and that the rest is therefore subjected to a pressure = 0.
From this follows:
Se free area ot surface of impact — (1 ca S
~!’ total area of surface of impact v

_ free surface of distance spheres 11+
| ge P = Sa a ee 1 — — —
total surface of distance spheres 8 v
11d
! 1 Sak
iP 8 v Oo b : ; _
and so = = 1 — — — with neglect of the terms of higher
ss b ov :
pee

order.

The importance of the proof completed in this way, lies for me
in the fact, that it makes use of the idea of systems of molecules
whose intra-molecular forces need not be introduced into the equation
of the virial, provided we adopt the pressure integrated over the
whole volume of these systems in the virial. I need not point out
the great advantages of such a point of view, already cursorily
mentioned by vax per Wa ts in his dissertation, and later worked
out; the communications of VAN DER Waals on the equation of state
and the theory of cyclic motion are striking evidences of its value.

Now it is true that there is a difference between our case and
the cases, to which this view is applied in the communications

in connection with the volume of the distance spheres, which are cut by the sur- _
face of impact. This correction would come to an increase of the volume to be
integrated with that part of the distance spheres that is found between the surface
of impact and the outer wall, but it is clear that this volume may be neglected
with the same right as the total volume enclosed by those two surfaces,

( 805 )

mentioned. For in the latter we suppose the existence of really
permanent systems of atoms, whereas in our case two molecules
Whose distance spheres cover each other partially, and which are
therefore thought as a system, remain only together for an exceedingly
short time. But we see that we get to the right result by assuming,
that also the part of the surface of impact lying within the distance
spheres, is part of a ‘system’, and that therefore the foree exerted
on if, does not count’). This result isa priori by no means improbable,
for this part of the surface of impact has exactly the same essential
property as the other parts of ‘‘systems’’ viz. of falling within distance
spheres, whereas in the communications mentioned this hy pothesis
for the surface of impact was not necessary, because there the
systems are characterized by other properties which do not distinguish
the surface of impact viz. that it is part of the same system for a
comparatively long time.

§ 5. The result obtained in the preceding §, enables us now to
use also the first method of reasoning of VAN Der Waats for the
determination of the final form without making use of the virial.
For we have seen that the pressure P on the wall, when the
pressure on the distance spheres P' is determined by

free ae meat me
P total “e? of surface of umpact Pe
p< tes. ue eS

~——- surface of distance spheres
total

Now the pressure on the distance spberes is, as appears from
Ciausivus’ formula for the length of path, proportional to:
free

——— surface of distance spheres
total

available volume
so that we find from this for P:

free : y
——— area of the surface of impact
, total

| eects pee

available volume

') The real significance of the introduction of these systems may be expressed
in this way, that we think the situation of one given moment as fixed, and take
info account the systems of more than one distance sphere formed in this way.
This removes also what is paradoxal in the supposition (see v. p. Waats Jr. loc.
cit. p. 644) that the pressure is 0 in those places which have just experienced a
collision or will soon experience one, viz. the points in the distance spheres. For
in this fixed state those points are really exempted from collisions from all other
molecules than those belonging to their system, and whose pressure may therefore
be considered as an intra-molecular force.

( 806 )

The signification of 7 we find by equating the volume of the
molecules to zero; it appears then, that 7= FT, so that the equation
of state becomes

available volume — RP
=. — i

free :
Yotal “ec of surface of impact
identical with (9).

Equation (10) shows us at the same time, what is the physical
significance of the quantities used by van per Waats Jr. in his proof
with the aid of the virial. For he integrates the pressure P over the
volume 7, the pressure P’ over the volume 4, so that the equation
of state becomes:

tree : 3
surface distance spheres

(»+ =| ee pe caake = RT ae

2 free : : +
area of surface of impact

total

which is, moreover, at once seen, when we read the cited paper
attentively. (Specially p. 492).

Though it is not clear to me, why we must integrate here over
half the volume of the distance spheres, I must acknowledge that
the result — to which we can also get without the proof in question
by simply putting the results (6) and (9) identical — is correct. For
calculations formula (11) which agrees closest with the original form
of vAN DER Waats, may be of use. I had hoped that [ should be
able to use the formula obtained in this way for removing the
remaining discrepancies between experiment and theory, at least

” . (Ta
partially, specially the great difference in the value of ( *) :
pé a

As yet these efforts have not met with the desired success, and it
is obvious, that this will not be possible, before we know e.g. the
numerator of (11) much more accurately than we do now. It is clear
that this numerator in virtue of its physical signification, can never
become zero for volumes larger than the minimum volume; now we
: : 11d
know this numerator only in the shape 1 reteoite expression
which becomes zero tor very much larger volumes, nay even for
the ordinary liquid volumes. For these volumes therefore the appli-
LEA
cation of the correction 1 — ra will be injurious, instead of advant-
ageous. Not before the mathematical form of two of the three quan-

( 807 )

WF free free ae a
tities : surface distance spheres ; area of surface of impact:

total total
available volume, is more accurately known, we shall be justified
in expecting better concordance of experiment and theory.

Physics. — “Note on Sypxry Youne’s law of distillation.’ By
Miss J. Revpier. (Communicated by Prof. J. D. VAN DER
WAALS).

Some time ago SypNrEY YounG gave a law of fractional distillation’),
which seems very strange at first sight. According to this jaw in
distillations with an efficient still, the weight of distillate coming over
below the middle point of the boiling temperatures of the components
would be almost equal to the weight of the most volatile component,
also when the separation is far from perfect. This concordance
would be so close, that Youne could even base a general law of
quantitative analysis on it, at least for substances whose boiling
points were not too near to each other. Now it seemed, however,
unlikely, that this law should always hold, quite independent of the
nature of the Zv-curves and of the composition of the mixture
from which we = start. Therefore | have distilled some mixtures,
inter alia also with Youne’s evaporator still head.

| began with some of the examples chosen by Youne, and I found
really that they confirmed the law. Then I tried to determine the
limits of its validity by taking a mixture with very steep 7’v-line,
so that I could closely examine, what happens, when the distillation
is broken off above or below the mean boiling point. I took for
this benzene (boiling point 79°,6) and aniline ‘boiling point 180°)
and began with such a composition, that the imitial boiling point
lay wready above the middle point, thinking that Youne’s law would
be sure not to hold in this case. Yet also now the law was confirmed,
but the process of the distillation revealed also the character of the rule.
For it appeared that independent of the composition of the mixture,

even when it consisted of 4 °/, benzene and 96 °/, aniline, and so

0
a thermometer, which IT had placed in the liquid, pointed to almost
180° already in the beginning of the distillation, the temperature in
the still head remained constant at 79° for a long time, and rose
then suddenly very rapidly to 180°, so that the distillation might
have been broken off with the same result very far above and

1) J. Chem. Soc. 81 752,

( 808 )

below the middle point 129°\8. It appeared in other words, that
with Youna’s still head an almost perfect separation was reached
already in a single distillation. That the law under consideration
holds in this case, is self-evident.

| found also there where the 7'r-line is less steep, as for benzene
and toluene, that the thermometer remained in the neighbourhood of
the boiling point of the most volatile substance during the greater
part of the distillation, and then suddenly rose rapidly, quickly passing
through the middle temperature, so that here too the breaking off
at the middle temperature is not essential.

Where it is essential as with distillations with less efficient stil
head or for mixtures with very flat) Zv-line, the law does not
hold. As an instance I give the three following distillations, the first
of which, where a mixture with very steep Zv-line is distilled with
the evaporator, conforms to the law; whereas the second, where the
same mixture is distilled with an ordinary straight tube and specially
the third where a mixture with flat 7’-line is distilled with the
evaporator, deviate from the law.

Weight of the

ie oT : me over below midde
Still head. Component Boiling point | components [OME d
temp. im gr.
in gr.
— a ——> ec SF Ch Om Oe es ees sn eee es sn ee nn nw... nn eee ee
Evaporator jenzene 79°.6 6O.S8 1¢@ 60,6
Toluene 110°,8 34,6

Straight

‘abe jonzene 719°.6 30,0
Toluene 110°.8 500 } M2
. yp “| strs -=—- = --
Evaporator an fone 4d 4 0 11,4 1077

chlorate

Benzene

In aecordanee with this Youne himself gives his law only for
mixtures which are not difficult to separate distilled with an efficient
still head.

[ think that IT am justified in coneluding that the law is simply
based on the separation of the mixture in its components, and that
we have to inelude under what Youne calls: a far from perfect
separation, only those cases, where at the end of the distillation a
small fraction of the most volatile substance is left in the recipient

( 809 )

and a small fraction of the least volatile is present in the distillate.
That the two quantities will then differ little in weight and therefore
the deviation from the law is comparatively small, is not strange in
my opinion.

I think to have shown in this way, that Youne’s rule is a proof
of the excellent way in which Youne’s still heads work, but that
from a point of view of quantitative analysis we must only take
this rule as an application of the most obvious Operation, viz that of
separating a substance in pure state froma mixture and then weighing
it separately.

Physical Lab. of the University. Amsterdam.
Physics. — ‘“Hlectromagnetic phenomena in a system moving with

any velocity smaller than that of light.” By Prot. H. A. Lorentz.

§ 1. The problem of determining the influence exerted on electric
and optical phenomena by a translation, such as all systems have in
virtue of the Earth’s annual motion, admits of a comparatively
simple solution, so long as only those terms need be taken into
account, which are proportional to the first power of the ratio
between the velocity of translation w and the velocity of light c¢.

Cases in which quantities of the second order, i.e. of the order —,
. c

may be perceptible, present more difficulties. The first example of
this kind is Micurtson’s well known interference-experiment, the
negative result of which has led Firz Grratp and myself to the
conclusion that the dimensions of solid bodies are slightly altered
by their motion through the aether.

Some new experiments in which a second order effect was sought
for have recently been published. RayiriGH*) and Brack?) have
examined the question whether the Earth’s motion may cause a
body to become doubly refracting: at first sight this might be
expected, if the just mentioned change of dimensions is admitted.
Both physicists have however come to a negative result.

In the second place Trovron and Nose *) have endeavoured to
detect a turning couple acting on a charged condenser, whose plates
make a certain angle with the direction of translation. The theory

‘) Rayteien, Phil. Mag. (6) 4 (1902), p. 678.
2) Brace, Phil. Mag. (6) 7 (1904), p. 317.
*) Trouron and Nogie, London Roy. Soc. Trans. A 202 (1903), p. 165.

( 810 )

of electrons, unless it be modified by some new hypothesis, would
undoubtedly require the existence of such a couple. In order to
see this, it will suffice to consider a condenser with aether as
dielectricum. It} may be shown that in every electrostatic system,
moving with a velocity w'), there is a certain amount of ‘“electro-
magnetic momentum’. If we represent this, in direetion and magni-
tude, by a vector ©, the couple in question will be determined by

the vector product *)
yy 50] 9 GS. Fs See ae ae ee

Now, if the axis of 2 is chosen perpendicular to the condenser
plates, the velocity w having any direction we like, and if 7 is
the energy of the condenser, calculated in the ordinary way, the
components of @ are given") by the following formulae, which are
exact up to the first order:

2U 2U

Substituting these values in (1), we get for the components of
the couple, up to terms of the second order,
20 2U
Wy We, — — We Wz, 0.

2
a2

€

These expressions show that the axis of the couple lies in the
plane of the plates, perpendicular to the translation. If @ is the angle
between the velocity and the normal to the plates, the moment of the

couple will be — w? sim 2a@; it tends to turn the condenser into such

(
a position that the plates are parallel to the Karth’s motion.

In the apparatus of Trovton and Nosrir the condenser was
fixed to the beam of a torsion-balance, sufficiently delicate to be
deflected by a couple of the above order of magnitude. No effeet

could however be observed.

) 2. The experiments of which T have spoken are not the only
reason for whieh a new examination of the problems connected
with the motion of the Earth is desirable. Potrncark*) has objected

') A vector will be denoted by a German letter, its magnitude by the corre-
sponding Latin letter.

*) See my article: Weiterbildung der Maxwetu’schen Theorie. Electronentheorie
in the Mathem, Eneyclopiidie V 14, § 21, a. (This article will be quoted as M. E.)

*) M. E, § 56, c.

4) Powcarsé, Rapports du Congrés de physique de 1900, Paris, 1, p. 22, 23.

( 811 )

to the existing theory of electric and optical phenomena in’ moving
bodies that, in order to explain Micnkenson’s negative result, the
introduction of a new hypothesis has been required, and that the
same necessity may occur each time new facts will be brought to light.
Surely, this course of inventing special hypotheses for each new expe-
rimental result is somewhat artificial. If would be more satisfactory,
if it were possible to show, by means of certain fundamental assumptions,
and without neglecting terms of one order of magnitude or another,
that many electromagnetic actions are entirely independent of the
motion of the system. Some years ago, I have already sought to
frame a theory of this kind’). I believe now to be able to treat
the subject with a better result. The only restriction as regards the
velocity will be that it be smaller than that of light.

§ 3. I shall start from the fundamental equations of the theory
of electrons *). Let 0 be the dielectric displacement in the aether,
the magnetic force, @ the volume-density of the charge of an
electron, » the velocity of a point of such a particle, and f the
electric force, i.e. the force, reckoned per unit charge, which is
exerted by the aether on a volume-element of an electron. Then,
if we use a fixed system of coordinates,

div 0 = By dir fy ye

rot fy = — (d + Oy).

5 ee ete |
rot d = — — fy,

ia
= >) 4 —[v. b].

I shall now suppose that the system as a whole moves in the
direction of « with a constant velocity mw, and IT shall denote bij u
any velocity a point of an electron may have in addition to this,
so. that

9, =w-- uy, ty =-Uy, Y2 = Uz.

If the equations (2) are at the same time referred to axes moving

with the system, they become

1) Lorentz, Zittingsverslag Akad. v. Wet., 7 (1899), p. 507; Amsterdam Proe.,
1898—99, p. 427.
2) M. EL, § 2.

( 812 )
dw) = @, div h = 0,

Ob- 05, 1/0 P “ee l |
fee : — : 1 Ree ee, fy
oy 02 c (5 a =A ¢ Q (we + Uy );

05, Oh- Pay | 0 i

Oz. a ae & : =) Oy SE ae
My Oe ¢ eeys fpliae
Ou Oy c \ Ot Ow ce
00- 03, Lal 0
cemic wag sD) De»

0d, 0d. 1 fo 0

a oa sta "aa .

1
fz — Dx + Fi (uy h- = ue h, );
c
‘ 1 1
i, = oy — = whe + = (u, hy — u, bz),

: 1 LS
f. = d. + — wh, + — (1 by — ty br).
€ c

§ 4. We shall further transform these formulae by a change of

variables. Putting
c? Z
ae ae ke,

C7 —w"

(3)

and understanding by / another numerical quantity, to be deter-

mined further on, I take as new independent variables

a = k l av b y — Ly 9 Z' == i <5

1 k uw hk uw
d',. == d, ; 0’, Sa d, ae a ay i v- +. -_— h, ‘
[? -? ‘ e [? Ap:
1 hk mu I: TG
l) A — 4 ly, 9 ly Ui — P fy / -+ Pe Og . i) S = esi fy. Se dy e
/? ‘ [? ¢ [? ¢ f

for which, on account of (38), we may also write

w w
dD. — EY, , d, = ke (+ ae ke } dD = ke (*. = “Hy )
c c .

bz == y's, by = a (s Me 2s hs ) em ie (. + =e )
C ce.

( 813 )

As to the coefficient 7, it is to be considered as a function of w,
whose value is 1 for «=O, and which, for small values of 2, differs
from unity no more than by an amount of the second order.

The variable ¢’ may be called the “local time’; indeed, for 4 = 1,
/— 1 it becomes identical with what I have formerly understood by
this name.

If, finally, we put

1
LB OQ — 0 rat . . . . . . . ° (7)
k? = = w', , ku, =w,, Bs Sy oP tN

these latter quantities being considered as the components of a new
vector wu, the equations take the following form:

“rat wu’, ' ‘
die Sel ee 5 at) == 0;
ty

t! { ! 1 dd’ ’ ! Q

ro —— ——— oO ul - “ ° . é e

) c or . ( )
1 oh’

ie c Ot

1 Ul ' Ul t 2 Ww Lj !
ie Fb Er. : (u,h.— wh, +P. = (u', 0, + u’. d',),

2 2 1 > ; Bw
te Gln nis) lb, ee
x k > k c h c? ; ,
f i? 8g P 1 ( ! f ' ! [ ! ) P w ' db!
2 ES SS Ss i iil lid | ee TS
Zz p Dx + I ; Wa Dy y Ya Bios uu; 0 -

The meaning of the symbols div’ and rot’ in (9) is similar to that
of dw and rot in (2); only, the differentations with respect to 7, y, 2
are to be replaced by the corresponding ones with respect tor’, y’, 2’.

§ 5. The equations (9) lead to the conclusion that the vectors
db’ and §' may be represented by means of a scalar potential g’ and
a vector potential a’. These potentials satisfy the equations ')

a 1 0%’
A —p — ba. ia ed QO, . ° . . . . (11)
t a’ 1
| edt WORE aa =e ay ae ee re (12)

and in terms of them 9’ and §' are given by

1) M. E., §§ 4 and 10,

( 814 )

] any ‘are uw ron
= — = de grad lags arad Qay + . . . (15)
c Of : ty
bh’ = rot' a’, = ‘ . . - ° F (14)
g* 0? 0?

The symbol Z' is an abbreviation for .—~ +4- and grad'g’

denotes a vector whose components are coy re
Ow Oy’ Oz

. The expression

grad a, has a similar meaning.

In order to obtain the solution of (11) and (12) in a simple form,
we may take ww, 4,2) as the coordinates of a point 7” in a space
S’, and aseribe to this point, for each value of ¢, the values of
Q,u.g.a, belonging to the corresponding point P (x, 7, 2) of the
electromagnetic system. For a definite value / of the fourth independent
variable, the potentials g’ and a’ in the point 7? of the system or in
the corresponding point 2’ of the space S', are given by ')

1 xi. 4
g=— (Sas. . ois eit

1 pond Pee |
ee [Fas > a
Axe r

Here dS’ is an element of the space S', 7’ its distance from

’ and the vector

/
ge’ uw’, such as they are in the element dS’, for the value ¢’ —— of
c

and the brackets serve to denote the quantity @

the fourth independent variable.
Instead of (15) and (16) we may also write, taking into account

(4) and (7),

ee eo
v= | iS... | 4
dn r

a eT es
gf st oe a AL ed

Ame x”
the integrations now extending over the electromagnetic system itself.
It should be kept in mind that in these formulae +’ does not denote
the distance between the element ZS and the point (x,y, 2) for which
the calculation is to be performed. If the element lies at the point
(v,, Y,,2,), We must take
de (w—wa,)? + (y —y,)? -+ (e- =2,)":

It is also to be remembered that, if we wish to determine yg’ and

1) M. E., §§ 5 and 10.

