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FOR EDVCATION
FOR SCIENCE

LIBRARY

OF

THE AMERICAN MUSEUM

OF

NATURAL HISTORY

Koninklijke Akademie van Wetenschappen
te Amsterdam.

PROCEEDINGS

OF THE

RCT TON OF SCTBENGCHS

WAS) Bp AO Jes Gan) Ve:
(2rd PART)

AMSTERDAM,
JOHANNES MULLER.
June 1906.

(Translated from: Verslagen van de Gewone Vergaderingen der Wis- en Natuurkundige
Afdeeling van 30 December 1905 tot 27 April 1906. DI. XIV.)

GROENTEN (DES:

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Proceedings of the Meeting of December 30

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KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING

of Saturday December 30, 1905.

IGC

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige

Afdeeling van Zaterdag 25 November 1905, Dl. XIV).

GON ELEN NE Ss:

A. F. Hotteman and F. H, van per Laan: “The bromination of toluene”, p. 512.

A. Wicumayy: “On fragments of rocks from the Ardennes found in the diluvium of the
Netherlands North of the Rhine”, p. 518. (With one plate).

H. W. Bakmus Roozeroom: “The boiling points of saturated solutions in binary systems in
which a compound occurs”, p. 536.

P. van Rompurcn and W. van Dorssen: “The reduction of acraldehyde and some derivatives
of s. divinylglycol (3. 4 dihydroxy 1. 5 hexadiene)”, p. 541.

P. van RomBvreH and N. H. Conen: “The occurrence of S-amyrine acetate in some varieties
of gutta percha”, p. 544.

W. Kapreyn: “The quotient of two successive Bessel functions”, p. 547.

J.P. vaN per Srok: “On frequency curves of barometric heights”, p. 549.

L. J. J. Muskexs: “Anatomical research about cerebellar connections”. (Communicated by
Prof. C. Wik ier), p. 563.

P. van Rompurcu and W. van Dorsser: “On the simplest hydrocarbon with two conjugated
systems of double bonds, 1. 3. 5 hexatriene”, p. 565

A. Sits: “On the hidden equilibria in the p‚z-sections below the eutectic point”. (Commu-
nicated by Prof. H. W. Bakuvis RoozeBoom), p. 568. (With one plate).

A. Saurs: “On the phenomena which occur when the plaitpoint curve meets the three phase
line of a dissociating binary compound”. (Communicated by Prof. H. W. Baxuuis RoozEsoom),
p- 571. (With one plate).

J. J. van Laar: “On the course of the spinodal and the plaitpoint lines for binary mixtures
of normal substances”. 3rd Communication. (Communicated by Prof. H. A. Lorentz), p. 578.
(With one plate).

H. A. Lorentz: “The absorption and emission lines of gaseous bodies”, p. 591.

Proceedings Royal Acad. Amsterdam. Vol. VIII.

( 512 )

Chemistry. — “The bromination of toluene’. By Prof. A. F.

HorLeMAN and Dr. F. H. van DER Laan.

(Communicated in the meeting of October 28, 1905).

In the reaction between toluene and bromine we have a striking
example of the influence exerted on the nature of the product of
reaction by experimental conditions. About this the following is
known:

1. Influence of temperature. In the dark and at a low tempera-
ture there is formed a mixture of bromotoluenes; on the other hand
benzyl bromide is formed at the boiling point of toluene.

2. Influence of light. At a low temperature benzyl bromide is
exclusively formed; the same takes place at the boiling temperature.

3. Injluence of catalyzers. Through their action the bromination
takes place exclusively in the core, even in full daylight and at
an elevated temperature.

If we make a closer study of the papers which have appeared
as to this reaction it strikes us, as in so many other cases, that the
virtually known suffers from much uncertainty owing to an insuffi-
cient observance of the quantitative proportions. When, for instance,
SCHRAMM states that on bromination in sunlight benzyl bromide is
exclusively formed, a doubt arises as to the correctness of this view,
as the only proof he adduces is that the boiling point of his product
lies at 195°—205°; his boiling point limits are therefore so wide
apart that they suggest rather the presence than the total absence
of isomers. As regards the bromotoluenes formed in the reaction,
it was known that these are ortho- and paura-bromotoluene. But the
question, in what proportion those are formed under the influence
of the three above factors, has only been made the subject of greatly
varying conjectures and rough estimates. Nothing was known also
as to the nature of the products of reaction which are formed in
the dark at temperatures between the ordinary and the boiling point
of toluene (110°).

There was, therefore, every reason to again study this interesting
reaction and to try to solve the following questions:

In how far is the composition of the reaction-mixture dependent
1. on the temperature; 2. on the action of light; 3. on the presence
of catalyzers.

In my laboratory, first at Groningen, afterwards at Amsterdam,
Dr. VAN DER Laan has made a contribution to the resolution of these
questions by means of a careful experimental research ; he commenced

(513 )

by making sure of the absolute purity of his toluene and bromine
by means of special methods of purifying; for details his dissertation
and his paper in the “Recueil” (next appearing) should be consulted.

As the composition of the reaction mixture consisting of orthe-
parabromotoluene and benzyl bromide had to be determined, but as
no method for this was available, it was necessary to work out a
suitable process; in order to do this it was necessary to first possess
the three said substances in a chemically pure state so as to be able
to make artificial mixtures for testing the analytical methods.

The preparation of parabromotoluene and of benzyl chloride presented
no difficulties. The first substance was obtained from paratoluidine
by diazotation, and as this is a solid it could be readily freed from
any adhering traces of its isomers by reerystallisation from ligroin
and thus yield a parabromotoluene also free from its isomers. Benzyl
bromide was made from benzyl aleohol and hydrobromie acid. On
the other hand the preparation of pure orthobromotoluene was not
so easy. This was also prepared from the corresponding toluidine,
but the difficulty was to obtain the latter in a pure condition. This
was overcome in the manner previously communicated (These Proc.
VII p. 395).

In the actual investigation a large excess of toluene was always
taken (8 mols. toluene to 1 mol. of bromine) so as to avoid for certain
the formation of higher substitution products. Besides the three above
mentioned substances the reaction mixture contains, therefore, a large
quantity of toluene: hydrogen bromide is also. present and often
also a small quantity of free bromine, especially in the reactions
which were executed in the dark. This reaction product was now
analysed quantitatively as follows: A slow current of air removed
almost quantitatively the hydrogen bromide, which was absorbed in
water and titrated: the quantity thus found is equivalent to and
serves as a measure for the brominated products. In order to free
the liquid from any free bromine, and to determine the amount of
the same, it is poured into a solution of potassium iodide and the
liberated iodine titrated with thiosulphate. The liquid is now washed
with water, dried, and the toluene is distilled off in an airbath
heated by boiling amyl alcohol. On taking the sp. gr. of the distilled
toluene it appeared that this had not carried over any brominated
products to speak of.

After these operations the liquid now only consisted of the bromo-
toluenes and benzyl bromide besides also a small quantity of toluene.
In this mixture the benzyl bromide can be estimated by means of
alcoholic silver nitrate which yields silver bromide quantitatively.

36*

( 514)

In order to determine in what proportion ortho- and parabromo-
toluene are present, it was necessary to remove the benzyl bromide
from the mixture. This was done by bringing it into contact with
dimethylaniline. There is then formed quantitatively an ammonium
bromide, the bulk of which is deposited as a crystalline mass. By
washing the residual liquid with very dilute nitric acid the excess
of dimethyl aniline and the still dissolved ammonium bromide
are removed so that we obtain finally a liquid consisting merely of
the „bromotoluenes. When dried and distilled in vacuo it is ready
for the determination of the isomers. This was done by determining
the solidifying point of this purified liquid. By means of the solidi-
fying point curve previously constructed by Dr. vaN DER Laan, the
composition of the mixture could be at once ascertained from the
said point. By the analysis of a series of made up mixtures he was
satisfied that this method of analysis gives results accurate within
about 1 percent and is therefore sufficiently accurate for the purpose
intended.

With the aid of the method described Dr. van per Laan obtained
the following results.

1. Influence of temperature. The flask containing the mixture of
bromine and toluene was kept carefully in the dark. Observations
were made at 25°, 50°, 75° and 100°. At 25° the reaction took
place very slowly and even after a week the bromine had not alto-_
gether disappeared. At 50° this was already the case in 3 days.
The subjoined table contains the analyses of the reaction mixtures.
The figures given are each the mean of 3 or 4 concordant determinations.

From this it appears that in the dark a regular increase of the
benzyl bromide content takes place with a rising temperature. From
a graphical extrapolation it appears that benzyl bromide is no longer
formed below 17°, but, on the other hand, above 83° it is the sole
reaction product. These conclusions, however, must still be confirmed
experimentally. The proportion in which ortho- and parabromotoluene
are formed also alters somewhat in favour of the first-named isomer.
A determination of the sp. gr. of the mixture showed that this does
not contain any of the higher brominated substances. The mixture
obtained at 25° had a sp. gr. of 1.3598 at 64°.6 whilst a mixture of
the two isomers in the same proportion shows a sp. gr. of 1.3598
at 64°.

2. Injluence of light. As already observed, Schramm claims to
have obtained exclusively benzylbromide when brominating at low
temperature in full sunlight, although his experimental data create

(515)
TAB i Bk

-
Composition of the brominatingproduct | Composition of the mixture

Temp. ortho para benzyl bromide| ortho + para
bromotoluene | | bromotoluene
95 350) | 53.9 10.6 39.7 | 60.3
50 | 23.5 32.8 43.7 11.8 | 58.2
75 6.2 Ted | 86.3 45.3 | 54.7
100 — — 100 — =

some doubt about this. In diffuse daylight ortho- and parabromo-
toluene are also formed according to him ; ERDMANN, on the other
hand, stated that benzylbromide is the sole product. The observations
of Dr. Var DER Laan confirm those of ERrpMaNN. In diffuse daylight
the bromination proceeds very rapidly at 25°; in about 10 minutes
all the bromine has disappeared. The analysis of the product gave
99°/, of benzylbromide. From this it follows that pure benzylbromide
can be readily prepared in this manner. BrirsteiN, who attempted
this previously, arrived at the opposite result. This, however, was
caused by the fact that he exposed to the light a mixture of bromine
and toluene in equivalent proportions at the temperature of boiling
toluene. Operating in this manner we obtain indeed a produet with-
out a constant boiling point which on fractionation appears to con-
tain products boiling at higher temperatures. If, however, working
in the light and at 100°, only one mol. of bromine is used for 10
mols. of toluene, the formation of these higher boiling substances is
prevented. The excess of toluene is readily removed by distillation.
After a distillation in vacuo Dr. Vax per Laan obtained a product
solidifying at — 4°.3 of a sp. gr. 1.38887 at 65°.5 whilst these con-
stants, according to his observations, are — 3°.9 and 1.3858 at 65°.5
for pure benzylbromide from benzylaleohol. The benzylbromide thus
prepared contains, therefore, less than 0.5°/, of impurities.

3. Injluence of Catalyzers. As the influence of light is, as we
have seen, very great, all the experiments with catalyzers were made
in complete darkness. Of these were tested : antimonytribromide,
aluminiumbromide, ferricbromide and phosphorustribromide. Of the
first three it is stated that they favour the bromination in the core,
of the latter that it accelerates the formation of benzylbromide. The
observations of Dr, Van per LAAN are in harmony with this. The

( 516 )

temperature at which the reaction was tried was 50°, and the action

of the catalyzers was determined in such a manner that increasing
quantities of them were added and the composition of the reaction
product determined each time.
A feeble catalyzer was found in antimony tribromide as shown in
the subjoined table.
TA Bae alle

Temp. 50°; 50 eM.* toluene + 3 cM.’ bromine. Dark.

Mol SbBr, En Composition of the brominatingproduct
on 1 mol Br, | ortho | para ortho | para | benzyl bromide
bromotoluene bromotoluene |
0.00 HS | 58.9 23.5 3258 43.7
0.0017 40.1 59.9 29.4 33.4 449
0.0084 38.9 61.4 24.0 | 37.8 | 38.2
0.016 38.3 61.7 26.0 420 | 32.0
0.034 38.9 61.1 28.0 4a A | 27.9
0.089 — — — — | 18.7

The quantity of benzylbromide diminishes with increasing quan-
tities of the catalyzer but is not inversely proportional; the decrease
is much less. The proportion of ortho- and parabromotoluene under-
goes but a slight modification.

Aluminiumbromide, however, acts very energetically, as very small
quantities prevent the formation of benzylbromide. The experiments
were conducted by adding a little aluminiumpowder to the mixture
of toluene and bromine, thereby converting it rapidly into the
bromide. The following figures were obtained :

TAB alo) ens SDE
Temp. 50’; 50 cM." toluene + 2.5 ¢.M.* bromine. Dark.

Composition of the

Mol AlBr; Benzyl- | - mixture,
on 1 mol Br, |_ bromide | ortho ee
bromotoluene
0 | 48.7 MS |) BBD
0.002 | 43.4 43.9 56.4

0.006 0 44.3

dj
1

|

|
0,004 0.5 (2) AAO 55.4
0,017 0 49.2

Whereas SbBr, modifies the proportion of ortho-para slightly in
favour of the para there is present here a much stronger influence
of AlBr, in favour of the ortho.

Particularly interesting here is the influence on the amount of
benzyl bromide. Although with only 0.002 mol. no modification of
those. proportions is perceptible, this becomes so pronounced with
double the quantity that practically no more benzyl bromide is
formed. This result is very striking and deserves a closer study.

With ferric bromide this phenomenon was repeated; this appeared
to be a still more powerful catalyzer than aluminium bromide, as
the limit of its aetivity is situated still considerably lower as may

be seen from the subjoined table:

MU AX 18} 1, JD, NAG

Temp. 50°; 50 eM.* toluene + 2.5 eM.* bromine. Dark.
Composition of the
Mol Fe Br, | Benzyl- | mixture,

on 1 mol Br, | bromide | ortho | Dan

| bromotoluene

0 43.7 AA 8 58.2
0.0007 wis | 36.9 |. e384
0.001 7.8 ze au
0.002 0 36.0 64.0
0.006 0 37.9 62.4
0.01 | 0 37.0 63 0

Here, the quantity of ortho is again depressed by the catalyzer.

With phosphorus trichloride as catalyzer Dr. van per Laan has
only made one experiment which, in accordance with ERDMANN’s
investigatfon, gave an increase in the amount of benzyl bromide.

AS Be bl NE

Temp. 51°; 50 ¢M.* toluene + 3 eM.* bromine. Dark.

Mol P Br, Benzyl- Bromotoluenes

on 4 mol Br, | bromide ortho para
0 45.4 1.8 58.2

0,02 54.7 4l 4 | 58.6

( 518 )

The quantity of benzyl bromide has therefore, much increased
but the proportion ortho-para has kept fairly well unaltered.

For further particulars as to these researches VAN DER LAAN’s
original dissertation should be consulted. An article by him on
this subject will also appear, shortly, in the “Recueil”.

Amsterdam, Sept. '05. Chemical Laboratory of the University.
Geology. — “On fragments of rocks from the Ardennes found in

the Diluvium of the Netherlands North of the Rhine.” By
Prof. A. WICHMANN.

(Communicated in the meeting of November 25, 1905)

Ever since the 18 Century, the attention of geologists has been
drawn to the boulders scattered about our heathgrounds and in opposition
to the various and oftentimes curious theories started to account for
their presence there, A. Vosmarr then already expressed the opinion
that they had been transported from elsewhere by “A Mighty Flood”. *)
A little later, A. Brugmans?) and after him S. J. Brugmans *) pointed
to Scandinavia as the original home of these erratics ; but this view,
though shared by a few other scientists, was not generally adopted
until after the publication of J. F. L. Hausmany’s treatise *). It seemed
then as if the only question still remaining to be solved, was in what
way and by what road this transport had been affected. Little or
no thought was given to the possibility that other countries might
be also accountable for their origin.

It was not until 1844 that W. C. H. Srarine, whilst investigating
the nature of these boulders, discovered that at least those composed
of sandstone and quartzite, were found as well in the Ardennes, in
the districts of Berg and Mark, at the foot of the Harz Mountains

1) JOHANNES van Lier. Oudheidkundige brieven, bevattende eene verhandelin s
over de manier van Begraven, en over de Lijkbussen, Wapenen,: Veld- en Eere-
teekens der oude Germaner. Uitgegeven.... door A. Vosmaer. ‘s-Gravenhage 1760,
jos AN, O Ml LO:

2) Sermo publicus, de monumentis variarum mutatationum, quas Belgii foederati
solum aliquando passum fuit. Verhandelingen ter nasporinge van de Wetten en
Gesteldheid onzes Vaderlands. 1. Groningen 1773, p. 504, 508.

3) Lithologia Groningana. Groningae 1781. Preface p. 2, 3.

1) Verhandelingen over den oorsprong der Graniet en andere primitieve Rots-
blokken, die over de vlakten der Nederlanden en van het Noordelijk Duitschland
verspreid liggen. Natuurk. Verhandelingen der Hollandsche Maatsch. van Wetensch.
XIX, Haarlem 1831, p. 341—349.

as in Seandinavia*). It is to be noted that on his first geological map
these diluvial beds are not marked out in separate divisions *).

Two years later, however, his attention was arrested by the pecu-
liarity that, wbile in Twente and in the Eastern part of Salland and
probably over the whole extent of the Veluwe, the principal con-
stituents of these erratics were quartzite, red or blackish jasper, near
the Havelter hill, before Steenwijk when one comes from the side
of Meppel, one suddenly finds the detritus to consist entirely of
flints. He noticed the same phenomenon near Steenwijk, the Steen-
wijkerwold and even near Vollenhove *). These facts led him to con-
clude that two distinct diluvial deposits had taken place, i.e. one
of “siliceous material” transported from the Baltic and another
“composed of quartz” derived from the Ardennes.

In 1854 Srarinc had modified his theories. To the siliceous for-
mation he gave the name of ‘Scandinavian Diluvium’”, and the
quartz, which he no longer regarded as derived from the Ardennes,
received the appellation of “Diluviam of the Rhine’, whicb also
included the deposits between the Meuse and the Rhine; and the
beds situated South of the river Lek received the name of Diluvium
of the Meuse. He was careful to add however that: “it would be
wrong to deduce from these appellations that Scandinavia alone was
responsible for the diluvial formation in the North of Holland, and
the Ardennes, or the mountains of what at present is known as the
basin of the Meuse, for that of one of its Southern parts and the
Rhine for that of the other.” *) :

Six years later STARING again proposed another division which he
then considered decisive. Leaving the boundaries of the Scandinavian
Diluvium and those of the Meuse unaltered, the limits of the diluvium
of the Rhine were confined to those parts of the Netherlands lying
between the Rhine and the Meuse. The formation North of the Rhine
and South of the Vecht was indicated by the name of “mixed dilu-
vium’’*), which therefore included the provinces of Overijsel, Guelders,
Utrecht, and the district of the Gooi in North Holland. The charac-
teristic feature of this diluvium is the presence of erratics from

4) De Aardkunde en de Landbouw in Nederland. Zwolle 1844, p. 14.

*) Proef eener geologische kaart van de Nederlanden. Groningen 1844.

5) De Aardkunde van Salland en het Land van Vollenhove. Zwolle 1846,
[Do teh, Se)

*) Het eiland Urk volgens den Hoogleeraar Harrine en het Nederlandsche dilu-
vium. Verhandel. uitgegeven door de Commissie belast met het vervaardigen eener
geologische. kaart van Nederland. Il. Haarlem 1854, p. 167 m. kaart.

5) De Bodem van Nederland. Il. Haarlem 1860, p. 54—56, Pl. 1,

( 520 )

Seandinavia, from Hanover, from the mountains along the banks of
the Rhine and from the Ardennes; but STARING was unable accurately
to define which erratics had been transported by the Rhine and
which by the Meuse.

“By far the largest portion of the quartzites, sandstones, pudding-
“stones and slates, found in those parts of the diluvium, which are
“situated to the South of the Seandinavian drift, are derived from the
“Devonian strata of the Rhine and the Ardennes.” *) Neither did
STARING succeed in proving that the erraties in the diluvium of the
Meuse had originally come from the Ardennes. “The gravel and the
‘“flints of the Meuse are similar to those of the Veluwe, with the
“important difference, however, that no fragments of plutonic rocks
“are found among them.” ’)

Although for the last ten years the erratics transported from the
North of Europe have been the subject of much careful investigation,
little interest has been bestowed on those derived from Southern parts.
This neglect is due in a great measure to the very nature of those
rocks. The first actual proof that detritus from the Ardennes has
been carried North of the Rhine, was supplied by J. Lorm when
he discovered a Rhynchonella Thurmanni near Wageningen *); but
until now scarcely any further progress has been made in the study
of this question.

The difficulty of tracing to their original home the boulders trans-
ported from the Ardennes, lies in the first place in the necessity of
leaving out of consideration, fragments of those rocks which are
represented both in the diluvium of the Rhine and in that of the
Meuse, for it is impossible to determine the exact districts to which
they originally belonged. In the second place, it is a well known
fact that the greater part of the Ardennes is very poor in fossils,
so that the chance of finding fossiliferous specimens among the diluvial
erraties is almost nil; — and thirdly, some of the very characteristic
rocks, e.g. the phyllites, are much too soft to offer adequate resis-
tance to the accidents of transportation. However, as I hope to show
in the following pages sufficient material from various formations

JE Ge ye BY
3) 1G CE ie le
3) Contributions à la géologie des Pays-Bas. Archives Teyler (2) III. Haarlem

1887, p. 80.

Postscript: Fern. Roemer has already mentioned silicified specimens of Stepha-
noceras coronatum, found in the boulders near Winterswijk, Guelders. (N. Jahrb.
f. Min. 1854, p. 322, 323). These looked exactly like those occurring in the jurassic
layers of Northern France. See also Cl. Schlüter in Zeitschr. d. D. geolog. Ges.
XLIX, 1897, f, 486.

(521)

remains to prove that the erraties traceable to the Ardennes may
claim a considerable share in the formation of the mixed diluvium 1).

Cambrian system. The principal part of the Ardennes is built
up of layers belonging to the Cambrian system, which A. Dumont
originally sub-divided into three groups, namely Devillian, Revinian
and Salmian*). The Devillian and Revinian systems were afterwards
united by J. Gosserer, *) into one series, called the devillo-revinian,
which consists of phyllites, alternating with bands of greyish black
and dark bluish grey quartzites. These layers may be seen exposed
principally near Revin and Deville, on the banks of the Meuse, near
Roeroi and Stavelot, and also near Givonne, to the north of Sedan. *)
These quartzites are often erossed in various directions by fine veins
of quartz and a distinetive feature by which they are easily
recognized — they often contain small cubes of pyrite, which 7

some cases has been in a greater or lesser degree changed into
hydroxyde of iron. Now and then specimens are found in which
the orginal mineral has entirely disappeared, only the impression of the
eubes being left. J. pr Winpr®) has given microscopical descriptions
of these crystalline quartzites, but has omitted to mention one
special characteristic in which they show great conformity with the
phyllites. In reference to the latter, E. Grinirz was the first to point
out that the enclosed crystals of magnetite and pyrite are sur-
rounded by a zone of quartz, thus forming elongated lenses. 4)
From the manner in which these minerals have grown together,
as well as the chlorite, he was led to the conclusion that they
were coeval. This theory has been refuted by A. Renarp. Although,
with Grinitz, he believes the magnetites and pyrites to have
been formed at the same time as the mass of the rocks, he

1) In all probability this share will be found to be much larger than is thought
at present, because a great many rocky fragments, among others quartzites and
sandstones, are now ascribed to the diluvium of the Rhine although they are also
present in that of the Meuse.

2) Mémoire sur les terrains Ardennais et Rhénan-Mémoires de l'Acad.-rov. de
Belgique XX. Bruxelles 1847, p. S.

8) Esquisse géologique du nord de la France. Lille, 1880, p. 19.

4) It cannot be made out which of these localities have provided the boulders.
They are represented in the accompanying map sas if they were coming from
Revin, the chief locality.

5) Sur les relations lithologiques entre les roches considérées comme cambrien-
nes des massifs de Rocroi, du Brabant et de Stavelot. Mém. cour. de l’Aead. roy.
de Belgique LVI. Bruxelles 1898, p. 21, 68.

©) Der Phyllit von Rimognes in den Ardennen. TscHermax’s Mineralog. und
Petrogr. Mitthlg. Ill. Wien. 1880, p. 533,

(529)

considers the zone of quartz surrounding these minerals to be of
secondary origin, and that pressure on both sides had caused eavities
which afterwards have been filled up with quartz. >) Some time
before, A. Davuprée had already furnished a description of trans-
formed erystals of pyrites found near Rimognes.*) The studies of
other kinds of rocks led to the same conclusion.*) An analysis of
the pyritiferous quartzites of the Cambrian system affords: still better
proof of the secondary origin of this quartz, because in this case
the rock itself is composed of this mineral. When examining specimens,
it is easy to observe the sharp contrast between the two formations.
The quartz which has formed itself around the pyrite, is clear and
transparent, seldom contains enclosures, and is built up of
fibres which stand perpendicular on the erystals of pyrite. The
same structure is seen in the parts which form the veins. L. DE
Dorporor, who has written on the same subject, is inclined to regard
this quartz as chalcedony. *)

sy the aid of this data it has not been difficult to prove that
erratics of this kind have been widely dispersed, and it is very
probable that in the course of time their presence will be signalized
from many other places besides those we here indicate.

1. Province Utrecht: Railway cutting near Rhenen, on the river
Lek, Darthuizer Berg, sandpit to the North of Rijsenburg, railway
cutting at Maarn, the heath near the pyramid of Austerlitz, near
Zeist, Heidebosch near the House ter Heide, between the stations
de Bilt and Zeist, to the rear of Houderinge near de Bilt, Soester Berg.

2. Province of North-Holland: Hilversum and the sandy tract to
the North of Larenberg.

3. Province of Guelders: Heath near Epe, Bennekom near Wage-
ningen, Eerbeek near Dieren, at several places around Eibergen
Borculo, Groenlo and Hettenheuvel near Doetichem.

4. Province of Overijsel: Heriker Berg near Markelo.

1) Recherches sur la composition et la structure des phyllades ardennais. Bull.
du Musée roy. d’hist. nat. de Belgique. IL Bruxelles 1883, p. 134—135.

2) Etudes synthétiques de géologie expérimentale. I. Paris 1879, p. 443.

3) H. Lorerz. Jeber Transversalschieferung und verwandte Erschemungen im
thiiringischen Schiefergebirge. Jahrbuch der k. preuss. geolog. Landesanstalt für
1881. Berlin 1882, p. 283 —289.

Hans Reuscu. Bömmelöen og Karmöen met omgivelser. Kristiania 1888, p. 69, 70.

Arrr. Harker. On “Eyes” of Pyrites and other Minerals in Slate. Geolog.
Magazine (3) VI. London L889, p. 396, 397.

4) Quelques observations sur les cubes de pyrite des quartzites revimens. Anu,
Soc. géolog. de Belgique. XXXL Liége 1903—04. Mém. p. 505.

( 523 )

It stands to reason that erratics of this type must be more plentiful
still in the district South of the Rhine; in fact, similar quartzites
have been found in the diluvium of the Meuse for a long time past.
In the Province of Limburg they are looked upon as the most com-
mon kind of erraties. ApH. ERrENs came across one 3 M. high, 2.6 M.
long and 0.6 M. broad *). According to this author, they are also
found in quantities in the Province of North Brabant, although they
are not so large as those of Limburg. J. Lork found rocks of this
composition on the heaths at Mook and at Schaik, also in South Holland
on the beach of Springer in Goedereede and near Rockanje in the
island of Voorne.

“Porphyroids.” But the most conclusive proofs that immense quan-
tities of rocky fragments must have been transported from the Ardennes,
are furnished by the so-called Porphyroids. This rocky formation is
confined to the districts of Revin and Deville, where, more particu-
larly in the neighbourhood of Laifour and Mairus, they form
dikes from 0.1 to 20 M. wide, corresponding to the layers of the
devillo-revinian group. At present only 17 places are known where
this exceedingly characteristic formation ®) may be encountered.
Dispersed in a bluish gray or greyish groundmass, may be seen
porphyritic crystals of bluish quartz and of feldspar. Owing to
their peculiar position and their schistose structure, many geologists
have classified these rocks among the series of crystalline
schists,
Cu. pe LA VarrÉr Poussin and A Renarp, who have given the

— whilst others have ascribed to them an eruptive origin.
most detailed description of these rocks, favoured the former view *);
Barrois, DAUBREÉR, GOSSELET, von LAsAULX and others, on the con-
trary, justly considered them to be quartzporphyry, an opinion which
A. Rerarp also finally accepted.

Although these porphyroids can have but a minimum share in the
formation of the Ardennes, they are frequently met with in diluvial
deposits. In Belgium, G. Dewarqer only noticed them near Liege‘),

which proves that but little attention has been paid to them in that

1) Recherches sur les formations diluviennes du sud des Pays-Bas. Archives
Teyler (2) Ill. 6eme partie. Haarlem 1891, p. 23.

2) J. Gosserer. L’Ardenne. Paris 1888, p. 86.

5) Mémoire sur les caractéres mineralogiques et stratigraphiques des roches dites
plutoniennes de la Belgique. Mémoires cour. ete. de l’Acad. roy. de Belgique XL.
Bruxelles 1876, p. 237—247 (also Zeitschr. d. D. geol. Ges. 1876, p. 750—769).

4) Prodrome d'une description géologique de la Belgique. Bruxelles et Liége
1868, p. 237. }

or

24 )

country *), for Arpa. ErENs mentions not less than 15 gravel-pits in
the neighbourhood of Maastricht in which he found fragments of
these rocks, one being 0.6 M. long and 0.5 M. thick. The most
easterly place of deposit known at present is Simpelveld’). Not long
ago, Mr. L. Rurren brought me several specimens dug up in the
neighbourhood of Sittard. From observations of Erexs, it would appear
that these erratics are scarce in the Province of North Brabant. He
himself found a nice piece at Mook ®, and J. Lori a fragment
between Bladel and Postel.

North of the Rhine they have been discovered in the railway cuttings
near Rhenen and also near Maarn (in the latter locality the fragment
was over ‘/, M. in diameter), and on the Soester Berg, in the Province
of Utrecht. Another piece was found near Eibergen, in Guelders and
finally Erens mentions having seen in the Geological Museum, at
Leiden, a fragment found in Overijsel : unfortunately he does not
state the exact spot at which it was found ‘).

2. Carboniferous system. Frrp. Roemer has given a description
of u few fragments of black carboniferous limestones containing
Productus striatus Fisch. found in the Gooi, near Hilversum and
sent to him for analysis by Srarinc. He came to the conclusion that
they were derived from the carboniferous limestone of the district
between Aix-la-Chapelle and Stolberg ®).

STARING on the contrary believed them to have been transported
from Visé on the Meuse, in Belgium, and based his opinion on the
similarity of their composition with the limestone found in that part
and also on the almost total absence of this rock from Westphalia.®)
Although fragments of carboniferous limestone from Ratingen, N.W.
of Dusseldorf, might have found their way to the Netherlands, the
fact that no traces of the said fossil have ever been observed in
those rocks‘), evidently keeps them outside the discussion. It is
true that in the district between Aix-la-Chapelle and Stolberg, the

1) J. Lori e.g. found several fragments near Lancklaer on the Zuid-Willemscanal.

*) Note sur les roches cristallines recueillies dans les dépots de transport dans
la partie méridionale du Limbourg hollandais. Ann. de la Soc. géolog. de Belgigue.
XVI. 1888—89. Liége. Mém. p. 417—420.

5) Recherches sur les formations diluviennes du sud des Pays-Bas. Archives
Teyler (2) III. 6ième partie. Haarlem 1891. p. 23, 33.

4) Recherches sur les formations diluviennes. |. c. p. 67.

6) Ueber Holländische Diluvial-Geschiebe. Neues Jahrb. f. Mineralogie. 1857, p. 389.

5) De Bodem van Nederland. IL. Haarlem 1860, p. 96.

7) H. von Deenen. Erläuterungen zur geologischen Karte des Rheinlandes und
der Provinz Westfalen. Il Bonn 1884, p. 216.

( 525 )

Productus striatus is occasionally met with *), but, like many other
fossils, it is extremely rare.*) The probability of one of these
specimens having been transported to the Gooi becomes therefore
nil. On the other hand, as SrarixG had already pointed out, they are
very common at Visé in Belgium, consequently we are justified in
concluding that the above mentioned fragments must be referred to.
that locality.

Other fossil mentioned by Roemer is the Goniatites sphaericus
Mart. (Glyphioceras sphaericum), a specimen of which had been
found near Holten, in Overijsel, and whose original birth-place he
claims to have been the valley of the Roer. This fossil, however,
is found both at Ratingen and Visé: nothing definite can therefore
be said with regard to the place of its origin. I may here mention
that in 1899, Dr. E. Corris brought me a fine specimen, well
preserved and but little polished, which had been picked up in
the gravel of a garden at Utrecht and was very probably brought
from the Lek.

In the railway cutting near Maarn, to the East of Driebergen, I
found in 1893 a block of crinoidal limestone weighing as much
as 97 K.G. In that same cutting repeatedly were observed pieces
of compact black limestone. In 1895, fragments of a very beautiful
erinoidal limestone were found in the grounds of the villa Houde-
ringe, near De Bilt, at a depth of abont 1 M. Other pieces of
black and next to these of grayish compact limestone were found
in a railway cutting half way between the stations of De Bilt and
Soest. On the whole, therefore, it cannot be said that rocks of this
type are largely represented in the diluvial deposits under considera-
tion. This is probably owing in a large measure to the sandy nature
of the diluvium of those parts which allows the moisture of the
atmosphere to penetrate to the limestone and gradually dissolve it.
The same physical conditions are probably also responsible for the
paucity of erratics of this description in the Provinces of North-
Brabant and Limburg, and in the Campine. A. Erexs found fragments
of erinoidal limestone near Oudenbosch, *) E. Drnvavx of earboni-

1) H. von Decuen. |. c. p. 211.

2) C. Dantz did not even come across a single specimen in the district of Aix-
la-Chapelle. (Der Kohlenkalk in der Umgebung von Aachen. Zeitschr. d. D. geolog.
Ges. XLV. Berlin 1893. p. 611).

5) L. G. De Konincx. Recherches sur les animaux fossiles. Lère partie. Mono-
graphie des genres Productus et Chonetes. Liége 1847. p. 30.

4) Recherches sur les formations diluviennes 1. c. p. 67.

( 526 )

ferous limestone in a gravel pit at Gelieren near Genck *) and J.
Lorié at Smeermaes and Lancklaer, on the Zuid-Willems canal.

The original home of these various limestones cannot be determined
with any certainty. However, as numerous layers of erinoidal lime-
stone are present in the districts of Aix-la-Chapelle and Stolberg ?)
as well as in the valley of the Meuse, more especially near Dinant,
it seems rational that we should in the first place look to these parts
for their origin’). In any case they must have been transported
along the Meuse, for the district Aix-la-Chapelle—Stolberg is drained
by the Geul, the Inde and the Worm, which all three flow into
the Meuse.

Finally Romer gives in his treatise a description of fragments of
phthanite, found near Ootmarsum, in Overijsel, which he thinks
derived from the layers of culm on the lower Rhine. This conjecture
is not inadmissible, but at the same time the fact must not be
overlooked that this kind of rock is also plentiful in the valley of
the Meuse.

Jurassic System (Oxfordian). In the foregoing pages mention has
already been made of a piece of brownish yellow sandy clay, found
by J. Lorn on the Wageninger hill (Guelders) in which was inbedded
a perfect specimen of Rhynehonella Thurmanni Voltz, in every respect
similar to the fossils of this species found at Vieil-Saint-Rémy, to the
South-West of Mezieres in the department of the Ardennes‘). This
is the’ only fossil of this type discovered in our country, although
in the diluvium of South Limbourg and Northern Belgium, jurassic

1) Les anciens dépôts de transport de la Meuse, appartenant 4 l’assise moséenne
observés dans les ballasticres de Gelieren près Genck en Campine. Ann. Soe. géol.
de Belgique XIV. 1886—87. Liége 1887, Mém. p. 103.

Here again, as at Maarn, he ascribed their presence to an “accident”.

2) J. Betsser. Ueber Struktur und Zusammensetzung des Kohlenkalks in der
Umgebung von Aachen. Verhandl. naturh. Vereins Rheinl. u. Westf. XXXIX. Bonn
1882. Corresp. Bl. p. 92.

5) Ep. Duronr. Notice sur les gîtes de fossiles du calcaire des bandes carboniféres
de Flourens et de Dinant. Bull. Acad. roy. de Belgique (2) XII Bruxelles 1861 p. 293.

Ep. Dupont. Essai d'une carte géologique des environs de Dinant |. ce. (2) XX.
1865. p. 621, 622, 629.

Ep. Doroxr. Carte géologique des environs de Dinant. Bull. Soc. geol. de Fr. (2)
XXIV. Paris 1866—67 p. 672, 673.

Ep. Dupont et MreneL Mourton, Explication de Ja feuille de Dinant. Musée d’hist.
nat. de Belgique. Service de la carte géolog. du Royaume. Bruxelles 1883, p. 9,
26, 33, 34, 53 et passim.

4) Contributions à la géologie des Pays-Bas. Archives Teyler (2) II. Haarlem
1887, p. 10.

C

( 527 )

fossils have been frequently met with. We find them already men-
tioned by J. T. BINKHORST VAN DEN BINKHORST ').

Fr. SeGHers discovered a Rhynchonella and part of an Ammonites
at Genck?). Close to this place, at Gelieren, E. Dervaux frequently
came across remains of “calcaire a Chailles” *). C. Mararse gave a
description of petrified Nerinea found at Rothem and an Isastraea at
Jambes, near Namur‘). A. Erens mentions a few other fossils *) and
finally we have an account of a yellow oolite, discovered by E. van
DEN BROECK among the erratics of the Meuse, and here we call
attention to the peculiar siliceous oolites scattered about the plateau of
the Meuse and which probably belong to the jurassic system ®). As
yet no trace of similar oolites has been discovered North of the Rhine,
but J. LormÉ noticed some in the borings of a well at Mariendaal,
near Grave’). A few weeks ago Mr. L. Rurren found a small pebble
in the diluvium at Kollenberg, near Sittard.

Tertiary system. (Eocene). Very interesting are the accounts of
the discovery of erratics comprising specimens of Numiulina laevigata
Lam. Ferp. Roemer has given a description of a fragment of this
kind derived from Holten, in Overijsel, but believed it to have only
accidentally found its way among the erratics*). STARING made
mention of a couple of rounded-off pieces of hornstone, one of which
had been found on the rising ground of Hellendoorn and the other
on the Steenshul, near Oldebroek, and which he referred to the Alps?
“If we did not know the place where these specimens were obtained,
“we should be rather inclined to think they came from a collection
“in which the objects had been confused and believe these rocks to

1) Esquisse géologique et paléontologique des couches crétacées du Limbourg.
Maastricht 1859. p. 7.

2) Ann. de la Soc. malacolog. de Belgique X. Bruxelles 1875. Bull. p. XXXIV.

3) Les anciens dépdts de transport de la Meuse, appartenant a l'assise moséenne
observés dans les ballastiéres de Gelieren près Genck en Campine. Bull. Soc.
géolog. de Belgique XIV. 1886/87. Liége. 1887. Mem. p. 102.

4) Sur quelques fossiles du diluvium. Ann. Soc. malacolog. de Belgique X.
Bruxelles 1875. Bull. p. IV.

5) Note sur les roches cristallines |. c. p. 413.

6) E. vaN DEN Broeck. Les cailloux oolithiques des graviers tertiaires des hauts
plateaux de la Meuse. Bull. Soc. belge de Géologie III. Bruxelles 1890 p. 404—412,

X. Sramrer. Origine des cailloux oolithiques des couches à cailloux blancs du
bassin de la Meuse. Ann. Soc. géolog. de Belgique XVIII. 1890—92, p. CV, 92.

E. van pen Broeck. Coup d'oeil synthétique sur l’Oligocéne belge. Bull. Soc. belge
de Géologie VII. Bruxelles 1893 p. 25, 266.

7) Beschrijving van eenige nieuwe grondboringen, Verhandel. K. Akademie v. W.
Qde sectie. VI, N. 6. Amsterdam 1899, p. 33.

8) Ueber Holländische Diluvial-Geschiebe. Neues Jahrb. f. Min. 1857, p. 392,

37
Proceedings Royal Acad. Amsterdam. Vol. VIII.

( 528 )

“have been picked up near Brussels *)”. K. Martin?) and J. Lorié*)
in fact assign them also to that locality; they forget, however, that
no strata of nummulitie limestone are known to exist there *). Their
origin lies much farther South. In 1863 J. Gosserrr had already
indicated the original source of these “silex à Nummulites”, of which
a few years later he published a description °). They are dispersed
in large quantities in the arrondissement of Avesnes, in the department
du Nord, more especially in the environs of Trélon") where, on
account of their hardness, they are frequently used for the paving
of roads.

Since then numerous fragments of this rock have also been found
in Belgium, specially on the plateau situated between the Meuse and
the Sambre, e.g. around Silenrieux, Sivry, Clermont, ete., as well
as in parts lying further West ‘).

The second question which we have to examine, is the period at
which these rocky fragments from the Ardennes have been trans-
ported to districts at present situated North of the Rhine. The view
expressed by SrariNG that this transport has taken place before the
deposition of Scandinavian erratics, seems at present also satisfactorily
established, for those carried by the Meuse. In the railway cuttings
at Maarn and Rhenen, rocks of diverse origin lie together in friendly

1) De Bodem van Nederland. Il. Haarlem 1860, p. 89.

2) Niederländische und Nordwestdeutsche Sedimentärgeschiebe. Leiden 1878, p. 37.

8) Les métamorphoses de I’Hscaut et de la Meuse. Bull. Soc. belge de Géologie,
IX. 1895 Bruxelles 1895—96, Mém. p. 60.

4) E. van pew Broeck. A propos de lorigine des Nummulites laevigata du gravier
de base du Laekénien. Bull. Soc. belge de Géologie. XVI. 1902. p. 580.

5) De l’extension des couches à Nummulites laevigata dans le nord de la France,
Bull. Soe, géolog. de la France (8) If. 1873—74. Paris 1874, p. 51—58. See also
Ann. Soc. géol. du Nord. 1. 1870—74. Lille, p. 36.

6) Compte-rendu de lexcursion du 7 Septembre [1874] a Trélon I. e. p. 681.
Leriche. L’Eocéne des environs de Trélon. Ann. Soc. géol. du Nord. XXXII. Lille
L903 pelo:

7) Micue, Mourton, Sur les amas de sable et les blocs de grés dissiminés a la
surface des collines famenniennes dans |’Entre-Sambre-et-Meuse. Bull. Acad. roy.
de Belgique (3) VII. Bruxelles 1884, p. 301—303.

A. Ruror. Sur lage de grés de Fayat. Bull. Soc. belge de Géologie I, 1887,
p. 47. i

L. Bayer. Première note sur quelques dépôts tertiaires de l’Entre-Sambre-et-Meuse.
Bull. Soc. belge de Géologie X, 1896. Bruxelles 1897—99 p. 139—140.

G. Veter. De l’extension des sables éoeènes laekéniens à travers la Hesbaye et la
Haute Belgique. Ann. Soc. géolog. de Belgique, XXV, 1897—98. Liége, p. CLXV.

A. Briarr. Notice deseriplive des terrains terliaires el erétacés de Entre-Sambre-
et-Meuse. Ann. Soc. géolog. de Belgique XV, 1887—88, p. 17,

( 529 )

juxtaposition and intermixture, which proves that they must have
been carried together and at the same time to the place where they
are found at present. From the shape of the front moraine, we con-
clude that the direction of the transport was from the North-East.
The erraties nowadays found at the surface have been gradually
denuded by the action of water and wind. It is therefore evident
that originally these erratics were transported much farther to the
North and East, than their present place of deposit, because they
were seized by the advancing Baltic icestream and carried along
together with the material of its moraine. We are therefore justified
in fixing the period of the transport of the boulders from the Rhine
and Meuse at the commencement of the epoch of maximum glaciation
(Saxonian).

A far greater difficulty presents itself when we attempt to deter-
mine in what way this transport has taken place, for it can only
have been effected by the agency of a river or a glacier. The
hypothesis that all these boulders should have been carried along
by the Meuse in its downward course, is scarcely admissible. Even
leaving out of account the finding of rocky fragments from the
Ardennes on the strands of Goedereede and Voorne — not to
speak of Suffolk, in England — there remains a large tract of land
105 K.M. long stretching from Utrecht to Eibergen, over which these
erratics are dispersed in the shape of a crescent. If carried by the
Meuse, its mouths must have extended over a very large area. But
a greater objection to this theory is that, in that case, they must have
been transported across the Rhine (at present the IJsel) because
rocks of this kind are found at places to the Kast of this river
(Doetichem, Eibergen, Markelo). Finally, some of these blocks are
so large that they could not possibly have been transported by a
river. Besides, some of them present no marks of polish, which is
another argument against their transport by running water.

For the better understanding of these objections we quote a few
examples from the Province of Limburg and the Campine. A. Erens
found in the environs of Maastricht numerous large blocks of Cam-
brian quartzites, one of which was 3 M. high, 2,6 M. long and
0,6 M. in width, computed to weigh about 12400 K.G. '). More
important still are the blocks of sandstone found in the diluvium
of the Campine at Holsteen-Molenheide, near Zonhoven, in the neigh-
bourhood of Hasselt, BE. Drtvavux noticed blocks measuring from 4

1) Note sur les roches cristallines 1. c.p. 412, 417. Mr. L. Rurren informed
me that in the neighbourhood of Sittard similar boulders reach a diameter of
ane) WG

dd

( 530 )

to 36 M. cub, weighing from 10600 to 95400 K.G. 1). He believed
them to belong to the landenian stage of the eocene system. His
opinion, that they covered the plateau of the Ardennes (where
Cu. Barros was the first to discover similar masses *), to a height
of 672 M., has been much contested. E. van DEN BrorckK classed these
sandstones first among the triassic system *), afterward referred them
to the oligocene system ‘), and finally suggested they might either be
oligocene, miocene or pliocene, but certainly not eocene®). G. DEWALQUE
pronounced them to be miocene °), whilst O. van ErrBORN sought
their origin in the pliocene system’), more especially in the diestian
group *), but was of opinion that they must be regarded as the
remains of a ‘delta caillouteux” *). M. Mourton, on the contrary,
held that they had been formed in the’ vicinity of their present place
of deposit, by the fusion of the “sable de Moll” **), an opinion
which cannot be maintained, because similar blocks are present in
the diluvium of Maastricht where no trace of this sand exists '*).

J. GossELET compares these rocks with the freshwater-quartzites of the
diluvium of the Rhine and, with reason, thinks that they belong
to the oligocene system **). At all events it is universally admitted
that the Ardennes have been covered by extensive layers of tertiary

1) Description sommaire des blocs colossaux de grès blanc cristallins provenant
de l'étage landénien supérieur... en différents points de la Campine limbour-
geoise. Ann. Soc. géolog. de Belgique XIV. 1886—87. Liége 1887. Mém. p. 117 —130.

2) Sur l’étendue du système tertiaire inférieur dans les Ardennes. Ann. Soc.
géol. du Nord. VL Lille 1879, p. 371.

3) Ann Soc. roy. malacolog. de Belgique XVI. Bruxelles 1880. Bull. p. LXXIV.

4) Note préliminaire sur le niveau straligraphique de la Belgique et de Ja région
d'origine de certains des blocs de grés quartzeux de la Moyenne et de la Basse-
Belgique. Bull. Soc. belge de Géologie IX. 1895. Bruxelles Proc. verb. p. 94—99.

5) Les grès erratiques du sud du Démer et dans la région de Heurcx. Bull.
Soc. belge de Géologie XV. 1901. Bruxelles 1902. Proc. verb. p. 628.

6) Ann. Soc. géolog. de Belgique. XIV. 1886—87. Liege 1887. Bull. p. 18.

7) Le Quaternaire dans le sud de la Belgique. Bull. Soc. belge de Géolog. XV.
1901. Proc. verb. p. 662.

8) Quelques mots au sujet des divers niveaux gréseux du tertiaire supérieur
dans le nord de la Belgique. 1. c. p. 632.

9) Contribution à Étude des Klages rupélien, boldérien, diestien et poederlien,
l. e. XVI. 1902. Mém. p. 65.

10) Compte rendu de l’excursion géologique en Campine les 23, 24 et 25 sep-
tembre. 1]. e. XIII. 1899, Mém. p. 205, 213, 214.

1) Arpa. Enens. Note sur les roches eristallines 1. c. Pl. NUL

2) L’Ardenne. Paris 1888, p. 833,

(5340)

system, as has been pointed out by M. Lonmsr >), X. Srainime ®),
J. Corner *) and others.

Before stating our reasons for supposing the presence of a gla-
cier in the Ardennes during the second glacial period, we are
willing to admit that J. Gosskrer, who of all geologistst knew most
of this mountain range, remarked in reference to this hypothesis :
“on nen trouve aucun indice serieux’’ *). Indeed we have but few
indications in support of it. The first to draw attention to this ques-
tion was Fr. van Horen, who at the time of the making of the rail-
way line between Tirlemont and Jodoigne, found near Bost blocks of
quartzites from the Ardennes which presented marks quite similar
to the striae caused by glaciers. Van Horen, however, did not feel
justified in drawing from this discovery the conclusion of the former
existence of a glacier °). A year later C. Mararsr observed similar
marks on blocks of quartzites on the banks of the Grande Geete,
close to the spot formerly occupied by the Abbey of Ramez-les-
Jochelette, about 10 K.M. from Bost*). G. Drwarqor believed to have
seen unmistakable striae on blocks of quartzites in the valley of the
Amblève, near Stavelot, on the “Hohe Venn”). E. Drtvaux also
noticed these horizontally parallel scratches, but believes them to
have been produced by a “torrent entrainant et roulant péle-méle
des sables et des cailloux.” *).

Finally, South of Stavelot, on the road to Somagne, G. DewaLQue
discovered giants’ kettles formed by the agency of glaciers’). It is
regrettable to find that the more detailed study of this subject has
been much impeded by the practice in Belgium of giving the name

1) Les depôts tertiaires de la haute Belgique. Ann. Soc.-géolog. de Belgique XV.
Liége 1887—88. Mém. p. 59.

*) Le grés blanc de Maizeroul. Ann. Soc. géolog. de Belgique XVIIL. Liége
1890—91. Mém. p. 61.

8) Etude sur I’Evolution des Rivières belges. Ann. Soc. géol. de Belgique XXXI.
1903 —04. Mém. p. 317, 355.

4) L’Ardenne, p. 843.

5) Note sur quelques points relatifs à la géologie des environs de Tirlemont.
Bull. Acad. roy. de Belgique (2) XXV. Bruxelles 1868, p. 645, 664; 1 Pl.

6) Roches usées avec cannelures de la vallée de la Be Geethe. 1. c. (2)
XXVII, 1879, p. 682—685.

7) Sur la présence de stries glaciaires dans la vallée de Amblève. Ann. Soc.
géolog. de Belgique. XII. 1884—85. Liège. 1885. Bull. p. 157—158.

5) Note succincte sur l’excursion de la Societé géologique à Spa, Sravrror et
LAMMERSDORF en aôut-septembre 1885. Ann. Soc. roy. malacol. de Belgique XX.
Bruxelles 1885, Mém. p. 19.

9) Marmites de géants près de Stavelot. Ann. Soc. géol. de Belgique. XXV.
1897—98, p. CXXXVIII.

of pseudoglacial to all kinds of bosses and scratches which elsewhere
would searcely be so called, because they do not in the leest resemble
the striae of glaciers *).

This absence of positive characteristics is however easily explained.
Leaving alone the fact that as yet no thorough investigation of the
subject has been made, the condition of the Ardennes themselves
are very unfavorable to research. Its dense forests, fens and heaths
make it difficult to reach the surface of the rocks, whose harder
layers are only capable of preserving marks. The reason why so
few traces are found on the sides of the valleys and on the plateau
of the Meuse becomes plain, when we remember that during the
period following the receding of the Northern glacier, the waters
of the Meuse rose 200 M. above the level of the sea, and not only
filled the whole valley but inundated the plateau of the Meuse and
thus destroyed the traces left by the glacier.

Of this we find the clearest proofs in the terraces which have
retained their boulders. *) Besides, exactly the same thing happened
with the Rhine and its tributaries. The sand and small pebbles
carried along by their waters must necessarily have almost entirely
obliterated the marks of the glaciers left on the rocks *).

Striae, however, are not the only evidences of the action of a

1) X. Sramrer. Stries pseudo-glaciaires en Belgique. Bull. Soc. belge de Géologie
X. Bruxelles 1896. Pr. verb. p. 212—216.

E. van pen Broeck. Contributions à l'étude des phénomènes d’altérations
dont l'interprétation erronée pourrait faite croire à Vexistanee de stries glaciaires.
1, e. XIII. 1899. Mém. p. 323—334. Pl. XX.

G. Siwoens. Sur une roche présentant des stries pseudo -glaciaires en Condroz.
l. c. Pr. verb. p. 222—223.

2) É. Duponr et M. Mouron. Explication de la feuille de Dinant. Bruxelles
1883, p. 100.

A. Rutor. Résultats de quelques explorations dans Je Quaternaire de la Meuse.
Bull. Soc. belge de Géologie. XIV. Bruxelles 1900. Pr. vorb. p. 259, 260.

X. Srarier. Le cours de la Meuse depuis l'ère tertiaire l.c. VIII. 1894 Mém,
p. 84. Pl. VII.

E. van peN Broeck. Coup d'oeil synthétique sur l’Oligocéne belge et les obser-
vations sur le Tongrien supérieur du Brabant l.e. VII. 1893, p. 255, 256, 266.

E. van pen Broeck. Exposé sommaire des observations et découvertes stratigra-
phiques et paléontologiques faites dans les dépôts marins et fluvio-marins du Lim-
bourg pendant les années 1880—81. Ann. Soc. roy. malacolog. de Belgique XVI,
Bruxelles 1881. Bull. p. CXXV—CXLII.

8) It might be suggested that the transport of these boulders had taken place by
means of ice-floes, but Mr. Lonesr has demonstrated in the most positive manner
that these ice-masses are incapable of effecting a notable removal. He comes to
the conclusion that among the present climatic conditions no explanation can be

( 533 )

glacier and one might reasonably expect to find in the valleys
some remains of the wall of moraines. That this is not the case
may be accounted for by the supposition that the great Baltic ice-
stream has travelled farther south and in its course also destroyed
these evidences. As there exists a great diversity of opinion with
respect to this forward movement of the ice-stream, it seems necessary
here to state what is known of the dispersion of Scandinavian
erraties in the Provinces of Limburg and North-Brabant and the
Campine.

As long ago as 1778, J. A. pr Luc mentions the discovery of
blocks of granite between Postel and Alfen, and also near Lommel
and Helchteren'). Subsequently, J. J. p'OMauvs D'HarLOY drew
attention to the numerous blocks of granite and other fragments of
“primordial” rocks found on the heath of the Campine. “La quan-
“tité de ces blocs doit être été immense; car quoiqu’on fasse
“un grand usage pour paver les rues, ainsi que pour faire des
“jetées le long de la mer et des rivieres, on en voit beaucoups
“dans les bruyeres’.?) And Eneetspact—Larivibre adds the infor-
mation that some of these blocks of granite measured several
M. eub.*) Somewhat later again, J. G. S. van Brepa mentioned
the finding of two pebbles of granite in the subsoil of Maastricht,
very justly remarking that these rocks must be regarded of later
date than those transported from the Ardennes *). At that time he
already spoke of blocks of granite found at Oudenbosch, in North-
Brabant °). Starve expressed the opinion that these erratics had been

brought there by “some accidental means or other” ©, although a
short time before Norsert pr War. had recorded the finding, at
Weelde, 10 K.M. to the NNE. of Turnhout and also at Poppel,

found for the transport of the blocks of quartzites from the Ardennes. (Sur le
transport et le déplacement des cailloux volumineux de l’Ambléve. Ann. Soc.
géol. de Belgique. XVIII. Liége 1890—91. Bull. p. GVI[—CIX).

1) Lettres physiques et morales sur l'histoire de la terre et de l'homme. IV.
Paris et La Haye 1779, p. 54, 57.

2) Mémoires pour servir à la description geologique des Pays-Bas, de la Flandre
et de quelques contrées voisines. Namur. 1828, p. 204, 205.

3) Considérations sur les blocs erratiques et roches primordiales Bruxelles. 1829
(fide P. Cocers. Ann. Soc. roy. malacolog. de Belgique. XVI. 1881, Bull. p. LIV).

4) Natuurk. Verhandel. van de Holl. Maatsch. v. Wetensch. XIX. Haarlem
1831, p. 390.

®) The biggest one originally weighed +5300 K.G. (V. Becker). Het zwerfblok
van Oudenbosch en zijne omgeving. Studiën op Godsdienstig, Wetensch. en
Letterk. Gebied, XXX. Utrecht. 1888, p. 25).

6) De bodem van Nederland Il. Haarlem 1860, p. 78.

( 534 )

half-way between the last-named place and Tilburg, of erratics one
of which weighed 200 K.G. *). G. Derwaqve then again mentioned
two pebbles of granite found in the neighbourhood of Maastricht’).
It is only during the last ten years that a deeper interest has been
taken in the study of this subject, with the result that the presence
of erratics of Northern origin has been ascertained in several places,
as we gather from the writings of C. Bamps, V. BrCKER, E. VAN DEN
BrorcK, P. Coarrs, E. Dervaux, G. DeEWALQUE, A. Erens, O. vAN
ErrTBORN, J. Lormé, A. Renarp and Cx. pr LA VALLÉE— Poussin.

Another fact worthy of notice is the presence, at these very places,
of boulders derived from the district of the Rhine. The first indications
of such finds, by G. Drewarque, are rather questionable. They were
fragments of rocks from the lava of Niedermendig, near Andernach,
frequently met with in the valley of the Ambleve, but were believed
to have been fragments of mill-stones, formerly used at Stavelot and
Malmedy. Subsequently E. Detvavx found a few pieces of lava and
pumice stone in the diluvium of the Campine *); but it was A. Erens
who discovered and described a great number of rocks derived from
the Rhine district, composed of lava from Niedermendig, pumice
stone and ‘Taunus-quartzite*). These were followed at a later
period by trachyte from the Drachenfels, basalt and hornblende-
andesite from the Siebengebirge, and melaphyre and agate from the
basin of the Nahe‘). The discovery of these fragments in the North
of Limburg admits of no other interpretation than that these recks
must have been carried South, simultaneously with the detritus from
Scandinavia.

It cannot be denied that fewer erraties from Seandinavian rocks
are found South of the Rhine than North of it. We give the following
reasons in explanation of this fact: 1st. During the progress of the
Baltic icestream in a South-Western direction, the Scandinavian drift
must already have Jost a certain portion of its material by the mix-
ture of the debris of its own moraine with that of other sources;
2d. It must have suffered further loss by mixing with the moraine

1) Bull. Soc. paléontolog. Bruxelles p. 36. (Séance du 5 Septembre 1858).

2) Prodrome d'une description géologique de la Belgique. Bruxelles et Liége.
1868, p. 237.

3) Les anciens dépôts de transport de la Meuse. Ann. Soc. géol. de Belgique
XIV. 1886—87. Mém. p. 102.

4) Note sur les roches cristallines... Ann. Soc. géolog. de Belgique XVI. 1888—
89. Mém. p. 414, 439—441, 444,

6) Recherches sur les formations diluviennes du sud des Pays-Bas. Archives
Teyler (2) III, 6°™¢ partie. Haarlem 1891. Tableaux synoptiques I—V,

A. WICHMANN. “On fragments of rocks from the Ardennes found in the Diluvium
of the Netherlands North of the Rhine.”

Groningen
.

Leeuwarden

Amsterdam

EN Renswoude
Maar

@ sGravenhage

: <
a

Rotterdam

\} Oudenbosch

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Grinoid Limes. —.—.-- f A = \

9 Vieil Saint Re A

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Proceedings Royal Acad. Amsterdam. Vol. VIII.

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( 535 )

debris of the glacier from the Ardennes; 3"¢. The melting process
commenced soon after reaching its Southern limit. It was only during
its receding course that the Baltic ice-stream remained for some time
stationary, and in this period of inaction was formed the front
moraine extending from the South coast of the Zuiderzee to Grebbe
and further as shown by J. Lorré'), over Nimeguen to Crefeld.
The glacierformations, at present situated South of the Rhine, were
afterwards, i. e., during the inter-glacial period, exposed to the turbulent
waters of the Meuse, which, as has been stated above, rose 200 M.
above the level of the sea, at least between Namur and Dinant, —
proof of which is afforded by the high terrace. Although this terrace
slopes down towards the North, near Nimeguen, it still reaches a
height of between 50 and 100 M. + A.P.?). Owing to this action
of the Meuse, the erratics found in North-Brabant and Limburg are
generally smaller and more polished than those of the diluvial depo-
sits North of the Rhine. And lastly, a great portion of the glacier
formation has got hidden from view by the large alluvial tract of
the Rhine delta, which has been formed after the breach of this
river at Nimeguen and subsequent alterations of the level by dis-
locations.

Anyhow, it is entirely out of the question to admit that in the
beginning of the quarternary period the Meuse had its outlet into the
sea, a little North of Maastricht and formed there an estuary, —
a theory put forwards by M. Mourton*) and A. Ruror *). As J. Lorié
justly observes, not a single indication exists of the sea having
extended so far inland.

1) J. Lor. Le Rhin et le glacier scandinave quaternaire. Bull. Soc. belge de
Géologie XVI. 1902. Mém. p. 129—153. N. VIIL

4) Le. p. 181. The high terrace of the valley of the Meuse is generally
considered of pliocene formation, but the presence of Scandinavian erratics in
places situated farther North, e.g. Mook, Nimeguen, etc., proves that it must have
been formed after the receding of the Baltic ice-stream.

3) Les mers quaternaires en Belgique. Bull. Acad. roy. de Belgique (3) XXXIL.
Bruxelles 1896 p. 671—711. La faune marine du quaternaire moséen revelée par
les sondages de SrryBeeK (Meerle) et de Worret, près de Hoogsrrarren en Cam-
pine. |. c. (3) XXXII. 1897, p. 776—782.

4) Les origines du quaternaire de la Belgique. Bull. Soc. belge de Géologie. XI.
Bruxelles 1897, p. 117.

5) De hoogvenen en de gedaantewisseling der Maas in Noord-Brabant en Limburg.
Verhandel. K. Akad. van W. Tweede Sectie III]. No. 7. Amsterdam 1894, p. 10,

( 536 )

Chemistry. — “The boiling points of saturated solutions in binary
systems in which a compound occurs”. By Prof. H. W.
Baknuis RoozeBoom.

(Communicated in the meeting of November 25, 1905).

In a previous communication’) it has been ascertained what
branches in the. three-phase lines for solid, liquid and vapour may
occur in binary systems in which a solid compound appears, namely
for the three cases that:

a. the vapour pressure of the liquid mixtures diminishes gradually
from the component A to the component B;

6. liquid mixtures occur with a minimum pressure;

ec. liquid mixtures occur with a maximum pressure.

For the right understanding of the behaviour of such systems it
is particularly desirable to ascertain what is the order of the pheno-
mena which appear with different mixing proportions of the components |
when these, at a constant pressure, are brought from low to high
temperatures.

If those pressures are very low the mixtures, at a sufficiently
low temperature, are completely solid, and on elevation of the
temperature, they pass gradually and, at last, completely into vapour,
therefore simply a sublimation occurs.

Ifthe pressures are sufficiently high (in the case of components
which are not too volatile, 1 atm. is quite sufficient), the solid sub-
stances pass gradually and, at last, completely into liquid and these
liquids evaporate at still higher temperatures. In this case, fusion
takes place first and evaporation afterwards.

With moderate pressures, however, the melting and evaporation
phenomena partly coincide, namely when pressures are chosen which
occur on the three-phase lines of the components or the compound.

What cases may be distinguished when no solid compound appears
has been fully investigated previously, by me. *)

Particular attention has been called to the fact that the three-
phase line of the component B may be sometimes intersected twice
at the same pressure, which is possible when this line exhibits the
branches Ia and Ib, described in the previous communication. (See
line BD in fig. 1 and 6). In such a case two separate boiling

1) These Proc. VIII, p. 455. I learned that Dr. Sarrs had also come to the
conclusion that the minimum on the three-phase line did not coincide with
point Tak.

2) Heterogene Gleichgewichte. Heft 2. p. 338, et seq.

(537 )

points of solutions saturated with solid B oceur, one on branch 1)
and another on branch Ja. At the last point, boiling does not take
place on heating but on cooling. The ¢, «-figures at a constant
pressure have been deduced by me, and the phenomena, in solutions
of salts in water and of sulphur in carbon disulphide, have been
demonstrated by Smits and pe Kock.

The figures 1, 3, 5, 6 show at once that this same case may

also occur in solutions saturated with a compound of the two com-
ponents as soon as their three-phase line shows branch 14 as well
as 1a. Examples of two boiling points of the saturated solution have
not thus far been noticed in binary compounds although they should
be far from rare.
-In compounds where, among the saturated solutions, there is
present one with a minimum pressure (Fig. 3), a second boiling
point of the saturated solution might occur with solutions either
richer in A or in B; in fact a third boiling point at the side of
the solution richer in B would be possible if the point D in fig. 3
were situated so low that, at the same pressure, the branches D7’,
TT, and TH could be intersected in succession. The saturated
solution would then in succession first disappear, then reappear to
finally disappear once more. Examples belonging to this case have
thus far not been sufficiently studied.

If branch 3 of the three-phase line exists for the solutions richer
in B (GD in Fig. 1 and 6, GH in Fig. 3 and 5), then if this
line is crossed, there occurs at a constant pressure a boiling point
of the saturated solution of a different nature from that on branch 1.
The ¢, z-figure of such a case is quite analogous to that derived by
me *) for saturated solutions of the component A whose three-phase
line in Fig. 1, 3, 5 always indicates branch 3. On boiling the solution
saturated with A the following transformation takes place :

solid + liquid — vapour.

As solid and liquid now pass together into vapour in a definite
proportion, it now depends on the quantity of those two phases
which of the two disappears at the boiling point. This case occurs
for instance on the three-phase line for ice in systems of water and
little volatile substances as salts, also on the three-phase line for
solid CO, in mixtures of CO, with less volatile substances such as
alcohol.

The same must now also serve for compounds’ in so far branch 3
occurs therein. Among the binary systems whose liquid-vapour pres-

1) Heter. Gleichg. IL. 341 et seq.

( 538)

sure always diminishes from A to B, the branch 3 has thus far only
been found with ICI, and ICI, as observed in the previous communi-
cation. From STORTENBEKER’s experiments, it may be deduced that for
ICI, the branch 3 extends from 34° at 100 mm. to 22°7 at 42 mm.,
for IC] from 22° at 24 mM. to 8’ at 11 mM. The peculiar boiling
phenomenon is, therefore, only possible between these temperatures
and pressures, but has not been expressly stated in the solutions
saturated with IC], or ICL.

In binary systems in which a liquid with a minimum pressure
occurs on the three-phase line of the compound, branch 38 must
always appear as shown in fig. 3 or 5. Among the examples cited
in the previous communication, there are sure to be found some
where the simultaneous boiling of the solid phase and the solution
may take place at 1 atm. pressure.

Another kind of boiling-phenomenon may, finally, take place on
branch 2 of the three-phase line of a compound. This branch cannot
occur with the components, for the peculiarity of the branch consists
in this that the saturated solution contains an excess of the compo-
nent B, whilst the saturated vapour contains an excess of A; the
compound is, therefore, the phase whose composition is situated
between those of the two others. This is, of course, only possible
with a compound and not with one of the components.

According to Fig. 1, 3, 5, 6 of the previous communication branch
2 must oceur with all compounds where coexisting liquids with an
excess of B are possible, for it commences immediately at the
melting point.

Now, this is possible with a number of hydrated salts which,
below their melting point, yield saturated solutions with excess of
salt; but the appertaining pressures are then generally so small that
the boiling phenomenon cannot be readily observed. In the case of
salt-hydrates which occur at a higher temperature so that the equi-
librium-pressure on their three-phase line might amount to | atm.,
the solutions richer in salt seem to be very rare and no example is
known to me. :

An example is, however, known if H,O is replaced by NH,. With
the compound NH, Br.3NH,, branch 2 appears and the pressures
are even greater than 1 atm. In this case the boiling phenomenon
has been observed by me.

Branch 2 has, however, been met repeatedly in my previous
researches on gas-hydrates where water is then the component 5. If
we now take those hydrates near solutions with more water the

( 539 )

vapour generally contains but little water, and we are dealing with
branch 2.

The conversion now taking place with heat supply at a constant
pressure is:

solid — liquid + vapour.

In all those cases it is, therefore, not the liquid which boils but
the compound. The gas is very plainly seen to emanate from the
erystals lying in the liquid, whilst the latter does not diminish but
increases. The phenomenon has been very plainly observed with the
two hydrates of HCl and of H Br and with those of SO, and CI,
With the last two and with HCLH,O it could be observed at 1 atm.
pressure.

It must also exist with ICl but limited between 27° at 39 mm.,
and 22° at 24 mm., much more plainly with IC], where it may
appear between the melting point 101° at 16 atm. and 34° at 100 mm.
Between this a three-phase pressure of 760 mm. occurs at 64°, and
at the said temperature it may, therefore, be observed in an open
apparatus. Solid ICI, breaks up into a liquid with 63 and into a
vapour with 89 atom-percent of chlorine.

That similar phenomena may also appear in compounds which are
very stable at a lower temperature, has recently been demonstrated
by Aten in the case of Bi,S,. This sulphide breaks up at 760° into
a liquid containing 55 atom-percent of S and a vapour consisting
almost exclusively of S. Therefore, the actual melting point of the
sulphide cannot be determined at 1 atm. pressure. A similar behaviour
may be expected of many compounds having a melting point situated
much higher than the boiling point of one of its components, such
as in the case of oxides, sulphides, phosphides ete.

We must point out another peculiarity which distinguishes the
boiling phenomena on branch 2 from those on branches 1 and 3.
The liquids and vapours belonging to the latter are both either richer
in A or richer in B than the compound : consequently the boiling
phenomena concerned are observed in systems consisting of the com-
pound with a smaller or larger excess of one of the components.
On branch 2 however the vapour is richer in A and the liquid
richer in B, therefore the boiling phenomenon can occur in mixtures
of the compound with A as well as with B. In the first case such
a system, below the boiling point at the existing pressure, consists
of compound + vapour and the liquid appears only at the boiling
point, in the second case, the system below the boiling point eon-
sists of compound + liquid and the vapour appears at the boiling

(540 )

point. In the particular case that the compound was perfectly pure,
liquid and vapour should appear both together at the boiling point.

This may be made plain by the example of TCI. The whole
i, a-figure at 1 atm. is schematically represented by fig. 7.

CL

Ww ial hd
Breed. Fig. 8.

in which ¢, represents the temperature (64°) in question. In the different
regions G represents vapour and £ liquid. The further parts of the
figure are entirely dominated in their relative situation by that of
the three-phase lines. On this entirely depends which branches of a
particular three-phase line will be intersected at the same pressure.
In fig. 1 (previous communication) a simultaneous intersection of the
branches Ia and Id is only possible on the three-phase line of the
compound. If, however, as with [Cl,, the melting point / lies at a
high pressure, a simultaneous intersection of 15 with 2 or 3 is
possible. This is why in Fig. 7, besides the boiling point ¢, on branch
2, ¢, also occurs as boiling point on branch 15.

The pressure of 1 atm. is also higher for I Cl or I than their
three-phase line, consequently for these compositions, melting and
boiling phenomena occur quite separately and the melting point lines
of IC] and I run quite below the boiling point line.

If we take a pressure somewhat lower than 100 mm. we obtain
a ¢,w-figure 8. For ICl, we now have again ¢, as boiling point
on branch If and ¢, as boiling point on branch 3. For I Cl, melting
and boiling are still quite distinct but at a pressure below 100 mm,

(541 )

the three-phase line for solid iodine is intersected both on branch
15 and Ja and therefore the complication in the figure occurs at
the side of the iodine.

Still greater complications may appear when according to Fig. 3
(previous communication) there exist liquids with a minimum pressure
and when consequently the branches 15, fa and 15 can also appear
at the side of the liquids richer in B, whose intersection at an equal
pressure may coincide eventually with those of branch 2 or branch
3. When such systems have been more closely investigated it will
not prove difficult to give detailed f, z-figures for the same.

Chemistry. — “The reduction of acraldehyde and some derivatives
of s. divinyl glycol (3.4 dihydroxy 1.5 hevadiene)’. By Prof.
7
P. van Rompurcu and W. van. Dorssen.

(Communicated in the Meeting of November 25, 1905)

The reduction of acraldehyde (acroleine) with sodium amalgam *)
as well as with zine and hydrochloric acid *) has been studied by
LINNEMANN, who states that he has obtained in the first case propyl
and isopropyl alcohol, in the second ease isopropyl and allyl alcohol,
also a substance called acropinacone of the composition C,H,,O,, or
rather a product of non-constant boiling point, of which the fractions
boiling between 160°—170° and 170°—180° gave, on analysis, values
which led to this formula.

Cravs ®) could not confirm the results of Linnemann as regards the
formation of sopropyl alcohol in the reduction with zine and hydro-
chloric acid.

GRINER *) has also repeated LINNEMANN’s experiments with the object
of preparing acropinacone (divinylglycol) but only obtained very small
quantities of a liquid without constant boiling point which bore no
resemblance to the glycol which, however, was obtained by him
in fairly large quantity by reduction of acraldehyde in acetie acid
solution with a copper-zine couple. The other products of the reaction
have not been further described by the author.

If we consider the formula of acraldehyde in connection with the

1) Ann. d. Chem. u. Pharm. 125 (1863) S. 315.
2) Ibid Suppl. Il (1864—1865) S. 257.

3) B. B. IIL (1870) S. 404.

4) Ann, d. Phys, et Chim. [6] 26 (1892). p. 369.

( 542)

views of Trier on the addition of hydrogen to conjugated systems
of unsaturated compounds, then on reducing

CH, CH,
| |
CH we might expect CH ,
| 49 || pOH
C C
NH SH

an unsaturated aleohol which, however, by intramolecular atomic
RNA

shifting would be converted into ne , propylaldehyde.
H

On further reduction this would form propyl alcohol, a substance
which actually occurs among the products of the reduction.

Up to the present, propylaldehyde has not been found among the
substances formed in the reduction of acraldehyde.

We have, however, succeeded in showing that, although no free
propylaldehyde may be present, a derivative of this substance is
formed under certain conditions so that the intermediate formation of
the said aldehyde is not at all improbable.

First of all the reduction with zine and hydrochloric acid in ethereal
solution according to LiNNEMANN has been studied, but we succeeded
no more than GRrINER in isolating a well defined product — besides
allyl aleohol and perhaps smaller quantities of propyl! alcohol;
generally, the substance obtained, which boiled between 158°—164°,
contained much chlorine.

If, however, we allow zine dust to act on a mixture of acraldehyde
and glacial acetic acid ') then, in addition to allyl and propyl alcohol,
a neutral liquid is formed (b.p. 170 ) from which, after fractionating
in vacuo, a product may be obtained boiling between 59°5—60° at
15 mm. The analysis and the vapour density lead to the formula
CHO

The compound is not decomposed by potassium hydroxide ; neither
sodium nor phosphorus pentachloride have any action; it cannot be
benzoylated with benzoyl chloride and pyridine. This sufficiently
proves the absence of OH groups.

The said properties, however, render it very probable that the
substance is an ether. By dilute acids it is hydrolysed although but
slowly. An aldehyde-like odour appears but, as the reaction proceeds,
the mass becomes so dark with formation of brownish-black resinous

1) The action of various reducing agents on acraldehyde has been studied. The
results will be published in due course.

( 543 )

produets that we have not, as yet, succeeded in isolating well-defined
compounds.

Bromine is readily absorbed by it and that in a quantity which
points to the presence of two double bonds. If we work with a
solution of carbon tetrachloride at a low temperature, but little hydrogen
bromide is formed.

From a substance of the formula C,H,,O, a great many isomers
are, of course, possible. We cannot enter here into a description of
the different experiments made in order to elucidate the structure of
the product obtained, but we may state that we have finally succeeded
by means of a synthesis, which leaves no doubt whatever.

If, on s.-divinyl glycol which, thanks to the beautiful researches
of GRINER, may be readily prepared, propylaldehyde is allowed to
act for 6 days at 90°, a substance is obtained identical with the one
described above.

(Sp. gr. at 12° of the synthetic product 0.9392
ee ee ee OLS Al Gs 0.9416
Refraction at 12° of the synthetic „ 1.4434
EN OL 1.4430.)

As to the synthetic product, propylidene s. divinylethylene ether,
must be given the formula :

CH,

|
CH

EEA
CHO,

| CH—CH,—CH
CH—0”

On

|

CH,
the original must also be considered as a derivative of propylaldehyde.
It is, of course, possible that there might be formed at first an
analogous acraldehyde derivative, which afterwards got converted
into a propylaldehyde derivative, but considering the comparative
difficulty with which the vinyl group combines with hydrogen, this
looks less probable.

As one of us (v. R.) explained many years ago, s. divinylglycol
ov 3.4 dihydroxy 1.5 bexadiene would form an excellent eer for the
preparation of the hydrocarbon CH, = CH — CH = CH — CH = CH,,
otherwise hexatriene 1.3.5.

Different methods which we have tried have not led to the desired

38

Proceedings Royal Acad. Amsterdam. Vol. VIII.

(544)

end. At last we think we have succeeded by making use of the
diformate of s.-divinyl glycol, a compound which may be prepared
by heating this glycol for a short time with formic acid.

By fractionating in vacuo, the diformate is obtained as a colourless
liquid which at a pressure of 20 mm. boils at 109° and has a sp. gr.
of 1.0747 at 11°. A determination of the formic acid (by saponifica-
tion) gave the amount required for diformate.

In a communication about to follow, the hydrocarbon prepared
from the diformate and the method of its preparation will be fully
described.

University Org. Chem. Lab. Utrecht.

Chemistry. — “The occurrence of B-amyrine acetate in some varieties
of gutta percha’. By Prof. P. van Rompuren and N. H. Conen,

(Communicated in the meeting of November 25, 1905).

Last year, a compound melting at 234° was found by one of
us (v. R.) in the gutta percha of Payena Leerii’) of which it could
be stated that it is nof identical with lupeol cinnamate, which occurs
in many varieties of gutta percha; the quantity was then too small
for further research. Since then a little more of that product was
prepared so that it could be proved that on treatment with alcoholic
potash it yields acetic acid and an alcohol melting at 195°,

In these Proc. of June 25, 1905 p. 137 it was stated that the
same product has been found by one of us (C.) in the “djelutung”
derived from the juice of varieties of Dyera. The identity was shown
by a comparison of the melting points and by melting point deter-
minations of mixtures of the two substances.

A sufficient quantity was now at disposal to determine the nature
of the compound.

In the first place, the substance was recrystallised a few times and
finally obtained in beautiful, long, hard needles which melted at
235° (corr. m. p. 240°—-241°).

On analysis (combustion with lead chromate) the following results
were obtained :

Calculated for C,,H,,O,
C 81.96, 82.08. C 82.06
H 11.24, 11.27. EO APA

The compound was found to be dextrorotatory. For the specifie
rotatory power in a chloroform solution |[@|p = 81°.1 was found.

As stated above, the substance melting at 285° when boiled with

1) B. B. 37 (1904) S. 3443.

(545 )

alcoholic potash yields acetic acid, which was converted into the silver
salt. A silver determination gave 64.2 °/,, theory 64.67 °/,.
The alcohol formed on saponification was a colorless substance

erystallising in long, thin needles and melting at 195° (corr. m. p.
197°—197.°5).

The elementary analysis (with lead chromate) gave:

Calculated for C,,H,,O.
C 84.27, 84.12, 84.32 84.50
Feld OW, AO Aa go 11.76

This alcohol has also a dextrorotatory power. In a chloroform solution
it has [@¢]p = 88°, and in a benzene solution [a@]p = 98°.

On treatment with benzoyl chloride and pyridine, the alcohol readily
yields a benzoate which erystallises in beautiful rectangular little
plates and melts at 230° (corr. m.p. 234°—235°).

After perusing the literature, it now appeared that the alcohol
melting at 195° is identical with B-amyrine which occurs in elemi
resin and has been investigated and described with great care by
VESTERBERG '). Not only do the melting points of the alcohol obtained
from Payena Leerii-gutta percha and “djelutung”, of the acetate
and the benzoate agree perfectly with the melting points determined
by VesrTERBERG for g-amyrine and its acetate and benzoate, but in
addition the values found for the specific rotatory power of the alcohol
from “djelutung” and its acetate differ so little from those which he
states for B-amyrine and its acetate *) that the difference may be safely
ascribed to experimental errors caused by working with dilute solutions.

B-Amyrine has also been found afterwards by Tscntrcn *) in the
resin of Protium Carana. It is stated, however, to differ from the
common g-amyrine by being optically inactive, which seems some-
what strange. It should be remarked, however, that the cinnamic
ester of lupeol described by Tscrrrern *) about the same period under
the name of erystal-albane was also declared to be inactive, although
we have found this substance having a decided dextrorotatory power.
A further investigation is therefore a desideratum.

Marek °) has obtained from the milky juice of Asclepias syriaca a
substance melting at 232°—2338°, the melting point of which could
be raised by repeated crystallisation to 289°—240°. Its analysis led

1) B. B. 20 (1887) S. 1242; 23 (1890) S. 3196.
2) VesrerBere states for B-amyrine (in benzene) [z]p = 99°81.
for the acetate (in benzene) [2]p = 78°.6.
3) Arch. d. Pharm. 241 S. 149.
4) Ibid 241 S. 483.
5) Journ. prakt. Chem. Bd. GS (1903) S. 385 and 449,
38*

( 546 )

to the formula C,,H,,0, and on saponification it yielded acetie acid
and an alcohol melting at 192°—193° having the formula C,,H,,0.
The benzoate from the alcohol melted at 229°—230°.

It can hardly be doubted that Marek has been working with the
acetic ester of g-amyrine. Fortunately, he has not given a name to
the product isolated by him, and hence, has not unnecessarily
increased the already existing confusion.

Undoubtedly, the enormous number of substances said to be obtained
from different resins and milky juices will, on closer investigation,
be reduced to a more modest number and it will often be shown
that pure substances described by different names are one and the
same, but could not be identified owing to incomplete description.
In other cases, names may have been given wrongly to mixtures or
impure substances.

Although it may seem superfluous, it is as well to again point
out how necessary it is, when investigating a natural product, to
purify the components as completely as possible, to fully describe
the properties and particularly to introduce no new names unless
one feels certain of really dealing with a new product.

A short time ago, Tscurrcn *) communicated the results of an
investigation of the components of Balata. From this was isolated a
crystallised substance called «-balalbane melting at 231°, the analysis
of which led to the formula C,,H,,O,

(found C 81.19 H 10.38. calculated C 81.82 H 10.64).

