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KONINKLIJKE AKADEMIE

VAN _WETENSCHAPPEN
:- TE AMSTERDAM -:-

PROCEEDINGS OF THE
See MON @r SCIENCES

VOLUME XVI
C= 2*PART — )

aS MULLER :—: AMSTERDAM
: AUGUST 1914 :

(Translated from: Verslagen van de Gewone Vergaderingen der Wis- en Natuurkundige
Afdeeling van 27 December 1913 tot 24 April 1914, Dl. XXII.)

CON THEN TS.

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KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEERTING
of Saturday December 27, 1913.
Vou XVI.

President: Prof. H. A. Lorentz.
Secretary: Prof. P. Zeeman.

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 27 December 1913, Dl. XXII).

GiOeN ae 2B ING ae Sr

J. W. vax Wisner: “On the metamorphosis of Amphioxus lanceolatus’’, p. 574.

J. G. Rurerrs: “Applications of Sonrr’s extension of ABEL’s integralequation.” (Communi-
eated by Prof. W. Karrryy), p, 583.

P. Eurexresr: “A mechanical theorem of Borrzmann and its relation to the theory of
energy quanta”. (Communicated by Prof. H. A. Lorenrz), p. 591.

FP. A. H. Semrememakers : “Equilibria in ternary systems” XT., p. 597.

HW. J. Hampurcer: “The effect of subcutancous turpentine-injections on the chemotaxis of
remote places.” (After experiments by Dr. J. Burrenuvis), p. 609.

W. UH. Anisz: “Adjustment to light in oats”. (Communicated by Prof. F. A. F.C. Wexv),
p- 615.

Ernst Conen and W. D. Herperman: *'The allotropy of copper.” J, p. 628.

Erxsr Conen: “The metastability of the metals in consequence of allotropy and its signi-
ficanee for chemistry, physics and technics”, p. 632.

A. J. P. van pen Broek: “On pteric sutures and pteric bones in the human skull. (Com-
municated by Prof. L. Bork), p. 634.

L. K. Worrr: “On the formation of antibodies after injection of sensitized antigens”. First
communication. (Communicated by Prof. C. Eraxman), p. 640.

Bucexe Desois: “On the relation between the quantity of brain and the size of the body
in vertebrates”. (Communicated by Prof. H. Zwaarpremaken), p. 647.

W. H. Kersom: “On the question whether at the absolute zero entropy changes on mixing”.
(Communicated by Prof. H. Kamertincit Ones), p. 669.

Hl. Kawerninan Onnes: “Further experiments with liquid helium. H. On the electrical
resistance ete. (continued), VIIL The sudden disappearance of the ordinary resistance of
tin, and the super-conductive state of lead”, p. 673.

H. Kameruincn Oxnes and Arnerr Perrier: “Magnetic researches. X. Apparatus for the
general cryomagnetic investigation of substances of small susceptibility”, p. 689.

A. Sits: “The application of the theory of allotropy to electromotive equilibria”. (Commu

nicated by Prof. J. D. van per WaAans), p. 699.

Proceedings Royal Acad. Amsterdam. Vol. XVI.

574

Anatomy. “On the Metamorphosis of Amphiorus lanceolatis”
By Prof. J. W. van W1JHE.

(Communicated. in the meeting of April 25, 1913).

Amphioxus still continues to be one of the most interesting objects
for the morphology of vertebrates, though the time is past in which
he was almost considered as their ancestor. It is now pretty well
generally admitted, that Amphioxus is not the grandfather of
vertebrates. It has appeared that his organisation deviates so strongly
from what must be regarded as the original type, that some morpho-
logists do not take him for a genuine grand-father, but for a step-
orand-father, who, in reality, does not belong at all to the family,
and only confuses its relations.

There have been morphologists, and perhaps there are still some,
whose theories appeared to be so much at variance with the orga-
nisation of Amphioxus, that they have proposed to strike him out
from the group to which vertebrates belong, and if they had been
able would willingly have brought him back to the group of snails,
to which Pziias in his time supposed him to belong, and for that
reason gave him the name of Limax lanceolatus.

Though these investigators could not deny, that Amphioxus is
affined to vertebrates, in order to save their theories, they were
obliged to declare, that this relation is such a distant one, that it
is certainly not necessary to make allowance for his organisation.

When however this organisation, both anatomically and embry-
ologically *), became better known, it appeared more and more
that Amphioxus shows indeed in many respects a very primitive
organisation, which must be taken as point of issue for that of the
higher vertebrates, whilst it presents, in other respects, such peculiar
phenomena, that these must doubtlessly be regarded as deviations
from types, that are represented among vertebrates.

I shall by-and-by discuss one of the most remarkable ie lations.
It is the placing of the mouth and the gill-slits in the larva before
the metamorphosis.

') How slowly our knowledge in this respect increases may appear from the
fact, that the celebrated morphologist Batrour was in 1882 still of opinion that
Amphioxus should possess no ventral nerve-roots, whilst, with regard to the
dorsal nerve-rools, one is still searching where the cells lie, which, in vertebrates,
form the spinal ganglia. 1 have discovered under the atrial-epithelium that covers
the liver, the intestine and gut an enormously large number of splendid multipolar
ganglion-cells, whose axis-cylinder runs along the dorsal nerve-roots to the
spinal cord,

After the expiration of the embryonal period one distinguishes
three stages in the development of Amphioxus: 1*t the stage of the
larval erowth ; 2nd the stage of tiie metamorphosis; 3'¢ the stage
of the postlarval growth.

At the beginning of the first stage the larva is 1 m.m. long; at
the end of it it has reached a length of between 4 and 5 m.m. At
the beginning of this period only the first gill-slit is formed, behind
it are gradually developed a second, a third ete. till a number of
14 to 16 is reached. All these gill-slits belong morphologically to
the left side of the body; those of the right side appear only in
the period of the metamorphosis. During the stage of the larval
growth constantly new muscle-segments (myotomes) are added to
the posterior part of the body, but at the beginning of the meta-
morphosis this number is already complete. The animal is then
only + to 5 m.m. long, but it posesses already the complete number
of 60 muscle-segments with the nerves appertaining to them, which
are also found in the full-grown animal which is almost a finger long.

During the comparatively long time of the metamorphosis, which
is divided by Wier into 8 subdivisions, astonishing changes take
place, not so much in the nervous or muscular system (with the
exception of the gill-muscles), but especially in the shape and the
placing of the mouth and of the gill-slits.

The animal does not grow during the metamorphosis, for its
length amounts, both at the beginning and at the end, to between
4 and 5 m.m.’). Differences in length do not indicate here a further
development. A larva that is half a millimeter longer than another
needs not be older than the latter, but is often younger. It has even
appeared to me that, during the first half of the metamorphosis, the
length rather decreases somewhat’ than increases, but the individual
differences are too numerous to state this phenomenon as certain. |
am of opinion, that the fact that the larva does not grow during
the metamorphosis, must be attributed to its not taking food during
this period. Presently I shall revert to the grounds of this.

Before the metamorphosis both the mouth and the gill-slits lie .
perfectly asymmetrically ; the mouth does not lie medianly and
ventrally as with all vertebrates, but on tke left-side of the body,
and of the gill-slits is only the row of the later left-side extant.
They behave very curiously, for they do not originate on the left-side,
but apparently in the median plane, whilst the foremost of the

1) Larvas from the neighbourhood of Messina are during the metamorphosis still

smaller. According to the statements of the authors their length amounts to an
average only to 3!/, mm,

Qn7™

of

row soon remove temporarily to the right-side of the larva. They
open freely outward and not in a gill-eavity or atrium, which is only
formed during the metamorphosis by the fusion of a longitudinal
fold, which has formed itself, during the larval growth period, on the
left-side of the body over the gill-slits with a similar fold, which has
developed itself on the right-side of the body.

During the metamorphosis appears likewise the right row of the
vill-slits 8, rarely 7 or 9, in number — which do not open directly
outward but in the gill-eavity. The slits of the left side, which had
temporarily removed to the right side, return now to the side to
which they belong.

f can confirm Wix.iny’s observation, that the first left gill-slit
aborts, and that also the 10% to the 16% disappear during the
metamorphosis. At the end of the metamorphosis the young animal
is then symmetrical with regard to the gill-slits, and there are 8 of
them on the left-side corresponding with the eight on the right-side.
It is of secondary importance that the symmetry is somewhat oblique;
every left gill-slit does not lie exactly directly opposite the right
one, but half the width of the slit more rostral. A similar oblique
symmetry is likewise shown by the nerves and muscles of the body
of the left-side compared with those of the right-side of the animal.

With the exception of the foremost slit, which remains undivided,
as long as the animal lives, each slit is divided into two parts, in
a longitudinal direction, by a clasp or “tongue” growing from the
dorsal rim, till it reaches the ventral rim with which it fuses.

Directly after the metamorphosis the animal possesses thus, both
on the right and on the left side, a row of 8 (rarely 7 or 9) gill-slits.
During the rapid growth that follows now, this number regularly
increases during the whole life-time of the animal, because constantly
au new pair of slits develop themselves at the hindmost part of the
oill-basket.

But afier the metamorphosis the mouth’) seems to be a symmetrical
organ; it is no longer situated distinctly on the left-side of the body
as in the larval growth-period, but more ventrally and almost halved
by the median plane as with all vertebrates.

The symmetrical placing of the gil-slits is real; since 1893 I have
demonstrated however that the symmetrical placing of the mouth of
Amphioxus is only so in appearance. In reality the mouth, also of
the full-grown Amphioxus. is an organ of the left-side; for its inner
parietes are exclusively provided for by nerves of the left-side, and

') Not to be mistaken for the mouth of the larva, see the conclusion of this article.

Lode
vii

its muscles belong all to those of the left-side. No nerve and no
muscle of the right-side tales part in the provision of the mouth-cavity,

Here we are in the presence of a remarkable phenomenon: ‘The
mouth of Amphioxus, as organ of the left-side, cannot be homologous
with the unpaired mouth of vertebrates always developing symme-
trically. and we must surmise that on the right-side of the young
larva a similar organ as the mouth, a counterpart of it, is found.
This organ is, as I indicated a long time ago already, the so-called
club-shaped gland and the mouth together with this gland form
morphologically the first pair of gill-slits of the Anmphioxus-larva,

Instead of gill-s/ts, it is more correct to speak of gill-pouches,
for in all vertebrates, without any exception, a gill-slit is formed,
because a pouch-shaped projecting part of the gut reaches the epidermis,
fuses with it on that spot, and afterwards splits to the outside.
With Amphioxus this is exactly the same; here also is every gill-slit
formed as a pouch-shaped projecting part of the gut, and _ splits
afterwards — before the metamorphosis — to the outside, after the
beginning of the metamorphosis, towards the gill-cavity (the atrium).
The epithelium of a gill-pouch can partly differentiate to glandular-
epithelium, in this way.e. g. in all vertebrates the thymus if formed,
a glandulous organ, from the epithelium of some gill-pouches.

The club-shaped gland possesses all the essential distinctive pro-
perties of a gill-pouch; it is formed on the right-side of the body
as a projecting part of the gut, which opens afterwards to the
outside and possesses then two openings one inside in the pharynx,
the other to the outside.

Though the greater part of its epithelium has differentiated into
glandular epithelium, IT found however laterally from it ‘a ring-
shaped strip of ciliated epithelium, corresponding entirely to. that
of the other gill-pouches.

The outside opening of the club-shaped gland is in the beginning
placed near to or in the median plane; afterwards it removes in
front of the mouth to the left-side of the body. This is again one
of the remarkable phenomena of asymmetry in the larva of Amphi-
oxus, the explanation of which I intend to give in my detailed
paper '), as it would lead me too far here. The club-shaped gland
disappears in the course of the metamorphosis, and does not leave
any vestige behind. :

Has the mouth of the Amphioxus-larva originally also been a
gill-slit? In my opinion there is no doubt about if. [It is true that

1) This paper was offered last winter te be published in the transactions ol
the Academy.

it does not originate as a pouch-shaped projecting part, but this is
impossible, because in the place where the mouth of the young larva
will open, the pharynx lies already directly against the epidermis.
Neither is a ciliated gill-epithelinm formed in this place, but one
has no right to expect it here, because the function of a mouth is
so entirely different from that of a oill-slit. On the other hand
the mouth possesses another lasting distinetive property, which is
peculiar to every gill-slit during the period of growth, but disappears
from these slits in the course of the metamorphosis. I found namely,
that each gill-slit of the young larva is accompanied in front and
behind by a strong gill-muscle, the fibres of which, for the greater
part, run in a transversal direction with regard to the axis of the
body. Some fibres however, surround the outside gill-opening and
form a sphincter round if.

The mouth-opening is likewise enclosed by two such muscles.
They degenerate also, but they are not lost without leaving a trace,
as the gill-muscles proper. but produce the lip-muscles and the
ring-shaped sphincter of the velum.

Mouth and club-shaped gland are counterparts, for they originate
“one under the second myotome of the left-side, the other under the
second myotome of the right-side of the body.

In vertebrates the first pair of gill-slits originates nearly under
the second myotome, of which in the head of Selachians nine are
formed, as | demonstrated more than 30 years ago for the genere
Seyllium and Pristurius '). In Selachians the first gill-slit does not any
longer function as such either; in rays it serves to admit instead of
to let out the respiration-water, and in some sharks this slit, known
by the name of spiracle, is shut by the fusion of its parietes. The
mouth of Amphioxus is, according to what has just been seen,
homologous with the left spiracle of Selachians, and serves, just as
ii rays, to ingest the respiration-water, but this water contains here
the necessary nutriment for the animal.

If now the mouth of the Amphioxus-larva was originally the first
gill-slit, then a primitive mouth, homologous with that of vertebrates,
must have been extant before this secondary mouth.

This primitive mouth is, in my opinion, represented by the opening

') Braus pretends that not 9 but at least 11 should be formed. A repeated
investigation, which will be published afterwards, has taught me that my number
9 for Seyllium and Pristurius is correct, and may be admilted as the normai one
for Selachians. In some genera however vertebrate elements fuse secondarily with
the skull,

579

of the so-called praeoral pit, which is formed as a sejoined part of
the pharynx and soon opens to the outside.

In aceordance with this view is the place where the thyroid
gland of Amphioxus originates. In all vertebrates this gland is formed
as a median outgrowth of the epithelium of the pharyna immediately
behind the mouth, between the first pair of gili-slits, if they are
taken as fused with their ventral extremities. If now we see in the
mouth of Amphioxus the homologue of that of vertebrates, then, in
an incomprehensible way, the thyroid gland of Amphioxus would
be formed in front of the mouth instead of behind it.

What explanation can now be given of the fact, that Amphioxus
has lost its primitive mouth and has obtained secondarily the first

gill-slit as mouth, whilst in the stage of the larval growth — now
letting alone the club-shaped gland — not the gill-slits of the right-
g I : g g

side, but only those of the left-side open to the exterior and moreover
in the median plane, whilst they even partly remove temporarily
to the right-side?

The key to this explanation is, in my opinion, to be found in
the movement of the young embryo which has been observed by
Harscurk. This embryo moves, turning on its longitudinal axis,
helicoidally forward; the rotation takes place from right to left.

If now one admits that ancestors of Amphioxus have moved
forward in this way, to which they may have been induced, because
they missed an auditive or equilibrium-organ, the trace of which
does not even appear in Amphioxus, then it is to be understood
that the left first gill-slit must have bad the predominance over the
medianly placed primitive mouth as opening for the admittance of
water, which must serve at the same time both for respiration and
for nutrition. The following gill-slits had to evacuate the respiration-
water, but this evacuation was for the slits on the left-side impeded
by’
from right to left, the following gill-slits on the left-side would be

the way of moving of the animal. On account of the rotation

inclined to ingest water instead of evacuating it, and therefore
they were obliged to remove from this side to the median plane,
or still better to the right-side, where the evacuation of the respi-
ration-water was exactly facilitated in consequence of the movement.

By this removal, however, came the original gill-slits of the right-
side in a tight place; they remained little, and this is the reason
why in the Amphioxus-larva, they appear only in the period of the
metamorphosis.

When later ancestors of Amphioxus gave up their swimming way
of living and buried themselves into the sand, as he does still now,

d80

fo dash forward from it with the quickness of an arrow, when he
is disturbed, and then fo return immediately again into the sand,
ihe reason for asymmetry did not exist any longer, the gill-basket
became symmetrical again, and the mouth also tried to assume
a symmetrical position, though if could only apparently suceeed in
it, as it is an organ of the left-side.

It is not to be wondered at, that there are investigators who
oppose these views, because they cannot admit that such an ancestral
organ, as the primitive mouth, should have had to give way to a
secondary mouth. They admit, that ancestors of Amphioxus, which
gave up the swimming way of living, have first passed through a
period, in which they lay on the sand in the way of flat-fishes in-
stead of burying themselves into it ; that then the mouth has removed
to the left side, just as, with flat-fishes, one eye, which otherwise
would be direeted downward to the bottom of the sea, removes to
the upperside.

This theory is untenable especially for three reasons :

d'y. The mouth of the Amphioxus-larva does not originate
medianly to remove afterwards to the left-side. It originates on the
contrary on the left-side to take afterwards a pseudo-median position.

2ly. There is no reason why a median organ, when removing to
the left-side should lose its nerves and muscles of the right-side.
Not a vestige of such a phenomenon can e.g. be discovered in the
heart and the stomach of man, which are for the greater part
situated on the left-side.

3. One of the characteristic properties of the second myotome
of Selachians is the facet, that its cavity remains, for a long time,
in communication with the part of the body-cavity that is situated
in the lower jaw and is*known by the name of mandibular cavity.
This communication continues fo exist for a lone time after the
cavities of the following myotomes have sejoined from the body-
cavity.

The same is the case with the larva of Amphioxus, and in order
to make out, whether the mouth of this larva corresponds, either
with that of vertebrates, or with their foremost left gill-slit, one
need only state, whether the mandibular cavity of the Amphioxus-
larva is situated before or behind the opening of the mouth.

On the base of investigations of GonpscuMiprt made on an_affined
larva, called by him Ataphioxides, (and in the beginning supposed
to be a developed form) I surmised at the time, that I could solve
this dilemma in the sense that really the mouth of Amphioxides
lies behind the mandibular cavity. In a later publication GoLpscnMipT

581

has not contradicted this conclusion, but Mac-Bripr asserted in 1909
that in the Amphioxus-larva the mandibular cavity should lie behind
the mouth. When I had the privilege of receiving a few years ago
Amphioxus-larvas from the Zoological stations at Naples and = in
Helgoland, my attention was specially directed to this point, and
I found in all the series of my sections of the larval growth-period,
but also in the beginning of the metamorphosis, that the mandibular
cavity does not run behind the mouth-opening, as Mac-Bripr asserts,
but before it. In| my opinion it has hereby been definitely proved
that the mouth-opening of the Amphioxus-larva is homologous with
the left spiracle of Selachians.

In the course of the metamorphosis the mandibular cavity develops
round the mouth, first in the shape of a horse-shoe and after-
wards in the shape of a ring, because the extremities of the horse-shoe
unite themselves with each other behind the mouth and form the
ring-shaped cavity of the velum. As soon as this cavity has assumed
the shape of a ring, one can of course no longer see, whether it
was situated originally before or behind the mouth.

Finally I may be allowed to give a short communication of the
remarkable variations which the mouth of the larva undergoes, of
which we know already from Harscupk that it invaginates to the
inside und transits into the ring-shaped »velum-fold, which, in the
full-grown animal, separates the mouth-cavity from the throat
(pharynx). This invagination is accompanied, during the metamor-
phosis, by the formation of a longitudinal fold of the skin, extending
along the left side of the mouth of the iarva and of the praeoral pit.

Hereby is formed an open cavity before the mouth of the larva:
the mouth-cavity of the full-grown animal, in which likewise the
praeoral pit is lodged, and which, by a longitudinal slit alone which
the cirri sprout forth, opens to the outside. This slit is known
as the mouth-slit of the developed animal.

At the end of the embryonal period. when the larva is only
1 mm. long, and the first gill-slit is on the point of opening to
the exterior, the mouth is a little almost round opening on the
left-side of the body under the second myotome. It lies then oppo-
site the club-shaped gland, which is found under the second myotome
of the right-side.

With the growth of the larva the mouth-opening, which is now oval
and becomes afterwards slit-shaped, increases giganticly in length.
When three gill-slits are extant, the mouth reaches as far to the
back as the baek-rim of the first slit, and at the end of the larval
growth-period it reaches even the back-rim of the fourth ov fifth

582

vill-slit. This gigantic enlargement?) of the mouth indicates that the
larva, during its growth, must be a very gluttonous animal, if the
words gigantic and gluttonous may be applied to an animal that is
not even 5 m.m. long. The gluttony is also of a very inoffensive
nature and consists in swallowing water, for only minimal remnants
of food are found in the gut.

During the metamorphosis remarkable modifications oeeur at the
mouth of the larva.

One modification regards its size. In the first half of the period
of metamorphosis the gigantic mouth becomes constantly smaller,
(ill, in the middle of this period, it is an extremely little round
hole. But for a little sickle-shaped slit this hole is moreover closed
by the formation, at the rostral rim, of the first tentacle in the
shape of a little tongue.

Now the falling asunder and the resorption of the gill-muscles is
in full swing. The fibres of these muscles let loose from their
insertions and have partly been broken into pieces. Just like the
loosened cells of the club-shaped gland these pieces float in the
fluid that is found in the body-cavity.

From this phenomenon, from the cessation of the growth and
from the minimal size of the mouth I deduce, that the animal
ceases to take food from outside, and continues to live at the
expense of part of its own texture: the gill-muscles and the cells of
the club-shaped gland.

Obviously the gill-muscles bave become superfluous, in conse-
quence of the formation of the atrinm, which now regulates for the
ereater part the movements of respiration. No trace of gill-muscles
appears at the slits of the right-side of the body, which never open
directly to exterior, but only indirectly by means of the atrium.

In the second half of the metamorphosis the mouth enlarges
again gradually, and becomes the opening of the ‘‘velum”, round
which three more tentacles develop, completing the number of
four, which this opening is provided with.

The diminution of the mouth has already partly been observed
by Leeros, but vehemently contested by WiLiey, who supposes this
diminution to Le only apparent, an optical effect, caused by the
rotation of the mouth on a sagittal axis.

According to Wittny, who does not base his views on the study
of sections, but only on that of the larva in foto, this rotation should
commence already at the beginning of the metamorphosis. I found

1) This enlargement of the mouth contributes to the temporary removal of the
foremost gill-slits of the left-side to the right-side.

583

however that this rotation, which is incomprehensibly denied by
Lecros does not set in before the mouth has reached its minimal
size, consequently in the middle of the period of the metamorphosis.
In consequence of this rotation the rostral rim of the mouth of the
larva becomes right-rim, whilst at the same time the posterior rim
becomes left-rim.

The mouth-opening having become velaropening lies now sym-
metrically with regard to the median plane, but the nerves, that
surround it, indicate that if continues to be an organ of the
lefiside.

In the higher animals the middle-ear originates from the first
gill-pouch, whilst amphioxus lacks the auditive organ entirely. If
we wish to express ourselves in a popular way, we may say, as
I did already on a former opportunity: Amphioxus cannot hear;
he eats however with the teft ear, and has consequently lost the
mouth.

Mathematics. — “Applications of Soninv’s extension of Apet’s
itegralequation.” By Dr. J. G. Rurerrs. (Communicated by
Prof. W. Kaptryy).

(Communicated in the meeting of September 27, 1913).

Sonne") has given to Apen’s integralequation an extension which
comes to the following.
The unknown funetion w in the equation

fa) = | UTC ==) ) (ces) che ein Paerenee es (lice)
a
is determined by
1) == foe §)/ '(S)d§ . Sl alae | Souls (2a)
e
a
where we suppose fo) to be finite and continuous, /'\r) finite,
as<a<bh, and f(a) =0. Moreover 6 and yp are connected in the
following way :
Suppose
Cy) = eon yin Se ue
0 gy) 0

1) Acta Matem. 4; 1884.

584.

then if

Cm dy
n= = = oo -
. T(m—A +1) I'(n-+-)
we shall find
2. yo cor
Ap (@) Sa —* = ayy a” and o(2) = «#—U—) > by, 2",
0 0

and at the same time we find 2 bound to the condition 1>4>0.

This vather intricate connection between yw and o greatly limits
the number of applications with some practical significance. As a
matier of faet Soninn gives two, for the third furnishes nothing new

as we shall see.
1. Apen’s equation appears when in (la) we take: yp (e)=
1

—=—(1 >A4>0). By this a,=1, a,=0(@u> 9); “by ‘whieh

¢, = TA—A+), cn =O (m > 0) and therefore
(y) I(1—A) :
gy) = —7fl : es
AC (U2)
furtheron
1
a — c a || 0
" I'(1—2) i Bree)
and therefore
1 sin Ax

b, = ——— — 5 ee (0) 0).
= Playray eae Cee)
Finally follows:
sin Ax 1
o(«) = ——_ . ——..
iv avila

Substitution of yw and 6 in (1a) and (14) now gives us:

ale Bae GHG

f(a) = | AS) as aye =| SG
J (@—8) x J (ws?
a a

2. For the second application Sontne starts from *) :

a fi © ; i: stele):

q(y) = PU—Ae + = r—4 FS — see

'
i) m.

em (2) cart’ yr

; thus @,,—= Rie
m! ia ( m! 1 (m—A +

so that

Cy == M(1—aA)

1) The factor f (1—.) is added for practical reasons.

]

by which
2Va 2m
E (—n(%
OSS mae ar
w(2) ( m 0 m! P(m—2A-+-1)
Further we tind
f @)
ail!
ere aS
Cree

1

Omen

so that

thus

by whie

6 (w

(1

2|&

Cy

n! P(n+2)'

sin Ae I(A)

9

1
T(l—A) "nl T(e+))

by, —
h
eVarvn
sin dr 1'(a) ei OL
(es f=
J o nT (n+A)
1—
ZN =e esas F
(=) Vv eel ry) (iz Vi).
(la) and

6) pass into

f(«e) = r—iy(

with
il— sin Am I(A)

u(v)—= ——_———___—_
fy

—

For

__ tl sin Ax V'(A)

By substitution of these values of w and o we see that

follow from
already noticed. The forms of ABEL appear when we take

ig
(Su)

4

J fea a (ey ences

this some important relations as SONINI

MN l—,
aoa (0 ome ED rca aN
G) fw —§) [jj (2@V w—S) 7s (S)ds. (36)

TV (m—a-+1)
a ( ; ae (zy) ‘

0

——()

3. As third application SONNE gives:

g (y) = P(l--4) A 42y)- 0) = S (—1p

by which

586

P' (m—a--1) (—1) zm
i (ll) - en, Qy S “-
m. mi!
thus
Pr, (zx)m ema
. = OSS lyn xe
w (x) t : ( ) ae =}
Further ensues
1 1 Kl ce (n+ cates
= — (1 +-2y)! fs = = > ( {yn f (2y)".
gly) P(l—A) M(1—2) F(a) 0 n!

so that
q ae ee (—1)" P(n-EA—1) ; (A= 1) sind or (1)? 2”
i —— “a Th = gi >on

ka 4 n- fd nl Te Sa
and therefore

(A—1) sin hx ay = Ge G 1)r (G ww)"

6 (x) = —

EL 4 0 nt(n-+a—1)’ a
to which Sonine gives another form, which is, however, not correct.
It would be better to write for it:
sin da 1 n oh ane) :
O(a == - — (1 =) S(—1)r he At ee ;
ae al—) 1 nl (n+A—1)_

for indeed it is now again evident that for =O we find yw and o
assuming the form as in § 1.

Substitution of y and o in (la) and (16) (Sonne leaves this out)

now gives:
x

Bods
e—Ar—5

(@ =| Vig (3) Ne I ermecoL oe ee fo (210
J (2) =e (s) (da)

a

sin ha 7 fF 6) - 1—A) sinha 4
u(y [a eae "(sa
by ae

s)' = sf

a -Ajner(w- Sy | Ue

niapa—ly \

my nt (n4+-2—1)

a
As 1>4>0 and f@=0, we find that by means of partial
integration the last integral, passes into :

a

w—eé n—-).—2
froze 1)" 2s ee

n!
so that
sin dx (° f'(§) _ (l—A)sinda (e—2-—1
u(x) = - —_ d§ — ——— : elds le. (4a
Oe es ee ee

That (4a) and (4/) do not stand for anything new, we shall
immediately see by substituting

587

FT (e) = (Caf, (w) and w (w) =——Cme™ 0,1 (2) \ 5
where (4a) takes at once the form of ABgEL’s equation and (4)) as
its solution can easily be reduced to its ordinary form.
In the following paragraphs we: shall be led to really new appli-
cations.

4. Let in the first place

1—)

AGL aT TO
gy)=T (1-A) (1-277?) 2 = To (-—1)" ; (ey)2",
—h 0 m:
Fi (ee
Ca)
where, by application of
Va
(a) (a+ +) = sarc o LINE) a GMa BS ono 115)
we find that
7) 2 1—2
ri P{ m+
= : . =) ——— =z gm, C5,,21a 0
: PA VAs 4 ( ) mit Pe

A 1—a
r( — =| yf (» + =)

am = - i( 1) Ly

WY 2 m! T(2nm—Aa+1) 2

$—$—____— - 4 Gm) = OF

so that:

zu \2m
r ——)| m Aa 5
Ts \ EDs ( ( 2 ) h ye
aN (ce) ed = > —— ———————— (1 ( Ie x (zx)
a 0 Zl 2 2x =
mir( — + 1) %
2
Furthermore we find

1-1
1 1 Is I = r(- 5) )

SSS USE) . 2(-1)r———_ — ey)2”
gy) TA) "| ae rasan") fae

by which, on account of (5):

588

: 2 1-a
(A—1) r(=) Ree r(— )
es Pa SU AT (= 2

a e a A = I) = moo — gn , day4 =)

be, — = 7 ae : aa ( —] ) = —_————.g2n —
22“ ax 4 n! P\(2n--A)

so that

9
a

A\ sin ax Pa (¢ ) wens —1
: eS (— 1)n Se See aT

O(v) = (Aa—1) r(

2, Lyn <—__.. —__
a, I ( ) 2 2n+2—1
nl In + 7

For z=0O we are evidently again in the special case of ABEL’s
problem (§ 1).

2 \2n
sin Au i “ A\ snka (5) ants 1
- ; D7 be :

Let us now substitute y and 6 now found in (1@) and (10), we
then arrive at the integralequation

ih aN fe :
f= r(i— =)(4) fo-9 21; fo(a--8)} ul) a8, (Ga)

to which belongs as solution:

sin Ax a S
u(e) = pe = | I (s) i
7 « (a — l

ae : ; 7 ; = z\2n
sin Aw (1L—A) I @ os | %. G) (w—§)24+—1
2 a 11 S75

7 6a\%
= fv (S) a ( ) ( on +i—1
ni IY n + a5

As 1>2>0, f(a) =0 and /(x) is finite the last integral passes
by means of partial integration into

e
a

89

(2) eames)
nl r(. ~ 3) \

o

{ f@& |= (yp
re: 1
a

so that we find

sin ho pr(e :
u (z) = ea Fs) de
14 ( r —§)!~
: >
: (60)

x we
sind (1-2) A (2 3 S/o oaa\
= ead | |) (5) (an (a-§ § (w—E)? (na 1s F

5. In a similar way we find by starting from

h
2 mn I Be i =
oS OP =A), 2 (w+ 2

=| :
gy)=T(1-A) (+277?) 2 = en ae ST (ey)?
0 me é
ies
2
and
PF A 1
1 1 ES if ® ee oa: :
v0) ra Hoe? : a EE Perna le
NY, = \ }
GY) r(1-a) (5-1) 0 U
successively
1—

I= -AN 2 (202
ap(z) = (| oi: (“) 7 4) (zz),

~ \2n
sin At 1 aie A+1)\ sinda 2) (3) gen+r—l
——(Z-2) — }—— (-1)rp——
wv

2n-+- 4-2

d
: tr (wint)

We can again notice here that for z=O the special forms appear
as with ABEL’s problem.
Substitution in (1a) and (14) furnishes the integralequation

4 1 (2G ga “ Bee yee
he) = { 5 lta) fe-s 2 Lip 2 (w—§)} u(§)ds, (7a)

with its solution ;

6(@) == a 5

Proceedings Royal Acad. Amsterdam. Vol. XVI.

x.
sin Ae

u(av) =

a

590

I'(S)

x J («—s)'—
a

|e iy be)

ds —

get |

sin hex (2- }) (- aay
pene! yas. 1 aay;
= 7 ur(n4t) i \

of which the last integral can be brought by partial integrating into

the form:

5 (2n + 2—1) (a — §)22+-2

frau AS 1) ——

a a Pan
e | ; n! r(o 4. es )
z\2n ;

Wee Okaas
a

= (—1) ce
: nt r(n4 5)

ie (w

2n + 24 — 2

ot §)2n+4—2

n+ ——

by partial integrating the last part we find for it,

f\-) (2) =[ f © 46:

zr

a

lie

= (—1)"-

fe nt r( +

( a

1)

?

if we put:

Summarizing we arrive at the following form for the solution

of (7a):

x
snk at i § :
= \eaar

a

bs aaalt
(e—§)2

(1)
pe) +2 a

-
=

/

591

Physics. — “A mechanical theorem of BourzMann and its relation
to the theory of energy quanta’. By Prof. P. Kurenresr.
(Communicated by Prof. H. A. Lorentz).

(Communicated in the meeting of November 29, 1913).

When black or also not black radiation is compressed reversibly
and adiabatically by compression of a perfectly reflecting enclosure,
it is known that the following takes place: The frequency », and
the energy £, of each of the principal modes of vibration of the
cavity increase during the compression in such a way that we get:

Ep
P

for each of the infinitely many principal vibrations.

Relation (1) is of fundamental importance for the purely
thermodynamic derivation of Wien’s law; it is no less so for every
Statistic theory of radiation, which is to remain in keeping with
the second law of thermodynamics'). In particular it is also the
basis of PLaNnck’s assumption of differences of energy : *)

Es OU edhe Nady Sp to, aon a ase, (2)

Y

Of late PLanck’s supposition (2) of the original region (Conient
of energy of systems vibrating sinusoidally) has been applied to a
rapidly extending region. Of course tentatively. Two questions arise:

1. Does there continue to exist an adiabatic relation analogous
to equation (1) in the transition of systems vibrating sinusoidally
(in which the motion is governed by linear differential equations
with constant coefficients) to general systems ?

1) P, Enrenrest. Welche Ziige der Lichtquantenhypothese spielen in der
Theorie der Wirmestrahlung eine wesentliche Rolle? Ann. d. Phys. 36 (1911)
p- 91; § 5.

2) By way of elucidation: differences of energy e. g. of the form

&
= — OF hy Oly as
v
would lead to a conflict with the second law of thermodynamics. It is known
that PuancK arrived at (2) by first carrying out his combinatory calculation in

general on the assumption
nD) go FU) 6 BO) nae
and by then determining the form of f(v) from the condition that the formula of
radiation found by the combinatory way shall satisfy WiEn’s law. Thus he brought
his energy quanta implicite in harmony both with relation (1) and with the second
law of thermodynamics.
38%

592

2: If sso how ean it be applied heuristically, when PLAaNck’s
assumption (2) is extended to systems vibrating not sinusoidally ?

The answer to the first question is in the affirmative. In the
search for the extension of the adiabatic relation (1) I perceived
that such an extension, and indeed a surprisingly far-reaching one,
follows immediately from a mechanic theorem found by BoLrzMaNnn
and Craustus independently of each other (see § 1).

For the present I can only answer the second question by giving
au example (§ 3). The difficulaes which in general present them-

selves in this —- Prof. Einstein drew my attention to the most
troublesome one (§ 4) in a conversation — I have stated in § 2,

3, 4, without being able to remove them.

Another objection may be raised against the whole viz.: there is
no sense — it may be argued — in combining a thesis, which is -
derived on the premise of the mechanical equations with the anti-
mechanical hypothesis of energy quanta. Answer: Wirn’s law holds
out the hope to us that results which may be derived from classical
mechanics and electrodynamics by the consideration of macroscopic-
adiabatie processes, will continue to be valid in the future mechanies
of energy quanta.

§ 1. Let g,,---, q be the coordinates of a mechanic system.
The potential energy ® may depend, besides on the coordinates q,
also on some “slowly variable parameters” 7,,7,,... Let the kinetic
energy 7’ of the system be an homogeneous, Guadratie function of
the velocities g,, and contain in its coefficients besides the q’s, even-
tually also the 7’s.

Let further the system possess the following properties : For definite
but arbitrarily chosen values of tle parameters 7',, 7,,.... all the motions
of the system are periodical, no matter with what initial phase
(Qise) Un. Pry» Pn) the system begins. The period P will in general
not only depend on the values of 7,,7,,..... but also on the phase
(Jo: Po)s With which the system begins.

By changing the parameters 7,,7,,..... infinitely slowly we can
transform every original motion (A) of the system into another (Bb).
This particular mode of influencing the system is called “adiabatic
influencing’ of the motion.

1?

If moreover the respective periods of the motion are indicated by
P, and Pp, or their reciprocal values (the ‘“frequencies”’) by va
and rp, and further the temporal mean of the kinetic energy by
Z'4 and Z’z, then

Ti 7
a) =i) Thee ae ate Ee)
VIA VD/B

With adiabatic influencing of a periodic system the quotient of
the temporal mean of the kinetic energy and of the frequency
remains unchanged (adiabatic relation).

If Jd’ denotes an infinitesimal adiabatic change, P the original

period, then :
T aP
a la Ge Ol ED)
v 0

(The action calculated over a period remains constant on adiabatic
influencing). The last assertion is nothing but a special case of the
thesis of Bottzmann, Craustus and Sziiy, the derivation and formu-
lation of which may be found in Bonrzmany’s “Vorlesungen iiber
Mechanik’’, Vol. II, § 48. *)

§ 2. Remarks.
a. In the ease that there is no potential energy at all in the system,
or that the potential energy is in a fixed ratio to the kinetic energy *),

E
a(S) =0 de GG 16te Sco cae at ror re Aaa)
>

holds at the same time as equation (//) (compare equation (1) for
systems vibrating sinusoidally). But it is noteworthy that (//’) only holds
in such particular cases, and is not of such general application as (//).

b. A practical extension of thesis (/) to non-periodical motions

the relation

would be very desirable. That if is not at once possible, follows
immediately from early investigations by Bonrzmann*). [| prefer not
to follow the way which Bo.itzmMann chose to extend his thesis to
non-periodical systems *), because it essentially rests on the untenable °)
hypothesis of ergodes.

c. In case the adiabatic influencing leads to some singular motions,
in which a periodic motion begins to detach itself into two or more
separate motions, assertion (if) must be modified accordingly.

1) Original papers: L. Botrzmann, Wissensch. Abh. I. p. 23, p. 229. R. Crausius,
Pogg. Ann. 142 p. 433. Samy, Pogg. Ann. 145.
2) »=T7' for systems vibrating sinusoidally, when the potential energy in the
state of equilibriam is taken zero.
~ 3) L. Botrzmann, Ges. Abh. IL p. 126 (1877); Vorles. tib. Mechanik If § 41.
*) Ges. Abh. Il p. 132, 139, 153.
») P.u. T. Earenresr Mathem. Encykl. 1V. 32 § 10a (Rosenruat, Ann. d. Phys.
42 (1913) p. 796; M. PLancnerer, Ann. d. Phys. (1913) 42 p. 1061.

594

Example’). Let a point move to and fro free from forces ina
tube closed on either side. Let a repulsive field of force arise and
increase infinitely slowly in the middle of the tube. At last a moment
comes when the point with its store of kinetic energy cannot get
any longer through that ‘wall’, and only moves to and fro in one
half of the tube. If this field of force is of infinitely small extension,
the kinetic energy of the motion is the same at the end as at the
beginning ; the frequency on the other hand is twice the value, for
the path has been halved. Accordingly the original motion has split
up into two distinct separated branches during the adiabatic influencing.

§ 3. An example may illustrate the way in which the “adiabatic
relation” I may be applied. This example refers to the extension of
PLANcK’s assumption (5) from resonators vibrating sinusoidally to
rotating dipoles.

A fixed dipole may be suspended so that it can revolve freely
round the z-axis. Parallel to the z-axis a very strong directional
field is made to aet. We first consider infinitely small oscillations
of the dipole. The angle of rotation may be denoted by g, the cor-
responding moment (moment of inertia X angular velocity) by p,
the frequency of the oscillation by »,. According to PLanck’s
assumption (2) the image point (q,p) of sach a dipole can lie
» nowhere else in the (q,p)-plane than on certain ellipses, which

belong to the quantities of energy O,dy,, 2hy,,.... and for which
therefore :

iE Lan h aL h

= ea: 9° “9? ® (el ovieise hee Ss . . . (3)

We have namely (sinus vibration !):

The infinite number of points of rest and equilibrium :

p10 Gi) star) Ste aes Sedo ao
belong to the value of the enersy ¢ == /0!

Some congruent ellipses, which have these points (5) as centres,
belong to the value «= nhp,.

We now consider an adiabatic influencing of such an_ initial
motion of the dipole by an infinitely slow change of the orientating
field of force, and eventually also of the moment of inertia. In this
Way if is possible to convert the infinitely small oscillations into

') Mr. K. Herzrerp gave this example on the occasion of a discussion.

ogo

oscillations of finite amplitude, till at last the dipole changes its
form of motion and begins to rotate to the right or to the left; at
first still noticeably irregularly, at last with constant velocity of
rotation. When we consult Fig. 1, the continuous change of the
motion will become clear, particularly also the transition through
the singular motion GH. A complete oscillation corresponds in the
final state to a double rotation of the uniformly rotating dipole

(O<q< 4a): ABE. Hence if we wish to derive the kinetic energy
T, of the uniform rotation by the aid of the “adiabatic relation”
from the mean kinetic energy 7’, of the original oscillatory motion,
we must take as corresponding period the time

gr Re CO CMR umes = Se Reina (0)

where g, is the constant velocity of rotation of the dipole ; so as
corresponding frequency

Then according to (7) (I) and (3), we have

i 4nT, 7 h h h
a fd OG A ar bs La Cece (Sh)
vy /, h vy}, 2 2 2

or also, as

ioe ale) 22 ee)

5O6

vee ee rerak (10)")
Pi {or da La HE

If other values of p were admitted for a uniformly rotating dipole,
it would be possible that by reversal of the described adiabatic process
sinusoidal vibrations were obtained, with an amount of energy which
would come in collision with PLANOK’s assumptions (3) and (2).

If we have .V dipoles, and if with given total energy, we wish
to caleulate the “most probable” distribution of the dipoles over the
possible motions (10), it is still to be fixed by definition to what
regions’ in the (q,p)-plane the same probability must be assigned.
By the “adiabatic influencing” every separate ellipse of PLANck’s in
the (q, p)-plane passes finally into a definite pair of straight lines of
the length of 22, which le symmetrically on either side of the
g-axis. If in the statistic treatment of dipoles vibrating sinusoidally
with PLanck we consider all the separate ellipses as regions of
equal probability, we are naturally led to treat the just-mentioned
pairs of lines for the uniformly rotating dipoles as regions of equal
probability *) (Hypothesis A). However natural this may be, yet it
is a new hypothesis. Is this hypothesis inevitable ?

Seemingly the following course is open. Let us start from
dipoles vibrating sinusoidally (frequeney »,), which are distributed
over Pranck’s ellipses in the most probable manner. Apply the
above-described ‘adiabatic influencing” to all the poles at the same
time. Then an entirely definite distribution of the -dipoles over
the different modes of motion is obtained finally (10). This distri-
bution (distribution 4) is, however, another than follows as the most
“probable” from the hypothesis A (distribution A). Is distribution. 6
to be taken as the distribution which corresponds with the state of
equilibruim, and is therefore the distribution A and the hypothesis
A to be rejected? The remarks made in the following § try to
demonsirate that the distribution B cannot be considered as a distri-
bution of equilibrium.

§ 4. In case of adiabatic compression black radiation is trans-
‘) In my monograph: “Bemerk, betreffs der specif. Wirme zweiatomiger Gase”’,
Verh. d. deutsch. phys. Ges. 15 (1913) p. 453, I have erroneously put:

ee SO p= eee

This, however, has no further influence on the derivations given there than that
the numerical value of the moment of inertia J, of the hydrogen molecule calculated
finally must be divided by four.

®) P. Enrenvesr. Bemerk. betreffs der specif. Wiirme zweiatomiger Gase. Verh.
d. deutschen phys. Ges. 15 (1913) p. 453.

formed into black radiation as well when there is a “black grain”
in the contracting reflecting enclosure, as in the absence of such a
“eatalyser”. Else we should get into collision with the second law
of thermodynamies.') If there are Vo monatomic molecules in a
vessel with rough walls, distributed according to Maxweni’s law,
and if this ideal gas is compressed by an infinitely slow shifting
of the walls of the vessel, the distribution finally follows again
Maxwei’s law, both when the molecules during the compression
ean collide,~ and when they could penetrate perfectly through each
other. Probably more examples might be found in which through
an “adiabatic influencing’ of the separate degrees of freedom a
state of equilibrium arises from a state of equilibrium.*) But in
general this is not the case, e.g. for molecules consisting of more
than one atom or for mon-atomic molecules on which an external
field of force acts. *)

Chemistry. — “Hquilibria tn ternary systems. XI?’ By Prof.
q Y sy: y)
F. A. H. ScHREINEMAKERS.

In all our previous communications we have always contemplated
the case that the occurring solid substances are ternary compounds.
Now we shall assume that a binary compound occurs.

It is evident that we may deduce the saturationcurves under their
own vapour-pressure and the boilingpointcurves of a binary compound
in the same way as has been done in the previous communications
for a ternary compound.

We take a compound composed of B and C, we represent this
in fig. 1 by the point # on the side BC of the components-triangle
ABC. We now take a definite temperature 7’ and a pressure P in
such a way, that no vapour can be formed and the isotherm consists
only of the saturationcurve of /’. This is represented in fig. 1 by
curve pq.

On decrease of P, a gasregion occurs somewhere and also the
region —(, which separates gas- and liquidregion from each other.

1) M. Pranex, Wiirmtestrablung Il. Aufl. § 71.

*) The two mentioned cases have this in common that the pressure only depends
on the total energy of the system, and not on its distribution over the different
degrees of freedom

3) In an analogous way we can see that a canonical ensemble of gases
“ec

generally does of remain canonical after an “adiabatic influencing”.

598

These regions may arise either any-
where within the triangle, or on one
of the sides or in one of the angular-
points; in fig. 1 we may think them
arisen in the angular-point C.; Also two
or more of these regions may be formed
in different points of the triangle and
they may come together later in diffe-
rent ways.
‘A We will distinguish now three prin-
Fig. 1. cipal cases according to the phenomena
in the binary system BC.

I. The equilibrium liquid-gas of the binary system BC’ shows
neither a maximum- nor a minimumpoint of pressure. The pressure
of every liquid consisting of B and C’ is situated, therefore, between
the pressure of the pure substances B and C.

II and III. The equilibrium liquid-gas of the binary system BC
shows a maximum- or a minimumpoint of pressure.

We take at first the case mentioned sub I; we assume, for fixing
the ideas, that the pressure decreases from C' to B. The result of
this is that every heterogeneous region L—G, at every temperature
and under every pressure, intersects only once the side BC (fig. 1)
and that this region on decrease of /P with its liquid-line ahead
moves along BC from Cto 6. Of course it is indifferent, where the
gasregion and the region L£—G' arise, on condition that this does
not occur in a point of the side LC (excepted in Citself). Decreasing
the pressure, a pressure Py, occurs, under which the liquidcurve of the
region LG and the saturationcurve of / obtain at first a common
point; we shall call this point J/. Py, therefore, is the highest
pressure, under which the system /’-++ ZL -+ G occurs.

When JW is situated within the triangle, then, as was formerly
deduced, M is a point of contact of the two curves and F, J and
the corresponding vapourpoint J/, are situated on a straight line.
The point J then is a point of maximum pressure of the saturation-
curve under its own vapourpressure.

When J/ is situated on the side BC of the triangle, e.g. in the
point p of figure 1, the points /’, p, and the corresponding vapour-
point on the side LC are, therefore, also situated on a straight line ;
then usually the two curves do not come in contact with one another. If
we imagine in fig. 1 the liquideurve drawn through p, the two curves
will come in contact with one another in p only exceptionally. The
pressure P, is then the highest pressure under which the system

599

F+L+G occurs, but the point p is not a point of maximum
pressure of the saturationcurve under its own vapourpressure (we
will refer to this later).

On further decrease of pressure one or more points of intersection
are found, therefore also one or more threephasetriangles; the different
diagrams may be easily deduced in the same way as in communication I.

On further decrease of pressure we attain a pressure P,, under
which the contemplated curves have for the last time a common
point; we call this point m. P,, therefore is the lowest pressure
under which the system /’+ £-+G ean still occur and the points
F, m and the corresponding vapourpoint m, are situated again ona
straight line. When m is situated within the triangle, it is again a
point of contact and also a point of minimum pressure of the satu-
rationcurve under its Own vapourpressure. When i is situated on
the side BC of the triangle, (we imagine in fig. 1 the liquid curve
of the region LG through the point g) the two curves do not come
in contact with one another in g, and g is not a point of minimum
pressure of the saturation curve under its Own vapourpressure.
Of course P, is the lowest pressure under which the system #’-+- L + G
may yet occur.

Now we will deduce some saturationcurves under their own
vapourpressure.

T< Tx. At first we choose a tempera-
ture 7’ lower than the point of maximum
sublimation 7’x of the binary compound F.
In a similar way as we have deduced fig. 11 (1)
for the general case, we now find a diagram
us is drawn in fig. 2. In this figure however
only a part of the componenttriangle ABC
is drawn; the line 4, #n is a part of the
side BC. Curve habn is the saturationcurve
under its Own vapourpressure, /,a,b,n, the
corresponding vapourcurve; we shall call
also here both the curves circumphased.

At the deduction of this diagram we have

assumed, that on these curves neither a point
of maximum- nor a point of minimum pressure occurs ; the pressure
increases from n to /, without being however in 2 a minimum and
in h a maximum. From the deduction it follows also that the sides
solid-liquid and solid-gas of the threephasetriangles must have a
position with respect to one another as is drawn in the triangles

Faa, and Fbé,.

600

Formerly (communication V and VI) we have deduced several
rules for the movement of the sides of a threephasetriangle on change
of pressure. When a saturationcurve under its own vapourpressure
and its corresponding vapourcurve are removed comparatively far
from the point /’, the formation of vapour from /’ + ZL takes place
on increase of volume and the formation of liquid from /’-+- G on
decrease of volume. The threephasetriangle turns on increase of
pressure in such a way that the conjugationline solid-vapour goes
ahead; on decrease of pressure it turns in opposite direction. If in
fic. 2 we make triangle aa, or (bb, turn towards higher or lower
pressures, we see that these movements are in accordance with the
previous rules.

Also we may imagine on curve jan a point of maximum pressure
M and on eurve h,a,6,n, the corresponding point V7,; the points F,
M and M, are then situated on a straight line. The pressure then
increases from and n towards M. Triangle /‘aa, must then also have
another position as is drawn in fig. 2; the line /a@ must viz. be
situated closer to the side /h, than the line /a,. Therefore, when
we take two threephasetriangles, situated on different sides of the
line FMM,, they turn their sides solid—gas towards each other.
We see that this is also in accordance with our previous considerations.

We may also imagine a point of minimum pressure m on curve

habn and the corresponding point m, on curve

h,a,b,n,. Triangle 66, must then have another

position; the line /%, must then be situated
4 closer to the side /’n than the line /%.

Th< T< Tp. We now take a temperature

7 higher than the point of maximum sublimation

7’'x, but lower than the minimum-meltingpoint
Tv of the substance /”. In a similar way as

a, is circumphased, curve /,a,b,7, exphased. Fur-

we have deduced for the general case fig. 7 (1),

we now find a diagram as fig. 3. Curve habn

x

Wie. | ther, if is assumed again that on these curves

neither a point of maximum- nor a point of
minimum pressure occurs. Because the points @ and a, are removed
comparatively far from the point /’, the above mentioned rule
applies again to the moving of triangle /aa, on change of pressure;
we see that ifs turning is in accordance with this rule.
It is different with triangle /’)),, its points 6 and 6, are to
, Let us at first contemplate the
equilibrium /°-+- liquid »—+ vapour n, of the binary system BC.

be imagined close to » and

601

Beeause we have in this system a temperature between 7’, and 7’p,
between the three phases the reaction: #Z liquid m+ vapour n,
takes place from left to right with increase of volume. We compare
now the ternary equilibrium /’-+ liquid 4+ vapour 6,, wherein
6 and 6, differ but little from ” and ,, with the previous system.
We then see that as well the formation of vapour from /-++
vapour 4 as also the formation of liquid from /’+ vapour 4, takes
place with increase of volume. According to the rule deduced in
communication VI, the sides solid-liquid and solid-vapour of the
threephasetriangle must then approach one another on increase of
P and separate from one another on decrease of P. We see that
the movement of, #4), in fig. 3 is in accordance with this rule.

The occurrence of a point of maximum- or minimumpressure can
be easily examined by the reader.

Tr< T. We now take a temperature 7’ a little higher than the
minimummeltingpoint 7 of the substance /. We then must distinguish
two cases, according as the substance expands or contracts on
melting. We only take the first case. In a similar way as is deduced
for the general case fig. 12 (I), we now find a diagram as fig. 4,
wherein the two curves are exphased. Further, it is assumed again
that on these curves neither a point of maximum nor a point of
minimumpressure occurs. From the deduction
of the diagram, it follows that #7, of the
threephasetriangle /’aa, is situated always
between Fa and /h,. When the points a
and a, are situated in the vicinity of and
n,, Kaa, turns, as is clear from the figure,
in such a way on decrease of pressure, that
the line Fa goes ahead. When a and a,
are situated however, in the vicinity of /
and /,, ‘aa, turns on decrease of pressure
in such a way that /a, goes ahead. This
turning is in accordance with the rules,
deduced in communication VI. Let us firstly
contemplate the equilibrium /’+ ZL, + G,,
of the binary system LC. Herein the reaction

Fig. 4. [nl + Gn, takes place from left to right
with decrease of volume. Let us now take the system /’ + L, + Go,
of which the points a and a, are situated in the immediate vicinity
of n and n,. At the formation. of vapour from /#'+ L the volume
will decrease, at the formation of liquid from /#’-+ G,, the volume
will increase.

602

According to the rule, deduced in communication VI aa, must
on increase of pressure turn in such a way that the line a goes
ahead. This is in accordance with fig. 4.

In the same way it is deduced that triangle /aa,, when aand a,
are situated in the vicinity of 2 and /,, must turn on increase of
pressure in such a way that the line Ha, goes ahead.

Also, however, curves of quite another form may occur, viz. closed
curves; these are, therefore, situated completely within the triangle
and they are exphased. We imagine e.g. in fig 12 (1) the component
triangle to be drawn in such a way that the point /’ is situated
on the side BC and that the two curves fall within the triangle.
Both the curves then show a point of maximum- and a point of
minimumpressure. While a binary compound generally may be in
equilibrium, in addition to a series of ternary solutions, yet also with
two binary solutions, in the above mentioned case, therefore, it is
no more the case; now it may be only in equilibrium with ternary

solutions.

Drawing the saturationcurves under their own vapourpressure and
their corresponding vapourcurves for different temperatures, we may
distinguish two principal types; these are represented in fig. 5 and
6. In both the figures, however, the vapourcurves are omitted. At
temperatures below the minimum meltingpoint 7’ the saturation-
curves under their own vapour pressure are circumphased; at 7'r
the curve goes through # and above 7p they are exphased. In
fig. 5 they disappear in a point 4 on the side, in fig. 6 in a point
R within the triangle.

605

At first let us contemplate fig. 5. The arrows indicate the direction
in which the pressure increases, therefore, it is assumed that on
these curves-neither a point of maximum- nor a point of minimum-
pressure occurs. When this however is the case, these points form the
limit-eurve, formerly treated, which is easy to draw in the figure.

The saturationcurves disappear at 7’z in the point //; the corre-
sponding vapourcurves disappear at the same time in the point //,,
which is not drawn. We see from fig. 5 that 777 is the highest
temperature at which, in the binary system BC, the equilibrium
F+L+4G ean still oecur. In this case 777 is also the highest
temperature at which in the ternary system the equilibrium /’+- L + @
ean still occur.

In fig. 6 the saturationcurve of the temperature 777 does not
disappear in the point /Z; it forms a closed curve, which touches
the side of the triangle in a point H. On further increase of tem-
perature it comes completely within the triangle and disappears in
a point #. It is evident that these closed curves, and also the not-
closed curves, being situated in the vicinity, show a point of maximum-
and a point of minimumpressure. In this case, therefore, a limit-curve
exists, going through the point AR. The curves situated at a greater
distance, need not necessarily show this point of maximum and that
of minimumpressure.

If it is imagined viz. that these points, on extension of the
curves, continue to approach closer to the side BC and that they
coincide with this at last; the point of maximumpressure disappears
somewhere between H and C, the point of minimumpressure between
Hand & on the side LC. The limit-curve then terminates in both
these points.

Also we see from the figure that the highest temperature (7'p)
at which in the ternary system the equilibrium “+ 2+ G may
still oceur, is higher than 7’7.

In figs. 5 and 6 the curves of different temperatures are all drawn
in a same plane. Imagining however perpendicular to this plane a
temperature axis and the curves to be drawn in space according to
their temperature, the saturationsurface of / under its own vapour-
pressure arises. In a similar way the corresponding vapoursurface
arises.

In the surfaces belonging to fig. 5 the highest points (#7 and #,)
are situated on the side-plane BCT’; in the surfaces belonging to
fig. 6 the highest points (# and &,) are situated within the prism
and not on the sideplane BCT’

604

Deducing the boilingpointcurves for different pressures we refind
again the figures 2, 3, and 4 and figures 5 and 6 deduced from
these. The arrows must then be drawn however in opposite direction
so that in the figs. 2, 8, and 4 7), is the lowest and 7}, the highest
temperature at which the equilibrium /’+- L +- G@ oceurs.

We must still contemplate the cases Il and IIT namely that the
vapourpressurecurve of the binary system BC shows a point of
maximum, or a point of minimum pressure. After the previous
general considerations on the occurrence of ternary points of maximum-
and of minimum-pressure, this need not to be considered here.

Now we shall contemplate some points more in detail. When /
is a binary compound of the composition 0, 8, 1—@ (therefore ¢=0)
[er + (y—B)s] dx + [es + (y—BA)t]dy=0. . . . (A)
applies to its saturationcurve at a constant 7’ and P.
The liquid curve of the region LG is fixed by:
[(e,—a)r + (y,—y)s] de 4 [(@,—a)s + (y,—y)] dy =0. . @Q)
We now imagine in fig. 1 that the liquid curve of the region LG
: dy . ae
is drawn through the point p or q; we now contemplate - in this
f Lk
point p or gq for both the curves. Because in this point «=O and
Lim. ar = R7 ix follows for the saturation curve that:

dy tT + (y—B)s
ay ep ee CE er. ((S!
GE (v2) a

and for the liquid curve of the region LG that :

wv
Si Were Se (y,—Y)s
dy v : ;
we Ne ee eee eee
\ dx J =o (y,—y)t :
From (3) and (4) it follows that the tangents on both the curves
in the point p have usually a different position, so that the two
curves do not come in contact with one another. When (8) is
accidentally equal to (4), the two curves touch one another in p or
q. This will be the case when:
a Lv y,—B
yy = es | (y—P) ort == es ee (5)
fb a y—B
Later we shall see that in this case their point of contact p or ¢
is then also a point of maximum- or of minimumpressure of a
saturationcurve under its own vapour pressure or of a boiling point
curve.

605

In order to find the saturationcurve under its own vapourpressure
we put in (8) and (9) (Il) a=0. We obtain:
[wr + (y —B)s] de + [es + (yA dy = AUP. . . (6)
[(a,—2)r + (y,—y)s] de + [(7,—2)s + (y,—y)t] dy = CdP . (7)
In the terminating point of this curve on the side LC (therefore
in the points 2 and n of figs. 2, 3, and 4), 7 =0. We find from
(6) and (7):

vy
(2) 1-9-8) le -1)

— ., | — = Sey UG)
RT \de}z=0 (y,—8)V+ ¥—y.)o + B—-9) V7
In order to find the boilingpointeurve we must substitute in (6)

and (7) AdP by — BdT and CdP by — DdT. We then find:

&
1 (2) sity) ( 1) é
RT : da pear (y, —B)H + (y—y,)q -b (@—y)H, . (i )
From (8) it follows that in a terminatingpoint of the saturation-

curve under its own vapourpressure on one of the sides (points /

dP
and n of fig. 2, 3,and 4) — has a definite value different from zero
Av

so that the pressure is in the terminatingpoint neither a maximum
nor a minimum. The same follows from (9) for the temperature in
the terminatingpoint of a boilingpointcurve.
In the binary system BC’ the relation between a change of P
and 7’ in the equilibrium #’+ LZ -+ G is fixed by:
(3) _ %—8)R + Y—y.)n + B- yA,
aT),=0 (y,—B)V + (y—y,)? + (B-¥)M,
From (8), (9), and (40) it now follows that:

dP an dP
(SZ) ; (=) = Al cae o> (tt)
\ da ra da | r=0 dil r=0

In order to see the meaning of this we imagine a graphical
representation of P and 7’ of the binary equilibrium #-+ L + G.
We will call that part of the P,7-curve on which the pressure
increases when raising the temperature, the ascending branch, the

(10)

part on which the pressure decreases when lowering the temperature

d
the descending branch. In the ascending branch ape positive, in

4h
the descending branch it is negative; from (11) it follows, that
aP aT : : PAE :
a and a have in the ascending branch the opposite sign and in
a“ Lv

the descending branch the same sign. We find therefore :
39
Proceedings Royal Acad. Amsterdam. Vol, XVI.

606

When the binary equilibrium /-+ L-+G is situated in an
ascending branch of its ?,7-curve, addition of a third substance has
an opposite influence on the pressure (at constant temperature) and
on the temperature (under constant pressure). When addition of a
third substance e. g. increases the pressure (at constant 7’) it will
decrease the boiling point (under a constant pressure).

When the binary equilibrium + L-+ G is situated in an de-
scending branch of its P,7’ curve addition of a third substance has
the same influence on the pressure (at constant 7’) and on the
temperature (under constant P). When addition of a third substance
increases for instance the pressure (at constant 7’) it will also
increase the boilingpoint (under constant P).

These rules are also true when / is instead of a combination one
of the components e.g. Bb or C.

We will now still examine, in what case the pressure (at constant 7’)
of the binary equilibrium /’-++- ZL + G is increased or decreased by
addition of a third substance. We may express this also in the
following way: in what case does the pressure along a saturationcurve
under its Own vapourpressure from one of its terminatingpoints (/
and m in figs. 2, 3, and 4) increase or decrease?

We take for this formula (8), which indicates the relation between
the change of pressure dP and the quantity dz of the new substance.

Between the 3 phases of the binary equilibrium #-+ 2+ Ga
reaction may always take place. We let the reaction take place in
such a way that 1 quantity of vapour occurs. The occurring change
of volume we call AV. The denominator of (8) becomes then
(8—y) AV, so that we may write:

ae (=) it ig a7 Lh Sa
Jigs dz )1—0 AV a p—y
We now take the ternary equilibrium F4AL+4G wherein L and
G contain still only a little of the third substance. The line solid-
liquid (a or Fb in figs. 2—4) then intersects the X-axis (side CA
of the componenttriangle) in a point at the distance S from C.
The line solid-gas (a, or Fb, figs. 2—4) intersects this Y-axis ina
point at the distance S, from C. We take S and S, positive, when
the points of intersection are situated on the right, negative, when
they are on the left of C. S and S, are fixed by

‘——_— SEE ee ees)

Substituting @—y and 8—y, from (13) in (12) we find:

607

] =) rau ] fie i S Md
Ride Aver = Ns Ait Wee

From this relation it follows that the sign of the change of pressure
depends on the sign of AV. Now AV is almost always positive
for the binary equilibrium / + Z-+ G and negative only between
the points /’ and # (figs. 5 and 6). Further it follows that the sign
of the change of pressure is not fixed by the ratio «, : x (the partition
of the third substance between gas and liquid), but by the ratio
S:S,; therefore this is by the ratio of the parts which the lines
Fa and Fa, or Fb and Fb, cut off from the X-axis. We may consider
S and S, also as the perspective projections of « and wz, from
the point # on the X-axis. We shall call for that reason S the
perspective concentration of the new substance in the liquid, and
S, that of the new substance in the vapour. These perspective con-
centrations can be as well positive as negative.

From (14) we can now easily deduce for the addition of a new
substance :

1. The formation of vapour in the binary system #'+ 1+ G
takes place with increase of volume (A) > 0).

When in liquid and vapour the new substance has perspective
concentrations of opposite sign, the pressure increases.

When in liquid and vapour the new substance has perspective
concentrations of the same sign, the pressure increases, when the
perspective concentration (apart from the sign) of the new substance is
greater in the vapour than in the liquid, the pressure decreases when
the reverse is the case.

2. The formation of vapour in the binary system #’-+- L -+ G
takes place with decrease of volume (AV < 0).

The changes of pressure take place in opposite direction as sub 1.
It may be considered with this, that 4V < Ois the case only between
Ty and Ty, therefore between the minimum-melting point of / and
the point of maximum-temperature of the binary system /’-+ L-+ G.

When we take a threephasetriangle in the vicinity of the side BC,
its angle /’ is either a little greater than O° (Maa, and F'dd, in tig. 2)
or a little smaller than 180° (/°)4, in fig. 3). We will call the three-
phasetriangle in the first case acute-angled, in the second case obtuse-
angled. We may express the previous rules also in the following way:

1. The formation of vapour in the binary system #+ 2+ G4
takes place with increase of volume (AV > 0).

An obtuse-angled threephasetriangle moves on increase of pressure
both its sides solid—liquid and solid—gas towards each other and
on decrease of pressure away from each other.

og*

608

An acute-angled threephasetriangle moves on increase of pressure
with the side solid—gas ahead, on decrease of pressure with the
side solid—liquid ahead.

2. The formation of vapour in the binary system ”-+ L + G
takes place with decrease of volume (AV < 0).

The triangles move in the opposite direction as sub 1..

We see that the position of the threephasetriangles in the figs.
2—4 are in accordance with these rules.

In a similar way as we have converted (8) into (14), we may
deduce from (9) :

1 aT ae S
Bae Sa), oe coat 3 S| <=) 1 mnt
RT) \ az J AW 2 S,

AW represents here the heat that is required to form 1 quantity
of vapour. The same rules as above may be deduced from this,
we must then however replace increase of pressure by decrease of
T and deerease of pressure by increase of 7.

We should have been able to deduce the rules, deduced above,
for the movement of the threephase triangles on change of pressure
and temperature, from the rules found in Communication V and VI.

As a particular case of the above-discussed we may put the
question: what influence has a third substance on the binary equi-
librium #’+ 1+ G when this is situated in the point of maximum
sublimation or in the minimummelting point of the substance

In the point of maximum sublimation the binary vapour has the

same composition as the substance /’,; therefore 7, = @. The vapour-
saturationcurve under its Own vapour-pressure goes through the point
J’ (in this transition-case between the figures 2 and 38 n, coincides
therefore with /”). When we put in (8) and (9) y, =8, we find:

i Oe 1 By i dP = ferry 16
oe kas Wak ae =f anc RT?’ an bodes AW Wek (16)

Herein )’,—v is the increase of volume on sublimation, AW the
heat of sublimation of the substance /*. Therefore, both are positive.
From (16) it now follows :

when the equilibrium #-+ 2+ G is situated in the point of
maximum sublimation of the substance F’, addition of a third substance
will increase the pressure (7’ constant) and decrease the temperature
(P constant).

In the minimum-melting point the binary liquid has the same com-
position as the substance /’, therefore y ==. The saturationcurve
under its Own vapour-pressure gues therefore through point #. (In
this transition-case between figs. 3 and 4, n, therefore, coincides with

609

F). When we put in (8) and (9) y= 3, then it follows :

1h ay TS es a a. ene rs
ae em pp

Herein )/—v is the increase of volume on melting, AW the heat
of melting of the substance /#. V—v can be as well positive as
negative, AW is always positive. From (17) it now follows that:

when the equilibrium /’+ + G is situated in the minimum-
meltingpoint of the substance /’, addition of a third substance will
increase the pressure (7’ constant), when the substance melts with
increase of volume (V > v) and decrease when the substance melts
with decrease of volume (V<v). The temperature (P constant)
is lowered.

We may express the above-stated also in the following way:

from F' the pressure increases along the vapoursaturationcurve
under its own vapour-pressure going through /’ and the temperature
decreases along the boilingpointeurve going through /.

From /' the pressure. increases along the saturationcurve under
its Own yvapourpressure going through /’, when /’ melts with in-
crease of volume and the pressure decreases when /’ melts with
decrease of volume. Along the boilingpointcurve going through /
the pressure decreases from I’.

Also we should be able to examine what influence has a third
substance on the binary equilibrium + 4+ G, when this is
situated in the point of maximum temperature (point // in figs. 5
and 6) or in the point of maximum pressure of its P,7-curve. We
refer to this later.

(To be continued).

Physiology. — “Vhe ejject of subcutaneous turpentine-injections on
the chemotaais of remote places.” By Prof. H. J. Hamburger.
After experiments by Dr. J. Burrnnnuts.

(Communicated in the meeting of November 29, 1915).

On a former occasion the attention was drawn to the favourable
effect of slight amounts of turpentine on the rapidity of phagocytosis.")
In a dilution of 1; 100.000 an increase was found of 24.7 °/, and
even in a dilution of 1: 500.000 an increase of 16

oy;

fo:

1) Hameurcer, pe Haan and BuBanovic: On the effect of Chloroform, lodoform
and other substances dissoluble in fat, on Phagocytosis. Proceedings of the Meeting

of Jan. 28, 1911, p. 913.

610

Elsewhere’) we have pointed out that the result agrees with a
ereat number of clinical experiences. The gynaecologist Focuirr from
Lyons for example has successfully applied turpentine in the treat-
ment of puerperal fever. For this purpose he injects turpentine under
the skin which gives rise to an abscess in this place and the fever
soon disappears.

Focnier thinks that the abscess attracts the noxious substances
which cause the fever, thus rendering them inactive. He speaks of
an “Absees de fixation”.

In veterinary circles this treatment has caused much enthusiasm.
The pneumonia (crupposa) of horses is at present chiefly and success-
fully treated with turpentine-injections. In the veterinary School at
Utrecht for instance J. J. Wustmr adopted this method with excellent
results.

He justly doubts, however, whether we are right in assuming an
“absees de fixation”. No plausible reasons can be adduced for this
hypothesis. Therefore he is more inclined to attribute this favourable
result to an improved action of the heart.

It seems not impossible to me that this factor has to be reckoned
with. But it is certainly not the only one; for in-Denmark the same
treatment is successfully applied to chronic mastitis of the cow. And
a better action of the heart, such as is often necessary in pneumonia,
would be of no avail here.

Therefore we have asked ourselves if this favourable effect of
turpentine may not be explained by assuming that this substance enters
the circulation from the place of injection as a weak solution, thus
stimulating the phagocytosis also in the hearths of the disease, which
would assist the curative process.

From a technical point of view, however, it is very difficult to
investigate the degree of phagocytosis in an inflamed centre and to
determine thus whether the activity of the phagocytes has increased.

This seemed possible, however, by chemotactical experiments.

For this purpose, just as in the case of Calcium, two methods
were adopted *).

The first method consisted in capillary tubes, filled with an extract
of coli bacteria, being placed under the skin of one of the hind legs

') Hampurcer: Physikalisch-chemische Untersuchungen iiber Phagozyten. Ihre
Bedeutung vom allgemein biologischen und pathologischen Gesichtspunkt. Wies-
baden, J. F. Beramann, 1912, p. 159.

2

*) Cf. Hampurcer. The effect of slight quantities of Calcium on the motion of
the phagocytes. Proceedings of the Meeting of May 28, 1910.

611

of a rabbit at the inside of the thigh. These extracts also contained
traces of turpentine.

Similar tubes were placed at the other hind leg with the same
contents, but without turpentine.

After 20 hours the leucocyte columns, which owing to chemotaxis
had entered the tubes, were measured. This rendered it possible to
establish if, and if so, to what extent, turpentine had promoted
chemotaxis and stimulated the phagocytes.

The second method consisted in 0.3 ce. of turpentine being injected
under the breast skin of some rabbits; it was then determined if a
greater amount of leucocytes had entered the capillary tubes with
coli-extract, than if the same rabbits had been injected with 0.3 ce.
of NaCl-solution instead of 0.3 ce. of turpentine.

Before stating the results obtained on the effect of turpentine we
shall communicate a series of experiments which were made _ to
ascertain the degree of accuracy of the method. In four rabbits
capillary tubes are placed right and left under the skin of the leg.
These tubes are filled with the same extract of coli-bacteria in NaCl

0,9 °/,.
The following table will require no further explanation.
TAN IE IL
Effect of extract of Coli-bacteria on chemotaxis.

Left leg. Right leg. |

| Extract of Colibac- | Extract of Colibac-

| teria in 0.99%9 NaCl | teria in 0.9% NaCl |

|
Rabbit 1 | Total of 4 leucocyte- 4.1 mm 4.5 mm + 0.4

| columns after
2 hours}

fe r 6:3) 25 aay — 0.8
oe: ; 5.6, | 5.5 Osi
eae! Fe | RAD 24 | BO =r Or

This table shows that the greatest deviation amounts to 0.8, whilst

the deviation in all 4 rabbits together oniy comes to 0,9 mm.
First method.

Under these circumstances it could be established now, to what
extent an addition of turpentine fo an extract of B. Coli in NaCl-
solution would affect the degree of chemotaxis. ')

1) The technical details were about the same as those we described in Vircnow’s
Archiv B. CLVIL p. 329, 1899 and in “Physik. Chemische Untersuchungen tiber
Phagozyten”. Beramanyn 1912. p. 94 foll. Only instead of cork paraffin was used
to keep the capillary tubes in their places.

612

For this purpose we used capillary tubes with extract of bacteria-
eoli in NaCl 0,9 °/,, in which 1: 100.000 turpentine had been dissolved.

In cach rabbit 4 capillary tubes with and 4 without turpentine
were placed on one side under the skin of the leg. After 20 hours
they were taken away, and the lengths of the leucocyte-columns
were measured.

Table Hl gives the results of this experiment.

1 7A BLE A

Effect of extract of Coli-bacteria on chemotaxis.

Right leg.
Left leg. : :
| Coli-bacteria extract Eat
| \e aoe Des Ee ++1:100.000 turpentine
| |
Rabbit 5 Total of 4 leucocyte- 4.8 mm 4.6 mm — 0.2
columns after |
20 hours,
> 6 7 Se Cia: ASS. os + 1.6
. 7 “ 4.— , | Dees a + 1.1
ns 8 F 4.58 3 O24, + 1.6
: 9 . Aah os a5 ey + 1.1
+ Oo RON =, Theil: hs a0
oetii 2 20a | ge + 0.9

In 6 of the 7 cases, therefore, the turpentine in a concentration
of 1: 100.000 has stimulated the chemotaxis.

In order to investigate if rabbit 5 made an exception to the rule,
or if a mistake had been made in the experiment, the experiment
was repeated with the same rabbit in the same places. It was found
then that the values became 5,1 and 6.8 respectively. In this case
{oo an increased chemotaxis has, therefore, been established.

We subjoin an experiment with a weaker turpentine-solution viz.
with turpentine 1: 500.000. Cf. table III.

These results show that an addition of turpentine 1 : 500.000 has
had a much more favourable effect still on the chemotaxis than
turpentine 1: 100.000.

Elsewhere') a more detailed account of the experiments will be
published.

1) In the dissertation (Bern) of Mr- J, Burrennuis.

613

Te AVByicsees In:

Effect of coli-bacteria-extract on chemotaxis.

| Right leg. |
ethan reer eee re etna ofcoli-bacteria|
| in 0.9%) NaCl in 0.9%) NaCl my
| ay) |-+1:500.000 turpentine,
Rabbit 12 Total of leucocyte-) 4.9 mm 6.4 mm +.1.5
‘columns after 20 hrs
is ; | 45 , | sie oes
eS | ; | Ae Bru + 1.6
Soa 5% | , | 36). BAI ex + 1.8
a 16))| 4 | 4.4, Nae 40.4
” 17 ” | 6.1 ” | 8.1 ” | -f 2
> ese | 6-2: gee 5 aero

Second method.

As we observed before, the second method of investigation consist-
ed in turpentine being injected subcutaneously in the lower chest
to enable it to spread through the body with the blood, thus entering
also into the lymph of the hind leg, where tubes with extracts of
bacteria in NaCl 0,9°/, had been placed. The experiment showed
that turpentine entered the system but slowly. For when after 7
days the injectionplace was opened, the mucous mass which came
out still strongly smelled of turpentine. Turpentine, indeed, does not
dissolve readily in watery fluids.

Since in different rabbits the chemotactical action is not the same,
the columns of each rabbit were measured without anything being
injected. When this had been determined half the rabbits were
injected under the breast with 0.8 cem. of turpentine and the other
half, as a test, with 0.3 cem. of NaCl-solution 0.9°/,.

Five or six hours after injection the capillary tubes were placed
under the skin and they were removed after 20 hours. The following
table gives a survey of the results obtained.

Now if we compare the total of the differences of 2, 4, 6, 8 and
10 which comes to + 6,1 mm. with the total of the differences of
1, 3, 5, 7 and 9, which amounts to —90,1, then it appears that the
subcutaneous injection of turpentine has evidently stimulated the
chemotaxis.

It must therefore be concluded that, in accordance with our hypo-

614

TA Bae SIV.

Effect of the subcutaneous injection of turpentine on chemotaxis.

| Length of 4 leucocytecolumns

ee the injection After mee acne of 0.3 cc,| Difference
of NaCl or of of turpentine or NaCl 0.9%o
turpentine |
Rabbit 1 | 6.6 mm Turpentine 7.4 , | -+ 1.8 (Turpent.)
i ae? 6:6. NaCl 5 | Ge O9(NaCl
‘ 3 | 023m, NaCl 5.9 |) = OFS 1(NaGl)
; 4 | 533): .,, Turpentine 5.8, 0 (Turpent.)
Sy ES NaCl 5.5» | + 0.7 (NaC)
, 6 | Gig | Turpentine 7.2 , + 1.2 (Turpent.)
ei Bae NaCl 6 cee + 1.3 (NaCl)
4 8 | 4.4 , Turpentine 7.1 , | + 2.7 (Turpent.)
See) | aio % NaCl 403 ve — 0.6 (NaCl)
5 104 5.8 Turpentine 6.2mm | -+ 0.4 (Turpent.)
| |

thesis, turpentine has gradually been removed from the place of
injection to different parts of the body. also to the blood-vessels of
the leg where turpentine was imparted to the lymph, which had
a favourable effect on the chemotaxis.

Repeated injection of turpentine in diluted solution.

If this view was correct then it might be expected that an injection
of turpentine in a diluted solution, if repeated a few times, would
likewise effect an increased chemotaxis.

This would, moreover, prove that the salutary therapeutic effect
of the turpentine would be entirely independent of the notion ‘“absces
de fixation”. At the same time this might lead to the application of
turpentine in human pathology being resorted to more frequentiy,
for in spite of the success obtained by Focarrr and others after him,
it is a wellknown fact that the subcutaneous injection is, if possible,
avoided because the sterile abscess, caused by it, is so extremely
painful. Indeed when we see bow, after the abscess has existed for
some days, the mass taken out, which still smells of turpentine, is

615

a mucous one, if becomes evident what destruction the turpentine
has caused there.

We investigated therefore whether the chemotaxis could not like-
wise be stimulated by injecting subcutaneously a solution of turpen-
tine in NaCl 0.9°/, in a concentraton of 1: 10.000, instead of pure
turpentine.

Provisional experiments have indeed shown that this has a favour-
able effect on chemotaxis. It was not considerable however.

Probably this must be attributed to the ineffective manner in
which the experiments were carried out. In the first place too little
was injected viz. only 5 times 5 cc. of a turpentine solution of
41: 10.000, which means only a total amount of 0.0025 ce. of turpen-
tine. But especially too much time elapsed between the injections
so that the turpentine injected, had ample opportunity to be secreted
in large quantities by the kidneys, whilst the method of injection
adopted by Focnimr creates a reserve of turpentine, from whence
turpentine is continually yielded to the circulation.

In subsequent experiments, which, owing to lack of time, could
not be carried out as yet, the above-mentioned consideration will
be taken into account.

As the technical difficulties attending turpentine-injections are being
removed, it will be possible to make use of these injections much
more frequently in human pathology ; meanwhile it may now be
concluded already from the foregoing experiments that turpentine
also stimulates chemotaxis in remote places. Further we may infer
from the greater mobility of the phagocytes, which is indeed also
the foundation of an increased chemotaxis, that in those places the
phagocytosis will be stimulated likewise.

Groningen, November 1913. Physiological Laboratory.

Botany. —. “Adjustment to light in oats’ By W. H. Arisz. (Com-
municated by Prof. Went).

Communicated in the meeting of November 29, 1913).
5
§ 1. Introduction.

In this preliminary communication there will be considered a
number of phenomena which are generally grouped as adjustment
phenomena (German: “Stimmung’’). By functional adjustment — is
usually meant the state of an organ which determines the effect

with which the latter reacts to a stimulus of a certain strength.

616

A change in adjustment is therefore made evident by a change in
ihe reaction to a stimulus of the same intensity. Thus it has been
known for a long time that plants grown in the light do not show
ihe same sensitiveness to unilateral illumination as etiolated ones.
PrincsHeim'), in a series of investigations, has attempted to obtain
a more detailed knowledge of these processes and quite recently
there appeared a paper by Criark*) which, as an extension of
Princsnem’s work, possesses in many ways points of contact with
the results about to be described. Crark’s conelusions and my own
differ on a fundamental point, namely the validity of the energy
law for negative reactions.

There are also striking differences with regard to our observations
on the influence of omnilateral preliminary and after-illumination.
Since Crark’s paper fortunately appeared before the close of the
present investigation, | have been able to test his results by control
experiments, which, at least with regard to the influence of omnilateral
after-illumination, have sufficiently explained the divergence in our
results. For a further explanation and for theoretical considerations
I must, however, refer to the detailed account of my investigations,
about to be published elsewhere.

§ 2. Method.

My method is in principle the same as that of Princsuemt and of
Crark. These investigators obtained the omnilateral illumination by
causing pots with seedlings to rotate on a elinostat round a vertical
axis in front of the souree of light. The objections to this method
are that owing to the excentric position of most of the plants, the
latter do not receive equal quantities of light on all sides, while
moreover, on account of the large numbers of plants in each pot,
they are continually getting into each other’s shadow. Owing to the
kindness of Prof. Went I was able to use an apparatus specially built
for these experiments. It is a kind of multiclinostat, in which 20
pots can rotate simultaneously each on its own axis. The arrangement
is such, that when the source of light is one metre from the instrument,
the possibility is excluded of the plants getting into each ather’s
shadow. The time for a revolution varies from 4 seconds to 4 minutes,
whilst a brake with an electrical contact makes it possible to
ilJuminate during an integral number of revolutions. Since the plants
rotate round their own axis, it is possible to use fairly large velocities

1) Coun’s Beitriige Bd. 9. 1909. Bd. 10. 1910
2) Zeitschr. f. Bot. Bd. 5, H. 10. 1913.

without fear of centrifugal force. In the series of experiments now
published, the rotation velocity was always 5 sec. The source of
light was a Nernst projectionlamp fed by a current maintained
constant. The light from the lamp, which was placed outside the
dark room, passed through a cooling apparatus with running water
and then through a diaphragm into the dark room. By interposing
plates of frosted and of milk glass the intensity of the light could
be changed in a few seconds. A greater intensity than 450 candles-
metre was not obtainable with this lamp at the distance at which
the multiclinostat was placed. The experiments described below,
with unilateral illumination at greater intensities were carried out
with the aid of a projection are lamp which gave at 1 metre an
intensity of 4600 candle-metre power. The numbers referring to the
latter illuminations have no claim to great accuracy.

The experiments were carried out in a small dark room in the
experimental hothouse of the laboratory. This small space could be
maintained at 23° C. by means of an electric heating apparatus and
regulator.

§ 3. Omnilateral fore-illumination followed by

unilateral after-illumination

In order to determine the state of sensitiveness of a plant at a
given moment, the plant must be exposed to unilateral illumination
at this moment and the resultant reaction must be observed. In the
course of the investigation it was found desirable to make a rule
of following the process of curvature, for the first two hours. A
longer period was not required for after two hours no further photo-
tropic phenomena became visible. The investigation aimed at observing
how a plant behaves towards unilateral illumination of various
intensities, after previous exposures of varying duration and intensity.
In order to determine the state of sensitiveness exactly at the end
of the preliminary illumination it is necessary to supply the quantity
of energy of the unilateral after-illumination in as short a time as
possible. How desirable this is will be seen especially from a con-
sideration of the processes discussed below, affecting the return of
sensitiveness. In contradistinction to Princsnem and to Crark, I did
therefore not always use the same intensity for the unilateral after-
illumination as had been employed when the plants were rotating.

On the contrary, an attempt was made to supply the plants in
as short a time as possible with a definite amount of energy, which
attempt was only limited at the higher amounts by the available

618

supply of light. I have investigated the influence of omnilateral
fore-illumination by allowing the plants to rotate for various periods
of time at 5 different intensities, of 5.5, 12.14, 25, 100 and 450
candle metre power. The results of the first four series are summa-
rized in tables. Without going into points of agreement and difference,
which would require detailed discussion, I here only wish to remark,
that Table I is comparable with the investigation of PrincsHEM
(second paper IV) and that my table HII shows agreement with
Crark’s figure 2.

It is especially by a consideration of table I, where the preliminary
illumination is weakest, namely 5.5 candle metre power, that we
can most readily obtain some idea of the influence of omnilateral
fore-illumination. A survey of the first six vertical columns of this
table, in which the unilateral after-illumination was 22—1000 C.M.S.,
reveals that a fore-illumination of 100 seconds already requires an
after-illumination of 60 C. M. S. to bring about a curvature, whereas
after 10 seconds 22 C. M. S. were able to do this. After still longer
preliminary illumination not much- more energy need be supplied
and 120 C. M. 8. always gives a definite positive curvature. We
may therefore conclude that the sensitiveness has been diminished
by the fore-illumination.

A second phenomenon is observed when the amount of the energy
of the after-illumination is increased (the last three columns of
table I). As I have previously *) shown these large amounts of energy
(more than 4000 C. M.S.) bring about negative curvatures. Even
after brief fore-illumination these negative curvatures occur after
large amounts of energy, but now the phenomenon is observed, that
after preliminary exposures of 5 minutes or longer, these negative
curvatures become feebler, and already after 20 minutes they are
no longer obtainable. Then positive curvatures occur, which are
extremely feeble at 27000 C. M. S. and become more clearly visible
at 18500 and 4500 C. M.S. After 1 hour’s fore-illamination the
positive curvature is even very marked at 4500 C. M. S.

This second phenomenon, which, as will be explained more fully
at the end of this paper, I wish to consider as the typical ‘adjustment
phenomenon” must therefore be formulated as the fact, that after a
certain duration of the preliminary exposure, it is no longer possible
to obtain negative curvatures at a certain intensity of unilateral
after-illumination.

If we compare with this the other tables we find that also at

') Proc. Kon. Akad. vy. Wetensch. Amsterdam Sept. 1913.

Explanation of signs,

++ all plants show definite positive curvature.

+-+ all plants show strong positive curvature.

0 no plants curved.

— all plants show definite negative curvature.

+? a few plants show slight positive curvature.

—? a few plants show slight negative curvature.

Two different signs placed in the same space e.g. + means that the reaction
after about 1 hour was according to the first of these, after about 2 hours according
to the second.

No previous illumination.

| Energy of the unilateral illumination in C. M. S,
No previous

22 | 44 | 60 | 120 500 | 1000 | 4500 | 13.500 | 27.000
se pst eta || ee aa A

ae ata wl |
TA BY EU
{ntensity of the omnilateral fore-illumination 5.5 C.M.

illumination

= - _— {_]

sos Energy of the unilateral after-illumination in C. M. S.

Soe | | | |

wee 4X5.58X5.5 5 12 |10 & 12/5 & 100/10 & 100/10 & 450/30 & 450/60 & 450
Ace 22 | 44 60 120 | 500 | 1000 | 4500 13.500 | 27.000
ea ea tata cht ec tahetediasten | | Eee le = oi
100 sec. | o | +2) + [| ++] +4] 4 = =
3 min | Fes? | ae Bp Sarat la eget) ie =

5 min oj; o}] + }4++] ++] + | -? | 2

|

20 min + }4+] 4+} 4] |]

1 hour Oe) ee euae ee

TAG Beles all
Intensity of the omnilateral fore-illumination 121 €C. M.

|
Duration of Energy of the unilateral after-illumination in C. M. S.

omnilateral fore- _- Azs :
illumination. | 22 | 44 | 60 | 120 | 500 | 1000 | 4500 |13.500| 27.000

Pee Pe | eee |e eee |) ae

|
36 sec. | a ee ae (ese abate See | a are | i
100 sec. | 0 | 0 0 | +? |4++) ++] +? sof lye
3 min | | P=0 | 2 +? | too | +2 | —? | eese
5 min. | | 0 | 0 0 + | +5 +? | =,
20 min. Oo} +) +} t+] +} ++

1 hour. a0 |) arse | Sep 4 See Se eas

620

Tf ABE ESI

Intensity of the omnilateral fore-illumination 25 C, M.

|
|

Duration of Energy of the unilateral after-illumination in C. M. S.

omnilateral fore-. — = i ay s ae eee
illumination 22 44 | 60 | 120 | 500 | 1000 | 4500 | 13.500 | 27.000
10 sec. 0 +? | | +} f+ ]) + + = a
36SEC; | | | 0 | +? +? — — =
100 sec. | Oi wale? ? steel p39) =
3 min. | | | | 0 0 0 =) = =
5 min, | | | | 0 0 +9 a ot
20 min. | poe +) 44] 4+] ++ | ++
shoGrTAN ae ee yleeeal 0 | sed ele eas ee ee
IASB LE IV.

Intensity of the ommndélateral fore-illumination 100 C. M.

Duration of Energy of the unilateral after-illumination in C. M. S.

omnilateral fore- - |
illumination | 22. || 44 | 60 | 120 | 500 1000 | 4500 | 13.500) 27.000
| |

10 sec. 0 | 0 Oe oi ++} — | — =
36 sec. | 30 | oO 0 = no =
100 sec. Oe a | 0 0 Ee ? =)
5 min. | od) | 0 0 0 +? ++
20 min. | | | | 0 ah ae ane
1 hour. + t+ )/ 4+] 4+

these intensities of fore-illumination the sensitiveness to the positive
reaction diminishes at first. Whereas at 12.1 C. M. (table ID it was
always possible to obtain a positive effect, this is not so at stronger
intensities. At 25 C. M. and 100 C. M. (tables III and IV) it is no
longer possible to bring about a positive curvature after a fore-
illumination of 100 seconds.

Just as in table I the possibility of obtaining negative curvatures
disappears with increased duration of the preliminary exposure, we
see also from tables II, Ill, and IV, after a certain period of fore-

621

illumination, that the strongest unilateral after-illuminations no longer
bring about negative curvatures. While at 5.5 C. M. the positive
curvatures only occur after a fore-illumination of 20 minutes, we
see that with more intense fore-illumination strong positive curva-
tures already occur in plants which had only 5 minutes fore-illu-
mination.

Tables I] and III show a further feature to this extent, that
with more prolonged fore-illumination smaller quantities of energy
suffice to give again a positive reaction, i.e. the plants become as
it were more sensitive. The four tables show gradual transition and
present a concordant picture. All tables demonstrate the existence
side by side of at least two different processes.

In the first place after any preliminary illumination a larger
amount of energy is required to bring about a positive reaction.
Secondly after a certain duration of the preliminary illumination the
capacity of giving negative curvatures is lost more or less completely ;
after more prolonged fore-illuminations only positive curvatures occur.
This second process, the adjustment phenomenon, recalls the phenomena
which are known to occur with unilateral illumination of greater
duration. In that case also the capacity of giving negative curvatures
is lost and after prolonged illumination only positive curvatures appear.
Let us therefore first consider unilateral illuminations of great
duration.

§ 4. Unilateral illuminations of great duration.

A preliminary idea may be obtained from the following table of
intensities from 1.4 to about 20000 candle metre power.

TA Bel EW;

Unilateral illumination.

Intensity in candle metre power.

] ] | ] | |

ely 55 | 12 | 100 | 450 | 1800 4600 20000
Negative = ———
curvature | = + 4000 C. M. S. limit not determined ;
begins at Fs) | at about
= + 10.000 M.C.S. neg.
Negative curvature ‘nn :
Mwave | e& | 9900 18000) 90000 | 135000 72900 | + 18000 | + 20000
curvature at n |
s
Duration of 3S
stimulus for 2 30min./25min. 15 min.) 5 min. | 40 sec. 4 sec. 1 sec,
sec. positive
curvature |
40

Proceedings Royal Acad. Amsterdam. Vol. XVI.

622

Unilateral illumination according to CLARK.

[repose I | 16 100 400 2500
| | | }
Negative curva- | ee ee
ture begins at | 500—900 + 900 + 2000—2500
Second positive | |
curv. begins at | 2300 7500 18000 | 34000 | 480000 | 4500000

At 1.4 metre-candlepower only positive curvatures are found, but at
each greater intensity there is a larger or smaller range of energy
in which negative curvatures occur. Although the accuracy of the
determination of the strongest light intensities was not very great,
we may nevertheless say that, at all intensities from 5.5 C.M. onwards,
there is a range over which negative curvatures are present. At
5.5 C.M. this range is very small, the curvatures which occur are
very feeble and a positive one always precedes them. This range
first increases at greater intensities and then diminishes again, but
even at the greatest intensity employed, namely 20000 C.M., it was
possible to obtain a negative curvature after stimulation for about
half a second. If we, however, compare with this the values published
by Crark for the appearance of a negative curvature, there is a very
striking difference. For the first positive reaction the energy law is
valid according to Cruark, but not for the negative one. The great
discrepancy between our figures depends on the phenomena at small
intensifies. For larger ones CLARK agrees in finding the negative
reaction at a constant amount of energy, but for feebler intensities
he considers that a negative curvature occurs after muuch smaller
amounts of energy. The cause of the discrepancy is CLark’s method
of working, as I have been able to show by control experiments.
A plant which executes a positive phototropic curvature assumes a
position in which its apex is stimulated by gravity. When the reaction
caused by the last stimulus is stronger than the phototropic one, the
plant assumes an upright position, which greatly resembles that due
to a negative phototropic curvature succeeding a positive one. For an
amount of energy from 500—2000 C. M.S. Crark has mistaken this
geotropic erection for negative phototropic curvatares.’) Had he made
his plants, after illumination, rotate on a clinostat round a horizontal
axis he would have seen no trace of a negative curvature. I desire to
emphasize here, that in all my experiments control observations were
made on a clinostat; by this means alone it is possible to obtain

') Prof. Josr was so kind as to inform me by letter, that Cuark never rotated
his plants round a horizontal axis on a clinostat.

623

‘certainty with regard to the occurrence of a negative phototropic
curvature. We have thus to consider the fact that at small intensities
no negative curvatures were observed, whereas at greater intensities,
as indeed Crark also found, after stimulation with a definite amount
of energy the plants curve negatively. CLArk’s observations were
entirely at variance with the energy law. The question now arises,
whether the facts, as above set forth, necessitate a limitation of the
energy law to smaller amounts of energy. It seems to me that from
the data obtained for negative curvatures we may not draw the
conclusion that the energy law is invalid for small intensities and a
long duration of the stimulus. There are so many facts in favour of
the general validity of this law that it is safer to assume that the
occurrence of negative curvature is mot entirely dependent on a
definite quantity of energy. It is necessary that this quantity should
be supplied within a certain time, for otherwise, owing to processes
to be discussed below, the effect is so much diminished, that the
excitation, which is required for the negative curvature, is no longer
reached.

In place of the negative curvature there arises again at all inten-
sities employed a positive one, when the illumination is continued
for a longer period. For this second positive curvature also there is
a striking discrepancy between C1ark’s figures and my own. My
figures (as indeed those of Cuark) show convincingly that the oceur-
rence of the second positive curvature is not dependent on a definite
quantity of energy.

If we take into consideration the well-known fact, that it is not
even necessary to supply this energy unilaterally, but that the latter
as Princsurim has shown, may be partially replaced by an illumi-
nation from the opposite side, then the hypothesis presents itself to
us that this second positive curvature arises through a process which
is independent of the direction of illumination. Tis process results
in a lowering of the excitation. In this train of thought there is
therefore no essential difference between the first and the second
positive curvature. On further consideration of the tables an additional
conclusion may be drawn. We see that the duration of stimulus,
i.e. the time during which illumination was necessary to induce the
second positive curvature, decreases continuously at greater intensities,
that is to say, that the intensity of the process, through which the
excitation diminishes is greater according as the quantity of energy
supplied per unit of time increases. We see therefore in unilateral
illumination the same process which we have studied as adjustment
phenomenon with omnilateral fore-illumination. In that case also

40%

624

the action of this process became evident after a certain period of
preliminary illumination by the disappearance of the possibility of
inducing negative curvatures and the exclusive appearance of positive

ones.
§ 5. The fading phenomenon (“Abklingen”).

Ommilateral preliminary illuminations render possible the closer
study of a phenomenon, which is generally called fading of
an excitation. By omnilateral stimulation of a plant for a longer
or shorter time we obtain as response a certain insensitiveness. We

Tt ALBEE avi:
Fading of an omnilateral preliminary illumination.

Time between Energy of the unilateral after-illumination in C. M. S.
fore- and after- |———————__— - Sar apa a ——
illumination 22 | 44 125 250 500 | 1000 | 4500 | 13.500 27.000
| a |
| | | |
at once lie Peet aca) 0 =?) | a
|
1 min. | | | +? | sae ee | — | =
5 min. | = ae acoelesrs eb amie usec =
20 min, qe | te | eR | EE | Sata rae
bhour | + | 4+ /4++ /4++ (44+ ]}4+) + | 0 |

no fore- Bt jae Se ae tear | SHY aly aoe | rs

illumination | |
During 100 sec. omnilateral fore-illumination with an intensity ef 25 C. M.

Ty AGB SESE avile
Fading of an omnilateral preliminary illumination.
Time between Energy of the unilateral after-illumination in C. M.S.
fore- and after | ; — eee
illumination 22 44 125 250 | 500 1000 | 4500 | 13.500 27.000
| |
at once 0 se erie ae see) ces
1 min. | Pere etapa Pare | =}
5 min. | jo? | sPealesse | bebe ete ctertt ia
20 min. (4+? +4 )+4+ | +4) ++ f+ + =E?
1 hour +? | + | + fet. | oleae | so | ja an _?
no fore- | :
illumination alco atale | feat inate = | ar a6 —_ _

During 20 minutes omnilateral fore-illumination with an intensity of 25 C. M.

625

ean then see how this insensitiveness gradually disappears again;
for this purpose the plant must be left in the dark for some time
and the slight residual sensitiveness which remains at that moment
must be determined by observing the magnitude of the reaction to
a given stimulus. In tables VI and VII the values are given relating
to a preliminary illumination of 25 candle-meter power during
100 sees. and 20 mins. respectively (see also table III).

From table VI we see that the possibility of obtaining positive
curvatures has returned after only one minute has elapsed between
the end of the omnilateral illumination and the beginning of the
after-illumination. After 1 hour the original sensitiveness for the
positive reaction has returned more or less completely. It is however
remarkable that at 4500 C. M.S. after an interval of 5 mins. between
fore- and after-illumination no negative curvature occurs again, but
instead a strong positive one. We see that here also through the
omuilateral illumination during 100 secs. the adjustment process has
been put into action, which process has continued in the dark and
resulted in the large quantity of energy giving not a negative but
a positive curvature. But the intensity of this process also diminishes
in the long run, so that after 60 minutes the negative reaction again
begins to be evident.

In table VII we see the return of the sensitiveness for positive
curvature as well as the possibility of a negative reaction. In this
case, however, neither the original sensitiveness for positive curvatures,
nor that for negative ones is completely reestablished after 1 hour.

§ 6. Omnilateral after-illumination.

Following Privesnum, [ investigated together with omnilateral
fore-illumination, the influence of an omnilateral after-illumination.
The simplest case imaginable, with two successive illuminations, 1s
that of a brief illumination from one side followed by one of equal
strength from the opposite side. Then the result is that the plant
remains straight. If there is an interval between the two exposures
even of only 2 minutes, the curvatures occur separately, so that
there is first a curvature in the direction of the first exposure and
then in that of the second.

TABLE Vil

105 C.M.S. (715) immediately afterwards in the opposite direction 105 CMS (7x15).
No curvature.

1 min. Fp No curvature
2 min, » apex curves first one way, then the other way
4 min. » first one way, then slightly the other way

8 min, » first one way then strongly the other way

626

Chark also paid attention to bilateral illumination and since his
results differ from my own, I made a series of observations, collected
here in table IX, for special comparison with his figure 7. This
table refers to successive illumination from two sides with an intensity
of 16 candle metre power. After the first exposure the plants were
turned through 480° and illuminated from the opposite side. It is
found that as long as a certain interval elapses between the beginning
of the two stimuli, each is expressed independently. If for instance

TAB EvERIxX.
Successive illumination from two sides,

Duration of the | Duration of the second exposure
first | i.
exposure. 10 sec. 30 sec. 60 sec. 90 sec. | 180 sec. | 600 sec.
7 , | |
30 sec. + 0 = = = =
60 sec. +b ao | ae | anit | = =
90 sec. be | + | 4+ | ant | = | =
180 sec. fe | ant + | zt | els | aL
200 sec. =p ES Eleaf = = +
600 sec. + | + + | + + 7

Intensity of both exposures 16 candle metre power.
-- signifies curvature in the direction of the first illumination.
— signifies curvature in the direction of the second illumination.
the illumination is first for 60 see. from one side, and is then
followed at onee by the same quantity of energy from the opposite
TABI Ex:
Unilateral illumination followed by omnilateral after-illumination.

Duration of the Duration of the omnilateral after iliumination

unilateral 3S

_ fore-illumination | 35 sec. 100 sec. | 300 sec. | 600 sec.
|
30 see. ++ + = Oy
|
60 sec. ye eae | ai || ellie! | ie
} |
= | | alte | |
180 sec, -+ | top ie + | =
300 sec. + | +? | +? | =

Intensity of fore- and after-illumination 12 candle metre power.
+ signifies curvature in the direction of the first (unilateral) illumination.
— signifies curvature in a direction opposite to that of the first illumination,

627

side, the two curvatures occur separately one after the other. CLARK
makes no mention of the first occurrence of the curvature in the
direction of the first illumination, and this deprives the phenomenon
of its surprising feature.

Let us finally consider table X for an omnilateral after-illumi-
nation. Although carried out with a somewhat weaker intensity, it
may very well be compared with Crark’s fig. 4. In this case also
CLARK makes no mention of the positive curvature which occurs
first and only gives the negative values. Had the after-illumination
here not been omnilateral, no new result would have been obtained,
but since all sides were afterwards exposed to an equal amount of
energy, the phenomenon is somewhat more complicated. We must
come to the very plausible conclusion, that after-illumination has
not the same effect on all sides, but has a different effect on the
side which had already been illuminated unilaterally. This results
in a separate production of the curvatures, first in the direction of
the first illumination and then in the opposite one. There is not the
slightest reason to call a curvature, in a direction opposite to the
first illumination, negative.