( 815 )

a’ for the instant, at which the local time in P is ¢’, we must take

0 and ow’, such as they are in the element @S at the instant at
.

which the loeal time of that element is / — —

§ 6. It will suffice for our purpose to consider two special cases.
The first is that of an electrostatic system, i, e. a system having
no other motion but the translation with the velocity 7. In this case
wu’ = 0, and therefore, by (12), a’ = 0. Also, ¢’ is independent of ¢’,
so that the equations (11), (15) and (14) reduce to

A'p =— 0; | (19)

> —— grad. ¢g', f' — 0. \

After having determined the vector 0’ by means of these equations,
we know also the electric force acting on electrons that belong to
the system. For these the formulae (10) become, since u’ = 0,

iy 2

= = I= d', fy —— k d'y, fz — a ee . . . . . (20)

The result may be put in a simple form if we compare the moving

system S with which we are concerned, to another electrostatic

system 2’ which remains at rest and into which > is changed, if
the dimensions parallel to the axis of « are multiplied by 4/, and
the dimensions which have the direction of 7 or that of z, by /,
a deformation for which (4/,/,/) is an appropriate symbol. In this
new system, which we may suppose to be placed in the above
mentioned space S$’, we shall give to the density the value 9’,
determined by (7), so that the charges of corresponding elements of
volume and of corresponding electrons are the same in + and &".
Then we shall obtain the forces acting on the electrons of the moving
system 2, if we first determine the corresponding forces in ", and
next multiply their components in the direction of the axis of . by

2
P, and their components perpendicular to that axis by a This is

conveniently expressed by the formula
7 - I ~ a
B=(% py a ie ad eee

It is further to be remarked that, after having found »d’ by (19),
we can easily calculate the electromagnetic momentum in the moving
system, or rather its component in the direction of the motion.
Indeed, the formula

( 816 )

OM f
6= ftr.o)as

shows that
4 eS'¢
ee | (d, hb: — d- h,) dS
=== (

Therefore, by (6), since h! =
kl
= | (bd, * +p.")dS./. (22

2
‘

kltw fC.
oS. = | (d,7 + d-") dS:

§ 7. Our second special case is that of a particle having an elee-

tric moment, i. e. a small space JS, with a total charge fe dS =k
7

but with such a distribution of density, that the integrals fe wdS8,
4

fe yd 8, fe S have values differing from 0.
‘ e

Let X,y,z be the coordinates, taken relatively to a fixed point A
of the particle, which may be called its centre, and let the electric
moment be defined as a veetor » whose components are

Pz = | oxdS, py =r oy dS, i. = | ozds.... . ieee

d vps << d i i d As
F — Eh Ol, ae, = Py =) 04, 28, i =— [e wdS . (ea
dt . ‘e dt et dt -

Of course, if X, y, Z are treated as infinitely small, uy, uy, we must
he so likewise. We shall neglect squares and products of these six
quantities.

We shall now apply the equation (17) to the determination of
the sealar potential g’ for an exterior point P (7, y, 2), at finite distance
from the polarized particle, and for the instant at which the local
time of this point has some definite value ¢. In doing so, we shall
give the symbol |g], which, in (17), relates to the instant at which

'
,

‘| . . . . . . . .
the local time in dS is ¢ ,aslightly different meaning. Distinguishing

z
by 7’, the value of 7 for the centre A, we shall understand by ,@|
the value of the density existing in the element dS at the point

r
(x, Y, Z), at the instant ¢, at which the local time of A is ’——.
c

It may be seen from (5) that this instant precedes that for which
we have to take the numerator in (17) by

j w kr j—r' : 8 oe dr KS Or" Or’
2 ——___. — #? _-x-+——( x — — + Z—
€ eh C Ps c Ow ay. 0

units of time. In this last expression we may put for the differen-

tial coefficients their values at the point AL.
In (17) we have now to replace [oe] by

do et Or' 07" dr’ \ [ 00 pa
lel +H ox 2] 45 = (xx He agen ae =) eI Nee

do ' : ist re
where 7 relates again to the time ¢,. Now, the value of ¢ for

which the caleulations are to be performed having been chosen, this
time ¢, will be a function of the coordinates «, y,z of the exterior
point P. The value of {@] will therefore depend on these coordinates

in such a way that

d[o] k 1 Or' [ 0g

i .. Wimoe Ei oe
by which (25) becomes

,w. [90 d[Q] d[e] d[Q]
[el +e ex | 32] — (x Ou y Oy ge Oz

Again, if eee we understand by 7 what has above been

1
called 7’,, the factor — must be replaced by
7

t
,

1 ore l a KI 07 1
iar os ~v5(5 he eye

so that after all, in the integral (17), the element d Sis multiplied by

Lo| = [| 0xle] 9Oyle] 9 Zl]

7" Ot Ox Oy 7 dz 7'

This is simpler than the primitive form, because neither 7’, nor
the time for which the quantities enc!osed in brackets are to be

BY }2 w

taken, depend on w, ¥, 2. Using (23) and remembering that fi odS=0

we get
apt, [me] L peledy 2d, atop
cra 4ac*r'| Ot 4a lov r' Oy x

a formula in which all the enclosed quantities are to s a for
the imstant at which the local time of the centre of the particle is

'
PP
pe SRD

€
We shall conclude these calculations by introducing a new vector
yp, whose components are

Proceedings Royal Acad, Amsterdam. Vol, VL.

( 818 )

Pr = klpr, Py —l py, 2 lpe, . . « - (26)
passing at the same time to .’,7/’,2',/ as independent variables. The
final result is

pf a Bal eed Gel Pal ee
— Ager’ ot Aa lode’ -' oy dz’ (7

As to the formula (18) for the vector potential, its transformation
is less complicate, because it contains the infinitely small vector w’.
Having regard to (8), (24), (26) and (5), I find

i Opal
4Aacr Ot

The field produced by the polarized particle is now wholly deter-
mined. The formula (13) leads to

ee eee eee oR lem eee! s
Sis 4axeot? + 1 4 wee | de’ r a a dz’ or!
and the vector §' is given by (14). We may further use the equations
(20), instead of the original formulae (10‘, if we wish to consider
the forces exerted by the polarized particle on a similar one placed
at some distance. Indeed, in the second particle, as well as in the
first, the velocities ' may be held to be infinitely small.

It is to be remarked that the formulae for a system without
translation are implied in what precedes. For such a system the
quantities with accents become identical to the corresponding ones
without accents; also 4;=1 and /—1. The components of (27) are
at the same time those of the electric force which is exerted by one
polarized particle on another.

(27)

§ 8. Thus far we have only used the fundamental equations
without any new assumptions. I shall now suppose that the electrons,
which I take to be spheres of radius R in the state of rest, have
their dimensions changed by the effect of a translation, the dimensions
in the direction of motion becoming kl times and those in perpen-
dicular directions / times smaller.

jer ee
In this deformation, which may be represented by G —, 7,
kh tae
each element of volume is understood to preserve its charge.

Our assumption amounts to saying that in an electrostatic system
~, moving with a velocity aw, all electrons are flattened ellipsoids
with their smaller axes in the direction of motion. If now, in order
to apply the theorem of § 6, we subject the system to the defor-
mation (A/,/,/), we shall have again spherical electrons of radius 7,

( 819 )

Hence, if we alter the relative position of the centres of the electrons
in by applying the deformation (4/, /, /), and if, in the points
thus obtained, we place the centres of electrons that remain at rest,
we shall get a system, identical to the imaginary system ’, of
which we have spoken in § 6. The forees in this system and those
in + will bear to each other the relation expressed by (21).

In the second place I shall suppose that the forces between unchar-
ged particles, as well as those between such particles and electrons, are
influenced by a translation in quite the same way as the electric forces
in an electrostatic system. In other terms, whatever be the nature of
the particles composing a ponderable body, so long as they do not
move relatively to each other, we shall have between the forces
acting in a system (2") without, and the same system () with a
translation, the relation specified in (21), if, as regards the relative
position of the particles, =’ is got from Y by the deformation (A/, /, /),

Lh
or = from ' by the deformation (F 7? +)

We see by this that, as soon as the resulting force is 0 for a
particle in =’, the same must be true for the corresponding particle
in +. Consequently, if, neglecting the effects of molecular motion,
we suppose each particle of a solid body to be in equilibrium under
the action of the attractions and repulsions exerted by its neighbours,
and if we take for granted that there is but one configuration of
equilibrium, we may draw the conclusion that the system ’, if the
velocity ™ is imparted to it, will of self change into the system
+. In other terms, the translation will produce the deformation

ptt
Moe by:

The case of molecular motion will be considered in § 12.

It will easily be seen that the hypothesis that has formerly been
made in connexion with MicHELson’s experiment, is implied in what
has now been said. However, the present hypothesis is more general
because the only limitation imposed on the motion is that its velocity’
be smaller than that of light.

§ 9. We are now in a position to calculate the electromagnetic
momentum of a single electron. For simplicity’s sake I shall suppose
the charge ¢ to be uniformly distributed over the surface, so long
as the electron remains at rest. Then, a distribution of the same
kind will exist in the system SS’ with which we are concerned in
the last integral of (22). Hence

54*

and

e
oS. = PC hs lw.

It must be observed that the product 4/ is a function of w and
that, for reasons of symmetry, the vector © has the direction of the
translation. In general, representing by w the velocity of this motion,
we have the vector equation

§ = a tt ree Aree le
62acR oem

Now, every change in the motion of a system will entail a cor-
responding change in the electromagnetic momentum and will there-
fore require a certain force, which is given in direction and mag-
nitude by

aS ee, ee
we a Ki

Strictly speaking, the formula (28) may only be applied in the
ease of a uniform rectilinear translation. On account of this circum-
stance — though (29) is always true — the theory of rapidly varying
motions of an electron becomes very complicated, the more so, because
the hypothesis of § 8 would imply that the direction and amount of
the deformation are continually changing. It is even hardly probable
that the form of the electron will be determined solely by the
velocity existing at the moment considered.

Nevertheless, provided the changes in the state of motion be suf-
ficiently slow, we shall get a satisfactory approximation by using (28)
at every instant. The application of (29) to such a quasi-stationary
translation, as it has been called by ABRAHAM’), is a very simple
matter. Let, at a certain instant, j, be the acceleration in the direction
of the path, and j, the acceleration perpendicular to it. Then the force
® will consist of two components, having the directions of these acce-
lerations and which are given by

% = ta: ond ee a
if
2 r . 5 2
a ta sl ee and m, = oe ees + - Spee
bach de back

Hence, in phenomena in which there is an acceleration in the

') Apranam, Wied. Ann, 10 (1903), p. 100,

( 821 )

direction of motion, the electron behaves as if it had a mass m,, in
those in which the acceleration is normal to the path, as if the
mass were m,. These quantities m, and m, may therefore properly
be called the “longitudinal” and “transverse” electromagnetic masses
of the electron. I shall suppose that there ts no other, no “true? or
“material” mass.

mw?

Since & and / differ from unity by quantities of the order —, we

9?
c?

find for very small velocities

m, = mM, = broth

This is the mass with which we are concerned, if there are small
vibratory motions of the electrons in a system without translation.
If, on the contrary, motions of this kind are going on in a body
moving with the velocity w in the direction of the axis of z, we
shall have to reckon with the mass m,, as given by (30), if we con-
sider the vibrations parallel to that axis, and with the mass m,, if
we treat of those that are parallel to OY or OZ. Therefore, in
short terms, referring by the index + to a moving system and by
=' to one that remains at rest,

mS) = (ent) (2), ee en)

§ 10. We can now proceed to examine the influence of the Earth’s
motion on optical phenomena in a system of transparent bodies. In
discussing this problem we shall fix our attention on the variable
electric moments in the particles or “atoms” of the ~ystem. To these
moments we may apply what has been said in § 7. For the sake
of simplicity we shall suppose that, in each particle, the charge is
concentrated in a certain number of separate electrons, and that the
“elastic” forces that act on one of these and, conjointly with the
electric forces, determine its motion, have their origin within the
bounds of the same atom.

I shall show that, if we start from any given state of motion if
a system without translation, we may deduce from it a corresponding
state that can exist in the same system after a translation has been
imparted to it, the kind of correspondence being as specified in
what follows.

a. Let A’,, A’,, A’,, ete. be the centres of the particles in
the system without translation (2'); neglecting molecular motions
we shall take these points to remain at rest. The system of points.

( 822 )

A,, A,, Ay, ete., formed by the centres of the particles in the moving
system 2, is obtained from A’, A’,, A’, ete. by means of a deformation

Loe mer
& qT ~} According to what has been said in § 8, the centres
will of themselves take these positions A’, A’,, A’,, ete. if originally,
before there was a translation, they occupied the positions ,, .A,, A,, ete.

We may conceive any point /” in the space of the system +" to
be deplaced by the above deformation, so that a definite point ? of
corresponds to it. For two corresponding points /” and P we shall
define corresponding instants, the one belonging to /”, the other to
P, by stating that the true time at the first instant is equal to the
local time, as determined by (5) for the point /, at the second instant.
3y corresponding times for two corresponding particles we shall
understand times that may be said to correspond, if we fix our
attention on the centres A’ and A of these particles.

}. As regards the interior state of the atoms, we shall assume that
the configuration of a particle A in = at a certain time may be

Poet
derived by means of the deformation ( 7 7) from the confi-
guration of the corresponding particle in ”’, such as it is at the
corresponding instant. In so far as this assumption relates to the form
of the electrons themselves, it is implied in the first hypothesis of § 8.

Obviously, if we start from a state really existing in the system
~’, we have now completely defined a state of the moving system +.
The question remains however, whether this state will likewise be
a possible one.

In order to judge this, we may remark in the first place that
the electric moments which we have supposed to exist in the moving
system and which we shall denote by », will be certain definite
functions of the coordinates 7, y, 2 of the centres A of the particles,
or, as we shall say, of the coordinates of the particles themselves,
and of the time ¢. The equations which express the relations between
y on one hand and «, y, z, ¢ on the other, may be replaced by other
equations, containing the vectors p’ defined by (26) and the quantities
w’,y’,2’,t’ detined by (4) and (5). Now, by the above assumptions
a and #, if in a particle A of the moving system, whose coordinates
are ©, y, 2, we find an electric moment »p at the time ¢, or at the
local time ¢’, the vector p’ given by (26) will be the moment which
exists in the other system at the true time ¢’ in a particle whose
coordinates are x’, y’, 2’. It appears in this way that the equations
between p’, 2’, y’, 2’, ¢ are the same for both systems, the diffe-
rence being only this, that for the system +’ without translation

( 823 )

these symbols indieate the moment, the coordinates and the true time,
Whereas their meaning is different for the moving system, p’, 0, y/, 27, U
being here related to the moment »p, the coordinates wv, y, 2 and the
general time ¢ in the manner expressed by (26), (4) and (5).

It has already been stated that the equation (27) applies to both
systems. The vector d’ will therefore be the same in >’ and X,
provided we always compare corresponding places and times. How-
ever, this vector has not the same meaning in the two cases. In +’
it represents the electric force, in it is related to this force in
the way expressed by (20). We may therefore conclude that the
electric forces acting, in + and in Y’, on corresponding particles at
corresponding instants, bear to each other the relation determined by
(21). In virtue of our assumption 4, taken in connexion with the second
hypothesis of § 8, the same relation will exist between the “elastic”
forces; consequently, the formula (21) may also be regarded as
indicating the relation between the total forces, acting on corresponding
electrons, at corresponding instants.

It is clear that the state we have ele to exist in the moving
system will really be possible if, in + and 2’, the products of the
mass m and the acceleration of an electron are to each other in the
same relation as the forces, i.e. if

[es g2
mj (2) == (". rs “| UL j (=’) ° ° ° ° ° (52)

Now, we have for tbe accelerations

ea ara ice -
Di ee (=), - 6 2 + « « (83)

as may be deduced from (4) and (5), and combining this with (32),
we find for the masses
m (=) = (Kl, kl, hl) m €')
If this is compared to (81), it appears that, whatever be the value
of /, the condition is always satisfied, as regards the masses with

Which we have to reckon when we consider vibrations perpen-
dicular to the translation. The only condition we have to impose on
/ is therefore

d(klu
(lw) oe
dw

But, on account of (3),
d(kw)

—<u :

so that we must put

( 824 )

dl
—=-—|@, |] = const.
dw

The value of the constant must be unity, because we know already
that, for w= 0,!—1.

We are therefore led to suppose that the influence of a translation
on the dimensions (of the separate electrons and of a ponderable body
as a whole) is confined to those that have the direction of the motion,
these becoming k times smaller than they are in the state of rest. It
this hypothesis is added to those we have already made, we may be
sure that two states, the one in the moving system, the other in the
same system while at rest, corresponding as stated above, may both be
possible. Moreover, this correspondence is not limited to the electric
moments of the particles. In corresponding points that are situated
either in the aether between the particles, or in that surrounding the
ponderable bodies, we shall find at corresponding times the same
vector d’ and, as is easily shown, the same vector )’. We may sum
up by saying: If, in the system without translation, there is a state
of motion in which, at a definite place, the components of », > and
) are certain functions of the time, then the same system after it
has been put in motion (and thereby deformed) can be the seat of
a state of motion in which, at the corresponding place, the com-
ponents of p’, d’ and b’ are the same functions of the local time.

There is one point which requires further consideration. The values
of the masses m, and m, having been deduced from the theory of
quasi-stationary motion, the question arises, whether we are justified
in reckoning with them in the case of the rapid vibrations of light.
Now it is found on closer examination that the motion of an electron
may be treated as quasi-stationary if it changes very little during
the time a light-wave takes to travel over a distance equal to the
diameter. This condition is fulfilled in optical phenomena, because
the diameter of an electron is extremely small in comparison with
the wave-length.

§ 11. It is easily seen that the proposed theory can account for a
large number of facts.

Let us take in the first place the case of a system without trans-
lation, in some parts of which we have continually »=0, >= 0,
6=0. Then, in the corresponding state for the moving system, we
shall have in corresponding parts (or, as we may say, in the same
parts of the deformed system) p' = 0, 0’ = 0, l’=0. These equations
implying » = 0, }=0, § =0, as is seen by (26) and (6), it appears

that those parts which are dark while the system is at rest, will remain
so after it has beem put in motion. [ft will therefore be impossible
to detect an influence of the Earth’s motion on any optical experi-
ment, made with a terrestrial source of light, in which the geome-
trical distribution of light and darkness is observed. Many experi-
ments on interference and diffraction belong to this class.

In the second place, if in two points of a system, rays of light
of the same state of polarization are propagated in the same direction,
the ratio between the amplitudes in these points may be shown not
to be altered by a translation. The latter remark applies to those
experiments in which the intensities in adjacent parts of the field
of view are compared.

The above conclusions confirm the vesults | have formerly obtained
by a similar train of reasoning, in which however the terms of the
second order were neglected. They also contain an explanation of
MICHELSON’s negative result, more general and of somewhat different
form than the one previously given, and they show why Ray rien
and Brace could find no signs of double refraction produced by
the motion of the Earth.

As to the experiments of Trouton and Nosiz, their negative result
becomes at once clear, if we admit the hypotheses of § 8. It may be
inferred from these and from our last assumption (§ 10) that the only
effect of the translation must have been a contraction of the whole
system of electrons and other particles constituting the charged
condenser and the beam and thread of the torsion-balanee. Such a
contraction does not give rise to a sensible change of direction.