No acids were found by TscuircH on saponification with aleoholie
potash as he only looked for crystallised acids *). This made one of
us (C.) think that Balata might perhaps also contain acetic esters
and that the «-balalbane might be identical with g-amyrine acetate.

It was not difficult to isolate by Tscurrcn’s method the product
melting at 231°.

By repeated recrystallisation from acetone, the melting point rose
to 235°. On saponification, acetic acid was obtained, also an alcohol
melting at 195°. Ester and alcohol mixed, respectively, with g-amyrine
acetate and g-amyrine gave no lowering of the melting point, so
that a-balalbane is nothing else but g-amyrine acetate; the name
a-balalbane may, therefore, be struck out.

University Org. Chem. Lab., Utrecht.

1) Ann. d. Pharm. 243 (1905) S. 358.

2) Tsemrem comes to the conclusion that there exist gutta perchas which yield
no cinnamie acid on treatment with alcoholic potash, but | have demonstrated
this fact previously (B. B, 37 S. 3434), (v. R.).

eer Re

(547 )

Mathematics. — “The quotient of two successive Bessel Functions.”
By Prof. W. Kaprnyn.

If 7’+(z) and /%z) represent two successive Bessel Functions of
the first kind, the quotient may be expanded as follows:
Vian)
T(z)
Of course this equation holds for all values of z within a circle
whose radius is equal to the modulus of the first root of the
equation /*(z) = 0, zero excepted. Eurer and Jacot have determined
the first coefficients of this expansion; we wish to determine the
general coefficient.
Starting from the known development 8
RE (Ean rz Ks
Md AE

=fetfetfrAe +t...

a2

kad

2(v-+3) — etc.

2(p-+ 2) —

and putting
—w 2 p= Ap
the question reduces to the determination of the general coefficient
in the following equation:
v
a, +e
a, + ete.

Ps
Let — stand for the approximating fractions of the continued

“on

fraction in the first member, and let
Oan =v, + vy, e+ vy, ve? +... 4+ pp ar
Qan =H, teu, e+... + po
Oren == 7 = ita Sl ae nee Ani
Qo oe 205 Se ae, i Se we? Es ty et!

= fie — fix? + ft? — ete.

Qe == Het... bar
Ci — & =e &, © == sees = Es vs

where
n nt
Ps mi + 1 s= ay
when 7” even, and
eed n+1
n= OS == er

when n is odd, then we find

( 548 )

< 2
art! a,” ar! no 0 CRE Anti Frnt — (— 1)h er an on Te AE
Ni 02 tno Op_-9- . . 90

Rey 4n—1 0 Oe 00)

—1

n
In this equation / stands for — — 1 if m is even and for

when n is odd. If now we replace a, by 2(»-+ p)= 2b, we
obtain the following results. Firstly

gn lbnkibjnel Da | Bn es + Bat Ont Supt =

9
2 ye:
Ans el ta! EN
7.) %,) Oe 55 €
' ' ' '
An Xn Un : En
Ln 2 2 2 2
(ji) mo ve (YE
( ) Ae UB ss ne . 0 ( )
2 2 2
Ane eo oes 0
Zn Kn — 1 0 Me ee)

if 2 is an even number, and secondly

Q2n+ 1 bint! br+l S00 Byte bn43 Fh One bin
2 2

' ' ' !
a %, t EN

no iy l

a)

( 549 )

if 2 is an odd number, where
(2n — p— 1) (2n — p — 2)... (2n — 2p)

Àp = p! ET bn —pt-2.…. Dan— pi

' (2n — p — 2) (Qn — p — 3)... (2n — 2p — 1)

Ap = pl bn —p +2... b2n—p—2
. (2n — p — 3) (2n — p — 4)... (2n — 2p — 2)

Ep =S p! : : bn—p +2... bon—p—s

, ie APS)

Ep p!

en
(2n — p — 1) (2n — p—2)...(2n — 2p)

A = a bre en |
(2n — p — 2) (2n — p — 3)... (2n — 2p — 1)

B a by +1... 52n—p—2
(2n — p — 3) (2n — p — 4)... (2n — 2p — 2)

Up = ; Oy noe ban —p—3

Pp:
(n —p +1) (n —p)...(n — 2p + 2)
= 7 bo +-1... On—p+1:
Pp:
It is of importance to remark that
Mees ii tn —2 = (n—1) bp —1, Ons — ete:

and that the determinants in the second members of the equations
(I) and (II) after the substitution b,=r + p, are respectively poly-

3 n(n — 2) (n — 1)?
nomia of degrees i and

in v.

Meteorology. — “On frequency curves of barometric heights.” By
Dr. J. P. vAN DER STOK.

1. The records of barometric heights, corrected for temperature,
observed at Helder three times a day during the years August 1843
to July 1904, have been chosen as an appropriate material for this
inquiry into the nature of barometric frequency curves. The number
of observations for each month amounts to: |

January 5673 July 5673
February 5169 August 5766
March 5646 September 5560
April 5490 October 5766
May 5673 November 5580
June 5490 December 5766

Total 67252

( 550 )

40° OE =

So ae

TABLE I. Frequencies in 10.000 of deviations of barometric heights; positive and negative being taken together.
Nov, May
£ Jan. | Febr. March, Apr. | May | June July | Aug. | Sept. | Oct. | Nov. | Dec, — PE a
Febroy Seph, Aug.
0 — 0.5 mm. | 381 420 AAT 493 612 705 767 704 559 419 357 377 384 472 697
0.5— 1.5 680 837 798 | 1028 | 1176 | 1486 | 1493 | 1405 | 1410 865 726 755 749 950 1390
1.5— 2.5 712 779 821 | 1040 | 1170 | 1367 | 1456 | 1369 | 1048 861 750 706 737 943 1340
2.5— 3.5 735 752 841 | 4010 | 14164 | 1191 | 1285 | 1292 | 1000 837 737 680 726 922 1233
3.5— 4.5 703 799 826 893 | 1020 | 1140 | 1124 | 1156 950 771 684 662 | 712 860 1102
4,5— 5.5 679 775 702 907 952 933 998 | 1016 876 775 686 724 716 815 975
5.5— 6.5 660 683 754 825 809 804 807 806 783 801 715 660 | 679 790 806
6.5— 7.5 647 | 615 | 637 | 733 | 767 | 746 | 602 | 651 | 713 | 728 | 655 | 601 | 630 703 634
7.5— 8.5 636 605 606 633 607 572 428 509 684 638 668 637, 637 640 529
5 564 | 564 | 579 | 533 | 486 | 402 | 3057] 393 | 550 | 582 | 610 | “553 | 573 561 356
5 528 493) || 532.1. 45971) SDA 26 233) 2BOP |) A685) S72 aie BS Ten ade 19 595 508 279
5 498 | 425 | 459 | 362 | 964 | 477 | 479 | 466 | 354 | 452 | 546 || 478 | 485 406 194
5 421 | 353 | 406 | 281°} 199 | 105 | 128 | 444 | 983 | 347 | 460 | 445 | 420 329 136
5 338 | 342 | 344 | 225 | 12 66 78 1B) CARY | Baik | Giese 280 86
967 | 302 | 249, 166 73 4A 42 LESSORS OTE A GHDIE Wy ep tat iol 199 51
243 270 235 102 59 32 28 28 88 226 249 307 267 163 37
238 213 238 91 60 22 22 12 50 133 195 268 229 128 | 99
995 | 154 | 452 59 32 9 13 9 36) AAB 5st ZOL ES ot 16
188 | 127 99 42 12 3 7 8 35 67 | 445 | 447 | 444 6 8
129 | 146 84 37 10 3 5 4 29 439) Ado PSE 90 48 5
94 80 a) | OB 7 3 5 17 53 86 | 941 88 38 4
76 64 29 17 4 4 8 | 30 620 70 68 Ome ts 28
67 56 42 12 3 1 10 16 ZA | 60 56 20 1
69 35 16 8 6 17 20 RDS AG 49 |
59 19 18 5 4 | 40 16 | 28 31 9
42 93 13 il are] 4 Ad) allo 27 29 9
29 18 u D) Loa 2 10 20 19 5
29 22 6 2 B © dn By 21 5
17 14 sletje al 2 2 AT 13 45) | 4
8 u 6 | 4 2 2 40 | 40 10 | oh |
7 14 9 | Zn 6 12 9 3
| 40 u 55 | 2 SN EO Adee |
6 7 4 | DES pol eG hell
h 3 | Dl ES 3
1 1 | 2 Ll
1 ( | dele
35.5—36.5 4 0 | Se
5.5 87.5 3 0 0 1
8.5 1 0 0 0
5—39.5 4 1 5 9

Dn odes

Differences, W-—b, between observed frequencies and frequ. calculated according to exponential law ;

in 10.000 for every month, in 40.000 for the seasons.

TABLE II.

Sums.

ay 2

=

Es

28 ERE5E

re at see

ST ML eee ee AAA VE AE me
zu

5 “qaaata REE Reade "sasasRO Tes
5 = NA S = Ss

Sd | |

< Bain ae eee: CEG ee
= TO Om rN HASAN BRASS SSS AN =
a AAN NE Ee
s ee ee DID =O OO =D NE A
2 SIS SS Ue OSI CANET =a =—s= ss
Zi
i mint el Aa ln
OOS AF OG eer =o AMDOANMONONIeYo—s
ISIS ICONS CRISES EGTA ty COIN OD GN OD isd

bc Mel ne zie NA AL acd stale talbal

Pe 5

jn =

©

ae |

eb

=)

<
ee
=)
BUHL ++i EL H+
® zt > cS

i=} : =

S

and

ue
a
< nn
g |asseegsarssnageestnengegsenten
a
= IId tt a al
nce Mr AAS ONLSWALAHSHAWDNWIAN
rey SSD St GN = OD en TON == =
o
EI IEN IE AE tI
: SINE ERSORTEDNS IEEE se
5 OUD Tt OE 0) OO 1D ON mn CO) GI
Tr EE u ee eN
Ee CCS: AO ac
wy

TABLE III. Skew-differences, P—N, of positive and negative deviations.

| | | Sums.
e Jan. | Febr. | March | Apr. May | June July | Aug. | Sept. | Oct. Nov. Dec. Nov. Mech ADE May
| ile. Sept.—Oct. Aug.
0.5— 1.5 6 al 31 0 16 80 43 1|— 46 23 12 15 54 7 140
4.5— 2.5 LONS 55 |. 406 18 | 4139 | 144 77 48 71 22 62 91 280 318
2.5— 3.5 25 56 81 | 4199 54 | 415 79 | 46%) 68 37 69 60 210 308 412
3.5— 4.5 93 75 16} 435 4h | 414 75 92 90 ef || 150 20 238 302 325
k5— 5.5 GaP PON A AAT Ore zor 136 50 86 57 86 | 60| $30 332 345
Ae Gos VEY OR TON et 78 | 4380 496 | 85 83) 94 86 | 400 368 398
Bras kde HM || flag 37 48 74 97 | 95 438 | bi 45 | 356 395 256
1.5— 8.5 | 402 83 16 | 443 Al 4h 4A 138 94 60 89 334 4AA 126
8.5— 9.5 198 108 | 43 93 26 | — 20 | 5 19'| 44%) 62) 404] 97 437 | 249, 30
9 5 74 dd 40 15 19 | — 40 | — 31 —28 | 38 40) 409) 408) 368 173 — 50
a Pe 288) 5 | == 5619 OV ASN Ir ADE LORE EON PARA zene | naan 98 BAN:
5 77 25 OW || ee As |) Ul Ns EL | = A | 3 3} 442 47 O61) ath — 194
50 32 17 25 | Bl SEE Ope 7 93 | 57 232 40 — 145
AB 19 OTA AOS OND 35 OON SIE 103 3 — 116
ee Aaa late 3 aen (= 180i) 7308 ZONE eN tenis E33 BOs Made BE ang = 89
5 4h | A OYA es BB} | eS) | = LOS EO EG Gy) es EY En 20 | — 100 — ay
an) || 5 2 OM 23 SONS ABS SOR S36 | — 938) |= — "37 23 | — | — 99 =! 50
BN 951) ONE SRAD 3 7 8 | — 31 | — 43 | — 39 | — 41 | — 107 | — 119 — 30
BD QO ZON AO SN NN NEN ZON LONG an 408 — oy
Dee AN) Si I) — 3/— 5/]—17| — 33 | — 26 | — 27 | — 107 | — 108 a AIG
| oe SOS = Oey aes Avs FS a) Sie S| LOONT =
he [24d 190 | 96 youn 3 — 1/—10|— 146} — 31 | — 38) — 442 | — 64 eN
da EN EEE | | | redder SS AS SA Ei
Hate Ee | ANA SAN Eel EE LE as,
En | 999) aguas 07 ET ee as i es a) ee O7 ety
25,5- 6.5 | —27|—148|/—44|)— 2 — &| — 9 | — 40) SE 75] = 49
DENG OTe OOM ON Galt | ln Os VA EB
Dr Dsl ly es tk | SSO =d ES Et
98.5—29.5 |— 8|—11|/— 6/— 4 — 2|— 2|—10|—10 | — 39| — 44
DONS 3050 Ne | HE Pe 5 967) 2. 44
30.5—31.5 | — 40) —41;— 3 | PN Se eh eed
ARE ee ee | NR JO | Se ag
32.5—33.5 |= 4] — 3 | | | Oil Spo
B ti dl) | — Oi 2
34053505 | — i A | | = aie 3
ONIN — — 3 | — 7
36.5—37.5 | — 3 0 | | 0|/— 3
3.75—38 .5 — 1 0 | | | 0) — 4
38.5 enz. LA — 14, | | | | | arn Rik 7 | |

In registering the observations the decimals have been omitted, so
that the number of occurrences corresponding with a height of P
mm. ineludes all values between P + 0.5 and P — 0.5 mm.

Owing to this simplification the amount of labour is less than
would appear from the great number of data. The next work to do
was to multiply the frequency numbers with a factor such that the
total number for each month amounted to 10.000. The frequencies
thus obtained correspond with expressions for the probability of
occurrence expressed in 10.000" parts of unity. Then the average
height was calculated and, by means of simple, linear interpolation
the whole curve shifted in such a manner that the new frequencies
correspond with deviations from the average value expressed in
multiples of whole numbers. This has been done not only with a view
of abridging the computations of the moments of the second and
third order but principally in order to obtain an evaluation of the
skewness of the curves, which may be defined as the inequality of
frequency for equal positive and negative deviations from the arith-
metical mean. If of such a series of data the frequencies corresponding
with equal deviations are taken together, no account being taken
of their sign, the skewness is eliminated, and the numbers obtained
in this way may be considered as belonging to a symmetrical curve
(Table I).

For this curve we calculate the factor of precision (stability) and
investigate in how far the actual curve agrees or disagrees with the
curve of the normal exponential law (Table I).

As has been mentioned above, the inequalities of frequencies for
equal deviations of opposite sign have been taken as a measure of
the skewness.

Tables I—III show, separately for each month, the sums and differ-
ences thus formed. The numbers of Table I added to those of Table II
will give twice the number of frequencies corresponding to positive
deviations, their differences being twice that corresponding to negative
deviations. The values given for Winter, Summer and Spring-
Autumn are obtained by taking together the corresponding numbers
in the same Tables; consequently they are not quite identical with
the numbers which would have been obtained if the frequencies for
these seasons had been calculated from the absolute heights, instead
of, as has been done here, from the deviations ; in the latter the
annual variation has been left out of consideration. The annual varia-
tion, however, being very small, this will not influence the results
to an appreciable degree.

2. Table IV shows the results of the treatment of the frequencies
given in Table I, as indicated. If the deviation from the arith-
metical mean is denoted by «, then:

Tey 1 1 2 M?
Mal / ke REE oat rs ‚Ws 2 = .
n—l n My/2 a oe

TABLE IV.
M 3 eae eas x

| | | =:
Jan. 10.261 mM. | 8.272 mM, | 0.0689 | 0.0682 | 3.081
Febr. 9.522 | 7.597 | 0.0743 | 0.0743 | 3.441
Mrch. 8.969 | 7.194 | 0.0788 | 0.0784 | 3.409
Apr. 7.280 | 5.864 0.0971 | 0.0962 | 3.083
May 6.218 5.022 | 0.1136 | 0.419% | 3.067
June 5.301 | 4.392 | 0.1312 | 0.4305 | 3.442
July || 5.276 | 4.169 | 0.1340 | 0.4354 | 3.204
Aug. || 5.374 | 4.300 | 0.1316 | 0.1312 | 3.495
Sept. 6.972 | 5,602 | 0.1014 | 0.4007 | 3 098
Oct. 8.372 | 6.832 | 0.0845 | 0.0826 | 3.003
Nov. 9.490 9.006 | 0.0745 | 0.0725 | 2.974
Dec. || 10:085 8.173 \_0.0701 | 0.0690 | 3.045

From this summary it appears that the frequency curve of baro-
metric heights, as derived from observations made at Helder, shows
systematic departures from the normal curve corresponding to the
exponential law. For all months (except February and July) 4 is
greater than /’; in February these factors are equal and the curve
is nearly a normal one, in July 4/ >>.

In agreement with this result the calculated value of a is always
(except in the two months mentioned) less than its true value; the
departures from the normal law are greatest in winter, smallest in
summer time,

It may be noticed that the departures from the normal curve,
given in table Il, are generally of an opposite sign to those which
are found in the great majority of series of errors: whereas for
the latter the rule holds that small deviations occur oftener than is
required by the normal Jaw (in which case 4 > h and 2 cale. > 2),

here the reverse obtains, the frequency of barometric heights showing
a deficit for small and a surplus for moderate deviations.

In an earlier paper (this volume p. 314) I have shown that, in
taking together series with different factors of steadiness, each series
occurring with equal subfrequency, we must expect to find too great
a number of small deviations.

From this follows the apparently somewhat paradoxical conclusion,
that a sum of frequency numbers as those of barometric deviations,
all showing negative differences for small deviations, may, when
taken together, lead to a resulting curve in which these differences
have vanished or even turned positive.

This conclusion is of some importance because an investigation
into the frequency of barometric heights, in which the different
months are not treated separately, may lead to normal curves (the
skewness being left out of account) whereas in fact no normal curve
exists and appears only as an artificial consequence of the combi-
nation of incomparable frequency numbers.

The exceptional behaviour of the months of February and July might
then be explained by assuming that the different series of barometric
curves corresponding with different winds (barometric windrose) are
more differentiated in these two months than in the other ones.

A second remark is that frequency numbers as given in Table I
capnot be accepted as a measure for the variability of the atmo-
spheric pressure in the course of a month, at least not if we adhere
to the conception of this variability as generally admitted.

On the one hand we have here to do with the superposition of
two kinds of variability, 1st the secular variability as shown by the
variability from year to year of monthly means and 2ed the vari-
ability from day to day, which might be called the interior variability
for the month in question ; it is the latter definition which corresponds
with the usual conception.

On the other hand, daily means or observations taken at fixed
hours are by no means to be regarded as being independent of
each other.

The questions, therefore, arise: bow can we separate the two kinds
of variability, and to what degree are daily mean values of baro-
metric observations to be taken as dependent upon each other in
the different months.

For a knowledge of the climate of a place the latter question is
of importance ; it might also be formulated thus : what is the average
duration of a barometric disturbance, a question which can hardly
be answered by means of direct investigation,

( 556 )

TABLE V.
en | En L. OER | I woe He L. WB
0— 0.5 sis | 496 | 4-19 | 145455 118 472 | — 2%
05—4.5 || 1025 996 | +29 | 415.5-16.5 125 Ee
15-25 || 1001 | 962 | +39 | 46.5-17.5 || 400 | 404 | — 4
2.5— 3.5 056 ys | + | 17.518.5 75 ri Ne eee,
5 4.5 || 888 | 875 | 443 | 185495 58 | = 7
4.5— 5.5 846 826 + 20 19.5—20.5 43 45 — 2
5.5— 6:5 756 7 | — 4 | 90.5225 33 Paes ee oa
6.5— 7.5 574 676 | — 2 | U.5—2.5 25 DER Say
7.5— 8.5 591 608 | —17 | 22.5—-93.5 21 16 | +4 5
8.5— 9.5 519 526 — 7 93.5—94.5 13 42 + 1
9.510 5 437 459 | —22 | 24.5—95.5 13 | DSS 26
10.5—11.5 363 384 | —2 | 25.5—26.5 10 biens
44.5—12.5 304 [| 322 | — 18 | 26.5—97.5 7 sold
12. 5—13.5 24h 268 | — 4 | 27.5—98.5 6 gE:
13. 514.5 aon | miesje Ssst et: 13 2

The first problem is identical with the calculation of the prob-
ability of an event a+, when a and 6 follow the normal law and
are independent of each other.

This problem of the superposition of two laws of errors has been
already treated by Busser’) and subsequently p'Ocaaxe *) gave a
general solution for the superposition of several groups of errors.

It appears that, if H be the factor of stability of the secular and
h, that of the interior variability, the resulting deviations also follow
the normal law, the new factor 4 being determined by:

From the values of given in Table IV and those of H calcu-
lated from monthly means we can, therefore, deduce that of A, :

1) Untersuchungen über die Walhrscheinlichkeit der Beobachtungsfehler. Astr.
Nachr. XV, 1838.

2) Sur la composition des lois d’erreurs de situation d'un point. G B, Acad.
sc. CXVIII, 1894.

( 557 )

Hh

= ee 8 eed on Ul
; V H? — }3 ”

By the following reasoning the second problem may also be easily
solved.

The total mean value for a given month, as calculated from 7
monthly means, must be the same as that deduced from MN cor-
responding daily means.

The mean error (incertitude) of the total mean is, as monthly
means may be considered to be independent of each other:

(ee M,

n(n—=l) Vn

For the mean incertitude deduced in the same manner from
observations made three times each day :

M

2

VN

too small a value would be found as these observations are certainly
not independent of each other; therefore, if the number of obser-
vations which, on the average, constitute an independent group be
called p, we must have:

M, END
NT
If we wish to express the average duration of a disturbance D
in numbers of days, we have, in our case:
i) loge N h? N
UE (Sin He In

(2)

Table VI shows the values of the interior variability 4, thus
calculated by means of form. (1) and the duration D of a barometric
disturbance.

It appears | from these results that, on the average, the duration
of a barometric disturbance at Helder is in:

Winter 6.90 days

Summer 4.89). = |.

Spring-Autumn 6.04 „
or in round numbers resp. 7, 6 and 5 days in winter, spring-
autumn and summer.

3. It would perhaps not be impossible, and it certainly must be

( 558 )

TABLE VI.

i eK he cel ERD

Jan. || 0.4441 | 0.0689 | 0.0787 | 7.52
| |

Febr. 0.1458 0.0743 | 0.0864 7:46

March|| 0.1682 | 0.0788 | 0.082 | 6.82
| 7

Apr. || 0.2105 | 0.0971 | 0.109% | 6.49

May 0 „1136 0.1226 | 4.46

Go
o
So

June 0.3181 0.1312 0.1440 5g
July 0.3392 0.1340 0.1459 | 4.92

Aug. 0.3330 0.1316 | 0.4432 | 5.00

Sept. 0.2350 | 0.1014 | 0.1123 5.74
Oct. 0.2113 0.0845 0.0926 5.12
Nov. 0.1892 0.0745 0.0810 | 4.81

Dec. 0.1419 0.0701 0.0806 7.82

|

the final aim in inquiries of this kind to come to a rational expres-
sion for the frequency of barometric deviations as a funetion of the
distance of centres of depressions and of their average depth and
extent but, even if we assume the most simple relations between
pressure and distance of the centrum, we must expect to find rather
complicated, exponential expressions, which can be treated only by
expansion into series. It is, therefore, desirable to summarize the
characteristics of the frequency curve in an empirical formula of
the form:
e H(A + Ba + Ca? + De? + Eet). . « « « (3)
The constants of this formula can be easily determined and, if we
succeed in establishing a rational expression, there will probably be
no difficulty in indicating their meteorological meaning.
The frequency curve, positive and negative deviations being taken
together (Table I), is then represented by the expression :
GF = PP (A Cot 4 Ex'),. .

which represents a symmetrical curve, and the formula for the
differences of Table III becomes:

Vo = Ze (Br = Dai). es EERE)

If, as in our ease, the deviations rz are departures from the arith-
metical mean,

( 559 )

i ive) ae
fz ars [2 =F 5 [ee de — SU
0

0 0

ao 0

[z= Citi (le tebe fre di OR (6)

0 0
For the determination of the constants of form. (4) we then have
the four relations:
C 132 HT
_ ==

A+

OH? | AH Va
26: 2.4 #
A+ oY Pe Hu,
44 80 1 85 B_ Mn, Ne
2H?" 4H Va
ae 4C ts AOE ee
2H?" A

Multiplying resp. by 1,—8, + 3 and—1 and adding, we find:
P= oH bo —e=0

Ou, du, 1
a= —— , ) = —_, ¢ = —_,
5 u V/a u, ur
or, because:
1 1 1
fy Wyn u, Dj’ Us AE Vz
le 3H? 3H ;
- SON Se eee (Sh)
ge h? h'

From this equation possible values for M can be derived, but not
in an advantageous manner as the quantities h, A and h" generally
are only slightly different.

In practice, i.e. if we come to expression (4) by expansion of a
theoretical formula, the problem will probably be less difficult, as
the constants H and A or H and / will not be independent of each
other, and it will be possible to reduce the four equations (7) to three
or two.

In this preliminary investigation we confine ourselves to the most
simple case that M= h which, as it will appear, leads to satisfactory
results.

Putting

we find:

39
Proceedings Royal Acad. Amsterdam. Vol. VIII.

( 560 )

Aix hie sk
Ca = 12K
Ein = — 4 nn ee)
The position of the points of intersection of the observed frequency
curve with that calculated by assuming the simple exponential law
to hold good (the points where in Table I] the numbers change their
sign) is determined by the equation :

(A + Ca? + Ka) Va —h=)0,

Oke:
gee Bae ——f oe a 5 (Lil)
h? 4,
0.525 1.651
«== 7 ° a, = - 7 5

In fact Table I] shows that there are no more than two well
defined points of intersection, which justifies the omission of higher
powers than the fourth in form. (4).

Tabel VII shows the values of the constants of (4) and the values
of « calculated with the help of form. (9) and (10).

It is evident that, if form. (4) and the values of its constants
determined in the way indicated give a good representation of the
observed facts, the values of the coefficient A must be nearly equal

TABLE VII.

A | | |

| Calculated, Observed.

|

Jan. | 37710 * | 381 10! 227107 | — 3610 | 7.62 | 23.96
Febr. | 419 420 | 0 | 0 7.07 22.99
March 438 | 447 | 142 5 35 | 6.66 | 20.95
Apr. | 532 | 493 310 — 4182 | 5.44 | 47 00
May | 620 61 |. 662 | — 456 | 4.62 | 14.53
June | 728 | 705 | 532 ee | 4.00 | 12.58
July | 779 767 | — 1581 | 1008 | 3.92 | 12.32
|
Aug. za | 704 588 | — 340 3.99 | 42.55
Sept. | 500 559 491 | — 168 5.48 | 16.28
Oct. | 444 19 940 | — 94 6.24 | 19.54
| | |
Nov. | 386 357 772 | — 143 7.05) | 22546
Dec. | 377 | 37 | . 372 aes | 7.49 | 93.55

ee ee

——

rae op Oe Geeta

( 561 )

to the frequencies corresponding with the deviations 0—0.5 mm,
as given in Table I, so that the greater or less degree of agreement
between these values may be taken as a criterion for the proposed
assumption M= h.

In order to show that this agreement is fairly satisfactory, the
observed frequencies between the limits O and 0.5 are given once
more besides the calculated values of A.

If we compare the situation of the intersection points as shown in
Table II and as calculated according to form. (10), we see that the
situation of the first point of intersection agrees well with the
observed facts, but that the second points «,, as calculated, cor-
respond with greater deviations than occur in reality.

As this second point of intersection naturally coincides with small
frequencies the degree of precision of which is questionable, it seems
difficult to decide whether these differences may be ascribed to
insufficiency of material, to the omission of a possible fourth term in
form. (4), or to an error introduced by the supposition /7 = / ; as the
calculated values of @, are jointly too great, the latter cause has to
be regarded as the most probable one.

4. The fact that in Table III, in which a measure is given for
the skewness of the curves, except for ¢= 0, only one zero-value
occurs, proves that in form. (5) the addition of a third term is cer-
tainly not required. The calculation of the constants B and D as well
as the determination of the point of intersection ? can, therefore,
easily be made.

AS:
if Verdi)
0
we find immediately :
B 3 D 0
+ 9 h2 — os . (11)
whereas :
zi By ep
[rde gtper=rn. Aa oo (ile)

denotes the surplus of positive over negative deviations.
If we take the absolute sum of positive and negative deviations
as a measure for the skewness s:

ip ‚© t
sp tn=2f Y da = ras? | Yaz — ?,
0 0 0

39*

w

( 562 )

or:
tot | Zar . 4)
2
The situation of the point of intersection ? is determined by the
equation :
Bi Ds=0 . .-.) 2 ee
By (11) and (12):
B=3h'», D= hd RE)
BR Ig ee ENE
With the help of (13) we find from these values:
sv (LH 4e),
En ashy) i PEE or ot 3 UM)
YP Di n
By means of the values rv or s, to be taken from Table III, the
constants of form (5) as well as the position of the point of inter-
section can, therefore, be determined ; we choose », so that a com-
parison of the calculated and observed values of ’/, or?/, may serve
as a criterion for the method followed in calculating the constants
of the empirical formula.
TABLE VIII.

dend ; ee
Jan. | 707><10-4| 150010 *| 4014407? | — 32107 | 47.8
Febr. 606 | 1184 | 100 — 37 [4615
March | 467 | 993 | 87 | — 36 15.5
Apr. | 639 | 1277 + 484 | — 144 12.6
May | 498 | 576 | 163 — 144 10.5
June | 483 | 668 | 49 — 286 9.3
July | 486 | 998 | 262 [8 REE
Aug. | 496 | 908 | 295 | ob | 9.3
Sept | 463 | 4073 | 143 | 2/98 12.4
Oct. | 429 748 92 — 4 14.5
Nov. 599 1467 100 de 16.4

Dec. 605 1309 89 | — 29 (4725

Mean 528 1053

( 565

—

The average values of r and s show a satisfactory agreement
with the form. 17):

s 053 ‘
== 1-99

Y 025
From the aggregate values given in Table III for three seasons
we find:

Sums.

p Rn p+-h=s s p/n
Winter 3849 1340 5189 Ie ie OE 2.87
Spring-Autumn 2959 937 3896 9.74 3.16
Summer 2380 747 3127 7.82 3.19

For the values of 3 in these three seasons:
Observ. Tab. Il Cale. Tab: VII

Winter Il 17.05
Spring-Autumn 14 13.68
Summer 9.5 9:99
Anatomy. — “Anatomical research about cerebellar connections.”

By L. J. J. Muskens. (second communication). (Communicated
by Prof. C. WINKLER).

A comparative examination into different species of mammals 1
have thought desirable in order to get information about the course
of the axis-erlinders arising from the cortex cerebelli. The develop-
ment of our knowledge in this matter in the last 15 years has
resulted in that at the present time the following question has been
placed in the center of diseussion : do the strands of fibres, which
form the superior Crus cerebelli, arise from the cortex cerebelli stric-
tiore sensu or have we to regard the basal cerebellar nuclei as an
undispensable intermediary for all these cortico-fugal nervefibres ? On
the one hand we find in some rodentia in the lobus petrosus cere-
belli exclusively cortex and white matter (squirrel), on the other hand
we find in others (rabbit) equally a part of the nucleus dentatus
situated in the pedunele of that lobe. In both animals the lobus
petrosus is situated in a separate bony hole. We find in this lobe
therefore a very fortunate opportunity for operative procedure therein,
leaving the other neighbouring central structures and also the semi-
circular canals intact. We can here in a comparative physiological
way find an answer on the above question and at the same time
avoid a large cranial aperture,

( 564)

Since Marcm stated, that after large lesions. as hemi-exstirpation
of the cerebellum a number of merve-strands degenerate up to the
mesencephalon and down to the spinal cord, it is notable, that subse-
quently Manam, [Ferrier and Turner, R. Russkut, Tromas and
especially ProBsr and vaN GEHUCHTEN have more and more directed
their attention to smaller and smaller lesions, so that it became
more and more clear, that most of the degenerations, found by Marcut,
were caused by affection of neighbouring parts. Finally have CLARKE
and Horsey recently succeeded in stating definitely, that all fibres of
the superior crus cerebelli do not arise from the cortex, but from
the basal nuclei. Their material was larger than that of any of the
precedent investigators and only very limited exstirpations, mostly
without any lesion of the nuelei, were used. If the lesion was
limited and the cerebellar cortex exclusively hurt, never the dege-
neration was found further than the nuclei. They stated moreover,
which parts of the cortex are directly connected with special parts
of the basal nuclei.

Independently of this result the examination of my own material
(experiments on the lobus petrosus in different rodentia) tends clearly
to reinforce their conclusion. Whereas in the case of the squirrel (where
only cortical and white matter in the lobus petrosus cerebelli —- inex-
actly called floceulus — can be hurt) the degeneration stops short in
the lateral part of the dentate nucleus, we find in the rabbit always
a part — especially and exclusively the middle third part of the
superior crus cerebelli on cross section — degenerated. These dege-
nerated fibres could be followed in the series of sections up to the
lesion. Here, in the case of the rabbit, we had removed a number of
ganglioncells, situated in the peduncle of the lobus petrosus and
being contiguous to the nucleus dentatus.

We see therefore that as well the Marcni-work in the same spe-
cies as experiments in kin animal groups lead to the same
answer to our question viz. that only the ganglioncells of the basal
nuclei and not the cells of Purkinsé, have to be regarded as the
origin of the degenerations after the cerebellar lesion. The last reserve
left in this matter by Epinenr can therefore, so it appears to me,
be abandoned. |

In accordance with the above investigators and also with my
former communication in These Proc. VII p. 202 about experi-
ments in rabbits [ could not find in the spinal cord of the
squirrels, examined, any degeneration. Regarding the middle cere-
bellar pedunele, the relations are more complicated and: need further
research.

Chemistry. — “On the simplest hydrocarbon with two conjugated
systems of double bonds, 1.3.5. hevatriene.” By Prof. P. vax

RompurGH and W. van Dorssen.

In 1878 Tinpen *) advanced the hypothesis that the terpenes might

be derivatives of a hydrocarbon of the formula :
CH, = CH — CH = CH — CH = CH.

At the meeting of the Assoc. franc. pour lavane. des Sciences in
Paris 28 Aug. 1878, FRANCHIMONT pronounced the same opinion and
suggested that this compound might, perhaps, be obtained by elimi-
nating of the two chlorine atoms from acrolein chloride. The efforts
made by one of us (v. R.) many yearsago to prepare that hydrocarbon
in this manner did not prove successful. The researches on terpenes
which afterwards definitely led to the result that, in the ease of
these substances, we are dealing with cyclic compounds made the
above cited hydrocarbon recede into the background.

The views of THLE on conjugated systems of double bonds, and
the researches originated therefrom, in addition to the studies on the
aliphatic terpenes myreene and ocimene, hydrocarbons in which the
existence of three double-bonds has been proved by different inves-
tigators, have again drawn our attention to the 1.3.5 hexatriene,
because it would represent the simplest hydrocarbon in which occur
three double linkings that also form two conjugated systems.

One of us (v. R.) has pointed out previously that one of the
methods which might lead to the desired product consists in the
action of metals on 3.4 dichloro-1.5 hexadiene.

The investigations of Grinpr*) have acquainted us with the ana-
logous bromine compound which is formed by the action of phos-
phorus tribromide ons. divinyl glycol. We have treated this substance,
prepared according to Gringr’s directions, with metals but have not
yet succeeded in preparing the hydrocarbon in that way. There was
however, another way still at our disposal to gain our object, namely,
by starting from s. divinyl glycol and converting this into a formic ester.

It is known that the formates of polyhydrie alcohols, in which occur
a OH-group and a formic acid-residue connected with two C-atoms
linked together, yield, on heating, unsaturated compounds with eli-
mination of carbon dioxide and water. It was now obvious to prepare
the monoformate of divinyl glycol. We endeavoured to do this by
heating this glycol with oxalic acid but obtained, mainly, brownish

1) Journ. chem. Soc. 1878. p. 80.
*) Ann. d. Chim. et d, Phys. [6] 26 (1892) p. 305,

( 566 )

compounds not looking fit for further investigation. By cautious
treatment with formic acid the diformate was, however, readily
obtained (see p. 544).

In order to convert this into the hydrocarbon, a reaction was
applied which one of us had previously used for preparing allyl
aleohol from the diformate of glycerol, and which consists in heating
that compound with glycerol.

And, indeed, a mixture of the diformate of divinyl glycol with
the glycol when heated slowly, first at 165° and then gradually to
200°, evolves carbon dioxide and a little carbon monoxide and yields
a distillate consisting of two layers, the upper one of which consists
of a hydrocarbon.

The triformate of glycerol, like the diformate of divinyl glycol,
may be distilled without notable decomposition by heating it some-
what rapidly at the ordinary pressure. Recently one of us (v. R.) found
however that it is decomposed by prolonged heating at a temperature
a little below the boiling point and it then yields the same decom-
position products as the diformate of glycerol.

If now the diformate of s. divinyl glycol is heated at 165° and
the temperature allowed to rise very slowly, an evolution of gas is
observed and in the receiver is collected a liquid consisting of two
layers. The upper layer again consists of a hydrocarbon identical
with the one cited above.

Probably, the simplest way to explain this reaction is to assume
that the diformate contains a little monoformate which is decomposed
in the desired sense, with formation of water which in turn regene-
rates monoformate from the diformate. Finally, a residue consisting
of glycol (respectively, polyglycols) is obtained and in the distillate
a little formic acid is found, besides water, whilst the gases evolved
consist of carbon dioxide and carbon monoxide. The last method
appears to give a better yield than the first one.

The hydrocarbon formed is separated and distilled, the portion
distilling up to 95° being collected. It is then dried over a piece
of caustic potash, which also removes traces of formic acid and then
rectified a few times over metallic sodium.

It then forms a colourless, strongly refractive liquid with a slight
pungent odour; in contact with the air it appears to slowly oxidise.
The boiling point lies between 77°—82°, the main fraction boils
between 78°,5—80° (corr. ; pressure 766 m.m.)

The analysis and the vapour density gave values leading to the
composition C, H,.

For the physical constants of the main fraction was found ;

Np, 1.49856.

If we calculate the molecular refraction from these data, with the
aid of the formula of Lorentz—Lorenz, we find J/R = 31,03,
whilst for C,H, is found MA—=28.53 assuming that the hydrocarbon
possesses three double bonds, and making use of the atomic refrac-
tions of Conrapy') and the increment for the double bond.

The difference of 2,5 between the calculated and found molecular
refraction is a striking one. According to BrÜHL*) excesses always
occur with substances with a conjugated system of double bonds.
In the aliphatic terpene ocimene, an excess (to the extent of 1.76)
is also found, and this assumes an extraordinarily large proportion
in the case of allo-ocimene. *)

As regards the structural formula of the hydrocarbon obtained,
its formation from

CH,=CH—CH—CH—CH=CH,
OH OH
by the elimination of the two OH-groups by means of formie acid
points to the formula:

CH,=—CH—CH—CH--CH—CH,
which indeed represents 1.3.5-hexatriene.
A glance at this formula shows that it may appear in two geo-

metrical isomeric forms, namely in the eis and trans form‘):

CH,=CH—CH CH,—CH—CH
|} and ||
C,H=CH—CH HC—CH=CH,. :

If, with Trmre®), we accept partial valencies the formula of
1.3.5-hexatriene should be written:

==. —
CH,=CH—CH—CH—CH=—CH,
Unsaturated hydrocarbons with a conjugated system readily take
1, Zeitschr. physik. Chem. 3, 226.
2) B.B. 38, 768.
3) C. J. Exkraar, Dissertation 1905. Compare literature on the subject p. 87.
4) Probably, the hydrocarkon is a mixture of both. In the fractionation, besides
the main fraction, a distillate could be obtained boiting between 77.5? and 78°.5
(sp. gray 0.7558, Anjo 1.494 MR 30.8), also a final fraction boiling between
80°—82° (sp. grag 0.7584, noo 1.503, MR 31.2). We hope to repeat the expe-
riment on a larger scale.
®) Ann. 306. 94,

( 568 )

up hydrogen on treatment with absolute alcohol and metallie sodium.
In the reduetion of our own hydrocarbon, 2.4 bexadiene might be
expected in the first place, although, a priori the formation of other
hexadienes is not to be excluded. In the 2.4 hexadiene

CH, — CH = CH — CH = CH — CH,,
we have again, however a compound with a conjugated system
which might be further hydrogenated to hexene 3.

In fact, our hydrocarbon when treated with boiling absolute
alcohol and metallic sodium takes up hydrogen. The study of the
product (or products) of the reaction is not facilitated by the contra-
dictory statements found in the literature about the hexadienes. A
future communication will treat more extensively of this reaction and
also of the original hydrocarbon whose structure we will try to deter-
mine also by other methods. We may state further that a dibromine
addition compound has been prepared melting at 89—90° and a
tetra-compound melting at 115°,

University. Org. Chem. Lab. Utrecht.

Chemistry. — “On the hidden equilibria in the p,a-sections below
the eutectic point’. By Dr. A. Suits. (Communicated by Prof.

H. W. Bakuvis RoozrBoom).

The p,e-sections of binary systems in the neighbourhood of the
eutectic point have been fully discussed by Bakuuis RoozrBoom *); in
this the course of the solubility isotherms in the unstable and metastable
region were, however, not examined. This problem could only be
taken in hand after vay per Waars’ paper*) on: “The equilibrium
between a solid body and a fluid phase, especially in the neigh-
bourhood of the critical state” had been published.

Availing myself of this paper I shall discuss the just-mentioned
problem, and show briefly in what way the stable region is connected
with the metastable and unstable region.

If for the two substances A and B the volume in solid state is
larger than in liquid state, these substances will have negative melting-

: dp : ;
point curves, 1. e. Ss will be negative, and the melting-point curve
will therefore pass to lower temperatures with increase of pressure. If
1) Die Heterogene Gleichgewichte 2, 139 (1904).
2) These Proceedings Oct. 31, 1903, 439,

en, a

Ee ar oe

( 569 )

this case occurs, the eutectic melting-point curve, furnished by the system
A + B will generally present the same course. This case is rare.

As, however, Baknuis RoozeBoom already observed '), a negative
eutectic melting-point curve is also possible, when only the melting-
point curve of one substance is negative, provided-the negative course
of one melting-point curve be stronger than the positive course of the
other. To this belong all eryo-hydrate lines.

In the P,7-projection fig. 1 it bas been assumed (which, however,
is of minor importance here) that the negative course of the eutectic
melting-point curve results from negative melting-point curves of the
substances A and JB.

The particularity attending the negative course of the eutectic
melting-point curve, is this, that a p,v-section corresponding with a
temperature below the eutectic point, will contain a region for S4 + 1
and a region for Sp + L, separated by a liquid region L. The
limits of this liquid region are given by solubility isotherms, which
according to VAN DER Waars’ theory, are portions of two continuous |
curves indicating the fluid phases which can coexist with the solid
substance A respectively 4, and which have been called de solubility
isotherms.

The regions for S4 + G and Sy + Lresp. Sp + Gand Sp + L
below the eutectic point being separated by a region for Sy + Sp,
the question which I wished to solve came to this: “what is the
course of the two solubility isotherms in the region for S4 + Sp”.

In order to answer this question we first examine what is the
p.x-section which corresponds with a temperature above the eutectic
point, but below the melting points of the two components. The
temperature which I have chosen for this purpose, is denoted by
Lt, in the P,7-projection. The p-r-section corresponding with this is
represented in fig. 2. As van DER Waats has proved that the solu-
bility isotherm has two vertical tangents for the case 7, <_v¢ , but
only one vertical tangent for the case vr, > vy two continuous solu-
bility isotherms with one vertical tangent have been drawn in this
p-a-section; for the one solubility isotherm this vertical tangent lies
at the liquid point ZL, and for the other at the vapour point G.
We see further that the branches which separate the liquid region
L from the regions for S4 + L and Sy + L diverge towards higher
pressure. The portion of the liquid-vapour-region L + G, which may
be realized in stable condition, lies between the two three phase
pressure lines Sy GL and Spl G. If we now examine a pre-section,

1) Loe, cit. p. 418,

(570 )

corresponding with the eutectie temperature, denoted by ¢, in the
P.T-projection, we get what is represented in fig. 2. The two three
phase pressure lines S4-+- G+ L and Sp + L + G have both
descended, the former, however, stronger than the latter, and they
have finally coincided.

The two solubility isotherms intersect besides in the unstable region,
also in the points G and £. While the point of intersection G indi-
cates the possibility of a coexistence of S4 + Sp + G, the second
point of intersection “ indicates the possibility of a coexistence of
Sa + Sp + 4, and when at a definite temperature, as is the case
here the two points le on the same pressure line, this means that
at that temperature the four phases Sy + Sg + L + G@ can coexist,
provided the pressure be equal to that indicated by the horizontal
line which joins the four coexisting states. At a higher pressure the
regions for S4+Z and S;+ LZ are separated by the triangular
region for L.

In order to get a clear idea of the form which the pe-section
assumes at a temperature 7,, lying somewhat below the eutectic
temperature, it is necessary to draw the metastable branches of the
lines for S4 + Lap + Gap, tor Sp + Lap+Gapz and for La NG
as has been done in fig. 1. We see then, that the situation of the
first two three phase lines is just the reverse of that of the stable
branches. For the stable branches that for S4 + Lan + Gan lies,
namely, above that for Sy + Lap + Gap, for the metastable branches
the reverse is the case. If, taking this into consideration, we now
draw the pa-seetion corresponding with the temperature ¢,, we get
fig. 4, from which we see that the tirst point of intersection of
the two solubility isotherms has moved upwards, and the second
downwards. The first point of intersection denotes, as has been
said, the coexistence of Sy+ Sp + G, and the second the coexistence
of Sat Sp-+ L; at constant temperature these three phase equilibria
are only possible at one pressure, because we have here a system
of two components, hence for pressures between the two points of
intersection mentioned there must be change of the three phase
equilibria into a two phase system, where the two three phase
pressure lines form the limits of a new two phase region, vis. for
Sa SB. 3

The second point of intersection of the solubility isotherms which
causes the occurrence of the three phases S4 + Sp + L lies here
in agreement with the dotted line traced in the P,7-projection for
the temperature ¢, at a pressure below that of the supercooled liquid
of pure A.

A. SMITS. “On the hidden equilibria in the px-sections below the eutéctive point.”

Proceedings Royal Acad. Amsterdam. Vol. VIII.

( 574 )

It is further te be seen in this p‚v-section, that the two metastable
three phase pressure lines for S4 + G+ L and for Sg+ LG
lie above the stable three phase pressure line for S4 + Sp + G,
and that the first lies between the two others. At the same time we
see that the character of the solubility isotherms does not change,
the only modification which is brought about for each of the isotherms
compared with the usual case is this that the metastable part is
enlarged.

If we now take a temperature which lies still somewhat lower,
viz. ¢,, we get a p,v-section as represented in fig. 5. All the three
phase pressure lines have diverged, and descended, except that for
Sa + Sp + L, which has strongly ascended. The second point of
intersection lies now, in agreement with what the dotted line for the
temperature f, traced in the P,7-projection shows, far above the
point indicating the vapour tension of the supercooled liquid of A.
The metastable part of the two solubility isotherms has greatly in-
creased, and with it the region for S4 + Sp. With further decrease
of temperature the character of the modifications in the p,v-section
remains the same, so that it is unnecessary to examine another.

If we had applied the same considerations to the case that the
eutectic melting-point curve has a positive course, we should. with the
exception of the unstable region, have found but one (lower) point
of “intersection for the solubility isotherms, for the branches which
gave a second (higher) point of intersection in the case under dis-
eussion, recede continually from each other.

I have not represented this latter case, as it yields nothing special.

The case treated shows once more, how the examination of the
equilibria which are hidden from our eyes, may contribute to widen
our insight into those accessible to experiment.

Amsterdam, December 1905.

Anorganie Chemical laboratory of the University.

Chemistry. — “On the phenomena which occur when the plaitpoint-
curve meets the three phase line of a dissociating binary
compound”. By Dr. A. Smits. (Communicated by Prof. H. W.
Bakutis RooseBoom).

1. In a previous paper‘) I have already pointed out, that the
interesting systems metal-oxygen, metal-hydrogen and metal-nitrogen,
to which we may still add many of the systems metal-halogen, and
metaloxyde-acidanhydride, belong to the type ether-anthraquinone,

) Zeitschr, f. physik. chem. 51, 193 (1905.)

but they are more complicated, because here the components may
combine.

Now from a chemical point of view it is of the highest impor-
tance to examine also these more complicated phenomena, in order
to obtain in this way a general insight into the phenomena of equi-
librium for the case that compounds are raised to high temperatures,
and placed under such a pressure that critical phenomena are found
with saturated solutions. As yet any insight into this was wanting.

By bringing the results of my investigation on ether-anthraquinone
in connection with the cases lately discussed by me in a. paper:
“Contribution to the knowledge of the PX and the PT-lines for the
case that two substances enter into a combination which is disso-
ciated in the liquid and the gas phase”), I have succeeded in
arriving at a clear conception of the above mentioned phenomena.

In all the cases which 1 shall shortly discuss here, I start from
the supposition that the compound under consideration is miscible
with both components in fluid state in all proportions. On the whole
our knowledge as to this is exceedingly slight, nor is there the least
certainty on this head for the substances which I shall adduce here
as examples.

2. First of all I shall consider the case, that two substances
A and B yield a dissociating compound A, B,, the melting point of
which lies above the critical temperature of the substance. A. This
case is met with in the system CaQ—CQO,. If now the solubility of
the compound A,, B, in A is still slight at the critical temperature
of A, the continuous plaitpoint curve, which starts at the critical point
of A (CO,) and terminates in the eritieal point of B (CaO) will meet
the solubility curve of A, B, (CaCO,) in fluid A (CO,) in two points.
That the point p exists has already been demonstrated by Dr. BGCHNER *);
in temperature this point lies only slightly above 31°, the solubility
of CaCO, in fluid CO, being still very slight at this temperature

This case has been represented in Fig. 1. The upper half of this
diagram contains the projection of the spacial figure on the PT-plane;
the lower half represents the projection of the two phase regions *)
coevisting with solid substance, and the plaitpoint curve. The com-
bination of these two projections seems to me the simplest way of

1) These Proc., June 1905, p. 200.

2) Thesis for the doctorate, 106. (1905).

35) At first 1 gave the name of (ree phase regions to these regions because,
though they indicate only fwo phases, a third coexists with them. It seems,
however, better to me to speak of two phase regions coexisting with solid substance,
which term I shall use henceforth.

representation for a first investigation of these problems. For the sake
of clearness | must draw attention to the fact, that in the T-X-pro-
jection the lines aE, Ep, qFE’ and K’c are the solubility curves,
whereas ak, E‚p, gF’EH,’ and E,’
the P-T-projection, however, we get one three phase line for each

c represent the vapour lines. In

pair of two corresponding lines for the liquid and gas phases coexist-
ing with solid substance. These three phase lines are indicated
by A+L+G, A, B, +L+G and B+1.+4G in the P-T-projection.

The first meeting of a solubility curve with the plaitpoint curve
takes place in p and the seeond in q. According to var DER WAALS’
theory a continuous transition from the solubility curve into the
coexisting vapour curve takes place in these two points. If we take once
more the system CO,—CaQ as an example, p indicates the critical
point of the saturated solution of CaCO, in fluid carbonic acid, and
q the critical point of another solution saturated with CaCO, witha
much larger concentration of CaCQ,.

Between these points p and g a fluid phase may oecur alone or
by the side of solid A,, B,(CaCO,), and- in the neighbourhood of
these points the phenomenon of retrograde solidification must present
itself. I will further emphatically point out here, that it is assumed,
as is easily seen in the T-X-projection, that near the melting point
the difference of the volatility of the components is not so
large as to prevent the occurrence of a vapour of the composition
of the compound. The point F’, where the composition of the vapour
is the same as that of the compound, is the maximum-sublimation
point and the point F, where the concentration of the liquid is the
same as that of the compound, is the minimum melting point, or the
). What I did not vet
show in my previous paper is this that two lines start from the
points HF and HE’, which pass continuously into each other at K.
These lines form the continuous bounding curve of the two sheets
of the PTX-surface for the composition of the compound. The con-
tinuous bounding curve touches the plaitpoint curve in K, so that
K denotes the critical point of the dissociating compound. That this
point KK does not constitute a special point of the continuous plait-
point curve is due to the fact that when the compound is assumed
to dissociate, the critical point of the liquid compound does not
essentially differ from that of the liquids with other compositions.

In fig. 1a the projection of the two phase regions coexisting with
solid substance is represented, and also that of the plaitpoint curve

melting point under the three phase pressure '

1) These Proc., June 1905, p. 200.

(574)

on the p-v-plane: further the solubility isotherms corresponding with
the temperatures of the points p and q are indicated, from which
the phenomenon of retrograde solidification appears clearly.

3. In the ease discussed the situation of the points p and q
depends on different properties of the compound and its components.
In special cases it will, therefore, depend on this, on what part of
the three phase line of the compound the point q lies. Undoubtedly
there will be many cases where this point falls below the melting
point. Probably this case will occur the sooner the more the volatility
of the two components differs. In this paper, however, I continue to
assume, that a vapour of the composition of the compound may exist.

In this different cases may present themselves, which each call for
a separate discussion. So highly remarkable phenomena make e. g.
their appearance, when the plaitpoint curve cuts the three phase line
of the compound between the melting point and the maximum subli-
mation point. I shall, however, discuss this case and some others in
another paper, and restrict myself now to the phenomena, which
occur, when the point of intersection g, as has been drawn in Fig. 2,
lies not only below the melting point of the compound, but also
below the maximum sublimation point. Also in this case the posst-
bility is excluded that the de melts, and the only way in which
the solid compound can vanish, is by evaporation.

The line for solid A,, B, + a which would touch the three phase
line A, B,-+L-+G in the maximum sublimation point, if this
point existed, runs on uninterruptedly to infinity, at least when no
further complications appear.

The T-X-projection occurring in fig. 2 may contribute te elucidate
some points. As is to ‘be seen there, the two phase region £’, qi’
coexisting with the solid compound, does not possess any liquid
or vapour of the composition of the compound, which is in harmony
with the supposition, that the points F and F’ are wanting.

In fig. 2a I have traced the projection of the two phase regions
coexisting with solid substance, and of the plaitpoint curve om the
p-z-plane. Further there are some solubility isotherms in this dia-
eram, which require a few words of explanation,

The curve fGecf’ denotes the solubility isotherm for a temperature
somewhat below that of the point g. If we now consider the tem-
perature of the point g, we get a solubility isotherm which touches
in gq, and which has two more points of inflection, as is indicated
by the curve /, G,q,gf'. At a higher temperature we get a solu-
bility isotherm, which does not touch any more, and from which
the two points of inflection may disappear.

+. In the third place I will point out what I have already demon-
strated in a previous publication *), that when the tension of a com-
pound is smaller at its melting point than that of the components,
a three phase curve may occur with a very peculiar shape, viz
with one minimum and two maxima.

Let us now consider the case that the melting point of this com-
pound lies above the critical temperatures of the components, then
the very peculiar phenomenon may present itself, that what occurred
once in the system ether and anthraquinone, is here to be realized
twice, and that the solubility curve which runs from one eutectic
point to the other, meets the plaitpoint curve four times, which
appears in the PT-projection fig. 3 as a four times repeated inter-
section of the three phase curve A,,B,-+-L+G and the continuous
plaitpoint curve 6ALd in the points p, q,q' and p’.

It appears from the PT and TX-projections that for all possible
concentrations a range of temperature may be pointed out, within
which the solid compound can only coexist with a fluid phase.
When, however, which is conceivable, the portions cut out of the
three phase line have no range of temperature in common, the
temperature regions for solid + fluid, lie above each other, and so
we have no symmetrical phenomena for any temperature on both
sides of the line for A,,B, in the PT-projection.

The systems hydrogen-water and oxygen-water belong to the type
ether-anthraquinone when the components are miscible in all propor-
tions. Each of these systems will then yield a point p anda point q.
Supposing, which is, however, highly improbable, that by the appli-
cation of a catalyser we could bring about equilibrium between
oxygen, hydrogen and water vapour at any temperature, we should
get a continuous three phase line for ice + L-+ G as is indicated
in fig. 3, and also one continuous plaitpoint curve. The equilibrium
with water, however, lying theoretically almost quite on the side of
water at lower temperatures, we should commit a practically un-
appreciable error, when we tried to realize at these lower temperatures
the diagram drawn here by starting in one case from ice, resp.
water -+ hydrogen, and in another case from ice, resp. water +
oxygen.

This example, however, is not suitable for illustration of the
assumed case, because for this purpose we require a compound
which appreciably dissociates at its melting point. I have only men-
tioned the system H,—QO, to show how remarkable this system is.

It is very probable that systems are to be found, with which the

1) loc cit.
40
Proceedings Royal Acad. Amsterdam. Vol, VIII.

( 576 )

supposed case may be realized without excessive experimental
difficulties. This may succeed with NH, HCI. A system for which
fig. 3 holds, presents also this particularity, that we have here a
P, T, X-surface of two sheets with a minimum curve bounded on the
upper side by a continuous plaitpoint curve, which, in consequence
of the great difference between the critical temperatures of the
compound and the components might possibly have the shape
described here.

Prof. Van per Waars was so kind as to draw my attention to
the particularities of the P,T, X-surface of two sheets, which may
be derived directly from those of a surface with a maximum curve,
by simply reversing everything. The minimum curve, i.e. the locus
of all points for which the concentration of liquid and vapour are
the same, forms here the lower boundary of the projection of the
P, T, X-surface of two sheets on the P, T-plane. This curve is repre-
sented in fig. 3 by the dotted line LZ’, which touches the plaitpoint
curve at £, and the continuous three phase line at N. This point
AV, lying between the minimum Jf in the three phase line and the
maximum sublimation point /”, as I have shown in a paper forwarded
to the Zeitschr. f. phys. Chem. towards the end of September, is
a point where the concentration of the vapour is equal to that of
the liquid, and is therefore at the same line a point of the minimum
curve, which becomes metastable on the left of _N. The peculiar
feature in the P, T, X-surface of-two sheets drawn here manifests
itself, when the bounding curves are traced for different concentrations.

It appears then, that if we come from the side of B, the con-
centration of the point £ is the first, at which the bounding curve
presents some particularity. At this concentration we get, viz., two
bounding curves, which starting from Q and S, terminate at L in
a so-called cusp, as is here once more separately represented.

L

q
S

With a concentration somewhat richer in A we get now two
bounding curves which pass continuously into each other. The con-
tinuous transition takes place where the bounding curve touches the
plaitpoint curve. Further this continuous bounding curve shows this
particularity that the two branches touch each other near the critical

. pe
‘
: |
|
, =
3
a
(
Pd
:
;
| i
i ,
I
Í i
. | L
i bi
= a eel a a Se
Nel
4 a |

A. SMITS. “On the phenomena which occur when the plaitpoint curve meets the three phase line of
a dissociating binary compound.”

Tig | Fig. la, Fig 2

Fig. 2,

Fig. 3.

Proceedings Royal Acad, Amsterdam. Vol VIJL

The point of tangeney m lies on the minimum curve.
With concentrations still richer in A, the character of the bound-
ing curves remains the same, only the point m shifts along the

minimum curve towards M, so that, when we choose the concen-
tration corresponding with the point NV, the bounding curve gets
this shape, where the vapour branch as well as the liquid branch
touches the three phase line at J.

N

If we now pass on to greater concentration of A, we get again
bounding curves of the usual form, for the point of tangency m lies
now in the metastable region. If the critical point of the bounding
curve, coincides with the maximum temperature of the plaitpoint
curve then m lies at the absolute zero point. Leaving further parti-
cularities undiseussed, I will only just point out that the minimum
curve, beyond the point N towards lower temperatures, lies below
the three phase line, which is necessary, because the supersaturate
solution has a smaller vapour tension than a saturate one and it is

wanted for the realisation of the metastable branch of the minimum
curve that the solid substance does not make its appearance.

Now as to the T-X-projection on fig. 8 we may still remark,
that in accordance with the foregoing remark the liquid line q£’ Ng’
euts the vapour line gf Ng’ in N at a temperature and pressure
lying somewhat below that of the maximum sublimation point F”,
but slightly above that of the minimum point J/ of the three phase
line. In MN vapour and liquid are therefore of the same concen-
tration, but this is not the case at the minimum MM.

In fig. 3a the projection is represented of the two phase regions
coexisting with solid substance on the p,z-plane, which diagram does
not call for further elucidation.

Amsterdam, Deeember 1905.

Anorganie-Chemical-laboratory of the University.
40%

( 578 )

Chemistry. — “On the course of the spinodal and the plaitpoint
lines for binary mixtures of normal substances.” By J. J.
vaN Laar. (Third communication). (Communicated by Prof.
H. A. Lorentz).

1. In my last paper *) on the above mentioned subject I discussed
the general equations of the spinodal and the plaitpoint lines, viz.
RT =f (v, x) and Fv, «)=0 (derived in a previous communication ®))
for the special case b‚=b,, i.e. 7 = 6, when a denotes the ratio

7
2

48 Pz > hi
of the critical pressures —, and @ that of the critical temperatures 7
Pi 1
of the components. (The higher critical temperature is always 7).
I started from var per Waars’ equation of state, where b was
assumed to be independent of v and 7’, while further in the quadratic

equations :
b =(l—2)? b, + 2u(1—2) b,, Heb,

le = (La, + 2 (le) a, + eta,
it was assumed that
+3) 3 a Vaan 2 en
which reduces the above expressions to
b= (1—2z)b, + wb,
a= ((l—2) Va, He Va)’.

Henceforward we shall indicate by the name normal (binary)
mixtures such mixtures, the components of which are not only simple,
but where both the relations (1) may be considered as satisfied.

‚The discussion in question led to the occurrence of two separate
branches of the plaitpoint line (see plate loc. cit.), which present
a double point at a definite value of 6 (fig 4). If 6< 2,89
(when 6, =,), we have the normal shape, represented in fig. 2; if
6 > 2,89, we find the abnormal shape, represented in fig. 1, which
as yet has been only considered possible for mixtures, of which at
least one of the components is associating (abnormal). (C,H, + CH,OH,
C,H, + H,O, SO, + H,O, Ether + H,0).

The possibility of a third case was also briefly mentioned (see
fig. 3), examples of which have been described inter alia by KuENEN
(C,H, + C,H, OH, ete.) ; but this case was not further discussed, nor
the connodal relations and three phase equilibria, which, for the

1) These Proc., June 1905, p. 144.
2) These Proc., April 1905, p. 646.

(575 )

rest, were already known. (The chief points had already been
previously described by KorrewEG and van per WaAAts).

In a later paper’) the place of the double point, the knowledge
of which is important, because it indicates the separation of two
very different types, was determined for the perfectly general case

dS by and the discussion of the shape of the plaitpoint line was

extended to the case a =d, i.e. to the case which is of frequent
occurrence, that the critical pressures of the two components are
equal. In this latter case it was inter alia found, that not before
6>9,9 the case of fig. 1 loc. cit. is found.

I further derived from the perfectly general expression :

sie ee WG

RT Sat 5 ey iE) ee
of the plaitpoint line also the initial course, viz. rig , chiefly
1 av Jo

in connection with opinions expressed previously on this point:

As I remarked before (loc. cit. p. 34), van per Waars had already
drawn up the differential equation of the plaitpoint line, and drawn
a series of general conclusions from it. Also in a few papers of very
recent date *) he has demonstrated in his own masterly way how
far we may get with general thermodynamical considerations and
general relations, derived from the equation of state. But seeing that
VAN DER Waats himself in his Ternary Systems IV (These Proc. V,
p. 1—2) with perfect justice emphatically points out the absurdity
of the often prevailing opinion as if an equation of state should not
be required for the knowledge of the binary systems, I have consi-
dered it not unprofitable to transform the difjerential equation of the

eee _ Of Af (dv
plaitpoint line, viz. — + — | , where f represents the second
de dv \dw/y7 .
member of RT =/(v,«) — the equation of the spinodal lines —

by means of the equation of state into a finite relation /(v,«), which
in combination with RT = /(v, v7) expresses the plaitpoint line in the
usual data 7,v, 7. This enabled me to get acquainted with new par-
ticulars concerning its course (inter alia its splitting up into two
separate branches), and to examine this course in its details more closely

1) Arch. Treyter (2) X, Première partie, p. 1—26 (1905).

2) These Proc. VIII, p. 144.

3) These Proc, VIII, p.271—298,. The first mentioned paper was cited by me
(loc. cit. p. 34), so it has by no means “been overlooked’, that already ten years
ago van DER Waats determined the principal properties of the eritical line, (cf
v. p. Waars loc. cit. p. 271).

( 580 )

than has been done up to now. L also pointed out (loc. cit. p. 15)
that already before me Korrmwec has tried to find a finite expression
for the plaitpoint line, but has not fully succeeded in this. His dis-
cussion extends after all only over the special case *) 6,=b,—6,,, a,=a,
(but a, = xa,), whereas in my paper cited it was assumed in the

discussion that 6, = b,, but that a, E a,(anda,, = Va,4,)-Kowrewee’s

paper is of the highest importance, specially with regard to the
connodal relations, which are often so intricate, and to which we
shall presently come back.

The equation of the plaitpoint line once being derived in the above
mentioned finite form, it was hardly any difficulty to derive also

leefde
for the expression T\ Ge Jr the side of lower critical temperature
1 Ax 0

Ps

and a =—
Tr, Pr

occur. In Van DER Waars’ paper mentioned by me in the paper
cited, again only the general differential equation for the expression
mentioned is given. (cf. (9) p. 89).

an accurate expression, in which only the quantities 9 = —

2. Some important points are left for discussion.

1st The ‘discussion of the transition case at the double point, with
regard to the shape of the spinodal lines ete; and the discussion of
the possibility of the 38°4 case (loc. cit. fig. 3).

2nd The treatment of the special case 6 = 1.

3 The different connodal relations in the three chief cases and
in the transition case.

4th The particularity of the cusp at R,, R, and R/ in the p,7-
representations of the three cases (loc. cit. la, 2a and 34).

5th The question concerning the occurrence of a minimum critical
temperature, and in connection with this of a mawvimum vapour
pressure.

Let us in accordance with our last paper (loc. cit. p. 144) begin
with the fifth point.

a. Minimum-critical temperature.
In this paper I derived the formula:

alb 1 Lis ; IEN
7 (G2) de A 4 tE : (2)

1) Arch. Neérl. 24 (1891), p. 297, 324, 337 and 341.

nt een

(581 )
Putting A <0, we get:

av. (1 hV =) Ei

Jt
i.e.
Jt
6 < a
(hh ve)
or
An v/a
OZ rn ee (3)
(3 Val)
This gives the following synopsis:
a Wat ee As “ile 1 4 9 16 25
O< */, l oo 2 ln etn Bey Ke

6 always being assumed 1 (7, is the lower of the two critical
temperatures), a minimum critical temperature can only occur, when
a, i. e. the ratio of the two critical pressures > ‘/,,.

If ~="/,, this takes place for all values of 0; if'#='/,, only
for values of 6 between 1 and 2; ete. etc. (For a = 1,a minimum
occurs in the above series of extreme values for 6, viz. 6 = 1).
Now in by far the most cases 2 will probably lie between í and 4,
so that @ will always have to be quite near 1, if a minimum critical
temperature is to be found.

Let us take as an illustration the normal substances C,H, and
N,O, investigated by Kurnen. There
= 7 om
ple Oe pan erp re 1,00.

45 273 + 35
According to the above rule, 6 has to be smaller than 1,04, if 7,
is to be minimum. This is the case here. KueNeN found really a
minimum value for 7%.

We also call attention to the fact that when 5, == b,, so 7=6,

no value of 6 exists >> 1 satisfying the inequality (3). For6=a—1 (a,=a,,
6, = 6,) the two members are equal, and the line of the eritical
temperatures is a straight line. The foregoing is in perfect concordance
with what we have derived in a previous paper with regard to this
point (loc. cit. p. 43).

Also in the special case a= 1 evidently not a single value of
@ exists greater than 1, which satisfies (3). But in the case d= 1

there is always a value of x conceivable, yielding a minimum for

(582 )

T,. Evidently in this case / must be greater than '/,, as
A(x) —9(V x)? 4-6 a—1= (Wal) (4/71),
and hence 2>>7/,,, in agreement with what has already been

found above.

b. Maximum of vapour pressure. As is known, this will oceur at
higher temperatures, when at /ower temperatures in the case of a three
phase equilibrium the three phase pressure does not lie between the
vapour pressures of the two components, but is greater than either. The
concentration «, of the vapour lies then between the concentrations
zv, and w, of the two liquid phases. On the side of the lower critical
temperature 2, >, will always have to be satisfied.

Let us now try to determine the condition for this.

For equilibrium between the phase 1 and 3 we have evidently
when u, and gy represent the molecular potentials of the two components:

(Ua), = (Ua), ; (uo), = (u), ’
or

02
¢.—(2 ie =). + RTlog(1—wx,) = Ca— (2- se) HRTlog(l—e,)

2 2
C4— (e+a — a) +RTloge, =Co— (2+ | oe) +RTloge,
é 1 6 3

where @ = { ple —pv, and C, and C), are functions of the tem-

perature.
Subtraction of the two equations yields :
02 ic 02 —2,
— + RT log == — + RT ae f
Oz, U, mede, Vs
or

la, 2, 1 roe 02
log = =S ;
Dode =d RT | 0x, “1

as has been repeatedly derived before, inter alia by van per Waars.
02

Now we found before for — (Le. p 649 formula (3) and p. 650):
ar

02 ee

or

Hence we bave for e =0, when a =a,:

hr 0E) 1 1
(= — Se) —=2Wa (Wa, — Va.) is -- =) —a,(b,—b,) Ge == =|
Ox, Ow, r=0 Vs v, Be v,?

a va) (» +5) (oy

(583)

1
so that we get at low temperatures (when— and — may be neglected
t v, '

3 3

and v, = 6, may be put):

ac : ed i abh) 2Va,(Va,—V%) a
0 RT b? b

1 1

From this we see already, that when $b, =), (w= 48), so

Z,\.
Va, >> Va, (because 6 must be larger than 1), then (eo *:) is always
zer eA

negative, i.e. ©,<a,. Hence just as little a three phase pressure >
than the two vapour branches, as a minimum critical temperature.
Let us now proceed te derive the eondition for 7, >, from (4).

a
Then (sividing by En ) we must get:

la

Va
b (igo) 2(Va,—Va,),
1
wie:
b
BL se Aly,
Va,
b, 1 Va, 6
te S = — TR «| 1 =
or as ae Une VEE
6 ed
a= Je ijl en
from which follows :
Ed
4 aa 4
< 2Vx—1 6)

Hence this eondition is another than the condition (3) for the
minimum critical temperature, and we shall at once examine in
how far the two conditions include or exelude each other.

No more than for a—6 does a value of @ satisfy the above
inequality for 7—1.1f 4 = 1, then, provided Ya >'/,, 7—2Ya4+1
must be >> 0; and as this will always be satisfied, 2, will be >a,
for 6=1 on the side of the first component, when 2>'/,. (We

found only then a minimum critical temperature for 6=1, when

a>!)

We can now easily prove, that always :
Aa Va Ed
SS u
(8 Va—l) aal
when 2 >> !/, For the above leads to:
B Valt > 4 a (2 Val),

i.e. to m—2Va4+1> 0, which is again always satisfied.

( 584 )

Hence we have for a >> !/,:

If there is a minimum critical temperature, then also a, >, \but
not necessarily vice versa); if not #, > «,, then there is 0 minimum
of 7. (Again the reverse need not be true).

If a should be < '/,, then never vw, > x,, while 7, is only minimum,
when (3) is satisfied, viz. if 7 > */,,. But this exceptional case, viz.
that for 9 >1 the value of z remains below '/,, will be very rare.

It appears therefore convincingly from the above, that the two
conditions include each other often, but by no means always.

Just one example: “ther + H,0.
UEFA 2 1 195

poy a=

iba yey SR
Here 273 4 195 36

— 5,42, Va =2,85. The

51,0

>

’
6< 1,39, there will be a minimum critical temperature, and hence
also av, >a, according to the above rule. In fact the second member
of (5) = 1,46, and A being < 1,39, so a fortiori A << 1,46.

What is found, is in harmony with experiment, as the three phase
pressure was found larger than the vapour pressure of ether.

Let us now take CH, + H,0.

Here the three phase pressure was found smaller than that of
C,H,. Let us now examine if the inequality of (5) predicts the same. As

273 + 364 195

=S ie =S

TEE 45,2

= 1,39. As therefore

second member of (3) becomes therefore =

= 4,31, |/x = 2,08, so we find

9

for es? — the value 1,36. And so 2,07 is not << 1,386 now. Here
2Va—l ;
too the rule holds again.

According to the above rule there is now not a minimum critical
temperature either. The second member of (3) becomes now a =1,31,

’

and 2,07 is still less < 1,31 than < 1,36.

The two examples are illustrations of the first principal type,
where a plaitpoint curve runs from C, to A, and one from C, to C,.

The reader will observe, that water serves here as 2"? component,
so a very abnormal substance. But we must bear in mind, that in
the neighbourhood of «=O, where both the rules hold, the liquid
phase consists almost entirely of ether (resp. C,H,), so that the water
present may be considered as almost perfectly normal on account
of the extremely high degree of dilution.

For the sake of completeness we mention that two other known
examples, which with those mentioned are about the only ones

(585)

known, or rather investigated, which belong to Type 1, both follow
the rule derived.
With C,H, -+- CH,OH @ is viz. 1,69, a = 1,63, so on account

of ~=6, «, cannot be >er, And with SO, + H,O, 9 —1,49,
m= 2,47, Wa=1,57, hence the second member of (5) = 1,15. And
1,49 is not << 1,15, so x, is also not >>. This implies again that
no minimum critical temperature is found.

So the fact that of the four mixtures C,H, + CH,OH,, C,H, + H,O,
SO,-+H,O and ether + H,O only the last has a three phase
pressure greater than the vapour pressures of the two components,

is in perfect harmony with the theoretical derivations given above.

3. Let us now briefly discuss the third point, viz. the connodal
relations. As we are guided by the different figures of the adjoined
plate, a few words will suffice. The essential part was already given
by me in a few suggestions in one of my last papers (loc. cit.
p. 37 at the foot and p. 38 at the top; p. 44 at the foot and p. 45
at the top; p. 48 in the middle), where I referred to Korrewra’s
well-known papers, with regard to the neighbourhood of the points
R, and Zi, and to some papers by van per Waats, with regard to
the points FR, and £&', with the third principal type.

Now we may add to this, that recently van per Waars [in the
Proceedings of the same Meeting as in which my first paper on the
spinodal and the plaitpoint lines was published (Meeting of March 25
1905)| has given an addition to his former considerations concerning
the just mentioned third type, in agreement with what Korrrwne
derived for this case already 14 years ago (loc. cit. p. 316—318,
figs. 30—35). We have reproduced this course of transformation in
our figs. 9, 10 and 11, but now in connection with our former
considerations on the course of the plaitpoint line. So also in
other cases.

a. Principal type I (figs. 1—6).
In fig. 1 we see the gradual transformation of the principal
; 5 : £
(transverse) plait, when the temperature falls from += — = 2,37

’
0

at C, to 0,80. (These numerical values relate to special case b,=6,,
but when ee the relations are modified only numerically, as 1

have demonstrated in the above cited paper in the Arch. Teyler).
She

T, is the temperature of the point C,, and is put = 1. 6= T

1

( 586 )

is here =4. (ef. for these and other data the already repeatedly
mentioned paper in these proceedings).

The plaitpoint 7? has strongly shifted to the side of the small
volumes ; there is always equilibrium between a gas phase 3 anda
liquid phase 2, which is comparatively rich in the 2"d component.
With smaller volumes the gas phase 3 is practically equal to a
liquid phase, but the transition is gradual. (The full-traced border
curves of tbe plaits in their », v-projection, on which the straight
node lines rest, represent everywhere the connodal lines; the dotted
lines always represent the spinodal curves; the plaitpoint line is
indicated by crosses).

At t=1,6 and +r=1 we see the connodal lines in the figure.
If r is somewhat below 1, e.g. 0,98, a connodal line arises running
at a short distance round C,, while the large connodal line shifts
its plaitpoint further to C,. At r= 0,97 the two plaits meet in a
homogeneous double point‘). At still lower temperatures we have an
open plait, of which the two branches of the eonnodal line recede
towards the right and the left, and which is traced for t= 0,8. Up
to the highest pressures, x, and «, continue to differ, and it is no
longer possible to mix the two phases to one homogeneous liquid
phase by pressure, however great. With values of 7’ between 7,
and 0,977, the homogeneity reached at a certain high pressure was
again broken at still higher pressure, after which the two phases
diverge more and more up to a certain limit.

In fig. 2 an important moment has been represented. At t= 0.63
the spinodal curve touches namely the plaitpoint line C,A in A,
and from this moment a new closed connodal line begins to appear
of the shape as is represented in fig. 3 (r = 0,62) within the connodal
line proper. The spinodal line touches that isolated curve twice, Le.
in the plaitpoints p and p' [all this has been fully explained by
Korrewre (loc. cit.)|, which for t= 0,63 coincide to a so-called
“point double hétérogene” in R‚*).” The connodal line in question
does not yet present, however, realizable equilibria, because that line
lies on the y-surface above the tangent plane to the connodal line
proper, which determines the phases 3 and 2,

1) In fig. 1 the spinodal lines seem to touch each other in this double point ;
of course this has to be an intersection.

2) It need hardly be mentioned, that every time only one, after the contact at Ry
two points of the plaitpoint line correspond with the temperature of the spinodal
and connodal line under consideration. All the other points of the plaitpoint line
which is every time projected as a whole, belong to other, lower and higher tem-

peratures.

( 587 )

Fig. 3a gives an enlarged, schematical representation of that iso-
lated connodal line, where some straight lines represent the “hidden”,
non-realizable equilibria. The points a and a’, and in the same way
6 and 4’ are corresponding points. The “tail” at 0’ is always directed
towards the side of the plaitpoint (which has already disappeared in
our diagram) of the principal plait, the “point” at a lies on the
opposite side.

We point out that the shape of the spinodal line, as is drawn
in figs.3 and 3a, implies, that it touches the plaitpoint line in the
peculiar way, indicated in fig. 2. In the immediate neighbourhood of
, the uppermost portion lies left of the common tangent, the lower-
most portion on its right.

At somewhat lower temperatures, in our example at t= 0,61
fig. 4), the isolated connodal line begins to touch (in M) the connodal
‘line proper, and from this moment one of the two new plaitpoints,
viz. p, will become the plaitpoint of a new branch plait, which has
thus arisen from the principal plait in the way described above.
Cf. e.g. fig. 5, where r= 0,60. The point p' is always unrealizable,
and this continues so down to the absolute zero, where the plaitpoint
line terminates in A. On the other hand all the plaitpoints P from
M to C, will form realizable plaitpoints of the new plait.

In fig. + phase 3 begins to split up into two new phases, the gas
phase proper 3, anda new liquid phase 1, rich in the 1st component
of the mixture. There is a three phase /ine, the beginning of a three
phase triangle (see fig. 5), which continues to exist from this point
down to the lowest temperatures.

In fig.5 it is also seen how the connodal line which passed on
uninterruptedly before, but which is now broken off in the angles
1 and 3 of the three phase triangle, proceeds on the y-surface.
With this- corresponds the well-known “ridge” on the connodal line
at 2.

At t=0,59 the new plaitpoint P reaches the lower critical tem-
perature C,, and from this moment the branch plait is always open
on the side «=O, and this continues so down to the lowest
temperatures.

The p‚v-representations are omitted for want of space.

Fig. 6 gives the p,7-diagram of the plaitpoint lines. Noteworthy is,
that we meet with a cusp in the line C,A at F,, where the spinodal
line touches the plaitpoint line (cf. fig. 2). We shall prove this further
on. As we have already shown in our former paper, the pressure p
approaches —27p, at A, where 7=0. (This derivation holds

(588 )

evidently also for the general case that 120), Comparison with

fig.4 teaches us, that the point J/, where the three phase pressure
begins, lies at a temperature lower than that of R,. If the three
phase pressure lies between the vapour pressures of the two com-
ponents (the full-traced curves starting from C, and C, represent the
vapour tension lines), in other words if 2, >>, then fig. 6 holds;
if on the other hand #, >>, and the three phase pressure always
higher than the vapour pressure of the two components, then fig. 6a
holds. The line C,R shows then a minimum. (In the figure the three
phase pressure line is always denoted by AAA).

b. Principal type LI.

After what has been discussed above, the relations for this type
may be made sufficiently clear even without diagrams. At a tem-
perature somewhat lower than that of 2,, where the spinodal line
again touches the plaitpoint line (now C,A) a three phase equilibrium
again prevails. Now the gas phase 3 does not split up into 3 and
1, as with type I, but the liquid phase 2 into two liquid phases 2
and 1. Just as with type I the plaitpoints from M (between A, and
C,) to A were unrealizable (cf. also fig. 6), those from J/ (now between
R, and C,) to A are now also unrealizable. The three phase equi-
librium formed continues to exist down to the lowest temperatures.
Here the same phenomenon of the minimum critical temperature in
the neighbourhood of C, is met with as with type I. At tempera-
tures lower than 7’—0,96 7, the two liquid phases 1 and 2 are
no longer to be mixed to one homogeneous phase by pressure,
however great.

The successive p, z-lines are again omitted.

Finally we find in fig. 7 the p,Z-representation. The three phase
pressure line lies here between the two vapour pressure lines, so
that ze, <<, on the border near «= 0.

e. Principal type LLL

The possibility of this type for mixtures of normal substances will
be examined separately afterwards. When it occurs (inter alia for
mixtures of C,H, with C,H,OH,, etc,, for triethylamine and water),
then the plaitpoint line CC, has the shape drawn in fig. 8.

If we pass downward from the higher critical temperature at C,,
a double plaitpoint will again occur at PR, at the temperature indi-
cated by f,, hence formation of an isolated connodal line as in fig. 3,
at somewhat lower temperature, This goes on till at ¢, the closed

= =— a *

Lee Aa

( 589 )

curve in Jf" begins to get outside, i.e. outside the connodal line
proper of the principal plait, at which the phase 3 begins to split
up into 3 and 1 just as in fig. 4, This splitting up itself is repre-
sented at ¢, in fig. 9. A three phase equilibrium has formed then
just as in fig.5. The shape of the different connodal lines is still
quite the same as in the analogous case in fig. 5, only the plaitpoint
P of the principal plait had already disappeared there. This course
has already been given by Korrrwec, as was mentioned above, and
VAN DER Waars, too, has accepted it in one of his last papers (loc.
cit.) on the transformation of a principal plait into a branch plait
and the reverse.

The three phase equilibrium established is however not of long
duration as we shall see. At still somewhat lower temperature 7, a
very interesting transformation takes place (see fig. 10), also men-
tioned by Kortrewee (loc. cit. p. 318, fig. 34), and later by vaN DER
Waats (Le). The small letters a, b, c,d and a’, b', c'‚, d' placed in fig. 9
give a clear idea of the transformation.

