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KONINKLIJKE AKADEMIE
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PROCEEDINGS OF THE
oe LION OF SCIENCES

VOLUME XVIII
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JOHANNES MULLER :—: AMSTERDAM
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(Translated from: Verslagen van de Gewone Vergaderingen der
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Proceedings of the Meeting of May 29, 1915 (No. 1)

» > > » » June 26, 1915 (N° 2).
> >» > » » September 25, 1915 (N°. 3) .

» » » » NO AED TEE OSS

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCES IDINGS Ole Wiel] IMiNSsi2 1p INKe
of Saturday May 29, 1915.
Vor. XVIII.

President: Prof. H. A. LORENTZ.
Secretary: Prof. P. ZEEMAN.

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

Natuurkundige Afdeeling van Zaterdag 29 Mei 1915, DI. XXIV).

CONTENTS.

J. BOEKE: “On the structure and the innervation of the musculus sphincter pupillae and the musculus
ciliaris of the bird’s eye”, p. 2.

C. G. S. SANDBERG: “How volcanism might be explained”. (Communicated by Prof. C. E. A.
WICHMANN), p. 10.

J. WOLTJER JR.: “Observation of the moon during the Eclipse of the sun on Aug. 21 1914 and of the
Transit of Mercury on Nov. 7 1914, made in the Leiden Observatory. (Communicated by Prof.
E. F. VAN DE SANDE BAKHUYZEN), p. 16.

W. A. MIJSBERG: “On the structure of the muscular abdominal wall of Primates”. (Communicated
by Prof. L. BOLK), p. 19.

S. DE BOER: “On the heart-rhythm”. II]. (Communicated by Prof. J. K. A. WERTHEIM SALOMONSON),
p. 34.

JAN DE VRIES: “A particular bilinear congruence of rational twisted quintics”, p. 39.

JAN DE VRIES: “Bilinear congruences of elliptic and hyperelliptic twisted quintics”, p. 43.

L. E. J. BROUWER: “Remark on inner limiting sets”, p. 48.

F. M. JAEGER: “Investigations on PASTEUR's Principle of the Relation between Molecular and
Physical Dissymmetry” IL. (Communicated by Prof. H. HAGA), p. 49. (With one plate).

F. M. JAEGER and JUL. KAHN: “Investigations on the Temperature-Coefficients of the free Molecular
Surface-Energy_of Liquids at Temperatures from —80° to 16500 C.” IX. The Surface-Energy of
homologous Aliphatic Amines. (Communicated by Prof. P. VAN ROMBURGH), p. 75.

ERNST COHEN and S. WOLFF: “The Allotropy of Sodium” I, p. 91.

P. VAN ROMBURGH: “Action of methylethylketone on 2. 3.4.6. tetranitrophenylmethyinitramine”, p. 98.

L. H. SIERTSEMA: “The magnetic rotation of the polarisation plane in titanium tetrachloride”. I,
(Communicated by Prof. H. A. LORENTZ), p. 101.

A. SMITS and S. C. BOKHORST: “On Tension Lines of the System Phosphorus”. IV, (Communicated
by Prof. J. D. VAN DER WAALS), p. 106.

F. A. H. SCHREINEMAKERS: “In-, mono- and divariant equilibria”. I, p. 116.

F. A. H. SCHREINEMAKERS and Miss W. C. DE BAAT: “Compounds of the Arsenious Oxide”, II. p. 126.

Proceedings Royal Acad. Amsterdam, Vol, XVIII.

Anatomy. — “On the structure and the innervation of the musculus
sphincter pupillae and the musculus ciliaris of the bird's eye.”
By Prot. J. Borkr. (With 12 figures).

(Communicated in the meeting of April 23, 1915).

In a former communication’) I deseribed the innervation, the
relations between the muscle-cells and the nerve-endings, of the ciliary
muscle of the human eye, as a type of plain muscular tissue. A
subsequent examination of frontal sections through the iris-muscles
taught me, that, as far as my preparations showed me, the relations
between the efferent nerve-endings and the muscle-cells of the sphincter
pupillae in the iris of the human eye are essentially the same as
in the ciliary muscle. In connection with these observations it seemed
to be of interest to study somewhat more closely the structure and
the innervation of the intrinsic eye-ball-muscles (sphincter and dila-
tator pupillae, ciliary muscles) of the bird’s eye.

For indeed, both from the physiological and the morphological
point of view, this comparison of the iris- and ciliary muscles of
mammals and birds seems to be of interest. The swift and complex
accomodation (lens and cornea), the swift and varying play of the
muscles of the iris and their rôle in accomodation, the peculiar diffe-
rences in the function of the eyes in birds of different kinds and
habits (birds of prey, fastflying birds, day and night-birds, diving
birds ete.) make such a comparison of the details of the nerve-supply
tempting. And beside these physiological differences the ciliary and
iris-muscles of birds present such striking morphological characteristics,
that these alone would make a comparison of the avian and mam-
malian eye-muscles valuable.

The intrinsic muscles of the avian eye, both the muscles of the
iris (with the exception of the dilatator pupillae) and the ciliary
muscle, are distinguished from the homologous muscles of mammals
by their being composed of striated muscle-fibres, as was known
since the classical researches of Brücke and Möürrer.

In the vertebrate series this cross-striation of the inner muscles of
the eye-ball is only found in reptiles and birds. As was mentioned
above, it is met with both in the muscles of the iris and of the
corpus ciliare. Only the so-called dilatator pupillae of the membrane
of Brucn, as it was shown by the interesting and thorough researches
of GRYNFELLT, ANDREAR, ZIETZSCHMANN, VON SziLy and others, does not
show any vestige of eross-striation.

1) Proceedings of the meeting of Jan. 30, 1915. Royal Academy of science,
Amsterdam, p. 982—989.

By this eross-striation the muscle-fibres of the iris and the corpus
ciliare may be compared with the group of voluntary musele-fibres,
but when we study somewhat more closely their form and structure,
there appear quite a number of minor differences, which bring them
into a closer vicinity to the heart-musele fibres.

In the first place the musele-fibres of the iris and the corpus
ciliare, as was shown as far back as 1883 by GrBERG, do not possess
the tough, thickened cellmembrane commonly known as sarcolemma.
Here the plasma and the myofibrilla contained in the sarcoplasma
are surrounded by an extremely thin and delicate membrane, rein-
forced by the closely applied bodies of connective-tissue cells, and
often it is practically impossible to demonstrate the membranous
covering of the fibres, which might be called a sarcolemma apart
from this connective tissue.

In the second place these muscle-fibres contain a very considerable
amount of sarcoplasm and only a comparatively small number of
contractile striated fibrillae. These fibrillae are usually gathered toge-
ther into a number of columnlike or platelike bundles, which we
may call with Scuirer among others the sarcostyles.

In thin musele-fibres these fibrilbundles are distributed rather regu-
larly throughout the whole muscle-fibre, and, when cut in transverse
sections, present the picture of fig. 1 and fig. 5.

In the larger muscle-fibres these fibrilbundles or sarcostyles are
arranged in a curious manner, in flattened bundles, folded or curved
round, and lying in a large amount of sarcoplasm; the structure

Fig. 1. Fig. 2.

Fig. 3. Fig. 4. Fig. 5.
Fig. 1—5 cross sections of muscle-fibres of the muse. sphincter
pupillae of a full-grown fowl. Magn. 1600.
1*

and arrangement of the contractile elements of these large fibres is
better elucidated by regarding the cross-sections figured in fig. 2, 4,
and 5 than by a long-winded description. Especially in the transverse
sections of the larger muscle-fibres of the sphincter pupillae of full-
grown fowls this arrangement of the sarcostyles in flattened and
curved bundles is clearly shown.

The sarcoplasm between the folded and curved sareostyles is in
most cases of a very loose reticular slightly granular appearance.
Outside the column of fibrilbundles and platelike bands the sarco-
plasm is generally of a more coarsely granular structure and sur-
rounds the contractile elements on all sides, often in a thick layer.
Sometimes this granular appearance is seen throughout the whole
of the transverse section of a muscle-fiber. At intervals this layer of
sarcoplasm lying outside the column of sarcostyles is so thick, that
it not only surrounds the bundle of sarcostyles at all sides, but is
seen projecting beyond the line of the surface of the fibre, forming
a sort of protuberance on the side of the fibre (fig. 2, fig. 6); this
accumulation of sarcoplasm always contains several nuclei ; which
however, are found also here and there in the loosely reticulated
sarcoplasm between the sarcostyles (fig. 5). These sarcoplasmatic
protuberances may be compared with the granular expansions first

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Fig. 6 and 7 Longitudinal sections of striated muscle-fibres of the iris of
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noticed by Doyire in insects, and with the “soles” of the muscle-
fibres of the vertebrates. Only here they are found in a large num-
ber on the same muscle-fibre, and only one or two of them serve
as a “bed” or “sole” for the efferent nerve-endings (fig. 1, fig. 5, fig. 8).

Through this abundance of sarcoplasm, the curious arrangement
of the sarcostyles and the local protuberances of sarcoplasm on the
side of it, the muscle-fibre already acquires a very curious appearance.
This is still accentuated by the third fact to be mentioned here,
viz. that the muscle-fibres are not the independent, threadlike, straight
elements, running from one end of the muscle to the other, as is
the case in most of the sceletal muscles, but that in the iris of the
birds the muscle-fibres are branched, interwoven, and not only that
they divide, but the fibres anastomose through these side-branches
(cf. GrBrrG), so that there is established a continuity of the fibres
throughout the whole ring of the iris instead of a tissue containing
only distinct separate fibres. This syneytium of sarcoplasmatic elements
with bundles of fibrillae running through it in complete continuity
over a great distance gives the muscles of the avian iris a striking
resemblance to the cardiae muscle-fibres of the mammalian or avian
heart, with the only restriction that in the sphincter iridis the con-
nections between the different musclefibres do not come so much to the
foreground as in the heart muscle, and that the individuality of the
musclefibres is better preserved than it is the case in the myo-cardium,

In connection with this branching, dividing and anastomosing of
the different muscle fibres of the iris muscle a curious phenomenon
may be mentioned here, of which an example is drawn in fig. 6,
When we study tangential (frontal) sections of the iris, in which the
whole system of the fibres of the sphincter pupillae is shown parallel
to the surface, we meet in these sections both the circular fibres
running around the pupil (the sphincter pupillae) and the radiating
fibres, cut in longitudinal direction. We can state in these sections
throughout the whole depth of the sphincter muscle, but especially
in the dorsal part of the stroma iridis, the presence of a number
of radiating fibres running between the bundles of the circular tibres,
at right angles to the direction of the circular fibres, but lying in
the same plain. These radiating muscle fibres are apparently independent
of the circular fibres, and this is what we should expect, in corre-
spondence with the antagonistic function, which we should be inclined
to ascribe to the two sorts of fibres. But then this independency is
often only apparent, and one often finds a connection between the
two sets of fibres, even in the way figured in fig. 6, where a
muscle-fibre belonging to the circular system of the sphincter pupillae

divides into two branches running at right angles to the mother-
fibre, and thus forming a radiating fibre of the second system. The
curving round of the sarcostyles, the place of these fibril-bundles in
the sarcoplasm, the whole aspect of the T-shaped muscle-fibre, drawn
in the figure as accurately as possible, leave as if seems no doubt
as to the accuracy of the observation. And indeed, even GEBERG
as long ago as 1583, seems to have seen something like it, where
he says: “wo wir es, wie es so oft an unseren Object der Fall ist,
mit vielfach und mitunder senkrecht gegen einander sich verzweigenden
Muskelfasern zu thun haben’,... (le. p. 14).

Thus we must regard the muscular system of the iris in a certain
sense as a syncytium, composed of elements, connected with each
other, and in which the fibres of the circular system are in an
organic connection with the radiating fibres of the iris musculature.

Entirely independent of this system remains the so-called membrane
of Brucu, composed of fibres (or elongated cells) running only in a
radiary direction and remaining through life in close connection with
the epithelium of the iris, which do not show any vestige of eross-
striation, and to which must be ascribed exclusively, according to
ZIRTZSCHMANN, the function of a real dilatator pupillae.

In the muscular sheet of the iris of the human eye, being composed
of plain muscle-cells, this organic connection between the sphincter
muscle and the dilatatory fibres converging towards the pupil, is of
‘course not easily to be stated with accuracy. But the study of thin
tangential (frontal) sections through the iris gives one the impression,
that even here similar relations exist.

In my former communication I described the interesting relations
existing between the efferent nerve-endings and the muscle-cells of
the musculus ciliaris of the human eye. The small dimensions of
the muscular elements of the human corpus ciliare and the closely
interwoven nerve plexus make it very difficult to get a clear picture
of the numerical relations between the nerve-endings and the musele-
cells. The terminations of the efferent nerves seemed to be present
in two distinct types (compare the figures of the communication
mentioned above), as small rings or loops and as small networks,
but I could not get a distinct answer to the question whether these
two types of intraplasmatic nerve-endings belong to two different
kinds of efferent nerves or to nerve-fibres of the same kind and
the same source.

Kasier to determine are the relations between the efferent nerves
and the muscular elements in the bird’s eye,

=
(

According to the current opinion, in man and mammals, in Which
the relations between the nerves and the muscle-cells of the: iris are
studied profoundly, the sphincter pupillae is innervated by means of
the ganglion ciliare and the third nerve, the dilatator pupillae how-
ever gets its nervous supply from the sympathetic nerve, by means
of the superiorcervical ganglion, the ganglion ciliare and the nervi
ciliares longi. Stimulation of the nervus oculomotorius causes the
pupil to contract, stimulation of the cervical sympathetic causes the
pupil to enlarge. The real innervation of the membrane of Brucu
is not known. Only Rerzivs (1893) asserts to have seen in albinotic
rabbits very delicate non-medullated nerve-fibres running towards
the fibres or cells of this membrane and ending in very small knobs
lying against the surface of the membrane. In birds, where the
structure of the iris-muscles and the function of the sphincter and
dilatata pupillae have been studied very profoundly of late years,
there is no unanimity of opinion about the relations between efferent
nerves and the different muscular systems. GnrperG and Merkicn
are of opinion that both the circular and the radiating muscle-
fibres of the iris are innervated by inedullated nerve-fibres coming
from the same source. About the innervation of the membrane of
Brucu in the bird’s eye we know nothing exactly.

Cross sections and especially longitudinal (frontal) sections through
well-impregnated preparations of the iris of fowls and pigeons stained
after the method of Brerscnowsky and treated afterwards with
chloride of gold, haematoxylin and eosin showed the following facts.

In the iris-stroma we find the bundles and plexus of nerve-fibres,
containing medullated and non-medullated fibers, as they were described
by GeBrerG and others. :

The thick medullated nerve-fibres running between the muscular
elements of the sphincter pupillae supply them with terminations,
which may be compared with the motor nerve-endings (end-plates
of KueNeN) of the voluntary muscle-fibres.

On the muscle-fibres both of the musculus ciliaris and of the
sphineter pupillae these efferent nerve-terminations are loose, provided
with only a few branches and small endrings or delicate endnets.
The motor nerve-fibre usually enters the muscle-fibre at one of the
sarcoplasmatic protuberances described above (fig. 9 and 10) and in
transverse sections through the muscle-fibres the hypolemmal position
of these nerve-endings is clearly to be seen (fig. 1 and 5). Under a
very high power even in these muscles the existence of a periter-
minal network in the sarcoplasm and the intimate connections
between this periterminal network and the nerve-termination on one

Fig. 8. Muscle-fibre from the musculus ciliaris of a full-grown fowl
with double innervation. af = accessory nerve-termination. 7 = common
motor nerve-ending.

Fig. 9 and 10. Muscle-fibres of the sphincter pupillae of the eye of a full-grown
fowl, showing double innervation.

hand and the contractile fibrils, the sarcostyles on the other hand,
could be stated with accuracy. I often got the impression that the
delicate nerve-fibrils of the motor nerve-ending, after entering the
muscle-fibre, run round the sarcoplasmatic prominence, encircling it,
and then follow the direstion of the sarcostyles for some distance
before breaking up in endrings or endnets. These motor nerve-endrings
I found both in the circular fibres of the sphineter pupillae and in
the radiating fibres. The innervation of the membrane of Brucu I
could not make out.

Beside these motor nerve-endings at the end of medullated nerve-fibres
there exist in the sphincter pupillae and in the musculus ciliaris of
the bird’s eye just as in the voluntary sceletal muscles the very
delicate, non-medullated nerve-fibres with their small, loosely arranged,
delicate endings, entering the muscle-fibers independently of the
motor nerve-terminations mentioned above, which I described in the
voluntary muscles of the body as “accessory nerve-terminations”’,
and which could be traced to the nervus sympathicus. In fig. 8, 9,
and 10 are given some examples of these accessory nerve-endings
on muscle-fibres of the sphincter pupillae and the musculus ciliaris.

As far as I could gather from my preparations, the delicate non-
medullated nerve-fibres ending in the small “accessory” terminations
on the muscle-fibres, remained independent of the medullated nerves.

Whether we are entitled to ascribe to these accessory nerve-fibres
even bere an influence on the tonus of the iris- and ciliary muscles,
and what are the relations of these nerve-fibers to the sympathetic
nerve, are questions not to be debated here. There is here a wide
field lying open for experimental study.

In conclusion some words may be added about the question,
whether ganglioncells are present in the corpus ciliare or in the
stroma of the iris or not. Several authors (e.g. Rerzius) denied the
existence of these ganglioncells, others, as C. Krause, H. MéLiEr, and
in later years especially GeBere, described small groups of ganglion-
cells and separate cells appearing alongside the nerve-fibre bundles,
others, as AGABABow, found ganglioncells only in the course of the
vasomotor nerves. Finally Ineris Pottock found in 1912 that after
the exstirpation of the ganglion ciliare or of the superior cervical
sympathetic ganglion the nerves of the corpus ciliare and iris did
not degenerate. This fact would point to the conclusion, that in the
corpus ciliare and the iris the ganglioncells are as abundant as they
are in the terminal sympathetic ganglia in the intestinal wall in the
nerve plexus of AvwrBacH and MuissNer.

In my preparations of the corpus ciliare and iris, stained after

the method of Birnscnowsky, ganglioncells were scarce, and in fact
I often looked in vain for them. It was only in the nerve plexus

5 En - = |

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Sip aes EE eS Neri 5 Et

Fig. 11, 12 and 13. Ganglioncells from the plexus ciaris
of the human eye.
of the corpus ciliare that ganglioncells were to be found, of the
type figured in fig. 11, 12 and 13. It therefore seems improbable
that they should exist in the numbers required for the theory of
Inctis Porrock. So from this point of view too renewed research is
necessary and especially it will be necessary to verify the interesting
results of the last-named author.
Leiden, April 1915.

Geology. — “How volcanism might be explained.” By Dr. C.G.S.
SANDBERG. (Communicated by Prof. Dr. C. E. A. WIcHMANN).

(Communicated in the meeting of April 23, 1915).

To explain the phenomenon of voleanic eruptions and the mode
of their origin, it has long been considered necessary to assume that
large quantities of sea-water were suddenly brought in contact with
incandescent and liquid magma, by means of deep-reaching fissures
or crevasses in the erust of the earth.

The fact that the gaseous voleanic emanations showed some similarity
with the constituent elements of sea water and the proximity of
the seat of voleanic activity to marine areas, led to our looking
for a causal connection between these phenomena.

The theory built up on it is now acknowledged untenable,
both as some voleanic areas proved to be situated at considerable
distance from the sea and because it was admitted impossible for
sea water to penetrate to the magma along a fissure, only to be
violently expelled again along another, a more difficult passage.

A. Davsrée (1) experimentally tried to establish the possibility of
the necessary explosive energy, being furnished by the contact of
water, reaching magma by capillary attraction, through the sediment-
ary strata; this assumption equally proved untenable however.

In short we may say that since, the solution of the problem has
been sought in connection with the action of radioactive elements
of the interior of the earth, with cosmic influences (solar and lunar
attraction, maxima and minima of sun spots, ete.) or else in connec-
tion with mountainfolding. At the same time it was considered
admissable to accept that both, the eruptive power and the presence
of vapours and gases, ave primordial elements of the magma (2).

Lately A. Brun (8) denied the existence of water-vapour in large
quantities in voleanic emanations, an assertion which has been
refuted by the results of L. Day and E. 5. SurpnerD’s researches (4).

When now we examine the way in which volcanic regions are
distributed over the earth, we notice that their situation coincides
in general with the steep flanks of the G. A.*) which are, according
to the doctrine of isostatic movements of the earth’s crust, the faulted
and fissured regions of our globe.

In the author’s opinion it would not seem improbable, that a
causal connection exists between the faulted condition of these regions
and the occurrence of volcanism at those very places.

The products of erosion of the G. A. transported to the G.S. are
deposited in sea- ater.

Those sediments consequently consist of solid elements mixed with
sea-water.

In the G.S. the liquid constituents of the upper layers surpass
the solid material (Deep-sea ooze).

As sedimentation progresses, the proportion of solid material in the
mixture increases, through entassement.

Ultimately the water contents of the sedimentary deposit will not
exceed the capacity of the total of capillary- (pore-)spaces, left between
the adjacent particles of solid material, of which the sediment is
built up. *)

') In what follows the initials G. A. and G. S. will be used respectively for the
words Geo-anticlinal and Geo-synclinal.
*) The question whether larger Cavities must be considered existable at very

To arrive at an appreciation of the quantity of sea water, which
thus could possibly be contained in sedimentary strata, we have
first to examine what the pore space in sedimentary strata can
amount to.

If the constituting elements were perfectly spherical, the amount
of pore space would depend only on the way of their being piled
up, and would vary between the values of 25,95 to 47,64 volume
percentage (5) (6) (7).

As the constituting elements are not perfectly spherical however,
the pore space of sediments has to be determined empirically ; it
was found to vary between the values of 16 to 70 volume per-
centages‘). And it is a remarkable fact that pore space-capacity of
sedimentary strata increases with the diminution of their constituting
elements.

The above holds for deposits situated relatively near to the surface;
the question is now whether we may accept a similar conclusion
for deposits situated at very great depths beneath the surface?

The overwhelming amounts of oil, water and gas met with in
sedimentary strata at depths of 1000 meters and more, already seem
to point towards such conclusion not being unlikely.

But we have more direct indications to go by in the ascertained
pore space of Dakota sandstone (Cenomanian) and the Potsdam
sandstone (Paleozoic).

The researches of F. H. Kine showed that, under their hydro-
statie levels, the Dakota sandstone 15 to 38 and the considerably
older Potsdam-sandstone contains 10 to 38 volume percentages of
water’) (5).

The first mentioned deposit extends over an area of over 900,000
km? the latter over an area of more than 350,000 km? both
with an average thickness of about 300 meters.

The former is covered in the Denver District by more recent
deposits having a total thickness of 2000 m., the latter by a series
great depths, is left undiscussed here; should we accept the possibility of it, the
proportion of occluded water might be greater still.

1) loc. cit. (7) p. 127 and (5).

2) It is true that Newent found that a marble only contained 0,629/, of water.
But as a marble is not a sedimentary deposit but a modification of it, this per-
centage (as little as that of eruptive rocks) may not be taken as a basis for an
appreciation of the amount of water which can be stored up in the pore-space of
sedimentary strata, laid down in the G.S. The only conclusion we might perhaps
be allowed to draw from it is, that as the percentage is yet considerable relatively,
in spite of the intense metamorphism the deposit underwent since its deposition
the original contents must have been much greater.

of more recent deposits, the total thickness of which amounts, for
the paleozoic only, to over 12.000 m. in the Apallachian.

Here then we have an instance of well developed, similarly con-
stituted sediments, deposited over vast areas, differing considerably
in age and covered under layers of sediments, whose thickness
amounts to 2000 m. and 12.000 m. and more.

Yet their pore-space was and is, very nearly identie, and more-
over coincides with that of similar sediments which both are recent
and situated close to the surface. (5).

On the ground of these facts, the conclusion does not seem un-
warranted, that the pore space now proved to exist in these sand-
stones, was also present in them when they were still lying in the
G.S. covered up by a powerful mass of more than 2000 m. and
12000 m. thickness.

It would not be difficult to increase the instances given above.

If it seems legitimate, on the ground of the above detailed facts
to conclude that pore space in sedimentary rocks is existable at
depths of more than 12.000 m., the recently published results of
F. D. Apams’s researches and L. IF. Kiye’s calculations proved that
we may yet expect them to exist at far greater depths, even when
those pore spaces were not filled up by some hquid or gas imprisoned
in them.

_ Were these pore spaces filled with a liquid or gas, we might
expect them to be still extant at depths where the temperature is
so high, that under its influence the sediments would liquefy.

The question is now whether we may take it as probable, that
the water originally occluded in these sedimentary deposits, will
not have been expelled from there (by the tension of the vapour-
converted water of underlying strata), long before those sediments
could have reached the zone of liquefaction.

For should the water (vapour) still fill the pore-spaces, a sufficiently
sound basis for explaining the origin and mechanism of volcanism
were to be found, in the quantity of occluded water (vapour) and
the high tensions acquired by it, under the influence of excessive
high temperatures reigning in the magmatic zone.

The sedimentary rock would gradually pass into a plastic and
liquid condition, during its downward course in the G. S.

And as the steep flank of the G. A. adjacent to the G. S. constitute
a faulted and fissured region, the possibility might not be considered
excluded that part of those vapour-tensions will discharge themselves
into those fissures, thus creating the voleanie phenomenon at the
surface of the earth.

Another possibility which we might conceive, would be that
under the influence of these tensions the covering sedimentary masses
in the G. S. were upheaved.

That might ultimately lead to the formation of overthrust planes
(nappes de charriages), through a lateral bulging out of the raised
up masses.

At last a local rupture through the enveloping strata might give
birth to voleanic eruptions, which then might be sub-marine.

We might conceive the mechanism of voleanism in this way.

When by the action due to isostatic influences, a fissure or fault
be engendered in the region of the steep flank of the G. A., or when
in the raised up part of the G. 5. a rupture should result from the
high tensions prevailing there, the vapour tensions existing in the
vicinity of such faults or fissures would discharge themselves entirely
or partly in such fissure or fault.

Part of the plastic (or liquid) rock would be carried along, as
water overcharged with carbon-dioxide is carried along by sudden
and sufficient relief of pressure.

The subsidence of sedimentary deposits ever continuing, through
accumulation of the products of erosion in the G.S., water (vapour-)
charged sediments would ever and anon be conducted into the
regions of excessive high temperatures; this might account for the
periodicity of volcanism *).

Thus the appearance of volcanism might be expected in those
regions of the earth, situated outside the G.S., which by some cause
or other, are moving in centripetal direction or have lately done so.

Should on this basis a solution be offered for a certain amount
of questions regarding the mechanism and origin of volcanism, the
question still remains whether it may be considered plausible that
the sea water imprisoned in the pore spaces of sedimentary strata,
may be there still when these sediments have reached depths where
liquefying temperatures are reigning.

The vapour tensions, it might be argued, there prevailing, must
have expelled all the water once occluded in the pore space of these
sediments, long before such deposits could have reached the vicinity
of the regions of those high temperatures.

It is known however that the frictional resistance of liquids in
capillary channels is considerable, being for a given flow, per unit

1) I might be allowed to draw the attention to the fact that the absence of
water in liquid state on the moon, and the absence of erosion, sedimentation and
isostatic movements as a consequence of it, may perhaps stand in causal relation
to the absence of periodicity of lunar volcanism, in contrast with terrestrial voleanism,

of time, in direct ratio to the length and in inverse ratio to the
fourth power of the radius of the channel.

How considerable this resistance is in relatively porous rock, as
eg. the grès bigarré, is shown by A. Dausríp, in a note on his
experiments about capillary attraction.

Davprek draws attention to the fact that a thin dise of sandstone
2em. thick, which completely shuts off a basin partly filled with
water, is able to prevent water-vapour to escape (through the body
of the rock) even when the vapour has acquired a tension of several
atmospheres.

When now we take into consideration that the ratio of the dia-
meters of capillary channels in sands and those in clays may be
as from 1000 to 1, we shall be able to form an idea of the excessive
resistances prevailling in finegrained sediments. (In inverse ratio to
the fourth power of the radius).

Where moreover, the researches in folded areas have shown that
the magnitudes of such fine-grained sedimentary (argilieeous-, imper-
meable-) strata may amount to hundreds and even thousands of meters
in thickness, covering the total extent of the G.S., it does not seem
unwarranted to pose the possibility of such impermeable strata
preventing the water (vaponr) occupying the capillary channels of the
sedimentary deposits, from being expelled therefrom by the influence
of the high temperatures and tensions engendered in those strata,
on their way down to the zone of liquefaction.

This contribution purposes to point out a direction in which it
might be considered possible to look for a satisfactory solution of
the problem of the origin and the mechanism of volcanism.

(In the paper now in course of preparation, in collaboration with
others, and which we hope to be able to publish in the Journal of
Geology (Chicago, U.S.A.) before long, we intend to calculate the
values of vapour-tensions at temperatures of 1000°—1200° C. in
connection with the quantity of water supposed to be oceluded in
the sedimentary strata and their respective volumes; further to
approximate the frictional resistance in sedimentary strata built up
from clay and (or) sand, in order to approximate how thick a body
of clay or sand should be, so that the frictional resistance (in its
capillary channels) be sufficient to prevent the water oceluded in
the underlying sedimentary masses, to be expelled therefrom).

LITERATURE.

1. A. DAUBRÉE. Etudes synthétiques de Géologie expérimentale. Paris 1879,
2. T. v. Worrr. Der Vulkanismus. Berlin 1914.

A. Brun. Recherches sur l'exhalation volcanique. Genève 1911.

. L. Day and E. S. SHepHerD. Water and volcanic activity. Bull. Geol. Soe.
Am. Vol. 24 1913 p. 573—606.

5. T. H. Kine. Principles and conditions of the movements of coun
we An, rep. U. S. Geol. Surv. 1897—98 Pt. II.

6. CG. R. van Hise. A treatise on Metamorphism U. S. Geol. Surv. waan
1904 p. 1382 and 133.

7. J. Verstuys. Het beginsel der beweging van het grondwater. Amsterdam

1912 p. 126 et seq. See also: E. RAMANN. Bodenkunde. Berlin 1911; Verslag

van eene Commissie van de Kon. Ak. y. W. te Amsterdam. 1887, and others.

8. F. D. Apams and L. V. Kina. Journal of geology Vol. XX No. 2 p. 97—
138. 1912.
Astronomy. — “Observation of the moon during the Eclipse of the

sun on Aug. 21 1914 and of the Transit of Mercury on
Nov. 7 1914, made in the Leiden Observatory. By J. Wortser
Jr. (Communicated by Prof. EB. F. van DE SANDE BAKHUYZEN).

(Communicated in the meeting of April 23, 1915).
I. SorAr-mcLiPsn or Avausr 21, 1914.

During the eclipse of Aug. 21 1914, sun and moon passed over
the meridian. At the suggestion of Professor B. F. van DE SANDE
Baknuyzen I have observed the declination of the south-limb of the
moon with the transit-circle. The results of this observation ineluding
details concerning the method of reduction will be given here.

In order to obtain as large a number of pointings as possible
Professor Baknuyzen kindly undertook the reading of the microscopes
(including those for the observation of the nadir).

The observed declination depends on the observation of the nadir.
As two of the pointings had naturally to be made far outside the
meridian, it was necessary to give special attention to the inclination
and curvature of the horizontal wires. In 1911 an investigation on
these points had been made; for this purpose a collimator provided
with a level had been mounted on the south-pier; by means of
one of the foot-serews the middle of the two horizontal wires of
the collimator was pointed on various points of the horizontal wires
of the meridian-telescope; by reading the level each time the ineli-
nation of the optical axis of the collimator becomes known and
thus that of the line from the middle of the objective to the special
point of the horizontal wire on which has been pointed.

The pointings were made on five different points of each wire,

viz. on the centre and on two points on either side, one about half-
way between the middle and the extreme vertical wire, and another
just beyond the latter. In this manner the following corrections were
deduced, to be applied to the declinations deduced from pointings at
these points:
Clamp West wire a: —0'12 +0"15 07.00 —0'11 —0".33
wire 6: —0".67 0".00 07.00 + 0".04 — 0".08
The points are given in order, starting from the side of the clamp.

The first and third pointing on the south-limb of the moon were
made on wire a, the second on wire 5. The following corrections
to be applied to the zenith-distance were computed: --0."17 —O".02
+ 0"41.

On the ground of a number of nadir-determinations 6".43 was
found as representing half the distance of the two horizontal wires.
The refraction was calculated from tables in manuscript which are
used in the observatory; these are based on Besser’s constant and
Rapav’s theory. From observations made at the observatory it appears
that this refraction has to be diminished by 0.2 °/,, and this correction
has therefore been applied.

For the mean latitude of Leiden I have taken as the most probable
value 52°9’/19".80. The correction for the motion of the pole was
deduced from the paper by ALsrecnt (A. N. 4749) for a moment
1.2 of a year prior to the eclipse; in this manner account was
taken of the 14-monthly motion, but an error is introduced
in the annual term. This error, however, seemed unimportant and
in this way I found Ag = + 0".09') and therefore for the instan-
tanious latitude 52°9/19".89; this value?) was used in the reductions.

In order to pass from the observed declination of the limb to
that of the centre of the moon I have taken into account the irre-
gularities of the limb, which were very distinetly visible as-the dark
dise of the moon was projected on the bright dise of the sun. Using
the profile given by Hayn (A. N. 4724) I have made a drawing of
the part of the limb which was visible in the telescope and by the
aid of notes, taken down during the observation, about the manner
in which the pointings had been made, the corrections were estimated
which had to be applied to the declinations as reduced with a mean
radius of the moon; these corrections came to — 07.70, — 1.90,

1) Dr. Zwiers from a preliminary discussion of the latest results for the motion
of the pole, in continuation of his paper in these Proceedings for 1911, finds
do = -+0”.14 (however not including the z-term).

2) From the preliminary results of ArBrecurt (A. N. 4802) for the variation of
latitude in the year 1914 I find ~g = + 0”.20 (added June 1915).

Proceedings Royal Acad. Amsterdam. Vol, XVIII.

1".90. For the mean radius the value 2 = 932".58 was taken,
which is the value adopted by Nerwcomp in his last great work
on the motion of the moon, as if seemed to me that the radius to
be used in occultations must be the same as the mean radius of
the very sharp profile of the moon which projects itself on the
bright dise of the sun.

; 1
In the computation of the parallax IT have assumed — — for the

ade

ellipticity of the earth, both for the caleulation of the reduction to
geocentric latitude and of the radius-veetor of the earth at the place
of observation, and for deducing the constant of the sine-parallax.
I therefore assumed for the constant 38422".47 (Newcoms, Astr. Pap.
IX 1 p. 44) and a correction of + 0".40 was applied to the N. A.
value. The observations were made in the position of the instrument :
Clamp-West and Circle A. was read; for the reduction of the declination
so found to the mean of the two circles and the four positions of
the instrument (objective and ocular-end can be interchanged and the
instrument can be reversed) according to the investigations made in
the observatory a correction of -++ O".11 must be applied to the
declination. Moreover for the reduction to Avwers’s system a correc-
tion of —O".16 has to be applied, for that to Newcomp’s system
one of — 07.04.

The observations and their reduction are given in the following
table; the first column indicates whether or not a reversing prism
was used; the second column contains the hour-angle, at which the
observation was made; the third the mean of the four microscopes
for the moon; the fourth the same for the nadir; the fifth the sum
of the corrections for division-errors, run, reduction to the meridian,
flexure of the instrument, irregularities of the limb, distance, ineli-
nation and curvature of the wires, the sixth the correction for refrae-
tion; the seventh the zenith-distance obtained in that manner and
the eighth the geocentric declination of the centre of the moon.

4 al EG Zenith-dist. Declination
t Limb Nadir | Corr. Refr. | limb | centre

without pr. rae 140° 17/57/28 0°7' 41”56| —8”02 | 47/15 |39° 50’ 3045 | roe 12'98"52
with pr. | +14 | 17’ 2148 | A | +442 | 47/16 51 2/82 12/12/45
without pr. | +91 | 171450 | | oso 47717 51 24/03 11/5151
| | | |
By reducing the first and the third declination to the moment of
the second one we finally obtain: d = + 13° 12’ 12"39
12.45
11.80

The last pointing was made very near the end of the field and
has therefore a smaller weight than the others. Taking the mean
of the three with weights 1, 1, 4 we find: J=-+13°12'12"30;
reducing to the mean of the two circles and the four positions of
the instrument we get: d= + 13°12’ 12"41; finally we find for
the declination

Dp 0 eee Time of observ.
reduced to Auwers’s system: d=-+ 13° 12’ 12°25 53n45m9s4

ne) » NEWCOMB's ,, :d=-+13° 12’ 12'37

1 M.T. Greenw.

A comparison with the Nautical Almanac gives:
OI XQ

Observ.— Caleul.: Auwers’s system: — 3.56

NEwcombp’s ,, : —o 46.
Il. Transit or Mercury on November 7 1914.

Using the great refractor of the observatory (aperture 266 mm.)
I tried to observe the moments of inner and outer contact. At the
first two contacts the sky was clouded over, so that only the last
two could be observed. The power used was 170. As the moment
of inner contact | took the breaking of the thread of light.
The times observed are
last inner contact: 2h 6™ 245.8 M.T. Greenwich
» Outer ERROR dd 55 5
A comparison with the Nautical Almanac gives as the difference
calculation minus observation:
last inner contact + 1657
» outer 2 + 115,
Leiden, April 1915.

Anatomy. — “On the structure of the muscular abdominal wail
of Primates.” By W. A. Muspira. (Communicated by Prof.
Dr. L Bork).

(Communieated in the meeting of April 23, 1915).

In the publications relating to the myology of Primates, the
muscles of the abdomen are usually discussed very superficially, and
where that discussion is a more elaborate one, that greater elaboration
is as a rule restricted to an excessively accurate description of the
origins of these muscles. Less attention however is paid to the way
in which these muscles contribute to the formation of the sheath
of the M. rectus; no publication is even known to me, in which

something is communicated about the comparative anatomy of the
rectal sheath of Primates. This stbject however deserves greater
attention, as from a few stray communications it appears, that the
structure of the sheath of the different species of Primates can show
rather considerable differences.

I shall communicate here shortly the results of an investigation
into the comparative anatomy of the sheath of the rectus muscle
made by me in the Anatomical Laboratory of Amsterdam. In this
communication I shall leave Prosimiae entirely out of consideration,
and consequently restrict myself to Simiae (Platyrrhini and Katarrhini)
and Hominidae.

On the Membrana abdominis intermedia.

As the first result of my investigation I can communicate, that
with all monkeys examined by me, both Katarrhini and Platyrrhini,
a fourth element participates in the formation of the sheath of the
M. reetus, besides the three flat muscles of the abdomen. Between
the M. obliquus externus abdominis and the M. obliquus internus
abdominis a fascial membrane is namely found. This membrane
is solid, admits of a good free preparation, consequently it distin-
guishes itself obviously from the flimsy connective tissue, which is
found in man between the flat muscles of the abdomen. In the lite-
rature this membrane is not mentioned; I shall designate it as
Membrana abdominis intermedia. The anatomical lines of demarca-
tion of this membrane can distinctly be indicated. In the caudal
part the origin is immediately connected with that of the M. obliq.
int.: the membrana interm. is attached to the fascia lumbodorsalis,
crista iliaca, spina iliaca anterior and follows also in a caudal
direction the orige of the M. obliq. int so that — with a powerful
development of the membrane — its last fibres are attached to the
ramus superior ossis pubis. Sometimes however it cannot be followed
as far as the origins indicated here; in these cases it is closely con-
nected with the M. obliq. int., because it originates in the perimysium
externum of the latter at some distance from the origo of that muscle.
Jn the cranial part the origin of the membrane cannot be indicated
so exactly: it is namely continued between the M. obliq. ext. and
the thoracal wall, and looses itself in the flimsy connective tissue
that is found here. An origin from ribs can consequently not be
ascertained.

In a median direction the membrane passes into the sheath of the
M. rectus in the forming of which it takes part with the three flat
muscles of the abdomen.

What is now the signification that must be attributed to this mem-
brane occurring so constantly in monkeys 7

One might be inclined to regard the membrane as a condensation
of the intermuscular connective tissue; for likewise in man one often
sees that from the flimsy connective tissue between the abdo-
minal muscles fascial membranes can develop to increase the solidity
of the abdominal wall. There are however objections that tell against
this view: in the first place it cannot be explained in this way,
why in many Simiae such a membrane does exist between the
M. obliq. ext. and the M. obliq. int., but no vestige of fascial tissue
between M. obliq. int. and M. transv. is to be found ; secondly it
cannot be comprehended in this way, why the membrane possesses
such distinct anatomical lines of demarcation; thirdly the great
independence that this membrane possesses tells against this view.
With most Platyrrhini e. g. the membrane runs in the cranial part
behind the M. rectus, in the caudal part in front of it; it changes
consequently its course with regard to this muscle and moreover
independently of the abdominal museles between which it is situated.

From these objections appears distinctly, that the membrane may
by no means be regarded as a simple local condensation of inter-
muscular connective tissue. Most admissible it is to consider it as a
rudiment of a muscle that has existed on this spot with lower
vertebrates. With this hypothesis all the properties of the membrane
— as its sharp anatomical lines of demarcation, its independence — can
easily be explained. The correctness of this view is moreover
proved by a discovery with Siamang. With a Siamanga syndactylus
I found namely muscular fibres running in the membrane ; these
muscular fibres form a bundle of 8 mm. wide and 4.5 em. long,
which bundle is situated between the point of the last rib and the
crista iliaca. The fibres do however not originate in the rib, but
about */, em. caudally from the point of the last rib the muscular
fibres appear in the membrane. The fibres run almost vertically down-
ward, their direction corresponds with that of the fibres of the
M. oblig. ext. The fibres are inserted into the erista iliaca, a little
behind the spina iliaca anterior. The muscle possesses moreover still
a smaller head, arising from the fascia lumbodorsalis.

As now, in the direction of the ventral medianline, the membr.
interm. is directly connected with this muscle, and as moreover the
origin of the muscular fibres is not situated at the last rib, but the
fibres appear in the membrane at a little distance caudally from
the rib, if is clear that this muscle with Siamang is the last remain-
ing part of a musele which, with phylogenetically older forms, was

situated on the spot of the membrane. Indeed we know, that with
Urodele Ampbibia and with Reptilia the abdominal wall is composed
of more muscles than with Primates. The ontogeny and phylogeny
of the abdominal muscles of lower Vertebrates (Pisces, Amphibia,
Reptilia) has been accurately explained to us by the investigations
of Mavcrer'). It is especially the structure of the muscular abdo-
minal wall of the Urodele Amphibia that is of great interest for us ;
the abdominal muscles of Pisces still show very simple conditions,
whilst the conditions of the abdominal muscles of Anure Amphibia
and Reptilia can very well be deduced from those of Urodeles.

Urodele Amphibia possess four collateral abdominal muscles. Most
superficially are situated two muscles, the fibres of which have
an obliquely descending direction: a M. obliq. ext. superficialis and
a M. oblig. ext. profundus. The direction of the fibres of these
muscles differs little; that of the deep muscle is somewhat less oblique.
Under the Museuli obliq. ext. one finds a M. obliq. int. with an
obliquely ascending direction of the fibres, and abdominally from it
lies the M. transversus, the fibres of which run in a transversal
direction. Mavrer distinguishes these muscles in primary and second-
ary ones. The primary muscles: M. obliq: int., M. obliq. ext. prof.
and M. rectus profundus occur with the larva; the secondary ones:
M. obliq. ext. superfic., M. transv. and M. rectus superficialis come
into existence at the end of the larva-life by delamination of the
younger cells at the surface of the primary muscles. From the
development it is obvious, that the M. obliq. int. and the M. obliq.
ext. prof. are dorsally connected with each other in the myotome
and can never extend beyond the line of demarcation between the
ventral and the dorsal musculature, the lateral line; ven-
trally both muscles are conneeted in the M. rectus profundus. The
direction of their fibres changes here gradually from an oblique one
into the longitudinal one of the M. rectus prof. The M. obliq. ext.
superf. and the M. transv. however can extend dorsally from the
lateral line, and from the beginning they possess an aponeurosis
which runs before, resp. behind, the system of the Musculi reeti to
the linea alba.
1) £. MAURER, Der Aufbau und die Entwicklung der ventralen Rumpfmuskulatur
bei den urodelen Amphibien und deren Beziehung zu den gleichen Muskeln der
Selachier und Teleostier. Morph. Jahrb. 18 Bd. 1892.

F. Maurer. Die ventrale Rumpfmuskulatur der anuren Amphibien. Morph.
Jahrb. 22 Bd. 1894. ;

F. Maurer. Die ventrale Rumpfmuskulatur einiger Reptilien, eine vergleichend-
anatomische Untersuchung. Festschrift zum 70 Geburtstage von CARL GEGENBAUR,
1896.

Which are now the homologies between the abdominal muscles
of Primates and those of lower Vertebrates? That the M. transv.
and the M. obliq. int. of man are homologous with the homonymous
muscles of Urodela is obvious, on account of the corresponding
direction of the fibres and the corresponding direction of the inter-
costal nerve between the two muscles. There are however different
views concerning the M. obliq. ext. GrGeNBAUR reckons this muscle
together with the Musculi intercostales externi to the layer of the
M. obliq. ext. prof. of Urodeles; in this case the M. obliq. ext. super.
of Urodeles could be found back in the Musculi serrati postici of
man. According to Eiser *) the M. obliq. ext. and the Musculi
serrati postici belong to the layer of the M. obliq. ext. superficialis;
the M. obliq. ext. prof. of Urodeles is to be found back in the
Museuli intercostales externi and the “tiefe Zacken des M. oblig.
ext. abdominis’. By these Eisire understands small bundles of
muscles, which, as he communicates, oceur frequently under the
cranial origins of the M. obliq. ext. of man. They originate likewise
from the ribs, are separated by some connective tissue from the
M. obliq. ext. lying superficially from them, have an almost trans-
versal direction and lose themselves at last in the anterior lamella
of the sheath of the M. rectus.

The anatomy of the ventral trunkmusculature of man however
cannot give us certainty with regard to the origin of the M. obliq.
ext. As, however, with other Primates between this muscle and the
M. oblig. int. a membrane occurs that can be conceived as the
remaining part of an abdominal muscle, the situation becomes
clearer. Superticially from the M. oblig. int. we find first a muscle
reduced to a membrane and then a well developed muscle entirely
independent of each other; it is thus without more obvious, that
the more superficial one of these two layers must be homologous
with the M. obliq. ext. supertic., the deeper one with the M. obliq.
ext. prof. of Urodeles. Consequently the M. obliq. ext. of Primates
is homologous with the M. obliq. ext. supertic., whilst the Membrana
abdominis intermedia is the homologon of the Musculus obliq. ext.
profundus of Urodeles.

The direction of the fibres of the M. obliq. ext. prof. of Urodeles
differs little from that of the M. obliq. ext. superfie. The abdominal
muscle, which with ancestral forms of Primates was found in the
place of the Membrana intermedia, will also in all probability, with,
regard to the direction of its fibres, have corresponded with the
M. obliq. ext. (superficialis !) of Primates.

1) P. ErsLer. Die Muskeln des Stammes. Jena 1912.

In accordance with this is the fact, that the fibres of the “M. obliq.
ext. prof.” — for this name should be applied to the muscle —
found by me with Siamang show a direction that is almost parallel
with that of the fibres of the M. obliq. ext.

Further 1 will still remark in this connection, that according to
Tusrur ) and Le Dousre*) several investigators have described by
different names, and especially by that of “M rectus lateralis” as
variations muscles of man, situated between the Museuli oblig.
externus and internus and corresponding in the direction of their
fibres with the M. obliq. ext. In the most typical eases this “M.
rectus lateralis” originates from the 9" to the 11' rib, runs then
almost vertically downwards and-is inserted into the erista iliaca.
It is obvious that we have to do here with the remaining part of
the M. obliq. ext. prof., occurring as atavism, which muscle normal-
ly has been entirely reduced in man, whilst not even a membrane
has remained. The variation has been described by the name of M.
rectus lateralis. This name, though with regard to the direction of
the fibres very correct, is however not preferable, as it could give
rise to the entirely wrong notion, that this muscle is connected in
some way or other with the M. rectus abdominis. In fact the two
have nothing to do with each other. Consequently we had better
call this variation M. obliq. ext. profundus, a name to which, as
comparative anatomy teaches us, it has an indisputable right.

In conclusion be remarked that, in accordance with Eiser, |
think it likely, that the deep origins of the M. obliq. ext. (vide
before) described by him, can also be considered as remaining parts
of the M. obliq. ext. prof.

It still remains to trace the relation the Membr. abdominis inter-
media bears to the M. rectus: the membrane namely, as I commu-
nicated already takes part in the formation of the sheath of the M.
rectus. With the description of the structure of the sheath of the
different monkeys the relation of the membrane to the M. rectus
will consequently likewise be discussed.

On the structure of the sheath of the M. rectus of Primates.

The relations the four elements, that compose the rectal sheath,
bear to the M. rectus with the different monkeys will be briefly

DL. Tesrur. Les anomalies musculaires chez l'homme, expliquées par ]’anatomie
comparée, leur importance en anthropologie, Paris. 1884.

2) A. F. Le Dousre. Traité des variations du système musculair de homme et
= leur signification au point de vue de l'anthropologie zoologique. Paris. 1897,

‘
described with the help of text-figures, representing diagrammatic
transversal sections through the sheath. In all sections the M. obliq.
ext. is represented by a dotted line, the Membrana abdominis inter-
media by a point-dash-line, the M. obliq. int. by an uninterrupted
line, and the M. transversus by a dash-line. ;

The structure of the rectal sheath of Primates shows considerable
differences. It is however possible to unite all those cases under
one point of view; it will appear that in this way a more primitive
condition and relations that have removed from the original condition,
can be distinguished. The succession in which the rectal sheath of
the different Primates will be described is such, that I shall begin
with a condition of which afterwards it will appear, that it is the
most original one, and conclude with the description of the structure
of the sheath of such monkeys, which have farthest removed from
the primitive condition.

Fig. 1a represents a transversal section through the sheath of the
M. rectus of Ateles paniscus, close under the caudal edge of the

Fig. 1. Ateles paniscus. Fig. 2. Ateles hypoxanthus.
‚a. = Linea alba.
= Musc. rectus abdominis.
= M. transversus abdominis.
= M. obliquus internus abdom.
— Membrana abdominis intermedia:
= M, obliquus externus abdom.

poten

Fig. 4 Homo.

Cebus capucinus.
(Scheme of Platyrrhini).

Ris. 3:

emnopithecus entellus.

(Scheme of Katarrhini).

Ss.

Cercopithecus cynosuru

sternum. The M. obliq. ext. (4) passes in front of the M. rectus, the
Membr. interm. (3), the M. obliq. int. (2) and the M. transv. (1)
form the posterior lamella of the sheath. These relations exist however
only in the cranial */, part of the sheath; in the caudal part the
M. obliq. ext. remains before the M. rectus, the M. obliq. int. and
the M. transv. behind it, but the Membr. interm. passes at the lateral
edge of the M. rectus into the perimysium externum of this muscle,
(fig. 1). These relations continue to exist till the symphysis. (Com-
pare the sagittal section, fig. 1c).

With an Ateles hypovanthus examined by me the relation of the
M. obl. int. and Membr. intermedia to the M. rectus was different
from that with Ateles paniscus. The M. obliq. ext. passes entirely
before, the M. transv. entirely behind the M. rectus; the relations
the Membr. interm. and the M. obliq. int. bear to the M. rectus are
however not the same in all the parts of their course; in the cranial
part both run behind the M. rectus (fig. 2a). About 6 em. caudally
from the inferior edge of the sternum (the total distance sternum-
symphysis amounts to 12 em.) the membrane splits into two layers
one of which is passing before, the other behind the M. rectus.
The M. obliq. int. continues to send its aponeurosis itito the posterior
lamella of the sheath (fig. 24). 2'/, em. eranially from the symphysis
the two layers of the membrane terminate almost simultaneously ; at
the same time the M. obliq. int. changes its relation to the M. rectus:
from here its aponeurosis divides itself into two layers, which include
the M. rectus (vide fig. 2c). Fig. 2d gives an illustration of these
different anatomical relations.

The third fig. relates to the rectal sheath of Cebus Capucinus.
The M. oblig. ext. passes entirely before, the M. transv. entirely
behind the M. rectus. The Membr. interm. passes in the cranial
part, just like the M. obliq. int, behind the M. rectus (fig. 8a); ina
caudal direction it splits into two layers, enclosing the M. rectus,
the M. obliq. int. does provisionally not change its relation to the
M. rectus (fig. 3). Then the dorsal layer of the membrane disappears
and thereupon the membrane passes entirely into the anterior lamella
of the sheath (fig. 3c). A little farther caudally the aponeurosis of
the M. obliq. int. splits into two layers (fig. 3d); then the deep layer
disappears, so that in the caudal part the posterior lamella of the
rectal sheath consists only of the aponeurosis of the M. transversus,
whilst the other three elements pass in front of the M. rectus
(fig. 3e and 3/).

With the condition of the rectal sheath found with Cehus

capucinus, corresponds the structure of the sheath of all other

Platyrrhini (Mycetes niger, Chrysothrix sciurea and _ Hapale).

In fig.4 are represented sections through the sheath of the M. rectus
of Man. The M. obliq. ext. passes entirely in front of the M. rectus,
the Membr. interm. fails. Cranially from the linea Douglasii the
M. oblig. int. possesses two layers, and the M. transv. extends behind
the M. rectus (fig. 47), caudally from the linea semicircularis the
aponeuroses of the three flat muscles of the abdomen are situated
on the anterior surface of the M. rectus (fig. 46 and 4c).

The 5 figure relates to the sheath of a Cercopithecus cynosurus.
As appears from the sections, the M. obliq. ext. and the membr.
interm. pass entirely in front of the M. rectus, the M. obliq. int.
which runs also before the M. rectus, possesses moreover in its
most cranial part for a short distance a layer which passes behind
the M. rectus (fig. 5a); soon however this layer ceases (fig. 50).
The M. transversus, which in the cranial part extends behind the
M. rectus, sends in the caudal third part its aponeurosis likewise
before the M. rectus (fig. Sc and 5d).

Figure 6 relates to the vagina M. reeti of Semnopithecus entellus.
The M. obliq. ext., the Membr. interm. and the M. obliq. int. pass
entirely in front of the M. rectus. The M. transv. however runs in
the cranial */, part of the sheath behind the M. rectus (fig. 6a), in
the caudal 4 part its aponeurosis takes part in the forming of the
anterior lamella of the sheath (fig. 65 and 6c). A condition of the
vagina M. recti as represented in fig. 6, can be admitted as normal
for Katarrhint; 1 found it with Cercopithecus patas, Macacus eyno-
molgus, Colobus gueresa, Semnopithecus entellas, Cynocephalus
hamadryas, Siamanga syndactylus, Orang utan.

From this short description it appears that monkeys show great
differences with regard to the composition of their rectal sheath,
differences of such importance, that it seems in the beginning
difficult to see a connection between all the conditions that present
themselves. It will consequently be our task to try and find such a
connection founded on the evidences given above. With this purpose
we shall trace of each of the four elements that take part in the
forming of the sheath separately how the relation is it bears to
the M. rectus with the different Primates.

With Platyrrhini the M. transversus passes entirely into the post-
erior wall of the sheath, with Katarrhini and with man this con-
dition exists only in the cranial part; in the caudal third or fourth
parts the M. transv. takes part in the forming of the anterior wall
of the skeath; with a Macacus rhesus [ dissected, the aponeurosis

possessed at this passage for a short distance two layers, with the
other Katarrhini and with man the M. transv. suddenly, with an
acute line, modifies its course behind the M. rectus into a course
in front of the latter.

The condition of the M. transversus, as it shows itself with Kata-
rrhini and with man, is certainly not a primary one. The anatomy
of the sheath of the M. rectus of Amphibia and Reptilia teaches us
that there the M. transv. runs entirely behind the M. rectus, and
the ontogeny of the abdominal musculature of Urodeles shows us
that this condition is the primary one. As now moreover with all
Platyrrhini the M. transv. passes behind the M. rectus, there can no
longer exist any doubt; decidedly the relation which with Katarrhini
and with man the M. transversus bears to the M. rectus is a second-
ary one. With ancestral forms of monkeys of the old world and
of man the M. transversus ran behind the M. rectus, as it does
still with Platyrrhini. In the phylogenetical development of these
groups of Primates an influence has been at work, in consequence
of which the M. rectus pierces in the caudal part the M. transv.,
so that the latter muscle in the caudal part is found on the anterior
surface of the M. rectus.

With most Katarrhini the M. transv. modifies its relation to the
M. recius suddenly, in an acute line; with Macacus rhesus the
aponeurosis of the M. transv. possessed at the modification of its
direction for a short distance two layers, i.e. the M. rectus does
not pierce the M. transversus here abruptly, at right angles, but
gradually, so that the M. rectus is situated for a short distance in
the mass of the M. transversus.

The relation of the M. obliquus mternus to the M. rectus shows
with the different monkeys also great differences. With Katarrhini
the M. oblig. int. runs entirely before the M. rectus; with Ateles
paniscus on the contrary entirely behind that muscle. With all
Platyrrhini, with the exception of Ateles paniseus, with man and
also with a Cercopithecus cynosurus L examined, we find conditions
in which the relation of the internus aponeurosis to the M. rectus
is quite different in the cranial part from that in the caudal one. With
the majority of Platyrrhini we find that the internus apeunorosis
runs in the cranial part behind the M. reetus, and in the caudal
part before the M. rectus; consequently the M. rectus pierces the
M. oblig. int.;, usually the piercing takes place gradually at an
acute angle, so that the internus aponeurosis possesses for a short
distance two layers. With Ateles hypoxanthus the aponeurosis runs
in the cranial part behind the M. rectus and includes in the caudal

part this musele with two layers; with man and with Cercopitheeus
eynosurus on the contrary the M. obliq. int. shows in the cranial
part two layers, and passes caudally entirely into the anterior wall
of the Vagina M. reeti.

In the relation the M. obliq. int. bears to the M. rectus conse-
quently three types can be distinguished: the M. obliq. int. runs
either entirely behind the M. rectus, or passes entirely into the
anterior lamella of the sheath, or behaves differently, with regard to
the M. rectus, in the cranial part than in the caudal part; now the
question rises which of. these conditions is the original one. It is
self-evident, that the condition of the M. obliq. int. in which the
relation to the M. rectus in the cranial part is so quite different
from that in the caudal part will not bave existed with the ancestral
forms of Primates. With these doubtless the relation of the M. obliq.
int. to the M. rectus will have answered to one of the two other
types; consequently the M. obliq. int. has originally taken part either
in the forming of the anterior or in that of the posterior lamella
of the sheath of the M. rectus.

As we are compelled to admit with regard to the M. transversus,
that this muscle was pierced in the course of the phylogeny by the
M. rectus, it is a priori very likely that the piercing of the M. obliq.
int. will depend upon the same cause that also brings about the
modification in the course of the M. transv. From this simple con-
sideration results the conclusion that originally the M. obliq. int.
passed presumably behind the M. rectus.

Comparative anatomy can likewise support our view, that originally
with Primates the M. obliq. int. is situated behind the M. rectus. If
namely we consider the relation of this muscle to the M. reetus
with different Vertebrates (Maurer) we find that with Urodeles the
M. obliq. int. passes continuously into the M. reetus, with Anures
this muscle exists only in the larva, with Reptiles, however, we find,
that, where a M. obliq. int. exists as such, it has disengaged itself
from the system of the Musculi recti and possesses an aponeurosis,
that runs behind the M. rectus abdominis.

The Membrana abdominis intermedia with all Katarrhini takes
part in the forming of the anterior lamella of the sheath ; this cannot
be otherwise, as both the M. obliq. ext. and the M. obliq. int. pass
in front of the M. rectus. In case, however, as with Platyrrhini, the
M. obliq. int. in the cranial part lies behind the M. rectus, the
membrane also lies in the cranial part behind it. In the caudal
part we find nowhere the membrane behind the M. rectus: with
Ateles paniscus it is connected at the lateral edge with the peri-

mysium exierntiim of this muscle, with the other Platyrrhini it runs
in the caudal part in front of the M. rectus.

Again the question rises what the original relation of the membrane
to the M. rectus was. As in secondary situations of the Musculi
oblig. int. and transversus the membrane is found in front of the
M. rectus, and in the primary condition on the contrary, the mem-
brane, — in the cranial part at least — passes behind the M. rectus,
we may suppose, that, most likely, the Membr. abdominis inter-
media was originally situated behind the M. rectus. This view is
strengthened by considerations of the same nature as those, which
we communicated regarding the M. obliq. int.; only the comparative
anatomical argument cannot be applied here.

With all examined Primates the M. obliquits externas passes in
front of the M. rectus.

The four elements that compose the sheath of the M. reetus will
have taken part in the forming of the sheath, as ancestral forms of the
now living Simiae and of man possessed, in such a way that the
M. obliq. ext. passed in front of the M. rectus, whilst the three
other elements formed the posterior lamella of the sheath.

In the phylogenetical development, however, an influence appeared,
which brought about a variation in this structure, in consequence of
which the M. rectus began to show an inclination to pierce the three
elements lying behind it. This piercing begins in the caudal part.
The first modification that oceurs, consists in the fact, that the Membr.
intermedia changes the relation it bears to the M. rectus and is
found to be situated in the caudal part in front of the M. rectus.
Whilst the piercing-process in the membrane is continuing, the M.
oblig. int. in the caudal part begins to modify its direction with
regard to the M. rectus.

When then the caudal part of the M. rectus has taken its place
between the Museuli obliq. and transy., the piercing-process can begin
to extend itself also over the M. transversus. The modification of
direction of the latter is always restricted to the caudal part, the
piercing of the Membr. interm. and of the M. obliq. int. by the
M. rectus can however become a complete one, i.e. the piercing
can go so far, that in the end both elements are situated entirely
in front of the M. rectus.

In the phylogenetical development which has taken place in the
different genera of Primates, the factor, that modified the topography
of the flat abdominal muscles with regard to the M. rectus, made
itself felt in varying degrees, so that the Primates that live at the
present moment, find themselves in all sorts of phases of transformation,

The original condition of Membr. interm., M. obliq. int. and M.
transv. has least changed with Ateles paniscus. With this monkey
the M. transv. and the M. obliq. int. still show their original rela-
tion to the M. rectus; the Membr. interm. lies in the cranial part
also behind the M. rectus, passes then, however, into the perimysium
externum of that muscle. This relation must be regarded as a con-
dition, in which the M. rectus is situated in the mass of the mem-
brane, in other words: there exists here a beginning piercing of the
membrane by the M. rectus. With the other Platyrrhini the piereing
process has gone further than with Ateles paniscus, and the mem-
brane lies then in the caudal part before the M. rectus. At the same
time the piercing-process has with them extended over the M. obliq.
int.; the M. transversus, however, passes still entirely behind the
M. rectus.

The monkeys of the old world have removed farthest from the
original condition of the structure of their sheath: with them the
piercing of the Membr. interm. and of the M. obliq. int. is complete,
whilst the M. transv. in the caudal part also modifies its direction
with regard to the M. rectus. The structure of the sheath of the
M. rectus of man forms the connecting link between those of Platy-
rrhini and Katarrhini. This vagina is less original than that of Platy-
rrhini, as in man the piercing-process extends also over the M. trans-
versus, but because the piercing of the M. oblig. int. by the M. rectus
is not yet complete, the sheath of man is at the same time more
original than that of Katarrbini.

The linea semicireularis Douglasii is the line along which the
transversus aponeurosis modifies its direction with regard to the
M. rectus; it is formed by the last fibres of the M. transversus,
which proceed behind the M. rectus towards the linea alba (with
man the last fibres of the posterior layer of the aponeurosis of the
M. obliq. int. take moreover part in the formation of the linea).
The possession of a linea Douglasii does consequently mean, that
the piercing-process that takes place in the sheath of the M. rectus,
has advanced so much, that also the M. transversus is pierced in
the caudal part by the M. rectus. By this explanation a new light
is thrown on the dark question about the signification of the linea,
a question, that, notwithstanding the different hypotheses that have
been suggested, in order to explain this phenomenon in tke posterior
lamella of the rectal sheath, has not yet found a satisfactory solution.
We need by no means be astonished at this fact, as, indeed, all
investigators, who have hitherto occupied themselves with this quest-

ion, have regarded the formation of the linea Douglasii as an
independent process, because they were not acquainted with the
considerations communicated above, from which appears that the
formation of the linea is but part of a more comprehensive process,
which takes place in the rectal sheath.

Among the different theories that have been suggested about the
signification of the linea Douglasii, that of GRGENBAUR has become
most generally known. His hypothesis, in which the views of Rerzius
and Herre are united, makes the Vesica urinaria and the Vasa
epigastrica inferiora responsible for the occurrence of the linea
Douglasii.

Objections have been made against this theory and against those
of Dovetas and of Sorcerer, from which objections we must conclude
that these hypotheses are incorrect. Only the theory of Eisier’),
which is supported by the results of ontogeny and comparative
anatomy, stands unattacked at the present moment. EisLeR seeks the
cause of the formation of the linea in the protuberation of the anterior
abdominal wall, indicated as processus vaginalis, because this processus
compels the fibres of the Museuli oblig. int. and transversus, which
run eranially from the processus behind the M. rectus to give way
ventralwards there, where the processus is, and to remove before
the M. rectus.

It is obvious that the hypothesis of Eister cannot be correct, for
it tries likewise only to find a cause for the piercing of the M.
transversus by the M. rectus; like all other theories previously
suggested, it regards the formation of the linea Douglasii as an inde-
pendent process, whilst it must only be regarded as the last phase
of the piercing process that takes place in the rectal sheath.

It is consequently completely irrational to indicate for the formation
of the linea Douglasii a cause that does not explain at the same
time the other modifications occurring in the construction of the
sheath. The question about the cause of the linea semicircularis
must be replaced by the question about the inclination of the M.
rectus to pierce the three elements, that originally formed the posterior
lamella of the sheath of the M. rectus. Further investigations will
perhaps give an answer to this question; for the present moment
only the fact of the piercing can be ascertained.

1) In P. Erster. “Ueber die nächste Ursache der Linea semicircularis Douglasii
Verhandl. der Anat. Gesellschaft 1898” one finds described all the theories about
the cause of the linea, indicated here.

Proceedings Royal Acad. Amsterdam. Vol. XVIII,

Physiology. — “On the heart-rhythm.” UI. By Dr. S. pr Boer.
(Communicated by Prof. J. K. A. Werrtnem SALOMONSON).

(Communicated in the meeting of April 23, 1915,)
On the components of the a-v-interval.

In the estimation of the disturbances of the rhythmic funetions of
the heart the a-v-interval plays a comparatively important part. It
is consequently of great interest to know exactly by what factors
the duration of this interval is determined. When determining this
interval, we measure the time that elapses between the beginning
of the auricle-systole and the beginning of the next following systole
of the ventricle. What we determine in this way is consequently
not only the time of transmission of the stimulus from the place of
entrance into the auricle till the time of entrance into the ventricle;
for it is obvious that, in our determination, we have not left out of
account the time that the stimulus has required to exert influence
upon the ventricle, i.e. the time of the latent stimulation. If now we
make our estimation by means of mechanical curves, then the latter
amount is rather important, but with electrograms this latent time
exists likewise.

It is now my intention to represent this with some curves.

In Fig. I we see two rows of curves of a suspended frog’s heart;
the rhythm of auricle and ventricle is halved. A stimulator is applied
to the basis ventriculi by which we administer at the end of the
diastole an extra-stimulus (the closing strokes at which the signal
goes down are prevented, the opening strokes — motion of the signal
upwards — reach the ventricle). The first stimulus of the upper row
of curves falls in the refractory period. The second opening stroke,
which takes place later in the heart-period occasions an extra-systole
with a rather long latent period. After this extra-systole follows the
auricle-systole of the normal rhythm, the a-v-interval between this
auricle-systole, and the then following systole of the ventricle is almost
twice as long as the a-v-interval of the normal rhythm. It is obvious,
that the cause thereof is to be found in the decreased irritability of
the ventricle-musculature by the shortening of the preceding pause, the
stimulus coming from the auricle requires more time to exert influence
upon the ventricle.

In the second row of this figure we see a repetition of this
phenomenon with the same result for a stimulus occurring a little
earlier. We see here, at the same time, that the latent time after
an extra-stimnlus is the longer in proportion as the stimulus takes
place earlier in the heart-period. This figure illustrates likewise

upon the metabolic

n
>
u
=

1d av-interval by a

lhe closing-stimula (motion

gthene

auricle-

a len

= 7

after

lace

)

normal rhythm is followed with

the

2\ row repetition of this experiment with the same result:

wt poisoned wilh veratrine
ol

of the signal downward) are prevented.

2" opening-stimulus, which takes |

ae es
fy = n
bn th oi
Ui rn ae
> of se
= Ss
Se os =
7 jet n
nD as ==
a en Ee a
m=) SUN ee Ol aw
er
= o ~
Bo es) Ee
ESE 5
BS eS en 5

condition of the heart-musculature. I found this fact everywhere
contirmed in my frog’s hearts poisoned with veratrine,

By a second observation of my frog’s hearts poisoned with vera-
trine, it is shown, that the duration of the a-v-interval in unchanged

metabolic condition of the ventricle-muscle can depend upon the
condition of the transmission-systems from the point of beginning in
the auricle to that of the ventricle. If namely first the ventricle-
rhythm has been halved and afterwards the rhythm of the auricle, then
I saw after the latter halving the a-v-interval considerably reduced.

AN ‘
Fig. 2.

Halving of the ventriele-rhythm during the first 3 systoles, whilst the
rhythm of the auricle is still normal. Thereupon the rhythm of the auricle
halves likewise. The a-r-interval is then considerably shortened.

As an example we cite as follows: In Fig. 2 we see a row of
curves of a suspended frog’s heart, represented 40 min. after the
injection of 10 drops of acetas veratrini into the abdominal cavity.
During the first three systoles the rhythm of the ventricle is halved,
whilst the auricle-rhythm is still undisturbed. After this the following
auricle-systole falls out, so that on each then succeeding ventricle-
systole an auricle-systole appears. It is remarkable how considerably
the a-v-interval is now shortened. Apart from the influence of the
hiatus, that during some succeeding systoles can improve the meta-
bolie condition of the heart-muscle, the condition of the ventricle-

Fig. 3.

The lower row of curves was represented 5 minutes after the row

of curves of fig. 2 with greater rapidity of the drum. The a-v-

interval is still considerably shortened. The upper row of curves

was represented 10 min. before that of fig. 2. Time 1 see.

musculature remains unaltered, for the ventricle continues to pulsate
in the same rhythm. The condition however of the track of the
transmission of stimula from the point of beginning in the auricle
{o that in the ventricle has changed.

Formerly the stimulus was twice transmitied during one ventricle-
systole along this track, now only once; formerly on each ventricle-
systole two auricle-systoles occurred, now only one. *)

That the hiatus, caused by the falling out of one auricle-systole
is indeed not the cause of the shortening of the «-v-interval is
proved by the further progress of the curves. Thus we see in the
Jower row of curves of Fig. 3, which is represented 5 minutes after
that of the former figure, the a-v-interval still constantly shortened.
The upper-row of curves of Fig. 3 was registered 10 min. before
that of Fig. 2. We must pay attention to the fact that, when noting
down the curves of Fig. 3, the rotations of the drum were quicker,
and for the lower row again quicker than for the upper row ;
consequently the curves are drawn out more in width.

Fig. 4.

During the first 4 systoles halving of the ventricle-rhythm.
Thereupon the rhythm of the auricle halves likewise. The
first auricle-systole that falls out ought to have stood on the 5th
ventricle systole. This is the cause that there occurs no
hiatus. The «-v-interval after it is shortened. The curves show
the falling out of every 2nd auricle-systole as the tops of the
ventricle-curves become rounder.

We see in Fig. 4 another example. Half an hour after the in-
jection of 8 drops of 1°/, acetas veratrini the ventricle-rhythm of
this frog’s heart was halved, half an hour later when a few times
variations of the ventricle-rhythm had taken place, the rhythm of
the auricle halves. The first auricle-systole falls out on the top of
the fifth ventricle-systole of the figure. The acute ventricle-top
becomes by the falling out of the auricle-systole, that stood on its
top, obtuse and rounded off (by looking at the heart I have also
observed that afterwards on each auricle- one ventricle-systole
occurred). Because the first auricle-systole, which falls out, ought
to have come on the top of the ventricle-curve no hiatus occurs now.
The shortening of the a-v-interval is also here obvious. By exact
measurement we see, that after the halving of the auricle-rhythm

1) The stage of the latent irritation of the auricle will certainly be shortened,
but we may safely admit, that this has no influence on the q-v-interval, only the
si-d-interval is shortened by it.

the a-v-interval is not suddenly reduced to the definitive extent, but
becomes smaller from systole to systole; thus before this halving
the a-v-interval amounts to 1'/, see., for the first systole after the
halving of the auricle-rhythm 1'/,, for the second 1'/,, till for the
fifth, sixth and seventh this amount is 1 sec; 1'/, min. later (vide
Fig. 5 lower row) this amount is likewise still 1 sec. Tne upper-
row of curves of Fig. 5 has been represented 15 min. before the
lower. Here we see a variation of rhythm of the ventricle.

Fig. 5.

The lower row of curves has been represented 1!/, minutes

after the curves of fig. 4. The a-v-interval is still shortened. The

upper row has been represented 15 minutes before the lower.
We see hereupon a variation of rhythm of the ventricle.

When estimating the variations of the q-v-interval we must con-
sequently always ask, which amount of it must be attributed to the
transmission of stimuli, and which amount is caused by the possibility
of exerting influence upon the ventricle-musculature. So the shortening
of the a-v-interval after the halving of the ventricle-rhythm must
be attributed to the improved possibility of exerting influence upon
the ventricle-musculature. [f the rhythm of the auricle halves at the
same time as that of the ventricle, then both factors contribute to
the shortening of the a-v-interval.

For the extra-systole after irritation of the auricle both factors
contribute to lengthen the q-v-interval, for the then succeeding post-
compensatory systole to shorten the a-v-interval. For the post-com-
pensatory systole after extra-irritation of the ventricle the a-v-interval
is again shortened by the possibility of exerting influence more
rapidly upon the ventricle-musculature.

We shall however continue to speak of the power of transmis-
sion of the connecting-systems, and estimate this in accordance with
the a-v or P-R-interval, but the above evidence must guide us when
drawing our conclusions.

Along a quite different way I showed that the ventricle-systoles
have a latent stage for the irritation coming from the auricle, of a

duration that changes in aecordance with the metabolic situation of
the ventricle-musculature. I found in fact that the duration of the
R-V-interval (this name IT gave to the interval between the beginning
of the f-oscillation of the ventricle-electogram and the beginning of
the ventricle-suspensioncurve belonging to it) increases considerably
after poisoning with veratrine; when then the ventricle-rhythm halves
this R-V-interval decreases again, and increases afterwards again
when the poisoning-process continues. *)

Mathematics. — “A particular bilinear congruence of rational
twisted quintics”. By Prof. J. pr Vrins.

(Communicated in the meeting of April 23, 1915).

1. In a communication in these Proceedings of March 27" last,
(volume XVII, p. 1250) | considered a congruence of rational twisted
quinties, o°, which is determined by a net of cubic surfaces the base
of which consists of a twisted cubic, a straight line and three fun-
damental points. We arrive at a [@°| differing from this by starting
from a net of cubic ruled surfaces A’ having a straight line g as
nodal line. Two arbitrary surfaces of that net have another @° in
common, which is rational, because it has g as a quadrisecant. An
arbitrarily chosen third surface intersects g° eight times on q, con-
sequently seven times outside g; hence all base-curves 9° of the
pencils (#*) comprised in the net have seven fundamental points
Fr in common.

The congruence [@°] consists therefore of the curves 9°, which
intersect the straight line q four times and pass through seven points F.

2. The hyperboloid f,?, containing the straight line g and the
six points Fr(k=2 to 7), has with an A’ of the net another
rational curve e,* in common of which g is a trisecant. This @,* is

ok
a component part of a degenerate curve of the congruence; the
second component part is the straight line 7,, which connects #,
with the point #,, where 9,‘ moreover intersects the plane (/, q).
To each ray of the plane pencil (7,) belongs on the other hand a

1) Erelong an elaborate communication about this subject will appear in “The
Journal of Physiology.” Compare fig. 2, 3, 4 and 5 of communication I: “On the
heart-rhythm” by Dr. S. pe Boer. Koninkl. Akademie van Wetenschappen at
Amsterdam. Verslag van de gewone vergadering der Wis- en Natuurk. Afdeeling
van 30 Januari 1915. Deel XXII, p. 1026 and 1027, Proceedings of the meeting
of Saturday February 27 1915. Vol XVII p. 1075.

rational 0,‘, with which it is connected into a degenerate 9°. For
through any point of a straight line 7, pass o' ruled surfaces /?,
which have 7, in common; so they pass all moreover through a
rational 9%, of which g is a trisecant. All pencils (/*) which arise
when 7, is made to revolve round #, have in common the degene-
rate ruled surface composed of the plane (/,q) and F,’. These two
figures have in common, besides q, a straight line p,, which is
apparently the locus of the point R, = (7,, 0,*)-

Through the five points /% (4 = 3 to 7) a twisted cubic Gi may
be laid intersecting g twice. If AR, and &, are its points of inter-
section with the planes (#,q) and (/,q), the straight lines r, = F, R,
and 7,=F,R, form with gf, a degenerate 9°. Apparently 9, forms
with g the intersection of the hyperboloids #,* and A,’

The congruence therefore contains seven systems of degenerate

curves (9%, rk) and 21 degenerate figures (93, rk, 71).

3. Any curve g° intersecting the singular quadrisecant q in a
point S belongs to the base of a pencil of which all the surfaces
touch each other in S. In order to determine the locus of those
curves, I consider two arbitrary pencils of the net | R*]. If to each
ruled surface of the first pencil the two ruled surfaces of the second
pencil are associated, which touch the first ruled surface in S, the
pencils are in a correspondence (2,2). To the figure of order 12,
which they produce, the common ruled surface belongs twice. The
curves 9° passing through S form therefore a surface 2°. This sur-
face must be a monoid as an arbitrary straight line drawn through
S is chord of one curve 09°, consequently intersects =*° outside S
in one point only. From the consideration of a plane section it
ensues as a matter of course that q is a quadruple straight line of
the monoid.

Through the quintuple point S pass the seven straight lines F‚S.
An arbitrary 9° of the congruence intersects >* only on g and in
the points /#; from this it ensues at once that the monoid has
seven nodes Fr.

If 2° is projected from S on a plane y, the system oo of the
curves in which the monoid is intersected by a pencil of planes
finds its representation in a pencil of curves g°‚ passing through
the images fj, of the points #%. One of these curves has apparently
a node in Fx; the remaining curves will therefore have in F;’ the
tangent in common. 2° has in that case the same tangent plane in
all the points of SF}: the monoid has seven torsal straight lines SF,

The curves 9° lying on =* are represented by a pencil of rational
curves pf passing through the seven points /”, and thrice through
the intersection Q of qg. To that pencil belong seven surfaces each
consisting of a straight line Q/"; and a nodal ¢* passing through
the remaining points 7”. Such a figure is the image of a degenerate
e°, of which the eo“ passes through S; while the straight line 7 is

produced by the intersection of the plane (/;,q).

4. The surface 4 formed by the curves y*, which intersect a
straight line /, has g as a sertuple straight line; for in its intersections
with a monoid =° the line / meets six curves 9° passing through
the vertex S of the monoid.

The section of 4A with the plane (#,q) consists of the sextuple
straight line q and three straight lines r,; of these, one is intersected
by 7, the other two are indicated by the two curves @,‘, which
rest on 7 (§2). The surface A is therefore of order nine; it has
seven triple points Fr, and contains 21 straight lines r.

The order of A may also be determined as follows. As in § 3
I consider two pencils (R°). If each two ruled surfaces intersecting
on / are associated to each other, a correspondence (3,3) arises. The
figure produced by it is of order 18 and consists of three times
the ruled surface which the pencils have in common and the sur-
face A; this surface is consequently of order nine.

A plane 2 passing through / intersects A° along a curve À“. The
curve g°, which has / as a chord (hence is nodal curve of A®*) passes
through two of the intersections of / and À*; in each of the remain-
ing six intersections 2 is touched by a o°. The locus of the points
in which a plane p is touched by curves 9° is therefore a curve
of order six, p°‚ with quintuple point S,—= (q, 4).

With an arbitrary surface 4’ this curve has, outside S,,6 X 9 —
5 X 6= 24 points in common. The curves touching a plane p form
therefore a surface of order 24, D**,

A monoid =° has with g°, outside S,, moreover 6 x 6 —5 «4
= 16 points in common; on g° lie therefore the points of contact
of 16 curves 9° passing through the vertex of 2%, in other words
®* has q as sivteenfold straight line.

An arbitrary 9° therefore intersects ®*' 64 times on q; as the
remaining 56 intersections are united in the points #, ®** has seven
octuple points F.

The hyperboloid R* has, outside S,, seven points in common with
gy’; in those ‘points y is touched by as many rational curves 9!.
The corresponding straight lines 7, lie on ©‘. The section of this

surface with (#,g) consists of q and 8 straight lines 7,. The eighth
of those straight lines belongs to a degenerate 9°, which touches p
improperly.

The plane y has in common with **, besides two times the curve
of contact y, another curve y'*, which has a sextuple point in S,.
Outside S, the curves vy" and p'* have moreover 6 X 12 — 5 « 6= 42
points in common; from this it ensues that each plane is osculated
by 21 curves ¢’.

The curve wp° along which the plane wp is touched by Y**, has
in common with *', outside the intersection of gq, moreover
6 X 24 — 5 X 16 = 64 points. Two arbitrary planes are therefore
touched by 64 curves Q’.

5. Any straight line ¢, containing three points of a g°, is a sin-
gular trisecant. For through ¢ passes one R*; the remaining ruled
surfaces of the net intersect it therefore in the triplets of an invo-
lution so that it is trisecant for o' curves 9°. From this it ensues
that the singular trisecants form a congruence. As each g° is inter-
sected in each of its points by three trisecants, the congruence [t]
is of order three.

The fundamental points F' are singular points of [t|; for each of
those points bears oo! singular trisecants. The cone ©, which they
form, has in common with the cone S*, which projects an arbitrary
o° out of F, three straight lines ¢, which are nodal edges of ®*, and
further the straight lines to the remaining six points £. From this
it ensues that = is a cubic cone. The points are consequently
singular points of the third order for the congruence of rays [t].

The trisecants of @° form a ruled surface X*, on which 9° is
a triple curve *).

The axial ruled surface % formed by the straight lines f, resting
on a straight line « has therefore with a g° in common the 24
points, in which ¢° is intersected by the eight trisecants resting on
a. Outside these points they have only in common the seven points
F, which, however, are threefold on U. We conclude from this that
U must be a ruled surface of order nine. As a is a triple straight
line on it, a plane passing through « possesses moreover six straight
lines t. The congruence of rays [t] is therefore of class six.

In connection with this the plane F,F,F, contains, besides the

1) The points of support of the trisecants form the pairs of an involutorial
correspondence (6). The involution J;, which the planes passing through a straight
line 7 produce on g°, has apparently 24 pairs in common with (6); consequently
eight trisecants rest on /. >

three straight lines FF, F,F,, F,F,, three trisecants, consecutively
passing through F), F,, F,.

The three straight lines ¢, meeting in an arbitrary point P, are
nodal lines on the surface 11°, containing the points of support of
the chords drawn through P of the curves of the [g°|]. With the
cone which projects the o° passing through P, H* has, besides
this g*, only straight lines passing through P in common; they
are the three trisecants out of P, which are nodal lines for both
surfaces, and the seven singular bisecants PH. From the con-
sideration of the points which JZ* has in common with an
arbitrary 9° follows that this surface has nodes in the seven funda-
mental points.

For a point S of the singular quadrisecant II passes into the
monoid =*.

Mathematics. — “Bilinear congruences of elliptic and hyperelliptic
twisted quintics.” By Prof. JAN pr Vaes.

(Communicated in the meeting of April 23, 1915).

1. We consider a net of cubic surfaces ®* of which all figures
have a rational quartic, o', in common. Two arbitrary #* have
moreover an elliptic quintic @° in common, resting on o* in ten points.
A third surface of the net therefore intersects 9°, outside o*, in jive
points J; they form with o* the base of the net. As a ®* passing
through 13 points of o* wholly contains this curve, only four of the
points /; may be taken arbitrarily for the determination of the net.
The base-curves 9° of tbe pencils of the net form a bilinear congruence,
with singular curve o* and five fundamental points Fr.

The singular curve of may be replaced by the figure composed of
a o* with one of its secants, or by the figure composed of two conics,
which have one point in common, or by the figure consisting of a
conic and two straight lines intersecting it.

2. The curves @°‚, which intersect o* in the singular points S,
form a cubic surface S*, with node S, which belongs to the net;
S is therefore a singular point of order three. The monoids =*
belonging to two points S have o* and a curve 9° in common ;
through two points of o* passes therefore in general one curve g°.
The groups of 10 points which of has in common with the curves
of the congruence form therefore an involution of the second rank.

On of lie consequently 36 pairs of points, each bearing oo! curves
e°; in other words, the net contains 36 dimonoids, of which the
two nodes are lying on o*. The congruence further contains 24
curves 0°, which osculate the singular curve o*.

The curves 0° lying on the monoid 2%, are, by central projection
out of S, represented by a pencil of plane curves p*,‚ with two double
base-points and eight single base-points; to it belong the images of
the five fundamental points. The remaining three are the intersections
of three singular bisecants 6; through each point of such a straight
line passes a 0° of &*. The two nodes are the intersections of two
singular trisecants t; each straight line ¢ is moreover intersected
in two points by each 9° of the monoid; for two 9° the line ¢ is
a tangent. The three straight lines 6, and the two straight lines ¢
lie of course on 2’; the sixth straight line passing through S is a
trisecant d of o*. It is component part of a degenerate 9°; for all

passing through an arbitrary point of d contain this straight line
and have moreover another elliptic curve 9‘ in common.

8. The locus of the straight lines d is the hyperboloid A*, which
may be laid through o*. The latter. has with a monoid =* the
singular curve 6 and two trisecants d in common. Consequently *
contains a straight line d not passing through S ; the curve g* coupled
to this straight line must contain the point S. It is represented by
a curve *, containing the intersections of the straight lines ¢, 6 and
the images of the points /’, while the line connecting the intersections
of the two singular trisecants is the image of the SE line d
belonging to this 94

The locus - of the curves of has in common with 2* the curves
ot and two curves 9%; so it is a surface of order four, A*. With
A* the surface A“ has in common the curve o*; the remaining
section is a rational curve d*, being the locus of the point D = (d, 9).
As the trisecants of d* form the second system of straight lines of A?,
Jd and o* have. ten points in common. This is confirmed by the
observation that the pairs d, e* determine on o* a correspondence
(7, 3), which has the said ten points as coincidences.

4. The locus of the pairs of points which the curves g° have
in common with their chords drawn through a point P is a surface
TM, with a quadruple point P. The tangents in P form the cone #*,
which projects the curve 9° laid through P; the two trisecants tof
this curve are nodal edges of that cone and at the same time nodal
lines of 41°. The cone, which projects o* out of P has-in common

with &* the 10 edges containing the points of intersection of o* and
e°; the remaining 6 common edges q are singular bisecants. For ¢
is chord of the curve o° passing through P, and moreover of a 0°
intersecting it on 6%, but in that case it must be chord. of oo
curves 0°. The surface *, which may be laid through g, o* and 0°
does belong to the net; the other surfaces of this net consequently

intersect this net in the pairs of a quadratic involution ; in other
words, q is a singular bisecant. ee

The six straight lines g lie apparently on 47°; this surface also
contains the five straight lines /;,—= PH}, which, as the above men-
tioned straight lines 4, are particular (parabolic) singular bisecants ;
through each point / passes a 0°, which has its second point of
support in /’, so that the involution of the points of support is
parabolic. The section of 71" and S* apparently consists of a o?,
two straight lines ¢ (which are nodal lines for both surfaces) five
straight lines f and six straight lines ¢.

For a point S of the singular curve 6‘ the surface 17° consists of two
parts: the monoid 2* and a cubic cone formed by the singular bisecants
gq, which intersect of in S. As a plane contains four points $,
consequently 4 >< 3 straight lines g, the singular bisecants form a
congruence of rays (6, 12), belonging to the complex of secants
of of, which congruence of rays possesses in o* a singular curve of
order three.

5. The singular trisecants ¢ form, as has been proved;a congru-
ence of rays of order two. The latter has the-five fundamental
points # as singular points, for each of those points bears ce!
straight lines ¢, which form a cone £. With the cone §*, which
projects an arbitrary ef out of £, © has the four straight lines to’
the remaining points in common and further the two straight lines’

passing through /\ As these straight lines are nodal edges of 8*,
= must be a quadrie cone. The congruence [t] has therefore jive
singular points of order two.

The trisecants ¢ of an elliptic g° form ') a ruled surface X*, with
nodal curve o°. The axial ruled surface A formed by the straight
lines ¢ which intersect a given straight line a, has in common
with an arbitrary 9° in the first place 5 3 points, in which g° is
intersected by the five straight lines ¢ resting on a. Moreover they
have in common the five points #, which, however, are nodes of U.
Consequently A is a ruled surface of order five. As a is nodal line

1) Vid. e.g. my paper in volume IL (p. 374) of these Proceedings,

of *, a plane passing through a@ contains three straight lines more
hence the singular trisecants form a congruence (2, 3).

6. A straight line / intersects three curves o° of a monoid >’;
consequently o* is a triple curve on the surface A formed by the
o°, intersecting /. As two surfaces A*, outside of, bave but « cur-
ves 9° in common, we have 2? = 5z + 36, hence «= 9. An arbi-
trary curve g° intersects 4’ on o* in 10 X 3 points, consequently
fifteen times in Ft; so A° has five triple points Fy. On A’ lie (§ 3)
six straight lines and sir elliptic curves 0*
chord, is a nodal curve.

In a plane 2 passing through /, the congruence |o*| determines
a quintuple-involution possessing four singular points S of order three.
It transforms a straight line / into a curve 2° with four triple
points, and has a curve of coincidence of order six, y*, with four
nodes S. With an arbitrary surface 4° the curve 7’, has outside
Sr 9X 6—4x« 3 X2=30 points in common. The curves o*,
touching a plane p, consequently form a surface ®*°; on it of isa
decuple curve (=" intersects y°, outside Sz, in 3 X 6 — 4 x 2 points)
while FF, are decuple points (an arbitrary ¢° intersects °°, out-
side of, in 5 X 30 — 10 10 points).

® has in common with gy another curve g'*, possessing four
sextuple points S; it touches gy" in 20 points; gy is therefore
osculated by thirty curves 9°.

Two surfaces &°° have, outside of, 100 curves g° in common,

two planes are therefore touched by 100 curves 9°.

; the 0°, for which / is a

7. When all the surfaces #* of a net have an elliptic twisted
curve 6* in common, the variable base-curves 9° of the pencils
comprised in the net form a bilinear congruence of hyperelliptic
curves. Each g° rests in eiyht points on o* and has with an arbitrary
surface ®* moreover seven fundamental points Fp in common. As
the net is completely determined by of and five points #, the points
F cannot be taken arbitrarily.

The singular curve o* may be replaced by the figure composed
of a curve 0? and one of its chords, or by two conics having two
points in common. *)

8. The monoid =, which has the singular point S as node

1) In both cases a %, containing 12 points of the base-figure, will contain it
entirely. This elucidates the fact that #3 needs only to be laid through 12 points
of the elliptic «* in order to contain it entirely.

and belongs to the net [®*]|, again contains all the 9° intersecting
the singular curve o* in S. In representing S* on a plane p the
system of those curves passes into a pencil of hyperelliptie curves
g*, with a double base-point and 12 simple base-points. The first is
the intersection of a singular trisecant ¢, consequently of a straight
line passing through S, which is moreover twice intersected by all
the o° lying on &".

To the simple base-points belong the central projections of the 7
fundamental points. The remaining five are singular bisecants b,
consequently straight lines, which have a second point in common
with any o° passing through S. With the trisecant already men-

tioned they form the six straight lines of 2* passing through S. The
straight lines 4, are, as well as the straight lines / passing through

the fundamental points, parabolic bisecants.

9. In the same way as above (§ 4) it is proved that an arbitrary
point bears eight singular bisecants q, i.e. straight lines, which are
intersected by [@*| in the pairs of an involution; they belong to
the complex of secants of 6*. The straight lines g passing through
a point S of of again form a cubic cone, so that |q| is a congruence
of rays (8, 12).

The singular trisecants ¢ form a congruence of order one, which
has the points F as singular points. The singular cone © belonging to
HF is a quadrie cone as it has in common with the cone 3‘, which projeets
an arbitrary v° out of #, six straight lines FJ’ and a trisecant t,
which is nodal edge of 7%. As the trisecants of 9° form a ruled
surface X?, the axial ruled surface %, belonging to a straight line
a, has in common with a o° the six points of support of two
trisecants and the seven nodes /, consequently is of order four.
But in that case [7] is of clrss three, consequently the congruence
of the bisecants of a cubic t°, passing through the seven points #.

As in § 6 we find that two arbitrary straight lines are intersected
by nine curves 9°, that two arbitrary planes are touched by « hundred
curves, that there are thirty curves osculating a given plane.

Here too, the fundamental points are triple on A’, decuple on ®°,

Mathematics. — “Remark on inner limiting sets’. By Prof. L. E.J.
BROUWER.

(Communicated in the meeting of April 23, 1915).

The notion of inner limiting set i.e. the set of all the points
common to a series of sets of regions, was prepared by Boret '),
and fully developed by Young’). The two principal theorems about
this class of sets are the following :

1. An inner limiting set containing a component dense in itself,
has the continuous potency.

2. A countable set containing no component dense in itself, is an
inner limiting set.

The former theorem has been proved by Youre, first for the
linear domain, then for the space of nm dimensions *). The latter
theorem has been proved for the first time by Hopson‘). It is true
that this theorem ean be considered as a corollary of the following
theorem enunciated somewhat before by Youne®):

3. If Q be an arbitrary set of points, an inner limiting set ewists
containing besides Q only limiting points of the ultimate coherence ®)
of Q;

but this theorem was deduced by Youne*) from the property :
“Each of the successive adherences’) of a set of points consists
entirely of points which are limiting points of every preceding
adherence’, and the proof given by Youne for this property is
erroneous *), so that undoubtedly the priority for the proof of theorem
2 belongs to Hopson.

We can, however, arrive at theorem 2 in a much simpler way

1) Lecons sur la théorie des fonctions, p. 44.

2) Leipziger Ber. 1903, p. 288; Proc. London M. S. (2) 3, p. 372.

3) Leipziger Ber. 1903, p. 289—292; Proc. London M. S. (2) 3, p. 372—3874.
These proofs are referred to not quite exactly by ScHOENFLIES, Bericht über die
Mengenlehre II, p. 81 and Entwickelung der Mengenlehre I, p. 356.

+) Proc. London M. S. (2) 2, p. 316—323.

5) Proc. London M. S. (2) 1, p. 262—266.

6) Youna, Quarterly Journ of Math. vol. 35, p. 113.

7) Cantor, Acta Mathematica 7, p. 110.

8) Quarterly Journ. of Math., vol. 35, p. 115. The error is contained in the
sentence (line 8—6 from the bottom): “Thus P, being a limiting point of every
one of the derived coherences, is a limiting point of F”. A correct proof of
the property in question was communicated to me about two years ago by
G. CHisHoLM YouNG.

than Hopson and Youne did, by means of the following *) proof of
theorem 3, which is valid for the space of 1 dimensions:

For each positive integer » we describe round each point g of Q
as centre with a radius smaller than ¢, (lim e, == 0) a sphere which,
if q is a point of the adherence (Qc#a, excludes all points of the
derived set of Qc? In this way for each positive integer r a set of
regions ./, containing Q is determined.

The inner limiting set D(./,) then possesses the property required.
For, if p be a limiting point of Q not belonging to Q and not being
a limiting point of the ultimate coherence of Q, a transfinite number r,,

exists with the property that p is not a limiting point of Qe ‘7, but for
any «<t, is a limiting point of Qc’. Then on one hand p is
excluded by every sphere described round a point of © Qe7a, on
tp
the other hand a positive integer 6, exists so that p is excluded by
every sphere described for a v>>o, round a point of Qc’. Hence
p lies outside every -/, for which r > o,, so that p cannot belong
to D(J,). Thus the theorem has been established.

Chemistry. — ““/nvestigations on Pastwur’s Principle of the Rela-
tion between Molecular and Physical Dissymmetry.” IL. By
Prof. Dr. F. M. Janerr. (Communicated by Prof. H. Haca).

(Communicated in the meeting of April 23, 1915).

§ 1. In the following are reviewed the results of the erystallo-
graphical investigations upon which the conclusions explained in the
previous paper’) are founded.

I. Racemic Luteo- Triethylenediamine-Cobaltibromide.
Formula: {Co (Aein),} Br, + 3 H,O.

This compound was prepared by two methods: 1. Starting from
praseo-diethylenediamine-dichloro-cobaltichloride: {Co (Aein), CL} Cl, by
heating with ethylenediamine and precipitating with a concentrated
solution of sodiumbromide; 2. By heating purpureo-pentamine-

1) This proof was communicated about two years ago to SCHOENFLIES, who
on p. 356 of his Entwickelung der Mengenlehre I, applies it to prove the follow-
ing special case of theorem 2: “Every component of a countable closed set is
an inner limiting set”. Comp. Hopson, le. p. 320: “Every reducible set is an
inner limiting set”.

2) Vid. These Proceedings, March 1915.

Proceedings Royal Acad. Amsterdam, Vol. XVIII,

chlorocobaltichloride : ee CI, with three molecules of tri-

ethylenediamine for a considerable time, and precipitating the compound
with sodiumbromide.

A. The salt prepared by the method indicated sub 1 is deposited
from the yellow-brown solutions as hexagonal plates of red-brown
or orange colour, or in the shape of hexagonal, short prisms. (fig „La
and 15).

Pseudo-ditrigonal-scalenoédrical, but probably really monoclinic

a: C15 06794:

The compound is almost perfectly isomorphous with the corre-
sponding chloride; however the cleavage differs in the two salts.

Observed Forms: c= {0001}, most prominent and giving good
images; == MOTO}, often very well developed, shows however in
most eases broken faces, giving multiple reflections; r= HOi,
sometimes small, but occasionally rather large; r’ = {1017}, often
absent, several times very narrow, and in rare cases as well developed

as r: perhaps s = $4263}, occasionally visible as an extremely
| I ; i
narrow blunting.
Angular Values : Measured: Calculated :

y+ e= (1011): (0001) = *38°-7' as

r tm== (1011): (1010) = 5150 51053!
DRU (1010) : (0110) — 60 2 60 0
e 1 s == (0001): (4263) — ca. 54o 54 9
» : r==(1011):(101)= — 64 38

Fig. 1.
Racemic Triethylenediamine-Cobaltibromide.

A perfect cleavage oceurs parallel to {0001}. Plates perpendicular
to the c-axis are however completely dark in no situation between
crossed nicols, if the light is polarized parallel. Occasionally they
appear to be composed of lamellae parallel to {0001}, like the well-
known mica-piles of Reusch and Marrarp, as might also be proved
perhaps by the often observed anomalies of the angular values.

The erystals are optically-uniaxial ; the birefringence is of a negative
character. They do not show a rotatory polarisation ; their dichroism

is clearly visible: on {1010} for vibrations parallel to the c-axis
orange-red, for those perpendicular to the former orange-yellow. The
specific weight of the crystals was determined at 25° C. pycno-
metrically : de == 1.845; the molecular volume!) is thus: 577.8,
and the topical axes x: w = 10,9400 : 7,4328.

B. The substance prepared from purpureo-dichloro-salt crystallised
from its aqueous solution in the shape of hexagonal plates, which
will commonly show not only ec and m, but also 7 and 7’. The
optical behaviour and the angular values agree completely with
those of the previously described salt. Further, we obtained the same
modifications in separating the bromo-tartrate into its optically active
forms as in the first case; also the ¢/-bromo-tartrate was here identical
with that obtained from the first salt. There cannot be any doubt,
but that the two bromides are quite identical; the specific gravity of
the last crystals also, being found at: 1.142 at 25°C., is in agreement
with this supposition.

With the kind assistance of my colleague Haca a beautiful RÖNTGEN-
ogram of these hexagonal plates was made. The stereographic
projection of it is reproduced on Plate I, in A. It appears now, that
there is no ditrigonal symmetry at all: the photo reveals only a
single plane of symmetry, as if a mere monoclinic-domatic symmetry
were present. For the present no other explanation can be given
here, than the supposition of the crystral being only a pseudotrigonal
complex of perhaps monoclinic lamellae; in every case the very
perfect approximation of that complex to a real ditrigonal crystal is
a quite remarkable fact; it remains yet very strange however, why
only a single plane of symmetry will appear in this image.

IT. Dewtrogyratory Luteo- Tricthylenediamine-Cobaltibromide.
Formula: {Co (Aein),} Br, + 2 H,0.

The compound was obtained by the transformation of the racemic
salt in aqueous solution into the corresponding d-bromo-d-tartrate
by means of silver-d-tartrate and afterwards fractionated crystallisation.
The d-bromo-d-tartrate which is deposited first and whose beautiful
erystals are also described in the following, is then treated with HBr
to convert it into the dextrogyratory bromide; the same happened
with the -bromo-d-tartrate, which can be obtained only in the form
of a colloidal mass. The rotation of the two salts in aqueous solutions
appeared to be really equal but of opposite direction.

1) In the following calculations we adopted 2M instead of M as the molecular
weight of the racemic compounds. This latter one is undoubtedly also present still
in the aqueous solutions of the salts.

Big erystals, occasionally a ce.m. in volume; they are brownish
red, in most eases thick prisms with beautifully developed, lustrous
faces. Commonly they are flattened parallel to two opposite faces of
ms; also the dodecahedrical crystals were observed, which are described
in the case of the laevogyratory antipode.

Ditetragonal-bipyramidal.
anos OBE):

Observed Forms: m = $110}, in most cases predominant, sometimes
giving multiple images; o = {101{, with great, lustrous faces, allowing
very accurate measurements; w = {201}, well developed, but often
absent. (fig. 2a and 26).

Angular Values : Measured: Calculated:
O10 NONE MOU 8h —
m0) =O DE SS 6
m:m=—(110):(110)= 90 1 90 0
OS Cay == (OID) BEDI)

Onna — (201) (IO)

Fig. 2.

Dextrogyratory Triethylenediamine-
Cobaltibromide.

A distinct cleavage could not be stated.

On {110} the extinction is normal; the crystals are not appreciably
dichroitic. They are uniaxial, with negative birefringence. They
show a strong rotatory polarisation: a plate perpendicular to the
optical axis appeared to be strongly dextrogyratory: about 25° or 30°
for the transmitted orange-red light, and a thickness of 1 m.m. If
a similarly directed plate of the laevogyratory salt is combined with
it, one sees the spirals of Airy very distinctly like four dark beams,
radiating from the centrum of the image into direction of motion of
the hands of a clock, if the dextrogyratory plate is the upper-one
of the two.

The specifie weight of the erystrals was at 25° C.: dao = 1.971;
the molecular volume is thus: 261.29, and the topical parameters are :,

%:W: ao = 6,7759 : 6,7759 : 5,6910.

By means of a diluted solution of potassiumchlorate, finally corro~

sionfigures on {110} could be obtained, having the shape of kites or
long hexagons; they appeared symmetrical with respect to a horizontal
and to a vertical plane. From this and the holohedrical development
of the erystals, it must be concluded that they can not be considered
to have tetragonal-trapezohedrical symmetry, but that they must be
described as of ditetragonal-bipyramidal symmetry.

On the rotation in solution and its dispersion, the data of the
previous paper can be consulted.

The RönrarNogram obtained of a plate perpendicular to the c-axis
was too imperfect, to make a good reproduction possible. Thus on
Plate / in B we have given its steveographical projection ; it appears
to possess all the symmetry-elements of a ditetragonal-bipyramidal
crystal, and inter alia the four vertical symmetry-planes and the
quaternary axis can be easily distinguished. In reality the photo for
the laevogyratory salt, notwithstanding its imperfection, appeared to
be identical with that of the dextrogyratory salt. In all cases studied
up till now, we have found the Ronrennograms of the dextro- and
laevogyratory crystals always identical, just as the theory of the
phenomenon postulates: so in the cases of quartz, cinnabar, ete.
However we found in these investigations some quite remarkable
facts, which are already partially described in these Proceedings
(March 1915), and which ean lead to a perhaps justifiable doubt about the
correctness of the suppositions accepted hitherto about the explanation
of the symmetry-properties of the RöÖNrGerNograms, notwithstanding
the above-mentioned agreement of facts and theory in the case of
the optically active crystals.

In any case it appeared not to be possible to prove in this way
the presence of enantiomorphous forms.

All experiments made with the purpose of obtaining limiting
erystalfaces, which could demonstrate the hemihedrical character of
the crystals, either by crystallisation from neutral or alkaline or
acid solutions, either by addition of other salts to the aqueous
solutions, — were without any other result, than that of ahvays
giving holohedrical crystal-forms. In connection with the above-
mentioned experience, we have no reason to suppose the occurrence
of hemihedrical crystals in this case.

The optical rotation of the crystals must thus be ascribed wholly
to the optically active molecules themselves, which here build up
the holohedrical molecular configuration of the crystals. In the same
way, as e.g. sodiumchlorate is a salt, whose (active molecules are
arranged in a hemihedrical space-lattice, which causes the rotatory
power of the crystals, — in the same way we must suppose the

reverse case to be present here, where a holohedrical molecular
structure will thus be built up by optically active molecules.

LI. \n connection with the foregoing description of the dextro-
gyratory antipode, the erystal forms of the corresponding bromo-
aud chlorotartrates, from which the active eompound could be
prepared, may here be described in detail also.

The dd’-luteo-triethylenediamine-cobaltichlorotartrate, as well as
the corresponding — dd’-luteo-triethylenediamine-cobaltibromotartrate,
erystallise from the solutions of the racemic chloride, resp. bromide,
after being mixed with silver-d-tartrate-solutions, in the shape of
hard, very beautiful, translucid and commonly big erystals. If elimi-
nated from the original solution, this last will solidify, after having
been again concentrated and some more of the above-mentioned
crystals having been separated, into a brownish-red jelly, which for
the greater part represents the d/’-bromotartrate, and which after
treatment with HBr, will give the laevogyratory antipode, besides
some of the racemic compound. After a considerable time the jelly
of the d/’-bromotartrate often gradually transforms into a erypto-
crystalline mass.

a. dd’-Luteo- Triethylenediamine-Cobaltichlorotartrate.
; Am 8!
Formula: {Co (Aein), '
Je (C,OH,)

Big lustrous, brownish-yellow erystals (fig. 3), which commonly
have the aspect of oblique parallelopipeda.
Triclinic-ped ial.
MPO Te == OAL ibs Osi

A= 108° 421/,’ a = 102° 20/
B = 102° 46’ B == 101° 16’
C= 98°11,’ y= 95° 167/,’

Observed Forms: a= {100} and a’ = {100},
large and lustrous ; GO == {010}, c= {00k
and c/ = {001}, equally large and well reflect- —
ing; r={101}, well developed; g= {011}, about
as large as 7; m= {230}, only very narrow, and
often totally absent. The angular values oscillate,

as in the case of the bromotartrate, not unappre- Fig. 3.
ciably : deviations of 0°30’ to 1° are not seldom dd’-Triethylenediamine-
found with different individuals. A distinct Che

cleavage was not found,

ur
ie

Angular Values: Observed: Calculated:

a:b —(100):(010) = *81° 584 —

bre —=(010):(001)— *76 174 —

a:c ==(100):(001)—= *77 14 ==

a:r =—(100):(101) = *38 11 -

qi¢ =(011):(001)— *28 26 =

q:b =(011):(010)= 47 504 47° 504

rie =(101):(001)= 39 3 39 8

atm = (100):(230)—= 46 594 46 49

A distinct dichroism was not observed. On all faces the extinction

was oblique, but the extinction-angle on the prism-faces was only
small with respect to the direction of the c-axis, — which is in
agreement with the evident approximation to monoclinic symmetry,
this last one can be easily seen, if the forms a and 6 are taken as
{170}, resp. {110}, while c remains {001}.

bh. dd’-Luteo-Triethylenediamine-Cobaltibromotartrate.

Formula: {Co (Aein),} Fay H)

Big, very lustrous, perfectly transparent crystals (fig. 4), which
are wholly analogous to those of the corresponding chlorotartrate.
The angular values oscillate here still a little more than in the
preceding case; but undoubtedly the erystals are completely isomor-
phous with the above-mentioned ones,

Triclinic-pedial.

a:b:c= 0.6208:1: 0.6528.

a = 102° 50?/,' A=104° 8!
B= 100° 35 B=102° 7
y= 95° 14 C= 97° 55

Observed forms: b= {010} and b'= {010} large
and lustrous ; a = {100} and a’ = {100}, c = {001}
and: "¢ — (001, all about equally well developed
and giving good images; 7 =}LO1}, well develo-
ped and lustrous; 7° = {101} commonly absent ;
0 = {113} small, but allowing exact measure-

ments; v' = {032} narrow and somewhat dull.
The angular values oscillate with different indivi- Fig. 4.

ae tert Af We oe » dd’-Triethylenediamine-
duals not unappreciably, with differences of about 1°. Gopaltibromotartrate.

~~
56

Angular Values: Measured: Calculated ;

rb (100) ea (ON == 82cm —

bert (Ol0) (OOM SET:

ac (OON OON —
6

o: 6 = (113): (010) = *66 56
err = (001): (101) = *39 37 =

a:r =(100):(101) = 38 23 38°16!
ore =(113):(001)= 21 39 21 7
o:a =(118):(100) = 84 46 84 42
cq = (001): (032) = 50 38 50 493

No distinct cleavage could be stated.
On all faces the extinction-angles are other than rectangles; the
crystals have a sherry-like colour, and are not distinctly dichroitie.

IV. Laevogyratory Luteo- Triethylenediamine-Cobaltibromide.
Formula: {Co (Aewm),} Br, +2H, 0.

Big, brownish-red, commonly rhombic dodecahedrically shaped,
very lustrous crystals, which make very accurate measurements
possible.

Ditetragonal-bipyramidal.
D= ade)

Observed Forms: im = {110}, usually as largely developed as v,
giving the erystals thereby the aspect of rhombiedodecahedrons
(fig. 5); sometimes however m is strongly predominant either with
all its faces or with two parallel ones only, in such a way that the
erystals get a column-shaped or tabular aspect. Further: 0 = {101},
big and lustrous ; rarely : w = {201}, small but very easily measu-
rable. The faces of {110} sometimes give multiple images.

Angular Values : Observed : Calculated : SEN

o zo =(l01):(O11) = *54° 6 ea EAP

0 :m==(101):(110)= 62 55 62957 Ln

6 1 = (ON. OD 80 7 DE

Dei = (PAI) 5 (UO) =S UD ts 19 124 Fig. 5.

wim = (201):(110) = 5230 52 35 Teter ne
baltibromide.

No distinct cleavage was found,

Prof. Dr. F. M. JAEGER, ,,Investigations on Pasteur’s Principle of the
Relation between Molecular and Physical Dissymmetry.” Il.

A. Stereographical Projection of the Röntgenogram of the pseudo-ditrigonal
racemic [Co (Aein);] Br; + 3H,O; plate perpendicular to the c-axis.

B. Stereographical Projection of the Réntgenogram of dextrogyratory- and laevo-
gyratory [Co Aein)3] + 2H O; plate perpendicular to the c-axis.

With respect to the symmetry of the crystals the same can be
said as in the case of the dextrogyratory compound. Corrosion-expe-
riments on the faces {101} and {110} by means of water, mixtures
of water and alcohol, etc. in most case gave irregularly defined
corrosion-figures, which had the character of elevations.

The crystals are uniaxial with negative birefringence ; like those
of the dextrogyratory component they show a strong circular pola-
risation in the direction of the optical axis, which for a plate of
about 1 mm. thickness appeared to be equal and directed oppositely
to that of the dextrogyratory crystals.

On superposition of a dextro- and laevogyratory crystal, the latter
being the upper, the Atry-spirals are nicely seen, with their direction
of rotation just opposite to that mentioned in the description of the
dextrogyratory crystals.

The specific gravity of the crystals was pycnometrically deter-
le)

mined and found to be de —= 1.972; the molecular volume thus

is: 261.19, and the topical parameters are : y : py: w =
= 6.7589 : 5.6767.

V. Racemic Luteo-Triethylenediamine-Cobaltinitrate.
Formula: {Co (Aein),} (NO),

This compound was prepared by treatment of the racemic bromide
in aqueous solution with a warm solution of the quantity of silver-
nitrate calculated. The solution separated from the precipitated
silver-bromide was sufficiently concentrated on the waterbath ; at
roomtemperatnre dark red or brownish red, big, hemimorphic
crystals will be separated.

In general the parameters and angular values appear to be the
same as previously published (Z. f. Kryst. 39. 548. (1904). The
figure reproduced there however must now be changed, because the
hemimorphy is now clearly demonstrated ; further a wrong value
of the angle 0: q was introduced in the deseription, evidently by an
accidental interchange of the symbols {021} and {120}. For the
purpose of comparison of the calculated parameters with those of
the optically active forms, we have, contrary to the common usage
the polar binary axis as the a-axis.

1) These incorrect data are also reproduced in Groru’s Cliemische Krystallographie,
Il. 140, (1908) ; they must be corrected there by the numbers given here.

58
Rhombic-pyramidal.

a:b:c = 0.8079 :1:1,1279.

Observed forms: o = $112}, large and lustrous; a = {100}, smaller,
but also giving beautiful images; m= (7203, almost equally well
developed as 0, sometimes even with yet larger faces; p= {120},
appreciably smaller than m, but very lustrous; 4 = {010} narrow ;
c= {001} commonly absent, but if present well developed and giving good
images; w= (112, with very small but lustrous faces; a’ = {1003
almost in every case absent, but sometimes present as a very narrow
blunting of the intersection (120): (120). The crystals possess com-
monly a very peculiar irregularly-tetrahedrical habit, with prominent
faces of o and im.

Fig. 6.
Racemic Triethylenediamine-Cobaltinitrate.

Angular Values : Observed : Calculated:
PED (UU =S IN A —
o:0 ==(112):(112) = *49 38 =

o:0 =(112):(112)= 96 11 96° 12’
o:m=(112):(120)= 85 18 85 13
o:p =(112):(120)= 50 53 50 56
bn ==.(010) = (120) == ot ad Wale
a:p =(100):(120)= 58 10 58 15
pip ==(120):(120) = 116 20 116 30
m:m == (120): (120) =116 17 116 30

62 @ = (O01) (12) = 4 54 41 54
wo: = (112):(112)= 49 36 49 38

A distinct cleavage was not found.
On {100} and {001} diagonal extinction.

The specific gravity of the crystals was determined at 25° C. pycnome-
o

trically to be: d ET 1.709; the molecular volume is thus 497.64.

Topical parameters: 4: W: © = 6,6037: 8,1740: 9.2194.

The compound does not change the direction of the plane of
polarisation of the incident light.

VI. Laevogyratory Luteo-Triethylenediamine-Cobalti-nitrate.
Formula: {Co (Aein),} (NO,),-

The compound was prepared from the bromide by means of
silvernitrate in small excess and at lower temperature; after sepa-
rating from the silverbromide, the solution obtained was concentrated
on the waterbath. From this solution, which thus contained a slight
excess of silvernitrate, big, dark-red crystals were obtained, which
gave splendid images, and made very accurate measurements possible.

The crystals, which have the habit of thick, trapezohedrically or
pentagonally bounded plates, are usually developed parallel to oppo-
site faces of the prism. They are extraordinarily rich in faces, and
geometrically very well built; commonly the faces of the forms
O11}, {021}, {211} and {010}, are only partially present, a fact, which
in connection with the peculiar distortion of the crystals, often
impedes appreciably the exact crystallographical analyses of them.

Rhombic-bisphenoidic.
an bre 0.8647 = 1: 05983:

Observed Forms: a= $100}, well developed and giving beautiful
images; m — {110}; larger than a, giving good reflections; r= {101},
somewhat smaller than m, but in most cases equally well developed ;
o= {111}, giving good images and relatively large; s = 211} narrower,
but reflecting well; q = {O11}; and p= {021}, usually with only
half the number of their faces present, but developed rather largely ;
4 = {010}, narrower than a and reflecting well.

Angular Values: Observed: Calculated:
a zm =(100):(110) = *40° 51) —
a or) (OO) (AMIN os —
0 :m==(111):(110) = 47 28 47° 33!
m:m==(110):(110) = 98 18 98 18
r:m==(101):(110) = 64 304 64 304
0: o=(111):(111) = 84 58 84 54
6: s—=(010):(211) = 70 41 70 41
r:q=(101):(011)= 45 1
ro (101):(111) = 26 22 26 12
o : b=(111):(010) = 68 48 63 48
b:m=—=(010):(110) = 49 4 49 9
a: r= (100):(101)—= 55 15 55 19
ms: qg==(110):(011)= 70 21 70 23
m: p= (110):(021) = 59 43 59 5
p: o=(021):(11) = 35 43 35 43

D Bd (1 ): (110) = -84 33 84 244 Fig. 7

ee (101) B (211) = 27 13 27 94 Laevagyratory Triethylenedia-
js wt i mine-Cobaltinitrate.

m: 3 (ON (A) san US 21

ri p=(101): (021) = 58 20 58 103
gop = (OLD) (O2 = 9
a:s—=(100):(211)= 40 4 40 63
g: s=(011):(211)= 49 56 49 534
g:0=(01):(111)= 30 48 30 42
0: s==(111):(211) = 19 15 19 114
b : qg==(010):(011) = 59 4 59 6}
b : p=(010):(021) = 39 58 39 53
A distinct cleavage was not observed.

On {100} and {O10}, also on {101} and {110} everywhere a normal

extinction was found. The crystals are not appreciably dichroitic.
A 25°
The specific gravity of the crystals at 25° C was: d om 1.729:

the molecular volume is thus: 245.91. Topical parameters :
%:W:@ = 6.7486 : 7.8046 : 4.6695.

61
VII. Dextroguratory Luteo-Triethylenediamine-Cohaltinitrate,
Formula: {Co (Aein),} (NO),

This compound was prepared in perfectly analogous way to the
left-handed isomeride. From its aqueous solutions it crystallises as
dark red, very large erystals with rectangular outlines. They are
also very beautifully developed and give sharp images; the habit
as well as the limiting planes are quite analogous to those of the
laevogyratory component, but the crystals were in general not so
strangely distorted, and they had somewhat smaller dimensions. They
are the complete mirror-images of the crystals previously described.

Rhombic--bisphenoidic.
a:6:¢= 0.8652 :1:0.6009.

Observed Forms: a= {100} and m= $110}, both reflecting very well;
m is somewhat more largely developed than a, and the crystals
usually appear flattened parallel to two opposite faces of {110}.
Further-on: 7 = {101}, well developed, and like o = 144}, giving very
sharp images; s = {211}, small and showing in most cases only two
faces; g = {011}, very small; p= {120} and 6 = {010}, extremely
narrow and reflecting badly, often absent (fig. 8).

Angular Values: Observed: Calculated :
a %m = (100): (110) = *40° 52

0 :m=(111):(110) = *47 26 =
a zo = (100):(111)= 59 18 59° 14
rm :m = (101):(110) = 64 31 64 26%
(OO) CLO == Spee oon als

o tr == (111):(101) = 26 32 26 25

m:m = (110) : (110) = 98 14 98 12

yp tr =(101):(T01I)= 69 31 69 34
bh :s =(010):(211)= 70 87 70 394

oro (1M): (lll 85 8-85 5
miq ==(110):(01!1)= 70 16 70 13
rig =(lelj:(Oll) = 45 20 45 7
m:p = (110):(120)= 18 55 19 64
b sp =(010):(120)= 30 0 30 14
is Sti == (OUMYS(yss ZI) ch A)
bo =(010):(111)= 63 40 63 44

Topical parameters: y: wp: wo = 6,7467 : 7,: 7979: 4,6856.

Fig. 8.
Dextrogyratory Triethy-
lenediamine-Cobaltinitrate

A distinct cleavage was not observed.

On {100}, {110} and {101} the extinction is
normal; the crystals are not distinctly dichro-
itic. The plane of the optical axes is {001};
probably the 6-axis is first bisectrix. The
apparent axial angle is great, the dispersion
has no exceptional value; round the a-axis
it is @ >v, with a negative character of the
birefringence.

The specific weight of the crystals at 25° C.

5°
was determined at d on 1,725; the mole-
cular volume consequently is 246,51.

VILL. Racemic Luteo- Triethylenediamine-Cobalti-iodide.

Formula: {Co (Aein),} J, + 1 H,O

The compound was prepared from the corre-
sponding bromide by double decomposition with
a solution of potassium-iodide; the precipitate
was washed and reerystallised from warm water.
On slow evaporation of tbe saturated solution, the
small crystals can grow to fairly big individuals.

Splendid, dark-red to red-brown, very lustrous

and clear crystals of octahedrical habit. The Fig. 9.
angular values of the different individuals may Racemie
differ about 20'; every crystal as a whole how- _Triethylenediamine-
ever is geometrically very well built. Cobalti-iodide.

Rhombie-bipyramidal.

a:b:e=0,8700: | : 1.7399.

The crystals may be considered as pseudo-tetragonal, if the b-axis
is chosen as the pseudo-quaternary axis.

Observed Forms: o={112, and q=021}, about equally well
developed; the faces of g are sometimes a little smaller than those
of o, but both give very sharp images. Furthermore c= {O01}, much
smaller but giving good reflections; w={111}, very narrow and
somewhat dull, but quite measurable; 5 = {010}, extremely narrow

and reflecting badly ;

v={101}, rare and almost imperceptible.

Angular values: Observed: Caleulated:
0:0 = (112): (112) — #(53° 19! =
e:q = (001): (021) = #73 58 =
ero = (001): (112) = 53 39 4522 ae!
o:w = {112):(111) = 16 tds | GEND
w:w==(111):(11T) = 41 35. Al 20
q:q = (021): (021) = 30 AES
q:b = (021): (010) = 16) 2 MAGER
o:q = (112): (021) = 48 NS ATG
e:# —(001):(101) =S circa 45 — 44 593
ara == (101): (101) = 89: 520 Oren

A distinct cleavage could not be observed.

On {O01} diagonal extinction: the crystals are not perceptibly
diehroitie. The plane of the optical axis is {010}; the c-axis is first
bisectrix. The apparent optical angle is very small.

The specific gravity of the crystals at 25° C. was pyenometrically
determined de = 2.270; the molecular volume is thus: 562.10.

Topical parameters: 4: : w = 6.2532 : 7.1877 : 12.5070.

IX. Dextrogyratory Luteo- Triethylenediamine-Cobalti-iodide.
Formula: {Co(Aein),} J, + 1 H,0.

_ This compound was prepared by the precipitation of a solution
of the dextrogyratory bromide with a concentrated solution of
potassium-iodide; the precipitate was washed out and recrystallised
from warm water. Analysis showed, that the compound, just like
the racemic one, crystallizes with 1 molecule of water.

Long, dark-red, in transmitted light, blood-red needles, with lustrous
faces. All faces of the prism-zone, with the exception of those of
the forms {100} and {010}, are vertically striated; the vertical zone
furthermore shows many vicinal forms, which make it often diffi-
cult, to find the exact angular values. (fig. 10).

Rhombic-bipyramidal.
a@: bc = 0.8276: 1: 017386:

Observed Forms: m = {340}, the largest of all prism-faces, giving
like all prismatic faces, multiple reflections and diffraction-images ;
6 = {010}, and a= {100}, somewhat narrower, but giving sharp
reflections; p = {120} and s = {3.16.0}, both narrower than a, with
s in most cases again smaller than p; g = {OI}, well developed,
but with rather appreciably oscillating angular values; 7 = 1102),

giving very sharp reflections and easily measurable; ; ¢ = {104} and
o=}101}, small but distinetly reflecting; = {071}, very small
and dull.

The habit of the crystals is elongated parallel to the c-axis.

A distinct cleavage was not observed.

On all faces of the vertical zone a normal extinction is found;
no appreciable dichroism. The plane of the optical axes is {001},
with the /-axis as first bisectrix. The apparent axial angle is very
small; the dispersion is strong: 9 << vr. The birefringence is positive.

The specific gravity of the crystals at 25°C. was: die = 2.289;
the molecular-volume is thus: 278,72.

Topical parameters : YW: wo = 6,3699 : 7,6968 : 5,684.
Angular Forms : Observed : Calculated :
a:r == (100) : (102) =*65° 577 —
p:q = (120) : (O11) =*59 2 —
r:q == (102) : (011) = 42 48 42° 44’

r:p = (102) : (120) = 77 41 77 50

a:m== (100) : (340) = 47 50 47 49

mep == (SLO AEO ESA

p:s == (120) :(3.16.0) = 18 20 18 224

sbr (3-16.0) (OU Op == EO eo

rir = (102) : (102) = 48 12 48 6

mig == (340) : (011) = 63 40 63 53

q:q = (011) : (OT) = 72 52 72 54

b:q = (010) : (011) = 58 34 58 33

rst = (101) : (104) = 11 38 11 284 Fig. 10.
t :t = (104) : (104) = 25 15 25 74 ee
roo == (102) (0) LS vee ae mine-Coballti-
oa = (101) 2 (00), = AES MS gee.
b:w = (010) : (071) = 10 59 10 563

On {100} we obtained with mixtures of alcohol and water very
long, acute, hexagonal corrosion-figures and irregularly bordered
rectangular elevations arranged in long rows. On the other hand
we obtained on the faces of the prism triangular and trapezium-
shaped corrosion-figures, which proved beyond doubt the presence of
a horizontal symmetry-plane, parallel to (//{001}).

The RöNrerxogram of a plate parallel to //{001} was very irre-
cular and rudimentary, very probably however at least one single
symmetry-plane might be present.

X. Laevogyratory Luteo-Triethylenediamine-Cobalti-iodide.

Formula: {Co (Aein),} J, + 1 H,0.

This antipode was prepared in a quite analogous way to that indi-
cated in the case of the dextrogyratory component, and recrystallised
from warm water. The crystals also contain, according to analysis,
1 molecule of water of crystallisation. They may grow to considerable
size: one individual had a volume of more than 0.5 cem.

Flat, dark-red to blood-red crystals, with lustrous faces, which
give multiple reflections however, especially in the prism-zone.

Observed Forms: p =: }120!, large, but giving multiple images ;
q=3011}, also largely developed, and better reflecting than p;
6 = {010}, very lustrous and well reflecting ; 7 = {102}, small, but
very lustrous and well measurable; 7 = {340}, very narrow ;
6 = {101}, very small, and often absent ; @ = {100}, extremely narrow.

The habit is somewhat elongated with respect to the c-axis.
(fig. 11).

Rhombic-bipyramidal.

a@:6:¢ = 0.8256 : 1: 0.7395.

Angular Values: Observed: Calculated:
b: p = (010): (120) = *31° 12) —

q:q = (011): (011) =*72 58 =

b:q =(010):(611) = 53 31 53° 31’
a:p =(109):(120)—= 58 43 58 48
rin =(102):(102) — 48 10 48 154
r:6=(102):(101) = 17 52 17 434
8 (oO) (ONT) = bo) 22) 59) 926

Fig. 11.
Laevogyratory
ene (SLOD le NOs Voy 57 Triethylenediamine-
Cobalti-iodide.

No distinct cleavage was observed; one parallel to {001} may
perhaps be supposed.

The optical orientation is the same as in the case of the dextro-
gyratory compound.

€ Oo

25
, = 2.288: the

The specific gravity of the crystals at 25° Cis: d 4

molecular volume is thus: 278.84.

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

Topical parameter: 4: w: w = 6.3580 : 7,7010 : 5.6950,

With cold water we obtained on {010} elongated, commonly
irregularly shaped corrosion-figures. They seem to be symmetrical
with respect to 100%, but perfect certainty could not be procured,
notwithstanding many attempts made for this purpose.

XI. Racemic Luteo- Triethylenediamine-Cobalti-rhodanide.
Formula : {Co (Aein),} (CNS),.

The compound was prepared by double composition of the racemic
bromide with a concentrated solution of petassinmrhodanide, washing
the yellow precipitate, and reerystallising from hot water. The erys-
tals grow to rather large individuals in the solution, saturated at
room-temperature and have a flat, spindle-like shape. According to
analysis, they are anhydrous.

Red-yellow or yellow-brown, flat, spindle-shaped, acute, often
distorted crystals, which are easily measurable.

thombic-bipyramidal.
a:b:c= 0.8405: 1 : 0.8130.

Observed Forms: s = $201}, prominent and reflecting well, but
sometimes giving multiple images; 5 = {010} and p = {120}, giving
extremely sharp reflections, and thus exactly measurable ; m= {110},
lustrous, somewhat smaller than p; o = {211{ and x = {S24 as
narrow bluntings. The crystals are elongated parallel to the h-axis,
in several cases also parallel the a-xis; in the last mentioned case
the habit of the small erystals is the acute, spindle-like one already
described. (fig. 12 a, 6 and €).

Fig. 12.

Racemie Triethylenediamine-Cobalti-rhodanide.

Angular Values: Observed: Calculated :
$+ e==(201):(001) = *62° 40° —

Ce (OLON (LOSS ORE =
(ODE (LOOPS ORE O2 OI
AZOREN OO OD EE ONE
DAO a ELD toe 5 Ge ee

es ZOEN ZOE 625 52) 62 59:
joe == (UPD VE Brive EEL tb Bi Bir)
si (82) (201) ——29) Gr 729 2
OF DS(ON (i = te) Ne) tie) Be
oa Oe 1.20, Ab 20 288

A distinct cleavage was not observed.

In the zone of the ortho-diagonal the extinction is everywhere
normal ; the crystals are not distinctly diehroitie. On {120} triangular
corrosionfigures were obtained. which were in agreement with the
symmetry mentioned.

The specific weight of the crystals was at 25° C. pyenometrically
determined to be: de 1.511; the molecular volume is: 547.24.

Topical parameters: x: A: @ = 7.8053 : 9.2864 : 7.5499.

NII. Devtrogyratory Luteo-Triethylenediamine-Cobalti-rhodanide.
Formula: {Co(Aein),}(CNS),.

The active compounds were prepared from the dextro- or laevo-
gyratory bromides in a quite analogous way, as indicated by the
racemic rhodanide. Analysis proved that these optically active modi-
fications erystallise without water of crystallisation.

Beautifully formed, orange to blood-red, splendidly reflecting, quadran-
gular thick plates or flattened, shortprismatic, small crystals, whieh
make accurate measurements quite possible. They are extraordinarily
rich in faces, and geometrically generally very well built. (fig. 13).

Rhombic-bipyramidal.
a:b6:c= 0.8494 : 1 : 0.8376.

Observed Forms: ¢ = {001}, in most cases predominant and always
well developed; g = {O11}, with large faces; r= {101}, also large,
but narrower than q; « = }LOO}{, well developed and giving excel-
lent images, just like 4 = }OLO}, whose faces are somewhat narrower ;

s = {201} and ¢= {012}, well developed; there are commonly only
two faces of the form ¢ present.

Further : 0 = {121}, showing among all pyramids present the lar-
gest faces; w= {111}, somewhat smaller than 0; 4 = {122}, very
small, but giving distinct images; m = {110} and p= {120}, very
small and subsidiary, but measurable.

Fig. 13.

Dextrogyratory Triethylenediamine-
Cobalti-rhodanide.

Angular Values: Observed: Calculated:
og = (001) (OS LERT zn
nk q = (101): (C11) = *56 56 —
r:s=—=(l0l):(201)—= 18 23 18° 31
ec :r=—=(00l):(101)—= 44 39 44 36
s : a=(201):(100)—= 26 58 26 53
b:g=(010):(O11) = 50 2 50
s : g=(201):(011)= 69 39 69 42
C2 t — (OOM) (Ol2) 2
ts g@=(Ol2) (Old SS 7 46 SET 133
7 3 w = (101): (11H = 5
w:o=(iijj:(lij= 19 9 19 1
o : b= (12T):(010) = 40 3 39 584
ce: h==(001):(122)= 44 4 44 1

1
h: o=(122):(121)= 73 0 73 23
er o=(001):(121) = 62 51 62 464
0: o=(121):(121)= 80 6 79 57
o: q=(121):(011)= 81 56 81 53}
0: p= (123120) LI deren
a:m==(100):(110)= 40 15 40 21
m: b=(110):(010) = 49 45 49 39
a + w= (100j:(111) = 52 44 52 55
wim == (111): (110)= 87 46 37 42
wis e=(1'1):(001)= 52 24 52 18

A distinet cleavage was not observed.

On {001}, {011} and {101} everywhere normal extinction. The
erystals are not appreciably dichroitic. The optical axial plane is
{100}; the apparent axial angle is small, and the c-axis is first
bisectrix.

The specific weight of the substance at 25°C was found to be:

25°

d 4° = 1.502; the molecular volume is: 275.26.

Topical parameters: y:p: w = 6.1893 : 7.2867 : 6.1034.

With tepid water on {001} beautiful corrosion-figures were obtained
after short treatment. They represented rectangular, pyramidal eleva-
tions, which were distinctly symmetrical with respect to the planes
{100} and {010}. Consequently the crystals must be considered as
having bipyramidal symmetry ; with mixtures of alcohol and water
rectangular, bilateral-symmetrical corrosion-figures were also obtained,
which are in agreement with the holohedrical symmetry of the
rhombic system.

XIII. Laevogyratory Luteo-Triethylenediamine-Cobalti-rhodanide.

Formula: {Co(Aein),}(CNS),.

Thick, short-prismatic, orange- or blood-red needles, which are
very well built, and which give excellent images. Although the
habit is different from that of the dextrogyratory compound, the
erystalform is evidently quite the same.

Rhombic-bipyramidal.
a:b6:c= 0.8494: 1: 0.8375.

Observed Forms: 6 = {010}, predominant and, like « = {100},
which is also well developed, giving excellent images; c= {001},
small but very lustrous; s= {201} and r= 101}, rather large;
q = 011}, somewhat larger yet, and like both foregoing forms,
reflecting excellently ; m= {110}, about as broad as 7, and reflecting
well; p= {120!, narrow and a little duller; 0 = {121}, well deve-
loped; w= {111}, with small faces between o and r. The habit is
short-prismatic with respect to the c-axis, with predominance of

010} and {100}. (Fig. 14).

Angular Values: Observed: Calculated:

gag == (00 Wi (OlT) = *39° 54 —

r:q — (101): (OL) = *56 56 a3

(OLDE (ON0) 0) = One O ND:

ars == (100): (201) = 26 53 26 53

zen SDN Its) oetan dk “331

An =D WS 44 34 44 36

aen LOOD 40 22 40 21

mp — (110): (120) = OW 3 LO LD,

p:b = (120): (010) = 30 35 30 29

De (COOS 40 0 39 583 Fig. 14.
Ce (EON 50 0 50 14 Laevogyratory
ma = (101) ene eN PE
Man (LIN) Si GIA) = 30 329 26

A distinet cleavage could not be found.
The optical properties are the same as indicated in the previous
case.

Ths specifie gravity of the ervstals was pycnometrically determined
. le}

to be: d HE = 1.496; the molecular volume is: 276.37.
Fopical parameters x: wp: ow = 6.1979 : 7.2968 : 6.1110.
Of a plate parallel to {O01} we obtained a Röntgenogram which

notwithstanding its imperfectness, in every case showed the presence
of at least one plane of symmetry.

NIV. Racemic Luteo- Triethylenediamine- Cobalti-perchlorate
Formula: {Co (Aein),} (CIO)

4/8°

The salt was prepared by double decomposition between the racemic
bromide and silver-perchlorate.

It is rather difficult to obtain well developed crystals of this
compound; commonly thin, reetangular, tabular crystals are obtained

possessing round edges and giving considerably oscillating angular
values; or they are complicated intergrowths of extremely thin plates
arranged in rosettes. Between crossed nicols such intergrowths will
in no situation show a complete extinction, but lamellar polarisation
and high interference-colours, in some cases also a mosaic-like structure :

Finally we succeeded in making the necessary measurements with
the rectangular, tabular crystals.

Rhombic-bipyramidal.
epee — 08569": 1. 2.7751.

Fig. 15.
Racemic Triethylenediamine-
Cobaltiperchlorate.

Observed Forms: c= {001}, large and lustrous, in most cases
striated parallel to the intersection: c:q; r == {102}, 0 = {111} and
q= {011}, about equaliy largely developed; commonly q gives the
better, + the feebler images. Finally again: s = {101}, narrow, but
easily measurable. The habit is tabular parallel to {001}, with a
slight elongation parallel to the b-axis.

Angular Values : Observed : Calculated:
e:q==(001):(011) =*70° 1 —

etr=(001):(102)=*58 20 —

e:o0=(001):(111)= 77 10 76° 49'
cis =(001):(101)—= 72 56 72 504
sts = (101): (107) 1
rir = (102):(102) = 63 35 63 20
q:q¢=(011):(011)= 40 2 39 38
»:s = (102):(101) = 14 38 14 36

oo
rag
Go
oo
rss

On {O01} the extinction is perpendicular and parallel with respect
to the intersections c:7 and c:q. The plane of the optical axes is
{O10}; the crystals are distinctly dichroitic, namely orange for
vibrations parallel to the plane of the optical axes, orange-yellow
for such as are perpendicular to it.

The specifie weight of the crystals at 25°,1 C. was : « se 1.878;
the molecular volume is thus: 572.72

Topical parameters :y : wp: w = 5.3314: 6.2217 : 17.2660.

XV. Dewtrogyratory Luteo-Triethylenediamine-Cobalti-perchlorate.
Formula: {Co (Aein),} (CO).

The compound was prepared by transformation of the d-bromide
by means of a solution of silver-perchlorate. The salt erystallizes
from its aqueous solution in the shape of flat, brownish-red, very

lusirous crystals, which show rather strong oscillations of their
angular values, especially in the vertical zone. (Fig. 16).
They are rhombic bisphenoidic.

Qos C= LOT 2G OESO

Observed Forms: 6 = 3010}, strongly predominant and rather
sharply reflecting; a= {100}, very narrow or wholly absent, but
with some crystals prominent; im = }110{, well developed, giving
however multiple images; r= {101} and ¢=}O11}, giving very
sharp reflections; o = {111}, in most cases broader and larger than
o= Hi; this last form reflects very well.

Angular Values: Observed: Caleulated:

Dn (OW) (ODIS Ei -

bo =(010) : (OEI) "60 EL — ae
gq = (011):(011)= 68 26 68° 26' - El
0 :r =(111):(101)= 29 46 29 46 À
Beem = (010): (110) — 48 28 4e ik |
mia —=(110):(100)—= 46 32 46 354 |

rar = (101):(101)= 65 30 65 30
mig =(110):(011I)= 65 48 65 583

gir OLIE (LOU) = 46 4 45 56 pe
nm (101) (110) = 68" 16) 468) 10s ON
ato =(100):(111)= 62 3 61 59} Fig. 16.
; Dextrogyratory
Heo SCs @Obhss 46 OM 4) (a Triethylenediamine-
Cobalti-perchlorate.

b :w —(010)'(1T1)= 60 16 60 14
wir =(111):(101)= 29 50 29 46

No distinet cleavage was observed.
The specifie gravity of the crystals was pyenometrically determined
ĳjRO

25
at 25° C., and found to be d 4° = 1.881, the molecular volume is

thus: 285.80, and the topical axes are: 4: py: w= 7.7731 : 7.3526 :
5.004,

18
NVI. Laerogyratory Triethylenediamine-Cobalti-perchlorate.
Formula: {Co (Aein),} (CIO), .

This salt was prepared from the corresponding -bromide by means
of silver-perchlorate, and the concentrated solution afterwards slowly
evaporated at 15°C.

From an aqueous solution, still containing a trace of the silver-
salt in excess, the salt crystallized in the form of beautiful, spheno-
idie crystals (fig. 177), which immediately showed the presence of
hemihedrical symmetry. From the pure solutions in most cases the
flat, rectangular crystals, reproduced in fig. 176 were obtained; they
had a brownish-red or brownish-yellow colour, and show more
constant angular values than the sphenoidie crystals, whose angles
oscillate und which possess considerable geometrical anomalies.

Evidently these kinds of crystals are however quite identical.

Rhombic-bisphenoidic.

a:b:e=1.0580: 1 : 0.6806.

Observed Forms: b = {010}, highly predominant, and reflecting
well; the faces are however often spoiled, and then give multiple
reflections. Further m= {110}, giving good images and about as

a Fig. 17. b

Laevogyratory Triethylenediamine-Cobaltiperchlorate.

large as ¢ = {011}, which form shows very lustrous faces; 7 = {101},
giving sharp images, and very well developed, about as large as
o = {111}; w = {171} on the contrary small, and rather dull, although
giving well defined images; « = {100}, very narrow and dull. In

the erystals drawn in fig. 17a, the form o = {111} is predominant;
Oo 114) small and narrow, 6 = {O10}, narrow but reflecting well,
like @= {100}, which form is developed about equally to it; ¢ = {O01}
in most cases absent, but rarely present with only one single curved
and rudimentary face.

Angular Values: Observed: Calculated:
De DOD (GUND) = SOS ia —

ben (ONO IOS LN —

b : qg==(010):(011)= 55 48 55° 46!
a :m—=(100):(110) = 46 39 46 37
9: q= (011): (11) = 68 28 68 2
w:b==(111):(010) = 60 13 60 12
w: r=(lID:(101)—= 29 49 29 45
r + a==(101):(100)= 5

y+ r==(101):(101)= 65 48 65 36
a: o==(100):(111)= 62 0 62 0
e :o=(001):(111)= 43 0 43 8
0 :M@=(11l):(111l)= 93 48 93 44
m: o—=(111):(111I)= 5 55
o?w—=(111):(111)= 59 50 59 32
o : o=(1ll):(111)= 8

No distinct cleavage could be observed.

Feebly dichroitic: on {010} for vibrations parallel to the a-axis
orange-yellow ; for those perpendicular to these, yellow-orange.

The plane of the optical axis is {001}; the a-axis is probably first
bisectrix.

The specifie gravity of the crystals was pycnometrically determined to

25° Ee are

be: d AT 1.888; the moleenlar volume is thus: 284.74.

Topical parameters: p:p:w =: 7.7657 : 7.38399 : 4.9955.

NVI. Racemic Triethylenediamine-Cobalti-nitrite.
Formula: {Co(Aein),} (NO,),

Thin, orange-yellow, in thicker layers orange-brown, hexagonal
plates, often showing mutilated faces, and intergrowths parallel {OOOJ{,
mm == (4010) : (0110) = 60°; m : ¢ = 1010) : (0001) = 90°.

The erystals are uniaxial and negative.

The optically active components are so highly soluble that it was
impossible up to now, to obtain crystals suitable for measurements.

About the general conclusions, relating to the facts here described,
vid. Publication I (March 1915) on this same subject.

Laboratory for Inorganic and Physical
Chemistry of the University.
Groningen, March 1915.

Chemistry. — ‘J/nvestiyations on the Temperature-Coefficients of
the free Molecular Surface-Energy of Liquids at Tempera-
tures from — 80° to 1650° C° IX. The Surface-Energy of
homologous Aliphatic Amines. By Prof. F. M. Jarerr and
Dr. Jur. Kann. (Communicated by Prof. P. van ROMBURGH).

(Communicated in the meeting of April 23, 1915).

$ 1. During the continuation of our studies regarding the influence
of special substitutions in the molecules on the specifie and mole-
cular surface-energy of homologous compounds, our attention was
drawn to the fact, that the free surface-energy and its temperature-
coetficient in the case of organic derivatives of the trivalent nitrogen often
show remarkably low values. We therefore determined to study
systematically a greater number of the homologous series of the
aliphatic amines in the way previously deseribed. The results of these
investigations are communicated in the following pages.

A single determination of the yalue of the free surface-energy of
carefully purified and dried anhydrous ammonia: NH, taught us
that with this mother-substance itself, even at lower temperatures,
the value of y is a relatively small one.

We found at — 73° C. for the specific surface-tension of liquid
ammonia: about 37 Erg pro cm’. *), a value considerably different
from the sparsely published data in literature regarding the surface-
energy of this liquid. As we had at the moment no means of
maintaining constant lower temperatures for a longer time, we could
not for the present continue these experiments further ; however we
hope to be able to return to these researches later on.

1) The radius of the capillar tube was: 0.04595 e.m., the depth of immersion :
0.1 mm. The maximum pressure observed was: 1,210 mm, of mercury of O° C.

The 23 compounds of this homologous series studied here are:

Methyl-, Dimethyl-, and Trimethylamine; Ethyl-, Diethyl-, and
Triethylamine ; norms. Propyl-, Dipropyl-, and Tripropylamine ; 1so-
propylamine; Allylamine; norm. Butylamine; Tsobutyl-, Diisobutyl-,
and Triisobutylamine ; tertiary Butylamine; norm. Amylamine; Isoamyl-,
and Diisoamylamine ; tertiary Amylamine; norm. Heayl-, and Isoheayl-
amine; norm. Heptylamine; while for the purpose of comparison
the measurements of Kormamide are reproduced here also.

The pure amines were first dried by means of metallic sodium or
potassiumhydroxide, then fractionated in vacuo over KOH ; because
of the inevitable bumping of the liquid, the thermometer-readings
oscillated within limits of about 2”.

The specific gravity must be determinated with most of these
substances by means of a volumeter, because of their volatility and
their tendency to attract carbondioxide and water-vapour from the
atmosphere. Especially in the case of the lower-boiling amines these
experiments appeared to be highly cumbersome and demanded much
time; however we think the obtained results to be exact within
about 0.1°/,, which must be quite sufficient for the use here made
of them.

Molecular Surface-Energy
» in Erg pro c.m?,

980
950

260. me,
S070 60° 530: 4030 20°90 OJO LO IO AO IO OO TSO VCO HOTLO VO MOK 700770 Temperature

Fig. 1. Primary Amines.

—12 1.005 1340.1 Ald 0.696 | 272.9

8 £ cury of in Dynes Ere praca. | = Erg. pro cm?.
& | OC: | |

nm 7 aay ae vet ST : 7 TE ME
— 70 1.324 1764.8 29.2 0.759 346.7
—49 | 1.225 | 1633.2 26.5 0.736 321.2
— 20 1.068 1423.9 23.0 0.705 286.9
—18 | 1.049 1399.8 22.7 0.702 283.9

Molecular weight: 31.05. Radius of the Capillary tube: 0.03343 em.
Depth: 0.1 mm.

The dry amine boils under atmospheric pressure at —6° C. At —79° it is
still a thin fluid mass, without any trace of beginuing crystallisation.
At the boilingpoint the value of / can only slightly differ from: 20.9 Erg. pro cm?.

The specific gravity was determined by means of a volumeter: at —79°C.
it was: 0.7691; at 0° C. 0.6831. At ¢° it may be calculated from: Ayo =
= 0.6831— 0.00109 ¢.

The temperature-coefficient of » increases gradually at higher temperatu-
res: between —70° and —20° C. it is: 1.20; between —20° and —18° C. it
is: 1.50; and between —18° and —12°: 1.83 Erg. per degree.

Il.

Dimethylamine: (CH), NH.

— = en - = ——— SS
|
|

Maximum Pressure H |
Molecular

| Specific | Surface-

Surface-
tension 7 in
| Erg. pro cm2.

in mm. mer-

Temperature
fay

| .
| nt ME Dynes | | (Erg. pro cm?.
—18 0.842 | 1121.4 ZNA en NE
—50 0.745 995.5 22.5 | 0.730 | 351.4
—23 0.672 897.0 20.2 0103 | 323,5
0 0.606 807.9 18.1 0.680 | 296.4
5 0.586 | 183,5 Adie 0.675 | 291.3
= _ —_—— | — | | —
Molecular weight: 45.06. Radius of the Capillary tube: 0.04595 cm.

Depth: 0.1 mm.

The liquid boils at +-7.°95; at —76° C, it is not yet solidified. At the
boilingpoint ~ has the value: 175 Erg. per cm?. The specific weight at 0° C.
was: 0.6804; at —79° C.: 0758; at t°C.: it is: d4. = 0.6804—0.0009886 t.

The temperature-coefficient of „ has a mean value of 110 Erg. per degree,

gravity do, energy » in |

|
|
|
|
|

Trimethylamine: (CH3)3N.

2 Maximum Pressure H ;
iS = | Surface: Molecular
5 Saale ee | tension , in ey | Surface- |
a in mm. mer- “2 | gravity d,.| energy zin
g 5 cury of in Dynes | Ens pee ee a ; 2, |
& 0° C. | | Erg. pro cm |
a — ee — —— — en en = Se = es —— a =
Tk} aha O2 1102.5 24.8 0.748 456.6
—52 | 0.737 983.7 2282 0.725 417.4
—32 |- 0.678 | 897.8 20.0 0.704 383.5
=. | 0.627 834.8 18.6 0.691 361.0
—4 | 0.583 Annee 17.3 0.675 | 341.1
(oe ae.” ee A ae TE ase ee en Tl Ar |
Molecular weight: 59 10. Radius of the Capillary tube: 0.04595 em.

|
Depth: 01 mm.

The liquid boils at about —3° C.; even at —75° C. it was still as thin
as water, aud no trace of crystallisation could be observed. The sp-cific
gravity at 0° C. was: 0.6709; at —79° C.: 0.7537; at 1° C. is A 40 = 0.6709—

—0.001048 ¢. The temperature-coefficient of 4 decreases slowly with rising
temperature: between —73° and —52° C. it is: 1.89; between —52° C, and
—19° C.: 1.71; and between —19° and —4° C.: 1.33 Erg. per degree.

IV.

Ethylamine: (C.H;) . NH».

2 Maximum Pressure H _,
a} | 3 | Molecular |
aS ate Een Be urface- specifi | Surf
50 : ‚tension Zin | Pee - Ure
ag | in mm. mer- | gravily a energy win
Bam cury of in Dynes Bee Uae oo Erg. pro em?
= pc.) |
| = = — | 5 —=< —— === = ———S
ea bor Nep 20.1 | 0.785 433.1
—33. 0.807 1078.1 24.6 | 0.741 380.5
—21.5 0.773 1030.6 23.4 | 0.729 365.9
0 0.709 945.2 21.4 | 0.708 341.1
9.9 0.676 901.2 20.4 | 0.698 328.4
el a EE NEEN ND Oe Ue
Molecular weight: 45.07. Radius of the Capillary tube: 0.04595 cm, |

Depth: 0.1 mm.

The amine boils at 20° C.; even at —76° it is liquid stitl. At the boiling-
point 7 is about: 19.9 Erg. pro cm?. The specific weight at 0° C. was volu-
metrically determined to be: dyo= 0.708 at U° C.; and 0.790 at —79° C. At
ter @ sik 181: do = 0.7085—0.001032 ¢. |

The temperature-coefficient of » is constant and 1.25 Erg. per degree.

Diethylamine: (C,H;)o NH.

= Maximum Pressure U

le, Surf Molecular
5 on = urface- aie
ES tersion 7 in Specific Surface-
a in mm. mer img | gravity d,.| energy» in |
Ei 5 cury of in Dynes Ere PAGE 5 Erg. pro em?.
a OAT:

21.5 | 0.765 1019.9 23.0 0.752 486.2

Oa 0.693 923.9 20.8 0.731 448.1

10 0.655 873.8 19.7 0.720 428.8
23.4 0.616 819.5 18.3 0.708 402.8

35 0.587 781.4 17.4 0.695 387.7

45 | 0.568 754.5 16.6 0.626 373.1

| |

Molecular weight: 73.10. Radius of the Capillary tube: 0.04595 em.

Depth: 0.1 mm.

The amine boils at 56° C. and erystallises at about —40° C. At the boiling-
point 7 possesses the value: 16.2 Erg. pro em2. The specific gravity at 0°C.
was: 0.7315; at 25° C.: 0.7045; at 50° C.: 0.677. At 1° in general: do =
= 0.7315 — 0.00107 t—0,000000 t (2.

The temperature coefficient of » has a mean value of: 1.69 Erg. per degree.

Triethylamine: (C.H;)3 N.

= Maximum Pressure H |
= | Smrfae. | Molecular
On : - Specific Surface-
ended tension yin pegs 8 2
& . in mm. mer- 4 Erg. pro cm? gravily dy.) energy » in
2 = cury of in Dynes z | Erg. procm2,
& | ORG: L
| le} .
—70. 0.929 1238.5 28.1 0.816 698.5 |
—20.5 0.740 985.5 Doel 0.769 571.5 |
| 0 0.658 887.0 20.0 0.749 52674
25.6 | 0.596 794.6 17.8 0125 4718.8
41.2 | 0.572 153.1 16.7 0.710 455.5
Bogie 0.505 681.1 15.8 0.695 437.1
10.4 | 0.478 637.3 14.1 0.681 | 395.4
84.3 | 0.453 603.9 133 0.667 | 378.2 |
Molecular weight: 101.13. Radius of the Capillary tube: 0.04676 cm. |
|

Depth: 0.1 mm.

The liquid boils under 762 mm. at 87° or 89° C. Even at —72° the amine
is still a thin liquid. The specific weight was determined volumetrically:
at 0° C. it was: 0.7495; at 25° C.: 0.7255; at 50° C.: 0701. At t° C: do =
= 0.7495—0.00095 t—0.0000004 t?. At the boilingpoint ~ has the value: 12.8 Erg.

The temperature-coéfficient of » decreases gradually with increasing tem-
perature: between —70° and —20° C. it is: 2.56; hetween — 20°C and0°C.:
2.20; between 0° and 26° C.: 1.86; and between 26° and 84° C.: 1.71 Erg.
per degree Celsius.

VII.

normal Propylamine: C,H,NH).

Depth: 0.1 mm.

The liquid boils under a pressure of 760 mm. constantly at 47.°5 C.; at
—72° C. it is still very thin. The density at 0° C. is: 0,741; at 25° C.:0,714;
at 40° C.: 0.698. At t° in general: dy, = 0.741— 0.001075 ¢, At the boilingpoint
the value of x is: 17.5 Erg.

The temperature-coefficient of » is fairly constant and equal to: 1,54 Erg.
per degree.

VIII.

Dipropylamine: (C3;H7).NH.

104.5 0.453 603.9 13.8 0.662 394.3

Molecular weight: 101.10. Radius of the Capillary tube: 0.04777 cm; in the
measurements indicated by *, the radius was:
0.04839 cm.
Depth: 0.1 mm.

Under a pressure of 762 mm. the liquid boils at 110.95 C. Even at —78°C.
it remained clear, but solidifies afterwards into a mass of white crystals,
melting at —45° C. At the boilingpoint ,—13.9 Erg. pro cm?. The specific
weight at 0° C. was: 0.7565; at 25° C.: 0.733; at 50° C.: 0710. At t° C. itis:
Ayo = 0.7565 —0.00095 ¢ + 0.0000004 t2. The temperature-coefficient of » decreases
gradually with increasing temperature: it is 2.38 between —20° and 48° C;

between 48° and 65° C.: 219; between 65° and 81° C.:1.89; between 81°
and 104° C.: 1.69 Erg.

IX.

Tripropylamine : (C3H-;)3N.

© Maximum Pressure H | | |
5 dj Stare Molecular
a2 lr Specific Surface-
2° i | venlo Dt gravity d energy „in
in mm. mer- 2 | ° Yu
5 5 net in Dynes Bie sPEveI, Erg. pro cm?.
a — Er En de = ae SS SS mn
—Tl1 0.977 | 1302.5 30.6 0.830 | 948.2
—20.5 0.816 | 1087.9 25.6 0.789 | 820.6
0 0.758 | 1010.4 23.6 0.773 | 166.9
25.6 0.693 | 923.9 DG 0.753 | 710.9
40.5 0.647 862.6 20.1 0.741 | 671.8
55.5 0.607 810.5 18.8 | 0.729 | 635.2
80.2 0.545 | 726.6 16.8 | 0.709 578.3
92.2 0.513 684.4 15.8 0.699 | 549.0
116.1 0.460 613.5 14.1 | 0.680 | 499.0
*136 0.421 561.3 12.6 0.664 453.1
*149.5 | 0.385 BiSiG) wel © AIDS 0.653 Js 418.2

Molecular weight: 143.18. Et of Nee Oes tube: 0.04792 em. ; in ie
observations indicated by *, the radius was:
0.04670 cm.
Depth: 0.1 mm.

The amine boils constantly at 157° C. and 765 mm. pressure. Even at —79°
it remains liquid. The specific gravity was determined with the aid of a
volumeter: at 0° C. it was 0.773; at 25° C.: 0.753; at 50° C.: 0.733. At t°
generally: do = 0 773—0.0008 t. At the boilingpoint ~ was about: 10.9 Erg.

The temperature coefficient of » is fairly constant; its mean value is:
241 Erg. per degree.

Isopropylamine: C,H7N Hp.

2 Maximum Pressure HZ |
3 5 le Eds | | Molecular
5 o TE ES. | mam | tension yin | Specific | Surface- |
ao in mm, mer- Breen remaeeray ity dgo | energy « in |
ia cury of in Dynes 8 P > | Erg. pro em2, |
= OIC: | | | |
ae ee AS =! == Se |
a |
—79 0.929 | 1238.5 28.1 0.781 502.7 |
—10.5 | 0.734 975.7 21.8 0.728 | 408.7 |
aah 0.636. | 852.0 19.4 0.709 antes |
1 0.596 | 794.6 Ned) 0.694 342.6
25.2 0.564 | 151.9 6 0.684 328.3
Molecular weight: 59.09. Radius of the Capillary tube: 0.04676 em. |

Depth: 0.1 mm.

The amine boils at 33 —35° C., under 760 mm. The specific gravity at |
18° C. is: 0691; the other values were calculated by adopting 0.001 as the
mean pinparaine coefficient, which may not deviate much from the
true value of it. At the hoilingpoir t z has the value: 16.0 Erg.

The temperature-coefficient of » is fairly constant, and in mean: 1.76 Erg.
per degree Celsius.

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

XI.

Allylamine: C,H;. NH.

Under a pressure of 751 mm. the substarce boils at 53° C. At the boiling-
point x has the value of 20.6 Erg. pro cm°. The specific gravity at 0° C.
was: 0.785; at 25° C.: 0.757; at 50° C.: 0.730. At ° in general: d4. = 0.785— 0.0011 t.

The temperature-coefficient of » oscillates round a mean value of: 1.40

Erg. per degree.

Depth: 0.1 mm.

|
5 Maximum Pressure U | Meens
Seay. oe zb ee Siete ae ee cee
® o : | tension yin | ame a Bet en
a in mm. mer- | gravity do! energy pi
2 £ cury of | in Dynes | HT EE | ll Erg. pro em?2.
a 0° C. | | |
if | Sell En || |
2 1 eo | a oe ry... <a Te ] Pi
—15 | 1.547 2064.0 34.2 | 0.867 | 557.5 |
}—15 | 1.265 1687.1 27.9 | 0.801 | 479.5
ON LSO NN LSA 26.0 | 0.785 | 452-9
Ormel A 11220AR IN LOST 24.7 | OTT
ZO IO 2 1429.8 23.6 | 0.163 | 418.9
29.5 1.031 137609 Di | 0.752 | 406.9
40 0.979 | 1304.2 | 21.5 | 0.741 389.2
50.5 | 0.935 | 1245. 1 | 20.5 | 105730 | 374.8
aie Me as | |
|
Molecular weight: 57.07. Radius of the Capillary tube: 0.03343 cm. |

XII.

normal Butylamine: C,H ,N Hb.

2 Maximum Pressure H Mole
ES Surface-
BS ae
5 o 4 | tension xin ae Surface-
a in mm. mer- | gravity d energy » in
a = Cony ane in Dynes | Ets: procm?. | 2 Erg. pro cm?,
a 0° C.

= — d = SS == == — =

—21 0.853 1137.6 | 26.1 0.785 536.2

0 0.779 1038.6 23.8 0.764 497.9

2559 0.695 926.6 | 212 oe 453.5
41 0.650 866.6 | 19.7 0.723 427.5
55 0.606 808.4 | 18.4 0.709 404.6
70.8 0.574 765.2 | 17.4 0.693 388.5

Molecular weight: 73.1.

Radius of the Capillary tube: 0.04676 em.
Depth: 0.1 mm.

Under a pressure of 760.5 mm., the boilingpoint was 76° —78° C. The
liquid erystallises in a bath of solid carbondioxide and alcool, and then melts
at —46° C. At the boilingpoint x has the value: 17.0 Erg. The specific weight

at 0° C. is: 0.764; at 25° C.: 0.739; at 40° C.: 0.727. At t°C.:d

= 0.764 —0.001 ¢.

The temperature-coefficient of # decreases gradually with increasing tem-
perature: between —21° and 0° C. it is : 1.82; between 0° and 25° C.: 1.75;
between 25° and 55° C.: 164; and between 55° and 71° C, : 1.02 Erg. per degree.

XII.

Isobutylamine: C‚HoNHo.

2 Maximum Pressure H | hetis
5 5
Ts AT DEK. Sai ERGE Specific | Surface-
Foo : | tension 7 in oe af
By inmm.mer- | Erg. pro em? gravity do energy v in
ks, cury of in Dynes Erg. pro cm?
2 o
= Oo.
|
all EN >. see eee or ae =F
10 | 0.931 1243.5 | 28.9 0.812 | 580.5
—20.5 | 0.779 pee zh re part
OF 0.730 973. | : | : 4
Fae) 0.666 887.9 | 20.4 0.724 442.3
41.8 0.626 831.2 18.8 0.706 414.5 |
55.8 0.574 761.0 | Thai 0.692 395.5 |
|

Radius of the Capillary tube : 0.04676 cm.
Depth: 0.1 mm.

Under a pressure of 760.5 mm. the amine boils at 67°—689 C. At —70°
it is still liquid and not viscous. At 0 C. the specific weight was: 0.750;
at 25° C.: 0.724; at 50° C.: 0.698. At t° C. it can be calculated from the
formula: d4. = 0.7505 — 0.00104 ¢,

The temperature-coefficient of » oscillates somewhat round a mean value
of: 1.44 Erg. per degree.

Molecular weight: 73.10.

Diisobutylamine: {(C'H). CH. CH},

© Maximum Pressure //
3 Entre Molecular
: 3 en fonelan sine | ee | Surface-
a. in mm. mer- 2 | gravity do | energy “in
88 curyof | in Dynes | Erg: Procm?. 4 LE >
& 0e. | 3 | | Erg. pro em?.
i 3e _
72° 0.994 1325.2 29.9 0.825 868.5
—22.5 0.838 1124.4 25.4 0.782 764.6
0 0.769 1026.4 23.2 0.763 | 709.9
10 0.731 974.9 21.9 0.754 675.5
250 0.691 | 924.0 20.7 0.743 | 644.8
35.2 0.660 879.9 19.7 0.733 619.2
45 0.634 842.8 18.8 0.724 595.8
56.7 0.605 | 802.6 17.8 0.714 | 569.3
63 0.583 | Uta 17/2, 0.709 | 552.7
* 809 0.515 | 686.6 15.9 0.693 | 518.8
* 104.5 | 0.459 611.9 14.1 0.673 | 469.1
E125 0.408 544.3 1285 0.656 | 423.1
: EED en
Molecular weight: 129.16. Radius of the Capillary tube: 0.04595 cm. ; with

the measurements, indicated by *, the radius
was: 0.04777 cm.
Depth: 0.1 mm.

Under a pressure of 760 mm. the amine boils constantly at 142°C. At —78°
the I'quid becomes very viscous, but does not crystallize. At the boilingpoint
x has the value: 11.3 Erg. pro cm? The density was volumetrically deter-
mined; it was fuuud at 0° C.: 0763; at 25° C.: 0.741; at 50° C.: 0.72U. At t°
therefore: do = 0.763—0.00086 t. The temperature-coefficient of » is in gene-

ral: 2.40 Erg. per degree.

Triisobutylamine: (C‚Ho);N.

El Maximum Pressure H
5 Sartack 3 Molecular
sO in 4
abe tension x in Specific Surface-
a in mm. mer- : gravity d,.| energy » in
5 5 cury of in Dynes Supa = Erg. pro cm?,
al 0e C
Le)
—21 1.026 1367.9 24.5 0.797 | 926.2
0 0.982 1309.1 23.4 0.782 | 895.9
20.5 0.932 1243.1 2 0.767 861.0
35.3 0.894 1191.9 21.3 0.757 833.4
50.5 0.862 1149.2 20.5 0.745 810.6
65.5 0.825 1100.1 19.6 0.733 783.5
75.5 0.798 1063.9 18.9 0.725 761.1
90.3 0.758 1010.6 18.0 0.713 732.9
99.8 0.726 968. 1 Aha 0.704 706.3
115.1 0.684 911.9 16.2 0.692 672.9
124.5 0.652 869.2 15.4 0.683 645.3
139 0.612 814.0 14.4 0.672 610.0
155.8 0.563 751.0 13.3 0.654 573.6
170 0.519 693.0 1252, 0.640 533.9
185 0.471 627.0 11.0 0.626 488.5
Molecular weight: 185.26. Radius of the Capillary tube: 0.03636 cm.

Depth: 0.1 mm.

The amine boils under a pressure of 754 mm. constantly at 189° C. In a
bath of solid carbondioxide and alcool it solidifies, and will melt afterwards
at —24° C. At the boilingpoint the value of x is: 10.6 Erg. The specific
weight was detormined by means of a volumeter: at 0° C. it was found:
0.782; at 25° C.: 0.764; at 50° C.: 0.745. At t° generally: do = 0.782—

—0.0007 £—0.0000008 #2, The temperature-coefficient of # increases gradually
with rise of temperature: between —21° and 0° it is: 1.44; between 0° and
100°: 1.86; between 100° and 185° C. its mean value is: 2,61 Erg. per degree Celsius.

XVI.

tertiary Butylamine: (CH3)3.C. NA).

2 Maximum Pressure H
je é ‘Surface: Molecular
Eo ; tension Xin | oe Surface-
jen 10 mm. mer- 5 5 gravi y | energy im
5 : cury of in Dynes | Ere-proemf. = Erg. pro cm?.
a O9: |
EES AE
SD aos 1364.0 | 22.5 0.147 | 47k
| —15 0.956 12745. 4 a0 0.732 | 452.6
0 0.884 1177.7 19.4 0.716 | 423.8
10 0.840 1120.2 18.4 0.106 | 405.7
20 0.797 1061.0 17.4 0.694 | 388.1
29.5 0.749 999.0 16.4 0.685 369.0
40.5 0.698 930.6 15.3 0.672 | 348.6
Molecular weight: 73.1. Radius of the Capillary tube: 0.03343 cm.

Depth: 01 mm.

The amine boils at 44° C. under a pressure of 757 mm. In a bath of solid
carbondioxide and alcohol, it crystallizes readily at —54° C. At the boiling-
point x has about the value: 14.9 Erg. pro cm?. The density at 0° C. was:
0716; at 25°: 0689; at 40° C.: 0.672; in general at #° C.: dy. = 0.716 —

—0.001048 t—0.000001 #2. The temperature-coefficient of » is between —30°

XVII.

normal Amylamine: C; 4); Ho.

© Maximum Pressure H
5 S Molecular
3 © OE Specific Surface-
cd in mm. me era Ken pa d energy „ in
Au . Ts yr | 7)
8 2 pany oe in Dynes Erg. pro. em?, =| Erg pro cm?
is .
Di 0.861 1146.7 25.9 0.791 505.1
0 0.789 1054.7 24.1 0.770 563.5
Done 0.730 973.2 21.9 0.746 Bose
41.2 0.669 895.3 20.4 0.731 494.0
ba 0.641 858. 1 19.2 0.718 470.5
10.9 0.601 800.7 17.9 0.705 444.1
85.0 0.568 762.1 17.0 0.692 427.0
99.8 0.526 701.1 15.6 0.681 396.0

Radius of the Capillary tube : 0.04676 cm.
Depth: 0.1 mm.

The liquid boils at 103°—104° C. under a pressure of 762 mm. At —79°
it solidifies and crystallizes in needles, which melt at — 38° C. The specific
gravity was determined by means of a volumeter; at 0° C, it was found
to be: 0.770; at 25° C.: 0.746; at 50° C.: 0.723. In general at #° C.: djo=

= 0.770— 0.00098 ¢ + 0.0000008 #2. |
The temperature-coefficient of » has a mean value of 1.68 Erg. per degree. |

Molecular weight: 87.11.

XVIII.

Isoamylamine: C;H,,N Ap.

© Maximum Pressure H
A ee Molecular
s 5 BIRD. RISE Renae Specific Suiface-
oO : | | EA . .
a ia mm. mer- | | . gravity d energy /” in
8 8 Gon oF | in Dynes Erg. pro.ems..) = Erg pro em’,
a ORG: |
SAIS Ge oe Py
—69° 1.010 1346.5 30.9 0.840 682.1
—20.5 0.780 1042.0 | 25.9 0.791 595 1
0 0.779 1038.6 Zone 0.771 553.9
735), -15) 0.701 934.6 212 0.747 506.1
41.3 0.661 879.5 19.8 0.734 478.2
55.8 0.612 818.8 18.6 0.720 455.1
70.5 0.589 784.0 17.6 0.705 | 436.7
85.8 0.520 693.3 15.6 0.692 | 391.9

Molecular weight: 87.12.

Radius of the Capillary tube : 0.04676 cm.

Depth: 0,1 mm.

Under a pressure of 761 mm. the amine boils at 95°—97°. At —72° C. it
is still a thin liquid. The epceifie gravity at 0° C. was: 0.771; at 25° C.:
0.747; at 50° C : 0.724, At t°C. in general: dy. — 0.771— 0.00098 t + 0.0000008 ¢?.

The temperature-coefficient of » oscillates somewhat round a mean value

of 1.88 Erg. per degree.

XIX.

Temperature
bne (0,

The liquid boils constantly at 188° C. and 760 m.m. In solid carbondioxide
and alcohol the amine solidifies, and melts then at —44° C. At the boiling-
poiot x has the value: 10.2 Erg. pro cm?. The specific weight was volume-
trically determined; it was 0.784 at 0° C.; 0.764 at 25° C.; 0.745 at 50° C,
At t° C. in general: dyo = 0.784 — 0.00084 ¢ + 0.0000008 2. The temperature-

Diisoamylamine: [(C 3). CH .CH,. CH‚], NH.

| Maximum Pressure H
|

in mm. mer-

Surface-
tension 7 in

Specific
gravity d 40

Molecular
Surface-
energy in

one ot in Dynes | nee ee Erg. pro cm?.
; Mie ; |
0.838 NID 26.5 | 0.801 894.9
0.778 1037.4 24.6 05784 SANT
0.698 930.6 | OM | 0.760 759.0
0.647 S626 uel 20.1 | 0.746 ahs
| 0.612 816.4 19.0 0-732) 9) Testes
| 0.578 770.3 17.9 0.721 648.4
0.518 690.8 | 16.0 0.705 588.3
0.475 633.3 14.6 0.691 | 544.0
0.413 550.6 12.6 0.675 | 476.9
0.354 411.9 10.8 0.659 | 415.4

was: 0.04839 c.m.
Depth: 0.1 m.m.

coefficient of » has a mean value of: 2.37 Erg. pro degree.

XX,

tertiary Amylamine: (C43), (C,H;) C. NAQ.

© Maximum Pressure H Mol
8 5 Surface. che es ecular
oc i e | ieden IE @ me
a in mm. mer- | | gr gy ui
I 8 cury of | in Dynes DE = Erg. pro em?.
= 0° C.
TA EN —- =| == == == ==
— 710 1.252 1669.1 27.6 0.830 | 695.9
—19 1.101 | 1466.5 | 24.2 0.786 605.0
0 1.018 1357.2 | 22.4 0.756 554.7
9.5 0.983 | 1310.5 21.6 0.747 530.3
20 0.935 | 1245.1 20.5 | 0.736 498 .2
29.3 0.895 1199.3 19.7 | 0.727 | 474.9
40.5 0.854 1138.5 18.7 | 0.716 | 446.3
50.5 0.812 1082.9 | 17.8 | 0.707 | 421.5
60 0.758 1011.0 | 16.6, | 0.697 |: SN
70 0.709 945.2 | 1555 | 0.688 344.9

Under a pressure of 757 mm. the amine boils at 76°.56 C. At —78° it is
still a thia liquid, without any trace of crystallisation. At the boilingpoint
y has about the value: 15.0 Erg. The specific gravity was determined by
means of a volumeter. At U° C. it was: 0.756; at 25° C.: 0.731; at 50° C.:

| Molecular weight: 87 11.

Radius of the Capillary tube: 0.03343 cm.

Depth: 0.1 mm.

0.707; at t° C. in general: d4o = 0.756 — 0.00102 ¢ + 0.00000u8 72.

The temperature-coefficient of » is between —70° and 50° C. fairly con-
stant; its mean value is: 2.54 Erg. Above 50° it increases to about: 3.9 Erg.

XXL.

normal Hexylamine: CgH,3.N Ho.

5 Maximum Pressure H
5 en queraic: Molecular
5 iS Ti RE Specific Surface-
a in mm. mer- „…g | gravity do | energy » in
5 5 Ge in Dynes Drewe, 5 Erg. pro cm?.
— 18° 1.171 1562. 1 28.0 0.801 104.7
0 ee 1499.8 26.9 0.785 686.2
20.4 1.058 1410.5 22 0.767 652.8
35.1 1.010 1347.6 24.1 0.754 631.5
50 0.956 1274.6 22.9 0.740 607.6
65 0.911 1215.6 | De 0.725 583.7
14.8 0.884 1179.3 21.0 0.715 570.1
90.4 0.832 1109.2 19.8 0.700 545.2
99.8 | 0.795 1059.9 18.9 0.689 525.9
116 0.728 972.5 17.4 0.673 491.8
124.5 0.696 929.3 16.5 0.664 470.6

Radius of the Capillary tube: 0.03636 cm.
Depth: 0.1 mm.

The substance boils at 129°—130° C. under a pressure of 742 mm.; it
solidifies in solid carbondioxide and alcohol and melts then at —19° C. At
the boilingpoint x has the value: 16.0 Erg. The specific gravity at 0° C. is: 0 7855;
at 25° C.: 0.763; at 40° C.: 0.749. At t° C.: d4o = 0.7855—0.00088 ¢—0.0000008 2,

The coefficient of # is originally small: about 1.03 between —18° and 0° C.;
between 0° and 75° C, it is almost constant, with 1.55 Erg. as a mean value;
above 75° C. it increases gradually from 1.55 Erg. to 2.50 Erg. per degree.

Molecular weight: 101.13.

Isohexylamine: (CH3), CH. CH). CH;. CH, NH.

|
2 Maximum Pressure H |
8 5 Surface: ” Molecular
3° in mm. mer nage Be af
a, „mer- 7 o| energy „ in
5 | eury of in Dynes Erg. pro cm2, 4 ie hema
a ; |
|
— 150 1.307 1862.5 | 30.8 | 0.840 751.0 |
—20.8 1.203 1603.8 26.5 0.798 668.6
0 1.126 1501.6 24.8 0.780 635.3 |
10 1.096 1461.2 | 24.1 0.771 622.2 |
20 1.074 | 1430.2 23.3 0.762 606.3 |
29.8 1.021 1359.7 | 22.5 | 0.754 589.5 |
40.5| 0.991 [920.2 Ah Se af Ona 5163 |
60 0.924 1231.9 | 20.3 | 0.724 546.5
70 0.894 1191.9 | 19.6 | 0.716 532.1
80 0.861 1148.6 18.9 0.707 516.9
90 | 0.828 1103.9 18.1 | 0.698 499.3
100 0.795 1059.9 17.4 | 0.686 485.6
110.2 0.765 1019.9 16.7 | 0.676 470.6 |
121 0.726 969.1 15.9 0.665 453.0

Molecular weight: 101.13. Radius of the Capillary tube: 0.03343 cm.
Depth: 0.1 mM.

The amine boils at 123° C. under a pressure of 751 mm. Even at —79°
it is still a thin liquid. At the boilivogpoint tho value of x will be about:
15.8 Erg pro cm’. The specific gravity was determined by the aid of a
volumeter; at 0° C. it is: 0.780; at 25° C.: 0.758; at 50° C.: 0.735. At te
generally: Ayo = 0.780—0.00086 ¢ — 0.0000008 2. The temperature-coefficient

of # oscillates round a mean value of: 1.51 Erg. per degree.

XXill.

normal Heptylamine: C,H; NH.

|
|
|
|
|

© Maximum Pressure H |
5 Sne eN Surface. 8 Molecular
se | in mm. mer- | si eee, abt e an
aug : - ; Erg. pro cm?, | BF&VEY yo | ED re
5 | guano | in Dynes Uns Erg. pro cm?2.
|
le)
—18.5 | 0.902 | 1202.4 27.5 0.804 7152.8
Onn 0.857 | 1142.5 | 26.1 0.787 724.7
2023 0.793 | 1057.2 | 24.1 0.765 681.9
AID 0.744 993.0 22 0.750 650.9
56 0.714 950.8 | 21.5 0.737 623.7
70.9 0.663 886.2 | 20.3 0.723 596.4
84.5 0.634 845.2 | 19.1 0.711 567.5
100 0.607 809.2 | 18.3 0.697 551.0
ed 5e2 0.541 724.1 17.0 0.684 518.3
*130.8 0.545 | 723.8 | 15.7 | 0.669 485.8
R45. 0.507 | 673.2 | 14.4 0.657 451.0

Molecular weight: 115.15. Radius of the Capillary tube: 0.04676 em. ; in the
measurements indicated by *, this radius was:
0.04529 cm.
Depth: 0.1 mm.

Under a pressure of 761 mm. the amine boils at 152°-- 154° C. The liquid
can be undercooled, but finally solidifies in a bath of carbondioxide and alcohol
into a colourless crystal-aggregation, melting at —18° C. Above 130° a slow
decomposition is observable. At 0° C. the density is: Ayo = 0.7875 ; at 25° Cr:

0,7650; at 40° C.: 0.7515. At t° C. it can be calculated from the formula:
yo = 0.7875—0.0008 t.

The temperature-coefficient of « increases gradually at higher temperatures:
between —-18° and 6° C.: 1.52 Erg.; between 0° and 25°C.: 1.69; between
25° and 71° C.: 1.87; and between 71° and 145°: 1.96 Erg. per degree, as
a mean value.

XXIV.
Formamide: ZCONH,.
[ia eae te Wall
Maximum Pressure HZ | | |

| Surface-
| tension 7 in

|
|
|
|

Molecular
Specific Surface-
gravity dy.) energy „in

|
| in mm. mer-
|

Temperature
men

+0 1.875 | 2499.7 | 59.6 i674 Bee
29.9 1.806 | 2407.3 | 56.6 1.136 | 566
48.1 1.755 2340.3 55.1 1.120 551
65 1.702 | 2269.2 53.4 1.107 534
80.7 1.661 | 2214.8 52.1 1.094 521
104.5 1.598 | 2131.0 50.1 1.080 | 501
123.2 1.551 | 2068.2 48.6 LOT ee "agp
152 1.460 1946.8 45.7 1

„058 | 456

Molecular weight: 45.03. Radius of the Capillary tube: 0.04777 cm. ; in the
observations indicated by *, the radius was:
0.04839 cm.
Depth: 0.1 mm.

Under a pressure of about 18 mm., the liquid boils at 114°. In a freezing
mixture it solidifies into an aggregate of white crystals, which melts at
—5° C. Above 145° C. a gradual decomposition under development of gas-
bubbles, is observed; the ,-t-curve then rapidly falls towards the ¢-axis.
a neg eere menn ns essen st tn coin ensnemdtne tenen msterdam nn

$ 3. The results obtained are reviewed in the Tables [--XXIV
above, while the relations of the corresponding g-t-curves can be
seen from the fig. 1—8.

Molecular Surface-Energy
pin Erg pro c.m?.

260
-S0 7060-5040 3O 20°10 O° 10° 20 JO 40° JOAO 10 80° RO 700 01010 ASO T0100" Temperature
Fig. 2. Secondary Amines.
From these experiments it appears in the first instance, that the

substitution of H-atoms in the ammonia-molecule by hydrocarbon-
radicals, makes the surface-energy of the liquid compounds at the

same temperatures increase regularly; and that, — pecularities left
out of question, — that increase goes in general parallel to the

augmentation of the number of C- and H-atoms. That however,
even with the same number of C- and H-atoms, the special con-
figuration of the molecule plays an important rôle in this, can soon
be seen: e.g. the u-t-curves for (C,H,)NH, are not only situated
above those for (CH,), NV, etc, but it is also quite clear from fig. 1—3
that generally in the case of correspondingly built-up isomer amines,
those with normal hydrocarbon-chains generally possess at any tem-
perature a greater surface-tension than those with ramified hydrocarbon-
chains; and that generally the surface-tension of such isomerides under
the same conditions appears to be the lower, the more ramified the
hydrocarbon-chains are (e.g. butyl-, isobutyl-, and 37Y butyl-amines ;
in the same way the corresp. amylamincs between 10° and 70°; ete.)

Molecular Surface-Energy
u in Erg pro cm?,

80°70" 60°50°-40-30°20°I0° O° 10° 20°30 40° 50° 60°10" 80° HO WO MOTI HSO LAT 10010" Temperature

Fig. 3. Tertiary Amines.

On a comparison of the primary, secondary and tertiary amines
of the same alkyl-radical, it appears that the temperature-coefficients
of u are often analogous for 194 and 3% amines, but smaller than
those for the Zev amines.

However it becomes also clear, that a direct comparison of the
u-f-curves with the aim of studying the influence of the substitution
by hydroearbon-radicals in homologous compounds, may properly
be made only in the case of amines of the same fundamental con-
figuration; as e.g. by comparison of all primary, or all secondary,
resp. tertiary amines, with each other. (fig. 1, 2 and 3). Really then
the regular increase of the values of uw in these cases, if substitution
occurs by more complicated hydrocarbon-radicals, comes to the fore
in a most striking way.

With respect to the temperature-coefficients of u it may be remarked
that these generally appear rather small; the smallest values being
present in the case of primary amines (1.2—1.8), while in the case
of secondary amines these values are often somewhat greater (1.7—2.3),
and just as with the tertiary amines, approach gradually to the
values observed with other organic compounds. However, these rules
are not without exceptions: e.g. in the case of d/methylamine the

0
value of en appears beyond doubt to be smaller than with mono-

methylamine.

Finally the increase of the surface-energy by substitution of H-
atoms also appears here, as formerly stated, to be appreciably greater
if substitution occurs by wnasaturated, than by saturated hydrocarbon-
radicals: a comparison of the data for allylamine on the one side,
and of propyl-, and tsopropylamine on the other side, soon convinces
of the truth of this.

Lastly we may draw attention here to the data regarding the
formamide, which are also reproduced among those of the derivatives
of trivalent nitrogen. Although this compound does not possess more
than a single C-atom, the value of u nevertheless appears here to
be much greater than e.g. for (CH,)NH,, demonstrating the special
influence of the strongly electronegative oxygen-atom, and more
especially of the unsaturated carbonyl-radical, in a perfectly clear way.

Moreover this liquid, which in several respects shows some ana-
logy with the strongly dissociating solvents, appears to possess a

Sen
very small temperature-coefficient —: on an average about 0.89 Erg.

Ot
per degree. It would be of interest to study the behaviour of inorganic
salts if dissolved in this liquid, with respect to the electric current.
In analogy to the case of water, one would be inclined to conclude

0
in this case from the exceptionally small value of = that the liquid

formamide might be highly associated.

Laboratory for Inorganic and
Groningen, April 1915. Physical Chemistry of the University.

Chemistry. — “The Allotropy of Sodium.” I. By Prof. Ernst
Conen and Dr. S. Worrer.

(Communicated in the meeting of April 23, 1915).

1. Some time ago Ernst Conen and G. pe Bruin!) relying on
the determinations by Hzer Grirritus’) of the true specific heat of
sodium, proved that this metal shows allotropy and that the sub-
stance known hitherto as “sodium” is a metastable system in con-
sequence of the simultaneous presence of a- and g-sodium.

1) These Proc. 28, 896 (1915).
?) Proc. Roy. Soc. London 89, (A) 561 (1914),

Some preliminary determinations carried out by Grirritas proved
that the densities of the two modifications are different (at the same
temperature) and that this difference is of the order of 1 : 7000.
The modification formed by quenching cet. par. has the greater
specifie volume.

The investigations to be described below were carried out in order
to fix the limits of stability of both modifications, viz. to investigate
whether sodium is enantiotropic *) or monotropic.

2. Although the change of volume which accompanies the trans-
formation of «-sodium into g-sodium is small according to GrirrirHs’
measurements, yet the use of the dilatometer is suitable, if certain
precautions are taken, which enable us to carry out exact measure-
ments with this instrument.

These precautions are:

a. A large dilatometer must be used; we employed an instrument
of about 380 ce.

b. The bore of the capillary tube must be small (Bore of our
tube 1.2 mm.). 2

c. The quantity of liquid put in, (rock oil) must be as small as
possible.

d. The temperature at which the readings are taken must be
constant within some thousandths of a degree.

3. Special care has to be taken in filling the dilatometer. This
operation was carried out in the following manner: The metal
(sodium in rods from KaArrLBauM-Berlin, comp. $ 6 and 8) was melted
under petroleum in a Jena-glass flask. The rock oil had been
prepared in the way to be described in § 4, while the metal had
been treated in a special manner (comp. § 5). The flask O (Fig. 1) is put
into an oil bath RR, heated to 130°. Pieces of sodium are added
until there are about 400 ec. of molten metal in 0.)

The dilatometer after being filled with rock oil, is placed in the
same bath. O and G are connected by means of a glass tube PLH
the end of which (in G) is drawn out. :

The neck of the dilatometer is connected with a tube Z by
means of rubber tubing X.

1) In the paper mentioned above [These Proc. 23, 896 (1915)] the opinion was
expressed that there exists a transition point between 0° and 90°.

2) Generally there are formed spheres of metal which do not coalesce unless
the mo'ten metal is cooled below the melting point and gently stirred at the
same lime,

W represents a water pump, while B and C are filter flasks.
F represents a clip, S a rubber stopper through which the tube
PLH passes.

O is left open at J/. A manganin wire N,N, serves as a heater ;
5 or 6 storage cells are used as a source of current, whilst a
regulating resistance and an ammeter are put in the circuit.

The purpose of the wire N,N, is to heat that part of PLH
which is not heated by the oil bath, above the melting temperature
of sodium in order to prevent the solidification of the molten metal
when flowing from 0 to G. The wire is separated from the wall
of the tube by means of asbestos paper. In order to prevent loss of
heat the wire is also covered with asbestos paper. The oil bath is
heated to 130° and when the metal has entirely melted the stop-
cock Z is shut, the heating current started, and the pump JV put
in action. As soon as the tube J/ is sufficiently heated the clip /
is cautiously opened. The molten metal flows into the dilatometer
and displaces the rock oil present which flows into the flask C.

As soon as the sodium reaches /’ (the dilatometer being then full
of the metal) it solidifies, as the side tube is at room temperature.
In this way suction stops automatically *). The stopper S is now
removed while the tube PLH is taken out of the dilatometer. The
level of the metal falls and the rock oil present protects the sodium
from oxidation.

After the solidification of the metal which is accompanied by a

1) If any molten metal should still pass over, it enters the flask C containing
some rock oi! which covers the metal.

decrease of volume of about 2.5 percent, the capillary tube is sealed
at the bulb. After having been filled up with rock oil (by means
of an air pump) the instrument is ready for use. It may be pointed
out that only a few ce. of rock oil were used (comp. § 2. c.).

4. The petroleum used was prepared as follows: After having
been heated for 24 hours at 100° in contact with sodium, it was
distilled off from the metal. The part distilling below 175° was
not used; the remaining liquid was kept in contact with sodium
and used for the experiments.

5. In order to get the metal free from oxide the method described
by v. Rossen Hooeenpuk v. BreiswijK') may be followed. Small
pieces of the metal are put into benzene to which small portions
of amylaleohol are cautiously added. When the metal has become
bright it is put into the rock oil prepared as described above.

6. We were not able to detect any impurity in 10 grams of the
metal.

7. We used the (electric) thermostat described by Ernst COHEN
and HerDERMAN in their investigations on cadmium’), which enabled
us to keep the temperature constant within some thousandths of a
degree. The thermometers used were compared with two instruments
checked by the Phys. Techn. Reichsanstalt at Charlottenburg-Berlin.

8. Before describing the measurements some remarks may be
made concerning the melting point of the metal experimented with.

As is generally known, metals show, even if they are pure, a range
of fusion. This can be determined here very exactly by dilatometric
measurements as the process of melting is accompanied by a marked
change of volume (about 2.5 per cent).

While the level of the meniscus remained constant at 97°.12
during 17 hours, there occurred a strong dilatation at 97°.22.

The beginning of solidification of the molten metal was determined
in the following way: We put 25 ce. of sodium into a wide glass
tube which contained some rock oil in order to prevent the metal
from oxidation. A BECKMANN thermometer (graduated to hundredths
of a degree) and a glass stirrer pass through a cork in the neck of
the tube. The whole was placed into an oil thermostat the temperature

1) Zeitschr. f. anorg. Chemie 74, 152 (1912).
2) Zeitschr. f. physik. Chemie 87, 409 (1914).

of which was kept constant within some thousandths of a degree.
Its temperature was 97°.10.

The tube and its contents is heated to 99° and put into the
thermostat. When the temperature of the metal had become 97°.10
the stirrer was put in motion. The temperature rose to 97°.51 and
remained constant for some time. The experiment was repeated,
the molten metal being cooled 0°.7 lower than before. After stirring
the temperature rose again to 97°.51.

The beginning of solidification consequently occurs at 97°.54,
while the range of melting covers 0°.3 C.

9. As the changes of volume which play a rôle in these inves-
tigations are only small, and as the glass of the dilatometer was
exposed in our experiments to sudden and strong changes of temper-
ature (about 100°) we thought it important to prove that the glass
used did not show thermal hysteresis. For this purpose we filled
our dilatometer with rock oil and heated it for some hours in a
thermostat at 95°.00. After having noted the place of the meniscus
(358.0) we dipped the instrument into petroleum which had been
cooled (by means of solid carbon dioxyde) to — 20° C. After half
an hour we put it again into the thermostat at 95°.00. After two
hours the level of oil was again 358.0. Twenty-four hours later it
had not changed: consequently thermal hysteresis had not occurred.

10. The dilatometer was now filled in the way described above
(comp. § 3) with molten sodium and some ce. of petroleum. After
this it was cooled very slowly in the thermostat to 15° C., so that
the metal might be transformed into the «-modification.

The following results were obtained (Comp. Table I).

TABLE I.

Temperature PO nS eur level Gm)
50° | 31, 0
68.5 | 16 5
90.0 | 19 | 0
96.0 | 22 | 0

At 97°.3 the melting of the metal occurred which is accompanied
by a very marked increase in volume.

o¢

11. In order to melt the metal entirely, the dilatometer was
heated to 100° C.; the change of volume having ceased, the metal
was chilled at 0° C.

The observations carried out with the chilled metal are given in
Table II.

TABLE Il.
Temperature | Doran of te or | Re tee
45.2 | 22 0
10.0 31 0
90.0 | 48 5
96.02 | 24 EH
96.02 | 72 Jig
96.02 144 a6
96.02 240 =10

At 97°.22 C. fusion had already begun to take place.

12. The measurements given in the tables I and If in conjunction
with those of GrirritHs which show that the 3-modifieation has cet.
par. a greater specific volume than the «-modification, indicate that
we have to deal with a case of monotropy.

13. That at 94° we have not passed beyond a transition point
may be proved by showing that the transformation velocity does
not increase at higher temperatures (which would be the case above
a transition point) but that there exists a maximum of velocity. This
may also occur with monotropic transformations (for instance in the
case of B-dibromproprionie acid *) and if this is really the case, it
indicates that the transition point which cannot be reached lies in
the neighbourhood of the melting point.

14. The following experiments show that we really have to deal
with such a case with sodium: the metal was melted in the dilato-
meter and chilled.

After this the transformation velocity (g-sodium — a-sodium) was
determined at different temperatures. (Duration of observations 48
hours). The velocity was found to be:

1) O. LEHMANN, Molekularphysik 1, 197. Leipzig 1888.

At 94°.4 3
95°.4 +
sl 2.

A maximum was thus found at 95°.4, viz. two degrees below
the melting point.

15. The facts stated in § 14 exclude the existence of pseudo-
monotropy, but we are able to go a step farther and, from what
has already been stated as well as from the phenomena immediately
to be described, can conclude that sodium is monotropic.

16. These phenomena are: The metal was cooled very slowly
in order to transform it into the «-modification. After this the dilato-
meter was kept at 97°.22, a temperature at which melting began.
(At 97°.12 melting does not take place). Table III gives the results:

TABLEAU:
Temp. 979.22 (= 5°.998 on BECKMANN's thermometer).

BRO BECKMANN | Time (minutes) | Level in mm,
5°998 0 | 268
5.998 16 | 214
5.998 51 279
5.998 | 83 284 1/5

The metal having been melted and chilled (tbe metal was now
present in the g8-modification) the dilatometer was brought back to
97°.22. Table IV gives the results:

TABLE IV.

Temp. 97°.22 (= 5°.998 on BECKMANN’s thermometer).
ee eV SS

Temp. OEREN _ Time (minutes) Level in mm.
5°998 0 266 !)
5.998 5 215
5.998 | 31 309
5.998 | 51 | 326
5.998 76 | 344

1) In order to use the same part of the capillary tube, the meniscus was brought
to the same point of the scale as with the experiments mentioned in Table III.

7
Proceedings Royal Acad. Amsterdam. Vol. XVIII.

17. From these tables it is evident that the velocity of melting
at the same temperature is cet. par. greater with #-sodium than
with e-sodium. Consequently the quantity of heat wanted to transform
1 gram of solid g-sodium into the molten state is less than that
which must be added for that purpose to the same quantity of
e-sodium. From tbis we may conclude that the transformation
B-sodium — a-sodium is accompanied by an evolution of heat. The
fact that this heat of transformation is positive, proves that if there
exists a transition point it is to be looked for in the direction of
higher temperatures '). The facts described in $ 14, prove that such a
transition point does not exist and consequently sodium is monotropic.

18. Finally it may be pointed out that Hagen *), who determined
the coefficient of dilation of sodium (between O° C. and its melting
point) by dilatometric measurements, was not able to observe these
phenomena as the quantity of metal used by him (40 grams) has
been too small.

The value of this physical constant determined by this author is
consequently fortuitous and must be redetermined with the pure
a- and 8-modifications.

We express our best thanks to Dr. H. R. Kruyr to whom we
are indebted for many valuable remarks.

Utrecht, April 1915. van ’T Horr-Laboratory.

Chemistry. — “Action of inethylethylketone on 2.3.4. 6. tetranitro-
phenylmethylnitramine’. By Prof. P. van RoMBURGH.

(Communicated in the meeting of April 23, 1915).

As stated by me previously *), this nitramine reacts readily with
alcohols and amines. Water also acts on it with formation of nitrous
acid and of 2.4.6. trinitromethylnitraminophenol. Whereas at the
ordinary temperature this action proceeds very slowly it takes place
fairly rapidly at boiling temperature.

In order to get to know more accurately the progressive change
of the reaction some previous investigations were made a few
years ago by me conjointly with Dr. SiNNiep, which gave the result

1) Baknvis RoozeBoom, Die heterogenen Gleichgewichte vom Standpunkte der
Phasenlehre. 1, 178; Braunschweig 1901.

2) Wied. Ann. 19, 436 (1883).

3) Rec. 8, 275 (1889).

that the nitramine, when dissolved in acetone, reacts very rapidly
with water even at the ordinary temperature, so that the preparation
of the phenol in this manner is a very simple one.

Now it did not seem devoid of importance to know something
more as to the rôle played here by the acetone and, therefore, |
have studied this reaction more closely. It appeared, however, that
great difficulties are experienced in the separation and identification
of the products generated in addition to hydroeyanie acid, which
forms abundantly, so that I thought it desirable to try whether
satisfactory results can be obtained more readily by using another
ketone, which then perhaps may serve to also elucidate the reaction
with acetone.

It now appeared that methylethylketone lends itself very well for
that purpose.

If, at the ordinary temperature, we dissolve the nitramine in so
much moist ketone that a concentrated solution is obtained, we notice
that the original pale yellow colour of the solution rapidly begins
to darken and soon after, a yellow produet crystallizes, which proved
to be the 2.4.6. trinitrometbylnitroaminophenol. In my experiments
I generally used 11 grams of nitramine, which I dissolved in 16 c.c.
of ketone to which 0.8 c.c. of water was added. At first, I took
more nitramine (33 grams—'/,, gram mol.) but then towards the
end of the operations explosions frequently took place.

If we decant the ketone solution from the crystals and subject
the same to a distillation (in the water-bath) an intensively yellow
coloured liquid with a peculiar odour passes over. It contains
hydrogen cyanide which was identified by the Prussian blue test.
The yellow colour, also the odour pointed to the presence of diacetyl.

If to the liquid we add a solution of silver nitrate to precipitate
the hydrogen cyanide and subsequently to the filtrate an excess of
ammonia a white voluminous precipitate is obtained which according
to Firtmic, Damier, and Kerver!) is characteristic of diacetyl. The
detection of the diacetyl by means of hydroxylamine presented,
owing to the excess of methylethylketone, a little difficulty.

Still, by using a liberal quantity of hydroxylamine I succeeded
in obtaining crystals of dimethyglyoxime, which gave with a nickel
salt and ammonia the characteristic red nickel compound.

In order to detect any volatile products eventually formed, the
flask which had been heated in the waterbath at 100° was evacuated
and placed in an oilbath heated at 120°. A substance began to

1) Ann. 249, 205 (1888).

100

distill which deposited in a erystalline form in the exit tube, when
the flask exploded with a loud report.

In subsequent experiments the heating was therefore solely con-
dueted in vacuo at 100° in a waterbath and in this way I also
succeeded in obtaining small quantities of crystals, which after being
pressed between paper melted at 76° and gave no depression of the
melting point witb «-/so-nitrosomethylethylketone. In addition there
distilled a little of a liquid acid, which, after neutralisation with sodium
carbonate solution gave with silver nitrate a white precipitate, which
on heating with water turned black.

If the nitramine is heated with moist methylethylketone a rather
violent action sets in, but otherwise the reaction proceeds as described
above. If we take ketone that has been dried over calcium chloride
we also get a yellow, diacetyl containing distillate.

If, however, we take nitramine that has been standing for some
days in a desiccator over sulphuric acid and ketone that has been
dried with phosphoric anhydride, no reaction takes place at the
ordinary temperature even after two days. On heating in the
waterbath the ketone passes over entirely colourless. If the distillation
is interrupted, the nitramine in the flask crystallizes unchanged. On
long continued heating in the waterbath the distillate first shows
traces of hydrogen cyanide and gradually also a faint yellow
coloration, which need cause no surprise because, on heating at 100°,
the nitramine itself yields traces of nitrous vapours. So much,
however, is pretty certain that in the experiment with moist ketone
the formation of the reaction products found will have to be attributed
largely to the action on the ketone of the nitrous acid generated by
the water, when the strongly acid phenol will also have exerted its
influence.

The fact that the reaction takes place so rapidly in the ketone
solution even at the ordinary temperature may be caused by the
great concentration, but there also exists the possibility that the
presence of the acetone accelerat s the reaction. Experiments to make
sure about this and also to study the influence of the water on the
nitramine in other indifferent solvents are in progress. In water-
saturated ether a conversion of nitramine into phenol also takes
place fairly rapidly.

Utrecht, Org. Chem. Lab. University.

101

Physics. — “The magnetic rotation of the polarisation plane in
titanium tetrachloride.” 1. By Prof. L. H. Stertsema. (Com-
municated by Prof. H. A. Lorentz).

(Communicated in the meeting of March 27, 1915).

Among the substances of which the magnetic rotation of the plane
of polarisation has been observed, titanium tetrachloride occupies a
particular place, first of all because it is the only diamagnetic sub-
stance known that presents negative magnetic rotation, and then
because it is unique in being a liquid, for which the negative
magnetic rotation can be observed without the interfering influence
of a solvent, and which is free from absorption bands almost over
the entire visible spectrum. Only in the extreme violet, according to
my observation at 2 0.420 u, an absorption limit is found.

The diamagnetic character has been ascertained by Verper *) and
by H. BrecqurreL*); observations on magnetic rotation have been
made by Verper ®), who only shows that the rotation is negative,
and about of the same amount as the positive rotation of water,
and by H. BrecQquereL *), who determines the magnetic rotation for
six FRAUNHOFER lines. It appears from these measurements that the
rotations are in inverse ratio to the fourth power of the wavelength,
hence they follow an entirely different law from that found for the
positive rotation.

An attempt to ascertain whether the later dispersion formulae
derived from the theory of electrons can be applied to this substance
made me realize the desirability of extending the material of obser-
vation by the carrying out of new measurements.

The measurements have been carried out by a penumbra method
and spectral analysis.

The liquid was in a glass tube of a length of 265 mm. and a
diameter of 25 mm., closed by plane-parallel glass plates 1 mm.
thick. This tube was placed in a coil of wire 182 mm. long, so
that the closing plates were a few centimetres outside the coil.

It appeared from a measurement with an empty test tube that
the magnetic rotation in the glass plates was imperceptible. The
coil contained 8186 windings; between the windings and the coil

IE, Verper, Ann. de Ch. et de Ph. (3) 52 p. 156 (1858).

2) H. BecquereL, Ann. de Ch. et de Ph, (5) 12 p. 63 (1877).

3) E. Verper, loc.cit.

4) H. BecquereL, Ann. de Ch. et de Ph. (5) 12 p. 35 (1877); C.R. 85 p. 1229
(1877).

102

there was a waterjacket, through which a stream of water could
be led. The projecting ends of the test tube are enclosed in cotton
wool to ensure a uniform temperature. The strength of current
amounted to about 2 amperes, and was read down to 0,002 ampere
on a carefully gauged ampere metre. Of the optical arrangement we
should mention the source of light (quartz amalgam lamp of HERARUS,
or arclamp), from which the beam of light passed through a penumbra
prism according to Jerver, with a penumbra angle of 2°, a colli-
mator, the slit of which was immediately behind the penumbra
nicol, the test tube, a nicol with 12 x 18 mm. aperture as analyzer,
the rotation of which could be read in minutes on a graduated
circle, and the prism with eye-piece of a HirGer spectroscope with
constant deviation. r

The line of demarcation of the penumbra nicol is placed hori-
zontally, so that when the arclamp is used we observe a spectrum
in the eye-glass consisting of two parts lying above each other and
divided by a sharp line. Through rotation of the prism different
parts of the spectrum can successively be brought in the middle of
the field of vision. If the current in the coil is closed, a black band
is observed in both parts of the spectrum. These two bands, how-
ever, are slightly displaced with respect to each other. Halfway
between them a place can always be indicated where the intensity
of the light is the same in the two parts. At this place the adjust-
ment was brought about by means of rotation of the analyzer causing
a displacement of both bands. For this purpose the eye-piece was
provided with a wide ocular slit. After reversal of the current this
adjustment was repeated; the angle over which the analyzer has
been turned, is double the angle over which the plane of polarisation
in the titanium chloride has been turned. In observations with the
quartz amalgam-lamp the collimator slit was taken pretty wide, which
caused a great many slit images to be seen in the reading glass, each
divided into two parts by a horizontal line. Just as above the adjust-
ment can then be made at equal luminous intensity of the two parts.

From readings of thermometers in the supply and the leading
off of the water in the jacket the temperature of the test tube can
be derived.

The first series of measurements have been carried out with the
quartz amalgam lamp. The slit images used for this are those cor-
responding to the lines :

He 5780, the two mercury lines lying close together. The images
of the two lines overlap for the greater part; the readings are
reckoned to correspond to the mean of the two wavelengths.

103

Hg 5461, the most intense mercury line.

Cd 5086, intense cadmium line.

ZnCd 4805, a blue zine and a cadmium line, almost coinciding.

Zn 4722, blue zine line.

Hg 4358, ,, mercury line.

For every slit image there have been made four readings, two
for every direction of current, the strength of the current having
been read every time. Then the angle between the two positions
of the analyzers has been derived from the means of the corre-
sponding readings, and the angle of rotation for 1 ampere found
through division by the sum of the two strengths of current that
differ but little.

The results of some six series of observations are recorded in
the subjoined table. «

Magnetic rotation in minutes, for 1 amp. |
Ain p i. FT aa ae ra | — -MiN-/eauss.cm.
te OAD Siet 5 6 Mean
| | | | |
0.5780 | 59.8 | 60.1 60.1 60.2 | 60.0 | 60.0 | 60.0 0.01618
0.5461 | 74.9 | 15.2 | 15r3s) AGO aeolian) ares | 15.1 0.02023
0.5086 | 101.6 | 101.0 | 100.1. 100.4 | 98.9 | 100.2 | 100.4 0.02705
0.4805 | 128.1 | 128.4 | 129.4 | 129.3 | 129.2 | 127.8 | 128.7 0.03468
0.4722 | 140.5 | 139.6 | 140.1 | 141.9 | 138.8 | 141.1 | 140.3 0.03782
0.4358 | 208.7 | 209.6 | 208.8 209.5 209.2 | 208.3 | 209.0 0.05633
| |

Then observations have been made with are light for a number
of different wavelengths. The wavelength was found by illuminating
the collimator slit by means of a mirror with a quartz amalgam
lamp, and adjustment to the slit images lying nearest to the place
in the spectrum where observations were to be*made. From this
the wavelength at the place of observation was derived by means
of a dispersion’ curve of the prism. These adjustments always took
place immediately before or after those of the position of the
analyzer.

To be able to caleulate the rotation constant @ per gauss cm.,
the test tube is then filled with distilled water, and the magnetic
rotation is measured for two different wavelengths. By the aid of
the constant of rotation for water and the magnetic rotation dispersion

104

as they were before determined by the author‘) these measurements
gave two values for the reduction factor, which agreed down to
0.1 °/,. Besides, some measurements with carbon disulphide have
been made, which sufficiently harmonized with those of water.
Carbon disulphide is less satisfactory for a measurement of the
magnetic field than water. The angles of rotation are then, indeed,
larger, but the greater temperature coefficient renders a greater
accuracy in the temperature determinations necessary, in consequence
of which an accurate result is after all more difficult to reach.

Further a number of measurements have been made with the
titanium chloride at different temperatures by cooling the water at
its entrance into the jacket by means of ice, or by raising the tem-
perature. The temperature coefficient of the constant of rotation
appeared, however, to be so small, that it could not be determined
with certainty from the observations. The thought of applying a
temperature correction has, therefore, been abandoned. In the mea-
surements with the quartz amalgam lamp the temperature was on
an average 17.9°, in those with the arclamp 13.4°.

The results of the measurements with the quartz lamp are recorded
in the last column of the above table; those with the are lamp
referring to observations on six different days, follow below.

The more recent theories of the magneto-optical phenomena which
are founded on the theory of electrons, show that there is a connec-
tion between the magnetic rotation of the plane of polarisation and
the Zeman effect, which the lines of the substance’s free vibrations
present. By starting from simplifying suppositions, and assuming one
free period, the magnetic rotation as far as the sign and the order
of magnitude is concerned, can in many cases be explained by the
assumption of a magnetic resolution of spectrum lines as it is given
by the elementary theory’). For a more complete explanation it is,
however, necessary to take more free vibrations into consideration.

It has appeared from investigations by Drupe and others that
the ordinary dispersion of transparent substances can generally be
represented by an expression with a small number of free vibrations,
among which ultrared ones, corresponding to vibrations of positively
charged particles, and one or more ultraviolet free vibrations of
negative particles. The ultraviolet frequencies cause the greater
part of the dispersion.

1) Versl. Kon. Ak. van Wet. 1896/97 p. 131. Comm. Leiden Suppl. 1. p. 76
Arch. Néerl. (2) 2 p. 366 (1899); (2) 6 p. 825 (1901).
*) These Proc, Vol. 5, p. 413, Comm. Leiden ‚N°. 82.

105

For a satisfactory explanation of the magnetic rotation the same
frequencies will have to be taken into consideration ; it should only

|—e min. /sauss, cm.

0.4723 0.03689
0.5601 0.01830
0.5245 0.02349
0.5097 | 0.02643
0.4840 0.03325
0.4623 | 0.04054
0.4436 | 0.04927
0.4355 0.05439
|
0.4495 | 0. 04686
0.4694 0.03778
0.4688 0.03843
0.4889 | 0.03170
0.6452 0.01083
0.5956 | 0.01471

be borne in mind that there is no occasion to assume magnetic
resolution for the ultrared frequencies ascribed to positively charged
particles, so that these need not occur in the expressions for the
magnetic rotation.

For most substances the magnetic rotation is positive. Theory
teaches that it can be caused by the magnetic resolution of an ultra-
violet spectral line of a sign as determined by the elementary theory
of the Zerman-effect. To explain negative rotation a magnetic resolu-
tion of an ultraviolet line of the abnormal sign must be assumed.
Such a resolution need not necessarily be accompanied with a positive
charge, of the vibrating particles. Voier *) demonstrates that in con-
sequence of couplings between vibrating electrons complicated reso-

1) W. Vorer. Ann. d, Phys. 45 p. 457. 1914.

106

lution figures, and also resolutions of the abnormal sign, can appear,
and that negative rotation might arise in consequence.

The thought suggests itself to try whether the observed rotation
constants can be explained in this way. For this purpose it is neces-
sary to represent these constants by a formula as required by
theory, with one or more ultraviolet frequencies. It will have to
appear at the same time that the index of refraction can be repre-
sented by a formula of the form required by theory, with the same
frequencies, besides ultrared ones.

It will be communicated in a following paper what a treatment
of the results of our observations in this sense will have yielded.

Chemistry. — “On Tension Lines of the System Phosphorus.” IV.
By Prof. A. Smits and S. C. Boxnorst. (Communicated by

Prof. J. D. van DER WAALS.)

(Communicated in the meeting of April 23, 1915.)

1. New determinations of the vapour pressure of liquid white
phosphorus.

In the first communication under this title *) among others the vapour
pressure line of the liquid white phosphorus was discussed. This
line, which had been determined by us according to the statical
and dynamical method up to 386°, had such a course, that it could
not be considered as the metastable prolongation of the vapour pres-
sure line of the liquid violet phosphorus.

Now it appeared that this result was to be ascribed to this that
the vapour pressure above 325° increased with the temperature to
an abnormal degree.

This circumstance added to the fact that the temperature was
always increased as quickly as possible in the vapour tension deter-
mination to prevent all the white phosphorus from being converted before
the determination could be made, led us to suppose that the results
might be faulty at these high temperatures in consequence of spon-
taneous heating of the mass brought about by the conversion:

white P— violet P + «a Cal.