§ 7. Summary.

In conclusion a few results of this investigation may be considered
in their mutual relationship.

The observations with dlateral tllimination (table VIIT) show, that
when we apply to a plant two stimuli by illuminating first one side
and then the opposite side, each stimulus results in a visible ipsi-
lateral curvature, as lone as a certain time intervenes between the
two exposures. This is very marked when the interval between the
two inductions is long and less so with progressively shorter inter-
vals until, when the interval is very short, only very slight apicai
curvatures are seen. This suggests that also when the two sides are
illuminated simultaneously, both stimuli would produce a tendency
to curve, which tendencies are not expressed because they are
simultaneous, equal and opposite, and therefore annul each other.

The phenomena of omnilateral illumination are in complete agree-
ment with this. Here also, under certain conditions, there may occur
a curvature towards that side, which has had no preliminary unilateral
illumination. An omnilateral illumination must therefore be regarded
as the summation of unilateral ones.

A series of experiments, which are not described here, has shown
me, that when a plant is illuminated simu/taneously from twe opposite

sides with the same intensity, and when the illumination is then
continued on one side, results are obtained completely analogous to
those with omnilateral instead of bilateral fore-illumination. It need
cause no surprise, that with a dz/ateral illumination, the excess
which must be given on one of the sides, to obtain an ipsilateral
curvature, must be greater, in proportion as the tendency to eur-
vature on the other side is stronger. This is the same phenomenon,
which we have observed after an omnilateral fore-illumination. The
quantity of energy, which had to be given in one direction, in order
to obtain a positive curvature, was greater in proportion as the
previous illumination was more intense.

There is no reason to regard this so-called smaller sensitiveness
of a previously illuminated plant, which only depends on the necessity
of overcoming a tendency to curve, as an adjustment phenomenon.
Rather should this name be reserved for the process which we
have here always called adjustment process. We have been able to
observe how it is affected both by unilateral and by omnilateral
illumination.

Bilateral illumination can also give some explanation of the fading
phenomenon (§ 5).

We saw that, as the intervals between the two opposite illumina-
tions become longer, the curvatures show better. This gives us
a new point of view with regard to the fading process, which the
omnilateral illumination enabled us to study.

Here, with the time which elapses between the first stimulation
(omnilateral fore-illumination) and the second one (unilateral after-
illumination), the power of the latter of becoming visible increases.
This manifests itself in the phenomenon that, the longer the interval
has lasted, the smaller is the amount of energy reauired to produce
a visible curvature. We must therefore assume that the gradual
return of the original sensitiveness is the result of the faet that a
tendency to curvature can express itself more strongly when a longer
period has elapsed since the last stimulation.

Utrecht, Botanical Laboratory.

Chemistry. — “The Allotropy of Copper” I. By Prof. Ernst

Conr~n and Mr. W. D. HrtprermMan.

ee)
tA

1. In studying the earlier literature on copper we found certain
indications which justified the presumption that this metal is capable
of existing in different allotropic modifications. This presumption had
been strengthened by the results of our investigations on tin, bismuth,
cadmium and zine.

629

We will discuss the indications referred to above in our detailed
paper in the Zeitschrift. fiir physikalisehe Chemie; here only two
points may be specially mentioned: 1. Marrnirssen and von Boss’)
found as early as fifty years ago, that wires of electrolytic copper had
changed their electric conduetivity (at O° C.) after having been heated
for some time at 100° ©. Table 1 illustrates this phenomenon.

LA BISEy I:
Wire | | Wire 2 | Wire 3
Conductivity | |
at Q° | at 0° | at 0°
|
Before heating | 99.526 | 100.021 | 100.327
aft. heat. 1 day at 100° 99.943 99.971 100.461
Soe 2 days 100" 101.097 100.268 100.563
ee ses) - cn) Momae | 100.524 | 100.645
» » 4 » 100°} 101.671 | 100.656 | 100.708
Sees 1002 moiege | 101.075 | 100.649
iGo =n, c1002 — | 401.230 | 100.708
- al

yn 1009 = 101.469 =

2. Even in those cases where pure copper was used, the values
given in the literature for the density of this metal differ amongst
themselves very considerably. ')

2. We carried out our experiments in the same way as those
described in our paper “On the Ailotropy of Zine’. *)

Electrolytic copper (KanLBaum — Berlin, “geraspelt’’) was brought
in quantities of 100 grams each into a porcelain crucible. The pure
metal was melted in an electric furnace, some charcoal powder
having been added to it. The melted material which showed a
brilliant surface was poured out into eytinders made of asbestos-paper.
As soon as the metal had solidified, the cylinders were chilled in
water and turned into thin shavings on a lathe.

55 grams of this material after having been washed with ether,
dilute nitric acid, water, aleohol, ether, and dried in vacuo over
sulphuric acid, were put into a pyenometer in order to determine
the density at 25° C. We then observed that the water meniscus in

1) Poaeenporre’s Ann. 115, 353 (1862).
1) Compare e.g. Kanueaum u. Sruxm, Zeilschr. f. anorg. Ghemie 46, 280 (1905)

*) Proceedings 16, 565 (1913).

630

ithe pyenometer was continually falling at constant temperature. The
same phenomenon was observed when the experiment was repeated.
This indicates that themetal undergoes some change at this temperature.
3. By manipulating very quickly we sneceeded in determining the
density at 25.0 We found in two independent experiments :

9ro

Zo.
d—— 8.889 and 8.890.
4°

Our thermometers had been compared with a standard of the
Phys. Techn. Reichsanstalt at Charlottenburg-Berlin.

After having heated the metal during 24 hours at 100° in a
solution of coppersulphate no change of density was observed. Re-
peating this experiment at 25°, we found

228)
Cae 8.899 and 8 900

These experiments prove that there is a transition temperature
between 25° and 100° C.

4. In order to fix this temperature more closely we carried out
a determination with the dilatometer, using 300 grams of our chilled
metal. The dilatometer (bore of the capillary tube 1 mm.) was filled
with paraftinoil, which had been heated for some hours in contact
with finely divided copper, until there was no more evolution of
easbubbles.

The dilatometer was now kept at different, but constant temperatures.

TABISE: 1.
Duration of Rise of level Rise of level in
Temperature measurements
in hours in mm. | mm_ per hour
eee ee
2520 0.5 —- 545 — 1090
45 .0 OR2 — 100 | — 500
69 .6 0.3 | Se ec
1.5 18 | ess |) eas
72 .0 4 + 10 + 2.5
72 .5 i | + 45 ) + 4
Teva) 0.5 + 6 | ==" 12
OMe 0.4 a4 | + 36
80 .9 0.4 a | + 7

Ma
635

We used the electrically heated thermostat, mentioned in our paper
on the allotropy of cadmium ').

The results are given in Table 2. (Zie p. 680).

5. This table shows that there is a transitionpoint at 71°.7 C.
From this we conelude that there exist two allotropic (enantiotropie)
modifications of copper. The phenomena may be described by the
equation :

(ier

Cu (a) Zar G (3)

6. It may be pointed out that the change in the dilatometer has
taken place with great velocity notwithstanding the fact that the
copper used in this experiment had not been in contaet with a
solution of coppersulphate. On the other hand there was a large
quantity of finely divided metal present. Here, as in the ease of
bismuth, tin ete, the presence of this powder suffices to accelerate
the transitionvelocity very strongly.

7. The following experiment proves that the velocity of the
reaction B-copper— @-copper decreases enormously, when this powder
is not present.

We took 200 grams of electrolytic copper, melted it in an electric
furnace and poured the metal into a melting-spoon, where a_ series
of thin rods was formed. These rods were chilled in water and put
into a dilatometer which was filled with paraffinoil. The apparatus
was kept during 14 days and mights in a_ thermostat at 25° C.
Practicaily no change occurred. The transition velocity of @-copper
into «copper is several thousand times smaller than if the finely
divided metal is present.

This phenomenon explains the fact that objects made of copper
disintegrate so slowly in daily life. It is exactly the retardation
observed in the experiment deseribed above, which makes possible
the use of copper in daily life. We meet here with the same
phenomena which have been described already in the case of tin,
bismuth, cadmium and zine.

8. Our experiments prove that we have to consider copper as a
metastable system («@+ 3 copper), which (below 71°.7 C.) is continu-
ously changing into the stable modification (e-copper). The very
strongly marked retardations have concealed the allotropic change
from the physicists and chemists who have studied this metal in
different directions.

9. Dr. Cu. M. van Drventrr has been so kind as to call our

1) Proceedings 16, 485 (1913),

632

attention to the following curious historical peeuliarity: Turopnrastt
(a pupil of AristoTLE) says in his book sagt avecs: xartiregor yco
gaci zai wchBdov dy Taxivae ev to Hovta aayou xai yeuwwovos
ortos veavizot, yadxor dé oaytvaw (It is told that tin and lead
melted sometimes in the Pontos when it was very cold in a strong
winter and that copper was disintegrated).

10. The properties of copper @ and 3 as well as some problems
relating to the technical use of copper will be discussed shortly.

vAN “tT Horr-Laboratory.
Utrecht, December 19138.

Chemistry. — ‘The metastability of the metals in consequence of
allotropy and its significance for Chemistry, Physics and

Technics.” By Prof. Ernst Conen.

1. The research which | have carried out during these last few
months in- collaboration with A. Iu. Tu. Morsveip and W. D. He_perman,
has proved that several metals which until now were only known
in one modification are capable of existing in two (or more) allotropic
forms. The continuation of these investigations will show if all
metals have this property, but we may even already conjecture that.
this will be the ease. A great many observations described in the earlier
literature afford evidence in this direction.

2. We were also able to state the fact that the pure metals as we
have known them until now are metastable systems consisting of two
(or more) allotropie forms. This is a consequence of the very strongly
marked retardation which accompanies the reversible change of these
aullotropic modifications both below and adove their transitionpoints.
Employing certain devices (using the metals in a very finely divided
state, adding an clectrolyte) it is possible to increase the transition-
velocity in such a degree, that the change of the metastable to the
stable form occurs within a short time.

As such changes are very often accompanied by marked changes
of volume, the material is generally disintegrated.

3. As until now, chemists and physicists have always dealt with
the «- and B-form together, ad/ the physical constants of metals, which
have been determined, refer to the complicated metastable systems.
These are entirely undefined as the quantities of the @- and 6-modifi-
‘ations they contain-are not known.

Now it is known that a special physical property of any substance
at a definite temperature and.pressure depends on its allotropic

633

condition. H. F. Werser') found the specific heat of carbon (at 10°C.)
0.1128 in the form of diamond
Oni604> » 9» graphite
ORGS) 7, Charcoal

Ernst Conren and EK. Gotpscumipr’) found that the density of white
tin is 7.28, that of gray tin 5.8 (at the same temperature) while
KovarO Honpa*) has stated that the specific magnetic susceptibility
(x X 10°) of white tin is + 0.025, while that of gray tin is — 0.35
‘at the same temperature. Here even the sign is changed. The existing
data on the physical constants of metals known until now are thus
to be considered as entirely fortuitous values which depend on the
previous thermal history of the material used. Those physical constants,
which refer to a well defined condition of the metal are so far
unknown. In order to determine these, and only these have a definite
signification and are reproducible, we shall have to carry out in the
future all measurements for the pure «, 8,y.... modifications of the
metals.

4. Considering for instance the important part which the specific
heats of the metals have played in chemistry and physics during
the last few years, it is evident thata revision of these constants is
wanted.

5, What has been said about the specific heat holds evidently for
every other physical constant. In our paper on the allotropy of
bismuth *) we pointed out, that numerous phenomena which had been
observed in the study of density, electric conductivity (also under
pressure) conductivity for heat, melting point, thermoelectric force,
the Hatt-effect ete. and which had not been explained, may find
their explanation if the facts recently found are taken into account.

6. In this way a new field of research for chemists as well as
for physicists presents itself. Whilst it will be the task of the chemist
to prepare the pure modifications and study their physico-chemical
properties, the physicist will require to turn his attention to the
determination of their physical constants.

7. From a physico-chemical standpoint it will be very important
to study the electromotive behaviour of the allotropic modifications
mentioned above. The transitioncell of the sixth kind which I

1) Pogg. Ann. 154, 367, 553 (1875).

2) Zeitschrift fiir physik. Chemie. 50, 225 (1905)

3) Ann. d. Physik 32, 1027 (1910) ; The Science Reports of the Tohoku Imp. Uniy.,
Sendai, Japan. 1, 1 (1912).

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

634

described several years ago') may be used for this purpose. In this
way it will not only be possible to determine the heat of transfor-
mation of the modifications, but also to study the equilibrium between
the different forms. Several interesting problems may find their solu-
tion in this way. I have carried out some preliminary experiments in
this direction (with cadmium) in collaboration with Mr. W. D.
HieLDERMAN.

8. The same may be said if we consider the numerous alloys
which have an industrial as well as a scientific interest.

The melting point curves have to be revised, taking into account
the allotropy of the components. Quite recently the important part
played by the previous thermal history of alloys has been discovered.
Dipprn”*) bas proved that the specifie heat of certain alloys is different
according as they are chilled or cooled slowly.

In explaining this fact, Dirprt has not been able to take into
account the allotropy of the components of the alloys he experi-
mented with, as our papers on this subject could not at that time
be known to him.

9. I hope to report shortly on the problems which have been
indicated here. We will then discuss also several phenomena which
are observed in industry, the corrosion of metals in contaet with
water, rusting of iron, the decay of aluminium objects ete.

Utrecht, December 1913. van “T Horr- Laboratory.

Anatomy. — “On pteric sutures and pteric bones in the human
skull”. a Prof. A. J. P. v. p. Broek. (Communicated by
Prof. L. Bor

It is well known that the pteric region of the skull shows different
relations in form and extension of the adjacent sutures as well as
in the existence of separate bones, the so called pteric bones, ossa
epipterica.

In most of the human skulls the parietal and the ala magna of
the sphenoid touch in a more or less extensive spheno-parietal suture.

In some skulls the frontal is reached by the temporal bone, then
a fronto-temporal suture is formed. In this case we speak of a
processus frontalis ossis temporalis.

The configuration of the pteric region can be influenced by the
utiles form, extension and situation of the pteric bones.

1) eitechr. f. physik. Chem. 30, 623 (1899).
2) Ann. d. Physik 42, 889 (1913).

635

An examination of the skulls of papuans, brought home by the
Lorentz’ expedition from Dutch South New-Guinea, augmented with
a number of papuan skulls, sent to me by the military-surgeon
pE Kock from the same district, showed such relations in the pteric
region, that made a closer examination necessary.

A study of the concerning literature teaches, that the different
investigations on the proc. frontalis as well as on the pteric bones
are nearly all of a statistical nature, and do not reckon with the
condition of the two opposite sides of the same skull. As a conse-
quence of this way of investigation, the different forms of processus
frontalis are always explained in the same way. Only Grouper’)
mentions two forms of a fronto-temporal suture.

The examination of 114 papuan skulls drew my attention to three
questions, viz. 1 that several forms of proc. frontalis must be dis-
cerned. 2 that for the judging of the character of a processus fron-
talis the two opposite sides of the same skull must be mutually
compared and 3 that the processus frontalis and the pteric bones
must be compared with each other.

Regarding the first point I observe that two forms of proc. frontalis
ossis temporalis must be distinguished. I call these two forms of
proc. frontalis type I and type II.

Type I shows a projecting part at the upper border of the squama
temporalis, as is seen in figure 1. By prolonging the suture between
temporale and the alisphenoid in upward direction, as is done in

SS SS
\ eS

We

Fig. 1. Fig. 2.

1) GRuser W.Uber die Verbindung der Schliafenbeinschuppe mit dem Stirnbeine. 1874.

636

figure 1 by a dotted line, it reaches the parietal (vide figure 1).
This is Gruper’s “mittelbare Verbindung’. Type IL shows a regular
enlargement of the whole squamosal in the direction of the frontal,
so, that a fronto-temporal suture is formed. This is GruBer’s ‘unmit-
telbare Verbindung’’. A junction of the second type can be combined
with a frontal process of the first type.

The number of examined skulls is 114; in 47 I found a fronto-
temporal suture i. e. in 41,14 °/,.

The skulls of the two different kinds are divided as follows.

In 34 eases we have a frontal process of the first type. In 13
cases the two sides of the skull are symmetrical. In 21 the frontal
process is only present at one side. 5 of the 13 skulls with symme-
trical frontal process show a combination of the first and the second
type, so that from the first type 8 are found with the frontal process
on both sides, to 21 with the front. proc. on one side; which means
that the unilateral presence is much more frequent than the bilateral.

In 13 skulls the second type was found. Of no less than 12 skulls
the two sides were symmetrial and only once I found a unilateral
enlargement of the squamosal, which proves that the bilateral presence
is much more frequent than the unilateral.

In the unilateral presence of a frontal process of the first type
I found this process 18 times on the left side of the skull against
6 times on the right one; so the left half of the skull surpasses
strongly the right one in this respect.

An investigation of the pteric region of the side of the skull
Opposite to a frontal process of the first type led to the following
facts :

I. Processus frontalis at the left side.

A spheno-parietal suture at the right side in 6 skulls.

An os epiptericum typicum,, —,, on ey aE a
Several ossa epipterica oe 8D i) spenluskulle
A temporal proc. at the frontal. ,, ia ai lee

II. Processus frontalis + os epiptericum at the left side.

An os epiptericum-typicum at the right side in 2 skulls.

Il Processus frontalis at the right side.

A spheno-parietal suture at the left side in 2 skulls.

An os epiptericum typicum,, ,, _ ,, iho ces re

Several ossa epipterica et ae Ree Stine, sk

A spheno-parietal suture is mostly found at the side opposite to
the frontal process (in 8 of 19 cases). This suture is not always
situated in the same place. Usually it lies at the level of the sutura

657

squamosa, so that the region of the frontal process is included in
the alisphenoid.

Sometimes the spheno-parietal suture lies at the level of the lower
border of the frontal process; so that the region of this process is
included in the parietal. The region of the frontal process of one
side can be included in the frontal, as is proved by a skull, which
presents at the left side a frontal process of the temporal and at
the right side a symmetrical temporal process of the frontal.

If at the side opposite to the frontal process one or more ossa
epipterica are found, the situation and extension of these bones are
equal {o those of the frontal process.

We find other relations in the skulls with frontal processus of the
second type. Here the enlargement of the squamosal is nearly always
absolutely symmetrical.

Only once did I find a second type of frontal process at one side
and an os epiptericum typicum at the other one.

I suppose that the question after genesis and significance of the
above mentioned two types of frontal processus must be answered
as follows.

The proc. frontalis of the first type is to be considered as the
homologon of an os epiptericum typicum. Following arguments led
me to this opinion.

In the first place it is possible that the region of a unilateral
proc. frontalis can be included at the opposite side in one of the
surrounding bones (sphenoid, frontal, parietal). N

In the second place it must be remembered that the ossa epipterica,
which are present at the side opposite to the frontal process, corre-
spund in their extension and situation to this process.

When we find a frontal process together with an os epipte-
ricum at the opposite side, these two correspond with the frontal
process.

At last I have to mention the great variability in form and
extension of the proc. frontalis. As | will explain further on, we
ean find that in a skull with a unilateral os epiptericum or ossa
epipterica the opposite side suows the same conditions as in a skull
with a unilateral processus frontalis of the first type.

The frontal process of the “second type, the enlargement of the
whole squamosal, conld be due fo two causes. In the first place we
can suppose that merely an enlargement of the squamosal is cause
of the exclusion of the alisphenoid from the frontal, in the seeond
place we can imagine that this enlargement is due to the opposition
to the squamosal of that part of the alisphenoid which is not

+1

Proceedings Royal Acad. Amsterdam. Vol. XVI.

338

cartilagineous preformed, viz. the os intertemporale from Rankx’).
Perhaps both ways of enlargement of the temporal in forward
direction occur; only ontogenetical and comparative anatomical
investigations could make out this question.
Ossa epipterica.
I have brought the ossa epipterica to the following types.
I. Os epiptericum bordering to fonr bones (frontal, parietal,
temporal, alisphenoid): os epiptericum typicum.
II. Os epiptericum, bordering to three bones.
a: frontal, parietal, alisphenoid: os epipt. anterius.
6: parietal, temporal, alisphenoid: os epipt. posterius
c: frontal, parietal, temporal: os epipt. superius
d: frontal, temporal, alisphenoid : os epipt. inferius.
III. Os epiptericum, bordering to two bones; i.e. presenting itself
as a sutural bone.
IV. Several ossa epipterica.
Thirty times I found an os epiptericum typicum
in 4 skulls on both sides
5, ita) fs ,, the right side
Fl el ess ,, the left side.
If an os epiptericum typicum is present on both sides of the
skull, the two bones are symmetrical in situation and extension.
If an os epiptericum is only present at one side of the skull we
find, when examining the other side of the same skull the follow-

ing cases:

I. Os epiptericum typicum at the right side

a frontal process at the left side in 4 skulls.
a spheno-parietal suture SA cil ae tame’, tO)
a frontal process and an os epiptericum ,, ,, 5, 5° » @ 3

Several ossa epipterice iam LL thse ies 23

II. Os epiptericum at the left side

a frontal process at the right side in 2 skulls.
a spheno-parietal suture ,, ., ,, Sey Le) > 9p
several ossa epipterica ;, -,, 5 piensa

This survey proves that the side of the skull, opposite to an os
1) Ranke. J. Ueber den Stirnfortsatz der Schliifenschuppe bei den Primaten,
Silzungsber. bayr. Akad. d. Wissensch 1898,

639

epiptericum ftypicum can show just the same condition as a skull
with a unilateral processus frontalis of the first type.

That in case of a unilateral os epiptericum typicum the right
side is predominant to the left one is due to the predominance of
the frontal process of the first type on the left side.

If at the side of the skull, opposite to an os epiptericum typicum
a spheno-parietal suture is found, then the same rules hold for the
situation of this suture as by a unilateral frontal process; that part
of the skull that lies symmetrical to the pteric bone ean be included
as well in the alisphenoid as in the frontal or parietal bone.

II. I found an os epiptericum of the second type in 7 skulls; in
one on both sides and symmetrical, in 5 on the right and in one
on the left side. This pteric bone was always combined with a
frontal process of the first type. For the composition of the pteric
region of the opposite side of the skull in a unilateral occurrence
of such a pteric bone can be referred to the description of the
frontal process.

Ill. An os epiptericum of this type I found only once in a skull
as a little sutural bone in a fronto-temporal suture.

1V. Several ossa epipterica I observed in 4 skulls; always two
bone-pieces were present. In 3 skulls they were on the right; in one
on the left side.

For the behaviour of the side of the skulls opposite to those
with two pteric bones, I refer to the descriptions before mentioned.

All in all I found pterie bones in 42 skulls, or 36.8 °/, that is
to say in 5 on both sides, in 23 on the right and in 14 skulls
on the left side.

This enumeration proves that pteric bones are more often found
on the right than on the left side, on the contrary the fusion of
the bone pieces in the pteric region with one of the surrounding
bones, specially the squamosal, happens more frequently on the left
than on the right side.

It is impossible to decide by this study the meaning of the
pteric bones.

The frequent occurrence of these separate bone-pieces in papuan-
skulls is not favourable for Ranknr’s theory, saying they ought to
be considered pathological.

Ontogenetical and comparative anatomical researches will be
necessary to explain this question of the anatomy of human skull.

41

640

Physiology. — “On the formation of antibodies after injection of
sensitized antigens.” By Wa. K. Wore. (Communieated by
Prof. C. Etskman.) (First Communication).

In 1902 Busrepka') communicated about a new way of rendering
trial animals immune against pest, cholera, and typhus. This way
of immunizing consisted in injecting the animals with the bacilli in
question (either dead or alive), the latter being first treated with an
antiserum specially prepared for them, and afterwards being again
freed from the superfluous serum.

It appeared that by this treatment the animals became immune
much sooner than after being injected with nontreated bacilli, that
their state of immunity lasted as long, and besides that by this
treatment the bacilli had lost their toxical qualities. Since then
Brsrepka’s method has been applied to a great many other bacteria,
and according to many authors. mostly with good results.

In a report about his method’) in 1910 Besrepka finishes, saying
that it has been shown that sensitizing procures the bacteria with
new qualities, so that now they become first class vaccins, vaccins
with a reliable, quick, innocuous, and lasting effect.

In defiance of this seem to be experiments by Netsser and
Lupowsk1*), voN Diinaurn *) and Sacus °) °).

Neisser and Lusowskt examined upon rabbits the production of
agglutinins against typbusbacilli, which were loaded with agglutinins
on one side, and by injection of nontreated bacilli on the other side.
They found that the former had much less effect than the latter.

It must be remarked that their treated bacilli were saturated to
a maximum with agglutinins and were then washed out again
several times‘).
hy . R. de l'Académie des Sciences, 2 June 1902.

) Bulletin de l'Institut Pasteur, 1910, p. 241.

5) Centr. f. Bakteriologie I, vol. 30, p. 4&3.

4) Miinch, Med. Woch. Schr. 1900, No. 20.

5) Centr. f. Bakteriologie I, vol. 30, p. 491.

6) 1 do not here wish to speak about immunizing by means of loxin-antitoxin
mixtures, which have again been brought to the fore by the latest investigations
of von Benning as to the way of fighting diptheria. For this consult Krerz
(Zeitschr. f. Heilkunde 1901, Heft 4) and J. Reuns (C.R. de la Soc. de Biol. 1901,
féyrier), who could not bring aboul immunisation by compensated mixtures, con-

to

trary to Bases, who could, and further von Beurina’s communications (D. Med.
Woch. 1913), who found that a mixture reacting neutrally for one kind of animal,
could still be toxical for another.

1) J. Reans (CG. R. de la Soc. de Biol. 1900, p. 1958) did not find a difference
in immunisation power belween agglutinated and nontreated bacilli.

641

Von Dineprn has described a single experiment about the immn-
nisation power of red corpuscles of the ox, loaded with amboceptor,
upon the rabbit. In his experimenting he found as good as no am-
boceptor formation.

Sacus has extended these experiments, and he found that the
amboceptorformation was a less good one, but that it certainly did
exist. He too communicates but one series of experiments with corpus-
cles saturated to a maximum.

I here do not wish to show the differences between HKrsrepKa’s
experiments and those of the Germans; this I will do ina following
communication. But for me this controversy was enough reason to
get some more insight into this question by more extensive experi-
ments. Besides, one argument caused me not to consider of general
value the result which the German investigators drew from their
experiments, viz. that antigens loaded with antibodies possess no or
very little immunisation power.

For it is a wellknown fact that, in order to get au immuneserum
with a high titre, one must inject antigen in question more than
once. The second and following injections are generally given to
an animal that already possesses a certain quantity of antibody,
even more than is necessary, to saturate the quantity of antigen
which is being injected. Now there is not so very much difference
between treating an animal for the second time, and injecting antigen +-
antibody at the same time into a nontreated animal. And from the
fact that a second injection of a previously treated animal does
possess immunisation power, I considered the opinion of v. DUNGERN
c.s. improbable.

Suchlike experiments have been made by Dr. Trinity according to
a communication given by him during a discussion in the bactereo-
logical section of the international congress in London. Then my
experiments were already in progress.

I started studying the origin of antibodies in rabbits after the
injection of heterogeneous red corpuscles loaded more or less with
amboceptor. I have especially taken care also to use red corpuscles,
loaded with litthe amboceptor, because it was possible that this would
furnish a clue to solve the difference.

As to the technic of the experiments see below:

A great number of rabbits (145—18) were always injected witb
foreign red corpuscles at the same time. The rabbits had never been
treated with the kind of blood in question before. With my later

experiments the animals were always first weighed and injected in

642

proportion to their weight. The corpuscles had always been freed
from serum by centrifuging and washing them with a saltsolntion.
Afier that they were digested for at least half an hour with the
antiserum which was beforehand heated to 56°. As, except for a
single exception, homologous (rabbits) serums were always used for
this aim, the washing away of the antiserum was not necessary
in my experiments, and consequently this was not done. Attention
was always paid to all the amboceptor being also absorbed.

In order to find out all about the rapidity of the production of the
amboceptors, the rabbits were bled from the earveins every two or
three days. (Always litle, ’/, cem. at the utmost). The serum which
was in this way obtained, was heated to 56° for half an hour.
That is how no allowance was made for the appearance of thermo-
labile amboceptors.') However, as appears from THieLE and EMBLETON’s
writing, these are never very numerous, and they soon disappear.

The rate of the amboceptor of the various rabbitserums of one
day was always defined with the same Guinea pigserum so that
the numbers are mutually to be compared. As unity of amboceptor
a serum was taken, 1 cem. of which together with */,, cem. com-
plement (fresh guineapigserum) was able to solve 1 cem. of a 5 °/,
suspension of the corpuscles in question, in half an hour at a tem-.
perature of 387°.

In the following list the A.-rabbits have been injected with non-
sensitized, the £.-rabbits with weakly sensitized, the C.-rabbits with
strongly sensitized red cells. The bloodquantity is unthinned blood;
so for 1 cem. 20 unities amboceptor are equal to 1 dose.

Subcutaneous injection of sheepblood 1!/, ecm. per k.g. weight.

A nonsensitized

B sensitized with 6.6 dose Strength of the sensitized serum: !/gp99.
6 % 2 OOM With C all was also absorbed.
A
rabbit after days after7 days after L0days after 12 days after 14 days
121 "ho ‘hoo "Yoo "509 1/5 9 nearly
122 Vag dead intercurrent disease
123 + 1Hoq nearly 5 *
124 ! FA 100 dead
125 V9 nearly ooo Veo0 "500 "/s00

1) Turece and Empreron, Z. £. Immunititsforschung, XX, p. 1.

B
126
127
128
129
130

C

131
132
133
134
135
136

Tho
1/,9 nearly
< ho

1/,) nearly
< Wy

643

50
"oo
Moo
dead
1/199 largely

Moo
Moo
<"Nio

1/,) nearly

Noo
"/eo
50

/
y 200

1/199 nearly

dead
‘59
Moy

he <} 40

"Yo
Thy 0

V50
"oy
"ho

"Te00

Veo
hoo

'/199 nearly
oo

Result: Somewhat quicker formation of antibodies when injecting
nonsensitized red cells, and besides formation of somewhat higher
titre. But the difference is not much.

Il.

Intraperitoneal injection of horseblood !/; cem. per kg.

A nonsensitized.
B sensitized with 4 dose

C
A

rabbit

ali:
45

72
73
76
78
79

”

, 20

after 5 days
nearly 1/19

n

rabbitserum, strength 1/a99.

after 7 days
nearly 1/9
<"Nho

"ho

nearly 1/19
ho

< Mo
<A
< ho
< lho
<Nho

<tho
<a
<1
<Nio
nearly 1/9

aiter

10 days

nearly '/o9

”

”

”

”

“To
Y59
M59
Moo

<'ho

nearly 1/15

”

ho
< Myo
< ho

<ho
< "Mo
<Niho

"a9

“a

after 12 days
WEY)
"/20
"Yoo
"29
Mag

/
<'/ho
ho

‘ao
< Mo

< ‘Vio

tho
< "io
<Tho
"a9
"ao

Result: with none of the rabbits a high titre is to be found. But
the immunisation with the A rabbits is distinctly quicker and better

644

than with those of series B and C. The conduct of the A rabbits
is much more regular too; with 6 and C' there are much more
individual differences.

Ill.

Intravenous injection of oxblood 1.6 c.c.m. per k.g.
A nonsensitized.

B 1*/, dose ,
‘ rabbitserum strength 1/599.

C 95
A
rabbit weight after 2 days after 5 days after 9 days after 12 days after 14days
107 2100 <i <NMio Vivo "o00 Yooo largely
138 2100 <1 <ho “hoo Mooo nearly 1/99
109 2000 <l/, <Nig Mog nearly '/199 1/oo9 nearly
140. 2100 <i). <M lien a Vso nearly
108 2000 ass <Nho Ye0 Tio nearly 1/299
B
114 3200 <1, <0 "/s00 Y/sq9 nearly 1/;999 nearly
112 2600 <Vs <'ho “/a00 Yoon +» Yi00
115 2700 < Ys < ‘ho M500 1500 ” Mago
110 2350 <5 <Nhio Mono “Vaoo “00
116 2350 < Myo after |< 4/19 Vong after |1/509 "ooo
104 3100 <1) 4ds ae Wooo L1days}2/s500 W000
139 2300 died :
103 3300 . anaphylaxis
(G
106 1700 he <'io hoo Yooo nearly 1/199
113 2109 <5 <'ho Mag "hoo Thoo
121 1200 <Y5 <Nho 50 "/200 ‘000
142 1700 <5 <"Nhio Moo "ooo M09
125 1350 died
141 1550 5) | anaphylaxis
93 2200 ° |
Summary : ereat differences. But now the 6 rabbits (which

have been injected with weakly sensitized red cells) are quickest in

producing amboceptors.

The C rabbits finally lag behind a little, thongh not much, the
A and the B rabbits reach the same titre on an average. Soon after
the injection (5 minutes to ‘/, day) five rabbits died, 2.6 and 3 C
rabbits,

Consequently an intravenous injection of the same quanuty foreign
red cells is much more dangerous when they are loaded with

immune serum.

645

IV.

Intravenous injection 1/, ¢.c.m. per k.g. sheepblood.
A nonsensitized.

B sensitized with 4 unities dogserum, so heterogeneous serum
(6) : Palit 10) ene aps Strength: 1/149.
A

Before the injection
rabbit (The trialserums after 3days afterSdays after 7 days after 10 days
were not heated)

100 i 6 ho “Yeoo Yeo Mavoo
101 1/g Myo nearly og) nearly Yar Lodo
97 <5 < Mio *rovo ovo Vanoo
99 Ye < Mh) Thoo Taoo 1/500
98 < Ys < Vio : ut 200 Thooo 1/a000

B

96 Ys < thy Vao0 Vo 0 Mano
95 1f, nearly <M), “e00 Moo? T5900
92 "M/s ” < Myo Nooo Novo a 500
94 <I, <1) Te00 M00 U/yoognearly
93 < Ye < Tho 00 Maoo “ooo
C

90 < Ys < "io Ys ) Vr ow nearly Yano
91 V/s nearly < Wig A; ) Mo00 s oco
87 His ” < Iho Too "Yang Ya 9
89 Ye ” <p Mey Mano nearly 1/549
88 < Ye < Yio hoo 1100 “hoo

Summary: The rabbits treated here had only a small quantity of
normalamboceptors.

The C rabbits distinetly become immune more slowly than the A
and £& rabbits; the latter remain on the same level the first few
days; finally the A rabbits carry the victory as to titre.

The use of dogserum for sensitizing does not seem to be of any
influence here.

Ne

Intravenous injection of sheepblood. 1 eem. each rabbit. (The rabbits had about
the same weights, 2—3 kg.) Each group = 2 rabbits.

A nonsensitized.

B */, doses

C aM ”

ID} ey :

E 9h rabbit serum: strength !/599,. The red cells could
PF 50 . entirely absorb 150 doses.

G 100 ,

646

rabbit
A after 2 days after 5 days after 7 days after 1O days
8 ho weak 159 100 Yooo
x < Mio Vio weak Too weak Moo
B
9 Vy weak Mio “Yay weak M599 Weak
17 Mh ” "Yo 1500 ) Vs60
C
12 <Nhio <Nio M10 1/59 weak
R <M 149 weak Moy) weak Woo >
D
91 Vio 13 roo *hioo
33 Vo weak Mo) Mop 1/00
EK
24 Mo weak Mo “a9 55
18 Mho ” tho Moo 1/a00
iF
M 1/4. weak 1/)y weak 1/5) weak 1/-, weak
22 Mio "Meo "oo TO 3
G
25 ho ‘hy weak 1/5) weak Tog weak
14 < Why Moo Yeo "50 ”
H
16 Vio Moy Nov Too
15 hy weak 1, weak “hoy weak hoo
As far as results are to be drawn from this series — for the

rabbits have not been exactly injected in proportion to the weight
of their body—there does not seem to exist a great difference between
the various rabbits. The final result is somewhat better with A and
B than with the others; but the differences are small. The strongly
sensitized red cells (150 doses !) also had immunisation power.

At last I have made two more series of experiments, upon which
I will not dwell at length; with those the rate of amboceptor with
all the animals remained too low to be exactly measured, probably
by injecting too little blood: in one series no differences were to be
found, in the other the nonsensitized blood immunized a little better,
but the differences were small.

The final conclusion to be drawn from these series of experiments
may now follow :

In general one also succeeds in rousing amboceptors with sensitized

647

corpuscles. The strongly sensitized red cells mostly work less quickly ;
the serum of the rabbits gets a lower titre! But on a whole the
difference is not great, generally smaller than was found by Sacus
and von Dinerrn.

The weakly sensitized red cells are generally not inferior to the
nonsensitized as to immunisation power (in one series they even
worked somewhat more quickly); the final result is either the same
or a little less. In one series, with the treatment with red cells of
ox appeared the danger of intravenous injection of sensitized cor-
puseles: a number of rabbits died of anaphylaxis. As a rule however,
they could well stand the injections. I made one series of experi-
ments with injection (intraperitoneal) of sensitized and non sensitized
red cells of ox into rabbits, which a fortnight ago had already
had a first injection of red cells of ox, and which now all had an
equal titre (*/,,,). The rabbits that were injected with strongly sensi-
tized corpuscles all five died of anaphylaxis; of those that were
injected with weakly and nonsensitized corpuscles three died of five
resp. two of five of anaphylaxis.

So I did not continue those experiments.

December 1913. Laboratory of Path. Anatomy, Amsterdam.

Physiology. — ‘On the relation between the quantity of brain
and the size of the body in Vertebrates’. By Prof. Eugine
Dusois. (Communicated by Prof. H. ZWAaRDEMAKER).

Communicated in the meeting of November 29, 1913).
t=) )

It is obvious that, in general, in different species of animals,
the relative quantity of brain must be a measure for the degree of
the organisation of the nervous system. There are however still
other factors influencing the quantity of brain. In the first place
the size of the body, but especially also the age and the individual
deviations, further possible deviations caused by the living of the
animal out of the state of nature.

Of these factors the three last mentioned ones can easily be
excluded, the age, by choosing only full grown animals for compa-
rison, the individual deviations, by taking averages, or (which in
some cases may be preferred) by choosing individuals representing
the norm. Then remains still the factor of the size of the body.
Its influence cannot be appreciated by simply calculating the relative
quantity of brain. For a long time it has been known already that

648

in this way the required measure for the organisation of the
nervous system cannot be found, but on the contrary false relations
are obtained. Then Man is indeed not only inferior to some small
Monkeys but even to the. Mouse. The latter would then be four
times better provided with brain than the Brown Rat, ana the Cat
five times better than the Tiger or the Lion.

In general we find, not only in Mammals, but in all Verte-
brates, that the smaller species of closely allied animals, relatively
to the weight of their bodies, have a great quantity of brain.

If we exclude, however, as much as possible, the above mentioned
factors which, besides the size of the body, influence the quantity of
brain, if we thus compare animals taken in the state of nature,
which are as near as possible to one another, systematically, in their
manner of life and in the shape of their bodies, but differ as much
as possible in the size of their bodies, then it must be possible,
to discover at least, if it is not a simple proportion, some relation
existing between the quantity or mass of brain and the size, the
weight of the body.

About twenty years ago the necessary, trustworthy evidences,
chosen and explained with critical discernment, were very rare.
Thankfully it may be remembered here that it was Max Weser, who,
by procuring them, was one of the first that prepared the way for
the treatment of this problem, at least in so far as regards Mammals ').

At all events the size of the body remains a very important
factor amongst those determining the quantity of brain, for the Lion
e.@. possesses absolutely 7 times as much brain as the Cat, the
Brown Rat 6 times as much as the Mouse. Evidently the weight of
the brain is, after all, a (mathematical) function of the weight of the
body. If the quantity of brain does not inerease proportionally to the
volume of the body, expressed by the weight, it might be that this
is really the case with regard to the superficial dimensions, as being
proportional with the receptive sensitive surfaces and with the sections
of the muscles, thus measuring the passive and active relations of
the animal to the outer world, for which in this way the quantity
of brain can be a measure. Then, in animals equal in organisation
and shape, but not in size, the quantities of brain must increase as

9

the = power or the power 0.66.. of the weights of the bodies.

In those comparable Vertebrates of different sizes the longitu-
dinal dimension might likewise be the measure of the quantity of

1) Hspecially in his “Vorstudien tiber das Hirngewicht der Siugethiere’’. Fest-
schrift fir Cart Gr@EnBaur. Leipzig 1896.

649

brain, on account of the segmental structure, and the movement by
the contraction of muscle-fibres, working on levers proportional to
the length of the body in this tribe of animals.

Again, the extension or the specification of some definite receptive
surface (of sense) may likewise determine the quantity of brain. As
the former in its turn must be a (mathematical) function of the size
of the bocies of animals that are equal in shape and organisation,
it must, according to some (arithmetical) power-proportion of the
weight of the body, be one of the factors determining the quantity
of bra.

However insolvable, at first sight, the problem indicated by the

title of this communication may seem to be — as no organ is more
complicated of structure and in its physiology more obscure than
the brain — in this way it must be possible to make it fit

for solution. It must, at all events, be possible, likewise for
groups of animals of different grades of organisation, to repre-
sent the cephalisation by figures, and thus to compare them.

Be 7+ the required exponent of correlation (indicating the corre-
lation of the brain quantity to the mass of the body), be e¢ (ence-
phalon) the weight of the brain, s (soma) the weight of the body of
the smaller animal, / and SS the weight of the brain and the
weight of the body of the larger animal and & (kephalisation) the
coefficient of cephalisation, equal for both, then we have the following
equations :

EE eh S ie ksh
BEES IS! Sey

logE-log e

SSS Se
loy S- log s
Hy ie
k= —_ = —
SP s"
When working these equations by evidences contributed by Max
Weser and others J found in 1897") at a seven times repeated

1) The proportion of the weight of the brain to the size of the body in Mammals.
Verhandelingen der Kon. Akademie van Wetenschappen te Amsterdam. Volume
5. No. 10. Amsterdam 1597.

Also in French and German text: Sur le rapport du poids de l’encéphale
avec la grandeur du corps chez les Mammiferes. Bulletins de la Société d’An-
thropologie de Paris 1897. p. 337-376.

Ueber die Abhingigkeit des Hirngewichtes von der Kérpergrésse bei den
Sdogethieren. Archiv fiir Anthropologie. Band 25. Heft 1 und 2. Braunschweig
1897, p. 1-28.

650

calculation for each time two Mammals of different orders: Primates.

Ruminants, Carnivores, Rodents, always only values varying mutually

a

. "EPR 2) >
between 0.54 and 0.58, with an average of 0.56 or about = (393) 6 a <

Arranging according to #& calculated in this way, we see indeed
the great confusion prevailing in the arrangement of Mammals accord-
ing to the relative weights of their brains, give place, in a generally
satisfactory manner, to an arrangement that is pretty well in con-
formity with the natural system. A few deviations continue to exist,
the Elephant e. g. takes his place between Man and the Anthropoid
Apes, the Rodents deviate mutually very strongly. On the other
hand the different behaviour of Macrochiropteres and Microchiropteres
indicates rightly their different origin.

In 1905 the above-mentioned method of investigation was applied
to Birds by Louis Lapicqur and Pierre Girard’). By 5 comparisons
(Hooded Crow—Jay, Carrion Crow— Jay, Wild Duck—Summer Teal,
Silvery Gull—Sea Swallow, Buzzard—Kestrel) they obtained for +
a value that was so near the one I found for Mammals, that
their conclusion, that for Birds the same exponent of correlation
may be accepted, was entirely justified. According to the value of
the coefficient of cepbalisation calculated by this method, Birds,
though not entirely after the natural system, yet with regard to the
nearest affined ones, may be classified in a natural way. Parrots, the

Monkeys among Birds, stand highest in the list *).

Afterwards a few other comparisons (Swan—Summer Teal, Eagle—
Kestrel, Parrot— Parrakeet, which species showed greater differences
in the sizes of their bodies), could be added by Lapicqug*) to the
first 5 comparisons; in this way ‘still better results were obtained.

The 5 most thrustworthy comparisons gave now an average r—0.558.

This constant returning “of ‘cette puissance étrange”’ 0.56, the
meaning of which is absolutely incomprehensible according to
Lapicqusr *), likewise in Birds, where the anatomical composition
of the brain is certainly very different from that of Mammals, must
indeed be called exceedingly striking.

Under these circumstances it was of great interest to investigate

1) Comptes rendus des séances de |’Académie des Sciences. Paris 1905, 1, Tome
140, p. 1057—1059.

°) Bulletins du Muséum d’histoire naturelle. Paris 1909, p. 408—412.

8) Revue du Mois. Paris. 10 Avril 1908.

4) Revue du Mois. Avril 1908. p. 445. Further: Bulletins et Mémoires de la
Société d’ Anthropologie de Paris. Séance du 2 Mai 1907. 5me Série, Tome 8,
fasc. 3. Paris 1907, p. 261.

651

the relation between quantity of brain and size of the body likewise
for the lower classes of Vertebrates. This is connected here with
greater difficulties, for whereas in Birds the relative weight of
the brain is still of the same order of amount as in Mammals,
it descends in the inferior classes, both absolutely and relatively,
as low as to the order of magnitude of about '/,, of that of the two
highest classes. The quantities of brain we have to deal with are
thus absolutely little, and we can only make use of those rare
cases of the usually very scarce evidences about these classes, in
which the weights of the bodies show great differences. A few
accurate evidences are found in Wewcksr’s ‘‘Gewichtswerthe der
K6rperorgane bei dem Menschen und den Thieren”, published after
the author’s death by A. Branpr'). Further L. Laproqve and H. Lavarer *)
gave in 1908 some trustworthy determinations of weight, and lately
G. Wareriot, who had made himself conversant with the technical
method in the Laboratory of Lapicqur, published a great number of
weights of brains and bodies of Vertebrates, among which also
Reptiles and Amphibia, determined in Dahomey *).

As early as 1855 and 1856 E. Crisp gave trustworthy evidences
concerning a Reptile and a Fish ‘).

Among Warertor’s Reptiles were a Monitor and a Gecko, belonging
both to the same sub-order of the Lacertilia as likewise the Emerald-
Lizard, of which Lavcimr and Lapicqgué communicated the weight.

All were full-grown animals, the Monitor (Varanus niloticus) was
a subject of mean size; four individuals of the little Gecko (Hemi-
dactylus Brooki) were weighed and consequently average weights
can be calculated. The weight of the body of the Varanus is 1600
times that of the Gecko and almost 450 times that of the Emerald
Lizard. Under these circumstances trustworthy results may be expected.
A third good comparison of Reptiles affords a Viper (Vipera berus),
of which Crisp weighed 7 individuals, with a Cobra (Naja melano-
leuca) of Dahomey, weighing almost 28 times as much. A few other
Reptiles have been inserted into the following table. The values of
k& calculated with »—= 0.56 are likewise indicated in it, as well as
the average diameter of the eye-ball of some species °).
=i) Archiv fiir Anthropologie. Vol. 28 (Brauuschweig 1902), p.p. 55—61.

*) Comptes rendus. Soc. de Biologie. Paris 1908, Vol. 64. p. 1108.

8) Bulletins du Muséum d'Histoire naturelle. Paris 1912, p. 491.

4) E. Crisp, Proceed. Zool. Soc. London. Part. 23. (1855), p. 191. Ibid. Part 24.
(1856), p. 106.

5) N°. 7, 2 and 4 have been borrowed from Watertor (l.c.), 3 and 8 from
Lapicgue (l.c.) 5 from Crisp |.c. (1855), 6, 7 and 9 from Wetcker — Branpr (1.c.). —
An Alligator mississippiensis from Hropuicka, cited by Laricgue (Bull. et Mém. Soc,

| | Average
| idiameter
Sai IS anhaie) pe ontheeve
| | ball, in
at m.m,
z. Monitor (Varanus niloticus) (1) (7500. G.| 2.440G.| 0.0165 | 12.5
2, Little Gecko (Hemidactylus Brooki) (4) | 4.7 |0.043 0.0181 | 4.1
3. Emerald Lizard (Lacerta viridis) (aver.) 16.8 0.093 0.0191 | 5.8
4. Cobra (Naja melanoleuca) (1) 1770.0 | 0.646 0.0098 7.0
5. Common Viper (Vipera berus) (7) | 64.2 {0.105 | 0.0102 |
6. Common Lizard (Lacerta agilis) (2) | 12.507 0.076 0.0185
7. Slow Worm (Anguis fragilis) | 16.252 0.039 0.0082 |
| |
eas - é % 18.9 |0.037 | 0.0071} 2.8
g. Greek Tortoise (Testudo graeca) 993.58 0.360 | 0.0075 |

Herewith the following values for 7 are obtained. By comparison
of J with 2: 0.5476, of J with 3:0.5355, 4 with 5:0.5478. The
average for the examined Reptiles is 0.5436.

All these values are again so near to 0.55.., or °/9, that there
is no doubt but the same exponent of correlation may be accepted
for the three highest classes of Vertebrates. Here already I point to
the low value of 4 both of the Slow Worm (Anguis fragilis) and of
the Snakes in contradistinction to the Lizards.

Regarding Amphibia I have not been able to obtain entirely satis-
factory data for the calculation of r. The giants among these, as the
American Bullfrog (Rana mugiens or Catesbyana) and the Indian
Tiger-spotted Frog (Rana tigrina), reach only 5 times the size of the
nearest related species to be compared with. For the Bullfrog I have
calculated of Donapson’s*) 6 largest individuals the value of s 244.4 G.
and of ¢ 0.204 G. A comparison of the latter with our Waterfrog
(Rana esculenta), according to Lapicqur’s averages for s and e, gives
only an exponent of correlation of 0.38848. Compared with Lapicqug’s
Rana fusca (aver.) 7 becomes on the contrary — 0.5501. It seems
that the Bullfrog, at least in the organisation of the nervous system,

d’Anthrop. l.c. p. 263), with s = 11.34 KGM affords, as not full-grown, probably
too high a k (0.0268). For a *Crocodile” mentioned by Manouvrier (“Sur linterpré-
tation de la quantité dans l’encéphale”. Mémoires de la Société d’Anthropologie.
Paris 1885. 2me Série, Tome 5, 2me fase. p. 167) of about 70 KGM body weight,
we find k = 0.0290.

‘) Decennia! Publications. University of Chicago. Vol. X. (1902), p. 7 and Journal
vi Comparative Neurology. Vol. 8 (1898), p. 330.

653

is more closely allied with the European Landfrog than with the
Waterfrog. The similarity in the modus of living with the latter has
no influence in this respect. The following calculations of / for some
Amphibia prove indeed that other factors are predominant there.

Valuable evidence for the calculation of the exponent of correlation
for this class might be obtained from tke Japanese or the American
Gigantic Salamander (Megalobatrachus maximus and Cryptobranchus
Alleghaniensis). The former is certainly more than 100 times heavier
than the Spotted Landsalamander, and surpasses the Crested or Great
Newt more than 400 times in weight. But, as far as I know, this
evidence does not exist.

If we admit for Amphibia the same exponent of correlation as
for the three highest classes of Vertebrates, then we find the following
values for /.

Ss 15 Ne ae
1. Waterfrog (Rana esculenta) (aver.) | 44.5 G.) 0.106G. 0.0127
2. Leopard Frog (Rana virescens) (5) | 13ooe On 153— |NOLO138
3. Bullfrog (Rana Catesbyana) (6) 244.4 | 0.204 | 0.0094
4. Landfrog (Rana fusca) (aver.) | 53.0 | 0.088 | 0.0695
ys. Common Toad (Bufo vulgaris) (aver.) 44.5 | 0.073 | 0.0087
6. Shackletoad (Alytes obstetricans) (aver.) ged] | 0.041 | 0.0131
7. Treefrog (Hyla arborea) (aver.) | 4.8 | 0.043 | 0.0179
8. Spotted Landsalamander (Salamandra maculosa) (1) | 24.88 | 0.047 | 0.0078
g. Great Water-Newt (Triton cristatus) (2) ') | 7.46 | 0.019 | 0.0062

The comparatively high value of / in the two first mentioned
species, likewise in Alytes obstetricans and especially in the
Treefrog, has evidently some relation with a higher organisation of
the nervous system, and not with the surroundings in which the
animals live. Rana Catesbyana lives, as likewise R. esculenta and
R. virescens, in water, ranks however near to R. fusea, the Landfrog.
The deviation of & in this respect is in the latter analogous with

1) N’. 1, 4, 5, 6, 7 are borrowed from Lapicgue and Laverer (l.c.); 2 and 3
from Donatpson (Journal of Comparative Neurology. Vol. lO. (1900), p. 121 [the
5 largest Rana virescens (¢)|, Journal of Comparative Neurology. Vol. 8. (1898),
p. 330. Decennial Publications. Chicago. Vol. 10. (1902), p. 7 [the 6 largest Raua
Catesbyana]; 8 and 9 from Wetcker-Branpr (l.c., p. 57 and 58).

42

Proceedings Royal Acad. Amsterdam. Vol. XVI.

654

that of Salamanders and Newts, where the latter, which live
in water, have however lower cephalisation than the Landsala-
mander. In general the vaiue of & does not differ much from that
of Reptiles.

If now we find in the lowest class of Vertebrates, the Fishes,
for r the same value as for the three highest classes, then it is
certain that also in the Amphibia, which rank between them, the
same relation exists between weight of the body and weight of the brain.

Of the following evidence regarding Fishes the greater part has
been borrowed from Wretickrr-Branprt ').

SS) | E k
7. Carp (Cyprinus carpio) 1ST 23 Gael 270eGe 0.0190
2. Crucian (Carassius vulgaris) | 522 | 0.470 0.0186
3. Gudgeon (2) (Gobio fluviatilis) 42.196 | 0.159 0.0195
4. Perch (Perca fluviatilis) 67.27 | 0.162 0.0153
5. Stickleback (2) (Gasterosteus aculeatus) | 1.447 | 0.022 0.0179
6. Pike (Esox lucius) 2) |12700 4.860 0.0245
7. Conger (Conger vulgaris) 3) 10000 1.050 0.0060
8. Eel (Anguilla Anguilla) 3) | 650 | 0.170 0.0045

When comparing each time two, the nearest affined species, the
following values for r are found: J with 2: 0.5638, 7 with 3: 0.5522,
4 with 5: 0.5201, 6 with 2: 0.5949, 7 with 8: 0.6661.

With the exception of the last, to which I shall revert
afterwards, these values are also all near to 0.55... The average
of the four is 0.5576.

Eels (Muraenidae) excepted, the comparatively high values of
k:, in which most Fishes equal even the examined Reptiles, are
striking. In the low value of & in the Eels we find a similar pheno-
menon, the probable cause of which I shall indicate afterwards, as

1) L. c¢., p- 59-61. There 3 more perches. The statements for them deviate
however so much from what may be admitted as normal for this species, that
they cannot be used separately for trustworthy calculation of 7. Compared with
the 2 sticklebacks they give for ry values ranging from 0.437 to 0.644. The
average of 4 comparisons is 0.525.

2) I. Crisp in Proceed. Zool. Soc. London. Part. 24. (1856), p. 106.

3) L. Laprcgue, Bull. et Mém. Soc. d’Anthrop., Le. p. 263.

655
.

in the Snakes and the snake-shaped Slow Worm, but the deviation
is here still greater on account of a second cause.

The results obtained in this way seem to prove with certainty
the existence of a law that can be applied to all Vertebrates, indi-
eating the relation between quantity of brain and_ size of body.

In species of Vertebrates that are equal in organisation (syste-
matically), in their modus of living and in shape, the weights of the
brains are proportional to the */9 power of the weights of the bodies.

Before we try to discover the meaning of this law, it is
important to determine the value of the exponent of correlation for
the brainweight of large and small individuals in one and the same
species. The differences of size of the body are, in most cases, com-
paratively much less here than those between the species mutually,
and we are generally obliged to take averages of a great number
of individuals, to make the errors attending each special observation
balance as much as possible against one another. With the exception
of such species as the Dog, having many races of very different
sizes, the best evidences can consequently be found for Man.

The result | obtained in this respect for Man, in 1898, was com-
pletely contradictory to what I found for different species of Mammals.’)
The exponent of correlation proved to be an entirely different one.
For obvious reasons we cannot dispose, with regard to Man, for this
calculation of sufficient evidence, relating to normal weights of the
body belonging individually to the weights of the brain. In order
to be able to compare these quantities, we may follow two
indirect ways. In the first place it is possible to calculate the weight
of the brain of living Man. According to the method of Wetckur,
which has proved to be very trustworthy, | calculated the weights
of the brains of four groups, each of 10 strong, healthy, and not fat
young men, from the dimensions and shapes of their heads, which
evidences Orto Ammon had been kind enough to provide me with.
It had been ascertained for those 40 men that they did not 2row
any more. They were all small farmers and day-labourers from
Baden. In this way I found an exponent of correlation of about
0.25, the value 0.245 (of two of the six combinations possible) is
probably more correct.

Taking the second way I calculated + from the directly determined
weights of the brains of Englishmen (Londoners) with average
weights of bodies of men of the same social class, according to the

1) Ueber die Abhangigkeit des Hirngewichtes von der Kérpergrésse beim Menschen,
Archiv fiir Anthropologie. 4’. Bd 25. Heft 4. Braunschweig 1898, p. 493-441,

424

656

unsurpassed data of Joun Marsan"). Here the value of 0.219 was
found for 7.

I tried to explain that strongly deviating behaviour of individuals of
Man, differing in size, in comparison with species of Mammals of
different sizes, by the uncomparatively great supremacy of the brain
over other organs and parts of the skull in Man. The inferior augmen-
tation of the brain with tbe size of the body might be a consequence,
in my opinion then, of an exceptionally strong progressing folding of
the grey cortex, going hand in hand with that augmentation of the
brain as a whole. At the present state of our knowledge, now that
we know that in all Vertebrates in general, independently of
its shape and structure, the augmentation of the brain is equal for
all species that are of a similar organisation, the interpretation
then given, that can only be applied to Man, must be entirely
abandoned. I should certainly immediately have rejected it, if I had
known that, a few months previously in 1898, Lapicqur, when
applying the relation | had found for Mammals, to dogs of different
sizes, according to evidences borrowed from a series of Ricuet, had
obtained the same result, as | now found tor Man. That result had,
moreover, only been communicated by Lapicgur in a report of the
proceedings of the meeting of the Société de Biologie on the 15%
of January 1898, in hardly a single page of printing’) together with
the announcement of my memoir on Mammals.

His conclusion ran: “Tout ce que je veux établir aujourd'hui,
c'est que la puissance de P (the weight of the body), suivant laquelle
varie l’encéphale d’espece a espéce étant 0.55, dans lespece chien
cette puissance est 0.25, c’est a dire extreémement different”. Simul-
taneously with my paper on Man of 1898, in the “Archiv fiir An-
thropologie”’, Lapicque published with Durée another article *), in
which the authors communicate as briefly the result for the Dog,
mentioned above, and, on account of an examination of the chemical
composition of the brain, try to find an explanation of the exponent
found for this species in the relative amount of white and grey
1) On the relations between the weight of the brain and its parts, and the
stature and mass of the body. Journal of Anatomy and Physidlogy. Vol 26. London
1892. p. 445. There the weights of the bodies of living men, according to
Joun Beppoe (Memoirs. Anthrop. Soc. London. Vol. IIL. 1870, p. 533).

2) “Sur la relation du poids de l’encéphale au poids du corps” in “Comptes
rendus hebdomadaires des séances de la Société de Biologie”. Paris 1898. N°. 2
21 janvier 1898), p. 63.

3) “Sur le rapport entre la grandeur du corps et le développement de lencé-
phale”. In ‘Archives de Physiologie normale et pathologique”, N°. 4. Octobre 1898,
Paris. p. 763—773.

657

substance varying with the size. They ask themselves the question,
if the law found for the Dog may in general also be applied to
other species, and give a negative answer to it. “A priori, on doit
estimer que non, et nous avons soin de dire que notre étude porte
sur un cas particulier.” (p. 765). In conclusion they say: ‘Il y a
done, en passant des petits aux grands chiens, une différence sensible
de la composition chimique, et, par suite, Punité de poids ne repre-
sente pas pour les uns et pour les autres des valeurs physiologiques
identiques”’, (p. 773).

It is clear, that by Lapicque and by me, independently of each
other and unprejudiced, an identical result has been obtained for
two very different species of Mammals. If this circumstance increases
considerably the importance of this result, then it appears at the
same time that neither of us surmised he had found an interindi-
vidual exponent of correlation equal for all species.

Calculating the value of 7 for the dog found by Lapicqur,
proportional to the number of observations used for each comparison,
afterwards’) communicated by him, I find it to be — 0.285. When
he repeated the investigation applied to Man, which had caused me
to find the two above mentioned values of r 0.245 and 0.219, with
other evidences, according to the second method, he found for Man
0.23 and for Woman 0.224. A comparison of the averages of 7
larger with 7 smaller individuals of an American Squirrel (Sciurus
carolinensis), which 14 individuals with a smaller American species
(Sciurus carolinensis) (6 individuals) had furnished an exponent of
correlation of 0.56, gave an interindividual exponent of 0.20 °).
With two groups of 5 female Moles of Manouvrrer I find 0.284 °).
The average of these seven observations is 0,228.

A number of other comparisons, with less good evidences, however,
constantly furnished values that do not differ much from the average
found in this way. When I compare the above-mentioned weights
of the six largest Bullfrogs of Donatpson (I. ¢.) with the six next in
size of the same species, I find an exponent of correlation of 0,2516.

1) “Le poids encéphalique en fonction du poids corporel entre individus d’une
méme espéce’’. Bulletin et Mémoires de la Société d’Anthropologie de Paris. Séance
du 6 juin 1907. 5™© Série, Tome 8, fasc. 4, Paris 1908, p. 315.

2) Lapicgue, ‘Le poids encéphalique en fonction du poids corporel entre individus
d'une méme espéce’’, |. c. p. 327.

3) There must be errors in Manovuvrier’s statements (Mémoires Soc. d’Anthrop.
Paris 1885, p. 213 and p. 297) concerning two groups, each of 7,% moles, as the heavy
individuals should on an average only possess 1 mg. more brain than the lighter
ones; the average likewise points to these errors. Consequently these groups are
useless for the calculation of the interindividual 7.

658

Taking into consideration that the certainly still more correct lines
of DonaLpson *) give to 7 a value of 0.2316, we may call this result
very satisfactory. On grounds to be discussed afterwards we may
admit that indeed the exponent of correlation within the same species
of all Vertebrates is 0,22...

In my previous communication of the result for Mammals I had
borrowed, on behalf of a provisional comparison with Man, for the
calculation of / available evidences from the 24 edition (of 1893)
of Vimrorpt’s “Daten und Tabellen’. Calculating with the general
exponent of correlation 0,56 I found then a somewhat different value
of & for Man and for Woman. If I had made use. of more accurate
evidences, the cephalisation would have been found identical for the
two sexes, as-has indeed been proved by Lapicqur’) in 1907, and
at the same time it would have been proved that between Man and
Woman of different size the same exponent of correlation obtains as
between species that are equivalent with regard to the organisation
of the nervous system, but differ in the size of the body.

I can now affirm this by two more series of evidences. Placing
namely thé four groups of English men of average size, borrowed
from Marsaaty, used for my calculation of the exponent of corre-
Jation for Man, beside the four groups of average English women
of his Table XVIII (le., p. 498) we find 63685 G. and 54432 G. for
the average weight of the bodies and 1353.7 G. and 1233.2 G. for the
average weight of the brain. The result of the calculation is 7 = 0,594.

For the average weights of the brain of English and Scottish men
and women we obtain 1875 G. and 1235 G., according to seven different
observers, cited in the new edition of Virrorpt’s “Daten und Tabellen’’.*)
The weights of the body for full-grown men and women of that
nationality, according to Rogers, cited there, are 68010 G. and 52170
G. (deduction made for what Roperts indicates for the weight of
the clothes). With this value r can be ecaleulated at 0,568.

Calculating with the weights of the body according to Ropgrts
and the weights of the brain according to MarsuaL. we find 0,498.
The average of these three results is 0.558.

There are no sufficient evidences at hand for testing this sexual
difference in species of animals. KouLBrueeE*) gives the weights of

‘) For these comparisons 4 and e were borrowed from the graphical repre-
sentation in Donatpson’s publication of 1898 (J. c. p. 329).

*) “Le poids encephalique en fonction du poids corporel entre individus d’une
méme espéce’. |. c. p. 344,

8) Dritte Aufl. Jena 1906, p. 23—24, 75—76.

') Zeitschr. f. Anatomie und Morphologie. Bd. If (1900), p. 51—55d.

G59

the body of the Javanese Budeng (Semnopitheeus maurus and
pyrrhus) relating to 11 female and 7 male individuals and the
weights of the brain of 4 female and 3 male individuals. It is
a great pity that a few errors must have slipped into these precious
statements of the weights of the bodies‘). It is, however, possible to
calculate 0.553 or 0.536 for the imtersexual exponent of correlation,
either when correcting the presumable errors or when omitting
these erronical weights of the body.

What has been stated for Man, considered in connection with the
rational meaning of the exponent of correlation 0.55 still to be dis-
cussed, gives us already a right to admit that for Vertebrates in
general the following law exists: The seves differing in size of one
species are in the quantity of brain proportional to each other us two
different species with identical organisation of the nervous system.

The attention may here be called to the fact that this law is in
accordance with the result of the latest investigations about the
hereditary transmission of sex’), as with those of DumBar on the
sero-biological behaviour of the sexes in plants and animals.

Further I want to point out that there is a connection between
the relation of the two sexes found and the non-existence of the
disproportion in the relative length and thickness of the bones,
which is so striking a feature between the large and the small
individuals of one species. *) Both sexes behave, in this respect too,
as nearly related species of very different sizes.

*) The uniformity of the correlation found between quantity of
brain and size of body in all classes of Vertebrates, however
striking, cannot, properly, surprise us, as we did eliminate a priori
all other important influences on the quantity of the brain, save
the size of the body. That uniformity affords proof that indeed we
succeeded in eliminating those other influences and, moreover, that the
size of the body influences the quantity of the brain in the same
way in all classes.

One may, however, consider it strange that the well known in-
crease of the relative amount of white substance (composed chiefly
of medullated fibres) contrary to the grey substance (containing the

1) It seems indeed that in three cases pounds are written erroneously for kilos.

2) C. Cornrens and A. Gotpsmipt, Die Vererbung und Bestimmung des Geschlechtes.
Berlin 1913.

8) Species with a relatively slight difference of size (as e.g. Hylobates syndactylus
and H. leuciscus) show a disproportion in a reverted sense: between species of
very different size this is scarcely perceptible.

+) The passage between brackets is added in the English transtation.

660

bodies of nerve cells), an increase going on, systematically, with
increasing quantity of the entire brain, does not appreciably corrupt
those results.

It was this consideration that induced Dakré and Lapicaur to
investigate the chemical composition of the brain in large and small
dogs.*) From their results it is obvious that the real disproportion
between the two: constituents in large and small brains of nearly
related animals, though existing, is insignificant when compared
with what it seems to be on sections of those brains and from super-
ficial mathematical reflection. We may infer that the seemingly very
striking disproportion is, to a very large amount, corrected by other
variations going hand in hand with augmentation of the quantity
of brain, namely increasing thickness and folding of the cortex and
less rounded form (i.e. relatively more extended surfaces) of the
larger brain, these three processes (or two in the brains without
folding) tending to inerease the relative amount of grey substance.

The positive knowledge, obtained in this way, of the relation
between quantity of brain and size of the body, in species and indi-
viduals, gives now a meaning to that ‘puissance étrange” 0.55.. and
at the same time 0.22.. by which those relations are determined.

Referring to the arguments in my memoir of 1897 on the peculiar
relation of the eye to the size of the body, and continuing the
analysis of the exponent 0.56 or 0.55,., I believe that it will be
easy tO prove its rational character, as well as that of the exponent
0.22.. In this way the correlations we found are raised to the
rank of real biological laws.

In the memoir of 1897 I had already pointed out that the factor
that expresses the deviation from the simple relation between weight
of the brain and superficial dimension of the body is the cube-root
of the linear dimension of the body.

S55 can be analysed as follows:

eee 2) iris
A, 1S 0'66-—= 0 Say B. §022-+0.33 — 69) +4
2 2
as = Seals
L8

The relations found above can then be described as follows:
I. In species of Vertebrates that are alike in the organisation

*Sur le rapport entre la grandeur du corps et la développement de l’éncé-
phole.” lc. (1898).

661

of their nervous system and their shape, but differ in size, and also
in the two sexes of one and the same _ species, the quantity of
brain increases :

A. as the quotient of the superficial dimension and the cube-root
of the longitudinal dimension.

B. as the product of the longitudinal dimension and the square
of its cube-root.

Il. In individuals of one and the same species and of the same
sex, differing in size, the quantity of brain increases as the square
of the cube-root of the longitudinal dimension of the body.

Consequently we find between the exponents 0.22.. and 0.55.. a
relation of a simple nature.

2

Moreover the factor S°?2 or L? in B is the square of the deno-
minator in A.

The fact that, in different species, a factor determining the
quantity of brain is to be found in the superficial dimension of the
body, which is the measure of the sensitive surfaces as well as of
the muscular force, was discussed at large in my memoir of 1897.
It is neither incomprehensible, that individuals of different size in
one and the same species distinguish themselves from, for the rest
closely resembling species differing in size, because only in the latter
case an increase of the quantity of brain proportional to the longitudinal
dimension takes place, as a consequence of segmental growth, in-
crease of sensu-motorical unities in segmentically constituted species
of animals.

From the investigations of JI. Harpgsty ') it appears that in the
Elephant, which is 180000 times heavier than the Mouse, and in
Man, who is 38625 times heavier than the Mouse, the masses of
certain nerve-cells of the spinal-cord are proportional as the imagi-
nary longitudinal dimensions of the mentioned species.

If we admit that to every nerve-fibre a definite central cell-mass
answers, then these masses must increase with the number of nerve-
fibres, in segmentically constituted animals indeed as the longi-

tudinal dimension.
l

But what is then the meaning of L3?

The answer to this question was likewise prepared in my memoir
of 1897. It is to-be found in the very special relation between the
size of the eye and the body in animals of different sizes. The
longitudinal dimensions of the body and the eye of these animals

‘) Journal of Comparative Neurology. Vol. 12 (1902), p. 125—182.

662

are not proportional to each other, neither are they absolutely equal;
in other terms, the smaller animal has, in proportion to its body, a
large eye, yet it is absolutely surpassed by that of the larger animal.
We find here evidently a similar relation as between the weight of
the brain and that of the body, and can try to fix this relation in a
similar way, by caleulating an exponent of correlation.

Most fit for this comparative investigation are again species that
differ as much as possible in size, and have at the same time
absolutely large eyes. Instead of the simple diameter of the eye-ball
(which in its shape and in the thickness of the sclerotica is variable) it
is preferable to compare the linear sizes of the images on the retina. More
than twenty years ago Marruivssen') made exact measurements
of the sizes of the images on the retina, amongst others in Whales,
which together with others were already formerly discussed by
me. He does not indeed indicate the sizes of the animals them-
selves, but if we admit for them the averages of the full grown
species, then the error resulting from this insufficient information
cannot be very great.

Let us thus compare the largest of the four examined species of
Whalebone-Whales, Sibbald’s Fin-Whale, with the smallest, the
Humpback Whale, and calculate according to what exponent of
correlation of the length of the body proportionality with the size
of the image is obtained’).

Proportion of

linear sizes of the lengths of the body (2)

images (in Millimeters) (in Meters)
Larger Fin-Whale i |
(Balaenoptera Sibbaldi) | 39.78 | 30
| 15

and ,
30.23
Humpback-Whale |

(Megaptera Boops) |

We find then that on an average the lengths of the body must be
involved to the power 0.3964 to become proportional to the lengths

1) L. Marrutessen. Die neueren Fortschritte unserer Kentnis von dem optischen
Baue des Auges der Wirbelthiere. Festschrift fiir H. von Hetmnonrz 1891, p. 62-63.

2) The Porpoise (mentioned by Marrutessen as ‘Delphinus communis”’) and the
Whalebone-Whales belong to phylogenetically different orders, Ondontocetes and
Mysticetes, which differ greatly both in the relative size of the eye and in the
ephalisation (this in reverted proportion). Therefore they cannot be compared here.

663
8 9 7.6
of the images, i.e. almost VlorVS=S°"'!, correctly S°-!8? or VS.
In the interesting essay of Avuaust Pirrer') | find, in text and
in figures, statements both of the retina-surface and of the size
of the body of full-grown individuals of Hyperoodon rostratus,
the Bottlenose-Whale, and of Phoeaena communis, the Porpoise,
both Odontocetes. The lengths of the bodies are proportional as 6: 1,
and the diameters of the retina as 2:1. From this follows, that

SS \OuIS3)5. hai AG
those diameters increase as (=) = =
s s

In my memoir of 1897 a Lion was also compared with a Cat for
the calculation of the exponent of correlation. “The exponent of
correlation I found was 0.5466. The coefficient of cephalisation,
calculated with 0.55.., gives therefore a different result for them.
In order to obtain equality, the S of the Lion must only be a little
diminished (according to the proportion that presumably existed
between the two individuals examined by Marruiessen). Then the
proportion of lengths of the images in the eyes, measured for both

; 18.95 15/8
Species, = ——, is exactly equal to A F
11.80 8

An equal relation is found between the Sea-eagle and the Hawk.

The general validity of this relation is especially obvious when
comparing little animals with enormously Jarge ones. The shapes of
the bodies can then even be greatly different, if only there is no
great deviation in the coefficient of cephalisation. Among the animals
of which Marrninssen has measured the lengths of the images, are
also the Fox, the Cat and the Rabbit. The weights of the bodies of
these animals and also of that of Sibbald’s Fin-Whale, (of which
several individuals have been examined) are approximately known.

Between these the following relations are found:

Proportion of the

13
( s Me ana Kilograms | lengths of the
| s jimages (in Millim.)
|
| 0.133 |
Sibbald’s Fin-Whale and Fox | (eS) = 31643) | 22228 = 4903
6 | 9.42
100000 \0-133 39.78
| A SUG hy eee SS
: s » Cat | ( : ) 3.995 | gp = 3:31
| 7 100000 \0.133 esOn7e: he ee
“ » Rabbit | ( aaa) = 4.381 | 19 = 4329
| |
Average | —— 4.006 | — _ 3.974

|
‘) Zoologische Jahrbiicher. Abtheilung fiir Anatomie und Ontogenie der Thiere.
Jena 1903. p, 240, 243, 273 and 280.

664

Lapicgur has measured the diameters of the eyeballs of a number
of Vertebrates and found for Mammals an exponent of correlation

: zi 5 1 f
first of ane afterwards of —'). For the examined Mammals _ the

measurement of the diameter of the eye-ball was generally sufficient in
order to ascertain the size of the retina. He concludes then, as was
to be expected from what could be shown already in 1897, that
in most cases the size of the eye runs parallel with the weight of
the brain.

Those meritorious measurements of the eye-ball by Lapicqur thus
furnish a welcome affirmation of the results obtained here with regard
to the images on the retina. We may admit that the linear dimen-

5
sions of the images vary as y, iS OG yop
9 =

If the result had been “Sor S1'1--= £3, then we should have
here the same factor as in the coefficients for the brain, and we should
immediately be convinced of its rational character. Now it ean, again,
not be by chance only that even in apparently absurd compari-
sons (as those of Sibbald’s Fin-Whale with species of little land-
animals) that same exponent '/75 constantly returns. What is the meaning
of this facet?

The answer to this question too is not difficult, for 9: 7.5 =
0.66..:0.55... If now we consider that, in accordance with the
augmentation of the brain with the size of the species of animal, the
sensitive surfaces must increase in the same proportion to the superficial
dimension of the body, then it becomes comprehensible that the receptive
sense-elements in the retina do not remain entirely equally thiek
with the larger animal as with the smaller one, but become thicker
and less closely placed*), im the same proportion. For this reason
the number of the nerve-elements in the retina increases only linearly

9

1 2
9 9 =
as VS or 13, in the superficial dimension as V S?= S ® or S®-*2--

9

= L3 °

In this way a connection has been established between the expo-
nent of correlation for the eye and the exponent of correlation for

1) “La grandeur relative de l'oeil et ’appréciation du poids encéphalique’’. Comptes
rendus de l’Académie des Sciences. Paris, Tome 147, (1908), 2, p. 209. “Relation du
poids encéphalique a la surface rétinienne dans quelques ordres de Mammiferes”’. [bid.
Tome 151, (1910), 2, p. 1393. On lower Vertebrates: L. Lapicgue et H. Lauaira
in Comptes rendus de la Société de Biologie. Tome 64, (1908), p. 1108.

2) Compare the data in A. Pirrer, Organologie des Auges. 2nd Ed. Leipzig 1912.

the brain with the mass of the body, within one species, as well as
from species to species.
Still it remains, however, an open question why the lengths of the
images, as measured by the number of sense-eiements, increase
1

exactly as L3 = 1033...

In order to find an answer to if, we must consider, that the eye
distinguishes itself from the other senses by giving at a distance a
representation of the exact place of the energy-source that acts as a
stimulus. Consequently it orientates about the direction from which
that stimulus comes. Object and image, that is the place of the
stimulated sense-elements, answer to each other.

Under these circumstances the distance to the objects must
exactly stand in the mentioned relation to the linear dimension of the
body. Indeed the receptive nerve-elements of the retina placed in the
linear dimension of the image, increase then numerically in the propor-
tion of L°33- in the larger animal, their mass in the linear dimension
as L, their mass for the surface of the image as 47. But that mass
determines the amountof the transition of energy that is connected
with the stimulation of the sense-elements.

It appears now that the long since known intimate connection of
the organ of vision, as exquisite sense of room finding its principal
function in governing the movements, can be expressed in a definite
measure'). As in the movements of animals, differing in the size of
their bodies, the mass that is to be removed, increases in the pro-
portion of Z*, the muscle-power however only as L’, an L-fold
sensu-motorical stimulation is required for it. And as all senses are
more or less, as the optical sense is absolutely, organs of room,
their receptive elements must, in the aggregate, increase in mass in

1
that proportion of Z, that is in linear dimension as 1° in super-

» 9

ficial dimension as 1%, or S®. But the nerve-fibres, the peripherical
extremities of which are connected with sense-elements in the retina
and also in all other sensitive surfaces, and the corresponding cell
9) By
masses in the brain must increase as VS? = S9 = S022..,

S [?
The denominator of the coefficient —- can thus be explained as

L3
a relative reduction of the brain of the larger animal proportional

1) In a striking way this connection is demonstrated by Piérrer (1. ¢. p.p. 8d et
seq. and p.p. 402 et seq ).

666

to the relative reduction of the sizes of its images, a diminution of
the distance from the objects of his sphere of feeling and acting
and a diminution of the rapidity of movement in proportion to the
leneths of the bodies.

The conclusions we have thus obtained give an explanation of a
number of otherwise incomprehensible deviations in the value of the
coefficient of cephalisation.

For Bats J caleulated in 1897 a (mutual) exponent of correlation
of 0.66... It appears that it can be applied both to Macro- and to
Microchiropteres. A very large insectivorous Bat from Dahomey
(Scotophilus gigas) supplies a welcome control and affirmation of
my former results. In Bats the influence of the eye is almost

entirely excluded. The senses of touch and hearing determine the
i

quantity of brain and the factor S°''- or L? disappears. Calculated
with their own exponent of correlation the coefficient of cephalisation
still diminishes for the two phylogenetically different groups, of which
the Microchiropteres are lowest.

Rodents deviate mutually considerably in the values of their
cephalisation. This cannot be explained, as Lapicqueé surmises, by
different size of the eye, though it may play in some cases an in-
ferior part. It is the other senses especially, which, by taking the lead
in the nervous life of the animal, determine here the quantity of
brain. According to numerous evidences the cephalisation of the
Brown Rat and the Black Rat and likewise that of the Housemouse
is half that of Hares (and Rabbits) and only a third part of that of
Squirrels. In the Hares the sense of hearing, in the Squirrels, the
Desert Jerboa (Dipus) and the Garden Dormouse (Eliomys) especially the
organ of touch, on account of its high specification (in the hand), has
caused the increase of the brain.

The value of & falling very low in Shrews, is trebled with the
affined East-Indian Tupaja, which lives like the Squirrel.

Canides have about twice as high a cephalisation as Mustelides,
on account of the greater development of their senses of hearing
and of smell. Among the last-mentioned family, Otters are hand-
animals, and, for that reason, they surpass very considerably the
other Mustelides in their cephalisation. They reach the rank of Canides.

The Elephant surpasses the other Hoofed Mammals three times in ¢e-
phalisation. He ranks even much higher than the Anthropoid Apes. He
owes this to his trunk, which has become a prehensile and touch
hand, with high “specific energies”, and possesses the same combina-
tion with a chemical organ (here of smell) as the feelers of Ants.

667

Some of the American Monkeys (Ateles), which are higher cephalised
than the Monkeys of the Old World, not excepted the Anthropoid
Apes, obtained a third prehensile and touch hand in thew tail.

Man certainly likewise owes his high rank to his hand; his
cephalisation is almost equal to nearly four times that of Anthropoid
Apes, consequently he has risen still higher above the latter, than the
Squirrel above the Rat, or the Elephant above the other Hoofed Mammals.

Even in the Amphibia we see the cephalisation of the Treefrog,
which uses its fore-feet as hands, increasing considerably.

Among Birds, Owls have a high cephalisation, not so much on
account of their large night-eyes, which cause only an enlargement
of the images on the retina (in comparison with the Day-Birds of
Prey), without augmentation of central nerve-cell mass, but on account
of the extremely developed sense of touch in the skin and their
very quick ear. The touch-corpuscles at the base of the feathers are
incredibly numerous. ')

The Parrots owe the high value of their / to their handlike paw
and pincerlike beak.

In all these cases greater influence of the factor S°** by speci-
fication of the organ of touch occurs.

The comparatively high cephalisation of Sea-Mammals, usually
represented exaggerately (as few full-grown animals have been
examined), and that of the Hippotamus, bowever low in the general
organisation of the nervous system, can now easily be explained.

According to the evidence now available, the coefficient of cepha-
lisation of Seals can be computed at 0.6, that of Toothed Whales
(Odontocetes) at 0.7 and that of Whalebone Whales (Mysticetes) at
0.4. Seals owe their high cephalisation certainly partly to the
specifically high development of their sense of touch. But Odontocetes,
whose cephalisation is equal to that of Anthropoid Apes, lack
certainly a similar high development of the organ of touch. They
distinguish themselves from the plankton-eating Whalebone Whales
by seeking their subsisience at usually greater depth, even to where
perfect darkness prevails. In connection with this fact their eye is
smaller than that of Mysticetes, but they possess a still more developed
sense of hearing than the latter; in the quiet water of the great
deep this organ can function perfectly as a sense of room. In
all these Water-Mamuinals, but mostly in the Odontocetes amongst them,
the ear is the most important organ’). It is doubtless the crepuscular

1) E. Kiisrer, Morphol. Jahrb. Bd. 34. (1905), p. 126. :
*) G. Boenninanaus. Das Ohr des Zahnwales. Zoologische Jahrbticher. Bd. 19
1904). p. 338—339. — Compare O. Asst, Palaeobiologie. Stuttgart 1912, p. 458,

668

light prevailing in the water that makes other senses than the optical
one predominate in these Mammals, as likewise in the Fishes, and
probably in the Crocodiles (bearing very quick), in comparison with
Amphibia and most Reptiles. In the Fishes also the olfactory organ
and especially the sense-lines are predominant. This has caused
augmentation of the quantity of brain, because the surfaces of the
mentioned predominating organs of sense (in opposition to the eye,
which forms definite images) increase simply proportional to the super-
ficial dimension of the animal (consequently with the exponent of
correlation 0.66...). So in these animals a very considerable
increase of the quantity of brain does not signify a high degree
of organisation. Calculated by means of the exponent of correlation
0.66...) & becomes for Whalebone-Whales 0.07, for Toothed Whales
0.20 and for Seals 0.18.

In the Snakes and the Slow Worm and likewise in the Eels, on
the contrary, the great length of the body is the cause of the low
value of &, though this does not therefore indicate an inferior degree
of organisation. In proportion to the weight of the body the not
specialised segmental sensu-motorical unities are too equivalent for
a representation in the brain, proportional to that of other Reptiles
and Fishes. The body becomes thereby, as it were, to a certain
amount, a ballast for the brain. This is in a more literal sense the
case in the Tortoises. In the shell-bearing Vertebrates and also in the
elongated animals the influence of the factor S°*% in the analysis B
has thus diminished. In the Eels a second cause of diminution of the
quantity of brain exists moreover, in their life as animals of darkness,
by the disappearance for the greater part of the eye-factor S°?? in
the analysis 4B and at the same time of the eye-factor in the analysis
A (as in the Bats). On account of the latter circumstance their r
becomes == 0.66.

The influence of the not segmentally constituted eye im itself
remains in all cases restricted, from the nature of the factor S°??
which depends on it, and is thus less capable of increase. Even the
Horse, which possesses an absolutely larger (day-) eye than the
Elephant, rises still little above the average level of 4 for Mammals.
On the other band can the other factor S®*8, the segmental factor
in analysis B, grow, as it were, endlessly with the development of
“specific sense-energies” in the different segments. The tactile organs
have therefore always the lead with the higher organisation of the
nervous system. 25 November 1913.

669

Physics. — “On the question whether at the absolute zero entropy
changes on mixing.’ By Dr. W.H. Kursom. Supplement N°. 33
to the Communications from the Physical Laboratory at Leiden.
(Communicated by Prof. H. Kamuriincu Onnes).

§ 1. The formula for the entropy of the “gramme-molecule” of
a mixture of ideal, not reacting gases, for each of which pV=RT
is valid, contains the expression

= LUPOCNINC IG eSyh el see lal ve os ae, (CL)
if c, represents the number of gramme-molecules of the first com-
ponent, c, that of the second component ete., which are present in
the gramme-molecule of the mixture. > will indicate in this paper
a summation over the different components.

The expression (1) passes unchanged into the formula for the
entropy of the mixture, when this is transferred from an ideal gas
condition as considered above into other conditions.

According to PuLanck’s version of the Nernst heat theorem the
entropy of a one-component substance in a condensed state approaches
to a finite value, which is independent of the pressure and of the
special state of aggregation, when the absolute temperature approaches
to 0. That value may be taken as a suitable zero point for the
entropy of that substance in the condensed state.

As it is not immediately evident, how the other terms which
occur in the expression for the entropy of a mixture, can on ap-
proaching to 7’=0O furnish a compensation of the term written
above, it might be imagined, that for a mixture on approaching to
7'=O0 the entropy might not become O, notwithstanding this is the
case for the componenis.

In that case, however, at a temperature which differs little from
the absolute zero, any reversible isothermal change of the compo-
nents, in a condensed state, individually would be connected with
a development or absorption of heat, which approaches more rapidly
to O than the temperature. The reversible mixing of those components,
on the other hand, would be accompanied by a heat-effect, which
approaches to 0 as rapidly as (eventually more slowly than) the
temperature. In other words the mixing heat would be of a different
order of magnitude from the heat of each reversible isothermal
process performed with the components individually.

It seems to me that it is more natural to assume, that also fora
mivture the entropy at the absolute zero point is equal to 0, if this
is the case for the components by the choice of this point as a
zero point for the corresponding entropies.

43

Proceedings Royal Acad. Amsterdam. Vol. XVI.

670

Probably even the compensation referred to above already takes
place in the ideal gas state, at least if the volume of the mixture
is not inereased at too rapid a rate to «© as the temperature de-
creases to 0.

In aecordance with a remark by Nernst‘) we are practically
forced to assume that for the molecular translatory motion of a
gas on approaching to 7’=O at last the equipartition laws are no
more valid. For the determination of the temperature one can then
no more rely upon the gasthermometer. A method for the deter-
mination of the temperature, which is then suitable in theory, is
this that one derives the temperature from the energy density of the
radiation which is in equilibrium with it.

We shall consider the equilibrium between the molecular translatory
motion of the gas and the radiation subsequently at two temperatures
T and 7’'+ d7. The most obvious assumption is that to an increase
of the energy density of the gas an increase of the energy density
of tbe radiation corresponds which is in a finite ratio to the first,
in other words that

d= y BAT. |. Bin SR ee
where y has a finite, and at sufficiently low temperature a constant
value. In this equation U/ may represent the energy of the gramme-
molecule of the gas. The molecular volume is supposed not to
become © on approaching to 7’= 0.
From (2) follows that *)

: oU
fort 0 i: (57) =°- a hey Teh ine ea

V

The equation (2) has the same form as the corresponding relation
for a solid. Indeed it could hardly be assumed that the equilibrium
between the molecular motion of the gas molecules in colliding
against a solid and the radiation would be governed by quite a
different law from the equilibrium between the molecular motion in
a solid and the radiation.

From (2) and

| a ia eae tS oa

*) W. Nernst, Physik. Z.S. 13 (1912), p. 1066. Cf. also H. KamertinGu Onnes
and W. H. Kersom, Math. Enz. V 10, Leiden Comm. Suppl. N°. 23, note 517.

OT
ally to 78, as is indicated by (2), is not required, but that a decrease proportionally
to 7 would be sufficient.

U
2) It will be noticed that for the validity of (8) a decrease of( ) proportion
y

671

which relation remains valid, follows for 7’= 0

Ue oa ee os Ear :
i ae Os vence aa heats (5)

if S represents the entropy.

If we now calculate the change of entropy which occurs on mixing
two ideal gases (i.e. gases, in whose equation of state no members
occur which depend on the volume and the mutual attraction of
the molecules) by supposing this mixing to take place in a reversible
way at constant temperature, it follows from the last mentioned
relation that at the absolute zero the entropy change on mixing is
equal to 0.

§ 2. The theorem indicated in the former § may be further
elucidated by means of relations for the equation of state of an
ideal gas which I deduced in Suppl. N°. 30a (May °13). It seemed,
however, desirable to me as the foundations of the considerations
of § 1 not to make more assumptions than are strictly necessary.
For against several of the special assumptions of Suppl. N°. 30a,
particularly against the use of Dersin’s method in the way as is
done there for an ideal gas, more or less serious objections can be
made. All the same the deviations from the equipartition laws, which
will become apparent in the equation of state of an ideal monatomic
gas, are presumably given rightly in a qualitative sense by those
relations. Further it seems to me that one may expect with some
confidence that the order of magnitude of those deviations will agree
with that of the deviations given by the relations mentioned. For
this reason it seems to me to be not quite superfluous to indicate
here what may be derived for the entropy of an ideal mixture from
those relations.

a. From equation (1) of Suppl. N°. 30a with (2), (3), and (5) of
that paper follows for a one-component gas, if molec ten rotations
and intramolecular motions are left out of account’),

ae hy

hy a7,
S mel ta - —In{1—e - v? dy ; (6)

i: max fl hy
ekL _]
With

ae Tipe. és
Saag ar ees yh as)

1) This expression was already given by H. Terrope, Physik. Z.S. 14 (1913),
p: 212.

43%

and integrating partially as regards the second term under the
integral sign, (6) changes into

4 E378
S = 3Nk =f = ~ —lIn (=| Speen as (CS)
Fl Jor

for small values of a:

4
S=— 3Nk E (l—e-*) — 3

Hie ast eet 2 10
pT 5a” Sag eh eee

if B,, B,.... denote the Bernouillian coefficients.
a. Low temperatures. If of the development (9) we write down

6, . .
the first term only, we may put LF, with 4, according to Suppl.
No. 30a equation (18a) or (184). This gives
; S= ae V4T.6 sek. ie. =

if J denotes the molecular weight, and @ a constant which depends
on Pranck’s constants 4 and / and on the AvoGapro number.

According to (11), the volume being kept constant, the entropy
approaches to O for 7’= 0. It does so proportionally to 7", which
is in agreement with (2). The latter would not have been the case
if (see Suppl. No. 30a § 4c) the zero-point energy had not been
introduced in the theory, ef. H. Terropn, Physik. ZS. 14 (1913), p. 214.

8. High temperatures. Retaining in the development for high tem-
peratures only the first term which gives a deviation from the equi-
partition laws, we obtain :

ig ON eas NEE Le ME ate (13)
eB ar 1b75 7?
or
(3 1
S=Ni\— mn @MTV +447 0(8MTV) | . . (14)

where $ is a constant depending on h, &, and N.
33
The additive constant VA (4 + = Ing), with which the ‘chemi-

eal constant’? is connected, agrees with the expression obtained for
it by Trrrope Le. without the assumption of a zero-point energy.
b. From (11) and (14) the entropy of the molecular quantity of

673

an ideal miature, again leaving molecular rotations and intramolecular
motions out of account, may be easily derived if Gripes’ theorem,
according to waich the entropy of such a mixture is obtained by
calculating the entropy for each component as if it were present by
itself in the volume occupied by the mixture and adding the values
so obtained, is supposed to remain valid when the equipartition
laws no longer hold. We then obtain:
a. for low temperatures
saaryes, bt ee to Mee eeu pel ULSD)
C,
8. for high temperatures, retaining the first term which gives a
deviation from the equipartition laws:
3 3
S = Nk = In BT V7ls +

»)

= c,InM,— 2c, Ine, + 4+

a5 BPVIY. Seth Miro eRe ie saree yea. (107)

If at constant volume the temperature continually decreases, at
sufficiently low temperatures (for densities of the order of magnitude
of the normal density at extremely low temperatures, cf. Suppl.
N°. 30a § 56) a positive deviation from the equipartition value begins
to develop itself. This deviation finally causes the entropy for a
mixture also to approach to 0 proportionally to 7° as shown by
(16) instead of becoming — o.

Physics. — “Further experiments with liquid helium. H. On the
electrical resistance ete. (continued). VIL. The sudden disappear-
ance of the ordinary resistance of tin, and the super-conductive
state of lead.” By Prof. H. Kamernincn Onns.

(Communicated in the meeting of May 31, 1913).

§ 137). First observation of the phenomena. a. Passing from the
investigation of the super-conductive state of mercury to that of the
change in the resistance of various other metals when they are
cooled to helium temperatures, although I hoped to find more super-
conductors, I did not think it likely, judging from our experiences

1) The §§, tables and figures are numbered successively to those of Comm. VII
of this series. (These Proceedings May and June 1913).

674

with gold and platinum (see Comm. N°. 119, IIL and Comm. N°. 120,
IV of this series) that we should be able to get more than a systematic
survey of different cases of additive admixture-resistance (see Comm.
VII of this series § 10). Very soon, however, the surprising results
with tin and lead were obtained, which we mentioned in Comm.
VIL § 1 and § 12.

In the first place on Dec. 3% 1912 we investigated a wire of
pure tin, and perceived that this metal too, at helium temperatures
became super-conducting.

The tin was of the specially pure kind supplied by KaniBaum.
It was melted in a vacuum and poured into a glass capillary U-tube.
The capillary tube had tin branches at either end, by which the
conducting wires and the measuring wires were attached. The
resistance at the ordinary temperature, 290° K., was 0.27 &.

We found that at the boiling point of helium a small ordinary
resistance 1.3.10-* 2 remained. At 3° K. this had disappeared
(<< 10-6 2) and when the field of temperature between 4°.25 and
3° K. was gradually gone through, we found that the disappearance
took place suddenly at 3°.78 K.

In order to be better able to judge of the micro-residual resistance,
we tried to make a tin wire of greater resistance, in the same way
in which we had formerly succeeded in making a long thin lead
wire'). A steel core was covered with a substantial layer of pure
tin, and turned down on the lathe. Then with a razorshaped chisel
a thin spiral shaving was cut off’). This method, which seemed
preferable to drawing (comp. § 14a) by which the metal might
undergo a greater change, yields without difficulty wires of 0,01 mm?.
section. Several of these wires were then joined into one long wire
by melting them on to eachother, during which it was necessary to
carefully avoid the possibility of oxide being introduced into the
surfaces to be united. The tin wires, one of which 1.75 m. long
had a resistance of 19.2 2, and the other 1.5 m. long a resistance
of 6,7 2, were wound upon glass cylinders, between a spiral of
silk thread which separated the windings of the tin thread from
each other. Leading wires of tin fastened to the up turned ends of
the wire, were led downwards through the liquid and attached to
copper wires. With these resistances immersed in liquid helium the

1) KAMERLINGH ONNES and Benet BeckMAN. Comm. N°, 132c. Dec. 1912.

2) A few of the tin wires first made did not become super-conducting ; the inferior
method of working the metal had perhaps caused additive admixture resistance, or
more probably very insufficient continuity of material.

arteé

619

sudden disapparance was observed when the temperature fell to
3°.806 K. (boiling under 47 em. mercury pressure). At 3°.82 Kk.
fhe resistance of one was still 0.0183 2, of the other 0.00584, at
3°.785 K. of both < 10-6 2. In this case too the highest limit for
a possible micro-residual resistance was thus very low. We may put

w =

ea 10—7

273K.

Besides the sudden disappearance of the resistance of the wire,
we also observed, as in the mercury thread, that for each tempe-
rature below the vanishing point a threshold value for the current
density’) determined by this temperature, (in the case of the last
mentioned wire the threshold current was 0.28 amp. at 2°.785 K.)
could be fixed, below which the current passes without any perceptible
fall of potential, and above which it is accompanied by potential
phenomena, which (see § 14) increase rapidly with the increase of
the excess of the current above the threshold value. In a word, the
tin wire behaves below the vanishing temperature of the tin, 3°.8 K.,
qualitatively precisely the same as a thread of mercury below the
vanishing point of that metal.

u

8. Lead of Kanipaum, made into a wire in the same way as the
tin, 1.5 m. long and 10.8 2 resistance at ordinary temperature,
when it was immersed in liquid helium appeared to be super-
conducting, without the necessity of reducing the pressure at whieh
the helium boiled. When the temperature was raised as far as the
cryostat permitted, that is to 4°.29 K. (the pressure was raised 11 em.
mercury above 76 cm.) the lead remained super-conducting. The
temperature at which the ordinary resistance of the lead disappears
will probably, as indicated in § 15, not be far above the boiling
point of helium.

Whether this disappearance, as with mercury and tin, also takes
place suddenly, has yet to be investigated. For temperatures below
14° K., where lead has still a relatively high ordinary resistance,
and above 4°.3 K. where it has disappeared, we do not yet possess
a satisfactory cryostat. At the temperature just mentioned of 4°.29 K.
we found that the threshold value of the current was not yet reached
at 1.3 amp.

1) Concerning the dependence of the threshold value upon the dimensions of
the wire and the conditions under which the heat is given off, further investi-
gation is needed.

676

y. Besides lead and tin, amalgamated
{tin foil was investigated. We examined a
layer of it spread out on a mirror glass,
in which layer grooves were made in the
manner shown in fig. 8. In helium boiling
at atmospheric pressure, it appeared to
have lost the ordinary resistance (2.3 2
at 290° K.). At 4°.29 K. we found 0.12 amp.
for the threshold value of the current, and
a potential of 1.3.10~6 volt, at 0.30 amp.
19.8.10-© volt, and at 0.363 amp. 34.6.
10—* volt.

It is worth noticing that this amalgamated

LNT

tinfoil becomes more easily superconducting
than either tin or mercury. Perhaps the soft

ets ee tin-amalgam, though a solid solution (of
0 3 6 cM.

Fig. 8 Fig. 9 would only need to become a continuous

mercury in tin), bas this property. This

whole in order to provide a nonresisting path for the current beside
that of the free mereury ‘comp. (§ 9) or tin that might be present
in the tin foil.

§ 14. Further investigation of tin. The further investigation of tin
and lead does not form by any means a complete whole yet. Several
of the measurements we had in view were failures, so that the
resulfs attained are very disconnected; nevertheless, in connection
with our experiments with mercury, I think them worth communicating.

a. Methods of working the tin. In the previous § we said that
working the tin into a spiral shaving did not interfere with the
sudden disappearance of the resistance. What is of even more
importance is that the rolling out of the wire to a thickness of
0:01 mm. has not any influence upon the super-conducting state
either, so that we may feel confident that a very thin nonresisting
tinfoil could be made’).

We must remark that in working tin, heating must be avoided.
The increase of hardness which is caused in the drawing of metals
by the compression and stretching, which is accompanied by an

') The resistance of commercial tin foil, pasted on glass and cut out as in
fig. 9, appeared not to become zero,

677

increase of resistance and decrease of the temperature coefficient, is
removed in gold and platinum for instance, by heating. With tin,
on the other hand, heating is injurious, it causes the resistance to
increase '), moreover, it causes thin wires to go into angular formes *).
The threads we used were, therefore, not heated after being worked,
and showed regular curvatures when bent.

8 Potential phenomena in the super-conducting state. The following
observations allow us to judge of the highest limit of the possible
micro-residual resistance, and of the potential differences above the
threshold value of the current density just below the vanishing point.
They were made with a branching tin wire exactly like the one
used in the experiments with mercury of Table [V and V in Comm.
VI of this series, § 6 and 7. The resistance consisted of a principal
wire We 4 m. long, and mainly 0.0097 mm*. section *) with two

1) According to TAMMAXN and his school, the crystals are shattered by wire
drawing, and arranged in such a way that in the cases meant the resistance
increases. By heating, larger crystals are again formed, and the resistance resumes
its original value. In the investigations of KAmerLincH Onnes and Cray, (Gomm.
N°. 996 § 4, June 1907), it is pointed out that the additive resistance of platinum
and gold wires is always found greater by continued drawing even after heating
to glowing. We attributed this to the acquiring of admixtures through the drawing.
In gold it is possible to test for such small quantities of admixture as are here of
importance. In gold wires carefully drawn by Herarus (Comm. N’. 99¢ § 2, June
1907), under repeated treatment with acids, larger quantities of admixtures were
found in proportion as the resistance feli less at reduction to hydrogen tempera-
tures. At the same time it is possible that the drawing itself has an influence.
Hennine (Ann. d. Phys. 1913), thinking as we do, attributes the difference found
with his platinum thermometers in the temperature coefficient from that found by
us, to a larger amount of admixtures in our thermometer. The difference becomes
greater still, when we consider that HENNiING’s wire (0.05 mm.) was drawn out
further than ours (0.1 mm.) (which is of importance in the application to thermo-
metry). As mentioned above and as we found confirmed in comparing the wires
Pt; (0,1 mm.) and Pf; (0,05 mm.), thinner wires fall less in resistance, a result
by which we also explained, |. c., why Honsorn’s thick wires (0.2 mm.) showed
a greater fall than ours. Our wires were at the time most carefully drawn by
Heraeus from the purest platinum supplied by him. The platinum obtained by
HeraAgus later on may have been even parer. Improvement may also have been
made in the method of drawing the wires.

*) Where broken, tin wires exhibit comparatively large crystals. See also
§ 15 note 1.

5) In this investigation the section is deduced from the length of the wire and
the resistance at ordinary temperature. We only ascertained, whether this agreed
approximately with the result of direct measurement. The values given are there-
ore only to be considered as rough mean values.