Still somewhat lower, at ¢, (fig. 11), the plaits have reversed their
functions; the branch plait of fig. 9 has become a principal plait, and
reversely the principal plait has been transformed into a branch
plait. We may notice that the “tail” at 6 is always turned to the
side of the principal plait, both in fig. 9 and in fig. 11. Also the
“ridge” has changed its place after the transition of fig. 10.

And then the further transformation resumes its normal course.
There comes a moment, at f, (represented in fig. 8), that the isolated
connodal line of fig. 11 begins to retreat within the connodal line
proper of the principal plait. This takes place in WM’, and the three
phase equilibrium, which accordingly has been of very short dura-
tion, finishes. The two phases 1 and 2 have again coincided, and
after this we have only coexistence of 38 and 2, as before, and as
with type II before Min the neighbourhood of #,. The plaitpoint
P of the principal plait continues to exist for some time more, but
will soon also disappear (at C,) *) Also the closed connodal line
remains past J/' still for a short time within the connodal line
proper, gets smaller and smaller, and disappears at last at /?,', where
the spinodal line touches the plaitpoint line once more (fig. 8 at ¢,).
The temperature ¢,, is the lower critical temperature of the two
components, that of C,, and at still lower temperatures we begin
gradually to approach the second plaitpoint line Cd.

1) The temperature of B's (and M') may also be lower than that of C5. This
really occurs for the above mentioned mixtures. The point P of the principal
plait has then already disappeared before 1 and 2 coincide at M',

( 590 )

At ¢,, contact of a spinodal line and the plaitpoint line takes
place for the third time, viz. at the branch C,A mentioned. Again at
somewhat lower temperature a three phase equilibrium will be found
at M/ by the repeated splitting up of 2 into 1 and 2, and now for
good and all, down to the lowest temperatures. All this is quite
identical with the case treated with type II.

Theoretically of importance for this remarkable third (very ab-
normal) principal type is therefore this, that after the two liquid
phases 1 and 2 have become identical at J/’ (¢,), there must again
take place splitting up of the homogeneous liquid phases into two
separate phases with sufficient lowering of the temperature, viz. at
M, somewhat below R, (ef. also fig. 12).

We point out that the point M in fig.4 and 6, and in fig. 7 isa
so-called upper mixing-point, i.e. that at temperatures higher than the
temperatures corresponding with that point the two phases 3,1 or
2,1 will form one homogeneous phase. The same thing is also the
‘ase for the points J/ and J/" of figs. 8 and 12. Above the tempe-
rature of J/ 1 coincides with 2, above that of J/" again 1 with 3.
Jut the point M' is there a so-called /ower mixing-point, for at
temperatures Lower than that of J/' the phases 1 and 2, distinct at
higher temperatures, coincide to one homogeneous phase.

For the plaitpoint line C,C, of the third type (fig. 8) all the points,
lying between J/" somewhat before B, and J/' somewhat beyond
R',, are not to be realized. They form again the series of hidden
plaitpoints p'‚ indicated in the figs. 9—11.

The p, representations are again omitted.

In the figs.12 and 12a the p,7-representations of the plaitpoint
line are drawn of the type mentioned. We again notice the three
cusps R,, R, and R’,. In fig. 12 the three phase pressure lies between
the vapour pressures of the components; in fig. 12a above them.
C, R, has then again, as in fig. 6a, a retrogressive course.

We shall put off the discussion of the remaining points to a
following paper. Those points are: a. The transition case between
type I and II with the double point; b. the discussion of the possi-
bility of the occurrence of type III; ec. some remarks on the special
‘ase @ = 1; d., the proof, that in the p,7-representations the different
points #,, A, and #’, are cusps.

a

1 J.J. VAN LAAR. “On tho course of the spinodal and the plaitpoint lines for binary mixtures of ra
normal substances.” (Third communication).

A Gino

Fig. 11

Fig. 12a

(591 )

Physics. — “The absorption and emission lines of gaseous bodies.”
By Prof. H. A. Lorentz.

(Communicated in the Meetings of November and December 1905).

§ 1. The dispersion and absorption of light, as well as the
influence of certain ¢ircumstances on the bands or lines of absorp-
tion, can be explained by means of the hypothesis that the molecules
of ponderable bodies contain small particles that are set in vibration
by the periodic forces existing in a beam of light or radiant heat.
The connexion between the two first mentioned phenomena forms the
subject of the theory of anomalous dispersion that has been developed
by SELLMEYER, BoussiNesQ and Hermnortz, a theory that may readily
be reproduced in the language of electromagnetic theory, if the
small vibrating particles are supposed to have electric charges, so
that they may be called electrons. Among the changes in the lines
of absorption, those that are produced by an exterior magnetic field
are of paramount interest. Voret') has proposed a theory which
not only accounts for these modifications, the inverse ZEEMAN effect
as it may properly be called, but from which he has been able to
deduce the existence of several other phenomena, which are closely
allied to the magnetic splitting of spectral lines, and which have
been investigated by Hato’) and Grersr*) in the Amsterdam labo-
ratory. In this theory of Voicr there is hardly any question of the
mechanism by which the phenomena are produced. I have shown
however that equations corresponding to his and from which the
same conclusions may be drawn, may be established on the basis
of the theory of electrons, if we confine ourselves to the simpler
cases. In what follows I shall give some further development to
my former considerations on the subject, somewhat simplifying them
at the same time by the introduction of the notation I have used
in my articles in the Mathematical Encyclopedia.

1) W. Vorer, Theorie der magneto-optischen Erscheinungen. Ann. Phys. Chem.
67 (1899), p. 345; Weiteres zur Theorie des Zeeman-effectes, ibidem 68 (1899),
p. 352; Weiteres zur Theorie der magneto-optischen Wirkungen. Ann. Phys., 1
(1900), p. 389.

2) J.J. Haro, La rotation magnétique du plan de polarisation dans le voisinage
d'une bande d’absorption, Arch. Néerl., (2), 10 (1905), p. 148.

5) J. Geest, La double réfraction magnétique de la vapeur de sodium, Arch.
Néerl., (2), 10 (1905), p. 291. :

4) Lorentz, Sur la théorie des phénomènes magnéto-optiques récemment décou-
verts Rapports prés. au Congrès de physique, 1900, T. 3, p. 1.

41

Proceedings Royal Acad. Amsterdam. Vol. VIII,

(592 )

$ 2. We shall always consider a gaseous body. Let, in any point
of it, € be the electric force, the magnetic force, 9 the electrie
polarization and
the dieleetrie displacement. Then we have the general relations
Òh- 0), 1 0D: Ofc OH: 1 0D,

oy z c Ot Ry der Ve ett
0), 08; 1 0D:
== 2
Ow Oy c dt” ( )
dE, dE, EEE OE: 1,
Dael OZ sna) enor dE nnee OP en dt
ÒE, dE, 1 0:
ut eid : 3
Ow Oy é tol 6)

in which c is the velocity of light in the aether.

To these we must add the formulae expressing the connexion
between € and W, which we can find by starting from the equations
of motion for the vibrating electrons. For the sake of simplicity we
shall suppose each molecule to contain only one movable electron.
We shall write e for its charge, m for its mass and (x, y, 2) for.
its displacement from the position of equilibrium. Then, if MN is the
number of molecules per unit volume,

Y= Nex, p, = Ney, p.= Nez. . Ben (4)

§ 3. The movable electron is acted on by several forces. First,
in virtue of the state of all other molecules, except the one to which
it belongs, there is a force whose components per unit charge are
given by ')

Cz +aYr,, €,+ aPy, E+ ae,
a being a constant that may be shown to have the value '/, in
certain simple cases and which in general will not be widely different
from this. The components of the first force acting on the electron
are therefore
(EHaD), e(E, Hat), eG +aP) . . . (5)

In the second place we shall assume the existence of an elastic
force directed towards the position of equilibrium and proportional
to the displacement. We may write for its components

SE fy SS PL ee. Se
f being & constant whose value depends on the nature of the molecule.

1) Lorentz, Math. Eneycl. Bd. 5, Art. 14, §§ 35 and 36.

(593 )

If this were the only force, the electron could vibrate with a

frequency 7,, determined by
Es ne et er
m

In order to account for the absorption, one has often introduced
a resistance proportional to the velocity of the electron whose com-
ponents may be represented by

d d d
= ay, en (8)
if by g we denote a new constant.

We have finally to consider the forces due to the external mag-
netic field. We shall suppose this field to be constant and to have
the direction of the axis of z. If the strength of the field is H, the
components of the last mentioned force will be

eHdy eHdx :
(9)
chdit e dt

It must be observed that, in the formulae (2) and (3), we may
understand by the magnetic force that is due to the vibrations
in the beam of light and that may be conceived to be superimposed
on the constant magnetic force H.

§ 4. The equations of motion of the electron are

a’x dx eHdy
= E, + WK g§ — — —;
Tm At at TT
d*y dy eHdx
= Eee
Ae = Ege NN aH c dt
dz dz
CANET =e (€. ste Oe) cel nd Ten

These formulae may however be put in a form somewhat more
convenient for our purpose.

To this effect we shall divide by e, expressing at the same time
x,y,z in Po, P,, P-. This may be done by means of the relations (4).

Putting

a=” Se ed (10)
we find in this way
" whe =€.f aP:—/'P.— 9 a

41*

( 594 )

The equations may be further simplified, if, following a well
known method, we work with complex expressions, all containing
the time in the factor ett. If we introduce the three quantities

§=f"—a— mn’, . ss)
| N= AJ «fe a, 3 ee es
and
nH
Ge EE eo Ge oo (IE
7 cNe ee
the result becomes
€, =(E Hin) We — iS P,, |
E,=(E Hin) Py HE We, | ar eere
(EH in) De

$ 5. Before proceeding further, we shall try to form an idea of
the mechanism by which the absorption is produced. It seems difficult
to admit the real existence of a resistance proportional to the velo-
city such as is represented by the expressions (8). It is true that in the
theory of electrons a charged particle moving through the aether
is acted on by a certain force to which the name of resistance may
be applied, but this force is proportional to the differential coefficients
of the third order of x,y,z with respect to the time. Besides, as
we shall see later on, it is much too small to account for the absorp-
tion existing in many cases; we shall therefore begin by neglecting
it altogether, i.e. by supposing that a vibrating electron is not subject
to any force, exerted by the aether and tending to damp its vibrations.

However, if, in our case of gaseous bodies, we think of the mutual
encounters between the molecules, a way in which the regular
vibrations of light might be transformed into an inorderly motion
that may be called heat, can easily be conceived. As long as a mole-
cule is not struck by another, the movable electron contained within
it may be considered as free to follow the periodic electric forces
existing in the beam of light; it will therefore take a motion whose
amplitude would continually increase if the frequency of the incident
light corresponded exactly to that ofthe free vibrations of the electron.

In a short time however, the molecule will strike against another
particle, and it seems natural to suppose that by this encounter the
regular vibration set up in the molecule will be changed into a
motion of a wholly different kind. between this transformation and
the next encounter, there will again be an interval of time during
which a new regular vibration is given to the electron. It is clear
that in this way, as well as by a resistance proportional to the velo-

_— es

(595 )

city, the amplitude of the vibrations will be prevented from surpas-
sing a certain limit.

We should be led into serious mathematical difficulties, if, in
following up this idea, we were to consider the motions actually
taking place in a system of molecules. In order to simplify the
problem, without materially changing the circumstances of the case,
we shall suppose each molecule to remain in its place, the state of
vibration being disturbed over and over again by a large number of
blows, distributed in the system according to the laws of chance.
Let A be the number of blows that are given to MN molecules per
unit of time. Then

may be said to be the mean length of time during which the vibra-
tion in a molecule is left undisturbed. It may further be shown
that, at a definite instant, there are

molecules for which the time that has elapsed since the last blow
lies between ® and 9 + d%.

$ 6. We have now to compare the influence of the just men-
tioned blows with that of a resistance whose intensity is determined
by the coefficient g. In order to do this, we shall consider a mole-
cule acted on by an external electric force

aeint

in the direction of the axis of «.

If there is a resistance g, the displacement xX is given by the
equation

x

R dx
Nn kleen +aeent,
so that, if we confine ourselves to the particular solution in which
Xx contains the factor eint, and if we use the relation (7),
Es ae ind
m(n,? — n°) + ing
In the other case, if, between two successive blows, there is no
resistance, we must start from the equation of motion
x :
LO —fx+aeenr?

whose general solution is

elise (15)

x ER + Cyeimot + Coe imt. . . = (16)

By means of this formula we can calculate, for a definite instant

t, the mean value X for a large number of molecules, all acted on
by the same electric force aeint. Now, for each molecule, the con-

, dx.
stants C, and C, are determined by the values of x and immediately

: dx ie
after the last blow, i. e. by the values x, and (5) existing at
C
0
the time ¢—®%, if 9 is the interval that has elapsed since that blow.

We shall suppose that immediately after a blow all directions of
the displacement and the velocity of the electron are equally pro-

: dx
bable. Then the mean values of x, and (=) are 0, and we shall
at
0
find the exact value of x, if in the determination of C, and C,, we

dx
suppose X and a to vanish at the time ¢— 9.
¢

In this way, (16) becomes

ou aeent on 1 1 ae 2 el(m—n)s — 5 (: — i e—i(notn)s}
m(n,?—n*) 2 No 2 Ne

=:

= ln ,
From this x is found, if, after multiplying by —e * dd, we inte-
T

grate from 9—=0 to ®=o. If w is an imaginary constant, we have

oo
eu — 1
fe td = é
T l—uwut

Hence, after some transformations,

1 | ze

eee eee

: 1 5 sf imn
mi no jaa @ + 2—
T T

If this is compared with (15), it appears that, on account of the
blows, the phenomena will be the same as if there were a resistance
determined by

2m
GN ee ie CANE

T

and an elastic force having for its coefficient

Dlt ne tht. ENEN

( 597 )

Indeed, if the elastie force had the intensity corresponding to this
formula, the square of the frequency of the free vibrations would

1 :
have, by (7), the value m,*-++—. The equation (15) would then
> Lr

take the form (17).

In the next paragraphs the last term in (19) will however be
omitted.

As to the time rt, it will be found to be considerably shorter than
the time between two successive encounters of a molecule. Hence,
if we wish to maintain the conception here set forth, we must sup-
pose the regular succession of vibrations to be disturbed by some un-
known action much more rapidly than it would be by the encounters.

We may add that, even if there were a resistance proportional to
the velocity, the vibrations might be said to go on undisturbed only
for a limited length of time. On account of the damping their amplitude
would be considerably diminished in a time of the order of magnitude
= This is comparable to the value of t which, by (18), corresponds
to a given magnitude of g.

§ 7. The laws of propagation of electric vibrations are easily
deduced from our fundamental equations. We shall begin by sup-
posing that there is no external magnetic field, so that the terms
with § disappear from the equations (14).

Let the propagation take place in the direction of the axis of z
and let the components of the electromagnetic vectors all contain
the factor

OS iy Re ig craig ee (20)

in which it is the value of the constant g that will chiefly interest
us. There can exist a state of things, in which the electric vibrations
are parallel to OX and the magnetic ones parallel to O Y, so that
€,, P,, D, and HD, are the only components differing from 0. Since

differentiations with respect to ¢ and to z are equivalent to a
multiplication by #7 and by —ingq_ respectively, we have by
(2) and (3)
: 1 1
GI reas Gee
Hence
Dy =? gr,

and, in virtue of (1),
Pe = (cq? —1)&.
The first of the equations (14) leads therefore to the following

(598 )
formula, which may serve for the determination of q,

1

Pr 1 — EN

: S +1

Of course, q has a complex value. If, taking x and real, we put
1—ix

LS RM

the expression (20) becomes
ae
ee ies
so that the real parts of the quantities representing the vibrations
contain the factor
peepee

ene 28 rd ey AES

multiplied by the cosine or sine of

n (« == 5)
w
It appears from this that w may be called the velocity of propa-
gation and that the absorption is determined by x. If
nk
— zkh,

w

(index of absorption), we may infer from (23) that, while the vibra-

1
tions travel over a distance i? their amplitude is diminished in the

1
ratio of 1 to —.
e

In order to determine w and x, we have only to substitute (22)
in (21). We then get

(Ll — ix) 1
SS SS bap SSS
w SH 1
or, separating the real and the imaginary parts,
c? (1 — x?) § 2c? x 1
TEE Ne En on
PD) § + n ov? S + i?
from which we derive the formulae
EL Ir Er E
oo = sn ) a at 5 Ss : ded, eee (24)
Spry Th + 4%

EH 12 Ha’ §
= A eee
AE EDE a? En ( )

in which the radical must be taken with the positive sign.

a

edn and

( 599 )

If the different constants are known, we can calculate by these
formulae the velocity and the index of absorption for every value
of the frequency #; in doing so, we shall also get an idea about
the breadth and the intensity of the absorption band.

§ 8. In these questions much depends on ‚the value of 4. In the

special case §— 0), i.e. if the frequency is equal to, or at least only
a little different from that of the free vibrations, we have on account

of (25)
2 Dene
ae

From what has been said above, it may further be inferred that

along a distance equal to the wave-length in air, i.e. , the

nr
amplitude decreases in the ratio of 1 to

2acx

é

wo

Now, in the large majority of cases, the absorption along such a.

8 : 2 2mcx
distance is undoubtedly very feeble, so that —— must be a small
wo

n2,,2

number. The value of must be still smaller and this can only

be the case, if 4 is much larger than 1.
This being so, the radical in (25) may be replaced by an approxi-
mate value. Putting it in the form

Angee 1
Cae La Sy os
aa
we may in the first place observe, that, since 1 is large, the numerator
2§+1 will be very small in comparison with the denominator,

whatever be the value of §. Up to terms with the square of

2§-+1

we may therefore write for the radical

— St a?’
pee eed Ed
25+ 868 64-77)

and after some transformations
Gee Baie es
ow 8(8 +a)
As long as § is small in comparison with 7, the numerator of
this fraction may be replaced by 47. On the other hand, as

( 600 )

soon as § is of the same order of magnitude as 7? or surpasses
this quantity, the fraction becomes so small that it may be neglected,
and it will remain so, if we omit the term — 48 in the numerator.
We may therefore write in all cases
Ch __ y
oe 484-77)

so that the index of absorption becomes

n 1
kene En
2e SH
This formula shows that for 8=0 the index has its maximum
value
n
Ne ee ET
2en
and that for §—= + vy, it is vp? +1 times smaller.
The frequency corresponding to this value of § can easily be cal-
culated. If @ may be neglected, a question to which we shall return
in § 18, (41) may be put in the form

mnd Gon REE

>
>
>
—~
>=

s
Hence, for §= += vx
m (n? — n,?) = + vg = +t yng’,
or, on account of (10) and (18),

ee 5 2mpn
m(n? — n,*) = Erang= + — :
G

2vn

T
If » — n, is much smaller than 7,, we may also write
zj

es <= Ge eae Mo (2)
T

The preceding considerations lead to the well known conclusion,
somewhat paradoxal at first sight, that the intensity of the maximum
absorption increases by a diminution of the resistance, or by a lengthen-
ing of the time during which the vibrations go on undisturbed. In-
deed, if g is diminished or rv increased, it appears by (10) and (12)
that 2] becomes smaller and by (27) 4, will become larger. This result
may be understood, if we keep in mind that, in the case n= no,
the one most favourable to “optical resonance’, in molecules that
are left to themselves for a long time a large amount of vibratory
energy will have accumulated before a blow takes place. Though
the blows are rare, the amount of vibratory energy which is converted
into heat may therefore very well be large.

pn”

( 601 )

In another sense, however, the absorption may be said to be
diminished by an increase of t (or a diminution of g), the range
of wave-lengths to which it is confined, becoming narrower. This
follows immediately from the equation (26). Let a fixed value be
given to §, so that we fix our attention on a point of the spectrum,
situated at a definite distance from the place of maximum absorption,
and let 4 be gradually diminished. As soon as it has come below
8, further diminution will lead to smaller values of 4, i. e. to a
smaller breadth of the band.

If g is very small, or t very large, we shall observe a very nar-
row line of great intensity.

§ 9. The observation of the bands or lines of absorption, combined
with the knowledge that has been obtained by other means of some
of the quantities occurring in our formulae, enables us to determine
the time t and the number N of molecules per unit volume.

I shall perform these calculations for two rather different cases,
viz. for the absorption of dark rays of heat by carbonic dioxyd and
for the absorption in a sodium flame.

As soon as we know the breadth of the absorption band, or,
more exactly, at what distance from the middle of the band the
absorption has diminished in a certain ratio, the value of + may be
deduced from (29); we have only to remember that in this formula,
n is the frequency for which the index of absorption is yr? + 1 times
smaller than the maximum 7,

Anestrim') has found that in the absorption band of carbonic
dioxyd, whose middle corresponds to the wave-length 2 = 2,60 u,
the index of absorption has approximately diminished to 44, for

= 2,30 u. This diminution corresponding to r = 1, we have by (29)

1

ZEN — Nos
T

if 7, and n are the frequencies for the wave-lengths 2,60 u and 2,30 u.

In this way I find

<= 104 sec.

In the case of the absorption lines produced in the spectrum by
a sodium flame, we cannot say at what distance from the middle
the absorption has sunk to 3 /,. We must therefore deduce the value of
tT from the estimated breadth of the line. Though the value of v
corresponding to the border cannot be exactly indicated, we shall

LY Ke Anastrom, Beiträge zur Kenntniss der Absorption der Wärmestrahlen
durch die verschiedenen Bestandteile der Atmosphäre, Ann. Phys. Chem. 39 (1890),
p. 267 (see p. 280).

( 602 )

probably be not far wrong, if we suppose it to lie between 3 and 6;
this would imply that at the border the index of absorption lies be-

1 1
tween a k, and 5 ke, If therefore 2 relates to the border, the for-
: aq leave dl 1 \ 1
‘mula (29) shows that the limits for — are — (n— 1) and ie (n—n,).
T )

In Hat.o’s experiments the breadth of the D-lines was about
1 A. LE. The relation between 7 and the wave-length 2 heing

2e
PE
we find for that between small variations of the two quantities
dn = — zeg dà.

Hence, if we put dA=0,5 A. H.=0,5 X 10-8 em, we find
n — ny — 0,26 X 1012,
from which I infer that the value of rt lies between 12 Xx 10—! and
24 «x 10—!2 see.

§ 10. In the case of carbonic dioxyd the number MN may be
deduced from the measured intensity of absorption. In ANesTrom’s
experiments this amounted to 10,6 pCt. in a layer, 12 em. thick, |
and for 4= 2,60 u. The amplitude being diminished in the proportion
of 1 to et? in a layer whose thickness is z, and the intensity of
the rays being proportional to the square of the amplitude, we have

el — 0,894,

and
ko = 0,0046.
Now, by the formulae (27), (12), (10) and (18)
oo Ne'r
eden
Ee ER
et

Here + and i, are known by what precedes. As to the charge 6,
it is, in all probability, equal to that of an electrolytic ion of hydrogen.
It is therefore expressed in the usual electromagnetic units by
the number 1,3 X 102, and in the usual electrostatic units by
3,9 Xx 10-10, The unit of electricity used in our formulae being
Via 3,5 times smaller than the common electrostatic one, we
must put

mld 610-0. evt Za vr GED

( 608 )

In the case of the infra-red rays whose absorption has been
measured by AnestrOM we are probably concerned with the vibrations
of charged atoms of oxygen or carbon. The mass of an atom of
hydrogen being about 1,3 X 10-24 gramme, I shall take

m= 2 10528,

The result then becomes

N=6X 101,

§ 11. The above method is not available for a sodium flame.
Harro has however observed that the value of N for this body may
be deduced from his measurements of the magnetic rotation of the
plane of polarization and Gerst has shown that the magnetic double
refraction in the flame may serve for the same purpose. In what
follows I shall only use one of Harro's results.

In the first place it must be noticed that in the case to be con-

-
=

0 = S) 4
sidered, § is much larger and —— — much smaller than unity. The

3 + 1?

radical in (24) may therefore be replaced by

lee
ze Sa 4 ij
and the formula becomes
a =1+ EN .
w 2 (S? + n°)

Now, if there is an external magnetic field, the velocities of pro-
pagation , and ow, of right and left circularly polarized light can
be calculated by a similar formula. We have only to replace § by
§—S$ and by §+6.') From the results

Ee SS
sisi ee am == |l END See
Ma =o a ae an

we find for the angle of rotation per unit length

1 € ~ ) n Sie SH
g=—n = =
2 GG 4c

EE

In order to determine MN hy means of a measured value of g,

we begin by observing that, in virtue of the equation (28), for
which we may write

S= 2m n, (n, — 2),

each value of ¢ determines a certain point in the spectrum whose
distance from the middle of the band is proportional to &. At the

1) See Lorentz, Sur la théorie des phenomènes magnéto-optiques, ete., § 16,

( 604 )

border of the band (if there is no magnetic field) § has the value
va, the coefficient » being some moderate number, say between 3
and 6 ($9), and for one of the components of Zreman’s doublet we
have §=6¢. In the magnetic field used by Harro the distance of
the components from the middle of the original line amounted to
0,15 A. 2, half the breadth of the line being 0,5 A. #., as has
already been said.
We have therefore the following relation between 7 and $:

Gon = 0,15 40,5

3,3
N=

Bene ai SER

Yv

On the other hand, a point in the speetrum, at which the angle

of rotation per unit length was approximately equal to unity, was
(35

situated at a distance of 1,6 A. EL. (5 of the mutual distance of the

two D-lines) from the middle of the original line. This being 10 times

the distance from this line to one of the components, we have

approximately

SEON

On substituting this value and (32) in the formula (31), it appears

that the terms 7? may be omitted. Hence, if (13) is taken into account,

+

n Ne
g¢'=-0,005 — = 0,005 RE
p Ae ’ H ( )
or since g = 1 is,
Ne= 200 H.
The strength of the magnetie field in these experiments was 9000
in ordinary units, or

in those used in our equations. Taking for e the value (30), I finally find
NS 410

-§ 12. The value of 4 may likewise be calculated, both for the
carbonic dioxyde and for the sodium flame. In the first case we can
avail ourselves of the formula (27), in which &, is now known;
the result is

1

RT

— 2,5 X 10%.

1 —=

For the sodium flame we first draw from (33)

( 605 )

It

= 500
2

BOO == 0.01
C

and we then find by (32) the following limits for 4
550 and 270.

These results fully verify our assumption that 1% would be a
large number.

Finally we can compare the values we have found for r with
the period of the vibrations. In this way we see that in the flame
some six or twelve thousand vibrations follow each other in uninter-
rupted succession. In the carbonic dioxyd on the contrary no more
than a few vibrations can take place between two successive blows.

$ 13. After having found the number MN of molecules in the
sodium flame we can deduce from it the density d of the vapour of
sodium. In doing so, 1 shall suppose the molecules to be single atoms,
so that each has a mass equal to 23 times that of a mass of hydrogen.
Taking for this latter 1,3 10-74 gramme, I find

d= DU
This is not very different from the number 7109 found by Harro.

Harro has already pointed out that this value is very much smaller
than the density of the vapour really present in the flame; at least,
this must be concluded if we may apply a statement made by
E. Wirpemann, according to which a certain flame with which he
has worked contained per cm’. about 510-7 gramme of sodium.
Perhaps the difference must be explained by supposing that only
those particles that are in some peculiar state, a small portion of the
whole number, play a part in the phenomenon of absorption. This
would agree with the views to which Lenarp has been led by his
investigation of the emission by vapour of sodium.

It must be noticed that the value of ‚N we have calculated for
carbonic dioxyd warrants a similar conclusion. In the experiments of
Ayestrém the pressure was 739 mm. At this pressure and at 15°C.
the number of molecules per cm*. may be estimated at 3,2 x 1019,
This is 50 times the number we have found in § 10.

§ 14. An interesting result is obtained if the time + we have
calculated for carbonic dioxyd is compared with the mean lapse of
time between two successive encounters of a molecule. Under the
circumstances mentioned at the end of § 13, the mean length of the
free path is about 7 > 10 6 em. The molecular velocity being
4X 10+ em. per sec, this distance is travelled over in

( 606 )

1,8 X 10-10 sec.,

Le. in a time equal to 18000 times the value we have found for rt.
We see in this way that it cannot be the encounters between mole-
cules, by which the regular succession of vibrations comes to an end.
It seems to be disturbed much more rapidly by some other cause
which is at work within each molecule.

In the case of the sodium flame there is a similar difference
between the length of time tr and the mean interval between two
encounters.

§ 15. We shall now return for a moment to the resistance that
has been spoken of in § 5, the only one that is really exerted by
the aether. This resistance is intimately connected with the radiation
issuing from a vibrating electron, and if a beam of light were
weakened by its influence, this would be due to part of the incident
energy being withdrawn from the beam and emitted again into the
aether. Of course, this could hardly be called an absorption. But,
apart from this objection, we can easily show that the resistance in
question is much too small to account for the diminution of intensity
that is really observed. Its component in the direction of « is

eo dx:
6e? dt’

or, for harmonie vibrations of frequency 7,

nie dx
6e? dt
Comparing this with (8), we find
net
g=-= é
; 62c

This amounts to 2,0 x 10-2! for carbonic dioxyd (for the wave-
length 2=2,60u ($ 9)) and to 4,0 X10 2 in the case of the
sodium tlame. These numbers are far below those which result from
(18), if we substitute the value that has been calculated for r. We
then get, for carbonic dioxyd 4,0 x 10-%, and for the sodium flame
a number between 1,2 X 10-16 and 0,6 X 10-16,

§ 16. It has already been shown in $ 8 that an increase of 1
broadens the absorption band, diminishing at the same time the ab-
sorption in its middle. Indeed, in many eases we may say that
the broader the band, the feebler is the absorption for a definite
kind of rays.

The question now arises what is the total amount of energy

( 607.)

absorbed by a layer of given thickness z, if the incident beam con-

tains all wave-lengths occurring in the part of the spectrum occupied

by the absorption band. In treating this problem, I shall suppose

the energy to be uniformly distributed over this range of frequencies,

so that, if we write /dn for the incident energy, in so far as it

belongs to wave-lengths between n and n+ dn, I is a constant.
The total amount of energy absorbed is then given by

ANSA NIS Ne NONO GEN (84)

Now, if the coefficient g and the time r were independent of the
density of the gas, both § and 4 would be inversely proportional to
NV; this results from (10), (12) and (28). The equation (26) shows
that under these circumstances and for a given value of n, 4 is
proportional to NV. The value of A will therefore be determined by
the product Nz. This means that the total absorption would solely
depend on the quantity of gas contained in a layer of the given
thickness, whose boundary surfaces have unit of area; if the same
quantity were compressed within a layer of a thickness } 2, the
absorption would not be altered.

The result is different, if g and t+ depend on the density. In order
to examine this point, I shall take z to be so small that 1
may be replaced by 242 — 2k*z?, so that (84) becomes

Se Uy! |= fa — ef k'dn
0 0

Let us further confine ourselves to an absorption band, so narrow,
that we may put

e — 2ke

ue EN 15)

NCP NG EE)
en
== ng k= 5 ET zi eer tos! (Gis)
Introducing §, instead of nm, and extending the integrations from
5—=—oa to§=-++, as may indeed be done, | find from (35)

x I 1
A= — [| z—— 2
2em! 4cg' ‘

or, on account of (10),

axl
A=

2em

1
Ne' z — — (Ne? z)? |
4cg

Two conelusions follow from this result. First, the absorption in
an infinitely thin layer of given thickness does not depend on the
42
Proceedings Royal Acad. Amsterdam. Vol. VIII.

( 608 )

value of g. In the second place, if the layer is so thick that the
second term in the formula has a certain influence, for a given
value of Ve, the amount of absorption will increase with g. It will
therefore increase by a compression of the gas, if by this means the
coefficient g takes a larger value. An effect of this kind has really
been observed by Anastrom ') in his experiments on the absorption
produced by carbonic dioxyde.

This result could have been predicted by theory if the idea that
the succession of regular vibrations would be disturbed by the colli-
sions between the molecules had been confirmed ; then, by an increase
of the density, the time + would become shorter and the formula (18)
would give a larger value for the coefficient g. As it is, the vibra-
tions must be supposed to be disturbed by some other cause (§ 14)
and we can only infer from Ayasrrom’s measurements that the influ-
ence of this cause must depend in some unknown way on the density
of the gas.

§ 17. Thus far, we have constantly assumed in our calculations
that the coefficient 9 is very much larger than unity ; this hypothesis
has been confirmed by the values given in § 12 and, to judge from
these numbers, it would even seem hardly probable that a can in
any case have a value equal to, or smaller than 1. Yet, there is a
phenomenon which can only be explained by aseribing to a a small
value. This is the dissvmmetry of the Zurman effect, which has been
predicted by Voier’s theory *) and has shown itself in some experi-
ments of ZrrMAN®). In so far as we are here concerned with it, it
consists in a small inequality, observable only in weak magnetic
fields, of the distances at which the two outer components of the
triplet are situated from the place of the original spectral line.
Whereas in strong fields the position of these components is deter-
mined by the equations §=-+ 6 and §=- 6, it corresponds to
s—0 and §=—1, if the magnetic intensity is very small.

Voigr has immediately pointed out that the dissymmetry can only
exist, if 4 is not very large. Yet, from the fact that the effect could
searcely be detected by Zmnman, he concludes that the coefficient must

1) Anasrrim, Über die Abhängigkeit der Absorption der Gase, besonders der
Kohlensiiure, von der Dichte, Ann. Phys., 6 (1901), p. 163.

2) Vorer, Uber eine Dissymmetrie der Zeemay’schen normalen Triplets, Ann.
Phys. 1 (1900), p. 376.

5) Zeeman, Some observations concerning an asymmetrical change of the spectral
lines of iron, radiating in « magnetic field, These Proceedings, I (1900), p. 298.

na enten

( 609 )

have been rather larger than unity. In my opinion, we must go
farther than that and ascribe to 4 a value, not sensibly above 1,
my argument being that the dissymmetry can only make itself felt,
if the difference between the distances from the original line to the
two components in question is not very much smaller than the breadth
of the line.

We know already (§ 9) that § =O at the middle of the line and
=r, at the border. Now, if 4 were sensibly larger than 1, the

Ss

places corresponding to $—0 and §=—1, i.e. the places occupied
by the two components in a weak field, would lie within the
breadth of the original line; it would therefore be impossible to
discern the want of symmetry.

§ 18. Whatever be the exact value of 4, ZeeMAN’s experiments
on this point show at all events that under favourable circumstances
a displacement of a line, corresponding to a change from §= 0 to
§ =1, or to a change

1

2m'n,

asc elas ew. +. (88)

of the frequency, is large enough to be seen. But, if such is the
case, we shall no longer be right, if we discuss the value of §, in
omitting quantities that are but a few times smaller than unity.
A quantity of this kind is the term « in the equation (11), which
as has already been mentioned, is but little different from ‘'/;, and
which we have omitted in all our calculations. If we wish to take
it into account, we shall find that all that precedes will still hold,
provided only we replace #, by the quantity 7',, determined by
ig = =I amok toh aioe = st oe Peten (3)
Indeed, (28) may then be written in the form

2
a

En (EF

and the place of maximum absorption, the middle of the line, will
correspond to the frequency m,, exactly as it formerly corresponded
to the frequeney 1.

Now, by (7) and (10)

SEK
and by (39)
19 ‘ a ; a
VZ mi na, ZEN — ere et (40)
aa 0
or, on account of (10),
a Ne?
ie = Ny — enn . . . . . . . (41)
2 Ny In

We learn from this equation that an increase of the density must

( 610 )

give rise to a small displacement of the absorption line towards
the side of the larger wave-lengths. A shift of this kind has been
observed by Humeurrys and Monrer in their investigation of the in-
fluence of pressure on the position of spectral lines. However, as
the formula (41) does not lead to the laws the two physicists have
established for the new phenomenon, I do not pretend to have
given an explanation of it.

Nevertheless we may be sure that in those cases in which the
dissymmetry of the Zreman effect can be detected, the last term in
(41), which in fact is of the same order of magnitude as the expres-
sion (88), can have an influence on the position of a spectral line
that is not wholly to be neglected.

On the other hand, it now becomes clear that, in the case of a
large value of 7, the term @ in (11) may certainly be neglected, its
influence on the position of the middle of the line being much smaller
than the breadth. *)

§ 19. We shall conclude by examining the influence of the last
term in (19), which we have likewise omitted. If we replace 7 by

} A Ef m/ ;
f + a and, in virtue of (10), 7’ by /' + —, which I shall denote by
T t° :

«

(7'), and if this time we neglect the term a@, the formula (11) may
again be written in the form (28). Indeed, if we put

i 1
Ware = en = iy AF =a) ’ . . . . 5 A (42)
we shall have
§ = m (n',? — rn’).

Instead of (42) we may write

1
=n i ed

oT
an equation which shows that the absorption band lies somewhat more
towards the side of the smaller wave-lengths than would correspond
to the frequeney 7, and that its position would be shifted a little,
if the time t were altered in one way or another ($ 16). These displa-

') Prof. Junius has called my attention to the fact that in many cases the absorp-
tion lines are considerably broadened by the change in the course of the rays that
can be produced in a non-homogeneous medium by anomalous dispersion. In the
experiments. of Harro, | have discussed, this phenomenon seems to have had no

influence. This may be inferred from the circumstance that the emission lines of

his flame had about the same breadth as the absorption lines,

ee

——— nnen

(COS)

cements would however be much smaller than half the breadth of
the band. This is easily seen, if we divide the value of 7”, — 7,
calculated from (43) by the value of » — 7, that is given by (29).
The result jd

1

c
2
2vn,t

is (ef. $12) a small fraction, because ‚rt is equal to the number of
vibrations during the time rt, multiplied by 2 2.

(January 25, 1906).

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,

PROCEEDINGS OF THE MEETING
of Saturday January 27, 1906.

DOG

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 27 Januari 1906, Dl. XIV).

SC OWN Mee NEE Ss:

F. M. Jarcer: “Contribution to the knowledge of the isomorphous substitution of the
elements Fluorine, Chlorine, Bromine and Iodine, in organic molecules”. (Communicated by
Prof, A. P. N. FRANCHIMONT), p. 614. (With one plate).

L. van Irarrie: “On catalases of the blood”. (Communicated by Prof. C. A. PEKELHARING), p. 623.

L. van Irarmie: “On the differentiation of fluids of the body, containing proteid”. (Commu-
nicated by Prof. C. A. PEKELHARING), p. 628.

O. Postma: “Some remarks on the quantity H in Botrzmann’s “Vorlesungen über Gastheorie”.
“_(Communicated by Prof. H. A. Lorentz), p. 630.

F. A. F. C. Went: “Some remarks on the work of Mr. A. A. Perre, entitled: “An enumeration
of the vascular plants known from Surinam, together with their distribution and synonymy”,
* p. 639.

W. Karrern: “The quotient of two successive Bessel functions’, (2nd paper), p. 640.

H. J. Zwiers: “Researches on the orbit of the periodic comet Holmes and on the perturbations
' of its elliptic motion”. (Communicated by Prof. H. G. van pr Sanpe BAKHUYZEN), p. 642.
“LS. Orysrers: “On the motion of a metal wire through a lump of ice”. (Communicated by
Prof. H. A. Lorentz), p. 653.

P. P. C. Hork: “On the Polyandry of Scalpellum Stearnsi”, p. 659.

Jan DE Vries: “A group of complexes of rays whose singular surface consists of a scroll and
a number of planes”, p. 662.

Crystallography. — “Contribution to the knowledge of the isomor-
phous substitution of the elements Fluorine, Chlorine, Bromine
and Iodine, in organic molecules”. By Dr. F. M. Janenr.
(Communicated by Prof. A. P. N. FRANCHIMONT).

(Communicated in the meeting of November 25, 1905).

Some time ago a paper was published by GossNer *) on the erystal-
forms of Chlorobromonitrophenol, Dibromonitrophenol and Lodobromo-
nitrophenol being an experimental contribution to the knowledge of

1) B. Gossner, Krystallographische Untersuchung organischer Halogenverbin-
dungen. Ein Beitrag zur Kenntniss der Isomorphie von Cl, Br und J. Zeitschr. f.
Krystall. Bd. 40. (1905). 78—85.

43

Proceedings Royal Acad. Amsterdam. Vol. VIII.

( 614 )

the isomorphous substitution of the halogens C7, Br and / in organic
molecules. The author first gives a short résumé of the chief series
of inorganic compounds where C/-, Br- and /-compounds have been
compared in regard to their crystal-form. Even in cases where a
direct analogy in form does not occur an isodimorphism may be
always proved to exist.

The /-compounds differ in most cases from the others as regards
their behaviour.

Only a few complete series of analogous halogen derivatives of
organic compounds have been investigated and in no case as to
their mutual behaviour in the liquid state.

A complete crystallographical investigation was made of : p-Chloro-,
p-Bromo- and p-lodoacetanilide *), the melting points of which are
respectively, 179°, 1674° and 181°. The Bromo- and the Zodo-com-
pounds are both monoclinic, the Chloro-compound differs and is
rhombic. The Br- and the /-compound present in symmetry and
parameters a distinct analogy with the rhombic C/-compound; the
plane of cleavage is, however, a totally different one *).

Cl-compound: Rhombo-pyramidal.

a:b:c=1,3347 :1 : 0,6857 ; 8 = 90°0'. Cleavable towards {100}.

Br-compound : monoelino-prismatic. *)

a:b:ce=1,3895:1:0,7221; 8=90°19'. Cleavable towards {301}.
J-compound: monoclino-prismatic. *)
a:b:e=1,4185:1:0,7415; 8—90°29'. Cleavable towards {301}.

GossNERr *) proved that the C/-compound is dimorphous and also
that it possesses a more labile monoclinic form. On the other hand,
the Br- and /-compounds are certainly also d/morphous but here
the rhombic modification is the more labile. The more labile and
the more stable modifications possess very analogous parameters,
although their molecular structures are different. He thinks however
that the drregular positions of the melting points may be satisfac-
torily explained from all this.

On the other hand, in the series Chlorobromo-, Dibromo- and
Lodobromonitrophenol, all three derivatives are directly-isomorphous
with each other. (Structure: (OH):(NO,): Bre=1:2:4; Cl, Br
and J on 6). ;

1) B. Gossner, Z. f. Kryst. 38. 156—158. (1904).

2) Fers, Z. f. Kryst. 32. 386 (1900); Idem 32. 406.

8) Mian, Z. f. Kryst. 4. 335; Fers, Z. f. Kryst. 37. (1903). 469; Witson, Z. f.
Kryst. 36. 86. Abstract; Panepranco, Z. f. Kryst. 4. 393.

4) Sanson, Z. f. Kryst. 18. 102.

5) Gossner, Z. f. Kryst. 88. 156—158.

(615 )

This is the first properly investigated series of halogen-substitution
products in organic chemistry where C/, Br, and J replace each
other in a directly isomorphous manner.

Notwithstanding this complete isomorphism there occurs here a
remarkable abnormality in the position of the melting points, just
as in the case of the isodimorphous p-Halogen acetanilides. This
abnormality cannot, therefore, be explained in the manner described
above; in fact it is quite incomprehensible:

Cl-compound: m.p. 112° C. Spee. gr. 2,114 Mol. Vol. 118,7
Br- A Lore Dd (a ye Saad Ga eee Pa ASA 4, 5, AAT
I- 5 m.p. 104° C. 3 £82,045 7"; ) 3 129,03

In this case it is the /-compound which exhibits an abnormal
melting point.

From all this it is evident that there is still something strange,
as regards the mutual morphotropous relations of the halogens, at
least, in the case of organic compounds: Some facts relating thereto
will therefore be communicated in what follows.

I have, frequently, published papers on the Methyl esters of p-
Chloro-, and p-Bromobenzoie acid *). The Chloro- and Bromo-deriva-
tive each appeared to possess a different form, whereas the melting
point line of binary mixtures should lead to the conclusion that an
isodimorphism was present here, with a melting point line of the
rising type, although it seemed impossible then to define by physico-
chemical methods the limits of mixing for the two kinds of mixed
erystals.

In order to treat the existing problem as fully as possible, I
prepared first of all the corresponding //wore- and Zodo-compound.

p-Fluorotoluene kindly presented to me by Prof. HorLeMAN was
oxidised with KMnO, in alkaline solution, the p-Flworobenzoic acid
was separated with HCl and then esterified by means of methyl
alcohol and hydrogen chloride. The ester, which has a strong odour
of .uniseseed oil, is a liquid rendering measurements impossible, but
on the other hand the acid could be measured crystallographically.

p--Toluidine was diazotised and converted by means of KT into
p-lodotoluene, this was distilled with steam, recrystallised and oxidised
as directed to p-Jodobenzoic acid. In the same manner, p-Aminobenzoic
acid was converted by diazotation ete. into its acid and this was

1) Jaeger, Neues Jahrb. f. Miner. Geol. und Palaeont. (1903). Beil. Bd. 1—28;
Zeits. f. Kryst. 38. (1903). 279—301.
43%

( 616 )

purified by sublimation. Both Jodobenzoic acids thus obtained. were
then esterified by means of methyl alcohol and HCl.
The product so obtained was purified by repeated recrystallisation
from boiling alcohol until the melting point became constant at 114°.
The methyl ester of p-lodobenzoic acid m.p. 114° erystallises from
ether + alcohol in colourless needles, having a faint odour of aniseseed
oil, which are very neatly formed, and exhibit the form of fig. 8.

Rhombo-bipyramidal.
a:b:e=1,4144:1 : 0,8187.

Forms observed; a = {100}, predominant, very strongly lustrous,
sometimes with delicate, vertical stripes; p = {210}, very sharply
reflecting; 6 — {110}, narrow, often absent, but yields very sharp
reflexes; v= {122} and » = {011}, well-developed; o = {112}, very
small and often absent altogether.

Habit: flattened towards {100}, with tendency parallel to the c-axis.

Angular measurements:
Measured: Calculated:
a: p = (100) : (210) S*So dark ==
b:v = (010) : (122) =*51 49 —
b : p = (010) : (210) = 54 44!/,

v:v = (122) : (122) = 76°23’ 76°22’
b: r= (010) : 011) = 50 24'/, 50 41°/,
@:0 = (100) :(122) == 77 29 77 23

v : 0 = (122) : (122) = 25 42 25 41
r:7 = (011) : (O11) = 79 12 Todd:

ù sr = (122): (011) =12 507/, 12 37
p:r = (210): (011) = 68 23 68 33
0: 0 == (422) 42) SAT OY, 16 43'/,
0:0 = (112) : (112) = 43 3 42 55'/,

Cleavable towards {010}.

The optical axial plane is {001} with the d-axis as first bissectrix.
The apparent axial angle in a-monobromonaphthalene is about 80°;
the dispersion is e <v. On a, p and 6 orientated extinction.

The sp. gr. of the ae is: 2,020 at 10°; the equivalent volume
— 129,7.

Topic axes x: pw: w = 6,8179 : 4,8208 : 3,9464.

From the above it follows that the /-compound is perfectly iso-
morphous with the analogous Br-eompound. By way of comparison

(6E)

some of the chief data observed in both compounds are placed here
in juxtaposition :

p-lodobenzoic Ester : p-Bromobenzoic Ester:
Rhombo-bipyramidal Rhombo-bipyramidal
a:6:c= 1,4144:1 : 0,8187 a:b6:¢c=1,3967 : 1 : 0,8402
Forms: Forms:

{100}, {010}, {011}, {210}, (1123, {122}. {100}, {010}, (O1 13, {210}, 112}, 1122}
On {100} delicate stripes On {100} delicate stripes
parallel c-axis. parallel c-axis.

Cleavable along 6. Imperfectly cleavable along 6.
Axial plane is {001}; 1st Diag. is hb. Axial plane is {010}; 1st Diag. is b.
Angles: Angles:
G3 pi— 3016) a: p = 34°56’
OE v 91°49’ by 51°10!
0:0 = 42°55 etc. 0:0 = 43°50" etc.

The dispersion in the /-derivative is of an opposite character to
that in the Br-compound; the apparent axial angles are almost equal
if that of the /-derivative is measured in a-Bromonaphthalene and
that of the Br-derivative in oil of Cassia.

It seems remarkable, that in our case the Bromo- and Zodo-com-
pounds behave in an analogous manner and that it is the Chloro-
compound which exhibits here a deviating character.

In order to show the further relation of the three compounds the
binary melting point lines were determined and represented in fig. 9.

The melting point line Br-/-compound does not deviate markedly
from the straight line, the difference is really negligeable. The lowering
of the melting point of the /-derivate is, therefore, practically directly
proportional to the number of added molecules of the Br-compound.

The melting point lines C/-/- and C/-Br-compound take an analogous
course, that is to say, all the melting points lie between the lowest
and the highest melting point. Both melting point lines belong to
the rising type of RoozeBoom, which may occur in isodimorphous
substances. The lower branch and the mixing limits could not be
found by thermometrical methods. The existence of these two branches
may indeed be proved, and they are even situated at some considerable
distance from the top branches — at least at the side of the com-
pounds having the highest melting points — as was found by Dr.
B. R. DE Bruyn. It is, however, not possible to determine this line
with sufficient accuracy. The progressive change of the cooling-curve
is of such a nature that a discontinuity is observed from which we

( 618 )

may draw the above mentioned conclusion that the lower branch of

the melting point line — at least at the side of the rhombic mixed
crystals — is situated at a fairly considerable distance from the upper
sel Ln

: 0
Ô (24 0 Ó GO 90 700
100 90 80 70 60 40 30 20 10 a

Fig. 9. Binary melting point lines of the three halogenised benzoic methyl esters.

branch. This change in direction of the cooling line is, however, so
slight, that the true situation of the point on the lower branch cannot
be indicated with certainty.

The determination of the mixing limits by an investigation of the
solid phases, which are in equilibrium with solutions of known con-
tent, met with difficulties of an analytical character. An effort was,
therefore, made to determine those mixing limits by the crystallo-
graphic process. For that purpose solutions were prepared of mixtures
of the two esters, for instance of the chloro- and the bromo-ester,

( 619 )

in ether + alcohol, and the homogeneous mixed crystals obtained
on slow evaporation were individually investigated crystallographic-
ally and then their melting point was taken, namely the temperature
at which the last particle of solid matter disappears in the surrounding
fused mass. If one may assume that this last solid particle, in each
of the cases investigated, is really in state equilibrium in regard
to the fused mass, the temperature thus found, by comparison with
the already found upper branch, indicates the molecule-percentage
composition of the mixed erystal under investigation.

If we take little of the Br-ester and much of the Cl-ester, we
obtain from the alcoholic solution monoclinic mixed crystals which
possess quite the form and angular values of monoclinic Cl-ester
itself. Of such crystals the melting point never exceeded 46'/,°. If
the proportion of the components is reversed mixed crystals of a
rhombie form are deposited quite analogous to the Br-ester. These
crystals gave melting points from 79'/,° down to 47° ; but not lower.

Assuming that the melting point of the end terms of the mono-
clinic series does not differ practically from 47°, it then looks as
if rhombic mixed phases may exist which, at 47° as transition tem-
perature, attach themselves immediately to the monoclinic terms. I
have found, however, that rhombic mixed crystals with various melt-
ing points kept together in a closed tube for four months become
turbid and partially opaque with a rough surface as soon as their
melting point falls below 65°. It is also remarkable that the rhombic
mixed phases of this kind are more and more badly formed and curve-
planed, and that they become more distorted, as if existing in a kind of
enforced condition, when their composition begins to differ from that at
65° towards the monoclinic side. It seems to me that when accepting
the above hypothesis, all rhombic mixed phases below 65° represent
metastable conditions, which, in the solid state, are very slowly
broken up, to be partly converted into monoclinic terms.

That is to say the melting figure takes schematically the form of
fig. 9; the said metastable conditions are then points situated on the
extended part of the lower branch to the right, which indicates the
composition of the rhombic mixed crystals coexisting with the fused
mass. The stable hiatus in the mixing series then extends from 18°/,
to 60°/, of the Br-compound.

From all this it follows that in consequence of the very slow
conversion of the mixed crystals, no sharp determination of the
mixing limits can be made in this manner when less than 60°/,
Br-ester of monoclinic character is present.

In the system C/-ester + /-ester the matter is still more troublesome.

( 620 )

There, the end term of the monoclinic mixing series is ‘situated
still much closer to the axis than in the case mentioned. In conse-
quence of the very great difference in solubility of the C/-, and the
[-compound we never obtain here from alcoholic solutions anything
else but rhombic very delicate needles, while the monoclinic phases
erystallise so indistinctly that they are quite unsuitable for a serious
investigation.

The Br-, and the /-ester readily erystallise together in all propor-
tions with angular values which differ but little from those of the
components. No optical anomalies could be found in such mixed
phases. From this it follows that to those two halogen substitution
products belongs au analogous molecular structure. Their molecular
volumes in the solid condition agree indeed very well; the difference
is smaller than between tbat of the Cl-, and Br-compounds.

As regards the lowering of the melting point of the compound
melting at the higher temperature by addition of the one melting
at the lower temperature, this is not proportionate to the number of
added molecules, as in the system Br- + /-compound. In the
mixtures of C/- and J-ester, the observed values are always situated
on a curve which oceurs above the line of the proportionate lowering
of the melting point; in the system Cl- and Br-ester, on a two-
periodic curve which occurs below the said straight line.

It must also be observed that the mixed phases deposited from
alcoholic solutions possess a larger content in the compound melting
at the higher temperature than the solution from which they have
formed. For instance, from a solution containing 20°/, of Br-ester
and 80°/, of Cl-ester, mixed (rhombic) crystals were at first depo-
sited which melted at 57° corresponding with a considerably higher
percentage of the Ar-compound.

The Chloro-compound which is monoclinic with:
a:b:c=1,8626:1:3,4260, and 6= 64°18’

and the forms:
a={100}, c=(001}, r= $102}, p—{2 103, t—=(01 1, o=fT11}, c= {111}, {113}.
presents a habit which is not at all like that of the two other deri-
vatives, although that habit, as shown in fig. 1—5, is in a high
degree variable, according to the choice of the solvent and tempe-
rature of crystallisation.

The habit of the Br- and /-compound is on the other hand per-
fectly analogous ; in the /-ester it is, moreover, very constant under
different conditions of crystallisation (fig. 8) whilst it is still some-

( 6214 )

what changeable in the Br-ester (fig. 6 and 7), although no longer
so strong as in the C/-derivative. With an increasing atomie weight
of the halogens, the changeability of the erystal-habit, owing to a
change in conditions of crystallisation, decreases considerably and
gradually.

The sp. gr. of the three compounds, their equivalent volume and
their topic parameters are :
Cl-ester: de = 1,382; V=123,37 .y: wp: =5,1731:2,7774: 9.5153.
Br-ester: d,,o = 1,689; V—=127,29.p:w: w —=6,6611 : 4,7691 : 4,0070.
Jester: do = 2,020; V = 129,70. 4: W: w = 6,8179 : 4,8208 : 3,9464.

It must be remarked here that the melting points of the three
esters increase regularly by 35'/,° notwithstanding the difference in
erystalform : 44°—79*/,°—114°.

The above admits of no other explanation than the assumption
that all three halogenised esters are dimorphous. The C/-ester must
still exist in a more labile rhombic form and the Br- and J-esters
in a more labile monoclinic form. In one of Bruni’s communications *)
a “monoclinic’* p-Bromobenzoic Methyl Ester is described by an
Italian investigator with the object of proving an “isomorphism”
with the analogous p-Nitrobenzoic ester. The given measurements
have, however, absolutely no connection with those applied to the
p-Chlorobenzoate, so that this monoclinic form can in no case be
the one intended. Moréover, none of the measured angular values
of the p-Bromo-derivative agree with those obtained by myself. It
appears to me doubtful whether the measurements mentioned in
Bruni’s paper are really correct or it may be that the operator has
really not been working with p-Bromobenzoic Methyl ester at all.
All efforts made by me to obtain from this substance a crystal form
different to the rhombic one proved fruitless, whilst in the Italian
treatise, the supposed “monoclinic” form is represented as a perfectly
stable one which, therefore, occurs continuously.

In order to prove an eventually existing dimorphism of these sub-
stances, I have made use of LeEHMANN's microscopical method with the
aid of the crystallisation microscope constructed by him. It appeared,
however, that in none of these cases a positive result could be
obtained. I think that in the case of each of these substances, I can
notice two different ways of. crystallisation under the microscope,
namely long, rather delicate needles and also parallelogram-limited

1) Brunt and Papoa, Gazz. Chimic. Ital. (1904). 84a. 133—143 ; Rendic. Lincei
(1903). 5a, 12. 348.

( 622 )

flat needles which exhibit higher interference colours and like the
first named extinguish normally on the longitudinal direction. Howe-
ver, the difference — if present at all — is so indistinct that taking
into consideration the inclination of these substances to alter their
crystal-habiousit under var circumstances in so high a degree, I dare
not conclude to an already proved dimorphism, Experiments with
mixtures richer or poorer in Chloro-ester also exhibited the same
properties. It is, therefore, quite possible that we have two forms
for each of the three substances, but this has not yet been proved
and also it could not be ascertained whether in the given circum-
stances both eventually present forms stood to each other in the
position of monotropy or enantiotropy.

A few short data as to the halogenised benzoic acids deserve mention.

1. p-Chlorobenzoic acid m.p. 243° has been measured by Fers
(Zeitschr. f. Kryst. 32, (1900) 389). It is monoelino-prismatie, with
a:b:c=1,2738:1 :3,3397, and 8 = 78°24}'. The forms observed
have intricate symbols; besides a = {100} and c = {001}, he finds
d = {207}, o = {111}, e= {233}, u = {322}, v = {411}. Sp.gr. = 1,541.

2. p-Fluorobenzoie acid m.p. 182° synthesised by me is also
monoclino-prismatic. If to the forms occurring here we assign
the symbols: a = {100}, c = {001}, 7 = {203}, s = {403}, and g={043},
the indices being therefore analogous to those given above, the
parameters become :

a:6:¢6=1,1917 :1:3:1825
p= 18 16"

Although there exists here an undeniable difference in habit, I
think I may still conclude that there is a direct isomorphism of
the Chloro- and Fluoro-compound. A distinct plane of cleavage was
not found. The melting point of p-/luorebenzoic acid is also elevated
by addition of the C/-compound.

Angular values:

csr = 69°56'
aag == IL5 LN
ge =d
Cad =S Ue)
Cg dS

Meg

The habit is thin-tabled towards c. with a rectangular cireum-
ference. The crystals were obtained from alcohol + ether and were
generally badly formed. The extinction on c is orientated.

F. M. JAEGER. Contribution to the knowledge of the isomorphous substitution of the elements Fluorine,
Chlorine, Bromine and Iodine in organic molecules.

Fig. | Fig. 2

p-Chlorobenzoic Methyl ester
From methyl alcohol, at a higher temperature.

Fig. 4.

p-Chlorobenzoic Methyl ester.

From methyl alcohol, at a lower temperature

Fig. 3.
c
p-Chlorobenzoic Methyl ester.
From ethyl alcohol, at a higher temperature.
a’
Fig 6.
a

p-Chlorobenzoic Methyl ester.
From methyl alcohol, at a higher temperature.

Fig. 5.
ART =
Aa, fs ee
En
EE
p-Bromobenzoic Methyl ester.
p-Chlorobenzoic Methyl! ester. From methyl alcohol
From ether, at a lower temperature Fig. 8
| ae
w* eN
. a

p-Bromobenzoic Methyl ester. al

From ether. p-lodobenzoic Methyl! ester
From ethyl alcohol + ether,

Proceedings Royal Acad, Amsterdam Vol. VIII.

( 623 )

3. _p-Bromobenzoice acid, m.p. 252° was obtained by me in tiny
crystals from ethyl acetate + benzene but they were very badly
formed. They are monoclinie and probably quite isomorphous with
the two other acids. The angle of inclination amounts to about 78°/,°.

4. p-lodobenzoic acid has not as yet been obtained in measurable
crystals owing to its little solubility in most of the organic solvents.
Its melting point is situated at 267°, therefore higher than that of
the Br-derivative. A direct isomorphism with the three other halogen
benzoie acids is not improbable.

Physiology. — “On catalases of the blood’. By L. van Irarur.
(Communicated by Prof. C. A. PEKELHARING.)

(Communicated in the meeting of December 30, 1905).

The discovery made by Tuénarp that bloodfibrine possesses the
property of decomposing hydrogenperoxide has also been extended
to defibrinated blood, by ScHönBriN (Journ. f. prakt. Chemie 89,
22). It has found a practical application in the judicial investi-
gation on bloodtraces and has been the object of manifold scientific
investigations. A resuming report precedes the investigations by
SENTER (Das Wasserstofisuperoxyd zersetzende Enzym des Blutes.
Zeitschr. f. physik. Chemie 44 |1903] 257—318) to whose work we
refer the reader. SenTER calls the enzyme which he has isolated
from blood Haemase whereas I myself prefer to use the name
of catalase, which has been given by Lorw (Catalase, A new enzym
of general occurrence, Report N°. 68 U. S. Depart. of Agriculture.
Washington).

Although the catalases, those enzymes which are able to split
H,O, in water and oxygen, are universally scattered in the vegetable
and animal kingdom, it has as yet not been possible to isolate one
of these bodies in state of purity.

Although different phenomena indicate that there exist more than
one catalase (apart from Lorw’s a- and @-varieties) it ‚has been
impossible as yet to discern them.

The following communication gives a new contribution to the
properties of the catalases of the blood, which may perhaps lead to
a differentation of the catalases, and which at least gives an opportunity
of dividing the catalases of some animals into two groups.

To Mr. C. J. Konine at Bussum I owe the communication that
human-blood diluted from 1—1000 heated at 63° for half an hour,

( 624 )

still contains a quantity of catalase whereas ox-blood under the
same conditions no longer contains any catalase after half an hour.
Want of time prevented the above mentioned gentleman from pene-
trating any further in this matter, so that he left the treatment of
this subject to me.

The loss of activity of the catalase of the blood by heating has
been investigated for ox-blood by Senter (Lc. p. 293). Those
investigations show that a diluted bloodsolution loses its activity in
a quarter of an hour at 65°, that the rapidity of decomposition is
considerably smaller at 55° and that the solution after having been
heated for three hours at 45° still contains 60°/, of the catalystic
power, .which it possessed originally.

Moreover it appeared that the loss of activity is not proportional
to the present quantity of the enzyme, but that this phenomenon
takes place with constant rapidity. I thought it useful to investigate
the observed phenomenon with regard to some species of blood *)
more closely and to see at the same time if it was possible to
render the catalasereaction serviceable to the distinguishing of different
species of blood.

Method of investigation. 5 cM* of the different species of blood in
a dilution of 1—1000 are heated for half an hour at 63°, then
cooled down to 15° and mixed with 3 cM*. of a hydrogenperoxide
solution of 1°/,. The mixture is put into a fermentation tube, such
as are used at the investigation of urine on glucose. If the mixture
still contains catalase the developing of oxygen begins within a few
minutes so that by the development of this gas it is indicated whether
catalase of the blood is present or not.

Human- and monkey-blood (Macacus cynomolgus) investigated in
this way appeared to contain still catalase after having been heated
at 63° for half an hour, whereas the blood of horses, oxen, pigs,
goats, sheep, rabbits, cavies, rats, hares, chickens, pigeons, fish (flounder)
and frogs did not show any reaction after the described treatment
with H,O, and did not split off oxygen within 3 hours.

Now the blood of some of these animals contains only a small
quantity of catalase, but in the liver this substance is present in
greater quantity. According to Barrerrr and Stern (Compt. rendus
138 |1904], 923-924) 10 mG. blood of a frog produces after being
mixed with H,O, of 1°/,, 7.5 cM.’ oxygen in 5 minutes, whereas

1) For the providing of species of blood 1 am indebted to Messrs. W. C. Scrummer
and M. G. pe Bruin, of the veterinary school at Utrecht and to Dr. J. Birrrxorer,
director of the zoological gardens at Rotterdam.

( 625 )

an equal quantity of the liver liberates 295 eM.* oxygen in the
same time.

The liver of a frog was mixed with purified sand, and the mixture
thus obtained was shaken with water. A drop of the decanted
liquid called about in a H,O,-solution a turbulent development of O.
If 5 cM.* of the liquid was heated for half an hour it lost the power
of decomposing H,O, quite, so that also with a considerable original
catalytic power the above mentioned time is sufficient to make that
power disappear.

In order to get an insight into the rapidity with which the catalase
of the blood loses its activity I put into practice the following method
of investigation for some species of blood.

5 cM.* of the bloodsolution (1—1000) were put in some test-tubes;
the tubes and their contents were heated for some time varying
from O—110 minutes in the thermostate at 63°, then cooled down
to 15° and mixed with 10 or 20 cM.* of a H,O,-solution of 1°/,.
The action having taken place, for 1°/, hour at 15°, the catalase-
action was interrupted by adding 10 cM.’ diluted sulphuric acid
and the quantity of hydrogenperoxide, which had not been decom-
posed was immediately titrated back with '/,, N. Kaliumpermanganatic
solution. While the not heated bloodsolution indicates the quantity
of H,O, which is decomposed by 5 milligrams of the used blood-
species, it could be investigated at an arbitrary point of time in how
far the catalytic action had been weakened by the heating.

At the used degree of concentration an oxidation of the catalytic
may originate by the H,O, (Senter Ze. 279) but I would not reject
the advantages which are offered by larger concentration as it was
not wanted to get in the first place absolute figures.

In the table mentioned below the results of my investigations are
written down while the graphic representation gives a more ample
survey. ;

It is peculiar that here as well as at the blood investigations of
Untennuta and those of Neisser and Sacus (Berl. klin. Wochenschr.
1905 N°. 44) the bloodspecies of related animals (man and monkey)
show a relation with regard to catalytic power concerning the
absolute strength as well as the greater resistance against the increase
of temperature.

I think I may deduce from these investigations that the catalases
occurring in the blood of different species of animals are not identical.
My own observations, it is true extend to some individuals of the
different species of animals only, but from reports of BarrLu and

( 626 )

Action of diluted bloodsolutions (4 — 1000) on hydrogenperoxide solutions (containing 1 pct. H,O,) after 5 cM’.
of the bloodsolution having been kept at 63° for the mentioned number of minutes and cooled down
to 15°. Time of the influence of the H,O,, one and a half hour at 15°.

mm

Time of Number of milligrams H,O, decomposed by Developed quantity O in cM$. (0° — 760 mM.
the heating
at 63° in | Human Mon- Horse Horse Ox Goat | Pigeon || Human Mon-| Horse Horse Ox Goat | Pigeon
i blood Le blood blood | blood | blood blood blood KO Blgad blood | blood blood blood
minutes. blood | (arterial) | (venous) blood | (arterial) |(venous)
OO
0 407.8 |107.3 66.6 43.9 90.7 8.8 0.7 3155 308 2.19 1.44 0.68 0.29 0.02
5 93.5 9.7 4.9 0 3.07 0.32 0.16 0
10 76.5 84.5 0 0 4A Sil 0 OMG, ON 0 0 0.13 0.10 0
15 68.9 ORO, des 2.26 0.07 0.04 |
20 48.3 57.6 0 0 49, 0.5 1.58 1.89 0 0 0.04 0.016
95 — 0.2 0 0.006 0
30 28.9 44.4 0 0 0.95 1.45 0 0
35 a
40 16.8 26 2 0.55 0.86
45
Dl 10.2 16 7 0.33 0.55 |
55 |
60 8.7 10.0 0.29 0.33
65
70 5.4 6.3 0.48 0.20
75
80 3.9 — 0.13 —
85
90 3.0 3.6 0.10 0.12
95
400 2.2 2.9 0.07 0.095
105
110 1.4 0.046 | |

( 627 )

Harrr (Soc. biol. 57 [1904] 264) it appeared already that the same
organs of animals of the same species contain mostly about equal
quantities of catalase and that this quantity is not dependent on the

mG. H,0,

no

Number of milligrams HO, decomposed
5 by five milligrams of different bloodspecies
after their having been heated at 63° for
some minutes in a dilution of 1 : 1000.

fen
rts.
Sites,

85 90 95 1eo fos 10
Human blood.
soon eee e nn eenen Monkey. blood.
Se ne , Horse blood (arterial).
=.= Horsesblood) (venous):
snoeren OX blood:
eG oatbloade
ee bigeons blood:

temperature of the body nor on the metabolism. To illustrate the
catalytic power of the bloodspecies which I investigated quantitati-
vely I add a short survey,

( 628 )

Quantity of oxygen in cM.* (0°—760 mAL.) obtained from the
action of 1 cM.* blood on a solution of H, O, of 1°/,.
Man 710
Monkey 706
Horse (venous) 288
Horse (arterial) 438

Ox 136
Goat 58
Pigeon 4

Utrecht, December 1905.

Physiology. — “On the differentiation of fluids of the body,
containing proteid.” By L. van Irarum. (Communicated by
Prof. C. A. PEKELHARING).

(Communicated in the meeting of December 30, 1905).

For the research of blood, sperm and other fluids of the body,
containing proteid, the phenomenon, that even traces of these sub-
stances are able to decompose hydrogenperoxide, has been used for
a long time already. If a drop of a hydrogenperoxide-solution is
put on an object on which blood or sperm was dried up, develop-
ment of gas is observed, even by the presence of traces of blood or
sperm which give rise to the forming of froth, when blood is
present. As the experiment can already be taken with some fibres,
and the splitting off of oxygen can be traced under the microscope,
it has often rendered me good services in examining on behalf of
the court of justice, at the preliminary-examinations. If then no oxygen
is liberated and the object on which dubious stains occur, has not
been exposed to a temperature higher than 65°, it may be concluded
from the fact that no reaction occurs, that blood and sperm were
absent.

It was obvious to try to render the result of the experiments
communicated in the preceding paper, serviceable to the distinguishing
of the blood of men, resp. monkeys, from the blood of other species
of animals. Not every one is in the possession of the serum. of
Untennvt or of the sera recommended by Nuisser and Sacus (Berl.
klin. Wochenschr. 1905, number 44) for the anti-complementary
influence, while it may be moreover of great value to the court of

justice to have within some hours the certainty whether bloodstains
appearing on an object, originate from human blood (in our country
of course monkey blood may as a rule be left unconsidered).

It is now indeed possible to show the presence of human blood
(resp. of the monkey) in older stains with the aid of the catalase of
the blood. I wish to draw the attention to this that the presence of
blood must have been proved by a preceding microscopical, chemical
or spectroscopical investigation because other fluids of the body too
(sperm and milk) cause a reaction of catalase.

The method of investigation is simple. If the dubious blood trace
is dried on some tissue, a piece of it is extracted with water at the
ordinary temperature and the extract is divided into two parts. One
part is mixed with a solution of hydrogenperoxide of 1°/, and the
mixture is put into a fermentation tube. The other part is heated
for half an hour in a waterbath at 68°, then cooled down to 15°
and after having been mixed with a solution of H,O, it is also put

a
into a fermentation tube. If within some hours oxygen develops in
both tubes, it may be concluded that human — (resp. monkey-)

blood is present; the quantity of oxygen in the second tube is of
course smaller than that in the first. When active catalase of the
blood is present the splitting off of oxygen begins soon after the
mixing, and is finished in some hours.

If however only in the first tube oxygen is split off and the
second tube does not show any development of gas, it follows that
the catalase of the blood has become inactive by the heating to 63°
for half an hour, and that the dubious blood does not originate
from man or monkey.

I was in the opportunity of applying these experiments to fresh
bloodstains of man, dog, ox and horse and to bloodstains on linen
from the year 1903 originating from man, oxen, horses, goats and
pigs. The old bloodstains gave the same results as the fresh blood.

If we dispose of more bloodstains we can follow the process of
the reaction somewhat quantitatively by preparing for instance a
larger quantity of extract with water, dividing this in parts of 5 cM.*,
heating this to 63° during different periods in test-tubes and mixing
it with H,O, and titrating it, as has been communicated in the
preceding paper. The peculiar process of the reaction, graphically
expressed, does not give a representation of the absolute quantity
of the catalase of the blood which is present, but is so characteristic
that human- (and monkey-) blood can be easily distinguished from
that of another species of animal, even in the dried state.

44
Proceedings Royal Acad. Amsterdam. Vol. VIII.

( 630 )

It is hardly necessary to mention separately that the reaction of
the catalase can be made serviceable to the distinguishing of mother’s
and cow’s milk.

Cow’s milk which has been heated to 63° for half an hour no
longer possesses the property of decomposing H,O,, a property
which mother’s milk still possesses in a rather considerable measure
under the same circumstance.

In a mother’s milk which I thank to the kind interference of
Prof. Kouwrr I found the following results, but it should be
observed that the action of the milk on the solution of hydrogen-
peroxide found place in the nitrometer of LuNee and that I read off
the volume of the developed oxygen after twelve hours :

5 cM.* mother’s milk not heated gave 24.8 cM.*? oxygen.
Did en » heated to 68° for «
quarter of an hour gave 18.5 „ A
5 2, 2, 2) bed 3 ” ”? ” >, 7.5 ” 2,
dur Sr be 5 » for an hour > 4:08 4
Utrecht, December 1905.
Physics. — “Some remarks on the quantity H in BoLtzMANN’s

“Vorlesungen über Gastheorie’” By O. Postma. (Communi-
cated by Prof. H. A. Lorentz).

(Communicated in the meeting of December 30, 1905).

§ 1. It seems to me that some of the views advanced in one of
the first paragraphs of the above mentioned work, are inaccurate;
and it may be desirable to draw attention to this fact, because
several considerations of BoLtTzMaNN and others are based on them.
1 mean § 6 on the “Mathematische Bedeutung der Grosse MH”.

In the ease of a gas the molecules of which are all of the same

type, this quantity is represented by [fli de. Now, in $ 5, assum-

ing that the gas is of the simplest nature and that the motion of
the molecules is “molecular-ungeordnet”, BorrzMANN has shown that,
in general, the quantity M decreases by the collisions and is minimum
in the stationary state.

Such a gas would therefore move of its own accord to the
stationary state i.e. with Maxwerr’s distribution of velocities, as
BoLrzMANN shows further on.

Now it is demonstrated in § 6 that the quantity H has also

( 631 )

another meaning, and that the circumstance that H is minimum
implies that the probability of the corresponding distribution of velo-
cities, indicated by the function f, is maximum. Afterwards the
connection between H and the entropy is indicated in $ 8 on the
“Physikalische Bedeutung der Grösse HZ”.

The meaning of H in question being very incompletely derived
in §6, we shall have to consult Vol. 76 of the Sitzungsberichte der
Wiener Akad., to which BontzmMann refers, and Vol. 72, to which
he refers in Vol. 76.

In $ 6 p. 40, BorrzManN begins with the following reasoning:
“Für alle Zusammenstösse, für welche der Geschwindigkeitspunkt
des einen der stossenden Molekiile vor dem Zusammenstosse in einem
unendlich kleinen Volumelemente lag, befindet sich derselbe, wie
wir sahen, bei Constanz aller anderen, den Zusammenstoss charakte-
risirenden Variabeln nach dem Stosse wieder in einem Volumelement
von genau gleicher Grösse. Theilen wir daher den ganzen Raum
in sehr viele (§) gleichgrosse Volumenelemente w (Zellen), so ist die
Anwesenheit des Geschwindigkeitspunktes eines Molekuls in jedem
solchen Volumenelemente mit der Anwesenheit in jedem anderen
Volumenelemente als ein gleichmöglicher Fall zu betrachten, gerade
so wie früher der Zug einer weissen oder einer schwarzen oder
einer blauer Kugel.”

So it is as if the velocities were assigned to the molecules by
taking for every molecule a slip of paper from a box, which box
would be filled with slips of paper each indicating a unit of volume
of the “whole space”. The probabilities a priori are therefore equal
that the components of the velocity §, 7,6 lie between two values
which differ d&, dy, dS.

Here at least something has been adduced to account for the fact
that these probabilities are equal, which has not been attempted in
Vol. 76 of the W. S. We have to derive it from the fact, that at
a collision the “points of velocity” skip from a certain volume into
one of the same size (cf. the “daher” of the quotation). For me
this has, however, by no means convincing force; for that one point
always skips from a volume to one of the same size does not prove
that it can just as well be found in any volume of the same size.
We shall presently show that this can hardly be assumed.

But let us first proceed. Let us assume n molecules are to have
a velocity, then the probability a priori that of them mn, @ have their
“point of velocity” in the first volume w, n, w in the second volume

8 : E n!
ete. is proportional to 7 = GRE ‚ Where (n,+-n, +...) w=n.
,@)!(n,w)!...
44*

( 632)

P
If we now assume that for p! may be taken vaal) ‚ we get
é
IZ=—a(n,ln, +n, ln, +...) + C, and so Z is maximum when
w (n,ln,+n,ln,+..) is minimum or when [Peo G8 dE dn dS

is minimum, or when Mis minimum, if we have a simple gas.

The distribution of the velocities f (815) for which Mis minimum,
is therefore also that with the greatest probability, concludes BOLTZMANN.
So the stationary state with Maxwerr’s distribution of velocities is at
the same time the most probable (p. 42).

This, however, follows by no means from the above, for the
stationary state is that, for which the change of H with the time in
consequence of the collisions — 0, whereas the most probable state
here is that for which every conceivable variation of the numerator
of Z—0:

Not before the condition is taken into consideration that the kinetic
energy of 7 molecules must have a definite value, as BOLTZMANN does
in Vol. 76 and 72, it can appear whether the result is the same.

Now

Jo Jo fo

H= ip Hb uc PENS) Uf (E48) dE dy a

=o = 00
must be minimum, while the conditions
nea dar
n =| f fre n S) dE dy dS
iy Hy er

and
id ar
ba tl [fete eorengdans
Sear
exist, when m is the mass of every molecule, and Z the kinetic
energy of m molecules.
In Vol. 72 p. 450 Botrzmann gives the solution of this, and it
appears that when no external forces exist,
ifEns)+atu.tmE +77 +5)=0
where 2 and u are constants which are still to be determined.
From this follows Maxwerr’s distribution of velocities.
But what probability problem has now been solved? I cannot see
that any has been solved but the following: From a box with slips
of paper, each indicating a volume element, one has been taken at

( 633 )

random for each of the m molecules of a certain quantity of gas;
the “point of velocity’ of the molecule was every time placed in
the volume element extracted. The n velocities which have been
extracted chanced to be such that the sum of the energies of the
molecules has a definite value 1. What distribution of the velocities
among those 7 molecules is now a posteriori the most probable?

The most probable is therefore the distribution of Maxwerr. But
this is a problem without importance for the gas theory. For itis
easy to see that the mean velocity indicated by the slips of paper
in the box is infinitely large, so that if from this » slips of paper
are taken at random, in general the mean velocity, which is indicated
by them, is also infinitely large, and there is only an infinitely small
chance, that the energy of the m molecules becomes finite. If we
now see that of every finite gas-mass the energy is finite, we cannot
assume that the velocities would have been assigned to the molecules
in the way mentioned above. The chances a priori for every velocity
must, therefore, not be considered as equal.

The mean velocity in the box may be calculated as follows.

If in the unity of volume there are c points of velocity, then in
a spherical shell with radius 7 and thickness dr there are: 4 a 7? ¢ dr.
The sum of the velocities now is dar? cdr, and so for a sphere
with radius r=ar‘tc. The number of points of velocity in the

4
sphere is 5 xr’ Cc, so the mean velocity = a”

For the whole space, therefore, the mean velocity is infinitely
large. In this way it is proved that the hypothesis of the equality
of the chances a priori is inaccurate, and so also the result that
MAXWELL’s distribution of velocities is the most probable state.

§ 2. Of course nothing is said here in derogation of the proof,
that Maxwerr's law holds in the stationary state, which BOLTZMANN
gives in the §§ preceding § 6 and in $ 7. But it is incorrect to
speak of transition of probable to improbable states when the meaning
is from stationary to non-stationary states. This incorrect view gives
rise to wrong considerations when BorTzMaNN discusses the fiction
of the reversal of the molecular velocities in the last part of § 6.

It is assumed there, that a gas has originally a “molecular-unge-
ordnet” but “improbable” distribution e.g. all molecules have the same
velocity. The gas moves now to the stationary state with Maxwerr’s
distribution of velocities. But before it is reached, all velocities are
reversed, which causes the same conditions to be passed through
but now in reversed succession. This will cause H to increase. Is

( 634 )

dH
this not incompatible with § 5, where it is proved that pet! only
¢

be negative or zero? No, says Bonrzman, for the reversed motion is
not one for which this theorem holds, because the motion is “molecular
geordnet”. For the molecules, which a molecule with a certain velocity
meets, are not taken at haphazard from the whole number but
their velocities are connected with that of the molecule under con-
sideration. This is specially clear when at the moment of reversal
the motion had not yet lasted long.

Now, however, BOLTZMANN meets with another dfficulty, which is
to be removed. Does the increase of H not also clash with the laws
of probability, as the smallest H gives the most probable state ?

No, for the increase of 7 is only improbable, not impossible.

This difficulty seems to me to have only been raised by the in-
correct view discussed above. The smallest /7 is not the most pro-
bable. Moreover we do not do justice to the subjectivity of statements
concerning probability, when we speak of a transition from pro-
bable to improbable states, as if objective properties of substances
are expressed in this way. BoLtTzMANN loses repeatedly sight of this;
particularly at the end of the second part of his “Gastheorie”.

In my opinion the views on this matter of Dr. A. PANNEKOEK, occurring
in these Proceedings, Vol. VI, p. 42 *) are not perfectly correct either.

The latter assumes also that in the above mentioned case of
reversal the reversed motion is “molecular-geordnet”, and tries now to
make clear what this means. With perfect justice he says, that it
does not mean, as seems to be sometimes assumed, that the state
may be calculated beforehand; this might also be done in the original
case if the initial state was known. Now, however, we get the im-

1) Another remark on this subject. Under 2 we read: “one more remark, however
is to be added”, on which something follows, that does not supplement what has
been said, but is in direct opposition to it. Moreover, the author seems to con-
found the collisions in the fictitious system (after reversal of the motions) and what
BorrzMAnN calls the collisions of the opposite kind.

For it is not correct that the points Q)Q,', 2, R,' return to P, P;'in the reversed
system; by reversal of the volocity we get a point of velocity lying diametrically
opposite to the first.

Also 3 gives rise to different questions. As e.g. is it allogether correct that in
the statistical way of treatment the direction of the normal of collision is consi-
dered as independent of the velocities? It can certainly not be independent of the
relative velocity? And further: does the fact, that in the calculations it is assumed
that the molecules do not hinder each other when colliding against a third, give
sufficient justification for calling the radius of a molecule small of the first order
with respect to the distances of the molecules ?

( 635 )

pression that Dr. PANNEKOEK considers as the distinctive feature which
renders the original motion “ungeordnet” its dissipating influence, and
that which makes us call the reversed motion “geordnet” its bringing
the velocity points nearer together. When in consequence of the col-
lisions the “points of velocity” get dissipated the state would be “unge-
ordnet”, when they draw nearer to each other, it is ‘“geordnet”. But
this holds only in this special case, and it might just as well be just
the reverse.