1) These Proc. Vol. XYI, p. 1174.

107

As this conversion is accompanied by a pretty
great generation of heat (4.4 Cal. at the ordinary
temp.), and the velocity of this reaction is already
pretty great above 325°, it would be possible that
the temperature of the phosphorus had been higher
than that of the surrounding bath, whereas it had
been assumed that inside and outside the apparatus
there always prevailed the same temperature.

To avoid this possible error, not the temperature
of the bath, but that of the phosphorus had to be
measured.

For this purpose with application of the dynamic
method according to SmirH') the tube of the thermo-
element was fused into the vapour pressure apparatus,
so that always the temperature of the phosphorus
was determined.

Afterwards when it had appeared that through
the contact with stearine the boiling point of the
phosphorus was absolutely not influenced, the apparatus was used
represented in fig. 1. Into the inner tube a which has a constriction
at c a resistance thermometer has been fused, which reaches to the
lowest widening. This inner tube is filled up to above the constric-
tion with pure white phosphorus, which is then shut off by a layer
of stearine. All this takes place in vacuum. In the outer jacket e
also stearine is brought, which is heated under different pressures.

Just as for the other apparatus also now the temperature is
determined at which the phosphorus under a definite pressure begins
to boil. This method has this advantage that without any difficulty
the experiment can be made with larger quantities, and the tempe-
rature can be indicated very quickly and very accurately.

By these two improved methods the following results were now
found :

Fig. 1.

| =
| Pressure

Temp | in atm.
331.8° 2.47
332.9° 2.61
342.0 | 2.95

355.7 3.88

1) Americ. Chem. Soc. 82, 897 (1910).

108

2. The vapour pressure formula for the liquid phosphorus.

When we supplement our former measurements up to 300° by

the above mentioned results, we get what follows:

0.04
0.07
0.09
0.18
0.20
0.32
0.42
0.54

t Tip. Vee en Tin p
169.0 | —1423.| 0.69 | 261.4 | — 198
181.3 | —1208 | 0.74 | 265.5 | — 162
185.5 | —1104 | 1.00 | 280.5 | — 0
206.9 | — 823 | 1.38 | 298.6 | + 185
210.0 | —777 | 2.47 | 331.8 | + 541
229.8 | — 573 | 2.61 | 332.9 | + 582
237.9 | — 443 | 2.95 | 342.0 + 665
252.0 | — 323 | 3.88 | 355.7 =} 852

That the last four points fit in very well with the others, follows
clearly from the following graphical representation (Fig. 2), in

kelde je

25000
: ~
24000)

al
|
|

meene
\
BN
peat
faa

TH
ee
= EERENS ea
EE
ME TOOT CO eee

EEH MERA

4u000 [ 1g 7
gnc HEHE
0000 A El Ei
8000 i tr

500

600

2000

109

which the quantity 7m p is plotted as function of 7’ (the line al).
We see from this that the different points yield an almost straight
line, whose shape is exceedingly little concave with respect to the
temperature axis. This had accordingly proved that the preceding
determinations had been vitiated by the spontaneous heating of the
white phosphorus in conversion.

If in the same diagram we now give 7’/np as function of T'also
for the liquid violet phosphorus, we get the already discussed straight
line ed.

The consideration of these two lines a) and cd brings us at once
to the conviction that they belong together, i.e. that they are two
parts of one and the same curve, the intermediate part of which
cannot be realized here.

It follows then from this that the second part cd cannot be
perfectly straight in reality, no more than the first part ab, and
that there must be a rational formula to be found, which represents
both portions with sufficient accuracy.

To find this formula the following course is taken.

The line a4 which represents 7’/np as function of 7’ for the liquid
white phosphorus, is only very slightly curved. If we now assume
for a moment that this line is straight, then as was already shown
before, the constant C can be found by the aid of two points,
on the application of the relations:

ry. Q am

ED aaa Me eee ACL)
and

gal Q alla td

Dib, =— or OW, fe Oo. UO Mine tee te ioe (2)

If this value of C is substituted in one of the above equations,
then follows from this the value for Q, which indicates the molecular
heat of evaporation.

If this is done, we find Q= 1217 kg. cal, 9.96 kg. cal. being
found for the mol. heat of evaporation of the liquid violet phosphorus.
The latter result was obtained in the same way as here the Q for
the liquid white phosphorus was calculated viz. on the assumption
that Q is no temperature function.

Now this is, evidently, indeed not the case, for 7'/n p plotted as
function of 7’ is no perfectly straight line.

We can now accept by approximation that 12.17 kg. cal. is the
mean value of the heat of evaporation of the liquid white phosphorus
in the temperature interval from 160° to 360°, and that this heat

110

of evaporation will therefore about agree with the mean temperature
of 260°. Thus we can also consider the value of 9.96 kg. cal. as
the mean heat of evaporation of the liquid violet phosphorus over the
temperature range from 512° to 630 , so that this heat of evaporation
will about hold for the mean temperature of 571°. Thus we arrive
at the result that the heat of evaporation from 260° to 571° decreases
by 2210 gr. cal., so that we have at a rough approximation

dQ
08e
AT (4)
If we now start from the equation:
dinp Q
de Te 5

and write:
On= OQ, 4-¢T . 2 te ae
we find by integration:

inp = Sr Teo, ., ie
and as according to (6)
dQr _
dee

we can substitute the value given by (4) for a. Then equation (7)
becomes

ip es
np R

==13.59)In T A0 U) . 5). ENEN

To see whether this formula satisfied, the following graphical
method was applied: Let us write equation (8) as follows :

Tlnp + 3.59 Tin T = — S CLS 2 . eee
we see at once that when this relation satisfies, (7/n p + 3,59 Tin T)
plotted as function of 7, will have to yield a straight line.

As appears from fig. 2, the thus obtained points lie really on a
straight line ef, so that it has thus been proved that the relation -
(6) represents the change of the heat of evaporation with the tem-
perature with sufficient accuracy.

In ease of an exceptionally rapid heating, when the result was of
course less accurate, a pressure of 7,36 atm. was observed at 409°,3,
from which the value 1362 follows for Z'/np. In comparison with the

1) We may just state here that instead of 3.59 we might as well have taken
3 or 4, for the course’ by which we have come to this value, is a rough approxi-
mation.

111

line diseussed just now this value is slightly too low; this proves
that the vapour was no longer perfectly saturate with respect to the
white liquid phosphorus, which we think by no means astonishing.

By means of the linear relation (9) the constant C may now again
be easily found in the following way from the value which the first
member possesses at two different temperatures.

T, np, + 3.59 T, In T, = — R ROM ees Fess ee 10)
REE bee 0 OA
T, np, + 3.59 7, in T, = — R ACER a Bass. (CLL)

from which follows that:
(Timp, + 3.597 nT) — (Flap, + 3.597 InT,)
En, 5 T,--T, RT
In this way we find C = 37.62.
If we substitute this value in (9), we get:

==tga: … (12)

Q
Tinp + 3.59 Tin T= — A TEA A Smet se và ALE)
1

3. Calculation of Q, and of the vapour tension.
; Q
By means of this relation we can now calculate the value of =

from the different observations.
The result of this caleulation is recorded in the following table.
(see p. 112).

: : Q ‘ nae
In the fifth column the found values for Al are given, which give

as mean the value 8257, from which follows that Q, = 16,35 kgs. cal.

The sixth column gives the discrepancies which the different results
present from the mean, and it appears from this that they are com-
paratively small, and now exhibit the positive sign, now the nega-
tive sign.

If this value for = is substituted in equation (13), we get:

Dip NT ST OTRS ADL)
by the aid of which we can now calculate the pressures for the
different observation temperatures.

We find the result of this calculation in column 7.

These calculated pressures harmonize on the whole as well with
the observed ones, as can be desired under the given circumstances,
This is shown most convincingly by the last column, which gives
the difference between the caleulated and the observed pressure. It
is evident that this difference should not be considered in itself, but

DRO Cie

WO Chi O

RL er, SG a

p in
atm.
0.05
0.08
0.09
0.17
0.19

| 0.32
0.40

0.55
0.68

| 0.75

1.02 |

1.46
2.65
2.70

| 3.13

3.88

8.10)

222

23.9
31.6
32.2

| 32.7
| 33.5

34.2
35.1
35.4
35.9

| 37.8

39.2
40.4
41.3

| 44.9

| 47.7
| 49.1

49.6 |

53.9
55.5
56.2
57.8
58.5

| Calc. |

++++4+4+44

113

in connection with the absolute value found in the first or in the
sixth column.
Besides the vapour pressure line of violet phosphorus, also that for
liquid phosphorus is indicated in fig. 4, from which it is seen how
the observed vapour pressures lie on the line drawn according to
formula (14).

0 TE re 500 GOD
Fig. 3.

4. Conclusions.

The result of this investigation is so important for this reason
that it was not known before whether there was any connection
between the liquid white, and the liquid violet phosphorus. BAKHUIs
RoozrBooM ') pointed out the possibility that the liquid white phos-
phorus had to be looked upon as supercooled liquid violet phosphorus,
but he also expressed the opinion that it might also be that the
phosphorus entirely agreed with the cyanogen, and that the vapour
pressure line of the liquid white phosphorus terminated below the
melting-point of the violet form in a critical point.

Up to a short time ago we thought for three reasons that this
latter supposition of Bakuuis RoozreBooM's would be the correct one.
First of all the shape of the vapour pressure line of the liquid
white phosphorus found some time ago pointed to the fact that this
line could not be the prolongation of that of the liquid violet one.
In the second place it could be calculated from the determinations
of Aston and Ramsay’) of the surface tension that the liquid white
phosphorus must reach its critical point at + 422°. And in the third
1) Lehrbuch Heterog. Gleichgewichte 171 and 176.

2) Journ Chem. Soc. 65, 175 (1894).

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

place the peculiar way in which, as Srock and Gomotka ') were the
first to find, red phosphorus can suddenly deposit from supercooled
molten violet phosphorus and its vapour, seemed to point to a cri-
tical phenomenon.

In virtue of these three circumstances which seem to be in agree-
ment with each other, we concluded phosphorus and cyanogen to be
systems of the same type, and devised a diagram for the pseudo
system of phosphorus, wbich was in close connection of that of
cyanogen.

Now for the first time the question raised by Bakuuis RoozrBoom,
has been answered, and it has now appeared that the three above
mentioned circumstances misled us at first. Phosphorus does not
belong to the same type as cyanogen and the liquid white phosphorus
must be really taken as supercooled liqnid violet phosphorus.

The first determinations of the vapour tension were faulty at the
highest temperature. Aston and Ramsay’s determinations of the surface
tension of liquid white phosphorus (which were only two, indeed)
appear not to justify a calculation of the critical temperature, and
the just mentioned phenomenon, which was observed by Stock and
GoMoLKA, must be ascribed to this that the number of nuclei posses-
ses a strongly pronounced maximum at a definite degree of super-
cooling, so that a spontaneous crystallisation, which proceeds with
very great velocity, suddenly occurs there.

We see with great satisfaction that the system phosphorus can
be represented in a simpler way than we thought at first in eon-
sequence of the non-existence of the supposed complication.

The P,7-projection of the system phosphorus for so far as it is
known now, is schematically represented in the subjoined fig. 6.

1) Ber. 42, 4510 (1909).

115

With regard to the 7'X-fig. we must point out, that as was
already remarked by us before *), the pseudo-system of the phospho-
rus is most probably ternary, and that the third kind of molecules
which has been left unconsidered up to now, plays probably a
principal part in the change of the point of solidification of the
white phosphorus. To simplify the representation we can disregard
this third kind of molecules and take the pseudo system as binary,
at least when our point of consideration is the connection between
the white and the violet phosphorus.

Now the difference in properties between the white and the violet
phosphorus, just as the difference in volatility and melting point
suggest with great probability that we have to do here with a
system of molecule-kinds, which differ in size. Hence we have
probably to do here with the case of association, and the violet

1) Z. f. phys. Chem. 88, 621 (1914).

116

phosphorus will differ from the white chiefly in this that it contains
a much larger proportion of associated molecules.

In this case the pseudo system, as was already explained several
times, will possess no eutectic point, and then this pseudo system
with the unary system lying in if, can be given schematically by
fie. 5. If the pseudo-component @ was isomer of «, also a figure
like fig. 6 would be possible.

Note. When according to form. 14 we calculate the vressure corresponding
with the temperature of 695°, which is the eritical temperature of the liquid phos-
phorus according to W. A. WaHL’s measurements, we find 82.2 atm. This is
therefore the critical pressure, for which we found 83.56 in our preceding com-
munication by means of the assumed linear relation.

When we calculate the 6-value from the critical pressure 82,2 atm. and the
absolute critical temperature of 696° + 273° = 968°, and from this the size of the
phosphorus molecule, we find 4.33; we found 4.26 before, which makes no
difference of any importance.

According to the formula:

8 T np, —T,lnp 2
ee ee
1 Ir 1 2
the following values are found for the value of f at different temperatures:

from 200° to 300° f= 3,11

» 300° , 400° f= 2,84

, 400° , 500° f= 2,60

„ 300° , 600° f= 2,40

Amsterdam, April 19, 1915. Anorg. Chemic. Laboratory
of the University.

Chemistry. — “J/n-, mono- and divartant equilibria’ 1. By Prof.
F. A. H. ScHREINEMAKERS.

1. Introduction.

When 2 -+ 2 phases occur in an equilibrium, which is composed
of n substances, then it is invariant; the composition of the phases,
the pressure and the temperature are perfectly defined then. In a
P,T-diagram this equilibrium is represented by a point; we shall
call this pressure and this temperature P, and 7,

As this equilibrium is completely determined in every respect
neither the composition of the phases, nor the pressure or the
temperature can change on addition or withdrawal of heat or on

1) In the preceding communication the term Zpy, had been erroneously omitted.

‘ality

a change of volume. Then, however, a reaction occurs, at which
the quantities of some phases increase, those of other phases decrease,
and only after disappearance of one of the phases, pressure, tempe-
rature and composition of the phases can change.

May the composition of a phase /’, be given by the quantities

INGEDEELD = (na), and Le or (an (ae). ea)
that of a phase /’, by:
EDC Nen ren) an ALOE (Grip (ay CL)
of the m components. We express in the same way the compositions
of the phases /,, ,,.../,49. Let occur between these n + 2 phases
the reaction :
Ur Et PS ae oe) pth — O (1)
y,f, means 7, quantities of the phase /’,, each of which has the
composition given above; y,/, ete. have the same meaning. It is
evident that these reaction-coefficients y,...¥4,42 cannot have all the
same sign. In order to know reaction (1) it is not necessary to know
the n-+2 reactioncoefficients y, ...%,42 themselves, the reaction is
viz. determined by their -+ 1 relations.
From the condition, that at the reaction the total quantity of
each of the m components rests unchanged, the n relations follow :

Vat Ya FH Ya Hoen + Ine = 0 \
Yr (Gy). + Ya (ra + Ys (ida HH Ynte (Japa = 0 |
Yi (), zie Va (v4), ata Ys (x,); ar Sans Yn4+2 (@.)n42 == 0 | 8 e (2)

vy (Eri) + 5 (@n—1), += Ui (Gri); - - + Ynt2 (@n—1)n-++2 == (I)

As we have only n conditions for the determination of then +1
ratios, (2) and therefore also (1) may be satisfied in infinitely many
ways, or in other words: the reaction between the » + 2 phases
-of an invariant equilibrium can take place in intinitely many ways.

Now we put the condition that the totalvolume remains the
same at the reaction; the reaction is then: “isovolumetrical’. When
we represent the volumina of the above-mentioned quantities of the
phases F,, F, etc. by v,, v, ete. then it follows:

Un ar O05 ap dy ap ser ae Ure SW cB

Now we have n+ 1 equations [viz. the equations (2) and
equation (3)|; the 2+ 1 ratios of the reaction-coefficients are conse-
quently determined and therefore also the proceeding of the reaction
(1). Consequently we find that an isovolumetrical reaction between the
n + 2 phases of an invariant equilibrium is completely determined.

118

We might just as well have posed instead of (8) the condition
that the reaction takes place without addition or withdrawal of heat.
As the entropy remains the same then, we call such a reaction an
“jsentropical reaction’. When we represent the entropies by 7,, 7, ete.,
then the condition is:

OP gw ruta cru ace ar Unu = Oe

Then we have again n + 1 equations, so that also an isentropical
reaction between the „+ 2 phases of an invariant equilibrium is
completely defined.

It is evident that the coefficients y,, y, ete. in the isovolumetrical
reaction (1) are others than in the isentropical reaction (1). Further
it is also evident that, dependent on the direction of the reaction,
we must add or withdraw heat with an isovolumetrical reaction
and that we must change the volume with an isentropical reaction.

Now we imagine at 7, and under P, that the 7 + 2 phases
I,...F,42 are together; we let the isovolumetrical or isentropical
reaction take place and we let this proceed until one of the phases
disappears. Then an equilibrium of 2 components in 7 + 1 phases
arises, which is consequently monovariant. In this way 2 + 2 mono-
variant equilibria may occur. As in each of these equilibria one of
the phases of the invariant point fails, we represent, for the sake
of abbreviation, a monovariant equilibrium by putting between
parentheses the missing phase. Consequently we shall represent the
equilibrium /,-+ y+... 2.42 by (4), the equilibrium + 2, +
Ed... Ene by (4), ete. From the invariant equilibrium, there-
fore, the #2 monovariant equilibria (/,), (P,), 4). (Pu 42)
may occur.

Each monovariant equilibrium exists at a whole series of tem-
peratures and corresponding pressures; consequently it is represented
in the P,7-diagram by a curve, which goes through the invariant
point P, 7’. Therefore in this point „+ 2 curves intersect one
another. Each of these curves is divided by the invariant point into
two parts; the one represents stable conditions the other metastable
conditions. We shall always dot tlie metastable part. (See e. g. the
fig. 1, in which these curves are indicated in the same way as the
equilibria, which they represent).

When we consider only stable conditions, we may say: n + 2
monovariant curves proceed from an invariant point of a system
of m components.

In order to define the direction of these curves in the P, 7-diagram,
we may use the following thesis'): the systems which are formed
on addition of heat at an isovolumetrical reaction exist at higher
— those which are formed on withdrawal of heat exist at lower
temperatures. The systems which are formed on decrease of volume
at an isentropical reaction exist under higher — those which are
formed on increase of volume exist under lower pressures.

Let us consider now the equilibrium (/,) = 7, + F,+...Fi+42,
which is represented in fig. 1 by curve (/) at a temperature 7’,
and under a pressure P,, which are represented by the point «.
On addition of heat under a constant pressure or on change of
volume at a constant temperature a reaction, which is completely
defined, occurs between these n-+1 phases. Let us write this reaction:

Vala Ui Das Yn NE: (5)

The x relations between the n+ 1 reaction-coefficients are fixed
then by-the equations (2) in which, however, we must omit all
terms which refer to the phase /,, [consequently 4, (7,),, (w,), ete. |.

Now we let reaction (5) occur until one of the phases of the
equilibrium (/,) disappears; then an equilibrium of 7” phases
arises, which is consequently bivariant. In all # +1 bivariant
equilibria can arise from the equilibrium (/’,). As in each of these
equilibria two of the phases of the invariant point are wanting, we
represent a bivariant equilibrium by putting between parentheses
the failing phases. (/’,/,) represents consequently the equilibrium
FPy+F,+..-Fi4e From the equilibrium (/,), therefore, the
bivariant equilibria (#4), (CELE ae Ch Bees} may arise in the
manner, which is treated above.

In a bivariant equilibrium P and 7 can be considered as inde-
pendent variables; each bivariant equilibrium can, therefore, be
represented in the P,7-diagram by the points of the plane of this
diagram, consequently by a region.

Consequently n-+ 1 bivariant regions, which may arise from the
equilibrium (/), go through each monovariant curve (/). Each of
these regions is divided into two parts by the curve (F)\); the one
part represents stable conditions, the other metastable conditions.
When we limit ourselves to the stable parts of these regions, we
may say: in a system of 7 components n-+ 1 bivariant regions
start from each monovariant curve.

1 F. A. H. SCHREINEMAKERS. Heterog. Gleichgewichte von H. W. Baxuuis
Roozesoom, Ill’: we find herein the proofs for ternary systems on p. 220—221
and 298—301. These, however, are also true for systems of components.

120

The n+ 1 regions starting in fig. 1 from curve (/,), are situated
partly at the one and partly at the other side of this curve; also
it is evident that the regions, which are situated on the same side
of the curve, cover one another. Hence it follows immediately that
several bivariant equilibria can occur under a given P and at a
given 7.

In order to determine on which side of the curve (/,) the stable
part e.g. (PF) of a bivariant region is situated, we let the reaction
(5) take place in such a way, that the phase /’, disappears from
the equilibrium (/,). This may always take place, when the quantity
of F, in the equilibrium (#,) has been taken small enough. If we
let this reaction proceed under a constant pressure, we have to state
whether heat must be added or supplied, when we let it take place
at a constant temperature, we must determine whether the volume
increases or decreases. We may then apply the following rules:
at the right of the curve we find the bivariant equilibria, which
arise on addition of heat; at the left of the curve those which arise
on withdrawal of heat. Above the curve we find the bivariant equi-
libria, which arise on decrease of volume; beneath the curve those,
which arise on increase of volume.

For the meaning of “at the right”, “at the left”, “beneath” and
“above” is assumed that the P- and 7-axes are situated as in fig. 1.

When we apply the considerations, mentioned above, to each of
the n+ 2 curves (F)...(/,42) then we obtain the division of
the 4 (n+2)(n-+1) divariant regions between the different curves and
around the point 0.

The following is apparent from the previous considerations. When
we know the compositions of the phases, which occur in an inva-
riant point and the changes in entropy and volume which take place
at the reactions, then we are able to determine in the P,7-diagram
the curves starting from this point and the division of the bivariant
regions.

2. Some general properties.

Now we will put the question whether anything may be deduced
concerning the position of the curves and the regions with respect
to one another, when we know the compositions of the phases only
and not the changes of entropy and volume which the reactions involve.

This question is already dissolved for binary *) and ternary ’)

1) F. A. H. ScurememaKkers, Z. f. Phys. Chemie 82 59 (1913) and F. E. C.
ScHEFFER, these Communications October 1912.

2) F. A. H. ScHreINEMAKERS, Die heterogenen Gleichgewichte von BAKHUIs
RoozeBoom III’ 218,

121

systems, the way which we have followed then [viz. with the aid
of the graphical representation of the y- and the &-function] is not
appropriate however to be applied to systems with more components.
The following method is much simpler and leads to the result
desired for any system.

We consider an invariant point with the phases /, /,,.../i42
and two of the curves starting from this point, viz. (4) = #, +
+ F,+...Fi4e and (fF) = Ff, + Frye. (see fig. 1). Between
the stable parts of these curves the region #4) = F, + fF, +... Foe
is situated. When we consider stable conditions only, this region
terminates at the one side in curve (/’,), at the other side in curve
(F,). Now it is the question in which of the two angles (/,) O (F,)
the region (#,/) is situated, viz. in the angle which is smaller or
; in the angle which is larger than 180°.
The first case has been drawn in fig. 1
in the latter case the region (F',F,)
should extend itself over the metastable
parts of the curve (#,) and (F,). We
call the angle of the region (#,F) in
the point o the region-angle of (FF) ;
we can prove now: “a region-angle is

Fig. 1. always smaller than 180°.”

In order to prove this we imagine in fig. 1 the region (#,F) in
the angle (/)o0(/,), which is larger than 180°. The stable part
of this region then extends itself on both sides of the metastable
part of curve (/,) and also of (#). This now is in contradiction
with the property that the stable part of each region, which may
arise from a curve, is situated only at one side of this curve. Hence
it follows, therefore, that the region-angle must be smaller than 180°.

Therefore, when we will draw in tig. 1 the region (/’,F,), this
must be situated in the angle (/,) O(F,), which is smaller than
180°. As in fig. 1 (/,) and (F,) are drawn on different sides of
(F,), the regions (PF) and (FF) fall outside one another; when
we had taken (F,) and (#,) on the same side of (/), the two
regions should partly cover one another.

Another property is the following: every region, which extends
itself over the metastable or stable part of a curve (/,) contains the
phase #),, or in other words: each region which is intersected by
the stable or the metastable part of a curve (#)) contains the phase
Fy. In an invariant point the n +2 phases FF... Hye occur;
consequently arround this point 5 (n + 2) (n +1) bivariant regions
extend themselves, In „+1 of these regions the phase /’, is wanting,

122

viz. in (FF), FP)... (Figs); in all the other [viz. in $n (n41)
regions| it is present however. The same applies to every other phase.

Now we imagine in fig 1 the curves (PF), (F,)...(Pr42) to be
drawn. The n + 1 regions in which the phase /, does not occur,
all start from the stable part of the curve (£); none of those
regions can therefore, extend itself over the stable part of curve
(/’,). When, therefore a region extends itself over the stable part
of the curve (/,), then it must consequently contain the phase F,.
As every region-angle is however smaller than 180°, none of the
n +1 regions, in which the phase PF, does not occur, can extend
itself over the metastable part of the curve (4); the regions, which
extend themselves over this part, consequently contain all the phase F’,.

Consequently we find: each region, which extends itself over the
metastable or stable part of a curve (H), contains the phase /,.

We must keep in mind with this that the metastable part of a
curve is always covered by one or more regions, but this is not
always the case with the stable part. Further it is also apparent
that the reverse of the previous thesis viz. “all regions which contain
themselves the phase #, extend themselves over the metastable or
stable part of the curve (/,)” need not be true; tbis is only always
the case in unary systems. Later we shall still refer to these and
other properties.

Now we shall deduce a thesis, which is of great importance for
the determination of the position of the curves with respect to one
another. For fixing the ideas we take an invariant point with the
phases ‚FF, F, and F, and we consider the curve 1) =
LF, HF, + F, starting from this point. Between the four phases
of this equilibrium on addition or withdrawal of heat a reaction
occurs, which is, as we have seen above, completely defined by the
compositions of the phases. Let this reaction be for instance:

pp SP FO en ne

Consequently four bivariant regions start from the curve (/)
vz. BFF, FFF, FFF, and F,F,f,. It follows fromag
that the regions #, F, F, and F, F, F, are situated at the one side
and the regions F, F,F, and F, F, F, at the other side of curve
(HF). We write this:

Ten ze A Hel
VN din EEA:
VNT IE LOD

When we should know the changes in entropy and volume,

123

occurring with reaction (6), then we could, as we have seen above,
indicate at which side (viz. at the right, at the left, above or
beneath) of curve (#,) each of these regions is situated. As this is
not the case, we only know that the regions, which are written
in (7) at the right of the vertical line, are situated at the one side
and those, which are written at the left of this line, are situated at
the other side of (/,). Each of the four regions is limited, besides
by curve (/) also still by another curve, viz. the region F, F, F,
B ZEP, by (Ff), BEF; by (P‚) and FFF by (Fi).
When we keep in mind now that every region-angle is smaller than
180°, then it is evident that the curves (/,) and (/,) are situated
at the one side and the curves (/,) and (/’,) at the other side of
curve (/’,). We shall represent this in future in the following way :
PEER ee ev en ER om (B)

EE) O)NIENE)-. « - - 2. - (9)

This means: when reaction 8 occurs between the phases of curve
(F,), then the curves (/’,) and (/’,) are situated at the one side and
the curves (/’,) and (/’,) are situated at the other side of curve (/,).

As the previous considerations are completely valid in general, we
find the following. When we know of a system of #-components
the compositions of the 7 + 1 phases of a curve (/’,), then also the
reaction is known between these n-+ 1 phases /,, F,... Fite.
With the aid of this reaction we can divide the curves (4), (4) … Up»)
into two groups in such a way, that the one group is situated at
the one side and the other group at the other side of curve (/,).

As we may act in the same way with each of the other curves,
we find:

When we know the compositions of the + 2 phases /,, /,,...Fi42,
which occur in an invariant point, we can with respect to each of
the curves (1), 4’)... (Fe) divide the n +1 remaining curves
into two groups in such a way that the one group is situated at
the one side and the other group is situated at the other side of the
curve under consideration.

Now we shall apply the rule which is treated above, to some
eases in order to deduce the position of the different curves with
respect to one another. In order to simplify the discussions, we shall
distinguish instead of “at the one” and “at the other side” of a
curve “at the right” and “at the left”. For this we imagine that we
find ourselves on this curve facing tbe stable part and turning our
back towards the stable part. Consequently in fig. 1 (#) is situated
at the right and (/’,) at the left of (#); (F,) is situated at the right

124

and (4) at the left of (/,); (F‚) is situated at the right and (F,)
at the left of (#,).

3. Unary systems.

In an invariant point of a unary system three phases /,, F, and
F, oeeur; consequently the point is a triplepoint. Three curves
(F), (F,) and (/,) start from this point, further the three regions
of Ff, F, and F, occur. From our previous considerations the
well-known property immediately follows: the region of F, covers
the metastable part of curve (F,)=F,-+ F,, the region of FP,
covers the metastable part of curve (/',) = F, + F, and the region
of F, covers the metastable part of curve (Ff) = F, + FK.

4. Binary systems’).

In an invariant point of a binary system four phases occur;
consequently this point is a quadruple point. When we omit, as we
shall do in the following, the letter / in the notation and when
we keep the index only, then we may call these phases 1, 2, 3
and 4. The four curves (1), (2), (8) and (4) are starting from this
quadruple point, further we find $(7+2)(m+1)=6 regions viz.
12, 18, 14, 23, 24 and 34.

We call the two components of which the system is composed,
A and B; the four phases may be represented then by four points
of a line AB. In fig. 2 we have assumed that each phase contains
the two components; it is evident however, that /’, can also represent
the substance A and F, the substance B.

Now we shall deduce with the aid of the former rules the situa-
tion of the four curves with respect to one another. As F, is
situated between /’, and F, (fig. 2) we find:

ZZA 4 . i. 2 oS Se
(2) (S)G) (4)...
As F, is situated between /, and F, it follows:
3d. 2% 2 so
GD OD EN

Now we draw in a P,7-diagram (fig. 2) quite arbitrarily the two
curves (1) and (38); for fixing the ideas we draw (3) at the left of (1).

1) For another deduction see also F. A. SCHREINEMAKERS (l.c.) and F. E. C.
SCHEFFER (l.c).

125

We firstly determine now the position of (2). It is apparent from
equation 11 that the curves (1) and (2) are situated at different sides of
(3); as (1) is taken at the right of (3), (2) must, therefore, be situ-
ated at the left of (3). It is apparent from equation 15 that the
curves (2) and (8) are situated at different
sides of (1); as (38) has been taken at the
left of (1), (2) must consequently be situated
at the right of (1).

Therefore, we find: curve (2) is situated
at the left of (8) and at the right of (4);
it is situated, therefore, as is drawn in
fig. 2 between the metastable parts of (1)
and (3).

Now we determine the position of (4).
It is apparent from equation 11 that (1)
and (4) are situated at the same side of (3); (4) is, therefore, situated
at the right of (3). It is apparent from equation (13) that (3) and
(4) are situated at different sides of (1); consequently (4) is situated
at the right of (1).

Consequently we find: curve (4) is situated at the right of (1)
and (3); it is situated, therefore, as is also drawn in fig. 2, between
the stable part of (1) and the metastable part of (3).

From fig. 2 still follow the relations:

eee os wy (14) Se leptin ot +78, 2 (16)

and

(2) |(4)|Q) (3). (15) (EPNM ay Gy. 4)

As the position of the curves with respect to one another, is
already fixed in fig. 2, we need no more the relations 14—17, they
may however be useful as a confirmation. From (15) follows that
(1) and (3) are situated at the one side and (2) at tbe other side of
(4); in accordance with (17) (1) and (4) are situated at the one
side and (8) at the other side of (2). We see that this is in accord-
ance with fig. 2. Consequently we find the following rule:

when we call, going from the one component towards the other,
the phases occurring in a quadruplepoint F,, /,, 7, and /, then
the order of succession of the curves, if we move in the P, 7-diagram
around the quadruplepoint, is 1, 3, 2, 4 or reversally.

We have assumed at the deduction above that curve (3) is
situated at the left of (1); when we take (3) at the right of (1)
we find the same order of succession.

126

Now we shall seek the position of the 6 bivariant regions. From
curve (l)= 2 +3 +44 the regions 23, 24 and 34 are starting. The
region 23 extends itself between the curves (1) and (4); it is indicated
in fig. 2 by 23. The region 24 is situated between the curves (1)
and (3); the region 34 is situated between the curves (1) and (2)
and therefore, extends itself over curve (2) [fig. 2|. [We keep in
mind with this that each region-angle is smaller than 180°. |

When we act in the same way with the regions which start from
the curves (2), (3) and (4) we find a partition of the regions as in
fig. 2.

Previously we have deduced: each region, which extends itself over
the stable or metastable part of curve (/,) contains the phase F,.
We see the confirmation of this rule in fig. 2. The metastable part of
curve (1) intersects the region 14, the stable part of this curve the
region 12; both the regions contain the phase 1. The metastable part
of curve (2) intersects the regions 12 and 24, which contain both
the phase 2; the metastable part of curve (8) intersects the regions
13 and 34 which contain both the phase 3. The metastable part of
curve (4) intersects the region 14, the stable part of this curve is
covered by the region 34; both the regions contain the phase 4.

The following is apparent from the preceding considerations. In
all binary systems the partition and the position of the curves and
the regions will respect to one another starting from a quadruple-
point, is always the same; it can be represented by fig. 2.

(To be continued).

Chemistry. — “Compounds of the Arsenious Owide.” Il. By Prof.
F. A. H. Scuremnemakers and Miss W.C. pr Baar.

a. Introduction.

By Réporrr') and others compounds are prepared of the As,O,
with halogenides of potassium, sodium and ammonium.

These compounds were obtained by treating solutions of arsenites
(viz. solutions of As,Q, in a base) with the corresponding halogenides.

Rüporrr describes the compound As,O,.NH,Cl, which we have
found also; he also deseribes the compound (As,O,),. KCl. which
we have not found.

In order to obtain these compounds, we have, however, worked
in quite another manner; for this we have brought together water,

1) Fr. Rüporrr. Ber. 19 2668 (1886), 21 3051 (1888).

127

As,O, and the halogenide, consequently without first dissolving
As,O, in a base. Therefore, we had to deal with equilibria in the
ternary systems: water-As, V,-halogenide.

Of course we have to bear in mind in judging the results,
that the possibility is never excluded that besides the compounds
which have shown themselves, others might exist, that even the
compounds fuund might be metastable.

b. The system: H,O — As,O, — KCI at 30°.

In this system at 30° the two components As,V, and AC! occur
as solid phases and further a compound, which we shall call D.
The composition of this compound is defined with the aid of the
rest-method, but is not known exactly. It is sure, however, that it
has not the composition: (As,O,), KCH; it is about (As, 0), ACD,

(As, O,), (KCH), ; we shall refer to this further.

In fig. 1 in which the point 7 indicates the component AC! the
isotherm of 30° is represented schematically, this isotherm consists
of three branches;

ab represents the solutions, saturated with As,O,
be 9) Eh] 2? ” > D
ed 5c ze si En EOL

The composition of the solution 6, which is saturated with As, OD, + D,
has not been defined. It is apparent from table 1 that its percentage
of KC! will be between 10,37 and 11.22 °/, and that its percentage
of As,O, will be somewhat higher than 2.46°/,. Further it is
apparent from table 1 that the solubility of As,O, with increasing
percentage of KC/ of the solution increases a little, viz. from 2.26°/,
to a little over 2.46 °/,; consequently the point 6 is situated somewhat

further from the side WZ than the point

Jl 0, a. Further it is apparent from table 1

that the solubility of the compound D
decreases at increasing percentage of
KCl of the solutions, viz. of over
2.46°/, to about 0.78°/, (in table 1 the
average of N°. 12 and 13); curve dc ap-

a proaches, the side WZin fig. 1 therefore
Ww d Z from b. Consequently we see that the

Fig. 1- solubility of As,O, increases at first a
little by adding ACV, until the compound D is separated, after which
the solubility decreases. [from 2.26°/, in pure water (point a) towards
0.78 °/, in a solution saturated with AC7 (point c)].

128

No other points besides both the terminating points ¢ and d have
been defined of curve cd, which represents the solutions saturated
with ACV.

We find united in table 1 the results of the different analyses ;
all the small bottles have been shaken in a thermostat during from
three to five weeks. Although the s,Q, and the compound D formed
both an extremely fine powder, the eye could easily distinguish them
by their different behaviour on sinking.

ABs Eek

Composition in percentages by weight at 30°

of the solution of the rest

No. | op, As;O3 | % KCl | 4% As203 | % KCI | solid phase

1 | 2.26 0 — | =) eee
2 2.40 6.58 84.05 | 1.05 | 2

3 2.46 10.37 82.48 2.13 :

4 2.10 11.22 36.84 17.07 D

5 1.77 13.59 18.74 | 15.88 A

6 1.52 15.89 31.45 20.06 .
wy hee 17.72 32.81 | 20.62 r
8 7 11-10 20.67 19.73 21.75 î

9 | 0.995 | 22.38 23.53 22.31 y
10 | 0.898 | 22.92 11.36 | 23.12 .
u 0.841 | 25.23 26.93 24.70 | ;
12 | 0.783 | 26.96 12.23 | 28.16 | D+KC
13 | 0.777 MEL | (8) (32) | D+KCI
14 | 0 OE | =e = | Kel

The solubility of KCl in pure water (n°. 14 of table 1) has not
been determined but has been taken from the tables of LANDoLT-
BORNSTEIN.

As table I shows, besides the compositions of several solutions,
also the rests belonging to them, are determined; the numbers placed
between parentheses in n°. 13 indicate however the composition of
the complex. In order to examine if in the determinations errors might
have occurred by analysis or anything else, several complexes were

129
weighed accurately ; this complex must then be situated on a straight
line with the solution and the rest formed from this. This was
always the case in this examination.

When in fig. 1 we draw the conjugationlines, which unite the
solutions of branch he with the corresponding rests, those do not go,
as is drawn in fig. 1, through the same point D. When we call
the percentages of As,O0, and water of a solution Y; and IV), those
of the corresponding rest Y, and W,, and when we call JV the
percentage of As,O, of the point D (the point of intersection of the
line liquid-rest with the side As,O,—W) then we find:

Tae dl X Wr

eae
t TW

When we calculate with the aid of this formula Y‚ for the deter-
minations 4—11 of table 1, we find

UB 29: 16-35: 75.52; 75.45; 75.04; 77.86; 75.65; 76:30.
As the compound As,0,. KC! contains 72.6°/, As,O, and the com-

pound (As,0,), KCl contains 84.1 °/, As,O;, the point D, therefore
cannot represent this compound, it is more probably (As, 0), (KCH).

which contains 76.1°/, As,0, or (As,0), (KC), which contains

76.9°/, As,O,. When we take the average of the eight determina-
tions, then we find 76.08 °/, As,O,, which is in accordance with the
composition of (As,0,), (KCH.

When we draw in fig. 1 the line WD, we see that this does not
intersect the saturationcarve of D, but that of the As,O,. Conse-
quently the compound is not soluble in water without decomposition,
but is decomposed with separation of As, 0O,.

c. The system: H,O—As,O0,—N4H,Cl at 30°.

In this system both the components As,O, and NH,Cland further
a compound D occur at 30°. We found for the composition of
this compound, which is determined with the aid of the rest-method,

As,0,. NH,CI

We may represent the isotherm of 30° in this system again
schematically by fig. 1; the anglepoint 7 represents then the V//,C/
and the point D the compound As,O,.NH,Cl. Consequently the
isotherm consists again of three branches, viz. :

ab, the saturationcurve of As,0,
OG; 3: ” jn AS Oe ENG)
CU as, +5 a NEEGL

Proceedings Royal Acad. Amsterdam. Vol, XVIII.

130

It is apparent from table 2 that the solubility of the As,O, remains
invariable within the errors of analysis on increasing percentage of
NH,Cl of the solutions. The solution (point 6) which contains 7.08°/,
NH,Cl, contains 2.28°/, As,O,, while the aqueous saturated solution
(point a) contains 2.26°/, As,O,. Further it appears from table 2
that the solubility of the compound decreases on increasing percentage
of NH,C/ of the solutions; in point 4 (N°.3 in table 2) the solution
contains still 2.28°/, As,Q,, in the solution, saturated with NH,C7-+ D
(point c; N°. 9 in table 2) the percentage of As,O, is however
lowered to 0.291°/,. Consequently the <As,O, is less soluble in a
solution, saturated with N//,C! than in a saturated solution of A CZ.

Only the terminatingpoinis ¢ and d of curve cd, which represents
the solutions saturated with NH,C/, have been determined.

In table 2 the results of the determinations are united; all the
small bottles have been shaken during 3 to 5 weeks in a thermostat.
Also here, although the As,0, and the compound are both an
extremely fine powder, the eye could easily distinguish them by
their different behaviour on sinking.

TrASBalEm2:

Composition in percentages by weight at 30°

of the solution | of the rest
NO. | Oo AsO, | 00 NH4CI | 0/0 AsO; | %0 NH4CL | solid phase
1 2.26 0 yy Aisa As,03
2 2.29 3.86 82.55 0.34 | 5
3 2.28 7.08 73.09 6.67 | As,O3 + As,03.NH,Cl
4 1.31 9.08 44.50 | 15.90 | As,O3.NH,Cl
5 0.993 11.76 48.35 | 17.09 7
6 0.490 21.09 21.43 | 20.93 3
7 0.432 24.61 47.11 22.14 | :
8 0.398 27.18 39.13 23.81 8
9 0.291 29.52 (8) | (35) | As,O3.NHyCI+NH,CI
10 0 29.3 = ae NH,CI

The solubility of the NH,C! in pure water (N°. 10 of table 2) is
not determined, but taken from the tables of LANpoLT-BÖRNSTEIN, the

131

numbers placed between parentheses do not indicate the composition
of the rest but that of the complex.

When we draw in fig. 1 the line WD, then we see that it does
intersect curve ab, but not be. The compound 45,0, . NH,CI is,
consequently decomposed by water with separation of As,O,.

d. The system H,O—As,0,-—NaCl.

In this system at 30° only the two components As,0, and NaCl
occur as solid phases, we have not found a compound.

We may represent the isotherm schematically by fig. 2; then the
anglepoint Z represents the NaC/. Consequently the isotherm consists
of two branches, viz. :

ab the saturationcurve of As,O,

be ,, Ae Nar
It is apparent from table 3 that the solu-
H4,0, bility of As,O, decreases with increasing

percentage of NaC/ of the solutions. The

saturated aqueous solution of As,O, contains

viz. 2.26°/, As,O,, the solution saturated

with NaC/-+ As,0, contains only 1.58°/,

w oo@ 1 7 As,0,. As a saturated solution of AC/ con-

e: tains 0.78°/, As,O, and a solution saturated

Ee with NH,Cl 0.291°/, As,O,, it is apparent

that As,O, is expelled least by NaC/ and the most by NH,Cl from
its solution.

dA BE Etc:

Composition in percentages by weight at 30°

of the solution of the rest
No. | 0,A203 | %NaCl | A03 | %% NaCl | solid phase
| [ |
1 2.26 0 Pari As20;
2 2.18 5.93 (5) | (16) 5
3 2.04 11.49 (10) | (14) 8
4 1.88 16.86 (15) (12) ‘
5 1.71 22.06 74.12 | 5.90 8
6 1.58 26.17 Go) I 2) As,O;--NaCl
7 0 26.5 SM Men NaCl

132

In table 3 the results of the determinations are united, all the
small bottles have been shaken during three to five weeks in a
thermostat.

The solubility of the NaCl in pure water (N°. 7 of table 3) is
taken from the tables of LaNpour-BögrNsrerN; the numbers placed
between parentheses indicate again the compositions of the complexes
(consequently not of rests).

(To be continued).

(July 18, 1915).

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING

of Saturday June 26, 1915.
Vor. XVIII.

President: Prof. H. A. LORENTZ.
Secretary: Prof. P. ZEEMAN.

(Translated from: Verslag van de gewone vergadering der Wis- en
Natuurkundige Afdeeling van Zaterdag 26 Juni 1915, DI. XXIV).

CONTENTS.

H. A. LORENTZ: “The width of spectral lines”, p. 134.

W. REINDERS and F. GOUDRIAAN: “Equilibria in the system Cu—S—O; the roasting reaction process
with copper.” (Communicated by Prof. S. HOOGEWERFF), p. 150.

H. ZWAARDEMAKER: “On measurement of sound”, p. 165.

E. H. BücHNER: “The viscosity of colloidal solutions.” (Communicated by Prof. A. F. HOLLEMAN),
p. 170.

P. EHRENFEST: “Some Remarks on the Capillarity Theory of the Crystalline Form”. (Communicated
by Prof. H. A. LORENTZ), p. 173.

A. W. K. DE JONG: “Action of sun-light on the cinnamic acids”, p. 181.

J. J. VAN LAAR: “Some Remarks on the Osmotic Pressure”. (Commucicated by Prof. H. A. LORENTZ),
p. 184.

J. A. J. BARGE: “On the metamerological signification of the craniovertebral interval.” (Communi-
cated by Prof. L. BOLK), p. 191.

J. A. J. BARGE: “The genetical signification of some atlas-variations”. (Communicated by Prof.
L. BOLK), p. 201.

A. WICHMANN: “On phosphorite of the isle of Ajawi”, p. 214.

W. and J. DOCTERS VAN LEEUWEN-REIJNVAAN: “On the germination of the seeds of some Javanese
Loranthaceae”. (Communicated by Prof. F. A. F. C. WENT), p. 220.

S. DE BOER: “On the heart-rhythm”. IV. Heart-alternation (Communicated by Prof. J. K. A.
WERTHEIM SALOMONSON), p. 231.

W. EINTHOVEN, F. L. BERGANSIUS and J. BIJTEL: “Upon the simultaneous registration of electric
phenomena by means of two or more galvanometers, and upon its application to electro-
cardiography”, p. 242.

P. WEISS and Miss E. D. BRUINS: “The magnetic susceptibility and the number of magnetons of
nickel in solutions of nickelsalts”. (Communicated by Prof. H. A. LORENTZ), p. 246.

P. WEISS and Miss C. A. FRANKAMP: “Magneto-chemical researches on ferrous salts in solution”,
(Communicated by Prof. H. A. LORENTZ), p. 254.

Miss H. J. VAN LUTSENBURG MAAS and G. VAN ITERSON Jr.: “A microsaccharimeter”. (Communi-
cated by Prof. M. W. BEIJERINCK), p. 258. (With one plate).

F. M. JAEGER and JUL. KAHN: “Investigations on the Temperature-Coefficients of the Free Molecular
Surface-Energy of Liquids between _ 80° and 1650° C. X. Measurements Relating to a Series
of Aliphatic Compounds”, p. 269.

F. M. JAEGER and JUL. KAHN: Ibid. XI. “The Surface-Tension of homologous Triglycerides of the
fatty Acids”, p. 285.

F. M. JAEGER and JUL. KAHN: Ibid XII. “The Surface-Energy of the Isotropous and Anisotropous
Liquid Phases of some Aromatic Azoxy-Compounds and of Anisaldazine”, p. 297.

M. W. BEVJERINCK: “Crystallysed Starch”, p. 305. (With one plate).

J. P. VAN DER STOK: “On the relation between meteorological conditions in the Netherlands and
some circumjacent places. Atmospheric Pressure”, p. 310.

J. P. VAN DER STOK: “On the relation between meteorological conditions in the Netherlands and
some circumjacent places. Difference of atmospheric pressure and wind”, p. 321.

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

134

G.J. ELIAS: “On a General Electromagnetic Thesis and its Application to the Magnetic State ofa
Twisted Iron Bar”. (Communicated by Prof. H. A. LORENTZ), p. 327.

A. SMITS: “Molecular-Allotropy and Phase-Allotropy in Organic Chemistry”. (Communicated by Prof.
J. D. VAN DER WAALS), p. 346. :

A. SMITS: “The Apparent Contradiction between Theory and Practice in the Crystallisation of Allotropic
Substances from Different Solvents”. (Communicated by Prof. J. D. VAN DER WAALS), p. 363.
DEVENDRA NATH BHATTACHARYYA and NILRATAN DHAR: “Stpersaturation and release of super-

saturation”. (Communicated by Prof. ERNST COHEN), p. 369.

DEVENDRA NATH BHATTACHARYYA and NILRATAN DHAR: “Temperature-coefficient of conductivity
in alcoholic solutions, and extension of KOHLRAUSCH’s hypothesis to alcoholic solutions”. (Com-
municated by Prof. ERNST COHEN), p. 373.

DEVENDRA NATH BHATTACHARYYA and NILRATAN DHAR: “Velocity of ions at 0° C.” (Communicated
by Prof. ERNST COHEN), p. 375.

NILRATAN DHAR: “Properties of elements and the periodic system”. (Communicated by Prof. ERNST
COHEN), p. 384.

P. ZEEMAN: “FRESNEL’s coefficient for light of different colours”. (Second part), p. 398. (With one
plate).

H. KAMERLINGH ONNES, C. DORSMAN and G. HOLST: “Isothermals of diatomic substances and their
binary mixtures. XV. Vapour pressures of oxygen and critical point of oxygen and nitrogen”.
(Errata to Comm. NO. 1456 from the Physical Laboratory at Leiden, Jan. 1914), p. 409,

Physics. — “The width of spectral lines.’ By Prof. H. A. Lorentz.
(Communicated in the meeting of June 27, 1914).

§ 4. In order to account for the absorption of light we may
suppose the molecules to contain electrons which are set vibrating
by the incident rays and experience a resistance to their motion.

If we suppose that an electron is drawn towards its position of
equilibrium by a quasi-elastic force and that the resistance is pro-
portional to the velocity, the vibrations are determined by the
equation

mr=—fr—gr+eE, 2 ne a, OU
where the vector r means the displacement from the position of
equilibrium and E the electric force in the incident light. The mass
and the charge are represented by m and e, whereas f and g
are the constants for the quasi-elastic force and the resistance.

The theory takes its simplest form for a gaseous body of not too
great a density; to this case I shall here confine myself. If there
are several groups of electrons, those which belong to the same
group being equal and equally displaced, we may write for the
electric moment per unit of volume

=SNer, zo
where the sign = refers to the different groups and MN means the
number of electrons per unit of volume for each group. The di-
electric displacement is given by

and in addition to these formulae we have the general equations

135
rot H = E D,
C

1p
rot E= ——H.
c

(H magnetic force, c velocity of light in the aether).

We shall, in the usual way, represent the vibrations of the system
by means of complex expressions, so that, if 2 is the frequency,
all variable quantities contain the factor

gint,

— J
ry = —
m

the frequency of the free vibrations, we find from (1) and (2)
re Saenen VE
mln, —n*) Jing
A beam of light travelling in the direction of the axis of #, may
be represented by expressions for E, D and H, containing the factor

Cn
in (: — Le)
e CRN
where (uw) may be called the “complex index of refraction.” For this
quantity we find from the above equations
Ne?

m(n,?—n*) + ing :

Introducing

@i=14+2z (3)
§ 2. If now we put

ich

ne Ee ce (0)

u will be the real index of refraction and / the index of absorption.
The meaning of the latter is, that the intensity of a beam of light
travelling over a distance d, is diminished in the ratio of 1 to

Cane BEY kh eee ae (5)

By means of (3) u and A may be determined for each frequency
of the light.

If the values of nm, for the different groups of electrons are suffi-
ciently different from each other, there will be a certain number of
separate maxima of absorption. In this ease we may treat the phenomena
belonging to each of these maxima with sufficient approximation by
supposing only one group of corpuscles to be present.

Thus (3) becomes

10*

136

Ne’
=| Ee ae ry ‘ e e
(u) A mn, —n?) + ing (6)
and if we put
N 2
edn in ce ieee
Nog

we find the following values for the case n =n,, Le. for the maxi-
mum of absorption
(u,)? = 1—a,
2u, = VI He +1,
ch:

doei

The last equation shows that the smaller the coefficient of resist-
ance g, the greater will be the value of h,; small resistances give
rise to a strong maximum of absorption. We can in this respect
distinguish two extreme cases; viz. that @ is much greater and that
it is considerably smaller than unity. In the first case we have
approximately

and in the second case

Se. 2. 4 oe eee

If we write 2, for the wave-length in the aether, corresponding
to m,, we have

ie ote
Now, according to (5) the decrease in intensity over a wave-length’s

distance is given by

el Re OE Ee ho te (9)

and we see therefore that this decrease will be considerable if a >> 1
and very small if a << 1.

§ 3. The width of the bands of absorption may likewise be
deduced from equation (6). Indeed, if m is made to differ from 7, in
one direction or the other, the term m(n,’—n*) gains in importance
in comparison with 72g; when it has reached a value equal to a
few times ng, the index of absorption has become considerably
smaller than A. As the ratio of m(n,?—n’) to ng is of the same
order of magnitude as that of 2mn,(n—n,) to n‚g, we may say that for

137

nen ee Soest dnc, ts Wome, condi)
2m

where s is a moderate number, the absorption is much smaller than
for n—n,. Hence, the absolute value of (10) will give us some idea
of half the width of the absorption band. The smaller the coefficient
of resistance, the narrower the band is seen to be. A strong maxi-
mum of absorption and a small width will be found together, whereas
in the case of a feeble maximum we shall find a broad band.

For values of n, differing so much from n, that 7mg may be
treated as a small quantity compared with m(n,’—n’), we may
replace (6) by

Ne’ iNne’g
(u)? =1 IE TEN ae 23
m(n,?—n’?) m*(n,°>—n’*)

Supposing further that the real part on the right hand side is
positive and much greater than the imaginary one, we find approxi-
mately

Ne’
2—1 eee
a 15 m(n,?—n*)
Ne?n®

Emad VEE TR gq.
2ucm?(n,*—n*)?

The last formula shows that the absorption at a rather large
distance from the maximum increases with the coefficient of resist-
ance, just the reverse of what we found for the maximum itself.

For values of g, so great that a << 1, the equations become less
complicated. Indeed, for this case (6) may be written
1 Ne?
2° m(n,?—n?) + ing
and this, combined with (4), leads to the values

1 Ne?m(n,?—n’)
WS 1 a 9 RP) =F aac

m?(n?—n,")* + n?q?
1 Ne’n’g

Files m*(n?—n,?)? + n° 9?

(wy) = 1+

This last equation shows that for n =n,

„Nef
e= 2eg’
agreeing with (8), and that at the distance from the maximum deter-
mined by (10), the index of absorption has become s? + 1 times
smaller than /,.

138

§ 4. The above has been known for a long time and has been
repeated here as an introduction only to some further considerations.
These will be limited to lines in the visible and the ultraviolet
spectrum, i.e. to lines which in all probability are due to vibrations
of negative electrons.

We shall also confine ourselves to such problems as may be treated
without going deeply into the mechanism of the absorption. There are
good grounds for this restriction, for it must be owned that in many
cases we are very uncertain about the true nature of the phenomenon.

In the case of a vibrating electron there is always a resistance of
one kind, viz. the force that is represented by

6x0?
if v is the velocity. For harmonic vibrations we may write for it
en’
bac
so that it proves to be proportional to the velocity and opposite to
it. If this “radiation resistance”, as it may appropriately be called,
because it is intimately connected with the radiation issuing from
the particle, is the only one, we must substitute in the above for-
mulae for the coefficient g the value

Vv,

ome rl
G —— . . . . . . . .
I Bare? ( )
Replacing here n by n, we deduce from form. (7)
62 Ne? aye
oS eS N Ee
De 4?

0
Now .V2,*, the number of vibrating electrons in a “cubic wave-
length” will have in many cases a high value. Hence, on our
present assumption, « would be very great and for rays of frequency
, the weakening would be considerable even over a distance of

one wave-length only. Indeed, one finds for the exponent in (9)

2a = — MENE 5.4 2
It must be remarked here that in the case now under consider-
ation, we cannot speak of true “absorption”, ie. of transformation
of the vibrations into irregular heat motion, but only of a “scattering”
of the light by the vibrating electrons, so that 4 may properly be

called the “index of extinction’.
Formula (11) leads to a very small value for the width of the
dark line. Indeed, using (10) and replacing n by n, in (11), we
easily find for the width measured by the difference of wave-length

139

between the borders

2
e’nd
Ai zn
mn Ome*m

or
Ah = 227 sk,
after substitution of the well known value
e?
Orc. R
(R radius of the electron) for the (electromagnetic) mass m.
Now we have

so that for s= 10
Aa=12.10-2% em = 0,0012 AU... . . . « (13)

This is a very small width indeed.

We shall soon see however that equations (12) and (13) apply
to the ideal case only of molecules having no velocity of translation.
In reality, on account of the heat motion of the molecules a “line
of extinction” will be much broader than is given by (13) and less
strong at the middle than we should infer from (12).

One remark more has to be made about the radiation resistance.
Though the extinction to which it gives rise, quickly decreases as
the frequency n deviates more and more from the frequency 7,,
yet in the case of thick layers of gas it remains observable at a
considerable distance from n,. We may suppose e.g. that in the case
of atmospheric air, 2, belongs to a point in the ultraviolet. Now, if
for light in the visible spectrum, we calculate the extinction corre-
sponding to the coefficient g,, we find exactly the well known
formula of Rayurren which agrees in a satisfactory way with obser-
vations.

§ 5. As the radiation resistance does not give rise to any true
absorption, we must look for another explanation of this pheno-
menon. We can hardly think of a real friction or viscosity, but we
may suppose that the vibrations of the electrons which are excited
by the incident light cannot go on regularly for a long time, but
are disturbed over and over again by collisions or impacts which
convert them into irregular heat motion. It can be shown‘) that
this leads to the same effect as a frictional resistance and that the

1) H. A. Lorentz, The absorption and emission lines of gaseous bodies, Proc.
Amsterdam Acad. 8 (1905), p. 591.

140

formulae of $$ 1 and 2 may still be used, provided we substitute for
the coefficient g the value

n= nn ee

Here r denotes the average time between two succeeding collisions
of one and the same electron. The formula is based on the assump-
tion that each collision wholly destroys the original vibration. If
some part of it remained after an impact, we should have to take
for t a larger or smaller multiple of the time between two collisions.
We may also remark that the expression (14) has a more general
meaning. We may understand by + the time during which a vibration
can go on without being much disturbed or considerably damped,
and use the formula, whatever be the cause of the disturbance or
the damping. If there were e.g. a true frictional resistance the equation
for the free vibrations would be

OS dijk
and we should have
21 AR
: == t

m 4m?

The time during which the amplitude decreases in the ratio e: 1
would therefore be
2m
SS)
9,
which agrees with (14). Thus, the formula also applies to cases in
which there is a radiation resistance only; for g we have then to
substitute the value (11).

Returning to the question of impacts, we may remark that in the
case of a gaseous medium, it would be natural to take for r in (14)
the mean time between two collisions of a molecule. There are,
however, cases where we find in this way a value much too high
for 4,-

Let us consider e.g. the propagation of yellow light (2 = 6000 A. U.)
through air of O° and under a pressure of 76 em, and compare the
values of g, and g,. In calculating this latter coefficient we shall
use the values holding for nitrogen. If « denoies the mean velocity
of the molecules, / the mean length of path between two collisions,

l
we find, putting r—-—, from (14) and (11)
u

ga IEN SL

gj war ce) ARI

141

With 2=6.10—5 cm, /= 9,4.10-6 em, uw = 4,93.104 em/sec., and
the above value of R, the ratio becomes

Le 172.
Ji

Now, we found in $ 3 that, at a rather large distance from 7, ,
the index of absorption is proportional to g. Our calculation therefore
shows that the collisions would cause an extinction 172 times stronger
than that to which the radiation resistance gives rise. As the latter
leads to Rayiuicn’s formula which has been confirmed by the obser-
vations, we must conclude that the effect of the collisions is much
less than we supposed it to be. Thus, when light is propagated in
air the electric moment which is excited in a molecule must remain
nearly unchanged in direction and magnitude during an impact.

Of course, notwithstanding this, it may very well be that in the
neighbourhood of », and under special circumstances the collisions
disturb the vibrations. Recently Stark has given good reasons for
supposing that the electric field round a charged particle changes
the vibrations of a neighbouring molecule in such a way that a
broadening of the spectral line is brought about.

$ 6. It has often been remarked that, according to DorPrLer’s
principle, the molecular motion must give rise to a broadening of the
spectral lines. We shall first consider this effect for the case of an
emission line, on the assumption that there are no other causes for a
broadening.

Let »,, the frequency of the vibrations within the molecules, be
the same for all the particles and let € denote the component of the
velocity of a molecule along a line directed towards the observer,
§ being positive when the molecule approaches the observer, and
negative in the opposite case. Then the observed frequency is given by

5
nn! +5).
c

The change in frequency expressed in terms of »,, i.e. the fraction
N—nN,
OI .
0
which also represents the ratio of the change of wave-length to

4,, is therefore given by

OSS i od aetna airs. (Le)

Let us further write N for the number of molecules per unit of
volume and wu? for the mean square of their velocity. Then we find

142

for the number of particles for which the velocity & lies between §
and §-++ ds, and the change of frequency between the corresponding
values w and w + do,

EL a

ow 5 é 2u? d& . . e . . . . (16)
or

aa 3c?

OR Sty

DE a Ne 2u? dw 5 p 7 ps d 4 (1 7)

This last expression immediately determines the distribution of
light in the emission line. The borders of the line may be taken to
correspond to the values of w for which the exponent becomes —1,
Ie 10

EE
n= a

3 c

so that the width is determined by

Mealy ee
Omen

If «w is of the order of 5.10% em/see and 2, of the order of 6000 AU;

this 4A will be about !/¢0 A.U. This is a very small width; yet,
it far exceeds the value which, starting from the value of g,,
we found ($ 4) for the breadth of an absorption line, and which
would also belong to an emission line, if we had to reckon with
the radiation resistance only. The cause of the difference is that

NSK mn. Elen Ie 4 ols)

The conclusions drawn from (17) about the width of the lines are
in good agreement with the results of several physicists; they are
strikingly confirmed by the experiments of Buisson and Fasry’) on the
emission of helium, krypton, and neon in GrissLer tubes. These
observations show at the same time that in these rarefied gases there
are no resistances whose coefficient does not fulfil the condition
(18), and which, acting by themselves, would therefore give rise to
a width comparable with that arising from molecular motion, or
ereater than it. If there had been resistances of_ this kind, the
observed width would have been found greater than is required by
Dorrpuer’s principle.

1) H. Buisson et Cu. Farry, La largeur des raies spectrales et la théorie ciné
lique des gaz, Journal de Physique (5) 2 (1912), p. 442.

143

$ 7. We shall now pass on to consider the influence of mole-
cular motion on an absorption line. We shall suppose that there is
a radiation resistance only, or at any rate that there are only

4 = u
resistances whose coefficients g are much smaller than mn,— so
6

that, acting by themselves, they would produce a much smaller
width than the one we calculated in $ 6. Cases of somewhat
greater density are hereby excluded.

The problem is easily solved if, after having grouped the mole-
cules according to their velocity of translation, we substitute for
each group a proper value of m, in the expression for the electric
moment and then take the sum over all the groups in the way
shown in equation (3).

Let & be the velocity of translation of a molecule in the direction
of the beam of light and let one of the groups contain particles with
velocities between § and §-+ ds. In (3) we must then replace NV
by 46) or (17). Farther it is clear that the particles in question will

resonate with light of the frequency 2, (: + ) =n, (1 + w) in the
CG

same way as they would with light of the frequency n, if they
had no velocity of translation. We therefore write 2, (1 + w) instead
of n,. We shall also put

(en USE) at or oo Se on Gee LED)
so that » determines the difference between the frequency of the inci-
dent light and n,, and we shall confine ourselves to small values
of », as we may do in the case of narrow lines. Then, for small
values of w, the only ones for which (17) has an appreciable mag-
nitude, we may write

[rn (L+o)]? — n° = 2n,?(w—).

Moreover, since 7 will differ very little from m, we may in the
term ing replace n by nm, and consider g as a constant, though in
reality this coefficient may depend on n (as g, does according to (11)).

Putting further

g k 20
2mn, — . . . . . . . . . . (2 )
we find
— +2 3c?
vel 8 Nee? ot dw
(D= fie Br Es
2 2% mun,’ w—v+ik

—- 00

or, if we introduce

144

as a new variable and put

[Ae eae is! 3h,

Nee? ;
wett 2. (PQ, . » > Sane
22° mun,
where
+
w
iPS jh ee TWP dw ,
wi +k?
and
+o ;
Q=k] — e—Piwt+)? dw.
w? +k?

We observe that these formulae determine the indices of refraction
and of absorption for hght whose frequency is given by (19).

§ 8. We may now avail ourselves of the circumstance that,
according to (20), (21) and the inequality (18), which we suppose
to hold for g,

RIEN. . . 3 4

In the first place we find by a simple transformation

P — | — rd = fe gw)? ze Cat) dw :
w? + k?
0
showing that P=O for »>=—o, v=O and y= + o, that the
sign of P is always opposite to that of p, and that Pr) = — P(+-r).

We have therefore only to consider positive values of rv. For these
the absolute value of P lies beneath

ml — WN — ET wt) dw,

w
0

1
== mas eg fe2qhw —e gw} dw.

w
0
Developing
ew — e—-2g vw

in a series according to the ascending bongs of 2q?rw and inte-
grating each term separately we find

145

gages 0 1
R=2WVar.erl 1 = dn
ae ( TAS. (Oana )

where
L—Gnb--
The expression #& has a maximum for «= 0.83.
This greatest value is 1.92, so that in all cases
|P|< 1,92.

The integral Q can be evaluated by remarking that the fraction
EEE is a maximum for w=O and becomes very much smaller
than this maximum when the absolute value of w exceeds a certain
limit w,, which is a moderate multiple of 4. The interval (—w,, +-w,)
therefore contributes by far the greater part to the value of Q. Now,
in this interval, as is shown by the inequality (23), the function

ew”)?
differs very little from the value
emd
corresponding to w == 0. We may therefore write
+o

albe he se
OS emt ——~— == we-F™,
w? dk?

=o
It is remarkable that /, and therefore the coefficient g have dis-
appeared from the result.
We see by these considerations that P is smaller than the highest
value of Q. Thus, if even for that highest value of Q the factor
of ¢ in (22) is small compared with unity, this will also be true of

IE Neo
Ze:
2 20 mun,”

we may then deduce from (22)

l 3 Nee?
walt — ——. (P—iQ).
ZJ mun,
Combining this with (4), we find, first the value of the real index
of refraction, which we shall not now consider, and secondly that

of the index of absorption 4, viz. (if in (4) too we replace n by n,)
1 3 Ne?
— be a eo",
4 2 mun,

3c?
y2

khair We ee (2A)

il 3 Ne? |
= eA aN on, SA ee ee
: 4 2 4 MUN, (25)

This is the maximum value of the index of absorption which is
found at the middle of the line (» = 0).

Whether the supposition that the coefficient of # in (22) is much
smaller than unity be right, may be decided by calculating /,. For
it is evident that this supposition is equivalent to the inequality

hyd, EG ils
it requires therefore that the absorption over a distance of one
wave-length is small.

If this is not the case we may not use (24). However, by combining
(22) and (4), we then find

where gp may differ considerably from 1, and 4, still has the value
determined by (25). (This will however no longer be the index of
absorption for » = 0.)

Formula (25) may be so transformed that it becomes fit for
numerical calculation. If we express w in the absolute temperature
T and the molecular weight M of the gas, N in Tand the pressure
p (in mm. of mercury), 2, in the wave-length 4, (in AU), substituting
also the values for e and m, we find

M
Neier pa ie ae

We shall now make some applications of these results.

$ 9. Woop’s remarkable experiments’) on the scattering of the
rays of the ultraviolet mercury line 42536 by mercury vapour have
shown that even at ordinary temperatures this scattering is very
considerable. The intensity of the beam decreases to half its original
value over a distance of 5 mm.

The vapour pressure at this temperature is about p= 0,001 and
putting M—=200 and 7’= 290 I find from (26) a value a little
above 400 for 4, This is much too high compared with Woop's
result. It must however be borne in mind that the beam for which
he measured the extinction contained a small interval of frequencies,
so that we are concerned, not only with the value of /,, but also
with those of A4 which correspond to small positive and negative
values of » and may be considerably smaller than h,. However,

1) R. W. Woop, Selective reflexion, scattering and absorption by resonating gas-
molecules, Phil. Mag. (6) 23 (1912), p. 689.

147

since Woop has found the scattered rays to be unpolarized, I am
rather doubtful as to the propriety of applying the above theory to
his experiments. For this reason, I shall no longer dwell on this
question. *) I shall only add that the value 4, whick we found, leads
to a value of 4,2, considerably below 1.

§ 10. The formulae (24) and (25) may also be used for calcula-
ting the total absorption, integrated over the whole width of the
line, for a certain thickness of a given gas. On the other hand this
absorption can be measured by a simple photometric experiment,
Dr. G. J. Erras was so kind as to do this for iodine vapour.

A beam of yellow light was passed through an evacuated tube
containing some small iodine crystals and heated to 89° C. The
beam was obtained by isolating from the spectrum of an are lamp
a portion corresponding to the distance between the D lines. In a
layer of 2 em. the absorption amounted to 15 °/,.

In discussing this result, [ shall remark in the first place that the
distribution of light in an absorption band will depend on different
circumstances, e.g. on the thickness of the gas traversed. It may be
that at the middle of the line and within a certain distance from
it practically all light is absorbed, the absorption diminishing gradu-
ally on both sides. However this may be, one can always define
a certain width 42, such that the amount of light absorbed by the
gas is equal to the quantity of light that is found in the incident
rays within the interval A2. The magnitude of A2, which we may
call the “effective” width of the line, can be immediately deduced
from a photometric measurement.

The absorption spectrum of iodine vapour has a very complicated
structure, containing somewhat over 100 lines between the D lines.
Dr. Erras’s observation shows that the effective widths of all these
lines taken together amount to 15°/, of the distance between the D

lines, i.e. to 0,9 A.U. We shall therefore not be far from the mark
if for one line we put on an average
Al, = 0.008 A.U.

If /da is the intensity of the incident light within the interval
di, we have for the absorption over the whole width of a line by

a layer of thickness d
1 fe) di.

1) According to more recent measurements by A. v. Matinowsky (Resonanz-
strahlung des Quecksilberdampfes, Ann. d. Physik 44 (1914), p. 935) Jo = 1,55.

148
Hence

fo ANNAE

by which we can calculate the maximum absorption index h,.
For this purpose we develop e-?/¢ in a series and integrate

between the limits » =— oo and rv = + o, after having substituted
for A the value (24) and replaced dà by 4, dr. Putting
2h,d=«
we find
yt ty ee
en VA 20 sb A,

With the values w=—=1,88.10* emyssee and 4, = 5893 A. U. the
quantity on the right hand side of this equation becomes 1,50 and
we find

a= 2h, 0=4,1
approximately, showing that the absorption at the middle of the line
must have been more than 98°/,. As d=2 cm, the index of
absorption itself is found to be about

he 02 fom

§ 11. Now this value is widely different from the one that follows
from (26). At 89°C. the pressure of iodine vapour is about 24 mm.
Using this value and putting 4, = 5893 A.U., T = 362, M= 254,
we get from (26)

=De IMME iem:

The great difference between this number and the former one
may be accounted for by supposing that a very small part (about
one twenty millionth) only of the molecules are active in producing
the absorption, so far as one line is concerned, a conclusion agreeing
with that to which one has been led by other lines of research.

It must however be remarked that perhaps the fundamental sup-
position expressed in equation (1) does not correspond to reality and
must be replaced by a more general one. Instead of thinking of a
vibrating negative electron we may simply suppose that under the
influence of the incident light an alternating electric moment p is
induced in a particle. Equation (1) then takes the form

p + «p + 6p =7E
in which @, 2, and y are certain constants, the first of which deter-
mines the resistance, while 8 has the value n,*. We are again led
to equation (24), but instead of (25) we get an expression which

149

contains y. Of this coefficient we can say nothing without making
special hypotheses.

§ 12. Finally we shall shortly discuss the question whether the
width of FRrAUNHOFER’s lines in the spectrum of the sun can teach
us something about the quantity of the absorbing vapour which
produces them. Let us consider an arbitrarily chosen rather fine line,
the calcium line 4 5868. Its width is certainly smaller than 0,1 A. Ue

by which I mean that, 0,05 A.U. from the middle, the intensity of
1

the light amounts to more than the part — of that which is seen at
é

a small distance from the line and which would exist in the place
of the line itself if no calcium vapour were present.

If dis the thickness of the traversed layer of calcium vapour we
may write, giving to v the value that corresponds to the above
mentioned distance of 0,05 AU.

Qhd<1,

so that

We can calculate the right hand side of this inequality if we
make an assumption concerning the temperature 7’ of the absorbing
layer. For 7'—6000° we find in this way h,fd< 7,0 and for
T = 3000° h‚d < 98.

Now, if it were allowed to use the formula (26), this upper limit
for h‚d would lead to a similar one for pd. We should have for
T = 6000°, pd <0,0015 and for 7’= 3000°, pd << 0,0074. As p
represents the pressure expressed in mm. of mercury, whereas J is
expressed in cm., we might infer from these numbers that the quantity
of calcium vapour which produces the line in question is very small.
Some reserve however must be made here. It may very well be
that a small part only of the calcium atoms take part in the absorp-
tion. Then the above inequalities will still hold, provided we
understand by p the pressure of the “active” vapour. If we mean
by p the total pressure of the calcium vapour present we should
have to multiply the given numbers by 107, if one ten millionth
part of the atoms were active (comp. § 11). For the first temperature
this would give pd < 15000 and for the second pd < 74000. The
last of these numbers corresponds e.g. to a thickness of 0.75 km.
if the pressure is 1 mm. of mercury.

If we wish to abstain from all suppositions on the nature of the

Proceedings Royal Acad. Amsterdam. Vol. XVIII,

150

vibrating particles (comp. the end of the preceding $) we can say
nothing about pd and must confine ourselves to a conclusion con-
cerning /,d. However this may be, it seems rather probable that
the finest lines in the spectrum of the sun are caused by relatively
small quantities of the absorbing gases.

It ought also to be remarked that the problem is, strictly speaking,
less simple than we have put it here. We have reasoned as if a small
quantity of an absorbing vapour were present in front of a radiating
body giving rise to a continuous spectrum. In this spectrum there will
then be a fine absorption line. In reality, however, if there is very
rare calcium vapour in a certain layer, there will be vapour ot
somewhat greater density at a greater depth in the sun’s atmosphere.
For a satisfactory theory of the phenomena it would be necessary
to explain why this latter vapour does not give rise to a broader
absorption line, but must rather be considered as belonging to the
mass to which the continuous spectrum is due.

Chemistry. — “quilibria in the system Cu—S—O,; the roasting
reaction process with copper.’ By Prof. W. Ruinpers and
F. GOUDRIAAN. (Communicated by Prof. HOOGEWERFF).

(Communicated in the meeting of May 29, 1915.)

1. In the metallurgy of copper the reactions, which may oecur
between the roasting products of the partly burnt copper ore, play
an important role; in special conditions they can lead in a direct
manner to the separation of metal. Usually it is assumed that these
reactions take place according to the subjoined equations *):

Cu,S + 2 Cu0 = 4 Cu + SO,

Cu,S + 2 Cu,O = 6 Cu + SO,

Cu,S + 3 CuO = 3 Cu + Cu,O + SO,
Cu,S + 6 CuO = 4Cu,O + SO,

Cu,S + CuSO, = 3 Cu + 2 50,

Cu,S + 4 CuSO, = 6 CuO +5 S0,.

Systematic researches as to this process, which seems very com-
plicated owing to the large number of possible phases, are exceedingly
scarce. The only observations worth mentioning are those of R.
Scuenck and W. HrMPELMANN ®); they determined p 7-lines for mixtures
of Cu,S—Cu,O0, Cu,S—CuSO, and Cu—CuS0O,. As these observations
are incomplete and their conclusions in many points unsatisfactory,

1) SCHNABEL, Handb. der Metallhiittenkunde I 176 (1901).
2) Metall und Erz, 1, 283 (1913). Z. f. angew. Chemie 26, 646 (1913).

151

& new investigation as to the equilibria in this system appeared to
us as being very desirable. The results obtained thus far, which
differ in some respects from the data already known, will be stated
here in brief.

2. The theoretical points of view which guided us here are the
same as those described in the system Pb—S—O *).

In order to find out whether cuprous oxide forms with cuprous
sulphide a stable phase-pair and also to measure the SO,-pressures,
a very intimate mixture of these substances was heated in a porcelain
tube connected with an open manometer and a mercury air-pump.
The heating took place in a Heraeus oven; the measuring of the
temperature was carried out with a Pt-PtRh-thermocell which had
been carefully set on the melting points of tin, lead, zine, antimony
and silver and which was checked a few times during the experiments.

The Cu,O was obtained by reduction of an alkaline CuSO, solution
with glucose, it was dried in a vacuum at 800°—400° and contained
88.64°/, of Cu. The Cu,S was a preparation of KaurBaum which,
mixed with a small quantity of sulphur, was heated for some time
in a current of hydrogen at 500°—600° and so got the theoretical
composition.

The equilibria pressures could be attained very readily from both
sides; the values obtained from SO,-evolution and SO,-adsorption
only differed 2—3 mm. Also, after evacuation the same pressures
were always again obtained; they are united in table 1, where the
pressure is expressed in mm. mercury at 0°.

TABLE]. 2Cu,O + CuS 2 6Cu + SO, (fig. 3 line III).

T p
586 73
607 120
636 179
650 222
669 | 289
691 | 390
710 488
730 599

1) W. Rerpers, These Proc. 23, 596 (1914).
11*

152

The reaction product was obtained by evacuating a few times
more; it was a cindery, copper-coloured mass in which metallic
particles were easily discernible; sulphate could not be detected.
Cu,0O+Cu,S thus form a stable phase-pair and as the diagonal
Cu,O—Cu,S cuts the diagonal Cu—CuSO, (see fig. 1), it follows
that Cu+-CuSO, must be metastable in presence of each other.

3. By now combining the other phases that are stable between
+ 300° and 900° two and two with each other and heating in
evacuated, sealed tubes we were able to record which of these
phase-pairs can be considered as the stable ones. First of all were
chosen the combinations Cu,S--CuO and Cu,O0—CuSO,.

A mixture of equal mols. of the last named substances when
heated during 6—7 hours at 450°—480° remained completely un-
changed, not a trace of sulphide could be detected. On the other
hand, mixtures of Cu,S and CuO appeared to undergo a very strong
change at this temperature; the colour changed from black to
brownish-red and on extraction with cold, recently boiled water a
blue-coloured filtrate was obtained which gave a strong sulphate
reaction. The sulphate soluble in water was determined quantitatively
as BaSO,. From 1.1182 grams of a mixture containing 2 mols. CuO
on 1 mol. Cu,S was thus obtained 0.1729 gram of BaSO, corre-
sponding with 0.118 gram of CuSO,; the mixture, after heating,
therefore contained 10.6°/, of CuSO,. This quite agrees with the
amount of CuSO, calculated on the supposition that the conversion
of the mixture takes place according to the equation:

Cu,S + 9 CuO = 5Cu,0 + CuSO,
namely 10.58°/, of CuSQ,.

Hence, we come to the conclusion that Cu,O0 + CuSO, forms
the stable and Cu,S+CuO the metastable phase-pair.

4. In a similar manner we investigated the combinations CauS—
Cu,O and CuSO,—Cu,S. It was a priori improbable that the first-
named pair should be stable as according to the observations of
PrEUNER and BrockmM6ner'), the dissociation of CuS into Cu‚S + S
becomes already measurable at 450°. In fact, it appeared that the
colour of the CuS—Cu,O mixtures had been changed from dark
brown to grey after 5 hours’ heating at 300°—320°; a considerable
quantity of sulphate had been formed. This, after extraction with
cold, recently boiled water, was determined as BaSO,. From 0.8722

1) Zeitschr. phys. Chem. 81, 129, (1912).

153

gram of a mixture containing 9 mols CuS to 4 mols. Cu,O 0.1274
gram of BaSO, was obtained in this manner so that the mass, after
heating, contains 10.0°/, of CuSO,. If the mass had been converted
entirely according to

9 CuS + 4Cu,0 = 8 Cu,S + CuSO,
the CuSO, content ought to be 11.15°/,. Hence, it had been converted
to a very considerable extent.

In good agreement herewith was the fact that a mixture of Cu,S
and CuSO, did not at all change at this temperature; it retained
its colour and remained powdery *).

Hence, Cu,S—CuSO, forms the stable, CuS—Cu,O the metastable
phase-pair.

5. On the strength of the above orientating experiments it seemed
probable that we must imagine the stable equilibria in the system

Fig. 1.

Cu—S—O to be as follows. Fig. 1 represents a horizontal projection
on the ground plane of a figure in space which holds for a constant
temperature and where the vapour pressure p is plotted on the
vertical axis.

Mixtures of CuS and CuSO, will at a given temperature give the
highest SO,-pressure, namely the one related to the monovariant
equilibrium :

3 CuS + CuSO, 2 2Cu,S+ 280,. . . . . D

1) This is in contradiction with the observations of Scuenck and HempeLMANN,
who record a melt between CuSO, and Cu,S, already at 300°.

154

If, by removing each time the SO, formed, we allow this reaction
to take place completely, either a mixture of CuS and Cu,S or one
of Cu,S and CuSO, will remain.

On increasing the temperature the first will be converted
completely into Cu,S with elimination of sulphur according to
2CuS = Cu,S +5. This reaction has been completely confirmed by
the experiments of PREUNER and BROCKMÖLLER.

The mixture of Cu,S and CuSO, will form Cu,O with evolution
of SO, and yield pressures appertaining to the monovariant equilibrium :

Cu,5 + 2 CuSO, 22 Cu,0 + 350, . 2

Of this process the reaction product must be a mixture of Cu,O
and Cu,S or of Cu,O and CuSO, according to whether it contained
originally an excess of Cu,S or of CuSO,

In the first case will take place the reaction

2Cu,O + Cu,S = 6Cu-+ S80, . . 2 ie
which leads to the equilibria pressures mentioned in table I.

Mixtures of Cu,O and CuSO, will, at a continued increase of
temperature, form as a third phase either CuO, or an intermediate
basie copper sulphate between CuO and CuSO,. In connexion with
the experiments of Woniur and his coadjutors*) it was probable
that a role is played here by the basic sulphate CuO .CuSO, so
that we shall obtain first of all the monovariant equilibrium :

4CuSO, + Cu,0 23CuO CuSO, +50, . . . (IV)
and then
CuOCuSO, + CuO 24Cu0 +50, ... (MW)

Finally, we will, therefore, have left a mixture of CuO and Cu,O
or of CuO and CuO. CuSO,. The latter will then dissociate according
to: CuO. CuSO, 2 2CuO + S0,, whereas at a still higher temperature
occurs the dissociation of CuO into Cu,O + 0%).

6. The above considerations have been completely confirmed by
our pressure measurements.

Pressures appertaining to the monovariant equilibrium: 3CuS +
CuSO, = 2Cu,S + 250, were obtained by starting from an intimate
mixture of CuS and CuSO,.

The CuSO, was obtained by dehydrating pure crystallised CuSO, .
5H,0 an! heating at 800°—400° in order to eliminate any free
siou vie acid eventually present. CuS was prepared by precipitating
a fe oiv aed souten of CusO, with H,S at the ordinary tempe-

ij Ber der deutschen chem. Gesellschaft 41, 703 (1908),
2) L. Wouter. Zeitschr. f. Elektroch. 12, 784 (1906), _

159

rature and heating the precipitate so obtained, after drying at 200°—
250°, in a current of H,S. In order to remove occluded gases it was
then again heated in a vacuum at 300°—350°. It contained 66.2°/,
of Cu (theory 66.46°/,).

The SO, evolution is already perceptible at + 150°, but the
reaction velocity at this temperature is so trifling, that it is
practically impossible to attain the equilibrium by heating at a con-
stant temperature. Hence, the mass was first heated at a higher
temperature (usually 220°—240°) until a considerable quantity of
SO, had evolved and then cooled very gradually until a temperature
was reached where adsorption of SO, occurred. Now, this tempera-
ture was kept constant for a considerable time, small quantities of
SO, were frequently withdrawn and it was recorded whether any
further absorption took place or not. In this manner it was possible to
restrict the equilibrium pressure within 20— 30 m.m, ; closer limits
could not be obtained in this very slowly progressing reaction.
Table II represents the results.

TABLE Il. 3CuS + CuSO, 2Cu,S + 280, (fig. 2 line 1).

Dj P

95 180
121 246
159 443
175 716

These pressures were always again attained after a few evacuations.
The reaction product at the end of the measurements was still ina
powdery condition, the colour had changed from black to grey.
Cu,O could not be detected. The pressures measured will, therefore,
relate indeed to the above-cited monovariant equilibrium.

7. In exactly the same manner the reaction Cu,5 + 2 CuSO, 2
2 Cu,0 + 350, was investigated. This also proceeds very slowly at
temperatures where the equilibrium pressure is less than 1 atmos-
phere, so that it is here also impracticable to attain the equilibrium
by heating at constant temperature. Hence, it was necessary to approxi-
mate the pressure in the same manner as detailed above.

As it appeared very soon that our observations differed very much

156

from those of SCHENCK and HeMPELMANN, we repeated the pressure
measurements with mixtures of different composition. From table IIL
wherein the results are indicated, it appears, however, that this
exerts no influence on the equilibrium pressure, so that the existence
of solid solutions is excluded.

TABLE III. CS + 2CuSO, = 2Cu.0 + 3SO, (fig. 2 line II).

2 CuSO, on 1 Cw. | 1 CuSO, on 1 Cu,S.
— |

ie | p

300 | 185 le cal Ale dan

310 | 148 | 351 228

350 | 210 | 315 350

360 245 |

317.5 285 |

300 443 |

400 517 |

We have not been able to confirm the phenomenon observed by
the said investigators that, above 300°, the equilibrium pressure first
attains a maximum value and then falls to a constant terminal value.
Although we kept the mixture, after the setting in of the equilibrium,
for fully 5 X 24 hours at + 320°, no adsorption was noticed {In the
case of other mixtures where the measurements were executed as
rapidly as possible, we also could not notice anything of the pheno-
menon.

Notwithstanding the heating at 420°—425° the reaction product,
afier the end of the operations, was a strongly caked but non fused
mass in which red Cu,O particles were distinetly discernible. The
above pressures therefore relate undoubtedly to the equilibrium
between the solid phases Cu,O, Cu,S, and Cusd,.

We must, therfore, unerly reject the concluson of SCHENCK and

BMP ul MANN as fo bar appease Of a q pe ott in this system
wiel would be sitaatel „tt 800 (| t= 20d in 30),-pressure and
waere CajO, Cus and Cus0, shouul Goexst vr pecsence of a liquid

phase and a gaseous phase. Even at 430° we could not yet observe
the appearance of a liquid phase.

8. “This contradiction induced us to try and find the initial
melting points of mixtures of Cu,S and CuSO, by the thermic
process. For this purpose they were heated in a glass tube placed
in an electric oven whilst the heating curve could be recorded with
a silver-constantane thermo-cell. The tube was furnished with an
exit tube; the gas developed during the measurement was thus
carried off, adsorbed in alkali and finally determined. The rise in
temperature amounted to 3° per minute; the starting of the fusion
was characterized by a very pronounced inflexion in the heating
line. For instance, with a mixture of 25 grams of CuSO, and 25
grams of Cu,S (about 1 mol. CuSO, to 1 mol. Cu,S) the constancy
of the temperature amounted to + 5 minutes, after which a regular
rise of 2—3° per 1’ again set in. With mixtures of different com-
position were obtained initial melting points which differed only 1—2°.

The mean value amounts to 484°. During the observation there
was evolved, when using 25 grams of mixture, on an average 160
mg. of SO,, from which we deduced that the mixture can have been
converted at most to the extent of 2°/,. The value found can, there-
fore, be but a very little too low.

Pp
700 T. 3CuS + CuSO, = 2 Cu,S +2 SO,.

IL. Cu,S + 2CuS0,= 2 Cu,0 +3 S0,.

200 300 350 400

En
Fig
Le

SO, very powerfully, heating in a
sealed apparatus was not possible.

By exactly the same method the initial melting points of ternary
mixtures of CuSO,, Cu,S, and Cu,O were recorded. Also here, the
results obtained with mixtures of different composition only differed

As the fused mass evolves

158

1—2° and the thermie effect was very considerable. On an average
was found: 457°. The SO, evolved amounted to average 40 mg.
per 25 grams of mixture.

The ternary eutecticum is, therefore, situated but a little lower
than the binary one of mixtures of Cu,S and CuSO,; the liquidum
region in the triangle Cu,S—Cu0—CuSO, will exhibit a strongly
one-sided situation towards the Cu,S—CuSO, side. As the liquid is
very viscous and the evolution of gas a violent one, we have not,
up to the present, succeeded in determining the composition of the
eutectica. Hence, we can only say this that they will only be
permanent under a high SO,-pressure and will, at the ordinary
pressure, decompose rapidly with formation of Cu,O. From our
dissociation experiments with mixtures of Cu,S—-CuSO, we calculate
for the SO,-tension at the initial melting point + 1.5 atmospheres.
A quintuple point between the solid phases Cu,O, CuS, CuSO,, the
liquid and the gaseous phase will, therefore, appear at about the
above pressure.

9. Mixtures of CuSO, and Cu,O will react with formation of
the basic sulphate CuO .CuSO,.

In order to study this reaction more closely, pressure measurements
were executed with these mixtures also. In contrast with the former
equilibria the pressure rapidly sets in; usually the equilibrium state
is attained after 15—20 minutes; the adsorption also proceeds
rapidly. The values attained from both sides only differed 2—3 mm.;
hence, the dissociation line is sharply determinable. The SO,-evolution
became discernible at + 480°; after evacuation the same pressures
were again obtained. The results are given in table IV.

TABLE IV. 4 CuSO4 + Cu,0 3 CuO . CuSO, + SO, (fig. 3 line IV).

t p
552 48
573 71
582 87
592 114
604 | 168
625 317
648 502

159

After only a little SO, had been withdrawn the reaction product
consisted of a powdery, but slightly caked brownish-red mass.

10. At 570°, SO, was now constantly being withdrawn from
the mixture and each time the equilibrium pressure was measured,
This remained the same until suddenly a strong depression was
observed. A series of points of this newly attained equilibrium was
determined; it is about equally sharply noticeable as the former.
The values return, after evacuation, again very exactly. The results
obtained are those of table V 1=t series.

In order to ascertain whether this last equilibrium really relates
to the basic sulphate CuO.CuSO,, and hence may be represented by :
CuO.CuSO, + Cu,O 2 3 CuO + SO,
it was endeavoured to obtain this sulphate in a pure condition.
Wönrer*) and otbers recommend heating CuSO, at + 800’ in a
current of SO,; it is then, however, mixed with a small quantity
of Cu,O. We have repeated this process, but it appeared that in
this manner are obtained strongly caked, red masses very rich in
Cu,O. Consequently we have abandoned this method and endeavoured
to obtain the compound in a pure condition by heating CuSO, in a
current of air at 720°—740°. This gave better results; the product
was coloured a pure yellow and yielded on analysis 66.21°/, CuSO,

(theory for CuO.CuSO, 66.62°/,).

TABLE V. CuOCuSO, + Cu,0 = 4 CuO + SO, (fig. 3 line V).

Ist series. | 2nd series.
Ee ps
t Pp | t P

644 39.5 655 54
666 52 679 76
684 86 699 115
703 | 131.5 105 133
125 215 723 205
736 292 149 386
754 419

1) L. Wouter, W. PrüppeMANN and P. Wouter, Ber. der deutschen chem, Ges. 41.
710 (1908),

160

A mixture of equal mols. of tbis basic sulphate and Cu,O yielded
the pressures of table V 2°¢ series. As both series of observations
entirely agree, we may be sure that they relate to a same mono-
variant equilibrium, namely between CuO .CuSO,, Cu,O, CuO and
the gaseous phase. As the equilibrium pressure does not alter after
withdrawal of SO,, that is after variation in the relation of Cu,O
and CuO, the miscibility of these phases, noticed by Wönrer'!) at
higher temperatures, will be slight in this temperature-range, so that
they will both continue to exist.

Finally, the SO, was withdrawn completely, so that only CuO
could remain, as we had started from equimolecular quantities of
basie sulphate and Cu,O. We have been able to demonstrate that
this was really the case by measuring the dissociation hereof in
Cu,O and O,. Here we found at 944°...36 m.m. and at 958°...
49 m.m., observations which entirely agree with those of Wönrer
for pure CuO.

11. With the above mentioned equilibria in the ternary system
Cu-S-O are connected the dissociation equilibria of pure CuSO, and
CuO . CuSO,. ;

These have been determined by Wönrer and his co-workers.

On a closer scrutiny of. the values given by them it appeared
that the p-7-lines that can be construed thereof intersect each other,
which would lead to the improbable conclusion that the basic sulphate
is only stable above + 625° and must dissociate below this tem-
perature into CuO and CuSO,. Hence, we were obliged to doubt
the correctness of their determinations.

As, however, the accurate knowledge of the dissociation line of

the basie salt was of importance to us because — as will be seen
in $ 14 — the equilibrium pressure of reaction V can be calculated

therefrom, we have once more determined the dissociation lines of
the normal and of the basic sulphate. The results differ considerably
from those of WOHLER.

Both equilibria can be attained very readily and the pressures
obtained by evolution and absorption do not differ more than 2—3 m.m. ;
after evacuation they accurately resume the same value. By way
of a check a series of observations were executed in the dissociation
of the normal sulphate where platinum gauze was tied round the
porcelain tube with the substance. A priori it was probable, however,
that even without addition of this catalyst the equilibrium in the

1) L. Wouter, c.s, loc.cit.

161

gaseous phase would be attained because the copper compounds
themselves have a catalytic action at the temperatures here employed’).
Table VI where the 1st series has been executed without, and the
2nd with addition of platinum confirms this entirely.

12. The gas mixture was withdrawn a few times by suction until
a fall took place in the equilibrium pressure; the reaction product
was then analysed and gave the proportion 2CuO: SO, = 1 : 0.98.
This product gave afterwards the pressures of table VII, these
always returned after continued evacuation, until finally the pressure
fell to that of the equilibrium 4Cu0 = 2Cu,0 + O,. Further basic
sulphates are, therefore, not capable of existence at these temperatures.

TABLE VI. 2CuSO, 2 CuOCuSO, + SO3 [SO, + 1/2 0,] (fig. 3, line VI).

Ist series | 2nd series

Ë I} 8
t P | t P
680 34 | 682 37
710 76 711 80
730 131 | 732 | 142
740 169 150 235
760 287 | 710 | 371
780 442

TABLE VII. CuOCuSO, 2 2 CuO + SO; [SO, + '),0,] (fig. 3, line VI).

t | P
740 61
760 84
780 144
800 224
810 284
820 345

1) BopensteiN and Fink. Zeitschr. f. physik. Chem. 60, 46 (1907).
L. Wouter, W. PLünDeMANN and P. Wouter, Zeitschr. f. phys. Chem. 62, 641 (1908).

162

13. The bad agreement existing between the observations of Wönrer
and his co-workers and our own, made us doubt for a moment
whether our apparatus arrangement might he the cause of the diffe-
rences. For a small quantity of SO, was deposited in the capillary
which connected the reaction tube with the manometer. Theoreti-
eally, it is very improbable that this phenomenon can have any
influence on the equilibrium pressure, for as soon as SO, disappears
from the gas mixture which is in contact with the solid substance
in the reaction tube, dissociation will again set in, until the original
SO,-pressure has again been attained. Only in those parts of the
apparatus where there is no longer any contact between gas and
solid substance and where moreover the temperature is low enough,
in other words in the capillary, a permanent decrease of the SO,-
tension can take place. Here, then forms a gas mixture of SO, and
Ox
measurements of Wönrer and co-workers. Our gas mixture, however,
is not indifferent but can on cooling, be reabsorbed completely by
the solid substance. It was, in fact, always observed that after heating
at a higher temperature followed by cooling, the equilibrium pressure

which plays the same role as the interlinked air cushion in the

UL. 2Cu,0 +Cu,S # 6Cu + SO, .
IZ. 4CuS0, +Cu,0 + 3Cu0CuSO, + SO, .
YZ. CuOCuSO, + Cu,0 =3CxO0+SO,.
VI. 2CuS0, = Cu0CuSo, + SO; .

P. lyr. CuO CuSO, * 2CUO + SO, .
500 .
IL

4,00 Yv Ww
300 j
200
100

550 600 650 700 750 800 °C

Fig. 3.

163

set in very exactly on the lower value appertaining to this lower
temperature.

A few check experiments with ferric sulphate, executed in the
same apparatus yielded equilibria pressures agreeing entirely with
the values indicated by BopENstEIN ’).

The results are given below. The deviations answer to a difference
in temperature of 1—2°.

t | PBODENSTEIN | PR. and G.

650 | 124 | 116 |
670 | 193 181 |
689 | 319 317 |

14. If we again consider the monovariant equilibrium,

CuO . CuSO, + Cu,0 S4Cu0+S0,. . . . (V)

we can imagine this to have originated in the following manner :
0). CusO; AGO SOLE sa CD

SO; 2250, EO. tes ses Pe ES)

CuO OZ 2CuOe ys > SOV ELD)

The gaseous phase consists both in reaction (V) and reaction (VII)

of a mixture of SO,, SO, and O,. If we call the partial pressures
of these gases at a given temperature :
for V respectively, ‚pso, 5 ;950,» «PO,» the total pressure P,
» VII ” 1PS0s> 1PS0, > PO nn » P,
the homogeneous equilibrium in the gaseous phase will be as follows :
1 1
SO. + 5P 0, „_1PSO, + ;PO,
at V Kp er EE andre PS
sPSOs „PS
Hence it follows that, at the same temperature
DSO, POs!" __ ;PSO,- PO,
sPSO, . „PS
The coexistence of the phases Cu,O and CuO at V now demands
that the partial oxygen pressure in this equilibrium is equal to a
dissociation pressure of pure CuO into Cu,O and QO,. If we call
the latter P,, then ‚po, must be = P,.
Likewise does the coexistence of the solid phases CuO . CuSO, and

a or et |)

1) Zeitschr. f. Elektrochemie 16, 912. (1900).

164

CuO at V demand that the SO,-pressure of V is equal to that ot VIL
so that „psos = sPsos-

These relations substituted in (a) give:
PSO, > PO; = Pil so.
In this ,pso, and ‚po, may be calculated from the observations
of the total pressure P, if the dissociation degree a of the SO, is
known. Then we have:

2a a
iP

„DSO = ——— and DO
ik 2 2+e 7 iE 2 2+¢a 7

and hence, substituted
Ja a
el = P's. ps,
mn $ 214 ap SEOs

Pilz a =
PS0, = > +> - Va (24 a)
PN Pole Cte a

I= ar sPSO, + 1P50

In this last equation ‚pso, will be very great in proportion to the
two other terms; at the first approximation the total pressure of
reaction V might be put equal to ,psoq-

or:

and

15. From the foregoing it appears that it is possible to calculate
the equilibrium pressure of V if we know:

a. the dissociation pressure at the equilibrium VII;

Db. the dissociation degree of the SO, at the pressures of VII;

c. the dissociation pressure of CuO.

The first quantity is known from our determinations given in table
VII. The second can be calculated accurately from the careful
investigations of BopeNsTEIN and Pont’). We have done this for
various temperatures and pressures which are interpolated graphi-
cally from our measurements of VII (see column 5 of table VIII).

The dissociation pressure of CuO into Cu,O and O, is extrapolated
from the observations of WO6HLER’) with the aid of the formula

/ 14000

og P, == 13,077 — FF

which agrees excellently with his observations.
With the aid of formula (c) the equilibria pressures P, have been

1) Zeitschr. f. Elektroch. 11, 373 (1905).
2) Zeitschr. f. Elektroch. 12, 704 (1906).

165

ealeulated for a series of temperatures and compared with the values
found experimentally. They are collected in table VIII.

TEAB IRE BVIE

t Jl P, Ps a | Ps (calculated) | Ps (observed)
\
ld NS
F 720° 993 33 0.0951 0.895 211 195
740 1013 | 55 0.1803 | 0.915 338 308
760 1033 90 | 0.3342 0.921 | 526 500
780 | 1053 | 144 | 0.6054 | 0.907 | 784 810
|

Considering the inaccuracy of the extrapolation of P, over fully
200° below the field of observation, the agreement may be called
a complete one. It furnishes a proof of the correctness of our mea-
surements as well as of those of Wönrer in connexion with the dis-
sociation of copper oxide.

Delft, Inorg. and phys. chem. laboratory
of the Technical University.

Physiology. — “On measurement of sound.” By Prof. H. ZwAARDE-
MAKER.

(Communicated in the meeting of April 1915.)

I have previously pointed out the benefit to be derived from Lord
RaYLEIGH’s arrangement, if we wish to perform a relative or even
an absolute measurement of sound. Originally’) it was applied to
the measurement of stationary sound-waves. W. K6nic*) extended
its use to the theory of progressive waves in detail. It also enabled
W. ZerNov®) to carry out experiments on the intensity of the
human voice. All earlier researchers and myself at first also, gave
to the mirror, which was placed obliquely to the sound-wave, a
peculiar position by attaching to it a small magnet. I now departed
from this principle, at first by bifilar suspension, afterwards by simply
hanging the mirror up by a long Wollaston fibre, flattened or not. *)

1) Lord Rayreren. Scientific Papers. Vol Il, p. 132.

2) W. Könre. Ann. d. Physik. Bd. 42 and 43, 1891.

2) W. Zernov. Ann. d. Physik. (4). Bd 24 p. 79, 1908.

4) H. ZWAARDEMAKER. “On hearing-apparatus”’. Ned. Tijdschrift v. Geneesk.
1912, Il. p. 1101. Proc. of the meeting-of 27 Sept. 1913. Vol. 22. p. 273,
Congress at Delft, March 1913, Multiple resonantie. Ned. Tijdschr. v. Geneesk.,
1913. Il. p. 640.

Proceedings Royal Acad. Amsterdam. Vol. XVIIL

166

To my knowledge Zrrnov was the first to place the measuring
mirror in a space entirely free from resonance. To increase the
sensitiveness I took some years later, for application to medical
problems, an afferent tube of the dimensions of the auditory canal
and the auricle. This enables us to perform an accurate measurement
even of whispered speechsounds. However, occasional currents of air
must be arrested by putting a very small plug of cotton-wool in
the artificial auditory canal. The mirror is placed at an angle of
45° close in front of the aperture of the tube, so that the sound-
wave, issuing from the auditory canal is driven against it as fully
as possible. The mirror is consequently tilted with maximum power
to a more transversal position.

If weak sounds in the speechzone a, to e, are to be measured,
it will be well to use large receiving funnels. Phonograph horns in
their various shapes will be found to work very well. Small am-
plitudes are recorded more accurately, when the scale is placed at
a great distance. Then, however, a constant position of rest is ex-
pedient, which is hardly practicable, unless the streams of air in
funnel and auditory canal are removed through the insertion of an
india-rubber diaphragm of the size of a phonograph membrane.
Cover-glass or thin mica will do as well. Thus I was in a position
to establish the ratio of the average intensities of whispered and
spoken sounds. The experiment was made (together with Dr. Reurer)
with 20 monosyllabic, aequisonorous and aequidistant words. The ratio
appeared to be 1: 170. (The intensity is in the ratio of 1: 170, the distance
at which sounds are heard of 1: 18)*). The modifying influence of
funnel and membrane may be controlled by going through the gamut
first with a simple physiological conducting tube and afterwards with
the same tube associated with a funnel and phonograph membrane.

In the following pages I shall briefly state the rules which have
proved generally reliable in measuring sound.

§ 1. Physiological measurement of sound.

When the measurement of sounds with regard to their audibility
is the subject under consideration, it is permissible to use an arti-
ficial auricle and an artificial auditory canal to direct the sound-
wave on to the measuring mirror. Provided the resonance of the
artificial conduit be equal to that of the natural canal, nothing
foreign is added to the sound, for when perceived by the human
ear, it is transmitted through a similar tube. The artificial canal

1) Proceedings of the 14th Dutch Congress for Phys. and Med. at Delft.

167

used by me, has with a small plug of cotton-wool a tone of reson-
ance equivalent to f,, without a plug to e,. The funnel in front of
it was different in either experiment. When it was simply a flat
wooden platter, a peculiar resonance was not noticeable.

The degree of sensitiveness is. inversely proportional to the size
of the mirror. A mirror of 2 mm. in diameter and 60 w thickness,
hung up by a Wollaston fibre of 2u have thus far proved to be
the smallest dimensions for easy handling. In the same proportion
the auditory canal should also be made narrower. Since we
generally experiment on continuous waves (only e, yields a sta-
tionary wave), the distance at which the mirror is placed is of little
consequence, provided it be axial. The sensitiveness is about inversely
proportional to the distance from the aperture. It is remarkable that
acoustic attraction will often concur in the case of powerful sounds.
It should be precluded by all means. ') Electric attraction is obviated
by connecting the auditory canal with the point, from which the
mirror is suspended, by a small metallic chain. Should rather high
tensions occur in the neigbourhood, also a conductive connection to
the earth should be constituted.

In physiological experiments the walls of the space in which the
mirror is suspended, are generally lined with gauze, which method
was also followed by ZerrNov. To this there can be hardly any
objection, when experimenting with receiving funnels, the progres-
sive sound being in large part transmitted to the mirror along the
artificial canal. What is conducted from other quarters may be
disregarded altogether. }

The afferent tube is fitted to a copper plate. A more accurate
axial position must be effected by means of three adjusting screws
at the foot of the apparatus. The distance from the mirror to the
aperture of the tube is determined by a horizontal measuring
microscope mounted on a heavy vertical Lerrz-stand.

§ 2. Physical measurement.

If instead of experimenting on the intensity of audible sounds
we wish to determine the objective intensity of a pure sound-
motion, auricle and auditory canal are of course disturbances. For
this purpose a conduit of a more physical nature is desirable.
The simplest is either a tube or a cone. A tube, if short, is liable
to become a resonator with a very sharp and narrow resonance.

1) Attraction seemingly acoustic, but in reality involved by eddies, will occur
with any fine puncture in the canal or in the membrane.

1 hes

168

Mr. Ws. van per Erst, assistant in our laboratory, established the
resonance curves of such small resonators by shutting off one end
of the tube with wax and placing a suitable mirror before the open
end. In very long tubes the tone of resonance is so low, that it
need not be taken into account. Earlier experiments on the propa-
gation of sound in air showed that there is a marked decrease in
the velocity of propagation, when the tubes are narrower than
4 mm. This at least is the case, when they are made of india-rubber.
It must be deemed advisable, therefore, to take glass or metallic pipes of
no less than + 4 mm. in diameter. A mirror of, say 3 mm. diame-
ter, placed just in front of a straight-cut aperture, will be found very
suitable in most cases. Still, for very high tones even this pipe is
too narrow, as was demonstrated by researches years ago‘). The
tones of GALTON’s whistle (six-legerlined octave) change, when passing
through a canal of from 3—-5 mm. bore, which after the foregoing
need not cause surprise, the tones lying near the upper limit of
musical sounds. We found it suitable to provide the afferent tubes
with leaden taps*). The sound conducted to the measuring apparatus,
may be generated at a considerable distance.

Another simple conduit is the cone. The funnel may be given an
angle of 40° and a mouth of 50 cm’. Some American hearing
apparatus (operaphone) are provided with a similar funnel. HELMHOLTZ
discusses its resonance in his “Tonempfindungen”. The one
I used, resounds to d,. This is easy to determine when an opening
is left in the apex of 2 mm., before which the RayLeiGH mirror is
placed. The latter will deflect considerably, when the tone. of
resonance is given. With all other tones the waves will be progres-
sive, the cone being merely an indifferent receiving funnel. Again
a small plug of cotton wool had to be used to arrest disturbing
streams of air.

§ 3. Point-shaped soundsources.

Outlets in the shape of a mere puncture are obtainable through
a fine orifice, say of 1 mm. 1. in a little leaden dise that serves
for a septum in a speaking tube; 2. in the covering disc of the
air-chamber of a thermoteleplione. In either case the mirror is placed -
right opposite to the fine opening, through which the sound is con-

1) H. T. Minkema, On the sensitiveness of the human ear to the various tones
of the gamut. Dissertation Utrecht 1905.

2) H. pe Groor, Zschr. f. Sinnesphysiologie Bd. 44 S. 18 (experiments by
Dr. vaN Mens) and these Proceedings Vol. 14 p. 758 (experiments by Dr. P.
NIKIFOROWSKY). |

169

ducted. Either method allows of altering the sound at will, the
number of sounds and intensities, transmissible through a long, wide
pipe to the diaphragm, being indefinite. The tones embraced by the
thermotelephone are also a great many, from the low, non-coalescent
tone of an interruptor to the high hissing-sound *). Likewise the
intensity of the thermotelephone-sound can be varied through artificial
appliances within far-extended limits. Selection occurs with the latter
appliance only as far as the peculiar tone of the air-chamber is con-
cerned, but when the air-chamber is small — as is deemed advisable —
it is so high, that it may be left out of calculation.

Both methods yield progressive soundwaves, whose energy is
constantly procured by the generator, and emerges through the point-
shaped orifice of 1 mm. If the latter is in circuit with an air-chamber,
through which the sound is conveyed to the measuring mirror, the
results vary roughly according to the size ‘of the chamber. The
differences are markedly perceptible with an outlet of ‘/, mm. in
diameter. As original sound-generator may be used a telephone,
actuated by: an electrically driven tuning fork or a large powerful
organpipe.

§ 4. Investigation of resonators.

The mode of arrangement can also be easily applied to test reso-
nators. When a puncture (2 mm.) is made in the wall of the reso-
nator, right opposite to the mouth, the sound passing through it
may readily be directed on to RaYreiH’s mirror via a canal of the
same bore’). It will be expedient, however, to arrest by means of
a very small plug of cottonwool or a piece of lint, the streams of
air escaping, like the sound, through the fine opening of the resonator.
Without this precaution the mirror will never be steady, not even
in a perfectly quiet environment.

The sound thus emitted through the puncture, is made up of
progressive waves. By means of a long tube it can also be sent to
a comparatively long distance, provided that fresh acoustic energy
be constantly supplied through the orifice. The energy collected and
adjusted in the resonator, emerges via the fine opening, as well as
through the wide orifice. A mirror, subjected to these progressive
waves, deflects, when the amplitudes are small, proportionally to the
amount of acoustic energy produced. Spherical resonators yield fairly

1) According to the assistant W. v. p. Ersr the pitch agrees with the tone of
resonance of a Cs resonator (8000 v. d.).
2) H. ZWAARDEMAKER, Multiple resonantie. Ned. Tijdsch. v. Gen. 1913, II. p. 640.

170

symmetrical resonance curves (see le. p. 642); those generated by
paraboloid-shaped resonators or such as are more complicated, like
some hearing apparatus, are surprisingly variable *).

A very curious shape of resonators is offered by tbe familiar shells,
found on the beach after stormy weather, and in which the mur-
muring of the rolling waves is heard. Here numerous tones coalesce
into a murmur. Testing them involves peculiar difficulties for the
very reason, that narrow conduits are not appropriated to the exa-
mination of high tones. Nonetheless the difficulty can be overcome
by exposing the measuring mirror directly to the point-shaped outlets,
afforded by the fine openings in the wall of the shell.

Chemistry. — “The viscosity of cotloidal solutions.” By Dr. E. H.
Bicunwr. (Communicated by Prof. A. F. Hort.eMan.)

According to Einstein, the viscosity of a liquid, in which a great
number of particles are floating, is connected with the relative total
volume of the particles. If the viscosity of the pure liquid is repre-
sented by z, that of the suspension by 2’, and its volume by », if
further v’ is the total volume of the suspended particles, then

'
ae

= 2,5—
z Vv

This formula has been applied to gamboge suspensions by BANCELIN,
who obtained fairly satisfactory results; the factor had to be taken,
however, 2,9 instead of 2,5. Admitting the formula to be correct,
we may, conversely, calculate the volume of the floating particles
from measurements of the viscosity. If, then, we determine the
number of the particles (e.g. ultramicroscopically), the volume of
one separate particle may even be deduced.

The application of this formula to colloidal solutions will greatly
deepen our insight in the nature of these systems. We might feel
some doubt, whether the suppositions, made by Ernstein, when
deducing the formula, hold good in the case of colloidal solutions,
the particles of which are so much smaller. But Ernster himself
has applied it to sugar solutions, and has calculated from the result,
in connection with determinations of the diffusion constant, AVOGADRO’S
number. The fact, that he found in this way 6,6.107*, shows, that
his assumptions are not far from being correct. For the rest, 1 have
found, that even several observations on the viscosity of ordinary

1) H. ZWAARDEMAKER. These Proceedings, Vol. 16, p. 496.

solutions may be represented by the same formula, as I hope to
show in a more detailed paper. There is, therefore, no objection to
the application of the formula to colloidal solutions, which, according
to modern theory, stand between the ordinary solutions and the
suspensions or emulsions, and differ from these only with regard to
the size of the ‘dissolved’ particles. For the present, it is not of
much importance, that the value of the factor is not yet absolutely
settled. In this communication, I only wish to show at least quali-
tatively, that the colloid particles are combined with a quantity
of the solvent. For instance, the ultramicroscopically visible particles
of a ferric hydroxide solution consist of a number of molecules
ferric hydroxide and a number of molecules water ; these are moving
as an aggregate in the surrounding liquid. A great viscosity is
to be ascribed to a great volume of the colloid particles, either
they are very great themselves, or they take up much water. It
must be pointed out, that, when comparing different solutions,
one ought to express the concentration in volume percentage, because
according to the point of view here adopted, the viscosity depends
only on the volume of the dissolved particles.

The idea may also be applied to ordinary molecular solutions.
The fact, that the viscosity of solutions of electrolytes is often
relatively large, may be brought in connection with the property of
the ions, to combine with or to envelop themselves by water, a
faculty of which numerous investigators have furnished proof on
the most different grounds. In accordance with this conception, the
salt solutions, the ions of which show the smallest tendency to
hydration, exhibit the smallest viscosity. But, for the present, I
will not enter further into this question.

I have only to communicate measurements of two substances,
molybdenum blue (Mo, O,?) and iron hydroxide. I have determined
at 30° and 40° the viscosity and specific gravity of some solutions
of varying concentrations. The values for the two temperatures diffe-
ring only slightly, the communication of the results at 30° will be
sufticient. In the subjoined table 2’ represents the viscosity of the
solution, that of water being taken = 1, v’ the volume of the particles,

deduced from z’ according to ZA; v is put equal to 1 ce.
The concentration of the solutions c is expressed in g per c.c.; d’
is the density thereof. As dissolved substance I regard the molyb-
denum blue, dried at 100°, respectively the ferric hydroxide : Fe(OH), .
The concentration of the solutions of the former is known, for they
are made by weighing; the content of the latter is determined iodo-

172

metrically, the hydroxide having been first converted into chloride.

Molybdenum blue Ferric hydroxide

c | d' 3! v' c d’ 8! v'

0.0199 | 1.014 1.042 0.017 0.014 | 1.011 | 1.034 0.014

0337 | 1.022 | 1.066 026 037 | 1.026 | 1.082 033
0511 | 1.034 | 1.091 036 074 | 1.051 \ 1.192 077
0969 | 1.064 | 1.168 Rr |

1943 | 1.137 | 1.390 156

From this table we deduce at once, that the volume of the dispersed
particles is considerably greater than would be expected, if these par-
ticles consisted of molybdenum blue, resp. iron hydroxide only. The
specifie gravity of the molybdenum blue used was found to be 3,1
at 12°, that of the iron hydroxide may be put equal to about 4.
The volume of .0511 g¢ molybdenum blue in the solid state is there-
fore .O17 ec, and here we calculate for the dissolved particles
‚036 ec, more than the double value. For the iron hydroxide the
proportion is still greater, and even rises to about 4. These results
show conclusively that the colloid particles condense water mole-
cules around themselves or combine with them, and that the hydroxide
takes up more water than the molybdenum blue. Although it has
often been maintained that such dispersed particles would be composed
of colloid and water, it has, I think, never been so clearly demon-
strated by experiment.

We may also proceed in a slightly different manner, and calculate
the density of the particles. Let us imagine a volume v of the liquid,
in which particles having the total volume v’ and the density D
are floating; the total weight of the particles being consequently v’ D.
Let further d’ represent the density of the solution, and vd’ its weight.
Now, the volume of the “free” water, that is the water, which is
not combined with colloid particles, will be v—v’ ; if its density be
called d, then we have

v' D = vd' — (v—v'’) d.
D=—(@'-d+4.
v

Therefore

173

2,5

As the specific gravity of the solution must be determined for the
viscosity measurements, it is easy to deduce the specific gravity of
the particles. We find for molybdenum blue 1,83 to 1,93; for iron
hydroxide 1,66 to 1,8. In this manner too, it becomes clear, that the
particles suspended in the liquid cannot consist only of dissolved
substance, the density of which is 5 or 4, but must also contain
water. As has already been pointed out, the qualitative value of
these conclusions is not attacked, if it should appear, that instead of

U U
v

v
2,5—, for instance, 3— must be written. Neither would this be the
v v

case, when we introduce into Ernstein’s formula the second power of

es is necessary for the more concentrated solutions.

{ hope to discuss later from the standpoint taken in this paper,
the viscosity measurements previously published by other observers,
A preliminary investigation already led to remarkable results, but
a great part of what is known, cannot serve my purpose ; I propose
to fill up this lacuna by new determinations, and to discuss then at
length the many questions, which arise in this field.

Inorg. Chem. Lab.
University of Amsterdam.

Physics. — “Some Remarks on the Capillarity Theory of the Crystal-
line Form’. By Prof. P. Earenrest. (Communicated by Prof.
H. A. Lorentz).

(Communicated in the meeting of May 29, 1915).

§ 1. As is known, W. Gipps') and P. Curie) have set forth the
following view, and given further thermodynamic grounds for it.
A crystal in a solution is in thermodynamic equilibrium only when
it has that shape in which its surface energy has a smaller value
than for any other shape with the same content. That this equilibrium

1) W. GrBBs: Thermodyn. Studiën p. 320.

?) P. Curie: Bull. de la Soc. Min. de France 8 (1885) p. 145 of Oeuvres p. 153.
Cf. for the relations between the theories of GrBBs and Curie:

J, J. P. Vateton: Kristalvorm en oplosbaarheid. Proefschr. Amsterdam 1915,
Ber. d. Sächs. Ges. d. Wiss. 67, (1915).

174

shape is not the sphere (i.e. the form with the smallest surface) but
a polyhedron, is according to Gisss and Curie owing to the following
circumstance. The surface energy of a surface element depends in
a crystalline substance on the orientation of the surface element
with respect to the crystalline substance, i.e. on the indices of the
surface elements, and this in different ways for different substances.
If 4,,4,,45,... are the capillarity constants of the differently
orientated bounding planes; S,, $,, Sit .. the corresponding areas of
the surfaces, V the volume of the crystal, then the equilibrium
form is characterised by the condition:
= k, S,= min. for V =€onst: . . 9.) ee
G. Wore’) has derived a remarkably elegant geometrical property
of the equilibrium diagrams from (1), which greatly facilitates the
following expositions: In a figure characterised by the minimum
condition (1) there always exists a point W (we will call this Wurrr’s
point) lying so that the distances n,,n,,.... of the different surfaces
S,,S,... from W are directly proportional to the constants &,, h,,...
, ben Eh skinken ee EN
This theorem of Wutrr’s immediately furnishes a construction of
the equilibrium figure, if for every direction of the normal the
corresponding value of # has been given. Draw from an arbitrary
point W of the space in all directions lines whose lengths are propor-
tional to the corresponding 4’s and apply planes normal to them
through their endpoints: then there remains a space in the neigh-
bourbood of IV, where none of these planes enters — this space is
the required crystalline form. It is seen here at once that surfaces
with a comparatively large value of / lie so far from JV, that they
cannot constitute a part of the boundaries of the crystal ?).
We derive the “law of the (small) rational indices” therefore
in this theory in consequence of this that the surfaces with small

n 2 8

index values in general must also possess particularly small capilla-
rity constants 4.

1) G. Worrr: Zschr. f. Krystallogr. 34 (1901) p. 449. The proof, which Wurrr
had given in an imperfect form, has been improved by Hitron afterwards:

H. HiroN Centralbl. f. Miner. 1901 p. 753 = Mathem. Crystallogi. (Oxford 1903)
p. 106. Cf. H. LreBMANN. z. f. Kryst. 53 (1914) p. 171:

2%) Let in the regular system e.g. the k’s of cube planes be %}, those of the
octahedron planes ky. It is required for the octahedron planes to occur by the
side of those of the cube that:

Vs ve

See: CURIE loc. cit. and Wurrr loc. cit.

175

As is known, this theory of Gisss and Corie’s plays a very im-
portant part in the erystallographical literature. Frequent erystallo-
graphical applications have been made of it’); it has been now and
then extended by the introduction of ‘side energies” and “angular
point energies” by the side of “surface energies” #,, k,..., and by
making the former have a share in the determination of the equilibrium
figure *); of late years criticism has not been wanting either, which
now and then even comes to a full rejection of Grsss and Curtn’s view”)

On the other hand it seems that except Sonnke’s indications ‘),
which concur with Bravais’ views, no attempts have been made as
yet to interpret the energetic theory of GiBBs and Curie in a mole-
cular scheme. Such an attempt would be the more desirable as there
is in this region a whole series of dark or paradoxical points to be
analysed.

In view of the great difficulties which are to be overcome here,
J should like to confine myself to a single of these points, and
demonstrate how this can entirely be elucidated by the aid of an
extreme simplified molecular scheme. It is seen the more clearly
on this occasion how much there remains to be done to elucidate
other points.

§ 2. Does the capillarity constant of a crystal plane depend con-
tinuously or discontinuously on its orientation? The problem of the
vicinal planes.

The polyhedrical shape of the crystals and the law of the small
rational indices easily gives rise to the supposition of a discontinuous
dependence ; accordingly it seems to have been made, at least impli-
citly by most erystallographers, as soon as they made use of Gipps
and Curte’s theory. Explicitly it is found expressed in two often

1) Chiefly to be able to draw some conclusions on the structure from the
crystal form see: Weoporow, Z. f. Kryst. Vol. 34—53, compare also the appli-
cation to twin formations H. Hirron. The energy of twin crystals. Mineralog.
Magazine 15 (1909) p. 245.

2) BRILLOUIN. Ann. Chim. Phys [7] 6 (1895) p. 540; Vernapsky. Bull. de la
Soc. Imp. de Naturalistes de Moscou 1902 p. 495; P. PAwrow. Zschr. f. Kryst.
40 (1905) 189; 42 (1906) 120; Zschr. f. phys. Ch. 72 (1910) p. 385.

8) A. BertHoup. Journ. de Chim. phys. 10 (1912) p. 624; G. Frieper. Journ.
de chim. phys. 11 (1913) p. 478. — Cf. also J. J. P. VALEron. Thesis for the
doctorate. loc. cit.

4) F. Sonnxe. Ueber Spaltungsflächen und natürliche Krystallfl. Z. f. Kryst. 18
(1888) p. 214.

176

cited papers by F. Sonnke and G. Worrr *). Both these authors
namely assume that the capillarity constant of a crystal plane (apart
from a factor which continuously changes with the orientation) is
in inverse ratio to the net density of the plane in question *).

This net density, however, is, as is known, a very discontinuous
function of the orientation: thus for irrationally orieutated planes,
which have been rotated however little with respect to the plane
(1,4, 1), the net density would still be infinitely small in proportion
to that of the plane (1, 1,1). Here the exceptional function of the
planes with the smallest indices is at once seen.

In spite of this appeal to the relation with the net density the
supposition that the capillarity constant depends discontinuously on
the orientation, will yet be thought very uncommon, if not quite
paradoxical! Besides it involves a great difficulty for the frequent
occurrence of the so-called “vicinal planes”. *)

For according to Sounke and Werrr these planes with particularly
large indices (which are practically irrationally orientated) would
possess extraordinarily large surface energy. Of course we are willing
to admit deviations from the theoretical equilibrium figure, taking
into consideration the small disturbances which are never entirely
to be excluded (fluctuations of temperature, disturbances in the con-
centration ete.) But yet totally unexplained and even paradoxical it
remains when these slight disturbances give rise exactly to those planes
with extremely large surface energy, and particularly those which lie
very near to the planes with particularly small surface-energy ‘).

1) F. Sounxe. Zeitschr. f. Krystallogr. 13 (1888) p. 221; G. Wutrr. Zeitschr. f.
Krystallogr. 4 (1901) p. 526. Gress and Curie do not give any further indication
on the continuous or discontinuous character of the dependence.

2) Wutrr gives this formula and characterises the gist of SonnKe’s conceplion,
partly in Sounke’s own words in the following way: “Nach Sohnke muss ein
Zusammenhang zwischen der Oberflichenergie einer Kristallfläche und ihrer Flachen-
dichtigkeit bestehen. Nämlich für eine kläche von dichtester Besetzung können die
Molekularkräfte keine Arbeit mehr leisten, weil die Theilehen einander nicht weiter
genähert werden können: die potentielle Energie einer solchen Fläche muss also
ein Minimum sein. In dem Masse, als die Flächendichtigkeiteu der verschiedenen
Krystallflächen geringere sind, müssen die Oberflächenergieen (Capillarconstanten)
grösser sein....

5) By “vicinal planes” we understand planes which differ exceedingly little in
situation from the planes with small indices.

4) H. Miers, Rep. of the Brit. Assoc. 1894 p. 654; Z. f. Kr. 9 (1904) p. 220
bas demonstrated experimentally through accurate goniometric measurements during
the growth of alumn crystals, that the planes with small indices in this case (1, 1, 1),
practically. never occur, but nearly always vicinal planes. Cf. also CG. Vrora, Z. f.
Kr. 35 p. 332.

$ 3. Geometrical-physical interpretation of the capillary-constant for
a special molecular scheme ; the surface energy appears then as continuous
function of the orientation, and yet produces a polyhedron as equili-
brium figure. The function of the ‘vicinal planes”.

To throw this point into strong relief, the point which is our only
purpose here, we make use of an exceedingly simplified molecular
scheme :

1. a two-dimensional scheme instead of a three dimensional one ;

2. we leave the thermal motion out of account and accordingly
we simply seek the molecular groupings with the smallest potential
energy ;

3. the molecules may be squares, which tend to adjust their sides
close against each other. (We might as well use circular molecules
with four points of valency).

Let an enormously large number of such square molecules be
given. We seek that grouping at which the maximum “saturation”
of the molecules has set in. Complete saturation, at which all the
molecule sides are occupied, is of course impossible — at least the

Big. 1.
extreme edge of the “crystal” consists of unsaturate molecule sides.
Let in fig. 1 the line AGCDE... be a portion of the “real” edge,
the line ACH... a portion of the “apparent” edge. Let us put:

ABC = Ao ‘and! AG = Xe
then:
Lo = (cos p + sing) As.
The maximum saturation has evidently been reached for that
grouping of the molecules, for which the length of the real edge, i.e:

EO == Sees ogee (2)

178

happens to be as small as possible. Hence the quantity:
k= (cos (pict si PE. el > oo Ce eee
plays the part of the capillarity factor in our scheme.

It is seen that:

A. the capillarity factor & is here a continuous function of the
orientation of the element of the apparent edge, which is the subject
in view here. (To get a graphical representation, & should be con-
sidered as function of the direction of the normals to the edge
element, and distances should be projected from a point W in all
directions, which are proportional with the values of & for this
direction of the normals. We obtain the curve dotted in figure (2),
which is composed of 4 ares of a circle.

Fig. 2.

B. Yet the “equilibrium form” corresponding to it is a square.
This is immediately to be seen by the aid of the construction men-
tioned in § 1. See fig. 2: W is Wuxrr’s point: WN is proportional
to & for this direction of the normal. If the straight line AZ is
constructed for all directions WAN, they envelop conjointly the
square drawn in fig. 2.*)

C. The occurrence of “vicinal planes” involves in our scheme no
deviation worth mentioning from the minimum of energy. For our
k depends continuously on the orientation, and the vicinal planes
are only exceedingly little rotated with respect to the planes of the
form of equilibrium. Here the contrast with Soanke and Woter’s
supposition stands out very clearly.

D. Strictly speaking the form of equilibrium can do without vicinal

1) By slight changes in the definition of the scheme another dependence of k
on the orientation can be obtained, hence other equilibrium polygons.

179

planes only in particular cases. Indeed: if the number of molecules
happens to be the square of a whole number, then the form of
equilibrium is exactly a square. When however successively more
molecules are added, they must adjust themselves somewhere against
the square to get maximum saturation, which leads to vicinal planes.

(In the formulae of § 1 this circumstance remains concealed,
because there it is considered that the minimum must be determined
with respect to infinitesimal changes of form. Here we realize,
however, that it is a question of addition or displacement of a:
whole number of molecules).

§ 4. Observations. A. If a certain number of molecules is originally
grouped in the form of two squares of different sizes, potential
energy may be still diminished by the removal of a row of molecules
from the small square, which are then laid against the large square.
Decrease of energy also takes place when a rectangular grouping
is changed into a square one. Until we take the temperature motion
into consideration and consider the process of solution and sublima-
tion, we can of course not ascertain whether in our molecular
scheme these transitions will take place spontaneously. A somewhat
trustworthy treatment of this question seems difficult to me, because
for this the unevennesses of the edge are to be considered, i.e. those
molecules which at a given moment are only bound singly or doubly,
and not threefold.

B. It has been experimentally proved that for erystal powder e.g.
of gypsum with a radius of about one micron the saturation concen-
tration of the solution around it still appreciably depends on the
radius. But for a radius of some microns this dependence already
loses its significance with respect to disturbances of various nature.
In virtue of this doubts will rise as to whether the changes discussed
under A will appear spontaneously, and whether the actually occurring
crystalline forms really agree with a minimum of surface energy *).
Shortly ago VaLeron*) defined this view in the following way:

“For microscopic and submicroscopic crystals the surface energy
has a measurable influence on the solubility. Such erystals can be
in equilibrium with a solution only when their form corresponds
with the minimum of surface energy. For macroscopic crystals this

1) A. Bertuoup, Journ. de Chim. Phys. 10 (1912) p. 624. — G. Frrieper, Journ.
de Chim. Phys. 11 (1913) p. 478.

2) Le. p. 42. Compare there the fuller report of Huterr’s experiments. Z. f. phys
Chem 37 (1901) 385 with crystal powder of gypsym and barium sulphate.

180

influence is practically not existing. With regard to the crystalline
form the equilibrium of these erystals is indifferent.

C. For our special model the whole still unused store of energy
may be comprised in the one expression

ak As

with which the surface energy of the crystal corresponds in the three
dimensional case; by the side of this there is left nothing that could
answer to an energy of angular points or sides in the three-
dimensional case, with which BrirLoviN, VeERNADSKY and Pawrow *)
work. Now however the model can be made more general by
making e.g. moreover those isotropic attractive forces act between
the molecules, with which LarLacr, Gauss, and vAN DER W aars work
witb action spheres, which still contain many molecules’). It remains
noteworthy that then actually special side and angular point energies
appear, whose numerical value remains undetermined for the present *).

D. We have for the present not entered any further into the
molecular interpretation of the cleavage directions. More recent views
on this head are found in a study of P. P. Ewarp *) on the structure
of diamond. It would be interesting to ascertain whether one has
also as a rule to do with vicinal planes of the ideal cleavage planes
in the cleavage process. For the rest it would not be sufficient for
a complete analysis of the cleavage process to ascertain what cleavage
planes break a minimum of bindings; also the elastic deformation
preceding the cleaving is in principle a factor to determine the orien-
tation of the cleavage planes.

1) See the citations § 1.

2) In this connection it may be mentioned that Einstein Ann. d. Phys. 34 (1911)
p. 165, comes to the conclusion from the law of Eörvös that also in liquids an
attraction may be assumed only between those neighbouring molecules that are
in immediate contact.

8) In the current derivation of the fundamental equations of the capillarity the
terms in question vanish, because in a certain point of the derivation the assump-
tion is made use of that the curvature rays of the surface remain everywhere
above a definite finite value. Cf. among others H. Minxowsk, Art. Kapillaritat,
Math. Encykl. V. 9, § 14, transition between equation (24) and (26). First of all
this supposition does not hold for erystal sides and angles, but moreover also
e.g. at the side in which three liquids are in contact with each other. BRILLOUIN,
Ann Chim. et Phys. [7] 6 (1895) p. 540 has demonstrated that the structure of
the groove which is formed when glass and other substances are scratched is
chiefly determined by the side and angular point energy.

4) Ann. d. Phys. 44 (1914) p. 281.

181

Chemistry. — “Action of sun-light on the cvinnamic acids”. By
Dr. A. W. K. pe Jone. 5

The continued investigation has shown that the peculiar behaviour
of cinnamic acid in the solid condition under the influence of sun-
light must be attributed to the ease with which it passes into the
metastable form. This metastable condition has been described first
by O. LeaMann *) in 1885. Ertenmeyer Jr. has communicated a very
lengthy investigation as to the existence of different forms of cinnamic
acid in the Ber. D. Ch. G. and further in the Biochem. Zeitschr.
He comes to the conclusion that of the normal ecinnamic acid
there exist four different modifications, namely «- and 3-Storax cinnamic
acid and «- and g-Hetero cinnamiec acid. Cinnamic acid derived from
plants consists of Storax cinnamic acid with but 0,5°/, of the Hetero-
acid whilst synthetic einnamie acid is a mixture of about equal parts
of those acids. On heating their aqueous or dilute-aleoholic solutions
the a-acids are converted into the g-acids. In Ber. 39 p. 1581, Ber.
42 p. 509 and Biochem. Zeitschr. 34 p. 355 some further conversions
of the «- into the g-acids, and the reverse phenomenon, are commu-
nicated. The cinnamic acid used in my experiments was Storax
cinnamic acid (probably derived from hydrolysed coca-acids; see
previous communication) as it was deposited from alcohol in the
well-formed, thick prismatic crystals of Storax cinnamie acid (in
Ber. 42, p. 504 are found the photographs of the various forms).
On repeatedly reerystallising from warm 95°/, alcohol which took
place in the said experiments the «-Storax einnamie acid is converted
more or less into the @-acid. This mixture ‘when illuminated always
yielded «- and g-truxillie acid. The transformation into g-acid was
much promoted, because after dissolving the einnamic acid in aleohol
the solution was made to evaporate rapidly by the shaking of the
dish. For it was noticed that when an alcoholic solution of «-Storax
cinnamic acid is poured on to a glass plate and the aleohol allowed
to evaporate rapidly by blowing, only erystals of 8-Storax cinnamic
acid are formed. These crystals when illuminated gave only }-truxillic
acid whereas the prismatic crystals of the «-Storax cinnamic acid
gave only e-truxillic acid. The crushing of the crystals caused no
change in the action of the light.

From the research is thus shown that «-Storax einnamic acid gives
a-truxillie acid when illuminated in the solid condition, whilst under
the same circumstances, 8-truxillic acid is formed from the 8-Storax acid.

1) Ber. 43, 461 (1910); Granam Orro’s Lehrbuch der Chemie Bd. I, 3e
Abth., p. 57.
13
Proceedings Royal Acad. Amsterdam. Vol. XVIII.

182

As to the connexion existing between «- and B-Storax cinnamie
acid, nothing is as yet known with certainty.

The oceurrence of differently crystallised forms of a substance
may be generally attributed to polymerism, isomerism or polymorphism.

In the first case the one form is a polymeride of the other and
thus possesses a double or multiple molecular weight, in the second
case the molecular weight is the same but the structure of the
molecule is different, whereas in the latter case where the difference
exists only in the solid condition and disappears both in the liquid
and the gas the arrangement of the molecules in the ‘“Raumgitter”’
is accepted by some as the cause of the difference whilst others
think that in this ease also, a chemical difference between the solid
forms is very probable *).

There has been no lack of efforts to determine the connexion
between the different forms of the cinnamic acids.

According to ErLENMEYER Jr.*) there exist eight forms of cinnamic
acid, namely four of the normal and four having as type a//ocinnamic
acid. The first four appertain to each other two and two and
according to ERLENMEYER, these pairs should exhibit differences in
the benzene nucleus.

Among the four a//oacids we find mentioned, in addition to the
three known acids, also a triclinic cinnamic acid, which he noticed
a few times during his research, but of which the mode of formation
is as yet quite obscure. ErLeNMeYeR sees in the different crystallised
forms different chemical substances and endeavours to explain this
case of isomerism.

I eannot find his effort, which he himself wishes to be looked:
upon as a sketch, a very happy one.

He reverts to the antiquated idea where the properties of a double
bond are explained by the presence of a single bond and free affini-
lies or as some express it, unoccupied affinity positions. Then, he
assumes that on turning one of the two carbon tetrahedrons, between
which the double bond exists, three different metastable forms ean
occur dependent on the different position of the groups on the one
carbon tetrahedron in regard to that of the other one. In this manner
he arrives at six different forms all capable of occurring in left- and
right-handed modifications. Three thereof belong to the type of the
normal cinnamic acid and three to that of the adloacid.

1) O. Lenman writes in “Die neue Welt der flüssigen Kristalle” 1911 p. SI:
“daraus folgt aber lediglich, dass diese chemischen Methoden nicht ausreichend >
sind, jede Verschiedenheit der Molekiile zu entdecken und dass man polymorphe

Modifikationen nicht olme weiteres als chemisch identisch betrachten darf,”
*) Biochem. Zeitschrift 35, 149 (1911) and following.

183

_ Opposed to this stands the view of BurmanN ') that the differences
of the adloacids must be attributed to trimorphism whereas Riper
and Gonpscumipt *) consider the occurrence of «- and 8-Storax cinna-
mic acid as a typical case of dimorphism.

The changes which «- and @8-Storax cinnamie acid suffer in sun-
light afford us a view on the difference existing between these acids
in the solid condition. The polymerisation products of these acids
are, as we noticed, «- and g-truxillie acid to which are attributed
the following formulae as being the most likely :

a-truxillie acid 8-truxillic acid

On CH —CH-— COOH © CH, —-CH — CH — COOH

| | | |
HOOG — CH — CH — C,H, C,H, — CH — CH — COOR

As to the position of the groups with regard to the plane of the
d-ring not much is known; in the case of 2-truxillie acid the proba-
bility is that the COOH groups are found at the same side.

From these structural formulae it is plainly perceptible that one
molecule of these truxillie acids is generated from two molecules of
cinnamie acid and that the different manner in which the combination

takes place gives rise to the occurrence of two truxillic acids.

Hence it must be assumed that there exists between «- and g-
truxillie acid such a difference that the first, by the action of
light, renders possible only a bond such as oceurs in e-truxillie acid,
whereas the #-Storax cinnamic acid must be such that only the
binding as present in p-truxillie acid can take place exclusively.

A different placing of the groups in the molecule in regard to
each other, which EmrieNMBYER suggests to explain the difference
between «- and B-. cinnamic acid cannot avail us as even then for
each formula the linking of two molecules can always take place
in such a manner that both «- and ?-truxillic acid can form.

If, however, we assume that the position of the molecules in the
erystals is different for the two acids, a different bond due to the
action of light might be coupled with this. The different behaviour
of the acids might then be looked for in a different arrangement
of the molecules in the ‘‘Raumegitter”’.

The following hypothesis may also be proposed. As is well known‘),
most probably all organic acids dissolved in hydroxyl-free solvents
possess double molecules. Hence there is a great probability that in

1) Per. 42, 184 (1909). Ber. 43, 569 (1910).

2) Ber. 43, 461 (1910).

3) Van ‘t Horr, Vorlesungen über theoretische und physikalische Chemie, zweites
Heft, pg. 52.

13*

184

the solid condition at least double molecules occur. The difference
between «- and B-cinnamic acid might then have its origin in the
manner in which the single molecules are placed in the double
molecule.

The difference between these two assumptions consists in this that
the first admits of a difference in the solid condition only, whereas
the second renders possible a difference for the solution also.

A further investigation will have to decide which representation
is in harmony with the facts. I hope to revert to this in detail,
shortly.

Physics. — “Some Remarks on the Osmotic Pressure’. By Dr.
J. J. van LAAR. (Communicated by Prof. H. A. Lorentz).

(Communicated in the meeting of May 29, 1915).

With much interest I read Prof. Enrenrest’s paper [in the
Proceedings of this Academy (April 1915)| on the kinetic inter-
pretation of the osmotic pressure.

However, I can concur neither with the deeper ground of his
interesting considerations, nor with the “Remarks” that are added
to them, which in some respect may be considered as resulting from
the foregoing considerations.

Prof. Enrenrest knows that I feel a special interest in the osmotic
pressure and its correct interpretation, so that he will no doubt
excuse me if I once more return to it.

I will therefore briefly summarize my objections, already set
forth in different papers’), in a number of Theses.

Tuesis I. The results of a kinetic theory must necessarily be in
accordance with the established results of Thermodynamics.

If the results of the kinetic theory differ from those of Thermo-
dynamics, the kinetic theory in question is not valid.

Tuesis Il. Through the equating of the molecular thermodynamic
potentials of the water in the solution and of the pure water outside
it [there exists namely only thermodynamic equilibrium between
the ‘water’ on either side of the membrane, as this is supposed to
be permeable only to water] the thermodynamic theory leads to’)

1) See particularly: Sechs Vorträge (1906), p. 17—36, and These Proc. of
June 1806, p. 53 et seq. Also Zeitschr. f. physik. Ch. 64, p. 629 et seq. (1905).

2) I gave this simple derivation already in 1894 (Zeitschr. f. physik. Ch. 15,
p, 463 et seq).

185

u (x p) = u (9, Po),
when u(v,p) is the molecular potential of the water in the solution
(in which x is the molecular concentration of the dissolved substance,
p the pressure of equilibrium), and u(O, p,) that of the pure water
(in which the concentration of the dissolved substance is 0, the
pressure of equilibrium p,).

Now:
az, p) = f(Z) + pre + ax* + RT log (1—zx)
ulo, p.) = f(T) + Por
and hence as in dilute solutions v, (the molecular volume of the

water in the solution) can be equated to v,') (the molecular volume
of the pure water):

(p—p.)% = — RT log (A— x) + az’,
or

RT
I Pt ferred eea Ten her (1)

when z represents the “osmotic” pressure. In this a is the so-called
“influencing” coefficient in consequence of the interaction of the
molecules of the solvent and those of the dissolved substance. It is
known that « is represented by the expression *) :

= a,b,’ +4,6,’—2a,,6,b,

— ’

in which the numerator passes into (6,/.a,— 6,Va,)*, when a,, =V aya,
can be put.

Tursis III. All kinetic theories, therefore, which for non-diluted
solutions lead to expressions which remind directly of the equation
of state of gases and liquids (e.g. with v—é ete., and without loga-
rithmic member) must be rejected. (Therefore the theories of Winp,
Stern and others).

Tuesis IV. For very diluted solutions (I) passes into
fide:

Van ’r Horr’s well-known equation. Yet it is easy to see that the
deviations for non-diluted solutions are much slighter than those for

1) wv, and v only differing in a quantity of the order z?, the difference can
always be thought included in the term ux?

2) See among others Z. f. ph. Ch. 63 (1908), p. 227228 (Die Schmelz- und
Erstarrungskurven etc).

186

the corresponding non-ideal gas state. (Cf. Sechs Vorträge p. 29—30,
and the cited paper in These Proe., p. 57 et seg).

Already from this we are led to surmise that the so-called osmotie
pressure has an entirely different ground from what the analogy of
the behaviour of the dissolved substance to that of the same sub-
stance in the corresponding gas state would lead us to suspect, and
that there is here no close relation, only analogy. Particularly the
occurrence of the term — log (1 — «) (which only passes into z at
v=) in the expression (1) for the osmotic pressure should have
admonished to caution. This term continues to exist in the most
dilute solutions.

Tresis V. If actually the osmotic pressure was caused by the
pressure of the dissolved substance (the old theory revived !), as
Enrenrest also assumes again, the pressure of the “sugar” molecules
against the semi-permeable membrane would cause the reverse of what
is actually observed. Then there would namely no water pass from
the side of the pure solvent through the membrane into the solution,

and give rise to the hydrostatic counterpressure — 2 in the
ascension tube of the osmometer — but this water would on the

contrary be checked, since the pressure in the solution would be
ereater from the outset than in the pure water !

Thesis VI. In reality the osmotic pressure is caused by the water,
penetrating through the semi-permeable membrane ito the sugar
solution, which gives rise to a hydrostatic pressure, which prevents
the further intrusion of the water. This excess of pressure a = p — p,
is the so-called “osmotic pressure’ of the solution.

Tuesis VII. Every theory, which would try to interpret the oceur-
rence of the osmotic pressure Kinetically, should be based on the
diffusion of the water molecules on both sides of the membrane.
Quite generally one- can assume then two solutions of different con-
centration v, and wv, on both sides of the membrane. If one confines
oneself to a solution of the concentration v« and pure water, one
has what follows: In the unity of time there diffuse a certain
number of water molecules of the pure water towards the solution,
and another number from the solution towards the water. But on
account of the solution containing less water than the pure water,
there will go — parallel with the prevailing diffusion pressure —
more particles of the water to the solution than the reverse.

In ordinary circumstances the dissolved substance (sugar) would

187

also diffuse, but this diffusion is now arrested by the semi-permeable
membrane, so that the diffusion is only brought about by the water.

Tuesis VIII. Apart from what actually takes place on or in the
semi-permeable membrane — hence when simply an imaginary mem-
brane is taken, which does allow one sort of molecules to pass
through, but not the other kind — it is easy to determine the just
mentioned numbers of diffusing molecules according to BorrzManN’s
method (in agreement with the kinetic interpretation of the thermo-
dynamic potential). (See among others Sechs Vorträge p. 20—21).
Then the required logarithmic member arises of its own accord.

Tuesis IX. If there is nteraction between the two kinds of
molecules, another term ev? simply arises by the side of —logd—2a).
If however «=O, as is the case for so-called ideal solutions (this
is also the “imaginary”? case to which E. alludes in his Remarks)
all the above remarks continue to be valid unimpaired — which is in
contradiction with E.’s view in his Remarks. The diffusion, the
intrusion of the water till the required excess of pressure has been
reached — everything remains the same.

E.’s opinion that the rise of the water in the osmometer can only
take place through the three factors named by him, of which the
interaction of the two kinds of molecules is one, must therefore be
rejected with the greatest decision.

To what absurdities this conception would lead appears from this
that when as dissolved substance a substance is taken with a very
high critical temperature, and when this substance yet forms an
“ideal” solution with water, without interaction (4 = 0), as is the
ease with many organic substances (also sugar), the partial vapour
pressure of that dissolved substance (e.g. sugar) is vanishingly small
with respect to that of water. So there does not take place any
“evaporation” at all. According to EK. the vapour pressure of the
Sugar would become equal to the osmotic pressure — which for a
normal solution amounts to no less than 24 atmospheres! In reality
the partial pressure of the dissolved sugar will perhaps amount to
a billionth m.m. in the imaginary case mentioned by E. (sugar is
about in that case).

Tuesis X. It appears in my opinion sufficiently from the above
that the kinetic interpretation of the osmotic pressure — which is
always reappearing again in new forms — is moving and has moved
in a wrong direction, and should again be founded on the simple

188

diffusion phenomenon, as was indicated by me already more than
20 years ago, and was further worked out by me ten years ago
(Sechs Vorträge |. c.).

OBSERVATIONS. Though I wish a long otium cum dignitate to
all incorrect kinetic theories, | would by no means be considered a
personal foe to the osmotic pressure — the significance of which for
the theory of the dilute solutions was set forth by van ’r Horr in
the ingenious way characteristic of him.

My earlier and later opposition was only directed against two
later introduced abuses (with which Prof. Earenrest of course entirely
agrees), namely :

1. Against the extension of the idea (thought as reality) to isolated
homogeneous solutions (i.e. when no semipermeable membrane is
thought to exist), in which of course no real pressure of 24 atms.
for every dissolved gr. mol. occurs.

2. Against the practical application of the idea to non-diluted
solutions, which application I thought undesirable in view of the
inaccuracies which then occur and which are not to be ascertained
— which can give rise to very erroneous conclusions (and have
indeed done so!). Then the general theory of the thermodynamic
potential (or free energy) is the obvious and sure way.

The evxistence of the osmotic pressure has never been called in
question by me. One does not give calculations and interpretations
of something that does not exist! But it exists only in a solution
that is separated by a semi permeable membrane from the pure solvent
(or from a solution of slighter concentration) — and manifests itself
then through a diffusion pressure from the pure solvent towards
the solution (so just the reverse of what the kinetic interpreters
imagine).

That the above described osmotic diffusion pressure for exceed-
ingly diluted solutions has a value as if the sugar molecules in the
sugar solution in the corresponding ideal gas state exert this pres-
sure, is a mere coincidence, only owing to the term — log (J—2)
of the so-called GrBBs’ paradox; which term, as we know, is kine-
tically in connection with the diffusion tendency of the components
of the mixture.

Only a kinetie theory of the osmotic pressure which starts from
the diffusion phenomenon, arrives at the term in question (Sechs
Vorträge, S. 20—21); all other theories, which imagine the pressure
in the sugar solution, only come to non-logarithmical expressions
wih stanly e (resp. €, U '/—), etc), which owing to their deri-

189

vation of course remind of the ordinary gas pressure, (law of Borre,
or for non-diluted solutions the formula of vaN DER Waars), but which
are to be called inaccurate in the most absolute sense.

Fontanivent sur Clarens, April, 1915.
Appendix during the correction.

In a correspondence on this subject with Prof. Enrenrest (Prof.
Lorentz was namely so kind as to send him my article) it has
become still clearer to me to what E.’s result, which in my opinion
is erroneous, is to be ascribed.

In his considerations he namely assumes (this had not appeared
to me from his paper) that the molecules of the substances do not
exert any action on each other, i.e. that all the forces and actions,
also those in the collisions, are neglected. (that the attractive forces
are neglected, does not affect the correctness or incorrectness of the
calculations). Prof. E. expresses this by saying: The water is quite
unaffected by the sugar present, and vice versa.

This is the very core of the problem. When the water is not
affected by the sugar present, then g(r)= (0), and no longer
u(x) = (0) + RT log (lr). In other words: B. works with substances
for which Gipps’s paradox has disappeared, and which have therefore
become entirely free from thermodynamics. Hence he could not

possibly find the expression — loy (1—v) corresponding to it.
Such extra-stellary, thermodynamic-free substances have of course
lost all diffusion tendency — which just causes the phenomenon of

the osmotic pressure. For if the water is quite unaffected by the
sugar present, there exists no impetus any longer for the water to
be displaced, so that the disturbed equilibrium (between concentrations
zw and O, or x, and wr) is reestablished.

As so many before him, Prof. B. has in my opinion allowed
himself be carried away (see e.g. p. 1241 of his paper) by the striking
analogy, which was already mentioned in Thesis IV above. That
we can only speak of analogy here, is no doubt clear after all that
was remarked above. The analogy pressure of E. and others acts
namely precisely in the opposite sense from the real osmotic pressure.
In the limiting case it is not v that is found instead of — loy (1—.),
but — wv! This mistaken opposite pressure is of course the conse-
quence of the perfect freedom of the sugar molecules assumed by
EB. and others, which molecules now begin to exert a pressure of
24 atms. per gr. mol. on the semi-permeable wall — a pressure
which of course is not exerted for ordinary solutions as we know

them on earth. And where E. speaks in his paper of the kinetic
interpretation of the osmotic pressure, it seems to me that he too
should work with substances as they exist on earth, and not with
such where Thermodynamics is eliminated.

For through the elimination of the actions between the molecules
just the “according-to-probability unordered kinetic” element (the
kinetic equivalent of Thermodynamies), which is brought about by
the mutual collisions has been done away with, and only the
“roughly kinetic” element remains, which then, moreover, leads to
to tbe opposite result.

In conclusion [ can adduce no better evidence of the validity of
my considerations than the following.

For a gas mixture (even if necessary of ideal gases) of e.g. O, in
N, — separated from pure N, by asemi-permeable membrane, which
does not let through O, — the osmotic pressure would just as for
liquid mixtures, be represented by the above equation (1). Here
too the gas mixture would rise in an ascension tube (in consequence
of the diffusion tendency of the pure nitrogen) till the necessary
counter pressure had been reached, which then prevented the further
intrusion of the nitrogen. But here too “the osmotic pressure” starts
from the pure nitrogen outside the mixiure, and not from the O, in
the mixture. That there is here no question of a separate excess of
pressure of the O,, appears from this that at the beginning of the
experiment the gas pressures on the two sides of the membrane are
perfectly the same, (both = 1 atm.), the sum of the partial pressures
of the O,-+ that of the N, of course being precisely equal to the
pressure of the N, on the other side of the membrane. The excess
of pressure does not make its appearance until after the appearance
of the diffusion — and arises, as has been said, from the pure
nitrogen.

These observations, which in my opinion are conclusive for this
problem, have already been made and elaborated in my Lehrbuch
der Mathematischen Chemie (1901), p. 380-—81.

4 May. 1915.

191

Anatomy. — “On the metamerological signification of the cranio-
vertebral interval.” By Dr. J. A. J. Barer. (Communicated
by Prof. L. Bork).

(Communicated in the meeting of May 29, 1915).

In the so exceedingly extensive literature concerning the history
of the development of vertebral column and cranium two problems
chiefly draw continually the attention: the so-called resegmentation
of the vertebral column (Neugliederung der Wirbelsäule) and the
metamery of the cranium.

Both problems have been studied circumstantially, and the biblio-
graphy of both can boast of classical essays from the best days of
morphology. The more remarkable it must be ealled, that the two
fundamental views, that served as a guide to the numerous investi-
gators in this department, and, which, at presentat least, in principle,
are pretty well generally admitted, have constantly been studied
separately, and never yet in their mutual relation.

It is especially to this fact that 1 wish to fix the attention in this
communication, in order to show in this way at the same time, how
for this reason the signification of important carefully stated facts
has remained unobserved.

Since GorrHn and Oxen expressed in the “Vertebral theory of the
cranium” for the first time the idea, that the bones of the cranium,
at least those of mammals, could be grouped into a number of
segments, which show some similarity with vertebrae, the doctrine
concerning the metamery of the cranium has passed through a long
period of development. It is superfluous to describe here this histo-
rical development already for this reason that most of the manuals
give a summary of this idea more detailed than seems desirable in
the short compass of this communication.

It may suffice to point out, that the question that was put when
this problem was investigated, has constantly varied, and that the phases
of development of this idea can probably be best characterized by
the following formulations of the problem.

1. Are there evidences that prove, that the cranium has been con-
structed of a number of segments corresponding to vertebrae ?

2. Is the cranium, or at least part of it, formed in its embryonal
development in a similar way and of equivalent material as the
vertebral column ?*

3. Are there indications, that make it probable, that at least part

192

of the cranium was segmented in a previous period of the phylo-
genetical development ?

In this last form the problem is at the present moment still being
discussed, though the arguments that are now brought forward to
enable us to come to an affirmative answer of this question, are of a
character quite different from those which GEGENBAUR, who was the first
to formulate it in this way, developed for it. At present the state of
the problem is indeed so, that a positive answer of the question is
no longer contested by any of the investigators, and they only do
not agree in stating how great the part of the cranium is, over
which the mentioned segmentation extends.

In connection with the much earlier ontogenetical investigations
of RATHKE, GEGENBAUR distinguished in the cranium 2 parts, a frontal
not segmented part and a posterior segmented part. The two parts
are designated as the vertebral part and the praevertebral one.

According to GEGENBAUR, who formed his theory from the pheno-
mena of the Selachier-cranium, the vertebral part would form by
far the greater part of the cranium ; only the region in which the
N. opticus and the N. olfactorins pierce through the skull, would
belong to the praevertebral region. The vertebral part constructed
by fusion of about 9 cranial vertebrae would be primary, and it
is only after concrescence of these elements, that the praevertebral
part would have been developed by exerescence in a frontal direction
of the cartilageous part formed in the above mentioned manner,
under adaptation to the olfactory groove and the optical organ.

We do not find with GEGENBAUR a primitive part of the cranium, —
principally to be distinguished from the other segmented part of the
cranium —, which ought to be maintained as real primordial cranium
contrary to the vertebral column. The body of vertebrates consisted
of a number of equivalent segments. The frontal part of these has
fused for the formation of the cranium, the posterior part forms the
vertebral column, Secondarily, by excrescence, an unsegmented part
has still been added to the segmented part of the cranium.

STÖnHR added to this the opinion that the number of segments
used for the construction of the cranium is not constant, and con-
tinually increases in the series of vertebrates. The craniovertebral
interval shifts consequently more and more in a caudal direction.
Other investigators could confirm the correctness of this view.
SAGEMEHL succeeded in showing, that the cranium of higher developed
pisees and of amniotes has increased in a caudal direction with 3
vertebrae. This cranium would consequently be the Selachiercranium

193

Augmented with 3 vertebrae. With regard to the formation of the
Selachiercranium SAGEMEHL is of the same opinion as GEGENBAUER. It
would namely have taken existence from metameres. It is however
of great importance to remark here, that, according to SaGument,
these metameres had not yet the character of vertebrae, and that
consequently the fusion-progress of these metameres in order to form
the Selachier-cranium is not equivalent to the addition of the 3
vertebrae to the Selachier-eranium, which we observe with higher
pisces and amniotes.

SAGEMEHL calls the Selachier cranium protometamere, the cranium
enlarged by the addition of 3 vertebrae auximetamere.

Van Wijgr showed that with Selachiers 9 segments (primordial
vertebrae, somites) can be distinguished at the dorsal head mesoderm,
which correspond entirely with and are equivalent to those of the
trunkregion. GEGENBAUER’s view, that the head would be nothing
else but a transformed part of the trunk, was certainly supported
by this discovery. Van Wisun's discoveries were however not of
such great signification for the skeleton, as he could show, it is
true, that sclerotomes originated from the primordial vertebrae, but
it appeared likewise from his investigations, that this segmentation
of the primitive formation of the skeleton was immediately again
suppressed.

The investigations of Froriep are of great importance for the
problem of the cranium metamery.

Froriep likewise distinguishes 2 parts of the cranium, one formerly
segmented part and one unsegmented part. In this respect he con-
sequently agrees with GEGENBAUR. Not so however with regard to
the place of the boundary-line between the two regions. According
to GRGENBAUR this boundary-line would be situated far frontally, and
the unsegmented part would be restrieted to the part of the cranium,
formed secondarily in the neighbourhood of the olfactory groove
and the optical organ. Frokimp however admits as boundary-line
between the two regions the spot, where the N. Vagus pierces through
the base of the skull. The earlier segmented part is thus, according
to Frormpr, but very small and confines itself only to the occipital
region. Frorike showed now that with cow and hen this occipital
part behaves ontogenetically as the frontal part of the vertebral
column, and consequently shows likewise the design of primordial
vertrebrae, vertebral arches and nerves, whilst in the region lying
before the vagus nothing is perceptible that could be compared to
the segmentation in the spinal trunk-region. In accordance herewith
Froriep distinguishes in the cranium a spinal and a praespinal part.

Lod

What Frorine could show with regard to the N. hypoglossus is
likewise of importance. He found namely in the course of this
cerebral nerve, always conceived as purely motorical, spinalganglions,
and so it was obvious that this nerve would be nothing else than
the complex of the nerves belonging to the spinal cranium-region.

This view of Frorirp’s concerning the spinal character of the
occipital region of the cranium finds in reality no longer con-
tradiction. From all sides confirmations of his discoveries have come
also with other species of animals. Everywhere it has been possible
to indicate that embryonally the occipital part of the cranium shows
great similarity with the vertebral column. The part of the problem
regarding the metamery of the cranium has ceased to be’a problem.
At best there is only question of the number of metameres, that
can be distinguished in the spinal part. The question after the origin
and the eventual segmentation of the part in front of the N. vagus
still remains. On this point the views are still divided. For us it
has for this moment no interest.

What is interesting for us, is the fact, that the most caudal part
of the cranium, i.e. the occipital part, shows distinct proofs of a
previous segmentation which corresponds entirely with that of the
region of the vertebral column. It is of importance to emphasize
here already that the above mentioned segmentation is a segmenta-
tion of metameres or primordial vertebrae with myotome and selero-
tome, not a segmentation in vertebrae.

The second problem mentioned in the beginning is the so-called
re-segmentation of the vertebral column (Neugliederung der Wirbel-
säule). The quintessence of this problem is the question, whether the
intervertebral joints with a full-grown individual are the same as
the intervals found embryonally between the primordial vertebrae.
In other terms, whether the intersegmental and the intervertebral
intervals are the same, and the cartilageous and the osseous verte-
brate originate from the sclerotome of one primordial vertebra
(metamere.)

Remak already answered this in the negative. Van Barr admitted
still that the embryonal primordial vertebrae correspond with the
permanent later vertebrae. Remax showed that in the primordial
vertebrae the intervertebral musculature originated, and at the same
time the blastema, from whieh the permanent vertebrae take their
origin. According to him the permanent vertebra is formed in this way :
The primitive vertebral bodies (sclerotomes they are called at present)
originating in the primordial vertebrae (metameres) fuse together, and,
at the same time, new intervals come into existence for the secondary

195

(permanent) vertebrae in the middle between the original intervals.
A secondary (permanent) vertebra consists consequently of the caudal
and cranial halves of two adjoining primitive vertebrae fused together.
According to Remak there was in the development of the vertebral
column one moment, in which the blastema, from which the vertebrae
will originate, is entirely unsegmented. For a considerable time
Remak’s theory about the “re-segmentation of the vertebral column”
has not been recognised by many anatomists. Recent investigations
however have done justice to him. Especially the investigations of
v. Epner have turned the scale here, and in the first place the
discovery of the so-called intervertebral-fissure.

On the frontal section through an embryo (ef. fig. 1) one sees
on either side of the chorda the bodies of the primordial vertebrae.

JS.

Fig. 1.
Frontal section through an embryo of Tropidonotus natrix (after v. Meyer).
ch = chorda dorsalis; Ls. = intervertebral fissure ;

ais. =arteria interprotovertebralis ; ».c. = myocoel.
At a certain stage of the development one sees occur in it the
differentiation that causes the formation of the products that are
derived from it.

The primordial vertebra, in which the primordial vertebraleavity
is situated, shows a medial and a lateral lamella. The lateral lamella
is the ecutislamella, from which the derm with adnexa takes its
origin; the medial one is the muscle-lamella from which the muscu-
lature develops itself. Moreover originates from this medial lamella
of the primordial segment the blastema (mesenchym) from which

196

the skeleton will form itself, and with Amniotes a rather considerable
part of it is used. This mesenchym accumulates between the chorda
and the medial lamella of the primordial vertebra, so that the
primordial vertebrae are pushed in a lateral direction from the
chorda. The intervals between the different primordial segments are
distinetly indicated by the transversal course of the intersegmental-
or interprotovertebral vessels.

What is now v. EBNER’s discovery ?

This that from the lumen of the primordial vertebra a narrow
fissure runs in a medial direction to quite near the chorda. This
fissure, called by v. EBNer intervertebral-fissure divides each segment
into a clearly defined anterior and a posterior (cranial and caudal)
half. With Tropidonotus natrix (upon which v. EBNeR made his first
investigations) this fissure is most distinet in the neighbourhood of
the spinalganglions. More dorsally it disappears; ventrally it can
easily be followed as far as the region of the chorda. As was said
this fissure was first observed by v. Esner in Tropidonotus natrix
and afterwards it was shown by the same investigator in hens,
mice and bats. This discovery was soon confirmed by other investi-
gators with other animals and also with man. The existence of the
fissure is no longer contested. Van EBNER could also already show
that the intervertebral fissures agreed completely with the joints of
the later permanent vertebrae. According to him they disappear in
the end in the dense mass of tissue, in which afterwards the articular
cavities between the vertebrae occur.

The permanent vertebrae come now into existence each in the
region that is limited between 2 intervertebral-fissures. Consequently
each vertebra belongs to two segments and is constructed of the
caudal half of a diseretional segment and the cranial half of the
next following one. This agrees consequently entirely with Remak’s
assertion cited above, with this difference however, that the inter-
vertebral-fissures that indicate the intervals between the permanent
vertebrae, can already be observed when the intervals between the
segments have not yet disappeared, so that the unsegmented blastema,
which, according to Remak, should exist for some time, does in reality
not occur.

After this explanation it is obvious what must be understood by
re-segmentation of the vertebral column. The segmentation that is
expressed by the permanent vertebrae, is different from that which
is given by the primordial vertebrae; a new and another segmen-
tation has taken place.

How do now the fused caudal and cranial segments behave in

19%

the forming of the vertebra? This depends upon the species of
animal in question. With some animals we see that the originally
caudal half and the originally cranial half have an equal part in
the forming of the vertebra. With most higher Amniotes and like-
wise with man we see however that, at least as regards the ver-
tebral arch, the caudal segmenthalf becomes predominant, whilst the
cranial one, partly because the spinal-nerve and the spinalganglion
belonging to it always lie in it, gets more into the background. It
is not my intention to enter into further particulars about the share
that the two segmenthalves have in the forming of the vertebra. The
statements of the divers investigators diverge, which must be partly
attributed to the certainly very great difficulties of the investigation,
partly to the fact mentioned already above, that the relations with
the different species of animals are not the same in this respect.
I will only emphatically point out, that in what way the segment-
halves may behave in definite cases in the forming of the vertebra,
they naturally possess a complete potency, in such a measure that
from each of the two halves under special circumstances a complete
vertebra can be formed. A proof of this are the so called em-
bolomere or rhachitome vertebrae, which occur frequently with
Anamnia, but are likewise found with Amniotes, which was first
shown by Gorrne with Lacerta viridis, afterwards by MAnNer with
Angius and by ScHauinsLanD with Sphenodon, Castor fiber and
Cetaceae.

After this very short explanation of what is essential in the meta-
mery of the cranium and the re-segmentation of the vertebral column
we shall examine, to what consequence these two dogmas lead in
the ontogeny of the cranio-vertebral region.

If the doctrine of the metamery of the cranium according to
Froriep and the later investigators is correct, and for the present
there is no reason to doubt of it, then we must represent to ourselves
the region of the spinal part of the cranium (the praespinal part
can, as falling beyond tbe cranio-vertebral region, remain out of
consideration) and of the vertebral column in a very young stage
of embryonal development, as an uninterrupted row of anatomically
(not morphologically) equivalent scleromeres, as is represented schema-
tically in Fig. 2.

Axially the chorda(ch.) extends, through these scleromeres, the
cranial and caudal boundaries of which are indicated by the arteriae
intersegmentales (a.2.s. interprotovertebrales). Laterally from the scle-
romeres one sees the myotome belonging to the connected segment

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

198

with in it the myocoel (m.c.) which is continued in a medial direction
in the intervertebral fissure (/.7.7.) of von EBNer to quite near the

ch. = chorda dorsalis; 7.8. = nervus spinalis; @.7.s. = arteria interprotovertebralis ;

m.c. = myocoel ; 7.7.v. = intervertebral fissure.

chorda. The seleromere is divided, as was described above, by
this intervertebral fissure into two halves, a cranial half and a
caudal half. In the cranial half we see the N. spinalis (m.s.), the
caudal half is represented striped in conformity with the fact that
it is as a rule considerably stronger tinged. Somewhere in this row
of scleromeres, which encloses consequently the spinal part of the
skull and the immediately adjoining part of the vertebral column
at some period or other of the development the eranio-vertebral
interval will manifest itself.

What is interesting for us at the occurrence of this interval is
not the question, where it will present itself, in this sense, as if it
were of importance for us, how many scleromeres will join the
cranium. This problem remains here entirely out of consideration.
What we want to know of the interval is, whether it coincides

199

with the interval between the scleromeres or with the intervertebral
fissure of von Epner. Though, as far as I know, the question as
such has never been put, it can however be answered with certainty
from the literature. It has indeed always been found *) (cf. the well
known investigations of Froriep, Wwiss, Gaupp, BARDEEN and others)
and my own investigations on sheep-embryones confirm this in every
respect, that the craniovertebral interval coincides with a segment
or scleromere interval, and that the most caudal part of the cranium
is always formed by a caudal segment-half. This can be most easily
ascertained by paying attention to the nerves. The nerve running
in the cranial half of the scleromere, the caudal half of which forms
the most caudal part of the cranium, forms with the two nerves
of the two scleromeres lying in a cranial direction from it, the roots
of the N. hypoglossus; the nerve in the cranial half of the next
following segment in caudal direction, is the free 1st cervical-nerve
running outside the cranium (c.f. Fig. 3). The caudal half of the
last segment belonging to the cranium is always strongly developed
and by its intensive colour distinctly to be distinguished from the
weakly tinged cranial half of the in caudal direction next following
segment belonging to the region of the vertebral column, in which
cranial half always the first cervical-nerve is found.

If now we pay careful attention to the fact ascertained by obser-
vation, that the cranio-vertebral interval is an intersegmental one,
it appears immediately that necessarily, in consequence of the process
of the resegmentation of the vertebral column, one segment-half
remains between the first cervical vertebra and the occipital bone.
An illustration of this offers fig. 3.

We see in it as in Fig. 2 a representation of a row of segments,
in which axially the chorda extends itself, and which in a lateral
direction are limited by the myotomes somewhat further differentiated
in comparison with Fig. 2, from which the myocoel has disappeared.
Here the caudal half is likewise striped; in the cranial segment-half
the spinal-nerve (n.s.) is indicated whilst the intersegmental vessels
(a.2.s.) limit the segments. The line 4.5. represents the cranioverte-
bral interval situated intersegmentally.

In the process of the resegmentation described above, the vertebrae
are formed from the segments in such a way that the caudal half
of each segment fuses with the cranial half of the next following
segment in a caudal direction. So e.g. the caudal half of the fourth
segment (S. /V) will fuse with the cranial half of the fifth segment

1) These statements only regard Amniotes.

14%

200

(S. V), the caudal half of S. 777 with the cranial half of S. 1V,
the caudal half of S. // with the cranial half of S. ///, and the
caudal half of S. / with the cranial half of S. //, and in this way

ch.

Of
Es,

nd
Yi if
Ny

A Bre :
a n.C
SI,
NC U
Sr |
; Viel
Sm |
V.c.mz
Siv |
V.c.mv

Fig 3.

ch. = chorda dorsalis ; 1. = myotome ; /.7.c = intervertebral fissure ; @.7.s. = arteria
interprotovertebralis ; A.B. = cranio-vertebral interval; .c. J = 1st cervical nerve;
n.c. IT = nd cervical nerve.

resp. the 4th, 3rd, 2nd and 1st cervical vertebrae will be formed.

If we call the cranial half a, the caudal one 5, we can say in
general that the nt" vertebra is formed by the fusion of Sn. d
with S(n+1)a; the n™ vertebra has consequently for metamere
formula Snb+ S(n+1)a. From the first segment remains now
the cranial half S. Ja, for it remains separated from the caudal
half of the segment lying cranially from it by the cranio-vertebral
interval,

The conclusion from this demonstration that has issued from no
other premises than from the law of the resegmentation of the
vertebral column and from the fact, that the cranio-vertebral interval
is an intersegmental one, must consequently be, that between the

201

cranium and the vertebral column a free segmenthalf is found, that
has certainly an osteogenetical, perhaps even a hemispondylogene-
tical potency.

It is now the question whether this potency is activated, and if
so, what phenomena are the results of this activication. Though it
is not the intention of this communication to give a categorical
answer to the question submitted here, I will however indicate
already the direction in which, according to my opinion, the answer
must be looked for, and fix the attention to the fact that in the
cranio-vertebral region a great many phenomena present themselves,
the morphological signification of which has as yet not by far been
defined in the same way by all investigators. I have here especially
an eye to the variations of the atlas in the region of the sulcus
arteriae vertebralis, to the different phenomena on which in fact
the Pro-atlashypothesis of ALBRucnt is founded, to the concrescentia
atlanto-occipitalis and the manifestation of the occipital vertebra.

I think, that all these phenomena can be brought under one
point of view, namely the existence of the above mentioned segment-
half Za.

A further investigation into this question will form the subject
of a following communication,

Anatomy. — “The genetical signification of some atlas-variations’’.
By Dr. J. A. J. Bares. (Communicated by Prof. L. Bork).

In the previous communication, “On the metamerological signification
of the cranio-vertebral interval” I have fixed the attention to the
fact, verified also by investigation, that between the atlas and the
caudal boundary of the cranium, in consequence of the intersegmental
position of the craniovertebral interval and of the process of the
re-segmentation of the vertebral column, necessarily a free halt-
segment must exist, indicated for the sake of brevity as the semi-
segment Ia.

At the end of this communication the question was raised, to what
phenomena the activation of the osteogenetic potency, doubtlessly
existing in this semi-segment, would give rise, and the provisional
answer to this question was, that, in my opinion, it would probably
be possible to trace a relation between the established existence of
the semi-segment and a series of phenomena in the cranio-vertebral

202

region, namely the atlas-variations, the Pro-atlas of ALBrecut, the
conereseentia atlanto-oecipitalis and the manifestation of the occipital
vertebra.

In this second communication I intend to trace the signification
of the existence of the semi-segment for the morphological explanation
of the atlas-variations.

The fact that I wish to discuss in the first place these atlas-
variations finds its foundation among others in the circumstance that
it is just the study of these variations that has been the nearest induce-
ment to state the existence of the semi-segment Ia described in the
previous communication.

In the description of the human atlas it is always indicated, that
the most lateral part of the arcus posterior, namely that part that
borders immediately on the massa lateralis is characterized by a
notch. This notch, called suleus arteriae vertebralis, is caused by
the arteria vertebralis, which after having passed through the foramen
transversarium atlantis bends behind the massae laterales and crosses
the arcus posterior together with the first cervical-nerve, before it
pierces the membrana atlanto-occipitalis. The degree of development
of this notch shows a great deal of variability. Now it is flat and
shallow, now one sees that it has been transformed into a channel
shut off from all sides, because an osseous bridge extends itself
from the posterior rim of the massae laterale to the upper-rim of
the arcus posterior, so that one must then speak of a canalis or
foramen arteriae vertebralis. This latter condition occurs frequently,
witness the fact, that nearly all text-books call the attention to it
in their descriptions of the atlas.

The nomenclature, however, of this variation, both of the osseous
bridge, mentioned above, and of the channel or foramen the eranial
border of which is formed by the bridge, varies so very much, that
it is almost as arbitrary to find out oneself a name for it, as to
make a choice from the numerous existing names. In my opinion
foramen atlantoideum posterius (Bork) and foramen arcuale (GAvrP)
are the simplest among the denominations of the above-mentioned
foramen. I shall call the osseous bridge over this foramen ponticulus
posterior.

Beside this variation of the human atlas a second is known,
which occurs less frequently. It consists herein, that from the lateral
side of the upper-rim of the massa lateralis an -osseous bridge
xends to the most lateral part of the upper-rim of the processus

dove cus athints. Here is consequently the arteria vertebralis

| ), a bone, now together with the ramus anterior of the

203

first cervical nerve, and in this way a short channel or ring-shaped
opening is formed. To indicate this opening Bork uses the name of
foramen atlantoideum laterale, whilst Gavre proposes to borrow the
denomination that the veterinary surgeons (ELLENBERGER and Baum)
give to its homologon, constantly occurring with many animals, the
foramen alare. The osseous bridge that shuts off this foramen at
the top I call ponticulus lateralis.

As I remarked already previously both variations are known in
literature. Le Doupie') indicates the frequency of the foramen
atlant. posterior and the ponticulus lateralis as 11.7°/, that of the
foramen atlantoideum and the ponticulus lateralis as 1.8°/,.

In the collection of atlases of the Anatomical Laboratory in
Amsterdam, I found among 3360 atlases 77 or 2.5°/, with foramen
atlantoideum laterale and 355 or 10.6°/, with foramen atlantoideum
posterius. The numbers resulting from the examination of this material,
which is at least twice as large as the complete collective tables from
which Le Dousrr calculated his percentage do consequently not
considerably deviate from the latter.

The simultaneous occurrence of these two variations at the same
atlas has a.o. been described by Bork *), who found a combination of
a foramen atlantoideum laterale and a bilateral foramen atlantoideum
posterius on the right side.

Lr DovBLe (le.s.) mentions likewise a case in which on the right
side the two foramina with the ponticuli belonging to them were
simultaneously present.

From the material that was at my disposal, I could select a
series, in which all imaginable coincidences occur, as appears from
the following summary :

1. For. atl. lat. bilateral For. atl. post. bilateral with 2 specimens

U 855° 5 * he KOMEN SR re
ON On 5 ee Lel S
reo) totheleft „ —… ., bilateral 4 ® A
5) ig) nn Os 5 , totheleft ,, 4 i
TN Te tar on etn ha eee RE Es
ewe, right, r Ddilatemly m0 Ks
eee SS , O stothelettr ass ¥
Dn Ca eee een ed 3
io. 5. 4, mMissine 5 5 » lateral „124 5
ih, EN 5 oy as) a tomthelletiqged 2a
Ne se 25 Di EN or eo ri 5

1) Le Dovpre. Les variations de la colonne vertébrale.
2) L. Bork. De variaties in het grensgebied tusschen hoofd en halswervel-

204

The two most remarkable cases of this series are doubtless the
two specimina mentioned first, as to my knowledge they have not
yet been described. One of them is represented in Fig. 1.

*g “2,
7 2
= |

Fig. 1.
Atlas with bilateral ponticulus lateralis and bilateral
ponticulus posterior.

Rises the question about the morphological signification of these
variations.

Among the investigators that have tried to give an answer to this
question, there are especially three, who claim the attention here,
viz. Le DovBre, BorK and pr Bur et.

Le Dovgre explains the occurrence of the above-described pontieuli
posteriores simply mechanically and regards it as ossification of a
ligament, which in most cases is found between the upper-posterior-rim
of the massae laterales and the upper-rim of the most lateral part
of the arcus posterior atlantis. This ossification would take place
under the influence of the pulsations of the arteria vertebralis.

In consequence of the curving of this artery at this place the
convexity of which is directed backwards, every pulse-gulf would
push the above-described ligament backward; thereby a traction
would be occasioned on the periost of the atlas on the spot where
the ligament is fastened and under the influence of the stimulus the
osteogenetic potency of the periost would be increased. Lr DouBrE
cites, as an explanation of the occurrence of the ponticuli laterales,
an ossification of a ligament occasioned by the same causes.

It seems to me very improbable that the cause of the formation
of the mentioned variations is to be found in the pulsations of the
A. vertebralis. In the first place it is very improbable that a so
typical variation should exclusively be dependent upon outward
circumstances, the more so, as these circumstances are pretty well
constantly existing, and the frequency of the variation, though not
unimportant, is after all not so great as might be expected in

kolom bij den mensch en hunne beteekenis. Nederl. Tijdschr. v. Geneesk. 1899
Oi, A HTO, ID IL

L. Bork. Zur Frage der Assimilation des Atlas am Schädel beim Menschen.
Anat. Auzeiger Bd. XXVIII,

205

accordance with the pretty well constant occurrence of the above-
mentioned ligaments and the not less constant pulsation of the A
vertebralis. There are however still other considerations that, in our
opinion, make Lr Dovstn’s explanation appear less acceptable.
Suppose even that the stimulus of the periost caused by the pulsation
of the A. vertebralis should in reality be the cause of the occurrence
of the ponticuli posteriores and laterales, then it would at all events
be at least astonishing that the results of this process, naturally some-
what slow, could already be observed at a youthful age, and yet this
is the case, as I have been able to ascertain with several atlases of
the collection | have examined. The extraordinarily powerful way,
in which in many cases both the pontieuli posteriores and the
ponticuli laterales can be developed make us likewise doubt the
correctness of Lr Dovusir’s explanation of the discussed variations,
the more so, as it is generally known, that osseous tissue reacts
on the pulsations of the vesselwall rather with atrophy than with
hypertrophy.

This doubt becomes still greater if we also consider the results
of comparative anatomical investigation which were also known
to Lr Dovusie. For then it appears that with many groups of mam-
mals, and among these also primates, the ponticuli and foramini,
occurring with man only as variations, are constant and normal
parts of the atlas.

Bork has laid, as far as it regards Primates, a stress upon this
fact, which was already known to MrrkKer. He demonstrates that
namely ihe normal human atlas has been developed by reduction
from the more complete form, as it is met with among Primates
a.o. with Cynocephalides. This reduction regards in the first place
the topmost limitation of the canalis arteriae vertebralis, with
Cynocephalides still completely extant, of which first the most lateral
part (the ponticulus lateralis) afterwards also the medial part (the
ponticulus posterior) disappears, by which process the channel is
changed into a notch.

The repeated occurrence of these ponticuli must consequently most
probably be regarded as a common atavism; ponticulus posterior
and ponticulus lateralis are with the human atlas regressive variations.
According to this notion the signification of- this variation is in
comparison with Lr DouBre's view a quite different one. The prin-
cipal cause of its occurrence is now not to be found in outward
circumstances, however favourable their influence may for the rest
be upon the process, but in a generally occurring inclination of
reproducing phylogenetically older forms.

906

If we desist from trying to give an answer to the question after the
influences that have brought about the reduction of the human atlas
in the above-mentioned parts, the interpretation of the reoccurrence of
the ponticuli laterales and posteriores as regressive variation gives
certainly a satisfactory explanation of this phenomenon, as entering
upon further details of the problem would immediately lead us to
the department of general biology and specially to that of the pheno-
mena of heredity.

The way in which pr Burt’), the third of the above-mentioned
investigators, has treated the problem differs principally from that
of the former. In the views hitherto reproduced there was only an
attempt to answer the question after the signification and the origin
of the ponticuli posteriores and laterales with the human atlas.

De BerLer puts the question in a different way by taking likewise
into account with this question the homologa of these elements, as
they constantly occur — as has already been mentioned — with many
mammals. By doing so the problem assumes a more general nature,
and may be formulated as follows:

“What is the signification of the foramen arcuale and alare of the
mammal atlas and of the parts lying eranially from it?”

When answering this question pe Burrer points out the possibility
that the arcus posterior atlantis should not be equivalent to the
arcus posterior of the other vertebrae, in this sense namely, that
foreign elements lying originally cranially from it should have
assimilated with the arcus posterior atlantis, and as original source
of these elements he indicates the so-called proatlas.

1 cannot treat pe Buruer’s view completely within the compass
of tbis communication. The notion proatlas has in the course of
time gradually been modified and is even now by no means accu-
rately defined, so that an effectual discussion of pr Burret’s view
that the ponticulus posterior and lateral might be homologised with
the proatlas requires necessarily an accurate definition of the proatlas.
I hope to do so in a subsequent communication, which will be entirely
devoted to the Proatlas-problem; now I can, whilst explaining my
own view, only enter upon DE BURLET's opinion in so far as he
admits the possibility that elements having originally extended cra-
nially from the arcus posterior atlantis sbould have assimilated with
it, and the posterior arch of the atlas should consequently not be
homologous with the posterior arch of the other vertebrae.

1) De Burver. H. M. — Ueber einen rudimentären Wirbelkörper an der Spitze
des Dens Epistrophei bei einem Embryo von Bradypus cuculli. Morphol. Jahrb.
Bd. XLV. H 3.

207

In order to examine in how far the possibility expressed here is
likewise a reality, we ought in the first place to remember what has
been said in the previous communication on the metamerological
signification of the cranio-vertebral interval about the metamere
relation of the vertebrae.

From the generally admitted and in fact ascertained law of the
re-segmentation of the vertebral column we have then deduced that
in general the nt vertebra has been constructed from the caudal
half of the nm scleromere and the cranial half of the (m+ 4)"
scleromere, so that the metamere formula of the vertebrae is
Viertebra) 2 = Snb + S (n+) a.

If now we admit that the atlas, with regard to its metamere
relations, is entirely equivalent to the other vertebrae and that
consequently the above-mentioned formula likewise holds good
for the atlas, then follows from it necessarily (supposing » == 1),
that the atlas would be constructed from the caudal half of the
first segment and the cranial half of the second one.

Let us now regard in this connection the position of the ponticuli
posteriores and laterales.

Fig. 2.
Ch = chorda m = myotome; AB = cranio-vertebral interval;
SI= Ist Segment; SIl=2d Segment, ete. a= cranial
semi-segment; b= caudal semi-segment; n.c.1= le cer-
vicalnerve; v.c. Il = axis.

To the nature of the ponticuli belongs that they form the cranial
extremity resp. of the foramen arcuale and of the foramen alare,
through which foramina the first cervical nerve passes. Both the
ponticuli are consequently always situated cranially from this first
cervical-nerve. Fig. 2 however teaches us, according to the law,

208

that the spinal-nerve is always situated in the cranial half of the
sclerotome to which it belongs, that the first cervical-nerve does not
belong to the semi-segments from which the atlas is constructed, at
least not, if we maintain that the atlas is equivalent to the other
vertebrae and that its formula is SIb + Slla. If now the 1“ spinal-
nerve is situated in the cranial semi-segment Ia, as is in every
respeet confirmed by investigation, then a fortiori the ponticulus
lying eranially from this nerve must be reckoned to the same semi-
segment, at all events most certainly not to the caudal semi-segment
Id. If consequently a ponticulus is present, then it follows necessarily
from the fact, that the pontieulus has been formed in the cranial
semi-sclerotome Ia (it remains separated from the caudal half of the
last sclerotome of the cranium by the cranio-vertebral interval
situated intersegmentally) that indeed the atlas is no longer equivalent
to the other vertebrae, but is constructed instead of 3 semi-sclerotomes
and not of 2 and consequently the formula must run: Sla+Sl64 Sila.

Hereby an answer is given both to the question put by pe BurLer
after the signification and the origin of the ponticuli posteriores and
laterales, occurring with man as a variation and with many mammals
constantly, and in the first instance to the question formulated in
the beginning of this communication, if activation can occur of the
osteogenetic potency of the “free” semi-segment Ia, and if so, to what
phenomena this activation will give rise.

The answer to the first question must be that, on account of the
existence of the Ponticuli posteriores and laterales, the atlas may
most decidedly not be called equivalent to the other vertebrae, but
that, in comparison with the other vertebrae, it has enlarged itself,
as was likewise supposed by pr Buriet by assimilation of a cranially
lying element originating in the semi-segment Ia.

The answer to the second question must be, that activation
of the osteogenetic potency of the semi-segment Ia is doubtlessly
possible, and that one of the phenomena, by which this activation is
characterized, consists in the occurrence of the ponticuli posteriores
and laterales, which limit cranially the foramina arcualia and
alaria. We can imagine this process thus, that in that region of
the semi-segment Ia, that corresponds with the areus posterior
vertebrae (the region of the body of the vertebra remains for the
present out of discussion) on account of the influence of the ossi-
ficating poteney existing in it, an osseous arch is formed, be it
usually only weak, which assimilates with the arcus posterior atlantis
and leaves, when doing so, a necessary opening for the passage of
the n. cervicalis I and the a. vertebralis, the foramen arcuale. The

209

same holds for the region of the processus transyersus. There is
likewise formed in the semi-segment Ia an osseous piece connected
with the osseous arch in the region of the arcus posterior, which,
whilst leaving the required room for the passage of a. vertebralis
and ramus anterior n. cervicalis, (foramen alare) assimilates with
the processus transversus.

If this representation is correct, it is self-evident to admit, that
besides the above-mentioned ponticuli other elements can be indicated
in the dorsal region of the atlas, which must be reduced to the semi-
sclerotome Ia. Hereby I have especially in view the cranial half of
the massae laterales and the central part of the arcus posterior,
situated between the place of insertion of the ponticuli posteriores
into the posterior arch. With regard to the massae laterales we
need only pay attention to the fact, that both the ponticuli originate
at its upper-resp. posterior and lateral rim, and that this place of
origin resp. the part of the massa lateralis projecting most posteriously
and laterally is likewise always situated cranially from the 1* spinal-
nerve; for on this spot we see, with somewhat strong development,
the two ponticuli assimilate into each other. Consequently we are
compelled to admit that here also is a part lying in the most
cranial region of the massae laterales, which just like both the ponticuli
has originated from the semi-segment Ia. A difficulty however
presents itself here for fixing the boundary-line between the regions
of the semi-segments Ia and 15. There was no difficulty in this
respect for the ponticuli, as all that lies cranially from the first
spinal-nerve i.e. over the foramen arcuale or alare does certainly
not belong to Id. and there is not a single inducement to admit
that anything of the region lying caudally with regard to that nerve,
should belong to the semi-segment la. Here however it is different,
the massae laterales show neither with the full-grown atlas nor
with the young one a relief of any morphological signification, as
the for. arcuale or the for. alare doubtlessly is, and that would
allow to indicate the boundary-line between the semi-segment Ta and 1d.
We can consequently say indeed, that in all probability part of the
massae laterales still belongs to the semi-segment la, for the present
it is however impossible to say which part belongs to it.

For the above-mentioned central part of the arcus posterior it is
easier. Also in this region it is, as we saw, a priori probable, that
the activation of the osteogenetic potency of the semi-segment la
does not remain restricted to the ponticuli posteriores and laterales,
but extends itself between the points of insertion of the ponticuli
into the arcus posterior, and consequently forms an in the median

210
line uninterrupted osseous arch. As a rule the boundary-line between
the regions belonging to Sla and SI5 cannot be observed here,
no more as with the massae laterales, for the simple reason that no
passage required for nerve or bloodvessel keeps the regions separated.

It seems to me to be here the place to fix the attention to
peculiarities occurring rather frequently at the ossification of the
posterior arch of the atlas. In some cases namely one sees either
in the median line, or immediately on either side of if, openings in
the arcus posterior. The occurrence of these foramina is not entirely
unknown. Le DovBrr mentions them in his repeatedly cited work,
when he says on p. 88 that sometimes the tubereulum posterior
atlantis is replaced “par une dépression plus ou moins profonde,
dans laquelle on trouve par exception un foramen minuscule, qui
est lorigine d’une canalicule, qui s’ouvre en avant dans la cavité
rachidienne”. The author does however not attach any signification
to it, nor does he try to give an explanation of it.

The mentioned opening, which might be distinguished as foramen
arcuale medianum or mediale, occurs rather frequently in those
atlases, where the process of ossification is not yet completed, but
it is not entirely wanting in the normal, well developed atlas, as
I could ascertain in the material examined by me. Usually, as
likewise Le Dovus.e indicates, the variation remains restricted to a
depression lying in the region of the tuberculum posterius, now of
a fantastical shape, now, and this rather frequently, in the form of
a rather deep notch running transversally, the two extremities of
which are still a little deeper. In fig. 8, 4, and 5 I have represented
some forms of this variation, as I found them in full-grown atlases

Fig. 3.
Atlas with foramen arcuale medianum.

among the material examined by me, Fig. 3 represents an atlas, in
which the for the rest strongly developed arcus posterior shows in
the median-line a round opening (foramen arcuale medianum) lying
in a little eavity. In fig. 4 we find the representation of an atlas,
the posierior part of which is characterized by a transversal notch
extending over a rather large distance. In the bottom of this notch
we find on either side of the median-line an opening (foramen

211

arenale) which is considerably larger on the left side than on the

Fig. 4.
Atlas with foramina arcualia medialia.

right one, and at last Fig. 5 gives us the representation of an atlas,
which is already remarkable on account of the existence of a strongly
developed bi-lateral ponticulus posterior, but which shows moreover
an extraordinary deep depression (impressio mediana arcus posterioris)
lying in the centre of ihe areus posterior, a piercing ofthe posterior
arch as in the specimens represented in fig. 3 and 4 is however not
found here.

Fig. 5.
Atlas with impressio mediana arcus posterioris.

In the occurrence of these variations, to which till now but little
attention has been paid, I suppose, | may see a proof for the view
described above and a priori probable, that also the central part of
the arcus posterior atlantis contains elements that must be reduced
to the above-mentioned semi-segment Ia. In that case the notch
running transversally, and the foramina arcualia medialia or mediana,
eventually occurring in it, would indicate the boundary-line between
semi-segment Ia and semi-segment Id.

If this supposition agrees with the actual fact, it follows from
what has been said, that also in case the ponticuli posteriores and
laterales have not developed, as is most frequently the case with
man, the atlas cannot be called equivalent to the other vertebrae,
but that also in normal circumstances it has been built of elements
belonging to 3 semi-segments.

I have projected Fig. 6 (p. 212) in order to give a concise survey
of the manner in which I conceive the part that the semi-segment
la has in the construction of the atlas with the variations deseribed

212

above, in proportion to the degree of the activation of the osteo:
genetic potency contained in it.

The figure represents 4 human atlasforms A, B, C, and D. The
parts that have originated with certainty from the semi-sclerotome
Ia are represented black; those of which this is very probable and
for which in many cases the region of extension can be limited
are hatched.

A gives the scheme of the normal atlas without any variation.
We find in it,as belonging with great probability to the semi-segment
Ia, the most cranial part of the central part of the posterior arch.

Sa
Sey

Fig. 6.

In B we find the ponticuli posteriores occurring bi-laterally re-
presented black; the part of the arcus posterior lying between the
two places of insertion of the ponticuli into the posterior arch is
hatched as in A. The part of the atlas belonging to semi-segment
la represents now an arch lying between the posterior rim of the
massae laterales and assimilated with it and with the central part
of the arcus posterior.

C differs from the preceding form only by the occurrence of the
ponticuli laterales, likewise represented black, by which the osseous

218

arch originating from semi-segment Ia has been enlarged in a lateral
direction; whilst in D the foramen arcuale medianum is indicated
as the very probable natural limitation of semi-segment Ia opposite
to semi-segment 15.

A indicates consequently the minimal degree, D the maximal
degree of activation of the osteogenetie potency in the semi-segment Ia.

On purpose I have not represented in these schemes the share
that semi-segment Ia@ would have in the structure of the massae
laterales. As long as this part of the atlas does not show a relief,
by which we could indicate the boundary-line between the semi-
segments Ia and 15, I do not think myself justified to insert it
in a scheme, however probable the view may be theoretically.

Briefly expressed the following has been demonstrated in this
communication :

Ist. As was ascertained by Bork, we have to see in the occurrence
of ponticuli posteriores and laterales in the human atlas nothing
else than an atavistic variation, as the form of the atlas occurring
normally with man has originated by reduction from the mammal-
atlas, in which the mentioned ponticuli usually occur constantly.

2. The ponticuli posteriores and laterales, whether they occur as
a variation, as with man, or are constant, as with most of the
mammals, belong to the semi-segment Ia

In all cases in which the mentioned ponticuli are extant, the atlas
is certainly not equivalent to the other vertebrae, as the formula
for the atlas must then be Sla + SI+ + Slla. Consequently pr Buriet’s
supposition that elements that originally were situated cranially, have
assimilated with the atlas, is correct.

3. The variations of the atlas designated as foramina arcualia
medialia or mediana are most likely the proof, that also the part
of the arcus posterior, in so far as it is situated cranially from the
mentioned foramina, extending between the two places of insertion
of the ponticuli posteriores must be reduced to the semi-segment Ia.

4. The fact that the two mentioned ponticuli belong to the semi-
segment Ia is the proof, that activation of the osteogenetie potency
existing in this semi-segment is possible.

15
Proceedings Royal Acad. Amsterdam. Vol. XVIII.

214

Mineralogy. — “On phosphorite of the isle of Ajawi’. By Prof.
A. WICHMANN.

(Communicated in the meeting of May 29, 1915).

The isle of Ajawi or Mios Kairú, situated at 0°16'/,’ S. Lat. and
135°5’ E. Long. northwest of the Schouten Islands was discovered
on Febr. the 15% 1700 by Wirrram Dampier. When he intended
to sail between this island and the neighbouring isle of Aifondi he
scarcely escaped being shipwrecked. This fortunate escape indu-
ced him to call this group the Providence Islands’). Though it
was afterwards often enough seen, Ajawi was never visited by
Europeans. When the New Guinea Expedition of 1903 was on their
way to the Mapia Islands, they were of opinion that they should
not let the opportunity pass by to take likewise a view of this
isolated island.

After Aifondi was left in the morning of the 19" of July by
the government steamer “Zeemeeuw”, Ajawi was reached after
3'/, hours’ steaming. Already from a distance it appeared that the
island, covered with forests, was low, but that the eastern part was
formed by rocks of a} phantastic shape. At about 2 km. distance
from the south-coast the ship cast anchor in 13 fathoms, whereupon
the yawl took all the participants to the south-west-corner. This part,
rising hardly 3 m. above the level of the sea, consists of coral sand
with blocks of coral besides boulders of a white rather gross-grained
and hard but porous limestone which contains, according to L. Rurren,
numerous specimens of Rotalia. They call the attention to the fact
that the rock must be considered as subrecent®). The ground is
covered by a thin forest, consisting of specimens of Pandanus, about
16 m. high, in which enormous flocks of the beautiful Nicobara
pigeons (Caloenas nicobarica) nestle*). There were no human inhabi-
tants and from the absence of coconut-palms the conclusion may
be drawn, that permanent settlements have never existed.

In the eastern and north-eastern part of the island compact lime-
stones occur, which however differ from the above-mentioned ones.

!) A Voyage to New Holland, etc. in the year 1699. A Collection of Voyages
3d ed. 3. London 1729, p. 195. On the map Ajawi was indicated as Little Provi-
dence and Aifondi as Great Providence.

2) Foraminiferen-fiihrende Gesteine von Niederländisch Neu-Guinea. Nova Guinea
6. 2. Leiden 1914, p. 30.

3) Maatschappij ter bevordering van het Natuurkundig Onderzoek der Neder-
landsche Koloniën. Bulletin No. 46. 1903, p.p. 35—36. — H. A. Lorentz, Eenige
maanden onder de Papoea's. Leiden 1905, p p. 201 —202.

They are dense, of a whitish grey colour, and contain specimens of
Globigerina, so that they are perhaps of equal age as similar rocks
that are found likewise in islands to the North of New Guinea, and
according to RurreN are not younger than old-miocene’).

The most important rock of the island is however formed by the
above-mentioned + 16 m. high pbantastie rocks, some of which are
likewise found isolated in the neighbourhood of the eastern shore.
This rock, hitherto unknown in the Dutch East Indies, is a phosphorite
which shows great resemblance to the phosphates of other islands
of the Pacific. It is of a yellow to reddish-brown colour and some-
times of a pitchlike appearance. Angular, yellowish-white parts give
to the rock a brecciated character. The specific weight amounts to
2.78 and the hardness is = 6.

In thin sections the rock has under the microscope the appearance
of a light-yellowish, structureless mass, intersected with fine and
irregular fissures. Some parts of the thin sections are rather opaque,
but everywhere dispersed are dark dots which are apparently of
an organic origin. Though amorphous the phosphorite shows a slight
double-refraction, in which the interference-colours do not surpass
the iron-grey of the first order. In some parts one discovers through
the phosphate cavities filled up in zones that remind entirely of
the formation of agates (fig. 1), a phenomenon that is quite common
in phosphates from the Pacific *).

1) 1. c. p. 29—81.
2) CARL ELSCHNER. Corallogene Phosphat-Inseln Austral-Oceaniens und ihre
Produkte. Lübeck 1913, p. 55, pl. Ila. Such like phosphate-agates are found in

the Isle of Nauru itself in rather large pieces (l. c. pl. VIllb).
15*

216

An incomplete analysis made by Dr. Max Bucuyer at Heidelberg
gave the following result:

PAO zei A ee tabs
COP Se, se eon
Ne? O2 Ce Ae ce CANET ee PADD
CaO)... sa Ge eee STEDE
MgO’ 2) Koet OE PA
BOO BEDE ea en ne AAS)
H?O from) 44042508 €. 3:86
insoluble residue . . . 019

86.75

Qualitatively still a considerably large quantity of organic matter
and moreover fluorine and traces of chlorine was shown. The com-
position points to the fact, that 68.90°/, tricaleium-phosphate ought
to be present in the rock, which is less than with most of the
phosphates from the Pacific, whose typical representatives contain
38 to 40°/, P?0%.

Whereas 31.53°/, P*0* require for the formation of the caleium-
triphosphate 37.37°/, CaO, for the likewise occurring 7.31°/, CO?
however no less than 9.30°/, CaO is required for CaCO*, there isa
residue of phosphoric acid extant that can only be bound to the
magnesium and the iron. Further it appeared that not the entire
CaCO* is mechanically mixed with the other substances. When it was
namely removed by means of acetic acid, the treatment with hydro-
chlorie acid showed a very perceptible development of carbondioxyde,
so that we have decidedly to do with a earbono-phosphate, which are
likewise the minerals Dahllite, Podolite and Francolite. The Nauruite,
moreover always contains fluorine, as likewise the phosphorite of Ajawi.

P. Hamprucnu gives as formula for this mineral

3 (Ca?P?08). CaCO? . Cal, *)

C. ErscHNeR on the contrary

CaO |
x Ca?P:0° + {Ca(OH)*f, in which x=3 to 5%)
CaF?

It is however clear, that with the impurities, that are found in
all phosphates from the Pacific, it is for the present decidedly
impossible to find a satisfactory formula.

1) |. e. p. 680.
2) Entstehung, Bildung und Lagerung des Phosphats auf Nauru. Zeitschr. Gesellsch.
f. Erdkunde. Berlin 1912, p. 59.

21¢

With regard to the origin of the phosphorite of Ajawi there can
exist no doubt, but it was formed in the same way as the other
phosphates from the Pacific. From the investigations made in this
respect appeared that those islands were in former times atolls or
at least contained lagoons, into which the exerements of the birds
producing guano were washed by the atmospheric waters. The
phosphoric acid that had become free by the dissolution was the
cause that the coral-limestone surrounding the lagoons was changed
into phosphorite. The coral fragments that had come down to the
bottom of the lagoons, the boulders of limestone ete. were likewise
submitted to a similar metamorphosis, and were afterwards cemented
into a compact rock *).

Wherever such like phosphorites of coral islands make them-
selves apparent, it can only be the consequence of negative level-
changes. For this reason the rocks of Ajawi are to be considered
as the ruins of an original atoll, which has obtained its present shape
after subsequent upheaval by the waves of the sea.

Now the question still needs to be answered, in what way the
absence of phosphorite in the islands of the Indian Archipelago can
be explained. For Ajawi belongs already to the territory of the
Pacifie Ocean, and Christmas Island, 10°25’, S. Lat. 105°42’ E.
Long.?), rich in phosphorite is, it is true, situated in the Indian Ocean,
but its distance from the west-point of Java amounts to 420 km.,
so that it does not form any longer part of the Archipelago.

As we have seen the conditions for the formation of phosphorite
in the Pacific were: the existence of coral islands with lagoons and
further deposits of guano. There is no doubt but there existed also
during the tertiary period a great number of coral islands. Neither
is it hazardous to suppose that in some of them settlements of guano-
producing birds were found. Consequently it seems to me that the
third condition — the existence of lagoons — was not complied
with, from which would follow that no more at that time than at
the present moment there were atolls in existence. At any case,

1) O. Srurzer. Ueber Phosphatlagerstiilten. Zeitschrift für praktische Geologie
19. Berlin 1911, pp. 81—82. — O. Srurzer. Die wichtigsten Lagerstitten der
Nichterze 1. Berlin 1911, pp. 438—440. — PauL Hamsrucu. Entstehung, Bildung
und Lagerung des Phosphats auf Nauru. Zeitschr. Gesellsch. f. Erdkunde. Berlin
1912, p. 679. — Already as early as 1896 Ap. CARNOT (Sur la mode de formation
des gites sédimentaires de phosphate de chaux. Compt. rend. Acad. des Se. 128.
Paris, pp. 724—729) proved, that in general phosphorite and phosphate-chalk are
to be considered as shore- and lagoon-formations.

*) CHARLES W. AnpRews. A Monograph of Christmas Island (Indian Ocean).
London 1900, pp. 289—291.

218

they cannot have played a significant part. All this is of greater
significance, if we cast a look at the condition of the few guano-
deposits that are found in the Indian Archipelago.

For a long time it has been known that guano occurs in the
Baars Island, or Kabia') the west-point of which is situated at
6°50'55" S.Lat. and 122°12'20" E.Long.’). In 1877 an application
for preliminary exploration was made but “it was found inap-
propriate for being granted” *). Apparently that refusal was the
consequence of an investigation made by J. Brenspacn and G. A. L.
W. Son in the beginning of Dec. 1877 the result of which was not
favourable *). Notwithstanding this we read in a report over 1879,
that a concession was granted for the time of 10 years against
payment of f 1 per bouw (7096'/, m*.) to J. H. pre Siso and Tu.
C. Dryspate at Kupang ®). According to C. C. Tromp a certain
quantity of that guano had already been shipped to England, but
the exploration had afterwards to be stopped on account of the
depressed market °).

When Cary Risse had however paid a visit to the island in 1882
he wrote, that “ein durch die tropischen Regengiisse sehr ausgelaugter
und deshalb minderwertiger Guano ausgefiihrt wird.” ’) At last
Max Weer described Kabia as an upheaved coral reef, the rocks
and trees of which were covered by a white bed of excrements
originating from Sula pisatrir, Sula fusca and Tachypetes ariél*),

The second finding-place of guano has become known by F. H.
GuILLEMARD, who found it on the cliffs of Batu Kapal situated near
the north-point of the isle of Lembé (eastward of the N.E. point
of the isle of Celebes, but it was taken for chalk’). As appeared

}) According to H. D. E. EnsenHarp the real name is Kawi Kawijang. (Het
eiland Saleyer. Bijdr. tot de T. L en Vk. (4) 8. ’s Gravenhage 1884, p. 264).

2) J. A. C. Ovupemans. Verslag van de bepaling der geographische ligging van
punten in Straat Makassar etc. Natuurk. Tijdschr. Ned. Indië. 31. Batavia 1871,
p. 146 (table).

5) Jaarboek van het Mijnwezen in Ned. Indië. 1878. 2. p. 233.

4) J. E. Teysmann. Bekort verslag eener Botanische dienstreis naar bet Gouver-
nement Celebes ete. Natuurk. Tijdschr. v. Ned. Ind. 30. Batavia 1878, p. 119.

5) Jaarboek van het Mijnwezen. Amsterdam 1879. 2, p. 201.

Tijdschr. voor Nijverheid en Landbouw Ned. Ind 25. Batavia 1880, p. 554.
Oscar Scureipex CARL Ripge's Reisen in der Südsee. Deutsche geograph.

‚der «Oo. Hremen iS) p 374

5) Maatschappij ler bevordering van het Natuurk. Onderzoek der Nederl. Koloniën
B letin N. 53, 1900, p 7. — Max Wegen, Introduction et description de l'expé-
dilion. Siboga-Expeditie 1. Leiden 1402, p. 94

9 The Cruise of the Murchesa to Kamschatka and New Guinea. 2. 2d ed.
London 1889, p. 533.

219

however from the investigations of SipNey J. Hickson, the cliffs
consisting of limestone were covered by a thin bed of guano, which
seen from a distance looked like chalk’).

The third and last finding-place was traced by J. J. PANNEKOEK
VAN RHEDEN in Pulu Batu, a little island near Pulu Seraya ketjil,
westward of Flores”). The guano forms there only a thin bed spread
over the surface of a few ares, the quantity was valued at only
about one hundred cubic meters *).

From the description, at all events of that of the two first-
mentioned places, it appears that the guano was leached, i.e. a not
unimportant part of the phosphoric acic had found its way to the
sea, by which the formation of phosphorite, as under equal circum-
stances in every monsoon-territory, was prevented.

The guano-beds in limestone-grottoes originating chiefly from bats
will be preserved from such a fate. The quantity of these formations
is however usually very slight, as will appear from the following
summary.

In the S. and E. department of Borneo the grottoes of Mount
Hapu are especially known, in these grottoes the existing guano-
bed attains a thickness of at least 2 m. The quantity of guano that
is found in the grottoes of Mount Lampinet was even valued at
10000 tons’). It is however far surpassed by that of the grottoes
of Gomanton on the river Kinabatangan in British North Borneo
where it is said that the thickness of the gnano-beds amounts to
50 feet *).

The bottom of the numerous limestone-grottoes in Sarawak is
likewise usually covered with a bed of bat- and bird-guano some-
times mixed with river-mud. It is however of no significance °).

1) Omzwervingen in Noord Celebes. Tijdschr. Ned. Aard. Genootsch. (2) 4. M.
U. A. 1887, p. 135. — A Naturalist in Celebes. London 1889, p. 33.

2) Overzicht van de geographische en geologische gegevens verkregen bij de
Mijnbouwkundig-geologische verkenning van het Eiland Flores in 1910 en 1911.
Jaarboek van het Mijnwezen 40, 1911. Batavia 1913, p. 226.

3) P. J. Mater, Scheikundig onderzoek van Vogelmest, afkomstig uit de grotten
van den Goenoeng Hapoe in de afdeeling Riam Kanan en Kiwa (Zuid- en Ooster-
afdeeling van Borneo). Natuurk. Tijdschr. Ned. Ind. 29, Batavia 1867, p. 114—129.

*) Die Vogelnestgrotten von Gomanton auf Nord Borneo. Globus 46. 1884,
p. 31, according to the North Borneo Herald of Ist March 1884. — H. Prypr. An
Account of a Visit to the Bird’s nest Caves of British North Borneo. Proceed.
Zoolog. Soc. London 1884, p. 532—538. — D.D. Davy, On the Caves containing
Edible bird’s nests in Britisch North Borneo. Ibid. 1888, p. 108—116.

5) A. Harr Everett. Report on the Exploration of the Caves of Borneo. Proc.
Roy. Soc. 30. London 1880, blz. 310—313. — Tu. Posewrrz. Höhlenforschungen
in Borneo. Das Ausland 61, Stuttgart-München 1880, pp. 612—613.

220

In Sumatra the Lyang-na-Muwap in the department of Padang
Lawas, residency of Tapanuli, is especially known, the bottom of
which is covered by a bed of guano of a thickness of 2 feet'). The
grotto in the isle of Kluwang (5°8’ S. Lat, 95°17’ B. Long.), near
the west-coast of Atjeh, contains likewise rather much guano ’).

Numerous are the cavities in limestone in Java, that contain
guano. Similar deposits are nowhere missing where swallows or
bats are nestling. Some of them were carefully examined, but not
a single one is of any significance *).

Nothing has ever become known of an investigation whether in
any of the above-mentioned grottoes phosphatisation has taken place
i.e. whether the existing guano has caused a metamorphosis of the
limestone into phosphorite.

Botany. — “On the germination of the seeds of some Javanese
Loranthaceae.” By Dr. W. and Mrs. J. Docters van LEEUWEN-
ReIJNVAAN. (Communieated by Prof. F. A. F. C. Went).

(Communicated in the meeting of April 23, 1915).
1. Introduction.

Only a few investigations have been published on the Javanese
Loranthaceae. The last carried out by KoERNICKE *) appeared in
the Annales du Jardin botanique de Buitenzorg some years ago. It
deals chiefly with the adult life of these plants. Already long before
this ariicle appeared we had occasionally been occupied with experi-
nents on the germ nation of various species of Loranthus. Mr. Korr-
NICKE wrote to us (in 1911) that he had also taken with bim material

1, R. G. van DER Bor. De Lijang na Moewap en de legende daaraan verbon-
den. Tijdschr. voor Ind. Taal-, Land- en Volkenk. 37, latavia 1894, p. 201.