It need hardly be said that the present theory is put forward with
all due reserve. Though it seems to me that it can account for all
well established facts, it leads to some consequences that cannot as
yet be put to the test of experiment. One of these is that the result
of MicHELSON’s experiment must remain negative, if the interfering
rays of light are made to travel through some ponderable transparent
body.

Our assumption about the contraction of the electrons cannot in
itself be pronounced to be either plausible or inadmissible. What
we know about the nature of electrons is very little and the only
means of pushing our way farther will be to test such hypotheses
as | have here made. Of course, there will be difficulties, e.g. as soon
as we come to consider the rotation of electrons. Perhaps we shall
have to suppose that in those phenomena in which, if there is no
translation, spherical electrons rotate about a diameter, the points of
the electrons in the moving system will describe elliptic paths,

corresponding, in the manner specified in § 10, to the cireular paths
described in the other case.

§ 12. It remains to say some words about molecular motion. We
may conceive that bodies in which this has a sensible influence or
even predominates, undergo the same deformation as the systems of
particles of constant relative position of which alone we have spoken
till now. Indeed, in two systems of molecules +’ and Y, the first
without and the second with a translation, we may imagine molecular
motions corresponding to each other in such a way that, ifa particle
in X has a certain position at a definite instant, a particle in Y
occupies at the corresponding instant the corresponding position. This
being assumed, we may use the reiation (83) between the accelera-
tions in all those cases in which the velocity of molecular motion
is very small as compared to w. In these cases the molecular forces
may be taken to be determined by the relative positions, indepen-
dently of the velocities of molecular motion. If, finally, we suppose
these forces to be limited to such small distances that, for particles
acting on each other, the difference of local times may be neglected,
one of the particles, together with those which lie in its sphere of
autraction or repulsion, will form a system which undergoes the
often mentioned deformation. In virtue of the second hypothesis
of § 8 we may therefore apply to the resulting molecular force
acting on a particle, the equation (21). Consequently, the proper
relation between the forces and the accelerations will exist in the two
cases, if we suppose that the masses of all particles are influenced
hy a translation to the same degree as the electromagnetie masses of
the electrons.

§ 13. The values (80) which I have found for the longitudinal and
transverse masses of an electron, expressed in terms of its velocity, are
not the same as those that have been formerly obtained by ABRAHAM.
The ground for this difference is solely to be sought in the cireum-
stance that, in his theory, the electrons are treated as spheres of
invariable dimensions. Now, as regards the transverse mass, the
results of ABRAHAM have been confirmed in a most remarkable way
by IKXAUPMANN’s measurements of the deflexion of radium-rays in
electric and magnetic fields. Therefore, if there is not to be a most
serious objection to the theory I have now proposed, it must be
possible to show that those measurements agree with my values
nearly as well as with those of ABRAHAM.

1 shall begin by discussing two of the series of measurements

( 827 )

published by KaurMaxn') in 1902. From each series he has deduced

two quantities y and 6, the “reduced” electric and magnetic deflexions,
w

which are related as follows to the ratio @=—:

C U7] .
Bah, WO= Ee (34)
Here y (8) is such a function, that the transverse mass is given by
3 e ~,
m,=— . —— w(8),- - « «» « » « (89)

4° 62c?R
whereas 4, ank /, are constant in each series.
It appears from the second of the formulae (80) that my theory
leads likewise to an equation of the form (55); only ABRAHAM’s
function yw (8) must be replaced by

ap ee
a es Bp):

vo
Hence, my theory requires that, if we substitute this value for
yw (8) in (34), these equations shall still hold. Of course, in seeking
io obtain a good agreement, we shall be justified in giving to /, and 4,
other values than those of KAUrMANN, and in taking for every measure-
ment a proper value of the velocity w, or of the ratio B. Writing

sk,, —k’, and #' for the new values, we may put (34) in the form
1? 4 2 «

PS ak S MD os Bk Fe
7
and
bes ?
(he 6°) ae :
KAUFMANN has tested his equations by choosing for /, such a value
that, calculating 8 and 4, by means of (34), he got values for this
latter number that remained constant in each series as well as might
be. This constancy was the proof of a sufficient agreement.
I have followed a similar method, using however some of the
numbers calculated by Katrmany. I have computed for éach measure-
meut the value of the expression

Hel = By PG) Hy eo FF Oe
that may be got from (387) combined with the second of the equations
(84). The values of w(3) and £, have been taken from KavrMany’s
tables and for 3’ I have substituted the value he has found for 8,
multiplied by s, the latter coefficient being chosen with a view to

se Sola

') Kaurmann, Physik. Zeitschr. 4 (1902), p. 58.

( 828 )

obtaining a good constaney of (88). The results are contained in the
following tables, corresponding to the tables [1] and LV in KavrmMann’s

paper.
III. s = 0,933.

6 v(B) m4 B' kg!
0.851 2.447 1.721 0.794 | 2.246
0.766 1.860 | 1.736 : 0.715 | 2.958
0.727 1.78 | 41.73 | 0.678 | 9.956
0.6615 1.66 | Lidar FSO Ot | 2 256
0.6075 4.595 | 4.655 | 0.567 24175

IV. s = 0,954.
<= —— ———
B (6) | ke B' ke!
ee oe oe =" lesneees — = eS
0,963 Sea | 8 12 0.919 10.36
0.949 2.86 | 71.99 | 0.905 9.70
0.933 2.73 | 7.46 | 0.800 | 9.98
0.883 2.31 | 8.32 | 0.842 | 410.36
0.860 2 A995 | 8.09 0.820 | 10.15
0.830 2.06 8.413 0.792 | 10.23
0.801 1.96 8.13 0.764 10.98
0.777 1289 8.04 0.744 | 10.20
0.752 4-83... 11-8302 Oia 10.22
0.732 4.7% | 7.97 0.698 | 40.48

The constancy of 2’, is seen to come out no less satisfactory than
that of /,, the more so as in each case the value of s has been
determined by means of only two measurements. The coefficient has
been so chosen that for these two observations, which were in Table
Ill the first and the last but one, and in Table IV the first and the
last, the values of 4’, should be proportional to those of /,.

I shall next consider two series from a later publication by KAUFMANN’),
which have been caleulated by Renew?) by means of the method of

1) Kavemany, GOtl. Nachr. Math. phys. KL, 1903, p. 90.
2) Ruxce, ibidem, p. 326.

( 829 )

least squares, the coefficients 4, and /, having been determined in
such a way, that the values of 4, calculated, for each observed §,
from KAvFMANN’s equations (34), agree as closely as may be with
the observed values of 7.

I have determined by the same condition, likewise using the method
of least squares, the constants @ and 4 in the formula

Ui == as? — bo! ;
which may be deduced from my equations (56) and (37). Knowing
a and 4, I find B for each measurement by means of the relation

C
B=Va-.
y

For two plates on which KavurmMann had measured the electric and
magnetic deflexions, the results are as follows, the deflexions being
given in centimeters.

I have not found time for calculating the other tables in KAUFMANN’S
paper. As they begin, like the table for Plate 15, with a rather
large negative difference between the values of 4 which have been
deduced from the observations and calculated by Rung, we may
expect a satisfactory agreement with my formulae.

§ 14. I take this opportunity for mentioning an experiment that

Plate N°. 15. a= 0,06489, 4 = 0,3039.

| D | B

: ¢ IGateulated | - | Calculated | | Calculated by

Observed. | by R. | Diff. | by a | Dit: 4} = : ‘

| | | | om need
0.1495 | 0.0388 | 0.0404 | — 46 | 0.0400 | — 419 | 0.987 | 0.951
0.199 | 0.0548 | 00550 | — 2] 0.0552 | ==) Bl VG. 96% | 0.918
0.2475 | 0.0716 | 0.0710 | + 6| 0.075 | + 1| 0.930 | 0.881
0.296 0.0806 | 0.0887 | + 9| 0.085 | + 1!/ 0.899 | 0.842
0.3435 | 0.1080 | 0.1081 | a5) Af | 0.1090 | —10| 0.3847 | 0.803
0.391 | 0.1290 | 0.1297 pos 7 | 0.1305 | — 15 0.804 | 0.763
0.437 | 0.1524 | 0.4597 | — 3 0.4532 | — 8| 0.763 | 0.727
0.4825 | 0.1788 | 0.4777 | +41] 0.4777 | +44] 0.72% | 0.692
0 | | 0.660

5963 | 0.9033 | 0.9039 | — 61 0.9033 | 0} 0.688

( 830°)

Plate N°. 19. a = 0,05867, 6 = 0,2591.

% | B
; |

; Ghsecve: ee Dirt. oe Dit. | ae Ss
ee ea
0.1495 0.040% 0 0388 + 46 0.0379 +25 | 0.990 | 0.954
0.199 0.0529 | 0.0597 | 4+ 2) 0.052 | 47 | 0.969 | 0.998
0.247 | 0.0678 | 0067 | + 3] 0.0674 | +4 | 0.939 | 0.888

| |
0.296 | 0.0834 | 0.082 | — 8} 0.084% | —140 | 0.902 | 0.849
0.3435 | 04019 | 0.1022 | — 3| 0.1096 | —7 | 0.862 | 0.811
0.391 0.1219 | 0.192 | — 3! 0.199% | —7 | 0992 | 0.773
0.437 | 0.1499 | 0.1484 | — 5] 0.4437 | —8 | 0.782 | 0.736
0.4825 0 1660 0.1665 — 5 0.1664 | —"4 | 0.744 | 0.702
0.5265 0.1916 0.1906 = $10, 0.192 | 444 | 0.709 | 0.671

has been made by Trovuton’) at the suggestion of Firz Grra.p, and
in which it was tried to observe the existence of a sudden impulse
acting on a condenser at the moment of charging or discharging;
for this purpose the condenser was suspended by a torsion-balance,
with ifs plates parallel to the Earth’s motion. For forming an
estimate of the effect that may be expected, it will suffice to consider
a condenser with aether as dielectricum. Now, if the apparatus is
charged, there will be (§ 1) an electromagnetic momentum
2U

6} —— wD.

Terms of the third and higher orders are here neglected). This
momentum being produced at the moment of charging, and dis-
appearing at that of discharging, the condenser must experience in
the first case an impulse — @ and in the second an impulse + 6.
However Trovuron has not been able to observe these jerks.
| believe it may be shown (though his calculations have led him
fo a different conclusion) that the sensibility of the apparatus was
far from sufficient for the object Trovuron had in view.
Representing, as before, by Ll’ the energy of the charged condenser
') Trovrox, Dublin Roy, Sec. Trans. (2) 7 (1902), p. 379 (This paper may also

be found in The scientific writings of Firz Geran, edited by Larmor, Dublin and
London 1902, p. 557).

( 831 )

in the state of rest, and by (’-+ UL” the energy in the state of motion,
we have by the formulae of this paper, up to the terms of the
second order,

an. expression, agreeing in order of magnitude with the value used
by Trocron for estimating the effect.

The intensity of the sudden jerk or impulse will therefore be — .
w

Now, supposing the apparatus to be initially at rest, we may
compare the deflexion «, produced by this impulse, to the deflexion
a which may be given to the torsion-balance by means of a constant
couple A, acting during half the vibration time. We may also
consider the case in which a swinging motion has already been set
up; then the impulse, applied at the moment in which the apparatus
passes through the position of equilibrium, will alter the amplitude
by a certain amount ? and a similar effect 3’ may be caused by
letting the couple A’ act during the swing from one extreme position
to the other. Let 7 be the period of swinging and / the distance
from the condenser to the thread of the torsion-balance. Then it is
easily found that

e ¢ <0"
ene KT w

According to TrovTon’s statements (7’ amounted to one or two
ergs, and the smallest couple by which a sensible deflexion could be
produced was estimated at 7,5 C.G.S.-units. If we substitute this
value for A and take into account that the velocity of the Earth’s
motion is 3 x 10° ¢.M. per sec., we immediately see that (39) must
have been a very small fraction.

(39)

Mathematics. — “Uhservation on the paper cominunicated on
Febr. 27% 1904 by Mr. Brocwer: ”On a decomposition of the
continuous motion about a point O of S, into two continuous
motions about O of S,'s.” By Dr. E. Janyxe. (Communicated
by Prof. D. J. Kortewese.)

The above mentioned paper is connected with investigations of
Frerp. Caspary and with works published by me in the years
1896—1901. Mr. Brouwer not referring to these, I take the liberty
to remark the following: Problems of the theory of the thetafune-
tions on one hand and of mechanics on the other hand have led

( 832 )

me to relate the rotation in S, to two rotations in S,. The relations
between the elements of the four-dimensional rotation and the elements
of the two threedimensional rotations belonging to it have been
explicidy pointed out by me in ‘“Sitzungsberichte der Berliner
Akademie” of July 30% 1896 and in the “Journal fiir die reine
und angewandte Mathematik” Vol. 118, p. 215, 1897. I have
particularly found that the components of the velocity of the first
rotation are easily deduced from the components of the velocity of
the two others (compare also my lecture at the ‘“Naturforscher Ver-
sammlung’” at Hamburg 1901: “On rotations in fourdimensional
spaces,” (Ueber Drehungen im vierdimensionalen Raum).

Mr. Brouwer arrives in his paper also at these results though in
a different way, namely geometrically, whilst I have worked alge-
braically. Mr. Brouwer arrives at a decomposition (“Zerlegung”) of
the fourdimensional rotation into two threedimensional ones, whilst
I use the expression coordination (“Zauordnung”).

Berlin, March 28%, 1904.

Mathematics. — “Alyebraic deduction of the decomposability of
the continuous motion about a fixed point of S, into those of
two S,s’. By Mr. L. E. J. Brovwrr. (Communicated by
Prof. KorTEWwEs).

As the position of S, is determined with respect to a fixed system
of axes by siv independent variables and that of S, with respect to
a fixed system of axes by three independent variables we understand
at once that in an infinite number of ways two S, motions can be
coordinated to an S, motion, so that position and velocities of S, are
determined by position and velocities of the two S,’s. On such a
coordination Mr. JAHNKE has been engaged in the papers mentioned
above and has deduced the relations between positions and veiocities
of S, and the two S,’s. Interpreted geometrically his coordination
amounts to the following: Let us suppose in S, a fixed system of
axes X, X, X, X,, and a movable one Y, Y, Y, Y,; let us con-
sider the part equiangular to the right of the double rotation, which
transfers Y, Y, Y, X, into Y, Y, Y, Y,; let us add to it an equal
equiangular double rotation to the left (namely equal with respect to
the system of axes Y, VY, NX, X,; only with respect to a definite

2 1

system of axes can we call an equiangular double rotation to the
right and one to the left equal); the resulting rotation becomes a single

( 838 )

rotation parallel to the space Y, NY, .Y, which would transfer the
system of axes .Y, YY, Y, into an other 7, 7, Z,. Thus to each
position }” with respect to XY, Y, Y, , answers a position 7 with
respect to .Y, Y, X,, and by interchanging right and left, in an
analogous manner a position (7 with respect to Y, , Y,; and we
may consider the positions 7 and // as coordinated to the position )’”.

Not immediately to be seen are the two following properties of
the S, motion geometrically deduced in what was communicated in
the February meeting.

Ist. The continuous motion of S, can be decomposed, that is:
independent of the choice of a system of axes two definite three-
foldly infinite motion groups exist in SS, in such a way that an
arbitrary motion can be composed out of two motions each of which
belongs to one of the groups mentioned.

Qed. The continuous motion of S, can be decomposed into two
S,; motions, that is, two twodimensional manifoldnesses (namely
those of the systems of planes equiangular to the right and to
the left) exist in S, in such a way that each of the motion
groups mentioned transforms the elements of one of them into
each other and leaves the other unchanged; to which further-
more we can allow twodimensional Euclidean stars to answer in
such a way that to congruent combinations in one of the manifold-
nesses congruent combinations of the Euclidean stars correspond,
that to the corresponding motion group of S, answers the motion group
of the Euclidean star movable as a solid and that to congruent
combinations in the motion group of S, answer congruent combinations
in the motion group of the Euclidean star movable as a solid: reason
why we may call the two twodimensional manifoldnesses fivodiinen-
sional Euclidean stars and the motion groups of S, transforming them
Euclidean threedimensional motion groups about a piced pout.

We shall now see how we can arrive algebraically at both results.

Mr. JAHNKE takes from Caspary the so called ‘Elementary trans-
formation” (see a.o. Jahresbericht der Deutschen Mathematiker-
Vereiniging XI, 4, 1902, p. 180 and F. Caspary, Zur Theorie der
Thitafunctionen mit zwet Arqumenten, Cretix’s Journal, vol. 94, page
75), which has the property that an arbitrary congruent transformation
of S, can be replaced by two successive elementary transformations.
The name “Elementary rotation” (Elementardrehung) of Mr. JAHNKE
seems to me less fortunate, because it is asymmetric transformation,
not a rotation. The real meaning of the “Elementary transformation’
will be made clear furtheron. For the present we remind the readers
of its determinant type (see Jahresbericht, 1. ¢., page 180).

Proceedings Royal Acad, Amsterdam. Vol. VI.

, ake *, a,
1 rr 5 ‘a
~ ae 1 7 3
5; 2 . . . . > (I)
—7, a, 1 Tw,
X, TU, aX, —#,

and we notice that it does not represent a group and does not
possess any threedimensional properties (it does after composition
with itself, compare for instance the theorem of Mr. Janyke, Jahres-
bericht, l. ¢., page 182: “Jede endliche Drehung im &, lasst sich als
eine Zusammensetzung aus einer Elementardrehung im #, mit sich
selbst auffassen’”’’); which operation is for the rest bound to a once
chosen system of axes).

We shall now deduce two different determinant types likewise
determined by a system of cosines of direction %,, 7,, 7,4, which
do represent a group and have threedimensional properties. Those
will be the determinants of equiangular double rotation to the
right and to the left.

Let us solve the a@’s out of the equations (/7) (see Proceedings of
March 19%, 1904, page 721); then we have

PFE, ge — he hp re \

ieee een Chee aetna os. kag) See (a).

berg Es Gy ot a le
a, = 2,8, — *, 8, — x, B, — x, B,

Thus the determinant type of the equiangular double rotation to
the right is

7, NX, —H, = ee
— FH Mi 4 ig 1 |
3 4 1 2
. . -})
a, —, x, , |
ea | et eee 1%,

Directly can be verified that this determinant type forms a group.

Likewise we deduce for the equiangular double rotation to the left
(7, x, 7, %,), transferring the vector (@, @, a, a,) into (@, 8, B, B,), the
relations :

1— — %, 8, — “2, Bs + 1, B, + x, B, |
= Xf; a Be
ee es

re a,—— zB, —2, 8, — 7,8, — 2, 8,

1) “Each finite rotation in S, can be regarded as a composition of an elementary
rotation in S, with itself,”

— SS

( 835 )

from which ensues the determinant type for equiangular double
rotation to the left:

—x, —27, a is
1, —%, —2 x |

; : S| Oe eR.
—X, a, —42, on
—a, —7, —2, —2,!

and for this too the property of a group can be verified.