For what does “molecular-ungeordnet” mean. This appears when we
examine the place where BortzManN introduces this idea. We find it
p. 20 in the formula (17): 2) = ® F, dw,. Here ® represents the
sum of the contents of all the oblique eylindres, into which a mole-
cule of the 2°¢ kind must get in order to collide with one of the
1st kind. The formula now expresses that the molecules of the 2"4
are, in proportion to the volume, as numerous in all these eylindres
together as in the whole gas mass, or that these cylindres constitute
a quantity taken at random from the gas mass with regard to the
molecules of the 2d kind.

Now in my opinion an “ungeordnete” distribution might very well
be imagined, in which the points of velocity are more dissipated
than in the stationary state. And of a gas in such a state the points
of velocity would be brought nearer together by the collisions till
Maxwerr’s distribution of velocity is reached.

§ 3. With reference to the foregoing Prof. Lorentz was so kind
as to direct my attention to the work of Jeans on the kinetic
theory *). In this work a derivation of Maxwerr’s distribution of
velocities occurs, which is called a new one by the author, but which
essentially agrees with the reasoning of BorTZMANN in the above
mentioned § 6 on the “Mathematische Bedeutung der Grösse H”,
though the outward form is quite different. It is true that an impor-
tant improvement has been made, which for the first time renders
it in reality a derivation of the law; it is viz. not only demonstrated
there, that the most probable state of a gas is that, for which the
distribution of velocities in question occurs, but also that the chance
is very great that a state will make its appearance, differing but
very little from the most probable: for when it is only known that
a state is the most probable, its probability may yet be so very small,
that it does not say anything as to whether that state will occur or not.

Accordingly Jeans calls this most probable state the “normal state”,
in which he is now perfectly justified.

1) “The dynamical Theory of Gases” by J. H. Jeans; Cambridge, 1904,

( 636 )

The “normal” state is now the same as the “stationary” state.
However, the same objection applies to this derivation as to that
of BOLTZMANN.

Jrans calls his method “The method of General Dynamics” in
opposition to the usual one, with the aid of collisions, which he
calls “The statistical Method”. This name, however, does not seem
very appropriate to me; the considerations here are just as much
statistical as in the usual method. Dynamics do not play any part
in it but this, that the state of a gas with MN molecules, so deter-
mined by 6 N-coordinates and components of velocity, is represented
by a point in a 6 N-dimensional space, and that now the change
of state of the gas runs parallel with the motion of this point in the
generalized space.

A great number of possible states gives therefore a great number
of points, and their changes a great number of orbits, the general
course of which is to be studied. Instead of with these mathematical
points we may also imagine the generalized space to be filled with
an homogeneous liquid, the motion of which we must examine, |
which then according to the author is a “steady-motion” in hydro-
dynamic sense, the stream-lines of which are determined by the
property that their energy is constant.

This, however, brings us about to the end of the dynamic conside-
rations. They form an illustration, but nothing is proved by them.

The author now examines, what part of the generalized space is
taken up by points representing systems of a certain state. But this
is the same as what BorrzManNN calls the probability of a system of a
certain state. Both represent the proportion of the number of systems
of equal possibility possessing a certain property, to the total number
of systems. The objections to be made to the expression for the
probability hold also for that of the part of the space.

JEANS treats successively two problems :

1. What part of the generalized space is occupied by the systems
with a certain distribution of the coordinates of the molecules (or
what chance is there of a certain distribution of density of the gas)
and in connection with this: how are the systems distributed in
that space with regard to the distribution of the coordinates.

2. What part of the generalized space is occupied by the systems
with a certain distribution of velocities of the molecules (or what
chance is there of such a distribution) and how are the systems
distributed in that space with regard to the distribution of velocities ?

Only the first problem is fully treated by Jeans; for the second,
the most important, we are referred to the first.

( 637 )

It is then assumed that the gas is inclosed in a vessel with
capacity 2, divided into m elements @, so that nw=. We imagine
now a certain distribution of density, at which a, molecules are
placed in the first element of volume, a, in the second ete. The
number of ways, in which MN molecules may be distributed over the
n elements, so that every time this distribution of density exists is

N! :
——_—_—__—_—_—_. For each of these ways every molecule must be
On Loot ‘ :

placed in a certain element of volume from the m2 and so the
] th

representative point’ is restricted to the — part of the whole
n

generalized space, in the same way with the following, so “the repre-
sentative points will oecupy the fraction n—‘ of the whole of the
generalised space”. This is in somewhat different words nothing but
“the chance of each of the combinations is „A, and the reasoning
rests evidently on the assumption that each molecule has every time
an equal chance to any place in the vessel.
The representative points of the systems with this distribution of
velocities occupy therefore together a part of the generalized space
N!
= ——_—_——— n- (which therefore represents the total chance; an
(Teel Cold eC ne
expression agreeing perfectly with the chance of a certain distribution of
denoities in $ 1). After a similar reduction as in BorrTzMannN follows

5
‘ 5 A nn ee
from this: the part of the generalized space (chance) = Se ee
==
(2aN) 2
Sn
E IL 1 nas
where K,=—Y (ast — log — in the above mentioned distri-
N mm 2 MN -
s—l

bution (A). Now, neglecting 4 by the side of «, we may consider
Ka as a special value of the general function:

oe nada d
== DC U Ze
5 2 HE a vy | s 4

integrated over the vessel, where p represents the molecular density
as function of the coordinates of an arbitrary point, and », the
mean density throughout the vessel. A’ is a function corresponding
closely with Botrzmann’s //, specially when we leave out the
constants and write:

{Ge a {> logy de dy dz just as H was ii (tous da dy de;

p is the density function, just as f is the function of velocity.

( 638 )

K is now minimum when a, =a, = etc. or when » = constant.
It is obvious that this also means “the part of the generalized space”,
is maximum or the chance is maximum. So on the above assump-
tion the most probable distribution is that of uniform density.

Now JraNs proves further, that also by far the greater part of
the generalized space contains systems which differ infinitely little
from these with minimum A, so that this state may be called the
normal one. Expressed in the other way this is, that the chance is
infinitely great of a state deviating infinitely little from the most
probable state. Though Jeans’ proof does not seem faultless to me
(no sufficient attention is paid, in my opinion, to the order of mag-
nitude of infinitesimals) yet the result seems to me to follow from
BrrnouLirs theorem, provided “systems differing infinitely little” is
taken in the proper sense.

So Jeans concludes: it is clear that the gas-masses with uniform
density. will represent the ordinary case.

The second problem might be treated in the same way. Instead
of the molecules which are to be distributed over the elements of
volume of the vessel, we have now the velocity points of the
molecules which are to be distributed over the elements of volume
of the whole space. We get now in the same way for the part of
the generalized space occupied by systems with a certain distribution

N!
of velocities, the expression —
Dl Ghd sos Gi

2
large. According to the other mode of expression this is again the
chance to that distribution of velocities. 7

The treatment of the problem is further the same as that of the
first, but now we have to do with the quantity H. And finally it
may be proved, that by far the greater part of the generalized space
is occupied by systems which differ very little from that with mini-
mum MH or the normal state is that for which H is about minimum,
from which, taking into account the condition that the energy = £,
Maxwerr’s distribution of velocities follows.

Now it is, however, clear that the same objection may be raised
to this reasoning as to that of BOLTZMANN.

The above expression for the part of the generalized space (or
the chance) rests on the assumption that the representative points
are distributed uniformly throughout the generalized space also here,
or that for every molecule the chance that the point of velocity
gets into a certain element of volume, is independent of the place
of that element. What now does the condition, that the energy
=F, mean? Either that attention has been paid to it in the distri-

n—N, but now WN is infinitely

( 639 )

bution of velocities or not. If no attention has been paid to it, it
is not to be accepted that the energy always becomes finite (see $ 1);
if attention has been paid to it, the chance a priori can no longer
be taken equal for each element of volume, and the above expression
is faulty, and so also the further reasoning.

So it seems to me that also this derivation of Juans must be
considered as incorrect’).

Botany. — Some remarks on the work of Mr. A. A. Purre,
entitled: “An enumeration of the vascular plants known from
Surinam, together with their distribution and synonymy.” By
Prof. F. A. F. C: Went. :

Mr. Purrr has worked out the botanical material collected by the
expeditions of the last years, of one of which he was a member
himself. He has also tried to render our knowledge of the flora of
Surinam more complete by incorporating into his work the older
collections which are preserved at Leyden, Utrecht, Göttingen, Berlin,
Kew Gardens and in the British Museum.

In this way a total number of 2100 vascular plants appeared to
be known for Surinam and although it may be said with certainty
that this number is far from representing the real number of species,
occurring in our colony, yet we must appreciate that here for the
first time a comprehensive idea is given of the flora of Surinam.

Without entering into further details it must be mentioned that
the author is led to the important result that phytogeographically
Surinam belongs to the Hylaea, the region of the Amazon river,
with the exception perhaps of the still unknown territory west of
the Wilhelmina range. The Hylaea would then extend from the
mouth of the Amazon river over French Guyana and Surinam and
gradually form a narrow littoral strip in British Guyana, finally
passing into the Orinoco district. As a consequence of this the
conception must be given up that across Surinam there is found a
continuous savanah district, such as occurs in Demerara and more to
the west; where savanahs are found in our colony their presence
must be entirely attributed to local influence of the soil.

1) Jeans’ derivation occurs for the first time in the Philos. Magazine VI, 5, 1903,
under the title of “The Kinetic Theory of Gases developed from a New Standpoint”
p. 597, That also the “molecular ungeordnet” hypothesis is implied, which Jeans
denies, is proved by Bursury in the same magazine VI, 6, 1903 in an article
on “Mr. J, H. Jeans’ Theory of Gases” p. 529. ;

( 640 )

Mathematics. — “The quotient of two successive Bessel Functions”.
(2"4 paper). By Prof. W. Kaprryn.

In our preceding paper we gave the value of the general coefficient
of the expansion

TH! (2)

Iz)

=fethe thet...

Now we wish to draw the attention to a couple of relations which
exist between these coefficients. The first is obtained from a particular
integral of the following differential equation of Riccati

du
ee Av dOr vn 5. > 9 (i)

Putting
at

Z

204144,

this differential equation reduces to

UI

du je
en fut +204] uy,$2=0.

Repeating this process, it is evident that the equation (1) is satisfied
by the continued fraction

a2
z

ZE EET 2
DE) = 2?
dare 243) — etc.
. ; P+1(z)
which represents the value of — z RO
Introducing therefore
u=—/f, 2? —f,2z*—f, 2 — ete.

in the equation (1) we have
2~+)A7A=1
2p m= Dar Sada + Jada te «> Te Sn a
where) 7 == dl, 243 ver
The second relation may be deduced from our former equation

la, Ce th Che el &, |

atlas an” AH hen 1)’
An 2 Xn—2 ly 20, 9...00

Ann WY Ooo OO

( 641)

where
ap —2(v + p),
(2n — p—1) ...(2n — 2p)
= p!
(2n — p — 2)... (2n — 2p — 1)
Ap == 7
Pp:

ap Ap +1,..42n—p—1

Ap + 1...42n— p —2

(n—p+1). .(u— 2p + 2)
EN sl

Ap A1... An —p +1

n—l 4
when 7 is odd.

n : A
and A stands for = — 1 when « is even or for 5

pe

Putting a, = 26, this equation may be written

22n+t1 bl oun see bn Ond Jr = D,, . . aire (2)
and it is found that the determinant D, satisfies the condition

Ne

ID}, — nb, oe by Dy = Baten by . b, oar bal ID -f-

9)? 1

oe

n—2.n—3 .n—4 b
+ a) es

the last term being

Ivor iby aan ba Diet.

lf
— 1)? — WN onale ds eline colle lon
DE EEn bn,

to| =

when 7 is an even number, and
n—l

ODE Cae bye Ort eat Dee
2 2
when 7 is odd.
Substituting in this equation D, by their values from (2) we get
this second relation between the coefficients /,

n—l

= 2
N—p)..-(n—2y c
ey Sup a
p=0

(p +1)! 25, … byt16n—pti wee Ont

Finally we will show that from the recurrent relation between
the determinants D, the value of

; Jn
Lim =!
n=@ Sit
may be deduced. For the series
fethet fete.

is converging when

( 642 )

| f, |
Lim En P< II

n=@o|l Jn
or when
7,
| 2 < Lim Sas
n= Jn
Now
ye WS p b . b 1 7D) il
Lim SE SD) 1 nl
Jn+1 ID).
therefore

a

Lim b, + «bpp Dai en TON
Dy

: ea sal Ay on alt JO ED G2 \
Lim 1 ate! D: see? =(5) etc.

and finally

a \? a‘ a\°
2 2 2

== — — etc.
b, 2/50, 3/b,b,b,

Hence it is evident that @ is a root of the equation /’(z) =O as
might be expected.

Astronomy. — “Researches on the orbit of the periodic comet
Holmes and on the perturbations of its elliptic motion.” By
Dr. H. J. Zwiers. (Communicated by Prof. H. G. van DE
SANDE BAKHUIJZEN.)

In 1902, after the reappearance of the comet Holmes in 1899—
1900 I published in full the results which I had derived from the
investigation of the observations after its return.') With the most
accurate elements which I had been able to deduce from its appearance
in 1892 —93 I had calculated in advance the perturbations arising
from the action of Jupiter and of Saturnus and at first also of
the earth and thence I have derived a system of elements for 1899
September 9.0 mean time Greenwich, which served as a basis for
an ephemeris published in No. 3553 of the Astron. Nachrichten.
By means of this ephemeris the comet has been rediscovered at
the Lick Observatory and the relatively small difference between the
observed and the computed place proved that the elements of the

1) Recherches sur l'orbite de la cométe périodique de Holmes et sur les perturbations
de son mouvement elliptique, par Dr. H. J. Zwiers, Deuxième mémoire. Leyde,
E. J. Brill, 1902.

( 643 )

orbit found for 1892 and the computation of the perturbations which
had been based on them were very nearly correct.

The observations in 1899 and 1900 furnished me with sufficient
material to apply to the elements such small corrections as brought
the remaining differences between the predicted and the observed
positions within the limits of ordinary errors of observation. The
system of elements obtained thus, which satisfied both the appearance
of 1892—93 and that of 1899—1900 and which in my “Deuxième
Mémoire” p. 78 has been recorded as “Systeme VII’, must naturally
furnish the basis for further investigations. Therefore I shall give
it here in its general features.

System VII.
Epoch 1899 June 11.0 mean time of Greenw.
Osculation 1899 September 9.0 „ „ ,, 4
M, = 22661" 3264
Ee lb, 183879r
log a= 0.558 1320.0
p= 24°17! 23'54
e= 0.4113532
i— 20°48' 9"84
mw = 345 48 38.06 } 1899.0
S = 331 43 18.24
i= 20 48 10.29 |
a = 345 49 28.27 | 1900.0
% = 331 44 8.95 |

Although the corrections which had to be applied to the elements
in consequence of the new observations were small, I immediately
after the publication of those researches resolved to repeat the compu-
tation of the perturbations between 1892 and 1900 with the new
elements and to extend it to all the planets of which the disturbing
effect could not a priori be neglected as being insensible. This
elaborate investigation, which necessarily required a new discussion
of the two appearances of the comet, was however only partly
finished when in 1905 the preparation for the third appearance had
to be taken in hand.

I have then started from system VII, which though not perfect, yet
satisfied all practical demands. I did not venture, however, to use
those elements without more for the computation of the places at
the return of the comet in 1906. It is true that the disturbing planets,
especially Jupiter, whose influence is by far the greatest, remained
at a considerable distance during the entire revolution of the comet,
yet the feeble light of the comet in 1899—1900 and the difficulty

( 644 )

experienced by most observers to properly identify the comet in the
midst of numerous faint nebulae near the apparent orbit, made me
fear that such a rough ephemeris of the apparent places for 1906
might prove insufficient for rediscovering it and observing it.

In the autumn of 1905, I therefore resolved to derive the pertur-
bations which the comet would suffer on its path between the perihelion
passages of 1899 and 1906. The original plan of also computing the
perturbations arising from the action of Saturnus had to be given

-up through lack of time. And so Jupiter remained the only disturbing
planet. The method I chose was that of the variation of the elliptic
constants; I also chose an interval of 80 days, because former
investigations had shown that the accuracy, attainable by it was
more than sufficient for my purpose. In former researches we have
always adopted the rule that for each new epoch the small varia-
tions which the elements had undergone during the course of the
last interval were to be applied to them. The computations required
for this implied, however, an amount of labour not to be underrated,
and as in this case the computations could have only a preliminary
character I could leave aside these small corrections by which in this
case only small quantities of the second order were neglected. Thus
the above mentioned system VII was used as a basis for the com-
putation of perturbations for the entire revolution. The places of
the disturbing planet are taken from the Nautical Almanac; the
longitudes only were reduced to the equinox of 1900.0 by applying
the precession. The neglection of the small corrections for nutation
and for the variation in the obliquity of the ecliptic cannot have
any perceptible influence on the perturbations caused by the planet.

Instead of the elaborate tables of perturbations I shall for shortness
communicate only the summed series, namely the quantities Hf for
the mean daily motion and the quantities 47 for the other elements.
By working out each table the reader will be able to form a judgment
on the accuracy reached. The initial constants printed in big figures,
which in the construction of the tables were derived from the first

dE ; 5
values of (E representing one of the 6 elements) and from their
differences up to //V are chosen so that the integrals disappear for
1899 September 9 as lower limit. Up to 1900 February 16 the
derivatives could be borrowed from the tables which I have commu-
nicated in my Deuxieéme Mémoire ps. 26—32; with regard, however

d
to the interval chosen now I had to multiply = by 4, and the

other derivatives of the elements by 2.

TABLES OF THE JUPITER PERTURBATIONS.

1899

1900

1901

1902

1903

1905

1906

Dates | t | I u M hd p
| 1 ]
Jan. 12 " | " aes 21 5730 " u 1
+ 4.536 7.382 + 0.176/+ 413.677/— 29.200
April 2 | | — 8.4814
; oi |H 2.690-+ 6.991) nou 4.983/+ 6.957/\— 16.451
une 2 | — 1.5328)
+ 0.760 3.297 | 2.505 2.601— 4.611
Sept. 9 | + 0.2737 5
— 0.625— 3.826) — 2.530— 3.150 4.197
Nov. 28 | — 1.2125 |
— 1.018— 13.652) — 5.973— 13.460\4+ 11.287
Febr. 16 | — _4.2367/ :
— 0.203— 25.174 — 6.752— 28.616H- 18.278
May 7 | — 7.5053 5
+ 1.867— 37.406) — 5.822— 47.169 26.379
July 26 | — 10.1533)
+ 5 MS— 49.494) |= 4.954— 67.123 36.268
Oct. 14 — 114.6218 |
+ 9.397|\— 60.732! — 6.051|— 86.516 48.205
Jan. 2 | |} — 414.5478
i E + 14 489 — 70.570) |— 10.874/— 103.621)4+ 62.168
rch 2 | — 9.6867)
+ 20.135 — 78.624 |— 20.923 — 117.008|+- 77.946
June 11 — 5,8601
|e 26.049'— 84.681 |— 37.388|— 125.552 95.199
Aug. 30 nee a 0.0784, ; | ‘ k 8
+ 1.931 — 88.702) |— 61.130/— 128.426)4 113.505
Nov. 18 | + 8.2654 be ae
-++ 37.487 — 90.817) — 92.674,— 125.094|+ 132.387
Febr. 6 _ | + 18.8492! : :
+ 42.443 — 91.315) |— 1382.210)— 115.298) 151.344
April 27 | + 31.9635]
+ 46.560— 90.624 — 179.598|— 99.047)+ 169.854
July 16 | + 47.8025 ail
| 4 49.651|— 89.287 |— 234.380/— 76.601|-+ 187.497
Oct. 4 | | 4 66.5527 al
+ 51.593 — 87.924! — 295.802! 48 .453\+- 203.590
Dec. 23 + 88.4279
-++ 52.337 — 87.192) — 362.844 — 15.304 217.927
Mrch 13 | + 113.6611
+ 51.916— 87.735) — 434.253 21.975 230.081
June 4 | + 142.5014
+ 50.444— 90.131) — 508.617/-+ 62.385|+ 239,783
Aug. 20 |} 4+ 475.2199; nm
| + 48.115 — 94.838 — 584.410 -+ 104.856|+ 246.855
Nov. 8 ‚+ 242.0688, | É | 5
| + 45.193 — 102.143) ‚— 660.082 + 148.3144 251.221
Jan. 27 | | | 4 953.3579 | |
| 4. 44.996— 112 115) — 734.136, 191.752|4- 252.903
April16 | | + 299.3790 5 d E
+ 38 875 — 124.566) — 805.2164 234 308\+ 252.014
July 5 | + 350.4492 |
+ 36.183 — 139.032 — 872.1764 275.334\4+ 248.718
Sept. 23 eee EN É |
+ 34.243 — 154.764 — 934.123 + 314.438) 243.224
Dec. 12 | + 469.1545 he
+ 33.309 — 170.745) — 990.396 + 351.479|+ 235.703
Mrch 2 + 537.6167) |
+ 33.518 — 185.739) \—1040.430/+ 386.444 226.250
May 21 | + 612.8073
5; + 34.834 — 198.384) —1083,432/ + 419 1294 214.885
Aug. 9 + 695. 2691 E
+. 36.981 — 207.384 —1117.855/-++ 448.580/+- 201.767
Oct. 28 + 785.4184 5
+ 39.372 — 211.929 —1141 2144+ 472.756 187.961
Jan. 16 + 883.0549 ij
+ 1,116) 212.537 —1152.415)-+ 490.526/+ 176.821
April 6 + 986.3401
+ 41.312)— 212.305 —1158.665 + 508.036)+- 173.909
June 25 44090. 7444 |
45

Proceedings Royal Acad. Amsterdam. Vol. VIII.

( 646 )

By means of these tables it is not difficult to integrate the pertur-
bations for an arbitrary epoch according to the known expressions
of the mechanical quadrature. As a new osculation epoch I have
chosen

1906 January 16.0 mean time Greenwich
and I have found:

NE ADEN A M= —8'32'48
d
A= ses WG — 4 883"5368
A,M = — 1147'7070 An=+8' 2"08

Ag=+3' 2"01
hence the new elements become:

epoch and osculation 1906 January 16.0 mean time Greenwich
M, = 1266412"148
u — 517"447665
log a = 0. 557 4267.74
p = 24° 20' 2555
e= 0. 412 1574
i= 20°48'50"63
a = 345 5730.35 ) 1900.0
SX = 331 40 36.47

From these disturbed elements we derive for the time of perihelion
passage
1906 March 14.1804 mean time Greenwich
while the original system VII, without regard to the perturbations
during the period since 1899 June would give
1906 March 13.8083.

If we take into account that the small retardation of not yet 9
hours is compensated by an increased longitude of the perihelion of
8’, we find a posteriori confirmed, what could have been foreseen,
that the perturbations during the second revolution have only slightly
affected the places of the comet in space.

By reducing the elements 7, 7 and §% to the mean equinox of
1906.0 I find

i= 20°48'53"30 |
a 346 231.63 > 1906.0.
Sb = 331 45 40.75 |

In order to compute from these elements an ephemeris I have

| Il

derived the following expressions for the heliocentric coordinates of
the comet referred to the equator :

( 647 )

az = [9.993 7731.9] sin (v + 77° 37' 2485)
y = [9.876 2012.2] sin (v — 20 58 31.25)
z = [9.832 7001.5] sin (v — 1 47 16.19)

The coefficients in square brackets are logarithms; the quantity v
denotes the true anomaly of the comet.

By means of the expressions above given the heliocentric coordi-
nates have been derived from 4 to 4 days for mean noon at
Greenwich; the coordinates of the sun were taken from the Nautical
Almanac after having been reduced to the mean equinox of the
beginning of the year. In the reduction of the mean places to
apparent ones the aberration terms are omitted, because, as it is
known, the influence of the aberration for the bodies of our solar
system can be more simply accounted for by subtracting from the
times of observation the equation of light. In the two following
tables which contain the apparent places of the comet in a« and
d I have therefore added in column 9 for each date the equation
of light expressed in mean solar days. The 4" column gives the
logarithms of the geocentric distance. As first date I have chosen
May 1st because I had derived from a preliminary computation that
before that time there would be no chance to discover the comet
owing to its small apparent distance from the sun and its large
distance from the earth. The possibility did not seem excluded,
however, that by means of powerful telescopes or sensitive photo-
graphic plates the comet might be discovered in January 1906.
Therefore I have derived positions for that month and sent a short
ephemeris to Prof. Kreutz, who in a circular has communicated
it to astronomers. To give a clear idea of the apparent orbit of the
comet and also because the published places were not pertectly
correct owing to a small reduction error, I here shall give the
correct results from 4 to 4 days. Up to now (February 14) no tidings
about the discovery have arrived, at which we need not wonder
if we consider the cloudiness and especially the southern and
generally unfavourable position.

The next table gives the apparent positions of the comet for the last
8 months of the year. The direct computations have been made from
4 to 4 days; between them one date has been interpolated taking
into account the fourth differences.

As a measure for the probable brightness we generally calculate

4 1
the quantity 7=-——,. Although on account of the irregular varia-
ro

S

tion of the comet’s light it is not certain that the brightness will be
45*

( 648 )

PLACES OF THE COMET BEFORE THE CONJUNCTION.

1906 apparent « | apparent ¢ log p s | H
h ms SR
Jan. 1 20 45 1.65 = 223) a7 0.47858 0.017373 | 0.0230
5 53 18.18 — 20 26 48.41 „48066 456 „0229
9 21 1 33.24 — 19 29 15.4 „48257 533 „0229
13 9 46.66 — 18 30 24.6 „48431 603 „0228
17 17 58.35 — 17 30 17.8 „48590 668 „0228
21 26 8.26 — 16 28 58.8 A8733 726 „0228
25 34 16.26 — 15 26 28.4 „48860 778 „0227
29 42 22.19 — 14 22 50.3 „48971 824 „0227
Febr. 2 50 25.91 — 1318 7.8 „49067 863 „0227
6 58 27.36 — 12 12 24.5 „49147 896 „0227
10 22 6 26.56 — 1 5 43.5 49213 923 „0227

proportional to M, I for completeness have added this quantity to
the table from 4 to 4 days. In 1892—98 this so-called ‘theoretical
brightness” varied between 0.075 and 0.012.

Because the elements adopted for 1900 might still require small
corrections, and as up to 1906 only the principal perturbation by Jupiter
has been taken into account, it is not improbable that when the
comet happens to be discovered there will be some difference between
the observed and these computed places. In order to facilitate the
search for astronomers who possess the needed instruments for
finding it, 1 have repeated the calculation of the places first on the
supposition that the comet will pass through its perihelion 4 days
earlier, and secondly that it will pass 4 days later than would
follow from the most probable elements. Although the adopted
latitude of + 4 days will probably be much larger than the
real error in the accepted time of passage through the perihelion
I give the results as obtained from direct calculation. The following
table contains the variations in right ascension and declination for
the two suppositions; column A log@ gives the corrections which
would have to be applied to the 5% decimal of log eg from the ephe-
meris communicated before,

( 649 )

APPARENT PLACES OF THE COMET FROM MAY 1 TO
DECEMBER 31, 1906,
FOR OF MEAN TIME AT GREENWICH.

1906 | ‘ | 3
May 4 | 040 15.98 | + 12 49 44.3
3 44 0.82 | +43 25 36.3
5 47 46.93 | +44 12.9
7 BA 31.54 36 58.4
9 55 16.77 | + 45 12 97.8
u 59 1.94 47 48.8
13 | 4 247.03 | 44693 1.3
45 6 32.06 58 4.7
17 10 417.02 | +4417 32 58.6
19 14 1.90 | 448 7 42.8
1 17 46.67 42 16.7
23 U 31.32 | +4 19 16 39.8
25 25 15.84 50 51.9
27 29 0.0 | + 20 2459.4
29 32 44.40 58 40.9
31 36 98.40 | +4 91 32 17.0
June 2 40 12.99 | 499 5 40.5
A 43 55.83 38 51.0
6 47 39.93 | 4 23 44 48.3
8. | 51 99.42 hh 32.4
10 55 5.37 | JAAT 2.4
12 58 48.06 49 18.9
14 | 2 230.46 | +9591 0.5
16 6 12.51 53 9.8
18 95448 | 4 26 2% 43.6
20 13 35.40 56 2.8
22 1716.13 | +27 7.1
24 20 56.31 57 56.2
26 24 35.89 | + 98 28 30.0

log p 5 H
47733 0.017 322 | 0.0240
47632 282
47528 241 „0241
41421 199
47312 156 „0242
47200 111
47084 066 „0243
„46966 019
46844 0.016 972 0244
„46719 923
„46591 873 „0246
„46460 822
„46326 770 „0247
46189 717
46048 663 „0248
45904 608
45757 552 „0250
„45607 495
45453 437 0252
45296 378
„45137 317 „0253
LATA 256
„44807 194 „0255
44637 131
4444 067 „0257
„44287 001
A407 0.015 935 „0259
„43923 868
43736 799 „0261

1906 a ) log ¢ s
bh m s : ik el |

June 28 | 2 28 14.81 + 98 58 48.2 | 9.43545 | 0.015 730
31 53.03 + 29 98 50.8 „43350 660
July 2 35 30.49 58 37.7 43152 589
4 39 7.15 + 30 28 8.8 42951 517
6 42 42.95 57 24.2 12746 4k
8 46 17.85 31 96 24.4 42538 370
10 49 51.75 55 8.4 12326 295
12 53 24.59 + 32 23 37.4 421 219
14 56 56.26 51 50 9 41892 143
16 | 3 0 26.67 + 33 19 49.4 44669 | 065
18 3 55.70 47 32.1 v2 | 0.014 987
20 7 23.4 + 34 14 59.8 MU 907
22 10 49.18 42, 12.4 „40978 827
24 14 13.40 EE OEE „40740 746
26 17 35.80 35 52.2 40499 665
28 20 56.25 + 36 249.8 A024 582
30 24 14.64 98 32.6 „40006 499
Aug. 1 27 30.86 54 31.0 „30755 416
3 30 44.79 +. 37 20 15.2 „39500 331
5 33 56.32 45 45.6 39241 216
7 37 5.28 + 3841 2.7 „38079 160
9 MO 11.54 36 6.8 „38714 074

1 43 14.91 + 39 058.0 38446 | 0.013 oss
13 46 15.20 25 36.8 „38174 900
15 49 12.25 50 3.3 „37899 813
17 52 5.8% + 40 14 17.8 „37621 724
19 54 55.77 38 20.5 „37340 636
21 57 41.84 JA 2115 „37057 541
23 | 4 0 93.84 25 50.9 „36771 458
25 3 1.59 49 19.0 „36482 369
27 5 34.86 +. 42 12 35.9 „36191 280

0.0264

„0266

„0269

„0271

„0277

„0281

„0284

„0288

„0291

„0300

„0304

„0308

„0313

Oct.

22 54.34
24 37 12
26 12.92
27 4.47
29 2.48
30 15.71
31 20.90
32 17.81
33 6.20
33 45.85
34 16.56
34 38.08
34 50.16
34 52.61
34 45.25
34 27.94
34 0.56
33 23.06
32 35.43
31 37.75
30 30.16
29 12.87
27 46.15
26 10.32

}

4+ 42 35 M,8
58 36.9
4 43 2 2.3
43 55.4
4+. 44 6 19.0
28 32.3
50 35.4
4+ 45 42 27.0
34 7.7
55 36 6
4. 46 16 53.0
37 56.4
58 44.9
+ 47 19 18.3
od done
59 34.3
4 48 19 14.3
38 33.8
57 31.0
4+ 4916 3.6
34 9.6
51 46.5
+50 851.4
95 21.4
41 13.3
56 93.7
4 51 10 49.4
24 26.0
37 14.0
49 0.8
59 51.9

c=
0.35899 0.013 191 0.0318
„35605 102
„35308 013 „0323
„35010 | 0.012 924
„34112 835 „0329
„34412 747
34412 659 „0334
„33812 572
„33512 485 „0339
„33212 399
„32913 314 „0345
„32615 230
„32320 147 „0350
„32027 066
„31737 0.011 985 „0356
„31450 907
„31168 830 „0361
„30891 154
„30618 681 „0366
„30351 609
„30042 540 „0370
„29840 473
„29595 409 „0375
„29359 347
„234 288 „0378
„28919 232
28715 180 „0381
28523 130
28345 085 „0383
28181 043
28031 005 „0384

(652)

1206 A 8
oct. 30 | #247575 | 450 9 4.4
Nov. 1 29 32.88 18 25.1
3 20 32.19 2% 0.8

5 18 24.96 32 25.2

7 16 9.72 37 35.5

9 13 40.98 4A 29.2

u 11 23.70 4h 4.0

13 8 53.82 45 18.4

15 6 20.53 45 11.0

17 3 44.79 43 4.2

19 1 7.59 40 48.9

21 | 3 58 29.91 36 35.4

23 55 52.74 31 4.4

25 53 17.00 % 8.9

27 50 43.59 16 0.8

29 48 13.36 6 39.9

Dec. 4 4547.40 | + 5156 9.2
3 43 25.56 44 39.6

5 MA 9.42 31 53.9

7 38 59.30 18 17.3

9 36 55.80 3 47.5

u 34 59.40 | + 50 48 29.0

13 33 10.58 32 26.7

15 31 20.73 15 45.9

17 29 57.49 | ++ 40 58 31.6

19 28 33.19 40 49.4

21 27 17.93 29 43.8

23 26 11.50 4 20.5

25 25 13.95 + 48 45 43 9

27 24 95.92 26 58.7

29 23 45.29 8 88

31 23 14.07 + 47 49 18.0

log p | EG, i oH

„28010
„28178
„28568
„28578
„28810
„29062
„20334
„29627
„29939
„30270
„30619
„30984
„31365

„33039
„33489

0.010

0.014

0.012

971
941
916

0.0384

„0383

„0380

„0376

„0371

„0365

„0848

„0337

„0326

„0314

„0302

„0289

„0262

„0249

( 653 )

VARIATIONS OF a, d AND log FOR THE ALTERED TIME OF PASSAGE

THROUGH THE PERIHELION.

T=—A4 days T=+-4 days

May 5 | 4 31348 | 4+ 38 55/2 | + 931 | — 3.13.49 39215 | — 988
> oa | + 392.45 | 4 3693.2 | 4+ 994] — 3.99.19] — 37 38| — 297
June 6 + 3 33.07 + 33 10.6 | + 355 | — 3 33.23 | — 33 58.3 | — 359
>» 29 | 4 346.412 |-4+ 29 19.9 | + 43] — 3 46.62 | — 30 13.4 | — 418
July 8 [+4 1.95 | HU 55.8|H469| — 4 2.30 | — 95 53.4 | — 476
> a |4a18sel 490 44/45] —490.42|— A 4,4 | — 500
Aug. 9 | -+ 4 38.61 | + 14 54.2 | + 567 | — 44.55 | — 15 55.9 | — 576
» 2 [45 240| 4 939.3| 4+ 606] —5 6.87 | —10M.7| — 616
Sept. 10 | +5 31.9714 444.9] + 692] — 538.29 | — 5 45.9 | — 642
» 26 |+6 9.74 | + 39.2 | + 640 | — 6 18.02 | — 1 49.4 | — 649
Oct. 42 465591 | — 4 274 6M 7 50 vs = 627
» 2 | +74403|— 93.3| +566] — 754.54 | — 1 90.9 | — 569
Nov. 13 + 8 15.71 | + 415.2 | + 475 | — 8 23.95 | — 619.7 | — 474
» 29 |+ 8 10.71 | + 10.42.4 | + 361 | — 8 14.80 | — 12 50.9 | — 356
Dec. 15 + 7 29 + 15 44.7 | + 247 Se 80.69) — Ae TES | — 241
| |

Leyden, January 1906.

Physics. — “On the motion of a metal wire through a lump of ice”.

By L. S. ORNSTEIN. (Communicated by Prof. H. A. Lorentz).

In a well known experiment on the regelation of ice a metal
wire charged with weights is placed on a lump of ice. It moves
slowly through the ice, while on the upper side new ice is formed;
after a short time the motion takes place with uniform velocity. This
phenomenon is explained by the fact, that if we increase the pressure
the meltingpoint is lowered.

In order to caleulate the velocity of the wire I shall consider an
infinite circular cylinder which is moved through an infinite Jump

( 654 )

of ice by a force perpendicular to its axis. The phenomenon is
the same in each normal section. I suppose round the wire a
layer of water whose thickness is small in comparison with the
diameter of the wire. At the bounding surface of water and ice
there is a pressure, which decreases from the lower to the upper
side of the boundary. This pressure depends on the force by which
the wire is acted on pro unit of length. As the motion is very
slow the temperature in each point may be supposed to be the
-meltingpoint corresponding to the pressure existing in the point.
The flow of heat, determined by the distribution of temperature
is the same as if the wire were at rest. At the upperside of the
bounding surface of ice and water heat flows away and water is
frozen, at the lower side the ice is melted by the heat that is carried
towards the surface. If we can determine the quantity that is melted
we shall be able to determine the velocity acquired by the wire.

Let M be the centre of the circular section of the wire and Zi
the radius, the boundary between ice and water being a circle of
radius R +d.

The pressure at the
circle A'B'C' in any point
i may be represented by
the formula

p=p,tbesg,
p being the angle between
the radius M/Z’ and the line
MA which has been taken
for axis of ordinates. The
corresponding temperature

18
dt
i=, +3(S) COS,
dp},

dt
(=) being the change of
dp),

the meltingpoint per unit increase of pressure near 0° C.

Let £,, be the coefficient of conductivity within the circle ABC,
that of the layer of water, and 4, that of the ice without AB'C'.
The differential equation for the temperature is in every one of
these fields

k

2

0°t Oe
Ov? | Oy?

The conditions at the limits of the fields are:

Ot Ot,
deat ABC, ile k, i) =; 3 ;
On 1 On a
dt Ì
Zat ABC ft, =t,,4,-0 (=) cos p,
dp)
3. at infinite distance t, =t,.

The normal at ABC coinciding with the radius.
The formulae:

t, =t, + B,.r cos p in the wire,

C
t‚=t, + B,rcos gy + Ee cosp in the layer of water,

C
Si + = cosy in the surrounding ice

satisfy the equations r being the distance from the point M. For
the coefficients I find the relations
C

Br == B, + ail

C
ky B, = k, @ aa z)

ze Cant Os =(5) 1
7" (R+d) (Bd? \ dp), Rd
Neglecting powers of d/R I find

dt
C, (or) et)
Rt UR, HU/R(k —&)
(5) (k, +h)
dp), :

n= 5

1 RH +4/R(k, —',)}
For an element WF’ of A’B’C’ the flow of heat into the ice
towards the surfaces amounts to:
— k, es
R-+d’
if we write dp for the angle E’ MI”. Hence the total quantity of

heat conducted through the ice towards the surface A’5’ per unit
of time:

cos pd ,

n/2

k, 6 be üm (5
as dp Jeng M= 3 dp B

In the layer of water the flow of heat per unit of time is for ZF”

( 656 )

C, )
Rd)

— (R + d) dp cos pk, @ --
and for A’B’ totally

Ö: dt Nm (A:
sl Rn ei p
k,(R +d) (». a jo (el Nn ne

Of course as much heat is lost at the surface B’C’ as is conducted
towards A/B’; and the melted and frozen quantities of ice and water
will therefore be equal. W being the quantity of heat that is required
for the melting of a gramme of ice, the melted quantity is

k, U p(k, —k dt

9 E kelk) + a | b (=)

SRE) dp),

W. ;

If S, is the specifie gravity of ice, the volume of this quantity is:

k, —4/R(k,—k It

of, hae Se

En k +4/R(k, —k,) dp 0

WS,

On the other hand, if the eylinder moves with a uniform velocity
v a volume .

2 Rv.
is melted. So we find for the value of »

k,+4/pr(k, —k,) dp),
RW S, :

To express 6 in the force P acting per unit of length of the
cylinder we have only to notice that an element KY = Rdg is
acted on by a force per unit of surface p cos p = (p‚ + b cos p) cos gp.
Hence :

CS —

PS af. cos p +- b cos? p) Rdg = nbk
0

The velocity C in case P= 1 is found to be

At k, —4/ p(k, —k
(5) E | RE, ) A |
dp 0 ka +4/R(k, — &,)
x R? WS,
We can find another expression for d/p if we pay attention to the
motion of the water. If we conceive the wire to be at rest but

the ice moving along it, we shall see at the limit A'S’ water con-
tinually streaming into the channel AS A'S’ while it streams out of

Cc=—

U).

( 657 )

it and freezes at the part BC of the surface. The velocity of the
ice being » we find for the quantity of water entering through /'/”
(R + d)v cos g dg.

This is also the difference between the quantities flowing across
FF' and EE’ upwards.

This quantity can also be determined by means of the hydro-
dynamical equations. Take for axis of § a circle with radius R + 4d
and for axis of % a radius of the circle. The forces acting on an
element KLOP are in equilibrium. Writing wuz for the velocity
parallel to the axis of &, u for the coefficient of viscosity, neglecting
the velocity w, and taking the intersection of the § circle, with
EE’ for origin of coordinates we have:

0? uz _ bsng
giro stale
At the circle AB, uz = 0, at A'B', uz

> sing, therefore:

Bt US £
Ee — fee = hag an)
and the quantity streaming across LE’ is
+d],
fu dy =— =| a Bike SIL,
a TR

the difference between the quantities of water flowing across FF’
and EE' will therefore ee

bd’ vd
12 R cos pdp
and we have, B powers of Dn
bd?
U 12u R . . . . . - & . (ZI?)

In the experiments the wires become curved. I suppose the wire
to be perfectly flexible and the stress to have the same value S in
all its parts; the force per unit of length perpendicular to the wire
is given in each point by

=

ds
dw being the angle between two consecutive tangents to the curve.
The curvature being not large we can use the coefficient given by
(7) to find the normal velocity arising from this force. This velocity is

es
ds

( 658 )
In a time dt the element ds of the wire describes a surface
d
CS ds dt.
ds

If the wire at the ends is vertical the whole wire will therefore
describe an area

5 dw
afcs ds =7 CS dt.

s
0

Now if the velocity of the wire is v, and the distance between
the vertical ends d,, the same area will be vd, so that we have

acs
v= (IIT)
d,
or if the angle between the ends is 2a, and P the weight at each end,
2aCP F
UE ter Hen iy y 5) (UE)
d, sin a

We shall next consider the form taken by the wire if it descends
as a whole with uniform velocity. It is determined by the condition
dw da

or

ded ds
As 9 dw=ds, 9 being the radius of curvature, this equation becomes

Taking the axis of 2 horizontal at the highest point of the line,
the axis of y vertical downwards we have for x= 0,

therefore

The normal pressure at the highest point is
Sa
d

Sn =>

( 659 )

In order to find the formula (//*) for curved wires we can put,
approximately, for 5 its value at the point c=0 y=0.
So that we may put for

By this the formula (II*) gives

d 8
Ee Te 53) aN USS 0 ay
12ud,\ Rk

S being equal to the weight hanging at each end.
If the angle between the tangents at the ends is 2a, we have
other formulae. The equation of the curve becomes

and the velocity, if P is again the weight at each end
_ 2aCP

v <a .
d,sina

(LLT)

By the hydrodynamical method the same velocity is found to be

EN Sn a\? a
” 12nd, sina B Wa ee va ed ct)

Dr. J. H. MeerBurG has made a series of experiments, of which
he will communicate the results at a later opportunity. The agree-
ment with the theory is not very satisfactory. It must be noticed
however that d is very small. The roughness of the surface of the
wire will therefore greatly increase the resistance to the motion of
the water, so that the result of the hydrodynamical method can no
longer be considered as correct.

Zoology. — “On the Polyandry of Scalpellum Stearns’ by P. P.
C. Hork.

One of the largest forms of the genus Scalpellum which is so
rich in species is Scalpellum Stearnsi, Prtssry from shallow water
near the coast of Japan.

This species is represented by two varieties or sub-species in the
collection of Cirripedes made by the Siboga Expedition in the waters
of the Dutch East Indies and handed over to me for description. Both
forms agree in the main with Pinspry’s species — they differ, however,

( 660 )

in some regards from one another as well as from the Japan species.
I made the acquaintance of the latter by studying a few samples
which were kindly lent me from the Berlin museum by the Director
(Prof. K. Morsrus) and by the curator of the Crustacea Department
(Prof. W. WeLTNER).

Apart from PirsBry *), the Japan species has also been named
and deseribed by Fiscunr*); one of the two varieties from the
Malay Archipelago has of late again met with the same fate from
ANNANDALE *), who tried to introduce it into the literature of the
Cirripedia as a new species.

Yet, though we dispose at present of three names and three
fairly extensive descriptions for this species, a very curious pheno-
menon in the life-history of the reproductive period of this Scalpellum
has hitherto escaped the attention of its describers ; for I can hardly
believe that they could have discovered this peculiarity and yet
not mentioned it in their papers.

PirsBry says of this species (and FrscHer in this regard quite agrees
with him) that it was found in shallow water in Japan. The speci-
mens of the Berlin Museum were from Nagasaki and apparently also
from coastal waters. Those of the Siboga Expedition are from four
different stations the depths of: which range from 204 to 450 m.
ANNANDALE had a single specimen at his disposal, caught in Bali
Straits at a depth of 160 fathoms, about 290 m.

Scalpellum Stearnsi belongs to the unisexual species of the genus:
the large specimens with fully developed capitulum of a length of
about 5 em. and with (for a species of Scalpellum) very long pedun-
cles (of 5—9 em. length) are the females. The males (which should
not be called ‘‘complemental” males in this case) are looked for in
vain at the place they ordinarily occupy, viz., at the inner side of
the scutum, near the occludent margin, a little in front of or above
the adductor muscle, in a duplicature of the sac or mantle which
covers the valves of the capitulum on their inner surface. They are
not to be found there — and I think this explains why they escaped the
attention of the earlier describers. Darwin discovered that the little
males in one of the species (in Sc. rostratum, DARWIN) were attached
as three little parasites to the body of the hermaphrodite, close
under the labrum, between it and the adductor muscle almost in
the median line of the body — but even at that place they are not

1) Proceed. Acad. Nat. Sci. Philadelphia. 1890. p. 441—443.
?) Bullet. Soc. Zool. d. France. XVI, 1891. p. 116—118.
3) Memoirs Asiatic Soc. of Bengal. I. N°. 5. 1905. p. 74—77.

( 661 )

to be found in Se. Stearnsi. I noted, however, that that part of the
sac or mantle, which unites the two scuta behind or beneath the
adductor muscle and which can be better seen by moving the two
scuta slightly from one another, in the largest and oldest specimen
of the collection, showed a crusty and grainy surface — just as if
a Flustra or other Bryozoon were attached to it. Investigating a part
of that crusty covering I easily found that each grain represented
a male and that over a hundred of these were attached to the same
female. Each male is inclosed in a kind of capsule (a thickening of
the mantle) and that part of the mantle-surface which is opposite
the head-end with the prehensile antennae forms a little elevation
over the surface of the capsule. They are in parts so closely
placed as to flatten one another mutually. Their dimensions are
0.7 < 0.5 mm. — they are even small for males of Scalpellum.
Their structure agrees with that of the males of several other species
of this genus: round about the opening of the mantle, at the extremity
of the little elevation over the surface of the chitinous capsule, four
rudimentary valves are observed. What I think, so far as my experience
goes, is characteristic for this species, is that short rudimentary
tentacles are attached to the surface of the mantle between (alternating
with) the small valves, little appendages — which of course have
nothing in common with the articulated antennae or other limbs of
the Cirripedes. Should any doubt remain, as to whether these little
parasites really represented the males of this species, these tentacles
might be used to dissipate it. A few small, quite young females, in
which the capitulum however was already furnished with calcareous
valves and the whole appearance of which corresponded with an
early condition of fullgrown females, were found attached to the
surface of the capitulum of one of the large specimens. Now, these
little females are furnished with the same tentacles. They are
embryological organs, which of course may have importance froma
morphological or phylogenetic point of view, but which have dis-
appeared in the fullgrown females. In the young females they occupy
the same place as in the males, viz. at the free extremity (the tip)
of the capitulum attached to the chitinous surface between the two
calcareous plates which represent the terga, near the anterior extremity
of the orifice — in the females large, in the males relatively much
smaller — which gives entrance to the cavity in which the animal’s
body is lodged.

I do not believe that examples are known in animals so highly
developed as Cirripedia of such a pronounced polyandry as in this
species of Scalpellum. As a rule, the number of males found attached

46

Proceedings Royal Acad. Amsterdam. Vol VIII.

( 662 )

to the capitulum of the female or of the hermaphrodite is one at
each side only, in some species it is two or three and the largest
number I have observed was five. How can we explain that there
is a species with such a large number as the case mentioned? I
have tried in vain to find an explanation. We do not know much of
the habits of these animals. It is hardly admissible that the great
number of males should be connected with the depth at which they
live, for (1) the same species which is found in the Malay Archipe-
lago at a depth of 200—400 m. lives in the Japan sea in shallow
water, and (2) we know species living in coastal waters and others
found in depths of over 1800 m., all of which have two males
only. A connection exists no doubt between the place where the
little males are found attached and their great number —~ but I
am at a loss to understand what the relation may be. The eggs
of these Cirripedes are fecundated at the moment they are excluded
and form two leaves (the so-called ovigerous lamellae) which remain
in the sack or mantle-cavity of the female until the eggs hatch out.
If the males are attached at the margin of the mantle-cavity, the
chance that the eggs will be impregnated is of course larger than
in the case when they are attached at a greater distance, as in
Se. Stearnsi. So it is easily understood that in the latter case a
greater number of males would be required — but why did they
choose for attachment a place which is less favourable for impregnation?
Because they were so numerous and did not find space enough at
the ordinary place?

v

Mathematics. — “A group of complexes of rays whose singular
surfaces consist of a scroll and a number of planes’. By
Prof. JAN DE VRIES.

1. The generatrices of a rational scroll can be arranged in the
groups of an involution /,; to this end we have but to arrange
their traces on an arbitrary plane in the groups of an J,. If we
consider each pair of lines /,/ of J, as directrices of a linear con-
gruence, it immediately occurs to us to examine the complex of
rays I which is the compound of the o* congruences determined
by it.

Let the scroll or be of order n and let it have an (n—1)-fold
directrix d. The generatrices / form a fundamental involution J,—1,
each group of which consists of the (n—1) right lines, coinciding
in a point of d. This /,-,; has evidently (m—2) (p—1) pairs in

( 663 )

common with the given [hs so on d lie as many points of intersec-
tion H of pairs /,/ of the involution /,. Each ray through a point HT
belongs to the complex I, likewise each ray in the connecting
plane 4 of the right lines /,/; i. o. w. the complex has (n—2) (p—1)
principal points H and (n—-2) (p—1) principal planes h.

2. On an arbitrary plane « a rational curve c with (m—1)-fold
point D is determined by oe”. The rays of the complex lying in a
envelop a curve (@) of class (n—1) (p—1), the curve of involution
(director curve) of /', in which the points of c* are arranged by
the given /,. *)

So the complex is of order (n—1) (p—).

The line of intersection of « with a principal plane 4 being a
ray of I, the curve of the complex (@) touches.all principal planes.

If @ is made to pass through a right line / of 9”, then (a) splits
up into the pencils having for vertices the traces L’ of the (p—1)
rays conjugate to / and into a curve of order (n—2) (p—1), the
curve of the involution of 7", on the curve c™—! which @ has in
common with 9” besides. So a tangent plane of 9” is a singular
plane of I.

The singular surface consists of a scroll and the principal planes.

When a tangent plane contains one -of the principal points it passes
in general through the directrix d, therefore through all principal
points. Then (a) splits up into (n—2) (p—1) pencils (H) and (p—1)
pencils (L’).

Of the n—1 generatrices / through a point H, two, /, and /,,
form a pair of J/,. If we bring «a through one of the remaining
right lines /, (k=1 to n—3), then (a) consists of (p—1) pencils with
vertices L',, the pencil (H) and a curve of class (n —2) (p—1)—1.

In an arbitrary plane through H the curve of the complex (a)
consists of the pencil (H) and a curve of order (n—1) (p—1)—1.

3. The rays of the complex through an arbitrary point A
envelop a cone (A) of order (m—1) (p—1) passing through the
principal points.

If A lies on 9” cone (A) consists of (p—1) concentric pencils and
a cone of order (n—2) (p— 1).

If we assume A in a principal plane / then only one pencil
separates itself from the cone of the complex.

1) ['y has (n—1) (p—1) pairs in common with the involution Ip which an
arbitrary pencil determines on cr.

( 664 )

If A is taken on the line of intersection of two planes h, two
pencils are separated from the cone. Three pencils are obtained
when A is point of intersection of three principal planes.

If we take A on the curve ec”? which a plane 4 has in common
with o” then (A) consists of p concentric pencils and a cone of
order (n—2) (p—1)—1.

If A is a point of intersection of @" with two principal planes
the number of pencils evidently becomes (p+-1).

4. The curve of the complex (a) is of order (p—1) (2n-4-p—6)’).
It possesses } (p — 1) (p — 2) (n — 2) threefold tangents *) which are
transversals of as many triplets of right lines belonging to a group
of J,. The cone of the complex (A) possessing evidently as many
threefold edges, the scrolls each having three conjugate right lines /
as directrices form together a congruence y of order and class
4 (p — 1) (p — 2) (n — 2).

Each principal point H is for this congruence a singular point of
order (p — 2); the singular cone is broken up into (p— 2) pencils.

Each principal plane 4 is a singular plane of order (p— 2) and
contains (p — 2) pencils of rays of congruence.

5. The right lines resting on four lines / belonging to a group
of J, form a scroll enclosed in PF, of which the order is going to
be determined.

Each transversal ¢ of three conjugate right lines /,,/,,/, and the
arbitrary right line « intersects still (n — 3) generatrices m of 0”.
To each of these right lines m can be made to correspond the (p — 3)
right lines / forming with /,,7,,2, a group of J,.

To each ray / belong (p —1), triplets /,,/,, 2,, so 2(—1), trans-
versals ¢ and therefore 2 (n — 3) (p —-1), rays m.

The congruence (1,1) of the right lines resting on m and a has
with the congruence y in common (n — 2) (p — 1) (p — 2) rays t,
so that to m are conjugate (m — 2)\p—1)(p — 2) (p—8) right
lines J’.

Now each transversal of four lines / belonging to a group of J,
evidently gives four coincidences of the correspondence (/' , m).

1) The characteristic numbers of the curve of involution of an J, on arational
c" are found in the dissertation of Jon. A. Vreeswijk Jr. (Involuties op rationale
krommen, Utrecht 1905, page 38).

2) See also my paper “Complexes of rays in relation to a rational skew curve”
(These Proceedings, VI, page 12).

( 665 )

Consequently the scroll of the transversals of quadruplets of the

1
involution is of order B (p —1) (p — 2) (p — 3) (dn — 9).
Each principal point and each principal plane of I bears

1
5 (P—2) (p—3) right lines of this scroll.

6. If o” possesses also a single directrix e all principal planes of
I’ pass through e and the complex is in itself dual.

il
If o” has a nodal curve J of order 5 (n — 2) (n — 1) each gene-

ratrix 7 rests in (n— 2) points on d, and is thus cut by (n — 2)
right lines /. By this the generatrices are arranged in a symmetric
correspondence of order (n— 2), having with /, given on 0” in
common (n— 2) (p— 1) points H. So the complex has again
(n — 2) (p —1) principal points and as many principal planes.

In like manner the order of F remains the same. But now the
curve of the complex can break up on account of its plane contain-
ing two or three principal points by which two or three pencils
are separated. Besides « can contain still a right line /. So here
the degenerations of («) are dually opposed to those of the cone (A).

(February 21, 1906).

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KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,

PROCEEDINGS OF THE MEETING
of Saturday February 24, 1906.

DOG

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 24 Februari 1906, Dl. XIV).

COEN a aN eS

W.H. Jurivs: “A new method for determining the rate of decrease of the radiating power
from the center toward the limb of the solar disk”, p. 668. (With one plate).

A. F. HorrEMAN: “On the nitration of ortho- and metadibromobenzene”, p. 678.

J. J. Buanksma: “The introduction of halogen atoms into the benzene core in the reduction
of aromatic nitro-compounds”. (Communicated by Prof. A. F. Horreman), p. 680,

F. A. F. C. Went and A. H. Braauw: “On a case of apogamy observed ‚with Dasylirion
acrotrichum Zuce.”, p. 684.

J. C. Kapreyn: “On the parallax of the nebulae”, p. 691.

J. J. van Laar: “On the course of melting-point curves for compounds which are partially
dissociated in the liquid phase, the proportion of the products of dissociation being arbitrary”.
(Communicated by Prof. H. W. Bakuuis RoozrBoom), p. 699.

C. J. ENKLAAR: “On ocimene and myrcene, a contribution to the knowledge of the aliphatic
terpenes”. (Communicated by Prof. P. van Rompurcn), p. 714.

C. J. ENkraar: “On some aliphatic terpene alcohols”. (Communicated by Prof, P. van
RomBurGH), p. 723.

H. B. A. BockwiykeEL: “On the propagation of light in a biaxial crystal around a centre of
vibration”. (Communicated by Prof. H. A. Lorentz), p. 728.

K. Martin: “On brackish and fresh water deposits of the river Silat in Western—Borneo”, p. 742.

Physics. “A new method for determining the rate of decrease
of the radiating power froin the center toward the limb of
the solar disk”. By Prof. W. H. Junius.

(Communicated in the Meeting of January 27, 1906)

The brightness of the solar disk is known to diminish considerably
from the center toward the limb. Although this prominent feature
of the solar phenomenon should be among the first accounted for in
every theory of the Sun, it leads to problems presenting so many
difficulties, that a satisfactory explanation is, until now, altogether
wanting. And even the empirical study of the law according to
which the radiating power varies across the disk, is not very advanced.

What we know about the question is founded on researches in

47
Proceedings Royal Acad. Amsterdam. Vol. VIII.

( 668 )

which either a photometer, or a thermopile, a bolometer or a radio-
micrometer was used for exploring an image of the Sun. The results
obtained by different observers are rather discordant’). This may be
partly due to instrumental or accidental errors, but there is also a
systematical error which must have influenced similarly all of the
results thus obtained, and which proceeds from the scattering of the
rays by the terrestrial atmosphere. In any point of an image of the
Sun is not only to be found the radiation coming from the corre-
sponding point of tbe disk, but, besides, some diffused radiation
proceeding from other parts of the disk. This disturbing effect will,
of course, vary in magnitude with the condition of our atmosphere,
but it will always act in a levelling way, parts of the image lying
near the edge receiving more diffused radiation from the middle
parts of the disk, than receive the central parts of the image from
the marginal parts of the disk.

We may completely avoid this source of error by using a method
in which the radiating power of the different parts of the disk is
calculated from observations made on the occasion of a total eclipse
of the Sun.

Let us suppose tbe curve, representing the intensity of the ‘solar
radiation from the first until the fourth contact as a function of time,
to be exactly known?). The curve will show us by how much the
total radiation has increased or decreased between any two epochs.
Every (positive or negative) increment is exclusively due to rays
coming from that strip of the solar disk through which the Moon’s
limb has appeared to move between those very epochs.

Suppose the time after third contact to be divided into equal
intervals of, say, 2 minutes, and the position of the Moon’s limb
at the end of each interval delineated on the solar disk, then the
latter will be divided into 39 narrow strips, successively contributing
the known quantities a, b, c, d,.. to the total radiation.

Now, let us distinguish m concentric zones on the solar disk and
denote by wz, ze , . . 7, the radiation coming from these zones per

1) Cf. J. Scuremer, Strahlung und Temperatur der Sonne, p. 43—49 (1899).

2) It is well known that, at Burgos, the observation of the eclipse of August 30,
1905, has not been favoured with a clear sky (Cf. the Preliminary Report in the
Proceedings of the Meeting of November 25, 1905). Nevertheless, the measurements
of total radiation have yielded some results of sufficient accuracy to justify that,
in our present investigation, we make use of the radiation curve then secured.
Further particulars regarding the observations will soon be published in the
complete report on our expedition.

( 669 )

unit surface. (According to results obtained by LANGLEY and by Frost
we shall suppose the radiating power to vary only with the distance
from the center, not with the position angle). One of the strips will
contribute to the radiation :

dan 0. ap = ee = = On Bs

if it cuts out of the first zone an area d,, out of the second zone
an area d, ete. The next strip contributes :

EE dad ETB see En Xr
and so on. We get 39 equations from which z,, ws, … z, may be
resolved.

Determination of the coefficients of the n unknown quantities.

I have found the coefficients d,, d, . . . &, €, . . . by weighing.
On a piece of excellent homogeneous paper the solar disk was drawn
and divided into a suitable number of concentric zones, which were
intersected by ares representing the Moon’s limb in its successive
positions. The following astronomical data, necessary for making the
drawing, have been kindly procured to me by prof. A. A. Niranp.

contact I II Ill IV

position angle 293°,4 104°,5 304°,9 114°,9

local time 23337105 0°51™58s 055m 39s 2h42™ 14s
Moon’s radius : Sun’s radius — 132,8 : 126,8.

Now the strips were carefully separated from each other and
weighed (for subsequent control). Then each strip was cut along
the zone circles, and the pieces were weighed separately. In order
to make the pieces recognizable, the zones had all been differently
painted, each with a narrow line of water-colour. The weighings,
which were accurate to half a milligram, gave the coefficients of
the unknown quantities 2, zz....2,. So the unit of area, adopted
for measuring the surface of the solar disk, corresponds to a piece
of our drawing paper weighing 1 milligram.

The breadth of each of the outer five concentric zones was '/,,
of the Sun’s radius; then came seven zones with breadth '/,, of the
radius each, leaving round the center a circle with radius '/,,. The
average distances of the zones from the center, expressed in thou-
sandth parts of the radius, will now be used as indices a, 8.... of
our 13 unknown quantities; so these will be written :

Dors © RT Eier Penn Goreng le

>» V4oor Paoor Uaoor Vicor Yor

47%

925? Pars 825? “775 700 600 500

sa 8 a Ss ee

WW ME We WN Need Aleh is Veet settee

. &

126% Torn

662 mrs +101 zoe,

28 morst 59 w,,,+84 morst 1 mas

18 worst 29 #,,,+50,5¢,,,177. «,,,+ 1,52,,,

18 w,,,+ 19 «#,,,+27,50,,,+46° 7,,,169,50,,,+ 2 ro,

10-#,,,+ 14 #,,,+19 2,,,+28' @,,,140 #,,,166 zoo

8 oort 10 a ,f12 @,,+15. 2,118 @,,, +97 fy +98 ao,

7 mok Stash 9 wey, +10,52,,,112,50,,,430 e548 Zooo ll 500

6 mrs 6,5¢,,,+ 7 Lorst 8 ont 9 Dirt 23 Drood 28,599 +40 Zoot 49 400

Oort 6 Daas 7 Derst 8 Daas 8 Det 19 Broo 21 Beg 20 ® 599-99 Dsoot 36 © 300
Soth 6 most 6,Smsrst 7 Rost 7 #,,+16 By T1752 499 FH 19500 22000400 +26,52,,,+31 KENT
bros tee WO saret ClO ny psf Damned Byog $15.5 ary op + 16,505 917,54 559+ 18,52 499-+ 18,52. 21,5,,,+ 20,52, 00

95M 575 + 6 Toast 6,57; + 7 Beast 7 @7,415 Drood 154500 +16,5255)+17 Dsoot 17452300 +18 Lao +19 Lio +8,

On p. 670 the equations are written out. We have confined our-
selves to 13 equations; increasing this number would not have led
to greater accuracy, as the values of a,b,c... had to be found from
the radiation curve, that is by graphical interpolation, in which pro-
cess. it is understood that all of the observations have already been
taken into consideration.

Determination of the constant terms of the equations.

Table I contains the results of the observations made at Burgos
with our actinometer. The second column gives the galvanometer
deflections, from which the numbers of the third column, representing
the intensity of the radiation, are calculated *).

Owing to the clouds there are large gaps in the series of obser-
vations; but nevertheless, after the results had been plotted down,
we saw that there was only little room left for fancy when drawing
the radiation curve in such a way, that closest agreement with the
observational data was obtained. As a matter of course the curve
has not been drawn between the series of points, but so as to join
the highest points, for the observed values could only be too small.
Only one exception is made to this rule, the value found at 0° 17™ 3s
being very probably too high by some error or instrumental dis-
turbance. £

The middle part of the radiation curve has been reproduced on
the annexed plate. For determining a, b, c, . . . we have used the
part included between 0° 55m and 1" 37m, which was very carefully
constructed on a larger scale. It deserves notice that the relative
accuracy of the small ordinates (corresponding to few minutes after
totality) is nearly as great as that of the larger ones, because
the galvanometer deflections from which they were calculated are
all lying between 118 and 347 scale divisions. Table II refers to
this part of the radiation curve. In the second column are given
the ordinates of the curve at the epochs O° 55"408 and every
two minutes later; the unit corresponds to an intensity = 1000.

1) Particulars concerning the connection between the numbers of these two
columns will be found in the forthcoming report on the Dutch expedition. The
method and the instruments used al Burgos were the same that are described in;
“Total Eclipse of the Sun, May 18, 1901. Reports on the Dutch Expedition to
Karang Sago, Sumatra, N’. 4: Heat Radiation of the Sun during the Eclipse”, by
W. H. Juuus. The numbers of the third column are proportional to the total
radiation coming from a circular patch of the sky, 3° in diameter, with the Sun
in its center. '

( 672 )

EAB ME
| Galvano- | Intensity
Time. meter- of Time.
deflections | radiation.
hm s h m s
29 28 48 280 1750000 0 20 48
36 0 231 1444000 || 2nd contact 51 58
38 33 287 1794000 5303
54 28
46 58 £87 1794000 55 18
51 38 270 1688000 || 3rd contact 55 40
53 49 260.5 1631000 55 58
56 8 278 1745000 57 58
58 33
93 458 256 1610000 59 13
8 3 283.5 1786000 59 53
9 56 284.5 1792000 AIS
41 44 275 1736000 2 28
Ast contact 33 8 3) 08)
35 48 226 1430000
38 3 256.5 1625000 7 38
WW 38 269.5 4709000
4A 38 270 1712000 U 15
42, 48 270.5 1715000 22 3
4h 0 260 1649000 3
45 33 25085 1646000 93 58
46 38 256.5 1627000 MU 53
47 52 248.5 1566000 25 53
48 53 950.5 1589000 26 53
50 8 249 1580000 D753
bl 33 244 1529000 98 58
53 8 23315 1483000 30 8
boro 997 1442000 31 8
56 33 226 1435000 32 11
58 23 216.5 1376000 33 13
34 20
OMT 23 192 1222000 35 25
8 53 184 1170000 36 34
10 28 4677 1127000
11 43 Ur 5) 1091000 DY nde)
1313 |_ 165.5 | 1054000 38
14 58 159 1013C00 || 4th contact 12 24
3 150 956000 13 18
19 28 136 867000 14 20

Galvano-
meter-
deflections.

128.5

w

rs

a
or or on

Intensity
of
radiation.

819000

635000
665000
676000
722000
745000
776000
805000
832000
865000
897C00
926000
950000
981000
1007000
1037000
1060000

1506000
1581000

1648000
1657000

( 673 )

But this observational curve has to be corrected, owing to the
circumstance that in the lapse of time considered the Sun’s altitude
has diminished. We may proceed as follows. Apart from a possible
influence of sun-spots or faculae there is no reason why the eclipse
curve would not be symmetrical if the Sun’s altitude (and the con-
dition of. our atmosphere) reinained constant. Between 23 and 41
the variation of altitude is very small. Now taking 0° 53™ 50s as

TABLE II. TABLE III.
Ordinates Orden
. f
Time Woe corrected Increments
radiation radiation
curve.
curve.
x eae | Radiation per unit surface
0 55 40 0 0 ant re of the concentric zones of
5740 | 20.4 0 A | a the solar disk.
32.4 =h ‘
59 40 55 sj)
JEG Sm 5d5
4 1 40 91.0 91.0
45.5=d Frog = 0.2160
3 40 136.5 136.5
50.5 =e Car — 0.2504
5 40 187 187
Dn == Lr 03023
7 40 240 AA
DONE Ls — 023290
9 40 296 297
58 =h Kroo = O 3488
41 40 354 355 ;
ay) Si Leo) — 0.3662
13 40 Zel2 Alk
CU SS Eg — 0.3843
15 40 472 474
61 —=k Lio — 0-53
17 40 532 535
627 L440 = 0.4278
19 40 594 597
62 =m Lano — 04240
21 40 655 659 6
62 =n X19) = 0.4380
23 40 717 721
Ë OND xX) = 0.4388
25 40 776 783
61.5= p
27 40 834.5 844.5
61 =g
29 40 891.5 905.5
60.5=r
31 40 947 966
60 s
33 40 | 1001 1026
59.5= 7
35 40 | 1053.5 1085.5

the epoch of mid-eclipse, we draw a horizontal line through a point
m corresponding to that epoch. The line cuts the descending branch
of the curve in /; we make mn—m/ and thus find a point n of
the hypothetical radiation curve for constant altitude of the Sun.
Acting in a similar way for a few more points, we get an idea of
the magnitude of the smoothly increasing correction which is to be
applied to the ordinates of the ascending branch. K. Anestr6m’s
measures of the intensity of the radiation for different altitudes of
the Sun ') have also been considered in determining the correction.

The third column of Table [ contains the ordinates of the corrected
curve; in the fourth column are given their successive increments
which, of course, are the values to be assigned to the absolute terms
of our equations.

Results.

The solution of the equations leads to the numbers of Table III;
the results—are plotted down in fig. 2 on the plate. Through these
points we have drawn a curve satisfying the condition that its
curvature should gradually diminish; it shows us the law of variation,
of the radiating power from the edge toward the center of the solar
disk, Putting the ordinate at the center equal to 100 and expressing
the other ordinates in the same unit, we get numbers comparable
with the results obtained by other investigators.

The comparison with the spectro-photometric observations by
H. C. Voerr ®) and with the measurements of total radiation made
with a radio-micrometer by Wiutson*) and with a thermopile by
Frost‘), is given in Table IV. We add in Table V the results of a
spectro-bolometric investigation by Very *), as these numbers have
been used by Very and by Scuusrer ®) in testing their explanations
of the phenomenon.

According to Frost’s measurements the total radiation appears to
diminish from the center toward the limb in about the same pro-
portion as the radiation of wave-length 650uu, whereas my numbers
Show a decrease very similar to that exhibited by rays of wave-

1) K. Anosrrön Intensité de la radiation solaire à différentes altitudes. Recherches
faites à Ténériffe 1895 et 1896.

2) H. C. Voeer, Ber. d. Berl. Akad. 1877, p. 104.

3) W. E. Wuson, Proc. Roy. Irish Acad. [3], Vol. 2, p. 299, (1892).

4) E. B. Frost, Astron. Nachr. 130: (1892), p. 129.

5) F, W. Very, Astroph. Journ. 16 (1902), p. 73.

6) A. Scuuster, Astroph. Journ. 16 (1902), p. 820; 21 (1905), p. 258.

( 673 )

TAB

L E

IV.

Distance| H. C. VoGEL’s spectro-photometric measurements,

from

Total radiation.

Gee | ee prea Aes ee baits Receiver in solar Eclipse.
of. = — 7—473)510—515)573—585 |658—666 image. curve.
disk. pe wp pp. pp py. pp. Wirson | Frost | JuLIus
0.0 100.0 | 100.0 | 400.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0
0.1, Ce || SEE 99.7 99.7 99.8 EEN) 99.9 99.9 99.8
0.2 98.5 98.7 98.8 98.7 99:2 99 5 99.6 99.4 | 98.6
0.3 96.3 96.8 97.2 96.9 98.2 98.9 98.8 98.4 96.6
0.4 {3.4 94.4 94.7 94.3 96.7 98.0 97.3 96.3 94.0
0.5 88.7 90.2 91.3 90.7 94.5 | {6.7 95.3 93.6 90.3
0.6 82.4 84.9 87.0 86.2 90.9 | 94.8 92.5 89 8 85.5
0.7 74.4 71.8 80.8 80.0 84.5 91.0 88.7 84 6 79 5
0.75 69.4 73.0 76.7 | 75.9 | 804 | 88.1 oes
0.8 63.7 67.0 Tiled 70 9 74.6 84.3 83.9 11.9 70.4
0.85 56 7 59.6 65.5 64.7 ZE 79 0 63.5
0.9 47.7 50.2 57.6 56.6 59.0 71.0 | 74.9 | 68.0 | 55.0
0.95 34.7 35.0 45.6 44.0 46.0 58.0 | | (60.5) | 440
1.0 13.0 14.0 16.0 16.0 25.0 30.0 45 A (24.0)
PAB LRA
Distance | F. W. Very’s spectro-bolometric measurements. sie sic
cantar | MG u | MB np | 550nu | 6l5pu | 781 pe | 1040ux | 1500 pp
0.5 85.8 90.2 93.3 94 8 G44 94.3 95.9
0.75 74.4 76.4 83.1 84.5 88.5 89.4 95.0
0.95 47 A 46.2 58.7 68.1 74.9 76.5 85.6

length 540uu. At first sight the evidence is in favour of the results
obtained by Frost, because the maximum of the curve representing
the energy in the solar spectrum (or perhaps rather the “center of
gravity” of the enclosed surface) lies closer to 650uu than to 510uu.
But this argument fails; for the measurements of Voerr and those
of Frost are all disturbed alike by atmospheric diffusion. Had the
spectro-photometric observations been free from this influence, then

the rate of decrease of the

radiation from the center toward the

( 676 )

limb would doubtless have been found quicker for all wave-lengths,
and, very probably, the distribution for the region 650ug would have
proved to agree better with my results than with the uncorrected
values of Frosr.

WirsoN’s measurements seem to have been influenced by other
causes of error still, besides atmospheric scattering, as his nambers
are greater than those obtained by Frost, and harmonize not as well
as the latter with the spectro-photometric series.

The observations of Very have given considerably greater ratios
in the marginal regions than those of Voce. Mr. Very himself points
out the difference, and remarks that the bolometer has an advantage
over the eye in the red where the heat is great; but I may suggest,
on the other hand, that instrumental errors (reflection or scattering
of light by prisms, lenses, tubes, ete.) are easier discovered and
corrected in spectro-photometric than in speectro-bolometrie work.

It seems to me that observing an eclipse-curve by means of a
very simple but sensitive actinometer, without lenses or mirrors,
must yield results concerning the radiation of different parts of the
solar disk which deserve more confidence than the values hitherto
obtained in other ways. I wish to lay stress upon the advantages of
our method, rather than on the reliability of the numbers secured
at Burgos under not very favourable circumstances. In a clear sky
the shape of the eclipse curve will easily be found with very great
accuracy.

The same method will also be applicable with radiations covering
limited parts of the spectrum, if we only put suitable ray-filters
before the opening of one of the diaphragms in the actinometer. It
may even be possible, in a future eclipse, to use an arrangement
which brings several ray-filters by turns before the opening ; thus,
when disposing of a quick galvanometer, one would be able to
simultaneously determine, with one actinometer, the eclipse curves
for rays belonging to five or more regions of the spectrum, and the
results would be independent of selective atmospheric scattering.

Remarks on the hypotheses used for explaining the distribution of
the radiating power on the solar disk.

The diminution of the intensity of radiation toward the limb is
almost generally ascribed to absorption of the rays by the solar
atmosphere '), and it is supposed that, in absence of that atmosphere,

1) J. Scuetner goes as far as to say: “Eine andere Deutung des Lichtabfalls ist
nicht zulässig.”’ (Strahlung und Temperatur der Sonne. p. 40).

(877)

the photosphere would show itself as an equally luminous disk. But
then it appears to be impossible to find such values for the thick-
ness of that atmosphere and for its coefficient of absorption, as to
give a law for the rate of diminution of brightness, consistent with
observation. Very!) e.g. when attributing the effect to absorption
only, arrives at the absurd result that we should have to assume
that the absorptive power toward the limb is smaller than that nearer
the center. He, therefore, suggests the existence of other influences
which, combining with the absorbent process, would reconcile theory
to observed facts. Diffraction by fine particles, columnar structure
of the solar atmosphere, irregularity of the photospheric surface, are
thus introduced.

ScHUSTER *), on the other hand, is of opinion that the difficulty
which has been felt in explaining the law of variation of intensity
across the solar disk is easily removed by placing the absorbing
layer sufficiently near the photosphere and taking account of the
radiation which this layer, owing to its high temperature, must itself
emit. He then really finds values for the absorption and the emission
of that layer, harmonizing with the results of Very’s and Witson’s *)
measurements, and also with the properties of the energy curve of
the spectrum of a black body at different temperatures. But, for all
that, serious doubts as to the correctness of the premise and the
conclusions must subsist.

Indeed, the calculations of Schuster as well as those of Very,
Witson, LANGLEY, PrickERING and others, concerning the same subject,
are based on the assumption that the light travels along straight
lines through the solar gases, whereas everybody who has duly
noticed A. Scumipt’s “Strahlenbrechung auf der Sonne” will at the
least have to give in that rays coming from the outer zones of the
disk must have followed curved paths through the solar atmosphere.
By this circumstance the said calculations lose their convincing power..

And besides, the fundamental idea that a considerable portion of
the photospheric radiation should be absorbed by a thin atmosphere,
encounters a difficulty of greater importance still. This point, I
think, has also first been moved by A. Scumipt. What becomes of
the absorbed energy accumulating in the atmosphere ? According to
SCHUSTER e.g. (le. p. 322) the atmosphere transmits largely */, of

1) F. W. Very. The absorptive power of the solar atmosphere. Astroph. Journ.
16, p. 73—91, (1902).

2) A. Scucster. Astroph. Journ. 16, p.320—327, (1902); 21, p. 258—261, (1905).

3) W. B. Wirson and A. A, Rampaut. Proc. Roy. Irish Acad. [3], 2, p. 299—
334, (1892).

( 678 )

the radiation emitted by the photosphere ; so it stops almost °/,, and
only a small fraction of this absorbed energy leaves the Sun in the
form of radiation, emitted by the atmosphere itself. After all, more
than half of the radiation coming from the photosphere is retained
by the absorbing layer, and we cannot suppose it to go back to
the interior without violating the second law of thermodynamics,
As long as it has not been shown how the solar atmosphere may
get rid of that immense quantity of energy continually supplied and
never radiated, similar considerations will remain very unsatisfactory.

Our problem appears to be much less intricate when viewed from
the stand-point taken by Scumipr'), though the mathematical treat-
ment will not be easy. A uniformly luminous sphere surrounded
by a concentric, perfectly transparent refracting envelope, will offer
the aspect of a disk the brightness of which diminishes towards the
limb. This has been established approximately by Scumipr for the case
of a homogeneous, sharply limited envelope. It is easily understood
that a similar result must be obtained when assuming a transparent
atmosphere of gradually decreasing density and refractive power ;
but then, of course, the rate at which the luminosity varies on the
disk will depend on the law of density variation. We may proceed
a little farther, and accept Scumipr’s hypothesis that the incandescent
core of the Sun is not a sphere with a sharp boundary, but a gaseous
body the density and radiating power of which are smoothly dimi-
nishing along the radius. In this way, I think, we dispose of pre-
mises from which it seems possible to derive an explanation of the
general aspect of the solar disk without involving into such serious
difficulties as were hitherto encountered.

Chemistry. — “On the nitration of ortho- and metadibromobenzene.”
By Prof. A. F. HOLLEMAN.

(Communicated in the meeting of January 27, 1906).

After the disturbing influence which the halogen atoms exercise
on each other's directing influence in regard to the nitro-group, had
been noticed in the nitration of the dichlorobenzenes, it was necessary
to extend this research to the nitration of the dibromobenzenes so
as to be able to find the connection between the results with the
dichloro- and dibromocompounds and to compare the same with the
result of the nitration of the corresponding monohalogen benzenes.

1) A. Scum, Physik. Zeitschr. 4, 282, 341, 453, 476 ; 5, 67, 528. (1903 and 1904),

ay H. JULIUS. A new method for determining the rate of decrease of the radiating power
from the center toward the limb of the solar disk.

Middle part of the radiation curve obtained during the solar eclipse
of August 30. 1905.

1200000

1100000

1000000

900000

800000

700000

600000

500000

400000

300000

200000

100000

{
50 Oh vio 20 20 40 50 it 10 20 ?0 40 50 2

Radiating power across the solar disk.

“OD OE VE Tan
Edge. Center,

Proceedings Royal Acad. Amsterdam. Vol. VIII.

mat

1

( 679 )

The necessary experiments have been considerably delayed, because
it appeared that the ortho- and meta-dibromobenzenes had not as
yet been obtained in a perfectly pure condition, and the search for
a good method absorbed much time. We have at last succeeded in
preparing m-dibromobenzene from perfectly pure m-bromoaniline by
diazotation in a dilute hydrobromie acid solution, according to a
direction given by ErpMann for another purpose. Meta-dibromobenzene
has a sp. gr. of 1.960 at 18.5°, and solidifies at — 7°. It is true
that F. Scuirr incidentally mentions (M. 11, 335) that he has met
with m-dibromobenzene solidifying at + 1°, without saying how he
has obtained the same, but there is good reason for doubting the
correctness of this statement. In this case, the product obtained by
me and my coadjutors (Siks, SLurrer) with its 8° lower solidifying
point should contain about 16°/, of impurities. In the nitration of
our m-dibromobenzene, however, a product is obtained having a
sp. gr. such as was to be expected from a mixture of the isomers
(Br : Br? : NO,*) and (Br': Br* : NO,?) brought together in the propor-
tion indicated by the solidifying point, so that a contamination of
our preparation with such a large quantity of another substance is
altogether out of the question ; moreover, on distillation our preparation
yielded two fractions within one degree which both possessed
practically the same sp. gr. and solidifying point.

O-dibromobenzene which was obtained in an analogous manner
from o-bromoaniline, had a sp. gr. of 1.996 at 11° and solidified
at + 6°.

The preparation of the six dibromonitrobenzenes was carried out
in a manner analogous to that of the six dichloronitrobenzenes,
described by me in the “Recueil” 28, 357.

The composition of the products of nitration of the dibromobenzenes
was determined from their solidifying point and their sp. gr. and
led to the results united in the subjoined table with the composition
of the products of nitration of the dichlorobenzenes. The temperature
of the nitration was 0°. (See p. 680).

In ortho-dibromobenzene the disturbance of the directing power of
the one halogen atom owing to the presence of the other one is,
therefore, much less than in the case of orthodichlorobenzene because
in the first one 18.3 and in the second only 7.2°/, of by-product
is formed, whilst monobromo- and monochlorobenzene yield, respec-
tively, 29.8 and 37.6°/, of by-product. On the other hand, the
disturbance caused by the entry of the nitro-group between the two
halogen atoms in m-dibromobenzene is very nearly equal to that in
m-dichlorobenzene, therefore much larger in regard to the ortho-

( 680 )

Quantity of (Quantity of by-prod. in
by-product in °/, 100 parts of main prod.
|

0-C,1T,Cl, 7.2 7.8
m-C,H,Cly 4.0 | 4A
o-C,H,Bry | 18.3 | 22.4
m-C‚H,Br, 4.6 4.8
C,H,Cl 29.8 42.0
C,H,Br 27.6 60.5

compounds. One would feel inclined to attribute this to “steric
disturbances” introduced into Organic Chemistry by V. Mrwer, were
it not that the specific volume of chlorine and of bromine in the
dichloro- and bibromovenzenes differs but little.