2) L. H. Watton, Klouwang et ses Grottes. Côtes ouest d’Atchin. Ann. de
Extreme Orient 2. Paris 1879—80, p. 41. — X. Brau DE SAINT-Por-Lras. La
Cote de Poivre. Voyage a Sumatra. Paris 1891, p. 224. — Zeemansgids voor
den Oost-Indischen Archipel 1, 2e druk. ’s Gravenhage 1904, p. 450.

3) D. W. Rosr van Tonnineen. Scheikundig onderzoek van eene meststof (guano)
afkomstig uit de afdeeling Grissee. Natuurk. Tijdsch. Ned. Indië 9. Batavia 1855,

pp. 157 168. — P. F. H. Frompere. Verslag over den aard en de bruikbaarheid
der dierlijke meststof aanwezig in de grot Poeljakwang te Grissee. Ibid. pp. 169—
19. J. C. Beryevor Moens. Guano van Telok Djambi, residentie Krawang.

ibid. 35. 1863, p. 327 —328.
4) M. KoerNieke, Biologische Studien an Loranthaceae. Ann. d. Jard. Bot. de
Buitenzorg, 3e Supplément, p. 665. 1910,

221

from Java for the study of the germination and would shortly
publish a paper on the subject. We thereupon abandoned the inves-
tigation, but having heard nothing further from Kogrnickr, we took
it up again and were thus able to collect a fairly large quantity
of material.

Some time ago, however, we learned that Korrnicke had read a
paper on this subject at Vienna, but we did not receive a copy of
this, so that we are still in ignorance as to what was dealt with in
this paper. For the present we do not intend therefore to give a
complete survey of our work. Our results concerning germination
form, however, a complete whole and this instalment can probably
confirm or extend Koxrrnickr’s paper. Later we may have an oppor-
tunity of considering some points further.

A few notes on the germination of these species are given in
GorBer’s work *) and Wiesner’) also discusses certain points.

As is known, the fruits or rather pseudocarps of Loranthus are
one-seeded. The pericarp is succulent and contains a large amount
of sugar. The testa is very thin and is surrounded by a layer of
mucilage varying in thickness, which is very sticky in some species,
e.g. in Loranthus pentandrus. Within the testa lies the endosperm
and in the longitudinal axis of the latter the green embryo is found
consisting of a hypocotyl and two small, thin cotyledons.

We had at our disposal material from Viscum articulatum L. and
V. orientale Bl, also the following species of Loranthus whose names
were determined by the kindness of Dr. J. J. Smita: first a species
indicated as N°. 5, which is probably identical with L. suhumbellatus Bl,
further Loranthus chrysanthus Bl, L. fasciculatus Bl, L. pentandrus L.,
L. ferrugineus Bl, a species indicated as N°. 6 which resembles
L. Schultesii Don. as well as L. atropurpureus Bl, but whose flowers
are larger and leaves less hirsute, also N°. 8 which is probably
identical with ZL. fuscus Bl. and finally ZL. praelongus Bl

It is not always easy to collect a sufficient supply of ripe fruits.
Various birds are very fond of them and look for them especially
in the early morning. Moreover they eat the seeds before they are
quite ripe. We succeeded in getting together a sufficient quantity of
fruits either by enclosing the plants or by collecting the fruits of those
plants which had been strongly occupied by the great red, vicious

1) K. Gorse, Pflanzenbiologische Schilderungen. Teil I, 1889, p. 156.

2) J. Wiesner, Vergleich. physiol. Studien über die Keimung europäischer und
tropischer Arten von Viscum und Loranthus, Sitz. Ber. d. Kais Ak. d. Wissensch.
Wien, Bd. 103. Abt. I. 1894, p. 403.

222

tree ants, Ovcophila smaragdina Em., which are evidently avoided
by birds. [

At first it appeared to us that the germination varies greatly among
different species of Loranthaceae, but on closer investigation we found
that a number of types of germination can be distinguished which
are readily deducible from one another.

2. Viseum articulatum L.

So far as is known, these plants are almost exclusively found
parasitic on Loranthus pentandrus. Cases have, however, been recorded
in which this plant occurred on other hosts. We only succeeded in
finding one such case. The Viscum-plants were growing on a young
tree of a Symplocos species in the Tolomaja mountains in such
numbers on the branches and stem and had such a peculiar habit,
that we did not at first recognise them.

Sometimes it seems as if a plant of V. articulatum is growing
on a host other than Loranthus but on closer examination this is
found not to be the case. The leaves of the Loranthus are sometimes
entirely eaten away by caterpillars (Deltas species). Microscopic exa-
mination of the branch on which the Viscum grows alone can
give certainty in this case.

At various times we sowed seeds of this species of Visewm on
many kinds of plants, but none germinated. If the seeds are sown
on Loranthus pentandrus, then development takes place with great
certaintv. We do not know the reason for this.

The fruits are almost spherical and in colour white. The seeds
are juicy and flat, 3 by 2} m.m. and about } m.m. thick. They
easily adhere and germination takes place fairly quickly. The first
day after the seeds have been set, no great change is observable.
On the second day a small green point appears from the edge of
the seed. This gradually develops into a thin green filament of about
‘mm. in length. The apex of this bends towards the branch of
the host in consequence of negative heliotropism, as can easily be
demonstrated and as has long been known in the case of European
Viscum. The green filament is none other than the hypocotyl of the
seedling grown out. Its apex attaches itself to the bark of the host
and then begins to swell up a little to a small discoid sucker.

The seed sometimes remains for several weeks in this stage of
development. It swells up so as to become rounder. After about
four weeks (in the rainy season somewhat earlier, in the dry some-
what later) the seed becomes loosened from the substratum, where-

223

upon the hypocotyl extends. The seed then stands on a straight
green stalk. The cotyledons now draw nourishment from the endo-
sperm, the testa shrivels and falls off and the cotyledons bend away
from each other. In the meantime the haustorium has also penetrated
into the bark of the host and the plant begins its proper mode of
life. In comparison with European species of Viscum, germination
proceeds quickly and the further development in particular takes
place more quickly, but in the species of Loranthus which we have
investigated the development of the seeds proceeds even much more
rapidly.

3. Viscum orientale Bu.

In our neighbourhood this plant is not so common as the previous
species. We had therefore not much material at our disposal. The
fruits and seeds closely resemble those of Viscum articulatum, but
are somewhat smaller. Germination proceeds exactly in the same
way, although somewhat more slowly. Seeds, which were set on
November 26", showed four days later commencement of growth
of the hypocotyl. On December 6" the apex of the hypocotyl had
become applied to the substratuin. There was no trace of any thicken-
ing of the extremity. At the end of January the hypocotyl was
again straightened out and only after a few weeks the cotyledons
made their appearance from the seed.

4. Species of Loranthus.

Among the species of Loranthus which we investigated three
types of germination can be distinguished. The simplest case is that
in which germination takes place in much the same manner as in
Viscum.

We have not been able to find from the literature at our disposal
in what manner germination takes place in the European species
of Loranthus. H. York") describes the development of an American
Loranthacea: Phoradendron flavescens Nutr. where germination,
as we shall later show in greater detail, corresponds in many respects
with that of the species of Loranthus which we have investigated.

5. Loranthus subumbellatus Bu. (?)

This species is very common, both in the plains and on the

1) H. York. The analomy and some of the biological aspects of the “American”
Mistletoe. Bull. of the University of Texas. No, 20. 1909.

Nw
bo
i>

mountains. Tbe plants grow on all kinds of hosts, and, in contrast
with most other members of this genus, are also often found on
species of Ficus. They are rather conspicuous by reason of their
bright green foliage and the bright yellow colour of their ripe fruits.
These fruits are spindle-shaped and pointed at both ends. The green
seeds are also spindle shaped and are enclosed in a thick layer of
juicy fruit-flesh. The layer of mucilage is not so strongly developed
as in other species of Loranthus and is really found only at one
end of the seed.

This is the part of the seed which in the fruit is turned towards
the fruit-stalk. The seeds are not attached by their lateral edge,
but at the extremity, and the connection with the substratum is not
so firm as in other species. After a good shower of rain the seeds
may be seen hanging by a thread of mucilage, loosened from the
substratum. On drying they usually attach themselves again to
the stem. In the course of a day the mucilage becomes, however, so
hard that the seed remains fixed in its place. There appear on the
side of the seed opposite the substratum five small, soft, white pro-
tuberances, which are placed in a ring round the apex. If these
portions are removed, the extremity of the endosperm and the apex
of the hypocotyl become visible.

The embryo consists of a well-developed hypocotyl, whose extremity
is already enlarged in the seed to a discoid sucker with glutinous
apex, and of two cotyledons. The latter are bright green like the
rest of the embryo and about 1 m.m. long. The germination of these
seeds is attached to a branch, the apex of the hypocotyl begins to
emerge from between the soft bosses. After 24 hours the hypocotyl
already projects one or two m.m. from the seed. The hypocotyl
continues to develop until it is a green filament 5—7 m.m. in length.
The apex becomes broader and broader and continually more sticky,
After 36 hours a curvature of the filament becomes visible and
usually the substratum is already reached after two days. The dise
is then attached to the surface of the host and becomes very much
broader.

After a few days the mucilage layer by means of which the seed
was fastened to the substratum becomes loose and the hypocotyl
now begins to straighten itself again. The seed is thus drawn away
from the branch and then stands up erect on a green stalk 7—9 m.m.
in length. The endosperm is now used up and the testa falls off
afier a few days and then the two cotyledons spread themselves out flat.

This brings germination proper to an end. In the meantime the
haustorium has made itself a way into the host.

225

As can be seen from the above description, this species of Loran-
thus develops in much the same way as Viscum.

A clear figure of the germination of this Loranthus is given in the
well-known work of GoreBer *), already quoted. The name of the
Loranthus described is however not given there.

6 and 7. Loranthus spec. 6 and L. chrysanthus Bl.

The first species of Loranthus is very common in several places
in the neighbourhood of Semarang, especially on neglected coffee-
plants of the natives. We found the second species in large numbers
on the slopes of Merbabu and Telamaja at a height of 1000—2000
metres. The fruits of the two species, closely resemble each other,
as do the plants themselves. Those of JL. spec. 6 are somewhat
smaller and less thickly covered with brown scales. The fruits are
pear-shaped with a fairly long stalk which becomes much curved
on ripening. The ripe berries are orange-brown in colour. They are
greedily eaten by birds, which swallow the entire fruit. The seeds are
dropped with the faeces and sometimes attach themselves in masses
to the branches.

The shape of the seed differs from that of the previously described
species of Loranthus. The latter was round in transverse section,
whilst a section of the seed of L. spec. 6 is square. At one end it
is broad and there occur in a line with the four edges four small,
. succulent, white protuberances. At their other end the seeds become
gradually narrower and terminate in a long, thin white stalk. This
stalk is the central portion of the fruit stalk. Although this white
stalk easily breaks off, it is almost always seen in seeds when ger-
minating in the open. These seeds have traversed the intestinal canal.
Round the seed itself and the stalk there is a thin, but very gluti-
nous, partly green layer of mucilage, by means of which the seeds
of this species of Loranthus are very firmly fastened to their substratum.
' The greater part of the seed consists of a white endosperm in
which the small green embryo is imbedded. This embryo is com-
posed of a short, thin cylindrical hypocotyl ending in a point, and
of two very small cotyledons. They are rather difficult to distinguish,
since they form a prolongation, as it were, of the cylindrical hypo-
cotyl. The latter, whose apex, in contradistinction to that of the
previous species of Loranthus, is not at all broadened, lies entirely
within the testa. The testa is however perforated in the middle,
exactly at the spot where the hypocotyl is applied to the testa. The

1) R. GoeBeL loc. cit p. 156. Figure 64 A.

226

hole is small and quite diffieult to see, but yet large enough to
form an outlet for the thin hypocotyl.

Germination takes place fairly rapidly. Its commencement is diffi-
cult to distinguish through the tough green layer of mucilage. This
must be removed by means of a needle, which is hardly possible
until the seeds have been soaked for some time in water to soften
them. A few hours after the seed has become fixed, the apex of the
hypocotyl begins to emerge and the next day there can be clearly
seen a fine green point protruding from the hole in the testa.

As soon as this protrudes half a millimetre out of the seed, the
growing stem begins to turn towards the substratum, keeping close
to the testa, so that it cannot be traced through the layer of mucilage.
Later it often bends still further and grows for a short distance
between the testa and the substratum. The apex of the hypocotyl
is not broadened and does not apply itself with its extreme point
to the substratum, but sideways. Gradually there is a broadening of
that part of the hypocotyl, which lies against the branch. The hypo-
cotyl is now as it were drawn ont of the testa and the basal por-
tions of the cotyledons also appear outside the seed. For the most
part, however, the cotyledons remain hidden within the seed. The
upper side of the hypocotyl and the bases of the cotyledons also
soon appear outside the layer of mucilage and are very obvious by
reason of their bright green colour. The seed reaches this stage
after two or three days according to circumstances. Still a day later
a small green point appears on the upper side of the hypocotyl,
and later yet another. After a short time these are seen to be the
first green leaves of the plant. At first we took this to be the
development of adventitious buds, but the process is, however, much
simpler. The two cotyledons separate a little at their base, so that
a narrow slit is visible, from which the growing point of the embryo
grows out. Generally the embryo turns itself in coming out, in such
a way that the slit between the two colyledons faces upwards.
Occasionally this opening lies more to the side and then the leaves
of course also appear laterally.

The two leaves grow very slowly and the hypocotyl broadens
itself at the same time. After a few weeks the haustorium penetrates
into the bark of the host.

8. Loranthus fuscus Bl. (?)

We found this species in large quantities as a parasite on plants
of Lespedeza cytisoides, which were very common on the slopes of

227

the Merbabu Mountain at a height of 2000—2500 Metres. With
regard to its manner of growth this species of Loranthus resembles
the two previous ones, but the leaves are not covered with scales,
and the flowers and fruits are much smaller. The seeds are also
quadrangular and quite of the same structure as those of Loranthus
spec. 6. The mucilage layer was also the same, as were the first
stages of germination as far as we saw them — we remained for
two days on the top of Merbabu.

9. Loranthus fasciculatus Bl.

We found a species of Loranthus which was noticeable because
of its small leaves and the flowers coloured dark-red at their base
on a gigantic tree of Ficus retusa in the neighbourhood of Getasan,
a village at an altitude of about 1100 Metres at the foot of Merbabu.

The fruits resemble in shape those of ZL. subumbellatus, but were
somewhat smaller and of a beautiful red colour like currants. The
fleshy part of the fruit was especially well developed, so that the
seeds were very small, hardly 2 millimetres in length. Moreover
the mucilage layer was not so strongly developed. The seeds of this
species also were quadrangular, the edges more or less rounded off.
We were only able to observe the germination for a few days.
The tirst stages completely agreed with those of the three foregoing
species of Loranthus.

10. Loranthus pentandrus L.

This species is, in Semarang at any rate, the commonest Loran-
thus. It is a vigorous plant which grows very quickly and of which
the stems, a metre in length, for the most part hang down from
the branches of the host. The fruits are fairly large, about 10
millimeters long and 4—5 mm. thick. They have the shape of a
truncated cone and are orange-red in colour. Mature fruits are
seldom found on the plants, because when still green and almost
ripe, they are eaten by birds. The germination of these nearly ripe
fruits, however, takes place just as well as that of the completely
ripe ones. Naturally the latter germinate more rapidly, but
germination takes place so quickly in this species, that one sees
little difference.

In contradistinetion to the fruits of the foregoing species of Loran-
thus which are usually swallowed entire by birds, so that the seeds
arrive on the branches of the host with the ejecta, the fruits of

228

L. pentandrus are generally pealed by the birds one by one. Then
the birds, usually species of thrushes rub off the very sticky seeds
from their beaks on to the branches. It is obvious that by such
a method, the chance of a seed arriving at a place suitable for its
development is much greater than was the case in the previously
mentioned species.

Naturally they are often found on branches of Loranthus pen-
tandrus itself and young seedlings can always be found on it in
great numbers. This fact was also observed by Kogrnicke *). But
this does not imply, that we can now speak of Loranthus as a
parasite on Loranthus itself. All the cases figured by KoERNICKE
refer only to seedlings. We have never yet met with adult plants
of Loranthus growing on another species of Loranthus. Seedlings
are often also found on dead branches, which, because they are
leafless, offer a favourite support to birds. But this does not permit
us to say that species of Loranthus can be parasitic on dead wood.

In comparison with the size of the fruit the seeds are relatively
small, about 4—5 mm. The testa is, as in the other species, very
thin and encloses a great quantity of endusperm. At the extremity
which is in the fruit turned towards the apex, there are 5 muci-
laginous, filamentous protuberances, about 3 mm. long, which cover
the apex of the seed and make it appear to be therefore about
7 mm. long.

Their removal from the seed is not prejudicial to germination and
is indeed often brought about by the agency of birds. The green
apex of the hypocotyl is then seen which hence protrudes slightly
from the seed. The apex is already markedly swollen, when the
fruit is still not quite ripe. In proportion to the quantity of endosperm
the embryo is rather small. It consists of a short hypocotyl, which,
as has already been said, is swollen at its free extremity into a
knob and of a pair of very short, flat cotyledons, which reach to
about the centre of the endosperm.

If the seeds are stuck on a branch, then, at least if it does not
rain, a few hours afterwards the mucilaginous protuberances of the
seed are seen to begin to dry up and the green knob of the hypo-
cotyl becomes visible.

At the same time this knob swells up and grows with one lateral
edge towards the branch, so that a large swelling arises at the
extremity of the seed. Its lower side lies against the branch and
adheres to it. This occurs in the course of one to three days.
Gradually also that part of the hypocotyl which was concealed in

1 M. KorrNIoKE. loc. cit. p. 690.

229

the seed, is drawn out in consequence of the growth of its anterior
part, but since this concealed portion is very short, very little of
this can be seen in the beginning. The bases of the cotyledons also
just become visible and the terminal bud, which is concealed between
the two cotyledons grows out. First a small leaf appears, then
another. But this growth is much slower than at the commencement
of germination. After a few weeks they are usually one centimetre
in length. It is only when the stem begins to lengthen, sometimes
not until after a few months, that development proceeds again at a
greater rate. Long before this the white haustorium has already
penetrated into the host.

11. Loranthus praelongus Bu.
This is the largest species of Loranthus which we found in Java.
g |

It can grow on a variety of trees, but for the most part we found
them on Ficus species, including Micus elastica. Specimens with

pendulous branches 4—5 meters in length, are not uncommon. The
inflorescence is a thick crowded raceme. The flowers are very long
and orange-yellow in colour. The fruits are sessile, as broad as
those of the former species, but somewhat shorter. Moreover the
seeds are somewhat more crowded. The structure is identical with
that of Loranthus pentandrus and germination takes place in the

same way.
12. Conclusion.

The first impression gained with regard to the germination of
species of Loranthus is that it proceeds very differently in various
species. But investigation has shown that this difference is only
apparent.

The germination, as described above for species of Vésewm and
agreeing completely with that of Wiscum album, might be considered
the simplest stage. This germination-process may be compared with
that of epiphyte seeds, as GorBer') has already noticed. In species
of Aeschynanthus*) and Dischidia*) the hypocotyl also appears first
from the seed. It bends towards the bark of the host and attaches

1) K. GoeBer. loc. cit. p. 156.

2) Idem p. 155. Figure 63.

5) W. and J. Docrers van LEEUWEN—REIJNVAAN. Beiträge zur Kenninis der
Lebensweise einiger Dischidia-Arten. Ann. d. Jard. bot. de Buitenzorg. XXVI.
1913. p. 68.

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

230
itself to it by means of a ring of fine hairs. Not until later do the
cotyledons appear.

The germination of Loranthus subumbellatus (2) quite agrees with
this. In this species also the cotyledons become the first leaves of
the young plant. In the other species of Loranthus which we inves-
tigated this is no longer the case. In these the cotvledons (except
their bases) remain completely concealed in the endosperm, and
serve to carry the food hence to the hypocotyl and do not later
function as leaves of the plant.

In Loranthus spec. N°. 6, chrysanthus, fuscus(?) and fasciculatus
the hypocotyl is still placed completely within the testa. On germin-
ation it becomes visible and grows along the testa towards the
bark of the host. The embryo now pushes itself so far out of the
seed that the bases of the cotyledons appear and the terminal bud
is able to grow out.

In Loranthus pentandrus and praelongus the apex of the hypocotyl
is in the first place already outside the testa and in the second
place the apex is swollen into a knob. Here there is no question
of a curvature of the hypocotyl, as in all the other species. The
knob grows, at the side which is turned to the host, towards the
latter’s bark. The hypocotyl in the seed is further so short that
the bases of the cotyledons almost at once come to lie outside the
seed. So far as germination is concerned this species of Loranthus
may be considered the most specialised. The germination is here the
most rapid and the seedlings are the earliest to reach their host.

The germination of an American Loranthacea i.e. Phoradendron
flavescens Nutt. has been investigated by York *), who found that
in this species germination takes place in the same way as in
Loranthus spec. 6 investigated by us. But the cotyledons remain
functional much longer. First the embryonic root is formed; the
endosperm often remains united to the cotyledons for more than a
year. Generally these shrivel up and disappear. Rarely the stem
develops from the terminal bud between the cotyledons. Usually the
shoots arise from adventitious buds, which develop on the terminal
dise of the hypocotyl by means of which the latter is united to
the host.

Semarang, Java.

‘)) Oley Chis Tap {s

231

Physiology. — “On the heart-rhythm. 4% Communication. Heart-
alternation.” By Dr. S. pr Borr. (Communicated by Prof.
J. K. A. WerrHem SALOMONSON.)

(Communicated in the meeting of May 25, 1915).

Physiologists and clinical men have repeatedly discovered an
alternating activity of the central organ of the circulation of
the blood. By experiments this phenomenon was likewise brought
about in different ways. So could Horrmann (1) cause his stopping
frog’s heart preparations to make for some time alternatingly stronger
and weaker pulsations by passing from a slow stimulation-frequency
to a quicker. Rümke (2) made frog’s hearts alternate by poisoning
them with antiarine. Muskurs (3) obtained heart-allernation by
poisoning frog’s hearts with digitalisdyalysate. Also by other poi-
sons as aconitine and glyoxyle-acid an alternating activity of the
heart is obtained. Gaskerr (4) could make the heart-alternation in
frog’s hearts disappear by Vagus-stimulation, whilst Frépúricq (5) could
produce heart-alternation in narcotized dogs by stimulation of the
accelerantes. There exists very little certainty about the explanation
of this phenomenon. Muskens, TRENDELENBURG (6) and HERING (7) on
one side attribute the alternating weak pulsations of the heart to
asystoly of part of the ventricle-musculature. Wernckrsacn (8) con-
tradicts this view, he admits likewise this cause for the alternating
activity of the heart, but distinguishes moreover another reason for
the phenomenon. Clinical experience taught him that p. alternans,
apart from its occurrence in paroxysmal tachycardies, is almost
exclusively discovered, when the arterial pressure of the blood has
increased (chron. nephritis) and the elasticity of the arterial wall has
decreased. He considers in this respect alternation more as a pulse-
phenomenon than as a heart-phenomenon. Under the influence of
little irregularities the filling of the ventricle and the arterial resistance
vary alternatingly, so that with constant contractility of the heart-
muscle the result of the systoles varied alternatingly.

My experiments) treat of extirpated frog’s hearts: for the alter-
nating activity of these this peripherie cause is consequently excluded.
If a frog’s heart is extirpated and suspended, sometimes alternatingly
high and low curves are obtained. I give an example of this in fig. 1.
(next page).

1) The experiments were made on hibernated specimens of rana esculenta in
the months of February and March 1915. Preliminary communication published in
the Zentrallblatt fiir Physiologie (9).

16*

232

During the large systoles I saw in this experiment the whole
ventricle contract, whilst during the little systoles the point remained

Cute

—

Fig. 1.
in rest. After this suspended heart had written for some time alter-
nation-curves, these curves suddenly changed into curves of equal
height. This transition can be seen in the figure. For a very short
time these curves continued to be of equal height, to change again into
alternation. The second row of curves of the figure was written
down 5 minutes after the first. The transition of the alternation into
the curves of equal height is brought about, because the little curves
increase in height, whilst the height of the large curves gradually
decreases. The height of the normal curves is in the end between
that of the large ones and the little ones of the alternation. I
found this confirmed in a great number of experiments. This
can be beautifully seen in fig. 1. [ have not observed here the
transition of these normal curves into the alternation. After I
had replaced the drum to begin the second row, the alternation
existed already again. The distances between the initial points of
the ventricle-systoles of the alternation-row are equal, but because
the large systoles are wider, the ventricle-pauses are of unequal
duration. The little systoles follow after a shorter pause than the
large ones. And it is the preceding pause that is of consequence.
The dimension of the systole is in general dependent upon the
duration of the preceding pause and of the dimension of the systole
that has preceded this pause. If a systole after a short pause succeeds

a large systole then it is little, and on the other hand a systole is
large, when the preceding systole is little and the preceding pause long.

Repeatedly I saw the alternation change into halving of rhythm.
Fig. 2, lower row of curves, shows an instance of it. After I had
suspended this heart, the systoles were all equally high; after a
short time this row of curves changed into alternation. When this

Pe me nennen -- —

234

had existed for about one minute, halving of rhythm oceurred. In
this halved rhythm the heart continued to pulsate for more than
2'/, minutes, after which the usual rhythm returned, in the beginning
with systoles of equal height. After this slow rhythm the height of
the systoles gradually decreases. The preceding slow rhythm had
contributed to make the first systoles higher. The first systole of
Wig. 2 is the 15 after the halved stage. The systoles continue here
to decrease in height. From the 6 systole in this figure the alter-
nation is distinctly extant. We see now the little systole constantly
diminish in height, till the rhythm halves again. I hope to give an
explanation of this fact at the end. Conducted by this observation
which I made several times myself, from which appeared, that
alternation oecurs as a transition from the normal rhythm into the
halved one, and conducted by the well known clinical observation
that p. alternation occurs especially with paroxysmal tachycardies,
I have tried to produce heart-alternation in my frogs in a simple
way. The result answered entirely to my expectations. I suspended
in the usual way an extirpated frog’s heart, and raised then the
temperature of the sinus venosus by making a het Ringersolution
trickle on it.

My intention was to make the impulsions proceed from the sinus
venosus to the ventricle in a quicker tempo, whilst the temperature
of the ventricle remained the same. As I expected the ventricle
began indeed to pulsate in alternation. Fig. 3 (at V. sinus venosus
calefied). In this way I could cause nearly every extirpated frog’s
heart to pulsate alternatingly. Thus [ suspended e.g. 28 March
10 froe’s hearts and found with 9 of these alternation after calefaction
of the sinus venosus, with the 10% polygeminy occurred. (Every 4
to 8 systoles 1 ventricle-systole fell out here). Refrigeration of the
sinus venosus was then again sufficient to change the alternation
again into the normal rhythm. (Fig. 4 at A sin. venosus refrigerated).

Alternation as transition between the normal and the halved rhythm
occurred hereby likewise frequently.

So we see in Fig. 5 upper row at V, on account of calefaction
of the sinus venosus, alternation appear which disappears again at
A in consequence of refrigeration. In the lower row occur a few
curves of another heart in the halved rhythm between the alternation-
pulsations (at V the sin. venosus is here likewise calefied, at A
refrigerated).

Sometimes I obtained in this experiment for a short time heart-
alternation, but often also the heart continued to pulsate for a long
time in alternation. It makes the impression that the average normal

235

height of the systole lies between the two of the alternation, whilst
during the alternation there exists an oscillation round this average.
This is in accordance with the conception that the height of the
systole is direct proportional to the duration of the preceding pauses.
The duration of the pause in the normal rhythm is also the average

Fig 4.

236

of the long and the short pauses during the alternation. When once
pulsating in alternation the heart continues of itself to oscillate round
this average. Every large systole is followed by a shorter pause, so
that there are two reasons, why every following systole will be
little, namely :

1. the short preceding pause.

2. the fact that the preceding systoles are large.

And so, conversely, every little systole will be followed by a
large one. This will be so, because the preceding systole is little,
and the preceding pause long. For this reason a once existing
alternation easily continues.

Now I thought it desirable to study this heart-phenomenon likewise
with the string-galvanometer. The communications on this subject
are so contradictory that I felt the desire to study the action-currents
of the simple frog’s heart possessing but one ventricle during the
alternation. My experiment facilitated my investigations considerably ;
I could now at any time by any method make hearts pulsate alter-
natingly ; [.deducted the action-currents in the usual way from the
point and the basis or anricle. I represent here in Fig. 6 the sus-
pension-curve and the electrogram of a frog’s heart that by itself
was pulsating alternatingly. (Fig. 6. Time in ‘/, sec.) After the sixth
systole I refrigerated the sinus venosus by pouring a little chlorie
ethyl on if.

We see in the row of curves the /-oscillations remain equally
large. The slow 7-oscillations are for the little systoles considerably
larger than for the large ones. The consequence of this is, that the
electric curves alternate over against the mechanical ones in an
Opposite sense.

And this can easily be explained. The negativities of the basis
and of the point are transmitted from the ventricle to the measuring-
apparatus. These negativities demonstrate themselves there in opposite
signs. In so far as consequently the basis- and the point-negativities
coincide, they are subtracted from each other. Jn the mechanical
curves however the point and the basisalterations sum up. The greater
the mechanical curve is, i.e. the more the point takes part in it,
the smaller the electric curve becomes. With the low curves conse-
quently is in the electrogram the incision from the top into the
electrograms smaller than with the large curves (indicated by two
arrows in Fig. 6). The depth of the incision is indicated by the
measure in which the point interferes with the basis.

That indeed during the little curves the point is in rest can espe-
cially distinetly be seen, when the difference in dimension of the

The little curves of the alter-

es in the electrograms more as mono-
ree ones represent more diphasic curves.

gly pronounced.

is stron

nation-pairs express themselv

two systoles

whilst the lar

The part of the point consequently participates, also in an elee

phasic curves

tric

239

of stimula through the basis-part, till the stimulus has proceeded so
far, that the negativity begins to show itself also at the point-pole.
As long as the basis-region continues to pulsate in its full extent,
the A will consequently remain equally high. (If at least the

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240

transmission-veloeity of the stimulus is not considerably disturbed;
for if the stimulus transmits itself slower, the point will interfere
later with the basis, and thereby the height will be able to increase
already). The influence of the refrigeration of the sinus venosus on
the eleetrograms and the mechanical curves is here entirely a con-
sequence of variation of frequency. The duration of the /-oscillation
becomes shorter on account of the improved transmission of excitation
after the longer pauses, but the duration and height of the 7-oscil-
lation likewise inerease considerably. The mechanogram likewise
inereases in height and duration.

A well-defined example of transition of alternation into the normal
rhythm represents Fig. 7. The height of the mechanograms of the
normal rhythm stands between the heights of the alternation-systoles.
In the eleetrograms the same ‘proportion is found back for the
heights of the Zoscillations, and likewise for the depths of the
incisions, caused in the electrograms by the interference of the apex
negativity with the negativity of the basis.

In Fig. 8 (page 238) we see an alternation that I had caused
by calefaction of the sinus venosus, change again into the normal
one by refrigeration of the sinus (the moment of refrigeration is
indicated by the signal) Occasionally the alternation was only to
be ascertained by a difference in height of the 7-oscillations. The
highest 7”s belonged then to the lowest systoles. This can only be
explained by an inferior interference of the apex-part with the basis.

Not always, however, does the point participate less during the
little systoles; in some cases the electogram can only be understood,
if alternatingly we admit a diminished participation of the basis, or
also, if alternatingly now the basis, now the point pulsated.

So Fig. 9 (page 239) allows us to doubt, whether here the little
systoles are occasioned by exclusively basis-systoles.

I have another representation in which during the little systoles
for the greater part the point pulsates, and during the large systoles
the basis does so. These however are exceptions. As a rule I observed
that during the little svstoles the point does not participate. In
nearly all vepresentations the large systole begins later after the
expiration of the preceding systole than the little one. This can
distinctly be observed from the electrograms. Consequently besides the
systoles the pauses alternate also, whilst an alternation in the duration
of the heartperiods does not occur. After it bas appeared from the
electrograms, that the heart-alternation of the extirpated frog’s heart
is caused by partial asystole of part of the ventricle-musculature
(mostly of the point), Fig. 2 suddenly becomes also more intelligible.

241

We see here alternation gradually change into halving of the rhythm,

most probably of the ventricle only. I often observed this halving

of the rhythm after alternation. The alternation is here consequently

a form of transition between the normal rhythm and the halved

one, as I fonnd in my frog’s hearts poisoned with veratrine repeatedly

bi- and trigeminus as transition between these two rhythms. The

transition is here gradual; the more we approach the halved rhythm,

the lower the little alternation-systole beecmes. During the little

systole a constantly greater part of the beartpoirt remains in rest.

in Fie. 10 T have indicated by

Lo lines drawn transversally over the

ventricle the frontier between the

part of the ventricle that pulsates

during the little systole, and the

part that remains in rest. The part

under the lie pulsates consequently

during one alternationpair once, and

this part becomes constantly larger,

4 the line rises gradually. So we come

to the conclusion that as soon as

the alternation occurs, halving of

Wig. 10. rhythm of part of the ventricle-

musculature takes place. The part of which the rhythm halves

becomes constantly larger and larger, till at last the rhythm of the

whole ventricle halves. The lines in the fig. indieate thus, how
far the contraction continues alternatingly in the ventricle.

By this investigation into the potential differences which exist in
the ventricle during the alternation-curves it is at the same time
clearly indicated that we must conceive the ventricle-electrogram as a
product of interference of the negativities at the basis and the point.

LITERATURE.

1. F. B. Hormann: Ueber die Aenderung des Contractions ablaufes am Ventrikel
und Vorhofe des Froschherzens bei Frequenziinderung und im hypodynamen
Zustande. Prrücers Archiv. 84, 1901 Seite 130.

2. CG. L. Rümke. De werking van antiarine op het hart. Nederl. Tijdschr. v.
Geneesk. 1902, I. no. 15 blz. 869.

3. L. J. J. Muskens. Bijdrage tot de kennis van zenuwinvloed op de hartwerking.
Koninklyke Akademie van Wetenschappen te Amsterdam. Verslag van de gewone
vergadering der Wis- en Natuurk. afdeeling van 26 April 1907. (These Proceedings
Vol. 10, p. 78).

4. W. H. GAsKELL. On the rhythm of the heart of the frog and on the nature

24)

of the action of the Vagus nerve. Philosoph. Trans R. S. 1882. CLX XII 993-—
1033 (p. 1017—1018) 5 pl.
5. H. Fripiricg. Pouls alternant produit chez le chien chloralisé par excitation
des nerfs accélérateurs du coeur. Archives internationales de Physiologie 1912. p. 47.
6. W. TRENDELENBURG. Untersuchungen über das Verhalten des Herzmuskels
bei rhythmischer electrischer Reizung. ENGELMANNS Archiv. f. Physiologie 1903, S. 271.
7. H. E. Herina. Das Wesen des Herzalternans Münch. Med. Wochenschr.
1908 Seite 1417.

8. kK. F. WenckupacuH. Die unregelmiissige Herztätigkeit und ihre klinische
Bedeutung 1914 Seite 198—215.

9. S. pr Boer. Herzalternans. Zentralblatt für Physiologie, Pd. XXX, N® 4,
Seite 149 (15 Mei 1915).

Physiology. — “Upon the simultaneous registration of electric
phenomena by means of two or more galvanometers, and
upon its application to electro-cardiography” By W. Evr-
HOVEN, F. L. Bereansius, and J. Brorer.

(Communicated in the meeting of May 29, 1915).

For a long time the need has been felt of a simultaneous regis-
tration of electric phenomena by means of two, or three galvanometers.
This is evident from the experiments made by Burr, Garren, Horr-
MAN, Lewis, WiLrrams, and others.

Speaking generally, three methods may be distinguished:

A. That in which two galvanometers are placed side by side.
Each of the instruments is illuminated by a separate lamp, while
the rays which proceed from the projection-oculars form two fields
of illumination one beside the other on the horizontal slit, behind
which the photographic plate is moved in a vertical direction.

The time-registration can be obtained by a single spoke-dise, the
number of spokes of which may be 10, or a multiple of ten. The
dise must be placed in such a position that its centre falls in the
line, which, running about parallel with the slit, connects the optical
axes of the two galvanometers. This can easily be done with great
accuracy, so that no greater error need occur than say 0,01 part
of the distance which divides one spoke from another. Care must
also be taken that by a suitable placing of the lenses the images
of the spokes on the slit are sharply defined.

B. Another method consists in stretching two strings across the
same magnetic field. The Cambridge Scientific Instrument Comp.
provides a double string-holder on their model of galvanometer, in
which two strings are held at a distance of 0.5 mm. from each other.

If a strong magnification were used with this arrangement without
any further arrangements the images in the field of projection would
fall so far apart that the apparatus would be useless in practice.
With a magnification of 600, the images of the strings would lie
30 em. apart. To avoid this difficulty, the rays which are directed
upon the slit by the projection-ocular, are changed in direction by
a pair of achromatic prisms in such a manner, that the images of
the strings come to lie at a convenient distance from one another
upon the slit. A rectangular screen, placed at some distance in front
of the slit, divides the two fields formed by the prisms, and forms
a fine line of shadow upon the sensitive plate.

C. The third method of combination of galyanometers may
perhaps be called the most elegant, but it demands a very careful
adjustment. The principle of this method is that the two galvano-
meters are placed one behind the other, with the optical axes falling
in the same line.

Midway between the projection-objective of the first galvanometer
and the illumination-objective of the second a combination of lenses
is introduced which may be compared to a double ocular, and
which the firm of Cart Zwiss have been kind enough to construct
at our request. This system is placed at such a distance from the
two above mentioned objectives, that the spherical and chromatic
aberrations of the image are compensated as well as possible.

The string which is nearest to the lamp is first projected in: the
new Zeiss-system, a second time in the optieal field of the second
string; a third time in the projection-ocular, and finally a fourth
time upon the sensitive plate.

Although great demands are made upon the optical apparatus in
order to insure sharpness in this fourth image, yet the curves show
that the method leads to very satisfactory results. The images are
so sharp and full of contrast, that it is sometimes almost impossible
to distinguish between the image of the first and that of the second
string. This may be seen for instance in the curves in the thesis
of Dr. BarrarrD, in which heart sounds and E.K.G. were simulta-
neously registered by the method in question.

In applying the method of simultaneous registration to electro-
cardiography special precautions must be taken. In this paper we
discuss the use of thrée galvanometers at once.

If an E.K.G. is made with only one derivation, regulating the
sensitivity of the galvanometer in the usual way, each centimetre
of an ordinate of the curve represents a potential difference of 1

DAA

millivolt, and this potential difference would actually exist between
the places of derivation, if these were not connected to the galvano-
meter.

If the body is connected to a second galvanometer, the deflections
of the first will be diminished, and this will be increasingly the case
in proportion as the second galvanometer possesses less resistance.
By a third connection the results are again reduced, and the question
therefore arises: How is the sensitivity of the three galvanometers
to be regulated, so that they will simultaneously inseribe curves
which will fulfil the conditions required: The centimetres of the
ordinates must always represent the millivolts of the potential oseil-
lations which oceur between two points of derivation of a body,
when the body itself is still free from all connections.

As long as only one galvanometer is connected to the body, at
the sudden application of ¢ millivolts in the circuit the image of the
string must be deflected by e cms. If there are three galvanometers
connected to the body at the same time, by the application of 2
millivolts the deflection must be more than e ems. In a particular
ease with the simultaneons derivations I, II], and III, we will call
the deflections required £,, ME, and #,. These deflections can be
calculated by means of the laws of distribution of currents from
the potential difference e applied each time, the resistances of the
body 4, /, and /,, and the galvanometer resistances g,, g,, and g;.

The result may be obtained in the simplest and at the same time
most practical way, by using the method of the equilateral triangle. *)

In this model of the human body the resistances of the body in
the three derivations are equal. If /,, /,, and /, really differ from
one another, they can be made equal by means of rheostats, or in

/ ll
the adjustments a mean resistance /= At — may be used.
In almost all cases this last method which is simpler in practiee, is
amply accurate enough.
The galvanometer-resistances must be actually made equal to each
other, by the addition of rheostat resistances to the two smallest

ones. We then write 9, =9, —=9, —4@-

l
If --=a, the deflection required is for each of the three string
PAG]

images /’= e(1 + a) centimetres.
We may remark in passing that at the application of e millivolts
1) Comp. “Ueber die Richtung und die manifeste Grösse der Potentialschwan-

kungen im menschlichen Herzen”, u. s. w. Prrücer’s Archiv für die ges. Physio-
logie. Bd. 150. p. 275, 1913.

245

in one of the galvanometer circuits all three of the string images
show a deflection. If the sensitivity of the strings is properly regu-
lated the string image into the circuit of which the potential
difference is introduced will be deflected by 4 ems and each of the
e ems.

other string images by //
The following case may serve as an example. In the experimental
subject Hu the resistances of the body are
/, = 1200 Ohms
(PK ae
l; == ON 5.
from which it follows that the mean resistance is / = 1000 Ohms.
Two galvanometer resistances of 4400 and 4000 Ohms are raised
by means of rheostats to 6200 Ohms and thus made equal to the
third galvanometer resistance. We then get
g = 6200, a= 5 = 0,08, and E>e(i-+ a) =—1,08 cm.

The sensitivity of each galvanometer must therefore be regulated
in such a way that when in one of the circuits one millivolt is
introduced, the string image that belongs to that cireuit will show
a deflection of 10.8 mms. The other string images will be deflected
by 0.8 mms.

The curves obtained in this way show a complete agreement
within the limits of observation with the formula quoted. In the
measurement of a curve of complicated shape with a strongly negative
peak Ry, no deviation was found to be larger than 0.1 mm.

The simultaneous registration of the E. K.G. by three derivations
has provided a new and not unwelcome proof of the accuracy with
which the string galvanometer is capable of reproducing the potential
oscillations of the human heart. For the direct practical proof that the
formula for the three derivations is right, can only be given, when
each of the three curves is accurate in itself.

It is worth mentioning, that the object can be obtained with the
ordinary commercial string galvanometers. Our curves are obtained
partly with the original model, partly with the double string-holder
of the Cambridge model.

The method here described further opens the possibility of deter-
mining the manifest value and the direction of the potential difference
in the heart itself, in an easy and certain way. If, in the measure-
ments, one is obliged to use curves which have been registered one
after the other, one often meets with difficulties. If the curves have
a complicated form it is not always easy to ascertain the corresponding

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

246

phases of a heart period that has been registered by derivation 1,
for instance, and of another period by derivation II or III.

Moreover, one heart contraction is not exactly like another. At a
superticial glance the E.K.G. of the same series, appear so similar
to one another, that one would take one period for the reproduction
of another, but, when measured, numerous small differences appear
which impede the accurate calculation of the direction and the
manifest value of the potential difference. All these difficulties disappear
when the E.K.G. is registered by the three derivations simultaneously.

The method is of service not only physiologically, but also clinically.
For the object of practical cardiography is not to ascertain the
potential difference that exists between one hand and another, or a
hand and a foot, but to obtain an insight into the working of the
heart itself *).

Physics. — “The magnetic susceptibility and the number of mag-
netons of nickel in solutions of nickelsalts.’ By P. Weiss
and Miss B. D. Bruins. (Communicated by Prof. H. A.
LORENTZ.)

$ 1. The purpose of this research was to investigate, how in
connection with the magnetontheory the magnetic susceptibility of
nickel in solutions of nickelsalts depends on the concentration of
nickel in the solution. The research was made after QuINcKE’s method
improved by PiccarD?).

Before and after every series of measurements water was measured
of which the specifie susceptibility or coefficient of magnetisation
has of late years been determined with great accuracy after different
methods.

For this coefficient Sfive gives: —0.725.10-§ at 22° C.*)
Piccarp : —0.71938.10— ,, 20° C-%)
pr Haas and DraAPIER: — 0.721.106 ,, 21° C.%)

In the following calculations has been used the value given by
PICCARD Yare 200: == — Ond 93 HOE:

The coefficient of magnetisation X/ of the solution is calculated
with the formula:

1) The complete account of the above investigation will appear elsewhere.

*) Die Magnetisierungskoeffizienten des Wassers und des Sauerstoffs. Promotions-
arbeit von A. Prccarp. Arch. de Genève 1913.

5) Sùve. Paris 1912. Thése. Ann. Chim. phys. (8) 27 p. 189—244. 1912.

') De Haas und DRAPIER. Annalen der Physik. Band 42. p. 673—684, 1913.

247

a ere k
hye = rs + ni Awater -— 7 5 pte ary Midde MIB)

where: h, =the measured ascension of the solution.
k, =the susceptibility of the air which is above the meniscus
of the solution. At 20°C. and a pressure of 760 mm.
k = 0.0294 . 10-6.

293)?
Therefore 4, = 0.0294.10-t ® ( je

(G5 ORNE
where p, indicates the atmospheric pressure decreased
with the moisture of the air.
y¥, =the density of the solution.
h =the measured ascension of the water.
k =the susceptibility of the air which is above the meniscus
of the water.
y =the density of the water.
If the solution contains 2°/, of the nickelsalt, we have according
to WIEDEMANN’s law:
WA: (100 —2@) Xwater + EANi salt
EL 100 a
This %yisai multiphed by the molecular weight of the nickelsalt
in question gives the molecular coefficient of magnetisation y”.
From 4" the coefficient of magnetisation 4%, of the nickelatom has

(LI)

been deduced by making a correction for the diamagnetism of the
anion.
These were taken :

mt OOR OS
Cle
7 en 37 —6
So, = 3371 5 1100)
yn == = (Nt). MOS
(NO,), iy

which values have been deduced from those given by Pascar by
making a correction for the value of Ywarer, Which Pascar has taken
— 0.75 . 10-6.

The formula 6, =W(XN- BRT) gives o, the magnetic moment of
the nickel pro gramatom at the absolute zero of temperature.

n= finally gives the number of magnetons of the nickelatom.

1123,5
§ 2. In the first place the aqueous solutions of NiSO,, NiCl, and
Ni(NO,), were investigated.
They have been prepared from distilled water and cobaltfree
nickelsalts from KaHLBAUM.
aie

248

The concentration has been determined by analyzing the most
concentrated solution after the electrolytic method *) with a platinum
net for cathode and a platinum spiral for anode. The rest of the solu-
tions were obtained from the analyzed by dilution. In order to
insure accuracy some have been analyzed. For example the results
of two analyses of a solution, which ought to contain 3,641 °/, NiCl,
according to the way it was prepared, were found to be 3,643°/, and
3,640 °/, NiCl,.

The following table gives the results obtained ; in the fifth column
are mentioned the values of Xy; reduced to 20° C. according to
Curmw's law (comp. $ 5).

Aqueous solutions of NiSO,.

Jo NISO,| 7 | XMigo,.105| ¥%,. 108 | AE ore Me

param. | 24.1542)| 201.6 | 443.7 447.3 445.2 16.05
param. | 16.345 | 291.3 444.0 447.1 445.0 16.05
param. | 10.341 | 290.4 444.7 448.4 444.4 16.05
param. 3.116 | 290.2 446.6 450.3 446.0 16.07
Average: 445.1 16.06

Aqueous solutions of NiCl.

99 NiC 7E, NiCl, „105 | IN: 105 | XX; 200 C, + 105 | n

param. | 22.690 3) | 289.3 | 446.6 450.7 | 445.0 16.05
param. | 16.121 2893 | 447.2 451.2 445.5 16.06
param. 95164) | 291.2 444.8 448.8 446.1 16.07
param. 5.890 291.1 443.6 447.6 444.7 16.05
param. 3.641 290.9 | 443.4 447.5 444,3 16,04
param. 3.156 | 289.2 446.2 450.2 444.4 16.02
diam. | 1.244 | 290.8 444.3 448.3 444.9 16.05
diam. | 0.623 290.8 | 4428 | 446.8 443.4 | 16.03

Average: 444.8 16.05

1) Treadwell. Quantitative Analyse.

2) Average of the results of two analyses: 24.154 and 24.154.
3) Average of the results of two analyses: 22,695 and 22,685.
4) Average of the results of two analyses: 9,513 and 9,519.

249

Aqueous solutions of Ni(NO3).

0/)Ni(NO3)> ip | KNi(NO,),* 107} Ay; 105 | XNigvec,- 108) rn
param. | 37.164!) | 289.4 445.9 449,5 444.0 16.03
param. 26.953 289.4 447.9 451.5 445,9 16.07
param. 14.873 289.3 447.9 451.5 445.8 16.07
param. 7.098 289.3 448.0 451.7 446.0 16.07
diam. 1.016 289.2 447.8 | 4514 | 445,5 16.06
Average: 445.4 16.06

Before we draw conclusions from the results obtained their accuracy
must be tested. The error in the value used for ywater is not greater
than 3°/,, at most*), from these, 2°/,, are a consequence of the error
in the measurement of the normal electromagnetic field. The propor-
tion of the susceptibility of the solution to that of the water, how-
ever, is independent of the error in the field; as in this research
the proportion of the susceptibility of the solution to that of the
water has really been determined, it is only the inaccuracy in the
determination of the ascension, which was 1°/,, at most, which con-
sists in that proportion obtained, while in the final results the error
Of water remains as well. From the results of the analyses it is
evident, that the error in the concentration always remains below 1°/,,.

Thus within the limits of experimental accuracy the value of Renee
and also the number of magnetons seems to be independent of the
nature of the salt and of the concentration of the solution. This
result agrees with that of Cabrera’), who from his research about
the aqueous solutions of nickelsalts also concluded the atomsuscepti-
bility to be independent of the concentration and the nature of the
salt. For the number of magnetons of the nickelatom in solutions
of NiSO,, NiCl,, and Ni(NO,), he respectively gives the numbers
16,07, 16,03 and 16,02.

The number of magnetons of nickel in dissolved nickelsalts thus
seems to be a whole number within the limits of experimental
accuracy and as such supports the magneton theory.

§ 3. Then the ammoniacal solutions of nickelsalts were investigated.

1) The analyses gave 37,1649/) and 37.131°/), the former value has been taken,
because the second is less reliable.

2) A. PrccArp, ibid. p. 53.

3) CABRERA, Morres et Guzman, Arch. de Genève T. XXXVII, p. 330, 1914,

250,

If ammonia is added to an aqueous solution of a nickelsalt, we get
the blue coloured solution of the complex nickel-ammonia compound.
As with these solutions the strong evaporation of the ammonia
makes it impossible to determine with sufficient accuracy the correction
for the magnetic susceptibility of the air, these measurements were
carried out under an atmosphere of hydrogen and ammonia, which
was obtained by leading the hydrogen through an aqueous NH,-solution
of about the same NH,-concentration as the solution to be investigated.
The magnetic susceptibility of this atmosphere is so small, that it
may be taken equal to zero, thus formula (I) becomes, as with these
measurements the water measurements also were made under a
hydrogenatmosphere :
h

=S Was. 2
h

The calculation of Yv: sa, from Xr with the ammoniacal solutions
is. performed analogous to the calculation of Xn; sat from Xr, with
the aqueous solutions. However not only the susceptibility of the
water but also that of the ammonia must be taken into account.

The measurements of aqueous ammonia solutions gave for XNu, :

— 0,947.10—-6
— 0,950.10—6
— 0,942.10—6
— 0,954.10-6

Average: — 0,948.10—6
while Pascar gives: ny, = — 0,881.10-°.
Instead of formula (II) we get:

as (L00 —e—y) Awater = ANH, + a XNi salt <a r)

where @ indicates the percentage of nickelsalt, y that of ammonia.

As from some experiments in the beginning it was evident, that
with a certam concentration of the nickelsalt within the limits of
experimental accuracy a fixed value was found for Xn; sur calculated
with formula (LL) for diferent NH,-concentrations, the conclusion may
be drawn that %yq, has the same value no matter in what degree
the ammonia is bound to the nickelsalt or finds itself free in
Le solution. The susceptibility therefore may be assumed as an
additive property and the correction for the ammonia may be
deduced from the whole ammonia quantity.

The following table gives the results obtained with the ammonical
solutions :

251

Ammoniacal solutions of NiSO4.')

0/0 NiSO4| Oo NH3 | di NiSO,* 105 k Ni: 105! Ni 200, - 105 n

param. | 4.441 8.628 | 2901 | 419.7 | 423.4 | 419.2 | 15.58
param. 3.244 8.061 | 290.0 | 419.9 | 423.6 | 419.3 15.58
diam. | 2:52 6.225 | 290.0 | 420.3 | 424.0 | 419.7 | 1559
diam. 1.522 6.557 2931 | 415.1 | 418,7 | 418.9 | 15.57
diam. 1.078 3.479 291.0 | 420.5 | 424,2 | 421.2 | 15.62
diam. 0.535 2.937 | 291.1 | 421.0 | 424.7 | 421.9 | 15.63

Average: 420.0 15.59

Ammoniacal solutions of NiCL.?)
0, oNiCl, O/ NH3 | T | NiCl, . 105 Ini „105 | (Ni 200 C.* 105 | n
param. 4,342 6.875 | 290.9 417.6 | 421.6 418.6 | 15.57
param. 3.141 7.517 | 291.0 417.0 | 421.0 | 418.2 | 15.56
diam. | 2209 | 6.704 | 2804 4182 | 4223 417.1 15.54
| | |
diam. 1,688 4,478 290.8 | 411,5 | 4215 418.4 | 15.56
diam. 1.197 | 3744 | 2894 | 420.1 | 424.2 419.0 | 15.58
| | |
diam. 0.569 | 1.901 | 289.5 4215 | 4256 | 420.5 15.60
Average: 418.6 15.57

Ammoniacal solutions of Ni(NO3)3.3)

OoNi(NO3) | %/0 NH; | T | ANiNOss: 108 ea XNi ooo. 105. |
param. 5.276 5.520 290% | 4112 | 420.8 | 417.8 | 15.55
param.) 4.262 | 6.692 | 290.9 ANTS | A228) 418.1 | 15.56
diam. | 3.032 | 4.566 | 291.2 418.5 | 422.1 | 419.5 | 15.58
diam. | 2.556 5.639 | 289.6 | 421.0 | 424.6 | 419.7 | 15.59
diam | 1919 | 5.512 205 4210 | 4247 | 419.6 | 15.59
diam. | 1.041 | 4918 | 289.5 420.7 424.4 | 419,3 15.58
—— Average: 419,0 15,51

1) These solutions were prepared by dilution, and mixture of an aqueous NiSQ,-
solution, for which two analyses gave 16,587 and 16,592°/, NiSO, and a solution of
ammonia in water, for which two analyses gave 11,53 and 11,49°/, NH. The
ammonia analyses were performed by titration with 1/) normal chlorie acid.

*) These solutions were prepared by dilution and mixture of an aqueous NiCl-
solution for which two analyses gave 17.216 and 17.190 °%/) NiCl, and a solution
of ammona in water for which two analyses gave 11.782 and 11.783 °/, NH3.

3) These solutions were prepared by dilution and mixture of an aqueous so!ution
of Ni(NOs)., for which two analyses gave 19.539 and 19.514 %, Ni(NO3); and the
same NHj-sotution in water as with the ammoniacal NiCl-solutions.

252

From the results obtained the conclusion may be drawn, that for
the ammoniacal solutions Nea and also the numbers of magnetons
+ - ue

are somewhat smaller than the corresponding quantities for the
aqueous solutions. For the three salts investigated this difference is
the same within the limits of experimental accuracy, for instance
this difference is for the number of magnetons 0.47 0.48 and 0.49
respectively for the NiSO,, NiCl, and Ni(NO,), solution.

§ 4. Addition of H,SO, to a aqueous solution of NiSO, and of
(NH,),SO, to an ammonical solution of NiSO, evidently was without
influence on the number of magnetons:

7, NiSO, _ °/, H, SO, n
3.619 16.01
3.241 9.493 16.02

*/, NiSO, NH, °/, (NH,),80, n
3.659 8.308 15.46
3.187 7.238 12.884 15.48

§ 5. Finally it has been investigated how A, depends on the

temperature, by measurements of a aqueous NiCl,-solution at 6°.0,
16°.7 and 89°.7 C. and of an ammoniacal NiCl,-solution at 6°.7,
18°.6; 20°22, and 562220:

As only that part of the tube which was in the magnetic field
had the temperature 7, while the rest of the tube and the basin in
which the end of the tube bad been immersed were at the tempe-
rature © C. of the room, a correction must be made for the inhomo-
geneity of the liquid in the tube and the basin; therefore formula (I’)
becomes :
hee

Xr = Ywater

Where 7? indicates the density of the solution at the temperature 77,
and y, the density of the solution at the temperature ¢.
The coefficients of dilatation necessary for the calculation of yr
have been determined:
Coefficient of dilatation of an aqueous NiCl,-solution containing
4.614°/, NiCl, between 5°.0 C. and 187.8 C.: 0.00021
between 5°.9 C. and 22°.0 C,: 0.00017
Average: 0.00019

253

between 18°.8 C. and 89°.5 C.: 0.00042
between 22°.0 C. and 90°.3 C.: 0.00044

Average: 0.00043

Coefficient of dilatation of the solution containing 4.611 °/, NiCl, and
6.782 °/, NH, between 4°.8 U. and 19°.1 C.: 0.00023
between 3°.7 C. and 19°.8 C.: 0.00018

Average: 0.00020

between 19°.4 C. and 59°.0 C.: 0.00037
between 19°.8 C. and 60°.8 C.: 0.00039

Average: 0.00038
These measurements were also executed under a hydrogen atmos-
phere and gave the following results:

el EN
VoNiCk | T — | Xyj- 105 | ASZ
| | | |
| | |

4614 | 2790 | 4667 | 1302 | 19C.

461 289.7 | 450.7 | 1306 | 16.7
4.614 | 3627 | 357.7 | 1.297 | 184

Average: 1.302
Be 7’ caleulated from the above average 444.8 for

gives 1.303.

ya
Axi 20°C.

Oo NiCl | %NH3 | TF |Xy;,-105| AG-7 | ¢
| |

4.611 6.782 207.7 4349 | 1.216 | 20.9
4.611 6.782 | 291.8 418.9 1.222 18.8

4.605 | 6.800 | 293.2 | 4182 | 1.226 21.2
| |

4,605 | 6800 | 3292 | 3723 | 1.226 | 20.6

Average: 1.223
Ni. T calculated from the above average 418.6 for 48, gives
1.226.
From the results obtained it is evident, that within the limits of
experimental accuracy the atomsusceptibility of nickel in solutions
of nickelsalts follows Curin’s law.

Zürich, July 1914. Eidgenössisches Physikgebüude.

254

Physics. — “Magneto-chemical researches on ferrous salts in solution”.
By P. Weiss and Miss C. A. Frankamp. (Communicated by
Prof. H. A. Lorentz).

The investigation included ferrous sulfate 7 aq. and the ammoniacal
double-salt thereof, ferrous-ammonium sulfate 6 aq.

According to the method of Quincke, as it has been finally improved
by Piccarp'), the ascension is measured of the solution, placed
between the pole-pieces of a Werss-magnet. Standard-liquid is distilled
water, which is also used in preparing the solutions.

According to the equation:

soe ho, tale)
0 sol. C Q

we are able to deduce the coefficient of magnetisation from the
ascension; y being this coefficient, ~’

the one, belonging to water,
k,, and k,, the susceptibilities of air at the average temperatures of
the experiment, finally 4 and h’ the ascensions of the solution and
of water respectively.

The meaning of the o’s is evident.

By means of the theorem of WIEDEMANN

Hv U
nii ni fi
4 ( aE + To %

x being the percentage in weight of the salt without aq, % has been
calculated, which, multiplied by the molecular weight of the salt,
gives the molecular coefficient of magnetisation.

After correction as to the diamagnetism of the other elements,
the atomic coefficient of magnetisation of iron %, is obtained, from
which, by means of the well-known formulae:

2 On, =V BRT Ya

and

the number of magnetons may be derived; 0, being the maximum
value of the molecular magnetisation at the absolute zero, whereas
1423.5 indicates the average value of the so-called grammagneton *).

Since ferrous-salts, and ferrous sulfate in particular, are easily
oxydated when exposed to the air and even in solutions, we soon
carried out our measurements in a magnetical-indifferent atmosphere

1) A. Piecarp. Diss. 1913 Zürich.
2) P, Weiss. Physik. Zeitschrift 1911 S- 955.

255

of hydrogen, which at the same time simplified our calculations
considerably.

Henceforth the solutions were prepared with boiled water.

They were analyzed as well by precipitating with ammonia as by
reducing with potassiumpermanganate '); in the first case we oxydated
with nitric acid till the entire transformation into ferric-salt had
taken place; whereas in the second case the permanganate was
tested with oxalate; the second method proved sodium the most
reliable (accuracy 4 °/,,).

Save the ferrous sulfate of Merck, all the material was provided
by KAHLBAUM.

The ferrous ammoniumsulfate was the so-called ‘“Manganfreie
Morsche Salz’. On account of the ferric-salts, examined till then ®,
we could expect a dependence of the number of magnetons on the
concentration with ferrous-salts as well.

However, our experiments showed an absolute constancy of this
number as may be seen from the following tables:

TABLE I. Ferrous-sulfate.

X.106 solution | %,.104 after correction) n= 11235 Te 0/ of salt
— 0.321 123.3 | 26.49 288.6 0.488
— 0.319 122.9 26.48 288.6 0.492
— 0.306 121.9 | 26.46 290.7 0.512
— 0.0014 122.6 26.45 288.8 | 0885
-- 0.0223 122.4 26.56 291.1 | 0.915
+ 0.2724 121.9 | 26.46 290.7 1.229
+ 1.256 122.0 26,45 290.3 2.445
+ 2.358 122.0 26.47 290.7 3.810
+ 6.140 121.1 26.52 294.1 8.560
+ 8.100 123.3 26.56 289.6 10.800
+ 9.010 121.4 2657 | 242 | 12,100
+ 12.160 | 123.1 | 26.55 2898 | 15.800
+ 12.420 122.8 | 26.56 290.9 | 16.170
+ 15.870 | 121.2 | 2654 | 2042 20.700

Average value of n — 26.51.

1) TREADWELL, Quantitative Analyse.
2) B. CABRERA et E. Montes, Mai 1913 Arch. des Se. Ph. et N. Genève, whose
results were on the whole confirmed by our own experiments (not published though).

256

TABLE II. Ferrous-ammoniumsulfate.

% . 106 solution | %,.104after correct. | n= is | L 0 of salt
— 0.609 121.5 26.49 293.2 0.2503
— 0.606 121.6 26.49 292.2 | 0.2549
— 0.602 | 120.8 26.45 292.5 0.2639
— 0.512 120.6 26.47 294.4 0.485
— 0.407 121.3 26.47 292.3 0.726
— 0.397 12) 26.49 293.0 0.751
— 0.057 123.1 26.54 289.3 1.520
40.135 | 122.3 26.50 290 8 1.975
40.152 122.7 26.48 289 2 2.007
0.544 122.4 26.44 280.0 | 2.918
+ 0.563 121.2 26.44 292 0 2.980
+ 0.570 122.0 26.46 2905 2.990
++ 0.587 | 121.9 2645 | 2905 | 3.030
+ 1.204 | 121.6 | 26.48 291 8 4.470
+ 1.179 | 121.2 26.44 2918 | 4430
+ 1.440 | 122.9 | 2652 | 2806 5.000
+ 1.877 | 122.0 | 26.50 | 2912 | 6.020
+ 3.510 | 122.6 26.53 | 2904 9.750
+ 3.580 | 121.7 26.44 | 290.9 | 9.980
43880 | 121.5 2650 | 2924 10.710
+ 4,740 | 122.9 2657 | 2908 | 12570
+ 5.820 | 122.5 2650 | 2019 | 15.120
+ 6.890 | 123.3 26.59 290 4 17.450

Average value of n — 26.49,

However, in the lower concentrations, the state of things never
seemed so simple — now the number of magnetons rose to 27 and
higher, now it fell to 26.

The thought of traces of impurity suggested itself first; or perhaps
the salt contained an excess of acid, however small it might be.

Yet, a great many experiments, where solutions were measured
with widely different additions of sulphuric acid, showed again and

din

257

again the independence of such influences — and as moreover it
was evident from these experiments that solutions, thus prepared,
were more constant and therefore more fit for experiment, we finally
carried out our measurements of the lower concentrations on acid
solutions only.

So here too the constancy of 2 showed itself.

To be able to calculate the results, special measurements were
required on sulphuric acid and out of the following dates the
average value for lower concentrations x .10° = — 0.358 is used.

The dates, marked * are taken from CABRERA ’).

TABLE III. Sulphuric acid.

Nas IGS Olo

—0.358 8.250
—0.336* 9.282*
—0.350 | 24.110
—0.352 | 27.150
—0.364 43.500
—0.357 46.200
—0.379* | 60.300*

—0.389 90.800
—0.392 90.800

Notwithstanding this, there still remained the first deviations in
the strongly diluted solutions and the question was to which cause
they ought to be attributed.

It was natural to consider the increased magnetisation as the effect
of oxydation, the more so since Casrera and we found higher
values for the ferric sulfate.

However, a solution of 0.25°/, with an excess of acid of 1.04°/,,
gave, after having been heated in boiling water and cooled again,
exactly the same value.

This experiment might be considered as a disproof. At the same
time it shows how the addition of an acid is an essential condition
to the constancy of the solution, so that finally the chief cause seems
to be the hydrolysis, which is checked by the acid.

1) CABRERA, Arch. des Sc. Ph. et Nat. Dec. 1913 Genève.

558

If, on the other hand, we could further the hydrolysis, and thus
accelerate the “transformation in time” which showed itself in many
cases, a positive proof would be given.

Since, however, traces of NaOH already form a fine granular
precipitate, such an experiment seems to be excluded from measurement.

The chemical complications, which in particular for iron-salts are
so numerous, constantly impede the investigation of these salts.

Zürich Jali 1914. Physikgebaiide des Eidgenissischen
Polytechnikums.

Microbiology. — “A microsacchartmeter”. By Miss. H. J. van
LutsenpurGc Maas and Prof. G. van ITerson Jr. (Communicated
by Prof. M. W. BeIERINCK.)

In the conscientious and extensive work of A. J. Kruyver: “Bio-
chemische suikerbepalingen” *) (Biochemical Sugaranalysis) a fermen-
tation-saccharimeter is described, which enables us to quantitative
fermentations under perfect sterile circumstances. The quantities of
the different fermentable sugars, possibly at the same time present,
are to be calculated from the quantities carbonic acid, produced in
such an apparatus from a fixed volume liquid by different ferments.

The rich material, which Krurver published, shows in a convincing
way, how this apparatus gives a most. satisfactory and at the
same time simple solution for the problem of quantitative sugar-
determinations by means of the fermentation-method. Such a solu-
tion has in spite of the researches of many predecessors never been
found.

The application of this method in studying biological questions,
from which Kruyver gives already some interesting examples, promises
most important results.

By no means the fermentation-saccharimeter, whose description
will follow, will be able to supersede the apparatus, used by Kr.urver.
The latter will always be preferred when accuracy is required
and a sufficient quantity of the sugars is to be had. The reason
why, will be explained later, we only mention it here, because the
applicability of the here described method is justified by the results,
found with the apparatus of which Krurver gives the description.

In the first place some remarks may follow on this last appara-
tus and the limits of what can be attained will be indicated.

1) Published by E. J. Britt at Leiden, 1914.

259

In the current form the apparatus wants about 1 ce. liquid to
ferment. By taking a smaller size this volume can be reduced to
0.5 ec, but the accuracy
the convex mercury meniscus). For constructive and practical reasons
it seems impossible to reduce the size more.

The quantity of fermentable sugar, used in the apparatus of
ordinary size is about 40 mgr. (corresponding with 10 ce. CO)
and should not be less than 4 mgr. The last limit is determined by
the circumstance, that almost an equal volume of the earbonie acid
as is produced from this quantity of sugar by the fermentation is
soluble in 1 ce. of the sufficiently fermented liquid under average
barometric pressure and at the temperature of the room. By applying
a manipulation, viz. the addition of a known, small quantity ferment-
able sugar, it is possible to determine smaller quantities of sugar
with this apparatus, but the analysis is not very accurate in that
case. With the developing of small quantities of carbonic acid the
influence of the factor, which is to be charged for the gas, dissolved

of the reading diminishes (influence of

in the fermented liquid, is comparatively very large, and just this
factor is by the changing composition of that liquid always some-
what uncertain.

The inoculation-material for this apparatus is a small quantity of
yeast, which is taken from a tube-culture with the aid of a thick
platinum needle. That yeast quantity is so chosen by Kuvyver, in
connection with a research of JopLBaupr, that the proportion yeast
to sugar is about 1:2. The influence of the autofermentation is can-
celled. With this yeast-concentration the fermentable sugars have
usually completely disappeared after about 40 hours (when raffinose
is present the time, necessary for the fermentation is much longer).
This long fermentation makes it necessary to sterilize carefully the ap-
paratus, the fermenting mixture and the mercury, shutting off the liquid.

For many biological researches a method for quantitative sugar-
analysis would be desirable for quantities smaller than 1 ee. and
often it will be necessary to estimate smaller portions than 4 mer.
with greater accuracy than is possible with the aid of the mani-
pulation in the apparatus referred to. Therefore now an apparatus
will be described with which this purpose can be reached. The
quantities of sugar, which can be fermented are between 3.5 mgr.
and 0.1 mgr. and a drop of 0.010 ce. will be sufficient to perform
the analysis, though it is preferable to take a larger quantity of
the liquid. Moreover it will be evident that with this new method
the fermentation will be much sooner finished than with the old
one, so that no sterile circumstances are necessary.

260
$ 1. Description of the microsaccharimeter.

The principal part of the microsaccharimeter (see the Plate _, tig. 1)
is made of a capillary tube of thick glass, with an inner diameter
of about 2.8 mm. At a short distance from one of the ends this
tube has been blown to a cylindric reservoir, the content of which
is about 1 ec. and with a short neck. The other end of the tube has
been enlarged to a funnel, of a content of about 1.5 ec. The length of
the glass apparatus, measured from the point on the utmost right to
the utmost left is about 35 em. (in connect with the usual dimensions
of the thermostats). The capillary tube has such a curve under the
reservoir that the longest, straight part (see fig. 1) mounts to about
half way the reservoir. This long straight part has been calibrated ;
the scale-division is in parts, each from 0.01 ec. The zero-point
is as near as possible to the downward directed curve and the
division continues till the upward bent. With the here mentioned
dimensions this division will go to about 0.9 ec. and it is desirable,
that it should not be much shorter. The dimensions are for the rest
so chosen, that the content of the reservoir is a bit smaller than
that of the bent and straight part of the capillary tube and the
funnel together, a circumstance, which is to be observed by the
constructor of the apparatus. The finishing of the neck of the small
reservoir is to be done carefully. The opening of that neck is
upward somewhat enlarged in a conical form, while also from the
very short, narrow part of this opening downward a very regular
conical transition must be (see fig. 3).

The glass apparatus is placed on a small stand (see fig. 2), made
from a wooden platter (5.5 x 38 cm’.), on which a wooden block
has been fastened, that bears a cork clamp. This clamp is made
from a conical cork of good quality (largest diameter 4 em, high
3.5 em.). This cork has on the short side a groove, which continues
to some distance from the large side. The curved part of the
capillary tube fits in this groove. The cork is further on at two
sides filed parabolical (see fig. 2).

The glass apparatus is to be fixed in every desired stand by a
brass pin with winged nut, fitting in the cork just above the curve
of the capillary tube. By removing the brass pin the glass apparatus
can be taken from the stand, which is necessary to clean it. To
sterilize the apparatus is superfluous, but it should be dried carefully.

The two mercury levels, being after the fermentation in the reser-
voir and in the divided part of the capillary tube, can be placed
on the same height by different simple ways. A rather good method

Miss H. J. VAN LUTSENBURG MAAS and Mr. G. VAN ITERSON Jr: “A microsaccharimeter.”

EE,

LET

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

261

is by using an apparatus as shown in figure 4. This apparatus bears
a pin, which can be moved over a vertical stand. The pin reaches
before the microsaccharimeter, when the stand is placed behind it.
To compare the mercury levels all is placed on an exactly horizontal
table and by removing the apparatus over this table and changing
the angle between the capillary tube and the platter, the two levels
ean be brought on exactly the same height.

For using this microsaccharimeter we want (besides different
ferment-cultures): dried and cleaned mercury, paraffin with a melting-
point of about 55° C., red sealing-wax of superior quality, some
metal spatulas, a platinum spatula in a needle-holder, a number of
dropping syringes, some capillary tubes (diameter 1 mm.), some
small sterile glass tubes with cotton-wool stops and sterile main-water.*)

$ 2. Preparation of the yeasts.

For a quantitative analysis with the microsaccharimeter the yeast
is to be submitted to a very simple preparation. The yeast quantity,
used in this apparatus is in proportion to the quantity of sugar
rather large. So the volume of the carbonic acid, developed out of
the glycogen present in the yeast can often be very important com-
pared to the gas, produced by the fermentation of the sugar. This
difficulty is to be prevented ; before bringing the yeast in the appa-
ratus, it is made free from glycogen by auto-fermentation.

The different ferments are the best cultivated in the ordinary
culture-tubes on the surface of malt-gelatine. When tubes of a large
size are used, one contains enough yeast to do at least six quanti-
tative determinations with the microsaccharimeter. With the aid of
a sterile platinum spatula the yeast is to be carefully taken from the
gelatine-surface and divided in some ce. sterile main water in a glass
tube stopped with cotton wool. Then the tubes with the different
yeasis are placed in a thermostat at 380° C. With the aid of the
iodine reaction it can be settled that under these circumstances all
the glycogen has disappeared by auto-fermentation after four hours.

After this preparation the yeast has sunk to the bottom of the
tube and the water, standing above, can easily be taken away
with a dropping syringe. For this no sterile syringe is wanted,
but for each other kind of yeast a new or cleaned one is to be
used.

1) The microsaccharimeter is to be had at J. CG. Th. Marius, Lim., Utrecht
the ferment cultures at the “Centralstelle fiir Pilzkulturen” at Amsterdam.

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

262

In the water above the yeast but little carbon dioxide is dissolved
In the following calculation the water has been supposed to contain
no carboni¢ acid, so a small, practically to be neglected, mistake is made.
This mistake is completely to be avoided by refreshing the water above
the sunken yeast, which too should be taken away with a dropping
syringe. The sunken yeast is divided in the remaining water and
brought into the saccharimeter with a capillary tube.

§ 3. Method of using.

In the first place the microsaccharimeter is to be filled with a
certain quantity of dried, cleaned mercury.

The nut-wing is unscrewed and the glass apparatus placed as
fig. 2 shows. The filling is done by the funnel, with a dropping
syringe. When the funnel is full, it is carefully raised; the mercury
streams to the reservoir A and remains partly in the capillary tube.
The next lowering of the funnel makes the mercury stream partly
back. By addition or removal of mercury tbe quantity can be
taken so, that the reservoir with its neck and the capillary tube is
filled as far as or just past the zero-point. To control this, the funnel is
raised till the mereury reaches the border of the opening of the
neck; the mercury will then be adjusted at zero, or between the
first marks. After the apparatus has been filled with mercury, it
is placed in the original position and with the aid of a metal spatula
a bit of paraffin, melted on that spatula, is spread on the polished
surface of the neck.

Only a thin cover is wanted, but it should reach the border of
the opening; it is even to be preferred to cover the inner-wall of this
neck over a short distance, but it is not necessary.

Now the nut-wing is fastened, but so, that the glass apparatus
can still be moved in the cork and remains in every required posi-
tion, when released. Then the apparatus is placed so that the
tangentplane to the mercury level in the neck coincides with the
paraffin cover. Therefore the eye is kept in the tangent-plane to
this surface and the funnel is to be raised till the mercury meniscus
can just be seen. In this phase the first reading of the mercury
in the calibrated tube is made.

By the action of the capillarity in that calibrated tube a strongly
convex meniscus is formed and the position of the utmost tangent-
plane is to be read without difficulty with the naked eye up to in
tenth parts of the calibration.

Next a drop of the fermenting liquid is brought on the mercury

268

and on the surface of the neck with the aid of a dropping syringe.
The size of this drop is to be regulated by the quantity of sugar to be
fermented. This quantity ought not to surpass 3.5 mgr. and practi-
cally not to sink under 0,1 mgr. The concentration of the solution
should be more than 0,4°/,. Good results are to be had with a
3°/, sugar solution, from which it is best to take drops of 0,06—
0,08 cc.

After this the funnel is carefully lowered; thereby the drop of
liquid is drawn into the apparatus. This can be performed without
any loss of liquid, if only the paraffin cover have been laid down in
the right way on the neck of the reservoir. Should however any
liquid be left behind, then this has to be removed with a small
piece of filter-paper. ~

The meniscus of the solution in the upper part of the neck will
be convex, especially when some paraffine had been brought along the
inner side of the neck. This shape of the meniscus can be obtained
in the best way by making the solution rise from a lower part of
the neck up to the top, taking care however, not to have it lowered
under tbe narrow part. In this way it is possible to bring the
tangent-plane at the meniscus on the level of the upper surface of
the neck. After fixing the apparatus in this position, the 274 reading
of the meniscus of the mercury in the straight capillary glass tube
is made.

The difference between the two first readings gives: the volume
of the sugar solution to an accuracy of 0,001 ce.

Now again the liquid is a bit lowered, but not so far as to reach
the narrow part. Then, with a thin capillary glass tube, we add a drop
of yeast-suspension, which has been prepared previously as already
indicated. The drop is carefully thrown into the apparatus, until the
meniscus, which again will be convex, reaches the same level as
mentioned before. Now the 38’7eading is taken. :

The difference between the 3rd. and the 2nd. reading gives: the
volume of the added yeast-suspension. Care must be taken that to
1 part of sugar about from 5 to 8 parts of yeast be added (weighed in
living state)'). With sugar concentrations of about 3 per cent and with
suspensions of yeast, prepared in the described way, this can be
done by taking the volume of the suspension nearly the same as that
of the sugar solution.

After this 8rd. reading the liquid is allowed to go down to the
narrow part of the neck; there the meniscus will be decidedly con-
1) Just by the choice of these large quantities of yeast, the fermentation-time

is much reduced, compared with the duration of the analysis, made by Kruyver.
iis

264

save. Then one melts some paraffine on a small metallic spatula and
lets it flow along the inner side of the neck on the surface of the
liquid. In this way it is possible to fill up the whole upper part of
the neck with paraffin, without any difficulty and with a startling
result. No air bubble ought to be present between the liquid and
the paraffin, but no difficulties will arise, should a bubble be present,
provided its volume is small compared with that of the carbon dioxide,
evolved by the fermentation. Once the paraffin solidified, the
4 reading is made.

After this the apparatus can be sealed definitively, for which sealing-
wax was used, as paraffine shrinks, when it solidifies and easily gets
loose from the glass. The application of the sealing-wax is as
follow. At the outer side of the round upper part of the neck,
a ring of paraffin is taken away with a small knife. Care should
be taken, not to damage the stop of paraffin, which seals off the liquid
in the neck. Now on a small metallic spatula some sealing-wax is
liquefied by heating and the melted wax is put on the part of the
neck, from which the paraffin had been taken away. Not before the
wax is well fixed on the glass, a drop of liquefied wax is put on
the paraffin stop. Now the whole closure can be perfected by adding
more sealing-wax.

This done, one puts the apparatus in the thermostat of 30° C.,
fixing it in the position of figure 2. The fermentation will be com-
pletely finished within 6 hours’). This time past, the apparatus is
taken from the thermostat and fastened in such a position, that the
mercury in the capillary tube and in the reservoir are on about
the same level. Two hours are quite sufficient to have the apparatus
cooled to the temperature of the air. The 5% reading is then made,
but not before the mercury in the tube and in the reservoir is
carefully placed on the same level. This can be done, as already
indicated, by means of the small auxiliary apparatus, described in
§ 1. As the same time the temperature of the air and the barometer
are read. Now all data, necessary for the calculation of the analysis
are known.

In the experiments, dealed with in § 5 of this communication,
the preparation of the yeast took place in the morning; the miero-
saccharimeters were put into the thermostat at about 3 o’clock in the
afternoon and were taken out of the thermostat in the evening of
the same day. The last reading was made next morning.

1) Till now, we did not yet study the fermentation of raffinose with this appas
ratus, it seems possible, that this sugar will ask a longer time to ferment completely.

265
§ 4. How to calculate the results.

The difference between the 5” and the 4% reading gives: the
volume of the gaseous carbon dioxide, present in the apparatus at
the end of the fermentation. Another portion of carbonic acid
however is retained by the liquid and this portion too has to be
taken into account. Now Kruyver observed, that when sugar is
fermented in yeast-extract at 15° C. and 760 mm., in 1 ce. of
the liquid a quantity of carbonic acid is left behind which has a
volume of 1.2 cc. at O° C. and 760 mm. (provided that super-
saturation of the liquid is avoided). By Bonr and Bock however
it was pointed out that at 15° C. and 760 mm. pure water retains
a volume of carbonic acid, which after reduction to 0° C. and 760 mm.
amounts to 1.019 ce. The fact that Kiuyver found more, can be
explained by the special nature of his liquid.

Though in our experiments the carbon dioxide was not dissolved
in pure water, as every fermented liquid retains alcohol, yet our
liquid approaches more to pure water than yeast-extract. It is very
probable, that under these circumsiances the foresaid number falls
between the two numbers, mentioned above. Moreover our readings
were made at temperatures between 17° and 20° C. Now the
solubility of carbon dioxide diminishes rather rapidly, when the
temperature rises. After Bonr and Bock the foresaid volume becomes
0.878 ec. at 20° C.

For these reasons we assume the forementioned volume, under
thes conditions of our experiments, to be 1 ec. This simplifies the
calculation.

The total volume of carbon dioxide of 0° C. and 760 mm. now
can be found by reducing at first the gaseous carbon dioxide to
that temperature and pressure, which may be done quite efficiently
by means of a table, published by Kuiuyver’). This done, the volume
of all the liquid is to be added (viz. the difference between the 3rd.
and the Ith. reading).

Krurver made a large number of determinations of the volume
of carbon dioxide (reduced to O° C. and 760 mm.), obtainable
with 6 different species of yeasts from 40 mer. of 8 different
sugars in the apparatus, used by him (see table XXVIII of his
publication). Then also the number of milligrammes of sugar, equi-
valent to 1 ee. of CO, at that temperature and under normal
pressure were known. We have limited our experiments for the

266

yeasts to Saccharomyces cerevisiae (press-yeast), Torula dattila and
Torula monosa, and for the sugars to glucose, fructose, saccharose
and maltose. Especially the quantitative determination of these
sugars, separately or as mixtures will be required in biological research
work. Now these determinations are possible with the 3 yeasts
mentioned, with this exception alone, that glucose and fructose
are always found together. The first of the 3 yeasts is capable to
ferment the 4 sugars, the second the monoses and saccharose and
the last ferments only monoses. >

Now Ktvyver established, that out of the 4 mentioned sugars in
his apparatus nearly the theoretical quantity of carbon dioxide is
produced. Certainly in our microsaccharimeter we may expect no
smaller quantity of this gas, as reproduction of yeast is practically
impossible within the 6 hours of our experiments, whilst under the
circumstances of Kruyver some reproduction may be expected.
Therefore we took the theoretical value to make our calculations.
This means, that we supposed a yield of 1 ce. of carbon dioxide
(of O° C. and 760 m.m.) to be equivalent to 4.05 mgr. of absolutely
dried hexose (respectively to 4,45 mgr. hexose-hydrate, containing
1 H,O) and to 3,85 mgr. of absolutely dried bihexose (respectively
to 4,05 mer. of bihexose-hydrate, containing 1 H‚O).

§ 5. Numerical illustration.

Here follow some examples of determinations, which we performed
with the microsaccharimeter. We give only a small number of
applications of this apparatus on the analysis of natural products,
as we intend to publish a more detailed communication on this
subject later on. Here we principally mention the results of fermentations
with sugar solutions; we took the most pure sugars to be got. Thus,
with the numbers published here, we intend to demonstrate the
applicability of the method.

1. A 3 per cent. solution of glucosehydrate was fermented by °
Torula monosa. The readings were successively: 0,012; 0,070;
0,128; 0,138 and 0,486 ce. The last reading was made at 19°C.
and under a pressure ‘of 767 m.m.

The gaseous carbon dioxide, present in the apparatus after the
fermention, was 0,303 ec. After reduction to O° C. and 760 mm.
this becomes 0,286 ec. The volume of the liquid in tbe apparatus
is found to be 0,116 ec. Thus, the whole volume of carbon dioxide
of O° and 760 mm, obtained by the fermentation, may be supposed
to be 0,402 cc, e

267

This carbon dioxide is equivalent to 0,402 x 4,45 = 1,78 mer.
of glucosehydrate. Originally the apparatus received 0,058 cc. of
liquid, corresponding to 1,74 mgr. of glucosehydrate.

2. With 7. monosa we fermented a 1 per cent. solution of glucose-
hydrate. The successive readings were: 0,020; 0,030; 0,044 ; 0,053 ;
0,059 ce. The last reading was taken at 19° C. and 760 mm. The
quantity of gaseous carbon dioxide in the apparatus after fermentation
is found to be 0,006 ce.; after reduction to 0° C. and 760 mm.
this volume remains the same. The volume of liquid was 0,021 ce.
Consequently the total amount of carbonic acid of O° and 760 mm.
may be assumed to be 0,027 ec. This gives 0,027 > 4,45 = 0,12 mer.
glucosehydrate, whereas we took 0,10 mgr.

3. In a similar way we obtained the following results by
fermenting other solutions of glucosehydrate with 7. monosa. The
two corresponding numbers are placed one beneath the other.

daken: 1:89 1.77 141 1.35 1.59 1.59 1.83 1.74 1.89 mer.
Found: 1.74 1.78 141 1.38 1.57 1.64 1.81 1.78 1.86 mer.

Taken: 2.01 0.34 0.30 0.21 0.19 010 216 1.71 0.84 mer.
Found: 1.99 0.38 0.29 0.26 0.22 0.12 2.20 1.65 0.93 mer.

4. Solutions of glucosehydrate, fermented by 7. dattila gave the
following results :
Taken: 1.29 2.67 1.62 2.04 1.68 1.32 1.89 1.56 1.65 1.98 1.89 mer.
Found: 1.54 2.65 1.74 1.94 1.62 1.34 1.93 1.60 1.78 1.93 1.65 mgr.
5. In the same way we found by fermenting solutions of glucose-
hydrate with S. cerevisiae (press-yeast) :
Taken: 1.56 1.83 2.18 2.13 2.04 1.80 2.31 1.50 mgr.
Found: 1.62 1.90 2.18 2.14 2.20 2.16 2.38 1.82 mer.
6. Quantitative determinations of fructose by fermenting with
T. monosa gave us:
Taken: 1.65 1.68 1.26 2.01 2.25 mer.
Found: 1.58 1.69 1.23 1.97 2.10 mer.
7. From similar determinations of fructose, fermented by 7. dat-
tila resulted :
Taken: 1.47 1.62 0.99 1.44 1.89 1.50 mer.
Found: 1.67 1.88 1.12 1.44 1.88 1.64 mer.
8. The results of fermenting fructose with $. cerevisiae were these:
Taken: 1.56 1.68 1.80 1.56 1.41 1.68 mer.
Found: 1.5) 1.81 1.80 1.60 1.15 1.63 mer.

268

9. Saccharose, fermented with 7. dattila gave:
Taken :1.65 1.80 1.68 2.49 2.19 2.31 2.25 0.78 2.13 1.31 1.59 mgr.
Found: 1.66 1.76 1.76 2.47 2.27 2.20 2.17 0.82 2.13 1.38 1.67 mgr.
Taken :1.86 1.71 1.62 1.592.314 1.741.31 1.65 1.77 1.77 2.10 1.83 mgr.
Found: 1.971.783 1.68 1.58 2.21 1.80 1.38 1.64 1.81 1.83 2.17 1.95 mgr.
10. Solutions of saccharose with S. cerevisiae gave the following
numbers :
Taken: 1.41 1.53 2.19 2.25 2.70 1.23 2.13 1.50 1.59 1.59 mer.
Found: 1.72 1.62 2.25 2.35 2.53 1.34 2.16 1.70 1.62 1.75 mgr.
Taken: 1.65 1.80 1.47 mgr.
Found: 1.93 1.90 1.59 mgr.
11. Solutions of maltose, fermented with JS. cererisiae:
Taken: 1.26 1.80 2.46 2.31 1.83 1.65 2.52 1.86 1.68 1.35 1.38 mgr.
Found: 1.88 1.72 2.82 232 1.72 1.52 2.42 1.66 1.55 1.30 1.51 mer.

12. With a solution, containing 3 per cent. glucosehydrate, 3 per
cet. saccharose ard 3 per cent. maltosehydrate, we undertook three
fermentations, viz. with 7. monosa, 7. dattila and S. cerevisiae. With
T. monosa the carbonic acid obtained from 0,045 ce. of the solution
was 0,326 cc, with 7. dattila 0,633 cc. from 0,045 cc. and with
S. cerevisiae 0,932 ce. from 0,043 ce; all gasvolumes being reduced
to 0° C, and 760 mm. From these numbers we calculate that of
1 ce. of the solution 7,1; 14,1 and 21,7 ec. of carbon dioxide will
be obtained by each of the 3 yeasts. Consequently there were
obtained 7,1 ce. from monoses (here from glucose-hydrate), 7,0 ce.
from saccharose and 7,6 ee. from maltosehydrate. This means a
composition of the solution of 3,1 per cent. of glucosehydrate, 2,7
per cent, of saccharose and 3,1 per cent. of maltosehydrate.

13. Other determinations with solutions of the same composition
gave the following results:

2,85 °/, glucosehydraat; 3,2 °/, saccharose; 2,7 °/, maltosehydrate.
2,98 °/, De 3,19 °/, - 2,84 °/, J

The three last numbers were calculated from the results of ana-
lysis, made in triplo.

14. Juice, pressed from a slice of orange, was diluted with water
to the threefold of the original volume and the diluted juice was
fermented with the three different yeasts. One ec. of this liquid
practically gave the same amount of carbon dioxide, when fermented
with 7. dutta and with S. cerevisiae, so that maltose was absent.
Tue composition of the undiiuted sap was calculated as to be: 2,6
per cent of monoses and 3,1 per cent, of saccharose,

269

15. Nectar from Nicotiana affinis, after dilution to about the
threefold of the original volume, was fermented with S. cerevisiae.
Two drops from the same flower were brought into two small platinum
scales and herein the water was added. (The weighings were made
with a torsion-balance, accurate to 0,1 mgr). The two analyses,
made separately gave as results: 33,9 and 34,4 per cent. of sugar
in the undiluted nectar; the sugar being calculated as hexose.

In studying the numbers published here, one will see, that on the
whole the results obtained with the microsaccharimeter, were quite
satisfactory. Add to this, that sugar determinations by chemical
analysis too are of no great accuracy, whilst here we took only a
few milligrammes of sugar. For the study of a large number of
biological problems the accuracy that was reached here, certainly
will be quite sufficient.

Laboratory for Microscopical Anatomy of the
Technical Academy.
Delft, July 1915.
EXPLICATION OF PLATE.

Figure 1. Longitudinal section of the glass apparatus of the microsaccharimeter.

Figure 2. General view of the microsaccharimeter (the glass apparatus fixed
in the cork clamp).

Figure 3. Longitudinal section of the neck (enlarged) of the microsaccharimeter,
filled with mercury, as for the 1th. reading.

Figure 4. Auxiliary apparatus, which may be used to place the mercury in the
tube and the reservoir on the same level.

Chemistry. — “Investigations on the Temperature-Coefficients of the
Free Molecular Surface-Energy of Liquids between —80°
and 1650° C.” &. Measurements Relating to a Series of Ali-
phatic Compounds. By Prof. F. M. Janerr and Dr. Jur. Kann.

§ 1. For the purpose of comparison of the variations, which
oceur in the values of the molecular surface-energy of several deri-
vatives of the aliphatic series, when simple substitutions have been
made in them, it appeared necessary also to investigate in detail the
surface-tension and its temperature-coefficient of the following com-
pounds: Lthyl-vodide, Ethylene-chloride, Ethylidene-chloride, Acetylene-
tetrachloride, Acetylene-tetrabromide, Epichlorohydrine, Carbonbisulphide,
Methylalcohol, Formic Acid, Mono-, Di- and Trichloroacetic Acid,
Levulinie Acid, Nitromethane, Bromonitromethane, Capronitrile, Di-
methylsuccinate, Diethylbromoisosuccinate, and Acetylacetone.

270

In the following we publish the results of the measurements with
these derivatives.

The determination of the specific gravity was made either by means
of the pycnometer, or by means of volumeters especially constructed
for that purpose, and which were previously accurately calibrated.
If both these methods could not be applied, the determinations were
made by the aid of a hydrostatic method, which some time ago
was developed by the first-named of us originally for the purpose
of measuring the densities of molten salts and liquid magmata at
very high temperatures, and which will be described in detail on
a future suitable occasion. By preliminary experiments and by com-
parison of the results thus obtained with those collected by other
methods, the applicability and reliability of the method were proved
and the degree of accuracy established ; the last appeared to be no
less than that reached by the usual way of measuring.

§ 2.
IL

| Ethyl-lodide: C,H;J.

| 2 : Maximum Pressure H Z Molens
BG urface- :

ie oe litendion an Specific Surface-

205 1.427 1903.1 32.5 |. 2.024 | sam

| 0 1.337 1782.7 30.4 1.979 | 551.4

2054 1.238 1650.9 28.1 1.934 517.6
40.4 | 1.143 1524.8 25.9 1.895 483.6
64.8 | 1.023 1364.3 23.1 | 1.845 439.0
Molecular weight: 152.88. Radius of the Capillary tube: 0.03489 cm.

Depth: 0.1 mm.

This carefully purified liquid boils under a pressure of 760 mm. at 72°.5C.;
according to TIMMERMANS it solidifies at —110°.9 C. At the boilingpoint 7 has
the value: 22.3 Erg.

The temperature-coefficient of » is between —20° and 0° C.:1.43; between
0’ and 20°.4 C.: 1.65; and between 20° and 65° C.: 1.84 Erg per degree:
evidently therefore it gradually increases with rising temperature.

II.

Ethylene-chloride: C‚H4Cl,

|
v Maximum Pressure H Molec
£5 Er Surface- Ees ne ae ar
Bid in mm mer Snes sn dr ne |
5 | 1 | hl |
5 ES Ze in Dynes Erg pro cm, | 4° Erg pro oni: |
“20° 1.176 1567.8 | 31.2 1.311 664,4 |
al 1.080 1439.8 | 34.1 | 1.283 617.9
9.9 0.961 1281.2 30.1 1.239 558.2
48 0.880 1173.8 27.5 1.213 511,2
58.9 0.831 1107.7 25.9 1.197 491.5
86 0.733 977.2 ZZ 1.158 440.4

Molecular weight: 98.95. Radius of the Capillary tube: 0.04839 cm; in the obser-
vations indicated by *, the radius was: 0.04867 cm.
Depth: 0.1 mm.

Under a pressure of 770 mm. the liquid boils constantly at 86° C. In solid
carbondioxide and alcohol it crystallizes and melts at —31° C. At the boiling-
point x has the value: 23.6 Erg.

The density at 15° C. was: 1.2609; at 25° C.: 1.2463; at 50° C.: 1.2103. At
P C.: d4o = 1.2826—0.001446 tf,

The temperature-coefficient of » has a mean value of: 2.16 Erg per degree.

UL.

Ethylidene-chloride: CH; . CHC

v Maximum Pressure 7
Zij TE Surface- Molecular
5e in mm. mer eenn zn Say | e ae
a. in : - | : nergy # in
Ee cury of in Dynes OE | Erg. pro cm2,
(= 0° C. |
16 1.144 1525.2 | 35.9 1.329 635.4
—21 0.903 1203.9 28.3 1.240 524.5
0 0.819 1091.1 2 1.207 | 485.0
30.4 0.722 963.0 22.4 1.159 | 434.3
47.8 0.663 | 884.4 20.6 1.130 | 406 2 |
60.9 0.626 834.9 | 19.4 1.109 | 387.4 |
- EEA ee ee om:
Molecular weight: 98.95. Radius of the Capillary tube: 0.04839 cm.;

in the observations indicated by *, the radius
was: 0.04867 cm.
Depth 0.1 mm.

The liquid boils at 60°.9 C. under a pressure of 770 mm. At — 80° C. it
becomes turbid, but does not crystallize. According to TIMMERMANS the sub-
stance melts at —96°.6 C. At the boiling-point the value of 7 is 19.4 Erg.
pro cm?. The density at 15’ C. was: 1.1830; at f° C.: d4o = 1.2069—0.0016
t + 0.00000015 #. :

The temperature-coefficient of » decreases gradually with rise of temperature:
between —76° and —21°C. it is: 2.00; between —21° and 0° C.: 1.88; between
0° and 30°.4C.: 1.66; between 30°.4C. and 47°.8C.: 1.61; and between 47°.8
and 60°.9C.: 1.43 Erg. per degree. The »-tcurve is therefore a concave one.

272

IV.

Acetylene-tetrachloride: C,H2Cl,.

v Maximum Pressure 7
Sy oleae ia in Sien Molecular
8 ° | in mm. mer | tension. in ee ae
a In . - wil pe
sE cury of in Dynes |Erg- pro cm? 4° Erg. pro cm?,
Fe On:
El 1.254 1672.4 39.4 | 1.657 856.2
Sed 1.171 1561.5 36.7 1.620 | 809.6
29.9 | 1.054 1405.2 2 1.570 736.6
47.4 0.983 | 1310.2 30.5 1.544 | 694.7
58.3 0.936 1248.2 29.0 | 1.526 | 665.8
87.1 0.834 1111.8 25 | 1.488 600.0
103.2 0.784 | 1045.7 24.1 1.468 567.7
WG 0.725 967.1 2252 1.452 526.8
127.8 0.694 925.8 Dit 1.440 505.9
Molecular weight: 167.86. Radius of the Capillary tube: 0.04839 cm.;

with the measurements indicated by *, the
radius was: 0.04867 cm.
Depth: 0.1 mm.

The liquid boils at 146°.3 under 758 mm. mercury. In solid carbondioxide
| and alcohol it solidifies, and then melts at —50° C. At the boiling-point 7 is
about: 20.5 Erg. pro cm? The specific gravity at 25’ C. is: 1.5779; at 50°C:
1.5394; at 75°C.: 1.5042; at £9: dygo = 1,6197—0.001738 f + 0.00000264 #2.
The temperature-coefficient of » is fairly constant; its mean value is 2.36
Erg. per degree.

273

Molecular Surface-Energy
vin Erg. pro cm?

1260
1220
1180
1140
1100
1060
1020
980
940
900
860
820
780
740
700
660
620
580
540
500
460

420

380 de:
5 Temperature
-80° -60° -40° -20° O° 20° 40° 60° 80° 10C° 120° 140° 160° P

Fig. 1.

Acetylene-tetrabromide: C,H,Br,.
v Maximum Pressure H
fete el ; Sine Molecular
5 o ee ee | tension x in sie Surface-
i . mer- gravity d,, | energy » in
ES cury of in Dynes Erg pro cm’, 2
2 0°°C. Erg pro cm2,
ie 1.698 2264.2 53.1 3.039 1246.1
pets) 1.624 2165.6 50.7 2.996 1201.2
30.4 1.510 2012.8 | 46.7 2.934 1122.0
4786 ° ladon RIE Oe 44.6 2.897 1080.5
59.6 1.398 1864.0 43.1 2.871 1050.5
87.2 1.296 1727.6 | 39.8 2.814 983.1
102.1 1.240 1653.2 | 38.0 2.780 946.3
| 117.8 1.178 1570.6 | 36.0 2.747 903.6
127.3 1.144 1525.1 | 34.9 2.736 878.4
154.1 | 1.042 1388.7 31.6 2.669 808.6
175,5 0.964 1285.4 29.1 2.620 753.8
|

Molecular weight: 345.46. Radius of the Capillary tube: 0.04839 cm.; in the
observations indicated by *, it was : 0.04867 cm.
Depth: 0.1 mm.

The bromide boils constantly at 132° under a pressure of 20 mm. In ice
and salt it solidifies, after undercooling to —24?C., and melts at—3°C. On
heating above 190° C. it is decomposed.

The density was at 50? C.: 2.8920; at 75° C.: 2.8390; at 100° C.: 2.7852. At
t C. in general: d4o = 2.9956 0.°0204 t—0.00000064 #2.

The temperature-coefficient of » is fairly constant; its mean value is:

|
|
|
|
|

2.51 Erg. per degree.
: VI.
ZON
Epichlorohydrine: CH,C!. CH . CH.
v | Maximum Pressure H |
3g | Gurfaces ; Molecular
Bo in mm. mer kenen Zn wee a
= | : TI Erg pro cm? 40 | Je
5 | cu of | in Dynes sp Erg pro cm‘,
|*_21° 1.288 | 1717.7 41.o- | 1,228 |> “Game
eae ES 1.196 1594.5 38.0 1.205 | 686.4
30.3 1.079 1438.3 34.0 1.170 | 626.3
46.5 1.014 1351.5 31.9 1.147 | 595.5
59.8 0.958 1277.1 30.1 1131 | 567.1
86.2 0.865 1153.1 27.1 1.095 521.7
102.8 0.815 1087.0 255 1.071 498.2
117.5 | 0.772 1029.1 24.1 1.049 | 477.5

Molecular weight: 92.50. Radius of the Capillary tube: 0.04839 cm.; in the mea-
surements, indicated by*, the radius was: 0.04867 cm.

Depth: 0.1 mm. |

Under a pressure of 758 mm., the liquid boils at 117° C.;inabath of solid |
carbondioxide and alcohol it crystallises, and melts then at —48° C. At the

boilingpoint x is about: 24.1 Erg.

The density at 20° C. was: 1.1812; at 50° C.: 1.1436; at 75° C.: 1.1101.

| At tf? C.: dgo = 1,2046 —0.00114 t—0.0000016 #2, |

The temperature-coefficient of » is originally: 2.04 Erg; but from 86° C.
upwards it decreases continually to 1.41 Erg per degree.

VIL.

Carbonbisulphide : CS,

v | Maximum Pressure H |

3 Len Molecular

S TRR | ; 5 Specific | Surface-

oro Of. | | tension x in | 5 3

5 ey (pint cam ger hes 5 NEsore len? gravity dy, | energy » in

Ë ae in Dynes. | | Erg pro cm?,
EED. 1.931 2574.4 44.3 | 1.398 | 636.5
—21 1.602 2146.0 36.8 Ak 323 | 548.6

0 1.483 1977.1 | 33.9 1.292 513.4
21.5 1.354 1805.1 | 30.9 1.262 415.3
40.9 1.245 1659.8 28.3 | 1232 | 442.3
pi gee we Kd „ul a Ka
Molecular. weight: 76.14. ; Radius of the Capillary tube: 0.03489 cm.

Depth: 0.1 mm.

The liquid was distilled several times, then shaken with mercury and
again subjected to fractional distillation in an atmosphere of nitrogen after
being completely dried. It boils at 46.8 C. constantly; it solidifies (TIMMER-
MANS) at — 111°.6 C. At the boiling-point x has the value: 273 Erg. The
specific gravity at 0° C. was: 1.2921; at 20° C.: 1.261; at 46° C.: 1226. In
general at £° C.: dgo = 1.2921 —0.00147 ¢.

The temperature-coefficient of » is constant; its value is 1.75 Erg per degree.

VIII. -

Methylalcohol: CH30H.

|
|

© Maximum Pressure H
Sj Surface- eases
Si oh : : Specific Surface-
ae in mm. mer- | Pe hl Bie dio | energy » in
| . > i 2 1 o | Be
5 5 cury of in Dynes Epgipreccms. sal Erg pro cm?,
mn OMGE | |
I. = ast en = |
le]
—15 1.246 1661.2 29.8 0.878 327.8
—20 1.043 1391.8 24.9 0.828 284.8
0 0.986 1314.6 23.5 0.810 272.8
20.8 0.924 | 1232.0 22.0 | 0.792 259.2
35.3. | 0.882 1177.0 21.0 0.778 250.4
50.1 | 0.841 | 1121.2 20.0 | 0.765 | 241.2
65 0.794 | 1058.6 | 18.8 0.752 | 229.3
. | |

Radius of Capillary tube: 0.03536 cm.
Depth: 0.1 mm.

The aleohol was obtained in an anhydrous state by boiling with dry calcium-
oxide for several days; then it was carefully distilled. Under a pressure of
752 mm. it boils at from 65 .5 to 65.8 C.; at this temperature the value of x is:
18.7 Erg. It solidifies at —97 .1 C. (TIMMERMANS). The specific gravity was
calculated from the formula: dyo = 0,8102 —0.000905 £—0.000000085 72.

The temperature-coefficient of » is very small: as a mean value about
0.67 Erg per degree. :

Molecular weight: 32.03.

276

IX.

Formic Acid: HCO. OH.

2 Maximum Pressure
Sie Sud Molecular
hed | Arrr el : … | Specific Surface-
3 o ; tension 7 in a 7 cnc ; a

in mm. mer- > | gravi > | energy w i

5 5 cury of | in Dynes | Exe DRO Cus - Erg pro cm2
= 02 C.

le)

9.2 1.596 2128.6 38.1 1.233 425.5
alee 18555 2073.7 Bee 1.218 418.8
BORG 1.510 2013.2 | 36.1 1.200 410.5
50.4 1.444 1925.1 34.5 1.181 396.5
64.8 1.386 1874.6 33.1 1.162 384.6
75.3 1.354 1787.6 32.0 1.149 374.6
90 1.263 1684.9 30.1 1.130 356.3
99.8 eli 1622.5 29.0 1.117 346.0
Molecular weight: 46.02. Radius of the Capillary tube: 0.03636 cm.

Depth: 0.1 mm.

The acid solidifies below 0° C., and then melts again at + 6° C. It boils
under a pressure of 762 mm. at 101° C.; at this temperature 7 has the value:
28.8 Erg. The density was calculated from the equation: dyo = 1.2441—
—0.001249 t—0.000000181 7.

The temperature-coefficient of » is between 9° and 35°: 0.57 Erg.; between
35° and 75° C,: 0.90 Erg.; between 75° and 100° C.: 1.15 Erg. per degree.

Monochloroacetic Acid: CH2C!. COOH.

|
|
}
|
|

2 Maximum Pressure HZ Moleent
rame Surface- ae is Ee a
z Sin mm. m | IEEE adt d ae En
in mm. mer- | k
5 5 cure in Dynes Ergopro eme) = Erg pro cm?.
Saen 1072 1429.2 33.3 1.352 565.0
92 | 1.042 1389.8 32.4 1,339 | 5538
118.5 0.970 | 1293.8 30.1 1.305 522.9
"136.2 02932) 1242.0 28.1 1.285 | 493.2
"149.4 | 0.883 | 1175.3 26.6 1.260 | 473.0
*176.3 0.184 | 1045.0 23.5 | 1.235 423.5

| Molecular weight: 94.49 Radius of the Capillary tube: 0.04792 cm.; the mea-

surements indicated with * were made with atube
whose radius was: 0 04670 cm.
Depth: 6.1 mm.

At a pressure of 20 mm. the acid boils constantly at 101° C. The melting-
point was 62°.5 C. The density was at 75° C.: 1.3576; at 100° C.: 1.3261;
at 125° C.: 1.2933. In general at C.: dyo = 1.3878 0.001182 (t—50°)—0.00000104
(£— 50°).

The temperaturecoefficient of » increases gradually with rise of tempera-
ture: between 80° and 92° C.: 0.96; between 92° and 118° C.: 1.14; between
118° and 149° C.: 1.61; and between 149° and 176° C.: 1.84 Erg per degree.

271

Molecular Surface-Energy
v in Erg pro cm?2.

580
540
500
460
420
330
340
300

260

220
-B80° -60° -40° -20° 0° 20° 40° 60° 80° 100°

Temperature

Fig. 2.

Molecular Surface-Energy
«in Erg pro cm?2.

660
620
580
540
500
460

420

380
-B0° -60° -40° -20° O° 20° 40° 60° 80° 100°

Temperature

Fig. 3.

19
Proceedings Royal Acad. Amsterdam. Vol. XVIIL.

Dichloroacetic Acid: CHC/,. COOH.

® Maximum Pressure H
5 afl Sd Molecular
ge hia mm. mer | Pensten eae acute pa in
5 | 2 o B
é 5 EIS in Dynes | Exe pie eu. 3 Erg pro em?.
| | | =
ar a —
0 1.228 1637.2 38.1 1.592 796.5
PA Sate |) 1.143 1523.4 BE) | 12557, 726.5
41 1.096 1460.6 34.0 | 1.535 691.8
55.9 1.052 | 1402.3 32.6 | 1515 | 655.3
80.2 0.980 1306.4 30.3 1.488 605.3
92 0.945 1260.5 29.2 1.444 571.8
117 0.905 1206.2 21.9 1.431 | 539.8
S130 508 0.842 112281 A 1.405 | 481.4
"149.3 0.803 1070.7 24.0 1.387 456.0
el 6N2 0.719 959.3 21.4 1.349 400.6

| | | |
| |

Molecular weight: 128.95. Radius of the Capillary tube: 0.04792 cm.;inthe obser-
vations indicated by *, this radius was : 0.04670 cm.
Depth: 0.1 mm.

The acid boils at 192°.5 C. under a pressure of 763 mm.; on cooling it
solidifies and melts again at +10’ C.

The density at 12’ C. was: 1.5759; at 75° C.: 1.4891; at 100° C. 1.4547;
© C.: dgo = 1.5924—0.001378 t The temperature-coefficients of # oscillates

beyond a mean value of about 2.30 Erg per degree.

= = es — =~ =4

XII.

Molecular weight: 163.40. Radius ofthe Capillary tube: 0.04792 cm; in the obser-

Trichloroacetic Acid: CCl;. COOH.

® Maximum Pressure H |

hen _ ERGE | Molecular
5: lia e \ tereion ein B | aoe )

in mm. mer- | » in |

5 5 EE in Dynes Erg procent. | = (Erg pro cm?
Drs | 7 | :

80.2 | 0.902 1202.0 27.8 | 1.575 613.8

92 0.876 | 1168.6 | 21.0 | 1.556 601.0 |
117.5 0.814 1085.2 2081 1.515 568.7 |
*136.5 0.784 | 1045.0 23.4 1.484 537.6 |
*149.2 0.746 994.6 2959. 9) | 1 Ae5 514.4
“176.1 0.665 886.5 19.7 | 1.415 | 467.1
*196 0.607 809.2 17.8 | 1.378 | 429.6 |

vations marked by * the radius was: 0.04670 cm.
Depth: 0.1 mm.

Under a pressure of 765 mm. the acid boils at 195.°5 C.; under 21 mm.
at 107° C. The melting-point was 57°5 C.

The specific gravity at 752 C. was: 1.5829; at 100° C.: 1.5451; at 125? C.:
1.5082; at #2 C. d4o —1.6216—0.001566 (¢—50°)—0.00000072 (¢ 50 )?.

The temperature-coefficient of » originally increases with rise of tempera-
ture: between 80° and 92° C.: 1.09; between 92° and 117° C.: 1.27; between |
117° and 136° C.: 1.63; afterwards it remains fairly constant at 1.82 Erg
per degree.

279

XIII.

Levulinic Acid: CH3. CO. CHz. CH). COOH.

® Maximum Pressure H
a G Surtees Molecular |
ue in mm. mer | stensions, Da ae | aa |
= 6 - : | 2 | gravity d,. | energy « in
5 iS cay of | in Dynes | Erg pro cm’. \Erg pro cm?.
o uk j j i 7 |
2555 1,304 | 1738.2 39.7 1.135 868.1
41.1 1.268 | 1691.0 | 38.6 1.123 850. 1
60.1 1.220 1626.6 Sil 1.109 823.9
81.5 1.166 1554.5 39.5 1.093 796.0
95.1 1.130 | 1506.4 34.4 1.083 716.1
115 1.082 1442.1 32.9 | 1.068 749.2

Radius of the Capillary tube: 0.04660 cm. |
Depth: 0.1 mm.

Under atmospheric pressure the acid boils at 1539.5 C. Above 100° C. it
is soon coloured yellowish and gets a special odour; the measurements were
thus stopped because of the evident decomposition. The melting-point is
339 G. At 25° C. the density is: dgo=1.1351; at 50° C.: 1.1140; at 75° C.:
1.0924; at f in general: d4o == 1.1557 - 0.000814 ¢— 0.0000004 #2.

The temperature-coefficient of » is almost constant and has thesmall mean |
value: 1.33 Erg per degree.

Molecular weight: 116.06.

XIV.

Nitromethane: CH;NO,.

v Maximum Pressure H melee
Eis | Surface- | USS els
= BRE Et | DH Specific | Surface-
ac inmm. mer- | Bas ma ent gravity d, | energy « in
5 = a ‚in Dynes | Sp (Erg pro cm2,
| | | | |
“21.5 | 1.279 1705.4 40.6 1.199 557.6
20 1.202 1602.6 38.1 1.166 533.1
30.1 1.091 | 1454.8 34.3 128 492.1
46.3 1.026 1368.1 | 32.2 | 1.100 468.4
58.7 0.979 | 1306.0 30.8 1.086 | 451.9
86.2 0.868 | 1157.3 | 27.2 | 1.056 | 406.6
101.4 0.812 1082.9 | 25.4 | 1.040 | 383.6
|

Radius of the Capillary tube: 0.04839 cm; in
the observations indicated by *, the radius |
was: 0.04867 cm.

Depth: 0.1 mm.

The nitromethane boils at 102° C. under a pressure of 760 mm. On cooling |
below —24° C. it solidifies and melts at —17’C.; according to WALDEN the |
melting point is —26°.5 C. At the boiling-point ~ has the value: 25.3 Erg
pro cm.? The specific gravity at 15 C. is: dgo = 1.1437 at 25°: 1.1297; 50° C::
1.0970; in general: d4o = 1.1657—0.0015052 ¢ | 0.000002629 #2.

The temperature-coefficient of » evidently increases with rising temperature;
between —21° and 0° it is: 1.14; between 0° and 59°: 1.38; between 59° and |
101° C.; 158; being thus appreciably under Eötvös’ normal-value of 2.2 Erg.

19*

Molecular weight: 61.03.

280

XV.
Bromonitromethane CH,(NO,)Br.
v Maximum Pressure H
2G = Surface-
go adenine tension 7 in
in mm. - |
ks cury of in Dynes Erg pro cm?.
ol es (ee
= 18.5 1.512 2015.9 48.3
0 1.431 1907.2 45.7
Zoe 1.337 1782.1 42.7
40.5 1.280 1707.0 40.9
55.5 1.227 1636.1 39.2 |
80 1.139 1519.2 36.4
92.2 1.105 1473.2 35.3
116 1.002 1335.6 32.0 |
*135.8 0.919 1224.8 28.6

Molecular weight: 139.99. Radius of the Capillary
tube: 0.04792 cm.; with the
observations indicated by *,
the radius was: R=0.04670cm.
Depth: 0.1 min.

Under a pressure of 765 mm. the liquid boils at
152°.5 C.; in a bath of solid carbondioxide and
alcohol it soon solidifies into a hard mass of
crystals, melting at — 28° C.

XVI.
Capronitrile: C;H,,CN.

v Maximum Pressure H
ae San Molecular
= F
go ae rel | tension x in ae pee
n mm. mer- 3 i o | energy «in
5 5 A in Dynes | Erg pro cm? 4 Erg pro cm?.
le}
*—22 | 0.903 1204.1 28.7 0.854 673.6
SO kel 0.854 1138.3 21.1 | 0.835 645.6
29.9 0.781 1041.5 24.6 | 0.810 598.1
47.9 0.735 979.5 231 0.793 569.6
59.7 0.704 938.2 221 0.782 550.0
86 | 0.635 847.3 19.9 | 0.757 506.1
101.8 0.592 789.4 18.5 | 0.740 H 477.7
ales 0.555 739.8 17.3 0.723 453.7
127.4 0.530 106.7 16.5 0.713 436.8
151.8 0.465 619.9 14.4 0.684 391.9

Molecular weight: 97.10. Radius of the Capillary tube : 0.04839 cm.; in the mea-
surements indicated by *, the radius was: 0.04867 cm.
Depth: 0.1 mm.

This very ill-smelling liquid boils constantly at 157° C. under a pressure of
762 us In solid carbondioxide and alcohol, it solidifies and melts again at
—45° C.

The density is at 24° C.: 0.8147; at 50° C: 0.7914; at 75° C.: 0.7675. At
t° C.: d4o = 0.8347 - 0.000806 t—0.0000012 £2.

The temperature-coefficient of » has between 0° and 127° C. amean value
of about 1.63 Erg per degree, and above the last temperature a somewhat |
greater value: 1.84 Erg. :

Molecular Surface-Energy
yin Erg pro cm2.

900
860
820
780

740
- 700
660
620

580

540

. Temperature
O° 20° 40° 60° 80° 100° 120° 140° 160° 180° 200°

Fig. 4
XVII.
Dimethyl-Succinate: CH3;0.CO.CH,.CH,.CO.OCH;.
er Maximum Pressure H a | EE
a0 FE | een Specific | Surface-
Soc ’ | tension x in de A el :
a. in mm. mer- | | > | gravity do | energy « in |
ES A ere) | Erg pro cm?. 4° | 2
Ë le In Dynes | Erg pro cm?. |
25.2 1.123 1497.2 | 34.1 1.115 879.6
40.4 1.085 | 1446.5 | 33.1 1.097 863.1
54 1.015 1353.2 30.9 | 1.082 | 813.2
75.9 0.932 12425 | 28.3 | 08 756.0 |
95 0.870 1160.6 | 26.4 GEOI 1D |
116 0.806 1069.5 | 24.3 1.014 | 667.8
135 0.745 993.6 | 2255 | 0.995 626.2 |
150 0.694 925.0 20.9 | 0.980 587.6 |
176.2 0.585 119.9 | 17.5 0.955 500.5
== — ——— = |

Molecular weight: 146.08. Radius of the Capillary tube: 0,04670 cm. |

Depth: 0.1 mm. |

Under a pressure of 25 mm. the liquid boils at 103°.5 C.; the melting-point
of the crystals is 18°.2C. The specific gravity at 25° C. was: 1.1149; at 50° C.:
1.0865; at 75° C.: 1.0589; at #° in general: ago = 1.1441 — 0.001184 ¢-+ 0.00000064 £.

The temperature-coefficient of » is fairly constant up to 150° C. its mean |
value being: 2.32 Erg. per degree. Above 150° however it increases rapidly, |
perhaps caused by a beginning decomposition. |

XVIII.

Diethyl-Bromoisosuccinate: CH;.CBr(CO.OC,H;5)9- |

v Maximum Pressure H
Eis Surf Molecular
ae) urface- Specifi ae
Bee mm. mer tension 2 Ii Ei d cr
a. in 4 - 5 py
ES cury of in Dynes Erg pro cm?, 4 2
© | 0°°C. Erg procm
le) |
—21 1.155 1539.8 35.0 1.377 1131.3
0 1.079 1439.0 | 32.7 1.350 1071.0
207108 1.005 1340.5 | 30.4 1.318 1011.6
40.3 | 0.960 | 1280.5 29.0 1.300 974.0
52.8 | 0.918 | 1223.9 21.8 1.284 | 941.4
OS 0.861 | 1147.7 | 26.0 1.257 893.0
95.4 0.809 | 1079.2 24.4 1.232 849.4
114 | 0.752 1002.6 22.6 1.211 | 795.8
134.1 | 0.698 | 930.6 | 20.9 1.189 145.0
| 152 | 0.652 869.4 | 19.5 1.169 703.0
| 176 | 0.581 115.1 | USS 1.144 632.7
| 197 | 0.499 | 665.3 | 14.7 1.121 544.9
| | | |
Molecular weight: 253.03. Radius of the Capillary tube: 0.04670 cm.
Depth: 0.1 mm.

Under a pressure of 13 mm. the liquid boils at 122? C. At —79° C. it
becomes turbid and very viscous, but does not solidify. Above 176° a slow
decomposition sets in, and the 7-fcurve then rapidly falls towards the taxis,
The specific gravity at 25° C. is: 1.3183; at 50° C.: 1.2875; at 75° C.: 1.2575.
At # in general it is calculated from: a@4o = 1.3499—0.00128 ¢ + 0.00000064 72.

| The temperature-coefficient of » is fairly constant up to 176°; its mean
value is about: 2.54 Erg. per degree.

XIX.
Acetylacetone: CH; .CO. CH, . CO. CH.
v | Maximum Pressure H_ |
2G lee : ee Molecular
aie | | tension 2 in Benes pe.
a |. | in mm. mer- 3 |E 2, | gravity dy. | energy « in
Eos cury of | in Dynes | 77S Procm Erg procm?2.
i ORE: | | |
9° ot | agape” |) 3a 0) ee
0 1.041 | 1387.7 31.6 0.998 681.9
Dt 0.956 | 1274.5 29.2 0.972 641.4
40.5 | 0.912 | 1216.3 PAST 0.957 614.8
54.5 | 0.867 1156.3 26.3 0.943 589.5
HO 0.805 1073.3 24.4 0.923 554.8
4.8 | 0.752 1002.6 22.7 0.906 | 522.6
115 | 0.687 916.5 20.7 0.889 482.5
Wes | 0.623 830.6 18.7 0.873 441.2
ae ee AA |
| Molecular weight: 100.06. Radius of the Capillary tube: 0.04670 cm.
Depth: 0.1 mm.

Under a pressure of 755 mm. the liquid boils at 1377.5 C. In a bath of
solid carbondioxide and alcohol it crystallizes; the crystals melt at —30’ C.
| At 25 C. the specific gravity is: 0.9721; at 50° C.: 0.9475; at 75° C.: 0.9241.
At t° C.: d4o = 0.9979 —0.001056 ¢ + 0.00000096 2.

The #-tcurve has a peculiar shape, which is probably connected with the
transformation of the keto 2 enol-equilibrium : between —21° and 0° en

is: 217 Erg, and decreases between 54° and 76° to 1.60; afterwards it
increases gradually to 2.06 Erg.

28.

Molecular Surface-Energy
yin Erg pro cm?

1140
1100
1060
1020
980
940
900
860
820
780
740
700
660
620
580
540

500
-40°-20° 0° 20° 40° 60° 80° 100° 120° 140° 160° 180° 200° 220°
igo:

Temp.

$ 3. The results reviewed in Tables 1
duced in Fig. 1

In general the shape of the u-tcurves, as determined by the values
of the temperature-coefficients of u, appears to be quite analogous
in the case of derivatives of similar constitution : it is so in the
case of all halogen-derivatives of the hbydroearbons (Fig. 1), in the
case of the alcohols and water (Fig. 2), and in that of the neutral
ethers of two-basie acids (Fig. 5).

In the case of ethylene-, and of ethylidene-chloride (Fig. 1), the
different situation of the two chlorine-atoms in their molecules,
appears in these cases to cause an appreciable difference of the values
of u at corresponding temperatures: thus such isomerides evidently
do not possess the same surface-energy, as has been occasionally
suspected by previous authors (Fevsrer). With the increase of the

atomic weight of the halogen (ef. acetylene-tetrabromide and -tetra-

19 and graphically repro-

5, give rise to the following general remarks.

284

chloride) the surface-energy u also increases. Substitution of hydrogen-
atoms by the negative oxygen-atom has in the same way a magni-
fying influence on the original values of u.

In the case of the alcohols (fig. 2) the values of u, and also those
of the temperature-coefficient of gw, increase regularly with the
increase of the alkyl-radical ; water however has evidently a special place.

In the case of Acetic and Monochloro-, and Trichloroacetic Acids,

0
g increases regularly with the content of halogen, while 5 in these

cases is quite analogous. Dichloroacetic Acid however shows a much
larger temperature-coefficient, as a consequence of which the values
of u below 126° C. appear to be greater, above 126° however to
be smaller than in the case of monochloroacetic acid. It must be
mentioned also as a remarkable fact that the u-f-curve for Formic
Acid is entirely situated above that for Acetic Acid, while at the
same time the value of 5 for the formic acid appears to be
unusually small. The special and diverging character of the formic
acid shows itself in a most striking way in this fact too.

Diethylmalonate and Dimethylsuccinate (fig. 5) show within a
rather considerable temperature-range, almost the same values of u;
furthermore a comparison of the g-t-eurves of dimethylsuccinate
and dimethyltartrate clearly demonstrates the strongly magnifying
power of the substitution of two hydrogen-atoms by the typically
negative hydroxyl-groups. This inerease of the molecular surface-
energy by the substitution of negative elements of radicals into the
original molecules, according to these data and those formerly published
seems to be a quite general phenomenon.

Vi respect to the temperature-coetticients themselves, it may
be reaarked that in the case of the halogen-derivatives of the
hydro-carbons they seem to be not unappreciably variable with the
temperature im the case of ethyliodide and ethylidenechloride, and
also in the case of epichlorohydrine from (1,43 to 1,88 Erg.). In the
case of the symmetrically constituted compounds: ethylenechloride,
and tetrachloro-, resp. tetrabromo-acetylene, they may be considered
to be constant, while they furthermore appear to increase regularly
with the augmenting content of the halogen:

For C,H,Cl,: 2,16 Erg per degree.
For C,H,Cl,: 2,36 Erg per degree.
For C,H,Br,: 2,51 Erg per degree.

285

0
In the case of the alcohols and water, the values of = are

remarkably small; also in the case of the alcohols a regular increase
with growing molecular weight is observable :

0
While in the case of water the value of = is 1,0 Erg per degree,

it is for CH,OH: 0,67 Erg per degree.
for C,H,OH: 0,94 Erg per degree.
and for C,H,OH: 1,10 Erg per degree.
On later occasions other regularities of this kind will be pointed out.

Groningen, Holland, June 1915.
Laboratory for Physical and Inorganic
Chemistry of the University.

Chemistry. — “Investigations on the Temperature-Coefficients of
the free Molecular Surface-Energy of Liquids between — 80°
and 1650° C” XI. The Surface-Tension of homologous
Triglycerides of the fatty Acids. By Prof. F. M. Jarcer and
Dr. Jur. Kann.

$1. In the following we give the measurements made with
the neutral ethers of glycerol and the fatty acids. The information
about the surface-energy of the simple fats and its temperature-
coefficient must be considered of high importance for practical reasons,
because it allows conclusions to be made about the corresponding
values for the natural fats, those being mixtures of the simple fats.
The temperature-coefficient of ge appears furthermore to have very
exceptional values for some of these derivatives which may be con-
sidered as a fact in many respects also of interest from a theoretical
point of view.

Finally we give here again some measurements of the specific
surface-energy 4 and its temperature-coefficient, for natural butter
and for margarine, which measurements were made with the
purpose of finding out, if a reliable criterion could perhaps be
obtained for the discrimination of pure natural butter from that
which had been adulterated by vegetable fats. Although the temperature-
coefficient of y in the case of margarine evidently differs from that
for natural butter, we think these differences too slight to found

286
a reliable method upon these for the decision of the said questions.

§ 2. The eleven compounds investigated are:

Glycerol, Glyceryltriformiate, Glyceryltriacetate, Glyceryltributyrate,
Glyceryltricaproate, Glyceryltricaprylate, Glyceryltricaprinate, Glyceryl-
trilaurinate, Glyceryltripalmitate, Gilyceryltristearate and Glyceryl-
trioleate.

The butter and margarine used were both of the best kind; when
molten, a heavier white precipitate is formed, consisting of salts and
other components, mixed with water. Of course the measurements
relating to such liquids can only have a relative value; but in any
case they do not indicate any clearly evident difference between the
two kinds of fats.

Glycerol: CH,OH.CHOH.CH,OH.

v Maximum Pressure H

eee Ss Molecular

BG B f urface- Specifi Surf

ik in mm. mer enon al | ZE p | nen
. = 2 ol BP

5 5 cury of in Dynes Erg pro cms = Erg pro cm?

fe WIE

o |

OM “(ea Bai) (ca. 4100) (ca. 88) 1.272 (ca. 1546)

13.5 (ca. 2.4) (ca. 3200) (ca. 69) 1.264 (ca. 1221)

26 2.297 3062.4 66.1 1.258 1156.5
35 2.182 2909.0 62.7 15251 1101.0
50.2 2.085 2780.1 59.9 1.242 1057.0

| (ais) 2.023 2697.8 58.1 1.233 1030.2
74.5 2.010 | 2679.5 : Dill 15227 1026.5
90.8 1.975 | 2633.6 | 56.7 1.218 1013.5
104.1 1.941 9588. | 55E 1.212 999.0
121 1.913 2551.4 54.9 1.200 | 991.2
130 1,886 2514.4 54.1 1.194 980.0
151 1.783 2378.1 ooi lS 2 931.9
171 1.708 2277.0 48.9 1.169 898.4
184.5 1.660 2213.0 47.5 1.162 876.2
202 1.585 2113.1 45.3 1.152 840.5
Molecular weight: 92.06. Radius of the Capillary tube: 0.04374 cm.

Depth: 0.1 mm.

The anhydrous compound melts at 19° C.; it can however be enormously
| undercooled; at —180? C. it becomes a glassy mass. The glycerol boils at
} 290° C., and under a pressure of 12mm. at 180° C. The specific gravity at

20° CG. is: 1.2604; at 50°C: 1.2420; at 100° C.: 1.1636. At fin general: d4o =
— 1.2720—0.000576 t—0.00000064 #. The temperature-coefficient of » oscillates
irregularly: in the beginning (from 13° to 50°) it is relatively great: 6.1 to
2.9 Erg.; then it decreases (between 50° and 200° C.) on: 1.8 to 1.5 Erg. per

degree. The irregularities are undoubtedly connected with the embarrassing |
measurements in the case of this highly viscous liquid, especially at lower |
temperatures. |

287

Glyceryltriformiate: C3H;(O . COH)3. |

ke)

—20 (1.972) (2629.1) (56.0) 1.352 (1438.7)

0 152 2335.8 | 49.6 1.332 1287.0
13.5 1.705 2273.1 48.3 1.318 | 126221
26 1.629 2171.9 46.7 1.305 | 1228.4
35 1.598 2130.7 45.8 1.296 1210.3
50.3 1.536 2048.4 | 44.0 | 1.281 1171.8
64.7 1 488 | 1983.6 42.6 1.266 1143.5
15.2 1.452 1934.1 41.5 1.256 1119.8
91.2 1.385 1847.2 39.6 1.240 1077.8
105 1.347 1797.0 38.5 16225 1056.4
121 1.279 1705.5 36.5 1.210 1009.7
130.4 ZO 1671.8 35.8 1.200 995.9
151 1.182 1575.8 Soul 1.179 948.5
170 1.096 1461.2 31.1 1.159 885.4
184.8 1.015 1353.2 28.8 1.144 827.1

Molecular weight: 176.06. Radius of the Capillary tube: 0.04374 cm.; in the
determinations indicated by *, it was: 0.04320 cm.
Depth: 0.1 mm.

The ether was prepared by Prof. VAN RoMBURGH (Proc. Kon. Ak. v. Wet.
Amsterdam 9, (109), (1907)) and kindly lent to me for the purpose of measu-
rement. Under a pressure of 14 mm. it boils constantly at 147° C.; in a
refrigerant mixture of alcohol and solid carbondioxide it crystallises slowly,
and then melts at 18° C. At — 20°C. the viscosity of the liquid is too great,
to allow reliable measurements. Above 140? a slow decomposition sets in, acid
vapours being evolved; the z-tcurve therefore falls more rapidly to the axis.

At the boilingpoint (266° C.) x has a value of about 16.5 Erg.

The specific gravity at 50’ C. was: 1.2812; at 75° C.: 1.2560; at 100° C.:
1.2305. At #2 C.: dyo = 1.3319—0.001014 4,

The temperature-coefficient of » is up to 150° C. fairly constant, and oscillates
round a mean value of 2.20 Erg per degree; later on it increases, because of
the reasons mentioned above, very rapidly to about 3.6 Erg per degree.

Il.

Glyceryltriacetate: C3H,(O.CO.CH3)3.

yv Maximum Pressure H

3 3 % Sie Molecular

5e in mm. me Pensioner eee ee
in mm. mer- ‚

5 5 gaen in Dynes | Erg pro cm? 42 Erg pro cm?
Zan 1.580 2106.7 37.8 1212 1204.9
0 1.543 2057.2 36.9 1.187 1192.6
21 1.488 1983.8 35.6 1.161 1167.8
35.2 1.456 1941.7 34.8 1.144 1152.8
50.2 1.419 1892.1 33.9 1.127 1134.2
65 1.382 1842.7 33.0 1.110 1115.3
he 1.349 1798.9 S202 1.100 1092.4
90.2 1.300 1732.6 31.0 1.085 1063.8
99.8 1.262 1683.1 30.1 | 1.075 1039.3
115 1.200 1600.7 28.6 | 1.060 996.8
125 1.160 1546.5 27.6 1.051 967.4
139.8 1.089 1452.1 25.9 1.040 914.2
155 1.027 1369.6 24.4 1.028 868.0
169.2 0.977 1303.6 23.2 1.016 831.8
185.2 0.916 1221.1 PANT 1.007 782.6
200.3 0.862 1149.6 20.4 0.997 740.6

Molecular weight: 218.1.

Radius of the Capillary tube: 0.03636 cm.
Depth: 0.1 mm.

At —78° C. the liquid gets glassy; at —20° it is again very viscous. Under
a pressure of 40 mm. the liquid boils at 172°.5 C.; under atmospheric pres-
sure at 260° C. The density at 25°C. is: 1.1562; at 50’ C.: 1.1271; at 75° C.:
1.1001; at 100 C.: 1.0752. At 2 C.: dqo = 1.1874—0.00129 f + 0 0000017 2.

The temperature-coefficient of » increases gradually with rising temperature;
between —19° and 0’ C. it is: 0.64 Erg.; between 0? and 21° C.: 0.92 Erg.;
between 21° and 35° C.: 1.05 Erg.; between 35° and 65° C.: 1.26 Erg.; between

65 and 100°C.: 2.20 Erg.; between 100° and 170’C.: 2.89 Erg.; and between
170°? and 200° C. almost 3.0 Erg. per degree.

989

IV.

Glyceryltributyrate: C,H;(O.CO.C3H;)3.

Maximum Pressure H |
RIS Surface-
| | tension x in

Temperature
iy 2 (E

|
|

Specific

Molecular
Surface-

in mm. mer- | » | gravity d,, | energy » in
cury Oo | in Dynes Erg BROT Des | ea Erg pro cm2.
0° C. | | |
| |
fe)
—20.5 1.381 1841.1 33.0 1.080 1411.8
0 1.333 1776.7 31.8 1.060 1377.5
BONNIE! 1283 | 1710.7 30.6 1.040 1342.4
BENE 1.246" | 1661.2 29.7 1.024 1316.5
50.3 1213008 1672 28.9 1.011 1292.0
64:8 |. 1.173 1561.7 27.9 1.005 1252.2
15.3 1.142 1523.7 27.2 0.998 1226.5
90.2 1.101 1467.8 26.2 0.979 1196.6
99.8 1.074 1431.8 25.5 0.966 1177.3
115.2 1.031 1375.2 94.5. - 7 |) KOBA ae” 11385
125.3 1.001 1333.3 23.7 | 0.948 | 1106.0
140 0.943 1259.1 22.4 | 0.939 | 1052.0
156 _\ 0.899 1199.2 21.3 OEE || SON
170.8 0.854 1138.5 20.2 WEET | SCO
184.5 0.817 1089.1 | 19.4 0.900 937.2
200.8 0.776 | 1034.0 | 18.3 0.890 890.7

’

Molecular weight: 302.2.
Depth: 0.1 mm.

Radius of the Capillary tube: 0.03636 cm.

Under atmospheric pressure the liquid boils at 286° C. The density at
50° C. is: 1.0110; at 75° C.: 0.9982; at 100° C.: 0.9664. At ¢ C.: in general

d4o = 1.0596—0.00101 ¢ + 0.0000008 #.

The temperature-coefficient of » originally increases gradually from 1.70 Erg.
between —20° and 50° C., and 2.42 Erg: between 50’ and 115' C., to 3.44
Erg between 115° and 140° C. Afterwards it again decreases somewhat:
between 140° and 201° C. its mean value is about 2.63 Erg per degree.

290

Glyceryltricapronate: C3H;(O .CO.C;H,))s.

v Maximum Pressure
5 Ua ee i Sr e Molecular
go | Ae tension 7 in an Surface- |
in mm. mer- » | gravi o | energy » in
EE cury of in Dynes Erg pro cm. 4 2
2 0°G. Erg pro cm?.
(oe)
—20 1.395 | 1859.2 33.4 1.028 1739.3
0 1316/0) MTBAEB AN 31.5 1.011 1658.4
21 1.250 1666.6 | 29.9 | 0.993 1593.4
cor 1213 | 1617.2 29.0 0.982 1557.0
50.1 1.180 | 1573.2 28.2 0.970 1526.4
64.8 | 1.147 | 1529.2 21.4 0.958 1495.5
Ros 1,123 1496.3 26.8 0.949 1472.0
90 1.085 1446.7 25.9 0.938 1433.7
99.8 1.061 1414.5 25.3 0.931 1407.4
115.3 1.034 1376.5 24.6 0.919 1380.1
125 1.004 1338.5 23.9 0.905 1354.9
141 0.972 1295.9 23.0 0.900 1308.7
155.8 0.932 1243.1 22.2 0.890 1272.6
169.5 0.897 1190.6 2158 0.880 1230.3
185 0.862 1149.7 20.5 0.871 1192.2
200 0.825 1100.1 19.6 0.860 1149.6

Molecular weight: 386.3. Radius of the Capillary tube: 0.03636 cm.

Depth: 0.1 mm.

In a refrigerant bath of solid carbondioxide and alcohol, the liquid gets
very viscous, and then solidifies very slowly at —60° C. At 50° C. the density
was: 0.9699; at 75° C.: 0.9501; at 100° C.: 0.9309. At 2 C.: dyo = 1.0113-—
—0,000852 ¢ + 0.00000048 #2.

The values of En decrease with increasing temperature gradually from 4.04

Erg per degree at —20’ C. to 2.54 Erg at 35 C. Afterwards they remain
relatively constant, and oscillate somewhat round a mean value of 2.49 Erg
per degree.

291

Vi.

Glyceryltricaprylate: C,H;(O.CO.C7H\5)3.

Y i ressure H |
5 Maximum Presst ay OEIeRiEE
Bo nn | eee rin | as | Scie

} in . mer- gravity do | energy » i
EE curyof | in Dynes | Erg pro cm? 5 see ne
& Ove. | | | ae
| | |

o | |

0 1.258 1677.7 30.1 0.967 1861.8
21 1.218 1623.8 29.1 0.950 | 1821.3
35.1 1.194 1588.2 28.4 0.939 | 1791.4
50.3 1.156 1541.2 27.6 0.927 | 1756.0
65.3 1.126 1501.6 26.9 0.915 1726.3
rf 1.106 1474.2 26.4 0.908 | 1702.9
90.3 1.073 1430.1 25.6 0.897 1664.8
99.8 1.052 1402.7 25.1 0.890 | 1640.8
MSO 1.015 1353. 2 | 24.2 0.879 1595. 2
125.2 | 0.994 1325.7 | 23.1 0.871 1571.7
140.2 | 0.961 1281.6 22.9 0.861 1530.5
154.8 | 0.924 1231.9 | 22.0 0.852 | 1480.6
OFS) | 0.902 1202.5 A5 0.842 | 1458.4
185.8 0.863 1151.8 | 20.5 0.831 1402.8
200.2 0.826 1103.8 19.7 0.822 1357.9

Molecular weight: 470.4.
Depth: 0.1 mm.

Radius of the Capillary tube: 0.03636 cm.

The compound solidifies at —22° C. slowly into acolourless crystal-aggre-

gation; it melts again at +9’ C.

The density at 50° C. is: 0.9273; at 75° C.: 0.9082; at 100° C.: 0.8897. At

LRE: Ajo = 0.9673 — 0.000824 ¢ + 0.00000048 #.

The temperature-coefficient of » is between 0° and 76°

GA R2 2E:

between 76° and 155 C. its mean value is about: 2.65 Erg; and between 155°

and 200° C.: about 2.9 Erg per degree.

299

VIL.

Glyceryltricaprinate: C,H;(O.CO.CyH;9)3.

v Maximum Pressure H M

By : Gapaces lolecular
5 7 in mm. mer tension x ‘in Ee e ae
os rea oe Erg pro cm? BY G40 Be
Ee cury of in Dynes Sp Erg pro cm2.
Ee Oor:

35.4 0.956 1275.7 27.6 0.923 1965.0
50.2 0.940 1253.2 Diet | 0.912 1944.9
65.3 0.915 1220.9 26.4 0.902 1908.6
74. 0.902 1202.5 26.0 0.895 1889.5
90.5 0.867 1156.8 25.0 0.884 1831.9
104.1 0.834 1113.9 24.1 0.875 1778.0
121 0.803 1068.1 23.0 0.863 1712.6
130.3 0.779 1037.8 22.4 0.856 1677.0
151 0.740 985.1 2158 0.842 1612.1
172 0.708 950.1 20.2 0.827 1547.4
184.9 0.681 913.8 19.5 0.818 1504.7
201.2 0.655 873.2 18.8 0.807 1463.9
Molecular weight: 554.49. Radius of the Capillary tube: 0.04374 cm.
Depth: 0.1 mm.

The substance melts at 31°.1 C. The density at 50° C. is: 0.9126; at 75° C.:
0.8950; at 100° C.: 0.8777. At f° C.: d4o = 0.9475—0.000698 f.

The temperature-coefficient of # has a mean value of about 3,09 Erg per
degree.

VIII.
Glyceryltrilaurinate : C3H;(O.CO. C,H23)3.

® Maximum Pressure H
Bs Sirrce: Molecular
5 ei in mer. fensionyein B aan ae
a. mm. mer- 7 ravi 5 gy # in
ES f : Erg pro cm?. 4
é Ge in Dynes Erg pro cm?.

64.7 1.209 1611.7 29.2 | 0801 | 23885

75.1 1.180 1573.2 | 28.5 0.885 2293.1

90 1.147 1529.1 2181 | 0.876 | 2343-4

99.8 1.122 1496.2 27.1 0.870 2205.1
114.8 1.093 1456.1 | 26.4 0.561 | 216155
126 1.064 1419.2 | 25.1 0.853 21189
139 1.040 1386.2 25.1 | 0.846 2080.9

156 0.997 1331.4 | 24.1 0.828 2026.8
170 0.978 1303.9 | 23.6 0.824 1991.1
185 0.949 1261.8 | 22.8 0.815 | 1937.8
200 | 0.916 1221.1 22.1 0.804 1895.4

| |
Molecular weight: 638.59. Radius of the Capillary tube: 0.03636 cm. |
Depth: 0.1 mm.
The compound melts at 46°.5 C. The specific gravity at 75° C. is: 0.8842;

at 100° C.: 0.8676; at 125° C.: 0.8507. In general at © C.: dgo = 0.9005—

0.00060 (t—50 ) ~- 0.00000024 (t—50°)2.

The temperature-coefficient of » oscillates somewhat round a mean value of:
3.33 Erg pro degree.

Glyceryltripalmitate : C,H; (O. CO, C15H31)3.

|
v Maximum Pressure H MSlecuf
BG Surface- Specifi En ae au
5 ke in mm. mer deren sauna B
a. . 2 pp
E 5 cury of in Dynes Ere ano cme = Erg pro cm?
= Oe
64.3 1.287 1715.7 | 30.4 | 0.877 | 2863.4
75.3 1.257 1675.8 20 | 0.870 2812.5
90 1.206 1610.4 28.5 | 0.862 21955,
99.8 1.182 | 1575.8 27.8 | 0.854 2665.3
115 1.139 | 1518.2 26.8 0.845 2587.7
125.5 1.124 1496.2 26.4 | 0.834 2571.4
140.2 1.077 | 1435.6 25.6 | 0.828 2505.6
154.8 1.060 1413.7 24.9 | 0.816 2460.9
170 1.031 1375.2 24.2 0.805 2413.4
184.8 1.000 1333.2 | 23.4 0.794 2355.2
200 0.963 | 1288. 1 | 22.6 | 0.781 2299.8
|

Radius of the Capillary tube: 0.03636 cm.
Depth: 0.1 mm.

Molecular weight 801.74.

The compound melts at 65°.1 C.; the metastable form melts at 46° C.

The specific gravity was at 75° C.: 0.8702; at 100? C.: 0.8544; at 125°C.:
0.8377. In general at ¢? C.: dg4o = 0.8851 0.000578 (f — 50°) — 0.00000079 (¢— 50°)?.

The temperature-coefficient of » is up to 90°C. about 5.55 Erg per degree;
afterwards it decreases gradually from 5.10 Erg to 3.41 Erg per degree. |

kK = — a = ee

Glyceryltristearate: C3H5(O. CO. C‚7H.5)3.

© Maximum Pressure H |
5 Surf Molecular |
eS urftace- Ss ifi Surf
So ; | tension ~ in : one ¥ aie eS
a jin mm. mer-| | | Ere pro cm2, | Stavity deo | energy # in |
5 = cary of in Dynes | sp | |Erg pro cm’,
121° 0.908 1210.5 | 26.0 0.840 2104.0 |
130 0.886 1181.2 | 25.3 0.834 (204308 ||
151 0.822 1095.9 2320 0.820 2483.6 |
169 0.784 1045.2 | 22.3 0.807 | 2382.0
185 0.741 987.9 21.1 0.794 2278.3
201.2 0.725 966.6 19.8 0.782 | 2159.8
Molecular weight: 890.88 Radius of the Capillary tube: 0.04374 cm. |
Depth: 0.1 mm.

The ether melts at 71°.6 C.; its metastable form at 55° C. From 75° to
120° C. the value of y changes only inconsiderably: from 26.9 Erg at 74?.6C. |
to 26.5 Erg at 120° C. Above 120° C. the curve falls gradually; only this
part of it is drawn in the diagram.

The density at 75° C. was: 0.8704; at 100° C.: 0.8542; at 125° C.: 0.8373.
At t° C.: dgo = 0.8859 0.000606 (*—50 )—0.00000056 (*—50 )?.

The temperature-coefficient of » oscillates round a mean value of 6.75 Erg
per degree.

20
Proceedings Royal Acad. Amsterdam. Vol. XVIII.

294

0 1.535 2046.2 gu 0.937 3580

21 1.436 1914.2 34.8 0.920 3391

9519 1.375 1833.1 33.3 0.909 3271

50.1 1.335 1780.9 32.4 0.899 3206

65 1.304 1738.2 31.6 0.888 3153 |

15.8 7b} 1696.0 30.8 0.881 3089 |

90 1.233 1643.6 29.9 0.872 3019

99.8 1.209 1611.8 29.3 0.866 2972 |
114.8 1.180 1573.2 28.6 0.857 2922

125,2 1.159 1545.7 28.1 0.850 2886

141 1.131 1507.1 27.4 0.842 | 2832
154.8 1.106 | 1474.2 26.8 0.834 2788

170 1.081 | 1441.2 26.2 0.829 2736
185 1.056 1408 1 25.6 0.821 2691
200.6 1.031 1375.1 25.0 0.813 2645

= E E ET = |
Molecular weight: 884.82. Radius of the Capillary tube: 0.03636 cm.
Depth: 0.1 m.m.

The liquid solidifies at about — 17° C. slowly, after becoming very viscous
at that temperature.

The density at 50° C. was; 0.8992; at 75° C.; 0.8822; at 100° C.: 0.8665.
At © C.: d4o = 0.9371 — 0.00081 t+ 0.00000104 2.

The temperature-coefficient of “ decreases gradually with rising temperature,
and rather greatly from about 14 to 84 Erg. between — 17? and 21° C, to
4.7 Erg. between 21° and 90° C., and 3.25 Erg. between 90° and 200° C. |

= |

Radius of the Capillary tube: 0.04667 cm. |
| Depth: 0.1 mm.

995

XIII.
Margarine.
Maximum Pressure 1
Temperature Surface-tension x
Am OC : in Erg. pro cm?
in mi mercury in Dynes
40.2 1.009 | 1345.6 31.0
54.1 0.952 | 12684 | 20.3
76.2 0.886 1181.2 27.2
94.8 0.829 1105.6 | 258
116.5 0.795 1060.1 244

Radius of the Capillary tube: 0.04667 cm.
Depth: 0.1 mm.

Specific Surface-energy 7
in Erg pro cm?.

SS
40° 50° 60° 70° 80° 90° 100° 110° 120° Temperature

Specific Surface-energy of Butter and of Margarine.

§ 3. The results here obtained lead to the following remarks.
The absolute values of u evidently increase in a regular and pro-
minent way with augmenting carbon-content of the fatty acid; in
the case of the ethers of the higher fatty acids they reach a mag-
nitude quite comparable with that observed in the case of some
molten inorganic salts. This fact certainly runs in some respects
parallel with the strong increase of the molecular weight of these fats.
At the same time the temperature-coéfficients of u regularly
increase, with exception of the first term of the series, as can be seen

from the following data:
20*

296

Triformiate: 2,20—3,6

Triacetate: 1,05—1,26—2,20—2,89—3,0
Tributyrate: 1,70—2,42—2,60
Tricapronate : 2,49 :

Tricaprylate: 2,12—2,65—2,90
Tricaprinate: 3,09

Trilaurate: 3,33

Tripalmitate: 5,55—5,1—8,41

Tristearate: 6,75

Trioleate : RAD

It will be remarked, that the g-t-curve for trioleate is wholly
situated above that for ¢ristearate, which clearly demonstrates that
in the ease of the same number of carbon-atoms, the values of u
for the derivative of the wnsaturated acid will be greater than those
for the derivative of the saturated acid with the same number of
carbon-atoms.

Furthermore attention must be drawn to the fact that for the
first five members of the series = increases with rise of tempera-
ture; for tricaprinate, trilaurate and tristearate however it remains
rather constant, while for tripalmitate, trioleate just as for glycerol *)
itself, it decreases with rising temperature.

Most of the changes mentioned thus appear to occur in quite a regular
way. It is at the moment hardly possible to give any probable expla-
nation of the enormously great values of the temperature-coefficient
of u in the case of the higher members of this series.

With respect to the investigation of butter and margarine, we found

0
for the butter studied here a value of = of about: 0,055 Erg, and

for the margarine of about: 0.087 Erg pro degree. The absolute
values of 4 however deviate only slightly for the two complex fats ;
at 50°C. both liquids must have about the same specific surface-
energy of 29,8 Erg.
Laboratory for Physical and Inorganic
Chemistry of the University.
Groningen, June 1915.

0
1) For glycerol — varies between 1,8 and 1,5 Erg pro cm?,

297

Chemistry. — “Jnvestiyations on the Temperature-Coefficients of
the free Molecular Surface-Energy of Liquids between —80°
~ and 1650° C.” XII. The Surface-Energy of the Isotropous
and Anisotropous Liquid Phases of some Aromatic Azoxy-
Compounds and of Anisaldazine. By Prof. F, M, Janenr and

Dr, Jur. Kann.

§ 1. With the purpose of elucidating better the significance of
the temperature-coefficients of the free molecular surface-energy u
of liquids as a criterion for the degree to which these liquids are
associated, we have now extended our measurements to some of
these compounds which show wore than one liquid phase and of
which all, with the exception of the last, are optically anisotropous.

There can hardly be a doubt any longer that these anisotropous
liquids should be considered really as quite homogeneous liquid
phases of very peculiar molecular structure, while the mutual
relations of these anisotropous phases to the isotropous phase on the
one side and to the solid phase on the other, are quite analogous
to those commonly observed in the cases of polymorphism.

The successive anisotropous liquids, which reveal themselves in
the case of some of these substances and which in the case of
enantiotropic transformations can exist within a proper, sharply
limited temperature-range, may be distinguished according to the
explanation given by the most probable hypothesis yet suggested,
by a motion of the molecules in “swarms”, which decrease in com-
plexity after each higher transformation-temperature has been passed;
these molecules themselves probably have moreover an atomistic
structure, causing a general shape which is in one direction of space
considerably more elongated than in the two directions perpendicular
to the first.

By this hypothesis it thus becomes highly probable, that the
dsotropous liquid, which always appears at the highest transition-
point, will possess a much less complex structure than the foregoing
anisotropous liquids, — a supposition which will be found to agree
entirely with our usual ideas about the progress of a dissociation
occurring with increase of temperature.

If the hypothesis accepted till now was right, that a smaller value

0
of = than the normal of 2,2 erg stated by Hörvös, indicates an

association, but that a larger value than 2,2 Erg pro degree points
to a dissociation of the liquid, — we may expect here that the

298

Aro
mean value of the coefficient = at temperatures helow the transition-

point of the anisotropous liquid will appear to be smaller than that
of the isotropous liquid above the transformationpoint. The following
measurements were made to verify this conclusion by means of
experiments.

$ 2. The substances investigated here are in the first place the
following compounds often studied already, which have been purified
here with the utmost care :

para-Azoay-Anisol: CH,O.C,H,.N,0.C,H,.OCH,;
f == WAC and ti 367 CG,
para-Azoxy-Phenetol: C,H,O.C,H,.N,0.C,H,.OC,A, ;
(= 138 Cand 4. — 168" 1C-
and
para-Anisaldazine : CH, O.C,H,.CH:N.N:CH.C,H,.OCH, ;
(== 169" Cand 130

The last mentioned substance was prepared from p-anisaldehyde
and hydrazine-sulphate; it was purified by repeated crystallisation
from boiling benzene.

Furthermore we choose: Lthyl-para-Azoxybenzoate: C,H,O.CO.C,
H,.N,O.C,H,.CO.OC,H,, which was purified by reerystallisation
from a mixture of chloroform and benzene. The beautifully erys-
tallized compound shows the transition-temperatures: ¢, = 114° C.
and ¢, = 121°C. Finally we prepared, for other purposes also, a
quantity of Lthyl-para-Ethorybenzalamino-a-Methyleinnamylate: C,H,
0.C,H,.CH: N.C,H,.CH: (CH,).CO.OC,H, for the transitiontempe-
ratures we found: f, = 95° C. and ¢, = 117°,8C., which numbers
do not agree with those given in the literature on this compound.

The purity of the three first-named substances is above all doubt;
as for the two last mentioned compounds the certainty is somewhat
less, but it is very probable that the impurities possibly intermingled
with them, are not of any considerable importance. Since the beha-
viour of the three first substances differs appreciably from that of
the last two, the resp. u-t-curves are placed in two different diagrams.

299

para-Azoxy-Anisol: C3HO 5 Ce Hi . N20 ° Cs Hi ° OCH.

5 Maximum Pressure H | Mier
ch Surface- 3 te
ss tenen So Surface-
in mm. mer- 2 | gravity do | energy v in
EE cury of | in Dynes | Erg pro cm?. 4 2
2 en Yi Erg pro cm?,
|
iis: 1.136 1515.2 40.1 154 kN 1463.3
120 1.104 1472.3 | 39.0 1.166 1427.3
126 1.067 1422.8 | 37.7 1.159 1385.2
129.5 1.034 | 1378.5 | 36.4 1.156 1339.8
oon) 1.072 | 1429.1 | 37.8 1152 1394.6
138.1 OUT 1435-8 57150 1.142 1406.4
144.5 1.056 1407.7 Sie 1.136 1385.2
155.2 1.025 1366.0 36.0 1.126 1348.5
160.5 1.003 1338.8 35.5 1.124 SSU)
174.5 0.977 1302.0 | 34.2 oul 1292.0
190 0.940 1253.2 | 33.0 1.100 1255.5
211 0.897 1195.7 | 31.4 1.080 | 1209.4
| | eel es
Molecular weight: 258.14. Radius of the Capillary tube: 0.05425 cm.

Depth: 0.1 mm.

The compound was purified by repeated crystallisations. At 114° C. the
solid phase begins to transform into an orange anisotropous liquid, which

at 133°.5 C. is almost, at 138° completely, clear and transparent.

The temperature-coefficient of » is remarkably great for the anisotropous
liquid: between 115° and 126° C. about 7.1 Erg per degree, between 126° and
133° even 12.2 Erg per degree. For the isotropous liquid however it decreases
gradually from the transition-temperature from 3.45 Erg to 2.20 Erg at 190° C,

para-Azoxyphenetol : C,)H;0.C,;H4N,0.C,H40C, Hs.
v Maximum Pressure H
SA om Surf | Molecular
SO ene ae Specific | Surf
00 eal tension x in on ze | nn
a. | inmm.mer- ; Ere pro cm?, | Sravity d4o „in
5 = guty oF in Dynes ae | Erg pro cm?.
142.5 0.882 1198.0 31.6 1,094 1292.5
147.5 0.875 1165.9 30.7 1.089 | 1259.5
151.8 | 0.854 1138.5 30.0 1.084 1234.6
159) | 0 827 1102.2 29.0 1.076 1199.4
164 | 0.813 1085.0 | 28.3 | 1.072 | 1173.3
168.5 0.835 1113.2 | 29.3 1.068 1217.6
1145 | 0.814 1087.4 28.6 1.053 | 1200.0
190 0.779 | 1038.5 27.3 1.039 1155.7
2055 7} 0.742 | 990.8 26.2 | 1.026 1118.5
219 0.722 | 962.6 25.2 1.014 1084.2
Molecular weight: 286.17. Radius of the Capillary tube: 0.05425 cm.

Depth: 0.1 mm.

This beautifully crystallised compound is transformed into an anisotropous
liquid at 138° C., which becomes transparent at 168° C. With this compound
thus once more he fact is proved that the temperature-coefficient of » for

| the anisotropous liquid is abnormally high: it decreases gradually from 6,60
| Erg. at 143°C. to 489 Erg. between 159° and 164°, and then increases suddenly
under change of the algebraic sign, to 9.84 Erg. For the isotropous liquid

it is nearly constant; its mean value is 2.6 Erg. per degree.

Molecular Surface-Energy
in Erg pro cm?,

1470
1440
1410
1380
1350
1320
1290
1260
1230
1200
1170
1140

1110

1080
80° 90° 100° 110° 120° 130° 140° 150° 160° 170° 180° 190° 200° 210° 220° 230°

Fig. 1. Temperature

Molecular Surface-Energy
sin Erg pro cm’.

1380

1350

1320

1290

1260

1230

1200

1170

1140

1110

1080

80° 90° 100° 110° 120° 130° 140° 150° 160° 170° 180° 190° 200° 210° 220° 230°
igi 2:
Il.
Anisaldazine: CH30. CoHyCH:N.N: CH. CoH; . OCH.
v Maximum Pressure H Motked
EG Surface- Specifi Si ee on
5° in m Spe ues an : ee
a. in mm. mer- | ye
ES cury of in Dynes | Erg pro cm? 4° Erg pro cm2.
U o
= ORG:
171 0.932 1242.5 32.1 1051 | 1291.2
173.5 0.911 1214.0 31.4 1.049 | 1264.7
174.5 0.902 1203.5 31.1 | 1.048 | 1253.4
176.5 0.886 1181.2 30.5 1.046 1230.8
178 0 865 1154.8 29.9 1.044 1208.0
179 0.845 1128.4 29.4 1.043 1188.7
180.5 0.908 1210.5 31.2 1.035 1267.9
185 0.886 1181.2 | 30.4 1.031 1238.6
195 0.851 1134.5 29.2 1.023 1195.9
204.5 0.822 1096.4 28.3 | 1.015 1165.1
219 0.800 | 1067.1 27.4 | 1.002 1137.8
230.5 0.789 1044.7 26.8 | 0.993 1119.6
> = + — - —— — = | - — —
Molecular weight: 268.14. Radius of the Capillary tube: 0.05301 cm.
Depth: 0.1 mm. ;

The compound was prepared from anisaldehyde and hydrazinesulphate in
cold aqueous solution, and repeatedly crystallized from boiling benzene.
The beautiful yellow crystals are at 169°C. transformed into an isotropous
liquid, which at 180? C. gets clear and isotropous. The density of the isotro
pous liquid was: 1.0313 at 185° C.; at 205° C.: 1.0150; at 225° G.: 0.9977.
At © C. in general: d4o = 1.0355—0.0007775 (£—180 )—0.00000125 (t—180°)2.
For the anisotropous liquid the density at 173° C. was: 1.0486; at 180° C.:
MOTO ate ZG do = 1.0516—0.001 (¢ - 170 ). In this case also the tempera-

ture-coefficient of » is for the anisotropous liquid exceptionally great : between
171° and 176° about: 11.0 Erg, afterwards 15.2 and even 19.3 Erg per degree.
For the isotropous liquid it rapidly decreases with rise of temperature : At the
transitionpoint : 6.5 Erg, then 4.27 ; 3.25 ; and finally 1.88 and 1.53 Erg per degree.

302

IV.

Ethyl-para-Azoxybenzoate: C,H;0.CO.C,H4.N.0.C,H4.CO.0C2H;.

® Maximum Pressure H
Sir Shirtcen Molecular
a 9 ; . Specific Surface-
ER in mm. mer SCO gravity d energy » in

=} 7 2 o p
5 = city of zal in Dynes Ereipro En 5 Erg pro cm?

| |

° |
114 | 0.789 | 1052.6 27.0 1.176 1185.6
116 0.788 1049.4 26.9 1.174 | 1182.5
118 0.776 1034.6 26.5 1.172 | 1166.3
119 0.764 1018.3 26.1 1.170 | 1150.0
120 0.762 | 1014.3 26.0 1.168 1146.9
121 0.832 | 1109.2 28.5 1.148 1271.7
124 0.809 1079.0 27.7 1.145 1238.1
125 0.779 1038.4 26.7 1.144 | 1194.2
130 0.774 1030.3 26.5 1.141 ee KES
140 0.768 1023.9 26.2 1.135 1178.0
150 0.770 1027.1 26.3 1.128 1187.4
160 0.771 1030.0 26.3 1.121 1192.3
170 0.770 1027.1 26.3 | 1.114 1197.3
180 0.799 1065.2 2k | 1.108 1247.3
190 0.804 1072.2 27.5 | 1.102 | 1261.0
200 | 0.793 1057.2 27.1 1.096 | | 12472
210 0.762 1011.0 | 26.1 1.090 1205.6
220 0.757 1005.1 | P2531 1.084 1191.2
230 0.741 | 987.9 2573 | 1.079 1176.5
Molecular weight: 342.18. Radius of the Capillary tube: 0.05301 cm.

Depth: 0.1 mm.

The beautiful orange-coloured crystals are at 114° C. transformed into the
anisotropous liquid, which at 121’ C. is changed into the clear, amorphous
one. All measurements were repeated after crystallisations of the substance
used in mixtures of chloroform and benzene; as the peculiarities were observed
again every time, they must be considered as essential features of the substance.

In this case also the temperature-coefficient of » is abnormally high:
irregularly oscillating, but with a mean value of about 7.2 Erg. per degree.
Then » increases suddenly with rise of temperature, and afterwards falls
rapidly and irregularly in the isotropous liquid; then it increases again slowly
to a maximum at about 190° C., to decrease afterwards slowly, and reach a
final gradient of about 1.45 Erg. per degree. Very complicated reactions seem
indeed to take place in this liquid.

303

Vv.
Ethyl-para-Ethoxybenzalamino-«-Methylcinnamate :
C.H50 . CgH,.CH:N.CgH,. CH: C(CH3) C. OOC,Hs.
v Maximum Pressure H Moleeutay |
BG Surface- |
5° in mm. mer tenn ee ae |
as : a) Erg pro cm?2. 24 ie
aS cury of in Dynes SP ° | Erg pro cm? |
= 0e C. |
85 0.843 ior sik oane PE 1324.7
94.5 0.837 1112.9 | 28.5 | 1.068 1321.2
99 0.831 1108.0 | 28.3 1 064 | 815: |
105.5 0.829 | 1104.7 28.1 1.058 | 1310.9 |
111 0.822 1095.8 27.9 | 1.053 | 1305.7 |
115.3 0.819 1090.9 27.8 | 1.049 | 1304.3 |
117.6 0.843 1123.7 28.7 | 1.045 1350.0
123.7 0.831 1107.8 28.3 | 1.040 | 1335.4
130.5 0.828 1101.9 28.1 1.034 1331.1
139 0.825 1099.9 28.0 1.027 1332.4
149 9.822 1095.8 27.9 | 1.018 1335.4
159 0.819 1091.9 27.8 | 1.010 1337.6
168.5 0.818 1089.8 27.8 1,002 1344.8
179 0.816 1085.8 27.7 0.993 1348.0
2 | 7 Len J | eae}
Molecular weight: 337.11. Radius of the Capillary tube: 0.05265. |
Depth: 0.1 mm.

The compound was prepared by the method described by W. KasTEN
(Dissertation, HALLE, 1909 p. 41), and purified by repeated crystallisations.
Contrary to the data given there, we found the transition-points to be: 95° C.
into the anisotropous, greenishly opalescent liquid, and 117°.8 C. into the
amorphous liquid. If every crystallisation-germ is excluded, the liquid can be
undercooled to about 79°; it remains then only slightly viscous, and has a
yellow colour. In this case also the temperature-coefficient of the surface-
energy is extremely small; nor does the break in the curve at the transition-
temperature seem to be of any considerable magnitude.

The density at 95° C. was: 1.0673; at 115° C. 1.0491. For the anisotropous
liquid the density may thus be calculated from: do = 1.0809 — 0,000905 (t— 80 ).

For the isotropous liquid at 120° was found: 1.0428; at 140° C.: 1.0257; at
160° C.: 1.0086. In general at ¢ C.: dyo = 1.0599—0 000855 (f—100°). (Only to

be used for temperatures from 117? upwards).

With the exception of the sudden increase of » in the neighbourhood of
117° C., the temperature-coefficient of » is here exceptionally small; for the
isotropous liquid moreover it increases gradually with rise of temperature,
and with a gradient of about 0.33 Erg per degree. The entire behaviour is
very strange and enigmatic.

4. =o

§ 3. If now we review in the first instance the results obtained
with the three first-mentioned compounds, it will immediately attract
attention that the corresponding g-f-curves have all a completely
analogous shape: this shows two branches, of which the first has
regard to the anisotropous, the second to the isotropous liquid

304

phase, and in all cases without eaception the first branch falls
with increase of temperature more rapidly than the second. The
result is thus just opposite to what we should expect if we founded
our Opinion on the mentioned hypotheses about the molecular state
of the two liquid phases; and with regard to the great probability of
the correctness of these views, the fact observed may be considered
as a rather strong argument against the opinion, that it is right

Ou
to consider the smaller or greater values of oe 38 8 somewhat sure
t

criterion for the judgment of the degree of an occurring dissociation
in the liquids.

lt will be remarked further that the mutual position of the two
branches of the curve always indicates a sudden increase of the
value of u at the transformation from the anisotropous-liquid into
the isotropous-liquid condition. This discontinuity does not set in
precisely at the transition-temperature: from the observations it
seems rather probable, that it occurs in a continuous way, and
already starts at temperatures below the transition-temperature.

In that case the two branches could perhaps be linked together in
the way indicated in the diagrams by dotted lines (fig. 1).

Now although in the cases of both ethers fvo branches were also
present in the u-f-curves (fig. 2), and here too u seems to increase
suddenly at the transformation into the isotropous-liquid state, another
remarkable peculiarity reveals itself here in so far, as the values of
u for the isotropous-liquid phase fall in the beginning with increase
of temperature and then increase again to a flatter or steeper maxi-
mum in the curve. It can hardly be doubted that these phenomena
are real ones; in these isotropous liquids we were therefore forced
to see the first instances of liquids, whose free surface-energy
increases with a rise of temperature. The explanation of such an
abnormal phenomenon must be found in the algebraic sign of the
heat-effect which accompanies the eventually isothermical enlarge-
ment of the surface-layer of the liquid. What peculiarities of the
molecular structure of these isotropous liquids could be the cause
of such abnormal heat-effect, is for the moment incomprehensible
and very difficult to imagine. In any case the said phenomena
indicate the presence of molecular conditions in these liquids,
differing of course very much from those, which are intrinsic for
most of the common isotropous liquids.

Laboratory for Inorganic and Physical
Chemistry of the University.
Groningen, June 1915.

305
Botany. — “Crystallised Starch”. By Prof. Dr. M. W. BrineiNck.

The fact that starch erystallises easily is not generally known. It
is true that ArrHur Meyer supported the view that the starch grain
is a sphero-erystal, *) but convincing figures he does not give; his
considerations are hypothetical and not decisive as he did not make
any microscopical examination on soluble starch. Moreover, the
highest temperature used by him was but 145° C., and he conti-
nued the heating not long enough.

Most species of starch, such as that of potato, wheat, barley, rye,
rice, maize, behave as follows.

When a 10°/, solution, after previous boiling and gelatinising in
distilled water, is heated during fifteen minutes or half an hour at
150° to 160°C., the grains dissolve to a perfectly clear, transparent
liquid, in which, at slow cooling, a crystalline deposit sets off,
consisting of very fine needles, which are either isolated or united
in groups of various shapes, not seldom resembling natural starch,
and which must undoubtedly be considered as crystallised starch
on account of their behaviour towards diastase and chemical reagents.

The free needles, measuring but few microns or parts of microns,
make the impression of an amorphous sediment. The groups, formed
by longer needles have the shape of corn-sheaves or bundles of
arrows (bolidesms); or of dises (bolidises), reminding in size and
form of the red blood-cells ; or they are more or less regular globules
(spherites or sphero-crystals), from whose surface, however, here
and there project the crystal needles.

Potato starch is very well apt to produce bolidesms and sphero-
erystals; it is sufficient to heat to 150° C., during a quarter
of an hour, a 10°/, solution in distilled water, previously boiled
and gelatinised. After being kept 24 hours in a cold room
loose needles, bolidesms or sphero-crystals are precipitated, and
their crystalline nature is easily observable. What circumstances
determine the union of the needles to bundles is not yet well
known, but certainly slowness of crystallisation favours it, and the
concentration has also some influence. Not seldom the whole deposit
consists of a magnificent mass of sphero-erystals (Fig. 1). The discs,
to which I shall return presently, are formed from potato starch
at a somewhat lower temperature than the needles mentioned here.

') Untersuchungen über Stärkekörner, Jena, 1895 Beiträge zur Kenntnis der
Stärkegallerten, Kolloidchemische Beihefte Bd. 5, Pag. 1. 1913. The observations
and opinions of Bürsenrr, Untersuchungen über Strukturen, Pag. 283, Leipzig 1898,
are obscure,

306
The two constituents of the starch grain, which I described earlier, *)
namely the amylopectose, non-soluble at boiling, which forms the
wall of the starch grain, and the granulose (amylose), which does
dissolve at boiling and forms the inner part, change both at 150°
C. into erystallisable starch.

It is not difficult to convert 40°/, of the original starch into
needles or sphero-crystals. With a lower temperature or a shorter
time of heating the quantity of starch, which crystallises increases,
but at the same time the needles become shorter and less distinet.
When heated at 110° to 120° C. the solution, at first perfectly
clear, quite coagulates at cooling and becomes white as porcelain.
This coagulated substance or gel, must also be considered as con-
sisting of crystals, but the needles are nearly, or in fact ultra-
microscopic. They do not show any orientation.

As the temperature is taken higher, the quantity of dextrine, which
does not erystallise, increases. The iodine reaction shows that this
dextrine contains much erythrodextrine at lower temperatures, and
at higher consists only of leukodextrine, colouring light brown. At
temperatures of from 160° to 170° C. the 10°/, potato starch quite
changes into dextrine in from half an hour to three quarters of an
hour; besides, the presence of sugar, susceptible to alcoholic fer-
mentation, may then already be observed.

The sphero-crystals and needles of the starch dissolve, when
heated in water, more slowly than soluble starch, which I ascribe
to the greater size of the artificial needles, compared with that of
the needles composing the natural and soluble starch. These needles
consist in my opinion of a substance (granulose) impermeable to
water, so that the dissolving must begin at the outside and will be
the slower as the needles are thicker.

At 70° C. the solubility becomes very great, without any sign
of production of paste or of gelatinising. With iodine the colour
of the solution is pure blue. The effect of diastase on the granulose
needles is as usual: erythrodiastase extracted from crude barley-
flower, forms erythrodextrine and maltose, whilst leukodiastase pre-
pared from malt, produces leukodextrine and maltose.

Of erystallisable dextrine and amylodextrine, so munch discussed
in literature, I. perceived nothing in my experiments; the latter
substance is evidently erystallised starch, with so much erythro- or
leukodextrine between the needles, that the pure blue iodine colour
of the granulose is modified to violet or reddish brown. When the

1) Proceedings of the Academy of Sciences. Amsterdam, 11 April, 1912.

307
erystalline mass, which in fact sometimes colours red with iodine,
is washed out with much water, the dextrine, and with it the
“amylodextrine reaction” quite disappears, to make place for
pure blue.

The crystals may also be obtained from soluble potato starch.
Such starch is prepared by keeping raw starch during 10 days under
10°/,-ie cold hydrochloric acid.

Crystal dises (bolidises) result very easily from wheat starch.
The heating must be somewhat longer and the temperature higher
than for potato starch. Besides, it is more difficult to obtain a per-
fectly clear solution from wheat paste.

Fig. 3 shows, 230 times magnified, the dises formed in a beaker-
glass of 100 cm*, in which wheat starch, previously boiled in distilled
water, is heated to 160° ©. The dises are thinnest in the middle
and from this centre the needles radiate. The discs resemble natural
wheat starch as well in shape as in size. With polarised light 1 could
not, however, perceive anything of the axial cross, which is so very
obvious in natural starch. | suppose that it does exist, but is too
feeble to be observed. It is, namely, a fact that the structure of
the spherites and discs is much looser than that of natural starch,
so that in a volume unit of the latter many more needles occur
than in the discs and spherites. If now the double refraction of the
separate needles be not great, their united power in the dises need
not necessarily show the same as is seen in the natural grains.

That the double refraction of the common starch grains reposes
on their crystalline nature and not on tangential and radial tensions,
may be concluded from the fact, that the axial cross is in the usual
way perceptible in soluble starch. As this substance is prepared with
strong hydrochloric acid, whereby from 10 to 16°/, of the dry
substance is extracted, it must be concluded that all tensions, originally
present in the grain, disappear.

That the dises may also be obtained from potato starch is demon-
strated in Fig. 3, where 10°/, potato starch, after boiling and gela-
tinising in distilled water, in a 100 em° beakerglass, heated to 125° C.
during 3'/, hour, and after 24 hours of crystallisation in a room of
about 16° C., is figured 600 times magnified.

By moving the coverglass on the slide, many discs may be
observed laterally, as is clearly seen in the photo. In the preparation
of wheat starch used for fig. 3, all the grains are lying on their
broad side.

The crystal dises of the starch are now and then referred to in
literature as “JACQUELAIN discs”, but without any allusion to their

308
erystalline structure. JACQUBLAIN himself, who first mentioned these
grains, called them “granules de fécule”. *)

After having become acquainted with the deseribed facts and
found them confirmed for other species of starch, | convinced myself
that the natural starch grain also is built up of erystal needles
radiating from the dot or hilum. This may best be seen in soluble
potato starch, very cautiously heated in the microscopic preparation
on the slide under the coverglass, when all the stages of the dissolving
in hot water can be followed. The tiny radiating crystal needles
then become visible in a ring-shaped arrangement, such as might
be expected from the structure of the starch grain itself. It seems
that the length of the needles corresponds with the thickness of the
rings.

From the preceding I conclude, that the formation of the starch
grain takes place in the following way. The amyloplast produces
granulose, which in the interior crystallises to small spherites, just
as in a solution. But this granulose production occurs periodically,
and so the process of crystallisation gives rise to the formation of
the layers of the grain.

To explain the great difference existing between starch gelatinised
at 100° C. and that heated to 150° and 160° C. it must be accepted
that in the starch grain, beside the granulose, an incrustating
substance exists, functioning asa “protecting colloid”, whose presence
makes the needles remain sbort, the shorter the more of the colloid
is present. It remains active unto about 100° C., but above
this temperature it slowly decomposes, quite to vanish at about
150°. €.

The hypothesis that this protecting colloid might be a phosphoric
ester of granulose; is contrary to the properties of soluble starch,
for this behaves at erystallisation of the solutions, prepared between
100° and 150° C., precisely in the same manner as natural starch
so that the protecting colloid is still present in this substance, whereas
it might be expected that an ester would be decomposed by the
strong, 10°/,-ic hydrochloric acid used for its preparation.

Perhaps the colloid is the amyloplast itself, which, at the formation
of the starch grain, remains partly enclosed between the fine granulose
needles. Its greatest accumulation would then occur in the amylo-
pectose wall of the grain, which does not yet dissolve at boiling.

1) J A. JACQUELAIN, Mémoire sur la fécule. Annales de Chimie et de Physique.
T. 63, Pag. 173, Paris 1840. Much in this treatise is incorrect and obscure, else
the dises would certainly already earlier have drawn general attention.

ee eT os,

Fig. 2 (600). Fig. 4 (200)

9
Proceedings Royal Acad. Amsterdam. Vol. XVIII.

309

That no difference could be found in the rate of nitrogen between
the granulose and the amylopectose of the starch grain, to which
circumstance I directed attention in my communication of 11 April
1912, I ascribe to the extremely small absolute rate of nitrogen in
both constituents; but I think that the relative difference is con-
siderable.

I will not omit to draw attention to the existence of starch species,
which after heating, do not erystallise in the usual way. To these
belongs arrowroot. If a 10°/, paste of arrowroot is precisely treated
as above described, it becomes after cooling, as usually, turbid and
precipitates; but instead of a crystalline deposit we find in the
microscopic preparation drops of various sizes, and homogeneous struc-
ture (Fig. 4), which later, however, become turbid and granulous.
With iodine these drops turn deep blue and evidently consist of
granulose like the crystal needles of the other starch species. The
liquid between the drops is also a granulose solution, but less con-
centrated. The drops remind of a heavy oil, but they differ from it
by such a small surface tension that notwithstanding their liquid
state many may be pear- or egg shaped, and even pointed. Double
refraction I could not perceive, but, nevertheless, I think it probable
that they must be reckoned to the liquid crystals. That after some
time the drops become turbid can be explained by the growing in
length and thickness of the ultra-microscopic needles, which constitute
the liquid crystal drops, hence, by the same process of crystallisation
by which the needles originate.

The facts here briefly described deserve further attention from a
physico-chemical view.

EXPLANATION OF THE FIGURES.

Fig. 1 (600). Sphero-crystals of 10°/) potato starch, half an hour at 150° GC,

Fig. 2 (600). Bolidises or JacgueLatn dises of potato starch, half an hour at
125° C.

Fig. 3 (230). Bolidises or Jacquenat discs of wheat starch, three quarters of
an hour at 160° C.

Fig. 4 (200). Drops or liquid crystals of 10°/) arrowroot, three quarters of an
hour at 140° C., coloured with iodine.

21
Proceedings Royal Acad. Amsterdam. Vol. XVIII.

310

Meteorology. — “On the relation between meteorological conditions
in the Netherlands and some circumjacent places. Atmospheric
Pressure.” By Dr. J. P. vAN DER STOK.

(Communicated in the meeting of May 29, 1915).

1. For the knowledge of the climate of a country as also for
the forecasting of the weather, it is of importance to investigate in
how far a relation exists between the meteorological conditions
within a limited region and in circumjacent places, chosen for this
purpose, and to what degree local influences are felt.

Statistical methods, leading to empirical, numerical relations,
involve the objection that many peculiarities, especially secondary
phenomena, disappear by the collective treatment, but by their means
existing relations may become more prominent, which necessarily
remain unobserved by those who, for many years, have made a
special study of the individual phenomena and, if no new relations
are brought to light, quantitative rules are substituted for qualitative
knowledge. As the most simple and principal problem, the question
will be examined, what relation exists between the oscillations of the
atmospheric pressure at de Bilt and the oscillations at a few surround-
ing places.

The isobars for different months and the corresponding average
values of the wind show that this relation can hardly be the same
in different seasons. We come to the same conclusion by investigating
the relation existing between barometric oscillations within the region
of high pressure near the Azores and of low pressure near Iceland,
by which the climate of Western Europe is considerably affected.

Each factor indicates that the observations made during the months
of January, February, and December are the fittest material for this
inquiry which, therefore, is restricted to the wintermonths.

2. The method followed is simple, but necessarily laborious.

If the deviations from the average barometric height at a central
point and the cireumjacent stations be denoted by «,, a7, ....2,, then,
the quantities under consideration being small, a linear relation may
be assumed to exist

== bits 1210 ta vertand ae, Oe
and the coefficients h can be calculated by means of the method of
least squares from the n—1 equations formed by multiplying the
equations (1) successively by x,,2;...2, and addition of the total
number of equations.

31i

Putting

De DN)
= 6;” eee (2)
: n n0,0,

where » denotes the number of equations, ¢ the standard deviation
and 7, the correlation-coefficient (cc) between a, and ay, the n—1
equations deduced from (1) can be substituted by the equivalent set
of equations :

tin SSS ae Weg ar rin ge edo dha: 1

rs ars; tr Ag tr 9s, oi ee AnTan

hes
t
il

Pin = 4,7 On -+ A313n ze G4? 4n |. «dn
By the quantities « thus calculated, the quantities 4 become

oO oO
b,. =a, ’ b — EN BS: An -
2 3 n
Obviously the equation (1) holds good only to a limited degree
because the data are necessarily incomplete; a measure of the com-

pleteness is obtained by putting

Re, = F,
from which
Dey
R=
> 2

ay
or, by substitution of the values (2):
En =a,” 4 + ik An
+ 2a,a,7,, + 2a,0,7,,-+ « 2a,arron
—+-.2a,0,7,, + 20,4,7,,-.. 2a,dnrsp
+ Dan 10rt n= n
The quantity represents the general c.c. of equations (1) and
the probable error of one determination of , becomes
w= ao, V1—R? a= 0.67449
The partial c.c., defined as the ¢c.c. between #, and «, when all
other values rv are zero, is calculated by solving also the equations
ig ’ OR Sec oo tii, = Id
and is given by the expression
Opg = V ba bop -

the sign of o being that of the quantities 0.

21"

312
For the probable error of the c.c., Pearson gives the formula

f= 1—7*
le am) Vn
It holds good for the case of normal distribution of deviations
and the ce. is considered to be reliable when / is considerably
smaller than the c.e. itself; in the following tables

gif

3. The monthly mean values of barometric height in Iceland and
the region of the Azores are compiled from Danish and Portuguese
annals for the 36 years 1875—1910.

The Iceland values are obtained by taking the average of three
stations namely: Berufjord, Grimsey and Stykkisholm.

From the Portuguese observations average values were calculated
for two stations: Punta Delgada (Azores) and Funchal (Madeira);
for the years 1906—1910 Horta was substituted for Funchal.

The monthly means thus obtained and considered as normal
values, are shown in Table I; they are uncorrected for height above
sealevel, this correction being unnecessary for the calculation of
deviations, and given only to show the correspondence existing
between the annual variation of the differences of pressure and the
c.c. of table II.

ee | | | |

January 65.0 48,3 | +16.7 | July 65.7 56.4 | + 9.3

February 64.2 50.6 | 13.6 | August 64.4 | 56.0 8.4

March 63.3 53.0 | 10.3 || September | 63.9 | 53.6 10.3

April 63.6 56.6 7.0 | October 62.4 | 53.8 8.6

May 63.7 59.3 | 4.4 | November 63.0 | 52.5 10.5

June 65.3 57,7 | 7.6 | December 64.3 | 48.5 15.8

It appears from these data that the differences of atmospheric
pressure are greatest in the winter months and smallest in May.
Table Il shows the results of the calculation relating to the deviations
from the normal values of table I.

313

TAB ESI
Standard deviations and correlation coefficients Iceland =1, Azores = 2.

0, 6, Js q bio bar
| |
January 6.31 mm. | 2.86 mm. | EE OEE
February | 7.00 | 3.97 | — 0.595 | 8.2 | — 1.048 | — 0.337
March 5.30 | 3.07 | — 0.620 | 9.0 | — 1.071 | — 0.359
|
April 3.83 | 2.24 PZ 0:48 5.6) |= 0,82 | 00288
May 2.96 | 1.51 = 0.365 |) 3.7 es 0. 100 |) —-0),186
ime - | 3.32 | 1.39 | — 0.396 | 4.2 | — 0.946 | — 0.166
July 2.64 | 1.25 1 = ..0.845r|) Stol = Orem 0164
August | 3.01 1.21 = 0)376:|) 30001 0:03 ORS
September | 3.56 1.18 —0:Â85 | 5.) =f, ASA ORL 62
October 4.36 kaal | — 0.469 | 5.3 | — 0.885 | — 0.249
November | 5.52. 2.87 — 0.421 | 4.5 | — 0.810 | — 0.219
|
December | 5.04 2.97 | ES) raar Geeren Orgs
|

These results show, with a certainty much greater than can be
obtained by graphic representations that the antagonism between
the barometric oscillations in the region of the Azores and the
northern parts of the Atlantic Ocean is evident in every month.
From the regular course of the values of 7, in the summer months
as well as in winter, the conclusion may be drawn that a value
of g=3.5 indicates a reliable result, for, if the four months: May—
August were taken together, the same value 7 = 0.37 would be
obtained, but now with a factor of accuracy twice as great, or g = 7.5.

In his extensive investigation of correlations between monthly
oscillations of atmospheric pressure and temperature at 49 stations
in the northern hemisphere during the three winter months of the
years 1897—1906, Exner’) gives the value = — 0.479 (q = 5.0)
for the e.c. between Stykkisholm and Punta Delgada which cor-
respond well with the data of table II, and the fact that, by using a
number of observations four times as great, a greater value is found
may be considered as proof of the reliability of the results obtained.

4. For an investigation of the relation between oscillations of
atmospheric pressure at different places, the “Dekadenbericht” edited

1) F. M. Exner, Ueber monatliche Witterungsanomalien auf der nördlichen
Erdhälfte im Winter. Sitz. Ber. Akad. d. W. Wien 122, 1913 (1105—1240).

314

by the “Deutsche Seewarte” contains valuable data: commencing
in 1900, this publication gives ten-day means of barometric heights,
in such a way that three average values are always formed for
each month. At the same time normal values are given so that
deviations from the normals can be formed at once for the purpose
of further treatment. In accordance with the results of Table II,
the inquiry is restricted to the winter months from December 1900
to February 1914 as being the most disturbed; the number of
observations therefore amounts to 126.

From the stations in this publication the following places were
chosen, in the equations represented by their rank-number; the
values 6 are the standard deviations.

1. Helder 6, = 6.96 mm.

2. Valencia (W. coast Ireland) 0, = SOR

3. Clermont (S. France) 6, =o 00m

4. Milan (N. Italy) Or 0102

5. Neufahrwasser (Baltic Sea coast, Prussia) 6, = 6.30 _,,

6. Christiansund (W. coast Norway) 6, = 8.4905
TABLE III.

Correlation-coefficiénts r, factors of precision q and distances D.
Helder —Valencia . . . . | ri = 0.170 q = 30.8 | DESM
Helder Clermont. . . . | ryz = 0.127 251 | 79.25

|
Helder—Milan . . . .. | m4=0511 11.5 8°.0
Helder—Neufahrwasser . . | rs = 0.633 17.6 8°.35
Helder—Christiansund . . | rig = 0.609 | 164 | 10°.3
Valencia—Clermont . . . | r23 = 0.704 | 23.2 10°.7
Valencia—Milan ... . | r24 = 0.380 | 14 140,3
Valencia—Neufahrwasser | 725 = 0.247 | 4.4 17°.4
Valencia—Christiansund. . | r26‚— 0.310 5.1 | 140,7
ont Mia raa =0.645 | 184 | 40,2
Clermont —Neufahrwasser . | 35 = 0.246 | 44 | 130.15
Clermont —Christiansund . | 73g = 0.058 | 1.0 125
Milan—Neufahrwasser . . r45 = 0.370 | 7.1 | 10°.8
Milan—Christiansund . . | ryg=0.095 | eG ay) dd Od
Neufahrw.—Christiansund . sg = 0.746 | 28.0 | 109,4

315

In Table III (p. 314) the different correlation coefficients are
given and the distances between the stations expressed in degrees
of the great circle corresponding to about 111 k.m.

For ascertaining meteorological conditions, the regression-equations
(preferably called meteorological condition equations) are of greater
importance than these general, interdependent correlation coefficients,

R
v, = 0.238 #7, 4+ 0.520 #,+0.011 w, 40.201 #,4+0.292 2, 0.943
x, = 0.928 x,+ 0.416 x, —0.096 «,—0.485 #,—0.112 2, 0.830
x, = 0 680 w, 4-9.109 w, 4- 0.242 x,—0.026 w, —0.836 x, 0.908 Wr Be)
&, = 0.038 x, —0.076 x, 4-0 594 #,+0.353 #,—0.150 a, 0.672 |
av, = 0.457 v,— 0.259 x, — 0.054 #,+0.250 7,+0.396 2, 0.843 |
©, = 0.929 #,+0.063 #, —0.822 wr, —0.150 wv, 40.578, 0.878

The partial c.c. calculated from the coefficients of these equations
are given in Table IV, arranged according to their magnitude.

TABLE IV. Partial correlation-coefficients.

Helder— Clermont . . . . | 0.594 | Valencia—Christiansund. . | 0.084
Helder—Christiansund . . | 0.521 || Helder—Milan . . . . . | 0.020
Neufahrw. — Christiansund . 0.476 Clermont —Neufahrwasser . | — 0.037
Helder—Valencia . . . . 0.470 Valencia—Milan | —0.085
Milan—Clermont . .. . 0.379 || Milan—Christansund . . | —0.150
Helder—Neufahrwasser . . 0.303 || Valencia—Neufahrwasser . | — 0.355
Milan--Neufahrwasser . . 0.297 | Clermont—Christiansund | —0.526

|
|
Valencia—Clermont . . . 0.213 |

From these results it appears that the choice of the stations was
good, except Milan which, although at about the same distance from
Helder as Clermont, still exercises a much smaller influence.

Clermont and Milan being at a mutual distance of only 4°.2, it
is possible that this result is due to purely arithmetical reasons;
the method followed involves that two stations near to each other
must be considered as one, because it depends on incalculable factors
how the common effect is distributed over either point, this being
of no importance for the result.

If this were the case, however, the partial c.c. between Clermont
and Milan ought to be nearly equal to unity, which is contradicted
by the c.c.: 0.379.

316

It appears, therefore, that Milan is situated out of the circle of
influence, which from a meteorological point of view is perfectly clear
because here the influence of the Alpine montain chains and the
Mediterranean prevails, the equations (4) are, therefore, actually based
upon only four points, situated round Helder and the first equation
proves that these are sufficient to account for the barometric oscil-
lations in the central point to an extent of 94 °/,.

As it may be assumed that this percentage would increase by
augmenting the number of stations, it appears from this equation
that local disturbances have only a subordinate influence. Whether
this statement is also applicable to the summer months can only be
proved by experiment.

Another result is that the meteorological field cannot be considered
as uniform in different directions, the influence of Clermont being
twice as great as that of Valencia at a slightly greater distance
from Helder.

It may be, further, remarked that the central point, without
exception, plays a more important part in the equations for the
surrounding stations than, inversely, the latter for Helder; which is
easily understood because the central point represents the meteoro-
logical conditions common to the whole field of disturbance. In the
partial ¢.c. this asymmetry disappears and for these quantities the
question arises whether and to what degree the relations are dependent
on the distance.

Assuming that this relation can be taken as linear so that

el — kD:
where ) denotes the distance, expressed in degrees and / a constant,
we find for Valencia, Clermont and Christiansund for / respectively :
0.0576 0.0560 0.0465
for Neufahrwasser the somewhat different value: 0.0834.

According to this relation the partial c.c. at equal distances of 5°
would be

@.,== 0.711 9, = 0.720 9,, = 0.583 9, = 0.767.

Finally the remarkable fact may be noticed that the same negative
correlation, observed between the region of the Azores and Iceland
at a distance of about 35°, appears to exist, and with the same
magnitude, between the stations Clermont and Christiansund at about
half the distance.

5. In order to come to a conclusion concerning the results obtained,

317

it seemed desirable to institute a similar inquiry based upon other
data and partly other stations.

For this. purpose daily observations made at 7 a.m. as published
in different weather bulletins and inscribed in registers at de Bilt,
were chosen.

A first group of stations is: 1. de Bilt, 2. Ile d’Aix (W. coast
France), 3. Dresden, 4. Lerwick (Shetland Isles). The distances between
de Bilt and the surrounding stations are:

1:38) DAO SS ON,
the azimuths:
N217°11'E , N97°44 E , N338°59' Z ,
the mutual angular distance, therefore, about 120°.

The data are observations made during the winter months of January,
February, December 1912, January, February, December 1913 and
January, February 1914, in total 240 observations.

The standard deviations are:

GD On —— (oO, On — 1-0 0ny Oy Ont

bo
>
>
>
>
>=
:

The correlation coefficients :
Ta AEN we tet OLE jn — UD
EADE A A EU
The criterion q="/; for the reliability of the ee. calculated,
mentioned above, cannot be applied in this case (as it was for ten day
and monthly means) because daily observations are by no means
to be considered as independent data.
The condition-equations calculated from these values are as follows:
vw, = 0.395 w, + 0.568 «, + 0.2342, R, =0957
@, = 1.370 x, — 0.525 «, — 0.3462, R, =0.821 |
2, = 1.207 2, — 0.821 7, —02052, R,=0.905 \
2, = 2.042 x, — 0.8738 v, — 0.842e, R,=0.751

. (5)

The partial c.c., the mutual distances, the variation k of the partial
c.c. per degree of distance and the partial cc. for equal distances
of 5° from the centre are:

ONS 0.735 k,, = 0.0358 Oi =S 0.821
0,,=0.828 k,—=0.0318 _ Q,,— 0 841
Or OON! k,, = 0.0351 0,, = 0.824
Mean 0.03842 Mean 0.829

Q,,=— 0411 Dy, = 119.10

Qc Dias) De = Veh

0,,= — 0415 Dy Std? 130

318

6. A second set of four stations is:

1. De Bilt, 2. Valencia, 3. Mülhausen i. B. and 4. Sylt (W. coast

Schleswig Holstein).

The distances from de Bilt to the surrounding stations are respect-

ively :
9°.48, 4°57, 3°.39

the azimuths :

N 32° 40' E, N 161° 32’ Z, N 275° 13' E.

For these places the angular distance is likewise about 120°, and

they differ 60° with the stations mentioned sub 5,
The standard deviations are
Ot== 8.20) 6, —— 10,8259 0. HD 0 SS ED rn
The correlation coefficients :
r= 9.683 , vr, =0818 , »,,—0.864
7 END en NOES ne or DE
from which the following condition-equations derive :
zw, = 0.140 2, + 0.494, — 0.5102, R, =0.976
&, = 2.417 «, — 0.852 2, —1.9342, R, = 0.722
w, = 1.457 a, — 0.146 2, — 0.653, R, 0.905

„== 1.595 a, — 0.188 2, — 0.6932, R, = 0.934

U, ==

|
\

- (6)

For the partial ee, the distances not yet mentioned, the variation
ke for one degree distance and the c.e. for equal distances of 5°,

we find:

k=5

Ono = 0.583 he 0.0441 Di 0.780
v‚, — 0.848 k,, = 0.0332 0,, = 0.834
on 10-902 Ki, =2020290 Ci, = 02855
Mean 0.0354 Mean 0.823

0,, = — 0.352 Dl 0

0,, = — 0.440 Dy = 11245

Os == 0.672 iD, LILY

Either group proves that barometric oscillations in a central point
may be determined with great accuracy from only three well chosen
stations; the condition-equations for de Bilt (v,) show even a greater
value of # than the corresponding equations (4) and the equations
for the three easterly stations: Dresden, Miilhausen and Sylt all
show a value greater than 0.9. As one would perhaps be inclined
to overrate the value of such a cc. for an actual calculation, it
seems not superfluous to remark that if — as in this case — the
standard deviation is relatively great, a large value of c.c. may

319

leave a pretty large margin of uncertainty. According to the formula
given in § 2 the probable errors of a determination from (5) and
(6) for de Bilt with R=0.957 and 0.976 resp. are 1.62 and
1.21 m.m.; they prove however, as well as equ. (4) that local
influences play an unimportant part.

In the same manner as from (4), it appears from (5) and (6) that
the influence of the eastern stations Mülhausen, Dresden and Sylt
is considerably greater than that of the western stations: Valencia,
Tle d'Aix and Lerwick.

For the partial ee. between Helder and Valencia we have found
0.470 (Table IV) whereas for that between de Bilt and Valencia, as
deduced from (6), we find 0.583, an agreement which can be
considered fairly satisfactory if we take into account that the data
used in computing these values are totally different.

As mentioned in § 3, for the first series general normal values
have been used, given in the “Berichte” so that it is possible that
in this case the sum of the deviations for each station is not exactly
equal to zero which, of course, would influence the value of the c.c.

It is, however, more probable that the cause of this disagreement
must be ascribed to an insufficiency of the number of observations
used in § 5 and $ 6, because the values of & found in the first
investigation (§ +) are all greater than those derived from the groups
treated in $ 5 and $ 6, from which a generally smaller value of
the ¢.c. would follow. Owing to the mutual dependence a number
of 240 daily observations cannot be considered as equivalent to 126
tenday means and it is a general law in statistical investigations
that the computed relations show a tendency to give smaller limiting
values as the data increase in number.

7. Finally the question may be put, what will the condition
equation become when the two groups of three surrounding stations
are taken together so that the deviation of atmospheric pressure in
the central point is determined by 6 circumjacent stations within
angular distance of about 60°.

The numeration of the stations then becomes :

1. de Bilt 5. Dresden
2. Valencia 6. Sylt
3. Ile d’Aix 7. Lerwick

4. Miilhausen

The c¢.c. computed in $ 5 and § 6 and all products can be used

320

for this purpose so that the labour entailed for this calculation was
relatively small.

The values not yet given are:

Poy == WHOA) üm (belt) rj = 0.744
NE 0,360 in Oe
r,, = 0.548 (Pa Ul
T= 0.888 Pe, — 0.848

And the condition equation becomes :
v, = 0.140 #,—0.069 w, + 0.624 wv, —0.101 wv, +
10.538 2,40.015 o,. . « . nn

It appears from (7) that the methods of computation followed in
this inquiry fails in this case in so far that, owing to the insufficient
distances between successive stations, negative coefficients now appear
in the equations. Obviously they are due to a mutual distribution
of common influence which must be considered as unreal and as a
mere arithmetical result.

Equation (7), therefore, shows a great resemblance to the first of
he equations (6); the coefficients are alternatively small or even
negative and if we reduce the equation to one with three terms by
an equal distribution of the odd over the even coefficients so that
for example:

0.069 + 0101 B

0.539,

coëff. x, = 0.624 =

we find the following equation little different from (6)
v, = 0.113 z, + 0.539 a, + 0.495 z,

In equation (7) the prevailing influence of the stations Mülhausen
and Sylt is still more conspicuous than in the results of other groups.

A calculation of the remaining equation and of partial e.e. would
in this case have no meaning.

Taken as a whole equation (7) is to be considered as an im-
provement because the general correlation-coefficient is very large
namely

R= 0.9953
from which follows, for the calculation of one value, the probable
error:

w= 0.589 mm.

321

Meteorology. — “On the relation between meteorological conditions
in the Netherlands and some circumjacent places. Difference
of atmospheric pressure and wind.” By Dr. J. P. vaN DER STOK.

1. In previous communications it was proved that the relation
between direction and magnitude of the gradient of atmospheric
pressure on the one hand, and force and angle of deviation (between
wind and gradient) of the wind on the other hand is not a constant
quantity, but varies with the azimuth of the gradient *) and with
increase and decrease of pressure difference *).

If we select from the gradients, as calculated for the Netherlands
and published in the weather charts, those pointing to eight points
of the compass, then, for the period 1904—1910, the wind at De
Bilt and the whole year, we find the following results:

TABLE I. Average values of angle of deviation @ and force of the wind

(Beaufort scale) for different directions of unity gradient.

Direction. | Number of observations Average force ET SS
NE = „Onl 5.8

gradient | 450° | 679.5 | 90° | Sum 45° | 67°5| 90° Ee: 2s
N 208 | 165 | 66 | 439 129°) 18 2.0 1.86 | 60°
NE 44 | 123 | 112 | 279 1.8 | 1.9 | 2.0 [1.93 | 73
E 17 44 | 59 | 120 SHOP 25E ES 2 NEZ Oma
SE 14 | 54 | 42 | 110 3.4 |2.9 |3.2 | 3.06 | 73
Ss so | u | 39 | 179 2.2 | 2.0 | 2.0 | 2.05 | 64
SW 38 | 92] 51 | 181 EN ON EG EA 7 | 69
w donne aat BBs |, 116 2:1) E28 28e If ande 62
NW 180 | 122 | 29 | 331 1.9 | 2.0 | 2.3 | 1.95] 57

Total | 645 | 744 | 426 | 1815 | Aver. 1.94 | 2.03 | 2.30 | 2.05 | 64.8

Various objections against the method followed in this inquiry
may be raised.
Angles of deviation smaller than 45° are left out of consideration

1) On the angle of deviation between gradient of atmospheric pressure and air
motion. Amsterdam. Proc. Sci. K. Akad. Wet. 14, 1912 (865—875).

2) The relation between changes of the weather and local phenomena. Ibid. 14,
1912 (856—865),

399

because these are usually associated with feeble wind forces, sd
that the direction becomes uncertain.

It appears however from the large frequencies for a = 45° and
N and NW directions of the gradient (208 and 180), greater than
any other, that the omission of smaller values of a in these cases
certainly gives too great a value for the average angle of deviation,
whereas for E and SE directions of the gradient the influence of
smaller values than 45° are compensated by those greater than 90°.
The results of this inquiry are therefore to be considered as doubtful,
not only in an absolute but also in a relative sense.

A more serious objection against this method is that it appears
from table I that the meteorological field is by no means to be
taken as uniform: easterly and south-easterly gradients are generally
associated with wind forces and angles of deviation considerably
greater than northerly and north-westerly directed gradients. The
frequencies indicate that a gradient of a given magnitude and direction
may be accompanied by different forces and angles of deviation so
that the gradient, calculated as a vesultant difference of pressure in
a central point and four circumjacent stations cannot be considered
as a reliable measure of the wind. A positive difference in a given
direction does not exercise the same influence as a negative difference
in the opposite direction. If, therefore, we wish to investigate this
relation, the computation of a resultant must be avoided and each
direction is to be taken into account with its proper coefficient of
influence.

2. To this purpose differences of atmospheric pressure between
Flushing on the one hand and Valencia, Biarritz, Munich, Neufahr-
wasser and Lerwick in the other hand are associated with the wind
at the first named station, as published in the annals of the K. N.
M. Institute for each day of the eight months: January, February,
December 1912 and 1913, and January, February 1914. The average
differences for the whole period are:

1. Flushing—Valencia + 5.8 mm.
De A —Biarritz = is)
3, Ps —Munich des
4. … —Neufahrwasser -+ 0.4
5. „ —Lerwick + 7.9.

The average wind at Flushing during the same period is:

3.70 m.p.s. S 25°36’ W
W,, = — 3.34 N component

W. = — 1.60 E component.

323

The length D and the azimuth A of the ares joining Flushing
and the other stations are:
te dD = BPS! A= N 278°41’ E

2. 8°40’ 205°31’
3. 6°8’ 119°39’
4. 9°23’ 66°4’
5. 9°8' 345°4’

Denoting the deviations from the average values of the pressure
differences by «v,, «,...#;, and those of the north- and east com-
ponents of the wind, by «x, and 2,, and further assuming that a linear
relation is justified we can put:

tO. at Oe. EEN One
EN RN = Dd an

The treatment was the same as explained in a previous paper
and the following results were obtained :

7, = + 0.383 1 = — 0.456 6, = 8.47 mm.

T;3 = — 0.185 == + 0.256 On lo

’,, = — 0.354 r= Oste Oe (ee

?,, = + 0.297 ’,, = + 0.300 Or

T,, = + 0.576 Ve = — 0.561 GS EG op
Pr, = — 0.116 r,, = + 0.313 6, = 4.55 m.p.s.
r,; = — 0.201 T,, = + 0.765 OO Ol
’,, = + 0.290 Ny, = + 0.522

’,; = — 0.491 My, = — 0.375

Ps = + 0.197 ?,, = — 0.463

The condition equations then become:
a, = — 0.134 7, + 0.002 a, + 0.537 z, + 0.061 w, — 0.128 x,
x, = + 0.089 2, + 0.426 a, + 0.293 2, — 0.227 a, — 0.155 x,

The general correlation coefficient of the first equation (N. com-
ponent) is A=0.825, of the second equation (E. component) R=0.870.
It follows from these results that the actual pressure differences,
deduced from observations made at 5 circumjacent stations enable
us to account for the wind blowing in the centre to a degree of
85°/, or, in other words, the expected deviation from the mean value
with an average uncertainty of 6, = + 4.55 and o, = + 6.01 as a
first, rough approximation of the wind components is improved by
equation (1) with

(4)

— == 415)
WAR: 0 IS :
(A — V1—R’) x 10C spe Pel cent

It appears from equ. (1) that a positive gradient in the direction

354

of Valencia produces a SE wind, in the direction of Biarritz an E,
of Munich a NE, of Neufahrwasser a NW, and of Lerwick a SW
wind and further, that, although the distance from Flushing is
about the same, Biarritz exercises a much stronger influence than
Valencia. These results are in accordance with the experience afforded
by the study of the weather charts, but they give quantitative
relations by means of which a calculation of the resulting wind
hecomes possible.

With the help of equ. (1) it is possible to demonstrate in a more
conspicuous manner the influence of the gradient direction on the
velocity of the wind and the angle of deviation by putting the
question: which wind will be caused by or, rather, will be associated
with a fictitious distribution where the pressure difference in the
whole field is uniform and represented by isobars, successively drawn
in the directions of eight principal points of the compass, and at
distances from each other equal to unity (1 mm. per degree of
latitude).

Denoting the distance of a station from Flushing by WD, the
azimuth of the joining are by A, the azimuth of the gradient
by « and the average difference of pressure by , then

av; = D cos (A; — a) — B;
where 7 is to be given successively the values 1 to 5.

The components of the wind then follow from the values com-
puted from (1):

W,=w, +a, Wed dol

The results of this calculation are given in table II.

TWANB RISE sI

ity ey Sb | |

N | 54 | Naer 68°

NE | 5.29 | 294 69

E | 5.53 349 79

SE Jn SDA 35 80

s 8.35 67 67

SW | 1.55 97 52

w Ad 139 49

NW 4.90 | 198 63

325

According to the expectation formulated in § 1, by this improved
method a smaller minimum value is found for the angle of deviation
than in table I; at the same time the positions of the maxima and
minima are somewhat shifted.

It may be noticed that for the correlation between Munich and
Lerwick for pressure differences a negative value, 7,, =— 0.491
has been found of the same order of magnitude as the partia/ corre-
lation of deviations from pressure between Clermont and Christiansund
viz. —0.536, and between the region of the Azores and Iceland.

The laborious calculations of partial corr. coeff. may, therefore,
aften be avoided by forming difjerences, by which process large
common influences are eliminated.

3. For a third investigation the average wind for the Nether-
lands has been calculated (for the same period as mentioned in § 2
and 7 a.m.) from the stations De Bilt, Flushing, Helder, and Groningen
and this average wind has been associated with pressure differences
between De Bilt on the one hand and Sylt, Dresden, Miilhausen,
Ile d’Aix, Valencia, and Lerwick on the other hand; the azimuths
of these stations differ about 60° C.

The ranknumbers, average values and standard deviations now
become :

Pressure Average

differences differences Standard deviation
1. De Bilt—Sylt + 1.58 mm. 6, = 4.96 mm.
2 „ _— Dresden — 1.99 On 416
3 » —Miilhausen reve (in 6, — 4.74
4. » -—-lle d Aix — 1.48 Sa 6.08
5 » _— Valencia + 5.31 6, = 8.47
6 » — Lerwick + 7.95 Me Sti ey

Wind ;
7. North-component — 2.63’ m.p.s. o,=3.61 m.p.s.
8. East-component — 0.95 Os 4.52

The correlation-coefficients are:

EE on OA eee oan
r = Og rr OR 2S 0.989
r= W520. fe 0.688! or 043
A == 0.253 Ve 0.246 Mi + 0.763
My, = + 0.546

22
Proceedings Royal Acad. Amsterdam. Vol, XVIII.

326
p= 0168 7,,=+0.782 r,,— + 0.300

r‚ = — 0.820 Ps = + 0.014 P's, = — 0.398

rs, = — 0.508 Ts = + 0.323
Ts = + 0.354 == + 0.624 T,, = — 0.635
,, = — 0.061 Ts = + 0.687 Ps = — 0.535

The condition equations reduced from these values are:
2,—=—0.085., +0.3962,-+0.2552,—0.03827,—0.0602,—0.1032,
“= —0.239.xv,— 0.3462, +0.4547, -+0.0682,-+-0.08327,—0.1292,
with the general correlation-coefficients :

ii, = 08065 7h, 00

With respect to a first expectation with the average uncertainty
o, and o, the expectation has been, therefore, improved respectively
48 and 65 percent, and the computation with the help of 6 stations
affords an improvement with respect to the use of 5 stations with
only 5°/, for the north-component, but with 15°/, for the east-com-
ponent. The probable uncertainty becomes + 1.24 and + 1.05 m.p.s.

(2)

TVACBIEE SUT
Direction Direction Wind- | Angle of
gradient wind velocity deviation
—
N N 231° E | 3.43 m.p.s. ole
NNE | 258 | 3.39 56
NE 285 | 3535 60
ENE 309 3.56 62
E 338 3.76 68
ESE 3 4.11 70
SE | 25 4.44 70
SSE | 45 4.96 67
Ss 62 5.28 62
SSW | 80 5.46 51
SW | 96 5.39 | 51
WSW 114 | 5.14 | 47
W | 133 4.73 43
WNW | 54-42 | 42
NW | 178 3.86 43
NNW 204 3.58 | 41

327

Table III (p. 326) shows the values of the wind velocity, the
direction of the wind and the angle of deviation as calculated from
equation (2) for 16 different directions of the gradient and a uniform
field of 1 mm. difference of pressure per degree of latitude.

A comparison of these results with those of table II shows that
the use of an average wind for the whole country has induced a
more regular course in the numbers, but also that considerable
differences are due to this method. The wind velocity and the angles
of deviation have become smaller as also the azimuths and wind
directions. From this result we may conclude that the northerly
stations behave differently in many respects from Flushing and that
a combination as made in this inquiry is not desirable.

Physics. — “Ona General Electromagnetic Thesis and its Application
to the Magnetic State of a Twisted Iron Bar’. By Dr. G.J.

Erras. (Communicated by Prof. H. A. Lorenz).

(Communicated in the meeting of May 29, 1915).