678

sentinel wires Ws4 and IWsg') of 0.8 im. length and about 0.02 mm?.
section, wound round a glass tube and insulated with silk. We found,
(Febr. 1913) *):

TA Bal JE VAL |

Resistance of a bare tin wire at, and a little below 3°,8 K. |
Section of We: 0.0097 mm2,

WSA USB | 2G
Ite ee =
| Current density 0.61 amp./mm2 in C.
Sheets) 164 6.84. 10-3 © 6.50.10—-3 © 69.6.10-3 0
82 5.50 0.90 34,9
.19 2.82 0.03 1.23
. 785 Vet) 0 0
.18 0.7 0 0
svi) 0.15 0 0
.14 0.02 0 0
72 0 0 oan
Current density in C 154 amp./mm? (and higher ?)
1°26 | 0 0 0

With a coil of 252 windings of tin wire insulated by picéin (see
§ 16) of 0.014 mm?’. section, (with pieces of 0.02, 0.012 and 0.03)
and 79 2 resistance at ordinary temperature 290° K., the disappearance
of the resistance was followed, at three different current strengths
as in § 8 was done with mercury. We found :

1) The object of the sentinel wires was the same as in VII § 6. We had namely
calculated on sending much stronger currents through than we actually did, and
on that supposition it was necessary to make sure that no JoULE heat penetrated
to the wire from elsewhere.

2) In one of the sentinel wires Ws there is obviously a thinner place which
causes locally a much greater current density than the mean. Probably the same
case occurs flere as in the experiments with mercury in Table IV, but here the
disappearance of the resistance at lower temperature makes it improbable that the
tin wire should be interrupted by a foreign resistance.

| Ti AD Bawa lXe
Disappearance of the resistance of a tin wire, under reduced giving off
of heat, at different currents.
— rs. oes 5 SE ae ee ee. 4
Af 0.004 amp. | 0.04 amp. | 0.4 amp. | 0.6 amp. | 1.0 amp.
aa ee : — meas

3,82 K. 0.0533 (2 | 0.0535 0.0536 2 |

805 500 534 536

79 488 533

785 425

78 162 508

165 0.00137

315 0.00005 0.0039

714 1 14 0.0532

.72 0.000000 | 0.00025

.70

.68 0.000012

66 0.000000 | 0.0050 |

64 |

5A 38—CsCid|

«42 22 |

.28 10

125 0.0002
2.69 0.000012

.35 | | 0.000000

1.6 | 0.000000 | great

This table gives in general the same as fig. 6 and 7 of § 8.
The disappearance of the resistance extends over a much larger
field of temperature than with the mercury thread, probably because
the giving off of heat is considerably reduced by the winding up
of the wire protected by picéin; which is probably also the reason
why at the lowest temperature the strength of the current cannot
be raised above 0.8 amp. and the threshold value of the current
density therefore only reaches 56 amp/min’.

680

y. Experiments concerning the influence of the contact with an
ordinary conductor of a metal which can become super-conducting,
upon its super-conducting properties, were in continuation of those
of § 10 made with tin in two different ways, first with a german
silver tube, which was tinned, and through the layer of tin of
which a spiral was cut, and second with a constantin wire which
was tinned. In the first experiment the resistance did not disappear,
in the second, as already said in § 10, it did; from which we
conclude that the continuity of the layer of tin in the first case was
not sufficient. In the second experiment the threshold value was,
however, also very low, even at the lowest temperature 1.°6 K. it
remained below 0.095 amp. for the bare wire immersed in liquid
helium. It is simplest to assume in the mean time, that the layer
of tin becomes super-conducting, but that the section of it, which
was, deduced from the resistance, 0,0125 mm’., according to measure-
ments down to O,1 mm’*., was very small here and there. There
was in this case no reason to suppose a want of contact between
tin and constantin, as in the corresponding experiment with mercury
between it and the steel.

§ 15. Further examination of lead. In the first place we will
mention a few experiments on the heating of a wire which was at
a temperature below the vanishing point, which correspond to those

TA ByL EX. |
Potential differences in a lead wire carrying
a current
/=—6 M,, section = 0.014 mm2.

T Current density |Potential difference
| in amp/mm? in microvolts

|

| aXe eee Hl
- |

|

Je tea 560 | 0.0
| | 645 0.2
| 675 3.5
| 695 5
| 710 6
720 | 10
750 | 19

| 791 (¢\* bah40

very great

681

in Table VI for mercury. The lead resistances were arranged exactly
like the tin resistances described in§14, the bare wires were wound
upon glass between silk. With a wire of 0.025 mm’. section
(10.8 2 resistance at ordinary temperature) containing six joints,
which were made with a miniature hydrogen flame, we ascertained
that joints do not interfere with the experiments. The results (Febr.
1913) with one of the wires (92 2 at ordinary temperature) are con-
tained in Table X (the observations were confirmed later on repetition).

A similar experiment with the wire containing six joints at less
low temperature gave ; .

ae i
|
|

AWB EVE. Xie |
Threshold value of current

density for bare lead wire of |

section 0.025 mm2. |

T Threshold value |
in amp/mm2 |

At a current density of 940 the wire was dammaged (calefaction °)
and upon repetition it appeared that it was broken.

Similar conditions of external conduction of heat to those of the
tin coil described in § 14, prevailed in a lead wire (see § 16) of

| Te ANB LSE XI:
| Potential difference in a lead wire carrying a current |

with reduced external conduction of heat.
5555 0M. section = 0.014 mm2
| T | Current density (Potential difference
| in amp/mm2 in microvolts |
| ——e = Ti = === —— SSE — SSS = =
| 40.25 K. | 33 0.03
| | 36 0.65 |
| | 38 ied
| | 40.2 1.35
| | 41.3 22.0
Loe 60 Bal
=|

682

1000 windings (resistance at ordinary temperature, 290° K., 773 2)
insulated by silk soaked in liquid helium. We found: (See table XII
p. 681).

Judging by this we may perhaps estimate that the lower limit of

0

° 4 g A ) 410 20 30
Fig. 10. Fig. 11.
the threshold value at 4°.25 K. given above cannot be raised much,
and that the vanishing point for lead lies at about 6° K.

683

Further, measurements were made with lead wires placed in a
vacuum, the object of which is obvious by § 12. The apparatus
which served for this consists (see fig. 10 and fig. 11, face view and
diagram of d with detail figures) of a glass reservoir immersed in
liquid helium, carried by a long narrow glass tube fixed into the
lid of the eryostat. The reservoir d can be evacuated through the
tube c (the tap a@ allows it then to be connected to a tube filled
with charcoal which is immersed in liquid air); through the indicator
gauge 6 we can make sure that the apparatus is not cracked in
cooling.

In the apparatus shown in the fig. there are two lead wires (see
diagram); we were only able to do the measurements with one.
Four short tubes are blown into the upper part of the reservoir
to receive. the lead wires (see detail figures); upon these tubes after
platinizing and copperplating caps are soldered with tin inte whieh
the thicker top ends of the wires are soldered with Woop-metal ’).

Rolled out lead wires are fastened to the wires that project from
the covers, and run down along the reservoir, insulated from each
other with silk and then up again through the liquid helium.

We found with a part of the wire of Table XI:

TABLE XIII

Threshold value of current
\density of a lead wire in vacuo;)
section !/79 mm2,

T Current density
| in amp/mm2

ly 407257 | > 270
| |

The experiment is incomplete as the threshold value was not
reached. ;

We made similar apparatus with tin wire; the observations with
tin in vacuo have, however, not succeeded yet.

§ 16. Remarks in connection with the experiments with tin and lead.
a. Our results with tin and lead make it seem probable that

1) It is not possible to solder tin wires into the covers with Woop-metal : as
coming in contact with the tin the melted Woop-metal, as it seems, penetrates
by capillary action amongst the tin crystals which makes the wire brittle and
break in two. The tin wires must therefore be melted to the tinned covers, which
is possible, by their being provided like the lead wires with sealed on thicker ends.

684

all metals, or at least a class of them, if they can be procured
sufficiently pure, pass into the super-conducting state when reduced
io a low enough temperature. Perhaps in all it weuld also be
suddenly. But the additive admixture-resistance which ean be caused
by mere traces of admixtures, will in general make the detection
of the phenomena a difficult one.

8. A number of experiments with resistance-free conductors of
which several suggest themselves at once, now that we can use the
easily workable super-conductors tin and lead, can be undertaken
with good prospect of success *).

In this way the preparing of nonresisting coils of wire, with a
great number of windings in a small space, changes from a theo-
retical possibility into a practical one. We come to new difficulties
when we want not only to make a nonresisting coil, but to supply
it as a magnetic coil with a strong current *).

I have been engaged for some time making a preliminary estima-
tion of these difficulties *).

The coils mentioned in § 14 and § 15 were made chiefly for
this purpose. The first of tin wire insulated with picéin, contained
on dem. length in a layer of 7 mm. thickness 300 windings of
‘/,, mm?*. section (the resistance at ordinary temp. was 19 2).
While a current of 8 amp. could be sent through the wire before
it was wound when immersed in liquid helium, without reaching
the threshold value of current density (see § 14) the coil came to
the threshold value at 1.0 amp. The number of ampere windings
per em?. of a section through the axis was about 400. The second
coil was wound of lead wire of '/,, mm*. section, and contained in
a length of 1 em. 1000 windings in a layer of 1 cm. thickness.
The resistance at ordinary temperature was 773 8. The insulation
of the wires in each layer was obtained by silk threads, between
the different layers a thin piece of silk was placed. I thought that
the liquid helium penetrating into the coil through this texture would
cause the heat to be given off more easily all over the coil, while

') In our first paper about the disappearance of thesresistance of mercury we
mentioned that this opened a‘new field of experiment. That mercury is liquid at
ordinary temperature was, however, a serious hindrance to entering it.

3) A coil of this kind one would wish to place in the interferrum of a very
large electromagnet of Wetss, in the same way as the auxiliary coils contemplated
by him, in order to further raise the field. The field that is added by the coil
would in that case have to be greater than what would be sacrified by enlarging
the interferrum to make room for the cooling appliances.

8) A possible difficulty was pointed out in note 2 § 4.

685

it was not certain (comp. the remarks about mercury in glass in
§ 7 and § 11 Comm. VII of this series) that the picéin remained
adherent to the tin wire everywhere. Through this coil a current of
0.8 amp. (see § 15) could be sent, without the threshold value being
reached. The number of ampere windings per cm’. was then about
800. If the disturbing potential phenomena had not been greater
than with the shorter wire of the same section which was washed.
by liquid helium over its entire surface, and if the difficulty mentioned
in note 2 §4 does not come into play, it would have been possible
to supply this coil with up to 9000 ampere windings per em’. If,
therefore, the potential phenomena which frustrated this in the
experiment reported, in accordance with the opinion expressed in
Comm. N°. VII of this series, particularly in § 11, may be ascribed
to “bad places” in the wire, and if we may therefore be confident
that they can be removed (for instance by fractionising the wire)
and if moreover the magnetic field of the coil itself does not produce
any disturbance (note 2 § 4) then this miniature coil may be the
prototype of magnetic coils without iron, by which in future much
stronger magnetic fields may be realised than are at present reached
in the interferrum of the strongest electromagnets ').

1) J. Perrin (Soc. d. phys. 19 Avril 1907) made the saggestion of a field of
100000 gauss being produced over a fairly large space, by coils without iron,
cooled in liquid air. Ch. Fapry (Journ. d. Phys Févr. 1910) worked out this idea.
He finds that the energy absorbed in such a coil, in watts is represented by the
formula

Wore? ke

where @ is a length in centrimetres, which determines the size of the coil, for a
cylindrical one the radius of the internal space, » the ratio of the metallic area in
a section through the coil at right angles to the windings to the area of this
section, K a purely numerical coefficient, which depends upon the form of the
coil, and which in cylindrical coils with wire of equal section does not differ much
from 0,18, ; the specific resistance of the metal of the windings in ohms. centi-
metre, H the magnetic field in gauss.

In order to get the desired field of 100000 gauss in a coil with an internal
space of 1 cm. radius, with copper as metal, and cooling by liquid air 100 kilo-
watt would be necessary, putting A at 0.20 and » at 1,5 (which last number
might well be 6 times as large). The electric energy supply, as FaBRy remarks,
would give no real difficulty, but it would arise from the development of JouLs
heat in the small volume of the coil to the amount of 25 kilogramme calories per
sec. which in order to be carried off by evaporation of liquid air would require
about 0,4 litre per second, let us say about 1500 litres per hour.

We may add to Fapry’s objection that the preparation of 1 litre of liquid air
per hour is at present to be reckoned as requiring not much tess than !/, KW.
According to this standard, 7 times as much work would be necessary for the

44

Proceedings Royal Acad. Amsterdam. Vol, XVI.

656

y. Certainty that the potential phenomena observed are due to
such imperfections in the wire would be of no less value for another
tempting group of experiments. As soon as the super-conductivity of
mercury was established, the question foreed itself upon me, in
connection with the great value which according to the electron
‘theory of metals is ascribed to the free path of the electrons *) (comp.
§ 12 8), whether electrons moving at speeds by which they cannot
penetrate a thin plate, e.g. a Lenarp’s window of solid mercury, at
temperatures near the ordinary temperature *), or at least not without a
change of direction, would be able to do this better if the foil were

cooling than for the current. By a judicious use of the cold of the vapours this
number can be reduced, but the proportion will remain unfavourable.

Moreover, as FApRY shows, the dimensions determined by a, to make it pos-
sible for the heat to be carried off, would need to be much larger, by which at
the same time the amount of liquid gas used becomes greater. The cost of
carrying out PrRRIN’s plan even with liquid air might be about comparable to
that of building a cruiser!

If we calculate in the same way the cooling with liquid hydrogen in the case
of silver and if we assume that the resistance of silver (according to KAMERLINGH
OnNeES and Guay) at the boiling point of hydrogen is 0,009 of that at the ordinary
temperature, we arrive at a more favourable figure, namely, that al a=1 cm.,
700 liters of liquid hydrogen would be needed per hour, but the ratio of cooling
work and electric work becomes more unfavourable yet, putting the preparation
of a litre of liquid hydrogen in the same way as above at 1!/, K. W. But the
figure for liquid hydrogen would also on the ground mentioned above have to be
considerably increased. Although an installation which will give as much liquid
hydrogen as is necessary for the cooling could be made after the pattern of the
present Leiden plant, it would be of such an extraordinary size that with liquid
hydrogen also, the method described perhaps involves more difficulties than a
further increase of the size of the coil, in order to be able to cool with running
water (as introduced by Werss) while this method also has its advantages with
a view to the use of the field.

The possibility of using the super-conductors tin anl Jead, gives a new depar-
ture to the idea of Perrin of procuring a stronger magnetic field py the use
of coils without iron. With super-conductors no JouLe heat needs to be carried
off (or at any rate only 10° times less than with ordinary conductors) and thus
with currents below the threshold value the difficulties mentioned above disappear.
If the conditions mentioned in the text can be fulfilled, then even a coil of 25 cm.
diameter of lead wire, constructed as the one in § 15, immersed in helium, could
give a field of 100000 gauss, without perceptible het being developed in the
coil. Some such apparatus could be made at Leiden if a relatively modest
financial support were obtained. In the mean time this remark may serve to put
the problem of very strong magnetic fields which are becoming indispensable for
various investigations in new form.

1) Comp. note 3 p. 1113. Leiden. Comm. N°. 119. Kebr. 1911.

2) Whether the same electron passes through, or whether tbe movement is
carried from the one to the other, does not affect the experimental question.

687

superconductive. Now that super-condueting plates of tin and lead can
be made, the experiments on this subject are made practicable, and
the plan of making these has assumed a promising form, since [|
have obtained the prospect of doing it with Lenarp himself, which
I highly value. If the potential phenomena are caused by local
disturbances, we may expect that in experiments with thin plates,
by a correct choice of the places to be experimented upon, they will
be of little importance. If, as might be imagined according to § 4,
the potential phenomena are connected with peculiarities in the
movements of the electrons, then they would be of prime impor-
tance in phenomena such as we have here under consideration.

Jd. The correspondence of the potential phenomena in tin and lead
to those in mercury is very striking. As regards tin, it was stated
already in § 18a, and further investigation has confirmed it and also
extended to lead. All the considerations with regard to them for the
case of mercury can thus immediately be applied to tin and lead.
On the other hand the latter may serve to elucidate the doubtful
points in mercury.

With the bare tin wires at 4°.245 K. measurements were made
which acquaint us with the amount of heat, given off to the liquid
helium above the vanishing point; whether it is proportional to the
surface of the wire, as is to be expected, when the heat is mainly
given off to the liquid, could not be settled yet. With the rolled
out tin wire, with which the various measurements were successful,
it was great, which corresponds to the fact that here the ratio
between the heat-conveying surface and the heat developed is very
favourable. It was estimated at 0.5 watt per 1 degree difference of
temperature. Still at 1°.6 K., 1.4 microwatt caused a local rise of
temperature to the vanishing point. As in § 11 we deduce from
this that the whole development of heat is local. The hypothesis
that in this way ‘“‘bad places” show themselves is confirmed by the
fact that through a wire like this at the boiling point of helium,
therefore above the vanishing point, a current of 9 amp. could be
sent, and all the Journ heat was absorbed by the liquid helium,
while with a current only a little stronger the wire gave way
(presumably by the forming round the wire of a vapour bubble in
the helium, which caused calefaction in the wire).

The different threshold values for the bare lead wire and the
lead coil § 15, and for the bare tin wire and the tin coil § 14,
may throw light upon the influence of more or less easy conditions
of heat loss. The phenomena at the disappearance of the resistance
with the bare tin wire with sentinel wires make the hypothesis

44%

688

followed out in § 12 improbable, namely that the mereury below
the vanishing point comes away from the glass or at least does not
give off heat to it at a difference of temperature. The correspond-
ence of the disappearance of the resistance in the tin wire with
sentinel wires and in the mercury thread is explained most simply
by assuming a local rise of temperature in both, while for both
below the vanishing point the same opportunity remains for giving
off heat, but does not take piace owing to absence of rise of
temperature.

Here, therefore, the “bad places” mentioned in § 11 (comp. § 12a,
note 1 p. 118) would again remain as the sole explanation. It is
however suspicious that in the coil of lead wire at 1°.6 K. 56
amp./mm’, was found as the threshold value, while with lead in
a vacuum 270 amp./mm*. at 4°.26 K. was reached without a trace
of potential phenomena.

Finally we point out that the threshold values of current density
far below the vanishing point im the wires of the three different
metals differ very little. We found for the highest limit of the
possible micro-residual resistance determined by the threshold value
in proportion to that at the ordinary temperature

w ~
20.45 Kh

with MERCURY. ae Ke 2.10—10
e730 K
é 18h 5
tin — <Q Gril O10
w
273° K
1Osk

lead < 0.5 10—10

"9730 K

In view of so much correspondence and such regularity of the
character of all the potential phenomena, it still remains doubtful
whether besides the disturbances which we have adduced to explain
them, there may not be at the bottom of them peculiarities in the
movement of the electrons, which may be more clearly revealed by
the experiments indicated in y.

Having completed the series H of my experiments with liquid
helium I wish to express my thanks to Mr. G. Host, assistant at
the Physical Laboratory, for the devotion with which he has helped
me, and to Mr. G. J. Fim, chief of the technical department of the
eryogemic laboratory, and Mr. O. Kessenrine, glassblower to the
laboratory, for their important help in the arrangement of the
experiments and manufacturing of the apparatus.

689

Physics. — “Magnetic researches. X. Apparatus for the general
eryomagnetic investigation of substances of small susceptibility.”
By Prof. H. Kameritincn Onnes and Dr. Apert Perrier.
Communication N°. 139a from the Physical Laboratory at
Leiden. (Communicated by Prof. H. Kameriincn ONNEs).

(Communicated in the meeting of October 25, 1913).

§ 1. Introduction. This paper contains the full description of the
apparatus used in the investigation of Communication III (Comm.
N°. 122a, continued in IV, Comm. N°. 124) of this series (Proceed-
ings of May 1911). Various circumstances have retarded the extensive
deseription which was promised there instead of the rough sketeh.

The construction of the apparatus to be deseribed forms part ofa
more general scheme to gradually obtaii the necessary appliances
for the investigation of weak magnetisation at low temperature. In
doing this we did not confine our attention to special measurements,
but intended to enlarge with as many appliances as possible the
almost completely unknown “technique” of investigations in this field.

On the one hand the measurement of magnetic forces, on the
other that of magnetic couples suggest themselves. The ballistic
method (measurement of flux) is only applied in the stndy of ferro-
magnetism *).

The method of couples is specially suitable for crystals and for
isotropic bodies, which by their shape are seemingly magnetically
anisotropic (e.g. ellipsoids). The apparatus with which our first
measurements on the susceptibility of liquid and solid oxygen were
made (Comm. N°. 116, Proceedings April 1910) is based on this method.*)
In a modified form this piece of apparatus will, we hope, be soon
utilized in the cryomagnetic investigation of crystals.

In measuring forces a non-homogeneous field is used. Two cases
have to be distinguished here.

For an object of small dimensions (the volume of which is v and
the volume-susceptibility A’) placed in the plane of symmetry between
the poles of a magnet the force in the direction of the middle of
the interferrum is given by

Oe
F=vkH —
dy
where H indicates the intensity of the field and y the coordinate at
right angles to the field.

1) In some cases which we will not dwell upon here this method might be
resorted to.

*) The apparatus used by Weiss and KameruincH Onnes for the investigation of
ferromagnetism at low temperature (Comm. N° 114) belongs to the same type,

690

Mor an object in the shape of a rod of uniform section s, the axis
of which is in the plane of symmetry of the poles and passes through
the middle of the interferrum, the relation is

K

F——s(H" —- H")

my
a

if H" and H’ are the values of the field-strength at the ends of the
rod. When dealing with bodies of small dimensions by the method of

0H
Faraday, the spherical object is placed where iz. therefore the
Y

force is a maximum. This is the method of procedure specially used
by Curt in his classical researches.

The rod-method, though applied long ago for measuring the suscep-
tibility of liquids by Quinckr’s method, was hardly used at all in
investigations on solids until 1910, when Pascan adopted it in his
important series of magneto-chemical researches ').

This is certainly curious, as the principle of the method is very
simple and direct, but even more so as the disposition itself offers
important advantages over the other methods. If one end of the rod
is placed in the middle of the interferrum and care is taken that
the other end is as far removed from it as possible, 7" obtains a
maximum value and #H' remains a quantity which may be neglected
or need only be taken into account as a correction.

The susceptibility is thus given by a single field-strength which

oH ;
is much more easily determined than the product /7/ ae has
to be derived from several values of AH, not to mention the fact,
that the measurement itself of H in the middle of the interferrum,
where the field is most nearly uniform, can be carried out much
more accurately than at the point where the field is least uniform.

An absolute measurement by this method can therefore lead to a
much more trustworthy result. Moreover in using a rod a much
higher sensibility can be obtained, on the one hand because a larger
quantity of the substance can be utilized, on the other hand because
the intensity of the field in the middle of the interferrum can be
raised to a much higher value without any objection, which is not
by any means the case in the other method. Finally, as the field
near the middle of the interferrum can usually be made approxi-
mately homogeneous over a space of 1 ce., it is of no great import-
ance at what point exactly within that space the end of the rod

1) P. Pascat, G@ R. 150, p. 1054. 1910. The priority of this application belongs
to Govy. G.R. 109, p. 935. 1889.

691

under investigation is placed, so that as regards this a rough adjust-
ment will be sufficient ; the exact opposite holds when it is desired
to place a body at the place of maximum action.

There are cases, however, in which only the method of maximum
attraction can be applied, e.g. when the susceptibility depends on
the field or when the available quantity of the substance is limited
(e.g. on account of its rarity).

On the ground of the above considerations we have made it our
object to construct a piece of apparatus which.in the first place is
suitable for measurements with objects in the shape of an elongated
cylinder, which may further, without important change, be adapted
to the study of small objects placed at the point of maximum-attraction
and finally, in addition to being suitable for solids, may also be
used for the investigation of liquids, either by enclosing them in the
movable part of the apparatus or by surrounding it as a bath.

The ease with which our apparatus may be adapted to the various
requirements has shown itself a great advantage in our experiments ').

§ 2. General arrangement of the apparatus (comp. figure and
perspective drawing). The main part of the apparatus is a carrier
movably suspended along the axis of an enclosure which has the
shape of a body of revolution. This enclosure is closed airtight,
seeing that it must be capable of being exhausted and that it must
be possible to maintain throughout the apparatus any pressure below
atmospheric. This requirement from the side of eryogenics has its
influence on the choice of most other parts.

The carrier the motion of which is guided along the vertical, carries
at its lower end the experimental object which is placed between
the poles of an electro-magnet with horizontal axis. The magnetic
attraction or repulsion acts along the vertical and is measured by
compensating it by means of the electromagnetic attraction of two
co-axial magnetic coils, one of which is attached to the carrier while
the other one is fixed. The force between the two coils is given by

1) We may here recapitulate the various apparatus which in the mean time
form the complete scheme planned by us:
depending on the use of a. apparatus with ellipsoid (Comm. N°. 116)
couples db. ms for crystals (to be constructed)

Beperdineten ticrusero! | c. hydrostatic apparatus (Comm. No. 116)

ae d. apparatus for objects in the shape of

spheres or eylinders (this Comm.)
a. has been used for liquid and solid oxygen, c¢. for liquid gases, d. for liquified
or solidified gases and various solids.

692

693

F = Ci, tf, where 7, and /¢ represent the currents in the movable
and fixed coils and ¢ is a constant which is determined once for all
by using known forces (weights) ’).

The electromagnetic compensation has for its sole object making
a balance with the forces to be measured: the weight of the carrier
itself is balanced /ydrostatically by means of two floats immersed
in mercury; the principle is therefore similar to that of a constant-
volume hydrometer.

§ 3. The various parts of the apparatus.

a. The enclosure of the cryostat. The space inside the enclosure
A of the apparatus is divided by screens /#, which prevent exchange
of heat between the two parts. The cryogenic part below the screens
contains everything connected with the establishment of low tem-
peratures, in the chamber above the screens which remains practi-
cally at constant temperature, all the delicate parts for the measure-
ment of the forces are brought together.

The wall of the cryogenic space below /# is of german silver. It
is joined airtight by means of the india-rubber ring A, to the
vaenum glass A, which contains the bath of liquid gas. The liquid
gas is supplied by the german silver tube A,, the vapours are
earried off by A,. The steel capillary of a heliamthermometer 77
is soldered through the wall of the cap.

The upper part of the vacuum-glass is comparatively wide (6 cms),
so that the liquid level falls very slowly during the evaporation,
which as we shall see is of importance. By means of the copper
ting A,
the cap, that the considerable forces arising from changes of internal

and the rods A, the vacuumelass is firmly connected to

pressure may not change its position.

1) For keeping in equilibrium an apparatus of the general type under consider-
ation any kind of force may be used which can be changed gradually without
touching the carrier. We can thus work equally well with a given compensating
force (definite weights) and changing field (regulating the current through the
electromagnet) as with a given field and changing electromagnetic compensating
force. When our apparatus was first constructed we did not possess the necessary
appliances for accurate field-‘measurements, and in examining the dependence of
the phenomena on the temperature we had to make ourselves independent of the
change of the field by confining ourselves to the investigation of the magnetisation at
different temperatures at a few field-stengths chosen beforehand and kept constant
each time during the experiments

For a modification in which the electromagnetic compensation is replaced by
a compensation by weights we refer to a forthcoming description of the appa-
ratus which was used in their investigations by Kameruincn Onnes and OostEeRHuIs
(Comm. n°, 1296 etc.).

694

The part of the enclosure above the screens / is entirely of brass
with the exception of tube A,, which is glass.

At A, and at the joint with the upper part of the enclosure
above N,, A,, (the letter is omitted in the figure,) the parts fit each
other with friction, which is of great convenience in the building
up of the apparatus.

At the upper end the enclosure A is enlarged to a wide chamber
containing the parts which serve to keep the carrier afloat. It is
closed by an arched cover A,,, which again fits on the wall with
friction. To this part of the enclosure is attached the german silver
tube B,B, which narrows down towards the bottom and to which
is fastened at B, the spring which guides the movable carrier in a
vertical direction and the two stopping pins 6,, which prevent the
earrier from moving too far up or down. ’*)

The enclosure further serves to suspend the entire apparatus from
two horizontal beams; by means of the ball socket C,C, the direc-
tion of the axis of the apparatus may be changed, without altering
its height. The plate C, bears with three adjusting serews C, on
the ground plate C,, which in its turn is fixed to the beams, and
may be shifted in a hvurizontal plane in two directions at right
angles to each other by means of the serews C,. With the adjusting
screws the apparatus may be moved 3 ems up or down; this is
necessary in using Farapay’s method in order to jind the maximum
foree by displacing the apparatus with respect to the electromagnet.

b. The movable carrier with adjuncts. In the figure the carrier
is indicated by Af. It consists of a long thinwalled tube of brass,
at the same time light and firm, lengthened by a narrow german
silver tube which at its end carries a thread W,. The experimental
objects are also fitted with german silver top-pieces, which may be
screwed on to M,. They are thus easily attached to and detached
from the carrier. At convenient heights the brass tube is provided
with the following parts: the springs A, and #, which guide the
motion, the marks .W, for the purpose of reading the position of
the carrier, a stopping ring 6, for confining the motion between
the pins, the electromagnetic coil JM, moving with the carrier, the
carriers /’, of the floats and a seale M,. As regards these various
parts the following may be added.

1) The german silver tube might without disadvantage have been replaced by
a simpler arrangement; in the design experiments were contemplated which were
not carried out. If due care is taken, the stopping pins may also be dispensed
with.

695

c. Vertical guidance of the carrier. The space between the
experimental objects and the inner wall of the vacuum-glass can
sometimes not be more than a few tenths of a millimetre when
measurements with strong fields are to be made; with the slightest
movement: of the axis of the carrier from its original position owing
to a small asymmetry in the action of the electromagnet or any
other cause the carrier would not be able to move up and down
freely. This difficulty was quite satisfactorily overcome by guiding
the carrier in its up and down motion by the aid of two flattened
spiral springs '). The outer end of both is fastened to the stationary
part of the apparatus, the inner end to the carrier and the plane
of the springs is placed at right angles to the axis of the carrier.
By the device of using flat springs a movement of the middle in
the plane of each of the spirals is almost completely prevented.
Usually the upper spring Fk, attached to the carrier remains the
same, while each separate experimental object is provided with its
own spring, which is removed from the apparatus with the object.

d. The hydrometric equilibrium. To keep the carrier afloat on
mereury the upper chamber of the apparatus is provided with a
ring-shaped trough @ (in our experiments of glass, later on of china)
which is centred on the axis of the carrier. The latter is fitted with
a horizontal arm /’,, in which at both ends are fixed the tubes of
the floats #,, glass bulbs, the shape of which is not unlike a flattened
ellipsoid. The tubes of these bulbs which are of very small section
are the only part that projects above the mercury. The section has
to be small in order that the upward pressure of the mercury shall
vary very little, if the apparatus is to be sensitive to a very small
change of the vertical force acting on it. But the size cannot fall
below a certain limit, because the tubes must also serve to com-
pensate the diminution in upward pressure in the bath on the ex-
perimental object, owing to evaporation.

This compensation is effected by raising the level of the mercury.
For this purpose use is made of a plunger ),, a small glass flask
of a shape corresponding to that of the trough which is moved up
and down by means of a rod D, with thread and milled head D,
passing through a stuffing box D,. This contrivance, which was found

1) Springs of that kind are made by cutting on the lathe a spiral groove 0.2
to 0.38 m.m. wide in a plate of german silver (comp. perspective figures R,R,).
By giving different widths to the spiral strip for a given diameter springs may be
obtained of any desired degree of sensibility. The inner end is soldered to a small
tube, the outer end is fixed in a clamping screw.

696

very serviceable supplies the advantage that at the beginning the
hydrostatic pressure of the bath need only be approximately com-
pensated, which is done by placing a weight about equal to the
pressure on the scale J/,; the accurate adjustment is made afterwards
by regulating the level of the mercury.

e. The electromagnetic compensation. The fixed coil .V, consists of
1275 turns of insulated copper wire, wound on a brass frame,
sliding closely over the outside of the enclosure; the coil rests on
the ring N, and is fixed at the top by the screw V,. The movable
coil M/, has on the one hand to be as light as possible, on the other
it has to produce as great a force as possible; account was therefore
taken of the fact that for a given weight it is an advantage to
make the radius of the coil large and the number of turns small.
The coil contains 248 turns (d= 0.7 mm.) in two layers, wound on
a thin-walled ebonite tube, which is held between two supporting
brass rings M,M, in the shape of wheels, which may be clamped
to the carrier at ,the desired height.

The wire which carries the current to the movable coil passes
through and is insulated from the cover G, and is connected to the
clamping screw G, of the upper spiral spring; the current passes
through this spring to the ring by which it is attached and which
is insulated with ebonite, along the wire G, to the coil and back
through the carrier itself, the rod of the floats, a platinum wire
dipping in the mereury, the mercury and finally a second platinum
wire, which carries the current to the cover.

The electromagnetic system is calibrated once for all by fixing
to the lower end instead of the experimental object a small scale,
on which definite weights are placed, and regulating the current
until the balance is obtained.

The level at which the carrier floats, is read on a glass plate J/,
with a seale division in tenths of a millimetre, which is focussed
with a microscope Z, magnifying about 40 times. For this purpose
a window of thick plane-parallel glass is sealed on to an opening
in the glass tube A,. On the side opposite to the microscope behind
the tube an electric glowlamp is placed in such a position that the
scale divisions are seen light on a half-dark background: in this
manner it may be very sharply determined when the cross fibre of
the microscope exactly coincides with the division.

§ 4. The experimental tubes. The substances investigated by us
(salts, powdered metal) are all enclosed in glass tubes, concerning
which the following may be mentioned.

It is desirable, that the upward pressure due to the bath changes
as little as possible when the liquid level falls through evaporation ;
for this reason the tubes end at the top in thin glass rods J/, of

2to 2.5 mm. diameter. The lower spiral spring /, and the thread
by means of which the tube is screwed to the carrier are sealed to
this rod with some Knorinsky glue. As regards the shape of the tube
we have used different forms. Tubes as shown at S, are used for
substances of high susceptibility, for which the magnetic action on the
glass or on the bath plays a subordinate part, so that for them it may
be entirely neglected or else a correction may be easily applied. The
tube is filled with the substance, when it is still open, at the bottom
putting in small quantities at the time, which are evenly compressed
in order to obtain a tight filling and at the same time a uniform
density throughout the whole tube; the substance is then closed in
with a small plug of glass wool to prevent its being heated during
the sealing of the tube and the tube is sealed off at the air-pump.
The smaller the susceptibility of the substance the greater influence
the susceptibility of the air would have and the morene cessary it is
to be assured of a good vacuum; a high vacuum, however, is
obviously unnecessary.

In cases where account has to be taken of the susceptibility of
the glass, which may give rise to fairly strong forces'), tubes of
type S, are used, the lower half of which, separated from the upper
half by a glass partition, is exhausted. When this partition is placed
on the level of the axis of the poles, the correction for the elass
disappears, as it is divided symmetrically with respect to the axis;
the susceptibility of the substance is in that case directly compared
with that of the vacuum. Type S,, which does not require further
explanation is meant for the measurement of the susceptibility of
the liquid in the bath.

§ 5. Additional apparatus. The electromagnet is a copy of Wriss’s
electromagnet which was used in previous researches of this series.
The yoke is, however, placed horizontally this time, in order to
leave the space below the apparatus completely free (comp. per-
spective drawing). Usually poles were used of the shape shown,
the flat end-faces of which had a diameter of 40 mms. At a polar
distance of 15 to 20 mms. the topographical inequality of the field
about the middle of the interferrum was not above 0.1 °/, within a

') Te suscepubilily of glass at low temperature was determined by us in
- Comm. No, 124a, p. 6.

698

distance of 1 em. The field-strengths were measured with a Corron-
balance of the usual pattern by W. C. Weser of Ziirich.

The circuits of the fixed and movable coils are entirely independ-
ent of each other: each of them contains an accurate ammeter, a
commutator and rheostats, in which the current is reversed on com-
mutation, in order to neutralise any magnetic influence on the ammeters.
They are within reach of the observer seated in front of the microscope.

The field-strengih of the electromagnet 1s given by the current
flowing through it; the field was not adjusted until the magnetising
current had been “several times reversed.

If the evaporation of the bath in the apparatus as described is
too strong, as is the case when liquid hydrogen is used, it is dimi-
nished by surrounding the bottom half of the vacuam-glass with a
vacuum-elass with liquid air.

§ 6. Method of observation. Passing by certain simplifications
whieh were often possible we proceeded as follows.

The enclosure and the carrier (without experimental tube) are
first adjusted so that the common axis is vertical and passes through
the centre of the interferrum. When this position is arrived at, the
apparatus is not moved sideways any more.

The experimental tube is then serewed to the carrier and its
spring clamped. By means of the weight on scale J/, the carrier is
made to float on the mercury approximately at the desired level
and care is taken that the movable coil has the correct position
relatively to the fixed coil. The apparatus as a whele is then moved
in a vertical direction until the lower end of the experimental cylinder
falls about in the line of the axis of the poles, after which the
cylinder is adjusted more accurately by turning the apparatus about
the ball socket C,. When finally the poles have been brought at the
right distance, everything is ready for the observations at ordinary
temperature.

In changing to low temperatures as much weight is added to the
seale as agrees approximately with the upward pressure of the bath
to be expected and the cover is fastened to the apparatus air-tight
by means of the india-rubber ring; after drawing out the poles, the
vacuum-glass is placed carefully round the experimental tube, con-
nected airtight and centred in a manner similar to that used in the
apparatus of Weiss and Kamrrtinen Onnes. After having made sure
that everything is airtight, the liquid gas is admitted to the vacuum-
glass, the poles are brought back to their position, and the carrier
is adjusted to its zero by means of the plunger; the currents in the

699

large electromagnet 7, and in the fixed coil 7¢ are adjusted to suitable
whole numbers and the current 7, (in the movable coil) regulated
by a gradual change of the resistance until the carrier has come back
to the zero. The current 7, is then noted down and the operations are
repeated for the 4 possible combinations of the currents 7%, 7 and
i, . Before and after each observation the zero-position of the carrier
is observed or again adjusted; when the change amounts to only a
few tenths of a millimetre, there is no objection to do this, more
simply than by means of the plunger, by shifting the microscope
a little.
(To be continued).

Chemistry. — “The application of the theory of allotropy to electro-
motive equilibria.’ By Prof. A. Smirs. (Communicated by
Prof. J. D. van per WaAAts.)

1. I communicated already before') that the investigation for
testing the theory of allotropy with different elements and anorganic
as well as organic compounds was in progress. The investigation of
the metals, which had been started with tin and mercury, was
somewhat delayed, because all the time had to be devoted to the
study of phosphorus and mercury-iodide, so that only comparatively
shortly ago the metals could be taken in hand again.

As may be supposed as known, the theory of allotropy rests on
this fundamental assumption that every phase of a system that
behaves as a unary one is at the least built up of two kinds of
molecules which are in internal equilibrium, and must necessarily
be taken as the components of a pseudo-system. This theory com-
prises, therefore, all possible states of aggregation of a substance, and on
account of the importance of its conclusions its principial interest lies
in the region that has been least investigated up to now, viz. that
of the solid state.

Now it is clear that the experiments which are carried out to
test this theory are undertaken in the first place to prove that the
different states of aggregation and particularly the solid phases of a
substance which presents the phenomenon of allotropy, are really
mixtures, and in internal equilibrium, for every time that this
succeeds a confirmation of the said theory has been found. In the
second place an attempt may be made by a continuation of the in-

1) These Proceedings, April 26, 1912, XIV, p. i199,

700

vestigation to find something about the type of the pseudo-system,
which is, of course, a far more difficult problem.

2. The test may now take place in different ways:

a. by an inquiry into the influence of the previous treatment on
the point of solidification, resp. melting point, point of transition ete.

b. by an inquiry into the influence of the previous treatment on
the solubility.

c. by an inquiry into the influence of the previous treatment on
the specific gravity, the viscosity, the index of refraction, the specific
heat, and further on every other property of the substance.

d. by the study of any temperature function, in which a con-
firmation of the said theory may follow from the way in which
this function varies with temperature.

Besides in this way the theory of allotropy can probably also be
tested in another way, by the fact that as I observed already before’)
it may be expected that the different kings of molecules of a same
substance will in genera! differ in reactive power.

On that occasion I already pointed out that by means of this the
passivity of the metals might be explained, hence also the permanent
or periodic changes in the potential difference between metal and
electrolyte, in the solution of some metals by an electrolytic way,
so that when this view should prove correct, a new means would
have been found to prove the complexity of the metals in the
study of the phenomenon of passivity brought about by a purely
chemical or by an electrolytic way.

As I am of opinion that the experiment really shows the validity
of the above mentioned supposition, { will expound here further
how the electrolytic deposition and soiution of metals must be con-
sidered in the light of the theory of allotropy, and at what conclu-
sions we then arrive.

3. When we have a metal that shows the phenomenon of allotropy,
different kinds of molecules will be present in this metal. To simplify
the matter as much as possible, let us assume that molecules M/,
occur by the side of mon-atomic molecules 4/. When this metal is
immersed in an electrolyte and emits ions, two different kinds of
ions will be emitted; if the metal as ion, carries three positive charges
per atom they will be the ions 1°" and M/,** on the supposition made.

Up to now it has always been assumed that a metal emits only
one kind of ions, now the theory, however, states that when one
of the coexisting phases is in internal equilibrium, the other must

\) These Proceedings, May 31, 1913, XV1, p. 191.

701

also be in internal equilibrium, so that when in the metal the molecules
M and M, are in equilibrium, there will be equilibrium between the
ions Mf and M,** in the electrolyte. So the simplest assumption
is this that the different ions are emitted by the metal, though this
need not take place in the ratio in which they are present as molecules
in the metal. In this way we then arrive at the result that the unary
electromotive equilibrium may be considered as a special equilibrium
in the series of electromotive equilibria of homogeneous mixed crystals,
which we may imagine as being built up of the molecules J
and M, in different ratio.

Let us now suppose that fig. 11) for a definite 7’ P and a definite
total metal-ion concentration indicates the potential difference A
between electrolyte and metal as function of the concentration.

The point a denotes the potential of a solution of an J/-salt of

definite metal-ion concentration containing exclusively 1/°’-ions, with

1 (Cf. Retnpers. Zeitschr. f. Phys. Chem. 42, 225 (1902).

Proceedings Royal Acad. Amsterdam. Vol. XVI,

702

regard to a metal merged in this solution, which is thought to be
entirely built up of M/-molecules.

The point 6 denotes the same thing for a solution of the same
metal-ion concentration as the just-mentioned solution, but containing
exclusively J/,**'-ions, a metal being immersed in this solution which
consists exclusively of M,-molecules. The metal J is here supposed
to be a base state, and M, to be a noble state of the same metal.

Now it has been assumed in fig 1 that the metals 17 and M, are
miscible to a limited degree in the solid state with the assumed 7’
and P. The two branches of the interrupted series of mixing are
indicated by the lines ad and eh, the solutions which can be in
electromotive equilibrium with these metal phases being indicated by
ac and ch. The line cde denotes the three-phase electromotive equili-
brium. In general this three-phase equilibrium can also lie above the
potential difference of the two metals, but this case is not considered
here, because we shall no doubt always have to do with association
in metals, in which it is to be expected that the metal phase will
contain more of the’most composite pseudo-component than the coexist-
ing solution.

The phases coexisting in case of electromotive equilibrium of
course lie on a horizontal line, which, the A,z-figure being given,
and the potential difference being known, immediately enables us to
know the concentration of the coexisting phases.

Now we may of course apply Van Laar’s') formula for the
potential difference between mixed crystals of two metals and electrolyte
also to the case supposed here. Considering that for electromotive
equilibrium

+ +

[Re eS SE rr.)

VME ve

+ oF

in which pj and wy, are the mol.-potentials of the °° and M,**
ions in the electrolyte, and uy and wy, those of the molecules
M and M, in the metal, ry and vy, representing the number of
charges of the different metal-ions, we arrive at the following relation
for the potential difference
RT. Ky(l—a) RT Kye

In - — In —,
PME Ci vu,e Cy?

jh (2)

It follows from this formula, in which as I showed before, A’yz

1) Chem. Weekbl. 41, 1905.
Lehrbuch der Theoretischen Elektrochemie.

703

and Ay, indieate the saturation concentrations of the metal-ions
M~ and M,***), that
1 l

(“3 i a oe (3)
Cu Sn Cig, oh

and as in the case supposed here

DM see 8, pots ese fon oA)
we get:

4. The A, x figure 1, drawn here, holds for the case that the two
kinds of molecules and the two kinds of ions cannot be converted
into each other. If, however, an internal equilibrium is established,
only electromotive equilibrium is possible, when the coexisting phases
are both in internal equilibrium. This is immediately seen in the
following way. Equation 1 runs

+ +
UM—UM UM; — UM,
vue VM é
Now
YM, = 2vy
so that
+ +
2um — 2um— UM, — UM,
or
+
20M — mM, =2Um— bu, =~ > » . »11(6)

from which follows that when in case of electromotive equilibrium
internal equilibrium prevails in the electrolyte between the metal-
ions, for which:

at ar

24M = UM,

a consequence of this is that:
2uM = UM

or in words that internal equilibrium must then also prevail in the
metal, and vice versa. As is directly to be seen, the same conclusion
follows from equation \5), when we assume the validity of the law
of the chemical mass-action also in this case. As said before the
A,a-tigure holds for a definite 7’, P and total metal-ion concentration.

The internal equilibrium in the metal phase is perfectly detined
for definite 7’ and P. The internal metal-ion equilibrium in the

es) These Proc. May 9 1906. IX p. 2.

704

electrolyte, however, is dependent on the concentration ; Cy, resp. Cy,
varies with the total concentration, and together with it according
to equation (2) also the potential difference A. If, therefore, also the
total metal-ion concentration has been fixed, everything is perfectly
dete rininate.

Let us put that for given 7’, P and total metal-ion concentration,
for which our Fig. 1 holds, the internal equilibrium between the
metal-ions is indicated by the point 7, it follows from the A, - figure
that for unary electromotive equilibrium the solution 4 will coexist
with the metal phase S for a potential difference indicated by the
situation of the line ZS. It has been said that the internal equilibrium
in the metal phase is solely determined by 7’ and P, i.e. the point
y, but the situation of S in the A, x-figure depends of course on the
total metal-ion concentration in the electrolyte.

We see, however, that when we prolong the lines ac and ad
metastable, the same solution Z can be in unary electromotive
equilibrium with another metal phase fora higher potential difference,
viz. with the phase S’. This second unary electromotive equilibrium
is, however, metastable, whereas the first is stable.

If we first of all assume that we have ahvays to do with internal
equilibrium we may question what will happen when the solution
Z is electrolysed, while the total metal-ion concentration is kept
constant. It is clear that for the separation of a metal phase, in
which another internal equilibrium prevails than in the electrolyte,
a molecular transformation will be necessary, which in our case
consists of the reaction 2!@— M,. We now see from Fig. 1 that
the metastable phase S’ lies much closer to the liquid 4’ than the
stable phase S to the liquid phase L. Jt follows from this that the
deposition of the metastable metal S’ requires a much smaller internal
transformation than that of S, and the consequence of this will
be that when electrolytic metal depositions is carried out at tempera-
tures al which the velocity of transformation of the metastabie modi-
jication to the stable modification is small, the metastable state is
deposited. i

It is, therefore, seen from this that for so far as Ostwaup’s “Gesetz
der Umaivandlungsstufen” holds also here, the explanation is quite
analogous to that given by me for the succession in the appearance
of different allotropic states of the same substance in the cases in
which the deposition was not effected by the supply of electric
energy '). On that oceasioa I already pointed out that Ostwa.p’s rule

1) Zeitschr. f. phys. Chem. 84, 385 (1918).

705

need not necessarily alvays be valid, and here too exceptions may
be expected, when viz. the metastable and stable solid phases differ
only little in concentration.

5. We have discussed the phenomenon of electrolysis here on
the supposition that the internal equilibrium in both phases sets in
with so great a velocity that at any moment internal equilibrium
prevails, but this is a limiting case, and it is certain that the setting
in of the internal equilibrium at least at the ordinary temperature,
requires an appreciable space of time. It is therefore of importance
to ascertain what the phenomena will be when the setting in of the
internal equilibrium cannot keep pace with the changes of concen-
tration caused by the electrolytic process.

For this purpose it is simplest first of all to assume the other
limiting case, viz. that the internal transformations are entire/y wanting
during the experiment. We think two rods of the same metal J/,
which have somehow assumed internal equilibrium at the temperature
and the pressure for which Fig. 1 holds. These rods are used as
electrodes, and placed in some salt solution of the same metal, and
of a concentration, for which Fig. 1 also holds. Suppose internal
equilibrium also to exist in the solution, then both metal electrodes
are in electromotive equilibrium with the solution and the coexisting
phases are indicated in Fig. 1 by the points S and Z. Then we
think a negative catalyst to be added, after which there can be no
question any more of the setting in of internal equilibrium.

Fig. 2 represents the potential differences, which exist between

the two electrodes and the electrolyte. The distance ch = de indicates

é | he

a £

Rig 2:

the potential of the solution with respect to the metal electrodes.
So the situation of ed agrees with the potential of the electrolyte,
and that of the lines a) and ef with the potentials of the two metal
electrodes I and II. So the potential of the electrolyte is here positive
with respect to that of the metal electrodes.

Let us now connect the two metal electrodes with the poles of a
battery; let us put I to be the positive, and II the negative pole,
then electrode 1 will be dissolved, whereas metal from the electrolyte
deposits on the electrode II. If we again imagine the total metal ion

706

conceniration kept artificially constant, Fig. I can account to us for
what will happen.

If positive electricity is applied to electrode I, the electromotive
equilibrium is broken for a moment, and a new electromotive
equilibrium sets in, in consequence of molecules of the metal I being
dissolved as positive ions. If the ions M7 and JM,** entered the
solution in the same ratio as they were present as molecules in the
metal, the composition of the metal would not change while the
electrolyte gets richer in J/,**-ions. It is clear that as we now
exclude internal transformations, in this way there cannot be question
any more of a renewed setting in of the electromotive equilibrium.
If the metal-ions entered the solution exactly in the same ratio in
which they are already present in the electrolyte, the concentration
of the metal phase would change, whereas that of the electrolyte
remained the same, which could not lead to a renewed setting in
of the electromotive equilibrium either.

Thus we-see that the metal phase will emit J/°” and J/,**-ions
in ‘a ratio lying between ZL and JS; in consequence of which both
phases become richer in J/,, and two phases can therefore form
again, which can be in electromotive equilibrium with each other.
On supply of positive electricity to the electrode I the potential
difference A will, therefore, have to descend, and when the dotted
line pq in Fig. 1 indicates the potential difference zero, it is even
possible ‘that the potential difference A at electrode I becomes negative.

What will take place at the other electrode Il? At this electrode
metal will be deposited, and it is easy to see that assuming that at
first the stable phase S separates, the different metal-ions will be
discharged in a ratio lying between 4 and S, because only in this
way a renewed setting in of the electromotive equilibrium is possible.
Hence the coexisting phases will become richer in J7 on the side
of the metal-deposition, and the potential difference will become
greater positive. For a definite potential difference indicated by the
line ce another metal phase d will arise by the side of the metal
phase e, and when the electric current continues to pass through,
the potential difference remains constant fill the metal ions in the
electrolyte depositing on the metal phase e, have converted this
latter phase, at least superficially, into the metal phase d. Then the
potential difference can increase again, and the metal phase moves
along the line da and the electrolyte along ca.

So we may conclude from the foregoing that when the current
has continued to pass for some time, figure 2 of the potential differénces
may have been changed into figure 3.

107

Though at first there did not exist a potential difference between
T and TI, this will, indeed, be the case after some time, because ™m

i ie 4

consequence of the electrolytic process, one metal electrode has become
less base or even noble, whereas-on the other hand the other electrode
has become baser.

As has been said, in many cases the metastable state will separate,
and then part of the potential difference is, of course, to be attributed
to this. This, however, does not affect the nature of the phenomenon.

6. Here, however, the limiting case has been assumed that the
metal molecules and ions are not transformed into each other at all
during the experiment, which, however, will not, be the case in
general. As a rule the system will not entirely behave as a unary
one with regard to the metal molecules and ions, nor will it behave
entirely as a pseudo-system, and for this very reason exceedingly
remarkable phenomena may present themselves. Thus it has been
found that in some eases periodic oscillations occur in the potential
difference in the above described experiment, which, as I stated
before, seems to indicate that the internal transformations at first
are slackened~ by negative catalytic influences, which however,
after a certain degree of metastability has been reached, are no
longer able to maintain the formed metastable state, so that all at
once an internal transformaticn may setin, which propagates with
great rapidity all over the metastable metal surface. When this
transformation, in which internal equilibrium has been more or
less approached, has taken place, the same phenomenon may
repeat itself. I have already pointed out that the negative catalytic
influence is probably exerted here by a trace of oxygen dissolved
in the metal, which iniluence can, of course, also be active when
no periodic oscillations in the potential difference occur, but a
continuous change in the same direction.

708

In this connection it may be pointed out that explosive antimony
is probably a metal phase which is far removed from the state of
internal equilibrium, and in which the internal transformations are
impeded by the dissolved antimony-chloride.

7. In connection with the foregoing it is desirable to draw attention
to this that according to these considerations the contact with the
solution of a salt of the metal must have an accelerating influence on
the setting in of the internal equilibrium of the metal.

In general we shall namely be no doubt justified in assuming
that the internal metal-ion equilibrium establishes itself pretty rapidly
in the electrolyte at the ordinary temperature and pressure, whereas
under the same circumstances the metal probably will not get in
equilibrium or exceedingly slowly. If we imagine the case that at
the ordinary temperature and pressure a metal is immersed into the
solution of a salt of this metal, then, assuming the same case as
represented in figure 1, the metal will contain too many molecules
or too many molecules J/,. The electrolyte, which indeed is
thought to be in internal equilibrium cannot be in electromotive
equilibrium with this metal, and the consequence of this is that both the
electrolyte and the metal will tend to reach this electromotive equi-
librium. Put that the metal contains too many JZ molecules, then
M,*** ions will deposit from the electrolyte on the metal, and M
molecules will be sent as ions in solution by the metal. In the
electrolyte the ion concentration now remains constant in consequence
of internal transformations, but the concentration in the surface of
the metal changes in such a way that it finally agrees with the
internal equilibrium. So the surface of the metal has reached internal
equilibrium by means of the electrolyte, and now the possibility is
given that also the layers that lie deeper will assume internal
equilibrium by self-gratting.

If the temperature is that of the transition point, the electrolyte
lies exactly in ¢ (Mig. 1) with internal equilibrium, and above this
temperature on the line ac. At the point of transition the electrolyte
will greatly promote the internal equilibrium both in the metal
phase e, and in the metal phase d@ for the just-mentioned reasons.

8. In conclusion IT will direct attention to another circumstance
which may be expected with great probability on the ground of
the considerations of the theory of allotropy.

If for the sake of simplicity we retain the case of a metal con-

709

sisting of molecules M and J,, then it is clear that as we have
assigned three positive charges to every atom as ion, the molecules
MCI, and M, Cl, will be formed on solution of this metal in hy-
drochlorie acid. The solid salt which may be separated from this
solution will also contain both kinds of molecules, and in the state
of internal equilibrium in a ratio which is entirely determined by
T and P. Let us now suppose that this salt is reduced with hydrogen
at a temperature as low as possible, then when the temperature is
too low for the setting in of the internal equilibrium of the mole-
ecules M and J/,, a metal will form, which as far as infernal con-
centration is concerned, may differ very much from the metal as
we know it. If the obtained metal relatively contains more simple
molecules than in the state of internal equilibrium, it will contain
a greater reactive power, because probably an association will be
generally attended with a decrease of chemical activity.

In this way perhaps the pyrophoric phenomenon will have to be
explained, which has already been observed for different metals, and
which disappéars again when the metal is heated at higher temperature.

I have now briefly indicated the different directions in which for
some time the metals have been studied in my laboratory.

SU! MOM ALR Y:

In this paper the theory of allotropy was applied to the electro-
motive equilibrium between metal and electrolyte, in which it appeared
that a metal exhibiting the phenomenon of allotropy, and consequently
composed of different kinds of molecules (different in degree of asso-
ciation), immersed in an electrolyte, will emit different kinds of ions.
By means of this it could be demonstrated that the unary electro-
motive equilibrium belongs to the A,-figure of a pseudo-system,
which system might be realized for the case that the different kinds
of metal molecules and ions could not be transformed into each other
e.g. by the presence of a negative catalyst.

The application of this new view to the phenomenon of electrolysis
led to the following results.

In the first place it could be made clear that and why with electro-
lytie metal deposition in many cases not the stable but the metastable
phase will be obtained. In the second place the theory showed that
when the internal transformations under negative catalytic influences
fail to appear or are impeded, the metal that is made to dissolve

710

by an electrolytic way, will get nobler superficially '), whereas the
newly deposited metal will be daser*) than what went into solution.

In the third place it was made probable that also the periodic
oscillations in the potential difference, which point to a periodic
enobling of the metal surface may be accounted for from the same
point of view.

In the fourth place it was demonstrated why the contact of a
metal with the solution of one of its salts must exert an accelerating
influence on the setting in of the internal equilibrium of the metal.

Finally attention was drawn to the possibility that on reduction
of metal compounds at low temperatures metal masses are obtained
which are far from the state of internal equilibrium, and can exhibit
an abnormally great chemical activity. This will be the case when
they differ from the ordinary metal states by a greater content of the
more simply composed kinds of molecules. The pyrophoric states
observed for some metals are possibly to be explai ned in this way.

Anorg. chemic. laboratory
Amsterdam, Dec. 20, 1918. of the University.

1) This may also mean: becomes less base.
ae pce “pee » nobie.

(January 29, 1914).

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING
of Saturday January 31, 1914.
Vout XVI.

=D OG
President: Prof. H. A. Lorentz.
Secretary: Prof. P. Zeeman.

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 31 Januari 1914, Dl. XXII).

SO eNe Fa aNy FES"

?

H. R. Kruyr: “Pseudoternary systems of acid anhydrides and water. I. Phthalic anhydride’

wo

(Communicated by Prof. Ernst Comen), p. 71

J. Borsrxen and P. EB. Verxapr: “The mechanism of the acid formation of aliphatic acid
anhydrides in an excess of water”. (Communicated by Prof. A. ¥. HoiiEMman), p. 718.

JAN DE Vries: “Bilinear congruences and complexes of plane algebraic curves’, p. 726.

Jan DE Vries: “A bilinear congruence of twisted quarties of the first species’, p. 733.

F. A. OH. Scurememakers: “Equilibria in ternary systems” XII., p. 739.

Pu. Konystamm and K. W. Warsrra: “An apparatus for the determination of gas isotherms
up to about 3000 atms.” (Communicated by Prof. J. D. VAN DER WAALS), p. 754.

L. Rurren: “Elephas antiquus Fale. from the river Waal near Nijmegen”. (Communicated
by Prof. A. WicHMAnNN), p. 769.

H. J. Backer: “On the nitration of methylurea”. (Communicated by Prof. A. P. N.
Francurmonr), p. 770.

A. H. Braauw: “The primary photo-growth reactions and the cause of the positive photc-
tropism in Phycomyces nitens.” (Communicated by Prof. F. A. F. C. Went), p. 774.

Al. Kameriincu Onnes and Apert Perrier: “Magnetic researches. X. Apparatus for the

general cryomagnetic investigation or substances of small susceptibility”.(Continued), p. 786.

46
Proceedings Royal Acad, Amsterdam, Vol. XVI.

712

Chemistry. — ‘“Pseudoternary systems of acid anhydrides and
water. 1. Phthalic anhydride.” By Dr. H. R. Kruyr. (Com-
municated by Prof. Ernst Coney).

(Communicated in the meeting of December 27, 1913).

For reasons, which will be further explained in a following treatise
of this series, the knowledge of the heterogeneous equilibria in
systems of acid anhydrides and water seemed to me of importance.
The only quantitative investigation that has been made on_ this
subject is found in the dissertation of E. van pr Stapr') and relates
to phthalie- and succinic anhydride. The results thereof may be
summarised as follows: If we shake the acid with water at a
definite temperature we soon attain an equilibriam; if, however, we
shake the anhydride with water, we notice a continuous rise of the
total-solubility*) at which values are attained far above the solubility
of the acid; then follows a period of fall quite as regular as the
previous rise, no discontinuity occurs in this process; finally we
again arrive, at the solubility of the acid. These results suggest the
following interpretation: the anhydride has a greater solubility than
the acid, hence occurs the provisional high total concentration, but

Z

w 2 A

Fig. 1.
1) Amsterdam 1901. Also Zeitschr. f. physik. Chem. 31, 250 (1899) and 41,
353 (1902),
2) By this is meant the acid concentration as found by titration which represents
the sum of the acid- and anhydride molecules.

713

gradually the anhydride disappears by conversion into the acid and
so we again finish with the acid-solubility.

This explanation, however cannot be satisfactory, for it is assumed
herein that the phase equilibria set in while the reaction equilibrium
is modifying the condition in the homogeneous solution. Thus we
have a pseudoternary system: water-anhydride-acid (W-A-Z). In
fig. 1 has been drawn the solubility-isotherm, the equilibrium line
will about coincide with the axis WZ. The position of a and 6 is
given by the assumed difference in solubility between the acid and
the anhydride. If now we shake water and anhydride the solution
will about follow the lines Wd and dc; in ¢ the solubility of the
phthalic acid has been attained and if then a fall occurs in the
total solubility this means to say that solid phthalic acid has deposited.
But then the equilibrium is non-variant (p,f) and hence a fall cannot
take place immediately after a rise; no continuous maximum can
follow, but a Jong stop at the highest concentration must oceur. Now
this was not observed by VAN DE STapT; on repeating the experiment
at 20° I also noticed that the concentration of a solution when shaken
with phthalic anhydride in a rotating flask did not come to a
standstill, but passed continuously through a maximum value.

In Table I this frequently repeated experiment is indicated. NV/10
sodium hydroxide was used for the titration with phenolphthalein
as indicator.

TABLE I.
3.17 gr. Phtalicanhydride + 90 cc. water.
Concentration in
No. Time
millimols per L.
1 V/, hour Le)
2 Vy » 34.4
3 3/4 > 55.1
4 ll, » 46.2
5 1h , 41.3
6 4 >» | 36.4

The solubility of phtbalic acid is 35.2 millimols p. litre; it was
always attained the next day.
46*

714

It should be noticed that in the interval between experiments 3
ang 4+ a finely divided solid mass had deposited (which very much
impedes the filtration through cotton wool) ; indeed the experiments
following have really been carried out with the two solid phases,
anhydride and acid; even after experiment 6 a few long needles of
anhydride were still readily visible.

Afterwards the shaking bottle was provided with acid as well as
with anhydride so as to determine the position of point c. Now
indeed a composition was attained that remained fairly constant for
a longer time (see the first two columns of table II). But it seems
peculiar that 1. the value found lies but little above the sclubility
of the phthalie acid and 2. that the value was found to differ in
different experimental series. In the dissertation of VAN DE STADT we
also find in the second table on page 49 an extremely smooth maximum
as the progress of the solubility in the presence of the two solid phases.

Perhaps an explanation may be found here owing to a peculiar
relation between the velocities of attainment of the homogeneous
and heterogeneous equilibria. As this necessitates the knowledge of
the proportion of anhydride to acid in the various solutions this
proportion was determined. The chemical method applied by Lumrmre
and Barpmr') in the study of the equilibrium in the homogeneous
system acetic-anhydride-water proved impracticable here, but the
electric conductivity power previously applied by Vorrman*) and by
Riverr and Sipewick*) in the study of the progressive change of the
reaction in homogeneous systems, seemed to furnish a better method.*)

In order to render unnecessary the repeated withdrawal of large
volumes of liquid a small plunging electrode was constructed with
a capacity that just required suitable resistances for liquids used in
these experiments.

We made use of pe Haegn’s phthalic anhydride (m.p. 130°.6 in
VAN E1k’s apparatus); phthalic acid was prepared from that anhydride
by complete hydratation ; titre and conductivity power of the saturated
solution appeared to be independent of the quantity of solid phase,
hence foreign substances were absent. By numerous determinations
with concordant results we found for the solution saturated with
phthalic acid :

1) Bull. Soe. Chem. de France [3] 33, 783 (1905).

2) Diss. Groningen 1903, Rec. d. Trav. Chim. d, Pays-Bas 23, 265 (1904).

8) Journ. Chem, Soc. 97, 732 and 1677 (1910).

4) The method also has been applied by Boisexen and his collaborators, cf.
Ree. d. Tray. Chim. d. Pays Bas 1912 and these Proceedings, (Note added in the
English translation).

715

35.2 millimol. p. litre spec. cond. power 0.001952.

If we take w, for 20° on 0.3838, Ostwatn’s law of dilution then
yields 4 = 0.117, which result was put to the test in a number of
solutions. The acid concentration may now be calculated from the
specific conductivity power ').

The experiments were carried out by rotating a small flask in
‘the usual manner in a_ thermostat. The conductivity vessel was
furnished with a trebly perforated stopper. Through the stopper was
put the plunging electrode, also a little tube leading to the cotton-
wool filter and another one to which suction could be applied.
Immediately after 11 ce. of the liquid had been withdrawn the
resistance was measured in the usual manner (Waxratstonn bridge,
alternating current and telephone); 10 ce. were then pipetted off
and _ titrated.

In Table 2 is found the complete composition of the solutions which
are shaken with the two solid phases. We notice that although a
totally stationary maximum value was not found, it is very surprising
to find how remarkably little anhydride is contained in the solutions
which during about two hours still change but little in composition.

TABLE Il.

2.05 gr. acid + 2.72 gr. anhydride -++ 90 cc. water.

Time | Titration Spec.cond.power, Acid \Aahivdride| Maximum average |
11min.) 40.0 0.001970 | 35.8 |) 4.2

oT > 42.1 Paz eal) RST 4.4

65 > 41.1. | 2002 | 36.8 | 4.3 37.0 acid

96 > 41.5 | 20022 | 36.8 | 4.7 4.4 anhydride
147 » 40:7 | 1995 36.6 Mes WY) |

Hence a large solubility of the anhydride molecules appears but
little probable. It is interesting to notice that these solutions contain
more phthalic acid than the purely aqueous ones. The solubility ot
the acid is thus much promoted by the anhydride present.

Fig. 2 appears to be the most appropriate one for expressing
these results.

1) As to the neglecting of the influence of the anhydride on the conductivity
power see Riverr and Smwewick (l.c.).

716

W
6 Fig. 2- . S

a lies at a greater concentration than 6, the solution ¢ contains more
acid than a. Looking at the presumably very slight solubility of the
anhydride and the fairly large reaction velocity of the hydratation
(four times greater’) than that of acetic and succinic anhydride) it
will be understood why in different experimental series were found
maximum values which mutually slightly differed. (Some tritration
values from different series: 41,4 — 41,4, 44,0 — 44,3 — 44,5). Three
processes are taking place continuously: solution of anhydride,
hydratation thereof and crystallisation of phthalic acid. The latter
will no doubt take place spontaneously as a large quantity of tinely
divided solid phase is present: the second takes place fairly rapidly
and the first is evidently not rapid enough to maintain the condition
of the point c. That appears from table 3 where this last reaction

TABLE III.
2.25 gr. acid + 4.37 gr. finely powdered anhydride —- 90 cc. water.
Time Titration | Spec. cond. Power Acid Anhydride
30 min. | An} 7] 0.002050 38.5 Dee
60"; 44.5 2056 38.7 5.8
| 101 , 44.1 2056 38.7 5.4
Isa 42.7 2027 Siial! 5.0
222%.) | 40.8 1986 36.3 4.5
|

fl 7

was promoted by adding a large quantity of finely powdered anhydride.

If we compare these results with those of Table 2, we notice
ihat now indeed the anhydride-concentration has risen: as the acid
concentration also lies higher this is evidently also promoted by the
concentration increase of the other pseudo-component.

It now still remained to be seen whether the internal composition
of the liquids which are shaken with anhydride only, agrees with
the conclusions drawn from the above experiments.

In Table IV is shown the result of a measurement.

TABLE IV.
3.11 gr. anhydride + 90 cc. water.

Time Titration | Spec. cond. Power | Acid | Anhydride |
— u = = —_ = a

25 min. 29.2 0.001663 | 26.3 2.9
50 > 54.5 2286 a7 | ie |
iS) > 47.2 2193 43.6 3.6

From this we notice that the large total-solubility found when
shaking with anhydride is mainly an acid-solubility. In another
series, for instance, 43.6 acid: 7.7 anhydride was found for the
composition at the greatest total solubility. More than the sixth part
can therefore never be put to the account of the anhydride. As
originally no solid phthalic acid is present as a solid phase we are
presumably dealing here with supersaturated solutions, although on
the other hand, anhydride and acid seem to promote each others
solubility. It is therefore, intelligible that, after the maximum has
been attained we can plainly observe the separation of the phthalic
acid in the liquid and also that the liquidum phase gets impoverished
both in acid and anhydride. As regards the acid this is presumably
the case in a much higher degree than indicated in Table 4 as the
withdrawal, after the maximum concentration has been passed,
always takes a few minutes on account of the clogging of the filter
by the deposited exceedingly finely divided phthalic acid. In the
meanwhile of course, a little of the anhydride from the clear
liquid in the conductivity vessel becomes hydrated again before the
measurement could be executed and thus a somewhat too high acid
and a somewhat too low anhydride concentration is found.

718

The progressive change of the solubility is also characterised by
the fact that after about 25 minutes, when the solubility of phthalie
acid (35.2 millimol. per litre) has not yet been attained, the condition
is already such that the solution contains a preponderance of acid.
The idea that phthalic anhydride should be readily soluble is, therefore,
without any foundation; the anhydride concentration can, moreover,
not be calculated by simply deducting the solubility of the acid in
water from the total solubility.

This last experimental series therefore also confirms our contention :
the anhydride passes into solution as such and then becomes hydrated
and this so rapidly in comparison with its solubility velocity that
the non-variant (p,é) equilibrium is not attained, or at least not
permanently so. The anhydride, if we will not eredit it with an
abnormally small solubility velocity (for which there exists no reason,
just the contrary), has a much smaller solubility than the acid.

No measurements have as yet been carried out with succinic
anhydride, but looking at the parallel behaviour of the two acid
anhydrides similar relations may be expected there also.

Owing to the peculiar relations between the homogeneous and the
heterogeneous reaction velocities in this kind of systems, we are
here at the limitation where we may still speak of actual pseudo
ternary systems. In connection therewith and other correlated questions
the investigation of different systems is being continued.

Utrecht, Dec. 1913. van “? Hore-Laboratory.

Chemistry. — “The mechanism of the acid formation of aliphatic
acid anhydrides in an excess of water’. By Prot. J. BousEKen
and P. E. Verkapr. (Communicated by Prof. Hoieman).

(Communicated in the meeting of December 27, 1913).

The communication of Wirspon and Sipewick ') on the hydratation
of some acid anhydrides induces us to give a short résumé of the
results obtained by us when investigating the hydratation of the
aliphatic acid anhydrides.

This investigation *) has already been announced by one of us
some time ago. He had found that the hydratation constant of the
eyclic acid anhydrides was connected with the dissociation constant
of the acids formed thereof. As it was his intention to get to know

1) Soc. 108, 1959 (1913).

*) Recueil 31, 90 (1912).

119

something about the ring tension eventually occurring in those acid
anhydrides, it had to be decided whether the dissociation constant
of the acids was the only or principal factor which, besides that
ring tension, could exert an influence on the hydratation velocity.
The hydratation of the anhydrides of the fatty acids seemed to him the
most appropriate one, because in this the factor of the ring tension
is excluded, whilst that of the dissociation constant can be readily
applied. Moreover, the values of the dissociation constants of the
fatty acids do not diverge much, so that other factors can exert
their influence distinctly. While the detailed account of this invest-
igation will be published in another form'), we give here a short
summary of the results obtained.

The hydratation velocity of the acid anhydrides was determined
in the manner indicated by VorrmMan?), namely by measuring the
conductivity of the aqueous solutions in which it is assumed that
only the acid determines the conductivity and that this is not
modified by the anhydride still present.

The conductivity of the acids and the dissociation constant to be
deduced therefrom had to be accurately known, because from the
conductivity found in the hydratation the concentration of the acid
formed (and consequently that of the anhydride consumed) had to
be calculated. As the values given in the literature for the diss,
const. often differ considerably, we judged it necessary to make
new determinations thereof.

They were carried out in the usual manner already frequently
deseribed by us.

A correction for the conductivity of the water itself (1--1.5 & 10—6)
was not applied, because this conductivity is caused in the carefully

Dissociation-constants of the fatty acids.

| | | |

| es |) es KES MOE | TEGO’
= |
acetic acid — 387 | -— | 1.82
propionic ,, 241 384 ARS | 11
n. butyric ,, 239 381 E55) 1.47
isobutyric ,, 239 381 | At 53) | 1.44

isopropylacetic acid) oo 378 -- 1.68

1) Dissertation of P. E. VerKave to appear shortly.
*) Recueil 23, 265 (1902). Dissertation Groningen 1903.

720

cleaned Jena vessels by carbon dioxide and the dissociation thereof
is practically repelled by the fatty acids.

The constant given above for7zsopropylacetic acid (= 1.68) has
been found equal for both the commercial and synthetic product.
As the former is contaminated with methylethylacetic acid and as
the constant thereof does not differ much from that of the pure
isovalerianic acid'), this was to be expeeted.

The measurements of the hydratation velocity were executed in
the same manner as those described previously.*) The anhydride

Propionicanhydride 0°. | Aceticanhydride 25°.0.
t x c | 0.4343 °7| t y c | 0.4343 425
Le |
0 0.0,598 0.00481 — | 0 | 0.03132 | 0.00674 =
3 664 594 | 0.00689 | 1 1555 937 0.0721
4 685 631 691 | 11/5 164 | 0.01048 700
5 105 668 695 | 2 172 1151 7113
6 725 701 686 | 21o 1795 1250 718
7 745 740 700 || 3 186 1341 718
8 764 7167 679 || 3!/, 192 1425 113
9 780 809 699 4 1965 1486 703
11 815 879 706 | 41), 2015 1560 106
13 844 940 699 | 5 206 1628 704
15 874 | 0.01002 698 || 51/2 2095 1680 703
17 902 1070 708 8 213 1734 | 705
20 938 1150 698 | oo 2505 2380 | —
23 973 1238 7104
mean: 0.4343 225 = 0.0709.

26 | 0.0;1008 | 1325 712

29 1037 1401 112 ||

32 1064 1473 | 711 |

36 | 1098 1563 | 710 |

% 1407 | | 2013 en

mean: 0.4343 k? = 0.00700.

1) Biturrzer, Sitz. Ber. Ak. Wien 1899, p. 416.
2) Rec. 31, 80 (1912),

721

was shaken with previously warmed (cooled) conductivity water
and then filtered rapidly into the resistance vessel.
As O0-point was taken the moment that the irregular initial reaction
was over and the bridge readings could take place accurately.
Subjoined are found some of these measurements. (See p. 720).
In this manner the following constants were obtained for different
acid anhydrides.

Hydratation-constants of the fatty anhydrides.

Values found by
0.4343 29) 0.4343 b25 RiveTr, WILSDON and

SIDGWICK.
acetic anhydride = | 0.0713 | 0.0701
propionic _, 0.00700 0.0372 | 0.0372
n. butyric, 0.00471 | 0.0243 | 0.0204
isobutyric ,, 0.00454 0.0227
aceticpropionicanhydride = 0.0522

This table contains a résumé of the constants obtained at an
anhydride concentration of 0.01 —0.02 normal. We chose this small
concentration, because it had been noticed by Sipewick and his
coadjutors') that the constant decreases when a much greater con-
centration is taken and also because the higher fatty acids were
soluble to the extent of about 0.03 normal only.

Only under these conditions could the constants obtained be com-
pared mutually.

a. From these data it follows in the first place that the influence
of the temperature is about the same for the fatty acids mutually :

he?
—foracetic acid =5.07)

0

propionic ,, = 5.3
n. butyric, == 5-2
isobutyrie ,, = 9.0;

and differs considerably from that found previously for the cyclic
anhy drides. *)

1) Soc. 97, 732 (1910), 101, 1708 (1912) and 108, 1959 (1913),

*) This has been deduced from the above measurements in connexion with those
of Riverr and Sipewick (I.c.) and Orton and Jones. Soc. 101, 1708 (1912).

3) Recueil 31, 80 (1912).

722

6. For itso and n butyric acid the proportion of the hydratation
constants = 1:1,04, and 1:1,07 respectively; that of the dissocia-
tion constants 1:1,01, and 1:1,02 respectively. The branching of
a saturated group, appears therefore to exert but little influence on
the velocity of hydratation. This is in accordance with the fact that
the hydratation constants of the two isomeric s dimethylsuceinie an-
hydrides are proportional to the dissociation constants of the correlated
acids. *)

c. If now we assume provisionally that, other influences being
equal, the hydratation constant is proportional to the dissociation
constant, the specific influence of the saturated group may then be
expressed in figures.

Therefore we have only got to divide the hydratation constants
by the dissociation constants; we then obtain, for the influence of
this group, for instance at 25°:

Proportion
For acetic acid 3.92 « 10-3
1.36
For propionic ,, 2.89 < 10-3
1:75
so2) ai DUILYITIC ats, 1e6o x 105

5 isobutyrie ,, 1558 SadOs?

From the corresponding values for butyric acid and isobutyrie
anhydride follows that the influence of the configuration of the group
in regard to other influences must be trifling (see 6).

The influence of the mass must be, however, very great as the
retardation that occurs by the introduction of two methyl groups in
the acetic anhydride (= 1.36) is less than that observed by intro-
ducing those same groups into the propionic anhydride (= 1.75).

This stronger retarding influence of the ethyl than that of the
methyl group also appears from what has been found in the case
of the mixed acetic propionic anhydride. The constant thereof lies
between the two constants of the acetic and propionic anhydride,
but slightly more towards the constant of propionic anhydride.

In the case of the isovaleric anhydride we have met with very
great difficulties; the solubility of this substance in water is exceed-
ingly small so that we could not get solutions containing more
than 0,005 mol. °/,.

Owing, however, to the very small velocity with which the
hydratation took place and the fairly great conductivity of the iso-
valerie acid the process could be traced very accurately,

1) Rec. 31, 80 (1912).

723

Here it appeared that there was no question of a constant; the
caleulated constant decreased, but so regularly and (after elimination
of all possible disturbing influences) so very concordantly, that we
were able to conclude that this decrease might be traced to a very
definite cause.

The subjoined table shows one of the many measurements.

Isovaleric anhydride at 25°.0.

d Z c 0.4343 425
0 | 0.0,670 | 0.00210 a
1 694 224 | 0.0247
3 721 244 | 209
5 151 264 209
| 782 280 201
9 804 204 195
mH 822 306 188
14 843 321 179
Tee) | 863 335 174
20 879 345 | 166
25 §99 360 | 156
30 o14 71 | 146
37 929 384 139
45 940 392 123
55 953 401 M1
0 0.031027 463 =

When the constants obtained in the different measurements were

plotted against the time, we could draw through the points thus
obtained smooth curves which either coincided or ran completely
parallel’), a sign that not only were we not dealing with experi-
mental errors, but that the fall must be attributed to a disturbing
reaction and, looking at the regularity, to a follow-reaction.
1) The latter, because the readings did not always commence exactly at the
same moment after the anhydride had been dissolved, as the filtration sometimes
took a little longer and because the temperature equilibrium in the resistance
vessel was not always attained in the same time.

724

In consequence of VorrMman’s observations (I. ¢.) we first believed
that the anhydride might be polymerised and that a succession of
depolymerisation and hydratation was measured. As, however, the
anhydride did not give the least indications of polymerisation even
in strongly associating liquids, C,H, and C,H,NO,, we gave up this
idea in favour of the following assumption.

We can imagine the process to be divided into two phases: the
first is the union with water or the hydratation proper; the second
is the splitting of the hydrate into two molecules of acid.

Now in the case of the lower acid anhydrides the first process
will take place very rapidly causing the second one to be measured
only; hence, the reaction exhibits the form of the simple unimole-
cular change.

If the velocity of the first in regard to the second is no longer
practically infinite, we are then dealing with the succession of two
unimolecular processes occurring in the same direction and the uni-
molecular-caleulated constant will exhibit a regular change *).

We give here three of these observation series obtained with very
carefully purified synthetic ¢sovaleric anhydride.

Falling constant of the hydratation of the c¢sovaleric anhydride.

Constant
S< 106
2000

1800

1600

1400

1200

1000
0-point 0-point 0-point time 2/; mm. = 1’.
ist Series 2nd Series 3rd Series

The further discussion of these observations in connection with the

1) Osrwaup. Lehrbuch Allg. Ch. Il, 2, 286.

129

relation applying to the unimolecular follow reactions will be
given elsewhere; we call, however, already now the attention to
the fact that BenratH') has found that in glacial acetic acid the
reaction between equivalent quantities of water and acetic anhydride
proceeds unimolecularly, which can only be explained by assuming
that in glacial acetic acid they are dissolved jointly as hydrate (in
fact that the hydration proceeds exceedingly rapidly) and that this
hydrate splits up into the acid molecules °*).

Further, we have also succeeded in demonstrating the formation
of other additional compounds with the acid anhydrides of which
those with zsovaleric anhydride exhibit a greater stability than those
with the lower acid anhydrides.

Thus we could isolate the additive products of hydroferricyanic
acid with zsovaleric and heptylic anhydride in a crystalline condition
and analyse the same whereas these two gave with 70°/, perchloric
acid colorations that pointed to additive action.

With great probability we may conclude already now that the
conversion of acid anhydrides into acids proceeds in two phases;
presumably there first takes place a linking of the anhydride to the
watermolecules which occurs very rapidly with the lower terms ;
this is then sueceeded by the splitting reaction which takes place
more slowly.

The analogy existing between the acid anhydrides, the esters, and
the ethers and between the acid formation, the saponification and
the alcohol formation causes the elucidation of the first reaction to
become of a more general significance.

If, on further working out the results obtained, it appears that
the process studied by us proves with certainty the linking of water
followed by hydrolysis, we may expect this to be also the case with
the other processes mentioned.

Like in so many other chemical transformations we again get here
the impression that the reaction proper is preceded by a previous
stage, namely the mutual influence of the molecules.

This is often shown by the formation of an additive product, but
here, as in the case of the catalytic phenomena, the reaction proper
will proceed more rapidly when this additive product forms more
quickly and possesses less stability.

1) Z. Ph. Ch. 67. 501 (1909).

°) BenratH measures the density of a mixture of acetic anhydride, glacial acetic
acid and water during the hydration; he finds a change in density of about one
unit in the second decimal.

726

SUMMARY.

1. We determined the progressive change of the acid formation
from some aliphatic saturated acid anhydrides in presence
of an excess of water at 0° and 25°.

2. In the ease of the lower acid anhydrides including the butyric
acids this proved to be a unimolecular reaction with a relative
small temperature coefficient.

3. As from previous investigations it had appeared that the
reaction constant is closely connected with the dissociation
constant of the acids forming, it could be deduced, by elimi-
nating this influence, that the hydratation constant decreases
as the mass of the saturated group increases, and that the
branching of the saturated carbon chain has little influence
on this constant.

4. From the fall of the “constant” for the acid formation from
zsovaleric anhydride it was deduced that the formation of acid
usually takes place in two phases: a. Absorption of water,
b. splitting of the hydrate; that with the lower acid anhydrides
the first reaction occurs very rapidly so that only the last
unimolecular reaction gets measured; that in the case of the
zsovaleric anhydride the first reaction no longer takes place
infinitely in regard to the second so that we must get the
image of a follow-reaction with unequal reaction constants.

Delft, December 1913.
Lab. Org. Chem. Techn. Univ., Delft.

Mathematics. — <“<Bilinear congruences and complexes of plane
algebraic curves.” By Prof. Jan pu Vrins.

1. We shall consider a doubly infinite system of plane curves
of order », consequently a congruence [y”|. We suppose that through

an arbitrary point only one curve passes, and that an arbitrary

straight line is eut in m points by only one curve. The congruence
is in that case of the first order, and of the jirst class; we shall
call it for the sake of brevity a bilinear congruence.

As a y of the congruence is determined by a straight line 7 of
its plane y, all planes g must pass through a fixed point /’, which
we shall call the pole.

A ray / passing through J (polar ray) bears @* planes g; the
curves y" lying in it form a surface S of order (n-+/), for any
point of 7/ lies on only one curve y”.

727

We consider now the surfaces 2”+!, belonging to the rays f and
?#’; they have in common the y” lying in the plane (//’), and intersect
further along a curve 6 of order (n?+-n-+1}, which passes through /”’).

Through a point S of 6 pass two curves y”, the planes of which
contain successively the straight lines / and /’. S is therefore a
singular point and lies consequently in oo’ curves y". The planes of
these y form the pencil with axis /S; the curves themselves lie
on a "tl, which has a node in S; for a straight line passing
through S meets "+? in (n—-1) points situated outside JS.

Let 7” be an arbitrary ray through F, s= /S a bisecant of the
curve o; y” in the plane (/"s) passes through S. The surface =
belonging to /” contains therefore the curve o and the latter is
base-curve of the net which is formed by the w* surfaces +. The
y” which is determined by an arbitrary point P, forms with o the
base of a pencil belonging to the net.
only; consequently it rests in n(n + 1) points on the singular curve
o*+"+!, while its plane cuts o still in the pole /’.

A y" can meet an arbitrary surface >”+', in singular points S

A bilinear congruence |y"| consists of the curves y", which cut a
twisted curve of the order (n? +n-+ 1) in (n+ 1) points, and send
their planes through a fixed point of that curve”).

The curve 6 may be represented by

a” bn en
x x xv =0,
Cty Ba Yr
hence the |="+'| by
mn u Y
ar bn en == ();
aL xz az
ty Bx Yxz
and the congruence {y”’| by the relations
ga" + obr + rr=—0, Ox + Of, + Tyr = 0.
Y x zc

2. The surface + formed by the y”, which rest in a singular

1) ¢ is of the rank n(2n?-++n-+ 1) and the genus 2” (n—1) (2n-+ 1); it sends
272 (n2+ 1) bisecants through one point.

2) For 2 = 2 this has been pointed out by Monresano (‘Su di un sistema lineare
di coniche nello spazio’’, Aft) di Torino, XXVI, p. 660—690). GopEaux arrived
at the congruence [y”] by inquiring into /inear congruences of y” of the genus
Vo (n — 1) (1 —2), which possess one singular curve, on which the ;” rest each
in a(n-+1) points. (“Sulle congruenze lineari di curve piane dotate di una sola
curva singolare”, Rend. di Pulermo, XXXIV, p. 288—300).

47

Proceedings Royal Acad. Amsterdam. Vol. XVI.

728

point SS on 6, is cut in (n-+-1) points by an arbitrary straight

line 7; consequently 6 is an (n + 1)-fold curve on the surface A of

the curves y", which are cut by 7. As two surfaces 4 apart from

o can only have in common a number of y”, which agrees with

the order of A, we have for the determination of that order ” the relation
v= ne + (n + 1)? (rn? + n+ 1);

from which ensues «= (n + 1)’.

The y® resting on a straight line 1 form a surface of order
(x + 1)? on which the y", of which the plane passes through 1, ts an

/
n-fold curve ; the singular curve ts (n + 1)-fold.

A is eut n(n-+1)* times by an arbitrary y” of the congruence ;
from this appears again that y” rests in 2(n-—+ 1) points on o,

Two arbitrary straight lines are cut by (n+ 1)? curves of the
congruence.

A plane # passing through / intersects -/ moreover along a curve,
which is apparently cut nm (n—1) times on 7 by the y”, of which
the plane passes through 7; in each of the remaining (+ 1)?—1—
n(n—1) = 8n points @ is touched by a y”.

The curves y", which touch a given plane have their points of
contact on a curve of order 3n, which possesses (n*+-n-+-1) double points.

The last mentioned observation ensues from the fact that the
surface ’+!, which has a node in a singular point S, is cut by
y along a curve with node S; is therefore touched in S by two y”.

The curve gy” found just now is the locus of the coincidences of
the involution formed from collinear sets of 2 points in which gy is

eut by [y*].

3. The surface 4 belonging to an arbitrary straight line, not
lying in g, has apart from the (nv? + 2+ 1) points S 38n(2+1)?—
2 (n+1) (n?-+-n+1) = (n-+1) (n?-+-n—2) = (n-+2) (n?—1) points in
common with gy,

There are (n+ 2)(n?—1) curves in [y"], which touch a given
plane, and at the same time cut a given straight line.

We can arrive at the last mentioned result in an other way yet.

The surface 2”+!, which contains the y", the planes of which
pass through a polar ray f, is cut by a straight line 7 in (nm + 1)
points; so the planes of (2 -+ i) curves y” pass through /, which
curves rest on /, Consequently the planes of the y” lying on 4 envelop
a cone of class (n +1).

A plane g cuts S"+! along a curve g’+!, which passes through

the point of intersection of /, and sends (n+-1)n—2 = (n-+-2)(n—1)

729

tangents through that point. From this follows that the planes of
the y", touching y, envelop a cone of class (n+-2)(n—1).

Each common tangent plane of the two cones, contains a y”, which
cuts / and touches y; for the number of those curves we find there-
fore again (n-+-2) (n?—1).

The two cones of class (n+-2)(n ey which are enveloped by the
planes of the y”, which touch two given planes have (n+2)? (n—1)
tangent planes in common. As many curves 7" consequently touch
two given planes.

4. A surface ="t', belonging to the polar ray /, contains a
number of y” with a node; such a y” is the intersection of S with
a tangent plane passing through //.

In order to determine the number of those planes, we consider
the points which S outside /, has in common with the polar surfaces
a” and B" of two points A and # lying on /. A plane » passing
through / cuts these surfaces along two curves a’—! and 6"—!, which
cut 7 in two groups of (m—1) points A, and By. If w is made to
revolve round /, these sets of (n—1) points describe two projective
involutions so that a borrernondence @—T 2—1) arises on f In
each coincidence C, f is cut by two curves a”—!, 6’—! lying in the
same plane gy; there «@” and ” have therefore the same tangent
plane which contains at the same time the tangent of the curve
gy of the order (n?—1), which a” and p” have in common, apart from /.

The 2(n—1) points C’ are at the same time the coincidences of
the involution of the nt degree, which is determined on 7 by the
curve y”, out of which & is built up; in each point C, & is there-
fore touched by the plane y and moreover by the curve yg. Conse-
quently @ has on f 4(n—1) points in common with ; the number
of intersecting points of g and + lying eee 7 amounts therefore
to (n’—1)(n-+-1) — 4(n=1) = (n—1)?(n-+8).!

Through each polar ray / pass eee the planes of
(n—1)?(n-++3) nodal curves y”).

The planes of the nodal curves y") envelop a cone of class
(n—1)?(n-++3); the ee of the +”, which rest on a straight line /,
envelop a cone of class (n+1). From this follows that the nodal
curves y"> form a surface & of order (n+8) (n+1) (n—1)?

On a straight line f lie m (n—1)? (n-+8) points of the nodal curves
y’e, of which the planes pass through 7; in the pole /' the surface
A is cut by f in (n-+3) (n—1)’*. points.

1) For » + 1= 3, we duly find the five pairs of lines which rest on a straight
line of a cubic surface.

47%

730

Let S be a point of the singular eurve 6; the ray FS is eutin S
by the (n-++8) (n--1)? curves ye”, of which the planes pass through FS.

In connection with what was mentioned above we may therefore
conclude that the singular curve o is (n+3)(n—1)?-fold on the
surface A.

5. If all y" pass through the pole /’, so that the latter is a
fundamental point of the congruence, then all surfaces "+! have
a node in J’. Two surfaces have four points in /’ in common in
that case; one of them belongs to the y", which forms part of the
intersection, consequently the szagular curve o has now a triple point
in /. In an arbitrary plane g passing through /’ the two = have
(n + 1)?—4 points in common, apart from /, (n—1) of those
points lie on the common y”, the remaining (72’-+-7—2) on 6.

In those points 6 is cut by the curve of the congruence lying in
g. The curves y” consequently pass through the triple point of the
singular curve, and rest moreover in (7#-+-2) (n—1) other points on it.

Any plane passing through a tangent % in # to 6 contains a ¥",
which touches ¢ in /’. In the plane passing through two of those
tangents lies therefore a yo”, which has a node in /. Each of the
three bitangent planes of o@ which are determined by the three
tangents in / contains therefore a ys" with node /.

The quadric> cones of contact in / of the surfaces of the net
[+"+!] form apparently a net which has as base edges the three
tangents of the singular curve 6. To that net belongs the figure
consisting of the plane ¢ ¢ with an arbitrary plane passing through
tn; so the net ["+1| contains three systems of surfaces, which
have a biplanar point in #’; the edge of the pair of planes into
which the cone of contact degenerates lies in one of the three
planes ¢ t.

6. We shall now consider a triply infinite system of plane algebraic
curves y", which form a bilinear complex {y”}"). In an arbitrary
plane lies therefore one y", and the curves y”, which pass through,
a point P, lie in the planes of a pencil (cone of the first class) ;
the axis p of that pencil we shall call for the sake of brevity, the
axis of P.

The curves of fy”}, of which the planes pass through an arbitrary
straight line + form apparently a surface of order (n-+-1), which we

1) The bilinear complexes of conics have been fully treated by D. Monresano
(“1 complessi bilineari di coniche nello spazio”, Atti R. Ace. Napoli, XV, ser.
2a, n°. 8).

731

shall indicate by 2."+!'. Through a point P of 7 passes only one
y", namely the curve lying in the plane (pr).

The surface ,”+! belonging to an axis p has a node in P; for
a line / passing through P cuts the y” of the plane (p/) in (n—1)
points lying outside P.

If ry is made to revolve in a plane ~ around a point O then
“St! describes a pencil. In order to determine the surface 2 which
passes through an arbitrary point P, we have only to find the ray
r, which cuts the axis p of P. The base of this pencil consists of
the curve y" lying in ¢ and a twisted curve g’t"t!, which cuts
y" in n(r+1) points.

Any point P of this curve lies on o' curves y”; its axes p must
meet all the rays of the pencil (OV, y), consequently pass through O.

To the net of rays of the straight lines 7, lying in g, corresponds
a net of surfaces Y,”+!. Through two arbitrary points 2, P’ passes
the surface belonging to the straight line 7, which cuts the axis p,p’.

7. Let us now consider the surfaces of this net belonging to
three straight lines, 7,7’,7" of g, which do not pass through one
point. The curve y*t"t!, which two of these surfaces have in com-
mon, cuts the third surface in (n+1) (n°+n-+1) points. To these
points belong n(n-+-1) points of the y” lying in ¢.

Let H be one of the remaining (n+4) (n?-+-n+1)— (a4+)n=
(n+1)(n?+-1) intersections. Through // pass the curves y” lying in
the three planes which connect H/ with 7,7’, 7",; these planes do not
belong to a pencil, consequently // bears «* curves y” and is therefore
a cardinal point (fundamental point) of the complex fy"}. Any straight
line through H is apparently an axis and determines by means of
its intersection with gy, a pencil (S"+!), consequently a curve ge” t"t!.

The complex Sy} has (n+1)(n?+1) cardinal points; they are at
the same time cardinal points of the complex of rays tp} and of the
complex of curves jo},

The cardinal points are apparently base points of the net {2 s+}}
belonging to the plane yv, or, more exactly expressed, of all the nets
which are indicated by the planes ~ in space.

8. Let us now consider the curves of }y"} which send their planes
through an arbitrary point /. Through a point P passes the y" of
the plane (/p); through a straight line r passes the plane (/) and
this plane contains one y”. So we have set apart out of the complex
a bilinear congruence {y"\ which has J” as pole. Its polar rays are
the axes p of the points P of the singular curve ot"t!; they

732

project this curve out of the pole # lying on it, consequently form
a cone of order n(n--l). From this follows that the aves of $y"} form
a complea of rays of order nn-+-1).

In any plane passing through a cardinal point H lies a y", which
passes through 7. The o* y" passing through H form therefore a
special congruence [y"], which has Has fundamental point; the
singular curve 6 of this congruence has therefore a triple point in
H (§ 5); it is the o*, which has H; as pole.

Each point H is triple point of a singular curve 6, which passes
through the remaining cardinal points.

This curve is base curve of a net of surfaces 2, which have all
a node in /7.

The planes of the nodal. curves y”> envelop a surface of class
(n—1)?(n-++3), for this is the number of tangent planes of >,"T!,
which pass through a straight line r (§ 4).

The curves y"> form apparently a congruence of which the order

and class are (n—1)’(n+8).

9. We now assume a tetrahedron of coordinates and consider
the net of surfaces Y belonging to the straight lines of the plane
«,=0. This net may then be represented by

b> dn,
eh
Gey 7 Wa Caen

The cardinal points are therefore found from

CR y qd” a |

—))5

| a» d”, |

a
v

:

» |
3 U4 |

| | any bn 2 Cp dn -
|| = ; é — Q. x
} vy a 3 Us

From this ensues readily that the curves of the complex may be

represented by the relations:
aa", +Bb",4+ yo"z+dd";=0 , ax, +Px,+yx,+dz,—0.

If we consider here «@, 8, 7 as given, but # as variable, then there
arises by elimination of d the above mentioned equation of the surface
> belonging to the straight line #,=0, ar,+3u,+ya, = 0.

For the curves passing through a point JY” is

= aar= e Bon + ever + dd®? = 0 and Say, = 0.
BOs oie + | , - i, 4 : yy

‘4

By elimination of a@,3,y,d out of these equations and 2 «a= 0,
Savr,=0, we find for the surface ="+' belonging to Y, the
equation

| no a
y, we &, a | 0.
The axis of Y is indicated by

| ¥% a" aps || = 9.

733

In order to determine the surface "+! belonging to the straight
line whicn joins the points VY and Z, one has to eliminate «, 8, y, d
out of Say, = 0, Yaz, =0, Yar,=—O0 and + aa» —0; then one
finds

| Wn ea we a | =9,
while the straight line }’Z is indicated by
|| GY, ante =O.

Through the point X pass the axes of the points ), for which

we have

Yi a a, Die a eae

| Ye
Op bn Hi ee and Gm ae 20)
Ys CF iy | YO x,
These surfaces of order (n+-1) have the curve
ey br ie
== (0)
| Ys or vs

in common, which is of order nr, but is not situated on the two
other surfaces of order (n-++1), which are indicated by
| yr. a a, || =0
The last mentioned relations determine therefore a curve of order
(n? + n-+ 1) as locus of the points Y. From this ensues again that
the axes form a complex of rays of order n (2 -+1).

Mathematics. — “A bilinear congruence of twisted quartics of the

Jirst species.” By Prof. Jan DE Vrigs.

1. As we know, we distinguish with congruences of algebraic
twisted curves two characteristic numbers, ealled order and class.

The order indicates how many curves pass through an arbitrary
point, the class the number of curves which have an arbitrarily
chosen straight line as a bisecant. If both numbers are one the
congruence is called bi/inear. In volume XVI of the Rend. del Cire.
mat. di Palermo (p. 210) E. Vensront has proved that there exist
principally two kinds of bilinear congruences of twisted cubies. An
analogous inquiry concerning congruences of twisted quartics of the

first species, o*, has not been made till now. *)

1) The bilinear congruences of conics lave been treated by Monresano (Atti di
Torino XXVII p. 660).

734

In a communication which appeared in Volume XIV of these
Proceedings, 1 have (p. 255) considered the bilinear congruence [¢'],
which arises if the quadries of two pencils are made to intersect. *)

It is not difficult to understand that no bilinear congruences
of curves of a higher order can be produced by two pencils of
surfaces. For, if these pencils are of the degrees m and n, they
intersect an arbitrary line in two involutions of the degrees yr and
n and these have in common & = (m—1) (n—1) pairs; so we find
a congruence [o”"| of the tirst order, and the class’ (m—1)(n—4) ;
only for m=n=2 we find k=1.

2. In order to arrive at another group of bilinear congruences,
I consider a net of cubic surfaces [®*]. Through an arbitrary point
P pass o* surfaces ®*, which form a pencil included in the net,
of which pencil the base curve in the general case will be a twisted
curve 9° of genus 10. All the curves gy" included in the net conse-
quently form a congruence of order one. On an arbitrary line the
net determines a ecubie involution of the second rank; the latter
possesses as we know a neutral pair N,, N,; all the @’ through
N, pass through MN, as well, consequently the congruence is also
of the first class, therefore bilinear.

9

If all the ®* have a eurve in common, the curves 0°

Ss

degenerate
into an invariable and a variable part, and a bilinear congruence of
curves of a lower order is found. We shall now consider the case
in which we have to do with a congruence [9*].

3. Let e® be a twisted curve of order five, and let the genus be
2, so the remaining section of a ®* and a @®’, which have a straight
line in common. Any surface ®* passing through 14 points of 9°
contains this curve*); consequently the #* passing through o* and
three arbitrarily chosen points H/,, H/,, 7,, form a net. Two of these
surfaces have besides 9°, a e* of the 41st species in common, which
intersects @° in eight points*). With a third #*, ¢* has 12 points in
common, of which 8 he on 0°, the other four, and to them belong
of course H,, H, and H, lie apparently on all ®*, therefore on

© 4
all Q. 2

1) If the bases of the two pencils have a straight line in common, one of the
two congruences [9°] found by Veneronr arises.

2) R. Sruam, Synthetische Untersuchungen tiber Fldchen dadritter Ordnung
(1867, p 234). P. H. Scuoure, La courbe d'intersection de deux surfaces
cubiques et ses dégénerations (Archives Teyler 1901, t. VIJ, p. 219). M. Sruyvarrt,
Cing études de géométrie analytique (Mem. Soc. Liége, 1907, t. VII, p. 40).

8) Scnoure, (l. c. p. 241), Stuyvarrt, (I. c. p. 41).

7395
Here we have consequently a bilinear congruence {o'| with four
cardinal points Hy, and a singular curve g*°; ie. all g* pass through
the four cardinal points and rest in 8 points on y*’).

4. let ¢ be a trisecant of 0°; the pencil of net surfaces determined
by a point of ¢ has for base the complex of 9°, 7 and a plane cubic
y’®, which bas a point 7 with ¢ in common, and 5 points with 9’.
This y*? must contain the four cardinal points H; consequently the
cardinal points are situated in a plane ¢.

Any curve y’ connects the 4 cardinal points and the 5 points R;,
in which 9° cuts the plane v, with the intersecting point 7’ of the
trisecapt belonging to it. As the trisecants form the quadratic ruled
surface ®?, on which 6° lies, the points A, together with 7’ may
be connected by a conic t’.

The curves y* form a pencil with base (/%, Hx); any y* intersects
rt in the point 7, through which the straight line ¢ passes, which,
considered together with y* belongs to the congruence | 0*|’).

The locus of the degenerate figures (y* +t) is apparently the com-
plex of ®* and gy, and consequently belongs to the net [@°].

5. Let & be one of the four bisecants of @°®, which pass through
the cardinal point AH. All the ®* which contain 4, have moreover

a e*® in common, which has % as bisecant and rests in 6 points on 9°.

s

Consequently there are sirteen figures (9° + 6) in [Q').