Perhaps it is rather the atomic weight of chlorine and bromine
which has some connection with the above. For further particulars
concerning this research the “Recueil” should be consulted.

Amsterdam, Org. chem. Lab. of the University, January 1906.

Chemistry. — “The introduction of halogen atoms into the benzene
core in the reduction of aromatic nitro-compounds”’. By
Dr. J. J. BrANKsMA. (Communicated by Prof. A. F. HoLLeMAN).

(Communicated in the meeting of January 27, 1906).

Some time ago I cited and communicated some experiments *)
which showed that, in some cases, in the reduction of aromatic
nitrocompounds, halogen atoms may be removed from the benzene
core. In 1901 an article by Prinnow’) appeared in which a
fairly large number of cases are mentioned, where halogen atoms
are introduced into the benzene core in the reduction of aromatic
nitrocompounds. Piynow endeavours to find the conditions under
which this secondary reaction is as much as possible prevented in
order to prevent formation of halogenised amidocompounds as by-
products, alongside the amidocompounds.

1) Proc. 30 March 1904, Recueil 24, 320.
2) Journ. für Prakt. Chem. (2) 63, 352.

( 681 )

So when I obtained 5-chloro-4-6-dibromo-2-amido-m-xylene as by-
product. in the reduction of 4-6-dibromo-2-nitro-m-xylene, I tried to
CH, CH,

introduce halogen atoms into the core, taking the simplest case,
namely, the reduction of nitrobenzene with tin and hydrochlorid acid.

As is well-known, various intermediate products are formed in
the reduction of nitrobenzene to aniline. The formation of chloro-
aniline from nitrobenzene may be explained in the following manner: *)

C,H,NO, + 4H =—C,H,NHOH + H,0
C,H,NHOH + HCI = C,H,NHCI + H,O
C,H,NHCI — CIC,H,NH, (0. + p.).

The fact that, in the reduction of nitrobenzene, phenylhydroxylamine
occurs as an intermediate compound, has been demonstrated by
BAMBERGER, who has also proved that, on boiling phenylhydroxylamine
with hydrochloric acid, o- and p-chloroaniline are formed *). It has
also been proved by Lös that o- and p-chloroanilines are formed in
the electrolytic reduction of nitrobenzene in alcoholic hydrochloric
acid solution *). The object of the experiments to be described was
to try and conduct the reduction of nitrobenzene with tin and hydro-
chlorie acid in such a manner that instead of aniline, as much as
possible chloroaniline was formed.

The experiment had, therefore, to be carried out in such a way,
that the phenylhydroxylamine formed was not at once further reduced
to aniline, but to give this substance an opportunity to be converted
into chloroaniline, under the influence of hydrochlorie acid. The
conditions were also to be such that the phenylchloroamine C,H,NHCI,
which is formed intermediary, could be readily converted into chloro-
aniline.

The intramolecular conversion of phenylchloroamine into o- and
p-chloroaniline is, bowever, but little known, as the first substance
is very unstable but the conditions under which acetylchloroanilide
is converted into p-chloroacetanilide have been closely investigated.
It has been shown that this reaction is very much. accelerated by
increase of the temperature and also by addition of hydrochlorid acid *).

1) Los, Die Electrochemie der Organischen Verbindungen p. 166, 3e Auflage (1905).
2) Ber. 28, 451. Bampercer and LaAcutt, Ber. 34, 1503.

3) Ber. 29, 1896.

4) Benper, Ber. 19, 2273. Branxsma, Recueil 21, 366, 22, 290.

( 682 )

If, on account of the analogy between phenyl-chloroamine and
acetylchlorophenylamine, we assume that in the case of the first sub-
stance the velocity of the conversion into o- and p-chloroaniline is
also strongly accelerated by elevation of temperature and addition
of hydrochloric acid, the conditions for obtaining chloroaniline instead
of aniline, in the reduction of nitrobenzene with tin and hydrochloric
acid, are as follows:

1. Slow reduction, or addition of tin in small quantities at the
time, in order not to at-once reduce the phenylhydroxylamine to
aniline.

2. Excess of hydrochloric acid so as to rapidly convert the phenyl-
chloroamine formed into chloroaniline.

3. The reaction should take place at the boiling temperature, as
elevation of temperature also promotes this conversion.

The experiment was now conducted as follows:

10 ce. of nitrobenzene were dissolved in 100 ce. of alcohol and
200 ce. of 25 °/, hydrochloric acid were added. This solution was
boiled over the naked flame, whilst 15 grams of tin were added
through the reflux condenser in small portions. Each time, after
adding a small amount of tin, the boiling was continued until every-
thing had dissolved before adding a fresh portion. The experiment
lasted six hours. The unaltered nitrobenzene was now removed by
steam, the residue was rendered alkaline and the aniline and chloro-
aniline recovered by distillation in steam.

In this way, 6.5 gram of oil were obtained. The greater portion
of this oil was distilled between 182° and 225°, the residue solidified
in the distilling flask, and proved to be p-chloroaniline (m. p. 70°).
The oil consisted of aniline and o- and p-chloroaniline.

From a chlorine determination according to Carius, it appeared
that the mixture consisted of 55°/, of chloroaniline and 45°/, of aniline.

If the reduction experiment was made with SnCl, and HCI (o--p)
chloroaniline (53°/,) were formed together with aniline. In this case,
the stannous chloride was also added in small portions, so as to
give the intermediary formed phenylhydroxylamine an opportunity
of being converted into o- and p-chloroaniline. Nitroso-benzene gives
the same result *).

In the same manner, the reduction of nitrobenzene with tin and
hydrobromie gave a mixture of aniline and (v- and p)-bromoaniline.

At present it is still difficult to predict which aromatic nitro-

') Cf. Gorpscuaipr, Zeitschrift für Phys. Chem: 48, 435.

( 683°)

compounds will yield a large quantity of halogenised by-products on
reduction with tin and hydrochloric acid. It would be necessary to
know something more about the reduction velocity of the nitrocom-
pounds *) (and of the intermediary formed hydroxylaminederivatives),
and about the intramolecular conversion velocities of the halogen-
phenylamines.

It is known, for instance, that o-nitrotoluene gives a large amount
of chlorinated by-product on reduction with tin and hydrochloric
acid *). The o-tolylbydroxylamine formed as intermediate product is,
therefore converted here into 5-chlorotoluidine, and the reduction ex-
periments of GorpscHMIDT *) on o-nitrotoluene are in agreement with
this. GoLpscummr has shown that, with increase of the temperature
the reduction velocity also increases, whilst an elevation of temperature
also increases the conversion velocity of the halogenphenylamines.
It now appears that this last reaction is the most strongly accelerated,
for the amount of halogenised by-products increases with elevation of
the temperature ‘).

Resumé. It has been shown that the reduction of nitrobenzene with
tin (or Sn Cl,) and hydrochloric acid may be carried out in such a
manner that p-chloroaniline occurs as the main product. The cause
of this must be explained by the fact that, in the reduction of
nitrobenzene, phenylhydroxylamine occurs as an intermediate product.
As on reduction of all aromatic nitrocompounds, hydroxylamine
derivatives are formed as intermediate compounds, we shall generally
notice on reduction of such nitrocompounds with tin and hydrochloric
acid, besides amidocompounds, also halogenised amidocompounds
(with halogen atoms o- or p- in regard to the NH, group), whilst
the quantity of these two last substances will be dependent on the
conditions under which the reduction is carried out. In some cases
no halogen atoms are introduced, but they are even eliminated from
the benzene core °).

I hope to record more fully further experiments in the Recueil
later on.

Amsterdam, January 1906.

1) See the note on the preceeding page.

?) Bemsrein and Künreere, Ann, 156, 81. HorremAN and Junaus, Chemisch Week-
blad II. 553.

SMI?
4) Pinnow, I. €.
5) Recueil 24, 320.
48
Proceedings Royal Acad. Amsterdam. Vol. VIIL

( 684 )

Botany. — “On a case of apogamy observed with Dasylirion
acrotrichum Zucc.” By Prof. F. A. F. C. Went and A. H.
BLAAUW.

In the summer of 1904 a specimen of Dasylirion acrotrichum Zuce.
was in bloom in the Utrecht Botanical Garden. The home of this
tree-like Liliacea is in Mexico; on a short stem it bears a bundle
of flat leaves with thorny margins. Although the plant is pretty
often cultivated in European botanical gardens it is very seldom seen
in bloom. Hence constant attention was paid to the here mentioned
specimen. The inflorescence was two metres long; the principal axis
was ramified and had a great number of steeply erected lateral axes
in the axils of bracts; each of these carried some 50 to 150
unstalked female flowers. Dasylirion is dioecious so that male flowers
were entirely absent.

Each flower had a perianth consisting of six green leaflets and a
pistil; this latter consisted of a triangular ovary with a short style
and three stigmas. The ovary was unilocular and had on its bottom
three ovules.

After the flowers had finished blooming it seemed as if some
ovaries began to swell. As there could be no question of fertilisation
in the absence of male sexual organs, it was thought that perhaps
a new case of apogamy or parthenogenesis was present here. The
ovaries were now regularly examined ; they more and more assumed
the appearance of little fruits, looked like small nuts provided with
three wings and strongly reminded one of the fruitlets of Rheum.
It appeared that many ovules swelled, but never more than one in
each ovary. Not nearly in all flowers this phenomenon was observed,
in no more than 10 to 40 percent it was at all visible.

For a detailed investigation these ovules were now fixed in
FiLemMina’s fixing solution (the weak solution) and then washed in
the usual manner and gradually placed in strong alcohol. This was
done for the first time on August 15; from 158 ovaries 49 ovules
were obtained, i.e. 31 percent. This was a maximum, however, for
when later material was collected in the same way on August 22,
September 3, 10, 13, 19 and 25, October 8 and 22, November 12,
December 15 and 24 and on January 19, 1905, each time more and
more ovules appeared to be unfit for use, as they began to wrinkle.
Such as looked more or less swollen were fixed ; among these some
had grown thicker and finally the impression was that some seeds
had ripened. But ultimately not a single germinable seed appeared
to be on the plant and after January 19 no material fit for investi-

( 685 )

gation could be got. Nothwithstanding this the preserved material was
examined, since it was possible that only the unfavourable conditions
under which Dasylirion lived in the Botanical Garden at Utrecht,
were the reason why no ripe seed was formed.

On microscopical examination phenomena were indeed observed
which seemed to point to apogamy or parthenogenesis, but the mate-
rial proved insufficient to obtain a consistent result. Leaving apart
even the already mentioned fact that not a single ripe seed was
produced, the number of ovules in which ultimately anything parti-
cular could be observed, was extremely small. For microscopic
examination revealed that most ovules which outwardly showed
nothing abnormal, were yet already in all stages of disorganisation.

Although we are unable to offer a finished investigation, yet it
seemed desirable to us to publish what we have seen. For Dasylirion
blooms so seldom in Europe that for us the chance of finishing our
investigation is practically nihil, while now at least attention has
been drawn to it, so that perhaps in the mother country of the plant
some one may feel inclined to re-examine it.

Moreover the number of known cases of apogamy or partheno-
genesis is so small that there is every reason to publish each new
case. And finally the material examined by us presents some points
which deserve attention for special reasons.

The fixed material was embedded in paraffin, cut with the micro-
tome and then stained, as a rule with saffranine only, sometimes
with saffranine, gentian violet and orange G.

The ovules of Dasylirion are anatropous and furnished with two
integuments ; the outer one consists, besides of an exterior and inte-
rior epiderm, of cells, situated rather irregularly in 2 to 4 rows ;
towards the chalaza it is much more strongly developed. The inner
integument consists of two layers of closely adjacent cells. The
micropyle is formed by the inner integument only, the edges of
which are strongly swollen — the cells are larger and the thickness
is bere about four cells — and are closely adjacent, so that they
only leave a narrow slit between them.

The tissue of the nucellus is small-celled near the chalaza, but for
the rest it consists of large cells with very little protoplasm and
apparently very much cell-sap. The more peripheral cells are smaller,
their cell-walls are perpendicular to the integument, especially near
the micropyle, but the others are greatly lengthened in the direction
of the chalaza so that they have become tube-shaped. These tubes
are often more or less bent, so that longitudinal sections present an
appearance which is rather difficult to disentangle. The swelling of

48*

( 686 )

the ovules was in many cases to be ascribed to the strong turges-
cence of these nucellus-cells only ; in older stages also the cells or
the outer integument began to increase their volume, evidently also
by the increase of the cell-sap only.

These strongly lengthened nucellus cells at first caused us to believe
that more than one embryosac is formed, but an accurate examination
of the preparations finally gave us the conviction that only one
embryosac is found. Certainty on this point will be obtained only by
investigating the development and for this purpose the collected
material was unsuitable, for also in the youngest ovules the embryosac
was already completely formed. It is long-drawn, somewhat in the
shape of a dumb-bell, at the base extending near the chalaza, at the
top near the micropyle surrounded by a single layer of nucellus cells.

Now it appeared that in the great majority of these embryosacs
nothing particular could be observed; sometimes a little protoplasm
or more or less disorganised and swollen masses, but no egg-appa-
ratus, no polar nuclei and no antipodal cells, so that presumably in
nearly all the ovules a disorganisation had already taken place before
they were fixed.

Only a few ovules presented more particularities and these we
shall describe here, in the first place those where a young embryo
was found.

In an ovule, collected on August 22, there is found at the top of
the embryosac and filling this part of the latter entirely, a cellular
body with eight normal looking nuclei, making the impression of an
embryo. The rest of the embryosac is empty and only some disor-
ganised masses lie in it; of an endosperm nothing can be seen, no
more than of antipodals or embryosac-nucleus ; concerning this latter,
however, the possibility must be granted that it has fallen from the
preparation during the staining, although we do not think this probable.

In an ovule, collected on September 10, the top of the embryosac
is filled by a cell-mass of some 20 to 30 cells, the walls of which
are strongly swollen; the nuclei are small and are in a state of
disorganisation as well as the rest of the protoplast. The whole makes
the impression of a more or less disorganised embryo. Further there
is in the embrosae a pretty large quantity of protoplasm in which
we could find no nuclei.

Finally we found in an ovule, collected on August 22, a still
larger cellular body, reminding us of an embryo. It consists of about 40
cells, the contents of which are still more disorganised, with swollen
cell-walls which strongly absorb staining substances. Having regard
to the former two preparations we are of opinion that this also

( 687 )

must be looked upon as an embryo, the development of which has
already for some time been stopped and which is now in progress
of disorganisation. Also here nothing peculiar was further found
in the embryosac.

Of course we looked also for the presence of an egg-apparatus,
especially in the younger stages, but there is only one preparation
in which anything of this kind can be detected. It is an ovule,
collected on August 22, where in the top of the embryosac three
cells are found, two shorter ones with distinet nuclei and a third
which is larger with disorganised cell-contents in which the nucleus
can still be discovered, however. We believe this to be the egg,
the others synergids. Here also nothing else is found in the embryosac
except protoplasm, which stains strongly.

In 10 other ovules an endosperm was observed in various stages
of development. It must be stated at once that in none of these
anything of the nature of an embryo is seen. Although it may be
objected that for some ovules the series of sections is not complete,
yet this is certainly not the case with the majority. Especially where
the micropyle is seen in the section, the embryo would be sure to
be observed if it were there, but also in this case no trace of it
can be found. So we arrive at the conclusion that here an endosperm
has been formed without the embryo having developed.

An ovule, collected on August 15, shows the smallest quantity
of endosperm. The upper part (*/, to */,) of the embryosac is filled
up with it. The shape of the embryosac has been changed; it is
swollen, has become cylindrical or somewhat broader towards the
bottom, has a thickness of O,4 mm., while the nucellus has a
maximum diameter of 1,0 mm. The lower part of the embryosac in
which no endosperm is found, has entirely collapsed and has evidently
been squeezed by the surrounding cells. This same shape of the
embryosac was met with only once without an endosperm having
been formed in it, namely in an ovule, collected on the same day.
In the lining protoplasmatie layer no nuclei could be seen, but still
we believe that this was a first beginning of the formation of an
endosperm. Now the endosperm of the just-mentioned ovule consists
of thin-walled cells of varying size; normal nuclear divisions occur
but also nuclei of abnormal size with a number of nucleoli, indicating
fragmentation. At one of the sides of the embryosac the formation
of the endosperm has not yet been completed.

Curiously enough the next stage in the development of the endos-
perm was observed with an ovule, fixed on December 15. Here the
greater part of the tissue of the nucellus has been displaced, so that

( 688 )

it forms only a narrow layer round the endosperm, somewhat
thicker near the chalaza (greatest thickness of the embryosac 1,2 mm.,
of the nucellus 1,5 mm.). Here also the lower part of the embryosac
is not filled, but is entirely abortive. The endosperm-cells are of
rather unequal size, most nuclei do not look normal, but still divisional
stages occur; in the more peripheral cells small grains which strongly
absorb staining substances appear outside the nucleus. As in some
other cases, the impression is got here that the formation of the
endosperm takes place rather irregularly, as if in various spots within
the embryosac pieces of endosperm-tissue would form which grow
towards each other so that seemingly more than one endosperm lies
in the embryosac. At any rate this seems to be so when one limits
his attention to one preparation; by comparing, however, the different
successive sections of one ovule there finally appears to be only one
mass of endosperm. The formation of the endosperm begins in the
lining of the wall of the embryosac and from there proceeds inwardly ;
in this process the cavity is gradually filled up, the endosperm now
meets itself from various sides and it is these divisional lines that
remain visible.

That the formation of an endosperm starts indeed at the periphery
of the embryosac, appears e.g. from an ovule, collected on Septem-
ber 19. Here the size of the whole endosperm is greater than in
the already mentioned ovules (diameter 1,85 mm.), so that only a
very narrow layer of nucellus-tissue is visible all round, mostly at
the chalaza (greatest diameter of the nucellus 1,4 mm.); but the
whole endosperm is hollow and in this cavity remnants of the proto-
plasm of the embryosac are visible. The endosperm-cells are here
of very different sizes and so also the nuclei vary much. Some of
them look normal, show karyokinesis, others are enlarged, have
assumed all sorts of capricious shapes, the number of nucleoli has
greatly increased and a number of fragmentation stages can be observed.

Two ovules, collected on September 10, show a still further
developed endosperm. The nucellus tissue has been more displaced,
the shape of the endosperm-cells is pretty regular, their cell-wall
is somewhat thickened, the nuclei are almost normal; in any case
there is much less indication of fragmentation than with the just
mentioned ovule.

In an ovule, collected on September 19, the endosperm is so
strongly developed that of the nucellus tissue hardly anything remains
visible. This also applies to the cases which will be described
presently. The endosperm-cells have strongly thickened but still
fairly gelatinous walls; the contents of the cells consist of a number

( 689 )

of small grains which stained very strongly and which somehow
make the impression of nucleoli; of a nucleus nothing is found any
longer, unless we apply the name to some thick, coloured masses.

Three ovules, fixed on December 15, all showed the same picture.
A strongly developed endosperm is present with very thick cell-
walls, absorbing saffranine more or less, and protoplasts which are
entirely foamy and in which nothing of a finer structure is found.
This endosperm must evidently be reckoned among the horny ones;
it was extremely difficult to cut. Sections of the ovules could only
be made after treatment with hydrofluoric acid. It is not impossible,
of course, that the foamy appearance of the protoplasts must be
ascribed to this treatment, although we do not think this probable
on account of other experience with this method. In the endosperm
some fissures are visible, the last remnants of the cavity of the
embry osae.

Finally an ovule with an endosperm was found among the material
collected on January 19. Here also cutting was only possible after
treatment with hydrofluoric acid. The endosperm is entirely dis-
organised, borders of cells can scarcely be recognised. No more than
in the preceding cases we think this must be ascribed to the manner
of treatment.

We have now described all cases of formation of an endosperm,
observed by us. It will have been noticed that the order is not
chronological, the arrangement was such that we gradually proceeded
from the least developed to the complete endosperm. From this it
follows already that the formation of an endosperm takes place very
irregularly with these ovules, sets in now sooner, then later, and
that the endosperm may pass into disorganisation at various stages
of development.

Summarising, it appears that with Dasylirion acrotrichum an endo-
sperm is formed without fertilisation. This endosperm finally disorga-
nises ; it may do so already at a pretty early stage of development,
but it may also first attain its complete development. But an embryo
could never be found together with such an endosperm. From this
it does not follow, however, that it could never be formed together
with an endosperm, especially since in three ovules — in which,
to be sure, no endosperm was formed — in the top of the embryosac
a cell-body was found which we take to be an embryo, which how-
ever very soon passes into a state of disorganisation.

One may now ask to what cause this disorganisation must be
ascribed. It might be suspected that the circumstances of this Dasylirion
were abnormal. Although we grant that these were different from

( 690 )

the conditions in the mother country of the plant, yet we must
remark that the plant was in the open air for a long time before and
after it had bloomed during the very hot summer of 1904 and that there
was no question of this specimen being sickly. We venture another
supposition: to us it seems that this plant makes, so to say, an
attempt to apogamous development, but that these endeavours do not
succeed. For this would plead that the endosperm develops here
independently of an eventual formation of an embryo and that the
embryo is sometimes planned, but never grows to any considerable
size. If this be the case, in the mother country of the plant similar
phenomena should be observed, but at the same time normal ferti-
lisation and seed-formation. We ought to know the development of
the embryosac, in order to know why the apogamy is unsuccessful
here, even though the plant makes an attempt in this direction. If
in the embryosac mother-cell a reduction division has taken place,
this would be very easy to understand and it would also explain
the greater facility with which the endosperm is formed. For, after
fusion of the two polar nuclei the normal number of chromosomes
of the 2z-generation (not, of course, of the endosperm) would be
re-established again; we have tried to determine this number and it
seemed to us to be 20 to 24. But as long as we do not know how
the endosperm is formed this determination is of little value; for
we owe to TrruB*) the knowledge of a case of endosperm formation,
with Balanophora elongata, where the endosperm nuclei are formed
by division of one of the two polar nuclei. It is, to be sure, the
only case on record where an embryosac fills with endosperm,
without a ‘normal embryo being formed. In this respect the ovules
of Dasylirion, described by us, could be compared with Balanophora. —
On the other hand there is this great difference, that with Balanophora
an embryo is later formed from part of the endosperm and of this
there is no question with Dasylirion.

We put the word apogamy at the head of this communication
because it leaves unsettled whether here phenomena of parthenogenesis
were indeed observed. It is an open question to what extent the
development of an endosperm without previous fusion of the polar
nuclei with one of the generative nuclei of the pollen tube can be
brought under one of these conceptions. Those who will not use
ihe word fertilisation in the case of endosperm formation, like
STRASBURGER, Will object to it; those who embrace the opposite view,

1) M. Trevus. L’organe femelle et ’Apogamie du Balanophora elongata Bl. Ann.

du Jardin botan. de Buitenzorg XV. 1898 p. 1. See also J. P. Lorsy, Balanophora
globosa Jungh. Ann. du Jardin botan. de Buitenzorg 2me Série I. 1899, p. 174,

( 691 )

like GuienarpD and Bonnier, will think the use of these terms
admissible. Although we incline towards this latter opinion, we shall
not dwell on this point here.

But we think it desirable to point out that a closer study of
unfertilised ovules, especially of dioecious plants will perhaps yield
surprising results. Since we know through Logs that chemical stimuli
may cause the development of an egg, the possibility must be granted
that this may also be the case with higher plants. When a normal
fertilisation does not take place, such chemical stimuli would at any
rate render a beginning of development possible. Looked at from
this point of view the case of Dasylirion is perhaps important, but,
as we stated already at the beginning of this communication, only
an investigation in the natural place of occurrence of the plant can
give an answer to this and allied questions.

Astronomy. — “On the parallax of the nebulae’. By Prof. J. C.
I APTEYN.

Up to the present time we know hardly anything about the distance
of the nebulae. On the whole they do not allow of the most accurate
measurement, and as a consequence direct determination of parallax
is generally to be considered as hopeless. A few endeavours made
for particularly regular nebulae have not led to any positive result.

The proper motions (p.m.) seem more promising, at least for the
purpose of getting general notions about the distances of these objects.

Spectroscopic measurements of radial motion show that the real
velocities of the nebulae are quite of the order of those of the stars.
Therefore, as soon as we find the astronomical proper motion of
any nebula, we conclude, with some degree of probability, that its
distance is of the order of that of the stars with equal p. m.

Meanwhile it may be considered to be a fact, most clearly brought
out just by the observations presently to be discussed. that as yet
p.m. of a nebula has not been proved with certainty in a single case.
It does not follow that these p.m. are necessarily very small. The
time during which the position of these bodies has been determined
with precision, is still short, the errors of the observations are large.
The effect of these errors on the annual p. m. may easily amount
to 0"2 or 0'3,

We might endeavour to lessen the influence of the errors of
observation by determining not the individual motions but the mean
p.m. of a considerable number of nebulae.

( 692 )

If this succeeded we might then compare this mean p.m. with
the mean p. m. of different classes of stars, the mean distance of
which is known with some approximation or, better perhaps, with
the mean radial velocity of the nebulae determined by the spectro-
scope. The comparison would lead at once to ideas about the real
distances.

Unfortunately the mean of a great number of observed p.m. will
not be materially more correct than the individual values, if the total
proper motion is small. The cause of this lies in the fact that in such
a case the effect of a determined error of observation is not at all
cancelled by an equal but opposite error of observation. Suppose for
instance two nebulae both having in reality a p. m. of O"01. For
the first let the error of observation be 0’10 in the direction of the
p. m. For the second assume an equal error in a direction opposed
to the p. m. The observed p. m. of the first nebula will be 0"11,
that of the second 0"09. Taking the mean of the two we are not
brought nearer to the real value.

For this reason we shall not be led to any valuable result in
this way, even if our material consists of very numerous objects, as
long as the errors of observation exceed the real p. m.

The difficulty here considered would vanish if, instead of the total
p. m., we could avail ourselves of some component of the p. m.,
which in different direction would have different sign. In this case,
if systematic errors can be avoided or determined, the accuracy would
increase as the square root of the number of objects included.

Such a component of the p. m. is that in the direction towards
the Antapex. From this component we may derive the mean paral-
lactic p. m. which is a measure of the mean parallax.

I will not here stop to consider the hypothesis involved. It must
be sufficient to state that it assumes that the sum of the projections
on some determined direction of the peculiar p. m. vanishes in the
case of very numerous nebulae or, which comes much to the same
that the peculiar p. m. may be treated as errors of observations.

Let

h be the linear annual motion of the solar system;

@ the distance of a nebula from that system ;

4 the angular distance of this nebula from the Apex of the solar
motion ; ;

v, t the components of the observed p. m. in the direction towards
the Antapex and at right angles to that direction ;

p the component of the peculiar p. m. in the direction towards
the Antapex.

( 693 )

The parallactic p.m, shall then be:
h

—sndA=v—p.
o

If this equation is written out for each individual nebula and if,
after that, we take the mean of all the equations, the quantities p will

disappear and we obtain the mean value of =, which is the secular
Q
parallax.
Or rather :
As we may treat the quantities p as if they were errors of obser-
vation, which mix up with the real errors of the observed quantities
v, we may write out for each nebula an equation of the form

on
SOLE a o oo wo oo (II)

9

If then we assume that the distance o is the same for all the
nebulae, we may solve the whole of the equations (J) by the method
of least squares.

I have long wished to apply this method in order to get some
more certainty about the position of the nebulae in space, but I have
been restrained by the extent of the work connected with such an
enterprise.

The difficulty has disappeared since the publication, a few years
ago, of a paper by Dr. MöÖNNICHMEYER assistant at the Observatory of
Bonn (Veröff. der Kön. Sternw. zu Bonn. N°. 1). In this paper all
the materials available at the time of its appearance have been
brought together in a way which, for my purpose, leaves little to
be desired.

This paper contains the observations of Dr. MöNNIcHMEYER himself.
They bear on no less than 208 objects, mostly chosen among such
nebulae as can be measured with considerable or at least moderate
precision. Dr. MénnicoMeyeR has collected besides, all previous obser-
vations of these objects. I have confined myself to the observations
of those nebulae for which all the observers have used the same
star or stars of comparison. I have further rejected the observations
of those objects for which MÖNNICHMEYER did not succeed in deter-
mining the personal errors. The observations which thus have served
for the investigation are those of MÖNNrcHMEYER’s paper pages 59—70,
from which have been excluded, in the first place, those objects
which in the list of pages 15—17, second column, have been denoted
by the letter M; further the planetary nebulae, the clusters and the
ring-nebula h 2028.

( 694 )

There remain 168 nebulae.

A good judgment about the accuracy of the observations may be
obtained by the probable error derived by Monnicumnyerr for his
own observations on page 9. For the other observers I have availed
myself of the data contained on pages 18—25.

The aceuracy was found little different for the several observers
with the exception of RimKerr.

I therefore simply assumed the weights to be proportional to the
number of observations. For Rümker only the weight was reduced
in the proportion of three to one. For Scumipt the number of obser-
vations is not given. For reasons given by MénnicuMryer they are
“immerhin etwas fraglich” (l. e. page 14). The results of Scumipr
got the weight of only a single observation for that reason.

An_ overwhelming majority of the observations has been made
between 1861—1869 and 1883—1893. It was possible therefore in
nearly every case to contract all the observations in two normal
differences from which the proper motion and its weight could be
derived at once without any serious loss of accuracy.
From these p.m. I then derived the components t and v, assuming
for the position of the Apex, the coordinates

Ars — Dione Drs — + 29557

The whole of the materials was divided into the three classes of
MÖNNICHMEYER. They are described by him on page 9 of his paper
in the following way:

Class I. Nebulae with starlike nucleus not fainter than 11 mag-
nitude ;

Class IL. Nebulae with moderately condensed nucleus not fainter
than 11 magnitude;

Class III. Difficult objects, in the first place irregular nebulae
without any sharply marked point; furthermore all very faint objects
and the very oblong nebulae.

Most of the objects have been classified by MÖNNrcnmeyer himself
on page 9 of his paper. The nebulae wanting in this list have been
classified by myself, in accordance with the descriptions on p.p. 27—54,
as follows: Ah 693, 1088, 1225 in Class I; A 421, 1017, 1212, 1221,
1251, 3683 in Class II; 2 316, 1461 in Class III.

The p.m. as derived are relative p.m.; they are the motions
relative to the comparison stars. MÖNNICHMEYER has investigated the
p.m. of the comparison stars themselves; he has found a sensible
p.m. for only 7 of the objects used for my investigation. The
following table contains his results for these 7 stars.

Star of used for Eb: i

mag. fla {to in arc v Sin 4
Comp. nebula er. circle

s | " " ”

45 6.0 h 132 |H 0.0140 | — 0.089 | 0.227 + 0.225 | 0.94
90 8.8 h 805 4 .0237 | — .170 „352 — 156 | 1.00
129 6.1 h- 1471 |— .0170 | — .127 „257 + .255 | 0.97
164 ileal h 1329 — .013 „00 „192 + 167 | 0.99
168 955 M 90 + .014 „00 „204 — .180 | 0.98
208 4.7 Il 542 |— .0050 | + .010 „075 + .055 | 0.80
242 6.6 h 2050 |— .0134 | — .152 „199 — .197 | 0.45

These p.m. were applied by Ménnicumnyer before he derived his
definitive differences in @ and Jd (Neb.-Star). In no other case a
correction for the p.m. of the comparison stars was applied.

The majority of the observers used the ringmicrometer.

The principal error to be feared for observation with this micro-
meter is the personal error in right ascension. MÖNNICHMEYER has
devoted the utmost care to their determination. Notwithstanding this
it may be considered a fortunate circumstance that this error has no
influence on the result for the mean parallactie motion, at least in
the ideal case that the nebulae are distributed uniformly over the
right ascensions from 0 to 24 hours.

For it seems highly probable that the distance of the nebulae is
not systematically different in the different hours of right ascension.
This being so the personal error will vitiate the parallactic p.m. of
the nebulae at the same distance in right ascension on both sides
of the apex, to the same extent but in opposite directions.

It is true that the distribution in right ascension is far from being
uniform; still we may be sure that whatever residual personal
errors may still exist in the materials of MONNICHMEYER, must appear
considerably diminished in the result. Meanwhile I have tried to
obtain some idea about the possible amount of these residual errors
in the following way.

I computed the average proper motion in right ascension for each
hour separately. Taking the simple mean of all these hourly averages
we may expect to get a result in which not only the peculiar proper
motions, but, as explained just now, also the parallactic motions
shall have vanished.

( 696 )

This final result may therefore be assumed to represent the residual
influence of the personal errors on the p.m.

For the value uz of this mean I find

He = — 0.5000 4

In deriving this result the hours with many nebulae did not get
any greater weight than the hours with only a few objects. Owing
to this cause the final weight is found to be only 0.4 of what it
would have been had the distribution been uniform.

We shall get a result of appreciably greater weight if in the first
place we combine by twos the hours lying symmetrically in respect
to the apex. In these mean values the parallactic motion is already
eliminated; we may therefore further combine the twelve partial
results having regard to their individual weights.

In this way I find

Hx = + 0.50006.

It thus appears that MénnicuMnyEr has succeeded remarkably well
in getting rid of the influence of the personal errors.

As mentioned just now these errors appear still further diminished
in the result for the parallactic motion.

There thus seems to be ample reason for neglecting any further
consideration of them. In order to enable the reader to get at once
a pretty good insight in the accuracy really obtained, I have divided
the whole of the material not only into the three classes fof
Monnicumeyer, but I have subdivided each of them into a certain
number of sections, each of about the same weight.

I thus got the following summary. (See p. 697).

The values of t have been included in the table merely in order
to show that in them too no traces of any personal error are visible.

In order to get the yearly parallaxes z, I have divided the secular

h 5
parallaxes — by 4.20; this number being, according to CAMPBELL’s
Qe

determination, the number of solar distances covered by the solar
system in a year in its motion through space.

The probable errors were derived in the hypothesis that the com-
ponent v is wholly due to errors of observation.

If we compute the probable error of one of our 13 results from
their internal agreement we get 0."023. This number differs very
little from the values directly found. Here again we have an indication
that systematic errors must be small.

The last row of numbers contains the simple averages of the 13
individual results.

Class a | ae Tt 5 pe a pe.
hm m y si ) Ù L
0.0 — 5.33 | 13 | + 0.014 | — 0 039 | + 0.023 | — 0.009 | + 0.0055
5.33—10.57 | 12 | — 0435; + .051 022 | + .012 5
I 10.57—12.22 | 10 |— .04 | + .034 023 | + .008 98
12.22-12.45 9 |— .004 | — .027 022 | — 006% 5
12.45— 0. 0 | 10 | — .008 | + .013 025 | + .003 59
0.0 — 9.50) 12 | + .021 | + 0.014 | + 0.019 | + .003 4s
9.50—11.10 | 10 | — .004 | — .016 .019 | — .004 4
Il 11.40—12.16 | 11 | — .008 | — .037 ‚020 | — .009 5
| 12.16-12.28 | 12 | + .O19 | — .040 „020 | — .0095 5
12.28— 0.0] 14 | + .0005/ — .040 „020 | — .0095 5
0.0 —412.14 | 20 | + .030 | + 0.016 | + 0.019 | + .004 45
Ill 12.14—12.32 | 16 |— .04 | + .038 ‚019 | + .009 45
12.32— 0.0} 19 |+ .Ol6 | — 036% ‚018 | — .009 4
Simple B IJ yy iM L
mean of | 168 — 0.004 — 0.005 + 0.005 — .0013 + 0.0012
13 results

We thus finally get for the mean yearly parallax
— 0"0013 + 0"0012 (168 nebulae). . . . . (3)

This is the parallax relative to stars of comparison the mean

magnitude of which is
8.75

Meanwhile, as mentioned before, MÖNNICHMEYER applied p. in. to
7 of his 183 stars of comparison.

If he had refrained from doing so, we should have found the
parallax O’0004 smaller. We thus have in conclusion:

Mean parallax of the 168 nebulae relative to stars of comparison
of the mean magnitude 8.75.

=O OOET =O. OLF (PE) sete eee ee)

In N°. 8 of the Publ. of the Astr. Laboratory at Groningen the
mean parallax of the stars of magnitude 8.75 was found to be

ONDER 0, gee emir en

To this value we might apply two corrections:

( 698 )

1st. Because, since the publication of the paper mentioned, our
knowledge about the sun’s velocity has made considerable progress ;

2nd. Beeause in its derivation a slight mistake was discovered.

I shall not apply any correction, however, because the two cor-
rections nearly compensate each other for the magnitude 8.75. There
is a fair prospect of the possibility of materially improving the values
given in Publication 8 before long. It seems advisable to wait for
such improvements before we alter these determinations.

If for this reason we provisionally adopt the value (5) we get:

Mean absolute parallax of the 168 nebulae

0"0046 + O'0012 (p.e) a ee)

This result is somewhat less reliable, however, than (5) because
of the additional uncertainty in the absolute parallax of the stars of
comparison.

The value (6) agrees nearly with the mean parallax of the stars
of the tenth magnitude.

I shall not insist on the exact amount brought out for the parallax.
I shall only direct the attention to the fact that from observations
covering only a period of somewhat over thirty years, we get a
probable error of hardly over 0.001. If this is the case with visual
observations we may look for really excellent results by photography.

The best measurable nebulae must be generally the smaller ones.
The number of these which can be photographed is enormous.

With his Bruce-telescope (opening 40 centim., foc. dist. 202 centim.)
Max Worrr obtained in 150 minutes a single photograph of the
region near 31 Comae, containing 1528 measurable nebulae (Publ.
Königstuhl I p. 127).

This richness of material will enable us to confine ourselves provi-
sionally to those nebulae which allow of a very accurate measurement.

Personal errors must disappear because we shall certainly succeed
in nearly every case in making our pointings on the same point for
the several epochs. The peculiar p. m. will be the more thoroughly
eliminated the more extensive our material; especially if this material
is distributed over the whole of the sky. Errors in the precession
have no influence at least on the value of the relative parallax.

I am convinced that by photography we may obtain, even within
ten years, results which will far surpass in accuracy those of the
present paper. Thus we may hope, in the near future, to reach
a fairly satisfactory solution of the vexed question respecting the
position of the nebulae in space.

The same treatment to which we have here subjected the nebulae
may of course also be applied to other objects. We have already

( 699 )

undertaken that of the Helium-stars and might perhaps afterwards
try the same method for the stars of Pickrrine’s 5 Type.

In concluding it is only just to say that, whatever be the merit
of the present investigation, it belongs mainly to Dr MÖNNICHMEYER.
As compared with his careful and elaborate labour, that spent on
the derivation of the present result is quite insignificant.

Chemistry. — “On the course of melting-point curves for compounds
which are partially dissociated in the liquid phase, the proportion
of the products of dissociation being arbitrary”, by J. J. van
Laar. (Communicated by Prof. H. W. Baknuis RoozeBoom).

1. It is well known, that a liquid mixture of e.g. two compo-
nents 1A and B, which can form a compound A, B, reaches its
maximum point of solidification, when the ratio of the molecular
quantities of the two components is as r,:»,, in other words when
there is no excess of one of the products of dissociation of the com-
pound A,, B.

_ Expressed differently: when we determine the points of solidification

of a series of liquid mixtures of A, B and the compound with

increasing excess 2 of one of the products of dissociation of the
dT

compound under consideration, then (== for the curve of soli-

dification or melting-point line thus formed.

Hence the melting-point curve of a compound, with increasing
addition x of one of the products of dissociation, will have an
horizontal direction at xw=0O, as soon as there is but the
slightest dissociation of the compound in the liquid phase. If there
is no dissociation at all, the admixture may be considered as an
alien, indifferent substance, and the initial direction of the melting-
point curve will show all at once the normal descending course at
mk

As will also appear from the following computation, the initial
horizontal course will of course pass the sooner into a descending
course, the slighter the dissociation of the compound is.

dT

The peculiarity mentioned of (
at

) becoming zero with the slight-
0

est trace of dissociation of the compound, was already proved by
Prof. Lorentz in 1892, on the occasion of an investigation of
STORTENBEKER on chlorine-iodides'). Prof. vaN per Waars too has

1) Z. f. Ph. Ch. 10, bl. 194 et seq.

49
Proceedings Royal Acad. Amsterdam. Vol. VIII.

( 700 )

proved this property, induced by a statement made by Le CHATELIER !).
The proof given does not directly bear, however, on the case that
in the liquid phase also the compound (vAN DER Waars’ so-called
complex molecule of salt and water) is found by the side of the
products of dissociation.

2. Here follows another simple and quite general proof of the
property in question, in which specially the condition in the liquid
phase is taken into consideration, in which by the side of the com-
pound the products of dissociation oecur in varying quantities.

Let us suppose there three kinds of molecules:

those of the compound A,, B, ; number n, = 1—e
those of A ; re Ni Pie
those of B; 5 n, = vate.

So a is the degree of dissociation of the compound, and z the
excess of B e.g.

Now from the property, that the molecular potentials of these three
substances, viz. #4, wt, and w,, are homogeneous functions of the Oth
degree with respect to the numbers of molecules, follows immediately :

‘ du, du,
Dj n, ar ds
dz

0
Ae

du 8
j ZO) or ER

dx

Here the differentiations with respect to z are to be taken total,
so that e.g.:
du, Ou, , Op, da
de 0a da da’

i.e. at constant temperature.

[The above property is proved (loc. cit.) as follows. We have viz.
in consequence of the mentioned peculiarity of the functions py, u,
and u,:

Ou Ou Ou
ede Se |)
a On, - On, ane On,
Ou Ou Ou His
Corer (awe ni emg
0 1 2

On On, TO On

2 2

0 : On, 0Z dz
So also zi being equal to en etc. (fo u = — and ip, =a)

1) Verslagen Kon. Akad. van Wetenschappen (4) V, p. 385 (1897).
2) These and the following properties were already proved by me in 1894. See
Z. f. Ph. Ch. 15, p. 459 et seq. (‘Ueber die genauen Formeln, etc.”).

(701 )

Ou, Ou, Ou, |
ate == (()
=e On, = On, eee On, |

Ou, Ou, Ou, |

=n, — =0
Re
So if we pass rea He aes n,, nm, and n, (of which there

are only two independently variable) to the variables @ and x, we
have also:

5 du, Oe
bat haa eda |

fi 0
nn

da
The first equation multiplied by Ee and added to the second,
at
gives immediately (1). |
Now follows from the equilibrium of dissociation :

— Myo + 1H, + Pall, = 0

1) We can easily test the truth of these simple properties by supposing the
functions g'o w'; and yz’, constant in:

: 8 l—a
Hoo BE log rs

u =n’, + BT log *
mee
N

1a
N’
til Tog

: : Se od
Then we have immediately (having divided by RZ’) after differentiation ED
a

taking into consideration that

N=1+ (wv, +7,—lhe4e«=1+4 ate,

for the first member:

(1 — a)

lo
tels x] + eetl
a JV a

4 —
via nat ZN
6
Pec ee ea ag gta ct ya A wg ee eee
N N
After differentiation Le we find for the first member:

1
vate NIT
Sn

N ; 7 N Rr

(l—a)

1
ny + v,a

— {+ eats)

And according to what has been proved, this will continue to be true, also
when u'o, gr and y's are still functions of z and z.

49*

( 702 )

‘immediately, after total Bearer with respect to x (7' constant):

2 du
PR +» — + Yv,

EO ~ 2 [eee
dx i)

And from (1) and Dn follows, that when n,:n,=»,:7, (i.e. z=0),
we have necessarily

a ee eS

5 8 Se: 8

So the becoming zero of el is the primary moment, on account of
&

dali ;
which also (5) will have to be O in the presence of a solid phase:
aL 0

with change ef «2 (with which also @ changes) the mol. potential
of the unsplit compound does, namely, not change when x«=0. [This
property will evidently also continue to hold for an arbitrary number
of splitting products].

3

dT 5 ad ; Sop
That now also i= = 0, follows from the condition of equilibrium:
at

0
ml ie ols 0,
when u is the mol. potential of the soiid phase. Total differentiation
with respect to 7’ dh viz. :

da:
zr WH) te (Ce == Ho) a= 9

\ eh eee fi 0 sa and £=(2 0 da
in which IT is again or + — a ar) , an EE + de

d
But ar (— a ——

hence also:

= when Q is the total heat of melting,
Q dude, _
Ee
because u (in the solid phase) is independent of x. Hence:

pp do
dT da 4

pl , . ait 5
z= = 0, also —-=0O, and in this way the proposition is
ae axe

proved. When in the liquid phase there is no excess of one of the
products of dissociation, but instead an indifferent substance, then
there are four kinds of molecules, with molecular quantities resp. :

Cee APRON ee DCT iy ts

( 703 )

Instead of (1) we get now:

du, du, i du, du, 0: ie
SS =— n= == = . . . .
a du nee dx * da aM da ) @)
u, du, EL 2
And as n, Ge = qe Temains finite at # — 0, viz. RT, from (1°)
ax wv
; du,
and (2) will now not follow == 0, wien RHO, (oi DERDE
ar

ry

di
is always satisfied in this case). And consequently St will not be 0.
ar

du f
| hat x ae continues to have a finite value at ,=0, follows from this,
at

oe. lu We AET ND
that u, =u', + RT log — yields ~2 =? + - , hence
N° da da v N dz

du', _& T dN

- | , in which the expression between

du,
a—— RT
dx arse |= de N de

|

du
always remains finite. At «=O we h therefore x =|
ti

3. We now proceed to derive an expression for the course of the
melting-point curve in the case of increasing excess of one of the
products of dissociation in the liquid phase.

Let us for this purpose suppose, that in this phase there are present
(in Gr. mol.) 1—a AB and wx B, while the 1 — 2 AB is disso-
ciated to an amount @. We have then:

AB A B
(1 — a) (1 — 2) a (1 — 2) a (1 — ©) 4x,
together 1 + a (1 — x) molecules.

We suppose then, that the compound consists of 1 mol. A and
1 mol. 4, which simplifies the calculations.

The equilibrium between the solid phase and the non-dissociated
molecules in the liquid phase yields:

fo = (Mo 0
or (the terms with 7’/og T on either side cancel each other)

i= =S
em oP =e, — Gf + RT bg OED,

1) This too is easy to test, when uw’), w'j, elc. are considered as constant, so
that e.g. in

l1—a ou 1
= RT log —— , —~ b N= ,
u ZW + On ae ecomes ia dl ete

( 704 )

or with e = % le eef kT a,
with ¢, — e= | €, 3 alt mt

a
— (- + kT — +) =q (so that q is the pure latent heat of melting

of the compound, without the heat of dissociation, which is still to
be added), and with c,—c=y:
(1 — @)(l — 2)
Lexi Sry

For the determination of y may serve, that at «= Oand 7'= 7,,
a becomes a,, hence:

= YT — RT log

l—a
= YT, — RT, log ——.
an se ee
Hence we finally get:
1 ines
ME == RIT bg eae
1 0 1 + a (1 — x)

=
or

— log

“1—a, 14+a(1—z2z) ste (5)

EN ee 1
(= 7) Ê

In this derivation it has also been supposed, that the liquid mixture
is a so-called {deaf mixture, i.e. that terms, referring to the influence
of the components inter se, have been left out. It is known that
these terms are of the second degree with respect to a. Equation (5)
represents therefore the course of the “ideal” melting-point curve in
our case.

Further the degree of dissociation « occurring there is given by
the equation (here too the above mentioned terms are left out, so
that the simple law of mass-action is supposed to hold):

a (1—2) a(l—2) + # . (1— a) (ert) ae

Me ky aa. N =

or
a(a(l—a) +a) _
(le) (la (le)

In this K is now no longer a function of « according to the above
supposition, but it is one of 7.

Even if we would solve « from this quadratic equation, and sub-
stitute it in (5), we should have gained but little, because A contains
T in a rather intricate way. Therefore the only thing we can do, is
to try and find an approximate expression, which only holds for

(6)

small values of 2.

( 705 )

; drs
After that a general expression for ER will be given.
av

In order to find the approximate ex-

Tab pression in question for the course of
the eurve 7A, we suppose for the

present, that @ does vary with 2, but

To not with 7. In the result we have then _
A simply to replace q by the total heat
B of melting at ec —0 Q,=q+a, (A is
the heat of dissociation), in order to
introduce the variability of «a with 7’.
(see appendix).
0 From (6) follows now immediately

the quadratic equation

=

a? (l—«) + av — TER

al

By putting «=O, we see that is then —a,’. According to

IE
the above provisional assumption it is now supposed, that also for
values of 7, lower than 7,, the value of «, holding for «=O and
T = T,, remains unchanged. Therefore in the equation

a (Lr) + ax — a, = 0
a, is no longer a function of 7. So we find for «:

— Wad Vie’ Ha, (lr)

a ==
Wor
and hence
(a 1 Se — | re da (l—e)

le
In consequence of this we get:
L-)(l Dele
l4a(l eel ed

so that we find for the quotient occurring under the sign log in (5):

1e We? He (1— 2)

Ae el 4 :
or also after multiplication of numerator and denominator by
1 Yr:

(a+ a") (Ll —e) +, 2? —2(1 — IE) V
(1 — a,’) (Ll — 2) :

( 706 )

Let us now approximate Va,?(1 — 2) + ‚et = VA —a+ Is

for small values of z.
We shall find:

pe Od ie
2 ie 2
ay a

as he (l—e 1 — 5 «,°)
+ as Sse DÛ ° &

0 ay

4

a, WV, multiplied by 2— 2, yields then:

af? G5 55 ai (=S Ja...

This, subtracted from (1 + a,?) (1 — x) + */, x’, gives:

l—a 1 —a,
OA ee

ay ay

If now finally this formula is divided by (1 — «,°) (1 — a), we get:

En ats ad

mee | a l—

Equation (5) changes now into:

| (2), Cae
\
(

4 ne a, |= ball
a l1—z TN

Notice, that the term ‘with « does not occur, in consequence of

dT fe :
which ( ) satisfies the condition of becoming 0.
at

If higher powers than 2* are neglected, the above becomes:

a? (1 + 2) —@ 1 1
BG ae NEE

or also, if we now replace q by Q, (see above) and 77, by 7,’,
which does not bring about a change in the coefficient of 2°, as

RST)

pers) eee
en Meme
which approximate expression holds for not too small values of
a (e.g. « ='/,) at least up to values of z=0,1. We see, that
T,—T is not proportional to z, for small values of x, but pro-
portional to 2*. Hence instead of the usual straight downward course

( 707 )

of the melting-point curve at the beginning, it presents now an
almost horizontal course.

Observation.

Equation (5) enables us also to compute the melting-point tem-
perature 7, of the unsplit compound (i.e. unsplit in the liquid
phase). (cf. fig. 1).

Then we have namely a=0, «=0, and we get, supposing

MW OP 5 Opi asl 1
log = = ’
WS CRM EIEN CE

from which follows:
1 i R 1
di Fate ay Sala a ate ga
q 1—a,

Of) = OF

rl

dl
4. We shall now derive the general expression for a all over
ak

the line 7, A, in which it is only supposed that we have to do
with ideal mixtures in the liquid phase, so that the terms, referring
to the influence inter se of the different components, are again left
out. But besides on 2, « will now also depend on 7’.

In two different ways we can arrive at the correct expression
dT
da”
First of all by total differentiation of the equation (5) with respect
(1 — a) (1 — 2) :
ees)

d log c, ite dloge,\ de q
dT de Jrdf RT*

for

to 7. We get then, calling the fraction

hence
d log c,
dT oe dau
de — q dloge,
RE NAT
dloge, Ologe, Òloge, da
Now ——=-—~— —=
de 0x Oa da
1 a 1 lr da
le 1+a(l—2) la 1+a(1—z2)/ de
1 2e da

ee eee

(l—e)(1+a(l—a)) (le) (la (l—a)) da’

( 708 )

da 8 Aer
Hence we must calculate = From (6) follows:
ar

Lge 8 ia et EON
ade «ta(1—zx) da l—a dz
1
-- Tl |- a+ Aln =
After reduction we find from this:
da a (1 — «)
fe a + 2a(1— 2) ~ me
Substitution yields now:
dloge, __ 1 a (2—2)
ie datt Aaen

v

~ (1a) (e+ 2a (1—2))

d log c,

ap Ce find in the same way:

For

dloge, Ologe, Òloge, da _dloge, da
LO MOE Oxi dl nr
because c, is not directly dependent on 7. This gives further (see
above):

dloge, 2—2 da
TENEN
da
So we calculate ae From (6) follows:
1 da le) da 1 da lt da 2
adt #«+ta(1—2) ITT lad? 1-a(—a) dT? RT’
0 log K AE
Ss Sr Rr when 2 represents the heat of dissociation.

By solution and reduction we find:

da 4 a(1—a) (14a (1—a)) (e+e (1—a)) (2)

ATR RTS at2a (le)
In consequence of this we get:
dloge, _ 2 a(2—2)(e«+a(1—2a))
dT RT v+2a(1l—2)
d log ¢, d log e,

If we now substitute the values found for and ———
da d1

( 709 )

7

the last equation for a we get finally:
T

RT? — =
dn l—a vt2a(l_—e)
de — (2—2) (e+e(1—2) _’
+a \
: u+2a(1—z2)
Le.
dT Vh a 8
dans Oele en (8)

when for q+ ete. is written Q, i.e. the total heat of melting.
This formula, combined with (6), indicates therefore the direction
of the melting-point curve throughout its course.
In the second place we could have derived the same expression
from tbe general equation (4). As namely yu, = u, + RT loge,
du, RT dloge,

we have — = , assuming u, to be independent of «, and
dx dx
hence:
5 _,, d loge
Eee
dT da
dx Q
5 8 _ dloge,
Substitution of the above found value of

— yields immediately

an
(8). But now we have still to prove, that really the total heat Q is
represented by

(2—2) (ea (1—a))
i a
a+2a(1—z2)

Q=¢q+ (9)

This takes place in the following way. If a quantity dn of solid
substance passes into the liquid phase, the total quantity of heat
absorbed is evidently :

d
qdn + addn + (l—e) À a dn.
dn

For g is the pure latent heat of melting, if only non-dissociated
molecules are formed. But of the dn mols. an amount edn is dis-
sociated; the heat required is a dn.2. Finally the existing condition
of dissociation « of the 1—z mols. will be changed by the addition

da
of dn new mols., namely to an amount (1— ) Tut For (1—2)a
an

dissociated mols. become (1—.) (a + da).

( 710 )

: da dada m
Now —=——. And from 1—r=n, e= m follows «= p
dn da dn m+n
dx m g da da
rence =—_— Sh On tt
dn (m+n)? dx de

Dividing by dn, we find therefore for the total quantity of heat,
absorbed per Gr. mol.:
da

Q=g tad — a«(l—a)— 2.

du
bete ‚da
Substitution of ae from («) yields then after a slight transformation (9).
at

Let us now put «=O, then we find from (8) on account of the

factor 2:
ak 0 3
=== SS UN ne vree a
=i (8°)

If a is very small, this horizontal course does not continue long.

For with small 2 we may write:
dT Jee Gy

dx Q a+2a ;

As soon therefore as w becomes so large thet 2a is small with

respect to wv, the fraction —~— approaches — = 1, and the normal
wt2ea a ‘

course is restored. The greater therefore a, the longer the almost

horizontal course will maintain itself in the neighbourhood of 77.

aH

If « absolute = 0, then may be replaced by =)

av
a +2a (1—a)
from the beginning, and we have immediately the normal course,
given by
dT Wh Jagd
dx TE q

dT e Res
dx fe: q :

Also 7, and 7, then coincide.

’

yielding :

5. In fig. 1 also the line 7,B has been drawn. This would be the
melting-point line, when instead of an excess of one of the products
of dissociation, an excess of an indifferent substance C was added.

The equation (5) remains then the same. But now (6) becomes
different. We have now namely :

(rit)
AB A B C
(1—a) (1—z) a(1—) a(l1—.) is
together again 1 + a (1—.) molecules.
Hence the dissociation isotherm becomes:
a(l—e#) a(l—e) (1—a) (1—2)
NEA SENA Nes

— K,

or
a 1—z

ee 10
la 1+a(1—z) a CS

Now « does not decrease with xv, but increase. The added indifferent
substance C may viz. be considered as ‘‘diluent’’, whereas in the
preceding question the addition of one of the products of dissociation
depresses the degree of dissociation «.

If we solve from (10) again a, we find in this case:

K K
a? (lr) + AT — — 0;
IE TEE
B tti 0, it in that À > that
q= d ars again € SS 7 OS € Je
y putting z ‚ it appears again tha LEK a, so that. we

must solve a from
a'(l--a) + aan — a, = 0,
in which «, is again provisionally assumed to be independent of 7.
(Cf. $ 3).
Now we find:

a= a, fet + Vaer (le |]: (1— 2),

(l—a) (Le) = (le) — a, |[— Var + Y]

1 aE a (1—z) == 1 a ay = adt Si Vv]
The quantity occurring in (5) under the sign log becomes then:

(le) Hater — a
ESCH Ae
Now Vilas" + (—z) = 1—*/,2—'/,(l—e,?)z?...., so that the
above hon passes into
1—a,— /.(L —a,)(2 + dal + all —a,*)x*...
1+ a, —’/,a@,(1 + @,)« —'*/, el — EE.

i. e. into
(1 —a,)[ 1 — */,(2 + @,)e + Vell + @,)x med,
( =F a) Te et = sae to(1 a a)” 00 -|

or into

(742 )

1l—a, 1 1 ee
—— [le fat].
TE tos

Owing to this we get:

q (1 1
Og NN se ee [Og ell, me

17 (9 slee
w + /,(2 + @,)a =P In 0)

or

2 2 . a] RT,
or finally, substituting, Q,=q-+a,2 for q (cf. $3), and Tt Q x
0
fors 1:

eee | RAN
TT = 0 fae 1+ %/,a,— )e jee (BO)

° Qo
which approximate expression will now at least hold for values of
x < 0,26.

F a 3 3
6. A general expression for — in the case in question may be
av

most conveniently calculated from (4). (ef. §4). Then we get:

RT? d loge,
dT 4 de
da Q 4
where
dloge, Ologe, Òloge,da _
de — — Òz da de
1 Jt da

— (i=a)(i+e(l—2)) (l—a)(1-a(1—2)) de!

da y 2
But now = is different. From (6¢) we find viz.:
at

2 da 1 da 1 1 { da
SE = = met (l=
ads 1—adz 1—z2 — 1+a(i—2)| da
yielding :
da__—_ a(1—a)
dx (1—x)(2—az) ’
so no longer negative, but positive as it should be (see above). After
substitution we get:
dloge, 1 a(2—2)

de en (1—«#)1+a(1—2)) in (1—«#)(2—aa)(1-+-a(1—2) ) ae

92

a

(eZ ae)’

(gal
so that we find :
aT PEE A 2

dx Q lr 2—azx

(11)

: da Bs ae
In this Q is again =gq Had —a(l —e) = i. After substitution of
at

- : da }
the just found value for ay this becomes:
U

2
Q=q+a5—— (12)
AU
For «=O (11) becomes now:
TES vo sae Sl Me ce A
|= aa

So the melting-point curve has now also at 7’= 7, a perfectly
normal course.

For practical purposes we can determine more or less accurately
the value of a, from the approximate equation (Sa) (for small values
of «), which according to (7) renders also an estimation of 7%, possible.
The value of Q, must then of course be known. It can, however,
also be calculated from the accurate determination of the initial course
of 7,B (with indifferent admixture), according to equation (11a).

7

C
If we then determine a once more for that same line for 7 = 0,1
at
or 0,2 e.g., we can find Q by means of (11), i.e.
l—a) a
g+ ee OEE

2—ax

supposing that we may put « =a, by first approximation. We find
then by subtraction of the above found value of q + @,4 the value
(l—a,)z

2—a, #

of «2 , so that of 4 separately. Also q is then separately

known.

Appendiz. The approximate equations (5°) and (5%) might also
have been derived from:

dT d°1 den
sik EN Eil fire 1] x aro
Cry evel ra aac ced

yy

F 5 ae 11
With (5e) we find then easily from the value (8) for = that
at

( 714 )

dT eae aN al aN (ei lone eae
AE NE in + 2 da}, «a, ee Qs Qa

BT 3 (dT ekke:
and = ie In this it is noteworthy, that on account of
0

„3 5 ; ;
Ge tie, Os

1 1
Q=g + E — «(l—2z) Z| 4 also 5) ==)
dx da },

ED BT din
With (5%) we shall find from (11): (=) = ——— ; ( In

da Q, da?
2RT.\ (aT dQ
=| 1+ 1/,¢,———](—]. Here too (—}]=0.
( ne OF NG ) - da},
Chemistry. — “On ocimene and myrcene, a contribution to the

knowledge of the aliphatic terpenes.” By Dr. C. J. ENKLAAR.
(Communicated by Prof. P. van Rompuren).

(Communicated in the meeting of Januari 27, 1906).

The aliphatic terpene group, discovered in 1890 by Srmmrxr *), is
characterised by the absence of closed rings; the terpenes of this
group possess, therefore, three double links in an open chain. The
first aliphatic terpene described was anhydro-geraniol, which SEMMLER
prepared *) from the aliphatic terpéne alcoho! geraniol by heating
the same with potassium hydrosulphate. This terpene has not yet
been obtained pure, and has been but tittle investigated. A naturally
occurring terpene of this group was found by Power and Kruger *)
in oil of Bay (the ethereal oil of Myrcia acris D. C.); it was called
by them myrcene. The sp. gr. (0,861 at 15°) was much lower than
that of the cyclic terpenes (0,840—0,860), the molecular refraction
and the addition of bromine pointed to the presence of three double
links. With permanganate myrcene yielded some succinic acid, on
treatment with mixed sulphuric and glacial acetic acid an alcohol
was obtained, having the odour of oil of bergamotte, which was
taken for linaloöl on account of its oxidation to citral. Myrcene oxi-
dised in contact with the air, and polymerised even at the ordinary
temperature. In his studies on cacutchouc Harries *) has for some
time considered these polymerisation products as closely allied or iden-
1) Ber. 28, 2965 (1890) and 24, 201 and 682 (1891).
*) Ber. 24, 682 (1891).

3) Pharm. Rundschau (New-York) 1895, no. 18.
4) Ber. 35, 3256 (1902).

(715 )

tical with caoutchouec, on account of similar nitrites being formed
from them.

On treatment with sodium and aleohol, Semurer ‘) obtained from
myrcene a dihydromyreene, which induced him to suppose the presence
in myrcene of a conjugate system of doubie links. In connection
with the formation of suceinie acid from myrcene, and of laevulinic
acid from dihydromyrcene, he constructed the following formulae :

for myrcene: for dihydromyrcene :
} C—C C C—C
NS LN oN te aa te Sl
ag C= ¢ C=C C—C
Va he ZA ind 4"
C CSC C C—C
8 7 8 7

For a long time, myrcene remained the only known naturally
occurring alliphatie terpene. CraPMaN*) also found it in the oil of hops,
Power and KreBer®) rendered its presence probable in the ethereal
oil from the leaves of the Sassafras tree, BARBIER *) in the ethereal
oil of Lippia citriodora. At Buitenzorg, however, van Romsureu °)
found that the leaves of a variety (sub-variety) of Ocimum Basili-
cum Ls. contained an ethereal oil, in which occurred a still unknown
aliphatic terpene which he called ocimene. Apart from its odour it
was distinguished from myrcene by a greater index of refraction, a
more powerful absorption of oxygen, and by the peculiarity of passing
into an isomer at its boiling point at the ordinary pressure. The
molecular refraction of ocimene gave a considerably higher value
than the calculated value for C,,H,, so that the proof of the aliphatic
character of ocimene was, as yet, wanting.

The further investigation of ocimene was yielded to me by Prof.
VAN RompureH; the ocimene formed the subject of my dissertation’).
My research, which at first concerned only ocimene, had soon to
be extended to the aliphatic terpenes in general, particularly to
myrcene and the isomer formed from ocimene.

1) Ber. 34, 3122 (1901).

2) Journ. of the Chem. Soc. Trans. 6%, 54 (1895) and 83, 505 (1903).

3) Pharm. Review 1896, Chem. Centr. Bl. 1897, II, 42,

4) Bull. Soc. Chim. [3], 25, 691 (1901).

5) Verslagen van ’sLands Plantentuin te Buitenzorg, 1899, p. 48, and These
Proe. IL p. 454.

6) C. J. ENKLAAR, „Over ocimeen en myrceen, eene bijdrage tot de kennis van
de aliphatische terpenen”. Acad. proefschrift, Utrecht, Dec. 1905. A more extended
communication will appear in the Rec. des Trav. d. chim. des Pays-Bas.

50

Proceedings Royal Acad. Amsterdam. Vol. VIII.

( 746 )

The three aliphatic terpenes investigated by me (the isomer of
ocimene proved later on to be also an aliphatic terpene) form together
a closely related, natural group which, according to my struc-
tural formulae, embraces the dehydratation products of the terpene
aleohol, linaloöl, which occurs so widely in the vegetable kingdom.
The ocimene obtained by distillation in vacuo over metallic sodium
is an optically inactive liquid of an agreeable ester-like odour, which
possesses the following constants :

sp. Sr, nd.,, b.p. at 30 mM. b.p. at ordinary pressure.

0,8031 1,4857 81° 172°,5.

Whilst it boils constantly at diminished pressure, the boiling point
at the ordinary pressure does not remain constant for a minute, and
after 25 minutes the original product is found to be nearly wholly
converted into an isomer, which boils 17° higher than ocimene. By
fractionation in vacuo it may be obtained pure, and it then possesses
the following constants *) :

Spots, nd. b.p. at 12 mM. b.p. at 750 mM.
0,8182 1,5296 (ou 188°.

The myrcene was partly prepared by myself from the oil of Bay,
for another part I used a myrcene, most willingly held at my
disposal by the firm of Scurmmen and Co. In accordance with others,
I found for the myreene the following constants:

Sp. 88s; HG sr b.p. at 760 mM.
0,8013 1,4700 166°

At the ordinary temperature these terpenes are stable, except
myrcene, which then undergoes a slow polymerisation; the isomer
of ocimene is pretty soon altered in strong daylight. The chemical
reagents which can be absorbed by unsaturated compounds are
readily taken up by these terpenes. Up to the present, however it
has not been possible to isolate well-defined additive products, with
the exception of the compound formed from myrcene and hydrogen.
Crystallised derivatives of these terpenes are as yet quite unknown,
which very much impedes their detection in ethereal oils and their
investigation. If the chemistry of the aliphatic terpenes is not to
experience the same fate as that of the cyclic terpenes before WArLACH’s
researches, it now becomes all important, to devise a further charac-
teristic, based, if possible, on crystallised derivatives. The following

1) This change of ocimene into an isomer has been noticed and already communi-
cated by vaN Rompureu (l.c.). The constants I found agree with those previonsyl
observed by im. I followed his directions for the preparation of ocimene from
the ethereal oil.

CH)

contains a deseription of some derivatives obtained from the terpenes
ocimene and myrcene; from ocimene and myrcene a crystallised
dihydrotetrabromide (m. p. 88°), from ocimene a* phenylurethane
(m. p. 72°) from the new terpene alcohol ocimenol, obtained from
ocimene, from myrcene a phenylurethane (m. p. 68°) from the corre-
sponding terpene alcohol, myreenol, which had not yet been recognised
as a new product.

As will be shown, the preparation of these crystallised derivatives
enabled me to confirm with certainty certain facts already surmised
and to find a few new ones of great importance for the further research.

As regards the additive experiments, it may be mentioned, that in
the bromination the final point is difficult to observe on account of
colorations; in the case of both ocimene and its isomer the quantity
absorbed seemed to point to the presence of three double links.
Of some more importance is the behaviour of these substances
towards oxygen. With some other unsaturated hydrocarbons they
share the property of absorbing oxygen. The isomer of ocimene does
this in a very striking manner. When a glass plate is moistened
with this liquid, if is found to be changed after half an hour into
a film or resinous crust. Ocimene does this also very strongly,
myrcene a little less. The final point of the absorption seems to be
reached after the fixation of two atoms of oxygen’).

I have specially investigated the behaviour of ocimene towards
permanganate. There is no question here of the isolation of glycols
such as Wacyer has obtained from many unsaturated substances.
Even should a glycol be formed with a same number of carbon
atoms as ocimene, this is very rapidly oxidised by the permanganate.
As oxidation products are formed in large quantities carbonic acid,
acetic acid, oxalic acid, acetone and a small portion of higher fatty
acids, also traces of some non-volatile acids, among which is perhaps
pyruvic acid. In a very weak solution of acetone, the oxidation
takes place more moderately. After the absorption of 9 atoms of
oxygen the discoloration of the permanganate ceases; according to
my determinations 25°/, of the ocimene is then oxidised to carbon
dioxide. The greater part of the oxidation products is, however,
volatile with the acetone; a very small quantity of a sirupy glycol
gave on oxidation with hydrogenperoxide a little carbonic acid,
acetone, acetic acid and in addition a fair amount of a non-volatile
acid, which is probably malonic acid. It is remarkable, however,

1) In connection with the researches of Enerer on the oxygen absorption of

the fulvenes and of Watiacu on that of phellandrene, I hope to further investigate
this matter,

50*

( 718 )

that in the oxidation in acetone solution no acids higher than acetic
acid were formed and besides not a trace of oxalic acid with hydrogen-
peroxide. I am therefore of opinion that those substances owe their
origin to migration of double links during the oxidation. All
this causes that, I, for one, consider the structural formulae based
on oxidation experiments with such very changeable substances as
very untrustworthy. One should also be very careful in drawing
conclusions from the isolation of small quantities of the more typical
decomposition products, as these may have been yielded by impurities.

Notwithstanding the beautiful researches of T1EMANN and SEMMLER *)
on geranial, citral, etc, the structural formulae of none of the mem-
bers of the aliphatic terpene group seems to have been sufficiently
established as was only recently shown by Harries oxidations with
ozone *).

Meanwhile I had tried, whether ocimene could be hydrogenised
like myrcene by means of sodium and alcohol. This proved to be
the case. Ocimene, therefore, also contains a conjugate system of
double links. The hydro-product, which I obtained, had the eompo-
sition C©,,H,,*) (I will call it in future dihydro-ocimene) ; it is a
very mobile liquid of an agreeabie odour. For its constants I found
the following values :

sp. gY.,, nd.,, b.p. at 761 mm.

0,7792 1,4507 166°—168°
whilst SEMMLER *) states for dihydromyrcene :

sp. gr. nd. b.p.

0,7802 1,4501 171°,5—172°,5.

The temperature, at which the specific gravity was determined,
and the barometric pressure at the boiling point are not stated; at
770 mM., the boiling point of dihydro-ocimene is, however, but
little higher. Owing to this difference of 6° in the boiling point of

1) Ber. 28, 2126 (1895).

2) Ber. 36, 1933, 2998, 3001, 3658; and 3%, 612, 839, also Harries und
Scuauwecker, Ber. 34, 2987 (1901) and Harries, Lehrbuch der Org. Chem. by
V. Meyer und P. Jacogson, Il, 754. The above-standing was written before the
latest publication of Harries on this subject appeared (Lieb. Ann. Jan. 1906).

3) In the combustion of these substances with copper oxide in an open tube
the carbon is often found a good deal too low, but in the closed tube with lead
chromate the exact values are always obtained. On the strength of his analyses,
Cuapman also concluded at first to the presence in oil of hops of a hydrocarbon
CjoH,g which by further investigation proved to be myrcene.

4) 1. ¢.

( 719 )

the said hydrocarbons, these were not considered as identical in the
provisional communication. A second point of difference was the
obtainment of a crystalline bromide from dihydro-ocimene. When,
afterwards, I repeated SEMMLER’s experiments, I found the boiling
point of dihydromyrcene to be the same as that of dihydro-ocimene,
whilst the other constants (as far as could be ascertained) agreed
with those of Semmier; I found the following values:

sp. gT.,, ne, b.p. at 761 mm.
0,7852 1,4514 166°—168°

Like Sremmrer, I found that myrcene and its hydro-product have
the same boiling point so that, probably, Semmrer’s statement is
based on a mistake; for other investigators also state 166° as. being
the boiling point of myrcene.

The now probable identity of the hydro-products became a certainty
by the bromination of dihydromyrcene. As stated, dihydro-ocimene
had given me on bromination a crystalline bromide; from the oil
obtained at first, it erystallises to the extent of 12—14°/,. After
repeated crystallisations from methyl alcohol it forms snow-white
erystals which melt, sharply, at 88°. Analysis and determination of
molecular weight pointed to the composition C,,H,,Br,. In most of
the organic solvents. this bromide is readily soluble, but in methyl
alcohol only to the extent of 1,2°/,; on boiling with sodium hydroxide
and also with silver oxide and water an oil smelling of peppermint
is obtained. From dihydromyrcene I now obtained the same bromide.
The oil obtained by Srmmuer soon solidifies when, after being purified,
it is put away to erystallise in a cool place; by applying a little
artifice I succeeded in instantly inducing the crystallisation. The
identity was proved by the fact that this bromide like all its mixtures
with dihydro-ocimenetetrabromide, melted, sharply, at 88° and also
that the solubility of dihydro-ocimenebromide was practically not
affected by addition of this substance.

This now completely proves:

1. that both ocimene and myrcene are aliphatic terpenes.

2. that the dihydroproducts of these terpenes are identical.

From this it follows — and this is probably of more importance
still — that we may now deduce the structural formulae of ocimene
and myrcene from the obtained data.

As regards myrcene, owing to its connection with citral and
-dipentene*), it was already fairly certain that, like all aliphatic

1) Power and Kteser, |. c.

( 720 )

terpenederivatives as yet known, it is a derivative of dimethyl- ~
2-6 octane :
H, Hs B;
C C—C
NE Hy? NSE
C—C C — CH,
PA 3 6
C
H,
On account of the proved identity of the bromides, ocimene should

also possess this carbon skeleton. Now when we accept the correct-
ness of the hydrogenation principle of conjugate systems *):

H,C — CH,

beto on snot oe
ZR EERENS JA Ale EN

it is, in the carbon branch formation of dimethyl 2— 6-oetane, only

then possible for different triënes to give identical diénes, when these

triënes possess the following conjugate systems:

SD CNS \ 7 |
0 C-—C and )—= C es C= Cre
via 2 3 : He : a 2 3 oa wo 6 ee
: At C “C=C
it”

and when the third double link occupies the same position in both
formulae, and is not conjugate with the other double links. For
this third double link 1 or 2 is the only possible position ; on
account of my experiences as to the oxidation of ocimene, I should
be inclined to accept the position 2, although the position 1 has still
quite as much right of existence*). Perhaps, as SEMMLER believes,
myreene may contain both forms (ortho and pseudo form).

Dihydro-ocimene and dihydromyrcene then assume the formula of
dimethyl 2—6 octadiéne 2—6 :

1) For exact details and the literature of this hydrogenation principle, I must
refer to my dissertation p. 26.1 wish only to point out particularly, that my rule is not
based on the theory of Turete, but has been deduced in a purely empirical manner.
I, therefore, make a distinction between the addition of hydrogen and that of other
substances which may prove more complicated.

2) Admitting for this third double link the position I, yet another couple of
formulae seems possible; on account of other facts the latter must however be
rejected.

C C—C
oN Yes EON
—iÛ C—C
we 3 Us
C C—C
8 7

which has already been agreed to by SemMmier on other grounds.
Which of the above formulae, however, belongs to ocimene and
which to myrcene? A choice is only possible on the strength of other
data. As has been stated, SemmreRr had assigned to myrcene for-
mula IL on account of the formation of succinic acid in the oxida-
tion. Independently of him and these considerations, I had constructed
for ocimene formula I as the result of my oxidation experiments,
but without attaching any value to this. A closer consideration of
the above formulae, coupled with the peculiar behaviour of ocimene
on heating, as observed by van Rompureu, led me to the discovery
of a fact, which rendered a choice possible with great certainty.

In one respect formula I differs characteristically from formula II
namely by the presence of the double link 5, which forms an
asymmetric system with the carbon atoms combined thereby and the
groups attached thereto, and so gives an opportunity for the existence
of a geometric isomerism. The transformation of ocimene into its
isomer led me to think that these two substances might be geome-
trically (stereo-) isomeric. Geometrical isomers are often readily con-
verted into each other on warming ; for instance, WisLrceNus noticed the
transformation of the one bromobutylene into the other on distillation.
The hypothesis advanced by me was easy to verify for on hydro-
genation the same dihydro-ocimene ought to be formed from the
isomer as from the ocimene itself. This proved indeed to be the case.
The physical constants of these materials were indeed identical as
is shown from the following table :

Spe Gr... nd.,, b.p. at 761 mM.
dihydro-ocimene 0,7792 1,4507 166°—168°
dihydro-isomere 0,7793 1,4516 167°—168°

whilst the original products exhibit strong differences as is shown
from the subjoined '):

Sp ern, nd. b.p. at 760 mM.
ocimene 0,8031 1,4857 172°,5
isomer 0,8133 1,5447 188°

1} The constants of the isomer have been determined with the aid of a purer
preparation than those previously communicated. On heating ocimene some by-
products seem to be formed.

( 322)

With this I consider the identity of these hydro-products and the
geometrical isomerism of the terpenes as proved. The isomer of
ocimene I will call in future allo-ocimene. It is remarkable that
allo-ocimene deviates 6,31 from the theory of Brinn; its index of
refraction is also greater than that of the hydrocarbon and it has
also a strong dispersion power. This, as Brinn thinks *), is perhaps
connected with the presence of a conjugate system of double links.
Provisionally, one should be careful in drawing conclusions as other
substances also exhibit such differences. Allo-ocimene is, however,
in this respect a unicum in organic chemistry. Dihydro-ocimene on
the other hand exhibits the correct refraction. The deduced geo-
metrically isomerism was also very much supported by the behaviour
of the isomer towards a mixture of sulphuric and glacial acetic acid.
Whilst ocimene remains for the greater part unchanged and is, to
a small extent, converted into an alcohol, allo-ocimene is for the
greater part converted into a polymerisation product, whilst there
is left a small quantity of terpene, which proved to be nothing else
but ocimene. This typical difference between the two ocimenes is
perhaps connected. with the particular tension which the ethylene
link may attain here. Possibly, at the moment this ethylene link
opens, the two connected atoms of three molecules combine to form
a cycle of six atoms; a substituted hexa-hydrobenzene derivative
would then be formed; the polymerisation product would be this
triterpene.

The regeneration of ocimene from allo-ocimene under the influence
of dilute acids renders the analogy complete with the isomerism of
fumaric and maleïnie acid. After what has been said, it is no longer
doubtful, that ocimene, which possesses the double link 5, is repre-
sented by formula I, whilst myrcene is represented by formula I,
which has now been deduced independently of the results of the
oxidation. But few instances of geometrical isomerism have been
noticed with hydrocarbons and this is the first known in the terpene
series. It seems to me not impossible that the absence of the cyclic
link has given nature the opportunity of forming a labile geometrical
isomer; it is remarkable, however, that this has taken place without
any admixture of allo-ocimene. I hesitate to pronounce just now an
opinion as to the nature of that geometrical isomerism with ocimene
and allo-ocimene; the following projection formulae seem to me the
most probable.

2) Ber. 88, 761 (1905).

( 723 )

I am still engaged with this
geometrical isomerism and the
other substances described. I

3 soon hope to make a further

ocimene: C=C re C—~.© communication about the

A ins er: alcohols formed from these
C C=C terpenes.

© © Of late, after this research

Net 4 had already been partly

C finished, SABATIER and SENDE-

I RENS have made some valu-

C able additions to our methods

Ray? of research of the unsaturated

allo-ocimene : C compounds. I am engaged in

| applying the same to the

He. — > aliphatic terpene group and to

SN the sesquiterpenes. Dihydro-

f C= ‘ ocimene, which cannot be

A further hydrogenised by so-

(mate dium and aleohol, eagerly

absorbs hydrogen at 180°

under the influence of reduced nickel; a nearly odourless liquid is

formed which boils at a considerably lower temperature and contains

only traces of the original product. It consists, probably, of dimethyl-

2.6.octane, the as yet unknown foundation of the aliphatic terpene

group. The aliphatic terpene-alcohol, geraniol, also reacts with nickel

and hydrogen; the reaction product is a liquid, possessing a particular

odour; it contains, besides some water, a hydrocarbon, which probably

is identical with the hydrocarbon, obtained from dihydroacimene

and a substance of a higher boiling point, which I suppose to be the

saturated alcohol, corresponding with geraniol.

C

Chemistry. — “On some aliphatic terpene alcohols.” By Dr. C.J.
ENKLAAR. (Communicated by Prof. P. van Rompuren).
(Communicated in the meeting of January 27, 1906).

According to the process of Bertram and WarBauM ') terpene
alcohols may be obtained from terpenes by digesting their solution
in glacial acetic acid for some hours with dilute sulphuric acid at
50°—60°. The aliphatic terpene ocimene, discovered by van ROMBURGH

1) D. R. Pat. No. 80711, Journ. f. Prakt. Chem. 49. 1. Also compare WaArLAcH

and Waker, Ann. 271, 285, and Power and Kieser, Pharm. Rundschau (N.-York)
1895, No. 3.

(724 )

and investigated by myself‘), was treated by me in this way *).
The greater half of the ocimene operated upon was recovered
unaltered while a small portion underwent polymerisation. At the
same time an alcohol was formed, the quantity of which was about
10°/, of the ocimene used. This alcohol was an agreeably smelling
liquid, which gave the following constants :

Sper nd; B.p. at 10 mm. Mol. Refraction (M.R.)
0.901 4.4900 Os 49.22
(calculated for C,,H,,0|> is: MR = 48.86)

The analysis had given the composition C,,H,,0.

This alcohol, probably an aliphatic terpene alcohol is, therefore,
formed by the addition of the elements of water to ocimene. In
properties it does not correspond with any of the already known
aliphatic terpene alcohols, as is shown by the following table:

Spy Sta nd B.p. at 10 mm.
geraniol : 0,882 LAY. 116°
nerol °) : 0,881+ 112°
myrcenol (BARBIER) : 0,901 1.477 99°
linaloöl : OISTOE 1,464 86°

On account of its formation from ocimene, I call this new alcohol
ocimenol. The-investigation of this ocimenol is still of a provisional
character.

The beautifully crystallised phenylurethane, which I could prepare
from it in good yield, renders it possible to characterise and readily
investigate the alcohol. This urethane, when recrystallised from dilute
alcohol, forms white needle-shaped crystals, which melt without
decomposition at 72°, whilst according to the analysis, it has the
composition C,, H,,0,N. I am still occupied with the regeneration
of ocimenol from its urethane and the closer investigation of these
substances; however from the fair yield of this urethane, and the
absence of oily by-products, it seems that the product obtained from
ocimene is mainly a simple alcohol.

For me, the study of this alcohol was of particular importance
as I wanted to compare ocimene in this respect with myrcene.
Several investigators have been already occupied with the alcohol,

1) Compare my previous paper and my dissertation.

2) | worked according to the directions of Power and Kregen. 100 parts of
terpene were heated with 250 parts of glacial acetic acid and 10 parts of 50°/,
sulphuric acid for three hours at 40°.

3) Nerol is distinguished from geraniol by a more delicate odour of roses, by
not combining with calcium chloride and by yielding a diphenylurethane melting at 52°.