WieDEMANN has already observed that in a longitudinally resp.
circularly magnetized iron bar a circular resp. longitudinal magneti-
sation arises in consequence of torsion. Moreover he discovered that
a bar which is at the same time longitudinally and circularly
magnetized, is twisted. These observations formed the starting point
of the following considerations.

In a magnetic field, in which the magnetic induction can be an
arbitrary vector function of the magnetic force variable from point
to point, whereas the media in the field can be anisotropic also with
respect to the conductivity, but in which no phenomena of hysteresis
occur, the equation

rif Siam hon tn Genito mee 0)
5
holds for the magnetic field energy.

In this 7 means the current in a circuit M, the induction flux
passing through this circuit, « representing the ratio of the electro-
magnetic to the electrostatic unity of electricity. The summation
extends over all the circuits, the integration covering a range from
M for i=0 to the final value which J/ assumes.

1) In this and following formulae Lorentz's system of unilies is used.

22%

328

1. Let us now consider two linear conductors (circuits), in whieh
currents 7, and 7, run. Let M, be the induction flux passing through
the first, M, that through the second wire. If M, and M, change
infinitely little, then follows from (1)

1
dT —— (i,dM, + i, dM),
C
for which we may put:

AT = = d (i, M, +i, M,) = M, di, — - M, di,.
The first member of this equation is a total differential, as 7’ is
perfectly determined by 7, and 7,, hence
M, di, + M, di,
must also be a total differential, from which follows:
0M, 0M, ,

dd,

i.e. the increase of the induction flux passing through the first

circuit, caused by an infinitely small current variation in the second,

is equal to the increase of induction flux passing through the second
circuit, caused by an equal change of current in the first.

An increase of the induction flux JM will give rise to an electrical

impulse, in which through every section of the circuit the quantity

of electricity

i aos on

1dM

de = — — —

c W

passes, if w represents the resistance of the circuit. The negative
sign means that the direction of the current, is in lefthand cyclical
order with the increase of the induction flux.

If now the current 7, increases by the infinitely small amount of
di, the induction flux through the second circuit will increase by:

AM, .
dM, == = dis.

Hence for a short time an induction current will pass through the
second conductor. If after the lapse of this time the current in this
conductor has again the same value as before, then the “integral
current’, i.e. the total quantity of electricity set in motion by the
induction current amounts to:

1) For so far as | have been able to ascertain, this relation, as well as those
following later (3), (8), (15) and (17) is new.

329

1 ae 1 OM, ..
de, = — —. =— di

6
CS c.w, Ot,

In the same way for an infinitesimal change of 7, the integral
current in the first conductor will amount to

1 OM, …
de, = — — di.
Cc. Ww, dy
If di, = di, it follows from this by the aid of (2)
de Oa Went el ce re pe. MOD

de
1

de
If by — resp. — we denote the quotient of the integral current
di, 3

in the first resp. second conductor and the change of current in
the second resp. first conductor, we may also write:

e é
“ag BEA Cae teeter cle LO)
In case the permeability is independent of the intensity of the
field, so that D in general is a linear vector function of 5, both
Hand B are linear functions of 7, and #, hence J/, and J, too.

Then we may write:
M,=1L,,i, + Ld

mees (4)

M, aw Ent SF Lt

From (2) then follows the known thesis:
VE NEE Dr TE re en ls MEN

Le. with equal currents in the two circuits the first sends as many
induction lines through the second as the second through the first.
For this case the magnetic field energy becomes according to (1):

2
€ 2

1 ej ete
or Olen Fore gues ay ye 106)
If the current in the first circuit increases by d?,, then the integral
current in the second amounts to:
dM, L
2 SS —

2
C.W, C.W,

atc

On increase of the current in the second conductor by d
integral current:

, the

flows through the first.
Both expressions can be integrated. If e, resp. e, represent the
integral currents, which pass through the first resp. second circuit

330

on increase of the current in the second resp. first circuit to the same
amount 7, the relation
CUE We oe en eet OO 5 = (7)

exists between these quantities.

2. We shall now consider the case that the function which
represents the relation between 3 and 9 is variable in some parts
of the field. This variability is meant in very general sense: we may
e.g. imagine it as a dependence of volume, pressure, temperature
etc. or as variations in consequence of elastic deformations, while also
motions of the particles of the medium may be understood by it.
We except, however, such changes which are attended with motions
of the enrrent conductors or parts of them. Let the variability be
expressed by means of the general coordinate a. Then the induction
flux through the circuits will in general depend on «. With a varia-
tion of « the relation (2) holds both before and after the change,
so that we get:

00M, 0 0M,
de di, Oa di, ;
for which we may write, seeing that
1 1
—dM, = — w‚de, dM, = —- w‚de,

C C

0 de, Of 2, ‘
lanen): RN

when we attach analogous signification to the partial differential

A de de, E
quotients ae and vi as above for (8). If the resistances are not
la t,
dependent on @, we get:
0 de, 0 de, 7
U = SS SS "USS SS . . . . . .
Ti di, Ou - di, da (8)

We may express this relation in the following words: Successively
we measure four quantities of electricity: 1. the integral current
(de): in the first conductor, which is the result of the change da,
whilst the currents ¢, and 7, run through the two conduetors ;
2. the integral current (de,);,i,, which flows in the second conductor
under the same circumstances; 3. the integral current (dE) in teek in
the first conductor, which is the resnlt of the same change as under
1, with this difference however, that the current in the second
conductor is 7,-- di; 4. the integral current (de); + aii, in the second
conductor, which is the consequence of the same change as under

EKE

331

2, with this difference, however, that the current in the first con-
ductor is #% + di.

Now according to (8’) the difference of (de,);,,;, and (de); + ai,
multiplied by the resistance of the first conductor must be equal to
the difference of (de,);,,;, and (de,);, 4 a,;,, multiplied by the resistance
of the second conductor.

If the relation between 3 and £ is linear, then on change of «
the relation (7) will hold, both before and after the change, so that
we have quite generally

0 0
=~ (WENNEN) ENE es rom (9)
a da
If the resistances are not dependent on « we have
de, de

2
WU Se ee ee eee ae eee C9
Oa * 0a (9)

i.e. when in the first circuit there runs a current 7, the second being
without current, and the change da is accompanied with an integral
current de, in the second conductor, then the product of de, with
the resistance of the second circuit will be equal to the product of
the resistance of the first circuit with the integral current de,, which
flows through the first circuit in consequence of the change de,
when the current 7 now exists in the second conductor, the first
being currentless.

3. Up to now we only considered linear conductors. In order
to be able to apply the above derived relations to three-dimensional
conductors, we shall first prove a general thesis.

We imagine an arbitrary conductor in which certain electrical
forces are active. Let the conductor be an anisotropic body, of
such a symmetry, however, that there are three main directions
which are vertical with respect to each other, in which the current
coincides with the electrical force. In this case:

Fz
Js zo € J et (10)

in which

Now let a system of electrical forces € give rise to a current
JD, the system € giving rise to a current J@). Then the follow-
ing equation will hold for every volume element, as is easy to
see by the aid of (10):

332

(ED. $P) ZED. 4).
Integrated with respect to an arbitrary volume of the conductor
this yields:

(EW. ID) .dS=f(G@.30).dS. . . . « GI)

This we apply to a conductor consisting of two parts, one of
which, A, is a three-dimensional body, whereas the other, B, which
is to be considered as linear, is in contact with the three-dimensional
part in its initial point P and its final point Q. Let us suppose
in the linear part a galvanometer G, which we use to measure the
current / in the linear part. The case that arbitrary electrical forces
are active in this system, e.g. originating from induction actions
which can vary from moment to moment, we shall denote by (1).
In case (2) on the other hand we imagine a constant electromotive
force to act in the linear part. Then there will exist a potential
difference yq—yp between the points Q and P.

In both cases we divide the three-dimensional part A into the
eireuits that compose the current. Let us call the current in each
circuit ¢ and let us denote an element of the circuit by ds, then
the relation (11) gives:

zen ‚d2) de [EU 40 dal.

In this the integration takes place along the circuits, the summa-
tion extending over all the circuits. In the lefthand member we
may write D= Wat p), when w) denotes the resistance of
a circuit in case (2). For every circuit this current is multiplied by
the linear integral of the electrical force in case (1) along the circuit.
In the righthand member we shall have to distinguish between
circuits which are closed in themselves inside the part <A, and
circuits which start in Q and terminate in P. For the first kind:

ee 0
Jem to= ;

EO = — vp.

seeing that

For the second kind:

(2)
fe dst) = pq — PP,
Ma)

further holding for this:

333

when / is the current measured by the aid of the galvanometer

G. If we divide both parts by gag—yp, we get finally:

es! @) P
VN MS ds),
w2) s(2)

(12)

or expressed in words: the total current flowing through the linear
part B is obtained by division of the part A into those circuits which
are the consequence of the presence of a constant electromotive force
in the linear part B, by integration of the electric force € along
every circuit, by division every time of these line integrals by tbe
resistance of the circuit, and by taking finally the sum of all these

quotients.

If we now call an element of a circuit in case (2) briefly ds, we

can, with the omission of the indices, also write:

— >=

Wis
- ic ds.
w) s

Hence we may assign an imaginary current to every circuit

P
zl a
(== [Ede
Ww
Q
from which follows:
P
I n= | &, ds.
%
On the other hand:
Q
i. W, = |G, as
P

holds according to the law of Onm for the linear part,
represents the resistance of this.
By adding the two last relations we get:

w+ IW, = fe, ds,

in which the integration is extended all along the circuit.

je dere,

w w

we get:

when W,

If we put:

(13)

and further by summation over all the circuits and introduction of:

Su rel 1
2, Su! EEE
w W,
if JW, is the resistance of the part A,
W E W E

1 5 a ee ahs baa

ls 2
WW wv Ww
if W is the resistance of the whole system.

Ww
If now by w we represent a resistance which is Wi times as
1
great as that of the circuit between Q and P, we get:
E
IZESTE

The resistance w introduced here is practically the resistance of
a circuit closed in itself, to which the circuits of case (2) discussed
above can be supplemented by continuation into the linear part of
the conductor. The summation is extended here over all the cireuits
of the case indicated above by (2).

5. We shall now consider the case of two current conductors of
the kind considered just now, so each consisting of a three-dimensional
and a linear part. When currents pass through these conductors,
either in one of them or in both, and we want to examine the
induction action which is the consequence of a change, either of
the current in these conductors or of the properties of the surrounding
field, then we may, therefore, according to what was derived just
now, divide these conductors into the circuits which are the conse-
quence of the presence of a constant electromotive force in the
linear part of these conductors, examine the induction action in each
of these cireuits and take the sum of these.

Let the resistances of the conductors be IW, and W,, the currents,
measured in the linear part, £, and /,. We shall examine the
influence of a change of these currents. We can now divide the
first conduetor into mm circuits, each with a current 7,, the second
into ” circuits, each with a current 7,, so that we shall have:

JE Suk == nije

The resistance of each circuit of the first conductor amounts to
m.W,, of the second conductor to n.W,, as the electromotive
force must be taken the same for all of them on division into circuits.
If we increase the current in every circuit of the second conductor
by di, then the total induction flux through the pt? circuit of the
first conductor will be increased by :

935

OM»

dM, =d.
n 29

As the resistance of every circuit amounts to m.W, we get for
the integral current, which flows through the linear part of the
first conductor:

de == = eS eae
e ae a
em. W rm n Vis,4

For this may also be written:
di, aM

Sey
—— il

de, = — 5
1 .
emn.Wim n di29

In the same way the integral current

jf eS
“S| Stim ee eD ep

flows through the linear part of the second conductor on a change
dl, of the current in the first conductor.

If
dT
then follows, when (2) is used:
Wi ste We delice El rellen on
In general:
AD ee (15)
on ave

in which the meaning of the differential quotients is analagous to
that which was attached to them above in (3).

This relation is analagous to (8). It holds quite generally, so long
as D is a univalent function of $, which, however, can be quite
arbitrary for the rest.

If the permeability is independent of the strength of the field,
so that there exists a linear relation between ® and 6, we shall
be able to integrate equation (15). So we get:

A RY ME ID,

analogous to relation (7). Here just as there e, resp. e, will mean
the integral currents which flow through the linear part of the first
resp. second conductor, when the current in the second resp. first
conductor inereases from zero to the same value I, the other con-
ductor being without current.

5. Just as we did before in the case of two circuits we can also

336

now consider the case of an infinitely small change of the function
which indicates the relation between B and , in some parts of the
field, as result of an infinitely small change of a general coordinate a.

In general (15) will be valid both before and after the change
of a, so that analogous to (8) we get from this:

0 = dd DE, de, “=
dates DL Mee * Or oe
If the resistances remain unchanged we get analogous to (8’):
0 de 0 de
= SS = WwW — — , S| ee
‘01, 0a “OL, de Cy

which relation is also open to analogous interpretation.
In the special case of a linear relation between 8 and 0 we
shall get in the same way analogous to (9):

® ar no Daca eee (18)
da hie da Pet arn
which becomes for invariable resistances:
rn ee (18')
0a * 0a

Here e, and e, have the same signification as above in (16).

6. We now inquire into the work of the ponderomotive forces,
being accompanied with a modification in the magnetic field, which
is the consequence of the infinitely small change de. We assume
that at the change da the external electromotive forces remain un-
changed, and likewise the coefficients 6, which in the most general
case determine the relation between the electrical force and the
current.

If & represents the electric force, and <° the external electromotive
force, then the quantity of energy

WE + Ee). 3}. dS. dt.
will be consumed as Joure heat in the volume element dS in the
time dt.

On the other hand the energy supplied by the current generators
in the time dt is:

(Ee. 9) .dS . di.
The difference of these two expressions:
—(€.$).dS.dt
passes into other modes of energy. Integrated with respect to all
the conductors this becomes:

83%

fe dis ab

3 =e curl D,

If we introduce

and if we make use of the known thesis of the vector calculus that
the following equation holds generally :

div [UB] = B curl U—A curl B
then we get for the above expression:

— ef (curl ©, 5) dS. dt + ef dir [€, H| dS. dt
Introducing further :
2 —

and making use of Gauss’s theorem, we get:

dd . aes
if 5 5) Jos ‚dt +c] [€, D], do. dt.

The second term vanishes, as on the surfaces of the current con-
ductors the normal component of {&, | is continuous, and the
integral amounts to zero over the plane in infinity. Accordingly the
first term only remains. This will have to be equal to the increase of
the energy of the magnetic field and the work of the ponderomotive
forces. Hence we get:

ar+aa=((2 pasar

Per volume and time unity:
d8
aT + dA=|[ —, ) | dt.

For the energy of the magnetic field per volume unity the expression :

§
r= | (Ba)
0
holds generally.

With the change da we shall get:
gap

ah mas fan

in which Jd represents the change of the final value of 9, and
D' the value of DB corresponding to in the changed state. Now
we get:

338
Hdi
—aa={ (6 moan (a8, 5)

0
from which easily follows:

gle
1A = — ne
dA milk 5) da
0

Integrated with respect to the whole field this becomes:

dA dS ie er fl
=; f fe .d 8. da (19)

We can always split up the vector 9 into two parts, 9°, for
which holds div 6°=0, and ', for which holds cur’ 5' =0").
Taking into consideration that generally

fas(a.B) = 0
on integration over the whole space, when

dv =O, eurl DO,

0
a f ds fs di
da

Making use of the equation :
B= DH MW,

0
a fi ds fees zE fas fmaor) . da.
da

As in the first term we can again split up ® into )° and #', in
which 5° is independent of « — 5° being determined by the current
XY — and as the product 5*d ò° integrated over the whole field
yields zero, this term will vanish, so that there remains:

14 = fas (5 a9? ae eS

owt rl:
In this — denotes the change of the magnetisation in consequence
a

we get:

of a change de, in which the external electromotive forces and also
the coefficients determining the conductivity, remain unchanged.
1) In Batra we shall understand by {° the intensity of the field as it would
be without the presence of the iron, ® representing the real strength of the field.
The difference is \}.

339

7. We shall now consider a special case. Let us imagine a
system of two currents, one passing through a vertical cylindrical
iron bar, the other through a vertical solenoid which is concentric
with the iron bar. We suppose the iron bar, whose length is assu-
med to be large with respect to the diameter, to be in the middle
part of the solenoid, and that the latter on both sides projects far
beyond the bar. For the present we assume for simplicity’s sake
that the permeability of the iron has a constant value.

The first current /, gives rise to a circular magnetisation in the
iron, the second /, to a longitudinal magnetisation. If /, and J,
are in righthand cyclical order the corresponding strengths of the
field ),° and ,° are so too.

The resistances of the conductors are called W, and W,.

We can now twist the iron bar, /, being =/ and /,=0; in
consequence of this three main directions will arise in the iron with
different permeability, which will also cause a longitudinal magneti-
sation in the bar, which is accompanied with an impulse of current
in the second conductor. Likewise we may twist the bar when
/,=0 and /,=/J, which gives vise to a circular magnetisation of
the bar, and accompanying this an impulse of current in the first
conductor. We shall compute for both cases the quantities of elec-
tricity which pass through every section in consequence of the
impulses of current.

If the radius of the iron bar is FR, then
a

he j
Ot. Rc

scot

holds for the intensity of te field °, inside the iron at the distance
r from the axis of the cylinder.

If the solenoid has m windings per unity of length, the intensity

of the field in the middle part in which the iron bar is found, is;

We shall assume the bar, which has a length /, to be twisted
over an angle g=/Jl.a, and this in such a way that while one
extremity, where the current /, enters, is held fast, the other extre-
mity is twisted over an angle ¢ in the sense of the current /,. In
consequence of this an originally square surface element with sides
of a length one of a cylinder surface concentric with the axis of
the bar, with radius 7, will assume a rhombic shape.

In this the angle which the sides of the rhomb, which were
originally parallel to the axis, form with the direction of the axis,

340)

becomes equal to r «, so long as the second and higher powers of
a are neglected. The diagonals of the rhomb become resp. :

V2(l + tre) and V2(l—4ra),
hence the ratio between this and the original length resp.
14 4ra and 1—tra.

We call the direction of the strength of the field 6°, 2, that of the
strength of the field °, y.

In consequence of the twisting the considered surface element has
obtained two main directions, which coincide with the diagonals of
the rhomb'). We call the direction of the diagonal which falls between
the positive a-direction and the positive y-direction, u, that of the
other diagonal v. In the direction w the iron is elongated, in the
direction v compressed. The elongation resp. compression amounts
to ra per unity of length. Let / . 2 be the increase of the permeability
in a certain direction, when the elongation per unity of length
amounts to 2 in that direction, the compression per unity of length
normal to that direction being of the same value. Then

U =H kra wy =u—tkra.

We assume / to be independent of the strength of the field.

If we further assume the angles which the directions « and v
form with « and y to amount to 45°, which is permissible so long
as we confine ourselves to quantities of the first order in @, we get:

Du = 4 V2 (De + Dy)
Dy = 1 V2 (— Hz + Dy)
and further, as:
Be Bi = pe Des

A u 5 p 3 5 5
Bu = V2 (De HDi) + $hray2 (Ge + B)

= ld ak VE :
B= TG VA He + Dy) + phray2 (— De + Dy):

from which follows:
Br =u de + ihre Dy
B, =u Dy + bkr De.

We see that here the relation u,,—=«,, holding universally for
anisotropie media with three mutually normal main directions is
satisfied.

In the twisted bar 9, has everywhere the same value at a certain
distance from the axis, when we move along a circle normal to
the axis, as there is radial symmetry with respect to this axis. The

1) The third radially directed main direction may be left out of consideration,
as no change takes place in that direction.

sil
line integral of 9, along this circle amounts therefore to 277. 9;
‚this line integral also amounts to 2a7.,°, so that we get:
Dies ae
We shall further assume the length of the bar to be large with
respect to its diameter, in which case the influence of the magnetisation
at the extremities in the determination of the field intensity inside
the bar in ease of longitudinal magnetisation will be small, so that
we may assume
Me
Inside the bar the following equations hold
M= uh,’ + 4 kra h,°
RK == OA Jt 0

nh oF

kra D,
The change of the magnetic induction within the bar in consequence
of the twisting amounts to

AY, = 4 kre Die
AD, kra DY

In the same way we have for the magnetisation :

M, == *. DP + 4b kra D°
ME He

Also outside the magnetic induction changes in consequence of
the twisting. On account of the change of %, the quantity of
magnetism will namely change at the extremities of the bar which
will give rise to a change of strength of the field outside the bar.
If there was no iron inside the solenoid, and if this was infinitely
long, the change of the magnetism at the extremities would not
give rise to an induction current at all, because every quantity of
magnetism sends its induction lines through the windings lying on
either side, and the sense of rotation of the indueed electric force
is directed for the windings on one side opposite to that on the other
side. We commit an error on account of the presence of the iron
inside the solenoid in as much as the magnetic induction inside
the iron does not change in the same way as that outside it. As
we have, however, assumed that as far as the magnetic induction
inside the iron is concerned, we may disregard the magnetism at
the extremities, we may also leave this error out of account.

In order to calculate the induction impulse, we must therefore
integrate the just mentioned amounts of 4%, and 4%, inside the
bar over the surface which is surrounded by every circuit, and then
sum up over all the circuits.

We explicitly excepted (§ 2 above) movements of the current

Proceedings Royal Acad. Amsterdam, Vol. XVIII,

342

conductors. Here, however, such movements occur in consequence
of the twisting. Now in case of longitudinal magnetisation of the
bar the movement of matter, which is the consequence of the tor-
sion, will give rise to an induction impulse in radial direction, which
has no influence on the induction impulse in longitudinal direction.
In the case of circular magnetisation on the other hand no induction
lines will be cut by the matter on twisting, so that no induction
impulse takes place. The movement of the substance will, therefore,
have no influence in these cases on the induction impulses, which
are accordingly exclusively the consequence of the change of the
properties of the substance.

A. If we now first suppose /,=J/,/,=0, hence the case of
circular magnetisation, then :

Lee rl ;
Do = DER DE == ()
klar®
A Ds AS, = 0.
An R?.¢

Now Ad, must be integrated over all the surface elements which
are normal to the direction y, so over all the windings of the sole-
noid. The increase of the flux of induction through one winding
amounts to:
kIaR?

*R
AM, = 22 | Ad, .rdr =
0
As there are m./. windings to the length / of the bar, the total
increase of the induction flux will be m./. A My, and the electricity
set in motion:

& ml. klak?
1 = aware
If we introduce the angle of twisting y—=Jl.a, we get:
mgklk?
Mga ee 21
2 8W,.¢ an)

With a positive value of & we come to the conclusion that for
the considered twisting the sense in which the impulse takes place,
is in lefthand eyelieal order with the current /.

In the other circuit the impulse is zero, as AB, =

B. Let us now suppose J, = 0, /, = J, hence the case of longi-
tudinal magnetisation; then:

or e= 7
Sf=0 f=

343

AS, = mkrol Ad, = 0.
ac
In order to calculate the impulse in the first circuit, we shall
divide the first conductor into conducting tubes, which each of them
again consists of circuits. Let the conducting tubes, which are con-
centric and cylindrical in the iron, have a radius 7 there and a
thickness dr. When we then give them dimensions proportional! to
this in the other parts of the conductor, the resistance of such a
tube will be:
R?
ws W.
2r dr :
The increase of the induction flux through the surface surrounded
by every circuit belonging to the conducting tube, amounts to:
R

NM EI | an Ae ;

mlkLa (R*—r°).

The quantity of electricity set in motion in the conductor, now
becomes, when we make use of the mode of caleulation explained
in § 3, which finds expression in (14):

R
AM, mikla (°__ 3 mlkLak?
=DE Rk? — 7°) rdr = — ———_ ,
cr 2h? W ct 3 Wc
0
With introduction of the angle of twisting g this becomes:
mopkL k?
i, == So (22)
8 W 1e

Hence from (21) and (22) we find really

ennen
in agreement with (18’).

If & is positive, then the sense in which the impulse takes place,
is in lefthand cyclical order with the current /.

As 4%, = 0, the impulse in the second conductor is zero.

We may assume that the circuits run parallel to the axis over
the greater part of the length. The direction of the current can,
however, be different for different circuits. In this case we shall be
allowed to use the formula (13) for the real current. It follows
from this that the circuits where the motion of electricity is zero,
will lie on a cylinder surface, the radius 7 of which is given by
the equation:

1
AS

€

23*

344

in which W,, is the resistance of the linear part of the circuit.

From this we get:
a 2W—W,,
r=R in
2W,
When W,

», is small compared with W,, 7 will differ little from
R. As a rule, however, the reverse will be the case, from which
ensues that 7 approaches the value $22. We can calenlate the
current through the central part of the bar by means of the relation
(13). For this we get:

AG) ET

AT (24)
32 (WW)

mykl.R? 2W,— =)
Gece:
When W,—W’,, is small with respect to W, this quantity of
electricity will become much larger than e,; it can become arbitrarily
large with respect to e, when IV,—JV,, is made small enough
with respect to IW. On the other hand when W,, was small with
respect to W,, e, would differ only little from e,.
Let us now suppose that a current /, runs in the first conductor, a
current /, in the second. We assume that then the state of equilibriam
is characterized by this that the bar is twisted over an angle « per unity
of length. The torsion couple amounting to KR“. a, the elastic energy
of the bar is $A R*.a*?./ in the twisted state. We make this state
undergo an infinitesimal change so that « increases by the amount
da. Then the elastic energy increases by the amount AR‘ a/da,
the work of the ponderomotive forces being found from (20) for the
considered change, which formula, after introduction of M, and M,,
produces

> 1
dA = 4 k. def» . JD ayy MSS 3e mlk JL Heli . da.

In case of equilibrium this work must be equal to the increase
of the elastic energy, from which we find for the angle «:

titre kmI I, (25)
Sc KR?
The whole torsion becomes:
ook kmll,I, (25)
Sc KR?

If # is positive, then with the given current directions of /, and
/, the bar will be twisted so that when the extremity where /,
enters, is kept in fixed position, the other extremity is rotated in
the sense of the current /,, hence counter clockwise, when we

345

look towards this extremity. Of course the sense of the rotation
changes on reversal of one of the currents.

Hence the bar assumes the shape of a righthand screw, when the
currents 7, and /, are in righthand cyclical order. Further the angle
over which the bar is twisted, is proportional to the total number
of windings of the solenoid, which falls on the length of the bar,
to the intensities of the currents, and in inverse ratio to the square
of the radius.

Above we found an expression for the work of the ponderomotive
forces dA on the increase of the torsion dea. If the torsion amounts
to a, we can integrate this expression, through which we get:

1
Aas mikiqgn te Tek

We find this work back in the first place in the elastic energy
U of the bar. If into the expression for this } AR‘ ag, we introduce
the above found expression for «‚ we get for this:

—,mkoy I, I, R’.

The rest, which is of the same amount as U, is converted into
kinetic energy, or when we make the motion take place infinitely
slowly by means of external couples, into external work.

Let us now inquire into the increase of magnetic field energy.
For this purpose we make use of the expression:

r={as{ 5a,

which can be easily derived from (1).
Here we introduce:

an ls a m 7
De = Ick? Dy = nae
1 krtal
AB: 5 mkra Ji. Ay ==

We get then:
Gi 5 e 6 3 1
(AND = fas feaa Be + H,d A B) = ae TO ae Ik
Hence
1
Pee Cy AN T= mpk I, I, RR.
c

On the other hand on account of the torsion the quantity of
electricity

is circulated in the first conductor. The electromotive force in that
conductor amounts to #,—/,. W,. In consequence of the circu-
lation of the quantity of electricity ¢,, the generator of the current
yields, besides the Jour heat, the quantity of energy — He, which
amounts to:

VULE
en

We find in the same way that after subtraction of the JouLE
heat, an equal amount of energy is yielded by the second generator
of current. Together the total quantity of energy yielded by the
generator of current, amounts therefore to:

1
— mgpk I,I,R’,
4¢?

which corresponds with the value A + 47, required for the work
of the ponderomotive forces and the increase of the magnetic energy.

Chemistry. — “Molecular-Allotropy and Phase-Allotropy in Organic
Chemistry.” By Prof. A. Smirs. (Communicated by Prof. J.
D. vaN DER Waals).

1. Survey of organic pseudo-systems.

I have indicated the appearance of a substance in two or more
similar phases by the name phase-allotropy, and the occurrence of
different kinds of molecules of the same substance by the name of
molecular-allotropy. It may be assumed as known that one of the
conclusions to which the theory of allotropy leads, is this that phase-
allotropy is based on molecular-allotropy.

The region in which the existence of molecular allotropy is easiest
to demonstrate is the region of organic chemistry, and 1 think that
[ have to attribute this fact to this that the velocity of conversion
between the different kinds of molecules which present the pheno-
menon of isomery or polymery, is on the whole much smaller in
organic chemistry than in anorganie chemistry ; in organic substances
it seems even not perceptible in many cases. The substances, for
which this is, however, the case, and which were formerly called

347

tautomers, are comparatively few as yet, but undoubtedly their
number will increase as the experiment is made more refined.

It is obvious that a test of the just mentioned conclusion from
the theory of allotropy will be most easily carried out in the region
of organic chemistry, but on the other hand a test in the region of
anorganie chemistry will be, especially for elements, of greater scien-
tific interest.

Accordingly the research is continued both in anorganie and
organic domain, and the purpose of this communication is to draw
attention to the gigantic field of research which is opened up for
us in organic region for a study in this direction.

Bancrort') was the first to take into account the influence of the
time in the study of systems of organie substances which can occur
in two different forms. In this consideration he came to three cases.

1. The time element vanishes in consequence of the practically
immediate setting in of the (internal) equilibrium.

2. The setting in of the (internal) equilibrium takes place so
slowly that so-called “false equilibria” occur, for which case BaKnHurs
RoozeBoom *) derived different 7, X-figures. ;

3. The (internal) equilibrium sets in with such a velocity that
the system behaves as a binary one in case of rapid working, as a
unary one in case of slow working.

The substances belonging to the latter group, and their number
is undoubtedly enormously great especially in the domain of organic
chemistry, yield very satisfactory material of research.

Bancrorr was the first who discovered a pseudo binary system in
dichlorostilbene examined by Zixcke*) and explained its behaviour.
Zieke had discovered that when the form with the highest melting
point was kept in molten condition for a long time (200°), there
took place a lowering of the point of solidification from 192° to
160°, which was to be attributed, as Bancrorr stated, to this that
the substance had assumed (internal) equilibrium at 200°, in which
the molecules of one form had been partially converted to those of
the other form.

Among the organic substances which can occur in different isomer
forms, variations of the melting point are met with in very many
cases according to the literature, which variations must be attributed
to a conversion in the direction of the internal equilibrium or to a
retardation of the setting in of the internal equilibrium.

2) Z. f. phys. Chem. 28. 289 (1899).
3) Lieb. Ann. 198. 115 (1879).

348

Specially the group of the owimes furnishes several examples. In
this respect we may mention in the first place acetaldoxvim studied
by Dunstan and Dymonp'), and later more closely examined by
CARVETH °).

Further may be mentioned benzaldorim, for which the first data
have been given by BrCKMANN®), the discoverer of the isomerie con-
versions of these substances. This substance was more closely in-
vestigated by Cameron’), whose results were later tested and im-
proved by Scuonvers’s study ®). CarverH’) investigated also another
ovim, viz. anisoldoxim, of which BrckMaNn’) had also found two
isomers.

A very interesting substance is the henzilorthocarbonie acid, of
which Grarse and Jurrarp *) found two distinetly different
crystallized products, one white, the other yellow.

While enantiotropy is a very frequently occurring phenomenon
in anorganic chemistry, we find this phenomenon only exceedingly
rarely mentioned in the organic literature. We should undoubtedly be
mistaken if we supposed that it must be inferred from this that
the phenomenon of enantiotropy in organic region is met with only
by great exception. In the first place this circumstance is much
sooner to be ascribed to this that on account of the slight velocity
of conversion between the different kinds of molecules of organic
substances, the phenomenon of enantiotropy manifests itself much
less easily, and in the second place to the absolute absence of an
accurate systematic investigation in this direction.

It is, however, known of benzilorthocarbonic acid that it is enantio-
tropic. Socn’) has namely demonstrated this with certainty, and
considerably extended Graxsn’s ‘’) investigation.

We have further a very important group of allotropic substances
with distinet transformation in the Aefo- and enol compounds.

Wo xr'') devoted an investigation to formylphenyl acetic ester, of

1) Journ. chem. Soc. 61, 470 (1892); 65, 206 (1894).
2) Journ. phys. chem. 2, 159 (1898).

3) Ber. 20, 2768 (1887); 37, 3042 (1902).
) Journ. phys. chem. 2, 409 (1898).

5) Dissertatie 43.

6) Journ. phys. chem. 3, 437 (1899).

7) Ber. 23, 2103 (1890).

8) Ber. 21. 2003 (1888).

9) Journ. phys. chem. 2, 364 (1898).

10) Ber. 23, 1344 (1890).

11) Journ, phys. chem. 4, 123 (1900).

349

which Wisnicenvs') had discovered two modifications a few years
before, viz. the solid keto and the liquid enol compound.

Of late a number of investigations on other substances with inter-
molecular transformation have been published by Dimrotn?). These
very interesting publications treat molecular conversions in derivatives
of triazol, in different solvents.

One of the isomers is always an acid which can be determined
titrimetrically, which may be called a very favourable circumstance
for the study of the phenomena of conversion.

Another substance whose peculiar behaviour has already induced
many investigators to occupy themselves with it, is the hydrazon of
acetaldehyde, of which Fiscuur*) discovered two modifications.

BAMBERGER and PemseL*) undertook a further investigation, a few
years later also LocKEMANN and Ligscnr*), and six years later Laws
and Siwewick"), but none of these investigators has succeeded in
unravelling the behaviour of this peculiar substance.

P. nitrobenzal-phenyl-methyl-hydrazon, investigated by Backer‘) is
another hydrazon which shows great resemblance with the former.
Also this substance possesses, two modifications, a red and a yellow
one, but it is not known as yet, in what relation these forms are
to each other.

The system wrewin-ammoniumeyanate, farther examined by WALKER
and HamBry *), just as the system su/pho-ureum-ammontumsulphoeyanate
studied by Vornarp®) Wappen"), ReyNorps and Werner"), Finp-
LAY '*), and finally by Smrrs and Kerrner**), likewise belong to the
organic pseudo-systems, just as cyanoyen-paracyanogen investigated
by TeRWEN ®) and cyanogenichydrogente acid, cyaniric acid and
cyamelide investigated by Troost and HaurereuILLE **).

1) Ber. 20, 2933 (1887); 28, 767 (1895).

2) Ber, 35, 4041 (1902); Lieb. Ann 335, 1 (1904); 888, 143 (1905), 364, 183
(1909); 373, 336 (1910), 377, 127 (1910).

8) Ber. 29, 795 (1896).

*) Ber. 36, “5 (1903)

5) Lieb. Ann. 342, 14 (1905).

6) Journ. Chem. Soc. 99, 2085 (1911).

7) Dissertation, Leiden 1911.

8) Journ. chem. Soc. 67, 746 (1895).

9) Ber. 7, 92 (1874).

10) Journ. phys. chem. 2, 525 (1898).

U) Journ. chem. Soc: 83, 1 (1903).

12) Journ. chem. Soc. 85, 403 (1904).

15) These Proc. Vol. 15, p. 683 (1912).

14) Dissertation Amsterdam 1913.

la) Compt. rend 66, 795; 67, 1345.

350

Among the organic nitro compounds there are some that belong
to the group of the pseudo acids, as was found by Hanrscu') and
HOLLEMAN*) in the investigation of brominephenylnitromethane and of
phenylnitromethane; these substances too are to be counted among the
pseudo systems.

The same thing may be remarked about the dimethy/ketol, examined
by Prcumann and Danu*), the benzolazocyanogen acetic ester studied
by FE. Krückeere *), Kirpine’s benzylidenehydrindon*), and tolane-
dibromide*) of Limpricnr and Scuwanert.

Also in the domain of structure isomery, tautomery or internal
transformation has been observed. PoraKk?) found a fine example
of this in the para- and metabenzoldisulphonic acid and Smits and
VIXSRBOXSE *) in methylrhodanide and methylmustard oil. In connection
with this Trrwen*) advanced the supposition that the structure
isomers should be tautomers that very slowly pass into each other.

2. Discussion of the binary pseudoternary systems consisting
of an allotropic substance and a solvent.

The survey of organic substances given here, of which it is
certain that they are psendo systems, can by no means lay claim
to completeness, nor did we try to reach it. Our purpose was only
to demonstrate by a mere enumeration of some facts, how enormously
large is the territory in organic region, on which the theory of
allotropy might be tested.

Here and there an attempt has been made to find a connection
between the pseudo binary and the unary melting-point diagram,
but this study has never been exhaustive.

Barcrorr and his pupils have proceeded furthest in this direction,
but the theory of allotropy requires more at present.

Nor has a systematical investigation of tautomeric substances with
a solvent, so that we get a pseudo ternary system to study, in
which the situation of the isotherm for the internal equilibrium in

1) Ber. 29, 699, 2251 and 2253 (1896).
2) Kon. Akad. van Wetensch. Vol. XIV (1906).
8) Ber. 28, 2421 (1890).
4) J. f. prakt. Chem. [2] 46, 579 (1892).
2» 5 7 „ 47, 591 (1893).
5) Journ. chem. Soc. 65, 499 (1894).
6) Lieb. Ann. 145, 348 (1868).
7) Thesis for the Doctorate, Amsterdam.
5) These Proc. Vol. 16, p. 33.
‘) Thesis for the Doctorate Amsterdam

dol

the liquid phase leads to the knowledge which solid phase at a
definite temperature is the stable one, which the metastable, been
sufficiently carried out as yet.

As we shall show presently, Dimrota has indeed, made very
important investigations in this directions, but an investigation carried
through systematically at different constant temperatures only can
bring us further here.

To show this it is necessary to subject Dimrotn’s important work,
which is of great interest for us here, to a closer examination.

DimrotH') has made use here of van ‘r Horr’s formula’) about
the change of the equilibrium through the solvent, but in a some-
what modified convenient form, viz. in this shape:

Ca La
EE
B Lg
in which C4 and Cg indicate the concentrations of the substances
A and B in the state of (internal) equilibrium at a definite tempe-
rature.

La and Lg are the concentrations of saturation of A and B in
the pure solvent at the same temperature, G being a constant inde-
pendent of the solvent.

Dimrortu, now, points out that important conclusions can be drawn
from this relation, which are of great importance for the preparation
of isomers transforming themselves into each other.

He says: suppose that for a certain temperature G = 1, it follows
from this that when at this temperature we have saturated an
arbitrary solvent with the two isomers A and £, and solid A and
B lie on the bottom, the whole system remains unchanged in equi-
librium. It might have been stated here that the temperature at
which this takes place, would be the point of transition between
A and 5, the temperature, therefore, at which the two solid phases
A and B are in equilibrium.

Se Ca _ La
1G < 1, then ———
LB

Cp
respect to two solid isomers A and 5 will contain more A than
corresponds to the state of equilibrium. A consequence of this is
that A is converted to B in the liquid, 5 erystallizing out, and
solid A going into solution, till the solid A has entirely disappeared.
The reverse will take place when G > 1. In connection with these

considerations he says: “Bringt man also zwei wechselseitig mit

}) Lieb. Ann. 377, 133 (1910).
?) Vorlesungen über theor. u. phys. Chemie, 219,

In this case the solution saturate with

ausreichender Geschwindigkeit umwandelbare Isomere mit einer zur
Lösung unzureichenden Menge eines Lösungsmittels zusammen, so
muss, wenn der Satz von van ’t Horr zu Recht besteht, die Richtung
des sich abspielenden Isomerisationsvorganges ausschliesslich von
der Konstanten G abhängen, also gänzlich unabhängig sein von
der Natur des Lösungsmittels”.

Experience, says Dimroru, is however in conflict with this, for
it often occurs that it is possible to convert isomers into each other
by treatment with different solvents.

He refers in particular to the investigation of E. BAMBERGER *) on
the isomers of nitroformaldehydrazons, the a-form of which is
converted by water or alcohol into the g-form, the g-modification
being reversely transformed into the «-modification by benzene,
chloroform, or ligroine.

In this connection he states explicitly: “Es kann kein Zweifel
sein, dass diese mit Erfolg geübte Laboratoriumspraxis mit dem
van “Tt Horr’schen Satze in Widerspruch steht.”

This statement may seem somewhat strange, as in a test by
means of the amnoderivatives of triazol carbonic ester, which show
the following conversion,

C,H,
| H
N N
YX zs pa
H,N—C N C,H,NH—C N
les >
ROOC—C—_N ROOC—C—N
1 Phenyl-5-aminotriazol- 5 Anilinotriazol-
carbonie ester (neutral) carbonie ester (acid)

Divrorn himself found a very fine confirmation, so that doubt of
the true interpretation of the said laboratory experience was sooner
to be expected.

Dimroru determined the concentration of the two isomers C4 and
Cy in different solvents, in which the isomers had assumed equili-
brium at = 60° under influence of the catalytic action of a trace
of acid.

Further the solubility of each of the isomers, so L4 and Lp,
was determined at the same temperature in the same solvent, and
then the quantity G caleulated by means of equation (1).

The investigation of the isomers of the ethyl resp. methyl ester
yielded the following interesting result:

1) Ber. 34. 2001 (1901).

Methyl ester.

Ether 21.7 53.0 0.4

Methylalcohol 2.3 7.0 0.33
Toluol 1.8 4.3 0.33
Benzene 1.02 SA 0532
Nitrobenzene 0.8 Dine, | 0.36
Chloroform 0.32 leste 0532,

On the whole @ yields a good constant value. As the value of
G happens to be larger than 1 for the ethyl ester, and smaller
than 1 for the methyl ester, it was to be foreseen that when the
two isomers of the ethyl ester at 60 are left in contact with the
saturate solution, the neutral form vanishes entirely, whereas the
reverse must take place with the methyl ester. Experiment was in
perfect harmony with this, so that the investigation of these isomers
yielded a fine qualitative confirmation.

3. A relation of general validity, by means of which both for
isomers and for polymers it can be decided in an exceedingly simple
way which modification is the stable one.

The substances discussed here present the phenomenon of mole-
cular allotropy, because they are built up of two kinds of molecules.
Besides they present the phenomenon of phase allotropy, because
the substance appears in two solid phases.

Hence the substance without solvent belongs to the pseudo binary
systems, and only when the different kinds of molecules in the

S54.

homogeneous phase(s) are in internal equilibrium, the system behaves
as a unary substance, i.e. as a substance of one component.

When we consider the behaviour of the two modifications with
a solvent, we have a pseudo ternary system, which becomes binary
when the different kinds of molecules assume internal equilibrium
in the homogeneous phases.

To set forth the cases discussed by Dimrorn in the most easily
comprehensible way, I will follow the method which I discussed
already before in the publication : “Das Gesetz der Umwandlungs-
stufen Osrwarps im Lichte der Theorie der Allotropie” *).

Ca A
Ql; a
Fig. 1.

At the angles of the equilateral triangle Fig. 1 the letters A, B,
and Care placed, of which A and 5 represent the pseudo-compo-
nents, which are miscible in the solid state to a limited degree, C
denoting the solvent.

In this triangle have been given among others the solubility
isotherm of the mixed crystal series AA, represented by the curve

) Z. f. phys. Chem, 84, 385 (1913).

355

al, and that of the mixed crystal series BB,, represented by the
curve OL, for a definite temperature, so that the point of intersection
L indicates the saturate solution coexisting with the mixed erystal
phases A, and 5.

We imagine the solutions here also in equilibrium with their
vapour, in consequence of which the pressure is therefore not constant.

The vapour isotherm belonging to the solubility isotherm aZ is
the line a,G, that which belongs to the solubility isotherm (Z is
denoted by 6,G, so that G represents the vapour phase coexisting
with the saturate liquid and the two solid phases A, and B, at
the four phase equilibrium.

If now CL,L, represents the isotherm of the internal equilibrium
in the liquid phase, i.e. the line that indicates how the internal
equilibrium between A and ZB in the liquid phase shifts through
change of the concentration of the solvent C, we see immediately
that as this line cuts the solubility isotherm of the mixed crystal
series AA, (point ZL), in case of internal equilibrium between A
and B of all the saturated solutions only the saturate solution L,
is stable, which then of course will coexist with a mixed crystal
phase which is likewise in internal equilibrium, and is denoted here
by A.

Besides these also the isotherm of the internal equilibrium in the
vapour CG,G, is indicated. This line cuts the vapour isotherm
a,G in G,, so that it immediately follows from this that in case of
internal equilibrium of all the saturated vapours only the vapour
G', is stable, so that the phases A,, L,, and G, coexist in the stable
three phase equilibrium solid-liquid-vapour.

It is known that the concentration of an arbitrary phase can
immediately be given. Thus the concentration of the liquid phase
L, is found by a line being drawn in this point parallel to the side
CB, and another parallel to the side CA, as this has been done
in fig. 1. One line meets the side AB in h, and the other in 4.
The number of gr. mol. A to 1 gr. mol. total or xv is now given
by Bh, the number of gr. mol. B or y by Ak, and the number of
gr. mol. solvent C or 1—a—y by Ak.

I may further assume as known that if our end in view is only
the ratio of the concentrations A and 4, e.g. in the same point L,
this is also directly found when a straight line is drawn through
the points C and LZ. This line meets the side AB in the point d.
The ratio of the concentrations of A and 5 is the same in every
point of the line Cd, hence it is in d also the same as in LZ. Im
d this ratio is:

558

Bd Bh «@
Ad Ak y

Now it is perfectly clear that when the isotherm for the internal
liquid equilibrium passes exactly through the point Z, or the point
of intersection of the two liquid isotherms, this implies that at the
considered temperature the solution saturate with respect to the
mixed erystal phases A, and B, is exactly in internal equilibrium.
Accordingly it follows immediately from this, that also the coexisting
solid phases will be in internal equilibrium in this case, and besides
that also the vapour coexisting with Z will be in internal equili-
brium. The vapour G lying in the point of intersection of the two
vapour isotherms will, therefore, in this case have to lie on the
equilibrium isotherm for the vapour.

In this case, which presents itself at the transition temperature of
the two modifications, we get a coincidence of the points L, and L,
G, and G, A, and A,, B, and B. Then coincide also the points e
and d, g and f, which indicate the concentrations, the liquid phases,
and the vapour phases as far as the substances A and & are con-
cerned.

To simplity the discussion we shall now denote the concentration
by small letters when the system is in internal equilibrium, capitals
being used when the system is not in internal equilibrium.

The ratio of the concentration between .4 and 5 will therefore

Ane ee EL En
be indicated by in the liquid £, and by — in the liquid Z,.
je YL

In accordance with this the ratio between A and JA in the vapour
p

: 5 a X, 5 d,
G is then indicated by and that in the vapour G, by ae

7 Ya
Thus the ratio of concentration of A and B is denoted by —
SI
Ús
in the solid phase A,, and that in the phase A, by = — , that in
Ys,
Xs ; Xs
B, being given by wal and that in B, by —.
Sp Usa

For the temperature of the point of transition the following simple
equations hold :

UL Xr 2) sy, Xz, In
/ CRM Oi, BE 3
YL L Ys, 8)
ig) =) Ses (3) te _ Xs (5)

Vy My a, - Ve

357

At another temperature, however, we get the following relations:

BDS. Df : ay AM ONG,
oF ee ee ed men (8)
Jen i Xy (7) ape f Xs, 9
ae me
About the factors f we will only state here that they are in
connection with each other and become at the same time —1 at

the temperature of transition.

These relations (6) and (9) are of general validity, and of these
relations equation (6) is the most suitable to decide which modification
is the stable one at a definite temperature. :

Let us suppose that 7, >1, ie. that the case presents itself
indicated in fig. 1. The internal equilibrium Ze, requires here
a greater concentration of A, than prevails in the solution L. If
therefore at first we have the saturate solution Z in coexistence with
the two mixed crystal phases A, and B,, the transformation

Bs A

will take place in the solution, which renders the solution unsa-
turate with respect to B-mixed crystals, and supersaturate with
respect to A-mixed crystals, with this consequence that B-mixed
erystals dissolve, and A-mixed crystals deposit. This process continues
till the B-mixed crystals have entirely disappeared, and a solution
L, is left, in which A and B are in internal equilibrium, which
solution coexists with a mixed crystal phase A,, which is then also
in internal equilibrium.

For the case /< 1 we then get the reverse.

It is now perfectly clear that by consideration of the relations
(7) or (8) and (9) we come to the same conclusion.

These now are all self-evident relations, which, indeed, only allow
of a qualitative test, but which have this advantage, that as has
been said, they have general validity.

It will repeatedly happen that we do not know which of the two
forms of a substance is the stable modification at a definite tempe-
rature, and then equation (6), as has been shown, indicates an exceed-
ingly simple way to decide this.

At the said temperature we determine the concentrations of A
and B in the solution, which is saturute with respect to the two solid

phases A, and B, (which will be mixed crystals). Thus we find cl
ih

: é 5 arne TL
What is particular about this method is this that — does not refer

YL
24
Proceedings Royal Acad. Amsterdam. Vol. XVIII.

358

to an arbitrary solution in which A and B are in internal equilibrium,
but very specially to the solution L,. We therefore take a part of
the saturate solution with some crystals of the two solid phases,
and let the internal equilibrium set in at the same temperature, at
which one kind of erystals disappears (except at the point of
transition). We now determine the concentration of A and B in

Fig. 2.

< ; = uv . . . e 7 . .
this solution, and thus find —, in which it is perfectly indifferent
y
whether these concentrations are great or small. If we now caleu-
late the quotient :
UL
YL _
XL = fh
Yr
we know with perfect certainty that without any exception A will
be stable when f/> 1, and that B will be stable when f <1.

359

In this method it is quite immaterial whether A and B are
isomers or polymers. Whatever molecular weights we may assume
for the calculation of the concentration ratios between A and B,
whether these are correct or wrong, all this is of no importance
whatever, because the factor /, is not affected at all by this.

3. Drrotu’s relation for isomers.
The relation of Dimrorn.

PE Mid re SA cia Ag RN io

is not universally valid, and this is already seen by this that here

Ege ' ; oni
En is written instead of x’ in which £4 indicates the solubility of
B AL

A in the pure solvent. 7 is therefore „ot the ratio of concentration
of A and B in the liquid Z saturated with respect to A and 5 in
Fig 1, but:
Ca Cb
DN HE and Zg= a

This circumstance is to be explained by this that Dimroth’s
formula only holds for the ideal case that even to the liquid and
the vapour phases saturated with respect to the solid phases the laws
for the ideal solutions and gases may be applied, so that also a
mutual influencing between A and B is excluded.

Accordingly it need not astonish us that this relation of Dimroru
has a very limited validity, but on the other hand it can also give
us further information about these ideal cases.

I shall demonstrate this by the aid of fig. 2, which likewise holds
for an ideal ternary system. We see that this fig. differs from fig. 1;
first in this that the solubility isotherms, at least for so far as they
represent stable states, are straight lines, which join the points a
resp. a, with the angular point B, and the points 6 resp. 6, with
the angular point A, which expresses that the substances A and 6
do not influence each other’s solubility. Secondly it is noteworthy
that the isotherms for the internal liquid resp. vapour equilibrium
are also straight lines, because it is supposed here that A and 5
are isomers. And in the third place it is assumed that A and £
do not form mixed erystals.

For the internal equilibrium in every liquid phase, hence also in
L,, holds:

24*

360

> UL
LT

and for that in the coexisting vapour phase G,

(11)

If now, as was supposed above, the laws for the ideal solutions
and gases may be applied, Henry's law will also hold both with
regard to 4 and to B for all the coexisting liquid and vapour
phases to be considered here, independent whether or no internal
equilibrium prevails in these phases.

If we now consider that in the application of Henry's law the
concentrations must be indicated per volume unity, we get what
follows :

If the liquid possesses a, gr. mol. A per 1 gr. mol. total, and if
this quantity of 1 gr. mol. occupies a volume of vz eem, the con-

centration per liter of solution is =

If further the concentration of A in the coexisting vapour is 2,
gr. mol. per gr. mol. total, and if the volume of this quantity of
1 gr. mol. gas at the considered temperature and the prevailing
vapour tension amounts to vg eem, the concentration of A in the

k 3 . : 1000 x,
vapour is per liter of gas mixture ata wat
q
If we now apply Henry’s law, we may write:

1000 ey, 1000 Xy

CU ees Vy (12)
1000, 1000 X, É
Vg Vy

and
1000y, 1000 Y7

VL Wg
8 ijs ae
1000 e, 1000 X,

Vg Ve

If now the quotients of the first member of equations (12) and (13)
hold for the ratio of concentrations of the substances A and B
between the coexisting phases ZL, and G,, which are in internal
equilibrium, and are also saturate with respect to solid A, we see
that these quotients are equal to the corresponding ratios in the
coexisting phases 1 and G, which are not in internal equilibrium
and are saturate with respect to solid A and solid 5.

361

From equation (12) (13) now follows the relation:

EL XL

pi oe te (14)
ay Al Xy AF

Ig Y,

from which it appears that in the ideal case the factors f, and f,
of equations (6) and (7) become equal, so that the relative distance
in concentration, as far as A and B are concerned, has the same
value for the coexisting liquid and vapour-phase L and G in the
four phase equilibrium of the pseudo ternary system as the relative
distance between the internal equilibria Lo and Go in the binary system.
Equation (14), therefore, says with reference to fig. 2 that:
Be Bd
Bg By
Ag Af
If we now write equation (14) in the form:
wy Xp wg Xg
TAR ED Yg Y,
we may remark that according to Dimrorn’s terminology :

(16)

tg Xy
Yg Y,
If we introduce also this substitution, we get:

= &.

fp Ge

aa AEON OEL 7)

whereas Dimrorn wrote:
Ca La
Ce Lp

Now Xp and Yy indicate the concentrations of A and B in the
solution ZL (see fig. 2), which is saturate with respect to A and B,
La and Lg representing the saturation concentrations of A resp. B
in the pure solvent.

As a rule these are of course not the same quantities, but when,
as in the ideal case, the substances A and B do not influence each
other’s solubility, this zs the case, as also appears from fig. 2, for
from this follows immediately :

GAGE VLS

Ca Bd wr Xe,
Aant Adan en
so that Dimrotu’s formula is perfectly correct for the ideal case.

La= (19)

362

We must finally still point out here that in contradistinction with

: ie ON , Canes é
equation (6) the quotient in equation (17) and C m equation
UL B

(18) ús the ratio of concentration of A and B in an arbitrary solu-
tion, in which A and B are in internal equilibrium.

4. The relation for the case of polymery.

Up to now we have supposed that A and B are isomers, but
the same considerations are valid for the case of polymery.

Put the case that B is a polymer of A, and that the internal
equilibrium is represented by:

Bia

then the just given derivation may be applied also here. We must
only bear in mind that to get a relation that is analogous to equa-
tion (16) i.e. in which the expression for the equilibrium constant
in the liquid- and gasphase occurs, we must apply Henry’s law to
those concentrations of A and B which occur in the equation for
the equilibrium constant. Hence we consider the concentration z? of
A, and y of B.

In this way we then get the relation:

ay, eS xy : Xx

zene) Se OA
YL Te de XG (20)

This equation expresses, indeed, the same thing as equation (16),
which holds for isomers, but differs from it in shape. Of course
this equation, too, can only be applied to the ideal case, and only
then, written in the form:

oe SA

Ús Sloe
it can be used to examine which modification is the stable one at
a certain temperature. This is however, only possible when we know
the size of the different kinds of molecules. Now the great advantage
of equation 6 is evident, as this can be applied, without the size
of the molecules of A and B being known.

In this communication I have tried to treat the problem in the
simplest way possible; in the next the relations considered here will
be derived by a thermodynamic way, and there the significance of
the phenomena known in practice which seem in conflict with this
theory, will also be pointed out.

cha otard eon

Amsterdam, 23 June 1915. Anorg. Chem. Laboratory
of the University.

363

Chemistry. — “The Apparent Contradiction between Theory and
Practice in the Crystallisation of Allotropic Substances from
Different Solvents’. By Prof. A. Sirs. (Communicated by
Prof. J. D. van DER WaAats).

1. Derivation of the equation for the connection between the satu-
ration concentrations and those of the internal equilibrium.

In this communication [ will give in the first place the thermo-
dynamic derivation of the equations derived in the first communi-
cation on this subject in simpler but less rigorous way.

We shall suppose for this purpose that in a homogeneous phase,
a gas phase or a solution, at a definite temperature and pressure
between two kinds of molecules of the same substance the following
equilibrium prevails :

OE DE ee ie AE i a ee (1!)

We further suppose that in two separate spaces at the same
temperature the solid substances A and B are in equilibrium with
their saturate vapour resp. solution, hence:

EEEN an CE PE BE)
Be GE Tae rte A hee HeT (SN

Now we shall assume that », mol. of solid A by the aid of the
homogeneous phase, which is a gas resp. a liquid phase, is converted
into », mol. of solid 5.

In the first process, which we shall consider now, the homogeneous
phase is thought to be a gas phase, in which internal equilibrium
prevails, and in the second process the homogeneous phase is thought
to be a solution, in which the kinds of molecules A and B are
likewise in internal equilibrium. In these two cases the increase of
the molecular potential Svu must, of course, be the same.

Before proceeding to the first process, I will first observe, that
for the increase of the molecular potential or:

= (vu)s = Psp — Msgs + + + + - + (4)
may be written:

SUD Us PS Pals PAG GEDAAGD PUG 4g FP UG {Pits (5)

in which wg, and ue, represent the molecular potentials of A and

B in the saturate vapour.
For the heterogeneous equilibrium between solid A and its vapour
and solid 6 and its vapour hold the following relations:

364

Usp = UG, OF Mllep— PGR © > + 2s (6)
and

Us UG, OF Pills FPUG © ss (7)
By combination of (5) with (6) and (7) we then get:
= (PW) =P GR VG «2 eee (8)

If we now express the internal equilibrium potentials of gaseous
A and B by;
! '
wae, and we,
then
PUG, =vWG =
for internal equilibrium, so that instead of (8) we may also write:

= (vp); = PUG — Pl G + PWG, 1,06) OS (9)

in which »,ug,,—¥.tGp, represents the work done or gained when
we give the equilibrium potential to rv, mol. of gaseous B, which
possess the mol. potential of the saturate vapour, and thus
Pp, ue, — En En
represents the work performed or gained when rv, mol. of gaseous
A are brought from the equilibrium potential on the potential of the
saturate vapour.
These two values for the work are easy to compute.
We start from the equation:
dp = — ndr udp «9. 2) EE)
hence
(du); =vdp nn = 2) >
or

Wr= map = RTlnp + C

from which follows that:
uw Cy = RTlnp'4 + C

and ue = RTinpa + C
or
WG, — 4G, = RTIn i = RTIn at EN
hence
CAs
PWG, — PUG, =P, RTIn G <a eee)

‘Ag

365

In the same way we get for:

CB;
PUGg — MUG, — vs Rin De (14)
G
so that equation (9) now assumes the following form:
CB; C's
On. + vy, RTIn 7
G G
Now we can apply the same considerations for the case that the
homogeneous phase, in which there is internal equilibrium, is a
solution (second process); then we get instead of equation (15):

mY Ul
CB, C

!
DI

> (vu)s=v, RTIn

Ay,

> (vu)s= v, RTIn + v, RTin
Ca

(16)
5

As 2 (vu)s has the same value in the two cases, the second
member of equation (15) will be equal to the second member of
equation (16).

Then follows from equation (15) and (16), that:

all 1 ld) id
Ca, Ga; Cae

Lg GA Cc"? : CH (17)
Es neg

The concentrations provided with accents indicate the internal

equilibrium concentrations, and those without accents the saturation

concentrations.
Let us suppose that we have to do with isomers, then:

hence:

Ti ree (18)

This equation is the same as equation (16) in the first communi-
cation. +)
If we have the case of polymery, and if e.g.
a =2 and rl
the general equation (17) passes into:

fol c? oy Cc?
dy of Ay A, A,

== nn
5 5 CB, Cn CE,

PE)

1) See preceding communication p. 361.

366

This equation is again the same as equation (20) in the first
communication.

2. Apparent contradiction between theory and practice.

Dimroti'), who wrote equation (18) as follows:

C'4 Cr

fi ie

- = (Gk ke ae Oo (EU
CB, CB,

has pointed out that, the direction of the isomeration being exclusively
dependent on the factor G, this must be independent of the nature
of the solvent.

Experience, says Dimrorn, is in contradiction with this, for it is
known that isomers can be transformed into each other by treat-
ment with different solvents.

In this connection I must point out in tbe first place that there
can be question of a test of formula (20) only when we start from
a solution saturate with respect to A and B im contact with the
two solid phases. Only in one case there will then come no change
in this state, viz. when the temperature of the system is exactly
the transition temperature of the two solid phases. In all other cases
a transformation will take place ‘dependent of the solvent, in which
the metastable solid modification disappears, and the stable one
remains. For some systems this transformation will proceed slowly,
but then we must try to accelerate the process catalytically.

When, working in {his way, we find deviations, it will no doubt
have to be ascribed to this that equation (20) is applied to non-ideal
cases, or to the ease of polymers. That practice is really in agreement
with theory, can be demonstrated in such a case in a simple way
by application of the wrversally holding equation (6) of the preceding
communication :

in the way indicated there.

That isomers can be converted into each other by treatment with
different solvents is an entirely different phenomenon. By this we
understand namely that when e.g. the «-form is dissolved in a certain
solvent, and we then bring the solution to erystallisation in some
way or other, the g-form appears.

1) Lieb. Ann. 377, 127 (1910).

367

We should, however, bear in mind that the formulae discussed
here refer to equilibria, whereas the last mentioned phenomenon is
a question of number of nuclei and spontaneous crystallisation.

I discussed this question already fully on an earlier occasion *),
so that T will only say a few words about it here.

Suppose that at a definite temperature and pressure, the situation
of the solubility isotherms a and bL and that of the line for the
internal equilibrium in the liquid phase is as is indicated in fig. 1;

Ë a A

Fig. 1.
then we see immediately that from an supersaturate solution, in which
A and B are in internal equilibrium, the stable modification A, or
the metastable modification B, can deposit. The liquid Z, is namely
the stable saturate solution coexisting with A,, Z’, indicating the
metastable saturate solution, which is in equilibrium with B. If
the solutions 1, and ZL’, lie under the point ZL, i. e. if LZ’, and L,
contain more of the pseudo-component A than £, and if these points,

1) Zeitschr. f. phys. Chem. 84 (1913).

368

as in fig. 1, lie pretty much on the B-side, it may occur that in
consequence of the greater concentration of B than of A, the number
of nuclei for the metastable modification B, reaches that value first,
at which spontaneous crystallisation sets in. In this case, therefore,
the metastable modification deposits from the supersaturate solution,
and if under the given circumstances the velocity of @onversion is
small, the metastable modification that has crystallized out, con-
tinues to exist.

If, therefore, the situation is as Fig. 1 indicates, it is very well
A, is dissolved in C at
higher temperature, ie. at such a temperature that the internal
equilibrium is entirely or almost entirely established, the metastable
form is deposited when the solution is cooled.

For one solvent the situation will be as is indicated in Fig. 1,
whereas this situation will be less one-sided when another solvent
is used, and in this probably lies the explanation of the fact that
by means of one solvent from the stable form the metastable form can be

possible that when the stable modification

369

obtained, whereas another solvent always yields the stable modification.

If, therefore, the line for the internal equilibrium as Fig. 2 shows,
lies above L, i.e. if at the considered temperature B, is stable, and
L, and L’, lie greatly on the A-side, then for the same reason the
possibility is to be expected that when B, is dissolved in C, the
metastable modification A, deposits from the supersaturate solution
at lower temperature.

Where this phenomenon presents itself it will be an interesting
problem to determine the situation of the points Z, L,, and //, at
a definite temperature, to find out in this way in how far the given
explanation is the true one.

Amsterdam, 24 June 1915. Anorg. Chem. Lab. of the University.

Chemistry. — “Supersaturation and release of supersaturation.”
By DevenpraA Nata BHATTACHARYYA and Ninratan Daar.
(Communicated by Prof. Ernst COHEN).

The older literature on supersaturation, chiefly works of Gay
Lussac '), Scuweiccrr *), Ziz*), Tomson *), Ogprn °), and others,
abounds with evidences showing that the phenomenon is rather
common.

But after that, the general idea of the chemists was that only
few substances could form supersaturated solutions.

But now a days chemists have recognised again that the pheno-
menon is common. Thus Merpergprr | Principles of Chemistry, English
translation (1905), p. 93] states that salts which separate out with
water of crystallisation and form several erystallohydrates yield
snpersaturated solutions with the greatest ease, and the phenomenon
is much more common than was previously imagined. OstwaLp
has studied this case very thoroughly and is of opinion that this is
very common. Turron also mentions in his book, “Crystals” (p. 238)
that supersaturation is a phenomenon of frequent occurrence.

But the reminiscence of the old idea is still unconsciously present
in the popular mind. For demonstration experiments, sodium acetate,
or sodium sulphate, or sodium thiosulphate is invariably taken. Also

1) Ann, Chim. 87, 225; Schw. 9, 70; Ann, Chim. Phys, 11, 301.
2) Schw. 9, 79.

5) Schw. 15, 160.

4) Ann. Phil. 19, 169.

5) N. Ed. Phil. J. 13, 309

370

the idea is predominant that only hydrated salts can be easily supers
saturated. Sodium chlorate is cited as a solitary example of an
anhydrous salt capable of forming supersaturated solution. Again,
no systematic work of a quantitative character is available in this
direction. These led to the present investigation of showing the
general tendency of almost all substances of forming supersaturated
solutions.

At first qualitative experiments were done with varied substances.
These were all performed in well cleaned, steamed test tubes fitted
with similarly operated corks. The solution is boiled for a few
minutes till all the particles of the substance on the side of the test
tube have been dissolved away by the steam, the cork is immediately
put in, and the hot solution, then, is glided over the side of the
tube twice or thrice. The tube is then held under the tap and
cooled down to the room temperature. The corks were always
moist when they were inserted thus insuring against germ crystals
being carried in that way. In open tubes the solution might evaporate
and deposit minute crystals on the sides, which would then at once.
release the supersaturation.

But such things can hardly take place in this case, because the
solution is in a partial vacuum saturated with water vapour. With
ordinary amount of precaution many supersaturated solutions were
prepared in this way which would not deposit crystals even when
shaken vigorously.

Thus it has been found that tartaric acid, citric acid, magnesium
sulphate, lead acetate, cobalt chloride, microcosmic salt, sodium
formate, ammonium acetate, copper sulphate, borax form highly
supersaturated solutions. In the case of tartaric and citrie acids the
supersaturated solution is very much viscous, and even on the
addition of a small germ crystal of the acid, some time elapses
before crystallisation takes place, because the velocity of crystalli-
sation depends on the fluidity of the solution.

In the ease of lead nitrate, barium nitrate, ammonium chloride,
strontium chloride, barium chloride, manganese chloride, potassium
ferrocyanide, potassium sulphate, zine sulphate, nickel sulphate, cobalt
sulphate, barium chlorate, sodium chlorate, sodium bromate, sodium
nitrate, ammonium nitrate, ammonium oxalate, oxalic acid, the
amount of supersaturation is not as extensive as in the case of the
previously mentioned group.

The sparingly soluble organic acids, namely, salicylic, benzoic,
hippurie, succinic, cinnamic, gallic, phthalic acids can be supersatu-
rated. Substances like potassium chlorate, cadmium iodide, borie

374
acid also admit of supersaturation. But in all these cases, the amount
of substance held in excess though appreciable, is small.

Copper chloride and nickel chloride which are highly soluble,
can form fairly supersaturated solutions, but the range of dilution
in which they can exist as such in good stability, is rather
limited.

Thus it is shown qualitatively that the phenomenon of super-
saturation is perfectly general, and all sorts of substances, hydrated
or anhydrous, sparingly soluble or highly soluble, can form super-
saturated solutions.

Now, experiments of a quantitative character were under-
taken with a series of substances. The experiments were
conducted in the following way: A bulb was blown at
one end of a tube of about 10 mm. diameter, and a
portion towards the other end drawn out a little so as to
form a constriction there. The tube was then very care-
fully washed and steamed to dissolve away any nuclei,
carefully dried, and weighed. A weighed amount of the
pure dry substance was introduced into it, a little water
was added to it, and a supersaturated solution produced
by properly adjusting the amount of the solvent by boiling.
The solution was freely boiled so that every particle on
the side of the tube passed into solution. The tube was

then partially cooled under the tap, and carefully sealed at the con-
striction by means of a blow-pipe. The solution was then rolled
over the stem of the bulb to mix with the condensed droplets of
water there, and thus a homogeneous solution was obtained. The
tube was then thoroughly cooled and placed in a quiet place with
a thermometer to indicate the temperature. The drawn out portion
of the tube was dried, and this weighed with the sealed bulb, gave
the weight of water added.

To reach the maximum amount of supersaturation, which can
be maintained under ordinary circumstances for an hour or so, the
method of trial was adopted. The solution was often boiled a little
and cooled down in tap water to see whether crystals appear
immediately. By a little practice no difficulty was felt to judge in
this way whether the solution would erystallise shortly or not. The
tube was sealed when this stage was reached.

The time for which the solution remained supersaturated, as well
as the temperature at which crystallisation set in were carefully
observed.

The following table shows the experimental data. The solubility

of the substance was obtained from Srtpeta’s Solubilities of Inor-
ganic and Organic substances. The solubilities were calculated as
grams of anhydrous substances per L gram of water. The substances
appear in the list in the order of their water of crystallisation, and
of their solubility. The substances crystallised in all cases in 1 to
5 hours after the sealing of the tubes.

Besides these, some 30 tubes were sealed with solutions of less
supersaturation. They were watched for 3 months, in which time
very few crystallised.

From the above tables it will be seen that no perfectly general
deduction is obtainable; but the following facts are observable;

a. Hydrates easily form supersaturated solution.

6. Supersaturation is common in easily soluble substances.

c. Also the phenomenon is common in those snbstances, which
easily form big well-defined crystals.

Physico-chemical Laboratory, Presidency College, Calcutta.

Chemistry. — “ Temperature-coefficient of conductivity in alcoholic
solutions, and extension of Konurauscn’s hypothesis to alcoholic
solutions.” By Drvenpra Nato BHATTACHARYYA and _NILRATAN
Duar. (Communicated by Prof. Erxsv COHEN).

In a former paper’), the results of conductivity measurements
of ten sodium salts in alcoholic solutions were published. The mea-
surements were carried out at three temperatures, and in this paper
the values of the temperature coefficient of conductivity are calculated
and some deductions made from the results.

If we suppose that the conductivity increases proportionally with
the temperature, i.e. the conductivity is a linear function of the
temperature, we find the following values for the temperature coefti-
cient of conductivity of the ten sodium salts in aleoholie solutions
investigated: (see table p. 374).

It is evident from the above table that in all cases the value of
the temperature coefficient is about 0.024. Now, from the researches
of Bouty*) it is seen that the temperature coefficient of fluidity of
aleohol is about 0.024 per degree centigrade. Thus for almost all
the salts studied, the temperature coefficient of conductivity in aleo-
holie solutions is equal to the temperature coefficient of fluidity
of the solutions; because the solutions being very dilute, their viscosities
are practically identical to that of the pure solvent, namely alcohol.

1) Zeitschr. fiir anorg. Chemic 82, 357 (1913).
2) Jour. de Physique (2). 3, 351 (1884).

Ww
Or

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

374

' : = a v ae

| Temperature- Temperature-
sait en ND
| 5° C 30° C.

I. NaClO; | 0.018 | 0.027 | 1774.332
IL. NaCl | 0.016 | 0.026 1623.888
II. NaNO; | 0.019 | 0.026 | 1180.694
IV. NaNO, | 0.024 0.027 | 1916.937
V. NaCNS | 0.022 | 0.028 | 2208.451
VI. Na,PtCl, hel) vid 015 eel hoon 4236 .345
VII. Sodium propionate | 0.023 | 0.024 993.517

VIII. Sodium butyrate | 0.027 | 0.025 1320 .672
IX. Sour benzoate | 0.015 | 0.024 | 685.179
X. Sodium Salicylate 0.013 | 0.023 1306. 449

From a consideration of equal effect of temperature on the con-
ductivity and fluidity of aqueous electrolytic solutions of pure water,
KonrravscH ') presents the hypothesis that, round every ion, and
moving along with it, there is an atmosphere of the solvent whose
dimension is determined by the individual characteristics of the ion;
and the electrolytic resistance of an ion is a frictional resistance
which inereases with the extension of the atmosphere, the direct
action between the ion and the outer portion of the solvent dimin-
ishing as the atmosphere becomes of greater thickness. This hypo-
thesis is in agreement with the fact that the most sluggish ions
have the temperature coefficient of resistance very like the tempe-
rature coefficient of viscosity of the solvent. The hypothesis is in
further agreement with the circumstance that the temperature formula
for the mobility of the ions shows in all cases a convergence towards
the zero value between — 35° C. and — 41° C., the zero value of
the fluidity of water being reached at — 34° C.

From our work it is evident that the same hypothesis may be
applied equally in alcoholic solutions. The electrolyte binds with
it a few molecules of the solvent, the alcohol, which forms an
atmosphere round it, and it moves through the solution with this
alcoholic atmosphere surrounding it. The frictional resistance it meets,
is not the frictional resistance between the ions and the solvent
alcohol, but it is the frictional resistance of the alcoholic atmosphere
round the ions against the solvent molecules.

Chemical Laboratory, Presidency College, Calcutta.

1) Proc. Roy. Soc. 1903, 71, 338.

Bib

Chemistry. — “Velocity of tons at 0 C°” By Duvenpra Nati
BHATTACHARYYA and Nivraran Duar. (Communicated by
Prof. Ernst COHEN).

From time to time attempts have been made to determine accu-
rately the mobilities of ions at 0°. But there is no systematic work
in this line; only isolated cases have been investigated. Even the
velocity of hydrion at O° is uncertain. An exact idea of our very
much incomplete knowledge would be obtained from the following
summary of the work previously done.

Woop ') was the first investigator in this line. Het determined the
molecular conductivities of sodium chloride, potassium chloride,
dichloracetic acid, and trichloracetic acid at O°, and at various
dilutions. But his measurements are inaccurate as will be shown
subsequently. ARCHIBALD *), Barnes *) and Konrrauscu *) also studied
some electrolytes. WuHrTHAM *) accurately determined the conductivi-
ties of some electrolytes at 0°; but he did not attempt in deducing
the velocities of individual ions at O° from his measurements.
KAHLENBERG °), and Jones and his pupils’) also studied some cases,
but their measurements are not accurate. The measurements of
Noyes and Coorper*) agreed with those of Wurrnam. Evidently
no systematic work is done in this line.

The ionic mobilities of various ions are fairly accurately known
at 18° or at 25° (Norges and Fatk — J. Amer. Chem. Soc. 88
(1911), 1436). But the value for hydrion (H°) is not exactly certain
even at 18° or 25°. Osrwarp®) first used the value 342 at 25°, and
then raised it to 347 in Lehrbuch der Chemie 1893, 2, 675. Konr-
RAUSCH’S*’) provisional value was 318 at 18° or 352 at 25°. Until
recently, these values were accepted. Noyrs*'), and then Noyes and
SAMMET '*) obtained the unexpectedly high value of 365 at 25°. Rorn-

1) Phil. Mag. 1896 (5) XLI, 117.
2) Trans. Nov. Sco. Inst. Sci X, 33, 1898.
8) ibid X, 139, 1899.
4) Ann. Phys. Chem. 1898, 66, 785—825
5) Phil. Trans. 1900.

Proc. Roy. Soc. 71, 354 (1903).
6) Journal. Phys. Chem. 5, 339 (1901).
7) Amer. Chem. Journ. 25, 349 (1901); 26, 428 (1901); 34, 557 (1905).
5) Carnegie Institution Publications 63, 47 (1907).
9) Zeit. Phys. Chem. 1888, 2, 842.
10) Leitvermögen der Elektrolyte pp. 107—110, 200.
11) Zeit. Phys. Chem. 1901, 36, 63—82.
12) Zeit. Phys. Chem. 1903, 43, 49.

25%

376

MUND and Drucker!) suggested the value 338 at 25°; and then
Drucker *) used the value 312 at 18° and 345 at 25°. Again,
Drucker *), GoopwiN and HaskeLL *), and WuernaM ‘), by combining
their molecular conductivity measurements with the transference
ratios obtained by Jann and his pupils, and Tower deduced the
mean value for hydrion equal to 313 at 18° or 346 at 25°. Konr-
RAUSCH °) again, and JAHN and his pupils °), declared the most
probable value of hydrion to be 315 at 18° or 348 at 25°. Gorkr *)
obtained the value 353 at 25° from measurements of picric acid.
Noyrs and Karo % came to the value 315 at 18° or 348 at 25°
from migration ratios of nitric and bydrochlorie acids. Drucker and
KrsNJarr 7°) again gave the value 313 at 18° or 346 at 25°. It
would be quite evident from these that the value for hydrion is
far from being correctly known.

Now, by applying KonurauscH’s formula for the temperature
coefficient of mobility we can get the values of ions at O° from the
values given at 18 or 25°. But this empirical formula holds good
with rigidity in the neighbourhood of 18°; so results deduced at
0 are rather uncertain. Moreover KonrrauscH himself has changed
these values of temperature coefficients many umes. For comparison,
are added below the tables (see p. 416) of temperature coefficients («)
as published by KonrrauscuH '*) in 1901, and 1908.

Thus extrapolation to O° is rather uncertain. With a view to deter-
mine exactly the ionic velocities at O°, this investigation was under-
taken. Noyes and Fark '®) have given very accurate tables collected
from the work of numerous investigators for the transference numbers
of various substances at almost infinite dilution and at O°. From the
molecular conductivity determination at 0°, the sum of the ionie

oe : ; ; u,
velocities at O° is obtained (since wo = uw + v), and — is taken
v

1) Zeit. Phys. Chem. 1903, 46, 827.

*) Zeit. Phys. Chem. 1904, 49, 563.

8) Zeit. Elektrochem. 1907, 18, 81.

4) Proc. Amer. Acad. 1904, 40, 399.

5) Zeit. Phys. Chem. 1906, 55, 200.

6) Zeit. Elektrochem. 1907, 13, 333.

7) Zeit. Phys. Chem. 1907, 58, 641.

5) Zeit. Phys. Chem. 1908, 61, 495.

9 Zeit. Phys. Chem. 1908, 62, 420.

10) Zeit. Phys. Chem. 1908, 62, 731.

11) Sitzungsber. d. Berl. Akad. 1901, 1026; 1902, 572; Proc. Roy. Soe. 71, 338
(1903). Zeit. Elektrochem. 14 (1908), 129.

12) loc. cit.

fons 1901 1908 |
A, 18 ‘18 |
Lio + 0.0261 + 0.0265
Nae + 0.0245 + 0.0244
Ko + 0.0220 + 0.0217
Rie + 0.0217 + 0.0214
Ag? + 0.0231 + 0.0229 |
He + 0.0154 + 0.0154
cl’ + 0.0215 + 0.0216
F’ + 0.0232 + 0.0238 |
|
V + 0.0206 + 0.0213 |

The water used in these experiments was carefully purified by
Jones and Mackay’s') method, and collected in wellsteamed resistance
glass vessels. Freshly purified water was used in all experiments.
The conductivity of the water used varied from 4 X 106 to

ad Sat O°.

The measurements were carried out by the alternating current-
telephone method ‘in a closed well platinised cell, with a thermo-

meter tightly fitting its mouth. In our
bot and moist climate, moisture con-
denses in the interior of vessels sur-
rounded with ice; so there is the danger
of dilution of the solutions in open
mouth cells; but this difficulty is removed
by having closed vessel for putting in
solution. The bath was of pure melting ice.

The temperature as indicated by the
thermometer was kept constant for
-nearly half an hour, and then readings
were taken. The cell was now taken
out of the bath and made to attain the
ordinary laboratory temperature, and
diluted with calibrated standard pipettes.

Merck’s chemically pure substances were purified by repeated erystal-
lisation and dried according to the nature of the substance in question.
Hydrochloric acid was prepared by dissolving in conductivity

1) Zeit. Phys. Chem. 22, 237, (1897).

water hydrochloric acid gas evolved out of the ordinary pure con-

centrated hydrochloric acid.

Concentrations of solutions were obtained in most cases by volu-
metric method, and the results were mostly checked by the con-
centrations obtained from the weights of the salts dissolved.

The following tables give the values of the molecular conductivities

obtained :
1. Hydrochloric acid.

Molecular
Dilution conductivity

31.963 237.0
63.926 259.8
127.852 201.5
255.104 | 262.9
511.408 263.8
1022.816 264.2
2045 .632 264.3
4091. 264 264.4

Thus / obtained = 264.4.

The value of vj calculated with
KOHLRAUSCH’S ionic velocities and

temperature coefficients = 265.8.
UI. Lithium Chl ride.

Dilution | py
1.437 47.0
14.874 53.2
29.748 55.6
59.496 | 57.5
118.992 | 59.2
237.984 59.7
475.968 | 59.9
951.936 60.1
1903.872 60.1

obtained — 60.1

vo
“” Calculated from KOHLRAUSCH’S

data = 60.5.

Il Ammonium Chloride,

Dilution My
9.984 66.5
19.968 73.8
39.936 | 75.3
79.872 76.0
159.744 78.4
319.488 79.2
638.976 79.7
1277.952 79.9
2555.904 80.0

Thus ”… obtained = 80.0
% calculated from KOHLRAUSCH’S
data = 81.7.

IV. Strontium Chloride.

Equivalent | Equivalent

dilution | My
19.516 | 53.2
30.152 | 61.3
18.304 | 64.0
156.608 | 66.0
3132165 4 RGO
626.432 | 68.8
1252.864 | 70.7
2505. 728 | 71.9
5011.456 | 72.3

gp is taken to be 72.5
“gy calculated from KOHLRAUSCH’S
data = 73.1.

379

V. Magnesium Chloride. VI. Ammonium Nitrate.

|
Equivalent | Equivalent

dilution | My ° Dg Ran
[SRA iad PE |
30.396 58.8 Boogie |). 17:1
60.792 59.5 60.462 78.6
121.584 60.5 120.924 | 79.2
243.168 62.3 241.848 | 79.7
486.336 | 64.0 483.696 80.0
972.672 | 65.3 967.392 80.2
1945.344 66.1 1934.784 | 80.2
3890.688 | 66.4 3869.568 | 80.3

Lo is taken to be 66.6
“gp calculated from KOHLRAUSCH’S

Lp obtained = 50.3
gq calculated from KOHLRAUSCH’S

data = 68.3 data = 80.3
VII. Sodium Nitrate. VIII. Potassium Nitrate.
Dilution My Dilution | My
22.271 62.6 39.068 | 78.4
44.554 63.7 78.136 | 80.3
89.108 65.1 156.272 81.3
178.216 65.8 312.544 | 82.5
|
356.432 | 66.0 625.088 | 83.0
112.864 | 66.5 1250. 176 83.2
1425.728 | 66.8 2500.352 | 83.3
2851 .456 66.9 5000.704 | 83.4

Pep obtained = 66.9
Pp calculated from KOHLRAUSCH’S
data = 66.1

“ obtained = 83.4
’g calculated from KOHLRAUSCH’S
data = 81.1

380

IX. Ammonium Sulphate. X. Potassium Sulphate.
Equivalent | Equivalent Equivalent Equivalent
dilution Wy .; dilution Py
53.633 825, 33.156 72.9
107.267 76.7 66.312 | (eet
214.534 19.2 132.624 79.0
429.068 | 80.6 265.248 81.9
858. 136 81.3 530.496 | 83.5
1746: 202 1) 8126 1060. 992 84.0
3432.544 81.7 2121.984 | 84.2
Yo taken to be 81.8 ” taken to be 84.4
Y%g Calculated from KOHLRAUSCH's Y’g calculated from KOHLRAUSCH's
data = 82.4. data = 83.2.
XI. Sodium Sulphate. XII. Calcium Sulphate.
Equivalent Equivalent Equivalent | Equivalent
dilution conductivity dilution My
17.325 55.9 467.913 63.3
34.651 58.2 935.826 67.7
69.302 | 61.6 1871.652 | 71.0
138.604 63.8 3743.304 filed
277.208 65.9
| to is taken to be 72.
554.416 67.1
1108.832 | 67.9
2217.664 68.1
4435 .323 68.2

Y’e Obtained — 68.2 ,
” calculated from KOHLRAUSCH’S
data = 68.3.

XIII. Magnesium Bromide.

Equivalent | Equivalent
dilution Pe

44.182 59.3
88.365 | 61.8
176.730 | 63.7
353.460 | 65.1
706.920 66.1
1413.840 66.9
2827 ..680 67.3

381

XIV. Calcium Bromide.

Equivalent |

dilution

21.333
42.667
85.334
170.668
341.336
682.672
1365 .344
27130. 688

Equivalent

H.
fav:

62.7
65.0
66.8
68.4
69.5
10.4
11.0
lee

Ye is taken to be 67.5
"ep Calculated from KOHLRAUSCH’S
data — 69.3

Now, Noyes and Fark!) give the cation transference numbers
for HCl and NH,CI at O° at almost infinite dilution as 0.847 and
0.490 respectively. By using these values, the ionic velocities are
calculated from uz, determinations for HCI and NH,Cl. Thus,

Yq Obtained = 71.2

Cation transport |

Substance | Ionic velocities

number
SE—E———————— —— 1 ——— => EE =. =
| H* 223.9
HCl 264.4 | 0.847
| Gie” "40.5% 3]
| zE
|
| NH, 39.2
NGE CIO 80.0 | 0.490 |
| | | GI 40.8

| | |

Now, the ionie velocity of Cl’ is taken as 40.8 as the more

accurate figure, and from it the following ionic velocities are deduced
by applying Konrrauscnr’s law fg, == uv

Substance

. Equivalent “5 lonic velocities
LiCl 60.5 | Lit = 19.3
Sr Cl 72.5 | pSr = 31.7
Mg Cla_ | 66.6 | y‚Mg““=25.8

Again, by using these values, other ionic velocities are calculated
as is shown in the following table:
1) Loe. cit.

| Equi- | Peaounianie Required ionic

It would be noticed from the column headed “Remarks” that in
no case have ionic velocities differed by more than 0.3, as obtained
from different sources.

Below, is added a comparative table of the ionic velocities as
obtained by this direct method, and as obtained from Konrrauscm’s
table’) by calculating with his temperature coefficients:

‘ Velocities at 0? C as Velocities as calculated

lons obtained directly with temp. coefficients.

HC | 223.9 224.3
NH4 | 39.2 40.2
Bis 19.3 | 19.0
Na’ 25.6 | 26.0
K* 42.1 |

WiGac 29.5 |

ie St ea Sie |

to Mg” | 25.8 |

Cl 40.8

NO’; | 41.3

Br’ 41.7

yp SO’ 42.6

1) Loc. cit.

Evidently then, the temperature coefficients of KoHLRravuscH can
not be relied on to obtain accurate values at 0° C.

Woop’) has given the following values for u at 0°: for KCl =
77.8, for NaCl = 65.0, for dichloracetie acid = 227.0, for trichlor-
acetic acid = 224.7. Thus from the values obtained by me it is
seen that his values for KCl and NaCl are a little too low, whilst
his values for the acids are very much too low, since the most
probable value of H° is 223.9.

JOHNSTON’S*) rough estimation of the value of H° at O° = 240 is
also far from being correct.

Noyes and Srrwart*) have deduced values for H° in an indirect
way which can hardly be relied on. Whilst from data for HCI they
obtained the velocity for H° at 0° = 224, they, at the same time
obtained, by considering H,SO, in the same way the value 235 at 0°.

Noyes and Cooper *) give 81.4 as the value of u for KCl at
O°; but it is a little too low.

Jones and West’) have given «ug at 0° for NH,Cl = 74.84;
evidently it is too low.

Jones and CALDWELL®) give the value for ammonium nitrate
= 78.0, which is a value a little too low.

KAHLENBERG’) obtains for strontium nitrate the value 66.1. Evidently
it is too low, since the correct value would be about 31.7 + 41.38 =
(emoe cit).

Hint and Sircar*) take a very high value for H° at 0°. They
write: For uy in the case of hydrogen fluoride, we have taken
the number 364 at 18° and 325 at O°. The first number is derived
from the ionic conductivities at 18° which are 318 for the hydrogen
ion and 46.6 for the fluorine ion. The second number is derived
from the following data:

“OsTWALD gives 325 as the ionic conductivity of the hydrogen
ion at 25°; at 18° the value is 318 (KourrauscH and v. STEINWERR,
Sitz.-ber. Berlin. Akad. 1902), being a fall of one unit per degree.
Hence at 0° the value would be approximately 300. Correcting
the ionic conductivity of fluorine for temperature, the temperature
coefficient being 0.0238, we get the value at 0° = 26.6. The sum

1) Loc. cit. ;

2) J. Amer. Chem. Soc. 31, 1015 (1909).

5) J. Amer. Chem. Soc. 32, (1910), 1140—1141.

*) Carnegie Institution Publications 63, 47 (1907).

5) Amer. Chem. Jour. 34, 557 (1905).

8) Amer. Chem. Jour. 25, 349 (1901).

7) Jour. Phys. Chem. 5, 339 (1901).

8) Proc. Roy. Soc, Vol. 83 A, p. 130.

354

of these ionic conductivities is 326. This number may be derived
in another way. H. E. Jones gives 380 as the limiting value for
HF at 25°. The value as calculated above for 18° is 364. The
difference per degree is 2.3 units, hence the value at 0° is 324.
The approximate correctness of the number 325 is shown by the
fact that if we assume the amount of dissociation to be little affected
by temperature, at any rate in the more concentrated solutions, we

0° 18
get a= a . Substituting 0.0576 for a and 18.30 for
Ue U

u, which is the value for the acid of 29.83 °/,, we get ug — 318
(at O°).

“The temperature coefficient for H at 18° is about 0.0153. If this
is used to calculate the limiting value for the hydrogen ion at 0°,
the number for g°° becomes very much lower than any of these
3 numbers given above, and as a coefficient is only correct in the
neighbourhood of 18° we discard this method of calculating.”

It is evident that Hir and Sircar have calculated u at O° for
HF assuming a very high value for H°. Their value for H° at O°
is about 100 units higher than the value obtained in this investi-
gation in the direet way. Consequently all their calculations for
the degree of dissociation of HF with this value for H° are not
reliable.

Chemical Laboratory,

Presidency College, Calcutta.

Chemistry. — “Properties of elements and the periodic system”. By
NILRATAN Duar. (Communicated by Prof. Ernst Conen).

In a former paper (Duar Zeit. Elektro-Chem. (1913) it has been
shown that the heats of ionisation of elements and the temperature
coefficient of mobility of ions are periodic functions of their atomie
weights. In this paper it will be shown that some other properties
are also periodic functions of their atomic weights.

Surface tension, capillary rise ete.

The surface tension of liquids being an important property has
been investigated by various workers. There are several methods
of determining the value of the surface tension of liquids, the most
important ones are (1) the rise in a capillary tube, (2) measurements

385

of bubbles and drops by Quincku, Macin and Wirpervorce, 8) deter-
mination by means of ripples (Lord Rarreren Phil. Mag. XXX
p. 386), 4) Lenarv’s (Wied. Ann. XXX p. 209) method of determ-
ination by oscillations of a spherical drop of liquid, (5) determination
by the size of drops (Rarrrien Phil. Mog. 48, p. 321) (6) Winnermry’s
method of measuring the downward pull exerted by a liquid on a
thin plate of glass or metal partly immersed in the liquid, (7) JArGER’s
method of measuring the least pressure which will force bubbles
of air from the narrow orifice of a capillary tube dipping into the
liquid, (8) by measuring the pull required to drag a plate of known
area away from the surface of a liquid ete.

Besides (vy) the surface tension, another constant is sometimes
employed; it is called specific cohesion, and is usually denoted by
a’. The relation between a* and (y) is expressed as follows:
me 27 : mises ee ted ae
a = = = specific cohesion, where -/ = density of the liquid, whence
since (y)='/,rhd (where r=radius of the capillary tube, =
= rise in the tube), it is seen that the specific cohesion is measured
by the height to which a liquid rises in a capillary tube of unit
radius.

WarpeN [Zeit. Phys. Chem. 65, 129, 257 (1908)| has recently
found that specifie cohesion may be applied in another way to esti-
mate the degree of association of both liquids and solids. A com-
parison of the experimental data showed the relationship

AT constant = 17.9
where 7, is the latent heat of vaporisation at a boiling point and
a’ the specifie cohesion at the same temperature. Combining this
expression with Trouton’s rule, we see that the molecular cohesion
of a liquid at its boiling point is proportional to the boiling temper-
ature expressed on the absolute scale. This relation holds only for
non-associated liquids.

Moreover WALDEN points out that if substances are in corresponding
states at their melting points, there would be a similar relation
between the latent heat of fusion and the specific cohesion at the
melting point.

The specitie cohesion of fused metals and salts has been investi-
gated by Quincku in a very thorough manner. The measurements
were obtained from the weight of falling drops of a liquid, or from
the curvature of flat drops of the solidified material.

It was found (Pogg. Ann. 185, 643, 1868) that all salts and
metals and some organic substances near their melting points have

386

specific cohesions which are simple multiples of the constant number
4.3. For various reasons it seems clear that these relations are only
apparent. In the first place, the divergence from the constant is in
many cases considerable.

Moreover there are errors of experiment [ef. Meyer. Wied. Ann.
54, 415 (1895); Lonnsrer. ibid. 54, 722 (1895) ete). Under the
stress of criticism: (ibid, 58, 1070 (1894), 61, 267 (1897)), ()UINCKE
somewhat modified his views.

It has now been found out that the specific cohesion of elements
is a periodic function of their atomie weights.

The following data are collected from the works of various investi-

Name of elements. Specific Cohesion.

————————

Sb 7.635
Pb | 8.339
Bree: | 3.895
Cd 16.84
25.81

K 85.74
Cu 14.44
Na | 52.97
Pd | 25.26
P 4.475
Pt | 17.88
Hg 8.234
S | 4.28
Se 3.42
Ag 15.94
Bi 8.019
Zn | 24.05
Sn | 16.75
Cl | 4.176
| 3.018

N | 2.541

Specific cohesion of elements

— > Atomic weigths of elements

Fig. 1.
gators using the previously described methods. By plotting the
following data, well-defined periodic curves are obtained.

From the curve it is seen that the alkali metals Jie on the top
most points, whilst Zn,Cd and Hg lie on a straight line on the descending
portion of the curve. P,As,Sb, and bi occupy similar positions in the
minima.

Temperature coefficient. of electric conductivity of elements.

The reciprocal of the resistance of a conductor is called its con-
ductivity. Thus if S is the conductivity of a wire, Onm’s law is
expressed by C= SH. In the same way the specifie conductivity
is the reciprocal of the specific resistance and is connected with the
conductivity by the relation S—=ms//, where / is the length and s
the cross section; the conductivity is directly proportional to the
cross section and inversely proportional to the length.

In the case of pure metals the specific conductivity always decreases
with increase of temperature. Dewar and Femina have shown that
at absolute zero the resistance of all pure metals approximates to
zero. As a result it has been found that if A, is the resistance of
a platinum wire at the temperature £ C. on the air thermometer
and Mè, is the resistance at a temperature of O° C., then the connection
between these quantities can be expressed by an equation of the form

R,/R, = 1 + at + Bt’.
In the expression « and 3 are constants which vary very slightly

from one specimen of wire to another. The value of these constants

388

is determined by measuring the resistance of the wire at three known
temperatures. Just as Konrrauscu has shown that the effect of tem-
perature on the conductivity of a solution is very nearly linear, so
over comparatively small ranges of temperature the increase of
resistance of pure metals is very nearly proportional to the increase
in temperature. Hence if /2, is the resistance at a standard temperature,
say O°? ©. and 7, the resistance at a temperature f, then we may
express the relation between Zi, and /?, by an expression of the
form R,= R,(1-+at), where «= 0.00366. There are distinct variations
in the value of @, from one element to another.

It has now been observed that the temperature coefficient of electric
conductivity of elements is distinctly a periodic property of the elements.

By plotting the values of the temperature coefficients given in
Lanpotr and Bornsruin’s tables well marked periodic curves are
obtained.

Temperature _
coefficient of electric

conductivity

hg Te

Sn
5

> Atomic weights of elements
Fig. 2.

Elements of the same group lie very nearly on a straight line
and oceupy similar positions on the curve.

This curve resembles the one that is obtained by plotting the
temperature coefticient of ionic mobility of elements (ef. Daar loc. cit.).

389

Temperature coefficient of conductivity of heat.

The change of thermai conduction with temperature was noticed
by ForBrs [ Phil. Trans. Roy. Soc. Edin. Vol. 33 (1862), p. 133].
Generally there is a decrease of conductivity with inerease of tem-
perature and as a similar decrease takes place in the electric con-
duetivity of metals, it was supposed by Forses that in general the
thermal conductivities of metals like their electric, diminished with
rise of temperature.

WiIEDEMANN and Franz |Pogg. Ann. 89, (1853), 497] appeared to
show that there is some connection between conducting power for
heat and for electricity.

For the metals were found not only to follow the same order for
the two conductivities, but in many cases the numbers bore nearly
the same ratio to each other.

More recent work has confirmed this supposition. The following
are some of the values for metals of the ratio of the thermal con-
ductivity and the electrical conductivity or 4'c at 18° C. as deter-
mined by JarGER and DinsseLnorst |Phys. Tech. Reichsanstalt Wiss.
Abh. 3, (1900) i; together with the themperature coefficient of the ratio.

10—10 5 Temp. coeff.

Cu 6.65 0.0039
Ag | 6.86 | 0.0037
Au 7.09 0.0037
Zn 6.72 0.0038
Cd 7.06 0.0037
Pb 7.15 0.0040
Sn 7.35 0.0034

The electron theory of conduction for heat and for electricity gives
an explanation of the connection between the two quantities.

According to that theory the ratio should be proportional to the
absolute temperature i.e. should have a temp. coeff. 0.00367 and at
0? C., its value should be 6.3 > 10°. The temperature coefficient
of heat conductivity has been determined by Lorenz {Wied. Ann.
18, 422, 582 (1881)], Srewarr [Proc. Roy. Soc. 58, 151 (1893),
Lees (Phil. Trans. A. 188, 481 (1892) | ete.

But the data of only a few elements are available, so it is im-
possible to obtain a curve with the insufficient data, which at present

26
Proceedings Royal Acad. Amsterdam. Vol. XVIII.

390

we can have. It has already been found that the conductivity of heat
and electricity is a periodic function of the atomic weights of elements
and now it is seen that the temperature coefficient of electric con-
ductivity of metals is also a periodic function of the atomic weights
and as the two properties, as has been already observed, are very
much related, it seems very probable that the temperature coefficient
of the conductivity of heat of elements would also be a periodic
function of their atomic weights.

Torsional rigidity, Youne’s modulus and their temperature coef-
ficients.
The following table is obtained from LaNporr und BöRNSTEIN’s

T
|

Metals | E | o, | T is
At | e510 | 21.3 | 2580 | 24.7
Pb | 1493 | — | 550 | 78.7
Ga dronk 2450 | 46.7
Cs — — — 180
Fe | 18347 | 2.25 | 7337 | 3.04
Au | 7580 = 2850 | 3.01
K = = — 14150
Cu | 9807 | 3.63 | 3967 | 4.49
Li | — = —! aan
Mg | 4260 | — 1710 | 302
Na — — — 130
Ni | 20300 | 2.46 | 7820 | 3.28
Pd | 11284 | 1.98 | 4613 2.7
Pt | 16029 | 0.73 | 6594 1.78
Rb ze a de, hy
Ag | 7790 | 7.65 | 2960 | 8.21
Bi | 3190 | — | 1240 =
Zn | 10300 | — | 3880 =
Sn | 5410 1730 | 82

Tabellen. / represents the Youne’s modulus, A, its temperature
coefficient. 7' indicates the values of torsional rigidity and A, its
temperature coefficient.

391

From the above table it is seen that in these properties also there
are distinct indications of periodicity. The transitional elements
Fe and Ni have practically equal values for these properties.

As the atomic weight of elements in the same periodic group
increases the value for Youna’s modulus and torsional rigidity decreases.
In the sub group B of the first group of periodic classification (Cu,
Ag, Au), gold having the highest atomic weight has the smallest
values for Yotne’s modulus and torsional rigidity. Similar are the
behaviours of zinc, cadmium, tin and lead.

Sufficient data are available in the case of the temperature coefficient
of torsional rigidity and hence distinct periodic curves are obtained ;
the alkali metals, Li, K, Na, Rb and Cs lie on the topmost points
whilst copper, silver and gold lie on a straight line on the minima.

Temperature coefficient of
Torsional rigidity of elements.

Pt
9
| Atomic
\| weights
| :
mg,
he
Je Au

Fig. 3.

Specific heat. During recent years the determination of specific
heats of substances at low temperatures was attracting the attention
of numerous investigators. :

RicHarps and Jackson (Zeit. Phys. Chem, 1910. 70, 414) have
carefully determined the specific heats of various elements between
— 188° and + 20°. From their experimental data, they come to
the conclusion that the atomic heats of various elements between
the above range of temperature conform approximately to DuLone
and Prrrr’s law, the value of the constant being 5.3. There are

26%

392

certain deviations and these show distinct periodicity, the general tendency
being towards increasing atomic heat with increasing atomie weight.

Scuimer (Zeit. Phys. Chem. 1910. 71, 257) has determined the
specific heats of many elements at various temperatures (e.g. —150°,
— 00", OMELENE

From his work he concludes that the atomic heats diverge in a
marked way as the temperature falls, whilst conversely a rise of
temperature produces, as is well known, a marked convergence
towards a fixed value for all elements.

Evidently, it is seen from the above investigations, that there are
distinct indications showing the period nature of atomic heats at
low temperatures.

Very recently a decided advance in this direction was made by
Dewar [Proec. Roy. Soc. A. Vol. 89 p. 158 (1913)]. He determined
the specific heats of 53 elements between the boiling points of liquid
nitrogen and hydrogen at about 50° absolute.

When the atomic heats are plotted in terms of their atomic
weights they reveal definitely a periodic variation resembling gener-
ally the well-known Lornar Meyer atomic volume curve.

The author concludes that if experiments were similarly made
between the boiling points of hydrogen and helium then in all proba-
bility the atomie heats would be all very small and nearly constant.

However interesting these results may be there is a great difticulty
in these investigations. The temperature range is very high with
these workers. In the case of Ricuarps of JAcKson’s experiments it
was about 200° and in the case of Drwar’s it was 57°.5.

From these works only the mean specific heat between so large
a range of temperature is available and not the specific beats at a
fixed temperature. Since there is a marked variation of specific
heats with temperature, the results obtained in experiments carried
on with large range of temperature lose much of their significance.

Nernst and his pupils have determined the specifie heats at low
temperatures (Jour. de Phys. tome IX, 1910, p. 721); E. H. GRIF-
rirus and E. Grireitas have also attacked the same problem (Phil.
Trans. 1913 A 213, 119). These experiments are advantageous,
since the temperature range is very small. In Nernst’s experiments
it is only 2°.7 C. It is well known that the atomic heats of
elements can be calculated from Ernsrein’s formula

e
US

ae 2
eee)

457%

393

where R is a gas constant, equal to 1.98 gram calories, for Pb a = 58,
=O LO:
In the following tables (see p. 431) the values of atomic heats
of lead and silver at various temperatures are recorded.

Lead (atomic heat).

Absolute NERNST’S | Calc. from | Cale. from
temp. observed value | EINSTEIN GRIFFITHS
| |
62° 5.63 | 5.58 | 5.62
66° | 5.68 | 5.63 | 5.64
79° 5.69 | 5.75 | 5.68

DeEwar’s value at about 50° abs, = 4.96

Silver (atomic heat).

64° 32 3.61 -

84° 4.43 4.44 | —

86° | 4.40 4.50 | =

DEwAR’s value at 50° abs. = 2.62.

Though Nernst’s, Einstein's and Grireirus’ values agree with each
other, Drwar’s values are divergent owing to a large range of
temperature.

GrirfitHs and GrirrirHs have calculated the following values of
ihewatomiesheatssat ——2 lon OC All 3-54. He— Oh (orm Gules
Zn 4204 Ap 95.378, Cd = 4.95, Sn = £997, Pb 4.927.

These figures also do not agree with the statement of Dewar
that atomic heats of elements between the boiling points of liquid
hydrogen and helium would be all very small and nearly constant.
Evidently Dewars data show the mean atomic heat between his
experimental range of temperature.

Since the product of atomic weight and specific heat at the ordinary
temperature is very nearly constant, if we plot the atomic heats at
the ordinary temperature against the atomic weights, we shall geta
straight line parallel to the axis representing the atomic weights.
On the other hand by plotting the specific heats of elements at the
ordinary temperature against their atomic weights, very nearly a
rectangular hyperbola is obtained, since the product of specific heat
and atomic weight is constant.

This non-periodie curve is quite unique amongst the physical

8394

properties of the elements, since almost all important physical pro-
perties are periodic functions of their atomic weights.

3y plotting Dewars’s values of specific heat at about 50° absolute,
we get a distinet periodic curve; evidently at about 50° absolute,

—— Specific heat of elements at 50° absolute

——— Atomic weights of elements

Fig. 4.

specific heat, like other pbysical properties of elements, is a periodic
function of the atomic weight of the elements. The alkali metals,
lithium, sodium, potassium, rubidium, caesium ete. lie on a straight
line at the top of the curve. The halogen elements lie on a straight
line on the ascending portion of the curve near the alkali metals,
on the descending portion nearing the alkali metals lie Mg, Ca, Sr
ete. S, Se and Te may be connected by a straight line. So also Zn,
Cd and Hg. The platinum metals, (Osmium, iridium, platinum,
ruthenium, rhodium, and palladium) lie on the minima of the curves.

Coefficient of linear expansion. The researches of Fizeau show
that the volatile elements occurring in the ascending curve possess,
almost without exception, a larger coefficient of expansion by heat
between 0° and 100° than the not easily fusible elements occupying
the minimum of LotHar Mryer’s curve.

Similar vague suggestions are collected in Lortmar Meyer’s “Theories
of Chemistry” Eng. Trans. p. 181 from the works of CARNELLY
(Journ. Chem. Soe. 1879, 565); Wiese (Ber. 1878, 2289; 1880,
1258); Raoun Picrer (Compt. rend. 1879 LXXXVIII, 855) on the

relations between melting point, expansion ete. But no definite
statement of the periodicity of coefficient of linear expansion of
elements with their atomic weights is available.

Griinuisen [ Ann. Phys. 1910 (IV), 38, 33—64] has found that the
observed expansion of metals by heat is, in general, in close agree-
ment with that required by ‘uieseN’s (Ber. Deut. Phys. Ges. 1908,
6, 947) exponential formula /,—/, = y (Te Te) and this agree-
ment is particularly good at low temperatures. The experimental
given e is a periodic function of the atomic weight of the metal and
that its maximum values are reached when the atomic volumes are
at their respective minima. It has now been found out that the
coefficient of linear expansion of elements is also a periodic property.

> Coefficient of linear expansion

mmm Atomic weights of elements
Fig. 5.

By plotting the values given in LaNpoLr und Bornsrein’s Tabellen
well defined periodic curves are obtained. The alkali metals lie on
the topmost points, whilst S, Se and Te lie on a straight line on
the ascending portions of the curve.

Cu, Ag and Gold, as well as As, Sb and Bi oceur in similar
positions in the minima.

Molecular Magnetic Rotation.

If we imagine a layer of unit length of any substance placed in
a magnetic field of unit intensity and traversed by a beam of homo-

396

geneous plane polarised light in the direction of the lines of force
of the field, then the rotation which the plane of polarisation under-
goes at a known temperature is the absolute magnetic rotation of
the substance.

Generally we do not require the absolute value and the relative
value with reference to a standard substance is sufficient.

Perkin, the veteran worker in this line, chose water as the stan-
dard substance.

Hence denoting the specific rotation by 7 we have the expression,

a ;
y=, where a is the rotation of the given substance .-. M (mole-
a
: : a dm :
cular magnetic rotation) = - ee where m and d are respectively
ade

the molecular weight and density of the substance and u and d the
corresponding values for the standard (since in Perkin’s work, tubes
of equal length were always used).

The magnetic rotation of the plane of polarised light is measured
in the same way as the permanent rotation of a substance, but the
apparatus is more complex, since an arrangement for placing the
substance in a magnetic field is provided. The tube containing the
liquid is placed either between the poles or as in Prrkin’s latest
form of apparatus in the hollow cone of a powerful electromagnet.
The chief precaution to be observed in addition to those of an
ordinary polarimetric determination, is in preserving a constant strength
of the magnetic field.

The rotations of the standard and of the substance are measured
in the same tube under identical conditions of temperature and
magnetic intensity [Perkin, Trans. chem. Soc. 421 (1884); 69 1025
(1896); 89, 605 (1906) }.

From an exhaustive study of organic compounds, Perkin has shown
that the addition of CH, causes an approximately constant increase
in molecular rotation and this increase is very nearly the same in
different classes of compounds. Perkin has calculated the average
value for CH, from a wider range of material and he found that
CH: = 15023:

If there are n CH, groups in a compound whose molecular rota-
tion is M, then the expression —na (1.023) == represents the
rotatory effect of the remainder of the molecule. In a large number
of organic compounds it is seen that S is approximately constant
for all the higher members of a given series. Thus S is called the
series constant. The series constant 0.508 of the normal paraffins
Cn Mo 2 is obtained by subtracting the value of CH, from the

397

rotation of any member of the series. This residue must represent
the value for 2 H, since Cn Ho, 42 — nCH,=2H. Hence we
may write 2 0.508 or the value of hydrogen as 0.254. Then
again, it is known that CH, = 1.028, whence by deducting the value
of 2 H we may obtain the value for carbon = 0.515. Again, when
hydrogen is removed from a compound and replaced by chlorine,
there is an increase in rotatory power of 1.480; hence the value
for chlorine may be assumed to be 1.480 + 0.254 = 1.734. Similarly,
bromine and iodine may be caleulated to be equivalent to 3.562
and 7.757 respectively.

It has been found out that molecular magnetic rotation of elements
is also a periodic function of their atomic weights.

|
5 /
2 |
3 /
©
=
= /
2
vu
5
ao
os
= en
-
=
=
i>)
&
©
=
ct f
\/
“ sod
y /
ke ve
Mg
EN wa
; 2

> Atomic weights of elemants

Fig. 6.

The curve is obtained from the following data (see table p. 436)
collected from the works of different investigators.

398

Magnetic rotatory power.

| Observed by

Name of

Element PERKIN | HUMBURG
H | 0.254 | =
C (in Ketones) | 0.850 | —
O(inOH) | 0.191 | =
Br | 3.562 | 3.563
CI AAG aw
I | Ue | —
N | 0.717 | —
Na Ie 0558
K ey Rea Wl
Li il 124. | —
Ca Pe =
Mg | 2.029 | =

Distinct periodic curves are obtained. The halogen elements occupy
the topmost points.

Physico-Chemical Laboratory, Presidency College, Calcutta.
y y y

Physics. — “Fresnei’s coefficient for light of different colours.”
(Second part). By Prof. P. Zeeman.

(Communicated in the meeting of May 29, 1915)

A first series of experiments was made with yellow, green, and
violet (4358) mercury light. As FresneL’s coefficient changes only
slowly with the wavelength, such a high homogeneity of the incident
light is unnecessary. With regard to the intensity of the light it is
even recommendable to work with a limited part of a continuous
spectrum. In a second series of experiments I therefore analysed
the light of an electric are (12 Amp.) with a spectroscope of constant
deviation, which I had arranged as a monochromator by taking
away the eye-piece and replacing it by a slit. The monochromator
had been calibrated with mercury and helium lines. The prism stood
on a table, which could be turned by means of a screw. Each

reading on the scale attached to this screw gave the mean wave-
length of the light used with an accuracy of a few ANGsTROM-units.
By repeating the calibration during the experiments it was proved,
that this mean wavelength could always be reproduced with the
above mentioned accuracy. This now is more than sufficient, as for
instance in the green part of the spectrum a change of 4 = 5400
into 25500 and at the greatest possible velocity of the water
the shift of the interference fringes becomes 0.660 instead of 0.675
of the distance between two fringes. Even a change of 10 A.U.
in the wavelength of the light used corresponds to 0,0015 only of
the distance between the interference fringes, while the probable
error of the final result is of the order of magnitude of 0.005.

In order to determine the place of the interference fringes | used
two or rather three different methods and in a few experiments
only eye observations were made. In one series of experiments a
wire-net, which could be turned and shifted was adjusted in the
focal plane s (see Fig. 1)'). In the focal plane of the telescope / we
took photos of the interference fringes, while care was taken that
one wire was parallel to the fringes and that the other passed
through the middle of the field.

An advantage of this method is, that the interchanging of the
photographie plates in the focal plane of f does not disturb the
relative position of the interference fringes and the wires. With
this method however it is rather difficult to adjust the wire-net
accurately as it is so far away from the observer. Moreover the
net must be very fine because of the strong magnifying power of
the telescope. On the proposal of Prof. Woop I used in a second
method Rowranrp’s artifice’) for the comparison of spectra. RowLanp
puts in front of the photographic plate a brass plate with longi-
tudinal aperture of the same width as the thickness of the plate,
which could turn round a horizontal axis in front of the photo-
graphic plate. The rotation could easily be limited to an angle of
90°. By means of two fine quartz wires adjusted perpendicular to
the plane of the brass plate the position of the plate could be
measured accurately and corrected if necessary.

Two photos taken by this method are reproduced in the Plate
(Fig. 4 and 5). The onter system of interference fringes has been
obtained while the water was streaming in one direction; the inner
system corresponds to a current in the opposite direction.

Fig. 5 shows also the shadow of the fine quartz wires.
ie 1) See the first part.

2) Ames, Phil Mag. (5) 27, 369. 1889,

400

Though this method gives a clear survey of the shift of the inter-
ference fringes and e. g. shows immediately, that the shift for red
light (Fig. 4) differs from that for violet (Fig. 5), it is not very fit
to obtain quantitative results. By a detailed investigation I found,
that the uncertainty of the measurements was greater than I had
expected from eye observations. A disadvantage of this method
is first, that for the measurement of the negative we must once
point on an interference fringe and then on the two pieces of a
broken fringe. For spectral lines this does not matter much, but the
difficulty becomes greater for the more hazy interference fringes. It
is however an essential disadvantage of this method that pointings
‘annot be made on corresponding points of the interference fringes.

Quite satisfying results I got with the third method,
concerning which I shall give some details. In the
focal plane of the telescope a system of wires as
is shown in fig. 4 was adjusted. There are three
vertical wires (and one horizontal wire), so that
we can always choose the best one asa fixed mark
and read along the horizontal wire. It is very
improbable that the three wires are all badly situated with respect to
the interference fringes. Just behind the cross wires the photographie
plate is adjusted on a plate-holder which is mounted independently of
the telescope with the cross wires. The photographic plate can be brought
in the right position and slidden to take suecessive photos without
touching the telescope. Examples of the obtained photos are repro-
duced on the Plate (Fig. la—3é), 4 or 5 times enlarged. The photos
la and 1%, 2a and 25 ete. belong together. Comparing two such
photos the shift of the interference fringes is evident. The dis-
placement is also given on the Plate in parts of the distance between

Fig. 4.

two fringes. As mentioned above the measurement was made along
the horizontal wire.

The width of the interference fringes can be chosen according
to the circumstances. p gives the pressure of the water in kilograms
per em?‚ measured during the streaming of the water with a mano-
meter coupled to the main tube, just before it divides into two
less wide ones. The times of exposition for the making of the
negatives amounted between 3 and 5 minutes. It therefore sufficed
to read the pressure of the water each 30 seconds. The mean of
these readings was taken as the pressure during the measurement.
The variations in the pressure most times amounted only to some
hundredth parts of a kilogram. If by accident (what happened very

401

seldom) the variation in pressure was greater, the corresponding
measurement was not used.
If 2/ is the length of the whole water-column that is in motion,
the double shift to be expected is
1 i du
SUL — —~—— — Ju?
(DG
: : Wimax: ee (EL)
aavs
expressed in parts of the distance between two fringes, Wmax is the
axial velocity, while u, 2, and c are respectively the index of
refraction of the water, the wavelength of the light used, and c the
velocity of light in vacuo.
For / has been taken 302,0 em ; that is the distance between corres-
ponding points of contact of the dotted lines with the axis in the head-

€

pieces at the ends of the tube (see fig. 3). [f the current in the
tubes was governed by the laws of Porsrcunn for viscous fluids, the
maximum velocity would be equal to twice the mean velocity and
the distribution of the velocities over the transverse section would
be represented by a parabola. In our experiments however the
velocity of the water was more uniform; we are in the region of
the turbulent motion. From the axis of the tube towards the side
the velocity decreases much more slowly than in the case of a
parabolic distribution and finally only decreases very rapidly. In the
neighbourhood of the axis of the tube there is thus a considerable
region, where the velocity may be regarded as being constant, at
least more constant than in the case of a distribution of the velocities
according to Potsrui.Le. From numerous and very careful researches
of American engineers!) the ratio of the mean velocity to that
along the axis of the tube has been deduced. The result was always
found in the neighbourhood of 0,84, so that the mean velocity w,
becomes w, = 0,84 Max.

The mean velocity for a definite pressure was determined by
measuring the quantity of the fluid that streamed ont in a certain
time or rather the time (about half an hour) necessary to let stream
out 10 m*. By the latter method the determination was independent
of the excentricity of the scale division, which gives the volume
of the water that has passed through the watermeter. For the
pressures used between 1.95 and 2.40 kg/em* it was proved, that

1) Wims, HurBeL and Frenkett, Trans. Am. Soc. of Civ. Eng. Vol. 47. 1902.

Lawrence and Braunwortx ibid. Vol. 57. 1906.

Cf. also R. Bier. Heft 44 der Mitteilungen über Forschungsarbeiten heraus-
gegeben v. Ver. deutsch. Ing. 1907,

402

the connection between the mean velocity (the volume) and the
pressure could be represented by a parabolic curve. So it was
possible to reduce observations at a pressure p to a standard pressure
(for which 2,14 k.g.cm* was chosen) by multiplying the shift of
2.14

the interference fringe, measured at the pressure p, by |
P

graphically by means of the curve.

Before relating the obtained results I shall give in extension an
arbitrary example of one of the 32 determinations of the change
of phase. The four cocks in Fig. 25 (first communication) will be
called A, B, C, D respectively.

Photo n°. 154 wavelength 4580 A.U.

Photo a. Photo b.

B, D open; A, C shut. A, C open; B, D shut.
Pressure on manometer. Pressure on manometer.
2.12 215
2.14 2.14
2.14 Deke
Daler 2.18
2.18 PAV
2.18 2.16
2.16 2.18

Mean: 2.16 2.16

Mean pressure during the experiment 2.16 k.g./em?.
We have mentioned already that the given pressures refer to the
times 0, 30", 60" ete.
Measurement of photo N°. 154 a. Readings with the Zeiss-compa-
rator in m.m.

on the interference fringes. on the fixed wire.
54.217 53.091 52.689
224 591 686
220 599 688
218 593 692
225 599 689
219 594 688
225 598 52.689
223 600
Mean: 54.221 53.596 thus middle: 53.908
52.689
Distance between 5, = 0.625 Distance from 1.219

the fringes the fixed wire

403

Measurement of photo N°. 154 6. Readings :
on the interference fringes. on the fixed wire.
53.675 53.037 52.264
675 O41 265
680 046 266
681 045 262
683 051 52.264
680 046
686 046
683 O44
Mean: 53.680 53.044 Thus middle: 53.359
52.264
Distance between J. = 0.636 IE ee from 1.095
the fringes : the fixed wire
0.625 :
Mean distance of the fringes 0.636 0.630

Shift of the fringes by the motion 1.219 — 1.095 = 0.124 or
reckoned in the right direction 0.630 — 0.124 = 0.506.
Thus shift in parts of the fringe distance
A= age == 0803" for pi 2.16" keen”.
630
thus A= 0,799) for: p= 2.14 -kg//em*.

The obtained results may be summarized in a table.

Shift of the interference fringes by reversing the direction of the
current.
p=214 kg/em?. w,=465em/sec. naz = 553.6 cm/sec.

Number of

ARIAN Ap, Ar JAPEN experiments
4500 0.786 0.825 0.826 + 0.007 6
4580 0.771 0.808 0.808 + 0.005 6
5461 0.637 0.660 0.656 + 0.005 q
6440 0.534 0.551 0.542 i
6870 0.500 0.513 0.511 + 0.007 10

Under Ap, and A7 are given the shifts calculated with the formula
with FrrsNer’s coefficient without the term of dispersion for
the value wins = 553.6 cm/sec. belonging to p= 2.14. Under Ag,
are found the observed shifts with the probable error in the final
reading. The number of experiments is given in the last column.

404

For the reading at 2 6443 no probable error is given as only one
reading was made for that colour. The agreement of the experiments
with the formula of Lorentz is evident.

In Fig. 5 I have represented graphically the results obtained. For
4 4500 and 2 4580 the theoretically and experimentally determined
points coincide. Perhaps it is interesting to give also the values of
FRESNEL’S coefficient «:

Zim AS. Er, Er exp
4500 0.443 0.464 0.465
4580 0.442 0.463 0.463
5461 0.439 0.454 0.451
6870 0.435 0.447 0.445
1 1 A du :
Here ep, =de >_> And eem. is found from
De u ud

the numbers in the fourth column of the table concerning the shift of

the interference fringes (under Lea) by multiplication by sh
WW. Wmaz.

A few words may be said concerning the determination of the mean
velocity w,— 465 em/sec., p = 214 k.g./em*?, whieh was important
for the interpretation of our observations. We have mentioned already
that there was a watermeter in the main tube. This meter (of the
WotrMann-type) ran very regularly, so that no vibrations were
transferred to the system of tubes. It was destined however for
large quantities. Its errors were known in rough approximation only.
If the meter was supposed to indicate accurately, we found taking
into consideration the above mentioned precaution (see p. 401) concern-
ing the reading at a complete rotation of the nands of the counting-
piece, », = 475 em/sec, p = 2.14 k.g./sec. With this value I found
a difference of about 2.1 °/, between the results of my experiments
and the formula of Lorentz. In order to investigate, whether this
difference might be aseribed to an error in the watermeter, [ decided
to put a more accurate measuring apparatus at the end of the system
of tubes to control the first watermeter. With extreme kindness
Mr. Ing. PeNNiK, Director of the Amsterdam waterworks put at
my disposal a calibrated so-called “Ster” meter, which begins to
indicate at a quantity of 10 L. per hour and which indicates accu-
rately for 30 L. and more per hour. If this “Ster” meter was con-
nected to the end of the system of tubes, while the principal cock
was quite open, the mechanical vibrations of the systems would

P. ZEEMAN: “ON FRESNEL’S COEFFICIENT FOR LIGHT OF DIFFERENT COLOURS” (2nd PART.)

Current
first
direction.

la A = 6870 p = 213 2a A= 4580 p = 2.16 3a A = 4580 p = 2.26

Current
opposite
direction,

ib A = 6870 p = 2.13 2b A= 4580 p = 2.16 3b 2 = 4580 p = 2,26
From aand b : A=0.522 A = 0.803 A=0:812

4 A = 6870 p= 221 5 A= 4500 p=2.30
A = 0.53 A = 0.86

Proceedings Royal Acad. Amsterdam, Vol. XVIII. HELIOTYPIE, VAN LEER, AMSTERDAM

405

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Proceedings Royal Acad. Amsterdam. Vol. XVIII

406

have been propagated from the “Stermeter” and have badly influenced
the optical observations.

The only purpose however was to compare the indications of the
two meters. By two independent, quite corresponding measurements
on different days it was proved, that the large meter gave 10000 L.,
when the accurate “Ster” meter registrated 9810 L. only. This is
a difference of 1.9°/,. Now the error of the “Ster” meter itself
is about 0.2°/, as had been determined by direct measurement
of the volume transmitted to a large tank on the grounds of the
waterworks. Altogether, taking the error of 0.2°/, with the right
sign, the error in the indication of the large watermeter amounts
to 2.1°/,, We have seen already, that theory and experiment
agree extremely well, if we introduce this correction, which reduces
the values of w, from 475 e.m./sec. to 465 c.m./sec. for p= 2.14
k.g./e.m*.

The value of w, at p=2.1+ K.g./e.m.* may thus be regarded as
well established and the same may be said of the value of /, at least
within the limits of the accuracy of the final result. About the
factor 0.84 however some doubt may exist. Therefore it seems to
us interesting to show, that even if the absolute value of the Lorentz
dispersion-term might have been determined less accurately than has
been the case, there might have been drawn a conclusion about the
necessary existence of this term '). This conclusion is independent of
the values gwen to l and wac :

For, writing down equation (4) for two different colours with the
wavelengths A, and 2, we see, that J, maz, and c fall out by the
division. The ratio of the shifts 42, and A), becomes then according

to LORENTZ
(— 1 mee EE
A), u he u, dà, A,

A (jede BR
u u, da, J A,

and according to FRESNEL

1) I will still make one remark. If we wished to explain the difference of 5 0/,
between our observations and the formula of FresneL by an error in the factor
0,84, we should have to change this factor into 0,88 in order to obtain coin-
cidence of the experimental curve and that of Fresyer. But such a great inaccuracy
does by no means exist in that factor.

Eee ee ee (i)
A, 5
2 (a)
u) A,
0

Ay
Taking A, = 4500, 2,= 6870 we find from (6) am ag from

= =1,608, whereas the experiment (Table p. 403) gives P= 616.

Bar. 4, = 4580, A, = 6820 the ratios become respectively 1,542,
dipvo, 1,581.

So there is only a difference of 0,5 resp. 0,4°/, between the
formula of Lorentz and the experiments, but a difference of 2,2
resp. 2,0°/, between these and the formula of Fresnen. *)

Even if we had not succeeded in giving to /, pq, and the co-
efficient 0.84 very probable values, even then the result of our ex-
periments had been very favourable to equation (5).

(5)

Further we must mention, that the light beam was limited by
rings of tin-foil toa width of 11 m.m., whereas the glass plates allowed
a beam of 18 m.m. diameter to pass along the axis, the horizontal
„tubes through which the water flows being of an inner diameter of
40 m.m. By this precaution the optically effective change of the velo-
city over the section of the tube is diminished and this is also the
case with the broadening of the interference fringes caused by the
curving of the wavefronts by inequality of the velocities in them.

Sometimes (not always) there is a small change in the distance
between the interference fringes after reversing the direction of the

water current. It is easily proved, that, neglecting

G: quantities of the second order, we get a right result

by dividing the mean value of the distance between

the interference fringes before and after change of
the current in the shift of the fringes.

Let d, and 4, be the distances between the fringes
in the two cases and a, and a, the shifts of them
from the original position OO’. From the measure-

o dd
» 1 3 . .
Fig. 6. ments we find — or rather the double of this.
1 J;
a GEEL aps 5
We want to know —=-—. The difference between the first and the

1 8

second expression gives the error we make. Let us put

1) Our conclusion is conlirmed by a recent, more accurate series of observations.
[Note to the translation).

408

J, =d--—2
J,=0-+ a
where w represents a small quantity.
a, 4-4, ay Dn .
We calculate how much are differs from zero.
ao Or
i B 3 a, Ja, a —a,27 a SER
It is easily found that —— -- _—_ e=. —_, an
. 20 da 2d d 2d’

error of the second order of magnitude.

wv
In the example on p. 402 a is equal to , so that the change
€

100
in the distance between the fringes might be still 4 or 5 times
greater without making the error larger than 1 per thousand.

In the above cited paper') JAvMANN derives on p. 462 with his

N . El)
theory for the FresNer-coefficient the formula $ ———, where n
Nn
the index of refraction for very long waves and „ that for the
colour considered.

For water n,? = 80.0 and n?yq = 1.78, so that JAUMANN finds for
the Fresnet-coefficient of sodium light 0.488. This value does not
agree with the result of our experiments and these are so accurate,

that- we may say with security, that the theory of JAUMANN is in

filet

conflict with reality. There is still another point of disagreement
between experiment and this theory. The latter gives for decreasing
wavelength a decrease of the Fresnet-coefficient, while the experi-
ments (see p. 404) prove the contrary.

Resuming we may say, that we have repeated FResNEL’s experiment
with different colours and have proved the exactness of the FRESNEL
1 __À du ait Rab alone
eyeticient | ris sais: ae within the limits of the experimental

lend
errors. It is perhaps interesting to notice that the relative values of ez
for different colours have also been confirmed by these experiments,
because these relative values are independent of the effective
length of the moving watercolumn and of the exact value of a
numerical coefficient that was put equal to 0,84. So the measurements
from which the absolute value of the Fresne.-coefficient has been
derived, might be considered as an experimental determination of the
PatiO Wyay : 10, The Fizwav-effeet would from this point of view form
the fixed theoretical base, as it is an effect of the first order, quite
based on the ascertained fundamental equations of electrodynamics,

*) See the first part of this paper.

409

Physics. — “Jsothermals of diatomic substances and thew binary
mixtures. XV. Vapour pressures of oxygen and critical point
of oxygen and nitrogen”. By Prof. H. KAMERLINGH ONNEs,
C. Dorsman and G. Horst. Zrrata to Communication N°. 145%
from the Physical Laboratory at Leiden, Jan. 1914).

In the Proceedings of the Meeting of January 30, 1915 p. 952
table I is to be read:

TAB TE 15

| Vapour pressure of oxygen.

Beg coy ere ee eee We aarivatmn:
| issie | ner 9.096
| 149,25 | 123.84 | 12.506
138.95 | 134.14 21.328
138,92 | 134.17 21.342
135.96 137.13 24.528
130.64 | 14245 30.914
125.28 147.81 38.571
121.34 151.75 45.138
121.33 151.76 45.142
121.31 151.78 45.217
120.02 153.07 47.258
118.88 154.21 49.640
p. 953 in table IL:
iA BEE

| Critical point of oxygen.

| Ap = —118°.82 C. 7, = 154°.27K. Pp = 49.713 atm. |

(September 8, 1915).

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING

of Saturday September 25, 1915.
VoL. XVIII.

President: Prof. H. A. LORENTZ.
Secretary: Prof. P. ZEEMAN.

(Translated from: Verslag van de gewone vergadering der Wis- en
Natuurkundige Afdeeling van Zaterdag 25 September 1915, DI. XXIV).

CONTENTS.

P. ZEEMAN: “On the passage of light through the slit of a spectroscope”, p. 412.

G. A. F. MOLENGRAAFF: “On the occurrence of nodules of manganese in mesozoic deep-sea deposits
from Borneo, Timor, and Rotti, their significance and mode of formation”, p. 415. (With one plate).

JAN DE VRIES: “Bilinear congruences of twisted curves, which are determined by nets of cubic
surfaces”, p. 431.

Cus. H. VAN Os: “Associated points with respect to a complex of quadrics”. (Communicated by Prof.
JAN DE VRIES, p. 441.

F. E. C. SCHEFFER: “On the allotropy of the ammonium halides” I. (Communicated by Prof. A. F.
HOLLEMAN), p. 446.

H. KAMERLINGH ONNES, C. DORSMAN and G. HOLST: “Isothermals of di-atomic substances and their
binary mixtures. XVII. Preliminary measurements concerning the isothermal of hydrogen at
20° C. from 60 to 90 atmospheres”, p. 458.

H. KAMERLINGH ONNES, C. A. CROMMELIN and Miss E. I. SMID: “Isothermals of di-atomic substances
pa eet binary mixtures. XVIII. The isothermal of hydrogen at 20° C. from 60—100 atmospheres”,

C. ie CROMMELIN and Miss E. I. SMID: “Comparison of a pressure-balance of SCHÄFFER and
BUDENBERG with the open standard-gauge of the Leiden Physical Laboratory between 20 and
100 atmospheres, as a contribution to the theory of the pressure-balance”. (Communicated by
Prof. H. KAMERLINGH ONNES), p. 472. (With one plate).

W. H. KEESOM and H. KAMERLINGH ONNES: “The specific heat at low temperatures. II, Measurements
on the specific heat of copper between 14 and 90° K.”, p. 484.

H. KAMERLINGH ONNES and SOPHUS WEBER: “Further exper ments with liquid helium. O. On the
measurement of very low temperatures. XXV. The determination of the temperatures which
are obtained with liquid helium, especially in connection with measurements of the vapour-

ressure of helium”, p. 493.

H. KAMERLINGH ONNES: “Methods and apparatus used in the cryogenic laboratory. XVI. The
neon-cycle”, p. 507.

H. KAMERLINGH ONNES and C. A. CROMMELIN: “Isothermals of monatomic gases and of their
binary mixtures. XVII. Isothermals of neon and preliminary determinations concerning the
liquid condition of neon”, p. 515.

S. H. KOORDERS: “Sloanea javanica (Miquel) Sszyszylowicz, a remarkable tree growing wild in the
jungle of Depok, which is maintained as a nature reserve’. (Contribution to the Flora of Java,
part VIII). (Communicated by Prof. M. W. BEIJERINCK), p. 521.

A. F. C. WENT and A. A. L. RUTGERS: “On the influence of external conditions on the flowering
of Dendrobinm crumenatum Lindl”, p. 526.

A. H. SCHREINEMAKERS: “In-, mono- and divariant equilibria” II, p. 531.

. HAGA and F. M. JAEGER: On the Symmetry of the RONTGEN-patterns of Trigonal and Hexagonal
Crystals, and on Normal and Abnormal Diffraction-Images of birefringent Crystals in general”,
a: 542. (With 7 plates).

H. HAGA and F. M. JAEGER: “On the Symmetry of the RONTGEN-patterns of Rhombic Crystals”. I,

p. 559. With 4 plates).
K. BEER Jr. “The Physiology of the Air-bladder of Fishes”. III. (Communicated by Prof. MAX WEBER),
572

p. 572.
Erratum, p. 582.

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

412

Physics. — “On the passage of light through the slit of a spee-
troscope.” By Prof. P. Zeeman.

(Communicated in the meeting of June 26 1915).

Though the full resolving power of a spectroscope can be reached
with an infinitely narrow slit only, we can get a near approach to
it with a very narrow slit already.

This is evident, when with Scnusrer *) we introduce the so-called

: : : : F j4
“normal” width of the slit d defined by the relation d = 775’ Where

f is the focal distance of the collimator objective with the diameter
D and A the wavelength of the incident light. For an exceedingly
narrow slit the ‘purity’ ?) of the speetrum becomes equal to the
resolving power. For normal width the purity is only 1,4°/, below
its maximum value. With a slit of twice the normal width we get
about the double quantity of light, while the purity deviates 5,7°/,
only from the maximum value. More than four times the normal
width of the slit must never be taken, for then the purity of the
spectrum decreases rapidly, while even for an infinitely wide slit the
intensity of the light never exceeds four times the value obtainable
with normal width.

Resuming, we may conclude that for sufficiently intense sources

“ as : ae
of light a width of slit in the neighbourhood CD is the best. A nar-

rower slit causes loss of light without gain in resolving power and a
wider one already soon decreases the resolving power considerably. As
example I choose a collimator with a lens, for which D= 15 em.,
f=325 em, while 2 may be 5 X 10” cm. Then we have

ph
ad=— = 00027 mm:
4D

Some time ago*) I pointed out, that by very narrow slits the
observation of the polarized components of magnetically resolved
lines may be rendered very difficult. When gradually the slit was
made narrower, the (electric) vibrations that are perpendicular to
the length of the slit, are hardly transmitted at last.

It seems interesting to communicate some measurements concern-

A. Scuuster. The optics of the spectroscope Astrophys. Journ. 21, 197. 1905,

2) Scuusrer. Le. See also eg Zeeman. Researches in magneto-optics. p 7. London,
Macmillan, 1913.

) “On the polarisation impressed upon light by traversing the slit of a spec-
troscope and some errors resulting therefrom.’ These Proceedings p. 599. October 1912.

413

ing the width of slit necessary for the appearance of ‘the mentioned
polarisation phenomena. Then we can get an idea in how far we
must expect disturbances caused by the narrowness of the slit.

With the arrangement shown in Fig. 1 the relative decrease in
intensity of the horizontal vibrations may easily be measured.

Monochromatic green light falls upon a slit S, behind which a
calcite rhomb K is placed at such a distance that two adjacent images
of the slit are formed, one containing the vertical vibrations, the other
the horizontal ones. By means of a nicol N the intensity of the
two images may be made equal.

Fig. 1. Fig. 2.

Let (fig. 2) OP and OQ be the directions of the vibrations in the
two images. If the direction of vibration of the nicol is perpendi-
cular to PQ, the condition for equal intensities of the two images
will be tg. a= OP: OQ. The ratio of the intensities of the horizontal
and vertical vibrations is then given by tga.

A first experiment was made with a slit (of platinoid) from a
spectroscope with constant deviation of HrLeer.

The results are contained in the following table:

green light

width of slit

A Pae tang. a
0.010 ei
|
0.004 | 0.5
0.002 0.3
0.001 0.2

és

+14

The value of the width of the slit for tang. a=—= 1 is that for
which the first extinction of the horizontal vibrations becomes per-
ceptible.

A second series of observations has been made with a slit (also
of platinoid) belonging to the collimator of an echelon spectroscope
and for two different colours.

red light green light
RH be “ai itil (is
in mm. | tang 2 in mm, | tens @
0.0017 ! 0.0015 1
0.0015 0.7 0.0013 0.6
0.0013 0.5 0.0010 05
0.0010 0.3 0.0007 0.3
0.0005 0 0.0004 | 0

Interesting is the difference in absolute width at which for the
two slits the same phenomena occur. For, though the measurements
may not claim great accuracy, yet the different behaviour in the
two cases seems to be beyond doubt. Very probably the form of
the edges of the slit is here of much importance. The variation
with wavelength has the direction we should expect.

We also made some experiments with white light. When the slit
is gradually narrowed the image formed by the horizontal vibrations
becomes fainter and at the same time of bluish hue.

So we come to the result that with widths of slit often used
with spectroscopes in laboratories, polarisation phenomena are already

Pie
of some importance. The greater the ratio S— is taken, the less

D
these appearances will be noticed. So with the 75 feet spectrograph
of the Mount Wilson Solar observatory we surely shall not see anything
of the mentioned polarisation phenomena.

Recently a problem connected with the passage of light through
wu narrow slit has been treated theoretically by RArrriGH in a paper:
“On the Passage of waves through fine slits in thin opaque screens” *).
But as is observed by RarrrieH: “It may be well to emphasize
that the calculations of this paper relate to an aperture in an infi-

1) RAYLEIGH. Proc. R. S. London. Vol 89. 194. 1914.

415

nitely thin perfectly conducting sereen. We could scarcely be sure
beforehand that the conditions are sufficiently satisfied even by a
scratch upon a silver deposit. The case of an ordinary spectroscope
slit is quite different. It seems that here the polarisation observed
with the finest practicable slits corresponds to that from the less
fine scratches on silver deposits”.

With tbe last words RayieieH refers to an observation by Fizrau,
who on scratching in a silver layer on glass perceived that the
transmitted light was polarized perpendicularly to the direction of
the scratch, if the width of the latter was 455 mm. If this width
however was estimated at z>4o> mm. the polarisation was in the
direction of the seratch, viz. the electric vibrations were chiefly
perpendicular to it. With spectroscope slits the latter case does not
occur.

It will be remembered that pv Bois and Ruprns') found with a
wire grating a point of invetsion for ultra-red light, just as Fizwav
observed with scratches.

Geology. — “On the occurrence of nodules of manganese in
mesozoic deep-sea deposits from Borneo, Timor, and Rotti,
their significance and mode of formation”. By Prof. G. A.
F. MOrENGRAAFF.

(Communicated in the meeting of January 30, 1915).

The question whether deep-sea deposits, and more especially
oceanic abysmal deposits, of earlier geological ages, take part in
more or less appreciable degree in the formation of the existing
continental masses, may be considered of prime importance for the
solution of several geological problems. If answered in the affirma-
tive, the conclusion at once follows that movements of the earth’s
crust must have taken place of an amplitude, sufficiently great, to
bring deposits formed at a depth of 5000 metres or more, above
the surface of the sea.

Some twenty years ago the opinion prevailed, that true abysmal
deposits of former geological ages, had nowhere been proved, with
certainty, to exist in the continental areas. It must be admitted that
at that time, deseriptions of occurrences of such abysmal deposits
were scanty and far from convincing. This may have been partly
caused by the fact, that fossil deep-sea deposits are not conspicuous

1) H. pu Bois and H. Rusens. Ber. Berl. Akademie 1129, 1892,

416

as such, and that the organisms they contain, being only clearly
visible with the aid of a strong pocket lens, or a microscope, are
easily overlooked.

At all events, Murray and Renarp, in their classical treatise on
recent deep-sea deposits, were very sceptical with regard to the
question whether these play a role of any importance in the
structure of the continents, as can clearly be proved by the following
quotations : “With some doubtful exceptions it has been impossible
to recognise in the rocks of the continents formations identical with
these (i. e. the recent) pelagic deposits”, *) and “It seems doubtful if
the deposits of the abysmal areas have in the past taken any part
in the formation of the existing continental masses”. *)

Later, it must be admitted, strong proofs have been given ®) of
the deep-sea character of certain red shales with radiolaria, and
certain cherts and hornstones with radiolaria, the former being the
fossil equivalents of the recent red clay, the latter, the typical
radiolarites, being the fossil equivalents of the recent radiolarian ooze.
And it also has been pointed out that their occurrences in the
continents, must be found strictly limited to folded mountain ranges of
recent and earlier ages i. e. to the movable or geosynelinal areas
of the earth’s crust’) and cannot be expected to occur in the original
stable or continental masses i. e. the “aires continentales” in the
sense of Have. Although it has thus been distinctly proved that the
occurrences of deep-sea deposits of earlier ages in the continental
masses cannot be regarded as “some doubtful exceptions” yet, as
is clearly reflected in the most modern handbooks of geology, the
doubt regarding their importance has not yet been dispelled.

One of the most prominent American geologists recently in a
study on the testimony of the deep-sea deposits *) strongly supports
the view held by Murray and Renarp in 1891.

It is evident that in proportion to the strength of the arguments

1) Report on the scientific results of the voyage of H. M. S. Challenger. J.
Murray and A. F. Renarp. Deep-sea deposits, p 189, London 1891.

2) Ibidem, Introduction p. XXIX,

8) See i. a. G. A. F. Motencraarr. Geological explorations in Central Borneo
p. 91 and aon pp. 439—442. Leiden 1900 and G. Sretmann. Geol. Beobachtungen
in den Alpen. 2. Die Scuarpr’sche Ueberfaltungstheorie und die geologische Bedeu-
tung der meene und der ophiolitischen Massengesteine. Berichte d. naturfor.
Ges. zu Freiburg XVI, p. 33, 1905.

4) G. A. F. Moreneraarr. On oceanic deep-sea deposits of Central-Borneo. Proc.
of the Royal Academy of Sciences, Amsterdam XII, p. 141. Amsterdam. 1909.

5) T C. Cuamperuin. Diastrophism and the formative processes. V. The testimony
of the deep-sea deposits. Journal of Geology XXII p. 137, 1914.

417

afforded for the identity between a// the characteristics of the rocks
which are maintained to be the fossil equivalents of the recent
deep-sea deposits and of those latter deposits themselves the probabi-
lity must increase of this equivalency being generally accepted. Up
to the present it must be admitted, notwithstanding the almost
absolute similarity, which has been proved to exist between recent
radiolarian ooze, and triassic and jurassic radiolarites from some
Alpine localities, from Borneo, and some other islands in the East
Indian archipelago, one tmportant and remarkable characteristic of
recent abysmal deposits, i.e. the concentration of oxides of mangunese
in nodules has hitherto never been observed in fossil deep-sea
deposits forming part of continental areas *).

To what extent, and in which way manganese nodules are

characteristic of abysmal deposits?

The accumulation of oxide of manganese or shortly of manganese
in recent deep-sea deposits is very striking; almost without exception
manganese *) is found in all deep-sea deposits. Coneretions of man-
ganese of various dimensions are especially abundant in true abysmal
deposits, i.e. the red clay and the radiolarian ooze.

Murray *) in his latest book on deep-sea deposits remarks: ‘The

oxydes of iron and manganese... in certain abysmal regions of the
ocean... form concretions of larger or smaller size, which are

among the most striking characteristics of the oceanic red clay.”
The question arises, whether, and to what extent, nodules of
manganese must be considered characteristic exclusively of abysmal
deposits; do they occur in such deposits on/y or also elsewhere?
In the report of the Challenger-expedition, and in the memoir of
Murray and Horr *) quoted above it is reported that such nodules
of manganese have been dredged from shallow depths, and that they
have been found to occur there even in abundance, in some places,

t) Pumper says about this while treating the probability of the occurrence of
deep-sea deposits in former geological formations: “Auck sind meinens Wissens
die für recente Tiefseeablagerungen so charakteristischen Manganknollen . . .
bisher noch aus keiner Formation bekannt geworden.’ KE. Pumper. Ueber das
Problem der Schichtung und über Schichtbildung am Boden der heutigen Meere.
Zeitschr. d. deutschen geol. Ges. LX, p. 356, 1908.

2) T. Murray and A. F. Renarp say: “Rarely can a large sample of any mud,
clay or ooze be examined with care without traces of the oxides of this metal
being discovered, either as coatings or minute grains.”

8) J. Murray and J. Hsorr. The depths of the ocean, p. 155, Londen 1912,

4) Ic. p. 157.

418

where voleanie material forms a large proportion of the constituents
of the deposit on the bottom of the sea.

In the Kara-sea, highly ferruginous nodules of manganese have
been brought to the surface from terrigenous muds, at a moderate
depth by the Netherlands Arctic expedition in the years 1882/83.

During the Siboga-expedition, Weener, in the deep-sea basins of
the Netherlands East-Indian archipelago, has found manganese
nodules on one spot only between the islands of Letti and Timor, at
a depth of 1224 metres, in mud containing a strong proportion of
terrigenous material, being in no way a true pelagic deposit; man-
ganese forming an incrustation on a fragment of dead coral, has
moreover been observed in a sample dredged from a depth of 1633
metres, between the islands of Misol and Ceram. *)

As to the fossil occurrences, I have found in Upper-Triassie deposits,
on the eiland of Timor, roots of Crinoids which certainly did not
grow on the bottom of an ocean of abysmal depth, heavily incrus-
stated with a coating of concretionary manganese.

Nodules and concretions of manganese therefore are not charac-
teristic of abysmal deposits in this way, that from the occurrence
of such concretions in a certain deposit, one would be justified in
concluding that the deposit could be nothing else than an abysmal
deposit and could only have been formed on the bottom of a very
deep ocean. On the contrary, concretions of manganese have been
formed on the bottom of all oceans in varying depths when the
conditions for their formation were favourable.

Murray and Renard maintain — and I have no reason to diverge
from this opinion — that these favourable conditions are afforded
by the presence of basic volcanic material in an easily decomposable
form. As soon as this condition is fulfilled the possibility is realized
for the formation of concretions of manganese, but the chemical
process of their growth is a very slow one, as has been amply
proved by the researches of the Challenger-expedition. In shallow
seas, especially at small distances from the mainland, sediments derived
from land or from a planctonic and neritic fauna accumulate rapidly, so
rapidly indeed, that there is only a remote chance of finding by
dredging, concretions of manganese, which in the mud in odd places
grow very slowly. In abysmal seas far from land very different
conditions prevail, the rate of accumulation of sediment is an
extremely slow one there, the afflux of terrigenous material is
reduced almost to nil, whereas from the plankton only the siliceous

Ei Siboga-Expeditie I, M. Weger. Introduction et description de lexpédition,
p. 81 and p. 137. Leiden 1902,

Plate I.

G. A. F. MOLENGRAAFF. “On the occurrence of nodules of manganese in
mesozoic deep-sea deposits of Borneo, Timor and Rotti, their signifi-
cance and their mode of formation.”

Fig. 1. Manganese nodule in jurassic marl with chert-nodules and
radiolaria from Sua Lain, Island of Rotti. Original size.

Fig. 2. Manganese nodule in triassic deep-sea deposits, in the vicinity of the
mountain Somoholle, district Beboki, Island of Timor. Original size.

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

419

tests i.e. these of radiolaria and diatoms reach the bottom, the
caleareous test being dissolved by the cold water of the deep seas
with its high ratio of oxygenium and carbonic acid held in solution,
before they reach the bottom. The growth of the coneretions of
manganese, however, is not hampered in these depths; on the contrary
it even appears as if in abysmal depths in water of a temperature
very near the freezing point and containing much oxygenium in
solution, the conditions for the formation of concretions of oxydes of
manganese, are more favourable than in shallow seas, provided that
traces of volcanic material occur as a source of manganese from
whence the manganese could have been derived. Thus, concretions
of manganese, slow as they are in their process of formation, and
inconspicuous as they are in sediments in places where the rate of
accumulation is rapid, can become an important constituent where
the rate of accumulation of a deposit is extremely slow, as is the
case in the abysmal areas.

Consequently concretions of manganese are in this manner charac-
teristic of abysmal deposits that they may form an important per-
centage in proportion to other constituents exclusively in such deposits.

And from this it is easy to conclude that coneretions of manga-
nese are characteristic of abysmal deposits in the same manner as
the tests of radiolaria. The latter sink to the bottom of the ocean
from the plankton everywhere within the limits of their geographical
distribution, just as well near the mainland as far from the shore.
Near the land these tests, owing to their minuteness, however, dis-
appear being incorporated in enormous quantities of other chiefly
terrigenous material which there comes to deposition; far from land,
on the contrary, at the bottom of the very deep ocean-basins at
depths over 5000 metres, where calcareous tests sinking down are
dissolved before reaching the bottom of the ocean, these siliceous
tests, small as is their individual mass, may form a great, sometimes
a preponderating portion of whatsoever is deposited.

It is therefore quite justifiable to maintain, that radiolaria and
concretions of manganese, form part of the most characteristic con-
stituents of abysmal oceanic deposits, and further that nodules of
manganese containing radiolaria almost with certainty must have
been formed in the deeper portions of the ocean basins.

Localities where concretions of manganese have been found
in deep-sea deposits of mesozoic age.

Concretions of manganese have been discovered by the geological

420

expedition to the islands of the Timor group in 1910—1912 in
triassie and jurassic deep-sea deposits, on the Island of Timor, and
also well developed in similar jurassic deposits on the Island of Rotti,
and previously, (in 1894, and later) I had noticed them in abysmal
deposits of the precretaceous probably jurassic Danau formation,
occurring in West and East Borneo.

Rock specimens were collected by the undermentioned observers,
and their examination has afforded proof from which several dedue-
tions have been included in this paper.

a. In 1894 in Central Borneo by the author.

6. In 1898--1900 in the basin of the Mahakkam River by Prof. A.
W, NreuweNHurs.

c. In 1902 in the Long Keloh, a small branch of the Long Kelai,
which is one of the great tributaries of the Berau-stream in East-
Borneo, by Mr. van MAARSEVEEN, :

d. in 1911, on the island of Timor by the Netherlands Timor-
expedition led by the author,

e. in 1911 and 1912, on the island of Rotti, by Dr. H. A. BROUWER,
one of the members of the same expedition.

All the specimens collected with the exception only of these of
Central-Borneo are stored in the geological museum of the Technical
Highschool at Delft.

On the mode of occurrence of the manganese in the rocks.

In the rocks just mentioned the manganese has been concentrated
in various ways:

1. As grains, i.e. minute concretions, frequently only recognisable
as such under the microscope, occurring throughout the rock. This
form of concentration is very common in red shales, which are the
equivalent of recent red clays. These shales vary in colour from
brick red to chocolate brown, they invariably include a noticeable
proportion of silica, (in places a little lime) and, in varying quantities,
tests of radiolaria. The characteristic red colouration is due to the
presence of oxide of iron, and this tint deepens into chocolate brown
in proportion to the increase in the percentage of manganese,
entering into the composition of the rock.

This mode of accumulation is of almost general occurrence in
all deep-sea deposits containing much clay’), but is of less import-
i 1) In modern deep-sea deposits the bulk of the manganese is just as well con-
centrated in small grains, causing the brownish red and chocolate brown colour
of the deep sea silt, especially of the red-clay of the Pacifie and the Indian Ocean.
Compare J. Murray and A. F. Renarp le. p. 191, p. 341 and Pl. XXII fig. 1.

421

ance, and may even be wanting in siliceous deposits, i.e. the cherts
and hornstones, which are predominantly composed of tests of
radiolaria.

I have observed manganese accumulated as grains in the following
deep-sea rocks :

a. in red limeless siliceous clayshales with radioloria, probably
of jurassic age, which are the prevailing rocks in the entire area of
the Danau-formation of Central-Borneo, and in lesser quantities also
in the cherts, jaspers and hornstones, which occur interstratified
between the layers of the clayshales.

b. in red and brown, mostly limeless, siliceous clayshales of triassic
age in several localities spread over the island of Timor, and also
less abundant in the nodules and layers of chert and hornstone
accompanying these shales.

c. in siliceous limestones, marls') and more or less siliceous and
calcareous clayshales with radiolaria, as well as in the nodules and
layers of hornstone contained in those rocks of jurassic age which
occur very plentiful in a great portion of the island of Timor.

d. in jurassic deep-sea deposits on the island of Rotti*), being
identical which those just mentioned from Timor.

Probably the precipitation and accumulation of manganese is
always initiated by the formation of such grains and a gradual
transition can be observed between this mode of concentration and
others by which the ore is more strongly localized.

2. as nodules. Nodules of manganese are accumulations or rather
concretions. of larger size than grains, being either perfectly round,
or more irregular and nodular, but always well rounded‘). They

1) The strong proportion of lime contained in these rocks gives rise to the
question, whether the jurassic deep-sea deposits of Timor and Rotti, although
they are formed far from land and thus truly oceanic, might have been deposited
in water less deep than the sea, in which the entirely limeless precretaceous
deep-sea deposits of the Danau-formation of Central-Borneo have been formed
The author intends to discuss elsewhere the far-reaching problem, connected with
this question.

2) Possibly also triassie and cretaceous deposits are comprised within this series
of folded strata. Compare H. A. Brouwer. Voorloopig overzicht der geologie van
het eiland Rotti. Tijdschr Kon. Ned. Aardr. Genootsch 2, XXXI, p. 614, 1914,

3) As far as the shape is concerned, the nodules found in radiolarites of jurassic
age on tle island of Rotti, are in every respect similar to those which have been
dredged at great depths from the bottom of the ocean Compare J. Murray and
J. Hsort. The depths of the ocean p. 156: “The commonest form of the
manganese nodules is that of more or less rounded nodules . . . looking like
marbles at one place, like potatoes or like cricket balls at other places”.

422

are found both in the red deep-sea shale and in the hornstone and
chert with radiolaria (radiolarite).

As to their occurrence the following information may be given:

a. The author possesses from the island of Borneo a single,
mediumsized nodule, only collected by van MAARsEVEEN in chert
from the Danau-formation in the bed of the Long Keloh river in
Kast-Borneo.

6. On the island of Timor nodules of manganese have been
observed in several places in deep-sea deposits; a very beautiful
specimen (PI. I, fig. 2) was collected in clayshale with radiolaria,
probably of triassic age near the hill Somoholle in the Beboki-district,
about 720 metres above sea-level.

c. On the island of Rotti nodules of manganese were found in
several localities in siliceous limestones, marls, siliceous and calca-
reous clayshales with nodules and flat coucretions of chert all of
jurassic age, which are full of tests of radiolaria. Exceedingly well
preserved are the nodules of manganese in rocks from fatu Sua Lain’)
on the north coast of Rotti and the author refers to this locality
where in the following pages he describes the composition and the
mode of formation of these nodules. They are always macroscopic-
ally well demarcated from the enclosing rock and in consequence
of their greater resistance to weathering they gradually more and
more protude from the red shales, and white marls in which they
are found included, and thus often get detached from the rocks by
the process of weathering. Such detached nodules of manganese can be
‘collected in quantities on the beach near Sua Lain. Thus there is
evidently a great chance that these loose nodules may be incorporated
later on in younger deposits. VERBEEK, on the island of Rotti near
Bebalain, has found nodules of manganese in marls of plistocene
age. I have examined these nodules, and have found that they
contain radiolaria identical to those which occur in the nodules
found “in situ” in radiolarites.of jurassic age at different localities
on the island of Rotti. These nodules of Bebalain evidently have
not originated in the marls of plistocene age, but have been in-
corporated as such in the rock.

3. as slabs or flat concretions. The concretions of mangenese often,
are flat, and in this case more or less restricted to definite layers
of great horizontal extent; in this way true bedded manganese
deposits may originate.

!) Fatu = isolated rock or isolated group of rocks. R. D. M. VerBrex gives a
picture of the Fatu Sua Lain in his report on the geology of the Moluccas. Jaar-
boek van het Mijnwezen. 37. Wetensch. ged. p. 317 Batavia 1908.

423

Manganese accumulated in this manner has been found by the
author in more than one locality.

A good example of this mode of occurrence is given in a complex
of upper-triassic deep-sea deposits in the left slope of the valley of
the Noil Bisnain, near the track from Kapan to Fatu Naisusu
(commonly called the rock of Kapan) in Middle Timor. The ore-
bearing portion of this complex of strata is 25 metres thick, and
about 10 beds of manganese are found in it closely connected with
variegated, siliceous clayshales and cherts with radiolaria, the entire
complex being intercalated in strata containing limestones with tests
of Radiolaria and shells of Halobia. The beds of manganese vary in
thickness between 2 and 30 centimeters. Microscopical examination
reveals traces of tests of radiolaria in the ore as well as in the rock.

4. in thin films on fragments of rock formed by the infiltration
of manganese in cracks of the rock from which these fragments
were derived.

In this way manganese is found infiltrated in the cracks of all
the shales and in the majority of the cherts of the abysmal series
on the islands of Borneo, Timor, and Rotti.

The chemical composition of the nodules of manganese.

I am indebted to Prof. H. Ter Mevien in Delft for a chemical
analysis of a nodule of manganese taken from a marl bed with
concretions of hornstone, from Sua Lain mentioned previously.

The result of the analysis in as follows:

Nodule of manganese from Sua Lain °

SiO, 2.9)
Fe,O, + Al,0, 2.3

MnO, 57.7

MnO 10.5

CoO 0.3

BaO 17

CaO 5.6

Na,O dell

CO, small quantity

The substance loses 1.05°/, of its weight at a temperature of
125° ©. and 15.3°/, on roasting.
A similar analysis has been made by Mr. G. WrrrevreN of the

1) In the original Dutch edition of this paper erroneously the figure 2.09 has
been given for the percentage of SiQ,.

424

small nodules of manganese mentioned above, which have been
collected by VerBreK*) in plistocene marl near Bebalain on the island
of Rotti. The result of their analyses was as follows:

Nodule of manganese from Bebalain

SiO, 3.44
Al,O, =

FeO, 1.45
MnO, 62.06
MnO 6.03
Ba0 9.18
0) 8.86
= ane not determined

alkalis

Obviously there is a great similarity in chemical composition
between the concretions of manganese from Sua Lain and those of
Bebalain. Baryum figures highly in both the analyses. Comparing
these two analyses with 45 analyses*) made from concretions of
manganese dredged by the Challenger from recent deep-sea deposits,
the proportion of iron proves to be low in the mesozoiec nodules of
Rotti. In recent nodules of manganese from the deep-sea the propor-
tion of iron, determined as oxyde of iron, varies from 6.46 to 46.4.
The proportion of manganese determined as MnO, in these two
extreme cases proved to be 63.23 and 14.82 respectively.

On the relations between the concentration of manganese in the
form of grains and of nodules.

It is not an easy matter to study the manner in which the aecu-
mulation of manganese in recent deep-sea oozes takes place, because
in the process of dredging the samples from a great depth, the
sediment is agitated more or less and therefore the sample does
not show any more the original position and mutual arrangement
of the grains and the nodules of manganese in the mud or ooze
at the bottom of the ocean. As soon as, however, the deep-sea
ooze is cemented into rock as is the case with these deposits of
former geological ages the mutual arrangement of the grains and
nodules of manganese is no more modified, and can be studied under
the microscope in slides made of these rocks. These slides will show

‘) R. D. M. VERBEEK le. p. 393.
3) J. Murray and A. F. Renard lc. p. 464—487.

425

so to say the process of the accuinulation of the manganese in full
progress but fixed or petrified at a certain moment.

Rocks from certain localities on the island of Rotti, which proved
to be suitable for microscopical examination, have been studied by
the author, and therefore a few words on the mode of occurrence
of these rocks may serve as an introduction, before the results of
this study will be dealt with.

On the island of Rotti deep-sea deposits, both of triassie and of
jurassic age occur, but concretions of manganese in their original
position, have as yet only been found in sediments the jurassic age
of which has been determined in more than one locality. These
sedimentary rocks are characteristically exposed in the rocky
cliffs of Sua Lain near Termanoe situated on the north coast?) of
the island.

They are well stratified here, and the strata folded and tilted, but
not so disturbed, that the original sequence of the beds could not be
determined with certainty.

The bulk of this complex of strata is composed of true abysmal
deposits in which exclusively tests of radiolaria occur, but in the
same complex also limestones are found which contain both radio-
laria and belemnites of jurassic*) age. The geological age of these
deep-sea deposits bas thus been proved beyond doubt.

The deep-sea deposits are here represented by siliceous and slightly
calcareous red clay shales, which pass into reddish marls and lime-
stones in proportion as the content of lime in the rock increases,
the latter containing numerous concentrations of silica in nodules
grouped together in more or less distinct layers. The shales, marls,
limestones and cherts are completely studded with tests of radiolaria.
Manganese is concentrated irregularly in fairly equal proportions,
however, in the calcareous clay shale, in the siliceous limestone

1) H. A. Brouwer. l.c p. 614.

2) WicHMANN, who in his journey to the island of Rotti in the year 1889 visited
Sua Lain, reports as follows on the geological structure of this groups of rocks:
“Der Fels besteht aus einem wahrscheinlich tertiären Kalkstein, die sehr reich an
Foraminiferen, namentlich Globigerinen ist und ausserdem von zahlreichen Kalk-
spathlrümmern durchzogen wird.” (A. Wichmann, Tijdschr. Kon. Ned. Aardr.
Genootsch. 2, IX, p. 231, 1892). This statement is erroneous. VerBeeK has proved
that the rock is not filled by tests of Globigerina but of Radioloria and Hinpe takes
them to be of triassic age. (compare: R. D. M. Verperxk le. p. 317 and G. J.
Hinpe, ibid. p. 696) moreover, in the numerous samples, taken by Brouwer from
the strata of these rocks, no Globigerina, but exclusively Radiolaria are found, whereas
it follows from the Belemnites, occurring in the same complex of strata, that
these rocks cannot possibly be of tertiary age.”

426

and in the chert. Manganese is present in small grains and in
nodules, which are either spheroidal (PI. I, fig. 1) or possess various
irregular, often flat cake-like shapes, but are always rounded.

Microscopical examination shows that the ore is fonnd as black
dust all through the rock, and that if is, moreover, concentrated on
numerous spots in Jarger grains, which tend to cluster together. In
some spots these grains are so congregated together that with the
naked eye the presence of a concretion of pure manganese is sur-
mised, but the microscope reveals that in such a case the grains,
though very closely packed together and thus resembling a cloud,
still remain isolated from each other.

In other spots the accumulation is still more compact and a true
concretion or nodule is thus formed, composed exclusively of man-
ganese and tests of ‘radiolaria.

Surrounding such a nodule or concretion, there is generally a
concentration of the grains of ore, forming an opaque halo or border,
which however rapidly diminishes in density with increasing distance
from the nodule.

The larger and smaller nodules are more or less arranged and con-
nected together in layers, thus tending to form beds or flat deposits
of manganese. In recent deep-sea deposits flat concretions forming
a kind of cake or slab of ore are similarly found. *)

A great number of slides of nodules have been examined under
the microscope in order to determine whether, in the interior of
the nodulus, particles of minerals or remains of organisms were
present, that had acted as a centre or nucleus, around which the
ore had grown, thus. giving rise to a econcentrical structure of
the nodule around one or more nuclei. As a rule no nuclei and no
arrangement in concentric layers have been found within the nodules.
Sometimes the manganese is first deposited within the tests of
radiolaria, and the author has found cherts in which the accumu-
lation of manganese has remained strictly limited to the interior of
the tests of radiolaria. In some cases the nodules may grow from
such filled tests as centres, and thus polynucleal concretions may
be formed. This is, however, rather of rare occurrence, and as a
rule no nucleus whatever, and no concentric arrangement could be
detected in the fossil nodules’).

1) J. Murray and A. E. Renarp. lc. Pl. Ill fig. 3.

2) In this respect there is a difference between the fossil nodules of manganese
and those of the existing deep-seas, for the Jatter very often, although not always,
show a concentric arrangement around a nucleus as e.g. around a crystal of phil-
lipsite, a shark’s tooth or an otolith of a cetacean. It is clear that otoliths could

427

Polished slabs of nodules, examined in reflected light, in many
cases proved to be better fitted for microscopic study than slides,
the coherence in the nodulus being often not sufficient for the
preparation of thin slides.

In cases where slides of sufficient thinness could be made, the
effect was striking, the perforated tests of the radiolaria, which are
composed of silica, and are distinctly pellucid, contrasting strongly
with the completely opaque manganese both without and within.

On the mode of accumulation of manganese in the deep-sea ooze.

From the mutual relations between grains and nodules of manganese
in mesozoic deep-sea deposits and the pecularities of the occurrence
of radiolaria therein, deductions may be made regarding the mode
of accumulation of ore in deep-sea ooze.

Manganese is precipitated on numerous spots as minute grains in
the deep-sea ooze, which is a siliceous and somewhat argillaceous
colloid in which tests of radiolaria are found suspended. In some
places the precipitation is evidently more rapid than in others, and
thus grains of different size are formed, all of them floating in a
similar manner to the tests of radiolaria in the siliceous colloid. It
appears that by mutual attraction’) the grains pack together and
thus form stronger and stronger centra of attraction for other grains,
forming eventually clouds, which on closer packing together, are
gradually transformed into concretions or nodules, composed of pure ore.

During this process of gradual concentration of the ore into nodules,
the tests of radiolaria are surrounded by the ore, without being shifted
from their position, and finally are found in the nodules just at these
places where they had been floating, suspended in the ooze. As long
as the ooze remains viscous, a nodule once formed, continues to be
a centre of attraction and collecting more and more minute grains of

not be expected in jurassic deposits, but sharks’ teeth and remains of other animals
as e.g. belemnites could be expected to occur as nuclei in the jurassie nodules of
manganese This difference, certainly, is remarkable, and as yet cannot be explained,
but not tov much importance ought to be attached to it, according to the author’s
opinion, firstly because many nodules from recent deep-sea deposits in a similar manner
do not show a concentrical structure, and secondly because the fossil nodules,
which hitherto have been examined microscopically, come from three localities
only, not far distant from each other, all from the island of Rotti.

1) The existence of this attraction is deduced by the author from the observed
facts, without giving an explanation of its cause; a fair proportion of iron always
entering into the composition of the nodules of manganese it might be suggested
that magnetic forces could be the cause of tae mutual attraction of the small grains.

28
Proceedings Royal Acad. Amsterdam. Vol. XVIII.

428

ore, becomes surrounded by a kind of halo in which grains of
ore travelling slowly towards the focus of attraction, become more
numerous than at a certain distance from the growing nodule
beyond its sphere of influence, where the grains are found equally
distributed in the ooze. The grains, it may be safely admitted,
travel very slowly towards the larger nodules, and evidently the
position of the tests of radiolaria in the ooze is not altered by their
slow movement. The radiolaria are just as numerous and are spread
in the same irregular manner both without or within the nodules.

Although the mode of formation of the concretions by the close
packing together of grains of manganese fairly well explains the
observed facts, it is, however, not quite clear how finally concretions
are formed, composed of manganese and tests of radiolaria exclusively
without traces of the ooze being enclosed.

It might be supposed that in the ooze diffusion currents around the
growing nodules, carrying manganese in solution towards them are
stronger around grains which are larger, and that consequently the
latter grow faster, and by their growth may incorporate and absorb
the smaller ones, and finally by this process a concretion or nodule
may be formed. Also in this case the tests of radiolaria might be
surrounded and absorbed by the growing concretions without being
shifted from their original position, but it is not possible to explain
why in this case halos of higher concentration with minute grains
of manganese abundantly in suspension, should be found around the
larger grains.

Probably these two processes collaborate in the mode of formation of
the nodules, firstly growth by precipitation of manganese from con-
vergent diffusion currents and secondly growth by accumulation and
packing of preexisting minute grains ').

The result is the formation of a concretion with fairly well demar-
cated outlines, surrounded by a cloud of smaller grains rapidly
diminishing in density. The concretion itself is composed almost

1) In the discussion following on the reading of this paper Mr. Wicamann
remarked that according to his opinion, the nodules in deep-sea deposits are not
formed by anorganic processes, but by biochemical processes caused by bacteria
He drew the attention of the members to experiments made by Mr. BererINck,
who proved the existence of bacteria possessing the quality to precipitate manga-
nese as superoxyde from solutions of carbonate of manganese. The author admitted
the possibility of such biochemical processes as the cause of the accumulation of
manganese in deep-sea ooze, but he pointed out that hitherto the existence of
bacterial life in abysmal depths had not been proved. Compare M. W. BEIJERINGK.
Oxidation of mangano carbinate by microbes. Proc. of the section of sciences
of the Kon. Akad. der Wetensch. Amsterdam XVI I. p 397, 1914.

429

exclusively of manganese but as a rule *) contains numerous tests of
radiolaria, which in the nodules show a lack of any regular arrange-
ment just as is the case outside the nodules in the surrounding ooze.

The mutual relation between the accumulation of manganese
and of silica.

The study of fossil deep-sea deposits reveals that, before these
deposits had been converted into rock, the silica in the ooze has
been concentrated in the same manner as the manganese, with this
difference only, that the concretions of silica, as chert, or hornstone
have much greater dimensions, and are far more numerous than
those of manganese.

Silica just as well as manganese is accumulated in fossil deep-sea
deposits in concretions or nodules of manifold shapes, originally having
been formed in an ooze or colloid, which itself by cementation (petri-
fication) has been converted later into siliceous clayshale, marl or lime-
stone.*) The process of aggregation of the silica is, however, posterior
to that of the manganese. The silica, in concentrating, not only
envelops, and encloses, the tests of radiolaria which float suspended in
the ooze, but in the same way also the nodules of manganese. Both,
the tests of the radiolaria and the nodules of manganese, remain
in their places, and, being enveloped by the silica, are not shifted
from their original position.

The radiolarites (radiolarian rocks) from the island of Rotti thus
prove that in their origin and development the nodules of manganese
are absolutely independent of those formed of silica; they are just
as numerous within as without the nodules of hornstone, and frequently
one nodule of manganese is found enclosed partially by hornstone,
and partially by siliceous clayshale or marl. Radiolaria occur just
as plentiful and scattered in the same way in the nodules of man-
ganese, in the concretions of hornstone, and in the surrounding clay-
shale of marly clayshale.

It is further obvious that the two processes of the accumulation
of manganese and of silica are not only entirely independent of
each other, but are also not synchronous; in fact, the process, i.e.
1) On the island of Rotti the author has found several jurassic nodules of man-
ganese containing hardly any test of radiolaria.

*) According to the results of an analysis, for which I am indebted to Mr. J. pe
Vries, in a siliceous limestone with nodules both of manganese and hornstone,
the proportion of silica of the rock outside of the nodules of hornstone amounted
to 4.94°/,, notwithstanding obviously the bulk of the silica in this rock had been
concentrated into the nodules of hornstone.

28*

430

the accumulation of the manganese, must have reached its final
stage, before the second commenced. This is quite in harmony
with the testimony given by modern deep-sea deposits. Nodules of
manganese are found in abundance in the deep-sea oozes, but concre-
tions of silica e.g. as nodules of hornstone, have not yet been met
with. Obviously, in the recent deep-sea oozes (especially in the red
clay and the radiolarian ooze), the process of accumulation of man-
ganese partly has been completed, partly is still in full progress,
but the process of concentration of silica into hornstone, chert, jasper
ete. has not yet commenced.

It might be qnestioned, whether possibly the concentration of the
manganese and a fortiori of the silica, might have taken place after
the deep-sea deposits, by diastrophism, had been brought into the
position, where they take part now in the formation of mountain-
ranges. This question has to be answered in the negative; the con-
cretions of manganese and those of silica have been influenced by
the mountain-building processes precisely ‘in the same way as the
rocks in which they are found enclosed, and it is easy to prove
that before the mountain-making processes came into Operation they
had already been solidified, and had attained their full size.

It is only the last of the possible modes of accumulation mentioned
on p. 421—423 ie. the infiltration of manganese in the cracks of the
rocks, which according to the opinion of the author has taken place
entirely, or almost entirely after the deep-sea ooze had been solidified
into firm rock, and had been crushed more or less by pressure.

Iron and manganese are generally found together in cracks of
fossil deep-sea deposits, especially in cherts. In some places, as is
the case in West-Borneo, iron predominates, in other places, as in
East-Borneo, manganese prevails. In case of strong pressure the chert
is often converted into a crush breccia cemented by manganiferous
iron-ore. Frequently the chert is then found altered into white amorphous
silica, in which case beautiful rocks originate, being composed of a
mosaic of pure white angular fragments, cemented by chocolate-brown
films of iron-ore. *)

1) G. A. F. Moteneraarr, Geological explorations in Central-Borneo, p. 92, 1902.

431

Mathematics. — “Bilinear congruences of twisted curves, which
are determined by nets of cubic surfaces.” By Prof. Jan pr Vries.

(Communicated in the meeting of May 29, 1915)

1. The base-curves 0° of the pencils belonging to a general net
[®*] of cubic surfaces, form a bilinear congruence. For through an
arbitrary point passes one curve 9’, and the involution of the second
rank, which the net determines on an arbitrary straight line, has
one neutral pair, so that there is one @° for which that straight line
is bisecant.

The 27 base-points of the net are fundamental points of the
congruence. Any straight line / passing through one of those points
F is singular bisecant; for through any point of f passes a 9’, at
the same time containing /. As the points of support of the curves
resting on / form a parabolic involution, f may be called a parabolic
bisecant.

Let ¢ be a trisecant of a 9’; through an arbitrary point of ¢
passes one ®*, and this surface contains all the points of t. By the
remaining surfaces of the net, ¢ is intersected in the triplets of an
involution; consequently ¢ is a singular trisecant. The singular trise-
cants therefore form a congruence of rays; it 1s at the same time
the congruence of the straight lines lying on the surfaces of the net.

A curve 9° has 18 apparent nodes, is therefore of genus 10. The
cone of order eight 4°, projecting it out of one of the points /” has
therefore 11 double edges ¢’).

Any point F is a singular point for the congruence [4], conse-
quently vertex of a cone € formed by trisecants f. With 4° this cone
has, besides the 26 straight lines FF’ to the remaining fundamental
points, the 11 double edges of 4° in common. Consequently £ is a
cone of order six; the congruence [f| has therefore 27 singular
points of order sia.

The trisecants of a 0° form a ruled surface, on which 0° is an
elevenfold curve. With an arbitrary surface * this ruled surface
has moreover the 27 straight lines of #* in common; the complete
section is consequently a figure of order 126, and the ruled surface
in question has the order 42.

Let us now consider the axial ruled surface U, formed by the
rays of the congruence [tf] resting on a straight line a. With an
arbitrary e° it has first in common the 27 sextuple points /’; the

1) A curve ¢” wilh h apparent nodes is intersected in each of ils points by
h — (n—2) trisecants.

432

remaining intersections lie three by three on the 42 trisecants of 9’,
resting on a. From this it follows that U is a ruled surface of order
32. As an arbitrary point bears e/even straight lines ¢, a is elevenfold
straight line of U, and a plane passing through « contains more-
over 21 straight lines ¢. The singular trisecants form therefore a
congruence (11, 21).

In order to investigate whether the congruence |g’| possesses
other singular bisecants besides, we consider the surface 7, which
contains the points of support of the chords, which the curves 9°
send through a given point P. A straight line 7 passing through P,
is, in general, chord of one 9’, therefore contains two points of 7
lying outside P. One of those points of support comes in P, as soon
as 7 becomes chord of the @’, passing through P. The cone S* pro-
jecting this 9° out of P, is therefore the cone of contact of the
octuple point P and M is of order 10. The 11 straight lines t
passing through P are nodal edges of St* and at the same time
nodal lines of M'°. The complete section of these two surfaces
consists of the 11 double lines mentioned, the curve 9%, and the 27
straight lines P/F. From this it ensues that the straight lines f are
the only singular bisecants.

With an arbitrary og° °° has the points of support of the 18
chords in common, which the curve sends through /; the remaining
54 intersections lie in the points #’; consequently J/*® has nodes
in the 27 fundamental points.

2. If two surfaces ®* touch each other, the point of contact D
is node of their section d° and at the same time node of a surface
belonging to the net. The locus of D is a curve d**. In order to
find the Jocus of the nodal curves d°, we consider two pencils of
the net. Each surface of the first pencil has 72 points D in common
with d**, is therefore touched by 72 surfaces of the second pencil;
by this a correspondence (72,72) is determined between those pencils.
The intersections of homologous surfaces with a straight line / are
homologous points in a correspondence (216,216); and both peneils
produce therefore a figure of order 432. But the surface that the
pencils have in common has been assigned 72 times to itself; the
real product is therefore of order 216 only. From this it appears
that the nodal curves 6° form a: surface of order 216, 4".

An arbitrary v° can intersect this surface in the points F only;

consequently A*’® has the fundamental points as 72-fold points.

8. The pencils mentioned above are brought in a correspondence

433

(3,3), when each two surfaces, intersecting on a straight line /, are
considered as homologous. It is found then that the locus of the
curves 0°, resting on /, is a surface -/ of order nine, which has the
fundamental points as triple points.*)

Two straight lines are therefore intersected by nine curves v°.

The curves g°, intersecting a straight line f, form therefore a
surface of order six, with nodes /.

A plane passing through /, intersects 4’ moreover along a curve 2°,
the latter has in common with / the points of support of the curve ©”,
which has / as chord (nodal curve of A‘). In each of the remaining
points of intersection of / with 4° the plane is touched by curves og’.
The points, in which a plane p is touched by curves of the con-
gruence lie therefore in a curve g°. The latter is the curve of coin-
cidence of the nonuple involution which [9"| determines in ; this
involution possesses no exceptional points; each point belongs to
one group.

As each point of intersection of ¢
to an arbitrary straight line / indicates a curve 9°, which touches p
and rests on /, the curves 9’ touching y form a surface ®**. This
surface has moreover in common with p a curve gp“; as the latter
can only touch the curve °, there are 126 curves @°, osculating a
given plane.

If the curve g° is brought in connection with the surface U’,

* with a surface 4° belonging

belonging to a plane w, then it appears that two arbitrary planes
9

are touched by 324 curves 9’.

4. If the surfaces of a net [#°] have the straight line q in
common, the base-curves g° of the pencils form a bilinear congruence
with singular quadrisecant q. As a o° is cut by a surface ®, outside
q, in 20 points, the congruence has 20 fundamental points #.

Each point S of q is singular; the co’ curves 9° passing through
S form a monoid * belonging to the net, with nodal point in S.
In order to confirm this more specially we consider two pencils of
the net, and make them projective by associating any two surfaces,
which touch in S. The figure which they produce then consists of
the common fignre of the pencils and the monoid *.

If * is represented by central projection out of S on a plane
g, the images of the curves 9° form a pencil of curves gv’. The
image of the quadrisecant is triple base-point, the images of the five
trisecants ¢, which a e* sends moreover through S, are double base-
points. The remaining 20 base-points are the images of the points

1) A p® which does not intersect 7 will cut ..° only in the 27 points F.

434

F. The five straight lines ¢ lie, like g, entirely on 2’; they are
apparently singular trisecants. Each straight line ¢ is intersected by
the curves o° in JS, and in a pair of an involution.

Two monoids have the straight line q and a g° in common. Conse-
quently in general a curve of the congruence is determined by two
of its intersections with g. The sets of four points of support form
therefore an involution of the second rank. So there are on gq three
pairs of points, which each bear o' curves g°; in other words, the
net contains three binodal surfaces, of which the two nodes lie on
g. We may further observe that q is stationary tangent of six 9°
and bitangent of four @°.

Each trisecant ¢ of a g° is singular (§ 1); the straight lines ¢
form a congruence of order 8, with 20 singular points #. The
cone 37, with vertex #, which projects a 9°, has 8 double edges
and contains 19 straight lines FF’; from this it ensues that the
straight lines passing through / form a cone -°%, so that / appears
to be a singular point of order five.

in any plane passing through q lie 6 chords of a 9°, through any
point of g pass 8 chords. The straight lines resting on g and twice
on 0°, form therefore a ruled surface of order 14. As they belong
to the trisecants of the figure (q, 9“), the trisecants of g° must form
a ruled surface of order 28.

Let us now again consider the axial ruled surface 4, formed by
the trisecants resting on the straight line a. With a definite 9° U
has the 20 quintuple points / and 28 triplets of points of support
in common; from this it ensnes that 4 is of order 23. The singular
trisecants consequently form a congruence (8, 15).

5. The surface MH is here of order 9; it contains q and has 20
nodes F (§ 1). Its section with the cone, 3%’, which projects the 9°
laid through P, consists of that curve, 8 singular trisecants (which
are nodal lines for both surfaces) the 20 singular bisecants PF (each
with a parabolic involution of points of support) and moreover three
straight lines 6, which apparently must also be singular bisecants.
These straight lines we find moreover by paying attention to the
intersections of $7 with q; to them belong the four points, which
q has in common with the @* projected by that cone. If S is one
of the remaining three intersections the straight line PS belongs to
a ®* of the net, is consequently cut by that net in the pairs of an
involution and is therefore bisecant of oot curves 0°.

For a point S of g HZ consists of the monoid =* and a cone of
order six. For, a bisecant of a g° not laid through S is at the same

435

time bisecant of a ¢* belonging to 2%, consequently a singular
bisecant 6. The locus of the straight lines 6 drawn through S
forms therefore with =* the surface JI. An arbitrary plane
consequently contains six straight lines 6, and the singular bisecants
form a conqruence (3,6). The three rays b out of a point P lie in
the plane (Pq); the six rays in a plane 2 meet in the point (zg).

The curves 0° meeting a straight line / form again a surface A’.
On it g is triple straight line, for each monoid =* contains three
curves resting on / and meeting in S. Two surfaces 4 have besides
q the 9 curves 9° in common, resting in the two straight lines /.
The points / appear this time again to be triple.

In a plane p the congruence [g°] determines an octuple involution,
which possesses a singular point of order three (intersection S of q).
The curve of coincidence p° (§ 3) has now a node S.

As 4’ and ¢" have now, outside S, 48 points in common, the
curves 0°, which touch the plane y, form a surface ®**. On it ¢
is a 16-fold straight line; for the monoid that has an arbitrary point
of q as vertex, cuts g°‚ outside q, in 16 points. The plane p cuts
®** moreover along a curve g** with 12-fold point S. The curves
g?° and " have 24 intersections in S; as their remaining common
points must coincide in pairs, there are 96 curves g° osculating g.

The curve p° has with the surface ¥** (belonging to a plane
yp) 6 X 48 — 2 X 16 = 256 points in common outside q; there are
consequently 256 curves @* which touch two given planes.

6. If the surfaces ®* of a net have two non-intersecting straight
lines g and q’ in common, they determine a bilinear congruence of
twisted curves 0’, of genus four, for which g and q’ are singular
quadrisecants; it has 13 fundamental points F. The curves 9’ have
11 apparent nodes.

If the monoid +* containing the curves 0’, which intersect g in S,
is represented in the usual way, the system of those curves passes
into a pencil of curves p°‚ which has a triple base-point on g and
double base-points in the intersections of three other straight lines ¢
of the monoid; the remaining .base-points are the images of the
points /, and the intersections of the two straight lines 5*, which
may moreover be drawn on * through S (and which apparently
rest on q’). The straight lines 6* are singular bisecants (parabolic
bisecants), the straight lines ¢ are singular trisecants. The locus of
the singular bisecants 6* is a ruled surface of order four with nodal
lines q and q’.

Through an arbitrary point P pass six singular trisecants; they

436

are nodal lines of the surface 7° determined by P and nodal edges
of the cone £°, which projects the curve 9? laid through P. These
two surfaces have besides that @’ and the six straight lines ¢, more-
over the 13 parabolic bisecants PF and four singular bisecants b
in common. The straight lines 6 are found back if ®* is brought to
intersection with g and q’; on each of the singular quadrisecants
rest therefore two straight lines 5.

Each point of q or q’ bears a cone of order 5 (completing >?
into a surface 17°) formed by singular bisecants. The singular
bisecants consequently form two congruences (2,5).

The locus of the trisecants of the figure (g, q’, 97) consists of four
ruled surfaces, together forming a figure of order 42. The straight
lines intersecting g, q’ and eo’ apparently form a ruled surface 2°.
The bisecants of 9’ resting on q or on gq’ lie on a %* with quin-
tuple straight line. Consequently the trisecants ¢ of 9’? will form a
N20 (with sextuple curve 9’).

According to the method followed above (§§ 1, 4) we find now
that the singular trisecants t form a congruence (6, 10), possessing
in the 18 fundamental points / singular points of order six.

On two arbitrary straight lines nine curves of the congruence rest
now too. The surface 4° has two triple straight lines, q and q’. In
a plane p arises a septuple involution with a curve of coincidence
y* possessing “vo nodes, where the involution has singular points of
order three. The curves 9’ touching y, form a ®** with 14-fold
straight lines g and q’.

There are 70 curves 9’ osculating a plane vy, and 196 curves
touching two given planes.

7. If the surfaces ®* of a net have a conic o° in common they
determine a bilinear congruence of twisted curves 9’, of genus five.
Every 9’ rests in six points on the singular conic o°. The congruence
possesses consequently 15 fundamental points F.

In representing the monoid =*, containing the curves e’, which
intersect 6? in a point S, the system of those curves passes into a
pencil of curves p°. They have five nodes in the intersections of the
singular trisecants ¢, meeting in S; the remaining base-points are
the images of the 15 points F, and the intersection of the straight
line 6* of *, which forms with the 5 straight lines ¢ the set
of six straight lines passing through S. Apparently 4* is here also
a singular bisecant (parabolic bisecant).

The surface * belonging to a point P and the corresponding
cone £° have in common a g’, five singular trisecants ¢ (nodal lines

437

for both surfaces), the 15 parabolic bisecants PF and si singular
bisecants b.

For a point S of 6? H* consists of the monoid 2* and a cone
of order five formed by straight lines 6. Hence the singular bisecants
b form a congruence (6, 10).

Let us now consider the straight lines which intersect the figure
(07, 6?) thrice, consequently form together a figure of order 42. Any
point of 65° bears 10 chords of 9’; in the plane o of that conic
there are 6 of them, viz. the straight lines connecting the 6 inter-
sections of o? and ef with the point AR, which ge’ has moreover in
common with o. The chords of 9’ meeting 6? consequently form a
N°. The chords of 65° meeting 9’, form the plane pencil (2, 0).
Consequently the trisecants of 9’ form a .t”’.

In connection with this we easily find now that the singular
trisecants form a congruence (5,10) possessing 15 singular points £
of order four.

The surface A’ has now a triple conic, 6’, and 15 triple points
F. In a plane p [97] determines again a septuple involution with
two singular points of order three. In connection with this we find
for this congruence [97] the same characteristic number as for the
[o’| treated in § 6.

8. Passing on to congruences of twisted curves 9g", we suppose
in the first place, that the surfaces of [®*] have three non-inter-
secting straight lines qg,q',g" in common. They are then singular
quadrisecants of the congruence [9°]; consequently the curves g°
one) pass through six fundamental points #.

The curves «° intersecting g in S form again a monoid >*. They
are represented by a pencil (°), having a triple base-point on q and
double base-points in the intersections of two straight lines ¢ To
the base belong further the images of the points /’ and the intersections
of two straight lines 6* (singular bisecants).

(genus

The sixth straight line of 2%, passing through S, is component
part of a degenerate curve g°. It is the transversal d of gq’ and q"
passing through S; for through an arbitrary point of that transversal
pass oo! surfaces ¢* having d in common and therefore intersecting
moreover along a curve 6° (of genus one), which has g,q',q" as
trisecants. The planes (dq') and (dgq") each intersect 2* along one
of the straight lines 4%.

The ruled surface D* with directrices g,q,q" contains all the
straight lines d forming the second system of straight lines. With a
monoid >* D* has three straight lines d in common of which one

438

passes through S. Consequently there lie on * two curves d°,
which pass through S. The locus A of the curves d* has consequently
three nodal lines q,q',q"; its section with a 2% consists further of
three curves d°, is therefore of order 21. Hence A is a surface of
order seven.

The figures (d, d°) determine on q a correspondence (38,2); so there
lie on q five points D = (d, 0°). The locus of the points D is therefore
a twisted curve (D)°, intersecting each of the straight lines q, q', q"
five times.

Now D? and A’ have the three straight lines q and the curve
(Dy in common, consequently another figure of order two. This
figure must consist of two straight lines d, hence there is a figure
of [y"] consisting of two straight lines d and a curve d*. This curve
has q,q',q" as bisecants and intersects D? moreover in two points D.

Through an arbitrary point P pass five singular trisecants; they
are nodal lines of 77’ and 8*. These surfaces have moreover in
common the curve 9%, laid through P, the six parabolic bisecants

PF and three straight lines 6. The straight lines b are determined
by the points which the straight lines q outside the curve ef have

in common with the cone %*°; hence they are singular bisecants.

If P is supposed to be on gq, Jf is replaced by the figure com-
posed of &* and a cone (6)'. The singular bisecants form consequently
three congruences (1, 4).

The locus of the straight lines which intersect a figure (9°, q,q',¢')
thrice, consists of the hyperboloid (q q' q'), three ruled surfaces 2t*
with nodal lines q, g' and the ruled surface of the trisecants of @°;
this is therefore of order 16.

From this it is now deduced, in the way followed before, that
the singular trisecants form a congruence (5, 6) possessing six singular
points # of order three.

The surface 4’ has three triple straight lines q, q', q'. In a plane
the congruence [0°] determines a sextuple involution with three singular
points of order three, which are at the same time nodes of the curve of

coincidence p°. The curves «°, touching gy, form a ** with 12-fold

straight lines q, q', q". There are 48 curves 0°, osculating one plane,
and 144 curves touching two planes.

9. Let us now consider the case that all the surfaces of the net

{®*| have in common a conic 5? and a straight line g not inter-

secting it. Any two surfaces then determine a twisted curve 9,

NS
2

which rests in six points on v°, in four points on q. A third surface
intersects 9" moreover in eight points. The congruence [9°] possesses

’

439

therefore eight fundamental points F. The curves o° have eight
apparent nodes, they are consequently of genus two.

The monoid +* belonging to a point S of the singular quadri-
secant q contains a singular trisecant passing through S. From the
image of 2° it appears that the remaining four straight lines of Y*
passing through S are singular bisecants b*.

The curves g° intersecting the singular conic 6? in a point S*
also form a monoid =*. These curves are represented by a pencil
(g°), which has double base-points in the intersections of the four
singular trisecants t meeting in S*. The simple base-points are the
images of the 8 points /’ and the intersection of a singular bisecant b*.

The sixth straight line passing through S* must be component
part of a compound g°. lt must cut 6? and q, belongs therefore to
the plane pencil in the plane o of 6’, which has the point Q of q
as vertex.

Any ray d of that plane pencil is component part of a degenerate
o', for an arbitrary point of d determines a pencil (#*) of which
all figures pass through d, consequently have a curve g° in common
besides, which intersects o* four times, g three times, consequently
possesses four apparent nodes. To the surfaces ®* passing through
the figure (0°, g, d, d°) belongs the figure composed of the plane o and
the Ayperboloid D* passing through q and the points /’; this dege-
nerate figure apparently replaces the monoid belonging to Q. The
hyperboloid D? is the locus of the curves d°; its intersection d? on
6 contains the points D = (d, 0°); all curves d° pass through the
four intersections of d* with o.

From the consideration of the surfaces ZI and &*, which are
determined by a point P it follows readily that P bears five singular
bisecants 5. Four of these straight lines rest on 6’, the fifth on g.
Any point of o* or of g is the vertex of a cone of order four, formed
by straight lines 6. The singular bisecants consequently form two

congruences ; a congruence (1,4) with directrix g, a congruence (4,8)
with singular curve o°.

The singular trisecants ¢ form a congrüuence possessing eight sin-
gular points, /, of order three. The trisecants of a 9° form a ruled
surface '*. In connection with this we find that the straight lines
t determine a congruence (4,6).

As [o°] again intersects a plane p along a sextuple involution with
three singular points of order three, we find for the characteristic
numbers connected with it the same values as in § 8.

10. A net [%*], of which the figures have a cubic o* (or a

+40

degeneration of it) in common, determines a congruence of twisted
curves 0°, of genus three, intersecting the singular curve o° eight
times '). The congruence possesses accordingly ten fundamental
points F.

As o° has seven apparent nodes, 6°

is intersected in each of its
points S by three singular trisecants t. Using the image of the
monoid + belonging to S, we find that the remaining three straight
lines of 2? meeting in S are singular bisecants b*.

Through an arbitrary point P pass seven singular bisecants 5.
Each point of o* is vertex of a cone of order four formed by
straight lines 6. From this it ensnes that the singular bisecants form
a congruence (7,12).

The singular trisecants form a congruence (3,6) with ten singular
points, /’, of order three.

The characteristic numbers, connected with the surface 4’, have
the same values as with the congruence […°] already dealt with.

11. The surfaces of a net [ ®*], which have a plane curve 6? in
common, determine a congruence of twisted curves 9° of genus four,
which possesses twelve fundamental points F.

As o° has now six apparent nodes, each point S of the singular
curve o° bears two singular trisecants.

To the surfaces “* passing through a figure (0°, 9°) belongs a
figure consisting of the plane 5 of o* and a hyperboloid; 9° is there-
fore the complete section of a hyperboloid with a cubic surface.
In connection with this the curves 9° intersecting o* in a point S,
form a hyperboloid S*, passing through the points #. The surfaces
>? form a pencil?) with base-curve B*, which determines in 6 a
pencil of conics g*?. Any point of the plane o bears therefore a
jigure consisting of a 9° and the curve p*.

The section of o with the surface 4 belonging to the straight
line / consists of the nodal curve 6? and the conics 9° intersected
by 7; hence A is of order eight.

Two surfaces A° have the singular curve 60°, the curve #*, and

eight curves 9° in common.
a If 6 is replaced by a conic -2 and a straight line s intersecting it, we under-
stand easily that any 0% has five points in common with s°, and three points
with s.

2) The net [3] may be represented by the equation

aat + Alan + by? wv) + u (an Ter a) 0.

Through a point of 2,=0 passes the pencil for which 1+a+p=0. It
consists therefore of the plane z,=0, and the pencil a (be? — C°) — C° = 0,
with base-curve bz? =0, ca? 0.

441

The sextuple involution, which |g*] determines in a plane gy, has
three singular points S of order two lying in a straight line s and
(in the intersections of 3%) four singular points of order one, whieh
are completed into sets of six by the pairs of an involution lying on s.

Any trisecant ¢ of a g° is trisecant of oo* curves of the congruence
and in particular of a figure (¢*, 6"). The congruence of the singular
trisecants is therefore identical with the congruence of the chords
of gf, is consequently a (2, 6).

The cone projecting a 9° out of one of its points has in common
with 5? the 6 intersections of the two curves; the remaining 9 points
determine each a singular bisecant 0.

The surface J’ belonging to a point S of o* consists of S*, the
plane 5 (of which any straight line is singular bisecant) and a cone
(Db). Consequently the singular bisecants b form a congruence (9, 12).

A plane p contains a curve g° being the locus of the points of
contact of curves e°. As g* has 34 points in common with 4°,
outside 6°, the curves ¢° touching y form a **, which is moreover
intersected by p in a curve ¢**. As g° is intersected by an arbitrary
=? in 10 points, o® is decuple curve of *; so y?* has three
octuple points S. From this it ensues further that g° and g*‘, apart
from the points S, have 96 points in common, so that p is osculated
by 48 curves 0°.

As ¢* has outside 6? 140 points in common with 9 there are
140 curves e° touching two planes.

The bilinear congruences of twisted curves g° and gy‘, which are
determined by nets of cubic surfaces I have considered in commu-
nications published in volume XVII, p. 1250, in volume XVIII,
p. 43 and in vol. XVI, p. 7383 and 1186 of these Proceedings. The
congruence of twisted cubies determined by a [#*] was extensively
treated by Srvyvarrt (Bull. Acad. de Belgique, 1907, p. 470—514).

Mathematics. — “Associated points with respect to a complex of
quadrics.” By Crs. H. van Os. (Communicated by Professor
JAN DE VRIES).

(Communicated in the meeting of May 29, 1915).

Let a triply infinite linear system (complex) be given of quadries
®*, The surfaces passing through a point P form a net and have
moreover seven points @ in common. if we associate those points
to P we get a correspondence, which will be considered here.

449

§ 1. We first prove the proposition: Any straight line / joining
two associated points P and (QQ contains an involution of pairs
of associated points. Any pencil of the complex has one ®? in com-
mon with the net determined by P and Q, and intersects / there-
fore along an involution containing the pair of points P, Q. If two
pencils have one ®* in common (if they “intersect” as we shall say
for the sake of brevity) the associated involutions have moreover
one pair of points in common and so coincide. If the two pencils
do not intersect a third may be introduced intersecting each of them
and it may be seen that the involutions coincide in that case too.
All pencils therefore intersect / along the same involution, any pair
of points of it consequently determines an infinite number of pencils,
sets apart a net out of the complex, by which the proposition has
been proved.

§ 2. Let us determine the locus of the points P coinciding with
one of their associated points. For this purpose we determine the
number of those points lying on the section 9* of two #* of the
complex. The sets of eight associated points on of are cut out
on @° by the # of a pencil (®?) from the complex. Now a pencil
(®?) contains sixteen (®*), touching a twisted quartic of the first
kind; this is easily seen by making the curve to degenerate into a
quadrilateral, each of the sides of which touches then at two ®?,
while through each angle passes one ®?, which must be counted
twice.') The number of points lying on e* amounts therefore to 16,
their locus is therefore a surface of order four, A*.

§ 8. What is the locus of the points Q, if P describes a straight
line 7?.

Any © of the complex intersects / in two points P, and so con-
tains also the 14 points Q associated to them; the locus of these
points is therefore a curve of order seven, 9’. It has in common
with / the four intersections of {and A‘.

A plane V passing through / intersects 97 outside 7 moreover in
3 points Q, each associated to a point P of l. The 3 joining lines
PQ, which we shall indicate by g,, g, and g, contain each an
involution of associated points.

The locus of the points P of VV, for which one of the associated
points Q lies in V consists of these straight lines and of the section
c* of V with A“. Now this locus is the section of V with the surface

1) Vide ZBUTHEN, Lehrbuch der abzählenden Methoden der Geometrie,
Teubner 1914.

REVIEW OF THE THEORETICALLY PREDICTED SYMMETRY OF RONTGEN-PATTERNS OF UNIAXIAL CRYSTALS, FOR PLATES PARALLEL TO THE

BASAL FACE, AND TO THOSE OF THE FIRST AND SECOND PRISM.

I. Tetragonal System.

Symmetry of the

Seriesnumber Indic h Elements of Symmetry | Röntgenpaitern öntgenpattern Röntgenpattern « Representative
of the Class aeakton GELE in the | for a plate parallel to | for a plate parallel to | for a plate parallel to i ee
oe Symmetry: | Osei, considered Crystals ie p fooi: fe p final: : f p ‘11 a 9 | Crystalspecies :
9 | Tetragonal-bisphenoidal | A4 (also = A») A single quaternary axis | A single horizontal plane A single horizontal plane \No mineral known
of symmetry of symmetry |
10 ‚*Tetragonal-pyramidal Ay A single quaternary axis | A single horizontal plane A single horizontal plane | Wulfenite
= of symmetry of symmetry |
II | Tetragonal-scalenohe- Ay (also — A» 2 Aj’; A quaternary axis ; 2 >< 2| Two perpendic. planes of Two perpendic. planes of Urea; Potassium-
drical 2Sv" planes of symmetry | symmetry;the perpen-| symmetry; the perpen-| Aydrophosphate |
| dic. to the photograph. dic, to the photograph.
Í | plate is a binary axis plate is a binary axis
12 *Tetragonal-trapezohe- | Ay; 2Ay', 2 Ao” A quaternary axis; 2 <2) Two perpendie. planes of ‚Two perpendic. planes of, Nickelsulphate
drical | planes of symmetry | symmetry; the perpen- symmetry; the perpen- (6 H‚O)
| dic, to the photograph: dic. to the photograph.
plate is a binary axis, plate is a binary axis |
13 Tetragonal-bipyramidal A4; HS; C A single quaternary axis A single horizontal plate A single horizontal plane \ Scheelite; Ery-
Ë | of symmetry of symmetry thrite
14 Ditetragonal-pyramidal | Ay; 2Sy’; 2Sy" A quaternary axis;2><2 Two perpendic. planes of | Two perpendic. planes of Penta-Erythrite
planes of symmetry symmetry; the perpen-, symmetry; the perpen-
dic. to the photograph., dic. to the photograph.
| plate is a binary axis) plate is a binary axis |
15 Ditetragonal-bipyrami- ; 2A,"; HS; A quaternary axis; 2>< 2 | Two perpendic. planes of | Two perpendic. planes of |Rutile; Cassiterite;
dal KG planes of symmetry | symmetry ; the perpen-| symmetry; the perpen-| Potasstumferro-
dic. to the photograph.| dic. to the photograph. cyanide (mimetic)
plate is a binary axis| plate is a binary axis
Il. Trigonal System.
B Symmetry of the Symmetry of the Symmetry of the
er nee Indication of the Elements Oty SUITE Réntgenpattern | Kortenaer ROrlserbadern Representative
Of MIE Class zj : im tne or a plate parallel to | for a plate parallel to | for a plate parallel to i
of Symmetry: Crystal Symmetry; considered Crystals ps ie Pi Bi p Ei f pla ar Crystalspecies ;
{0001} : }1010} {1270}:
|
16 *Trigonal-pyramidal Az. A single ternary axis No symmetry at all | No symmetry at all | ST ete
= (3H20)
17 | Trigonal-rhombohe- A; (also = Ag); C A single ternary axis No symmetry at all No symmetry at all | Phenakite; Dolo-
| _ drical mite
18 *Trigonal-trapezohe- Ag; 3A, A ternary axis; three | A single vertical plane Theperpendic.totheplate Quarz, Cinnabar
| _ drical planes of symmetry of symmetry is a single binary axis |
19 | Trigonal-bipyramidal As; HS A single senary axis | A single horizontal plane A single horizontal plane No mineral known
A of symmetry of symmetry |
20 Ditrigonal-pyramidal | Aj; 3Sv A single ternary axis | A single vertical plane | The perpendic.totheplate) Zurmaline
| = of symmetry is a single binary axis
21 Ditrigonal-scalenohe- | A, (also = Ag); 3 Av; A single ternary axis | A single vertical plane The perpendic. to the plate! Calcite
drical 3sv5 CG | |_ of symmetry is a single binary axis |
22 Ditrigonal-bipyramidal | As; 3A,; HS; 3Sv A senary axis; and 2><3 | Two perpendic. planes of | Two perpendic. planes of {No mineral known
| planes of symmetry symmetry; the perpen- symmetry ; the perpen- |
| | dic. to the photograph. dic. to the photograph.
| plate is a binary axis, plate is a binary axis
Ill. Hexagonal System.
23 |*Hexagonal-pyramidal As ‚A single senary axis A single horizontal plane A single horizontal plane, Nephelite
of symmetry ‚_of symmetry | |
24 \"Hexagonal-trapezohe- Ag; 3A2; 3 Ag’ A senary axis and 2 >< 3 | Two perpendic. planes of | Two perpendic. planes of | Antimonylbarium-|
drical | planes of symmetry symmetry; the perpen-| symmetry; the perpen-| tartrate + Pot-
| | dic. to the photograph.| dic. to thephotograph.| assiumnitrate
| plate is a binary axis| plate is a binary axis
25 Hexagonal-bipyramidal | Ag; HS; C A single senary axis A single horizontal plane | A single horizontal plane | Apatite
of symmetry of symmetry
26 Dihexagonal-pyramidal | Ag; 3Sy; 3Sv | A senary axis and 2><3 | Two perpendic. planes of | Two perpendic, planes of | Zincite; Wurtsite
| planes ot symmetry symmetry; the perpen-| symmetry; the perpen-
| dic. to the photograph.| dic. to the photograph.
| plate is a binary axis) plate is a binary azis
27 Dihexagonal-bipyrami- | Ag; 3A.; 3A2'; HS; | A senary axis and 2><3 | Two perpendic. planes of | Two perpendic. planes of | Beryl
dal 3Sv; 3Sv'; C planes of symmetry | symmetry; the perpen-| symmetry; the perpen-
| | dic. to the photograph.| dic to the photograph. |
plate is a binary axis} plate is a binary axis!

It may be generally remarked here, that planes of symmetry perpendicular to the photographic plate, will be manifested in the Röntgenpattern by their
resp. intersections with the plane of the photographic plate; and that in the case, where the perpendicular to the plate corresponds to the direction ofa binary
axis, this will appear in the pattern, as if a symmetry-centre in the photo were present. Binary axes in a plane parallel to that of the photographic plate are
of course not revealed in the diffraction-pattern.

N.B. The symmetry-elements of the Crystals are indicated as follows: An

=symmetry-axis of the first order, with a period of a An =symmetry-axis of the
second order (axis of composed symmetry) of the period É

n
and planes are discerned by accents; C — centre of symmetry. The optical axis is always supposed to be vertical; the cristallographical principal axis of
the same direction is discerned as the c-axis. In the case of the trigonal crystals, the symbols of Bravais are used; in the case of hexagonal and trigonal
crystals both, the direction of the face (1010) is supposed to be parallel to that of (100) in the tetragonal crystals, and just so that of (1210) parallel to
that of (010) in the case of tetragonal forms. In some trigonal crystals, the plates were cut parallel to (0110) and (2110), what does not involve any
appreciable difference for the considered problem, but makes it necessary to compare more directly the corresponding patterns with those obtained from

tetragonal crystals cut parallel to (110) and (110). The symmetry-classes indicated by * are those, whose crystals can appear in enantiomorphous forms.
(Enantiomorphism).

; HS =a horizontal plane of symmetry; Sv = vertical plane of symmetry; unequivalent axes

443

of the points Q, which are associated to the points P of V, this is
consequently a surface of order seven, ®'.

This order is also easily found from the number of intersections
with a ef of the complex; the latter intersects V in 4 points P,
contains, therefore 28 points Q, associated to it.

The joining lines of associated points apparently form a con-
eruence (7,3).

§ 4. If the straight line / is one of the straight lines PQ, con-
sidered in $ 1, a ®* of the complex will intersect the straight line
/ in two associated points, consequently contain six points only,
which are associated to points of /. The locus of those points is
therefore a twisted cubic g°. The curve 9’ has been replaced here
by the figure composed of / and the e* counted twice. The latter
intersects 7 in two of the four points which / has in common
with A‘; the two others are the double points of the involution
lying on PQ.

Let us bring through PQ a plane V, in which PQ stands there-
fore for the straight line g,. This plane intersects @* moreover in a
point & outside g,; the joining lines of R with the two points
on g, associated to it, must be the straight lines g, and g,. We
see therefore that the three intersections of g,, g, and g, are
mutually associated and that each plane V contains one set of three
associated points.

A o* of the complex passing through two associated points lying
on g,, intersects ®’ further in the 6 points associated to them and in
the 14 points associated to its two other intersections with V. As
the total number of intersections must be 28, the 6 points mentioned
first are nodes of ®’. The three @° belonging to g,, g, and g, are
therefore nodal curves of ®'.

A o* passing through the three intersections of g,, g, and g, inter-
sects ®’ further in the 5 points associated to them and in the 7 points
associated to the fourth intersection of e* and V. From this it easily
ensues that the five points mentioned are triple points of ®’.

$ 5. If P lies on A* one of the associated points coincides with
P. If R is one of the others the locus of R may be inquired into.

A o* of the complex intersects A* in 16 points, contains therefore
the 16 > 6 — 96 points FR associated to them; that locus is con-
sequently a surface of order 24, A**.

A‘ and A** intersect in a curve of order 96; it will, however,
degenerate :

29
Proceedings Royal Acad. Amsterdam. Vol. XVIII.

444

- d.-in-het locus of the points P, coinciding with two of the points
associated to them. A* and 4** touch each other along this curve.

2. in the locus of the points P, coinciding with one of their
associated ones while two more of the other points associated to
them coincide as well.

§ 6. In order to find the first of these curves we investigate the
locus of the points R, associated to the points of the section cf of
V with A‘.

A ®* of the complex intersects c* in 8 points, contains therefore
8 x 6=—48 points R, so that the locus of A is a curve of order
24, 07%.

The curve 0%! intersects V in 24 points, of which 2 lie on each
of the three straight lines g, and these are associated to the inter-
sections of g with the associated 9’; there remain 18, which must
lie on cf, and in each of which the point P coinciding already
with Q coincides now moreover with PR.

The locus wanted. is therefore a curve of order eighteen, 9*°.

§ 7. The @°* found just now intersects A‘ in 96 points; 36 of
them are lying in the just found intersections with c*, the 60 remain-
ing ones lie on A‘, coincide consequently with one of the associated
ones while two others coincide on cf. We see therefore that the
second of the curves mentioned in § 5 is really of order 60.

§ 8. The * of the complex passing through a point P of A‘,
have a common tangent ¢ in P. As they form a net two more points
are necessary to determine one of them.

We now take these points infinitely near P, and in such a way,
that they do not le with ¢ in one plane. The surface ®* thus
determined has two different tangent planes in P, must therefore
be a cone which has P as vertex. A‘ ús therefore nothing but the
locus of the vertices of the cones of the complex.

§ 9.- The involution /° considered here is a particular case of
an /* investigated by Prof. JAN pe Vries’). Three arbitrary pencils
(®*?) had been given there. Through a point P passes out of each of
them one P°; these 3 * will intersect moreover in 7 points outside
P. If we associate these to P we get the /* meant.

The /* considered above is acquired by taking the 3 pencils as
belonging to one and the same complex; in that case the three ®

1) These Proceedings volume XXI, p. 431.

445

passing through P determine a net and have the base-points of this
net in common. ,

For the more general /* the proposition of § 1 does not hold
good; consequently the joining lines of associated points form a
complex of rays instead of a congruence of rays.

The locus of the coincidences is now a surface of order 8; the
curve associated to a straight line / is of order 23, the surface
associated to a plane V is also of order 23. The question arises
how the results obtained above are connected with the properties
of those more general /°.

$ 10. If the 3 pencils (@°) lie in the same complex oc! pencils
(4?) may be introduced intersecting the three given pencils. If the ®*
of the complex are represented by the points of a tridimensional space,
the (A?) are represented by the generatrices of the ruled surface
having the images of the given ®* as directrices.