A third group of complex figures is formed by pairs of conics
(a, 87). Let a be a conic passing through H,, //,, intersecting 9° in
4 points, the ®* passing through «* and @* have an other conic p* in
common, which intersects @ in 2 points, e* in 4 points and passes
through //,, H,

The number of «a? we deduce using the law of permanency of the
number. We replace 9° by the complex of a o* and a o?, which
have three points in common; through a point P pass consequently
3 straight lines, which rest on o* and o?; with the biseeant of o°
they form the 4 straight lines which replace the 4 bisecants of 0° ;
consequently (6° + 0*) is to be considered as a degeneration of vy’.
In any plane passing through H/, and H, lies a conic gy? connecting
these points with 3 points of 6°; as the straight line H,H, cannot

1) If the base of the net consists of a curve ¢%, of genus 3, and a cardinal
poimt H, the second bilinear congruence [o%] is formed.

*) That the figure (y?+4-¢) is a special case of a o*, appears from the fact that
through an arbitrarily chosen point P, two straight lines may be drawn which
intersect ,* and ¢; they replace the bisecants which .* sends out through P.

736

apparently be a part of a degenerate y*, the gy? form a quadric.
This is cut by 6° in 4 points; among them are the 3 common points
of o*® and o°; through the fourth intersecting point passes a g?,
which has four points in common with the figure (o* + 0°).

From this we conelude that one conic a can be drawn through H,
and /7,. As each a’ is coupled with a p? (which passes in that case

through H, and #H,), [@*| contains three figures (a? + B?).

6. Through a point S of the singular curve y' pass oo! curves @'.
They cut the plane g in the points H. To this sysiem of o* belongs,
however, also the figure consisting of the trisecant ¢ passing through
S and a y* lying in g. From this ensues that the locus of the 94
meeting in S, is a cubie surface 2*, passing through 0° aud the
points 7, and consequently belongs to the net [*].

An arbitrary line passing through S, is a bisecant of one 0%,
and so intersects >, apart from S in one point. Consequently 2?
has a double point in S. Through S pass 6 straight lines of S°,
one of them is of course the ¢ mentioned before ; each of the remaining
5 is a bisecant p of w* curves 9*, so a singular bisecant.

All the @* intersecting p twice pass through S; so they determine
on pa parabolic involution, of which all pairs have the point Sin
common; we shall call p a singular bisecant of the first species.

Through each point of 9° pass therefore five singular bisecants of
the Jirst species.

Any line h passing through a cardinal point H is as well a
singular bisecant of the first species.

The monoids +* having two points of @° as double points, inter-
sect apart from o° in a o*. Through any two points S passes
therefore only one curve of the congruence.

7. Let g be a bisecant of a g*, and at the same time a secant
of o'. The surface ®* passing through 9° and o* and a point of q
contains g, and belongs to the net {*|. Consequently all * passing
through a point Q of gq will cut this straight line moreover in a
second point QQ’. Consequently g is a bisecant of oo* curves o*, and
the pairs of the intersections Q,Q’ form an involution. We call qa
singular bisecant of the second species.

In order to find the number of lines ¢ that pass through a point
P, we consider the cubie cone k*, which out of P projects the 0%
containing P, and the cone &* which has P as vertex and 9° as
curve of direction. To the 15 common generatrices belong the lines

drawn to the eight intersecting points of g* and g°. The remaining

737

7 are bisecants of g' intersecting g°, therefore lines g. Consequently
the lines g form a congruence of order seven.

We can also arrive at this result in another way. A straight line
passing through P is generally speaking, a bisecant of one 0'; we
call R, R’ its intersections with o* and consider the surface a, which
is the locus of the pairs R, Rk’. On any generatrix of the cone k*
one of those points lies in P, hence a has in P a triple point with
k* as tangent cone; 2 is consequently a surface of order 5. It passes
through o*, and has nodes in the four cardinal points. For an arbi-
trary g* has in common with a the intersections with the bisecants
which it sends through P, and in 8 points of @’, so twice in each
point /7,

Now 2° and #* have in common the e* which passes through ?;
further they can, by reason of the definition of a, only have lines
in common which contain o' pairs R&R, Rk’ each. Therefore e/even
singular bisecants pass through P. To these the four straight lines
hy, = PH), belong; for through any point of PH, passes ao, which
meets this straight line again in the cardinal point H;, so that P//; is
a singular straight line of the first species (which, however, does
not rest on g*, and consequently may not be interchanged with a
straight line p). The remaining 7 singular bisecants passing through
P are therefore straight lines ¢.

For a point S of 0° the surface 2° degenerates, and consists of
the monoid * with node S and a quadratic cone, formed by the
straight lines g, which intersect 9° in S.

In an arbitrary plane lie five points of e°, consequently 10 straight
lines g; they belong therefore to a congruence of rays of class ten.

The singular bisecants of the second species form a congruence
(7, 10), which has 9° as a singular curve.

The section of 2° with a plane passing through P is a curve
with a triple point, consequently of class 14, of its tangents 8 pass
through P. Therefore the tangents of the curves 9* form a complex
of order eight.

N

which we intend to determine the order x. Any monoid #* contains
three 9', which intersect /, and rest in the vertex S on 9°; conse-
quently 9° is a triple curve of A.

The surfaces A, A’ belonging to two lines /, /’ have, besides the
threefold curve 9° only the x curves 9* in common, resting on /
and /’. So we have the relation x? = 4% + 37.5, hence x — 9.

On 4° lies one trisecant ¢; for the curve y*, which intersects /,

8. The 9* which [intersect a given line /, form a surface A, of

738

determines on t® the point 7 of the triseeant with which it forms
a degenerate @* (§ 4).

The curve e*;, which has / as a bisecant belongs to two points
of /, and is consequently a twofold curve of 4’.

The locus of the 9@* intersected by / is therefore a surfuce of order
* and two straight

nine with a twofold curve e*1, a triple curve @

lines 7 and ¢.

9. A plane through / intersects A’ in a curve 4°; the latter has
the two intersections of e*; and six points R in common with 7; in
each point 2, 2 is touched by a ¢*.

The points in which a plane is touched by curves g* lie therefore
on a curve y"; it is the curve of coincidences of the quadruple
involution @*, in which the plane 2 is intersected by the congruences
[e*].

The five intersections S; of 9° with 4 are apparently singular
points of Q*; to S; are namely conjugated o° triplets of points,
lying on the cubic curve o*,, with double point S¢, in which the
monoid ®* (with vertex /S;) is intersected by 4. In S, 4 is therefore
touched by two et; the curve of coincidences y’ has consequently
nodes in each of the five points S;, and in S; the same tangents
aS On.

Any point D of the conic d* through S; is the intersection of a
trisecant ¢, consequently determines a quadruple, of which the
remaining three points are produced by the intersection of the curve
y® coupled with ¢ On the section J of @ we have therefore a cubic
involution /*, of which the groups are completed into quadruples
of (Q* by the points D. It is evident that Q*, as long as 4 remains
an arbitrary plane, cannot possess any other collinear triplets.

In each of the points of intersection 7,, 7, of f with 1? (§ 4) a
t is cut by a y*, consequently these points are coincidences of the
Q‘. The remaining coincidences, lying on /, belong to the involution
F*, from this appears again that the order of the curve of coinci-
dences is sv.

As the singular point S, lies on d° and therefore may be considered
as a point D, the curve 6,° is intersected by / in a triplet of the
cubic involution /,*, of which the groups are completed into quad-
ruples of Q' by S,. As J,° cannot possess a second collinear
triplet, it is not a central involution; so it can be determined in
o' ways by a pencil of conics of which the base points are S,,
an arbitrary point of o,°, and moreover two points of the line /.

739

10. Any coincidence of the @Q* is completed into a quadruple
by two complementary points. The locus J of those points which
we shall call the complementary curve has apparently quadruple
points in S;; for J,’ has four coincidences. Of the four coincidences
of F*, four of the complementary points lie on d°; with this conic
the curve Jd has therefore 4+ 5 > 4 = 24 points in common.
Consequently the complementary curve is of order 12.

The curves 09%, which touch the plane 2 in the points of the
curve of coincidences y'°, intersect 4 moreover on the complementary
eurve d’?; so they form a surface of order 24, which passes eight
times through the curve ¢’.

This surface is intersected by .a plane 4’ along a curve of order
24 with 5 octuple points S;. As the curve of coincidences y'* lying
in A’ has double points in ‘S; the two curves outside S; have
24 6—5 « 8 X 2=—64 points in common. Consequently there are
64 curves 0', touching two given planes.

The surface A® belonging to the straight line / intersects an
arbitrary plane g along a curve ’, which has 5 triple points on
vo’. As the curve of coincidences g* lying in ~ has 5 nodes on ¢',
it intersects ~® moreover in 9 >< 6—5 & 3 & 2 = 24 points. From
this appears once more that the curves o*, which touch a given
plane, form a surface of order 24. At the same time, the fact that
the complementary curve is of order 12, is confirmed.

Chemistry. — ‘“Hquilibria in ternary systems”. XII. By Prof.
SCHREINEMAKERS.

We have seen in the previous communication that the saturation-
curve under its own vapour-pressure of the temperature 777 (the
point of maximumtemperature of the binary system /”’-+ L + G)
is either a point [fig. 5 (XI)| or a curve [fig. 6 (XI)]. We shall now
examine this case more in detail.

dy é ; ;

If we calculate aE for this curve in the point H from (6) and (7)
(XI), then we find an infinitely great value. The curve going through
Al in fig. 6 (XT) and the curve disappearing in H of figure 5 (XI)
come in contact, therefore, in /7 with the side BC. Now we take
a temperature somewhat lower than 777. The saturationcurve under
its Own vapour-pressure terminates then in two points m and h
situated on different sides of and very close to H. {nm and / in fig.
4—6 (XI) may be imagined very close to H.| As the saturationcurve

740

under ifs own vapour-pressure touches BC in H, the tangent in
n and the tangent in / to the curve, going through these points,
will yet be almost parallel BC.

Because the equilibria /’-+ liquid n+ vapourn, and F' + liquid
h + vapour h, differ but very little from one another, the perspective
concentrations S and S, (see the previous communication) will be,
on addition of a third substance, also approximately equal. Therefore,
when in the one equilibrium S>S,, this is also the case in the
other. Of course the same applies to S< S,. Now we distinguish,
according as the substance expands or contracts on melting, two
principal cases.

1. F expands on melting (V > v). The point H is then situ-
ated with respect to /’ as in fig. 4—6 (XI) viz. between / and C,
but close to /’; AV is negative between F and H, positive in the
other points of LC. From the situation of m and / with respect to
F’, it follows that S and S, are both positive. We distinguish S> 8S,
and S< &,.

a. S>8S,. As AV is positive in h and negative in n, it follows
from our previous communication that the pressure decreases from
h along the saturationcurve under its Own vapour-pressure and it
increases from 7. In which direction shall this curve now proceed
from A? As the tangent in coincides almost with BC, the curve
must go from / either almost in the direction towards m or almost
in opposite direction. We find the first in fig. 5, the second in
fig. 6 (XI). In order to determine this direction, it is to be consi-
dered that the region L-—G shifts on decrease of pressure from h
towards m, so that the pressure decreases in this direction. As .
the pressure along the saturationcurve under its own vapour-pressure
must also deerease from h, this curve must therefore, also go from
i almost in the direction towards mn. It has, therefore, from h a
direction as in fig. 5 (XI). As the tangent in » coincides almost
with BC, the curve must go from v either almost in the direction
towards 4 or almost in opposite direction. Considering that the region
L—G shifts on inerease of pressure from » towards /, so that the
pressure increases from m towards / and further that the pressure
along the saturationcurve under its own vapour-pressure must also
inerease from mn, we see that this curve must go, therefore, also
from 7 almost in the direction towards /.

The saturationcurve under its own vapour-pressure has, therefore,
a form as curve hn in fig. 5 (XI); it is situated, therefore, close to
the side BC and it disappears at 77 in the point /Z.

b, S<S,. In a similar way as above we find that the pressure

741

along the saturationcurve under its own vapour-pressure increases
from h and decreases from 7. Further we find that this curve must
have in the vicinity of m and / a direction as in fig. 6 (XI). As
further the pressure in / is greater than in n, therefore on this
curve as well a point of maximum- as a point of minimumpressure
must be situated. Consequently, we obtain a curve /n, as in fig. 6 (XI),
this does not disappear at the temperature 77, but it forms a curve,
touching the side BC in H.

2. # melts with decrease of volume (V < v). Now the points
H and H, are no more situated, as in the previous case, between
F and C. From the binary equilibrium “+ 2+ G it follows that
H is situated between F and 4; the point H, may be imagined as
well between /’ and Cas between /’ and B. In the last case H,
should be situated between /’ and // and therefore very close to /7;
the region Z—G should then be very narrow in the vicinity of the
side BC, which is only possible in very exceptional cases. Therefore
we consider only the first case: // is situated between F’ and B,
and H, between F' and C.

If we take two points n and fh close to H and the corre-
sponding points n, and h, close to H, then we see that S and S,
have an opposite sign. If further we keep in mind that AV is
negative between /’ and H and positive in the other points of BC,
then it follows, in a similar way as above, that curve nh must have
a form as in fig. 5 (XI). Therefore, it disappears at 777 in the point //.
Consequently, we obtain a diagram as in fig. 5 (XI), but with this
difference, that H/ is situated now between /’ and JZ.

Contemplating the boilingpointeurves of /’, we obtain diagrams
as fig. 5 and 6 (XI), the arrows must then however, indicate in
Opposite direction. Further we must imagine the point of maximum
temperature H to be replaced by the point of maximum pressure
Q of the binary equilibrium /-+ 1+ G. AW is negative between
F and Q, positive in the other points of BC. From the position of
Q and Q, with respect to VF, it follows that S and S, are both
positive. We distingnish two cases.

a. S>S,. We find that the boilingpointeurve fn has a form as
in fig. 5 (XT); the arrows must, however, indicate in opposite direction.
Therefore, this curve disappears under the pressure Pg in the point Q.

b6. S<S,. The boilingpointeurve 4m has a form as in fig. 6 (XI) ;
the arrows must, however, indicate in opposite direction. Therefore
the curve does not disappear in (Q under the pressure Pq.

If we sum together the results obtained above, we have ;

742

1. /? melts with increase of volume. The saturationcurve under
its Own vapour-pressure disappears, when is raised the temperature
in H |fig. 4 (X1I] when the concentration of the new substance is
greater in the liqnid than in the vapour. It does not disappear in
H |fig. 6 (XI)| when the concentration of the new substance is
smaller in the liquid than in the vapour.

2. # melts with decrease of volume. The saturationcurve under
its OWn vapour-pressure disappears, when is raised the temperature
in H |Fig. 5 (XD, wherein however H must be situated between
F and B]

3. The boilingpointeurve disappears, on increase of P in Q
[fig. 5 (X1)j, when the concentration of the new substance is greater
in the liquid than in the vapour. It does not disappear in Q [fig. 6
(XI)| when the concentration of the new substance is smaller in the
liquid than in the vapour. We mean of course, with “concentration”
above “perspective concentration”.

Now we will deduce in another way the relations in the vicinity
of the point H or Q. The saturationcurve under its own vapour-
pressure is fixed by the equations (4) (II), when we put therein a=0
and when we keep ZV constant. As og: etc. become infinitely
great for «= 0, we shall put

eNO INC HER eo oof co oo (Il)
so that all differential quotients of U with respect to 2, remain finite.
We put in the same way :

ZU Rae, loge es
so that the same applies to U,. Then we have :
0Z OU # oZ 0U 0Z OU
Fie ak RT (1 + logz) ; i oe OP ae
and similar relations for 7, and U).
The equations 1 (I) then become :

(8)

0U oO :
uw + (y—B) SNS al Pt Of Se A Be om! «((45)
Oa ; Oy
aU, sus atom :
v= + (y,—8)— + RkTx,—U, +$=0 (5)
0x, Oy,
IU 0U
<= RPI A dog 2) ===) ag en)
0a : Ow,
CNG © ONG)
= — ear EP Tat)

dy dy,

743

In the points H and H, of figs. 4—6 (XI), the pressure is equal
tora Oand ty — 0) further wer put 7 —(@), and! = (@,),.
For a point in the vicinity of BC on this saturationcurve under its own
vapour-pressure, the pressure is P77+dP, a=§, 1, =§,, y=(y), +%
and y, = (y,)o + 1.-

In the points H and #7, themselves the binary equilibrium /’-+- 1 + G
exists; to this ae

Ct aa o+ 60 aa Pt SAB)

wherein the pressure is equal to Py, y=(y), ¥,=(y,), and U
and U/, are independent of w and v%,.
We now take the condition (6), from this it follows :

Pe ee oe 9
tae ae Ei S(\G os “eee, 5 (8)
Therefore, we obtain for very small values of w and 2,

= 1 ou OU
og in é bkty dee (Il)
LE SUT pir & =) ee

or

Be eKee ries ve antes waar’ Glen)

wherein is determined in (10).
We now take the condition (7); in this we put the pressure
P equal to Py+dP, C= Gee =§&.,y=(y), t+ and Y.=(y,)o+n,-
If we expand both terms of (7) into a series and consider tnat
in the ae H (8) is satisfied, then we find:

Peet. ear as. ea. WAS ant +5 Sat
av. av 2)
params ans mae aera eh
0?U 0?U 07U
Herein 7 = s= t= ; these values must be kept, as

Ou? dxdy oy?
they are in the point H. The second member of (12) is indicated by
| ],; this means that we deduce the second member from the first by
substituting §,, 7,, s,, ¢, etc. for §, 7, s, t etc. Now we expand (4)
into a series; if we keep in mind, that in the point # (8) is again
satisfied, and that 2 and 2, must be put equal to zero, then we
find a series, which we write in the following form:

OV ov
— (V—v)dP — 3{ - dP? H=(
REE + 4 ty? — (V—») & 3) +R + (y—B)L=0 (18)
In F& only terms occur, which are intinitely small with respect
48 .
Proceedings Royal Acad. Amsterdam. Vol. XVI.

744

to those, which are already written down, viz. §*, $y, ete. EdP
and dP are wanting. L represents the first term of (412). For the
sake of simplification (y,) has been replaced by y.

If we expand (5) into a series, we find :
oV, dv
oP Of

RTE, +43t,n,2—(V,—v) dP i( APR, (8) E50 (14)

Herein R, contains only terms, infinitely small with respect to
those preceding, , represents the second term of (12); (y,), has
been replaced by ¥,.

Now, in the point /7 the denominator of (8) (XI) is equal to zero,
therefore :

(y, -A—)V+t(y—y,)r+6—y V,=?.

We write this condition in the form:

eS Sy ee

Now we have the four relations (11), (12), (13) and (14) between
the five variables. If we multiply (18) with y,— and (14) with
(y—é) then follows:

jlRpe+ tay a = Nae les
y,— af ein 1 ae | fe a z] Mee
(Y, re) v i) g ') 2 AY OP ¢

ot ; OV, Ov :
= (y—8)| RT §, +340, 4 aP dP CPF) ss

These equations may be satistied when we take § and §, of the
order dP? and 4 and 4, of the order dP. From (12), (13) and (14)
then follows:

(16)

ty + OM as n, + oN dP (17)
ay nh on bes ce
i) («- ~) OP hades is Set ee (18)
Oy ;
nn (« = ) EPP Klin ds (19)
mn: a ee ¢

These last three equations are, as is seen immediately, dependent
on one another. Substituting 9 from (18) and 4, from (19) in (16
Sea hid: ‘

Pan) eed bt Ov P) (y p) =| ea GH! 5 5 (20)

Herein §,:$§ is fixed by (11); further is:

Se
S

745

ay OV, *_(y,-6) oV : 3) oV Ov, 21
mea) a ay) ap W) spt 0 Dap ©

1

From (18) now foliows:

2RT| (yn — Ay a2 le=— ie Oa lan OR)
S

From (22) it follows that the saturationeurve under its own
vapour-pressure under consideration is in the vicinity of the point
A |fig. 4—6 (XI)]} a parabola, which touches the side BC in H.
From (18) and (20) follows the change of § and 4 along this curve
at a small change of pressure dP.

We can find the meaning of a (22) in the following way.

We represent the length of Cp or Cq [fig 1 (XI)] by Y, the
length of the part, which is cut off by the liquid curve of the
region 1 —G from CB by y. Then we have:

a. Vi—v Ov, rey Vi—V OV dy, ps V,—V_ ov, .
yae=6. OF IP 0, “dP yy. On

Herein ¢, and V, refer to the point of intersection of the satura-
tioncurve with BC. Now we put:
Y¥—y=l
2

d cai
c ’ ‘falculate — anc
an we Calcu dP dP?

. For this it may be considered that

V, depends on P and Y, V on P and y and JV, on P and y,.
If now the saturationcurve of /’ and the liquid-curve of the region
L—G go both through the point 17, then (15) is satisfied; also at
the same time V, becomes = V and ¢, —¢. Then we find:

dl d’l

ape and GY —B)Gi 4) a a oath oe 8 (PD)

Substituting this value of a in (20), we find after deduction with
the aid of (48) (XI) and (11)

aT (ee Ne a ae 25
: ( —;)§= UA) aps a See (20)
and
S #8 (y — I
2ar.K(1 -;)§= Le eE ae. 1(08)
M1

dv\? dP?
Ae)

wherein ¢>>0; that there may be agreement with our figures, we

take y— y, > 0.
We now distinguish two cases,

4 g*

746
iS d?] ; ee ke,
le ie z and a have the same sign. From (26) it follows

9; QE
that § is positive, so that the parabola. touches BC in H and is
further situated within the triangle [fig. 6 (XI)]. This is apparent
also yet from (25), as § becomes positive as well for dP positive
as negative.

S al
2. 1—— and dP? have an opposite sign. From (26) it follows
—O; ¢

that § is negative. Therefore the parabola touches LC in H, but is
further situated outside the triangle. Therefore a similar parabola
may be imagined in fig. 5(X1). Then only its point #7 represents a
liquid, its other points have no meaning.

( d?l
From our deduction of ——- and —— in the point //, follows :
dP Ge”
é la ee
Y—y=}. NE
; Set

Now, in the point H of fig. 4—6 (XI) Y—~y, therefore also
dl? 4
ae becomes positive, as well on increase as on decrease of pressure.
dP?

When, however, the point // is situated on the other side of £,

2

< ; ad .
then )’—y and therefore also —— becomes negative.
; aR: ie

We now consider some cases.
se 4 y - al
1. F melts with inerease of volume (V > 2). ap:

> 0. Sand S,

positive.

a. S>S,. From (26) follows: the saturationcurve under its
own vapourpressure is a parabola, which touches BC in H, but is
situated further outside the triangle [fig. 5 (XTI)].

b. S<S,. From (26) follows: the saturationcurve under its
own vapourpressure is a parabola, which touches BC in H, but is
further situated within the triangle. | fig. 6 (X1)].
d*l
—_< 0.
aiB?

2. F melts with decrease of volume (V < v).

We take again S and S, with opposite sign.

As sub d.a. In fig. 5 (XD) the point 7 must be imagined on the
other side of /, therefore, between / and B and H, between
and (C.

From (18) it follows that 2 changes sign with dP, as in the

point H the coefticient of dP is negative, 4 and dP must have the
opposite sign. Therefore, the pressure increases in the direction in

747

which a decreases and reversally. We see that this is in agreement
with the direction of the arrows in fig. 5 and 6 (XI).

If it is desired to know the influence of a small change of 7
on the position of the saturationcurve under its own vapour pressure
going through H, we must also include terms with d7’ in the
previous expansions into a series. Now U=Z— RT x loy a therefore,

0U
= — H — fz log x, therefore in the point A (« = 0) itself

or
0U
— —— H.

oT

c we : OH

In the right member of (12), therefore, must be added — a dT
Ou
. <7 yy . » dH,
and terms with &d7’ and yd7’; in the left member — —? (/7.

Y
In (13) must be added (H—y,) d7; in (14) (H,—»,) aT, in order
to distinguish the codrdinate 4, the entropy of the solid substance
F is indicated by yp.
In the first member of (16) must be added: (y,—~) (H—y,) dT;
in the second member (y—®) (//,—y.).
From (13) follows :

dV
i) = (« = A) dP +...
dy /

dV,
t.y4,=(e— a) dP+...
Oy,

As we must substitute these values in (16), it is apparent that
we. may neglect the other terms. As

from (14)

AW
(G—y,)2 =, —y) 1 + Y—8) 2, = =p) 7

we obtain:

s:|. AW
2RT | na —f) | §—a.dP* + (y—8). “apa dT
)

or, after deduction:

S dl W
Dae Ka (Vi NG it (yy) ta 2
( 5) (y Ys) Fp T di ( 7)
and:
: S t(y—y,) dl AW
Whee lk — ae 7 SOME, AOS
( ae ACh; weg Ne")
te ses
Yy

From (28) it follows that not only the saturationcurve under its

748

own vapour-pressure, going through #H, but also those which are
situated in the vicinity of HZ are parabolas.

In the point /7 of figs. 5--6 (XI) AJ is negative, when / is
situated on the other side of 7, AW is positive. From (28) it now
follows:

when the curve, touching in // is situated outside the triangle
|fig. 5 (XI)|, it shifts on decrease of 7, within the triangle [curve
An in fig. 5 (XD]

when the curve, touching in // is situated within the triangle
[fig. 6 (XD], it shifts on increase of 7 within the triangle [the
closed curve in fig. 6 (XD] and on decrease of 7’ partly outside
the triangle. Therefore, curve /n of fig. 6 (XI) must be imagined
to be closed by a part /n situated outside the triangle; this part,
however, has no physical meaning.

In fig. 1 three curves are drawn through /’; F/ is the liquid-
curve of the region L—G at the temperature 7’p and under the
pressure Py, therefore at the minimummeltingpoint of /’; #K is
the boilingpointeurve and /’s the saturationcurve under its own
vapourpressure. The two first curves are but partly drawn. We
now construe in /’ a tangent to each of these curves. With the
aid of the formulas from the previous communication, we find:

for the tangent to the liquidecurve (/7/) of the region LG:

v

a= 1) RT + (y,—B)s

dx}, (y,—B)t io

for the tangent (/’Z,) to the boilingpointeurve (1K):

fs D

——1]RT —)s-— RT—
He (“ ) eT’ + (y,—B)s Be a) i D RT a
(FZ hae (y,—B6)t ~ \da), B (y,—B£)t )

and for the tangent (/’Z,) to the saturationcurve under its own

vapourpressure (L's):
E

x G

21 a ee Renn
dy ne, ( i ) tL + (y, B) s v Fi 2 dy C RT oe
(z\= aS: (y,—B)t _ a a An (y,—A)t ee)

Now we take again the most probable case that BC—AD is
positive (communication II). That there may be agreement with the
figs. 5 and 6 (XI) and fig. 1, we take V >v therefore A positive.
As further y,—( is negative, we can deduce:

dy dy dy
(3) 2 (3). Ze @) )

749

The curves 77, Fk and Fs must, therefore, be situated with
respect to one another as in fig. 1.
When V<v, therefore A is negative, then it follows:

dy dy dy E
os = ~ Mente 6 ee (Oo
(3) > (2) Z te) Co

The point H and therefore also the point s, must be imagined,
however in this case, also in fig. 1 on the other side of /. In
agreement with (38) #7 comes then between the two other curves.

Now we shall consider the solutionpath consisting of a straight line
of F/ under its own vapourpressure or in short the solutionpath of
We take viz. ithe system “+ 1+ G, but we take care that the
quantity of vapour is always very small. On change of 7’ the liquid
traces a straight line going through /’, which we have called the
solution- or cristallisationpath of #. In fig. l three similar solution-
paths FZ, FZ,, and FZ, are drawn.

Let us consider now the binary equilibrium “+ 1+ G. In fig. 2
its P,7-curve is represented by HFU, Q is the point of maximum-
pressure, H the point of maximumtemperature; /” is the minimum-
meltingpoint, A the point of maximumsublimation of the compound.
ak is the sublimation-, /d the meltingeurve. Curve L/'U touches
Fd in F and ak in XK. It is apparent from the direction of the
meltingcurve that we assume V > v in agreement with fig. 1.

Fig. 1.

When the solutionpath FZ in fig. 1 coincides with /U, its
P,T-curve in tig. 2 is, therefore, represented by UAKF'; when /Z
coincides in fig. 1 with /'Z, it is represented in fig. 2 by MHF.
When the solutionpath FZ in fig 1 turns from the position /'U/

750

towards FH, its corresponding P,7-curve must therefore change
from UKE into LHI. Now we shall examine this more in detail.

The saturationecurves under their own vapourpressure have, in the
vicinity of H either a form as in fig. 5 (XI) or as in fig. 6 (XJ);
we assume that they have a form as in fig. 5(XI). In fig. 1 the curve
surrounded by F's, and F's, itself represent saturationcurves under
their own vapourpressure; the arrows indicate the direction of
increasing pressure.

The boilingpoint curves have also a position as in fig. 5 (XI);
we must consider, however, that H is replaced by the point of
maximumpressure Q and that the arrows point in opposite direc-
tion. Two of these curves are drawn in fig. 1, one in the vicinity
of Q and curve Fk; the latter is indicated for a part only.

Now we imagine in fig. 1 a solutionpath between FH and FZ,.
Imagining in this figure still many other saturation-curves under
their own vapourpressure to be drawn, then we see that some of
these are not intersected by this path, other ones twice, and others
again once. Further we see that one of these curves touches this
path; we call that point of contact /7’.

From this it follows: at first the temperature increases along this
solutionpath from /’ up to H’ and after that it decreases. Further
it follows: Vy is lower than 77:

Imagining yet many other boilingpoint-curves to be drawn in
fig. 1, then we see that one of these touches the solutionpath in
a point that we shall call Q’. Now we deduce: the pressure in-
ereases along this solutionpath from # up to Q’ and after that it
decreases. Further it follows: P@ is smaller than Pa.

Now it follows from this all that the P,7-curve belonging to this
solutionpath has a form in fig. 2 as curve b/ with a point of
maximumpressure in @Q’ and a point of maximumtemperature in //’.

As long as the solutionpath in fig. 1 is situated between /’/ and
FZ,, the P,T-curves retain a form as bF in fig. 2; according as
the path, however, approaches closer to /’Z,, the points Q’ and H’
come closer to /. When the path coincides with /Z,, H’ coincides
with / and the P,7-curve has a form as Z,F in fig. 2 with a
point of maximumpressure Q’’. The tangent in / stands vertically.

To see this, it must be considered that the line /’Z, touches in
F the saturationeurve under its own vapourpressure going through
(Fs in fig. 1). Going from F, along an infinitely small distance, along
curve Fs and therefore also along the tangent /’Z,, the pressure
increases while the temperature remains constant. As dP, therefore,
is positive, and ¢7’ is zero, the P,7-curve therefore, in fig. 2, along

751

a small distance, must point vertically upwards, so that it has there
a vertical tangent. Considering the saturationcurves under their own
vapourpressure, we see that /’Z, intersects only curves of tempe-
ratures lower than 77, so that the temperature decreases along
FZ, from F.

Considering the boilingpointenrves, we see that the same still
applies to these as to a solutionpath, situated between /’/ and F'Z,.
The pressure, therefore, increases at first from /’ and after that it
decreases. From all this it follows that the P, 7-curve has, therefore,
a form as curve OF in fig. 2.

Let us now take a solutionpath between /’Z, and FZ,. It is easy
to see ‘that the P,7-curve retains a form as FZ, in fig. 2, with
this difference, however, that the tangent in /” stands no longer
vertically. The curve proceeds viz. from /' immediately towards
higher pressures and lower temperatures. According as the solution-
path in fig. 1 comes closer to /Z,, in fig. 2 the point of maxi-
mumpressure (" approaches closer to /. When the solutionpath
coincides with FZ,, (" coincides with F, and in figure 2. the
P,T-curve obtains a form as Z,/ with a horizontal tangent in F’.

In order to see this, we consider the solutionpath #7, which
touches the boilingpointeurve FX in F’. (tig. 1). Going from F’along
an infinitely small distance along curve /X and, therefore, also
along the tangent #7, the temperature decreases, while the pres-
sure remains constant. As d7’,, therefore, is negative and dP is zero,
the P, 7-curve must, therefore, from /’ over a small distance point
horizontally towards the left; consequently it has a horizontal tangent
mm, 2,

We now take a solutionpath 7, situated between FU and
F Z,. \t follows from a consideration of the saturationcurves under
their own vapourpressure and the boilingpointcurves in the vicinity
of F, that pressure and temperature decrease from F. The P, 7-
curve is represented in fig. 2 by #' Z, it proceeds from F' towards
lower temperatures and pressures.

At the deduction of fig. 2 it is assumed that the saturationcurves
under their own vapourpressure and the boilingpointeurves have a
form as in fig. 1. Curve Fs and Fk are drawn herein in the
vicinity of /’, concave towards //. When in /’ they turn their convex
side towards H, then curve Fs will intersect its tangent /’Z, still
in another point and curve FA its tangent /'Z,. Although then in
fig. 2 the tangent in / to Z, # remains horizontal and the tangent
to Z,F vertical, all curves will obtain a somewhat different
form in the vicinity of / (we may also compare the previously

752

treated P, 7 diagrams for the case that # is a ternary compound).
After the previous considerations, the reader can easily deduce
the P, T diagram for the solutionpaths of /, when the curves are
situated as in fig. 6 (XI).
Formerly [5 (1V)] we have deduced for a solutionpath
dP DM—BN
dT CM—AN
now, as a=O, herein is:
M = a’? r+2 x (y—B)s+(y—B)’ t
N= «x (e,—2)r + [«(y.—y) + (.—2) ¥—B)] 8 + G1 —y) Y—B) t
In the point / becomes 2 =O and y= 8, therefore M =O and
N =O. Let us now contemplate a solution path and let us call the
angle, which it forms with the X-axis, y. If we imagine for the

(34)

sake of simplicity that the coordinatesystem is rectangular, then it
follows: coly. p= «: (y—Bs). We then obtain:

M wrcotgg + 2x8 + (y—p)t
N («, -«) rv cotg p + [(y, — y) cotg p + #,—a]s + (y,—y)t
In the point /” becomes «= 0 and y=@ therefore:
M RT
eesti : er 5)

N a, me
(= —_ 1) KT +- (y,—) (s + ttg¢@)

wv

The question now arises, what P, 7’curve touches the meltingline
Fd in F. For this must, according to (34):
DM—BN B
CM—AN A

therefore, J: N = 0. It is apparent from (85) that this is only the
case when ty is infinitely great, consequently for g = 90° and
¢ = 270°. Then the solutionpath coincides either with FZ or with
FU (fig. 1). Therefore, both the binary solutionpaths EF and UF
only touch in #' the meltingline #d; the ternary paths do not touch
this meltingline.

In order that the tangent to the P, 7’curve of a solutionpath may
be vertical in / we have, according to (34) CY—AN=0. As M:N
is fixed by (85), it follows that this is the case, when

av I ae
—~—1)RT + (y,—8) s—RT

av

td ff — ==

(y,—B)t
From (381) it follows that in F this solutionpath must touch the
saturationcurve under its own vapourpressure going through the

7353

point F [eurve Fs fig. 1], the required solutionpath is, therefore, /’Z,.

If we require a solutionpath, whose P,T curve has a horizontal
tangent in F’, we must, as follows from 34) put DIJ—BN = 0.
From this now follows:

bi ore).
iC ite 1) RT + (y, —8)s— RI
x B
(v, -e p)t

From this it follows, in connection with (30) that in /' the
solutionpath must touch the boilingpointcurve going through the point
F {eurve £% in fig. 1]; the wanted solutionpath is, therefore, /Z,.

Now it follows from the previous considerations: in the P, 7’ dia-
gram (fig. 2), none of the ternary solutionpaths touches the meltingline
Fd in #; the solutionpath, touching in /’ in the concentration-
diagram (fig. 1) the saturationcurve under its own vapour-pressure
going through /, has in the P,7’diagram a vertical tangent in /’;
the solutionpath, in the concentrationdiagram touching the boiling-
pointcurve going through /’, has a horizontal tangent in /’ in the
P,T diagram.

It is evident that the above-mentioned rules apply quite generally
no matter whether the relations of fig. 5 (XI) or 6 (XI) occur or
the curves in F# are concave or convex towards /.

In fig. 1 Fl represents the liquideurve of a region LG’, now we
imagine a solutionpath, touching curve /7/ in /. The direction of

gp = — (37)

?

. : , s a
this solutionpath is, therefore, fixed by (29). In order to find ar
¢

in the point F of this path, we must, therefore, substitute the second
term of (29) in (35) for tgy. We then find an infinitely great value
for (85). From (34) now follows :

He HT 3 on
Cn Caan Ch Ae
Mt Gata ee ies

wv

The latter part of (88) indicates the direction of the P,7-curve
of the evaporationline of the liquid /’. This line is traced, when
we melt the substance / and when we regulate after that the
temperature and the pressure in such a way that the liquid remains
in equilibrium with an infinitely small quantity of vapour. Therefore
the liquid retains the composition /# during this. This curve is
represented in fig. 3 (III) by Fe, the pressure and the temperature
increase from /’ along this curve.

Consequently we find: the solutionpath, touching in / in the

754

concentration-diagram the liquid curve of the region Z-G (curve 7
in fig. 1) going through /’, has in the P,7-diagram the same tangent
in /’ as the evaporationline of the liquid / starting from F’.

If we compare the P,7-diagram of the solutionpaths of a binary
compound / (fig. 2) with those of a ternary compound F'| fig. 4 (IV)
and 1-3 (V)], then we see very great differences in the vicinity
of the point /. We find these differences also in the concentration-
diagrams. When viz. in fig. 1. in the point / we construct tangents
io the curves F7, Fk and Fs going through the point /, three
different tangents arise. If /# is a ternary compound, as e.g. in
fig. 1 (IV), then these curves touch one another in #’ and the three
tangents coincide in the line X/’Y.

All this is based on the following. When / isa binary compound,
a new substance must be added, in order to trace a ternary solution-
path from /. When, however, / is a ternary compound, we add no
new substance in order to trace a solutionpath, from /’, but substances,
which are already present in the melted F.

(To be continued).

Physics. “An apparatus for the determination of gas isotherms up
to about 3000 atms.” Van per Waats-fund researches N°. 5.
By Prof. Pa. Konnstamm and K. W.Watzsrra. (Communicated
by Prof. van DER Waals).

(Communicated in the meeting of December 27, 1918).

As is known the material for testing the theory of the equation
of state at very high pressures consists almost exclusively of what
Amacat has published in his famous papers. It seems desirable for
different reasons to extend this material. Quite apart from the desirability
to get to know the behaviour of other gases than those examined
by Amacar — we think in the first place of the mon-atomic gases —
Amacat’s work itself gives rise to different questions, which can
only be decided by means of new experiments.

First of all it is known that Amacat does not give the direct
results of his observations; he only publishes the results of a graphical
interpolation between these observations. The question rises how
great the deviations are between the interpolated and the real
observations, and whether another way of interpolation had been
possible. Nor can the probable experimental error of Amagat’s
observations be inferred from his experiments. And it has finally

755

appeared that there are discrepancies between some of AMAGAT’s
results inter se, as well as between AmaGar’s observations on hydrogen
at high pressures on one side, and ScHALKWIK’s very accurate
observations for low pressures on the other side '

For all these reasons it seemed desirable to construct an apparatus
with which gas-isotherms might be measured up to the highest
attainable pressures. And as it is self-evident that the cost of such
a set of apparatus could not be defrayed from the ordinary means
of a laboratory, the board of the van per Waats-fund resolved
already in 1904 to grant money for this purpose. It is owing
to the strong support given by the van per Waats-fund all these
years that we are now able to communicate the first results. Our
cordial thanks are due to the board of the van pur Waatrs-fund,
and further to all who helped to support the fund.

In the following pages we shall of course not give an account of
all the difficulties that confronted us, and the way in which they

WL were finally surmounted. We shall confine
ourselves to a description of the arrangement
in its present form, and only mention in a
few words now and then what considerations
have led to this final form. We shall sue-
ae essively discuss the measurement of the

itm T pressure, the volume, and the temperature.

A. Measurement of the Pressure.

The measurement of the pressure in abso-
lute measure takes place by means of ScHArrs
and BuDENBERG’s pressure balance. In eee
this apparatus consists of a steel piece A
(fig. 1) with cylindric boring, which at
about half the height passes into a wider
cylindric boring. <A differential piston B
fits in this bormg, which piston is ground
into the two cylindres with the utmost eare.
By means of a side tube the cavity C can
be connected with the space where the
D pressure is to be measured. This side tube
and the space under the piston are filled

Fig. 1. with machine oil. By means of a mould,

1) Brinkman, Thesis for the Doctorate, Amsterdam p. 34.
Scuarkwisk. Thesis for the Doctorate, Leiden 1908, p. 120 et. seq.
Keesom. Thesis for the Doctorate, 1904, p. 57.

which has been prepared and measured with the utmost care, the
two apertures in the steel piece A and the two sections of the
cylindre 6 are ground in such a way that the difference between
the larger and the smaller section bas a definite size, e.g. 1 em’.
If we now suppose a pressure e.g. of 800 kg. per cm’ to prevail
in the space C, and no friction to be present, the piston 6 would
be foreed upwards with a force of 800 kg. If on the plate D,
which is connected with 4 by means of the socket joint / we
put so many weights that they together with 6, D, / and the
joining-rod J” weigh exactly 800 kg., the whole apparatus is exactly

in equilibrium. If the total weight amounts to 801 kg. — we
still suppose absence of friction — the piston descends till the

liquid in C and the space in connection with it is compressed so
much that there prevails a pressure of 801 kg. per em? in C.
If the total weight amounts to 799 kg., the piston rises till the
pressure in C' has fallen to 799 kg. per cm?. On account ofthe
song friction of the piston very tightly fitting in the cylindre
nothing, however, is to be observed of these movements. [In fact
the plate 0 can easily be loaded with 10 or 20 kg. too much or
too little without any movement being perceived on a manometer
connected with C. If, however, the piston 5 with the plate D and
all the weights lying on it are made to rotate round their axis, it
appears that this rotation has practically annihilated all the friction.
[t will appear from the description of our experiments that the
remaining friction will lie far below 10 gr. at low pressures, and
that it can certainly not be so much as 50 gr. for pressures of
2500 ke.

We cannot account for this most remarkable property, though it
is of course clear that the fact that C’ is filled with machine oil,
and that this oil penetrates between piston and cylindre wall plays
an important part in this. It is known that also in AMAGAT’s mano-
ineter the great decrease of friction when the piston moves with
respect to the eylindre wall is utilized. But in AMaGat’s mano-
meter ') the piston must be moved to the left and the right by hand,
also during the measurement. The mode of construction of SCHAFFER
and BuprENBERG’s pressure balance evades this by making the whole
mass of the weights, for the large model up to 1250 kg., for the
small one up to 250 kg. rotate with the piston 6. After these

1) This manometer is generally called after Desaorre; according to Amagat,
however, the first idea came from Gauty—Cazatar. And we owe to Amacart the
great improvement, which rendered the instrument for the first time adapted for
really accurate measurements, nl. the free movability of the pistons.

757

weights have once been set rotating by the hand or in another
way, the apparatus may be left to itself. The kinetic energy of the
rotation is so great that the apparatus continues rotating for a
considerable time, at any rate long enough to perform a pressure
measurement. Only on account of this circumstance it is possible
fully to avail oneself of the absence of friction in consequence of
the rotation, for it appears that any, also the lightest, touch of the
apparatus brings about inerease or decrease of the pressure in C)
as it is not possible in doing so not to exert a force on the piston
B in vertical direction. If the space C' is connected with a sensible
manoscope (and the volumemeter itself served as such in our expe-
riments) every touching of the piston, also the slightest, betrays
itself immediately by a deviation of the manoscope. Measurements
may, therefore, only be made when the apparatus is in rotation, and
entirely left to itself.

A second circumstance, on account of which in our opinion
ScHirrer and BupEnpEra’s pressure balance may claim to be considered
as an improvement compared with AMaGat’s manomeier, is this that
the differential piston as well as the cylindre consist of one piece,
and ean therefore be completely finished as a whole on the lathe.
As is known AmaGat’s manometer makes use of two pistons of
different section, which are connected with each other. In the vessel
where the great pressure which is to be measured, prevails, there is
a small piston, accurately ground in, and the force with which it
is expelled is transmitted to a large piston, which can move in a
second vessel; the pressure in this latter vessel is measured by
means of mercury. In this construction it is, however, not to be
avoided that the axes of the two pistons are not entirely each other's
prolongation, which must give rise to wrenchings and frictions. To
prevent these the pistons must, of course, not be so tightly ground
in as would otherwise be possible. It is known that Amacat there-
fore uses molasses as transmission liquid in his manometer, beeause
else the transmission liquid would flow away too quickly, whereas
in ScHArFER and BupEnpere’s pressure balance thin machine oil suffices.

On the other hand ScHiresr and Buprnpere’s pressure balance
shares a drawback with AmaGaT’s manometer, which as far as |
know, Waenrr') was the first to point out in his investigation of
an AMAGAT manometer. AMAGAT himself took as effective area of
the piston, i.e. as area on which the pressure acts to the outside,
simply the section of the piston itself. Wacnur, however, points out
that the liquid which is pressed through between piston and cylindre

1) Thesis for the Doctorate. Miinchen 1904. Ann, d. Phys. (4) 15, p. 906,

758

wall exerts a friction foree on the cylindrical surface of the piston,
and that in consequence of this the force which drives the piston
out must really be greater than the amount which can be caiculated
from the section of the piston and the pressure. Or in other words
the effective area of the piston must be greater than the real section.
By means of hydro-dynamic considerations WaGNER now comes to
the conclusion that the difference will depend on the width of the
eylindre in which the piston moves. Half the difference between
piston and cylindre section will namely have to be added to the
piston section to determine the true effective area. Hence WaGner
did not only very accurately determine the piston section, as AMAGAT
did, but also the cylindre diameters (at least for the two small steel
pistons which he used). The difference between the two diameters
amounted to about 0,01 mm.; it is therefore by no means insigni-
ficant for a total amount of about 5 mm.

Waanur has, however, also determined the effective area by a
direct experimental way, by namely ascertaining with what weights
the pistons must be loaded to balance a pressure which is direetly
measured by means of a mercury column. And he then arrives at
a very remarkable result. For whereas the measurement yielded
5,128 resp. 4,076 mm. for the piston diameters, 5,188 resp. 4,088
for the cylindre diameters, which according to the above would give
5,133 resp. 4,082 for the effective area, the direct experimental
equation yielded 5,127 resp. 4,076, i.e. exactly the sections of the
pistons without any correction. Evidently Wagner has not pointed
this out, because in his first investigation the direct experimental
determination of the effective area of the large piston of the AMaGar-
manometer yielded 40,189, whereas the section of the piston itself
amounted only to 40.176.’). In a later investigation, however, which
was undertaken in collaboration with P. P. Koc’), Waanrr repeated
these determinations. He now finds in measurements which he con-
siders more accurate than the earlier ones again 5,128 for the
effective area of the small piston, but 40.164 for that of the large
one, i.e. even a little less than the real section. Accordingly these
determinations cannot give support to the theory of the increase of
the effective area in consequence of the friction on the cylindrical
surface derived hydrodynamically. *)

1) Le. p. 919.

2) Ann. d. Phys. (4) 31, p. 48.

®) Some particulars in Brieman’s interesting experiments (Proc. Amer. Acad.
XLIV p. 201) seem to point in the same direction, but whether this supposition is
true cannot be inferred from the communication with certainty. We shall, therefore, |
not enter any further into this.

759

This question which is of fundamental importance for all absolute
pressure measurement, cannot be considered as decided as yet. Nor
can our experiments at this moment give a decision, because we
have not yet been able to compare one of our pressure balances
directly with an open manometer with transmission for sufficiently
high pressures (60 to 100 atm.). The indirect comparison obtained
by the very close agreement of our hydrcegen-isotherm with that of
SCHALKWIUJK, seems to point in the same direction as WaGner’s
experiments, that namely actually effective and real area coincide.
Nevertheless a direct comparison remains, of course, a matter of
the highest importance for all our measurements and we greatly
hope, therefore, to be able to carry out a comparison before long.

In what precedes we have discussed the principle of ScHArrEr
and Bupunpere’s pressure balances. We should now discuss for a
moment the execution of it in practice. For the lower pressures —
up to 250 atm. — this is very simple indeed. The cylindre A (fig. 2)
rests ‘on a heavy cast tripod, which again is supported on a stand,

49
Proceedings Royal Acad. Amsterdam. Vol. XVI.

8 mites LTT

761

which can be put in the required position by means of adjusting
serews. On the plate D an iron weight is placed, weighing with B, 2,
F, and D together exactly 25 kg. Then plate-shaped weights of 25,
10 ete. to 1 kg. and lower are put on it with a slit, which enables
them to slide round the rod /.. The whole apparatus is set rotating
by hand.

For higher pressures the gauge cannot be worked solely by the
hand. The “head” of the pressure balance (the piece A with the
piston #, fig. 1) is mounted here on an iron stand 2 mm. high,
which by accurate levelling has been adjusted, and rests on a
separate heavy stone foundation. Weights of 100 ke. tie round the
rod /’ (fig. 3) in rings, on which they rest. These rings are connected
by means of two bars G and the distances between the rings are
taken so that between two weights there always remains a space
of 2 cm.

The rods G are provided at their upper ends with screw thread,
and are in this way carried by the nuts #/ (fig. 3a)?), which rest
on the top plate of the iron stand, and are fixed by bent pieces L.
The nuts Hf are provided on the outside with teeth, in which a
worm /t catches. By means of this the nuts AZ can be turned, and
in this way the rods G and all the rings attached to them can be
adjusted higher or lower. When the rods are turned down, first the
lowest weight will get to lie on the plate YD; this weight has been
taken so that together with the plate D, the rods / and £Z, and
the piston it weighs exactly 100 kg. If the rods G are turned still
lower down, another weight of exactly 100 ke. will rest on this
weight etc. In this way the piston can in all be loaded with 1150 ke.
If the worm is turned in the opposite direction, the ring-system rises,
and lifts up the weights one after another, which relieves D. By
means of a transmission with two loose pulleys and a fast pulley
the worm is driven from a shaft, which in its turn is set going by
an electromotor of 1 H.P. Two belts run over the loose pulleys, a
crossed one and a straight one. By a simple adjusting apparatus
either the one or the other can be transferred to the interjacent fast
pulley, by which weights are put on or taken off. Smaller weights are put
on by the hand on the plate D’, which is fastened on the rod L’

In the second place it is necessary to get a mechanical arrange-
ment to set the pressure balance rotating. For this purpose a toothed
wheel M*) (Fig. 34) has been fixed on the rod /’, which engages

1) Fig. 8a gives a view from below, omitting the plate on which everything
rests. In Fig. 3 the nuts H are hidden behind the worm K and the rod on which
it is fastened.

*) In Fig. 3 M is hidden behind JN.
49*

762

a second toothed wheel N. M is about 32 mm. high, N only
23 mm. This is necessary because the toothed wheel JN is rigidly
adjusted at a fixed height, whereas JJ moves up and down with
the rod /, and therefore with the piston 6 in the eylindre A, for
so far as the cylindre A leaves room for it, ie. about 2'/, em. The
toothed wheels J/ and N must be able to engage each other at
every position made possible by the space left.

By the plate O turning round 7, N can now be put in two
positions: so that its teeth catch in J/, and so that the two toothed
wheels are clear of each other. When once the weights have been
well set rotating, NV is placed in the latter position, and fixed, so
that the toothed wheels no longer catch into each other, and the piston Bb
therefore with the weights attached to it rotates perfectly freely,

and no other forces act on it than gravity and the pressure of the
liquid. .V is driven by the worm &. The latter receives its motion
by means of a transmission with fast and loose pulleys from the
shaft, which is set going by the electromotor. To prevent the toothed
wheels from breaking, or connections from being strained when the
belt should be transferred from the fast to the loose pulley, the
toothed wheels catching into each other and the weights being in
strong rotation, V is provided with a free-wheel S, as is also in use
for bicycles. It is therefore possible by setting the worm in motion,
to make .V and with it J/ and the weights rotate, but a rotation
of W only sets N, and not the worm going.

It is self-evident that the pressure indicated by the pressure balance,

763

is the pressure at C (fig. 1). The pressure at the place where one
wants to know it, in casu at the place where the isotherm measure-
ments take place, must be derived from that in C’ by means of a
correction for the hydrostatic pressure difference in C and the first-
mentioned place.

The measurement of the pressures above 1250 kg. takes place in
exactly the same way, only then the “head” A is exchanged for another
cylindre and piston whose effective area is only ‘/, em.’ instead of 1 em?.
With this “head” therefore pressures of 5000 Kg. per em? might be
attained. The firm Scuirrer and Brprenserc, however, informed us
in 1906 when they prepared the apparatus, that already at about
4000 atm. a permanent change of form of the ecylindre A was to
be feared in consequence of a transgression of the limit of elasticity
of the steel, so that this pressure could not be exceeded for the
pressure balance. Since then Bripcman has succeeded in far exceeding
this- limit of pressure by means of apparatus of newer kinds of steel.
The question, however, remains whether his apparatus could be
modified for the determination of gas isotherms. Apart from the
much greater complexity and dimension of the apparatus also the
question of a transmission liquid which could be used in the absolute
pressure gauge, is to be considered. The machine oils, which we
always used as transmission liquid in the following investigations,
because they besi remove the friction between the cylindre and piston,
begin to be so viscous already at room temperature and 38000 atm.,
that the pressure gauge begins to be slow in its indications, and
also the transmission of the pressure in the narrow channels becomes
highly uncertain. For this reason we have for the present confined
ourselves to pressures below 3000 atm.

The very great value of the viscosity of the mineral oils at high
pressures is ascribed by Tammann and Bripeman to the solidification
of these substances. With the apparatus, however, described in N°. 4
of these communications (These Proc. XV p. 1021) nothing is to
be perceived of a deposition of salid substance at these pressures.
The oil remains as transparent when this pressure is approached as
it was at first, nor is anything to be observed of crystallisation. We
have, therefore, only to do with a very viscous fluid, possibly a
continuous transition mito an amorphous solid phase.

B. The volume measurement.

For the measurement of volume we have made use of a some-
what modified method of the electric contacts. Just as with AMAGar,

764

platinum wires about 1 mm. thick were originally sealed into a
elass tube. It appeared, however, that such sealing places were no
longer to be trusted after the tube had been compressed to e. g.
2500 atm. Sometimes they lasted some time longer, often however
they already came forth cracked from the pressure apparatus, and
in any case the reliability was exceedingly slight. AmagaT too
complains of the great fragility of his tubes. An investigation under-
taken specially for this end showed that the cause of the phenomenon
will be found in the difference of compressibility between enamel
elass and platinum, in consequence of which the connection between
the wire and the glass is lost at high pressures.

This gave an indication of the way in which improvement was
to be expected. If only the platinum wires are taken exceedingly
thin, the change of volume cannot be so great that detaching is to
be feared. Glass tubes in which capillary wires of 0.0856 mm. of
Hartmann and Braun were sealed, appeared really not to lose anyfhing
of their strength, not even when they had been kept at 3000 atm.
for a long time. It is, however, not possible to seal in these wires
in such a way that the mercury forms contact against a loose point
of them; it is self-evident that they are too limp for this. This
difficulty can be overcome by not letting a bit of wire stick out in
the tube, but by sealing in the wire at both its extremities. The
whole tube is therefore made as follows. A thick-walled capillary
tube of Jena enamel glass is blown out to small reservoirs in 15
or 20 places. At the top there is a somewhat larger reservoir, above
which the tube is drawn out to a very narrow capillary. Under the
said widening there are a number of very small reservoirs, which
pass into reservoirs that become gradually larger, to distribute the
points as uniformly as possible over the isotherm that is to be
determined. Now the tube is cut through at the places between the
reservoirs, which have kept their normal thickness of wall; a
platinum wire of the said strength is laid between the two ends, so
that the wire projects outside on either side, and then the glass is
fused together again. In this the wire is bent downward in a point
to get a sharper contact with the mercury. Then the projecting ends
are connected with a spiral of the same platinum wire, which is
attached to the tube by means of ‘‘zapon’’-lac and gelatin. (See Fig. 4.
For clearness’ sake the wire is drawn beside the tube. Fig. 5 gives
the real position). If the mereury is quite at the bottom of the
tube, the resistance between the two leads is the total amount
of the platinum spiral, e.g. 150 Ohms. As soon, however, as the
mercury has risen to the second contact 6, the resistance AB e.g.

ty
Saad

765

i

ANT)

BST PACA AUN AAT VANAYAYASSTAVAVAVAVAVAWAVDSSANAUSTUIVTESUANTARTE

Fig. 5,

Fig. 4.

766

10 © me. is short-civeuited, and so on at every following contact.

If we place the whole of the platinum wire in a Wheatstone
bridge, it is clear that when the gas is compressed, so when the
mercury in the tube rises, the resistance will be subjected to abrupt
changes. This is observed by replacing the galvanometer needle of
the bridge at zero, whenever a part of the platinum resistance has
been shunted out by the mercury. At the outset of the experiment,
when the measuring tube is still entirely filled with gas, the resistance
of the whole platinum wire, which we shall call the volume wire,
is in the bridge. Whenever a reservoir has been filled with mercury,
the part of the volume wire wrapped round that reservoir, is short
circuited.

The resistances of the different parts of which the volume wire
consists, are known by the gauging of the measuring tubes. We
shall now proceed to a discussion of this gauging.

An exceedingly narrow capillary CD is sealed to the measuring
tube. This capillary has the same length as the measuring tube and
is bent somewhat further round. The measuring tube is still open
at the top, and bas a prolongation /#, to which a rubber tube can
be fastened. An accurate scale-division G is attached to the narrow
capillary. The capillary is drawn out thin at the top and bent.

If the end PD is put in a vessel with mercury, the tubes will be
filled with mercury, when the air is sucked off at “. When the
mercury in the measuring tube is close to a point of contact, the
mercury can be made to move to and fro past it by suction or pres-
sure with two pumps’) connected with / by means of a three-way
cock. The volume wire is then again inserted into a WHEATSTONE
bridge. The galvanometer needle deviates whenever the place of
contact is passed. At the same time the mercury in the narrow
capillary tube passes up and down alone the scale. After some
practice it is not diffienlt to read the position of the mercury in
the latter tube at the moment that the galvanometer needle deviates.
The best way to do this is of course when the mercury in the
measuring tube rises, because the meniscus has then the same position
as during the measurements.

If this has been done at a place of contact, the mercury may be
pressed from the reservoir under it by increase of pressure of E,
and the quantity that flows out at D may be received in a weighing
bottle; then the level of the mereury in the capillary tube is again
observed at the moment that the galvanometer deviates. It is clear

') Two cycle pumps, in one of which the leather valve has been put reversed.

5
767

that in the meantime the resistance has changed, and the resistance
in the resistance box must also be changed.

It is simple to determine the volume that was occupied by the
mercury between the two places of contact. Let G be the weight
of the expelled mercury, S, and S, the scalar heights which have
been read, and / the weight of one sealar division of mercury, then
{G@ + (S,—S,)f}: A is equal to the required volume. (A is the specific
weight at the temperature used). In this way the great advantage
is reached that in the measurement any cocks and other movable
parts are avoided.

Thus the different reservoirs are calibrated. The upmost reservoir
is in an exceptional case. First of all there is no place of contact in
it. It would not be practicable to make one there. Besides, to clean
the tube after contamination the upmost point must be knocked off.
In order to enable us yet to accurately know the volume of the
upmost reservoir every time, the tube is drawn out very thin at the
top. On this narrow part lines are etched at some millimeters’ dis-
tance. When the tube is quite filled with mercury, the positions of
the mercury at the etched lines can every time be compared with
the position of the mercury along the scale. Thus the volumes can
be expressed and calculated from line to line in sealar divisions,
and also those from one of these lines to the upmost contact, after
a quantity of mercury has been expelled.

To determine the weight of a scalar division of mercury, we
make use of one of the places of contact. When the deviation of the
galvanometer needle has been compared with the level of the mercury
along the scale, we press out a drop of mercury, and again compare
the mercury level with the same place of contact. The decrease of
height agrees with the expelled drop of mercury, which is weighed,
and then the scale is at least partially gauged. This can be done
for different parts of the scale. Care can further be taken always
to work within a certain, pretty small part of the scale. And the
tube being very narrow, the differences of position are only to be
taken into account as a correction.

During the measurements the whole tube is of course placed ina
thermostat. On account of the length of the tube the thermostat is thus
constructed. A glass tube of + 6 cm. diameter passes at the bottom into
a narrower tube, which is connected by a rubber tube with a large
copper mixing vessel, where the water is kept at the desired temperature
by means of a toluol-thermoregulator, stirrer, and burner. The glass
tube is placed so high with respect to the liquid level in the mixing
vessel that the measuring tube which is to be gauged, is quite

768

immersed in the water; only the bent point D, in which there is
no mercury during the measurements, projects above the water. By
means of a water-jet air pump the water from the glass tube is
sucked up, and conveyed to the mixing vessel, in the same way as
the mereury is sucked up and thrown over (by air being sucked
up at the same time) in the well-known KantBaum air pump. The
water from the mixing vessel flows of its own accord to the thermo-
stat through the connection at the bottom, which secures a strong
water current. Thus the required accuracy, at the utmost 0°.1,
is easily obtamed. Eventual variations in temperature can be taken
into account, when the weight of the total quantity of mereury in
the two tubes is known. This quantity is every time determined by
pressing the remaining mercury from the tubes and weighing it
when the last reservoir has been gauged. As a rule the temperature
variations were not worth mentioning, and it was not necessary to
apply temperature corrections.

When a measuring tube must be cleaned on account of conta-
minations, a piece may every time be knocked off at the top. After
the cleaning the tube is fused to at the next line. This can be done
so accurately, and the capillary is so narrow here, that it may be
assumed that the volume of the tube is diminished by the known
volume between the lines.

It is unnecessary to apply more than ten lines. After so many
cleanings, the volume wire is damaged as a rule, if the tube was
not broken before, and to repair the volume wire is very difficult. A
newly wrapped tube is, indeed, always rubbed with zapon lac, but
in the long run this measure is no safeguard for the thin volume wire.

That in this way an exceedingly accurate calibration is obtained,
may appear from the following example. The values give the total
volumes from the upper end of the tube to the different places of
contact at two different calibrations.

7.0561 | 7.0554 20.0667 | 20.0590
7.4216 | 7.4281 25.0062 | 25.0078
8.0137 8.0121 34.5016 34.5005
8.8849 | 8.8843 43.7536 | 43.7516
11.5623 | 11.5595 85.4267 | 85.4287
14.9740 | 14.9709 87.5029 | 87.5008

2 90.3264 | 90.3269

The differences are at most '/,,,, of the values themselves, mostly
however much smaller, and for the large volumes they are even of
the order of 1 to 100.000. The mean error may safely be put at no
more than one to 10.000, an acenracy which is certainly not reached
for other sources of error in these measurements. Of course the values
directly give only the volumes at the temperature and the pressure
of the gauging. For other temperatures and pressures corrections must
be applied, which we shall discuss in one of the following papers.

Amsterdam. Physical Laboratory of the University.

Geology. — “Elephas antiquis Fale. from the river Waal near
Nijmegen.”, By Dr. L. Rurren. (Communicated by Prof. Dr.
A. WICHMANN).

The dredging-works in the river Waal in the neighbourhood of
Nijmegen have brought to light already many a finding of diluvial
mammals.

By much the greater part of the bones found belong — as indeed
nearly all remains of mammals dredged from our rivers — either
to animals of the mammoth fauna’) or to animals of the postglacial
fauna.

An exception to this rule is the fragment of a molar of Hlephas
meridionalis from the river Waal near Nijmegen,*) and this finding
proved that in the sub-soil of the neighbourhood of Nijmegen also
pliocene deposits must be found.

Mr. G. M. Kam of Nijmegen, who collects with laudable ardour
all remains of mammals that are found in the neighbourhood of
this town, showed me a short time ago a number of newly found
iypical molars of Elephas primigenius Blum. and moreover a molar
belonging doubtlessly to 27. antiquus Fale., and which had been
dredged from the river Waal, as were likewise the mammoth teeth.

Though the great stratigraphical value formerly aseribed to Hlephas
antiquus, has somewhat depreciated, because it is supposed from later
discoveries that the antiquus-fauna and the primiyenius-fauna, differ
more facially than stratigraphically from each other,*) it seems
however that, for our country, the rare fossils that are known of
the antiquus-fauna are older than the remains of the primigenius-
fauna.

1) L. Rurren. Die diluvialen Siugetiere der Niederlande, Diss. Utrecht, 1909,

*) L. Rutten. lbid., p. 15—16.

8) A.o. W. Soercer, Elephas trogontherii Pohl. und Elephas antiquus Fale.
Palaeontographica. LX. 1912.

770

The newly found molar is most likely a third genuine molar of
the left lower-jaw. It is much worn out by mastication, so that at
the frontal side a few lamillas
have already disappeared. Extant
are still —1/,1l2e at 221 x68
>< 117 mm. During the wearing-
out mastication there are formed
on each lamina first a median,

tape-shaped and two lateral, ring-shaped figures, which remain a
long time separated, but finally fuse into a distinctly rhombie figure, ©
so that the mastication-figures of two succeeding lamellas touch
each other in the middle. (fig. 1). The enamel is 2'/,—3 mm. thick
and strongly plaited. The mentioned dimensions and characteristics
are all extremely typical for Hlephas antiquus Fale.

The molar was not much worn out and between the laminas it
contained still a little ferruginous quartz-sand and some small pebbels

of quartzite.

Much less typical is the remnant of mastication of another molar,
belonging likewise most likely to El. antiquus. (fig. 2).

It contains still 4 laminae of 55 >< 56 mm.
and is most likely a fragment of a first genuine
molar of the upper-jaw. The very strongly plaited
enamel is 2—2'/, mm. thick. The figures of
mastication can hardly be called rhombic; we
must however take into consideration that these

Fig. 2. figures lose their typical character in the same
measure as a molar is worn out by mastication. This fossil can-
not possibly belong to AU. primiyenius; on account of its narrowness
the molar shows the greatest affinity with EV. atiquus.

Chemistry. — “On the nitration of methylurea.” By Dr. H. J.
Backpr. (Communicated by Prof. FRANCHIMONT).

The behaviour of methylurea and of ethylurea on nitration is
considered as a remarkable instance of the different influence which
the methyl and ethyl group can exert on the properties of a compound.’)

Drener and von Prcumann *) have stated that with methylurea the
nitration takes place at the zmno-nitrogen atom, whereas according

1) DeqNerR and von Prcumann, B. 80, 654 (1897). Also compare V. MEYER
and Jacosson’s Lehrb. d. Org. Chemie 1?, 1394 (1013).
2) B. 30, 652 (1897).

(il

to THiete and Lacuman') ethylurea is nitrated at the amino-nitrogen
atom. The nitration products thus should be :

a, a-methyInitro-urea, CH,-N(NO,)-CO-NH,,
a, b-aethyInitro-urea, C,H,-NH-CO-NH-NO,.

It has now been found that the idea as to the nitration of
methylurea is not correct.

D. and v. P. carried out the reaction by treating the sulphuric
acid solution of methylurea at a low teinperature with the theore-
tical quantity of ethyl nitrate. As products, they obtained methyl-
nitramine and a methylnitro-urea melting with decomposition at
156—157°.

I have carried out the nitration in various ways, namely with the
theoretical quantity of ethyl nitrate or absolute nitric acid in sul-
phurie acid solution, and also by introducing the nitric acid compound
of methylurea into sulphuric acid. Invariably, a compound was obtained
decomposing between 90 and 100° with evolution of gas and having
the composition of methylnitro-urea; methylnitramine was not formed.

If this product is dissolved in cold aqueous ammonia and then
mixed with dilute sulphuric acid, methylInitro-urea is precipitated,
inelting with decomposition against 159°.

D. and v. P. state that this compound is decomposed by ammonia
at 100° and then yields methylnitramine; from this they conclude
that it consists of a,a-methy]nitro-urea.

It has now appeared, however, that this compound m.p. 159° is
the a,b-methylnitro-urea; I have proved this structure firstly by
reduction to the corresponding semicarbazide and further by studying
the behaviour towards different bases.

a. Reduction. This was carried out electrochemically, because
also in the. non-substituted urea the electrical reduction gives far
better results than the chemical one’). The operation took place in
dilute sulphuric acid with a cathode of tinned copper gauze.

The generated product with benzaldehyde gave a semicarbazone
m.p. 166°. From the latter was formed, on heating with diiute sul-
phurie acid, the free methylsemicarbazide m.p. 118°. This compound
when decomposed by alkalis gave the non-substituted hydrazine
N,H,, and, hence, cannot be anything else but the hydrazinoformic-
methylamide NH,-NH-CO-NH-CH,. Consequently the nitrocompound
was the a, b-methyl-nitro-urea NH(NO,)-CO-NH-CH,.

In order to further contirm this conclusion the methylsemicarbazide

“1) A. 288, 285 (1895).
2) R. 81, 25 (1912).

772
was also prepared synthetically from methyl/socyanate and hydrazine:
NH,-NH, + CO : N-CH, = NH,-NH-CO-NH-CH,.

The product m.p. 118° proved to be identical with the methyl-
semicarbazide obtained by reduction. The above-mentioned conden-
sation product with benzaldehyde (m.p. 166°) and the semicarbazones
formed with other aldehydes were also identical.

b. Decomposition by bases. The reaction with bases
affords a suitable means of deciding whether we are dealing witha
primary nitramine or with an alkylnitramide. A primary nitramide
Ac-NH-NO,. will, on hydrolysis, yield nitramide NH,NO,, from which
is formed on subsequent decomposition nitrous oxide N,O, but an
alkylnitramide Ac-N(NO,)R gives the monoalkylnitramine RNHNO,.

Hence, the reaction of the a,a- and the a,/-methylnitro-urea will
be expressed by the following equations :

a,a —. CH,-N(NO,)-CO-NH, -- 3KOH =

— CH.-N-NO-K + K.CO, -- NH, 2 HO) eee
a,b —. CH,-NH-CO-NHNO,-+ 2 KOH =
= OHNE. -- K,CO, = N.0 42 8,0 0) ee

The methylnitro-urea m.p. 159° on heating with bases gives one
mol. of nitrous oxide; in addition methylamine is formed but no
methylnitramine. These observations all agree with equation II, but
they all are opposed to equation I.

The reaction of primary nitramides and alkylnitramides with
ammonia differs somewhat from that with alkalis, but is still quite
as useful for distinguishing the two classes. The decomposition of
the two isomers by ammonia is represented by the following equations :

a,a — . CH,-N(NO,)-CO-NH, + 2 NH, =

— CH,-N-NO,NH, + NH,-CO-NH, . . (ID)
a,b — . CH,-NH-CO-NH-NO, + NH, =
== CH,-NH-CO-NH, + N,O-4H,O . =) ay

The compound m.p. 159° gives on decomposition by ammonia
methylurea (identified in the form of its nitroso-derivative) and no
methylnitramine is formed. This tallies with equation IV, but not
with equation IIL.

The reactions with alkalis and ammonia therefore prove that the
methylnitro-urea m.p. 159° is, indeed, the a,d-compound.

Further, I have investigated the crude nitration product before
it was treated with ammonia.

This produet which melts very unsharply (at about 90°—100°)

773

with evolution of gas, has the empirical composition of methy|nitro-
urea and yet on purifying with ammonia, we obtain only about
half the weight of a,b-methylnitro-urea. Hence the presumption that
the admixture consists of the isomere, a,a-methylnitro-urea,

As a matter of fact, on treating this crude product with alkalis
or ammonia, methylnitramine is formed which I was able to show
by the melting point and other properties. On decomposing with
baryta water a quantity of methylnitramine was obtained, pointing
to the presence of 40°/, a, a-methylnitro-urea.

The quantity of nitrous oxide formed on heating with potassium
hydroxide indicated 55°/, of a,6-compound in the mixture.

I

Summary of the results.

1. On nitrating methylurea in sulphuric acid solution a mixture
is formed of the two isomeric mononitro-derivatives.

2. On treating this mixture with cold ammonia solution, the a, a-
methylnitro-urea is decomposed, whilst the a, 6-compound is converted
into its ammonium salt and is obtained in a pure condition by
addition of an acid.

The strueture of this a, d-methyInitro-urea is proved:

a. by reduction: hydrazino-formic-methylamide NH,-NH-CO-NH-CH,
is formed, the composition of which is proved analytically (formation
of hydrazine on heating with alkalis) and synthetically (preparation
from N,H, and CONCH,).

b. by the decomposition with alkalis and ammonia, which agrees
in all respects with the formula of the a, 6-compound and is opposed
to the formula of the a, a-compound.

3. The mixture of the isomers found in one of the nitration
experiments contained about 55°/, of the a, b-methylnitro-urea and,
as appears from the decomposition with bases, fully 40°/, of the
a, a-compound.

4. The essential difference in the behaviour of methylurea and
ethylurea towards nitration agents, as accepted up to the present,
is herewith annulled. .

The experimental details and the new compounds obtained in
this study will be described elsewhere.

774

Botany. — “The primary photo-growthreaction and the cause of the
positive phototropism in Phycomyces nitens.’ By Dr. A. H.
Biaauw. (Communicated by Prof. F. A. F. C. Went.)

(Communicated in the meeting of December 27, 1913).

There are numerous investigations of the curvature movements,
which plants execute, when energy is supplied unilaterally in the form
of light or warmth, or when the organs of plants are displaced from
the position, which they naturally occupy with respect to gravity.

The investigation of these “‘tropistic’ movements, has proceeded
especially in recent years with greater precision, after it was found
in 1908, that for the understanding of these curvature-phenomena it
is necessary to observe the effect of definite quantities of energy. But
whilst in this way more and more data have been collected, concerning
the curving of organs as a result of a unilateral action of energy, there
lagged bebind all the more the study of the effect of energy, when
applied to the organs not asymmetrically but radially. The occurrence
of curvatures as a result of asymmetrical forces, is a phenomenon
so striking, that it is easy to understand that much more attention
has been paid to the study of curvatures than to phenomena, which
occur when the quantities of energy are supplied radially symmetrie-
ally to the organs of the plant. Yet it is as a matter of fact more
natural to investigate first the influence exercised on an organ by
energy, such as light or warmth, when its action is distributed uni-
formly on all sides of that organ, and only afterwards to consider
as a special case what happens, when the energy reaches the plant
not equilateraily, but from one definite side.

Now since it is a very important and well-known phenomenon,
that the plant reacts to this asymmetric energy in a striking manner
controlled by fixed laws, it was hardly conceivable that the plant
would not also react distinctly in the more general case in which
the energy acts radially symmetrically. With this equilateral action a
marked curvature was no longer to be expected, but it was possible
that any reaction taking place might not be limited to certain che-
mical changes in the cells, difficult to demonstrate, but might express
itself more clearly in a change in the rate of growth, which change
might be susceptible of measurement.

After earlier investigations with light applied unilaterally, it seemed
to me desirable in consequence of the above considerations to pass
no further judgment as to the value and essence of curvature
reactions, until a further inquiry had been made into the way in
which a growing organ reacts when light, warmth or centrifugal force

775

acts in definite quantity on that organ uniformly from all sides.
The first results of such an inquiry with respect to light will now
be described.

For various reasons I have chosen in the first place the sporan-
giophores of Phycomyces as objects for investigation. The most im-
portant of these reasons was, that it was obviously desirable first to
trace the influence of light on a single cell and only then to in-
vestigate it in multicellular organs such as the stem and the root
of higher plants.

I have postponed for later more detailed description an account
of the arrangement for securing a constant temperature, of the method
of cultivation and of other details. | will here only mention, that
the fungus was grown at the same constant temperature at which
the experiment was afterwards carried out. During the experiments
the temperature remained constant within ‘/,,° C. I found that a
rapid rise of temperature of, for example, only '/,,0 C., may exercise
a considerable influence on the rate of growth of the sporangio-
phores, if it be only for a few minutes.

It can be noticed, that with the small, but sudden rise of */,,° C.
the vate of growth may for a short time decrease by as much as
25°/,, and then only rise again to the normal. In this case it is
perhaps not the temperature itself, which directly affects growth,
but a brief change in the degree of humidity of the atmosphere
round the plant. I hope to deal with this more in detail. The chief
point here is to show, how important it is to attain a high degree
of constancy in experiments of this nature.

In the experiments sporangiophores are used, which are three to
four em. high. It is known from Errera’s investigation (Bot. Zeitung
42« Jahrg. 1884) that they are then in a condition, in which they
possess a maximal and practically constant growth.

The sporangiophore employed, is placed in the centre of a box,
which remains therefore at a very constant temperature and in which
the atmosphere has a rather high degree of humidity, which throughout
the experiment remains quite constant. The growth is observed through
a double plate of thick glass, by means of a telescope placed outside
the box and magnifying 40 times. The light for the observation was
obtained from a weak, red lamp, which was switched on only during
the observation, for as short a time as possible; its feeble light, also
passing through a double glass plate, forms a silhouette of the plant
on a red background. The illumination of the plant, placed in a
central position, is carried out by allowing light to fall from above
through a double plate of glass. Whilst the plant is prevented from

50

Proceedings Royal Acad. Amsterdam, Vol. XVI.

776

being illuminated directly from above, the light first falls on 8 little
mirrors, which are arranged in a circle at equal distances round the
central sporangiophore at an angle of 45° with respect to the incident
rays. In this way the sporangiophore receives radially symmetrically

the same illumination on 8 sides. For various reasons — to be later
dealt with in greater detail — this arrangement was the more
satisfactory.

The growth of the sporangiophore is always determined before
illumination by several observations at intervals of 5 to 10 min.
Whilst the variation in growth of different sporangiophores is consi-
derable, the growth of any individual one in successive minutes is
very uniform, especially when it is remembered with regard to the
figures found, that with observations at short intervals the error of
observation may be fairly large, because with weak, red light the
measurement must always be made fairly rapidly. The figures of
growth in the dark agree very well with those of Errera. In the
first series of experiments with 8-sided illumination at 22° C. tigures
were mostly found, which fell below the maximal growth according
to Errrra, in the later experiments with unilateral illumination at
18°.3C., after the method of culture bad been somewhat modified,
a value was generally found which agreed with the values found
by Errwra during maximal growth. The eventual relative variations
in the rate of growth caused by the influence of light were however
more important than the absolute rate.

In the first experiments the plant was illuminated via the mirrors
on each of the 8 sides with 14 metre candle power during 15 sec.,
that is, eight times the quantity, which, given by one mirror only,
would have effected a decided curvature. When a growing cell
receives this amount of illumination, a very striking reaction of the
growth takes place. This reaction is all the more marked, the closer
the observations after illumination follow each other; for this reason
observations were made as far as possible every two minutes after
illumination. We then notice:

1. that immediately after illumination growth still remains the same
for about 3 min.

2. that after about 38 min. growth at once markedly increases to
reach a maximum 4'/, to 8 min. after illumination; with this
quantity of light the maximum is usually not less than 2 or 3 times
the normal rate of growth.

3. that afterwards the rate of growth again diminishes to its normal
value which is reached about 7—16 min. after illumination.

4, that often liowever the rate sinks to LO to 30°/, below its

777
normal value for some minutes, and then later becomes quite normal
again.

This is a short résumé of the reaction, which these growing cells
execute after illumination by the above-mentioned definite quantity
of light and there was among the dozens of cells, which I investigated
in this manner not a single one which did not clearly show this
remarkably strong reaction. Moreover the phenomenon equally occurred
both in slow-growing and in rapidly growing cells.

Of this series of experiments, only a few examples will for the
sake of brevity, be given in tables I, Ul, and III, of which the third
is also represented graphically in fig. 1. If observations are not made
every two minutes but at long intervals, the reaction then does not
appear to be so striking, whilst with observations made at still
shorter intervals than two minutes, for a very short time perhaps a
still higher figure for the maximum growth might be found, than
has here been noted in observations taken every two minutes.

If the cell is illuminated with the same intensity of light for a
4 times shorter period, there likewise always occurs a distinct
acceleration of growth, but the latter reaches a somewhat lower
value, about 1'/, to 2 times the normal; if the illumination is 4 times
as strong and 4 times as long, that is to say 16 times as great,
then growth increases not nearly so much as with the lesser illumination
and reaches a value of 1'/, to 1'/, times the normal.

Whilst these experiments are being continued in greater detail and
more accurately in order to determine on the one band, with how
small a quantity of light a measurable reaction still occurs and to
trace, on the other hand, what happens further after giving a much
greater quantity of light, my immediate purpose is to report the fact,
that the growth of the cells responds with a sharply accentuated
reaction to illumination with a certain quantity of light, a reaction
which shows the typical character of what hitherto has been called
in botanical literature a stimulus-reaction. This reaction of growth
to light I should like to name photo-growth-reaction, but considering,
that many as yet unanalysed phenomena in which light has an
influence on growth or form, may also be included under this general
name, I will in order to prevent confusion, distinguish this reaction
as primary photo-growth-reaction. In the case of an accel ration
of growth we can then speak of a positive, in the case of rel. dation
of a negative photo-growth-reaction.

With regard to the existence of a sharply-detined reaction of this
kind, practically nothing can be deduced from the literature-references,
at least the general opinion about the influence of light on growth

50*

778

TABLE I.
At 2.383/,; p. m. illuminated on 8 sides with
14 metre-candle power for 15 sec.

r Position of the Increase in length

ee a Sporangium. per minute in
ae ee one scale division = scale-divisions

49 if

2.3215 481),

2.4015 55 1/4 | a

2.421), 57 } oes

2.441), 61 ) ;

2.4615 651), a

2.4815 67! i

2.5015 69 eth

TABLE II.

At 4.32 p. m. illuminated with + 14 metre-candle
power for 15 sec. on 8 sides.

Position of the Increase in length
Time of
Sporangium. per minute in
observation :
one scale division = scale-division
49»
4.15 25
| 0.87
4,221), 3115
0.88
4.31 39
; 1.00
4.33 41
{ 0.80
4351/5 43 }
> 1.83
4.37 4534 )
t 1.50
4.381, 48 )
; 1.33
4.40 50
1.00
4.411, 51 1p )
0.67
4.43 5215
0.58
4.46 541),
0.55
4.51 57!/5
0.81
4.55 603);

a
~1
te)

TABLE III.
A specimen of weak growth illuminated at 2.52 p. m.
with 14 metre-candle-power for 15 sec. on 8 sides.
Position of the Increase in length
Time of
Sporangium per minute in
observation.
one scale division = scale division.
Oy
2.3915 39
0.36
2.50!/5 43
PISOY 4 Illumination 0.33
2.5315 44 )
; 0.40
2.56 45 }
( 0.50
2.58 46
> 0.75
3 p.m. 47/5
0.75
cae 49 )
t 0.50
3.4 50
¢ 0.50
Spell 5115 )
> 0.35
3.12 531,
‘ 0.38
3.22 57

° 2 y 6 Co JOM 16 I LOMN ZZ LY EC WOO:

Fig. 1. Graphical representation of a case of positive photo-growth-
reaction (Table Ill). The arrow gives the moment at which there was
illumination for 15 sec. with 14 metre-candle-power, on 8 sides. The
abscissa gives the time in minutes, the ordinate the ratio of the rates
of growth,

780

is completely at variance with these facts. In the first place so far
as concerns the positive or negative influence of light. The general
conception, supported by numerous facts, is that light in general
exercises a retarding influence on growth. In Prevrrr’s P/lanzen-
phystologie (2e Aufl. 1904, Bd. IL. blz. 108) as a result of facts then
known this conception is thus formulated: ‘Innerhalb der zulassigen
Lichtgrenzen wird, so weit bekannt, in der phototonischen Pflanze
durch Verminderung der Beleuchtung eine gewisse Beschieuniging,
durch Zunahme der Helligkeit eine gewisse Verlangsamung der
Zuwachsbewegung bewirkt”.

In particular this was also deduced from the experiments of ViNEs
(Arb. Wiirzburg IT, 1878), who observed the growth of the sporangio-
phores of Phycomyces every hour or half hour in daylight and in
the dark and found a slightly smaller growth in the light period
than in the dark. In this investigation, as in that of others, too large
and too indefinite quantities of light were used; moreover most
investigators, including Vinns, used intermittent stimulation, for

which reason the influence of illumination made itself felt as an
after «fect also in the dark periods and conversely. Further in Vings’
expe eis the temperature is very variable, in some it changed

for ¢ le from 22'/,° C.—26° C.

Whust nearly all earlier investigators found a smaller growth
in the light than in the dark, Hetene Jacosr (Sitzwngsber. d. K. Ak.
d. W. <2. Wien, Abt. I, Bd. 120, 1911) made the statement that,
for example, plants of Triticum and Phaseolus, which had been
illuminated 24 hours before for a fairly short time, had become
slightly larger, than the non-illuminated controls. In this investigation,
however, the growth was not measured until 24 hours later and
then only with the naked eye, whilst the humidity and the tempe-
rature varied very greatly during many experiments. In comparison
with this Vines’ investigation of 1878 may almost be called modern,
for he worked with a telescope, ensured a fairly constant humidity
and did not wait for 24 hours before taking his readings.

Further more the representation in the literature of the nature of
the growth reaction induced by light is at variance with the above
facts. The current conception of this nature issummarised by Prerrer
as follows (blz. 109): ‘“Selbst bei dem Uebergang von einer hellen
Beleuchtung zu voller Finsterniss, oder umgekehrt, wird die Wachs-
thumsschnelligkeit gewéhnlich nur um 5—80°/,, selten um 50 °/,
oder mehr beschleunigt, resp. verlangsamt, und bei schwacherem
Beleuchtungswechsel lasst sich eine Reaktion nicht immer nach-
weisen’. Prrrrer further indicates, that a change in the rate of

781

growth does not occur rapidly but gradually, and concludes:
“Neben dieser allmahlichen Verschiebung der Wachsthumsschnelligkeit
scheint durch einen plotzlichen Beleuchtungswechsel der Regel nach
keine auffallige transitorische Reaktion veranlasst zu werden’.

These conceptions, which contrast with the photo-growth-reaction
now demonstrated in Phycomyces, are caused by various facts:
that very large quantities of light were used, which greatly exceeded
the optimum; that the illumination was very prolonged, so that the
plant partly adjusted itself again to the light; that the illumination
was frequently intermittent, so that the phenomenon was not analysed,
but became more complex; and because observations were made
at too great intervals, so that the values for a possibly accentuated
reaction were lost in a more average value.

TABLE IV.
From 1.11/, p.m. to 1.2'/, p.m. unilateral.
Illumination with 14 metre candle power for 60 sec.
Increase in length
Time of Position ofthe, |
per minutes Remarks.
observation. sporangium.
in scale divisions
1.371!/ p.m. 40 )
, 1.07
1.51 1p 55
| ‘ 1.00
1.58 1/2 62
2. 1'/,—21/, | Illumination 0.85
2. 5p 68 )
; 2.00
| 1
‘ 2.00
2. 9 15 1}
1.20
2.114, 78 B
| , 25)
2.13 1p 801/. }
5 [0.88] *) Begin. of pos. curvature.
2.151p | (821/4] )
§ {0.88] Increasing curvature.
2.179 [84 ] )
\ [0.75] ” ”
2.1915 [85/3]
*) From this time onwards the amount of growth is uncertain on
| account of the occurrence of the curvature.

782

After the completion of these experiments with Phycomyces I hope
to study the behaviour of the stem and the root in higher plants.

After the phenomenon described above had been established qua-
litatively, I was naturally curious as to how far this photo-growth-
reaction was related to the well-known phototropism of Phycomyces.
In order to investigate this, the plant was illuminated unilaterally
with, for example, 14 metre candle power during 60 sec. and at
the same time the growth and the occurrence of a curvature were
watched through a telescope.

It was then found that — excluding the special. case, which is
described below — a_ positive curvature never appears, unless the

above-described acceleration of growth has previously taken place. The
positive photo-growth-reaction occurs in the usual manner after
about 3 min. — this time of reaction can with the weakest illumi-
nations rise to 7 min. — it reaches its maximum, then the rate ot
erowth diminishes again, and from this moment does the positive
phototropic curvature become visible, which, according to the con-
ditions of illumination becomes more or less strong. A few examples
ave given in tables IV and V.

TABLE V.
‘From 3.41 to 3.42 p.m. unilateral illumination with 14 metre candle power for 60sec.
ee ee = =
Increase in length |
Time of Position of the }
a | per minute Remarks
observation | Sporangium. |
| in scale divisions |
me £.| args = wala = oe
|
3.2519 p.m. 30 |
| 1.00
3.33 | 371, |
3.413.42 | Illumination | 0.95
3.43 | 47 I
Hee as} |
3.45 | 49 1/4 )
1.50
O24 | 521),
| 1.50
3.49 5514 } | Beginning of curvature
¢ [1.00]
3.51 [57 1/4] j | Obvious curvature
‘ [0.88]
3.53 (59 J ) Increasing curvature
[1.00]
3:05 (61 ] ; 5

783

When one considers that the rays, which practically ran parallel,
fall on the sporangiophores, as on a cylindrical lens, then the course
of the rays in the body of the cell can be conceived as in fig. 2.
It will be seen that the illumination of the front and of the back
of the cell necessarily must differ
rather widely. There passes indeed
as much light through the front-
half as through the back half,
but by far the greater part of

Saas the posterior wall the peripheral
protoplasm is more strongly illu-
Fig. 2. minated than that of the anterior
wall: in the middle of the posterior wall about twice as strongly
as in the middle of the anterior wall. With illumination which is
neither too strong nor too weak, the photo-growth reaction of both
sides commences at the same moment after about 3 min., but this
acceleration of growth continues at the end of the reaction somewhat
longer at the back than at the front and consequently after the cell
has shown a certain acceleration of growth, a curvature arises by
the action from that side, which is most strongly illuminated.

The experiments concerning the absence of positive curvature and
occurrence of a negative one with large quantities of ligbt, will be
continued in connection with results, to be obtained with the photo-
growth-reaction after omnilateral strong illumination. But in my
Opinion the explanation of the positive phototropism in Phycomyces
has already been given by the above, and moreover I found in the
following facts new supports for this conclusion.

I subsequently investigated what happens, when the unilateral
illumination is made weaker so that the lower limit of phototropism
is approached. We may now expect, according to the course of the
rays (see fig. 2) that a quantity of light would finally be reached,
which is too smal] to effect an increased stretching of the cell-wall
on the anterior side, but in consequence of refraction is just sufficient
to cause acceleration of growth on the posterior side. And that is
indeed what is found! Table VI gives an example of the different
eases of this kind which I observed.

In this way acceleration of growth was no longer observed ; at
the moment at which it would otherwise oecur —- that is after a
reaction-time of 5—7 min. with this very weak illumination —
the growth of the most strongly illuminated part of the cell-wall
only is accelerated and the only result is a curvature, which is weak
and often disappears again after a few minutes.

TABLE VI. |
At 3.40 p.m. unilateral illumination with about 2!/, metre-candle for 4 sec.
| Increase in length
Time of | Position of the | ,
per minute Remarks
observation | Sporangium
in scale divisions
3.183), p.m. 30 |
: \ 0.92
| 3,303/4 41 |}
‘ 0.96
3.37 47 |
3.40 Illumination | 1.00
3.41 51 )
, 1.00
3.43 53 1)
¢ 0.88
3.451/4 | 55 )
‘ 1.00
3.4714 57 ) | Beginning of curvature
1.00
| 3.4914 | 59 | ‘ Increasing curvature
| 1.00
| 3.514 61 | Curvature stops
3.56 1/4 | 65 1/5 | Curvature goes back

The curvature is thus seen to occur with a very small quantity
of light (2'/, to 10 metre-candle-seconds) and these curvatures, which
already appear after 5—-7 min. and are mostly weak, have not been
noticed by me before. Formerly I found a curvature only with the
most sensitive specimens, for example, after 50 metre-candle-seconds.
That was the curvature discussed above which occurs, when the
acceleration of growth has already passed off and of which the
reaction-time (observations being made with a telescope) amounts to
8-—15 min. at least. We see therefore, that as a necessary result of
the photo-growth-reaction and the refraction of light, weaker curva-
tures also oeeur with still less illumination and these of necessity
have a rather shorter reaction-time.

Whilst then these small curvatures are visible with 2'/, to 10
Metre-candle-seconds in proof of a liminal local acceleration of the
stretching of the cell wall, there occurs with a slightly stronger
illumination or with the same illumination in “more. sensitive”
specimens — a reaction, which also could have been anticipated.
In such cases, as those of table VII the quantity of light is just

785

sufficient to cause a slight acceleration of growth in the anterior
wall. Since the posterior side is somewhat more strongly illuminated
than the anterior one, which only just reacts, the posterior side
therefore begins to react sooner: after 4 to 5 min. a very slight
curvature occurs, after about 7 min. the anterior wall also reacts,
the very slight curvature does not continue or may even disappear,
but a distinct acceleration of growth of the entire cell can be observed
and as this passes off, there again occurs also a very slight curvature,
since the rather more strongly illuminated posterior wall not only
begins to react earlier, but continues to react somewhat longer
than the anterior wall, which falls tust within the reach of a growth
acceleration. The phototropic curvature is thus divided here into

| TABLE VII.
At 4.11/, p.m. unilateral illumination with ‘about 2!/. metre candle power for 5 sec.
- | Increase in length |
Time of Position of the
per minute | Remarks
observations sporangium |
in scale-divisions |
——- —— = — = = = = SS, —
3.42 AT, )
\ 0.97
3.491), 541/, )
‘ 0.96 |
3.55 60 | |
4. 11h | Illumination | 1.00
4. 2% 67 )
‘ 1.00 |
4. 41 691/ )
4. 64% we ) Beginning of curvature
> 1.25 |
4, 8h 74 Curvature slightly greater
Whee 63
4.1014 TI, | Curvature no greater
1.50
4.121 801/, Curvature back
, 1.10
4.15 83 ;
5 0.80
4.17, 85 |) Curvature again
( 0.75
4.191, 861, ) 6 Very feeble curvature
.83
4.221, 89 ) Curvature no greater

two and both parts remain very slight. If somewhat more light is
supplied, the reaction-times of the anterior and the posterior-wall

786

become very much the same and the curvature — and that is the
definitive phototropic curvature of Phycomyces — only appears after
the maximum of the acceleration of growth, because the growth-
reaction of the less illuminated anterior wall diminishes somewhat
more rapidly than that of the posterior wall.

To be on the safe side I will not extend the scope of these facts
further than to the positive phototropism of Phycomyces, but of this
phenomenon | think, that proof has now been furnished, that the
appearance of these curvatures is the result of an asymmetrical modi-
fication of the growth of different sides of the cell, caused by the
asymmetrical ilumination of these sides; that for this case therefore

pE Canponin’s simple and ancient theory — more particularly in
contradiction to the later conception of Sacas — is reestablished and
with this a theory of a perception of the light-direction itself ts
superfluous.

In the meantime I do not wish to generalize, but only to await
the results of further investigations, which are being continued in
various directions, on Phycomyces and on the root and stem of higher
plants. Only, in my opinion, for no single one of these cases can
any decisive proof in the literature be found against DE CaNnDOoLLn’s
theory.

Finally I desire to express my great indebtedness for the facilities
afforded me in the Laboratory of the Tryner Foundation, for carrying
out these experiments and it is no mere formality, that I tender
my thanks especially to the conservator, Jhr. Dr. G. Enras, for his
assistance and interest in the arrangements for this investigation.

Haarlem, Dee. 1018.

Physics. — “Magnetic researches. X. Apparatus for the general
eryomagnetic investigation of substances of small susceptibility.”
By H. Kamerninen Onnes and ALpert Perrrer. Communication
N°. 139a from the Physical Laboratory at Leiden. (Continued).
(Communicated by Prof. H. KAMERLINGH ONNES.)

§ 7. Sources of error. Sensibility. Accuracy. Disturbing magnetic
influences. The action of the magnet upon the carrier without the
experimental tube appeared to be negligible, even when the lower
end of the carrier was reduced to the temperature of liquid hydrogen.
The action upon the coil of the carrier was also imperceptible even
when a much stronger current 2%, was passed through this coil than

787

was used in our experiments'). Moreover, even if it should be of
any importance, it would be eliminated by the above indicated
method of observation. The influence of the stationary coil upon the
higher conducting spring is probably not negligible, but it cannot
cause any errors, as neither in the calibration nor in the observations
is anything changed in this spring.

It may also be mentioned that by the manner in which the con-
ductors are arranged, in connection with the order in’ which
readings are taken, any influence of the electro-magnet or the
rheostats upon the ammeters or of these upon each other, are elimi-
nated. These influences are moreover very small.

Capillary action. At first we were rather uneasy about the capillary
action between the rods of the floats and the mercury surface, and
between the carriers of the experimental tube and the surface of
the liquid in the bath. The regular return of the carriers to the
same zero, proved that no disturbances from these causes oceurred
in our expveriments. We had always given great care to keeping the
mercury surface as pure as possible.

Vibrations. Vibrations of the ground have a very injurious effect
upon the observations, as they are reproduced in the apparatus,
greatly magnified, and are likely to cause troublesome swinging of
the floating carrier. Vibrations in the microscope caused by the
vibration of the ground, which troubled us at first, could be avoided
by fixing the microscope more firmly.

The carrier is moved by every change of the forces that act
upon it, which causes vertical oscillations of great amplitude. To
damp these, glass wings are attached to the floats, so that after 2
or 3 swings they come to rest. Finally, the vapour bubbles
that constantly rise in the bath, cause small vertical movements of
the carrier, which are more marked, the greater the density of the
liquid gas is. Against these vibrations the comparatively large inert
mass — about 200 grams — of the carrier combined with the
damping just mentioned, proved to be the best expedient. The
damping could as a matter of fact have been made much greater,
without any difficulty. But it was better not to go any further, as it
would have made the movements of the apparatus aperiodic, and
a few swings were very useful to bring the influence of the capil-
lary action upon the carriers each time to the same value.

1) When the axis of the coil falls exactly in the plane of symmetry of the poles
and goes through the middie of the interferrum this force is strictly zero,

788

Sources of error in the experimental objects themselves.

For the calculation of the specific magnetisation,we need to know
the mass per unit of length of the substance with which the ex-
perimental tube is filled The total mass which the tube contains
‘an be ascertained as accurately as we wish, but the length over
which it is spread in the tube, owing to the irregularity of the
extremities cannot be determined more accurately than within
0.2 to 0.8 m.m.

Further, it is assumed in the calculation that it is evenly distri-
bated over the whole tube which cannot be strictly accurate, owing
to slight differences in diameter and slight differences in the degree
of closeness which is attained in filling to different heights, but this
error is certainly small, and only influences the absolute value of
the calculated susceptibility; if the same experimental tube is used
in the same position at the various temperatures, this error has no
effect upon the relative results, which are the principle object of
our research.

The relative results may however become inaccurate, if between
two experiments at different temperatures, some anisotropic grains,
which together form an isotropic mass, each take a different direction,
e.g. so that the line of greatest susceptibility in them approaches
the direction of the lines of force, since the mean susceptibility of
the group will thereby be changed. We can avoid that this happens
unnoticed, by taking the observations at low temperature between
two observations at ordinary temperature. To answer the more
general question in’ how far an apparent isotropy can be obtained
with substances which are in reality anisotropic, by pressing them
in a more or less finely granulated condition into tubes of 5 to 8 m.m.
we can, without changing the conditions in any other respect. repeat
the experiments after having brought the experimental tube into
another direction relatively to the lines of force, by turning it on
its axis. In doubtful cases we applied this method.

Numerical data: The coils described, can carry currents of
6 amp. (/7) and 1,5 amp. (¢n) respectively, for a quarter of an hour ;
the foree which they then exert upon each other is about 25 grams.
In the given arrangement this may therefore be regarded as the
limit of the foree whieh can be measured with the apparatus. Under
favourable circumstances (little vibration) a change of 0,001 gram
in the force acting upon the carrier can be observed. Generally
speaking, the para-magnetie substances examined caused attractions
of a few grams, sometimes even more. The accuracy of the results

789

is therefore more limited by the accuracy of the ammeters, than by
that of the apparatus itself. With two of the ammeters, in each of
which we constantly adjusted on one of the seale divisions, it was
possible to bring the relative sensibility to within a thousandth. The
third was almost equally accurate. In the relative measurements of
the susceptibility calculated, we can thus rely in general upon an
accuracy of 0,2 to 0,3°/,. The absolute accuracy suffers somewhat
from the fact that we are not certain of the homogeneity of the
experimental object (see above); but it is principally limited by the
accuracy of the determination of the magnetic field, the square of
which occurs in the formula for the susceptibility, and not by that
of the apparatus.

There is one more important factor to be considered, viz. the
constancy of the temperature of the bath. Disturbances in this will
have a different effect with different substances, as the change in
the susceptibility with the temperature is very unequal for different
substances, especially when we approach the absolute zero.

In our experiments in general we did not observe any disturbances
from irregularity of temperature. Only in the case of gadolinium
sulphate, the susceptibility of which changes most with the temperature
(1°/, for 0,2 degrees at 20° K.) the measurements in different fields
(at different moments therefore) did not agree so well with each other
as might have been expected if we only considered the accuracy
of the magnetic determinations.

(February 26, 1914).

: : as ae - ii,

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ee

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING
of Saturday February 28, 1914.
Vout XVI.

President: Prof. H. A. Lorenrz.
Secretary: Prof. P. Zeeman. :

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 28 Februari 1914, Dl. XXII).

CORNET sEeN eS

H. Haca and F. M. Jarcrer: “Ronreenpatterns of Boracite, obtained above and below
its inversion-temperature”’, p. 792. (With one plate).

F. M. Jancer and Ayr. Stuex: “On temperature-measurements of anisotropous bodies by
means of radiation-pyrometers”. (Communicated by Pref. H. Haca), p. 799.

Ernst Conen: “Allotropy and electromotive Equilibrium’, p. 807.

J. J. van Laar: “A new relation between the critical quantities, and on the unity of all the
substances in their thermic behaviour”. (Communicated by Prof. H. A. Lorenz), p. 808.

Pu. Konnstamm and K. W. Watsrra: “An apparatus for the determination of gas isotherms
up to about 3000 atm.” (Continuation), (Communicated by Prof. J. D. van per Waats),
p. 822. :

J. A. Honine: “Experiments on Hybridisation with Canna indica”. (Communicated by Prof
F. A. ¥. C. Went), p. 835.

F. A. H. Scurememaxkers: “Equilibria in ternary systems” XIII, p. 841.

F. M. Jarncer and H. S. van Ktooster: “Studies in the Field of Silicate Chemistry. I. On
Compounds of Lithinmoxide and Silica. (Communicated by Prof, P. van Rompuren), p. 857.

J. D. van per Waats: “The volume of molecules and the volume of the component atoms”.
p. 880.

J. BE. pk Vos van Sreenwiusk: “Investigation of the inequalities of approximately monthly
period in the longitude of the moon according to the meridian observations at Greenwich.”
Addendum. (Communicated by Prof. E. F. van pe Sanpr BaknuyzeEn), p. 890.

E. Oosternuis: “Magnetic researches. XI, Modification in the cryomagnetic apparatus of
Kameriiwcn Onnes and Perrier”. (Communicated by Prof. H. Kamertincn Onnes),
p- 892.

Avsert Perrier and H. Kameriinen Onnes: “Magnetic researches. XII. The susceptibility
of solid oxygen in two form;”, p. 894.

Avpert Perrier and H. Kameriincn Onnes: “Magnetic .researches XIII. The susceptibility
of liquid mixtures of oxygen and nitrogen, and the influence of the mutual distance
of the molecules upon paramagnetism”, p. 901.

H. Kameruixncu Onnes and E. Oosteruuis: “Magnetic researches. XIV. On paramagnetism
at low temperatures”. (Continuation of VID), p. 917.