If we call (I’) the determinant type formed by interchange of the
rows and columns of (1), we can remark :

If we reverse the signs in the bottom row of type (ID type (1’)

appears.
If we reverse the signs in the last column of type (III) type (I)
appears.

If we ask ourselves whether each arbitrary congruent transformation
can be replaced by the succession of a transformation (III) and a
transformation (Il) the answer must be affirmative; for we shall have
but to take those transformations (III) and (II) belonging to the
transformations (I) which when successively applied transfer the
given initial position into the given final one. (For those two ways
only the intermediate positions will differ in as far as they will be
each other’s reflection with regard to their _Y,-avxis.)

This is the algebraic proof of 1°.

At the same time it has become evident that the meaning of
the type (I) is an arbitrary equiangular double rotation to the
right preceded by a reflection according to the .Y,-axis (that is the
X,-axis of the initial position) or an arbitrary equiangular double
rotation to the left followed by a reflection according to the X,-axis
(that is the Y,-axis of the final position), and that the meaning of
the type (1) is an arbitrary equiangular double rotation to the right
followed by a reflection according to the Y,-axis or an arbitrary
equiangular double rotation to the left preceded by a reflection according
to the _Y,-axis.

Thus according to a preceding communication made in this meeting
of the Academy (see page 785) it has been proved that the types (I)
and (I') represent the most general symmetric transformation of S,,
of which the determinant type has been simplified only by particular
choice of the system of coordinates.

We shall now give a proof for 2°.

Out of the relations (a) for equiangular double rotation to the

ww ue

20*

( 836 )

right we deduce, representing for shortness’ sake a’, a’, — a’, a’, ete.
by §:, Gic; 6.6 ,— Pip. cle. by zy ee
S93 (% 7 +4 )Xast (WRF Hy sho + (3% — MyM) g— (Ay + Hs Vag
+ (7+ 1) + (Hg — HM a,
§ 5, (41%, — 7H Asst hrs? Vhs: — (5 1 ha +
(23+, % fis Ks4)
§ (7, +20 Nas tH dt (1% 3— 2H ,)(Xe +X.) +
+ (73° fa (AYP Ae Va
—— (0,° 1-7) host I ha (4 + 2%) hed
+ (70, — 7% X12 +Fs5)
Yas ( 2, — 4%) ast Xad— (As +8 hart +H Wat
+ (2,0, +2, 1 )(X1a+Hs4)
& = (27,, +77 )\Xas tis) + (45% — 2,2) Ns +2) —
(0 Py hat (A + haw
from which ensues:
EE (219 2 Hy has thas) + 2( + 5% Ns t+ he)
+ 2(2,%, —9 7X12 +Xs,)
€,,4§.,=2(9,7%,—2%,%,) sth) + (4 4+2,'—2,— 2, Wa Phd tT
Ff 2(2,% +, \ fre + ha4)
E +8, 2(r, 8, 42,2) Hast tr + 2( 5% — 7,2 )Xsr + Xa
+ (9,74 22 — 9 — 2, Vs +h)

= ==, a
Gu — Sis — X38 — Mis

S51 ae So4 = Xa. — Kas
wae? - par ini Sie
Sie S34 — ais hs4°

So also if we eall 4,, ete. the coefficients of position of a plane
before the equiangular double rotation to the right and wy, etc. the
coefficients of position after it:

4,44, (22 +97 — 2° — 7,’ )\(Uas tia) + 2(2,%, +20 ,)(%, +b) +
2 (20,0, — 7, )(M, Fils 4)
Ag A, =" (2,2, — 1% ,)(Uas +H) + Fo? — 2 *)(U,, +H)
+ 2( 2077, + EH My Mss)
As A, ,=2(2,7,+7,%,)(U,, +41) + 2(%,%,— 7, %,)(Uy, +H.) +
+(9,° +27 —2,?—%,’)( 1. Has)
Ass ae Ay, = Uss — Ui
As — 4eg = Msi — Mag
A, — Ay = Bye — Bee

(-837))

In an analogous way we deduce from the relations (4) for an
equiangular double rotation to the left the following relations between
the coefficients of position of a plane before and after the rotation:

Ass + fig = Mas H+ bag
As, + As, = Ur + Mas
Ais + Aa, = Ua + Ua
dys 4, $82 — Hr,’ — 2," (Us — By.) + 2( F431 — Ua) +
+ 2(% 7, — 7% ,)(U,.—Us,)
Ay 4, = 2(%, 1, — 1% V3 — Hy 4) ih (2? 4 72 —1,°— 2's. — ba) +
+ 2(27,77, +, %,)(U,.—Us,)
4, a— 45,2 (7,0, + ,0,)(U,3—Hy,.) + 2(2,%,— 2, 2%,)(U,,—B a) +

ar Ey — 2

As now (4,, + 4,,)? = land XS (4,,—4,,)? = 1 and the determinant
nitaZ—x7—a,* 2(2,2,+2,7,) 2(7,7,—7,7,) bed
2(2,%,—27,7,) x +a7—ai—a 2(2,%,127,2,) | (Ly)
2(9,7,+27,7,) 2(,%, —21,%,) x,°+2,'

represents the general congruent ea eae Meo
about a fixed point expressed in the four parameters of homogeneity,
we can regard the motion group with the determinant type (ID
as a congruent motion group of the twodimensional Euclidean
star of the (4j-+4g4)’s and the motion group with the determinant
type (IJ) as a congruent motion group of the twodimensional
Euclidean star of the (4,-—A,4)’s; namely according to the determinant
type ([V) about an axis with cosines of direction
leaky Ty x,

Vie 40- ws, Vie?
over an angle equal to 2a arc COs X,.

Let us call the S, of the (4;.+4a4)’s “the representing space to the
right” or the S, of S, and the S, of the (4c—Ans)’s the “representing
space to the left” of the S, of S,, then we find that to two equiangular
double rotations to the right (left) (7,' 7,' 2,' 2,/) and (2," a," 7," a,''
of S, whose angles of rotation are are cos 2, and are cos x," and whose
systems of planes of apt make an angle with each other equal to

eyes bor
are coe gaia est =, (see Proceedings, March, 1904, page 724)
VYi—z,” . V1—
correspond two rotations ie S, (S)) over angles 2 are cos 2’, and 2 are cos x,",
x,'x,"+2,'x,"+a,'x,"

Vi—2z,” . Vi—a,"

whose axes make an angle equal to are cos

( 838 )

with each other. So to congruent combinations in the group of
the equiangular double rotations to the right (left) in S, correspond
congruent combinations in the motion group of JS, (Sj. As moreover
the

As3 =e As
Ass ei Ass
Ars =e As

of a plane are the cosines of direction of the representant of the
system equiangular to the right with that plane with respect to the
system of axes OX, Y,Z, (defined Proceedings March1904, p. 728),
and likewise

Ass Sie a
a5; = Aas
A, po. Ass

the cosines of direction of the representant of the system equiangular
io the left with that plane with respect to the system of axes
OX, Y,Z (defined in the same place) the S, and S;introduced just
now prove to be identical with those introduced here formerly (see
Proceedings March, 1904, p. 725) so that they represent not only
by their motions the equiangular motion groups of S, to the right
and to the left, but also by their vectors the systems of planes equi-
angular to the right and to the left (with direction of rotation) of
S, and so that the angle of the representing vectors is the angle of
the systems of planes themselves.

So also to congruent combinations in the twodimensional mani-
foldness formed by the equiangular systems of planes to the right
(left) correspond congruent combinations in JS, (S,). This is an algebraic
proof for 2"¢. to its full extent.

This deduction has at the same time made clear the meaning of
the four parameters of homogeneity for the general congruent three-
dimensional transformation about a fixed point, namely the cosines
of direction of the vector indicating the corresponding equiangular
double rotation to the right (left) of au jS, of which this S, is
the S,.(S) and the system of axes in S, the system OX, Y,Z,

(OX; Y; Z).

( 839 )

Zoology. — “On the relationship of various invertebrate phyla.”
By Prof. A. A. W. Husrecar.

In an elaborate paper entitled “Beitrage zu einer Trophocdéltheorie,”’
published in 1903 in the 38th volume of the “Jenaische Zeitschrift
fiir Naturwissenschaft,’ Prof. Arnoip Lane of Ziirich (p. 68— 77)
gives a clear exposition of what has been, in his opinion, the phy-
logenesis of the Annelids.

In this pedigree he places, beginning with a protocoelenterate,
a ctenophore-like being, a plathelminth, an intermediate form resem-
bling a triclade, an animal in the shape of a leech which already
possesses metameric segmentation and finally a proto-annelid,

The grounds on which he bases this phylogenesis, compel us to
acknowledge important relations between these animal groups. But
whether this kinship testities to a descent in the order given by Lang,
or whether the order has for the greater part been a reversed one,
deserves to be examined more closely.

In my opinion there Ctenophores should not be placed at the
beginning of the series, nor are they to be considered as links between
Coelenterates and worms, but they have to be looked upon as animals,
which form the last offshoots of an evolutionary series, leading from
the Annelids via the Hirudimia and the Plathelminthes. Of these
latter there have been some which gradually assumed a pelagic
mode of life and have become Ctenophora, the external resem-
blance of which with transparent jelly-fish seemed to justify their
being placed by the side of the Coelenterates.

Let us first test the grounds on which that combination has until
now been defended (see e.g. G. C. Bourne in Ray Lankester’s
Treatise on Zoology, 1900).

The presence of a gastro-vascular system and the absence of an
independent coelom, as well as the presence of a subepithelial
nerveplexus are characteristics which can be found not only with
the Coelenterates, but also to a great extent with the Plathel-
minths,

The tentacles of the Ctenophores have quite wrongly been compared
to those of the medusae, while the analogy of the adhesive cells
of the Ctenophora with the nematocysts of the Cnidaria is also
defective. And if nematocysts should be found in some Ctenophora,
no conclusions should be based on this, because they also occur in
Molluses, Plathelminths and Nemertines.

The absence of nephridia, the general structural proportions and
the gelatinous composition of part of the organism are details which

( 840 )

by no means interfere with a view which would see in the Cteno-
phora Plathelminths that have become pelagic.

That the connection which Haxrcken intended to establish between
Coelenterates and Ctenophora, when describing Ctenaria ctenophora,
is an imaginary one, has already repeatedly been shown, so e. g.
by R. Hertwie (‘Jen. Zeitschr”’. Bd. 14, p. 444), G. C. Bourne
(I. c. p. 445) and others. The first-mentioned author says emphati-
cally (1. e. p. 445): “Die Ctenophoren sind Organismen welche sich
yon den iibrigen Coelenteraten sehr weit entfernen.”” Also KorscHELT
and Hriper in their excellent handbook on the embryology of the
invertebrates are inclined (p. 100) to look upon the Ctenophora rather
as an independent branch of the animal kingdom, the connection of
which with that of the Coelenterates lies far backward. On the other
hand they point out unmistakable relations between the phylogenesis
of the Ctenophora and that of the Bilateria (Annelids, Arthropoda,
Molluses ete.). They expressly add that the side-branch of the animal
kingdom on whieh the Ctenophora are placed cannot be consulered
as having furnished a starting-poit for higher animal forms.

Ctenoplana and Coeloplana are consequently not considered by
them as advancing steps of development in the direction of the Plat-
helminths, but as aberrant, creeping Ctenophora. LaneG himself has
acknowledged on page 72 of his great handbook that the place
of the Ctenophora among the other Cnidaria is a very problematical
one and that their embryology distinguishes them from all Cnidaria.

So there can be no doubt, considering all this, that the tie
which nowadays keeps together the Ctenophora with the Coelente-
rates has of late years been considerably slackened. One effort and
it may be entirely removed °).

What on the other hand have we to. think about possible relations
between Ctenophora and Plathelminths? These relations appear espe-
cially striking to those who have oecupied themselves with the
embryological development of both classes.

Thus SeELeNKA has already in 1881 summarized this analogy under
twelve heads (zur Entwickelungsgeschichte der Seeplanarien, 5. 288).
Also Lane in his monograph on Polyeclads (1884) has emphatically
pleaded for that relationship, although in a separate paragraph he
acknowledges the existence of real difficulties. Also in his most recent
paper he adheres to the same opinion.

The discovery of two very peculiar genera of animals has still more

1) A paper, published very recently in the Zoologische Anzeiger (Bd. 27, p. 223)
on a new, much simplified Ctenophore, does not, as its author Dawyporr sug-
gests, strengthen the bond between Coelenterates and Ctenophora.

ee el

( 841°)

emphasized the problem of the relationship between Ctenophora and
Plathelminths, I mean Ctenoplana and Coeloplana. In different degree
they unite properties of both classes as has already been clearly eluci-
dated by their discoverers: Korornerr and KowaLewsky. Yet neither
Bourne who prepared the Ctenophora for Ray Laykester’s large
Textbook of Zoology, nor Korscuett and Heimer in their handbook
mentioned above, nor Wininy, who lately studied Ctenoplana in a
living condition, are really convineed of the possibility of a derivation
of Plathelminths from Ctenophores, in which case these two genera
should have to be considered as intermediate forms in that direction.

So WILLEY e.g. points out that if is not very probable that littoral
forms would have sprung from pelagic ones, whereas generally
the contrary is observed. This would according to him have been
a reversion of the natural sequence. The future will show, in
my opinion, that the difficulties mentioned, and raised by such able
experts, will for the greater part vanish as soon as relationships
“against the grain’, i.e. in the timnatural order, are no longer
accepted, but when both genera are considered as gradually mutating
Plathelminths which are already fairly on the way of assuming
etenophoran habitus,

From what precedes we may at any rate infer that whereas the
Coelenterate relationship of the Ctenophora has faded, their compa-
rability with the Plathelminths has come to the fore.

The data for judging in how far a derivation of the Annelids from
Plathelminths might be possible are given in extenso especially in
Lane’s earlier and later publications, more particularly in his well
known Gundapaper (1881) of which he has given an improved and
partly modified edition in his most recent essay, quoted in the
beginning. So I need only refer to this latest paper here.

I for my part must now try to show that a derivation im. the
opposite direction presents no difficulties. We then should look upon
Plathelminths and Ctenophores no longer as ancestral forms but as
modified and in many respects unilaterally modified descendants of
~a more primitive, Annelid-like type.

Lane has already in his Polyelad-monograph (p. 674) openly
declared himself against such a view. Yet in the twenty years which
have since elapsed, various considerations have changed and it seems
that CaLpweLt’s view (Proc. R. Soe. 1882 no, 222) has become
more probable again, according to which “there is a presumption .
that in fact Platyelminths are degenerate Enterocoeles.”’

1 should be willing like to undertake the defence of this thesis
and to see in the Plathelminths degenerate forms in whieh the

( 842 )

coelom has almost entirely disappeared, while the genital apparatus
has obtained a maximum degree of complication.

At the outset it seems to me to be less probable that at the base
of the pedigree of the Annelids such animals should stand like the
hermaphrodite Plathelminths with their ovaries, testes, vitellaria, so
greatly varying in size and shape; with their shell-glands, ootype,
clirus, penes, uterus, spermatheca, ete., not even to mention the
vitello-intestinal, the Laurer- and other canals. Does not this very
complication force us to place such animal forms rather in the
peripheral branches than near the root of any pedigree ?

On the other hand we can state that in those Polychaeta which
have retained archaic characters, such as Polygordius, Protodrilus and
Saccocirrus, various peculiarities draw our attention which in Plathel-
minths are further developed. So the phylogenesis of the Plathel-
minths would not necessarily have to be so long, via Polychaeta,
Oligochaeta, Hirudinea, but the type of Plathelminths might already
at an early period have been a deviation of the original coelomatous
ancestral forms, while in the course of this evolutionary process also
the present Oligochaeta and Hirudinea might have sprung off laterally.

Meanwhile the stronges argument for the degeneration of the
Plathelminths seems to me to be found in their early ontogenesis.

When we consider this in the light which not long ago especially
American workers have procured to us, we ought to pay attention
to the phenomena of ce//-lineage: the descent of special groups of
tissue from certain mothercells. Winison, Coxkurx, Mrap and others
have shown us the way here.

Of paramount importance is the fact that Annelids (Polychaeta
Oligochaeta, Hirudinea) and Molluses in those earliest phases of
development show a striking uniformity and that e.g. in all of them
the couple of mothercells of the so-called mesoblast-bands, within which
the coelom and metamerism appear first, originate in a_ similar
manner from one cell, the oldest, unpaired, mesodermic mother-cell,
belonging to the 64-cellular cleavage phase.

This cell lies in the second quartet of cells reckoned from the vege-
tative pole and is produced by a plane of division slanting to the left.
The next cleavage always divides this cell into a right and left
mesodermic cell; these two develop into the paired mesodermic bands.

All this is always observed in the animal phyla above-mentioned. Con-
cerning the Plathelminths Lane provided us already twenty years ago
with extensive data, which however do not constitute an unbroken
series such as is necessary for establishing the cell-lineage. Such
a series was given us a few years ago (1898) for Leptoplana

( 843 )

by E. B. Wirtsox (Annals of the New-York Academy of Sciences,
vol. XI p. 15). From his publication we may conclude as follows:

1. That a cell-couple as represented by Lana for Discocoelis, is
also present in Leptoplana, which Mrap has compared to the mother-
cells of the mesoblastbands of Annelids and Molluses, although from
this cell-couple 710 mesoblast develops i either YJOnUs of Plathelminths.

2. That, moreover, with Leptoplana, four cells of the second cell-
quartet (counted from above) become the mother-cells of “larval mesen-
chym’, that they remove to the interior and that by further subdivision
they gradually furnish the whole mesoblast of Leptoplana. This origin
of the mesoblast in Plathelminths was also already known to LANG.

3. That also with Molluses (Unio, Crepidula) and probably also
with certain Annelids (Aricia), beside the two symmetrical mesoblast
bands still another source of mesoblastic tissue occurs, which is
directly comparable to the source of larval mesenchym mentioned
in 2, and that also these mesenchym mother-cells originate from cells
belonging to the ectoblast quartet, as with the Plathelminths.

4. That consequently it may be considered a settled fact that
with Annelids and Molluscs the mesoblast has a twofold origin ').

Conkhin (Vol. XIII, Journal of Morphology, p. 151) has emphasized
that thus mesoblast is furnished by each of the four quadrants,
viz. the mesenchym by the micromeres of the second quartet
of A, B, and C, the mesoderm-bands by D.

This latter phenomenon is always connected with lengthening of
the body and with teloblastie growth, even with animals like Lamel-
libranchia and Gastropoda, although the latter are not generally
Jooked upon as longitudinally developed forms. From this Conkiin
justly inferred that the radial mesoblast has a still more primitive
character than the bilateral.

Whoever considers more closely the correspondence here noticed
in the development of the Polyclada with that of the Annelids and
Molluses, will have to acknowledge that only that solution can be
satisfactory which considers the two ceils, mentioned in 1, as the last
remnant of the no longer fully developing mesoblast-bands with
the degeneration of which the disappearance of the coelom and of
a distinct metamerism has gone hand in hand.