For a point P on the base-curve 2‘ of a (4°) the three ®* from
the given pencils passing through P belong to (4°), consequently
they have 2* in common. Jor such a point P the associated points
Q become therefore indefinite, if we start for the definition of the Z*
from the three pencils (#*) instead of directly from the complex.

In order to find the locus of P, we observe that the ®#° of the
three pencils (@* belonging to one and the same pencil (4?) are
projectively associated to each other, as immediately follows from
the representation mentioned. The base-curves 4‘ are consequently
sections of corresponding surfaces * out of two projectively
associated pencils; their locus is therefore a surface of order four, Q'.

§ 11. If starting from the more general /*, the given pencils ®? are
allowed to change in such a way that they come to lie in the same com-
plex, the occurrence of £2* will apparently cause various degenerations.

As the points associated to a point P of @* are indefinite they
may also be considered as coinciding with P, and consequently the
surface A* of the coincidences of the general /* will degenerate into
A‘ and 2%.

A straight line / intersects 2‘ in 4 points, intersects therefore
four 4‘, the 9?’ associated in the general case to / degenerates
consequently into the v7 found above and those four 2‘.

A plane V passing through / intersects °° in general in 15 points
outside /, of these 12 lie now on &*‘, which are associated by 3’s
to 4 points of /.

From the section of V with the associated surface ** the section

29*

446

with @* is therefore separated thrice, and as this section must
be counted once more as part of the section with A*, 7" has
degenerated into the surface & found above and in the four times
counted surface $'.

§ 12. On each of the straight lines PQ considered in § 1 lies
an involution of associated points, of which the double points are
situated on A‘. If these are associated to each other an involution
on A* is obtained. It has been deduced in a different way by Srorm
(Die Lehre von den geometrischen Verwandtschaften, Vol. III, p. 409).
He proves among others that in this way to each plane section c*
of A‘ a twisted curve 0° of order six and rank sixteen is associated.

Chemistry. — “On the allotropy of the ammonium halides I.”
By Dr. F. KE. C. Scuerrer. (Communicated by Prof. A. F.
HOLLEMAN).

(Communicated in the meeting of June 26, 1915).

1. /ntroduction. In the literature, in particular in the erystallogra-
phical literature, there are a number of papers to be found which lead
us to the conclusion that ammonium chloride and ammonium bromide
can occur in two different crystalline forms. Thus Sras *) found that
the transparent crystalline mass which deposits from the vapour of
subliming ammonium chloride, comes off from the wall when cocled,
and becomes opaque; he also states that the specifie weight of the
transparent and the opaque ammonium chloride are different. Though
Sras does not enter into further details about these phenomena, these
experiments would already be sufficient to suggest dimorphy here.
It is remarkable that Stas has evidently succeeded in cooling the
transparent ammonium chloride, which according to the above is
metastable at the ordinary temperature, to room temperature without
the conversion taking place, the more so because in the papers that
have appeared later no indications are to be found for this possi-
bility. Gossner*), who repeated Stas’ sublimation experiment, says
that generally conversion sets in already during the sublimation, and
the clear crystals can only be preserved for a short time.

LEHMANN®) was the first to conclude to dimorphy; he tried

!) Sras Untersuchungen über die Gesetze der chemischen Proportionen u. s. w.
übersetzt von Aronstetn. S. 55 (1867. ;

2) Gossner, Zeitschr. f. Kryst. 38 110 (1903).

8) LEHMANN, Zeitschr. f. Kryst. 10 321 (1885).

447

to prove this by crystallisation experiments of a mixture of ammo-
nium chloride, bromide, and iodide from aqueous solution. With a
suitable choice of the concentrations he succeeded on cooling in
obtaining a ecubie kind of erystal, which is transformed on further
cooling to the well-known skeletons, which the chloride and bromide
of ammonium exhibit at the ordinary temperature. It is evident that
only the appearance of a transformation can prove the dimorphy of
the halogen salts; for ammonium chloride and bromide have the
skeleton form at the ordinary temperature, whereas ammonium iodide
crystallizes into cubi. From a solution which contains a mixture of
the salts, both ecubi and skeletons can deposit. According to Leamann
the transformation must be explained in this way that mixed crystals
of the skeleton type are converted to cubic mixed crystals, in which
then at the same time interchange of substance with the solution
will take place. That in mixtures of the three salts two kinds of
mixed erystals occur, becomes also probable because of the very
close crystallographic resemblance of NH,Cl and NH,br, and from
the limited miscibility of NH,Cl and NH,I, which Gossyer ') observed.

According to Krickmeypr’*) NH,Cl and KCl show limited misci-
bility. Grorn*) expressed the supposition in virtue of this isodimorphy
that the crystalline form of the ammonium chloride, which can form
at higher temperature, would be isomorphous with KCl. Warracr)
points out in his treatise that if this supposition is correet, this would
lead to a very remarkable conclusion. As KCl belongs to the penta-
gonikositetrahedrical class of symmetry, this would also have to be
the case for the form of the ammonium chloride, which is meta-
stable at the ordinary temperature, and which I shall call the 8-form
in what follows. As, however, «-ammonium chloride also belongs to
the same class of symmetry, we should have two modifications with
the same crystallographical symmetry. Then we should be obliged
in my opinion to seek the difference between the two modifications
in a different structure of the molecule. Ammonium chloride and bro-
mide would then be very suitable examples for a test of Prof. Sirs’
theory of the allotropy ; according to this theory the phenomenon
of allotropy is namely generally explained by the assumption of
different kinds of molecules. If we consider that the above mentioned
experiments of LenMaNN render it probable that NH,Cl and NH,Br
can dissolve in NH,I with formation of cubic mixed crystals, and

1) Gossner, Zeitschr. f. Kryst. 40. 70 (1905).

2) Krickmeyer, Zeitschr. f. physik. Chemie. 21. 72 (1896).

3) Grotu, Chem. Kristall. [. 167.

4) Wattace, Centralblatt fiir Mineralogie u.s. w. 1910 S. 33,

448

that NH,I probably crystallizes pentagonikositetrahedrically, we should
arrive by the same train of reasoning as above at the conclusion
that « and g-ammonium chloride are both pentagonikositetrahedrical.

An entirely different indication for the existence of two modifi-
cations has been found by Prof. Zeeman and HooGeNsooM *). In the
research of the birefringency of the ammonium chloride cloud in
the electric field it appeared that this can have a different sign and
that also the reversal of sign of the refraction can be demonstrated.
These phenomena are explained by the assumption that the refraction
of positive and negative sign must be due resp. to the two ammo-
nium chloride modifications.

The above mentioned experiments prove that ammonium chloride
occurs in two modifications, but whether we have to do here with
enantiotropy or monotropy cannot be inferred from the above.

Wa ace’), however, has shown of late that NH,Cl and NH,br
are enantiotropic. From cooling curves he found the points of transi-
tion resp. at 159° and 109°. By the aid of Leamann’s Heating mi-
croscope he could directly observe the conversion; besides, dilato-
metric determinations furnished a confirmation of these results. For
NH,I no transition could be observed.

2. The question whether ammonium chloride shows allotropy
is of importance in connection with JoHNnson’s well-known experiment’),
according to which dry and somewhat moist ammonium chloride
have the same vapour pressure, though in the first case the partial
dissociation of the vapour in ammonia and hydrochloric acid does
not take place. Prof. ABgrec, in whose laboratory these experiments
were carried out, considered this fact as in contradiction with our
views on chemical equilibrium phenomena‘). In the discussion of
these experiments I proved before that JoHNson’s experiment leads
to the conclusion that the thermodynamic potentials of the solid
substance in dry and moist state are different*); I did not venture,
then, however, to give an explanation of this difference in thermo-
dynamic potential; especially as the occurrence of allotropy for
NH,Cl was not known to me then, and even though NH,Cl were
allotropie, the connection with JonNsoN’s experiment would require
a separate proof. Besides the possibility did not seem excluded

1) Zeeman and Hoocenpoom, These Proc. XIV, p. 558 and 786 XV, p. 178.

2) WALLACE |. c.

5) Jounson, Zeitschr. f physik. Chemie 61. 457. (1908)

4) ABEGG, Zeitschr f. physik. Chemie 61. 455 (1908).

®) Scuurrer, Dissertatie Amsterdam 1909. Zeitschr. f. physik. Chem. 72. 451. (1910).

449

to me that the entropy would undergo a modification through the
presence of some water as catalyst’). Before the publication of my
thesis for the doctorate Prof. Weescnmiper led by slightly different
considerations, had pointed out that the explanation of JoHNson’s
experiment might among others be found by the assumption of two
modifications of the ammonium chloride’). When now Wa .uacr’s
paper came under my notice, “and I learned from it that ammo-
nium chloride shows enantiotropy, I have come to the conelusion in
connection with the above that I could investigate the possibility of
the explanation which Prof. We«eGsoreIDeR considered the most pro-
bable. First of all J] have repeated WarLacE’s experiments for this
purpose; it appeared to me already at the first thermical determina-
tion that really NH,Cl is enantiotropic, but that the temperature of
transition had to deviate appreciably from the value given by
Warracr. In what follows 1 will begin with a description of the
experiments which I have carried out to define the point of transi-
tion of ammonium chloride as accurately as possible.

3. Thermic determination of the point of transition of ammo-
nium chloride.

A test tube with ammonium chloride crystals was heated in an
oil bath at about 200°, and then placed on cotton wool in a wider
tube. Observation of the temperature every half minute showed the
temperature to remain constant at about 174°. If I placed a tube at
room temperature in the oilbath of 200°, again in an air jacket,
then the temperature-time-curve appeared to exhibit a horizontal
part about 187°. Repetition of these experiments at lower tempera-
ture of the oil bath and with use of a second oil bath for the cooling
curves produced but little change in the temporary constancy of the
temperature. We must therefore deduce from these observations that
ammonium chloride possesses a point of transition between 174°
and 187°, which is found too low on cooling and too high on
heating, through the conversion of the modifications proceeding too
slowly at the point of transition to consume the supplied heat im-
mediately and to supply the removed heat immediately again. The
point of transition could not be defined more accurately in con-
sequence of this retardation of the conversion. These experiments,
however, lead me to the conclusion that the temperature of 159°,
which Warracm gives for the point of transition, is indeed, con-
siderably too low.

1) KonnstamM and ScrerFer, These Proc. XVII p. 789, (1910/11).

2) WeEGSCHEIDER, Zeitschr. f. physik. Chemie. 65. 97 (1908).

450

4. Vapour pressure measurements.

It follows from the observations of the vapour pressure of solid
ammonium chloride through extrapolation that the detection of the
transition temperature through observation of a discontinuity in the
vapour pressure line would require an exceedingly accurate pressure
measurement; the pressure at 180° only amounts to a few milli-
meters of mercury.

I have, therefore, tried to find a discontinuity in the three-phase
line SLG of the system NH,Cl— H‚O. For if we measure the vapour
pressures of the saturate solutions, the transition temperature will
remain unchanged, at least if the solid substance does not absorb
water in appreciable quantities. The vapour pressure measurements,
performed by means of Cailletet tube and air manometer according
to the well-known method, yielded no break which could be demon-
strated with certainty when the accuracy was about '/,, atm. As
I however want these vapour pressure measurements for the deter-
minations of § 5, I have inserted some of the found pressures in table 1.

TABLE 1.
| Pressure | Pressure
Temperature (in atmospheres) Temperature (in atmospheres)
|
160.0 3.25 185,1 | 5.4
164.9 3.6 189.1 5.8
Lule 4.1 194.5 6.4
176.9 4.6 198.9 6.9
|
182.5 5.1 199.6 | 7.0

5. Determinations of the solubility of ammonium chloride in water
at temperatures between 160° and 205°.

Another method for the determination of the transition point
is found in the determination of the discontinuity in the liquid
branch of the above mentioned three phase line SLG in the system
NH,CI— H,O. It is known that the liquid points can only be deter-
mined by approximation directly by means of fused tubes. In a
liquid point the system can namely exist entirely as liquid phase
which is just saturate with solid substance, the pressure being exactly
equal to that of the vapour which might coexist with the liquid
phase. If we observe in a tube the vanishing point of the erystals,
we determine the liquid point of a mixture indicated by the con-
centration of the liquid at the disappearance of the last crystals; we

451

must, therefore, then think the vapour as removed. It is clear tbat
the weighed quantities must then be corrected for the quantity of
substance which is found, in the vapour phase at the vanishing
point. For this, volume and pressure of the vapour must be known.
In the observation of the vanishing point the position of the meniscus
was for this purpose indicated on the tube by means of a writing-
diamond. The volume of the vapour, which practically consists
of water here, as the vapour pressure of NH,Cl is negligible at
all the observed temperatures, was then measured after the tube
had been cut open, with water from a burette. The pressure could
be read from table I and then the quantity of water in the vapour
could be calculated by the aid of the laws of Boyre and GarLussac.
On account of the deviation from the gas-laws this calculation is of
course not quite accurate, but the correction being small, this method
of determination is, after all, accurate enough for this purpose. It
is, of course, necessary to take the vapour space as small as possible.

First the tubes were filled with ammonium chloride and weighed ;
then from a burette, a definite quantity of distilled water was
added and brought into the tube through the capillary connecting
tube and stem by repeated heating and cooling. The tube (of com-
bustion glass) was then fused to in the lighting gas oxygen flame,
and weighed again. The determinations marked by crosses in table 2,
were carried out in tubes of from 25 to 30 grams; these were
weighed down to half milligrams. In later determinations the weight
of the tubes of about 15 grams was determined down to tenths of
milligrams. As the weighing of the tubes can easily give rise to
errors on account of the large surface, I think that less value is to
be attached to the determinations marked with crosses than to the
Others. In the second and third columns of table 2 the weighed
quantity of substance is given; the fourth column gives the observed
vanishing points, which were determined in an oilbath, electrically
heated by 220 Volts of alternate current, which was regulated by the
insertion of incandescent lamps. Uniformity of temperature in the
oilbath was ensured by rapid stirring. The fifth column gives the
quantities of water in the vapour at the vanishing point calculated
according to the above given method; the sixth column contains the
corrected quantity of water; the seventh the quantity of grams of
NH,Cl to 100 grams of water in the liquid saturate with gas and
solid substance. Finally the eighth column gives the value for — log x,
in which # represents the number of molecules of NH,Cl present in
one mol. of the mixture. Hence w is given by:

452

g
Myc Bn ll
9 100 E20
Myu,ci. Mp,o
in which g represents the values of the seventh column.
To set forth the discontinuity in the solubility line under vapour —

TABLE 2.

Vanishing points of the solid substance in NH,Cl—H,0 mixtures
MNH4CI = 53.50 ; MH,0 = 18.016.

Weight Weight | Weight | Grams of |

Nek a Sater iewat le NEE | —logx| 103 es
NH,Cl | H,0 in es (corr.) RDE 1b

1 1942.8 | 1539.8 | 162.9 1.0 1538.8 126.26 | 0.52534 2.2941
2 X | 1634.0 | 1271.0 | 165.65) 3.5 | 1267.5 128.91 0.51906 | 2.2797
3 2463.4 | 1853.7 | 169.5 0.9 1852.8 132.95 | 0.50973 2.2599
d 2293.8 | 1696.0 | 172.0 1.9 1694.1 135.40 | 0.50427 2.2472
5 2444.7 | 1748.0 | 176.1 1.7 1746.3 139.99 0.49437 2.2267
6 > | 1638.0 | 1163.5 Wi 4.0 1159.5 141.27 | 0.49169 | 2.2212
1 2087.1 | 1464.6 | 178.55) 3.0 1461.6 142.79 | 0.48855 2.2146
8 | 2189.5 | 1533.6 | 178.95 Sal 1530.5 143.06 | 0.48799 | 2.2126
9 X | 1399.0 9615 | 181.05) 3.5 958.0 146.03 | 0.48199 | 2.2024
TOR | 1424.0 973.0 | VESTE eto 968.5 147.03 | 0.4800° 2.1999
11 | 2479.5 | 1695.2 | 182.2 0.6 1694.6 146.32 | 0.48142 | 2.1968
12 xX | 1838.0 | 1246.0 | 183.05, 35 1242.5 147.95 | 0.47823 2.1928
13 X | 1917.5 | 1285.5 | 184.55) 3.5 1282.0 149,57 | 0.47505 2.1855
149 162125 | 1070.0 | 187.3 4.0 1066.0 152.1! | 0.47019 2.1725
15 | 2309.9 | 1520.2 1879] 12 | 15190 | 15207 | 0.47027 | 2.1697
16 X | 1525.0 | 998.5 | 189.1 50 993.5 153.50 | 0.46758 | 2.1640
17 2169.6 1409.5 190.15 2.0 1407.5 154.15 0.46638 2.1591
18 | 2336.1 | 1505 8 | Ere 1504.1 155.3! | 0.46424 2.1519
19 2510.4 | 1592.4 | 194.7 | 251 1589.7 157.9! 0.45952 | 2.138!
20 2421.1 | 1502.2 | 199.1 2.4 1499.8 161.48 | 0.45329 | 2.1182
21 2556.6 | 1574.0 200.5 2.1 1571.9 162.64 | 0.45119 2.1119
22 | 2246.2 | 1351.5 |205.0| 44 1347.1 166.74 | 0.44423 | 2.0920

453

pressure as clearly as possible 1 have not considered the solubility
as function of the temperature, but led by the theoretical expression
for the solubility curve in its simplest shape :

!
I have calculated the values of log » and = (eighth and ninth columns

of table 2), and drawn them as ordinate and abscissa in the graphical
representation (fig. 1). The temperature range being small here I

Fig. 1.

expected the above expression to account satisfactorily for the obser-
vations ; the observations below and those above the transition point
will present a straight line in this case. It appears from the graphi-
cal representation that really two straight lines can be drawn through
the observed points so that the deviations occur irregularly on either
side of these lines; at the same time in the tracing of these lines
the probably smaller accuracy of the first determinations has been
taken into account. I have calculated the values of @ and 5 for
both lines from the graphical representation; the equations of the
lines drawn are:

454

464.5

— loge = EN 0.5400 (below the transition point) and
327.8 an :

— loge = ae ae 0.2412 (above the transition point).

To get an idea of the extent of the experimental errors I have
compared the values of g calculated according to the above expres-
sions in table 3 with the values of the seventh column of table 2.
It will be clear from the last column of table 3 that the agreement

1 1629 | 126.15 126.26 +0.1!
2 X | 165.65 128.95 128.9! — 0,04
3 169.5 132.95 132.95 | 0.0
4 172.0 135.6! | 135.40 | —0.2!
5 176.1 140.03 139.99 | —0.04
6 X | 177.2 141,24 141.27 | +0.03
7 178.55 142.73 142.79 +0.08
8 178.95 143,17 | 143,08 —0.1!
9 X | 181.05 145.52 146.03 0.5!
10 X | 181.75 146.31 147.03 | 40.72
| 1822 | 146.82 146.32 —0.50
12 X | 183.05 147.78 147.98 | -+0.15
13 X | 18455 | 149.48 14957 | 40.09
14 X | 187.3 151.72 152.11 | +039
15 187.9 152.21 15207 | Os
16 > | 189.1 153.19 153.50 | 03
17 190.15 «154.06 154.15 40.09
180 ere | 155.33 155.31 | —0.02
19 | 194.7 | 17e 157.9! 0.09
20 199.1 161.52 | 161.48 —0.09
21 | 2005 | 16279 | 162.64 —0.06
22 205.0 166.54 166.74 0.20

455

is satisfactory; the maximum error in the value of g amounts to
5°/,,; for 14 of the 22 observations the deviation is even smaller
than 1°/,,.

When we calculate the point of intersection of the two lines, we
find 184.5° for the transition temperature. In my opinion this value
can only depart a few tenths of degrees from the real point os
transition.

In these experiments the transition point could not directly be
determined optically; I have thought only a few times that I could
detect a difference in the appearance of tbe crystals above and below
the transition point.

6. Thermic determination of the transition point of ammonium
chloride by means of catalysts.

After the determination of the transition point from the solubilities
in water I have resumed the original thermic determinations, and
I have tried to find catalysts which can annul the retardation in
the conversion at the point of transition. For this purpose I have
looked for substances which are liquid at the transition point, and
of which it could be expected that they react only little, if at all,
to ammonium chloride. The number of available substances is not
large; glycerine is very suitable for this purpose. A quantity of
ammonium chloride was uniformly moistened in a mortar with a
few drops of glycerine, and conveyed to a test tube. By placing
this in an oilbath above the point of transition and then in a bath

NH, Ct
Glycerine 183.7 - 104

190

185

180

Mammite 183.1- 184.3

185.

Without 173-977 Time in minutes.
180)

Fig. 2.

456

below this point | have determined a series of heating and cooling
curves, the best examples of which are represented in the graphical
representation (fig. 2). Descending we found 188°.7, rising 184.°7.
At the same time it will appear from the graphical representation
that the curves exhibit resp. a minintum and a maximum, which
points to this that the conversion at first proceeds only slowly, but
soon becomes constant so that the supplied resp. discharged heat
and the thermal effect of the conversion compensate each other.

A second couple of curves, for which mannite acts as catalyst,
presents only little more diverging values. Also the results of a few
more substances used are reported in table 4.

It is clear that the catalysts counteract the retardation in the
conversion of the solid substance in a more or less degree, and that
this is particularly the case for glycerine and mannite, where the
limits for the point of transition from 13° (see §3) to 1°, resp. 1°.6
have contracted. Moreover it appears that the retardation in the
conversion without catalysts is much smaller in case of heating than
in case of cooling. If, however, we imagine that also when catalysts
are used this difference in retardation continues relatively to exist,
then the point of transition would be calculated at 184.5° in the
experiment with glycerine, at 184.4° in that with mannite, in perfect
harmony with the experiments of § 5. :

7. Accordingly the experiments of § 5 and 6 yield the result
that the point of transition of ammonium chloride has been fixed
at 184.5° with a possible error of a few tenths of a degree. The
value given by Warrace (see § 1) is therefore more than 25° too low.

8. Demonstration of the allotropy of ammonium chloride. The —
transition from the g- into the «-form cannot be demonstrated by
crystallisation of an aqueous solution under atmospheric pressure,

457

as the transition point lies too far above the boiling point, so that
thie B-crystals cannot be obtained metastable from these solutions
either. I have, therefore, tried to make the transition suitable
for demonstration by crystallisation from another solvent. The ex-
periments of § 6 led me to surmise that glycerine would be suitable
for this. If on an object glass we evaporise a solution saturated at
the ordinary temperature to initial crystallisation, and if then we
place the object glass under the microscope, we can clearly observe
the cubi deposited in the heat. After some time a transformation
then takes place, which propagates through the solid mass, and at
the same time we see crystal skeletons of the known shape appear
from the cubi. [ have been able to demonstrate this transition by
means of microscopic projection at the latest Physical and Medical
Congress. The demonstration is still easier to carry out with ammonium
bromide, as the point of transition lies at still lower temperature
here, which I shall show in a following paper. The phenomena
are entirely the same for ammonium chloride and bromide.

9. Allotropy or tsomery. The phenomena which are explained by
the assumption of more kinds of molecules, are expressed by a great
number of names in the literature. Among these phenomena the
occurrence of a substance in several solid phases will also often, if
not always, have to be reckoned. In organic chemistry we have,
namely, many examples of substances which can occur in two or
more solid states, to which different molecular structure is assigned
(tantomery, desmotropy). In $ 1 I discussed an indication for the
occurrence of two kinds of molecules also for ammonium chloride.

A rational collective name for the occurrence of more than one
kind of molecules and more than one solid phase has however not
yet been adopted, and yet this seems very desirable. The advantage
lies in this that general thermodynamical relations (for homogeneous
and heterogeneous equilibria) hold for both phenomena, which equations
are therefore independent of the more subtle differences in structure
of the molecules. Thermodynamically desmotropy, tautomery, isomery,
metamery, allelotropy, pseudomery ete. etc. are namely perfectly equi-
valent, at least for so far as they refer resp. to homogeneous or
heterogeneous states. If we consider which of the available denomi-
nations is suitable as a collective name, only allotropy and isomery
present themselves for consideration in my opinion. The word isomery,
however, is pretty generally current for the occurrence of molecules
of equal molecular. weight, which differ only in way of binding.
There is no objection in my opinion to the use of allotropy as a

458

collective name. This word is generally only used when elements
occur in more than one solid state; that this word should also be
used for compounds is only an advantage, for there is no reason
whatever to assume an essential difference for the phenomenon for
elements and compounds. Besides we find allotropy used already
several times for compounds; moreover we find it already applied
to non-solid states; thus oxygen is often called allotropic, when the
occurrence of oxygen as ozone and ordinary oxygen is referred to.

Why then should not we generally indicate the occurrence of
different kinds of molecules by allotropy? In this sense it was
already used by Prof. Surrs in his theoretical considerations. Rationally
the occurrence of two or more solid states is then to be called phase-
allotropy, the occurrence of more kinds of molecules molecular-allotropy.
Phase allotropy will then in virtue of the above often, if not always,
find its ground in molecular allotropy *).

Nothing is known of structure and size of the molecules in solid
state for ammonium chloride. In connection with the above this
sufficiently \justifies the choice of the title of this paper in my opinion.
: Anorganic Chemical Laboratory of

the University of Amsterdam.

Physics. — “/sothermals of di-atomic substances and their binary
mixtures. NVI. Preliminary measurements concerning the
isothermal of hydrogen at 20° C. from 60 to 90 atmospheres”.
By H. KaAMERLINGH Onnes, C. Dorsman and G. Horst. (Comm.
146a from the Physical Laboratory at Leiden).

(Communicated in the meeting of June 26, 1915).

1. Introduction. For a long time it has been the intention to
extend the determination of isothermals of gases at low temperatures
to pressures beyond the limit of 60 atmospheres, which had been
fixed in the first stage of the Leiden investigations. In Communication
106 (April 1908) mention was made of a first step taken towards
the realisation of that project.

On the basis of the data concerning the tensile strength of glass,
published on that occasion, (about) fifteen manometer-tubes had been
constructed, by which the divided open manometer (Comm. 44)
could be extended in such a manner, that the entire height of
mercury would correspond to a pressure of 120 atmospheres. These

1) Sirs. Zeitschr. f. physik. Chemie, 89 257 (1915).

459

high-pressure tubes with the boards to which they are attached were
fitted to a wall of the working room, which also contains the
standard-gauge of 60 atmospheres, in the same manner as the tubes
of the latter. Originally it was intended (comp. Comm. 106) to fit
up this wall with similar auxiliary apparatus as belong to the
manometer-tubes of the 60 atmospheres-gauge, such as: pressure-
connections to join the different manometer-tubes in series and to
bring up the pressure, measuring rods suspended in cardanie rings
beside the manometer-tubes used for measuring the height of the
mercury columns, ete. It was further the intention to set up telescopes
with which to take the readings on the new tubes in the same
manner as with the standard-gauge of 60 atmospheres and finally
to connect together all the tubes to one gauge of 120 atmospheres.

Want of room in the laboratory, however, prevented the execution
of this plan; it would have been necessary to reserve the working-
room completely for the gauges, which it was impossible to do.
For this reason it was resolved in the measurements above 60
atmospheres to proceed by an indirect method.

For measurements in the pressure-range in question a standard-
differential-manometer was constructed consisting of as many tubes
for pressures above 60 atmospheres as would be necessary to
supplement a pressure of about 60 atmospheres to the highest
pressure to be measured. To obtain this differential gauge use is
made of the same auxiliary apparatus, as serves for the measurements
below 60 atmospheres, pressure-connections, taps, measuring-rods,
telescopes, ete. but the tubes used for measuring pressures below
60 atmospheres are replaced by the desired number of high-pressure
tubes, which are mounted in the place of the former. The high-
pressure tubes are joined to the system of pressure-connections and
connected up in series in the same manner as with the divided
open gauge and the pressures are regulated in such a manner, that
in the upper space of the first tube of the series the pressure is
about 60 atmospheres, and that the mercury-surface in the lower
space of the last tube is subjected to the pressure to be measured.
The pressure of about 60 atmospheres in the upper space of the
first tube of the series is measured with a subsidiary manometer,
which only serves as a pressure-indicator, the readings of which
give the pressure in absolute measure by a calibration with the
Open standard gauge of 60 atmospheres.

If a pressure-indicator is available of sufficient accuracy for
pressures of about 60 atmospheres, this method has the advantage,
that the number of mercury-surfaces which have to be read becomes

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

460

much smaller and that thereby the time required for a complete
measurement is considerably shortened, which will as a rule
increase the accuracy of a measurement, specially in view of the
constancy of the room-temperature. The indicator used by us was
the closed working manometer going from 20 to 60 atmospheres
which was referred to in Comm. 78 and 97a and which we shall
call J/,,.. Its accuracy at 60 atmospheres can be put at about 55.

At the time when Comm. 106 was published some progress had
been made beyond the condition described in Comm. 100, not only
with the pressure-measurement, but also with the arrangement of
the further apparatus required for the higher pressures. This progress
especially concerns a new auxiliary manometer, a closed hydrogen-
manometer of very nearly the same model as J/,,, but arranged
for the pressure-range of 60—120 atmospheres. This manometer
which we shall call J/,,, is represented diagrammatically in Plate 1
of communication 146c. M,, will similarly be found represented as
C in Pl. I of Comm. 97a fig. 1. Both are constructed according to
the system described in communication 50. J/,,, has a vessel twice
as large a M

When the pressure-cylinders in the apparatus of Comm. 50 were
made, the MANNESMANN-process was not yet available. It was utilized,
however, in the construction of J/,,, and the pressure-cylinder can
thus stand a much higher pressure. There is moreover an improvement
in the mounting of the manometer, which consists principally in the
mercury entering the cylinder from below, as in the elosed mano-
meters described in Comm. 50. The mounting is for the rest in
every respect similar to that of the pressure-cylinder, represented in
fig. 3 Plate I Comm. 97a.

The measuring tube of the manometer had been calibrated with
great care by Dr. C. Braak. We completed the manometer and
filled it with distilled hydrogen (Comm. 94 f, XIV). For its further
arrangement and the method of using it in the experiments we may
refer to previous communications. ;

By means of the completed apparatus it was possible to carry
out the calibration of M,,, with the standardmanometer and obtain
data in connection with the question which interested us more
particularly as to whether AmaGat’s observations which only start
at 100 atmospheres would join on properly to accurate measurements
with the open gauge. SCHALKWIJK's measurements with the aid of
the same open gauge and the accurate piezometers of Comm. 50 had
given rise to some doubt on this point (comp. Comm. 70 cont.
towards the end). But as those measurements had not gone beyond

461

60 atmospheres, it was quite possible, that the extrapolation on
which the above conclusion was based would turn out to be imper-
missible.

It had been our intention to carry the calibration of a working-
manometer for pressures above 60 atmospheres and the determination
of the isothermals of hydrogen at 20° C. up to 100 atmospheres.
But when we had reached 90 atmospheres the connections in the
pressure-system turned out less perfectly tight as was desirable. The
mercury-surfaces were not completely still and to attain this it
appeared necessary to affect certain improvements. But it was not
till 1915 that these were carried out (comp. next Comm. 1465).
Soon after the measurements mentioned above which were made in
1911, our work was interrupted by the departure of one of us and
remained thus confined to a few preliminary. determinations which
do not extend beyond 90 atmospheres.

2. Arrangement of the divided open gauge for measurements from
60 to 100 atmospheres. The connections of the apparatus, already
roughly indicated in section 1, are shown in the Plate belonging to
Comm. 146c (these Proceedings below p. 472).

The figure differs from the earlier representation of the gauge by
the manner in which the tubes of the open gauge which had now
to serve for the measurement of 60 to 100 atmospheres are joined
up: the same arrangement has been used in the measurements of
the next communication. As will.be seen, the first five tubes have
been left intact, while the remaining tubes were replaced by tubes
of greater wall-strength, destined for pressures from 60 to 100
atmospheres and tested to a pressure double of what they are
intended to be used at.

This arrangement has the advantage that the first five tubes
which go up to 20 atmospheres remain available as a separate open
gauge, and this is necessary, because they are not only used as a
standard-manometer, but also regularly as working-manometer for
the range below 20 atmospheres and in this respect supplement the
manometer which we have described in previous communications,
going from 20 to 60 atmospheres, which above we called J/,,. In
the open gauge up to 20 atmospheres, J/,, and M
a set of three manometers which embrace the whole range of pres- |

12) We thus possess
sure, through which the isothermals at low temperatures are measured
in the Leiden-Laboratory at the present time.
The steel capillary on the left of tube B, which normally is
coupled to the T-piece 7’, is now connected toa tube which through
ane
30

462

the stop-cock A, puts B, into communication with the manometer
M,,. To begin with, when the pressure is first admitted, the stop-
cocks K,- K,,, Kaar Ky, Kar Kas, Ky, Koe Ko, are all opentana
the pressure is raised to about 60 atmospheres, when the mercury
in M,, will rise very nearly to the top, whereas the mercury surfaces
in the open gauge will remain where they are. A,, is then closed
and the pressure is further raised, whereby the mercury in the
manometer-tubes goes up in the usual way and thus indicates the
excess of the pressure above the pressure of about 60 atmospheres,
which is read on J/,,. In this manner the tubes 4, ete. are put in
series behind J/,, as indicated in section 1. Further details of the
arrangement will be sufficiently clear from an inspection of the
Plate without any further description.

If it is desirable to be able to use the two parts of the open
gauge simultaneously, viz. the first five tubes as open gauge up to
20 atmospheres and the next ten as differential manometer from
60 to 100, or also to connect them up into a single open gauge
from O—60 atmospheres, this is easily attained by means of a side
connection to the pressure-cylinder with T-piece and two stop-cocks
at the branching-point, as was actually the case in our experiments.

With the above arrangement of the manometer it was impossible
to go beyond 100 atmospheres. In order to continue the measure-
ment in a similar way, the open gauge of 20 atmospheres remaining
available, it will be necessary to have a new index-manometer on
which 100 atmospheres may be read to replace J/,,, with the
addition of five suitable tubes to be joined up asa differential mano-
meter for the difference between 100 and 120 atmospheres.

3. The normal volume. As mentioned above, the reading-tube
of the manometer had been carefully calibrated. The comparison
with the open standard-gauge could therefore serve at the same
time as a determination of the isothermal of hydrogen at 20° C.

It was even possible to determine accurately the normal volume
before and after the compression, because the vessel of the mano-
meter (of the pattern of Comm. 50) is provided at its lower end
with a small U-tube, also calibrated and containing the mercury
which closes the tube, when it is not immersed in the mercury of
the pressure-cylinder. :

At the same time in our experiments this was not done. In a
first determination of the isothermal of hydrogen trom 60 to 100
atmospheres we thought ourselves justified in using an indirect
determination of the normal volume, obtained by calculation from

463

a reading of M,,, at a pressure which was also read on J/,, and
therefore accurately known through the direct comparison with the
open standard-gauge. For this calculation the formula is available
which represents ScHALKWIJK’s observations within the limits of their
accuracy (Comm. 70).

Three measurements were made yielding the following data. The
deviations from the mean are not higher than y3l5>. The result may
certainly be called satisfactory, considering that M/,, gives the pressure

TABLE I.

|
Vag p | Normal vol.

13 Febr. 1911 | 1.76969 c.M3, 62.504 atm. | 99.568 c.M3

| |
21 „ „ [176633 „ |62802 , |99.601 ,

HD 1.76017 ,, |63:039 *, ‚99.618 5

Mean 995% „

in this case with an accuracy of zoop, as was confirmed moreover
by a special comparison with the open gauge of 0—60, and that
the reading of the volume in J/,,, was not more accurate than
to about 1 part in 10000. The mean was therefore taken as the
normal volume.

4. Results. Only one series of measurements was made. The
calculation for J/,, and for the open gauge were exactly as formerly.
The only point to be mentioned is, that the corrections for the
weight of the air-columns of the open gauge were calculated using
the densities as given in the tables which Brinkman deduced from
AMAGAT’s observations. (Comp. also Comm. 146c). Table Il (p. 468)
gives the results of the measurements.

The deviations from the values which would follow from SCHALK-
wisk’s formula are all with the exception of the first in the same
direction. Except in the doubtful observation corresponding to the
density 80, the deviation is only about 1 in 1500, the mean positive
deviation (leaving out of account the observation at d4 = 80) 0.0008
falls on the limit of what may be considered as established, con-
sidering the degree of accuracy of the observations. The fifth column
of Table Il contains for the highest pressures the values according
to the formula which was calculated from the series in Comm. 70
derived from AmaGat’s observations and given by SCHALKWIJK at

464

TABLE II.
Isothermals of hydrogen at 20° C.
dy Pp P24(W) POR ScHarkwux, PPA, AMAGAT

60.120 67.101 1.11610 1.11625

64.059 | 71.729 1.11966 1.11936

67.507 | 15.797 1.12281 | 1.12211

70.531 | 79.344 | 1.12494 | 1.12454

13853 | 83266 | 11246 | - 1.12723

71.470 | 87.580 | 1.13043 | 1.13017 1.13227 »
[79.852 90.509 | 1.13349 1.13213 1.13425]

the end of Comm. 70. No great value can be ascribed to the extra-
polation by means of this formula, which is valid for pressures
above 100 atmospheres from 100 down to 60 atmospheres, but in
the neighbourhood of 90 atmospheres the formula probably represents
correctly to one or two parts in a thousand what would follow
from AMaGatT’s observations.

Leaving out of account the observation at 90 atmospheres on the
ground of a priori doubt as to its accuracy, although from the
next communication it will appear, that it is really affected by a
much smaller error tban tbe others and that it would lead to a
different conclusion, our results would seem to show, that an extra-
polation above 60 atmospheres with ScHaLKwIJK’s formula calculated
for 4 to 60 atmospheres, although not giving the same accuracy in
that region, is still sufficiently accurate to support the suggestion,
that Amacat’s value at 100 atmospheres is too high. The error
would however be-less than zt;, the amount deduced from SCHALK-
wiJK’s formula.

465

Physics. — “Jsothermals of di-atomic substances and their binary
mixtures. XVIII. The isothermal of hydrogen at 20° C. from
60—100 atmospheres” By H. KAMERLINGH Onnes, C. A.
Crommenin and Miss EB. I. Sur. (Communication 1465 from
the Physical Laboratory at Leiden).

(Communicated in the meeting of June 26, 1915).

1. Introduction. The measurements communicated in this paper
are a revision and extension of those of the preceding communication.
They are to be looked upon as a first part of a more accurate
investigation to obtain a bridge between the accurate isothermal at
20° C. and between 4 and 60 atmospheres, determined by ScHALKWIJK’),
and AmaGat’s isothermals *), which only begin at 100 atmospheres.

Previous determinations by KAMERLINGH ONNEs and HyNDMAN *) were
made with the same ultimate aim in view. They were made with
the piezometers for low temperatures and gave the same values as
SCHALKWIJK's measurements with the piezometers for ordinary tem-
perature. On this ground measurements at O° C. with the same
piezometers for low temperatures could be undertaken with confi-
dence. In the paper by KAMERLINGH ONNes and HynpMaAN quoted above
a determination of the isothermal for 0° C. was published which
was replaced by a more accurate one in a later communication *).
It will be necessary to repeat the latter investigation and extend it
to 100 atmospheres in order to obtain the desired connection with
AmaGat’s work. In addition it will be necessary to undertake a
determination with ScHaLKWIJK's piezometer IV, provided with a
vessel of twice the volume, and thus extending from 60 to 120
atmospheres ; as a continuation of work with a somewhat different
object, viz. the investigation of the isothermal of 20° C. arranged
to reach a higher accuracy. For it will now also be our object to
know this isothermal from 60 to 120 atmospheres with an accuracy
of 1 in tenthousand.

In the mean time, while this investigation of the highest accuracy
is still in abeyance, the necessary calibration of the working mano-

1) J, CG. Senarkwijk, These Proceedings 4, p. 107, 1901, Comm. 70 (cont),
Dissertation, Amsterdam, 1902.

2) E. H. Amacar. Ann. de chim. et de phys. (6). 29. p. 68, 505, 1893

8) H. Kamertineh Onnes and H. H. F. Hynpman, These Proc. 4. p. 761,
1902, Comm. 78.

4) H. KAMeRLINGH Onnes and C. Braak, These Proc. 10, p 413, 1907, Comm.
100a and 1005. C. Braak, Dissertation, Leiden, 1907.

466

meter M,,, with the open standard-gauge (as carried out in the
preliminary measurements of the preceding communication) afforded
an opportunity for measuring the isothermal of hydrogen at 20° C.
up to 100 atmospheres, with an accuracy of 1 in 3000 or 4000,
as required in the investigations with piezometers for low tempera-
tures which will go up to 100 atmospheres and first of all in the
investigation of the isothermal of 0° C. to 100 atmospheres mentioned
above. The calibration of M,,, also served as a link in the compa-
rison of a pressure-balance of Scuanrrer and Bupenpere with the
open standard-gauge which will be dealt with in the next commu-
nication 146c.

2. As regards the experimental method we can be short, as itis
fully described in the preceding and in the next communication, the
latter of which also containing a plate. We only mention, that we
considered it advisable to compare once more the closed manometer
M,, at a few pressures with the open gauge, seeing that several
years had elapsed since the last comparison and that on one occasion
a small change of the normal volume had been noticed.

Table I contains the results of this comparison, O. M. standing
for “open manometer”.

In view of the accuracy of the two instruments it will be seen,
that the correspondence which is obtained must be called completely
satisfactory.

The method differed from that of the preliminary determination
of the preceding communication by the normal volume of J/,,, being
directly measured, in order to obtain a determination of the isothermal
as independent as possible.

The results of these measurements were as follows:

467

Measurement I: 102.875 ecc.
4 re KOE A % 5
he Wile SKOLIEE Sen

In taking the mean the second measurement was given half the
weight of the other two, on the ground that it does not agree well
with the others and that an irregularity must have occurred in it,
as was also clearly shown by a discussion of the observed temperature,
pressure and barometer in connection with each other. The mean
was thus taken at 102.863 ce.

3. Results. These are collected in Table IL. The pressures are
given in international atmospheres (75.9488 ems. mercury at Leiden),
in the densities (74) the normal density and in the volumes (v4) the
normal volume is taken as unit.

TABLE II.
Isothermal of hydrogen 20° C.

Pp | dy 1D,

65.247 | 58.500 | 1.11533 |
73.019 | 65.205 | 1.12075
71.363 | 68.826 | 1.12404
| 81.188 | 72.059 | 1.12670
85.133 | 75.374 | 1.12948
1.13198

96.490 84.817 1.13765

100.336 87.979 1.14047

|
92.677 | 81.660 | 1.13493
|

As regards the representation of these observations by a series
with ascending powers of d4*) the question arose as to whether
they could be represented by ScHaLKwuk’s formula for 4 to 60
atmospheres

pva = 1.07258 + 0.6671 X 10-8 d4 + 0.993 X 10-6 d4?
in other words, whether ScHALKWIJK's formula, which holds up to
60 atmospheres, could be extrapolated as far as 100.

1) H. Kamertinen Onnes, These Proceedings 4, p. 175, 1901. Comm. NO. 71.

468

Table III contains the results of a comparison of our observations
with ScHALKWIJK’s formula:

TABLE III. Comparison with SCHALKWIJK’s formula.
pu, (W) pu, (R) WR abs. W—R in 00
1.11533 1.11499 + 0.00034 + 0.03
2075 2028 | 47 4
2404 2317 87 8
2670 2578 92 8
7 2948 2847 101 9
3198 3068 130 12
3493 3364 129 12
3765 3627 138 12
4047 3892 155 14 |

4. Discussion. As will be seen from Table III, the deviations
from ScHALKWIJK’s formula follow a very distinct systematic course;
near 60 atmospheres they are still small, bat at higher pressures
they become much larger and largely exceed the limits of our accuracy.

In deducing a new formula we have assumed for A4o ') at O°C.
the value given by KAMERLINGH Onnes and BRAAK A 49 = 0.99942,
which gives at 20° A4o— 1.07261 and calculated B4 and
C4 by the method of least squares from all the observations from
4 to 100 atmospheres, viz. those of ScHaALKWIJK and those of this
paper; the formula thus represents the isothermal of hydrogen of
20° from 4 to 100 atmospheres.

Table IV gives the deviations from this formula of ScHALKWIJK’s
observations, those of the preceding and those of the present com-
munication.

The observations of the preceding communication have not been
used in the calculation of the constants of the formula. They are
however given in the Table. It has to be mentioned, that in the
preceding communication the normal volume was calculated by
means of ScnaLKWIJK’s formula, whereas now it seemed preferable
to determine it with our own more final one. The figures are

1) For the notation used for the virial-coefficients comp. Comm. 71.

469

TABLE IV. Isothermal of hydrogen 20° C.
4—100 atm.

pv y=1.07261--0.6571210—8 d 4 +1.2926>< 10-6 dy

pu, (W) | py | W—Rabs. | WOR
1.07677 | 1.07676 + 1.00001 0.00
7197 7811 = 14 ee ea
7982 7970 os 12 1
8160 8125 = 35 3
8141 8138 op 3 0
8321 8295 ai 26 kie
„| 8383 8393 = 10 Er |
=| 8770 8719 + 51 + 5
2 “ 9023 9012 le 11 er ed
a 9125 9108 ijn 17 SER
9318 9343 en 25 zo
9491 9517 ESS dee 2
9636 9618 ijs 18 i
1.10093 | 1.10110 en 18 NS
0647 0650 ae 3 0
[1187 1186 5 29 ERS
8 (1.11636 | 1.11676 — 0.00040 — 0.04
= 1992 1998 = 6 St
: 2307 2284 B 23 PD
&\ 2520 2535 = 15 SEAN
= 2712 2816 a 44 ze) Ma
Z| 3069 3123 = 54 EN
ED 3375 3329 a 46 A <A
d | 1.11533 | 1.11547 — 0.00014 — 0.01
| 2075 2096 Dn 21 =4t2
= 2404 2396 dE sed
Z| 2610 2667 ss, 0
= 2048 2048 0 0
& 3198 3179 ze 19 += 3
gl 3493 3489 ae 0
Z 3765 3765
Z\ 4047 4042 a 0

470

g thus somewhat different to what would
follow from Table I of the previous paper.

The deviations are graphically represented
in fig. 1. It is very striking, how much the
accuracy of the measurements has been

increased since previous determinations. The
circumstances under which they were carried

out (very constant room-temperature, entire
absence. of leakages, etc.) were extremely

favourable and, as great care was bestowed
on the measurements, it appears that they

have reached the full measure of accuracy
of which they are capable.

The accuracy of zooo to rotor, which

would follow from the excellent agreement
of our results with the formula can only

be a relative accuracy in view of the un-
certainty of the normal volume (see above).
It must therefore be ascribed to an accidental

K.ONNES. OORSMAN.HOLST.

Rigel.

VY K.ONNES. CROMMELIN. SMID.

concurrence of favourable circumstances, that
the agreement with SCHALKWIJK's observa-
tions is so very close. As the matter stands,
the portion of the isothermal determined by
him is continued without any discontinuity
by that of our experiments.

The figure also contains the value of
pva for 20° C. and 100.atmospheres, which
would follow fram Amacar’s observations
according to the principles developed in
Comm. 71 and which has been calculated by
a formula given by ScHALKWIJK. The devia-
epe 2 2! tion of this value from that given by our
formula is only 1 in 1000. This accordance
with Amacat’s observations may be called excellent, especially when
we consider, that the calenlation is as a matter of fact of the nature

of an extrapolation, albeit one which exceeds the limits of the
observation by very little only, as in Amacat’s work the isothermal
of 0° C. is the only one which goes down to 100 atmospheres. We
can therefore now set aside the supposition, made before, that
Amacat’s value at 100 atmospheres might be too high by 1 in 500.
This supposition was based on ScnaukwiJk's determinations up to

471

60 atmospheres and the measurements of the preceding paper going
up to 90 atmospheres had not been able to refute it, although they
tended to show, that the polynome of three terms by which
SCHALKWIJK's pv4 had been represented using least squares did not
hold accurately at the higher pressures. The agreement of 1 in 1000,
with AMAGAT now obtained justifies the expectation that a deter-
mination of the isothermal of 0° C. at 100 atmospheres made with
the degree of accuracy which we have now reached, will completely
confirm Amacat’s direct observation at this point. Our results are
thus well qualified to confirm the high value of Amacar’s excellent
work.
It appears that in the series

(On D4

Da
the term — may be neglected. The value of 64 which follows
(2)

from our results is in good agreement with the values calculated
by KAMERLINGH Onnes and Braak and by ScmarKwiJk from their
determinations of isothermals. If the various B4-values are represented
as a function of the temperature, they show only small deviations
from the curve which may be drawn through them. The 4 4-values
according to AMAGAT are very considerably higher.

Whereas 54 thus agrees well with what was to be expected in
connection with previous observations, it is otherwise with Cy.
Judging by the C4-values of KAMERLINGH ONNes and Braak at low
temperatures and those according to Amacar at ordinary and higher
temperatures, at 20° a value of C4 of about 0,6 > 10~-° would be
expected, whereas we find a value of C4 which is more than twice
as high. It is less astonishing, that ScHALKWIJK’s C'4 viz. 0,993 >< 10— is
also considerably higher than what had to be expected, because at
the highest density reached by him the value of the term Cada’ is
no more than about 0,008, so that only a very small accuracy
could be expected here; in our observations on the other hand the
term Cyd4? rises at the highest density to nearly 1°/, of pv4, so
that the accuracy, although still only small, might be expected to
be many times higher.

We have in vain looked for errors in our observations, which
might account for this nnexpeetedly high value of C4. As mentioned
above the observations were somewhat imperfect as regards the
normal volume, for the rest they left nothing to be desired. Neither
could the supposition of a small error having crept in the calibration

472

of the top of the manometertube give an explanation, unless this
error were supposed to have been of an amount entirely excluded
by the measurements themselves. Naturally it might be questioned,
whether the term in v7? left out can represent the course of the
isothermals in this region with an accuracy corresponding to the
accuracy of the observations. The observations in this region are
much more accurate than for the rest of the isothermals, the study
of which as a whole led to the selection of the polynome in the
given form for the purpose of representing the complete net of
isothermals. The circumstance, that the deviations in the range below
60 atmospheres show a systematic change, may possibly be a sign,
that the development which was chosen is actually not quite sufficient
for the present purpose.

In a subsequent paper our observations will be discussed in con-
nection with the further, fairly numerous observational data concerning
the equation of state for hydrogen.

Physics. — “Comparison of a pressure-balance of ScHirrer and
BuDENBERG with the open standard-gauge of the Leiden Physical
Laboratory between 20 and 100 atmospheres, as a contribution
to the theory of the pressure-balance.” By Dr. C. A. CROMMELIN
and Miss EK. I. Smip. (Comm. N°. 146c from the Physical
Laboratory at Leiden).

(Communicated in the meeting of June 26, 1915).

1. Introduction. Object of the investigation. The measurements
undertaken to extend the determination of the isothermal of hydrogen
at ordinary temperature from 60 to 100 atmospheres, which are
described in the preceding communication, afforded a welcome
opportunity for carrying out a comparison planned a long time ago
of the pressure-balance of ScHirrer and BUDENBERG with the open
manometer of the Physical Laboratory at Leiden.

In the isothermal-determinations of gases under high pressure
undertaken at Amsterdam by Prof. Kounstamm with the apparatus
belonging to the van per Waats-fund the pressure-measurements
are based on the indications of a pressure-balance by SCHAFFER
and BupDeNBERG, and the unit in which the volume of the gas
in the observations under high pressures is expressed is also
dependent upon the indications of a pressure-balance of that kind.

473

In fact this “normal volume” is derived by Konnstamm and Warsrra *)
from the volume which corresponds to the pressure given by the
pressure-balance according to the isothermal of hydrogen as deter-
mined by SCHALKWIJK ®) at Leiden by means of the open manometer
of KaAMERLINGH ONNes ®). In order to reduce the observed pressures
and volumes in the investigations by KonnNsramM and Wazstra to
real pressures and volumes, which are required for the deduction of
the equation of state, an investigation as to the real pressure,
corresponding to a definite indication of the pressure-balance, is thus
indispensable.

As the open manometer in question allows absolute pressure-
measurements up to 120 atmospheres of great accuracy, a calibration
of the small pressure-balance, used in the experiments of KouNsTaMM
and Waistra, would at any rate yield the normal volume belonging
to the measurements at lower pressures.

Independently of the absolute calibration itself of the pressure-
balance in the region explored, the comparison of this balance with
the open gauge was also of great value for forming an estimate of
the accuracy of the determination of the very high pressures. The
desirability of such comparison was insisted upon by KonnstamM
and Warsrra not long ago.

Of the theory of the pressure-balance only little is known and
even that has not been at all adequately tested by experiment.
Worst of all the experiments made so far do not confirm the theory.
We are chiefly referring to B, WaGner’s*) investigation, whose calcu-
lations about an AmaGat-gauge are also mutatis mutandis applicable
to a pressure-balance. Wacnrr calculates the force which the cylinder
of an AMAGAT-gauge experiences owing to the viscosity of the oil
which flows through the narrow interspace between piston and
cylinder and finds that this force cannot always be neglected in the
practice of accurate measurements. In order to calculate the true
pressure from the indications of the gauge a correction has to be
applied to the latter, but since in the. expression for the force,
besides constants of the instrument, only the pressure occurs as a

1) PH. Konnstamm and K. W Warsrra. These Proceedings 16. p. 754, 822.
1913 and 17 p. 203. 1914 and K. W. Warsrra, Dissertation Amsterdam 1914,
where also a description of the pressure-balance will be found.

2) J. G. ScHALKWIJK. These Proceedings 3. p. 421, 481 1901. Comm. 67 and
Dissertation, Amsterdam, 1902.

5) H. KAMERLINGH Onnes. These Proceedings 1. p. 213. 1898. Comm. 44.

4) E. Waener, Dissertation, München, 1904 and Ann. d. Phys. (4) 15 p. 906,
1901. Comp. also G. Krein, Dissertation Techn. Hochsch. Berlin, 1909.

474

factor, the correction can be made to the sectional area on which
the pressure acts; the area thus corrected, the “functional” area, is
therefore according to Wacner’s theoretical deductions a constant
for the instrument and naturally differs a little from the real area.
Waarmwr determined the functional area of his AmaGat-gauge by
means of experiments at low pressure, he also measured the real
area and found the two exactly equal! This result is in contradiction
with the theory, and, assuming WaGwner’s experiments to be trust-
worthy, this would indicate, that the theory is not so simple and
that there are possibly other factors which might influence the
functional area, in which case it might very well happen that the
functional area would turn out to be dependent on the pressure.

Before this matter can be cleared up, i.e. before a revised theory
of the pressure-balance can be tested by experiment, it will be
necessary to study the instrument as fully as possible from an
experimental point of view, i.e. to compare its indications over as
wide a range of pressures as possible with those of a standard-
manometer and on the other hand to make very accurate measurements
of the dimensions of its various parts. On the basis of these data
it will then perhaps be possible to build up a more exact theory.

If it appeared that the functional area in accordance with WAGNER’s
theory were independent of the pressure over the whole range of
comparison, one would be justified in extrapolating beyond the
region, where the comparison with the open gauge is possible (i.e.
above 120 atmospheres), and thus in calculating the actual pressure
at 250 atmospheres from the indication of the balance with the
same functional area as was found say at 100 atmospheres; the
large pressure-balance of the van per Waats-fund which has
a range from 250 to 5000 atmospheres could then be compared
with the small balance at 250 atmospheres and in this manner the
pressures on the isothermals of hydrogen measured by KonnstamM
and Warsrra with both instruments could be corrected using the
functional area thus determined.

So far we have not gone beyond 100 atmospheres with the
comparison, as it was made in connection with the determination ;
of the isothermal of 20° C. dealt with in the preceding communication.
The range from 60 to 100 atmospheres gave sufficient data for the
purposes of the investigation: they show the desirability of a further
systematic investigation of various questions in connection with the
theory of the pressure-balance; but this investigation can be carried
out, independently of the apparatus in the possession of the laboratory.
We resolved to defer the continuation of the measurements, which

475

become more an more difficult as the pressure rises, until the
above investigation should have been carried out.

2. Experimental method. A simultaneous reading of the open
gauge and the pressure-balance turned out to be practically impos-
sible. In fact in the pressure-balance the pressure in the oil-passages
is only constant, while the piston with its weights is turning freely,
and this motion does not continue longer than a few minutes at
the utmost; when the rotation has come to a stop and the piston
is again set in motion by hand, there are always, however carefully
the operation is conducted, sma!l vertical forces exerted on the piston
which are propagated in the tubes as pressure-impulses and disturb
the pressure-equilibrium. On the other band the various readings on
the open gauge require much more time than the two or three
minutes which the pressure-balance, while left to itself, allows; in
fact, when all the tubes are at the proper pressure, a complete
reading carried out by two cooperating observers requires about
three quarters of an hour.

A simultaneous reading of pressure-balance and open gauge being
therefore attented with practically unsurmountable difficulties, we
resolved to carry out the comparison through the intermediary of
the two closed hydrogen-manometers of the Leiden-Laboratory
M,, and M,,,, the former of which has a range from 20 to 60
atmospheres, the latter from 60 to 120. We already will mention
here, that this procedure did not impair the accuracy aimed at in
any respect, as will moreover appear from the discussion in the
next section.

The accompanying plate shows the open manometer QV. M., the two
closed manometers /,, and J/,,, and the pressure-balance D. B.
with its oil-forcing pump 0. P. besides the connections and stop-
cocks by which the various apparatus are joined up together. The
construction and method of working of the various gauges having
been repeatedly described and represented need not be gone into
on this occasion *).

A small complication arose in connection with the transmission

1) Open manometer: H. Kamertincu Onnes. These Proceedings I. p. 213. 1898.
Comm. 44, and J. G Senarkwik Dissertation, Amsterdam 1902. H. KAMERLINGH
Onnes, C. Dorsman and G. Horst These Proc. Supra Comm. 146a. Manometer
M,,: H. Kamerunen Onnes and H. H. F. Hynpuan, These Proceedings 4. p. 761.
1902, Comm. 78. § 17, H. KamerringH Onnes and C. BRAAK. These Proceedings
9 p. 754. 1906. Comm. 97a, § 3. Manometer Mog: These Proceedings Supra.
Comm. 146a, 146b. Pressure-balance: Pu. Konnsramm and K. W. Warsrra Il. c.c.

Proceedings Royal Acad. Amsterdam. Vol. X VIIL

+76

of the pressure from the oil-passages of the pressure-balance to the
tubes of the Leiden-manometers, in which compressed air is always
used for transmitting the pressure. This transmission was at first
carried out by means of the steel tube D, with its level-gauge P,.
The level of the oil in it could be easily kept up at the desired
height by the aid of the oil-pump 0. P. When this arrangement
had been in use for some time, it appeared that small changes of
pressure in the oil of the pressure-balance, produced by the addition
of small weights on the piston, were but very slowly and gradually
transmitted to the manometers J/,, and J/,,,; it was therefore
desirable to transmit the pressure in the oil of the pressure-balance
to the mereury of the closed gauges by means of tubes exclusively
filled with liquid, eliminating all air connections. This arrangement
could be easily applied to M,,, by screwing a steel tube with a
level-gauge P, to the tap A,, (the object proper of which is to fill
the manometer with mereury, when being mounted). Beyond this
gauge P,.a second gauge P, was mounted and the latter was in
connection with the oil-passages. Between the mercury in the lower
half of P, and the oil in the upper half of P, the pressure was
transmitted by means of glycerine.

Our procedure was to bring up the pressure at first in the usual
manner with compressed air; if the stop-cock A,, was then opened
and ,, and A, closed, the pressure-transmission exclusively by
means of liquids was realized. The pressure was further raised by
means of the oil-pump. This arrangement completely answered our
expectations : pressure-changes of boo in fhe oil of the pressure-

balance were now instantaneously indicated on J/,,,.

3. Accuracy. An opinion as to the accuracy which may be ex-
pected may be formed by giving some data respecting the absolute
and relative accuracy of the indications of the various instruments.

The open manometer, when free of leakages and with a room-
temperature which is carefully kept constant, gives with certainty
an accuracy (absolute) of 0.01 °/,.

The manometer J/,,, if the reading is certain to 0.1 mm. — which
is undoubtedly to be attained — guarantees

at 20 atmospheres an accuracy of 0.008 ° ,
=v 60 55 ER # », 0.020 °/,

For the manometer J/,,, the following figures hold:
at 65 atmospheres an accuracy of 0.007 °/,

,, LOO 5 5 5 OO LO

477

The accuracy given for the two closed manometers is not only a
relative one, but for a large number of points an absolute one as
well, seeing that both instruments have been directly compared with
the open manometer at those points. As to the pressure-balance,
neither with respect to the absolute nor to the relative accuracy
was anything known with certainty at the beginning of our invest-
igation. It had only been found, that the sensitivity of adjustment in
the neighbourhood of a definite pressure is very high and certainly
amounts to 0.02°/, or even 0.01°/,. As an instance, the pressuretrans-
mission through liquids being used, and the pressure-balance being
loaded with 65 kilogrammes, the addition of 10 grammes to that
load could be observed on M,,, with absolute certainty. The data
regarding the accuracy of the pressure-balance which we have now
obtained by our investigation will be given further down, when the
results are discussed.

4. The calculations. The reduction of the indications of the open
manometer is very simple in principle; the various corrections,
however, require some care, if an accuracy of 0.01 °/, is to be
guaranteed. These corrections have all been fully discussed by
ScHALKWIJK in his Dissertation, so that we may confine ourselves to
a few remarks. The correction for the weight of the columns of
compressed air, which transmit the pressure from each tube to the
next, becomes considerable at the higher pressures. Instead of air
hydrogen might be used’), which would yield a double advantage:
in the first place the correction thereby becomes ten times smaller
and secondly the isothermal for hydrogen at 20° is at present very
accurately known up to 100 atmospheres’), so that the correction
ean be calculated with great accuracy. It is true, that this method
requires very pure hydrogen being available, in order to be certain
of the specifie gravity, but at the present time hydrogen prepared
in the cryogenic laboratory by distillation is so absolutely pure, that
an influence on the specific gravity of traces of admixed air, which
is relatively large, need not be feared. We have ascertained, how-
ever, that for pressures up to 100 atmospheres it is not yet necessary
1) This method was recommended by H. Kamertineu Onnes in 1898; comp.
These Proceedings 1, p. 213, 1898, Comm, N”. 44.

2) J. CG. Senarkwik, These Proceedings 3, p. 421, 481, 1901. Comm. N°. 67.
These Proceedings 4, p. 23, 29, 35 1901, Comm. N?. 70, Dissertation, Amsterdam,
1902 H. Kamertingu Onnes, C. A. GROMMELIN and Miss. E. I. Smip, These Proceed-
ings supra. Comm. N°. 146b. For the temperature correction compare the
empirical equation of state of H. Kamertineu Onnes in the paper by J. P. Darron.
These Proceedings 11, p. 863, 1909. Comm. N°, 109a.

31*

478

to introduce this complication and we have therefore preferred to
calculate the corrections for air.

For this purpose Amacat’s’) isothermals are available which have
been represented in different ways by equations by Brinkman’) and
by KamertincH Onnes*): from these equatious tables of correction
were drawn up. The corrections calculated by the two methods
agree to 0.5 mm. even at 100 atmospheres. As will appear further
down the results prove, that in this manner the correction is ap-
proximated with sufficient accuracy.

The correction for the compression of the mercury remains small,
it is true, even at 100 atmospheres, but still comes into account.
For this correction we have also calculated a table, based on the
compressibility of 0.00000392 according to AMAGAT.

There was no need for a correction for the flow of the mercury
through the tubes, fully discussed by SCHALKWIJK, as the mercury
did not move at all. Thanks to the steel connecting tubes being
soldered to the glass tubes, to the fibre-washers and to all the
couplings being immersed in oil*) we succeeded in obtaining the
open manometer completely free of leakages even at 100 atmospheres,
while at the same time the room-temperature was kept constant so
successfully (owing to steam-heating, improved illumination by metal-
wire lamps, which give very little heat ete.) that even with the
very lengthy readings at the higher pressures there was hardly any
sign of flow in the tubes.

The corrections for capillary depression have not been applied.
A discussion showed, that the algebraic sum of these corrections
would have no influence on the accuracy aimed at, especially if
by tapping the tubes care was taken to obtain well-shaped convex
menisci®). As a matter of fact the correction would have been very
difficult, seeing that with the illumination used the height of the
menisci could not be determined with the telescopes which served
for reading the mercury-surtaces.

The further corrections do not require any special mention. The
method of reducing the indications of the manometers J/,, and W,,,
do not call for any remarks either. As regards the load on the

DE. H. AmAGAT, Ann de chim. et de phys. (6) 29, Juni and Augustus 1893.

2) C. H. BRINKMAN, Dissertation, Amsterdam, 1904,

3) Zie J. P. Darron, These Proceedings 11, p. 874, 1909 § 2 Comm. N°. 109c.

4) The oil-vessels in question are not shown in the somewhat diagrammatic
figure. For some of the improvements mentioned here compare H. KAMERLINGH
ONNEs, These Proceedings 8, p. 75, 1905, Comm. N°. 946.

5) Here again the results prove the reasoning to have been correct.

479

pressure-balance, it has to be kept in mind, that it consists of the
total weight of piston and imposed weights, with the addition of
the atmospheric pressure multiplied by the functional section.

The pressure of the atmosphere at Leiden is taken as equivalent
to 75,9488 cms. mercury, one atmosphere being equal to 1,0336
kilogrammes.

5. Measurements and results. As explained in $ 2 the meas-
urements consisted in (1) a comparison of M,, and M,,, with the
open manometer, (2) a comparison of the pressure-balance with
M,, and M,,,.

We will first discuss the measurements between 20 and 60 atmos-
pheres carried out by means of M,,.

Before undertaking the comparison of M/,, with the pressure-
balance we made sure by means of a comparison of J/,, with the
open manometer (fully described in the preceding communication),
that the indications of the closed manometer still deserve the con-
fidence which had always been given them in recent years. As
shown in that communication the result of this comparison was,
that since the last comparison ') a few years ago the closed mano-
meter bad not undergone any change.

The comparison of J/,, with the pressure-balance was carried
out as follows. The pressure having been adjusted at a chosen value,
the pressure-balance was set in rotation and we waited, until the
mercury-surface in J/,, did not change any more. The pressure was
in this case transmitted from air to oil and as the pressure-impulses
which are due to the setting and keeping in motion of the pressure-
balance are only very tardily propagated to Mit appeared possible
to turn the pressure-balance without any modification of the position
of the mercury-column being noticeable. A reading was taken, when
the mereury-surface had been constant for a considerable time.

Table I gives the results of two series of measurements. For the
measnrements of June 22 the pressure-balance was once more carefully
centred, as we thought that the adjustment had not been quite
perfect.

The observations marked with an asterisk were calculated by
means of ScuALKWIJK’s isothermal and in these observations the
manometer has thus not merely been used as an indicator. The
concordance between the two kinds of observations appeared, however,
to be so excellent, that it was considered unnecessary to establish

1) These Proceedings supra, Comm N°, 1465, § 3.

+80

the pressure by direct measurement with the open manometer for
the points in question.

We now proceed to the measurements from 60 to 100 atmospheres
carried out by means of M

In this case we could not check the readings by means of the
isothermal and the calibration, as the comparison of a few years
ago') did not appear to have fully given the desired accuracy; this
was the reason, why it was repeated together with the present

TABLE I. Comparison pressure-balance with Mog. 2) al
| 5 Weights on eae ER Reciprocal | Functional

Date | Nt. | balance in Kilogrammesper Section in | Section
| kilogrammes 5, atm. pressure cm—, Be:
6 Febr. 1915 1 | 21.650 | 21.72 1.0036 0.9964
ix 255650 | as | 36 64
mr 31.410 31.520 35 65
VIII" 36.000 36.121 33 61
11 41.760 41.895 32 68
vi 46.050 46.188 30 70
Iv: 50.130 50.269 28 72
vr 55.710 | 55.848 25 75
Vv | 61.300 61.445 24 76
22 June 1915 | VIII 25.000 25.089 | 1.003 0.9965
I* 30.000 30.086 28 72
vir 35.000 35.092 26 | 74
I 40.000 40.114 28 72
vr 45.000 | 45.098 Ss 78
tite 50.000 50.120 24 16
Vv" 55.000 | 55.112 20 | 80
IV 60.000 | 60.112 i9 | si

determinations and replaced by a new calibration ®). In this region
we have therefore made the comparison at a larger number of

1) These Proceedings Supra Comm. 146a.

2) The arrangement of the tables is somewhat different from that in the original
Dutch. publication.

3) These Proceedings Supra Comm 1465.

481

TABLE Il. Comparison pressure-balance with Mio.

| Weights en Wie onan Reciprocal | Functional |
Date N°. atance in Kilogr. perem?,/ Section in | Section
= li Kloos atm. | ressure | cm—, rien j
27 March 1915 I 67.000 67.143 1.0021 0.9979
Il 71.050 71.210 22 78
UI 75.000 15.147 19 81
Iv 79.650 79.865 21 | 73
Vv 83.500 83.729 21 13
VI 87.550 87.795 | 28 72
VII 01.050 | 91.201 26 74
VIII 95.550 95.790 25 75
IX 99.500 99.815 31 69
X | 103.500 103.884 gan 63
29 March 1915 X 67.200 | _ 67.329 1.0019 0.9981
IX 71.100 41236 =} 19 | 81
VIII 75.100 75.248 19 81
VII | 79.600 | 79.776 22 78
VI 83.050 | 83.329 33 67
v | e1.550 | 87.145 22 78
IV 91.050 | 91.292 26 74
Ill 95.450 95.694 25 75
Il 99.350 | 99.667 32 68
I | 103.350 103.686 32 68
24 June 1915 u | 75.000 | 75.181 | 1.025 | 0.9975
VII | 80.000 | 80.216 21 73
I | 85.000 85.234 21 73
VIII 90.000 90.271 30 70
Iv 95.000 95.298 31 69
IX | 100 000 100.362 | 36 64

482

TABLE II continued. Comparison pressure-balance with Moo.

| B Pressure accor- B

| pate’ | | pressure (dmg Mail fomchonal | Funetionl

; deel diminished by er in cm?2.
| atm. press.
23 April 1915 I 67.000 67.174 1.0026 | 0.9974
II 71-000 71.212 29 1
Il 75.000 15217 29 71
IV 79.000 79.239 30 70
v 83.000 83.268 32 68
VI 87.000 87.263 30 70
VII 91.000 91.294 32 68
VIII 95.000 | 95.338 | 35 65
IX 99.000 99.383 | 38 | 62
X | 103.000 | 103.406 30 | 61
| 24 April 1915 x | 67.000 67.174 1.0026 0.9974
| IX 71.000 71.180 26 74
VIII 75.000 75.229 30 70
VII 79.000 79.259 32 68
VI 83.000 83.272 32 68
Vv 87.000 81.208 | 32 68
IV 91.000 91.313 4 | 66
ill 95.000 95.328 34 66
Il 99.000 99.395 39 | 61
| 1 | 103.000 103.423 41 59
|

18 June 1915 I 70.000 | 70.185 1.0026 | 0.9974
Iv | 80.000 80.263 32 | 68
V 90.000 90.295 32 68
VI | 100.000 100.390 39 | 61
Pis June dois) x 70.000 | 70.181 | 1.0025 0.9975
| IX 80.000 | 80.256 32 68
| VIII 90.000 90.301 33. | 67
| VII | 100.000 | 100.360 36 | 64
19 June 1915 | mt | 70.000 | 70.179 1.0025 | 0.9975
| ee ELV: 80.000 80.247 30 70
| V | 90.000 90.286 31 69
VI | 100.000 100.375 37 63

C. A. CROMMELIN and/¢ Leiden Physical Laboratory between 20 and 100
atmospheres, as a contrib

i —— SS ae

C. A. CROMMELIN and Miss E. I. SMID: “Comparison of a pressure-balance of Schä i i
haffer and Budenberg with the ly
atmospheres, as a contribution to the theory of the pressure-balance of S. and B”, il open standard-gauge of the Lelden Physical Laboratory between 20 and 100

483

points. After the completion of the investigation described in the
preceding communication the various points could be each separately
checked by a comparison with the isothermal deduced from the
points combined. If the manometer had been filled with a different
gas or an arbitrary mixture of gases, it would have served. its
purpose as an intermediary between pressure-balance and open
manometer equally well.

Table II contains the results of the comparison of the pressure-
balance with MM,,,, extending over the range from 60 to 100 atmos-
pheres. The measurements of March 27 and 29 and June 24 were
made with the air-liquid transmission of pressure, as had been those
with M/,,, whereas in those of April 23 and 24 and June 18 and
19 use was made of the liquid system mercury-glycerine-oil which
was arranged later on as described in one of the preceding sections.

6. Discussion. The results of all the measurements as contained
in the above tables lead to the following conclusions:

1. The functional section is not independent of the pressure, but
as the pressure rises above 20 atmospheres it increases, goes through
a greatest value at about 70 atmospheres and then diminishes with
greater rapidity as far as the comparison reached. The greatest
deviation is 0.0020.

2. When the determinations were repeated, the same value was
not always found for the functional section, the greatest deviation
being about 0.0005 in this case.

3. The functional section differs from the geometrical section as
given by Scadrrer and BuperBerG (1 em’) by about 0.0030.

+. The sensitivity of the pressure-balance +50, thus far exceeds
its accuracy. If the latter is to be raised to the value of the sen-
sibility, the theory of the instrument will have to be developed and
means will have to be found to obtain constant results within the
limits of the sensibility. Probably in order to attain this accuracy
a pressure-balance will always directly or indirectly have to be
compared with an open manometer.

5. Pressures which have been measured with a Scuirrer and
BUDENBERG pressure-balance which has not been calibrated cannot at
present be estimated at a higher accuracy than about +4, provided
that the error in the area of the piston is not larger than 0,1 °/).

In conclusion we wish to thank Professor KAMERLINGH Onnes and
Professor Kounstamm for their sustained interest in our work.

484

Physics. — “The specific heat at low temperatures. Il. Measurements
on the specifie heat of copper between 14 and 90° K.” By
W. H. Kersom and H. KAMERLINGB Onnes. Communication
N°. 147a from the Physical Laboratory at Leiden. (Commu-
nicated by Prof. H. KAMERLINGH ONNEs).

(Communicated in the meeting of June 26, 1915).

§ 1. In Comm. N°. 148 (Oct. 1914, These Proceedings Dee. 1914)
§ 6 we published a series of measurements on the specific heat of
copper between 15 and 22° K. We have since made some improve-
ments in the experimental arrangement, particularly as regards the
resistance measurement for the purpose of the determination of the
temperature increase in the calorimetric experiment. The determination
of the “sensitivity” of the THomson-bridge arrangement (cf. Comm.
N°. 143 § 2) was made this time by shunting the standard resistance
of 1 2 (ef. Comm. N°. 143 Fig. 5) by a known resistance and
reading the resulting galvanometer deflection. Irregularities as men-
tioned in Comm. N°. 148.§ 4 note 1 did not occur now.

At a new calibration of the thermometer wire Aus it appeared
not to have remained so constant, especially at liquid hydrogen
temperatures, as at the time of the measurements of Comm. N°. 143
we concluded from determinations in liquid hydrogen on two different
days (table | Comm. N°. 143), and also from the comparison of the
result of a control measurement’) at the boiling point of oxygen on
May 25 with the results of the measurements of May 18 1914. See
table I.

Hence the resistance of the gold wire Aw,3*), which is enclosed
in enamel between metal, appears to show small differences when
brought to the same temperature at different times. This behaviour
agrees with what has been experienced with wires sealed in glass:
ef. KAMERLINGE Onnes and Horst, Comm. N°. 14la § 4.

At liquid oxygen temperatures the differences are, however, so
small, that for the calorimetric determination at these temperatures.
they are unimportant. At liquid hydrogen temperatures account has
to be taken of these changes.

1) This control measurement, which was not mentioned in Comm. N°. 143, gave:
fh Wane
May 25 714 90.45 3.6616
2) The preliminary treatment consisted in (ef. Comm. N°. 143 § 3 : glowing
before the winding, then 6 times cooling in liquid air and allowing it to return
to room temperature, likewise 2 times in liquid hydrogen.

485

TABLE I. Resistance of Au,3

Standard-

W
NG ji W WwW
thermometer WMay 14
27 Febr.’15 Il 14.10 0.6164 | 1.0034
H» vapour pressure
HI | 16.97 | 0.6437 | anparatus 34
1 | 20.41 | 0.6952 | 33
25 Febr.’15 II | 56.94 | 2.0822 | |
Ill | 60.65 | 2.2582 | |
IV | 68.65 | 2.6385 | [1.0033] 2)
Pty
V | 77.93 | 3.0779 1.0010
VI | 86.41 | 3.4759
1 | 90.28 | 3.6550 | / 0.9999
30 April 15 II | 14.49 | 0.6188 | 1.0023
.97 | 0.6432 | 25
IV | 16.97 Pty)
Ill | 18.49 | 0.6633 | 24
1 \ 20.49 | 0.69545) | 15
12 May ’15 Il | 60.69 | 2.2580 | \
Ill | 68.77 | 2.6429 Pty with changed | — [1.0027] 2) |
| zero resistance, cal- |
IV | 77.84 | 3.0718 culated from the 1.0004
: | | resistance of Pf,, at
I | 89.89 | 3.6360 | points Ill and IV. | 0.9997
Vv | 89.89 | 3.6368 0.9999

This was done for the measurements treated in this paper by
determining for each series of measurements in liquid hydrogen a
point of the scale of Aw,3 with the aid of the temperature derived

from the pressure of the liquid hydrogen bath *).

!) Checked by comparison with the temperatures calculated from the pressure

of the bath.

2) It has appeared since that at this temperature the calibration of the auxiliary

thermometers used in the measurement of May ‘14 was less accurate.

3) In table I it appears from the measurements of April 30 ’15 that even in a
single series of measurements at hydrogen temperatures small changes in Aes
may occur. With a view to this fact we intend in future measurements to deter-
mine each time at least two points of the scale of Awc3, viz. one at the boiling

point and one at the melting point of hydrogen.

486

§ 2. Heat capacity of the core Kj). With a view to the irregu-
larities which had occurred in the measurements of 1914 (Comm.
N°. 143 $ 4) this heat capacity was determined once more. In these
measurements at a pressure of 75.6 cms. of the hydrogen bath,
which corresponds to 7’= 20.31, W Aug was found equal to 0.6940 2,
whereas according to the calibration of Febr. 27, ’15 this resistance
corresponds to 7’— 20.34. The difference between these two values
of 7’ corresponds to a displacement of the curve, which represents
the heat capacity of Ayj7 as a function of the temperature to an
amount of 0.3°/, of the heat capacity at 15° K., and to an appre-
ciably smaller amount at 20° K. As this is far within the limit ot
accuracy reached in the measurements the calibrations of 25/27 Febr.

"15 could be used for the calenlation of the temperatures.

TABLE Il. Heat capacity of the core Ky:

F a Peal Mean on Temperature _ Heat capacity _
| temperature | increase an Joulesld eeen

21 Jan.’15 II | 14.815 1.018 0.714

II 15.07 1.174 0.732

IV 15.87 1.227 | 0.822

Vv 18.02 1.171 1.082

vie. » “0:56 0.895 | 1.419

T |) 202865 1.005 | 1.488

VII | 25.40 0.856 | 2.29

Vill 30.33 | 0.939 | 3.325

ee he SEEN 0.856 6.23

Kye oes 0.736 9.43

28 Jan. 15 I | 60.13 1.024 12.66

mn | 61.04 0.993 12.73

lI | 70.40 0.834 | 15.27

IV | 80.58 0.718 | 17.44

vo “1-10 | 0.701 | 17.95

| vi | 89.015 =| 0.768 | 19.45

VII 89.575 0.758 19.49

The heat capacity appears to be a little smaller in the region
of the liquid hydrogen temperatures in these measurements than at

487

those of 1914, viz. 0.023 joules/degree at 15° K., and 0.038 joules/
degree at 20° K.')

This difference can be explained by the fact that for the meas-
urements of 1915 on Ay,) for the wires which carry the heating
current a little less platinum had been used. This circumstance was
taken into account as far as possible.

$ 3. Atomic heat of copper.*) For the measurements the same
block of copper was used as for those of Comm. N°. 143 $ 6:
electrolytic copper of Ferrer and Guitiaume, 596,0 grammes.

As a check on the purity of the copper after the measurements
a strip was cut from the block; the strip was filed to a rectangular
section, then rolled and annealed. The resistance was then measured
at room temperature and in liquid hydrogen‘).

1) The measurements of 1914 being corrected for the change of Aves.

*) The atomic heat of copper has already been measured between 23 and
88° K. by W. Nernst, Ann. d Phys. (4) 36 (1911), p. 395.

3) We took advantage of this opportunity to test at the same time the purity
of the lead which we had used for the measurements on this metal of Gomm.

N°. 143, and to invest gate the influence of the treatment of the metal on the
decrease of the resistance. The results are collected in the following table.

Woo36K Wie K | “i493°K 1 — . 2H

Wie o|Pusec Vuec) CL

ee Ee RE CE
Copper filed | 0.01287 | 0.01229 0.00426
9 rolled 0.02359 0.02311 0.02295 420

ni if and

annealed 0.01042 0.00982 430
Lead cut 0.02827 0.01229 411
» rolled 0.02828 , 0.01222 410

These data lead to the following conclusions regarding the influence of the
treatment of the metal on the change of the resistance with change of temperature:

For copper rolling diminishes the decrease of the resistance between room tem-
perature and the boiling point of hydrogen in a large degree.

By subsequent annealing the influence of rolling the copper is not only annulled,
but the decrease of the resistance between the temperatures mentioned above is
now even greater than that of copper which has not been rolled and annealed;
apparently annealing has also annulled the influence of previous mechanical treatment
(filing), probably in consequence of the fact that the metal has united again to
larger crystals.

The temperature-coefficient at hydrogen temperatures undergoes only a small
change by the manipulations mentioned above.

The change of the resistance of lead suffers no or only a small change by rolling.

488

W
en = (0102 at 20 ASK
Wansec. :

= 0.0098 at 14.9° K. *)

The temperature coefficient at 10° C.
measurements at O and 20° C.:

1 dw
Woo. dT

These values point to a high degree of purity, which is certainly
sufficient for the measurements on the atomic heat *).

In the measurements in hydrogen at a pressure of the bath of
75.2 ems, to which belongs 7’= 20.30, Au.3 was found equal to
0.69382 2. According to the calibration of Febr. 15 this resistance
corresponds to 7’ 20.29. The agreement between these values of

was also determined by

= 0.00430 at 10° C.

TABLE III. Atomic heat of copper.
i | ‘ Ee BE eee a pee ST
N?. hemiperatiee re in leore uel degree K. 6
degree K. a | C,
16 Dec. 14 II 14.51 1.206 2.246 0.0396 330
Ill 15.595 0.955 2.791 506 326
IV 17.17 | 1.047 3.691 687 325
Vv 20.195 | 1.065 5.959 0.1155 321
I 20.745 | 0.880 6.255 1217 324
VI 25.37 0.918 11.42 234 319
VII | 29.73 | 0.667 18.01 377 317
VIII | 40.22 | 0.822 40.55 870 315
IX 50.04 0.672 66.38 1.434 315
15 Jan. ’15 I 59.75 0.537 94.42 2.06 310.5
II 60.33 0.540 95.40 2.08 312
Ill 69.66 0.598 118.2 2.59 | 2.58 | 313
IV | 80.32 0.588 137.7 3.055 3.04 | 317
Vv 88.86 | 0.532 151.85 3.37 | 3.35 | 321
VI 89.38 | 0.522 | 1548 3.44 | 3.42 | 316.5

1) Cf. also H. Kamerunen Onnes and B. Beckman. Comm. N°. 129a, Table VII.
*) GE for instance W. Meissner, Ann. d. Phys. (4) 47 (14 Sept. 1915), p. 1001.
[Added in the translation].

489

7 is sufficient to calculate the temperatures from that calibration.

In Fig. 1*) the results of our measurements are represented. In
the upper lefthand diagram the region up to 25° K. is represented
on a larger scale.’)

0225

0,175

0,125

+ 4 = gs0
| ut goo
10 20 T 30 40 so 60 70 30 so
Fig. 1.

The curve has been calculated from Desie’s formula*) with
6 = 315. Drrije's formula appears again to be capable of repre-

senting the atomic heat over a large region — the ratio of the
largest to the smallest value of the measured atomic heats amounts
to more than 80 — with a good approximation.

In table IV we have compared the atomic heats of copper in the
region of the liquid hydrogen temperatures with the 7'’-law derived
by Desi for low temperatures:

he 3
C, = 464.1 5
ad

1) In Fig. 1 the vertical line which indicates 7’= 80 has been drawn inaccura-
tely ; it has to be moved 1.25 mm. to the right. [Note added in the translation].

2) At 88° K. our resulls agree fairly well with those found by Nernst l.c., at
the lower temperatures (83°— 23° K.) our values are smaller

8) P. Depte. Ann. d. Phys. (4) 39 (191%), p 789.

490

TABLE IV. Copper.
3 C, eale Obs.—Cale.
No. jr a et
| | v | | (0 = 325.1) | | in Oo
i = = | = hl SO aa =
16 Dec. 714
II 14.51 0.0396 329.6 0.0412 —0.0016 | —4.0
Il 15.595 | 506 326.3 512 — 6 =e
| |
IV 17.17 687 | 324.6, 684 + 3 Vena
Vv | 20.195 0.1155 321.1] 0.11125 +- . 425, eee
I ey > 324.1| 1206 4 7 eae
| | mean 325.1)
| |

In these measurements, which are more accurate than those of
July “14 (Comm. N°. 143 $ 6), a small deviation from the 7*-law
shows itself. The deviation is in the sense that at decreasing tem-
perature the atomic heat decreases more rapidly than follows from
the 7°-law.

The deviation becomes still more apparent, if one compares the
atomic heat over the whole region of the measurements of this paper
with Desise’s general formula for the atomic heat, ef. tig. 1 and the
values of @ in table III.

In the liquid. hydrogen region and above it, up to 40° K., the
values of 6 decrease continually (fig. 2). Im this respect the

SIET Ti

324

31%

| 312

Fig. 2.

behaviour of copper differs from that of lead. For the latter metal
the values of @ increase with increasing temperature in the liquid

491

hydrogen region, and begin to decrease beyond about 30° K. *)

§ 4. Table V contains values of the energy U, which are derived

1) Our results point

TABLE V. Copper.
T | in ane 7 Ou
20 0.557 0.02785 | 322
30 2.86 0.0952 | 320
40 8.94 0.223 317
50 | 20.31 0.406 | 3165
60 | 37.8 0.629 315
70" |e Blt 0.873 314
80 | 89.4 1.118 314
90) 420.7 1.352 315

further to an increase of @ for copper above 70° K. It is

true, that the increase hardly exceeds the degree of accuracy reached in our
measurements, but meanwhile it finds a confirmation in the results obtained by
SCHIMPFF, ZS. physik. Chem. 71 (1910), p. 257, by RicHarps and Jackson, ZS.
physik. Chem. 70 (1910), p. 414, by Korer, Ann. d. Phys. (4) 36 (1911), p. 49,
R. Ewarp Ann. d. Phys. (4) 44 (1914), p. 1213 and by Rorra. Gazz. chim.
44 | (1914), p. 646, at temperatures between that of liquid air and room tem-
perature or 0° C. respectively. A curve which is drawn through our results below

90° K., and which represents the observations mentioned above as follows:

RICHARDS and JACKSON.

Interval of p
Temperature nn | Obs.—Calc.
— a from curve | observed | ae
83—290° K. 0.0790 0.0786 —0.0004
SCHIMPFF.
194 - 290 0.0879 0.0880 fe 1
85—293 0.0794 0.0789 — 5
83.5— 190 0.0710 0.0720 oh 10
KOREF.
196.5 — 273.1 0.0873 0.0878 -- 5
82.0—191.1 0.0708 0.0722 + 14 i
EwALD.
197.9—273.1 0.0874 0.0881 En Ie 1 \
82—191.5 0.0709 0.0720 4- 11
ROLLA.
198.2—273.1 0.0874 0.0860 — 14

gives ia. the following values of Cp:

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

492

by graphical integration from a curve which has been drawn through
the experimental points of fig. 1, with an extrapolation below 14° K. on
the basis of the assumption that the 7”-law is the ultimate limiting law.

The last column gives the values @, calculated from a = —

yy?

being derived from DeBie’s formula for the energy:

LE
Se, Cl ande
(== OINE 1 = || ==
a) &é—1
0

The change of 6, with 7 has the effect of making the values of
8, which are derived directly from the atomic heats, differ some-
what from those of 6@,.

For copper 6, appears to decrease with increasing temperature in
the region of 20 to 70 K., the rate of decrease being more rapid
at the lower than at the higher temperatures of this region.

§ 5. The values of A, found in § 4 (and also those of 6, $ 3)
are smaller than those following from the formula given by DeBije
Le, whieh with the value found by Mitiikan for the AvoGaDro
number (ef. Suppl. N° 365, March ’14) changes to:

3,657.10-3 J
ra M lag "hels [7 (o)] /s ;
Wee itor JS) Ohe ABE Hop — NON Cle ds sees.

In LiINDEMANN's formula ®):

fame wos
oe hae
one finds for (u from 6= 315: n= Ter
whereas for #5 from 6 = 88 follows: kj = 2.81.10, where for
v, the values at 77=0,2 7, have been used.

T =120, 160, 200. 240, 280 ,
C, = 4.22, 485. 5.28, 5.60, 580%, from which we find:
§ = 3831 , 343 ,, 336 :

On the contrary the results of E. H. and Ezer GrirritHs, Phil. Trans. 214 A
(1914), p. 319, cannot be reconciled so easily with ours as can be seen from the
fact that they give: at 138° K. § = 278, at 149.5° K. 4 = 285

1) Calculated from: 18 C.: o=8,94, »=0.74.10-%, ¢=0,35

—191° G.: gu, 0,69.10-1?, 0,35.

The value of « at 18° C. has been taken from E. GRÜNEISEN Ann. d. Phys. (4)
25 (1908), p. 848, the change of | with temperature from E. GRÜNEISEN, Ann.
d. Phy-. (4) 33 (1910). p. 1264.

a has been assumed to change inappreciably with the temperature according to
E. GRÜNEISEN, Ann. d. Phys. (4) 33 (1910), p. 1272.

2) F. A. LINDEMANN, Physik. ZS. 11 (1910), p. 609.

493

As LINDUMANN’'s formula can be deduced‘) from the principle of
similarity, applied to solid substances, the data mentioned for /7, can
serve at the same time as a comparison of these two metals with
respect to that principle. In this comparison the change of 6 with
the temperature has, however, not been taken into account.

Physics. — “Further experiments with liquid helium. O. On the
measurement of very low temperatures. XXV. The determination
of the temperatures which are obtamed with liquid helium,
especially in connection with measurements of the vapour-
pressure of helium.” By H. Kamer.incu Onnes and SopnHus
WeBer. (Comm. 1475 from the Physical Laboratory at Leiden).

(Communicated in the meeting of June 26, 1915).

1. Introduction. In this paper will be given some new deter-
minations of vapour-pressures of helium based on more accurate
temperature-measurements, as also a contribution to the knowledge
of the correction for the thermal molecular pressure, which has to
be applied with constant volume-thermometers for low temperatures
with gas under diminished pressure, if the manometer is kept at the
ordinary temperature.*)

This correction was discussed in Comm. 1245 (Dec. 1911); an
estimate of its magnitude, which was necessary to form a judgment
of the value of the temperature-determinations, showed that its
influence would only exceed the limits of accuracy then given, viz.
0.1 of a degree, in the measurement of the lowest temperatures.

The present determinations of the boiling point of helium made
with the aid of a belium thermometer with mereury-manometer
arranged for more accurate measurements have enabled us to test
the accuracy of the temperature-determination in the previous series
of experiments with liquid helium, in whieh this point had also
been determined. It appears that the difference. of the previous
results from the present can be explained by the correction for the
thermal molecular pressure. This correction remains below the value,
then given for the limit of accuracy. As to the correction at the
lowest temperatures which were measured, this also appears to have
about the estimated magnitude. The previous measurements are thus
as a whole confirmed.

1) H. KAMERLINGH ONNES, Comm. N). 123 (June ’11).

2) Compare for a different arrangement the conclusion of § 7, Comm. Suppl. 34
(Sept. 1913), where the investigation contained in the present communication was
also announced.

32*

494

We have now for the first time made measurements with a helium
thermometer in which a heated-wire manometer according to KnuDsEN
serves as manometer (comp. § 7 Comm. Suppl. 34). With this thermo-
meter it will be possible to go to still lower temperatures than
heretofore. In these measurements the correction for the thermal
molecular pressure became even now of paramount importance. We
sueceeded in calculating a formula for this correction, albeit with
the aid of a hypothesis regarding the effective molecular free path
which leads to a semi-empirical relation.

The new constant in this formula which is a characteristic constant
for helium could be chosen such, that for all our measurements
with the thermometer with hot-wire-manometer a satisfactory agreement
was obtained with the thermometer with mercury-manometer.

2. Survey of the difficulties inherent in the determinations of the
lowest temperatures. All measurements of temperature in the helium-
region will ultimately have to be reduced to readings on a helium-
thermometer supposed to be filled with helium in the AvoGApro-
condition. Hence the importance of knowing, how to arrive at
accurate determinations with a helium-thermometer, even at very
low pressures. For measuring those temperatures, at which the
vapour-pressure of helium approaches a very small value, no other
helium-thermometers but those with gas at very low pressure can
be used, as the pressure in the thermometer must in any case remain
below the vapour-pressure corresponding to the temperature to be
measured.

Various circumstances thus render it difficult to raise the accuracy
to the level which would be permitted by the high degree of constancy
of the temperature of the helium-bath which can be attained when
the experiment is not unduly prolonged.

It will be necessary to take care that the following conditions ~
are fulfilled.

1. The dead ‘space, or rather that part of the dead space the
temperature of which is uncertain, must be made as small as possible.

2. The adjustment of the equilibrium must take place in a
sufficiently small time in order to prevent the temperature-changes
of the helium-bath affecting the measurements.

3. The deviations of the equation of state for the thermometric
gas from the Avocapro-condition must not come too much into account.

4. The correction for the thermal molecular pressure must not
become too large and this pressure must not reach a region, for
which the correction is less accurately known.

495,

It will be seen that these requirements cannot all be fultilled
at the same time. A small value of (1) goes together with a large
value of (2) and similarly a minimum of (8) corresponds to a
maximum of (4).

All we can do therefore is choosing the construction of the
thermometer such that in the intended measurements an optimum
is attained as regards satisfying the mutually conflicting requirements.

A calculation of the order of magnitude of each of the afore-
mentioned disturbances, uncertainties or corrections will in general
sufficiently enable us to reach our object.

It is clear, that we have to devote our attention particularly to
the capillary which connects the reservoir (at low temperature) with
the manometer (at the ordinary temperature).

As regards (1), the uncertainty regarding the distribution of tem-
perature along the capillary makes itself principally felt in the lowest,
coldest part of the capillary, where the density of the gas is highest;
the narrower this part in proportion to the rest, the smaller the
uncertainty will be.

It would of course be advisable, if possible, to avoid the calcu-
lation of the correction for that part of the dead-space which is
dependent on the capillary by placing an auxiliary capillary according
to Cuapruis beside (he capillary of the thermometer.*) In our case
we were unable to utilize this device owing to want of space in
the cryostat. It was all the more important, therefore, to take the
lower part of the capillary as narrow as possible, from which it
follows in view of (2), that the capillary must be taken wider
higher up.

At the lowest temperatures the question becomes of importance,
whether helium still follows the gaseous laws. On the one hand the

B
term — in the equation of state pv = A + — has to be considered,
v v

where B for a reduced temperature say of 0.2 acquires a fairly
high value, so that the correction to be made on account of 5 may
obtain an important influenee. As long as the equation of state for
helium is no better known than is at present the case and the
calculation has to be made with the “mean” equation of state accord-
ing to the law of corresponding states, great uncertainty exists with
regard to this correction. On the other hand it might be a question,
whether A may still be taken directly proportional to 7’ or whether

1 We are dealing here exclusively with the constant-volume thermometer. A

subsequent Communication will deal with the use of thermometers at constant
pressure,

496

an absolute zero-point pressure according to the theory of quanta
ought not to be introduced.

In both respects the difficulty might be sufficiently avoided by
simply taking the melting-point pressure of the thermometer sufficiently
small, but in that case, as already pointed out, the thermal molecular
pressure begins to give difficulties which ultimately exceed all the

2h
others. In fact this pressure depends upon the ratio co where A

is the radius of the capillary and 4 the mean free path.

Whereas we know the condition of the pressure-equilibrium
between the bulb of the thermometer and the manometer, when
the temperatures of both are given for the two extreme cases
Oe al IR 4 = es ;
SS and = this is no longer the case for intermediate
values of this fraction. In ordinary gas-thermometers with a melt-

ing-point pressure of about the normal atmospheric pressure,
2)
the condition ee is very nearly satisfied and the pressures p,

at the top and p, at the bottom of the capillary, where the tem-
peratures are 7, (normal) and 7’, (to be measured) respectively,
may be taken as equal. As we shall see, this is by no means allowed
when temperatures are to be measured at which the vapour-pressure
of helium is no more than afew millimeters. In thermometers which
are adapted to this object considerable corrections have to be dealt
with, as will appear in the measurements to be discussed in this
paper, indeed the question naturally arises, whether in this case it
is not preferable in the temperature-measurement to start from the

ENNE ee REE
condition of equilibrium for PES Mi SS.

3. Description of the two thermometers.

The thermometer with mercury-manometer (fig. 1) was the improved
form of that in Comm. 119 as described in Comm. 1245. The bulb
Th, had about three times greater capacity, 23.95 ce., and the
capillary consisted of three parts, the first starting from below
C,—C, 15.3 ems. of 0.0362 em. radius, the next C,—C,. 9.80 ems.
of 0.0783 em., the third C.—-Cy 22.59 ems. of 0.0947 em. (the
upper 5,25 em. having 0,090 em, radius). To the top of the glass
capillary (being another part of 5,55 em. of 0,090 em. radius) was
soldered (entering over this same length) a copper capillary of
1.2 mm. diameter, which was connected to the mercury manometer,

497

first described in Comm.119 Pl. TL and more recently in Comm. 1245
Pl. I fig. 3 and specially designed for thermometrie work. After
the improvement of Comm. 1244 this manometer had only under-
gone a slight modifieation: in addition to the glass-tap in the glass
capillary leading to the copper one, a side-tap has been added whose
object is to connect the thermometer with the mercury-airpump if
required.

Fig. 1. Fig. 2.

The part of the dead space of the thermometer which during the
measurements remains at room-temperature had a volume of 4.87 cc.
The second thermometer (fig. 3) was provided with a very small
heated-wire manometer’) &, designed to measure small pressures
with sufficient accuracy. The bulb of the thermometer had the same
volume as that of the first thermometer 23.956 ec. and the capillary
was constructed in exactly the same way as with the latter. [he
part of the dead space which in this thermometer did not assume
the low temperature was 2.67 ce; the heated-wire manometer stood

DH, KAMERLINGH Onnes and SopHus WeBeER, Comm N’. 1375,

498

in ice. Previously this instrument had been carefully calibrated with
the aid of a set of pipettes with pure helium. We are glad to offer
Mr. P. G. Carn our thanks for his assistance in this work.

4. Results. The thermometers were mounted side by side in the
helium-eryostat, which was vigorously stirred by means of a pump-
stirrer. The bulbs were surrounded by brass tubes in order to protect
them from radiation through the liquid helium. The vapour pressures
of helium were corrected for the aerostatic difference of pressure
between the helium liquid surface and the vapour-pressure manometer.

Two series of observations were made. In the first Mr. Cuapputs

Vapour-pressures and thermometer-readings with helium. 1st series.
2 Thermometer with | Thermometer with
Test ||| mercury-manometer heated-wire manometer
28 g Poo = 25.738 cms | Po c= 5.240 cms
SEE il} — —— |
RES | Mutual | | Mutual
ag Uncorrected qe deviations | Uncorrected Tea need deviations
> ‘| of obs. “| \ of obs.
Tr = ] es = =- = = — =
| 156.6 | 4.205 K. 3 0.5% || 4°.468 K. 2 0.29%
564.5 | 4.155 a =" Vis
363.3 || 3.800 OEZ 0.2
| 359.5 || 3.535 3 0.25 |
| | ||
| 4.4 1.478 2 225 | 1.774 2 0.2
|
Vapour-pressures and thermometer-readings with helium. 2nd series.
\2 Thermometer with | Thermometer with
as | mercury manometer | heated-wire manometer
os 5 | Poe c= 25.358 cms | Poe C.S 1.2509 cms
[LEE | an gi
|S.5 5 || | Mutual Mutual
ag Uncorrected A NUE deviations | Uncorrected T Auber deviations
> | ORDE 6 | | “| of obs.
751.5 || 4.215 K. 2 0.1% «| |
| | HH
| 157.4 | || 5°.472 K. Ze A Ol
4.15|| 1.509 2 1.0 In 22558 2 4h Ont
756.5 4.219 2 0.1 |
| \} |
| 156.4 | | 5.470 2 0.1
| | II

499

the melting-point pressure of the helium-thermometer with mercury-
manometer was 25.738 ems. mercury, that of the helium-thermometer
with heated wire manometer 5.240 cms. In the second series these
pressures were 25.358 ems. and 1.2059 em. mercury respectively.
The vapour-pressure measurements were conducted in the same
manner as before (comm. 119 and 1245). The results were as follows
(uncorrected 7’ stands for 7’ not corrected for B and for thermal
molecular pressure *):

The first column gives the vapour-pressure of helium at the
corresponding temperature, the second the temperature as calculated
with the aid of the ordinary gas-laws (with b=0). The great
difference between the temperatures found in this way with the two
thermometers is very striking, especially in the last series of meas-
urements in which the melting-point pressure of the second thermo-
meter was very low. The influence of the thermal molecular pressure
causes a temperature of 5°.5 to be found instead of 4°.2.

5. Correction for the thermal molecular pressure. Expressions for
the thermal molecular pressure which are valid for the ranges

2h 2R 4 3
OS Si or 10< = <a have been developed by Kyupsen. !t is

clear, that the choice of the two limits 1 and 10 has been somewhat
arbitrary, but we may assume, that, when these limits are attended
to, the uncertainty of the results of calculation by means of these
formulae, supposing the constants which occur in them to be known,
is on the average smaller than 1°/,. KNupsrn’s formulae do not hold

9
for the intermediate range of 1 < SE <10.

The condition of pressure-equilibrium in a tube with a gradient
of temperature is in KNuDskN's notation
= ()

1
2nR(M + B) + ak? =
C

dp. :
Tk here the pressure-gradient, R the radius, J/ the tangential

force per cm?. exerted by the gas on the wall in consequence of

1) In controlling the calculations it was found that small errors and uncertainties
remain about the data for calculating the gas contained in the capillary, which
can change the numbers for the uncorrected 7 by some thousandths of a degree.
The necessary corrections are inside the limits of the experimental errors. So we
have left them mixed up with the latter. As soon as we shall have an opportunity
to compare the present determinations with more accurate ones, we can perhaps
return to this point. (Added in the English translation).

500

the temperature-slope and B the tangential force which the gas
owing to its flow back along the axis of the tube exerts on the wall.
M and B according to Kyupsun *) are thus given by:

Bye dQ Oy d2
Me ke Nm 2) — = he
128 dl 128.0,30967 dl
and
3 ap dp mr i
Ba Bh k, 2 Dn where a = 3% ae

N the number of molecules per ce, 7 the mass of a molecule, 4
the viscosity and 4 the mean free path.

If 2 is not small as compared to &, we may not assume, as is
done in the derivation of the formulae, that a molecule in a collision
with a second molecule possesses the velocity corresponding to the
temperature at a point at a distance 2; in that case the collisions
with the wall have also to be taken into account. The paths described
by the molecules since the last collision are then found as follows:

In a disk of unit length cut out from the tube there are aM

re)
molecules and therefore «RN — mutual collisions occur per second
and 2a2R14 N@ collisions with the wall; the joint number of
collisions is thus

2
2aRiN2Q + RIN per second,

1 1
and each molecule collides (or + 5) 2 times, while describing a
path 2. The path described without collision is therefore on the

average

This leads to the following condition of equilibrium

tar i de nk Redp ey
2ak| — —k, Nm2 - Te ~~ , — See die = (I)
128 a “dl 256.0,30967 2 dl
boj OR

as 74 = 0,30967 Nm 22 or

1) M. Knupsen, Ann. d. Phys. 33, p. 1435, 1910. 31, p. 633, 1910 and 31,
p. 205, 1910 and SopHus Weser, Leiden, Comm. 137c.

2) The temperature change of the coefficient of accommodation for collisions
with the wall is disregarded on account of its smallness.

501

d 3 d2 1
Be k ate od)

PLD ETA ONK
2 0,30967.256 2

2R d, d& ale
As for — =0 we have P — or = iy + it follows,
a p 2 Pa T,
. 4 2R
that £, —— for —=0.
3 a
In the ease, that — becomes large, we obtain
drops A OH
EDO
ro ARA Jill

or introducing
nr neat:
hs — -
8 0,30967? po, 273
where g, is the density of the gas at O° and 1 dyne per e.m.’,
we get the formula

25 See lige T aT
0,30967.2737 o, A? kh, c
1+ T

pdp

calculating, like KNupseN, with SUrHERLAND’s formula (which however
is no longer applicable at temperatures below those of liquid air)
and calling the viscosity at 0° C. 9).
Knupsen has determined the value of 4, and #%, for hydrogen and
k
oxygen and found = = 2.0 and ti

“9

It is easily shown, that our formula (1) differs from KNupsEN’s

I
formula only by the factor EE which has no influence for

QR
2R
high values of =
It is therefore obvious, that the factor 4, in (1), if this equation
2h 2
is to hold for all values of mr. cannot be a constant, seeing that

2k
for all gases it approaches the value % for ii 0 and that for

5 2k
high values of a it becomes 2.3 for oxygen and hydrogen.

It is further to be remembered that in the theoretical deduction

502

of the relation between heat-conduction and friction numerically
correct results can only be arrived at by taking for the mean free
path in the case of conduction a somewhat higher value than that
which follows from internal friction. In other words the velocity of
the molecules at a collision is not that which corresponds to the
temperature at a distance 2, but at a distance «2, where « is 2.5
for monatomic gases and 1.7 for di-atomic gases. If we introdnee
this into the expression for J/ we obtain, as found by Kyepsen,
taking £,=1, for di-atomic gases Jk, = 1.7 Xx 4 for high values of

2k
== Or
2

;, = 2.3. For helium we shall have to take £, = 2,5.4=3.33:

for this gas &, thus changes between the limits */, and 3.3. The
question, as to how #, depends upon the mean free path will have
to be decided by experiment. This problem is analogous to that
concerning the relation between heat-conduction and friction, when
there is also slipping along the wall. Keeping that in view we have
ventured to make a simple assumption which does not clash with
the available experimental data and explains the nature of the
deviations between our thermometers with different melting-point
pressures as well as possible. In bow far this assumption may be
correct, can only .be settled by future experiments. In the mean
time it may perhaps be considered as a rough representation of
what will be found, when this problem, which is of great importance
for the insight into the mechanism of heat-conduction and internal
friction, will be specially taken up. The assumption in question is, that

heteen De

In this formula c, and ec, are two coefficients, c, having a special
value for each gas and being 0.550 for belium and ec, differing for
monatomic and diatomic gases. For the former ¢, = 2.5 and for
the latter c, == 1.7.

If we abandon the assumption, that 4, == 4 x 2.5 for large values

2R ;
of zE there is an additional constant c, available to adapt the
formula to our observations. A very good agreement is in that case
obtained with ec, == 2.865 and c,—=0.3101'). The corrections obtained

is the value of the power of 7’ in the viscosily-law for helium,

5038

Returning to our equation (1) we have for a monatomic gas
2k

i! er
dp en 1 dT

Zed d
p Is ee: Te ae
eae Ls eer a)

where for helium ec, = 0.1190 5.
We have now to express 7’ as a function of p and 2.
7
of bydrogen (comp. Comm. N°. 1345 March 1913) and as the thermo-
meter-corrections are almost entirely due to that part of the ca-
pillary which is at a higher temperature than 20° K., we may
apply this formula to the whole temperature-range in the form

Nt
MN EN 4

According to the expression for à given above, we have:

digp = (1 + n) dig T — dlga.

2 0.647
As the relation 7 Sal ) holds down to the boiling point

or also
digp = (A + n) dlgT + dlqy
it
2h
— DE F

With y as independent variable we may therefore write:

| ‘dp = 3 | : k, dy
2 ¥ y{(A+y) (1+e,y) (1 +7) Sea 3

The correction consists in our case in the sum of three corrections
for the different parts of the capillary, each with a different R.
For each of the three parts the integral might be easily found by
mechanical quadrature, taking .into account the changing valug of
k,, as soon as the limits of the integration are known. We may
also for the sake of simplicity divide each part into smaller parts
such, that in the integration a mean value may be assumed for 4.
The limits are each time determined by the value of the viscosity

; : : ; dp
1) It follows from this expression, that there is a maximum value of 7
a
(S. WeBeER Comm. N°. 137c Sept. 1913). In arranging the measurements in
question care must be taken that at the place where this maximum occurs the
distribution of temperature is known as accurately as possible.
The determination of this maximum may possibly be of importance in the

investigation of the relation between kj and Sn

504

of helium corresponding to the temperature and the density, as also
by the value of the radius at the ends of the given portions of
the tube’).

As the density depends on p as well as on 7’ and as p varies
along the tube, the limits at the ends of the various parts will
depend upon the local values of p themselves: of these only that
at the top of the capillary is immediately known, whereas at the
bottom the density is approximately known, it is true, but neither
p nor 7. It is therefore necessary to proceed by successive approxi-
mation and starting at the top to calculate the diminution of pressure
assuming as a first approximation p == constant equal to the value
at the top of that portion of the tube, and then, using the distribution
of pressure which is found and the known distribution of temperature
to improve the calculation, ete.

The uncertainty regarding the distribution of temperature along
the capillary is of course a source of error, but as a rule the errors
arising from this uncertainty are not of any importance, especially
because usually, according as this uncertainty is greater for a given
portion of the tube, its contribution to the total correction for the
molecular pressure becomes smaller. Finally for that portion which
reaches down to the range of temperatures which have to be deter-
mined by the thermometer itself the contribution to the correction
can be entirely neglected. The most important contribution to the
correction is due to the upper part of the capillary.

5. Corrected temperatures. Applying the corrections on the basis
of the pressure-distribution along the capillary, as found by the
above calculation, the following results are obtained: (see tabel II
p. 505).

The values between brackets ( ) refer to the calculation with the
more empirical values of ec, and c,, introduced solely with a view
to the observations witbout taking into account the theoretical
limiting values.

Caleulating the correction of the helium-thermometer with mereury-
manometer by means of the formulae tested in the above series of
observations, we find (considering only the most reliable observations
(see table IIL p. 505).

1) If afterwards a changing value of m were found for helium at the lower
temperatures, as in other gases, the same formula will be applicable, for each
piece into which the tube is divided its own value of ” being introduced.

505-

TABLE IJ. Temperature-measurements in the helium-region with
the heated wire helium-thermometer.
| S
amour Series I. Dop, =5, 240 cm. | Series Il. poe, = 1, 2059 cm.
pressure of | j
the bath T uncorr. T corr. | Tuncorr. T corr.
Wiis Vi [ {
756.6 mm. 4.468 K. 4.260 K. (4.230),
757.4 | 5.472 K. |4:245 K. (4.207)
564.5 | 4,155 (3.937 (3.912), | |
363.3 | 3.800 3.587 (3.568)
was RR 11.495 (1.490)
4.16 | |’ “2,558 |1.445 _ (1.461)
157.4 | | 5.472 4.245 (4.207)

TAB IEN

Vapour-pressures of helium measured by the helium-thermometer with
mercury-manometer and corrected for the thermal molecular pressure.

Vapour- || Accurate series 1913. | Series 1911.
pressure of - == aes n
helium in | ||
mms. | T uncorr. de COM: | T uncorr. T corr.
| fe) ke)
160 4.29 K. 4.22 K. (4.21)
757.5 || 4.215 K. [4.204 K. (4.208) ||
565 | 3.97 3.90 (3.89)
359.5 3.535 3.519 (3.516) |,
197 | 3.26 3.18 (3.17)
By "ll | 2.34 2.25 (2.24)
4.15 || 1.509 1.480 (1.475) |
3 | 1.47 | 1.36 (1.35)
il

In the same manner the vapour-pressure above the boiling point
is found as follows (Comm. N°. 1245, p. 16): (see tabel IV p. 506).
The corrections to be applied to the temperature-values as given
in previous communications will be seen to be but small. Both the

506

TAB GE MV.
Vapour-pressures measured by the helium-
thermometer with mercury-manometer,
corrected for thermal molecular pressure

(above the boiling point).
P T uncorr. T corr.
Lt once BTR Ce ern ean
767 mm. 4.28 K. 4.22 K. (4.21)
|
1329 4.97 4.91 (4.90)
1520 5.10 5.05 (5.04)
1569 "| 5.15 5.10 (5.09)
|
1668 | DAD Sab (5 A16)
1718 5.25 5.20 (5.19)
crit.

boiling point and the critical point go down a little, but the change
is within the limits of accuracy as previously given. The conclusions
formerly drawn from the temperature-measurements thus remain
valid, especially the rapid change of the constant fin VAN DER WAAIS’s
vapour-pressure law which we inferred at the time.

With the chosen pressures in the helium-thermometer with mercury-
manometer the correction for 4 becomes of minor importance.

At the boiling point of helium it is too small to have any influence.
According to Comm. N°. 1195 § 5 in po=kT+— we found
Baoar K = — 0.000047 and we thus bave with poco = 25.5 ec. at

5
4e OOK el + 0.000128.

It is true, that at lower temperatures, as discussed in § 1, B
becomes much larger. An extrapolation according to the “mean”
equation of state, in itself certainly little justified, would give.
By 50%. = 56.1 Byoo; x. Even on this supposition an error of only
2°/, or 0,03 degrees would have to be expected from B being
neglected. This deviation is smaller than the uncertainty of the cor-
rection for the thermal molecular pressure.

When the melting-point pressure in the thermometer with heated-
wire manometer is as low as it was taken in the above 2nd series,
the uncertainty regarding the last-named correction becomes predo-
minant. From this it appears, that a very accurate knowledge of

1) W. H. Kersom, Suppl. N°. 30, p. 12.

507

the thermal molecular pressure will be needed, if values of B are
to be derived from the comparison of thermometers with different
initial pressure. The same is true with respect to possible correc-
tions for deviations, as predicted by the theory of quanta.

7. Approximate formula for the vapour-pressure of helium. We
did not succeed in representing our observations by NeRNsT’s vapour-
pressure formula, treated as interpolation-formula.

The Bosr-RANKiNg form ’)

1 1 1
lg Pom.Hg = Zs Br 60 7: + D 7:

gave with
A= -+ 3.7290, BSS 05 B OMS ORS D=+4.3634
the results shown in Table V

TABLE V. Vapour-pressure of helium.
T | Pobs. Peale
1475 K. | 0.415 em. 0.419 cm.
| 3.516 35.95 35 50
|
4,205 75.15 16.38
4.9 | 132.9 136.5
fete 25-416 166.8 | 162.1

Even with this formula containing four constants the observations
appear to agree only very imperfectly.

Physics. — Methods and apparatus used in the cryogenic laboratory.
NVI. The neon-cycle. By H. KAMERLINGH Onnes. (Comm.
147c from the Physical Laboratory at Leiden).

(Communicated in the Meeting of June 26, 1915).

1. Introduction. In several accurate investigations on the law
of dependence on the temperature of the properties of substances
the difficulty is encountered, when going below 55° K., that not
till 20° K. is reached liquid baths of the desired constancy are again
available. The gap between 55° K. and 20° K. in a range which other:

1) G. A. CROMMELIN, Comm. NO, 138c,
33
Proceedings Royal Acad. Amsterdam, Vol. XVIII.

508

wise extends far in both directions without any break and in which
the temperature is under complete control from 90° K. to 55° K. by
means of liquid oxygen and from 20° K. to 14° K. of liquid
hydrogen, -— this gap is all the more to be regretted as in the
absence of a liquid bath comparisons of auxiliary thermometers with
the helium- or hydrogen-thermometer in this region of temperatures
are completely wanting. It would be specially valuable, if this gap
could be filled for the lower portions of the temperature-range in
question by tbe addition of a portion above the boiling point of
hydrogen joining on to the range of reduced temperatures which is
governed by hydrogen between 20° K. and 14° K. As instances of
investigations for which this extension would be greatly desired we
can name (besides the equations of state of hydrogen and neon) that
of paramagnetic susceptibility, that of specifie heat, and that of
galvanic resistance.

We have now succeeded in utilizing neon for this purpose.
During the experiments which have led to this result some thermal
quantities of neon were determined, which will be discussed in the
next communication (147d, these Proceedings) by Dr. CROMMELN and
myself. Amongst other data the boiling point of neon was found at
about 27° K. and the triple-point at about 24.5° K. By using neon
exactly in the same way as hydrogen, the range of 14°—20° K.
can, therefore, now practically be extended from 14° K. to 27° K.
As we have also found, that there is no serious difficulty in con-
structing cryostats for pressures some atmospheres above the normal
(e. g. with hydrogen it is possible to go from 20° to 25° K.), a
pressure-cryostat with neon will probably allow us to ascend to
a temperature of 34° K., by which it would become possible to
study by the eye the critical phenomena of hydrogen in a bath of
liquid neon. A future communication conjointly with Dr. CROMMELIN
will, | hope, deal with an investigation of this question.

Further as regards the region from 34° to 55° K., we may
mention even now, that one of the next communications will contain
a description of an arrangement by which I have succeeded by a
satisfactory method by means of hydrogen-vapour heated to the
desired temperature in obtaining constant temperatures in this region.
In a further communication to be given conjointly with Dr. CROMMELIN,
which will follow soou afterwards we hope to give an experimental
determination of the critical temperature of neon (compare our
Comm. 147d below) made by means of this new arrangement.
The same arrangement may also be utilized in the temperature-
region from 20°—384° K. But for most experiments, particularly

509

when phenomena have to be followed by the eve, the cryostat with
liquid neon is very much to preferred.

It was gratefully mentioned before, when the attempts to arrange
a neon-cryostat were discussed for the first time (Comm. 112 June
1909), that the gas was very kindly put at our disposal by Mr. G.
Craupe and the “Société d’Air Liquide” in Paris. This gas was
rich in neon and from it the large quantity of pure neon which is
now in circulation in the laboratory has been separated (Comp.
Leiden Comm. Suppl. 214 p. 40—41). It is there described, how
by a preliminary purification of the crude gas by means of freezing
in liquid hydrogen, pumping off the helium and separation of the
large quantity of nitrogen present, a gas was obtained almost totally
free from hydrogen and helium and principally only containing some
nitrogen. Continued fractionation further diminished the quantity of
the admixtures and the ultimate purification was conducted by
means of the neon cycle itself and the removal of the last traces of
oxygen and nitrogen by the aid of carbon cooled in liquid air.

2. The neon-liquefactor and neon-cryostat. These are combined
into one piece of apparatus (see fig. 1 below). The liquefactor
somewhat resembles in its construction the apparatus for the puri-
fication of hydrogen (Comm. 1095 March 1909). The cryostat is
constructed exactly as the helium-cryostat in its most recent form
(Comm. 123, June 1911). The connection between liquefactor and
cryostat is essentially the same as that between the helium-lique-
factor and the helium-cryostat of Leiden. Comm. Suppl. 21 fig. 5
(Oct. 1910). To facilitate a comparison with the helium-cryostat,
the parts of the neon-liquefactor in fig. 1 are marked with the same
letters as the corresponding paris of the helium-eryostat in the
Plate of Comm. 123. For parts of modified construction, but of
analogous purpose accented letters have been used.

The principle of the apparatus (comp. fig. 1) consists in this, that
in the liquefactor the neon is made to condense on a spiral a, a, a,
(comp. a,a@,@, in Plate of Comm. 1095), which is cooled below the
boiling point of neon by means of liquid hydrogen. From the coils
of this spiral the liquefied neon flows down into the eryostat. If
locally the temperature of the cooling-spiral descends below the
melting-point of neon, the substance will there be deposited as a
solid crust on the spiral. The external surface of the spiral, where
this happens, and the remaining free passages between the spiral
and the vessel, inside which the spiral is suspended are so large,
that a considerable quantity of solid neon can be deposited in this

33*

510

Fig. 1.

manner, without the apparatus becoming plugged. As soon as the
lower part of the spiral returns to a temperature above the melting-
point, the neon melts, drips down and flows into the cryostat.

In applying this principle of liquefying the neon by cooling with

liquid hydrogen the difficulty lies in the circumstance, that the
boiling-point and melting-point of neon are only a few degrees apart.
„The coustruction of our apparatus is specially designed to meet the
difficulty arising from the almost unavoidable freezing of the neon.
If we had applied Linpw’s principle of liquefaction on neon, cooled
only in liquid air, and had thus liquefied neon in the same manner
as Dewar first showed, how to liquefy hydrogen, this difficulty
of the neon freezing would not be encountered. But in that case the
other difficulty would make itself felt, that only a part of the
available gas appears as liquid in the bath. As long as neon is still
so difficult to obtain as at present, this objection weighs very much
more than that inherent in the principle of our apparatus. Moreover
as we have the excellent lydrogen-cycle ready at our disposal, it
would be much more complicated constructing a separate neon-cycle
with liquid-air cooling only, than following the method adopted. In
future, when neon will be equally easily obtained as at present
hydrogen and there will thus be no necessity for anxiously guarding
against the smallest loss and such a loss will be considered in the
same light as a loss of hydrogen is now, it will become more
profitable to prepare the liquid hydrogen itself by means of a neon-
eyele. For that case a purifying-apparatus of neon by means of
liquid neon, similar to that of hydrogen described in Comm. 109,
will be practically a necessity. If the neon is not completely deprived
beforehand of the less volatile admixtures, such as nitrogen, the
narrow tubes of the regenerator-spiral, throngh which the gas is
made to flow during its expansion, would be apt to get plugged. In
the method chosen by us it is of no account, whether the neon
still contains a few percentages of the less volatile constituents, like
nitrogen. Without obstructing the passages they are deposited on the
less cooled upper parts of the spiral, while the neon is liquefied or
solidified on the lower coils. If the temperature of the cooling spiral
is so regulated that the vapour-pressure of neon at that temperature
is above one atmosphere, while the solid nitrogen and oxygen have
still only a negligible vapour-pressure, all the liquid and solid neon
which might be present will evaporate and the less volatile admix-
tures of the neon can all be retained in the apparatus and so
removed from it. This procedure may be utilized for the purification
of the neon (see § 3). We will however at present adhere to the
supposition, made in the beginning of our description, that the neon
is already pure.

The liquid neon flowing down from the spiral is caught (fig. 1)
in the silvered vacuum-vessel with silvered draw-off-tube 2,3 and

512

then flows through the small stop-cock Mja into the vacuum-vessel
S, of the cryostat; for the description of the cryostat and its pump-
stirrer we may refer to Comm. 1235, where the lettering is identical. -
The difference between the valve used at present (for details see
separate drawing in fig. 1) and that of Comm. 1235 is of minor
importance and consists in the valve not having a turning movement,
but moving vertically up and down, being guided by the two rods
Haro and carried by the german-silver strip “47. The small stop-
cock is connected to the orifice Har; by means of two german-silver
rings Marg and Zoro.

Fig. 1 represents the condition, in which the cryostat contains a
helium-thermometer 7%,” with capillary Zh,” (as in the Plate of
Comm. 1285, this time however the thermometer used in Comm. 147),
a resistance @Au, as in the same Plate, and moreover a piece of
apparatus for the measurement of the vapour-pressure of hydrogen
above its boiling point (vessel P,, which contains the liquid hydrogen,
besides tube and capillary P,, P;, P, for connection with the further
apparatus): the measurements with this arrangement will be dealt
with in a communication to be made conjointly with Mr. P. G. Cara.

Two tubes are attached to the cover of the cryostat, S’, (comp.
figure of Plate in Comm. 24, where however the corresponding
letter is wanting) and .S’, leading to a manometer and the apparatus
(comp. § 3) for regulating the temperature in the cryostat.

The temperature in the cooling-spiral a, a, in the liquefactor, a,
being protected from supply of heat by a covering of wool, may
be regulated by the aid of the thermometer /, /, /; /:/,, exactly as
in the apparatus for the purification of hydrogen, for the description
of which we may again refer to Comm. 109.

Care has to be taken, that only liquid neon can enter the draw-
off tube. For this purpose a small vessel @ is contrived, which fits
in the vacuum-vessel with a thin layer of flannel; it is open at the
bottom and just above the opening 8, carries a filter 8,, which can
be warmed by means of hydrogen of ordinary temperature which
can be blown through the tube «‚ and the small spiral «, ; by which
means the temperature of the draw-off tube can be permanently
kept above that of the melting-point of neon. Solid and less volatile
substance, say nitrogen, which might fall down, is retained on the
filter and if the nitrogen which has collected there happened to
melt by the temperature rising it flows on the small tray y, where
it remains while only liquid neon can flow down’).

') In order to make the arrangement completely adequate — solid nitrogen is

lighter than liquid neon — this tray should be provided with a standing-up rim
of gauze, which was not yet the case.

513

3. The neon-cycle. This cycle is very similar to that of helium
(Comm. 108 July 1908). The neon is stocked under compression in
one or more receivers fF, (fig. 2). From FR, the gas is made to
flow into the gasometers G',, G,, floating in oil and arranged exactly
as in the hydrogen-cycle (Comm. 94/7, June 1906), the oil being
here also freed from air and moisture.

Jf necessary, the neon, before it is brought into circulation, can

Fig 2.

514

be drawn under pressure through carbon, cooled with liquid air,
by means of the compressor with mercury-piston Q (compare Comm.
54 Jan. 1900) and returned to R, or to the gasometer in purified
condition. The carbon is contained in Z, (which is cooled) and Z,
(a reserve tube), copper bardsoldered receivers which may be exhausted
by the mercury-airpump (vac in the figure) at red heat. The remaining
gas is transferred by the air-pump to a gasholder for impure neon.
The way of using the cocks and the object of the safety-tube 7’,
which in ease of need takes back the gas to the gasholder for impure
neon, as also of stop-cock 2 will be clear without special elucidation.

The eryostat is-filled with the pure neon from the gasometer by
stop-cock 4 through a drying-tube D, immersed in liquid air; from
here it flows with stop-cock 6 open by c’, (comp. fig 1) into the
liquefactor, from which as explained in § 2 the liquefied neon flows
down into the cryostat. The vaporized neon escapes through /S’, to the
gasometers G, and G,. When the cryostat is filled the small cock
Eer, and stop-cock 6 are closed. The neon which might then evaporate
in the liquefactor may escape through stop-cock 8 into the gasholder
for impure neon.

As usual the cryostat has attached to it a safety-tube X; the gas
which might escape through it is caught in the small safety-gaso-
meter Gv. When the small cock Z7, is closed, the temperature of
the bath may be regulated in the usual manner according to the
indication of manometer J/ and with the aid of the differential-
manometer shown beside it (comp. Comm. 83, Dec. 1902) by opening
7 more or less.

The apparatus itself and the connections may be evacuated by
manipulating stop-cocks 10 and 11. The exhaustion is performed
before the experiment to make sure of a proper operation of the
cryostat and again after the completion of the experiment to transfer
the gas contained in the apparatus back to the gasholder for impure
neon. Before proceeding to the latter operation the liquid neon is
transferred to the gasometers G, and G,, either by allowing the
liquid to evaporate with the cryostat connected to the gasometers,
or bv flowing the liquid to the gasometers by pressure through the
syphontube 4, allowing the liquid neon to evaporate in the passages
on its way to the gasometers, or finally by pumping the liquid out
and forcing it into the gasometers with the Siemens-pump JV’. The
gas which is left in the Siemens-pump is transferred by the mercury-
pump to the gasholder for impure neon with all the other gas
remaining in the whole apparatus and connections at the end of
the experiment as already mentioned.

515

To prevent too rapid an evaporation of the bath the cryostat-
vessel S, (fig. 1) is protected by a tube with liquid air.

If the available neon is not quite pure and if it is still desired
to start the work with it without the previous purification by means
of the circulation under pressure over carbon cooled in liquid air,
it will be possible instead of the drying tube DY, to insert between
4 and 5 a earbon-tube D, arranged for purification under ordinary
air-pressure, immersed in liquid-air with a drying-apparatus preceding it.

In the experiments the liquid gas in the bath was always obtained
in a perfectly transparent condition. Only the first quantity of
liquid neon which flows into the cryostat-vessel and evaporates there
very rapidly, left behind a little of a white substance (solid nitrogen
or solid air?) which dissolved again in the liquid gas which flows
in afterwards. A slight ring-shaped deposit was also noticed above
the liquid surface in the evaporation of the bath. The gas had thus
not been quite pure; as a matter of fact this can hardly be expected,
as long as it is allowed to come into contact with the oil of the
gasometers. The use of the latter, however, simplifies the operations
considerably, and the very slight impurity does not give the least
trouble.

It was found that the quantity of liquid in the bath could be
made as much as 400 ce.

I am glad to thank Mr. G. J. Frum, chief instrumentmaker in
the eryogenie laboratory, once again for his help in the construction
of the apparatus described in this paper.

Physics. — ‘“Jsothermals of monatomic gases and of their binary
mivtures XVII. Isothermals of neon and preliminary deter-
minations concerning the liquid condition of neon.” By Prof. H.
KaAMERLINGH Onnes and C. A. CROMMELJN. (Communication
147d from the Physical Laboratory at Leiden).

(Communicated in the meeting of June 26, 1915).

1. Asothermals of neon. This section contains a first instalment
of the isothermal-determinations, by which we hope to obtain the
equation of state of neon at low temperatures. The isothermals of
O° C. and 20° C. have been investigated from 20 —93 and from
20—84 atmospheres respectively; they give sufficient data for the
connections which are required for the reduction of the observations
concerning the isothermals of lower temperatures. Parts of isothermals
for —182°.6 C., —200°1 C., —208.°1 C., — 213°.1 C. and —217°.5 C.
are also given, which may serve as a first survey and even now

516

allow a preliminary application of the law of corresponding states
to be made.

In Table | and IL the symbols 4, p, d4, and v4, have the usual
meaning.

TABLE I. Isothermals of neon.

Series|No.| @ | p dy i < Ee calc.—obs. “io
vi | 1 + 200,00) 22.804 | 21.046 | 1.0835 | 1.0843 | —0.0008 | —0.06
vi | 2 25.015 | 23.052 | 852| 854|— 2 |—0.02
vi| 3 26.515 | 24.464 | 863| 862|+ 1 | 40.01
vi | 4 | 29.090 | 26.757 872| 85|— 3| —0.03
vi | 5 32.572 | 29.801 | 897| 9892) + 5 | +0.04

vil | 1 | 34.887 | 32.002 | 902| 904|— 2 | —0.02
VI | 6 35.423 | 32.441 | 017 | 907 |+ 10 | 40.09
VI 7 31.812 | 34.601 | 928 | 919 |H 9 | 40.08

vil | 2 39.168 | 35.843 | 928) 92% |H 2 | 40.02

VIII | 3 44.762 | 40.862 955) 956 1 | —0.01

VI) 5 54.149 49.213 | 1003 | 1005 | — 2 —0.02

VIII | 6 | 59.717 | 54.161 | 026 | 035|— 9 | —0.08

vill | 7 65.021 | 58.797 | 059| 063|— 41 —0.04

vill | 9 | 71.360 | 69.338 | 131 128 | + 3] 40.03

VII | 10 | 82.545 | 73.967| 160| 158|+ 2 | 40.02

VI 11 88.239 | 78.886 186 180 |=" eas | —0.03

VIII | 12 93.298 | 83.154 | 220, 217; + 3] 40.03

|
vi | 1| oo | 22.064 | 21.869 | 1.0089 | 1.0095 | —0.0006 | —0.06
Vil | 2 | 23.555 | 23-314 | 103] 101|+ 2| 40.02
vil | 3 | 95.867 | 25.558 | 121 | 12) + 9 | 40.09
vil | 4 | | 28.468 | 28.080 | 135) 124 | + | SOS
vil | 5 | 30.790 | 30.345 147 135 | Ae 12)) ae
De | 39.753 | 39.098 | 168 | B 10 | —0.10
IX | 2 44.892 | 44.030 | 196 | 203|— 7} -0.07
Ix | 5| 59.777 | 58.234 | 265| 279/— 14 | 0.14
IX] 6| | 66.104 | 64.135] 307| 311|— 4| —0.04
ix | ea | 74.059 | 71.495 | __ 359 353 | + 6) +0.06
IX | 8 19.108 | 76.127] 392| 380) + 12) +012
IX | 9 84.662 | 81.347 | 408 | 411|— 3 | —0.03

517

TABLE II. Isothermals of neon.

Series} NO. 6 P d A | PY, (obs.)
— == SSS I ek
V 1 | —182°.6 | [67.468 211.34 | 0.31924]
V 2 [14.232 234.61 | 31641]
V 3 [79.168 251.84 31436]

Ill 1 | —200°.1 61.657 263.71 | 0.23375

Ill 2 67.456 291.10 23172
lll 3 13.850 320.85 23017
Ill 4 79.923 348.59 22928

IV 1 | —208°.1 58.472 | 308.32 0.18965

ives | 2 64.451. | 345.22 18670
Heks 69.692 | 377.89 | 18443
Iv | 4 “14.532 | 409.18 18215
Iv |5 79.228 | 439.12 18043

II 1 | —213°.1 53.896 334.59 | 0.16108

Wee 59.769 | 382.03 | 15645
ie 66.271 | 435.46 | 15218
u | 4 22.858 | 484.75 | 15030
nm | 5 | 79.698 | 534.62 14908
1 | 1 | —217°.5 | 49.930 | 358.51 | 0.13927
Tey ie 53.528 | 305.62 13530
Be 59.618 | 458.40 13006
Loh | 64.975 | 511.85 | 12694
ee 11.649 | 571.69 | 12533 |
En ee 79.411 | 632.23 12561

2. Virial-coefficients. So far virial-coefficients have been calculated
for the temperatures of 20°C. and 0° C. only, in both cases using
least squares. The following values were found:

518

TABLE III. Virial-coefficients of neon.

0 | Ay B 42103 | C 4X 108
|
20° Gi -+ 1.0731 | + 0.51578 + 0.82778
0? + 0.99986 |

The differences between the observed values of pv, and those

+ 0.41334 + 1.1538

calculated with the above coefficients are found in Table I in the
last two columns. As the table shows, the isothermal of 20° C.
seems to be slightly more accurate than that of 0° C., a circumstance
which may be connected with the fact of its being more difficult
to keep a vessel at a constant temperature of O° C. than at one of
20° C., when an efficient thermostat is being used.

The communication of the value of the virial-coefficients for low
temperatures, as also the calculation of the BoyLe-point (Br

we defer to a subsequent paper.

3. Boiling point, vapour-pressures, liquid densities, triplepoint.

The vapour-pressures were directly determined as the pressures
of a bath of liquid neon, in which a helium-thermometer was
placed, the same as served for the measurements by KAMERLINGH
Onnes and Weer. ’)

The value found for the pressure at the triple-point differs but

TABLE IV.
Vapour-pressures and liquid densities of neon.

1) H. KAMERLINGH Onnes and S. WEBER, These Proceedings supra. Comm.
NO 1470.
2) Caleulated by interpolation.

519

little from that given Comm. 112, June 1909. Our results (yet of a
preliminary kind) were (see table IV p. 518).

The density of the liquid was measured by a small hydrometer
for densities of 1,20 to 1.30, floating in the bath, which after a
preliminary trial was specially made for this purpose.

4. Preliminary investigation of the behaviour of neon with respect
to the law of corresponding states.

The pieces of isothermals of low temperatures given in § 2 are
too short and have therefore too few characteristic features, to be
able to yield the critical constants of neon by the method of drawing
them in a logarithmie diagram and making this fit the logarithmic
diagram of another substance of known critical data, by parallel
motions in two directions.

They are still insufficient for this purpose, if the improved method
is used of taking as one of the coordinates in the diagram in which

WE
the isothermals are drawn the expression Te which has the same

value for all substances in corresponding states, so that now only
a motion in one direction is required. Definite results are to be
obtained, however, if in addition the value of the critical pressure
(Comm. 112 June 1909) is utilized, although it is only a preliminary
value. Following this plan we have placed the net of isothermals
2 pv : .

of neon in a Fie log p-diagram on top of that of hydrogen, oxygen
and argon and by ascertaining what temperatures the isothermals
which coincide belong to for each of the substances, we have arrived
at a few estimates of the critical temperature.

The results were as follows:

1. Hydrogen. (KAMERLINGH ONNES and BRAAK).

a. The isothermals —200.°1 yv, and — 217.°41 77, coincide and cover
each other completely over a long distance. Taking for the critical
temperature of hydrogen the value found experimentally by BuLLE
Onn, = —241.°14 C., we get

Onl Os Sans I) IE

b. The isothermals —182.°6y,—200.°67, coincide. This gives:
Din SS AD (Co, Whos SS BYES) I.

In this case we used also O7, —= —241.°14 C., but, as this value

belongs to monatomic hydrogen and hydrogen at —200° C. is certainly

520

not yet completely monatomic, whereas at the higher temperatures
much higher critical reduction-temperatures have undoubtedly to be
used, no weight can be attributed to the latter determination.

2. Oxygen (AMAGAT).

The isotbermals —198°.4y, and 0%, coincide, so that, with
Jy.0, = — 118°.84 C. (according to KaMERLINGH ONNES, Dorsman and
Horst),

Ot net Oe Dent

3. Argon (KAMERLINGH ONNEs and CROMMELIN).
a. The isothermals —217°.5y, and —87°.054, coincide. With

Oy Ay = —122°.44 C., according to CROMMELIN this leads to:
Ou ye == 298.92 CO, Tene 44°9 K:
h. The isothermals —200.°ly, and —-28°,, coincide; hence
ene = RRP Te aoe
c. The isothermals —1I91°y, and 0°4, coincide; which yields:
Opne = —227.°9 C., and Tyne = 45. 2. K.

It will be seen that on the one hand the two values obtained
from hydrogen and oxygen and on the other the three values from
argon agree closely, the mutual agreement between these two groups
of values being much less perfect.

[f, using the critical temperature as obtained by the comparison
with argon, the data of Table IV are plotted in the diagram of
reduced vapour-pressure curves (p as function of t‚ where t is the
reduced temperature for the several substances) and in that of the
reduced liquid- (and vapour-) densities (Comm. 131a fig. 3 Oct. 1912)
respectively, the curves for neon range themselves very well between
those of the other substances in their proper order.

Neon thus appears to correspond closely with argon and
to deviate from it in the direction indicated by its lower critical
temperature. We hope to be able soon to be in a position to com-
municate fuller data regarding the equation of state of neon, especially
to replace the preliminary measurement of the critical pressure by
a more accurate one and to give a direct determination of the critical
temperature.

We are glad to record our thanks to Mr. P. G. Carta for his
assistance in the investigation of the liquid state of neon.

521

Botany. — “Sloanea javanica (Miquel) Sszyszylowicz, a remarkable
tree growing wild in the jungle of Depok, which is maintained
as a nature reserve’. Contribution to the Flora of Java,
part VILS By Dr. S. H. Koorpers. (Communicated by
Prof. M. W. BeierINCk).

(Communicated in the meeting of June 26, 1915).

Original habitat. Between Batavia and Buitenzorg the jungle of
Depok has been constituted a permanent reserve since 1913 by the
Nederlandsch-Indische Vereeniging tot behoud van Natuurmonumen-
ten (Dutch-Eastindian Society for the Protection of Natural Monu-
ments), and here I found on March 15% last fruits, which [ immedi-
ately recognized as those of Sloanea javanica (Miquel)
Sszyszylowicz. The fruits were borne by two trees, which I
had ‘‘numbered” in 1914 (provided for botanical examination with
a number board and registered, as 232 and 39%). This observation
was especially interesting, sinee the original habitat of Sloanea
javanica has remained quite unknown to botanical literature
and to myself, although this javanese forest tree had already been
carefully described and figured half a century ago by Miquel in
the Annales Musei botanici 1 1865—1866 p. 65, table 3.

This fact, remarkable in itself, namely that an original habitat
of Sloanea javanica should remain unknown for almost half a cen-
tury, becomes all the more remarkable when considered in connect-
ion with the following facts:

Firstly, that the original habitat discovered by me namely the
forest of Depok, is in the neighbourhood of a scientific centre like
Buitenzorg.

Secondly, that especially in the last thirty years numerous per-
sons, including myself, have botanized in the above jungle.

Thirdly, that this forest tree, which had escaped notice for so
long, is found to be one of the largest trees of the wood.

Fourthly, that a herbarium specimen, collected by me in the forest
of Depok on August 27 1898 and provided with the correct native
name, has remained in the Buitenzorg Herbarium for 17 years,
without having its scientific name affixed to it, although the specimen
in question was within the immediate reach of anyone working in
the Buitenzorg Herbarium during these years.

The material collected by me in 1898, consisting of a few dry
sterile leaf twigs (Kds. n. 311183), remained quite undetermined

1) Compare Verslagen Kon. Acad. v. Wetenschappen, Amsterdam, Sept. 25 1909,
p. 300 and Nov. 27 1909, p. 488.

522

for thirteen years (until 1911) among the “Indeterminata’”’, no one
having even recognized the natural order. Then, in 1911, when
revising my herbarium collections for the Systematisches Verzeichnis
of Mrs. KooRDERS— SCHUMACHER, the twigs came again under my
eyes, and misled by an external resemblance to some species of
the genus Litsea, and in the absence of flowers and fruits, I labelled
them doubtfully as an undeterminable species of Litsea. Under
this preliminary determination, namely as Litsea? spee. div. the
above material (Kds. n. 31118) was first published in the Syste-
matisches Verzeichnis (1 Abteil § 1 Fam. 102, p. 34), with mention
of the station and time of collection.

Recently, on March 25%, when re-examining this 17 year old
herbarium material (Kds. n. 311188) I found that, without the least
doubt, it was identical with the fruiting twigs collected by me on
March 15% at the same spot, and then at once recognized as
Sloanea javanica; these twigs (Kds. n. 428138 and 42807 £)
were derived from two of my “numbered” trees (namely *) tree
23n and tree 397). The old herbarium material was also identical
with a specimen consisting only of leafy twigs (Kds. n. 42814 9),
which bore especially large leaves and had also been collected by
me in the jungle of Depok on March 15th, from a very young
unnumbered tree.

Geographical distribution. Whereas Sloanea Sigur may be
counted among the commonest forest trees of Western and Central
Java, as well as of Eastern Java, growing chiefly at an altitude of
600—1200 metres, and also occurs far outside Java, e.g. in India,
Sloanea javanica, which is sharply differentiated from the
former species by its not prickly fruits and entire petals, is so far
not known outside Java, and has not been found wild in Java
outside the forest of Depok.

Sloanea javanica is the only species of the subgenus Phoe-
nicospermum (Miq.) Schumann, in Engler and Prantl’s
Natürliehe Pflanzenfamilien III 6, (1890) 5. This subgenus was
formerly (1865—1866) erroneously published by Miquel as a
new genus, under the name Phoenicosperma.

Oecological conditions. In the very heterogeneous, shady nature-
reserve of Depok, lying at an altitude of about 100 metres above
sea-level, and consisting principally of evergreen trees with many

1) The letter 7 does not signify here number, but indicates the series to which
the trees numbered 23 and 39 belong.

523

climbing plants and a fairly rich under-growth, Sloanea javanica
only grows very sparsely, but is by no means rare, at least not in
young specimens. Adult trees, however, are only found in very
small numbers. The soil in the forest of Depok is fertile, and like
the climate, it is rather moist throughout almost the entire year.
With regard to rain-fall and location of this station (Depok) the
following data are taken from “Regenwaarnemingen in Ned. Indië”
II 4913) p. 66, published by the Royal magnetic and metereological
observatory of Batavia.

Depok is situated at an altitude of 93 metres above sea-level;
33 kilometres from the coast. Annual rainfall 3156 millimetres.
Monthly rainfall maxima 487 millimetres in November and 678
millimetres in April. Monthly minima of rainfall 95 millimetres in
June and 61 millimetres in August.

Means of distribution. The well developed, brilliantly coloured
arillus of the fairly large seeds, and the brilliant colour of the fruits
would already indicate that the distribution is effected by fructivorous
animals. Since the arillus has, however, an extraordinarily bitter
taste, many animals will probably soon drop the seeds they have
taken. The very scattered occurrence and the relatively small number
of specimens of this tree in the Depok forest may perhaps be
thus explained to some extent. [ myself have not yet observed
any transport of the seeds by animals. I did indeed observe on
March 31 that the numerous fruits lying below tree 89n had all,
without exception, been gnawed by animals before dehiscence. The
mature seeds, although damaged in some cases, were still within
the fruit. As far as Ll have been able to ascertain, this damage to
fallen fruits and also to fruits still on the tree, was probably all
due to monkeys (Semnopithecus) occurring near Depok in large
numbers. As a rule the strong woody pericarp was completely
gnawed away at or near the apex of the fruit, down to the arillus
of the seeds. The large embryo, which has a particularly ‘pleasant
taste, had only been eaten up in a few cases. Apparently the
intensely bitter arillus, which surrounds the greater part of the seed,
had protected it in most cases against the monkeys.

So it seems that Sloanea javanica depends for its means of
distribution on exozoie seed-distribution by small mammals and large
birds, which, having been: attracted by the brilliant colour of the
pericarp and arillus, take seeds from fruits which have opened, but
soon drop them again on account of the intensely bitter taste of
the arillus.

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

524

Season of flowering and fruiting. The two numbered trees (237 and
39n) fruited in March, the older specimen (397) very abundantly.
The flowering season is for Depok in the first half of the wet
monsoon (October—December).

Economic use. According to my native guides the wood is not
durable and is therefore only used as fire-wood, in spite of its large
dimensions. Formerly the dise-shaped wheels of pedatis (buffalo-carts),
were sometimes made from the thick plank-buttresses, found on the
roots of these, as of other trees. The older of the two trees mentioned
(89n) now within the wire fence of the nature reserve, still bears
clear traces of this custom, now obsolete for many years, for
evidently a wheel of a buffalo-cart has been cut out of one of the
plank-buttresses. Formerly the natives of Depok also prepared an oil
from the interior of the seeds (from the embryo). No other economic
application of Sloanea javanica is known.

Culture. On account of its size and fine arboreal habit, and of
the brilliant colour of its large fruits and seeds, this species deserves
to be cultivated as ornamental tree, at least in the lower districts
of Java. So far, however, Sloanea jevanica has not been
planted outside the Buitenzorg Gardens.

Description of the species. In 1894 Koorders and Valeton,
in their “Bijdragen tot de kennis der Boomsoorten van Java’, p. 240,
under “Aanmerkingen”, included anoteon Sloanea javanica, of
which the following is a translation: “The description of the leaves
from a living specimen in the Buitenzorg Gardens (VI. C. 94); the
rest according to Miquel le.” “The actual habitat is not known,
and the tree is only known from the above gardens, so that it
perhaps originates from one of the outer islands, and not from Java”.

“This species is still wanting in “Herb. Kds”. (Thus in Bijdragen
Booms. Java I).

I further wrote in 1912 in vol. IL. (p. 571) of my “Exkursionsflora
von Java” the following:

‘Java? Angeblich (nach Miquel Le.) wild in Java, jedoch
vermutlich dort nich ausserhalb des botanischen Gartens von Buitenzorg
vorkommend. Jedenfalls sah ich noch keine einwandfreie javanische
Spezimina”.

The finds and observations made in 1898 and in March 1915 in
the nature reserve of Depok have filled up in a gratifying manner
the lacuna in our knowledge of the habitat of this rare tree.

525

The examination of the specimens of Sloanea javanica
found in the forest of Depok, have shown me that the specific
description and figure, published by Miquel, is in the main,
correct, but requires amplification and, with regard to a few points,
also correction.

I confine myself here entirely to my observations on the material
from Depok (Herb. Kds. n. 42807 8, 42814 6, 42778 B, etc):

Tree attaining a height up to 25 metres. Trunk up to } metre
in diameter, fairly straight and sometimes columnar, with large
plank-buttresses formed by the roots, branching irregularly and
only high above the ground. Crown high, dense, irregular.
Bark externally dark grey, with watery sap (no latex and no
resin). Leaves with dark green upper surface, lower surface
bluish green; smooth and shiny on both sides. The leaves of very
young plants, only 2 metres high, may attain a length of 40 centi-
metres, but those of the fertile branches of a very old tree, 25
metres high, are only 10—20 centimetres long. Young twigs pale
green; older branches dark grey (not brown).

Fruits (ripe, but not yet dehisced): externally a beautiful orange
(not brick red). Mesocarp thick, woody, dry, grey, almest tasteless
and odourless. Endoearp thin, of a beautiful purple colour. Seeds
(ripe) almost completely enveloped by a fine orange yellow or orange
(not red), glistening, almost odourless and very bitter arillus. Testa
externally shiny black, crustaceous (not osseous). Endosperm small, opal-
white, fleshy. Embryo large, pure white, odourless, of pleasant taste.

Literature:

Sloanea javanica (Miquel) Sszyszylowiez in Engler’s
Botanische Jahrb. VI. (1885) 454; Sehumann in Engler und
Prantl, Natürl. Pflanzenfam. III. 6. (1890) 5; Koorders en
Valeton, Bijdragen Booms. Java I. (1894) 239; Koorders und
Valeton, Atlas Baumarten Java IL. (1914) Fig. 433; Koorders,
Exkursionsflora von Java. II. (1912) 571. (Here read line 17 from
foot of p.571 Miquel instead of: (Miq.) Sszysz.); Phoenicos-
perma javanica Miquel in Annales Mus. bot. Lugd. Bat. II.
(1865—1866) 68. t. 3; Echinocarpus tetragonus Teijsm. et
Binn., Catal. Hort. Bog. (1866) 184 (sine deseript.).

Trees grown in the Buitenzorg Gardens. Of Sloanea javanica
I already saw in last March correctly labelled Buitenzorg garden-
herbarium specimens of two trees, cultivated in the Hortus Bogoriensis
under numbers 92 and 94 in division VI. C. The latter of these two

34*

526

numbered trees from the Gardens (namely 94 VI. C.), was already
published by us in 1894 in Koorpers en Vareron, Bijdragen Booms.
Java I, p. 240, under the correct name Sloanea javanica
(Miquel) Sszyszylowiez.

An old garden collection-label of a sterile herbarium specimen
of tree 92 (VI. C.) indicates, that its numbered Hortus-tree was
formerly cultivated under the incorrect, and as far as I know
unpublished garden name of Elacocarpus stipularis Bl. var. latifolia.

Habit. In the fruiting season this forest giant with a trunk, more
than 12 metres in diameter, is very striking. The dark green crown
is then adorned by numerous fruits, almost as large as fists, extern-
ally orange, internally a beautiful purple and opening by four valves.
These generally contain 1—2, rarely 8—4 glistening jet black,
oblong, fairly large seeds, for the most part enveloped by an arillus
of a fine orange yellow colour. Except on account of the large
dimensions of the trunk, with the large plank-buttresses formed
by the roots, this tree is not very conspicuous outside the fruiting
season. Young trees easily escape the attention of the field botanist,
because this species, even in the sole original habitat so far known,
ie. in the forest of Depok, only occurs very scattered and does not
produce flowers and fruits until it has attained an advanced age;
a furtber reason why young speeimens are inconspicuous, is that
their leaves show such a close resemblance to those of some other
Javanese trees, as regards shape, size and innervation, that they are
only distinguished after close serutinizig. The latter reasons explain
the fact that the original habitat of Sloanea javanica
could have remained unknown for nearly half a century, in spite
of its situation near a scientific centre like Buitenzorg, in the forest
of Depok, often visited by many botanists.

Buitenzorg, April 9 1915.

Botany. — “On the influence of external conditions on the flowering of
- Dendrobium crumenatum Lindl.” By Prof. F. A. F.C.
Went and A. A. L. Rureers.

Dendrobium crumenatum is a small epiphytic Orchid, occurring
pretty frequently in the Dutch East Indies, and especially common
in Western Java, e.
attention of naturali

g. at Buitenzorg; it has often attracted the
sts by peculiarities of its flowering’). These

1) F. A. FP C. Went. Die Periodicität des Blühens von Dendrobium crumenatum
Lindl. Ann. d. Jard. bot de Buitenzorg, Supplément II, Leyde, 1898, p. 73—77.

527

peculiarities are so striking, that the plant has even received
a Duteh name and is known in Java as “duifjes”, in Singapore as
“pigeon orchid”. This name refers to the white flowers of a size
of about 3 centimetres, which appear simultaneously on many
plants and are all the more noticeable, because they remain open
only for a single day. Everywhere hundreds of these small, white
flowers are seen, which are, moreover, delicately scented. Next day
the phenomenon is over and only after several weeks, or even
months, the “pigeon orchids” again suddenly appear in full bloom ;
next day only faded flowers can be found.

We have now studied the phenomenon in question with plants
in their native habitat and with others, sent to Utrecht, which were
finally cultivated there in two different glass houses. A few results,
obtained by us in this manner, are briefly communicated here; for
further details we refer toa fuller paper, which will soon be published
elsewhere. We wish to emphasize, that we have not succeeded in
solving the problem completely, but nevertheless our observations
appear sufficient to deprive the phenomenon of its air of mystery.

In the first place we found that the interval between two succes-
sive flowering periods is subject to considerable variation; at Buiten-
zorg minima of 4 and 10 days, and a maximum of 94 days were
observed, but in Utrecht the intervals were generally much longer,
while in winter flowering cannot be observed at all.

Furthermore it became very evident, that external conditions
influence the outset of the flowering. Accordingly the time varies in
the East Indies from place to place, and only coincides occasionally
for neighbouring places, such as Meester Cornelis, Weltevreden and
Menes (March 14" 1913) or Maos, Klampok and Bandjarnegara
(March 26% 1913). Likewise the time of flowering often differed at
Utrecht in the two glass houses, in which temperature and humidity
were not kept equal; on the other hand the flowering period in
spring was once found to synchronize in glass houses at Utrecht,
Bonn and Hamburg.

When plants, previously grown at a spot A, and hence having
definite flowering days, are transferred to a spot B, they acquire
another flowering time, which is identical with that of plants grown
at B from the beginning... This was found on transporting plants
from various parts of Java and from Deli to Buitenzorg and con-
versely on moving plants from Buitenzorg to Medan. The same
change was observed in plants sent from the tropics to the hothouses
of European botanic gardens.

With respect to the question, what external factors play a part

528

in determining the flowering period, it should be noted that the two
above mentioned planthouses in Utrecht supply an indication, for
here the differences could at most extend to the amount of light,
the temperature and the degree of humidity of the air. Observations
at Buitenzorg (and also earlier ones at Tegal) have shown that the
light may here be dismissed from consideration, for the flowering
time is the same for plants growing in the shade as for those in
sunny places, although the wwuber of the flowers is evidently
determined to some extent by the amount of light. Temperature and
degree of humidity on the other hand, probably both influence the
flowering time, or sometimes the one and sometimes the other of
these factors. At Buitenzorg it was occasionally noticed that heavy
rains, following a period of drought, soon induced an abundant
flowering of Dendrobium crumenatum. On the other hand the co-
incidence of the spring flowering in planthouses at Bonn, Hamburg
and Utrecht can only be attributed to the temperature. During winter
the temperature of such houses is kept very constant; when in
spring the sun becomes more powerful, their temperature rises con-
siderably. It was indeed remarkable, that the above mentioned
coincidence was preceded by a period of bright, sunny weather
over the whole of Western Europe.

In what way can we now imagine the external conditions to
bring about the simultaneous flowering of very different individuals
of the same species? The explanation may be as follows: The buds
of this Dendrobium develop up to a certain stage, but cannot pass
it, unless certain favourable conditions are found in the environment,
e.g. of temperature or of humidity, or of both; then these conditions,
acting for a sufficient time, give an impulse, which carries the buds
to their last stage of development; it is further necessary that these
last stages should be gone through in a very short time.

What is observed in a state of nature is in complete agreement
with this explanation Not only are many flowers found at one time,
and few, or even a single one at another time, but different plants
do not behave in the same manner. We do not mean by this so
much that some plants always flower abundantly and others sparingly
(for this is more likely the result of internal disposition, of which
we know as yet very little) but rather, that on one and the same
plant sometimes many flowers unfold, sometimes only a few. The
favourable circumstances were present, but there were not always
the same number of buds in the sensitive stage, sometimes not even
a single one, so that there are flowering days when a given plant
unfolds no flower, other days, when the number of open flowers is

529

fairly large. Not only do different plants behave very unequally,
but the same is noticed on comparison of the various inflorescences
of the same plant.

Without careful inspection one gets the impression that the flowers
of this Dendrobium are solitary in the axils of the leaves; closer
observation, however, shows that these axils do not contain a solitary
flower, but an inflorescence, of which the axis remains extremely
short and generally only a single flower opens at a given time.
Sometimes, however, two open flowers are found together in the
inflorescence, very rarely even three. Now when careful notes are
made as to which inflorescences of a plant produce open flowers
at a given flowering period and subsequent flowering data are
compared with these, it is found, that in some cases a flower opens
in the inflorescence at each time of flowering and that at other
times it is left out one or more times. Nor is any order discernible
in the combination of inflorescences, which bear open flowers at
successive flowering periods. All this was of course to be expected
on the assumption that the unfolding of the flowers depends on the
presence of buds in a definite developmental stage at the moment
that favourable external conditions occur.

The question arises, whether a closer examination of the buds
gives any indication as to the nature of this stage of development.
The inflorescence is found to arise in the axil of a sheathing leaf
without lamina. The young bud is completely surrounded by the
sheath and the breaking through of this sheath is evidently difficult.
Each bud consists of a number of bud scales and the rudiments
proper of the flower. These bud scales completely surround the
interior of the bud and present themselves as closed sheaths, which
are hard and little permeable — so little, that a bud which has lain
in alcohol for some days, does not show internally a trace of this
liquid. When the interior of the bad has once broken through these
sheathing scales, the latter become fibrous and resemble straw, since
hardly anything remains beyond the vascular bundles. Every floral
bud is generally cut off from the outside world by two of these
scales; these must be broken through before the flower can open.
As long as the bud is not longer than 4—5 m.m. it remains between
these sheaths; at this stage all the floral parts are easily recognized,
although their dimensions are small; only the spur is not yet visible.
When the scales are broken through a sudden extension of all the
floral parts takes place and after a few days the flowers have opened.
Hence just before the flowering a number of buds are found, having
a length of 4—5 m.m., while immediately afterwards this number

530

is much smaller. An investigation at Utrecht on the size of the
adult floral buds, just before flowering, showed some diversity,
probably connected with the fact that not all buds opened on the
same day, and that the flowering extended over two days. This was
repeatedly the case at Utrechi, but also at Buitenzorg stragglers are
sometimes found, which only open on the day after the general
flowering, although it is not so common there as at Utrecht. Probably
this is due to a more rapid development under the favourable con-
ditions of the tropics. Careful observation indeed shows, that the
opening of the flowers is not absolutely synchronous and that it
takes place at different hours; nor is the end of the flowering
reached simultaneously, for it may vary by some hours or even by
half a day. Moreover the interval between opening and fading is not
identical for different flowers.

Attempts to induce flowering experimentally, by a choice of external
conditions, have not yet furnished any result. Such attempts are
rendered all the more difficult by the necessity of having plants
bearing buds at the desired stage of development.

The phenomena shown by Dendrobium crumenatum do not indeed,
differ fundamentally from those observed in other Orchids. In these
also the simultaneous flowering of different plants is often seen, but
it is less striking, because the flowering generally extends over days,
or sometimes even over weeks and hence one flower may open
several days before the other.

Still more generally the flowering of the “pigeon orchids” may
even be regarded as the extreme case of what is observed with
respect to the flowering of plants in our own climate. Here also,
for instance in spring-flowering plants, the floral buds reach an
advanced stage of development, which is not passed, until external
conditions are favourable and then simultaneous flowering of numerous
individuals occurs; the simultaneity is only less striking because the
last stages of development are gone through more slowly. Of late
these phenomena have been repeatedly investigated, e.g. by Kress;
a plant like Dendrobium crumenatum would perbaps be a suitable
experimental object for a further investigation of these cases.

Utrecht, August 1915,

531

Chemistry. — ‘“Jn-, mono- and divariant equilibria’? II.” By
Prof. F. A. H. SCHREINEMAKERS.

5. Ternary systems. *)

In an invariant point of a ternary system five phases occur,
which we will call 1, 2, 3, 4 and 5; consequently this point is a
quintuplepoint. Five curves, therefore, start from this point, which
we shall call (1), (2), (3), (4) and (5) according to our former
notation. Further we find 4 (7+ 2) (n+ 1) = 10 regions, viz. 123,
124, 184, 234, 125, 135, 235, 145, 245 and 345.

We call the three components of which the ternary system is
composed: A, B and C; the five phases then can be represented
by five points of the plane A BC. These five points may be situated
with respect to one another in three ways, as has been indicated in
figs. 1, 3 and 5. In fig. 1 they form the anglepoints of a quint-
angle; in fig. 3 they form the quadrangle 1 2 5 3, within which
the point 4 is situated; in fig. 5 they form the triangle 1 2 5, within
which the points 3 and 4 are situated.

We can however consider figs. 3 and 5 also as quintangles; in
each of them the sides have been drawn and the diagonals have
been dotted. We call fig. 3 a monoconcave and fig. 5 a biconcave
quintangle.

We are able to make of fig. 3 a monoconcave quintangle in different
ways; we do this, however, in the following way. We draw in the
quadrangle, within which the point 4 is situated, the diagonals 15
and 23. These divide the quadrangle into four triangles; the point 4
is situated within one of these triangles. Now we unite the angle-
points 1 and 2 of this triangle with the point 4 and we consider
the lines 14 and 24 as sides of the quintangle, so that a mono-
concave quintangle is formed.

In order to change fig. 5 into a quintangle we draw a straight
line through the points 8 and 4; this intersects two sides of the
triangle, in our case the sides 12 and 15. We now replace the side
12 by the two lines 14 and 24, the side 15 by the lines 13 and
35, so that a biconcave quintangle arises.

In the figs. 1, 3 and5 the anglepoints are numbered in the follow-
ing way. We take any anglepoint and we call this the point 1;
two diagonals start from this point. Now we go along one of

1) For another treatment confer F. A. H. ScHREINEMAKERS. Die heterogenen
Gleichgewichte von H. W. Baxuuis Roozesoom III’, 218,

532

these diagonals towards another anglepoint and we call this 2, from
this point we go again along a diagonal towards another anglepoint,
which we shall call 3; in the same way we go from point 3
towards point 4 and from this point towards point 5. (See the figs. 1,
3 and 5). We call this order of succession “the diagonal succession”.
It will appear from our further considerations for what reason this
definite order of succession has been chosen.

Type I. Now we shall deduce the P, 7-diagram when the five
phases form, as in fig. 1, the anglepoints of a convex quintangle.

As the lines 23 and 45 intersect one another, it follows for the
phases of curve (1):

2+3274+4+5 ne
2)(8) 14). (Oo, = ie
We find for the phases of curve (2):
3+42>1 5
ai ap a

(84 | @ | He
Now we draw in a P, 7-diagram (fig. 2) arbitrarily the curves
(1) and (2); for fixing the ideas we take (2) at the left of (1). With
regard to this the above mentioned reactions have been written at
once in such a way that also herein curve (2) is situated at the left
of (1). [For the distinction of “at the right” and “at the left” of a
curve we have previously assumed that we find ourselves in the
invariant point on this curve facing the stable part].

Fig. 1

Now we shall determine the position of curve (8). It is apparent
from the first reaction that the curves (2) and (8) are situated at
the same side of curve (1); as (2) is situated at the left of (1), (3)
must consequently be situated also at the left of (1).

It is apparent from the second reaction that (8) and (1) are
situated on different sides of (2); as, according to our assumption

533

curve (1) is situated at the right of (2), (8) must consequently be
situated at the left of (2).

Consequently we find: curve (3) is situated, at the left of (1) and
of (2); curve (8) is situated therefore, as is also drawn in fig. 2,
between the stable part of curve (2) and the metastable part of
curve (1).

Now we determine the position of curve (4). It follows from the
first reaction that (4) is situated at the right of (1); it is apparent
from the second reaction that (4) is situated at the left of (2). Curve
(4), therefore, as is also drawn in fig. 2, must be situated between
the metastable parts of the curves (1) and (2).

At last we have still to determine the position of curve (5). It
is apparent from the reactions above that curve (5) is situated at the
right of (1) and of (2). Consequently curve (5) is situated within
the angle, formed by the stable part of curve (1) and the metastable
part of curve (2). Within this angle we also find however the
metastable part of curve (3); consequently we now still have to
examine in what way curve (5) is situated with respect to curve (3).
We take for this the reaction between the phases of curve (3); we
find from fig. 1:

4+5271+4+2 | 3)
CROW M COM Migs ieee area

As we know already that (1) and (2) are situated at the right
of (3), we have written this reaction immediately in this way that
also herein (1) and (2) are situated at the right of (3). Prom this is
at once apparent that (5) must be situated at the left of (3).
According to the previous it is apparent, therefore, that curve (5)
must be situated between the metastable parts of the curves (2) and (3).

Besides the reactions 1, 2, and 3 we may still deduce two other
reactions from fig. 1; those reactions refer to the phases of the
curves (4) and (5). Although those reactions are no more wanted,
they may however be used as confirmation. We find:

1452243 14223844
OSIS “ W®/H|@Q@

The partition of the curves, which follows from this is also in
accordance with fig. 2.

Now we have still to deduce the partition of the regions. Between
the curves (1) and (2) the region (12) = 345 extends itself, between
(1) and (3) the region (13) = 245, between (1) and (4) the region
(14) = 235 and between (1) and (5) the region (15) = 234. When
drawing those regions we have to bear in mind that a region-angle

534

is always smaller than 180°. When we determine in a similar way
the position of the other regions, we find a partition as in fig. 2.

The following is apparent from fig. 2. When we move, starting
from a point of the curve (J), around the quintuplepoint, the succession
of the curves is: (1), (2), (3), (4), (5) or the reverse order (1), (5),
(4), (3), (2); we shall express this in the following way:

“The curves follow one another in diagonal order”.

Further it is apparent that the partition of the curves is symmetrical
in that respect, that we find between every two curves the meta-
stable part of another curve. Also we see that the regions are
divided symmetrically with respect to the different curves.

This symmetrical position of curves and regions with respect to
one another is based of course on fig. 1; this is viz. also symme-
trical in so far that each phase is situated outside the qnadrangle,
which is formed by the four other phases.

Further we see in fig. 2 again the confirmation of the rule that
each region which extends over the metastable or stable part of a
curve (/,) contains the phase #. Let us take e.g. curve (1); the
region 134 extends over the stable part of this curve, the regions
124, 125 and 135 extend over the metastable part; each of these
regions contains the phase 1.

Type Il. Now we consider the case that the five phases form
the anglepoints of a monoconcave quintangle (fig. 3). In order
to determine the position of the curves (1)—(5) we take the five

reactions :
4+5272+4+3 14+523+44 \
(4) (5) | (2) | 2) 8) (1) (5) | (2) | @) @
14+2+4524 2432145 ME:
(1) (2) (5) | 3) | @ (2) 8) | @® | Gd) ©)

4214283
(4) | (5) | 0) 2) B)

Now we draw in a /, 7-diagram (fig. 4) the curves (1) and (2);
for fixing the ideas we take (2) at the right of (1). According to
this the above-mentioned reactions, which refer to the phases of the
curves (1) and (2) have been written at once in such a way that
herein curve (2) is situated at the right of (1).

It follows at once from the first and the second of the reactions
above, that curve (3) is situated at the right of (1) and (2). Conse-
quently curve (8) is situated, as is also drawn in (fig. 4) within the

535

angle, which is formed by the stable part of curve (2) and the
metastable part of curve (1).

It also follows immediately from the first and the second of the
reactions above, that curve (4) is situated at the left of (1) and at
the right of (2). Curve (4) is consequently situated between the
metastable parts of the curves (1) and (2), and reversally the meta-
stable part of curve (4) is situated between the stable parts of the
curves (1) and (2). This is therefore drawn in fig. 4.

Fig. 3. Fig. 4.

It follows also from the first two reactions that curve (5) is
situated at the left of (1) and (2). Consequently curve (5) is situated
within the angle, which is formed by the stable part of curve (1)
and the metastable part of curve (2). [Confer fig. 4]. This angle,
however, is divided into two parts by the metastable part of curve
(3), so that we have still to know the position of (5) and (3) with
respect to one another. We can do this with the aid of the third of
the reactions mentioned above; from this it appears viz. that the
curves (1), (2), and (5) are situated on the same side of curve (3°;
curve (5) is consequently situated on the left side of (3), therefore,
within the angle, which is formed by the stable part of curve (1)
and the metastable part of curve (3). [Confer fig. 4].

We have used for the determination of the mutual position of
the five curves, the three first reactions only ; we see that the division
with vespect to the curves (4) and (5), which follows from the last
two reactions, is also in accordance with fig. 4.

When we determine, in the way treated above, the partition of
the regions, we find this as is indicated in fig. 4.

536

It is apparent from fig. + that again also in this case the curves
follow one another in diagonal succession. The partition of the curves
is no more symmetrical, however; between the curves (1) and (5)
and between (2) and (3) no metastable curve is found; between (1)
and (2) we find the metastable part of one curve | viz. of curve (4)];
between (8) and (4) and also between (4) and (5) we find two meta-
stable curves. This is also in accordance with fig. 3; herein phase
4 has a particular position with respect to the phases 1 and 2;
this is also the case in fig. 4 with curve (4) with respect to the
curves (1) and (2). In fig. 3 phase 4 has also a particular position
with respect to the phases 8 and 5; this is moreover the case in
fig. 4 with curve (4) with respect to the curves (3) and (5).

We see also in fig. 4 the confirmation of the rule, that each
region, which extends over the metastable or stable part of a curve
(/,), contains the phase /,. When we take e.g. curve (1); the
regions 124 and 134 extend themselves over the stable part of this
curve; the regions 125 and 135 extend themselves over the meta-
stable part; each of these regions contains the phase 1.

The regions 125 and 135 extend themselves over the metastable
parts of the curves (1) and (5); both the regions contain the phases 1
and 5. The region 124 extends itself over the curves (1) and (2);
it contains therefore the phases 1 and 2.

Type 111. Now we shall yet consider the case that the five phases
form the anglepoints of a biconvex quintangle (fig. 5). In order
io determine the position of the five curves with respect to one
another, we take the reactions:

Ve See el) Slide de
(2) (3) | @) | 4) 6) (3) | 2)! OQAa6
4214245 {edn 5
(4) | (8) | 4 (2) (5) (1) (2)5) | A1@B( ° -

142321
(1) (2) (3) | (5) | @

We now draw in a P,7-diagram (fig. 6) the curves (1) and (2);
we take curve (2) at the left side of (1). In connection with this
we have written both the first reactions immediately in such a way
that also herein (2) is situated at the left of (1).

The position of curve (3) follows also at once from both the
first reactions, viz. at the left of (1) and of (2), consequently we
have to draw in fig. 6 curve (3) within the angle, which is formed
by the stable part of curve (2) and the metastable part of curve (1).

537

Fig. 5. Fig. 6.

It follows also from both the tirst reactions that curve (4) is situated
on the righthand side of (1) and of (2); consequently it is situated
in fig. 6 within the angle, which is formed by the stable part of
curve (4) and the metastable part of (2). Within this angle, however,

also the metastable part of the curve (3) which has already been

determined, is situated; consequently we have yet to examine the
position of curve (4) with vespect to curve (3). This follows from
the third reaction; we know viz. already from the previous that (1)
and (2) are situated on the righthand side of (3) [in connection with
this the third reaction is written in such a way that herein (1) and
(2) are situated at the righthand side of (3)], so that (4) must be
situated at the left of (8). Hence it follows that (4) is situated within
the angle, formed by the metastable parts of curves (2) and (8).

It follows still also from both the first reactions that curve (5) is
situated at the right of (1) and of (2); consequently curve (5) must
be sitnated within the angle which is formed by the stable part of (1)
and the metastable part of (2). This angle is divided into three parts
by the stable part of curve (4) and the metastable part of curve (3),
so that we have still to examine within which of these parts the
curve (5) is situated. This appears immediately from the third reaction,
from which it is apparent that curve (5) is situated at the righthand
side of (3). Consequently curve (5) must be situated within the angle,
which is formed by the metastable part of curve (8) and the stable
part of curve (1).

We have only used the first three reactions for the determination
of the mutual position of the five curves. The partition of the curves,
which follows from both the last reactions, is also in accordance
with fig. 6.

538

When we determine, as has been indicated formerly, the partition
of the regions, then we find this as is indicated in fig. 6,

It is apparent from fig. 6 that also again in this case the curves
follow one another in diagonal succession. The partition of the
curves is not symmetrical. The phases 2 and 5 (fig. 5) are situated
in the same way with respect to 1, 3 and 4, the phases 3 and 4
with respect to 1, 2 and 5, while phase 1 has a particular position
with respect to the others. This shows itself therefore in the position
of the curves in fig. 6.

Also we see again in fig. 6 the confirmation of the rule, that each
region which extends itself over the metastable or stable part of a
curve (/p), contains the phase /p. The region 125 extends itself
over the metastable part of curve (1), the regions 124, 134 and 135
extend themselves over the stable part; each of these regions con-
tains the phase 1.

The metastable parts of the curves (1), (2) and (5) are situated in
the region, which is limited by the curves (3) and (4); this region
contains therefore the phases 1, 2 and 5.

When we combine the results, obtained above, then the following
is apparent.

1. Three types of -P, T-diagrams exist

a) as in fig. 2, when the five phases form the anglepoints of a
convex quintangle (fig. ae

bas in fig. 4, when the five phases form the anglepoints of a
monoconcave quintangle (fig. 3) ;

c) as in fig. 6, when the five phases form the anglepoints of a
biconcave quintangle.

2. The three types differ from ove another by the position of
the metastable parts of the curves and by the partition of the regions;
they are in accordance with one another in so far that the curves
follow one another in diagonal succession.

In order to formulate the obtained resulis in another way, we
shall call “a bundle’ a group of curves, which follow one another,
without metastable parts of curves occurring between them. Conse-
quently in fig. 6 (5), A) and (2) form a “bundle”, which we shall
call a “threecurvical’ bundle, as it consists of three curves; curve
(3) forms a “onecurvical” bundle, the same applies to curve (4).

In fic. & (4) and (5) form a “twoeurvical” bundle; the same
applies to (2) and (3); curve (4) forms a “onecurvical” bundle.

In fig. 2 each of the curves forms a “onecurvical” bundle. We

may express the results combined sub 1°, in the following way.

There exist three types of P, 7-diagrams; the five phases form
the anglepoints of :

a) a convex quintangle (fig. 1); then in the P, 7-diagram the
five curves form five “onecurvical” bundles (fig. 2).

6) a monoconcave quintangle (fig. 3); then in the P, 7-diagram
the five curves form two ‘twocurvical” and one ‘onecurvical”
bundle (fig. 4).

c) a biconcave quintangle (fig. 5); then in the P,7-diagram the
five curves form one “threecurvical” and two “onecurvical” bundles.
We can apply the obtained results also in the following way.

When we know the position of the five curves ofa P,T-diagram,
then we can easily determine to which of the types 2, + or 6 this
diagram belongs. Hence follows at once the position of the five
phases with respect to one another, viz. whether they form the
anglepoints of a convex, monoconcave or biconcave quintangle.

We shall discuss now an example of the partition of the curves,
starting from a quintuplepoint as is found experimentally in the
system: water, CuCl, and KC/. In this system occur as solid phases:
KCl, Cu(i,.2H,O and the doublesalts: CuCl,.2KC12H,O and
CuCl,. KCl. We use the following abbreviations: CuwCl,.2H,O=Cu, ;
CuCl,.2KCl2H,O = Diss and CuCl,.KCl= Dis. We represent by
G the vapour, which consists in this system of water only.

In fig. 7 the equilibria, experimentally defined, are represented ;
for the sake of clearness this figure is strongly schematized, otherwise
it would have to be much larger e.g. the point Cu, is situated far
too close to the point Cul, the point Dz far too close to the
side CuCl,—KCl, ete. Yet we have taken into consideration that
the different points which we have to consider, form together in
fig. 7 the same quintangles as this is really the case.

At the temperature 7’ = 56.1° oecurs the equilibrium:

Cu, + Diss + Din + Ly + CG
at 7’, = 93.3° oecurs the equilibrium :
KCH Dina + Dir + ii + G

As the vapour G' consists of water only, in fig. 7 the points W
and G coincide.

Of course five curves start from the point f, they are:

(Cu,)¢ = Dise Hr Dit + L + G
(Dy 22)¢= Cu, + Da +h + G
Di) = Cu, + Divot lL HG
(L)y == Cu, - Dias —J- Dia a. G
(Qe =Cu, + Dias + DittL

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

540

Fig. 7.

Fig. 8.

In order to indicate that these curves start from the point f,
outside the parentheses the letter f is written. In fig. 7 gf repre-
sents the solutions of the equilibrium (),,), fe those of the equili-
brium (Di22)¢ and fb those of the equilibrium (C’w,)7 The small
arrows indicate the direction in which the temperature increases.

Also from the point 6 five curves start; they are:

1) W. Meyernorrer. |Zeitschr. f. phys. Chem. 3, 336 (1889); 5, 97 (1890)]
defined the compositions of the solutions of the quadruplecurves.

J G. G. Vriens. [Zeitschr. f. phys. Chem. 7, 194 (1891)] has measured the
vapour-tensions of several points of these curves.

541

KC), == Diaz a Din 4- JL — G
(Diar = KCl H Dia HL HG
(Dii) — KCl ae Dias a £ -- G

(L), — KCl +- Dias 4- Dia — G
(G)p == 0G! == Daze + Dn =e L

The equilibria (Cu,)y and (KCl), are the same, as is apparent
from the occurring phases. In fig. 7 fb represents the solutions of
the equilibrium (KC), be represents the solutions of the equilibrium
(Dia), and ab those of the equilibrium (D114).

Fig. 8 gives a figure of the P,7-diagram, which is experimentally
defined *). This is somewhat schematized for the sake of clearness.
The point f represents the quintuplepoint with the phases:

Co, Dias, Din, Lp and G
the temperature is 56.1°, the pressure is + 73 mm. of mercury. The
curves (Cus), (D122), (L)¢ and (D,1)¢ starting from this point, have
been defined experimentally. Curve (G)p has not been defined; it
is apparent, however, that it must proceed in fig. 8 steeply onwards,
a little to the right or to the left.

The five phases of the quintuplepoint form a monoconcave
quintangle in fig. 7, its sides Gf, fCu2, Cuz Dir, Dia Dias and Doo G
are dotted in fig. 7. [The point f therefore, corresponds with the
point 4, the points G and Cu, with the points 1 and 2 of fig. 3].
When we take a diagonal succession of the phases, then we have,
starting from G:

G, Cus, Dias, Lr and Dn.
In the P,7-diagram consequently the succession

(G)p, (Cu), (Diao), (L)p (Disp

must occur, which is also found experimentally, as is apparent from
fig. 8. The metastable continuations of the curves are not drawn
in fig. 8; we find them by the same discussion, which has led us
to fig. 4. So far as some of these metastable conditions have been
realized, they are in accordance herewith.

The point 5 represents the quintuplepoint with the phases:

KC Diss ID cde ade:
the temperature is 93.3°, the pressure + 340 m.m. Hg. The curves,
starting from this point have been defined experimentally, except
curve (CG); it is apparent, however, that this must proceed in fig. 8
steeply onwards and a little to the right or to the left.

The five phases form a biconcave quintangle, the sides of
which are: W.6, 6.Dix, Dia. Diaz, Dias. KCl and KCl. G [The

1) J. G. CG. Vriens, Lc. fig. 6, p. 208.
35*

542

point D,\, therefore, corresponds with the point 1, the points 5 and
Di22 with the points 3 and 4 of fig. 5]. When we take a diagonal
succession of the phases, then we have, starting from point G: G,
Dise, Ly, KCl and Dis. In the P,7-diagram the succession of the

Guy

curves must be, therefore:
(Go, (Di22)5 (Lo, (KC, (Dino
As is apparent from fig. 8, this succession has been found also
experimentally. We find the metastable parts of these curves (not
drawn in fig. 8) by a similar discussion, as has led us to tig. 6.
(To be continued).

Crystallography. — “On the Symmetry of the Roxveun-patterns of
Trigonal and Hexagonal Crystals, and on Normal and Ab-
normal Diffraction-Images of birefringent Crystals in general.”
By Prof. H. Haca and Prof. F. M. JAEGER.

§ 1. In connection with the peculiar phenomena observed some
time ago with respect to a number of RÖNTGEN-patterns of birefringent,
and more especially of rhombic crystals'), we thought it necessary
to investigate in a rigorously systematical way, what kind of sym-
metry would be found in the diffraction-patterns of uniaxial crystals,
if radiated through in directions perpendicular to the optical axis.
For if the supposition were right, that the suppression of the sym-
metry-planes expected by theory in the RÖNTGeN-patterns of rhombic
crystals were connected in any way with the double refraction,
— as was thought at that time by one of us, — then we
might expect something of the kind also in the case of the patterns
obtained by means of planeparallel sections of uniaxial crystals, if
cut parallel to the optical axis, and radiated through in a direction
perpendicular to that axis.

To obtain the closest analogy in the orientation with that present
in the case of the rhombie crystals, which were always cut parallel
to the three pinacoïdal faces {100}, {O10} and {001}, we investigated
in the case of tetragonal crystals those sections, which were parallel
to the first and the second prisms {100} and {110}; in the case of
trigonal and hexagonal crystals we used in the same way the sections
parallel to the prism-faces {1010} and {1270}. In the last mentioned
crystals thus the seetions parallel to {1010} will be analogous to
those parallel to {100} in the case of rhombic crystals, the sections
parallel to {1210} corresponding in the same way to those parallel
to {O10} in the mentioned biaxial crystals.

1) These Proceedings, 17, 1204, (1915),

543

To deduce the symmetry of the RöÖNTGeN-patterns of these crystal-
sections, as it may be expected after the theory of the phenomenon,
it must be kept in mind, that this symmetry will be the same, as
in the case of the corresponding sections of a fictive crystal, whose
symmetry would be that of the investigated crystal after addition of the
symmetry-centre there-to. Indeed, for the phenomenon of the RÖNTGEN-
radiation the’ symmetry-centre would play the rôle of “additive”
symmetry-element; and inversely this supposition may be judged
satisfactorily proved, if the experiments will show on the other
hand a complete concordance between the facts and the theoretical
deduction.

In the accompanying table therefore the theoretically expected sym-
metry of the RöÖNrGeN-patterns, as deduced from the now adopted
theory, is summerized for all the optically uniaxial erystals from the
classes 9 to 27. From this table the expected symmetry of the
diffraction-image for all uniaxial crystals can immediately be seen.

§ 2. In the following pages we publish the results obtained in

544

the study of trigonal and hexagonal crystals; the data relating to
the investigations made with tetragonal crystals will be published
by us later-on in a separate communication.

Most of these researches were executed by means of RÖNTGEN-tubes
with platinum-anticathode, some of them, however, by the aid of
the Coorrper-tube with wolframium-anticathode and separate heating-
coil. In most of these experiments we used an apparatus, which
enabled us to make three RöÖNrarNograms (in the case of rhombic
crystals, by radiation along the three principal crystallographical
axes, or perpendicular to the first and second prism) at the same time.
This apparatus was arranged in the following way (vid. the hori-
zontal projection in fig. 1 p. 543).

On a 7-shaped brass support, provided with three levellingserews
S, (dimensions: 3 ¢.m. broad, 1 ¢.m. thick, longer beam: 28 e.m.,
shorter beam: 12,5 ¢.m.), three similar “erystal- and plate-holders”
D (vid. also fig. 2) were fixed in the right position by means of
strong screws. Every one of these bearers (fig. 2) consists of a brass
bar D of 1 e.m. thickness, whose
limiting faces are turned on the lathe
perfectly rectangularly and parallel
to each other. At the one end
is fixed the likewise rectangularly
turned-off plate-holder ZP, — whose
dimensions are 9,5 e‚m. broad, 12 e.m.
high and 3 m.m. thick; at the otber
end, however, the special erystal-
support A (high: 9 e.m., broad: 4 e.m.
and thick: 5 m.m.) was immovably

fixed by good serews. In a hole in

Fic. 2. K a brass tube of 8 e.m. length is

fixed, which is closed at both ends by two lead-cylinders e of 1 em,

length, these being pierced along their axes by a straight canal of

1 mm. diameter. An accurately fitting cover A (fig. 2) can be

pushed on that end of the brass tube, which is next to P; its

front face consists of a small brass plate with a central hole of
2 m.m. diameter.

The crystals were smoothly pressed against this brass plate, and
then held in position by means of sticking-wax.

As a result of the careful finishing of this apparatus, one could
be sure, that the RöÖNrGrN-rays, after having passed the small canals
in the lead cylinders, progress in a thin pencil, which is perpen-
dicular as well to the erystal-plate, as to the photographic plate.

545

The dimensions are chosen in such a way, that the distance from
the front face of the cover to the sensitive film in P is precisely
50 m.m.; of course the thickness of the fluorescent sereen and of
the two black paper covers, with which the plate and screen are
protected, are taken into account here.

The photographie plate, with the fluorescent ‘“‘Eresco’’-screen pressed
against the sensitive film, was wrapped in two covers of black paper
and then firmly pressed against P; it had an opening measuring
8 X 8 em, and the whole apparatus thus was held together much
in the same way as in the case of a photographic copying-press.

The three plate-bearers D could be adjusted into the right position
with sufficient accuracy by means of three straight, thin knitting-
needles, which after being pushed through the canals in the lead
cylinders, must meet in the same point A. For the purpose of making
the anti-cathode coincide with this point A, the wooden bearer of
the R6énrGEN-tube was fixed on a heavy brass support, which had
smoothly running sliding-motions in three perpendicular directions ;
thus it was made possible, to fix the RÖNTGeN-tube exactly in such
position that the three pencils of RÖNrGeN-rays generated three equally
strongly luminous little spots on a fluorescent screen, which was
placed behind P. In the plates P three central holes of 1 em. dia-
meter were bored to enable us to see these laminous spots. To protect
the photographic plate against undesired attack by direct or secondary
RontGen-rays, some larger lead screens were interposed between the
RöÖNrGeN-tube and the plate-holders with a total thickness of 2 ¢.m.;
in the same way the three crystal-, and plate-holders themselves
were surrounded by a lead cover, which could be closely fitted to
the large lead screens. In the backside face of the lead cover three
holes were bored, big enough to let the undiffracted RÖNTGEN-rays
freely pass.

An inconvenience, met with in our former experiments when using
the fluorescent screen, was the abnormal sizeof the central spot on the
photos, which spot would even seem still larger in the reproductions
from the negatives *). The extension of this spot must be caused by
the action of the secondary RÖNrGwN-rays, which were produced by
the passing of the undiffracted pencil through the glass and the
sensitive film; these secondary rays will provoke a rather strong
fluorescence of the vicinal parts of the screen and thus an intense

1) The diameter of the image of the undiffracted rays was about 2 m.m., as
can also be calculated from the used dimensions of our apparatus: by photographic
irradiation or by the mentioned secondary rays however, the central spot on the
photos appeared to be about 8 m.m. in some cases.

546

action on that place of the photographic plate. We were able to
eliminate this obstacle for the greater part, by eutting from the
centre of the sereen a small disc of about 1 ¢.m. diameter, and to
cover the inner rim of the hole with a layer of black ink. On the
photo however a very small halo was still visible in some cases ;
but this could be easily removed by covering the central part of
the negative during the reproduction with a small dise of black
paper. In this way the disturbance of the image by the above men-
tioned causes was finally completely prevented.

j 3. From the representative of each crystal-class, necessary for our
purpose, not all could be obtained in a sufficiently excellent quality,
or they could not be used from some other cause in our experiments.

So for instance the sodiwm-periodte-crystals were unsuitable, because
of their very rapidly occurring efflorescence and loss of their water
of crystallisation ; the crystals of benzi/ on the other hand appeared
to show optical anomalies and peculiar phenomena to be described
in a later communication. Notwithstanding much trouble it was
impossible to obtain larger crystals of cinnabar, which were not at
the same time twins or appeared to be too inhomogeneous. From
zincite we could have only badly disturbed and lamellar erystals ;
in the case of nephelite the obtained crystals still appeared finally
to be polysynthetie twins, notwithstanding the choice of very small,
clear-looking individuals.

Completely reliable results we obtained finally in the case of the
following minerals: phenakite, dolomite, quartz, turmaline, caleite,
apatite and beryl, while also our experience with some nephelite-
preparations, and with cinnabar cut perpendicularly to the c-axis,
can be judged as to be in agreement with the theoretical deduction.

§ 4. Description of the evamined substances.

a. Turmaline. For our observations we used a beautiful, dark
green turmaline-crystal of Brazil. The image obtained by radiation
through the direction of the optical axis, was already formerly
reproduced’); it possesses the expected symmetry, namely: one
ternary principal axis and three vertical symmetry-planes (vid. the
stereographical projection in fig. 1, Plate VI).

The first erystal-plate parallel to {1010} had a thickness of 3,05
m.m.; a second one however only of 1,15 m.m. Both images
(vid. Plate I, fig. 1 and 2, and Plate VI fig. 2.) show only one

1) Vid. these Proceedings, 17. 1204. (1915); Plate 1, fig. 4; Plate IV, fig. 4.

547

single plane of symmetry, perpendicular to the prism-face. The
spots in the image of the thick erystal-plate are very heavy and
not oval-shaped, but rectangular. We have already drawn attention
to this phenomenon on a previous occasion, in the cases of sodium-
chlorate, of sylvine*), ete.

It now becomes clear that it is principally connected with the
thickness of the crystal-plate: the formerly described patterns of
sodiumehlorate and sylvine are indeed also obtained by means of
very thick plates.

This peculiarity was also stated by usin many other cases, if thicker
plates of not very strongly absorbing substances were used in the
experiments; often the spots appear to be double ones in such
eases, which by joining finally give the impression of a more
or less rounded rectangular shape. We think that an explanation
can be given in this way: that in the case of not powerfully
absorbing substances so great a number of successive molecular layers
contribute to the intensity of the spot on the photographic plate,
that the images of the outer layers of the whole pile will appear
in a discernible distance from each other on the film, because of
ihe different distance of these outer layers from the sensitive plate.
If the spots thus properly produced will coalesce with each other,
the rounded rectangular shape of the resulting image is easily
explained.

The fourth turmaline-plate was cut parallel to 7210}; the RÖNTGEN-
pattern shows as a single symmetry-element, a binary axis coinciding
with the plate-normal. (Plate I, fig. 3). The results of the experiments
are therefore in this case in complete accordance with those of the
theoretical deductions.

b. Phenakite. We had at our disposition very beautiful, colourless
and lustrous phenakite-erystals from San Miguél, Minas Geraés, in Brazil.

The erystal plate cut perpendicularly to the c-axis, showed in
convergent polarized light, a uniaxial interference-image of positive
character; it manifested however a small abnormality in the form
of a feebly biaxial image with extremely small axial angle. However
this abnormality did not appear to have any influence on the diffraction-
pattern. The plate had a thickness of 1,1 mm.; the photographie
image was not very beautiful, and the most important spots appeared
to be covered by the strong irradiation of the central spot. Later-on
we obtained by means of our newer apparatus described previously,
a feeble but completely symmetrical image, which was used in the

1) Ibid. 1207, note 1.

548

construction of the stereographical projection in Plate VI, fig. 3.
Evidently there is only one ternary axis present, but no planes of
symmetry in the pattern.

The plate parallel to {1010} was 1,20 m.m., that parallel to {1210
was 1,15 m.m. thick; we obtained with them two very beautiful
photos, reproduced in Plate I, fig. 4 and Plate II, fig. 5; in these
photograms the direction of the c-axis is vertical. The diffraction-
patterns are wholly unsymmetrical ; the results are therefore exactly
what could be expected from the theory.

c. In the same symmetry-group also Dolomite must be placed.
From a splendid, perfectly translucid crystal of Binnenthal in
Switzerland, three faultless plates parallel to {0001}, {1010} and
{1210} were carefully cut. The plate perpendicular to the c-axis had
a thickness of 0,92 m.m.; the beautiful interference-image of negative
character appeared to be exactly centrical. The plate parallel to
{1010} was 1.14 m.m. thick; that parallel to {1210} was 1,11 mm.

The very beautiful diffraction-patterns obtained are reproduced in
fig. 6, 7 and 8 on Plate II, and in stereographical projection on
Plate VI, in fig. 4 to 6. The image perpendicular to the c-axis
possesses only a ternary axis; both the other images are completely
unsymmetrical, just as in the ease of phenakite. Also in this case
therefore experience and theoretical deduction are in full agreement
with each other.

d. Calcite. From a lustrous calcite-crystal from Zceland two plates
were cut: the plate parallel to {1010{, as well that parallel to {1210}
were 1,15 m.m. thick. Both images were too feeble to allow good
reproduction ; they are however reproduced as stereographical projec-
tions in fig. 7 and 8 on Plate VI. The RÖNrGeN-pattern for a plate
perpendicular to the c-axis was published some time ago by Brace *):
the image exhibits a ternary axis and three vertical planes of sym-
metry. The symmetry of all these patterns is the same, as was found
in the case of the furmaline, — just as could be expected from the
theory. It must be remarked that the image parallel to {1010},
although possessing only a single (vertical) plane of symmetry, shows,
however, a very strong approximation to a case, where two perpen-
dicular symmetry-planes were present.

e. Beryl. We had very beautiful plates at our disposition, cut
from a splendid, colourless, translucid erystal from the Aduntschilon-
mountains in the Transhaical. The plate parallel to {0001} had a

1) W. L. Brace Vid. Zeits. f. Anorg. Chem. 90. 206. (1914); Proc. Royal
Soc. A. 89 248. (1913).

549

thickness of 1.10 mm., that parallel to {1010} 1.17 mm., and that
parallel to {1210} 1.16 mm.

The diffraction-image parallel to 40001} (vid. Plate III, fig. 9),
shows a senary axis and six vertical planes of symmetry. Thus it
is again proved, that the beryl is really dihexagonal, and that the
arguments against this supposition, formerly brought to the fore by
Viora ®), can hardly be considered as valuable any more.

The two remaining images (Vid. Plate III, fig. 10 and Plate IV,
fig. 11) are, quite in concordance with the theory, symmetrical after
two perpendicular planes of symmetry. They are reproduced as stereo-
graphical projections in fig. 9—11, on Plate VJ. The image of the
plate parallel to }1010} appears to be somewhat sloping, evidently
caused by not wholly perfect orientation of the crystal-section.

jf. Apatite. From a beautiful erystal from Zllerthal, in Tyrol,
two plates were cut. The image of the plate parallel to {0001} was
reproduced already previously ®). The second plate was parallel to
{1010}; its thickness was 1,30 mm. The beautiful diffraction-pattern
is reproduced in fig. 12 on Plate IV, and both images as stereogra-
phical projections on Plate VI, fig. 12 and 18. The pattern parallel
to {1010} exhibits only one horizontal plane of symmetry, quite in
agreement with the theoretical expectations.

g. Quartz. From a translucid crystal from the St. Gothard four
plates were cut. The image of a plate perpendicular to the c-axis
was too feeble to make reproduction by any means possible. A sche-
matieal drawing of the most important, — and always double, —
spots, is given in fig. 14, Plate VII. The pattern shows a ternary
axis and three vertical planes of symmetry.

Two different plates, each of which was parallel to {1210}, and
having a thickness of 1,12, resp. 1,05 m.m., gave particularly
remarkable patterns. For although both plates were very accurately
orientated, and did not manifest, with the microscope, any differences,
nor any inhomogeneity discernible by optical means, — the image
obtained with the first mentioned plate appeared to be symmetrical
after two perpendicular planes; the other image however, notwith-
standing its being composed of precisely the same spots, showed
quite another distribution of their intensities, in such a way, that
the pattern was only symmetrical after a single binary avis. On
repeating the experiment with the first-mentioned quartz-plate, which

1) Vrora. Z. f. Kryst. 34. 381. (1901).
2) loco cit. 17. Plate I.

550

now was radiated through in another place, its abnormal syrametry
was found once more.

Here now we could, for the first time, observe in the case of
a uniaxial erystal a very particular abnormality: indeed it appears,
that properly a plane of symmetry perpendicular to the trigonal
axis seems to be added to the crystal, which involves at the same
time the addition of three new vertical planes of symmetry passing
through the c-axis, making this axis necessarily a senary one. In
the original negatives this different symmetry in both cases is very
evident, somewhat less, however, in the reproductions (Plate IV,
fig. 13 and 14); but the differences between the normal and the
abnormal pattern are clearly expressed in the stereographical projections,
which here are given together in fig. 3 and 4.

The same abnormality, ie. the addition of a horizontal plane of
symmetry perpendicular to the ternary axis, seems to be also present in
the RÖNTGEN-ogram, obtained with a crystal-plate parallel to {1010};
this plate had a thickness of 1,10 m.m. Although this plate was
parallel to the c-axis, it appeared to be not completely parallel to
the prismface; the pattern, which therefore very probably did not
show a true vertical symmetry-plane, is here not reproduced. The
stereographical projection of the normal patterns are given in fig. 14,
15 and 16, Plate VII.

A careful microscopical examination of both the plates parallel
to {1210}, did however not reveal any optical differences.

One might be inclined to suppose, that the plate parallel to (1210)
which had given the abnormal pattern, were really a twin-formation
after the brasilian rule; i.e. with a plane of (1210) being the twinning-
plane. Because perpendicularly to (1210) there is a binary axis
present, the RÖNrGeN-ogram therefore should indeed show a symmetry
with respect to two planes, perpendicular to each other. But by this
supposition it could never be made evident, that the diffraction-
pattern obtained with a plate cut from the same crystal parallel to
(1010), shows very probably also a horizontal plane of symmetry.
Thus the said explanation can hardly be considered a final one
already for the peculiar RÖNrGeN-patterns which were obtained
parallel to (1210) and to (1010). The observed abnormality therefore
cannot be said to be explained fully, and we intend to make
further experiments on this phenomenon in future.

h. Nephelite. From a small, clear crystal from the Vesuvius,
three crystal-plates were investigated. The plate perpendicular to
the optical axis showed a well-centred, uniaxial interference-image,
possessing only a slightly abnormal character. The plate had a

Plate 3, Stereograpcical Projection of the Röntgen-pattern of dextrogyratory
Quartz. Plate parallel to (1210). (Normal Image).

Fig, 4. Stereographical Projection of the Réntgen-pattern of dextrogyratory
Quartz. Plate parallel to (1 210). (Abnormal Image).

552

thickness of 0.70 m.m. The obtained diffraction-image was extremely
feeble: the spots, which, — as in the ease of the quartz, — were
all double-ones, — were situated very far from the centre and were
so feeble, as to make any reproduction impossible. It was however
possible to see, that the pattern possessed a senary axis (schematical
projection in fig. 17, Plate VII); mo vertical planes of symmetry
were present.

The plate parallel to {1010} was 0,78 m.m. thick, and gave a
rather good image, which as a stereographical projection is reproduced
on Plate VII, fig. 18. All spots here were also doubled, and the
axes of the oval impressions were inclined to each other, giving
to each pair of spots the shape of an arrow-point; this seems to
indicate a twin-formation of the used mineral. The pattern was
merely symmetrical after a horizontal plane. The third plate was
too disturbed and inhomogeneous, to give any suitable image.

?. That cinnabar, if radiated through in the direction of the c-axis,
will give a R6énTGEN-pattern, whose symmetry is in full concordance
with the theory, was already formerly recorded *). The stereographical
projection of the RÖNrGeN-ogram is reproduced here once more in
fig. 19, Plate VII. Finally in fig. 15, Plate V, the very beautiful
photo of pennine is reproduced; although this mineral’ is only
mimetic and clearly shows optical abnormalities, the structure of the
lamellae is evidently here a so regular and perfect one, that the whole
pile cannot be distinguished from a real trigonal erystal. Attention
must be drawn to the remarkable fact, just as formely stated in
the case of sylvine, that the central spot seems to irradiate in about
eighteen directions; it seems, that this irradiation is connected in
some way with the presence of certain gliding-planes in the erystal.
The thickness of the dark green, positively birefringent, and clearly
optically anomalous erystal-plate, was 0,81 m.m.

§ 4. If we now review all the results hitherto obtained in these
researches, it becomes clear, that, — with the exception of the
phenomena observed in the case of the two quartz-plates, which
phenomena undoubtedly are to be considered as true “abnormalities ’,—
the symmetry of the RÖNrGeN-patterns is always in agreement with
that predicted by the now adopted theory of the diffraction-phenomenon.
On the other hand the correctness of the supposed centrical symmetry
of the said phenomenon is thus sufficiently proved in this way.
Our experience can be considered evidently as a strong argumenta-

1) These Proceed. 17. p. 1204: vid. Plate IV, fig. 5.

553

tion against the supposition, that the particular fact of the dis-
appearance of certain symmetry-planes in the RÖNTGEN-patterns of
birefringent crystals would have anything to do with their optical
anisotropy. For if this were true, it would be hardly possible to
understand, why not one of the numerous patterns of uniaxial crystals,
which were radiated through in the direction of their optical axis,
and thus likewise are birefringent plates, exhibited the formerly
described phenomenon. On the other hand the case of the quartz-
images makes prudence necessary: for evidently the symmetry of
the patterns can by ‘yet partially unknown secondary causes, appear
otherwise than may be expected from the theory of the diffraction
phenomena, — as well of higher symmetry (quartz) as of lower
symmetry (rhombic crystals).

§ 5. In connection with these considerations, we have recom-
menced our studies with some optically biaxial (rhombic) crystals,
and have begun with a renewed investigation of the same, translucid
and very beautiful plate of hambergite parallel to {010}, which for-
merly*) had given aso strongly abnormal image. After having radiated
through in another place, we now repeatedly obtained a perfectly
normal diffraction-image, quite symmetrical after two perpendicular
planes. The normal pattern is reproduced in fig. 16, Plate V, as a
photo, and both images by the side of each other as stereographical
projections, in fig.5 and 6. Using the normal image as standard, it
may be called very remarkable, that the abnormal image appears in
comparison to it as a “distorted” normal pattern, as if the erystal-
plate were rotated round the vertical principal direction at a certain
angle. Very striking indeed is the completely different intensity-
distribution of the spots, and also their altered position in both
cases. Microscopically no differences could be found in the one place
of the plate and the other: with a very strong enlargement the
crystals showed certainly very small and long-shaped inclusions, but
these were in precisely the same way and arrangement present also
in both the other hambergite-plates, cut parallel to {100} and {001},
which plates however in striking contrast to the one mentioned,
always gave completely normal patterns. From this it must follow,
that these inclusions cannot be the cause of the phenomenon observed.

On repeating our experiments with the same plates of sodiwm-
ammoniumtartrate, as we used formerly, we obtained with the, —
now superficially somewhat rougher, — plate parallel to {100}, the
same abnormal pattern as previously: only a few of the spots

1) These Proceed. 17, 1204, Plate Il, fig. 8; Plate IV, fig. 11.

Fig. 5. Stereographical Projection of the Röntgen-pattern of
Hambergite. Plate parallel to 010). (Normal Image).

Fig. 6. Stereographical Projection of the Röntgen-pattern of
Hambergite. Plate parallel to (010). (Abnormal Image).

H. HAGA AND F. M. JAEGER. ON THE SYMMETRY OF THE RöNTGEN-PATTERNS PLATE I
OF TRIGONAL AND HEXAGONAL CRYSTALS, AND ON NORMAL AND ABNORMAL
DIFFRACTION-IMAGES OF BIREFRINGENT CRYSTALS IN GENERAL.

Fig. 1. Fig. 2.

Turmaline. Plate paralle! to (0110). Turmaline. Plate parallel to (0110).

Fig. 3.
Turmaline. Plate parallel to (1210).

Fig. 4.
Phenakite. Plate parallel to (0110).

Proceedings of the Acad. of Sciences, Amsterdam, Vol. XVIII. A° 1915/1916. HELIOTYPE, VAN LEER, AMSTERDAM

H. HAGA AND F. M. JAEGER. ON THE SYMMETRY OF THE RöNTGEN-PATTERNS PLATE Il.
OF TRIGONAL AND HEXAGONAL CRYSTALS, AND ON NORMAL AND ABNORMAL
DIFFRACTION-IMAGES OF BIREFRINGENT CRYSTALS IN GENERAL.

*
af Ld
hd ‘
. 7
’
*
;
'
’
‘
”~ ed „
Ed
. En: Pp
«i
~ si FE
=: « -
.
Fig. 5.
Phenakite. Plate parallel to (1210).
Fig. 6.
Dolomite. Plate parallel to (0001).
ee i
gd
“ oa
e - - aa had ®
„
Ld Se
id EN ‘
Ld
: ’
e ‘ ‘
\
B $ a
ry
Ld «
- - = -
… © pe jet
- *
>
Fig. 7. Fig. 8.
Dolomite. Plate parallel to (0110). Dolomite. Plate parallel to (1210).

Proceedings of the Acad. of Sciences, Amsterdam. XVIII. A° 1915/1916. HELIOTYPE , VAN LEER, AMSTERDAM

d HAGA AND F. M. JAEGER. ON THE SYMMETRY OF THE RöNTGEN-PATTERNS
JF TRIGONAL AND HEXAGONAL CRYSTALS, AND ON NORMAL AND ABNORMAL
DIFFRACTION-IMAGES OF BIREFRINGENT CRYSTALS IN GENERAL.

Fig. 10.

Fig. 9. 4
Beryl. Plate parallel to (0001).

Fig. 11.
Beryl. Plate parallel to (1210).

Beryl. Plate parallel to (1010).

PLATE IIL.

| Proceedings of the Acad. of Sciences, Amsterdam. XVIII. A° 1915/1916, HELIOTYPE , VAN LEER, AMSTERDAM

_H. HAGA AND F. M. JAEGER. ON THE SYMMETRY OF THE RöNTGEN-PATTERNS PLATE IV.
OF TRIGONAL AND HEXAGONAL CRYSTALS, AND ON NORMAL AND ABNORMAL
DIFFRACTION-IMAGES OF BIREFRINGENT CRYSTALS IN GENERAL.

‘

Fig. 12.
Apatite. Plate parallel to (1010).

Fig. 13.
Quarz. Plate parallel to (1210).
(Normal Pattern).

Fig. 14
Quarz. Plate parallel to (1210).
(Abnormal Pattern).

mee of the Acad. of Sciences, Amsterdam, Vol. XVIII. A° 1915/1916. HELIOTYPE , VAN LEER, AMSTERDAM

H. HAGA AND F. M. JAEGER. ON THE SYMMETRY OF THE RöNTGEN-PATTERNS PLATE V.
OF TRIGONAL AND HEXAGONAL CRYSTALS, AND ON NORMAL AND ABNORMAL
DIFFRACTION-IMAGES OF BIREFRINGENT CRYSTALS IN GENERAL.

> * - En -
e Ed > ae .
Sd ray -
4 IRE
Ld 5 - Ae
s , d bs ‘
>
B. "¢ ¢ ot
Ld
'
' ’ : ‘ ' j ‘ '
: ' '
; my Ks PJ .
« ” Ld
" pn Ld
e < ,
‘ Ld , a = , fi
. . = iggy © ® > = oe
ao
Fig. 15
Fig. 16,

Pennine. Plate parallel to (0001).
Hambergite. Plate parallel to (010).

(Normal Pattern).

-
ee .
b>,
/ ie
: ‘
‘
AN a” a
sé
-- d
ae .
Fig. 17.

Zinc-Sulphate Cleavage-lamella, exactly parallel to (010).
(The b-axis is Ist bissectrix).

Proceedings of the Acad. of Sciences, Amsterdam. XVIII. A° 1915/1916, HELIOTYPE, VAN LEER, AMSTERDAM

Fig. 4. Stereographical Projection of the Röntgenogramn
of Dolomite. Plate parallel to (0001).

_ Fig. 8. Stereographical Projection of the Rontgenogram

of Calcite. Plate parallel to (1210).

DET Se =

Prof. Dr. H. HAGA and Prof. Dr. F. M. JAEGER. "On the Symmetry of the Röntgen-patterns of Trigonal and Hexagonal Crystals,” etc, PLATE VI.

Fig. 1. Stereographical Projection of the Röntgenogram Fig. 2. Stereographical Projection of the Rontgenogram _ Fig. 3. Stercographical Projection of the Röntgenogram Fig 4. Stereographical Projection of the Réntgenogram
of Turmaline. Plate parallel to (0 001). of Turmaline. Plate parallel to (0110). of Phenakite, Plate parallel ta2(0 00 1)5 of Dolomite. Plate parallel to (0.00 1),

Fig. 5. Stercographical Projection of the Röntgenogram Fig. 6. Stereograpltical Projection of the Röntgenogram Fig. 7. Stereographical Projection of the Rontgenogram Fig. 8 Stereographical Projection of the Röntgenogram
of Dolomite. Plate parallel to (a1 To), of Dolomite. Plate parallel to (7270). of Calcite. Plate parallel to (1010). of Calcite. Plate parallel to (T2 Ta).

Fig. 9, Stereographical Projection of the Rontgenogram Fig. 10. Stereographical Projection of the Röntgenogram — Fig. 11. Stereographical Projection of
of Beryl. Plate parallel to (000 1), of Beryl, Plate parallel to (1010) of Beryl. Plate parallel to (T

e Rontgenogram Fig. 12. Stereographical Projection of the Röntgenogram
0). of Apatite. Plate parallel to (0001).

Fig. 13. Stereographical Projection of the Röntgenogram Fig. 14. Stereographical Projection of the Réntgenogram
of Apatite. Plate parallel to (1070). of dextrogyratory Quarz. Plate parallel to (0001).

Proceedings Royal Akad, Amsterdam. Vol. XXIV.

PLATE VII.

Fig. 15. Stereographical Projection of thefig. Stereographical Projection of the Röntgenogram
of dextrogyratory Quarz. Plate paralle of Nepheline. Plate parallel to (1210).

Fig. 19. Stereographical Projection of the 99. Stereographical Projection of the Röntgenogram
of dextrogyratory Cinnabar. Plate paralle) of dextrogyratory Sodium-Ammonium-Tartrate.
Plate parallel to (010). (Normal Image).