K. Marin: “At what time the Indian Archipelago is separated from the Tethys”, p. 921.

51
Proceedings Royal Acad. Amsterdam. Vol. XVI.

792

Mineralogy. — “Réniyenpatterns of Boracite, obtained above and —
below its inversion-temperature”. By Prof. H. Haga and Prof.

F. M. Jagger.

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

§ 1. Comparison of numerous photographie diffraction-patterns,
obtained by the method of Laug, Kyippine, and Friepricn, i.e. by the
transmission of ROnTeEN-rays through planparallel crystalplates, has
led with increasing evidence to the conviction, that the symmetry
of those patterns agrees with that of the space-lattice, which presents
itself as the very fundament of the molecular arrangement of
the investigated crystal. On this assumption, the new method of
research will be in future a very important manner to elucidate the
question, if with polymorphic changes, and principally in cases of
enantiotropic inversions in the neighbourhood of the critical inversion-
temperature, a change of the molecular arrangement takes place, or
if the cause of polymorphism must be attributed to a change only
of the erystalmolecules themselves.

This problem seemed to us of high importance, especially in the
ease of those remarkable reversible inversions, which are found in
a class of crystals, whose optical behaviour does not agree with
the symmetry of their external form, of their cohesion, ete., or
generally speaking: with their total crystallographic character ; so
that it has been a custom already from an early date, to discern these
cases as those of “optically anomalous” crystals. Of this elass of
mimetic crystals the minerals boracite: Mg. B,,O,,Cl,, and leucite :
K, Al,Si,Q,, may, after the investigations of MaLiarp, K1zn, ete.,
be considered to be typical representatives.

The boracite crystallizes in forms. which by no means can be
discerned from real hexakistetraédrical ones; even by the most
accurate goniometrical measurements it appeared to be impossible
to find any deviation of the external torm from those possessing the
above mentioned symmetry. On the other hand, however, the
optical investigations, and also those concerning the eorrosion-pheno-
mena, have shown with perfect evidence, that the crystals of boracite
possess no regular symmetry in the common way; they must be
considered as composed by a very complicated system of birefringent
lamellae, which according to their optical properties, cannot have
any higher symmetry than that of rhombic crystals; these lamellae
have intergrown in such a way, that their conglomerate corresponds,
with respect to its external form, very exactly with a true regular
crystal. More particularly the individuals of boracite seem to represent

H. HAGA and F. M. JAEGER. Réntgen-Patterns of Boracite below and
above its inversion-temperature.

Boracite 18° C. Distance: 42.5 mM. Boracite 300° C_ Distance- 61 mM

Ee;

Boracite 18° C_ Distance: 61 mM.

793

a polysynthetic twinformation of six hemimorphic rhombic crystals,
whose twinning-planes are those of the apparent rhombendodecahedron.
Normal to every plane of this form, the interference-image of a
biaxial crystal can be observed in convergent polarised light, the
plane of the optical axes being parallel to the longer diagonal of
each face of the pseudo-rhombendodecahedron. At temperatures between
260° and 280° C., the boracite suddenly becomes optically isotropous;
then it has got perfectly regular, and its optical properties are now
in complete agreement with its external form. On cooling, the
original birefringence returns as suddenly, as it has gone ; the crystal
represents afterwards again the case of an optically anomalous one.

These general considerations will be sufficient here for our pur-
pose ; therefore we will now begin the deseription of our experiments.

§ 2. The heating-apparatus. To fulfil the condition, that the
ROntTGEN-rays might be transmitted as well at higher as at lower
temperatures, a furnace of the form described here in detail, was
constructed.

A box «with double walls was made of polished brass; it
incloses the whole furnace like a screen, and is kept at a constant
temperature by means of a circulating stream of cold water. The
hollow box is composed of two separate parts: one of them Q,
bears a tube &, which can be connected with the RONTGEN-apparatus;
further it has a cylindrical hole z, serving as a canal for the thin
bundle of ROnrGuN-rays. Cold water enters the box at /; after cir-
culation it goes by V and & to the hollow cover Q,, and leaves
the apparatus at U/. The cover Q, is fixed in position on Q, by
means of three equidistant screws S. @, possesses at / an oblique
perforation, which serves for the adjustment of the thermoelement 7/.

The heating-coil D consists of platinum-wire, 0,4 m.m. in diameter ;
it enters the furnace at’ ?, where it is insulated from the brass box
by means of a porcelain-tube, and leaves the apparatus in the same
way by a second hole of this kind. The heating coil is wound
round a core of copper A‘), from which it is insulated by means
of a thin layer of asbestos-paper ; the coil needs to be applied only
in a single layer. The metal core A is held in a central position
by means of six pieces of carbon; all intervening space is filled
up with disks of heavy asbestos, cut in suitable dimensions.

1) For higher temperatures it must be recommended, to prepare this central
part of the furnace from nickel, or to coat it heavily with gold; for the highest
temperatures (up to 1600 C°.), alundwm-cores of the Norton Company in Worcester
(Mass.) U. S. A., are an excellent material.

51%

794

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f=) aera oa IL Ss (eek
LN CAARRARARARARBARRR f; YRS ISSA SESSA

\ N
\ N

SISA

Sa

\

isp | 3 LSSSSSSSSSSSSSSASSG -

N WW = ~ Wan

N SY CRE TREY ARES 2 [Vv] cose N

N N Y SNTOONST Cg SAMMONS Yj

. Zane Bi NN 0 he ZN ~
| |) 5 ee

os N es N Fan as se \ i SEED, EEE NANRNN PA

_N SRS A | OO eae GO N : pS =

N faa en) .

So 2a

KY Yy YY, a a N

Sess

CELLET LE Le

: [1d

N

Fig. 1.

795

The core A possesses a somewhat thinner wall at d, and is conical
excavated on the lathe, as indicated in the figure 1, with the purpose
to give the rather strongly deviating ROnrGEN-rays an opportunity
to reach the photographic plate without an interposing obstacle. The
farnace-chamber must be kept at a constant temperature however ;
therefore it is necessary, to shut it at JZ, and like-wise the cover
Q,, to protect the photographic plate from heat-radiation, at N,
by means of a thin plate of aluminium, which can be fixed or
removed by means of a copper-ring. In this way the heat is
sufficiently kept in the chamber, while the aluminium-screens do not
interpose any appreciable obstacle in the way of the ROnTGEN-rays.
The aluminium screens have, at 0, only a hole to introduce the
thermoelement Zh into the furnace. The erystal-plate p to be inves-
tigated, is fixed in position on a removable support, which can be
adjusted in the furnace-chamber by means of the buttons m, and
m,, and a bayonet-joint under the screws s, and s,, The crystal
is fixed on the support by means of the two metal springs v, and v,.
The furnace-coil can bear a maximum current of 5,5 Amperes ; with
this intensity a temperature of 800° C. or somewhat higher, can be
reached.

The connection of the furnace with the ROnrGEN-apparatus was
made in the following way. A brass plate was fixed in a vertical
position on a long horizontal rail; against the vertical end of the
plate a heavy lead-screen was fixed. In the brass plate a long brass
tube of about 7 ¢.m. is fixed, and adjusted in a horizontal position ;
this tube bears at the side where the furnace stands, (i.e. at this
side of the lead screen), a brass flange, which is turned off on the
lathe in such a way, that the plane of its border is accurately adjusted
perpendicularly to the direction of the emerging ROnrGEN-rays. The
tube A of the furnace just encircles the border of this flange. In
the brass tube two cylinders of lead, about 5 m.m. long, are arranged
at both terminals; they are fixed in such a way, that no rays can
escape otherwise, than through the 1 m.m. broad central canals,
which are pierced along the axes of the lead cylinders. As they are
accurately adjusted so, that the axes of the two cylinders are
lying in the same straight line, the direction of the bundle of R6nreEN-
rays (about 1 m.m. in diameter) is wholly determined, as it were
by means of a visor. Everywhere thick lead-plates are arranged so
as to prevent the R6énTGEN-ways from escaping otherwise, than
through the narrow canal.

The furnace, with ifs axis in horizontal position, is now connected
with the ROnreEN-apparatus, by pushing the tube / over the flange;

796

by a semi-cylindrical support, attached to the horizontal part of the
brass plate, it is borne up from beneath, while a copperwire, wrapped
round the double-walled cylinder of the furnace, helps to keep the
apparatus in its position. It is necessary of course, to adjust the
horizontal axis of the furnace exactly in the same level as the small
canal for the emerging rays. The whole arrangement of the RéntGEN-
tube, the lead sereen, ete., corresponds principally with that deseribed
formerly by one of us.')

§ 3. The material. The boracite, used in this investigation, was
from Sehnde, in Hannover. It crystallized in clear, pale blue-green
large crystals, showing the form {110}. Two planeparallel plates were
cut from a crystal, one perpendicular to a binary, the other one
perpendicular to a ternary axis of the apparent regular form,

Our experiments were only made with a plate, cut perpendicular
to a binary axis; at the same time such a plate must be perpendi-
cular to a quaternary axis of the Bravais’ space-lattice, if the crystal
is really of the regular system.

By microscopic investigation the strong birefringence of the erystal-
plate was easily demonstrated. It showed a typical polysynthetic
structure; between crossed nicols it was in no position totally dark,
but only locally. The composing lamellae showed high interference-
colours; in convergent polarized light an interference-image of a biaxial
crystal, almost perpendicular to an optical axis, was visible, with a
dispersion, which would be in agreement with rhombic symmetry.

When the crystal-plate was heated in the microscope-furnace, al-
ready described by one of us, — in which furnace the crystal rests
on the hot junction of the used thermoelement, — the polarisation-
colours between crossed nicols change gradually from violet to yellow,
blue and grey; then the field of the microscope gets dark suddenly
at 266° C. On cooling the birefringence returns as suddenly as it
disappeared ; 7¢ ts an extremely remarkable fact, thatalmost the same
lamellae return on that occasion, which were present already before
heating.

The experiment can be repeated arbitrarily ; thus we are quite
sure, that in our experiments at fully 300° C. the optically isotropous
form has alvays been present, while the birefringent one must have
returned always «after cooling to room-temperature.

§ 4. Our experiments now were made in such a way, that first
a Ronreun-photograph was taken, when the ecrystal-plate was out

1) H. Haga, Ann. d. Physik (4). 28. 439, 440. (1907).

GSN

of the furnace. Then the plate was fixed into the furnace, this was
heated to fully 300°C. and left at this temperature during one hour ;
only after that time, the second photograph was taken. When the
furnace had cooled down to room-temperature, a third photograph was
taken, whiie the plate remained in the furnace and in the same
position, as during the heating of it. The time of transmission
of the R6nrGEN-rays was 2 or 3 hours; this was shown to be suffi-
cient, if a phosphorescent screen behind the photographic plate
was used. The temperature of the furnace was under continuous
control by means of the thermoelement Zh. The obtained results
were 2s follows.

Let us study first fig. 31); it represents the image, obtained at
300° C. The crystal-plate was 1 m.m. thick, and was fixed at a
distance of 61 m.m. from the photographic plate. Notwithstanding
the fact, that the normal of the erystal-plate did not coincide abso-
lutely with the normal on the face of the hexahedron, one can conclude
from it, that the diffraction-pattern possesses a quaterny axis of
symmetry, —- just what might be expected in each of the three possible
Bravais’ space-lattices of the regular system.

In fig. 4 the pattern is reproduced, obtained after the furnace
has cooled down to room-temperature. The image is analogous to
that of fig. 38 in a misleading way ; however it doubtless differs from it.
Especially the following facts may be brought more into the fore-
ground: 1. in the quadrants to the right above and to the left
below, in the first row of spots from the centre, there are found
three small spots in close vicinity to each other; while at the same
place in the opposite quadrants only two of these are present: 2.
especially in fig. 2 it is very evident, that in both the rows, which
are most elongated. from the centre, there are only jive spots between
the two dark limiting ones, if the rows are situated at the opposite
ends of a vertical diameter of the plate; but in the corresponding
rows at the opposite ends of a horizontal diameter of the pattern,
there are about nie spots between the two darker ones, while the
spot in the midst of the row is darker than the otbers, and on both
sides accompanied by a feebler spot. On the original negative of
fig. 4 these differences could already be seen easily ; but much better
in the fig. 2, which represents the pattern obtained from a boracite-
plate, 1,8 m.m. thick, but at a distance of only 42,5 m.m. from the
photographic plate. Notwithstanding the fact, that this plate was not
cut absolutely parallel to the face of the hexahedron; however, the

1) We regret that the figures are only poor reproductions of the original réntgeno-
grains, so that some details cannot be distinguished on them.

798

above mentioned differences can easily be stated. Another point of
divergence of the figs. 3 and 4, which however does not relate
immediately to the difference in period of the symmetry-axis, —- is
the fact, that in the fig. 4 (also in fig. 2), there are always two
spots in the third row from the centre, which spots are missing
wholly in fig. 3. We must conclude from this, that, notwithstanding
the misleading analogy of figs. 2 and 4, with respect to fig. 3, the
former two do not possess more than a binary axis of symmetry ;
with respect to the fact, that most observers contribute rhombie
symmetry to the composing lamellae, it must be considered as highly
probable, that this binary axis of symmetry corresponds really with
a moleenlar arrangement of rhombic symmetry. In any case with
a space-lattice, which is relatively close to a regular arrangement : for,
as already mentioned, it was impossible till now, to state goniome-
trically any deviation of the pure regular crystal-form. However,
the R6éntgenogram shows this deviation with certainty, may it be
only by small differences, while a misleading similarity or analogy
with true regular symmetry remains present. This fact proves, that
in problems of this kind, in many cases the method of the RONTGEN- _
patterns will be of higher value, than the different methods used
~up to this date.

§ 5. The described experiments have thus demonstrated the fact,
that by heating to 266° C., simultaneously with its optical isotropy,
the boracite shows a slight molecular re-arrangement. The question,
if the dimorphism of the boracite is connected with a change in its
molecular arrangement, must, after what is found here, doubtlessly be
answered in the affirmative. *)

It makes only little diffeeence or none in this question, whether the
obtained images correspond perhaps only to the exclusive action of
one single kind of the atoms, constituting the chemical molecule of
boracite. For every kind of atoms of the molecule must be the
structure-unit of an individual space-lattice, and all those intergrown
space-lattices must be either congruent, or equal with respect to

!) Remarkable is also the granular character of the central spot on these
photographs: experiment taught us, that this fact 1s connected with the presence
of the two aluminium-screens M and N in the way of the Rénreen-rays. Especially
remarkable is the more or less regular hexagonal of hexaradiant shape of these
spots. Such an hexagonal image was also obtained by means of a thin alumi-
niumplate alone, about 1,55 mm. thick. It is not improbable, that this fact is
connected in some respect with the octahedral crystalform of the alummium;
perhaps the hexagonal image corresponds to six octahedron-faces as directions of
preference for the Rénreen-rays.

799

their symmetry, and at least in conformity with each other, with
rational proportions of their linear distances; and they must also
remain so, if their aggregation shall be crystallographically a possible
one. For that reason the changes in symmetry of one of these space-
lattices, must be connected with the same changes in the other ones;
it can hardly be hazardous, to conclude from the changes in the
Ronigenogram of one of them, with regard to the changes of the
other space-lattices. Besides it will seem somewhat improbable with
respect to the relatively shght change in molecular arrangement, that
at the same time no further change should accompany it, which
takes place within the demain of the composing molecules themselves.
For the birefringence is, even just a little below the inversion-
temperature, again very strong, but disappears at 266°C. quite
suddenly. It is diffienlt to believe, that so great a change could
only be attributed to the apparently not very great change in the
molecular arrangement. The conception, that the optical properties
partly, if not greatly, must be caused by the anisotropy of the
composing molecules themselves, more than by the structure of their
molecular aggregation, is often defended, just because it is able to
give a clear idea of the nature of optically-anomalous crystals. It
is true, our experiments have once more proved, that doubtlessly
the influence of the molecular arrangement is present; but perhaps
it is in this direction of research, that the cases are to be found,
which will allow a definitive conclusion with respect to the one or
the other of those views.

Experiments with /ewcite, in which the difficulties will be even
greater, because of the higher inversion-temperature and the much
slower transformation, are at present being made in our laboratories.

Groningen, January 1914.

Mineralogy. — “On temperature-measurements of anisotropous
bodies by means of radiation-pyrometers.” By Prof. Dr. F. M.
Jancger and Dr. Anv, Simex. (Communicated by Prof. Haga).

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

§ 1. In the study of the optical behaviour of white-hot silicates, it
accidentally happens that the temperature of the investigated objects
is measured by means of the now generally used radiation-pyrometers
of Wanner or of HoiporN—Kvr.Batm.

The temperature of the body, as determined in this way, generally
cannot coincide with its real temperature; for the mentioned pyro-

800

meters will indicate only that temperature, which an absolutely black
body should* possess, to show the same emission, that really is
observed by means of the pyrometer. Just because different objects
differ from the absolutely black state in an unequal degree, they will
seem to possess different radiation-temperatures, when heated to the
same temperature of ¢° C.

If the radiating object, as in the case of birefringent erystals, is
anisotropous with respect to its absorption for radiant energy, it must
be also anisotropous with vespect to its emission, in accordance with
Kircunorr’s fundamental law. Such a radiant anisotropous body will
behave therefore as if it had different temperatures in different
directions of vibration; its apparent radiation-temperature will not
be the same for different vibration-directions of its emitted radiation.

§ 2. Although this conclusion from KircnHorr’s law of radiation,
has been tested already occasionally by means of experiment’),
— as we learned however just after this investigation was finished, —
all those experiments were made at a time, when the construction
of radiationpyrometers, founded on the law of KircHHorr, and on
those of Wien and Pranck formulated since that date, had not yet
taken place: We thought it interesting, to demonstrate the said
phenomenon once more by means of a radiationpyrometer, as it is
used now in a very perfectly develloped form in all laboratories for
high temperature work, and thus to show at the same time again
the validity of Kircnnorr’s law, in qualitative respects, by means of
a striking experiment.

§ 3. Our experiments were made in the following way.

From a crystal of dark green turmaline of Arasi/, two small flat
cylinders of about 1 mm. thickness were prepared ; one of them had its
axis parallel to the crystallographical axis of the trigonal mineral,
the other one perpendicular to it. The form ofa cylinder was chosen,
1) Kircuuorr himself (Pogg. Ann. 109, 299. (1860) ), has already drawn this
conclusion from his theory, and tried to demonstrate it by experimenting with a
heated turmaline-crystal. The same experiment was repeated later on by Batrour
Stewart (Phil. Mag. (4). 2, 391. (1861)). Although both experiments can be
considered as proving the fact, they are not adapted to make a strong impression.
In 1902 however the law of KiacHHorr for this case was demonstrated in a
convincing and quantitative manner by Priiieer (Ann. d. Physik (4). '7, 106 (1902) ),
who measured by means oi a spectrophotometer, as well the difference in absorption
for the ordinary and extraordinary lightwaves, as the difference in emission of
white-hot turmaline for vibrations in the direction of the crystallographical axis,
and for those perpendicular to it.

801

to make the heat-transport between it and the walls of the furnace
as symmetrical as possible. The cylinders, which had a diameter
of about 2 or 3 mm., were carefully polished, and they were fixed
in the small resistance-furnace 4 (Fig. 1) by means of a fine platinuin-
wire, wrapped round their curved surfaces; the furnace was of the
type, used in this laboratory for microscopical purposes, and described
more in detail by one of us on another occasion *).

by means of the fine platinum-wire the small cylinder was fixed
just above the junction of the thermoelement 4, made of platinum-
platinumrhodium, and used in this furnace as the erystalsupport ;

Co
ig.

°

1) i M. Jazcer. Kine Anleitung zur Ausfiihrung exakter physiko-chemischer
Messungen bei hoheren Temperaturen; Groningen (1913), pag. 102, 103.

802

this thermoelement was connected with a sensitive direct-reading
galvanometer G. The furnace had an inside-winding of platinum-wire;
it was surrounded by a hollow mantle MW, in which continually a
stream of cold water was circulating. It was heated with direct
current of 220 Volt and 8—5 Amperes; the temperature was regulated
by means of a rheostate in such a way, as to be kept constant
at will at every height. The cylinder was fixed in such position,
that it remained at all sides equidistant from the furnace-walls, and that
it was situated in the very short part of the furnace, where no consider-
able fall of temperature along its axis, could be detected: Above the
furnace a movable diaphragm D was present, to make an entrance

to the measuring-apparatus possible only for the rays, coming froma
very small part of the surface of the glowing cylinder; a plane-convex
lense L, arranged above the furnace, allowed to observe a sharp image of
every chosen part of the glowing cylinder-surface, by means of the
telescope of the radiationpyrometer P.

This pyrometer P was of the HoLporn-KurLBaum-type, which is to be
preferred to the about equally accurate pyrometer of Wannur, because of
its giving an opportunity to observe the objects themselves in the hot
furnace sufficiently well. Before the objective of the pyrometer, a total-
reflecting prism (45°) .S was fixed, whose hypothenuse-side was heavily
coated with silver; it was fixed in an innerly:blackened tube, which at
the same time bore the rotating Nicol-prism M. This prism NV could
eventually be removed in an easy way, and, if necessary, be substituted
by another prism V’, to be fixed this time however at the opposite
end of the felescope, before the ocular. The telescope contained the
accurately calibrated incandescent-lamp //, which was lighted by
the current of two storage-cells 4. In the same circuit were present
two easily adjustable rheostates WV, and IJV,, and a milliampere-
meter /, provided with pointer and scale.

The calibration of the incandescent-lamp H between 600° and
LO00° C. gave the following results:

Intensity of current Number of milli-ampéres,

Temperature in ° C.: corresponding with a

in milli-amperes: temperature-rise of 1° C.:
ja ’
600° 318 | 0.38
700° 356 | 0.40
g00e° 396 | 0.44
900° 440 | 0.44

1000° 484

803

For temperatures under 800° C. if makes
evidently no difference for the adjustment of
the pyrometer, ifa monochromatic red glass
is placed before the ocular, or not. The
way, in which the wire of the incandes-
cent-lamp and the image of the heated
cylinder could be observed after the
diaphragm DD was removed, is visible from

fig. 2; the hot crystal there is indicated by
Fig, 2. p, while d represents the wire of the lamp.

§ 4. In first instance it was tried to find out, in what way this
apparatus would show the properties of an isotropous radiator.

For the purpose to be as much as possible in analogous conditions
as were present in the study of the expected phenomenon, these
experiments. were made with a turmaline-cylinder, with its flat end
cut perpendicularly to the optical. axis of the crystal. It could be
proved easily, that this crystalseclion, which was investigated at tem-
peratures ranging from 800° to 1000° C. showed in all directions
of vibration the same radiation-temperature: on rotating the nicol NV,
the intensity of the radiation was the same at every moment. This
observation proves also, that no disturbing polarisation-phenomena
were caused by the reflection of the light at the prism .S; the obser-
vations to be described further-on are thus proved to be quite inde-
pendent of the presence of this reflecting prism.

The object appeared, after removal of the nicol NV, to possess con-
siderably lower temperature, than the thermoelement indicated; the
differences between 700° and 800° are about 12°-—16° C., between
800° and 900° about 5°—12° C., between 900° and 1000° about
5° C. The indications of the galvanometer are therefore diminished
by these amounts, to find the true temperature of the object. Those
lower temperatures are probably partially caused by the fact, that
the small, but relatively thick cylinder was fixed at some distance
above the hot junction of the thermoelement, while a considerable
heat-conduction took place along the suspension-wires. The turmaline-
plate, cut perpendicularly to the optical axis, got soon opaque at a
temperature of 900° or JOO0° C.; the cylinder however, which was
eut parallel to this axis, remained transparent at 1000° C. for a
long time, so that it was possible to see the hot junction of the
thermoelement through it, although only very feebly. Finally however
also this section got opaque; the investigations with Harpmenr’s di-
chroscope e.g., are made all with such an opaque cylinder. Because

804

of the very steep temperature-fall in these small furnaees, the parts
of the furnace before and behind the radiating object were for the
greater part considerably cooler than the turmaline-plate itself.

§ 5. After it was demonstrated in this way, that the chosen appa-
rats was really suitable, to make accurate temperature-readings,
the other cylinder, cut parallel to the ervstallographical axis, was
fixed into the furnace in quite the same way. By a preliminary
optical investigation the direction of maximum light-absorption was
fixed, which direetion we will discern as &,,. The emitted light is
elliptically polarised; the intensity of the radiation for vibrations in
the two principal directions could be studied easily by rotating the
nicol iV.

a) In the field of the telescope, &,, may be in a vertical position.
The polarisator had its plane of vibration parallel to #,,; reading at
739° C.: 350 M.A. Ifthe polarisator NV is rotated over 90°, the intensity
of the current in the incandescent-lamp is only 344 M.A. at 739°C.
When the nicol is rotated over 360°, the following readings were
made in the four principal situations: 350 M A.; 344 M.A.; 351M.A.;
346 M. A.; finally once more: 351 M. A.

The apparent temperature of the small cylinder with respect to
vibrations in the direction of maximum absorption thus seems to be
clearly higher for 14° or 15° C., than in a direction perpendicular
to the first.

6b) Now F, was in a horizontal position; the plane of vibration of
the prism V is vertical. At 751°C. the readings were now: 351M.A.,
and after N being rotated over 90°, —356 M. A.

c) R, is replaced as in a); the polarisator has its plane of vibration
parallel with &,. Readings: at 756° C., first 358 M.A., and after
rotating NV over 90°: 352 M. A.

d) FR, is again horizontal. At 815° C. the readings of the milli-
amperemeter are: 376 M.A. and 381 M.A., according to the plane
of vibration of NV being perpendicular to, or parallel with &,.

e) KR, is now in a vertical position. Readings at 826° C. : 388 M.A.
and 388 M.A. If the nicol is removed, then the reading is in all
directions: 402 M.A.; the apparent increase of temperature is of course
explained by the light-absorption of nicol-, and prism-system. There-
fore all numbers of M.A., as they are found, need to be augmented
with 20 M.A., to get the true radiation-temperatures (Table).

/) The experiments mentioned d and e were now repeated, with

» 805

the use of a red, almost monochromatic glass on the ocular. As the
same readings were made as before, there seems to be no difference
of any appreciable amount between the two modes of observation.

g) If all nicols are removed, as well before as behind the pyro-
meter, the readings remain the same, if the furnace is turned over
some angle by means of the table of the microscope. Once more
thus the reflection at the prism S is demonstrated to have no real
effect on the results.

h) A nicol N’ is adjusted behind the pyrometer, and while F,,
has a fixed position, it is turned over O°, 45°,
The readings at 850°C. were:

and 90° respectively.

voiation of N’ over: Milli-Amperes :
Qo 415
45° 413
90° 409

2). Finally the nicol N was placed again before the pyrometer and
of course the other one was removed. At 898° C. the readings were now:
418 M. A. and 410 M. A.; at 963° C in the same way: 441 M.A.
and 447 M. A.

We can thus conclude from it:

| in I |

_ | Readings in M.A. as

ae terpe | they would be without
body in °C: | the absorption by the

Radiation-tem peratures |
| for vibrations in the two Differences :
principal directions:

| nicol :
|
Rm: Rm: Rm: Rm:

739° 370 en 364 735° en 720° 15°
751 | 376, 371 150. |, 737 13
756 | 318 , 372 755, 740 | 15
815 | 401, 396 8l1 800 Mm
826 | 408 , 403 824 , 816 | 8
850 | 415 , 409 846 , 831 15
890 | 435, 429 89, 875 | 14
808 438 ,, 430 895 , 878 | 17
969 467 ,, 461 961 , 948 13

Mean: 13°.5 (Ga

806

§ 6. It needs to be remarked, that from the individual differences
in sensitiveness of the human eye, evidently there result greater or
smaller values, than those given in column 4, if difierent observers
try to determine at the same time the apparent temperature-differences
between &,, and the direction perpendicular to it. So one of us
always found somewhat greater values, than the mean value of
column 4. But the difference itself as a real phenomenon remains without
any doubt.

§ 7. Finally we made also an experiment, in which the apparent
colder and hotter parts of the turmaline made the impression of being
in immediate contact with each other, and therefore could be com-
pared immediately, so that the phenomenon gets in this way
exceedingly striking.

The furnace was now fixed in a horizontal position, with its
central axis in the direction of the optical axis of the telescope; the
total reflecting prism can be removed in this case. before the objective
of the pyrometer, instead of the nicol VV, a Haipincer dichroscope-
ocular was adjusted in such a way, that two images, an ordinary
and an extraordinary one, of a small part of the crystal-surface,
were obtained; the object made therefore the impression of being
divided into two halves.

If all the circumstances of the experiment, e.g. the reversing effect of
the telescope, ete., were considered, it could be demonstrated, that
in the upper field) only lght was transmitted with a horizontal
vibration-plane, in the lower one only that with a vertical plane
of vibration; the last appeared to be the light of the extraordinary
waves. In the fig. 3 these vibration-directions are indicated by the
shadowing of the fields.

The temperature-measurements in both
images, — which could be performed in
an easy way, because the image of the

lampwire, on moving the eye before the

ocular, was seen by paralaxis now in the

upper, now in the lower field, — demon-
tl

strated, that at 769° C. the lower field
appeared to have a radiationtemperature of

Fig. 3. 757° C., the upper one however of 769° C.
In concordance with the well-known fact, that a turmaline-plate,
if parallel with the crystallographical axis, principally transmits
only the light of the extraordinary waves, which are vibrating i the
principal optical section of the crystal, — thus the direction of

4

807

the horizontal vibrations (i.e. of the ordinary waves), is at the
same time the direction of maximum light-absorption.

As the field A corresponds thus with that direction of vibration,
wherein the maximum absorption of the radiant energy takes place,
so the apparent temperature must also seem higher in that field,
— quite in accordance with the law of KircHHorr.

Groningen. Laboratory for Inorganic and
Physical Chemistry of the University.

Chemistry. — “‘Allotropy and electromotive Equilibrium.” By Prof.
Ernst Conen.

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

In the address on allotropy which I delivered on May 16% 1904
at the opening of the van “rt Horr-Laboratory at Utrecht (this adress
has been published as a pamphlet and also in the “Chemisch Week-
blad” *)) I ealled the attention of my audience to the importance of
a systematic study of this phenomenon. I also gave an outline of
the way to be followed in continuing the researches I had carried
out with my collaborators in this direction sinee the year 1899.

Since that time Mr. Smits at Amsterdam has also chosen allotropy
as a field of work. Into that matter I shall not enter further at
present. i

However attention may be called to the form which characterizes
Mr. A. Smits’ publications and which may give rise to a misunder-
standing.

This is strikingly shown in his paper in these Proceedings Vol. 16,
p. 708 (meeting of Dec. 27, 1913) where he says:

“Tn connection with the foregoing it is desirable to draw attention
to this that according to these considerations the contact with the
solution of a salt of the metal must have an accelerating influence
on the setting in of the internal equilibrium of the metal.”

Mr. A. Smits has written these words in italies; he has however
forgotten to mention in the text or in a footnote that this fact was
discovered and published 15 years ago by Ernst Conen and C. van
Eyk in their researches on the allotropy of tin’).

Moreover he forgets to point out that an explanation of this

1) Chem. Weekbl. 1, 481 (1903/04).
2) Zeitschr. f. physik. Chem. 30, 601 (1899),

Proceedings Royal Acad. Amsterdam. Vol. XVI.

808

phenomenon which is common knowledge now-a-days (and which
is mentioned even in elementary textbooks) was given by me 15
years ago') and that I myself and my collaborators made use of
it in our recent researches on the allotropy of bismuth, cadmium,
copper and zine.

The quotation reproduced above is so striking that discussion of
the other instances of the same kind is unnecessary.

I have always intended to abstain from any remarks on this point.
But as many colleagues both at home and abroad have taken
increasing umbrage at the procedure of Mr. A. Smits, I feel myself
reluctantly compelled to draw atttention *to the matter.

Utrecht, van ’t Horr-Laboratory.
January 1914.

Physics. — “A new relation between the critical quantities, and on
the unity of all the substances in their thermic behaviour.”
By J. J. van Laar. (Communicated by Prof. H. A. Lorunrz),

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

1. In my latest paper’) I have treated some relations also
derived by vAN per Waats — in which a perfectly accurate form
was substituted for the approximate one; I have proved that not
any factor 6 = /(v) by the side of %/,2, so not the factor (1—*/{7);,
added to it on account of the so-called quasi-association either, is

. . 7 4 f-1 Ecoéx.
able to account for the course of the function @=——. in
tke—1 did,

the neighbourhood ef the critical temperature (§ 3); 1 think I have
demonstrated that either a, or 6, or both must be functions of the
temperature (§ 4), and I have made a few more remarks about the
form of the reduced equation of state (§ 5). Now I wish to make
some remarks on the form of the dependence of the quantity 4 of
the volume v.

The temperature dependence will be considered in a subsequent
paper. I may, however, state already now that I have come to the
conclusion that this dependence too must be exclusively looked for in 4,
whereas a is assumed to be independent of the temperature. VAN
pEkR Waats seems finally also to have come to this conclusion, at

1) Zeitschr. f. physik. Chem. 30, 623 (1899).
*) These Proc. of Sept. 3, 1913, p. 44—59.

809

least I infer from an abstract in the Chem. Weekblad of Jan. 3,
1914, p. 29 of his most recent publication “Weiteres zur Zustands-
gleichung’” (summary of his latest Papers in these Proceedings of
Nov. and Dee. 1912, Jan. and Febr. 1913), that he has adopted
this opinion.

Thus the quantity 4 wonld control the whole thermic behaviour
of the different substances, and the variability of this quantity in

2

dependence on v, and also on 7’ would be the cause that this actual
behaviour deviates from that which would conform to van per WAALs’
ideal equation of state with @ and 6 constant.

Further it seems to appear more and more that all the causes
devised up to now, which were to account for the variability of 6,
yet jointly find their expression in one comparatively simple equation.

When the former supposition of perfectly hard and elastic spheres
is abandoned for that of a gradual exchange of the energy during
the collisions, in which at bottom the kinetic energy of the moving
and colliding molecules may be thought transferred to the interjacent
medium, which transition determines the external pressure — part
of the foundation of the before assumed correction on account of
apparent dininution is no longer valid, at least in its old form.

When the molecules are considered as pretty stable systems, the
volume of which varies only shghtly in consequence of the inerease
of the internal and the external pressure, a great part of the correction
introduced later on account of the real diminution, must no longer
be applied. We are led to this view when we consider how exceed-
ingly slight the influence of the temperature is just at higher tem-
peratures (we shall come back to this presently), so that if seems
that the molecule systems are only slightly modified in volume even
by the influence of the thermal motion (which will certainly be
more intense than that of the pressure). The rise of temperature
seems chiefly to have this influence that some molecules (the number
of which is indicated by the wellknown thermodynamic relations)
suddenly break up into simpler ones or the reverse), when the strong
chemical bond is broken for these molecules in consequence of the
too great intensity of the internal motions. Then in the “dissociating”’
substance there are simply two kinds of molecules, e.g. for N,O, the
molecules N,O, and NO,, but — as long as they exist individually —
both seem to be pretty insensible to changes of volume by tempera-
ture or pressure.

And finally — when the so-called quasi-association is considered
as a phenomenon inherent in the nature of things: 1 mean in this
sense that temporary molecule aggregations are naturally formed

02%

810

without any special cause, in consequence of collisions, and of the
temporarily acting strengthened attractive forces, or by other accidental

circumstances — so that this state of quasi-association ‘) for every
substance is quite determined by the value of the (reduced) tempe-
rature and of the volume — we are naturally led to combine all

the influences mentioned into one equation 6= f(v,7), of which at
present we only know the general form, without being able to define .
it more closely. It seems to me that the final decision — as regards
the derivation of the equation in question — will be given again
by the radiation theory and the theory of quanta.

2. Before giving the new relation between the critical quantities,
found by me some time ago, we may briefly state the results of
the foregoing paper, as far as the relations existing between the
critical quantities are concerned.

Ob 0°b
When 6=/(v) is assumed, and el and G2) is indicated by
U/k Uv Tk
6), and 6";, putting v,:b4—=7, it follows from the equation of state
RT a )
= —S= = . . . . . . . . a
P v—b v? (
; ; F dp d*p F
in the first place, by putting | —] and |—-}] =O (loc. cit. p. 45
z dv) T dv? ] 7
et seq.) :
pe OV Ce ole
a EE reese: 5
? 3 1— /;B k
when B",= vz b"¢: (L—O'p). :
Further
we 8 me ree 27 (r—1)? 2
RT, = 57 7 Fe in which 4, = ane | .
1 Higa oe a
a 21 | r—
0; = — 4, — ———— —— — 1 |
Re DY [ae i - ” | r 1—b; ||

In this 2, and A, are never far from 1; for substances that deviate
most from those which would correspond to the ideal VAN DER

Waats’s equation of state — the latter will henceforth be called
“ideal substances” for shortness — 2, and A, are both = 0,98.
For the so-called critical coefficient s= RT): prvg is found:
ppemastide aman ak RS is
Ar
in which 2,:4, may always be put = 1.

i) Which according to this view has therefore nothing to do with real associa-
tion, as for NO, and H,O, which is of entirely chemical nature.

S11

ip pe= t,he Mm, ove mn; 6 vy == B may be. put; the
reduced equation of state, in consequence of the mentioned relations,

becomes :
27:4, 7
(« + =) (n= 8) "arn ee or ee (O)
n

Another set of equations is found by the introduction of the
T' dp
pdt
on the temperature of the quantity 6 must be taken into account.
We easily find (see p. 56—57 loc. cit.):

es RT; (1+ Vk 2")
~ pe(ve—bx) ey)

T, (ab ;
when § represents we ( _}. Hence this becomes:
YE OT );.

ms r 1 r 2!
far ie gems )

*
If now the temperature-correction er 6", is represented by ~, and
P=

critical pressure coefficient 1 i But in this the dependence
k

if we bear in mind that s would be the value of /, when 6

(or a) were no function of the temperature, which value we shall
henceforth denote by /’, we have the relation:
r 718)

Ts — ; ge ha tee A
} r—l A,r—1 “)
in which
oh
ee Bete soe 6 yen o ((S))
ara
dé :
In this / is therefore the quantity (=) determinable experiment-
dm / |.

ally, which, however, will not appear as such in the different
relations. In them /’ oceurs systematically, which is connected with
J by the relation (5). Fortunately, however, y is always very small,
so that in a first approximation / may be substituted for /’. But
for the sake of accuracy we have everywhere in what follows not
identified /” with /.
When pe+ “/y,2 1S substituted for RZ’, :(v,—b,)
Fel ses 30 hale if
“7 ges at GaN me oF

follows from /” = RT: pe (ve —b;), so that we have also the relations:

812
3 8 At fl
ij) aed) et i — i bas ie fuer» eoegl(Oa)
pS 3 Zi 5)

while now the reduced equation of state may be written:

|
(«+7 ) oa) =m, eee) (C3)

n®

in which /’ will always be slightly smaller than //.

3. If we assume for an “ordinary substance’ (which is therefore
farthest from the above mentioned “ideal substance’) s=3,77‘*),
hence '/,=0,2653, then the value 2,12 corresponds to this for7,

with A,:4,=1 according to (3). :

Then the value 7,136 is found for /’ from (4) with 7: (7 —1)=1,893.
Since / will have to be somewhat greater than /’, as in (5) @ is
positive at any rate, but as for / experimentally a value is found
which for the said substances if not very near 7,14, yet lies only

little higher, we see confirmed here what I observed already above
(see also loc. cit. p. 57), that gm will be exceedingly small at the
critical temperature, and that therefore /’ and / will differ very little.
Further follows from f’ — J = 27: a,r’, with 27 : 7? = 27:4,494 —
= 6,008, for 2, the value 0,979 — 0,98.
And from /” =(4,:4,) x (8:(r—1)) the value .0,999°— detor

,:A, is then properly, found back with 8:(r—1)= 7,148, after

A

which 0,98 is also found for A,.

The quantities 2, and 2, will vary between 0,98 and 1, according
as one descends from “ordinary substances” to “ideal substances”
through the whole region of substances. In this 7 will at the same
time vary from 2,12 to 3; s from 3,77 to 2,67, and / from 7 to 4.

We further find for the relation for 4, indicated in (2):

1 = bi = 059085 ; bh; = OF0915:

The value of 8’, may be caleulated from (1). We then find:

8", = vy", — O5,) = — 0,4898 ; vb", = — 0,3996.

In the above we only apparently started from one fundamental
quantity, viz. s, from which we have calculated 7 = 2,12. For we
then made use of the circumstance that 2,: 2, = 1 may be put.

Strictly speaking we ought to have assumed fvo quantities, viz.

1) Mean of the values 3,766 for n-Penlane, 3,735 for i-Pentane, 3,796 for
Fluorbenzene.

813

s and 7, from which all the other quantities can then be calculated,
For r we could then have asswmed 2,12, and we had then found
4,:2,= 1. But it is better to start from two quantities, which are
experimentally determinable. And for the present s and /” seem the
most suitable, even though s depends on the accurate determination
of the critical density (which is often very difficult, and generally
takes place through the strictly speaking unpermissible prolongation
of the so called straight diameter’? —- unpermissible, because this
straight diameter exhibits a perceptible curvature c/ose to the critical
point), and though the determination of /” (supposing we may put
j’ =/) is from the nature of the thing always connected with not
very accurate calculations of pressure and temperature differences
close to the critical point.

We might eg. have assumed s= 3,77 and f=7, and we had
then also found 2,=—4,—0,98. And the equality of A, and a”,
would also have become clear for other substances, as Oxygen,
Argon ete., where another set of values for s and / had been
started from.'

We shall, however, immediately see that in consequence of the
new relation found by me instead of /’ and s another quantity can
be introduced, which in contrast with the two mentioned ones is
experimentally pretty sharply definable. We mean the direction of
the straight diameter, which can be determined very accurately from
observations even far below the critical temperature, and is at any
rate not affected by any uncertainty in the observations close to the
critical temperature. 7), and v; will, indeed, of course be of influence
in the determination of the “reduced” coefficient of direction.

If, as said, we take, however, for the present /” and s, we find
easily from the above relations :

ag oar ; Laas gee Sed a pt sa 3)

Further from /’ —1= 27:4, 1r° and /f’ =(a,:4,) X (8: (r—1)):

Dies 8 27 SENG
LS = = (: = *) SA eal aa vie (8)
sl J Saal ff

through which :

Pitees sees A Ne EES ea cr

ey

Finally we shall find :

2s(f'—1 LO k
1, =—L 3 (8)

In this particularly the last relation, viz. for 6";, is remarkably

814

simple, the more so as there occurs only one quantity, viz. 7’, in it.
For f// = f=4 we have ~’, =, as we should have.

4. If we may really put A,:4,—1, s is perfectly determined
by /” through the relation (y), and only one quantity either s or /”
suffices. Then we have only to put:

8f' 8s
= —. nL jf —=—=
8+f' 8--s
everywhere in the above. Further in (3) rs simply becomes = 8

and in (4) /’ will become = 8: (r—1).
Hence if we express everything in /', we have:

87’ Seah Die
St gag ee ee
s+) j j FD ae
Uo) , f'—4 :
a
8+) J

by the side of which we mention a few more earlier relations in
the new form :

n=8 ple 8) a

2
se
—=
lo 2)
~~

a Va SEe ote = EAE
when 2,=A, is represented by 2. We once more point out, that all
the foregoing relations hold quite generally and perfectly accurately,
but that the relations (7) and (8) will be dependent on the assumption
A,:4,=1. But this latter relation may be considered as perfectly
accurate.

Now

She a kG I Se
LE ae 3 Pk = 9G" ya»

is simply found for R7; and p;, so that we can calculate the quan-
tities « and /, very accurately from the observed critical pressure
and temperature.

As for the quantity 2, it is’) = 49:50 = 0,98 for /’ =7; for
Se = 6 .we find 243 :,245 =(0992)), for (7 o> we shaven

675 : 676 = 0,9985, and for // =4the value 1 is found. So whereas
ye de is pretty accurately = 1, A=4,=A, will in the utmost case

only deviate 2°/, from unity, and will approach more and more to
1 for substances with lower values for /’.

Let us now proceed to give the new relation and at the same
time introduce the reduced coefficient of direction of the straight
diameter y.

S15

5. A new relation.

1 found, namely, that remarkably enough, there always exists a
simple relation between the quantities r= vz: be and z= hy, :2
Not the approximate equality of s and s’ =v; :v,, brought forward
by van DER Waats, but another accurate relation. For though s
differs little from s’, yet the difference can amount to '/, of the
value, whereas the relation found by me seems perfectly accurate ;
the value of s:s’ can be calculated from it for every value of the
chosen independent parameter.

We know that according to the property of the ‘straight diameter”

4 (d, + d,)—1

when d, and d, represent the reduced densities of liquid and vapour.

When d, may be neglected with respect to d,, we have simply :
=1-4-y(1l—m),

which for m= 0 ap. ~ into $d, =1-+y or

dy = — = 2(1+y).

Here v, is therefore the fictitious extrapolated liquid volume at
the absolute zero-point; this volume can of course not be realized
for liquids, but in this ideal limiting case we may write 4, for it —
by 6, we must, therefore, understand the same thing as is understood
by v, Le. the smallest volume that a number of molecules lying
closely together, so that they are all in contact with each other,
can oceupy.

So if in future we represent the relation vz: v, by s’, and the
relation bz: 6, by z, we have:

eeicn Ma | (RS)

because r= vz: be. So far these equations do not contain anything

new; the last may serve to calculate 2, when y and + are known.
in w ae r ie be calculated from one of the equations (7), viz.
=1+ (8 . Thus ¢-=1,8 e.g. for an ordinary substance == 039;

ae AD) toe for argon (y=0,75, r= 2,33); z=1 for an
ideal substance (y = 0,5, r = 3
But now I found that always
9
—_— aa| . . . . . . . . . (10)

for the most different substances. In this form the relation was first
discovered by me. Thus among others:

M4 y > 4 2 °
For an ordinary substance (/” = 7,2) AS — 111 = 1,8
| g WeSC 1 — 2 = 15
» Argon (ji—=16) i 1331
; - 2
,, ideal substance (Ge=s4) i 7 = 1

in which the value of z in the first member was calculated from
(9), d.ce. ufrom z= 2 (SE) a

The relation (10) seems, therefore, to hold very accurately. It
comes) to thistitihat 7 — 1252 or

ve — Op mes

b]

Cen ea DE
hence
eat eit Cry aed eed oe (IL

If, namely, only for ideal substances we find v~ — 6; = 2 by, so
that then v, becomes 36, — now this property appears to continue
to hold for ad/ substances, if only in the second member 2 0, is
substituted for 26; (in which 6, is therefore always the volume v,
at 7’—O extrapolated from the equation of the straight diameter).
As therefore

= ey PYM Sige eal! !
Pi ; 01 2, (11a)

by
££ = 2'¥ (12)
b,
And this is what the new-found relation really comes to. In this
way we have for :
Ordinary substance re ))) cso
Argon ps (U5) z= 155)
Ideal substance ae (0)5) 2 =a

For an ideal substance we take y= 0,5, because there just as
for the other substanees the coefficient of direction has been taken
of the straight line which connects the eritical point with the point
d, at m=0O. The always slightly deviating direction of the locus
4(d,+d,) =f (m) close to the critical point would be = 0,4. (Com-
pare my earlier papers of 22 Nov. 1911, p. 488 et seq., of 24 Jan.
1912, p. 563 et seq. and 574, and of 25 April 1912, p.1091 1096).
That the so-called “straight diameter” really exhibits a slight curvature
at the last moment in the immediate neighbourhood of the critical

817

point, has been found among others by Carposo for different substances.
From the above a remarkable relation can still be derived, namely,

9
s’ — 2 being = z according to (11a), and z being according to (10) :
ee
2
gio ae
: al
or as r—1 is always =s: (/” —s) according to (a):
ss—2= of res 7
8
from which immediately follows:
Zi SBMS ARNE. Po oats a tee (LS)
Thus e.g.
Ordimary ‘substance: \|ics ="S,7' (4. 8 = 338) | = 716
Argon | 3,424 3,9 5,99
Ideal substance | 2,667 3 | 4

Here attention must once more be drawn to the difference between
s= RT,: prve and s'=v;:v,, which difference is, indeed, small,
but never negligible. Thus for an ideal substance s':s—°/,. The
empirical equalisation of s' and s would only lead to approximate
relations (v. D. W.), whereas our above empirical relations are perfectly
exact, and seem to hold accurately for all substances.

'

6. The found relation between z and + (in (10)), and in connection

with (9) therefore also between 7 and y — which relation will have
to be theoretically justified by the course of the function b= fv),
through which 6;:6, becomes — 2 y according to (12), which will
be discussed presently — now enables us in connection with the

assumption A,:2,— 1, to express a// the quantities relating to the
-equation of state in the one independent parameter y.

In the first place we choose y, because this quantity according to
(12) is in the closest relation with the course of the function 6 = f(v),
on which after all everything is founded: all the difference between
the great diversity of the substances. But in the second place because
this quantity y, as said, can be easily experimentally determined,
as for this purpose only a number of liquid- and vapour densities
must be determined not up to the critical temperature, but near to it.

From (9) and (10) follows with regard to r:
2(l+y) 2

a ae

hence

r= URS ae GE)
of
Then from (8), viz. rs = 8 <(A,:4,), when 4,:A, =1 is put,
i (15)
T= >———
1+y¥
follows for s, whereas from s'= 2(1-++ y), (see (9)), follows:
ss (+7)?
ean aie (16)
8 Ay
: 8
From /' = 8s: (8—s) (see a little above (7)), or also from /” = aa
Y el
according to (4) we derive:
PH Bye 0, 2 te

an exceedingly simple relation, which states that the critical coeffi-
cient of pressure f’*) will always be equal to eight times the reduced
coefficient of direction of the straight diameter.

From (7) follows for y:

27 ¥?
4=—______, (18)
Cay Cr)
Further according to (7) we have:
8y—1 2y—1)? by 2y—1)?
Te tpn ee ora a fe = Jie : Lees ) (19)
4y(1+-7) Ay (Lat y) deen he Oye
Then also according to (7):
vb" fi—4 2y—1
gs a ee le (20)

1b, f' 2y

Thus we arrive, substituting 6,:6, for 2y according to (12), at

the exceedingly simple relations at the critical point:
(ox—b,)? | uLOR a,
ost eres | , bbe oan + el Ce |e eee

From this we can already get an insight into the probable values
of 6’ and 6" also ovtside the critical point, and try to derive the
relation 6 = f(v) by integration. But this will be discussed later.

If we now finally summarize what has been found, in a table
in which some principal types of known substances have been
inserted, we get the following instructive summary, from which it
may be seen how the whole behaviour of the substance can be
deduced from one fundamental quantity — here the quantity y (also
='/,(by:6,)), the reduced coefficient of direction of the straight dia-
meter according to '/, (d, +d,)—1—=y(1—in). We may further
avail ourselves of the following table for the prediction of still un-
9) In which f’ is properly speaking =f:(1-+9), see (5). But /” always differs
exceedingly little from f.

819

known values (for helium and hydrogen e.g.) or for the correction
of already determined values (among others for oxygen).

Limiting |
substance) | | 2 eC ae! 4 1 | 8 | 0.9640.125 | 0.55

Ordinary | |
substances?) 0.9 | 1.8 | 2.11 | 3.8 | 3.79 |1.003 | 7.2 | 0.977/0.0936| 0.444

0.8 | 1.6 | 2.25 | 3.6 | 3.55 |1.0125) 6.4 | 0.9880,0625| 0.375

oxygen } |
Argon § 0.75 | 1.5 eae 3.5 | 3.43 1.02 | 6 0.992'0.0476) 0.333

Hydrogen? | 96 | 1.2 | 2.67/3.2 |3 /|1.067| 4.8 | 0.999:0.0104| 0.167
Helium § |
Ideal substance 0.5 | 1 | 3 3 2.67 |1.125 | 4 1 0 0

°
i

Now for H, has been found s = + 2,9, f= 4,83; so this agrees
very well with our type, where y=0,6 6=3, /' = 4,8). Ac-
cordingly we may expect for H/, a straight diameter, the reduced
coefficient of direction of which will amount to 0,6.

For helium has been found s=3,13, 7 > 4,46; this too may be
correct. If s is really 3,13, f would even be greater than 5. But if
jf is no more than 4,5, then y would be = 0,56, and s = 2,9, just
as for H,.

And, at last, for O, has been found s = 3,346, f = 5,76, y = 0,813,
where the values of s and / are in good harmony, but y deviates
greatly. For with f#=5,76 would correspond y=0,72, s = 3,349,
so that s as has been said, agrees beautifully, but y ought to be
considerably lower than 0,813. But here the fact may also have
influence that liquid oxygen is an associated liquid, and that hence
(just as for ethyl and methylaleohol, acetic acid, ete.) y is higher
than the normal value.

7. We will not drop this subject before having set forth a few
points. First: the circumstance, to which putting 2,:A,—=1 really
comes, is this. According to (7) A,:4,=s:8(1—*/-) and so when
/,=/, is assumed, this comes to this that s= 8/7’ :(8+ /”) (see
above (7)). This is experimentally satisfied. But further /” = 8y —
also in consequence of the new relation (12) — and according to
(21) b= (6; — 6,)? : by ve. The latter is in connection with the form

1) Substance with high molecular weight.
*) Mean of n-pentane, ?-pentaue, fluorbenzene, etc.

820

of the function )— fv), and so the particular form of this last
function is after all the deeper cause that both 4,—= 4,, and the
new relations found by me, viz. ve — bz = 2b, and bp:b,—=2y are
satisfied.

I further draw attention to the fact that the above relations only
remain valid as long as the law of equipartition continues to hold
at very low temperatures. | have convinced myself for argon that
the departures from this law even at the lowest temperatures, at
which vapour-pressure determinations ete. have still been made
below the critical temperature — among others at 90° K.— are
still so shght that they remain entirely below the errors of observation.
But this will be treated more fully in a following communication.
Whether this is the case at the critical temperatures of hydrogen
and helium, I have not yet examined. It is, however, very well
possible that for such exceedingly low absolute temperatures the
deviations are large enough to give rise to more or less considerable
deviations in the formulae. This can particularly affect the quantity
y, as the straight diameter extends to sull lower temperatures than
the critical temperatures.

Finally a few remarks on the way in which 4 depends on the
temperature. It has appeared to me that this variability is exceedingly
slight at higher temperatures, so that even at the critical temperature

06 :
of ordinary substances ar is still negligible (See § 1 and 2). This is
in agreement with what-I found before for H,*). For 0°, 100°, and
200° C. I found, namely, 6, constant = 917 10-® (p. 576, 580
and 582 loe. cit.). But 6, varied greatly. That 6, varied and even
apparently increased according to the relation b, — b,=VyT was
entirely owing to the form of the chosen function 6 = /(v), viz. the
wellknown “equation of state of the molecule” of van Der WAALS.

It has, however, become clear to me that this equation does not
hold, and is in contradiction to the above given accurate values 6’;
and B'y. The fact is this that 6 decreases at all temperatures, but the
more as the temperature is lower. Finally 6, will have become = 6,
at the absolute zero; hence no variation of 6 with the volume will then
be possible any more. For at a given temperature 4 moves between
b, (for v=) and b, (for v=v,). Now 4, is a temperature function,
and it moves from b,, (for T large) to 6, (for 70). Hence in a
b,v-diagram at high temperatures the curve 6= /f(v) will have a
pretty steep inclination from by = about 1,9 6, (for ordinary substances)

1) These Proc, of 24 April 1903, p. 573--589,

821

to b,. But at low temperatures this curve will approach the straight
line 6=6, more and more, moving from +, to 4,.

Now as has been said, the decrease of , with 7’ is so slow at
first that 6,= 6, at 7’ very great is not very different from 6, at
T;, when namely 7% is comparativeiy high, as for all “ordinary”
substances. Only at lower temperatures 6, decreases rapidly to 6.

OU:
In consequence of this Gi will, therefore, be comparatively very small

in the neighbourhood of 7%, but ie will assume a much greater
value.

So this accounts for the fact that for substances with /ow critical
temperatures, as O,, Argon, H, and Helium the.ratio b::6, becomes
smaller and smaller (see the table), which will cause the type to
approach more and more to that of the so-called ideal substance,
where vAN per’ Waats’ ideal equation of state with constant 6 will
hold. For once more: at lower temperatures 6, approaches 6, more
and more, and the distance between 6, and 6, disappears.

But that this is not the on/y cause of the change of type, so that
eg. Xenon with a comparatively high critical temperature (+ 16°,6 C.)
is identical in its behaviour with O,, where 7;—= — 119°C. — this is
perhaps owing to this that a second circumstance can be of influence

on the course of & as function of v, namely that the relation

0
which will probably depend on the structure of the molecule (com-

pound or simple as for argon, helium ete.), need not always be
= 1. This too will be discussed later.

Both the varying value of 6, with decrease of temperature, and
the variable value of v,:, according to the nature of the different
substances: these are the principal causes of the preservation of the
individuality of the great majority of substances also in their reduced
equation of state, so that these substances may he divided into diffe-
rent classes, ranging from the class of the “limiting substanee” with
high molecular weight, and of the ordinary substances, to that of
the “ideal” substance with extremely low eritical temperature, for
which would hold f~=4, r=3 and s=‘/,. But even helium (see
the table) is still a long way from this.

In a following paper we shall treat the form of the function
b=f(v), and test the found expressions by the values of & which
I have calculated for Argon.

I will communicate already here, that of the many expressions
which satisfy the relations (21), ie. which at 7% give the values of

822

b', for B"; indicated there, only some types lead to simple results’),
among others also (with some restriction, see later on) the exponen-
tial type proposed already before by Kampriincu ONNEs :

—a (v—v,)

b = bg — (b,—b,)e :

Already in 1901 (Archives Teyler (2) T. VII, Troisieme partie) I
tested (see p. 14 et seq.) the values of 4 for H, and CO, by this
equation *), and found a good agreement. But that I then found
deviations with respect to the critical quantities is simply owing to
this that I at the time did not take 6, variable with the tempera-
ture, and that therefore observations of H, at O° C. can by no means
give a final decision about the quantities at —241° C.

It is of course only of formal importance, when in the above
relation and others at last 6, and v, are replaced by critical quanti-
ties, so that the relations (21) are satisfied. But this will be discussed
in a subsequent paper.

Fontanivent sur Clarens, January 1914.

Physics. — “An apparatus for the determination of gas isotherms
up io about 8000 Atm.” (Continuation.) Vax per Waans-fund
researches N°. 6. By Prof. Pu. Kounstamm and Kk. W. Watstra.
(Communicated by Prof. J. D. van pER WAALS.)

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

B. The volume measurement. (Continuation).
CONVEYANCE OF THE GAS INTO THE MEASURING TUBE.

In the previous communication the question was answered how
the volume is determined of a quantity of gas which is in the
measuring tube, above mercury. Now we shall have to describe how
we get the gas quantity that is to be measured, in this position.
For this the most intricate part of the apparatus is required.

As is known AmaGat’s measuring tubes consisted of piezometers

’ é . b—b, b—b, n
1) Also v. p. Waats’ relation in the general form ——— = f | 1 :
v-—b by—b,
with by) constant gives perfectly impossible results, among others 7 varying between
8 and 30.
2) It is easy to see that the relation used there, viz.

4
=e
bbs (14 bee )
by the application of suitable substitutions for § and @ is identical with the above
relation,

823

of the well-known Caiierer form. The quantity of gas is measured
at low pressure, the piezometer is placed-in a steel vessel filled for
the greater part- with mercury and further with a transmission
liquid; and by then forcing up this liquid by means ofa hydrostatic
press we expel the gas from the piezometer reservoir, and convey
it to the calibrated stem. Through this way of procedure, however,
we are compelled to confine ourselves to a comparatively small
quantity of gas. For if we should want to start from e.g. 1 1. of
gas under normal circumstances, the steel pressure vessel must itself
have at least a capacity of 2 /. And to construct a vessel of such
a capacity, which can be perfectly closed, and does not leak at
3000 atm., is, if feasible, so expensive that its execution is entirely
out of the question. Yet it is very desirable not to work with small
quantities that the volumes may not become too small at high
pressure. To enable us to work with a quantity of gas of 1 /.
without the parts of the apparatus exposed to high pressures becoming
of too large dimensions, an apparatus was constructed which allows
us to compress the quantity of gas to be measured first to from
50 to 100 atm., and then convey it to the measuring tube proper.

A first requirement is that throughout the experiment the measuring
tube must be continually exposed to the same pressure outside and inside,
because else the thin glass tube of course at once gives way. Originally
it was the intention to convey the quantity of gas quantitatively into the
measuring tube, after its normal volume had been determined. Owing
to unforeseen difficulties, to which we shall revert further on, we
have not yet succeeded in realizing this quantitative transferrence,
so that in the experiments which will be deseribed in what follows,
the quantity of gas which was worked with, has been only deter-
mined by a measurement of its volume e.g. at 100 atm., the com-
pressibility between 1 and 100 atm. having to appear from separate
determinations. We shall discuss this more extensively Jater on in
the description of the experiments, and shall now first proceed to
give a description of the apparatus, used for the conveyance of the
gas into the measuring tube.

It consists of three pressure stages: an (unprotected) glass part
for the pressures below two atmospheres; a part that serves to
compress the gas from 2 to 50 or 100 atm.; and the measuring
part proper. The glass part consists of a vessel A of a capacity of
+1 /.*), placed in a copper thermostat with glass windows (repre-

1) As we have not made use of the accurate capacity of this vessel for the
experiments which will first be described, we shall not enter into a description of
its calibration as yet.

D3

Proceedings Royal Acad. Amsterdam. Vol. XVI.

824

sented schematically in fig. 6). At its bottom the vessel A passes
into atube 2, which is in connection by means of a side tube with
a GAEDE-airpump and other auxiliary apparatus to be used in the
filling. The tube £ passes through the bottom of the thermostat,
and is connected with a large pear-shaped mercury bulb by means
of a rubber tube.

@ oe

WAVY

825

At the top of the glass vessel there is a cock a, which, opened,
gives access to the glass tubing dc, which leads to the steel high
pressure cock C. This cock has been specially constructed for the
quantitative transferrence of gases, as was described in these Pro-
ceedings already before. ')

With this cock we reach the second ‘pressure stage”. It
consists chiefly of a large cast-iron vessel of more than 2 /.
capacity, which can be closed at the top with a heavy iron piece
F with bayonet joint and leather packing. This piece / is bored
through and a heavy glass tube /, of more than barometer height,
has been cemented in it. On its bottom this tube /’ is attached to
a glass jar G, of about 1 /. capacity; at its top it passes with a
sealing-wax joint into a steel capillary, which gives a connection
with the high-pressure-cock //, which can shut off the third “pressure
stage’.

The said cock C is fastened to the bottom of the iron vessel D;
the vertical opening is in connection with a thin glass tube /”’, of
a length of at least 80 em. When the piece / with the glass jar @
is placed into the iron vessel, the tube /” gets inside /, as is shown
in the figure. Through an aperture ¢ the vessel D is further in
connection with a steel tube 7, which connects D with the high
pressure-three-way-cock P, where the third pressure stage begins again.
The tube f is again connected with D by means of a steel-to-steel
closure, as was already described in this series of communications”).
On the steel tube /, the end-piece of which is ground conieal, a
double steel cone g is screwed, which is in its turn pressed against
D by means of a flange plate 4 with bolts, fastened in the iron
vessel D’ and nuts. (Cf. fig. 7). The closure of # in D is
elucidated by fig. 7a and 7b. A steel ring /, is pressed into a
leather ring /,, which is V-shaped in section by means of a plate
EH, fastened with serews on F (see the figure). The leather ring
extends through the pressure, presses therefore against / and D,
and effects in this way the closure. / is held in its place by a
piece D, with bayonet joint. When the projecting sectors D, are
rotated so that they get before the opening DV, of the rim D, (see
fig. 75), the piece D, can be taken out, and with it the piece LF
and (.

The highest pressure stage consists in the first place of the obser-
vation vessel proper L, a heavy steel tube of + 1m. length and

1) These Proc. XI, p. 915.
%) These Proc. XV, p. 1024 and fig. 2.
53%

826

1,65 em. bore, which is calculated to resist a pressure of 4000 atm
and is suspended on the ceiling by means of rods. At the bottom

Fig. 7. Fig. 7a.

L. is ‘closed by a shutter piece M, the construction of which we
shall discuss presently. J/ is bored through, and this boring terminates
in a steel tube N (fig. 11), to which the glass observation tube is

Fig. 70.

$27
“
fastened. The other side of the channel in the shutter piece J/ is
connected through a cone and nut A’) with a steel capillary tube
O, which leads to the before mentioned cock Hf. The construction
of this cock appears from fig. 8. The tube O always remains in
communication with the righthand side opening, which opens again
into a steel tube Q’, which leads further to the mercury vessel 2.
By opening or closing the cock H we can, however, bring OQ in
connection with, resp. shut off from the glass jar G in the iron
vessel D. The mercury vessel is by means of a steel tube S, in
communication with a high pressure cock 7”. which can effect or
prevent the communication with the steel tube S,. And finally this
tube JS, again leads to the before mentioned high pressure three-
way cock P. The construction of this cock appears from fig. 9.
The stopper ¢ enly serves to shut off an opening, through which
at the end of an experiment when one wants to lead back the gas
into the jar G, oil can escape. It is seen that S, is always in
communication with a third tube S,, but that a communication can
be made or broken off of |S, and S, with the tube 7 and so with
the second pressure stage by the opening or the closure of P. S,
terminates in a T-piece U/, which on one side is in communication
through the tube S, with the upper side of the observation vessel
Lin entirely the same way as the tube O with the bottom side,

S52

Fig. 9. Cock P.
on the other side through S, with the hydrostatic press, which
causes the pressure.

1) Cf. the description of these connections lower down.

828

By the aid of this arrangement it is now possible to fill the
measuring tube, which is fastened at NM on the piece M with the
gas that is to be measured, this glass tube being always subjected
to the same pressure on the inside and on the outside.

After the whole system of tubes and all the cocks ete. have been
cleaned, the mercury vessel # is filled entirely, and the vessel D
half with mereury. By the application of a slight pressure the
mereury in Q' rises, and fills the whole tube Q up to the cock H.
Then the cock 7’ is closed, so that the mercury in Q cannot moye
up and down any longer. When this pressure is applied, the vessel
LZ outside the glass tube has filled with the oil, which is used as
pressure transmission liquid. Now all the cocks except 7’ are opened,
and the whele system A abe Fh” FON is exhausted by means of the
GarpbE-pump. Then the mercury from PD rises in the jar G and
reaches barometric height between /’ and /’. Now the apparatus
may be rinsed once or twice with gas by admitting gas at B by
means of the mercury reservoir, and then making a vacuum with
the Ganpr-pump. If we now want to bring a definite measured
quantity of gas into the measuring tube, we close a, and admit a
quantity of gas into A. When the mercury reservoir is then raised,
a quantity of gas is isolated in A, the pressure, the volume, and the
temperature of which can be determined. If now the glass cock a@
is opened, the gas flows into the exhausted space c/”. Now the
mercury in /’ falls, and by raising the mercury reservoir which is
in communication with 6, we can now expel the gas from A to
D. If we want to do this quantitatively, we must raise the mercury
reservoir so much that the mercury overflows at 6, and fills the
whole tube 6c, and that at last it becomes visible at the upper end
of F. C is then closed. The gas is then under a pressure of about
one atmospkere in the jar D, and further in ON and in the
measuring tube.

By the hydrostatic press, resp. through the way S,US, Pfe we
now increase the pressure. The mercury in DY then descends outside
the jar G and rises inside it, and expels the gas more and more
from the jar towards /’. The pressure in the measuring tube then
rises, of course. But U7 being in communication with Z through S,,
the pressure inside and outside the measuring tube is always the
same. If we want to convey quantitatively, the pressure must be
raised so high that the gas has been entirely expelled by mercury
from G and #’, and the mercury has reached the steel capillary
above F’ and finally A. Then / is closed. Now the communication
between the inside and the outside of the measuring tube is broken.

829

We should, therefore, take care that in this condition no great
variations of pressure can take place, which might make the measur-
ing tube burst. This is controlled by a spring manometer, which
is in connection with the hydrostatic press. In the operation it appears,
however, that a few atmospheres’ difference of pressure is not yet
dangerous to the measuring tube. The dimensions of the measuring
tube must be so chosen in proportion to the jar G that all the gas
has been expelled from G and /’ by mercury before 80 to 100 atm.
have been reached, as the unprotected glass tube /’ cannot resist a
higher pressure. Now P is closed. This separates the high pressure
division, in which the measurements take place, entirely from the
second pressure stage, D ete. For // has already been closed (see above).
Now 7 is opened. This opens again the communication (by the
way S, US, PS, TS, RQHO) between the inside and the outside
of the measuring tube. If we now continue to raise the pressure by
the hydrostatic press, the mercury rises in Hf resp. O, and pushes
the gas further and further above it, till at last the mercury reaches
the tube \V and then the measuring tube. Still further increase of
pressure then brings the mercury into contact with the platinum
contacts in the measuring tube one after another. All through the
measuring tube remains constantly exposed to the same pressure
on the inside and on the outside. When we want to suspend the
measurements temporarily, this continues to be the case. For then
a cock in the hydrostatic press is closed which shuts the
conduit S,. The closure of the apparatus is so perfect that
when this cock is closed the high pressure stage (LHRTPU, and
the connecting system of tubes) can be left at a few hundreds
of atm.’s pressure for weeks, without a trace of leakage being
observed.

This perfect closure is obtained by the application of steel-to-
steel closure everywhere. Only in the cock 7’ it is inevitable that
liquid under high pressure is in contact with packing material. (In
the cocks P and // there is of course also packing material, but
this packing material belongs to the second “pressure stage’’).

All the couplings are again of the system indicated in fig. 7 and 8,
of course modified according to circumstances at the different places.
Thus the couplings for the cock P are represented by fig. 9. A
steel cone y is always found, which is then pressed against the piece
with which it is to be connected by a nut A or the flange plate h.
Jn the former case the thread of the screw is left-handed, so that
when the nuts A are turned on, the cone is screwed tighter, instead
of being unscrewed. This precaution is unnecessary in case of a

830

flange plate (fig. 7 and 9). The flange plate is pressed tight by bolts
and nuts.

We must discuss the piece J/, on which the glass measuring tube
is fastened, somewhat more fully. This fastening seemed an insuperable
difficulty for a long time. We have said up to now that the pressure
inside and outside the measuring tube was the same; this is true,
however, only by approximation. For the way R Q OM WN is filled
with mereury, the way RS )S,S,S, with oil, and the difference of
height of the measuring tube and & certainly amounting to 1.5 m.,
there prevails a pressure inside the measuring tube of about 2 atm.
less than outside it. The different kinds of cement which we used
to fasten the measuring tube on WV (CaiLLerer cement, with or without
shellac, sealing wax, also packing material put between, such as
ivory) were always cracked by the pressure, even though sometimes
only invisible cracks arose. On account of the excess of pressure
outside, oil then entered the tube from the outside, and rendered the
measurements impossible by contamination of the mercury.

At last it was resolved to platinize the measuring tube over some
centimeters’ distance on the bottom side, to coat this with copper,
and then to solder it to the copper tube / fastened on the steel piece
N (Fig. 10). Now it seemed that a solution was found, but a new
difficulty presented itself. When pressure brought the mereury into
the tube, it could come in contact with the tin when it passed the
place of soldering, and the amalgam formed contaminated the
measuring tube. To prevent this the tube was lengthened at the
bottom by a conical piece /, which titted in a conical part of the
steel pipe .V. Though it was tried, besides, to improve this closure
with zapon lac, the place of soldering was not yet sufficiently
protected. We then drew out the measuring tube some centimeters
into a point m. When the gas is compressed in the tube, part of it will
be enclosed in the small space 7 outside the drawn-out point. We must
then for the present give up the thought of a quantitative transferrence
of a quantity of gas. Besides, care should always be taken that
during the measurement of isotherms the mercury does not get below
the drawn-out point m, because then the quantity of gas in the
measuring tube might change. but that the soldering place now
remains separated from the mercury by gas up to high pressures,
is at present an indispensable advantage.

In the steel piece 7 there are four passages p, and through each
of them passes an insulated wire. The passages end at the top ina
conical widening. In this fits a conical ivory ring 7, and in this a
copper cone g. The wire insulated by the passage is soldered to the

831

bottom side of the cone. The upper side of tsvo of these cones is
connected. with beginning and end point of the volume wire. Only

Fig. 10.

the upper side is under pressure, and everything is close fitting on
account of the conieal form, so that now we have an insulated elec-
trical connection with the measuring tube.

A glass tube closed at the top, on which a platinum wire is
wound bifilarly is hung on the measuring tube. The ends of the
wire are connected with the two other copper cones.

We shall come back to this in the description of the temperature
measurement.

832
The hydrostatic press.

The pressure is furnished by a ScHArrer and BupenserG hydro-
static press of the known construction, only heavier than usual
according to the circumstances. This press is provided with 4 cocks

to the apparatus

to the pressure balance

lo the fore pump

Fig. 11.

(fig. 11). The tube |S, is in connection with one of them V,, and
it is this cock that is turned off when in the evening the work is
suspended after the measuring tube has been filled with gas. (ef.
above p. 829). V, can open, resp. break off the communication
with the large pressure balance. Here the tube ends, which joins
the pump with the “head” A and the space C' (fig. 1) of the
pressure balance. All the couplings are effected steel to steel as
above. V, is the exit-valve, V, bars the way to the fore pump.
This fore pump is an ordinary oil suction- and forcing pump, which
can carry the pressure up to 800 atm. So when the whole space
beyond V, has been filled up to that pressure, V, is closed, and
the pressure is further increased by means of the large wheel of
the press. On the way between V, and the fore pump there is still
a 4-ptece. The branch way which is formed here, may be shut
off by a high-pressure cock of ordinary construction. This branch

833

way leads on one side to the “head” of the little pressure balance,
on the other side to an accurate spring-manometer, which can
indicate up to 300 atm. As has been said above, during the
time that there is no communication between inside and outside of
the measuring tube the pressure is regulated with the aid of this
spring manometer.

On the large press stands a large spring manometer of SCHAFFHR
and BupENBERG, which can be used up to 5000 atm.; it serves for
a preliminary orientation about the prevailing pressure.

C. The temperature measurement.

It was originally the intention to measure the temperature im-
mediately by the side of the measuring tube, so inside the vessel L.
The third and fourth insulated wires in the piece J/ were at first
destined for this purpose. But an accurate preliminary investigation,
directed to this end, showed that no accurate temperature measure-
ment could thus be attained. For as Lisenr and Lussana have already
demonstrated, the resistance of a metal wire does not only change
in consequence of the temperature, but also through the pressure.
And this latter variation appeared to be by no means regular. After
increase of pressure a wire sometimes returned to its original re-
sistance at atmospheric pressure, sometimes permanent changes of
resistance appeared. Besides it would have to be ascertained empiri-
cally separately for every wire, how much the change of the resist-
ance with the pressure is, for these changes are by no means equal
for wires of seerhingly the same material. It is, however, required
for such a gauging of the resistance wire that the wire can be
placed under different pressures in the pressure apparatus, the tem-
perature being left constant. This can practically not be achieved in
another way than by enclosing the whole pressure apparatus in a
thermostat, and by taking, under the necessary precautions, the tem-
perature of the thermostat for the temperature of the resistance wire
under pressure. But then it is much simpler to apply the same thing
directly in the measurements, and assume then too the temperature
of the vessel ZL and its contents to be equal to that of the surround-
ing thermostat.

A thermoscope inside L is, however, indispensable then. In conse-
quence of the compression, resp. dilatation heat of the gas in the
measuring tube, namely, variations of temperature of the magnitude
of one degree occur inside L. If there is no thermoscope inside L,
much time may be needlessly lost in making sure that the stationary

834
state has returned in “4. The bifilarly wound wire now, placed on
the top of the measuring tube (ef. p. 831) supplies the want of sueh
a thermoscope. This resistance is led outside by the third and fourth
insulated wires of the piece J/, and brought in connection with a
Whearstonre bridge. The galvanometer of this combination indicates
if the stationary state has set in.

Separate experiments made at atmospheric pressure, so that a
resistance thermometer can be put in the space inside L, and moved
to and fro, have proved that when the stationary state in ZL has
set in, the same temperature prevails everywhere in L; at least for
the temperature at the top and the bottom of L (making use of the
thermostat which is to be described presently) no difference of 0°,01
could be demonstrated.

It also appeared that the temperature measured within Z and in
the thermostat that surrounds 4, agreed to within the same amount.
This was, however, not the case until not only the whole piece JZ,
but also the closing pieces J, projecting at the top and at the bottom,
and a part of the adjoining tubes had been enclosed in the thermostat.
In a smaller apparatus constructed first, in which the extremities of
L projected outside the thermostat, differences of the order of
magnitude of 1° could be demonstrated inside Z.

The arrangement of the thermostat can be sketched in a few
words. Round ZL on a steel cable W, which rfins over pulleys
fastened to the ceiling, hangs a plate-iron cylindre jacket Z balanced
by counterpoises ; it can be slid up and down a few d.m. On the
tube O, which leads from the eock H to JZ is placed oiltight by
by means of a packing box an iron circular plate X, whose section
is a little larger than that of the cylindre. At its bottom the cylindre
carries a flange, which can be fastened by bolts and nuts on the
plate, when the closing piece J and the tube U have been sufficiently
screwed tight by means of the nut A’ belonging to it. A leather
packing between flange and plate renders this closure oiltight. The
cylindre jacket remains open at the top. An oil pump worked by
the repeatedly mentioned transmission shaft then fills the whole
thermostat with oil from the large iron store reservoir. By means
of a stop-cock fastened in the plate Y (not drawn) and a hard lead
tubing connected with it, the oil can again be collected in this store
reservoir. In a fixed position attached to the cylindre jacket, and
therefore moving up and down with it is a stirrer, which when it
has been put in its place can again be set going by the transmission
shaft. Inside the cylindre a large toluol thermoregulator is suspended,
which is in connection with a gas flame which plays against the

835

plate-iron cylindre jacket. By its aid the temperature can be easily
kept constant to within 0°.01.

The temperature is determined by a platinum resistance thermo-
meter, which is inserted in a Wueatstonn bridge formed by a
Hartmann and brawn resistance box. The galvanometer is a HARTMANN
and Braun mirror galvanometer. The image of the incandescent rod
of a Nernst-lamp is thrown by a mirror and a lens on a large
seale fastened on the wall. The sensitiveness of the instrument is
such that a deviation of 0°.01 corresponds with a deviation of about
6 em. on the scale. So it can be seen all through tie room whether
the temperature remains constant, resp. how much it changes. The
indication of the thermoscope inside / is thrown on this screen in
the same way (only the Nernst-burner has here two incandescent
rods to distinguish it). Accordingly the observer, who is engaged
with the pressure balance or some other part of the apparatus, can
ascertain from far whether the stationary state has set in.

The resistance thermometer is gauged with the same leads and
in the same bridge arrangement as that with which the measurements
take place. For this purpose it is placed by the side of the chief-
temperature-normal of the laboratory in a tube filled with oil in the
thermostat which surrounds the vessel 4; the temperature is here
kept constant in the ordinary way.

Amsterdam. Physical Lab. of the University.

Botany. — “Experiments on Hybridisation with Canna indica.”
By J. A. Honinc. (Communicated by Prof. F. A. F.C. Wenr.)

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

Among the plants which my Javanese gardener planted in the
beginning of 1910 in order to make the empty space round the
house look somewhat like a garden, there were two varieties of
Canna, which occurred as escapes on the high bank of the Deli river.
One of them had leaves entirely green, green bracts, a green stem,
small red flowers, with yellowish labellum and fruits, which in an
unripe condition are green. This variety completely corresponds to
the plants, grown from seeds, which I received as Canna indica
from the Botanic gardens of Buitenzorg. The other had somewhat
darker leaves with a red edge and the flowers were also of a some-
what darker red. Further the stem was dark red as were the conical
papillae on the unripe fruits.

836

If Bauer’s “Hinfiihrung in die experimentelle Vererbungslehre”
had af that time already appeared, I should probably have chosen
two other forms, differimg in more characters, in order to be able
to investigate whether there exists a connection between reduction-
division and Mendelian segregation, as Bavurr considers possible.
Since there are only 38 chromosomes in the reproductive-cells of
Canna indica, only three characters can independently segregate
according to Mendel, if the hybrid-segregation is based on the division
of the chromosomes of the parents.

The chance that two varieties, which only differ outwardly by
ihe possession and absence of a red colour in almost all their aerial
organs, might differ in more than three characters, is at first sight
small. Yet this must be the case here, because from the proportions
in which the sclf-pollinated “red” plants segregate as well as from
those of the second generation of hybrids it is seen that even for
the red edge of the leaves alone the cooperation of three factors is
necessary, whilst the colour of the fruits requires at least one additional
factor. For this reason the hybridisations have from a theoretical
standpoint become of greater importance than I at first suspected.

The Canna indica without the red colouring matter has remained
constant to the fourth generation. I have had in all 165 specimens,
descendants of 14 mother-plants. All are descended from a single
“oreen” (7 11.

he “red” Canna on sowing was seen to be a hybrid. Only
from two specimens, & 4 and Fk 13 did I obtain seeds by self-
pollination, from most of the others only a little seed after free-
pollination. This fact makes it probable that these plants were
homozygotically “red”, because later I very often got few seeds or
none from the pure “red” individuals and a sufficient number from
the hybrids. Seeds were obtained after self-pollination from 20 des-
cendants of A 4 and from 25 of R 13 and although in many
cases the proportions, by reason of the small number of specimens,
were not wholly certain, yet it was established that segregation
occurs in three different ways:

a. In the proportion 3:1 (e.g. 27 red and 10 green; 44 red and
15 green; 69 red and 19 green; 24 red and 8 green).

/. In the proportion 9:7 (e.g. 146 red and 123 green |theoreti-
cally 151.2 red and 117.7 green]; 53 red and 38 green |theoreti-
cally 51.2 red and 39.8 green]; 31 red and 24 green [theor. 30.9
and 24.1]; 41 red and 29 green [theor. 39.4 and 30.6)).

c. As 27:37 (7 red and 10 green |theor. 7.2 and 9.8]; 11 red
and 15 green {theor. 11.0 and 15.0].

837

These proportions suggest segregation according to three Mendelian
factors and this is also completely confirmed by the proportion of
the second generation of hybrids. By means of the character of the
red leaf-edge the ‘red’ Canna can therefore be represented as
AABBCC and the pure green G 11 as aabbec.

Since R4 (9 red and 4 green), R4—1 (27 red and 10 green),
R4—1--1 (19 red and 7 green) and also the 4» generation
R4—i—1—1 (10 red and 8 green) segregate according to 3:1,
R4 must, at least if it is assumed that the three factors are ind e-
pendent of one another, be heterozygotic for one of these three
and homozygotic for the other two, eg. AaBBCC, which in the
following generation gives 1 AABBCC: 2 AaBBCC:1 aaBBCC. But
in that case descendants of R4 must segregate according to 3:1
in so far as they are not pure “red” or “green”. However R 4—1—11
segregated as 9:7 (146 red and 123 green) and R 4—1—14 likewise
(53 red and 38 green), These can therefore be represented for example
as AaBbCC or AaBBCc, because they are clearly heterogyzotic for
two factors instead of for one. Since now AaBbCC cannot be directly
derived from AaBBCC, we know that the representation AaBBCC
for A 4 is incorrect and that 24 also must have been heterozygotic
for at least two factors, but behaved as if this was so for only one
factor and that therefore in their Mendelian behaviour these two
factors were not independent of each other.

If we apply this same reasoning to Rk 13—1, which in like
manner segregates as 3:1 (namely 20 red and 9 green), whilst
FR 13—1—13 separates in the proportion 27 :.37 (7 red and 10 green)
then we come to the conelusion that R 13—1 must have been
heterozygotic for three factors, therefore Aa Bb Cc, and nevertheless
behaved as a hybrid with only one half-representative factor, in
other words, the three factors were not independent
but correlated as if there were only the one.

This is established by the second generation of crossing of “pure
red” with “pure green”. All the specimens of /', correspond to the
formula Aa bb Ce. Yet segregation took place in 42, as was also
the case with the self-pollinated offspring of R4 and R13, not only
according to 27:37, but also in the proportions 3:1 and 9: 7,
a3 the following table shows.

Probably it is no great error to say when considering all the
cases with more “green” than “red” individuals that they segregate
in the proportion of 27 red to 37 green, those with slightly more
“red” than “green” ones as belonging to those which segregate as
9:7 and thirdly, the cases with more than twice as many “ved”

838

di) AV BsIEsE:

Segregation in the second generation of hybrids after crossing of green with
pure red-edged specimens.

Second generation Theoretically
First generation ante = | = ee |
ber | red heey red fags
(G11—5) X(R13-4)R1 | 31 | 14) eat 27: 37 13.1 | ae
RSiaiieole |e 29 eal eee? 9:7 2B eA lmezeS
RA | 25 i A2e iets 21: 37? = &
(R134) X(GII—6)R1 | 52 | 28 | 24 9:7 29.25 | 22.75
R2 }_39 | 21 | 18 9:7 1Ore|) aren
(R 4—1) X(GN=5)R1 7 222 | 95 | 127 27: 37 93.6 | 128.3
R2 | 23 | 10 | 13 27 : 37 9.7 | 13.3
R318 | 8 | 10 27 : 37? = —
R4 | 195 | 83 | 112 Pe Sy] 82:3. | JIB
R5 | 58 | 28 | 30 27 : 312 24.5 | 33.5
Ro | 62 | 45 | 17 3:1 46.5 | 15.5
Ri Vial son | Al 21: 37 32.5 | 44.5
(R4-7)<(R4-4green)R 1 18 7 ll Zee Shp = “=
Roca) ate eas 9 27: 372 = =
R5 | 13 | 9 4 Sienise = =
R6 | 16 | 10 6 Ore at =
RT MhiS8h lS ale 20 21: 372 es =

as “green” as belonging to the category of those segregative as 3: 1.
When the figures of these three groups are added, the agreement of
the totals with the figures is, | think, complete :
op ee Se
Cc p,
Nature | Found Calevicvee
of segregation

red |green| red | green

| | | |
According to 3: 1 54 21 56525) |) 185

9:7 88 | 70 88.9 | 69.1

”)

27: 37| 319 | 403 |304.6 | 417.4

”

Parents which have a hybrid nature for three factors, can there-
fore distribute these three factors to their off-spring in different ways

839

and in such a manner that the proportional figures show that either
all three segregate independently of one another, or that two are
correlated and the third remains free or that all three are correlated.

On Bavr’s hypothesis this phenomenon is easily explained. The
factors A, 5, and C' may be distributed over the three chromosomes
as follows:

1. A, B, and C all in 1 chromosome, e.g. in /.

2. A and £6 together in one chromosome, e.g. in / and C' in
another, e.g, //.

3. A, B, and C in three different chromosomes e.g. A in J, B in
JE OOO Te IE

By substitution all other possible combinations can be found, which,
however, give no other proportional figures than the examples given,
which can be represented, as on page 148 of this book Baur repre-
sents them, e.g. by black for the chromosomes of the “red” plants
and white for the “green” ones. The formulae of the reproductive
cells appear then as follows:

IL
Zz
ZZ hi
[7
oi 0
Figure case | case I] ease II]
i ABC : A BC AB (6!
2 ABC ABC ABe
3 ABC ABe AbC
4 ABC ABe Abe
5 abe abc aBC
6 abe abC aBe
7 abe abe abc
8 abe abe abe
Number of combinations 2 4 8

o4
Proceedings Royal Acad. Amsterdam. Vol. XVI.

540

In the first case there arise only germ-cells of the constitution
ABC and abc. With self-pollination therefore segregation of 3 “red”
to 1 “green” must follow. In the second case there are four kinds
of pollen-grains and four kinds of ova, whereby /, will segregate
in the proportion of 9 “red” to 7 “green”. In the third case there
are eight different reproductive cells and segregation takes place in
the proportion of 27 “red” to 37 ‘green’.

Baur’s hypothetical example of Cannas, which differ in 3 char-
acters, refers to one leaf-, one stem-, and one floral character, which
should show independent Mendelian behaviour. We now find that,
if we hold to the existing ideas, three leaf characters, which one
might perhaps be inclined to assume were in one chromosome,
behave, as though they might be distributed over two or three
chromosomes, which would be an argument for the dissolution and
mixing-up of the chromosomes in the synapsis-stage.

The 17 green examples from (R 4—7) « (G@11—5) R6 have all
been planted out, most of them however died and only 6 grew
large enough to ascertain definitely that their leaf-edge completely
corresponded with the pure “green” descendants of G 11. They may
therefore indeed be represented as aabhcc. With respect to the fruits
however they differ. Whilst those from G11 and _ their offspring
possess at most a hardly noticeable red apex on some of the little
cones of the fruit wall, the ovaries of one of the “green” examples
of (R4—7) x (@11—5) R6 were clearly red, as was the case in
some of the examples, which had no red at all in the leaf-margin,
from (R4—7) « (G11—5) R,. A sister-specimen had, however, green
ovaries, so that for the factor red in the fruits the segregation indeed
occurs, independently therefore of the three leaf-edge factors, which

remain associated.

The great variability of the red in the fruits, even in one and
the same plant, is the reason for my failure to determine with
certainty the number of factors for it. I can only say that at least
one of them can behave as if it were independent of the three leaf-
edge factors.

So far the segregation of “red” and “green” has been spoken of
as if all “ereen” individuals were alike. In reality however this is
not so. With sowings, not older than 1 to 2 months, no distinction
can be made other than that between red-edged and green,
because nothing more can then be seen. If however ‘green’
specimens are planted out, then a few months later it is found that
some only are wholly green, as G11, but other specimens show a
narrow red edge on the upper half of the leaf, most distinetly at

841

the apex of the young rolled-up leaves. This is the only one of the
three factors which becomes separately visible. When it is present
heterozygotically, segregation takes place in the proportion of 3 with
and 1 without, for example, from /4—2 (green) — 3 I obtained
46 large plants, of which 35 had the narrow red edge and 11 were
without it. In the same way out of 35 specimens from 2 13—1—1
(green) 27 had it and 8 were without it.

In F2 of the crosses this segregation is also seen. Of 125 “green”
examples of (R 4—7) & (@11—5) R1 I obtained only 51 in bloom,
the others died by the continuous rain. With segregation in the
proportion of 27:37 (see the table) 8716 = 21 plants must occur,
which show the narrow red edge, as against 16 real “green” ones.
Calculated according to the proportion the number of those with
the narrow red edge is 28.94 and of “green” ones 22.05. The
figures found were 30 and 21, certainly a sufficient agreement. It
is perhaps not unnecessary to add that the 6 specimens which
remained from the 16 “green” ones from (ft 4—7 * (G 11—5) R6,
were really “green”, without the narrow red edge on the leaves.

New crossings of the same two forms but of different origin
have in the meantime been made, as also the crossing of R13—4—s5
with Canna glauea, which differ in at least ten characters and
probably in still more. The whole /'1 generation is however up
to the present only one specimen, of which the fertility is still
doubtful. The leaf shape is intermediate between ‘that of the parents:
the leaves have still something of the wax-like appearance of the

mother and the red edge of the father.
Medan (Sumatra), January 1914.

Chemistry. — “Hyuwilibiia in ternary systems.’ XIII. By Prof. F.
A. H. SOHREINEMAKERS.

Now we consider the case, that the substance F’ is one of the
components; it is evident that we can deduce then the saturation-
curves under their own vapourpressure and the boilingpointeurves
in the same way as is done in the previous communications for a
ternary and a binary compound.

We take the component / as solid substance and now we choose
a 7’ and P in such a way, that no vapour is formed and the
isotherm consists only of the saturationcurve rs of fig. 1, On decrease
of pressure anywhere a gasregion and the region LG occur. These
regions may arise in different points; in fig, 1 the region LG, the

54*

S42

liquideurve of which is indicated by ed, may be imagined arisen in
C. Also two or more of these regions can be formed in different
points of the triangle and they can later disappear and come together
in different ways.

We may now distinguish several principal cases, according to the
appearances in the binary systems BC and BA.

I. Neither in the binary system AC’ nor in the binary system BA
the equilibrium liquid—gas shows a point of maximum- or of
minimumpressure.

II. In the binary system BC or in the binary system AB or in
both these systems the equilibrium liquid—gas shows a point of
maximum- or minimum pressure. We only consider the first case,
so that a region LG intersects-only once as well the side BC as
the side LBA. We may distinguish the following cases :

1°. on decrease of pressure or increase of 7’ the region LG shifts
with its liquidline ahead along CB from C to 6, and along AB
from A to B.

2°. On decrease of pressure or increase of 7’ the region LG shifts
with its liquideurve ahead along LC from B to C, and along BA
from 6 to A. Consequently the movement is opposite to that sub 1°.
3°. On decrease of pressure or increase of 7’ the region LG shifts
with its liquideurve ahead firstly along CB from C to B, and after
this along BA from B to A or reversally from A along B to C.

In the case mentioned sub 1°.
it is to be imagined e.g., that the
gasregion arises on decrease of
pressure in C' (fig. 1), expands
then across the triangle, and attains
at last the point 4. The one
extremity of the region LG shifts
then on decrease of pressure with
its liquid line ahead from C'to B,
the other firstly from C to A and
subsequently from A to B. This
case may also be imagined. when

the gasregion arises in A or in a point of CA or anywhere within
the triangle. This case may yet also be imagined, when different
eas regions arise, e.g. in A and C, which coincide afterwards.

In the case sub 2° it is to be imagined, that the gasregion arises
in 6 on decrease of pressure; fy (fig. 1) may then represent the

8438

liquideurve of a region LG; the dotted curve situated in the vicinity
is the vapourcurve. On decrease of pressure this region LG’ shifts
along BC from B to. C and along BA from B to A.

In the case sub 3° we may imagine e.g. that on decrease of
pressure the region LG arises in C and disappears in A. On decrease
of pressure this region shifts with its liquideurve ahead along BC
from C to £ and along C4 from C to A. When the one extremity
is in 4, the other is still somewhere on CA: in fig. 1 Bu is the
liquideurve and Su, is the vapourcurve of a similar region. On
further decrease of pressure this region shifts towards point A; as
soon as the one extremity has left point 4, it obtains of course again
a certain breadth.

Let us at first consider the equilibrium B-+ ZL -+ G of the binary
system LC. If we represent the quantity of C in the liquid by y
and in the vapour by y, we have:

TO AWG,
(ESE LS) ME SG MALL oe en ee BG)
aT AV,
wherein:
A W,, YI r r Yy r
- == H, — y ——(H—n) en A Vy = V,—v——(V—v). (2)
le y y ,

Under a lower P and at a lower 7’ A WV, and AJ’, are positive.
Under a lower P and at a lower 7 the P7-curve will therefore
consist of an ascendant part. The question is whether this curve
will show in its subsequent course a point of maximum pressure
and a point of maximum temperature.

We shall call, as 6 is the solid substance, C' the solvent. y, <<y
means then, that the concentration of the solvent is smaller in the
vapour than in the liquid; or also (as 1—y, >> 1—y) that the con-
centration of the solid substance in the vapour is greater than in
the liquid. We shall express this in the following way: the solvent
is less volatile than the solid substance. y, >; means then: the
solvent is more volatile than the solid substance. We now distinguish
two cases.

y, < y. As H,—y is greater than H—y and V,—v > V—,
AW, and AV, can never become zero or negative. Therefore the
P, T-curve consists only of a part ascending with the temperature,
without a point of maximum pressure or of maximum temperature ;
it has its highest P and 7 in the minimum meltingpoint of the
solid substance.

y, >y. When y,:y is greater than 1, this quotient can yet be
smaller than (//,—y): (4H—1), so that in the P,7-curve the point
of maximum pressure and of maximum temperature are wanting.

S44

When however ¥,:7 becomes greater than (/7,—) : (H/— 4), while
it remains smaller than (V,—v):(V—v), only AW, can become
= 0 and consequently only a point of maximum pressure occurs.

In order that AV, may also become =0, V—v>0O and
as |’,—v is ordinarily ten thousand times as great as V—v, y,:y
must obtain a very great value. As A W, and AV, may become
=O, the P, 7-curve has then a point of maximum pressure and of
maximum temperature. Therefore we find: the P, 7-curve of the
binary equilibrium B-+ 1+ G is a curve ascending with the tem-
perature, when the solvent is less volatile or only a little more
volatile than the solid substance; it may show a point of maximum
pressure when the solvent is much more volatile than the solid sub-
stance; it may have, besides a point of maximum pressure, also a
point of maximum temperature, when the solvent is a thousand
times more volatile than the solid substance and this melts with
increase of volume. *)

Let us now consider the saturationcurves under their own vapour-
pressure of 8. For this we take firstly the case sub 1. We now
choose the P and 7 in such a way, that the saturationcurve of B
is represented by 7s and the liquideurve of the region LG by ed
in fig. 1. On decrease of pressure ed approaches to 7s. We assume
that the tirst common point arises by the coincidence of 7 and: s.
This point is represented in fig. 2 by /. In the same way as for
the case that the solid substance is a binary compound we can
prove, that ed and rs do not touch one another in h and that
although P;, is the highest pressure, under which the system
F+L+G oceurs, the point 4 is yet not a point of maximum
pressure of the saturationcurve under its Own vapourpressure. The
vapour corresponding with / is indicated in fig. 2 by 4,.

Lowering the pressure. still
more, the intersectingpoint of
ed and 7s of fig. 1, shifts
within the triangle; in fig. 2
a similar intersecting point is
represented by a and the cor-
responding vapourpoint by a.
From the manner in which the
three phase triangle arises, it
follows, that this must turn its

Nig. 2. side solid-gas (Ba,) towards BC.
When on further decrease of pressure the curves ed and’7s of

1) See also Pu. Kounstamm; these communications 15, (1907).

845

fig. 1 continue to intersect one another only in one point, under a
pressure P, the points s and d of fig. 1 coincide in a point 7 of
fig. 2; curve ed is then situated completely within the sector Br s.
Now the saturationcurve under its own vapourpressure is represented
in fig. 2 by dn and the corresponding vapoureurve by /,7, ; the pressure
increases in the direction of the arrows, therefore from 2 towards
h. Consequently P;, is the highest and P, the lowest pressure, under
which tbe equilibrium #’+ L-+ G occurs, 4 not being however a
point of maximum- and 7» a point of minimum pressure of the curve.
Further we see, that on change of pressure, the turning of the
threephase triangles Baa, and Bbb, is in accordance with the
rules formerly deduced.

We have assumed when deducing the above, that the curves ed
and rs of fig. 1 intersect one another only in one point under every
pressure. It is also possible, however, to imagine that after the forma-
tion of the first point of intersection, a second arises by the
coincidence of d and s (fig. 1). The liquideurve of the region LG
proceeds then in fig. 1 from s firstly outside and afterwards within
the sector Ars.On further decrease of pressure the two points of
intersection shift towards one another and coincide under a pressure
P,, in a point m not drawn in the figure; the corresponding vapour-
point m, is then situated on a straight line with m and L. The
pressure P,, is the lowest pressure under which the equilibrium
B+£+G may yet aceur; m and im, are points of minimum
pressure of the curves An and /h,n,.

It is evident from the manner in which arises the threephase
triangle 565, in the vicinity of LA that this now must have another
position than in fig. 2; its conjugation line solid-gas therefore 5d,
must be situated between bb and BA. Two three-phase triangles
situated on both sides of the point of minimum pressure turn there-
fore towards one another their sides solid-liquid.

In the two previous cases we have assumed, that the first common
point of ed and 7s arises by the coincidence of e and 7. We now
assume, that both the curves touch one another in a_ point J/
situated within the triangle; the corresponding vapour point J/, is
then situated on a straight line with J/ and &. The pressure Py, is
the lowest pressure under which the equilibrium 5 + LZ + G occurs.

On decrease of pressure two points of intersection of ed and rs
now arise; the one disappears, when 7 and e, the other when d
and s coincide. We then obtain again a saturationcurve under
its Own vapourpressure as im and a corresponding vapourcurve as
hn, in fig. 2; the points, M/ and /,, which are not drawn, are

S46

points of maximumpressure. It is evident, that in this case we must
imagine in tig. 2 the side Ba of the three phase triangle Baa,
between Ba, and BC.

When we consider in a similar way as above also the cases
sub 2° and 3°, we find:

the saturationcurves under their own vapourpressure have a
terminating point on BC and one on BA (curve An in fig. 2). On
this curve either a point of maximum or of minimum pressure occurs
or there oecurs none. The corresponding vapourcurve is situated with
respect to in in the case sub 1° as h,n,, in the case sub 2° as hyn,
and in the case sub 38° as hyn, (or hn).

Previously we have seen, that the saturationcurves under their own
vapourpressure of a ternary and a binary substance #’ become
exphased at temperatures above the minimum melting point of
F. At the deduetion of these curves for the binary compound
we have seen, that the point of maximum temperature of the binary
system /+L+G takes a prominent position and that these curves
occur in the vicinity of this point [point H in fig. 4—6 (XD}.
The same applies also to the saturation curves under their own
vapourpressure of the component 4; we shall not discuss these
here more in detail as similar appearances occur in the case of the
boilingpoint curve.

Let us now consider the boilingpoint curves of the component B;
firstly we take these curves under pressures lower than the pressure
in the minimum meltingpoint of 4; we then find: the boilingpoint
curves have a terminating point on AC and one on GA (curve
hn in fig. 2); on this curve, either a point of maximum- or minimum
temperature occurs or there is none. The corresponding vapourcurve is
situated with respect to in, in the case sub 1° as h,n,, in the case
2° as fn, and in the case sub 3° as hyn, (or hn,). If it is desired
that in fig. 2 the three phase triangles Baa, and bbb, retain their
position, the arrows must indicate in opposite direction and the
temperature increases, therefore, from / towards 7.

It follows from the previous deductions, in what direction the
threephase triangles solid-liquid-gas turn on change of pressure
at constant 7’), or on change of temperature (under constant P).
From this also follows the influence of a third substance on the
pressure (at constant 7’) or on the temperature (under constant P)
of the binary equilibrium B+ L-+ G.

We may also deduce these results in the following way. We

847

represent the quantity of A of a phase by « (or v,), the quantity of
C by y (or y,), and the quantity of B by 1—v—y (for 1--«7,—y,).
We put, therefore, the origin of our coordinatesystem in the angle
point B, the X-axis along the side BA, and the Y-axis alone the
side BC of the triangie. To the saturationcurve under its own
vapourpressure of B then applies :

(wr +- ys) de -- (as + yi)dy=AdP.'. . . . (8)
[(z, — «) r+ (y, — y)s| da + [(@#, — «)s + (y, — y) t] dy = CdP (A)
In order to have the boilingpoint curves, we must replace in (3)
AdP by — BdT and CdP by — DdT.
In the terminating point of both these curves on the side BC
2= 0. We then find:

?

wy yy % v,
z

1 /dP y 1 dT ya
ae — and — , — = ———.._ (5)
RI dt} —0 A Vy Janik dx Jr—o AWy

In the terminating point of both these curves on the side BA,
y = 0. We then tind:

1 dP y@ I dT = oY
eS (ee ——— sand. — = (OD
TRAE dy y=0 LWe RT° dy y=0 AW,

Herein is:

? zy r yy a
AV, = V, -—-v -- — (V—v) AV, = V, —+« — —(V—»)
a“ ; y
AW, ; AW,
aes): eee pene? ae ae Ht (ay:
IM ip 1 y

From this it is easily found, that the relation 11 (XI) and the
rules deduced from this apply also on the addition of a third
substance to the binary equilibrium B+ 1+ G.