1) 1 may briefly call attention to the fact that I also pleaded for a manyfold
origin of the mesoblast with mammals, on account of what had been found in
Tarsius (Verh. Kon. Ak. v. Wet. Amsterdam, vol. VIII n’. 6 1902, p.69) and that
I concluded from it that the mesoderm is not equivalent to the two primary germ-
layers, but that Kuervenpera was right when he qualified it as a complex of
originally independently developing organs.

( 844.)

To Jook upon them as potential mother-cells of those mesoblast-bands
would be against all known laws of heredity, where in all other points
there is so great a resemblance, also with regard to the mesenchym,
between this 64-ceilular stage and that of Annelids and Molluses and
where it would be entirely impossible — supposing evolution to have
followed the line: Coelenterates, Ctenophora, Plathelminths — to
derive the mesoblast-bands, which must anyhow lie accumulated in
the cells mentioned, from these preceding ancestral forms. On the
other hand it can easily be understood that these bands have gradually
assumed their present form and peculiar characteristics in the long
(and to us unknown) series of the ancestral forms of Annelids,
Molluses and Polyelada, and that with these latter and still more
with the Ctenophora (which have an ontogenesis so much resembling
that of the Polyelada,) the part played by these mesoblastic mother-cells
has again receded to the baeck-ground.

We must then, especially on account of what ontogenesis has
taught us, consider the Plathelminths as degenerate descendants of
Coelomata and so the = strobilation of the Cestoda, which are still
further degenerated by parasitism, again falls within the reach of an
explanation which would homologize it with the metamerie structure
of the Annelids.

How the gradual reduction leading from Polychaeta via Oligochaeta
and Hirudinea to Plathelminths, has left its traces in all the different
organs and tissues I will not develop more extensively here; I may
suppose these poimts to be generally known.

It is obvious, after what has preceded, that we ought not to attempt
to derive the metamerism of the Annelids from the pseudo-metamerism
of the Turbellaria as Lane does. I prefer to accept the hypothesis
formulated already in 1881 by Sepewick, according to which a longi-
tudinally extended, actinia-like being, possessing wormlike free motility,
formed the starting-point. Gradually cyclomerism was converted into
bilateral symmetry and linear metamerism, in the same way as now
already certain Actinia show a tendency to bilateral symmetry.

Ep. vAN BenepEn afterwards indicated (1894), though only in an
oral adress which has never been published, how SxpGwick’s view
might be extended to the Chordates. In 1902 in the ‘‘Verhandelingen”’
of this Academy, I have tested the possibility of applying Srp@wick’s
theory to the facts that are revealed to us by the development of
mammals. And the facility with which the explanation of Sepe@wick
can be extended both to Vertebrates and Invertebrates, is undoubtedly
an argument in its favour.

Lanc and Harscurk object that a prolonged actinialike being would

it tee

( 845 )

also. have possessed unpaired tentacles and an unpaired gastral division
in the median line. They forget that such an unpaired medial coelomic
cavity is already present in Balanoglossus and that LANGERHANS
(‘Zeitschr. fiir wiss. Zool.” Vol. 34. 1880) and Goopricu (Q. J.
Microsc. Se. Vol. 44, 1901) have also shown the existence of an
unpaired coelomic cavity in Saceocirrus, while cases of unpaired
median sensory spots could be enumerated in Coelomata. The well-
known antithesis of headsegment and pygidium as compared with
the trunk in the bilaterally metameric Coelomata is an argument
that goes far to meet Lane’s and HarscuEK’s contention.

Neoformation of segments, still pretty equally distributed with the
cyclomeric Coelenterates, but there also already variable, occurs with
the Coelomata exclusively at the posterior end and with many of
them only during embryonic life.

If we assume in accordance with E. van Brnepen (see Verh. Kon.
Akad. v. Wet. Amsterdam. Vol. VIII p. 69) that the stomodaeum
of an actinia-like ancestral form has been the precursor of the chorda
dorsalis, beside and above which the nerve-ring unites to a spinal
chord, while under it a connection between the stomodaeal fissure
(the chordal cavity) and the gastral diverticula (coelomic cavities)
can be observed, then it follows from this that the ancestral forms
of the aquatic Chordata are moved about in the water in a position
different from that of the ancestral Articulates by 180°. The mouth
of the Chordates would then have arisen later as a new formation,
as has already repeatedly been asserted. It is an undoubted simpli-
fication of our phylogenetic speculations if we are entitled to look
for this difference in orientation already in very early ancestral
forms and can so avoid Grorrroy St. Hinaire’s error who shifted
the process of reversion to a much later stage of development.

If thus the phylogenesis is very considerably shortened, I may
call attention to the fact that even with respect to the mammalian
foetal envelopes, I showed in the above-mentioned publication the
possibility of a similar shortening of their phylogenesis, by not
admitting that these embryonic coverings have originated from those of
reptiles and birds, as was done until now, but by considering them in
direct connection with larval envelopes of invertebrate ancestral forms.

In the grouping of bilaterally symmetrical, coelomatic animals
(resp. of such as have lost their coelom again) which has here
been attempted, important phyla (Nemertea, Nematoids’ Prosopygii,
Chaetognatha, etc.) have been left out of consideration.

There are still too many gaps in our knowledge of their anatomy

( 846 )

and their development, to enable us to form a correct judgment
about their exact position. .

With regard to the Nematoda I want to add that to me it seems
io be an error to look upon the parasitical Nematoda as descended
from those which are nowadays found living freely in the sea or
in fresh water or in moist soil. All these latter are far too uniform
to allow us to look upon them as ancestral forms. This phylum can
be better understood, when we consider the parasitical forms as the
older primitive ones and on the other hand derive the free-living
forms from them, as parasites which have adapted themselves
secondarily to a free existence. What the origin of the parasitical
Nematoda in their turn may have been remains an open question
for the present.

Of what has been briefly summarised above, I hope to give a
more elaborate exposition in the current number of the ‘“Jenaische
Zeitschrift. fiir Naturwissenschaft” which is now going through the
press, in which periodical also LANnG’s paper, which induced me to
write this article, appeared. To that number I refer for further
particulars.

Zoology. — Prof. Max Weber reads a paper: “On some of the
results of the Siboga-Expedition.”
(This paper will not be published in these Proceedings),
Anthropology. — Prof. L. Bonk reads a paper on: “ The dispersion
of the blondine and brunette type in our country.”

(This paper will not be published in these Proceedings).

Chemistry. — Prof. C. A. Losry pr Bruyn also in the name of
Dr. R. P. van Carncar presents a paper on: “Changes of
concentration in and crystallisation from solutions by centri-
Sugal power.”

(This paper will not be published in these Proceedings).

Chemistry. — Prof. C. A. Lopry pr Bruyn presents a paper of
Mr. ©. L. Juneis: “ Theoretical consideration concerning boundary
reactions which decline in two or more successive phases.”

(This paper will not be published in these Proceedings).
pa] |

(May 27, 1904),

CON: Pee: Nes.

ARSORPTION-COMPOUNDS which may change into chemical compounds or solutions. 368.

ACETANILIDE (Transformation of acetophenoxime into) and its velocity. 773.

ACETOPHENOXIME (Transformation of) into acetanilide and its velocity. 773.

acips (Action of hydrogen peroxyde on diketones 1, 2 and on z-ketonic). 715.

— (On the compounds of unsaturated ketones with). 325.

Arrica (Contributions to the determination of geographical positions on the West-
coast of). II. 426.

AFTER-IMAGES (On tactual). 481.

AGGREGATIONS (The representation of the continuity of the liquid and gaseous con-
ditions on the one hand and the various solid) on the other by the entropy-
volume-energy surface of GrpBs, 678.

AIRMANOMETER (The determination of the pressure with a closed). 510.

ALBERDA VAN EKENSTEIN (w.). Dibenzal- and benzalmethylglucosides. 452.

auLoys (The course of the melting-point-line of). 21.

Anatomy. A. J. P. van pen Broek: “The foetal membranes and the placenta of
Phoca vitulina.” 610.

Anthropology. L. Bork: “The dispersion of the blondine and brunette type in our
country.” 846,

apparatus (Description of an) for regulating the pressure when distilling under reduced
pressure. 665. .

— (Methods and) used in the Cryogenic Laboratory, VI. The methylchloride cir-
culation. 668.

AQUEOUS SOLUTIONS (A contribution to the knowledge of the course of the decrease
of the vapourtension for). 628.

ascus-ForM (The) of Aspergillus fumigatus Fresenius. 312.

ASPERGILLUs fumigatus Fresenius (The Ascus-form of). 312.

Astronomy. FE. F. van pE Sanpe Bakuuyzen : “Investigation of the errors cf the tables of
the moon of Hansen-Newcoms for the years 1895 —1902.” 370. 224 paper. 412. 422.

— C. Sanpers: “Contributions to the determination of geographical positions on
the West-coast of Africa.” IT, 426.

ATEN (a. H. W.) and H,. W. Baxuuts Roozesoom. Abnormal solubilitylines in

binary mixtures owing to the existence of compounds in the solution. 456.

— The melting point-lines of the system sulphur -++ chlorine. 599.

II CO NT) BeNe Ts:

BACTERIA (On the) which are active in flax-rotting. 462.

BAEYER’s tension theory (A quantitative research concerning). 410.

BAK HUIS ROOZEBOOM (H. W.) presents a paper of J. J. van Laan: “The course
of the melting-point-line of alloys.” 3rd communication. 21.

— The boiling-point-curves of the system sulphur and chlorine. 63.

— presents a paper of Dr. A. Smirs and L. K. Woxrr: “The velocity of trans-
formation of carbon monoxide.” IIL. 66.

— presents a paper of J. J. van Laan: “On the possible forms of the melting
point-curve for binary mixtures of isomorphous substances.” 151. 22¢ communi-
cation. 244.

— presents a paper of Dr. A. Sarvs: “The course of the solubility curve in the
region of critical temperatures of binary mixtures.” 171.224 communication, 484.

— The phenomena of solidification and transformation in the systems NH, NO,,
Ag NO, and KNO,, Ag NO. 259.

— The system Bromine + Iodine. 331.

— The sublimation lines of binary mixtures. 408.

— presents a paper of J. J, van Laan: “On the shape of melting point-curves
for binary mixtures, when the latent heat required for the mixing is very small
or = 0 in the two phases.” 518.

— presents a paper of Dr. A. Sirs: “A contribution to the knowledge of the
course of the decrease of the vapour tension for aqueous solutions.” 628.

— presents a paper of Prof. Euc. Dusors: “Facts leading to trace out the motion
and the origin of the underground water in our sea-provinces.” 738.

—and A. H. W. Arex. Abnormal solubility lines in binary mixtures owing to
ihe existence of compounds in the solution, 456.

— The meltingpoint lines of the system sulphur + chlorine. 599.
BAKHUYZEN (E. F. VAN DE SANDE). See SanpE Bakuuyzen (K. F. van De).

BaTrery (A) of standard-thermoelements and its use for thermoelectric determinations
of temperature. 642.

BECK MANN-rearrangement (The); transformation of acetophenoxime into acetanilide
and its velocity. 773.
BEEKMAN (J. w.) and A. F. Hoxtemay. Benzene fluoride and some of its deri-
vations. 327.
BEHRENS (vu. H.). The conduct of vegetal and animal fibers towards coal-tar
colours. 325.
BEMMELEN (J. M. VAN). Absorption-compounds which may change into chemical
compounds or solutions. 368.
BEMMELEN (Ww. VAN). The daily field of magnetic disturbance. 313.
BENZALMETHYLGLUCOSIDES (Dibenzal- and). 452.
BENZENE (On the substitution of the core of). 735.
— perivatives (Crystallographic and molecular symmetry of position isomeric). 406.
— FLUORIDE and some of its derivations, 327.

— (The nitration of). 659.

-BENZIDINE (The transformation of). 262.
BEIWERINCK (M. W.) and A. van Denpen. On the bacteria which are active in
flax-rotting, 462.
BIERENS DE HAAN (b.) (Extract of a letter of V. W1Luior on the work of);
“Théorie, propriétés, formules de transformation et méthodes d’évaluation des
intégrales définies.” 226.
BINARY MIXTURE (The y-surface in the neighbourhood of a) which behaves as a pure
substance. 649.
BINARY MIXTURES (The equations of state and the y-surface in the immediate neigh-
bourbood of the critical state for) with a small proportion of one of the compo-
nents (part 3). 59. (part 4). 115.
— (On the possible forms of the melting point-curve for) of isomorphous substances.
15], 2nd communication, 244.

— (The course of the solubility curve in the region of critical temperatures of).
171, 24 communication. 484.

— (The sublimation lines of). 408.

— (Abnormal solubility lines in) owing to the existence of compounds in the
solution, 456.

— (On the shape of meltingpoint-curves for) when the latent heat required for
the mixing is very small or=0 in the two phases. (3 communication), 518.
— (lsothermals of gravitation on the phenomena in the neighbourhood of the plait-

point for). 593.

BLANKSMA (J, J.). On the substitution of the core of Benzene. 735.

BLONDINE and brunette type (The dispersion of the) in our coantry. 846.

BOEKE (J.). On the development of the myocard in Teleosts. 218.

BOILING-POINT CURVES (The) of the system sulphur and chlorine. 63.

BOIS (H. E. J. G. DU). Hysteretic orientatic-phenomena. 597.

BOLK (L.) presents a paper of A. J. P. van DEN Broek: “The foetal membranes
and the placenta of Phoca vitulina.” 610.

— The dispersion of the blondine and brunette type in our country. 846.
BONNEMA (J. H.). A piece of lime-stone of the Ceratopyge-zone from the Dutch

diluvium. 319.
Botany. C. A. J. A. OupEMans and C.J. Kontne : “On a Sclerotinia hitherto unknown
and injurious to the cultivation of tobacco” (Sclerotinia Nicotianae Oud. et Koning).
48. Posteript. 85.
— Pu. van HakreveLD: “On the penetration into mercury of the roots of freely
floating germinating seeds.” 182,

— G. Grisys: “The Ascus-form of Aspergillus fumigatus Fresenius.” 312.

— C, A. J, A, OupemMans : “Exosporina Laricis Oud. — A new microscopic fungus
occurring on the Larch and very injurious to this tree.” 498.

— E. Verscuarre.r : “Determination of the action of poisons on plants.” 703.
BOULDER-CLAY BEDS (Deep) of a latter glacial period in North-Holland. 340.
BOUNDARY REACTIONS (Theoretical consideration concerning) which decline in two or

more successive phases. 846,

56*

IV € 0 NP ENE.

BRINKMAN (c. u.). The determination of the pressure with a closed airmano-
meter. 510.

BROEK (4. J. P. VAN DEN). The foetal membrane and the placenta of Phoca
vitulina. 610. -

BROMINE ++ lodine (ihe system). 331.

BROUWER (L. £. J.). On a decomposition of a continuous motion about a fixed
point O of S, into two continuous motions about O of S$,’s. 716. Observation of
Dr. E. JAHNKE. 831.

— On symmetric transformation of S, in connection with S, and Sz. 785.
— Algebraic deduction of the decomposability of the continuous motion about a
fixed point of S, into those of two S,’s. 832.

BRUNETTE TYPE (The dispersion of the blondine and) in our country. 846.

BRUYN (Cc. A. LOBRY DE). See Lopry pe Bruyn (C. A,).

BUYS-BALLO? medal (Extract from the Report made by the Committee for awarding
the). 78.

CALCAR (Rk. P. VAN) and C, A. Losry DE Bruyn. Changes of concentration in
and crystallisation from solutions by centrifugal power. 846,

CALIBRATION (The) of manometer and piezometer tubes. 532.

CARBON DIOXIDE (Isothermals of mixtures of oxygen). I. The calibration of manometer
and piezometer tubes. 532. If. The preparation of the mixtures and the com-
pressibility at small densities. 541, ILL. The determination of isothermals between
60 and 140 atmospheres, and between — 15° C. and + 60° C. 554, IV. Isother-
mals of pure carbon dioxide between 25° C. and 69° C. and between 60 and
140 atmospheres. 565. V. Isothermals of mixtures of the molecular compositions
0.1047 and 0.1994 of oxygen, and the comparison of them with those of pure
carbon dioxide. 577. VI. Influence of gravitation on the phenomena in the neigh-
bourhood of the plait point for binary mixtures. 593.

— (Isothermals of pure) between 25° C. and 66° C. and between 60 and 140
atmospheres. 565.

— (Isothermals of mixtures of the molecular compositions 0.1047 and 0.1994 of
oxygen, and the comparison of them with those of pure). 577.

CARBON MONOXIDE (The velocity of transformation of). I. 66.

CARDINAAL (J.) presents a paper of J. van DE GriEenD Jr.: “Rectifying curves.” 208.

CENTRIC DECOMPOSITION of polytopes, 366,

CENTRIFUGAL POWER (Changes of concentration in and crystallisation from solutions
by). 846.

CERATOPYGE-ZONE (A piece of limestone from the) of the Dutch diluvium. 319.

Chemistry. J. W. Diro: “The action of phosphorus on hydrazine.” 1.

— J. W. Commenix and Ernst Cowen: “The electromotive force of the
DanIELL-cells.” 4.

— J. J. van Laar: “The course of the melting-point-line of alloys” (3"4 com-
munication). 21.

— H. W. Baxuvis Roozesoom: “The boiling-point curves of the system sulphur

and chlorine.” 63,

CONTENTS v

Chemistry. A. Smirs and L. K. Woxrr: “The velocity of transformation of carbon
monoxide.” LL. 66.

— C. A. Lopry be Bruyn ‘and C. L. Juncius: “The condition of hydrates of
nickelsulphate in methylalcoholic solution.” 91.

— ©. A. Losey DE Bruyn and C. L. Juxezus: “The conductive power of hydrates
of nickelsulphate dissolved in methylaleohol.” 94.

— On intramolecular rearrangements. N°. 5. C. L. Junius: The mutual transfor-
mation of the two stereo-isomeric methyl-d-elucosides.” 99. NO. 6. H. Raven.
“The transformation of diphenylnitrosamine into p-nitroso-diphenylamine and its
velocity.” 267. N°. 7, C. A. Lopry pe Bruyn and C. H. Suurrer: “The Brcx-
MANN-rearrangement ; transformation of acetophenoxime into acetanilide and its
velocity.” 773. N® 8. C. L. Juneics: “The mutual transformation of the two
stereoisomeric pentacetates of d-glucose.” 779.

— S. Tymstra Bz.: ‘The electrolytic conductivity of solutions of sodium in mix-
tures of ethyl or methylaleohol and water.’ 104.

— J. J. van Laar: “On the possible forms of the meltingpoint-curve for binary
mixtures of isomorphous substances.” 151. 22¢ communication. 244.

— A. Smits: ‘The course of the solubility curve in the region of critical tem-
peratures of binary mixtures.” 171. 2"¢ communication. 484.

— A. F. HoLLEMan: “Preparation of Cyclohexanol.’’ 201,

— H. W. Bakuuis RoozEBoom; ‘“The phenomena of solidification and transformation
in the systems NH, NO;, Ag NO, and KNO,, Ag NO,.” 259.

— A. F. Hoieman and J. Porrer van Loon: “The transformation of benzidine.” 262,

— 8. Hoocewerrr and W. A. van Dorr: “On the compounds of unsaturated
ketones with acids.” 325.