Fig, 23. Stereographical Projection of the} 96. stereographical Projection (schematical) of the
of dextrogyratory Sodium-Ammoniumftgenogram of Zinc-sulphate. Plate parallel to (0 1 0).
Plate parallel to (010). (Abnormaormal Image, obtained with a perfectly clear lamella,
pared by cleavage, and exactly perpendicular to
the first bissectrix.

Proceedings Royal Acad. Vol. XXIj

Prof. Dr. H, HAGA and Prof. Dr. F. M. JAEGER. “On the Symmetry of the Röntgenpatterns of Trigonal and Hexagonal Crystals,” etc. PLATE VII.

Fig. 15. Stereographical Projection of the Réntgenogram Fig. 16. Stereographical Projection of the Röntgenogram Fig. 17. Stereographical Projection of the Röntgenogram Fig. 18. Stereographical Projection of the Rontgenogram
of dextrogyratory Quarz. Plate parallel to (1070). of dextrogyratory Quarz. Plate parallel to (T2To). of Nepheline. Plate parallel to (0001). (Schematical). of Nepheline. Plate parallel to (T2To).
(Normal Image). i

Fig, 19. Stereographical Projection of the Röntgenogram Fig. 20. Stereographical Projection of the Rontgenogram . 21, Stereographical Projection of the Röntgenogram Fig. 22 Stereographical Projection of the Röntgenogram
of dextrogyratory Cinnabar. Plate parallel to (0001). of dextrogyratory Sodium-Ammonium-Tartrate. of dextrogyratory Sodium-Ammonium-Tartrate. of dextrogyratory Sodium-Ammonium-Tartrate.
Plate parallel to (100). (Abnormal Image). Plate parallel to (100). (Normal Image). Plate parallel to (010), (Normal Image).

A
Fig. 23. Stereographical Projection of the Röntgenogram Fig. 24. Stereographical Projection of the Rontgenogram Fig. 25. Stereographical Projection of the Röntgenogram Fig. 26. Stereographical Projection (schematical) of the
of dextrogyratory Sodium-Ammonium-Tartrate. of dextrogyratory Sodium-Ammonium-Tartrate. Plate of dextrogyratory Sodium-Ammonium-Tartrate. Röntgenogram of Zinc-sulphate. Plate parallel to (0 1 0).
Plate parallel to (010). (Abnormal Image). parallel to (010). Abnormal Image, perpendicular Plate parallel to (001). Abnormal Image, obtained with a perfectly clear lamella,
to the first one, with the same position of the plate. prepared by cleavage, and exactly perpendicular to

the first bissectrix.

Proceedings Royal Acad. Vol. XXIV.

555

appeared to be absent on comparison with the former image. The
also superficially somewhat rougher plate parallel to {010} however,
gave now undoubtedly also an abnormal image, but as: a very
remarkable fact: just the other (second) plane of symmetry as before
was now manifested in the pattern, notwithstanding the same position
of the crystalplate! Formerly this plate had given an abnormal
image, which was symmetrical after the plane {001}; now it showed
a symmetry -plane parallel to {100}. As both plates of the tartrate
were superficially a little altered by a feebie efflorescence, we pre-
pared from a fresh, translucid crystal of the salt three new plates,
which were examined in the same way.

With these plates we were now able to obtain RÖNTGEN-patterns,
which were symmetrical after fo planes; in this way it was
possible at the same time to compare the partial symmetry of both
the abnormal images parallel to {OLO} with the normal pattern. The
three normal and the abnormal images are reproduced as stereo-
graphical projections in fig. 20 to 25 on Plate VII.

§ 6. We have convinced ourselves by especially arranged ex-
periments of the fact that a deviation from the true plane-parallel
shape of the hambergite-plate could not be the cause of the partial
symmetry of its pattern formerly obtained. Moreover, in our numerous
experiments with cordierite, with material from all localities, we
never obtained other images than abnormal ones, which were only
symmetrical after one single plane of symmetry. With this mineral the
phenomenon thus seems to manifest itself constantly. In our way of
experimenting, with the use of fixed, on the lathe rectangularly
turned-off crystal-supports, a somewhat appreciable deviation from
the true orientation is highly improbable. Moreover the same
crystals, adjusted by the same apparatus, appeared formerly often
to give quite normal patterns, if radiated through in one or two of
the other principal directions, so that a systematical error of the whole
arrangement can hardly be considered to be the cause of the pheno-
menon. If this were true, or if deviations in the right orientation
of the prepared erystal-sections were the cause of the phenomenon
observed, it could furthermore not be understood, why never a
distortion of the normal pattern after another direction than only
after the two principal ones of the plate, were till now observed.
The fact, that the planes of symmetry of the rhombic crystals just
play the preponderant rôle in this, proves sufficiently, that no
accidental causes are responsible here, but that these are of such

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

556

a nature, as to be connected intimately with the proper, internal
molecular structure of the crystals.

But a further and persuasive illustration of this question is given
also by the case of the rhombie zive-sulphate. Here we used a
splendid transparent erystal-plate, obtained by direct cleavage of the
erystal along the plane of perfect cleavability {O10}, whose perfectly
right orientation could be controlled very rigorously by optical
examination, the L-axis being at the same time the first biseetrix.
Notwithstanding this, however, the corresponding diffraction-image
appeared to be constantly abnormal, and to possess only one single
plane of symmetry parallel to {O01}, — i.e. parallel to the optical
axial plane. (Vid. Plate V, fig. 17 and Plate VII, fig. 26).

The above mentioned observations undoubtedly must bring the
conviction, that the cause of the observed phenomenon must be
ascribed to the erystal-plates themselves, — faultless as they may
appear even on more detailed examination. Indeed further experiments
taught us, that also with other rhombic crystals than with hambergite,
it is eventually possible to obtain perfectly normal patterns, with
the aid of the same apparatus. In the following paper we will
reproduce the photos and projections of the images, which we
obtained with the plates of a number of biaxial minerals and arti-
ficial substances, cut parallel to the three pinacoidal faces. They
will, besides some new cases of abnormal diffraction-patterns, also
show many, which indeed must be judged to be quite “normal”
ones; the fundamental exactness of the original theory thus being
convincingly proved. As Prof. Rinne of Leipzig, who supposed already
some time ago, that special secondary causes might be connected
with the observed phenomena, wrote to one of us, — he obtained
in the case of the anhydrite as well normal as abnormal diffraction-
images, and with ecalamine parallel to {010} only abnormal ones.
Witb respect to our own results with these minerals, we can refer
here to the following paper.

$ 7. As a result of our completed experiences, we finally can
make the statement, that the now adopted theory of the diffraction-
phenomena, really can describe sufficiently the general behaviour of
crystals with respect to RÖNTGEN-rays; and that the peculiar partial
symmetry of the RöÖNrGun-patterns, as observed till now in many
cases and especially with rhombic crystals, must be caused by secondary
circumstances, connected with a particular kind of disturbances of
the internal molecular structure of the crystals, and which at the
moment can be examined by no other physical means.

557

Of course the question immediately arises; of what kind are
these causes? On deviations in the right orientation of the crystal-
plates, — (which are always present in a less or higher degree), —
it is hardly necessary to expatiate: after a longer practice one
learns to evaluate quite exactly the smaller and very typical distor-
tions, arising from that source, and to pass over them as over the
typographical errors in an ordinary text. But the anomalies here
considered are of a totally different order; they must be caused by
a breaking-up of the stratographie position of the molecular layers,
by which certain parts of the parallel planes of the molecules will
be locally rotated round one of the principal directions in the crystal,
— in an analogous way, as on our earth the inversions and the
folding of geological strata may be observed. But in every case these
disturbances must be here of molecular dimensions ; they can evidently
not be studied or observed by other available means at the moment
than by the R6n7TGEn-radiation, because the crystal-medium, disturbed
in its molecular relations, behaves in respect to all other known
physical actions like a continuum, with exception just in respect to
the extremely small wave-lengths of the RÖNTGEN-rays.

If there are present in rhombic crystals some directions of higher
or less perfect cleavability, which are parallel to the principal sections
of the erystal, then it will be probable, that such “internal vicinal
planes” of the molecular layers will appear to be turned exactly
round these principal cleavage-directions as axes, — here round the
one, and there round the second of them. It will then depend on
the place, where the erystal will be radiated through, if the diffrae-
tion-image will show a symmetry after the one or after the perpen-
dicular plane. It must be remarked here however, that exactly in
the case of the sodiwnammoniumtartrate, where the mentioned
phenomenon was observed by us, mo such directions of typical
cleavability are present. It seems therefore, that the principal direc-
tions of the molecular structure can play this remarkable rôle also
in the case, that they are not at the same time directions of distinct
cleavability.

§ 8. We do not deny, that the explanation given here has some
weak points, especially if it must be supposed, that al/ molecular
layers, contained in the whole thickness of the erystal-plate, contri-
bute their part to the final impression on the photographic film,
while notwithstanding .that, only for a certain number of these
molecular layers the presence of such “internal vicinal planes” can
be accepted, because otherwise they would manifest themselves at

36*

558

the surface of the crystal-plates in some typical way, e.g. as irregu-
larities of that surface. In this connection it may be of interest to
mention the fact, that really in some few cases we found such
abnormal phenomena with erystalplates, cut parallel to some of such
“striated” faces of the erystal.

Moreover the question may arise: why is this abnormal behaviour
observed relatively so often in the case of biarial crystals, while it
oecurs evidently hardly ever in the case of uniaxial crystals ?

Finally we may yet draw attention to the following case: If a
pseudo-syymmetrical (mimetic) erystal is built-up by lower-symmetrical
lamellae, it cannot a priori be understood, why such a combination,
radiated through in the direction of the (new) optical axis, would
in any way manifest its polysynthetie twin-structure. Indeed this con-
clusion appears to be verified here by our experience with the pennine.
But if that lamellar structure can cause in any way the presence
of such “internal vicinal planes”, so that the molecular layers can
be turned a little round these two, three, four of six directions of
intergrowth, the possibility can then be foreseen, that these irregu-
larities will be brought uccidentally in one of these directions more
strongly to the fore, than in the remaining ones: that one direction
will then appear in the diffraction-pattern as a single plane of sym-
metry of it, and in this way the appearance of this can be considered
to be an indirect proof for the lamellar structure of the investigated
erystal. This was evidently the case with apophyllite *), henitoite *),
and the racemic triethylenediamine-cobalti-bromide*); moreover we found
it a short time ago also in the case of benzil, if cut perpendicular to
the optical axis of the pseudo-trigonal complex. We expect to elucidate
in every case these questions by systematical experiments, and especially
to determine finally the true nature of these internal disturbances, evi-
dently intimately connected with the normal molecular structure.

University- Laboratories for Physics and
Inorganical and Physical Chemistry.

Groningen, August 1915.

1) These Proceed. 4, 438.
2) Tbidem, 17. 1204. (1915), Plate IV, fig. 14. (1915).
3) lbidem, 18. 50. (1915).

559

Crystallography. — “On the Symmetry of the RÖntaeN-patterns
of Rhombic Crystals’. I. By Prof. H. Haga and Prof. F.M.
JAEGER.

§ 1. With the purpose to test yet further by experiments the
conclusions with respect to the special symmetry of the diffraction-
patterns of RÖNTGEN-rays in crystals, as may be derived from the
theory adopted till now, we have moreover made a series of experiments
with optically biaxial crystals. In the following pages are recorded
the results obtained in the investigations with rhombic crystals, and
especially with representatives from each of the possible symmetry-
classes of the rhombie system. As already formerly mentioned *),
the RÖNrGrN-patterns of plates from rhombic crystals of bisphenoidical,
pyramidal, or bipyramidal symmetry, must always show the symmetry
which would be observed in the analogous crystal-sections of the
rhombic-bipyramidal class. From this is deduced, that crystal-plates
cut parallel-to the three pinacoides {100}, {010} and {001}, in the case
of crystals of each of the three possible classes of this system will
give RÖNrGeN-patterns, which will always appear symmetrical with
respect to twoperpendicular planes of symmetry, if they are radiated
through in the direction of the plate-normal.

§ 2. The way, in which the true situation of the spots in the
diffraction-pattern, or more correctly : in its stereographical projection,
is related to the parameters a:b:e of such rhombic crystals, can
be elucidated more particularly as follows.

Let P in Fig. 1 be the plane of the photographie plate, and AC
the distance of the crystal from that plate. This distance (= A) was
in our experiments always 50 mm.’*); the diameter of the sphere
by means of which the stereographical projection on the plane P
will take place, is therefore always 100 mm. The viewpoint of tne
projection is 0; the planes VCY (= P), NCZ, and VCZare supposed
to coincide with (or to be parallel to) the three planes of symmetry
of rhombie-bipyramidal crystals. Let the parameter-quotient in the
directions CX, CY and CZ be: a:6:c, of which a and ec are
numbers, known by the measurements of the angular values, and
b is taken arbitrarily = 1.

If, now, Kz represents a “possible” zÔne-axis of the crystal, the

Cz 1 Ik ee ;
value of CK must be: om where Fi is the parameter-relation in

1) These Proceed. 17, 1204. (1915).
2) However attention must here be drawn to the remarks in § 4

the directions CY and CZ, while n is some integer. If Kz’ is

ape,
se a
equally such a zÔne-axis, then just in the same way Ss
: Y ¢ :
where m is also an integer. The projected spots S and S’, corre-
sponding with the reticular planes {101} and }011} of the erystal,

are therefore in the directions CX and CY of the stereographical

’

. . . . . . a
projection situated in distances from the central spot C, of: 24 —
C

2A _ 1004 100
and —, or in our case of: —— and — mm. In the same way for
C c (7

spots corresponding with the reticular planes of the symbols {hol}
1 100a 1 100

and {oA}, these distances from C, become: HGe mm.

The point of intersection M of both zÔne-circles, corresponding
with the zÔne-axes Kz, resp. Kz’, possessing the symbols [Aol] and
[ok1], represents the stereographical projection of a spot, corresponding
with a plane of the structure with the symbol (hkl; ete. In this
way it is possible to determine the indices of every spot in the

561

stereographical projection P by means of the existent zOne-relations,
and to investigate, which reticular planes will give the most intense
impressions on the photographie film; or, what is the same: it
will be possible to find out, in what way the spectral dissolving-
power of the different molecular planes is connected with their
reticular density.

We have chosen the case of a radiation perpendicular through a
plate parallel to {001}. In the same way however it can be found, that :
On {100} the spot corresponding with HOL, is situated in the direction

00 ¢
a
On {100} the spot corresponding with {110}, is situated in the direction

100
of the B-axis, at a distance of —— m.m.
a

On {010} the spot corresponding with {O11}, is situated in the direction
of C-axis, at a distance of 100 ec m.m.
On {010} the spot corresponding with {110}, is situated in the direction
of A-axis, at a distance of 100 « m.m.
all distances reckoned from the image-centre C'').

of C-axis, at a distance of m.m

_§ 3. If in this way the indices of the molecular planes are deter-
mined, it is possible to construct a stereographical projection of them,
and by means of this projection to execute the ordinary calculations,
as usual in crystallography. However it is also possible to construct
directly the stereographical projection of the reticular planes, with
which the spots on the photo correspond, from the stereographical
projection of the RÖNrGeN-pattern itself. The way to do this, is as follows:

The part to the right of fig. 2 relates to the original stereogra-
phical projection of the RöNTGeN-pattern of potassiumcehloride, obtained
by Brace, if the plate, cut parallel to a face of the cube, is
radiated through in a direction perpendicular to that face. The part
to the left of fig. 2 represents the stereographical projection of the
molecular planes of the erystalline structure, corresponding with the
spots in the part of fig. 2, situated to the right; the plane of projec-
tion is parallel to the same face of the cube. If now we again
pay attention for a moment to fig. 1, we shali find that in this figure

1) The relation between the situation of the spots on the photographical fi m,
and that of the corresponding points in the stereographical projection on P, can
also easily be seen from the fig. 1. For CS=24.tg 9 and CV = A.tg 29, it Vis
the original spot, and S its stereographical projection on P. If C} (= a) is measured
on the photography, then ig 2 —0,02a; from this andég~ are calculated,
and thus CS = 100¢g ¢ is found in mm..

562

the point z is the centre of a zone-cirele CMS, and thus also the
point of intersection of the zdne-axis AQ with the plane of the

photographie plate P, this being in fig. 2 the plane of projection of
the stereographical figure to the left.

tig. 2 Construction for the change of the Stereographical Projection of a RÖNTGEN-
pattern (to the right: potassiumchloride after Braga), into the Stereographical
Projection of the corresponding reticular planes of the Crystal-structure.

Let now m be the stereographical projection of the point Q, then,
if the polar circle to m is drawn, this cirele will contain all points,
that are the projections of all tautozonal reticular planes, having
KQ as their zone-axis. The azimuth of every spot in the plane P
and the azimuth of the stereographical pole of each corresponding
reticular plane in P always being equal, the place of every one of
these stereographical poles on the polar circle just obtained, may be
localised by joining the original spot, and to pass this straight line

563

through, until it intersects the constructed polar circle in the left
part of the figure.

“This point of intersection is the stereographical projection of the
molecular plane, which corresponds with the spot in the right part
of fig. 2. The points m can-be easily found from the points z by
an additional construction, in which a circle with a radius of 50 m.m.

is used; the contractions of the original distances to C, — which
thus can be represented by mz, — are moreover for spots in the

neighbourhood of C only so slight, that without considerable error,
instead of m, the point z itself may be used; but at greater distances
from C this of course is no longer allowable. The system of polar
circles and poles of reticular planes obtained in this way, will give
a direct review of the total zOne-velation and of the indices of the
molecular planes; while the calculation of the angles between the
poles of those reticular planes and the plotting of graphical con-
structions etc., can be made in the way usual in erystallonomy. It
is adviceable to keep the radius of the projection-circle in the left
part of fig. 2 equal to 2A (100 m.m.); then it is possible to execute
the different constructions by means of Werrr’s stereographical pro-
jection plat with a diameter of 20 e.m. The indices of the poles of
the reticular planes are the same as the original ones of the spots
in the projection to the right of fig. 2.

Finally we can express the different intensities of the spots in the
original figure, into the projection-figure of the corresponding molecular
planes to the left of fig. 2; in this way a further discussion of the
relations between the indices of the reticular planes and their
spectral-resolving power can be made, in the way indicated for the
first time by Braae.

§ 4. As an application of the discussions given above, we will
consider here more in detail the RÖNrGeN-patterns of the anhydrite.
The parameters of this mineral are: a:b: ¢ = 0.8932: 1 : 1.0008;
from this it follows, that for a distance of 100 m.m. between the
plane of projection P and the viewpoint O of the projection, the
projected spots for the faces {101}, {O11} and {110} will be situated
at the distances :

For a plate parallel to {100}:

in the direction of the C-axis at 112.04 m.m. from C
at as ES Ees amen: mel br 11: it Bs

For a plate parallel to {010}:

in the direction of the C-axis at 100.08 m.m. from C
Er ss RE RAISE SED bis ie

564

For a plate parallel to {001}:
in the direction of the A-axis at 89.25 m.m. from C
EE) ” ” EE) ” B-axis ” 99.92 EE) ” ” y

If now we calculate from the measured distances of the spots on
the photographie plate of anhydrite, using A — 50 m.m., the values
of ty 27, then v, and finally 100 tg gy, — we shall find that all these
calculated values are a little smaller than the corresponding rational
parts of the above mentioned fundamental distances in the directions
of the resp. axes: moreover, these calculated values all appear to
be diminished tn about the same ratio.

In the case of the photo parallel to {100} e.g. we measured for
some spots:

in the direction of the C-axis: 341.2 mm.; 24.1 mm. and 19.9 mm.
from the centre;

in the direction of the b-axis: 27.4 mm.; and 21.8 mm.

For the same points the calculated distances are:
in the direction of the C-axis: 32 mm.; 24.8 mm.; and 22.4 mm.
in the direction of the b-axis: 28 mm.; and 22.4 mm.

But caleulations and measurements now appear in much better
agreement with each other, if we suppose A during the experiment
to have had a smaller value, and to have been about 48,3 mm.

Now the thickness d of the erystalplate was in our case precisely
1,64 mm.; and thus we must conclude, that in this case we must
use in our ealeulations of the angles ~, for A not the value of the
distance from the front face of the erystal-plate to the photo-
eraphic film, but that from the hachward-face of it to the photo-
graphic plate.

In other analogous cases we indeed now learned, that if A was
supposed to be —50 mm., during the experiment, the distances
from the projected spots to the centre C appeared to be always
too small, if in the final projection the distance OP is always kept
= 100 mm.; but that ordinarily a sufficient agreement between
calculation and experiment would result; if A during the experiment
is supposed to be (50 —4d), where d is the thickness of the erystal-
plate used.

This influence of the plate-thickness becomes yet more evident, if
of the same crystal Rönrarr-patterns are obtained with plates of
very different thickness; for in that case the photos must manifest
different distances from C for the same spots. We were able to
observe something of the kind in the measurement of two analogous

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Fig. 3. Stereographical Projection of the Rönrarrogram of Anhydrite.
Plate parallel to (100).

photos of arragonite, obtained with erystalplates of different thickness.

Thus it seems undoubtedly necessary ; to take into consideration
the thickness of the erystal-plates in the calenlations of the angles p,
and to diminish the distance of 50 m.m., if rather thick plates are
used, with half the thickness of them '). The projections reproduced
on Plate IV of this paper all relate to such stereographical projec-
tions, for which the distance OP is 75 m.m.: in such cases the
diameter of the figure is also kept equal to 75 m.m. 4

In most of the drawings of Plate IV we have calculated the
symbols {hho}, fok} and {holtof the zdne-circles, (whose centres lie in
the direction of the axes), in the way formerly described ; the sym-
bols of the most important spots in the figure can then be imme-
diately seen from the indices of the zone-circles, after the method
mentioned above.

1) This is connected with the specifie absorbing power for Rénreen-rays of the
crystallised material. As this absorption is stronger, the distance of 50 m.m. will
have to be diminished with a smaller part of the thickness d.

Fig. 4.

Fig. 5.

Stereographical Projection of the R6NrGENogram of Anhydrite.
Plate parallel to (010).

\
a
0145

ae + ee +
wea of &

Stereographical Projection of the RönrGenogram of Anhydrite.
Plate parallel to (001).

567

In connection with the crystals investigated up to this moment;
the corresponding principal distances in the direction of the axes,
as in the case of anhydrite, may be recorded here *).

2 N 2 a Vee Tecan is = Bel 4
Aull assy 3 wo | av | 2E | be SEE E 32
St aS = wre Em | og am GOE s ia
aay = 5 Se Ns Zi |OES = 5
ur | = << ae) | n | Nd p} 5 oO
(ae c | 160.9 | 180.5 | 112.0 | 115.8 91.0 | 57.4 | 175.8 } 51.0 61.0 95.2
On {100}: fn
B-axis Fe | 176.5 | 189.2 | 111.9 | 160.7 | 125.2 | 102.0 | 211.1 | 121.4 | 127.6 | 170.3
C-axis 100c | 91.2 95.4 | 100.1 IDA 125 56.3. 83:3 | 42.0 41.8 | 55.8
On 3010}: | |
en. 56.7 52.8 89.3 62.2 79.9 98.0 | 47.4 82.3 18.3 58.7
100a |
A-axis—— | 62.1 55.4 | 89.2 | 86.4 109.9 | 174.1 56.9 | 196.0 | 163.9 | 105.1
On {001}: oo | | |
|z- -axis —— | 109.6 104.8 | 99.9 | 138.8 | 137.6 | 177.6 | 120.1 | 238.1 | 209.3 | 179.1

§ 5. In previous papers we already discussed some crystals of
rhombic symmetry, which will be reviewed again in connection
with what is mentioned above. However we will principally discuss
in this paper the results, to which our experiments till now have
led us, with respect to the following erystals : anhydrite; arragonite ;

- zinc-sulphate; topaz; struvite; l-asparagine and calamine. A following
communication will then contain the results with other rhombie
erystals, and at the same time we shall have then an opportunity
to draw the attention to some problems, which are connected with
the special choice of these crystals.

We will begin here with the erystals of the rhombic-bipyramidal
class first °).

. Anhydrite (CaSO,). The used anhydrite-erystal was from Srass-
FURT. It was lustrous and translueid, and evidently quite homogeneous.
Parallel to the three directions of cleavage: {100}, {O10} and {001},

1) Note A these numbers relate to a projection distance OP= 100 m.m.; our
figures then have also a diameter of 100 m.m. But for the drawings on Plate IV,
which are reduced to %/, size, all these values need to be also multiplied with 4/4.

2%) The erystals discussed in this paper are supposed to have such a position, that
their parameters become: anhydrite: a:b:c=0.8932:1:1.0008; arragonite:
a:b:c=0.6224:1:0.7206; zinc sulphate: a:b:c=0.9804:1:0.5631; topaz:
a:b:c=05285:1:0.9539; struvite: a:b:¢=0.5667:1:0.9121; calamine:

a:b:¢=0.7835:1:0.4778; lasparagine: a:b:c = 0.4737 : 1:0 8327; sodium-
ammonium-tartrate: a:b :¢ = 0.8233 :1:0.4200; hambergite: a:b :c¢= 0.7988:

1 0.7268.

568

three rather thick erystal-plates were prepared, whose thickness was
resp. 1.64 mm, 1,72 mm. and 2,09 mm. In this case and all others
here we experimented again with the fluorescent sereen ““Eresco”;
the time of exposition was ordinarily about 2,5 hours. In this case
of the anhydrite we used more particularly a Cooriper-tube, with a
wolframium-anticathode and separate heating-spiral.

The three photographs are reproduced in fig. 1—3 on Plate I;
their stereographical projections, already in fig. 3, 4 and 5 of the
text. All three images appear to be quite normal, and every one
has two perpendicular planes of symmetry ; the normal to the plate
(direction of radiation) is thus at the same time a binary axis of the
R6nTGEN-patterns.

Db. Arragonite (CaCO,). Our clear, lustrous crystals were from
Horscuerz in Bohemen. The erystal-plate parallel to {L00} had a
thiekness of 0,96 mm., that parallel to {010} 1,06 mm., and that
parallel to {001} 1,10 mm. The photos are reproduced in fig. + on
Plate I, and in fig. 5 and 6 on Plate II; their stereograpbical pro-
jections in fig. 1--3 on Plate IV. Also in this case the patterns
appear to be symmetrical with respect to two planes of symmetry
perpendicular to each other, just as might be predicted from theory.
In the image parallel to {001} moreover the well-known pseudo-
ditrigonal symmetry of the mineral is clearly recognisable.

c. Topaz. (AL, (F,OH), SiO,). The topaz-erystal used by us was
very homogeneous, vitreous and translucid; it possessed a yellowish
hue, and originated from Survony. The thickness of the three plates
parallel to {100}, {010} and {001}, was from 1,20 mm. to 1,27 mm.; the
time of exposition again two and a half hours. The plate parallel
to {OLO afterwards appeared to be a little inclined; therefore the
corresponding photo was not reproduced here, but solely those of the
other sections in fig. 7 and 8 on Plate II; their stereographical
projections are to be found in tig. 4—6 on Plate Ve

Also in this case all three patterns appear to be symmetrical after
two perpendicular planes, as might be expected from the theory.

To this same class belong furthermore the crystals of cordierite
and of hambergite, already previously *) discussed.

d. In the case of cordierite the patterns of crystal-plates parallel
to {100} and {010} appeared to be, till this moment, always abnormal,
notwithstanding the fact that erystals of several localities were used
in the experiments, and among these were present splendid, lustrous
erystals. Only the pattern obtained with a erystal-plate parallel to
{001}, appeared to exhibit the normal symmetry.

1) These Proceed. 17, 430, 1204. (1915).

_——

569

e. About the hambergite and its normal and abnormal images we
have said already something in the foregoing paper. In fig. 7—9
on Plate IV we reproduce here again the more exact stereographical
projections of the normal RÖNrGeN-patterns of this mineral, with
indication of the corresponding indices of the reticular planes.

$ 6. Of the rhombic-pyramidal class, to which thus belong the
hemimorphic crystals of the system, — we investigated here the
struvite (= magnesitum-ammonium-ortho-phosphate: (NH,)MgPO,+6H,0)),
and the calamine: Zn, (OB), SiO .

J. From a big, brownish yellow and only little translucid erystal
of struvite from Hompure, three plates were cut parallel to the three
pinacoides {100}, {010} and {O01}, whose thickness was from 1,20
to 1,26 mm. The time of exposition was two and a half hours.

The three very beautiful RöNrGeN-patterns are reproduced in the
fig. 9, 10 and 11 on Plate III, and as stereographical projections in
tig. 10—12 on Plate IV. Also in these images two planes of sym-
metry perperdicular to each other are evidently manifested ; notwith-
standing the polarity of the c-axis is very strongly revealed in the
erystals themselves, the result is also in this case in full agreement
with the theoretical prediction.

g. However in the case of calamine we obtained for crystal-plates
parallel to {100} and {010}, cut from a very beautiful crystal’),
always abnormal patterns, from which one parallel to {OLO} is re-
produced partially as a stereographical projection in fig. 13 of
Plate IV; the image parallel to {100} was quite analogous to that
parallel to ;010}, but it was too bad to allow in any way a repro-
duetion of it. Both patterns contained moreover such a great number
of very small and feeble spots, that also in the projection of fig. 13
on Plate IV, only the most important spots could be reproduced.

The RöÖnreerrogram of the ca/amine parallel to {001} however
was very beautifully regular (fig. 14 on Plate IV) and (fig. 12 on
Plate UI); quite in concordance with the theory, it is symmetrical
with respect to two planes perpendicular to each other. Why

it is the images parallel to {100} and {010{, — (corresponding with
those sections, that in the erystal itself do not possess the horizontal
plane of symmetry), — where the plane of symmetry parallel

to the c-axis is suppressed, can hardly be understood at this moment.

§ 7. Finally we used from the erystals of the rhombic-bisphenodical

') Por this very beautiful crystal we are much indebted to our colleague, Prof.
MOLENGRAAFF at Delft, whom we render our best thanks here once more.

570

class, besides the already formerly discussed erystals of d-sodium-
ammonium-tartrate, moreover : those of l-asparagine :(C,H,O,N,+H,0),
and of zine-su/phate: ZnS, + 7H,O; of these compounds both the
first named are optically active in solutions, while the zinc-su/phate
does not cbange the plane of polarisation of the light, when passing
through its solution.

h. Zinc-sulphate. From a beautiful erystal three rather thick plates
were cut: that parallel to {100} had a thickness of 2,11 mm., that
parallel to {OLO} of 3.30 mm., and that parallel to {001} of 3.10 mm.
Even with a time of exposition of two and a half hours, the patterns
parallel to {100} and {901} were too feeble, to allow of any repro-
duetion; but in fig. 15 and 16 their stereographical projections are
drawn.

These images are again symmetrical with respect to two perpen-
dicular planes However the pattern obtained with a plate parallel
to {O10} appeared to be always abnormal; the respective photo is
already reproduced in the foregoing paper on Plate V, while here
in fig. 17 on Plate IV its stereographical projection is represented.

This last fact is indeed of high importance for our problem: for
it may be supposed with good reason, that in eases, where such
erystal-plates are prepared by cleavage along planes of very perfect
cleavability, all chance to get a faulty orientation of the plate is
altogether eliminated. Now in our case the very perfect orientation
of this plate obtained by such cleavage, could moreover be very
rigorously tested, because of the fact that the b-axis, being the
direction through which radiation here takes place, is at the same
time the first bisectrix of the crystal. Indeed the interference-image
in convergent polarized light appeared after measuring with the
microscope, to be accurately centred, so that mo deviation between
the -axis and the normal on the plate could be found by any
means. And while now the orientation of the perfectly clear and
lustrous plate could hardly show any error exceeding a few minutes,
the image was in two repeated experiments, absolutely abnormal
in the way indicated here: evidently only the plane of symmetry
parallel to the plane of the optical axes has remained.

This fact must convince us in a striking way, that the abnor-
malities occurring in the case of such erystals cannot have their
origin in a faulty orientation of the erystal-sections. Indeed, they
must be caused by internal disturbances of the molecular structure,
which evidently, as here with the zinc-su/phate, cannot even be
discerned by the usual optical means. At the same time it appears
furthermore by this fact, that the probability of such “internal vicinal

<<< en on ~ ——eeee ee a

Sp | ee oe mn. En

í AEGER AND H. HAGA. ON THE SYMMETRY OF THE RöNTGEN-PATTERNS ; PLATE I.
d OF RHOMBIC CRYSTALS. I.

Fig. 1.
Anhydrite. Plate parallel to (100). :
Fig. 2.

Anhydrite. Plate parallel to (010).

Fig. 3. Fig. 4.
Anhydrite, Plate parallel to (001). Arregonite, Plate parallel to (100).

‘roceedings of the Acad. of Sciences, Amsterdam, Vol. XVIII. A? 1915/1916. HELIOTYPE, VAN LEER. AMSTERDAM.
3

PLATE II.

M. JAEGER AND H. HAGA. ON THE SYMMETRY OF THE RÖNTGEN-PATTERNS
OF RHOMBIC CRYSTALS. I.

Fig. 5.
Arragonite, Plate parallel to (010). Fig. 6
Arragonite. Plate parallel to (001).

Fig. 7. Fig. 8.
Topaz, Plate parallel to (100). Topaz. Plate parallel to (001).

HELIOTYPE, VAN LEER, AMSTERDAM

Proceedings of the Acad. of Sciences, Amsterdam. XVIII. A° 1915/1916.

.M. JAEGER AND H. HAGA. ON THE SYMMETRY OF THE RONTGEN-PATTERNS PLATE III.
OF RHOMBIC CRYSTALS. I.

Fig. 10.
Struvite. Plate parallel to (010).

"Struvite. Plate parallel to (100).

Fig. 11. Fig. 12.
Struvite, Plate parallel to (001). Calamine. Plate parallel to (001).

Proceedings of the Acad. of Sciences, Amsterdam. XVIII. A° 1915/1916. HELIOTYPE, VAN LEER, AMSTERDAM.

Plate IV

c!
Fig. 1. Stereographical Projection of the Rontgeno- Fig. 2. Stereographical Projection of the Röntgeno- Fig. 3, Stereographical Projection of the Röntgeno- Fig, 4. Stereographical Projection of the Rontgeno- Fig. 5, Stereographical Projection of the Röntgeno-
gram of Arragonite, Plate parallel ta (100). gram of Arragonite, Plate parallel to (010), gram of Arragonite. Plate parallel to (001), gram of Topaz, Plate parallel to (100). gram of Topaz, Plate parallel to (010)

Fig. 6, Stereographical Projection of the Röntgeno- Fig, 7. Stereographical Projection of the Réntgeno- Fig. 8. Stereographical Projection of the Röntgeno- Fig. 9. Stereographical Projection of the Rontgeno- Fig, 10. Stereographical Projection of the Röntgeno-
gram of Topaz. Plate parallel to (001) gram of Hambergite. Plate parallel to (100) gram of Hambergite. Plate parallel to (010), gram of Hambergite. Plate parallel to (001). gram of Struvite Plate parallel to (100).

Fig. 11, Stereographical Projection of the Röntgeno- Fig, 12, Stereograplical Projection of the Röntgeno- Fig. 13. Stereographical Projection of the Röntgeno- Fig. 14. Stereographical Projection of the Röntgeno- Fig, 15. Stereographical Projection of the Röntgeno-
gram of Struvite. Plate parallel to (010). gram of Struvite. Plate parallel to (001), gram of Calamine, Plate parallel to (010), gram of Calamine. Plate parallel to (001). gram of Zinc-sulphate. Plate parallel to (100),
(Schematical)

Fig. 16. Stereographical (schematical) Projection Fig. 17. Stereographical Projection of the Röntgeno- Fig. 18, Stereographical Projection of the Röntgeno- Fig. 19. Stereographical Projection of the Rontgeno-
of the Röntgenogram of Zinc sulphate. Plate parallel gram of Zinc-sulphate. Plate parallel to (001). gram of laevogyratory Asparagine. Plate parallel gram of laevogyratory Asparagine. Plate parallel
to (010). Abnormal Pattern, obtained with a perfectly to (100), to (001), (Schematical).
clear lamella prepared by cleavage, and exactly

perpendicular to the first bissectrix.

571

planes” is by no means diminished by the particular circumstance,
that the considered molecular layers are just those, which play the
role of directions of perfect cleavability in the erystals. (Thus being
perpendicular to the direction of minimal cohesion’).

?. The RöÖNraer-patterns of d-sodium-ammonium-tartrate, as well
the normal as the abnormal ones, and all particulars observed in
that case, have been discussed already in detail in our last paper.
We can here therefore refer to the resp. figures; only it may be
remembered here once more, that the patterns parallel to all three
pinacoidal faces, in the normal case appeared to be symmetrical
with respect to two perpendicular planes.

k. From big, colourless and perfectly transparent crystals of
laevogyratory asparagine, crystal-plates parallel to {100}, {010} and
{001} were cut. The plate parallel to {100} had a thickness of
1,21 mm., that parallel to {010}, of 1,06 mm., and that parallel to
{001}, of 1.22 mm.

The obtained RöNrGeN-patterns were all too feeble to make a
direct reproduction possible. But in fig. 18 and 19 on Plate IV
two of their stereographical projections are drawn. Also these images
evidently are symmetrical with respect to two perpendicular planes.
The third pattern was too disturbed to allow any valuable judgment
about this question.

§ 8. From these researches, which will be still completed, it
becomes clear even now, that in ordinary cases also with optically
biaxial crystals, the theoretical predictions are in full concordance
with experience.

The repeatedly observed suppression of one of the two expected
planes of symmetry in the R6nrGEN-patterns, must be considered
also in these cases as a peculiar “abnormality”, which undoubtedly
is caused by internal disturbances of molecular dimensions, whose
true nature however at this moment cannot yet be more sharply
defined.

University-Laboratories for Physics and for
Inorganic and Physical Chemistry.

Groningen, August 1915.

1) In this connection a remark made a short time ago by P. Enrenrest (these

Proceed. 18. 180. (1915) is of interest, consideriug the possibility of cleavage
along planes, which are “‘vicinal” with respect to such directions of perfect
cleavability.

Proceedings Royal Acad. Amsterdam. Vol. XVII

572

Zoology. — “The Physiology of the Air-bladder of Fishes.” (From
the Physiological Laboratory of the Amsterdam University.)

By Dr. K. Kureer Jr. (Communicated by Prof. Max Weger).

(Communicated in the meeting of May 29, 1915.)

I. The Ductus pneumaticus of the Physostomi.

Borre (1670) already demonstrated experimentally that a tench
when exposed to a lower pressure than the one under which it
lives, can allow air-bubbles to escape from the air-bladder by means
of the ductus pneumaticus. For a long time it was supposed that
this channel also served to lead into the air-bladder gases which
the fish had imbibed at the surface of the water. Evidently this
would only be possible if the tension of the gas in the bladder is
less than that of the atmosphere. The former being in a great
majority of instances greater than the latter, this mode of filling
the air-bladder is precluded. Besides a fish rising to the surface has
to leave its “plan des moindres efforts”, the plane where its S.G.=1.
At the surface the tension is less, the air-bladder expands, the fish
grows specifically lighter; it floats. To reach its static plane again
it has to perform muscular labour in a direction opposite to the
upward pressure. If it admitted air at the surface, which would
lower its statie plane in the water, the exertion in going down
again would have to be greater still. This view of the funetion
of the ductus has been relinquished by almost every one.

An annular muscle shuts off the entrance of the ductus into the
esophagus. Structuie and action of this muscle were first closely
studied by Geréror. He proved that this muscle has a tonic tension.
When a physostomus is exposed to a decreased pressure, air-bubbles
do not immediately escape from the mouth. Only when the decrease
amounts to about 5 centimetres of mereury the gas leaves the
bladder. At the death of the animal this tonus disappears. The
resistance which the sphincter offers to the air in the bladder is
reduced to about two fifths. The opening of the sphincter is brought
about under the influence of the central nerve-system. The muscles
get nerve-branches from the Ramus intestinalis Vagi. This appears
distinetly from the microscopic preparations (microtomic sections)
which 1 made of the sphincter and its surroundings. The gas-bubbles
are not emitted continually bat intermittently. This suggests the
probability that the tonus of the sphincter is relaxed every now

573

and then. A more accurate idea of the mechanism of this sphincter-
orifice was the object of this part of my investigations.

At the outset it must be observed that the pressure-decrease to
which a fish is submitted has to surpass a certain minimum before
the animal lets an air-bubble escape. Already at a smaller difference
in tension than that at which air-bubbles are sent forth, the fish
shows by the restless motion of its fins that it responds to this
difference. In the various species and also in the various individuals
of the same species the difference between the pressure-decrease at
which fin-reactions and at which air-bubbles appear is highly variable.
Besides the minimum change at which fin-reactions are observed
fluctuates strongly. Hence we shall have to experiment on as great
a number of animals as possible in order to obtain reliable results.

If a fish adapts itself to a modified pressure, this does not take
place at once. The relaxation of the sphincter seems to last but a
short time and may repeat itself at intervals as long as the fish
has not entirely adapted itself. The first air-bubble will be followed
after a shorter or longer time by others. Generally speaking the
interval between two air-bubbles will gradually become greater and
this is quite natural for after each air-bubble the fish becomes more
adapted to the new pressure. This lengthening of the intervals is,
however, by no means regular.

If for instance a fish is exposed for a long time at a stretch, to
a pressure-decrease which does not immediately cause air-bubbles
to escape, then the long action of this weak stimulus has the same
effect as the short action of the stronger one. It could not be de-
monstrated that the produet of time and degree of stimulus was a
constant one, but it was very evident that below a certain minimum
of pressure-difference no bubbles were emitted, and that above it,
at the inerease of the pressure-difference, the periods before the
emission of the first air-bubble grew smaller and smaller.

If a fish is narcotized then the sphineter-reflex, as was shown
by Guyinor, is retarded. The opening of the sphincter is the result
of the removal of the tonus in the muscle. It is an inhibitory reflex
removed by nargosis. I can confirm the results of GuysNor’s experiments.
It is remarkable that this reflex-retardation remains a long time
after the narcosis. First the respiratory rhythm grows normal, then
the equilibrium is restored, afterwards defensive reflexes, caused by
fright or decreased pressure manifest themselves. Only much later
the tonus-reflex of the sphincter becomes active again. It seems that
the centre whence the efferent part of this reflex proceeds remains

574

disturbed for a longer time than the centres of respiration, motion,
ete. The same retardation which is caused by narcosis also manifests
itself if the fish is exposed to the action of an electric current.

We shall now try to investigate the course of the inhibitory
sphincter reflex.

Guyinor states that in tench, carp, ete. a delay in the manifestation
of the refiex could be observed if the connection between the
forepart of the air-bladder and the perilymphatie space of the
vestibulary apparatus, which is formed by the so-called bones of
WeBer, was interrupted. If this view is correct, the function or at
least one of the functions of the bones of WerBer must consist in com-
municating to the brain modifications in the gas-tension of the bladder.
Air-bladder + organ of WeBerR must be looked upon, in accordance
with the views of Hasse, Briper and Happon and others, as a hydrostatic
organ. In this hydrostatic organ the ductus-sphineter acts as a
safety-valve by means of which a surplus of gas may be removed.

GurÉnor states that the emission of air-bubbles before the destruction
of this connection, set in at a pressure-decrease of + 4.5 centimetres
of mercury ; immediately after the operation it took place only after
a decrease of 12—14 centimetres of mercury.

In my preceding article (these Proceedings Vol. XXIII, p. 857) I
took exception to the technics of Gurúror's experiments. I feel
compelled to do the same now. GurÉror’s method is open to various
objections. It is based upon the most distal of the bones of Weger,
the Tripus, being detached from the side of the air-bladder; the
reaction of the fish is investigated immediately after the operation,
and the fish is killed immediately after this investigation.

Why was only the connection between air-bladder and Tripus
removed? Could not the air-bladder when it expands effect a pressure
on the Tripus, which could be transmitted to the vestibulary apparatus
by means of the rest of the organ of Weger? Why should the
fishes be killed immediately after the operation? Was it abso-
lutely impossible then that the retardation of the reflex was due to
the shock? Why was it not verified, in the case of some fishes at
least, that they reacted a few days after the operation exactly as they
did immediately after ?

These considerations induced me to test Guyinor’s experiments.

In two ways I tried to disrupt the connection in question. First
by making a ventral median section; thus I reached the body-cavity
and by moving a little hook past liver, intestine and genitals I tried
to destroy the connection. The sinus venosus rendered this operation

575

very difficult and the results were unsatisfactory, or rather they
agreed perfectly with those of GurÉnor.

The second way resembles much that of GurÉror. Sideways behind
the head a longitudinal cut was made in the muscles just where
the Tripus is situated. I reached the fossa auditoria of Weser, felt
my way by means of a thin hook until I felt the Tripus move,
then I caught firmly hold of it, detached it carefully from its
connection with the air-bladder on one side and the other bones of
Weger ‘on the other, and removed it from the body. Of course this
was done on either side.

The connection was now entirely removed.

The. results of these experiments are very striking. Whenever the
removal of the connection had been effected without giving rise to
hemorrhage during the operation, the pressure-decrease required to
bring about an emission of air-bubbles was no greater or hardly any
greater than before the operation. Only when the general condition
of the fish was a bad one, and immediately, after the operation,
a retardation was to be observed. Sometimes indeed, a retardation
could be observed in fishes which had only been submitted to a
beginning of an operation, which, moreover, had nothing to do with
the organ of Weber, or the muscles innervating the sphincter. If,
besides, we keep in view how long the retardation of the reflex
manifested itself after narcosis or after the recovery from the effect
of an electric current, we may be sure that GurÉror’s results must
be due to the shock.

Hence we conclude that the experiment of Gurtnor cannot be
adduced in support of the theory of Hasse c.s. regarding the function
of the air-bladder and the organ of WeBur.

To obtain greater certainty I also interrupted the hypothetical
reflex course in another spot.

If the sphincter-reflex is affected by the elimination of the organ
of Wesrr, this must also be the case if the connection between
brain and labyrinth is destroyed. Therefore I twice attempted to cut
the nervus octavus in tenches on one side and twice on both sides.
Technically this operation presented few difficulties. The fishes
remained alive for many days after the operation. Autopsy proved
that the operation had sueceeded. In none of these cases the emission
of air-bubbles had been retarded after the operation. The funetion
of the ductus-sphincter is entirely independent of the intact state of
the labyrinth.

Hence the afferent part of the inhibitory reflex course is not found
in the organ of Weger. It will probably have to be looked for in

576

the sensitive spinal nerve-ramifications, met with in: the air-bladder.

The efferent part of the reflex passes along the Rami intestinales
Vagi. This became evident when these two nerves were cut through.
It is very probable that the tensionand:the relaxation of the sphincter
are brought about: by different nerves; just as in the case of the
muscles of the bladder of: mammals.

Here: e.g. the sphineter:internus is relaxed (tonusinhibitton)-along the
nervus pelvicus, whilst the nervus hypogastricus effects the contraction
of this» muscle. ‘

What are the reasons for assuming such an:antagonistic@ innervation
also for the ductus sphincter ? The grounds for: this supposition are
of two kinds: and: derived: 1 from: experimental data; 2:from mieros-
copie observations.

1. Experiments. The sphincter is: innervated’ on both sides by a
branch of the Ramus intestinalis Vagi. [ have ent: through this
double “innervation: in two ways viz: immediately behind: the gill-
covery where the ramus intestinalis with the ramus: lateralis bends
away from the whole vagus. group, and: immediately near the
sphincter (by: making a median ventral cut). When :thewagusbranches
had been cut through near the gill-covers, the consequences; asregards
the: emission of air from the bladder, were the: following: 1. the
emission: was considerably retarded, 2, when air-bubbles:were emitted
the emission: no longer took place intermittently, but fora long time
at) a stretch.

Hence we must conclude that the vagus contains-inhibitory fibres
for the: sphineter-tonus.

If the vagus-braneh is cut through: immediately near the sphineter
the effect is different. The tonus-inhibition is: not retarded; but is no
longer intermittent either, and: the tonus decreases: more: and more
after the operation.

This result might be explained if it could be demonstrated that
the vagus branch near the sphineter also contains fibres: for the
preservation of the tonus (e.g: sympathetic fibres) the: cutting of
which caused the tonus- to disappear, thus entirely removing the
inhibition-delay.

2. Microscopic observations. What can we gather from the topo-
graphie studies of Cumvrer as regards the sympathetic nerve-system
of fishes, and our own histological and microscopic-anatomical resear-
ches on sphineterinnervation ?

Curvrer, divides the sympathetic system of fishes into three parts;
the cranial, the abdominal, and the caudal part. He deseribes the
connection which the ganglia of the first part form with brain and

a Br

577

gill-nerves and Ramus lateralis, and then describes how in the Labrax
lupus the R. intestinalis vagi forms near the division of the Arteria
coeliaca into Art. hepatoduodenale and Art. mesentero-spleniale, a
strong Plexus coeliacus with the N. splanchnieus, which originates
from the first abdominal sympathetic ganglion. No such plexus is
mentioned by Currvren in the case of Cyprinoids. As the latter
resembles Labrax in’ the main, there is no reason to assume that
though not mentioned it should not be found here. The probability
that the branch innervating the esophagus receives sympathetic fibres
by means of the splanchnicus is therefore very great, and becomes
practically a certainty if sympathetic fibres can be identified in the
thinnest nerve-ramifications on the muscular fibres.

We know that in the striated muscle three kinds of nerve-endings
may be met with. First the epilemmal sensible nerve-endings, secondly
the hypolemmal endings connected with nerve-fibres possessing a
myelin sheath; the so-called motorie endplates of Kiune, thirdly,
much more delicately shaped networks, always originating, as far
as we know, from the’ marrowless fibres, which are called accessory
endplates. Boekt describing this species takes them to be endings of
sympathetic fibres.

From pr Bowr’s publications we have known for a few years
that the sympathetic fibres maintain the tonus of the muscles.

The presence of accessory endplates in the sphincter ductus pneu-
matici has rendered in my opinion the antagonistic innervation very
probable.

For the study of the motorie endplates I used the silver-impreg-
nation of BiriscHowsky as prescribed by Borkr. The results, obtained

for the present by this method, are made clear in fig. 1—3.
Histological particulars concerning the course of the nerve-fibres and
the shape of the endplates may be omitted bere. The main point
is that in the muscle closing the esophagus and ductus motoric end
plates of 2 kinds may be met with.

The hypolemmal nerve-fibrils without a medullary sheath as far
as they could be traced, were thinner than those with one. The
endplates were less marked and mostly ended in simple loops.

Hence there are good reasons for assuming that the sphincter is
innervated in two ways, that the stimulation of the nervus sympathi-
cus keeps up the tonus, and that of the vagus removes it.

The easiest way of investigating the function of the ductus sphine-
ter is to expose the fish to a modified air-pressure.

578

There are, however, also other stimuli which act upon the “in-
hibitory reflex”, stimuli acting upon other senses than the hydrostatic
organ of sense (the air-bladder filled with gas) are also amongst them.

The following were made to act upon fishes: light stimuli, vibra-
tions of the water (whether they are to be viewed as sound or
sensory stimuli I shall leave undiscussed for the present), stimulation
of the static organ, chemical stimuli, enclosure in a narrow space
(this must pot be viewed as the stimulation of a certain organ of
sense, but as a means of exciting terror).

a. Light-stimuli.

The fishes in the experimental basin nearly always went to the
darkest part. If the basin is lighted up, they turn away from the
light, but do not become restless. This is the case, however, if the
basin is alternately lighted and darkened. If, for instance, the basin
is alternately lighted and darkened about 120 times a minute, the
fish begins to swim round uneasily, the respiration-rhythm rises
from about 50 to about 90 a minute, the mouth is opened every
now and then, and finally some air-bubbles escape.

6. Vibrations in the water. These are brought about by tapping
(with a stick) against the experiment-bottle which was in the basin,
and which contained the fish. The results agree with those mentioned
under a.

c. Stimulation of the statie® organ.

If a fish is placed in a bottle completely filled with water, which |
is closed by means of a tight fitting stopper, and if the bottle is
swiftly turned round in all directions, then the fish is compelled to
correct continually its statie position. Within a very short time such
an animal emits a number of air-bubbles.

d. Chemical stimuli.

When fishes are narcotized in the water with ether or chloroform,
they often emit air-bubbles.

e. Fishes enclosed in a narrow space, which are, for instance,
put in a jar below the surface of the water in the basin, emit a
few air-bubbles, swimming up and down meanwhile in a state of
great agitation.

We conclude from the preceding that as a result of greatly dif-
ferent sensory stimuli, besides swimming and respiratory movements,
the opening of the sphincter also manifests itself as a reflex.

Finally I wish to point out that these experiments with various
stimuli were also carried out with fishes that had been operated
upon. Thus I hoped to obtain a clue as to the direction in which

EET je , 5 ans
: bt Hen taal Jk
TICES A ae eek Se Loa

580

we shall have to look for an interpretation of the organ of Weber,
now that it has become evident that the view of GurÉror can no
longer be held.

The results of these experiments may be summarized as follows:

1. When the vagus-branches are cut through, the fishes no longer
emit air-bubbles, though they respond in a normal way to light-
alternations, vibrations and statie stimuli, by their swimming and
respiratory movements.

2. Destruction of the organ of Weser results in fishes responding
to light-stimuli (swimming, respiration, sometimes also air-bubble)
but not or very feebly to vibrations.

3. When the N. octavus is cut through, the fishes respond (and
that very violently) to changes in the light, but not to vibrations,
nor (which need scarcely be mentioned) to statie disturbances.

On comparing these results with those obtained formerly by means
of pressure-modification, we obtain the following survey.

Fishes

Vibrations
Static
disturbances
Narcosis

Reaction on
pressure-changes

Light alternation
Enclosure in
narrow space

Normal fish | + + | +4 +

cut on both sides |

|
|
| |
Vagus has been | 4 _— | ae |, a ds des ||
ee

Destruction of |
organ of WEBER | aE ac =r Gl emd sahekabs

N VIII has been |
cut on both sides aay ee eet te eee

[The first sign denotes reaction caused by swimming- or respiratory
movements, the second by the opening of the sphincter. |

Very curious is the disappearance of reactions to vibrations as
opposed to their remaining after pressure-modifications, when the
organ of Weser has been destroyed and the N VIII has been cut
through.

581

The sensitiveness of fishes to vibrations causing sound-sensations
in man, has been proved by Piper, who derived actioncurrents
from the N. octavus when the fish-labyrinth had been isolated, and
by Parker, who at the action of sound saw a number of fishes gather
at one side of the basin.

The Clupeides are very sensitive to vibrations. Would this perhaps
be due to the special direct connection these fishes bave between
air-bladder and vestibulary apparatus ?

I should say there are ample grounds for investigating if not the
view of KE. H. Weger, NusBaum and SrpoNrak and others, who see
in the organ of Wher a means to transmit vibrations which the
air-bladder receives from outside, to the vestibulary apparatus, must
be preferred to that of Hasse, Bripee and Happon, Gurúror, who
wish to connect this organ with the hydrostatic funetion of the
air-bladder.

Of course | do not for a moment lose sight of the importance
of the air-bladder as a hydrostatic organ of sense.

In my opinion it is, however, quite possible that further investi-
gations will prove that the air-bladder also serves to receive vibra-
tions and that the organ of WeBer has to transmit these vibrations
to the perilymph of the vestibulary apparatus.

Ty WG odie AA 10) RY AD
(concerning all three inferior parts of this treatise).

Baauont S., Zur Physiologie der Schwimmblase der Fische. Zeitschr. f. algem.
Physiol. Bd. VIII, 1908:

Braurort, L. F. pe, De zwemblaas der Malacopterygii. Akad. Proefschrift,
Amsterdam, 1908.

Boeke, J., Beiträge zur Kenntnis der motorischen Nervenendigungen. Intern.
Monatschr. f. Anat. u. Physiol. Bd. 28, Leipzig 1911.

Boer, S. pe, Die quergestreiften Muskeln erhalten ihre tonische Innervation
mittels der Verbindungsäste des Sympathicus (Thoracales autonomes System) Folia
Neurobiol. Bd. 7. Haarlem 1913.

Bour, G., The influence of section of the vagus-nerve on the disengagement of
gases in the airbladder of fishes. Journ. of Physiol. vol. 15, 1894,

CHARBONNEL-SALLE, L., Recherches experimentales sur les fonctions hydrostali-
ques de la vessie natatoire Ann. d. Se. Nat. (Zoologie), 1887.

CHevREL, R., Sur l’anatomie du systeme nerveux grand sympathique des Elas-
mobranches et des poisons osseux. Arch. de Zool. experim. et gener. T. 5, suppl.
1887—1890.

DeweKa, D., Zur Frage über den Bau der Schwimmblase, Zeitschr. f. Wiss.
Zool. Bd. 78, 1904.

Guyinot, E. Les fonctions de la vessie natatoire des poissons teleostiens. Thése
de la faculté de medicine de Paris, 1909.

582

Hasse, CG. Anatomische Studien. I. 1873.

Jager, A. Die Physiologie und Morphologie der Schwimmblase der Fische.
Inaugur. Dissert. Leipzig, 1903,

Kuiper, K. De functie van de zwemblaas bij eenige onzer zoetwatervisschen.
Akad. Proefschr. Amsterdam, 1914.

Moreau, A. Recherches physiologiques sur la vessie natatoire. Mémoires de Physio-
logie. Paris, 1877.

Nuspaum, J. u. Sportrak, S. Das anatomische Verhältnis zwischen dem Gehér-
organ und der Schwimmblase bei dem Schleimbeiszer (Cobitis fossilis). Anat. Anz.
Bd 14. 1899.

Parker, F. H. Sound as a directing influence in the movements of fishes. Bull
of the bureau of lisheries. Vol. 30, 1910.

Piper, H. Aktionsströme vom Labyrinth der Fische bei Schallreizung. Arch. f.
[Anat. u.] Physiol. 1910. Suppl.

Weser, E. H. De aure et auditu hominis et animalium. Pars I. Lipsiae, 1820.

Winterstein, H Beiträge zur Kenntniss der Fischatmung. Pfliiger’s Arch. Bd.
125. 190s.

Winterstein, H. Die physikalisch-chemischen Erscheinungen der Atmung. Handb. d,
vergl. Physiol. Bd. 1.

BRR A TUM;
In the Proceedings of the Meeting of December 30, 1914.

p. 905 line 7 of the 2°¢ column of table III: for 20.10° read 21.06

(October 30, 1915.)

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS

VOLUME XVIII
Now 4—5:

President: Prof. H. A. LORENTZ.
Secretary: Prof. P. ZEEMAN.

(Translated from: Verslag van de gewone vergadering der Wis- en
Natuurkundige Afdeeling, DI, XXIII and XXIV).

CONTENTS,

H. A. BROUWER: “Pneumatolytic hornfels from the hill countries of Siak (Sumatra)”. (Communicated
by Prof. G. A. F. MOLENGRAAFF), p. 584.

H. K. DE HAAs: “A Confirmation of the Principle of Relativity.” (Communicated by Prof. H. A.
LORENTZ), p. 591.

F. M. JAEGER and JUL. KAHN: “Investigations on the Temperature-Coefficients of the Free Mole-
cular Surface-Energy of Liquids from —80° to 1650° C. XIII. The Surface-Energy of position-
isomeric Benzene-Derivatives”, p. 595.

5, M. JAEGER and JUL. KAHN: “Ibid. XIV. Measurements of a Series of Aromatic and Heterocyclic
Substances”, p. 617.

W. H. KEESOM: “The second virial coefficient for rigid spherical molecules, whose mutual attraction
is equivalent to that of a quadruplet placed at their centre.” (Communicated by Prof. H.
KAMERLINGH ONNES), p. 636.

H. A. VERMEULEN: “The vagus-area in Camelopardalus Giraffe”. (Communicated by Prof. C.
WINKLER), p .647.

I. K. A. WERTHEIM SALOMONSON: “A difference between the action of light and of X-rays on the
photographic plate”, p. 671.

E. F. VAN DE SANDE BAKHUYZEN and C. DE JONG: “On the influence exercised by the systematic
connection between the parallax of the stars and their apparent distance from the galactic
plane upon the determination of the precessional constant and of the systematic proper
motions of the stars”. p. 683.

A. EINSTEIN and W. J. DE HAAS: “Experimental proof of the existence of Ampére’s molecular
currents.” (Communicated by Prof. H. A. LORENTZ), p. 696.

P. ZEEMAN: “On a possible influence of the FRESNEL-coefficient on solar phenomena’, p. 711.

L. BOLK: “On the Relation between the Dentition of Marsupials and that of Reptiles and Mono-

delphians”, p. 715.
W. E. RINGER: “Further researches on pure pepsin”. (Communicated by Prof. C. A. PEKELHARING).

p. 738.

A. W. K. DE JONG: “The action of sun-light on the cinnamic acids’, p. 751.

G. VAN ROMBURGH: “Nitro-derivatives of alkylbenzidines”. (Communicated by Prof. P. VAN ROM-
BURGH), p. 757.

J. DROSTE: “On the field of two spherical fixed centres in EINSTEIN’s theory of gravitation”.
(Communicated by Prof. H. A. LORENTZ), p. 760.

J. G. RUTGERS: “On a linear integral equation of VOLTERRA of the first kind, whose kernel contains
a function of BESSEL”. (Communicated by Prof. W. KAPTEYN). p. 769.

H. A. VERMEULEN: “On the conus medullaris of the domestic animals”. (Communicated by Prof.
C. WINKLER), p. 780.

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

584

A. SMITS: “On Critical Endpoints in Ternary Systems” Il. (Communicated by Prof. J. D. VAN DER
WAALS), p. 793.

A. SMITS and C. A. LOBRY DE BRUYN: “The Periodic Passivity of Iron”. (Communicated by Prof.
J. D. VAN DER WAALS), p. 807. With 2 plates).

F. ROELS: “On after-sounds”. (Communicated by Prof. A. ZWAARDEMAKER), p. 811.

F. A. H. SCHREINEMAKERS: “In-, mono- and divariant equilibria” III, p. 820.

G. HOLST: “On the measurement of very low temperatures. XXVI. The vapour-pressures of oxygen
and nitrogen according to the pressure-measurements by V. SIEMENS and the temperature-
determinations by KAMERLINGH ONNES c. s.”. (Communicated by Prof. H. KAMERLINGH ONNES',
p. 829.

J. E. VERSCHAFFELT: “The viscosity of liquefied gases”. I. The rotational oscillations of a sphere
in a viscous liquid” (Communicated by Prof. H. KAMERLINGH ONNES), p. 840.

J. E. VERSCHAFFELT: “Ibid.” II. On the similarity of the oscillations of spheres in viscous liquids”.
(Communicated by Prof. H. KAMERLINGH ONNES). p. 860.

W. H. KEESOM: “Two theorems concerning the second virial coefficient for rigid spherical mole-
cules which besides collisional forces only exert COULOMB-forces and for which the total
charge of the active agent is zero”. (Communicated by Prof. H. KAMERLINGH ONNES, p. 868.

G. HOLST and L. HAMBURGER: “Investigation of the equilibrium liquid-vapour of the system
argon-nitrogen”. (Communicated by Prof. H. KAMERLINGH ONNES). p. 872.

Petrography. — “Pneumatolytic hornfels from the hill countries of
Siak (Sumatray’. By Dr. H. A. Brouwer. (Communicated by
Prof. G. A. F. MOLENGRAAFF.)

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

The contact-phenomena described in a former communication, *)
on the southwestern side of the granitic area of Rokan are marked
by the occurrence, near the granites, of stratified granite-apophyses
and sehistose hornfels rich in felspar. From a preliminary exami-
nation of the homfels near the contact with granites from the hill
countries of Siak these rocks appear to show an entirely different

1) H. A. Brouwer, “On the granitic area of Rokan (Middle-Sumatra) and
on contact-phenomena in the surrounding schists’, these Proc. Vol. XVII (1915),
p 1190.

To the facts related there can be added that during an expedition along the
Rokan Kiri when its level was low, also to the right side of the Rokan similar
phenomena were observed on the south-western contact of the granites, as were
described from the Si Pakis. The first granites form an isolated little rock
emerging from the water near the right bank, whereas about 15 m. down the
river the contactmétamorphie schists with numerous granite-apophyses, which
occur in alternating layers with the schists, are uncovered in the right bank of the
river. Apophyses with a thickness varying from a few em. to at least 1 m. were
observed, the dip is again towards the granitic mass (e. g. Str. N. 20 W. dip
N.O.70° was measured). As a rule, the granite of the apophyses, just like near
Pakis, is very rich in biotite and shows parallel texture; here too, at a short
distance of the zone of apophyses, leucocratic granites with parallel texture are
found, beds of coarse and fine-granular rocks sometimes alternate. The thickness
of these beds varies from a few em. to several cm, they liave almost the same
strike and dip as the hornfels and granite apophyses (e. g. Str. N. 30 W. dip
N.O. 55°).

585

character; often the schistose structure has entirely disappeared,
whereas “felspathisation” as a characteristic contact-phenomenon is
missing. Tourmaline often occurs here in such large quantities at the
contact of the granites, that for the greater part the rocks consist
of this mineral. The tilted more or less schistose limestones with
graduations into sandstones, quartzites and hornfels of the Goenoeng
Soeligi, on the border of the hill countries of Siak and the subdi-
vision Boven Kampar of the government Sumatra’s Westkust, are
mainly covered to tbe North-Kast by sedimentary terrane. In the
beds of the Sei Lau and Set Rambei, which have their sources on
the Gs Soeligi, however, similar rocks are repeatedly uncovered.
Veins of quartz are numerous in these rocks. Near the top of the
Goenoeng Soeligi, N.W. and N.N.W. strikes with N.E. dips of
65° and 70° were measured, whereas to the North-East side of the
Gs Soeligi in the S* Lau, up the river from Kota Renah, N.W.
strikes and N.E. dips of 50° to 60° were found.

The occurrence of detached pieces and of weathering-products of
granite in the neighbourhood of Kota Renah (hill countries of Siak)
has already been mentioned by Everwijn!) (1864) whereas on a sketch-
map of Rorker*) granite is indicated in the last right branch of the
Sei Kalemboi, a right branch of the S* Lau. Further pebbles of
hornfels from the S* Lan have been collected and described by
VerBeeK ®). The “big, rounded diorite-stones” too, which EveRwIJN
found near and in the kampong Kota Renah, agree, judging from
his microscopical description, with some of our hornfels.

The occurrence of cassiterite, although not met with in the material
as yet examined, as a component of rocks in situ in the neighbour-
hood of Kota Renah is very probably in connection with the character
and distribution of alluvial tin-ore in the 5% Lau and its side-rivers.
Coarse and fine ore occur mixedly, the ore being often very sharp-
edged and sometimes intergrown with quartz, whereas it was not
found in the upper part of the 5S” Lau.

The examined granites «are rocks containing tourmaline and are
free from biotite, they were collected in the right bank of the last

1) R. EveRwijN. Verslag van een onderzoekingsreis in het rijk van Siak. Jaarb.
v. h. Mijrwezen v. N. O.-Indié 1874, and Natuurk. Tijdschr. v. Ned. Indië, vol.
XXIX, 1867.

2) Crarres M. Rouker. The alluvial tin-deposits of Siak, Sumatra. Trans.
Americ. Institute of Mining Engineers, vol. XX (1891), p. 50.

3) R. D. M. VerBeeK. Topographische en Geologische Beschrijving van een
Gedeelte van Sumatra's Westkust, Batavia 1883, p. 610, 612.

38*

586

right side-river of the S* Kalemboi near the Kampong Kota Renah.
Here we remark some tens of meters up the river, from the mouth,
first a larger intrusion of granite, and a few meters farther a
smaller intrusion which seems to be developed as a vein with N.W.
strike and a breadth of 1.8 m.

Coarse-granular parts alternate with fine-granular ones and por-
phyritie structures are found too. Polysynthetically twinned felspars
and untwinned ones, or felspars showing eross-hatching, can both
dominate so as to exclude the others. Further constituents are
quartz, muscovite, tourmaline and sometimes reddish-brown garnet,
iron ore missing almost entirely and only occurring as very fine
spots in the rocks. Further, some light-green chlorite was found in
a few samples when microscopically examined. The plagioclase
‘chiefly albite) shows only polysynthetical twins, according to the
albite-law. Whole crystals are sometimes characterised by eross-
hatching. However, part of the crystals often is untwinned, entirely
untwinned erystals also occurring. These untwinned parts sometimes
show parallel extinction, often their direction of extinction in sections
of the symmetrical zone was observed to cut in half the angle between
the directions of extinction of the polysynthetical twins; the untwinned
felspar often consists of irregular spots, which gradually pass into
one another and extinguish to different sides of the twinning plane,
their angle of extinction varying between the one of the distinctly
limited lamels and the one of the homogeneously extinguishing parts
mentioned above. These crystals apparently contain different gradua-
tions from microcline into orthoclase (extinction in sections perpen-
dicular to the positive bisectrix of the obtuse angle = 5°). Similar
graduations were described by the author in the microcline miero-
perthites of Transvaal foyaites'); they support the truth of the
conception of orthoclase as a microcline in which microscopically
no twinning can be observed.

-In the parts with porphyritic structure small crystals of musco-
vite, sometimes of quartz and felspar too, are to a small degree
enclosed by the larger felspar-crystals. The form of the larger
erystals of felspar, muscovite and quartz with respect to the ground-
mass, points to partly simultaneous crystallisation; in the ground-
mass the felspar often occurs in well developed elongated sections.

Varieties rich in garnet and tourmaline, near the contact with
the hornfels, show a beautiful poikilitical structure. Large erystals
of felspar include many small crystals of muscovite, of beautifully

1) H. A. Brouwer, Oorsprong en Samenstelling der Transvaalsche nephelien-
syenieten. ’s Gravenhage, 1910.

587

idomorphie tourmaline and garnet and also of quartz and felspar.
No ground-mass is observed here, the larger felspars closely adjoining
each other and the small crystals of the other minerals and of felspar
are disseminated in those larger crystals. The garnets are idiomorphie
and microscopically colourless (in thicker sections they show a
light rose colour). Exceptionally they are partly surrounded by a
tourmaline-crystal, tourmaline-crystals enclosed by garnet also occurring
occasionally. As a rule, tourmaline in the granites shows a beautiful
zonar structure, with often rather distinct light-blue central part
and a brown margin. Sometimes, between these zones an equally
distinct one of intermediate colour is found, or the colours graduate
into each other. Sometimes in zonar crystals a bluish central part
is seen with a pale-blue margin and an intermediate zone of light-
brown colour, differently coloured and repeatedly alternating zones
also being observed in some crystals. It is remarkable that in the
contiguous hornfels only brown and almost always homogeneously
coloured tourmalines occur. In the pieces of bornfels of the S° Lau
the zonar tourmalines were also found.

The contact-rocks have been examined near the contact with the
granites. There they are dark to nearly black-coloured, and often
even macroscopically a high percentage of mica can be seen, whereas
between the granites and these rocks sometimes a rather narrow
transition zone is found which is rich in tourmaline. At the very
contact we often see a zone which for the greater part consists of
tourmaline. Farther away from the granites, biotite occurs more
frequently, the percentage of tourmaline decreasing at the same time.
The biotitehornfels at the contact of the larger intrusion contain, as
a rule, much tourmaline, whereas along the contact of a narrow
tourmaline-bearing vein in the upper-Lau no tourmaline but only
traces of biotite could be observed as a contactphenomenon in
the schists, which for the rest were unaltered. The tourmaline of
the hornfels is almost always of homogeneous structure and of a
brown colour, exceptionally a marginal zone of darker brown colour
also occurs, but zones of blue tourmaline like those found in the
adjoining granites do not occur here. Garnet is often found in con-
siderable quantity in the contact-rocks. especially near the granites.

Sometimes between the quartztourmaline-roeks and the biotite-
hornfels a quartz-muscovite-zone was found of some mm.’s breadth
containing a small quantity of tourmaline, the muscovite of the zone
graduating farther from the contact into a mica of a pale brown
colour.

588

So we can distinguish near the contact of the granites successively:

1. A quartz-tourmaline zone of varying thickness (sometimes not
thicker than a few mm., sometimes entirely missing).

2. A quartz-muscovite zone with tourmaline, of some cm.’s breadth,
which is most times missing. :

3. A quartz-biotite zone. which also occurs at the very contact
of the granites.

In the quartz-tourmaline zone partly perhaps a marginal facies
of the granites — sometimes plenty of garnet and often in small
quantity some muscovite and apatite occur together with the main
constituents. The structure is sometimes beautifully poikilitic, larger
tourmaline crystals, sometimes reduced to skeletons, enclosing numerous
erains of quartz and sometimes also crystals of garnet and smaller
crystals of tourmaline. This zone often shows a mosaic structure,
which sometimes approaches to the hypidiomorphic granular structure,
these various structures graduate into each other, and in the granular
mixtures we sometimes see some larger crystals of tourmaline
with poikilitie structure. Again, the garnet often encloses small quartz-
crystals, even when it is itself enclosed by tourmaline. Often this
mineral is troubled by numerous inclusions, partly very fine ore-spots.
Occasionally, some irregularly limited and turbid felspar was
observed in this zone, which poikilitically enclosed quartz and also
muscovite. Between the granites and the quartz-tourmaline zone a
strong contrast can be seen microscopically, due to the differences
of structure, size of grain and constituent minerals. Between the
quartz-tourmaline zone and the granites sometimes a narrow zone
is observed, consisting of an aggregate of quartz-crystals only or
of quartz-crystals intermixed with very little tourmaline and musco-
vite or of a quartz-muscovite-mixture with much muscovite.

The quartz-muscovite-zone, which on several places was found
showing a thickness of some mm. only, between a quartz-tourmaline
zone of the same thickness containing much garnet and some mus-
covite and a quartz-biotite-zone containing less garnet, insensibly
graduates into the adjoining zones. In the quartz-muscovite zone
tourmaline-crystals still occur, which farther from the contact disappear
almost entirely. By the growing intensity of a brown colour, the
muscovite graduates farther from the contact into a pale brown mica.
The percentage of garnet is much smaller than in the quartz-tuur-
maline-zone and it remains almost constant in the quartz-biotite-zone.

The quartz-biotite-zone contains mostly tourmaline, sometimes
muscovite and garnet. As arule the quartz-tourmaline zone is between
it and the contact, occasionally it also oecurs at the very contact of

589

the granites. Thus e.g. from a quartz-tourmaline-zone of 4 mm.’s
breadth, the amount of biotite through a very narrow transitional
zone may increase to a large percentage in a quartz-biotite-zone
containing much tourmaline.

At 1'/, em. from the contact this percentage of tourmaline is still
considerable. The biotite is strongly pleochroic, from reddish-brown to
almost colourless; the tourmaline is found in small erystals in the
quartz-biotite-mixture, but for the greater part in larger crystals,
which enclose numerous grains of quartz and also small crystals of
garnet. This tourmaline with sieve-structure is sometimes idiomorphic
but most times shows irregular forms; in the former case we often
see flakes of biotite along the circumference of the crystal, from
which it is evident that they have more recently crystallised. The
garnet too is always idiomorphic with regard to biotite. In the
quartz-biotite-mixture lath-shaped sections of biotite are sometimes
rather numerous.

At another place near the contact we see that a small percentage of
biotite in a mixture of larger tourmaline-crystals with sieve-structure,
quartz and small garnets, has but slightly increased over a distance
of 2 em. Therefore the transitional zone to rocks containing more
biotite is much broader there. The biotite is again reddish-brown
and shows a strong pleochroism.

The presence of pale-brown mica in a quartz-biotite-zone, separated
from the tourmaline by rocks bearing a quartz-muscovite-zone, has
already been mentioned above.

If the quartz-tourmaline-zone does not exist, quartz-biotite hornfels
are found at the very contact of the granites. Tourmaline-quartz-
mixtures rich in garnet, and quartz-biotite-mixtures with tourmaline
and containing littie garnet, sometimes occur in the same section,
both at the very contact. Sometimes, muscovite occurs in a small
quantity together with biotite, and the contaci-rock is sometimes
separated from the granite by a narrow quartz-zone with or without
muscovite. The tourmaline occurring in varying quantity forms small
as well as larger crystals with sieve-structure. Small spots of ore
occur in small quantity; in parts which have more or less ellip-
tical forms and are free from tourmaline, the percentage of ore has
slightly increased.

In a specimen of the western contact of the dyke-shaped intrusion,
the quartz-tourmaline zone does not occur, and a fine-granular mixture
of quartz, biotite and muscovite with rather many small idiomorphie
tourmaline-erystals is seen. It is separated from the granites by a
narrow zone of quartz. Some spots of ore occur in these rocks, very

590

few larger quartz-crystals without inclusions being found in the fine-
granular mixture. At the eastern contact of this intrusion, or very
near to it, even muscovite bearing biotiteschists occurs, in which the
schistose structure has been preserved.

The detached pieces of hornfels already described by VerBekK,
which are found very frequently in the neighbourbood of Kota Renah
(similar rocks being met with by me even in the upper stream of the
Seit Lau as rocks in situ) prove the great extension of rocks similar
to those of the quartz-biotite zone which hitherto have been examined
by us only near the contact. They often contain green amphibole.
The other constituents are quartz, biotite, tourmaline, titanite, ilmenite,
‘aleite and pyrite.

Again, numerous pebbles of rocks similar to the quartz-tourmaline-
zone, were found in the rivers Lau and Pinggir, proving that
these rocks occur also elsewhere and of more considerable thickness.
Of the latter rocks, some with narrow veins of quartz were micro-
scopically examined,

The veins of quartz often — and chiefly in the marginal zone
— contain tourmaline, and are sometimes rich in muscovite. Oeca-
sionally in the marginal zone larger tourmaline-crystals (of sometimes
several mm.’s length) are deposed more or less perpendicular to the
plane of contact. As a rule, these tourmaline-erystals have a zonar
structure, just like the tourmaline of the granites, and contrary to
the tourmaline of the adjoining rocks, which most times has a
brown colour. Bluey and brown varieties can both occur as a
marginal zone, a repeated alternation of differently coloured zones
also being found. Especially at the contact of a vein containing much
muscovite, there could be clearly observed how a long erystal
of tourmaline, which was interrupted in the marginal zone, continued
at some distance in the fine-granular quartz-tourmaline-mixture of
the adjoining rock, which points to a partly simultaneous crystalli-
sation of the vein and the adjoining rock.

Like those of the granitic area of Rokan the contact-phenomena
described above show a pneumatolytie character. The phenomena
in the first mentioned area point to such relations of pressure and
temperature and to such a percentage of mineralisers as make granite
apophyses possible to be formed in alternating layers with the
surrounding rocks, and these rocks to be imbibed with mineralisers.
The missing of felspathisation in the contact rocks of the hill
countries of Siak can be explained by crystallisation at lower tem-
perature and pressure, and a lower percentage of mineralisers (espe-

591

cially of the alkalies), which occurred in sufficient quantity to make the
magma crystallise as a granite, but not in sufficient quantity to
cause felspathisation in the adjoining rocks. To match this supposi-
tion, the large extension of the granitic area of Rokan and the
occasional occurrence of small outcrops of granite in the hill countries of
Siak point to the fact that in the first mentioned area the granite
and the contact-rocks have been uncovered to a lower level by erosion.

Physics. — “A Confirmation of the Principle of Relativity”. By
Dr. H. K. pr Haas. (Communicated by Prof. H. A. Lorentz).

(Communicated in the meeting of June 26, i915). 8

The following considerations founded on a negative result of an
experimental research’) concerning the question: “does gravitation
require time for its extension in space?” corroborate one of the
principal theses of the principle of relativity with a greater degree
of accuracy, than is possible for light. Any effect resulting at any
moment from the relative motion of matter and ether, diame-
trically opposed to the motion of 30 km. + or — the component
of the motion toward the apex in the direction of these 30 km.
per second twelve hours later, can be excluded as regards gravi-

10,000
At the extremities of a torsion-balance two balls of equal weight
were hung, one of platinum ( sp. gr.: 21:5), the other of paraffin
(sp. gr.: 0°87).
The constants of the apparatus were:

1 \h
tation, with an accuracy ot ( ) ;

Weight: Grams: Moment of inertia (em?. gr.).
Platinum ball 11-6628 2189
Paraffin ball 11-6612 2199
Beam 21670 145
2 hooks (at ends of beam) 2 >{0:0364 14
Suspension-hook + mirror id
Q = 4550

The distance from the hooks at the extremities to the (middle)

suspension hook : 13:70 cm. + 0:01

The half period : Waa e40! Ee

1) For details see: Reports of the lectures delivered by members of the Bataafsch
Genootschap at Rotterdam. Vol. 1, 1915.

592

The distance between the mirror, which was attached to the
beam, and by which the ray of light was reflected, and the film,
on which the movements of the ray of light were photographed,

was : 410 em. + 0:5.
[t can be calculated from the formula ®= z Oe that
K(57-3°)

1 mm. permanent deviation of the distinctly observable image on
the film corresponded to a horizontal force normal to the beam ot
3-45 > 10-6 dynes on one of the balls or, of 2:96 x 107 dynes
per gram of mass of one ball.

The film was moved vertically about 3:4 mm. per hour, by means
of a registering timepiece, for 86 hours at a stretch, behind a narrow
horizontal slit in a light-proof case.

Every hour an illuminating apparatus, set in motion electrically
by means of a eloek-work, flashed a ray of light on the slit in such
a way that a time-line, divided into mm. was registered.

After many difficulties, caused by a sensitiveness to various dis-
turbances, which proved relatively great, and which prevented the
balance from acquiring a position of steady equilibrium, we succeeded
in registering nearly straight lines on several films, the deviation
from straight lines being less than 1 mm.

If we consider that an effect of the “ether wind” would be
perceptible to the left in the morning, to the right in the evening,
or the reverse, a force exerted on one of the balls, or more exact:
a difference of force, exerted on the two balls of 1:48 > 10—‘ dynes
per gram, may be considered excluded. It was shown that not even
so small a force was released, though the ether rushed through a
field of trillions of dynes of intermolecular attraction: for the field
of gravitation in one gram of platinum possesses trillions of dynes !

The order of magnitude (of the number of dynes) of total inter-
molecular attraction cannot be directly calculated for paraffin and
platinum, but it can be indirectly approximated from the total
amount of intermolecular attraction in 1 em’. of water; the physical
constants of paraffin and platinum required for a direct calculation,
are unknown. We base our indirect calculation on the supposition,
that the attraction between the molecules of liquids and of solids
is equal, if the specifie density is equal. The comparatively small
amount of heat, necessary to melt ice, and the slight linear con-
traction of melting ice, permit of this supposition. An error in
this calculation for water and ice of double or half the amount is
improbable.

For water the foree with which the outer layer of molecules is

593

drawn inward is 10700 atmospheres or 1:085 <10! dynes per em.’
(VAN DER WAALS).

The more central molecules attract each other no less; they also
attract each other with a force of 1:085 > 10!° dynes, because the
sphere of action of this attraction does not extend beyond the diameter
of one molecule. The radius of this sphere (7) is stated as 1-5 > 10~* em.
(Minkowski), the diameter of a molecule being 2:9 > 105.

There are about 3:45 >< 107 molecules to a cm., hence there is
the same number of layers. In the three directions of the sides
of 1 cm® of water, we find 3 x 1:085 « 10'°x 3:45 X 107 = 1:12
10!8 dynes of total intermolecular force. That the sphere of action
is smaller than the diameter of one molecule, on which the correctness
of the amount 1:12 1018 is based, may be verified by considering
the amount of heat necessary to evaporate 1 gram of water or even
of ice (0°62 calorie) as a measure of the work required to split up
1 gram into loose molecules. This work amounts to 260 K.gr.m.,
for 1 gram of ice, or 2:6 >< 10! erg. From the equation 2°6 >< 101° erg
=3 1:085 x 1010 dynes X 3:45 & 107 x 7,we find r = EAL SAO
henee smaller than the diameter of one molecule.

How much attraction do we find in platinum or in paraffin?

Van per Waats states that the intermolecular pressure is proportional
to the sp. gr“. This is also true of the sum of the attractions. In
balls of the same size it is therefore also proportional to the sp. gr’,
but in balls of the same weight, to the sp. gr, provided there
are equal numbers of layers of molecules per em.', which however
is not the case. The sp. gr. of platinum being 21:5 and the molecular
weight 194, it can be calculated that there are 1:26 X the number
of molecules in water per em*. In like manner it can be calculated
for paraffin, sp. gr. 0:87 and molecular weight (C,,H,,) 286, that it
contains per cm.’ 0.38 X the number of molecules in water per cm.".

In 1 gram of water we found the total intermolecular attraction
to be 1.12 X 10!8 dynes, we derive from this for
1 gram of platinum 1:12 x 10% x 215 X 1:26=30°5 > 10!8 dynes
1 gram of paraffin 1:12 < 1018 x 0:87 x 0:38 —= 0:37 x 10! dynes
in platinum per gram an excess of 30 10'8dynes.

If the motion of the ether through the two balls had caused any
aberration, we might reasonably assume that of the 0:37 ><10! dynes
per gram of paraffin an equal fraction had been diverted as of
0:37 X 1018 dynes in platinum; aberration-angles and aberration-
components, which may accompany them, are exclusively based on
ratios of velocity, and not on ratios of distance. The equal amounts

594

of aberration, which might be released from 0-37 >< 1018 dynes (pla-
tinum and paraffin), can never be demonstrated by means of a torsion-
balance, as this apparatus is fundamentally unsuitable for this
purpose.

But the torsion-balance would not fail to indicate any possible
variation of direction, i.e. aberration of the excess of 3 > 1019 dynes
per gram of platinum.

Of these 3 >< 10'9 dynes of attraction only $ are to be taken
into consideration for aberration, viz. only the sum of all the forces
in the 2 directions normal to the motion, but no forces parallel to
the direction of translation.

Let us now take into account that every single line of ferce,
acting at its extremities on two molecules, consists of two forces,
each equal to the tension along that line of force. It is true, that,
when the molecules are at rest, those two forces are exactly equal
and exactly opposed; their swm as such is nihil. But if there were
any effect of aberration, the aberration-components, though resulting
from opposed forces, would each be parallel to the direction of
motion; hence they would be mutually parallel and both point in
the same direction. Their su would manifest itself in the experiment.

For example: let us imagine two equal molecules, A and B,
attracting each other, when at rest, with a force A along the joining
line AB. If these molecules travel through the ether in a direction
normal to the joining line, and if gravitation requires time for its
extension, the agent acting on A will no longer reach point A along
BA, but along a diverging direction, forming an angle with AB
(conceived in the plane passing through AB and through the direction
of translation). The action which is not directed along the joining
line AB would produce a foree-component L AB in A, but in B
an equal component of force will originate, and the components of
the two will have the same direction in spite of their arising from
forces Of opposite directions. 4

We presume, in this experiment, that } > 28 10!® dynes of
attraction per gram are present in the platinum ball, of which the
presence of 1:48 10-7 dynes of aberration-component is excluded
in our straight registered line; not even 1-48 x 10-7 to 4 X 1019
dynes, i. e. not dE ‘< the total complex of forces manifested
itself outside the system.

In virtue of our mode of derivation, we shall assign no value to

the factor 2°7, and we shall round off our figures to powers of ten.
It follows from the straight registered line that the “ether wind”

595

did mot cause the direction of the intermolecular forces to deviate
from the direction required by Newton: an angle, namely, deviating

1
from the joining line, of the value Te can be exeluded; a deviation

between the direction indicated in tne law of Newton, namely the
joining line, and the direction of attraction through the relative ether
. . . . 1
motion of 2 X 30 km. per sec. remains below this amount of De
the deviation, provided: there be one, amounts to less than
imicron at a distance of 100 light-eenturies.

Chemistry. — “/nvestigations on the Temperature-Coefficients of
the Free Molecular Surface-Energy of Liquids from —80°
to 1650° C.” XIII. The Surface-Energy of position-isomeric
Benzene- Derivatives. By Prof. Dr. F. M. Jager and Dr. Jur. Kann.

(Communicated in the meeting of September 25, 1915)

§ 1. For the purpose of investigating the influence of the chemical
constitution of the liquids on the magnitude and on the temperature-
coefficients of the free surface-energy, we also made a series of
measurements with a number of benzene-derivatives, which are to
each other in relation of position-isomerides. The problem considered
seemed to us of yet greater importance, because i. a. in the already
previously mentioned paper of Fruster*), some position isomerides
were studied with this same purpose, and this author as a result
of his experiments concluded, that the surface-tensions of such
isomeric substances did not differ from each other in any appreciable
degree. His conclusion, founded only on a relatively small number of
data, seemed to us not too probable, judging from some experience
already gathered by us in the course of these investigations: for the
u-t-curves, determined by the first of us in the cases of dinethy!-
resorcinol and dimethyl-hydroquinone*), and also of mesitylene and
pseudocumene*), appeared to be clearly different for the two pairs of
isomerides.

Therefore it seemed of importance to extend such a comparison
of the magnitude of the surface-tension to a greater number of such
position-isomeric derivatives.

1) Feustet, Drude’s Annalen 16, 61. (1905).
2) F. M Jancer, these Proceedings, 23, 357, (1914).
3) F. M. Jarcer, these Proceedings, 23, 408, 409. (1914).

596

In the following paper we therefore publish the measurements
made with 36 position-isomeric substances: ortho-, meta-, and
para-Dinitrobenzene ; meta-, and para-Fluoronitrobenzene; ortho-, meta-,
and = para-Chloronitrobenzene; meta-"), and para-Dichlorobenzene ;
1-2-4, 1-3-4- and 1-4 2-Dichloronitiobenzenes ; ortho-, meta-, and para-
Bromonitrobenzene; ortho-, and meta-Jodonitrobenzene; ortho-*), and
para-Nitrotoluene ; ortho-, meta-, and para-Nitrophenol; ortho-*), and
para- Nitroanisol; ortho-, and para-Cresol; ortho-, and para-Chloro-
aniline; meta-, and para-Nitroaniline; 3-Nitro-, and 5-Nitro-ortho-
Toluidine, and 3- Nitro-para- Toluidine ; and finally the cyclic derivatives:
sylvestrene and terebene.

The purification of these compounds, as well as the determination
of the density, occurred in the same way as formerly deseribed. In
the case of some compounds evaporating rapidly already at the
meltingpoint, these determinations could not be made with satisfactory

exactitude.
§ 2.
1.
ortho-Dinitrobenzene: 1-2-C,H,(NOz)o.
ae Se
v Maximum Pressure H | |
= 5 Surin | Molecular |
Bo ke AD ed | tension yin | ae 5 a
; -| ravity d,.| energy win
ES : Erg. pro cm?2. | 49 |
2 | cu ot in Dynes | | Erg pro cm?
— = — — = r ——s
126 1.279 | 1705.0 | 38.4 | 1.305 979.2
| 140 1.230 1639.8 | 36.9 | 1.201 947.8
| A5Say |) a dees 1580.0 35.6 | 11276 923.4
176 1125 1499.8 33.6 | 1.259 877.6
194.4 1.082 | 1442.5 3253 1.245 | 849.9
209.1 1.034 1378.4 30.9 | 15235 817.5
| Molecular weight: 168.05. Radius of the Capillary tube: 0.04595 cm.
| Depth: 0.1 mm.
| Under a pressure of 30 mm. the substance boils at 194° C.; the melting-
| point was 117°C.
At 120° C. the density was: 1.3119; at 140° C.: 1.2915; at 160°C: 1,2737.

At f° C. in general : dyo = 1.3349 —0.001215 (t—100°) + 0.00000325 (¢— 100°).

The temperature-coefficient of » oscillates somewhat round a mean value
of: 1.95 Erg pro degree. |

EN F. M. Tacoun, these Proceedings, 23, 411, (1914).
2) F. M. Jaeger and M. J. Smir, these Proceedings, 23, 387, (1914)
5) F. M. Jarcer and Jur. Kann, ibidem, 23. 400, (1914).

597

meta-Dinitrobenzene: (1,3) o/s (NO).

@ Maximum Pressure H
a5 cj Eee ES Surface- , Molecular
ae |. | | tepsion i ee Vienna

in mm. mer- | ‚| gravity do | energy win |
ene ol ED | Erg pro cm’. 400
2 coe. | in Dynes | | Erg pro cm2. |
94.8 1.410 | 1880.3 42.3 1.361 | 1048.9
114.9 1.342 1788.9 40.2 | 1.340 | 1007.2
136 1.264 1688.5 38.1 | 1.316 966.1
155 1.209 1611.7 36.1 | 1.295 | 925.3
175.5 1.149 1532.1 34.3 1.271 | 890 3
191.2 1.103 | 1471.2 | 32.9 1.248 864.5
204.5 1.069 | 1425.0 | 31.8 1.235 841.4
Molecular weight: 168.05. Radius of the Capillary tube: 0.04595 cm.

The substance boils at 291°C. under a pressure of 756 mm.; it melts at 91° C.
At 120° C. the density was: 1.3349; at 140’ C.: 1.3149; at 160° C.: 1.2957,

Depth: 0.1 mm.

ALBA: do = 1.3557—0.00106 (£—100-)— 0.000001 (t—100°)?.

The temperature-coefficient of # is originally: 2.05 Erg; afterwards it

decreases slowly to about: 1.71 Erg pro degree.

para-Dinitrobenzene: 1-4 C,H, (NO).

IIL.

Maximum Pressure

Surface-

pte ake Lin mm. mer | 7 sey
cury of | in Dynes Erg. pro cm?.
ORE:
ee = EE gee | — nn | =
0 |
176.2 1.139 | 1518.5 34.4
196.5 1.080 1439.8 32.6
210 | 1.043 | 1391.0 31.5
226 1.007 1342.5 30.4

Molecular weight: 168.05. Radius of the Capillary tube:

0.04529 cm.
Depth: 0.1 mm.

The compound melts at 172° C.; it is very volatile and
sublimes readily.

IV.

meta-Fluoronitrobenzene : Cells (NOs) (1) Fz)

vw | Maximum Pressure H
3 5 reste Oo) 1 Molecular
5 df 5 mm ae | tension zin | ee sp
a. 1 a - | 1 energy „ In
5 7 cury of in Dynes | Bre Proycmé | ze Erg pro cm?,
= ONG: | |
EA ale DEN OE EDE SS
«0 1.274 | 1698.7 40.1 1.348 890.4
29.9 1.193 1590.9 Sil 1.314 837.9
41.8 | 1.137 1515.6 35.3 1.293 805.9
64.5 | 1.083 1444.4 | 33.6 1.274 714.7
80.8 1.031 1374.5 | 32.1 | 1.256 147.2
104.5 0.961 1281.1 29.7 1.232 700.3
122 | 0.914 | 1218.3 | 28.2 1.215 671.1
here 0.822 1095.9 25.4 1.187 613.9
178 | 0.741 988 .0 22.8 1.160 559.6
196 0.697 929.4 21.4 1.145 529.8

| | | /
Molecular weight: 141.04. Radius of the Capillary tube: 0.04777 cm.; with

the measurements indicated by *, it was:
0.04839 cm.
Depth: 0.1 mm. ;

The liquid boils constantly at 197.°5 C. and a pressure of 760 mm. It
solidifies on cooling very soon, and melts then at —1° C. At the boilingpoint
„ is about: 21.2 Erg pro cm?. The specific weight at 25° C. was: 1.3189; at
50° C.: 1.2905; at 75° C.: 1.2632; at 0°: dy. = 1.3484 0.001202 f + 0.00000088 2.

The temperature-coefficient of » oscillates round a mean value of 1.82 Erg |
pro degree.

V.
para-Fluoronitrobenzene: C,H, MO) 1) Fay

v Maximum Pressure 1

Sa he EN Stc: Molecular
5 a ; tension yin BE . Surface-
a in mm. mer- gravity | energy «in
ES cury of in Dynes — Erg pro cm?. el Erg pro cm2.
len WIE |
me 5 = Wes = —_ a

= - =
24.5 1.284 | Aarlen 38.4 1.325 862.5
31 1.269 | 1689.0 37.6 1.319 847.1
46.8 1.201 | 1601.1 35.9 1.301 816.2
60.4 1.149 | 1531.8 34.3 1.288 785.1
14.2 1.096 1461.2 32.8 1.270 157.8
89.3 1.050 1399.8 31.3 1.254 729.3
110 0.968 1292.8 29.0 1.229 684.4
124 0.931 1240.5 Paths 1.213 659.9
140.3 0.868 1157.8 25.9 1.193 623.9
156 0.805 1076.0 24.3 1.172 592.3
174.5 0.747 996.6 225 1.152 549.8
194.1 0.688 913.4 20.3 1.125 508.5
Molecular weight: 141.04. Radius of the Capillary tube: 0.04595 cm.
Depth: 0.1 mm.

The substance boils at 203.°5 C. under a pressure of 755 mm.; its melting-
point is 269.5 C. The specific gravity at 30° C. was: 1.3204; at 50° C.:
1.2986; at 75° C.: 1.2691. At f° in general: dyo= 1.3509 —0.00 10275 t—0.00000078 £.

At the boilingpoint x has the value: 19.3 Erg. The temperature-coefficient
of » is about 2.09 Erg pro degree, as a mean value.

Vi.

ortho-Chloronitrobenzene: C‚/4 WO) Ela);

v Maximum Pressure H

2G | Surface-

go AAN | tension / in

5 5 cury of in Dynes Erg pro cm?.
i OG:

= a ——— = oe

Slee 1.387 1849.8 41.6

46 1.330 1717.5 39.9
61.2 1.279 1706.2 38.3
73.5 022i 1638.7 36.9
~ 89 1.176 1567.8 Sdn
110 1.102 1470.2 32.9
124 1.056 1408.4 Seo
140 0.999 1330.9 29.6
155.5 0.960 1277.5 28.3
175 0.877 1171.0 26.1
194.5 0.824 1098.5 24.3
209.1 0.797 1062.0 2355

Molecular weight: 157.50.

meta-Chloronitrobenzene: C,H, WON) Ch3y-

Specific

Molecular
Surface-

gravity Ago | energy # in

mj
iw)
=I
(ee)

Erg pro cm2,

866.
818.
789.
749.

je uae.
674.
635.

|) 96218

DO al Ge ON == OD

Radius of the Capillary tube: 0.04595 cm.
Depth: 0.1 mm.
Under a pressure of 755 mm. the substance boils at 241°; it melts at 33° C
The density at 75° C. was: 1.3083; at 100° C.: 1.2812; at 125° C. : 1.2536.
At # C. in general: Ajo = 1.3866—0.001014 ¢—0.0000004 #2.

The temperature-coefficient of » is up to 195° C. fairly constant and equal

to 2.16 Erg pro degree as a mean value.

Wiis JS

v Maximum Pressure H
ae es Bie
Do :
a jin mm. mer-|
Es cury of in Dynes
io OF Cy

Le)
46.3 1.312 1749.7
60.5 1.258 1675.9
14.8 1.206 1608.4
90.3 1.148 1535.2
110 1.082 1442.4
eA 15037 1382.5
140.3 0.979 1304.4
155.2 0.928 1240.8
22 0.858 1147.0
194,2 0.806 1075.0
209.2 0.770 1026.6

Molecular weight: 157.50.

Surface-
tension / in

oo
Sc
ll OO ll DP OO I= Ow

Erg. pro cm?.

Specific

gravity dy

.339
ZI
„308
„201
„272
„256
2
„219
„194
slr
„154

Molecular
Surface-

o | energy » in

Erg. pro cm?.

943.4
908.
880.
846.
799.
711
139.
108.
666.
624.
601.

URODOOONWH

Radius of the Capillary tube: 0.04595 cm.
Depth: 0.1 mm.

The compound boils at 236° C. under a pressure of 756 mm. It melts at 449.5 C.
The density at 75° C. was: 1.3082; at 100° C.: 1.2816; at 125° C.: 1.2536;
Ete fe (Css Ayo = 1 3788 - 0.00086 # -0.000001 12 #?.

The temperature-coefficient of » between 46° and 194° C. is fairly constant;
its mean value is: 2.19 Erg pro degree.

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

600

VIII.

para-Chloronitrobenzene: C,H, WON) Clay:

7 Maximum Pressure |
= iS Se Molecular
5 ° inmm, m OE aon meee
a. in . mer- r p
EE | cury o in Dynes | Erg. preci? 4° | Erg. pro cm?
5 ;
= ORG: | |
= SSS = = = a oe = =
90 1.147 | 1529.1 34.3 1.293 842.8
110 1.080 | 1439.8 32.3 1.272 802.4
125 1.029 | 1374.0 30.9 1.256 774.1
139.9 0.992 | 1322.0 29.6 | 1.242 147.2
155 0.937 | 1252.6 28.2 11.225 718.3
175.2 0.882 1177.6 26.4 1.204 680.3
194.4 0.835 | IS 2 24.8 1.184 | 646.2
209.2 0.795 1059.9 23.5 1.169 617.6
EN Shs ce ene | MN SMC
Molecular weight: 157.50. Radius of the Capillary tube: 0.04595 cm.
Depth: 0.1 mm.
Under a pressure of 756 mm. the substance boils at 234° C.; it melts at 83°.5 C.
The density at 85° C. was: 1.2998; at 110° C.: 1.2722; at 135° C.: 1.2457, In
general at £° C.: dy. = 1.3285—0.00117 (60 ) + 0.00000088 (f— 60°).

The temperature-coefficient of » is fairly constant; its mean value is 1.88
Erg pro degree Celsius, |

IX.

para-Dichlorobenzene: 1-4-C,H, Clo.

| Maximum Pressure H

uo
5 | | Molecular-
EE: - | |
a 0 ena ‘ -| t pages | Specific \ Surface-
8 in mm. mer- | Ee | gravity do | energy «in
ze 8 | | /
Bes | scary of in Dynes | KS PRO En Erg pro cm? |
= OG. |
J } . ee | |
60%3a0| 0972 1294.7 29.4 | 15242 108.6
82.6 | 0.903 1204.4 21.4 | 1.218 669.0
95.1 0.872 1161.3 26.3 1.205 646.8
114 0.816 1087.9 24.6 1.185 611.7
130.4 0.768 1024.0 PA} 1.168 580.0 .
144.5 0.727 970.0 21.9 ee 2e
15.

166.5 se 40,671). )] 489466 97). a0. I gas aise |

Molecular weight: 146.95. Radius of the Capillary tube: 0.04660 cm.
| Depth: 0.1 mm.
The para-Dichlorobenzene boils under a pressure of 755 mm. at 173.95 C.;
it melts at 52° C.
At 75° C. the specific gravity was: 1.2261; at 100° C.: 1.1983; at 125°
(Cag IE Ne VEN GEE dyo = 1.2531—0.001064 (t—50°)—0.00000064 (¢ 50°)?.

The temperature-coefficient of » is constant: 1.83 Erg.

601

1-2-Dichloro-4-Nitrobenzene: C‚H3 Cl, (1,2) VO), 4)

ZT |

= |

te}

46 1.340 1787.5 40.2 1.490 1025.4 |
61 1.294 1724.4 | 38.7 1.471 995 .6 |
16.7 1.246 1660.5 31.2 1.454 964.5
95 1.217 1622.5 35.6 1.430 933.3
113.5 1.150 1533.2 34.0 1.407 901.1
136 1.074 1431.8 32.0 1.379 859.4
155.1 1.016 | 1355.0 30.3 1.356 823.0
177 0.948 | 1263.9 28.1 1.329 Te)
190.5 0.917 1217.9 26.8 alls 743.7
204 0.867 | 1155.9 | 25.6 | 1.295 717.0
Molecular weight: 191.95 Radius of the Capillary tube: 0.04595 cm.

Depth: 0.1 mm.

The meltingpoint of the compound is 43° C. The specific gravity at 75° C.
was : 1.4558, at 100° C.: 1.4266; at 125° C.: 1.3979. Att C.: dyo = 1.5464—

--0.001238 ¢ + 0.0000004 ¢.

The temperature-coefficient of » is rather constant; its mean value is: |

1.96 Erg pro degree.

1-3-Dichloro-4-Nitrobenzene: C,H, Ch 3) WON 4): |
v Maximum Pressure A |
ims Sree Molecular
cb ere | tension / in | satay Surface-
ai mer | Ere pro cm2, | Sravity do | energy « in
é Ee coy in Dynes ol: | Erg pro cm®*, |
35° INS 15 1833.1 41.3 | 1.487 1054.9
46.3 Plone 1787.4 40.1 | 1.475 1029.8
60.5 1.294 | 1724.4 38.8 1.460 1003.2
76.5 1.249 | 1665.7 Sao 1.443 972.0
95 1.176 1567.7 SOZ 1.421 926.7
114.9 1.104 1475.1 3323 1.399 885.8
136 1.042 1390.5 Siz2 1.373 840.4
155.1 0.982 1308.6 29.2 1.350 795.4
176 0.929 1246.0 2752 1.325 750.3
191 0.870 1158.7 20151 1.305 716.2
204 0.823 1096.8 24.4 1.289 685.5
Molecular weight: 191.95. Radius of the Capillary tube: 0.04595 cm.

Depth: 0.1 mm.

Under a pressure of 15 mm. the boilingpoint is 154° C. The meltingpoint
34° C. The specific gravity was hydrostatically determined: at 75°C. it was:
1.4149; at 125° C.: 1.3856. At ¢ C. it was in general;

1.4434; at 100° C.:
Ago = 1.5241—0.001028 £—0.00000064 #2.

The temperature-coefficient of » has a mean value of 2.16 Erg pro degree.

602

XII.

1-4-Dichloro-2-Nitrobenzene: C,H, Clay 4) (NO))():

| | [
KD Maximum Pressure H | | |
Six | Sirk Molecular
SO | uriace- Ss ifi S
Se tension yin | pecific | urface-
a. in mm. mer- : | gravity d,, | energy » in
ES cury of in Dynes Erg. pro cm? | 4 E 2
oss ae | rg. pro cm?,
60.5 1.281 | 1705.6 38.3 | 1.455 | 992.6
76 1.234 1645.2 37.1 | 1.438 969.0
95 | IN 2 | 1564.1 | 35.3 1.416 931.5
115 | 1.118 | 1491.1 33.6 | 1.393 896.4
136 | 1.053 | 1403.8 31.5 1.368 850.6
155 0.986 1314.4 29.5 | 1.344 | 806.0
5 | 0.938 | 1247.0 Di) 1.315 162.4
190.2 0.886 | 1181.2 26.4 1.298 738.3
204 | 0.840 | 1119.3 25.0 1.281 105.3
Molecular weight: 191.95. Radius of the Capillary tube: 0.04595 cm

Depth: 0.1 mm.

The compound boils at 267° C., and melts at 55° C. The specific weight
at 75° C. was 1.4390; at 100° C.: 1.4102; at 125° C.: 1.3804. In general at t°C.:
d4o = 1.5194—0.001012 ¢—0.0000008 #2,

The temperature-coefficient of # is fairly constant; its mean value is 2.01
Erg pro degree.

__Molecular Surface-energy
g in Erg pro em?
1000, 7

740

500
0° 20° 40° 60° 80° 100° 120° 140° 160° 180° 200° 220°C

Fig. 1.

Temperature

605

Molecular Surface-
Energy » in Erg pro cm?.

0° 20° 40° 60° 80° 100° 120° 140° 160° 180° zo0°G Temperature
Fig. 2.
XIII.

ortho-Bromonitrobenzene: C;H/, Bra Wor)

fe] |
46.3 1.405 1876.2 42.0 1.669 1027.5
61 1.353 1802.7 | 40.1 1.651 988. 1
76.5 1.303 1734.3 38.4 1.632 953.6
95.2 1.220 1627.3 | 36.3 1.608 | 910.4
116 1.156 1540.8 | 34.2 1.582 | 867. 1
136.2 1.076 | 1437.3 | 32.0 1.556 820.3
155.2 1.018 | 1358.0 | 30.1 1532 | 719.7
176.3 0.950 1266.6 | 28.1 1.505 736.6
191 0.908 1210.0 | 26.9 1.484 | LSI
204.5 0.867 1155.9 | 25.6 1.468 682.2

Radius of the Capillary tube: 0.04595 cm. |
Depth: 0.1 mm. |
The substance boils at 258°.5 C. under a pressure of 756 mm. it melts at
43E:
The specific gravity at 75° C. was: 1.6333; at 100 C.: 1.6020; at 125° C.:
1.5703. In general at 7? C.: dyo= 1.6642—0.001228 (¢--50° )—0.00000032 (t—50°)?.

The temperature-coefficient of » is fairly constant; its mean value is 2.19
| Erg pro degree.

Molecular weight: 201.96.

604

XIV.
meta-Bromonitrobenzene: C,H, Bra) WO) 3
at al * r ii |
2 { Maximum Pressure H 5 | Molse
Ed = te IRA sels Specific Surface-
rare elo ae do | energy vin |
a. in . mer-| 2 | gravi n p.
E 5 cury of | in Dynes | Erg pro cm’. | 4° Erg procm2.
ont | (Her (Cy | |
ee Ef = ==
61.5 1.347 1798.8 39.9 1.650 983.6
14 1.296 1730.0 | 38.6 | 1.634 | 957.8
89 1.256 1672.9 | 31d 1.616 927.4
110 1.164 1556.4 34.9 | 1,590 881.9
124 Leroi | 1512.8 33.4 1.572 850.4
139.8 1.085 | 1445.6 32.0 | 18558 | 821.4
156 1.032 1376.4 30.6 | 1.532 792.6
175, | 0.961 | 1303.0 28.8 | 1.506 154.5
194.4 | 0.910 | 1212.6 26.9 | 1.480 713.0
209 0.888 | 1179.3 25.9 | 1.459 | 693.0

Moleculair weight: 201.96.

Radius of the Capillary tube: 0.04595 cm.

Depth: 0.1 mm.

Under a pressure of 755 mm. the substance boils at 251° C.; it melts at 56°.5 C.

At 75° C. the density is: 1.6329;

at 100° C.: 1.6024; at 125° C.: 1.5710. In

general at f° C.: Aso = 1.6625 —0.001166 (¢—50°)—0.00000072 (t—50°)2.

value is: 2.04 Erg pro degree.

Up to 195° C. the temperature-coefficient of » is fairly constant; its mean

XV.

para-Bromonitrobenzene: CoHsBr (1) (NO2)4):

| 8 | Maximum Pressure H Maleentan

| erin eg] SUiface:
a in mm. mer- | energy 2 in |

LES cury of | in Dynes | Erg pro cm?
5 ;
ORE

| — re EEE == en =
127 1.116 1488.6 | 34.2 |
140.3 1.085 1445.9 | 33.1
155 1.025 1367.3 31.5
178 0.956 1274.5 29.3
194.5 0.908 1211.3 27.8

| 209.3 0.870 1159.9 26.6

| |

| Moleculair weight: 201.96. Radius of the Capillary

tube: 0.04595 cm. |
Depth: 0.1 mm.

Under a pressure of 758 mm. the compound
boils at 254° C.; it melts at 1279 C. At 140° already
it sublimes rather rapidly against the colder parts
of the capillar tube.

XVI.

ortho-lodonitrobenzene: C;H4 Jay (NO>)(9y.

v Maximum Pressure H len |
si E are. Surface- f poe car
5° in mm. m Been et Bn |
a. ‘in . mer- | 2 1 u
ES cury of in Dynes Eng Prova. En Erg pro cm?2. |
U fo}

= (HET (E
61 1.448 1930.5 43.1 | 1.938 1097.1
76.5 1.400 18665 / |) SLI 1.916 1069.6
95.2 1.339 11845 Jant sarge 0 ase || 0302
114.1 1.280 1706.2 38.0 | 1.863 993.1

136 1.209 1611.7 | 39.8 1.832 946.1
155.5 1.150 1533.1 34.0 | 1.805 907.5

176 1.085 1445.4 31.9 1.775 861.0

191 1.037 (3sa5er So TL 832.5
205 | 1.004 1338.5 | 29.5 1.734 808.7

Molecular weight: 248.90.

Radius of the Capillary tube: 0.04595 cm.
Depth: 0.1 mm.

The substance boils at 1622.5 C. under a pressure of 18 mm. it melts at
50° C. The specific gravity at 75° C. is: 1.9186; at 100? C.: 1.8831; at 125° C.:
1.8475. At @ C.: dyo = 1.9541 —0.001422 (£—50’).

The temperature-coefficient of » has a mean value of 1.98 Erg per degree.

|
|
|

XVII.
meta-lodonitrobenzene: C,H, Ja ) NOz(3)-
v Maximum Pressure 1
= Surface-
(©) mg ei — EE EEE .
5e in mm. mer- | LOE Bend
a. : - 2 | gravi
ES curyof | in Dynes | Erspro cm’. an
P)
= ORG:
pose 1.564 | 2086.2 | 41.3 1.981
“41.1 1.509 2010.7 45.4 1.960
*59.8 1.449 1929.4 43.4 1.935
*83 | 1.362 1815.4 41.0 1.902
95 1.324 1765.7 39.8 1.885
110 1.273 1696.8 | 38.2 1.864
124.5 1.224 | 1632.2 | 36.8 1.842
140.2 1.181 1572.8 | 35.3 1.821
156.1 1.124 1498.7 | Soni 1.797
170 1.084 1444.0 | 32.4 NES)
185.5. | 1.038 1381.6 | 30.9 1.752
198 0.999 1330.8 | 29.8 1.732
5.) | 0:957 |) W127673 | 28.6 1.688

Molecular weight: 24896. Radius of the Capillary tube: 0.04644 cm.; with the
observations indicated by *, it was 0.04660 cm.

Under a pressure of 14 mm. the boilingpoint was 153° C.; the substance
melts at 36°? C. It can remain in an undercooled state during a very long

Depth: 0.1 mm.

time, and crystallises extremely slowly.
At 50 C. the density was: 1.9477; at 75° C.: 1.9131; at 100° C.: 1.8778.

In general at # C.: dyo = 1.9816—0.001342 (t—25°)—0.00000056 (£—25°)?.

Molecular
Surface-
energy # in
Erg pro cm?. |

1186.8
1147.2
1106.1
1056.9
1032.2
998.1
969.2
936.8
902.3
874.7
841.5
817.7
798.4

Up to 198° C. the temperature-coefficient of » is fairly constant and hasa

mean value of: 2.16 Erg pro degree.

606

Molecular Surface-
Energy » in Erg vro cm’.
1040

1010
980
950

890

830
600

740

0° 20° 40° 60° 80° 100° 120° 140° 160° 180° 200° 220 240°C
Fig. 3.
XVIII.

Temperature

para-Nitrotoluene: CH; Er Ae WO), 4)

Maximum Pressure 1

v
ae. Surt Molecular
a U ——- — — . | :
go |. tension z in | Be ME

| | | |
le)

60.2 1.166 1554.5 35.5 efile 879.4
83.5 1.101 1467.8 33.5 1.098 836.9
95 1.069 1424.9 32.5 1.086 817.9
115 1.007 1343.3 30.6 1.066 | 719.7
130.1 0.956 1274.6 29.0 1.054 | 744.5
144.5 0.908 1210.3 27.5 1.040 | 112.3
166 + 0.827 1102.5 25.0 1.017 | 657.0
180.2 0.782 1042.9 23.6 0.995 629.6
194.5 0.738 982.8 22.1 0.973 598.4
214.6 0.659 876.9 19.9 0.954 546.0

Molecular weight: 137.1.
Depth: 0.1 mm.

Radius of the Capillary tube: 0.04660 cm.

The compound boils at 236° C. under a pressure of 755 mm.; the melting-

point was 57°.5 C.

The density at 75° C. was: 1.1038; at 100° C.: 1.0817; at 125° C.: 1.0576.

At f° C.: dgo = 1.1239—0.000764 (£—50°)—0.0000016 (t—50°)2.

The temperature-coefficient of » is originally (uP to 95°) about 1.77 Erg;
afterwards it becomes fairly constant and equal to 2.30 Erg pro degree.

XIX,

ortho-Nitrophenol: C,H, (OD, ) WVO) a):

v Maxi P.
2 aximum Pressure H ein ren
SO | ae Specific Surface-
ee in mm. mer. [eter ae dyo | energy / i

; - > | grav 5 rgy # in
Es <a DY Erg pro cm2. 4
& ee in Dynes Erg pro cm?.
52 1.289 1718.5 38.0 1.281 864.7
70 1.246 1660.0 36.6 1.264 | 840.3
90.2 Mane” 45805, | 34.8 (245 SOTO
108 1.134 | 1512.4 Sl 1.224 | 716.4 |
124.3 1.029 1374.4 31.2 1.206 | 739.1
140.1 1.014 1352.3 29.5 1.195 703.1
156 ORS 27241 27.5 (ITO GOTS
170 0.888 1184.4 25.6 1153 | 624.9
185.7 05805) °1073.2 23.0 Ee |. -Sb1kS
204 0.730 | 973.2 20.7 1.113 | 517.3
Molecular weight: 139.05. Radius of the Capillary tube: 0.04644 cm.

Depth: 0.1 mm.

The substance melts at 45° C. Under a pressure of 760 mm. it boils at |
214°.5 C. Above 209° C. a brown colouring is produced by gradual decom- |.
position.

The density at 75 C. was: 1.2583; at 100° C.: 1.2323; at 125° C,: 1.2052,
At £°C.: dygo = 1.2832—0,000974 (t—50°) —0.00000088 (t—50°)2.

The temperature-coefficient of » increases evidently with rise of temperature:
between 52° and 70° C.: 1.35 Erg; between 70° and 90°: 1.60; between 90°
and 108° C: 1.77; between 108° and 140° C.: 1.84; between 140° and 170° C.: |
2.61; and between 170° and 204° C.: about 3.20 Erg pro degree. Probably a
gradual decomposition of the substance occurs here, causing this increase of

E at higher temperatures.

XX. et

meta-Nitrophenol: CH, (OD) (NO, 3)

of the substance.
tee

= jin mm. mer-{ _ Erg pro cm2, | Sravity dyo | energy » in
5 ie Goren in Dynes ol} | Erg pro cm?2,
110 1354-5)" Is 48051. 2) dowd eth <aeome 914.0
125 1.338 | 1783.8 | 39.5 1.259 909.2
140.1 1,316 | 1754.5 | 38.8 1.249 897.9
15532 [ene | 1701.5 37.9 1.237 | 882.8
170 1.247 1662.4 36.7 | 15222 | 861.8
185.6 1.196 | 1594.4 35.1 | 120 | 831.0
201 1.146 1523.2 Soul | 1.191 | 790.7
218 1.051 | 1401.2 30.6 | 1.174 | 738.0

Molecular weight: 139.05. Radius of the Capillary tube: 0.04644 cm.
Depth: 0.1 mm.

The carefully purified substance melts at 96° C.

The density at 100° C. was: 1.2797; at 125° C.: 1.2588; at 150° C.: 1.2359.
At £° C.: dgo = 1.2797— 0.000716 (£—100 ) — 0.0000016 (ft—100°)2

The temperature-coefficient of » increases rapidly with rise of temperature:
between 110° and 140 C. it is: about 0.50 Erg; between 140° and 155° C.:
1.00; between 155° and 170° C.: 141; between 170° and 186° C.: 1.97; between
186° and 201° C.: 2.619; and between 201° and 218° C.: 31 Erg pro degree.
It is rather probable, that this fact is connected with a gradual decomposition |

para-Nitrophenol: C5, (OF) WON)

608

XXI.

| | |
9 Maximum Pressure H | Mole
Ss | olecular
> k LEN Surface- | :
Be | | nnn Sere | Surface-
a. ‘in mm. mer- gravity energy # in |
ha | cury of | in Dynes | BY8 pro cm? oe Erg pro cm?2.
nl | OBG |
E é DES WE nt oe] |
== as or : -
47 «9.4070 || 1906.0") Wes 1.213 | 989.4
130.5 | 1.452 1936.9 42.0 1.262 | 965.3
145.5 | 1.408 1877.1 40.6 1.249 | 939.6
162 15359 1815.3 39.1 | 1.234 912.2
176.5 5 Ul 1747.8 Sie | 1.222 885.3
196.5 1.241 1654.4 | 35.6 | 1.205 843.8
|
— = =- ———- ---=- —-= ~ ' — =) oe el —
Molecular weight: 139.05. Radius of the Capillary tube: 0.04529 cm. |

Depth: 0.1 mm.

The compound melts at 113° C. It sublimes rapidly and the measurements
are thus made much more difficult by the gradual reduction of the cross-
section of the capillary tube by the layers of crystals deposed there within.

The specific gravity at 120° C was: 1.2703; at 140° C.: 1.2532; at 160°C:
1.2361. At f° C.: dgo = 1.2874—0.000855(#—100~).

The temperature-coefficient of » is somewhat oscillating round a mean value

of 1.81 Erg pro degree.

XXII.

para-Nitroanisol: CH; OW) = Gglig - (NO2)¢4y-

Bis

| |

2 Maximum Pressure H | |
ZE. Sen Molecular
Bo Ta ECD Rn eae Surface-

ee |

60.5 34> | ea 40.9 1.216 1027.3
83 1.280 1706. 2 sont 1.194 994.1
95 1.243 1659.4 | 38.0 1.183 972.1
115.2 1.187 1582.5 36.1 1.165 932.9
130.6 1.148 1528325 | 34.6 1.149 902.5
144.5 1.096 1459.5 | 33.1 1.137 869.4
167.2 1.014 (gel > | 30.7 1.115 817.0
180.1 0.968 1291.8 20.3 1.101) Teens
194.5 0.909 1214.1 27.6 1.086 7417.5
220 0.814 - 1085.9 | 24.5 1.059 674.7

~ Molecular weight: 153.06.

Under atmospheric pressure the boilingpoint is 259° C. The substance

melts at 55° C.

Radius of the Capillary tube : 0.04660 cm.
Depth: 0.1 mm.

The density was at 75° C.: 1.2012; at 100°C.: 1.1775; at 125° C.: 1.1535;
at f° C.: d42 = 1.2246—0.00093 (t—50°) — 0.00000024 (t—05°)°.

The temperature-coefficient of # increases gradually with rising tempera-
ture: it is between 60° and 83° 1.49 Erg: between 83° and 95° C.: 1.93; |
between 95° C. and 131° C.: 1.97; between 131? and 180° C.: 2.35; between |

180° and 195° C.: 2.69; and between 195° and 220° C.: 2.80 Erg.

ortho-Cresol: CH3(1) .CsH4 (OM) 5);

v Maximum Pressure H
80 =

Do 2

a. |in mm. mer- ‘

es cury of in Dynes
sat ae:

5 === ae
40.3 1.142 1522.5
54.5 1.107 1475.8
15.6 1.047 1395.9
95 0.993 1323.3
116.2 0.918 1224.8
135 0.864 1152.0
151.5 0.814 1085.5
176 0.711 947.9

Molecular
Surface-
energy » in
Erg pro cm?. |

| |
Surface- :

tension % in ebecie |

Erg pro cm2. SCA djo

34.8 | 1.033
33.7 | 1.019
32.0 1.002
30.3 0.987
28.0 0.971
26.3 0.956
24.7 0.946
21.5 0.930

712.6
7155.0
725.0
693.5
647.8
614.8
| 581.5
OE

Depth: 0.1 mm.

Under a pressure of 755 mm. the ortho-cresol boils at 190°.2 C.; it melts
at 30° C. The specific weight at 25° C. is: 1.0458; at 50° C.: 1.0236; at
15° C.: 1.0027. At £° it is: dq4o = 1.0693—0.000966 ¢ + 0.00000104 #2.

XXIV.

25.6 1.135 1514.9
41 1.100 | 1465.4
60.2 1.042 1389.2
83 0.981 | 1309.0
95 0.946 1261.8
114.3 0.898 1195.5
130.5 0.849 1132.4
144.5 0.809 1079.1
166 0.746 | 994.2
180.9 0.701 926.6
194.5 0.639 851.9

Molecular weight: 108.06.

)

CHa) Cols Oy

| Surface- |

| tension x in
| Erg pro cm?

34.5
33.2
31.6
29.7 |
28.7
27.0
208
24.6
22.6
21.0
19.2

Specific

| gravity dyo

Molecular
Surface-
energy # in

Erg pro cm?.
|

|
|
|
|

167.
144.
115.
685
658.
629.
603.
580.
539.
504.
463.

ORWMWOMWOWA

Radius of the Capillary tube: 0.04660 cm.

Depth: 0.1 mm.

The substance boils at 200° C. under a pressure of one atmosphere. It
melts at 37° C. The specific weight at 25° C. was: 1.0309; at 50° C.: 1.0102;
at 75° C.: 0.9905; at f° C.: d4o = 1.0526—0.000888 f + 0.0000008 #2.

Molecular Surface-
Energy » in Erg pro cm?

1000
970
940
910
880
850
820
790
760
730
700
610
640
610
580
550
520
490
460

v Maximum Pressure H_ | |
Bes | Surface- | Molecular
EE tension xin | ae do | energy 1
| 5 SNE Erg provcm?,. | STAVEY 40: | Snerey sas
E> | cury of in Dynes | SP Erg pro cm?
= ORE
Ei ede ne Poel Sen eN
o | |
—19 1.444 | 1926.0 45.7 1.259 | 993.0
0 1.379 1839.2 43.6 1.239 | 957.6
29.7 1.300 | 1733.3 40.5 1.208 904.6
47.8 | 1.240 1653.7 38.6 1.190 870.8
64.8 | 1.180 1574.2 36.7 1.174 835.5
80.9 | 1.130 1507.3 Bol 1.160 | 805.5
104.5 | 1.055 1406.8 SE 1.140 759.1
125.1 0.977 1302.1 30.2 1.124 707.8
151.8 0.934 | 12452) 5 wel 28.8 lose 68355
177.5 0.883 | 1176.4 Biee 1.085 652.6
196.5 0.848 1130.4 26.1 | 1.073 630.9

Molecular weight: 127.52. Radius of the Capillary tube: 0.04777 cm.; with the
observations, indicated by *, it was: 0.04839 cm.
Depth. 0.1 mm.

The liquid boils under a pressure of 760 mm. at 210’.5 C. It can be strongly
undercooled, but after solidification it melts again at 0° C. At the boiling-
pointsyshas a value of: 25.3 Erg pro cm?

At 28°.5 C. the density is: 1.2178; at 50° C.: 1.1890; at 75° C.: 1.1660. At |
(2 C.: dgo = 1.2388 —0,001047 {+ 0.000001 £. |

The temperature-coefficient of » is below 125° C. fairly constant and has a mean
value of 1.97 Erg.: Afterwards it decreases to about 11 Erg pro degree. ;

XXVI.

para-Chloroaniline: C;H,. WI) : Clay

v Maximum Pressure 1
=e Surmaee: Molecular
al : : Specific Surface-
Ko tension 7 in : f
a < |in mm. mer- Ere procm2, | Sravity do | energy » in
=de) cury of in Dynes sp 2 Erg pro cm2,
vo
re ORE
le}
74.6 1.322 1762.5 37.8 1.166 | 864.5
90.6 1.262 1682.5 36:1 1.151 | 832.8
104.1 1.221 1627.9 34.9 1.139 | 810.7
121 1.166 1554.5 33.3 1.124 | 780.4
130.4 1.144 152582 | 32.6 1.116 | 7167.7
151 1.073 1431.1 30.6 1.097 728.8
170 1.015 1353.2 28.9 1.080 695.6
185 0.981 1307.7 | 27.9 1.067 | 676.9
| | |
Molecular weight: 127.52. Radius of the Capillary tube : 0.04374 cm.
Depth: 0.1 mm.

The compound was often recrystallised from mixtures of chloroform and
ether. The beautiful colourless crystals melt at 70° C.; the substance boils
at 232° C. The specific gravity at 70° C. is 1.1704; at 100° C.: 1.1432. At
170° the liquid becomes coloured deeply violet; the measurements therefore
were no longer continued. At the boilingpoint x must have a value not very
far deviating from 25,0 Erg. The density at © can be calculated from : d4o =
1.2337 — 0.000903 f.

The temperature-coefficient of » decreases a little with increasing tempe-
rature: between 74° and 91° C. it is about 1.98 Erg; between 170° and 185° C.:
1.24 Erg, oscillating thus round a mean value of about: 1.64 Erg pro degree.

XXVII.

meta-Nitro-Aniline: C;H, WI) NOx).

= — — | — me et =
124-2 1.410 1879.8 42.7 1.206 1006.7
140.5 1.357 1809.7 41.2 1.192 979.0
157 1.266 1684.5 39.7 | Walvie 951.4
170 1.274 1698.4 38.5 | 1.166 | 928.4
186.2 1.221 | 1631.6 31.0 1.152 | 899.4
201.3 1.184 1577.4 | 35.6 1.139 872.0

Radius of the Capillary tube: 0.04644 cm.

Depth: 0.1 mm.

The beautifully yellow coloured and well crystallised substance melts at
112° C.; while the liquid is heated above 200° C.,, it is gradually tinged
brownish by progressive decomposition, and therefore the measurements were
no further continued. Under the pressure of one atmosphere, the liquid boils
at 286° C. according to the data given in literature; however it must be decom-
posed partially already at that temperature.

At 120°C. the density was: 1.2095; at 140° C.: 1.1921; at 160°C.: 1.1747. At
t C. in general: ago = 1.2269 0.00087 (t—100°).

The temperature-coefficient of » is fairly constant; its mean value is:

1.74 Erg pro degree.

Molecular weight: 138.07.

|
|
|

612

XXVIII.

para-Nitroaniline: C6H4 WH»), 1) WO»), 4}

v Maximum Pressure H |
| = Geen = ee Surface
5 o lin CD | ‚tension / in
a, . mer- |
= & cury of | in Dynes Erg pro cm2. |
isa ORE: |
SS SSS SS SSS — == == en |
5 | |
151 | 1.601 2135.3 46.7
1D (5985 2048.4 | 44.8
184.5 1.496 | 1993.6 43.6

Molecular weight: 138.07. Radius of the Capillary
| tube: 0.04374 cm.
| Depth: 0.1 mm.

The beautiful, orange-yellow crystals melt at
147° C. The substance is so volatile above 180°,
that reliable measurements were no longer possible.

XXIX.

3-Nitro-ortho-Toluidine: CH.

105 1310 ||; 18265 39.2 1.186 | 996.8
12150 1.323 | 1764.9 37.9 Pout | 972.0
130 1.295 1726.5 37.0 1.164 | 952.7
151 | 1.231 | 1641.5 Sone 1.144 916.8
170 1.166 | 1549.7 33.4 1.128 878.2
184.8 1.124 | 1499.7 32.1 1.115 850.6
201.2 1.077 1435.8 30.7 1.101 | 820.3

Alt USE IVER? SE be EU OE | tte EEN
Molecular weight: 152.08. Radius of the Capillary tube: 0.04374 cm.

Depth: 0.1 mm.

The compound melts at 96° C. At 100° C. the density was: 1.1900; at
120° C.: 1.1722; 140° C.: 1.1546. At # C.: dgo = 1.1900—0.0008815 (t—100~).

Originally the temperature-coefficient of » is somewhat increasing: from |
1.27 Erg at 130° C. to 1.71 Erg at 151° C. Then it remains fairly constant, |
with a mean value of about: 1.9 Erg per degree. |

5-Nitro-ortho-Toluidine: CH) . CsH3 WD) o) ; WO) 5);

The beautiful yellow crystals melt at 128° C. Above 180° C. the volatili-
ty of the compound was too great, to make any reliable measurements
possible. |

XXXI.

3-Nitro-para-Toluidine : CHa 1) . CoH - WH), 4) WO) 3):

v Maximum Pressure H |
By Serre Molecular
=P OE | Erg pro cm2, | ST&VEY %4o | Se
5 7 cary (of in Dynes sp | | Erg pro cm2.
121° 1.274 1698.5 36.4 1.164 | 969.1
130.5 1.248 1664.2 SBT 1.156 943,1
151 1.134 1511.8 33.1 | 1.137 865.7
170.5 1.094 1458.6 312 | 1.120 807.0
185 1.045 1393.2 | 29.8 | 1.107 | 767.3
Molecular weight: 152.08. Radius of the Capillary tube: 0.04374 cm.

Depth: 0.1 mm.

The substance melts at 117° C. Above 180° C. the compound is so volatile,
that reliable measurements were hardly any more possible. The specific
gravity at 120° C. was: 1.1645; at 140° C.: 1.1468; at 160° C.: 1.1292. At¢’C.:
do = 1 1821 — 0 000882 (¢ —100 ).

The temperature-coeflicient of » is abnormally great; its mean value is
about: 3.08 Erg per degree.

Molecular Surface-
Energy » in Erg pro cm?

1120
1090
1060
1030
1000

970

10 5
40° 60° 80° 100° 120° 140° 160° 180° zoo°C emperature

Fig 5.
XXXIL

Sylvestrene: C, His

® Maximum Pressure H |
3 G vi i ___| Surface- | Molecular
este : | | tension / in Bme | Surface-
a. in mm. mer- | 5 ravi > | energy » in
B | cury of | in Dynes | PSE Sia 5 | Erg pro cm2.
ie 0° C. | |
|
o | |
| —70 | 1.139 1518.5 | San 0.923 | 979.2
| —20 | 0.964 1285.5 | 30.1 0.891 860.2
0 0.908 | 1210.5 28.3 0.878 | 816.8
25.8 | 0.833 1110.2 25.9 0.859 | 758.5
41 0.792 1055.9 24.6 0.847 12E
55.5 0.736 | 981.2 2852 0.841 | 689. 1
| 80.4 0.682 909.8 22 0.827 636.7
em 02 | 0.654 | 872.3 20.3 0.820 613.2
1 116.2; 4| 0.582 176.3 18.0 0.807 549.6
1*136 | 0.546 281 16.4 0.797 504.8
| *149.5 | 0.507 676.7 14.6 0.790 | 452.1

| |

Molecular weight: 136.13. Radius of the Capillary tube: 0.04792 cm.; with the
observations indicated by *, the radius was:

0.04670 cm.

Depth: 0.1 mm.

Under a pressure of 21 mm. it boils at 63°.5 C.; under atmospheric pres-
sure at 177° C. The specific gravity at 25° C. was: 0.8599; at 50° C.: 0.8409;
at 75° C.: 0.8209; at f° in general: ago = 0.8779 — 0.0007 £—0.0000008 #2.

| The temperature-coefficient of » is between —70° and 1362 C. fairly con-

rapidly and becomes 3.9 Erg.

stant; its mean value is: 2.28 Erg pro degree. Above 136° it increases

615

XXXIII.
= =
E Terebene: Co Hyg. |
+ eek
© Maximum Pressure H | Maleeal
BG Ë Surface-ten- / pe ae a
s 3 sion 7 in Specific | Surface-
vo . . | 5
a. in mm. mer- om2 | gravity do | energy # in |
5 5 cury of || in Dynes Erg pro em?. Ed Erg pro cm?
F 0e C |
| = A
aw 1.131 1508.6 | 35.8 0.956 | 976.2
*_22 0.968 1290.4 | 30.7 0.912 863.9
0 0.906 | 1208.2 | 28.7 0.893 819.0

29.9 0.825 | 1099.3 25.9 0.868 753.2

46.8 0.775 | 1033.2 24.3 0.853 714.9

58.3 0.744 991.9 23.4 0.844 693.4

86.3 0.673 | 896.9 | ZL 0.820 637.4

102.7 0.626 | 834.9 19.6 0.806 | 598.9

118 | 0.573 164.6 | 17.9 0.793 552.9

127.4 0.558 | 7143.9 | 17.4 0.786 540.6

153 0.499 | 665.4 15557 | 0.764 494.0

170 0.449 | 599.3 13.9 0.749 446.0
Molecular weight: 136.13. Radius of the Capillary tube: 0.04839 cm.; in the

measurements indicated by *, the radius was
0.04867 cm.; Depth: 0.1 mm.

Under a pressure of 761 mm. the liquid boils at 170° C.; at the boilingpoint
the value of y is about 13.7 Erg pro cm2. Even at —79° C. the compound is
not crystallised, but the liquid is turbid then. Probably it is a mixture of
isomerides.

The specific gravity at 25° C. is: 0.8721; at 50° C.: 0.8509; at 75° C.:

| 0.8298. At f° in general: Aho = 0,8932— 0.000846 4. The temperaturecoefficient
of » is in mean: 2.16 Erg pro degree, and fairly constant. |

$ 3. If we now review the results here obtained, it will appear
in first instance that such position-isomerie substances at the same
temperatures do „ot possess the same surface-energy in general, as
was formerly occasionally supposed. One cannot deny that the u-/-curves,
and especially those of the aromatic hydrocarbons, if substituted by
halogen-atoms or nitro-groups, often closely approach each other:
so e.g. with o- and m-Dinitrobenzene, with o-, m- and p-Chloronitro-
benzene; with o- and m-Bromonitrobenzene; with o- and p-Fluoro-
nitrobenzene; and with 1-2-4-, 1-4-2-, and 1-3-4- Dichloronitrobenzenes.
In the case of the nitrated phenols these curves deviate much more ;
but we must conclude this fo be caused by differences of the
internal structure of the mentioned compounds, which are undoubtedly
connected with the presence of the H-atom in the OH-group. For
while the mutual differences are rather great in the case of the
substituted phenols themselves, these differences will be strongly
diminished, if e.g. in the derivatives of polyvalent phenols one of

40
Proceedings Royal Acad. Amsterdam. Vol. XVIII.

616

the O#H-groups is substituted by an oxalkyl-group, as e.g. with
monomethylresorcinol and guajacol. These differences however are
completely reduced to the size found in the case of the above
mentioned substituted hydrocarbons, if a/l H-atoms of the OH-groups
present are esterified: between ortho-, and para-Nitroanisol e.g. the
deviation of the two curves is already much weaker, as in the case
of ortho-, and para-Nitrophenol itself, while it is yet more consider-
ably diminished in the case of Veratrol, Dimethylhydroquinone, where
the u-t-curves of the two last named substances even coincide almost
over their full length. If we now observe so much stronger differences
between e.g. ortho-, and para-Nitrophenol, than between their cor-
responding anisols, this could probably be considered as an indication,
th t the internal equilibrium in the liquid between the molecules with
the constitution of the pseudo-acid, and between those with the true
nitrophenol-formula, may be situated in the case of the ortho-
compound in such a way, that it much more approaches to the
side of the pseudo-acid, than in the case of the para-compound: a
circumstance probably caused by the more immediate vicinity of
OH-groups and NO,-radical in the case of the ortho-nitrophenol. In
the case of the corresponding «misols, they might then be supposed
to possess a quite analogous structure, no freely movable H-atom
being any more present.

Even in the cases, where the u--curves of such isomerides, approach
each other relatively closely, it can be often observed, that the values of

0
the temperature-coefficient = are evidently different, which thus deter-

mines the steeper or flatter shape of the curves.

Besides in the ease of the phenols, also somewhat greater differences
may be stated between isomeric aromatic bases, and between the
cresols. The abnormal shape of the curves with some of the considered
bases, undoubtedly must be partially explained by the alterations
and decompositions, which seem more easily to occur in the ease
of these compounds at higher temperatures, than with other substances.
Finally we can draw attention to the fact, that within the series
of the halogennitrobenzenes, just as within that of the halogenated
benzenes themselves, the values of u at the same temperatures appear
to be the greater, the higher the atomic weight of the halogen-atom
is. This fact is of course just opposite to that observed in the case
of the molten halogenides of the alcali-metals.

A general rule considering the relative magnitude of mg in the
case of ortho-, meta-, and para-monosubstitutionproduets, could not
be formulated. ; University-Laboratory for Inorganic
Groningen, August 1915. and Physical Chemistry.

617

Chemistry. — “Jnvestigations on the Temperature-Ccöffictents of
the Free Molecular Surface-Energy of Liquids from 2 SOC"
to 1650° C.” XIV. Measurements of a Series of Aromatic
and Heterocyclic Substances. By Prof. Dr. F. M. Janerr and
Dr. Jur. Kann.

(Communicated in the meeting of September 25, 1915).

§ 1. In the present paper the results are published, obtained with
the measurements of the surface-energy of the following 28 compounds ;
these measurements may be considered as a supplement of the
formerly published researches with aromatic and cyelic derivatives :

1-2-4-Chlorodinitrobenzene; para-Dibromobenzene; Lodobenzene; ortho-
Bromotoluene; Phenol; 1-2-4-Dinitrophenol; 2-4-6-Trichlorophenol;
para-Nitrophenetol; 2-Nitro-resorcine; Veratrol; 4-5-Dinitro-veratrol ;
Ethyl-Comamylate; Anisaldehyde; Benzophenone; 3-4-3'-4'- Tetra-chloro-
benzophenone; 2-4-2'-4'- Tetrachluirubenzophenonebichloride; Monome-
thylaniline; Nitrosomethylaniline; Diisobutylaniline; Diphenylamine ;
Dibenzylamine; Azoxybenzene; «-Dihydrocampholenic Acid; Ethyl-a-
Dihydro-campholenate ; «-Furfurol; Thiophene; and Piperidine.

The specific gravities were determined in the way previously
described, either by means of a dilatometer, or by the aid of the
pyenometer, or finally in some cases by a hydrostatical method.
Of some substances only such small quantities were available, that
it appeared impossible to determine these specifie weights with
sufficient exactitude; or there were other causes, which prohibited
these determinations in some cases. It is more especially the very
rapid evaporation of many of the higher melting substances, whicb
causes the formation of a crystalline layer round the fine platinum
suspension-wire of the immersion-conus, and which of course must
appear a serious obstacle for the exact determinations of the
density required.

‘ Al a

618

§ 2.
if
1-2-4-Chlorodinitrobenzene: CsCl) WO), 4):
En nd

2 Maximum Pressure H | Molecul
BS _ AET % 6 Surface- ees
= oneal be | tension in | oe A ee
a. in mm. mer- avi n ei
ES cury of in Dynes Exe Pro cuit: ae Erg pro cm?
uv |

= OG:

60.4 1.517 2021.3 45.5 1.515 | 1189.5
16.2 1.428 | 1954.8 43.9 1.497 1156.8
95 1.416 1884.4 42.2 1.477 | 1122.1
114 1.343 | 1791.0 | 40.4 1.455 / 1085.0
136 1.278 | 1703.8 38.3 1.432 1039.6
1551 1.219 1623.9 36.4 1.412 | 997.3
N75) 1.158 | 1544.0 34.5 | 1.391 | 954.7
190 1.101 1467.8 | 32.9 | 1.378 | 916.2
204.2 1.057 1408.0 | 3185 | 1.365 | 882.8

a |

Radius of the Capillary tube: 0.04595 cm.
Depth: 0.1 mm.

Molecular weight: 202.50.

The substance melts at 51° C.

The specific gravity at 75° C. was: 1.4982; at 100°C: 1.4706; at 125 C.:
1.4439. At f C.: dgo= 1.5267—0.001158 (¢ 50°) + 0.0000007 (£—50°)?.

The temperature coefficient of # is fairly constant ; its mean value is 2.23 Erg.
pro degree.

Il.

para-Dibromobenzene: 1-4-C,H,Br».

v Maximum Pressure H Motcent
BG = Surface- Specifi | a Bi ge
5 * in mm. m febsion ai gr bu | ere
a In . mer- 2 a | pe
Ee cury of in Dynes Erg Dro7cnit: 4° | Erg pro cm?.
vu
E ORE |
JEN A: ze : as = |
94.8 1.069 | 1424.9 32.0 1.840 | 813.4
115 | 1.008 | 1345.6 SUNS 1.807 | 7719.5
130.1 0.967 | 1289.2 28.8 1.782 741.8
144.5 0.923 1229.4 27.4 1.756 718.5
168.5 0.850 1133.0 | Zone | 1.715 671.3
180 | 0.810 | 1078.8 | 23.8 1.694 639.2
194.5 0.757 1009.2 2253 1.668 605.1
209 | 0.701 | 926.6 | 20.4 1.643 | 559.2
| | | |

Radius of the Capillary tube: 0.04660 cm.
Depth: 0.1 mm.

Under atmospheric. pressure the boiling point is 216? C. The substance
melts at 89° C. It sublimes already notoriously at rather low temperature (130°).

The density at 100° C. was: 1,8322; at 120° C.: 1.8000; at 140° C.: 1.7683.
At £ C. it is calculated from: d4o =1.8649—0.C0016475 (¢ 80°) —0.000000625
(t—80°)?.

The somewhat oscillating temperature-coefficient of » has below 195°C. a mean
value of about: 2.15 Erg pro degree.

Molecular weight: 235.79.

lodobenzene: C,H;J.

EY) Maximum Pressure
fn | Surt Molecular
oO | ea Specific Surface-
ue in mm. mer fension im stevia d energy v in
; - pi
EE P Erg pro cm2, ee) Gall
5 cue ol in Dynes Erg pro cm?
EN 1.375 1833.1 41.0 1.892 928.7
0 1.314 | 1751.6 39.1 1.861 895.5
25.4 152835) | 1644.5 Siok 1.823 861.4
40.4 1.188 1584.5 OON 1.801 835.7
54.1 1.144 1524.6 34.4 1.781 811.3
716.1 1.076 1434.7 32.3 1.747 711.6
95.1 1.015 1353.3 30.4 1.716 734.9
117.2 0.944 1260.5 28.2 1.683 690.6
135.1 0.857 1143.4 2055 1.659 630.5
150.5 0.803 1070.6 23.9 1.637 596.2
176 0.704 938.6 | 20.7 1.598 524.7
Molecular weight: 203.96. Radius of the Capillary tube: 0.04670cm.

Depth: 0.1 mm.

Under a pressure of 13 mm. the liquid boils constantly at 79° C. under
760 mm. at 188°.5 C.; on heating it becomes slightly coloured. In solid
carbondioxide and alcohol it solidifies into a hard crystalline mass, which
melts at — 26°? C.; according to TIMMERMANS at —31°.3 C. The specific
gravity at 25° C. was: 1.8230; at 50° C.: 1.7852; at 100° C.: 1.7090. At f° it
can be calculated from: djo = 1.8606 — 0.0015 f — 0.00000016 £.

The temperature-coefficient of » increases regularly with rising temperature:
between —21° C. and 76° C. its mean valueis:1.65; between 76° C. and 150° C : 2.46;
and above 150° C.: 2.80 Erg. The »-¢-curve therefore is concave towards the t-axis.

ortho-Bromotoluene : CH3(1). CoHsBrv2).

v Maximum Pressure H | | Hiniden
aS = is | Surface- ee 5 a oe
5 phi r | ia ae Baty d pe ee
a. in mm, mer- | | 5 win
& 5 cury of in Dynes | Erg le cm?. 4 Erg pro cm2,
= 0° C | |
3 | |
— 20 | 1.236 16478 ERA ani) Ie cod,e
Del ti 1569.3 36.5 1.447 878.9
25.8 1.102 1469.2 34.1 | 1.416 833.1
ag) 1.052 1402.3 32.5 | 1.399 | 800.4
55.5 1.002 1335.5 Biol 1.386 770.7
80 | 0.923 1231.2 28.6 1.352 720.6
92 0.886 1181.2 27.4 1.338 695.2
115.5 0.814 1085.1 | 25.1 1.310 645.8
*133.5| 0.784 1045.0 23.6 1.288 614.1
*149.5| 0.725 966.6 21.8 | 1.269 573.0
“175 0.634 845.2 18.9 1.239 504.7

Radius of the Capillary tube: 0.04792 cm. ;
with the determinations indicated by *, it
was: 0.04670 cm.

Depth: 0.1 mm.

Under a pressure of 755 mm. the liquid boils at 179° C. At —20° it beco-
mes turbid, and solidifies at a somewhat lower temperature into a white
crystalline mass, whose meltingpoint is: —27° C. The specific weight at
PbO Caisenl-4lis at oO Gs l.ooiO at 1OliGy nl Gone sauce sin Serena tens!
dyo = 1.4470—0.00119¢. The temperature-coefficient of » oscillates round a

mean value of 2.09 Erg pro degree.

Molecular weight: 170.98

620

Phenol: C,H;04.

© Maximum Pressure H
mute Sun Molecular
sd B RE Kn Specific | Surf
ae in mm. mer- | Pensions J Pk d nn
a. | . zi | 2 | hin
ik 4 tk | Erg pro cm?, 4°
| iS Coens in Dynes | | Erg pro cm?
41-2 1.207 1609.4 31.0 1.063 734.6
60.1 1.156 1538.9 Sone 1.043 707.8
82.1 1.090 1453.2 033 1.021 679.2
95.1 1.052 1400.8 32.0 1.019 653.5
115 0.980 1306.5 29.9 0.990 622.5
130.5 0.936 1245.6 28.3 0.979 593.6
144.5 0.868 1160.0 | 26.7 | 0.964 565.9
166 0.793 1057.2 24.1 0.951 515.4
180.5 0.719 958.6 | 21.8 0.940 469.8
|
— — en es | = — - = = =
Molecular weight: 94.05. Radius of the Capillary tube: 0.04660 cm.
Depth: 0.1 mm.
The compound boils at 180°.5C. under a pressure of 758 mm. The melting-
| point is 41° C. The specific gravity was determined by means of the hydro-
static method; at 50° C. it was: 1.0529; at 75° C.: 1.0272; at 100°C.: 1.0033.
At # C.: dgo = 1.1097—0,001208 ¢ + 0.00000144 £.

The temperature-coefficient of » is between 41° and 82° C.: 1.36; between

82° and 166° C.: 1.94 Erg.; above 166° C. it increases very rapidly.

The beautifully crystallised compound melts at 114°C. The specific gravity
at 120°? C. was: !.4309; at 140° C.: 1.4106; at 160° C.: 1.3898. At C.: d4go
= 1.4507—0.000962 (—100 ) — 0.00000062 (t—100°)2.
The temperature-coefficient of » has a mean value of about: 1.90 Erg per
degree.

621

VIL.
2-4-6-Trichlorophenol: C,H; (OH). Cl.

® Maximum Pressure HZ
2 Bs a Sinas \ Molecular
ae in mm. mer sae ee Bee

; - 5 ravi o | energy # in
EE cury of in Dynes Erg pro cm?. 4 2
© 05 C. Erg pro cm?2,
70.2 1.202 1600.8 36.3 AG4S5, he UUOd IRS
90 1.134 1522.4 | 34.7 1.466 | 911.6
109 1.095 1459.3 Bor | 1.438 880.8
124.9) | 1.040 1387.7 31.6 1.414 850.4
140.2 | 0.998 1328.7 30.0 1.386 818.2
156 0.941 1256.2 28.6 1.360 789.9
170 0.897 1195.9 2e 1.333 758.5
185.5 0.846 1127.9 25.5 1.308 722.8
196.5 0.803 1070.5 24.1 1.290 689.8

| |

Radius of the Capillary tube: 0.04644 cm.
Depth: 0.1 mm.

Under a pressure of 760 mm. the substance boils at 246° C. It melts at
69°.5 C. and evaporates rapidly on heating above the meltingpoint. Above
196° the liquid gets darker by a gradual decomposition. At 75° C. the density
was: 1.4901; at 100° C.: 1.4587; at 125° C.: 1.4294. At f° C.: dyo = 1.5236—
—0.001382 (¢— 50°)— 0.00000168 (£—50 )?.

The temperature-coefficient of » increases gradually with rise of tempera-
ture; between 70° and 109° C. it is about 1.57 Erg; between 109 and 185 C.:
2.07 Erg; and between 185° and 196°.5 C 3.02 Erg pro degree Celsius.

Molecular weight: 197.40.

|
|

VIII.

para-Nitrophenetol: CH, (NO). OCs 54)

Radius of the Capillary ‘tube: 0.04644 cm.
Depth: 0.1 mm.

The beautifully crystallised compound melts at 60° C.; under atmospheric
pressure it boils at 283° C. The specific gravity at 75° C. is: 1.1416; at 100° C.:
1.1176; at 125’ C.: 1.0937. At # C.: dgo = 1.1656—0.00096 (£—50 ).

The temperature-coefficient of » is fairly constant; its mean value is:
2.0 Erg pro degree.

Molecular weight: 167.08. _

v Maximum Pressure H
hve Surfaces Molecular
oS ar, rein F : Specific Surface-
Do ‘ | tension x in Sek d | in
a. in mm. mer- | | Er 2 | gravity do | energy » i
5.5 cury of i, Dynes Ere-proem) : Erg pro cm2,
ia ORG
70.2 1.164 1549.0 35.3 eda 963.9
90 1.096 1461.7 33.6 1.152 927.6
107.5 1.051 1401.7 32.2 | 1.111 910.6
124.5 | 1.004 | 1338.9 30.7 1.094 877.2
140 OLE ye i284e 29.3 1:079 | 184479
ey I) OLE Pa | 27.9 (HOG 4}, 81226
170 0.871 1162.9 | 26.7 1.051 784.0
185.6 | 0.840 1119.9 25.4 NOS |) TBEG
201 0.785 1048.8 24.1 1.020 1E (A5)
220 | 0.747 994.2 | 22.6 1.002 | 684.6
|

IX.

2-Nitroresorcinol: C,7,(OH),(NO,).

Maximum Pressure H
E aot Dt ee SED
beers | ‘ tension 7 in
in ; in mm. mer-
cury of in Dynes Erg pro cm.
Oe:
90.7 1,216 |, 1701-1 39.5
109.5 1.208 1610.6 37.4 |
125 1.150 1533.2 35.6
140 1.101 1466.6 34.0
156.2 | 1.037 1382.5 S2al
169.2 0.988 1317.8 30.6
185.5 0.940 1253.2 29.1

Molecular weight: 139.05. Radius of the Capillary tube:
0.04644 cm.
Depth: 0.1 mm.

The substance crystallises in bloodred crystals, and
melts at 85° C. At higher temperatures it is very volatile.
Above 180° C. the liquid becomes gradually darker by
oxydation and decomposition; thus the determinations were
no longer continued. (Added in the English translation.)

Veratrol: CalHs(OCH)2 Gs 2).

o | 1.345 1793.7 42.5 1.105 1062.4
29.9 | 1.209 | 1611.8 37.7 1.077 958.6
41.3 | 1.143 1524.09 35.6 1.059 915.4
64.5 | 1.083 1444.2 33.7 1.044 874.9
81.2 | 1.026 1367.9 31.9 1.029 836.2
104.5 | 0.945 1260.2 29.3 1.009 778.2
124.8 | 0.879 W123 2e 0.989 732.1
151.5 0.795 1058.2 24.4 0.967 666.6
178 | 0.719 | 958.8 22.1 0.943 614.0
196 | 0.678 904.3 20.8 0.928 584.1

Radius of the Capillary tube: 0.04777 cm.
with the measurements indicated by * if
was: 0.04839 cm.

Depth: 0.1 mm.

Under a pressure of 759 mm. the boilingpoint is 206° C. In a refrigerant
mixture it solidifies rapidly, and melts then again at + 22° C. At the boiling
point 7 will have about the value: 19.9 Erg pro cm?. The specific gravity at
25° C. was: 1.0812; at 50° C.: 1.0570; at 75° C.: 1.0325; at t?: dygo = 1.1051—
0.00095 t — 0.00000024 #2.

The temperature-coefficient of # is between 0° and 30° C. very great:3.47 |
Erg; between 30? and 150° it remains fairly constant, or only slowly decreasing |
from 2.42 to 2.36 Erg. Between 150° and 176° it decreases: 1.98 Erg, and
between 176° and 196° C.: 1.66 Erg, The curve thus is slightly concave. |

| “Molecular weight : 138.1,

625

XI
4-5-Dinitro-Veratrol : CH30.C,42(NO2),.OCH3.
Maximum Press H
5 5} 2 whee Surface Molecular
oe ta ej ten specific Surface-
Bin in mm. mer-| Ee pes gravity 4, | energy » in
5 = ony et in Dynes : Erg pro cm?.
130.8 1.349 1798.3 41.0 1.326 1268.0
144.5 1.307 1742.5 SON 1512 1236.5
167.2 | 1.236 1648.0 Sino 1.287 1183.1
182 1.178 1570.8 35.7 1.270 1136.3
194.5 P25; 1499 3 34.0 1251 1093.1
208 1.042 1389.2 S15 1.241 1018.2
Molecular weight: 228.06. Radius of the Capillary tube : 0.04660 cm.
Depth: 0.1 mm.

The compound was recrystallised from chloroform or ethylacetate; the
long, yellow needles melt sharply at 130°.5 C. On heating above ca. 160°C.,,
the liquid becomes gradually brownish. The specific gravity is at 140° C.:
1.3164; at 160? C.: 1.2948; and at 180° C.: 1.2726. At tf? C.: dgo = 1.3374—
0.001035 (£ — 120°) — 0.00000075 (¢ — 120°). The temperature-coefficient of »
increases rapidly with the temperature: between 130° and 167° C. it is: 2.32
Erg; between 167? and 182°C.: 3.17 Erg; between 182? and 194° C.: 3.45 Erg.
Above 198° C. the increase grows rapidly, to about 5.5 Erg at 208° C,,
indicating a decomposition setting in.

XII.
Ethyl-Cinnamylate: C,H; .CH: CH. COO (CH).
* :
g Maximum Pressure H 5 MENE
SO ze EE ag urface- 7 |
lon — |i. | | tension % in ne | eee:
& … |in mm. mer- | 4 gravity do | energy # in
B cury of in Dynes | Erg pro cm? 4 Erg pro cm?.
Be OKE
fe) |
Bowl 1.164 1552.6 | 36.5 1.045 | 1113.6
40.5 1.111 | 1481.5 34.8 1.032 1070.7
55.8 1.064 | 1418.5 33.3 1.018 1033.8
80 0.994 1325.2 31.0 0.997 975.9
92 0.956 1274.5 29.8 0.987 944.4
116.5 0.883 1176.9 27.5 0.966 884.1
*136 0.854 1139.2 26.0 0.953 843.5
*149.5 0.819 | 1092.1 24.9 0.941 814.6
* 176 0.732 976.4 222 0.922 736.3
*194.8 0.694 - 925.0 21.0 0.909 703.1

_ Molecular weight: 176.1. Radius of the Capillary tube: 0.04792 cm.; in the _
measurements indicated by*, it was: 0.04670 cm.
Depth: 0.1 mm.

Under a pressure of 755 mm. the liquid boils at 269° C.; at 158°C. under
a pressure of 21 mm. On cooling it solidifies soon and melts again at + 6°.5C.
The rapid decrease of the 7-f-curve above 194° C. indicates doubtless a be-
ginning decomposition. The specific weight at 25° C. is: 1.0457; at 50° C.;
1.0234; at 75° C.: 1.0018. At # it is calculated from: dyo = 1.0687—0.000934
t + 0.00000056 #.

The temperature-coefficient of » oscillates in a somewhat irregular way
round a rather considerable value of: 2.41 Erg pro degree.

XIII.

Anisaldehyde: CH30(1) . Coty. COH 4);
{
® Maximum Pressure H Mates
5 olecular
=e) gti rae Surface- :
Be in mm. mer (El Za ee, Ba
- 5 i o | energy «in
| ES cury of in Dynes Erg pro cm: 5 2
2 | oC. | Erg pro cm2,
o 1.489 | 19847 44.9 | 1.142 1087.2
24.5 1.386 1847.8 41.8 1.120 1025.4
3175 1.364 1818.9 40.9 1.114 1006.9
46.5 1.299 1741.1 39.5 1.101 980.1
61 1.268 1682.9 | 38.0 1.088 | 950.3
74.2 1.205 1609.3 36.5 1.077 919.0
90.3 | 1.159 1545.8 | 34.8 1.063 883.9
101 1.132 | 1506.8 SS 1.054 860.8
124 - 1.052 1400.8 | 31.3 1.030 811.9
140.2 0.996 | 1327.8 29.8 | 1.022 717.0
154.2 0.946 1262.3 28.4 1.009 746.9
175 0.882 | 1177.6 26.5 0.993 704.3
194.1 0.822 1095.7 24.5 0.977 658.3
210 | 0.770 1027.2 22.9 | 0.963 621.2 |
Molecular weight: 136.07. Radius of the Capillary tube: 0.04595 cm.
Depth: 0.1 mm.

|
The aldehyde boils under a pressure of 751 mm. at 246° C. At —12° it |
solidifies and melts again at + 2°.5 C.; according to WALDEN, the melting-
point is —2°C. The density at 25°C. is: 1.1199; at 50° C.: 1.0980; at 75°C.:
1.0764. In general at : d4o = 1.1421—0.000894 ¢ + 0,00000024 #.
The temperature-coefficient of » oscillates round a mean value of 2.06 Erg
pro degree.

XIV.
SOLE SO Gs; CO. C6Hs.
VT | |
Maxi Press H |

50.3 1.397 1862.5 40.0 | 1.087 | 121555

65 1.341 1787.9 38.4 | 1.075 | 111589

75 1.317 1755.9 Sica | 1.067 / 1160.0

91 1.255 1673.5 35.9 1.055 1112.8
104.1 | 1.214 1618.6 34.7 1.039 | 1086.7

121 | 1.165 1558.7 33.2 1.028 | 1047.1
130.5 1.138 1518.0 | 9285 1.021 | 1029.7

151 1.076 | 1435.7 | 30.7 1.003 984.3
171.8 | 1.015 | 1349.9 28.9 0.985 937.8
184.3 | 0.977 1303.1 27.8 0.973 909.5 |
200 0.925 1234.5 | 26.3 | 0.960 868.1

| | |
Molecular weight: 182.08. Radius of the Gail lane: 004374 cm.
Depth: 0.1 mm.

The compound was purified by repeated crystallisation from alcohol. It
melts at 48°.5 C.; its metastable form at 26°.5 C. Under atmospheric pressure
the boilingpoint is 305° C. The specific gravity at 50° C. is: 1.0869; at 75° C.:
1.0669; at 100° C.: 1.0464. At # C.: dyo = 1.1064—0. 00077(t—2 5°) — 0,0000004

(t—25°)2.
The temperature-coefficient of » has a mean value of 2.27 Erg per degree.

625

XV.

3-4-3/-4’-Tetrachlorobenzophenone:

| G,HSCh. CO. ChHGCL.
® Maximum Pressure 1
= 3 if Surface- |
5 o ; Ae tension x in |
a. in mm. mer-
5 5 cury of in Dynes Erg pro cm? |
= OMGE |
154 1.134 | 1511.7 | Spi
| 170 1.090 1453.1 Soni
186.5 1.037 1382.4 3251
201.8 | 0.993 1323.6 30.7
220 | 0.948 | 1263.7 29.3
|

Molecular weight: 319.88. Radius of the Capillary
tube: 0.04644 cm. |
Depth: 0.1 mm.

The colourless, beautifully crystallised substance
melts at 142° C,

The quantity available did not allow the deter-
mination of the specific weight of the liquid.

XVI.

2-4-2’'-4’-Tetrachlorobenzophenone-Dichloride: C,H3Cl, . CCL. CgH3Ch.

= B Erg pro cm?. 40
5 > cary ot in Dynes | ak | Erg pro cm?
A IED SEE -

156 | 1.037 1382.5 | 152 | 1.442 1270.7
170 1.002 1358.7 30.6 1.429 1253.8
185.5 | 0.994 1325.2 29.9 1.415 1233.2
199.2 0.969 1291.9 29.1 1.401 1208.2
218 | 0.943 1253.2 27.9 1.390 | 1164.5

Molecular weight: 374.80.

Depth: 0.1 mm.

Radius of the Capillary tube: 0.04644 cm.

The compound, which crystallises in beautiful, colourless crystals, melts at
140° C. At 145° C. the specific weight was: 1.4523; at 165° C.: 1.4336; at
185° C.: 1.4146. At £ C.: dyo = 1.4570—0.0009425 (¢—140°). The temperature-
coefficient of » increases rather rapidly with rise of temperature: between
156° and 170° C. it is: 1.21 Erg; between 170° and 185° C.: 1.33 Erg; between
185° and 199° C.: 1.82 Erg; and between 199° and 218° C.: 2.32 Erg per degree.

626

Molecular Surface-
Energy » in Erg pro cm?.

1330
1300
1270
1240
1210
1180
1150
1120
1090
1060
1030
1000

970

- Temperature
-5° 15° 35° 55° 75° 55° 115° 135° 155° 175° 195° 215° 235°

Fig. 1.

627

XVII.
Monomethylaniline: C,H; .NH(CH3).
v Maximum Pressure H
S Surtaae Molecular
5 ‘i Ty. en Specific Surface-
a. in mm. mer- ‚m2 | gravity do | energy » in
ES cury of in D Erg pro cm’. 5
ynes 2)
2 oC. Erg procm
Sik 1.332 1775.8 42.2 1.033 931.2
yw 1.268 1690.5 40.1 1.015 895.3
29.8 | 1.174 | 1565.8 36.7 0.985 835.9
49.3 1.106 1474.5 34.6 | 0.965 199.0
65 1.058 | 1410.9 33.0 0.952 | 768.9
80.9 1.005 1339.8 | 31.3 0.936 737.6
104.5 | 0.934: | 1245.2 29.0 0.915 693.8
122 0.879 1172.3 Pars) 0.899 | 660.9
T5254] 0.791 1055.0 24.5 0.872 605.3
178.8 | 0.713 | 950.4 22.0 0.850 552.9
195 | 0.672 895.9 20.7 0.837 525.6
Molecular weight: 107.08 Radius of the Capillary tube: 0.04777 cm.; with the
observations indicated by *, it was: 0.04839 cm.
Depth: 0.1 mm.
The substance boils constantly at 1959.5 C. under a pressure of 759 mm.

After strongly undercooling it solidifies and melts afterwards at —57° C. The |
specific weight at 25° C is: 0.9898; at 50° C.: 0.9656; at 75° C.: 0.9420; at
t© C,: dy> — 1.0146—0.001004 ¢ + 0.00000048 #?.

The temperature coefficient of » is fairly constant; its mean value is:
1.90 Erg pro degree.

para-Nitro-Monomethylaniline : C %q.(NACH3)1). NO2(4). |

2 | Maximum Pressure MH |

155.2 1.525 2032.1 | 46.3 1.20) sk “Iets
170 1.469 1958.2 | 45.2 1.189 | 1147.5
186 1.440 1919.7 43.7 5 UES
199 1.373 1830.3 | 41.5 1.165 1070.5
210 1.324 1765.7 | 40.1 1.156 1037.2
Molecular weight: 152.08. Radius of the Capillary tube: 0.04644 cm.

Depth: 0.1 mm.

The yellow crystals, which possess a beautiful pink lustre, melt at 152°C. |
Above 190° the liquid becomes gradually darker tinged; therefore the mea-
surements Were no longer continued. The specific gravity at 160° C. was:
1.1968; at 180° C.: 1.1807; at 200° C.: 1.1643. Att C.: dgo = 1.2049—0 0008125
(¢— 150°). The temperature-coefficient of » increases very rapidly with rise
of temperature: from 1.3 Erg at 155° C. to 3.3 Erg at 210° C. Evidently the
above mentioned decomposition must be considered the cause of this
phenomenon.

XIX.

Nitrosomethylaniline : C,H;.N(NO)CAz.

Molecular weight: 136.08.

|
v Maximum Pressure 7
BY Seen Molecular
je 5 (ry ri ihe Elan Specific ‚__Surface-
a> | in mm.mer- | | 2 | gravity do | energy win |
ENE cury of | in Dynes Erg pro Cmt, 4 2
& OC. | Erg pro cm2,
fe} |
0) 1.439 | 1919.1 | 45.7 1.143 1106.0
* 730.47 | 1.356 1808.1 43.0 ite ig 1056.8
46.9 | 1.314 | 1752.4 41.4 1.099 1028.5
58.6 | 1.280 1707.0 | 40.3 1.092 1005.4
85.9 1.190 1587.1 37.5 1.068 949.6
103.3 182 1508.6 35.6 1.054 909.4
117.6 | 1.079 1438 .3 33.9 1.041 873.2
127.4 | 1.048 1397.0 32.9 1.033 851.8
|

Radius of the Capillary tube: 0.04839 cm.; in
tle observations indicated by *, it was: 0.04867 cm.

Depth: 0.1 mm.

The substance boils constantly at 128° C. under a pressure of 760 mm. In
a mixture of ice and salt it solidifies, and melts afterwards at + 13° C.
Above 125° C. the liquid becomes gradually brownish by slow decomposition.
The specific gravity at 25° C. was: 1.1213; at 50°C. : 1.0995; at 75° C.: 1.0779.
At # C.: dyo = 1.1430 — 0.000868 ¢.

Originally the temperature-coefficient of » increases with rise of tempera-

ture from 1.63 Erg at 0? C. to 1.99 Erg at 30° C. Then it remains fairly

constant at 2.27 Erg pro degree.

PAD ESES

Diisobutylaniline: C;H;. N[CH). CH (CH3)o],.

v Maximum Pressure H

= WAE | |

Lie (1.118) (1490.0) | _ (87.0) 0.949 (1332.6)
OREN 1.049 1398. 1 | 32.8 0.932 1195.6
2600 0.959 1278.5 29.9 0.909 1108.2
40.7 | 0.908 | 1210.3 28.3 0.899 1056.7
Lala 0.864 | 1151.9 26.9 0.885 1015.0
80.2 | 0.800 1066.6 24.8 0.866 949.3
92.5 | 0.700 1026.7 23.9 0.860 919.1
115.5) | 0.711 947.4 2201 0.847 858.6

~ 135.3) | 0.678 903.6 20.5 0.836 803.4

*149.2 | 0.642 856.6 19.4 0.832 762.7

NOOI 0.577 | 769.2 17.4 0.823 689.1
*195.8 | 0.530 | 706.6 15.9 0.818 | 632.2

Molecular weight: 205.11.

Radius of the Capillary tube: 0.04792 cm. ;

in the measurements indicated by *, the
radius was: 0.04670 cm.

Depth: 0.1 mm.

The substance boils under a pressure of 21 mm. at 146°C. It remains in
liquid condition down to — 20° C., but is then very viscous; at —79° C. it
becomes glassy, but does not crystallise. Under atmospheric pressure the

liquid boils at 250° C. The specific gravity at 25° C.

is: 0.9099; at

50° C.: 0.8901; at 75° C.: 0.8725. At f° in general: dgo = 0.9319—0.000924 ¢ +

+ 0.00000176 £.

The temperature-coefficient of » is in the beginning (below 41° C.) almost .
3.43 Erg, afterwards very constant: 2.73 Erg pro degree. It is therefore rather
great, also at higher temperatures.

XXI.

Diphenylamine: (C,H;), NA.

v Maximum Pressure 1

5 Molecular
2G Surface- Specifi ae

Ze in mm Sion ut gr fe a A
a . mer- 5 avi p

5 = cury of in Dynes Ere Provan cy Erg pro cm2,
& ORE

60.5 1.284 1710.7 38.6 1.054 1143.3
76.8 1.230 1639.5 37.0 1.039 1106.4
95 iz 1570.4 S572 1.025 1062.1
114.2 1.103 1472.8 33.4 1.010 1017.8
136 1.041 1389.4 31.4 0.993 967.7
155 0.991 1321.2 29.7 | 0.980 923.4

Molecular weight: 169.89.

Radius of the capillary tube: 0.04595 cm.

Depth: 0.1 mm.

The substance boils at 179° C.; under a pressure of 12 mm. The melting-,
point is 54° C. Above 150° C. the liquid is soon coloured darkly; the mea-
surements therefore were no longer continued. The density at 75° C. was:
1.0412; at 100° C.: 1.0210; at 125° C.: 1.0022. In general at # C.: dyo=

= 1.0628—0,.000892 (£—50°) + 0.000001 12 (t—50°)?.

Dibenzylamine: (C,H; CH). NH.

Zon Cras

measurements

v Maximum Pressure H Wee reser
EG es Surface- Specifi cs ae Bs
ge in mm. mer Renpioim sage | Reels
ise 5 - al o p
EE cury of in Dynes | Erg pro.em’, | = Erg pro cm.
= ce |
o
—18.5 1.413 1883.6 43.3 1.060 1410.6
0 1.340 | 1787.8 41.1 | 1.045 1351.7
25.1 1.254 | 1683.5 38.5 1.024 1283.5
41.5 | 1.204 1603.9 36.7 1.011 1234.0
56 1.158 | 1543.7 35.4 0.999 1199.6
71 1.117 | 1489.2 34.1 | 0.988 1164.3
84.8 1.071 | 1437.3 Son 0.977 1138.4
100 1.039 1385. 1 31.7 0.963 1101.0
“116 1.026 1367.9 30.3 0.950 1061.9
* 130.5 0.977 1305.1 28.9 0.938 1021.5
*146 0.931 1242.6 2155 0.925 981.1
*162.5 0.900 1200.9 26.2 0.912 943.6
*176 0.853 1135.9 24.9 0.901 904.0
“196.8 0.803 | 1069.2 23.4 0.884 860.4
*209.5 0.772 1024.6 22.4 0.873 830.6
*228 0.713 949.4 20.7 0.858 716.4

0.04529 cm.
Depth: 0.1 mm.

the

| Molecular weight: 197.10. Radius of the Capillary tube: 0.04676 cm.; in the
indicated by *,

radius was

Under a pressure of 19 mm. the amine boils constantly at 186° C. At
— 70° it becomes a transparent glassy mass, but does not crystallise. The
| specific gravity was volumetrically determined: at 0° C. it was 1.045; at

1.024; at 50° C.: 1.004. Generally: ¢° C.:d4o = 1.045—0.00082 ¢.

The temperature-coefficient of » is oscillating round a mean value of : 2.53 Erg
pro degree Celsius.

Molecular weight

XXIII.

Azoxybenzene: C,H;. NO. C;Hs.

v Maximum Pressure H |
2G 2 ive Surface: | Molecular
Eon | RL | tension y in | sane | Surface-
ae , - ; Bre OEZ vity dyo energy » in
eo cury of in Dynes | SP | Erg pro cm?.
= OPKGS |
55.8 1.296 1725.4 39.3 1.133 1228.8
70.6 1.257 1676.0 38.3 1.121 1206.1
85 1.219 1625.2 Snil 1.110 1176.0
100 1.181 1579.9 35.9 1.098 1146.3
ei Wa) 1.180 1572.0 34.7 1.087 Tits ea
*130°5 1.139 | 1519.0 BOLD 1.074 1085.5
T4550 1.085 | 1448.8 all 1.063 1047.3
“162 1.050 | 1400.0 30.8 1.050 1013.2
*176 1.017 | 1355.4 29.7 1.039 983.9
*196.9 0.950 | 1265.5 2 1.022 927.7
*211 0.906 | 1210.1 26.6 1.011 | 897.3
*226 0.833 | 1110.5 | 24.2 1.000 | 822.4

: 1984. Radius of the Capillary tube: 0.04676 cm.; in the

measurements indicated by *, this radius was:
0.04529 cm.

Depth

: 0.1 mm.

At 36° C. the substance melts; the liquid is of a clear yellow colour. The
specific gravity at 50° C. was: 1.1373; at 75° C.: 1.1177; at 100° C.: 1.0982.
In general at 7° C.: dyo = 1.1764—0.000782 ¢.

The temperature-coefficient of » increases gradually with rise of temperature:
between 56° and 71° it is: C. 1.53 Erg; between 71° and 100° C : 1.96 Erg;
between 100° C. and 162° C.: 2.16 Erg: between 162° and 211° C.: 2.31 Erg
and above 211°C. increasing very rapidly, up to about 4.98 Erg per degree at

226° C., decomposition evidently setting in.

XXIV

z-Dihydrocampholenic Acid: C; He(C/3)3.CHo. COOH |

0.607

v Maximum Pressure 1 |
5 G = | Surface-
So Td tension / in
a. n : - 2
5 = cury of in Dynes | Erg pro cm’.
i ORT: |
|
oes Lesa) (2335.8) | (64.4)
0 1.102 1468.9 | 34.3
25 1.008 1344.7 | 31.4
ih, sects 0.960 1280.5 | 29.9
54.1 0.915 1220.5 28.5
1s 0.861 1147.5 26.8
hey I 0.813 1083.8 25.3
US 0.758 1010.7 23.6
134.3 0.723 963.6 22.5
150.5 | 0.684 912.2 2153
175.5 0636 41:9 | 19.8
800.4 | 18.9

does not crystallise.
is already very viscous.

The quantity of the liquid was too small to
permit the determination of its specific gravity.

Molecular weight: 170.14. Radius of the Capillary

tube: 0.04670 cm.
Depth: 0.1 mm

| At —79° the liquid becomes a glassy mass, but

At — 20° and 0° C. also it

631

XXV.

Aethyl-z-Dihydrocampholenate: (;¢(C43)3.CH2. COOC,Hs.

v Maximum Pressure H | | |
By See | Molecular
5 3 TN | | Venn Se are | Surface-
a. | k - 3 > | gravity do | energy win
5 =| any ot | in Dynes | En (es | : | Erg pro cm?2.
| |
o
Al 1.020 1359.9 | 31.0 0.961 1082.0
| On 0.964 1284.8 29.3 0.945 1034.2
2053: 0.893 | 1190.6 Zell 0.924 971.0
40.4 0.859 | 1145.2 26.0 0.912 939.8
54.1, 0.822 1095.9 24.9 0.901 907.3
75.5 | 0.768 1023.9 2332 0.884 856.2
95.5 0.714 951.9 2155 0.869 862.5
115.2) 0.673 | 896.2 20.2 0.852 764.0
134.8 0.620 826.5 18.6 0.837 T11.9
153 0.577 | 769.2 ies 0.822 670.2
176.1 0.517 689.5 15.4 0.804 605.4
194 | 0.456 | 5 0.789 537.4

|
|

f=?)
Oo
i)
de)
—
w

Molecular weight: 198.18. Radius of the Capillary tube: 0.04670 cm.
Depth: 0.1 mm.

Under a pressure of 20 mm. the colourless liquid boils at 147° C. At — 79° C.
it gets turbid and very viscous, but does not crystallise. The specific gravity
AERON is 0:9445) sat. 25°. Cy: 0/9250! Tats o0 RER 0.9045 Alwi> CG. -va4o—
= 0.9445 — 0.0008 f.

Below 176° C. the temperature-coefficient of » is relatively constant, with a
mean value of: 246 Erg pro degree.

41
Proceedings Royal Acad. Amsterdam. Vol. XVIII.

Molecular Surface-
Energy » in Erg. pro cm

„Temperature

140° 160° 180° 200° 220° 240

20° 0 20° 40° 60° 80° 100°120°

Big:

633

XXVI.

Furfurol: «-C,H;0. Ga 4

|
ay Maximum Pressure 1 |
Ea Ss Molecular
9 7] Kee Specifi Surface
5 : in mm. m kenbign: in poe 4 | BES in
Es in * Ere ° p
2 cury of | in Dynes Erg provem?, a Erg pro cm2. |
vo
= ONG:
*_22° 1.437 1915.8 45.7 1.211 921.8
0 1.368 1824.5 43.5 1.185 869.8 |
29.9 1.289 1719.3 40.7 1.151 806.3 |
46.8 1.214 1618.5 38.3 1.133 745.2 |
58.3 1.171 1561.2 37.0 1.119 713.9
86.5 1.072 1429.0 33.8 1.089 645.4 |
102.3 1.017 1355.5 32.0 1.074 599.3
117.7 0.961 1281.2 30.2 1.060 557.4 |
|

Radius of the Capillary tube: 0.04839 cm.; in the
observations indicated by *, it was: 0.04867 cm.
Depth: 0.1 mm.

The liquid boils at 162° and 761mm. mercury. The substace crystallises in
a bath of solid carbondioxide and alcohol, and melts then again at —31° C.;
according to WALDEN at —36° C Above 100° C. the liquid is rapidly oxydized,
and gets a brownish colour. At the boilingpoint, the value of „can only differ
slightly from: 25.4 Erg pro cm?2. The specific gravity at 25° C. was: 1.1563;
at 50°C.: 1.1287; at 75°C.: 1.1023; at f°: dgo=1.1851—0.001176 £4-0.00000096 £.

The temperature-coefficient » is almost constant, and has the mean value:
2.70 Erg pro degree; it is rather high.

Molecular weight: 96.03.

XXVII.
Thiophene: C,H,S.
v Maximum Pressure H
Elbe ne Molecular
Bo Tee : race Specific | Surface- |
ae in mm. mer- | ension x IN | gravity do | energy « in |
Es cury of in Dynes Erg pro cm? | Erg pro cm’,
2 oC. |
"19° 1.134 1512.3 | 36.0 110 | 64.6
ie 0 1.057 1409.5 | Sono 1.087 608.3
29.9 0.939 1252.3 | 29.5 1.051 | 547.8
47.3 0.874 1165.5 | 27.4 1.032 | Dim
58.7 0.834 1111.8 26.1 1.006 499.0
87 0.732 975.4 | 22.8 0.987 441.5

Radius of the Capillary tube: 0.04839 cm.; in the
measurements indicated by *, this radius was:
0.04867 cm.

Depth: 0.1 mm.

The liquid boils constantly at 87° C. under a pressure of 770 mm. In a
bath of solid carbondioxide and alcohol, the substance crystallises, and melts
at —29°.8 C.; according to TsAKALOTOS the meltingpoint is —37°.1 C. At
the boilingpoint x has the value: 22.8 Erg pro cm?.

At 0° C. the specific gravity is: 1.0873; at 25°C.: 1.0573; at 50° C.: 1.0285. |
At £ C.: d4o = 1.0873—0.001224 ¢-+- 0.00000096 #2, |

The temperature-coefficient of » is fairly constant, with a mean value of: |
1.90 Erg pro degree.

Molecular weight: 84.10.

41*

634

XXVIII

Piperidine: C;H\) > NH.

v Maximum Pressure H |
En Siere. Molecular
os yl | Ae | Specific | Surface-
a. in mm. mer- | “2 | gravity do | energy „in
En cury of in Dynes | EAE PICs 5 Erg pro cm?
o 0° C | |
= D
| |
le | | À
“19 1.041 1388.6 | 32.8 | 0.900 | 680.8
. 0 0.973 1297.7 | 30.6 0.882 643.7
29.4 0.876 1168.0 27.1 0.855 582.0
48 0.813 1084.3 | 25.1 0.838 546.3
64.5 0.753 1004.8 | 23.2 0.823 | Site
80.9 0.703 937.8 | 21.6 0.808 481.7
104.5. 0.628 | 837.4 19.2 0.786 | 436.2

Molecular weight : 85.10 Radius of the Capillary tube: 0.04777 cm. ; in the

Depth: 0.1 mm.

Under a pressure of 760 mm. the base boils at 108° C. On cooling it crys-
tallises, and melts afterwards at — 9° C.; according to MASCARELLI this tem-
perature would be — 13° C,; at the boiling point zis about: 19.7 Erg pro cm?
The specific gravity at 0° C. is: 0.8820; at 25° C.: 0.8586; at 50°C. : 0.8359.
At fe C.: dye = 0.8821 — 0.00092 ¢. The temperature-coefficient of » is fairly

constant: its mean value can be fixed upon 1.98 Erg pro degree.

Molecular Surface-
Energy u in Erg pro c.m?.

Temperature
“ 40° 60° 80° 100° 120°

Fig. 3.

635

$ 3. In connection with these data we can make the following
remarks.

The substitution of the bromine in bromobenzene by iodine, makes
the value of u at the same temperatures increase, just as we formerly
observed with the substitution of chlorine by bromine in the
chlorobenzene. This behaviour is evidently opposite to what was
formerly stated in the case cf the molten halogenides of the alcali-
metals. In agreement with our previous experiences, the substitution
of H in the benzene-nucleus by CH,, makes the value of u increase
(bromobenzene and o-bromotoluene); and the same holds good for
the substitution of H by a NO,-group, by halogenides, or by the
azoxy-radical; in general by substitution of HT by radicals built up
from strongly electronegative atoms. This seems to be a general
rule. An analogous phenomenon is observed, if aromatic hydrocarbon-
radicals substitute the H-atoms: a comparison of the /eay/-,
heptylamines with diphenyl-, and dibenzylamine makes this very
evident, and just in the same way a comparison of acetophenone
and benzophenone. The w-t-curve for ethylcinnamylate lies beneath
that for methylcinnamylate, and the same is the case with mono-
methylaniline in comparison with aniline itself. On the contrary, the
value of u for aniline is very much increased by substitution of the
H of the amino-group by two dsobutyl-radicals.

The addition of hydrogen in pyridine, this thus being transformed
into piperidine, makes the g-t-curve of the former compound lle
for thiophene it lies beneath that for piperidine.

Some curves for amylamines are reproduced here also for the
purpose of comparison. This is connected on the one hand with the
substitution of the atom \S/ in thiophene by the combination:

—N = CH—, and perhaps on the other hand with the presence of
the unsaturated C-atoms in pyridine, in comparison with those in
piperidine. However it must be remarked here at once, that evidently
this last may not be considered a general rule, as for instance the
curve of benzene lies lower than taat for cyclohexane. Certainly
a number of constitutive influences are superposed one upon the
other, thus prohibiting the statement of the precise connection between
the value of u and the degree of saturation of the C-atoms in this
vase, to a more or less degree.

We intend to finish here untill a later date the investigation of
organic compounds with the series here described.

University Laboratory for, Inorganic
/ Ue ‘
Groningen, August 1915. and Physical Chemistry.
heeds) 5 ! ¥

636

Physics. — The second virial coefficient for rigid spherical molecules,
‘whose mutual attraction is equivalent to that of a quadruplet
placed at their centre’. By Dr. W. H. Kersom. Supplement
No. 39a to the Communications from the Physical Laboratory
at Leiden. (Communicated by Prof. H. KAMERLINGH ONNES).

(Communicated in the meeting of September 25, 1915).

$ 1. This Communication forms a continuation of the investi-
gation started in Suppl. N°. 24 (April 12, these Proceedings June
12), the aim of which is to derive, on different suppositions concern-
ing structure and mutual interaction of the molecules, the first
terms in the development of the equation of state into ascending
powers of v—! as functions of the temperature, in order to compare
them with the available experimental material. It is obvious that
in this problem it is indicated to proceed step by step from the
simplest to more complicated suppositions.

In Suppl. N°. 246 § 6 the second virial coefficient, i.e. B in the
equation of state:

Jee AG)
Allo tte) zhe ie GEAN

was derived for rigid spheres of concentric structure, which carry
a doublet at their centre, or whose mutual attraction is equivalent
to that of such doublets. In a following paper it will be shown
i. a., that the limitation to molecules of concentric structure, observed
there, can be omitted as far as concerns the derivation of B.

In Suppl. N°. 25 (Sept. °12) I then showed that the way in which
the second virial coefficient of hydrogen between — 100° and + 100° C.
depends on the temperature agrees with that which was derived
for doublet-molecules of that structure.

Meanwhile it has, however, become evident especially by DeBue’s *)
investigation concerning dielectric constant and refractive index, that
the molecules of the diatomic elementary gases do not possess a
moment such as that of a doublet. The next step in the theoretical
development of the equation of state now seems to be, that the
next term of the development of the attractive potential outside the
spherical molecule into spherical harmonics, 1. e. that of the degree
3, is considered to be present alone. The corresponding surface
harmonie of the second order reduces to the zonal harmonic of the
second order for diatomic molecules, which in this paper as in Suppl.

1) Cf. P. Desise, Physik. ZS. 13 (1912), p. 97. W. CG. Manperstoot, Thesis for
the Doctorate, Utrecht 1914, p. 56. N. Bour, Phil. Mag. (6) 26 (1913), p. 866.

637

No. 24 we treat as bodies of revolution as regards their fields of
force. So we are led to the problem to deduce the second virial
coefficient for a system of rigid spheres, whose attraction is equi-
valent to that of a quadruplet with two coinciding axes, and which
is obtained when two doublets are placed along the same line with
two homonymous poles towards one another and their distance
approaches zero with maintenance of a finite quadruplet-moment *).

We place ourselves in this communication on the standpoint of
classical mechanics. The quantum theory only intervenes in so far
as the fact that according to that theory the rotations of a diatomic
molecule about one of its principal axes of inertia in consequence
of the smallness of the corresponding moment of inertia is not
influenced appreciably by the heat motion, is accounted for in our
treatment according to the principles of classical mechanics by
considering such a molecule as a body of revolution. We do not
consider here an influence, as given by the quantum theory, on the
rotations about the two other principal axes of inertia nor a possible
influence on the translational motion. If perhaps the bearing of the
resulis obtained in this paper is limited by this circumstance, still
they are in any case applicable to molecules for which these two
principal moments of inertia and eventually the molecular weight
in connection with the temperature region which is to be considered
are sufficiently large.

§ 2. As we explained in § 1 we will consider here the molecules
as rigid spheres of concentric structure *), with at their centre a
quadruplet which consists of two doublets whose axes lie in the same
line and have opposite directions, and which approach each other
indefinitely preserving, however, a finite quadruplet-moment.

For calculating the second virial coefficient we have again to
consider, just as in Suppl. N°. 24 a and 5, pairs of molecules which
at a given moment lie in each other’s sphere of action. The mutual
position of a pair can be specified in a way corresponding to that
followed in Suppl. N°. 245 § 6 in discussing the doublets, viz. by
the following coordinates (Fig. 1):

1s". the distance 7 between the centres;

1) J. CG. Maxwett. Electricity and Magnetism. 3rd ed. Vol. I, p. 197.

2) This expression is meant to indicate that the density is uniformly distributed
over concentric spherical layers. Yet the following deduction of B is also valid
if the density is distributed symmetrically about an axis, if this axis coincides
with the axis of the quadruplet. The result is, as far as regards B, even more
general and is also valid, if the density is distributed arbitrarily.

638

2.4. the angles 7, and @,, which the axes of the quadruplets make
with the line which joins the centres. For a closer definition of
these angles we choose in each molecule arbitrarily one of the two
equivalent directions on the axis as the positive direction; we choose
further as the positive direction on the line which joins the centres
the direction from the molecule whose position is determined by
the angle considered, towards the other molecule; 6, and 4, are
then the angles, from O to a, between the positive directions;

3, the angle p betweeh two half-planes each of which contains
the positive direction of the axis of one of the quadruplets and the
line joining the centres. This angle is further specified as in Suppl.
N°. 245 § 6, and goes from O to 22.

LE
Ko HETE .
Oe |
VON
vi 17
pn eae il

Fig. 1.

The method of Suppl. No. 245 $ 6 may then be applied imme-
diately to the problem dealt with here. It gives for the specific
heat at constant volume in the AvoGapro-state, assuming that the
spheres are smooth:

YA="/, B,
and for the second virial coefficient :
Bings — P) zot eee
where:
n= the number of molecules in the quantity of gas for which

the equation of state is derived,
6 = the diameter of the molecule and

DO TT AT «
oe
DRE i (e CDI) 9? sin A, sind, dr dO, d0,dp . . (3)

7000

In this formula
1

Mn
k is Pranck’s well known constant, whereas ws, is the potential
energy of the pair of quadruplets indicated by the index 1, when
the potential energy is put =O for r=o. Its value is given by:

h (4)

639

4p, = fl — 5 cos? 6, — 5 cos? 8, — 15 cos” O, cos” O, +
+ 2 (4 cos 6, cos 0, + sind, sin 0, cose), - - - + (9)

if u, represents the moment of the quadruplet.
We introduce:

3 a :
eee ee a
Nie Sera eo edie anny ee wea (0)
then v= the potential energy, when two molecules are touching

each other, the axes of the quadruplets being at right angles to
each other and to the line joining the centres.
We put further
W — 1—5 cos? 6, —5 cos? O,—15 cos? 0, cos” A, + 2 (4 cos O, cos O, +
+ sin @, sin @, cos p)°,

Or:
USAC (Ome a oe TD)
if
A = 2 (1-8 cost 0) (1 —3 co 0.) |
B=16 sin A, cos B, sin @, cos A, NS)
STENS |
so that

0° q -
up, = Vv — WP.
>»
Developing ¢~/“,—1 into a series of ascending powers of hug.
and integrating in (3) according to 7, we obtain‘):

tm 7 2
aad

P=to J (—1)"——— „oef if Wr sin 0, sin Ô,dÔ dO,dp . (9)

n=l Dn =) ni
000

If for the sake of brevity we write [Wv] for the integral in (9)
and correspondingly :

[Ar B2aCr] = | [arBucr sin Ó, sin 0, dé, |
on (10)
[ cos” op cos’ 2p] = | cos’ pp cos’ Zp dp,

Bee ie that [cos?-1¢~]—=0, |cos?12p] = 0, [cos?—1ep cos” pp] = 9
/ and 7 iu Gail positive integers, we find:

1) The quantities 7”, p, q.7,8, which we introduce temporarily in this § have a
meaning different from that in the other part of this paper and in an No. 24.

640
| u] zZz In LA] +
ms i [A"—2 B?] [eos?ep] + fe Nes C?] [cos 20] +

oe
8 ‘ Ad
‘ [A"-4 B*] [cost g] + 5 [A + B?C? |[ cos* gos? 2 q |+
n 4\_ :
is, a Lap
n\/9 MD n\(5 ned {
5 JA ENE
n N n\/6
ae « Jaren [cos*ip| + )G Jas B* C? | [eos* peos* Zip] +
)
aie 8 . An—6 B? C*] [cos? p cos* Ap] +
5 À [Z ] [eos® p cos* 2] +
n OR .
6 6

tr )
If we write:
A=2A, A,, A, = 1—3 cos? 6,
B= WG (B13. B= awd. cos, | (12)
C= CG. Cy SS sm iG,

then
[Ar Bo Cr] = tal [Ap Bu Cr]. 2 - - (13)
where the square brackets in the second member now refer to 6, only :
ae iH 5 vendor) dale
a
0
One finds

qr)!
APB UC] = ett anand |
(2p | + 4q+2 r+ D(2p + 4q-+-2r—1).. (2 2q + 1

- (14)
nee +2) ED
1/ pt+qt+r (p tqtr)( pt@atr-l)
from which formula also the special cases: [4,”], [4,”B,2¢] ete.,

may be derived.
Of these expressions [AP] can be calculated more easily from
the following relation:
9Dp--1

AP] = (IP Slik + [Adi seer eh NE
LA] nn ee

641

Further :

2 1
[eos?2 cp] = [cos?4 Zp] = 2a . ( A =
! q) 3

2q
(on) (oye d
[Leos?tgpeos?r" 2p |=2.2 ke >} j \5 { a HOC a - (16)
A vom q \f2r q \ 1 (ar a ") El
EE ON ONE

These formulae Ms ns

me le, RAe ca laseren
ER la ot Pt grs & zo26s CO +
(17)
40,2360 (hv) —0,1355 (hv)? + 0,1019 (ho)* … | \
so that

B=}n.4 xo* {1 —1.0667 (hv)? + 0.1741 (hv)? — 0.4738 (hv) + ae as)
+ 0.6252 (hv)’ —0.2360 (hv)® + 0.1355 (hv)’—0.1019 (hv).

$ 3. For the lower temperatures, e. g. at the Boyin-point (the
temperature at which BO), this series converges very slowly, so
that for them the terms given above are not sufficient.

At the inversion point of the Jouru-Kenvin effect for small densities
the term with (Aw) in (18) amounts to about 7/,,, of B, (= Ow),
the value to which B would approach for 77=o, if the equations
found here remained valid. Hence for the inversion point just
mentioned and for higher temperatures, the terms given above may
be considered to be sufficient, assuming that none of the following
terms is unexpectedly large. At 0.75 Tij» (eo) the above mentioned
term amounts to '/,, of 4,, so that on the same assumption we
may reckon upon an accuracy of about 1°/, (of B).

I have not sueceeded in deducing a series which is more suitable
for lower temperatures.

Just as for the (spherical) molecules, which bear a doublet at
their centre, so also for the quadruplets the term with 7~! is absent
in the series for B. Whereas, however, for the doublets all odd
powers are absent, here the higher odd powers appear in the series,
although the coefficient of 7 is still relatively small *):

Above 3 Tin» (e=o) with an accuracy of '/,,,, and above 1.2 aia)
with an accuracy of */,,., the first two terms in (18) are sufficient.
The dependence of B on temperature then agrees with the suppo-

1) The questions under what conditions in general the term with Tt, as also
the higher odd powers disappear from B. will be dealt with in a following paper
(Suppl. No. 390).

642

sition that in van DER Waars’ equation bw is independent of fand
aw is proportional to 7’-!. The latter assumption was already made
by Crausius, with a view to the vapour pressures of carbon dioxide.
A relation agreeing with

p=5,(1+ 3). a

(with a negative value of 4,) was also found by D. bertarior’)
to be suitable to represent the compressibility at densities near the
normal. In these investigations the approximate validity of that
relation was extended to much lower temperatures than those
indicated above. It will appear in the next $, that equation (18)
actually agrees with an equation of the form (19) down to an
appreciably lower temperature than those indicated above.

§ 4. For the purpose of a closer comparison between the second
virial coefficients of quadruplet-bearing molecules and of doublet-
bearing molecules we shall introduce as a reduction temperature a
temperature which is specific for each gas*). According to what
was said in § 3 about the region in which equation (18) is applicable
the inversion temperature of the Jourr-Kervin-effect at small densities
is a suitable one for this purpose. This temperature is found from
the relation:

db
=I = = (()-
an
or
pig ees)
ae ” a (hv) ro

Equation (18), and Suppl. N°. 245 equation (59) give respectively,
for quadruplets :
hviny(g=0) — 0.576,
for doublets :
hing) = 0.969.

If we’ call —-——- = fino) it follows further, that:
inv(e=0)

for quadruplets:

B = B,, {1 — 0.3539 tu) + 0.03827 fo) — 0.05215 te) + (20)
—5 - — 5 —7 A ee —és

+ 0 03964 fa) — 0.00862 tinny + 0.00285 fv) — 0.00123 € mn)

1) D. Berruezor. Trav. et Mém. Bur. Internat. des Poids el Mesures, t. 13 (1907).

2) Cf. H. KameruineH Onnes and W. H. Keesom. Die Zustandgleichung. Math.
Enc. V 10. Leiden Comm. Suppl. No. 23 § 28a.

643
for doublets :
B= B,, {1 — 0.3130 tiny — 0.01175 te) — 0,00044 timmy...) (21)

Table I contains some values calculated from (20) and (21)
respectively.

TABLE I.
B ae ae
T | /Bo

inv. C=O | quadr. doublets | v.p.WaaLs Se
| ERTHELOT

ie 00e, ils AIS 0.404 0.333 | 0.407

ee hg 0.660 | 0.675 0.5 | 0.667

1.5 0.847 0.859 0.667 0.852

2 | 0.914 | 0.921 0.15 | 0.917

3 | 0.961 | 0.965 0.833 | 0.963

4 | 0.978 0.980 0.875 | 0.979

The table also gives some values calculated from the equation
—1
Bi Ba Np 06 Ler PEREN TE
le ©} ‚1 0,5 fâno) ’ ( )
which follows from vAN DER Waars’ equation with constant aw, bw
and Ry, and some values calculated from the equation

BB {lb} en EEE

which is obtained from Craustus’ and BerrHeLor’s assumption:
aw- T-'.

As appears from table I, the difference between the values of B
for quadruplets and for doublets is small in the temperature region
considered here, i.e. above 0.75 Tin,(2=o0), viz. smaller than 1°/, of
ee or 4,3%, of B.

Hence the circumstance of a diatomic molecule possessing or not
possessing a doublet, has but a small influence on the dependence
of B on temperature in this temperature region. This leads one to
expect that in the considered region of temperature and density the
equation of state of diatomic compound gases and that of diatomic
elementary gases will not be easily distinguished from each other.

From table | it appears further, that the values of 5 for quadruplets
and for doublets both deviate very little from equation (23), viz.
over the whole region above 0.75 Tin»¢,—0) less than 0.6°/, of the
value of B, and less than 1.5°/, of the value of B.

644

$ 5. Hydrogen. Values of B for a diatomic gas in the tempe- _
rature region for which the terms given in (18) and (20) are sufficient
are only known as yet for hydrogen. For this substance in view
of its small molecular weight one has to pay particular attention
to a possible modification of the molecular translational motion
according to the quantum theory. According to it a correction
ought to be applied to the values of pv, before the equation of state
in the form (1) would be applicable. As that correction depends
on other powers of v than occur in the second member of (1), a
conclusion about that influence might be drawn for the temperature
region to be considered here from the agreement or disagreement
between the values of B calculated according to (1) without a
quantum-correction from measurements at higher pressures and from
such at densities near the normal one. The available experimental
material '), however, does not yet enable us to apply this test.
Meanwhile as mentioned above we will disregard a possible influence
for the temperature region under consideration. We shall also leave
out of account the possible influence on the value of the second
virial coefficient of those deviations from the equipartition laws,
which according to Euckrn’s measurements of the specific heat are
shown by the rotations about the axes at right angles to the line
joining the atomic centres, at least in the lowest part of the tem-
perature region under consideration.

In Suppl. N°. 25 (Sept. °12) it was shown that the dependence of
B on the temperature for temperatures above —100° C. agrees
with that which was derived for spherical molecules carrying a
doublet. From the agreement found in § 4 between the latter and
that for spherical molecules carrying a quadruplet in the temperature
region specified there it follows immediately that the values of B
for hydrogen in the temperature region under consideration ought
to be found in agreement with the dependence on temperature which
we derived for quadruplets.

To test this B/Bi» for hydrogen was represented in a diagram as
a function of 7/Tin~2—0) and compared with the values calculated
from (20) and (21) respectively. The values of B for hydrogen at
—140°, —104°, 0° and 100° C. were taken from KAMERLINGH ONNES
and Braak?), that for B at 20° C. from ScHaLKwIJK *) and from
KAMERLINGH ONNES, CROMMELIN and Miss Sip *). The temperature of
N 1) Cf W. J. Haas, Comm. NO. 12%a (April 12) § 4.

2) H. KAMERLINGH ONNES and C. BRAAK, Comm NO. 100 « and b (Nov. '07).
3) J. C.ScHALKWuRK. Thesis Amsterdam 1902. p. 116, also Leiden Comm. N°. 78 p. 22.
4) H. KAMERLINGH ONNES, C. A. GROMMELIN and Miss E. J. Sum. Comm. N°.
1465 (June 715).

645

the inversion point for the Joure-KerviN effect at small densities
(200.6° K.) was taken from the calculations by J. P. Darron’).
_ Bin the value of B for the just mentioned temperature, was calcu-
lated from the special reduced equation of state for hydrogen,
communicated in Comm. N°. 109a $ 7.

In this manner no sufficient agreement was, however, obtained,
neither with the quadruplet-equation, nor with the doublet-equation ;
the value for 100° C. deviates pretty considerably from the calcu-
lated curves.

This is to be ascribed chietly to the value, which is assumed for
Fine) The special equation of state used for the calculation of
ANP =0) appears to give a somewhat less perfect agreement with
experiment in this region than elsewhere, and this fact has a con-
siderable influence on the result obtained for Tea) in consequence
of the circumstance that for the determination of Pio, the value
of dB/dT is of great importance.

A value of Tio) was therefore subsequently deduced with the
aid of an equation which shows a good agreement in this region
of temperatures; for this purpose an equation of the form (19) was
chosen, and its constants were derived from the experimental data.
From the results of KAMBERLINGH Onnes and BRAAK we obtained:
Me ‚=194.5, Bx, np, = 0.000465.

Fig. 2 shows what agreement is

ij EN | pst “1 obtained with these values of the
Se a set | constants *). For comparison the
4 (eee i, curve following from vaN DER Waats’

Stuonners, | equation with constant aw, bw and

x DOUBLETS

|
L ~ 4 5
| | _ Ry is also represented.
as E | It appears now that, as expected,
a)

for the temperature region under
consideration the values of 5 for

Fig. 2. 5
8 hydrogen can be made to agree with

the equation derived for spherical molecules carrying a quadruplet,
just as well as with the equation derived for doublets.
From the value found for Bi, we obtain for o *):
O= 2-32-1058 em:

1) J. P. Dauron. Comm. N°. 109a@ (March 1909).
2) The values taken from the measurements by SCHALKWIJK, and by KAMER-
LINGH ONNES, CROMMELIN and Miss Smip are indicated by S and OCS respectively.
3) From BN inv = 0.000465, and Biny/B,, = 0.660 (table I), follows BN, =0.000705.
AN oC. = 0.99942 then gives Bo,, 0 000705. BM, = 0.000705X22412= 15.80=
=1N.470°. With WV = 6.06.102 according to MILLIKAN one obtains for the dia.

646

From Fino’) then follows: *)
v—=1,53.10-4
and using this value one obtains from (6) for the moment of the
quadruplet:
u, ==2,08.10-% [electrostatic units X ec.m”}.

If the quadruplet is assumed to consist of two positive charges e
at a distance d from each other, and midway between them a charge
— 2e, so that u, = 4 ed’, and if further e = the charge of an electron
= 4.77.10 0 (MrurrkAN), one finds

d = 0,92.10—8 em,

a value whose order of magnitude agrees properly with what the
distance of the positive nuclei of the two hydrogen atoms within
the molecule *) may be expected to be. It is to be kept in view,
however, that, properly speaking, with this distance of the charges
it would not be allowable to assume the charges to be situated
infinitely near to one and the same point, as is done in this paper.
By taking account of this circumstance one would presumably find
a smaller value of d.

$ 6. Resume.

1. For a system of rigid spherical molecules, whose mutual
attraction is equivalent to that of a quadruplet situated at their
centres the second virial coefficient is developed in a series of
ascending powers of 7-1,

2.. Above 0.75 Ti,,.;2—o0) the dependence of B on the temperature
for spherical molecules carrying a quadruplet nearly coincides with
that for molecules carrying a doublet and for both differs but little

from the relation B=B, {1 hij apie

3. The values of B for hydrogen from —100° to +100° C. may
‘be represented with sufficient accuracy by the equation derived for
spherical molecules carrying a quadruplet.

meter of the molecule the value mentioned in the text. For the meaning of the
indices N, 9 and M, cf. H. KAMERLINGE ONNes and W. H. Kersom, “Die
Zustandsgleichung”, Math. Enz. V 10, Leiden Comm. Suppl. N°. 23, Einheiten 0.

1) Calculated from Tin» (c=0) = 194.5, Avin = 0.576 (§ 4), equation (4), and k=
=S

*) According to P. DeBue, München Sitz. Ber. 1915, p. 1, that distance amounts
to 0.604.108 cm. DeBrje’s hydrogen molecule is, however, strongly paramagnetic
(its magnetic moment corresponds to 10 Weiss magnetons) so that the magnetic
properties of hydrogen are not represented accurately by this model, unless one
would assume with SOMMERFELD, Exster- and GerreL jubilee volume 1915,
p. 549, that the electrons in the hydrogen molecule in circulating in circular
orbits do not exert a magnetic action, and hence behave quite differently from
the electrons which in the experiment of Einstein and pe Haas cause the
magnetic moment of the iron molecules.

647

Anatomy. — “The vagus-area in Camelopardalus Giraffe’. By
Dr. H. A. Vermevuien. (Communicated by Prof. C. Winker).

(Communicated in the meeting of September 25, 1915).

LesBre, in his exhaustive treatise: “Recherches anatomiques sur les
Camélidés” (Archives du Muséum d’ Histoire naturelle de Lyon, Vol.
VIII. 1903), wrote that no nervus accessorius spinalis occurs in
these animals, and that the nervus laryngeus inferior does not follow
the usual recurrent course, but emerges together with the nervus
laryngeus superior from the vagus stem. LesBRE endeavoured to explain
the latter circumstance by expressing the supposition that the usual
course of the nervus recurrens would be useless by reason of the
unusual length of neck in the Camelidae; and he expressed the
desirability at the same time of the above relations being also studied
in the giraffe, whereby support might be found for his assumption, if
similar proportions were found in this extremely long-necked animal.

On a microscopical examination of the vagus area in Camelidae,
I saw that the nucleus accessorii spinalis is indeed present, and
that especially in the caudal third portion, the nucleus ambiguus is
but poorly developed in these animals. I also found several remark-
able relations, particularly of vagus and accessorius nuclei of
Camelidae *) which roused in me the desire to examine what the
circumstances might be in the giraffe. | was able to examine one
part only of the central nervous system of this class of animal, and
was enabled to do so by the courtesy of Dr. C. U. Arns Karpers,
Director of the Central Institute for Brain Research, at Amsterdam,
who kindly placed part of the material there at my disposal. This
consisted of the brain stem and a piece of the first cervical segment
of one specimen, and the first and second segments of another
specimen. In the latter preparation the nervi accessorii Willisii
could be seen perfectly intact in their usual course between the
roots of the two first cervical nerves, so that in this respect the
giraffe differs here at least, from the Camelidae. Of the portion
of cervical cord and vagus area of the former preparation about
2500 sections of 18 u have been coloured with eresil violet. From
a part of the second preparation alternating series have been
made according to Werieert Par and Van Gteson, while the other
part, for the fibre course, has been treated after Sarnpon’s method.

The illustrations given in this paper are, with the exception of

') H. A. Vermeuten. The vagus area in Camelidae. Kon. Acad, van Wetensch,
at Amsterdam. Meeting of 27th February 1915. Vol. XVII.

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

648

the schemata, traced from microphotos made in the above-mentioned
Institute.

The dorsal motor vagus nucleus. In no other mammal I have
ever examined, does such a large part of this nucleus lie in the
closed portion of the oblongata. In the hérse, the ox and the sheep
2/, of this nucleus lie spinally from the calamus, in the pig and
the dog it is nearly equally divided between the closed and the
open parts of the oblongata, in the goat, the lama and the camel
*/,, and in the giraffe no less than cc. ‘/, ave situated spinally from
the calamus (series of 1295 sections, 1007 of which spinal and 278
frontal from the calamus) (fig. 1). It makes its appearance with a
few cells at the usual place, dorso-laterally from the canalis centralis.
Some scores of sections frontally it is still poorly developed, and not
unfrequently is entirely absent. In spite of its defective development,
its appearance in this region varies. Sometimes a few cells are seen,
clustered in a small group, while again we see a greater number,
several of which have shifted into a more ventral level, or we see
a narrow row of cells running horizontally and spreading laterally.
Where in these last cases the cells, which in former sections lay

Calamus

a eee b
SS nn
Frontal Spinal

Fig. 1. Dorsal motor vagus nucleus of Giraffe.
a. Separate cell-group at the frontal pole.
b. Separate cell-groupe at the spinal pole.
c. Increases by fusion with nucleus XI.

000 nucleus motorius commissuralis vagi.

TAL
‘ar

| = Calamus

TE
LAL ARN

COOS TTT

649

EXPLANATION OF THE MARKS.