We may in the same way as in the previous communication in-
troduce also in (5) and (6) the perspective concentrations S and S,
of the new substance. Then S is the part cut off by the line B-
liquid, S, the part cut off by the line 4-vapour from the side CA
(fig. 2). When the binary equilibrium 6 -+- L + G is situated on
BC @=9), so that A is the new substance, these parts must of
course been measured from C’; when the binary equilibrium is situ-
ated on LA(y=0), so that C is the new substance, they must be
measured from A.

When the binary equilibrium 4-+ 1 + G is situated on the side
BC (2 = 0}, we find

848

q au , ov,
Se and S, =———
wry ry,

Substituting from this the values of y and y,, in (5), we find:

1 dP 1 ae i S
RT \de Zon AV, eo soe Sy,

1 dT +4 1 os ; =) |
RT? \@eJun LW, « 8,

As S and S, are very small we have equated, (1—S,) : (4—S) = 1.
When the binary equilibrium 5 -+ L -+ G is situated on the side
BA (y=0) we tind from (6)

1 dP 1 Y, 1 S
RT Nay py), =1ee Ve ic Gees |

and amereere. 5. (3)

18 sean LY ae v8 |
RE ale a WA, y ( 8,

We see that (7) and (8) are in accordance with (14) and (15) (XI);
we may deduce from this for the addition of a new substance to
the binary equilibrium 6 -+ L-+ G the same rules as was done in
communication XI for the equilibrium #-+ LZ + G. It is however
to be considered with this that now S and S, are positive. We see

oath

and

that the position of the threephase triangles in fig. 2 is in accordance
with these rules.

In communication XII we have deduced in different ways form
and position of the saturationcurves under their own vapourpressure
in the vicinity of the point of maximum temperature and of the
boilingpoint curves in the vicinity of the point of maximum pressure
of the binary equilibrium /’-+ 1 + G.

All this applies also when the solid substance is one of the com-
ponents. We must keep in mind that in the binary system 5+ LZ -+ G
there occurs not always a maximum of pressure and temperature,
which is indeed the case in the binary system /+ 2+ G. For that
reason we shall express these rules now in the following way.

Let in fig. 5 and 6 (XI) H be a point of maximum tempera-
ture of the binary equilibrium £-+ 1+ G. The saturationcurve
under its Own vapourpressure of 4 disappears on increase of 7’ in
H (fig. 5 (X1)|, when the concentration of the new substance in the
liquid is greater than in the vapour; it does not disappear in H
‘fig. 6 (XI)|, when the concentration of the new substance is smaller
in the liquid than in the vapour.

If we imagine in fig. 5 and 6 (XI) H to be replaced by the

849

point of maximum pressure (Q of the equilibrium B-- 1 -+ G and
the arrows in opposite direction, then we have: on increase of 1
the boilingpoint curve disappears in Q |fig. 5 (XI)|, when the con-
centration of the new substance is greater in the liquid than in the
vapour; it does not disappear in Q |fig. 6 (XI)], when the concen-
tration of the new substance is smaller in the liquid than in the vapour.

Of course we have meant above with concentration the perspective
concentration.

From the meaning of the perspective concentrations S and )S, of
a new substance, it follows immediately :

for equilibria in the vicinity of the side BC («#—0):

when S> 8, then also y,:y >> a@,:a and reversally,
VISION err ee Cameco shah alk ”

for equilibria in the vicinity of the side BA (y=0):

when S > 5S, then also x,: «> y,:y and reversally,
WGHET SIG St ch tae aya Nh :

On increase of pressure the boilingpointeurve in of fig. 2 changes
its position and form in order to disappear at last. This may take
place in different ways which we shall consider now. We have seen
at the deduction of the boilingpointeurves of the binary compound /’,
that the point of maximum pressure Q of the binary system /’-- 1 + G4
takes a prominent position, it is evident that this is also the case
with the boilingpoint curves of the substance 2.

We saw before that we may distingnish the three cases men-
tioned sub 1°, 2°, and 3° with regard to the movement of the
region LG on decrease of P or increase of 7. In the case mentioned
sub 1° as well the solvent Cas A is more volatile than the solid
substance 5. Therefore a point of maximum pressure of the binary
equilibrium b+ 1+ G can be situated either on BC' or not; the
same applies to the side BA.

In the case sub 2° both the solvents A and C' are less volatile
than the substance 4; therefore neither on BA nor on BC can a
point of maximum pressure be situated.

In the ease mentioned sub 3° C' is more volatile. A however less
volatile than the substance 4; therefore on BC either a point of maxi-
mum pressure occurs or it does not; this is however not possible on DA.

With regard to the occurrence of a point of maximum pressure in
both the binary systems b+ + G, we may, therefore, distinguish
three cases :

a.no point of maximum pressure occurs.
b. one Bi; ie x - LB
c. two’ points ,, i oceur.

850

In the case sub a the pressure of the binary equilibrium B+ 1+G
increases from C' along C4 and from A along AB up to B (fig. 2).
On inerease of pressure the points / and n shift therefore towards
5: under Pz (the pressure of the minimum meltingpoint of B) the
boilingpointeurve disappears in B.

In the case sub 4 one of the binary equilibria B+ L+G has a
maximum pressure, represented in fig. 3 by the point Q. Consequently
the pressure increases from C' along BC up to Q and from A firstly
aiong AB and afterwards along BC up to Q. Under pressures lower
than Pp the boilingpointeurves have therefore one extremity on AB

Ie; and one on BC between C and Q;
under pressures between Pg, and
Pe the one terminating point is situ-
ated on BQ and the other on CQ.

In the vicinity of the point Q the
boilingpointeurves may have two
kinds of form. In fig. 3 we have
assumed that they disappear in Q
on increase of pressure. In the other
C A case, which the reader may draw

Fig. 3. easily himself, there is one touching
the side BC in Q and they disappear in a point within the triangle.
A part of these curves has then necessarily a point of maximum-

and one of minimum temperature.

From the position of the boiling point curves in the vicinity of
the point Q it follows that S>>S, and therefore also y,:y > @,: a
is assumed or in words: if we add to the binary equilibrium 5+ L-+G
situated on the side BC (xo) the substance A, its perspective
concentration is greater in the liquid than in the vapour. If we consider
that AW, is positive between Q and C. and negative between
Q and JW’, then it follows from (5) or (7), that on the boiling point
curves in the vicinity of @ the temperature must increase in the
direction of the arrows.

In the case sub ¢ both the binary equilibria 5-+ L-+ G have a
point of maximum pressure, represented in fig. 4—6 by the points
Q and (Q’. We distinguish three types:

1. in the vicinity of the one point of maximum pressure | Q fig. 4]
S >> S,; in the vicinity of the other [Q’ tig4] S<S..

2. in the vicinity of both the points Q and Q’, S<S, (fig. 5).

3. in the vicinity of both the points Q and Q’ S>S, (fig. 6).

In each of these diagrams the pressure increases therefore along
BC from £6 and C to Q and along BA from B and A to Q’

851

Under pressures lower than P;;, the boiling point curve consists
therefore of one single branch with the one extremity ou CQ and
the other on AQ’; on this curve either a point of maximum (fig. 6)
or a point of minimum temperature (fig. 5) occurs or neither of
these points (fig. 4).

Under the pressure Pg now also the point 4 itself occurs, Pris
viz. the pressure of the minimum melting point or in this case as
#& is one of the components, therefore also the pressure in the

triplepoint of the substance 6; under this pressure exists the unary
equilibrium solid £-+ liquid B-+ vapour £. Consequently the
boilingpointeurve of the pressure Pg consists of a branch with

Fig. 5.

Fig. 6.

852

the one extremity on CQ and the other on AQ’ and of the isolated
point Bb (fig. 4—6).

On further increase of P boilingpointeurves now arise, consisting
of two branches separated from one another. In the vicinity of B
a new branch is viz. formed with the one end on BQ and the
other on bQ’ (fig. 4—6). On further increase of P both the branches
shift towards one another and under a definite pressure Px both
the branches come together in a point Y. This point YX is situated
1". on one of the sides LA or LC, 2°. within the triangle; in the
first case Y coincides with Q or QQ’. In fig. 4and 5 the two branches
come together in Q’, in fig. 6 in a point \ within the triangle.

In fig. 4 and 5 the boilingpointcurve of the pressure Pe forms,
therefore, a single branch. From our previous considerations it follows
that this is curved as a parabola in Q’ and touches the side BA in
this point. The temperature must increase in the direction of the
arrows along this curve in the vicinity of Q’.

On ‘further increase of pressure the boilingpointcurve shifts from
point Q’ (fig. 4 and 5) into the triangle and we may distinguish
two cases. Hither it disappears in the point Q on the side BC (fig. 4)
or it touehes the side BC in the point Q (fig. 5). In the latter case
it shifts on further increase of pressure from the point Q into the
triangle, so that a closed curve arises, which disappears in 2 some-
where within the triangle.

In fig. 6 the point VY in which the two branches of the boiling-
pointcurve come together, is situated within the triangle. Here we
have a case as was treated formerly in communication _X (fig. 5). On
further increase of pressure again two branches are formed, separated
from one another, which are situated now quite different than at first
and on which the points of maximumpressure are wanting. On further
increase of pressure the one disappears in Q and the other in Q’.

Besides the diagrams drawn in figs. 4-6, several others may be
imagined. For instance we may assume that the two branches of
the boilingpointeurve do not disappear in Q and Q’ as in fig. 6,
but that they touch in these points the sides of the triangle. The
boilingpointeurves then consist of two branches separated from one
another, which are both closed, and of which the one disappears
in a point between @ and X and the other in a point between
Q’ and X.

We may consider now more in detail the boilingpointcurves in
the vicinity of the point B; as in this point « becomes = 0 and
ye— 0, we pul:

853

Z=UART (a log a + y log yi +t RT («,-log x, + y, log y,)

We then find for the ean B+L+G in the vicinity of
the point B when we pute =§ 2, =§, y= y¥, =, P= Pp + dP
and T=T,-+dT:

SSS ih GH
RTE§ + RTy — (V—v) dP + (H—m) dT = 0 22 (9)
RTS, + RT, — (V,--v) dP + (H1,— nH) dT = 0
Herein, in order to distinguish the coordinate 4, the entropy of
the solid substance B is represented by ap.
In order to examine the influence of the pressure on the position
of the boilingpointeurves, we eliminate from (9) d7. We then obtain:

BC—AD
eee Oe
v

FD. Re ae eee (IU)

wherein BC — AD > 0. (See Comm. Ll).
When we put in (10) dP = 0, we obtain :
AWE AN, Om ies ove 2 Pathe)

the boilingpointeurve going through the point B.

At lirst we take AW, and AW, negative, so that the case treated
sub ¢ oceurs (fig. 4—6). From (11) it follows that § and 7 have the
opposite sign; the boilingpointcurve of the pressure Pz is situated,
therefore, excepted in the point # itself, completely outside the
triangle.

In figs 4 —6 a similar curve going through the point B is dotted
and a curve situated in the vicinity of B is extended outside the
triangle ; these parts situated outside the triangle have of course no
meaning for us. The direction of the boilingpointeurve going through
the point B, is fixed by 2W, and AW; if accidentally c=, therefore,

z y
also AW, = AW,, then this curve runs parallel to AC,

We now take a pressure somewhat higher than Pz, therefore dP
positive; the second term of (10) is, therefore, negative. From this
it follows that the curve cuts off a positive part 4 from the Y-axis
(BC) and a positive part § from the X-axis (GA), the curve is
situated, therefore, partly within the triangle as in figs 4—6 the
curve in the vicinity of L, partly drawn and partly dotted. In
accordance with what was treated sub c¢ (figs. 4—6) we find, there-
fore, that the boilingpoint curve shifts on increase of P from the
point 6 into the triangle.

In the same way it is apparent from (10) that under a pressure,
somewhat lower than Pz, therefore for /P negative, the curve cuts off a

854

negative part 4 from the Y-axis and also a negative part § froni
the \-axis. The boilingpointcurve is, therefore, situated completely
outside the triangle. Considering only the stable parts, therefore the
parts of these curves situated within the triangle, we can say:

On decrease of P the boilingpointcurve disappears in 5;

On increase of /P it arises in /& and shifts from this point into
the triangle.

The direction of the boilingpointeurve in the vicinity of B is

&
determined according to (10) by QW, and AW,. If we put 2s
: y &

then it follows in absolute value AW, > AW,. If we call the part,
which the curve cuts off from the X-axis (BA) §, and the part
which it cuts off from the Y-axis (BC) ,, then follows from (10)
5, = Yo:

is the ratio of the quantity of C in the vapour and in the

y
liquid, when we add a little C to the unary system solid 6 +
liquid B + vapour 4; we shall call this ratio the limit-ratio of C
in the equilibrium solid 6 + liquid 4 + vapour 4. The same

a “J¢ .
applies to on addition of A. We may now express what precedes
Lv
in such a way: when in the equilibrium solid 6B + liquid B +
vapour B the limit ratio of C is greater than that of A, the boil-
ingpointeurve cuts off a smaller part from the side BC than from
the side BA.

The above-mentioned rule applies only when AW, and AW, are
both negative, therefore, when the P,7-curve of each of the two
binary systems B+ 4+ G proceeds from £6 towards higher
pressures. .

yee é i] Uy, Bs : -

In figs. 4—6 in B is assumed “*>>— in accordance with this

y “
the boilingpointeurve, situated in the vicinity of 4 cuts off from
BC a smaller part than from BA.

When we take AV, and AW, positive, we have the case sub a.
From (10) and (11) it follows that the boilingpoimteurves in the
vicinity of B have the same position as in the case sub c; on change
of P they move, however, in opposite direction. On decrease of P
they shift viz. from £ into the triangle and on increase of P they
disappear in B.

Yy dh TEST i
When we take also here —>—, it follows that AW,<AW,; we
y oP
vow find: when in the equilibrium solid 4 -+ liquid 6 + vapour B the

855

limit-ratio of C is greater than that of A, the boilingpointcurve
cuts off a greater part from the side LC than from the side LA.

In the end AW, and AW, may have an opposite sign, so that
the case sub’ occurs. That there may be accordance with fig. 3, we
take AW, >0O and AW,< 0. From (11) it now follows that §
and » have the same sign, so that the boilingpointeurve going through
B must be situated within the triangle. We see that this is in
accordance with fig. 5.

If the pressure is a little raised, so that ¢/P is positive, it follows
from (10) that the boilingpointeurve cuts off a positive part a from
the Y-axis (BC) and a negative part § from the X-axis (BA).
If the pressure is lowered, so that /P is negative, then we find that
the curve cuts off a negative part 7 from the Y-axis (BC) and a
positive part § from the X-axis (A). If we imagine in fig. 3 some
boilingpointeurves still to be drawn in the vicinity of that going
through B and these extended outside the triangle as the sides AB
and CB, then we see that all this is in accordance with the previous
results. Considering only the parts of the curves, situated within the
triangle, it follows: the terminatingpoint of the boilingpointcurve
going through the point 4 shifts on decrease of P from / on the
side BA and on increase of ? from £ on the side BC.

Now we shall still examine how the temperature changes along a
boilingpointcurve in the vicinity of the point 5. For this we choose
a boilingpointeurve of a definite pressure Py, + dP, so that we must
assign a definite constant value to dP in (9). We then find:

/ ine
AW, at = RP . we = ESOP A Vt male katt)
AW, . dT = RT? e ==) We eE OA Ves 1 dP eee (IS)
wv y

As in (9) the temperature is put equal to T7g+dT, dT is,
therefore calculated from the point 5. Desiring to proceed from
the terminatingpoint of the boilingpointeurve on the Y-axis (BC),
we put d?’=dT", + dT’; herein d7”, is the change of 7’, wanted
to come from the point 4 in the terminatingpoint of the boiling-
pointeurve on the Y-axis and d7’ the change of temperature
from this terminatingpoint aleng the curve. We now have:
Peed... NV, -aP. Substituting in (2d? = dl -4-d7
we obtain:

7
y

; , ape { ¥ U1) 5
ES Wea ey a ( = — ‘ya. oy cea cee C14)
y ed
When we represent the change of temperature along the boiling-
ah)
Proceedings Royal Acad. Amsterdam. Vu!. \VI

856

pointeurve from its terminatingpoint on the X-axis (BA) by
we find from (13):

AW, . at, = Br ( BT i)

Let us firstly consider fig. 8, in the vicinity of the point B of this

figure is AW,<0 and A W,>0, therefore " Soe From (14)
-

and (15) it now follows that d7, and d7, are both negative. This

means that on a_ boilingpointeurve, situated in the vicinity of B,

the temperature decreases from the terminatingpoint sitpated in the

vicinity of 6. This is in accordance with fig. 3.

In fig. 4—6 we will assume a ee in order to remain in aceord-
ance with the direction of the boilingpointeurves, situated in the
vicinity of 6. As 4 W, and 4 W, are both negative, it follows from
(14) and (15) that d7, <0 and d7, >9. On a boilingpointeurve
situated in the vicinity of 6 the pressure, therefore, increases from
the terminatingpsint on BA (d7, >0) and it decreases from the
terminatingpoint on LC (d7,< 0). In conjunction with the length
of the parts, cut off by the curves from the sides BA and BC, we
may express this also in the following way: along a boilingpoint-
curve situated in the vicinity of B the teniperature increases in that
direction, in which this curve comes nearer to & (fig. 4—6).

In the case sub a A JV, and A Wy are both positive, we now
find the same rule as above for the change of temperature along a
boilingpointeurve situated in the vicinity of 2.

We may give a short résumé of some of the previous results in
the following way. For this we assume that in the equilibrium
solid B+ liquid b+ vapour 6 the limit-ratio of C' is greater than
that of A.

The two binary P,7-curves proceed from the point B towards
lower pressures ; consequently no point of maximumpressure occurs
[A W,>0 and A W, > 0; case sub a]. A boilingpointeurve situated
in the vicinity of B cuts off from the side BC a greater part than
from the side LA. The curve comes on decrease of P within the triangle.

6) One of the two binary 7, 7-curves proceeds from B towards lower
pressures and one towards higher pressures, consequently one point
of maximumpressure occurs [A IV, > 0 and A W,< 0; ease sub d.
fig. 3). The boilingpointeurve cuts off under pressures, somewhat
higher than Pp, a part from LC, under pressures, somewhat lower

857

than Pp, a part from BA. The curve remains, therefore, within the
triangle as well on inerease as on decrease of P.

c) Both the binary P, 7-curves proceed from the point 5 towards
higher pressures ; consequently two points of maximumpressure occur
[W.<0, A Wy<0; case sub c; fig. 4—6]. A boilingpointeurve
situated in the vicinity of B cuts off from the side LC a smaller
part than from the side BA. The curve comes, on increase of P,
within the triangle.

In each of the cases, mentioned sub a, 6, c, the temperature along
a boilingpointeurve situated in the vicinity of B, increases in that
direction in which this curve comes nearer to # (figs. 3—6).

(To be continued ).

Chemistry. — «Studies in the Field of Silicate-Chemistry: TL. On
Compounds of Lithiumoaide and Silica. By Prof. Dr. BF. M.
Jancer and Dr. H. S. van Kroostrr. (Communicated by Prof.

P. van RompBurGH.)

§ 1. In connection with a series of investigations going on in
this laboratory, on natural and synthetical lithiumaluminiumsilicates,
it seemed to us of importance once more to take up the study of
the binary system: lithiumoxide-silica, by means of the equipment
and methods, which are now at our disposal; only in this way it
seemed to us possible, to obtain thermical data, which are reliable
and reducible to the nitrogen gasthermometer. At the same time
we hoped to get information on the origin of in some respects rather
strongly deviating results of earlier investigators, who have occupied
themselves also with the study of these lithiumsilicates.

The two-componentsystem: Li,Q—siO, has already several times
been an object of research; thus some time ago by one of us‘),
using the method, already so often successfully employed upon metal-
alloys, of the crystallizationphenomena on cooling, which will show
themselves in such binary mixtures of varying composition. Later it
was studied in the same way by Enpe.t and Rieke *), who of course in
general also came to the same results, but who were not able finally to
answer the question, if a third compound, the lithiumbisilicate, could
separate from molten mixtures, like the ortho-, or meta-silicate.

1) H. S. van KuoosteEr, Dissertatie Groningen (1910); Zeits. f. anorg. Chemie
69, 136 (1910).
2) K EnpELL und R. Rieke, Sprechsaal, 44. No 46 (1910); 45. No 6 (1911),
55*

858

Again another problem originated from a publication of G. Frimpe.’),
who gave the description of a second modification of the metasilicate;
this new modification was never obtained either by Wa.nace *), or
by EnpreLi and Riexp, or by ourselves from a molten mass. On
the occasion of a renewed meltingpointdetermination, made by the first
of us*) in 1910 at the Geophysical Laboratory in Washington, a new
indication of an eventually appearing inversion was not found; at the
same time it was once more demonstrated by this study, that even
in this relatively favorable case, where the liquid was highly movable
and the erystallization-velocity of the silicate could be considered as
exceptionally great, the ‘“coolingmethod” was by no means adopted,
to give reliable and reproducible results. Other factors in the earlier
determinations, e.g. the use of crucibles and tubes of porous carbon,
and the insufficient control of the variations im chemical composition
of the studied mixtures, caused by the volatility of the lithium-oxide,
and finally the impossibility to reduce the existing thermical data
to the seale of the nitrogengasthermometer, — seemed to us a series
of reasons, to take up a new study of this binary system by means
of the gradually developed exact methods *).

§ 2. The necessary binary mixtures were prepared from the
purest lithiumearbonate and from pure, ground quartz of American
origin. The lithiumcarbonate was dried at 100° C.; there was a loss
of weight of only 0,05°/;. Only sodium could be detected spectros-
copically ; the quantity was however so small, that it could not be
determined by weight. using the amylaleohol-method. A trace of
iron was found also, but scarcely sufficient te give a reaction with
potassiumsulfocyanide as a pale pink colouring of the solution. The
lithium was weighed as lithiumsulphate; determined: 18,72°/, Lz,
calculated: 18,79°/, Zi.

The quartz lost on heating on the blast no more than 0,01°/, ;
a small trace of iron, less than 0,08°/,, appeared to ve the single
impurity. On evaporating with hydrofluoric acid in a platinum-dish,
no residue-was left; the used quartz therefore can be considered as
puressiOe)

1) G. I'RrepEL, Bull. de la Soc. Minér. 24, 141 (1901); HaurerguILLE et Mar-°
GOTTET, Compt. Rend. 93, 686 (1881).

2) R. CG. Wauuacg, Zeits. f. anorg. Chemie, 63, 1 (1909).

3) F. M. Jagcer, Journ. of the Wash. Acad. of Sciences, 1, 49 (1911).

4) FP. M. Jagger, Kine Anleitung zur Ausftihrung exakter physiko-chemischer
Messungen bei héheren ‘Temperaturen. Groningen, 1913,

®») Those preparations were supplied by Baker and ADAMSON; the used material
is the same as at the Geophysical Laboratory in Washingion, and employed for
standardizing purposes.

859

According to this high degree of purity of the components, all
the binary mixtures, employed in this research, were absolutely
white. They were obtained by heating weighed quantities of both
oxides in a finely divided state in platinum or nickel crucibles; this
manipulation was done in small resistance-furnaces, at temperatures
ranging from 900° to 1000° C., and every contact with a reducing
atmosphere was carefully avoided. After grinding down the masses
and sifting, they were treated in just the same way, ete., till the
whole preparation was shown to have a homogeneous composition.
Mixtures between ortho-, and meta-silicate were prepared from both
these compounds in quife the same way. The preparations were
analysed after HiLLepranp’s indications’), and always in duplo.

Every admixture of formed nickel-oxide was carefully avoided ;
mixtures rich in lithiumoxide however, needed to be heated in platinum
crucibles, because they would dissolve otherwise finely divided nickel,
which coloured the preparation with a beautiful violet hue. For
instance the orthosilicate could be obtained in this way, as a splendid,
intensively coloured, violet product. The study of mixtures, richer
in lithiumoxide, corresponding with the composition cf the ortho-
silicate was not possible in the usual way, both because of the vola-
ulity of the oxide at the prevailing temperatures, and by the fact,
that the lithiumperoxide Li,O,, generated at higher temperatures, will
very quickly attack the platinum and the wires of the thermoelements;
the platinum is superficially coated with a dull olive-green or greenish-
yellow layer, and every accurate temperature-measurement thus gets
practically impossible. Experiments, made in hermetically closed
platinum-vessels however, have given many good results, as will be
described further on, in § 12 of this paper.

§ 3. The temperatures of equilibrium were determined in the
way always used in this laboratory. A Wotrr-potentiometer (resis-
tance: 838 Ohm) with three decades, and with a constant resistance of
the galvanometer-circuit (Wrirs—DinsseLHorst), was employed, in
connection with a sensitive Ayrron-Maruer-movingcoilgalvanometer,
with high resistance, and short period, to compensate the momenta-
neous electromotive force of the thermoelement; the galvanometer
was calibrated and adjusted in such a way, that one microvolt
corresponded with a millimeter on the seale. The observations, made
with our thermoelements [I and II (platinum and platinumrhodium
(10°/,)-alloy) could be compared immediately with the nitrogengas-
thermometer, by means of calibration with a standardelement, cali-

') W. F. Hintepranp. Analysis of Silicate and Carbonate Rocks, 2nd. Edit. 1910.

860

brated in Washington, and by determination of the meltingpoints of
Na,SO, (884° C.), Li,SiO, (1201° C.), synthetical diopside (1391° C.),
and synthetical anorthite (1552° C.), with each of the three mentioned
thermoelements successively. The potentiometer-current was kept
constant at 0,002 Amperes ; two Weston-cells, connected in series,
and a Wouter auxiliary-rheostate, served as standard-electromotive
force; the Wusron-cells were constructed and controiled several
times at the Physical Laboratory of the University. The furnaces
used were platinum-resistance-furnaces with the heating-coil inside ;
they had the usual type, and their regulation was executed by means
of a decade-rheostate of manganin-wire. The heating-current was
direct current of 110 Volts and 20 or 30 Amperes.

§ 4. The components.

With respect to the components themselves, the following data
may be given. The relation between the three modifications of the
silicumdioxide: jS¢Q,, can be esteemed established in general lines
after the recent, most accurate research of C. N. Frnner (Amer.
Journal of Science, 36. 331 (1913)).

The inversiontemperature for B-quartz = tridymite lies at 870°
+ 10° C.; in the same way that for tridymite = cristobalite is deter-
mined at 1470° + 10° C. The three modifications are enantiotropic
forms, but the transformation-velocity is very small, and retardation-
phenomena, even in an enormously high degree, are almost always
present. This is the reason, why in nature some modifications of
SiO, often oceur within the stability-field of other forms.

Then there is at 575° C. an inversiontemperature for «- > 3-quartz;
at 117° C. one for a-— B-tridymite, at 163°C. one for p- — y-tridy-
mite; these inversions occur relatively fast. Probably the a-, and p-
forms of cristobalite are in less or more stable equilibrium with each
other at temperatures, situated between 198° and 274° C. The relations
of those modifications to each other are very complicated, but of no
direct interest for the present study.

The meltingpoint of cristobalite is very close to 1625°C.; the
liquid is a very viscous mass, which by rapid cooling changes into
the wellknown ‘“glass’’.

Quartz is optically casy to discriminate from both the other forms,
by the great differences of the refractive indices ; the discrimination
between tridy mite and eristobalite however is rather difficult.

The refractive indices of quartz are: me = 1.553 and n, = 1.544;
tiose for tridymite are: nz= 1.469, ny=1.473, while the true

861

angle of the optical axes 2V = about 35'/,°. For cristobalite these
values are: n, = 1,484, and n, = 1,487.

The Uthiumoaide: Li,O is only sparely known up to this date.
A deseription of it is to be found in an instructive paper of L.
Troost '), whose data we.in general could confirm. He obtained the
oxide from lithiumearbonate, by heating it at a high temperature in
the presence of coal in a platinum-crucible, and also by heating the
nitrate of lithium in silver crucibles at a red heat. The burning of
Jithinm in oxygen gave only partial results, as the protoxide: 7,0,
was formed. The presence of this peroxide causes the yellow colour
of the- product. Troosr describes the 47,0 as a white compound,
with cristalline rupture. We prepared the pure oxide after the method
of Dr Forcranp*), by heating lithiumearbonate in a platinum vessel
at 830°—900° C., while a current of dry hydrogen is run over it
continuously. We obtained in this way an absolutely white, cristal-
line product, which makes the impression of having been melted.
This however is not the case, as the aspect is caused by the melting
of the carbonate itself before its decomposition. For, as we found,
the oxide does nof melt under these circumstances, but can sublime
already under 1000° C.

We were able to confirm Troost’s observation, that pure Li,O
does not attack the platinum, even at very high temperatures, but
that the metal is attacked however, as soon as the oxide is heated
with it in an oxidizing atmosphere. The cause of this phenomenon

is the resulting peroxide, which attacks the platinum most intensily,
and gave to it the yellow or olive-green colour, which we have also
observed, whenever the lithiumorthosilicate was heated with
the metal. The view of the French author, that in absence of oxygen,
the 7,0 can be heated to a very high temperature, without melting,
is also quite right. We have made some experiments, to determine
its meltingpomt by means of the use of the “hollow thermoelement’,
— a method to be described further on, in the study of the
orthosilicate and the mixtures, rich in 7,0. It was found then, that
a heating to 1570° ©. (about 16400 M.V.) caused only a baking
together of the powder to a very hard mass, which was coloured
slightly yellowish by a trace of L7,0,, formed from 7,0 and the
small quantity of air, present in the platinum-bulb; however even
now the mass was probably not yet molten, nor at 1625°C., as we
found afterwards. Because the platinum is very soft at these tempe-
1) L. Troost. Ann. de Chim. et de Phys. (3). 51. 144, (1857).

*) De Forcrann. Compt. rend. 144. 1402, (1907).

862 ;
ratures, the platinombulb was inflated to a balloon, however with-
out Durstine.

Further we were able to determine the refractive indices and the
specific gravity of the pure oxide. Under the microscope the com-
pound appears as cristalline, irregularly shaped scales, with very
weak birefringence. Often they seem to be wholly isotropous, as if
they were glass. It may be, that the substance is finally yet of regu-
lar symmetry, for the weak birefringence often makes the impres-
sion of being only localised by tensions in the mass, more than of
a veal erystallographical anisotropy; and we found neither in any
case an interference-image in convergent polarised light, able to
prove that the compound belongs to one of the uniaxial classes.
Once some trigonally shaped plates were observed, which looked
like flat tetrahedrons or trigondodeecahedrons; but it was impossible
to prove this view. more exactly. The refractive index was found by
immersion: p= 1,644 + 0,002; so the refraction is relatively high,
this giving some evidence of the fact, why a great many hthiamalumi-
nosilicates, which are rich in 47,0, show higher refractive indices,
if they are richer in the oxide.

The specific gravity was determined by means of a pyenometer,
with ortho-chlorotoluene as a liquid; before it was found, that the
oxide does not attack this liquid in any appreciable way. As the
most probable value (from three determinations), we found: d,o=
2,013 + 0,015, at 25°,1 C.

The oxide dissolves slowly into water, without giving a great
heat-effect. The solution shows very strong alkaline reaction; it
tastes lixivial and at the same time somewhat bitter. With acids no
development of CO, was observed; so the product may be declared
free from carbonate.

§ 5. We have now given in the following table the obtained
results with mixtures of different composition; the numbers in the
7H) 8h, 9% and LO" columns are reduced on the gasthermometerscale
of Day and Sosman’), this being at the moment the most accurate one,
The composition of each mixture was determined a//er each experiment
by direct analysis, according to HILLeBRaNp’s*) indications for the
determination of the silicic acid. The thermoelements used, were
I in the furnace, II in the mass; they were read alternately every
half minute. Even with masses of hardly 1,5 gram, the heat-

') A. L. Day and R. B. Sosman, Carnegie-Publication No. 157 (1912),
2) W. I. Hittesranp, loco eitato.

863

effects could be fixed on the tempereture-time-curves very accurately ;
and if the furnace was run at a higher speed, again these temperatures
were reproducible within ea. 1°C; they therefore can be considered
as temperatures of true equilibrium.

Meltingpointdiagram of the Binary System: Liz0—SiOy.
(Thermoelement II] placed in the mass).

|
|
|

= lec Pec . |
Se| o# | 9 y
ma Gael Weare Caaseaiis Observed | Corr. Temp. Corr. Temp.
Ste Ae peratures No eee |
oc) £2 | 6& : | Temperatures | in intern.
Eu Res at | in Int. eo | Microvolts Tet LES
32) Ou. | O° | Microvolts: ree saree all
Zi Ne Hn | alt |
| 1st oazds Sivan tist 2d [st 2d Ist 2d
|Effect| Effect | Effect | Effect |Effect| Effect | Effect | .Effect
0 | 91.8 | 84.7 | 9902 | — | 1029 — 9866 == 1025.5 _—
1 | 89.0 | 80.0 | 9919 eel | 1030 — 9883 = 1027 —
3 | 85.3 | 74.2 | 9022] — | 1030.5| — | 9s86/ — | 1027 =
| | |
4 | 82.1 | 69.4 | 9920|/ — | 1030.5| — | 9884} — | 1027 —
| | | | |
5 | 79.6 | 65.9 | 9972 } | le = 9936 — 1032 —
6 | 75.7 | 60.7 | 9982 | 10958 | 1036 | 1118 | 9946 | 10918 | 1032.5 | 1115
7 | 71.1 | 54.9 | 9912 | 11624 | 1029.5 | 1174.5 | 9876 | 11580 | 1026 1170.5
|
8 66.67 49.7 | — 11992 = VZ2050 es — S944 — | 1201
9 | 63.9 | 46.7 | 9800 | 11908 | 1020 | 1198 9764 | 11860 | 1017 | 1194
10 | 62.4 | 45.1 | 9854 | 11622 | 1025 1174 9818 | 11578 | 1021.5 | 1170.5
11 | 57.4 | 40.0 | 9872 | 10680 | 1026.5 | 1094 | 9836 10640 | 10231092
|
12 | 52.8 | 35 9870 | 10732 | 1026.5 | 1096.5 | 9834 | 10692 | 1023. | 1097

Sy || OST Se

0

6

7 | 9850 | 11600 | 1024.5 | 1172 | 9814 | 11556 | 1021 | 1169.5
"14 | 49.9 | 33.0 | 9736 | 12154 | 1014.5 | 1218 | 9700 ene | 1011 | 1215
15 | 49.8 | 32.9 | 9812 | 12448 | 1021 | 1243 | 9776 | 12402 | 1018 | 1239
“16 49.2 | 92.4 | 12634 | ei ae ies | 1255
17 49.7 32.8 | 9826 12440 | 1022 | 1238 |) 9790 | 12394 | 1019 | 1238.5

|

* The marked preparations must accidentally have been changed before analysis;
we had however afterwards no means to ascertain this.

It may be remarked, that a preparation, having exactly the
composition of the orthosilicate, always gave a_ slight heat-effect,
corresponding with a eutectic temperature. We were able to show,
that the cause of this phenomenon is the high volatility of the
Li,O: after one single meltingpointdetermination, already a loss of L7,0

864

1700*
§
aay
aS 0
~ ’
= i
§ lors: 4
5 a
Tox | ©. lre00"
n ti]
+
fe ae
on Fe lea
ian :
aa j
aa '
15Q07 8 A 1300"
'
1470" i
R i
1
i
i
f
i
00 7400°
i
'
i
1
H
‘
'
i
i
1300" ; 71300‘
P255°
259 9
.
, ;
aTridymist i
2200" 130°
\ _
i
+
Wises ab
, 8
1 >
ate
nett
\
M0 1100"

c 1029°

100"

00
Bisilhast
as Tridyniat ae ieee 1
+ haste Oplossingen|| Metasiikaat
van as
Bisilikaat Bisilikaat in
Nec
LEG Metasi/jhaat \\Orthosi/ihaat
Yo 4, 930°

av)

&70~

p- Awarts
+

Bisi/thavt

800°
11,0.

=s'(( Li, 8t ©) 2

ae We ll
OS 77 1S BO RS MW OS 0

510,07 33S 90 9 $9 5S 00
Sumeastelling ia Melekuulprocenta
Fig. 1.
Temperatuar = Temperature. — Cristobaliet = Cristobalite. Tridymiet = Tridymite.
Bisilikaat = Bisilicate. Vaste oplossing van Bisilikaat in Metasilikaat = Solid solutions

J WNW WB HW

Samenstelling in Molekuul-

of Bisilicate in Metasilieate. @-Kwarts = @-Quartz.
procenten = Composition in Molecule-procents. Orthosilikaat = Orthosilicate.
of 0.4°/, could be stated. We finally obtained a temperature-time-

which the eutectic effect bad disappeared, starting with

curve, in
a mixture, which showed a small excess of the lithiumoxide ; the
meltingpoint was now at -12598 M.V. (corr.) corresponding with
1255°,5 C. This temperature we must consider as being the trne
orthosilicate, with an uncertainty of about

meltingpoint of the

S65

+ 3° C, caused by the variability in chemical composition as a
result of the extraordinary volatility of the lithiumoxide, which
will sublime already at temperatures, much lower than this melting-
temperature. Further below we will give the determinations of the
meltingpoint of the orthosilicate by means of a closed crucible and
a new method of observation; we shall see, that the true melting-
point does not differ appreciably from the here given value.

In fig. 1, we have composed these numbers graphically in
the usual way. At the same time also the results, of our experiments,
concerning the determination of the field, in which the bisilicate ean
exist in. contact with the liquid, are indicated in this figure. The
last mentioned determinations have given us much trouble, because
great difficulties were connected with the limitation of this very
narrow field of stability of the compound. We have only succeeded
by numerous quenching-experiments: preparations, heated during a
long time on known and constant temperatures, were momentaneously
chilled, and investigated in all details by means of the microscope.
Only in this way the place of the bisilicate in the series could be
fixed with sufficient accuracy ; the experiments on this subject are
described afterwards.

As a general result, we can thus say, that there are three com-
pounds: L7,,S¢O,, Li, SiO, and Li, Sz, O0,; the compound L757 O,,
proposed by Nicer on a very weak argumentation in no case
exists in contact with a molten mass; while the compound 47, Sz, O,
has evidently no real meltingpoint, but only a transformationtempe-
rature at 1032° C., at which if decomposes with deposition of some
metasilicate, or of a solid solution of a little of the bisilicate in an
excess of metasilicate'). We think we are right in this last view,
because the refractive indices of the needles of Lz, Si O,, which are
deposited at this temperature, have evidently somewhat lower values
(1.57 instead of 1.585 etc.), than the pure metasilicate.

The composition of both the eutectic mixtures /#, and £7, can be
indicated by :

ees (1022°C.): 55. Proc: of Weight S20; = 37.7 Mol. Proc.
of Si O,.
ane (10279 (C:) : 82;1.Proc. of Weight $20, = 69: Mol. Proce:

of Si Ox

§ 6. The lithiummetasilicate evystallizes from the thin molten mass
very

y rapidly; for this reason we succeeded in obtaining a “glass”
!) P. Nieewt, Journ.’of Amer. Chem. Soc. (1913); Zeits. f. anorg. Cliem. 84.,

263. (1913). In fig. 1 is wrongly written 1034° C, instead of 1032° C

566

of this substance only by cooling very small quantities of the com-
pound. The eristallized liquid consists of long, opaque, porcelain-like
looking needles, which show a principal and very complete cleavage
in the direction of their elongation; heavier individuals therefore
will decay very easily in a number of thin, felty needles, showing
normally orientated extinction. In the, zone of the longer axis we
could) measure some angles between 59° and 61°; this form of the
silicate seems to be the same as that, described by Havrrrnuitiy and
Marcorrer as rhombic, with pseudo-hexagonal symmetry. Doubtless
the silicate is biaxial, and probably monoclinic; the piane of the
optical axes parallel to the elongation of the needles, and perhaps
almost perpendicular to the formes }ltOO} or {O01}.

The silicate used was the
same, as formerly deseribed by
one of us’). Its analysis gaye
the following values :

Svo, 66.60°/,
Ii,O — 32.80°/,
Na, 0 O15
FeO, -- 00208
CaO 0.03°/,

99 on
There is thus about 0.3°/,
Li, too little. The metasilicate

Fie. 2. is decomposed by water, how-
Lithiummetasilicate (Enlargement 50 X<) ever much more slowly than the
(immersed in a liquid). ortho-silicate. Finally however
the water shows some alkaline reaction. The meltingpoint was determi-
ned with Sosman’s element C at 11954 M.V., corresponding with
1201°.8 C.; Day and Sosman determined 1200°.6 C. Another pre-
paration, (CRENSHAW), whose analysis gave the following numbers :

SiO, 65.89'/,
Ti0,. 32.83")
FeO 0.05"/,

Os oy

99. ie /

had a meltingpoint of 11930 M. V., or 1199,°8 C.; with the ther-
moelements G and // of Sosman and Day. The meltingpoint of pure

1) EF. M. Jagcer, Journ. of Wash. Acad. of Sciences 1. 49. (1911).

867

Ti,SiO,, can be indicated thus at 11944 + 12 M. V. or 1201° C.
+ 1°. The meltingpoint ean be localised so sharply on the heating-
eurves, that the compound can be used with success for calibration
purposes ; the temperature of equilibrium ts here really 7dependent
of the speed of heating, in very wide limits.

By means of the method of immersion, the refractive indices for
sodiumlight were determined on :

np = 1,609 + 0,004, for vibrations parallel to the direction ot
elongation of the needles,

np — 1,584 + 0,002, for vibrations, orientated perpendicularly
to the first direction.

The birefringence is strong and of positive character, being about
0,025. The specific gravity. at 25° ©. was: d, = 2,520. In fig. 2
a microphotograph of the crystallized meta-silicate between crossed
nicols is given while this is immersed in a liquid of about the same
refractive index.

With the aid of the method of quenching, used in this laboratory
with substances, heated at a constant temperature during a lone
time, we were able to get some g/ass of the metasilicate. As the.
compound crystallizes extraordinarily rapidly, it was only possible to
succeed by using very small quantities of the silicate, about 0,05
fo O,1 gram, wrapped in platinum-folium, and suddenly chilling
them by means of cold mercury. The refractive index of this glass was
found to be: np = 1,548 + 0,002 at 25° C; thus it appears to be
appreciably less than the smallest index of the crystallised substance.
The specific gravity of the glass was determined at : d, = 2,330, thus
being at 25° C. also much lower than for the crystallized substance.

§ 7. We found no indication whatever of an inversion tempera-
ture in heating and cooling our preparation; also in the microscopical
work we were not able to find any other modification of the meta-
silicate than the one just described.

However G. Frinpen') described in 1901 another form of lithi-
ummetasilicate, which he claimed to be trigonal and, strangely enough,
fo be homeomorphous with phenakite. He obtained this form of Li,Si0,
by heating the product, obtained by the reaction between Li,0,
S1O,, and muscovite in solution at 540° C. under pressure. His
results do not agree with those of Marcorrer and Havrarevuinie °),
who used LiS: as a flux, and obtained needles, to which they
attribute rhombic symmetry, with pseudo-hexagonal character.

1) G. Friepet, Bull. de la Soc. Miner. de France, 24, 147 (1901).

*) HAUTEFEUILLE and Margorvrer, ibid. 4, 241 (1881); Compt. rend., loco cit.

868

Just because neither we, nor our predecessors, ever found any
indication of another form of the metasilicate, than the mentioned
biaxial one, we wrote to Mr. Frinpen, asking him to send us a
sample of his modification. We wish to offer this mineralogist our
best thanks once more, for his aid and the trouble he has given
himself, to help to elucidate the complicated problem of those form-
deviations.

The preparation sent to us, soon appeared to be an aggregation
of flat needles, often radially ordered, which were however doubtless
hiavial. As was indicated on the label, they were obtained from
molten L7C/, showed a pale pink tinge, and an extinetion, directed
perpendicularly and parallel to their elongation ; the refractive index
for vibrations parallel to their direction of elongation, was:
np = 1,585 + 0,008, (being thus identical with tbat of our needles, per-
pendicularly to their elongation), while the refractive index for vibrations
oriéntated perpendicularly to the above, was: np = 1,563 + 0,002,
from which there results a birefringence of about : 0,022, being thus only
slightly less than for pure metasilicate. The flat needles showed at
their top-, and base-end, two small faces, making with the longer
edge of the crystals angles of respectively : 114°, 126°, and 120°.

In an experiment, where finely crushed /7,ScO, was heated during
eight hours with molten Z7C/ at 900° C. no other erystals were
obtained than the ordinary, biaxial needle-shaped form, which we
described already.

For another preparation of Mr. Frrepen, (with the number IV), also
obtained from molten 47C7, which preparation contained some metallic
copper‘), and some L7C/, we found: ny = 1.584 + 0.002, and
np = 1-574 + 0.002, the directions of the vibrations corresponding
with those, given earlier. The birefringence is thus now : 0.010 or
0.012; evidently the refractive index for vibrations in the elongation-
direction of the needles, seems to be variable. We think it not im-
probable, that a slight admixture in solid solution, of the bisilieate :
Li,Si,O, with its lower refractive index : ca 1.54, must be supposed,
to be the cause of this variability.

) 8. After having received the account of these experiments, Mr.
Frinpel was so kind as to repeat his experiments of 1901. Further
he suceeeded in finding again a preparation of the year 1898 (C;
exp. I, 1898), prepared by heating a solution of 2,5 grams of dried
SiO. and 0.65 eram of 47,0, with 6 grams of museovite at 540° C.
ar 2 2 b PS

‘) From the lining of the steelbomb, used in this and other experiments.

S69.

during 27 hours in a steelbomb lined with platinum. Of this preparation,
looking also like radial bundles of needles with trigonal symmetry,
we obtained some sections, normal to the axis of the needles. In
convergent polarized light it was in reality possible to observe an inter-
ference-image, closely similar to that of an optically uniaxial crysta! of
positive character; however, on moving the section and rotating the
table of the microscope, the image did not remain unaltered, but the
black cross opened its branches somewhat, and it was immediately
evident, that a dcaxial crystal, however with a
very small axial angle, was present. Of yet higher
importance however seemed the fact, that the
erystalplate showed itself in parallel polarized light,
to be composed of a number of sectors (fig. 3); in
every sector the black cross between crossed nicols

seems to open itself somewhat. It is hardly to be
Fig. 3. doubted, that a pseudo-symmetrie ageregation is
present here, with noticeable optical anomalies.

The repeated experiments of Mr. Frinpun gave, as he wrote us,
no other crystals whatever, than (iazial ones, with very small axial
angles, amounting occasionally to about 27°. The experiments were
made in these cases, by heating 2,68 grams of dry SvV, and 0.885 eranis
of Li,O0 (as hydroxyde) in solution, with a known quantity of finely
divided muscovite, at 545° or 550° C. during 30 hours. Also without
addition of mica, and at lower as well as at higher temperatures, the
same results were obtained. (A and 4, experiment XI, 1913).
Although all conditions of the earlier experiment I, 1898) were as
much as possible fulfilled, the obtained needles appeared however,
always to be biaxial: «w form of complete trigonal symmetry was
never produced in any of these cases.

The birefringence of the pseudo-trigonal needles of preparation
(I, 1898) was about: 0.021; that of the crystals from molten LiC/
was: 0,023 values do not differ noticeably from that, obtained by
us formerly with the biaxial silicate.

The preparations A and B, and XI, 1913, were investigated in
convergent and in parallel polarized light. Some sections, perpendicular
to the axis of the needles, are reproduced in fig. 4. Doubtless it must
result irom this, that .very complicated individuals and polysynthetic
twins of lamellae, crossing under 60°, are present; the pseudo-
trigonal habitus is caused thus by polysynthetic twinning.

The composing lamellae are all biaxial, the axial angle is very
small, and rarely exceeds, as ‘said already, 27°. By means
of the immersion-method we were able to determine with some of

ihese needles the following values for the refractive indices :
np = 1.600 + 0.003 for vibrations parallel to the longer axis of

the needles, and: np = 1.584 + 0.002 for vibrations, perpendicular
to the first named.

The question, whether the composing lamellae must be considered,
in ‘agreement with HavrernuinLe and Marcorrpr, as rhombic, is in
our mind, very doubtful. As already the French author himself
suggested, it is more probable to suppose monoclimic symmetry, and
a pseudo-trigonal aggregation of these monoclinic individuals. Indeed,
by such a polysynthethic twinformation, no pseudo-trigonal, but a
pseudo-hevagonal aggregation woult result, because the original axes
of binary period would involve a symmetry-axis of the whole strue-
ture, having a period of 60°.

The specific gravity of the modification ({, 1898) being: (d,,o =
= 2,529, is in complete agreement with that of our biaxial metasi-
lieate, which had: (72 = 2.520 at 25° ©.

Summarizing all these data, we must conclude from our experience
in this matter, that the so-called pseudo-trigonal modification of the
metasilicate can be no new modification of Li,S0,, but only a
polysynthetic twinformation of the original biaxial form, imitating
very closely a true trigonal individual.

This form with its apparent symmetry, must in questions of ther-
modynamical equilibria be considered as the same phase of the
compound, which is deposited from the molten mass ordinarily as
long, truly biaxial needles. In accordance with experience, brought
up to this date by the study of such mimetic crystals, it is just
quite clear, that no appreciable thermic effect. indicating some
noticeable, sudden difference in the total energy of the system, could
be detected in our experiments.

§ 9. The lithiumbisilicate: Li,Si,O, crystallizes from molten binary

871

mixtures of the same chemical composition, in the form of the great, flat
erystals, which are characterised by their tabular shape and _ their
peculiar aspect. Often they are recognisable (Fig. 5) by a system of
cleavage-directions, crossing each
other almost normally in three
directions of space ; the plates,
as if covered with a fine net-
work, are thus often bordered
by right angles. The symmetry
seems to be rhombic, or pro-
bably monoclimie ; the crystals
are biaxial, with positive charac-
ter of their birefringence, which
is about 0,020, — being slightly
less than for the metasilicate.

[he apparent axial angle is
: oe a ae _ .. probably rather great ; more or
Fig. 5. Lithiumbisilicate; cleavage-directions nade :
u less complicated twins are pre-
(enlargement 500 >).

a

sent. The figures 6 and 7 may
give some representation of the habitus of this compound, as it
looks between crossed nicols. The refractive indices are about :
1.545 and 1.525; it is very difficult to determine them accurately,
because the crystals are intergrown with fine, felty needles of tridy-
mite, or in some preparation with those of the metasilicate. The
peculiar cleavage-directions are in every case most typical for this
compound.

The specific gravity of the bisilicate was pycnometrically deter-
mined on: d,jo=2,454 at 25°.1C.

It was a difficult thing to fix the borders of the stability-tield
of this compound, in contact with a binary liquid. We succeeded,
by heating preparations of different composition, inclosed in’ thin
platinom-folium, at a constant temperature during a time ranging
from 20 to 60 minutes, in a quenching-furnace, and chilling the
preparations then suddenly in cold mercury ; in this way the momen-
tary state of the mixture is fixed, and can be studied by accurate
microscopical investigation.

The results of those experiments were the following:

Preparation N°. 3. Analysis: Weight Proc. of S’O, (= 74.2 Mol. Proc.).
Temperature
in M.V.:
8890 Wholly crystalline; much bisilicate, very little tridy mite.
56
Proceedings Royal Acad. Amsterdam. Vol. XVI.

—_——

Fig. 6. Lithiumbisilicate. (cleavage-directions; Fig. 7. Lithiumbisilicate. (Enlarg. 50 times).
enlargement: 50 times).

Temperature
in M.V.

9920 Little bisilieate; mostly feebly birefringent aggregates of
tridy mite.

9930 Idem.

10370 Mueh glass, in which imbedded extremely feebly birefringent
needles.

10970 Idem.

11570 Idem.

11770 Idem.

Preparation N°. 4, Analysis: 82.1°/, SvO, (= 69.4 Mol. Proc.).
Temperature
in M.V.:
9910 Crystalline, principally bisilicate, no tridymite in any appre-
ciable quantity.
9930 Very little bisilicate, many feebly birefringent aggregates; a
little glass.
9970 All glass.
Preparation N°. 9. Analysis: 79.9°/, SiO, (= 66.6 Mol. Proe.).
Temperature
in M.V.

9930 Bisilicate in typical form, often undulatory extinction, and

pellets:

finely intergrown with needles of impure metasilicate

np = 1.56 or 1.57.).

Temperature
nm M.V.

9950 Idem.

9962 About 10°/, glass; further as mentioned above.

9985 About 50°/, glass; imbedded bisilicate and needles.

9990 About 70—80"/, glass; needles of apparently impure metasilicate
j= ID Np

10005 About 90°/, glass; needles with mp—1.56 or 1.57.

10049 Almost all glass (72 = 1.536); locally a few needles.

Preparation N°. 6. Analysis: 75.7°/, ScO, (= 60.7 Mol. Proc.).

0

Temperature

in M.V.:

9930 Felty aggregations of metasilicate, intergrown with much
bisilicate.

9990 About 5°/, glass; metasilicate with 2p — 1.57.

10030 About 80°/, glass; felty birefringent needles.

We are of opinion, that in accordance with these results, the field,
in which the bisilicate can exist in contact with a binary liquid,
can be indicated as done in fig. 1; the compound must melf at
1032° C. under dissociation into metasilicate, and give a binary liquid
of shghtly varied composition. However, it seems, that no pure
metasilicate is deposited, but a very dilute solid solution of the
bisilicate in it; this we may conclude from the fact, that the refractive
indices of the needles are always somewhat less than those of the
pure compound.

§ 10. The third possible compound, existing in contact with its
binary liquid, the erthosilicate: Li,SiO,, was prepared in quite the
same way by heating of the tinely divided, thoroughly mixed
components. Although the mixture, in composition identical with
the compound, could also in this case be melted with a blast, if in
small quantity, it was necessary to keep the molten mass at 1500° C
for some time, to be sure, that practically all carbondioxide is
expelled. But then some /7,0 volatilizes, and thus the chemical
composition must be corrected again and again, till the required com-
position is reached. If, as is the case in the Fletcher-furnace, there
is*some watervapour present, the mass obtains afterwards a very
disagreeable odour of silicohydrogens. It seems, that the flame-gases

ob*

874

venerate platinum-silicides, which afterwards are decomposed by
watervapour under generation of silico-hydrogencompounds. The
platinumerucibles are strongly attacked by the L7,0,, which forms
from the orthosilicate, when melted in the air; the platinum is
coloured greenish or yellow, while the mass itself often looks
pale-pink.

The fact of the attacking of the platinum by the lithiumperoxide,
made it impossible to obtain reliable measurements with mixtures,
richer in Li,O than the orthosilicate, because the thermoelements are
spoiled in the same way as the crucibles, and are thus losing their
calibration. This fact must be kept in mind also, when meltingpoint
determinations of the orthosilicate are made.

The orthosilicate, if brought into cold water, is momentaneously
hydrolised by it; the solution shows a_ strong alkaline reaction.
Analogous decomposition finds place by the carbon dioxide and the
humidity of the atmosphere.

The heating of the orthosilicate in nickel crucibles, as already
mentioned, causes an intensive lilac colouring of the mass, probably
by diffusion of metallic nickel from the walls into the central part
of the substance. The colour is the same, as many nickel compounds
with complex ions show; it is not improbable, that the nickel is
present in these products in the colloidal form, as observed e.g. by
Lorenz ‘), in the electrolysis of some molten salts.

Microscopical investigation taught us, that the lilac product shows
the same polygonal or almost round, very thin seales as the pure
orthosilicate ; however, they were now tinged homogeneously violet,
and also often locally darker than in other places. These coloured
crystals are noticeable dichroitic, as is often observed in crystals,
which take some dyes in solid solution.

The refractive indices of this lilac substance did not differ appre-
ciably from those of the pure compound. By means of the immersion-
method, we found: n=1,595+ 0,005 and n, =1,610 + 0,005;
the birefringence is fairly strong, and about: 0,015 to 0,020. Often
a twinning is present, which reminds of that of albite. The specific
gravity was determine dpycnometrically, in toluene, to be: dye = 2,392
at 25,°1 C.; the coloured product showed a value slightly higher :
dyo = 2,415 at 25°,1 ©. Figure 8 may give a representation of
the compound between crossed nicols; some twins are also shown
in it.

1) Cf among others Lorenz, Elektrolyse der geschm. Salze Il. $, 40. (1905);
Gedenkboek Van Bemmeren, (1910). p. 395.

§ 11. The analysis of our
product thus obtained, gave
50,8°/, SiO, and 49,2°/, Li,0,
while one calculates : 50,25°/,
SiO, and 49,77°/, Li, O. So there
was an excess of 0,57°/, SvO,,
causing the small eutectic heat-
effect at 1020° ©. on the heating-
curve. The meltingpoint of this
substance, measured four times
with the element S,, was found
successively (without correction)
to be : 12463 M.V.; 12408 M.V.;
12399 M.V.; 12373 M.V.

The meltingpoint is thus con-

Fig. 8. Lithiumorthosilicate. (Enlargem.

50 times; in immersion-liquid). : ioe?
tinually lowered, which is caused

by the fact, that more and more 7,0 evaporates. and some L1,0,
is generated at the same time. On cooling, retardation of the crys-
tallization was observed to about 12280 M. V., depending upon the
speed of cooling; then, a sudden rise of temperature, caused by the
solidification of the mass was observed to 12320 M. V.

To find the trie meltingpoint, we started therefore with mixtures,
which had a slight excess of Z7,0; the experiment showed, that
uready afier one single determination, a loss of O,4 47,0 could be
proved, while a eutectic effect at 9775 M.V. became noticeable.
Finally some heatingeurves were obtained, showing no eutectic effect ;
the crystallized product gave, on analysing, 50,0°/, ZiQ0,. With
thermoelement II the meltingpoint was now 12590 M.V. (corr.),
corresponding with 1255°,5 C. + 3°.

By means of the method of the “hollow thermoelement” (vid. § 12),
we determined the meltingpoint to be: 1256°C.; as to the fact, that
this temperature could eventually rather correspond to a three-phase-
equilibrium, cf. § 12 and $13 7.

The refractive indices of the scale-shaped crystals were measured
by means of the immersion-method, and found to be np =1,614-+-0,003
and np = 1,594 + 0,003. The birefrmgence therefore was fairly
strong: about 0,020, perhaps somewhat less than for the metasilicate;
the same albite-like twinning as with the lilac crystals was also
observed in this colourless product.

The finely divided powder of the orthosilicate, like that of LeOH,
stimulaies intensively to sneezing.

876

§ 12. We have tried to gain some more data on the thermic
behaviour of mixtures, whose composition was lying between that
of Lr,ScO, and £7,0, and more particularly, with the aid of a
method, which possibly may open an important way in future, to get
results in those eases, where one of the components is highly volatile,
or changes in contact with the air. Therefore we shall deseribe it
shortly. The method is this, that crucibles are made from the purest
stock of platinum, like that used in drawing the wires of the thermo-
elements, which crucibles have the
shape and size, reproduced in fig 9a.
PE} WPt-Rho A platinumrhodiumwire of athermo-
element, about 0,6 m.m. thick, is
soldered to it at the bottom by
means of the oxygenflame; then
the erucible is filled with the finely
powdered material, with the aid of
the small funnel and hollow stem;
after cleaning it very well, a thick
platmumwire of the same diameter
as the stem is introduced into it,
and the crucible is melted off then
a. liye at the top. The platinumwire of the

Fig. 9, used thermoelement, also 0.6 m.m.

thick, is soldered then -with the oxygenflame at the top of the
crucible, and the other wire is bent as shown in the fig. 9b. Both
wires are isolated by means of porcelain capillary-tubes, and the
whole apparatus then fixed in a Marquarpr-tube and hung in the
furnace. The crucible must be in the region of the furnace, where
no appreciable temperature-gradient is present. In the immediate neigh-
bourhood of the crucible a second thermoelement is fixed in position;
then the meltingpoint of the substance can be determined in the
usual manner, by reading both thermoelements alternately every
half minute.

Some experiments with Li, Si O, immediately proved the method to be
completely adapted for our purposes: we found the meltingpoint not only
as sharp as formerly, but also the undercooling- and _ solidification-
phenomena gave perfectly analogous results, as in the case, where
open crucibles were used. The meltingpoint of Lz, Si O,, determined
in this way, was found at an E.M.F. of 11968 M.V.; as the cor-
rection of the thermoelement however was determined to be
—26 M.V., thus the temperature i.c. lies at 11942 M.V. or 1201° C.

We now tried first of all, to determine the meltingpoint of pure

877

Li,O in this way, if free from peroxide. Although the temperature was
increased up to 1625° C. this time, we were not able to find any
heat-effeet. The crucible was inflated like a balloon, but did not
erack. After being opened, we found the powder baked together,
however not molten. An unimportant trace of peroxide only was formed.
Therefore we inust conclude, that as Troost already pointed out, the
melting-point lies very high, — higher than can be determined by
means of our platinumresistance-furnaces and thermoelements. Probably
the meltingpoint will be in the neighbourhood of 1700° C.

Thirdly we determined the meltingpoint of the 7, .S7 O, quite in
the same way, and found it (without any correction), in several
determinations. at an E.M.F. of 12640 M.V., if the thick thermo-
element (0,6 m.m.) was used. As the correction of it was —35 M.V.
for this temperature, the true meltingpoint is 1256° C. (G. Th.), thus
not differing appreciably from the formerly obtained value. The
heat-effect was not large; but if the thermoelement is fixed in a
suitable way af the bottom, which must be bent a little inwardly,
the heat-effect is clearly localised on the heating-curves. On cooling,
we found a crystallization at 1249° C,

It is of course possible, that this temperature of 1256° C. indeed
corresponds to a steep and not very extended maximum in the curve,
However we made some more experiments, to find out the form of
the curve for mixtures, which are still richer in 47,0, by means
of the deseribed new method. With a mixture, corresponding to 54
weight-procents 17,0 (or 71 Mol. proce. 17,0), we found a good
observable heat-effect at 1405° C.; then the bulb cracked by the
enormous vapour-tension. Thus it ean be, judging from this, that the
temperature of 1256° C. must be considered rather as a temperature
of “transformation”, at which the orthosilicate melts under dissocia-
tion into Z2,O0, and into a liquid, whose composition is very close
to that of the pure compound.

§ 13. Microscopical investigations. All preparations were micros-
copically investigated, and the results were in every case compared
with those of the thermical determinations. It is an agreeable task to us,
to express our thanks once more to Dr. F. E. Wricur in Washington
for his kindness and readiness to look over our preparations again,
and for the information he has given us in some doubtful cases.

In general we can say, that the results of these investigations by
means of the microscopical method agree fairly well in all respects,
with the conclusions drawn from our thermical work. The prepara-

878

iions are ranged in the following, in series of increasing quantities
of SvO,.

a. 91.8 Weight Proc. SiO, (= 84.7 Mol. Proc.).

This preparation showed two components: firstly a substance of
weak birefringence and a_ refractive index of about 1.480. It is
present in irregular felty needles, spread through the other component,
or in corns of indefinite boundaries. This substance seems to be no
other than «-tridymite.

Another substance of stronger birefringence and of a_ positive
character, with a refractive index of about 1.545 is seen accompa-
nying it. The birefringence is about: 0.020, thus being a little less than
for the metasilicate. This component is the bisilicate: £7,S7,O,. Solid
solutions between this compound and S?O,, which we were inclined
to suppose, seem after Dr. Wricur’s judgment not to be present.

b. 89°/, ScO, (= 80 Mol. Proe.). This preparation is in all respects

analogous to the former one.

ig. 10. 89 Weight Proc. SvQy.

(Enlargement: 50 x}. Fig. 11. 85,29, SiO. (Enlargement: 50 X).
6.1 85.3%") S10) G42, Mole Proe:): t

The quantity of tridymite is considerably diminished; it is only
present in exceedingly small needles. The bisilieate presents itself in
tabular crystals, intergrown with tridymite. In convergent polarised
light, the substance is shown to be biaxial; however the axial angle
seems to be too large, to observe a complete interference-image.
Sometimes the crystals have the aspect as if subjected to torsion.

d.82.1°/, SiO, (= 69.4 Mol. Proc.). This preparation is almost homo-
geneous, and consists of tabular crystals; the macroscopical aspect

of the preparation gives already immediately the same impression.
Most characteristic is the system of cleavage-directions which seem
to cover the plates as with a fine net-work of lines in three direc-
tions, arranged perpendicularly to each other in space. The boundaries
of the tables are often rectangular; they show normal extinction.
The refractive indices are: 1.545 parallel to the axis of elongation
of the erystals, and 1.525 perpendicularly to it. The birefringence
is of positive character and about: 0.020.

Often twins or very complicated intergrowths occur.

Gy 09:6"), 1stO, (='66.0° Mol. Proc’):

The preparation is again fairly homogeneous. Only some fine
needles are found ‘locally on the table-shaped crystals, probably
representing the metasilicate. This fact would prove, that the bisilicate
will dissociate on melting. The birefringence is positive and about:
0.020; the refractive indices are found to be about: 1.545 and 1.530.
Many parallel intergrowths, and polysynthetical twins seem to be
present; the fine lines, indicating the system of cleavage-directions,

0

are here most typical. Locally the preparation shows a little quantity
of glass.

iia? VOM GIF

wove (= 605 Mol Proc:):

This preparation is inhomo-
geneous; longshaped needles,
with m = 1.585 and normal
extinction are intergrowr with
the grains and plates of the
bisilicate. The refractive indices
of the needles are somewhat
less than those for pure Z7,S70,;
we found e.g.: 1.595 and 1.569
in the same individuals.

Gs wld sv. (S-od-o Nol.
Proc.).

The quantity of the metasili-

cate is considerably increased ;
Fig. 12. 78,8 Weight Proc, SiO). (Enlarg.50X). for the remaining part just asf.

hy.) 66.7°/, StO, (=49.7 Mol. Proc.).

Homogeneous. It is the L7,S/0,, with all properties, formerly in-
dicated. The axial angle seems to be rather small.

i). 63.9°/, SiO, \=46.7 Mol. Proc.). In general lines this preparation
resembles the former; locally small grains of the orthosilicate,
with its weaker birefringence, but stronger refraction, are visible.

880

The following preparations are then analogous to 7; the quantity
of the metasilicate diminishes gradually, compared with the closely
intermixed orthosilicate, which presents itself in round or polygonal
corns, often twinned in a particular way. The preparations, which
are in gross composition very close to L7,S/O,, show the crystals of
the orthosilicate often in a highly altered condition; the immersion-
liquids also seem to be attacked by the expelled alkali, and measure-
ment is often impeded by it.

The fact, that the crystals of the orthosilicate appear often more
or less attacked under the microscope, could make more probable
the view, according to which the temperature of 1256° C. were rather a
“transformation’’-temperature than an ordinary meltingpoint; the
compound would be converted thus into a liquid, with partial dissociation.

In the principal outlines we may say, that the binary diagram
of SiO,—Li,O0 is known now. It will doubtlessly prove for the
present impossible, to investigate the behaviour of the components
at concentrations between orthosilicate and lithiumoxide in their
complete details, because of the enormous volatility of this oxide
at these extreme temperatures. -
Laboratory of Inorganic and
Groningen, February 1914. Physical Chemistry of the University.

Physics. —- “The volume of molecules and the volume of the com-
ponent atoms.” By Prof. J. D. van pur Waats.
(Communicated in the meeting of January 31, 1914).

I think I may assume as known that for normal substances the
volume of the molecules expressed in parts of the gas volume at
O° and 1 atmosphere pressure may be calculated in a simple way
by means of the critical quantities. When it is not yet taken into
account that the quantity 6 of the equation of state decreases with
v we find:

RT;

Pk

Tee 8 N28
* pe (+a) (12)
in which / represents 4 times the volume of the molecules. If we do
take into account that this faetor 4 diminishes when the volume, as
is the case for the eritical state, has decreased to almost 20, we find

== ffi

’y

by approximation:

Ss]

And if this factor 7 was really equally great for all substances,

* would be almost proportional to the size of the molecules. As
I].

it is not my purpose in this communication to caleulate the exact
numerical value of the size of the molecules, and in connection
with this the perfectly exact numerical value of the component atom
volumes, which perhaps is not yet feasible, among others on account
of the imperfect knowledge of the accurate value of 7% and pz, and
as this communication more bears the character of a preliminary

exploration of the territory, I shall assume the quantity = as a
Pk

numerical value, which is really, at least by approximation, pro-
portional to the size of the molecules and by the aid of this value
1 will investigate what follows for the size of the component atoms
from this size of the molecules. The quantities 7%, and p; are borrowed
from the exeellent Recueil des Constantes physiques by. Messrs.
ABRAHAM and SaceRDOTE.

As I expected the simplest relations for the saturated hydrocarbons,

rypy

: aes pee
I began with them, and the values of 7; p;, and follow here.

Pk
ae Pk a calculated
Pk

Methane 191,2 54,9 3,483 CH, 3,483
Ethane 305,16 48,86 6,2456 C,H, 6,243
Propane 370 45 82222 C,H. 9,003
Butane not given. 11,768
Pentane 470,2 33,08 14,236 C,H; 14,523
Isopentane 460,8 32598 14, @rlal e 14,523
Hexane 507,8 29,76 17,06 OAeh 17,283
Heptane 539,9 26,86 20,01 (OAsk Ss 20,043
Octane 569,2 24,64 23,1 Cons. 22,803
Decane 603,4 21,3 28,35 CHE 28,323

For the increase of the molecular volume in consequence of the
introduction of 1 atom C and 2 atoms H into tke molecule CH,,
we successively find the values:

~
Ww
oe

Ww we
» OD

iw)
aon
DP

Co_—
(Ju)
res

I “a

vo
Go

ww Ww

=
=
bo

and with Decane—Ethane

bo
~)
CO
pes

882

The inexplicably small amount for Propane is not able to take
away the impression that for these saturate hydrocarbons the volume
increases regularly and equally whenever 1 atom of © and 2 atoms
of H enter the molecule, and when we consider the almost perfect

a)

equality of = for Pentane and Isopentane, we come to the con-
clusion that at least in these cases a rearrangement of the atoms
is no influence of importance. If for the mean of the above values
(with the exelusion of 2,87) 2,76 is chosen, the volumes would be
as the calculated values of the preceding table indicate. It is seen
that except for Propane, the differences are small, and the question
suggests itself whether for this substance there is a cause of error
in the determination of the critical quantities, e.g. a certain degree
of impurity.

If in what follows the volume of the carbon atom is represented
by ©, and. the volume of the hydrogen atom by H, we have the
following two equations for the determination of these two quantities :

C+ 4H = 3,483
C+ 2H = 2,76")

TO9

0,425 RS
oye Jnl = — O}36Lomand C2203

Some other determinations which will be discussed presently, have
led me to consider C below 2 as possible. With C = 1,9. retaining
CH, = 3,483, H would be equal to 0,896. Tien CH, would have
fallen to 2,691, so it has changed only little. But whether one
assumes H = 0,3615 or H = 0,396, it appears that there is a great
difference with the volume of H or H, as it would follow from the
critival data of hydrogen. With 77, = 32 and p, = 19,4 we find
T).

= 1,65. And if we should assume the formula H, for the molecule
Vi:

as I also did at first, H = 0,825 would follow from this, a value
which is certainly not in harmeny with the above calculated value.
And tle difference is so great that I was already again on the verge
of concluding, as I had often supposed before, that it would be
impossible to get in this way to the knowledge of the size of the

1) From methylethylethylene(iso) which, the structure being disregarded, has

; ee? £2 LA RL 7 ‘ Balas Pad

CH) =5 (CH) as formula, we find —~ = 13,69, which would lead to CH, = 2,738.
Pk :

But from ethylene, which has 2 (CH,) as formula, we should find a somewhat

too great value, viz.: 2(CH,)=5,7 or GH, = 2,85. Is this substance somewhat

associating ?

583

atoms. Now however | bethought myself that [ had determined the
size of the hydrogen molecule already before, and that this size was
even the first molecule size that I had at least estimated. From
REGNAULT’s observations, in which the volume under 1 meter pressure
Was assumed as unity of volume, I had obtained values lying between
0,0005 and 0,0008, which for our unity of volume corresponds to

la al

0,00038, and 0,00006, from which for Ti a value would follow lying
Pk

between 0,95 and 1,5. And a value lying near 0,95 seems by far

more probable to me than the value which would follow from the

critical data, and leads me to conclude that at these low temperatures

hydrogen associates to double molecules for the greater part.

But nevertheless the value of the volume of the atom H remains
decidedly smaller when it is bound to '/, part of the atom C, than
when it is bound to a second atom H. And this is a result which
has always appeared correct to me, viz. that the size of the
volume of an atom is not only determined by its own nature, but
also by the nature of the atom,to which it is bound. This is of
ccurse in flat contradiction with the assumption that an atom is a
perfectly invariable corpuscle, not to be changed by any forces, not
by atomic forces either. With the molecules as wholes it must,
indeed, have the property in common of being invariable to forces
of collision of heat and of pressure. But when uniting with other
atoms, in which forces of higher order come into play, they behave,
I would almost say, as soft bodies, which can vary both with
regard to shape and to size. And the conception that an atom is an
orbit of electrons round a rigid centre formed by a point in which
the atomic weight is concentrated, or when the atom is bi-, tri- or

: . Urea Waid 1
tetravalent by 2, 3 or 4 orbits round centres in whieh eee Cr
of the atomic weight is concentrated — a conception called into

existence by the study of light phenomena ‘) — can give an explanation
of this. We have only to assume the velocity in the orbits large
with respect to the velocity of the thermal motion to account for
the apparent hardness, and only to assume rotation of the molecules
round one or more axes to convert orbits and planes to an apparent
volume. When we have two similar atoms which have united,
we have two orbits of electrons lying in the same plane, and
rotating in opposite direction. Where they are in contact or almost
in contact, the directions are in the same sense, hence we have

1) Cf. among others Dr. Bour, Phil, Mag. 1913.

884

attraction, just as this is the case with’ eleetrie currents in the
same direction. But when one of the atoms is replaced by one
of another nature, e.g. of greater atomic weight, the size of the
atom that has not been replaced, changes, because a stronger current
acts on it, 1.e. this atom becomes smaller, whereas the second atom
becomes Jarver than it would be if it had- continued to be united
with one.of ifs own nature, and the result ean be that the new
molecule is either greater, or smaller than, or has happened to remain
equal to half the volumes of the two molecules, the atoms of which
have been exchanged. But we do not yet know the degree of the
variability .

But let us after these speculative considerations return to the
investigation whether also other observations about the critical cireum-
stances are in agreement with the values of C and H, which we
have calculated above for the case of mutual binding.

It had already drawn my attention that = for isopentane had
is

been found somewhat smaller than for normal pentane, and that,
if this should also be the case for other iso-compounds, the earlier
calculations, in which these differences were not found, could not
be quite accurate. And strictly speaking already in the earlier ealcu-
lation it can be pointed out that there are differences which have
been neglected in this calculation. The volume for all atoms C e.g.
was put equal, though there always exist 2, viz. the outmost of the
chain, which are bound to 3 atoms H and 1 atom C, whereas there
are n—2 atoms C, which are bound to 2 atoms H and 2 atoms C,
and which will accordingly be smaller than the 2 outmost. For the
iso-compounds the case may even present itself that an atom is bound
to 1 atom of H and 3 atoms of C, and perhaps even that one atom
of C would be bound to 4 atoms of C. I was therefore glad that
for a few iso-compounds the quantities 7% and pk are determined
through investigations by Sypney Youne -— viz. for di-isopropyl
and di-isolutyl. For the former substance, for which, if the construe-
tion is disregarded, the composition is the same as that of Hexane,

ryy

“—416.3, and for the latter, the composition of which would be
Pk

Pp ‘k is se \
equal to that of Octane, — is equal to 22.4. For normal compounds
Pk
the values are 17,06 and 23,1 in the above list. Also for these
compounds the case occurs that the volume is smaller than for
normal ones, and even not inconsiderably.

But on account of the incertainties as to in what way and to

855

What degree the differences in size of the volume of the different C
atoms would have to be taken into account, I shall not attempt as
yet to calculate the found differences in size, at least not for the
present. For isobutyl, moreover, the difference in size amounts only
to 3 percent, and it always remains the question how far the accu-
racy of the determination of 77, and pz has been carried, and.in how
far the absolute purity of the substance and the equality of the factor
7 S< 2738
(+ aU—@
satisfied with the approximative calculations, which I have used above.

ean be relied on. | shall therefore for the present be

For the methyl, ethyl-, propyl-compounds etc. there is a whole
series of determinations of 7; and pz which can be of use for the
calculation of CH,. Then a new kind of atom, or a new group
of atoms, which we do not know as yet, is indeed added, but
when the new group of atoms is bound in these compounds in the

gal

an ke ?
same way, the difference in —, e.g. for the methyl- and ethyl-series,
Pk
can then enable us to determine the value of CH,. Thus we find the
following values :

igen
Tr Pk Pe Cie
Dike
Methyloxide (71-2 973753 7,55) 5,57 a
Ethyloxide NORGE DTS < 356 19 19k Ton ae

Methyl and ethyloxide 167,6 + 273 46,27 9,5

The value 2.78 coming so near the previous determination, I do

ry’

; Tr ;
not hesitate to call the value — for the third substance too small.
Pk

There the value 10.25 is to be expected instead of 9.5. If one should
assign the before given value also to the other H and C atoms,

gal

O =1,3 would follow from this, whereas O, = 3 follows from —!
Pl
Thus we find for:
te ra
-— difference
Pk
Methylacetate 10,95
Ethylaceiate 13,77 2,82
Propy lacetate 16,56 5,61

From this we should therefore derive CH, = 2,8. So the abnor-

S86

mality of acetic acid has disappeared in these compounds; of
these compounds and others examined by me the group CO, would
almost give the vaiue which follows from 7% and pz for CO, , viz. 4,14.

I choose three of the compounds of Cl, and © and H to see in
how far the others by means of the values calculated from these,
can be derived.

From the values of 7}. and p;, follows:

Chlorie ethy! C,H,Cl = 8,435
and C,H,Cl, = 10,61
and CHCl, = 10.

We find from this CI—H = 2,175, which means that if in these
compounds a hydrogen atom is substituted for the chlorine atom,
the volume increases by 2,175, a value which was found equal to
from 2,18 to 2,2 another time; a second equation is:

Cl,—H, = 9.39.

From these two equations follows Cl = 2,52 and H = 0,345 and
we find further C = 2,095, a value almost equal to that found before.

For carbon tetrachloride we find 12,175 for with these calenlated
je

values of Cl, H, and C, whereas the value found directly would be
egual to 12.4. But for CCIH, there is no sufficient agreement between
observation and calculation, and like other substances which have
been derived from CH, this substance yields a too large value and is
evidently associating. I am even astonished that the derivatives that
contain more chlorine behave evidently so normally. When we
compare the value found for Cl with that of the molecuie, viz.
4.45, it appears that the binding of C with Cl makes the atom Cl
larger than is the case with the binding of Cl with Cl. With the
values calculated from chlorine compounds we should find:

CH, = 3.475
CH, = 2.785

When these are compared with those found before:
CH, = 3.483

and . CH, = 2.76

there is reason for us to wonder that the entering of Cl into these
compounds hardly changes the values of C and H., if at all.
I shail now proceed to the amine compounds.

2 : : Ty.
We find for the ethyl amine compounds the values of —:
Pk

a

887

tri-ethylamine di-ethylamine and ethylamine
17.7 12.25 6.818
When the volume of C bound to N is represented by Cy and
that of C bound to C by C., we have the three following equations:
N43 (Cy + H, 4 C. + H,) = 17.7:
N+H+2(Cy +H, + C.+ H,) = 12.25
N+2H+(Cy+H,+C.+H,) =6.818

or —H+(Cy+ H,+ C+ H,) = 5.483
— 2H + 2(Cy + H. -+ C, + H,) = 10.915
and so Cy+ H,++ C. + H, = 5.483 of 5.457.

If we take the mean of these values, and if we take into consi-
deration that for C.+ 2H has been found before 2.76, we determine:
Cy+ 2H =2.71.

Hence the volume of C bound to N may be equated to that of
C bound to C.

If we do so, and calculate with it the value of the group (NH)),

the radieal of, the amine-compounds, we find:
(NH,) =1.3 about.

This value is much smaller than for NH,, which we call ammonia.
With T=132.3 and p= 109.6 we calculate this value at about
3.7. So there the question rises what difference there will be between
these two atom-groups. Perhaps it will have to be looked for in the
situation of the orbits of the electrons, which would then have to
lie in the equator plane of the trivalent nitrogen atom for ammonia.
and for amine in the meridian plane.

For propylamine we should find a slightly too high value, viz.

TN x :
2.84, for the value of CH, from — with (NH,) = 1.3, whereas we
Pk
found a somewhat too small value before for propane. I do not,
therefore, consider these differences as really existing. For dipropyl-
amine the value 1,3 + 1656— 17.86 might be ealeulated with

1.3 + 6CH,, whereas 17.47 follows from a Allowing for the
Pk
approximate character of our equations this may be considered as equal.
Bat the methylamines all yield a too high value, which I consider
aS a consequence of association, viz. 10.575 instead of 9.58, 7.43
instead of 6.82, and 5.944 instead of 4.06. With monomethylamine
there is, therefore, a high degree of association; about half the mole
cules are double molecules.
oF
Proceedings Royal Acad. Amsterdam. Vol. XVI.

588

I shall now proceed to discuss the substances in which the cyclic
bond of benzene occurs.

a al

For benzene itself we find ee a7) and for all the substances
Pk
in which this eyelic bond occurs, C,H, is smaller than would follow
from the saturate hydrocarbons. Of the substances in which the
grouping of C and H occurs, as this is the case for hydrocarbons,
6C alone would already have a value exceeding 12 or close to it.
So the question again rises for what special reasons the cyclic bond
of the 6 carbon atoms makes them smaller. Perhaps the closed
chain, the ends of which coincide, is the cause of this through the
mutual attraction of these ends.

That the binding of C to C with 38 valencies could account for
this, may be doubted for the present.

But whatever the cause may be — we shall assume C,H, = 11,73
for the cyclic binding, and take the former value for the atoms
further entering the molecule, which are grouped as in the saturate
hydrocarbons.

Tk eee P
For diphenyl we tind — = 24,17; it is, compared with benzene,
Pk
a little too great, or perhaps benzene is a little too small. By adding
2,76 to diphenyl we should get 26,93 for diphenyl methane whereas
Ty
27,3 would follow from ——. Whether these differences are the con-
Pk
sequence of our approvimate calculation, or whether they have a
real signification, 1 dare not decide. By the addition of CH, to ben-
Tk
zene 11,73 + 2,76 = 14,49 follows for toluine, whereas — yields 14,27.
Pk
We find further:

gal

Xylene (0) for —

the value 17,1, calculated from benzeney,

=
me ine 17,25
»” (m) LB] > ” > 17,64, bP) > 3 \
>” (Pp) be 99 29 ” 17,28; 33 99 9
; : Th, ; ee ;
Mesitylene for the value 19,3 , caleulateda from benzene 20,01
Pl
eye we 7
Durene \ SP th aa % 23,62, % Ls FA DAH A
Cumene PE Fp Se a 19745 o Pe 20,01
spe > © 0
Cymene PAR. Ac, i. hey fe si - MPT Tl

From Cresol (0) = 15,67 follows for — H + (O,H) the value 1,17.
If the two H cancel each other, we should have O = 1,17, whereas

889

we calenlated O =1,3 from the ethyl-oxides. If we had a priori
assumed O = 1.3, we should have calculated Cresol = 15,79.

I might add other examples to these, but those given here suftice
in my opinion to draw the following conclusions :

1. The volume of the molecules of normal substances may be
found from the critical circumstances.

2. The volume of the molecules is equal to the sum of the volumes
of the atoms contained in it.

3. The volume of an atom is not constant, but depends also on
the atoms to which it is bound, and the way in which it is bound
to others.

4. By normal substances we understand such as do not associate

or dissociate. For acetic acid 10.415 is found for — whereas C,H,O,

would lead to 7,823 at the most.

5. The view that the volume of an atom is determined by the
size of the orbits of the electrons holds out the prospect to determine
the modification of the size in case of mutual binding.

I had just commenced this investigation on the size of 6, when I
received the copies of nine treatises by Apert P. Matagws on the
value of a, in which very remarkable results have been obtained.
They appeared in the “Journal of Physical Chemistry” of 1913.

AE es EY SING aD) Xe

The comparison of Benzene with Naphthaline has given me the
conviction that the smallness of C,H,, as was indeed to be expected,
must not be ascribed to the H-atoms, but to the C-atoms. For

aad

naphthaline =e equal to 18.91. Now naphthaline is equal to twice
Pk
2 5
= benzene + 2C or — benzene 2H. We have, therefore, the
equations :
4

18.91, = - < 11.73 + 2C
and AS ot ; S173
or 18.91 = 15.64 + 2C
and 18,91 = 19.55 — 2H,

890

from which C= 1.635 and H= 0.82 is ecaleulated. The value of

H is of the former order of magnitude. But C has decreased to 0.8

of its former value. This appears still more clearly when benzene

is compared with hexamethylene or cyclohexane. With this latter

substance we have also the cyclic binding of 6 carbon atoms; only

the coincidence of two-valencies for carbon has disappeared. The
Ty. :

formula is C,H,, and — — 13.9. Hence the comparison with benzene
Pre

gives the two following equations:

6C+12H=13.9

and 6C+ 6H—11.738
or Li OS6N6
and S125 93

I will still give a few values calculated in the meantime, viz.

yropylbenzene, calculated with benzene and CH, = 2.76, equal to
A) 2 i

Ty)

k eee
20.01, — being equal to 19.772, and chlorobenzene with Cl—H =
Pk
2.185 calculated at 13.915 and found 14.18.

But all the nitriles appear to give much too high values of

=, and so for 6, and are associating in a high degree. Even benzo-
Pk
nitril, but this nitril in a less degree than the others.

Astronomy. — “Jnvestigation of the inequalities of approximately
monthly period in the longitude of the moon according to the
meridian observations at Greenwich’. Addendum. By J. E.
pr Vos VAN Sreenwisk. (Communicated by Prof. E. F. v. p.
SANDE BAkHUYZmN).

Professor BartermMann and Prof. Ernest Brown have both been
so kind as to point out to me, in letters to Prof. Baknuyzen, that
Brown’s theoretical value, quoted by me, for the motion of the
moon’s perigee (p. 140), which was taken from MJonthl. Not. 64
532, does not quite agree with his final result, which was published
by him in Memoirs R.A.S. 59, 94 (comp. also JMJonthl. Not. 70,
3). If we use the value assumed by me for the ellipticity of the
earth 1: 297.5, then the theoretical result for the sidereal motion
in a Julian year for 1850 becomes 146435'16, so that my result
from the observations 146435"31 is now only O"L5 greater, against
0'26 formerly.

891

We approach, therefore, the limits within which this difference
might be ascribed to the errors of observation. However, I now
think, that the difference which was found, smail as it is, still
deserves closer consideration, and this especially with regard to
the value which Newcomp has deduced for this motion from the
long series of observed occultations discussed by him in his lately
published posthumous paper Lesearches on the motion of the moon.
He found (p. 225) 146435"29 + 002, a result which appears
to be very accurate and which agrees almost exactly with mine.

This induced me to consider in how far the small difference
might be ascribed to inaccuracies in the values, deduced from
observations, on which the theoretical calculations are founded. Sueh
inaccuracies might occur in those parts of the motion of the perigee
which depend upon the figure of the earth and of the moon. The
latter part is very small, but probably also very uncertain. It must
be calculated from the libration-phenomena and Brown deduced
for it, from Hayn’s results, 003.

Much greater (6"4) is the influence of the ellipticity of the earth, or
more exactly of the -difference between its polar and equatorial
moment of inertia, which can be deduced both from the results of
gravity determinations and from measured terrestrial ares, by means
of relations that are connected with CLairaut’s theorem. However,
these deductions are open to erificism, as BarTERMANN also pointed
out. Still we see that, when the ellipticity of the earth is calculated
from the most reliable results, recently deduced from both classes
of observations the results agree well with each other, and this
makes it appear probable, that also the values deduced for the
difference of the moments of inertia and thereby for the constant
of the lunar perturbations would be fairly accurate.

From the gravity determinations Hertmert deduced 1: 298.3 a
few years ago, and recently Hayrorp and Bow deduced from deter-
minations in the United States 1: 298.4"). On the other hand,
Hayrorp, from his discussion of all the measured aresin the United
States found 1: 297.0, while in Kurope, from the Russio-Seandi-
navian are of meridian, 1: 298.6 was deduced. In the American
calculations reductions for isostatic compensation were applied.

According to these results the value adopted by me 1: 297.5
would appear to be too large rather than too small. But now it
is remarkable, that all lunar perturbations which are caused by the

1) A division of the 89 stations into 2 groups, an eastern and a western, led
to 1:297.8 and 1:299.6 respectively ; the addition to the 89 stations of 10 stations
in Alaska gave, however, as the result from all 1: 300.4.

892

figure of the earth would indicate a greater value for the ellipticity.
Amongst these perturbations there are four which have a somewhat
considerable coefficient :

J. a motion of the perigee;

2. a motion of the nodes;

3. a periodic inequality in the longitude;

4. a periodic inequality in the latitude.

The first of these. according to our results, would lead to 1: 294.38,
according to Newcome’s to 1: 294.6 ; the second, according to NEwcoms’s
results, would yield 1: 294.3 and the 4%, according to N»wcoms,
1: 293.7, while the 3"¢ which has a period of 18 years cannot be
used for our purpose on account of the unexplained inequalities of
long period in the mean longitude. Are these differences to be
regarded as real and would therefore the measurements made on
the surface of the earth not lead to an accurate determination of
the difference in the moments of inertia ?

On account of the possibility that other circumstances may
exercise an influence upon the motions of the perigee and node, the
periodie inequality in the latitude, which has a monthly period,
would certainly be the most likely to yield a decisive answer to
this question, if it were not that an error in the assumed obliquity
of the ecliptic has precisely the same influence upon the declination
of the moon as the inequality in the latitude. (See also Newcoms’s
very interesting Addendum to Chapter XI, p. 226).

‘

Physics. — “ Magnetic researches. X\. Modification in the cryomagnetic
apparatus of WKAMERLINGH ONNES and Perrier.” By Dr. E.
OostERHUIs. Communication N°. 1394 from the Physieal Labo-

ratory at Leiden. (Communicated by Prof. H. KAMERLINGH

ONNES).
(Communicated in the meeting of January 31, 1914.)

In the researches on patamagnetism at low temperatures, described
in Nes. VI, VII, and VIII of this series (Comm. N°. 1292, 132¢, 1342),
an apparatus was used, in the main the same as that constructed
by Kameriinch Onnes and Perrier, of which a complete description
is found in Comm. N°. 1397.

In one particular, however, a change was made in the apparatus.
The apparatus so changed, which was briefly indicated in § 1 of
Comm. N°. 129’, is here more fully described. The force acting

893

upon the experimental substance in the tube, when it is placed in
an inhomogeneous magnetic field, was measured in KAMERLINGH ONNES
and Perrimr’s apparatus by electro-magnetic compensation. This can
be replaced with advantage by a compensation by means of weights, an
opportunity for which is given by the scale Q placed upon the carrier *).

The hook S serves to move the weights on and off the scale, while
the apparatus remains air-tight; if can be moved from the outside,
through the opening OU. The rubber tube U is hermetically attached
to the rim of the opening QO, and also to the extremity of the hook ;
in this way, the tube and the hook together can be moved sufficiently *)
to be able to lift the weights from the wall table I and place
them on the scale, or vice versa. The glass plate 7 enables these
manipulations to be watched from the outside. To prevent the rubber
tube collapsing when there is a partial vacuum in the apparatus,
it is supported on the inside by a flexible spiral of steel wire. We
further refer to the figures, in which the upper portion of the apparatus,

1) In the apparatus described in Comm. N°. 139¢ there was also a scale fixed
at the top of the carrier; the weights placed upon it did not however serve to
measure the force, but only to obtain an approximate equilibrium against the
upward pressure of the liquid. (See § 3¢ Comm. N°, 1392).

*) Compare the similar arrangement for stirring in cryostats, Comm. N . 83 § 4.

894

as it appears after our moditication, is shown in section and seen
from above. The lower part remained unchanged ').

The arrangement here described has some advantages over that
with the electro-magnetic compensation. In the first place, a much
greater force SS can be measured by it, and moreover the method
of working is simpler, as now only one current (that of the electro-
magnet) has to be read, in the earlier arrangement three. On the
other hand, while in the former arrangement the current through
the electro-magnet was adjusted to certain fixed values, for which
the corresponding strengths of field were accurately measured, in
the modified arrangement it is best to place a certain weight upon
the scale, and to regulate the current through the electro-magnet,
until this weight is exactly compensated by the force exerted upon
the experimental substance by the magnetic field. As the strength
of field corresponding to this current must now be found by (graphic)
interpolation, it can now only be as accurately known as by the
method deseribed in Comm. N°. 1397, if the field has been determined
for a great number of current strengths. Naturally in the method
of compensation by weights we could also work with a few accurately
measured magnetic fields, if we had a sufficient number of small
weights at our disposal inside the apparatus; but working in this
way would greatly decrease the simplicity of the method. For this
reasou in these investigations by the method of compensation with
weights, the field for the Wnuiss electro-magnet for different strengths
of current, was very minutely studied.

Physics. — “‘Jlaynetic researches. XI. The susceptibility of solid
orygen in two forms”. By ALBERT Perrier and H. KAMERLINGH
Onnes. Communication N° 159¢ from the Physical Laboratory

at Leiden. (Communicated by Prof. H. KameriincH Onnxs.)

(Communicated in the meeting of January 51, 1914.)

§ 1. Introduction. A former investigation?) had led us to the

conclusion that the susceptibility of oxygen suddenly becomes consid-
erably smaller when this substance changes into the solid state.
1) The sectional drawing of the upper portion of the apparatus is drawn on
the same scale as the fig. in Comm. N°. 139a, and gives therefore, if placed upon
that, the complete drawing of the apparatus as used in the researches of Comm.
NY. 1296, 1382e and 134d. :

2, H. KameruineH Onnes and ALBert Perrier, Leiden Comm. N?. 116 and 124a.

895

How great the jump might be, was uncertain, owing to the absence
of a bath which would keep the temperature constant at which this
change takes place. We were therefore obliged to draw our conclusions
from what we observed during a gradual heating, at which the
temperature can be only imperfectly estimated. A further investigation
was therefore necessary. Moreover, in repeating our determinations,
we encountered the difficulty, that we found a different value for
the susceptibility of solid oxygen at the temperature of liquid hydrogen,
than in our first experiments, which were conducted according to a
different method. Although we thought we were justified (Comm. N°.
124) in considering that we had obtained reliable results only by
the second method, and that in the meantime we need not attach
any value to those obtained previously, it was still very desirable to
confirm the more recent value for the jump by new measurements.
Finally, in our experiments we came upon another problem that
required to be solved. We had noticed (see Comm N°. 122a May
1911) as Want') also observed later, that solid oxygen, besides
appearing in the blue-grey opaque form that it usually presents, also
occurs in a transparent vitreous form. This modification can optically
be very clearly distinguished from the liquid state. We conjectured
that the transition from the transparent condition to the other one
might be accompanied by a second jump in the magnetic condition,
followirg on that which took place on freezing. We wished to
ascertain the truth of this also.

§ 2. Arrangement of the experiments. For the magnetic determi-
nations, as in previous investigations, we made use of the method
of measuring the attraction which the magnetic field exerts upon a
rod of the experimental substance placed at right angles to the field
in the interferrum of an electro-magnet, and held suspended there
by a carrier with hydrometer-arrangement.

More specially the arrangement of the apparatus was in the main
the same as that used for our investigations of the liquid mixtures
of oxygen and nitrogen, of which we shall give a complete description
in the next paper (Comm. N’. 139d). We do not give it here,
because the investigation treated in this paper, is of a much more
preliminary character than our investigation of mixtures, confining
ourselves here in the main to that which is peculiar to our experiments
on solid oxygen. At the outset it should be mentioned that the way
in which the temporary connection was made between the carrier

') Zeitschrift fiir physikal. Chemie. Bd. 84 (1913).

896

and the apparatus which introduced the oxygen from outside, was
the same as in the experiments with mixtures of oxygen and nitrogen,

HE TINLEY

897

In the further deseription we shall assume that the drawing of the
apparatus as if is given in this paper will be consulted as a modifi-
cation together with that of the next paper (N°. 139d). The develop-
ment of the apparatus there described, from our original apparatus
and the modification due to Oostrruvis (Comm. N°. 1396) will be
obvious on gomparison with Comm. N°. 139d.

In the cryogenic part, we encountered in the first place a difficulty,
which so far had not been provided for. Measurements had to be
made at the temperatures between the melting-point of oxygen and
the boiling-point of hydrogen, as well as at the temperatures of
liquid and solid hydrogen. In order to be able to do this an arrange-
ment was made which permitted us to work both ina bath of liquid
hydrogen evaporating under various pressures, and in a bath of
hydrogen gas, the temperature of which can be regulated.

The arrangement consists principally in a circulation of hydrogen.
The hydrogen, after having been cooled to the boiling point, before
it comes in contact with the experimental object, passes over a
heating-spiral, in which Joutr heat is generated, and is thereby
heated to the desired temperature. The whole hydrogen circulation
is carefully shut off from the outside air. The gas streams from a
supply-cylinder in which it is kept under pressure, through a copper
spiral AZ, the glass tube CDL, which from CE is double-walled,
and silvered, and at /# is widened, to the experimental space in the
cryostat. It enters this through the twice bent double-walled tube
FG, which forms the downward continuation of the vacuum-vessel
of the cryostat. On the way down the gas is cooled by liquid air
at A (copper spiral), and is further cooled first by hydrogen vapour
and then by liquid hydrogen at £6 (glass spiral). At H the gas
passes along a resistance thermometer; at /’ is the heating wire, at
G in the lower part of the experimental space a resistance thermo-
meter.

By means of regulating resistances the current through the heating
wires is so regulated as to obtain the desired temperature in the
experimental space. In the upper part of this there is a helium
thermometer with a steel capillary, which forms part of our cryo-
magnetic apparatus in its usual form (Comm. N°. 159a). The gas
then rises further in the vacuum-vessel, and escapes through S into the
gasometer or the air-pump. The tubes A’ and JZ serve for leading
off hydrogen.

Of the various auxiliary apparatus we must further mention the
thick-walled copper tube J/, which surrounds the experimental tube,
and which serves to keep the temperature of the gas which sur-

898

rounds it even all over. Of course liquid hydrogen ean be introdu-
ced into the cryostat in the ordinary way, to immerse the experi-
mental tube in a bath of liquid hydrogen.

We had a good deal of difficulty in procuring a rod of solid
oxygen of about 5 or Gem. length that was completely homogeneous.
As in freezing the volume of the oxygen diminishes by about ‘/,
there is a great tendency to form hollows. A homogeneous rod can
only be obtained by allowing the liquid in the cylindrical mould to
gradually freeze from the bottom upwards. As soon as solid matter
settles in the neck of the tube, hollows must arise in the experimen-
tal mass, as the entrance of liquid oxygen is cut off '). The diffi-
culty of procuring an homogeneous cylinder was increased by the
fact that in our experiments the freezing had to take place inside
a silvered vacuum glass, and could therefore not be followed by
the eye.

In order to come a step nearer to the solution of this problem,
which still presents difficulties, we ‘made use of the possibility of
regulating at pleasure the heat conducting power of a double-walled
vacuum glass. The experimental tube in which the oxygen was frozen
was made double-walled (not silvered); as much hydrogen was put
in between the walls that the (small) pressure had exactly such a value,
that aecording to preliminary experiments in a transparent bath
the freezing took place under the most favourable circumstances.
It appeared to be favourable to this that in the upper part ofthe
tube fatent heat was developed by the condensation of the gaseous
oxygen which was admitted during the freezing. When a once for-
med stick partially melted, it was difficult to get it back into a
dense condition. The double wall of the experimental tube is there-
fore also of use to eliminate temporary irregularities in the temperature
of the surrounding bath (vapour or liquid). It was found that the
temperature-range of the transparent modification did not extend
more than 5 or 6 degrees below the melting point.

§ 3. Results. The figures in the following table are averages. To
be able to express the results in absolute measure, the fields are
measured in absolute measure, and the dimensions of the tubes
carefully determined. The tubes were of the symmetrical type (see
Comm. N°. 139 § 4), the lower part was evacuated, so that no

‘) We shall return later to the freezing of oxygen and the change from the
transparent to the opaque mass. When the access of gaseous oxygen is cut off,
a long shaped holiow usually forms which as it increases assumes the shape of
a worm fantastically coiled up in a confined space.

899

correction was needed for the magnetism of the bath or of the wall.
The oxygen used contained not more than 0,001 foreign admixtures.
The immediate result of the observations is the susceptibility A’ per
-unit of volume; to calculate the value of x, the specific susceptibility
(or specific magnetisation coefficient), we must know the density vy.
We have taken 1.44 for this, on the ground of our determinations
in 1910, and from a new one recently made, but neither determi-
nation can lay claim to great accuracy, so that the values of x (and
also of AK for the opaque modification if it should prove that in this
innumerable little splits are present) will have to be recalculated
when o is better known.
The four results refer to one freezing.

ALB EE

| Susceptibility of solid oxygen.

| |
Meri OSae|
alfa ae loca ees ae
Hp |
|
vap: | 43 | 166.1 | 115.3
| 20.3 Tous e\rasaeGe ||
EE tyes 171.3) 53.7
lig. {| 13.9 | 76.7 | 53.3

A new freezing gave two values for A near 165.5. 10—° (before
and after partial melting) at about the same temperature (280° C.).
This value is less to be relied upon than that in the Table. We had
very little time at our disposal for our joint work, and this was
even diminished by the apparatus being found somewhat deficient
in some points. On this account we had not time to test a tempera-
ture lying between the melting point and the transition point from
the transparent to the opaque modification. But we had already
postponed the resumption of our researches after the departure of
one of us from Leiden, for two years, and we shall not have an
opportunity in the near future to continue our joint research. We
therefore felt bound to publish what we had so far established.

This is, besides the numerical values of our table within the limits
of accuracy given for it, that the transition from the transparent

900

modification of oxygen to the opaque, which takes place at about

225° C., is not accompanied by any conspicuous magnetic modifi-
cation, so that it probably does not involve any important change
in molecular structure. Further, that in the whole range from the
freezing point of oxygen down to about —— 240° C. the susceptibility
is markedly less than in the liquid state. In this region it changes
little with the temperature, in fact increases slightly on cooling.
This does not seem to agree with the much smaller value which

the table gives for 253° ©. but here a phenomenon intervenes
which has not been observed before, viz. that at about — 240° C.

the susceptibility suddenly falls to about half its value. The exact
value of the temperature must still be more accurately determined ;
it is also not settled whether the transition is actually discontinuous
or is completed in a very small range of temperature (1 or 2 degrees).
The susceptibility falls in this transition to about the values that are
found in liquid hydrogen.

It will be seen that these last values agree with the values of
1911, within the limits of accuracy of the latter. The results of
1910 are thereby, as we expected, condemned, and the cause to
which we attributed the discrepancy between these results and
those of 1910, gains in probability at the same time.

As regards the change in the susceptibility below — 252°C. with
the temperature, although it is shght, yet it allows no doubt. that
it is a decrease. The observations permit the comparison of the
susceptibility at different temperatures at constant density without
the intervention of any correction. We have here, therefore, a
new example of a substance that follows Curir’s law at a higher
temperature, and on approaching the absolute zero completely
deviates from it. As the ratio of the susceptibilities observed above
and below the transformation point is

115.8
oD
it becomes probable that the exact value of the jump is precisely
2. For above 20° K, the magnetisation must still increase distinetly.