— Tu. H. Benrens: “The conduct of vegetal and animal fibers towards coal-tar-
colours.” 325.

— A. F. Honteman and J. W. Beekman: “Benzene fluoride and some of its
derivations.” 327,

— H. W. Bakkurs Roozesoom: “The system Bromine + Iodine.” 331,

— kh. O. Herzog: “On the action of Emulsin.” 332.

— J. M. van BemMeLen: “Absorption-compounds which may change into chemical
compounds or solutions.” 368,

— F. M. Jarcer: “Crystallographic and molecular symmetry of position isomeric
benzene derivatives.” 406.

— H. W. Baxuuis Roozesoom: “The sublimation lines of binary mixtures.” 408.

— A. FP. Hotteman and G. L. VorrMan: ‘‘A quantitative research corcerning
BakyeErs’s tension theory.” 410.

— W. ALBERDA vAN EkeEnsTEIN: “Dibenzal- and benzalmethylglucosides.” 452,

YI CONTENTS.

Chemistry. I]. W. Bakuvrs Roozepoom and A. H. W. Aven: “Abnormal solubility lines

in binary mixtures owing to the existence of compounds in the solution.” 456.

— J. J. van Laar: “On the shape of meltingpoint-curves for binary mixtures,
when the latent heat required for the mixing is very small or =O in the two
phases.” (3™4 communication). 518.

— H. W. Bakuurs Roozesoom and A. H. W. Aten: “The meltingpoint lines of
the system sulphur -+ chlorine.” 599.

— A. W. Visser: “Enzymactions considered as equilibria in a homogenous
system.” 605.

— A. Smits: “A contribution to the knowledge of the course of the decrease of
the vapour tension for aqueous solutions.” 628.

— A. F. HoLteman: “The nitration of Benzene fluoride.” 659.

— Jan Rutten: “Description of an apparatus for regulating the pressure when
distilling under reduced pressure.” 665.

— P. van RompurcH: “On Ocimene.” 700.

— P. van Rompurcu: “Additive compounds of s. trinitrobenzene.” 702.

— A. F. Hottrman: “Action of hydrogen peroxyde on diketones 1,2 and on a-
ketonic acids.” 715.

— C. A. Lopry pz Bruyn and L. k. Woirr: “Can the presence of the molecules
in solutions be proved by application of the optical method of TynpaLL.” 735.

— J. J. Buanksma: “On the substitution of the core of Benzene.” 735.

— ©. A. LosBry DE Bruyn and R. P. van Catcar: “Changes of concentration in
and crystallisation from solutions by centrifugal power.” 846.

— ©. L. Junerus: “Theoretical consideration concerning boundary reactions which
decline in two or more successive phases.” 846.

CHLORINE (The boiling-point curves of the system sulphur and). 63.

— (The meltingpoint lines of the system sulphur ++). 599.

CIRCLE POINTS at infinity (The singularities of the focal curve of a plane general curve
touching the line at infinity ¢ times and passing ¢ times through each of the
imaginary). 621.

cLAUSIUS and VAN DER Waats (On the equations of) for the mean length of path
and the number of collisions. 787.

COAL~TaR-coLouRS (The conduct of vegetal and animal fibers towards). 325.

COHEN (ERNST) and J, W. Commettn. The electromotive force of the DaNnrELL-
cells. 4.

COLLISIONS (On the equations of Cuausius and vaN DER Waats for the mean length
of path and the number of). 787.

COMMELIN (J. w.)and Ernst Conen. The electromotive force of the Danie.t-cells. 4.

COMPLEXES of rays (On) in relation to a rational skew curve. 12.

COMPONENTS of a quadruplet (On the double refraction in a magnetic field near the). 19.

compounbs (On the) of unsaturated ketones with acids, 325.

— (Absorption-compounds which may change into chemical) or solutions. 368.
— (Abnormal solubility lines in binary mixtures owing to the existence of) in the
solution, 456,

CONTENTS. Vil

compounps (Additive) of s. trinitrobenzene, 702.

COMPRESSIBILITY (The preparation of the mixtures and the) at small densities. 541.

CONCENTRATION (Changes of) in and crystallisation from solutions by centrifugal
power. 846,

CONDUCTIVE POWER (The) of hydrates of nickelsulphate dissolved in methylalcohol. 94.

conpuctivity (The electrolytic) of solutions of sodium in mixtures of ethyl- or methyl-
aleohol and water. 104.

conics (On systems of) belonging to involutions on rational curves. 505.

CONTINUITY (The representation of the) of the liquid and gaseous conditions on the
one hand and the various solid aggregations on the other by the entropy-volume-
energy surface of Gibs, 678.

CONTINUOUS MOTION (On a decomposition of a) about a fixed point O of S, into two
continuous motions about O of S,’s. 716. Observation of Dr. E, Jaunke. 8381.

— (Algebraic deduction of the decomposability of the) about a fixed point of S,
into those of two 8,’s. 832.

course (The) of the melting-point-line of alloys. 21.

— of the decrease (A contribution to the knowledge of the) of the vapour tension
for aqueous solutions. 628.

CRITICAL sTaTE (The equations of state and the y-surface in the immediate neigh-
bourhood of the), for binary mixtures with a small proportion of one of the
components (part 3). 59. (part 4). 115.

— (The equilibrium between a solid body and a fluid phase, especially in the
neighbourhood of the). 230. 224 part. 357.

CRITICAL TEMPERATURES (The course of the solubility curve in the region of) of
binary mixtures. 171. 224 communication. 484.

CROMMELIN (c. A.) and H. KameriincH OnneEs. On the measurement of very
low temperatures. VI. Improvements of the protected thermoelements; a battery
of standard-thermoelements and its use for thermoelectric determinations of tem-
perature. 642.

CRYOGENIC LABORATORY (Methods and apparatus used in the). VI. The methylchloride
circulation. 668.

CRYSTALLISATION (Changes of concentration in and) from solutions by centrifugal
power. 846.

CRYSTALLOGRAPHIC and molecular symmetry of position isomeric benzene derivatives, 406,

cuBIc cuRVE (The harmonic curves belonging to a given plane). 197.

curvE (The singularities of the focal curve of a plane general) touching the line at
infinity ¢ times and passing < times through each of the imaginary circle points
at infinity, 621.

— in 8, (PLicker’s numbers of a). 501.

CURVE IN space (The singularities of the focal curve of a), 17.

cuRVEs (An equation of reality for real and imaginary plane) with higher singila-
rities. 764,

— (Qn systems of conics belonging to involutions on rational), 505,
— (Fundamental involutions on rational) of order five. 508.

VITi AON OPS Bees:

curves (lhe harmonic) belonging to a given plane cubic curve. 197.
— (Rectifying). 208.

CYCLOHEXANOL (Preparation of). 201.

DAILY FIELD (The) of magnetic disturbance. 313.

DANIELL-CELLS (The electromotive force of the). 4. /

DECOMPOSABILITY (Algebraic deduction of the) of the continuous motion about a fixed ;
point of S, into those of two S,’s. 832. /

DEKHUYZEN (Mm. c.) and P. VeErMaat. On the epithelium of the surface of the
stomach. 30.

DELDEN (a. vaN) and M. W. BetsErtnck. On the bacteria which are active in |
flax-rotting. 462. |

DIBENZAL- and benzalmethylglucosides. 452.
DIFFERENTIAL EQUATION (On the) of Monee. 620.
DIKETONES 1,2 (Action of hydrogenperoxyde on) and on g-ketonie acids. 715. a

DILUvIUM (A piece of Jime-stone of the Ceratopyge-zone from the Dutch). 319.
DIPHENYLNITROSAMINE (The transformation of) into p-nitroso-diphenylamine and its |
velocity. 267. .
DISPERSION (The) of the blondine and brunette type in our country. 846.
— of light (Lhe periodicity of solar phenomena and the corresponding periodicity
in the variations of meteorological and earth-magnetic elements, explained by
the). 270.
D1ITO (J. w.). The action of phosphorus on hydrazine. 1.
DORP (W. a. VAN) and 8S. HoogEewErFr. On the compounds of unsaturated ketones
with acids. 325.
DUBOIS (EUG.). Deep boulder-clay beds of a latter glacial period in North-Holland. 340.
— Facts leading to trace out the motion and the origin of the underground water
in our sea-provinces. 738.
DIJK (G. VAN) and J. Kunst. A determination of the electrochemical equivalent of
silver. 441.
EARTH-MAGNETICAL elements (The periodicity of solar phenomena and the corres-
ponding periodicity in the variations of meteorological and), explained by the
dispersion of light. 270.
EFFECT (A new law concerning; the relation between stimulus and) (6 communi-
cation). 73. he
EINTHOVEN (W.). The string-galvanometer and the human electrocardiogram. 107.

— On some applications of the string-galvanometer. 707.

EKENSTEIN (W. ALBERDA VAN), See ALBERDA VAN EKENSTEIN (W.). F
ELECTROCARDIOGRAM (The string-galvanometer and the human), 107. |

BLECYROCHEMICAL equivalent of silver (A determination of the). 441. if

ELECTROLYSIS (Do the lons carry the solvent with them in). 97.

ELECTROMAGNETIC phenomena in a system moving with any velocity smaller than that
of light. 809.

ELECTROMOTIVE-FORCE (Lhe) of the Danie.u-cells. 4.

EMUISIN (On the action of). 332,

CO N TEN Ds: Ix

ENTROPY-VOLUME-ENERGY SURFACE of Gress (The representation of the continuity of
the liquid and gaseous conditions on the one hand and the various solid aggre-
gations on the other by the), 678.

ENZYMACTIONS considered as equilibria in a homogenous system. 605.

FPITHELIUM (On the) of the surface of the stomach. 30.

EQUATION OF conpDITION (The liquid state and the). 123.

EQUATION OF REALITY (An) for real and imaginary plane curves with higher singu-
larities. 764.

EQUATION OF STATE (On VAN DER Waals’). 794.

EQUATIONS (On the) of CLaustus and van pER Waats for the mean length of path
and the number of collisions. 787.

EQUATIONS OF STATE (The) and the -surface in the immediate neighbourhood of the
critical state for binary mixtures with @ small proportion of one of the compo-
nents (part 3). 59. (part 4). 115.

EQUILIBRIA (Enzymactions considered as) in a homogenous system. 605.

EQUILIBRIUM (The) between a solid body and a fluid phase, especially in the neigh-
bourhood of the critical state. 230. 2nd part. 357.

ETHYL- or methylalcohol (The electrolytic conductivity of solutions of sodium in
mixtures of). 104.

EXOSPORINA LARICIS OUD. — A new microscopic fungus occurring on the Larch and
very injurious to this tree. 498.

FIBERS (The conduct of vegetal and animal) towards coal-tar-colours. 325.

FLAX-ROTTING (On the bacteria which are active in). 462.

FOCAL cURVE (The singularities of the) of a curve in space. 17.

— (The singularities of the) of a plane general curve touching the line at infinity
o times and passing < times through each of the imaginary circle points at
infinity. 621.

FOETAL MEMBRANE (The) and the placenta of Phoca vitulina. 610.

FRANCHIMONT (a. P. N.) presents the dissertation of Dr. F. M. JageEr: “Cry-
stallographic and molecular symmetry of position isomeric benzene derivatives.’ 406.

ruNGUs (A new microscopic) occurring on the Larch and very injurious to this
tree. 498.

GaSEOus conditions (The representation of the continuity of the liquid and) on the
one hand and the various solid aggregations on the other by the entropy-volume-
energy surface of Gisss, 678.

GEEST (J.) and P, Zeeman. On the double refraction in a magnetic field near the
components of a quadruplet. 19.

GEOGRAPHICAL POSITIONS (Contributions tc the determination of) on the West-coast
of Africa. {I. 426. j

Geology. J. H. BonnemMa: “A piece of lime-stone of the Ceratopyge-zone from the
Dutch diluvium.” 319.

— Eva. Dusois: “Deep boulder-clay beds of a latter glacial period in North-
Holland.” 340.

x CONS Ee Ne TES:

Geology. Eve. Dusois: ‘Facts leading to trace out the motion and the origin of the
underground water in our sea-provinces.” 738.

G1BBs (The representation of the continuity of the liquid and gaseous conditions on
the one hand and the various solid aggregations on the other by the entropy-
volume-energy surface of). 678.

GLACIAL PERIOD (Deep boulder-clay beds of a latter) in North-Holland. 340.

cLucosE (The mutual transformation of the two stereoisomeric pentacetates of d-). 779.

GLucosIDES (The mutual transformation of the two stereoisomeric methyl-d-). 99.

GORTER (a.). The cause of sleep. 86.

GRAVITATION (Influence of) on the phenomena in the neighbourhood of the plaitpoint
for binary mixtures. 593. :

GRIEND JR. (J. vAN DE). Rectifying curves, 208.

GRIJNS (G.). The Ascus-form of Aspergillus fumigatus Fresenius. 312.

HAGA (d.). Extract from the Report made by the committee for awarding the Buys-
BaLLot medal. 78.

— presents a paper of G. van Disk and J. Kunst: “A determination of the electro-
chemical equivalent of silver.” 441.

HAMBURGER (H. J.) presents a paper of E, Hexma: “On the liberation of trypsin
from trypsin-zymogen.” 34.

HAPPEL (H.) and H, Kamertinen Onnes. The representation of the continuity of
the liquid and gaseous conditions on the one hand and the various solid aggre-
gations on the other by the entropy-volume-enerey surface of GipBs. 678.

HARREVELD (PH. VAN). On the penetration into mercury of the roots of freely
floating germinating seeds. 182.

HEKMA (k.). On the liberation of trypsin from trypsin-zymogen, 34.

HERZOG (Rk, O.). On the action of Emulsin. 332.

HOLLEMAN (A. F.). Preparation of Cyclohexanol. 201.

— The nitration of Benzene fluoride. 659.

—- Action of hydrogen peroxyde on diketones 1,2 and on g-ketonic acids. 715.

— and J. W. Beekman. Benzene fluoride and some of its derivations. 327.

— and J. Potrer van Loon. The transformation of benzidine. 262.

—and G. L. Vorrmayn. A quantitative research concerning Batyer’s tension
theory. 410.

HNOMOGENOUS SYSTEM (Enzymactions considered as equilibria in a). 605.

HOOGEWERFF (S.) presents a paper of Jan Rutren: “Description of an apparatus
for regulating the pressure when distilling under reduced pressure.” 665.

— and W. A. van Dorp. On the compounds of unsaturated ketones with acids. 325.

HUBRECHT (A, A. W.) presents a paper of Prof. Hans Srrauu: “The process of
involution of the mucous membrane of the uterus of Tarsius spectrum after
parturition.” 302.

— On the relationship of various invertebrate phyla. 839.
HYDRATES of nickelsulphate (The condition of) in methylalcoholic solution. 91.
— (The conductive power of) dissolved in methylalcohol. 94.

HYVRAZINE (The action of phosphorus on). 1.

—— —————-~*

CONTENTS. XI

HYDROGEN CYANIDE (The transformation of isonitrosoacetophenonsodium into sodium
benzoate and). 453.

HYDROGEN PEROXYDE (Action of) on diketones 1,2 and %-ketonic acids, 715,
HYSTERETIC orientatic-phenomena. 597.

INTEGRALES DEFINIES (Extract of a letter of V. Wiiuior on the work of D. Brerens
pE Haan: “Théorie, proprictés, formules de transformation et méthodes d’éyalua-
tion «les). 226.

INVERTEBRATE PHYLA (On the relationship of various), 839.

INVOLUTION (The process of) of the mucous membrane of the uterus of Tarsius spec-
trum after parturition. 302.

INVOLUTIONS (On systems of conics belonging to) on rational curves. 505.

— (Fundamental) on rational curves of order five. 508.

IODINE (The system Bromine +-). 331.

tons (Do the) carry the solvent with them in electrolysis. 97.

ISOMORPHOUS sURsTANCES (On the possible forms of the meltingpoint-curve for binary
mixtures of). 151. 2nd communication. 244.

ISONITROSOACETOPHENONSODIUM (The transformation of) into sodium benzoate and
hydrogen cyanide. 453.

ISOTHERMALS of mixtures of oxygen and carbon dioxide, I, The calibration of mano-
meter and piezometer tubes. 532. IJ. The preparation of the mixtures and the
compressibility at small densities. 541. III. The determination of isothermals
between 60 and 140 atmospheres, and between — 15° C. and + 60° C. 554.
IV. Isothermals of pure carbon dioxide between 25° C. and 60° C. and between
60 and 140 atmospheres. 565. V. Isothermals of mixtures of the molecular com-
positions 0.1047 and 0.1994 of oxygen, and the comparison of them with those
of pure carbon dioxide. 577. VI. Influence of gravitation on the phenomena in
the neighbourhood of the plaitpoint for binary mixtures. 593.

JAEGER (F. M.). Crystallographic and molecular symmetry of position isomeric benzene
derivatives. 406.

JAHNKE (E£.). Observation on the paper of Mr. Brouwer: “On a decomposition
of the continuous motion about a point O of S, into two continuous motions
about O of 8,’s. 831.

JULIUS (Ww. H.) presents a communication of J, W. ComMELIN and Ernst Conen:
“The electromotive force of the Danreut-cells.” 4.

— Extract from the Report made by the Committee for awarding the Buys-BaL.ot
medal. 78.

= The periodicity of solar phenomena and the corresponding periodicity in the
variations of meteorological and earth-magnetic elements, explained by the dis-
persion of light, 270. :

JuNG1US (c. L.). The mutual transformation of the two stereo-isomeric methyl-
d-glucosides. 99.

a
— The mutual transformation of the two stereo-isomeric pentacetates of d-glu-
cose, 779.

MII C80 ONT Ren se

yuNG1Uus (c. 1.). Theoretical consideration concerning boundary reactions which
decline in two or more successive phases. 846.

— and C. A. Losey ve Bruyn. The condition of hydrates of nickelsulphate in
methylalcohoJic solution. 91.

— The conductive power of hydrates of nickelsulphate dissolved in methyl-
alcohol. 94.

KAMERLINGH ONNES (H.) presents a paper of Dr. J. E. VERsCHAFFELT: ‘“Con-
tributions to the knowledge of van per Waats--surface. VJI. The equations
of state and the y-surface in the immediate neighbourhood of the critical state
for binary mixtures with a small proportion of one of the components (part 3).
59. (part 4). 115. VIII. The y-surface in the neighbourhood of a binary mixture
which behaves as a pure substance.” 649.

— presents a paper of W. H. Kersom: “IJsothermals of mixtures of oxygen and
carbon dioxide. I. The calibration of manometer and piezometer tubes. 532.
lI. The preparation of the mixtures and the compressibility at small densities.
541. III. The determination of isothermals between 60 and 140 atmospheres, and
between —15° C. and + 60° C. 554. LV. Isothermals of pure carbon dioxide
between 25° C. and 60° C, and between 60 and 140 atmospheres. 565. V. Iso-
thermals of mixtures of the molecular compositions 0.1047 and 0.1994 of oxygen
and the comparison of them with those of pure carbon dioxide. 577. VI. Influence
of gravitation on the phenomena in the neighbourhood of the plaitpoint for
binary mixtures.” 593.