( 725 )

which is formed from myrcene in the manner indicated; their state-
ments, however, are often diametrically opposed.

Power and Kinser‘), who first prepared it, took it to be linaloöl
on account of its odour and the formation of citral on oxidation
with chromic acid. Barpmr*) declared it to be a new alcohol; on
oxidation, he obtained no citral but another as yet unknown aldehyde.
From the results of the oxidations he deduced. for this aleohol, which
he named myrcenol, a structural formula, which had been given
already by Tiemann and SEMMLER to linaloöl. In a further research
on linaloöl, he gave as his opinion®) that it was not a simple
aleohol, but a mixture, and also that its main constituent was not
optically active, a reason why he rejected the formula of T. and S.
SEMMLER‘), however, looked upon myrcenol as a mixture already
partly converted into cyclic products, and upheld his linaloöl formula
against BARBIER’s objections.

I prepared the myrcenol according to the directions of Power and
Kirper. The greater part of the myrcene was recovered unaltered
(6°/,), a small portion polymerised whilst the alcohol had formed to
the amount of about 20°/,. For this alcohol distinguished from linaloöl
also by its intense, agreeable odour, I obtained the constants attributed
to it by Barrer, who, however, had a much langer quantity of the
aleohol at his disposal :

sp. Sr; nd,, Bp. at 10 mM. Mol. Refr.
myrcenol (£): 0,9032 1.4806 97—99° 48,44
E (B): 0,9012 1.47787 335 48,34

MR, calculated for C,,H‚, Ol, = 48,16

My analyses also pointed to the composition C,, H,,0. I do not
consider this aleohol to be perfectly pure as it has not got a quite
constant boiling point; it seems still to contain a more volatile fraction.

The closer investigation of this substance has, as stated, led to
differences of opinion. It seems to me that these have been caused
by the different methods used. The formation of citral in the oxidation
in acid solution is no reliable test for the presence of linaloöl as it
may be yielded also by other alcohols. Barger showed, however, that
on oxidation of myrcenol with chromic acid an aldehyde was formed,
having the same formula as citral, but not identical with the same.
He regenerated it, for instance, from its oxime, and obtained a

Doc:

2) Bull. Soc. Chem. [3], 25, 687 (1901).
3) Bull. Soc. Chem. [3]. 25, 828 (1901).
4) Ber. 34, 3122 (1901).

( 726 )

semicarbazone melting at 1975 whilst citralsemicarbazone melts
at 135°. Here we have a difference in the method of research.
Power and KrreBer tested for citral by converting it into citryl-
naphtoeinchonie acid; in this way a possibly formed ketone — I
presume myrcenol is a secondary aleohol — must have escaped their
notice, whilst a little citral thus detected may be simply a by-product.
On the other hand, semicarbazone, made use of by BARBIER, is
according to others unfit for testing for citral. BARBIER may have
obtained the semicarbazone from the eventually formed ketone, the
main product, whilst a little admixed citral may have given the
aldehyde reactions. Moreover BARBIER’s oxidations with permanganate
in aqueous solutions cannot be taken as decisive for the differen-
tiation of myrcenol and linaloöl *).

Instead of investigating the oxidation products of myrcenol, I have
prepared from the alcohol itself a crystallised derivative, in the form
of a phenyl-urethane, melting at 68°. The analysis again pointed to
the composition C,, H,,O,N. This urethane has been prepared in the
same manner as WaLBAuM and Hiruic’) prepared the phenyl-urethane
from linaloöl; the latter melts at 65°. By means of the phenyl-urethane
obtained from myrcenol, it could be decided very readily and distinetly,
that the alcohols, myrcenol and linaloöl, were totally different. The
mixture of racemic linalodlurethane and myrcenol-urethane melted
at 60°—62°; the depression of the melting point sufficiently proves
the non-identity. The alcohol, which is characterised by the phenyl-
urethane melting at 68°, is also the main product of crude myrcenol.
I obtained from this a yield of nearly 60 pCt. of crystallised urethane ;
besides this alcohol, a little linaloöl may possibly be contained in
the myrcenol (the hydration product of myrcene); the formation of
some oily urethane in presence of the crystallised substance might
even point to this. The facts mentioned render it possible, however, -
to decide the matter. By regenerating myrcenol from its urethane,
the properties of pure myrcenol may be ascertained. I am still engaged
with this. Of this alcohol, myrcenol, it may be stated that it is a
typical derivative of myrcene; its constants differ from those of
ocimenol, in the same manner as those of myrcene do from those
of ocimene; the tendency towards polymerisation of myrcenol is
still larger than that of myrcene. .

For ocimenol and myrcenol I devised provisional structural formulae’),
based on their formation from the terpenes ocimene and myrcene.

1) Compare previous communication.

3) Journ. f. prakt. Chem. 67, 323 (1903).
8) Dissertation, p. 73.

(Ca)

I have not been able to obtain the above racemic urethane of
linaloöl by mixing d- and /-linaloöl and preparing the urethane from
this racemic linaloöl; nothing but an oil was formed, which could
not be brought to erystallise. Still, from each oil separately (d-cori-
androl and Zlinaloöl, the latter obtained from ScrimmurL & Co.) I
obtained the urethanes at once erystalline. In order to obtain racemic
urethane, I was obliged to mix these urethanes of d- and /-linalodél
in the proportion of their optical activity. The latter, however, had
not been determined; in fact it was doubtful whether they were
optically active at all. WarBaum and Hurnie, who desired to prove
in this manner the identity of linaloöl derived from different ethereal
oils, have overlooked the fact, that alcohols of such varying optical
activity as those found with linaloöl (from 1° to 35°) could not yield
the same phenyl-urethane.

Racemie urethane has generally quite another melting point than
the pure optically active substance. I was, therefore, obliged to fill
this void in their research. I found that the yield of crystallised
urethane, which only amounts to 15°/,, when one works according to
their directions (time of reaction one week), may be increased to
85°/, increase of the time to three months. The urethanes formed,
which all melt at 65° are optically active in proportion with the
optical activity of the alcohols started from. They consist of mixtures
of racemic urethane (probably a racemic compound) with the opti-
cally active component, which in a pure condition shows a rotation
of 23°27’ in a 200 mM. tube and has the m.p. 66°. The rotation
of pure optically active linaloöl under the same conditions may also
be calculated from this; it then becomes 35° 27’, whereas the highest
observed rotation of the natural substance amounts to 35° 14’,
This alcohol appears, therefore, to be very strongly subject to race-
misation, even in nature. By the facts stated it has, therefore, been
proved that linaloöl consists of a simple optically active terpene
alcohol; the incorrectness of Barsier’s formula for linaloöl and
myrcenol has been demonstrated, whilst the linaloöl formula of
TreMANN and SEMMLER has received support.

( 7985)

Physics. — “On the propagation of light in a biavial crystal around
a centre of vibration.” By H. B. A. BockwinkeL. (Commu-
nicated by Prof. H. A. Lorentz).

(Communicated in the Meeting of January 1906).

In the electromagnetic theory of light, it is of interest to determine
the electromagnetic field in a crystal due to an action, taking place
in a certain centre QO. In order to fix the ideas, we shall assume,
that in an element of space t at the point O there are certain
periodic electromotive forces (1. M. F). There will then be a radiation
of energy from OQ in every direction, the amount of which will
depend on this direction with respect to that of the A. M. F.
and to those of the axes of electric symmetry. Our object is to
investigate this dependence, at least for points at a great distance
from O. We might for this purpose use the results of GRÜNWALD *);
this physicist however takes the equations in the form they assume
for a rigid elastic body and does not operate with an 2. M. F. as
mentioned above; we shall therefore treat the problem independently.
Our method will consist in reducing the question to one of plane
waves, by using a formula, proved by Prof. Lorentz. In this formula
a continuous function of the coordinates is represented by an integral
over the solid angles of all cones having their vertices in O and
filling the whole space. If the #. M. F. is Ee then

ake 1 FB
— for AE MW, . . . . . . . (1)

where dn is the element of a line of arbitrary direction within the
cone dw and ® a vector given by

Ba (ed, .. . |

the integral being taken over the plane, passing through the point
considered, perpendicularly to x. Hence, 28 depends on the coordi-
nates, but in such a way as to be constant in every plane perpen-
dicular to ». By (4) the original #. M. F. has now been decom-
posed into a great number of infinitely small vectors, the effect of
which can easily be calculated, each of them being constant in
planes of a certain direction. Thus we determine the field, produced
by each of the elements of the integral (1) and then compose all
the fields obtained in this way into one resulting field, which,

1) J. Grünwarp. Uber die Ausbreitung der Wellenbewegungen in optisch zwei-
achsigen elastischen Medien, Bottzmann Festschrift (1904), p. 518,

( 729 )

according to the principle of superposition, will really be the one
produced by the whole E. M. F. Each of the separate very small
fields will consist in a propagation of plane waves having the same
direction as the planes in which the corresponding element of the
E. M. F. is constant. The problem will therefore indeed be reduced
to one of plane waves.

§ 2. In order to find the small field, corresponding to a cone of
definite direction, we shall take a system of coordinates OX’, OY’,
OZ', the axis OZ' coinciding with the axis of the chosen cone and
OX', OY respectively with the two directions of the dielectric
displacement, belonging to plane waves, normal to OZ'. The wave
that has its dielectric displacement along OX' will be called “the
first wave’; the other “the second wave”.

Again we take a system of coordinates OX, OY, OZ, the axes
of which coincide with the axes of electric symmetry. ee the

components of the electric force along the first axes by €, €
Qn

ey ,

int
and supposing all quantities to contain the factor e fe have to
satisfy Ee following equations

An

A€ sadn. == ae (Er +€, )+e,,(€ y HE) He (Er + )|
An

Ag Eydie = Te fale HEI Hen Ey +69) +2, + )| (8)

4. 3 = C ce Fed €
Ag. dij Ec + €2)+e,,(Ey HE) + 6(Ee +]
kA c

It will not give rise to any misunderstanding that we have denoted
dw 0728
8x? Oz?”

The quantities e, occurring in these formulae, have particular
properties, because they relate to special directions. These properties
will show themselves in the following development. Since, according
to the preceding considerations, @ depends only upon 2’, we shall
find for € a solution, likewise containing only z’. By this hypothesis
the equations (3) become

here by €¢ the expression —

dE An?
S= Tr tu (Er) + (Ey + G + En (Ez + € |
dE An?

En en FE) Hen, (Ey + Gy + (Er HE | ®

0=s,, (Er + Er) ome Sar (Ey == &) + E32 (Er se Er)

( 730 )

§ 3. The last equation of (4) shows, that there is no dielectric
displacement in the z/-direction. Further it is evident from these

equations, that € has no share in the disturbance of the state of the

aether at a distant point. Indeed, ©", and Cy being zero, the equations
are satisfied by the solution

C2= 0, Cy On EE

At the distant point €£ is zero, therefore € is so likewise. Electro-
motive forces acting within a layer bounded by two parallel planes
and directed perpendicularly to these planes, do not therefore
produce any disturbance of equilibrium at a distant point.

We eliminate ©. between the first and the third and between the
second and the third equation.

This gives

0E An? 13 E1382 c ze
pe ete ae rent ( ee)

dE Anr? E38 EET -e si ; ke
02? oF, cr: (en — Ess Cz Pa Er) st Ea — Es, Er + €,) 5

According to what has already been said, these equations, if no
E. M. F. are acting, must have one solution in which ©, is zero,
and another in which ©, vanishes. This would follow from the
equations themselves, if we knew the above mentioned properties
of the quantities e‚ occurring in them. Conversely, we shall be able
to deduce these properties from the knowledge that the two solutions
must satisfy the equations. Indeed these solutions can only hold if

Ee G
13°23
Eig = Le — 0
E53
and 2 Cc? 2 c?
VS SS iis ERE
E15 E33
Emine E54 —
E35 E55

where V, and V, are the velocities of the plane waves in the two
cases. By this a ieee take the form
7g, 07E,1 An?
a = ac +) == GN
TV, T'V3

whereas the “third equation of (4) gives € when €, and €y are

known. We see from (5) that €, depends only on @;-, and G, only

on Cy, further that both equations have the same form, We can

( 731 )

therefore confine ourselves to considering only the first; in doing
so we shall write V instead of V,. We shall have to remember
however that after having found the result that is due to the X’-com-
ponents of the E. M. F. we have still to add to this a second amount
given by the Y’-component; this amount can be written down at
once by analogy with the first.

§ 4. The general solution of the equation

°C,” An? 5
pep ya
is given by
ut aed nz’ „2nz' z' „2nz'
‘ U — i— im U
ur TV e TV 1 EV fe VSN =
Ey = —-e Cy e dz' — ——e Ere zie (6)
TV IPE
| 92 n

The lower limit of these integrals is arbitrary, so that, as could
be expected, two arbitrary constants occur in the solution. It is
easily understood, that in the final result there will likewise be a
certain indefiniteness. Indeed both a propagation towards V and one from
O will be contained in it. It is sufficient for our present purpose to
consider only the first solution and in order to leave aside the second
we have to give completely definite values to the constants, as will
appear in the following manner. We consider the two planes perpen-
dicular to OZ’, tangent to the boundary surface of the space r; let
these planes be determined by the equations

zand eile
Then, since Ee stands for
1 9%
Rn dw,

it will differ from zero between the planes and will be zero in the
space outside them. The first integral of (6) must vanish for

ele

and the second for

This is only possible, if

9, << —h, and

Or h,.
For the rest g, and 7, may have any value satisfying these une-
qualities; it is evident that the result of the integrations will always
be the same, if we take into account what has been said about the

ol
Proceedings Royal Acad. Amsterdam. Vol. VIII.

( 732 )

values of Ee. We shall therefore put g, = —h, and g,=h,, so that
rz! zl Oz! Ae 2nz'
oe Ln ‘TV (O8y ‘Ty pa id en WIT (T
"8x TV oz? ° "8x TV- det A
— hy hy

§ 5. In effecting these integrations we have to distinguish whether
or no the point P, for which we intend to determine the’ state
of radiation, lies between the two just mentioned tangent planes. First
taking the latter case, the second integral of (7) is zero for positive
values of 2’, whereas in the first case we may take /, instead of
2’ for the upper limit. Integration by parts gives

ha _ 22! „2nz' hy ha Sere?
OB, fry, Be ‘Ty Zar (0Be irr”
En deli ral inr Ne deus
Zz z ze
—h, —h, —h,

Now € can only be represented by (1) if it is a continuous
function of the co-ordinates, but we may imagine nevertheless that
at the boundary of the space rt, W and 0%8/0z' have arbitrarily
small values. These quantities may therefore be taken zero at the
boundary; as to YW, this has already been done in the considerations
of the preceding paragraph. Hence the first term, given by the
integration by parts, vanishes; the second may again be integrated
by parts, so that finally

h Qnz! ha 2x2!
S 2 2 i
oF Tal a are mm, IC ae
Dr e Snare
in —h,

The exponential factor under the sign of integration may be
replaced by 1. Indeed, if a certain length /, of the same order of
magnitude as the linear dimensions of the space rt is very small in
comparison with the wavelength 2 of light, we may omit terms
T

l
7 and quantities of the order Er Now

containing products of

the integral taken over the portion of a plane z’ == const. lying

within rt. From this we infer

hy
„€
Ws dz! =e dt

ei

integrated over the volume t. We shall represent this integral by

(733)

-€ . <€ 5 r

Er, denoting by & a certain mean value of the A/-component of
> oD J

the E.M.F. within tr We may now write

ha An a
PR, Ty. Ant Ent
€ 2 = — ——__—_
02” rey
=p
Similarly
ha „2nz' é
Owe .* Ta _ Srey
der EE
—h,
an integral that has to be used for negative values of 2’ less
than — h,.
§ 6. If lastly
FIE h, <a 2! << h,

the point P lies between the tangent planes and doth integrals differ
from zero. We find by some transformations

Az’ 2! 2rz

2! nz. 2nz
OR, Ty , ÒW ‘Ty AES TJ 4x? J ' ry.
Se dei — i % e — —— 7 Wee !
i e a = x lz
02? dez! TV: mye oe
—h —h,
z' nz! nz!
OR) Ary 08,’ DEE ‚2 98 TV
— e == e i —Wy e —
027 dz! Ri
hg
2 rz’
Ant? zi
hog ee
Py}
hy

So that in this case the X’-component of the electric force is
given by

a 2 Brat) (20 i Qrz!
ide Ar Ant Ty TV
el tn ee We de! —
; al i) Vp :
—h,
Qnz’ he 2nz'

Since z' lies between —h, and h,, we may replace the exponential
factors by 1, both before and behind the sign of integration. Then
we find finally

dst. If P lies between the tangent planes

’ e
Ws inEyr

arp art

Ey =

(734)

2nd, If P lies outside these planes
a. For positive values of 2’

‚Az!
= ie 5 DA
DIV
b. For negative values of 2!
e 2 m2!
El = hek Vd

The Z’-component of the electric force consists of two parts, one
of which corresponds to €,, the other to €. Having already omitted
the Y’-compenent, we shall take only the first part, €, of the
Z’-component and add the second part Eva to the Y’-component
afterwards. Then by the third equation of (4)

Er OEE EEn Gye UO
8n? dz? En 82? dz?

It appears from this that outside the tangent planes € and G,,
are connected with each other in the way they always are in the
case of plane waves. We may therefore represent the electrie force

a’

by if 9 is the angle between this vector and the corresponding

cos 0

dielectric displacement in a system of plane waves. Finally we have
the following equations for the components of the electric force
along the axes of symmetry

z c° panes \
ima@yt ry
3 SS = d
©, 2T°V? cos a
Qnz!
imBGyt =
Gree TVG Rett (2)
y 2T°V? cos 9 a re
: e „nz!
yEnt Ary
Te d
E DT Vi cos 9 me

where a, 8 and y are the direction cosines of the electric force with
respect to the axes of symmetry. For negative values of 2 the same
formulae will apply, provided that z' be replaced by — 2’.

§ 7. In the preceding equations the symbols €, €, and €, were
used for the (small) electric force, produced by a single element of
the integral (1) in a point P, lying at a given distance 7 from the
origin O. We have seen that the expression for this small electric
force took a different form according to the point P lying or not

( 735 )

lying between the before mentioned tangent planes. Now the direc-
tions for which P lies inside these planes are those excluded by a
certain cone A, which may be defined as the locus of all normals to
another cone, having its vertex in P and tangent to the boundary
of the element of space rt. On the other hand, all directions of wave
normals, for which YL lies outside the tangent planes are included
by the cone A. It is clear that this cone will differ infinitely little
from the plane passing through O perpendicularly to OP.

We may therefore find the total electric force by integrating the
right hand members of the equations (8) with respect to all direc-
tions lying within A and then adding to the result the quantity
obtained by integrating the expressions relating to the remaining
directions. In effecting the first integration we must replace 2’ by
— 2 for negative values of z', according to the remark made at the
end of § 6. But we may as well limit the integration to half the
cone A multiplying the result by 2. Again, we may extend this
integration to the plane /’; indeed the right hand members of (8)
contain rt as a factor, so that it does not matter, whether or no an
infinitely small solid angle is included in this integration.

It remains to consider the expressions

ee tee oe eae
EZ ary: CS
2 1/0. &,, 0728," aa
Ems Es dw — —dw }——€,,
8x? \ dz’ enden Ens

which have to be integrated over all directions outside the cone JX.

Now, from these expressions we get the components along the
axes of symmetry by multiplying them by finite factors. It is easily
seen that terms already containing the factor t may therefore be
omitted, so that we may write

Ws
GC aT:v: dw,
€ 1/0 en er OZD
En = E 5 8 ~ | dw.
#1 Sieg tel gs Ta )

§ 8. We shall resolve this last vector into two other vectors,
the components of the first being

Ww €

AS. e
eene

3 2 a9

ary Es

and those of the second
1 dW. Ein 0728,"
a0; Eri = ( + ) dw.

827\ dz? Eo Oz.

( 736 )

The first vector has again the same direction as the electric force
in plane waves whose normal coincides with the direction we are
considering; its components along the axes of symmetry are therefore

ay BWB, ye,

= ES ily SE, SS i>) =“ (GS ie
Zes Ted y 27? V? cos 9 5 :

€; Tor:
27? V" cos 9

Now Ws, is of the order / and the integration is to be effected
over a solid angle of the order /. Thus, confining ourselves to
directions in a single plane passing through OP, we may regard as
constants the quantities a, V and cos 3, assigning to them the values
they take in the plane #.

We determine an arbitrary direction in the plane passing through
OP by the angle & which it makes with OP and its azimuth x
with respect to a fixed plane also passing through OP. Then —-

dw = sin § dé dy.

Now we have for the direction considered

Wy= of Ei do

the integral being extended to the portion inside r of a plane G,
passing through YP perpendicularly to that direction. If q is the
normal drawn from O towards G, we have

= r cos &,

|\dq| = rsin§ db,

giving

il

dw ‘= — |dq| dy,

=

and

Den

£ 1 a ee
erf Pap f Pedal

0

Here for each particular value of y, the latter integral is to be
extended to all values that can be given to & or g. Further

fe |dq| =f inl fe to={ (Sao,

do |dq|

whereas

is the element of volume of an infinitely small cylinder whose upper
and lower base are formed respectively by one of the surface
elements of G and of an infinitely near plane G', the generating
lines of the cylinder being perpendicular to G. It follows from
this that

( 737 )

Bi i do |dq|

is the volume-integral of ©, , taken over the whole volume of r.

We have already written for this integral ©) 1, denoting by ©) a
certain mean value ($ 5). Hence, the jist part of the components
of the electric force resulting from the integration with respect to

the directions outside the cone A, becomes

2 2 G
1 aG, t 1 BET
ZENE == dy, © =
ie zl cos Ù- : al en Tee Î
0 0
2
1 Er

TD Todt Lon eRe ne Te
‘ 27T?r J Vcosd es 6)
0

The second part results from a similar integration of the second
vector — ;

x 1 0728. OW,
Ey 0 ’ S= ( 2 Zi ae dw.

WCE tae es Der
Now it will appear: further on, that we can only determine the

exact value of those terms, in which the denominator contains the
first power of 7. We may therefore confine ourselves to such terms
in the whole course of our calculations. The cone over which we
have to integrate being of the order //r, we may omit terms, which
already contain 7 in the denominator. It will be evident therefore
that instead of

OWM 0728,

dz? Oe?
we may take the values of these quantities, corresponding to that
wave-normal, in the meridian plane passing through OP, which lies
at the same time in the plane /. If dz’ is a line-element of that
wave-normal, we have to consider the integrals

Otsen 2K,

ee and (SS dz!

ow
which evidently are zero, De being zero at the boundary of rt. It
appears in this way that we need not at all consider the second vector.

$ 9. We now proceed to effect the integration of the right hand

members of the equations (8) so far as is necessary in order to

7
w

L
obtain the terms with — We shall take the real parts of all expres-
2

( 738 )
sions and represent henceforth by © the whole electric force. Then,

JA t
if Ge = b cos 2a = we shall have

Bahyt 20 Zz
Cc = j ht Dj noe (UN
is T° Vcsd T ( =) if a?

integrated over all directions on that side of £ where z' has positive
values. We therefore obtain the resultant luminous vibration in an
arbitrary point P as the sum of small vibrations, belonging to a
great number of systems of plane waves of all possible directions.
These vibrations. differ from each other in amplitude and in phase.
The changes of phase are determined by those of the quantity

'

Vs
Since 7V means the wave-length in the crystal for the direction
considered and z' =r cos§, the phase will vary very much by small
variations of &, i.e., of the direction of the wave system in question.
There is one direction for which

TVs
takes a maximum value. This is the direction of the wave-normal
OQ to which OP corresponds as first ray. Indeed, 2/TV is
proportional to the time in which the vibrations of-a certain wave-
system arrive at P and this time is really a maximum for the
system whose normal is OQ. We shall prove, that the resultant
vibration at P is the same as it would be, if we had only to do
with wave systems of this latter direction and of directions in the
immediate vicinity of it. To this effect we shall fix our attention
on an arbitrary normal ON, making an angle © with OQ, writing
y for the azimuth of the plane NOQ with respect to a fixed plane,
which passes through OQ, and for which we might take the plane
POQ. We shall not however introduce w and ® as variables but p and
— = cos &,

if V, is the velocity of propagation of the plane wave, having OQ
for its normal. Further we put

2at 2ar

ce TV,

es)
= 9, dw=sn>— dudp.
du

Then

aby T j
ee © sin (gu — 2) sin dS day, os,

(739 )

if vo is the value of u for the direction OQ. Indeed the directions for
which w= const. lie on a cone surrounding the line OQ, just because
u is a maximum for that line. We first integrate with respect to w
and put

2

mab, t Le AE 12
Srna tee 7e. 0D
0
The result is

0
Cn = ff 0 sin oe — Ian en (5)

Uo

§ 10. An integral such as (13) has already been considered by
KircuHorr. For great values of g it approaches uniformly to zero
and at infinity it may be represented by a development of the form

OH as
ty
9 9

It is only the coefficient a, that can be found. Integration by parts
of the integral gives

0
fre sin (gu — h) du a (14)
a 9

g

The first term, taken by itself, gives a sufficiently exact result for
points P, lying at distances r from O, which are large in comparison
with the wavelength of light; in the following development we have
in view only such points as satisfy this condition. We put therefore

0
fF sn mW dr EOP TD ALOT 1

q

dv

Up
We shall first consider the part

2

f(0)cosh TV, 7 a) nmabyt. òf ;
bende Tkn ete
0

u=0
Now
„ 9 _ — A(cos)s Ò(cos5)
sane Òu —- (cost) Òu

Ou on 0 E 5 Ee Ve 0 Ve
Ò(cos5) _ Ò(cos5) | V ae | eal ee Ò(cosö) l= :

so that for u=0 or cos$=0

( 740 )

E fan) | == Ki Ò(cos®)
Ou u) V, Ò(cos5) 0

We may further deduce from the consideration of the spherical
triangle, defined by the directions ON, OQ and OP, that for u = 0

Ò(cos®) (dy
A(coss) ae Ga w= 0

so that
. 0? V /dy
sin — = — —_| ==
du Ju —o Le dp)u=o
and
f(O)cosh 1 Qat (7 aber
= = om cos — | ———_ dy.
g 2T?r T V *cosd
0

The real part of the expression (9), added to this result gives
exactly zero, so that, as we could have expected, there remains in
©. no term with only cos 21/7. We need hardly add that this is
equally the case with €, and €.

Finally we have to determine /(w,). Let us denote by 2 the
solid angle of a cone, formed by directions for which w is constant,
then

<7 ae
d2 = au f sin dS a BS 5 oo (U5)
du
0
Now by (12) we have
2
har na bz ON
jw) = — fe iel dp,
0

and with a view to (15) we may write for this

JW) = — de (=) :

T° V,*cosd, \ du Ju=u
The solid angle d@, of an infinitely small cone with axis OQ may
be found in the following manner. We imagine the wave-surface W,
passing through P, and the polar surface R of W with respect to
a sphere of radius unity. Then the point corresponding to P will be
the point of intersection Q of OQ and A. Further we take a point
P’ on OP prolonged, close to P and describe from P’ the cone
tangent to W. The normals drawn from QO to this cone will lie on
a second cone and this is the locus of all directions for which u

has the constant value

( 741 )

OP

—— cos wv,

OP
The infinitely small cone of normals will intersect R in a curve
lying in a plane, normal to OP; the plane touching £ at the point
Q is also normal to OP. Let these last two planes, which are
therefore parallel, cut OP in S’ and S. Then

GS>GOR AOS) OP = 13

and
u == OS’. OP cos F,
du, = — SS'. OP cos 3, .
Further
cos O
d2, = —— do,
0 OQ:

if do is the infinitely small surface of the just mentioned plane curve.
But we have also

do = 2n Vo, 0’, SS
if g, and 9’, are the two principal radii of curvature of Ff at the
point Q. Combining the obtained equations we find therefore

de EE TT
Wid Er OQNOP ~

1
or since OP =r and 00 == OP cos 0) indo
d2 IE
— = —2arV 0, 0, 0s’ 9,,
du u=Up
so that
yu,—h eo V.
fla) cos(gu,—h) na, bet Anr org seo? de —® cos (gue li)

TN T?V,? cos 9,
or by (13) and (14)

F cos (gu, —h) nabs, t Y¥0O,9', cos 9, 27 r

as) = — cos (: — )
g 1 5 Fe ib Po

if p, is the velocity of propagation of the ray OP, as it is defined
for plane waves. Thus the electric force appears to have the same
direction as it has for plane waves whose corresponding rays coincide
with OP. Its magnitude is given by

eee Thay tT VO, Qo cosy ad (-— ae
J Po

Anr

[3 Vo”
$ 11. We must add to this a second vibration which may be
obtained by the composition of all wave systems due to the Y’-com-
ponents of the infinitely small vectors into which the original
E. M. F. has been divided. It is this action we have left aside in

( 7427)

$ 3; the total electric force produced by it is given by
nb Te, 0, coed, 27 r

= cos i= = ||

Tl T Pr

if we distinguish by the index 1 the quantities corresponding to the
second plane wave for which OP is the direction of the ray. The
magnetic force too has in both cases the ordinary direction and may
be derived from the electric force by multiplying respectively by

C=

¢ ¢¢os 7D, € ccosd,

Se SL ie
Pes Ve Pa Va
so that the flow of energy is given by
c cos & c cos }
S= AR a el Geen
or
RON LL r
C= TV, cos T t— a
nc? b?y,t7 0, 9', cos* 9, | an r
: cos ge
Ti ZE Pr

The mean flow of energy per unit time is therefore
(ee |= =? 0, 0’, cos® 9, a. b?,, T° 0, Q', cos® *:|
Iie et ves :
The amount of energy travelling outwards in directions lying
within the cone of rays do’, is
r © do.
We may finally observe that the cone of corresponding wave-
normals has a solid angle

S=

do = 0 9' cos* 9. r° do!
so that the total amount of energy radiating from the centre may
be represented by the integral

p= eae sae
Tt NAV at eaves
It is only in the case of uniaxial crystals that this integral can
be further calculated.

Geology. — “On brackish and fresh water deposits of the river Silat
in Western-Borneo.” By Prof. K. MARTIN.

(This communication will not be published in these Proceedings).

ennn

(March 22, 1906).

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,

PROCEEDINGS OF THE MEETING
of Saturday March 31, 1906.

Ce

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige

Afdeeling van Zaterdag 31 Maart 1906, Dl. XIV).

COENEN, 22 Se

J. E. Verscuarrerr: “Contributions to the knowledge of van per Waars’ ¢-surface. X. On
the possibility of predicting the properties of mixtures from those of the components”. (Com-
municated by Prof. H. Kameriincn ONNes), p. 743. (With one plate).

J. E. Verscuarrerr: “Appendix to the communications published in the meetings of June 28,
September 1902 ‘and October 31, 1903”, p. 752.

P. H. Scroure: “A particular series of quadratic surfaces with eight common points and
eight common tangential planes”, p. 754.

W. pe Sirrer: “On the orbital planes of Jupiter’s satellites”. (Communicated by Prof.
J. C. Kapreyn), p. 767.

Physics. — “Contributions to the knowledge of vax pur Waars’
w-surface. NX. On the possibility of predicting the properties
of imirtures from those of the components” By Dr. J. E,
VERSCHAFFELT. Supplement no. 11 to the Communications from
the Physical Laboratory at Leiden. (Communicated by Prof.
H. KAMERLINGH ONNEsS).

(Communicated in the meeling of January 27, 1906).

1. In the following pages I intend to show that the original
equation of VAN DER Waars
RE va:
rg ni Nn Ne (B)

v— bz v

P=

where is put
az = a,, (1—a)? + 2a,, (le) 4 a,, 2?

be = b,, (1—a)? + 2b,, 4 (la) Hb, 2?
and where also are made the simplified suppositions *)

1) Comp. Kamertinen Onnes and Zaxrzewski, Suppl. no. 8, Proc. Sept. 24,
904, p. 227.

52
Proceedings Royal Acad. Amsterdam. Vol. VIIL

Ba Varden nt Ora kb 47 Or eee (3)

represents pretty well the special properties of mixtures. In cases
where we have no observations of mixtures of two substances,
the formulae given above will probably enable us to predict the
properties of the mixtures of those two substances by means of the
d's and 4’s — i.e. the critical elements — of the components; this
circumstance might be of some use in the choice of substances
whenever one wishes to observe definite phenomena in mixtures.
From formulae (1) and (3) we derive the formulae:

Te Tie
. is = oi (1) + us a
V pce V Pok V Pik (4)
E ane i. |
t _ To (eee Ue
Pak Pok Pik

which express how the critical elements 7, and p‚p of the mixture
taken as homogeneous depend on the composition ; from these formulae
also follows, as we know, a linear variation of the critical volume
va. That the second of the formulae (4) agrees well with the obser-
vations has been shown by vaN DER Waats'). As to the course of
Ver, the curve denoting the variation of that quantity with # not
only deviates considerably from a straight line *) (VERSCHAFFELT
and Kersom derive even from their experiments a maximum for
Vek) but also the quadratic formula cannot be brought to harmonize
with the observations *).

Not too much importance should be attached to this deviation ofa
quantity so closely connected with 6*); of higher import it seemed
to me to investigate in how far the formulae (4) accurately represent
the critical temperatures and pressures, as in connection with the
law of corresponding states, of which the approximate validity may
be considered to be established, these quantities entirely determine
the conduct of a mixture. But also here, of course, we should not
strain our expectations too high.

,

2. First I have computed from formulae (4) the values of the

quantities :

) Proceedings Nov. 1897.

2) Comp. KAMERLINGH Onnes and Rewaanum. Gomm. no. 59d, Proc. Sept. 29, 1900;
Brinkman, Thesis for the doctorate, Amsterdam 1904, p. 73.

8) Ibidem; comp. also Verscuarrerr, Gomm, Suppl. N°. 5.

4) For the possible causes of that deviation comp. BRINKMAN, loc., cit, p. 75.

(745 )
1 (dT or Ti por Tir por
a= —— | — }] = 2— — — — iI
Tor \ de J, Tor pik Tok Pik

5 1 (5 ke ) a Tik ( Pok be)
— = SS a ae ae ae Wh |
pok \ de Jo Tok Pik Pik

namely for those mixtures for which the « and 6 had been already
derived from the observations by the application of the law of cor-
responding states. The computed values are given in the following
table; the values in brackets follow from the observations.

(5)

CO, with CH,Cl «= 0,363 (0,378) B — — 0,149 (0,088)
CH,Cl with CO, ==10.270/(= 0.991) 0,068 (0,281)
CO, with H, —=10:978:(— 1,219) — 0,439 (— 1,645)
CO, with O, — 0,513 (— 0,6563) — 0,242 (— 1,0871)

Of principal importance are here the signs of the « and 2, and
in this respect there is a good agreement, when we except the 8 for
CO, with CH,Cl; I must remark, however, that from the experiments
of BRINKMAN a negative B is derived for this mixture *).

3. With the derived values of « and 8 we now, using the formulae
constructed by Kersom and me, might compute the quantities
delen dp.
p ‘Pxpl Ae
(Se : and others; but as our principal concern is the
0

dx dx

signs of those quantities, it is superfluous to perform these com-
putations. In fact, we immediately obtain a survey of the pro-
perties of the mixtures with a small proportion of one of the
components when we draw the values of « and 8 as I have done
before’); this time of course in a diagram, based no longer on the
empirical equation of state used then, but on equation (1). It is
still easier, by means of the formulae given in Comm. Suppl. n°. 5
(Proceedings May 30, 1903) to express the « and 3 in KortEwse’s*)
x and y, and then to use his diagram which, as is known, is
based on the original equation of state. Thus we find that the points
(a, B) — or (x,y) — lie exactly in the fields which correspond to the
properties of the mixtures; here also, therefore, the investigation has
a favourable result.

4. I shall now communicate some computed values of 77, and px
for the mixtures under consideration, and compare them with the
values derived from the observations. (See following table).

1) Loe. cit., p. 73; comp. also the table on the following page.
2) Comm. Suppl. no. 6, Proc. 30 May 1903.
3) Proc. 31 Jan. 1903.
52e

( 746 )

CH,Cl—CO, (BRINKMAN)

Computed Observed
Tok | pak Ta | pak
x—=0 (pure CH,Cl) 46.2 65.93 416.16 | 65.93
2 402.4 66.54 398.56 | 65.73
4 388.4 | 67.20 384.26 | 66.89
} 360.0 68.74 351.88 | 69.19
3 332.2 | 70.70 324.96 | 71.06
z=1 (pure CO,) 304.2 | 73.40 304.16 | 73.40

CO,—Hy (VERSCHAFFELT)

x=0 (pure CO,) 304.7 | 73.6 304.7 73.6
0.05 2899 | 72.0 287.8 68.4
0.01 275.2 70 2 273.6 63.5
0.02 | 245.7 66.4 248,7 54.8

“— (pure Hi) | 38.5 | 20 38.5 20

CO,—O, (KEESOM)
z=0 (pure CO,) | 304.02 | 72.93 304.02 | 72.93
0.4 998.6 | 71.47 | 985.68 | 67.70
0.2 273.0 69.24 272.92 | 67.30
x=1 (pure 0.) | 154.2 50.7 154-200 IE SOM
HCI—C3H, (Quint)

z=0 (pure HCI) | 3243 | 84.13 3924.3 | 84.43
0.1318 318.6 | 76.44 315.5) ONS
0.4035 | 310.9 | 64.89 303.0 boe
0.6167 307.2 57.75 299 4 58.6
0.7144 306.2 55.17 998.8 | 55.7
=d (pure C,H,) 304.9 48.94 304.9 48.94

On the whole the computed course of the Fr and p,, agrees
fairly well with the observations. The only important discrepancy is
that from the observations of mixtures of HCl and C,H, there follows
a minimum for the critical temperature, while the computation would
not have predicted this circumstance. This minimum, however, is not

very strongly pronounced; therefore I have investigated whether
perhaps the computation had predicted it for mixtures of NO and
C,H,, for which the minimum critical temperature is probably much
lower than that of the components. I really find on the side of ethane,
the component with the lowest critical temperature, « = — 0,019,
hence a negative value, which renders the existence of a minimum

critical temperature necessary.

>. After having shown by means of these few instances the
usefulness of formulae (4) for our purpose, I shall now closely
examine the course of the eritical lines, in order thenee to deduce
which conditions must be fulfilled by the critical elements of the
components, in order that the mixtures may show definite phenomena.

The shapes of these curves in the p7Z’ diagram have been deduced
by van per Waars from formulae (1) and (2)*) with the single
simplification 6,, = 4 (4,, + 4,,). What we shall find here will there-
fore be a special case of the more general forms found by vaN DER
Waars, namely the transition between the two cases a?,, > a, dy,
and a? < d,, dao, investigated by him.

ak Pxk 5
If we put VS and == — and moreover introduce the new

ok Pok
variable za, we may in our case write the equation of the
critical line:
zr (Wal) — ax (2, —1,) rr, Var)=0. «-. (6)

In the zr diagram therefore the critical line is a portion of a
hyperbola (see tig. 1), except when a, =r,, for then it is a portion
of a parabola (represented in fig. 1 by OAB; a straight line in the
pT diagram), and when z,=1 or Wa, == et, for then it is a
straight line (CD and OF).

In our drawing (fig. 1) one of the components always lies at the
point A, and we see that the form of the critical line is only deter-
mined by the relations ae and DÉ Besides, when we move the

Ok Pok
second component along one of the critical lines, the shape of that
line remains unchanged. *)

Fig. 1 therefore represents the forms which the critical line can
adopt in our ease. In order to show that the observed forms agree
with these in a satisfactory way, I have drawn in the same figure
1 the critical lines derived from the observations. The lines for

1) Versl, Kon, Akad, Nov, 1897.
*) As van pen Waaus (loe, cit.) has remarked in general,

( 748 )

mixtures of CO, with CH, Cl and of HCl with C,H, are drawn
twice in it, one time with the one component, the other time with the
other component at A. Of the lines for mixtures of carbon dioxide
with hydrogen or oxygen we could draw only a small portion in
the neighbourhood of carbon dioxide (point A).

These critical lines fit into the system of curves in a satisfactory
way, except the line CO,—O,. Also the beginning of the line
CO,—H, fits well into the diagram, but its further portion, if it is
to terminate at the point H,, cannot but deviate strongly from it.

6. The drawing of fig. 1 enables us also to determine how we
must choose the pure mixtures in order that the mixtures may
possess definite properties. “Van peR Waats (loc. cit.) has pointed
out the circumstance that the course of the critical lines (even when

Dee A, 4,,) excludes the existence of a maximum critical tempe-
rature or of a maximum or minimum critical pressure. Yet mixtures
occur which show') a minimum critical temperature, and in our

case we find as conditions for its existence *):

x, +1, >27, War, and also > 2 V/a.
The area, within which the second component must lie, if the
critical temperature is to reach a minimum for one of the mixtures,
is therefore bounded by the two curves

33
wT 22—2? and r= ——_,,
2z—1

represented in fig. 1 by OAF and GAH respectively. The first
line is one of the critical lines, namely that which has a vertical
tangent at a; the other contains all the points of the critical lines
where the tangent is vertical. It may be easily seen that the second
component must lie between those two curves, i.e. in the fields 2
and 8. On the strength of this we may predict that in general a
minimum critical temperature will be observed when the critical

1) The elements of the mixture for which the critical temperature is minimum,
are here determined by :

oh gg VD mn Va)
Amt AT tnt = 4 T,
—t, (a, —t.)®
Vy (a, +1,— 21, Wa.)
Wint VA
Wat) mt)

*) The general conditions for the existence of a minimum critical temperature
are given in the Molecular Theory of van DER Waats.

( 749 )

temperatures of the components differ little and the critical pressures
differ relatively much. It is known that experience confirms this
conclusion.

7. Now L shall try to find how the substances must be chosen
in order that one of the mixtures near the critical circumstances may
show a maximum — or a minimum — vapour pressure. At the critical
point (at the same time plaitpoint) of that mixture we then have,

He : Trt Upsk dp
RONG IE OAN —— (al
Prk IT rk k

As we have based our speculations on the original equation of

Ot
the value which follows from this equation, i.e. 4. Thus we find*)
that the area within which the second component must lie, is
bounded by the curves :

3 òp
state of vaN DER Waars, we must, strictly taken, use for (Ge)
k

D+?

Co 4 ean
2 ( ) PTA
represented by OAZ and KAL respectively in fig. 1. KAL is again
the critical line which shows at the point A itself the property

: 4 A : tdx
mentioned above, while OA/ combines all the points where -— = 4
adr
dz Eek F .
or mz, = 2. The second component must be situated between these
T

two lines, namely in field 3 or 4. ~

We may repeat that in order to observe the property under con-
sideration, the pure substances must be chosen so that the critical
temperatures differ little, but the values of the critical pressures
differ relatively much; however, the component with the higher
critical temperature must also have the higher critical pressure ®.

1) The elements of the mixture, of which the vapour pressure is maximum
or minimum, are given by

nit 20, Var Va Sr, pats Va,
mp 2 (x,—1,) Wart) ’ i nr, 1
9 (V2,—1) it Va)
TE f
ln |

?) The general conditions for the existence of a maximum or a minimum vapour
pressure have been derived by van per Waars (Versl. Kon. Ak. 1895/96).

My quotation of van Laar in the Dutch edition (same note) resulted from a
misunderstanding.

5) The latter does not always hold good, as for instance with mixtures of
CO, and CoH; (kuenen, Zeitschr, f. physik, Ghem., 24, 681, 1897),

(750 )

Hence a minimum critical temperature and a maximum vapour
pressure are two phenomena which as a rule oceur together, but
not necessarily; this is only the case in field 3.

From fig. 1 it appears that, according to our reasoning, only
a maximum vapour pressure is possible; yet we know that there
are mixtures which show a minimum vapour pressure, and it has
been proved by Kurnen’) that this phenomenon occurs even under
the critical circumstances. Here it seems that there is a fundamental
deviation from the observation. Nevertheless it is remarkable that
the mixtures which show a minimum vapour pressure are always
of such kind that at least one of the components is an anomalous
substance’); so that there is reason to suppose that with mixtures
of normal substances a minimum vapour pressure never occurs ; and
our speculations, which are based on the law of corresponding states,
are applicable to normal substances only.

8. Starting from the same suppositions as set forth here, van LAAR *)
has found an accurate expression for the projection of the plaitpoint
line on the vz-plane. I have tried to derive from this the equation
of the plaitpoint line in the p7’— hence also in the zt — diagram *),
but without success. Without therefore occupying myself further with
the general form which the plaitpoint line in our case takes in the zr-
diagram, 1 shall investigate a few points, namely the occurrence of
a maximum or a minimum plaitpoint temperature, and that of a maxi-
mum or a minimum plaitpoint pressure.

According to Krrsom’s °) formulae (2a) and (25) we have

Ina an tart ee j
De ine ae 2 [r, (3 inl) zer dt, Val
wh 0 Ld 1
ee (U)

il dpxpl ul 72 4/7 2 9 is =

oa oe == [z; (3 Vm, lk — 40,7, (9 VYx,—1) a da, |
Pok dx 0 A, J

bs d AT yp)

Tip
el and <Ois
av

Hence follows that the boundary between

formed by the curve:

1) Arch. Néerl., (2), 5, 306, 1900 (Livre jubilaire de H. A. Lorentz).

2?) For the bibliography of this cf. Harrman, Thesis for the doctorate, page 84,
Leiden 1899.

3) Proceedings April 22, 1905. /

4) By eliminating & and v between the equation of the vx projection of the
plaitpoint line, the equation of the spinodal surface (van Laan’s formula 6, loc,
cit.), and the equation of state,

9) Communication no, 75, Proceedings Dec, 28, 1901,

J. E. VEE
of

a4

J. E. VERSCHAFEFLT. “Contributions to the knowledge of VAN DER WAALS’ J-surface. X. On the possibility

of predicting the properties of mixtures from those of the components.”

Fig. 1.

Proceedings Royal Acad, Amsterdam. Vol. VIII.

boi )

42°
“ot Gey

represented in fig. 2 by the branches BAC and OD; to the left of
Topl
Av
component with the lower critical temperature, in other words: if
we put t,>1, there must be a minimum plaitpoint temperature
when the second component lies in the area AGCABDHA; in
general this will again occur when the critical temperatures differ
little, whereas the critical pressures differ much?). This does not
prove, however, that there may not be other circumstances for which
the plaitpoint temperature reaches a minimum.

If on the other hand we take A as a component with the higher
critical temperature, there must be a maximum plaitpoint temperature
when the second component lies in the area OHKX.’*) Neither here
is it proved that the phenomenon is restricted to that area.

it

<0, to the right > 0. If in consequence we take A as the

il Dap
9. The boundary between — aps = mon O and — = <0 is formed by the
curve
t? (82—1)? — 2rz* (5ze—1) 4+ 424 = 0,
dp xpl

=e is negative within that line and
ar

represented in fig. 2 by MAF;

positive beyond it. Whence follows that a minimum plaitpoint pres-
sure is impossible, at least little probable, while a maximum plait-
point pressure must occur when the second component lies within
the area ALKAF tT OMA; this will therefore in general be the
case when the critical temperatures differ much, which is confirmed by
experiment.

10. Finally, in order to show by means of an example that the
suppositions whence we started in the main represent precisely the

i) Cf. also van Laar, loc. cit., p. 585.

2) This is again the same condition as for the existence of a minimum critical

t ture; but as ESE : (6 — 42)?, d Topi be positive witl
emperature ; a a Es == 4 = 4 SSS tie: e€ positive w
P THN de Je 16 TEA st) ahi’

negative z, in other words: a minimum plaitpoint temperature requires a minimum
critical temperature, but not reversely. This may also be seen from fig. 2, where
I have once more drawn the line GAH of fig, 1 (dotted line),

8) An instance of this is probably not to be found,

course of the plaitpoint elements, I shall give here the results of a
computation which | have executed for CO, and H,.

x = 0 (pure CO.) Trp) = 304,1 Pop eee
01 295,8 90,8
0,2 287,4 108,7
0,3 274,8 124,8
0,4 260,4 140,0
0,5 244,3 153,9
0,6 22281 162,9
Di 194,0 164,5
0,8 157,0 152,5
0,9 108,8 115,2

#1 (pure Hs) 38,5 20

The course of the plaitpoint line resulting from this agrees with
fig. 9, plate 1 of Harrman’s Thesis for the doctorate; in reality,
however, the maximum of the plaitpoint pressure will lie much higher.

Physics. — “Appendix to Communication N°. 81”. (Proceedings
June 28 and September 27, 1902) and Supplement N°, 7
(Proceedings Oct. 31, 1903). By Dr. J. EB, VERSCHAFFELT.
Supplement N°. 12 to the Communications of the Physical
Laboratory at Leiden. (Communicated by Prof. H. KAMERLINGH
ONNES).

(Communicated in the meeting of January 27, 1906).

In the expression which I have given before (Comm. N°. 81 and
also Suppl. N°. 7) for the function y in the neighbourhood of the
plaitpoint an inaccuracy has remained. I have found that I have

neglected therein more than a mere linear function of w.

Vv
w = free + wy,

where J)’ represents a very large volume, then wy is the free energy
in the perfect gaseous state, with the exception of an error which
will be smaller as V itself becomes larger, and which vanishes
when we put V=o.

The first term of y, which depends on v, may be dissolved in the
following way:

If we write:

: (753)

Vv » V
Tk
fp dv = | pdv + fpdv.
v v i aT

r

V
The first part I have developed before, and X =e dv—RT log V

Th:

(V =o) is the w-function which has then been wrongly left out of
account. This function cannot be developed in the same manner as
the first integral, because the series used for that is no longer con-
vergent for large volumes; we must therefore turn to KAMERLINGH
ONNEs’ empirical equation of state.

When this equation of state is written in a reduced form, it also
represents the reduced equation of the isothermal of the mixture w,

”

at the reduced temperature t= —, so that
ak
V
V vat
vi pdv = Pak af Vay) —
UTE VI
ak
¥ 5
= RF (log Vlog vr) — = pat vr & zi) LS pat i= 2s =)
Hence the neglected z-function is:
eg,
: A? UTk Ae vin

and this may be developed again:
X= X, + Xe — er) + X, (w — ar)? +.....

where the co-efficients X,, X,, X, ete. are still functions of tempe-

rature. Fortunately the neglection of that function X has not influenced

the results in first. approximation; however in the formulae 4, 5,

12 and 13 of suppl. N°. 7 we have to add 2X, to the factor
RT

at, (1—aj)

754 )

Mathematics. — “A particular series of quadratic surfaces with
eight common points and eight common tangential planes.”
By Prof. P. H. ScHourr.

1. “In our space are given a fixed line and four projectively
related plane pencils of rays. To be found the common transversals
of the fixed line and a set of four corresponding rays.”

Notation’). We indicate the fixed line by @°, the vertices and
planes of the pencils of rays by O,, O,, O,,O, and ay, @,, a,, a@,,
four corresponding rays and their two transversals by LL, ll,
and /,/’, the pencils of rays themselves by (/,), (l,), (4), (l,) and the
pairs of points of intersection of /,/’ with each of the rays /,, 0,,/,, ¢, by
(SS) (95195), GS,, S',), (S,, S',)- Farther! the symbols NN
may represent the lines of intersection of the pairs of planes
(hy Gay (Gkig Cy to a (C5 Ge

2. The order of the locus of the pair of transversals J, /’ is easy
to deduct from its section with a@,, which consists of two parts: the
locus [(S,,,S,')| of the pair of points (S,,S,') and some generating
transversals. Each ray /, of the pencil (/,) containing a single pair
of points (S,, S,’), the locus [(S,,S,')] is an hyperelliptic curve the
order of which exceeds the number of times a transversal passes
through O, by two. Now three transversals pass through O,. By pro-
jeeting the pencils (/,), (/;) out of O, on a, we find namely in a, three
projectively related pencils (/,), /',), (/,) and now three times three cor-
responding rays /',,/,,/, pass through one and the same point, the
conies generated by the pairs {(/,), (/,)] and [(/), (/,)] having besides
O, three more points in common. So the locus [(S,, S',)] is a curve
c,° of order five having in QO, a threefold point; its genus is three.
Now that three transversals pass through QO, there must be according
to the principle of duality he three generating transversals in a.
And indeed, the peneils (/,), (/,), (Z,) do describe on the lines /,,,, /,,,,
,,, three projectively ne series of points (A,), (A,), (A,) where
three times three corresponding points A,, A,, A, lie on the same
right line a, the conies generated by the pairs [(A,), (A,)] and [(A,), (A,)]
possessing three more common tangents besides /,,,. So the total section
of «@, with the locus of the pair of transversals /,/ is a system of
order eight and this locus itself a scroll O* with a nodal curve of
order eighteen. The order of the nodal curve ensues even from the
fact that the surface O* must correspond in genus to c,°; moreover

1) For notation and reasoning see a former communication,

(755)

the eighteen points of intersection of the curve with @, are easy to
indicate.

The obtained surface (* is intersected by the given line / in eight
points. So in general there are eight lines resting on / and on four
corresponding rays /,, lll.

3. In the preceding we have assumed that four corresponding
rays /,, 1, U, 7, always admit of two common transversals, not
taking into account the possibility that four corresponding rays
have an hyperboloidie position. In the general case this singularity
does not occur; for the condition that four lines are situated hyper-
boloidically is a threefold one and the number of corresponding
quadruplets of rays is only singly infinite. However, this does not
prevent a proper selection of the data trom leading to projectively related
pencils with a quadruplet of corresponding rays lying hyperboloidi-
cally; to this end we have but to assume the points O,, O,, O,, O,
on four hyperboloidie lines /’,,/’,,/’,, U, and the planes a@,, a,, a, a,
through these same lines, and to fix the projective correspondence in
such a way that these four lines correspond.

If the case of four hyperboloidie rays /’,, l’,, /’,, /’, really occurs,
the scroll O* of the lines intersecting these four rays belongs to the
locus under consideration; we have thus further to investigate whether
this ©? joins the surface O* of the general case or whether this
surface breaks up in this special case into the surface 0? and a
completing surface O°. At the outset only the first possibility occurred
to me and I contented myself with developing grounds why this
elevation of the order of the locus from eight to ten need not really
clash with the wellkwown principle of the conservation of the number’),

Although at first sight it seems rather absurd that the infinitesimal
small difference between four nearly and four perfectly hyperboloidie
rays should rule the locus obtained by means of the remaining
quadruplets so as to let us find in the first ease an V* and in the second
an O*, yet as will be proved directly the second of the two sup-
positions mentioned above is the right one, not the first; so in that
sense this paper has had to be modified.

The surface O? of the common transversals of any hyperboloidic
quadruplet /’,,/’,,/’,,/’, contains these lines and so it must admit
of a transversal through each of the vertices O,, O,, O,, O, and in
each of the planes «,, a,,@,,a@,. The deduction of the order of the
locus O* has shown that through each of the four points 0 three

1) See for this a corresponding case of apparent contradiction in my “Mehrdimen-
sionale Geometrie", vol. I, page 263.

( 756 )

transversals pass and likewise there are three in each of the four
planes «. Hence the question, whether besides the scroll 0? a surface
O* or a surface O° presents itself, can be decided by the fact whether
the four generators through the points O and the four generators
in the planes @ are common to the two parts of the locus or not.
Now, as a matter of fact, those two parts can have but two gene-
rators in common, viz. those two common transversals of /’,, /’,, U, /,
joining the preceding pairs of transversals and the following of the
adjacent quadruplets. So the eight indicated transversals of U’,, 1’,, ’;, U’,
are not situated on the other part of the locus and consequently the
latter is cut by each of the planes @; according to a curve c* with
a node in QO; and two right lines; so the remaining part is a surface
O* with a nodal curve of order nine. For the scroll O* of genus
three appears instead a combination of a regulus O? and a seroll O°
of genus one cutting each other in two right lines and a twisted
curve of order ten.

From the preceding follows immediately what will happen when
the singularity of the hyperboloidie quadruplet presents itself more
than once. If two of those particular quadruplets are at hand O*
breaks up into three parts, two quadratic reguli and a scroll O*
with a twisted cubic as nodal curve; so the latter principal com-
ponent part of the locus is of genus zero and has with each of the
two quadratic surfaces two generating transversals and a twisted
curve of order six in common. If the projectively related pencils
contain three hyperboloidie quadruplets O* breaks up into four
quadratic reguli, three of which answer to these quadruplets whilst
the fourth, really the locus, is supplied by all the remaining qua-
druplets; the latter surface is intersected by each of the others
according to the edges of a skew quadrilateral, whilst these three
intersect each other in general according to twisted curves of order
four. And if there are four hyperboloidic quadruplets, as will
appear later on, all quadruplets are situated hyperboloidically; then
the case presents itself where the order of the locus, so far always
eight, becomes infinite.

4. The following simple example will show that it is not difficult
to choose the data so as to allow each quadruplet of corresponding
rays to lie hyperboloidically.

We imagine the four pencils (/,), (/,), (4), (/,) situated in the four
sides of a cube (fig. 1), we assume the vertices O,, O,, O,, O, of
the pencils in the centres of these sides and we allow those rays
1, /,,4, 4, to correspond which form the same angle g with their

2 6

projections on the plane through the four vertices when one keeps
in the same direction. To each quadruplet of corresponding rays
belongs a hyperboloid of revolution with OZ for axis and circle
O,0,0,0, as minimal circle (“cercle de gorge”), whilst the hyper-
boloids of revolution belonging to the various values of y, touching
each other according to that circle, form a tangential pencil as well
as an ordinary one. Each of those surfaces presents itself twice as
bearer of two reguli corresponding to two supplementary values
of g. In this case is a rule what was an exception above; here
the number to be found is infinite, as two lines satisfying the con-
ditions pass through each point of /’, the two generators of the surface
of this peculiar pencil passing through this point. Indeed, the case
of an infinite number of solutions makes its appearance even as
soon as there is only one hyperboloidie quadruplet and / is at the
same time director ray of the regulus determined by this quadruplet
as director rays; then through each point of / passes only one
line satisfying the question.

To simplify the representation the preceding particular case has
been taken on purpose as regularly as possible. The principal thing
is what the figure retains after a projective transformation, that
namely the vertices 0,, O,,0,, 0, lie in the same plane, that the
planes «,, ¢,,4@,,a, pass through the same point and that all quadratic
surfaces touch those planes in the vertices mentioned above; the
regular situation of the four vertices on the common minimal
circle is of secondary importance. —

This leads us to a new question, viz. whether it is impossible to find
four projectively related pencils of rays where each quadruplet of

( 758)

corresponding rays has hyperboloidie position, the vertices not lying
in the same plane, the bearing planes not passing through tbe same
same point and those planes not being touched in those vertices by
all quadratic surfaces herewith generated. Analytically as well as
geometrically we can convince ourselves in a simple way of the
reverse.

With respect to a rectangular system of coordinates O (XYZ) the
four pairs of equations.
y=perq| —y=prt+q y=—perq| —y= PETA
greats)’ —2=raets)’ ei z=—rets
represent four lines /,, /,,/,,7, with hyperboloidie position. For the
conditions under which the surface

av? + by? + cc? =1
contains one of those lines are
a+ bp? +er?=0, bpqg Hers=0, bq? Hes? =1,

any of the four lines being taken. Now these lines /,, /,, 7,7, hang
together in such a way, that by a rotation of 180°

round the axis OX the lines Jj, and / and likewise the lines lg and J, pass into each other.

OV os ly eo a, hp
OF MIER TLE Re ae ene NE

If now in a plane a, the line /, describes a pencil of rays with
O, as vertex, the lines /,, /,,7, will describe the pencils obtained by
making the pencil (/,) undergo a rotation of 180° round the axes
OX, OY, OZ, where the four vertices O,, O,, O,, O, will not lie
in the same plane, and the bearing planes will not pass through the
same point. And then is also excluded that the planes a,, «,, @,, a, are
touched in O,, O,, O,, O, by the generated quadratic surfaces. For two
quadratic surfaces touching each other in four points not situated in
one and the same plane coincide and the surfaces under consideration
do not.

Let us consider geometrically a more special case connected with
a regular tetrahedron. We siart from a cube and take (fig. 2) one
of the two groups of four not adjacent vertices A,A,A,A, as vertices
of this tetrahedron. Then the faces A,A,A,, A,A,A,, A,A,A,, A,A,A,
of this tetrahedron are the bearing planes a,, @,, a,,a,, the centres
of those equilateral triangles are the vertices O,, O,, O,, O, of those
pencils. And the rays 2, /,, 7, corresponding to an arbitrary ray /,
of the first pencil are found again by a rotation of 180° round
the lines OX, OY, OZ through the centre of the cube parallel
to the edges of the cube, which are at the same time the connecting
lines LE, FF’, GG' of centres of pairs of opposite edges of the

Fig. 2

tetrahedron. From. a simple inspection of the figure appears that
the three points, in which any of the faces of the tetrahedron is cut
by the corresponding three rays lying in the other faces, are situated
on the second asymptote of the hyperbola passing through the three
vertices of that face and having the fourth corresponding ray lying
in that face as an asymptote. So this ensues inter alia for the face
A,A,A, from the three relations:
ACRO 9) ALON == IDA. ABBA.

So already four lines rest on /,, /,,/,,7,, namely one in each face,

which proves that the lines /,, /,,/,;,/, have hyperboloidie position.

6. We leave our original problem for an other moment in order
to investigate first the series of quadratic surfaces furnished in the
last special case under consideration by the quadruplets of corre-
sponding rays. All these surfaces have eight points in common, the
four vertices O,, O,, O,, O, of the pencils and the four points O,,
O,, O,, O, symmetric to these with respect to the common centre
O; so they belong to the net N, of the quadratic surfaces deter-
mined by seven of those eight base-points O;, forming in their turn
the vertices of a cube. We can likewise point out eight common

53

Proceedings Royal Acad. Amsterdam. Vol. VIII.

( 760 )

tangential planes, the four planes «,, «,, @,, @, of the pencils of
rays and the planes a,, a@,, @,, @, parallel to the former and sym-
metric to these with respect to OU; so those quadratic surfaces are
a part of the tangential net N, determined by seven of those eight
base-planes «;, enclosing together a regular octahedron. So our series
of surfaces being formed by the surfaces common to V, and N,, can
be regarded as the intersection of those nets.

The tetrahedron of which the origin ( and the points X,, Y., Ze
at infinity of the axes of coordinates are the vertices is common
polar tetrahedron of all surfaces of the two nets N, and A. In
connection with this .V,, has instead of a single infinite number of
cones six pairs of planes, a pair through each of the edges of the
tetrahedron, and MN, contains instead of a single infinite number of
surfaces reduced to conics six pairs of points, a pair on each of the
edges of the tetrahedron. So we find the most general projective
trausformation of the series common to V, and N,, by starting from.
an arbitrary tetrahedron, an arbitrary point and an arbitrary plane
through this point and by then representing to ourselves the surfaces
having the given tetrahedron as polar tetrahedron, passing through
the given point and touching the given plane.

We prepare the deduction of the three characteristic numbers of
our series of surfaces by determining the locus of the points of contact
with one of the eight base-planes, say a. By considering the indicated
relation

A.C, = CA, , AD, == DA, . AB BER
between the two lines /, and /, (fig. 3), in which a, is cut by the
quadratic surface belonging to /,, we find immediately that B,, C,, D,
on A,A,, A,A,, A,A, describe projective series of points when /,
rotates round 0, and that /, envelops a conie described in triangle

( 761 )

A,A,A,; by determining for each of the pairs of projective series of
points on each of the bearers the point corresponding to the point
of intersection of the bearers reckoned to belong to the other series it
becomes evident that this conic touches the sides in the centres, so that
it is the inscribed cirele c?. The point of contact being the point of
intersection ZL, of /, and /,, the locus of this point is at the same
time the locus of the point of intersection of the corresponding rays
of the pencil (/,) of order one and the pencil (/',)? of order two
formed by the tangents /, of c?‚ thus a curve c* of order three with
O, as node and the tangents from (Q, to c’, i.e. the isotropic lines
through O, as nodal lines. This curve represented in fig. 4 touches
the sides of the triangle A,A,A, in the centres and has the points at

infinity of the sides as inflectional points; the inflectional asymptotes
run parallel to the sides at distances of four ninths of the height.
In normal coordinates its equation with respect to triangle A,A,A, is
ENEN > 2) — a DN
whilst the Pliicker numbers are
NZ 5 dal ~ ee,
ih ee a ib Oe
As is known we mean by the three characterizing numbers of a
simple infinite series of surfaces the numbers u, », @ indicating
successively how many surfaces of the series pass through any given
53*

point, touch any given line, touch any given plane. From the following
will be evident that in our case these numbers are 3, 6, 3.

All the surfaces of the net V, with the eight base-points O;, passing
moreover through any ninth point 0,, form a pencil with O as
common centre and OX, OY, OZ as common axes. Each surface
of that pencil touching one of the eight base-planes a; touches them
all, so it belongs to the series. A pencil of quadratic surfaces con-
taining three surfaces touching a given plane, we find w= 3.

All surfaces of the net MN, with eight base-planes a;, touching
moreover an arbitrary ninth plane @,, form a tangential pencil with
QO as common centre and ON, OY, OZ as common axes. Each
surface of that tangential pencil passing through one of the eight
base-points O;, contains all these, so it belongs to the series. So 9 = 3,
as three surfaces of a given tangential pencil pass through a given
point.

The number of surfaces of the series touching an arbitrary line
of the plane A,A,A, is three, because this line cuts the locus of the
points of contact (fig. 4) in three points. As the line is assumed in
a common tangential plane, each of those three cases counts twice;
so v = 6, as is immediately confirmed analytically.

So the indicated series of quadratic surfaces is a series (3, 6, 3).

Indeed, we also obtain a series with eight common points and
eight common tangential planes possessing the same characteristic
numbers (3, 6, 3) when starting from a common polar tetrahedron,
a point and a tangential plane not passing through this point.

7. We have two more points to consider with respect to our
original problem. Firstly, we wish to point out how the case in
whieh O*® breaks up into four quadratic reguli is easily realised ;
secondly, we must show that all quadruplets of corresponding rays
have hyperboloidic position as soon as this is the case with four
of those quadruplets.

When the original part of the locus O* is a regulus 0? the pairs
of transversals of the quadruplets of corresponding rays are the pairs
of generators of this regulus arrayed in a quadratic involution. If
such a quadratic involution of pairs of rays is cut by a plane situated
arbitrarily a quadratic involution of pairs of points is generated on a
conic; this involution is as one knows characterized by the property,
that the connecting lines of the points completing each other to a pair
pass through the same point. To realize the above-mentioned case of
decomposition of the loeus O* we start from an arbitrary regulus
VY’, whose generators we regard as paired off in involution in a

€ 163)

definite way, and from four arbitrary planes @,, @,, ¢,,.¢,- If then the
pencils of rays in those planes lying perspectively to the quadratic
involutions of points of the sections are taken as the projectively
related pencils of rays of the problem, then the surface (? is evidently
the integrating part of the corresponding surface O%, so this must
really also be completed to a surface of order eight by three other
reguli O°. To conform this we allow an analytical treatment to
follow this geometrical consideration.

We suppose the locus proper 0* to be decomposed into its genera-
tors by means of the equations

p+4q=0

r + das =0
and we assume that the generators belonging to 2== 0 and to 2 =
represent the double rays of the quadratic involution on (®%, i.e. that
in this involution the rays with the same absolute value of 4 correspond
to each other. Here p,q,7,s are general linear forms in w, y, 2,
according to the formula

BA ar Ue a wre = di no OSR

whilst the three planes of coordinates « = 0, y = 0, z = O and the plane
at infinity will do duty for the planes @,, @,,@,,a@, of the pencils of
rays to be found. The tracing of these pencils is simplified by repre-
senting the minors of the determinant

Py Ps Ps Ps |

A= Ja Ya Ist Je
ust rs U 3 Ms
| 8) Ss Sa 34

according to the elements pi, gi, 7: , si by Pi , Q: , Ri, Si
If we perform the described calculation with respect to the plane
uv =O, there is occasion to represent the equations
(Pa + 493) ¥ + (Ps + 29s) + Ps + AQ, = 0
(pe 4st @:; a2 483)! 2 =. 2 as, 0
determining together the point belonging to 4 of the conie of the
section, for shortness’sake by

(p + 49), =0
(rv + 23), = 0 |
Then

(Pf Ah PM + 4a) SO ses GL)

( 764 )
is an arbitrary line through point 4 and
Pat geurode) 5 PstAds Fu (ts +A Ss) 5 Path qe (rs tai ss)
Pa—A UES 1 jC 1 Pate a

Ts A83 8 T; A 8s À r,—As,

is the condition expressing that this line (1) through point 2 contains
at the same time the point — 2 and is thus the ray of the pencil
looked for, corresponding to the parametervalue 2. If for shortness’
sake we write here

| pit Ag: + ulmi + As) |
Pi — 2G: | == (I).
| WE Asi |
direct calculation affords
| Pi == Ang; | | % + As;
| pi — AQi | kj 7 — 238; ==)
| i À s; | Di 2 Qi
or
| Pi | vr;
qi | == Sy => 0,
| Ti — dS; | Pi — AG
or
ese aa
qi | —2) | 8; | + Au | 8; | == (i),
ri | dee i | | |
Ien
hee S, + Arle f
Q, JAP,

so the equation of the ray under consideration is

(GEAR) tag), EAR ae
which is reducible to
(Q, P ar S, 7), zi 2° (Ee q ste R, 8); = 0,
as the coefficient of the first power of A identically vanishes.

If now, for w= p,q,7,s, we understand by az, u, Uz, Uy the forms
into which w,2-—+u,y—+u,v+u, passes by omitting successively the
term with w, the term with y, the term with z or the constant term
and if 4 is substituted for 4? the four projectively related pencils are
represented in their planes by the equations

( 765 )
SLES Q, Pr HS rr +k CB Gk 0 \
45 S, ry = hk (AE, dy J- h, sy) ==) |
TET es OR Sn (Page = Ress) — 0 he
Mt. Q, Po ie S, Ve, = hk: ay To in Kh, 8) =!

For which values of / have these four rays hyperboloidie position ?

LES Oo,
(2)

To this end it is necessary and sufficient that the points at infinity of
I, I, UI lie on a right line. So for 4 we find the eubie equation:

0 » Q pst Si rsh Pi gst R, so), = Qi pet Spretk (Pigs Ri 52) |
je [Qe pst-Sorgh (Pa qa+-Ro s3) |, 0 > Qp+ Sanh (Ps Rosy) TO
| Qs pxt-Sprabk (Ps qo Rs 82); —[ Gaprt-Sar +k Pan H-Basi)], 0 |

So in reality three reguli have separated from the surface O*.

8. Finally we have still to indicate that all quadruplets of corre-
sponding rays lie hyperboloidically if four quadraplets do. This proof
we join on to the most general case of four arbitrary planes «a,
a,,a@, and four arbitrary points O,, O,, O,, O, in them. If A, A, A,
(A)
(/,) describe on the sides A,A,, A,A,, A,A, the projective series of
points (C), (D,), (B) possessing for /—=4 four triplets of points on
the same right line. In that ease the conics enveloped by the connect-
ing lines CLD, and D,B, have five common tangents, i.e. A,A, and
the four lines bearing corresponding triplets of points; then those
conics coincide. So the supposition of four such triplets leads to the
case that there is an infinite number of such triplets. But then in

is the face «‚ no longer equilateral, then the projective pencils (/,),

each of the four planes a,, @,, @,,@, lies a common transversal of
each corresponding quadruplet, ete.

We now conclude by showing that in order to determine four
projectively related pencils of rays with merely hyperboloidie qua-

druplets the four planes @,, @,,a@,,@, and the four vertices O,, O,,

4
O,, O, in them can be taken arbitrarily by showing that to aray /:
drawn arbitrarily in a, through ©, only a single triplet of rays
lll, of the remaining pencils corresponds, forming with /, four
lines with hyperboloidic position crossing each other.
If u‚r,eo represent successively the conditions that a quadratic
surface contains a point, touches a line and touches a plane, then
1
4
indicates according to Hurwitz the number of surfaces through an
arbitrary line, which satisfy the sixfold condition V, (Math. Ann,
vol, 10, page 354), So the number of quadratic surfaces through /,

Vp — 3y? (u + 0) + (3p? + 20 + 307) — 2(u* + 0°)

( 766 )

containing the points 0, 0,, 0, and touching the planes «,, @,, a,
is represented by

I
= weg? {2v" — Br? (u + 0) +» Bu? + 0 + By) — 2(w + Oh,
which in connection with the law of duality can be deduced to
1
= u'o' fy* — 3uv? + 3u7v + uro — 2u*}.

Out of the wellknown results (H. Scnupert, “Kalkül der abzählenden
Geometrie”, Leipzig, Teubner, 1879)

grot = 104, u*y?o° = 68, u've’ = 42, u r0 = 34, Ori
we find that there are five quadratic surfaces satisfying the given
conditions.

However it is now easy to see, that only one of those five
solutions furnishes four hyperboloidie lines /,, /,,7/,,7, crossing each
other. We find namely four solutions not to be used for our purpose
(fig. 5) if we determine /,,/,,/, in such a way so as to cut the given

P € 767. )

line 7,, or when having taken one of these three lines in that manner
we choose the other two in such a way that they both cut this
new line. So there is only one solution, in which the four lines
lll, 2, eross each other.

From the above consideration which can easily be confirmed
analytically ensues that the supposition of four planes «; given arbi-
trarily and of four vertices QO; given arbitrarily dominates the case
of four projective pencils of rays with merely hyperboloidie qua-
druplets to such an extent that the projective correspondence is fixed
by the condition of the hyperboloidic position. This now again includes
that the case of the three quadruplets with hyperboloidie position,
treated above in details, cannot present itself if the planes «; and
the points O; have been taken arbitrarily. For these three quadruplets
must also put in an appearance if we wish all quadruplets to have
hyperboloidie position, and they determine the projective relation
unequivocally, i.e. three hyperboloidie quadruplets lead here to pure
hyperboloidie quadruplets.

Not to get too redundant, we put aside the examination of the
less remarkable series of quadratic surfaces, answering to this most
general case of four pencils of rays with merely hyperboloidic
quadruplets.

Astronomy. — “On the orbital planes of Jupiter's satellites’. By
Dr. W. pe Sitter. (Communicated by Prof. J. C. Kaprryy).

The following pages contain a condensed summary of the results
of an investigation, which will soon be published in detail in the
“Annals of the Royal Observatory at the Cape of Good Hope”.
The material on which this investigation is based consists entirely
of observations made at the Cape Observatory, viz. :

1. Heliometer-observations made in 1891 by Gin and Finnay,
discussed by me and published in my inaugural dissertation. *)

2. Photographic plates taken at the Cape Observatory in 1891,
measured and discussed by me.

3. Heliometer-observations made in 1901 and 1902 by Cookson,
discussed by himself and published in Monthly Notices, June
1904 p. 728—747.

4. Photographie plates taken in 1903 and 1904, measured and
discussed by me.

1) Discussion of Heliometer-Observations of Jupiter's Satellites, Groningen J. B,
Worrers 1901,

( 768 )

My aim with this investigation was exclusively the determination
of the inclinations and nodes of the orbital planes of the satellites
and of the motions of these nodes. The plates of 1903 and 1904
were taken in order to provide a second epoch from which these
motions could be determined by a comparison with the observations
of 1891.

The fine series of observations, made by Mr. Bryan Cookson in
1901 and 1902 increases the weight of this determination considerably.

I have already pointed out, in the fourth chapter of my disserta-
tion, that the determination of the other elements, which must be
derived from the observed (jovicentric) longitudes, is probably suffi-
ciently provided for by the observations of eclipses. Moreover from
the observations mentioned above sub 1. and 3. a// elements were
determined.

Eelipse-observations are however not well adapted for the deter-
mination of the inclinations and nodes, which must be derived
from the observed latitudes, as I have shown, l.c. page 77. The
principal interest of the determination of the orbital planes lies in
the comparison with the observations of the large motions of the
nodes, which are demanded by the theory. Since these motions are
produced almost exclusively by the large polar compression of the
planet, the natural fundamental plane to which the latitudes must
be referred is the equator of Jupiter.

If we refer the positions of the satellites to a system of co-ordinate
axes, of which the axis of y is the projection on the sphere of a
line perpendicular to this fundamental plane (i. e. of Jupiter’s axis
of rotation), and the axis of w is the great circle through the centre
of the planet perpendicular to the axis of y, then for the determina-
tion of the inclinations and nodes the y co-ordinates of the satellites
are alone important. Only these co-ordinates have therefore been
measured. The plate was, by means of the position-circle with which
the Repsold measuring machine of the Astronomical Laboratory at
Groningen is provided, brought approximately in the position-angle
P+ 90°, where P is the position-angle of Jupiter’s adopted axis
of rotation. The plate then has a motion parallel to a straight line,
which nearly coincides with the axis of , and which is defined by
the axis of the cylinder which guides the plate-holder in its motion.
The co-ordinates perpendicular to this straight line were then measured
by the micrometer screw. These differ from the co-ordinates y only
by small corrections (refraction, orientation and scale-value). In this
method the measured quantities never exceed a few revolutions of
the serew, All errors of résean-lines, division errors of the scales,

( 769 )

error of projection, ete. are avoided. The straightness of the cylinder
was repeatedly tested by comparison with a stretched spiderline.
Its errors are certainly smaller than 0.2 micron. The position-angles
were read off by two microscopes, and the orientation of the plate
was determined from a pair of standard stars, which were for this
purpose photographed on each plate, and from trails of the satellites.
The errors of observation of the measures of the satellites are satis-
factory, distortion of the photographic film cannot be detected, and
the discussion of a dozen plates, which were specially taken for this
purpose, shows that the determination of the orientation from the
trails is always practically free from systematic errors, while the
same can be said of the determination from the standard stars under
certain conditions, which are however not always fultilled. The
accidental errors of both determinations are very small.

The image of the planet has not been measured. The observed
co-ordinates contain therefore an unknown additive constant (different
for each separate plate), which was eliminated by using in the
subsequent reductions the co-ordinates referred to the mean of all
the satellites occurring on the plate as origin. The equations of con-
dition and normal equations for these relative co-ordinates are very
simple and symmetrical. The limited space at my disposal prevents
me however from entering into more details regarding the measures
and reductions. I will at once state the results.

The unknowns which were determined from each opposition were
the corrections to the adopted values of the elements p and q of
the four satellites which are defined by the formulas:

paisn(— $b)

g =2c0s (— GM)
where 7 and 9, are the inclination and ascending node of the orbital
plane of the satellite referred to the fundamental plane. The longitude
of the node is counted from the ascending node of the plane of
Jupiter’s orbit on the fundamental plane. The quantities referring to
the four satellites are distinguished by the suffixed numerals 1 to 4.

The following table contains the results of the different series of
observations with their probable errors.

The values for 1891 (Heliometer) are those derived in my disser-
tation with a few unsignificant corrections in the last decimal places.
The results from the heliometer and those from the plates have been
combined with the relative weights 2 and 1.

The results for 1901 and 1902 are quoted from the communication
by Mr, Cooxsoy in the Monthly Notices,

I have however been compelled to reject Ap, and Ag, for 1901

(#10)

189175 1891.75 1891.75
Heliometer. Plates.

oO 5 o le}
Ap, | + 0.0409 + .0052 | + 0.0372
|
Ap, | 40404 36 |: 407334 360 |) 4) OB
3 | — 00AH 19 | — OO

Ap, | + 06424 12 | + 068 12 | + 0644 ° 9

+

20050 | + 0.0897 + 20038

Ap, | — -0033

H-

ag, | — 0.0259 + .0056 | — 0.028 + .0061 | — 0.0959 + °.0043

ag; | He soes | “ae costs’ 5 Oe

Ags | 068 90 | — 0784 B OE

ag, | — .0187 4 49, | = OS tie ee OE

1901.61 4902.62 | 1903.79 1904.89

| COOKSON. COOKSON. | Plates. | Plates.
Ap, + 0.0170 + 0077/4 00137 + 0072/4 0°o021 + °co6o|— 020028 + °0078
am ANB BO 0922 + HU OLH BB} OI A
Ap, |— .0148 + 36— .0072 + 28/— .0199-+ 22|— OM + 98
ap, | .0456 + 48+ .0658 + 15/4 0687 + 121 OH 48
ag, |— 0.0695 + .0084|— 0.0755 + .0065|— 0.0597 + .0048|— 0.0335 + 007
agg | A710 + 40 1860 + 0-210 + SJ MIL 48
Aq, |— 060 + 33— .0334 + B .049% 4 W— OMG + 2%
Ag, |— .0859 + A8— .0070-+ A4 .oosk + 44|— 02004 47

and 1902. Cookson found from the reduction of his observations
that the residuals could be much reduced by assuming in the latitude
of satellite IV an inequality of which the period is one half of the
periodic time of the satellite while the coefficient is about 50". I
have searched for this inequality in the observations of 1891, 1903
and 1904 and I ean confidently declare that in none of these years
there is even the slightest trace of any inequality of which the argu-
ment should be a multiple of the mean longitude of Sat. 1V. Since
also an inequality of this nature cannot be explained by the theory
I cannot but doubt its reality, and since the cause which has produced
this apparent inequality must necessarily also have affected the
determination of p, and q,, the safest course seemed to be to reject
the values of these elements found from the observations of 1901

(CAA)

-and 1902. All other corrections Ap and 4q derived from the obser-
vations are included in the following discussion, with weights in-
versely proportional to the squares of their probable errors and
corresponding to a p.e. of weight unity of + 0.°0050.

Before this discussion can be related the theoretical expressions
for p and q must be developed.

At the time when the analytical theory of the satellites was created
by LAGRANGE and Larrace, the eclipses were practically the only
phenomena of the satellites which were observed. For these the
natural fundamental plane is the plane containing the axis of the
shadow-cone, i.e. the plane of Jupiter’s orbit. This was accordingly
used by them. SovurLart, in his theory published in 1880, followed
their example.

The first thing which must be done before the theory can be
compared with modern observations is thus to reduce the expressions
for the latitudes referred to Jupiter’s orbit to latitudes referred to the
equator. This has already been done by Martu, who in 1891
published tables for the computation of the co-ordinates of the satel-
lites, based on SoviLiart’s theory (Monthly Notices, June 1891, pages
505—539).

Let J and N be the inclination and node *) of the orbital plane
of one of the satellites with reference to the orbit of Jupiter.
SoviLLarT’s theory then gives

Brain = > bijsin0; + u: wsin 6,
jl
; Ae ye @
I; cos N; = = bijsin0; + wi w sin G,
j=l |
In these formulae w and @, are the inclination and node of Jupiter’s
equator on its orbit. All longitudes are counted from the first point
of Aries. The quantities bj are constants, and the angles 6; vary
proportionally with the time. Of the constants 4; four only are
mutually independent. If we put:
— Yi bij = Gij Yj »
then the y; are constants. The multipliers oj; and u; and the coeffi-
cients of the time in the expressions for 6; are given by the theory
as functions of the masses, the compression of Jupiter and the mean
motions. The constants 6; are small numbers (the largest is 043 — 0.1944)
with the exception, of course, of those in the diagonal, 6; = 1. The
value of u; differs little from unity. The angles y; and 6; are what
Larracr calls the “inclinaisons et noeuds propres” of the satellites.

1) With node I mean ascending node, unless otherwise stated.