3 === hy KVR

For the ratio of the susceptibility of liquid oxygen and _ solid

oxygen at — 230° C. we find
313.3
ee
x 115.3

This value is less certain than that of 4,, for it contains the
uncertainty concerning the density of solid oxygen and that of the
change of susceptibility between --- 220° C. and — 280°C.

From our previous investigations we had inferred a sudden change

901

in the susceptibility to a fifth or sixth part of its value between the
liquid state and the solid state at hydrogen temperatures. It now
appears that a sudden change of this amount really exists, but takes
place in two parts, namely, once to ‘/, at freezing, and subsequently,

Eta)

T 1
| aed
| = |
300 =I Ti Pa |
| |
250 ~
] | |
| |
| |
220 ——+— ae ————
al | |
| |
—— ! ——
| |
| @---+~+ —— |
100 ' po pee
Ife: |
a 1 REA |
345 jae OS
i | | |
i | e
Ma MeN | ee | a | aa ace
F) 10 20 30 40 50 60 70 SOK

Vig, 2.
after the susceptibility has again increased a second time to 3 at
the transformation point — 240° C., after which the susceptibility
further decreases. In the accompanying figure our results are put
together.

Physics. — “Magnetic researches XIU. The susceptibility of
liquid mixtures of oxygen and nitrogen, and the influence of
the ‘mutual distance of the molecules upon paramagnetism.”
By Ausert Perrier and H. KaMerLincn Onnes. Communication
N°. 139d from the Physical Laboratory at Leiden. (Com-
municated by Prof. H. KameriincH ONvEs.)

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

§ 1. Introduction. In 1910 and 1911 we published experiments
upon the susceptibility of oxygen at very low temperatures, by
which it was demonstrated that the specific susceptibility of this
substance, which, in the gaseous form above 0° C. follows Curtn-
Lanervin’s law, deviates considerably from this law in the liquid
state at low temperatures, and even more so in the solid state.

Subsequently we have observed similar phenomena in other sub-
stances (paramagnetic salts). The (solid) substances referred to follow
Curtm’s law at ordinary temperature, and also at temperatures that
do not lie too far below it; but when the temperature falls to the

902

neighbourhood of the boiling point or the freezing point of hydrogen,
they deviate from the law im various degrees*), but always in the
direction of decrease of the susceptibility.

We think it advisable to recall here in a few words some of the
views and hypotheses which guided us in the above-mentioned
researches, in order to make clear the connection of the former ex-
periments to each other, and to the determinations we shall here
deal with, and to elucidate the object of these last.

When we began our magnetic investigations at low temperature
(in 1908) we wished, amongst other things, to test LanGcEvin’s recently
published theory of paramagnetism which leads to Curie’s law, at
low temperatures.

On this account (and on others, see Comm. N°. 116, § 1) it was
natura? we should begin with oxygen. The deviations that we found
in oxygen together with what we observed in other substances,
gave us ground to suppose phenomenologiecally that there would be
a law of corresponding conditions for the deviations from Curig’s
law. This again gave rise to the question of how Lanervin’s theory
would have to be supplemented in view of the new phenomena.
Our first idea was the possibility of polymerisation, which might
take the form of association in oxygen. As the degree of association
of liquid oxygen if diluted with a non-active substance, would be
changed, and as diamagnetic nitrogen could serve as such a substance,
we thought (see Comm. N°. 116, § 5) that by experiments on mix-
tures with this substance we should be able to ascertain whether it
was a case of polymerisation or not.

An experiment made witb a less satisfactory apparatus than that
which we now use, gave an indecisive result, and even led us to
a wrong conclusion, as it seemed to support our assumption of the
same change with temperature in the specific susceptibility of oxygen
independent of the distance that separated the molecules from
each other. In other words it still appeared possible to us that the
specific susceptibility of oxygen vapour at the boiling-point might
be the seme as that of liquid oxygen, and that therefore gaseous
oxygen at this temperature would deviate from Curir’s law to the
same extent as liquid oxygen. Our intention soon to make further
measurements on mixtures of oxygen and nitrogen, came to nothing,
as one of us left Leiden. It was a considerable time before we were
able to continue our experiments.

In the mean time, KameriinGH Onnes &nd Oosterutts’s investiga-

- 1) KamertingH Onnes and Perrirr, Comm. Nos. 116, 122a, 124a,

903

tions agaim raised the idea that the distance of the molecules in a
paramagnetic substance certainly has an influence upon the deviations
from Curin’s law. Their investigation of oxygen of more than 100
times the normal density (Comm. N°. 134d April 19138) demonstrated
more specially that the susceptibility for gaseous oxygen can be

represented down to — 130° C. with Curm’s constant, which holds
for the ordinary temperature, which indicated the possibility that
this might still be the case at — 183° C. This gave fresh support

to what they added at the end of their paper of Jan. 1918 (Comm.
N°. 132¢), showing the desirability of experiments upon the question,
whether the bringing of the molecules (or atoms) of a paramagnetic
substance to a greater distance from each other, influences in itself
the deviations from Curie’s law, and pointing out the importance
of the continuation of our experiments with liquid mixtures of oxygen
and nitrogen. *)

Before we could at last begin these experiments in 1913 the
importance of them was increased by yet another circumstance.
Besides the hypotheses considered in the above mentioned article,
hypotheses of another kind arose *).

With the former hypotheses, we do not interfere with the law of
equipartition, but assume either polymerisation, as in the above case,
or a subsiduary potential energy, a “molecular” field, the magnitude
of which is determined, not only by the field, but also by the amount
of one-sidedness of the direction of the molecular magnetic axes
(Weiss and Fox, KamertingH Onnes and QOostmruuis)*). In the new
type (OosTrrHuIs, Knresom) on the other hand a distribution of energy

1) Recently, Weiss (C. R. Dec. 1913) in deducing the distance law for the
molecular field in ferromagnelic substances (comp. § 4 this Comm.) points out the
importance of investigations of the same miterial at different densities. See also
G. Fox, Arch. d. Sc. phys. et natur. Genéve (4) XXXV. 1913.

2) As had been partly the case with the hypotheses of the first kind, so also
those of the new kind were partly suggested by our former magnetic investigations.

3) The hypothesis, that the resultant magnetic moment of the molecule changes,
can be introduced in two different ways. In the first place, by assuming polyme-
risation, as mentioned above. In the second place by supposing that the change
takes piace exclusively within the molecule itself. By continuous change of this
sort of course every deviation from Curie’s law may be explained. In that case
there can be no question of decision between the above mentioned types of theory.
The supposition referred to seems less acceptable also for this reason that in the
cases in which Weiss was led to assume a change in the molecular moment, this
was always a discontinuous alteration (by changes in the number of magnetons)
and ove which took place in all the molecules at once, while for the rest the
moment wilhin a definite temperature zone did not undergo any change.

53

Procecdigs Royal Acad. Aisterdiim Voi. XVI

904

is supposed, which is determined according to the quantum-theory.

In the extreme form of this type no other suppositions are intro-
duced than those of the quantum-theory. There is naturally room for
transitional forms between this extreme form and the other type of
hypothesis. These are got by assuming polymerisations or a mole-
cular field besides the quantum-theory.

It is now of importance, not only for magnetism, but also for the
law of molecular activity in general, to decide between these two
different types of hypothesis, by experiment. The most important for
this purpose are experiments in which the paramagnetic molecules
are brought to different distances from each other. For if the above
mentioned question should be answered in the negative and it should
be proved that the susceptibility per molecule remained the same
at whatever distance they are from each other, then all hypo-
theses of the first sort (mutual influences) would of course fall to
the ground. The measurements which should demonstrate this would
be an experimentum crucis.

The determination of the susceptibility of liquid mixtures of oxygen
and nitrogen claims the first place in experiments upon the influence
of the distance of the molecules upon the deviations from Curin’s
law. The liquid (paramagnetic) oxygen exercises no chemical influence
whatever upon the liquid (diamagnetic) nitrogen ; the two substances
can be mixed in any proportions, so that the distance of the para-
magnetic oxygen molecules can be increased at pleasure : the mixtures
remain moreover liquid down to a very low temperature, which is
of particular importance, if the theory of quanta is to be applied.
Experiments with these mixtures promised therefore a more distinet
and more immediate decision than those with crystals and solutions
of chemical compounds in different degrees of dilution’). In the
investigation now completed we have not been able to do more
than make a first survey of the difficult territory.

We here offer our sincere thanks to Dr. Oosternuts, who has eon-
tributed greatly to the suecess of our work, by very carefully measuring
out the field that served for our experiments, and by repeating certain
susceptibility determinations which were doubtful. His measurements
enabled us to introduce important corrections in our results.

1) With regard to these we may remark that the important investigations by
Cabrera and Motes (Arch; d. Geneve (4) XXXV, May 1913) of solutions of iron
salts are of a chemical nature and assume the validity of Curte’s law. Their object
is therefore quite different from ours, in which the point is to investigate the influence
of the distance of the molecules of a chemical element dissolved in another element,
upon a function of the temperature.

905

§ 2. Method. The measurements were made by the attraction
method, wiih a vertical cylinder of the substance to be investigated.
One of the extremities of the cylinder is placed in the middle of the
interferrum of an electromagnet. As in the apparatus previously
constructed by us‘) the cylinder was attached toa vertically running
carrier, and the forces were measured by a zero-method ; in this
the modification introduced by Oostmrivis’?) was made use of, viz.
the current through the electro-magnet was regulated, and therefore
the field adjusted, until there was equilibrium with marked weights.

While thus the magnetic part of the experiments is about the
same as that of the previous ones, the arrangement of the actual
experimental object demands a number of special apparatus and
precautions. A homogeneous mixture must be prepared of known
proportion, and in a proportion chosen at will, of two substances,
which are gaseous at ordinary temperature, and which are condensed
in the experimental tube.

In the first place a communication must be made through the
closed outer cover of the cryomagnetic apparatus (see description
loc. cit.) with the apparatus for mixing and measuring the gases.
For this purpose, the glass tube A (see fig. 1), which forms the
central part of the carrier, is bent round three times rectangularly
at #£; further it bears a horizontal tap C, and terminates in a
horizontal ground: joint YD, in which fits the ground extremity of
the tube #, which protrudes outside. This tube is enclosed in a thick
but elastic india-rubber covering, and can be pulled back about
2 centimetres, from outside, and made fast in this new position ;
in this way the connection with the carrier can be made; or the
latter can be left quite free, without the cover being opened. In the
same way the tap C can be manipulated from the outside by
means of a similar arrangement F’.

The necessity of the mixture being homogeneous, entails vigorous
stirring inside the experimental tube (the cylinder A, at the lower
end of the carrier). Even when the mixture is homogeneous in the
gaseous form, the oxygen which condenses more easily, will tend
to collect at the bottom in the carrier; this difficulty is overcome
by using astirrer consisting of a very long thin glass capillary tube
G, terminating in a small disk // (the actual stirrer), which carries
a little piece of iron (A) at the top; the whole of which can be
moved up and down through a distance equal to the height of the
experimental tube. This movement is set in motion by the attraction

1) See H. KamertineH Onnes and Atp. Perrier, Gomm. No. 139a.
*) E. Oosterauis, Comm. N°, 1390.

58%

< (NE

Fig. 1

SOT

of am electromagnet / upon the piece of iron A’; the electro-magnet
is moved from ontside the apparatus by means of two bronze strips
L, which run over the pullies WV and pass through the walls without
friction, terminating im two elastic enclosures similar to / and F.
These suspension-strips, which also serve as conductors tor the
electro-magnet, are moved by band.

The earriey is provided at #£ with a small stopper serving as a
safety valve, to guard against a casual excess of pressure in the
carrier during the measurements, when the tap is closed, bursting
the carrier.

The preparations for a series of measurements took place in the
following order: when the enclosure is found to be air-tight, a
sufficient weight is placed upon the plate Q to bring the carrier
to its lowest position; the connection with the tube /# ean then be
made, the tap C is then opened, and any gases that may be con-
tained in the carrier, are pumped out. Then the cryogen bath (of
pure liquid nitrogen) is made ready, and the temperature reduced
to a few degrees below the boiling-point by reduction of the pressure.
Finally the desired amount of pure oxygen, which has been previously
measured in a volumenometer resembling a T6rLER-pump, can be
condensed in the carrier, and then by means of the same instrument,
the quantity of pwre nitrogen required to completely fill the experi-
mental tube k. After this (€ is shut, D is disconnected, the gas
supply tube is pulled back and the overweight taken away ; the
carrier is them free, and completely closed against the vapour of the
bath. While the bath is beimg brought to atmospheric pressure, and
to: an even temperature, which is greatly promoted by the pump-stirrer
P*), whieh causes a vertical circulation in the whole bath, the
electro-magnet' which serves as stirrer for the mixture, is put in
motion, until the magnetic attraction, which is measured from time
to time, reaches a constant value.

The question of what the composition of the mixture is deserves
particular attention. A given weight of oxygen is introduced into
the tube, which spreads over a given volume, known by the eali-
bratiom of the experimental tube. The weight of oxygen per cm’.,
i. e. the concentration, is thus givem by immediate experiment,
whieh quantity is also the most inyportant from the magnetic point
of view, as the measurements im the first place give the suscepti-
bility of the mixture, and the concentration enables us to deduce
from it the specific magnetism which can be ascribed to the oxygen

1) See H. KAMERLINGH Onnes, Comm. No. 123, § 2.

90S

alone. To compensate the vacuum caused by the contraction of the
mixture by each decrease of temperature, we have each time added
pure nitrogen (stirring of course each time); our object was the
investigation of the influence of the mean distance of the paramag-
netic molecules upon the magnetisation, and the process described
above apparently comes to the determination of the changes in the
magnetisation with the temperature, for every mixture at constant
distance of the oxygen molecules.

After the measurements the vapour products were collected, and
analysed with pyrogallic acid. This analysis is a useful check, but
cannot lay claim to great accuracy, as the comparison with the
synthesis assumes the knowledge of the total quantity of condensed
nitrogen (including the amount added during the measurements), which
quantity is for various reasons somewhat uncertain. Moreover it is
necessary that the vapour products should be very completely col-
lected, as a considerable weight attaches to what is vaporised last,
as being almost pure oxygen. On the other hand we may remark
that the deduction of the concentration (see above) from the
synthesis presumes only an accurate knowledge of the weight of
orygen and not that of the nitrogen, and therefore can claim a
greater degree of accuracy.

The susceptibilities are expressed in absolute units by comparison
with that of pure liquid oxygen, which are previously measured in
absolute value by the method of rise’); this calibration comes simply
to this, that a series of measurements are made under the same
conditions as the former, but with pure oxygen instead of with the
mixtures. Moreover, a calculation of the absolute values based upon
the values of the field according to the measurements made by Dr.
OosteRHUIS in Leiden after the measurements, lead to results which
agreed with the experiments previously obtained, well within the
limits of experimental accuracy. Further the magnetic corrections
were applied for the glass of the carrier and for the nitrogen of the
bath as well as of the mixture *).

§ 3. Conclusions and expeximental results. The mean pumerical
data of the measurements are given in table I, where x signifies the
magnetisation of 1 gram of oxygen in each of the mixtures or in
the pure oxygen; for the latter the values are calculated on the

') KameRtINcH Onnes and Perrirr, Comm. No. 116. Cf. note 1, p. 912.

*) These corrections raust be made even in a purely relative measurement, as
they are by no means proportional to the susceptibility of the experimental object
taken as a whole.

909

basis of our measurements in 1910 (Comm. N°. 116); 9 is in each
case the weight of oxygen per cm*. (concentration), 4 the approximate
ratio between this weight and the corresponding one in the pure
liquid; 2 indieates to some extent the dilution (only approximately,
because with the method followed 4 changes with the temperature) ‘).

EABLET

Magnetisation-coefficients for oxygen. (77.°4 K—64.°2 K)

lo= atm. pressure) | (p = 300 mm.) | (p = 100 mm.)
Qo t X . 108 || t | X . 108 || t % . 106
liquid) 1.204 —195°.65 | 259.6 | | |
oxygen )) 1.235 | | —202°.23 | 271.4
pure} 1.267 | | '|—208°.8,| 284.9
| | | | |
- | 3n| | |
I | 0.745¢ | 5 || —195°.65 | 294.5 || —202°.2, | 314.5 || 208.8, | 336.5
te. | | |
2 | I 0 4019 | 3 | .79 | 336.7 || 2 S506) ||) la elt SOOK6
ft } 2 |
| 2 ( IM | 0.230, | i || .60 | 363.8 | . 393.0 || [423.5]
x | aera |
|=} iv |0.138| 3 || .65 | 383.6 || —202°.2, | 420.4 A 459.8
ee |
\ V_ | 0.080, | 75 || —195°.80 | 395.8 = = |==20858, |) 47240
extrapolated by |
., _ 0.03097 | | | |
, oe ae | —195°.65 400.0 || —202°.25 | 437.2 |—208°.8,| 482.2 |
(Weiss and PiccaRD } | | |
amc) | hea | | |
|

Table I shows at once this qualitative result: The specific mag-
netisation coefficient of oxygen becomes considerably greater, in pro-

1) The various numerical data upon which the results are based are not all of
the same degree of accuracy: the temperatures, measured by means of the pressure
under which the liquid boils, the same pressures beg chosen for the different
mixtures, may be compared in the one and the other mixture to 0.1°, the absolute
values, on the other hand, have the same degree of accuracy as the vapour
pressure curves.

The directly found (volume) susceptibilities of the mixtures, which are not in-
cluded in the table, may be compared with one another to about 0.3°/) on an average.
As regards the specific magnetisation coefficients, if these may be compared for
the same mixture at different temperatures with the same accuracy as the sus-
ceptibility, their uncertainty in absolute value is specially determined by that of
the concentration; we estimate it on an average at 1.5"/o, higher for the large
concentrations, lower for the smaller ones.

910

portion as the concentiation diminishes, i.e. the additive rule is by
no means followed in mixtures of oxygen and nitrogen. From a
somewhat more careful inspection, and the comparison with the
last row of the table, it appears further that aw7th increasing dilution
the magnetisation coefficient approaches to the values which satisfy
the inverse proportionality with the absolute temperature, starting from
the number lately obtained by Weiss and PiccarD tor gaseous oxygen
(see also Fig. 3).

Without anticipating in any way the theoretical interpretation of
these results, which will be treated im the next paragraph, we can
phenomenologically express them as follows: :

The deviaticns from Curti-Lanenvin’s law, shown by pure oaygen
at low temperature, are not an timmediate consequence of the change
of temperature, but are caused by the increase of the density on by
the distance between the molecules becoming smaller.

Finally, let us examine more closely the thermal change tor each
concentration, by plotting ‘/, as a function of 7’ (Fig. 2). We see at
once that the points obtained lie upon parallel straight lines; the

4400) 1] aa an

4900} ea : a —

Fig. 2.

change with the temperature can therefore be represented *) within
the limits of accuracy of the observations, by a relation of the form

.

') As was found by KamerunaH Onnes and Oosreruuts for liquid oxygen; Comm.
N°, 132¢.

91 |

¥(T +A): = const.,
in which only the parameter 4 changes from one concentration to
the other. Table Il shows this:

TABLE Ui.
| Hee)
Mixture A - a
| T=T14, T = 10.8, T = 64.2,
———————— A : |
I | 29.5 0.0315 | 0.0316 0.0315 |
| il 16.3 316 Sista Wie ewsis
| ll | 9.5 gigs) | 316) ho] [3125] |
IV | 4.5 314 | 316 | 316
| Vv | 2.2 316) ||| ~ 314
| Mean 0.03155

Therefore: the change in .density of the oxygen only alters the
specific magnetisation, without changing the Curi-constant.

The pure liquid oxygen seems to form an exception: the straight
line '/,= f(T) for this differs considerably in direction from that
for the mixtures. We would call attention to the faet, however, that
each mixture was examined at constant concentration (see § 2); while
this was not the case with pure oxygen, which shrinks considerably

on cooling (10°/, about between — 183° and — 210°); if we
calculate for any temperature (say —195°) the specific magnetisation

that pure oxygen would have at that temperature and at the densities
corresponding to the other temperatures, using the Curtm-constant
which is common to the mixtures at constant concentration, the
values obtained thus (see Fig. 3 the points indicated by blaek disks)
fall in a natural way upon the general curve, which gives the specific
magnetisation as a function of the concentration at the temperature
under consideration; the data obtained from these measurements form
therefore strong arguments im favour of the conclusion that in the
investigation of pure liquid oxygen at constant density a curve for the
change of the magnetisation would appear, which only differed from that
for the mixtures by a new translation. This causes the anomaly to
disappear. The strict experimental proof of this conclusion can only
be obtained by a great number of experiments with a very concen-
trated liquid, or by means of! a direet experiment, in which we begin

912

890 8 testo: H0= 100. —_—_
x
\y
380 3 —-— a
|
|
|S |
360 USGS b =|
| \
I) oN
\ |
340 t $< — 4
| x | |
\ | |
$20 — | a =
i] \
| \
| “
| INES
300 +--+ a - , |
|
|
.
2s0 |} — — |
<i}
1
INS
| | | | .
= 260 =r + 7B
r | | °
ot | | |
son | |
SS, 2405— —
~
i ese
99)
220 L 3|
Q on Q4 db 08 40 420° Ah

we odionr

with pure oxygen and for each decrease of temperature add the
necessary quantity of nitrogen *).

§ 4. Theoretical conclusions. We must call attention to the fact
that every theoretical interpretation of our results must account for
two different facts: in the first place for the change of the magne-
tisation with the density, and in the second place the parallelism

of the lines a)

It is plain that Lanenvin’s theory, only supplemented by the hypothesis
of the negative molecular fields, is sufficient to give the explanation.
In fact if NV represents the coefficient of the molecular field, it leads
to the law

1
a NO

=

e

or

¥(f + A)=C, where A = Cwo,

1) Experiments make it probable, that for gaseous oxygen x even at — 188°U.
does not deviate or at least (see the conclusion of § 4) deviates only very little
from Curie’s law. In the application of the ascension method y may therefore
not be supposed to be equal for the liquid and for the vapour, as was done in
formula (2) of Comm. No. 116, but a correction must be applied, whieh, however,
in our case remains within the limits of experimental error.

915

which agrees with the law following from Table IH, if we assume
that 4 or No decreases with the density.

This being established, the experiments further permit, and this
gives them an additional significance, to account for the aay in
which the molecular field changes with the density or with the distance
of the molecules.

We remark in the first place, that the accurate caiculation of the
molecular fields rests upon the knowledge of the deviations from
Curte’s /av, and not upon that of the susceptibilities themselves
[formula (1)|. It would therefore be necessary to know the specific
magnetisations in absolute value down to at least 0.1°/, in order to
be able to deduce the fields from them with sufficient certainty ;
this is especially the case for the great dilutions where the deviations
are extremely small. A determination of this degree of accuracy
demands in itself a long and difficult special investigation with
perfected apparatus.

The solution, if not completely found, may yet be brought within
narrow limits. The first question that then arises is, whether the
field is eqnal to a particular power of the distance of the molecules
i.e. of the density. If we suppose N = ag", then the molecular field
is ag"t!. At constant temperature '/, = /(@) is then a parabola of
the degree n + 1, with the axis vertical and the top on the axis of
ordinates. For n= 0, '/, is represented by a straight line.

4000/— ay eae a a ea |
| ry
} | W |
| A
| ia |
| | |
f
| | / |
3500} | ____ ——-! ae |
Ҥ $
RO nl |
% Qy |
° |
al
| Ape wal
3000 —
| |
- |
{Game Ame |
25k ST | [donee |
0 Or Os 06 08 410 4,4 1,4
mlm
Fig. 4.

In Fig. 4, the curve which our experimental data give for the
temperature 77°.45K. is shown; it deviates from the straight line,

914

but the deviations are not much greater than the errors of observation,
except for the most diluted mixture. Moreover the slight curvature
is im the opposite sense to all the parabolae for which n>0O. The
observations at concentrations smaller than 0.1 indicate that the
molecular field then begins to change more quickly, but they do
not justify the assertion that this is actually the case. It is therefore
not probable that the results can be represented by means of a
positive m (except for very great dilutions, for whieh we have not
a single indication); in order to elucidate this point we have also
constructed the curve */,= f(y), which with the same extremities
corresponds to n= 1, i.e. to the law that the molecular field would
be proportional to the square of the density or to the inverse sixth
power of the mean distance of the molecules; it is obvious that this
bears no resemblance to the experimental curve.

We assume therefore that the molecular field of oaygen changes
about proportionally to the density *).

This law, in the case of the appearance of a negative field
(assuming that this exists) for oxygen, differs totally from that at
which Weiss arrived, in the case of the positive molecular field with
alloys of ferromagnetic metals, for the dependence of .V upon the
density, and from which he inferred an influence according to the
inverse sixth power of the distance, which for that reason we have
just referred to. (From our law, in the same way, an influence
according to the inverse third power of the distance would follow).

At present, we need not see any contradiction between these two
results, as the conditions for which the two laws of distance hold
good, are quite different. This applies both to the nature of the
substances and to the. state of aggregation in which they were
examined. Moreover it must be particularly borne in mind that the
sign for the molecular field is different in both cases. The part of
the curves referring to the change of N with the concentration,
which Weiss makes use of in his theory, lies entirely in positive
fields, the transition to negative fields is curved. We are in complete
ignorance as to the origin of the mysterious influences which cause
the phenomena ascribed to the molecular field. There is no ground
therefore to expect that the two fields are subject to the same law.
Should it be confirmed that the two kinds of molecular field depend
upon the distance of the molecules according to different laws, we

) Cf. the next paper by KAMERLINGH ONNES and OosTeRHUIS, in which the
idea of the dependence of A on the concentration is extended to the “atomic
concentration” of the paramagnetic component in erystallized compounds, in the
first place in those containing water of crystallization.

915 -

might even see in this a proof that in the two cases influences are at
work which are the effect of different causes‘).

If we continue the idea that the deviations from Curiz’s law are
to be attributed to a negative field, we come with the value 0,03152
which we deduce for Curin’s constant, to 14.11 magnetons per
molecule of 2 rigidly connected atoms, while Weiss and Piccarp,
from their determination of the constant for gaseous oxygen arrive
at exactly 14. An error of 0.2 degrees in the lowest temperature
at which we made observations would explain this difference. So
there is no reason to take this observation as at variance with
the law of magnetons. [At the end of § 4 we have drawn attention
to a circumstance that would possibly explain the difference. (Added
in the translation) |.

Although the hypothesis of the negative molecular field is sufficient
to describe the phenomena, it is not devoid of interest to consider
in how far the other hypotheses can be reconciled to the observations.

As regards the polymerisation-hypothesis, it is not probable that
the association decreases as rapidly with the density at constant
temperature as would have to be the case if the experiments were
to be explained by it, nor that the result of a given form of the
hypothesis, which might give this change, would lead to the set of
parallel straight lines in fig. 2.

OostERHUIs’s hypothesis, that the energy of rotation should take
the form of

v.— hy hy
i 5
ekT__]

must he supplemented by a further hypothesis. It is in the: line
of the deduction to accept that the moment of inertia of the molecule
changes considerably by dilution, and increases to very great values.
Even in accepting this hypothesis it appears from ecaleulations by
Dr. OosteruuIs that the deviations of the curves calculated from the
set of the parallel straight lines in fig. 2 are too large to be explained
by experimental errors *).

1) The function ¢‘/s, which was given in a prelimmary note (Soc. Suisse de
physique, Frauenfeld 1913) was based upon data which later appeared to have
been insufficient in number, and before some subsequently calculated corrections
had been applied. The function may be correct for a range of weak concentrations.

2) In ‘these calculations OosTeRHuIS started from the values of ~ which were
deduced immediately from the experiments according to Table II, which in partic-
ular gives the most probable slope of the straight lines accepted to be parallel.

916

Finally we may remark that the supposition

f(T) eon cia oes eRe ee
combines the various hypotheses which we have explained above
(except that of polymerisation), and agrees with our experiments
if /( 7) is independent of the density, and .V of the temperature ').
It accounts for all phenomena which are expressed by a parallel
displacement whatever value is aseribed to /(7’), if only it remains
independent of the density.

(One can imagine that /(7’) is in reality of such a form that in
the temperature-range of our experiments it gives for x of the oxygen
in the liquid mixtures of oxygen and nitrogen a value which, while
being small for the large densities of oxygen, increases in passing
to more and more high dilutions, and approaches in the limit to a
value greater than that which with Curi’s law is obtained from
Wass and Piccarb’s experiments. If further experiments which may
be undertaken with a view to throwing light upon this point should
give a positive result, one could explain without relying upon expe-
‘/, being a little small
(given by C= 0,0815, see fig. 2). It would then be of interest to

rimental error the slope of our lines for

compare that result with what the investigation by IX AMERLINGH ONNiS
and OosTERHUIS on the susceptibility of gaseous oxygen at low tempe-
ratures will teach when extended to lower temperatures. It is not
entirely excluded that the nitrogen plays a different part from a
vacuum. Added in the translation.| (Cf. note 1 p. 915. Added in

going to press).

Since then Dr. Keesom has communicated to us that by calculating the values of 4
in giving to f(\7) [see formula (3)] either OosTERHUIs’s form, or the form wh'ch
Kresom has developed in Suppl. N’. 32a, whereby the values of ¢ are a little
changed, one obtains a_ satisfactory representation. The values of ~ are then in
agreement wilh the function «%/ for large values of «, which he arrives at (see a
paper of his to be published shortly). In his calculations Knzsom accepted the
number of magnetons of Wriss and Piccarp. His theory explains also that the
curve 1/, =f) of fig. & does not pass through the origin. [Note added in
going to press. |

1) F(T) vepresents$the energy of rotation as a function of the temperature. (3)
is only applicable to the range where the magnetisation is strictly parallel to the
field. Formula. (3) includes inter alia the vanishing of the CuRig point in ferro-
magnetic substances caused by zero energy deduced by Kersom (Leid. Com. Suppl.
N’. 32a@andb (1913).

(Regarding the influence of the density on f(7') in KeEsom’s theory see his next
paper, ef. also note 2 p. 6 of Suppl. N°. 32a. Added in going to press.|

917

Physics. — ‘“Maynetic researches. XIV. On paramagnetism at low
temperatures’. (Continuation of VII). By H. Kameriincu OnNzEs
and E. Oosternuts. Communication N°. 139¢ from the Physical

Laboratory at Leiden. Communicated by Prof. H. KamERLINGH
ONNES.

§ 15. Ferrous sulphate. (Continuation of HL § 2). The measurements
of the susceptibility of paramagnetic substances at low temperatures
were continued according to the method previously deseribed.

Crystallized ferrous sulphate, which had been already investigated
by KameruincH Onnes and Perrier (Comm. N°. 122a), was once
more very carefully prepared. by precipitating it out of its aqueous
* solution with alcohol. The values of the susceptibility found do not
entirely correspond to the previous ores, but the dependence on the
temperature is precisely the same, as is shown by the following
table, when compared with table Il of Comm. N°. J22a,

TABLE XII.

Crystallized ferrous sulphate FeSO,.7H,O
precipitated with alcohol.

| are |

| 18 eo wee toe 4. T. 106 | Bath

| es: — 2 —— zl =
| 292.°3K.| 42.4 12390 in air

| 71.3 160 12370 liquid

| 64.6 ie eet ot | 12340 nitrogen
| 202 eae oT 11590) ‘liquid

| Teiiees 786 13110 | hydrogen

§ 16. Palladium. Pure palladium (from Heranus) gave the
following figures: (see p. 918)

Palladium, it will be seen, deviates markedly from Curtn’s law.
Cur found just for this substance the law ~.7’= const. fairly well
confirmed. Honpa') (above ordinary temperature) and OwEn *) (below
ordinary temperature down to 100° K.) found deviations from Curin’s

: ; , . 1
law which agree very well with our results. The line — = /(7)
Pres

1) K. Honpa. Ann. d. Phys. 32, p. 1027, 1910.
*) M. Owen. Ann. d. Phys. 37, p. 657, 1912,

918

TABLE XIil.

Palladium.

Tels Neeeooetey Bath
201°.K. | 5.3 | imoair |
250 5.8 liquid
212 | 6.0 methyl chloride
170 6.9 liquid ethylene
71.3 | 8.1 ; |
| |
70.2 | 8.2 liquid nitrogen |
6416.» | "a8 | |
20.3 9.9 |
| ] liquid
| 17.9 10.2 f hydrogen
14.7 10S9)erea i

shows some irregularities, which are greater than we should have
expected considering the degree of accuracy of the experiments.

§ 17. Ferric ammoniumsulphate (tron alum).

This substance will be seen to follow Curin’s law throughout the
whole range of temperature that was examined. This, according to
the theory developed by Oostrrnuis in Suppl. No. 31, would be
owing to the great moment of inertia which a molecule of this
substance undoubtedly possesses.

It may also be explained by the theory which Fokx gives fol-
lowing Weiss (C. R. T. 157, p. 1145. 1913). In fact iron alum is a
substance crystallizing in the regular system and according to Fobx,

for such substances the line —— /(7’) will be a straight line at-all
Z
temperatures.

This property of ferric alum may also be regarded from another
point of view if we consider the latest results by KamErtincn Onnes and
Preise (Comm. N°. 139d). In § 3 we pointed out ‘that interposition
of water molecules between the molecules of ferrous sulphate, as
occurs when this salt crystallizes «with water of crystallisation, causes
the deviation from Curin’s law ‘to disappear, and thus diminishes A.

919

TABLE XIV.

| Ferric ammoniumsulfate Fe.(SO4)3. (NH4)2.SO, + 24H.0.

r. 1.103 ie TAOS Bath

290.°0 K, 30.4 8820 in air
169. 6 51.8 8790 liquid ethylene
ies ia S810) une

> liquid nitrogen
64. 6 137.0 850 |
20. 4 432 8810
[Tako lew “oR gsio0 | tiquid hydrogen
Ei a ad 5 8790

We found the same in § LO for manganese sulphate, and in § 11
we came to the conclusion that the decrease of A might be the
consequence of an increase in the distance of the paramagnetic
constituents of the salt. Finally we drew attention to the fact that
the transition of oxygen from the gaseous to the liquid form might
be accompanied by a change in A. Perrier and KAMERLINGH ONNxES
have now demonstrated that 4 decreases witli the dilution of oxygen
with nitrogen, and that the change of 4 with the density, which
must be assumed to find for liquid oxygen ai all temperatures | with
the help of the 4.) 7 corresponding to the liquid density oj, 7} from
4(P + Apitig 7) =C
the same number of magnetons as in the gas at ordinary temnerature,
agrees well with the change of A with the distance of the molecules,
which is found from the dilution of oxygen with nitrogen. By this
it has become evident that if A is the consequence of the existence
of a molecular field, this field decreases when the molecules are
brought to a greater distance from each other, and soon, at molecular

; : ale
concentrations of about 500° is no longer perceptible .

In ferric alum, the distance of the /e-atoms is of the same order
as that at which the molecular field of the oxygen molecules in
the solution of oxygen and nitrogen disappeared in KAMERLINGH ONNES
and Perrrier’s experiments. That this substance conforms to Curtz’s
law as far down as the freezing-point of hydrogen, may therefore
be due to the atoms of iron, at the atomic concentration in this
substance, being at a distance which permits them to behave like

og

Proceedings Rayal Acad. Amsterdam. Vol. XVI

920

those of a normal paramagnetic substance. Should this hypothesis be
correct, it would be of importance to take notice of the atomic
concentration, in studying paramagnetic substances. To determine
the number o; magnetons in a paramagnetic atom, we should therefore
have to take (complex) compounds, which fulfil this condition of
being sufficiently ‘diluted’. This condition is fulfilled by many
of the materials which have been used for the calculations about
magnetons *).

If we arrange the substances according to the vaiue of their
atomic concentration, we see that in general the deviations from
Curiz’s law at low temperatures seem to appear sooner in substances
with a high concentration. Oosrrrnuts’s calculations (Comm. Suppl.
N°. 31) give particulars of the amount of the deviation in different
substances. It will therefore be desirable, if we want to determine
the number of magnetons in an atom at low temperature, to go
down to very small concentrations. This is no difficulty for the
measurement, for, although the specific susceptibility at small
concentration is small, it increases considerably according to Curt’s
law for a given concentration with the transition to low temperatures.
We should come upon chemical ground if we were to discuss what
compounds would be suitable for this purpose. Double salts and
complex compounds seem to be particularly suitable, provided we
are able to apply the correction for diamagnetism.

It is very likely that with high atomic concentrations 4 may rise
to very high values. Something of this sort might be the case with
platinum (see § 12) and with the ferromagnetic substances the inves-
tigation of which first led Weiss and Foéx to the introduction of a
negative magnetic field.

For crystals, a ‘linear concentration” may have to be introduced.
The value of A for different directions would have to be brought
into connection with this.

In the further study of the deviation from Curie’s law, use will
have to be made of the results of Werner’s investigation of the
constitution of complex compounds on the one hand, and
on the other hand of the data which experiments upon the diffraction
of ROnreEn rays, such as Brage@ in particular has made, may yield.
What these can teach concerning the arrangement of the atoms and
the structure of the atomic lattice, is of great importance from the
above point of view. (To be continued).
2) In ferrie alum is realised a case of solution of a paramagnetic in a practically
neutral substance, of the same kind as that which Wetss considered by extra-

polation in his discussion of the ferro-magnetic alloys when he was searching for
the law of distance for the molecular field.

921

Geology. — “At what time the Indian Archipelago is separated
From the Tethys’. By Prof. K. Martin.

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

(This communicatien will not be published in these Proceedings).

(March 26, 1914).

tying ae
t ’ 4 Sy of

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HUA Pa ha ity , "yi d

PAA: Ay

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Reo. dee. ‘EAM (ile pill an ik Ag ‘nae
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. . » =. ‘ee
nd i
2
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KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING
of Saturday March 28, 1914.
VoL XVI.

Vice-President: Prof. D. J. Korvrwese.
Secretary: Prof. P. ZEEMan.

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Zaterdag 28 Maart 1914, Dl. XXII).

CLONE BIEN GaSe:

J.J. van Laar: “A new relation between the critical quantities, and on the unity of all
substances in their thermic behaviour”. (Communicated by Prof. H. A. Lorenrz), p. 924.

H. J. E. Bern: “The envelope of the osculating ellipses, which are described by the repre-
sentative point of a vibrating mechanism having two degrees of freedom of nearly equal
frequencies”. (Communicated by Prof. D. J. Korrewra), p. 938. (With one plate).

S. pe Borr: “On the reflectorical influence of the thoracal autonomical nervous system on the
rigor mortis in cold-blooded animals”. (Communicated by Prof. C. A. Prxeimartnc),
p. 952.

J. BorseKen and W. D. Conen: “On the reduction of aromatic ketones”. IT. (Communicated
by Prof. A. F. Horieman), p. 962.

A. J. yan Peski: “On a new method of preparing carboxylic anhydrides”. (Communicated
by Prof. S. Hoocrwerrr), p. 969.

W. P. A. Jonker: “Connexion between the adsorption-isotherm and the laws of Prousrand
Henry”. (Communicated by Prof. F. A. H. Scrrememaxers), p. 970.

Jax pe Vries: “Cubic involutions in the plane”, p. 974.

H. Kamertincu Onnes: “Further experiments with liquid helium I. The Hall-effect, and the
magnetic change in resistance at low temperatwes. 1X. The appearance of galvanic resistance
in supraconductors, which are brought into a magnetic field, at a threshold value of the
field”, p. 987.

J. K. A. Werrnem Saromonsoy : “Electrocardiograms of surviving human Embryos”, p, 992.

H. A. Brouwer: “On homoeogeneous inclusions of Kawah Idjen, Goentoer and Krakatau and
their connection with the surrounding eruptive rocks”. (Communicated by Prof. G. A. F.
MOLENGRAAFF), p. 995.

A. Smits, A. Kerrner and A. L. W. pe Ger: “On the pyrophoric phenomenon in metals.”
(Communicated by Prof. J. D. van per Waats), p. 999.

A. Suits: “Answer to Prof. E. Coney to his observations under the title of Allotropy and
Electromotive Equilibrium”. (Communicated by Prof. J. D. van per Waats), p. 1002.

60
Proceedings Royal Acad. Amsterdam, Vol, XVI.

24

Physics. — “A new relation between the critical quantities, and on
the unity of all substances in their thermic behaviour.” (Con-
tinuation.) By J. J. van Laar. (Communicated by Prof. H. A.

LORENTZ.)

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

8. The shape of the function b= f (v). After we have thus derived
some relations in the preceding paper‘), by means of which all the
critical quantities are expressed in the one quantity y, the reduced
coefficient of direction of the so-called “straight diameter’, we shall.
examine what forms of /= /(v) satisfy the relations found.

These relations, from which the table on p. 829 loc.cit. has been
calculated, are the following. {[Cf. also the formulae (14) and (21)
loc.cit. p. 818}.

by. Uk, It+y V};
2S SS ta — ss =—=>2(1+4+ })
Vo "Me if 9
(22)
SORT Sr. Sa) ee ae a
= pre) Vabys us be aye SEIS Gye
In this A is the factor in
8 a a
ie
OYA Niias Meare OE Tine

in which 4, =2,=A2 is put. The found values of 4, and 4, appeared,
namely, not to differ, and 4 is always in the neighbourhood of
unity. Though y varies from 0,9 for ‘normal’ substances to 0,5 for
‘ideal’ substances, 2 ranges only between the values 0,98 and 14.

We further found:
sgn dhe Na By 5 peg Gat 1 ili
1+y 4y(y+1) rae)

Pee Sf ea

: ene os p Tx. db
In this g = — Pe in which #',;= We saw that 6

is generally exceedingly small.
We may still remark that the relations for 6, and 6", may also

be written thus:

(by Tay v,)° by. = Vo
Bip, a eae yep MS ire tee
aS i ee ( k) (24)

1) These Proc p. 808.

925

Whieh enables us to find out something about the course of the
funetion =/(v'. For the sake of accuracy the original v, is every-
where written in the above formulae, and not the 6, put equal to
it. The quantity 7, is namely the liquid volume at 7’— 0 extra-
polated from the equation of the straight diameter. From '/, (d¢,--d,)—
=" 1 = y(d—~m) follows namely, when d, = 0 and m=—0, that the
reduced limit of density (d,),, i.e. v,: 0, becomes equal to s'=2 (1+).
It is this », which occurs in the above relations.

In virtue of the fact that when the limiting volume of 4 corre-
sponding to this limiting volume 7, ie. 6,, is assumed different
from v,, very intricate, if not impossible results are obtained for
b= f(v) — whereas the assumption 4,—=v, leads to comparatively
simple results, | have been led to identify 6, with v,. So we assume
that at the limiting value of v for 70 (calculated from the formula
of the straight diameter) also 4—=v, and so also Mo. Hence
what we call v, and 4, in what follows is the same as VAN DER

Waars understands by wv; and bj, *) with this difference, how-
‘db

ever, that (=) is not = 1, but always much smaller than 1, and
oh 0

will even appear to be =O (at y= '/,). That the latter is really

the case, follows also from this, that in the limiting case y= '‘/,

(ideal substances) — where therefore /,—4,, and the course of the

function = /f(v) is represented by a straight line parallel to the

y-axis — necessarily 6’, must be — 0.

Let us now proceed to determine the shape of the function
b= ff (v). According to what was observed in § 1 of the foregoing
paper, we consider the variation of 4 with the volume entirely as
an apparent change, and that chiefly on the ground of the joint
action of two influences, the diminution of the factor 4 in b,=4m
(m= nucleus volume of the molecules) to about 2m at 6, — at
least at the ordinary temperatures; and the simultaneously acting
influence of temiporary molecule aggregations (quasi association).
These two influences will make the quantity 6 in »—é diminish
from 4m to about 2m.

But at very low temperatures, at which 4, will approach more
and more to 4, (see § 7 loc. cit.) till 6,=6, at 7’=0, this varia-
bility disappears — and the question rises how this is possible.
Does 6,=2m then rise to b,=4m, or does 6, = 4m descend to

') These Proc. XV p. 1132 at the top, 1138 and p. 1142 at the top, where
everywhere tin = Oblim is assumed. On p 1138 also vdin=vo (from the straight
diameter) is put. Our v% and b, are therefore exactly the same quantities as
VAN DER WAALS’ Viim and Déim. A
60*

926

4, —=2m. The former is in contradiction with the experimental
result that 6,, and so also 6 decreases with decrease of temperature;
the latter seems in opposition to the theoretical result that for infini-
tely large volume 6, must always be = 4m, and cannot possibly
therefore assume the value 2m, however low the temperature may be.

Yet the latter is the only possible supposition. We shall return
to this at the close of this paper, and we shall then propose a
supposition which may be alleged as an explication of this appa-
rently so singular behaviour.

9. Let us first consider the forms which present themselves most
readily, but cannot satisfy the equations (24), in connection with
the convergency to 6, and %,.

When we put generally :

sf (2)
= by = as G) ; . 5 . . e . . (a)

in whieh /(v) is such that this function becomes = 0 for v= o,
and inereases with decreasing v, then

; (Uk
p= by 0A B =

baby = (by =). ai”) Ne st et Ocoee (CD)

(®
when we briefly write /(v) for / lah

From this follows :

hence also

by—br f( v) by — bz f'(r)

) SS pee ’ = — Tree
PACE) B? Ff (vr)
hence
b! by — be —f'(rr) h" bg — bk f'(ve)
Ne Ss 5 OO DE SES _ z
B I(vk) B* fv)

therefore
Ai | Woy)
OB fe)
but as according to (24) also
LE Aa LA
we have necessarily :

927

In consequence of this we have:

pag yy (Seo see
Op lo five)
from which follows for the relation (6, — 6;) : (6, —4,):
by — bi. ne bp. iy Ter) (a)
b, — b, 1 — be (—f'(vx))? =f" (ve)
The equation (4), written in the form :
J’)
Page rt 8 ¢ el
then becomes :
Be ge ty) On ()
1 — by (= fx)? : Fx)

in which 6; in given by (24).

First Example.
ie) = Pome |e
Then J) = afv ip) 10@318)i=— ——€ 4/4), and fe (v)=e—"/2 KO)
that we obtain :

vu v/
: b'y. CE k/e_— e /p
‘bt. = (b;. 5,) ———
1 —b; baie k/p

’

as (—f' (vx))* : f"@x) = e—vk/p
Hence we get:

ee ae
fy —SS — Ok
EET as ehh Oo - (25)

a]

b
oe ae ee eee
as 6 according to (c) = (b; — b,): (1 —- b's).

But the equation (25) — which in the neighbourhood of the eriti-
eal point of course perfectly accurately satisfies the conditions: 1)
that at v=o the value of 6 becomes properly 4, in connection
with (7), and 2) that the equation at vz for >; and 6", gives the
values determined by (24) — is quite deficient in the neighbourhood
of v,. It has, namely, also to satisfy there for small values of 6; — b,,
when y is near */, (ideal substances). Now in this case with 6), =
= (b.—b,)? : bv, (see (24)), and in regard of the circumstance that in
consequence of 6, becoming =O, unity may be written for 1—';,
for v= v,, b= b, we get:

=H
bi —- by (be — by)? de —b,
By ae OR er

’

925

in which within | | 1 has been omitted by the side of the infinitely
Jarge value of the exponential quantity. But now the first member
of this equation — 1, the second member becoming = 0X e”, hence
approaching o. Not until vz—v, should be of the order 6,—4,,
by which the exponential quantity could be made of the order
bgve: (be—5,)?, could the above equation be satisfied. But then v,

would get into the neighbourhood ‘of vy, when 6,—, approaches to

0
0, i.e. when y approaches to '/,, and this is impossible.

It is easy to see from the graphical representation that the indicated
Jv) intersects the v-axis already soon after vz, in consequence of
which / passes to negative values, so that there can be no question
of a convergency to the point v,, 4,.

And it is easy to see that this cannot be changed by changes in
the form of the chosen exponential function. Nor can KAMERLINGH
Onnes’ function satisfy. For this funetion, viz.

b = by — (bg — 6, )e—#—%) ,

and #, are

0

leading after substitution of v, and d,, through which »
eliminated, to

b = by ai, (b, os be»,

is identical with (6), when e—’/é is substituted for J(v), (@ satisfy
is then ='/g),. For it would inevitably lead to the rejected
equation (25).

And if this and suchlike functions are made to satisfy at 7,, 0,
— they will necessarily not satisfy at vz, dk, i.e. the values 6’,
and 6"; will then entirely differ from the theoretical values indicated
by (24).

Second example.

fe) = ( a

As 3 will disappear here, an exponent 4 must still be added to
satisfy the conditions (24), which exponent can then again be deter-
mined from (c), 6, being given by (d).

We now find:

. (e\- CD sd . » \— (+2)
AO) a 6( ) > Ff Moe =) ) 5
B, B

| f i, B Fi tl 6 (5 —h
g ance “(= yn) )? : Nhe 2 value ——— ‘
uid hence for (— /' (vx))? 7" (vr) the valu i

In consequence of this (e) becomes:

lie, Ye) te i vE\?
i ie = (pS a | Bae Thome i (2c
Me ( k a) cc by. 6 ] ( v ) | ( )

in which @ is determined through (c¢). (c¢) now becomes namely :

p=t—te+0(S) »

p

t
yielding
Uk

6+1=(1 — b4) (26a)

by. — b,
But here too there is no convergency for v,,6,. For small values
of by — 6, (26) namely approaches to

"h

Dig nbs | Lee \ EE %
SS a 2
by. Tim b, Vo

because 1 — b’; and (6 + 1):6 then approach to 1, while between
[ | again 1 has been omitted by the side of (vz: v,)’, which approaches
to infinite. The first member is —1, the second member approaching
to 0 <a”, hence to o.

Also when (v —v,)—% had been assumed, we should have found the
same impossibility ; even still intensified, because then (v, : y,) eK)
would have become [(ox—0,): (0, —v,) "Pe *), because of which
the root of the power would approach & for all the values of b; — 6, *).

In the same way the functions may be tested, in which v : (6—4,)
is written instead of v:f. The functions —/ (v) and /"(v) then
become somewhat more intricate, but the divergency at v,,
continues to exist.

And as for vAN per WaAALS’s equation in the general form

as len b—b, \” 97
aa =J = : . . e ° A (2 )

the so-called “equation of state of the molecule’ — this leads to
such complicated expressions for / and n, in order to satisfy the
relations (24), that no physical significance can possibly be assigned
to these expressions. Also when v—v, is substituted for v—b. We
shall, therefore, enter no further into all these calculations, and
leave their execution to the reader.

Before leaving this kind of functions, which all lead to failures,
I will just point out that if one should want e.g. to derive from the

0

bs AG B \9
1) Also the supposition / (v) =Nigaaa ‘ ) = (= ) leads to the same impos-
‘0 { 0

sibilities.

930

relations (24) by division, that also outside the critical point
6" b'
ee ei; b—b, .
one would easily find back (25) after integration of this differential
equation, But we know that this equation does not satisfy. Also
other obvious suppositions about 6” and 6’, which satisfy (24) at the
critical point, lead to such impossible final results.

10. We have now come to the forms, which lead to possible,
and at the same time not too intricate results, also as far as the”
convergency point v,,, is concerned. In all these forms the relation
(6 —b,):(v—v,) or also (6 — b,):(v—b) occurs by the side of
(6 —b,):(b, — 6,). In this respect the general form of VAN DER
Waats’s relation (27) is the best that can be assumed. Here every-
thing is reached that can be desired. The relation (6 — b,) : (v— 6)

approaches to a finite limiting value 7 at v=6=v,, when in the
,» 0, has been
properly warranted beforehand. Further 4 becomes 6= 6, for
v=o. But as has been said before —in order properly to obtain

second member /—= 4,, so that the convergenecy at v

the values given by (24) at vy, exceedingly intricate expressions must
be assigned to f and mn, in which for the case 4 = constant, Le.
br — b, or 6b, —b,=0 (y='7/,) f approaches to 0 and n to oo.
This is of course in itself nothing particular, as it is e.g. by no
means necessary that, as vAN pprR Waatis desires, Lim (b — 6,):

(v—v,), 1s == 1 or assumes another finite value; it can very well
become —O, as for values of v close to v, (orb) 6 can long have

assumed a value close to the limiting value },. Tbis is the more
apparent when we consider the case that 6 no longer changes at all,
or hardly changes (at += 1/,). The value of 5 can then be put
about —%, throughout its course, from v=o to v=v,, so that
the numerator of (6 — 4,):(e —v,) approaches much moré rapidly
(or infinitely more rapidly) to O than the denominator. Nor is a
very large value for n with small values of 6, — 6, impossible in
itself. :
But it is the exceeding intricacy of the expressions for 7 and n
that make us reject equation (27) in that form. And these intricate
results remain, so long as the exponent of (6 — 6,):(v— 4), which
is always =1 in (27), differs from that of 6 — 6,): (6, — 6,), viz. n.
Let us take generally :

b—b, ee a ly b—b, \* (270)
7) =a

931

and let us then calculate / and n for given value of 6. It soon
appears then that simplication is only found when 6 =n. The reader
may be left to ascertain this fact for himself.

Accordingly we shall only treat the case that 6 =n is put in
(27°) from the beginning. But first one more remark.

The equation (27a) is a special case of the general assumption :
7)
F (%)

in which /(v) approaches to 0 for v=o. We may, however, also
write for this :
‘(v
b — b, = (by — 6) (: - si )
F(%)

or still more general :
“b—b, \" ‘(v
cere WS Je) hae S25)
by — b, a

when /(v,) = Lim f(v) is denoted by a for v=v,. If we now take
for f(v) the special function [(6 —d,) : (v—v,)]|’. this passes into :

es Wea SU DY,
b,—b, = a \v- 2, ;

which corresponds with (27a), because a means the same thing as
J. We can, therefore, consider vaN Der Waats’s form as a special
case of the quite general form (28), when namely, (6—0,) : (v—v,)
is simply taken for /(v), and not this ratio to a certain power,
while also vAN DER Waats substitutes v—b for v—v,.

But whereas van pDrr Waats’s form with n=2, 06=1, f=1

= by (by b,)

or more, has a physical meaning, being related to the deformation
of the molecule by pressure and temperature (which deformation in
our theory —see § 1 of the preceding paper — may be considered
negligible, and has, therefore, been left out of account), our formula
is for the present without such a significance, and it must only be
considered as an empirical relation — just as many others, e.g. the
equation of the straight diameter, that for the vapour pressure, ete.
— to which possibly afterwards a physical meaning can be assigned,
in relation with the different factors which give rise to a quasi

variation of 6.
“b—b, \" 40 n
seas Von iy Tie(e eo a 4 (29)
bg —b, a \v—»,

So we put:
b—b,

in which a= Lim (

SF Uo

n
) at 70 — 0,0 OO wiles Oo == 0, is

assumed.

932

If for the sake of brevity we write 2 for (—d,):(v—v,), then

which with introduction of vj, and 6; passes into

bp—b, n ayn
— |= | — armen re whan! al tan LEX.
feo a te)

from which 6, can be computed, when a and n are known. Sub-

stitution yields :
b—b,\" a—ar “a
— ; . ° 5 . . . a
b.—b, a— ax} : )

in which a is therefore Lim «,”. Let us derive from this the values
of b' and 6". We find for 0’:

b b—b, n—l nan—l b—b, L b'
bth. Nop 0 tee ee eae (Gb) tee

hence for 6":

6" b-—b, \"—! (b')? bb, \7—2
———— n {| ——-—— + — n (n— 1); ——— =
b. —b, b.— 6, (6;.—6,)° by. —b,
n (n—1) ar—2 b—b, iy
— - — = + =e
a-—x}” (v—b,) v—b,

ner) b—b, b b"
an 2 Dk eit
a— xj (v—b,)* (v—b,)? r—b, |.

Hence at the critical point after multiplication by 6,—0,, resp.
— (b,—,)° :

' ae Sr b'k Uk " "ys
be |
a— Xp”

(n—1) a2 (xy? —b'p wy)? 4 ay} [2a7,°—2b'; ax? + 6", (b:—b,) xh| :

a—axj”

H

The first equation yields at once:

ake a pet!
b'p 1 t = ’
a—aj a—x Ij”

hence b',.a—=.apet', or

apt
a= (3)
b'k
The second gives:
. ry A F
— b" (bk—b,) (2 we ) — (n—1) (0%)? =
. a— xj

(n—1)(b'%)?axg"—2(n—1) b's ay™+— 26'% art! + (n—l)agrt? + Qayrt?

a— xp"

?

933

hence:
—b"7(be-b,)a —(n-1)(b'k)" (a ek") (n-1) (0) wg — Anb'k wg! +- (n+ Lyng.
As according to (24) — 6"s (hr—b,) = (bk —b,)? 1—O'n) : be ve, ie.
= b', (1—0';), we have also:
[o'~.—(6'r)?] @ = (n—1) (62)? a — 2nb'p apr! 4+ (n+-1) apr,
or
n (b'k}* a — b'p a — 2n bp eye) + (n+1) ayrt? = 0.
After substitution of xg+! for b'ga, and division by xz"+!, we get:
nb! — 1 —- 2n b'p + (n + 1) ap = 0,
or
(n + 1) ae — nb!’ = 1,
from which
l—xz
far De b'E
On account of the value found for a, we can now write for (29a):

b—b,\r ayer! -— b'p am
be — 6) ae +! — Up aen

or also

tH)? — b'k =
ob b, i)
ee eran a a ee (30)
b; — b, ze — bk
in which
b—b, bi —b, (bk—b,)? 1—aE
— 3° & = — ; bp=—— 3 n= ——_,,_ .. (30a)
v—b, VEU bk vk ae—b'k

while from («), (8) taken into consideration, follows:

be—b, n b'p ah? +1 ae
| ee (SOD)
Bye bk

11. It is easily seen that the found equation (30) fulfils all con-
ditions. In the first place we get properly

b,—6, Le wh:
be —b, ) pay

for v = © («= 0), which is in harmony with (302). Secondly the first
member —1 for v=vz (vz), the second member (vp —b'p) : (az— 6'p)
also becoming = 1. Thirdly for 6—=6,,v =v, the first member — 0,

bea

and the numerator of the second member = x, — ——, as x,”—=ais
aj

put. But 6',a@ = vpz’t', hence this numerator is also = 6.

By differentiation of (30), considering that there 6’, stands for

934

(by. — 6,)?: bp ve, which we shall call 8 for a moment, we find
further :

b—b, \"—_ BI 1 B b—d, U
n | ———— - <= ——_— — nan—l — —— + —— ],
bp —b, by—b, ek—B ay (v—b,)? v-b,

which becomes for vz:

ane geet
— aT oe — Ok Uk a
ae(ae—B) mr = Ray

from which immediately follows 6.=, ie. the value given by
(24). And with regard to 6";, from

b! bb, \2—1 B d b—b, b
S| | = —— en—iy — — + —— (a)
bp —b, \ be — »b, vk"(ap, — B) (v—b,)? v—d,

follows after a second differentiation, and substitution of vv; and
b= bh; (see also above):

B

es BM, (bi: oy b,| — (n = 1) Pe = ak (vk—B)

3) 5 O— 1) ay? (aj? — b'payx)? +

+ ay! [2 wp? — 2 by a? + b" 4 (6, — b,) wel |

yielding, when @ is written for 6';:

"(be — b,) (: ut )=e ~)e +8 & 1) (ex — 8) +2 |
or — 6"; (bk — 6) ce, = B (ae — B). (n + 1) ay

Now according to (80 (n+1) ( cc at Nea ae =1— 8;
hence

— b", (bo, — 6) = BU —p—)=—Se(1 — 5),
and now (24) is again satisfied.

After having thus carried out these control calculations, we return
to equation (30).

The quantity 6’, cannot be computed from. the above equation
(a) for 6', as the latter gives O=O for v,,6,. No more could 6",
be calculated from the general equation for 6". But since in the
neighbourhood of v,, 65:

ye b—b, pleat 1) pl 7
Carey === bg + /2 5 @—m) + os.
V—V,
: ' . lil) : a
evidently 6’, = Lim ——~ = .w,, and hence according to (306) = ya.
v—v
0

When we represent (6—4,) : (b,—6,) by Jd

930

follows from the above equation («) for 4’; or also, since 2 approaches
Ro oo Oe adap —= Ok:

' vi;
b noe = ae ae (w—b »)
Uj-—b'
Now «—b', = '/, 6", (v—yv,), hence:
C—O el
Bie OE hn ee eee
th v—v,

or also

b",(bk—b,) = 2(0',)’0" ele
since (b4-— b,) : (v—v,) = (br — 4,) : (6 —4,)) K (b— 4,) : w—%,)) =
===! x b.

With assumption of (30) the value of 4”, is therefore always = 0,
since d approaches to 0. The final course of the curve b= /(v) is
therefore straight, the coefficient of direction being indicated by
i Va.

That for v =o, in consequence of v — v, in the numerator of 2,
both 6’, and 6", become = 0, is self-evident.

Let us now examine the values of a and n for different values
of b;— 6, or of y.

When we substitute in m = (1—«z) : (we—'p) the values of wv, and
b'x, we get:

b.—b,
Ve—V
LS ee
be—b, (bx — 6,)°
Ve—Vv, Of Vk

€

or also, taking the relations (22) into account, i.e. d¢: 6, = 2y,
Mm:¥,=2(1+ y), in which 6,=—v,:

(: | Ge en)
N= I Ea tet lg ae i Se a :
2741 ayo aye l)

Hla
n= 8y(y + 1): @y—1) [470 + D — Gy + D@r—-D],
or
Sx(y +1 Qbp vp
i= eS seiner i nee oii. col (32h)
(2y—1) (4y+1) (6r—6,) (26% + 4,) 3
So the exponent n ranges from 3'/, (when y= 1) to » (when

y='/,). For ordinary substances (y=0,9) » becomes =46:171 =
== 3,72; for Argon (y—0,75) n= 5,25.

For the value of a, i. e. the limiting value x, of (6—b,) : (v—»,)

for' v=, 6=06,,. we ind’ from) #7, =a ayan sible aise sa05)

the value:
n n Lye 4 i) 5 il
Ci — aah ae = ana z - + (82)
2y+1 2 eee

in which %# possesses the value given by (31). This limiting value
vj, Which is at the same time = 4’, (see above) assumes for y =‘
the value :

1 35 8
- ee = 4/1359 (O53) fors yp — 10,9) themmralee
3) to)

0,8 ,37276 84

3 ae 5 D4 == ia x | 5315) 0) == 0,386 2 for = 0,75 the value
O15 7 214 75,25 e i ,
ne ee a5 = '/; < 1,814 = 0,268 ; while for y = 0,5 it properly op-

proaches 0 (6—4, then namely has become continually =O). For Viwnb!s)
then approaches unity, the factor (2y—1):(2y+-1) approaching to 0.
Accordingly for all “ordinary substances’, where y is about 0,9,
the line 6=/(v) will approach the point of convergency v,,), at
an angle of about 21° (¢g gy = 0,39).
In conclusion we will still discuss the value of 6, : be according
to (30°), viz. é

by - b, n vi);
f br. Es b, = rh-—O'
31/5 3
The limiting value of this for y =1 is evidently Oa ,2C/,;— in| —

| 16 = 1,158, which with 6; : 6,=2 leads tu bg : be =1,079.
3,72
For ordinary substances (y = 0,9) we find ke Weeh |=

= 74 senda oe —— al oalialidy leading with 0;:/0, = 18 to 0, ae

= 1,050, i. e. the normal value. For Argon (y= 0,75) the second

member becomes abe (e/a .)| = (21) 2116) se Ob 3e

which with 6,:6,=1,5 for 6,: 6; yields the value 1,018. Finally

for an ideal substance 4, : 6, = 1.

Equation (80) found by us, therefore, yields good results in every
respect, from v=o to v=v,, and that for all values of d, — 6d,
or of y. In addition it may once more be stated, that when 6 = 6,
in the first member, the second member too must be = 0, hence

Ue O'e (a: ve)", in consequence of which a=,” assumes the value

art: b'., thus properly the value given by (30°). It is also easy to
see that in the limiting case y—'‘/,, i.e. 6, = 6,, the equation (30)
passes into 6 =const.=,. For then 6',=0, and the second member
becomes constantly = 1, i.e. ) constant = b; = 4,.

12. It is self-evident that the equation (30) is not the only one
that will satisfy the different conditions. Thus in the second member
of (29) e.g. we might have assumed v —> in the denominator
instead of v—v,. A ealeulation quite analogous to that in § 10 would
then again have enabled us to find a set of values for » and a,
But then they would have been less simple than with v — v,. It is
easily seen that the result is obtained by substituting (1 --6',) :(1—6'x)
in 2 = (1—ay) : (we —b',) for unity, and 6: (1—0';,) for 6'"), so that
we then get:

1+ b", bk ny 2 Uke
7 Ges yeecd b r =9 ie ie cr
having
by—6, Dp Uh,
ene eres

The equation = /(v) itself becomes :

by far

RE Ee ris)
(= =) eos :(1—b'2) ;

But when we now wish to express 7 in 7 we get, instead of
n = 8y (y + 1): (2y—1) (4y + 1) according to (31), the less satisfactory
expression (10y + 1) :(2y—1) (4y-++1), in which 10y + 1 = 5h, + 6,):6,
has a much less simple signification than 8y ‘y+ l) = breve: 6,°.
We remind of the fact that 2 is now = (b; —~ 6,): (vp

And there will be no doubt that more such funetions are to be found,
which lead to more or less complicated expressions — but we confine
ourselves to the above.

by), lence

1) For where we found above b/; = xkr—! X (xk? — b'k Hk) 2 (@ — xen), a factor
1 — b'& will now occur by the side of xg’, so that after division of both members
by 1—b’¢ everywhere b’« has been replaced by 0’; :({—b'r). And in the equation
for b”r, [b'¢—(b's)2] a in the first member will be replaced by (0/%—(0'2)*) (a--vkr +1):
(1 — b’z)2, when both members are now divided by (1 — b’x\*. On account of this
b/:(1 —b’z) comes everywhere in the second member, where 6’ stood before,
while in the first member (b/¢—(b’))2)<(a+arr+!), is substituted for (b'—(b'7)2) a,
the consequence of which is that, after application of entirely the same reductions
as above, nb’, — 1 — 2nb’r+(n+1)ae=0 is replaced by nb'k: (1 — b’k) —
—(1+0’k): (1 — b’k) — Anb'k (1 — be) + (1 +1) oe = 0.

938

In our coneluding paper something will be said about the iempe-
rature influence, which will manifest itself by continual diminution
of b¢— b,, at first slowly, then more rapidly, as the absolute zero is
approached. Descending from high to low temperatures one can
therefore pass through all the types. If the eritical region of a substance
lies in the region of low temperatures, the critical quantities, and
also the isotherms in the neighbourhood of the eritical point, will
present, as far as the course of 6 is concerned, the little variable
type with slight 4,—4, (y in the neighbourhood of 0,5). But these
same substances will of course show the same variability of 6 as
the “ordinary” substances at high temperatures. Reversely the ordinary
substances, considered at low temperatures, will assume the Argon-,
Hydrogen- or Helium-type, with respect to the slight variability of
4 at these temperatures. Ete. Ete.

In this coneluding paper I shall also communicate the 4-values
for Argon I have calculated; besides I shall venture to give some
theoretical considerations concerning the diminution of the factor 4
in b, = 4m with fall of the temperature.

Fontanivent sur Clavens, February 1914.

Mathematics. — “The envelope of the osculating ellipses, which are
described by the representative point of a vibrating mechanism
having two degrees of freedom of nearly equal frequencies.”
By H.J. EK. Bern. (Communicated by Professor D. J. Kortawne).

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

§ 1. In my paper on the small oscillations of mechanisms with
two degrees of freedom '), Lissasous curves with their envelopes were
discussed, which envelopes form the boundaries of the domain of
motion. In a summarizing treatment of a more general problem *)
my further inquiries as to these envelopes have also been included.
These inquiries were extended over a system of Lissasous curves,
more general than the system which is of importance for the dynamical
problem. However the envelopes were considered exclusively from
a dynamical point of view, so that purely geometrical properties
together with the shape of the curves outside the domain of motion
remained unknown. Moreover what came to light about the shape
of the envelope remained for the greatey part restricted to simple
cases, e.g. in the case, formerly indicated by S— 2, to the symmet-
rical case, as quoted, indicated by p+q=—0 , /=0.

') These Proceedings pp. 619—635 and 735—-750 (1910).

*) Phil. Mag., sixth series Number 152 (1913).

939

In what follows for S— 2, the case of the equality of frequencies,
the envelope will be treated anew and from a more geometrical
point of view.

We shall therefore have to occupy ourselves with the envelope (L)
of the system of ellipses

= 6\cos : y¥ = V 136 cos (t—@),
in which § and y are two variable quantities in the most general

case connected by the relation :

j Ss
Ve (1—$) cos ¢ = — = [ate We o + gS + r-+ Ti 2.

By elimination of ¢ we tind for the equation of the ellipses
(A) (5) § (1—6) cos yg . wy + Sy? = §(1—S) sin? ep.

Let us now determine the reciprocal polar curves of these ellipses
with respect to the circle :
(C) oP
in the circumference of which circle the vertices are situated of the
rectangles, which are circumscribed to the ellipses (A), and have
their sides parallel with the axes. The envelope (“’) of this new
system of ellipses will be the reciprocal polar curve of the envelope
(£) wanted. (Cf. note p. 943).

The new system of ellipses appears to be given by :
(1') 622-2 VATE —S)cos‘p . ay + (13) Yr =

By elimination of gy between this equation and the given relation

1
4(ps + 95 -+ +- A r | wy*® — 1 — Sa? + ley -- (1—$) 77}?.

This equation contains § to a no higher order than two. The
equation of the envelope of (4') may consequently be written down
at once. After some reduction this equation of (Z') becomes :

—(4r 1 1?)(y?—a?)? —4p(1 +-luy—y")? + 4p(4r4-P a? yr
tq? a7? y* — 4q(1+ley—y’*)(y* —2’).

As (L') is now apparently of the fourth order, the envelope (L)
wanted is of the fourth class.

As (Z') in general as we shall see, has no double points or cusps,
it has been determined by this, that ) is of the twelfth order.

(L), like (L’), has the origin as centre.

If we multiply the equation found for (L’') by p, (the cases p = O
and jp == we shall consider separately in § 9) it appears that it
may be written thus :

between ¢ and y we find :

61
Proceedings Royal Acad. Amsterdam. Vol. XVL.

94.0,

(L') (qu? + 2play—(2p-+ q)y? + 2p)? = s\a* + 2(2p 4+ 1)e?y? 4+-y'},
where
s=—q —p(4r +P).

§ 2. It is evident from the equation just found that out of the
origin 4 bitangents may be drawn to (L’), given by
a — 2 (2p - 1) a*y? + y* = 0.
The 8 points of contact are lying on the conic

(K) qe* + 2play — (2p + g)y* + 2p = 0.

The bitangents are real or imaginary, according to p being positive
or negative. They form two pairs of perpendicular lies, lying sym-
metrically with regard to the axes and with regard to the straight
lines that bisect the angles of the axes.

If (K) has its axes along the axes of coordinates or along the
bisectrices, then (Z') and consequently (Z) as well will have those
lines as lines of symmetry. The first occurs for /= 0, the second
for p-+q—0. These two suppositions consequently give rise to the
same simplification in the shape of (Z). In the formerly amply dis-
cussed case that 70 as well as p+.q=0, (A) becomes a eirele
with p/2 as radius.

§ 3. Nodes of (1). Let us write the equation of (L’) found in
§ 1 in the shape
(O12 = LN
in which
FL eat ea ae Bee ai 22
Vs
and M and N are expressions of the second order, obtained by
separation of the expression w*—2(2p + 1)a*y? + y*, then we see,
that (1’) is touched in 4 points by each conie of the system,
VM +2201 N=),
in which 4 represents a parameter.
The separation of the expression mentioned, may be executed in
the following ways:
w?—2(2p + lay? + yt = (#? + 2V/p ey—y?)\(e*— 2 p ay—y’)
= (2? + 2p + 1 ay + y?)(@?—2V p + 1ay +y?)
= fat—(V 2p + 1— WV p(p + 1)y"} jw? —
—(V2p + 1+ 2V pip + 1))y".
The first way of separation Jeads to the following system of inscribed
conics

941

(a? + 2 2 A 1)e + 2 (2? + ly a A—1)ay—(A? +
s s
y 4
go Are) ai il
Ws Vs
The values of 2, other than 0 or o, for which this equation

represents a degeneration, viz. a meee into two pedals) straight
lines, are determined by the equation :

9, z
meet? ayy ae aa ray ee) Ait be ine gt) Lae = 0;

Each of the straight lines of a degeneration touches (Z’) in two
points, is therefore a bitangent of (’). If we write the equation of
such a straight line in the shape

av + by = 1,
then we see easily that we have
vt,
i.e. the 4 pairs of parallel bitangents touch (C).

We may observe that the system of conics to which we have
arrived is the system of ellipses (A’) itself, which is apparent, if we
replace the parameter § by 2, in such a way that :

—Apr =p? I?
4pS? -- 496 + 4dr + P= A :
4p A

Let us proceed now to the second way of separation. The equation
of the second system of inscribed conies and the equation determining
the degenerations may be written down. So we come again to 4
pairs of parallel bitangents of (L’); they appear to touch the hyperbola :

ne
Da
In the same way the third method of separating leads to 4 pairs
of parallel bitangents of (1’), which touch the hyperbola
1

21°

ey = —

Hence:
Of the 28 bitangents which the envelope (L’), possesses 4 pass
through O; the remaining ones are pairs of parallel lines ; 8 of them

touch the circle «*-+ y*=1, 8 the hyperbola a*--y? = — ———

1
and 8 the hyperbola «= — a:
We now transfer what we have found to (L):

61*

942

Of the 28 nodes of the envelope (L), 4 are lying at infinity,
8 on the circuinference of the circle a? + y? =1, 8 on the hyperbola
gi_y? = 2 : 1 and 8 on the hyperbola ay = — 2.

The 4 pairs of parallel asymptotes of (LZ), which correspond with
the bitangents of (L’) passing through O, touch the conic (A’), which
is the reciprocal polar curve of (XK).

The nodes of (Z) lying on (C), if they are real, are for the dynam-
ical problem under discussion the vertices of the quadrangular
figures, which as appeared before, may serve as envelopes; the
branches intersecting in those points meet perpendicularly, as was
proved for a more general case ').

§ 4. Asymptotes of (L). Besides the 4 pairs of parallel asymp-
totes, (1) has moreover generally speaking 4 asymptotes passing
through O, which are perpendicular to the asymptotes of (1).

Of (L’) two asy mptotical directions may coincide.

In this case the corresponding asymptotes do not pass through O,
but they are removed from © at equal distances. In that case on
the straight lines passing through O (ZL) has two cusps in which
the straight line is a tangent. The said straight line is to be consid-
ered to belong to (LZ); consequently (1) is degenerate.

Various shapes of (L’).

§ 5. The equation of (L£’) reads (§ 1):

tga? + 2play — (2p -+ q)y? + 2p}? = s fat -- 2(2p 4+ l)aty? + y%,
where

s= 9° —p(4r + 2).

lis shape will in the first place be dependent on the nature of
the bitangents drawn from Q, viz. whether they are imaginary
(p <0), or real (p > 0) and touch the curve in real points or are
isolated.

Further on the nature of the conic (A) which may be an ellipsis,
an hyperbola or a degeneration.

Finally on the reality of the asymptotes.

We can prove now, that (L’) has as many real asymptotical direc-
tions as it has pairs of real points of intersection with (C).

Let (cosa, sine) be the point of (C) lying on (L’), then we have:

1) Phil. Mag. 1. c., p. 297.

bs J

945

{q cos? a + 2pl cos a sin a—(2p + q) sin? a@ + 2p}? =
= s {cost a—2 (2p + 1) cos? a sin® a + sin‘ al.
If we write this in the form:
{q sin? a—2pl cos a sin a—(2p + q) cos* a}? =
= s {sin* a—2 (2p + 1) cos’ a sin? a + cos* a
then it is evident, that
y = — “& coiga
in an asymptotical direction of (L’).
If (Z’) touches (C), two asymptotical directions coincide, they are
perpendicular to the line that connecis O with the points of contact.

§ 6. (K) is an ellipsis.

1°. p> 0, consequently the bitangents from O are real. They
cut (A) in real points, in which points they touch (L’).

The bitangents divide the plane into 8 angles, in which

HH, = a*—2 (2p + 1) 2 y? + y*
is alternately positive and negative. (L’) lies for positive values of
s=q—p(4r+ /)

in the angles, where H, is positive.

Let us call the branches of (L’), which are lying in the one pair
of opposite angles, a, those which are situated in the other pair, 0.

Let us begin by giving positive values to s and let us first consider

a exclusively.

For so degeneration in two bitangents. For large values of s,
a consists of one branch with two asymptotes and four points of
inflexion. For decreasing values of s the angle between the asymp-
totes becomes smaller, the apices are removed from each other and
the points of intlexion move towards infinity. For a detinite value of s
the asymptotes are parallel. If there is a further decrease in s, a will
consist of two closed branches in which for another special value
of s points of osculation occur in the sides turned towards QO. Then
two points of inflexion appear in each branch and the branches
contract, till we have for sO degeneration in the ellipsis (A) ').

1) The case s = q?—p (4r + /?) =0 must be inquired into separately. For s = 0
is the condition that in the second part of the relation between ¢ and 9 (p. 939)
the root may be drawn. In this case (A’) represents two pencils of ellipses.
Consequently the required envelope (L) has now degenerated into 8 straight lines,
which are the polar lines of the base points of those pencils, and in (K’), which
is the polar curve of (K).

944

If we allow s to change from o into 0, 6 passes through an
equal change of shape. If we consider a and 6, however, together,
then the general and special values of s, for which two asympto-
tical directions coincide, and those for which points of osculation
occur, will not be the same for a and Ob.

if we take into consideration what has been observed in § 5 with
respect to the asymptotical directions of (1’) and its points of inter-
section with (C’), it is evident that we have to distinguish the fol-
lowing cases, which are represented in fig. 1 (with the exception
of the 3r¢):

1. a and #4 both cut (C’); they have each two_ intersecting
asymptotes.

2. a touches (C’), 6 cuts (C); a has two intersecting, 6 two paral-
lel asymptotes.

3. a lies outside (C’), 6 cuts (C’); a has two intersecting asymp-
totes, 6 consists of closed branches.

4. «a lies outside (C’), 6 touches (C’); a has two parallel asymp-
totes, 6 consists of closed branches.

5. a and & lie both outside (C’); both consist of closed branches.

In this we have not yet paid attention to the presence or absence
of the points of inflexion in the closed branches; the number of
cases would be increased by this.

It is evident that a value of s exists, below which points of inflexion
occur both in the closed branches @ and ¢., In that ease all the 28
bitangents of (4’) are real.

We have now allotted to s all positive values, for negative values
of s (Z’) lies in the other four angles. If we revolve the system of
axes 45°, we shall get the same cases again.

The value of p determines the situation of the bitangents drawn
from OV. For increasing values of p they move towards the axes,
for decreasing values of p towards the lines that bisect the axes-
angles. We shall have to consider the limit-cases separately.

§ 7. 2°. p <0, consequently the bitangents from O are imaginary.
For a very great value of s (which we have always to take posi-
tive here) (Z’) consists of a small closed branch, given by

w'—2(2p + 1) a*y* +. ys = :

symmetrical with regard to the axes and the bisectrices. It possesses

945

8 points of inflexion or none, according to p being a or

2
1
2a

We shall suppose p>—1. This is sufficient, for it is easy to
prove that (L’) for a value of p< —1 by revolving the system of
axes 45° passes into a curve answering to a value of p>—41.

If s decreases, the closed branch will increase while the symmetry
is lost. For a certain value of s it touches (C’) in two points. Then
it euts (C) in four points, in consequence of which according to the
observations made in § 5, infinite branches occur. For a smaller
value of s the closed branch which we shall call a, again touches
(C) internally in two points. Then a cuts (C) in 8 points.while new
infinite branches appear. If s decreases further, then @ touches (C)
externally in two points; two asymptotes of 6 become parallel.
Further a cuts (C’) moreover in 4 points while two asymptotes of
6 have become imaginary. After this external touching occurs again,
after which a has quite passed outside (C’). At the same time # has
become a closed branch. All the time a has remained inside (A), 6
outside (A), for (L’) cannot cut (A) now as H, cannot become
zero. It is evident, that, if (£’) has assumed the form of a ring, a
must have lost its points of inflexion if it possessed them. They will
have disappeared with four at a time. After the falling together of
two asymptotical directions, points of inflexion will occur in } so
that the closed branch 6 may possess 8 points of inflexion. On further
decrease of s these points of inflexion will disappear by four at a
time, while the branches a and } approach each other, in order to
coincide with (4) for s=0.

In Fig. 2 (Z’) is represented for a certain value of p< O (viz.
< —}3) for some values of s.

From the equation of (Z’) appears at once that for p= —1, (L’)
has degenerated into two conics; at the same time (ZL) has degener-
ated into two conics.

In the figures (A) and (C’) have not been drawn as intersecting;
it is easily shown that they cannot intersect each other if (A) is
an ellipsis.

§ 8. (K) ts an hiperbola.

1°. p > 0, so the bitangents from O are real.

From the equation of (A) we deduce easily that the angle of the
asyimptotes is always greater than 90°. Hence (A) will cut at least

946

2 of the bitangents from O. Of the 4 bitangents 0, 1 or 2 are
consequently isolated.

Fig. 3 refers to the case that two of the bitangents are isolated.
For a few positive and negative values of s, (Z’) has been drawn.

Fig. 4 refers to the case that 1 bitangent is isolated.

Fig. 5 to the case that none of the bitangents is isolated; (17)
therefore touches the 4 bitangents drawn from O in real points.

2°. p <0, so the bitangents from O are imaginary.

Fig. 6 gives a representation of this (p is supposed >> — 3),

(In the figures (A’) and (C) are represented as intersecting; this
is indeed always the case if (A) is an hyperbola).

(K) ts a degeneration.

As p -|-0 is supposed, we have only to consider the case of
degeneration in two parallel lines that touch (C). Generally speaking
we can say that substantially everything is as when () is an
hyperbola. Hf the bitangents are real they will generally touch (L’)
in real points.

§ 9. Special cases p=O0 and p=c. These cases had to be
considered separately (§ 1).

For p=0O and q-}-0 the first equation which we have found
in §1 for (Z’) passes into:

+ (4r + BP) (y? — 27)? + 4q? wy? + 49 (1 + lay — y’) (y? — 27) —— 0;

If we write:

then the equation becomes :

ita? + ley —(t + 1)y? + 1} (y? — 2°) = qa’y’,
(L’) has now a node in Q. For the rest various cases may occur
also here, which we are not going to consider separately.

If p =O and besides g = 0, then we have to consider the problem
separately (ef. note p. 143). It is evident then that (Z) consists of two
rectangles *).

For p=o and g=-o, the first equation of (L’') found in § 1
represents two hyperbolae, intersecting in the points (0, + 1); p= 2
involves, according to the relation between § and » (§ 1), $= 0.
There is therefore no question of an envelope (L’'). For p=o
and at the same time g —o the envelope must be found again.
It appears that (Z) consists of 2 rectangles ’).

1) Phil. Mag. p. 315.

*) Phil. Mag. p. 315,

94:7
Various shapes of the envelope (L).

§ 10. The number of various shapes which (Z’) and consequently
also (L) may assume is, as we have deduced in what precedes,
very great. In order to facilitate the survey of those various forms,
we shall begin with the case that p+ q¢=Oand at the same time
1=0. The equation of (Z’) runs:

Ge? +y?—2)' =s fo —2(1—2g)ety* ty} (s=9°-+4gr).

The equations of the 4t order in 4 as mentioned in § 3 are now
of a quadratic form. The situation of the double points of (1) may
therefore be determined by means of quadratic equations; of the
double poimts 8 are lying on the axes, 8 on the bisectrices. The
cases ¢g = 0 and ¢=« have been considered separately (§ 9).

For an arbitrary value of qg we have besides the values s = 0
and s =o, for which (L’) degenerates, two more special values of

s, viz. a value for which the asymptotical directions coincide in
pairs and one for which the points of inflexion coincide in pairs.
The asymptotical directions are determined by :
(q?—s) (x? —y")? + 4q(q—s) #*y? = 0.
They are real if qg’—s and q(qg—s) have different signs.
They coincide in pairs:
for s = q? (r = 0) with the directions of the axes,

1
POLES — J (-=;a-9) with the directions of the bisectrices.

; 1
For s = q’ the asymptotes are removed at a distance | / =
Sex|
1 —29
from 0, for s=gq at a distance - :
2 1—q

For s=q* (L’) touches (C) in 4 points, lying on the axes, for
s=q in 4 points on the bisectrices (§ 5).

If the points of inflexion coincide in pairs. those points are
situated either on the axes or on the bisectrices.

If they are lying on the axes at a distance a from Q, then the

equation should run :

(a? + y?—a’*)* = s' (&? —a’) (y?—a’).

From this we deduce :

7 ( i) 2 ae!
,{|r7r=—@q Serer (AT il— fe ety
~ (129) (1—29) q—1

The points of inflexion coincide in pairs on the biseetrices for:

945

1
Pike hip isthe
ee ( !) ps.

i — ee

Gas @Q—2 Ii

From what was observed in § 7 follows that we have to consider
for q negative values only, and positive ones smaller than unity.

The asymptotes, parallel to the axes, are real for all these
values of g.

The asymptotes, parallel to the bisectrices, are real for negative
values of g, imaginary for positive ones, smaller than unity.

The points where the points of inflexion coincide on the bisee-
trices, are always real.

The points where the points of inflexion coincide on the axes are
real for all negative values of gq, and further for positive values

1 1

of q, smaller than = For values of q between > and 1 they are
ol

imaginary. Further we observe that the value of s, for which these

: ; ; 1
points oceur, is between oo and q, if g les between Z and a s lies

1
between q and q’, if g lies between 0 and ©

After the deductions made in § 6 and § 7 and this § it will be
superfluous to give an explanation of fig. 7, where (L’) is repre-

sented for a negative value of g and some various values of s, and

]
fig. 8, where (L’) is represented for a positive value of a(<;}

§ 11. From the shape of (Z’) that of (Z) as reciprocal polar
curve may be at once deduced.
Let in the first place qg be negative. There are 4 pairs of parallel

1
asymptotes, touching at the cirele ay? =>. They are parallel

with the bitangents of (4’), passing through O. Let us now consider
various values of s.

s>qy. (r<0). Fig. 9. Besides the 8 asymptotes just mentioned
there are 4 more, which pass through O. The entire curve (Z) lies
outside (C’) and can therefore not be of any consequence as an
envelope. For on (C) the velocity of the moving point is 0; outside
(C’) the vis viva would be negative. In fact g’ is the greatest value
that s can have in the dynamical problem.

s=q. (=O). Fig. 10. The cusps have coincided in pairs in

949

the axes, with which the four asymptotes passing through O have
now coincided in pairs. (4) touches in 4 points at (C}.

The only forms of motion which the dynamical problem allows
of are an .\-vibration, and é a Y-vibration.

, fa x ieee
<s<iqg? | q? —— ae ‘>0). Fig. 11. (4) delimits two

a—2 ay = 2) ;

quadrilateral domains ' motion with vertices on (C)?)

2 We=
ay b= —— ies iad) i On the axes 4 pairs of cusps
(1-29)*

have coincided. (1) deviates only a little from the shape indi-
cated in Fig. 11.

Vege —. af Oana — Piggy 2s eSr cusps
(ARS Oy Fm (Ones 2q)
occur. (The “stirrups” lying within e domains of motion contribute
deed to the envelope).

iets ; ; : :
s—0 (-= — i): Fig. 13. Degeneration in 8 asymptotes.

Two domains of motion each bounded by a square.

We now get to the negative values of s. No figures have been
drawn for them as they are of exactly the same nature as those
for the positive values of s; we have only to revolve the figures

5°. Consequently :
7 lars ; 7)

oe 210) Spl = Sy . Fig. 12, having

(q— 9) G2);
revolved 45°.
‘ \
; ag—V(1 a)
—_ aia ‘VS Sea Here we have to take into
(qa) (q—2

consideration that the distance of the special points to O is another
one than for
F $

1—2y)? |

1) One domain of motion is bounded by two opposite branches a, as far as
they are lying inside (C), and the branches ) which pass through the points of
intersection of the just mentioned branches a with (C).

*) This Fig. and Fig. 18 we also find in a treatise of F. Kunin: ‘‘Uber den
Verlauf der Apet’schen Integrale bei den Curven vierten Grades”. (Math. Ann.
10. Bd, 1876).

950

1
A sit) tale
ys \ q(q V( :)

q<s Saas ae —(l—q) >r > — ; = : Ries de
74) 4 (q—2)
having revolved 45°.

cae (: = ia) : } Fig. 10, having revolved 45°. The distance
of the cusps to O has changed however.

s<a(+ > 70-0) Fig. 9, having revolved 45°

Let us now suppose that y ts positive and < 1.

s <1(*>; 0-0). Fig. 14. (Z) has no dynamical meaning for
the same reasons as in Fig. 9.

9 & pia): Fig. 15. The dynamical problem allows of

iwo simple vibrations only.

q? ee (a Te <7 a} Fig. 16. Two domains

(1—29)
of motion. *)
pe as I i rel . The cusps of the preceding Fig.
(1 —29)° (l—29)*
have coincided in pairs now.
g<s <q 2y T° <u: Soe C =e Fig. 16, from which the
au

cusps have ee

s=g’. (r=0). Fig. 17. (Z) has 4 points of contact with (C).
In the dynamical problem we are concerned with an asymptotical
approach to the X- or )-vibration. This case should be considered
as the transition between two domains of motion and a single domain
of motion.

“ea? contribute to the “envelope”. *)

1) Of the closed branch of (£) 4 parts lie inside (C). Each of the domains of
motion is bounded by 2 opposite parts and by the infinite branches that pass
through their final points.

*) The inner branch serves partly as exterior, partly as interior envelope. The
parts which, seen from the centre, are hollow, touch internally, the rest externally.

1
q W(t — t i)

8 2 elbaee (> = ——---+~____-_* ) The cusps of Fig. 18 have
(q—2)’ (q — 2)°
coincided in pairs.
; ae
q l aa—U(1—+4) yet
a G5: é A PRPS Ge a2 aa BLS: sel OID)
s= 0. (+ = — - i) Fig. 20. Degeneration in the circle viy=.

1
We have now supposed, that qy lies between O and we If q¢ lies

1 1
between y md we have a little change. Then the 8 cusps of

o

Fig. 14 would already have disappeared for s = q.
8 J PI 1
1 ae
For g between — and 2 the forms of the envelope, indicated by

Fig 16, do not exist.
For q positive and >1 no figures have been drawn for reasons
stated already.

§ 12. Let us now consider the shape of (/) in general, first in
case (A) is an ellipsis.

The symmetry with regard to the axes and the bisectrices does
not exist anymore now. The nodes, which for /=O lie on the
axes, lie for positive values of / in the second and the fourth
quadrant (§ 3); those which lie for p+ q¢=0 on the bisectrices

ei

have been removed for positive values of PTT into the direction of
P

the Y-axis (§ 3). The changes in form which (/) undergoes in con-

sequence of this are easily understood.

Other forms of (Z) are, however, possible.

Let us first suppose p >0O. We have to start now from the 5
cases mentioned in § 6.

In case 1, (LZ) has mainly the shape which has been represented
in Fig. 9, in which we have to take into consideration the observa-
tions just mentioned.

In case 5, (L) has, with due observation of these remarks, the
general shape of Fig. 11, or of Fig. 12, or it is a combination of

1) For gq =1 (S) consists of two circles; we have then the well known case
of the conical pendulum.

952

those two forms, i.e., the envelope of one system of osculating
ellipses has 4 cusps, the envelope of the other has none.

Case 2 is to be considered as a combination of Fig. 9 and Fig.
10. a touches (C’) in two points, 6 has two cusps on the line which
connects QO with the points of contaet of @ with (C’). The dynamical
problem allows of a single simple vibration.

Jase 3 gives rise to a combination of Fig. 10 and Fig. 11 (or
Fig. 12). There is one system of osculating ellipses.

Case 4 to a combination of Fig. 10 and Fig. 11 (or Fig. 12).
There is one system of osculating ellipses. Moreover the dynamical
problem allows of a simple vibration.

In the case p< 0 we have again in'the first place envelopes
corresponding in the main with those represented in the Fig. 14—20.
We should, however, bear in mind, that in general the cusps do
not disappear by 8 but by 4 at a time. There is for instance a
transitional form possible between Fig. 18 and Fig. 19 in which 4
cusps oecur, and in Fig. 14 and Fig. 15 4 cusps may have fallen
out. In order to obtain the other forms of the envelope we must
make use of the observation about (1%) in §.7.

Y

If the branch of (Z) lying outside (C’) touches (C’) in two points,
then the dynamical problem allows of one simple vibration. If (Z)
cuts (C’) in 4 points, then we get one of the two domains of motion
of Fig. 16, ete.

Is (4) an hyperbola or a degeneration then the various shapes of
(L) may be deduced in the same way from the Fig. 3—6.

Physiology. — “On the rejlectorical influence of the thoracal auto-
nomical nervous system on the rigor mort in cold-blooded
animals.” ‘). By S. pu Borr. (Communicated by Prof. C. A.
PRKELHARING.)

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

The rigor mortis that is caused by hardening and shortening of
the muscles begins in warm- and cold-blooded animals after the
circulation of the blood has stopped for some time, in warm-blooded
ones 5—8 hours, in cold-blooded ones 1—2 days. If with a muscle
that has been removed, we make provision for a sufficient supply
of oxygen, it mortifies without stiffening. A special chemical state

‘) According to experiments made in the physiological laboratory of the Uni-
versity of Amsterdam.

953

that is caused by a deficiency of oxygen, is consequently an indispen-
sable condition for rigor mortis of the muscles, Hermann showed
moreover that the process of rigor mortis is accelerated from the
central nervous system, whereas Ewanp ascribed this accelerating
influence to the labyrinth.

Last year I established, that, both for warm- and cold-blooded
animals, the tonus of the skeleton-muscles is entertained by impulses
reaching the muscles along the efferent, thoracal autonomical nerve-
tracks). I demonstrated this by the section of the Rami communi-
cantes on one side, after which the muscles of the same side become
atonic. In this way T could fully ascertain, by a physiological ex-
periment, the double innervation established by Borkr*) on account
of morphological investigations, and, at the same time, I could
establish the signification, which autonomic innervation has on the
transversally striped muscles. :

In the many operations that I made on frogs, | was struck by
the fact that, after death, the hind-lee of the operated side was still
supple, when the other hind-leg was already quite stiff. So on
January the 13 T cut the right Rami communicantis and_ the
sympathetic chain of a frog as high as possible. The next afternoon
at 6 o'clock the frog was no longer very active. On the 15 of
January I found it dead, all limbs were supple. Now f laid down
the frog with both hind-legs flexed in the same way. At 4 o'clock
of the afternoon the right fore- and hind-legs are still quite supple.
The left hind-leg however is, both in hip- and knee-joint, stiff in
flexed position with strengthened dorsalflexion in the foot-joint. The
left shoulder- and elbow-joint are also stiffened. The axis of the
body is flexed with the concave side to the left. These particulars
ean easily be observed in the photograph.

At half past five the condition is still unchanged.

At half past eight p. m. there is likewise a beginning of rigor
mortis in the right hind-leg and in the right shoulder. At eleven
o'clock the right fore- and hind-legs are also quite stiffened. On the
18 of January the rigor mortis has entirely ceased. This observa-
tion was made at a temperature of 17° Celsius. Consequently the
rigor mortis began, on the side where the Rami communicantes had
been cut, 7 hours later than on the other side, where the muscles
were still connected with the spinalcord by means of the autonomic
nerve-tracks. This observation induced me to a series of intentionally
1) Folio Neurobiologica Vil (1913) 378 and 837.

*) Verslag der Wis.- en Natuurk. Afd. Kon. Akad. vy. Wetensch. Amsterdam,
April 1909. Deel XVII, p. 1008—1012.

954

Frog of which the right Rr. communicantes have been cut through in
the begining stage of rigor mortis. The left shoulder and elbow
are stiffened, the left hind-leg is stiffened in flexed position both in
hip- and knee-joint with strengthened dorsal-flexion of the foot. The
axis of the body is bent with the concavity to the left.

The right fore- and hind-legs are still quite supple.

955

made experiments in which I removed, as much as possible, ineal-
cwable influences. 1 proceeded in the following manner:

A short time before I hung the frog in the damp case, or occasion-
ally a few days previously, I cut, on the right side, the Rami com-
municantes and the right sympathetic chain at the top. By binding
up the heart I killed the frog, then I passed a thread through the
two jaws, and on these I hung the frog in a closed, glass-case that
was kept damp by a wet sponge and by thoroughly wet filter-paper
on the bottom. The damp case was then placed in a room in which
the temperature was raised as high as 30° to 35° Celsius. The frog

was consequently placed in regularly heated damp surroundings.
By this higher temperature the process of rigor mortis is consider-
ably shortened. It could easily be observed in these frogs, that the
right hind-leg hung down suppler than the left one, that consequently
the tonus had disappeared from the muscles at the right side.

A short extract from the protocols may follow bere:

I. 17 January. All Rami communicantes of the right side are cut.
20 January: After the heart has been bound up the frog is hung in
the damp case.
4.30. Left hind-leg is drawn up, stiffness in hip, knee-joint and fool.
The left elbow-joint is stiffened, no difference is to be observed in the two
shoulder-joints
Right elbow and whole right hind leg are still supple.
5.30. Situation still the same.
9.30. The two hind-legs are hanging in stiffened tense and abduction
position; the two fore-legs stiffened in flexed position.
22 January. Rigor mortis has ceased.
ll. 21 January. 1.15. The Rv. communicantes are cut through.
1.30. The heart is bound up. The frog is hung in the case,
5.30. Left shoulder-joint is stiff, other joints are still supple.
7.30. Situation unchanged.
8.30. Beginning of rigor mortis of the left hip.
9. Right shoulder begins to become stiff.
10. Left elbow stiffened. ~
11.30. Left knee begins, to stiffen, the hip is quite stiff.
22 January. Stiffened tense and abduction position in all joints of the
hind-legs.
23 January. 9 a. m. The rigor mortis has ceased.
Il. 79 January. 11.15 a. m. The Rr. communicantes are cut through.
11.30. The frog is hung in the case after the heart has been bound up.
4. p. m. Heft fore-leg stiffened in tke elbow- and shoulder-joints, left
hind-leg is strongly flexed and stiffened in the hip, dorsal flexion and rigor
mortis of the foot-joint.
4.30. Left knee is becoming stiff.
5. p. m. Right elbow-joint, knee and hip begin to become stiff.
62
Proceedings Royal Acad. Amsterdam. Vol. XVI.

956

6. p. m. Entire rigor mortis with abduced and tense hind-legs and
expanded webs.

24 January. 12 a. m. The rigor mortis has ceased.

IV. 22 January. 11.15. The Rr. communicantes are cut through.

11.30, The frog is hung in the case after the heart has been bound up.

5. p. m. Beginning of rigor mortis in left elbow and shoulder.

9.30 p. m. Left fore-leg entirely stiffened, right one only in the shoulder-
joint. Left hip and knee entirely stiffened in fiexed position. Beginning cf
rigor mortis of right hip, right knee-joint is still supple. Right foot is still
supple, whilst the left one is entirely stiffened. The entire left hind-leg
hangs with strong flexion in the hip tense foot and expanded webs. The
right hind-leg hangs still in the usual slightly flexed position.

10.15. Situation unchanged.

11.30. The left hind-leg shows stiffened tense position, the right mip-joint
entirely stiffened, beginning of rigor mortis in the right knee and foot.
Temp. is 28° Celsius.

23 January 9 a. m. Both hind-legs are hanging in completely stiffened
tense and abduction posilion.

24 January. The rigor mortis has ceased.

V. 23 January. 8.45 a.m. The Rr. communicantes are cut through.

9 a. m. The frog is hung in the damp case after the heart has been
bound up.

1 p. m. Left shoulder and hip show more resistance than right ones.
Left hind-leg drawn up with strong dorsal flexion of the foot.

2 p. m. In left knee and foot more resistance than in right ones.

3 p.m. The right hip becomes also stilfer.

4 p.m. The two hind-legs are hanging in tense and abduction position.

VI. 24 January. 8.45 a. m. The Rr. communicantes are cut through.

9 a.m The frog is hung in the damp case.

12. Beginning of rigor mortis of left shoulder-joint.

4 p. m. Left hip shows more resistance than right one.

430. Left hind-leg stiffened, with strongly flexed hip, knee and foot

6 p. m. Left hind-leg still in stiffened flexed position. The right one is
sul quite supple. Both the shoulder-joints are stiffened.

8.80. Beginning of rigor mortis in the right hip.

9.30. Right hip entirely stiff, the knee is stili supple.

10.30. Right knee also entirely stiffened, the right foot is still supple.

26 January. 10 2. m. Both hind-legs are hanging in stiffened tense and
abduction position.

26 January 5 p.m. The rigor mortis has ceased.

VIL. 24 January. 9.15. The Rr. communicantes are cut through.
10 a. m. Frog hung in the case after the heart has been bound up.
5.30. Left hind-leg more flexed in the hip and with greater dorsal flexion
of the foot than right one.
6.30. When lifting the left hind-leg greater resistance than in the right one.
9.30. Stronger resistance in the left hip.
10.30, Left hip, knee and foot are stiff in flexed position, right hip be-
ginning of rigor mortis; right knee and foot still quite sapple.

if

Kr

)

co
~

‘

26 January. Both hind-legs ave hanging in stiffened extension- and
abduction-position (25 Jan. not controlled).
26 January. 5 p.m. Rigor mortis has ceased.

VIL. 26 January. 9.45. The Rr. communicantes are cut through.
10 a. m. Frog hung in the damp ease, after the heart has been bound up.
1 p. m. All joints still supple.
6 p. m. Left shoulder and elbow stiffened, slight rigor mortis in left hip.
9 p. m. Left hind-leg completely stiffened in tense position with expanded
webs.
Right shoulder and elbow also Stiff, but less so than left ones. Right hip
sliff in flexed-position, but right knee and foot are still supple.

So I have made a series of 20 experiments in which I always
found retardation of rigor mortis on that side where [had cut through
the Rr. communicantes. The process of rigor mortis is consequently
accelerated, when the muscles are connected with the central ner-
vous system by means of the efferent autonomic nerve-tracks. In
the first operation, which was performed at roomtemperature the
operated side stiffened at least 7 hours after the not operated one.
But also in experiments that | made at a temperature of over 30°
Celsius, the difference was even 1 or 2 hours. The experiments men-
tioned here were made on individuals of Rana esculenta. I made
also some experiments on Rana temporaria, in which the process of
rigor mortis went off quicker. In my opinion the reason of this is
to be found in the much thinner limbs by which the relation be-
tween volume and surface of the muscles becomes less favourable.
Hereby the mortification-process and the process of rigor mortis is
evidently promoted. The same difference between the operated and
the not operated side I observed here likewise. In all my experi-
ments it struck me immediately that of the fore-legs the shoulder, and
of the hind-legs the hip stiffens first. The knee however was now
stiff before the foot, now the reverse took place. With slight devia-
tions this occurred thus according to the law of Nystpn.