— Methods and apparatus used in the cryogenic laboratory. VI. The methylchloride
circulation. 668.

— presents a paper of Dr. L. H. Siertsema: “Investigation of a source of errors
in measurements of magnetic rotations of the plane of polarisation in absorbing
solutions.” 760.

— and C. A. CromMMELIN. On the measurement of very low temperatures. VI.
Improvements of the protected thermoelements; a battery of standard-thermo-
elements and its use for thermoelectric determinations of temperature. 642.

— and H. Happex. The representation of the continuity of the liquid and gaseous
conditions on the one hand and the various solid aggregations on the other by
the entropy-volume-energy surface of Gipss. 678,

KAPTEYN (W.). On the differential equation of Monee. 620.

KEESOM (W. H.). Isothermals of mixtures of oxygen and carbon dioxide, I. The
calibration of manometer and piezometer tubes. 532. II. The preparation of the
mixtures and the compressibility at small densities. 541. III. The determination
of isothermals between 60 and 140 atmospheres, and between — 15° C. and
+ 60° C. 554. IV. Isothermals of pure carbon dioxide between 25° C, and 60° C.
and between 60 and 140 atmospheres. 565, V. Isothermals of mixtures of the
molecular compositions 0.1047 and 0.1994 of oxygen, and the comparison of them
with those of pure carbon dioxide. 577. VI. Influence of gravitation on the

phenomena in the neighbourhood of the plaitpoint for binary mixtures. 593.

CO NFER? 8. XII

KETONES (On the compounds of unsaturated) with acids, 325.

F : ? Uy eS
KLUYVER (J. c.). Series derived from the series me 305.

KOHNSTAMM (PH.). On the equations of CLausius and VAN DER WAALS for the
mean length of path and the number of collisions, 787.

— On VAN DER WaAALs’ equation of stute. 794.
l

KONING (c. J.) and C. A.J, A, OupEMaNs. On a Sclerotinia hitherto unknown
and injurious to the cultivation of tobacco, (Sclerotinia Nicotianae Oud. et
Koning). 48. Posteript. 85.

KORTEWEG (bD. J.) presents a paper of L. E. J. Brouwer: “On a decomposition
of a continuous motion about a fixed point O of Sy into two continuous motions
about O of S,’s.” 716. Observation of Dr. E. Jaunke, 831.

— presents a paper of Frep. Scaun: “An equation of reality for real and imaginary
plane curves with higher singularities.” 764.

— presents a paper of L. E. J. BrouwEr: “On symmetric transformation of 8, in
connection with S$; and Sj.’ 785.

— presents a paper of L. E. J. Brouwer: “Algebraic deduction of the decompo-
sability of the continuous motion about a fixed point of 8, into those of two
8,’s." 832,

KUENEN (J. P.). On the critical mixing-point of the two liquids. 387,

KUNST (J.) and G. van Dix. A determination of the electrochemical equivalent of
silver. 441.

LAAR (J. J. VAN). The course of the meltingpoint-line of alloys. (3rd communi-
cation). 21.
— On the possible forms of the meltingpoint-curve for binary mixtures of isomor-

phous substances. 151. 2nd communication. 244.

— On the shape of meltingpoint-curves for binary mixtures, when the latent heat
required for the mixing is very small or =0 in the two phases. (3rd communi-
cation). 518.

LATERAL AREAS (Something concerning the growth of the) of the trunkdermatomata
on the caudal portion of the upper extremity. 392.
Law (A new) concerning the relation between stimulus and effect. (6th communi-
cation). 73.
— of distillation (Note on SypNEY Youna’s). 807.

LENGTH OF PATH (On the equations of CLaustts and vAN DER WaALs for the mean)
and the number of collisions. 787.

LIGHT (Electromagnetic phenomena in a system moving with any velocity smaller than
that of). 809.

LIME-STONE (A piece of) of the Ceratopyge-zone from the Dutch diluvium. 319.

LINE AT INFINITY (The singularities of the focal curve of the plane general curve
touching the) ¢ times and passing ¢ times through each of the imaginary circle

points at infinity. 621.

XTV: EoNTEN TSS.

11QUID and gaseous conditions (The representation of the continuity of the) on the
one hand and the various solid aggregations on the other by the entropy-volume-
energy surface of GrBBs. 678.

Liquips (On the critical mixing-point of the’ two). 387.

LIQUID sTATE (The) and the equation of condition, 123.

LOBRY DE BRUYN (C. A.) presents a paper of J. W. Dito: “The action of phos-
phorus on hydrazine.” 1.

— Do the Ions carry the solvent with them in electrolysis, 97.

— presents a paper “On intramolecular rearrangements,” N°. 5. C. L. Junetus:
“The mutual transformation of the two stereoisomeric methyl-d-glucosides.” 99.
N°. 6. H. Raken: “The transformation of diphenylnitrosamine into p-nitroso-
diphenylamine and its velocity.” 267. N°. 7. C. A. Lospry DE Bruyn and C, H.
Siurrer: “The BeckmMaNN-rearrangement ; transformation of acetophenoxime into
acetanilide and its velocity.” 773. N® 8. C. L. Junerus: “The mutual trans-

formation of the two stereoisomeric pentacetates of d-glucose.” 779.

— presents a paper of S. Tymsrra Bz.: “The electrolytic conductivity of solutions
of Sodium in mixtures of ethyl- or methylaleohol and water.” 104.

— presents a paper of Dr. TH. Weevers and Mrs. C. J. Wrevers—-pE Graarr:
“Investigations of some Xanthine derivatives in connection with the internal
mutation of plants.” 203.

— presents a paper of W. ALBERDA vaN ExkeENsTEIN: “Dibenzal- and benzal-
methylglucosides.”” 452. .

— presents a paper of ©. H. Sturrer: ‘The transformation of isonitrosoaceto-
phenonsodium into sodium benzoate and hydrogen cyanide.” 453.

— presents a paper of A. W. Visser: “Enzymactions considered as equilibria in
a homogenous system.” 605.

— presents a paper of Prof. P. van Rompureu: “On Ocimene.” 700,

— presents a paper of Prof. P. van RomBurGH: ‘Additive compounds of s. trinitro-
benzene.” 702.

— presents a paper of Prof. EH. VerscaarreLr: “Determination of the action of
poisons on plants.” 703.

— presents a paper of Dr. J. J. Buanxsma: “On the substitution of the core of
Benzene.” 725.

— presents a paper of C. L. Junerus: “Theoretical consideration concerning
boundary reactions which decline in two or more successive phases.” 846.

— and R, P. van Catcar, Changes of concentration in and crystallisation from
solutions by centrifugal power. 846.

—and C, L. Junerus. The condition of hydrates of nickelsulphate in methyl-
alcoholic solution, 91.

— The conductive power of hydrates of nickelsulphate dissolved in methylalcohol. 94.

— and L. k. Wotrr. Can the presence of the molecules in solutions be proved
by application of the optical method of TynDaLL? 735.

LOON (J. POTTER VAN). See PorreR vAN Loon (J.).

CON TEN TS. xv

LORENTZ (il. A.) presents a paper of A. PANNEKOEK: “Some remarks on the
reversibility of molecular motions.” 42.
— Electromagnetic phenomena in a system moving with any velocity smaller than
that of light. 809.
MAGNETIC DISTURBANCE (The daily field of), 313.
MAGNETIC FIELD (On the double refraction in a) near the components of a quadruplet. 19,
MAGNETIC ROTATIONS (Investigation of a source of errors in measurements of) of the
plane of polarisation in absorbing solutions. 760.
MANOMETER- and piezometertubes (The calibration of). 532.
MARTIN (k.) presents a paper of J. H. Bonnema: ‘‘A piece of lime-stone of the
Ceratopyge-zone from the Dutch diluvium.” 319.
— presents a paper of Prof. Eva. Dusois: “Deep boulder-clay beds of a iatter
glacial period in North-Holland.” 340.
Mathematics. J. pe Vries: “On complexes of rays in relation to a rational skew
curve.” 12:
— W. A. Verstuys: “The singularities of the focal curve of a curve in space.” 17.
— Jan pe Vries: “The harmonic curves belonging to a plane cubic curve.” 197.
— J. vAN DE GrRIEND Jr.: “Rectifying curves.” 208.
-— Extract of a letter of V. Wrinror on the work of D. Brerexs pr Haan:

“Théorie, propriétes, formules de transformation et méthodes d’évaluation des
intégrales définies.” 226.

33
— J. CG. Kuuyver: “Series derived from the series pm) 3052
m

— P. H. ScHoure: “Centric decomposition of polytopes.” 366.
— P. H. Scyoute: “PLicKker’s numbers of a curve in 8.” 501,

— Jan ve Vries: “On systems of conics belonging to involutions on rational
curves.” 505.

— Jan pE Vries: “Fundamental involutions on rational curves of order five.” 508.

— W. Kaprteyn: “On the differential equation of Moner.” 620.

— W. A. Verstuys: “The singularities of the focal curve of a plane general curve
touching the line at infinity ¢ times and passing ¢ times through each of the
imaginary circle points at infinity.” 621.

— W. A. Versiuys: “On the position of the three points which a twisted curve
has in common with its osculating plane.” 622.

— L. E. J. Brouwer: “On a decomposition of a continuous motion about a fixed
point O of S, into two continuous motions avout O of S,’s.” 716. Observation of
Dr. E. JaAHNKE. 831.

— Frep. Scouu: An equation of reality for real and imaginary plane curves with
higher singularities.” 764.

— P. H. Scnourr: “Regular projections of regular polytopes.” 783.

— L. I. J. Brouwer: “On symmetric transformation of $, in connection with
S; and Sj.” 785.

xVI CO N ENF 3.

Mathematics. L. E. J. Brouwer: “Algebraic deduction of the decomposability of the
continuous motion about a fixed point of S, into those of two S,’s.” 832.

MEASUREMENT (On the) of very low temperatures. VI. Improvements of the protected
thermoelements; a battery of standard-thermoelements and its use for thermoelectric
determinations of temperature. 642.

MEASUREMENTS (Investigation of a source of errors in) of magnetic rotations of the
plane of polarisation in absorbing solutions. 760.

MELTINGPO!NT-cURVE (On the possible forms of the) for binary mixtures for isomor-
phous substances. 151. (2nd communication). 244.

MELTINGPOINT-cURVES (On the shape of) for binary mixtures, when the latent heat
required for the mixing is very small or = 0 in the two phases. (3rd commu-
nication). 518.

MELTINGPOINT-LINE of alloys (The course of the). 21.

MELTINGPOINT-LINES (The) of the system sulphur + chlorine. 599.

meRcuRY (On the penetration into) of the roots of freely floating germinating seeds. 182.

METEOROLOGICAL and earth-magnetical elements (The periodicity of solar phenomena
and the corresponding periodicity in the variations of), explained by the dispers-
ion of light, 270.
Meteorology. Extract from the Report made by the Ccmmittee for awarding the Buys-
Bator medal. 78.
METHODS and apparatus used in the cryogenic Laboratory. VI. The methylchloride
circulation. €68.
METHYLALCOHOL (The conductive power of hydrates of nickelsulphate dissolved in). 94.
— and water (The electrolytic conductivity of solutions of sodium in mixtures of
ethyl-or). 104,
METHYLALCOHOLIC SOLUTION (‘The condition of hydrates of nickelsulphate in). 91.
METHYLCHLORIDE circulation (The). 668.
Microbiology. M. W. Berterinck and A, vaAN DeLpen: “On the bacteria which are
active in flax-rotting.”’ 462.
MIXING POINT (On the critical) of the two liquids. 387.
mMixTurEs of ethyl- or methylaleoho! and water (The electrolytic conductivity of
solutions of sodium in). 104.
— (The equations of state and the y-surface in the immediate neighbourhood of
the critical state for binary) with a small proportion of one of the components. 59.
— (Isothermals of) of oxygen and carbon dioxide. I. The calibration of manometer
and piezometertubes. 532. II]. The preparation of the mixtures and the com-
pressibility at small densities. 541. ILL The determination of isothermals between
60 and 140 atmospheres, and between — 15° ©. and + 60° C. 554. IV. Iso-
thermals of pure carbon dioxide between 25° C. and 60° C. and between 60
and 140 atmospheres. 565. V. Isothermals of mixtures of the molecular com-
positions 0.1047 and 0.1994 of oxygen, and the comparison of them with those
of pure carbon dioxide. 577. V1. Influence of gravitation on the phenomena in
the neighbourhood of the plaitpoint for binary mixtures. 593,

CONTENTS. XVII

MIXTURES (The preparation of the) and the compressibility at small densities. 541.
— ({sothermals of) of the molecular compositions 0.1047 and 0.1994 of oxygen,
and the comparison of them with those of pure carbon dioxide. 577.
MOLECULAR composiTions (Isothermals of mixtures of the) 0.1047 and 0.1994 of
oxygen, and the comparison of them with those of pure carbon «lioxide. 577.
MOLECULAR MOTIONS (Some remarks on the reversibility of). 42.
MOLECULES (Can the presence of the) in solutions be proved by application of the

optical method of TynDaLL. 735.
MOLL (J. w.) presents a paper of Pu. van HaRREVELD: “On the penetration into

mercury of the roots of freely floating germinating seeds.” 182.

MONGE (On the differential equation of). 620.

motion (Algebraic deduction of the decomposability of the continuous) about a fixed
point of S, into those of two S,’s. $32.

— (Facts leading to trace out the) and the origin of the underground water in

our sea-provinces. 738.

motions (On a decomposition of a continuous motion about a fixed point O of S
into two continuous) about O of S,’s. 716. Observation of Dr. E JaHnxe. 831.

MUCOUS MEMBRANE (The process of involution of the) of the uterus of Tarsius spec-
trum ufter parturition. 302.

MUTATION of plants (Investigations of some Xanthine derivatives in connection with
the internal). 203. '

MyocakD (On the development of the) in Teleosts. 218.

NITRATION (The) of Benzene fluoride, 659.

NORTH-HOLLAND (Deep boulder-clay beds of a latter glacial period in). 340.

NUMBERS (PLicKER’s) of a curve in S,. 501.

OCIMENE (On). 700.

ONNES (H. KAMERLINGH). See KamerLinco Onnes (H.).

OPTICAL METHOD of TyNDsLt (Can the presence of the molecules in solutions be proved
by application of the). 735.

ORIENTATIC-PHENOMENA (Hysteretic). 597.

oRIGIN (Facts leading to trace out the motion and the) of the underground water
in our sea-provinces. 738.

OSCULATING PLANE (On the position of the three points which a twisted curve has
in common with its). 622.

OUDEMANS (c. a. J. A.). Exosporina Laricis Oud. — A new microscopic fungus
occurring on the Larch and very injurious to this tree. 498.

—and C. J. Konine. On a Sclerotinia hitherto unknown and injurious to the

cultivation of tobacco (Sclerotinia Nicotianae Oup. et Konrne). 48. Posteript. 85.

OXYGEN and carbon dioxide (Isothermals of mixtures of). I. The calibration of mano-
meter and piezometertubes. 532. II. The preparation of the mixtures and the
compressibility at small densities. 541. III. The determination of isothermals

XVIII ClOCNGTREENEL 3S.

LV. Isothermals of pure carbon dioxide between 25° C. and 60° C. and between
60 and 140 atmospheres. 565. V. Isothermals of mixtures of the molecular com-
positions 0.1047 and 0.1994 of oxygen, and the comparison of them with those
of pure carbon dioxide. 577. VI. Influence of gravitation on the phenomena

in the neighbourhood of the plaitpoint for binary mixtures. 593.

oxYGEN (Isothermals of mixtures of the molecular compositions 0.1047 and 6.1994 of),
and the comparison of them with those of pure carbon dioxide, 577.

pANNEKOEK (A.). Some remarks on the reversibility of molecular motions. 42.
PEKELHARING (C. A.) presents a paper of Dr. M. C. Dexnuyzen and P. VERMaatT:
“On the epithelium cf the surface of the stomach.” 30.
— presents a paper of Dr. R. O. Herzoe: “On the action of Fmulsin.” 332.
PENTACETATES (The mutual transformation of the two stereoisomeric) of d-glucose. 112.

pertopicity (The) of solar phenomena and the corresponding periodicity in the
variations of meteorological and earth-magnetic elements, explained by the
dispersion of light. 270.

pHasEs (Theoretical consideration concerning boundary reactions which decline in
two or more successive). 846.

PHENOMENA of solidification (The) and transformation in the systems NHy NO,, Ag NO,
and KNO;, Ag NO;. 259.

PHOCA VITULINA (The foetal membrane and the placenta of). 610.
pHosPHorus (The action of) on hydrazine. 1.
PHYLA (On the relationship of various invertebrate), 839.
Physics. P. Zeeman and J. Geesr: “On the double refraction in a magnetic field near
the components of a quadruplet.” 19.
— A. PanneKoEK: “Some remarks on the reversibility of molecular motions.” 42,
— J. E. VerscuarreLt: “Contributions to the knowledge of vAN DER Waals
y-surface. VII. The equations of state and the y-surface in the immediate neigh-
bourhood of the critical state for binary mixtures with a small proportion of one
of the components. (part 3). 59. (part 4), 115. VIII. The p-surface in the neigh-
bourhood of a binary mixture which behaves as a pure substance. 649.
— J. D. van per Waats: “The liquid state and the equation of condition.” 123,
— J. D. van per Waats: “The equilibrium between a solid body and a fluid
phase, especially in the neighbourhood of the critical state.” 230, 2nd part. 357.
— W. H. Junius: “The periodicity of solar phenomena and the corresponding
periodicity in the variations of meteorological and earth-magnetic elements,
explained by the dispersion of light.” 270.
— J. P. Kuenen: “On the critical mixing-point of the two liquids.” 387.
— G. van Dik and J. Kunst: ,,A determination of the electrochemical equivalent
of silver.” 441.

— C. H. Brinkman: “The determination of the pressure with a closed airmano-
meter.” 510,

CONTENTS xIX

Physics. W. H. Kersom: “Isothermals of mixtures of oxygen and carbon dioxide. 1. The
calibration of manometer and piezometer tubes. 552. {L. The preparation of the
mixtures and the compressibility at small densities. 541. ILI. The determination
of isothermals between 60 and 140 atmospheres, and between — 15° C. and
+ 60° C. 554. IV. Isothermals of pure carbon dioxide between 25° C. and 60°
C. and between 60 and 140 atmospheres.” 565. V. Isothermals of mixtures of
the molecular compositions 0.1047 and 0.1994 of oxygen, and the comparison of
them with those of pure carbon dioxide. 577. VI. Influence of gravitation on the
phenomena in the neighbourhood of the plaitpoint for binary mixtures,” 593.

—H. E. J. G. pu Bois: “Hysteretic orientatic-phenomena.” 597.

— H. Kameriincu Onnes and C. A, CrommMenin: “On the measurement of very
low temperatures. VI. Improveinents of the protected thermoelements; a battery
of standard-thermoelements and its use for thermoelectric determinations of tem-
perature.” 642. .

— H. KamertincH Onnes: “Methods and apparatus used in the cryogenic Labo-
ratory. VI. The methylchloride circulation.” 668.