(27)
Let now om, and ws, be the inclination and the longitude (counted
from the first point of Aries) of the descending node of the plane
which I wish to adopt as the fundamental plane, referred to the
plane of Jupiters orbit. Longitudes in the fundumental plane are
counted from the node y, as zero.

Then if ¢ and gy are the inclination and node of the orbit of one
of the satellites referred to the fundamental plane, we have, neglecting
quantities of the third order in 7, Z and w‚:

isin $4 = I sin(N—Y,,)
1cos My = LI cos (N—y,) + w,

If further we introduce the notations

T= yw, — 6; w= yp, — 0, + 180°
v= yi sin TD; vt, = W sin W Re (2)
Yi yi cos Fi Yo = W cos YW —W,
then the expressions for p and q become:
ae = WGE Le 7 |
ae RG)
w= 45; Yj + (1 — Hi) ©, — Bi Yo |

MartH has adopted

w, = the value of w

WS ees » G4, + 180°
and has computed the values of p and q by the formulae (3), taking
Cie:

The unknowns y;, [%, x, and y, must be determined from the
equations (3). This is, of course, only possible if the coefficients
6; and w; are known. I have adopted these coefficients from
SOUILLART’s theory, as being the best available. They are very com-
plicated functions of the masses, the compression of Jupiter, and the
mean motions. As a rough approximation, we can say that the
coefficients 6 are proportional to the mass mj. Since the masses are
very imperfectly known, the same thing is true of the coefficients of
the equations (3). Therefore the results of the present discussion cannot
be considered as final, but the discussion will have to be repeated
when better values of the coefficients are available. The results here
derived will however doubtlessly represent a very fair approximation.

It may perhaps be mentioned that the uncertainty of these coeffi-

from SourLLart’s theory, *)

1) Marru has made one or two mistakes here, which will be duly mentioned
in the detailed publication, but as they have no influence on the result they can
be ignored at present.

(tee)

cients is not due to our ignorance with respect to the masses alone.
The values of these coefficients derived by Soum art from the same
masses and elements by two different methods of integration show
differences of such amount, that the consequent differences in the
computed values of p and qg are of the order of the errors of
observation. It is hardly to be expected that this defect in the theory
will be remedied before the equator is introduced instead of the
orbit as the fundamental plane of the theory. The coefficients adopted
by Marta and myself are those derived from the second method
of integration, which is also preferred by SoumLarr himself.

In the following discussions these coefficients are treated as absolute
constants. If we denote the corrections to the adopted values of
wv; and y; by dw; and dy;, then the unknowns

dw; Oy; % Yo
must be determined from the equations

= 64 Ox; — Wid = A pi | (4)

= 65 dyj — Hi Ye =A gi
The term (1 — u;)w, in the second equation (3) must, of course,
be treated as rigorously known.
The solution of the equations (4) is conducted in the following
manner. I define the quantities Aa; and Ax; by the equations

POs va Ai
ey a so o (8)
= 6; Ay; =Agqi

These equations are solved once and for all, and the solution is:

A x = = oj A p; | (6)
A yi = 265 Ag;
Further, if we put:
wi = = OF Wy
then the equations of condition become:
ee,
Syi — Wi Ye= gi

Next, if we denote the originally adopted values of 2; and y; by

vj, and y;, so that %=a;, + Oei, W=vi dyi, then the equations
become:

Ui — wi &, = Lio + Aa, (8)
Yi — Ui Yo = Yin + Ayi
In these equations 2; and y; are defined by the equations (2), where

dT;
the y; are constants, and T= 1%, + = (Lt). The unknowns, which
¢

<-

(774)

must be determined from the solution of the equations (8) are
dT;
wey Oe, iy Oey U SSS
2 dt

The values of = for the four satellites are however not mutually
independent. The theory gives these differential coefficients as functions
of the masses of the satellites and the compression of Jupiter. The
masses need not be considered here. I have tried to determine a
correction to m,, but this determination had too small a weight to
have any real value. The influence of the other masses is even
smaller.

The compression enters into the formulas through the factor Jb?,
where J is the well known constant, which is approximately equal
to o—'/, m (9 = ellipticity of the free surface, g = ratio of centri-
fugal force to gravity at the equator of Jupiter) and 5 is the equatorial
radius *) of the planet. '

If we introduce as unknown:

db?
==
Jb?
then the true values of the coefficients of ¢ are

dy ay;
dia Oa eds ae arg

The coefficients a; depend practically alone on the mean motions,

‘ dT;
and must be treated as absolute constants. They differ little from —

itself, and consequently the ratios of the motions of the nodes must
be considered as approximately constant. The adopted values accor-
ding to Souruart’s theory are (daily motions):

ir AT
EE ~-* | — 0°.007019
dt - dt ;

ar in
St) — 0°.033010 24 | — 0°.001898
dt 5 dt A

The 86 equations (8) thus contain the 11 unknowns

Yi Hi Do Yo %

These equations must be solved by successive approximations. The
conditions for the application of the method of least squares are far
from being fulfilled.

These approximations have been conducted in the following manner.

1) In the original Dutch 4 was erroneously stated to be the diameter, instead
of the radius.

Bree
(775 )
Let #,, 7, be approximate values of 2, and #,, thus 7, = Boo + de,
and y, = 7,, + dy, We have then:
vj — pil dw, = wi, + Levi + i! w,, |
Yi — pi Dy, = Yin + Ayi Hi yy,
If we suppose that the approximation «,, 7,, is already so good
that dv, and dy, can be neglected, then these equations become:

yisin Ty = vi, + Ax; Hui! 2,,
Yi cos FE = Yio + Ay, + ui! Yoo
Next I compute the quantities g; and G; from the equations:
gisin Gs = avi + Aaj Hui ee, |
gi 008 OF; = yp + A yi Hui Yoo
The other unknowns are then determined from the equations:

se ces 2())

eee (10)

eave ciety
te EE
dr

IRD. — a (t—t,) — G; + owe Ke We (12)

dr;

If these equations give constant values for y; and values of
dt

which can by an acceptable value of x be made consistent with
the theory, then the appromation is sufficient, if not, then a new
approximation must be made. As a first approximation I have assumed:

a

oo = Yoo = 0.

The equations (12) were then formed and solved. In this solution

|

dT:
I have determined the values of 7 for the four satellites separately
: 4

without introducing the theoretical ratios ab initio. The equations (12)
then consist of two sets for each satellite and each of these 8 sets
is independent of all others. The residuals which remain after the
substitution of the resulting values of the unknowns will be given
below together with those from the other solutions. The probable
error of unit weight was + 0°.0086.
The motions of the nodes in this solution are (Sol. I):
dT. ar,

== = 0%,01218 — = 0°.00587
dt dt
In dr,

dl = 0°,080266 —' = 0°.00189,
dt dt

If these are compared with the theoretical values, it appears at
once that their ratios are very different. The node of satellite I,
which according to the theory has a yearly motion of about 50°, in
this solution shows a motion of about 5°. The ratios of the three

54
Proceedings Royal Acad. Amsterdam. Vol, VIII.

( 776 )

other motions also differ considerably from their theoretical values.
Moreover the inelinations are far from constant, as will be seen at
once from an. inspection of the residuals A y.

a a 9 .
It must be mentioned that the value of a agrees approximately
(

with the value derived by Cookson from the observations of 1891,
1901 and 1902. This could have been expected since Cookson in
this determination also neglected the corrections to the position of

: am
the equator. The difference between CooksoN’s value of on and the

value of Sol. [ is not due to a bad agreement of the observations of
1903 and 1904 with those of 1901 and 1902 (which on the contrary
agree extremely well), but to the fact that in Sol. I the corrections
to the elements of the other satellites were eliminated by means of
the transformation from Ap and Aq to Ar and Ay, while Cookson
did not eliminate these corrections but neglected them.
I have now made a number of further solutions, in which I started
with approximate values w,, and y,,, and introduced the unknowns
Vi Fi,
thus rigorously subjeeting the motions of the nodes to the theoretical
condition. The unknowns dy, and x are badly separated. The
weight of the determination of x is considerably diminished by the
introduction as unknowns of the corrections to the position of the

JS x, JS 7, x,

equator. That this must of necessity be so, is easily seen. If we had
observations of only one satellite at two epochs, it would be impossible
to determine both the motion of the node and the equator. We
would in that case have only four data (the values of p and ¢ at
each of the epochs) for the determination of the five unknowns

dr ; : : : :
a x, and y,. Now x is practically determined from satellite
dt . r

II alone. The motions of the nodes of III] and IV are too slow,
and the inclination of I is too small, to allow a determination of
the motions of the nodes of these satellites to be made, the accuracy
of which would be even remotely comparable to that of sat. IL.
The motions of the nodes of I, HI and IV are derived theoretically
from that of II. If therefore the latter is known, each of the three
others provides a determination of the equator. Then the determina-
tion of x from II must be repeated with this new position of the

Von

used this method, but he rested content with the first approximation. His corrections
to the equator derived from satellites [IL and IV are in the same direction as the
values found by me,

(CST

The solution was not actually made in this way, but all equa-
tions were treated simultaneously. This consideration is only given
here to point out that the position of the equator is ultimately
determined by the condition that it shall be the same for the four
satellites, i.e. that the inclinations shall be constant, and the motions
of the nodes shall be consistent with the theoretical ratios. Since a
small displacement of the equator has a large influence on the
motions of the nodes, in consequence of the small inclinations, it
can be expected that the unknown z and the quantities which
determine the position of the equator will mutually diminish each
others weights. (That this decrease of weight is actually much more
marked in the case of y, than for «,, is accidental and depends on
the choice of the zero of longitudes).

By these considerations I have been led to try whether the value
of x could not be determined from a comparison with other obser-
vations. I have used the values of 6; for 1750 given by Dreramsrr.
A value of * was adopted, such that the value of 6, carried back
to 1750 from the modern observations would be nearly equal to
the value given by Detampre. The unknowns «,, ¥,, dy; and dT,
were then determined from the modern observations alone.

This gives solution VII. In solution VI on the other hand all
unknowns (inclusive of x) were determined from the modern obser-
vations. I give below the results from these two solutions, which I
consider as the best that can be derived with our present knowledge
of the masses. I do not venture to choose between the two solutions.
Probably au eventual correction of the coefficients 6; will tend to
reconcile the two solutions.

Instead of I; I give at once 6; =y, — I. The values are given
for 1900 Jan. 0 Greenwich Mean Noon.

Solution VI Solution VIL — Adopted values.
z, — 0°.0172 + °.0023 —0°.0177 + .°0022 0
Yo, + 9 0427 + .0043 +0 .0489 + . 0022 0
x — 0.0321 EE .0094 — 0.0126 0
Y. 0°.0259 + °.0032 0°.0248 + .0038 0°.0013
Ya 4696 + 27 4676 + 24 4694
1; „1926 + 40 1874 + 26 ‚1789
Ys 2540 + 34 „2504 + 25 „2254
6, 540,4 + 8°.5 54°.0 + 8°8 392-5
6, 293 .42 + 0.35 293 .10 + 0.29 273 32
6, 319.68 + 0 .77 319 .67 + 0.80 330 .59
6, 14 .40 + 0 .91 Toro Gr O55 7 ar

( 778 )

10
From the values of x we find the following values of =

=
10 2 :
el — 0°.13664 —. 0°.13932 — 0°.14105
a
10
en — 0 .032105 — 0 .032633 — 0 032974
dô, ee aes wa is
ae — 0 .006814 — 0. 006916 — 0 .006983
dé, oars
= 0 .001839 — 0 .001854 — 0 .001863
at

From the values of a, and y, we find for the inclination and node

of the equator on Lrverrimr’s orbit of Jupiter of 1900-0 :
wm —-8°.1107 + “0043 3°-1169 + °.0022 3°.0680
6 315.727 + ‘042 315.7385 =, 041 315.410 ;

With the exception of x all unknowns in the two solutions agree
within the sum of their probable errors, and with only one excep-
tion (y,) all the corrections to the adopted values are many times
larger than their probable errors.

The residuals of the two solutions VI and VII are given in the
following table together with those of Sol. I. The probable errors,
which have been added for comparison are somewhat larger than
those of the observed Ap and Aq, because by the transformation
from Lp and Aq to Ow and Ay, the p.e. must be somewhat
increased, even if we consider the coefficients oj as absolutely exact.

The p.e. of weight unity, which was + 0°.0086 for Sol. I, is
+ 0°.0065 for Sol. VI and + 0°.0064 for Sol. Vil. But it is chiefly
in their consistency with the theoretical conditions, that both solutions
are incomparably better than Sol. 1. The inclinations are now constant
within the probable errors. The residuals of the nodes only show a
systematic tendency for Satellite I (in Sol. VII, where the motions
of the nodes were not derived from the observations, also for Sat. II).
Still the agreement with the theoretical motions is much improved.
The value of E derived from Sol. VI irrespective of the theoretical

a
conditions would be 0°.1250, while the value corresponding to the
value of x in this solution is 0°.1366. This is a great improvement
compared with Sol. I (0°.0121).

The results for Sat. HI in 1901 and 1902, which in all solutions
eave large residuals, have in the solutions VI and VII been rejected.
This rejection has no appreciable influence on the values of the
unknowns, nor on the other residuals, but it reduces the p.e. of

(778)

Sol. J Sol. VI Sol. VHI
de

Ay sin AT Ay sin yAT AY sin yAT ,

1891 | +.0045 | —/0068 —:0003 | +:0005 H:0123 | +0047 -°0093
POO eee en don — SA 49 3 “401 |= 6g) Je 99
E OMEN Se SS 5 OE ve Sion
GE ere coe tr 99) = apes a ga, cate
DE A Aa gg te ag) rR

1891 | +.0030 #20138 ++.0002 | 4.0017 —.0008 | 4-.0016 4.0045
1901 | GO ts 137 — 240 | ee OES Ser ts 8
7 DE En EE Tae aan Soes + 29
DE a) oe KE Verken Wickens Nae, ae 400
04 | + 50 | SS PE Ne ONE | = Ag e108

|
1891 | +.0020 | +.0048 +4.0007 | — 0014 —.0029 | —.0013 —.0037
_)490f | = (40) -| — 437, = 33 |[— 478] [— 29]|/(— AS 24]
= 02 + 0 |— 14 — Te Ae B A en
5 B + B |F 32 + Ti MH 56 | + 10 + 62
DEE Ee OEE DE | 4h pees
|

1891 | +.0010 | —.0010 +.0001 | +.0013 —.0028 | +.0017 — .0031
1901) + 20 I BIJ 188]\[— 101][-+ 205) [— 1101 [4 200]
02; + 20 |[— SB 195]/[— s3}[— 466]|(— BSI 174]
Bosi i BRE Krt G40 =) = Teme
Ob ieee ORN AE = GO 80) .< ONE ERA

weight unity from + 0°.0072 and + 0°.0073 to + 0°.0065 and
+ 0°.0064 for the solutions VI and VIL respectively.
The values of 6;. carried back to 1750 are:

Sol. VI

Sol. 1
6, 151°.8
A, 282 .9
6, 110 .3

252°.4
333 .0
114 .2

Sol. VII Damoiseau Delambre
281°.0 282°.0 283°.3
338 .6 398 .0 BONED
AUT Gil Ba ea 105 .0

( 780 )

In conclusion T must express my deep sense of gratitude towards
Sir Davin Gur, who liberally placed the observations of the Cape
Observatory at my disposal, and was always ready to meet all my
wishes,

2

(April 24, 1906).

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,

PROCEEDINGS OF THE MEETING
of Friday April 27, 1906.

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige

Afdeeling van Zaterdag 31 Maart 1906, DI. XIV).

© ORNE Ne eS:

L. Bork: “On the relation between the teeth-formulas of the platyrrhine and catarrhine
Primates”, p. 781.

F. M. Jarcer: “A simple geometrical deduction of the relations existing between known and
unknown quantities, mentioned in the method of Vorer for determining the conductibility of
heat in crystals”. (Communicated by Prof. P. ZEEMAN), p. 793.

W. Burex: “On plants which in the natural state have the character of eversporting varieties
in the sense of the mutation theory”. (Communicated by Prof. J. W. Morr). p. 798.

H. Srraur: “The uterus of Erinaceus europaeus L. after parturition”. (Communicated by
Prof. A. A. W. Husrecut), p. 812.

P. Zeeman: “Magnetic resolution of spectral lines and magnetic force”, (Ist part) p. 814.
(With one plate).

JAN DE Vries: “Some properties of pencils of algebraic curves”, p. 817.

H. ZWAARDEMAKER: “On the strength of the reflex-stimuli as weak as possible”, p. 821.

Anatomy. — “On the relation between the teeth-formulas of the

platyrrhine and catarrhine Primates”. (Communicated by
Prof. L. Bork).

(Communicated in the meeting of March 31, 1906).

Among the anatomical characteristics by which the Primates of

the New-World — the platyrrhine apes are distinguished from
those of the Old-World — the catarrhine apes and man — the com-

position of the set of teeth takes a first place. They are charac-
terized because they possess in the upper and lower jaw one milk-
molar with premolar, which replaces this, more than the latter.

In simplified writing the set of teeth of catarrhine Primates may
be rendered by the following formula:

55
Proceedings Royal Acad. Amsterdam. Vol. VIII,

( 782 )

ell Gee
Zn alens Demets ee
PN EE
OEREN

in which the teeth of the permanent set of teeth are written with
a capital letter.

For the majority of the platyrrhine Primates the following formula
holds true :

DT WE KG Bib WEE
ANN ip ot WE
io Ih Os 8s Gime @) JUL
Yih, Al Go Gh 72

This last formula is only applicable to the family of Cebidae,
whereas the Hapalidae differ from them because they have a molar
less, so that the formula for their set of teeth becomes as follows:

PRES I, (Goi 2
he Ie has PP We
PY Oa Wey ak Ge PA WL
Wath, NAG By IE

The difference however in the set of teeth between Cebidae and
Hapalidae is for the present of less importance, the significance of
it will be shown later on. In the first place the attention should be
fixed on the principal difference between all platyrrhine Primates
on one side and all catarrhine ones on the other, i.e. the occurrence
of only two milkmolars and premolars with these and of three milk-
molars and premolars with those.

It is not doubtful that the set of teeth of catarrhine apes and of
man must be deduced from one that was composed like the set of
teeth of the now living Platyrrhines with three molars, so compared
with the set of teeth of those, the set of teeth of the catarrhine
Primates may be considered as reduced, the total number of teeth
is larger with the former than with the latter. In what way has
this reduction of the set of teeth come about, this is a question
which has been frequently put and which has been answered in diffe-
rent ways. An obvious conception is certainly this, that a milkmolar
with his replacing tooth, the premolar, has become lost. But which
of the row has disappeared? This question has been answered in
different ways. Whereas the Anthropologists in general are more
of the opinion that the last milkmolar and premolar have been
linked out, zoologists, palaeontologists and anatomists accept the view

( 783 )

that it has been the first, so that which follows immediately on
the caninetooth. The two opinions have in common that they link
out a milk molar and its replacing tooth from the continuity of the
tooth row. On account of this the two theories may be distinguished
as the excalation theories. I cannot agree with any of these opinions,
it appears to me that the reduction has been brought about in another
way, but this can only be explained more fully,’ when I shall have
brought forward what pleads for and what against each of the above
mentioned theories.

The Anthropologists look for their proof material, or perhaps more
exactly for the arguing of their theses in the variations in the set
of teeth, which occur with man. Of late DuckwortH among others
has again drawn attention to the fact that rudiments of a tooth, more
or less developed often appear between the last bicuspid tooth and
the first molar tooth especially in the upper jaw and what is especially
of importance, often on both sides. These rudiments are conical tooth-
points, now occurring single either on the inner or the outer border
of the alveolar margin, then again double on each of the two
borders simultaneously. And Duckworth does not hesitate to con-
sider these rudiments as the again visible traces of the linked out
third premolar: “on the whole we think that it is most reasonable
to adopt the view that they are aborted third premolars, which
constitute a human type of dentition similar to that of the New
World Apes’’). From the investigation of Duckworrn the following
must be mentioned. Firstly that the occurrence of these rudiments of
a third premolar is exceedingly different with the different races :
in 300 old Egyptian skulls he found no single case, on the other
hand in some thirty skulls of Australians he found these rudiments
seven times. The set of teeth of the natives of New-britam shows
this anomaly exceedingly often. With respect to the set of teeth of
the Anthropoids, DuckwortH mentions that with seven of the thirteen
skulls of gorillas, which he investigated, the rudiments in question
were present whereas on the other hand he found them nota single
time with Hylobates nor with Orang-outans or Chimpanzees.

The reasoning of those who think that the first milkmolar and
premolar, following on the canine tooth have fallen out, in the
passing from the platyrrhine form to the catarrhine form is of quite
a different nature. It is a fact which is generally acknowledged as
being true that originally the number of premolars of the primitive
Primates did not amount to three but to four; so that already the

1) W. H. L. Duckworrn. Studies in Anthropology. Cambridge 1904. p. 22.
55*

( 784 )

platyrrhines also, with their three premolars and milkmolars, possess
a reduced set of teeth, and indeed among the group, of the primitive
Primates which OsBorn puts together under the general name of
-+ Mesodonta, forms are found with which both in upper and lower
jaw still four premolars occur (+ Hyopsodus). According to the
investigations of Leene the number of four premolars has decreased
to three, because the premolar which follows immediately behind the
canine tooth — so the first or front of the row — has become lost.
As most convincing for this opinion of Lecur the set of + Micro-
choerus may count, where only three premolars occur in the upper
jaw, and still as many as four in the lower jaw, but of these the
first of the row has been reduced to a rudiment without function.
Where it is as good as proved that the reduction of four to three
premolars with the primitive Primates has been brought about by
the disappearance of the premolar following immediately behind the
canine tooth, where moreover we know that with other animals also
reduction of teeth may take place in this spot, there it is quite
comprehensible that the further reduction of four to three premolars
in the same place is localized. The difference between the two
explained opinions is easily made recognizable by writing down the
complete tooth formula of the primitive Primates and that of the
now living ones.

For the primitive Primates we get the following formula in which
the probably original number of /ncésivi has not been reckoned with :

JE De PR Ge Ne SEA ns Zare .
Telly Pare lay re eB NRE
TB USE a le app le 25 al Zion WG ll Ay Se
jh, WS BGS 5 VEA Ms Abs 8h. 25

For the Platyrrhines (Cebidae) the formula becomes :
ile We De GS le Jen Or De Bia. 4
dp Wee PGS ale Va aby JIG lS 5

Me Ve Dard. AM A Diese
DOED a. C5

B lly BS te
ite ile, Bs GE

is}
— 7
. .

According to the opinion of Anthropologists this formula becomes
for the catarrhine Primates:

TOL 724 5 Ss 2% OE
7 Der ol eres Bs She 0) 1 ae 2
ho RE TRE

ha Ì
te
bo
~
mi
hm S
o™ .
bo De
iss)

By We

so the milkmolars and premolars of man should be the original 2°¢
and 34,

According to the theory, mentioned in the second place, the for-
mula becomes :

JENS Bs Ge We JEE We Wee LE
eo Me PR es Te OOS BAR UE NS
LRT OM OPS MLR MER IES
Tee ene Wee On OR Se:

so that with man the original 3" and 4" milkmolar and premolar
would still exist.

The last mentioned opinion seemed to me also to be the most
acceptable. It pleads for it, that in a phylogenetically older stadium
the first milkmolar and its premolar had already become lost, and
if then one lets the second follow, the reduction-process is localized
and more continuity brought into it. The following can moreover
be said against the opinion of the Anthropologists, that the fourth
milkmolar and premolar with man should have been lost. It may
be justly supposed that only those teeth can reduce, which fulfill
the smallest function. And this now does not apply to the last milk-
molar and premolar. On the contrary. With the Platyrrhines we see,
that just that last molar does not only not stay behind by the others,
but is even the strongest developed of the three. So with those
forms, where we might with some right suppose at least some indi-
cation to a reduction of this tooth, we on the contrary find a pro-
gressive development. No single reason can be given why in the
middle of this toothrow a tooth should suddenly have disappeared,
and why a discontinuity of the set of teeth should have come about
by which the function would have suffered considerably, no single
indication can be found, neither in the ontogenetic nor in the full-
grown set of teeth, in the form of a diastem, that a tooth has really
become lost here, and so the first mode of explanation: that the
last milkmolar and its replacing tooth would have become lost, does
not seem probable to me.

But neither can the theory that at the passing from the platyrrhine
to the catarrhine type, the first milkmolar with the premolar belonging
to it, should have been linked out, satisfy me. The above mentioned
argument about it, is always only an argument per analogiam
without its being possible that a morphological proof for such a
reduction can be given. If the sets of teeth of Platyrrhines are com-
pared in particular with relation to the degree of development of
the first premolar nothing is found that points to a reduction of this

( 786 )

tooth, at least with the now living forms; on the contrary, the first
premolar is often stronger than the second (Cebus, Chrysothrix,
Mycetes, Hapale). Then not a single indication ean be observed in
the Ontogenese of the set of teeth of man, which indicates that a
tooth should have become lost behind the canine tooth, the papillae
succeed each other very regularly in their origin and place. Moreover
if it were right that a molar and a premolar became lost behind
the canine tooth the remarkable fact remains still unexplained, that a
rudimentary tooth appears so often between the first molar and the
last premolar.

So I cannot agree with either of the two opinions which prevail
now about the differentiation of the set of teeth of the Primates,
but I am of the opinion that it came about in quite another way.
To be short, my opinion about it is as follows: the set of teeth of
the catarrhine Primates has originated from that of the platyrrhines
by the disappearance of the last or third molar and of the last
or third premolar while the third milkmolar has lost its character
of temporary tooth and has become a permanent tooth.

This opinion is explained by the two following formulas. If we
overlook the original number of four milkmolars and premolars,
and number the elements of the platyrrhine set of teeth according
to their now present amount this set of teeth may be written
according to the following formula:

WEN CSTN ERE
We Une Cairdian re We Wlan Wl.
Oho. epe Oa nae iep Wns Wiha Wiles. ile

AEN

The eatarrhine set of teeth has originated from this, as P, and M,
have fallen away in the upper and lower jaw, whereas 1, becomes
M, in both jaws, by which as a matter of course M, of the
platyrrhines becomes M, of the catarrhines, the M, of the former
becomes M, of the latter. If it had remained the MZ, of the platyrrhines
would have become MZ, of the catarrhines. Those things are stated
in the following formula in which the reduced teeth are put between

parenthesis.

eh CEERD
Gao. ne OA Write Lilo Ml, Allee els
ie Lesions EA
LD OMEN BEEN:

So the differentiation of the set of teeth of the Primates is accord-

( 787 )

ing to my view more complicated than would have been the case
according to the two above mentioned excalation theories. ‘Two pheno-
mena may be distinguished in this process of development, namely
progressive development of one of the elements: 7, loses its character
of temporary element and becomes persistent, and the second pheno-
menon is the reduction of two other elements. These two elements
are at the extremity of each of the two tooth series, P, at the end
of the. series of replacing teeth, JZ, of the end of the series of
ihe teeth of the first generation. Contrary to the two above mentioned
excalation hypotheses I might distinguish the one defended by me
as the hypothesis of the terminal reduction. I shall try to show
the correctness of my Opinion.

If I let m, of the Platyrrhines become a persistent tooth, no
new principle is introduced into odontologie. For it is kwown to us
from other groups of animals that milk teeth may become persistent
teeth; I remind the reader of the Marsupialia, where but for some
exceptions the whole set of milk teeth has become a set of persistent
teeth except a single tooth. Furthermore to Erinacaeus, where according
to the investigations of Leeuw the so called persistent set of teeth
consists partly of milk teeth partly of permanent teeth. So my
opinion is nothing more than a new example of the tendeney also
observed elsewhere of a diphyodont set of teeth to pass into a
monophyodont. So against the principle as such there can be no
objection. :

As a first argument for the correctness of my opinion I state the
morphology of the milk molars in platyrrhines, L had the opportunity
of studying them from Hapale, Chrysothrix, Cebus, Mycetes, Pithecia
and Ateles. Without going into details it must only be mentioned here
that m, of the platyrrhines differs a great deal both in the compo-
sition of its crown and in the number of its fangs from m, or m,
and shows much resemblance to J/, of these apes.

lt is of much importance with this that m, is functionally a
higher developed tooth than its deciduous tooth P,, so that means
that at the moment that m, is replaced by P,, the set of teeth
becomes to a certain degree functionally inferior. So if m, becomes
persistent, this means a gain for the mechanism of the set of teeth.
This does not hold true for m, and m,, the replacing P, and P,
are functionally higher developed.

A second motive is derived from the development of the set of
teeth of the catarrhine Primates, in particular that of man. So according
to my opinion our first molar has passed from a milk tooth into
a persistent tooth in a relatively recent stadium, with the Platyr-

( 788 )

rhines it still belongs to the milk teeth. May this not be the
explanation of the fact that our first molar still breaks through
in connection with the teeth of the set of milk teeth, and still
before the appearance of the first replacing tooth, while the
second tooth appears only after a period of some years? By this
early appearance of our first molar it functionates indeed for
some time together with the complete set of milk teeth and so
according to my opinion the set of teeth of man still possesses in
this period a composition as in the first lifetime of the Platyrrhines.
Still more distinctly than from the time of the eruption this relation
appears when the first forming during the ontogonese is more closely
investigated. I derive the following about this from the wellknown
investigation of Rösr '). Between the 9" and 12% week of the faetal
development the papillae of the milk teeth are invaginated in the
dental band (Zahnleiste) which grows on uninterruptedly towards the
back, and already in the 17" week of the development the papilla
of the first molar is invaginated. So with man there is not the least
histogenetical discontinuity between the forming of the milk teeth
and of the first molar. Only after the course of a year, so
four months after the birth the dental band begins to grow on
towards the back and not before the 6% month after birth the
papilla of the second tooth is invaginated. So while J/, is formed
immediately after m, with man, a pause of about a year begins
after this first development. So both from morphology and ontogeny
arguments may be derived for the hypothesis that m, of the Platyr-
rhines is homological to J/, of the Catarrhines.

My hypothesis however still contains another element viz. the
reduction of P, and M, of the Platyrrhines.

Let us first consider the reduction of J/,. From my above men-
tioned deduction of the catarrhine set of teeth given in a formula,
follows that I come in conflict with a rather generally accepted
opinion that the three molars of the Catarrhines should be homo-
logue to the three molars of the Platyrrhines. According to my
opinion J/, of the Platyrrhines is homologue to J/, of the Catarrhines,
M, of those homologue to J/, of these, and in the set of teeth of the
Catarrhines the homologon of J/, of the Platyrrhines is wanting.
If this tooth should also appear by the last mentioned group
of Primates it would become a J/,. Now it is a fact that is
universally known that a more or less developed fourth molar
is not seldom with man and among the Anthropoids, especially

1) G. Röse, Ueber die Entwicklung der Zähne des Menschen. Arch. f. mikrosk,
Anat. Bnd, XX XVIII.

(4593)

with the Orang and Gorilla. Moreover ZvckeRrKANDL *) has shown
that the epithelial rudiment of a fourth molar of man is formed
with the majority of the individuals. This rudiment of a tooth
and the eventual eruption of the fourth molar were till now
phenomena which were somewhat difficult to interprete. There
was an inclination to keep this fourth molar with man for an
atavism and the set of teeth of man was deduced from a hypo-
thetical primitive form when the set of teeth contained four
molars. Here however the difficulty offers itself that among the
already numerous well known primitive Primates there has never been
found a form with four molars. ZuckERKANDL also reveals this diffi-
culty where he points to it that four molars should only appear with
the primitive forms of the carnivores. SELENKA?*) also, who found from
his rich material that with Orang in 20°/, of the cases appears a
fourth molar feels the mentioned difficulty and interprets the
variation in another way. It should not be atavism but a progressive
phenomenon in that sense, that the set of teeth of Orang is on the
way of bringing into development a fourth molar. It appears to
me that this explanation of SErLENKA is not correct. If this variation
were only known to us from Orang, no direct difficulties could be
stated against this hypothesis. But such a fourth molar also occurs
as I said before very often with man. And now it is not doubtful
that the extremity of the human set of teeth is in a state of regres-
sion, the third molar is always more or less reduced and even
according to the investigations of pr Trrra*) and others issues no
more with at least 12°/, of the recent Europeans. Where it
is now fixed that our set of teeth reduces at its extremity, the
formation and issue of a fourth molar can hardly be interpreted as
a progressive phenomenon.

The hypothesis brought forward by me gives a simple solution
of the difficulty. The fourth molar of man and of the Anthropoids
is indeed an atavism but does not refer back to a removed primi-
tive form unknown to us, but does not go any farther than to the
nearest past of the history of development of our set of teeth, it
is the homologon of M, of the Platyrrhines. And contemplated in
such a way the relatively frequent occurrence of it can no longer
surprise us.

1) E. ZuekerKANDL, Vierter Mahlzahn beim Menschen. Sitzungsber. der k. Akad.
d. Wiss. Wien Bnd. G.

*) E. Srerenka. Menschenaffen. Rassen, Schädel und Bezahnung des Orang Utan.
Wiesbaden 1898.

3) M. pe Terra. Beiträge zu einer Odontographie der Menschenrassen. Zürich 1905,

( 790 )

More direct proofs may however be cited for the conclusion that
M, of the Platyrrhines should be reduced. For if the sets of teeth of
different representatives of this group are investigated, it is undeni-
able that 7, is behind in development to M, and M,.

Not all Platyrrhines are alike in this regard, with some species the
set of teeth is apparently very constant with other it is more varia-
ble. A particularly fixed set of teeth Chrysothrix seems to possess. I
could at least find not a single deviation in the 130 skulls of Chry-
sothrix sciurea which I possess, no more in 60 skulls of Cebus fatuel-
lus, although the JZ, is already very much reduced with this species.
Ateles on the contrary seems to possess a set of teeth which is
richer in variations and Barrson') mentions three cases in which
the M, which is already reduced in this genus quite fails. The men-
tioned author points to it that in these cases Ateles possessed a
formula for its set of teeth which is typical for the second family
of the Platyrrhines — the Hapalidae. And in connection with this
I may now examine the set of teeth of the Hapalidae in the
light of my hypothesis. This hypothesis puts that 17, of the Pla-
tyrrhines became lost in passing to the catarrhine type, that m,
becomes M, and that P, no longer issues. Where a reduction
of M, is not seldom found with the Cebidae, and now and then
even it is quite wanting as an individual variation, there M* is
already constantly absent with the Hapalidae. So with these Pla-
tyrrhines one phase of the process has already been run through,
but not yet the second phase, the progression from m, to M,. So
according to my opinion the set of the Hapalidae does not stand
as a deviating form at the side of that of the other Platyrrhines,
but must be considered as an intermediate form, between the original
platyrrhine and the definite catarrhine set of teeth.

So we see that several phenomena plead for my opinion, that the
catarrhine set of teeth has not originated by an excalation but by a
terminal reduction, and I must stop at my assertion that, because
m, has become JM, the replacing tooth, which originally belonged
to-it, Le. P, no longer appears.

By this supposition, the observation of the anthropologists is done
justice to, that a rudimentary tooth does relatively often appear with
man and Gorilla between P, and J/,. When P, has only been sup-
pressed as a normal element of the set of teeth, in a relatively recent-
period of the development, than the supposition lies at hand, that this
tooth also like M, of the Platyrrhines ontogenetically will be formed

1) W. Bareson. Materials for the Study of Variation. London, 1894,

( 791 )

still. And it is my opinion that the rudiments of a tooth which so
often occur in the indicated place are indeed traces of the P, which
has got lost.

There could still be mentioned some more anomalies in the set
of teeth of man (the growing together of J/, with a superfluous
tooth, the pushing out of J/, and replacing by a new tooth (so
called third dentition) which would be explained by my hypothesis,
but I will not look more closely into this matter in this place.

By my opinion about the differentation of the set of teeth of the
Primates I come into conflict with a rather universally prevailing
opinion about the morphological significance of the first molar or
the Placentalia. This molar is universally considered with all Pla-
centalia as a perfectly homological element of: the set of teeth.
Thus says ScHLOSSER') e.g. speaking of the first molar of man:
“Niemand wird sicher die Homologie dieses Zahnes mit dem ersten
Molaren der übrigen Placentalier bestreiten dürfen”. Where I now
homologise M, of man with m, of the Platyrrhines I come into
conflict with this opinion. If we however try to find motives for the
above mentioned opinion in literature, we seek in vain. And so if
seems to me, that here we have to do with a dogma, which is not
without danger for the comparative anatomy of the set of teeth.
For it lies at hand that as soon as in the whole row of the Pla-
centalia one element of the set of teeth is fixed in its morphological
significance, that then the homologating of the other elements must
join itself to this aprioristical principle. And where such a thing is
possible to a certain degree with a canine tooth, which is sharply
distinguished from the other teeth by its peculiar form, it is absolutely
impossible with a definite molar which possesses no specifie mor-
phological qualities.

I cannot finish this communication before having pointed to a
phenomenon, which is immediately related to the here communicated
point of view. If we compare the set of teeth of man with that
of the other catarrhine Primates, it appears that the process, by
which the catarrhine set of the teeth orginated from the platyrrhine
type, is still progressive with man, and that the human set of teeth
is on its way to differentiate from that of the other Catarrhines in
the same way, as these differentiated from the Platyrrhines one time.
I shall try to show this in short. The still active differentiation of
the human set of teeth appears from different facts. First as to the
premolars. In comparison to all other Primates the premolars of men

') M. Scutosser. Das Milchgebiss der Säugetiere, Biol. Gentralblatt, Bnd. 10, blz. 89,

( 792 )

have been reduced considerably, and the 2.¢ premolar more than
the first. Where as the premolars in the upper jaw of all other
Catarrhines possess three and in the lower jaw two fangs, the
premolars of man have normaliter one single fang. That this
has originated from several, appears from the grooves on the
surface. Now it is not without significance that the first premolar
shows its origine of a form with several fangs, by a dividing of the
point of the fang. So P, is more reduced than P, with man. If
further the milkmolars, which temporarily precede the premolars
are compared, we state that the milkmolars differentiate progressively
in the group of the catarrhines, and this is especially the case with
the second milkmolar. The progression concerns especially the crown
of the teeth, the number of roots is two in the lower jaw, three in
the upper jaw.

So if we for a moment fix our attention exclusively on m, and
its replacing tooth P, with man, it appears that the first is in
progression, the second in regression, and that with man, the same
relation exists in regard to these two teeth as with m, and P, of
the Platyrrhines. When man namely pushes out his m, and replaces
it by P,, his set of teeth becomes functionally inferior, for instead
of a tooth with tive or four knobs on the crown and two or three
fangs there comes in its place a tooth with two cusps on the
smaller crown and only one root.

So we see, that the terminal element of -the dental band of
the second generation (P,) reduces with man. Still distinetly
may be seen the terminal reduction of the tooth band, of the
first generation, closing with J/,, for as is already mentioned our
M, no longer even issues in + 12°/, of all cases, and is always
behind in development, at least with more highly developed human
races. So the human set of teeth is characterized from the catarrhine
Primates by the following peculiarities ; the last molar is on its way
of reduction, the last premolar is on its way of reduction, the last
milkmolar has developed very progressively. So a trio of phenomena
which are entirely homological to those, by which the catarrhine set
of teeth has originated from the platyrrhine. Only one phase is still
wanting to the process, namely the remaining persistent of the last
milkmolar and the suppression of the last premolar. And this phase
also is reached now and then individually. This: among others
appears from what Maerror says: La persistance des grosses molai-
res temporaires (m,) s’observe tres-souvent, concurremment avec
absence congénitale ou Vatrophie des secondes prémolaires (P,)

( 793 )

Nous en connaissons de nombreux exemples*). If the stated phe-
nomena are connected with each other the conformity to the earlier
process of development of the set of teeth of the Primates as I take
it, immediately strikes the eye; and one would be inclined to this
thesis; In the future set of teeth of man P, will no longer erupt,
m, will have become persistent and functionate as J/,, but by the
simultaneous reduction of M/, the number of molars will not have
become larger than three.

So from this communication appears that the differentiation of the
entire set of teeth of the Primates is from my standpoint more in-
tricate than was supposed till now, but it seems to me that my
principle of the terminal reduction can better be brought into accord-
ance with the function of the set of teeth, and is based on a
larger number of facts than the hypothesis of the excalation.
What from a general point of view, also seems to me to plead
for my opinion is the fact, that in the exposition given by me the
development of the set of teeth has taken place without a disconti-
nuity in the toothrows at any time.

Physics. — “A simple geometrical deduction of the relations existing
between known and unknown quantities, mentioned in the
method of Vorer for determining the conductibility of heat
in crystals. By Dr. F. M. Jareer. (Communicated by Prof.
P. ZEEMAN.)

(Communicated in the meeting of March 31, 1906).

It is commonly known that about ten years ago W. Voier ’*)
indicated a method, based on a recognized principle of KircHHorr,
by which to determine the relative conductibility of heat in crystals
in the different directions. His mode of experimental examination
consists in the determination of the break which two isothermal lines
present at the boundary line of an artificial twin, the principal
directions of which form a given angle p with that line, whilst the
conduction of heat takes place along the line of limit. The isothermal
lines are rendered visible to the eye by the tracings formed by the
fusion of a mixture of elaidie acid and wax with which the plane
of the erystal has previously been covered.

1) E. Macrror. Traité des Anomalies du Systeme dentaire. Paris 1877. p. 221.
2) Vorer, Göttmger Nachrichten, 1896, Heft 3.

(794)

The method of Vorer is far more accurate than that of DE SÉNAR-
MONT *) or even of RÖNTGEN *), and, requiring for other purposes to
investigate the relative conductibility of heat in erystals, it was
obvious that 1 should make use of the method indicated by Vorer.

For a erystal, for which the rotatory coefficients, found in accord-
ance with the theory of G. C. Srokes ®), are —= 0, Vorer deducts
the relations required here by constructing the equations of the flow
of heat, conformable to the conditions of limit which are common
to the lateral boundaries of both plates; i.e. that along that line the
loss of temperature must be the same, and moreover that in a
direction normal to that boundary-line the entire flow of heat must
be the same in the two contiguous plates.

Prof. Lorentz had the kindness to derive the above mentioned
relations in an analogous manner and to note down the conditions
under which the break in the isothermal lines will reach its maximum.

If « be the break, and & the angle, formed in the plates by the
two principal directions, is 45°, the proportion of the two coefficients of

the conduction of heat in those directions, consequently En is found
3

as follows:

À +2,
tqé = (4,—4,) \ = 2)
ies

If p differs from 45°, Vorer finds in that case:
(Ad) sin 2p
(2, +2,)—(2,—4,) cos 2p"

which for g equal to 45° passes into the formula of Prof. Lorentz

tos =

: é : 5 g 5
by introducing ty 5 (= 198 according to Vorer’s deduction) instead
=

of tgs.
Instead of the complicated formulae which are required for the
determination of these relations, wé here give a simple geometrical

À
> : oe _ . tS a . bits
demonstration, which, besides presenting eu a form which is imme-

diately available for logarithmic calculations, possesses at the same
time the advantage of being easily discernible.

If, from a given point O in the centrum of a crystal, a flow of heat
can take place without interruption in all directions, the isothermal

1) pe SÉNARMONT, Compt. rend. 25, 459, 707. (1847).
2) Rönreen, Pogg. Ann. 151, 603, (1874).
5) Srokes, Gambr. and Dublin Math. Journal. 6 215, (1851).

(795)

surfaces in a similar plane of a crystal are, in most cases, concentric
and equiform three-axial ellipsoids whose half axes stand in the
relation of V2,,V2, and W2,; among these the so-called principal
ellipsoid 4, whose axes are V2,, V2, and VA, must here be kept
more especially in view.

In the present case we leave unnoticed the rotatory qualities of
the erystal, and suppose an infinitely thin plate, cut parellel to a
plane of thermic symmetry, whose principal direetions correspond to
the coordinate axes. Let fig. 1 represent the elliptic intersection
of the plate with the ellipsoid 4; the line traced by the melted wax
then has the direction of the tangent of the ellipse in the point
P(x'y’), given by the radius vector e, which may enelose the angle
p with the axis X. The flow of heat may thus proceed along 9,
being the boundary line. In this case the equation for the isothermal
line pq is:

! '
Le Uy
—=l,

X

Fig. 1.

Thus for the two sections Op and Og cut off on the two axes
the result is:

0, == ie 4, =
y 0 sin p
Og = fe fi —
© Qcosp
therefore :
On

(796 )

On the other hand however:

90 (v + =) == Cot (v “+ 5) -

(5 5 5 a 5
where 5 is half of the break of the isothermal lines at the boundary

al

Si =S ij

line OG.
The immediate conclusion is therefore :

Ze €
EN KON rn KN 5 oe a (()
A 2

From this equation the required proportion may be at onee dedu-
ced when p represents the direction of the plate and the value of
has been ascertained.

Moreover it will be easy to find the maximum of ¢ — and thus
reduce the errors of investigation to the lowest figures. Suppose

A : : ;
A=, the above stated formula, after a few goniometrical trans-
2

formations becomes :

jn g (A—1) sin 2g
EN (A= coal
aa: Air ; : A _ de p
This function will be a maximum for TE =—=1() sae:
ap

de _ 2{(A*—1) cos 2p — (AI),
dp A Ns pen
The maximum condition then becomes :
A—1 4,—A,
cos 2p = = ——_
ZEE AE
and the appertaining maximum break ¢ in the isothermal lines is
then expressed by :

é (4,—4,)

= ee ke ee

pm ee DD, (B)

In cases where the difference between 1/2, and p/2, is very small

and observation teaches that this is usually the case — the

notation may be:

E 4,—A,

tg 2 =. SSS . . . . . . . . C

"2 4,+4, ( ;

For practical purposes therefore, the theoretical maximum gw = 45°
may be taken as fairly accurate, so that then the twin plate with

( 797 )

the isothermal lines etc, takes the form of fig. 2. In that case it

follows from A:
7) & :
a lg (45° -L =): GROND MT Ce af (D)

2 a

Fig. 2.

. . . . € . .
By expressing fg as a function of fg 5 from (C) one obtains the

relation deduced by Prof. Lorentz ;

REE)
ee)
BiZh 2

Moreover from the geometrical solution here given the fact is again
brought to light that in general the angle y is not equal to 90°; in
other words in this simple but experimental way is proved by

1e

occular demonstration the truth of the statement already made by
Voier, that the isothermal lines in crystals do not generally stand
perpendicular to the direction of the flow of heat.

Along the thermic axes however this is the case, because the
tangent lines at the ellipses are there directed perpendicularly to
these axes.

From fig. 1 also follows the form of the break as a result of
2, ZI

I hope soon to communicate the results obtained in the measurement
of erystals by means of this method, together with a few observations
on tbe differences of these results with those, derived in the same
minerals by the usual methods of pn SÉNARMONT and RÖNTGEN.

56
Proceedings Royal Acad. Amsterdam. Vol. VIII.

( 798 )

Botany. — “On plants which in the natural state have the character
of eversporting varieties in the sense of the mutation theory.”
By Dr. W. Burcx. (Communicated by Prof. J. W. Mor.

(Communicated in the meeting of March 31, 1906).

An investigation of the causes of Cleistogamy *) showed that: 1
plants with closed flowers originated by mutation from plants with
chasmogamic flowers and 2 that they occur in the natural state,
partly as constant, partly as ever-sporting varieties.

In the course of this investigation the question arose whether other
wild-growing plants do not also have the character of ever-sporting
varieties.

Especially those plants were thought of that have bisexual and
unisexual flowers in one and the same individual or in which by
the side of bisexual, unisexual individuals are found and also those
plants among the dioecious ones that possess rudimentary stamens or
ovaries, from which may be inferred that they originated from plants
with bisexual flowers.

The agreement between unisexual, cleistogamic and filled flowers
pointed to the same origin, while the resemblance in the manner
in which unisexual flowers occur among the hermaphrodite ones and
closed flowers among the chasmogamic ones, justified the assumption
that in the monoecious and dioecious as well as in the cleistogamic
we bave ever-sporting and constant varieties.

This summer I tried to confirm this conception in a twofold manner,
firstly by cultivating the gyno-monoecious Satureja hortensis and
secondly by studying the different forms in which one and the same
andro-monoecious Umbellifer can occur in nature with regard to the
number of male flowers in proportion to that of the bisexual ones
and to the place which the male flowers occupy on the principal
and secondary axes.

To the results of the culture experiments I shall return afterwards
when I shall have had an occasion to repeat these experiments on
a larger scale and with more species. I will here only mention that
they showed that a gyno-monoecious Satureja hortensis begins its
period of flowering with producing bisexual flowers only, that not
until later, when the plant has grown stronger, a few female flowers
appear among the bisexual ones, that their number gradually increases

1) Die Mutation als Ursache der Kleistogamie. Recueil des Travaux Botaniques
Néerlandais Vol, II. 1905,

(799 )

in the following days until a definite maximum is reached, after
which it gradually decreases again until at the end of its flowering-
period the plant again produces bisexual flowers only.

Hence the female flower follows the law of periodicity established
by pr Vries for the occurrence of anomalies of various nature with
other plants and it may in this respect be put on a line with such
anomalies. It may be compared with the increased number of leaflets
of Trifolium pratense quinquefolium, with the filled flowers of
Ranunculus bulbosus semiplenus, with the ramified spikes of Plantago
lanceolata ramosa, ete.

In what follows I shall give the results obtained with the andro-
monoecious Umbelliferae.

The investigations of BEIJERINCK *), ScHurz®), Kircuner *), Mac
Lrop *), Loew 5), WARNSTORF ®), and others on the sexual relations
of the Umbelliferae have shown that by far the most species are
andro-monoecious and that besides in some of them forms occur with
female or with female and asexual flowers. Male flowers appeared
in this family to be as common as bisexual ones. Male individuals
are rare, however. Until now Zrinia glauca was considered the
only Umbellifer in Europe, known in the male form. From Scuurz’s
notes it appears, however, that in the environs of Halle a. S. also
male plants of Oenanthe fistulosa®) and Stum latifolium *) oceur,
while in this country also Heraclewm Sphondylium can occur in the
male form.

Far less general are female flowers. ScuuLz only mentions them
for (Eryngium campestre)?*), Trinia glauca, Pimpinella magna,

1) Bewerinck, Gynodioecie bei Daucus Carota L. Nederlandsch Kruidkundig Arch,
Tweede serie 4e Deel 1885, p. 345.

2) Aveusr Scnurz, Beiträge zur Kenntniss der Bestäubungseinrichtungen und
Geschlechtsvertheilung bei den Pflanzen. Bibliotheca botanica. Bd. If 1888, Heft 10
und Bd. Ill 1890, Heft 17.

3) O. Kircuyer, Flora von Stuttgart und Umgebung 1888.

4) J. Mac Leop, Over de bevruchting der bloemen in het Kempisch gedeelte van
Vlaanderen. Botanisch Jaarboek Dodonaea 1893 en 1894.

5) E. Loew, Blütenbiologische Floristik des mittleren und nördlichen Europa
sowie Grönlands. 1894.

6) CG. Warnstorr Blütenbiologische Beobachtungen aus der Ruppiner Flora im
Jahre 1895. Verhandlungen des botanischen Vereins der Provinz Brandenburg
Bd. XXXVII. Berlin 1896.

7) Scuutz, Beitr. I p. 47.

8) Scuutz, Beitr. I p. 48. '

9) In his note concerning this plant on page 42 of his first paper, female
flowers are not mentioned. So this is perhaps an error in the general summary
at the end of the second paper.

56*

( 800 )

P. saxifraga and Daucus Carota, for which latter plant BeIJERINCK
had already found them before.

In the long list of 66 European Umbelliferae in the Bliitenbiologische
Floristik of Lorw no more than 16 species occur that are only
known as bisexual plants whereas 40 are andromonoecious. It has
appeared since that with three of the plants mentioned as bisexual
also male flowers are found. Of Anethum graveolens, Aethusa
Cynapium and Heracleum Sphondylium namely, Warystorr found
andromonoecious forms in the environs of Neu-Ruppin; also in this
country they occur in this form. Of the 66 Umbelliferae that were
studied, the following remain of which until now no other than
bisexual plants are known:

Laserpitium pruthenicum, Peucedanum venetum, Crithmum mariti-
mum, Silaus pratensis, Seseli Hippomarathrum, S. annuum, Anthriscus
vulgaris, Bupleurum longifolium, falcatum, tenuissimum and Pleuro-
spermum austriacum, to which list I think must be added: Hryn-
gium maritimum, Berula angustifolia, Conium maculatum and
Helosciadium nodiflorum.

It is probable that of some of these plants andro-monoecious forms
will be found when they are examined over a larger part of their
region of occurrence, especially since it has appeared that the different
forms in which Umbelliferae can occur, are often spread over very
different and widely distant parts, so that, even though the species
mentioned be only known as hermaphrodite plants in a part of
Europe, the possibility must be granted that they occur in other
forms elsewhere.

Of Sium latifolium e.g., no other but the andro-monoecious form
is found in a great part of Middle Europe and until now only in
the environs of Halle a/S accompanied by the male form, evidently
only in a few specimens. Only in our country the bisexual form
is known.

Of Pimpinella magna the bisexual plant is only found in southern
Tyrol and Italy; the andro-monoecious on the other hand in the
whole of Middle Europe, while in southern Tyrol and Italy the
same plant also occurs with female and with female and asexual
flowers.

Of Oenanthe fistulosa the andro-monoecious plant is found every-
where, the male one until now only in the environs of Halle.

Of Aethusa Cynapium the hermaphrodite plant is known in the
whole of Middle Europe, the andro-monoecious one only in the
neighbourhood of Neu-Ruppin and of my residence.

Of Daucus Carota the andro-monoecious form is generally found,

( 801 )

the bisexual one until now only in Flanders *) and in this country *).

So it is not at all unlikely that of those species which until now
are known as bisexual only, later other forms will also be found,
and similarly it may be assumed that of the large number of Um-
belliferae of which now only the monoecious form is known, on
closer examination also the hermaphrodite or unisexual forms will
be found.

Meanwhile it is a very remarkable fact that by far the most
Umbeliiferae are andro-monoecious and that exactly these forms are
most generally spread.

Where male individuals are found they only occur in very
limited numbers as rare occurrences among the great majority of
andro-monoecious individuals.

This also holds for the hermaphrodite plants, at any rate for Daucus
Carota, Sium latifolium and Heracleum Sphondylium. Where these
and andro-monoecious plants occur together the number of bisexuals
is far less than that of the andro-monoecious ones. *)

This general occurrence of andro-monoecious forms gives a very
peculiar character to the family of the Umbelliferae. Nowhere in
the vegetable kingdom these forms are so prominent as here.

In other families with species that are rich in forms, as the
Labiatae, Alsineae, Sileneae and others, where gyno- and andro-
monoecious and female and male forms occur together with bisexual
ones, a similar preponderance of monoecious plants is not found
with a single species.

The rule is there that where the three forms occur together the
monoecious flowers are a minority with respect to the bisexual and
unisexual ones.

Next is conspicuous with the monoecious Umbelliferae the great
variety that may be observed in the occurrence of the male flowers
in the umbels of different order and the many mutually different
forms in which consequently oue and the same andro-monoecious
plant may occur.

Sometimes an individual is found which among the large number
of bisexual flowers has a relatively small number of male ones,
another time one in which the number of male flowers is not much

1) J. Srars. De bloemen van Daucus Carota L. Botanisch Jaarboek, Dodonaea
Jaargang I. 1889. p. 132.

2) I shall soon treat elsewhere the different forms in which the Umbelliferae,
occurring in this country, are met. :

3) Male Umbelliferae and exclusively bisexual species are very rare also outside
Europe. (See Drvpe Umbelliferae. Exater und Pranrt. Die natürl. Pflanzenfamilien
III. Teil, Abt. 8. p. 91).

( 802 )

less than that of the bisexual ones, and then again an individual in
which the male flowers are more numerous than the others, and
between these a long series of gradual transitions and intermediate
forms is found.

Not unfrequently the number of male flowers is greatly in excess
of the bisexuals. I met in this country plants of Heracleum Sphon-
dylium in which the inner umbellules of the umbel of the first order
and all other umbels of higher order were exclusively male and
similar plants are also found of Pastinaca sativa and Daucus Carota.
They are found spread among other individuals in which the propor-
tion of male to bisexual flowers is more favourable to the bisexuals
or where the number of males is even very small.

Some Umbelliferae are only known in an almost male form.
Kchinophora spinosa e. g. has one bisexual flower in the middle
of the umbel ; all other flowers are male. Also with Meum athaman-
ticum and Myrrhis odorata we may observe in the specimens cul-
tivated in this country in botanical gardens, how also there the
bisexual flower is superseded, so that the umbellules often do not
contain more than one. such flower.

An investigation of the andro-monoecious Umbelliferae shows us
at once that there is a certain regularity in the way in which the
male flowers occur. In the first place, when they appear for the
first time in an umbel of a certain order, their number as com-
pared with that of the bisexual flowers increases as we come to
umbels of higher order; and secondly, if in the peripheral umbellules
some male flowers occur among the bisexual ones, their part in
the constitution of the umbellules becomes greater as the umbellules
are more distant from the periphery.

Of Daucus Carota, Pastinaca sativa and Heracleum Sphondylium
whole series of specimens may be collected in the neighbourhood
of my residence, beginning with such which in all the umbels con-
tain only bisexual flowers up to forms which are almost or entirely
(H. Sphondylium) male. Among these specimens are found in which
the male flowers already appear in the very first umbel of the plant
by the side of other specimens in which the andro-monoecious cha-
racter only appears in the umbels of the second order or later still
in those of the third or fourth order. Now it is a constant rule that
if they appear for the first time in an umbel of a certain order they
will also appear in the umbels that develop later and that their
number in proportion to that of the bisexual flowers in the succes-
sive umbels goes on increasing.

( 803 )

Specimens which in no respect revealed their andro-monoecious
character during the whole summer, which only-late in summer
produced male flowers in the umbels of the third or fourth order
or sometimes entire male umbels, are found connected by interme-
diate forms with specimens which already in the very first umbels
contain male flowers.

Concerning the part occupied by male flowers in the constitution
of the peripheral and central umbellules, it must be remarked in
the first place that with all Umbelliferae whose umbels reach a
certain size, the peripheral umbellules consist of a larger number of
flowers than those that occupy the middle part of the umbel. In
some species those central umbellules may be very poor in flowers ;
with Daucus Carota the central umbellules often even consist of
only one flower.

When it was stated that the part occupied in the umbellules by
the male flowers becomes greater the more they are placed near
the centre of the umbel, this must be so understood that as the
umbellules become more distant from the periphery the number of
bisexual flowers decreases and does so much more rapidly than the
rumber of male flowers. Hence the inner umbellules are often
entirely male while the outer ones bear a number of bisexual
flowers.

This rule is not without exception, however. There are namely
Umbelliferae in the umbels of which the central umbellule occupies
the top of the principal axis of the umbel and may consequently
be distinguished as the top-umbellule.

Such top-umbellules are especially found with Carum Carvi and
Oenanthe fistulosa and occasionally, although not so regularly, also
with Daucus Carota. For such a top-umbellule now the rule does
not hold that the part occupied by the male flowers is greater than
in the surrounding umbellules. Such an umbellule contains a greater
quantity of bisexual flowers. With Carum Carvi I often found no
male flowers in the top-umbellule when all others, as well the
peripheral as the more inwardly situated umbellules had some of
them. In other specimens the number of male flowers in this top-
umbellule was smaller than in the other.

Of Oenanthe fistulosa the umbels of the second order are in this
country much larger than those of the first order; they consist of
five to eight umbellules and agree in their constitution almost entirely
with that, indicated by Scrurz for the umbellules of the first order.
Here as a rule a top-umbellule can be very easily distinguished; it
contains only a few (7 to 9) male flowers, but is for the rest entively

( 804 )

hermaphrodite, while the side-umbellules are generally exclusively
male. a

With Daucus Carota, where the umbellule as was remarked
above, often consists of no more than one flower, this latter is very
often hermaphrodite, also when the surrounding umbellules consist
entirely of male flowers. ;

It must still be remarked for the andro-monoecious Umbelliferae
that both sorts of flowers as a rule occupy a fixed place in the
umbellule.

In by far the most Umbelliferae the bisexual flowers are found
near the edge and the male ones in the middle.

Only a few make an exception to this rule; with Oenanthe jistulosa
and Sanicula europaea the opposite is found and with Astrantia the
bisexual flowers as a rule occupy a definite zone between the peri-
pheral and central male flowers. Advancing from the cireumference
to the centre we find there first one or two whorls of male flowers,
then a whorl of bisexual ones and finally at the centre male flo-
wers again.

But although it may be the rule for all other Umbelliferae that
in all the umbellules, containing the two forms of flowers, the her-
maphrodite ones are placed at the edge and the male ones in the
middle, an exception must be made for those Umbelliferae which
in the middle of the umbellules develop a top-flower, for this latter
is as a rule bisexual.

Such top-flowers are e.g. regularly found with Chaerophyllum and
with Meum; in each umbellule of Chaerophyllum temulum and Meum
athamanticum bisexual marginal flowers and a bisexual top-flower
are found and for the rest male flowers.

Also with Aegopodium Podograria, Carum Carvi and Daucus
Carota bisexual top-flowers are found in the umbellules, but in these
species this top-flower is not always found in all umbellules.

No extensive argument will be needed to understand that the two
forms of flowers, found in the same individual of the plants men-
tioned, may be considered, like the two flowers of a eleistogamic
plant, as two antagonistie characters which mutually exclude each
other and that consequently these plants may be compared with
ever-sporting varieties, originated by mutation, the existence of which
was shown by DE Vriks.

Every andro-monoecious Umbellifera of which we compare a
number of individuals among themselves, affords an opportunity for
noticing that the two antagonistic characters evidently fight for

( 805 )

supremacy, in which combat now one, then the other gains an
advantage.

But if of a species which is rich in forms we mutually compare
a fairly complete series of andro-monoecious forms, we are struck
by the circumstance that between these and the ever-sporting varieties
known until now, there is this important difference that while
with other ever-sporting varieties the original specifie character is
always more conspicuous than the racial character, here very often
the opposite takes place.

We met in what precedes plants like Myrrhis odorata, Meum
athamanticum or forms of Pastinaca sativa, Heracleum Sphondylium
and Daucus Carota, where the specitie character had been entirely
superseded by the racial character, and this raises the question whether
the andro-monoecious Umbelliferae, looked upon as races originated
by mutation, must be placed on a line with the above-mentioned
gyno-monoecious Satureja hortensis and other ever-sporting varieties.

We know from the theory of mutation that the interaction of two
antagonistic characters may show itself in more than one way and
that a character originated by mutation may be inherited in a different
degree in various plant-species, by which process various races are
formed.

To a race in which the anomaly comes only little to the front,
much less than the normal character, and which consequently is
hereditary in a small degree only, pr Vries has given the name of
a half-race, and the abnormal character he has called semi-latent.
That, however, among these half-races important differences may
occur in the measure in which the character is semi-latent, clearly
appeared from the statistical investigation of the half-races, e.g. of
Trifolium incarnatum quadrifolium and Trifolium pratense quinque-
folium.

It may be imagined that there exist races in which the two antago-
nistic characters possess nearly the same degree of heredity so that
then it is often difficult, under favourable circumstances, to settle
whether the specific or the racial character is more prominent and
sometimes even, when the conditions of life are very favourable,
the anomaly gets the upper hand. In such a race as well the specific
character as the anomaly are then to be considered as semi-active.
The statistical investigation of the anomalies has not yet revealed
that such races really exist.

But it may be further imagined that between these latter races
which pr Vries called middle-races and the constant varieties, in
which the specifie character is latent and the anomaly active, there

( 806 )

exist still other races in which the normal character is semi-latent
to a different degree.

Dr Vries thinks such cases possible, but until now they have not
yet been noticed *). Now the question arose to me whether in the
andro-monoecious Umbelliferae we may not have such races in which
the specific character has become semi-latent ? *)

Let us start our speculations with one of those Umbelliferae of
which besides andro-monoecious ones also hermaphrodite and male
forms are known, e.g. Heracleum Sphondylium.

As was remarked above, Heracleum Sphondylium appears in a
great part of Middle Europe as a hermaphrodite plant. In the
environs of Neu-Ruppin at the same time forms are however found
which are only bisexual in the umbels of the first order, whose
umbels of the second order are composed on half bisexual and half
male umbellules and whose umbels of the third order are exclusively
male, and which in consequence may be considered to produce about
as many male as bisexual flowers.

In this country now I found besides ‘the hermaphrodite and the
Neu-Ruppin middle forms a great variety of forms which may be
considered either as gradual transitions of those middle forms to
perfectly hermaphrodite ones or as gradual transitions of those middle
forms to perfectly male individuals, which latter occur also in this
country.

If we now for the present consider this andro-monoecious plant
which is so rich in forms as an ever-sporting variety, and if we
compare its properties with those of Trifolium pratense quinquefolium,
which has first been extensively dealt with by pr Vrins, and later
has been investigated in all its details by Miss Tammes ®), so that of
this race the properties are most completely known, then we begin
with asking what peculiarities Heraclewm should present if its mo-
noecious form- represented an ever-sporting variety.

Then we should observe:

1. that a strongly developed specimen, e.g. a plant with umbels
of the first to the fourth order, produces more male flowers than
an individual which has not succeeded in getting beyond the formation
of umbels of the first and second order.

1) De Vries, Mutationstheorie, I, p. 424.

2) In my article on cleistogamic plants I already briefly raised the question
whether Ruellia tuberosa, Impatiens noli tangere, Impatiens fulva, Amphicarpaea
monoica, Viola spec. div. are not in this condition.

3) Bot. Zeit. Iste. Abt., Heft XI, 1904.

( 807 )

2. that plants on fertile soil produce on the whole more male
flowers in proportion to the bisexual ones than plants on less fertile
soil.

3. that the male flowers only appear at a stage in which the
plant has grown stronger, that they gradually increase in number
as the individual grows stronger and gradually decrease in number
again when the plant has passed its highest point of development.

4. that in each umbel as well as in each umbellule which contains
both forms of flowers, the male flowers are preferably found in
those places which are most favourable with respect to nutrition.

It is not difficult to show that observation does not confirm these
four points.

Let us in the first place consider point 4.

There can be no doubt that (excepting the just mentioned terminal
umbellules and terminal flowers) the peripheral umbellules are more
favourably placed with regard to nutrition than the more inwardly
situated umbellules, and that in each umbellule the flowers at the
circumference also occupy a more favourable position than those in
the middle. This is seen not only by the inner umbellules being
less rich in flowers but also in the flowers becoming smaller the
further they are distant from the periphery; often the central flowers
do not reach their normal development or the setting of the fruit
does not take place. We see here the same with the umbels as with
long-drawn inflorescences like those of Capsella Bursa pastoris or
Pisum sativum, that namely the last-formed flowers, at the top of
the inflorescence, no longer reach their normal development on
account of insufficient nutrition. Further every umbellule (not only
a mixed one but also a purely hermaphrodite one} allows us to
notice that the peripheral flowers are ahead of the central ones in
their development.

And now we see with all Umbelliferae without exception:

that the peripheral umbellules retain their bisexual character longest,

that the male flowers always occur first at the centre of the umbel,

that where the umbellules are mixed, the number of bisexual
flowers always decreases from the periphery to the centre,

that the inner umbellules often are already entirely male when
the outer ones still contain bisexual flowers, and

that everywhere, except with Oenanthe fistulosa, Sanicula europaea
and Astrantia the marginal flowers in the umbellules are bisexual
and the central flowers male’).

1) I think an explanation may be found for the anomalous behaviour of these
three genera. [ cannot dwell on this point, however, in this short communica-

( 808 )

In other words, we may say that as well in the umbel as in the
umbellule the bisexual flowers always -occupy the place which is most
favourable with respect to nutrition.

That terminal umbellules and flowers are placed most favourably
is evident; it can be readily explained why a top-umbellule is often
richer in bisexual flowers than other umbellules from the centre
and why as a rule the top-flower of the umbellule is hermaphrodite.

That this position is by far the most advantageous can also be
inferred from the fact that often the top-flower is the only bisexual
one of the whole umbellule. So with Mewm athamanticum e.g. it is
very often found that in the umbels of the second order, the 6—8
inner umbellules possess no bisexual flowers at all; the only bisexual
flower of these umbellules is the top-flower. *)

So we see exactly the opposite from what we should observe if
the andro-monoecious plant represented an ever-sporting variety like

Trifolium pratense quinquefolium. It is not the male flower — the
anomaly — which is preferably found in the best places, but the

bisevual flower, and on further examination of the above points
1, 2 and 3 we shall again see how it is this latter that depends
on the nutritive conditions and in all respects behaves like a character
in a semi-latent condition opposed to the active condition of the
anomaly.

I pointed out already that with all andro-monoecious Umbelliferae
the umbel of the first order shows the anomaly least.

With very many forms the male flower appears first in the umbels
of the second order, with others in those of the third order, and
sometimes it is the umbel of the fourth order in which the male
flower appears first.

But where these flowers are already observed in the umbels of
the first order their number is there always less than in the umbels
of the second and higher orders.

The umbel of the first order consequently retains in all andro-
monoecious Umbelliferae the pure racial character longest.

If we remember that the umbel of the first order is at the same
time the terminal umbel of the plant and is extremely favourably
placed at the end of the principal axis with regard nutrition, we
cannot wonder at this, bearing in mind what was said when

tion. I shall return to it elsewhere when exposing the differences between the
forms occurring in this country and those that have been observed in other parts
of Europe.

1) This reminds us of what may be noticed with Hchinophora spinosa. Vide
supra.

( 809 )

discussing point 4. We find the already stated conception confirmed
that the bisexual flower, being in a latent condition with respect to
the anomaly, preferably occurs in the most favourable places.

We may also assume that the plant during the flowering of its
top-umbel, which only occurs after it has reached its full vegetative
development, is also in the strongest stage of its growth, in a stage
in which a good part of its nutritive material may be spent on the
development of its top-umbel, while all umbels that bud forth later,
are in less favourable conditions, first on account of their being
placed on lateral axes of the second or higher order and secondly
because a very great part of the nutritive material is spent on the
ripening of the fruit of the first umbel during the development of
the umbels of the second or at any rate higher orders. This would
explain why in the umbel of the second order the semi-latent bisexual
flower is no longer prominent in the same degree as in the terminal
umbel, and why in the umbels of the third and fourth order it more
and more gives way before the racial character.

This also explains why in very strong specimens the male flowers
first appear in the umbels of the third order, and why often with
Sium latifolium, Daucus Carota and others, not until late in summer,
when the plant has already passed its highest point of development,
male flowers and even male umbels appear in plants which in their
umbels of the first and second or first, second and third order have
exclusively produced bisexual flowers.

That in fact strongly developed specimens produce more bisexual
flowers than weak specimens was already noticed by Mac Lxop,

With strong specimens — he says in his note on Aegopodium
Podagraria — the umbels of the first order and with very strong

specimens also those of the second order consist almost exclusively
of hermaphrodite flowers, while with ordinary specimens the
umbellules in the umbels of the first order consist partly and in those
of the second order exclusively of male flowers. Also Scuu1z made
the same remark with Torilis Anthriscus and Pimpinella saxifraga
and personally I found the justness of his remark repeatedly confir-
med with Pimpinella magna, Aegopodium Podagraria, Aethusa
Cynapium, Astrantia major ete.

If now finally the numerical relations of the two flower-forms are
examined in umbels of such species as are found in large numbers
on soils of different constitution and fertility, the examination at once
shows that the number of bisexual flowers in a fertile place is
considerably greater than in a less fertile one. Anthriscus silvestris
and Chaerophyllum temulum are plants which in our country are

( 810 )

very general as well on sandy soil (at the edge of the dunes) as on
fertile claygrounds. Both plants can be best judged by the constitution
of the umbels of the second order.

Of Anthriscus silvestris the average constitution is :

on sandy soil on clay ground
of the six outer umbellules 4-538111-137 7-103+3-4¢
of the seven inner umbellules 2-498-+- 8-11¢ 6-78+4-7h

And of Chaerophyllum temulum :
of the outer umbellules 15§+10%+1% 203+7¢+1%

while the 2 or 3 innermost umbellules of the plants on sandy soil
are entirely male.

So the results are in perfect agreement with my observations on
the influence of the fertility of the soil on the appearance of chas-
mogamie flowers with Ruellia tuberosa at Batavia and with those
of GorBEL on the chasmogamic flowers with Zmpatiens noli tangere
in places of different fertility near Ambach *).

From what has been communicated here it appears that the andro-
monoecious Umbelliferae in the natural state have the character of
ever-sporting varieties in which the racial character, the bisexual
flower, is in a semi-latent condition.

By assuming this it becomes clear why the anomaly shows itself
least in the terminal umbel, why, afier it has once appeared, it
increases in number in the umbels of higher order, why in each
umbel the number of hermaphrodite flowers decreases from the
periphery to the centre, why in each umbellule the bisexual flowers
are placed at the circumference and the male ones at the centre and
why with those species in which the umbels have a top-umbellule,
this latter often has again relatively more bisexual flowers than the
surrounding umbellules and finally why, where in the umbellules
a top-flower is found, this is as a rule bisexual and holds out longest
when the umbellules grow more and more male, so that it often
still oceurs in such umbellules where the bisexual marginal flowers
have already had to give way to the male ones.

Although I am of opinion that many things plead for my conception,
yet I am perfectly aware that certainty about the true nature of the
race, about the influence of fluctuating variability on the numerical
relations between bisexual and male flowers, about the question
whether perhaps locally different varieties or ever-sporting varieties

1) Gorge. Die kleistogamen Blüten und die Anpassungstheorién, Biol. Centralbl.
Bd. XXIV. No. 24, p. 770,

( 811 j

may exist of one and the same Umbellifer and other related questions
can only be obtained by culture experiments and statistical investi-
gation.

Yet I thought it worth while to communicate these observations
although they must only be considered as an exposition of the
grounds why culture experiments were undertaken. It may be useful
to indicate these grounds, first because they support my conception
about the racial character of many cleistogamic plants, and further
because in my opinion we may certainly expect that besides monoe-
cious and cleistogamic plants, other plants in the natural state will
turn out to have the character of races originated by mutation, so
that this communication may to some extent draw attention to this
point.

The culture experiments will from the nature of the case occupy
a few years.

In the Ergänzungsband of Flora 1905, Heft I, p, 214, Gorpen
communicates as a sequel to his paper “Die kleistogamen Bliiten
und die Anpassungstheorien” the results of his continued culture
experiments with cleistogamie species of Viola. The results of his
experiments confirm his formerly pronounced opinion that the appea-
rance of a cleistogamic or chasmogamic flower depends entirely
on nutritive conditions. If these are favourable the chasmogamic
flower is seen to appear; in the opposite case the cleistogamic one
appears.

I communicated in my former article my objections to this con-
ception. I will now only remark that the influence of the nutritive
conditions shows itself in such a way that with favourable conditions
the semi-latent character is developed, and with unfavourable is
suppressed.

Now if in Gorger's experiments the chasmogamic flowering is
suppressed when the plant is under unfavourable conditions, this is
because Viola is an ever-sporting variety in which the chasmogamic
flower is in a semi-latent condition. If the cleistogamie Viola be-
longed to one of the other ever-sporting varieties, if e.g. it were
an ever-sporting variety like the gyno-monoecious form of Satureja
hortensis or Trifolium pratense quinquefolium in which the anomaly:
(the female flower and the composite leaf) is in a semi-latent con-
dition, then under favourable nutritive conditions the anomaly, the
cleistogamic flower and under less favourable conditions the chas-
mogamic flower would be fostered.

( 812 )

Zoology. — “The uterus of Evinaceus europaeus L. after parturi-
tion”. By Prof. H. SrranL, of Giessen. (Communicated by
Prof. A. A. W. Husrecut).

(Communicated in the meeting of March 31, 1906).

Through the obliging kindness of my colleague Prof. HuBrecur,
to whom I owe my sincere thanks, I was enabled to continue my
researches on the involution of the uterus post partum with a species
which, as far as I know, had not yet been studied in this respect.
The examination of a larger number of uteri of Erinaceus europaeus L.
made it possible sufficiently to investigate the regressive development
in question.

In the pregnant uterus of the hedgehog shortly before parturition,
pretty large foetal chambers are found, as was shown by Huprecut’s
extensive investigations. These chambers are entirely lined with
epithelium which extends a little under the edges of the discoid
placenta, the relative size of which is not very large. This placenta
consequently belongs to the stalked ones, although the stalk is a
very broad one.

The wall of the uterus of a hedgehog which was killed immediately
after parturition is accordingly almost entirely covered with an
epithelium which proved to consist of high, cylindrical cells. A
layer of epithelium is only wanting in a small antimesometral region
which is characterised as the site of the placenta by the large
vascular stumps.

Excepting the specimen just mentioned the time post partum could
not be determined in my preparations. So I had to arrange them in
a series according to the thickness of the uteri, beginning with such
as were still very thick and admitted of a determination of the number
of former foetal chambers by swellings corresponding to the placental
places and ending with others the appearance of which did not
reveal any traces of pregnancy. The sections obtained from such
uteri were in good agreement with each other and gave a sufficient
idea of the various stages of involution.

I will not give here a detailed description of the phases of the
retrogade development but only remark that the essential changes
occur in the connective tissue of the uterine mucous membrane and
in the glandular apparatus. The surface epithelium which with many
animals (e.g. with Putorius furo) undergoes considerable changes of
form, here shows these to a relatively smaller extent. They are
limited to the casting off of superfluous parts and to the change of

larger cells into smaller ones.

(zene)

The epithelial defect of the placental spot is covered by epithelium
advancing from the edges by a similar process as has become known
of late years for a number of other mammals. Since a spot without
epithelium is found in several stages, it must be assumed that the
covering of the gap does not take place so rapidly as e.g. in many
Rodents.

Characteristic for the connective tissue is the great abundance of
liquid in it; after parturition it appears to be of a loose irregular
texture and contains a considerable number of large blood- and
especially lymph-vessels, the former especially in the placental spot, the
latter spread over the. whole mucous membrane. In this connective
tissue during the first period following parturition only small and
irregularly shaped glands are found, with a low epithelium. These
glands occupy little place in the pretty thick mucous membrane.

In the completely retrograde uterus I find a mucous-connective
tissue which is not particularly strong and is rich in cells; in this
long glands reach in a very graceful and regular arrangement from
the inside of the uterus to the musculature, while larger blood- and
lymph-vessels are lacking in it. (see fig. 1 in Huprecut’s Studies in
Mammalian Embryology. Quart. journ. of micr. sc. vol. XXX. new
ser.). A comparison of these two stages, representing the beginning
and the end of the involution, shows the direction of the involution.
It consists, not to speak of the just mentioned minor changes in the
epithelium, in the connective tissue becoming more compact, the
total calibre becoming considerably less, and in a re-arrangement of
the glandular apparatus which is probably accompanied by a new-
formation, but certainly with a re-arrangement and considerable
lengthening of the single glandular tubes.

In the connective tissue it is not so much the single cells which
change (as is e.g. conspicuously the case with the female dog post
partum) as there is a clear indication that intercellular substances
diminish, which finally leads to a consolidation of the whole tissue.

At the same time the swollen lymph-vessels become smaller and
narrower as well as the stumps of the torn blood-vessels in the
placental spot, the trombi of which organise themselves. The retro-
gression at the placental spot takes place distinctly more slowly
than in the remaining mucous membrane so that the placental spot
is still recognised as something particular when the gap in the
epithelium has become completely covered.

The return of the glands to their regular form takes still more
time than that of the connective tissue, perhaps its last phase only
sets in with a new rut.

57

Proceedings Royal Acad. Amsterdam. Vol. VIII.

(Bids)

Comparing the puerperal involution of the uterus of the hedgehog
with the same process as it occurs in other mammals, hitherto studied,
we may state that in this respect the hedgehog occupies an intermediate
position between Rodents and Carnivora. It stands near the former
in the way in which the epithelium regresses, near some of the latter
in the regression of the layer of connective tissue, although im this
respect the analogy is not complete.

The more accurate details of the involutional processes of which
a short sketch is given here, will be published elsewhere.

Physics. — “Magnetic resolution of spectral lines and magnetic
force’. By Prof. P. Zeeman. (First part).

The intensity of a magnetic field may be defined by the amount
of splitting up of a given spectral line emitted by a source placed
in the field.

The distance of the outer components of a triplet can be measured
with great accuracy. The components of a line resolved by the
action of magnetism are of the same width as the original line and
the high degree of accuracy obtainable in the measurement of spec-
trum photographs is generally known.

We may call two magnetic intensities equal, when producing
equal amounts of separation of a spectral line, and we may call
two differences of magnetic intensilies equal, when the changes of
the distances of the components are the same. In this way we
obtain a scale of magnetic forces, the zero point and the magnitude
of the units can still however be chosen arbitrarily. All conditions
necessary for the indirect comparison of different intensities of a
quantity are fulfilled. *)

In this method of measuring magnetic forces we adopt a natural
unit of magnetic force.

In applying the specified method we need not know the functional
relation between magnetic force and magnetic separation of the
spectral lines. It is sufficient to know that this function is one-
valued. The most accurate measurements of the present time *)
and also theory render it extremely probable that the separation
of the spectral lines is proportional to the intensity of the field
wherein the source of light is placed. If this simple relation be

1) Comp. Runee, Maass und Messen. Encyclopiidie der mathematischen Wissensch.
Bd. V. I. 1903.

2) See specially: A, Färper, Uber das Zeeman-Phänomen. Ann. d. Phys. 9
p. 886. 1902,

(815)

the true one, then our scale of magnetie forces is identical with the
one commonly used.

We may then deduce from a given separation of a well-defined
spectral line the strength of a field in absolute measure, the constant
of reduction being once for all determined.

In the measurements of FäRBER*) relating to the lines 4678 Cd
and 4680 Zn (produced by a spark between zinc-cadmium electrodes)
the constant of reduction could be determined with a probable error
of far less then */,,)-

This method and all methods used till now for measuring
magnetic fields, give the intensity in a point. Or rather the mean
value in a small area (often rather extensive) or in a small space
is considered to be the intensity in a point of that area or of that
space.

The magnetic separation of the spectral lines enables us to measure
simultaneously the magnetic force in all points belonging to a
straight line.

In my experiments vacuum tubes charged with some mercury and
excited by a coil were used. The tubes had capillaries of 8 cm.
length, the interior diameters varying between '/, and '/, mm.
The shape of the tubes was that given by PascHeN *), also used by
Ruree and PascHeN in their investigation concerning the radiation of
mercury in the magnetic field.

A very moderate heating is required for the passage of the discharge,
the light in the capillary is then fairly intense, it becomes very
brilliant as soon as the tube is placed in the magnetic field.

It was noticed that for a given vapour density there exists a
definite intensity of field for which the luminosity is a maximum.
This is easily seen when putting on the current of a pu Bors half ring
electromagnet. Owing to the large inductance (relaxation time 50")
the intensity of the field rises gradually. If the vapour density in
the tube is not too high, there is clearly one moment of maximum
luminosity.

If with a given field the density of the vapour is well chosen, then
only a very moderate heating of the tube is sufficient for keeping
it luminous.