GEL: Oliva inferior EDA - Nucleus AG

UL/J/E « Nucl. = x , :
Nucl pd NW Nucl. 3.0L mn: Nucl. AE + (ervical zl

Fig. 3. Union of nucleus dorsalis moto-
rius vagi with nucleus accessoriï; shifting

a
Fig. 2.

mostly medial, have disappeared
in one or two sections, we are
struck by the strongly lateral
position of the cell group in the
direction of nucleus XI on the
border of the anterior and posterior
horns. Further frontally we see
the significance of this, for very
speedily the nucleus accessorii
appears at this place, and we
notice in 11 consecutive sections

DI
==
ss |
Sa a complete merging of the acces-
sorius and dorsal-motor vagus
nucleus (fig. 3), such as I have
shown, though ina lesser degree,
in the camel and the lama. In

the same region there are also

constant cells belonging to the

of vaguscells in a more ventral level. vagus group, which have sunk

49%

650

into a more ventral level; in general these more ventrally situated
cells are longer than those of the vagus type, and in this respect
bear more resemblance to those of the nucleus XI. (fig. 3). After the
dorsal motor vagus nucleus has separated from the accessorius
nucleus and the latter at this place has disappeared, except for
a few cells, the former numbers 15—16 cells, frequently to be seen
more or less clearly arranged in two rows one above the other. Rather
more frontally the nucleus XI manifests itself again more strongly
and shortly after it is clearly seen to unite with the vagus nucleus
in question. This time too they separate again, and the accessorius
nucleus disappears entirely or almost entirely, after which the dorsal
motor vagus nucleus appears as a loosely built group of cells, containing
on an average 20 cells. The whole is more or less oval, with the blunt
pole pointing laterally. Striking is the large size of the cell type in this
region; ventrally shifted cells are no longer to be seen. A few sections
more frontally the cell type becomes smaller again, and the nucleus
decreases considerably in size, containing in many sections not more
than 3 or 4 cells, the accessorius nucleus, however, soon appears
again, and the process of uniting with the vagus nucleus is gone
through for the third time. Now, however, the two nuclei are but
a short time united, and only in a few sections is the closer con-
nection between X and XI to be seen. Simultaneously, however,
vagus cells have shifted into a more ventral level. The whole
process, viz. the decrease in size of nucleus X dorsalis, then a union
with the accessorius nucleus, accompanied by a spreading of the
vagus cells into a more ventral region, takes place twice more,
though in lesser degree. In the giraffe the union of the dorsal motor
vagus nucleus with the accessorius nucleus thus successively occurs
at five consecutive places. (fig. 2). This takes place before anything
can be seen of the tongue nucleus. From this moment the dorsal
motor vagus nucleus occurs constantly ; it is loosely built and egg-
shaped, with the blunt pole pointing ventro-laterally, and contains
20—25, mostly large cells (maximal 50 u); a peculiarity here is,
that sometimes the laterally situated cells are of a larger type than
those lying more medially. As in the lama and the camel, the cell
groups from the right and left come right to the raphe and soon
we see here too a commissural motor vagus nucleus appear, as I
have described in the lama and camel. It appears near the spinal
pole of nucleus XII, is less developed than in Camelidae and not
constant in appearance (fig. 1, 2 and 4).

Whenever the tongue nucleus is well developed, the dorsal
motor vagus nucleus becomes much compacter and its ventro-

„-
aes
aa
ld blt
>
‘ pe 4
N wv
wrk sa
a
WED -
~<
. hen id
4 >
Ed

651

mu
. we
‘a’ af
> ~ b]
SF a
a wre oo De
2»
id
5 a
4
\
>

Wig. 4. Nucleus motorius commissuralis vagi. c, Canalis centralis

lateral part grows out into a curved point. Its base is then directed

das
44

<7 ,

type of cell predominating.

medio-dorsally, so that it more or
less assumes the forin of a sickle.
In a great number of sections we
see that many cells have shifted
ventrally, so that not unfrequently
an actual bridge has been formed
between it and the nucleus hypo-
glossi. It contains in this region
90—100 cells (fig. 5). More front-
ally the ventro-lateral pole sinks
more and more, and the nuclei
diverge to right and left. The
development of the nucleus is not
eqnal everywhere. At times it is
remarkably strong, with a large
At
other places the number of cells

Pig. 5. Sickle-shaped dorsal motor vagus js much smaller and the cell group

nucleus ; connection with nucleus XII.

shows gaps. In a following region

the form of the nucleus is irregular, as, besides the cells which have
moved ventrally, some cells have also dropped out in a dorso-lateral
direction; these are frequently classed in separate cell groups. Near
the calamus the nucleus becomes clumsy in form, separate loca-
lisations can now be clearly seen, owing to cell groups severing

Calamus

652

at
foe a”
ee!
y >
4 ee ae
A sew
Ak het ras Les,
ad = 3
Nl A
. a 3 5 Lee =
CN SU ee ere 8
Zn on A
See awa
Beg es a
le AL!
ee wie
2 a A
Ne Ww ae
á ¥
CORR ns?
IN
pda
AA, 4
: yaad aS
B
aK
Fig. 6.

Ventric.

h
i: àr
pré r
‘ 4
vk

653

dorso-medially and dorso-laterally from the large body (fig. 6). That
these groups belong to the vagus nucleus we learn from the sections
immediately frontal from the calamus, where it is seen that the
nucleus enlarges in the above direction by means of cells, which unite
with these cell groups. Also the ventro-lateral point stretches further
out (fig. 7); not unfrequently this is broken, so that the most distal portion
appears as a separate cell group. On this level many cell groups have
as many as c.c. 200 cells. Further frontally the ventro-lateral point
disappears, the dorso-lateral one becomes thicker, till the nucleus is
triangular in form with a broad base in the direction of the ependyma.
Now two or three independent cell-groups frequently appear in the
latero-dorsal portion, sometimes quite separate from the chief nucleus,
again connected with it by a few cells. (fig. 8) These can be seen
even when the chief nucleus has become considerably smaller,
which takes place at first medially; simultaneously the number of
cells in the whole nucleus decreases, so that it becomes looser.
According as the nucleus decreases in size, the cell-type becomes
smaller, till finally this cell-type, for this nucleus is a large one, is no
longer seen in the ventro-lateral, i.e. the oldest, portion. In the
giraffe it is remarkable that 20 sections more frontally from the
place where the dorsal motor vagus nucleus entirely disappeared,

Ventriculus

pe
4 4
7 FNS vue Ne
AST y)
IN ‘
ed
, b é
ry OA ee”)
tan s
i EEGA NEN A
-
5 ‘
eee of aE
4 4
se ~
a Kle
a’ Nd re
a FEA Ed
Us a“
>
<
sod Si agf! «©,
‘ IDC
4
enke
odd

Fig. 8.

654

it reappears as a small cell-group which is seen for about 40 sections
and then disappears definitively.

Nucleus ambiguus. In general the ambiguus is well developed
in the giraffe. In the most spinal portion alone, it is small, contains
8—12 cells only. On this level I have been able to show repeat-
edly and more distinctly than was the case in the camel and
the lama, the simultaneous presence of the nucleus dorsalis vagi,
the nucleus accessorii and the ambiguus. Near the spinal pole
of the tongue nucleus, however, the ambiguus of the giraffe
has often grown to a powerful nucleus which, though varying in size,
is seen to be constant in numerous sections. In the strongest
development at this place we see a loosely built nucleus of about
45 large cells, all arranged in a ventro-lateral direction (fig. 9).
Frequently the ventro-lateral part is noticeably more developed than
the rest. This portion soon grows out medially in a nearly horizontal

4
OJ ming ote rig
b = PENS ‘
8 ~ „-
4 yhs a OPA ENE
4 4 Kor es Pie
y En A > On ,
Ld ei, Sy an x r
5) DOOK | “ret je
x ot
x =
ov x
Fig. 9 Fig. 10.

direction with a particularly large cell-type, till the whole has more
or less the form of an equilateral triangle, with the fewest cells in
the centre and at the medial side (fig. 10). Sometimes in successive
sections we see mainly the basis of the triangle, so that the nucleus
then appears as a horizontal column consisting of extremely large
cells. In circa 300 successive sections the ambiguus in this region
is clearly visible in the form described above, after which it varies
very much, sometimes being altogether absent: in the most places,
however, it JS present in various forms, though less well developed
than before; we can distinguish two separate cell groups, a medio
dorsal and a ventro-lateral (nucleus laryngeus and nucleus cardiacus
of Kosaka and Yacira) or only the ventro-lateral part of it, sometimes
attached to these we see scattered cells which impart to the whole
a sort of form of a triangle in which the nucleus is seen more
spinally. We now see it growing gradually till it gets near the calamus,

655

and assuming the same forms as before. First a large loose group,
in which as many as 50 cells may be counted, and then the triangle
with all its derivatives, now mainly the base, again the base with
the lateral side or the whole triangle. Sometimes the three corners
are sharply defined by fine groups of cells, while here the characteristic
shape of the ambiguus with its dorso-medial and ventro-lateral parts
is also present. In the calamus there is again a decrease to 8—12
cells lying in ventro-lateral direction, while from the calamus to the
frontal pole of nucleus XII, the development is much less marked
than spinally from the calamus. The greatest number of cells
contained here by the ambiguus is 18—20, sometimesit is altogether
absent. At the frontal pole of the tongue nucleus we see very
clearly in few sections the sinking of a few ambiguus cells into a
more ventral level, and very soon the huge frontal bulging makes
its appearance. This grows to an irregular oval form, with a maximum
of 110 cells, the majority being large, genuine ambiguus cells. As
in the lama and the camel the cells here are mot crowded together
but lie rather scattered. Ventrally from this large group is a smaller

Wy one, consisting principally of cells of a
Mass ode much smaller type. Whether this group
Kopala ae ane wi too belongs to the ambiguus I do not
ce: >i ee venture to assert (fig. 2 and 11). As
dr A yy, «rt 4449 usual the bulging of the ambiguus begins
ay pie Noe eto decrease at the frontal pole of the
choi dorsal motor vagus nucleus and soon
Jr oe 7 after decreases rapidly. Ten sections before
SE its final disappearance it has still 25 cells.
ee ca In this animal the frontal pole of the

ig. 11.

ambiguus stretches 46 sections frontally
from the dorsal motor vagus nucleus (fig. 2), and reaches over a
stretch of 12 sections the region of the nucl. facialis. The remainder
of the ambiguus then lies dorso-medially from the caudal pole of
nucl. VII.

Nucleus accessor. In this series the first XI cells can be seen
on the border of the anterior and posterior horns, 1188 sections spinally
from the appearance of the nucleus motorius dorsalis vagi. These
increase and a group of 14 cells is soon present, of a smaller type
than the large motor cells of the anterior horn. It rapidly decreases
in size and soon disappears altogether at this place. Cells of a similar
type appear however in several sections, dorso-laterally from the
canalis centralis, further lateral than where the dorsal motor vagus

656

nucleus will presently appear; in other sections similar cells are to
be seen still further lateral in the grey matter, directly medial from
the angle between the anterior and posterior horns. Thereupon the
XI nucleus again appears at the sharply defined place described
above, and we can see how frontal horn cells of the lateral group
have risen so high that they lie in the grey matter between the
anterior and posterior horns and form a whole with nucleus XI, so
that the impression is repeatedly conveyed as if the XI nucleus at
that place is reinforced by frontal horn cells in its most ventral part,
or that the XI nucleus itself continues ventrally along the lateral
border of the frontal horn fig. 12). More frontally the XI nucleus developed
very differently, sometimes minimally, only to appear again stronger

eee

id # posterior

4 ron a horn
: oe > 4

n 1 D] 1

canalis ; i fazer

eentralis 5 = .

Fig. 12.
than before. It then contains as many as 32 cells. At the point of
greatest development it is pear-shaped, with the point projecting
laterally into the substantia reticularis; many cells exhibit a larger
type than formerly, and here also a contact with frontal horn elements
can be observed repeatedly (fig. 13).

When the nucleus again commences to decrease, we frequently
see that only the most lateral portion is developed, so that in these
sections it lies exclusively in the substantia reticularis: in other
places we see that only the middle part of the whole has disappeared
and that the nucleus then consists of a medial and a lateral portion,
the former at the usual place between the anterior and posterior horns:
the latter lying lateral from it in the substantia reticularis ‘fig. 14).

canalis
centralis j . be
« 4)

N Dow

Wig. 14.
a medial, 6 lateral part of X 1.

Fig. 13.

Likewise in this region it
can be seen ‘that cells some-
times occur medially from
the whole, in the so-called
middle horn, dorso-lateral:
from the canalis centralis, as
has been found before. Now
follow seores of sections in
which the XI nucleus is not
present at the usual place,

or but faintly indicated,
though lateral frontal-horn

cells with a strong upward ten-
dency can be seen, or cells
in a horizontal direction,
lateral in the middle horn.
This is followed again by a
marked bulging and laterally
by a growth of the XI nucleus
in the substantia reticularis
to a complex of a maximum
of 38 cells, after which the
reduction begins again under

the same conditions as before. Locally again one medial and
one lateral portion of the nucleus occurs, or either one of the two
portions, or cells in the middle horn are seen. The contact with
frontal horn cells is then present again. The same process repeats
itself several times and the medial part, in the direction therefore of the
place where the dorsal motor vagus nucleus will shortly appear,
is frequently met with better developed than before. In this series
we thus see in the first cervical segment, varying frequently at the
place already mentioned, an extremely poor development of the
accessorius nucleus, followed by a gradual strengthening and an
outgrowth of it, both in a medial and in a lateral direction, together
with a contact with front horn cells (or shifting in a ventro-lateral
direction) till the dorsal motor vagus nucleus appears and the
repeated merging of the latter with the XI nucleus begins, as has
been mentioned in the description of the said vagus nucleus (fig. 2). The
last union of the two nuclei occurs 40 sections spinally from the
appearance of the first XII cells, in a region where the frontal horns
are still well developed and nothing is to be seen of the oliva inferior.

Also in the Weicrrt-PaL, VAN Girson and SHELDON series the XI
nucleus was in the first cervical segment to be seen at the place
already indicated. The ending of the nervus accessorii could be traced
in many sections. Frequently we see several bundles leave through
the processus posterolateralis of ZieBeN, often three parallel to each
other, first an upward arch, parallel to the distal portion of the posterior
horn, and then laterally. These bundles do not leave the nucleus
directly, but first take a medial curve before leaving grey matter.
In a few preparations it was observed that fibres joined these bund-
les from a more centrally situated region, and also from a more
ventrally situated region. Besides the above bundles fibres also leave
the XI nucleus and a little further distally, directly i.e. without a
central curve. Also in the 2nd. cervical segment efferent XI roots
were to be seen, but far fewer in number and of poorer develop-
ment than in the 1st. Only in a few sections could indications of
the XI nucleus be demonstrated on the border of the anterior and
posterior horns, though in several sections cells could be seen in the
processus postero-lateralis, through which the efferent root takes its
way. Judging from the great decrease in the efferent XI roots in
the 2nd. cervical segment, it may be assumed that in the giraffe
the nervus accessorius spinalis extends only to the 2nd. cervical
segment, or perhaps a little further distally of it. In view, however,
of the important function this nerve has undoubtedly to fulfil in this

659

animal, it must not be considered impossible that the XI nucleus
extends still further and that XI fibres with cervical nerves leave more
distally, as is the case in the Camelidae, where a nervous accessorius
spinalis is entirely absent.

Nucleus hypoylossi. Before the appearance of the XII nucleus the
dorsal motor vagus nucleus is well developed and efferent XII fibres are
visible; the direct continuation of nucleus XII out of the frontal horn
grey matter can be clearly demonstrated in the giraffe as in the
lama and the camel (tig. 2), typical large front-horn cells shift to a
higher level and soon arrange themselves in a group of XII cells.
In this series this occurs 496 sections spinally from the calamus.
First a cell-group appears lying ventro-laterally from the canal and
consisting of 6—10 cells; this group retains the same degree of
development in many of the following sections. We see repeatedly
eells in this area between the dorsal motor vagus nucleus and the
tongue nucleus; they clearly belong to the vagus nucleus, in the
first place by reason of their type, but in the second place because
here there is always some distance between these ventral vagus cells and
the tongue nucleus (fig. 15). After this the nucleus XII grows out,
first dorso-laterally and then medially in the direction of the raphe.
The nucleus then contains 30—35 large cells, the majority attain
the maximum diameter of 85 u; only in the dorsolateral group are

Za a
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pees 4 Q | , Re EE
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; | a. s ~
ay, | {a 4 4 4
jl 4 { ‚ L

660

there often cells of a smaller type. Very shortly, in a more ventral
region than where the first XII cells had occurred and medially
from there a fourth group of cells appears, so that a large complex
is formed, shaped like a slanting quadrilateral, containing 70—90 cells.

Here we can clearly distinguish a ventro-medial, a ventro-lateral, a
dorso-medial and a dorso-lateral group. In many sections a few cells also
occur in the centrum, while in all there are numbers of cells between
the tongue nucleus and the dorsal motor vagus nucleus. Not un-
frequently an actual bridge exists between the two nuclei (nucleus
intermedius, fig. 16). Slightly more frontally both nuclei strike against
the raphe and 168 sections spinally from the calamus a few XII
cells appear in the raphe, whereupon a nucleus commissuralis hypo-
glossi makes its appearance (fig. 17). In this region many central

4 ad
a 2 Te , 4 a Sy - \
- 4
AOE wees bis
~ 4* r
rae ~ Fi, h (A dr Ad <& Re A
Reden NRE bj
4 Yo se | ¥ ff Pi es
& as de yv 4 a d as d. &
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ke r id 4h An 7 4 rk a
4 { Reo 4a é ao a Pi
~ he é
. eee, ae coat
-
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Fig. 17.

cells appear in the irregular quadrilateral tongue nucleus. The com-
missural tongue nucleus does not seem to follow any continuous
course, in a few consecutive sections it is present. Everywhere the
connecting cells are met with between the tongue nucleus and the
adjacent vagus nucleus. Now the XII nucleus begins to diminish in
size, it becomes loose in structure, and shows gaps at different
places, only the latero-dorsal and lateroventral portions remain
constant, even commissural cells are now and again seen and not
unfrequently the bridge to the dorsal motor vagus nucleus is com-
plete. Then the central cells disappear entirely, and the latero-ventral
portion also diminishes, so that it is mainly only the latero-dorsal
part and the cells connecting with the vagus nucleus which are
still properly visible. More frontally, more XII cells again appear and
the irregular quadrilateral gradually reappears though in a less marked

661

degree than before; the centrum remains poor in cells. This process
repeats itself for a third time; then practically all cells disappear, with
the exception of the dorso-lateral portion and the connecting bridge
with the X dorsalis; a few commissural cells still oecur occasionally.
In the calamus the grouping is different; the medial and dorso-lateral
groups merge into an elongated triangular whole, the apex of which
points ventrolaterally ; ventrally from this lie the ventro-medial and
the ventro-lateral groups, now fairly well on the same level (fig. 18).

sy =
vos 3
gerne i: laste
er aba
> EE
i v fee
RP
=d
kere
4 =
Sp ne
A
.
wv < ¢
Di 4
er 4 4 rh
YM a DS
\ b i
ash of {
4
x hie en,
, ‘ hed ae Pie
+
fai & = 4 IS wy 5 i
Ed
“|e
a = Ed ’
5 ee EZ ie
Pd be = Pa a >
.
À é ee A
< “ ae (i
fa Aes in „7
4 „ ee >
Ee a AE
4 ed <
Fig. 18.

Also in this region of the tongue nucleus a few cells can be observed
in the raphe; they no longer show, however, the striking hypo-
glossus type, but have become much smaller. The former group is
of the same shape as the nucleus hypoglossi in other animals,
triangular in form and with a majority of large cells, it lies medially
under the ependyma of the fourth ventricle; the ventral groups are
different, occasionally they converge so that we see a second tongue
nucleus ventrally from the usual tongue nucleus, built up of a
fairly broad horizontal row of cells, the cell-type of which has
erown smaller than of that lying dorsally (fig. 19); in general,
however, the ventral tongue nucleus consists of a medial and a
lateral portion. between the lateral portion and the dorsal tongue
nucleus we often find a few large XII cells (fig. 19); not unfre-

662

quently, however, the two main groups are quite separated from each
other. The medial group of the ventral tongue-nucleus has shifted
away from the raphe and simultaneously a small group of little
cells appear between the tongue nucleus and the raphe (nucleus
funiculi teretis) (fig. 19a); the bridge of connection with the vagus
nucleus bas vanished and in its place one or more small groups of
cells have appeared (nucleus intercalatus Staderini) (fig. 195). These

we sb
ges on oe
be
’ gei at Beal
cena bn
Ek pee >
Kn A
os 4<
Se: a 5 ne
rt aay
: 4
dorsalis SH chy ene |S
d i? a
BL i:
vi :
4 ‘
a ad 4 { 4 a
ne a Fn 4
=
4 4 ane
4 ‘,
AE sa

XII ventralis

-_ 4 a
> el
a = ak BS ave
— ° nd
Fig. 19.

lie thus laterally from the dorsal tongue nucleus, i.e. between the
latter and the dorsal motor vagus nucleus. Some cells of these
last groups are of a larger type than those of the group next the
raphe. The ventral tongue nucleus gradually diminishes; the cell
type has grown smaller, the medial portion disappears first, the
lateral portion, lying under the ventral point of XII. dorsalis remains
longest in existence (fig. 20). The cell-group between the raphe has
grown larger; it contains + 30 cells, many of a larger type than
these which first appear; soon similar cells also appear here in the
raphe, so that the two small cellular nuclei are connected medially
from the tongue nuclei by a group of cells. In this region too
we often see tiny cells and little cell-groups between tongue and
vagus nucleus. The distal nucleus soon completely disappears, but

U en ak

663

still further frontally the aspect changes again. The dorsal portion
of XII. dorsalis vanishes, the lateral portion of XII. ventralis again
appears, after which the latter combines with the rest of XII. dorsalis

<
. 4 . .
e oe ae
i, A a a
- NA EN Zp .
v3 pl .
a Patan we
ei) S : .
bs -
g * i) sie
nd . wt a
og -
ie “vO La
kel “a acs «
Zn N
nd ~ > ~
4 7 4 ix mM he
w ol

7 vr .
‘ en ZI dorsalis
OE « ERVEN 5

4 5 9?

~ a A 4 26

a ee 7/3 ventralis
Fig. 20.

to make one large whole; the cell-group nearest the raphe has
grown greatly, on the one hand it has extended medioventrally, on
the other hand it bas approached close to the ependyma; the little
cell-groups between XII. and X. dorsalis occur inconstantly, not
unfrequently a gradual parvo-cellular continuation of the nucleus
funiculi teretis can be seen into the nucleus intercalatus Staderini
over the tongue nucleus. The latter decreases rapidly in size; 168
sections frontally from the calamus it has disappeared ; the ventro-
lateral portion remains longest in existence.

The oliva inferior of the giraffe appears in the Jatero-ventral region
of the spinal pole of nucleus XII. and soon grows strongly in a medial
direction, which medial portion presently curves upwards and begins
to form a powerful lamel growing in a lateral direction. Very soon
the olives from the right and left join at the raphe and a little
further forward we can clearly see a connecting olive in the raphe.
Near the calamus the olives have again receded from the raphe
and the dorsal lamel loses itself in several cell-groups lying one

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

664

behind the other, in which the celltype in general is larger than it
was before. The strongly developed olive clearly bulges ventrally.
It diminishes first laterally, then ventrally, and extends 360 sections
frontally from the calamus, i.e. to just in front of the frontal end
of the ambiguus (36 sections). ;

The nucleus reticularis inferior makes its appearance 85 sections
spinally from the oliva inferior and dorso-laterally from it, with cells
which for reticular elements are small. Frequently it breaks up into
several cell-groups, locally we find also raphe cells in this spinal
portion ; more frontally it extends over the olive in a medial direc-
tion, whereby the inclination towards the formation of cellclusters
again shows itself, after which it begins to decrease in size spinally
from the calamus; the cell type becomes larger and the presence
of raphe cells more constant. As far as the front poles of the vagus
nuclei clusters of large cells next the raphe and of cells lying scat-
tered laterally from it can be observed, after which the former groups
become fewer and the latter still remain visible. In general the
nucleus reticularis inferior is poorly developed in the giraffe.

As regards the occurrence of the commissural motor vagus nucleus
in the giraffe, I refer to what I have remarked already in my paper
to the Kon. Acad. v. Wetensch. at Amsterdam. on Jan. 18, 1915,
The vagus area in Camelidae.

Although the presence of glands in the oesophagus and proven-
triculi of the giraffe has not yet been demonstrated, and this
argument cannot as yet be advanced for an extension of the
dorsal motor vagus nucleus with the commissural nucleus, yet the
extreme length of the gullet in this animal, even more than in
Camelidae, may be regarded as an argument in favour of the
above opinion. The enormous development of the tongue nucleus
and its extension with the commissural tongue nucleus has undoubt-
edly something to do with the extremely intensive use that the
giraffe makes of its tongue as a prehensile organ; as a rule this
animal feeds on the leaves from the tops of high palm-trees, seizing
them with its tongue and pulling them off. Regarding the significance
of the presence of a commissural nucleus funiculi teretis and its
direct passing into the nucleus intercalatus Staderini, | am not in a
position to give fuller details. The strikingly strong development of
a great part of the nucleus ambiguus spinally from the calamus
furnished a strong contrast with the appearance of the nucleus at
this place in Camelidae. I believe that a relation may be assumed
between the short recurrent course of the nervus laryngeus inferior

665

and the poor development of the nucleus ambiguus in its spinal third
part in Camelidae. If this be so, one might conclude, judging from the
strong development of the nucleus at this place in the giraffe, that the
nervus recurrens, even in this animal in spite of its long neck, well
deserves its name, in which case the highly exceptional condi-
tions of this nerve in Camelidae have wrongly been connected by
Luspre with the unusually long neck of these animals.

As regards the conditions of the nucleus accessorii in the giraffe
I wish to make the following observation. No agreement exists yet
as to the position, extent and nature of this nucleus. Most observers
are agreed upon the position of it in the first cervical segment,
viz. about the level of its leaving the nervus accessorius, on the
border of the anterior and posterior horns and their neighbourhood,
or, according to the nomenclature of Warpeyer, in the lateral
portion of the. middle horn. This position has already been fixed by
Crarke. Rorrer and Darkewitscu believed that here also the XI
nucleus was situated in the most ventro-lateral portion of the frontal
horn. According to Dress only the most dorsal of the'cells of this
group belong to the cells of the accessorius nucleus, while only
anterior horn roots arise in the ventral. He pointed out that in the
cranial part of the first cervical segment the XI nucleus shifts
to the anterior horn and then comes to lie sideways: Karser too
indicates that spinally from the first cervical segment the XI
nucleus shifts distally. According to OBerstriNer the said nucleus
lies first (Bh cervical segment) dorso-lateral in the anterior horn,
near its border; in a cerebral direction, however, it shifts cen-
trally, to pass over into the nucleus ambiguus. Casa indicates as
the position of the XI nucleus, as regards ihe spinal portion, the
lateral edge of the frontal horn, and more frontally the whole dorsal half
of that. Karerrs, found the nucleus on a frontal level, dorso-lateral from
the canalis centralis, spinally more latero-ventral towards the border of
anterior and posterior horns and finally latero-ventral from it. LANGELAAN
also describes the nucleus in the dorso-lateral portion of the front
horn, and from the illustration it appears that here too the boundary
between the anterior and posterior horns is meant. JacoBsonN and
WALTER assume ascending cells from the medial group of frontal born
cells to the nucleus accessorii; ZieHEN states that the nucleus in
question, in the 1s* cervical segment is formed by a pyramidal
protrusion of the gray matter radiating at the base of the anterior horn
into the substantia reticularis, which protrusion he names processus
postero-lateralis cornu anterioris, and which he regards as a direet
continuation of the dorso-lateral group of frontal horn cells.

43*

666

From what I have found in consecutive series of lama, camel
and giraffe, I believe I may conclude that spinally from the 1*.
cervical segment the nucleus accessorii gradually ascends out of the
latero-dorsal portion of the anterior horn, and thereby comes to lie
on the border of the anterior and posterior horns and that, when
once there, it can spread out both in a lateral direction into the
substantia reticularis and into the processus postero-lateralis, and in
a medial direction towards the central canal. The general opinion,
and the one still expressed by OsersteiNer in the latest edition of
his text book, viz. that the nucleus XI continues frontally into the
nucleus ambiguus, I am unable to share. In the first place 1 have
demonstrated the direct transition of the nucleus accessorii and the
nucleus motorius dorsalis vagi in Camelidae and much clearer
still in the giraffe, and I have, moreover, shown in these animals,
and especially in the last-mentioned, the simultaneous presence of
ambiguus and nucleus XI. For the same reasons | consider the
nomenclature in the atlas of WinkLer and Porter (Anatomical Guide
to Experimental Researches on the Cat’s Brain plate 35) in which
the nucleus of origin of the nervus accessorius spinalis is called
nucleus ambiguus inferior, not a happy one. As regards the connection of
nucleus XI with nucleus motorius dorsalis X in the spinal portion
of the oblongata I may mention that the observation made by
Karpers, who saw this union in embryos of sheep has been con-
firmed by myself in a calf’s foetus (4'/, months) and that I have
again found undoubted indications of such a connection in a
new-born lamb and in a new-born pig. (fig. 21)

As regards the spreading of the accessorius nucleus, it will be
known that this varies very much in a spinal direction, according
to the species of animal: the cerebral pole, however, is also described
very differently. v. GrnucnTen is of opinion that the frontal pole of this
nucleus should lie in the first cervical segment. Darkrwitscu, on the
other hand, gave the distal third portion of the oliva inferior, thus
quite in the hypoglossus region, v. BUNZL-FrDERN thinks it reaches
as far as the rise of nucleus XII, while GRABOWER and ZigHEN mention
the region of the pyramidal decussation. (ZieHeN, Nerven-system.)

In the giraffe this pole can be indicated directly behind the spinal
end of the tongue nucleus and the oliva inferior. In any case it
may be regarded as an established fact after what I have found in
Camelidae, and so clearly and repeatedly confirmed in the giraffe,
that the accessorius nucleus has also a bulbar part and that the
difference between a nervus accessorius spinalis and bulbaris, chal-
lenged by Casa and Kosaka, is correct.

667

The appearance of the nucleus XI, like that of the ambiguus, is
very different; in continuous series of the 1st. cervical segment and

Fig. 21. Calf's foetus about 4!/, months.

of the region of it lying here cranially, i.e. at the place where the
nucleus by reason of its position between anterior and posterior horns
is most sharply defined and therefore easiest to follow, this can
be seen very clearly and frequently in the neighbourhood of places
where the nucleus is very strongly developed, it will be found that
it is greatly reduced, often indeed quite absent. Drs has shown the
so-called rosary-shaped development of the nucleus accessorii in
longitudinal sections.

Also as regards the nature of the XI nucleus, various
opinions exist. Epinerr describes the motor bulbar nuclei as
continuations of the frontal horn grey matter, which have been
disturbed in their continuity, and explains the dorso-medial
position, with respect to the ventral system of most of
them as follows: owing to the upward rise of the central canal,
the motory regions lying below rise too, whereby the sensory regions
at the same time are pressed laterally. This conception cannot be
disputed as regards the tongue nucleus. As for the glosso-pharyngeo-
vago-accessorius system, however, the conclusion drawn by Kapprrs is

668

in contradiction to it. On the basis of his phylogenetic and
embryologie studies, Karpers came to the conviction that the
nucleus accessorii and the ambiguus have nothing to do with the
spinal system, but that both are direct continuations of the dorsal
motor vagus nucleus; the accessorius nucleus exhibits hereby the
peculiarity that it grows from its cerebral origin into the cervieal
cord, sometimes along almost its entire length. My confirmation of
this position of the XI nucleus and the dorsal motor vagus nucleus
in a calf’'s foetus, in ovis aries neonatus and sus scrofa domesticus
neonatus, of what Karpers found in embryos of sheep, and especially
the fact that the connection between these two nuclei is still to be
found in Camelidae and so clearly and repeatedly in the giraffe,
strengthen, in my opinion, Karpers’ theory to no small extent. Other
difficulties, however, present themselves with regard to this question.

Bork has described that also anterior horn roots leave with the nervus
accessorius, so that what has never yet been demonstrated in any
other place in the animal body takes place here, viz. that viscero-
motor and somatomotor fibres unite. I have now observed that
in the first cervical segment of the giraffe, cells from the anterior horn
join the accessorius nucleus. The question is now whether these are
genuine frontal horn cells or accessorius cells. Only from the first
cervical segment do we find frontally, the XI nucleus at the sharply
defined place, viz. or mainly at least, in the corner between the
anterior and posterior horns; if we follow this nucleus spinally we see
the connection with motor cells on the dorso-lateral border of the
frontal horn, but later we can affirm that the XI nucleus has disappeared
entirely from the corner indicated, although in this and even in
regions lying much more candally the nervus accessorius may arise
and „in that case its nucleus must still be present; in other words,
this nucleus may have sunk away in the midst of genuine frontal horn
cells and the derivatives of the dorsal motor vagus nucleus may
finally disappear in the middle of the motor elements of the grey
matter of the neck. There is therefore the possibility that the bundles
described by ‘Bork contain accessorius fibres after all, I will add,
however, immediately that I am willing to admit the possibility of
a simultaneous vise of XI and frontal horn roots, in the first place
because a priori the coincidence of viscero-motor and somato-
motor fibres must not be considered as impossible in view
of the fact that everywhere motory, sensory, and autonomic fibres
combine, and in the second place because of the fact that in
Camelidae XI fibres must necessarily originate together with
cervical nerves. These animals have a musculus trapezius,

669

a nucleus accessori spinalis and no nervus accessorius spinalis. (This
observation of Lusprn’s has been confirmed by Professor WinGarn
Topp of Cleveland in a letter directed to Dr. C. U. Ariins Karpers).

A more difficult question is presented in this respect by the dorsal
motor vagus nucleus itself. In the lower vertebrates numbers of
cells leave the spinal portion of the nucleus out of the connection
into a more ventral level; in the Alligator a part of the dorsal
motor vagus nucleus is even attached to the frontal horn grey matter,
and in birds to the tongue nucleus, which here forms the direct
continuation of this grey matter (Karpers). In mammals the rise of
the vagus and hypoglossus cells in the hypoglossus region between
the two nuclei is a common phenomenon, which undeniably is as
clearly seen in the giraffe as anywhere. Spinally from the nucleus
XII, however, it was apparent in many sections in the giraffe
series, that these ventral cells form one whole with a series of frontal
horn cells of small type, often an arched series of cells were even
noticeable, which began deep in the frontal horn and ended dorsally
from the central canal; the same was frequently observed in the
first cervical segment, i. e. spinally from the dorsal motor vagus
nucleus. My interest in this circumstance increased when I met the
same phenomenon, though in a much stronger degree, in my series
of the calf foetus, where these ventral cells of the said vagus nucleus,
reaching deep into the motor horn, are of much larger type. This
phenomenon was to be seen in this series, for instance, in these
sections where there was a connection between this vagus nucleus
and the XI nucleus (fig. 21). Thus in this respect also there are
very primitive conditions in the giraffe as in the tongue nucleus,
which I am unable to explain, the more so as I know nothing of
the rise of the nervus vagus in this animal.

CONCLUSIONS.

1. The nervus accessorius spinalis occurs in the 1** and 2™s cervical
segment in the giraffe as in the other mammais, with the exception
of Camelidae.

2. Spinally from the nucleus XII. the dorsal motor vagus
nucleus of the giraffe appears to be at five consecutive places in
direct connection with nucleus XI.

3. In the most spinal portion the dorsal motor vagus nucleus
of the giraffe does not occur constantly ; in front of its frontal pole,
there is still a small, quite separate, portion of this nucleus.

4. Frontally from the unions of Nucl. mot. X. dorsalis and

670

nucleus XI in the giraffe, a commissural motor vagus nucleus
occurs which is not continued.

5. In the first cervical segment it is repeatedly observable that
medial and central anterior horn cells of small type rise upwards like
an arch to above the central canal at exactly the place where
frontally from the nucleus mot. X dorsalis will appear; in the
most spinal portion of the vagus nucleus numbers of vagus cells
leave the connection for a more ventral level, and ina large portion
of the hypoglossus region this is so often the case that the vagus
and tongue nuclei are completely joined.

6. The ambiguus is strongly developed in a large part of that
portion of the nucleus which lies in the closed portion of the oblon-
gata, and occurs here often in forms which are not to be met with
in other animals; the frontal growth of the ambiguus is very strongly
developed and reaches the facialis region, somewhat cranially from
the frontal pole of nucleus X dorsalis.

7. In the giraffe the simultaneous presence of nucl. mot. dorsalis
vagi, nucleus access., and nucleus ambiguus is repeatedly to be
met with.

8. In the spinal end of the oblongata the main group of the
nucleus accessorii in the giraffe lies on the border of anterior and
posterior horns; this nucleus, however, repeatedly radiates both in
a medial and in a lateral direction. In the latter case the nucleus
frequently consists of 2 groups, the medial one being at the usual
place between the anterior and posterior horns, while the lateral one
lies in the substantia reticularis. Spinally from ‘this we see the direct
connection of the nucleus with the cells lying on the latero-dorsal
border of the frontal horn, and further spinally the nucleus does not
occur again on the border of the anterior and posterior horns ; behind
the first cervical segment thus it shifts in a latero-ventral direction.

9. The tongue nucleus in the giraffe is, in comparison with the
vagus nucleus, short but unusually strongly developed ; frontal from
the commissural motor vagus nucleus a commissural tongue nucleus
occurs, which like the one mentioned above, is not continuous, but
ends close to the calamus. In the same region the tongue nucleus
has an irregular quadrilateral shape, more frontally it splits into
a dorsal and a ventral portion.

10. The oliya inferior is strongly developed; there is a small
connecting olive; the nucleus reticularis inferior is poorly developed.

671

Physics. — “A difference between the action of light and of
X-rays on the photographic plate’. By Prof. 1. K. A. WerTHEIM
SALOMONSON.

(Communicated in the meeting of September 25, 1915).

In a series of experiments on the quantitative action of \-rays
and light on photographie plates, I found a characteristic difference
between the two kinds of rays.

In these experiments so-called exposure-scales were made by
exposing one half of a plate to regularly increasing light-quantities
and the other half in the same way to Röntgen-rays. Both halves
were developed at the same time in one developing tray and also
fixed simultaneously in one tray.

On each of the negatives we find a series of small fields, which
have been exposed to the action of light or of 2-rays of intensities
increasing in the ratio of 1, 2, 4, 8, 16 ete., and which show an
increasing density. On the half exposed to the X-rays the time of
exposure and the hardness of the rays are also recorded. The
transparency of each of the small fields is photometrically measured.
The reciproques of the figures obtained in this way give the
absorption-factor, the logarithm of which is the optical density. From
the figures for the density curves are drawn, the densities being
plotted as ordinates to the logarithms of the exposures as ordinates,
In this way we get the ‘characteristic curves” of the plates as used
by Herrer and Drirrietp, Eper and others.

The different precautions taken in these experiments need not be
described: sufficient be it that the exposures, once started, were
automatically carried out, and that any irregularities in the intensity of
the light and the X-radiation either could bear no influence on the
result or could be immediately detected.

Curves like these always show a curvature convex to the X-axis
corresponding to the underexposed part. The “correct exposures”
give a straight line. This part generally commences at a density
of roughly 0.5. The straight line prolonged to the axis of abscissae
meets it in the “point of inertia’ (Beharrungspunkt) which is used
by Hurrer and Drirrietp to indicate the “speed” of the plate. It is
almost entirely independent of the time of development, the kind
of developer used and its temperature, which influence only the
slope of the curve in the straight part. We also know that the
quantity of silver in a negative increases proportionally to the
logarithm of the exposure.

ARB MENE ml:

Negative 5A and 5B.

i p 2logetgp | R gq 2 log ctg pl
1 43°24’ 0.049 1 38°19/30” 0.204
2 39.55 30” 0.155 2 33.34 30 0.356
4 33.45 0.350 4 26.24 0.615
8 23.12 0.736 8 17.37 30 0.996
16 14.30 Wali 16 10.52 30 1.433
32 8.0 1.704 |
64 4.16 30 2.253
Negative 6 A and 6 B.
1 43°42’ 0.039 1 40°49'30” 0.127
2 40. 430” 0.150 2 36.12 0.271
4 35.15 0.301 4 29.31 30 0.494
8 24.54 0.667 8 226 0.783
16 16.13 30 1.072 16 15.27 sen laf
32 10. 130 1.505
64 8. 430 1.696
Negative 7A and 7B.
1 43°51’ 0.035 | 1 41° 630” 0.118
2 42. 3 0.090 2 38.18 0.205
4 Sia 0.219 4 33.25 30 0.361
8 30.1330” 0.469 8 26. 19 30 0.611
16 20.12 0.868 16 18.19 30 0.960
32 12 1.355
64 7.9 1.803
Negative 8A and 8B.
1 44° 0.030 1 3045’ 0.160
2 40.48’ 0.128 2 34.33 0.324
4 33.16 30” 0.366 + 26.43 30” 0.596
8 22.12 0.778 8 18.13 30 0.965
16 13.22 30 1.248 ° 16 11.18 1.399
32 8. 730 1.691
64 4.22 30 2.236

673

In the next table I give the result of the measurement of 4

pur of negatives.

672)

See p.

(

oe <> em eo
eee AN

675

The fact to which I wish to draw attention is, that for every
pair of negatives the characteristic curve for light slopes considerably
more than the one for X-rays. This is clearly shown in fig. 1—4.
Each of them contains two curves, the upper one showing the
action of light, the lower one the X-ray curve. The slope of these
curves always proved to be different in the manner indicated and
to be independent of the development if only both halves of the
plate were developed in the same tray for the same length of time
without undue restriction of the time. Changes in the development
merely caused changes in the slope of both curves at the same
time and in the same way.

We may expect a physical difference in the action of light and
of X-rays on the photographic plate. The sensitive layer strongly
absorbs light, whereas X-rays are only slightly absorbed. As we
know that the action of both kinds of rays increases with the
intensity, we may in the case of light look for a strong action at
the surface of the sensitive layer and for a markedly diminished
action in the lower strata of the emulsion. In the case of X-rays
which are not notably weakened after passing through the silver-
bromide-emulsion we may reasonably expect that the action in the
deeper layers is not less than the action on the surface. After
development the reduced silver should be nearly equally deposited
in every part of the gelatine layer if the negative had been obtained
with X-rays. Im light-negatives the silver would probably be
accumulated on the surface and only a slight amount would be
present in the deeper strata. Any one who has developed many light-
and X-ray-negatives knows, that with the former only the parts
exposed to the strongest lights are visible at the back after development
but before fixing, whereas properly developed unfixed ROnTGEN-
negatives present nearly the same appearance at the back as on
the front surface.

We may ask if this difference might be responsible for the
difference in the slope of the characteristic curves. It seems to me
that this is possible and even quite probable, if we consider the
question in the following way.

Let us first consider how the reduced silver is deposited in light-
and RöÖNrGrN-negatives. After this we shall see how this effects their
transparency.

We may represent the absorption of light and RÖNTGEN-rays in
the gelatinobromide-emulsion by the well-known formula

TI Pree a et ee (1)
in which JZ; is the intensity of the radiation after passing a layer

676

of thickness /, /, being the intensity of the radiation at the surface,
u the absorption coefficient of the absorbing medium for the
incident rays.
By multiplication by ¢, the time, and equating J)t= Q, and
1. t= iQ, we: gel;
= Qe. Lo) EN

a formula for the quantity of radiating energy at a distance of /
below the surface. Differentiating 2 gives:

=d UQ, pe tid -. '. ») jena ee
an expression for the light absorbed in a stratum of thickness d/
at a distance / below the surface. As the quantity of silver reduced
by development in this stratum is proportional to —dQ, we may put:

dAg=kQjnerid ... ... ae
which integrated gives:

Ag=KQ. (lede .
as a formula for the total quantity of reduced silver between the
surface and a layer at a distance / below it.

From (5) we deduce:

zg Kler) de J)
i.e. the increase of silver caused by an increase of exposure depends
on the absorptioncoefficient uw. If u is large the differentialquotient
is also large.

In order to calculate the density of the negative, we suppose
that the absorption in an infinitely thin layer is proportional to
the amount of silver in it and also with the intensity of the light
falling on it. Using (4) for the quantity of silver we get the equation:

—d Ty Sel). cK Owen

or after integration

vA
Ui aes Sgn ed

id
in which D is the density, /, the intensity of the light before, and
/, the same after passing through the negative.
From (8) we tind:
dn 2 Ke EE
dl
This last equation shows that the increase of density also depends
on the absorption coefficient u of the rays used in producing the
negative.

677

These formulae are only available in cases of underexposure. For
correct exposure we can get an expression by applying the empirical
formula given by Hurrer and DeurrieLp, This formula (10) “repre-
sents the necessary relation between the density and the exposure
which must be fulfilled if photography is true to nature” (Hurrer).

This formula-slightly modified is:

D=lg=a Jb Aga, +b,logQ. . . . (10)
t

in which a, a,, 6 and 6, are numerical constants, Ag the total

quantity of reduced silver, Q the total energy of the light. If we

use the expression for Ay from (5) in this formula we get:

if
D = log ie =a db Ag (1 —erl) =a, + b, log Q(L —e#!) . (11)
t

in which we have also corrected the value for Q by using (8) and
putting in it only that part of Q which really has been absorbed.

If the results of this discussion represent the facts with sufficient
accuracy, we may draw the conclusion, that between light- and
Röntgen-negatives still another point of difference should exist.

We may expect that in cases of the same density a light-negative
contains considerably less silver than a Röntgen-negative; in cases
of light- and Röntgen-negatives containing the same quantity of
reduced silver, the transparency of the latter will invariably be
greater.

In order to test the truth of these conclusions I asked my
assistant Dr. Karz to make a careful quantitative analysis of the
amount of silver in a set of larger plates forming together an ex-
posure-scale. The 10 plates measuring nearly 10 15 cm. were
cut from one plate 30 X 40 em. Five of them were used for the
lightseale, the other 5 for the Röntgen-exposure scale. The results
of all the measurements are given in table II. (See p. 678),

The vertical columns contain: Under Plate 42 the number of
each plate; under Q the relative quantities of light; under y we
find the reading of the polarisation photometer; under 2 log ctg p the
measured density, whereas the next column contains the most pro-
bable value for the calculated density, supposing a linear relation between
log Land log ctq p. The following vertical columns contain: the measured
quantity of silver on the whole surface of each plate, the exact
measured surface, the quantity of silver per square centimeter. In
the last column the most probable quantity of silver is given, cal-
culated on the supposition of a linear relation between loy Q and

678

A Bal Be aL
es ; 2 sae | me a
Ly 125907 0.663 0.6654 19.4 96.7 | 0.201 | 0.1954
Lo 2 | 14.341, 1.170 1.1590 28.6 93.7 | 0.306 | 0.3202
„L3 4 8.501 1.617 1.6526 39.9 88.4 | 0.452 | 0.4451
La 8 4.341, 2.194 2.1462 inl 99.7 | 0.578 | 0.5700
Ls |16| 2.484 | 2.619 2.6398 | 69.1 | 100.7 0.689 | 0.6948
Ri EES 0.228 15.1 93.6 | 0.161 | 0.1582
Rs Dale 0.397 21.0 97.3 | 0.216 | ..2190
R3 4 | 26.3 0.622 0.6272 | 26.4 94.6 | 0.279 (0.2798
Ry, 8 17.0 1.029 1.0187 | 32.4 | 96.1 | 0.338 |0.3406
Rs 16 ‚ 11.13% 1.405 1.4102 | 39.9 | 98.6 | 0.405 pa

Silver.
Fig. 6.

the quantity of silver per unit surface. The formulae used for the
calculation of the figures on the 5 column were
D, = 9.1708 + 0.4138 log (2)Q Q and Drp= 0.5473 + 0.3915 loge) Q.

The second formula was calculated from 3 figures only.

For the last column I used the formulae:

100 Ag, = 7.055 + 12.485 log2)Q and 100 Agr=9.74 + 6.08 loge) Q

We see immediately from the table, that the conclusion as to
the difference in the amount of silver contained in the film after
exposure to light and to X-rays seems to be true. We find that
L, and R, show only a slight difference in density viz. 0.663 and
0.622, the Röntgennegative being the more transparent one. Yet
this contains 0.279 mgr. of silver per unit whereas the denser light
negative contains only 0,201 mgr. The same thing is found for
L, and R,.

If two negatives with nearly the same quantity of silver be com-
pared, for instance L, and A&,. containing 0,201 and 0,216 mer.
of silver, we find the light-negative about 50 percent denser than
the Röntgennegative, which, however, contains more silver.

I must advance still another argument in favour of my theoretical
deductions. If these be true we ought also to expect differences in
the slope of the characteristic curves when ordinary light waves of
different length are used, the absorption-coefficients of which in
bromide-silver-gelatine is different. In Epmr’s Handbook of Photo-

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

680

graphy, Part III, we find on plate II a series of characteristic
curves pertaining to light of different wavelength between 4100 and
5100. The curve for 4600 shows maximal action and also maximal
slope. Experiments by Eprr on orthochromatic plates, the curves
of which are given on other plates, also prove the fact that stronger
absorption or a large value for wg concurs with stronger slope in
the curve.

Another fact mentioned by Eper (le. p. 223) is the greater density
of collodion negatives as compared with gelatine-negatives containing
the same amount of silver. As the former are notably thinner than
gelatinefilms this is equivalent to a larger absorption in the thinner
films. If, finally, the thickness of a layer containing a certain amount
of silver is so far reduced that the conditions, present in a silver-
mirror are approached, Eper finds that only 0,039 mgr. of silver per

TeANB NEE
ds dS : | Quotient
Number aL dR Quotient | Hardness ES

|5 A and B | .505 „409 | 1252 7.2 BENOIST | 1.250

|
6 AandB| .419 | .311 | 1.349 6.1 r | 1.336

1 AandB| .445 | .300 | 1.482 |42 , | 1.483

8 AandB| .468 | .401 LEN Gre PCE | 1.157

| 42 „489 „301 | 1.250 | |
Quotient

Hardness 4 5 6 a 8 9

681

square centimeter is sufficient to produce a density of 1.5 and 0.052
mgr. of silver a density of 2.0.

On the other hand I found in my experiments one fact that at
first sight did not agree with my deductions. If from the different
series of experiments given in table I and II we ealeulate the in-
crease of density with the increase of the action of the light and
of the Röntgenrays, we find the figures given in table III, graphi-
cally represented in fig. 7. (See p. 680).

The first column gives the number of the experiment, the second one
the increase of density when the action of light is doubled; the third
one the increase of density on doubling the action of the Röntgenrays

In the fourth column the quotient of the figures in the former
columns is given. The 5' column contains the penetrating power
of the X-rays expressed in degrees Brrorsr.

The figures in the 4 column are useful to indicate the amount
of difference in slope of the characteristic curves. If these be com-
pared with those for the hardness of the rays, we find the remark-
able fact, that the difference in slope is less for penetrating rays
than for rays from a lower-vacuum tube. This is best seen in the
curve of fig. 7 which shows an absolutely unexpected linear relation
between the quotient and the penetrating power. The figures in the
last column of table III are calculated with the linear equation :

Quot.: = 1.809 — 0.0776 Degrees BrNorsr.

Though this seemingly anomalous behaviour of the harder rays
might be caused in different ways, we cannot reasonably suspect a
secondary radiation originated in the gelatine bromide layer itself,
as this would occur in every part of the layer. We can only suppose
that the more penetrating rays are mixed with an exceedingly
absorbable radiation which is present to a far less extent in the
radiation of medium hardness. Perhaps a very absorbable radiation
might be generated by the harder X-rays by impact on the glass
support after their passage through the sensitive layer. If the primary
rays already contain a certain amount of soft rays, these may be
derived from the anticathode (as a soft characteristic platinum or
tungsten-radiation) or from the glass-bulb, or perhaps from the
envelope in which the plate was exposed to the rays. Between the
first and the last of these possibilities we must have the difference,
that in the first case the deepest parts of the gelatine layer contain
more silver than the surface, whereas in other cases the surface of
the gelatine will be richest in silver. In order to decide in this
question I asked Dr. Kiussens to make a few microscopic slides
from transverse sections of the gelatine layer of different negatives.

aar

682

Microphotographs of these, enlarged about 500 times show immediately
that the theoretical deductions in my paper are confirmed. In fig. 8
a transverse section through a light-negative shows a strong deposit
of silver in the upper part of the gelatinelayer and hardly any
silverparticles in the deeper strata. A section through a Röntgen-
film made with soft rays (8° Berorsr) is shown in fig. 9. The silver-
particles are almost equally distributed in the layer. From a negative
with hard X-rays (8° Brnotst) I got the photograph shown in fig. 10,

Fig. 10.
in which the surface of the gelatine contains more silverparticles
than the deeper strata. With rays of medium hardness I found a
more even distribution of the silver particles, showing that these
rays contained only a limited amount of extremely soft rays.

683

Astronomy. — “On the influence exercised by the systematic
connection between the parallax of the stars and their apparent
distance from the galactic plane. upon the determination of the
precessional constant and of the systematic proper motions of
the stars.” By Prof. E. F. van pr SANDE BAKHUYZEN and C. pr JONG.

(Communicated in the meeting of Sept. 25, 1915.)

Since the researches made by KarreyN, it may be regarded as
an established fact, that stars of a given magnitude are at a greater
mean distance from us, in proportion as they are nearer to the
galactic plane. At the galactic poles the mean parallax is found
to be about one and a half times as great as in the galactic plane
itself. As in the researches so fur undertaken concerning the pre-
cessional constant and the systematic proper motions of the stars
this connection had not been taken into consideration, it is obvious
that the determination of these quantities may be affected by syste-
matic errors. :

For some time it had been the intention of one of us to institute
a nearer investigation of this matter, all the more because it might
throw light upon a difference, found by Newcoms, between the values
of the piecession-constant, as deduced on the one hand from Right
Ascension- and on the other one from Declination-observations. Later on
it was noticed, that Newcoms himself had indicated the possibility of
such an explanation of the difference, (Prec. Const. p. 67 and 73) and
also that Eppineron in his well known monograph published last year,
“Stellar movements and the structure of the universe’, in pointing
out the desirability of taking the differences of distance into consi-
deration, had already made a beginning in this direction. At the
same time, he only deals with the influence of the inequality of the
distance upon the determination of the apex of the Parallactic
motion (p. 81—83), and only develops it in the case of the inves-
tigation being based upon stars which are evenly distributed over
the entire celestial sphere.

A new research, therefore, embracing the whole question, was by
no means superfluous. We have undertaken it, and in the following
paper we communicate our results. The term “Systematic proper
motions’ is here taken in a somewhat limited sense; it includes
only those motions which are functions of the spherical place of
the star, although the coefficients may still be dependent upon
their distance from us, and perhaps also upon the spectral type,
(we leave that here out of account). Systematic movements which

654

are the consequence of star-streams, or may be ascribed to an equi-
valent non-spherical distribution of the individual motions, which
we might call systematic proper motions of the second kind"), are
excluded from our investigation.

In the first place, then, the dependence of the parallax upon the
galactic latitude must be expressed in a simple formula; for the
derivation of this we have used the table given by Kaprryn and
Weersma in their paper Publ. Groningen 24, 15 In that table
values for the mean parallax are given for the magnitudes 3.0 to
11.0, and for galactic latitudes: between — 20° and + 20°, between
+ 20° and + 40° and between + 40° and + 90°. For all mag-
nitudes the same ratio is assumed: between a, and a, and with
sufficient accuracy for our purpose — the table is given as “quite
provisional” — we could put: zp —= 2, (1 + ¢ sin’ 8).

The three columns of Kapreyn and Weersma’s table were assumed
to apply to gal. latitudes of = 10°, + 30° and + 60°, and it appeared
that the coefficient c must be given a value between 0.60 and 0.70
We assumed therefore

3 = x, (1 + 0.65 sin? B)

The relation assumed by EDDINGTON is equivalent to a formula of
the same form with e = 0.60.

Our value for A must now be substituted in the equations for
the systematic proper motion, whereby, for the present, we confined
ourselves to the terms dependent upon a precession-correction and
upon the parallactic motion.

The usual equations are

X Ve
uw, cos d= A meosd + Ansind sina + — sina — — cosa
RK R
ig 7 7
4 = . .
us = — —cosd + Ancos a+ — sin d cos a + —sind sina
R R R

Substituting in these the value of R, expressed in A, and after-
wards, according to the formula

sin 8 = sin dcosi — cos d sin (a —0) sini

1) The frequency-surface may be more general than the ellipsoid, but must,
according to our definition, have a centre, as the part of the movement that
depends upon the spherical place (Systematic Prop. mot. Ist kind) is subtracted
from the total movement.

685

in which 9 and 7 represent the node and inclination of the galactic

plane in respect to the equator, expressing everything in equatorial

coordinates, we get, after the expansion of the powers and products

of the goniometrical functions of @, leaving the value of @, 7 and c for

the present undetermined :

uz cos S—= A m eos d —1 ¢ sin 2 i cos — sin2 d — Le sin 2i sin 0 — sin2 d
0 0

X x
+|4 DT + 1¢sin?i (2 + =, e982 @) 00 Sf
k, Yo
= Jd in 2 0 ee i Vikg
= sin® isin 2 O — cos° ¢ SU
+ ¢cos*t R, sin? d + esin? isin R, c La

= aaa -++ + sin? i sin 2 20- nd CON d a.
C s?
C

Y us at
+ 1 ¢ sin? 1 (2 — cos 2 0) — cos*, d c cos? 1 — sin? d | cos a
4 >
R, R,

x
+ E esin 2 isin DE sin 2d + esin 2d cos On sin2d | sin2a

sinda

X
+ E esin 2 i eos 0 R° sin 2d — +e sin 21 sin 0. — sin 2 j. s 2a

— | te sin® i cos 2 20— cos? S — Le sin” i sin 2 O — cos? d

Vo 0

x ve
+ | 4 ¢ sin? i sin 2 O — cos? d + Lesin® ieos 2 0 — cos? J | cos 3 a
R 0 R,
X
fo — —cosd + Hesin2isind — cos d sin? d—
R, Jan

7 7

/; Z
— Lesin 2icos 0 — cos dsin° d — } ¢ on cos? d — e cos? 1 — cos d sin? d
Et
0 0 0

q Xx pe
+ lz sin dte sin? isin 20 R -cos* dsind esin Pia 0082 0) = — cos* sind
0 0 Ry

y Z
+ ¢ cos? i — sin? BH esin 2 icos I — cos* dD sin d | sin a
Re R,

X X
e \ er; , 1 pn ams Deine Eet 2 TY
4 E n + pn J + Lesin?2 (2 — cos 2 A) Rp S sind +
0 o
> 5 5 2
= 9 . . 9 . . el Je, ) a 2 .
+ ecos?i— sin® d—+ esin? isin2/ — cos* dsind— esin 2isin 0 — cos* dsind [cost
Ike R, R

2 S
7
— | destin 2 icos O— cos d sin® d — Hesin 21 sin O — cos dsin? d —
Ine R,

686

4
— hkesin?isn20 Rp cos° d | sin2a

Xx ie
+ | hesin2isin 0 — cos dsin? d+ 3 csin2icosO — cos d sin’ d |
R, x.
are Z
+ 4 esin® i cos 2 0 — cos° d | cos2 a
Ry

Xd i :
—| tex sin? sin 2 20 =, cos" dsind 4+ +c sin? 1 eos 2 0 5008 bind [inde

Lo 0

X Jif
-~| 1 ¢ sin? i cos 20 — cos? db sin d — 4 ¢ sin® i sin2 O — cos’ dsind | cos 3a
Ik. Uk
[f in these general formulae we substitute:
0 = 16945" = 281°
is 68:
@G == (00),
we get:

x DA
{tz cos — A meosd — 0.02 — sin 2 Oa le sin 2 d

0 0

: X XO X Mw ;
+ | Ansin d+ RE 0.13 — sin? dH0.14— cos°d—0.05— cos°d [sin a
Ben Ik ieee R,
(es bie d+ 0.38 4 d 0.13 2 J
R, — R, cos’ d + z cos* d + R, sin® cos @
Y
0.13 sin 2 0.08 vin 24 | sin De

Y
0.12 Be ae suse

vr 0

Z }
bekenden

a
0.05 5 eo d + 0.12 om 0 [ease

EZ va
Me ire ere J 0.26 À R cos d sin? dS —0.04 RE cos d sin? d —

0 0 0

Z G
— 0.26 — cos° d — 0.13 — cos d sin? 6
R R

0 0

Myf X We le
+ EF sin d + 0.05 E cos” Osin d Old cos” dsind 0.18 — sin’ d+-

0 0 0 0

Z
+ 0.10 E cos” d sin | sin &

687

X X xX
a E nd R sin d + 0.38 R cos? S sin d + 0.13 R sin d +
0 0

VA Z
+ 0.05 — cos? d sin d + 0.52 — cos* dD sin d | cos a
Te Te

— | 0.04 a cos d sin? d + 0.26 za cos d sin? d + 0.10 a cos* d [sin 2 a
IR R ‘ R

0 0 0

= = nn 0 0) = s + 0 4 Tt Ss d
0.26 d vn d . 4 ‘0% J Ww Jd a Co, é COS ot
cos sin C sin R

0 0 0

X Me é
En | 00s R, cos? J sin d + AT cos” d sin ‘| sn da

} x He
+ | 0.12 — cos? db sin d — 0.05 — cos? d'sin d | cos 3 a
R, - R,

In many cases it is convenient to modify the formulae so that in
place of FR, they contain the mean distance F,, corresponding to .
the magnitude or the mean magnitude under consideration. We will
define this mean distance as the reciprocal value of the mean parallax,
and therefore put :

0
Rn — RS EET
1 40.65 >{ mean value sin 73

We must then integrate si °3 over the whole surface of the sphere,
and in this way we find: mean value of sin °8= 4, so that R, =
1.22 Ry, and this relation must be substituted in all the terms which
are dependent upon the parallactic motion.

To save space, we give below only the values of the numerical
coefficients in the new formulae containing B.

Coefficients in the formulae containing Rn.

MacOS
+1.00 — 0.02 +011

688

ni
— 0/82 OMO OSD

a 0.89 2004 SOM SEO ADE sina
+[+1.00 +082 +031 +011 + 0.04 + 0.43] cosa
000 2008 | sin 2a
= (a SSA Se a0 | cos 2a
+[+ 0.04 + 0.10 | sin 3a
+[+ 010 — 0.04 | cos 3a

Using these formulae we can now trace the influence which the
systematic difference in the distance of the stars of the same mag-
nitude will have upon the derivation of the precessional constant
and of the elements of the parallactic movement, and thus’ deduce
the corrections, which must be applied to results in the derivation
of which the differences of distance were not taken into account.
When we consider this question more closely, however, we soon
see that a sharp determination of the corrections, which would hold
for all the determinations of these constants hitherto made, is hardly
possible.

Even if we assume that the same law of mean variation of
distance with the gal. latitude holds for allindividual magnitudes, which
is perhaps still doubtful for the brightest classes *), it does not follow
that it will also hold for the mean magnitude of a material which
extends over several classes, as the distribution of the separate
magnitudes may be different for the different regions of the heavens.
The working of the simple law may also be disturbed, when, as
is often done, and frequently quite rightly, proper motions above
certain limits are excluded from the discussion.

Further, it is evident that the correct value of the necessary
corrections will be influenced by the manner, followed in each par-
ticular case, of establishing and solving the equations. Where the
separate determination of the various unknown quantities is just
possible, we may try to do so, or by preference take those which
would be determined with the least weight from other investigations.
There is, moreover, ample rooin for differences of opinion as to the
attribution of the weights, and often in different instances different
distributions of weights will recommend themselves. If there is reason
to believe that a group of stars belong together physically, this may
determine us to attribute to it the weight of only one star, and in
general, the discussion may be based upon the individual stars, or

1) Newcomp in his Precessyonal constant Section XIV p. 43—46, points out
the difficulties which the answering of this question presents.

689

upon larger or smaller trapezia in which the celestial sphere is divided.

Some investigators have made use of different methods and have
discussed and combined the respective results; Newcomg, in particular,
has done this in an admirable manner. It is therefore often difficult,
even for the results of one investigator, to fix the exact valne of,
the corrections to be applied to them, and whereas an accurate
knowledge of the foundation of our investigation, namely the exact
mean variation of the distances, is not yet attained, it would cer-
tainly not be worth while to make elaborate calculations concerning
the influence of this variation. We shall therefore only trace this
influence in a few simple suppositions concerning the method of
calculation followed. For this we use the formulae expressed in Zi, ,
as it can be seen at once that the values previously obtained for the
components of the parallactic motion will agree most nearly with
the corrected results for that distance.

In the first place we will consider the influence of the assumed
law of distances, upon the results for. the precessional constant.

a. Determination of the Precession from Right Ascensions. In
this deduction we may either determine the correction of the total
luni-solar precession Ap by expressing Am and An in it, or, elimi-
nating An by attributing equal weights to the results from groups
formed according to the A. R., confine ourselves to the determination
of Am; the influence of An disappears of course, when the material
used is symmetrically distributed over north and south declinations.
If we allow for the influence of An, the correction terms which
contain sim « must be taken into consideration, and we must

investigate how the influence of these terms will be divided between

8 A :
the term in An which contains sind and that in —, which is con-
Lin

stant for all declinations. Now owing to the approximate equality
of two coefficients the whole coefficient of sina is reduced to

; X 4
An sin d + 0.93 EO -, cos? d and, even without the rigorous
m Un

formation of the normal equations, it is clear that, for not too high
deelinations, the term with cos* d will principally influence the
parallactic motion.

So it follows that, even if we take the influence of An into account,
provided our stars are distributed over all R.A. and we do not
attribute too great differences of weight to the different groups, we
may practically only pay attention to the correction terms which
do not depend upon «. Calling the value of Am (variation in 100

690

years) which is found, if the correction terms are left out of con-
sideration, | Am], then

7 7

X }
[Am] = Am — 0.04 E sin d + 0.21 — sin d.

m m
If we accept for the mean distance of the BrapLey-stars (mean
magn. 5.5) according to Newcomp’s results: X = + 0".20, Y = — 2.60
and according to his table on p. 39, as a mean value sin d = + 0.20,
we get Am — [Am] + 0.11 or
corr. dp Newc. = + O".12.

A separate correction of Newcoms’s 7 zones (p. 39) gives the result
corr. dp = + 0".11. ‘

In the second place we compute the correction which must be
applied to the value of Am, deduced by Dyson and TrackKerar from
the comparison of GROOMBRIDGES catalogue with the second 10 year
catalogue. Taking 7.0 as the mean magnitude of the GROOMBRIDGE-
stars, and accordingly (see Newc. p. 34) adopting for A a small
value, putting Y — — 4%. 2”".60 = — 2".00, and accepting (Monthly
Not. 65, 440) as mean declination of the stars + 52°, we find for
the correction to be applied to [Am]: + 0".42 sin 52° = + 0'.33.

In general, if the difference of distances is disregarded, the
precessional constant deduced from the right ascensions will be too
small if we had used stars of north declination and too large if the
stars had south declination.

b. Determination of the precession from the Declinations. To trace
the errors made in this case, by the assumption of equal distances,
we must consider the terms containing cosa. We have two prin-

: EA Ke
cipal terms of this form: A xcosa and —— sin d cosa. Almost al-

m
ways, and unless the mean deel. of the stars in question is large, it
will be preferable to determine the sum of An and the influence
of X and then to substitute the value of derived from the R. A.
This is also Newcoms’s method, and we shall accordingly assume
that this has been done and put:
coeff. of cos a — — sin d = [An]

ni
then, after an easy transformation:
b get A X F,
[An] = An — (0.07 —0.20 cos? d) sin d R. + 0.04 cos* d sen Sd — +

m m

EEZ
+ 0.43 cos* d'sin d —.

““m

691

For Newcoms’s result from the Brapiry-stars we find, taking

Z
according to NewcomB — = + 1"50:

An = [An] — 0".00 + 0".02 — 0".13 = [An] — 0".11

so that
corr. dp Newc. = — 0.29.
As the first correction term is always small and the three others
; . X ) 4
have as factor cos? d sin d, while the sum 0.20 0.04 EE
mm m

— 0.437 has a considerable negative value, the precessional
an

constant from declinations will be found too large for stars with a

north declination, or when in the compared catalogues stars with

a north declination are preponderant, while stars with a south

declination will yield too small a value.

We have therefore arrived at the remarkable result that, in deriving
the precessional constant in the ordinary way, in which no attention
is paid to the dependence of the distances upon the galactic latitude,
from catalogues with preponderating north declinations the lunisolar
precession p is found /aryer from the declinations than from the
R.A., while the true value must lie between these two, and nearer
to the result from the R.A., and thus, to some extent at least, the
discrepancy found by Newcoms is accounted for. The values finally
assumed by Nrwcoms for dp and those corrected according to our
investigation are as follows:

Nrwcoms Corrected
dp from R.A. — 0.36 + 0.48
» Decl. + 1.12 + 0 .83

The difference found by NewcomB is thus reduced to half, and
no longer presents a serious difficulty.

It should be mentioned once more, that, after the completion of
our calculations, the explanation found here appeared to have
been suggested by NewcomB himself as a possible cause of the discre-
paney; so far his remarks upon this subject do not appear to have
received sufficient attention.

Distinguishing by the names of “vernal region” and “autumnal
region” the regions between R.A. 19°.5 and 55.5 and between
7h5 and 17".5, he says on p. 67: “A very little consideration
“will show that if the stars of a given apparent magnitude are
“farther away within the vernal region than within the autumnal

692

“region, then the smaller parallactic motions in the former region
“will tend to diminish the precession found from the right ascensions
“and increase that found from the deelinations”, while later on p. 71
in drawing up his final conclusions he says: “I have already
“remarked that a possible cause for the discrepancy..... EEE
matter of fact the galaxy, for the northern heaven is in the vernal
region, and for the southern in the autumnal one.

As NwewcomB further, according to observations of the sun and
of Mercury, considered as probable a correction of the assumed
centennial motion of the equinox in the system NV, by + 0".30, he
finally assumed óp = + 0".82. With this correction, our results
become

dp from A.R. + 0".78
from Deel. + 0.83

dp mean ao 0.80

so that the discrepancy would then vanish entirely. If we do not
accept the latter correction, our final result is

dp mean + O".66.

There is a striking agreement between the mean of the results
from « and d, as they are found by us, with that which Newcoms
found by eliminating the parallactie motion from the motions of the
individual stars, by a method corresponding in principle to one
given before by Kaprryn (use of the proper-motion-component rt).
NeEwcomB found in this way:

dp = + 0.64
or, if he accepted the corrected motion of the equinox, by estimation,
+ 0".84.

From this we get a strong impression that the principal un-
certainty which still remains in the precessional constant according
to the BRADLEY-stars, is not due to the method of treatment, but to
possible errors in the catalogues compared and particularly on the
one hand to an error in the equinox and on the other hand to
periodic errors in the declinations, the Adz.

The precession in R.A. (the value form) deduced from the Groom-
BRIDGE-stars by Dyson and THACKERAY, was already much larger
than the m according to Nrwcoms, and the discrepancy becomes
still greater by applying our corrections. Beside this result they deduced
a value for An from the R.A. and Decl.-observations together, which
is grounded upon the principle that from large and from small
proper motions the same R.A. of the apex must be found. It cannot

693

be seen at once, how the difference in distance of the stars
will affect the results by this method. This investigation gave
Apyewe. = +0".48, while the R.A. after applying our correction
gave Apnewe, = + 0".76 + 0".383 = + 1'.09. In these results too,
catalogue-errors probably play a considerable part.

Finally we must draw attention to the terms which we found,
depending upon 2e and 3e, amongst which there are some which
may attain values which can certainly not be neglected.

We have in R.A. the terms:

7 7

}
+ 0.11 sin 2d —- cos Za — 0.10 cos? d — cos 3a

mt m
that is for stars of the magnitude 5™.5:
— 0".29 sin 2d cos Ze + 0".26 cos? db cos 3a
and in Deel. to confine ourselves to the terms in 2a,

. 5

Z 5
— 0.08 cos? d — sin 2a — 0.20 cos? d—- cos 2a
mj m

that is for stars 5,5
— 0.12 cos” d'sin 2a — 0,30 cos? d cos 2a.

These terms will, when we do not take account of them in our
calculations, be added to the corresponding ones arising from periodic
catalogue-errors, and show all the more clearly, that no conelusions
can be easily drawn from limited areas of R.A., and that it is
advisable in investigations of this kind as far as, possible to give
equal weights to the different R.A.-groups.

In the second place we investigate the influence of the assumed
law of distances upon the determination of the parallactic motion.

We assume here that the A and Y-components are deduced
from the f.A. only, that is, from the terms which depend respectively
upon sie and cosa, and that for the determination of Y a value
of An is introduced, which is deduced from other terms (m in «‚ 7

in d). If we then indicate by lz. | the value which is found when

Un
we regard the distance as only dependent upon the magnitude, and
act in the same way with regard to the two other components,
and if we further apply a few simple transformations, as was
already partially done above, we get
X x yeh
=| Uda 0.04 bos" dT
Rin m Vijn

de X }
> |= 0.938—— — 0.04 cos* d — + 0.20 cos? d —

m Un tm

694

El == 0) 932 + 0.21 sin? eal + 0.08 sin? el + 0.10 cos? ze
Rin Rn Eem En Me

These equations contain in the correction-terms only cos*d and
sin? d, so that they do not disappear even by integration over the
whole sphere. We see thus, that, even when the stars used are
spread evenly over the whole sphere, 1*t the velocity-components
for the mean distance, corresponding to sin° = 4, are not equal
to those which are found in the assumption of equal distances, and
ged that the changes which Y, Y, and Z undergo are not proportional
to the quantities themselves, so that the place deduced for the apex
also undergoes a change. As we have: mean value of cos* d=,
m. v. of sin? d =+4, we find for the entire sky:

: ACT ey.

EE gs 0.03 Gn

Sm Lig

y Xx

= p98 =

Rn bn Een
AIS og ete ete
=| Lh. Rt Sj = : ==.
2). m Ry Je Rn, je Rn

Starting from the same values of the three components for the
BrADLEY-stars, as were accepted before, the corrected values for the
mean distance are as follows:

Original Corrected Correction
X + 07.20 + 0".14 — 0".06
Je — 2 .60 —2 43 +0 17
a 450 V4 51 +0 .04
and the R.A. and Decl. of the apex become:
Original Corrected Correction
A 274° 24 273° 20! —1° 4
D +30 0 + 31 48 +1 48

As we said at the beginning of this paper, this particular problem
appeared to have been already treated by Evpineron in his Stellar
movements p. S1—83. He found, starting from practically the same
data, but by an entirely different method, that A in particular will
need a correction, viz. of about —2.°4. The two results for A
agree tolerably well, and ours is also not accurate to a few minutes.
We find also an appreciable value for the correction of D, although
the Zcomponent remains almost unchanged.

The result found for the whole sky is equal to that for d= + 35°15!
As a second example we will calculate the corrections for d= 0.

695

x X Ji
- | = 0.98 — — 0.04 —
Ti Ee:

ye Nig X
— |= 1.13 — — 0.04 —
Fen Ry Rn

Z Z
— |= 1.03 —
Lijn Tú

and herewith we find, starting from the same original values as above,

Original Corrected Correction
Re + 0".20 Olid —0".09
Y 293.60 — 9.29 ld
Z + 1 .50 +1 .46 — 0.04
A 274°24’ 272°45’ — 1°39’
D + 30 0 + 32 32 + 2 32

The corrections to be applied differ not much, therefore, from
those in the first case.

As the components of the parallactie motion are thus found to
require appreciable corrections, those found above for the precession
are no longer quite correct, but their errors are of the same order
as other unavoidable inaccuracies in the calculation.

The result of our research is thus to show that in researches coneern-
ing precession and systematic proper motions it is necessary to take
into account the dependence of the mean distance upon the galactic
latitude: its influence upon both the precessional constant, and the
parallactic prop. motion cannot be neglected.

By taking this influence into account it is possible to bring into
fair agreement Newcoms’s results for the precessional constant found
from observations of R.A. and from those of Decl. For the present,
therefore, it is not necessary to follow Hoven and Harm, who
proceed from a new definition of the precession, by which this is
not to be determined with reference to the whole of the stars, but
with reference to the mean of the two star streams regarded as
of different strength in different parts of the sky: a method which,
moreover, as it would appear, involves great difficulties.

This, of course, does not mean that we can now rely upon the
precession, determined relatively to a large complex of stars, giving
us the true mechanical precession. To throw more light upon this
subject many more extensive researches will be necessary, in which
attention must also be paid to general rotations possibly occurring
in our system of stars, as first proposed by ScnHönreLp. lt seemed
premature to include terms of this kind in our present calculations.

Proceedings Royal Acad. Amsterdam. Vol. XVIII

696

Physics. — “Brperimental proof of the existence of Ampere’s
molecular currents.” By Prof. A. Einsrern and Dr. W. J. pr Haas.
(Communicated by Prof. H. A. Lorenrz),

(Communicated in the meeting of April 23, 1915).

_ When it had been discovered by Oxrstep that magnetic actions
are exerted not only by permanent magnets, but also by electric
currents, there seemed to be two entirely different ways in which
a magnetic field can be produced. This conception, however, could
hardly be considered as satisfactory and physicists soon tried to
refer the two actions to one and the same cause. AmpirE succeeded
in doing so by his celebrated hypothesis of currents circulating
around the molecules without encountering any resistance.

The same assumption is made in the theory of electrons in the
form e.g. in which it has been developed by H. A. Lorentz, the
only difference being that, like electric currents in general, the
molecular currents are now regarded as a circulation of elementary
charges or electrons.

It cannot be denied that these views call forth some objections.
One of these is even more serious than it was in Ampbre’s days;
it is difficult to conceive a circulation of electricity free from all
resistance and therefore continuing for ever. Indeed, according to
MAXWELL’s equations circulating electrons must lose their energy
by radiation; the molecules of a magnetic body would therefore
gradually lose their magnetic moment. Nothing of the kind having
ever been observed, the hypothesis seems irreconcilable with a
general validity of the fundamental laws of electromagnetism.

Again, the law of Curig-LANGrvIN requires that the magnetic
moment of a molecule shall be independent of the temperature, and
shall still exist at the absolute zero. The energy of the revolving
electrons would therefore be a true zero point energy. In the
opinion of many physicists however, the existence of an energy of
this kind is very improbable.

It appears by these remarks that after all as much may be said
in favour of AMmPÈre's hypothesis as against it and that the question
concerns important physical principles. We have therefore made
the experiments here to be described. by which we have been able
to show that the magnetic moment of an iron molecule is really
due to a circulation of electrons.

The possibility of an experimental proof lies in the fact that every
negative electron circulating in a closed path has a moment of

697

momentum in a direction opposite to the vector that represents its
magnetic moment, the ratio between the two moments having a
definite value which is independent of the geometric dimensions
and of the time of circulation. The magnetic molecule behaves as
a gyroscope whose axis coincides wich the direction of the magneti-
sation. Every change of magnetic state involves an alteration of
the orientation of the gvroscopes and of the moment of momentum
of the magnetic elements. In virtue of the law of conservation of
moment of momentum the change of ‘‘magnetic’ moment of momen-
tum must be compensated by an equal and opposite one in the
moment of momentum of ponderable matter. The magnetisation of a
body must therefore give rise to a couple, which makes the body
rotate. *)

1. Magnetic moment and moment of momentum of the molecule.
g

The magnetic moment of a current of intensity ¢ flowing along
a circle of area fis given by the formula
minn
or if the current consists in an electron circulating n times per
second by
Sai ee ote (1)
It may be represented by a vector perpendicular to the plane
of the circle, the positive direction of this vector corresponding in
the well-known way to the positive direction of the current.
The moment of momentum is
NE en eZ)
if we let coincide its positive direction with that of the magnetic
moment.
Hence :
2m

DE il RER EAN

€
„For a body in which a certain number of electrons are circulating,

this becomes
Qin

=m — — Em,
7

or if we denote the magnetisation Ym by /

1) This paper had gone to press when we learned that O. W. RicHARDSON
(Phys. Rev. Vol. 26, 1908 p. 248) had sought already for the effect in question, without
however obtaining a positive result.

45*

698

2m
=m = — (4)
é
§ 2. Consequence of the existence of a magnetic moment
of momentum.

Any change of the moment of momentum >M of a magnetized
body gives rise to a couple 4 determined by the vector equation
am

G=— 2

aat
= 1,13:107" — ot
dt
where the numerical coefficient has been deduced from the known
value of - for negative electrons.

It has been our aim to verify the relation expressed by (5). We
shall show in the first place that the calculated effect is not too
small to be observed. Let the body be an iron cylinder with radius
R, which can rotate about its vertical axis. We shall deduce from
(5) the angular velocity w the cylinder acquires by the reversal of
a longitudinal magnetisation, which we suppose to bave the satura-
tion value /,. Denoting by Q the moment of inertia of the cylinder,
and writing 4 for the above coefficient 1,18. 107, we find :

Qo = [dt fig
Now, if the saturation value of the magnetisation per cm° is 1000,
Me M
which is not a high estimate, we have /, = ze 1000. The moment
‘y
of inertia is Q= 4 WR’, and we find for R=O0,1 cm
: DEU Oe,
an angular velocity that can easily be observed.

§ 3. Description of the method.

At first sight it seems that equation (5) may be tested in the
following way. A soft iron cylinder C' is suspended by a thin wire
D coinciding with the axis of the cylinder prolonged, the period of
the torsional oscillations being a few seconds. Let the cylinder C
be surrounded by a coil A whose axis coincides with that of C.
Then, on reversing a current in A, a rotation of C ought to be
observed. In reality, however, this simple method cannot be thought
of. As the field of the coil will not be uniform the cylinder
would probably show highly irregular motions completely masking
the effect that is sought for.

699

Better results are obtained if the effect is magnified by reso-
nance. For this purpose an alternating current having the same or
nearly the same frequency as the oscillations of C about the wire
D is made to flow through the coil.

For the oscillations of C about the vertical axis under the influence
of the couple 6 we have the equation

B= Oe Oo Pa sn ke en)
in which the angle «, the deviation from the position of equilibrium
is reckoned positive in the same direction as the current in the wind-
ings. Q is the moment of inertia, © the torsion constant of the
wire and P a small coefficient of friction. Instead of @ and P we
shall introduce two new constants

Va P 5
Or DT gere Vee

the first of which is 27 times the free frequency, as it would be
in the absence of friction, whereas x is the constant of damping.
Indeed the free oscillations (the equation for which is deduced from
(6) by putting 6 —=0) are given by
a = Ce—*t cos (V w,? — x? t + p).
The differential equation (6) is easily solved if we develop 6 as
a function of ¢ in a Fourrer series. Now according to (5) 4 has

the same phase as aoe Hence, if the magnetisation were proportional
at

to the current we could directly represent 4 as a harmonie function
whose phase would be +. in advance of that of the current 7 in
the coil. The proportionality will, however, hold for small intensities
only. If the amplitude of 7 is made to increase so that the magneti-
sation approaches saturation, the magnetisation curve takes a differ-
ent form. Finally, for very large amplitudes of 7, the magnetisation
will suddenly pass from one saturation value into the opposite one,
simultaneously (except for a small difference of phase) with the
change of direction of the current. For this limiting case the cal-
culation will now be made.

The couple acting on the cylinder may be represented by fig. 1,
in which the sinusoid refers to the current 7’).

‘ dl ‘
1) The curve with the sharp peaks represents the value of —, to which the couple

dt
@ is proportional. It was obtained in the following way. The iron cylinder, which
had its right position along the axis of the coil K, was surrounded by a narrow
glass tube covered with windings and immediately beside this tube a similar one,
equal to it and covered in the same way, was placed. The windings of the two

700

Fig. 1.
Kach sharp peak corresponds to a reversal of the magnetisation
and we have for each of them

foa=+uar, EEE

Let the origin {== 0 coincide with a point in Fig. 1, where the
current passes from the negative to the positive direction. Then we
may write

1 =A sin Ot; Amen 2), EERE
and @ may be developed in a series
n=O
C= PSB cosinor ERE EO)
n=1

Of this series the first term only need be considered here, as the
effect corresponding to it is the only one that is multiplied by
resonance, so that the other terms have no sensible influence on the

motion of the cylinder. Now, multiplying (10) by cos wt and inte-
am
erating over a full period 7’=— we find

o
3m
» Oe) z
0 cos wt dt =— B.
A co)
7

On the left hand side @ is different from O only in the very small

JT
intervals at ¢= 0 and t=~—. For the first of these we may put
w

tubes were connected in such a way, that a current passing through them flowed
round the tubes in opposite directions.
Under these circumstances, the current induced in the windings is exactly pro-
; dl ah 5 : :
portional to Fe the demagnetizing action of the poles of the iron bar being
C

eliminated, as well as the induction due to the field of the coil K. The graph

‘ dl 4
for the induced current, and therefore for ai or 6 was obtained by means of an
oscillograph of SteMENs and Harske. The alternations of the current 7, repre-
sented by the sinusoid, were registered in the same way.

701

cos ot=1 and for the second cosmt=—=—1 so that we find,
using (8)
4
BNN oe Ee (EI
u 4

Instead of (6) we now get the equation
Bost Qed Oe baw. se.
the periodie solution of which is

1
a=— cos(wt—v), « . . « « « « (13)
u

if the constants w and v are determined by

u Gi v = (w,’—@’) Q (14)
usinv =2xwQ
Here the quantity w, to which we shall give the positive sign,
determines the amplitude whereas the phase of the oscillations is
given by the angle ». For the amplitude, which we shall denote
by |a|, we find

Ay lee
lq| == nn)

CE der 4x?

For w= w,‘it becomes a maximum |e|,, viz.

| ZN ar
ana OENE le (LG)

ke 4
As to the phase, we first remark that according to (14) In

for w=w,. If the frequency of the alternating current is higher

Jt
than that of the cylinder, we have v >> — and in the opposite case

Jt
nd When w is made to differ more and more from w‚, the

phase v approaches the value 2 in the first case and 0 in the second.
If the constant of damping * is small we may say that these
limiting values will be reached at rather small distances from w,
already. In our experiments this was really the case and we may
therefore say, excepting only values of w in the immediate neigh-
bourhood of w, that v=a for w >o, and v=0O for ww.
Taking into account what has been said about the positive direction
one will easily see that, if the current # and the deviation « had
the same phase, the eylinder would at every moment be deviated
in the direction the eurrent in the coil has just then. In reality the

702

phase of the oscillations of the cylinder is behind that of the current

by an amount v— =; this follows from (9) and (13). Remembering

further that in the deduction of (11) it has been assumed that
the circulating electrons are negative and that if they were positive
ones, the sign of B, and the phase of the effect would be reversed
we are led to the following conclusion :

Negative electrons.

w >w,. The phase of the oscillations of the cylinder is a quarter
of a period behind that of the current.
ow, It is a quarter of a period in advance.
=w,. The vibration has the same phase as the current.

Positive electrons.

w >w,. The phase of the oscillations of the cylinder is a quarter
of a period in advance of that of the current.

w <w,. It is a quarter of a period behind that of the current.

w =w,. The vibration of the cylinder and the current have opposite
phases.

It is important to notice that there is a quarter of a period
difference of phase between the active couple 6, cos wt and the
current == Asint and likewise between the active couple and
the alternating magnetisation. This is always so, independently of
the relative values of w and , and of the sign of the circulating
electrons.

§ 4. Short description of the apparatus.

The alternating field which has been mentioned several times
already was excited by two coils placed with their axes along the
same vertical line and with a distance of about 1 cm between
them. They were mounted on a brass foot to which three foot screws
could give different inclinations. The coils were connected in series
and gave a field of about 50 Gauss. The iron cylinder was suspended
along ‘their axis. This cylinder, 1.7 mm thick and in the first
experiments 7 em long, was carefully turned of soft iron. Centrally
in its top there was bored a narrow hole of diameter 0.3 mm in
which a fitting glass wire was sealed. At its middle the cylinder

703

wore a very light mirror made from a silvered microscope covering
glass. The light of a single wire lamp was thrown on the mirror
through the space between the two coils. The reflected rays formed
an image on a scale placed at a distance of 45 cm When the
cylinder was set vibrating this image was broadened into a band,
the width of which determined the double deviation.

In order to obtain resonance, it must of course be possible to
regulate the length of the glass wire. For this purpose we used a
clamping arrangement by which the glass wire could be tightly
held at different points of its length.

The clamp and the suspending wire with the cylinder could rotate
together about a vertical axis in a fixed column. The effective current
was read on a precision instrument. Finally, the whole apparatus
was surrounded by an arrangement by which the terrestrial magnetic
field could be compensated. We shall revert to it further on.

§ 5. The experiments.

Let us now examine the principal disturbing causes.

1. At the ends of the cylinder alternating poles are induced.
Acting on these the horizontal component of the terrestrial field can
give rise to a couple alternating with the same frequency as the
current and tending to rotate the cylinder about a horizontal
axis. (Effect 1).

Rotations of this kind have not, however, been observed by us.

2. According to the views of Wriss the ferromagnetic crystals
are lying irregularly in all directions. It may therefore happen
that some of them are directed in such a way that their magnetism
is not reversed by the alternating field. In this case there will be
a permanent horizontal component of the magnetisation, which,
acted upon by the alternating horizontal component of the magnetic
field in the coil, will give rise to an alternating couple around the
vertical axis with the same frequency and phase as the alternating
field (Effect Il).

3. The axis about which the cylinder rotates will not coincide
accurately with its magnetic axis.

A permanent horizontal magnetic foree such as that of terrestrial
magnetism, will therefore produce torsional oscillations of the cylinder.
The couple which excites these oscillations has the same phase as
the magnetisation and (in the case of strong currents) as the alter-
nating current itself.

4. It is easily seen that the Fovcaurr currents which are induced

704

in the cylinder cannot have any influence in our experiment, their
sole effect being a slight retardation of the magnetic reversals. So
far as we can see, the above effects are the only ones that have
the same frequency as the current in the coil and are therefore
magnified by resonance. When now the coil was connected to the
main alternating current conductors the image on the scale remained
perfectly at rest so long as the length of the suspending wire was
not such as to make the frequency of a free vibration of the eylin-
der coincide very nearly with that of the alternating field. The
resonance appeared and disappeared again by a change of length
of the wire by 1 mm, the whole length being 8 cm.

In order to find the length required for resonance and to make
sure that the suspended apparatus did not vibrate in one of its
higher modes, we used the following method by which we could
also determine the moment of inertia of the cylinder.

At the lower end of the iron cylinder we sealed a short copper
cross bar whose moment of inertia was 10,7.

For the moment of inertia of the cylinder calculation had given
0,0045.

It follows from this that the period of oscillation of the cylinder

10,7
becomes ke 00a = 48,8 times greater by adding the small cross
4 5

bar. If therefore we chose the length of the wire so as to have a
frequency 1 *) with the cross-bar, the frequency without it would
be about 48,8. This is nearly equal to the frequency of the alter-
nating current.

We were sure by this that the suspended system would vibrate
in its fundamental mode. In order to determine the moment of
inertia more accurately however, the cylinder was now placed
within. the coil and the length of the wire was increased until the
resonance was at its maximum. Then the frequency of the free
vibrations might be supposed to be equal to that of the alternating
current which was found to be 46,2. After this the arrangement
was removed from the coil and the cross bar fixed to it. We then
found the frequency 1,14. From these numbers we deduce

Q=10,7 (5) = 0,0065
TTN AD Tae

After these preparations it was found that Effect II, i.e. the

oscillation caused by permanent poles in the eylinder, was of no

1) By frequency we always mean the number of complete oscillations in a
second.”

705

importance. The double deviation remained unchanged when the
position of the axis of the coil with respect to a vertical line was
changed by means of the foot screws, a change which gave rise to
horizontal alternating fields.

Effect III, however, which was caused by the action which stati-
onary magnetic fields can exert on the alternating poles on account
of their excentric position could easily be observed. The double
deviation changed immediately when a permanent magnet was
brought near the coil. The influence of the terrestrial magnetism
was also apparent. When it was not compensated we got, in the
case of resonance, a broadening of the image on the scale up to
3 cm for a scale distance of 45 em. In all further experiments
the terrestrial field has therefore been compensated, the measure-
ments required for this being made with an earth inductor and a
ballistic galvanometer. The horizontal and vertical components of
the terrestrial field were compensated separately by means of hoops
of about 1 m. diameter on which copper wire was wound. The
current was taken from storage cells, and precision Amperemeters of
SIEMENS and Harske served for continually controlling its strength.

Whether the compensation was obtained could be tested by turning
the upper end of the suspending wire. The amplitude of the oscil-
lations changed by this so long as the terrestrial magnetism was
still acting on the iron magnetized by the alternating current. After
compensation however this azimuthal sensibility of the effect had
disappeared. After all there remained a well marked double devi-
ation of 4,5 mm.

We now had to make sure that this was really the effect we
sought for. For this purpose we first availed ourselves of the cir-
cumstance that the acting couple must differ a quarter of a period
in phase from the current and the magnetisation. We brought a
permanent magnet near the coil, thereby calling forth effect III
and adding to the couple B, cos wt, with which we are concerned,
a new one, which has the same or the opposite phase as the magne-
tisation and therefore differs a quarter of a period in phase from
B, cos wt. Whatever be the sign of this additional couple, the ampli-
tude of the resulting one must become larger than 5,. We found
indeed that the broadening of the image always increased when we
brought a magnet near the coil.

Further the theory requires that the magnitude of the effect depends
on the intensity of the alternating field in the same way as the
magnetisation itself. This was likewise confirmed by experiment.

Finally we shall compare the observed magnitude of the effect

706

with the theoretical one. If we take 1200 for the magnetisation
reached by the iron, we get (the volume of the cylinder being 0,16
em’) /;= 192. By direct observation of the oscillations in the alter-
nating field we found

K = 0,533.

As ( = 0,0065,
it follows from (16) that

le) = 0,0036.

For a scale distance of 45 em this gives for the double deviation
dla). 45 = 0,65; as has been said already, we have found 0,45 by
our experiments.

As to this difference we must observe that the theoretical value
is an upper limit, as the magnetism does not change its sign in-
stantaneously.

On account of the demagnetising influence of the free poles the
field in the coil must be rather strong if on its reversal the mag:
netisation is to take immediately a constant value in the new direction.

$ 6. Determination of the phase.

_ We have seen that the active couple differs a quarter of a period
in phase from the alternating magnetisation. Further it follows from
§ 3 that by comparing the phase of the effect (P,) with that of the
alternating current (P,) we shall be able to decide, whether the
electrons circulating round the iron molecules are really negative
ones. We have tried to effect this by proceeding in the following way.

The single wire lamp used for the scale reading was connected
with the main alternating current conductors in parallel with the
coil that contained the iron cylinder. If then we brought a perma-
nent. magnet near the lamp, the incandescent wire was set into
motion by alternating electromagnetic forces, so that, besides the
oscillations due to the vibrations of the mirror, the image also
performed those that were caused by the motion of the wire.

By observing whether the addition of this last vibration increased
or decreased the amplitude of the image, we could compare the
phase P, with that of the new vibrations. Now this latter is deter-
mined by the phase of the glowing wire and this in its turn depends
on the phase of the current in it, whereas the difference between
this phase and P, is determined by the self-induction of the coil.
It would therefore be possible to compare the phases P, and /,.

Unfortunately, when our experiments had been brought to a con-
clusion and one of us had left Berlin it came out that a mistake

707

had been made in the application of the method, so that we must

consider as a failure this part of our investigation. The negative

sign of the circulating electrons is however made very probable by

the agreement between the magnitude of the observed effect and
€

the value we have deduced for it from that of the ratio — for
m

negative electrons.

$ 7. More accurate measurements.

The measurements thus far deseribed furnished a satisfactory con-
firmation of the theory, but were much lacking in precision. The
tield in the coil was too weak practically to cause the sudden
reversals of the magnetisation assumed in the theory. Further the
coefficient of damping « could not be determined with any accuracy.
Even the question may arise whether the influence of the damping
is represented rightly by the term Pe in equation (6).

For these reasons we have somewhat modified our apparatus. In
order to quicken the reversals of the magnetisation we used instead
of the former short coil one of 62 em length (about 100 windings
to a em) the amplitude of whose field, for an effective strength of
1,45 Ampére was 260 Gauss in its central part and therefore 130
Gauss at the ends. In order to diminish the demagnetizing influence
of the poles we further used a cylinder of 16 em length and 0,17 em
diameter. The mirror was now suspended by a thin walled tube that was
sealed to the lower end of the iron cylinder. It just projected beneath
the lower end of the coil. In order to avoid a determination of the
coefficient of damping and assumptions about the law of damping
a series of experiments were made in which, for a definite length
of the wire, the amplitude |« was determined for different frequen-
cies of the alternating current, so that a “resonance curve” could
be drawn.

The alternating current was furnished by a generator placed in
the cellar of the building and moved by the current of a battery
of storage cells. The apparatus in the working room comprised a
variable resistance connected in parallel to the windings of the field
magnets. By varying this resistance we could change within certain
limits the exciting current in the motor and therefore the number
of its revolutions and the frequency of the induced alternating
current. The current which passed through the variable resistance
was controlled by an ampèremeter. When all other things were kept
constant the frequency of the alternating current was a function of

708

the strength of the current in the variable resistance. Besides we
used a resonance frequency meter of Hartmann and Braun, with
which we could accurately determine definite frequencies (45 ; 45,5;
46 up to 55). The intermediate frequencies were interpolated by
means of the ampèremeter. The amplitude of the vibrations of the
cylinder was measured in the same way as in the former experi-
ments. However, in order to increase the precision we now took a
scale distance of 145 cm.

In fig. 2 the results have been plotted graphically. The numbers

709

on the horizontal ') axis give the frequencies of the alternating
current, those on the vertical axis 10 times the double deviation in
centimeters. :

For the Eeen we each time used two points at the same
height combined with the ordinate of the highest point of the curve.
If for shortness’ sake we put

4) Is

it follows from (15) that

e/o
la! wo"

Now, if @,(>,) and w‚ (Cw) are the two values of w corre-
sponding to the same paoktude \a| we have the equations

En Eg + 4x? and am a\7 er — 453,
i |

By elimination of w, and x from these and from

A
f = 2x
loen
we find
we u ;
oe = (w,—wa,)’.
le lal eae

Let » be the difference in frequency of the two chosen points,

so that w, — w, = dar and let us put
a
cc
|@ lm

Then we find, after introducing the value of u

b
rao iain eZ ee ob nrs een er O7)

When the resonance curve has been drawn, (17) gives a value
of A for each ordinate |e|. If this value or what amounts to the

b? \ Ä :
same vf / 7 is constant, this proves that the influence of the

damping can really be represented by a linear term in the equation
of motion.
The following table contains the values of » and 5, taken from

b?
the diagram and those of » [ez ae have deduced from them.

1) If the figure is brought into the right position by a rotation of 90°,

nes | nit hoe dn
| |
15 0,0911 0,812 1,32 0,120
12 0,152 0,649 0,853 0,130
9 0,221 0,488 0,560 0,124
1 0,293 0,380 0,413 0,121
5 0,403 0,271 0,280 0,114
4 0,489 | 0,217 0,222 0,108
3 0,618 0,163 0,165 0,0957

The last column shows that for the greater deviations, not less
Sa
1—b?
being sufficiently constant. If we pass on to smaller ordinates this
quantity seems to decrease very rapidly. lt must be remarked how-
ever that the small ordinates cannot be measured with sufficient
precision. We shall therefore use the first four ordinates only. The
mean of the numbers deduced from them is

than 7 mm, the curve agrees satisfactorily with theory, | ZK

b?
1) NEN
152
Further it follows from the curve that
ae — 0,320. 10-2
(lm = 7454 —= et - .

The moment of inertia of the vibrating system was determined
by measuring the change of frequency produced by the addition of
a small moment of inertia, which is accurately known.

We found *) for it

Q = 0,0126

If now we take 1300 for the magnetization (calculated from the
hysteresis curve of the material and the constants of the coil) we
find for the magnetic moment of the cylinder

Ts 40;
With these numbers equation (17) leads to the value
1) Is may be mentioned here that, assuming a pure cylindrical form, we caleu-

lated for the moment of inertia of the cylinder without the glass tube and the
little mirror Q = 0,0102.

714

A= (0th

which agrees very well with the theoretical one 1,13. 10-7.

We must observe, however, that we cannot assign to our measu-
rements a greater precision than of 10°/,.

It seems to us that within these limits the theoretical conclusions
have been fairly confirmed by our observations..

The experiments have been carried out in the “Physikalisch-Tech-
nische Reichsanstalt”. We want to express our thanks for the appa-
ratus kindly placed at our disposition.

Physics. — “On a possible influence of the Frusner-coefficient on
solar phenomena’. By Prof. P. Zenman.

(Communicated in the meeting of September 25, 1915).
4 du
u dd
Lorentz in the expression for the Fresner coefficient (cf. also my
paper Vol. 18, p. 398 of these Proceedings) may give rise to a
change in the propagation of lightwaves if in a moving, refracting
medium a change of velocity occurs. | suppose the medium to have
everywhere the same density and to be flowing with a velocity v
parallel to the axis of X in a system of coordinates that is at rest with
respect to the observer. In the direction of the Z axis a velocity
gradient exists in such a way, that the velocity decreases with the
distance to the X axis and becomes zero at the distance z — A. If
now the incident lightbeam (with a plane wave front) is parallel to
the axis of X, the parts of the wave fronts which are near this
axis will be more carried with the medium than those at a greater
distance. The wave front will thus be rotated.

If the velocity decreases linearly in the direction of the Z axis
the wavefront will remain plane. In a time 4 the angle of rotation,

. Evt. : ú
(supposed to be small) will be a —- Ans where ¢ is the FRESNEL

We shall prove here, that the presence of the term — of

coefficient and where v and A have the above mentioned meaning.
More in general we may consider an element of the wave front

PRE RUr RoD .
and then write ae for x: Moreover ¢ may be expressed as a func-
az

tion of the velocity of light and the path through which the rays
have travelled, so that we find

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

712

In general this angle is infinitesimal, but it will take higher

a AL 2 1 2 du
values if ——- becomes very large. In the expression ¢, = 1 —— — ——
dà : u add
we only need to keep the last term, so that (1) becomes
Ad ee REL du l dv
Ze dn EE
da c/u dz dd ce dz

If the normal of the wave fronts forms an angle 7 with the
direction in which the gradient of the velocity changes most, we find
du l dv

==) BUG MS lok” EE
a DO sin 1 (3)

This equation makes it possible to construct the path of the light
ray starting from a given point in a given direction.

In order to show how great the influence of the dispersion term
may become in different cases I give here some tables referring to
water, carbonic disulphide and sodium vapour.

For water and carbonic disulphide we have calculated with the
data from well known tables the values of u for some values of 2

dn AE
(in A.U.) In the third column the values of — in cm.) are

given, while in the fourth the Fresne, coefficient ej is found.
The last column gives the value of the dispersion term separately.

For sodium I take the value of 4 and gj. from Woon’s') obser-
vations, made at 644° C.; now e, reduces to the dispersion term.

1.
The values of e, and of — = are only of interest as to the
C
order of magnitude.
Water.
ARo du 2 du
Aim A.U. u — | EL — — —
dà u dà
4500 1.3393 650 0.464 0.021
4580 1.3388 615 0.463 0.021
5461 1.3346 390 0.454 0.015
6440 ARS 270 0.449 0.013
6870 1.3308 216 0.447 0.012
Carbonic disulphide.
4358 1.6750 5000 0.774 0.130
5461 1.6370 1900 0.690 0.063
6870 1.6160 1200 0.668 0.051

1) Physical optics. p. 427. 1911

713

Sodium vapour.

Nut 9 du 2 du
Ain A.U. [Weta rr 7 za EL:
5882 0,9908
1,3.10° 7,8
5885 0,9870
8,1.10° 48
5886,6 0,9740
NT JU 102
5888,4 0,9443
2805" 105 2100
5889,6 0,614

In the application we are going to make of equation (2) « is
supposed small, so that we need not integrate over the path of the
ray. We suppose in the sun a radially rising, selectively absorb-
ing gas mass, in which a velocity gradient exists perpendicular to
the radius. Even without the density gradients, which are necessary
in the theory of Junivs, there must be here a deflection of the light
waves, especially for the wavelengths in the neighbourhood of the
absorption lines.

If we try to work out quantitatively the idea, on which rests
equation (2) we directly meet with the difficulty, that the necessary
data are failing. Still we may derive a conclusion from (2), be it
with little evidence, viz. that also with extremely small density of the
considered vapour there may exist an observable influence of the
FrrsneL coefficient on the light waves.

Let the radially ascending gas mass be found in the centre of
the visible solar disc and suppose that an objective of e.g. 30 em.
diameter be used for observation. The light cone proceeding from
the considered point of the sun has then (the distance of the earth
to the sun being 1,5.10'* em.), a value of - Dns — 2.10-12 in

1,5 x 1013
radials. A ray deviating with half this amount from the line that
connects the centre of the sun with the objective does not fall in
the telescope. A ray to the rim of the objective however needs a
deviation of the whole amount to fall beside the telescope.

For / we may take the depth of the “reversing layer’, viz. a
number of the order of 1000 k.m.

du
As to a according to the above mentioned observations of Woop,

this is in the neighbourhood of the sodium line and at 644° C. of

the order 10°. The density of sodium vapour is at 644° C. of the order

105. This follows from a calculation, which Mr. C. M. Hoocrnsoom,
46*

714

assistent at the Physical Laboratory, made at my request, using
the observations of HACKSsPILL *).

As to the density of the metal vapours on the sun, which give
rise to the finest lines in the solar spectrum, we may treat these
according to Lorentz”) as being very small. If p is the pressure in
mm. mercury of the metal vapour, / the length of the layer that
is traversed by the rays, Lorentz finds at 7’= 6000’ p/ < 0,0015
or pl< 15000 depending on the suppositions made. For /=10* ¢.m.
would follow p< 0,00015 mm. mercury in the latter case and
p <9,00015 10-7 mm. mercury in the former one. To the men-
tioned pressures correspond the densities 9.10? and 9.10,

du . ;
Let — = be proportional to the density, then we should find

da 10 BO = 10-" at 644° C. We shall
da il Ome
suppose this number to be still valid at 6000°.

For a=10-” and 4=—=6.10 cm. we then roughly find from

dv
equation (2) — — 50. This number and therefore the velocity

az
gradient becomes 107 times smaller, if we take 10~'' for the density
of the metallic vapour and still smaller, if we assign a higher value

for a density 9.10—'%

du :
to — — than we did above.
i

A few objections can be made to the application of the above
given discussion to the explanation of solar phenomena. I shall
mention these shortly.

Even if we confine ourselves to rays proceeding from one point of
the sun, there seems to be a difficulty in the fact, that while rays of a
definite wave length and definite direction are deflected away from
the objective, there are other rays of the same wavelength and
originally another direction, which are deflected towards the objec-
tive. This difficulty may be avoided by assuming a partition of
velocities symmetrical with respect to the line connecting sun and
objective. Then all rays that must be taken into consideration are
deflected. If now we had to consider the light from one point of
the sun only, we might directly conclude, that for the mentioned
small velocity gradients the deflection of the light rays must give
rise to observable phenomena. One of these phenomena would be
the occurrence of complicated changes closely connected with the

1) HacksrirL. Ann. de Chim. et de Phys. (8) 28, 676 and 661. 1913.
2) H. A. Lorentz. On the width of spectral lines. These proceedings, 23, 470. 1914,

715

dispersion bands of Junius, in the neighbourhood of the simple
absorption line that would be observed in a gas mass at rest. If
however instead of one point of the photosphere we consider a part
of observable apparent area we only get a mean effect, which will
be small.

Only a very special partition of the velocity may then give rise
to a strong action.

Large velocity gradients will occur in the neighbourhood of sur-
faces of discontinuity ; then hel may become very large and « even

de
of another order of magnitude. Ascending and descending currents
may be found in neighbouring parts of space. Currents in these two
directions may deflect the light, so that finally the light from a
finite part of the photosphere may be deflected.

The aim of this communication is only to call the attention of
astrophysicists to the fact, that under favourable circumstances the
simultaneous existence of velocity gradients and anomalous dispersion
in gases that are extremely rare and without deusity gradients, may
give rise to a deflection of Jight.

Anatomy. — “On the Relation between the Dentition of Marsu-
pials and that of Reptiles and Monodelphians.” (First Com-
munication). By Prof. L. Bork.

(Communicated in the Meeting of May 29, 1915).

On the morphologieal significance of the dentition of Marsupials
opinions have varied greatly in the course of time. The special
characteristic of this dentition, the almost entire absence of a teeth-
change, naturally gave rise to the question: with which of the two
sets of teeth of the Monodelphian mammals does that of the Mar-
supials correspond, with the deciduous or with the permanent set ?
Older authors, more particularly led by comparative anatomical
investigations, were generally of opinion that it must be considered
as identical with the permanent set of the Monodelphian mammals.
This was e.g. the opinion of Owen, Flower, OrprieLD Tuomas. With
the Marsupials the milk-dentition would, according to them, remain
undeveloped with the exception of a single tooth, namely the one
immediately preceding the first molar. In fact with most Marsupials
an existing tooth is here sooner or later expelled and replaced by

716

a successor, in the same way as happens in the Monodelphian
mammals with all the milk-teeth.

The opinion that the dentition of Marsupials corresponds with the
second set of teeth of the Monodelphians was generally held until
about 1890, when in a comparatively short time it gave way to
a different view. It was namely at that period that ontogenetical
researches came more to the fore and led not only to a change in
the conception about the Marsupial dentition, but also introduced new
ideas into odontology, which were the starting-point for so much
capriciousness in the interpretation of the phenomena and caused so
much diversity of opinion that in the casuistic literature on the onto-
genesis of the Marsupialian dentition one finds the different authors
continually at variance ; as soon as detailed questions are dealt with
there is hardly any agreement. This period in the history of odonto-
logy begins with the papers KÜKENTHAL, Leene and Ross. Especially
the researches and views of the first of these authors were of para-
mount importance for the new course.

However much these authors might differ in other respects, they
agreed on the point that the functionating dentition of the Marsupials
must be considered to correspond to the milk-dentition of the Mono-
delphians. And as to the tooth which precedes the first molar and
is replaced, it should be looked upon as a milk-tooth which is replaced
by the only developed tooth of the permanent dentition. In short,
while in the opinion of the older anatomists Marsupials only possess
the second set of teeth and of the first only temporarily a single
tooth, this opinion is reversed after 1890: Marsupials possess only
the milk-set and of the second one only a single tooth develops.
For KikentHaL and Rösr this tooth was the remnant of the lost
dentition, for Leren on the other hand it was the first element of
a new series of teeth, attaining full development in the Monodelphians.

When investigating the development of the dentition of a Marsupial,
preferably of a Polyprotodont, without being biased by existing
theories, one cannot help wondering a little at the weakness of the
grounds on which KikextHanL based his theory, the more so since
on a premise against which many objections might be raised he
wanted to introduce an entirely new conception into mammalian
odontology, a conception which made its confusing influence felt
over the whole range of this department of science. This conception
is the so-called prelacteal dentition. As such this author distinguishes
a dental series which would precede the milk-teeth series. Hence
we should have to distinguish in mammals at least three dentitions :
the prelacteal, the lacteal and the permanent one. Of these three the

717

lacteal would be the functionating dentition with Marsupials, of the
permanent one only a single tooth (the last premolar) would develop
and of the prelacteal one small teeth would be evolved but never
reach full development and always be reduced.

How did the investigators between 1890 and 1900 arrive at this
view ? Embryological investigation of the development of the Mar- ’
supialian dentition showed that also with this group of vertebrates
two dental series were undoubtedly evolved. And the topographical
relation of the tooth-germs of either series was exactly similar to
that which is found in the Anlage of the dentition of the Monodel-
phian mammals, viz. the germs of one series lie buccally of those
of the other series and alternate with them. Now it appeared, how-
ever, that otherwise than with the Monodelphian mammals, the teeth
of the buccal or outer set become rudimentary, while the germs of
the inner set develop into the functionating dentition. At first sight
this would seem to confirm the view of the older anatomists that
the functionating dentition of the Marsupials corresponds with the
second or permanent set of the Monodelphians, for also this latter
develops from the inner series of tooth-germs. If KükeNrHaL had only
given this obvious interpretation to his observations, as e.g. WiLson and
Hitt. *) did in 1897, much confusion and contradiction in odontological
literature would have been avoided. But KikentHan was led astray
by a histological phenomenon to which he attributed a paramount
and in my opinion erroneous significance. He saw namely that the
free border of the dental lamina, after the germs of the inner series
had evolved, became slightly thickened. This phenomenon drew his
particular attention and he attributed so great a significance to it that
it became the basis for his theory. He saw namely in this thickening
the indication of still another dental series, so that three sets of
teeth would evolve with Marsupials, an outer one, of which the
teeth show a rudimentary development and are afterwards reduced,
a middle one, the teeth of which form the functionating dentition,
and an inner one which however only appears as a thickening of
the free border of the dental lamina and of which only a single
tooth would develop — the only successional tooth of Marsupials.
I wish to point out at once, however, that no investigator has ever
observed in this slightly thickened free border of the dental lamina
anything that points to even a beginning of dental development.
Now this should raise our doubt whether in this thickening we may
see a phenomenon, actually pointing to a dental series which the

1) Development and succession of teeth in Perameles. Quat. Journ. of microse:
Sc. Vol. XXXIX. 1897.

718

Marsupials would have lost in their latest phylogenetical evolution.

Leren, who also assigned a definite significance to the free border
of the dental lamina, therefore gave another explanation which from
this point of view was more plausible, namely that it should not
be considered as the last trace of a lost dental series but as the
first indication of a new one. Lecue’s opinion found no adherents
and so the free border of the dental lamina was assumed by a group
of investigators, following KükeNTHAL, to prove that the Marsupials
‘must have lost a dental series. And once arrived at this point of
view these authors were now obliged to identify this series, being
the most inwardly situated, with the permanent set of teeth of the
Monodelphizn mammals and the middle series, which in Marsupials
develops into the functionating dentition, could then only be identified
with the milk-dentition of the higher mammals. *)

Now the difficulty arose how to explain the outer row of small
teeth which in Marsupialian embryos evolve and partially develop,
but are afterwards reduced. This led KükeNtTnHAL to introduce into
literature the conception of a prelacteal dental series, a dentition
which would precede the milk-teeth.

The reason why KükENTHAL attached so much importance to the
thickened border of the dental lamina is not very evident, the less
so as it created such a fundamental difference in the dental evoln-
tion between Didelphian and Monodelphian mammals. In both groups
the Anlage of two series of tooth-germs is found, an outer and an
inner one. But instead of identifying these two, the inner row of
the Didelphian mammals is identified by him with the outer row
of the Monodelphians, while the inner row of these latter is met
with in Marsupials as a simple thickening of the border of the dental
lamina in which never a trace of real dental evolution has been
observed, and the outer row is referred to a hypothetical dental
series which is supposed to have functionated in the hypothetical .
ancestors of the mammals. Now this interpretation seems rather
strained and moreover it must a priori be highly improbable that
the dental series which in the Monodelphian mammals has such a
preponderating significance as a permanent dentition would have
disappeared in the more primitive Didelphian mammals without
leaving a trace, even in the embryo. Placing ourselves for a moment
on KükeNrHar’s viewpoint that there have originally been three

1) The opinion that from this thickened edge of the dental lamina the only
tooth having a predecessor (Py) would originate, is wrong. This particular tooth
belongs to the series of the other functionating teeth and its Anlage is exactly
the same but only starts a little later than the other teeth.

719

series of teeth, we should expect that where the so-called prelacteal
dental series is still visible as a number of sniall but fully developed
teeth, also something would be seen of that inner row, since it is
this latter which develops so powerfully in the Monodelphian mam-
mals. And especially since according to Kiikentua: one of the teeth
of this inner row does not become rudimentary, but develops fully.)
So while one element of this inner row attains its full development,
the development of all the other would always have been completely
checked. This is exactly opposite to what is observed in the outer
one of the supposed three rows, which also does not produce fully
developed teeth, but the elements of which do often appear as well-
shaped little teeth that are reduced after having formed.

This difference in development between the outer and inner row
with Didelphian mammals could in my opinion only be explained
by assuming that the inner row were checked in its development
long before the outer one. But in this case the ancestral forms of
Marsupials would have possessed not three but only two dental series,
which would however not have agreed with the two series of the
Monodelphian mammals. ,

The preponderant and absolutely unjustified significance assigned
by KükeNrnar, Rösr and Depenporr to the thickening of the border
of the dental lamina of Marsupials has complicated the problems of
dentition in no small measure. Winson and Hint already showed
this in 1897 by pointing out in particular that in this thickened
lamina not the least traces of local thickening can be observed which
would indicate a commencing Anlage of any tooth. According to
them the free border of the dental lamina simply originates by
emancipation of the tooth-germs of the teethband.

So Kékrenruan postulated already three dental series for the
Marsupials: a prelacteal, a lacteal and a permanent one. But the
complications of this problem of dentition were not at an end yet.
For also at the lingual side of the Anlage of the molars the so-called
free teethband border was observed.

Now KükeNrnar and other authors are of opinion that the molars
originate by fusion of the Anlage of teeth of both series, namely
of elements of the lacteal and of the permanent dentition. By this
hypothesis one was obliged to assign to the free teethband border
lingually of the molars a different meaning from that lingually of
the more frontally situated teeth.

With these latter it was an indication of the lost series of per-

1) It has been remarked above that this opinion is erroneous.

720

manent teeth, but since these would with the Marsupials have also
been incorporated in the formation of the molars, the free teethband
border lingually of the Marsupialian molars could only have the
meaning of still a fourth series of teeth. In this way the idea of
a series of post-permanent teeth was introduced into odontological
literature.

Thus we see that only on account of the significance assigned to
the free teethband border the conceptions of prelacteal and post
permanent teeth were successively introduced into odontology and
that besides the identification of Didelphian and Monodelphian mam-
mals became different from that given by the older anatomists. Not
to mention more substantial objections which will be presently
explained, the general question is justified whether it was admissible
to build up such a far-reaching theory on such a feeble base and
to make morphological deductions of paramount importance from
such a weak starting-point to the reality of which objections might
moreover be raised. And if no other arguments had led me to
reject KükENrnar’s theory as erroneous, it would already have
appeared to me little plausible by its general internal weakness.

Still this theory has found several adherents. because no argument
could be adduced by which it could a priori be declared to be false;
besides the theory seemingly linked the phenomena of tooth-changing
in Reptiles and Monodelphian mammals. One of the characteristics
of the reptilian dentition is so-called polyphyodontism; during life
the process of tooth-changing is an unlimited one and a number of
dental series evolve in succession. With mammals on the other
hand tooth-changing occurs only once, they only develop two dental
series, are diphyodontic. Exceptionally also monopbyodontism is
found, no tooth-change taking plave. The indeed obvious view was
now generally held that the diphyodontism of Mammals had developed
out of the polyphyodontism of Reptiles, the number of tooth-changes
having gradually diminished to one and hence that of the dental
series to two. And on account of this view the idea that with
Marsupials indications of four dental series would be found, namely
a prelacteal, lacteal, permanent and postpermanent one, had nothing
objectionable. On the contrary this interpretation of phenomena
supported the apparently so logical deduction of diphyodontism from
polyphyodontism. So factors were certainly present which secured
a favourable reception for KükENTHAL’s theory.

Considerations of a more general kind would, as was stated above,
have already made this theory less acceptable for me. But my
object in this paper is not to point out the weak side of this theory

721

and so to arrive at the conclusion that it cannot be right. I propose
in what follows to investigate the morphological significance of the
Marsupialian dentition, starting from quite different viewpoints.

A few years ago the Proceedings of this Academy contained a
paper by myself on the relation between the mammalian and rep-
tilian dentition. In particular the question was dealt with whether
the diphyodontism of Mammals might be derived from the polyphy-
odontism of Reptiles by diminishing the number of tooth-changes.
In such a derivation it is tacitly assumed that the tooth-changing
process in Reptiles and in Mammals are identical phenomena. In
the paper mentioned and in later more extensive papers it has been
shown that this supposition is not correct. The tooth-changing process
of Reptiles and that of Mammals are two phenomena different in
principle. Hence we may not derive the diphyodontism of the latter
from the polyphyodontism of the former. And in order to prevent
confusion that might be caused by the meaning of these words in
which the older conception is reflected, it is desirable to drop these
terms and to indicate by other terms what is essential in the mam-
malian and reptilian dentition. These terms will be given presently.

In my investigation on the morphological significance of the Mar-
supialian dentition I have from the outset started from another point
of view than preceding authors. For them the question was in what
relation the dentition of the Didelphian mammals stands to that of
the Monodelphians, what could be found in Marsupials with their
absence of a tooth-change of the two dental series of the Mono-
delphians. For me the principal question was: to what extent do
we still find in Marsupials during the Anlage of the dentition phe-
nomena that are characteristic for the dentition of Reptiles? For a
right understanding of the answer to this question a short account
must precede of the chief evolutionary phenomena of the reptilian
dentition as compared with that of Mammals.

In the mentioned paper it has been shown that the reptilian
dentition originates from tooth-germs, evolving in two rows on the
teethband, one row on the buccal side close below the epithelium
of the cavity of the mouth and a second row on the free border
of the teethband. Both rows consequently lie as an outer and an
inner one with respect to one another, for which reason they are
distinguished as Exostichos and Endostichos. And since the first
Anlage of the dentition is double-rowed it may be indicated as
“distichical’’.

Another characteristic is that the tooth-germs of both rows alter-
nate with each other. First. the tooth-germs of the exostichical row

722

become visible and the teeth so evolved remain also in their develop-
ment a little in advance of those of the endostichical row. In Mam-
mals the same structural principle is met with. Here also the Anlage
of the dentition is in a buccal — exostichos — and in a lingual
row or endostichos and the elements of the two rows alternate as
with the Reptiles. Hence the dentition of both groups of vertebrates
is distichical in Anlage. In the course of its further development
however essential differences arise between the dentitions of Reptiles
and Monodelphian Mammals.

With the Reptiles the endostichical teeth are regularly intercalated
between the exostichical, so that in the functionating dentition the two
rows are fixed on or in the jaw in a single row. So it is charac-
teristie of the morphology of the reptilian dentition that in it the two
rows of teeth functionate simultaneously. I should like to express
this fact by calling the reptilian dentition ‘‘shamastichical”’. And since
at any rate in the beginning between every two exostichical teeth
an endostichical one is inserted and takes part in the construction
of the dentition, the mixing of the rows being thus a regular one,
also this fact might find expression in the characterisation of the
reptilian dentition. Hence the functionating dentition of the Reptiles
should be described as an “isocrasic hamastichical” one.

In regard to this characteristic a fundamental difference is now
met with between Reptiles and Monodelphian Mammals. Although
also with these latter the two dental rows evolve shortly after each
other, still the inner one or endostichos generally develops much more
slowly and its elements do not push themselves between those ot
tbe exostichos. This latter forms a compact dentition of which the
teeth pierce with a certain regularity and functionate during some
time, while the teeth of the endostichos remain below the surface,
developing slowly. When they have reached a certain degree of
development they gradually expel the teeth of the endostichos, i. e.
the milk-set, fill up their places and form the second or permanent
set. The typical difference between the reptilian and mammalian
dentition consequently is that the functionating dentition of the former
consists of elements of both rows, while on the other hand with
the mammals the two rows functionate one afier another. Hence I
distinguish the dentition of the Monodelphian mammals as chorissti-
chical as compared with the hamastichical one of the Reptiles. It
should be pointed out however that according to the investigations
of Leene the functionating dentition of Erinacidae also consists of a
mixture of elements of the rows. Probably this expresses the very
primitive character of this animal group.

723

In what precedes the chief characteristic of the nature of the tooth-
change in mammals has also been indicated: the endostichical row
expels the exostichical, in other words the two rows succeed one
another, there is a change of series. This form of tooth-change will
therefore be distinguished as “stichobolism”. With Reptiles the change
must have an entirely different character, as here the two rows
constitute simultaneously the functionating dentition, so that there
can be no question of substitution of one series by another. So with
Reptiles the change is of a much more elementary character. In this
group the productivity of the teeth-band does not stop with the
Anlage of a single exo- and endostichical dental series. On the
contrary, after the endostichical series has been evolved, a
third series appears which must be considered as the substituting
series of the first evolved exostichos. After this a fourth appears
which will replace the first endostichos and so on. The elements of
these subsequent series are formed by the matrices from which the
first two series came forth, in this way that a matrix first produces
an element for the first exostichos, then for the second exostichos
and so on. The second product of a matrix is destined to expel and
replace the first and is in its turn expelled by the third product.
All the products of the same matrix may be distinguished as a
dental family. With Reptiles every tooth is therefore to be considered
as a generation that will be replaced by a following younger generation,
produced by the same matrix. So an exostichical tooth will always
be expelled by an exostichical one. Consequently there are as many
matrices in the teeth-band as the dentition has functionating teeth.
These matrices go on producing continuously. With some Reptiles
the time between the formation of two dental generations is longer,
with others shorter, but there is no question of a change of series,
as the series functionate simultaneously. Here the change has the
characteristic that the members of a family, successively produced
by a matrix, replace each other. In contradistinetion to the stichobolism
of the Monodelphian mammals | propose to distinguish this process
as “merobolism”’.

What is now the relation between the mammalian dentition in
which only once an exo- and endostichical series is evolved and
the reptilian dentition in which a number of exo- and endostichical
series succeed each other like as many generations? The simplest
conception is that with Reptiles the dental matrix extends its produc-
tivity over the whole life of the individual, giving birth each time
to an elementary tooth, while on the other hand with Mammals the.
whole productivity of a dental matrix is exhausted in the formation

724

ot a single product, containing potentially a larger number of elementary
teeth, a number of dental generations. A whole dental family of
the Reptiles has as it were been condensed in a mammalian tooth.
This dental Anlage will therefore be distinguished as “symphyomeric”.

So the mammalian tooth is not identical with a reptilian one, but
represents all the generations which come forth from one matrix of
the teeth-band, i.e. a reptilian dental family. In most cases two,
sometimes three such generations can be recognised on the relief of
the mammalian teeth, they are according to their structure dimeric
or trimeric.

The reptilian teeth on the other hand are always monomeric, each
tooth corresponds to a single generation only, these generations
succeeding each other sometimes more sometimes less rapidly. In
contradistinetion to the symphyomerie dental Anlage of Mammals
the dentition of Reptiles must therefore be indicated as stoicheomeric.

Summarising the main points of the above comparison between
the dentitions of Reptiles and Monodelphian mammals, we have
what follows. The Anlage of the dentition is in both groups distich-
ical, the Anlage of the teeth with Monodelphian mammals sym-
phyomeric, with Reptiles stoicheomeric, the shape of the teeth witb
the Mammals dimeric, seldom tri- or polymeric, with the Reptiles
monomeric, the functionating dentition with the Monodelphian mam-
mals chorisstichical, with the Reptiles isocrasic hamastichical, the
tooth-change with the Mammals stichobolic, with the Reptiles merobolic.
Comparing this characterisation of the dentitions of the vertebrate
groups with the generally accepted one, that the dentition of Reptiles
is polyphyodontical, the teeth simple, with the Mammals the dentition
diphyodontical and the teeth partly composite, it would appear as
if I had made the difference between the two forms of dentition
larger. But this is not so much the case as it seems. The essential
difference is that by me the relation between the so-called polyphy-
odontism of the Reptiles and the diphyodontism of the Mammals is
rejected in principle, since the tooth-change is an entirely different pheno-
menon in these two groups. Directly related to this is the difference
in structure of the functionating dentition on which I have laid stress.

The differences described above are schematically represented in
fig. 1. Scheme A refers to the Reptiles, the exostichical teeth are
dotted, the arrows show the mechanism of the tooth-change. Scheme B
refers to the Monodelphian mammals. The dots and arrows have the
same meaning as in A.

Basing ourselves on what precedes we may answer the question
what place the dentition of the Didelphian mammals occupies in the

re”

725

Fig. 1.

system. It is easily perceived that for each of the above described
points of difference between the reptilian and monodelphian dentitions
this question must be put and answered separately. Now there are
three possibilities: a. it behaves like the reptilian dentition, 5. like
that of the Monodelphian mammals, and c. it occupies an intermediate
position and has points in common with both, so that it is no longer
a reptilian dentition but not yet in every respect that of a Monodel-
phian mammal. The answer, based on an investigation of a fair
number of young ones of several marsupial groups is given as suc-
cinetly as possible in the following table.

Reptiles Distichical stoicheomeric monomeric hamastichical merobolic
| | _ (isocrasic) |

This table shows that according to my investigations the Marsu-
pials agree with the Reptiles and the remaining mammals only in
regard to the Anlage of their dentition, since also with them it is
evolved in two rows: an exostichal and an endostichical one, but
that for the rest the Marsupials form in every respect a transition
between Reptiles and Monodelphian mammals.

This will be shown successively for each of the ontogenetical
and morphological properties of the dentition and the teeth. In this
first communication only the dentition as a whole will be dealt with,
in a following one the teeth as elements of the dentition will be
studzed more closely.

Concerning the dentition it will therefore be attempted to show

726

that its Anlage is distichical, i.e. that the Anlage has two rows,
while its final structure is hamastichical, i.e. that elements of both
rows contribute to the construction. As (o the distichical nature of
the marsupialian dentition, this can of course be shown best with
the dentition of polyprotodontic Marsupials.

The further discussion will be based on the partially developed
dentition of a pouch-young of Perameles obesula, starting with the
lower jaw. In fig. 2 this Anlage has been sketched. In agreement

Fig. 2.

with other authors I found here a number of evolved but not further
developing small teeth. These have been dotted in fig. 2.

The scheme in which the teeth are shown in their mutual topo-
graphical situation, represents the dental Anlage when the teeth-band
is viewed from the buceal side. It is evident that the tooth-germs
lie in two rows, one nearer the surface epithelium and one along
the lower margin of the teeth-band. There are eight teeth in the
exostichical row, numbered 1—8, the endostichical row also contains
eight teeth, indicated by a—h. The teeth of the two rows are clearly
seen to alternate. The object studied by me, from which fig. 2 has
been drawn, was at about the same stage of development of the
dentition as the object described as stage IV by Wirson and Hur
jn their monograph on the evolution of the dentition of Perameles.
Of the eight exostichical teeth only three attain further development,
namely the third, sixth and seventh in the row, the other are reduced.

The exostichical teeth are evolved from the lateral margin of the
teeth-band, as with the Reptiles. This is also the case with the
Monodelphian mammals, but still the Marsupials agree in this respect
much more with the Reptiles than with these mammals. How great
in young stages of development the agreement is between the Anlage
of the teeth of Marsupials and Reptiles, may be seen by comparing
figs. 3 and 4. In fig. 3 the teeth-band with the Anlage of an exostichical
and endostichical tooth of a young Lacerta is sketched, the exostichical
tooth lies parietally close below the epithelium of the cavity of the
mouth, the endostichical Anlage lies terminally. Fig. 4 is a repro-
duction of Wirson and Huxr'’s fig. 37 and refers to the Anlage of

Fig. 3. Fig 4.
teeth 3 and + in the scheme of fig. 2, at a stage of development
somewhat vounger than was at my disposal. The agreement is so
striking that only the more powerful development of the primitive:
pulp-cells in fig. 4 proves that it is not a teeth-band with dental

me ‘

ee ea

Fig. 5.

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

728

Anlage of a Reptile. Already Lxcun pointed out this agreement of
the teeth-band apparatus with the tooth-germs between Marsupials
and Reptiles for Myrmecobius (Morph. Jahrb. XX p. 118). This
author says in the place referred to: ‘‘dasz die erhaltenen Bilder in
Bezug auf die Beziehungen der Schmelzleiste des rudimentären
Zahns zur Leiste der persistierenden eben so sehr von den bei allen
übrigen Säugethieren vorkommenden Befunden abweichen, wie sie
an Zustände bei manchen Reptilien erinnern” (that the obtained
pictures in regard to the relations of the border of the teethband
of the rudimentary tooth to the teethband of the permanent teeth
differ as much from what is found with mammals as they remind
us of the conditions with many Reptiles).

As will be seen from fig. 3, of the exostichical teeth only three
develop, namely those numbered 3, 6, and 7. Especially the meaning
of tooth 3 and 7 is important for our further discussion and therefore
it is necessary that its exostichical nature is definitely proved. So
in fig. 5 some fifteen successive sections are given through the region
of the teeth-band, enclosed in fig. 2 between the lines A and 5.

In this region lies also the posterior end of the endostichical tooth
a, visible in the sections a, 6, and c as a terminal thickening of the
dental lamina. Then follows the exostichical tooth 2, already furnished
with a dentine cap, but otherwise rudimentary, sketched in sections
b-f. That this tooth is formed from the teeth-band not terminally
but parietally is clearly seen. Next comes the endostichical tooth 5,
the Anlage of which may be followed in the sections f-p as the
already terminally invaginated thickening of the dental lamina. But
before this Anlage is completed that of the exostichical tooth 3 appears.
That also this tooth is connected with the teeth-band not terminally
but parietally like the tooth 2 and consequently belongs to the
exostichos, is proved beyond doubt by the pictures. As an additional
proof the Anlage of tooth 6 and tooth 3 at a younger stage of
development is given in fig. 6. This is a reproduction of Wison
and Hrri’s fig. 34. In my opinion there can be no doubt as to the
exostichical nature of tooth 3 in Perameles. That so much stress is

Fig. 6.

729

laid on this point is on account ef the circumstance that while teeth
a and 6 will later develop into the first and second incisors, tooth
3 produces the third incisor. Now it follows from what precedes
that with Perameles the functionating incisors do not all originate
from a single dental series, but partly from the endostichos (=
permanent set of the Monodelphian mammals), partly from the
exostichos (= milk-set of the same mammalian group).

As to the dental Anlage of tooth 6, this will produce the last
premolar, the only tooth which, as we know, is replaced in the
marsupialian dentition and which in all respects behaves as a milk-
tooth. To this I shall return later. As to the manner of Anlage
and the relation between the tooth germ and the teeth-band there
is not the slightest difference between tooth 3 and 6. This is
acknowledged as well by Witson and Hr as by DrPerporr, although
this latter without any reason and quite erroneously simply considers
this as a secondary state. This view was forced upon the author
since otherwise he would according to his system necessarily have
arrived at the conclusion that tooth 3 and 6 belonged to the so-
called prelacteal dental series, while a complete development of
teeth of this series may not be assumed by adherents of a prelacteal
dental series. This is a very striking instance how strongly the
idea of a “‘prelacteal dentition” spoils objectivity in judging the
facts. Wison and Hitt, who like myself consider the row 1—8
in fig. 2 as the row of the milk-set, accordingly state expressly that
tooth 6 at its first appearance is evolved from the buccal wall of
the teeth-band and not terminally. Curiously enough however they
do not state this for tooth 3 and 7, although their drawings clearly
show such an Anlage at any rate for tooth 3, as will appear from
figure 6, here reproduced. Very peculiar is Drpenporr’s reasoning
concerning the remarkable situation of tooth 3. “Würde der Kiefer”,
he says on p. 255, “später nicht an Lange zunehmen, so hätten
wir im Bereiche der Incisivi von Perameles ebenfalls einen Zahn-
wechsel zu erwarten, in der Art, wie er wirklich bei den Diprot-
odontiern in der Prämolarenreihe vor sich geht” (If the jaw did
not later increase in length we should have to expect in the region
of the incisors of Perameles a tooth-change as it actually occurs
with the Diprotodontians in the premolar series). So he grants
indirectly that the Anlage of the developing tooth 3 in regard to
that of tooth 4 and c agrees entirely with the relation of a tooth-
germ of the milk-set to that of the permanent teeth.

For the genetical significance of the teeth constituting the dentition
of Perameles it is important emphatically to point out that the teeth

47*

730

3 and 6 which develop fully, belong to the same series and are
entirely equivalent to the rudimentary little teeth 1, 2, 4, 5, and 8,
Tooth 7 will presently be separately dealt with. Bearing in mind
that by the adherents of Kiikentnar’s theory these rudimentary little
teeth are adduced as a proof for the assumed prelacteal dentition,
the importance of the mentioned fact becomes evident. If we accept
KiikeNTHAL’s theory teeth 3 and 6 must be considered as prelacteal
teeth reaching development. This consequence however no adierent
of this theory has until now had the courage to accept. The view-
point of this paper is much simpler and more natural, the teeth
1—8 are exostichical (milk-teeth of the Monodelphians) and among
these 3 and 6 attain development and push themselves in between
the elements of the eudostichical teeth, as with the reptilianlike
ancestral forms also the remaining teeth of this series would have done.

The point of view of this paper leads in its consequences to
somewhat radical’ conclusions as to the relation of the incisors of
the Marsupials to those of the Monodelphian mammals. For if the
functionating incisors of the Marsupials are derived from the two
dental. series and so form a hamastichical row, they must not be
identified with the incisors of either set of teeth of the Monodelphians,
but with both. In other words the incisors of a polyprotodontian
Marsupial are identical with the incisors of both the milk-set and the
permanent set of the Monodelphians. By this conclusion it seems to me
that an existing difficulty in the comparison of the incisors of Monodel-
phian and Didelphian mammals is solved in a simple manner. The
largest number of incisors of the Monodelphian mammals is three, in
the permanent and milk-set together six. With the Marsupials five
develop at the utmost, although the Anlage of six is present. As
well in the permanent as in the milk-dentition at least three would
accordingly be lost with the Didelphians. But no trace of them has
ever been detected. And so there always remained an unbridged
gap between the two groups of mammals. In my opinion this gap
does not exist. The highest number of incisors, evolved with Marsu-
pials, was stated to be six.’) Woopwarp has found this number in
Petrogale. Of these six only three develop with Petrogale, namely
2, 4 and 6, while 1, 3 and 5 become rudimentary. It is clear that
here we have development of the incisors of the endostichical series
only, while the exostichical teeth do not develop. The three teeth
that become rudimentary must be identitied with the three milk-

1) The total number of rudimentary and developing teeth may occasionally be
larger than six in the domain of the incisors, e. g with Dasyurus, but this is
the result of a complication which will be explained in the following communication,

731

incisors of a Monodelphian mammal, the three that develop with
the three incisors of the permanent dentition. In this way a natural
connection is established between the number of incisors of the two
groups. Here I shall restrict myself to a simple mentioning of this
view, remarking in passing that e.g. of the five incisors developing
with Didelphis three will belong to one series, two to the other.
So the hamastichical character of the dentition is still very strongly
expressed there.

It has been shown above that also the series of incisors in the
lower jaw of Perameles is hamastichical, the first and second incisor
being endostichical, the third exostichical. For the upper jaw this
is not so easily proved, since there the incisors are evolved more
directly and individually from the buccal epithelium. Five incisors
develop here in all. As many are evolved in the lower jaw and
phenomena, observed in older specimens, rendered it probable that
also these five would be evolved in two rows. To prove this more
fully would take up too much space here. That the five incisors
in the upper jaw correspond with the five, evolved in the lower
jaw, follows still from the fact that rudimentary incisors do not
occur in the upper jaw.

I need not enlarge here on the exostichical character of tooth 6.
From this tooth-germ the premolar is formed which undergoes sub-
stitution. Now in the domain of tooth 6 and 7 an irregularity in
the constitution of the dentition is met with. As far as tooth 6 the
elements of the two series alfernate regularly and so after the exosti-
chical tooth 6 an endostichical one would have to follow. But this
tooth is still lacking at the stage of fig. 2. Still at the spot marked
by a cross the free border of the dental lamina is already slightly
thickened and with further development the endostichical tooth will
here be formed which is destined to replace the exostichical tuoth
3 (the third premolar). Witson and Hir have described these stages
more fully. It should be particularly .pointed out here that this sub-
stituting tooth is formed in the same way from the free border of
the dental lamina as the teeth a,b,c ete., for these also are formed
terminally. So the substituting tooth is isostichical with the teeth
a, b ete, the strong development of tooth six however seems to be
the cause of its later Anlage.

After tooth 6 now follows tooth 7 and concerning this one I
disagree with WirsoN and Hur in this respect that according to
my view also this dental Anlage, from which the first molar will
develop, belongs to the exostichos. If this view is right, this would
mean that with Perameles also the first molar belongs to the exo-

732

stichical dentition, i.e. the milk-dentition of the Monodelphians. It
may be stated at once that the same holds for the first molar of
the upper jaw set of Perameles.

It is easier to prove the correctness of this view for the lower
than for the upper jaw. Following up the Anlage of the tooth-germ
of the first molar in the lower jaw, it is clear that it does not
evolve from the free border of the dental lamina, but from the
labial wall, contrary to the second molar which is formed indeed
as an endostichical tooth from the free border of the dental lamina. But
in the lower jaw a more definite proof may be given, namely:
Following up the Anlage of M1 — i.e. tooth 7 — in the lower
jaw, one finds that very shortly before the posterior edge of this
Anlage the free end of the teeth-band produces a rudimentary tooth-
Anlage. This is indicated in fig. 2 by f, and in fig. 7 sections of

Fig. 7.

it on the right and left side of the jaw are drawn. The Anlage of
these rudimentary germs puts the exostichical nature of the first
molar beyond doubt. If these germs developed further- also tooth 7
would be expelled, as is in reality the case with tooth 6.

The first molar in the upper jaw has been said to belong also to
the exostichos. Here however J have found no trace of the corre-
sponding endostichical tooth. And the proof can here only be given
by a comparison of the topographical relation of the germs of the
first and second molar in regard to the dental lamina. Therefore in
fig. 58 thirteen sections are given of the Anlage of the first molar
and in fig. 9 of the second molar of the upper jaw. Especially for
those who are acquainted with the evolution of the reptilian dentition

733

it will be clear that in fig. 8 we have a so-called parietal dental
Anlage and in Fig. 9 a terminal one. For over the whole length of
the Anlage in fig. 8 the lamina ends in a free border and the place
where in the posterior part of the enamelling organ the connecting
strand between this organ and the dental lamina is attached to this
latter, furnishes a certain proof that this Anlage has been evolved
from the dental lamina shortly below the buccal epithelium. The
tooth-germ of the second molar, on the other hand, sketched in fig. 9,
begins as a thickening of the upper edge of the dental lamina and
retains this character over its whole Anlage. In the sections 9, 10,
41, and 12 the tooth is visible which is indicated in fig. 2 as tooth

734

8 and belongs to the exostichical series. This little tooth starts at the
same spot on the dental lamina as the connecting strand of the
enamelling organ and the first molar in fig. 8.

These brief indications may suffice here to prove that the first

Fig. 9.
so-called molar of Perameles is exostichical, i.e. a milk-tooth. From
what has been said here it becomes probable that the second molar
of Perameles is identical with the first molar of the Monodelphians.
For the first molar of Perameles is nothing else but the fourth milk-
molar which is not expelled and replaced like the third. The first

735

and second milk-molar are formed in Anlage (tooth 4 and 5 in the
scheme of fig. 2) but do not develop.

In what precedes it has in my opinion been definitely proved
that in its constitution the marsupialian dentition has an essential
characteristic in common with the reptilian dentition, namely bama-
stichism. For the dentition of Perameles chiefly consists of endosti-
chical teeth (these are the so-called permanent teeth of the Mono-
delphians), but of the exostichical series the third incisor and first
molar functionate permanently, the third milk-molar temporarily
together with these endostichical teeth. In the upper jaw with its
five incisors the hamastichical character is still more clearly perceived
since of these five incisors three belong to the exostichical and two
to the endostichical series.

It is remarkable that in literature one repeatedly comes across
remarks, presented in the shape of possibilities or surmises, which
tit in perfectly with the here briefly framed theory of the marsupia-
lian dentition. If these investigators had not always been influenced
by the opinion that the diphyodontism of Mammals and the poly-
phyodontism of Reptiles were identical, only quantitatively different
phenomena, a more correct conception of the marsupialian dentition
would in my opinion have sooner prevailed. But in this erroneous
premise the conceptions of prelacteal and postpermanent dentitions
were rooted and it was these which blocked the road for a right
understanding of ‘the marsupialian dentition. So e.g. Rösr says in
his investigation of the dental evolution of Marsupials: “Es scheint
mir sehr wahrscheinlich dasz auch bei Phalangista nicht allein der
letzte Prämolar, sondern auch der dritte Incisivus des Oberkiefers
aus der zweiten Zahnreihe entsteht.” (To me it seems very likely
that also with Phalangista not only the last premolar but also the
third incisor of the upper jaw is formed from the second dental
series). This statement of Rösr is similar to that of Drpenporr,
quoted above, who also, in this case for Perameles, expresses the
possibility that the incisors originate from the two dental series. *). The
significance of this fact for the identification of the incisors of Mar-
supials and Monodelphian Mammals has been explained above.

A very remarkable discussion as to the manner in which with
the Monodelphians the four milk-molars and their substituting teeth
have originated, is found in Woopwarp’s: “Development of the

1) In this respect Benstey’s statement is remarkable that with Didelphis the
incisors of the lower jaw do not stand in a single row, the second stands more
inwardly between the first and the third. (On the evolution of the Austratian Mar-
supialia. Transact. Linn, Soc. London. Vol. IX, p. 187)

736

Teeth of the Macropodidae” (Proc. Zool. Soc. 1893). The author
points out that with Amphilestes “there are 12 or 13 cheek-teeth
present, and no evidence of the presence of two sets of teeth. May
not the five posterior ones”, the anthor continues, “represent the
five molars (Bettongia) while the first 8 might be supposed to give
vise to the 8 premolars, (4 milk and 4 permanent) and by the
retardation of each alternate one the condition in the Placentalia
might be brought about, the 2"d, th, 6 and 8 being retarded
and displaced to form a second or replacing set, while the 4st,‚ 34,
Sh and 7' develop early and are replaced by the former” (loc. cit.
p. 470). So here the tooth-change is explained as a possible shifting
into two rows of a larger number of teeth in the most primitive
mammals,

If Woopwarp had known that two-rowedness is an essential
characteristic of the dentition of Reptiles and certainly also of the
Marsupials, he would have explained the relation between the
dentition of Amphilestes and the Marsupials with four premolars in
the opposite direction and then in my opinion correctly. It seems
to me that with Amphilestes hamasthichism is still fully expressed,
i. e. the four teeth of the endostichical row push themselves between
the four teeth of the exostichical row as with the Reptiles. In the
now living Marsupials this hamastichism has for the greater part
been lost by a number of exostichical teeth becoming rudimentary,
with the Placentalia it has been entirely lost exactly on account of
the more complete development of the exostichical teeth, by which
the endostichical ones were retarded and tbe foundation was laid
for a system of tooth-change, in which the exostichical teeth were
replaced by the endostichical.

Now this process deviates in its essential points entirely from
that of the Reptiles. But for a correct insight into these relations
the knowledge of the structural principle of the distichism of the
reptilian dentition was required. And in this communication it has
been proved in principle that this distichism leads with Reptiles
to a hamastichically built dentition, with the Monodelphian Mammals
to a chorisstichically built one, while the Marsupials form a transi-

tion between them, as their dentition is still partly hamastichical,
one element being with many forms replaced in the same manner
as with the Monodelphian mammals, so that also the phenomenon
of chorisstichism is already present in principle. But it should be
clearly pointed out that the question to what extent the marsupialian
dentition is still hamastichical will have to be solved for each form
separately.

737

A view, entirely agreeing with the principle developed in this
paper, has already been held by Wince in regard to the large
number of molars of Myrmecobius. This author is namely of opinion
that this large number must be explained by the non-expulsion of
milk-teeth. So also for this author the dentition of Myrmecobius at
any rate consists of a mixture of milk-teeth — exostichical teeth
in my nomenclature — and “permanent” i. e. endostichical teeth.
Also according to Wiee the dentition of the mentioned Marsupial
is consequently hamastichical.

Finally in this relation the results may be mentioned of Lecne’s
investigation of the dentition of Erinaceus which consists of elements
of the milk-set and of the permanent set. Whether this hamasti-
chism is a secondary acquisition or the direct continuation of the
original phylogenetic condition does not matter. However, this
phenomenon is certainly remarkable in a form which has remained
so primitive as Erinaceus. That besides hamastichism, be it to a
limited extent, may also re-appear in other Monodelphian mammals,
is proved by the dentition of the catarrhine Primates, in which the
first molar is an element of the milk-set, become permanent.

If we now return once more to our starting-point and compare
the here developed theory of the constitution of the marsapialian
dentition with the two existing theories, it appears to stand between
these two. While according to the older investigators the functionat-
ing dentition of the Marsupials corresponds with the permanent
dentition of the Monodelphians, according to the more recent workers
with the milk-dentition, it is in my opinien built up ef elements of
both, although in a very disproportional mixtnre. It is an aniso-
crasic, hamastichical dentition, betraying by its hamastichism its
nearer relation to the dentition of the Reptiles and certainly also
of the most primitive Mammals, and by its anisocrasy its progres-
sive character as compared with that of the Reptiles.

In this communication I have endeavoured to prove that the
Marsupialian dentition in its evolution and constitution still shows
relationship to that of the Reptiles, in a following one it will be
shown that also in the development and structure of the Marsupialian
tooth there exist points of agreement with the Reptilian teeth.

738

Physiology. — “Further researches on pure pepsin.” By Dr. W. E.
Ringer. (Communicated by Prof. C. A. PeEKELHARING.)

(Communicated in the meeting of ‘September 96, 1915).

Some years ago PeKELHARING and myself‘) found that pure pepsin
has not a so-called iso-electrie point, that is to savy, not with any
concentration of hydrogen-ions has it a minimal electric charge
with opposite charges on either side of this H-concentration. Pepsin
always appeared to be electro-negative and ever to move towards
the anode in the electric field. This result conflicted with the ex-
perience of Mrcnaerrs and DavrosonN? , who found in their pepsin
an iso-electric point at a concentration Cyy= 5.5 X 10-° (pay = 4.26).
We found, however, that when we add protein or albumoses to our
pepsin, the enzyme behaves as in the experiments of Mrcuarmis and
Davipsonn. It then educes an iso-electric point, more or less distinct
according to the amount of protein added. This may also happen
when the enzyme has been prepared under unfavourable cireum-
stances. MuicHarntis and Davipsoun made their experiments with
GruBLur’s pepsin, an impure commercial preparation. The impurities
of their pepsin are obviously responsible for their results.

In the meantime Micnaunis and Merperssonn *) have brought forward
another publication, in which they assert that pepsin is an enzyme,
obeying the laws of dissociation and of which the free cations act
proteolitically. We know now, especially after the important ex-
periments by SöÖRENSEN, that the H-ion-concentration is of great
importance for the action of hydrolitic enzymes. A number of enzymes
have been examined in this respect; it appeared that there is a

maximum action at a definite reaction; on either side of this optimal _

H-ion-concentration the action decreases at first slowly, then rapidly.
SÖRENSEN had already observed this phenomenon in his researches
on pepsin and had already determined the optimum. He cautiously
avoids accounting for this phenomenon and only states that the
location of the optimal reaction depends to some extent on circum-
stances; it shifts towards greater Cy; in prolonged digestion experi-
ments, which SOreNnsen ascribes to the fact that pepsin is rendered
inactive in solutions with small H-ion-concentrations. The longer
the period of digestion, the greater the effect of this lack of activity.

Micuartis and his co-workers, however, have endeavoured to

1) Zeitschr. f. physiol. Chem. Bnd. 75, S. 282 (1911),
*) Liochem. Zeitschr. Bnd. 28, S. 1 (1910).
5) Liochem. Zeitschr. Bnd. 65, S. 1 (1914).

739

account for the influence of the reaction on the enzymic activity.
They suppose this activity to have something to do with the electric
charge; they consider pepsin to be a so-called amphoteric substance,
which combines on either side of the iso-eleetrie point with bases
or acids, so that compounds are formed, which are in some measure
to be compared with salts.

According to them the compound containing acid becomes active;
when in solution it is, like salt, partly dissociated, and the pepsin-
ions are considered to be the active constituents. From this it seems
to follow that with a greater amount of acid the activity must
increase beyond the iso-electric point. As to a decrease with a still
greater amount of acid, Micnariis supposes that perhaps in that
case bivalent pepsin-ions may be formed without activity. He tries
to substantiate this view on the basis of experiments, just as he
does with other enzymes. He supposes the activity to vary in pro-
portion to the amount of pepsin-ions present in the ‘solution. Now
it should be observed that the curve representing the activity of
enzymes, such as pepsin, as a function of the H-ion-concentration
is comparatively only slightly typical and has, in still stronger acid
solutions, a rather abrupt rise up to the optimum and a less sudden
fall. All sorts of conjectures may induce one to suggest an approxi-
mate interpretation of such a curve, and it seems to me to be a
bold one to explain the phenomena in this case by supposing pepsin,
of which we really are still much in the dark, to form asalt when
combined with acids, and the electrically charged pepsin-ions to be
active in this process, and moreover by supposing bivalent-ions to
be educed when a second basic group of pepsin unites with acids,
and assuming these bivalent-ions to be inactive in contradistinction
to univalent-ions. This conjecture appears to be all the more hazard-
ous, as we had already denied the existence of the iso-electrie point.
Micnariis also asserts that the question of identity or non-identity
of pepsin and chymosin may be solved in such a sense, that pepsin
combined with bases (consequently beyond the iso-electric point)
acts as chymosin, in which case the pepsin-anions are supposed to
be inactive‘) as such.

With a view to further researches on the action of pepsin and
the nature of the action, it seemed to me to be of prime importance
to settle the question whether or not there is an iso-electrie point
in pepsin, once for all. Should our previous results be confirmed,
it would be incumbent upon me to study the peculiar action of

1) Cf. “Die Wasserstoffionenkonzentration.”” By L. Micwaeuis, (1914).

740

pepsin more closely, because then Mrcmamus’ way of solving the
problem would appear to be erroneous. I, therefore, made two sets
of experiments; in the first 1 watched the behaviour of pepsin in
the electric field as accurately as possible; in the second I tried to
study in a different way from Mrcnarus the bearing of the H-ion-
concentration on the enzymic action.

Above all I wanted an adequate quantity of pure pepsin. According
to PeKELHARING this is best obtained from the pure gastric juice of
a dog, provided with a Pawrow fistula in the stomach and in the
esophagus. Such a dog was at my disposal. It had been operated
upon by Prof. Lameris and produced 300—500 c.c, of gastric juice
after being given a fictitious meal two or three times a week.

The enzyme was prepared after Puxennarinc. The gastric juice
was dialyzed and subsequently centrifugalized. The precipitate obtained
was washed and dried (pepsin 1). The centrifuged fluid mixed with
its own volume of a saturated solution of ammonium-sulfate, yields
another precipitate that was filtered off, dialyzed, dissolved in hydro-
chlorie acid of about 0.05 n. at 37°, and dialyzed again. The greater
part of it is then thrown out of solution again (pepsin 2). By a
prolonged dialyzation of pepsin, precipitated by ammonium sulfate,
and by dissolving it in oxalic acid and dialyzing it again fora very
long time, I have succeeded in obtaining a chlorin-free pepsin. So
we know now that pure pepsin is free from phosphorus (PEKELHARING)
and from chlorine as well, and that the amount of chlorine in common
pepsin is to be aseribed to hydrochloric acid, either held back or
combined or adsorbed. The chlorine-free pepsin (3) I employed for
a good many experiments; its activity was equal to that of the
chlorine-containing pepsin 1 or 2.

First set. The behaviour of pure pepsin in the electric field.

In order to avoid as many disturbances in my experiments as
possible, I improved upon my previous method. First of all | raised
the capacity of the non-polarisable electrodes. I then placed the
whole apparatus in a thermostat at 25°, and finally, at least in the
conclusive largest set of tests, [ raised the specific gravity of the
pepsin solution by an indifferent, neutral substance with no affinity
for acids, viz. cane-sugar. The increased specific gravity, which I
had also applied in similar experiments with ptyalin, precludes
convection-streams of the fluids during the passage of the electric current.
By proceeding thus no manner of disturbance took place, although
the apparatus was an elaborate contrivance and consequently difficult

741

in handling. Still, however indifferent cane-sugar seems to be and
most likely will be in these experiments, it may be objected that
without this substance the process might have been different. I insist
upon saying therefore, that in an initial set of experiments, without
any addition, the results were quite the same, except an occasional
disturbance in one case. As in this set of experiments the specific
gravity of pepsin-solution and of the side-fluid was about the same,
the disturbance must have been due to a slight rise of the specific
gravity of the latter generated by the current, which necessarily
engendered a streaming of the fluids. The results obtained with
pepsin-solutions to which sugar had been added, are given in the
following table. It will be seen that in every experiment the movement
of pepsin was anodal; consequently it was charged negatively. In
an earlier publication we have already demonstrated that by the
addition of protein or albumoses an iso-eleetric point was in some
sense brought forth. I now repeated these experiments with albumoses,
which confirmed my former results, only the addition of the albumoses
had to be greater than before, which niust be ascribed to the higher
degree of purity of the pepsin.

This evidence goes to show that with a sufficient quantity of
albumoses the movement is reversed, though it never becomes
quite cathodic. It is remarkable that amino-acids do not seem to
unite with pepsin, although a combination (or an adsorption) was
expected in view of the opposite electrical charge.

We now know for certain, therefore, that pepsin has not an iso-
electric point. This being settled, something else requires considera-
tion, which at first sight seems to clash with our experience, viz.
the existence of a minimal solubility of the pure pepsin in the
neighbourhood of the neutral point (pn =4—5). However, we need
not wonder at this. Pepsin, surely, must not be bracketed with
ordinary proteins. It differs from them altogether, for instance
by the remarkable property to coagulate in hydrochloric acid
solution, when heated rapidly (PrKeLHARING). Still, this peculiar
behaviour of pepsin (no iso-eleetrie point and none the less a
minimal solubility) drew my attention. I have tried to learn
more about this. PeKELHARING has already put forward the hypo-
thesis that pepsin might be a combination of the real enzyme and
protein"). Granting this to be true, the behaviour in the electric
field can be accounted for, when the compound is decomposed in
acid solution. If it is not decomposed in a very faint acid

') Archives des Sciences biclogiques. Tome XI, p. 37 (1904).

TABLE I. Movement of pepsin in the electric field. To the pepsin-solution 10/9
cane-sugar is added. 20 mgr. of pepsin to 50 c.c. Estimation of the
amount of pepsin after METT.

EB as Digestive action of the
Normality of the | Normality of the | = Ss | mie pry ie hours
Nr. = OE
epsin-solution side-fluid 2 | se | — ven
| ee 2 | Eg | at the at the
| ee | Ax | cathode ‚__anode
|
1 phosphate-solution phosphate-solution) 100 5 0 5.8
Dra a pu =4. |
2 | 0.00155 Hydrochl.) 0.00136 Hydrochl., 120 5 0 4.4
| acid; acid,
3 | 0.00369 ĳ | 0.00330 i 100 5 0.5 4.5
|
4 | 0.00621 5 | 0.00582 5 100 | 5 0.14 Sl
| |
5 | 0.0058 0.0058 ; SOMS 0 3.8
6 | 0.0064 a 0.0058 5 80 5 0.48 3.5
7 | 0.0099 B 0.0103 7 90 5 1.0 4.3
8 | 0.0101 “4 0.0101 ï 80 5 0.2 3.4
9 | 0.0169 = 0.0165 i 100 5 1.4 4.8
10 | 0.0155 r, 0.0165 5 80::| 5 0 3.0
11 | 0.0314 ; 0.0287 i 95 5 0 2.8
12 | 0.0287 0.0291 90 5 0 P|
13 | 0.0582 0.0582 80 5 0 2.4
14 | 0.0595 0.0592 80 5 | 0 2.3
15 | 0.118 0.118 esra did 188
16 | 0.235 0.236 te Cat Rie aaa 1.0

TABLE II. Movement of pepsin after addition of albumoses or amino-acids; for
further details see Table I.

oenen SS neee ne eenn

=
ra) ; | = Digestion in
8 Xx | mgr. albumoses. | | = 48 hear mm.
an | ——| Tension | per tube
Wise \| eS Our own | | | is
BE pepsin-| side- | Volts | = | a
ES mevaraton feotuion| ta |E at
| | Al
Del | 20 0.0324 0.0310 60 | 5 | 0 tea
2 20 | 0.0165 |0.0155 | 80 | 5 | 0.2 | 1.6
| | | | | | |
320 0.0301 0.0301 ‚60 5 | 04) | ieee
4 | | 100 | 0.0314 | 0.0301 | 50 Belt 1.6
| | | | |
5 | 100 | | 0.0320 | 0.0301 , 50 Be dl 2082 le
6 | | 300 | 0.0310} 0.0803 50 |5 | 28 | 14
7 | 400 | | 0:0349 | 0/0310.) 50" SI Bult were ss
8 | | 100 mgr. glycocoll | 0.0330 0.0310, 50 | 5 | 0 1.4
9 500 „ 5 0.0369 | 0.0301 | 50 BAO 0.8
|
10 300 ,, leucin | 0.0310 | 0.0310 | 50 5 0 1.4

743

solution the minimal solubility would not be a matter of sur-
prise at all. Some of my experimental results lend support to the
view that pepsin is indeed a compound. Firstly the movement of
the enzyme in the electric field in acid solution appeared to be
anodal, that of the greater part of the protein cathodal. The separa-
tion, however, is by no means complete, nor can it be expected to
be so; perhaps the protein moving towards the cathode consists of
nothing else but decomposition products of pepsin. I have not been
able to ascertain this because of the incomplete separation and the
difficulty to procure larger quantities.

Secondly I have noted the quantities of H- and Cl-ions that are
combined with the pepsin in the hydrochloric acid solution. !f the
pepsin, prepared after PEKRLHARING, is the enzyme itself, it will unlike
protein, not combine chiefly with H-ions, but with Cl-ions, as it is
always charged negatively. If, however, pepsin is a compound of
protein and the enzyme, the protein-constituent will most likely
combine chiefly with H-ions, whereas the enzyme-constituent will
unite with Cl-ions only. The enzyme itself may be expected to weigh
very little indeed, and to combine with only an inappreciable quantity
of Cl-ions. It would follow then that in this case, after all, only small
differences between the pepsin and the ordinary protein can be
expected, and that at most there would be comparatively only a
small majority of combined Cl-ions. This supposition was borne out
by determinations, performed with very small electrodes, as the
ratios of the combined H-ions and the combined Cl-ions were in a
hydrochloric-acid concentration of

0.029 n "!/q, for pepsin 3.00 and for albumoses 3.06
of OL059 iin 55, 955 Sia A Sr AN 1.42
andeots OAT... «5, ER: Ds ae 5 1.12

In a still stronger hydrochloric acid, 0.235 n, the ratio was, it is
true, somewhat higher for pepsin than for albumoses, but with such
a strong acid the estimation is liable to so many errors, that the
results cannot be relied on.

The mere fact that the pepsin combines chiefly with H-ions, refutes
the hypothesis that all the pepsin, as we prepared it, is the enzyme
itself, the latter being invariably charged negatively. I, therefore,
maintain that my experiments confirm the supposition, that the pepsin,
as we prepared it after PEKELHARING, is a compound (or an adsorption
compound) of a highly complicated protein and the enzyme, the
latter being always charged negatively through combination with anions.
This combination of anions with the true enzyme betrays itself by

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

744

the ratio of the combined ions H/Cl being somewhat smaller for
pepsin than for albumoses.

„The researches on the ion-combinations have yielded various other
results: inter alia i found a more accurate value for the solubility
of mercuric chlorid than the one universally received.

Furthermore the determinations of the Cl-ion-combinations with
albumoses have clearly illustrated the dissociation of the protein
chlorids, but I cannot discuss this point any further here.

Second Set. Experiments on the conditions under which the action
of pepsin takes place.

From what has been said thus far it is evident that Mrcmarms’
views as to the action of pepsin are not all correct. I have, there-
fore, tried to use another method in my researches on this action.
For the present the study of the condition of the enzyme offered no
prospect, as all we know about it is, that it is charged negatively
and probably combined with anions. On the other hand more success
might attend an attempt to observe the substratum ; all the more so
because it had been given very little attention to as yet.

The condition of proteins in solution with regard to the reaction
and the presence of salts, has been extensively studied in recent years.
We know that proteins are capable of combining with acids and
bases; that the compounds, which are in some way similar to salts,
can dissociate like the latter, but also that at a more considerable
concentration of the acids or the bases, this dissociation is arrested.
Furthermore it is highly probable that the protein-ions, liberated at
the dissociation, hydrate and swell. The more powerful the electric
charge of the protein, the more intense the swelling will be. With
continual addition of acid to a protein solution the swelling is made
to pass through a maximum; the lessening of the swelling beyond
the maximum may be partly due to the reduced dissociation, but at
the same time to other causes also.

We also know that salts affect the condition of proteins and that
they are capable of exerting influence in various ways. In small
concentrations and in acid or alkaline solutions the inhibitory action
of salts with regard to the electric charge and the swelling plays
the principal part. Various salts act in a different manner according
to the ions they throw into solution; definite ions, especially the
sulfate-ion, are very powerful in arresting the swelling.

In observing the action of pepsin we, therefore, had to take into
account the condition of the protein. In my first set of experiments
I could readily do this by employing Grirzner’s method to deter-

745

mine the action of pepsin. Here the pepsin solution acts on carmin-
stained fibrin. The stain of the fluid varies with the quantity of fibrin
dissolved; the intensity of the stain, being an index of the peptic
action, is determined colorimetrically.

According to Micnar.is’ observations the action of pepsin depends
entirely on the H-ion-concentration, that is to say various acid.
render the pepsin equally active, provided only that this eoncen-
tration is the same for every one of them. In trying to ascertain
this after GrürzNer’s method, I arrived at different results. It appeared
first and foremost that the action of every acid corresponded to the
swelling of the fibrin. The optimum of the digestion lay at that
reaction which concurred with a maximum swelling. I found this
to be the case for hydrochloric acid, oxalic acid, lactic acid, phos-
phorie acid, sulfuric acid and citric acid. It is peculiar that in
acetic acid the swelling occurs not only in highly aqueous solutions,
but also in sparingly aqueous solutions, from which I inferred that
in the latter the swelling is brought about by the combination with
the acetic acid and not with water. Acetic acid and water are
similar in their behaviour also in other respects. Be this as it may,
the action of the pepsin corresponded to the swelling in solutions
containing much water, not in the sparingly aqueous solutions ;
probably the enzyme acts only on protein swollen up by water,
not by acetic acid.

When comparing the action in the various acid solutions at their
optimal H-ion-concentration, this action appeared to differ rather
much. On the ground of Micnannis’ views the optima as well as the
activity might be expected to be all alike for all acids. The con-
dition of the pepsin, as determined by the Cy, should, according to
Micwariis, be most favourable at a definite Cy, no matter by what
acid the Cy is evolved. As stated before, my results go ee this
theory, as is shown by the table on p. 746.

The values of py and C before the action of the pepsin illustrate
best the optimal reactions; after the digestion these values under-
went various changes in proportion to the progress of the digestion.
With sulfuric acid the reaction has even become alkaline, which is
owing to the peculiar action of sulfuric acid. | did not notice it
with any of the other acids, whatever the concentration may have
been. It seems that sulfuric acid has liberated the ammonia, with
which the carmin was still united, and that it was in its turn
combined with or adsorbed by the fibrin or the carmin. We see
now how much the optima (before the action of the pepsin) differ;
with pbosphorie acid the Cy is highest, 0.011; and with acetic acid

48*

746

TABLE III. The action of pepsin in different acid solutions at the optimal reactions.

Time: 5 minutes.

Estimation of the H-ions-

7 Sata ae
Se Sam geil concentration
bak = IG ae Zn
Acid and normality | Ee ger | ong Poa ‚after the digestion
| Zo Es | ore | igestion
ES ABE ISEB |T |
| ME SES | Pa | cx | Fan
Hydrochl. acid 0.016 | 3.1 21 1 2.05 | 0.0088 | 2.68 | 0.0021
Oxalic acid 0.030 | 2.65 | 2.2 0.8 2.13 | 0.0075 | 2.62 | 0.0024
| | | |
Lactic acid 0.180 \ 3.54 ZT ir vil 2.21 | 0.0062 | 2.61 | 0.0025
| | |
Phosphor. acid 0.074 | 3.10 20 ee 00 1.95 | 0.0113 | 2.31 | 0.0050
|
Sulfuric acid 0.010 | 0.58 trace | trace | 2.40 | 0.0040 | 7.23 | 5.8710-8
|
Acetic acid 0.670| 3.16 | 1.8 | 0.67 | 2.55 | 0.0028 | 3.18 | 0.00066
Citric acid EAR || ATH | 23 0.85 | 2.18 | 0.0067 | 2.56 | 0.0028

it is lowest, viz 0.003. It is also obvious how unlike the digestion
is with the various acids; also, however, that the swelling corresponds
fairly to this digestion, except with acetic acid, the behaviour of
which substance has already been discussed. What strikes us most
is the very low digestion in the sulfuric acid solution and the con-
currence of a minimal swelling. I, therefore, disagree with MicHarris
and his pupils with regard to their assertion that it is virtually
only the Ci which determines the action of the pepsin. Pepsin
works best in those solutions in which the proteins swell most. This
maximum by no means occurs at the same H-ion-concentration with
different acids; when the anion is highly hydrophilous, as is the
case with sulfuric acid, the action of this ion prevails even in com-
paratively slight concentration, the optimum of digestion then lies
at low Cir, and the digestion is inappreciable, since the swelling
can be but slight.

The relation between digestion and swelling becomes even more
manifest, when we study the influence of salts. Salts were known
to generally impede the action of pepsin. Even common salt does
so very strongly in a concentration as in seawater; the action of
sulfates especially is very inhibitory. Up to now notbing was known
about the cause of this action of salts. Micnaniis speaks of a “Salz-
wirkung”’ noticeable also in the shifting of the optima to the smaller
Cy. When looked upon from my standpoint, the action of the salts
is quite easy to explain and we are even enabled to say before-
hand which salts arrest the action considerably and which are only
slightly inhibitory, since salts markedly affect the swelling of protein

747

in dilute solutions and their influence increases according as their
ions are more hydrophilous. The salts of a definite metal (Na) have
been arranged in the order of the intensities of their inhibitory
influence upon the swelling. This series then shows the ions in
the order of their hydrophilous nature. The salts will impede the
action of the pepsin in the same order. In order to ascertain this,
I have made researches on seven salts of sodium, viz. citrate, acetate,
chloride, chlorate, nitrate, rhodanate and sulfate. A difficulty arose
in these experiments, viz. special caution was to be exercised to
prevent the salt from materially altering the Cy, as a change of
the Cy brings about a change of the charge of the protein and
consequently of the swelling. I fairly got over this difficulty by
taking the weak lactic acid. The measurements demonstrated that
the addition of salt caused only a slight change of the Cy. In
lactic acid solutions, with an acidity in the neighbourhood of the
optimum, the Cy can be allowed to fluctuate considerably before
any change in the digestion is noticeable. The changes noted by
me must, therefore, be ascribed to the action of the salt-ions.
Table IV shows the results of the experiments, in which the salt-
concentration was smallest; this enabled us to estimate the results
more correctly than with more considerable salt-concentrations,
which affect the swelling to such an extent as to render it almost
too small for a correct determination.

TABLE IV. Experiments on the influence of salts. The salt-concentration is in-
variably 0.0067 equivalent. Temperature 15°; concentration of the
lactic acid 0.18 n.

| silted fa Determination PH and cH
S It oA = | 54 | Ee city aie” ws, a eee 7 Swat
No a se | gee (Fe mee Before the action After the action
ESB dram 2 EIESE | 50 5 oS. of the pepsin | of the pepsin
it elected ates SINR em =
| | PH Cele) Pa? My Bes
1 | none 34 5 | 5.85 | 5.85 | 2.646 | 0.0023 | 2.248 | 0.0057
| | |
2 | citrate 26.8 5 |5.3 | 5.3 | 2.692 | 0.0020 | 2.420 | 0.0038
3 | acetate 26.5 5 | 5.1 5.1 2.760 | 0.0017 | 2.435 | 0.0037
4 | chloride | 25.4 5 4.8 4.8 2.592 | 0.0026 | 2.257 | 0.0055
er lechtorate 25.0 5 droes Solutions of chlorates cannot
: jie at be measured
6 | nitrate 23.8 | 5 4.8 4.8 2.548 | 0.0028 | 2.253 |
| | | 0.0056
7 | rhodanate | 18.1 9 AAW SE 2.513 | 0.0031 | 2.246 |
| | 0.0057
8 | sulfate loz 20 2.8 0.7 2.713 | 0.0019 | 2.288 |
| | 0.0052

748

This table clearly shows the inhibitory action of the salts and
at the same time their influence upon the swelling. It also appears
from these data that this influence and the inhibitory action proceed
collaterally. There is a slight deviation only with the nitrate in such
a sense, that the digesting action is a little more intense than with
the chlorate, which, however, may result from an experimental
error, the methods of estimating the swelling and the digestion being
comparatively rough.

With greater concentrations of the salts the order was modified
a little, but there was again the side-by-side progress just alluded
to; in these greater concentrations the Cu changes more considerably,
which renders it slightly more difficult to note the influence.

Accordingly the sodium salt experiments yield evidence confirm-
utory of the supposition that the action of the pepsin is determined
by the condition of the substrata.

In the above experiments the method used allowed me only to
make a rough estimation of the condition of the protein and of the
digestion. I, therefore, deemed it necessary to carry out some exper-
iments affording an opportunity to estimate them as correctly as
possible. It is very difficult to thoroughly study the condition of
the protein, the size of the molecules in the solution, the taking
up of water ete. The preceding tests, however, taught us that the
swelling seems to play a principal part, which in fact seemed
plausible from the very first.

This swelling can be determined in several ways; when working
with protein-solutions we determine it by noting the viscosity.
To work with solutions seemed to be the best method to arrive at
accurate determinations. Much more difficult it is to correetly
estimate the action of the pepsin. Here the formol-titration defeats
our purpose. I have employed a method, nsed also by SöRENSEN
and consisting in the determination of the amount of nitrogen, which
after the pepsin has been active for some time, can no more be
precipitated by tannin.

In determining the viscosity it should be borne in mind that it
quickly recedes in solutions containing a pretty large amount of
acid, especially in the first few minutes after the addition. It is
impossible to obtain a perfectly correct estimation of the initial
viscosity in solutions with differing amounts of acid; the maximum
for instance will always be found among the lower amounts of
acid. I found that this decrease in the viscosity is very much
quickened by pepsin, to such a degree that in a very few minutes
the rise of the viscosity by acid is no longer noticeable. From this

749

fact we may conclude, that the action caused by the acid alone may
be the same as that, brought about by pepsin in acid solution, though
it is slower. Both actions consist in splitting the large protein
molecules; the problem is really very complex; the splitting yields
new products with other properties, and consequently another
situation of the maximum of the swelling. The initial viscosity
determined directly after the addition of the acid, can only, if my
judgment be correct, be an index of the action, which the pepsin
can exert on the protein molecules present at the beginning. Most
likely the new products, gradually evolved, reach the maximum
swelling at another degree of acidity than the original protein.
Unfortunately these products of decomposition seem to have little
influence on the viscosity also in their swollen state, so that we
cannot observe the swelling with regard to these products with
great accuracy. From this it follows that we can hardly speak of
the maximum of swelling of dissolved protein with a definite amount
of acid at which pepsin acts best, but that in reality this maximum
must necessarily shift according to the formation of other substances,
even though the shifting cannot be extensive, because first of all,
the decomposition products are, as far as their properties are concerned,
very similar to the original protein, and secondly because with
pepsin the decomposition does not advance far. In addition there is
the practical difficulty that during the digestion the reaction must
necessarily change. We are also aware that pepsin, especially in
solutions with a very -small amount of acid and also in such as
have a large amount of it, gradually loses its activity. Finally, even
from the modification of the viscosity in the strong acid solutions,
without pepsin, it appears that the action of acid alone must not
be ignored.

When recapitulating we can state that:

1. Under the influence of the acid the maximum of the viscosity,
as determined by us, has shifted a little towards the small amounts
of acid.

2. The location of the maxima of the swelling cannot be expected
to be entirely constant, when the protein is split up; as yet we
cannot say in what direction the shifting takes place.

3. The activity of pepsin gradually slackens, especially in the
weak acid solutions, however also in very strong acid solutions. In
consequence of this, it is especially in prolonged experiments that
the optimum of the activity of pepsin shifts towards the stronger
acid solutions.

4. Also the acid itself occasions a certain digestion, which shows

750

itself especially in strong acid solutions and is instrumental in shifting
the optimum of digestion in pepsin-containing solutions towards the
stronger acid solutions.

I have expatiated on this point because the question is rather
knotty; also because I wanted to show that we cannot expect to
find complete concordance between maximum of swelling and optimum
of the action of pepsin. The results of a set of experiments with
dialyzed and filtered horse-serum have been tabulated in Table V.

TABLE V. Estimation of the action of pepsin upon dialyzed and filtered horse-
serum in 4 hrs. at 37°; estimation of the viscosity in these solutions
with inactive pepsin at 18°.

The pepsin-solution contained 50 mgr. of pepsin taken up in 50 c.c.
very dilute oxalic acid solution, 5 c.c. was used for every protein-solution.
The estimation of the viscosity was made 5 min. after the mixing of
the protein and the acid; for these tests the pepsin had been inactivated.
The estimations were made at 18°, since at 37° it was quite impossible
to obtain at all values representing the initial condition. Of course the
viscosimeter, the liquids, the pipettes etc. were heated up beforehand
to 18, so that after the mixing we had not to wait longer than five

minutes.
Ree eda eet eee Estimation py and c
Pee oo) Sea) sos oe
No Ne ze = before the action after the action
Sao (22 AGE of pepsin of pepsin
SEE ee dees
OS S| a) o NS j
5 ES aa
S+ |r o > Py | Cy Pa | CH
1 10 0 WAG I SSS) ||) waste} | 414106 | 5.462 | 3.454><10—6
|
2 9.7 0-3) 134.2)) 62110) = 37893 | 0.00013 | 4.407 | 3.92X10—5
3 | 9.3 | 0.7 | 163.8 | 13.07 | 3.141 | 0.00072 3.834 | 1.47X10A
4 | 9.0 | 1.0 | 178.8 | 18.03 | 2.695 | 0.0020 3.525 2.99<10-4
5 8.6 | 1.4 | 179.6 | 23.47 | 2.257 | 0.0055 | 3.246 | 5.67><10—-4
6 | 85240 MEBs) 2 ONZ FOREL S | 0.0106 2.809 | 0.00155
TL ON Phat 25, 162.5 25.66 | 1.744 | 0.018 | 2.175 | 0006
85) 6.5 | 3.5 | 148.0 | 25.09 | 1.436 | 0.0366 | 1.632, 0.0234
|
9 | 4.0} 6.0 | 142.2 | 25.09 | 1.150 | 0.0708 1.231 | 0.0588
Bie | |

When representing the viscosity graphically as a function of
pu, the maximum appears to lie at py—= 2.5. The optimum of the
peptic action lies at py—=41.7. SÖRENSEN'S values of the latter are
from 1.6—2.26 according to the duration of the digestion. In the
light of these very reliable values and the above mentioned causes
of the varying maxima of viscosity and swelling I am induced to

751

think that also these experiments are confirmatory of the hypothesis
that the action of pepsin is not determined by the H-ion-concentration
alone, but principally by the condition of the substratum and in the
first place by the swelling.

Of course the experiments with protein-solutions have to be continued
and extended to other acids and here also the influence of salts has
to be studied.

It is perhaps hardly necessary to add that other enzymes have to be
subjected to similar observations. The curve representing the viscosity
and consequently also the swelling as a function of py is strikingly
analogous to the curve representing the action of many hydrolitic
enzymes as a function of px; as with trypsin and also with ptyalin *).
We are, therefore, inclined to believe that with these enzymes also
the condition of the substrata plays a prominent part.

Chemistry. — “The action of sun-light on the cinnamic acids.”
By Dr. A. W. K. bE Jona.

(Communicated in the meeting of September 25, 1915).

For the continued research of «- and g-“Storax” cinnamie acid it
was necessary to possess a method by which large quantities of the
a-acid can be readily converted into the ?-acid.

The rapid evaporation of an alcoholic solution spread in a thin
layer on glass plates certainly provides the means of preparing the
B-acid on a small scale, but in this manner one is obliged to always
work with small quantities of solution, as otherwise crystals of the
a-acid soon occur beside those of the g-acid.

According to ERLENMEYER Jun.?) the @-acid is formed in the
following ways®*).

«-“Storax” cinnamie acid is dissolved in as little ether as possible
and precipitated with petroleum ether. If the ethereal solution is not
sufficiently concentrated «-acid only, or else a mixture of the two
acids, is formed.

A warm solution of the «-acid in dilute (75°/,) aleohol deposits
on cooling the (-acid.

1) Vide VAn Trier and Rineer’s publication in the Proceedings of the meeting
of Nov. 30, 1912, Vol. XXI. Part. I, p. 858 (1912).

2) Ber. 39, 1581 et seq. (1906).

3) In what manner LEHMANN has prepared the acid, I have not been able
to trace as the original literature is not obtainable in Java.

752

As a third method he mentions that on heating the a-acid above
its melting point the g-aeid is formed *).

The first two methods, however, do not always give the desired
result, according to ERLANMEYER. He writes): “In anderen Fallen
gelingt die Umwandlung aus noch unbekannten Gründen selbst bei
ölterer Wiederholung nicht.”

The third method given by him is not correct. Both the solidified
melt and the sublimate gave, on being illuminated, a-truxillie acid only.

After various experiments I observed that the g-acid is most
conveniently prepared by pouring an alcoholic solution of a-cinnamic
acid, saturated at the ordinary temperature, in a large quantity of
water with stirring. On being illuminated this product always
yielded g-truxillie acid only.

6-cinnamie acid may be also obtained by allowing warm solutions
of einnamie acid to erystallise. In this case the erystals are mostly
visible with the naked eye and the change into the «-acid can also
be traced.

If, however, we make a saturated aqueous solution at boiling
heat, filter the same rapidly through cottonwool and filter off the
erystallisations at intervals, the succeeding fractions appear to be
different. The fraction depositing at a high temperature yields
d-cinnamic acid, whereas at a lower temperature g-cinnamic acid
erystallises (as proved by illuminating).

Benzine and petroleum are very suitable liquids for readily tracing
the transformation of the einnamie acids. If we wish to prepare the
p-acid in this manner we must take care that the solution is not
too concentrated as otherwise plate-like crystals of @-cinnamic acid
will appear. The best thing is to cool locally (for instance the bottom
of the flask) a warm and not too strong benzene solutiun. Splendid
needles united in feathers are then formed. On these being left
undisturbed the crystals are seen to partly vanish, plate-like crystals
are formed and a few of the needles although retaining their original ,
shape are seen to become transformed into a series of adjacent
plates which convey the impression that they were tacked with the
original needles.

The lower the boiling point of the benzene and the greater the
concentration the more rapidly we notice the appearance of the
plates in addition to the little feathers.

As to the transformation of the p-“Storax” cinnamic acid into
the «-acid, ErreNMever also reports the following particulars.

1) See also: Bioch. Zeitschr. 34, 356. (1911).

2) Ber. 42, 509. (1909).

753

In dilute (75 °/,) alcoholic solution the transformation takes place
slowly and spontaneously and only at the end of 14 days has the
greater part of the g-acid disappeared *).

On repeated recrystallisation from ether or dissolving in absolute
alcohol, the g-acid is generally converted into the a-acid. In some
eases, however, it will remain unchanged for weeks. “Wie es
scheint spielt auch bei diesen Umwandlungen die Belichtung eine
wichtige Rolle, die aber noch der Aufklärung bedarf*)”. This last
remark looks to me as if he has occasionally mistaken the crystals.
Here, where the temperature is generally 10—20° higher, the trans-
formation of B-cinnamic acid in water, benzene or alcohol proceeded
very rapidly in a few days.

In a dry state and at the ordinary temperature the e-cinnamic
acid keeps unchanged for a very long time. The fine powder
obtained by pouring an alcoholic solution of cinnamic acid into water
is but very slowly converted even after an addition of g-cinnamic
acid. A specimen that had been mixed with 1°/, of cinnamic acid
after being kept in the dark for over a month gave, on illuminating
0.5 gram during one morning, 0.09 gram of e-acid and 0.10 gram
of g-truxillie acid.

On heating, however, the g-cinnamic acid, even without previous
fusion, is changed very rapidly into e-cinnamic acid. The higher
the temperature, the more rapidly the transformation.

From all these data it thus appears that at the ordinary and also
at a higher temperature the e«-cinnamic acid is the stable modification
and that the 3-acid, for this temperature range, is always metastable.

From the ready change of the 8-cinnamic acid into the «-acid it
may be explained that concentrated solutions, which commence to
crystallise at a higher temperature than the dilute ones, give a-cin-
namie acid, whereas from dilute solutions which erystallise at a
lower temperature, B-erystals are deposited.

We have already stated previously with a few words that —
considering it has been generally found in the case of the organic
acids that in some solvents (benzene, chloroform etc.) they oceur at
great concentration, almost exclusively, and at low concentrations
still partially, as double molecules — we must also assume that in
the solid condition at least double molecules oceur.

According to BECKMANN®) the formula of the double molecule in
a general form would be as follows:

1) Ber. 39, 1583. (1906).
2) Ber. 42, 509. (1909).
3) Z. f. ph. Ch. 6, 469. (1890).

| |
ROR

An objection to this formula is that two hydroxyl-groups are
found at one C-atom which is not possible because water would
then be readily split off.

The following formula appears to me to agree better with the
data. As is well-known alcohols have the power to form large
molecular compounds in the said solvents but only in concentrated
solutions, whereas the dilute solution contains single molecules.
Hence, we must assume that, in the acids, two causes are at work,
which by themselves are not capable of producing the effect, namely
the hydroxyl- and the CO-groups.

As the manner in which the OH-groups react on each other
cannot be properly represented in the formula as yet, the double
molecule might be represented as follows:

OHHO
ER:

For our purpose, however, it is for the moment of less importance
what idea one entertains as to the double molecule; it is certain,
however, that in the case of acids we generally notice that they
combine by means of their carboxyl-groups.

In the case of acids possessing two bonds in their molecule it is
very probable that on the transition of the liquid state into the solid
one, the attraction of the two bonds may direct the molecules.

Supposing the difference between «- and g-einnamic acid to consist
solely in a difference of position of the double molecules in the
“Raumgitter”” we might then arrive to the following schema which
elucidates the transformation of the acids into «- and 8-truxillie acid.

a
OHHO
C,H,CH=CH—C<0 >C—CH=CHC,H,
OHHO OHHO

C,H,—CH=CH-C < 6 > U-CH=CH—C,H,0,H,—CH=CH-C < 2 > 0-CH=CH-C,H,
Bp

OHHO
Zl ie
C,H,CH=CH—C < n > C—_CH—CHCO,H,

755

OHHO
C,H,CH=cH—C < 6) > Ù-—CH=CHCH,

Also when we assume that on solidifying a change in structure
of the double molecule takes place and that the formation of the
truxillic acids oecurs in the double molecule itself and not between
two double molecules it is possible to give structural formulae for

e- and g-einnamic acid.
a

C,H, CH — CH, — CO

4 Ns
O Ò

es ra
CO — CH, — CH C,H,
B
C,H, CH = CH — COH

i
GO

C,H, CH = CH _ You

In the first representation it is not evident why the structure of

should make the acid more stable than that of 8; in the second
representation this is, however, better visible, although a lactide of
the formula « will also not possess much stability. Yet there are
some facts which lead us to believe that the lactide formula is a
very probable one.

An argument in favour of this formula is furnished by the follow-
ing experiments.

The cinnamates, namely the acid potassium-, the normal potassium-,
the calcium- and the barium salt have on exposure to light, in the
solid condition always yielded g-truxillie acid only and not in one
instance a-truxillic acid, although their preparation had been modified
in different ways. The result was the same whether we started from
a- or from f-cinnamic acid; the temperature also made no difference.

No salts can, therefore, be derived from the «-acid.

If the difference between the «- and the s-cinnamic acid consisted
merely in the position of the molecules in the “Raumgitter” it would
be rather strange (when the e-arrangement is the more stable one)
that this grouping does not occur in the salts. If for the e-cinnamic
acid the lactide form is accepted, the non-existence of salts speaks
for itself.

We might argue that in the salts no double molecule need occur,
or else that these molecules possess a somewhat different structure ;
for the acid potassium salt, however, this does not do because the

756

acid molecule must, as in the case of the acids, be combined to
the potassium salt molecule, as the acid is very strongly combined
and cannot be extracted by ether from the solid powdered salt, as
has already been stated by ERLENMEYER ’).

The e-cinnamic acid would then be the lactide of 3-phenylhydra-
erylie acid.

It is known that the «-oxyacids on being heated in a vacuum
are converted into lactides; 3-oxyacids on heating give unsaturated
acids with elimination of water, whereas y- and d-oxyacids very
readily form lactones.

From this it appears that, as a rule, the substances possessing a
carboxyl- and a hydroxyl-group, always have a greater tendency to
split off water between these two groups, whether this takes place
between the groups of one molecule, or whether the reaction proceeds
between two molecules.

Only the g-oxyacids apparently make an exception.

The @-phenylhydracrylic acid, for instance, on being slowly heated
breaks up at 180° into cinnamic acid and water according to the
equation :

C,H,CHCH,COOH — C,H,CH=CHCOOH + H,0.
|
OH

With substances possessing no carboxylgroup this elimination of
water does not take place readily, as will appear from the following
examples :

(CH,), C,H,CH (OH) CH,CH,CH, boils at 270° *).

CH,CH(OH)C,H, (CH,), boils at 248° *).

O,H,CH,CH (OH) C,H, melts at 62° and distils unchanged *).

Non-aromatie secondary aleohols also generally boil unchanged *).
If, however, we assume that from the @-phenylhydracrylie acid a
lactide is first formed, this ready elimination of water becomes
comprehensible.

C,H,CHCH,CO
Ye EN
2 C,H,CHCH,COOH — 0 0—=2C,H,CH=CHCOOH
* ua
OH COCH,CHC,H,

The transformation of other 8-oxyacids, on heating, may be supposed
to take place in a corresponding manner.

1) Ber. 42, 515 (1909).

2) Bemsrtern II, p. 1067.

3) Ber. 31, 1008 (1898).

4) Ann, 155, 63 (1870).

5) C. 1901 I, p. 623.

757

Chemistry. — “Mitro-derivatives of alkylbenzidines”. By G. van
RomsBurcu. (Communicated by Prof. P. van Rompuren).

(Communicated in the meeting of October 30, 1915),

Mertens’) has obtained in 1877 as a byproduct in the nitration
of dimethylaniline an orange-yellow compound soluble with difficulty
in alcohol, which he named isodinitrodimethylaniline. From this was
obtained on boiling with concentrated nitric acid a product which
he again investigated a few years later’) and took it for dinitro-
phenylmethylnitramine. From this was formed on boiling with
phenol a splendid red coloured compound which was described as
tetranitrodimethylazobenzene. Shortly afterwards P. van RompureH*)
showed that these compounds found by Merrexs are derivatives of a
tetranitrobenzidine without, however, determining the position of the
nitro-groups.

I resolved to endeavour to elucidate the structure of these products,
and at the same time to study also a number of nitro compounds in
the alkylbenzidine series in addition to some reduction products thereof.

The tetranitrotetramethylbenzidine, which in the circumstances, is
formed only in small quantity, in the above nitration is obtained
in a yield of about 35°/, of the dimethylaniline employed, when
we operate as follows:

30 grams of dimethylaniline are dissolved in 900 c.c. of nitric acid
D. 1.11, which are cooled in ice-water to abont 5°. After thorough
shaking and leaving it for some time in the ice-water it is left at
the ordinary temperature. The product that has formed over night
is collected, boiled with alcohol and filtered through a hot water-
funnel. The substance so obtained is already very pure and, when
recrystallised from phenol, it decomposes at 272°.

Aqueous potassium hydroxide is supposed not to act on this
compound. I could, however, ascertain that on prolonged boiling
some formation of dimethylamine takes place.

The manner in which the product is formed justifies the belief that
the nitro-groups occupy the positions 3.3/.5.5/. For in the nitration
of dimethylaniline, as shown by Pinnow ®) there is formed, at least
in diluted sulphurie acid solution, some orthonitrodimethylaniline,
which product is not readily nitrated any further. As nitric acid of

1) Diss. Leiden, 1877.

2) Ber. d. D. Chem. Ges. 19, 2123 (1886).
8) Rec. d. Trav. Chim. 5, 240 (1886).

4) Ber. d. D. Chem. Ges. 32, 1666 (1899).

758

low concentration, such as used in the above experiment, may act
as an oxidiser, it is likely to attack this o-nitrodimethylaniline in
the still unoccupied para-positions and cause the formation of .
o.o’-dinitrotetramethylbenzidine, which is more readily capable of
further nitration, particularly in the presence of nitrous acid. As is
well-known, the nitro-group, in this prolonged nitration, exerts an
influence of such a kind that the newly entered nitro-groups arrange
themselves meta in regard to the previous ones.

It may also be possible that the dimethylamine itself is oxidised
directly to a benzidine derivative of which it may be assumed (in
analogy with different other benzene derivatives in which the para-
position in regard to the aminogroup has been occupied) that the
nitration will take place in a corresponding manner. Hence, I have
tried in the first place to prepare the 3.3’.5.5’ tetranitrotetramethyl-
benzidine synthetically.

After several vain efforts, to which ! will not now refer, I have
taken the following course.

I started from p.-diphenoldiethylether, which I prepared according
to Hirscn’s directions’) and then treated with fuming nitrie acid.
The dark coloured solution, on heating soon became pale yellow
and on cooling the tetranitrodiphenoldiethylether crystallises in long,
transparent colourless needles melting at 256°—257°.

Analysis: found 45.6 °/, C. 3.5°/,H- 1320

calculated for C,,H,,N,O,, 45.5 ,, 3:35 13:3

Of the tetranitrodiphenolether, [ placed 2 grams in a tube of
resistance glass and added a solution of 1 gram of dimethylamine
in 25 ce. of alcohol. The sealed tube was first placed in a boiling
water-bath, which caused the contents to slowly turn an orange-red.
I further also heated for some hours at 120° when it appeared that
a red crystalline mass had deposited. This product was collected
and washed with warm alcohol and warm water, when it appeared
that the compound dissolved in the latter. On addition of strong
hydrochloric acid to the red coloured solution, a yellow coloured com-
pound was precipitated which could be recrystallised from acetic
acid, and melted at 223°. It struck me as not being improbable
that this product was tetranitrodiphenol and indeed it caused no
lowering of the melting point when mixed with this substance.

As to its structure, the opinions remained, however, divided. By
boiling it with strong nitric acid I succeeded, as did ScumipT and
ScuuLtz*), in converting it into pierie acid, so that the position of the

1) Ber d. D. Chem. Ges. 22, 335 (1889).

2) Ann. d. Chemie 207, 334 (1881).

759

nitro-groups in this tetranitrodiphenol, and therefore also in the
ether obtained by me, must be 3.3'.5.5',

No tetranitrotetramethylbenzidine had formed meanwhile. Hence,
I made another experiment where I allowed monomethylamine to
act on the tetranitrodiphenoldiethylether. The contents of the tube
also turned orange-red when immersed in the boiling water-bath
and after the operation a red crystalline mass had again deposited
in the tube.

Again I washed with warm alcohol and warm water, but the
latter soon ran through colourless whilst a dark red crystalline mass
was left behind on the filter. It could be recrystallised from phenol.
The compound so obtained decomposed at 282°.

Hence, the synthesis of tetranitrodimethylbenzidine had been success-
ful and now it was also proved beyond doubt that it was a 3.3'.5.5/
compound, which, of course, also applies to the tetranitrotetramethy|-
benzidine and its derivatives.

The difficult decomposition by boiling aqueous potassium hydroxide
must be most likely attributed to the slight solubility of this
compound.

The above cited experiments now also paved the way for the
synthesis of all kinds of tetranitroalkylbenzidines.

For instance, I allowed ethylamine to act on ihe tetranitrodiphenol-
ether and obtained a compound which, when recrystallised from
ethyl benzoate, erystallises in yellowish-red small needles, which
melt at 248° with decomposition. This same substance, I also could
prepare from tetraethylbenzidine.

I have also allowed propyl-, /sopropyl- isobutyl- and allylamine
to react. The compounds so obtained are united in the following
table in which are also included the final nitration compounds
(nitramines) generated from the different products. All these nitra-
mines are of an extremely pale yellow colour.

Monoalkyl compounds corresponding
nitramines

Methyl red 284° (with decomp.) 230° (with decomp.)
ethyl yellowish-red 248° ,, ie 230 EN
propyl dark-red 202° so uke. =
isopropyl af One wee e 209°. ‘6
isobutyl - 194° 205 5
allyl yellowish-red 208° de sy ACO ns

With tin and hydrochloric acid the tetranitrotetramethyl- and
49
Proceedings Royal Acad. Amsterdam. Vol. XVIII.

760

the tetranitrodimethylbenzidine may be reduced, also the end nitration
product obtained from these compounds.

As these substances are practically insoluble in hydrochloric acid
the reaction proceeds very slowly; the two last named compounds
must be boiled for a considerable time before everything has passed
into solution. On cooling, the tin double salts erystallise in colourless
scales. | removed the tin with hydrogen sulphide and on adding
strong hydrochloric acid to the filtrates, | obtained the hydrochlorides
of tetraminotetramethyl- and of tetraminodimethylbenzidine in beauti-
ful, small, colourless needles.

The first product begins to darken at 240° and decomposes at
251°. It contains 4 mols. of hydrogen chloride and 2 mols. of water,

Analysis: Found: 39:4°/,C. 6.7°/,H 17.55

Calculated for C,,H,,N,O,Cl, 39.8 „ 66,, 174 ,,

The tetraminodimethylbenzidine which is formed both from the
tetranitrodimethylbenzidine and from the end product, erystallises
with + mols. of hydrogen chloride and 1 mol. of water.

Analysis: Found: 38.8°/,C 6.4°/,H 19.3°/,N

Calculated for C,,H,,N,OCI, 38.5 „ 58 ,, 19.3 ,,

I happened to succeed in diazotising these amino-compounds and
preparing from the same a number of colouring matters varying
in shade from red to bluish-violet, by linking them to suitable
substances such as the various naphthylaminosulphonie acids and
naphtholsulphonie acid. Some of these colouring matters exhibit the
property of dyeing cotton without the aid of a mordant.

Further particulars as to the compounds described in this article
will be published before long in the Ree. d. Trav. Chim.

Org. Chem. Lab. University, Utrecht.

Physics. — “On the field of two spherical fixed centres in EistriN’s
theory of gravitation”. By J. Droste. (Communicated by
Prof. H. A. Lorentz).

(Communicated in the meeting of October 30, 1915).

In a former communication') I calculated the field of a single
spherical centre and I investigated the motion of a particle in it.
I now proceed to calculate the field of two fixed spherical centres
according to the method followed by Lorenrz in calculating the
field of a single centre consisting of an incompressible fluid. It

761

differs from my former method in not using the symmetry of the
field for decreasing the number of functions to be calculated. This
would searcely be an advantage here, the functions having all the
same to be calculated from partial differential equations.

I have worked out the calculation on the supposition that the
bodies have invariable shape and volume, and I have carried the
calculation only to such an extent as is required by the precision
with which we are going to calculate the equations of motion of a
particle in it. As to this precision it will be sufficient that it furnishes
a first correction on the equations of motion as defined by classical
mechanics and Nrewron’s law.

§ 1. We call g®, y, c the values of the quantities g,, yo, WV —g,

as they would be if both centres were absent. If only the first centre
existed, these quantities would be 9+ gd, 7O-+y\0,e+¢); when

we have only the second centre we represent fhe by gl) gi),
y+ 72), c+-c®), and in the case of both centres we put:
90=9 AID AID + gor, vrt HD HO + yor, V-gae tet) HED He (1)

The quantities g!), y®, c are constants. We know already
Ge, ed, g®), yD, ¢ 5, they do not contain terms of order zero.
(We name one the order of a term such as 4/r or »°/c*). The
quantities g., yx, C finally do not contain any terms of lower order
than the second; it is they that must be calculated.

We now ae to substitute the expressions (1) in the equations

Ors. 4
~(v=9 g Yap 3 Jop. se) id (Soy + tay) . . e 5 (2)

Omitting all terms of higher order than the second, we have

se Òz,

= OY»
Vg belge

en 0} TEN 2) OY wv
(eh DHeDN raa Otra Dragen Og Dga (Een )

dws ei

Ty Oy.)
= CYap ah 0) gen! 0) ee En (ee) gi? +Yap jk Maen gend ) —
Oarg / ; ae ER Ow,
Oy)
=F (c+-c®)) (Yap! 0) + yap?) (gap a Jou" ey
wv, 3
Òy/D
+ (cyag (0) ¢ Jou? )) a Gey Yaa? 2) + Ya) 300) Jap) c2 j=
te

(2
Ön, Oe
+ (cya Gaps!) SE Gap! Yaa) ae Yap (0) Aly e(t) -

49%

762
We represent these fiv

terms
Substituting equations (1) in

successively by A, B, C, D, E.
LE 09 x2 OY re En Dad
A Ht V gE yp, etn Vig E yop tt
Prep Oa's Ow z

afsp Ou, Oarg
0, when o=—r) we obtain
—tin=te2

5 ny (0) Òg-/ òg-,@) Oye) yr? ay
YP } da 5 zi d " : +
Brp Ug Us

Oz Oa 3

dg \ sp-(2) ds pa (31) __(2)
4 dey ¢ De Yap) Ogee") | Over ) ( Yap 4 Òyrel? )
zip Van 02x

Bag 0e
Oz. (1) Over? Og, 2) Òy-s
Dn je EE
Oz, Oa, On, Oay
Og 1) dy (2) Bd en
+ 4de = Tre vi ded Yep :
Oty, Ou, Or, Sky,

represent the values of t, in the case of only
the first or second centre. We put

(2 — 1, when o==2

where ft) ZEN fol?)

4D)
— toy = — Kl

O+pt+¢.
In p and q we have considered, that 1e and ry are
zero, except when 8 =v resp. 3 — a. Moreover as terms to be dif-

ferentiated with respect to a, give zero, the field being stationary
we might everywhere replace y© and y by —1.
When we now put >

calculating

os EI) + £@) st So.

(2) becomes

7) >(2) (2) =
ae (A+ B+C+D+4+£)= (Dy 4. yr (eS + ley ) Pp gren
apy. Oks

As the field of each centre separately satisfies (2) we have
0B

(A D+E) =
2B. Oe,

Ein P aa q + Ses
by further reduction of A

oD re
ogi 0) Aya == KS

i Seog ee
apy. Oly apn 02s
We now have to consider that in neglecting terms of the

second

763

‚(1

lab
involves, exact up to terms of the second order inclusive,
0D Or

EE
afp. Oz, apy. Oz,

and higher orders go) == vy?) =0 if not a=b=4. This

when not o=»v=4. In the latter case

oD dg Ord De) Dy y(t)
Ds A ADE 44 ae) Aap leas st zo
app. Oe ne oe 5 Ok we eee Hr Òza Oatx
and

For p and q we find for the same reasons

Og Oi) | Oda Oy.)
ean 44 44 744 44
Ue: bef Ow, Oay in Ox; Òz, }

and

q=tdncS Og) at 09,42) 07440
4 Voy 2 On, Ò, Oa, Oa, .

Now, putting
944) =— cA and g,,") = — cn,

and neglecting quantities of order 2 in g,,!),9,42), Yq" 7442), cl
and c?), we find

nee

hal Tua =—, CNS — Fed, cd) = — Heu
and so
x OA Ou Le Ou 02 He OA Ou
pat ’ = — 3 Oort a -_— 5
P= AN dei dz) dede)! Je Sh IRIS
and in the case o=r =d
d OA Ou OL <0" Ou
2S =—3yAA+32¢ D SS SSS a 3 5
afg Oa, ule ae a O@e Ola,” ay. Oa a ate! Me a Oz Oty,

In consequence to all these considerations we get

= 04 Ou
Jao) A yov== 3 Ios dy4{ KAA + Mu +22 Dern +
x Ota Oty

02 Om Ou OA
af ea Tee ) b= ee

Oz, 0a, Òo-Òr,

Ou
Now, if everywhere we replace 22
x Obey Oi

we obtain

764

A (Gao Yar — 3 04 ds Au ze + d, Au) —

=14,,(u0d + 2Au) + 3 (

04 Ou Ou OA =
PETRE = eo

$ 2. We now have to substitute in (4) for 2 and u values that are

exact including terms of the first order. We find them from (2) by

omitting all terms of higher orders than the second. This gives us
— eo) Aye) = ED and — eg,20) Ayo?) == Seely

When o=vr=4 this becomes

xO xO
AL=~— or 0 and Ap—=— —* or On
C ¢

In these equations g, and eg, represent positive constants; the right
member of the first equation is different from zero only in the
interior of a sphere of radius 2, and the righthand member of the other
equation is different from zero only in a sphere of Radius &,.
From (5) we have

5 ee AP epee ia a

1 3c DE

Each equation (6) is valid onlv at a point outside the sphere the
radius of which occurs in it; within that sphere is

xO, x

: : Q
N= 5 (3R,?—r,*) and w= ge (hs 72") 0 (07
e c

We now substitute this in the righthand member of (4). Within the
first sphere that second member becomes

wo w,0, 7, (Òr,Òr, Or, Or, =
Jets yy eS SS + — Kin
; Rn Rt ‘r,\Òz-de, Oer dx, idd:

when we put

Rk? xy,R,
DI and o, = ——.
c 6e
In the interior of the second sphere we find in the same way
— h,,. Outside both spheres the right member of (4) will be

[le eo: esc
d0—d— Od

Tr, Ps BE Ta r,
Ow, Ox, O28, O25!
Considering (6) we thus find outside both spheres

ONO us Eas, fF ds, QS dS

— Q,, = 20,0,

Jas de Yar — (6d4 d4— doy)

5 be Say (7
Anr Aar 1 dar (7)

(1) (2)

TPs

765

the first integral is to be extended over the volume of the first
sphere, the second over the volume of the second, and the third
over the whole space outside both spheres. P, must be calculated
at a point near dS,; in the same way Q,, near dS and A, near
dS. r in each expression represents the distance from the point,
at which y,, is to be calculated, to the point near which the element
of volume is situated.

§ 3. From (7) we are able to calculate the function yo for all
values of 6 and rv. For the motion of a particle in the field of the
two centres only y,, is to be calculated if no terms of higher order
than the second are required. For this reason we will finish only
the calculation of y,,; at the same time we introduce the suppo-
sition ©,,— 0, which, in connexion with the supposition already
used of both centres remaining spherical under each other’s influence,
comes to the same thing as exclusion of any variation of shape and
volume. We then find

a, Oo; EE ef 1 fs Ns aay
7s An RJ rl Aak) rl,

2
(1) (2)

where /, denotes the distance from dS, to the centre of the second
sphere, and /, the distance from dS, to that of the first. In case the
mutual distance / of the centres or the distances 7, and 7, of these
centres from the point, in which y,, is required, is large with
respect te AR, and R, the value of the first integral will be 4a 22°: 3r,/
and of the second 47F,*: 3r,/. In this case we have

— 0,0, 5 1 1 9
Wi a rr di iB iT z etal at Wal Sees ( )

For the caleulation of the quantity y,, itself it is sufficient now
to know y,, and y,,@. From the equation

occurring on p. 1006 of my former communication, quoted above,
it follows that

9 a ROE 5 € nd
Oe ay fo, \) 50, and (@) — 2@2 late sw, 5,
Yau” CE WA SE MITE

Cat

and from this and (8), in connexion with (1),

1 20,/ 3w 20 510)
Ri! dens Drs 2( 4 2
Yas =| tae hans en ge

(9)

a i Jo, o, Hey € o, wi
Cw, aC eet a ==> ande 0; we E ts ae
1

2
we may replace w,*,@,*° and w‚w, by ah ‚hct and Ar
in the terms 5w,?: 2r,°, 5w,’: 2r,° and 5w,w,:7r,r,, and so we have
en

vy k, 5 C Ja 2
Wan = zi jie sir ) on Iet ( de )
Tj Vz ac wr, Ms

and from this
. DAE VEN Cot vh
daze |! (2 + en )| EC
NT n NT ie

§ 4. We now proceed to the calculation of the field of the
equations of motion of a particle in the field of the two fixed centres.
We put for abbreviation

(10)

SW ERM ECM olla,

w is a function of the coordinates. Let v be the velocity of the
particle and w, y,2 the cartesian coordinates. For Z we then get the
expression

L=Vei— wt 3 w? — ev?
and from this, expanding the root and neglecting terms of higher
order than the second,

vt
P=e (1—L/ce) =F 0? + fw —ferw* + tL wv? + Be

Instead of L we may use P in the principle of Hammon and
thus we find

d (0P oP “ad (OP oP 4 d (OP oP a
— —S FE =— ANGST — .
dt (7) Ow’ dt & Oy dt & ) Oz (18)

The first of these equations is

= = Ow . Ow « Ow
aut gp tal DE Gen

vu. Ow me
=de 5 —+4 5

767

Neglecting in these and the two other equations any terms of

the second order we get

B e Ow .. je Ow , Ow (14)
DES EZ EE en ae
ae” oy dz

and so

DE o (ee tase tes): Raber eli)
y

We now may everywhere replace in the terms of the second
order in the complete equations the quantities 2, YZ and vv by the
values taken from (14) and (14a). We then find

ee (« 2 rig Ow aes i) ars Ow Seay 5 NE)

Oy 0 Oy
Beli Ow .0w . Ow „de 4 Ow
z a + zZz a —3¢ (Hi
Bs nea ae ae os x

These are the equations of motion required. From them we can
deduce the equation of energy by multiplying the first by 2, the
second by y, and the third by z, and then adding them. So we get

-- EAD + 2 v? Ws eee ee
dt dt z dt

In as Dn (14a) we write the second term in the form

dw Wv d (x
2y? — = = —
dt c? dé \ 2c?
and this gives us

d 4
ae +a ew tte [=o a ee ages CLG)

On the other side we find from (13)

TE Ay Ve
HC OR May Se ben

1 4
ah bete et pew |=0. (00)

This agrees with (16) because the difference

d vt en 4 fees

—{ — — i v*w 5 CW
3 2 2

dt \ 8c?

is equal to

being zero on account of (14a) when terms of higher order than the
second are neglected.

§ 5. The equation of energy (together with the integral of angular
momentum) of the motion of a ‘particle in the field of two fixed
centres can be obtained rigorous in the following way.

It is clear that, whatever may be the influence of both centres
on each other, their field will be symmetrically situated, about an
axis. Choosing this axis for axis of w and calling 7 the distance of
the particle from that axis, p the angle between a fixed plane
through the axis and the plane through the axis and the particle,
we obtain

L = (ux? + 2p ar + or? + gry? + s),

u,p,v,qg,8 being functions of « and r. This will yield at once the
equations of motion

A(DIY ML a (dt)_dw daly
le mt zl Sells

From the third we get

OL gry

a SS ZEN A h, . . . . . . . 1%

in t (17)
and by multiplying them in succession by a, 7, p and adding them
we obtain

za ot ple Sey oe oe ag cee en
Here A and A are constants. From (17) and (18) it follows that
BUS As oe nn set. LS)

(18) represents the equation of energy, (19) the equation which cor-
responds to the integral of angular momentum. With the approxi-
mation with which we have contented ourselves in the former $$
gq = —1 and
sce? (l—2w + $v’).
so that we obtain
rig = Ac (l—2w + Zw). . . . « « (19a)

Without difficulty one sees that (18) agrees with (16/1). (19) enables

us to eliminate the variable p from the equations ef motion.

769

I take the opportunity to correct an error in my former communi-
cation (quoted above). On page 1003 in the equation that follows
equation (11) and in the next equation 37° P instead of r? (2P + Q)
is to be read. This makes (12) valid in any case (and not only in
the case of a liquid), even when S=|-0 r being < R. (13) of course
is valid only, as before, in the case of S being zero outside a
sphere of radius F at points in which r > Rk.