— H. Kameritncu Onnes and H. Happex: “The representation of the continuity
of the liquid and gaseous conditions on the one hand and the various solid
aggregations on the other by the entropy-volume-energy surface of GrBps.” 678.

— L. H. Srertsema: “Investigation of a source of errors in measurements of
magnetic rotations of the plane of polarisation in absorbing solutions.” 760.

— Pu. hounnstamm: “On the equations of CLausius and vAN DER Waals for the
mean length of path and the number of collisions.” 787.

— Pa. Kounsramm: “On van DER Waals’ equation of state.” 794.

— Miss J. Reupier: “Note on SypNEy Youne’s law of distillation.” 807.

— H. A. Loxentz: “Electromagnetic phenomena in a system moving with any
velocity smaller than that of light.” 809.

Physiology. M. C. Dexuvuyzen and P, Vermaat: “On the epithelium of the surface
of the stomach.” 30.

— E. Hexma: “On the liberation of trypsin from trypsin-zymogen.” 34.

= J, kK. A. WERTHEIM SaLomonson: “A new law concerning the relation between
stimulus and effect” (6t? communication), 73.

— A. Gorter: “The cause of sleep.” 86.

= W. Etnraoven : “The string galvanometer and the human electrocardiogram.” 107.

— J. Boexe: “On the development of the myocard in Teleosts.” 218.

— G, van RignBerk: “On the fact of sensible skin-areas dying away in a centri-
petal direction.” 346.

— C. Winter and G. van RiunBerK: “Something concerning the growth of the
lateral areas of the trunk-dermatomata on the caudal portion of the upper
extremity.” 392.

— J. K. A. WerrHemm Satomonson: “On tactual after-images.” 481.

— W. Etnruoven: “On some applications of the string-galvanometer.” 707.

Xx Goax?t? END s:

PIEZOMETERTUBES (The calibration of manometer and). 532.
PLACE (f.) presents a paper of Dr. J. Boeke: “On the development of the myocard
in Teleosts.” 218.
PLACENTA (The foetal membrane and the) of Phoea vitulina. 610.
PLAITPOINT (Influence of gravitation on the phenomena in the neighbourhood of the)
for binary mixtures. 593.
PLANE OF POLARISATION (Investigation of a source of errors in measurements of mag-
netic rotations of the) in absorbing solutions. 760.
PLANTS (Determination of the action of poisons on). 703.
— (Investigations of some Xanthine derivatives in connection with the internal
mutation of). 203.
PLtcCKER’s numbers of a curve in S,. 501.
point O of S, (On a decomposition of a continuous motion about a fixed) into two
continuous motions about O of S,’s. 716. Observation of Dr, E. JANKE. 831.
— of SS; (Algebraic deduction of the decomposability of the continuous motion
about a fixed) into those of two 83’s. 832.
pornts (On the position of the three) which a twisted curve has in common with its
osculating plane. 622.
poisons (Determination of the action of) on plants. 703.
POLYTOPES (Centric decomposition of). 866.
— (Regular projections of regular). 783.
POTTER VAN LOON (s.) and A, F. HoLteman. The transformation of benzidine. 262.

PRESSURE (The determination of the) with a closed airmanometer. 510,
— (Description of an apparatus for regulating the) when distitling under reduced

pressure. 665.

PROJECTIONS (Regular) of regular polytopes. 783.

quapruPLeT (On the double refraction in a magnetic field near the components of a). 19,

RAKEN (H.). The transformation of diphenylnitrosamine into p-nitroso-diphenylamine
and its velocity. 267.

REARRANGEMENT (The BECKMANN); transformation of acetophenoxime into acetanilide
and its velocity. 773.

PEARRANGEMENTS (On intramolecular). No. 5. C. L. Junezus: ‘The mutual transfor-
mation of the two stereo-isomeric methyl-d-glucosides.” 99. No. 6. H. RakEn:
“The transformation of diphenylnitrosamine into p-nitroso-diphenylamine and its
velocity.” 267. No. 7. C. A. Lopry bE Bruyn and C. H. Swurrer : “The Brck-
MANN-rearrangement: transformation of acetophenoxime into acetanilide and its
velocity.” 773. No. 8 C. L. Junerus: “The mutual transformation of the two
stereoisomeric pentacetates of d-glucose.” 779.

REFRACTION (On the double) in a magnetic field near the components of a qua-
druplet. 19.

REUDLER (J.). Note on SypNEY Youne’s law of distillation. 807.

REVERSIBILITY (Some remarks on the) of molecular motions. 42.

CONTENTS. XXI

ROMBURBGH (P. VAN). On Ocimene. 700.

— Additive compounds of s. trinitrobenzene. 702.

Roots (On the penetration into mercury of the) of freely floating germinating seeds, 182.

ROOZEBOOM (H. W. BAKHUTS). See Bakuuis RoozeBoom (H. W.).

RUTTEN (JAN). Description of an apparatus for i es the pressure when
distilling under reduced pressure. 665,

RIJNBERK (G. VAN). On the fact of sensible skin-areas dying away 1m a centripetal
direction. 346.

— and C. Winker. Structure and function of the trunk-dermatoma. IV. 347.

— Something concerning the growth of the lateral areas of the trunkdermatomata
on the caudal portion of the upper extremity. 392.

SANDE BAKHUYZEN (E. F. VAN DE). Investigations of the errors of the tables of
the moon of HanseN-NEwcoms for the years 1895—1902. 370. 24 paper. 412. 422.

— presents a paper of C. Sanpers: “Contributions to the determination of geogra-
phical positions on the West-coast of Africa.” II, 426.

SANDERs (c.). Contributions to the determination of geographical positions on the
West-coast of Africa. IT. 426.

SCHOUTE (P. H.) presents a paper of Dr. W. A. VersLuys: “The singularities of
the focal curve of a curve in space.” 17.

— Centric decomposition of polytopes. 366.

— P.tcker’s numbers of a curve in S,. 501.

— presents a paper of Dr. W. A. VersLuys: “The singularities of the focal curve
of a plane general curve touching the line at infinity ¢ times and passing ¢ times
through each of the imaginary circle points at infinity.” 621.

— presents a paper of Dr. W. A. Verstuys: “On the position of the three points
which a twistéd curve has in common with its osculating plane.” 622.

— Regular projections of regular polytopes. 783.

SCHUH (FRED.), An equation of reality for real and imaginary plane curves with
higher singularities. 764.

SCLEROTINIA (On a) hitherto unknown and injurious to the cultivation of tobacco
(Sclerotinia Nicotianae Oup. et Konine), 48. Postcript. 85.

SEA-PROVINCES (Facts leading to trace out the motion and the origin of the under-

ground water in our). 738.
SEEDS (On the penetration into mercury bes the roots of freely floating germinating). 182.

SERIES derived from the series > —~’. 305.

SIBOGA-ESPEDITION (On some of the es of the). §
SIERTSEMA (L. H.). Investigation of a source of errors in measurements of mag-

netic rotations of the plane of polarisation in absorbing solutions. 760.
SILVER (A determination of the electrochemical equivalent of). 441.
SKEW CURVE (On complexes of rays in relation to a rational). 12.
SKIN-AREAS (On the fact of sensible) dying away in a centripetal direction. 346.

SLEEP (The cause of). 86.

SXII CO NTE NTS:

SLUITER (c. H.). The transformation of isonitrosoacetophenonsodium into sodium
benzoate and hydrogen cyanide. 453.

— and C. A. Lopry pe Bruyn. The BreckMaNn-rearrangement ; transformation
of acetophenoxime into acetanilide and its velocity. 773.

sMITS (A.). The course of the solubility curve in the region of critical temperatures.

of binary mixtures. 171. 224 communication. 484.
— A contribution to the knowledge of the course of the decrease of the vapour
tension for aqueous solutions. 628.
— and L. K. Wotrr. The velocity of transformation of carbon monoxide. II. 66.
sopiuM (The electrolytic conductivity of solutions of) in mixtures of ethyl- or methyl-
alcohol and water. 104.

SODIUM BENZOATE (The transformation of isonitrosoacetophenonsodium into) and hydrogen
cyanide, 453.

SOLAR PHENOMENA (The periodicity of) and the corresponding periodicity in the
variations of meteorological and earth-magnetic elements, explained by the dis--
persion of light. 270.

SOLIDIFICATION (The phenomena of) and transformation in the systems NH,NO,,
AgNO, and KNO,, AgNO. 259.

SOLUBILITY CURVE (The course of the) in the region of critical temperatures of binary
mixtures. 171. 224 communication. 484.

SOLUBILITY LINES (Abnormal) in binary mixtures owing to the existence of compounds
in the solution. 456.

sOLUTIONS (Absorption-compounds which may change into chemical compounds or). 368..

— (Changes of concentration in and crystallisation from) by centrifugal power. 846.
— (Investigation of a source of errors in measurements of magnetic rotations of the
plane of polarisation in absorbing). 760.

SOLVENT (Do the Ions carry the) with them in electrolysis. 97.

SOURCE OF ERRORS (Investigation of a) in measurements of magnetic rotations of the
plane of polarisation in absorbing solutions. 760.

STANDARD-THERMOELEMENTS (A battery of) and its use for thermoelectric determinations.
of temperature. 642.

STIMULUs and effect (A new law concerning the relation between). (6th communi--
cation). 73.

STOK (J. P. VAN DER). Extract from the Report made by the committee for
awarding the Buys-BauLor medal. 78.

— presents a paper of Dr. W. van BemMeELen: “The daily field of magnetic distur--
bance.” 313.

stomacH (On the epithelium of the surface of the). 30.

STRAHL (HANS). The process of involution of the mucous membrane of the uterus
of Tarsius spectrum after parturition. 302.

STRING-GALVANOMETER (The) and the human electrocardiogram. 107.

— (On some applications of the). 707.

SUBLIMATION LINES (The) of binary mixtures. 408.

SUBSTITUTION (On the) of the core of Benzene. 735.

CON TEN TS: XXIII

suLPHUR and chlorine (The boiling-point curves of the system). 63.
— + chlorine (The meltingpoint lines of the system). 599.

-sURFACE (Contributions to the knowledge of van per Waats). VII. The equations
of state and the g-surface in the immediate neighbourhood of the critical state
for binary mixtures with a small proportion of one of the components (part 3).
59. (part 4). 115. VIIT. The y-surface in the neighbourhood of a binary mixture
which behaves as a pure substance. 649.

SYDNEY youNG’s law of distillation (Note on). 807.

SYMMETRY of position (Crystallographic and molecular) isomeric benzene derivatives. 406.

— sulphur and chlorine (The boiling-point curves of the), 63.
SYSTEM bromine ++ iodine (The). 331.
— sulphur + chlorine (The meltingpoint lines of the). 599.
— (Electromagnetic phenomena in a) moving with any velocity smaller than that
of light. 809.

sysTEMS NH,NO,, AgNO, and KNO,, AgNO, (Ihe phenomena of solidification and
transformation in the). 259.

— of conics (On) belonging to involutions on rational curves. 405.

TABLES OF THE MOON (Investigations of the errors of the) of HanseN-Newcoms for
the years 1895—1902. 379. 2nd paper. 412. 422.

TARSIUS spectrum (The process of involution of the mucous membrane of the uterus
of) after parturition. 302.

TELEOsTS (On the development of the myocard in). 218.

TEMPERATURES (On the measurement of very low). VI. Improvements of the protected
thermoelements; a battery of standard-thermoelements and its use of thermo-
electric determinations of temperature. 642.

“TENSION THEORY (A quantitative research concerning Bafyer’s.) 410.

Terrestrial Magnetism. W. van BemMELEN: “The daily field of magnetic disturbance.” 313.

THERMOELEMENTS (Improvements of the protected); a battery of standard-thermoelements
and its use for thermoelectric determinations of temperature. 642.

ropacco (On a Sclerotinia hitherto unknown and injurious to the cultivation of)
(Sclerotinia Nicotianae Oud. et Koning). 48. Postcript. 85.

TRANSFORMATION of acetophenoxime into acetanilide and its velocity. 773.

— (The phenomena of solidification and) in the systems NH,NO,;, AgNO; and
KNO;, AgNO3. 259.

— (The) of benzidine. 262.

— (The) of diphenylnitrosamine into p-nitroso-diphenylamine and its velocity. 267,

— (The) of isonitrosoacetophenonsodium into sodium benzoate and hydrogen
eyapide. 453.

— (The mutual) of the two stereo-isomeric methyl-d-glucosides. 99.

— (The mutual) of the two stereo-isomeric pentacetates of d-glucose. 779.

— (On symmetric) of S, in connection with S, and 8S; 785.

XXIV = CeO, NOT -E NSE.

TRINITROBENZENE (Additive compounds of s.). 702.
TRUNKDERMATOMATA (Something concerning the growth of the lateral areas of the)
on the caudal portion of the upper extremity. 392.
— (Structure and function of the). IV. 347.
TRYPSIN (On the liberation of) from trypsin-zymogen. 34.
TWISTED CURVE (On the position of the three points which a) has in common with
its osculating plane. 622.
TYMSTRA BZ. (s.). The electrolytic conductivity of solutions of sodiuin in mixtures
of ethyl- or methylalcohol and water. 104.
TYNDALL (Can the presence of the molecules in solutions be proved by application
of the optical method of). 735.
uterus of Tarsius spectrum (The process of involution of the mucous membrane of
the) after parturition. 302.
VAPOUR TENSION (A contribution to the knowledge of the course of the) for aqueous
solutions. 628.
Vegetable Physiology. Tu. Werevers and Mrs. C. J. Weevers—pe Graarr: “In-
vestigations of some Xanthine derivatives in connection with the internal mutations
of plants.” 203.
vELocity (Electromagnetic phenomena in a system moving with any) smaller than that
of light. 809.
— of transformation (The) of carbon monoxide. IL. 66.
verRMAAT (p.) and M. C. Dexsuyzey. On the epithelium of the surface of the
stomach. 30.
VERSCHAFFELT (E.). Determination of the action of poisons on plants. 703.
VERSCHAFFELT (J. E.). Contributions to the knowledge of van DER Waals
y-surface. VIL. The equations of state and the y¥-surface in the immediate neigh-
bourhood of the critical state for binary mixtures with a small proportion of one
of the components (part 3). 59. (part 4). 115. VIII. The y-surface in the neigh-
bourhood of a binary mixture which behaves as a pure substance. 649.
VERSLUYS (wW. A.). The singularities of the focal curve of a curve in space. 17.
— The singularities of the focal curve of a plane general curve touching the tine
at infinity o times and passing ¢ times through each of the imaginary circle
points at infinity. 621.
— On the position of the three points which a twisted curve has in common with
its osculating plane. 622.
VISSER (a. W.). Enzymuactions considered as equilibria in a homogenous system. 605.
VOERMAN (s. L.) and A. F. Hoiieman. A quantitative research concerning
Baryer’s tension theory. 410.
yYRIES (J. DE). On complexes of rays in relation to a rational skew curve. 12.
— The harmonic curves belonging to a given plane cubic curve. 197.
— On systems of conics belonging to involutions on rational curves. 505.

— Fundamental involutions on rational curves of order five. 508.

CONTENTS. XXV

WAALS (VAN DER) (On the equations of Craustus and) for the mean length of
path and the number of collisions. 787.

— y-surface (Contributions to the knowledge of}. VIL. The equations of state and
the y-surface in the immediate neighbourhood of the critical state for binary
mixtures with a small proportion of one of the components (part 8). 59. (part 4).
115. VILL. The y-surface in the neighbourhood of a binary mixture which behaves
as a pure substance. 649.

— equation of state (On). 794.

WAALS (J. D. VAN DER). The liquid state and the equation of condition. 123.

— The equilibrium between a solid body and a fluid phase, especially in the
neighbourhood of the critical state. 230. 2nd part. 357.

— presents a paper of Prof. J. P. Kugnen: “On the critical mixing-point of the
two liquids.” 387.

— presents a paper of C. H. Brtxkman: ‘The determination of the pressure with
a closed airmanometer.” 510.

— presents a paper of Prof. H. E. J. G. pu Bots: “Hysteretic orientatic-pheno-
mena’. 597.

— presents a paper of Dr. Pa. Kounstamm: “On the equations of CLaustus and
vAN DER Waats for the mean length of path and the number of collisions.” 787.

— presents a paper of Dr. Pu, Kowystamm: “On van DER Waals’ equation of
state.” 794.

— presents a paper of Miss J. ReupLer: “Note on SypNeY Youna’s law of distil-
lation.” 807.

waTER (Facts leading to trace out the motion and the origin of the underground)
in our sea-provinces. 738.

— (The electrolytic conductivity of solutions of sodiam in mixtures of ethyl- or
methylalcohol and). 104.

WEBER (MAX). On some of the results of the Siboga-Expedition. 846.
WEEVERS (TH.) and Mrs, C. J. WrevERs—pr Graarr. Investigations of some
Xanthine derivatives in connection with the internal mutation of plants. 203.
WENT (F. A. F. C.) presents a paper of Dr. G. Gruns: “The Ascus-form of Asper-

gillus fumigatus Fresenius.” 312.

WERTHEIM SALOMONSON (J. kK. A.). A new law concerning the relation between
stimulus and effect. 73.

— On tactual after-images. 481.

WILLtoT (v.). — Extract of a letter of — on the work of D. Brerens pe Haan:
“Théorie, propriétés, formules de transformation et méthodes d’évaluation des
intégrales définies.” 226.

WIND (c. H.). Extract from the Report made by the Committee for awarding the
Buys—Ba ior medal. 78.

WINKLER (c.) presents a paper of Prof. J. K. A. WerrnHem Satomonson: “A
new law concerning the relation between stimulus and effect.” (6th Communi-
cation). 73.

XxVI C(O: Not EANSTTS-

WINKLER (C.) presents a paper of Dr. A. Gorter: ‘The cause of sleep.” 86.

— presents a paper of Dr, G. van Runperk: “On the fact of sensible skin areas
dying away in a centripetal direction.” 346.

— presents a paper of Prof. J. K. A. WERTHEIM SaLomonson: “On tactual after-
images.” 481.

— and G. van RisnBerk, Structure and function of the trunk-dermatoma. IV. 347.

— Something concerning the growth of the lateral areas of the trunk-dermatomata
on the caudal portion of the upper extremity. 392.

WOLFF (r. kK.) and C, A. Lopry pe Bruyn. Can the presence of the molecules in
solutions be proved by application of the optical method of TyNDALL. 735.
WOLFF(L. kK.) and A. Smits. The velocity of transformation of carbon monoxide. II. 66.
XANTHINE DERIVATIVES (Investigations of some) in connection with the internal muta-

tion of plants. 203.
ZEEMAN (pP.). Extract from the Report made by the committee for awarding the
Buys—Ba ior medal. 78.
— and J. Grest. On the double refraction in a magnetic field near the components
of a quadruplet. 19.
Zoology. Hans Srrauu: “The process of involution of the mucous membrane of the
uterus of Tarsius spectrum after parturition.” 302.
— A. A. W. Husrecut: “On the relationship of various invertebrate phyla.” 839
— Max Wesrr: “On some of the results of the Siboga-Expedition.” 846.

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Physical & Proceedings of the Section
Applied Sci. of Sciences

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