When the tube is placed between the conical poles of a pv Bors
electromagnet and in a plane perpendicular to the line joining the
poles, there is of course a different field intensity in every point of

1) FäRrBenr. |. c.
*) PascreN, Eine Geisslersche Röhre zum Studium des Zeeman-effectes. Physik.
Zeitschr. p. 478. I. 1900,

57*

(816 )

the tube. Analysing the light of the different points of the tube
with a spectroscope, we find of course a different magnetic separation
for every point.

We can however speetroscopically analyse simultaneously the light
of all points of the tube.

We have only to focus an image of the tube upon the slit of the
spectroscope. This spectroscope must satisfy one condition. This con-
dition is that to every point of the slit there corresponds one point
of the spectral image. In the case of a prism spectroscope, of an
echelon spectroscope, and of a plane grating spectroscope, this condition
is clearly fulfilled, but the concave grating mounted in Row1ann’s
manner forms an exception. The use of the concave grating necessitates
in our case the employment of the method proposed by Runer and
PASCHEN ?).

My experiments were made in the above manner.

To illustrate this method I shall take the blue line of mercury (4359),
which divides into a sextet.

The distribution of the magnetic force in a plane perpendicular to
the axis of a pu Bors electromagnet with a distance of 4 mm. between
the poles is mapped out in a spindle-shaped magnetogram, of which
a part is reproduced in Fig. 1. This figure is from a negative enlarged
9 times. We may extinguish by means of a Nicol the light of the
inner components. At both sides two narrow lines remain, Fig. 2
is a natural size reproduction of a magnetogram taken under the
specified conditions. The duplication of the outer components is lost
in the reproduction. The extension of the field, mapped out by this
magnetogram, may be better understood if I observe that 1 mm. in the
focal plane of the spectroscope corresponds to 1.80 mm. in the plane
between the poles or 1 mm. in the latter plane to 0,556 mm. of the
negative. Hence in Fig. 1 5 mm. corresponds to 1 mm. between the
poles. The complete magnetogram gives the magnetic force in a line,
30 mm. in length. Using a lens of shorter focus we can represent,
of course, a greater part of the field. In the middle of the field the
magnetic force is about 24,000 C.G.S. A comparison of field strengths
can be made with a decidedly higher degree of accuracy than that
which is given above for an absolute measurement.

The method set forth above will be applied, of course, only in diffieult
cases. As long as our spectroscopes of great resolving power are
rather cumbersome, no practical application of the method is possible.

In many cases there will be great advantage in selecting a spectral
line which is tripled in the field.

1) Kayser. Handbuch Bd. I, p. 482,

P. ZEEMAN. “Magnetic resolution of spectral lines and magnetic force.’

Proceedings Royal Acad. Amsterdam. Vol. VIII.

( 817 )

The magnetisation of the spectral lines enables us to determine the
maximum value of the force with phenomena varying rapidly with
the time, and with non-uniform fields.

In some cases it is of great importance to follow the behaviour of
a spectral phenomenon with different strengths of field. The above
described method might then be called the method of the non-uniform
feld.

In a future communication I hope to study in this manner the
asymmetry of the separation of spectral lines in weak magnetic
fields, predicted from theory by Vorer. On a former occasion I have
communicated some experiments giving rather convincing evidence of
the existence of this asymmetry *).

In the mean time, I think that the developments lately given by
Lorentz *) make it desirable to corroborate the reasons for accepting
the existence of this extremely small asymmetry.

Mathematics. — “Some properties of pencils of algebraic curves”.
By Prof. JAN pe Vries.

§ 1. Let A be one of the n° basepoints of a pencil (c”) of curves
cn of order 7, B one of the remaining basepoints. If we make to
correspond to each c” the right line c° touching c" in A, then we
get as product of the projective pencils (c") and (c'), a curve 7’, of
order (7-1) forming the locus of the tangential points of A, i.e.
of the points which are determined by each ec” on its tangent cl.
This tangential curve has in A a threefold point where it is touched
by the inflectional tangents of three c? having in A an inflection;
it has been considered for the first time by Emm Weyr (Sitz. Ber.
Akad. in Wien, LXI, 82).

I shall now consider more in general the locus 7, of the mth
tangential points of A. The order of this curve is to be represented
by t(m), whilst a(m) and 807) are to indicate the number of branches
which 7 has in A and B.

Prof. P. H. Scuourr has drawn my attention to a paper inserted
by him in the Comptes Rendus de Académie des sciences, tome CI,
736, where the corresponding curve is treated for a cubic pencil.
I found that the numbers obtained there for » = 3 appear from the
results to be deduced here.

1) Zeeman. These Proceedings, December 1899.
2) Lorentz. These Proceedings, December 1905.

( 818 )

To determine the functions T(m), a(m) and p(m) I shall make use
of an auxiliary curve already used by Werr, which might be called
the antitangential curve of A. It contains the groups of m(m—1)—2
points A_;, having A as tangential point; so it passes three times
through A and once through all points B. So it has (2n? — n)
points in common with any c”‚ from which it is evident that it is of
order (27 — 1).

§ 2. The (m—1)" tangential curve (Am!) of A is cut by the
antitangential curve (A) of A, save in the base points, in the points
Amb having A as tangential point. Their number amounts to three
less than the number of tangents which 75, has in A, so a(m) — 3;
for, on the three c® which have in A an inflection A coincides with
one of its m* tangential points.

The three inflectional tangents being also tangents of the curve
(A—'), the tangential curve (A”—') and the antitangential curve
(A—') have 38a¢(m—1)+8 points in common in A. In each base-
point B lie 8 (@m—1) points of intersection. So

(2x — 1) rt (m — 1) = a (m) + 8a (m — 1) + (n° — 1) B(m—1). . (1)

A second relation is found by noticing that (A"™~!) has with the
antitangential curve of B, save the basis, the @(m) points in common
for which B is an m' tangential point. In B lie 38 (im — 1) points
of intersection, «(mm — 1) points of intersection lie in A, B(m— 1)
in each of the other basepoints. So

(2n — 1) t(m — 1) = Ben) + a(m — 1) + (n° 4- 1) Pm — 1) ~ (2)

With any c” the locus 7, has, save the basis, only the (m— 2)

points A) in common; so

n T(m) == a(m) + (nr? — 1) Bim) + (n — 2). eS. (B)

$ 3. To find a homogeneous equation of finite differences for the
determination of t(m) I eliminate from the three obtained relations
the quantities «/m) and p(m), and I find
nt(m) = n?(2n —1)r(m —1) — (n° + 2)fa(m— 1) + (n?—1)8(m—1)} + (n —2)™.
Here the expression within braces can be replaced on account
of (3) by nt(m— 1) — (n — rt, Then
t(m) = (rn? — n — 2) te(m— 1) 4+ (r+ 1)(n — 2)" 1. . (4)
So
t(m — 1) = (n? — n — 2) T(m — 2) + (n+ 1)(n — 2-2 (5)
Equations (4) and (5) finally furnish

T(m) — (n — 2)(n + 2) T(m — 1) + (n — 2) (rn 4 1) vn — 2) = 0 (6)

( 819 )

To determine a particular solution t(m) = ze we have
uv? — (n — 2) (n + 2)ea + (nxn — 2) (n + 1) = 0,
therefore

oS — 1 — OP on de

Consequently the general solution is

t(m) = ¢,(n* — n — 2)" Hen — 2)”.
To determine the constants c, and c, I substitute in (4) the known

values (n + 1) of x(1) and (n +1) n° —4) of x(2).

Now

n+ 1—=e, (n° — n— 2) He, (n — 2),

(n° — 4)(n + 1) =e, (n° — n — 2)? He, (n — 2)’.

Finally we find by elimination of c‚ and c,

perma

t (m) = (n + 1) (rn — 2m (7)
n
From (4) and (2) ensues
a (m) — B(m) = — 2 ja (m — 1) — B(m— 1),

so
a (m) — B (m) = (— 2)"—1fa (1) — B(I} = — (— 2)... (8)

Making use of (3) and (7) we now find
n° a (m) = (n — rin + Iml — Qn + 1} — (rn? — 1)(— 2)". (9)
n° B (m) = (n — 2yr-1f(n + Iml — 2n + 1} + (— 2)" . … ©. (10)

§ 4. For m=2 we find a(2) =n? + n—9; as A is inflection
for three curves ¢,, there are therefore (n° + — 12) curves on
which A coincides with its second tangential point. From this ensues
the wellknown result that A is point of contact of (n + 4) (n — 3)
double tangents.
“In a former paper’) I have brought into connection the locus of
the points of contact D of the double tangents with the locus of the
points W in which a ec” is cut by its double tangents. To determine,
how often a point D coincides with one of its tangential points I”
I consider the correspondence of the rays d= OD and w= OW
which the correspondence (), W) forms in a pencil with vertex 0.

As the curves (J) and (JW) are of orders (n — 3) (2n? + 5n— 6)
and 4 (7 — 4) (n — 3) (5n* + 5n —6), to each ray d correspond
(n — 4) (n — 3) (2n* + 5n — 6) rays w and to each ray w correspond
(n — 4) (n — 3) (On? + 5n — 6) rays d.

1) “On linear systems of algebraic plane curves.” Proc. April 22 1905, Vol. VII
(a), p. 710:

( 820 5

Because each of the 27 (n — 2) (n — 3) double tangents out of O
represents 2 (n —4) coincidences d= w, the number of coincidences
D — W is represented by

(n — 4) (n — 3) (2n? + 5n — 6) + (nm — 4) (n — 3) (on? 4- 5n — 6) —
— 4(n — 4) (n — 3) (n — 2) n = 3 (n — 4) (n — 3) (n? + Ón — 4).

In a pencil (c") we find that 3 (n — 4) (n — 3) (n* + 6n — 4) curves
have an inflection, of which the tangent touches the curve in one other
point more.

In the paper quoted above I thought I was able to determine this
number out of the points of intersection of the curves (D) and (IW);
here I overlooked the fact that a point of contact of a double tangent
can be tangential point W of another double tangent.

§ 5. To find the number of threefold tangents I consider the
correspondence between the rays projecting out of O two points
W and W’ lying on the same double tangent. The characterizing
number of this symmetric correspondence is evidently equal to
4 (n — 4) (n — 3) (Sn? + 5n — 6) (n — 5), whilst each double tangent
borne by O replaces 27 (n — 2) (n — 3) (n — 4) (n —5) coincidences.
The number of coincidences JV’ == JV’ amounts thus to

(n — 5) (n — 4) (n — 3) (5n? + 5n — 6 — 2n? + 4n).

As each threefold tangent bears three of these coincidences we
have the property :

In a pencil (c") we find that (n — 5) (n — 4) (n — 3) (n? + 3n — 2)

curves have a threefold tangent.

§ 6. In my paper indicated above I have tried to determine the
number of undulation-points out of the points of intersection of the
inflectional curve (7) with the locus of the points (V) which ec
determines on its inflectional tangents. As each inflection which is
also tangential point of another inflection is common to (J) and
(VV), the number found elsewhere is too large. The exact number I
can determine by means of the correspondence between the rays OF
and OV.

As the orders of (J) and (V) are 6(n—1) and 3(n—3)(n?-+2n—2)
and each of the 3x (n — 2) inflectional tangents drawn from O replaces
(n — 3) rays of coincidence, we get for the number of coincidences
I= V
6(n—1) (n—3) + B(n— 3) (n?4-2n—2)—8n(n—2) (n—3)= 6(n—3) (Bn—2).

In a pencil (et) we find that 6 (n — 3) (Bn — 2) curves have a
four-point tangent.

ete

( 821 )

$ 7. The curve of inflections (J) and the bitangential curve (D)
have in each of the 3 (n — 1)? nodes of (c”) in common a number

of 2 (z — 3) (x + 2) points.

For, out of a node we can draw to the c" to which it belongs
(n? —n—6) tangents, to be regarded as double tangents, whilst each
node of a ct is at the same time node of (/).

In each basepoint lie moreover 3 (7 + 4)(m — 3) points of inter-
section ($ 4). The remaining points common to (D) and (/) are
the inflections of which the tangent touches the c= once more (§ 4)
and the undulation-points (§ 6) where the two curves touch each
other.

Indeed, we have

6(n—1)? (n— 3) (n +2) + Bu (n+4) (n—3) + 3 (n— 4) (n—3) (n° + 6n—4) +
+ 12(n—3)(8n—2) = 6(n—1)*(n—3)(n42) + 3(n—3)(270°+6n?—16n48) =
= 6(n—1) (n—3) (2n?+5n—B),

and this is the product of the orders of (/) and (D).

Physiology. “On the strength of reflex stimuli as weak as possible.”
By Prof. H. ZWAARDEMAKER. (Report of a research made by
D. I. A. van REEKUM).

(Communicated in the meeting of March 31, 1906).

Investigated were chemical, thermal, mechanical and electrical

stimuli, which partly acted upon tbe skin partly on the sensible nerves

of the animals, which were experimented on.

§ 1. The chemical stimuli were applied by immerging the hind-
leg of a winterfrog in a little bowl with a solution of sulphuric

160
was withdrawn in the usual way from the influence of the cere-
brum. After the experiment the legs were washed with distilled
water and the experiment repeated after a pause of 5 minutes.
Neglecting the preliminary reflex, only a complete reflex was consi-
dered as a positive result. After-reflexes and general movements did
only show themselves when rather strong concentrations were used.

acid varying from */, to */;,°/, = to ) The spinal cord system

n

As a rule a */,, °/, eG solution of sulphuric acid may be accepted
3)

as the minimum stimulus which still produces reflexes. The retlex-

( 822 )

time at an immerging of the two legs was 10 seconds, at an immerging
of one leg 22 seconds.
It was calculated how much sulphuric acid disappeared in the

7

VW
skin of the frog, when '/,, °/, sulphuric acid (=) was used, respec-

tively how much was fixed by the excretion-products. This occurred
by titrating the immerging liquid with caustic soda (methylene orange
as indicator) before and after a series of 20 singular reflexes.

Then it appears that about */,, of the total quantity of the
used ‘sulphuric acid has been bound. Supposing the heat of reaction
of 2 aequivalents natron and | aequivalent sulphuric acid to be
31,4 great calories and supposing that our sulphuric acid has been
bound in a reaction of this kind then the heat of reaction of
the chemical process pro singular reflex, reckoned over the whole
immerged surface of the skin, amounts to 1,37 gram-calorie. It is evident
that only a small part of this supposed reaction can have taken
place in or near the terminations of the nerves and that this value
of 1,37 gram-calorie must be also a limit under which is situated
the heat of reaction.

This amount may surpass the real value of the reflex-stimulus
perhaps a million of times. By measuring the electrical conductivity
of the stimulating solution before and after the reflexes it was
controlled if anything else had passed into the immerging liquid
in the place of the disappeared sulphuric acid. This proved to
be the case for the increase of resistance of the liquid experi-
mented with, was greater than would follow from the decrease of
the sulphuric acid.

§ 2. As a thermal stimulus served immersion in cold or warm
water. The most favourable result was obtained by a decreasing dif-
ference of temperature between animal and water of 10° C. and
by an increasing difference of temperature of 15° C. The reservoir,
isolated by an asbestos envelope, in which the immersion of the frog
took place contained 50 eem. The immersion was performed once
and after that tbe reflex was waited for. Then it could be stated
that the temperature of the water increased on an average of 8
centigrades by the immersion of the heated frog and decreased on an
average of 22 centigrades by the immersion of the leg of a frog
which was cooled down. Some experiments already gave a reflex
before it had come to this. A sufficient quantity of refleses large
enough to avoid casualties, were accompanied by an increase of
temperature of 7 centigrades resp. a decrease of temperature of 19

( 823 )

centigrades. Consequently at these last experiments a quantity of
heat of 3,5 gr. calorie must have been withdrawn from the leg of
the frog, and 9,5 calorie have been added. This heat divided itself
during a reflex-time of average 7'/, sec. resp. 9 sec. over the whole
immerged part of the skin. Only a very small part will have come
to the benefit of the terminations of the nerves and what appears
as a reflex-stimulus may very well be millions of times smaller than
the total quantity of the heat which is given or taken up. The
above mentioned values have again only the significance of limit
values beneath which the heat resp. cold stimulus, which causes a
reflex movement, must be necessarily situated.

$ 3. To produce mechanical reflex-stimuli first falling mercury
drops were made use of *), afterwards a little ball of resin fastened
to a pig’s-bristle, which by an electrically moved tuning fork of
16 double vibrations was kept in a forced vibration of fixed ampli-
tude. In both cases as much as possible the lateral side of the
foot, where the corpuscula tactus are situated, was taken.

The mercury drops were all of the same size (average 100 mer.)
and were used to the number of 1 to 15, trickling down one after
the other. The height from which the drops were falling varied
from 1 to 20 em. At each experiment the vis viva was calculated
with which the drop came down on the skin of the animal. It was
obvious that for causing a reflex the vis viva had to be in minimo
686 ergs which amount was obtained by dropping 7 drops one after
the other from a falling height of 1 em. Once it was possible to
obtain a reflex by the fall of one drop from a height of 7 em.
which shows the same quantity of energy now contained in one
single stimulus without any summation.

The smallest results according to vis viva which still produce
a reflex were obtained with a little ball of resin of 7 milligram
which vibrated with an excursion of 5 mm. After a reflextime of
on an average 3 sec. the reflex movement was obtained. The
quantity of energy which was added to the skin in this way in
summing contains 212 ergs.

The result of the mechanical stimulation is quantitatively consi-
derably lower than the above mentioned chemical and caloric
stimulation. It leads to a minimnm, which however put together
in a restrict spot still possesses the peculiarity of having been
communicated to a part of the skin which probably is considerably

IE. A. Scuarer, Proc. Physiol. Soe. 26 Jan. ‘901.

( 824 )

larger than the surface of a corpusculum tactus. The divergency
between the quantity of energy applied and that which is used for
reflex-stimulus is in this last case not by far so great as in the
thermal forms of reflex stimulus. The simplest relation might be
expected in the very favourable case already mentioned, in which
only one drop of mercury falling from a height of 7 em. was used.
Meanwhile, with the ball of resin, still smaller values were obtained,
notwithstanding’ the summation was taken into the account, so that
we may accept, this most simple case has not at all been a most
favourable one.

§ 4. The electrical stimulation brought about by discharges of a con-
densator which was immediately before charged with a voltage varying
between O and 2 volts. The capacity of the condensators, which were
constructed in the laboratory from mica of different thickness and cover-
ings of tinfoil different in surface varied from 15d 10— to 4X
10-3m. F. They were wholly closed in by paraffine and verified by com-
paring with an air-condensator. The following stimuli were used:
firstly on the skin of the leg of the frog by means of little catches
of steel which surround the leg: secondly on the posterior roots of the
lumbal-cord, by means of platinum-electrodes set in paraffine, thirdly
on the nervus vagus of a rabbit by means of platinum-electrodes set
in ebonite. The stimuli were for the greater part supplied in series
with an interval of '/, sec. in a number varying between 1 and 15.
All those regulations took place automatically by properly isolated
swings and keys. The best results gave a condensator of 5910 m. F.

Skinreflexes (not ordened series)

(with condensator of 59.10—5 m.F.)

1 9 8 4 5 GZO oS TTR LEL fh steal fs a) 14 15 number of stimuli
| | | | |
121 | 108 | 158 | 98 | 76 | 34 | 31 | 40 ee | 20 | 6 | 6 | 2 | 5 | 10 number of observat.
| | |
0.87 | 0.81) 0.83 | 0.77) 0.77 | 0.75 | 0.74! 0.79 | 0.94 | 0.86 | 0.85 | 0.75 | 0.65) 0.62 | 0.67 javerage voltage

| |

| | |
22.32,19.35/20.32/17.49/17,49/16,59/16.15

| |

18.41,26.07/21.81/21,31/16.59/12,4611.3413.2denergy in 10—4

The above mentioned experiments were taken without a system.
Observing a more judicious succession of the stimuli more favourable
conditions of stimulation were obtained in the following series.

From this table it distinctly appears that the stimulus is limited
to the smallest quantity of energy when a condensator 0,00035 m. F.
is used. Then 1,4 & 10-4 ergs is sufficient on condition that
the stimulus is repeated three times with an interval of */, sec.
Consulting the experiments about reflexes which are not mentioned

Skinreflexes (ordened series)

(the average fur the different condensators).

|
Capacity | | Number | Energy
pacity | g

Voltage of of each stimulus
in m.F. | | stimuli in 10—4 ergs.
Cl
0.00025 0.40 2 2.0
0.00035 0.28 3 1.4
0.00059 0.24 8 407
0.0013 0.24 3 Se
0.004 0.34 15 Jara

in the tables a minimum value is obtained which is only slightly
larger, namely an amount of 5 & 10~4 ergs.

The result got at the last root of the lumbal region with frogs
cannot be given in one table as the individual experiments differed
too much and have not been numerous enough to fix the average.
In a very sensitive preparation when the above mentioned condensator
of 0,00035 m. F. was used, a distinct reflex was obtained with a single
discharge of only 8,6 >< 10~® ergs, a result which shows clearly that
in the experiments of Mr. van Reekum the reflex sensitiveness has
been considerably greater from the root than that from the skin. In a
single case there was even found a value still three times smaller.
The above stated number however was not obtained accidentally
but represents a whole series of observations (12 in number).

By central stimulation of the cervical part of the nervus vagus
of a rabbit reflex-changes of the breathing were caused, which could
be registered by means of the aerodromograph *). The said reflex
consists according to the intensity of the stimulus 1. if stimulating
with very weak discharges in a slight increase of frequency of
breathing and in an increase of the rapidity of the current of air in
in- and expiration 2. if stimulating with somewhat greater discharges,
an increase of the rapidity of the stream of air notwithstanding
decrease of frequency 3. stimulating with sufficient great discharges
a distinct decrease in rapidity of the stream of air and frequency
both. If we only examine the result mentioned in the third
case as the reflex on which we want to base our measurements,
the results of the experiments may be taken together as follows:

1) H. ZwaarpemakerR und C. D, Ouwenanp, Arch. f. Physiol. 1904. p. 241,

( 826 )

Breath-reflexes.

capacity | 15 successive discharges 1 discharge
ME | | energy. of the | energy
ae | voltage | stimulus | voltage in 104 ergs
| in 10—4 ergs

0.00015 | 0.47 | 0.2% | 0.23 0.40

0.000% | 043 | 0.24 | 0.21 0.55

0.00035 | 0.10 0.47 | 0.47 0.54
| | |

0.0059 | 0.09 0.24 | 0.16 0.76
| |

0.0013 | Ose 0.79 | 0.19 2.35

0.004 | 0.12 2.88 0.18 6.48

CONCLUSION.

The reflex stimuli of different kinds used as weak as possible on
eold- resp. warmblooded animals have in minimo very different
value. Thus one and the same effect was brought about by applica-
ting on the skin of a frog of an electric stimulus of 3,15 >» 10+ ergs
by a mechanical stimulus of 212 ergs, by a thermal stimulus of
11,5 mega-ergs and by a chemical stimulus of 57 mega-ergs. So
of all these forms of stimulus the electrical is the most favourable.
It may be still more favourable when we let the stimulus act not
on the skin but on a posterior lumbal root of the frog. Then 3 > 10 &
ergs is sufficient to cause a typical reflex and so the amount ap-
proaches to that which occurs with weak sensorial stimuli (light stimuli
vary in general between 1 X 10-10 as lowest and 6 X 10° as highest
value; acoustical stimuli between 0,3 >< 3—-* as lowest and 1 « 10°
as highest value’). What holds true for frogs, as a rule holds
true for mammals. From the nervus vagus there can be brought
about by central stimulation with an electrical stimulus of 0,17 X
10~4ergs a very marked change of breathing, whereas a few times
smaller value causes an indistinct but yet an unmistakable accele-
ration of breathing. Here also the minimum reflex stimuli have a
limit value of the order 1 x 10—® ergs.

1) Die physiol. wahrnehmbaren Energiewanderungen, Ergebnisse der Physiologie
Bd. IV. 1906. p. 423.

(May 25, 1906).

CONTENTS:

ABSORPTION and emission Jines (The) of gaseous bodies. 591.

aciD (The amides of g- and §-aminopropionic), 475.

acips (On colorimetry and « colorimetric method for determining the dissociation
constant of). 166.

— (Ester anhydrides of dibasic). 336.

ACRALDEHYDE (The reduction of) and some derivatives of s. divinylglycol (3.4 dihy-
droxy 1.5 hexadiene). 541.

ALGEBRAIC CURVES (Some properties of pencils of). S17.

ALGEBRAIC SURFACES (On pencils of). 29.

— (On the rank of the section of two). 52.

ALLYL FORMATE (On the action of ammonia and amives on). 138.

AMIDES (The) of z- and B-aminopropionie acid. 475.

AMINES (On the action of ammonia and) on allylformate. 138.

— (On the action of ammonia and) on formic esters of glycols and glycerol. 339.
AMMONIA (On the action of) and amines on allylformate. 138.

— (On the action of) and amines on formic esters of glycols and glycerol. 339.
AMYRINE-ACETATE (The occurrence of 3-) in some varieties of gutta-percha. 544.
Anatomy. L. Bork: ‘On the development of the cerebellum in man”. 1st part. 1.

2nd part. 85.
— A. J. P. VAN DEN BROEK : “On the sympathetic nervous system in Monotremes”. 91.
.— D.J. HutsHorr Por: “Bouk’s centra in the cerebellum of the mammalia”. 298.
— L. J. J. Muskens: “Anatomical research about cerebellar connections”. 563.
— L. Bork: “On the relation between the teeth-formulas of the platyrrhine and
catarrhine primates”. 751.
APOGAMY (On a case of) observed with Dasylirion acrotrichum Zucc. 684.
Astronomy. J. WeEpER: “Approximate formulae of a high degree of accuracy for the
ratio of the triangles in the determination of an elliptic orbit from three obser-
vations.” If. 104.
— J. A. C. OupeMans: “Supplement to the account of the determination of the
longitude of St. Denis (Island of Reunion), executed in 1874, containing also
a general account of the observation of the transit of Venus”. 110.

— H. G. van DE SANDE BAKHUYZEN: “Preliminary Report on the Dutch expedition
to Burgos for the observation of the total solar eclipse of August 30, 1905”. 501.

58

Tl CONTENTS.

Astronomy. H. J. Zwreus: ‘Researches on the orbit of the periodic comet Hormes and

on the perturbations of its elleptic motion”. 642.
— J.C. KarreyN: “On the parallax of the nebulae”. 691.
— W. pr Sirrpr: “On the orbital planes of Jupiter’s satellites”. 767.

atoms (The introduction of halogen) into the benzene core in the reduction of aromatic
nitro-compounds, 680.

AZOBENZENE, Stilbene and Dibenzyl (On Diphenylhydrazine, Hydrazobenzene and
Benzylaniline, and on the miscibility of the last two with) in the solid aggregate
condition. 466.

BACTERIA (Methan as carbon-food and source of energy for). 327.

BAKHUIS ROOZEBOOM (a. w.). The different branches of the three-phaselines
for solid, liquid, vapour in binary systems in which a compound occurs. 455.
— presents,a paper of Dr. F. M. Jancer: “On Diphenylhydrazine, Hydrazobenzene
and Benzylaniline, and on the miscibility of the last two with Azobenzene, Stil-
bene and Dibenzyl in the solid aggregate condition”. 466.

— The boiling points of saturated solutions in binary systems in which a compound
occurs. 536.

— presents a paper of Dr. A. Surrs: “On the hidden equilibria in the p, z-sections
below the eutectic point.” 568.

— presents a paper of Dr. A. Smits: “On the phenomena which oceur when the
plaitpoint curve meets the three phase line of a dissociating binary compound”. 571.

— presents a paper of J. J. van Laar: “On the course of melting-point curves
for compounds which are partially dissociated in the liquid phase, the proportion
of the products of dissociation being arbitrary’’. 699.

— and J. Ourte gr. The solubilities of the isomeric chromic chlorides. 66.

BAKHUYSEN (H. G. VAN DE SANDE). v. SANDE BAKHUYSEN (H. G. VAN DE).

BAROMETRIC HEIGHTS (On frequency curves of). 549.

BENZENE CORE (The introduction of halogen atoms into the) in the reduction of aromatic
nitro-compounds. 680. :

BENZYLANILINE (On Diphenylhydrazine, Hydrazobenzene and); and on the miscibility
of the last two with Azobenzene, Stilbene and Dibenzyl in the solid aggregate
condition. 466.

BESSEL FUNCTIONS (The quotient of two successive). I. 547. II. 640.

BEIJRRINCK (M. W.) presents a paper of N. L. SöHNGeN : “Methan as carbon-
food and source of energy for bacteria’. 327.

BINARY COMPOUND (On the phenomena which occur when the plaitpoint curve meets
the three phase line of a dissociating). 571.
BINARY MIxTURE (The molecular rise of the lower critical temperature of a) of normal

components. 144.
— (The properties of the sections of the surface of saturation of a) on the side of
the components. 280. ;
BINARY MIXTURES (On the course of the spinodal and the plaitpoint lines for) of normal
substances. 3rd communication, 578.

CONTENTS. Ill

BINARY SYSTEM (On the hidden equilibria in the p, 2-diagram of a) in consequence of
the appearance of solid substances. 196.
BINARY SYSTEMS (The different branches of the three-phaselines for solid, liquid,

vapour in) in which a compound occurs. 455.
— (The boiling points of saturated solutions in) in which a compound occurs. 536,

BLAAUW (A. H.) and F, A. F, C. Went. On a case of apogamy with Dasylirion
acrotrichum Zuce. 684.

BLANKSMA (J. J.). Nitration of symmetric nifrometaxylene. 70.

— The introduction of halogen atoms into the benzene core in the reduction of
aromatic nitro-compounds. 680.

— and F, M. Jarcer. On the six isomeric tribromoxylenes. 153.

BLOOD (On catalases cf the). 623.

BOCKWINCKEL (H. B. A). On the propagation of light in a biaxial crystal around
a centre of vibration. 728.

BOILING POINTS (The) of saturated solutions in binary systems in which a compound
occurs. 536.

BOLK’s CENTRA in the cerebellum of the mammalia. 298.

BOLK (L.). On the development of the cerebellum in man. Ist part. 1. 2nd part. 85.

— presents a paper of Dr. A. J. P. van DEN BROEK: “On the sympathetic nervous
system in Monotremes”. 91.

— On the relation between the teeth-formulas of the platyrrhine and catharrine
primates. 781.

BOLTZMANN’s Vorlesungen über Gastheorie (Some remarks on the quantity 7 in). 630.
Botany. HK. VerSCHAFFELT: “Some observations on the longitudinal growth of stems
and flower-stalks”. 8.

— Ff. A. F. C. Went: “Some remarks on the work of Dr. A. A. Pune: “An
enumeration of the vascular plants known from Surinam, together with their
distribution and synonymy”. 639.

— F. A. F.C. Went and A. H. Braauw: “On a case of apogamy observed with
Dasylirion acrotrichum Zuce.” 684.

— W. Burek: “On plants which in the natural state have the character of ever-
sporting varieties in the sense of the mutation theory”. 798.

BOUMAN (Z. P.). An article on the knowledge of the tetrahedral complex. 358,

BROEK (A, J. P. VAN DEN). On the sympathetic nervous system in Monotremes, 91.

BROMINATION (The) of toluene. 512.

BROMINE and iodine (Contribution to the knowledge of the isomorphous substitution
of the elements fluorine, chlorine,) in organic molecules. 614.

BU RCK (w.). On plants which in the natural state have the character of eversporting
varieties in the sense of the mutation theory. 798.

CARBON-FOOD (Methan as) and source of energy for bacteria, 327. :

CARDINAAL (J.) presents a paper of Dr. H. pr Vries: “Central projection in the
space of LoBaTSCHEFSKY”. Ist part. 359,

CATALASES (On) of the blood. 623,

Iv CO NATER NAS;

CAUCH Ys THEORY (Derivation of the fundamental equations of metallic reflection
from). 486.

CENTRAL PROJECTION in the space of LoparscuErsky. Ist part. 389.
CEREBELLAR connections (Anatomical research about). 563.

CEREBELLUM in man (On the development of the). Ist part. 1. 2nd part. 85.
— of the mammalia (Bork’s centra in the). 298.

Chemistry. J. J. van Laar: “On the shape of the plaitpoint curves for mixtures of
normal substances”. 2nd communication. 33.

— H. W. Bakgurs RoozeBoom and J. Orie sr: “The solubilities of the isomeric
chromic chlorides’. 66.

— J. J. Buanxsma: “Nitration of symmetric nitrometaxylene”. 70.

— F. M. Jarcrr: “On some derivatives of phenylearbamic acid’. 127.

— P. van Rompurcu : ‘On the presence of lupeol in some kinds of gutta-percha”. 137.

— P. van Rompurcu; “On the action of ammonia and amines on allyl formate”. 138.

— A. J. Urrer: “On the action of hydroeyanie acid on ketones”. 141.

— J. J. van Laar: “The molecular rise of the lower critical temperature of a
binary mixture of normal components”. 144,

— FF. M. JAEGER and J. J. Buanksma: “On the six isomeric tribromoxylenes”. 153.

— F. H. Eypman JR: “On colorimetry and a colorimetric method for determining
the dissociation constant of acids’. 166.

— D. Mor: “Ester anhydrides of dibasic acids”. 336.

— L. van lrauure: “Thalictrum aquilegifolium, a hydrogen cyanide-yielding plant”. 337.

— P. van ROMBURGH: “On the action of ammonia and amines on formic esters of
glycols and glycerol”. II. 339.

— W. A. van Dore and G. ©, A, van Dorp: “On the chlorides of maleic acid
and of fumarie acid and on some of their derivatives”. 387.

— H. W. Bakuuts RoozeBooM : “The different branches of the three-phaselines for
solid, liquid, vapour in binary systems in which a compound occurs”. 455.

— A, P. N. FRANCHIMONT and H. ERIEDMANN: “The amides of z- and -amino-
propionic acid”. 475.

— A. F. HorvEMAN and F. H. van DER Laan: “The bromination of toluene”. 512.

— H. W. Bakuuis RoozeBoom: “The boiling points of saturated solutions in
binary systems in which a compound oceurs”. 536.

— P. van Rompurcu and W. van Dorssen: “The reduction of acraldehyde and
some derivatives of s. divinylglycol (2.4 dihydroxy 1.5 hexadiene). 541.

— P. van RompurcH aud N. H. Conen: “The occurrence of 6-amyrineacetate in
some varieties of gutta-percha”. 544.

-- P. van Rompurcu and W. van Dorssen: “On the simplest hydrocarbon with
two conjugated systems of double bonds, 1. 3. 5. hexutriene”. 565.

— A. Smits: “On the hidden equilibria in the p, z-sections below the eutectic
point”. 568.

— A. Suits: “On the phenomena which occur when the plaitpoint curve meets

the three phaseline of a dissociating binary compound”. 571.

€ ON PE NTS, Vi

Chemistry. J. J. van Laar: “On the course of the spinodal and the plaitpoint lines
for binary mixtures of normal substances’. 3rd communication. 578.

— A. F. Hotteman: “On the nitration of ortho- and metadibromobenzene”. 678.

— J. J. BranksMa: “The introduction of halogen atoms into the benzene core in
the reduction of aromatic nitro-compounds’’. 680.

— J. J. van Laag: “On the course of melting-point curves for compounds which
are partially dissociated in the liquid phase, the proportion of the products of
dissociating being arbitrary”. 699.

— C. J. ENKLAAR: “On Ocimene and Myrcene, a contribution to the knowledge of
the aliphatic terpenes”. 714.

— C. J. ENKLAAR: “On some aliphatic terpene alcohols”. 723.

CHLORIDES (The solubilities of the isomeric chromic). 66,

— (On the) of maleic acid and of fumaric acid and on some of their derivatives. 387.

CHLORINE, bromine and iodine (Contribution to the knowledge of the isomorphous
substitution of the elements fluorine). 614.

CLIMATE (Oscillations of the solar activity and the). 20d communication, 155.

CLOCKS (HuyGENs’ sympathie) and related phenomena in connection with the principal
and the compound oscillations presenting themselves when two pendulums are
suspended to a mechanism with one degree of freedom. 436.

COHEN (N. H.) and P. van Rompuren. The occurrence of G-amyrine acetate in
some varieties of gutta percha. 544.

COLORIMETRY (On) and a colorimetric method for determining the dissociation constant
of acids. 166. '

COMET HOLMES (Researches on the orbit of the periodic) and on the perturbations of
its elliptic motion. 642. :

COMPLEX (An article on the knowledge of the tetrahedral). 358.

COMPLEXES of rays (A group of) whose singular surface consists of a scroll and a
number of planes. 662.

COMPONENTS (The molecular rise of the lower critical temperature of a binary mixture
of normal). 144.

— (Properties of the critical line (plaitpoint line) on the side of the). 271.

— (The properties of the sections of the surface of saturation of a binary mixture
on the side of the). 280.

— (The exact numerical values for the properties of the plaitpoint line on the side
of the). 289.

— (On the possibility of predicting the properties of mixtures from those of the). 743.

COMPOUNDS (On the course of meltingpoint curves for) which are partially dissociated
in the liquid phase, the proportion of the products of dissociation being arbitrary. 699.

CONDUCTIBILITY of heat in crystals (A simple geometrical deduction of the relations
existing between known and unknown quantities, mentioned in the method of
Vorer for deterniining the). 793:

CORALLIUM from Timor (On a new species of). 268.

CORONA (Measurement of the heat produced by the integral radiation of the) and of
the solar disk. 503.

CORTIS ORGAN (On the pressure of sound in). 60.

VI CONTENTS.

CRANIUM (The primordial) of Tarsius spectrum. 397,

CREATININ (On the excretion of) in man. 363.

CRITICAL LINE (plaitpoint line) (Properties of the) on the side of the components. 271.

CRYOGENIC LABORATORY (Methods and apparatus used in the). VIL. 77. VILL 79. IX. 82.

CRYOSTAT (A modified). 77.

— with liquid oxygen for temperatures below — 210°C. 79.

CRYSTAL (On the propagation of light in a biaxial) around a centre of vibration. 728.

Crystallography. F. M. Jarcer: “On Diphenylhydrazine, Hydrazobenzene and Benzyl-
aniline, and on the miscibility of the last two with Azobenzene, Stilbene and
Dibenzyl in the solid aggregate condition”. 466.

— F. M, Jarerr: “Contribution to the knowledge of the isomorphous substitution
of the elements fluorine, chlorine, bromine and iodine, in organic molecules”. 614.

CRYSTALS (A simple geometrical deduction of the relations existing between known and
unknown quantities, mentioned in the method of Vorer for determining the con-
ductibility of heat in), 793.

CURVE (The PLÜCKER equivalents of a cyclic point of a twisted). 498.

CYCLIC POINT (The Prücker equivalents of a) of a twisted curve. 498.

DASYLIRION ACROTRICHUM ZUCC. (On a case of apogamy observed with). 684.

pEposits (On brackish and fresh water) of the river Silat in Western-Borneo. 742.

DIBENZYL (On Diphenylhydrazine, Hydrazobenzene and Benzylaniline, and on the
miscibility of the last two with Azobenzene, Stilbene and) in the solid aggregate
condition. 466.

DILUVIUM of Holland (The geographical and geological signification of the Hondsrug,
and the examination of the erraties in the northern), 427.

— of the Netherlands North of the Rhine (On fragments of rocks from the Ardennes
found in the). 518.

DIPHENYLHYDRAZINE (On), Hydrazobenzene and Benzylaniline, and on the miscibility
of the last two with Azobenzene, Stilbene and Dibenzyl in the solid aggregate
condition. 466.

DISSOCIATION CONSTANT of acids (On colorimetry and a colorimetric method for deter-
mining the). 166.

DIVINYLGLYCOL (‘he reduction of acraldehyde and some derivatives of s.) (3.4 dihy-
droxy 1.5 hexadiene). 541,

DORP (w. A. and G. C. A. VAN). On the chlorides of maleic acid and of fumaric
acid and on some of their derivatives. 387.

DORSSEN (W. VAN) and P. van Romsureu. The reduction of acraldehyde and
some derivatives of s. divinylglycol (3.4 dihydroxy 1.5 hexadiene). 541.

— On the simplest hydrocarbon with two conjugated systems of double bonds
1.3.5 hexatriene. 565.

DUBOIS (£UG.). The geographical and geological signification of the Hondsrug,
and the examination of the erratics in the Northern diluvium of Holland. 427.

DYNAMIGS of the electron (Remarks concerning the). 477.

EASTON (c.). Oscillations of the solar activity and the climate. 2nd communication.
155,

COUN ESN DAS: Vil

EINTHOVEN (w.). Analysis of the curves obtained with the string galvanometer.
Mass and tension of the quartz wire and resistance to tle motion of the string. 210.

ELECTRON (Remarks concerning the dynamics of the). 477.

ELLIPTIC MOTION (Researches on the orbit of the periodic comet Hormes and on the
perturbations of its). 642.

ELLIPTIC ORBIT (Approximate formulae of a high degree of accuracy for the ratio of
the triangles in the determination of an) from three observations. I]. 104.

EMISSION LINES (‘The absorption and) of gaseous bodies. 591.

ENKLAAR (C. J.). On Ocimene and Myrcene, a contribution to the knowledge of
the aliphatic terpenes. 714.
— On some aliphatic terpene alcohols. 723.
EQuATIONS (Derivation of fundamental) of metallic reflection from Caucuiy’s theory. 486.
EQuILIBRIA (The Tz-) of solid and fluid phases for variable values of the pressure. 193.
— (On the hidden) in the pa-diagram of a binary system in consequence of the
appearance of solid substances. 196.
— (On the hidden) in the p,#-sections below the eutectic point. 568.
ERINACEUS EUROPAEUS L. (The uterus of) after parturition. 812.
ERRATICS (The geographical and geological signification of the Hondsrug, and the
examination of the) in the Northern Diluvium of Holland. 427.
ERRATUM. 426.
ESTER ANHYDRIDES of dibasic acids. 336.
EsTERS (On the action of ammonia and amines on formic) of glycols and glycerol. 339.
EUTECTIC POINT (On the hidden equilibria in the p‚p-sections below the). 568.
EYDMAN JR. (F. H.). On colorimetry and a colorimetric method for determining
the dissociation constant of acids. 166.
EXCRETION (On the) of creatinin in man. 363.
FISCHER (EUGEN). On the primordial cranium of Tarsius spectrum. 397.
FLOWER-STALKS (Some observations on the longitudinal growth of stems and). 8.
FLUIDS of the body (On the differentiation of), containing proteid. 628.
FLUORINE, chlorine, bromine and iodine (Contribution to the knowledge of the isomor-
phous substitution of the elements), in organic molecules. 614.
FRANCHIMONT (A. P. N.). presents a paper of Dr. D. Mor: “Ester anhydrides of
dibasic acids.” 336.
— presents a paper of Dr. F. M. JarGer: “Contribution to the knowledge of the
isomorphous substitution of the elements fluorine, chlorine, bromine and iodine,
in organie molecules.” 614.
— and H. FrreDMANN. The amides of z- and B-aminopropionie acid. 475.
FREQUENCY CURVES (On) of meteorological elements, 314.
— (On) of barometric heights. 549.
FRIEDMANN (H.) and A. P. N. Francuimont. The amides of z- and G-aminopro-
pionie acid, 475.
FUMARIC actb (On the chlorides of maleic acid and of) and on some of their derivatives, 387.
FUNCTIONS (The quotient of two successive BEssEL). [. 547. II. 640.

VIII CONTENTS.

GALVANOMETER (Analysis of the curves obtained with the string). Mass and tension
of the quartz wire and resistance to the motion of the string. 210.

GAs (Improvement to the open mercury manometer of reduced height with transference
of pressure by means of compressed). 75.

— (Improvement in the transference of pressure by compressed) especially for the

determination of isothermals. 76.

GASEOUS BODIES (The absorption and emission lines of). 591.

casEs (The purifying of) by cooling combined with compression especially the preparing
of pure hydrogen. 82. j

GASPHASE (Contribution to the knowledge of the ya- and the p7Z-lines for the case
that two substances enter into a combination which is dissociated in the liquid
and the). 200.

GASTHEORIE (Some remarks on the quantity in BOLTZMANN’s Vorlesungen über). 630.

Geology. H. G. Jonker: “Some observations on the geological structure and origin
of the Hondsrug”. 96.

— Eve. Dugors: “The geographical and geological signification of the Hondsrug,
and the examination of the erratics in the Northern Diluvium of Holland”. 427.

— C. BE. A. WrcHMANN: “On fragments of rocks from the Ardennes found in the
diluvium of the Netherlands North of the Rhine”. 518.

— K. Martin: “On brackish and fresh water deposits of the river Silat in Western-
Borneo.” 742.

GLycots and glycerol (On the action of ammonia and amines on formic esters of). 339.
GROWTH of stems and flower-stalks (Some observations on the longitudinal). 8.
GuTTA-PERcHA (On the presence of lupeol in some kinds of). 137.

— The occurrence of B-amyrine acetate in some varieties of). 544.

HAGA (H.) presents a paper of Dr. C. Scuoure: “Determination of the Thomson-eflect
in mercury”. 33).

HAMBURGER (H. J.). A method for determining the osmotic pressure of very small
quantities of liquid. 394.

Hear (On the radiation of) in a system of bodies having a uniform temperature. 401,

— (Measurement of the) produced by the integral radiation of the corona and of
the solar disk. 503.

— in crystals (A simple geometrical deduction of the relations existing between
known and unknown quantities, mentioned in the method of Vorer for deter-
mining the conductibility of). 793.

HEXATRIENE (On the simplest hydrocarbon with two conjugated systems of double bonds,
1, 3, 5). 565.
HICKSON (SYDNEY J.). On a new species of Corallium from Timor. 268.
HOEK (P. P. c.). On the polyandry of Scalpellum Stearnsi. 659.
HOLLEMAN (A. F.) presents a paper of Dr. J.J. Buanxsma: “Nitration of symmetric
nitrometaxylene.” 70.
— presents a paper of Dr. F. M. Jaraer and Dr. J. J. Buanksma: “On the six

isomeric tribromoxylenes,” 153.

C0) NDE NDS: IX

HOLLEMAN (a. F.). On the nitration of ortho- and metadibromobenzene. 678.
— presents a paper of Dr. J. J. Buanxsma: “The introduction of halogen atoms
into the benzene core in the reduction of aromatic nitro-compounds.” 680.

— and F. H. van DER Laan. The bromination of toluene. 512.

HOLMES (Researches on the orbit of the periodic comet) and on the perturbations
of its elliptic motion. 642.

HONDSRUG (Some observations on the geological structure and origin of the). 96.

— (The geographical and geological signification of the), and the examination cf
the erratics in the Northern Diluvium of Holland. 427.

HOOGEWERFF (s.) presents a paper of F. H. Eypman Jr: “On colorimetry and
a colorimetric method for determining the dissociation constant of acids.” 166.

HUBRECHT (a. a. W.) presents a paper of Prof. Eugen Frscurr: “On the primordial
cranium of Tarsius spectrum.” 397.

— presents a paper of Prof. H. Srraur: “The uterus of Erinaceus europaeus L.
after parturition.” 812. ; ,
HULSHOFF POL (od. J.). Bork’s centra in the cerebellum of the mammalia. 298.
HUYGENS’ sympathie clocks and related phenomena in connection with the principal
and the compound oscillations presenting themselves when two pendulums are

suspended to a mechanism with one degree of freedom. 436.

HYDRAZOBENZENE (On Diphenylhydrazine), and Benzylaniline, and on the miscibility
of the last two with Azobenzene, Stilbene and Dibenzyl in the solid aggregate
condition. 466.

HYDROCARBON (On the simplest) with two conjugated systems of double bonds 1, 3,5
hexatriene. 555.

HYDROCYANIC ACID (On the action of) on ketones, 141.

HYDROGEN (The purifying of gases by cooling combined with compression, especially
the preparing of pure). 82.

HYDROGEN CYANIDE-yielding-plant (Thalictrum aquilegifolium, a), 337.

ICE (On the motion of a metal wire through a lump of). 653.

INTEGRAL of Kummer (A definite). 350.

INTENSITIES of tones (On the ability of distinguishing). 421.

IODINE (Contribution to the knowledge of the isomorphous substitution of the elements
fluorine, chlorine, bromine and) in organic molecules. 614.

ISOMORPHOUS SUBSTITUTION (Contribution to the knowledge of the) of the elements
fluorine, chlorine, bromine and iodine, in organic molecules. 614.

ISOTHERMALS (Improvement in the transference of pressure by compressed gas especially
for the determination of). 76.

ITALLIE (L. van). Thalictrum aquilegifolium, a hydrogen cyanide-yielding plant. 337.

— On catalases of the blood. 623.
— On the differentiation of fluids of the body, containing proteid. 628.

- JAEGER (F. M.). On some derivatives of Phenylcarbamie acid. 127.

— On Diphenylhydrazine, Hydrazobenzene and Benzylaniline, and on the miscibility

of the last two with Azobenzene, Stilbene and Dibenzyl in the solid aggregate
condition. 466, ‘

x CONTENTS.

JAEGER (vr. M.). Contributions to the knowledge of the isomorphous substitution of
the elements fluorine, chlorine, bromine and iodine in organie molecules. 614.

A simple geometrical deduction of the relations existing between known and

unknown quantities, mentioned in the method of Vorer for determining the
conductibility of heat in erystals. 793.
— and J. J. BranksMa. On the six isomeric tribromoxylenes. 153.
JONKER (H. G.). Some observations on the geological structure and origin of the
Hondsrug. 96.

suurus (w. H,). Measurement of the heat produced by the integral radiation of
the corona and of the solar disk. 503. ~

— A new method for determining the rate of decrease of the radiating power
from the center toward the limb of the solar disk. 668.

JUPITER’s satellites (On the orbital planes of). 767.
KAMERLINGH ONNES (H.). Improvement to the open mercury manometer of
reduced height with transference of pressure by means of compressed gas, 75.

— Improvement in the transference of pressure by compressed gas especially for
the determination of isothermals. 76.

— Methods and apparatus used in the cryogenic laboratory. VII. A modified
eryostat. 77. VIIL Cryostat with liquid oxygen for temperatures below —210°C.
79. 1X. The purifying of gases by cooling combined with compression, especially
the preparing of pure hydrogen. 82.

— presents a paper of Dr. J. B. Verscuarre.t: “Contributions to the knowledge
of VAN DER Waals’ g-surface. X. On the possibility of predicting the properties
of mixtures from those of the components”. 743. 3

— presents a paper of Dr. J. B. VerscuarreLt: “Appendix to the communications
published in the meetings of June 28, September 27, 1902 and October 31,
1903”. 752.

KAPTEYN (J. C.). On the parallax of the nebulae. 691.

— presents a paper of Dr. W. pr Sirrer: “On the orbital planes of Jupiter’s

satellites”. 767.

KAPTEYN (w.). A definite integral of Kummer. 350.

— The quotient of two successive Bresser functions. L. 547. IL. 640.

KETONES (On the action of hydroeyanie acid on), 141.

KLUYVER (J. C.). A local probability problem. 341.

K OH NSTAMM (PH.) — Some remarks on Dr.— last papers (on the osmotic pressure). 49.

KORTEWEG (p. J.) presents a paper of Dr. W. A. VersLuys: “On the number of
common tangents of a curve and a surface”. 176.

-- HuyerNs’ sympathic clocks and related phenomena in connection with the
principal and the compound oscillations presenting themselves when two pendu-
lums are suspended to a mechanism with one degree of freedom. 436.

KUMMER (A definite integral of). 350.

LAAN (F. H. VAN DER) and A. F. Horteman. The bomination of toluene. 512.

LAAR (J. 3. VAN). On the shape of the plaitpoint curves for mixtures of normal
substances. 2nd communication. 33.

CONTENTS. : XI

LAAR (J. J. VAN). Some remarks on Dr, Pu. KoHNSTAMM’s last papers. 49.

— The molecular rise of the lower critical temperature of a binary mixture of
normal components. 144.

— On the course of the spinodal and the plaitpoint lines for binary mixtures of -
normal substances. 3rd communication. 578.

— On the course of melting-point curves for compounds which are partially dissociated
in the liquid phase, the propcrtion of the products of dissociation being arbitrary. 699.

LIGHT (On the theory of reflection of) by imperfectly transparent bodies. 377.

— (On the propagation of) in a biaxial erystal around a centre of vibration. 728.

LINES (Contribution to the knowledge of the pe- and pT-) for the case that two
substances enter into a combination which is dissociated in the liquid and the
gasphase, 200.

LIQUID (A method for determining the osmotic pressure of very small quantities of). 394.

— and the gasphase (Contribution to the knowledge of the pz- and the p7Z-lines for the
case that two substances enter into a combination which is dissociated in the). 200.

LIQUID PHASE (On the course of melting-point curves for compounds which are
partially dissociated in the) the proportion of the products of dissociation being
arbitrary. 699.

LOBATSCHEFSKY (Central projection in the space of). lst part. 389.

LONGITUDE of St. Denis (Island of Réunion) (Supplement to the account of the deter-
mination of the), executed in 1874, containing also a general account of the
observation of the transit of Venus. 110.

LORENTZ (H. A.) presents a paper of J. J. vaN Laar: “On the shape of the
plaitpoint curves for mixtures of normal substances”, 2nd communication. 33.

— presents a paper of J. J. van Laar: “Some remarks on Dr. Pu. Kounstamm’s
last papers”. 49.

— presents a paper of J. J. van Laar: “The molecular rise of the lower critical
temperature of a binary mixture of normal components”. 144.

— presents a paper of Prof. R. Sisstncu: “On the theory of reflection of light by
imperfectly transparent bodies”. 377.

— On the radiation of heat in a system of bodies having a uniform temperature. 401.

— presents a paper of Prof. R. Sissrncu: “Derivation of the fundamental equations
of metallic reflection from Caucuy’s theory”. 436.

— presents a paper of J. J. van Laar: “On the course of the spinodal and the
plaitpoint lines for binary mixtures of normal substances. (3rd communication). 578.

— The absorption and emission lines of gaseous bodies. 591.

— presents a paper of O. Postma; “Some remarks on the quantity H in Bourz-
MANN’s: Vorlesungen über Gastheorie”. 630.

— presents a paper of L, S. ORNsTEIN: “On the motion of a metal wire through a
lump of ice”. 653.

— presents a paper of H. B. A. BocKwiNKEL: “On the propagation of light in a
biaxial crystal around a centre of vibration”. 728.

LUPEOL (On the presence of) in some kinds of gutta percha. 137.
MAGNETIC FORCE (Magnetic resolution of spectral lines and). Ist part. 814.

XI CO N TENNIS,

MALEIC Acip (On the chlorides of) and of fumarie acid and on some of their deri-
vatives. 387.

MAMMALIA (Bonk’s centra in the cerebellum of the). 298.
MAN (On the development of the cerebellum in). 1st part. 1. 2nd part. 85.

— (On the excretion of creatinin in). 363.

MANOMETER (Improvement to the open mercury) of reduced height with transference
of pressure by means of compressed gas. 75.

MARTIN (K.) presents a paper of Dr. H. G. Jonker: “Some observations on the
geological structure and origin of the Hondsrug.” 96,

— presents a paper of Prof. Eve, Dusors: “The geographical and geological signi-
fication of the Hondsrug, and the examination of the erraties in the Northern
Diluvium of Holland.” 427.

— On brackish and fresh water deposits of the river Silat in Western-Borneo. 742.

Mathematics. Jan pr Vries: “On pencils of algebraic surfaces.” 29.

—- W. A. Verstuys: “On the rank of the section of two algebraic surfaces.” 62.

— W. A.Verstuys: “On the number of common tangents of a curve and a surface.” 176.

— J. C. Kruyver: “A local probability problem.” 341.

— W. KaprrryN: “A definite integral of Kummer.” 350.

— Z. P. Bouman: “An article on the knowledge of the tetrahedral complex.” 358.

— H. pe Vries: “Central projection in the space of Lobatschefsky.” (1st part). 389.

— D. J. Korrewee: “Huyeens’ sympathie clocks and related phenomena in
connection with the principal and the compound oscillations presenting them-
selves when two pendulums are suspended to a mechanism with one degree of
freedom.” 436.

— P. H. Scuoure: “A tortuous surface of order six and of genus zero in space
Sp, of four dimensions.” 489.

— W, A.VersLuys: “The PLicker equivalents of a cyclic point of a twisted curve.” 498.

— W. Karrnyn: “The quotient of two successive Bessel functions.” I. 547. IL. 640.

— Jan pe Vries: “A group of complexes of rays whose singular surface consists
of a seroll and a number of planes.” 662. =

— P. H. Scnoure: “A particular series of quadratic surfaces with eight common
points and eight common tangential planes.” 754.

— Jan DE Vries: “Some properties of pencils of algebraic curves.” 817.

MELTING POINT CURVES (On the course of) for compounds which are partially disso-
ciated in the liquid phase, the proportion of the products of dissociation being
arbitrary. 699.

MERCURY (Determination of the Thomson-effect in). 331.

METADIBROMOBENZENE (On the nitration of ortho-and). 678.

METAL WIRE (Qn the motion of a) through a lump of ice. 653.

Meteorology. C. Basron: “Oscillations of the solar activity and the climate”. 2ud com-
munication. 155.

— J. P. van pur Srox: “On frequency curves of meteorological elements”. 314.
— J. P. van per Srox: “On frequency curves of barometric heights”. 549.

CONTENTS. XII

METHAN as carbon-food and source of energy for bacteria. 327.

METHOD (A) for determining the osmotic pressure of very small quantities of liquid. 394,

METHOD of Vorer (A simple geometrical deduction of the relations existing between
known and unknown quantities, mentioned in the) for determining the conduc-
tibility of heat in crystals. 793.

METHODS and apparatus used in the Cryogenic Laboratory. VIL. A modified Cryostat.
77. VILL Cryostat with liquid oxygen for temperatures below — 210° C. 79. IX.
The purifying of gases by cooling combined with compression, especially the
preparing of pure hydrogen. 83.

Microbiology. N. L. SönneeN: “Methan as carbon-food and source of energy for
bacteria”. 327.
MIXTURES (On the possibility of predicting the properties of) from those of the com-

ponents. 743.

MIXTURES of normal substances (On the shape of the plaitpoint curves for). 2nd com-
munication. 33.

MOL (p.). Ester anhydrides of dibasic acids. 336.

MOLECULAR RiSE (The) of the lower critical temperature of a binary mixture of normal
components. 144.

MOLL (J. w.) presents a paper of Dr. W. Burck: “On plants which in the natural
state have the character of eversporting varieties in the sense of the mutation
theory”. 798.

MONOTREMES (On the sympathetic nervous system in). 91.

MUSKENS (L. J. J.). Anatomical research about cerebellar connections. 563.

MUTATION THEORY (On plants which in the natural state have the character of ever-
sporting varieties in the sense of the). 798.

MYRCENE (On Ocimene and), a contribution to the knowledge of the aliphatic terpenes.
714.

NEBULAE (On the parallax of the). 691.

NERVOUS SYSTEM (On the sympathetic) in Monotremes. 91.

NITRATION (On the) of brtho- and metadibromobenzene. 678.

— of symmetric nitrometaxylene. 70.

NITRO-coMPOUNDS (The introduction of halogen atoms into the benzene core in the
reduction of aromatic). 680.

NITROMETAXYLENE (Nitration of symmetric). 70.

NYLAND (A. A). The prismatic camera. 505.

OCIMENE (On) and Myrcene, a contribution to the knowledge of the aliphatic terpenes.
714.

OLIE sr. (J.) and H. W. Bakauis RoozeBooM. The solubilities of the isomeric chromic
chlorides, 66.

ONNES (H. KAMERUINGH). v. KAMERLINGH Onnzs (H.).

orBrr of the periodic comet Houmrs (Researches on the) and on the perturbations
of its elliptic motion. 642.

ORNSTEIN (1. s.). On the motion of a metal wire through a lump of ice. 653.

oriHo- and metadibromobenzene (On the nitration of). 678.

XIV CONTENTS.

OSCILLATIONS (HUYGENs’ sympathie clocks and related phenomena in connection with
the principal and the compound) presenting themselves when two pendulums
ure suspended to a mechanism with one degree of freedom. 436.

orpit of the periodic comet Houmes (Researches on the) and on the perturbations
of its elliptic motion. 642.

ORBITAL PLANEs (On the) of Jupiter’s satellites. 767.
OSMOTIC PRESSURE (Some remarks on Dr. Pu. Kounstamm’s last papers on the). 49.
— (A method for determining the) of very small quantities of liquid. 394.
OUDEMANS (J. A. C.). Supplement to the account of the determination of the
longitude of St. Denis (Island of Réunion), executed in 1874, containing also a
general account of the observation of the transit of Venus. 110.
PARALLAX (On the) of the nebulae. 691.
PEKELHARING (C. A.). On the excretion of creatinin in man. 363.
— presents a paper of Dr. L. van Irattie: “On catalases of the blood.” 623.

— presents a paper of Dr. L. van [rauutp: “On the differentiation of fluids of the
body, containing proteid.” 628.

prNcius (On) of algebraic surfaces. 29,

— (Some properties of) of algebraic curves. 817.

PHASE LINE (On the phenomena which occur when the plaitpoint curve meets the
three) of a dissociating binary compound. 571.

PHASE LINES (The different branches of the three-) for solid, liquid, vapour in binary
systems in which a compound occurs. 455.

PHASE PRESSURE (The shape of the sections of the surface of saturation normal to the
x axis, in case of a three) between two temperatures. 184,

puases (The Zz-equilibria of solid and fluid) for variable values of the pressure. 193.

PHENYLCARBAMIC ACID (On some derivatives of). 127.

Physics. J. J. van Laar: “Some remarks on Dr. Px. Konxsramm’s last papers”. 49.

— H. KAMERLINGH Onnes: “Improvement to the open mercury manometer of
reduced height with transference of pressure by means of compressed gas’ 75.

— H. Kameruincu Onnes: “Improvement in the transference of pressure by com-
pressed gas especially for the determination of isothermals”. 76.

— H. Kameruincu Onnes: ‘Methods and apparatus used in the eryogenie laboratory.
VII. A modified eryostat. 77. VILL. Cryostat with liquid oxygen for temperatures
below — 210° C. 79. IX. The purifying of gases by cooling combined with com-
pression, especially the preparing of pure hydrogen”. 82.

__ J. D. van per Waats: “The shape of the sections of the surface of saturation
normal to the a-axis, in case of a three phase pressure between two tempera-
tures”. 184.

— J. D. van per Waats: “Lhe Zr- equilibria of solid and fluid phases for variable
values of the pressure”. 193.

— A, Smirs: “On the hidden equilibria in the p‚r- diagram of a binary system in
consequence of the appearance of solid substances”. 196.

— A. Smits: “Contribution to the knowledge of the p.r- and the p7- lines for the
case that two substances enter into a combination which is dissociated in the

liquid and the gasphase”, 200,

CONTENTS. Xv

Physics. J. D. van per Waats: “Properties of the critical line (plaitpoint line) on

the side of the components.” 271.

— J. D. van per Waats: “The properties of the sections of the surface of
saturation of a binary mixture. on the side of the components.” 280.

— J. D. van per Waars: “The exact numerical values for the properties of the
plaitpoint line on the side of the components.” 289.

— ©. Scuours: “Determination of the Thomson-eflect in mercury”. 331.

— R. SrssineH! “ On the theory of reflection of light by imperfectly transparent
bodies”. 377.

— H. A. Lorentz: “On the radiation of heat in a system of bodies having a
uniform temperature”. 401.

— J. D. van per Waats Jr.: “Remarks concerning the dynamics of the
electron”. 477.

— R. Sissincu: “Derivation of the fundamental equations of metallic reflection
from CaucHy’s theory”. 486.
— H. A. Lorentz: “The absorption and emission lines of gaseous bodies”. 591.

— O. Posrma: “Some remarks on the quantity HZ in BOLTMANN's “Vorlesungen
über Gastheorie.” ” 630.

— L. S. Ornstein: “On the motion of a metal wire through a lump of ice”. 653.
— W. H. Junius: “A new method for determining the rate of decrease of the
radiating power from the center toward the limb of the solar disk”. 668.

— H. B. A. BockwinkeL: “On the propagation of light in a biaxial crystal around
a centre of vibration”. 728.

—- J. E. Verscuarrect: “Contributions to the knowledge of van DER Waars’ y-
surface. X. On the possibility of predicting the properties of mixtures from those
of the components.” 743.

— J. E‚ VerscnarreLr: “Appendix to the communications pablished in the mee-
tings of June 28, September 27, 1902 and October 31, 1903”. 752.

— KF. M. Jarcrr: “A simple geometrical deduction of ‘the relations between
known and unknown quantities, mentioned in the method of Vorer for deter-
mining the conductibility of heat in erystals”. 793.

— P. Zeeman: “Magnetic resolution of spectral lines and magnetic force”. Ist part.
814.

Physiology. H. Zwaarprmaker: “On the pressure of sound in Corti’s organ”. 60.
— W. Eryxtnoven: “Analysis of the curves obtained with the string galvano-

meter. Mass and tension of the quartz wire and resistance in the motion of the
- string”, 210.

— G. van Rynperx: “The designs on the skin of the vertebrates, considered in
their connection with the theory of segmentation”. 307.

— C. A. PEKELHARING: “On the excretion of creatinin in man”, 363.

— H. J. Hamsurcer: “A method for determining the osmotic pressure of very
small quantities of liquid”. 394,

— H. ZWAARDEMAKER: “On the ability of distinguishing intensities of tones”. 421.

— L van [rarr : “On catalases of the blood”. 623.

— L. van Ivantre: “On the differentiation of fluids of the body, containing pro-
teid”’, 628.

XVI CONTENTS

Physiology. H. ZWAARDEMAKER: “On the strength of the reflex-stimuli as weak as
possible”. 821.
PLAITPOINT CURVE (On the phenomena which occur when the) meets the three phase
line of a dissociating binary compound. 571.
PLAITPOINT CURVES (On the shape of the) for mixtures of normal substances. 2nd com-
munication. 33.
PLAITPOINT LINE (Properties of the critical line) on the side of the components. 271.
— (The exact numerical values for the properties of the) on the side of the com-
ponents. 289.
PLAITPOINT LINES (On the course of the spinodal and the) for binary mixtures of
normal substances. 38rd communication. 578.
PLANT (Thalictrum aquilegifolium, a hydrogen cyanide-yielding). 337.
PLANTS (An enumeration of the vascular) known from Surinam, together with their
distribution and synonymy. 639.
(On) which in the natura! state have the character of eversporting varieties “in
the sense of the mutation theory. 798.
PLUCKER equivalents (The) of a cyclic point of a twisted curve. 498,
POL (D. J. HULSHOFF). v. HutsHorr Por (D. J.)
POLYANDRY of Scalpellum Stearnsi (On the). 659.
POSTMA (0.). Some remarks on the quantity H in Boltzmann’s “Vorlesungen über
Gastheorie.” 630.
PRESSURE (Improvement to the open mercury manometer of reduced height with trans-
ference of) by means of compressed gas. 75.
— (Improvement in the transference of) by compressed gas especially for the deter-
mination of isothermals. 76.
— (The Tx-equilibria of solid and fluid phases for variable values of the). 193.
— of sound (On the) in Corti’s organ. 60.
PRIMATEs (On the relation between the teeth-formulas of the platyrrhine and catarrhine). 781.
PRISMATIC CAMERA (The). 505.
PROBABILITY PROBLEM (A local). 341.
proreip (On the differentiation of fluids of the body, containing). 628.
PULLE (A. A.). An enumeration of the vascular plants known from Surinam, re
with their distribution and synonymy. 639.
QUADRATIC SURFACES (A particular series of) with eight common points and eight
common tangential planes. 754.
quantrry ZZ (Some remarks on the) in BortzMann’s “Vorlesungen über Gastheorie.” 630.
QUARTZ wirp (Mass and tension of the) and resistance to the motion of the string. 210.
RADIATING POWER (A new method for determining the rate of decrease of the) from
the center toward the limb of the solar disk. 668.
RADIATION (Measurement of the heat produced by the integral) of the corona and the
solar disk. 503.
— of heat (On the) in a system of bodies having a uniform temperature. 401.
RATE OF DECREASE (A new method for determining the) of the radiating power from

the center toward the limb of the solar disk. 668,

CONTENTS, xVII

RATIO of the triangles (Approximate formulae of a high degree of accuracy for the)
in the determination of an elliptic orbit from three observations. Il. 104.

rays (A group of complexes of) whose singular surface consists of a scroll and a
number of planes. 662.
REFLECTION (Derivation of the fundamental equations of metallic) from Caucuy’s
theory. 486.
— of light (On the theory of) by imperfectly transparent bodies, 377.
REFLEX-STIMULI (On the strength of the) as weak as possible. 821.

rocks (On fragments of) from the Ardennes found in the diluvium of the Netherlands
North of the Rhine, 518.
ROMBURGH (P. VAN) presents a paper of Dr. F. M. Jarcer : “On some derivatives
of Phenylcarbamic acid.” 127.
— On the presence of lupeol in some kinds of gutta-percha. 137.
— Or the action of ammonia and amines on allyl formate. 138.
— presents a paper of Dr. A. J, Uurer: “On the action of hydrocyanic acid on
ketones”. 141,
— presents a paper of Dr. L. van Iraumm: “Thalictrum aquilegifolium, a hydrogen
cyanide-yielding plant”. 337.
— On the action of ammonia and amines on formic esters of glycols and glycerol. 339.
— presents a paper of Dr.C. J. ENKLaar : “On Ocimene and Myrcene, a contribution
to the knowledge of the aliphatic terpenes.” 714.
— presents a paper of Dr. C.J. ENKLAAR: “On some aliphatic terpene alcohols.” 723,
— and N. H. Conen: “The occurrence of @-amyrine acetate in some varieties of
gutta percha’. 544.
— and W. van Doxssen: “The reduction of acraldehyde and some derivatives of
s, divinylglycol (3.4 dihydroxy 1.5 hexadiene). 541.
— On the simplest hydrocarbon with two conjugated systems of double bonds,
1.3.5 hexatriene. 565.
ROOZEBOOM (H. W. BAKHUIS). v. BaKHurs Roozesoom (H. W.).
RIJNBERK (G. vAN). The designs on the skin of the vertebrates, considered in
their connection with the theory of segmentation. 307.
SANDE BAKHUYZEN (H.G, VAN DE) presents a paper of J. WEEDER: “Ap-
proximate formnlae of a high degree of accuracy for the ratio of the triangles
in the determination of an elliptic orbit from three observations”, II. 104,
— Preliminary Report on the Dutch expedition to Burgos for the observation of
the total solar eclipse of August 30, 1905, 501,
— presents a paper of Dr. H. J. Zwiers: “Researches on the orbit of the periodic
comet Holmes and on the perturbations of its elliptic motion”. 642.
SATELLITES (On the orbital planes of Jupiter’s). 767.
SCALPELLUM STEARNSI (On the polyandry of). 659.
scHourTe (c.). Determination of the Thomson-effect in mercury. 331,
SCHOUTE (P. H.) presents a communication Dr, W. A. VersLuys: “On the rank of
the section of two algebraic surfaces”, 52.

XVIII COONS DIEREN Les;

scHOUTE (P. H.). A tortuous surface of order six and of genus zero in space Sy,
of four dimensions, 489,

— presents a paper of Dr. W. A. Verstuys: “The PLicker equivalents of a cyclic
point of a twisted curve.” 498.

— A particular series of quadratic surfaces with eight common points and eight
common tangential planes. 754.

SECTION of two algebraic surfaces (On the rank of the). 52.
SECTIONS (On the hidden equilibria in the p,z-) below the eutectic point. 568.

SEGMENTATION (The designs on the skin of the vertebrates, considered in their con=
nection with the theory of). 307.

stLat in Western-Borneo (On brackish and fresh water deposits of the river). 742.

SISSINGH (R.). On the theory of reflection of light by imperfectly transparent
bodies. 377.

—- Derivation of fundamental equations of metallic reflection from CaucHy’s

theory. 486.

SITTER (w. DE). On the orbital planes of Jupiter’s satellites. 767.

sktN (The designs on the) of the vertebrates, considered in their connection with the
theory of segmentation. 307.

SMITS (A). On the hidden equilibria in the p‚x-diagram of a binary system in
consequence of the’ appearance of solid substances. 196.

— Contribution to the knowledge of the pa- and the pZ-lines for the case that two
substances enter into a combination which is dissociated in the liquid and the
gasphase. 200.

— On the hidden equilibria in the p,z-sections below the eutectic point. 568.

— On the phenomena which occur when the plaitpoint curve meets the three phase
line of a dissociating binary compound. 571.

SÖHNGEN (N. L.). Methan as carbon-food and source of energy for bacteria. 327.

SOLAR activity (Oscillations of the) and the climate. 2nd communication. 155.

SOLAR DISK (Measurement of the heat produced by the integral radiation of the corona
and of the). 503.

— (A new method for determining the rate of decrease of the radiating power
from the center toward the limb of the). 668.

SOLAR ECLIPSE (Preliminary Report on the Dutch expedition to Burgos for the obser-
vation of the) of August 30, 1905. 501.

— (Report on the operations with the two slit-spectrographs for the) of August

30, 1905. 506.

SOLUBILITIES (The) of the isomeric chromic chlorides. 66.

SOLUTIONS (The boiling points of saturated) in binary systems in which a compound
occurs. 536.

SOUND (On the pressure of) in Corti’s organ. 60.

SPACE Sp, (A tortuous surface of order six and of genus zero in) of four dimensions. 489.

— of LosarscuErsky (Central projection in the). Ist part. 389.

SPECTRAL LINES (Magnetic resolution of) and magnetic force. 1st part. 814,

en

CONTENTS. XIX

SPECTROGRAPHS (Report on the operations with the two slit-) for the solar eclipse of
August 30, 1905. 506.

SPICULES of sponges (On the structure of some siliceous). I. The styli of Tethya

lyncurium, 15,

SPINODAL and the plaitpoint lines (On the course of the) for binary mixtures of
normal substances. 3rd communication. 578.

SPONGES (On the structure of some siliceous spicules of). I. The styli of Tethya
Jyncurium. 15.

ST. DENIS (Island of Réunion) (Supplement to the account of the determination of
the longitude of), executed in 1874, containing also a general account of the
observation of the transit of Venus. 110.

sTEMs and flower-stalks (Some observations on the longitudinal growth of). 8.

STILBENE and Dibenzyl (On Diphenylhydrazine, Hydrazobenzene and Benzylaniline,
and on the miscibility of the last two with Azobenzene) in the solid aggregate
condition, 466.

STOK (J. P. VAN DER). On frequency curves of meteorological elements. 314.

— On frequency curves of barometric heights. 549.

STRAHL (H.). The uterus of Erinaceus europaeus L. after parturition. $12.

STRING (Mass and tension of the quartz wire and resistance to the motion of the). 210.

SUBSTANCES (On the hidden equilibria in the p,v-diagram of a binary system in conse-
quence of the appearence of solid). 196.

— (Contribution to the knowledge of the p,a-and the p,7- lines for the case that
two) enter into a combination which is dissociated in the liquid and the gasphase. 200.

SURFACE (A tortuous) of order six and of genus zero in space Sp, of four dimensions. 498.

J-surracr (Contributions to the knowledge of van per Waats’). X. On the possibi-
lity of predicting the properties of mixtures from those of the components. 743,

SURFACE OF SATURATION (The shape of the sections of the) normal to the a-axis, in case
of a three phase pressure between two temperatures. 184.

SURFACE OF SATURATION (The properties ot the sections of the) of a binary mixture
on the side of the components, 280.

SURFACES (A particular series of quadratic) with eight common points and eight
common tangential planes. 754.

SURINAM (An enumeration of the vascular plants known from) together with their
distribution and synonymy. 639.

TANGENTS (On the number of common) of a curve and a surface. 176.

TARSIUS SPECTRUM (On the primordial cranium of). 397.

TEETH-FORMULAS (On the relation between the) of the platyrrhine and catarrhine
primates. 781.

TEMPERATURE (The molecular rise of the lower critical) of a binary mixture of normal
components. 144.

— (On the radiation of heat in a system of bodies having a uniform). 401,

TEMPERATURES (The shape of the sections of the surface of saturation normal to the
x-axis, in case of a three phase pressure between two). L84.

— below —210°C, (Cryostat with liquid oxygen for). 79.

oe

XxX CONTENTS.

TERPENE ALCOHOLS (On some aliphatic). 723.

TERPENES (On Ocimene and Myrcene, a contribution to the knowledge of the aliphatic). 714.
TETHYA LYNCURIUM (The styli of). 15.

TETRAHEDRAL COMPLEX (An article on the knowledge of the). 358.

THALICTRUM AQUILEGIFOLIUM, a hydrogen cyanide-yielding plant. 337.

THEORY of reflection of light (On the) by imperfectly transparent bodies. 377.
THOMSON-EFFECT (Determination of the) in mercury. 331.

Timor (On a new species of Corallium from). 268.

TOLUENE (The bromination of). 512.

TONES (On the ability of distinguishing intensities of). 421.

TRANSIT of Venus (Supplement to the account of the determination of the longitude
of St. Denis (Island of Réunion), executed in 1874, containing also a general
account of the observation of the). 110.

TRIANGLES (Approximate formulae of a high degree of accuracy for the ratio of the)
in the determination of an elliptic orbit from three observations. II. 104,

TRIBROMOXYLENES (On the six isomeric). 153.

ULTEE (A. J.). On the action of hydrocyanic acid on ketones. 141.

uterus (The) of Erinaceus europaeus L. after parturition. 812.

VENUS (Supplement to the account of the determination of the longitude of St. Denis
(Island of Réunion), executed in 1874, containing also a general account of the
observation of the transit of). 110.

VERSCHAFFELT (E.). Some observations on the longitudinal growth of stems and
flower-stalks. 8.

VERSCHAFFELT (J. E). Contributions to the knowledge of vaN DER Waats’
p-surface. X. On the possibility of predicting the properties of mixtures from
those of the components. 743.

— Appendix to the communications published in the meetings of June 28, Sep-
tember 27, 1902 and October 31, 1903. 752.
VERSLUYS (w. A.). On the rank of the section of two algebraic surfaces. 52.
— On the number of common tangents of a curve and a surface. 176.
— The Prücker equivalents of a cyclic point of a twisted curve. 498,

VERTEBRATES (The designs on the skin of the), considered in their connection with
the theory of segmentation. 307.

VIBRATION (On the propagation of light in a biaxial crystal around a centre of). 728.

vorer (A simple geometrical deduction ot the relations existing between known and
unknown quantities, mentioned in the method of) for determining the conduc-
tibility of heat in erystals. 793.

VOSMAER (G. C.J.) and H. P. Wisman. On the structure of some siliceous
spicules of sponges. I. The styli of Tethya lyneurium. 15.

VRIES (H. DE). Central projection in the space of LoBarscuErsky. lst part. 389,

VRIES (HUGO DE) presents a communication of Prof. E. Verscuarrent: “Some
observations on the longitudinal growth of stems and flower-stalks”. 8,

VRIES (JAN DE). On pencils of algebraic surfaces, 29,

CONTENT SH, XXI

VRIES (JAN DE) presents a paper of Z. P, Bouman: “An article on the know-
ledge of the tetrahedral complex.” 358. Bay
— A group of complexes of rays whose singular surface consists of a scroll and a
number of planes. 662.
— Some properties of pencils of algebraic curves. 817.

WAALS (VAN DER) g-surface (Contributions to the knowledge of). X. On the
possibility of predicting the properties of mixtures from those of the components. 743,
WAALS (J, D. VAN DER). The shape of the sections of the surface of saturation
normal to the a-axis, in case of a three phase pressure between two temperatures. 184.
— The 7,x equilibria of solid and fluid phases for variable values of the pressure. 193.
— presents a paper of Dr. A. Sirs: “On the hidden equilibria in the p,e-diagram
of a binary system in consequence of the appearance of solid substances.” 196.
— presents a paper of Dr. A. Smits: ‘Contribution to the knowledge of the pz-
and the p7Z-lines for the case that two substances enter into a combination which
is dissociated in the liquid and the gasphase.” 200.
— Properties of the critical line (plaitpoint line) on the side of the components. 271.
— The properties of the sections of the surface of saturation of a binary mixture
on the side of the components. 280.
— The exact numerical values for the properties of the plaitpoint line on the side
of the components. 289. -
— presents a paper of Prof. J. D. van per Waars Jr: “Remarks concerning the
dynamics of the electron.” 477.
WAALS JR. (J. D VAN DER). Remarks concerning the dynamics of the electron. 477.
WEBER (MAX) presents a paper of Prof. Sypney J. Hickson: “On a new species
of Corallium from Timor.” 268.
WEEDER (J.). Approximate formulae of a high degree of accuracy for the ratio of the
triangles in the determination of an elliptic orbit from three observations. II. 104,
WENT (F. A. F. C.). Some remarks on the work of Mr. A. A. Pure, entitled: “An
enumeration of the vascular plants known from Surinam, together with their
distribution and synonymy.” 639.
— and A. H. Braauw. On a case of apogamy observed with Dasylirion acrotrichum
Zuce. 684,
WICHMANN (c. B‚ A). On fragments of rocks from the Ardennes found in the
diluvium of the Netherlands North of the Rhine. 518.
WILTERDINK (J. H.). Report on the operations with the two slit-spectrographs for
the solar eclipse of August 30, 1905. 506.
WIND (Cc. H.) presents a paper of C. Easton: “Oscillations of the solar activity and
the climate”, 2nd communication. 155.
WINKLER (C.) presents a paper of D. J. Hursuorr Por: ‘“Bork’s centra in the
cerebellum of the mammalia”. 298.
— presents a paper of Dr. G. van Risnperx: “The designs on the skin of the
vertebrates, considered in their connection with the theory of segmentation’’. 307.

— presents a paper of Dr. L. J. J. Muskens: “Anatomical research about cerebellar
connections,” 563,

XXII REGISTER.

WIJSMAN (H. P.) and G. U. J. Vosmaer. On the structure of some siliceous spi-
cules of sponges. I. The styli of Tethya lyncurium. 15,

ZEEMAN (P.) presents a paper of Dr. F. M. Jarcer: “A simple geometrical
deduction of the relations existing between known and unknown quantities,
mentioned in the method of Vorer for determining the conductibility of heat in
crystals.” 793.

— Magnetic resolution of spectral lines and magnetic force. Ist part. 814.

Zoology. G. C. J. Vosmarr and H. P. Wissman: “On the structure of some siliceous
spicules of sponges. J. The styli of Tethya lyncurium.” 15.

— Sypney J. Hickson: “On a new species of Corallium from Timor.” 268.
— Eveen Fiscuer: “On the primordial cranium of Tarsius spectrum.” 397,
— P. P. C. Hoek: “On the polyandry of Scalpellum Stearnsi.” 659.

— H. SrrauL: “The uterus of Erinaceus europaeus L. after parturition.” 812.

ZWAARDEMAKER (H.). On the pressure of sound in Corti’s organ. 50,

— On the ability of distinguishing intensities of tones. 421,
— On the strength of the reflex-stimuli as weak as possible. 821.

ZWIERS (H. J.). Researches on the orbit ot the periodic comet Houmes and on the
perturbations of its elliptic motion. 642.

Koninklijke Akademie van Wetenschappen
te Amsterdam.

PROCEEDINGS

OF THE

BE OTTON OF SCIEN Can

VOEDEN Me VEE

(2nd PART)

AMSTERDAM,
JOHANNES MULLER.
June 1906,

air

MALENE
1 00067624