Mathematics. — “On a linear integral equation of Vourerra of
the first kind, whose kernel contains a function of Brsswn.”
By Dr. J. G. Rurexrs. (Communicated by Prof. W. Karrryn).

(Communicated in the meeting of September 25, 1915).

Among the few applications given of Sonine’s extension of ABEL’s
integral equation’) we may arrange the integral equation :

fle) = ran) fen evens. zl)

with the solution:

i 1—)

sin Ax 1z là Aer 5 ERA nae te
up ra(5) fes > Ian(ieeBfO dE (2)

in which it is supposed: 0<4< 1, and the given function f'(w)
must satisfy the conditions that /(«) is an analytical function, f'(«)
finite with at most a finite number of discontinuities for a Se Sb,
and f(a) = 0.

In what follows we shall prove that (1) and (2)-may be directly
deduced by means of relations known in the theory of the functions
of Bresser. In this deduction it will moreover appear that the solution
of (1) only becomes the form (2) if a definite value is avoided and
consequently a great restriction is imposed on a certain parameter,
what is not strictly necessary. This special selection has moreover
the drawback that we only come to the solution of (1) under the
very restrictive condition 0 < (2) <1, whereas the more general
expression which we may find in this way, gives a solution under
the far more extensive condition #(4)< 1, The conditions which
the given function f(x) must satisfy will manifest themselves.

1) Sonine: Acta Matem. 4 (1884). These Proceedings XVI p. 583 (1913).

770
We shall also apply Vourrrra’s method to (1) and so we shall

be led to important conclusions.

We premise the well-known relation’):

Al.
y Jk dh

, AN Rw) > —1
Lolly’ a)da, Rio) Sin (3)

2 os
TEA | PD
1)

in
det (4) Te +
të tes
substitute in it: a= ——, y=2zV «—a, and replace » by —4, @ by
w—a
nm (n and m positive integers or zero), so as to get:

Lam (z Va = =

2 \n-+r+1 .
=] , > = — d (4)
= En) fe 5) 27 (eV w-§)(§-a)r tds, R(4)<1
(n+m)! (ata) 2 a
Vara a
ri and summate

We multiply both members of (4) by — { —
Tes
afterwards from n=O to n=. The first member may be reduced

by means of the relation *):

y n
g 2
—T,, » \/ =
nf EAD

n=0

and in the second member summation under the integral sign is
allowed on account of uniform convergence of the series arisen.

After some reduction we find:

(5) (@—aymtl)
TD (m-+2—aA)

Ea)? Im (i2V §—a)d&, Rid) <1.

(5)

(=) | (aA 5 In (Va). €

7
é

‚y= iV x—a, and replace

If we further substitute in (3) @=
va

v by w—1, 9 by m— g (m again positive integer or zero), we get

1) Nietsen: Handb. der Cylinderfunktionen 1904, p. 181 (8) slightly altered.

2) Nrersen. l.c. p. 97 (6).

fares

(ea)? I (iV x—a) =

Br —_ (6)
a B ug e )
(a) 2 Lamia). (Same dé,

é ae
Or
dd

= T'(m+1-- wu)

a
0< R(w)<m +1. |
These expressions (5) and (6), which in a sense may be considered
as each other’s reverses, enable us to arrive at (1) and (2).
vl : A iz \m
For this purpose we multiply both members of (5) by nl =) F(1-2)
and afterwards summate from 7 —~s tom == (in the second member
under the integral sign). Let us write:

HO 5 (—l)"a Le] iS le (7)
EN de TET SAN) May a RS
en RE
MEO > am Da In (eV a—a), … . . . (8)
then we get already:
T

Ica Dul8di, R(V<1. (1)

Ars
—

Plal= PL) ( 5 ) fe

iz \m
If we multiply both members of (6) by a (=) , the first member

by summation from m==s to m= om passes on account of (8) into
u(e), and if we execute the summation in the second member under
the integral sign, we find:

1—p.

12, \ SF . — Nee eat |
u(x) = ey fes EL) (i2V «—&) g (S) ds,
a

ae (— 1)"am le |
In med D= = Es = __ 4 \m—p
fe) m=s Ip (m + 1 — 1) (S a) |

O0O< R(u) <s+1 (s positive integer or zero).
It clearly appears now that only on account of the special selection
u =A this expression on account of (7) passes into:

(9)

sinan iz 5 TT , Se Oy
u (2) = (5) J (w—8) P Tan (iz Wa B)f(GdE. (2)

but we see at the same time arise as a condition R(4)>0; and as

772

in (1) RO)<1 was necessary, so we find apart from other condi-
tions, that (2) is a solution of (1), provided 0 < R(4) <1.

2. If we do not impose that great restriction on u in (9) (viz.
ua), but if we maintain its independence in reference to A; on
even in this case, apart from other conditions, represents a solution
(1) provided R(2) <1 is satisfied.

A simpler form may be given to (9) by using the following
definition :

for all values of p and g, which form exactly indicates for positive
integer values of q the q'" differential quotient of x. For the series
occurring in the second member of (9) under the integral sign, we

may then write:
( 1) 2\2m
— ma, =
En me 9
Sal

han P(m4-1l—u)

(§—a)"—" —

(10)
ivan 6
— Dir 5 en Nai (Sam =) — Dit re 5) |
; m=s I(m--2 —A) i —A)
1
on account of (7), or again Tina (el) (§) according to the

well-known notation by the whole index.
So we get for (9) the form:

sin da ia (C° ft me ve
e= PG) G) DP Lg mie Df CH IOU)

0< Ru) <s +1.

We now recognize at once (2) from (11) for u = À.

The remaining conditions, under which (11) will be a solution of
(1), are implied in the way of deducing these relations from (5)
and (6), in which we have carried out summations under the integral
sign.

So it is necessary that in (11) the series for fet) (w), ef. (10),
converges uniformly for a <a <b; if this condition is satisfied, the
series (8) for w(z) is uniformly convergent, as in the second member

773

‘ 1—p.
of (11):(@—&) 2? Z_a_,»(izV¥2—8S) is of order

fies Ru) > 0.

As a condition in the deducing of (1) from (5) it arises that (8)
must be uniformly convergent for a Se Sb, which bas the conse-
quence: /(«) continuous as R(A) <1.

We may therefore agree upon the following:

(a—a)1—?
having a =a as zero of order s [so that development (7) obtains],
and if the series, which we may draw up according to our defini-
tion for f(“+!— (a) [ef. (10)], converges uniformly for a <a <6, —
(11) will be a continuous solution of (1), provided R(4)< 1 and

O< RwW<cs+.

and u satis-
i.

1
J

is an analytical function, regular for a<7r<b,

3. For z=0, (1) passes into Aprr’s integral equation:
x
u(S) ae :
F(#) al (e=) ds, . . . . . . . (12)

for which we now find the solution in a general form by substi-
tuting in (11) also z=0, viz.
ws fe
an Age BA) AT LE
me Aa) J (eset
a

Qe Boh Wt uaa)

available under the same conditions as mentioned under I (§ 2).
AseL solved (12) on the supposition 0< R(A) < 1, and found as
solution (13), in which u= 42.

Liouvure *) extended Aprr’s problem to the supposition --n<
<R(4)<—n-+1 (n positive integer or zero) and found as solution
(13), in which w=n-+ À.

4. Let us now take (1) as a special case of Vorrerra’s integral
equation of the first kind, which has the general form:

/(0) = (Ke, Dude. Sime at, a (ELZEN

then (1) appears to ensue from this, if we take as kernel

“

Key =rd—a(5) oa * Te (eV Sey = (15)

1) Journ. de |'Ke. Polytechn , Cah. 21 (1832).

774

As to (14) the following theorems) obtain.

ij dK(w,§) :
A. If K, («,§)= K(2,§), K,(«,5) = —_—.,... K,(«,6)=

0" K(w,€)
re [See

Ön
Ont! Kla (a,6) 3 Neo
== - is finite for a<§ Sas

continuous and A, (w‚5) =

dart
and the discontinuities of AK: (z,8), if it has any, are regularly
distributed 7), and if moreover XK, (2,2) =0, K, @,2)=0,... Eee:

K,—1(a,2)=0, but Keo) =O for a<2<6, (14) will have ols one
continuous solution under the necessary and sufficient conditions:
Ka), f@). f CF Ne) Continuous for a<2<b and fla) S= f(a
=f44)=0. And this solution will be represented by the only
possible continuous solution of the integral equation of the second kind:

TL
fart (se) = Kr (wr) u (x) + Kri (#,8) (ENE ee (16)
OK (és, . O"—1K (#6),
Be ieee (GE (IE) PE DE ay (#8)
Ow Onl
oe = = On K(x,5) 2,8)
continuous for a<$<«#<b and K,(#.5)= 5 = (0< Rt
Pills
(a D= = n

in which G(z,§) and —

are also continuous for a S&<rS<b, and if

0G(ax,§)
Ow
moreover A,(a,2)=0, K,(#,2)=0,...K,«(2.2)=0, but Geo) 0
for a<a<b, — then (14) will have only one continuous solution
under the necessary and sufficient conditions: f(a), f'(@).… f(x) and

P(n)
ae Ae d$ continuous for a <a#<b,andf(aj=/'(a)=..=f/M@=
One (eE)

1—A,

sr And this solution will be represented by the only possible
continuous solution of the integral equation of the first kind:

Hee jude 0)

in which:

1) See for instance M. Bécuer: An introduction to the study of integral equa-
tions (1904) §§ 13, 14.

2) Viz. that the discontinuities lie on a finite number of curves with continu-
ously turning tangents in the space of the x£-plane considered, which are inter-
sected by lines // a- of S-axis always in a finite number of points.

and

JAS ,
L(a,5) = il GEN A 5. ea (RO)
(z SN ™(y— gy’ n

Theorem A may again be applied to equation (17), as the kernel
L(a,) satisfies already for »—O the conditions written down for
Kla,E).

We may moreover observe that, as sufficient though not necessary

~ FM Ë J 3
ee ds obtains: f(x) con-

(Hr,

tinuous and f@+(x) finite with St: a finite number of discontinuities
for wss 6.

In the first place we shall now prove that the special value (15)
for the kernel A (iv, §) satisfies the conditions mentioned in theorem
A or B and that in proportion as 2=—nor —n< RW) <—n+1
(n positive integer or zero).

a. Let us suppose 2== — n, (15) passes into:
A ne)
NTL — 2
K(«,§) = n! | — (a --§)2 I, (eVa) = nJ en ONE —(x—§)™
2 m=o ml (m+n)! ;

and we find:

“> \2m
ENEN =
OP K(a,8) ae ga ( ) ie

Kle 13 = / x =\ym-+n—p —
oA Sa dar mom! (m+n zj 5)
2 NID carl tS
== nl ( ) (e—§) 2 LF» (2 V «—&),
2
so that:

K,@,§, K, @ §)... Anti @,§) are continuous for a< Seb,
&) =

moreover Ae (a 2) = 0) 1G G2) = 0%. Krt =0, but
Ki (@, 2) S= 0) for a= a= 6:
Consequently for 2—vn the suppositions mentioned in theorem

A are satisfied by K(e,8), also if z= 0.

h. Let us further suppose 4=— n+ 2, (0 << R (2) <1), then:
50
Proceedings Royal Acad. Amsterdam. Vol. XVIII.

2 zt, En ER
K (a,§)—= T (n+1—aA,) ( =) (@—&) 2 In, (Vai =

= (A = = Se rn,
ne ue —o m! P(m- tn DI (8)

(—oe(5)
K, (2,8 Ji eye BS
a En Leak ee, m! T (m+n—p+1—,)

and consequently :

(x 6) ii a, —

; z \— "p+, ee sd.
ON (on Ne een (Va),

so that:

K, (@§), K (2,8). Kara, 5) are continuous for @ SES
moreover A, (a, ed K, (@, 2)=0,...K,-1(2,2)=0 for asen

G #,8 5 Fi
while K, (x, 6) = Al )_ in which:
(v8)
sds An
G («, 5) = P(n+1—a,) ex (a— 52 (Vas —é)
and
=
0G a, § 2 Na {a= —
ene) = — P(n+1—2,) | — («—S§) 2 Tri (eV 2—8),
Ox 2 LL
so that:

0G (a,&)

Ow
for a= 2\ 6:

Consequently for —n< R(4)<—n-+1 the supposition: mentioned
in theorem B are satisfied by A (z,5), also if z=

Summarizing we can already state that (1) has only one continuous
solution, provided R(z)< 1 and certain conditions for f(z) are
satisfied.

These necessary and sufficient conditions for fes) mentioned in
A or B are doubtlessly satistied if we impose on f(z) the conditions
mentioned under I (§ 2), so that we can complete [ in this way
that (11) under the conditions mentioned there is the only possible
continuous solution of (1). [This holds good for (13) as a solution
of (12)]. As a consequence of this (11) is invariable by changing
u within the limits indicated.

G (x,§) and are continuous for a <& <w« <b, and G(a,7)=—0

deld

In order to determine the solution of (1) according to Vourprra’s
method we have to investigate again the cases a and 5 separately.
a. Supposing that } —=— n and the given function f(v) satisfies
the conditions mentioned in theorem A, we have to consider the
equation of the second kind into which (16) passes for our case, viz.

tl) (gh eee (el oe ee ;
Pr Oe — je (SS (PAO)

Its solution is the absolutely and uniformly convergent series :

By el EE
zn fora) 1 2 By SS AE
ni ant iN Vat KEE,

a a

ERS
TEV En Em) , Pa lnEn) den. dS dE, wt NG

Een
a
which now moreover represents the only possible continuous solution

of (1) for 2= — n.
b. Supposing that à—=—n + À,(O << RA) <1) and f(w) satisfies

the conditions mentioned in theorem 5, we arrive at equation (17),
in which the kernel, represented by (19), passes for our case into

se 0 2 di < I-i, (2Vy—8)
1D 35 (3) (tee A) = =e 5 dy =

a NEA CAE AN)

so that (17) becomes:

F (@) = Din + 1 — à,) raf T, (eV a—&) u(§) dg. . (22

This integral equation of the first kind has as kernel:
K (a, &) = P(n + 1—4,) F'(An) I, (e Vat),
so that A, (w,r)=0 and we consequently arrive at its solution by
determining the solution of (16), in ;which n=O and / has been
replaced by /’; if we replace moreover 4, by n-+-4, (16), consider-
ing (18), assumes the following form:

x Ee 9)

1 hols z (DL (eV «—é)

(a= he Te) ge CLE
DLD Pet dede De Ta ans

~)
a

Its solution is the absolutely and uniformly convergent series:
50*

778

he: 1 d En fm (&) ds
‘ (ait an ee Jagen St

1 OM (zz Wad 7 (WEE, )
PT = =( I= =: NE
M(L— _3) P(n- 1) ml 2 De VER f

a a

in
|
‘es

“Ly (eV En 1—En — Em) d à LS (Em4i)
WE EEn dn } Eu — Emi) md )

dd. Em dEm .. dE dE,
a

which now represents moreover the only possible continuous solution

of (1) for —n< R(A<—n+1.

It is moreover important to observe, that though (1) for z=0
passes into the equation of Axper (12), the substitution of z=O in
(21) and (24) does not lead to its solution. As we saw, the kernel
K(v,§) continues to satisfy the conditions mentioned in theorem A
or B if z=O0, but, for 2=——n and z=0, Kral ee
that (16) is cancelled.

And if —n< R(4)< —n-+1 and z=0, (17) passes into

in zx
> ln)

le as dé — P(1 — A) P@ 4-2) fn (SD dE,
Te : a

from which the solution ensues directly :

%
snix F(a) d f@E)
x T(e+td) =| (c—é)'-@)

Wes

u (ce) =
under the conditions for / (2) mentioned in theorem Bb.

5. The expressions (21) and (24) may not be easily reduced,
even though we should make use of (7) and so we accept the
conditions mentioned under I (§2) for f(w). As in this case (11)
must represent the same v (x) we arrive at the following conclusions :

1. Not only (21) but also (11) with 4—W—n represents
the only possible continuous solution of (20), if the conditions
mentioned under I hold good for f(e). If we introduce some
Ber nisa ts ee)
simplification here by supposing RAD = p(x), we can say that
the integral equation of the second kind:

2 te Se) Mae. .
u (a) = p («) +5 - == ws) ds. 02> … (25)

has the only possible continuous solution :

x Lp

2 \\—P- a ee =
ne =(5) fen 2 Ig mea Bp EE, 0<R(u)<s+1 (26)

if the conditions are satisfied :

Il. g(a) is an analytical function, regular for a Sw Sb, which
has «=a as zero of order s; and the series for gy” (2), which we
may draw up by means of our definition, is uniformly convergent
fora a S 0.

So, not only (24) but also (11) with —n< R(4)< —n-+1 repre-
sents the only possible continuous solution of (23), if the conditions
mentioned under I hold good for f(z). Here too we can introduce
some simplification by writing Ans —= (a), so that of the

: P(1—a) T(n +2)
integral equation :

x T =
1 é Ro NL
MES ek F = GS) — dE +- — Al : ao) u(&) dà, |
dx} (a — Sti) 2 V x—t pan (247)
a a ij \
—n< R(4)< —n + 1 (n pos. integer or zero) |

the only possible continuous solution may be written in the form:

ze 1—p
iz \1—# == ; Te eT |
Wo=no-+i(S ) J (a) 9 glee Bp MEE 4 38)

OCRW SSH 1 |
under the conditions:
p(@) : gE be
UI ——_——— is an analytical function, regular for a<a <b,

(a—a)'\—o-)
having aa as zero of order s; and the series ensuing from it for
ptn) (z) is uniformly convergent for a <a <b.
at feld
2. As (21) with —————

— = #(t) and (26) both represent the only

possible continuous solution of (25), in the same way (24) with
f(a)
F(1l—2) M(n+a)

= g(v) and (28) both the only possible continuous

780

solution of (27), we arrive at the two important relations:

Aan Te NEE
ple) + (=) Af ee) ale — 5)

ml Vak WEE,
a a
Em —l

5 (2 DE — En)
he VE ry Em

(Emden. dE dE wae (29)

Sep
1

ANNE erf —_—— 223 :
= ( = | ic ee Haley Ve —£) plH(E)dE,

in which 0 < R(w) << s + 1, 2 JO, and the conditions: mentioned
under IL obtain.

al a) 3) Er 5 (zy fue rs EE) +
da (ri +) eG F Vat VEE, iid
Em 1

eed ¢(Sn-41)
xs A 7 Lem Lem. dé,dé= 30
J | (Sm—§m-+1)!~( ni) ie ik 8 din A )

E BE dé

gare Em =M «

a a
7

1—p. =o Sse las
= = iw 4- a(S ) Me —S) 2 Ter i) (iz Var — Syn (EE, |

in which —n< R(A}< —n 1 (n positive integer or zero),
O< Rw st 1, 2-0 and the conditions mentioned under [IL

obtain.

Anatomy. — “On the conus medullaris of the domestic animals.”
By Dr. H. A. VERMEULEN. (Communicated by Prof. C. WINKLER).

(Communicated in the meeting of October 30, 1915).

The material used in this research was derived from 4 horses,
a calf’s foetus of 4'/, months, 2 goats, 2 sheep, a pig’s foetus of 3
months, 3 dogs and a eat. Of that of 2 horses, 1 dog and 1 sheep
longitudinal sections were made, that of the other animals was
cut into transverse sections. (Paraffine inclusion, sections of 12—18 u,
colouring with cresil violet.)

In all our domestic animals the spinal cord reaches further in the
spinal canal than in human beings. Whereas in the latter the conus

781

medullaris reaches the second lumbal segment, in the carnivori this
passes the whole or almost all of the lumbar region of the vertebral
column, which in these animals is generally built up of seven,
sometimes of 6 vertebrae, while in the Ungulata, it can be traced as
far as the middle of the sacral portion of the vertebral column.
Similarly, the continuation of the conus and that of the surrounding
membranes, the filum terminale, extends in these animals, owing
to the stronger development of the tail column, further than in the
corresponding part of the human body. 5

Equus caballus. In the last lumbal segment the transverse section
of the medulla of the horse shows a heart shape, with the basis
turned ventrally (anterior) and the blunt point dorsally (posterior).
The anterior horns are well developed, the posterior horns are
large, with rounded, “much broadened tops turned towards the
periphery ; the substantia gelatinosa is characterised by a sharply
outlined fibre system. As well as in the ventral and in the
ventro-lateral portion of the anterior horn, numbers of large
cells are met with on the border of the anterior and posterior
horns; in the posterior horn we see scattered cells generally of a
somewhat smaller type. Occasionally these are fusiform or egg-shaped,
or more or less round, and they exhibit a marked accumulation of
pigment, which causes a morphological resemblance to the cells of
the spinal ganglion of the horse. Frequently we see a few cells,
sometimes clustered in small groups and of a narrow fusiform, in
the border zone of the posterior horn, most of them on its posterior
and outside edge. The septum longitudinale posterius is very thin
and the fissura longitudinalis anterior much narrower ou the periphery
than in the more central portion of it (fig. 1). The canalis centralis
is not obliterated, small coagulations are visible in the centrum but
the ciliated epithelium is quite intact. Remarkable is the great
number of small blood-vessels situated in its immediate neighbour-
hood. It shows a peculiar form (fig. 2). The posterior portion of it is
broad and rounded, and possesses two small pointed lateral recessus,
the anterior portion is smaller and likewise rounded off. At its
greatest breadth it measures 0.315 mm., while the greatest depth
is 0.365 mm. At the commencement of the sacral medulla the
heart shape becomes more distinct on section as the posterior pole
becomes more pointed. The canalis has shifted from the centrum in
a forward direction and has become rather narrower; the above
dimensions now are 0.216 mm. and 0.315 mm. respectively; the
section is that of a spindle with irregular walls, and the side pro-

782

jections in the posterior portion are but faintly indicated. The septum
posterior has meanwhile disappeared and the number of cells in

Equus (Fig. 1). Equus (ig. 2).

the anterior horn have greatly decreased, clusters of cells can be
seen longest ventrally and dorso-laterally on the border of the
anterior and posterior horns. In the sensory zone the large cells,
mentioned above, can still be seen, though not constantly, both in the
centrally situated cells and the fusiform border-cells.

Likewise fairly large oval, or more or less round cells, containing
pigment, can still be seen occasionally. The fissura longitudinalis
anterior is unchanged. In the following portion of the sacral medulla
these conditions are the same, with the exception of the section of
the central canal. This is now widest in the ventral (anterior) por-
tion, for there the wall is gently curved ventrally or flattened, the
dorsal (posterior) pole a blunt curve, and the side walls exhibit
several bulges. These at first number two on either side, one half
way up and one on the ventrally pointing basis. In many sections
they are seen symmetrically. The number of cells in the anterior horn
has grown small again, while in the sensory zone the various kinds
of cells appear now and then as before. This sensory zone has grown
much more massive, owing to the commissura grisea having become
thicker, the fissura anterior is smaller and no longer shows the
broadened central portion. Further back the sensory horns merge
almost to one mass, in which however, the two horns ean still be
separately distinguished for some time, as the round-fibred systems
keep their individuality (fig. 3). The conus which gradually decreases
in diameter, still exhibits the heartshaped form in section. The
anterior horn cells seen occasionally are few, and the central and
border cells are also scarce in the sensory area. The projections of
the central canal are larger, the epithelium is intact and soon a third
set of projections makes its appearance. The number of cells de-
creases, especially in the sensory portion, while the section loses its

783

heart-shaped form, owing to the conus becoming flatter. As the
fissura anterior is still present and the back wall of the conus rounds
off, the whole, on a section, now has the appearance of a kidney. The
flattening is a result of the diminishing of the sensory area. The
sectional view of the central canal again changes. The posterior
portion grows out in a point and before long almost touches the posterior
periphery of the conus, the side projections again increase in number,
new ones appear among the first, but neither constantly nor symme-
trically, while also small projections grow out of the posterior top
which has become flat. The canal now measures at the deepest part,
830 m.m., and its maximum breadth is 0.217 m.m. In another
horse these measurements were at this place 1.13 and 0.398 m.m.
The folds, four, five, and sometimes six in number on each side,
vary in size, the longer having secondary smaller ones (fig. 4).

Equus (Fig. 3) Equus (Fig. 4)
The conus is still kidney-shaped on section, occasionally a few cells
still occur, the posterior zone having no more large cells. After
this the canal breaks through on the posterior side, which break

Equus (Fig. 5). Equus (Fig. 6).

can be seen in a series of 62 consecutive sections of 18u, for a
length of fully 1 m.m. The opening, very narrow at first, gradually
widens to a maximum of 0.3 m.m. after which it becomes narrower
and the canal closes again, continuing for ‘/, m.m. nearly to the
apex of the conus.

The ciliated epithelium can still be seen quite intact in many
sections as far as the break in the border. In the conus medullaris

754

of the horse there is thus a cleft-like open communication of about
1 m.m. long and with a maximum breadth of 0.3 m.m. After this
cleft has closed the central canal attains its greatest depth, viz. 1.33
m.m., with a breadth of 0.382 m.m. The fissura anterior has dis-
appeared after the rupture, the kidney-form in section gives place to
an irregular round shape and afterwards, when the cross diameter
of the conus grows shorter, to a pear shape. Finally the anterior
portion of the canal is also pointed, whereby the frontal wall is
almost reached, but not broken through. The ventriculus terminalis
measures about 5.5 mm.

In two horses the end of the sacral medulla was cut longitudi-
nally for a length of 3.5 em. Here too it is seen that the central
canal, before it widens at the end of the conus into a ventriculus
terminalis is not everywhere equally wide. Cranially from the
ventriculus terminalis more widenings occur, in one case there was
even an elongated spindle-shaped widening, 2.5 m.m. in length, to be
seen right in front of the ventricle. Since the ventriculus proper was here
only 2.8 m.m., it is not impossible that this extreme broadening
belongs to it and that the ventriculus in this horse showed a bend.
The folds vary greatly in size, the smaller ones protruding at
right angles, the larger ones at an acute angle, while the longest
runs nearly parallel to the conus (fig. 7). The longest which I

Equus. Fig. 7.

observed was 5 mm. in length with a breadth of 0.250 mm. In
one case a narrow fold was to be seen close to the end of the canal,
so that the latter ended here in the form of a pitch-fork. The wall of
the ventriculus is much folded, some folds branch off again till the
whole has a very odd appearance
(fig. 8). The rupture seems to take
place near the end of the ventriculus.
Behind the ventriculus the conus
continues for 0.5 mm. more (fig. 8).
Equus. Fig. 8. Neither is the ventriculus obliterated,

although the epithelium here shows signs of degeneration.
Especially in the longitudinal sections fine large round cells con-

785

taining a great quantity of pigment are to be seen. Lt is not improbable
that these are central ganglion cells of spinal ganglions.

Bos taurus. (foetus of 4*/, months). On the border of the lumbal
and sacral portion the medulla shows a sectional view which
resembles exactly that of the closed portion of the medulla oblon-
gata of the cow, in the reverse way, however, for the cleft is
caused by the fissura anterior and thus lies here on the frontal side.
The walls of this fissure diverge widely and gradually slope into
the frontal wall. The strongly developed anterior horns are extremgly
rich in cells in the ventral portion; latero-dorsally on the border
of anterior and posterior horns no cells of a large type are met
with. As a rule three sharply defined cell-groups may be distinguished
in the anterior horn, one ventro-medial, one ventro-lateral and one
dorsally at the last-named. This dorso-lateral group is the most
constantly round in form and contains 30—40 cells, the two other
differ greatly in size and shape, owing to their often possessing
continuations which continue along the lateral and medial walls respec-
tively. The dorsal horns are broad and carry a heavy cap of
substantia gelatinosa Rolando, always clearly circumscribed on the
periphery by a fibre system. These horns are also rich in cells, of
a smaller type, however, than those of the anterior horns. The canalis
centralis is a recumbent oval in section, in width it measures 0.1 mm.
and in depth 0.07 mm.; the ciliated epithelium is very well developed.
The fissura anterior is shallow, regular in section and proceeds, as has
been remarked, with a pronounced curve into the frontal wall of
the medulla. In this foetal tissue the commissura grisea is very
slightly developed, when, strongly magnified, but few commissure
fibres can be detected, a circumstance which can be observed also
in the whole of the lumbal segment (fig. 9).

Caudally the cross diameter of the conus decreases, whereby the
form on section becomes compact, the central canal shifts in a
ventral direction and on section is seen to be round; the cell groups

Fig. 9. Fig. 10.
Bos taurus (Embryo 4!/; months).

756

in the anterior horn have grown fewer in number and smaller, the
commissura grisea begins to be clearly visible on the peripheral
portion and further develops rapidly and grows very rich in small
cells. The border zone of the posterior horns lies directly against
the periphery. Further caudally, in the medio-ventral portion of the
anterior horn, many cells again appear, and conspicuous is a well-defined
cell-group right and left of the canalis centralis. These groups built up
of typical anterior horn cells, can be traced for many sections (fig. 10).

The conus then becomes roundish in form, only broken in its
frontal wall by the shallow fissura anterior, the central canal has
become egg-shaped on section with the blunt end pointing ventrally ;
the septum posterius has disappeared; the commissura grisea is very
broad and rich in small cells, in the anterior horn a varyingly large
number of cells occur of a smaller type than before; after this the
conus flattens and its section shows the form of a kidney, the
central canal keeps its diameter and remains free; the number
of cells has diminished very greatly everywhere; in the anterior horn
we see exclusively small cells of 10—12 u, sometimes in groups
3—d. By the time the fissura anterior has disappeared, the frontal
wall of the conus is flattened, the posterior wall remains rounded,
the central canal is then rather wider, (0.13 > 0.1 mm.) and is also
flattened on the frontal side. Now the canal begins gradually to widen
into the ventriculus terminalis. First egg-shaped on section with the
pointed end towards the front, it further on expands backwards
whereby the posterior wall of the canal becomes flat. At the base
traces of folds can now and then be seen (fig. 11). The breadth
diameter of the conus diminishes greatly so that, when the canal has
reached its maximum breadth and its front and back walls have
very nearly reached the periphery, the whole canai is surrounded
by a narrow sfrip of conus-tissue (fig. 12). The ventriculus is then

Fig. 11. Fig. 12.
Bos taurus Embryo 4l/, month.

1.16 mm. deep and 0.250 mm. broad; the epithelium here shows
siens of degeneration, and cell remnants are present in the ventriculus.
Then the latter decreases in width and gradually becomes a narrow
groove; before the end, however, a slight widening takes place,

787

which bears traces of folds, and in which the epithelium appears
again to be quite intact. The whole ventriculus has a length of
3 mm., and there is no sign of any rupture. At the end of the
conus we find outside the continuation of the dura numerous spinal
ganglions, the largest with a diameter of 0.750 mm., while a few
smaller ones can be seen caudally from the conus (fig. 12).

Capra hircus. On the border of the last lumbal and the first
sacral segment the medulla is roundish on section, the anterior horns
are well developed and almost reach the periphery; they are very
rich in large cells, which also occur in the so-called middle-horn ; the
posterior horns, with their round, cap-like, broadened tops partly,
and rather more caudally entirely, reach the periphery. They contain
few large cells; the fibre-system round the substantia gelatinosa Rolandi
is also distinctly present. The section shows the canalis as an upright
oval, at this place it is 0.270 mm. deep and 0.1 mm. wide. The
septum posterius is very thin and the fissura anterior very narrow. The
canal is quite free, ventro-laterally we find on the right and left a
sharply defined fibre bundle, more or less round, with a diameter of
0.2 mm. These bundles are also present in the lumbal medulla and can
be traced far back’). Also in the second series they can equally
clearly be seen. Owing to the canal deepening caudally they gradually
come to lie right and left beside the canal (fig. 13). In this level the
conus is still round in section and numerous cells, though in general
of a smaller type than before, are met with in the anterior horns, as
also in the middle-horn and dorsally from the central canal. The
posterior horns are still poor in cells. More caudally the septum
posterius disappears and the whole posterior portion of the conus
is taken up by the sensory area, in which the two horns have
merged into one, the fissura anterior has grown very shallow, the
central canal has shifted further ventrally and has become wider,

i rat BW

/ Ret

Fig. 13. Capra hircus. Fig. 14. Capra hircus.

) According to Dexter these sharply cireumsciibed “intra kommissurale Ven-
tralbtindel” occur constantly in the Ruminants and in Pigs. (ErrenBereer, Hand-
buch der vergleichenden mikroskopischen Anatomie der Haustiere, Vol. Il, Page 214).

In the calf’s foetus they were not present.

788

especially in the ventral portion, in which portion folds occur.
In this respect there appear to be individual differences. In one
series they are very distinct. The posterior portion grows out in a
point, stretches as far as the back wall of the conus and even
pushes the latter outwards in a point at some places; the anterior
portion sends out strong folds at its base and somewhat higher
(fig. 14). Further back these increase till finally the whole ventricle
wall is folded. The greatest depth here measures 0.550 mm. the
greatest width 0.140 mm. In the other series the canal appeared
less deep here, though more than twice as broad; here the measu-
rements were 0.480 and 0.3 mm. respectively; the folds occur later,
are less numerous and much smaller. The ventriculus terminalis
of the goat is about 3 mm. long. The canal is not obliterated.

Ovis aries. The end of the lumbal medulla on section is round,
as is also the central canal. The latter is partially obliterated and
the epithelium also exhibits distinct signs of degeneration. As in the
goat, clearly defined bundles also occur ventrally from the canal:
here however, they lie nearer the median line and do not reach
so far caudally. The grey matter is less well developed than in
the goat and cells are fewer in number. The septum posterius is
partially cleft-shaped, the fissura anterior, as in the horse, is much
wider in the more central portion than at the surface.

Caudally the conus becomes heart-shaped in section, the canal
shifts in a ventral direction, deepens and broadens ventrally, and
then becomes bell-shaped in section, owing to the flattening of the
broad lower wall. Its depth and breadth are here 0.2 and 0.170 mm.
respectively. In this region we see, at the back, indications of folds
and the above-mentioned bundles will be found to lie immediately
against each other and right against the lower wall. More caudally
tbe canal becomes -narrower again, the septum posterius here is a
cleft almost as well developed as the fissura anterior, still further
back, the septum becomes shorter and we frequently see the remainder
of it as a small cleft-like space connected with the posterior wall
by a fine pia-bundle. At this juncture the conus is distinctly
kidney-shaped on section, cells are still present in all the sections,
the majority in the anterior horn but a few also in the posterior horn.
The central canal widens into the ventriculus terminalis, deepens
as it proceeds backwards and soon reaches the posterior circumference,
many sections show the wall at this place bulged in a point by
the ventriculus. Here shallow folds and short bulges are present
in the ventricle wail. (Fig. 15). The back wall of tae conus is

789

hereby rendered so thin that a break seems to have taken place
repeatedly. In the continuous series, however, we see distinctly
that there have been ruptures, the remains of which are frequently
to be seen, but where such is not the case or is doubtful, such
sections are followed by others in which the canal is closed.
The greatest depth of the ventriculus in this series is 0.670 mm.
and the maximum width is 0.250 mm., after which the canal grows
narrower. Although the walls are often irregular, distinet folds no
longer occur. The ventriculus is about + mm. long. Even at the

Fig. 15. Ovis aries. Fig. 16. Sus scrofa domesticus
(foetus 3 months).

end of the conus an occasional cell is to be found. Immediately
behind the end of the conus, beyond the continuation of the dura
lies a spinal ganglion which contains about 60 cells. In a longitu-
dinal section we see that the central canal itself is very irregular
in width, and that the folds are small and few in number.

Sus scrofa domesticus (foetus of 3 months). This material
appears to have suffered greatly and only the series of the
last portion of the conus has been successful. At this place the
conus is ~+ mm. in diameter, and round in section, the septum
posterius is not present and of the fissura anterior only a shallow
groove is left. No cells are to be observed. The canal no longer
lies in the centrum, it is a fairly narrow ellipsis in section, 0.3 mm.
deep and 0.07 mm. wide. Towards the back it widens 0.16 mm.
and the section becomes egg-shaped. On this level and also further
backwards we constantly find in the durapocket one or two spinal
ganglions of 0.250 mm. in diameter.’ The canal continues till it
strikes against the front and back walls of the conus (fig. 16), then
it widens in a ventral direction and finally decreases in width and

790

depth, at the end it is surrounded only by an extremely fine layer
of conus tissue. The widened portion of the canal is 1.5 mm. long,
the greatest depth measures 0.4 and the greatest breadth 0.18 mm.
No folds of the wall, nor any indications of such can be noticed.
Cell-remnants are present in the ventriculns. No more spinal ganglions
are seen at or near the top of the conus.

Canis familiaris. In carnivori the conus does not reach the sacral
canal. In the middle (he lumbal medulla is heart-shaped on section
with the blunt point directed backwards. The grey matter is very
strongly developed. Owing to the presence of the big commissura grisea
the fine septum posterius is very small. The central canal is an
irregular round, frequently it is a distinet pentagon on section, the
epithelium is poorly developed and even lost in several places;
many remnants of it are found in the central canal, which is also
wholly, or nearly wholly, obliterated, its depth and breadth are
practically equal, the diameter measures 0.17 mm. In the strongly
developed motor horns we find large cells ventrally only. The pos-
terior horns touch a large part of the back wall of the conus, the
border zone is not so sharply marked as in the Ungulates. In this
area too a few large cells occur. In general the medulla is poorer
in cells than the sacral medulla of ruminants (fig. 17). Further
back the conus becomes kidney-shaped on section and the canal
measures more in width than in depth, the broad base sometimes
arched, sometimes flat, measures 0.250 mm. and the depth 0.125 mm.
Here we find traces of folding at the base and sometimes also

Fig. 17. Canis familiaris. Fig. 18. Felis catis domest.

above. Now the formation of the ventricle commences, the canal
deepens towards the back; at first it is pointed in front and rounded
at the back, so that the whole in section becomes pear-shaped ;
later the base also rounds off so that it becomes an elongated oval,
after which it gradually decreases. In three dogs the measurements
were as follows: from the number of transverse sections the

wot

length of the ventriculus of one could be calculated to be 2.5 mm.
of another 2.25 mm. while of the third dog the longitudinal section
measured 3 mm. In the two first cases the greatest depth and breadth
were 0.4—0.17 mm. and 0.5—0.15 mm. respectively, and the great-
est depth in longitudinal section 0.515 mm. In longitudinal section
jt further appears that the canal does not run quite to the point of the
conus, but stops 0.225 mm, from it and that the portion of the canal
behind the ventricle exhibits slight differences in depth. Past the
conus very small ganglions are seen outside the membranes.

Felis catis domestica. In general we find here the same conditions
as in the dog. Owing as the fissura anterior disappears earlier the
section does not show the kidney shape after the heart shape, but
the conus here is more or less flattened at both poles, and later it
becomes oval and pear-shaped on section. Further the central canal
in the cat appears to have different diameter measurements at several
places, and is mostly obliterated. At first fusiform on section with
a depth of 0.30 mm. and a width of 0.166 mm. towards the back
it becomes roundish, with a section of 0.230 mm. and then points
in a ventral direction. At several places it exhibits small folds
in many sections of the ventriculus, these are symmetrically present
in the posterior third portion (fig. 18). Here the ventricle is 0.558 mm.
deep and 0.250 mm. wide, after which it gradually narrows to a
fine cleft which has also small folds. The whole ventriculus is
2.25 mm. long. At the end of the conus a few ganglion cells are
observed.

We see thus that of our domestic animals the horse exhibits
various peculiarities in the structure of the conus. Although the length
of the ventriculus terminalis is very small compared to that of
human beings at least, (man 8—10 mm., horse 5.5 mm.) this differ-
ence is certainly fully compensated by the particularly strong folds
of the ventricle walls and the numerous, frequently even strongly
developed folds of the canal before the ventricular widening.
This fold formation can be seen in a more or less degree in all
the other domestic animals with the exception perhaps of the pig,
but in none in such a degree of development as in the horse.
Further the rupture of the canal, the presence in the horse of a
neuroporus posterior and the striking abundance of blood-vessels in
the immediate proximity of the central canal. As regards the rupture,
STILLING has observed that the central canal breaks through at the

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

792

end of the conus, in some animals at the back wall, on others at
the frontal wall. Srmrine’s observations have been repeatedly refuted
by others, and hitherto the theory generally held was that such
a rupture does not occur, and that what Srmaine had seen
were only artefacta, which need occasion no surprise since
the conus wall, which surrounds the ventricle, is often extremely
thin. In my opinion the rupture is undeniable in the horse and I
connect it with the unusually rich fold formation, the presence of
numerous recessus and the great quantity of blood. For, owing to
these conditions, the resorption surface of the liquor cerebro-spinalis
and the degree of the power of resorption increases of the relative
tissues, which for an animal used for long and heavy labour and
therefore provided with a very powerful metabolism, cannot be
otherwise than of the greatest use. To this opinion I will here add
in passing that in none of our domestic animals are such frequent
disturbances of the central nervous system caused by stopping of the
liquor cerebro-spinalis to be met with as in the horse.

Remarkable is the occurrence of sharply defined bundles in the
motory region and in the immediate neighbourhood of the central
canal and the lumbal and sacral medulla of ruminants and pig, as
also the fact that about half-way in the development the commissura
grisea in the cow is locally developed and at other places has still
to be formed.

It is known that in human beings spinal ganglia can be seen
at the end of the medulla inside the dura-pocket. As regards the
horse I ean give no information on this point because the material
of these animals has been prepared for the investigation. Of the
other animals numerdus spinal ganglia occurred intra-durally only
in the pig (foetus): in several, these ganglia are seen caudally from
the conus. It is certainly remarkable that these ganglia, which in
higher levels have shifted peripherally into the foramina vertebralia,
have remained at the end of the medulla nearer their origin or
have been left behind at the end of the spinal canal. The fact that
they even remain within the membranes entitles us to assume that the
spinal ganglion cells of the terminal part of the medulla are more
inclined to keep their connection with the spinal cord, for which
reason [ venture to express the possibility that the cells rich in
pigment as described in the horse even might be central ganglion cells.

793
Chemistry. — “On Critical Endpoints in Ternary Systems’. MI.

By Prof. A. Smits. (Communicated by Prof. J. D. vaN Der W aars.)

(Communicated in the meeting of October 30, 1915).

1. Projections on the concentration triangle.

Already in a few earlier communications | have written on the
occurrence of ¢ritical endpoints in ternary systems’), specially because
this subject is of great importance for petrography and particularly
for the chemistry of the magma.

In my latest communication six cases have been successively dis-
cussed, the sixth of which referred to the occurrence of a binary
compound as solid phase.

The consideration of a case that a ternary compound occurs as
solid phase was then postponed till later, because it seemed to me
that this case would not be a subject of study for the present.

Soon after, howéver, Dr. Morey informed me that he was engaged
in the study of the ternary system H,O—SiO,—K,O in the Geo-
physical Laboratory of the Carnegie Institution of Washington, in
the course of which research he met with a case that had not yet
been treated by me, so that it had become desirable to extend my
earlier considerations.

I greatly desired, particularly because I knew Dr. Morey would
be interested, to undertake this work immediately after his commu-
nication, but want of time compelled me to put this off until now.

7 Case. Continuing our earlier considerations we shall therefore
begin with the case that the volatile component A gives critical
endpoints neither with B nor with C, but that a ternary compound
D, ocenrs, which more or less dissociates in the liquid and the
vapour phase, and which presents critical endpoints with A. This
case is schematically represented in fig. 1.

In this figure in the first place the ternary eutectic Jiquid and
vapour lines are given, so the liquids and the vapours that coexist
with two solid substances. In the second place the critical endpoint
curve has been given.

1) These Proc. XII, p. 342 and XV, p. 184.
li

794

Fig. 1.
Ds the least volatile; B more volatile than C; A very volatile.

The lines L,/L,/and G,'G’s \ 3 { A+-D;
melo WGL refer to the B+ D3
» yy Ly'L3 „ GG,’ | liquid resp. vapour C+ D3
pe ton, ae eee Gr phases coexisting ) 4+€
” „ Lobo! „ GG’ with A+B
cna LL en (Gace | BHC

The arrows on every curve indicate the direction towards higher
temperature.

The closed curve pq is the critical endpoint curve with the
ternary compound as solid phase. Hence critical phenomena take
place by the side of the solid ternary compound J, along this line.
The critical endpoints which are found starting from the ternary
compound D, and pure A lie in the points p and g. On addition
of B, as well as of C these points approach each other, till they
finally coincide. Now it has been assumed here that the ternary
compound can exist up to the highest eutectic temperature that
occurs in the ternary sytem.

If this is not the case, however, and if the ternary compound de-
composes before this temperature has been reached, so that a double
salt D, occurs as solid phase, the tigure becomes as indicated in
fig. 2.

Now the transformation points Z', and G', resp. Z', and G', occur

795

on the liquid and vapour lines which indicate the liquids and the
vapours coexisting with D,+ C and D, + B, from which points
new eutectic lines start indicating the following coexistences.

L',L, and G',G, for liquid or resp. vapour phases with C+ D,
IB IEE ” GAG. LE) LE) LE) EE) ” 2 LE) B a dD,
ode GG 55 a Ae k) 5 » D,+D,

It might happen that now again critical endpoints occur, and
now by the side of D, as solid substance, but this case we leave
out of consideration for the moment.

It is still noteworthy here that the critical endpoint curve might
also have been drawn in this way, that it intersects the lines G’,,
G', and L', L';. This intersection would then, however, have had
no physical signification, as the latter lines refer to other tempera-
tures than those for which the critical endpoint curve holds.

Ds the least volatile; Dj less volatile than B and C;

B more volatile than C; A very volatile.

8th Case. We will, however, examine the case that presents itself
when in the preceding case the ternary compound D, decomposes
before the critical endpoint q is reached, and when at higher tem-
peratures critical phenomena with solid D, occur instead of with
solid D,. When this case presents itself fig. 2 is changed into fig. 3.

Fig. 3.
D; the least volatile; D, less volatile than B and C;
B more volatile than C; A very volatile.

The particularity is here that the eutectic liquid-vapour lines
referring to the coexistence with D, + D,, merge continuously
into each other in the points p and p,, which are therefore two
double critical endpoints.

In these two points the two critical endpoint curves, that of D,
and of D,, intersect.

9 Case. Just as in the preceding case two double critical end-
points can present themselves, when besides the ternary compound,
also the component C with A exhibits critical endpoints. We then
get a structure as given in fig. 4.

The double-critical endpoints P, and P, are the points of inter-
section of two critical endpoint curves.

For one critical endpoint curve the ternary compound D, occurs
as solid phase, and for the other the component C. Of course the
corresponding continuous eutectic liquid vapour lines pass through
the two points of intersection. It has further been assumed in this
figure that just as in the preceding case a binary compound D, is
formed from the ternary compound at a temperature above the
critical endpoint p. If in the binary system A—B also critical end-
points occur, two double critical endpoints may arise also on that
side of the triangle, which we need not specially indicate here.

Fig. 4.
Ds the least volatile; D, less volatile than B and C;
B more volatile than C; A very volatile.

Besides a combination with fig. 3 can occur, but this case too
follows so easily from the preceding ones that this does not call
for a separate discussion either.

Thus it will also be clear that in the last case the two endpoint
curves coming from the sides AC and AB, which refer to the
coexistence of a critical phase with solid C resp. with solid B,
can come in contact with each other, as was drawn by mealready
before, (fig. 5 in communication IJ), and then this case can occur
e.g. combined with case 7 or 8.

What is, however, of more importance at the moment is the fact
that Dr. Morey in his study of the system H,O0—Si0,—K, 0, found
phenomena which point to this that this system as far as its main
points are concerned, must be probably classed with fig. 4, when
we namely put that A= H,O, C=SiO, and B=K,O. The system
H,O —SiO, gives two critical endpoints; further Dr. Morey has found
that in this system a ternary compound AKHSi,O, occurs, which
probably also shows two critical endpoints, the former lying at
+ 365°, the latter at + 500°. He has further found that this
ternary compound splits up at higher temperatures into the binary
compound K,Si,O,, and a solution rich in SiO,. Of course the
critical endpoint curve of the compound need not come in
contact with that of SiO,; this is however probably the case, and

798

then fig. 4 represents the phenomena schematically perfectly, at least
as far as the principal features are concerned, though the situation
of the vapour lines is much more one-sided than has been drawn
here. It is, however, not impossible, as Dr. Morey observes, that
also the binary compound yields critical endpoints, but this being
still unknown at the moment, we can leave this possible compli-
cation undiscussed for the present. Now the system studied by
Dr. Morey, however, is certainly still somewhat more complicated
than that indicated in fig. 4, for there occurs another ternary com-
pound there, viz. K,Si,0,H,O0. This ternary compound gives no
critical endpoints. The figure, however, changes only little, also
when this compound is considered.

1 5
Fig. 5.

Dz the least volatile; B more volatile than C; A very volatile.

This change will be applied later when the system has been more
closely investigated; probably A,S:,O,H,O will occur at lower
temperature, KHSi,O, at higher temperature. ;

In any case it seems probable to me that what is typical of the
said ternary system is indicated by fig. 4, and so this figure can
probably render good services as a guide in the continued research.

Case 10. Up to now cases have been considered which may
present themselves for ternary systems with one volatile component.

799

Now we will suppose that both A and B are volatile, and that a
ternary compound J, occurs, giving critical endpoints with A and
B, whereas C presents critical endpoints neither with A nor with
B. We then get fig. 5, which does not call for further elucidation.

Case 11. The case we are going to consider now only differs
from the preceding one in this that in the binary system A—C
critical endpoints occur. The critical endpoint curve for solid D and
solid C intersect, and give then rise to the origin of two double
critical endpoints #, and P,.

Fig. 6.
Ds the least volatile; B more volatile than C; A very volatile.

As it has been supposed that also B is volatile, critical endpoints
could also occur in the binary system BC, with this result that
also on this side double critical endpoints make their appearance.

Case 12. We shall now proceed to the case that the three com-
ponents are volatile, but form a ternary compound melting ata high
temperature and much less volatile, which yields critical endpoints
with the three components. Here too, as in the preceding cases,
unmixing in the liquid phases is excluded.

Fig. 7 represents the case supposed here in drawing, and shows
that the ternary compound PD, with all the mixtures gives critical
endpoints, so that two closed critical endpoint curves are formed,
an inner g-curve and an outer p-curve.

800

Fig. 7.
Ds very little volatile; A, B, and C very volatile.

If now in one of the binary systems a maximum critical tempe-
rature occurs, the possibility still exists that the ring is opened in
consequence of the continuous merging into each other of the p-
and the g-curve at two places.

Though the cases discussed here might be supplemented by a
number of others, | shall for the present drop the subject here, and
resume it again as soon as the experiment renders it desirable to
enter more deeply into these considerations or to extend them.

Ul. The P,T-figure.
Four phase lines and critical endpoint curves.

As in Dr. Morny’s research P-7-lines are determined it was
desirable to represent also these curves i.e. the four phase lines in
drawing for a few of the cases considered here.

When we examine the projections of the eutectic liquid and
vapour lines, taking the direction into account in which the temperature
rises, and bear in mind that where a eutectic line is cut by a line
joining the two coexisting solid phases with each other a maximum
temperature prevails, this derivation can on the whole easily be
given rougbly, provided the rules are made use of, giving the relative
situation of the four-phase lines round a definite quintuple point.

801

I will therefore first devote a few moments to the discussion of
the derivation of these rules.

If the concentrations of the coexisting phases in a system of an
arbitrary number of components have been given, there exist in the
P,T-figure definite relations for the relative situation of the lines
for monovariant equilibria. For quadruple points Dr. Scuerrnr has
derived a rule which indicates this relation, and which renders the
construction of the three phase lines possible, if the succession in
concentration of the four phases is known.') Afterwards the same
rule derived and formulated in a slightly different way, was
given by ScHreineMAkers.*) The situation of the four phase lines
round a quintuple point has already been described by ScHREINEMAKERS
in “Heterogene Gleichgewichte III 1”, the relations holding for them
have been lately elucidated further by him. *)

Fig. 8.

For the construction of the subjoined P,7-figures I have used
these relations availing myself of the following figures, which
1) These Proc. XV, p. 389. Z. f. phys. Chem 84. 707 (1913).

2) Z. f phys. Chem. 82, 59 (1913).
3) Verslag Kon. Akademie 25 Noy. 1915. (Not yet translated.)

802

Dr. Scnerrer had already derived in his cited investigation, but
which had been left unpublished, as the essential part appeared to
have been published already by SCHREINEMAKERS, and the derivation
of which only differs somewhat in form. In his investigation on the
quadruple point rule Scuerrer demonstrated that no two-phase coexist-
ence can exist over a spacial angle greater than 180°. Making use
of the filling up of the space round the quadruple line by two-
phase coexistences, he came to the quadruple point rule. The follow-
ing figures have been constructed by him through application of
the same principles for the quintuple points. The P,7-figures round
the quintuple point were derived through the application of the
principle of the filling up of the space round the quintuple point,
which is now four-dimensional, and must consist of three-phase
coexistences, combined with the rule that three phase coexistences
in stable state can only occur over angles which are smaller than 180°.

Fig. 9.

In the figures 8, 9, and 10 are given three-phase-coexistences
which suecessive regions have in common and which must lie

803

within an angle smaller than 180°. The coexistences between
immediately following four-phase lines have been omitted for the
sake of clearness.

If we know the situation of the five phases in the plane of con-
centration, it is easy to construct the subjoined P-7' figures. The
five points can namely lie in three different ways: they can forma
triangle with two points inside, a quadrangle with one point inside
it, or a pentagon.

These three cases correspond resp. with the figures 8, 9, and 10.
For the first case the figure is e.g. constructed in the following way.
We consider a certain division of the triangle in three phase
regions; this situation is then possible in one angle at the quin-
tuple point. If we now pass round the quintuple point it is possible
that by the side of three of the coexisting phases a fourth exists.
This fourth phase can lie inside or outside the three-phase coexistence
in question. We then get either a quadrangle, of which the four

phases can exist simultaneously, or a triangle with a point inside
it, which are all at the same time stable. If we take a definite

804

division as point of issue, the new division can come about in two
different ways.

In the P-7T-figures this comes to this that the region is enclosed
by two four-phase lines. The question is therefore reduced to this:
divide the concentration figure into triangles, and gradually change
this division, so that every time one fourphase coexistence shows
the transition. When the division has been modified five time, we
have passed round the quintuple point, and we have again the
original division.

In this way the three figures are easy to reconstruct. In the figures
the corresponding division is indicated in every region and it has
been indicated by hatching on the quadruple lines what four phase
coexistences make the transition between successive divisions possible.
Strictly speaking regions of one single homogeneous phase and the
two-phase coexistence would still have to be indicated in the con-
centration figures; for the survey and the construction these are,
however, not necessary. {When the four-phase line is passed some
three-phase coexistences are left undisturbed repeatedly. Thus it will
be clear among others that in fig. 10 the coexistence 125 is not
disturbed by the four-phase line 2345; it occurs both on the left

Fig. la.

805

and on the right of the four-phase line in question.

The reproduction of these figures 8, 9, 10, which were not published
by Dr. Scuerrer, seemed desirable to me, because though they
do not contain anything new, they can render good services in the
application on account of their great lucidity.

We can now represent the four-phase lines schematically for the
different cases.

Fig. la agrees with the case considered in fig. 1. Particularities do
not present themselves; it is only worthy of note that the four-

806

phase lines of AD,LG, CD,LG, and BD,LG possess temperature
maxima.

The ternary critical endpoint curve for the coexistence of the
solid ternary compound with the critical fluid phase is indicated by
a closed line, on which the critical endpoints p and qg oecur. By
the side of this line the symbol D, + (L = G) is written.

807

Fig. 2a is a little more intricate, because here the binary com-
pound D, is formed from the ternary compound D, at higher tem-
perature. This gives rise to two new quintuple points CD,D,LG
and BD,D,LG. Now the temperature maxima of the four phase
lines CD,LG and BD,LG have disappeared, and instead of this
the four-phase line D,D,LG now possesses a temperature-maximum.

Of the greatest importance, however, is the P-7' fig. 4a, which
corresponds with fig. 4.

In a binary system occur the critical endpoints S + (= 4G), in
consequence of the three-phase line S + 1 + G meeting the plait-
point curve £ = G, just as for the system ether-anthraquinone. In
a ternary system the critical endpoints S, + S,+(L=G) occur,
which I have called double critical endpoints, when the four-phase
line S, S, ZG meets the critical endpoint curves S, + (1 = G) and
S,+(L=G), which meeting must of course take place simulta-
neously. In fig. 4a the lines p‚rg, and P,RP,VP,, refer to the
critical endpoint curves C+(L=G) and D, + (L= G).

Where the four-phase line CD,LG meets these critical endpoint
curves, the double critical endpoints C+ D, + (L = G) oceur, from
which it therefore follows that this meeting must take place in the
points of intersection of the critical endpoint curves mentioned. The
double eritical endpoints P, and P, are connected by the critical
endpoint curve P,VP, the other half of this curve is metastable.

As has been said it is very well possible that this case occurs
in the system H,O—SiO, —K,O, but it is also possible that the critical
endpoint curves p‚rg, and P, RP, VP, do not intersect, and in this
case the four-pbase line CD,LG proceeds undisturbed from one
quintuple point to the other.

Dr. Morry’s investigation will be able to decide this point.

Anorgame Chemical

Amsterdam, Oct. 28, 1915. Laboratory of the University.

Chemistry. — “ The Periodic Passivity of Iron.” By Prof. A. Smits and
C. A. Losey DE BRUYN. (Communicated by Prof. van per W aars).

(Communicated in the meeting of October 30, 1915).

1. The periodic passivity on anodic polarisation.
As was already communicated before *) the passive state of iron
can be abolished by bringing the iron into contact with solutions

1) Chem. Weekblad 12, 678 (1915).

or
Lo

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

805

containing Cl’—Br’ and I’-ions, which ions must therefore be
considered as catalysts for the conversion of passive iron into
active iron.

In the course of the investigation on the passivity of iron the
question rose whether it would not be possible to call forth periodic
phenomena for instance by the addition of Cl-ions to the electrolyte
during the anodic polarisation.

According to our recent views. the internal equilibrium in the iron
surface is namely disturbed during the anodic polarisation, in con-
sequence of this that practically exclusively ferro-ions go into solution,
and the comparatively slow internal transformation ferri ferro in
the iron surface proceeds too slowly to keep pace with the going
into solution of ferro-ions. Hence the iron surface becomes richer in
ferro-ions and the potential difference iron electrolyte becomes less
strongly negative or positive.

Let us suppose that the electrolyte is ferrosulphate, and during
the anodic polarisation of an iron electrolyte with a very small
surface, we add ferrochloride, then the catalytic influence exercised
by the chlorine ion becomes noticeable by a decrease of the positive
potential difference, and when the addition of ferrochloride is con-
tinued, a pretty rapid and considerable decrease of the potential
difference appears at a given moment, and the iron has passed
from the passive state into the active state.

Without our entering into any further details it is clear that at
a velocity of solution of the iron determined by the density of
current it must be possible to find a concentration of chlorine ions,
at which at a definite moment the chance that the iron remains
passive is just as great as the chance that it becomes active or vice
versa. Let us now suppose that at this moment the density of the
current is somewhat diminished, then it may be expected that the
transition passive-active takes place, and while the iron-anode inthe
passive state only goes exceedingly little into solution, the iron,
having now become active, will be sent into solution to a very great
degree in the form of ferro-ions. Hence the contact of the Cl’-ions
with the iron-surface will diminish, and in consequence of this the
iron will again be brought back to the passive state.

As has been said, the iron dissolves but very sparingly in this
passive state, and the processes which now take place at the anode,
consist first of all in the discharge of the SO,-ions with the subse-
quent O,-generation, and secondly in an increase of concentration of
the Cl’-ions. This latter process will then again give rise to activation
and so on. This supposition was fully confirmed, and as the following

A. SMITS and C. A. LOBRY DE BRUYN: “Activation curves of iron’’.

0 Z A

igs 2:

Activation curves of iron after anodic polarisation in FeSO, (0.473 gr. mol. p. L.)

ay ” nj ” i i without FeCl
by > a aes ‘ 5 + 0.00024 gr. mol. ,
Cony 5 Nears ö ; & + 0.00036 - .
he . nk a 5 ‘ + 0,00048 , , E

The potential is indicated on the y-axis in Volt. with respect to the potential of

active iron in the same solution. The time is indicated on the x-axis in minutes.

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809

photographie reproductions (fig. 1) show, we have complete control
over the phenomenon 5. .

For a definite Cl-ion concentration the density of current is to be
chosen so that the time during which the most passive state prevails,
is about equally long as that during which the most active state
continues to exist. See tig. 1a.

If the density of current is made slightly greater, the passive state
continues to exist longer than the active state, which appears very
clearly from fig. 16. In the maxima the iron is passive, and in the
minima active. The oscillations in the potential which we have
observed here, are very great; the maxima and the minima lie 1,74
Volts apart, the duration of the periods amounting to 6.54 and 5.8
seconds. It is self-evident that the periodic phenomenon described
here only manifests itself clearly when the iron-surface is small. The
larger the iron-surface the smaller the chance that the iron is passive
or active all over its surface at the same moment : hence this pheno-
menon is less regular as the surface is taken larger, and vanishes
entirely for a large surface.

We will point out here that periodie phenomena during the elec-
trolytic solution of passifiable electrodes have already been observed
by different investigators, but none of these investigators has sue-
ceeded in calling forth a periodic phenomenon of such large regular
oscillations as here. 7

ADLER’), who has perhaps done the most meritorious work in
this region, obtained periodic oscillations in the potential difference
anode-electrolyte among others for iron by generating hydrogen at
the backside of the iron wall, part of which acted as anode. The
explanation is as follows: The hydrogen diffuses through the iron,
and arriving at the anodeside it can then exert its catalytic action.
Though ADLER’s view was different from ours we may say that here
too the periodic phenomenon was obtained by the use of a catalyst,
but here the catalyst enters through the metal, hence the pheno-
menon is brought about in another way than ours.

Further the iron in Aprer’s experiments remained a long time
passive and a very short time active, and the potential difference
only amounted to 180 millivolts, the phenomenon beine besides less
regular than ours. The curve found by him is represented to scale

1) The iron rod was not suspended on a platinum wire, but was cemented
with shellac in the short leg of a U-shaped tube. After it had appeared that
electrolytic iron behaves perfectly uniformly to iron with a sinall carbon-content,
we have afterwards always used the latter.

*) Z f. phys. Chem. 80, 385 (1912).

52*

810

in fig. de. The oscillations found by us are, as is shown in the
drawing, about ten times greater.

2. The influence of the Cl'-ion concentration on the shape of the
curve of activation.

Another question which likewise incited to research, was this:

When iron is made passive by anodic polarisation, e. g. in a
solution of ferro-sulphate, and then the current is interrupted, the
potential difference diminishes rapidly at first, then it changes little
for a short time, after which it finally descends again rapidly.

This discontinuity has been accounted for by Smits and ATEN *),
the explanation coming to this that in the transition passive —
active a state must be passed through at which two metal phases
exist side by side, which, in case electromotive equilibrium continued
to exist all the time, would have to give rise to a temporary occur-
rence of a constant potential difference.

When now chlorine ions in the form of ferro-chloride are added
to the solution of ferro-sulphate it may be expected that, the C/-ions
accelerating the internal transformation in the iron surface, this
discontinuity will become less distinct, and apparently vanishes
entirely at a certain C/’-ion concentration.

As the curves fig. 2 show this expectation has been entirely realized.

It is clear that the discontinuity which seems to have entirely
disappeared on the last photo, d fig. 2, would manifest itself again
clearly, when the velocity of revolution of the registration cylinder
was increased. We shall return to this later on. *)

That these remarkable results recorded here, which strongly
support the new views of the passivity, can be stated in such a
way that every particularity which tlie different figures contain, is
essential to the phenomenon, and is not a consequence of the inertia
of the galvanometer, we owe to this that the research could be
made with Dr. Morr's excellent galvanometer, which through its
quick and moreover perfectly aperiodic indication was eminently
suitable for these experiments.

The photographic representations have been made with Dr. Morr’s

1) These Proc. Vol. XVII, p. 680.

Chem. Weekblad 31, 678 (1915).

2) The curve d exhibits a hardly visible thickening on the original photo at the
place of the halting-point. In a subsequent communication the influence of the
extent of the iron-surface on the periodicity will be more particularly dealt with,
and further the periodie passivity at anodic polarisation of iron, the unprotected
surface of which is only partially immerged in a ferro-sulphate solution.

811

photographie registering apparatus, which he very kindly placed at
our disposition, and for which we gladly express our sincere thanks
to him once more here.

Anorg. Chem. Laboratory of the University.

Amsterdam, Oct. 28, 1915.

Physiology. — “On «after-sounds.” By Dr. F. Roers. (Communi-

cated by Prof. Dr. H. ZWAARDEMAKER).

(Communicated in the meeting of October 30, 1915).

In daily life after-sounds are rarely perceptible to the car of
normal man and even then they are vague and comparatively feeble
after violent detonations. We, therefore, had to apply rather potent
stimuli and to sereen our subjects from all disturbances above all
from the ordinary street-noises.

The GALTON- and EpriMann-whistles gave most satisfaction. The
subject was placed in the camera silenta of the Physiological Labo-
ratory at Utrecht; the head was fixed, the right ear at 2 em. dis-
tance and right in front of the embouchure of the whistle. At every
time an airstream of equal force was urged through the whistle by
the experimenter outside the camera. In the first experiments the
whistle was put into operation inside the camera by the experi-
menter, who also recorded the phenomena perceived by the subject.
Although we used our utmost endeavour to do this as noiselessly
as possible, it was detrimental to the production as well as to the
observation of the phenomena. We, therefore, resolved to separate
the experimenter from the subject. They spoke to each other by
telephone, which enabled the experimenter to perform tbe time-
measurements by means of a chronometer. The subject used the
telephone only for these measurements; for the description of the
nature of the phenomena he relied entirely upon his memory after
the experiment. This procedure was not open to objection as the
phenomena never took more time than 1'/, minute.

Before entering upon our experiment proper a series of respectively
100 and 50 preliminary tests were performed with our two subjects,
Prof. Dr. A. Micnorre from Louvain and Dr. Bakker from Batavia.
The total number of the subsequent conclusive tests amounted for
M to 148 and for B to 129,

812

They are distributed among the various stimuli as follows:

M | B. | PAIS Al Me Boe M. | B.
| | | |
el nobele Bek het) ed er loren 10 | 12
7 Soro Ga cal as re feat 0
2 8 | 6 | a3 | 12 | vl | ay | 20 | 22 es | 8 16
a | 8 Gaulianes | gE Net) | ds | 17 | 12 C7 2

The order of the stimuli varied regularly. As a rule stimuli of
the same pitch acted on the subject in 2 or 38 consecutive tests.
From 6 to 12 experiments were made in succession.

2
(1 see), feeble, and indistinct. Sometimes a short and slight sensation
of strain is perceived directly after or simultaneously with the
after-sound. Most often the subject announces a period of absolute
or relative silence (total absence or considerable decrease of intensity
of the murmurs usually perceived during a stay of some length in
the camera silenta). This interval generally links itself to the after-
sound. In half the cases it continues from 10—16 see. Little by
little the normal noises return intensified.

M. Directly after the stimulus an after-sound, being a typical
murmur with pitch (+ fis ,). The pitch disappears after a rather
short time; the murmur continues and while being broken from
time to time by feeble boundary tones, pulsations and the like,
passes into the normal noises after 15 to 27 sec.

/, B. The after-sound follows the stimulus instantaneously; it is
a short (+ 1 sec), feeble, shrill sound. It is closely followed by a
period of absolute or relative silence (1—13'/, sec.), which is grad-
ually filled by reinforeed normal noises. During the interval of
silence the subject is generally conscious of a slight sensation of
strain. Oceasionally the reinforced noises are interrupted by a musical
sound, of a pitch lying between that of the stimulus and that of
the succeeding after-sound. ;

M. In 5 out of 10 cases a typical murmur with pitch, is yielded
directly after the stimulus. The intensity of tone rapidly diminishes,
so that at last only the murmur remains. The tone heard in the
murmur, is higher than jis, and afterwards recurs once or twice.
In the other cases a tone is heard directly after the stimulus which,
while lowering rapidly, sinks into the afore-said typical murmur.

e,. B. The after-sound immediately following the stimulus is short

813

In its turn the latter gets lost again in the ordinary entotic noises.

J, B. Very likely the after-sound comes close upon the stimulus.
It is short (+ 1'/, sec.) and very high. Less often than in the case
of /, it is followed directly by an interval of absolute or relative
silence, as mostly a feeble musical tone is heard whose pitch lies
between that of the after-sound and the stimulus and whose duration
varies from 2—3'/, sec. :

Whenever the musical tone is not heard, the normal noises,
which, while intensifying gradually, follow the after-sound directly
or are heard after a space of absolute or relative silence, possess
a certain pitch. Eventually the space of silence lasts 5—9,5 sec.

M. In three cases a tone is heard instantly after the whistle is
blown. It is rather higher than fis,, gradually grows less intense,
to be replaced after 4—7 seconds by a typical murmur. In the
other cases the tone and the typical murmur occur simultaneously.
Its pitch (invariably + jis,) gets lost after 6—8 sec., when the pure
murmur continues to flow (as is ever the case) into the normai noises;
sometimes a strain is felt.

a,. B. The after-sound is short (+ 1'/, sec.), feeble, and high-pitched.
Only twice a vague sensation of strain is announced. Close upon
the after-sound follows a “dark” space (period of absolute or relative
silence of 10.5—11 sec.). At times it is succeeded by a feeble musi-
cal tone by the side of which the normal noises are generated and
reinforced so as to supersede the tone, whose pitch lies between
that of the after-sound and the stimulus. Every now and then a
high bird’s note interferes with these noises.

M. In every experiment the subject notices immediately after the
stimulus a murmur, with markedly varying pitch and intensity, the
former fluctuating between d, and «, The pitch gradually disap-
pears so that only the typical murmur is left. Occasionally a great
strain, which sometimes causes pain.

cis, B. Short (+ 1 sec.) and feeble after-sound, followed in 5 out
of 6 cases by a “dark” space, which lasts from 13 to 16 seconds.
Little by little the normal noises recur with growing intensity.

M. Immediately after the stimulus in all cases a murmur, evidently
of a definite pitch; it most often belongs to the 6 octave. The
intensity of the tone decreases by degrees, so that at last only a
typical murmur remains, in which, however, a pitch is still plainly
discernible. At times the quality of this murmur is modified, both
the intensity and the richness being diminished; the pitch also is
gradually lowered.

a, B. The after-sound is short (+ 1.1 sec), feeble and high. Some-

814

times it is followed by a feeble musical tone (3'/,—4 sec). Then a
period of absolute or relative silence sets in. In almost all cases
this “dark” interval commences immediately when the after-sound
has ceased; it takes 19'/,—20'/, see. Then the normal noises recur,
gradually intensified. Feeble bird’s notes of distinctly varying pitch
often mingle with the noises at more or jess regular intervals. Some-
times a strongly marked sensation of strain occurs in the gap of
absolute or comparative silence.

M. A murmur with pitch in almost all cases directly after the
production of the stimulus. The pitch is about 1*/, octave higher
than jis, At times only a tone is heard, sueceeded by a murmur
after 14—17 sec.

The pitch of the tone is modified in a few cases: being rather
low at first, it rises up to +d,. The intensity of tone and murmur
gradually lessens. The pulsations heard anterior to the production
of the stimulus recur during the experiment with augmented inten-
sity and with a decided pitch. Only once or twice the subject makes
mention of a sensation of strain.

c, B. The after-sound is short (+ 1,1 sec, feeble, and shrill. In
4 out of 6 cases it passes into a very feeble tone of different pitch
(lower than the after-sound, higher than the stimulus), lasting from
4—7'/, sec. A gap of absolute or relative silence immediately links
itself to it. The gap covers 14 to 25 seconds, whereas only 13—15
seconds are taken by the “dark” interval that follows the after-
sound. Ultimately the normal noises return gradually with aug-
mented intensity, intermitted by several high and feeble musical tones.
In one case only a slight sensation of strain.

M. Frequently, directly after the production of the stimulus a
murmur with piteh (+ c¢,,d,; duration 24—31 sec.) In a few cases
a pure tone is heard, which only somewhat later makes way for
the typical murmur, which in its turn passes into the normal noises,
broken now and again by pulsations and feeble cricket-chirps.

e, B. The duration of the after-sound, mostly forcible and very
high, .averages 2 sec. Directly after it a constantly feeble, musical
tone with a pitch, intermediate between that of the after-sound and
the stimulus. Sometimes the after-sound coalesces with the musical
tone so gradually that is seems to sound musical at the outset. The
tone continues from 1 to 18 seconds and is succeeded by a gap of
absolute or relative silence lasting from 3 to 34 sec. Finally the
normal noises slowly return with augmenting intensity. Only once
a sensation of strain is. recorded.

M. Almost always directly after the emission of the stimulus a

815

murmur with pitch (+ ¢,). Both tone and murmur soon get weaker
and weaker; when they have disappeared the normal noises are heard.

j, B. The after-sound is very forcible and high; its time averages
1°/, sec. It always makes way for a musical sound of a pitch lying
between that of after-sound and stimulus. Its intensity lessens
gradually, so that finally (in 3 cases after 4, 7 and 20°/, min.) an
absolute or relative silence ensues. This interval lasts about 6 sec,
after which not the normal noises are perceived, but again a musical
sound whose length varies from 7 to 18 sec. and with which the
gradually reinforeed normal noises coalesce, while being interrupted
every now and then by feeble bird’s notes. Ultimately the musical
tone flows together with the normal noises.

M. Only rarely does the subject observe a murmur with pitch
directly after the emission of the stimulus. While maintaining its
piteh (+ ¢,) till the end it gets gradually fainter and finally makes
way for the normal noises. Oftenest, however, the subject observes
instantly after the stimulus a powerful, highpitched tone (6th Octave)
of fairly long duration (7
the normal noises return.

a, B. The after-sound heard directly after the stimulus, is high
and powerful; its duration averages + 1'/, sec. In well nigh all

9 sec.), fading away slowly. In the end

cases it is succeeded by a musical sound of a pitch lying between
that of the after-sound and the stimulus and of a duration varying
from 2 to 4 sec. This sound makes way for a period of absolute
or relative silence, which is gradually filled by intensified normal
noises.

M. In 47 out of 20 cases a tone is heard instantly after the
stimulus is emitted. It gradually swells up to a maximum, reached
after 2 or 3 seconds. Then the tone dies out very slowly. Its pitch
is about that of the stimulus. Its length is considerable (21—65 sec.)
When lasting very long there is sometimes a breach of continuity ;
it is plainly audible, though it is, of course, comparatively feeble.
When discontinuous it sounds like a succession of pulsations of the
same periodicity with those observed by the subject when not ex-
perimented upon. In the end there is a recurrence of the ordinary
entotic noises.

In 3 cases the subject is for about 20—58 see. conscious of a
powerful, typical blowing noise immediately after the stimulus issues
from the whistle. It is discontinuous at rather regular intervals
and makes way for the normal noises, in which it may be distin-
guished a few times.

d, B. The after-sound is very high and powerful; its time averages

816

+ 1*/, sec. The subject often announces a regularly recurring
intense strain, which vanishes by slow degrees. In 11 out of 12
cases the after-sound is succeeded by a pause of absolute or relative
silence. In about half the cases it lasts 13—17 sec. when it is
filled by the gradually intensifying murmur. In the remaining
cases this pause is much shorter (8—10 sec.) and is filled not by
the normal noises, but by a second after-sound, a continuous tone
lasting +: 7—10 sec. and fading before the gradually intensifying
normal noises. In only one case does the second after-sound follow
the first immediately. Its pitch is lower than that of the first.

M. Close upon the issue of the stimulus a rapid tone, gradually
growing less intense, lying somewhere about a,. In well-nigh every
case it is succeeded by a vigorous blowing noise, which lasts from
65—93 sec; the niaximum of intensity is reached after 2'/,—3 see. ;
then it fades away extremely slowly and regularly. Sometimes it
recurs once or twice. In synchronism with this blowing noise pul-
sations are audible, weak as compared with the force of the blowing
noise (pitch = a,).
fB. The average duration of the after-sound, appearing at the
emission of the stimulus, is 2 sec. It is high (ericket-chirp), vigor-
ous, often extremely so. It is constantly succeeded by a period of
absolute or relative silence, (5—-16 sec); in this pause a strong sen-
sation of strain is often perceived. In some cases a second after-
sound is heard after the first, lower but of longer duration (8—7
sec.). In the majority of cases the pause is filled by gradually intensi-
fying normal noises broken by a few bird’s notes.

M. In some cases directly after the emission of the stimulus a
high-pitched tone, followed immediately by a typical, continuous
blowing noise (duration 69—87 sec). Mostly this noise is heard
close upon the stimulus. It is very powerful, sometimes with pitch
especially at the beginning. At times it is interrupted by the ordi-
nary pulsations. Finally the normal murmur returns.

a, B. The after-sound is comparatively long (+ 3 sec.), powerful
and high-pitehed (crieket-chirp) and seems to follow the stimulus
immediately. In most cases it is succeeded by a period of absolute
or relative silence (B —12'/, sev.), In one third of the cases, however,
the normal noises recur, either to continue with growing intensity,
or to make way for a second after-sound, most often a musical
sound lower and feebler than the first.

This after-sound covers about 4—13 sec. Ultimately it is also
replaced by the gradually intensifying normal noises.

M. Only in one of the 10 cases does the subject announce a short

817

Subject B.
6% | S * | Sensation | Period of absolute Blowing
SE 28 : ent 2nd after-sound ;
carey |e a) Ce of strain | or relative silence | noise.
Sal 24
Sie |) Ce) dE
es (6) 1 feeble | rarely, short 10—16
and slight |after Ist after-sound)
fo (6)\1 feeble | most often, 6 —13.5
notvery great|after 1st after-sound
22 (6)|1.25) feeble 5—9.5 2—3.5
lafter Ist after-sound| mostly after Ist
| after-sound
az (6)/1.3 | feeble (rarely, slight, 10.5—11 Short, after the
jafter lst after-sound, period of silence
cis3(6)| 1 feeble 13—16 | |
jafter Ist after-sound|
az (7)}1.1 | feeble | distinct, | 19.5 - 20.5 3.5—4
rather slight | In 6 cases after the |occasionally, feeble,
| 1st after-sound. | directly after the |
In one case after | first after-sound |
| the musical tone | |
following the |
after-sound. |
13—15 4—1.5
| In 4cases after the |In 4 cases directly
| musical tone, after the 1st
ca (6)|1.1 | feeble rarely, rather, 14—25 after-sound
slight In 2 cases after the
Ist after-sound
4 (6))2 mostly rarely 3—34 1—18
intense | after the musical | alwaysafter the 1st
| | tone following the after-sound
| after-sound |
fa (6)/1.75/intense | most often, 6 4—20.5
sometimes | after the musical | always after the 1st
| very intense | tone after-sound
ax(22)|1.25| intense | sometimes 18
almost always after| always after the Ist
the musical tone after-sound
a(12)}1.8 |intense| regularly (almost always after 7—10
the Ist after-sound ;/in five cases after
lin 6 cases: 8—10;\theperiod of silence
| in 5 cases:
| 5—16
f5(12)|2 often | regularly, after the Ist 3—7
very | often very | after-sound | in 3 cases after the
| intense | great period of silence
as(12),3 ‘intense rarely, slight 3—12.5 | 4—13
| | mostly after Ist | in 2 cases after the
| after-sound period of silence
e¢(16) 2.6 intense none | 2—10 | Gl
after the first hiss | During or
| after the 1st
after-sound
15—40
| Intermittent
(blow, sound.

818

Subject M.

Pitch of the | Duration of the
after-sound | after-sound (sec.)

es (1) In 6 cases murmur with slightly lower than fis,| tone: 2
pitch murmur: 15-21
In 1 case: tone

Ist After-sound

Ap (8) Murmur with pitch between d, and fis4

~
2
=>

ie)
id

” 5 » between d, and fis,

a3 (12) | In 11 cases murmur with | + 1'/, octave higher | tone: 14—17
pitch than fis,
In 1 case: tone

ca (7) In 4 cases murmur with
| pitch
In 3 cases: tone

H+

Cs, ds tone: 24—31

é, (8) In 6 cases murmur with | higher than c5
pitch
In 2 cases: tone

fy (12) | Nearly always tone + 6th octave tone: 7—9
a, (20) In 17 cases: tone mostly + €5 tone: 21—63 (not
In 3 cases: blowing sound continuous)

ds (17) Nearly always blowing sound ‚Blowing sound: 65—93

fs (10) 5 8 x el en „ :69—87

as (8) | Always : z NE » :46—11
| (not continuous)

€5)(8) sales 4 4 higher than cz Blowing sound : 13—35

cz (2) Typical murmur

‚No blowing sound |

tone directly after the stimulus. In the other cases a vigorous
blowing noise is observed, sometimes (especially at the commence-
ment) of a certain pitch (a boundary tone). Mostly the blowing
noise continues very vigorously, but not unintermittently, as in 5
of the 10 experiments it ceases altogether only after 46—71 sec.
In three experiments the noise disappears after 15 or 15,5 sec. Im
its final stage other phenomena are also discernible, such as pul-
sations etc.

819

e,. B. Immediately after the stimulus the after-sound, which is
powerful and high-pitched (cricket-chirp) (duration 2°/, sec.).

A highly powerful blowing noise in conjunction with the after-
sound and continuing when this has ceased. With one exception
(15.5 sec.) it continues for 3—-7 sec, to be succeeded by a gap of
absolute or relative silence (2—10 sec). Subsequently a second
discontinuous blowing noise is distinguished, slightly differing in
character from the first. The intervals are characterized by a slowly
increasing murmur. The second blowing noise disappears entirely
only after 15—40 sec. In the end the normal noises return while
intensifying gradually.

M. Immediately when the stimulus is emitted a blowing noise is
plainly audible, which especially in its initial phase, assumes a certain
piteh (higher than c,). The intensity of the noise lessens rapidly ;
after 2 or 3 sec. the subject has to concentrate his attention con-
siderably to follow it; in 7 cases it is inaudible after 13—15 sec.
Sometimes it is not continuous; the moment of its first disappearance
occurs after 4— 23 sec. Usually it is superseded by the normal noises.

c‚. M. Directly after the stimulus a typical murmur, heard also
before the experiment but less vigorously.

In the foregoing tables we give the principal data regarding the
character and the duration of the phenomena as apprehended by
our subjects when acted upon by the stimuli applied.

CONCLUSIONS.

1. Invariably a constant after-sound, differing individually has been
observed close upon the stimulus. With the lower stimuli it consists
chiefly in @ murmur of a certain pitch, while the latter prevails
before the discant. At one stage after the discant the after-sound
changes into a typical blowing noise.

The most forcible after-sound is yielded by the high discant. Its
duration varies from 2 to 30 sec. As for the pitch of the after-sound,
it is constantly higher than that of the stimulus. The lowest stimuli
as a rule yield the lowest after-sound; the highest are produced by
the highest stimuli.

2. An interval of 2—30 sec. is most offen filled by a second
after-sound, ‘lower than the first, mostly of longer duration and much
less distinguishable from the normal entotie noises.

820

Chemistry. — “Jn-, mono- and divariant equilibria.”. HI. By Prof.
SCHREINEMAKERS. ‘

(Communicated in the meeting of October 30, 1915),

Correction.

In the previous communication II, the figures 4 and 6, as will
have been obvious to the reader, have to be changed mutually.

6. Quaternary systems.

In an invariant point of a quaternary system six phases occur,
which we shall call A, B, C, D, Hand F; consequently this point is
a sextuplepoint. Six curves start from this point, therefore; in
accordance with our previous notation we ought to call them

(A), (B),.... (); here, however we shall represent them by A’, B,
C", D’, E' and F’. Further we find 4 (n + 2)(n +1) = 15 bivariant
regions.

When we call the components A,, A,, A, and K, and when we
represent them by the anglepoints of a regular tetrahedron, then
we are able to represent each phase, which contains these four
components, by a peint in the space. As in a sextuplepoint six
phases occur, consequently we have to consider six points in the
space and their position with respect to one another.

In general this representation in space can lead to difficulties for
the application to definite cases; for this reason we shall later indi-
cate a method, which leads easily towards the purpose in every
definite case. Here, however, we shall use the representation in
space in order to deduce the different types of the possible P,7-
diagrams.

When we consider the six points in the space, then they may
be situated with respect to one another as in the figs. 1, 3, 5, and 7:

In figs. 1 and 3 they form the anglepoints of an octohedron, viz.
of a solid which is limited by eight triangles. In each of these
oetohedrons we find twelve sides and three diagonals. [In fig. 1 AF,
EC and BD are the diagonals, in tig. 3 AF, EC and EF]. In
fig. 1 we find in each anglepoint four sides and one diagonal, in
fiz. 3 we find in the anglepoints / and / three sides and two
diagonals, in the anglepoints A and C four sides and one diagonal
and in the anglepoints B and D five sides only. As in fig. 1 the
“partition of the sides and the diagonals is a symmetrical one and,
however, in fig. 3 an asymmetrical one, we shall call tig. 1 asym-
metrical, fig. 3 an asymmetrical octohedron.

821

In fig. 5 five points form the anglepoints of a hexahedron
within which the point / is situated. When we omit the side-plane
BCD and when we unite F with B, C, and D, then again an
octohedron arises, which we shall call monoconcave.

In fig. 7 four of the points form the anglepoints of a tetra-
hedron, within which the points /# and # are situated. When
we unite /7 with the points 4, B and D, the point / with C, B
and D, and when we omit the side-planes ABD and CBD, then
a biconcave octohedron arises.

Type I. We shall deduce now the P,7-diagram, when the six
phases form the anglepoints of a symmetrical octohedron (tig. 1).
We may consider this solid as construed of the four tetrahedrons
CABD, EABD, FBCD and FBED, which terminate all in the
side BD.

In order to determine the reaction between the phases of the
monovariant equilibrium /”, we consider the hexahedron CADBE;
as the diagonal CF’ intersects the triangle ABD, this reaction is:

CHEZAHBHD

Henee it follows:

CAE Rt AGI

In order to define the reaction between the phases of the mono-
variant equilibrium 4’, we take the tetrahedron ACBDI; as the
diagonal Af” intersects the triangle BCD, we find for this reaction:

BY CR D AE

CAD EN EA Ee reen ver A (ON

Hence it follows:

We now draw in a P,7-diagram (fig. 2) in any way the curves
E' and FP’; for fixing the ideas we draw £” at the left of £’. [For
the definition of “at the left” and “at the right” of a curve we
have previously assumed that we find ourselves in the invariant
point on this curve, facing the stable part). In accordance with this
assumption (1) and (2) have been written also at once in such a
way that herein £/ is situated at the left of #”.

It now follows from (1) and (2) that C’ is sitnated at the left of
fF’ and E’; C” is situated, therefore, as has also been drawn in tig. 2
between the stable part of 4” and the metastable part of 4”.

Further it follows from (1) and (2) that the curves B’ and D’
are situated at the right of /” and at the left of 4’; they must,
therefore, as is also drawn in fig. 2, be situated between the meta-
stable parts of the curves 4” and F”’. The position of B’ and JD’

Fig. 1. Fig. 2.

with respect to one another is, however, not yet defined, we shall
refer to this later.

Further it follows from (1) and (2) that A’ is situated at the
right of ZF’ and WE’; consequently A’ is situated within the angle,
which is formed by the stable part of curve /” and the metastable
part of curve W’. As however also the metastable part of curve C”
is situated within this angle, we have still to define the position of
A’ with respect to this curve. For this we take the hexahedron
BCEFD,; as the diagonal BD intersects the triangle CHF, we find:

CoH FF | Al) BoD. oS

Hence it is apparent that ©’, 4” and /” must be situated at the
one side, B’ and D’ at the other side of A’; consequently A’ must
be situated between the stable part of /” and the metastable part
of C’.

In order to define the position of A’ and C” with respect to one
another, we might have considered also the hexadron DCEFB. As
the diagonal BD intersects the triangle CHF, we find:

BDC | AR nn EN

In accordance with what has been deduced above we find here
that B’ and D’ must be situated at the one side and A’, £’ and
F’ at the other side of curve C’.

In order to define the position of B’ and D’ with respect to one
another, we have to know the reactions, which occur in the mono-
variant systems 5’ and D’; we shall refer to this later.

When we introduce, as in the case of ternary systems. the idea

823

“bundle of curves’, then we may express the results in the following
way: when the six phases form the anglepoints of a symmetrical
octahedron, then the six monovariant curves form in the P, 7-diagram
three “twocurvieal” bundles.

Now we should yet also have to consider the bivariant regions ;
as, however, the reader can easily draw them in each of the P,7-
diagrams, we shall omit this. Later we shall, however, refer to an
example.

Type II. In fig. 3 the six pbases form the anglepoints of an
asymmetrical octohedron. We may consider this solid as to be
composed of three tetrahedrons, which terminate in the side BD.

In order to define the position of the curves with respect to curve
I’, we consider the hexahedron CADBE, hence we find:

GEAN AB EE

In order to find the position of the curves with respect to curve

i’, we consider the hexahedron ABDCF; hence we deduce:

Fig. 3.
BCD" BO Aenea ee TB)

Now we draw in a P,7-diagram (fig. 4) the curves 4’ and F’
and we take in this case /” at the left of 4’. For this reason (5)
and (6) have been written also in such a way that herein // is
situated at the left of 4”.

It follows from (5) and (6) that 4’ and D’ are situated both at
the right of /’ and at the left of /’; consequently, as is also drawn

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

824

in fig. 4, they must be situated between the metastable parts of L”
and £”. The position of B’ and D’ with respect to one another is,
however, not yet defined by this; we shall refer to this later.

Further it follows from (5) and (6) that C’ is situated at the left
of F” and “’; consequently C’ is situated within the angle which
is formed by the stable part of 4’ and the metastable part of #7’.

For the position of A’ it follows from (5) and (6) that A’ must
be situated at the right of #” and £”; consequently A’ is situated
in fig. 4 within the angle, which is formed by the stable part of
F’ and the metastable part of /’. As however this angle, is divided
into two parts by the metastable part of C’, we cannot tell yet
within which of those two angles we have to draw curve A’. In
order to examine this, we consider the hexahedron HBDCF; we
find from this:

HEFIAIB OD... . ) = aa

Hence it is apparent that we must find at the one side of A’ the
curves WE’ and F”, at the other side the curves B’, C’ and D’.
Consequently it follows from this that A’ must be situated between
the metastable parts of the curves C” and 4’.

We should have been able to find the same with the aid of the
hexahedron HALDI; hence it follows:

PIC \|A'BD!. >... el

Now it appears from this that we must find at the one side of
C’ the curves 4” and #”, at the other side the curves A’, B’ and D’.

It is apparent from fig. 4 that we may express the previous results
in the following way :

when the six phases form the anglepoints of an asymmetrical
octohedron, then the six monovariant curves form in the P, 7-diagram
four onecurvical and one twocurvical bundle.

Type Ill. In fig. 5 the six phases form the anglepoints of the
hexahedron EFLABDC, within which the point # is situated.
In order to transform this hexahedron into an octohedron, we
unite /’ with the three anglepoints of a definite side-plane of
the hexahedron; we find this side-plane in the following way. In
fig. 5 S represents the point of intersection of the diagonal CZ
with the triangle ABD. We imagine the hexahedron to be divided
into six tetrahedrons, which terminate in the point S. As tbe point
S is situated within the tetrahedron SSDC, we take for the side
plane, mentioned above, the triangle 5DC and we unite therefore
the point /” with the points B, C and D.

825

Consequently we may consider the solid as a monoconcave
octohedron, which is composed of the tetrahedrons HABD and
CABD, diminished with / BCD; these tetrahedrons terminate again,
the same as in the figs. 1 and 3 in the side BD.

a
Fig. 5. Fig. 6.

In order to define the position of the curves with respect to /”
and 4’, we consider the hexahedron WABDC and the tetrahedron
ABCD, within which the point # is situated. We find:

GENE ALB) sei Rn ven
and ba ial LATE SV Cc ae Ge MANEN LT EIND

Now we draw again in a P,7-diagram the curves #’ and /’
(fig. 6) and we take again 4H’ at the left of 4”.

In this connection (9) and (10) have been written at once in such
a way that also herein £’ is at the left of #7.

It follows from (9) and (10) that C’ must be situated at the left
of F’ and of 4”; consequently C’ must be situated within the
angle, which is formed by the stable part of 4’ and the metastable
part of PF’.

Further it is apparent from (9) and (10) that A’, 5’ and D’ must
be situated at the right of /’, but at the left of 4”; consequently
they are situated, as is also drawn in fig. 6 within the metastable
parts of H’ and F’.

Now we have still to define the position of the three curves A’,
B’ and D’ with respect to one another. From the tetrahedron
CBDE within which the point /’ is situated, it follows:

P| AC \SBAGE 1D ED area Nem sie tale ct CHE)
so that at the one side of A’ only F”, at the other side B’, C’, D’
53*

826

and #” must be situated. Consequently curve A’ is situated as is
drawn in fig. 6.

The contemplation of the hexahedron HABDF gives us:

EEOC? | ACB DO i GO A

but it does not teach us anything new.

Now we have still to define the position of B’ and D’ with
respect to one another; we shall refer to this later.

When we summarize the obtained results, we may say:

when the six phases form the anglepoints of a monoconcave
oetohedron, then the six monovariant curves form in the P, 7-
diagram one threecurvical, one twocurvical and one onecurvical bundle.

Type IV. In fig. 7 the six phases form the anglepoints of the
tetrahedron ABCD, within which the points / and F are situated.
The line HF’ intersects the triangles ABD and CBD; now we
unite E with A, B and D and also # with C, B and D. Conse-
quently we may consider the solid as a biconcave octohedron, which
is composed of the tetrahedron ABCD, diminished with the tetra-
hedrons HABD and FCBD. These three tetrahedrons terminate
again in the side BD.

From the position of the five phases of the equilibrium #” with
respect to one another we find:

BIELLA BCD, ann nn
It follows for the position of the equilibrium 4’:
ABCD | BY |E te ne

Now we draw in a P,7-diagram (fig. 8) again the curves /” and
LY and we take again ” at the left of /”, in accordance with this
also in (12) and (14) W/ is taken at the left of 47.

Fig. 7.

I neen

827

Now it follows from (13) and (14) that the bundle of the curves
A’, B’, C’ and D’ must be situated at the right of /” and at the
left of /’; therefore, these curves are situated, as is also drawn in
fig. 8, within the angle, which is formed by the metastable parts
of H’ and PF.

Now we have still to define the position of those four curves with
respect to one another. As the five phases of the equilibrium A’
form a tetrahedron LBCD, within which the point F is situated,
we find:

IP: | AGEN tO ERED oe SN ovens 32 yet, (ELN

Hence it follows that curve A’ must be situated as is drawn in
the figure.

The five phases of the equilibrium C” form the tetrahedron ALD,
within which the point /; hence it follows:

B Ca Ae Oe dey ENG)

Hence it is apparent that curve C” must be situated as is drawn
in the figure.

Later we shall define the position of the curves B’ and D’ with
respect to one another.

We have found the following above:

when the six phases form the anglepoints of a biconcave octohedron,
then the six monovariant curves form in the P,7-diagram one
fourcurvical and two onecurvical bundles.

Though we have deduced the four types of the P,7-diagrams
without knowing the position of the curves 5’ and D’ with respect
to one another, yet we shall define the position of the curves 5’
and D’ with respect to one another. For this we have to consider
the position of the five phases of each of the equilibria 5’ and D’.

For this we consider the line A/; this line intersects in each of
the solids (figs. 1, 3, 5 and 7) either the triangle BCE or the triangle
DCE. Now we assume that it intersects in each of these solids the
triangle BCL.

As the five phases of the equilibrium DD’ form the hexahedron
ACEBF, the diagonal of which intersects the triangle C/A, it follows:

AP || DG |RBACeE ee gers. es PCLT)

The five phases of the equilibrium 4’ form the anglepoints of
the hexahedron ACDEF. As, in accordance with our assumption
the line AF does not intersect the triangle CDE, the line CE will
intersect the triangle AFD. Hence it follows:

ENDE LAND ANNE TENEN)

It is apparent from (17) that in each of the figures 2, 4, 6 and

828

8, we must find at the one side of curve D’ the curves A’ and
FF’ and at the other side the curves B’, C’ and EH’. Therefore
curve D’ must be situated, as it is drawn in each of these figures.
Consequently also by this the place of curve B’ is defined.

We should have been able to deduce the same also from (18).

In each of the P,7-diagrams, when starting in a definite direction
from 4, the suecession of the curves is: B’D’A’F’ EC’. Im order
to understand the meaning of this succession, we shall bear in mind
the following. The points 5,D, and A of the solids, are particular
points, each defined in a particular way. BD is viz. the side in
which terminate the tetrahedrons, of which we imagined each octo-
hedron to be built up. On this side the point 5 occupies again a
special place, as we have assumed that tbe line AF’ intersects the
triangle BCL. Also the point A is a particular point, as the line
AF intersects the triangle BCE.

When we compare the succession of the curves in the P, 7-diagrams
with the succession of the anglepoints of the solids then we go in
these solids tirst along the sides from B towards D and afterwards
towards A. Starting from A we go along a diagonal, consequently
towards F’; starting from F we go along the other diagonal, conse-
quently towards # (figs. 3, 5 and 7) or, when no other diagonal
starts from # (fig, 1) we go along a side towards the point, which
is situated on the other side of the triangle ABD, consequently
also towards #. At last we go, starting from # along a diagonal,
consequently towards C.

When we summarize the results obtained above, the following is
apparent: ;

1. There exist four types of P,T-diagrams. Tke six phases form
the anglepoints of

a. a symmetrical octohedron (fig. 1); then in the P,7-diagram
the six curves form three twocurvical bundles (fig. 2);

b. an asymmetrical octohedron (fig. 3); then in the P, 7-diagram the
six curves form one twocurvical and four onecurvical bundles (fig. 4);

c. a monoconcave octohedron (fig. 5); then in the P,7-diagram
the six curves form one threecurvical, one twocurvical and one
onecurvical bundle (fig. 6);

d. a biconcave octohedron (fig. 7); then in the P,7-diagram the
six curves form one fourcurvical and two onecurvical bundles (fig. 8).

2. The four types are in accordance with one another in that
respect that the curves succeed one another in a same definite
succession. (To be continued).

i a a nn a

829

Physics. — “On the measurement of very low temperatures’. XXVI.
The vapour-pressures of oxygen and nitrogen according to the
pressure-measurements by v. SiRMENs and the temperature-
determinations by KamertincH Onnes c.s. By Dr. G. Horst.
(Communications from the Physical Laboratory at Leiden. 1487).
(Communicated by Prof. H. KaMERLINGH ONNrs).

(Communicated in the meeting of Sept. 25. 1915.)

$ 1. /ntroduction. The main object of this communication is a
correction of the calculation of the results contained in a paper by
H. von SieMeNs, Annalen der Physik Vol. 42, p. 871, 1913. Siemens
determined the vapour-pressure as a function of the temperature for
a number of substances using a platinum-resistance-thermometer.
This thermometer had been reduced to the Leiden: standard-platinum-
thermometer Pt, by means of Nernst’s linear reduction-formula.
For a handy calculation of the temperatures Sigmens used an
interpolation-table in which the resistance is given divided by the
resistance at O°C. below 80°K. for every two degrees and for
temperatures between 80°K. and 290°K. for every five degrees. For
this purpose he used the data of the Leiden-calibration of 1905—1906.
It has appeared, however, afterwards that this calibration does not

agree so well with subsequent ones as these among themselves and
that, particularly in the oxygen-region, considerable deviations occur
which must therefore also affect the results obtained by Siemens.
We will therefore begin by a detailed examination of these deviations.

» § 2. The calibration of Pt,.

The first comparison of this resistance-thermometer with the
hydrogen-thermometer was carried out in 1905—1906 by KAMeRLINGH
Onnes, BRAAK and Cray. The results are contained in the table on
p. 44 of Comm. 95e. Subsequently Pt, broke and was then once more
wound. The repaired thermometer was called Pf. It was again
compared with the hydrogen-thermometer in 1907. On page 5
of Comm. 101a its resistance at nine different temperatures is given.
Small differences showed themselves at the time up to 0,04 of a
degree. In the end of 1907 and the beginning of 1908 another
calibration was performed at six different points: the results were
published in Comm. 107a page 6.

In 1913 a new series of measurements was made by KaAMeRLINGH
Onnes and Horsr, the results being contained in Table 1 Comm. 141a
page 7.*)

1) An interpolation-formula representing these observations between 15° K. and
230°K. was given by Zernike. (These Proceedings Kon. Ak. v. Wet. X XIII, p. 742, 1914).

830

| TABLE 1.

Resistance of the platinum-thermometer Pf, by KAMERLINGH ONNES CS.
| BE ah | W :
T abs. scala | Wo, diff. | T abs scala | Wo diff.
{| |
| |
56° K. 0.10815 74°K. | 0.18252
374 | 427
57 11189 | 15 | 18679
394 427
58 11583 76 19106
401 428
59 11984 | 71 19534
406 || | 428
60 12390 wit 18 | 19962
409 I} 428
61 12799 79 20390
411 429
62 13210 | 80 | 20819
412 | 429
63 13622 | 81 | 21248
414 430
64 14036 | 82 21678
416 |! | 431
65 14452 || 83 | 22109
417 | | 431
66 14869 84 22540
418 430
67 15287 | 85 22970
420 | | 431
68 15707 | 86 23401
Bot, wit 430
GON 16128 | 87 23831
| 423 431
| 70 16551 | 88 24262
| 424 430
71 16975 89 | 24692 “
425 | | 431
72 17400 | 90 25123
426 | 430
73 ' 17826 | 91 25553
426 | |
|

On the basis of the results of the last three calibrations | have
now computed a new interpolation-table, in which the resistance-
ratio is given from 56°K. to 91°K. for every degree and from 90° K.
to 270° K. for every five degrees. This table ought to replace the
one given by SIeMENs and at the same time for temperatures below
80°K. supplement the full table computed by Hennyne'). ‘This addition
may be useful, although it must not be forgotten, that exactly in
the range below 80° K. the platinum-thermometer gives rise to
special difficulties *).

1) F. Henning Ann. d. Phys 40, p. 635, i913.
2) Comp. Comm. Leiden 14la § 6.

831

TABLE 1 (continued).

Resistance of the platinum-thermometer Pf, by KAMERLINGH ONNES C.S.

ae ee
T abs. scale | Wo | diff. T abs. scale | Wo | diff.
| |
90° K. | 0.25123 | 1859 K. | 0.64776
| 429.8 | 405.6
95 PPP || 190 66804
| ZEE | 404.4
100 29416 195 | 68826
| ew | 403.4
105 31552 | | 200 70843
| 425.6 | 402.8
110 33680 205 | 72857
| 423.8 | 402.2
115 35799 210 = 74868)"
422.2 | | | 401.8
120 37910 | | 215 | 76877
| 420.8 | 401.4
125 40014 | | 220 18884 | |
| 419.4 | 401.0
130 42111 | | | 225 |_80889
418.0 | | 400.6 |
135 44201 | 230 | 82892 |
416.6 | | 400.0 |
140 46284 || 235 | 84892 |
415.2 || | | 399.2 |
145 48360 | || 240 86888 |
VEEN Aj | 398.4 |
150 50429 | | 245 88880
412.6 | 397.8
155 52492 | 250 90869
ee 4th on a] | 397.0
160 54550 | | 255 92854 |
| | 411.0 396.2
165 | 56605 | | 260 | 94835
| | 410.4 | 305.4
170 58656 | 265 96812 | |
409.2 | | 304.4
175 60702 | 270 | 98784 | |
408.0 | | 393.4 |
180 62742 | EOD A=
406.8 |

The temperatures given in Table 1 are those read on the hydrogen-
thermometer and corrected to the absolute scale, for the latter pur-
pose the corrections as determined by KAMERLINGH Onnes and BRAAK *)
being used.

In order to be able to form an opinion of the accuracy of this
table I have calculated for all four calibrations the temperature

: V 4
corresponding to according to the table, and the deviations from
0
the temperatures, as observed.

1) Comm. Leiden 1015.

832

TABLE II.

Comparison of different calibrations of Pf,

observ. — calc.

ie | 273.09° K. | 273.09° K.
0.88180 | 243.24 243.29
76°15 214.35 | 214.34
| 64749 181.93 184.96
| 58345 169.24 169.28
| 43450 133.20 133.25
35486 | 114.26 | 114.30
25280 90.365 90.36
20013 | 78.12 | 11.97
15969 68.61 | 68.47 |
12539 60.36 60.34
10709 | 55.72 55.76

| Calibration 1907. Comm. 101a p. 105.

0.58426 169.44 169.44
51825 152.385 153.38
33265 | 109.025 109.02
25467 | 90.80 | 90.80 |
11028 | 56.57 56.56

Calibration 1905 1906. Comm. 95c p. 44.

As will be seen the first calibration shows pretty considerable
deviations, whereas the others are in very good agreement with
each other. Only at one point a deviation of 0.03 of a degree occurs,
which is not more than might be expected considering that the
accuracy of the hydrogen-thermometer is not much greater than

0.02 of a degree.

833

[ _

TABLE II (continued).
Comparison of different calibrations of Pf’, |
W T | Tone annleecl T |
W, table | foelie. seeie obs.- calc.
<<< —————— —$—— el)
Calibration 1907—1908. Comm. 107a p. 6.
0.25369 90.57 | 90.55 — 0.02
23647 86.57 | 86.55 — 0.02
22395 83.66 | 83.65 | — 0.01
10945 56.35 E 56.33 — 0.02
25294 | 90.40 90.41 | + 0.01
25044 89.82 | 89.85 sen 20:08 |
|
Calibration 1913. Comm. 14la p. 7.
0.90523 249.139 K. 249.139 K. | 0.00
82803 | 230.00 | 230.00 | 0.00
15511 211.60 211.60 | 0.00
68233 | 193.53 193.53 | 0.000
58820 170.40 170.39 Tp Rel fer oma!
54359 | 159.535 159.53 | —o.008 |
47389 | 142.66 | 142.66 0.00 |
25234 90.26 90.27 | + 0.01 |
23554 | 86.36 | 86.36 0.00 |
19925 | 71.91 | 71.91 | 0.00 |
15866 68.38 | 68.38 0.00
12622 60.57 60.57 0.00
11162 | 56.93 56.93 | 0.00

3. Comparison of Pt, with P,, of Hunnixe ').

We will now compare the scale as laid down in our table with
that determined by HeNNiNe for his platinum-thermometer P,,; for
this purpose Hrnnina’s values were first reduced to the absolute scale
according to KAMERLINGH ONNes and Braak’s corrections *).

1) F. Hennine. Ann. d. Phys. (40), 635, 1913.
2) Comm. Leiden 1015.

834
TABLE Ill.
Co mparison of the platinum-thermometer of KAMERLINGH ONNES c.s. (Pf)
with that of HENNING Py».
art ad ee |
ip | (7) a | A ) peel aa! A
= a a
80° K. 0.20819 0.20241 0.00578
100 | 29416 28881 535
120 | 37910 31432 | 478
140 46284 45874 410
160 54550 54200 350
180 62742 62448 | 294
| 200 | 70843 | 10624 | 219
220 | 78884 | 18137 147
240 86888 86787 101
260 94835 94786 049
273.09 1.— 1.— a=

We shall first try to reduce the two scales to each other by
means of Nernst’s linear formula. For this purpose we can utilize
the fact, that on both thermometers the boiling point of oxygen

Ww
was measured; at this point Pt, gave == 0.25176, “and

0
Ay

—— = 0.246317), so that in the formula

W W

W, WJ pe,
a = 0.007284.

If we do not want to go beyond an accuracy of >} of a degree,
we may use this linear relation’). A much closer correspondence
is obtained, however, if with Hrnninc*) we use a quadratic relation.

1) F. Hennine, Ann. d. Phys. (43), 282, 1914.

2) H. Scumanx. (Ann. d. Phys. (45), 706, 1914) states, that, for a = 0,03, a
differenee of 0,1—0,2 of a degree is to be expected, which agrees with the
difference found here of >; of a degree for 2 = 0,0073.

3) F. Henning. Ann. d. Phys (40), 635, 1913.

835

Even then, however, real deviations remain in the range 200° K. -
240° K. showing that the Leiden-temperature-scale lies here somewhat
above that of the Phys. Techn. Reichsanstalt.

TABLE IV.
Comparison of the linear and the quadratic deviation-formulae.
| | |
T 6 Wops oale | AT pp Pt | Vale ls Pl; —=Pt |
+) sNERNST |} - 32 | quadr. form. Î =
| BEREA eN Sl SN EAN |
80° K. 0.00578 0.00576 — 0.005 0.00578 | 0.00 |
100 535 Biden saa) Gea, 525 — 0.02
120 | 478 452 | — 0.06 410 «| — 0.02
140 | 410 301 | — 0.045 | 408 — 0.00
160 350 31 | — 0.045 | 355 + 0.01
180 294 271 | = 0406: | 296 | 0.00
200 219 212%) Savor | 235 | + 0.04
220 | 147 154 + 0.02 | 173 | + 0.06
240 | 101 06 | —0.01 | 108 + 0.02
260 | 049 | 038 | —0.03 | 044 — 0.01
273.09 0 OET 0 Loko 0
| | |

A good correspondence at the lower temperatures is obtained with
the following formula

Ww W Ww?
BEES == 0:00850 (1 = =) 0,00Nets | W==—_ }.
W, W, W,

The greatest deviation amounts to 0.06 of a degree at 220° K.
It would seem to me, that this formula cannot be far wrong, and
for the following reasons. Looking at fig. 2 on page 653 in HENNING’s
paper, we see that the curve 7’—7'c as a function of the tempera-
ture, in the temperature region under consideration, allows a small
shift upwards, without the agreement with the observations becoming
much impaired, which shows, that the deviation from CaLLENDar’s
formula begins even at a somewhat higher temperature.

In the range in question we can further utilize the freezing point
of mercury. HENNING!) has made a very accurate measurement of this

1) F. Hennine. Ann. d. Phys. (43), 282, 1914,

836

point, from which may be inferred that = = 0.84465 at this point.

According to the quadratic formula we should then have for
Ww : :
Pin W, — ().84593 corresponding to — 38°.84 C., whereas the tem-

perature-scale of the P. T. R. gives — 38°.89. Borrowing from
Hennine’s paper the results of other observers:

STEWART — 38.65

CHAPPUIS — 38.80 + 0.02

CHREE — 38.86

we see that the freezing point as determined by HeNNiNG, when
reduced to the Leiden scale, coincides exactly with the mean of the
other observers. Although this must, of course, not form the basis
of a final judgment on the difference of the two temperature-scales,
still we may see in it an indication of the cause of the deviation,
viz. too great a value having been attributed to CALLENDAR's formula
at temperatures below — 20° C.

Each fresh direct determination of the freezing point of mereury
may, moreover, lead to a decision in favour of one or the other of
the two temperature-scales.

Apart from the deviation just discussed, the agreement is a very
good one, no greater deviations occurring than of 0.02 of a degree.
It remains a matter for regret, however, that for Pt,’ the constants
of CALLENDAR’'s formula were not determined, before proceeding to
use the thermometer at low temperatures, which would have made
a more direet comparison possible. With a view to the great import-
ance of Pt,' for low temperature-thermometry it was not deemed
advisable to carry out the determination in question now. *)

§ 4. The vapour-pressure of oxygen.

KAMERLINGH ONNes and Braak have determined the vapour-pressure
of oxygen at four different temperatures. As the resistance of Pf,’ was
measured at the same time, these vapour-pressures may be reduced
io the temperature-scale as laid down in the above table.

We find, that the temperature corresponding to a given vapour-
pressure may be represented by the following formula which is of
RANKINE— VAN DER Waats.

Is 369.83
~~ 6.98460. — log p
Henninc also gives the vapour-pressure at a few temperatures in

the form as proposed by AuGusT

1) Comp Comm. Leiden N°. 1410

837

the neighbourhood of the boiling point. Calculating according to the
above formula the temperatures corresponding to these vapour-
pressures we do not find greater deviations than of 0.02 of a degree,
so that the temperature belonging to a given vapour-pressure is
pretty sure to be accurate to 0.02 of a degree.

TABLE V. |
Vapour-pressures of oxygen according to KAMERLINGH ONNES and BRAAK. |
7. pune | Table Tk.O,and B. | Tiormula
sete” = EAM EN = == |
0.25424 807.18 90.70° K. | 90.689 K. | 90.709 K.
25176 760.16 90.12 | 90.10 | 90.12
23647 516.19 86.57 86.55 | 86.57 |
22395 366. 24 | 83.66 83.65 | 83.66 |
| |
TABLE VI.
Vapour-pressures of oxygen according to HENNING.
Treduced to Pp | Te | ;
abs. scale ormula | UE
en = Be Se etl
88.305° K. | 626.7 | 88.315° K. — 0.01
88.805 659.8 88.79 + 0.015
90.115 - 158.0 | 90.095 . | + 0.02
90.114 758.7 | 90.105 + 0.01
90.171 764.0 | 90.17 0.00

By means of the formula given above the vapour-pressure mea-

surements by SieMENs may now be recalculated. Siemens gives the
resistance of his thermometer at an oxygen-pressure of 766.8 mm.,
where according to the formula 7’=— 90°,21 K. According to the
table at this point the resistance-ratio for P?', is 0.25211, whereas
for Stipmens’ thermometer it is 0.25923, so that « in Nerrnst’s linear
formula is equal to 0.00961; with this constant the thermometer may
be reduced to P?', and the temperatures may be calculated.

It follows from the value of @, in connection with what was found
above in the comparison between Pf, and P,,, that no greater

838

TABLE VII.

Vapour-pressures of oxygen.
Pressures by SIEMENS, temperature by KAMERLINGH
ONNES c.s, as calculated by Horst.

Ug | we CG) Tabs. scale | Pmm.
; pete: ee
32.507 | 0.25924 |0.25212 | 90.21° K. 766.8
30.083 | 0.23024 23193 | 85.52 457.6
27.341 | 0.21743 20991 | 80.40 239.5
25.068 | 0.19936 | 19167 | 76.14 129.5
| 23.262 | 0.18500; 17717 | 72.74 15.7
20.400 | 0.16224] 15419 | 67.31 28.07
18.244 | 0.14509 | 13687 | 63.16 11.52
16.648 | 0.13240 | 12406 | 60.04 | 5.49
16.253 | 0.12926) 12089 | 59.26 4.40
15.327 | 0.12189] 11345 | 57.40 2.68

accuracy may be expected than to about 0.05 of a degree. The
corrections for Srock’s thermometer also undergo a change and
become as given in Table VIII.

TABLE VIII.

Corrections for Stock’s thermometer according to Table VII.
‘obs. ‘corr. | | tops. | ‘corr.
Creer ees aes | se bok |
— 183 | — 183.969 C. | — 192 — 192.449 C,
— 184 — 184.90 | — 193 — 193.41
— 185 me 185583 | — 194 — 194.44
— 186 — 186.79 | — 195 — 195.42
— 187 — 181.16 | — 196 — 196.39
— 188 — 188.68 | — 197 -— 197.33
| — 189 — 189.62 || — 198 — 198.34
| — 190 — 190.54 | — 199 — 199.37
| — 191 — 191.50 | — 200 | — 200.40

839

§ 5. The vapour-pressures of nitrogen.

The deviations of the scale used by von Siemens from the Leiden
scale having been computed in the case of oxygen, SteMEns’ tempera-
tures for nitrogen can be corrected directly. Table IX gives the results.

TABLE IX. |
Vapour-pressures of nitrogen. |
Pressure by SIEMENS, temperature by K. ONNES C.S, |
as calculated by Horst. |
T abs. scale p m.m.
80.48° K. | 1086.0
79.82 1009.4 |
15.86 631.3 |
72.85 428.6
10.97 329.4
67.89 206.9
66.93 117.6 |
63.25 | 93.5
63.25 | 93.5 |
62.87 | 86.1
62.02 71.9
60.83 55.3
60.01 45.8
58.76 34.1
57.73 26.4
57.00 21.8

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

840

Physics. — “The viscosity of liquefied gases. I. The sotational
oscillations of a sphere in a viscous liquid.” By Prof. J. E.
VERSCHAFFBLT. Comm. N°, 1484 from the Physical Laboratory
at Leiden. (Communicated by Prof. H. KAMERLINGH ONNES).

(Communicated in the meeting of October 30, 1915).

1. With a view to an investigation of the viscosity of liquefied
gases at low temperatures, especially in the case of hydrogen, which
on the invitation of Professor KAMERLINGH Onnes | hope to under-
take, in conjunction with Mr. Ch. Nicaise, by the method of damped
rotational oscillations of a sphere suspended in the liquids in question,
I shall here give the theory of the method. The problem has been
dealt with before by a number of writers *) and the formulae which
embody the results of their calculations have also found application
in the discussion of different experiments; still [ do not consider it
superfluous to publish my method of dealing with the problem,
because in my opinion it is simpler and less involved than the one
followed by previous writers, while the formulae which I have
arrived at are much better adopted to numerical calculations.

The sphere will be supposed to swing freely about a diameter
under the action of a couple of forces (the torsional moment of the
suspension) the moment of which Me is proportional to the angle
of deflection «. In the absence of friction the sphere would perform
a harmonic oscillation with a time of swing given by:

K
aoe
K being the moment of inertia of the sphere about a diameter (or
more correctly the moment of inertia of the vibrating system of
which the sphere forms parts), J/ the angular moment per unit of
angle. If the sphere swings in a viscous liquid, the motion is damped
and it appears (although properly speaking an experimental confirm-
ation is lacking), that when the friction is not too strong the sphere
executes a damped harmonic vibration, according to the formula:

1) G. J. H. Lampe, Programm des stadt. Gymn. zu Danzig, 1866.

G. Kircnnorr, Vorlesungen über mathematische Physik, No. 26, 1877.

Ie. Kremencre, Wien Ber. Il. 84, 146, 1882,

G. G. Sroxes, Math. and Phys. Papers. Vol. V, p 207.

W. Konia, Wied. Ann. 32, 193, 1887.

H. Lams. Hydrodynamics, 1906, p. 571, 599, 581.

G. ZemPLÉN, Ann. d. Phys. 19, 783, 1906; 29, 899, 1909.

M. Brittouin. Lecons sur la viscosité des liquides et des gaz, 1907; lee partie
p. 96.

250

7 t
dae GO ve. ht a (2)

where 7’ is the new time of vibration and d the logarithmic decre-
ment of the elongations for one vibration.) The problem before us
is, how d and 7 depend upon the specific properties of the liquid,
in particular on the viscosity 7, and how 4 may be calculated from
observations on the two quantities in question.

2. We shall confine our investigation to the two cases in which
the liquid is either externally unlimited (i.e. practically speaking,
fills a space the dimensions of which are very large compared with
the radius of the sphere) or is limited by a stationary spherical
surface which is concentric with the oscillating sphere; in these
cases we may naturally assume, that the motion in the liquid is
such, that it divides itself into spherical, concentric layers, which
each separately oscillates as a solid shell about the same axis as the
sphere, with the same periodic time and the same logarithmic deere-
ment; it will be shown further down that this assumed state of
motion is actually a possible one, at least when the motion is very
slow’). In that case it is only the amplitude and the phase of the
motion which differ from one shell to another, and for a shell of

radius 7 we may therefore put:
t

= d- t
Gy == Ar ë 1 cos Ir (7 — 7) 4 . . e e "a (5)

where d, and yg, are functions of 7. If we further assume that the
liquid layer which is contiguous to the sphere, adheres to it, as is
well known to be generally the case, expression (3) must become
identical with (2) for r= R, thus ag =a and gr =O.

3. In order to find the functions ap and gp we proceed to estab-
lish the equation of motion for a spherical liquid shell. For this
purpose we shall consider the ring whose section is ABCD = r.de.dr
(comp. adjoining figure) and whose radius is 9 —=r cos. On its side-
faces AB and CD this ring according to our assumption does not
experience any friction; on the inner surface AB, owing to friction
against a shell closer to the centre, it experiences a tangential force

F per unit area in the direction of its motion, and on the outer
oe ; j OF
surface BC similarly a force — ( r+ = ar): writing down the
Or

1) If the motion of the sphere without friction were a compound harmonic motion,
as would be the case, if the sphere were coupled to other oscillating systems, the
motion with friction would be compounded of damped harmonie vibrations,

2) For the necessary condition of slowness of the motion see note in Comm N°, 148d.

54*

842

condition, that the work of these forces during a small angular dis-
placement equals the increase of the kinetic energy 3m, of the
ring, we find, when the density of the liquid is a,

ae : de, Pi OF ip \ ike aren dar
fy. 2arcose. rde .reose ——| F 4- —dr | Za (r Ir)? coster dens
Mr COS E. TC COS di Dr 7 ) FY
1 2 2 dvr
== 5: (3 mv,?) =2arcose.rde.dr.u. Ur
or
OF 3F Ov, 0° a,
— — == == OS € .
or , Ë Ot es Ot?

According to the elementary laws of internal friction the force 7
proportional to the velocity-gradient in the direction of the radius;
in determining this slope we must only take into account the gradient
which is due to the change of the angular velocity with 7*). The

de
ua

Or \ df
1) The gradient of velocity which is the consequence of a uniform rotation of
the liquid does not produce any friction. In the classical hydrodynamical theory
this results from the circumstance that in a uniform rotation there is no deformation
and consequently no stress. (Note added in the translation).

: : cr
velocity-gradient thus becomes equal to r cos a (ae) and therefore

843

dw
Mi mrien ee ie. ee) (4)
or
0a, :
when Ne ieee represents the angular velocity of the shell under con-

sideration and y the viscosity of the liquid. The equation of motion
of the sphericall shell may now be written in the form
Co 400 udo
te eee ees
Or? or òr 4 OF
4. This equation determines how w depends on 7; as it does
not contain the angle «, it is in accordance with our assumption,
that the individual shells oscillate to and fro as solid bodies *). As
regards the law of dependence of w on ¢, which we have already
presupposed in equation (3), it appears that it also is compatible
with (5); substituting (3) in (5) and expressing the condition, that
equation (5) must be fulfilled at all times (by putting the coefficients
of cos and sin equal to zero), two differential equations are obtained,
which do not contain the time and which determine the functions
da, and Gr.
This method is, however, very cumbrous. It is much simpler first
to reduce (3) to the form
<i

mats) t : t
pee # (« cos 2 T + ysin 2 =) Py enema ee st (0)

(5)

where w and y are new functions which for r= A become equal
to a and O respectively and are determined by the two differential
equations :
dement dia
dr® r dr
dy 4 dy u
dr? r dr ij nt Race oa
The simplest method of all is to consider (6) as the real part of
an exponential function

4- ke (de — Zy) = 0
nl
(7)

OO EEE ILS)

where uw and & are in general complex quantities; in that case (2)
is the real part of

1) It should not be overlooked that in this manner the possibility of the afore-
said assumption has been proved, not its necessity (for this proof, see Lams,
loc. cit). lt is moreover easily seen, that with a different law of friction, eg.
in which » would also depend on the velocity itself, the assumption would become
unallowable.

844

ht meee el ce
and w is a function of 7 only, which for r == A obtains the value
a. Putting
k=" +24 GV) = Se
it follows by equating (6) to the real part of (8) that
d 2m

as and ae EE

The real angular velocity w is the real part of the complex
quantity
D= kiek, ea U
the function w satisfying the equation

d'u 4 du ne u
A a Us « . . . . . . ( )

which is obtained by substituting (10) in (5). *)
5. The general solution of (11) is well known to be

C—

[Ae-tr (br + 1) + Be br (br — IJ,
(

3
or
it
“Ss [Pet (br + 1) + Qe! rl (br = De q 2)
7

where

1) Equation (10) is a particular solution of equation (5). The mode of motion
which it represents is, therefore, a possible one but not necessarily the actually
existing one. The reason why we only consider this solution is that we suppose
the sphere not to perform forced vibrations. In the case of a compound harmonic
motion w would consist of a number of terms, each with its own k, the w’s of
which would satisfy as many equations (11).

It is also obvious, that the condition of motion considered cannot exist from
the beginning, but can only be reached after a theoretically infinite period, so that
the motion of the sphere cannot correspond either to equation (2) from the moment
at which the motion begins. The experiments show, however, that the final
condition is practically reached after a comparatively short time (a few minutes),
i. e. very soon T and > have become constant; this may be expressed mathema-
tically by saying, that the assumed condition of motion is the limiting condition
to which the real motion approaches asymptotically and this approach is in general
so rapid, that even after a comparatively short time the deviations of the actual
motion from the final limit are within the limits of the errors of observation. The
question as to the real motion during the said period of approach is one which
would have to be settled by a separate theoretical and experimental investigation,
but is of no importance for our present purpose.

845

al hate ORE wane)
1

A, B, P and Q are complex constants which are determined by
the conditions at the boundaries.
In the first place we have u=a for r= R, so that
POR + DF Q@R—1)—ak*. . . .. (14)
If the liquid is unlimited or at any rate may practically be con-
sidered as unlimited, «=O for »=o; this leads to the condition
Q=0 (unless 6 were a pure imaginary quantity, i. e. were real,
in which case the motion would be aperiodic, a case which we do
not consider here), and therefore

i gaia eg aay ehh, tert AIG)

On the other hand, if the liquid is bounded by a stationary
spherical surface of radius FR’, the condition is that «#—O for
r= k’ at all times (again in the supposition tbat the liquid adheres
to the surface of the sphere) so that

Pe-WR'-R)(bR' +. 1) + Qe(R—-R(6R'—1)=0; . . (16)
in that case
__ ROR le Re re ak (bR' + De „—b(R'—R)
Mae SS —, (9)
D D

where
D=(bR + 1) (6R' — 1) ARR) — (6R — 1) (OR! + De IRD, (17)
so that

u == [br + 1) (BR' — 1) ERN) — (br — IOR! + 1) eH] (17)
td

6. If we put
VLS E (y + 1)
it follows that
py =H and Uy =k",
and therefore, seeing that y' and 7” from their nature represent
real quantities:

zel w IVES ke soi se

a EV rep Vó + An
oT

As a rule the circumstances under which the experiments are

. (18)

846

conducted are such, that d is a small number, of the order of
magnitude 0,1; in that case the expressions (18) can be developed
into series progressing according to the ascending powers of 4=

J
== 5> which teads to:

aly eee nt bat +.
genet a.
eee

Ain DE
b= YY [ata a—i% HOE | (20)

“7. As mentioned above in section 1, the real part of (8) may in
general be written in the form
a, = e't—'r [X, cos (k't—b"r) + Y, sin (k't—b"r)]

+ ekHPr [X, cos (k't+b"r) + Y, sin (k't+b"r)], . . (21)
where X,, X,, Y, and Y, are again functions of 7, but now real
quantities. This form shows, that the motion of the liquid is the
result of the propagation of two waves, the one moving away from
the oscillating sphere, the other moving towards the sphere; writing

(19)

so that

27 r
k't + b'r in the form = (: = 7): the speed of propagation appears

to be

kN 20 |
— b _— pr’
this velocity therefore depends not on the specitic properties of the
liquid only, but in addition on the time of swing of the sphere.
2

bil

For d very smail we have by (19%),

/ an Jh
alen en. .
ul u

When the liquid extends to infinity (practically), we have only to
deal with the former of the two waves: but when tbe liquid is
bounded, the wave which is emitted by the oscillating sphere is
reflected on the fixed wall, in such a manner that the phase is
reversed, and thereby the amplitude « becomes zero at the wall.

In addition the waves undergo a damping effect during propagation,

(22)

The wave-length is À =

847

in such a manner that, independently of the algebraic dependence
on 7, the amplitude is reduced in the ratio 4:1 over a distance 1,
where A =e”.

With a small value of d according to (20) the damping increases
as JT becomes smaller and with a sufficiently small value of 7’ it
may happen, that even a comparatively narrowly bounded liquid is
practically unbounded, because the motion which starts from the
sphere is practically completely damped, before it reaches the external
boundary; to this point we shall return later on ($ 12).

8. We can now proceed to calculate the time of swing and the
logarithmic decrement of the damped oscillations of the sphere from
the specifie constants of the liquid (viz. the viscosity 4 and the
density u). The equation of motion of the oscillating sphere is

aa f
Ke CTM =O ee Veh oe ee ES)
dt”
where C, the moment of the frictional forces, is given by (comp. $ 3)
+
“ y dw
C= — |F . 2nR’* cos’? ede = § nh | — (23')
Or Jr

According to (10) and (12) we may write
dw kekt 22 € b(r—R) 2 9 9 b R
en me r+ 3br+3)e—Or—&) — Q (b?r?— 3br+3) ebr li],

and therefore

dw kekt
a = — [PUR 30R+3) — Q ORR I=
r JR
1 l
— — —_[P(0?R?+3bR+3) — Q(6°R?—3bR+3)| —,
ak! dt
so that for the case of a damped harmonic motion we may write
da da 3 Ee
Gn 4 L dt + Me = 0, ) . . . . . . (24)
where

1) The equation once more expresses the fact that the sphere oscillates freely.
2) In the case of a not purely harmonic damped motion the proportionality of
de ; :
C with Fe no longer exists. As far as I can see, it is in that case impossible to
say, how in general C depends on the motion, so that it will then probably be
impossible to establish a general differential equation for ».

848

R*7

Lap (ORS bR4S)(bR'-!)e R24 (5? R2-3bRHIOR HIJ! R-BIJ (24)
D being the form given in (17). L is again a complex quantity. *)
When the liquid is (practically) unbounded and the motion periodic
(ie. Q=0), we have simply:
OR? + 36h + 3
bR +1

L={<2h'y

(25)

9. The expression (8’) actually satisfies the equation (24), when

k satisfies the equation
KRS + Lie tM == 0 HT ee EN

If we put again 1 = L’ + L'i, we find:

K(k —k") + Lk’ — D'R + M=0 and 2KER' + Lk" + L'k' =0, (26')
or according to (9’) and (1),
J? — Anr? — ques An ae + 47? Piet) and 4ad inn BE (27)

vi K wie K K

These are therefore the equations which determine 4’ and k",
and thus also d and 7’, under the given experimental conditions;
conversely they enable us to compute £’ and £” from the experi-
mental values of 7’ and d and thereby by the aid of (24) to
calculate 1.

From (27) it follows that:

TONIE Re LY Zar Te Ang 1:08)
KF Tee. | es el ree a

T—T
When d is a small number, as also y= a (as is usually the
0

case), we may write:

a tw HO) + Se HP) $d
— = — + wy 5 (tpr- y° oe | —— — 5 —) oie
K 7 t wt EW x?) +] 7! Ek

joa ll ay 43 Fy?
—= at y| 1+ ¥ Ee WN =S i wil MELK +...
K Ti w f 2w :

(25)

10. As we have been using complex quantities all along, we

1) The meaning of this is as follows: the real angle » satisfies equation (23),
where everything is veal, even C, the moment of the frictional forces, which is
determined by (23’) with w still real. If, however, a complex angle g is introduced,
the real part of which is the real 2, C will be the real part of (23’), where « must
be taken as a complex quantity, and this is at the same time the real part of

la : Bape 2
an expression of the form J. a where L is then similarly a complex quantity.
(

849
have not come across the fictitious addition to the moment of inertia
which usually occurs in problems of this kind. This addition does

not show itself, until the real part is extracted from equation (24).
This real part is equal to

da! da! da" ;
Ree tg geen gy ie es = eet (29)
having put a—=a + ei; and as is easily found from (8’)
da" daa! ed
i EO

so that

iN dia! kN de!
ea Eee a EM — 08 En ee (29)
( +) dt? al ( =) dt Teg Ce

which means an apparent increase of the moment of inertia by the

Eis
=)

Substituting the expression (2) in (29) and again expressing the
fact that for all values of ¢ the equation must be satisfied, by
equating to zero the coefficients of cos and sim, the same equations

(26’) are arrived at.

amount A’=

11. The separation of the general expression (24’) into its real
and imaginary parts is a troublesome performance, which is of no
practical value; the general expressions for Z' and L" are so involved,
that they are practically useless for the computation of 4 from the
observed values of 7’ and d by means of the equations (28). As a
matter of fact it is only under simplified conditions, that the deter-
mination of 4 by observation of the oscillations of a sphere is
practically possible. Now the whole problem becomes most simple,
when the liquid may be considered as unbounded; in that case
it follows from (25) which may also be written as

1) From (29) it also follows, that even in the case of friction in a liquid the
well-known equation

850

that

Uta (OR424 vR+1 j
4 == J bj ) =
peed URI 40" R |
5 . 27 (80)

1
L" = 8 aRbn — |
NVBR 1)?+.5"" R?

For a further approximation in the case, that the liquid may by
approximation be considered as unbounded, (24') can be developed
in the form of a series. For this purpose we write first:

YR? —3bR+3 bR+1

ge Ea _ e—25(R’—R)
en b°R°+3bR+3 OR?+3bR4+3 DR —1 x
Dirk. BRIL — .— RST BRO (24")
a ee, Ne
ORH1 bR'—1

when e—%®—R) is sufficiently small*), formula (25) will hold as a
first approximation; if necessary a first correction-term may be added
of the form

bR'—1

L, = 18 «Rd *y RR) | eae
ORL ORI

the value of which can be computed fairly easily, when an approximate
value has been found for 4.

1) If K(k) is replaced by the conjugate imaginary quantity kj, it is clear, that
the real part of 2 and also of z- do not undergo any change (bj and 5» are
similarly conjugate), so that exactly the same results must be obtained, in particular
the same equations (30). That this is actually true may be easily seen from the
fact that Zj and Zo according to (24’) are also conjugate imaginary.

We might even, in general, have represented the damped harmonic oscillation
by the real part of

aa, + a, =a,eht + a,ekst.
We should then have obtained
w= ku et + ku elst,

and have found, that z must satisfy the ee

aa a da, i pee = +} Vu 0
— —- a=10;
ar dt ;
which, owing to LZ’, = L’; and L”, = nha may also be written as:
da’ da! d (a",—a",)
Kea TEN DEE ge (0
dt? ek dt à dt

By putting @ =d, « may then be real (form. (2)).
*) The coefficients of this factor in (24”) cannot become infinite in this case,
on the contrary they donot differ much from unity.

851

12. In our experiments we intend to choose the conditions such
that the liquid may, at least approximately, be considered as unbounded;
moreover we shall arrange to make d small. It is easily found, what
conditions these simplifications are subject to.

Clearly it is necessary that the factor e#’—®) obtains so high a
value, that the terms containing this factor are sufficiently prepon-
derant; this condition does not necessarily involve a specially high
value of 6’, for if eg. R’ -R=—1 Le. if the distance of the two
spherical surfaces is only 1 em. (and this will be about the case
in our experiments) still even for 6’—10, the value of e’\R—®
will be as high as 10000 about. For water in C.G.S. units 7 = 0,01
and w=1, so that even with 7’=3, ie. a time of swing of 3
second, 6’ will reach the value 10, so that even in that case the
desired condition will be fulfilled of the wave-motion, which starts
from the oscillating sphere, when arriving at the external sphere,
being practically completely damped out (§7). If it is further taken
into account, that the oscillating sphere can only undergo an influence
from the bounding wall by the waves reflected on the wall returning
to the sphere and that the returning waves again undergo a damping
process, it becomes clear, that the damping on the way from the
inner sphere to the outer wall does not need to be so very complete,
in order to be able to consider the liquid as - being practically
unbounded.

This fact is also expressed in our equations (24") and (81). Prac-
tically (24") is identical with (25), or Z,—0, when ¢—?\R—-#) is
sufficiently small, i.e. when the damping over a distance 2(R’— R)
is sufficiently strong; in order that e-2E-—B) may be say ists
with k’—RK=1, even b’=3 would be sufficient and this would
still be the case for water with 7’ as high as 30. A somewhat
large time of swing of about that magnitude is favourable to the
readings from which the logarithmic decrement must be determined
and it is accordingly intended in our experiments to make the
periodic time about that size.

With R’—R=1 and 7'=30 even when working with water
the liquid can thus approximately be considered as unbounded. But,
moreover, it appears from (20) that with a given time of swing 0’
and 6" become greater, and therefore the conditions more favourable,

F afi lie ; : an Re ,
according as the ratio — is smaller; for very mobile liquids, like
u

ether and benzene, they would therefore be even more favourable
than with water, and, as the available data show, most favourable

852

of all for liquified gases. The oscillation-method appears thus a
particularly suitable one for liquid gases ‘).

13. With a view to our experiments it appeared to us desirable
to have a rough idea as to the value of the viscosity for liquid hydrogen,
say at the boiling point; an estimate may be obtained by the appli-
cation of the law of corresponding states. KAMERLINGH ONNES*) has
shown that for two different substances obeying this law the expres-

"We
must have the same value at corresponding temperatures, where
7;, and py, are the critical temperature and pressure and M the
molecular weight. It is therefore possible by the application of this
rule, which will be at least approximately valid, to calculate » for
hydrogen by comparison with a substance whose viscosity is known
over a somewhat wide range of temperatures, such as methyl-chloride
according to measurements by pe Haas*). For methyl-chloride 7;=416,

sions

Wiis axe
pr = 66 (atm.), M = 50, and therefore [7 — = 0,024; for hy-
pri M*

6 TE
drogen similarly 7,=31, pp=11, M= 2, so that | = 0,40.
k 4

The boiling point of hydrogen is 20°K. and the corresponding tempe-

416
rature for methyl chloride is 20 > Eer 268° K., or about 0° C., at

which temperature 4 for methyl chloride is 0,0022 ; it follows that for
hydrogen at 20° K. 0,40 7 = 0,024 .0,0022, which gives 1, — 0,00018.
As at this temperature the density of liquid hydrogen is about

0,071 +), we have “ = 0,0018.
u

') On the other hand, in ZemPLÉN’s experiments (Ann. d. Phys., 19, 783, 1906)
on the viscosity of air in which concentric spheres were used of 5 and 6 emis.
radius the condition of nearly complete damping of the reflected wave is not
satisfied by a long way; with » =0,0002, » =0,00012 and 7=30, b’=0,8 ie.
e—26(k’—k) = 1 about. The damping is thus so weak in this case that the first
correction-term (31) is not sufficient: we have therefore been obliged to abandon
our intention originally formed, of recalculating ZEMPLEN’s experiments by means
of our formulae.

*) Comm. phys. Lab. Leiden, n°. 12, p. 9.

5) Comm. phys. Lab. Leiden, n°. 12, p. 1

*) Comm. phys. Lab. Leiden, n°. 137d.

853

14. In all the above calculations it is assumed that the oscillations
of the sphere are only weakly damped; this condition can in any
case be satisfied, independentiv of the specific properties of the liquid.
For, even when Z’ obtains a high value, the logarithmic decrement,
by formula (28) can be made as smali as desired by giving the
oscillating system a bigh moment of inertia; this does not necessarily
involve a corresponding increase of the time of swing, because the
rotational moment J/ may still be chosen at will.

It is, moreover, easily seen, that for substances with a small value

of | the circumstances must again be the most favourable: according
u
to (28) and (30) it is exactly for these substances, that under other-

wise equal circumstances the oscillations of the sphere will be least
damped.

15. When equation (25) holds, the calculation of 4, the quantities
u, Rk, K, T,, T and J being known from the experiment, can be made
in a fairly simple manner. First L’ and L’’ are calculated with the
aid of equations (28) or, as the case may be, (28’). An approximate
value of 7 having been found, 4’ and 6" can be obtained in first
approximation by means of (20) and using these values a suffi-
ciently accurate value can in general be calculated from the terms

BR 1 1 .
p = RLY IR and 1 RED NR in equations (30).
Finally it only remains to solve the following quadratic equation

in Wi:

Rye — BH
(AS Pati TE BER (a)
An alternative method of calculation would be from
3L'
Yi = asten AAG

SaRyVull—g)

but in general this will yield a much less accurate value owing to

Gal

the smaller accuracy with which w= con is determined as com-

’

0
pared with d. Equation (4) ought rather to be looked upon as a

kind of check on the result obtained; but it may also render excel-
lent service for the purpose of obtaining an approximate value for
y, if this should not be known; in that case it is even sufficient to
neglect q with respect to 1.

854

16. As an example of a calculation the results of a preliminary
experiment made by Mr. Cu. Nrcarse in water of 20° C. may be
given here. A brass sphere of 1,927 em. radius and weighing
250,8 erms. was suspended from a wire of phosphorbronze, such
that in air the time of swing was 12,05 sec. ; immersed in a large
vessel with pure water the sphere had a periodic time of 12,24 sec.
the amplitude of the oscillations diminishing per time of swing in
a constant ratio, the natural logarithm of which was 0,1148 (it was
found that this did not increase appreciably, until much narrower
vessels were used, which shows that the liquid could be considered
as being practically unbounded). For this experiment we have
therefore R=1,927, K=372,5, T,=12,05 (properly speaking the
time of swing ought to have been measured in vacuo, but this
would not have made a difference within the limits of accuracy of
the observation) 7’ = 12,24, d=0,1145 (freed from the internal
friction of the wire)*) and u = 0,998.

This gives E = 0,0091 and w= en = 0,016, and therefore

5 s

within the limits of accuracy of the observation

dk awk
[i So e708 ek
0 1 0 pen
A first approximation with 9=— 0,01, gives b'=6"= a

therefore b’R = b6"R = 10, so that p= 0,05, ¢ = 0,004. The visco-
sity is now given by
2,05n + 0,966 Y= 0,1181,
hence:
Nos — 0,01014,

a value which agrees very well with the known data. The equation
with ZL” gives as a very rough verification — 0,010.

17. The formulae become even simpler, if }'R and 5'R are large
numbers (say of the order 1000); in that case we have:

R
ua) =. s -)
r

Ll == $0 R't'n ~, E38 oe Rib ay.

1) Observation gave §=0,1148; in air }=0,0011, of which, according to a
calculation of ZL’ with »=0,0002 and «=0,0012, the fraction 0,0008 is due
to the friction of the air, so that 0,0003 is left for the internal friction of the
suspension.

BES

If d is small at the same time, we have in first approximation

aw f
Bata yar| / ee ee iB)

from which, by (28')

Ce T—T J
6=4= Vaal 4 SS SS 35
3 K (yt, qe on ( )
This extreme case is discussed by Kircnnorr in his Vorlesungen
We nl,
über mathematische Physik, N°. 26; it occurs when ao Hee
ee

small number’). This case would be realized, if in a liquid
; U EN é
with small — (say a liquid gas) a large sphere was made to swing

quickly ; taking say „0001, in order to have 6’R=1000 with
R=10, it would be necessary for 7 to be 0,3. Apart from the not
very practical nature of these conditions, it may be considered very
doubtful, whether with the comparatively high velocities, involved in
a rapid vibration of that kind the preceding theory would still hold.
It seems to me, therefore, that the extreme case in question has no
experimental physical importance.

When 0’F and 6’’F are only moderately large L’ and L’’ may

| te cee
be developed according tot ascending powers of — and —— ; if in
: bR b"R

addition the series (20) and (28'), are introduced, and the development
is stopped at a definite point, formulae such as those of Lamem '),
Kiemencic”), BotrzmMann*) and Könre®) are obtained.

1) KircHHOFF assumes » to be very small, which must of course be taken to
mean: under otherwise normal circumstances, for, taken absolutely, it has no
sense to suppose a quantity which is not dimensionless to be very small, seeing
that the value depends on the choice of units. For the rest, the liquid need not
necessarily have a very small viscosity in order to obtain the simple case in
question ; a small friction would even be a disadvantage, if combined with a small

A F 5 2 ille ,
density, as in the case of gases. For air for instance— is about 0,2, and thus

much larger than for water, notwithstanding the much smaller value of »
(comp. 12 note).

2) loc. cit.

3) Vid. Lampe, Wien Ber. IL. 93, 291, 1886. These formulae are as a rule not
very suitable for accurate calculations, because a sufficient accuracy cannot be
obtained with only a few terms; as an instance, K6NIG’s experiments can be cal-
culated much more simply and accurately in the manner of section 15 of this
paper, than by Kéyra’s own method. From one of Kénia’s experiments (the last

Proceedings Royal Acad. Amsterdam. Vol. XVIII.

856

18. The opposite extreme case is that, in which 6R and HR’ —R)
are very small numbers; in that case &’ cannot of course be
infinite, i. e. the liquid must be bounded. With normal dimensions
of the spheres and usual times of swing this case might be realized
with liquids of very high viscosity; for ordinary liquids the time
of swing would have to be much greater than practice allows.

In that case (24’) leads to:

RR?

dan RR? a= Whee J?
therefore — Wiggs nT and — med oe

= 0

Seeing that by (22)

L=L' =8nRy and L'=0, .. . (86)

(37)

2nR Rk
alee
4 being the wave-length in the liquid, the physical meaning of the
given simplifying condition is thus, that the radii R and FR’ are
small as compared to the wavelength. In that case all the spherical
shells im the liquid swing practically in the same phase *) (vy, and y
are nearly zero, so that « becomes real; in that case w = 2 (sect. 4)
and equation (11) reduces to the first equation (7)); at the same
time approximately e—%(#’—%) = (RR) =1, ie. the waves are
propagated without being appreciably damped, as they move forward.
The resulting equation is this time :
R? R®— 4 ij

u=a4 = Rek? . . . . . . . (39)

b"R = ee

with sphere 3) I find for water of 15° „— 0,01103, whereas Könre himself found
0,01140.

1) This is the simplifying condition used by Zempién (Ann. d. Phys. (4) 19, 785, 1906)
as the basis in the deduction of the formulae which served for the calculation of
the results of his experiments; thereby he overlooked the fact, that in that case
his coefficient mm (our factor 0b’) is very small, so that cosm (R—r') and sin m
(R—r') ought to have been developed according to powers of m (R—7');
carrying out this development, his equation (14) leads to our equation (39) (it
may be noted here, thot a small error has crept into his equation (14); the terms
m2Rr? and m?2Rr‚? should be m?Rr and m?Rrz respectively). As a matter of fact
in Zewp.in’s experiments the assumed approximation is not applicable, for in his
case aA =9, and thus not large as compared to the radii of the spheres( & = 5,
?’ = 6); his result is, therefore, very doubtful. Later on (Ann. d. Physik. 29, 899,
1909) he discovered this himsolf and gave a more accurate treatment of the
problem; but owing to the very complicated nature of the correct formulae he
did not submit his experiments to a new calculation.

2) This distribution of velocities is the same as the one found for uniform
rotation comp. for instance Brittourn le. p. 89); this explains itself by the consi-

—

857

When $F and GR’ are only moderately small numbers, L’ and
L’” can be developed according to powers of those quantities ;. the
equations (36) are the first terms of the series which are obtained
in that manner. Probably 1 might be found by that method for
ordinary liquids at low temperature.

19. The formulae become also very simple, when k’—-R is
small with respect to Zit, a case which may possibly be of some
importance experimentally. In that case :

dm 40
Ni Ar Ee ER EN
ITE: (30)

R
= OENE Re ect ee Bat ae Ee (41)

20. Although probably aot of any practical utility I will for
the sake of completeness discuss the case, in which the oscillating
sphere is hollow, contains the liquid and swings about a smaller
fixed sphere. Seeing that our general discussion of the state of
motion in the liquid is not altered thereby, the preceding treatment
retains in general its validity ; the boundary-conditions also remain

Why

the same, so that equations (17) and (17’) remain valid. Only owing
to the fact that R >7r > RK’, it is now more logical to write

1
Cae [PeUR 7)(br—1) + Qe(R—)(br+1)], . . (42)
and the conditions at the boundaries now give
3 rar eh(R-R 1F3(b R'—1)e—4:R-R’)
ne wR (DRI + Det a ae — aR(bR'— 1e Os
D D
where

D= (6R — 1) (DR + 1) ARR) — (BR +1) (6R'— 1e -UR-R), (44)

As regards ZL, the expression given in (24) still holds for it,

except that it has to be provided with the negative sign, because

now that the sphere undergoes friction on the inside, the tangential
force is not / but — F (comp. sect. 3 and 8); we thus have”):

deration that, when the wave-length is large as compared to the radii of the
spheres, the condition may at any moment be cousidered as stationary.

1) This distribution of velocities agrees with that between two parallel planes,
which move with respect to each other’ at constant speed; this result could have

been expected.

2) All the formulae for this case are obtained from the corresponding ones in
» and 8 by giving R, R and r everywhere the opposite sign; this is quite
intelligible from a mathematical point of view.

55*

858

L ge,
Shan

(b? R?-3U.R+8)(bR'+1)e RF) 4 (b? R243 R+3)(bR'—1)e—4R-R](45)

For the rest no alterations have to be made to section 9 and the
calculation of y would proceed in the same manner as with an
internal oscillating sphere.

21. Another case which is of practical importance and has found
experimental application *), is that of a hollow sphere completely
filled with liquid which is made to swing. It may be expected that
this case ean be derived as a special case from our general formulae
by putting A’ =O. In that case according to (53):

ak?
(6R—1)ek + (bR + 1e bR

Pe RK — QbR — (46)

and
R® (br—1)e’r + (br + 1)e—4r
TR (OR -DERH(ORH 1e IR"
Physically, however, this is only possible, if for r— 0, w does
not become infinite and, as a matter of fact, it does not, for with
r=— 0, wu becomes

(47)

; R
(ORI) OR + (DRH Ie IR"
In the general case the liquid cannot be at rest at the centre:
the wave-motion starting from the oscillating sphere passes through
the centre and expands again beyond it; this may also be formulated
by saying, that the waves are reflected at the centre, this time as
upon a free boundary, i. e. without reversal of phase. Only when
OR is so large, that the motion is damped out before reaching the
centre, 1, =O practically and further

JRE ll
NSU A ee (49)

AD
u, == ab

(48)

22. In the case of a sphere filled with a liquid we have further
(by putting A’ = 0 in (45)):

(b?R?—3bR+3) eR — (DPR 3bR+3) eik

(6R—1) eR + (6R4-1) IR

If the wave-motion is damped out when arriving at the centre,

ie. if e-@® may be put very small, the value of 4 is given by

Leren ean Wale (51)

bk —1

which is obtained from (25) by reversing the sign of #; in the same

L=8ak'y (50)

1) H. v. Hermnorrz und G. v. Prorrowsk1, Wien. Ber. 40 (2), 607, 1860. H.
v. Hermnorrz, Wissensch. Abh., 1, p. 172.

G. ZemPréN, Ann. d. Phys., 19, 791, 1906; 29, 902, 1909.

Vid. also Lamp, Hydrodynamics, p. 578.

Fe nee eee ee nn a end

859

manner (30) will then give:

B DR
L'= rR'y| UR — 2+ sae |b
('R—1)? + UR?
1
LE! =8 wR*t"'n | 1 — ata det (02)
(DRI)? + 6° R?

The calculations are to be carried out as in § 15.

When 6’R and 6’’R are very large, the same formulae (33) are
arrived at as before, which means that, when the motion is com-
pletely extinguished at a very short distance from the oscillating
sphere, it makes no difference whether the friction is internal or
external; this might of course have been foreseen. *)

23. When ZA, and therefore also br, are very small, that is:
when the wavelength is very large compared to the radius of the
sphere, as would probably be the case with very viscous liquids
(comp. § 18), it follows from (49) that «=a, 1. e. the sphere swings
as a completely solid mass, as might have been expected a priori.
There will thus be no damping and the time of swing must be
that of a system the moment of inertia of which is equal to A with
the addition of the moment of inertia of the liquid.

This actually follows from the above formulae, for (50) then
reduces to

L=- 27 Ry = 4 rukk,
and introducing this into (26'), we find that
eer Nalin ae
(== (0 sd Ss Tie K’'),

where A’ = & zult’, the moment of inertia of the liquid. *)

1) In PiotRowski’s experiments the aforesaid condition was not fulfilled, no
more than in Kéniq@’s experiments; R was = 12,5, 7 = 30, and hence 4’R =7,5
about. Still this value is sufficiently large to make the application of (51) allow-
able, and as in Kémia’s experiments, this leads without difficulty to the value
of y. Similarly in ZeMpLEN’s experiments with air equation (51) is applicable to
the inside-friction on the oscillating sphere, for with » = 0,0012, „ = 0,0002,

= qth fe 1
7’ = 30 and R= 5 one finds 5’ = —— ==()}8' hence ¢—26R —e@—8 —_ —
yl 2000
about.
2) This result may be expressed as follows; L is imaginary in this case and
Li == 0 and LB ak",
showing that the addition to the moment of inertia (comp § 10), is here equal
to the actual moment of inertia of the liquid, and the equation of motion of the

sphere becomes (29):
EE
) ae + Ma! == 0.

(A+ K 5

860

Physics. — “The viscosity of liquefied gases IL. On the similarity
of the oscillations of spheres in viscous liquids.” By Prof.
J. E. Verscnaarrert. Comm. N°. 148¢ from the Physical
Laboratory at Leiden. (Communicated by Prof. H. KAMERLINGH
ONNES).

(Communicated in the meeting of October 30, 1915).

1. When two different spheres are swinging in two different
liquids, the question may be raised, whether the one movement
might be a conform representation of the second, that is to say,
whether it is possible in each of the two cases to choose the units
of length, mass and time such that, quantitatively, the two systems
become identical. It is easily seen, that in general this is not possible.

Indeed it is clear, that the numerical values of quantities of
dimension 0, such as: logarithmic decrements per time of swing of
the oscillations of the spheres, are not changed by a change of the
units. For two states of motion to be “similar”, the logarithmic
decrements have thus to be equal, which would naturally not be
the case in general. Similarly in order that there may be corre-
spondence in the two states of motion, the damping of the waves
over corresponding distances must be the same in both systems; as
the radii of the spheres are corresponding lengths, the quantity 6’ R,
according to the previous communication, would have to be numeric-
ally equal in the two systems; this again would not necessarily be
the case. In general therefore the two states of motion would not
be similar.

On the other hand, when a definite state of motion is given, it
is possible to produce a similar motion in a different liquid, and
we shall now inquire, to what conditions this similarity is subjected.

2. In the first place there must be similarity in the motions of
the spheres. These motions are represented by equation (2) of the
previous paper: we may also write this formula as follows

a = ae—* cos Anr — ael—* +21)" (real part),
t : : : : : :
where t = ri the time measured in the time of swing as unit;

if we take the time of swing in both cases as the unit of time, the
expression no longer contains anything specific, if at a given
moment a has the same value in both cases and d is also equal in
the two cases. We can of course arrange the experiments in such
a manner, that the first condition is satisfied; we shall see imme-
diately, how the second condition may be fulfilled.

861

In the second place the spherical shells, at corresponding distances,
must perform the same motion, reduced to the time of swing as
unit, that is in

a, = uekt — ue —2H2rijt
u must have the same value for corresponding values of 7 in the
two systems. Seeing that the radii of the spheres are corresponding
values of 7, we shall find all corresponding values of 7 by taking

equal multiples of A. Calling 0 = the reduced distance from the

centre, the function wv, reduced to the time of swing, must be the
same for reduced distances. For an unbounded liquid we have
according to (15)

1 Bol
1 potl en
o pak

where B=—OR; it appears, therefore, in order that this expression
may not contain any specifie quantity, that the quantities 5 must

. . ie .
be such in the two cases that 6,R,=0,R,. As 6= É len Te
1]

uk? 3 :
follows that En (—od-+ 227) must have the same value in both cases,
1

: ;
in other words ~— must have the same numerical value.
i]

In order therefore that similarity may exist between the two states
of motion, R and 7 cannot be chosen at will: the radii of the
spheres being given, at least one of the spheres must have a pre-
scribed time of swing and in order to obtain this value the moment
of inertia of the sphere and the rotational moment are at our disposal.
As we shall see, both these quantities are thereby completely determined.

3. The motion of the sphere is determined by equation (26), which
we may write in the form

er Ear Er ao
et de
If :7’——d-+ 22 is to have the same value in both cases,
ates ay M T:
the quantities a and = [ror DE have to be equal. Owing to the
ig Al Lies ak

i R'n1
equality of dR, the equality of involves on account of (25) that of = =
A

according to (28) the condition of the equality DE is then satisfied
0

862

at the same time and the periodic time of the damped vibrations
is in both cases the same multiple of the periodic time of the
undamped motion, or differently expressed: the reduced periodic
time is the same.
Then it appears that for the similarity of the two motions it is
necessary and sufficient that the expressions:
2 377
nat a2 |
ane
have the same value in both cases; for given Ff, and u these
equalities determine for one of the systems A and 7’, and therefore
also M, since:
- ‘ ws 1 wk? A K nk
K=C,uR and T, = — —, therefore M Ar — — Ci
Cn T 2

where C, and C, again stand for equal values in both cases. Each
system of values of C, and C, defines a state of motion, of which
there is thus a doubly infinite series.

If the oscillating system consisted of nothing but the sphere, we
should have K = 5 ay'R*, uw being the density of the sphere, and
in that case it follows from the required proportionality of A to
wR, that wo must be proportional to u, ie. the density of the sphere
would have to be the same multiple of the density of the liquid in
both cases. Seeing that the oscillating system can be more compli-
cated, the latter condition does not need to be fulfilled, if only X
has the required value.

4. We may conclude therefore that it is possible to obtain a
conform representation of the oscillating movement of a sphere in a
liquid, by taking a different sphere in a second liquid; the radius
of the second sphere may even be chosen arbitrarily, but the moment
of inertia of the vibrating system and the rotational moment are
then completely determined. That there is no similarity in general,
is due to the fact, that the motion depends upon five quantities:
y u, R,K and M, which can all be changed independently, whereas
by making a suitable choice of the fundamental units for each case
only three of these quantities can he made to assume equal values.
If in each case a system of units is chosen such that 7 =1,4—=1
and R= 1 it does not follow that A and M have the same value
in both systems; the equality of the values of A and Jf expressed
in the special units in the two systems is thus the condition to
which similarity is tied down.

863

5. In the above discussion we assumed the liquid to be unbounded,
but it is evident, that everything remains valid, when the liquid
is externally bounded by a sphere; the only additional condition
is that A’ must have the same reduced value in both systems.

By varying the ratio = in all possible ways (from O to oo) an infi-

nite series of similar cases is again obtained.

It is obvious that similarity may still exist, if the bounding sur-
faces were arbitvary, if only similar; the vibrating body would not
even have to be a sphere’). For this reason it would be possible to
make relative measurements of viscosities with “similar” apparatus
(in the simplest case with one apparatus); this might be done by
first determining the undamped time of vibration and the decrement
in a standard liquid (e. g. water’, then for the experiment in the
liquid which is to be examined first modifying the moment of
inertia of the vibrating system until condition (II) is satisfied, that
is: for the same apparatus increasing or diminisbing A’ proportion-
ally to w and finally changing the rotational couple until the
legarithmie decrement becomes the same as in the first liquid:
according to (1) the times of vibration of the undamped oscillations
for one and the same apparatus would then be proportional to -
and in this manner it would be possible to calculate 1.

It is obvious, however, that relative measurements of that nature
would be much more elaborate than absolute measurements by
direct calculation of 4 from experimental data obtained in the simple
cases, which were dealt with in the previous paper.

6. Returning to the case of a sphere oscillating in an externally
unbounded liquid, it was shown that all possible cases which can
occur can be realized by giving K and M, or K and 7’, all possible
values between O and o. In order to give a general survey of the
different cases I have calculated for special values of u, 9 and R
a few systems of values of A and 7, (or K and JZ) corresponding
to definite values of d and 7. To simplify the calculations I have
taken w=1,. y»=1 and R=I!1 (C.G.S. units), representing a
fictitious liquid which might, however, be realized at a special
temperature by mixing special real liquids. In that case, d and 7’
being given, A and 7, are determined by the equations (comp.
equations 18, 28 and 30)

1) This, of course, does not follow from the foregoing discussion but may be
proved in a more general way. (Note added in the translation.)

T= 100 rad
Bee | Tyee lt oe eee B IEN | mee!
To
0 | 10: 1 ow Ps 0.32 | 0.32 | 0.63 | 20 0.73
5x Diem 326 1652 85 HO. 14. 1 Coat 0r28 8.7 | 0.87
8x 1.107 | 9.1 4.4 | 145 | 0.11 | 0.90 | 0.22 | 70
Ox 0.657 | 15 1.8 | 18 0.10 | 0.95 | 0.21 | 66 (oo
9.9: | 0 wo 0 22 0:10 | 1.00.| 0.20 | 64E
T = 100=
d= Fi Na eee oN Mee | el be ee => |i
To
0 100= 1 oo oo 0.10 | 0.10 | 0.20 | 63 | 0.91
10z | 18.17 5.5 | 106 1.29 | 0.03 | 0.32 | 0.06 | 20 | 0.97
LONNIE 2.95 | 0.02 | 0.45 | 0.04 | 14 | 0.98
25x | 4.707 | 21 23.5 | 4.3 | 0.02 | 0.50 | 0.03 | 13 | 0.98
307 | 2.907 | 34 12:0 | 5.9.) 0.02.) 0.55: 4) 10:05 11 | 0.99
35 1.05 | 95 2.0 | 8.0 | 0.02 | 0.59 | 0.03 | 11 | 0.99
36 0 o 0 9.1 | 0.02 | 0.60 | 0.03 | 11 | 0.99
T = 1000:
a= ney |e KES S ee e | pee
To
0 1000= ree a> oo 0.03 | 0.03 | 0.06 | 200 | 0.97
80 18.8: | 53 | 104 1.18 | 0.00 | 0.28 | 0.01 | 22 1e
100: 11.4 | 88 | 61 1.9 | 0:00 | 0.32 | 0.01 | 20 In
120% 5.8r | 170 | 22.5 | 2.6 | 0.00 | 0.35 | 0.01 18 | 1.00
1307 3.0: | 330 | 6.6 | 2.9 | 0.00 | 0.36 | 0.01 18 | 1.00
135 0 co 0 3.2...) 0:00" | 10-375) (0201 18 | 1.00

T=r
5 Li ' 7
a= i= == i M= (= bj id À= L=
To
0 7 1 (oe) (oe) 1.00 1.00 2 6.3 0.37
7 0.157 1.3 10.8 ald 0.79 1527, 1.58 4.9 0.45
2 0.457 Die, 3.5 69 0.64 oo 1.29 4.0 0.53
3x 0.207 5 0.8 80 0.55 1.82 1.10 3.4 0.58
3.42 0 ee) 0 100 0.52 1.92 1.04 Siere) 0.60
’
T =2r=
é= Tj —= Ke M= = b'= V= == A=
To
0 Qn 1 oe) (eo) 0.71 0.71 1.41 8.8 0.49
ud 1.657 ile 23.1 34 0.56 0.90 ) len | 7.0 0.57
2a 1.107 1.8 8.6 29 0.46 1.10 0.90 5.8 0.63
3x 0.657 3.8 3.8 36 0.39 1.29 0.77 4.9 0.68
4x 0.30x 6.7 all 45 0.35 1.46 0.68 4.2 0.70
4.57 0 oo 0 51 0.33 1553 0.66 ded 0.71
T=4r
A Ji | :
Os 1 — == K= M= b'= b'= V= i= A=
To
0 Ar 1 fee) oe) 0.50 0.50 1.00 12.6 0.61
2 2.457 1.6 19.2 12.8 0.32 0.78 0.64 8.1 0.73
3x 1.657 2.4 10.8 16 0.28 0.91 0.54 6.9 0.76
4x 1.107 3.6 6.0 20 0.25 1.03 0.48 6.1 0.78
5x 0.607 6.7 est 2 0.22 1.14 0.43 555, 0.80
67 0.207 8 0.4 34 0.20 1.24 0.40 a 0.82
6.22 0 fe) 0 35 0.20 1.26 0.39 5.0 0.82

866
8 bee 1 Am
JRE a
3 K A A 427 + 0?
8a 1 tar ed
BK GEDE TLE

' Va OEVER le S+V 44x
— — ee , = KE
27 2T

By means of these relations the tables of page 864 and 865 have been

ce oe
obtained, which also contain the values of a the quantities >’ and
0
b", the velocity of propagation of the waves V, the wavelength 2 and

the damping-factor A —=e”, i.e. the ratio in which the amplitude
of the oscillation is reduced in a distance of 1 em.

‘aos REY
Om zoe
ee ee

EL:

1
AAU
NN

7. It appears from these tables that not every system of values
of 7 and d gives a possible system of values for AK and 7, or of
K and M. For d very small A and M are very iarge and in that
case 1, — 7’; as d diminishes, A, 7, and also M decrease, but,

867

whereas K and 7’, approach a final value of 0, M goes through a
minimum and then rises once more to a limiting value. Similarly
there is a maximum-value for ©, above which with a given 7 it
cannot rise; for higher values of d A would become negative and
T, imaginary; the limit lies at a higher value, as 7’ itself is larger,

but compared to 7’ it becomes smaller and smaller, so that

becomes itself zero for 7'— oo.

On the other hand to every finite system of values of K and M
corresponds a finite set of values for d and 7. In order to make
this clearer a graphical representation of the Tables may be given
in a K, M-diagram. Here the drawn-out curves are those along
which 7’ is constant, the dotted curves those for Ò = constant. A

: K
few 7, curves are also given = Const. | to which the corre-

NV,

sponding 7’ curves approach asymptotically.

8. The Tables and corresponding diagram can also be utilised
in a more general case; A must then be replaced by the charac-

teristic constant C, = - Rs and J/ by the characteristic constant
ul?

14 ul . . aa or tos
C RE The values given in the Tables for 7, 6, V,% and
1
; wd Pe tel
A =e’ are then in general those of —, DR, ——, and e—“k,
wh? if = edit

corresponding to a set of values of C, and C,; from those values
it is thus possible to calculate 7,6,V,4 and A under other more

a al

general circumstances. The value of d as well as that of 7 natu-
0

rally remain unaltered.

The above results can also be used to derive what happens when
one of the quantities is gradually altered, the others remaining the
same. As an example, without making any change in the adjustment
of the apparatus, liquids can be taken of increasing viscosity ; in
that case C, does not change, whereas C, diminishes continually ;
d and 7 are then found to increase gradually, V diminishes, 4
increases and A approaches the value 1.

868

Physics. — “Two theorems concerning the second virial coefficient
for rigid spherical molecules which besides collisional forces
only exert CovromB-forces and for which the total charge of
the active agent is zero”. By Dr. W. H. Krrsom. Supplement
No. 394 to the Communications from the Physical Laboratory
at Leiden. (Communicated by Prof. H. KAMERLINGH ONNES).

(Communicated in the meeting of October 29).

§ 1. In caleulating the second virial coefficient B in the equation
of state written in the form:

i IB: eC
Pint tem amie «> EN

for a system of rigid spherical molecules, which carry a doublet at
the centre (Suppl. No. 246, June 1912), the second term in the
development according to inverse powers of the temperature:

b
ae ee . 4 .
did not occur. This was also the case as regards all the higher odd
powers.

In treating rigid spnerical molecules which carry a quadruplet
of revolution-type in Suppl. No. 39a (see p. 636), the second term in (2)
was again found to be absent, but in this case the higher terms
with 6, etc. were present.

The question now arises whether general conditions can be given
for the structure of the molecules under which the second term
in (2) does not occur.

If, as will appear to be the case, such conditions can be given,
the next question is: can still further conditions be given under
which, if also satisfied by the molecules, no one of the odd powers
of 7-1 occurs in (2)?

In discussing these questions we shall place ourselves completely
on the basis of classical mechanics.

In that case the following theorems can be proved:

4. In the development of B the term with 7! does not occur
if the following conditions are fulfilled:

(A). a. the molecules behave at their collisions as rigid spheres,

hb. the attractive or repulsive forces’), which the molecules exert
on each other, originate from fixed points in the molecule, and can
be derived from a CovrouB law of force (inversely proportional to

b
BB ae
(lt 3+

1) Not including the collisional forces.

869

the second power of the distance between the attracting or repulsing
points), so that these forces might be ascribed to an electric agent, *)
possibly with multiple points ®,

c. the total quantity of the agent in each molecule = O (the
molecules behave as electrically neutral),

2. No odd power of 7! oceurs, if the following conditions
are fulfilled :

(B): a, b and c as above, and besides:

d. the molecule possesses, as regards its attractive and repulsive
forces, at least one axis of “inverse symmetry”, by which expression
we mean, that each volume element contains a quantity of the
agent (as indicated under 5) equal and opposite to that of the volume
element with which it coincides after a revolution about that axis
through an angle of 227/k, k being a whole and necessarily even
number *).

In this case B is an even funetion of the temperature.

The proof of these two theorems follows below in § 3 and 4.

If in the development of B according to (2) the second term
does not occur, the series for 5 reduces for high temperatures to:

b
ae (143) aah Baty ts? ARNE

This dependence of 5 on the temperature is the same as that
which follows from vAN DER WaAALs’ equation by putting dy =
constant, and assuming for aw with Crausrvs and D. BerrneLor:
aw — T-' (ef. Suppl. N°. 39a). Hence if the molecules satisfy the
conditions (A), then for high temperatures and at densities for which
only encounters of two molecules at a time have to be considered,
the equation of state in the form accepted by D. BertuELot would hold.

If the conditions (4) are fulfilled the agreement with BerraeLOoT's
equation of state is still closer in consequence of the absence of the
term b,/1°.

1) Or the supposition that electrodynamic forces (other than magnetic) need
not be considered.

2) In this, if need be, a magnetic agent may be included.

3) As examples of this we mention the cases, that a molecule contains two
posilive and two negalive charges situated at the corners of a square, the centre
of which coincides with that of the molecule. If the homonymous charges lie
diametrically opposite to each other, the molecule has one quadruple and two |
double axes of inverse symmetry. in the other case it has two double axes of
inverse symmetry. We have another example, where the charges form a figure of
revolution aboul an axis through the centre of the molecule, and the part on one
side of the equatorial plane is the “inverse image” of the part on the other side.

870

§ 2. The second virial coefficient for a gas the molecules of which
fulfil the conditions (A) can be deduced by the method given in
Suppl. N°. 24, for which method Borrzmann’s entropy principle
serves as basis. This deduction follows more particularly the lines
of the treatment in §§ 4 and 6 of that paper; it differs, however,
from that treatment in the following points:

1s". The three principal moments of inertia are now supposed to
be unequal. In this case also in determining micro-elements of equal
probability the expression dpd6dydydddy, pp, O and % being the
angles which determine the position of the principal axes of inertia
relative to a fixed system of coordinates, and , 4 and 7 being the
corresponding moments of momentum, may be replaced by dodydp,dq,dr,,
where do represents a surface element of the sphere of unit radius,
which serves for marking the position of one of the principal axes
of inertia, and »,, g, and r, represent the velocities of rotation
about the principal axes of inertia.

2d. For determining the relative position of the two members of
a pair of molecules, we now need, besides the coordinates r, 7,, 7,, 9,
which as in Suppl. N°. 246 § 6 and recently N°. 39a fix the distance
of the centres and the relative orientation of a definite arbitrarily chosen
principal axis of inertia of one molecule relative to the correspond-
ing axis of inertia of the other molecule, two more angles, which
for each molecule specify the azimuth of the plane going through
the principal axis of inertia mentioned above and a second principal
axis of inertia. As such we may choose the angle 7, between that
plane and the plane which contains the first principal axis of
inertia and the line joining the centres . y., and similarly z,, for
the second molecule, are counted from O to 227.

Quite analagously to Suppl. N°. 246 § 6 the foliowing result
is obtained :

B Anton
where now *):

T Tlie Zer

Er ii eae (e—hs1 1) * sin O, sin O,drdO,d0,dy,dy,dp. (5)

s0 0000

In this formula w;; is again the potential energy of a pair of mole-
cules in the position indicated by definite values of 7...q, the

1) As in P’ the manner in which the density is distributed over the spherical
molecule does not occur, it appears that the limitation to molecules of spherical
symmetry observed in Suppl. N°. 240 § 6, can be omitted (cf Suppl. N°. 59a
S 2 note).

871
potential energy for + = oo being chosen as zero. Further

1 i ; EN 5 :
a k being Prancr’s constant. Finally the attraction is sup-

posed to decrease sufficiently rapidly with increasing 7, for the integral
in (5) to be convergent.

§ 3. For the proof of the first of the theorems mentioned in § 1
we develop P’ according to ascending powers of h. The first term
becomes :

oo T TAnAT2T

— oe If fer sin 4, sin @, drd@,d6,dy,du,dy. . (6)

000000

The integration according to 6,, 7, and p, the coordinates 7, 6,
and y, being kept constant, must necessarily give 0, if the condi-
tions (A) are fulfilled. In fact the result of this integration can be
represented as the potential energy of a molecule 1 relative to a
great number of superposed molecules 2, all with the same centre,
but further as regards their orientations uniformly distributed over
all the possible positions. By this superposition at the limit a sphere
is obtained in which the agent is uniformly distributed over con-
centric shells. According to a well known theorem of the theory of
potential, the potential outside such a sphere is constant if the total
quantity of the agent acting according to CouromB’s law of the
inverse square of the distance equals 0; from this, together with
the assumption mentioned above about w,; becoming O for r= o,
follows the above result; the theorem in question is hereby proved.

§ 4. The odd powers of / in the development of P’ (§ 3) occur
in the following form:

1 1 Tae
a: ee ety! oes [ff ff finer B sin 7, sin @,drdG6,d0,dy,dy,dyp (7)

700000

q is here a whole positive number.

If the conditions (4) are fulfilled, the integration of this integral
according to 0,, y, and y,, the coordinates r, @, and y, being kept
constant, will again necessarily give 0. This results from the fact
that each contribution to the integral, obtained from positions of the
second molecule indicated by definite values of @,, x, and y, with
the ranges d0,, dé,, dp, is neutralized by the contribution obtained
from positions, which can be derived from the first by a revolution
through an angle of 22// about one of the axes of inverse symmetry.
With this the second theorem mentioned in § 1 is proved also.

Proceedings Royal Acad. Amsterdam, Vol. XVIII.

872

Physics. — “Investigation of the equilibrium liquid—vapour of the
system argon—nitrogen”. By G. Horsr and L. HAMBURGER.
(Communicated by Professor H. KAMERLINGH ONNEs.)

(Communicated in the Meeting of October 30, 1915).

Summary: L Introduction. Il. Preparation and analysis of the gases. 1. Pre-

paration. 2. Test of purity. 3. Methods of analysis. III. Temperature measurement.
IV Determination of the end-points of condensation. 1. Apparatus. 2 Vapourpressures
of oxygen, nitrogen and argon. 3. Mixtures. V. Determination of the points of
beginning cond nsation. 1. Apparatus. 2. Measurements. 3. Equation of state of
the mixtures. VI. Tx- and pa-diagrams. VII. Resumé.

1. Introduction.

Owing to the development in recent years of the incandescent-
lamp industry the problem of the technical preparation of argon
has come to the front. For this purpose it was natural that beside
chemical methods the cryogenic method should draw the attention.
As it is a simple matter to obtain mixtures of argon and nitrogen
by chemically removing the oxygen from oxygen-nitrogen mixtures
which are rich in argon, an investigation became desirable of the
behaviour of argon-nitrogen mixtures at low temperature with a
view to collecting useful data for a possible argon-nitrogen rectification.
This investigation has been carried out by us and we have determ-
ined the composition of the liquid and vapour phase as a function
of temperature and pressure in the corresponding range of temperatures.

U. Preparation and analysis of the gases.

1. Preparation.

The preparation of the gases was in general carried out in glass
apparatus which had been previously exhausted with a mercury
pump and liquid air to a pressure of 0.0003 to 0.001 mm. and
subsequently washed out with pure gas. For the calibration of our
thermometer the vapour-pressure of pure oxygen was used.

a. Oxygen.

This gas we prepared from recrystallised, dry potassium per-
manganate ; the first portion of the gas evolved was drawn away
and the rest of the oxygen formed was condensed ; the middle
fraction of the condensed gas was used.

b. Nitrogen.
This gas we prepared from ammonium sulphate, potassium
chromate and sodium nitrite; in the purification special attention

873

was given to the removal of nitric oxide (glowing copper); for
further details we refer to.a paper which will appear elsewhere.

In this case, as well as in that of oxygen, the purity of the gas
was proved inter alia by the equality of the vapour-pressures obtained
at the beginning and at the end of condensation.

e. Argon.

For this gas we could start from the strongly argonous gas-
mixtures which the firm of Linpr has recently brought into the
market. The final purification was effected by means of HreMper’s
mixture’) in a manner similar to that given by CROMMELIN *). The
only modification which we applied in our apparatus consisted in
each tube containing chemical substances which might develop im-
purities, such as water-vapour ete, or conversely might react with
them, being flanked at each end by cooling tubes immersed in
liquid oxygen. Care was taken, moreover, that during the complete
circulation-process the gas should be at a higher pressure than the
atmosphere throughout the whole apparatus.

Again in this case the final product was found to satisfy the test
of equal pressures at the beginning and the end of condensation.

d. The mixtures.

The mixtures were prepared by adding nitrogen to Linpg’s argon-
nitrogen mixtures after these had been freed from oxygen by means
of glowing copper. The nitrogen had been obtained from air by
liberation from oxygen. We gladly acknowledge our indebtedness
to Mr. H. Finrpo Jzn. for his kind collaboration in this part of our
work. In a few cases use was made of the method of diminishing
the percentage of nitrogen of Lipr’s mixtures (down to about 5°/,)
by means of a fraction-apparatus constructed by Mr. Finippo,

2. Test of purity.

The gases and mixtures were tested for the following impurities
or, if necessary, simultaneously freed from them.

a. Water-vapour and carbon dioxide were removed from the gases
which were kept above water, freed from air by boiling, by passing
them previously to the measurements through a couple of cooling
tubes immersed in liquid oxygen.

b. Hydrocarbons. It was found that these were not present: a
thin spiral wire of tungsten which was made to glow in the gas
mixture was found not to change in resistance *).

1) W. M. Heupen. Gasanal. Methoden, 3nd edition p. 151.
2) GC. A. Crommetin. Dissert. Leiden 1910.
5) Comp. L. HAMBURGER, Chem. Weekbl. 12, (1915) 62.

874

e. Oxygen was completely removed with yellow phosphorus.

d. Carbon monoxide. The gas was tested for this by means of
I,0,'): it was found not to contain more than '/,, °/,.

e. Hydrogen. In testing for this gas we used the method given
by Prrmmrs*). The gas contained less than 0.01 °/, of hydrogen.
We may add, that the gases were always condensed before they
were used in the measurements and that the liquefied gases were
then made to boil under reduced pressure; the vapour that was
drawn off must have contained the last traces of hydrogen present
and the small admixture of neon must also have been for the
greater part removed in this way.

Finally we may give the following data as providing a measure
of the purity of the gases.

A. Oxygen. The gas was analysed by means of copper
(immersed in an ammoniacal solution of ammonium carbonate),
later on with sodium hydrosulphite. It was found to contain more
than 99.9°/, of oxygen.

B. Nitrogen. Observations were made with nitrogen, obtained
from air by removal of oxygen, which corresponded completely to
those made with chemically prepared nitrogen, taking into account
the percentage of argon in air-nitrogen.

This correspondence, with such widely different methods of
preparation, may give us additional confidence that our gases were
satisfactorily free from impurities.

C. Argon. This substance was tested for absence of nitrogen
indirectly by means of the determination of the pressure at the
beginning and the end of condensation, but also more directly by
means of glow-discharges in potassium vapour (comp. 3) in which
no diminution of volume could be detected. (Comp. also the determ-
ination of specific gravity § 3c).

3. Methods of analysis. It follows from the above that the only
gas besides argon which could be present in the mixtures which
were intended for the measurements was nitrogen. This fact made
it possible to determine the percentage of nitrogen by means of a
baroscope. It appeared, however, that the sensitivity of the available
balance was not so high as we should have wished, in consequence
of whieh these determinations, at least in the most unfavourable

1) Comp. Dennis, Gas analysis (1913) p. 231 and 235.
2) Am. Chem. J. 16 259 (1894).

875

case, are not more accurate than to about 0.2°/,. Fortnnately we
were able to carry out the analysis more accurately by a chemical
method, which enabled us to attain an accuracy of 0.1°/,.*) We
shall begin by a description of the latter method.

A. Determination of the percentage of nitrogen in Ar—N miatures
by means of glow discharges in potassium vapour.

It has been long known *), that in electric discharges through gases
such as nitrogen, hydrogen ete. a chemical reaction may occur,
especially between the material of the cathode and the rarified gas.

Mry*) pointed out, that this provided a means of liberating rare
gases from admixtures. This method was further developed by
GEHLHOF*), who succeeded by means of glow discharges through
potassium vapour in preparing spectroscopically pure rare gases
comparatively rapidly although not in large quantities.

In order to adopt this method to a quantitative analysis of Ar — N
mixtures the following apparatus was constructed by us.

A definite quantity of the gas-sample which is collected above

1) The readings might have been further refined by the use of a cathetometer.
but we did not adopt this method, as an accuracy of 0,1 °/9 was sufficient for
our purpose.

2) Comp. G. Sater, Pogg. Ann. (158) 332, 1876. L Zexunver, Wied. Ann.
(52) 56, 1894.

3) Mey, Ann. d. Phys. 11 127 (1903). GeaLHorr and Rorrearprt, Verh. d. D.
phys. Ges. 12 411 (1910).

4) GeavHoFr, Verh. D. phys. Ges. 13 271 (1911).

876

mercury (fig. 1B) was drawn into the burette a (fig. 1A). Previously
the absorption-apparatus 4 and the T6pLER-pump c had been exhausted
by means of the mercury pump &; tap e was then closed and by
opening d the gas was transferred from the burette into 6 by means
of the mereury column in C. On the bottom of the absorption-
apparatus (fig. 1C) is the potassium, which is now heated to 200°C.
by means of a small electric furnace. An induction-coil is used to
send a glow-discharge through the evolved potassium-vapour.

After a few hours — the time required depends on the percentage
of nitrogen in the mixture — the unabsorbed portion is transferred

back to the burette by means of the Törrer-pump.

In using the method the question arises, whether the potassium
which may be deposited from the vapour on the cooler parts
of the absorption-vessel’) may possibly absorb argon at its large,
freshly formed surface. It is well known, that sublimated metals
may absorb at their finely divided surface even the rare gases.
Fortunately argon often does not show the phenomenon *). It appeared,
moreover, that in our case an absorption of this nature was impro-
bable, from the fact that, after the nitrogen had been absorbed,
there was always a residne of gas left which did not show any
further contraction however long it remained exposed to the glow-
discharge. In the mean time the potassium goes on evaporating and
depositing on the colder surfaces, so that the metallic surface is
constantly being renewed. If an appreciable absorption of argon .
took place, it would have been impossible to obtain a constant
final volume. It may finally be noted, that a sample of the pure
argon which we had prepared did not show any contraction in the
absorption-apparatus.

We have also tried to utilize for the purpose of analysis the
method of binding nitrogen recommended by Stark *) (electric dis-
charge through mercury vapour). It was found, however, that for
a sufficient rate of absorption we had to work at much lower
pressures — even when the electrodes were placed opposite each
other in the middle of the vessel. With potassium on the other hand
every gas-mixture, however high the percentage of nitrogen might
be, could be made to react with the metallic vapour at relatively
high pressures. *)

1) As well as the compound which is formed.

2) Travers. Proc. Roy. Soc. 60 449. Comp. also KorrscHürrer, Jahrb.
Radioakt. 9 402. (1912).

35) Phys. Zeitschr. 1913 p. 497.

4) It is very probable that the reaction is in general started by the splitting of

877

B. Determination of the percentage of nitrogen by means of a
baroscope.

For this purpose use was made of the difference in the upward
pressure produced by the gas-mixture on a glass body (volume about
300 e.m.*) which was suspended from one arm of a balance as
compared to an open glass vessel of an equal outer surface on the
other arm.

The apparatus was arranged in such a manner, that by the
turning of a properly shutting glass tap the arresting arrangement
of the balance could also be put into action in a high vacuum. The
pressures were read by means of a cathetometer.

The following data’) were used for the baroscope-determinations :
density of az, free from water-vapour and carbon dioxide, 45° N.L.,

sea-level, O° and 76 cm. 0.0012928
nitrogen (RayvLEiGH and Lepvc) 12514
argon (Watson) 17809

C. Results.

The following table (p. 878) (column 1—6) gives a survey of
different determinations by methods A and B.

In deducing the mean (column 6) we have attributed a double
weight to the determinations by method: A.

When the mean of the results by method A is compared with
those by method B, a systematic deviation will be seen to exist
which increases with the percentage of argon in the mixture. As
the baroscope had been previously calibrated with other gases (carbon
dioxide, nitrogen, air) with satisfactory results, we were led to
conjecture that the atomic weight of argon, respectively its specific
the nitrogen molecules by the electric discharge, the atoms which are formed
combining with the potassium. Strutt, (Proc. Royal Soc. Serie A 85 219 and
subsequent volumes) found that the re-combination of the N-atoms to molecules
(which do not react with the potassium) is much accelerated by an increase of
the pressure. This was the main ground, on which we chose the dimensions of
the absorption-vessel large as compared with those of the burette. (The low
pressure also facilitates the production of the discharge). The fact explains in
particular, why the time of absorption in our analyses increases with the percentage
of nitrogen in the mixtures. lt is also known (Srrurr l.c. comp. also Kornie
Zeitschr. f. Electroch. 1915. 1 June), that metallic vapours accelerate the molisa-
tion of nitrogen atoms. (An afterglow on interrupting the discharge was therefore
entirely absent in our apparatus). It is of course possible that mercury has this
property to a higher degree than potassium, although a different affinity of mer-
cury towards N may also play a part here; this might be one reason for the
stronger reaction of the polassium vapour

) LANDOLT-BöRNsTEIN Phys. Chem. Tabellen. 4th ed,

878

gravity, as at present assumed, was probably not entirely accurate,
and we made preparations for an accurate determination. A prelimi-
nary measurement gave the normal density as 0.001785'.

TABLE 1.
0; Method
Number Method AShN: | Method’ Ine
of the | El B eier |
gas- Ist de- |2nd de-| 3rd de- modified lue.
mixture. \termina-\termina- termina-, 0 N. Hele: | ie
tion. | tion. | tion. NEES.
It 82.6 82.6 -- 82.5 82.6 82.6 82.6
Il. OD 65.3 65.4 6550) «1172165235 Rayer 65.3
IIL. 31.4 31.6 — GEE 31.6? Si
|
IV. 9.9 9.9 — 9.76 | 9.9 | 10.25 10.0
V. belie || oe = 73.7 74.0 | 13.85 74.05
|
VI. 52.9 52.8 — 52.4 apud Sap 52.8
VII. 24.4 24,25 — 23.8 24.2 24.2 24.3
Bures) |
argon. $ 0.0 = —0.5 | 0.— | 0.0 0.0
i 3} 3. 4, 5. 6. | if Beal

The account of our investigation had already been written, when
a paper appeared by H. Scuurrze’) in which the specifie gravity
of argon is given as 0,00178376. When we use this value, we
obtain the results given in columns 7 and 8 of the above table.
The mean difference between the determinations with the baroscope
and those by method A is now only 0.04°/,, in other words there
is no sign now of a systematic deviation between the two methods.
This result proves on the one hand the reliability of method A and
may on the other hand be taken to confirm ScuuLtzr’s result. We
hope soon to be able to publish the results of a more accurate
direct determination.

WU Woz temperature measurement.

The measurements were made in a bath of liquid oxygen. In
the construction of the eryostat as well as of many other parts of
our apparatus we could avail ourselves of the experience gained
in the cryogenic Laboratory at Leiden, where one of us had the
advantage of working for several years under the guidance of

1 Ann. d. Physik 48 (1915) p. 269. Heft 2 published 14 Oct. *15.

879

Professor H. Kamuriincn ONNes. The temperatures were measured
with the aid of a platinum resistance-thermometer. The wire was
about 0,1 mm. in diameter and was wound bifilarly on a small tube
of Marquardt-material on which a double spiral groove had been
cut. At the ends of the tube stouter platinum wires were auto-
genically sealed on; to these wires the four copper leads were
soldered. Before using the thermometer it had been treated thermally
by a tenfold immersion in liquid air, each time followed by glowing
at about 700°. By that means a constant zero-point was obtained.
On three different days the resistance w, was found equal to
18.4695 2, 18.4697 2 and 18.4695 Q respectively ; it was measured
with a differential galvanometer by KorrrauscH’s method.

The calibration of the thermometer took place by using the vapour-
pressures of oxygen as determined by Kamerrincr ONNEs and BRAAK, *)
in the apparatus in which the end-points of the condensation were
determined. If p represents the vapour-pressure in mms., the relation
between 7’ and p in the range 83,5° and 90° abs. is: *)

369,83
~ 6,98460 — log. p

(Aal
The ratio — was determined at the same time.

‘ aed
For the Leiden standard platinum thermometer P27’, the ratio —
Wo

as a function of the temperature in the range of temperatures in
question is accurately known. It is therefore possible to calculate
the value of the constant @ in the linear relation which according
to Nernst holds for different thermometers :

a(2)\=«(1—2).
Wo Wo
With « = 0,00121 our thermometer could be reduced to Pt, and
this constant was therefore used in calculating the temperatures.
To test the apparatus which served for the determination of the
points of beginning condensation for its utility, the boiling point of
oxygen was also determined in it. The pressure was 762.4 mm.
According to the vapour-pressure formula this corresponds to a

. . w a .
temperature of 90°.15; the ratio gave 90°.16, which agrees very
w
0

closely. As @ was comparatively small for our thermometer *) and,

1) H. KAMERLINGH ONNEs en BRAAK. Comm. Leiden No. 107a.

2) G..Hotst. Comm. Leiden No. 148a.

8) H. ScHiMANK, (Ann. d. Phys. (45) 706, 1914), gives 0.1—0.2° as the
uncertainty for a =0.C3.

880

TABLE 2.
iz Ww
je AM En | a
Pmm Gr) Gr) Pr |
758. 1 90.10 | 0.25258 | 0.25166 0.00123
|
757.6 | 90:09 0.25251 0.25162 0.00119
593.2 | 87.82 | 0.24273 0.24184 0.00118
151.2 90.01 | 0.25220 0.25127 0.00124
Mean . . . 0.00121 |
a

as our platinum was obtained from Hreraevs like that of P//,, it is
very probable that the temperatures as given by us are correct to
about 0,02°.

IV. Determination of the end-points of condensation.

1. The apparatus. The end-points of condensation were measured
by means of a vapour-pressure apparatus provided with a stirrer,
as used by KuvereN. The small vessel was placed in a eryostat
which contained, beside the resistance-thermometer, a small pump
which provided a thorough circulation in the oxygen-bath. The tem-
perature was regulated by an adjustment of the pressure in the
cryostat. The constancy of the temperature during the measurements
was about 0,01°.

2. Vapouwr-pressures of oxygen, nitrogen and argon.

Beside the measurements which served as a calibration of our
thermometer we determined the vapour-pressure of oxygen at two
other temperatures.

| TABLE 3.
T calc.from |
T p vapour pressure
_ | _ formula
| 5 |
83.49 | 357.7 | 83.47
18.42 | 184.3 |. 18-81
| |

Whereas at 83°.5 the temperature as measured agrees with that
calculated from the vapour-pressure to within 0.02°, there is a
difference of 0.05° at 78°. It will therefore be advisable as a
precaution not to use the formula for 7 as a function of log p for
purposes of extrapolation.

ee ee ee

881

For nitrogen we found:

TABLE 4.
T P
80.88 1138.0
78.50 88.1 |
72.10 306.6 |
69.29 264.6
For argon :
TABLE 5.
T P
89.95 1001.0
|
87.78 801.7
87.76 802.2
| 84.02 533.9 |
83.84 522.6
83.78 518.7
83.71 514.1 |
| 83.62 509.2

and hence for the triple point 7’= 83°,81 p= 521,4 m.m.

We shall compare these figures with some recent ones of other
observers.

For oxygen the measurements by HenninG’) and by v. SIEMENS *)
may be used.

1
For all these measurements we have drawn log. p= f (=). The
1) F. Hennina. Ann. d. Phys. (43) 282, 1914.

2) H. v. Stemens. Ann. d. Phys. (42) 882, 1913. Comp. also G. Horsr. Comm.
Leiden N°. 148qa.

882

greatest differences with HENNING are about 0.02°, v. Sremens’s
measurements differing a little more at the lower temperatures, not
more than 0.06° however.

For nitrogen we can also compare our measurements with those
by v. Siemens; here again the difference is very small at the higher
pressures and increases as the temperature falls.

At the higher temperatures our measurements agree but moderately
with those of CROMMELIN*), even if we discard his lowest point which
he himself considers less accurate.

The values which we obtain for the vapour-pressures of pure
nitrogen by extrapolating the measurements with the argon-nitrogen
mixtures are in good agreement with our direct observations.

Argon has also been investigated by CROMMELIN®) in the same
temperature-range. His results correspond very well to ours.

There is only a small difference as regards the triple point. As
we made a number of observations in the immediate neighbourhood
of this point (fig. 2) and as our points fall very accurately on the
curve drawn through the other points determined by CromMEtin,
we think it probable that the triple point as determined by us is
to be preferred. The differences are for the rest of the order of
magnitude of the errors of observation.

Ss Oo. 1 oS
88h 8 78 18 ale ee eee
We Nr eae cs ae

Fig.2

1) GC. A. CROMMELIN. Comm. Leiden N°. 145d.
2) C. A. CROMMELIN. Comm. Leiden N°, 1385.

———— EE a

883

3. Mixtures.

For five mixtures the pressure at the end of the condensation
was measured at three different temperatures. Not more than 4 °/,
of the gas was uncondensed.

The composition of the mixtures was given above.

The results are contained in Table 6:

TABLE 6.
Mixture I. 82.6 Og. N. Mixture III. 31.59% N.
J Pmm | ii ees
82.63 1218.1 86.55 1162.3
18.53 781.5 83.47 852.2
| |
74.02 451.0 78.46 487.8 |
Mixture II. 65.3 Oo N. Mixture IV. 10.00, N.
If P T Pp
83.49 1175.9 89.86 | 1198.6
|
18.53 686.5 87.69 | 972.0
14.53 424.2 83.53 631.2
Mixture VIII (atmospheric nitrogen 99.— 9) N. (baroscope)).

T Pp
81.06 1151.6
18.435 863.5
711.295 350.9

: 1
When log. p was drawn as a function of = for argon, nitrogen

and the mixtures,a set of straight lines was obtained which converge
at higher temperatures. The values of p and 7’ which will be used
later on for the construction of the pz- and 7r-diagrams were taken
from this graphic representation.

584

V. Determination of the points of beginning condensation.

1. Apparatus.

The apparatus used for this purpose was arranged in the manner
of a constant volume gas-thermometer. Its vessel had a volume of
about 142 ce. and was provided at the lower end with a small
appendix 8 mms. long in which the liquid gas collected. In order
to make sure that equilibrium was attained the liquid could be
stirred by means of a small steel ball, which on closing a current
was drawn up in the field of a small electro-magnet with pole-
pieces cut at 45°. In calculating the changes of volume of the vessel
the coefficient of expansion was taken as 0.0000212, the mean of
the results obtained by Travers, SENTER and JAQVEROD!) and by
KAMERLINGH Onnes and Hrousr ®) for Thüringen-glass between O° and
—190°.

The measurement was conducted as follows: a measured quantity
of gas was transferred to the vessel and the pressure read at a
definite temperature; a second quantity of gas was then measured
and transferred to the vessel, and the pressure was read again,
ete. etc. until condensation set in. The vapour-pressure was then
measured at increasing densities of the vapour.

For a convenient measurement of the quantities of gas which were
added, the manometer-tube on the vessel-side was provided with a
seale-division and had been accurately calibrated. For the reading
of the pressures a cathetometer was sometimes used, sometimes a
vertical comparator with steel measuring-rod. In the latter case the
accuracy is smaller, but not smaller than about 0,1 mm.

2. The measurements.

; 5 pv
For each mixture at three different temperatures „Et was now

determined as a function of the pressure, where p is the pressure
of the mixture in mms. and v the volume of the gas in the vessel,
divided by the theoretical normal volume of the same quantity. *)
The point, where this curve shows a discontinuity, is the point of
beginning condensation in question.

For each quantity of gas which was added the normal volume
was each time calculated; this volume was diminished by the quantity
contained in the dead space and the capillary in order to obtain
the quantity of gas in the vessel.

1) TRAVERS, SENTER and JAQUEROD. Phil. Trans. A 200. p. 138.

2) H. KAMERLINGH ONNES and W. Heuser. Comm. Leiden No. 85.

3) H. KAMERLINGE ONNES and W. H. Kersom. Enc. d. Math. Wiss. Comm.
Leiden Suppl. 23.

TABLE 7.

Mixture V. 74.05 % N.
T=83.°54 RT = 0.30595 | 7 —78.°62 RT =0.2879
BS ? eu SO EVAE RT, Gey pu. SERT
TE 760 | 760 PS 760 | 760
0.4424 | 513.5 | 0.2991 | 0.00685 || 0.6956 | 308.9 | 0.2829 | 0.0050
3541 | 637.7 | 2973 | 0.00855 || 0.4421 | 482.1 | 0.28065) 0.00725
2853 | 786.4 2054 | 0.01055 || 0.35405 597.4 | 0.2785
2423 | 920.4} 2937) 0.01225 || 0.35405! 597.1 | 0.27835
2117 | 1044.9 | 2913 | 0.01465 || 0.2849 | 630.4 | 0.2365
1854 | 1079.8 | 2635 En 0.28495| 629.2 | 0.2360
1854 | 1079.0 | 2633 ae 0.2419 | 650.9 | 0.2073
1773 | 1088.9 | 2542 en
16825| 1099.1 | 2435 = |
Mixture V. 74.05 0, N. Mixture VI. 52.8 of) N 4
Eise RT —0.2102 T=85.03 | RTr—=03141
0.8861 | 228.6 | 0.2667 0.0035 || 1.3663 | 169.7 | 0.3123 0.0024
6954 | 290.0} 2655 | 0.0047 || 0.6310 | 373.0 | 0.3099 | 0.0048
5657 | 327.8 | 2443 = 0.2316 | 989.0 | 0.3016 | 0.0131
44135| 349.35; 2031 = 0.2144 | 1053.9 | 0.29745; = —
3530 | 363.2 | 1688 = 0.2078 | 1061.6 | 0.2905 | = —
0.2004 | 1065.3 | 0.2811) 9 —
Mixture VI. 52.8 % N. ar
T= 800.89 RT = 0.29625 | “T= 16°.225 RT=0.2791
1.3979 | 159.8 | 0.2041 | 0.00215 |} 1.3964 | 150.6 | 0.2769 | 0.0022
0.94595| 235.5 | 0.2933 | 0.00295 || 0.9439 | 221.7 | 0.2755 | 0.0036
0.7125 | 311.5 | 0.2923 | 0.00395 |] 0.7122°| 293.0 | 0.2748 | 0.0043
0.4697 | 468.4 | 0.2897 | 0.0065° || 0.6303 | 330.2 | 0.2741 | 0.0050
0.4047 | 541.8 | 0.2887 | 0.00755 || 0.5628°| 340.5 | 0.25235, —
0.37425| 584.1 | 0.2878 | 0.00845 || 0.4690 | 357.5 | 0.2208 a
0.3465 | 606.6 | 0.27675 a 0.40385| 379.8 | 0.1966 =
0.3069 | 624.0 | 0.25215 a
0.28075} 636.0 | 0.2351 a

886

TABLE 7. (Continued).

Mixture VII. 24.3%) N.

T= 90.11 RT = 0.3300 | T = 85.36 RT = 0.31265

rte: pv) |_ pv Bie pv) |_ po
Pors E45) zoo RTP on 4 (5) — 769 TRI

4.0803 61.1 | 0.3280 0.0020 4.079 SI SIR OES1OL 0.00255

0.5666 | 434.7 | 0.3243 0057 2.073 | 114.0 3110 00165
0.3170 766.0 0.3197 0103 1.0943 | 215.3 3102 | 00245
0.2959 | 819.6 | 0.3191 0109 0.4327 | 534.3 ‚ 30445 0082
0.2011 | 1186.7 | 0.3142 0158 0.3437 | 669.3 | 3029 00975
0.1928 | 1228.4 | 0.3118 = 0.3174 | 722.8 3021 01055
0.1882 | 1232.7 | 0.3054 = 0.3108 | 737.6 3018 01085
0.1795 | 1236.7 | 0.2923 = 0.3048 | 752.5 3018 01085

0.2956 | 756.2 2954 =
0.2867 | 758.6 2864 —

0.2743 | 762.5 2754 =
| |

T = 80.53 RT = 0.2950 | T = 80.53 RT = 0.2950
| |
4.018 | 54.6 | 0.2931 | 0.0019 || 0.59615) 368.0 | 0.2888 0062
2.072 | 107.6 | 0.2935 0015 |} 0.4923 | 429.5 | 0.2785 =
| 1.0942 | 202.9 | 0.2923 0027 || 0.4444 | 438.7 | 0.2567 —
0.8446 | 261.5 | 0.2908 0042 || 0.4324 | 439.3 | 0.2502 =
0.59615) 368.0 | 0.2888 0062 || 0.4212 | 439.45 | 0.2437 =

The first column of the above table 7 contains the volume of the
vessel v,, divided by the theoretical normal volume vj of the
quantity of gas which it contains.

5
For argon we assumed B == (SERRA)

Vthn

,, nitrogen ,, ao SUREEIGS)
for the mixtures intermediate values were taken.

1) H. KAMERLINGH ONNes and C. A. GromMeLIN, Comm. Leiden 1180.
*) Recueil des constantes p. 189.

887

The second column gives the pressures in mm. mercury, all
: pe
reduced to the same temperature, the third column gives =a and

)
the last i) — RT for the gaseous state.

Oey. 5 8 :
In fig. 3 = is drawn as a function of p for each of the
mixtures for the purpose of determining the pressure at which the
condensation begins.

100 200 300 400 500 600 700 800 900 1000 1100 1200
Fig.3.

Table 8 contains these pressures and the corresponding temper-
atures; it also gives the volumes of the saturated vapour expressed
in the theoretical normal volume as unit.

1
When log. p was represented as a function of f(z). a set of

straight lines was obtained, in this case also, As before, the values
which served for the construction of the final diagrams were derived
from these curves.
It may be mentioned, that with the last mixture of 24.3°/, N at
a temperature very little below 80°.50 the solid began to separate out.
57
Proceedings Royal Acad. Amsterdam. Vol. XVIII.

888

TABLE 8.

Mixture V. 74,050) N Mixture VI. 52.8 |) N
up up
f P 760 J T P 760 ze

83.54 1052 0.29185 0.2107 85.93 1053 0.30075 | 0.2171
18.62 507 0.27875 0.355 80.89 599 | 0.28795 | 0.365
13.78 316° 0.2652 0.638 76.225 | 330 0.27415 | 0.631

Mixture VII. 24.3 °/, N

up
ql p 760

90.11 1228.5 | 0.3138 0.1942
85.36 154 0.30175 0.304
80.53 427 0.28789 0.512

3. Equation of state of the mixtures.

av . . . .
Fig. (8) shows on inspection that ni is a linear function of p. It is

5
‘

1 : :
preferable, however, to choose — as the independent variable. The
v

equation of state for the mixtures under investigation. in the region

ENT) zon 500 4000 $000

889

in question can then be represented in the form
BN)
pu=RT(1+—)°.
v

1
In fig. 4 pv—RT is represented as a function of — for mixture VI.
U

We have computed the values of B in this equation and have
obtained the following results

TABLE 9.
Mixture V. 74.05 Oo N. | Mixture VL. 52.8 Oo N.
|
is F fore) ee t
| B | T B
— a | —_—-=-- — — —
83.54 00100 «|| 85.93 — 0.0096
{|
78.62 Sib | | 80.89 — 0.0103
| |
13.78 ODB, nz © jen 220. 0108. 9

rn = |
Mixture VII. 24.3 Of, N.

T B |
90.11 | — 0.0100
85.36 — 0.0107
80.53 SN ONOI22

Unfortunately so far determinations of B-values for argon at
these low temperatures have not been published®). For nitrogen
measurements by BrsteLMEYER and VALENTINER*) are available.

These measurements give B—=—0.0116 at 7’ = 81.4 in good
agreement with our results as regards the order of magnitude.

The equation of state finally enables us to calculate the volume
of the saturated vapour. This calculation we are, however, obliged
to defer. Table 8 gives the volumes of the saturated vapour for the
points which were experimentally determined.

Comm, Leiden Suppl. 23.

2) Weunderstand that the measurements of B for argon undertaken by KAMERLINGH
ONNEs and CROMMELIN in the Leiden Laboratory will not be completed for a
considerable time.

8) A. BESTELMEYER and S. VALENTINER. Ann. d. Phys. (15) 61, 1904.

890

VI. Tx- and pa-diagrams.

The data found above enable us to derive temperature-composition
as well as pressure-composition diagrams. The values which we
obtained are arranged in Table 10 on page 891; by means of these
a few Tx-curves were drawn (fig. 5) and the pz-diagram for
T= Soden DE

b 7 7) E)

FI0.5. Figs. a

It will be seen, that the difference in composition between the
liquid- and vapour-phases is a little smaller on the nitrogen- than
on the argon-side. A glance at the figure further shows, that in the
preparation by means of fractionation of argon from mixtures
containing only a few hundredths of argon no great advantage can
be gained from raising the pressure, althongh the advantages of a
better exchange of cold at the higher pressures must not be lost
sight of, where a technical method is concerned.

The change of the composition of the gas-phase with that of the
liqnid-phase satisfies the relation *) :

1) The Tx curves for p=50 have been dotted on the argonside, as the solid
makes its appearance here.
2) LEHFELDT, Phil. Mag. (5) 40 397 (1895).

891

’ log r' =a-+ blogr
where r’ represents the ratio of the components in the liquid and

y the same quantity in the vapour.

TABLE 10. 7—«-diagrams.
zoon. doe 50.0 Dn 16.0 Tp = a ol Tp = a
le) fe) ° ke)
0.0 83.45 87.26 89.93 94.18
10.0 81.42 85.25 87.98 92.32
End
: Bleo 78.65 82.40 85 .05° 89.29
o
65.3 15.86 79.41 81.95 85.97
cond.
82.6 14.82 18.30 80.76 84.70
100.0 13.81 11.28 19.711 83.57
Beginn 24.3 81.79 85.46 88.04 92.15
of 52.8 79.41 82.97 85.40 89.33
cond. 74.055 Uae 80.66 83.08 86.93
End
of 99.— 13.94 17.39 79.18 83.64
cond
p-x diagram for 7 — 5811
x Oo p. c.m
0.0 60.28
10.0 14.15
End
31.5 100.5
of
65.3 137.9
cond,
82.6 156.2
100.0 174.3
Beginn. 24.3 73.18
efi ail) DerSeEs 96.78
cond. 74.0° 124.2

892

TABLE 11. |

p=50.0 cm. | p = 76.0 cm. |

a= — 0.545 b = 1.08 a=—0496 | b6=1.06

T r’ Tcalc "found If if "calc "found |
76.00 jae 5.36 DRO 80.00 1.34 3.87 3.85
78.00 0.605 2.01 2.01 82.00 0.534 1.64 1.65
80.00 0.247 0.879 0.869 84.00 0.227 0.725 0.718
82.00 0.0695 0.269 0.270 86.00 0.0593 0.205 0.206

p= 1000 cm p = 150.0 cm
a=—04515 | b=104 a — — 0.3965 b = 1.03"
82.00 | 1.825 | 4.82 |. 4.81. ||-86.00 | 1.85 | 452 JD
84.00 | 0.706: | 1.94 | 1.93 || 88.00 | 0.750 | 1.83: | 1.84
86.0) | 0.305: 0.869 | 0.872s || 90.00 | 0.346 | 0.866 | 0.866
88.00 | 0.108' | 0.323 | 0.3245 || 92.00 | 0.134 | 0.348 | 0.348

T = 85°.11
a =— 0.466 b=1.11
Poem le rcalc "found

80.0 0.164 0.516 0.513

100.0 | 0.446 | 1.27 1.265
120.0 | 0.942 | 2.49 2.49
140.0 | 2.0675 | 5.06 | 5.06

|
| |

As appears from the above Table 11, the values of a and 5 in
the several 7w-diagrams change with" the pressure. In each diagram
taken separately the agreement between the calculated and found
values is very good.

The result that the liquid-curve in the pz-diagram (especially on

893

the nitrogen side) is only very faintly curved *) had been found
before in a series of unpublished preliminary determinations and
may be looked upon as an indirect confirmation of our observations
respecting the vapour-pressures of nitrogen (IV. 2).

The pa-diagrams shows that especially on the nitrogen-side, the
values of the composition of the liquid and vapour phases do not
differ much from each other. This would lead to the expectation
that the fractionation, especially of the mixtures with little argon,
will not be a very easy matter.

When the change with pressure of the composition of the phases
is taken into consideration, it follows that the differences in com-
position increase with diminishing pressure, so that a comparison of
the 7-x diagram for argon-nitrogen at 76.0 ems with Baty’s dia-
gram °*) for the fractionation of air puts the problem of the frac-
tionation of the mixtures in question in a iess unfavourable light.
At the same time it follows from our results, that the use of mixtures
with little argon will give considerable difficulty.

Vil. Resumé.

1. A method was worked out enabling us to determine the
composition of argon-nitrogen mixtures with an accuracy of 0,1 °/,
or, if need be, higher.

2. A systematic difference was found between the results of the
determinations with the baroscope and the method referred to under
1, which led us to the conclusion, independently of Scnvurze’s work
(Le), that the atomic weight of argon hitherto assumed might not
be quite exact. As this systematic difference disappears when
SCHULTZE's value is adopted, the latter is thereby rendered highly
probable. A preliminary direct determination gave a value in good
agreement with Scnurrze's result.

3. New measurements of vapour-pressures for oxygen, argon and
nitrogen are published and critically compared with those of previous
observers. The triple point of argon was determined with greater
accuracy.

4. The end-points of condensation of the argon-nitrogen mixtures
were determined with an accuracy corresponding to 0.02° in the
temperature.

1) Pointing to a simple behaviour of argon towards nitrogen.
2) Phil. Mag. 49 (1900) p. 517.

894

5. At the points of beginning condensation the accuracy is about
the same. The saturated vapour-volumes are given.
6. The observations with the mixtures are compared with the

pv B
equation of state in the form ao (2 + =). The accuracy
v

in ES was found to be about 0,1 Pin
760

7. Within the range of temperatures investigated log p for the

; ; ; 1
mixtures can be represented as a linear function of me both for the

points of beginning condensation and for the end-points.

8. The pe- and P'z-diagrams are established. As regards the com-
position of the gas-phase (7) and the liquid-phase (r’) they were
found to satisfy the relation log r/ =a + blog r.

9. Conclusions were drawn from the shape of the curves in the
diagrams in connection with a possible fractional distillation of
argon-nitrogen mixtures.

We are glad to be able here to express our sincere thanks to
Mr. G. L. F. Pures for the unstinted support afforded to us by
which this investigation was made possible.

We also wish to record our cordial thanks to Messrs. W. Koopman
and J. ScrarP pr Visser for their zealous assistance in carrying out
the measurements and calculations.

Physical and Chemical Laboratory of the Philips
Eindhoven. Incandescent-lamp works Ltd.

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AMNH LIBRARY

00139160

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