Further in all my experiments the flexors stiffened first and after-
wards the tensors. No exception was made in this respeet for the hind-
legs, so that at the end ofeach experiment the hind-legs were in
a tense position. Further I must point out that in all my experi-
ments the rigor mortis was accompanied by a shortening of the
muscles, first rigor mortis and shortening of the flexors, then of the
tensors.

Hermann, who first proved that the process of rigor mortis was
accelerated under the influence of the central nervous system, took
rigor mortis for a last contraction of the muscles. Because, as | have

62*

958

just shown, rigor mortis is influenced by the Central nervous
system along the autonomic nerve tracks, as is likewise the ease
with the muscle-tonus, 1 am of opinion that rigor mortis is a_ last
tonical muscle-shortening. This view is also entirely in keeping with
PEKELHARING’s *) investigations, who proved that the percentage of
creatine of the muscles increases with rigor mortis, as is likewise
the case with increased tonus.

Now the question arises: how is rigor mortis brought about ?
The usual explanation is, that through the mortification of the cen-
tral nervous system the muscles receive stimulants along the nerve-
tracks, and these stimulants accelerate rigor mortis. EwaLD was of
opinion that these stimulants originate in the labyrinth, whilst
Frercner proved that supply of oxygen makes the muscles mortify
without rigor mortis. [think lean now give amore general explana-
tion, corresponding with the facts that are known.

We know that rigor mortis only begins, when the circulation of
the blood has ceased. We obtain then in all tissues an aecumula-
tion of products of metabolism consequently suffocation. And
now it is known that, if we kill an animal by hemorrhage or
suffocate it by pinching off the trachea, that then, by the influ-
ence of the autonomic nervous system, the body shows manifold
irritation-situations: through tension of the arrectores pilorum the
hairs stand erect in the dorsal skin-regions of the trunk and in the
tail; the bladder empties itself and also the rectum. In an entirely
analogous way the sending of more powerful stimulants of the tonus
to the skeleton-muscles takes place. The stimulants running centri-
fugally, which during life-time entertain the muscle-tonus by means of
the thoracal autonomic nervous system, will now, at this inereased
irritability, after death cause a last powerful tonical shortening of
the muscles.

When I had established in this way, that the occurrence of rigor
mortis stands under the influence of the thoracal autonomic nervous
system the question rose, if, at least in frogs, this influence, just
like the tonus, as P. (. Bronperest *) has proved, is entertained
by stimulants produced along the posterior roots of the spinal cord.

In this direetion | made already 10 experiments. I cut the pos-
terior-roots $, 9, and 10 of a frog at one side. From the doctrine of
segmental anatomy we know, that these posterior roots contain the

sensitive nerve-tracts of the hind-leg.

1) Onderzoekingen van het Physiologisch Laboraterium te Utrecht 5de R. X1
pag. Ll. 1910.
*) P. Q. Bronperrstr, Over den tonus der willekeuvige spieren, Diss. Utrecht 1860.

959 !

Only such frogs as could still leap well after the operation, and
in which from the leg at the operated side no reflexes could be
excited, whilst it could be done at the other side, and that showed
the so-called “Hebephaenomenon” of Herinc were used for my
experiments. I add here a few protocols :

la.

Na.

6 February. Rana esculenta, of which posterior root 8, 9, and 10 of the
left side are cul. The frog continues leaping after the operation and makes
good use of the two hind-legs. The Jeft hind-leg shows after the leap anew
elevation of the foot as HerinG has observed. Reflexes at the left hind-leg
have ceased, a crossed reflex-movement through strong irritation of the right
hind-foot is observed. The reflexes at the right side are lively.

7 February 9.30. The frog which is in a very good condition is hung at
30° Cels. in the damp case after the heart has been bound up.

12.30. The right hind-leg shows increased dorsal flexion in the foot-joint.

1.30. The dorsal flexion of the right leg has increased; when lifting the
hind-legs a stronger resistance on the right side than on the left one, likewise
in the knee and the hip. Left hind-leg still supple. Both fore-legs are likewise
sul] supple.

2.30. Still the same situation as 1.30.

3.30. In right hind-leg still more resistance, left hind-leg still quile supple.

4 pm. Right hind-leg is in stiffened tense and abduction position with
expanded webs, foot-joint still supple.

5.30. The right hind-leg is quite stiffened in knee and hip, in the foot-
joint partial rigor mortis. The left hind-leg is supple in all jomts. On both
sides there is rigor mortis in shoulder and elbow.

8 February 10 a.m. The frog has been hanging from 5.30 last night in
the damp case at 15° Cels.

The right foot is now likewise stiffened, so that the right hind-leg stands
in entire tense and abduction position with expanded webs. The left lip is
entirely stiffened, left knee and foot-jcint are still movable.

9 February 10 am. The left leg is now aiso stiffened, only the knee
is still somewhat, but very little, less stiff than the right one. A
10 Februwry. Little Rana esculenta, of which on the 9th of Febr. posterior
roots 8, 9, and 10 have been cut, on the leftside. Mobility and reflexes
as with the former frog.

10 am. The heart is bound up. The animal is placed in the damp case
at 30° Cels. for the experiment.

1.30 p.m. The dorsal flexion of the right foot has increased, likewise the
hip flexion on the right side. Right hip begins to be stiffened, left hind-leg
is still quite supple.

2 p.m. On the right side increase of the phenomena, on the left side still supple.

2.30. Right hind-leg almost quite stiff in still slightly flexed position, left
hind-leg still supple.

3,30. Right hind-leg in stiffened tense and abduction position, the left
one is stiff in the hip; knee- and foot-joint of the left leg still supple.

4.30. Both hind-legs are hanging in sliffened tense- and abductionposition
with expanded webs

» 960

Illa Very large Esculent.

10 Febr. 10.45, The right posterior roots 8, 9, and 10 are cut.

11 p.m. After the heart has been bound up, the frog is placed in the
damp case at 30° Cels,

3.30 p.m. Rigor mortis in the left hip.

4.30. Left hind-foot is entirely stiffened, only the foot is still a little
moyable. The fight hind-leg is sull quile supple. Both fore-legs are stiff.
Now I remove the ease with the frog to a surrounding of 17.5° Cels.

11 Febr. 10 am. Right hind-leg is now likewise entirely stiffened, only
the foot is still parlly supple.

11 Febr. 5 p.m. The right hind-leg is still somewhat supple in the foot-joint.

12 Febr, Both hind-legs stiffened in all joints. "

Va. 10 Febr. The left dorsal roots 8, 9 and 10 of large Esculent are cul.

11 Febr. 9.80. Hung in damp case at 30° Cels.

11.30. Right hind-leg with expanded webs, when lifting it the right leg
shows increased resistance. Left hind-leg still quite supple.

{ p.m. Right hip rather stiff, left one still quite supple.

3 pm. Right hip rather stiff, right knee drawn up. Left hind-leg still
quite supple.

5 pm. Right hip entirely, knee- and foot-joint partly stiff, much increased
flexion position to the right. Left hind-leg still quite supple, the webs are
here expanded.

5.30. Right hind-leg stiff in flexion-position, only the foot-joint is partly
stiff; left hind-leg is still supple in all joints. Both fore-legs stiffened. Frog
is now placed in a surrounding of 15° Cels.

12 Febr. 9 a.m. Situation still exactly the same as last night at 5.30.
From this moment temperature at 30° Cels.

12 at noon. Left hind-leg begins to become stiff im knee and hip; right
foot-joint still partly stiff.

1.30 p.m. Right hind-leg also stiffened in the foot-joint, entire tense-
position ; left hind-leg in tense position stiff in knee and hip, left foot is
sull partly supple.

Va. 12 Febr. 9.45 am. Right dorsal root 8, 9, and 10 cut through,

10 p.m. The frog is hung in the damp case at 30° Cels.

1 pm. The left leg begins to drew up, the flexion in the Inp and the
dorsal flexion of the foot increase.

2 p.m. Left hip strongly flexed; left foot strongly dorsally flexed, on the
left side increased resistance when lifting. Right leg still supple.

4 p.m. Left hip entirely stiff, knee and foot begin to be stiffened. Right
hind-leg begins to draw up.

6 p.m Right hip and knee now likewise ‘partly still, foot is still supple.
Left hind-leg in tense position with still partly supple foot, right hind-leg
in flexion-position.

18 Febr, 10 a.m. Both legs ave hanging in stiffened tense- and abduction-
position with expanded webs.

From these experiments, which I intend to continue it appears
clearly, that the cutting of the appurtenant dorsal roots causes
retardation of the rigor mortis of the muscles.

961

In this way we have proved that the view of HerMANN is incor-
rect, according to which the influence of the central nervous system
on the occurrence of rigor mortis should be caused. by the
mortification of the higher centra by which impulses should be
driven towards the muscles. For in my experiments in whieh I cut
on one side the posterior roots, the way from the central nervous
system to the muscle is nowhere interrupted; only the supply of
reflexstimulants (from the proprioceptores) is prevented. Rigor mortis
is consequently also caused by a reflectoric process.

If we ask now how we are to understand the tonical innervation
for accelerating rigor mortis, the answer must run, in my opinion,
pretty well as follows.

We know from Frercner and Winrerstein that the indispensable
cause of rigor mortis is to be found in a chemical state of the
muscles, which is caused by want of oxygen.

This ‘chemical state” will certainly depend on the existence of
products of metabolism. It is for the present unknown which are
these products. There are however, I surmise, sufficient reasons to
admit that they are products of partial transmutation, for supply of
oxygen, which certainly encourages transmutation, prevents rigor mortis,
and ‘increase of temperature which also promotes transmutation,
accelerates rigor mortis.

We can reconcile these two facts in no other way than by ad-
mitting that in the first case the ample supply of oxygen causes the
processes of metabolism to take their normal courses to the end,
consequently to complete oxydations, during which then the obnoxious
intermediate products do not come into existence, or do not continue
to exist. In this way it is also comprehensible that increase of
temperature promotes rigor mortis so much,because with the metabolism,
taking place then with still greater rapidity and intensity, the want
of oxygen, resp. the deficit of oxygen, is felt so much the stronger.

If now in this respect we compare the two hindlegs of a frog
of which on one side the reflex-stimulants’ for the tonus have no
longer access, then the leg with intact reflex-track has muscles that
are in a state of tonus, whilst the tonus in the other side has dis-
appeared. The leg with muscles in tonus, requiring for the entertain-
ment of this situation more metabolism will consequently show a
more rapid and intensive accumulation of intermediate products of
metabolism than the atonic leg, which does notrequire so much
oxygen on account of less intensive metabolism.

962

Consequently the muscles that are in a state of tonus satisfy
better the indispensable condition of rigor mortis, namely suffocation,
than the atonic ones. The Jeg with tonus muscles also. satisfies
better the 2°¢ condition namely the condition of being influenced
by the nerves.

For these muscles constantly receive indeed stimulants by way
of reflection, whereas the other atonic leg remains without these
stimulants. The consequence of both the more intense alteration of
the chemical state and the influence of the reflection is that the leg
of which the tonus-reflection track remains uninjured, stiffens sooner
than the leg of which this reflection-track is interrupted at the
posterior roots or near the Rami communicantes. We must thus
consider the rigor mortis of the skeleton muscles as a last vital
demonstration of the muscles under the influence of suffocation,
whilst stimulants running along the tonus-reflection-track accelerate
this process. That rigor mortis is a last (tonical) contraction of the
muscles is apparent from the fact that the muscles that have lost
their irritability in an atmosphere of oxygen, can no more stiffen
or shorten under circumstances of suffocation.

Chemistry. — “On the reduction of aromatic ketones”. I. By
Prof. J. Bousexen and W. D. Conrn. (Communicated by
Prof. A. F. HoLiEman).

(Communicated in the Meeting of February 28, 1914).

In our previous communication on this subject *) we have assumed
that by reduction of the ketones the half pinacone molecule is in all
cases the sole direct reduction product.

If, in the position where that partial molecule is formed, there are
practically no OH-ions it polymerises immediately to pinacone.

In the presence of OH’, however, there was always found benz-
hydrole and the question arose whether this was caused by direct
reduction or by the transformation of the previously formed pinacone
into benzophenone and benzhydrole by the OH-ions.

These alternatives may be represented by the schemes

(C,H,),CO — (C,H,),COH > (C,H,),CHOH . . . (I)
(C,H,),CO — (C,H,),COH — [(C,H,),COH], > (C,H,),CHOH +
45 (OPER ECO: a1 by S50 rear ae eaeean GLL

1) Proc. XVI, 91 (1913).

963

If the latter is the case, the pinacones belonging to the ketones
which, in a neutral or very faintly alkaline medium, give much
hydrole must be decomposed by alkalis into a mixture of hydrole and
ketone much more rapidly than those which in the same cireum-
stances yield but little hydvole.

It may even be expected that the formation of hydrole and the
splitting of the pinacone by alkalis will proceed in a strongly
parallel manner.

This has now indeed proved to be the case. The greater the
decomposition velocity of the pinacone by alkalis, the smaller the
quantities formed in the reduction with aluminium amalgam.

With this is also proved that at the boundary layer of the amalgam
is present an excess of OH-ions which is only accessible to the pinacone
in its nascent state. If, for instance, pinacone is exposed to the action
of aluminium amalgam and 80°/, alcohol, it is practically not attacked,
moreover the proportion in which pinacone and hydrole are formed
is nearly independent of the duration of the reduction. (1s¢ commu-
nication p. 92).

The proportion of the quantities of pinacone and benzhydrole in
which these are formed during the reduction of thirteen aromatic
ketones with aluminium amalgam has been given in the 1s* eom-
munication p. 98.

The decomposition velocity of the pinacones was determined by
dissolving quantities of 0.5 gram in a mixture of 75 ee. of ether
and 5 ec. of alcohol diluting this solution to 105 ce. with aleoholic
solutions of potassium hydroxide of N/0.42, N/0.042 and N/0.0042
strength, respectively. The normalities of the solution thus become
0.4, 0.01, and O.00L.

These mixtures were kept for definite periods at 25°, then diluted
with cold water, agitated a few times with ether, the ethereal solution
was evaporated down rapidly and the residue digested with 80°/,
aleohol at 25° in the manner described previously (1. ¢. p. 9) in
order to get to know the quantities of undecomposed pinacone.

The subjoined table and graphic representations give a survey of
the results obtained.

The numbers of the lines in the graphic representations appertain
to the numbers with which the pinacones are indicated in the table ;
the percentages next to or below those numbers in the graphic
representation indicate the quantities of pinacone formed from the
respective ketones by reduction with aluminum amalgam in 80°/, aleohol.

From the graphic representation of the pinacone decomposition,
where, as observed above, are indicated the percentages of pinacone

964

which are formed in tae reduetion with aluminium amalgam, it
follows that these two phenomena proceed indeed in a completely
parallel manner.

oe ) : a
NEO CUS Time of action | Undecomposed

yy - 74
>jnacone. approximate : : id 3
Pin € ape in minutes. pinacone inmegr.

| concentration.
1) pinacone trom benzophenone 0.1 120 0
: 5 0.01 15 370
& 0.01 30 270
“ 0.01 60 60
; 0.001 15 500
5 0.001 30 498
* 0.001 60 488
2) pinacone from 2.chlorobenzophen 0.1 120 0
é 0.01 15 0
A 0.01 30 0
‘ 0.001 15 280
4 0.001 20 210
é 0.001 30 90
3) pinacone from 3.chlorobenzophen 0.001 15 0
* 0.001 25 0
4) pinacone from 4.chlorobenzophen 0.01 10 280
i ONO! 15 200
i 0.01 23 80
* 0.01 30 0
' 0.001 30 430
é. 0.001 60 370
5) pinacone from 4.bromobenzophen 0.01 10 270
4 0.01 15 190
i 0.01 30 0
‘ 0.001 30 440
5 0.001 60 380
6) pinacone from 44’chlorobenzophen 0.01 10 0
f 0.01 15 0
a 0.001 10 300
» 0.00] 15 200
. 0.001 25 0
7) pinacone fr. 4 methoxybenzophen 0.01 15 440
e 0.01 30 390
- 0.01 60 270
? Aa Sh not attacked
8) pinacone from 4 methyl benzophen 0.01 15 480
“3 | 0.01 30 450
‘. 0.01 60 370
is 0.001 15
* 0.001 30 not attacked
in 0.001 60
9) pinacone fr. 44’ dimethylbenzoph. 0.01 3 475
- 0.01 60 450
; 0.01 90 430
uy aie ion not attacked
3 0.1 90 0
10) pinacone fr.2’Cl 4 methyl benzoph. 0.01 10 260
3 0.01 15 180
” 0.01 30 0
‘ 0.001 | 30 430
* 0.001 60 370
11) pinacone fr.4’Cl4 methylbenzoph. 0.001 15 0
0.001 | 25 0

» i

Time in minutes

Time in minutes.

©

rr)

965

10+ 13%

90 450 ie 60 Je “0 J3o wu 0 a

2 Percentage of unsplit pinacone
Fig. I.

Decomposition of the pinacones in 0.017 NaOC,H;.

.

P 15%
1 = 32% /

4 14%

10> 19%

Percentage of unsplit pinacone.

Fig. 2.

Decomposition of the pinacones in 0.001 2 NaOC,Hs.

966

One gets the impression that in the reduction of benzophenone
and its derivatives, the oxygen only is attacked and that on gentle
reduction there takes place an exclusive addition of a hydrogen atom
to the oxygen. Whatever happens afterwards has nothing more to
do with that reduction.

If there are no OlH-ions, pinacone’) is formed, but if these are
present a splitting into hydrole and ketone takes place and the latter
can be again attacked by the hydrogen. If the hydroxyl-ions are
exclusively present in the boundary layer, we shall obtain a definite
proportion of’ pinacone and hydrole; if they are found also in the
solution in a sufficient concentration all the ketone is converted
into: hydrole.

In the case of a very violent reduction, for instance, with zinc amalgam and
strong hydrochloric acid*) the oxygen seems also to be attacked by preference
and becomes apparently completely detached; the residual molecular part now,
however, also absorbs hydrogen and is converted into hydrocarbon.

2. The progressive change of the gentle reduction is herewith
explained in general traits, at least in so far purely aromatic ketones
are concerned.

The hydrole formation thus depends in the first place on the
facility with which pinacone gets resolved and this is in a high degree
promoted by alkalis.

This action of bases, has meanwhile been much elucidated by the
researches of W. Scnenck, T. Weicker, and A. THau (B. 44, 11838
(1911) and 46, 2840 (1913). There it was shown that pinacones
form with the alkali metals compounds of the trivalent carbon, for
instance (C,H,), COK; we notice that the central C—C-bond, which in
the ketones is not particularly strong, becomes much looser still
under the influence of these metals so that the half pimacone mole-
cules, under the influence of the metal atom, can indeed lead a
free existence.

In the comparatively faintly alkaline solutions matters will not
proceed so far, but here those central carbon atoms can detach
themselves from each other in consequence of an intramolecular
displacement of atoms :

\C,H,), C—O..-H (C,H,), CO
C,H), 0. 0-H y (C,H) Cron

in which the mobile H-atoms will play a role.

1) We have exposed a whole series of ketones in absolute alcohol to the action
of light and never obtained a trace of hydrole.
2) EK. CLEMMENSEN, B. 46, 1837, (1913).

967

Montacnn') found some years ago that a number of aromatic
ketones are already reduced by boiling with alcoholic potassium
hydroxide ; it is very well possible that the strongly alkaline reaction
of the medium increases the affinity of the ketone oxygen for the
hydrogen of the alcohol molecules, so that also here half pinacone
mols. are formed*) as follows :

2 (C,H,), C—O... + C,H,O = C,H,O + 2 (C,H,), OH ete.

The phase of the entire pinacone mols. is very rapidly gone through
in this case.

It speaks for itself that this powerful affinity influence of the
medium will also make its action felt on other bonds in the molecule,
so that the entire phenylgroup may be resolved or halogen atoms
become “activated” as found by Monracnn, an action that ceases, or
becomes less, when the entire C = O-group is saturated with hydrogen.

Conversely, this influence itself will be modified by the nature of
the groups in the ketone and this the more so as the character of
that group differs more from that of the hydrogen atoms. In fact,
Monracne has found that the aminobenzophenones are absolutely not
affected by strong alcoholic potassium hydroxide.

3. This influence of the substituents on the stability of the central

pinacone-C—C bond in regard to alkalis can now be readily deduced
from Our measurements (see graphic representation A and B and table).

If we take the ordinary benzpinacone as the starting point, it
appears that the methyl- (9 and 8) and the methoxylgroup (7) in the
para-position render the molecule stable, on the other hand the
halogen atoms will render the said bond looser and this in the order
para (4), ortho (2), meta (table N°. 3). The para-placed bromine atom
(5) joins the chlorine atom; also in the pinacone from 4.4’ dichloro-
benzophenone (6) the bond is considerably looser than in the pinacone
from 4 chlorobenzophenone.

Whereas in the pinacone from 2 Cl 4’-methylbenzophenone the two
influences, as might be expected,counteract each other (10) it appears that
in the pinacone from 4 Cl 4’-methylbenzophenone (11) the methylgroup
unexpectedly promotes the loosening action of the eblorine atom.

The method followed by us thus indicates the way to mutually

1) Montaaye, Recueil 27, 327 (1908).

Moracne and Mont van Cuarente, R. 81, 298 (1912).

*) We may also express this as follows: the oxygen activated by the alkali
metal withdraws the hydrogen from the aleohol molecules,

968

compare the action of different substituents in a molecule on a defi-
nite bond of that same molecule. If we choose the decomposition
velocity of one of the pinacones as unit, the ratio of the velocities
of the other pinacones to this unit is then the measure of the
relative lability.

Thus we obtain for the decomposition in N/O0.01 sodium ethoxide:

for 4.4.4’.4’. tetramethylpinacone (9) = 0.1

4.4’, dimethylpinacone (8) = 0.18
4.4’. dimethoxylpinacone (7) = 0.45

[pinacone =) 5 |
2.2’. diC1 4.4’. dimethyl ,, (140) = 2.5
44s Gibromo. ssi) 2.4
14. dichloro 4, (by — 223

Moreover, owing to the nature of the measurements we cannot
attach to these figures more value than to an approximate deter-
mination.

4. With regard to the relative reduction velocity of the ketones
to pinacones these experiments tell us nothing. In order to get to
know something about this we must reduce the different ketones
under the same conditions, preferably in such a manner that nothing
but the pinacone is formed.

This now may be effeeted by exposing to light a solution of the
ketones in absolute aleohol when indeed a ready transformation into
pinacone and aldehyde takes place ‘).

As it concerns here the activation of the C-O-bond it is to be
expected that the relative extent of the influence of the substituents
in the benzene nuelens will show quite a different order than in
the pinacone resolution. We will refer to this in a future com-
munication,

Labor. Org. Chem. Techn. University.

Delft, February 1914.

1) This was slated long ago by Cramtctan and Sirper; we have pointed out in
our previous communication that in this neutral, or at most very faintly acid
medium no transformation of pinacone into hydrole is to be expected and that,
therefore, the absence of hydrole in this case is again a proof that the reaction

proper does not extend further than to the balf pinacone molecule.

969

Chemistry. — “On a new method of preparing carboxylic anhy-
drides”’. By A. J. vAN Peskr. (Communicated by Prof. S.
Hoogewerer).

(Communicated in the mecting of February 28, 1014).

Mersrens (Ann, 52, p. 276) was the first to obtain sulphoacetic
acid by the action of sulphuric anhydride or fuming sulphurie acid
on acetic acid at a somewhat elevated temperature.

The same compound was prepared afterwards by FRraNcHIMoNnT
froma sulphuric acid and acetic anhydride in which ease the reaction
takes place also at a higher temperature (Comp. Rend. 92, p. 1054
also this journal 1881 16). ‘In an analogous manner FRANCHIMONT
and others prepared some higher sulphoacids such as sulphopro-
pionic and sulpho-isobutyrie acid"). With regard to the formation
of sulphoacetic acid according to the last method, it has already
been suggested by Francmmonr that it was preceded by the for-
mation of acetylsulphuric acid. The correctness of this presumption
was proved by Stituicn by his isolation of the acetylsulphate of an
organic base obtained in the acetylation of nitroamidobenzyl-p-nitra-
niline with acetic anhydride and sulphuric acid. (Ber. 38, p. 1241).

I have now succeeded in demonstrating that when, during the
action of SO, on acetic acid, the temperature is kept below 0°
primary acetylsulphurie acid is formed, which only at a higher
temperature is transformed into sulphoacetie acid. The acetylsulphurie
acid thus prepared is quite identical with that obtained by mixing
acetic anhydride and sulphuric acid at a temperature below 0°.

Acetylsulphuric acid is capable of forming salts, the sodium
compound being prepared by adding anhydrous sodium acetate to
acetylsulphuric acid, when acetic acid is liberated. During this
reaction the temperature must be kept below O°. This sodium salt
is insoluble in acetic acid and may therefore be obtained in a pure
condition by collecting it on a filter and washing with, say, dry
ether. If this sodium salt is heated either by itself or suspended in
a liquid such as acetie acid or toluene it decomposes, as shown by
a quantitative analysis, into acetic anhydride and sodium pyrosul-
phate according to the equation :

2 CH,COSO,Na = (CH,CO),O + Na,S,O

If, however, the sodium salt is heated with sodium acetate in pre-

7

sence of acetic acid, double the amount of acetic anhydride is formed :
CH,COSO,Na -+ CH,COONa = (CH,CO),O + Na,SO,.

1) Mott v. CHaranve Rec. XXIV.

970

The anhydride, formed can be obtained by distillation, sodium
pyrosulphate being left benind in the first case and sodium sulphate
in the second case. The so obtained sodium pyrosulphate is very
voluminous and on distillation with acetic acid and sodium acetate
it again produces acetic anhydride. In this case refrigeration is not
necessary when adding together the three components. If, however,
the above pyrosulphate is first submitted to fusion a considerable
decrease in volume takes place and it is then no longer capable
of forming acetic anhydride, resembling in this respect a pyrosulphate
prepared in the usual manner.

In the action of sodium chloride on acetylsulphurie acid acetyl
chloride is formed. In a manner analogous to that of the preparation
of acetyTsulphurie acid from acetic acid and SO,, were prepared
butyrylsulphurie acid and benzoylsulphurie acid, from which were
obtained in a corresponding manner butyric- and benzoic anhydride,
respectively.

Chemistry. — “Connexion between the adsorption-isotherm and the
laws of Proust and Henry.” By Dr. W. P. A. Jonxur. (Com-
municated by Prof. ScHREINEMAKERS).

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

1. The adsorption-isotherm is of great importance for the stady
of the colloids. From various sides efforts have been made to find
a connexion between this law and other laws of physical chemistry.
Starting from the phase rule and the law of mass action which
both can be deduced from the two main laws of thermody-
namics, I have tried, in the subjoined lines, to trace the connexion
between the adsorption-isotherm, the division rule and the law of
constant proportions.

The question whether the phase rule may be applied unreservedly
to dispersive systems will not be discussed here.

2. Let us imagine three substances A, 4, and C. A and (C' form
two non-mixable phases. C we may eall the solvent (dispersive me-
dium). 2 is soluble in C and can give a “compound” with A. (What
kind of compound this is does not matter; it may be a chemical
compound or an adsorption compound, or an ordinary solution).

When the equilibrium has set in we have “=n -+2—v7; when
n= 3, r=2 and p and 7 are constant, /’ = 1, therefore, the system
is monovariant (p-7". Which variables can oceur here?

A and C' form two phases between which 4 can distribute itself,

971

Theretore, we are dealing with the concentrations of 4 in the two
phases. If we call the concentration of 4 in the dispersive medium:
. av . . .

e and that in the phase A: — (im agreement with the notation used by

m
FRrevNDLICH in his ‘Kapillarchemie’’) it follows that in the monovariant

av
(p-T’)-system must then be = /(c).
m

3. Only in the case where 6 in A yields a compound occurring
in a separate phase, the system becomes non-variant (p-7"), hence
ve

= « (constant)
m

so that the “compound” is independent of the concentration.

We then speak of a real chemical compound that conforms to
the “law of Proust”. This is in harmony with the idea of Watp,
who for years has been trying to demonstrate that the constant
composition, with which we credit our chemical compounds, is caused
by the manner in whieh we generate these compounds. For we
always utilise the oecurrence of new phases (distillation, crystal-
lisation, sublimation).

av
4. As a rule, however, — will be a funetion of ¢.
m

The nature of this function may be determined by means of the
law of mass action.

We now apply the same to the “compound” which & can form
with A and eall the number of gram. mols. of A, 6 and the com-
pound m, p and q, respectively.

Let the formula of the compound be A,, Bp: then if

q qd
mA + pBZq Amn By
q q

we get, according to the law of mass action,

wn vp
Ca UB
Sy ee Se Geb) Sor) Oe he eel)
CAB

In this only the concentrations in which £& appears are

changeable.

wv
If again we eall Cyz : and Cg:c then (1) passes into
mW

63
Proceedings Royal Acad. Amsterdam. Vol. XVI.

9) 1
in which @ is constant. If, further, we put —=— the well known
adsorption isotherm

m
is formed.

5. This isotherm is generally a parabolic curved line that runs
through the origin and the point (1a). From the value

1 on
—_— =a—.{|-— 1
de? n n
we

notice that the isotherm will turn the convex side towards the
1

c-axis, when —— 1 > 0, and the concave side when ——1 <0.
n nl
ia al ais D 1 4
The transition case lies at ——1=0.
nr
In

the subjoined figure the course of the curve has been drawn
for different values of

n

973

nn ‘
6. For — =—0, the isotherm passes into— = a, hence into a
nL We

straight line parallel to the C-axis. This compound is, therefore,
independent of the concentration and consequently a “true chemical
compound” obeying the law of Provusr (3).

i a : : ie
7. If —=1, —=«e becomes a straight line through the origin,
n mm =
. . a - .
which cuts the line —-=« in the point (1. «).
m

The quantity of the substance 6 that passes into the phase A is
then proportional to the amount of the substance # in the solvent C,
in other words, the law of division (Hrenry’s law applied to two
liquid phases) is complied with.

, v
In this case, in owe (4) p must be = q, so that the equation

of equilibrium now passes into:
mA+q@BaqAn B,
q
that is to say the substance 4 has the same number of atoms in
the solvent C and in the phase A. This is also assumed in the law
of division.

Some investigators are accustomed to speak of a “solid solution”
in ease the phase A is amorphous-solid. This denomination is likely
to lead to confusion with mixed crystals so that, in my opinion, it
would be better to use the expression “solution” if one does not
like to introduce the word “pseudo-solid”’,

8. If — > 1 the convex side of the curve is turned towards the
nt

C-axis. We obtain such a line when, for instance, we draw the
distribution of acetic acid in water and toluene. In such a case we
never speak of ‘adsorption’, but attribute the deviation from Henry's
law to “association”.
In fact, from the equation of equilibrium
mA+pB@qAn By
g q
it appears that the substance passes into the other phase as
> PR ; ; ;
B p> and being > 1, the number of atoms has increased.
qy 4
6: me

974

] ;
If — <1 we obtain those cases which we are accustomed to eall
nL

“adsorption”. Analogous to (8) we ought to attribute here the devia-
tion from Hpnry’s law to “dissociation”. But nothing of the kind
has been found experimentally.

10. Henee, in the above-mentioned matter, I believe I have
demonstrated that Henrys law (law of division) and the law of
Proust are special instances of the adsorption-isotherm. This is in
complete harmony with the results of the investigations recently
published by Reipers ') and GrorGikvics *).

Zwolle, February 1914.

Mathematics. — “Cubic involutions in the plane’. By Prof. Jan
DE VRIES.

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

1. The points of a plane form a cubic involution (triple involution)
if they are to be arranged in groups of three in such a way, that,
with the exception of a finite number of points, each point belongs
to one group only. Suchlike involutions are for instance determined
by linear congruences of twisted cubics. The best known is produced
by the intersection of the congruence of the twisted cubies, which
may be laid through five fixed points; it consists of o* polar
triangles of a definite conic (Reve, Die Geometrie der Lage, 3° Auflage,
2° Abtheiluny, p. 225). According to Caporats*) it may also be
determined by the common polar triangles of a conic and a cubic.
A quite independent treatment of this involution was given by
Dr W. van per Wovtpe ’).

In what follows only cubic involutions will be considered posses-
sing the property that an arbitrary line contains one pair only, and
is consequently the side of a single triangle of the involution. The

1) Kolloid. Zcitschr. 18 96 (1913).

*) Zeitschr. f physik. Chem. 84 353 (1918).

3) Teoremt sulle curve del terzo ordine (Transunti R. A. dei Lincei, ser. 3a,
vol. 1 (1877) or Memorie di geometria, Napoli 1888, p. 49). [fa3,=0 and 62, =0
are those curves, then the involution is determined by a@,a,a@,=0, b,b, = 0,
b, (ole =0, b. b,. ==):

t) The cubic involution of the first rank in the plane. (These Proceedings
volume XII, p. 751—759).

975

lines of the plane are then moreover arranged in a cubic involution,
It is further supposed that the points of a triplet are never collinear,
the lines of a triplet are never concurrent.

2. if each point P is associated to the opposite side p of the
triangle of involution & which is determined by P, a birational cor-
respondence (P,p). will arise. Let be the degree of that correspond-
ence; then the points P of a line 7 will correspond to the rays
p of a system with index m, in other words to the tangents of a
rational curve (jp), of class n; the rays p of a pencil with centre
FR pass into the points P of a rational curve (/)" of order n.

Between the points P of + and the points P*, where 7 is cut by
the lines p, exists a correspondence in which each point P deter-
mines one point P* while a point P* apparently determines 7
points P. So (n+ 1) points P lie on the corresponding line p= P’ P".

In that case one of the points P’ has coincided in a definite
direction p with P, while p has joined with p'. The coincidences of
the involution (?*) form therefore a curve of order (n+ 1), which
will be indicated by y’+!. In a similar way it is demonstrated that
the coincidences of the involution (p*) envelop a curve of class (7 + 1).

When P describes the line 7, the points P’ and P" deseribe a
curve of order (x + 3); for this curve has in common with 7 the
two vertices of the triangle of involution, of which one side falls
along r, and the (x + 1) coincidences P= 7”, indicated above; we
indicate it by means of the symbol 9”+%,

Analogously there belongs to a pencil of rays with its centre
in & a curve of class (7 + 3), which is enveloped by the lines p' and p”
of the triangles A, of which one side p passes through AR.

3. The two curves (p), and (p)', belonging to the lines 7 and 7
have the line p, which has been associated to the point of inter-
section (7), as common tangent. Each of the remaining common
tangents 6 is the side of two triangles 4, of which the opposite
vertices are respectively on 7 and 7’; 6 therefore bears a quadratic
involution I? of pairs (P’,P').

The pairs (p',p"), which form triangles of involution with a
singular straight line 6, envelop a curve (4). If it is of the class a,
then it has 6 as (u—1)-fold tangent, for through a point 6 passes
only one line p’. We call b a singular line of order w. The pairs
(p',p") form a quadratic involution on the rational curve (b). Its
curve of involution B, i. e. the locus of the point P— p'p", is a
curve of order (u—1); for it has with 6 only in common the points

976

in which this line is eut by the (a—1) rays p", with which 6 = p'
forms pairs of the quadratic involution.

As 3’! has apparently (u--1) points in common with 7, 6 is a
(u—1)-fold) tangent of the curve (y),. Hence 6, as common tangent
of the curves (p)x and (p)', must be taken into account (u—1)? times.
The number of singular lines 6 satisfies therefore the relation.

a (1) Sh ae a ee (C18)

The singular lines 6 are apparently fundamental lines of the
birational correspondence (P,)).

The curves (P)" belonging to the pencils that have & and L'
respectively as centres, pass through the point ?, which has been
associated to the common ray of those pencils. Each point 6, which
they have further in common has been associated to two different
rays p, is consequently a sigular point of (P*) and at the same
time a fundamental point of (P. p).

The pairs of points (?, P’), forming triangles 4 with 4 he on
a curve (4), which has 4 as (m—1)-fold point if its order is m;
then we call Ba singular point of order m. On this rational eurve,
the pairs (P, P") form a quadratic mvolution, in which B belongs
to (m—1) pairs; the line p— VP’ P" envelops therefore a curve of
mvolution of class (m—1).

From this ensues that 5 in the intersection of two curves
(Py must be. counted for (m—1)* points, so that the number of
points 5 has to satisfy the equation

> (/) 0) a — a eo at tc 4 (2)

4. The involution (7) may also have singular points A, for which
the pairs of points (?, P") form an involution /* on a line a; the
latter is then szmgular for the involution (p*) and the pairs (p', p")
belong to an involution of rays with A as centre; a and A we
call singular of the first order. The pairs (A, a) are apparently not
fundamental for the correspondence (P, p); we indicate their number
by «. If n=1, as for the involution of Revs, (cf. § 1), then there
are only singular points and lines of the first order; for now n°— 1=0.

Let us now consider the curves 9"t* and 6”+* belonging to the
lines 7 and s. A point of intersection P’ of 7» with o determines a
triangle of involution of which a second vertex P" lies on s; P" is
therefore a point of intersection of s with 9. The third vertex P
lies therefore on the two curves @ and o. They have also in common
the pair of points that forms a triplet of the (?*) with the point rs.
The remaining points of intersection of @ and o lie in singular

S

points A and B, for they belong each to two triangles of involution,
of which one has a vertex on 7, the other a vertex on s.

As the singular curve (5)” cuts each of the lines 7, s in m points,
o and o have an m-fold point in 5. The numbers m must therefore
satisfy the relation (n-++3)* = (n+3)+2-+a + Sm’ or

emt (na Tia) een ara (2)
In a similar way we find the relation
eee unin Dna ays SS ee ee (A)
From the relations') (1), (2), (38), (4) ensues moreover
Pe he Cre 1045.4 foe (0)
=(m—1)? = J(u-—1)’, , (6)
consequently
E> (27 — (2 V5 ee 1 ee sel)
and

Oe (2m— MO (ee. eee Be en n((9)

5. The points P’, P", of which the connecting line p_ passes
through /, lie on a curve ¢*, which has a node in &, and is touched
there by the lines HE’, HE".

If # is a singular point £ then this locus consists apparently
of (5) and a curve of order (4d—m). Hence m may be four at
most. If m= 3, «* degenerates into (4)* and a singular line.

Through #, six tangents pass to e*; each of these lines bears a
coincidence of the involution (7%). Such a line belongs to a group
of the involution (p*), in which p" is connected with p’. The
coincidences of (p*) envelop a curve y, of class three, reciprocally
corresponding to the curve y*, which contains the coincidences of (7°).

By complementary curve we shall understand the envelope of the

lines p, which form triplets with the coincidences of the (p*). From
what was stated above follows therefore, that the complementary
curve of the (p’) is of the swth class.
Analogously we find a complementary curve of the sixth order,
, as locus of the points P, which complete the coincidences of the
(P*) into triplets. It has nodes in all the singular points of (P*),
for each curve (4)" and each line a bears two coincidences, which
form triplets with the corresponding singular points.

As the curve (B)" has an (m-—1)-fold point in 2B, the curve of

pau

1) In my paper “A quadruple involution in the plane’ (These Proceedings vol.
XIII, p. 82) I have considered a (P3), which possesses a singular point of the
fourth order and six singular points of the second order. In correspondence to
the formulae mentioned above, 7 = 4 was found.

978

coincidences y"t passes also (vi—1) times through B. Consequently
vit! and x" have yet 6(% + 1}—2 S(m—1) points in common
besides the points 4; but these points must coincide in pairs in
points where the two curves touch, where consequently the three
points of a group of the (P") have coincided.
Now
25 = O(n + 1)—2 S(m—1) = 6(n + 1) —S(2m—1) + 2,
if Bp indicates the number of points 7.
by means of (8) we find further
2d=(n+1)4+a+P.
Let o represent the number of singular points (6 = «+ ~), we
have found then, that the involution (P*) is in possession of
C= b(t USE GO) st oe er ed)
groups of which the three points ? have coincided.
Apparently this is at the same time the number of groups of
(p’), which consist of three coincided lines.
If the number of singular points of the order / is represented by
o,, then it ensues from (2) and (8), as m <4,
96,+46,+6,=n—I1,. . (10)
76, +506, +306, + 6,=5(n ieee 5 | ((IkIt)
By elimination of 6, we find
17 5, +- 206, + 96,=(n 4+ 1) (52 — 7m). . . . (12)
So that if appears that m amounts at most to SVEN.

6. We shall now further consider the case n=2. From (m—1)
=3 follows at once, that (P*) possesses three singular points of
the second order A, (4 = 1, 2,3). The curves (;) associated to

them are conics, which contain involutions (P’,P"); the lines p on
Which those pairs are situated, pass through a point Ch.

The existence of three singular straight lines of the second order
ensues analogously from (u—1)? = 38; the points P, which with
the pairs on 4; form triangles of involution, lie on a line ¢x; the
sides of those triangles envelop a conic (b¢)’.

From (8) we further find @—6,; consequently there are six sin-
gular pairs (A,qa).

The correspondence (/?,p) is quadratic; Le are its fundamental
points, 6; its fundamental lines.

To an arbitrary line 7 is associated a curve 9°, which has nodes
in the three points 6 and in the point associated to r in the
quadratic correspondence. The pairs (P’,P") on this gwadrinodal

979

eurve form the only involution of pairs that can exist on a curve
of genus /wo; the straight lines p envelop a conic *).

If r contains a singular point A, 9° degenerates into the line @
and a 9‘; the latter will further degenerate as it must possess four
nodes, consequently is composed of two conics.

On a singular line a lie two coincidences of the involution
i? =(P’,P"); they are at the same time coincidences of the ()’).
The curve of coincidences y is of the third order, so a must contain
another coincidence. Let it be Q’= Q; Q’ forms a triangle of
involution 4 with A and a point Q" of a, but moreover a A with
Q and a point Q* lying outside 7. Consequently Q’ is a singular
point viz. a point 4, for the pairs 4,Q” and Q,Q* do not le on
one line.

The curve 0° belonging to a consists first of a itself and a conic
(5)’; the completing curve must also have arisen from singular
points. No second point 4 lies on a, for this line would then contain
four points of the curve of coincidences. Hence two more singular
points of the first order lie on a, A*, and A**. Each singular line a
contains therefore fvo points A and one point b. If a* cuts the
line a in S, then A* and S form a pair of the involution lying in
a; so that AA*S is a triangle of involution. Hence A is the point

of intersection of the singular lines a*, a**.

7. The connector of two singular points A, and <A; is not always
a singular line a. Let A; lie on az, A; then forms with A; and an-
other point Q of a, a triangle 4, so that A;,Q is the line a. If
A; lies on az, a passes consequently through Az.

Let us now consider the line that connects the centres of invo-
lution belonging to C, and C,. It contains a pair of points forming
a triplet with B,, and a pair that is completed into a triplet by b,.
Hence it is a singular line b; we call it 6,. The axis of involution
c, belonging to it, is apparently the line 6,4,; the three lines ¢
form the triangle 5, b,,,.

In the transformation (P,/”) c, corresponds with the figure com-
posed of 4, and the conics (6),*, (,)’. With y, it has in common
the coincidences lying in Bb, and 4,, its third point of intersection
with y* lies apparently in 4,c,. The singular line (, is transformed
by (P,P) into a figure of the fifth order; to this belongs 6, itself
and the line c, twice. As no point B lies on 4, it must connect

1) The quadrinodal curves «° | have treated in * Ueber Curven fiinfter Ord-
nung mit vier Doppelpunkten” (Sitz. ber. der Akad. d. Wiss. in Wien, vol. CIV,
p. 46—59).

980

.

two points A; the correponding lines a form the completing figure.

The conie (4,)° has in common with y* the two coincidences of
7? lying on it andthe coincidence of the (P*) lying on B. As it
cannot apparently contain a coincidence of an other /? it must pass

through B, and B,, while it touches y* in B,.

8. A conic is transformed by (P,P’) into a figure of the tenth
order. For the conic (B,)? it consists of twice (5,)* itself, the conies
(B,)’, (B,)* and two lines a; it bears consequently fvo points A,
which we shall indicate by A, and A,*. As these points each form
a triangle of involution with £4, and another point of (5,)*, the
lines a, and a,* pass through B,.

Analogously we shall indicate the singular lines which meet in
B, and in B,, by a,, a@,* and a,, a,*; the pomts A, and Ay fare
then situated on (B,)*; A, and A;* on (B,).

On a, two more points A are lying; one of them belongs to
(B,)?, the other to (B,)?; we may indicate them by A,* and A,*.

If we act analogously with the remaining points A and lines a,
then the sides a,, a,, a, of the triangle A,*A,*A,* will pass through
B,, B,, B,, and the same holds good concerning the sides a,*, a,*, a,*
of the triangle A,A,A,.

In connection with the symmetry, which is involved by the
quadratic correspondence (P,p), the lines 6,, 6,, 6, contain respecti-,
vely the pairs A,, A,*; A,, A,*; A,, A,*. The triangle of the lines
b has C,, C,, C, as vertices; analogously c,,c,,¢, are the sides of
Be). By.

The six points 4, and the three points 6 form with the six straight
lines a a configuration (9,, 6,) B*), the points A with the straight
line w and the straight lines / the reciprocal configuration (6,, 9,) B.

9. That the involution (/*) discussed above exists, may be proved
as follows.

We consider the congruence formed by the twisted cubies ¢*,
which pass through feo given points G, G* and has as bisecants
three given lines g,,92,g, °) By Aj and h*,, we indicate the trans-
versals of gz, gi, Which may be drawn out of G and G*.

Let us now consider the net of cubic surfaces ¥*, which pass

1) A configuration (9,63) A consists of two triplets of lmes , Po, P3; Qs Yar Is
and the 9 points (p;.q/)-

2) This congruence has been inquired into by analytic method by M. Sruyvaert
(‘Btude de quelques surfaces algébriques . .. ” Dissertation maugurale Gand,
Hoste, 1902).

981
through y,,4,,g, and G* and have a node in G. The base of this
net consists of the 6 lines 4,, 44,43) Myos/o3. 431; they form a dege-
nerate twisted curve of the 6" order with 7 apparent nodes. Every
two ¥Y* have moreover in common a twisted cubic, which passes
through G and G* and meets each of the lines g;, twice ; these curves
y* consequently form the above mentioned congruence.

Through an arbitrary point passes a pencil (¥*), hence one ¢’*.
On an arbitrary tine / the net determines a cubic involution of
the second rank; through the neutral points of this /*, passes a
curve g*, which has / as bisecant. The congruence |qv*| is therefore
bilinear.

Through a point S of y, pass «' curves y*, they lie on the hyper-
boloid H’, which is determined by S, G, G*, g,, g,- All the curves
¢* lying on H?, pass moreover through the point S’, in which //?
again cuts the line g,.

To |g'| belongs the figure formed by 4,, and a conie of the
pencil which is determined in the plane (G%y,) by the intersections
of 91,42, h,,, and the point G*. There are apparently 5 analogous
pencils of conics besides.

Let us now consider the surface 4 formed by the ¢*, which
meet the line /. Through each of the two points of intersection of
/ and H?’ passes a g', cutting g, in S. From this ensues that the
three lines yg; are double lines of 4. The lines hin, h* 7 lie on <A,
for / for instance meets a conic of the pencil indicated in the
plane (G*g,), and this pencil forms with /,, a ¢’.

We determine the order of 4 by seeking for its section with the
plane (G'g,). To it belong 1) the line g,, which counts twice, 2)
the conic in that plane, which rests on / and is completed by /,,*
into a gy’, 3) the lines 4,, and /,,, which are component parts of
two degenerate y*, of which the conic rests on /. From this ensues
that 4 is of the sazvth order.

10. If the congruence [y*| is made to intersect with a plane g,
a cubic involution (P*) arises, which has the intersections of the
lines gz, Agi, and h,;* as singular points. With the intersection 5,
of ge correspond viz. the intersections of the y*, which cut g already
in /?,; they lie as we saw on the intersection (B,)? of the hyperbo-
loid H belonging to 4,. To the intersection A, of 4,, corresponds
the /* on the intersection «, of the plane (G*q,), originating from
the pencil of conics in that plane, ete.

On (B,)? lie the intersections of 9,,9,,9:,4,, and h,,*, viz. the
points B,, B,, b,, A, and A,*; on the intersection a, of the plane

982

(G*qg,) we find the intersections B,, A,* and A,* of g,, ,,* and h,,*.
To the points P of the line 7 lying in ¢~ correspond the pairs of
points 2, P' lying on the curve of the fifth order, which gy has
moreover in Common with the surface A®; this curve passes through
the points A;, A;* and has the points A; as nodes.
So we jind a cubic involution possessing the same properties as
the cubic involution (P*) considered before.

ll. We are now going to consider the case that the plane @ is
laid through a straight line c. resting on g,,4,,g, and cutting these
lines in the points 6,, 4,, B,. The three hyperboloids /7 determined
by ‘these points have the line ¢ in common besides a conic g? through
G, G*, resting on c,g,,g, and g, and forming with ¢ a curve of
the jy*|. For the conics passing through (7, G* and cutting 9,, 9., 95)
form a surface of the fourth order, cut by ¢ in a point not lying
on one of the lines g. The three hyperboloids mentioned cut ~ along
three lines 6,,6,,6,, meeting in a point C not lying on c, where ¢?
intersects the plane g again.

The curves {g*]| passing throngh 4,, meet g in the pairs of points
P’, F", of an involution on 6,. So Ay, are now singular points of the
jirst order. C too is a singular pot now ; for the figure (gy, c) has
all the points of ¢ in common with g, so that each pair of ¢ corre-
sponds to C.

The conic (4,)? of the general case has been replaced here by the
pair of lines (4,,c); on 6, lie now the singular points A,, A,*.

The singular points and lines now form a configuration (10,, 10,),
viz. the well-known configuration of Desarcurs. For in the lines
b,, 6,, 6,, passing through C, the triangles A, A, A, and A,* A,* A,*
are inscribed, the pairs of corresponding ‘sides a,*, a, ; 4,*, dy 3 A,*, Ay
of which meet in the collinear points 6,, B,, B,.

From the curve v°, which in the general case corresponds to a
line 7, the line ¢ falls away ; in connection with this the curve of
coincidences y® passes into a conic.

On the 6’ with one node D, now associated to r, exists only one
involution of pairs; the points PP’, P", which form triangles of
involution with the points of 7, lie therefore on the lines p passing
through D; consequently n= 1.

This involution differs from the (?*) described by Rryr only in
this respect that the singular point C’ does not correspond to the
pairs of an /® on c, as all the points of c have been associated to C.

12. Another (/*) differing in this respect from the involution

983

of Reyer, is found as follows. We consider two pencils of conies,
which have a common base-point /; the remaining base-points we
eall F,, F,, F, and G,, G,, G,. If each conic through , 7%, is brought
into intersection with each conic through /7,G%, a (P*) is acquired,
possessing a singular point of the fourth order in /, and singular
points of the second order in /%,G% ')

If, however, the points G; lie on the rays HF;, then the dege-
nerate conics (HF,, F,/',) and (HG, G,G,) have in. common the line
ah a and fhe point H, = (F,F,, G,G,); now H, is a singular
point corresponding to a// the points of h,; consequently it is in the
same condition as the point C mentioned above. There are now two
more similar points still, 7, =(P,/,,G,G,) and H,=(F,£,,G,G,).

While with an arbitrary situation of the points / and G, a 97

corresponds to a straight line 7, which 9’ passes four times through

E and twice through /%, G;, this curve degenerates now into the

three lines A; F,.G and a o*, which has a node in the third

vertex D cf the triangle of involution, of which 7 is a side. On this
P’ and P" are now again collinear with D, so that »=1.

If G, is placed on EF, and G, on EF,, a special case of a (P°)
is found, where n= 2. The curve 9’ now loses only the’ straight
parts 4, and h,, consequently becomes a_9*° having nodes in £F, F,.
G, and PD; on this quadrinodal 9°, (P’, P") form again the involu-
tion of pairs, so that m appears to be 2. The singular points of the
second Ge are HL, F’,, G;, the singular points of the first order are
FF, G,, G,, H,, H,; but the last two have respectively been asso-
ciated to all the points of 4, and h,, while to each of the first four
a quadratic involution corresponds.

13. In the case 7=3 we have the relations
= (m—1)? =8 and a+ Sm? = 28.
The first holds in three ways, for
a DS CU IES Cale eats C2
But the first solution must be put aside at once. For by (P,P’) a line
r would be transformed into a 9°; for the connector of two singular
points of the 3'¢ order 9° would have the two corresponding curves
(B)* as component parts; but then there would be no figure corre-
sponding to the remaining points of the line in question.
The third solution too must be rejected, as, for 8 singular points
of the second order «+ 8 & 2° = 28; so a = —4 would: be found.

1) See my paper, referred to above, in volume XIII of these Proceedings (p.p. 90
and 91). The notation has been altered here.

For the further investigation there remains consequently the com-
bination. of one singular point of the 3'¢ order, and four singular
points of the 2°¢ order ; we shall indicate them by Cand 4, (k=1,2.3,4).
In addition to this we have moreover three singular points of the
first order A;.

Then there are further ¢hree singular lines of the 1s8* order, ap,
four singular lines of the second order and one singular line of the
third order.

The curve (C)* belonging to C has in C’ a node, which is at the
same time node of the curve of coincidence y'. The two curves
have in ( six points in common; so also six points outside C; to
them belong the two coincidences of the /* lying on (C)*; the
remaming four can only lie in the points B.

As (C’)' forms part of the curve ¢« ($5), belonging to C, a singular

line a, passes through C. With y*‘, a, has in common the coincidences

of the /* lying on it, and the two coincidences lying in C’; conse-
quently a, cannot contain any of the points 2. By the transformation
(P,P’) it is transformed now into a figute of the 6 order, of which
(C)® and a, itself form a part; so the figure consists further of the
singular lines a, and a,, belonging to two singular points A,, A,
lying on ay.

The singular line a, is transformed by (P?,P’) into a,, and a figure
of the 5' order, arising from singular points on that line. As a,
does not pass through C and as it must contain, besides the
coincidences of the /*, situated on it, two more coincidences which
can only lie in points 6, we conelude that it bears two points
B,, B, and the point A,. From this ensues at once, that a, too
passes through A,, and contains the points 5,, 5,.

We consider CU, 5,, 6,, A, as base-points of a pencil (g*) of conics;
C, B,, B,, A, as base-puints of a second pencil (w?). If each g’ is
made to intersect with each wp’, a (P*) will avise, having singular
points in C, b,, Ap (see § 12). If to each y is associated the w?,
which touches it in C, then the pencils rendered projective by it,
generate the figure ((’)* + a,; from this it is evident that (C’)* does
not only contain the points 4;, but also the singular point A, =
==) (U9... 1D i,):

It is easy to see now, that A,B,, A,B,, A,B,, and A,B, are the
singular lines of the 2°¢ order. For the ¢? formed by A,B, and
CB, is cut by (yp?) in a J? on A,B, and a series of points (P) on
ChL,; so CB, is the axis of the involution (p',p") belonging to A, B,.

As the axes of the involutions (p', p"), determined by the four
singular lines of the 2"°¢ order pass through one point C;, the centres

Sd

of the involutions (P’, ?") lying on the conies (4;)? will analogously
be collinear.

The line on which they lie contains four pairs (P?’, P"), which
form each a triangle of involution with one of the points 4;,; from
this we conclude that it is the singular line of 3"* order, which (p*)
must have.

14. Let now n=—4. As to a line r a y7 must correspond, no
singular point of the 34 order SS) can occur beside a singular
point of the 4 order S@ (see § 13). A simple investigation shows
that only two cases are possible, viz. (UL) one point S with six
points S@) or (2) three points S*, with three points S@) and one
point S.

The jirst case appears on further investigation to be realised
by the (/*) mentioned at the beginning of § 12") To the singular
point of the 4'" order, #, belongs a rational curve (/)*, which
passes also through the remaining singular points /;, Gy (& — 1, 2, 3).
Singular lines of the 2™¢ order are /y.#) and GG); the axes of
involutions (p', p") belonging to them we find in FF, and EG.

As these six axes meet in /, the singular line of 4% order will
contain the centres of the involutions /* on the conics (/%)?, (G),)’.

In the second case there are three singular points Cy), three points
By, one point A, and, analogously, thie lines cx), three lines
bi), one line a.

With the curve of coincidences y*, which possesses nodes in

yz, (C)* has in common the 2 coincidences of the /? lying on it,
and six points in C,; the remaining 7 points of intersection must lie
in singular points, consequently (C,)’ passes also through C,, C,, and Bp.

On (Cz)* lies therefore a point ?, which forms a A with Cy and
B,; hence (B,)’ passes through Cy.

The line a is transformed by (/, P’) into itself and a figure of
the 6 order, so, either into the three conies (B;)? or into two
curves (Cx)*’. But the second supposition is to be cancelled, because
a would contain 6 coincidences in that case, two of its /? and four
in the two points C. Consequently the points B,, 6,, B, lie on the
singular line a,

Analogously the singular lines 6,,,.6, meet in A.

Every singular line cz passes through a point Cz and completes
KG.) into’ as‘.

The curve of the 3'¢ class (c,), belonging to c, has c,, c,, bg as

1) See also my paper, referred to above, in volume XIII, p, 90, 91.

956

The curve (,), touches the three cj, (and /,).

To a come corresponds in the correspondence (P?, P’) a curve of
order 14; it consists for the conic 8,* passing through C,, C,, C;,
B,, B,, of three curves (C,)*, of (B,)’?, (B,)* and a singular line. As
B,° is the curve of involution of the involution (p', p"), which is
determined by that line, it is a singular line of the 3"¢ order, conse-
quently a line ec.

155 hor

six Singular points of the 3'¢ order and as many singular lines of .

5) a further investigation produces only a (P*) with

ihe 3 order. Through each of those points C), passes one of those
lines, c,. A combination of the curve (Cy)* with the curve y° makes
it clear that the first curve also passes through the remaining points C.
‘ To the conic y,’ passing through C,, C,,C,, C,, C, corresponds a
figure of the 16% order, composed of the 5 curves (C;)*, & == 6, and
a singular line, c,. So y,’ is the curve of involution belonging to ¢,.

This (P") may be produced by a net of cubic curves with base-
points Cy. All the curves determined by a point P form a pencil,
of which the missing base-points form with P a triplet of the
involution *).

16. For n=6 we find as the only solution of the relations (10)
and (11) o,=3, 6, = 2, o,=4. But this is to be rejected: For a
conie would have to be transformed by (2, P’) into a figure of the
18 order. To the conic passing through 3 points 4% and 2 points
3) would correspond the tigure composed of 3 curves (5)* and 2
curves (5), which is already of the 18 order.

For 2=7 we find no solution at all.

The results obtained are united in the following table

n 0, | oO, oO, oO; oO
ead |
] 10 | 10
2 6 3 9
3 3 4 1 5
4 6 1 G
AS Aso h 7
5 | 6 6

1) This (P3) is a plane section of a bilinear congruence of twisted cubies
indicated by Venrronr (Rend. Palermo, XVI, 210) and amply discussed by Stuyvaerr
(Bull, Acad. Belgique, 1907, p. 470).

957

From the relation (9) ensues moreover Jd=6. In all the (P*) occur
therefore six groups, of which the three points P have coincided into
one; in the (p*) belonging to them szv groups with united lines p.

Physics. Further Experiments with Liquid Helium. I. The Hatt-
effect, and the magnetic change in resistance at low tempera-
tures. IX. The appearance of galvanic resistance in supra-
conductors, which are brought into a magnetic field, at a
threshold value of the field”. By H. Kamertincn Onnes. Com-
munication No. 1897 from the Physical Laboratory at Leiden.

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

§ 1. Introduction, first experiments. In my last paper upon the
properties of supra-conductors, and in the summary of my experiments
in that direction which I wrote for the Third Internationa! Congress
of Refrigeration in Chicago (Sept. 19138, Leiden Comm. Suppl.
N°. 340), I frequently referred to the possibility of resistance being
generated in supra-conductors by the magnetic field. There were,
however, reasons to suppose that its amount would be small. The
question as to whether the threshold value of the current might be
connected with the magnetic resistance by the field of the current
itself becoming perceptible could be answered in the negative, as
we had then no reason to think of a jaw of increase of the resist-
ance with the field other than proportional to it, or to the square
of it, and the law of increase of the potential differences at currents
above the threshold value could not be reconciled with either
supposition. A direet proof that in supra-conductors only an insigni-
ficant resistance was originated by the magnetic field was found in
the fact that a coil with 1000 turns of lead wire wound within a
section of a square centimetre at right angles to the turns round a
space of | ¢.m. in diameter remained supra-conducting, even when
a current of 0.8 ampere was sent through it. The field ef the coil
itself amounted in that case to several hundred gauss, and a great
part of the turns were in a field of this order of magnitude, without
any resistance being observed. The inference was natural, that, even
if we should assume an increase with the square of the field, the
resistance would probably still remain of no importance even in fields
of 100 kilogauss. In my publication (see Report, Chicago, Suppl.
N°’. 344) I restricted my conclusion about the resistance in the
magnetic field to a limit of 1000 gauss, and I also remarked that
when if came to making use of the supra-conductors for the cop-
struction of strong magnets without iron, it would be necessary in
the first place to investigate what resistance the magnetic field would

64

Proceedings Royal Acad. Amsterdam. Vol. XVI.

955

generate in a supra-conductor, and I immediately prepared experi-
ments in connection with this. That I was firmly convinced that the
action would be only small, is shown by the fact that [ arranged
the apparatus for these experiments as if for a phenomenon that
could only be studied with profit in fields of 10 kilo-gauss, but it
now appears that even then without further preparation, I might
have made the observations described below quite easily with the
field of 2 kilo-gauss that I then had at my disposal.

For our experiments a coil was prepared as described above, but
wound non-inductively. When (17 January 1914) it was brought
into a field’ of 10 kilo-gauss, it showed a considerable resistance.
We had not been so successful in the constraction of this coil as in
the previous one, as it did not become supra-conducting. It was
therefore possible that not much value could be attached to this
experiment. A coil with tin wire prepared in the same way as the
above described non-inductive lead coil also showed a considerable
resistance in a field of 10 kilo-gauss when cooled to 2° K., which
decreased more slowly than proportionally, when the field was
reduced to 5 kilo-gauss. In this case again we had not succeeded
in making the coil so that it would become supra-conducting, but
(always assuming a vegular decrease with the field, and supposing
that the fact that the coil did not become supra-conducting only
gives a non-essential disturbance) the results of both experiments did
not seem to be reconcilable with the above mentioned observations,
in which the magnetic field generated no resistance in supra-conductors.

The first thing to do was therefore to repeat the experiments with
the coils of tin and lead, which had become supra-conducting in the
former experiments, notwithstanding that the windings were in a
magnetic field. That these coils were not wound induction-free, was
of no consequence, now that if was a question of such comparatively
large resistances.

§ 2. Further experiments with lead and tin which show a sudden
change in the resistance at a threshold value of the magnetic field.

The lead coil of Table XII Comm. N°. 133, as it was not wound
induction-free, was placed in the cryostat of the apparatus to be
described in a future paper for magnetic measurements in hquid
helium, so that the plane of the windings coincided with the lines
of force of the magnetic field which is to be applied. This last acts
therefore partly transversely upon the conductor (lines of force at
right angles to the current), partly longitudinally (lines of force in
the direction of the current).

It was first ascertained that the coil was supra-conducting at the

989

boiling-point of helium. Further that it remained supra-conducting
when a current of 0.4 ampere was sent through it; even then the
windings were in a not inconsiderable field of their own current.

For further confirmation it was ascertained that the current
actually passed through the windings by bringing a small cardani-
cally suspended magnet (pole seeker) near the cryostat ; it showed the
movements which were to be expected.

Then the magnetic field
was applied. With a field of
10 Kilogauss there was a

considerable resistance, at 5 = %-——— i

Kilo-gauss it was somewhat —————
less. This made it fairly cer- me (ae
: a: eal ale le
tain that the magnetic field Sa |
created resistance in supra-\W% | | |
conductors at larger intensi- F 10 =the t 5
ties, and not atsmalier ones.
The apparent contradiction

that so far had existed be- 9 500 «$000 1509 12000 Gaus
tween the different experi- Fig. 1.

ments, was hereby solved. Later it appeared that 500 gauss was
below the threshold value, and 700 above it. Further investigation
gave for the resistance (expressed in parts of the resistance at 0° C)
as function of the field, the curve that is given diagrammatically
completed in fig. 1. The numerical values, in so far as they are
necessary for the description of the phenomenon, can be read from
the figure, so that they need not be separately detailed here.

It will be seen that the transition from the supra-conducting con-
dition to the ordinary conducting condition through the magnetic
field takes place fairly suddenly. The curve, which represents the
change of the resistance with the field is closely analogous to that
which represents the change of the resistance with ihe temperature
‘comp. / 0,004 amp. in fig. 7 in Comm. N°. 133). The resistance
measurements were made with a current of 0,006 ampere. Of the
two curves in fig. 1, one refers to 4°.25 A, and the other to 2° KA.
The sudden change in the resistance moves at low temperatures
towards higher fields; beyond this point the resistance increases at
lower temperatures (2° K.) almost in the same way as at higher ones,
it seems as if the introduction of the magnetic field has the same effect
as heating the conductor.

The tin coil of Comm. N° 133 Table IX was examined in the
same way. With this too we have a result in which longitudinal

64*

990

and transverse effects are combined. At 4°,25 AK the tin is still in a

state of ordinary
250; = —
200 |
7
150} a se 4
JIE
hs Ye
400 + +. 4
w 105 |
Wo
T 50 = =
F)
d 2500 5000 7500 40000 Camas.
~
Lig 2.
this ease at the threshold

conductivity, the curve, which represents the

a function of
the field decreases in steep-
ness (see fig. 2) with a dimin-
ishing field and meets the

resistance as

axis of ordinates pretty nearly
parallel to the axis of abeis-
sae. The only thing, there-
fore, that is remarkable here
as compared to what is obser-
ved at higher temperatures, 1s
the decrease of the slope to
zero. There is no indication
of a sudden change.

With the supra-conduecting
tin at 2° A we find, as with
lead a sudden change, in

value of 200 gauss. In fact with tin at

2° AK we are much nearer to the temperature of sudden change for
the resistance (3°,8 A’) than in the case of lead (sudden change for
the resistance 6° A (?) (comp. Comm. N°. 133).

§ 3.
verse effect with lead.

Separate observations of the longitudinal and of the trans-

Pressed lead wire was wound on a plate, so as to cover it witha
few flat layers of insulated windings. The windings could be so directed
that the effect was entirely transverse, or almost entirely longitudinal.

The results for the tempera-
tures of 2° K and 4°.25 K
are given in the four curves
in fig. 3.

The sudden change in
both -effeets takes place

almost at the same threshold
value of the field. The long-
itudinal effect is weaker than
the effect. The
value of the effect at hydro-

transverse

gen temperatures was exam-
Dr. K. Hor
and I. take

ined by and

myself, this

opportunity to thank him

250

2500 5000 1500
Kig. 3.

1000 aa

gon

for his help. A paper on tne subject will be published shortly. It
appears from this that the effect which (see fig. 3, and in detail
fig. 4) changes little with the fall from 4°.25 A to 2° K, increases
considerably with the fall from 14° A’ to 4°,25 4K.

It is worthy of notice that the sudden change differs considerably
in magnitude with Pbxz and Phy. Possibly there is a difference
in the nature of the lead in the two coils. In fact at 20°

Wp x WPpor
= = 0,0284 and ——* =0,0274.

77

0 0
Amongst the different questions that arise, one is whether a lead
wire might be constructed in which the magnetic resistance, remaining
zero as far as the threshold value of the field, will further gradually
increase with the field from the value O upwards.

| a al A CF

40

20

ri)
ones
Wo

1e)

3000

1500 2000 2500

Wig, 4.

a 3500 Gauss.

There is no doubt that the phenomenon discovered here is con-
nected with the sudden appearence of ordinary resistance in the
supra-conductors at a certain temperature. The analogy between the
influence of heating upon the resistance and that of the introduction
of the magnetic field, is so far complete.

One would be inclined to assume that an energy of rotation
determined by the magnetic field might be simply added to the
energy of the irregular molecular motion. If, in the production of
the obstructions which determine the resistance we have to do with
dissociations in the sense, that movements of electrons in certain

992

paths become unstable at a dofinite temperatare, the magnetic cen-
trifugal foree might make there motions one-sidedly unstable at
another temperature,

If the creation of ordinary resistance in supra-conductors with
currents above a certain threshold value, which is fully described
in Comm. N°. 133, really is a peculiarity of the supra-conducting
metal, and not due to disturbances, then the new phenomenon might
also be connected with this property. In faet if it were once proved
— to use an image already introduced into my paper for the Con-
gress in Chicago — that the vibrators which cause the resistance
can only be set in motion when the stream of electrons passes them
with sufficient rapidity, then it wouid not be surprising that the
magnetic resistance does not arise until the rapidity of the circulating
motions of the electrons is great enough to carry the atoms with
it and set them in rotation, by which they can then disturb the
regular motion of the electrons.

Finally, it is certain that the phenomenon deseribed is connected
with the laws of magnetisation of supra-conductors which are as
yet unknown.

Before however drawing definite conclusions from the new phe-
nomenon, it is desirable to gather more experimental information
on the subject.

Physiology. — ‘“Flectrocardiograms of surviving human Embryos”.
3y Prof. J. K. A. WertHemm SALOMONSON.

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

By the kindness of Dr. H. Trrus, Professor of Obstetrics and
Gynaecology I was enabled to record the electrocardiograms of 3
human embryos, born after operation for extrauterine pregnancy ete.
The age of the embryos was given as about 6 weeks, 5 months
and 8 weeks and agreed with ihe length measurements.

As the operations were performed in the University Institute for
Obstetrics and Gynaecology, the embryo had to be sent to my labo-
ratory in the University hospital about one mile distant, there being
no telecardiographie connecticn between the two.

The embryo was put into a bottle containing a warm solution of
Rincer. In the laboratory it was immediately placed in the hot moist
chamber, which I had formerly used for my experiments with chicken
embryos. The leads to the Ermrnoven galvanometer were placed on
the upper part of the thorax and on the abdomen.

993

The first embryo gave only a few rather poor tracings. I suppose
that its early stage of development, the effects of the shaking during
transport and perhaps of a change of temperature may have been
the canse. From the second and third embryo I got a series of
satisfactory tracings.

I may be allowed to show first the tracings from the last embryo,
which were obtained on a plate moving 20 mm. a second, an en-
largement of 1100 times, and a string of high resistance and _ sensi-
bility adjusted to a 30 mm. deflection for 1 millivolt.

Looking at the tracings we immediately see that the heart action
was not entirely regular. The interval between two contractions is
not equal. The complexes occurring with every heart-beat also
showed a notable difference. In the first tracings we see two different
forms, alternating regularly. A little later an intermediate form
occurs a few times and in the last negatives we see only one of
the first complexes. As a point of interest we note the complete
absence of waves which might be identified as /-waves.

The different complexes bear a decided resemblance to heteroge-
netic complexes occurring after stimulation of the right and left
ventricle. A contraction showing the form of a 6-complex in which
there is a lesion of the right bundle, is followed each time by a
complex of the A-type, where the contraction is caused by stimu-
lation of the right bundle or the right ventricle.

Already in the fourth negative we see 4-complexes which are
not followed by an A-complex. In the 5‘ negative we find for the
last time two complexes slightly resembling A-iypes, but with a
much smaller amplitude and a few particulars that cause them to
be considered as intermediate or C-types. After this we see only B-
complexes with a very slowly decreasing amplitude. The last tracings
become very irregular and show many small anomalous complexes
of different types.

In the second embryo, measuring 26 centimetres, the thorax had
been opened by Prof. Treus, who was in doubt if the heart was
still beating. Here the contractions came in groups of 10—20 or
even 2
embryos.

The curves were traced with a velecity of 25 mm. per second ;

5 single beats, in the same way as was seen with chicken

the sensibility was adjusted at 10 mm. per millivolt.

All the contractions showed atypical complexes of the 4-form
starting with a descending curve, rising afterwards. Generally the
first contraction in a group was a rather small one, the next ones
being somewhat larger. The groups ended abruptly.

994

The first descending part in such a complex was generally inter-
rupted by a few short waves. after which the descent became
regular. The ascending part was less steep and ended in a blunt
summit. Before this last wave sometimes a small intermediate wave
could be detected.

About 10 minutes later between the regular complexes as described
above, other anomalous ones appeared, of a much longer duration.
The number of these grew, and the form first observed disappeared
entirely. At last the tracing showed merely a series of conti-
nuously changing, very abnormal complexes.

It is difficult to explain these tracings. We know of course that
they are related to extremely abnormal circumstances. We have
before us a heart, very imperfectly developed, the halves of which
freely communicate, the duetus Botalli still being largely open.
An embryo with such a heart is asphyxiated without the possibility
of a normal large or small circulation, as at the same time the ciren-
latory system is entirely void of blood, and the heart cannot pump
any other fluid into the placentary or proper circulatory system. The
consequences are not, even approximately, to be foreseen. We can
only consider one or two points.

The normal stimulus for the heart starts near the right venous
sinus. But in the long run this necessitates the presence of blood
in the vessels. If this is and remains absent, the sinus node stops
its work. In such a case other parts of the auriculo-ventricular
bundle may temporarily continue the work. In the embryo n°. 3
we find the evidence, that this occurs alternately in the left and right
part of the bundle, and later on only in the left part. The result
is a ventricular automatism. At last the left part of the bundle also
breaks down, but at this moment the overworked muscle contains
so much fatigue-products as to cause a “diathese de contracture”,
and to produce idiogenetic irregular ventricle contractions, originated
in the muscle-substance itself without the aid of the bundle of His-
Tawara. In the larger second embryo, with the exposed heart these
irregular spasmodic contractions occurring at the same time as the
lengthened complexes could easily be seen.

If the complexes produced by the second embryo may be con-
sidered as to be caused by a temporary ventricalar automatism, the
small waves in the commencement of the first descending part of
the wave may be taken as recurrent auricular waves. As these
commence about the same time as the ventricular complexes, the
starting point of the stimulus ought to be situated not in the ven-
tricle itself, but somewhere between the auricle and the ventricle.

995

In the common well-known atypical complexes of the -form we
never see this recurrent wave and in the rare clinical cases with
recurrent auricle wave it is seen after the R-wave. Though this
seeming discrepancy can be accounted for, we may perhaps find a
fuller explanation after a continued research.

Geology. —- “On homocogencous inclusions of Kawah Idjen, Goentoer
and Krakatau and their connection with the surrounding erup-
tive rocks.’ By H. A. Brouwrr. (Communicated by Prof. G.
A. F. Monencraarfr.)

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

From the study of homoeogeneous inclusions of eruptive rocks it
is apparent which rocks of great depth may crystallize out of the
mothermagma, and to which differentiations this magma was subject
during the formation of a certain volcanic complex, even when the
eruptive aequivalents of certain products of differentiation, occurring
among the inclusions, are not known among the volcanic rocks of
the complex. Further, they show us the conditions of crystallization
of certain minerals, which only under special conditions can be
formed out of a magma of a certain chemical constitution ’). For
the determination of the relative age of rocks of the same volcanic
complex the study of inclusions is an important resource, especially
for the Indian volcanoes, which for the greater part are built up from
loose rolled material, natural denudations being of little occurrence.

Kawah Idjen.

The volcanic products of the Kawah Idjen *) consist chiefly of cinders
and stones, which are partly hardened into a conglomerate and are
beautifully denudated in the precipitous walls that surround the lake
of the crater. Somewhat above the locks of the irrigation which
when the level is high unloads the lake, there begins a flow of
lavas that follows the left shore of the drainage. Along the precipi-
tous slope to the locks and in the stream of lavas, during a short
visit in August 1912, some homoeogeneous and enallogeneous inclu-
sions were collected. The enclosing rocks are hypersthene-augite-
andesytes, in which numerous light-coloured phenocrists of plagioclase
form a contrast with the gray to grayish black glassy groundmass.

1) A. Lacrorx, Les enclaves des roches voleaniques Macon 1594. Id. La Montagne,
Pelée et ses éruptions, Paris. 1904.

2) R. D. M. Verpeek and Vennema, Java en Madoera. J. p. 81. Amsterdam 1896.

996

Microscopically examined these plagioclases show kernels from labra-
dorite to bytownite, and a repeated alternation of more basic and
acidic layers; besides pale green augite which sometimes occurs as
twin crystals according to (100), and hypersthene with a distinct
pleochroism in pale green and pale brownish-yellow colours, we
occasionally also remark small ore-crystals among the phenocrists.
The glassy base is partly unglassed, and contains edges of plagioclase,
small pillars of both augite and hypersthene, and ore-crystals.

The bomoeogeneous inclusions are partly holocrystalline micro-
pyroxene diorites, partly they only differ from the surrounding rocks by
the strong increase of the crystals of plagioclase, augite, hypersthene
and ore in the groundmass, whereas the glass only occurs caught
between the crystalline constituents; they apparently have formed
crystalline parts in the rising magma, their total erystallisation occur-
ring simultaneously with that of the surrounding lavas. The miero-
diorites are partly rather abundant of ore and then appertain to a
cleavage product more basic than the surrounding lavas. Exception-
ally olivine, in a small quantity, was found among the constituents
of these inclusions while it is wholly absent in the examined samples
of the surrounding pyroxene andesites. The occurrence of olivine in-
dicates cleavage products of the common mothermagma in which this
mineral may crystallize, these cleavage products being known to us
from the olivine-containing pyroxene andesites and basalts of volea-
noes of the same complex *). (Merapi, Raoeng, Gd. Pondok, Koekoesan).

Coentoer.

During the ascension of the Goentoer in April 1913 a scattered
vegetation turned out to have reached the very top, whereas VERBEEK,
on the smooth cone that has but few incisions even now, did not
meet with a single trace of vegetation above the limit af 1000 m.
The rocks of the Goentoer complex, as far as they have been examined
by Lorn, Brnrens, Versnexk, and myself, are chiefly basalts, that
sometimes graduate into olivine-containing andesites, andesites without
olivine also occurring. The products of the youngest point of eruption
(the Goentoer properly speaking) which now only at the northwestern
side shows some vapor of water and SO, rising from it, but which
during the preceding century was frequently very active, consist of
streams of lavas and gravel, or big blocks of often very porous rocks,
which entirely cover the upper part of the streams of lava. As far
as they have been examined, they are all found to be olivine basalts,

1) L. D. M. Verseex and Fennema, loc. cit.

997

usually with numerous phenocrisis of plagioclase, sometimes besides
green augite also hypersthene occurring among the phenoerists.

The homoeogeneous inclusions have been gathered in porous frag-
ments along the slope above the hot springs of Tjipanas, near the
brink of the crater. They are chiefly rather fine-granular olivine
gabbroes, which by their pale colour distinctly contrast with the
dark lava. The percentage of olivine varies, but is usually rather
high. Some of the inclusions consist of basic plagioclase, green augite,
olivine and magnetite; the olivine crystals with more or less rounded
edges are often entirely surrounded by the augites, the latter being
angularly bounded with respect to the plagioclases. Hypersthene being
among the constituents there arise graduations into particular inelu-
sions in which augite is absent among the constituent minerals, a
strong brownish-black to brownish-yellow pleochroitic amphibole
and hypersthene both occurring in its place. In these inclusions also,
the plagioclase is rather well idiomorphically developed with respect
to amphibole and hypersthene, whereas olivine-crystals with rounded
edges and sometimes irregularly shaped are entirely enelosed by
amphibole and hypersthene. All these rgcks represent shapes of
different depths of olivine-basalts, the amphibole seems to be absent
in the effusive aequivalents and was either not produced, the cireum-
stances of crystallization being different, or it was wholly resorbed
after crystallization. On the contrary, the rounded shape of the olivine-
erystals with their spread framing by amphibole, indicates a resorp-
tion of the first-mentioned mineral in the holocrystalline rocks. The
inclusions without augite show a rare combination of minerals by
the absence of monoclinic pyroxene and the presence of olivine, this
mineral generally being absent in amphibole gabbroes and similar rocks.

Olivine-free inclusions are the aequivalents of more andesitic rocks,
which we know from other parts of the Goentoer complex. In a similar
inclusion there were recognized: plagioclase, both hypersthene and
augite, and magnetite. As a rule the plagioclases form the bigger
individuals not limited idiomorphically, which ina very large number
poikilitically surround small pyroxene crystals.

Krakatau.

During a visit to Krakatau in the beginning of May 1913, in
one of the basaltic windings west of the great winding of lyper-
sthene andesite’) angular fragments were collected of a light-coloured
fine- to coarser-granular rock, which microscopically examined turned

) R. D. M. Verperk, Krakatau, Il, p. 160. Batavia 1885

995

out to contain much quartz. Although acidie hypersthene andesites
mark the first and third period that Verbeek distinguishes in the
history of the voleano, the quartz has not been able to develop itself
as such, under the circumstances in which these rocks crystallized,
and is found in virtual state in the glass of the groundmass.

The surrounding basalt contains phenocrists of basic plagioclase
and a small quantity of olivine in a glassy mass with crystals of
more acidic plagioclase, augite and ore. The holocrystalline inclusions
of which the largest dimension measures 10 cm. consist of strongly
zonair plagioclases, quartz (a good deal of it fine-granophyrically
grown together with feldspar), worn dark minerals and ore. In the
fine-granophyrical conglomerations also kali-feldspar may be found.
The SiO, percentage varies, the chemical constitution of one of the
inclusions appearing from the following analysis (analyst F. G.
MANNHARDT):

SiO, | 64,14
TiO cen > SABs6
NOR eae TelGil
sles xit) |) ie 33a
FeO lea Brea
CaO Ha 5G O
MeO | 0,82
NasO' rel Aer
K,O [Weeo!oa
H,O 0,68 *)
Sum total | 100,73

Calculating the analyses according to the American system we
find a remarkable high percentage of SiO, that is not bound as a
silicate (about 38°/,).

{t appears from the above-said that the homoeogeneous inclusions
of the Kawah Idjen, according to their chemical constitution, show
but a few varying types; in connection with this fact the chemical
constitution of the andesites and basalt of the Idjen complex differ
but shghtly. *)

1) Loss by ignition. :

2) The basalt of the stream of lavas of the Merapi which flows into the sea
near Batoe Dodol on the straits of Bali contains (according to Stéur) 54°/9 SiO);
two pyroxene andesites of the Kawah Idjen contain 58°/) and 60°/, SiO,; and
among the rocks that were gathered by me during the eruption of the Raoeng
in 1913, on the northern slope of the voleano near the brink of the crater, some
amphibole-hypersthene-augiie-andesites with 63 °/) SiO, occur. Also the olivine-
containing basaltic cinders of the youngest Raoeng-eruption have a high SiO,

percentage (54/4).

999

Various aequivalents of the basalts and aequivalents of the andesitic
rocks of the Goentoer in a broader sense were found among the
homoeogeneous inclusions of the youngest eruptive products of the
(coentoer properly speaking.

The quartz-containing inclusions of the basalts of Krakatau illustrate
the presence of virtual quartz in the groundmass of the hypersthene
andesites of the first period, and would as well be the only traces of
differentiation in the mother-magma before the basaltic eruptions, if
not, not only the greater part, but all traces of the former basic
eruptions had disappeared by a fall-down.

The occurrence of augitefree plagioclase-hypersthene-amphibole-
olivine rocks as homoeogeneous: inclusions in the products of the
Goentoer teaches us that such combinations of minerals may at a
_ greater depth crystallize out of the basaltic magma.

It appears from the calculation of the norm that also the quartz-
containing inclusions of Krakatau belong to the rare combinations
of minerals because, according to the analyses calculated by Wasninc-
Ton no other rock belongs to the sub-class (Il. 3, 4, 3).

»

Chemistry. — “On the pyrophoric phenomenon in metals”. By
Prof. A. Smits, A. Kettner, and A. L. W. pe Gen. (A pre-
liminary communication). (Communicated by Prof. J. D. van

ppr WAALS).

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

In a previous communication ‘) it was pointed out that the
pyrophoric phenomenon would possibly have to be explained by
this that the metals obtained in the reduction of certain compounds
are comparatively far from the state of internal equilibrium and
show an abnormally great power of reaction in consequence of
an abnormally large content of the simpler kind of molecule.

The explanation for this phenomenon prevalent up to:now, which
is of more frequent ocenrrence than is perhaps supposed (we found
it with Cu, Bi, Pb, Ni, Fe) attributed the great reactive power to
the very finely divided state; so an explanation which is perfectly
analogous to that of the so called “chemical flag’ for phosphorus

Now the possibility might also be considered that in the liberation
of the metal a pyrophoric admixture is formed, or that the hydrogen

1) These Proc. XVI, p. 699.

1000

!
dissolves somewhat in the metal or becomes denser on the surface
and exercises a catalytic influence.

It has, however, appeared that pyrophoric iron may be obtained
when different iron compounds are heated for a short time in a
hydrogen current at + 350°. This sueceeds with ferro oxalate, ferro
iartrate, ferro chloride, and with the oxides of iron, from which
follows that no common admixture except hydrogen can be pointed
out bere, to whieh the pyrophoric property could be aseribed. Now
it appeared, however, that also pyrophoric iron can be obtained
when ferro oxalate is heated without contact with hydrogen, whieh
proves that the hydrogen certainly does not cause the pyrophorie
phenomenon. ')

To test the supposition expressed by one of us, it was examined
in the first place what the influence is of the temperature on the
pyrophoric phenomenon. Sealed to glass tubes with pyrophoric iron
were placed in a thermostat, which was regulated at different tem-
peratures between 250° and 340°. After a certain time the tubes
were taken from the bath and opened to find out if the iron was
still pyrophoric. The result is given in the following table:

Duration of the |

heating | Temperature | Result
| |
a week 250° still pyrophoric
4 ; | 290° | no longer pyrophoric
48 hours | 310° | hardly pyrophoric
24, | 340° no longer pyrophoric
|

The pyrophorie property of iron, therefore, vanishes with heating
to higher temperature. The rapidity with whieb this happens,
increases greatly with the temperature. 310° is about the temperature
at which the conversion has taken place almost completely in 48
hours.

That at this temperature a massing together of the powder should
have taken place, and that in consequence of this the pyrophorie
phenomenon would have disappeared, is pretty well out of the
question, and it was therefore of importance to make an attempt to
examine whether the transition pyrophoric won — non-pyrophoric

1) Turespautr [Bull. Soc. Ch. de Paris (3) 81, 135] found that when Bi-mellate
is heated in vacuo, pyrophoric Bi is formed; in the same way we obtained
pyrophoric bi from:the citrate.

1001

tron is attended with a variation of volume, as in this way an
important support might be given to the supposition of an internal
transformation.

In a dilatometer constructed specially for the purpose Fe,O, was
reduced with hydrogen under such circumstances (temp. and time)
that on the ground of experiments, previously taken, the iron could
certainly be assumed to be pyrophoric. Then the apparatus was
exhausted and filled with mercury, which had been boiled at the
arpump °*).

In connection with the experiments in sealed to glass tubes it
was to be expected that in case of one or two days’ heating nothing
could be observed until the neighbourhood of 300° is reached. In
agreement with this the following was found :

Sh dt Duration of Change of position of
Horpeiacine heating | the mercury meniscus
212° | 54 hours | 0 cm.
284° | 22 ee;; OF
320° Scene ‘+14 , Oncontinued
heating no change
| of volume took
place any
longer 2).

Accordingly it appeared most convincingly from the dilatometrie
investigation that a considerable increase of volume fakes place
exactly in the temperature region where the pyrophoric property of
the iron vanishes with such rapidity that it can no longer be
demonstrated after + 48 hours. In virtue of these preliminary
experiments it may, therefore, be considered as certain that the
transition of pyrophoric iron to ordinary iron is accompanied with
an increase of volume. The supposition that pyrophorie iron is iron
that is not in internal equilibrinm, has thereby greatly gained in
probability. In a subsequent communication it will be demonstrated
why pyrophoric iron must not be considered as a new modification
of iron.

Amsterdam, Febr. 27, 1914. Anorg. Chem. Lab. of the

University.

1) Tron and mercury were examined after the experiment was over, when the
mercury appeared to contain only exceedingly small traces of iron, and the iron
to be perfectly free from mercury.

*) At the end of the experiment the iron appeared to be no longer pyrophoric,

1002

Chemistry. — “Answer to Prof. E. Conn to his cbservations under
the title of Allotropy and Electromotive Equilibrium”. *) By
Prof. A. Smits. (Communicated by Prof. J.D. vax per Waals).

(Communicated in the meeting of Feb. 27, 1914).

Mr. Cony’s attack under the tithe of ‘“Allotropy and electro-
motive Equilibrium” induces me to make the following remarks.

Mr. Conpn seems to think it anything but correct that I have
ventured to enter a field of work, which bad been proclaimed his
territory of research in more than one address, treatise, and magazine.

This deed, however unpardonable it may appear in Mr. Conrn’s
eyes, may be very reasonably accounted for. If I had not seen a
chance to throw new light on the phenomenon of allotropy, I should
certainly not have occupied myself with it, as it would not have
prompted me so urgently to investigation then, but when a few
years ago | came to the conviction that the phenomenon of enantio-
tropy and monotropy and the allied phenomena might be united
under a new point of view, by the assumption that every phase of
an allotropic substance is built up of different kinds of molecules,
1 did not hesitate for a moment, but immediately set about to test
the drawn up theory with my pupils. This is the reason that of
late years I have studied the phenomenon of allotropy, and I do
not think that there is anything in the line of conduct followed by
me that can in the least rouse astonishment.

Further Mr. Conun considers it necessary to point out that the
form of my publications might give rise to misunderstanding, which
would appear from a passage occurring in my latest paper'), run-
ning: “In connection with the foregoing it is desirable to draw
aitention to this that according to these considerations the contact
with the solution of a salt of the metal must have an accelerating
influence on the setting in of the internal equilibrium of the metal.”

Mr. Conen has taken offence at this sentence, because according
to him | should have forgotten to mention that already fifteen years
avo this fact was found by him and Van Eyk, and has since been
explained by him.

This remark of Mr. Congn is very significant, for 1 do not think
that he could have made it apparent in a clearer manner that the
contents of my communication “The application of the theory of
allotropy to electromotive equilibria” have remained perfectly dark
to him.

1) These Proc. XVI p. 708.

1005

Messrs. Conkn and Van Eyk ') found that when e.@. white tin
is left in contact with a tin solution at a temperature lying under
the transition point, the conversion of the metastable white to the
stable grey tin is accelerated. Mr. Conmn’s explanation is this *) that
when once a trace of grey tin is present, the tin from the solution
will deposit in the grey moditication on the grey tin, in consequence
of the difference in “LOsungstension” of white tin and grey tin, the
white tin entering the solution. It is clear that all this refers to the
conversion of one modification to another or of one solid phase to
another.

My paper does not deal with the transformation which takes
place between two solid phases of an allotropic substance, but with
the chemical conversion which can oceur between the different kinds of
molecules in each of the solid phases according to the theory of
allotropy.

In the cited communication | namely pointed out that the just-men-
tioned theory states that a metal which presents the phenomenon of
allotropy, will contain different kinds of molecules. ‘To simplify
the case as much as possible I assumed that double molecules
M, occur by the side of simple molecules J/. If the metal is now
fo behave as a substance of one component, so in a unary way, it
is necessary that the different kinds of molecules in each of the
’ phases of the metal are in equilibrium, and as we have to do here
with an equilibrium between the kinds of molecules of one and the
same substance, the word ‘internal equilibrium” is used here to
distinguish it from other equilibria.

Up to now it has always been assumed that a metal emits only
one kind of ions into solution. In connection with the just-mentioned
internal equilibrium in the homogeneous meta! phase we come,
however, to the conclusion that the metal supposed here immersed
in an electrolyte will emit different ions, which, if the ion per
atom carries e.g. three positive charges, will be the ions J and
Ds |e

Just as the molecules Wand WV, in the homogeneous metal phase
can be in equilibrium, this will also be the case for the ions JM
and M,:::, and this equilibrium, too, may be called an internal
equilibrium.

Now 1| have among others pointed out that the metal can be in
unary electromotive equilibrium only when the different kinds of

1) Zeitschr. f. phys. Chem. 30, 601 (1899).

i eee » 30, 623 (1899).

65

Proceedings Royal Acad. Amsterdam. Vol. XVI.

1004

molecules in the metal and the different kinds of ions in the elee-
trolyte each in itself, are in internal equilibrium.

It is to be expected that at the ordinary temperature the internal
metal ion equilibrium sets in rapidly, whereas the metal in itself
at the ordinary temperature does not pass into, the state of internal
equilibrium, or only exceedingly slowly.

When, however, the metal is brought into contact with an electrolyte
which contains the ions of this metal, the surface of the metal, as
I have demonstrated, will assume internal equilibrium in consequence
of this that more of those ions in which the metal is deficient,
deposit as molecule from the electrolyte, or that the metal sends
more of those molecules as ion into solution which have too great
a concentration in the metal. These two processes, which dependent on
the concentration of the metal can also proceed simultaneously, bring
about that the concentration of the surface of the metal becomes
equal to that which corresponds to the internal metal equilibrinm
at the given temperature and pressure. In the maintaining of this
equilibrium between the molecules J/ and J/,, as well as in its
setting in, the electrolyte as connective link, will play an important part.

So it appears convincingly from what precedes, just as from my
previous communication that the quoted passage refers to the trans-
formations which take place when a metal phase which is not in
internal equilibrium, passes into the state of equilibrium.

Also where I mention the transition point, | have said: “At the
point of transition the electrolyte will greatly promote the internal
equilibrium both in the metal e, and in the metal phase d for the
just-mentioned reasons.”

The case referred to by Mr. Coney, the influence of an electrolyte
on the conversion of one moditication to another, | have therefore
left entirely out of consideration, and as it is not exactly practical
to mention the names of those who have occupied themselves with
other phenomena, there was no occasion for me to mention Mr. ConEn
in my preceding paper.

This will, however, be the case when I shall discuss also the
influence which Mr. Conmn has in view, when it will appear that
a deeper insight is attained just by means of the considerations given
in my preceding communication.

In conclusion in reference to the motive of Mr. Conmn’s attack,
which according to him is to be found in the fact that more and
more both Duteh and foreign colleagues should have objected 10 the
line of conduct followed by me, I will only remark that different
Dutch colleagues have expressed their sympathy with my work to

1005

me. And as Mr. Conen also mentions foreign countries, I may add
that I have, indeed, carried on a controversy with Mr. Tammany,
from which it therefore appears that on that side, as I had, indeed,
expected, 1 meet with opposition; but I may state that on the other
hand both before and after this controversy I have received expres-
sions of great sympathy with my views from very competent colleagues
from Germany, Sweden, England, and America, expressed in letters
or publications, which if this should be considered desirable, I shall
be glad to lay before the Committee of this Academy.
Amsterdain, Febr. 1914.

(April 28, 1914.)

a
o

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
: TE AMSTERDAM.
PROCEEDINGS OF THE MEETING
of Friday April 24, 1914.
Vout XVI.

Doce

President: Prof. H. A. Lorentz.
Secretary: Prof. P. Zeman.

(Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige
Afdeeling van Vrijdag 24 April 1914, Dl. XXII).

(SHO) ANAL Js ANP oS

Z. Kameriinc: “On the regulation of the trapspiration of Viscum album and Ripsalis Cassy tha.
A contribution to the knowledge’ of the antagonism between the guard cells of the
stomata and the adjacent cells of the epidermis”. (Communicated by Prof. M. W.
Brigerinck), p. 1008. (Wich one plate).

Tink Tammes: “The explanation of an apparent exception to Menpet’s law of segregation”.
(Communicated by Prof. J. W. Mort), p. 1021.

F. Tueunissen: “The arrangement of the motor roots and nuclei in the brain of Acipenser
ruthenus and Lepidosteus osseus”. (Communicated by Prof. L Bork), p. 10382.

C. E. Brnsamins: “On esophageal ausecaltation and the recording of esophageal heart sounds.”
(Communicated by Prof. H. ZwaarpEMAKeER), p. 1041. (With one plate).

J.J. van Laan: “A new relation between the critical quantities, and on the unity of all
substances in their thermic behaviour’. (Communicated by Prof. H. A. Lorentz), (Con-
tinued, p. 1047.

W. Remnpers: “The reciprocal pairs of salts KCl + NaNO, Ze NaCl-+ KNO, and the
manufacture of conversion salpetre”. (Communicated by Prof. FP. A. H.ScurerNeMakeErs),
p. 1065.

J. D. van per Waars: “On the critical density for associating substances”, p. 1076.

J. D. van per Waats Jr.: “On the law of partition of energy.” V. (Communicated by Prof.
J. D. vAN pkrR WAALS), p. 1082.

P. van Romeurcu and Miss ID. W. Wernsimnk: A new hydrocarbon from the pmacone of
methylethylketone,” p. 1088.

P. van Rompurcn and P. Murter: “1:3:5. hexatriene,” p. 1090.

J. BorseKeN and J. F. Carripre: “On dichloroacetylene.” (A warning). (Communicated
by Prof. A. F. Ho_iran), p. 1093.

FP. M. Jarcer: “On the Isomorphy of the Ethylsulphates of the Metals of the Rare Harths, and
on the problem of eventual morphotropic relations of these salts with analogous salts of
Scandium, Indium and Beryllium.” (Communicated by Prof. P. van RompureH), p. 1095.

J. H. Bonnema: “Contribution to the knowledge of the genus Kloedenella, Uxiricn and
Basster.” (Communicated by Prof. J. W. Mor1), p. 1105. (With one plate).

W. J. pe Haas: “The effect of temperature and fransverse magnetisation on the continuous-
current resistance of crystallized antimony.” (Communicated by Prof. pu Bors), p. 1110.

M. J. van Uven: “The theory of Bravais (on errors in space) for polydimensional space,
with applications to correlation” (Qommunicated by Prof. J. C. Kapreyn), p. 1124.

¥. A. H. Scurememaxers: “Equilibria in ternary systems.” XIV, p. 1136.

Hk. pe Vries and G. Scmaake: “On the singular solutions of ordinary and partial differen-
tialequations of the first order’, p. 1152.

J. P. Kurnen: “The diffusion-coefficient of gases and the viscosity of gas-mixtures”, p, 1162.

A. Sits: “The metastable continuation of the mixed crystal series of pseudo components in
connection with the phenomenon of allotropy.” (Communicated by Prof. J. D. vAN DER
WaAALs), p. 1167.

A. Smits, 8S. C. Boxuorsr and J. W. Terwen: “On the vapour pressure lines of the system
phosphorus.” I. (Communicated by Prof. J. D. van per Waats), p. 1174.

Jan dE ries: “A bilinear congruence of rationnl twisted quartics,” p. 1186.

W. Karreyn: “On Iiermire’s functions”, p. 1191.

M. W. Bewerrinck: “On the nitrate ferment and the formation of physiological species,” p. 1211.

66
Proceedings Royal Acad, Amsterdam, Vol, XVI.

1008

Botany. — “On the Regulation of the transpiration of Viscum
album and Rhipsalis Cassytha”. A contribution to the knowledge
of the antagonism between the guard cells of the stomata
and the adjacent cells of the epidermis. By Z. KAMERLING.
(Communicated by Prof. BrisErinck).

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

In recent years | have conducted numerous experiments to obtain
an insight into the need for water and the consumption of water in
various tropical plants. In continuation of these investigations, carried
out in Java and in Brazil, similar experiments have been undertaken
during the last few months in Holland with native plants. The
method of inquiry was almost always the same: leafy boughs were
cut off and hung up in the laboratory in the shade or exposed to the
sun in the habitat of the plant investigated; they were weighed
periodically at shorter or longer intervals.

By this method of experiment the extent of transpiration can be
determined when the tissues of the plant still possess their normal
water-content and also the nature of its modification, when the tissues
of the plant gradually lose water.

These experiments show that in many plants there is a continuous
and very considerable transpiration from the beginning of the expe-
riment until the leaves of the bough are dried up. In other species
the transpiration is more or less great at the beginning, but decreases
gradually so that finally it sinks to a minimum-value. This decrease
or regulation of transpiration is evidently due to the narrowing or
closing of the stomata, which in the different plants investigated may
occur more or less quickly and more or less extensively.

In some plants I found that in ecgntrast to the normal course
of the regulation, the intensity of transpiration increases distinetly at
the beginning and only afterwards diminishes in the usual way.
Such an irregularity, at least when there is no external influence at
work, such as temperature, illumination or conditions of humidity
or movement of the atmosphere, can hardly be explained otherwise
than by assuming that the aperture of the stomata in these cases first
dilates when the plant begins to wither and only afterwards constricts.

i observed this phenomenon very clearly in .Viscwn album in a
comparative experiment which | performed on the transpiration of
this plant and of some deciduous and evergreen woody plants.

It is unnecessary to publish here the detailed results. I append

1009

only the figures which have reference to the above-mentioned
irregularity in the regulation of transpiration.

The boughs for experiment were arranged at an open window,
where they were not reached by the sun before mid-day, and only
for a short time afterwards.

=
3 First bough s Ih -ceeohd bough | 3 Third bough
E experimented on £ | experimented on 5 experimented on |
| = Viscum album. = | Viscum album. 6 Viscum album. |
M \Weightingrammes| “ Weightingrammes| “ |Weightin grammes
vo} io} vo} |
| | | { |
|
| 9.25 21.5 grm. | Ox350 |) Mbeiseerm: 9.40 15.55 grm.
|
9.45} 21:2. 10) 8 5,55. 10. 15.50, |
HOsIGs| oto 1055: eerisee 10.20| 15.42 .
moras ..20.7 10.55| 15.0 , 10.55-|., 15-240
| |
15: |. 120.27 — itt 225) mean Tee 11:25) Wr taeda ae
11.45 | 19.82 , 1255; |e anion 12. 14.53,
Dh igesy Oeipe |) 13R220 1 2.15%) eisai
| |
BRoaaley SAT De" 8.35: |) | 1289200. 2 335°) i ae7s ais
| |

The results of these experiments are more intelligible when repre-
sented in the following way :

First bough experimented on.

Average |
Length of Total soe
i aaa aeIIN transpiration
period transpiration Fads math (ies

9.25 till 9.45 20 minutes | 300 milligrm. 75 milligrm.

OAs 10810) 625, | 200 . 40 .
10100 10045. \N35y * | 300 P 43 fs
POFASY = eel iSO! =; | 430 f 72 i
(iin Alay NST | 450 2 75 .
| 11.45 ad 1850, | 1520 F 56 :
OR eS Sone 95) 1100 X | 58 ‘

66"

1010

|
|

Second bough experimented on.

Average
| ied | transetation | #Bspiration in
| 9.35 till 10. | 25 minutes | 200 milligrams | 40 milligrams
[Osment 10215 | 15.) oer aN R50 i 50 Z
10.15, 4.10.55 |40, 1400 2s BO dae
10.55- 9° 11225: 1} 30 430 3 2 .
1.25 15 Soe SO) eee 1 h450 * 15 .
(Wt 55 en, 0 Qalseli40ige* aaloo0 32 5
fe cist nay 3, ani icone 300 19 :
Third bough experimented on. |
(a ek Ce er
| e | | verage |
| Bie om | Gisccietan | tr anspiralion in
9.40 till 10. | 20 minutes | 50 milligrams. 12.5 milligrams,
10." = 10220 © 20 am | 80 \ 20 Hs
| 10.20° , 10.55 | 35 ee fece . | 26 .
10255)e),, e250 130i | 300 . | 50
1.25 Weis eat 35 mvt tl 410s etm ‘
12 Sea hnlaye ais. 8 ae | 1380 ts | 5I i
alae a ee! | 400, Ie ,

The three boughs were cut off at the same time, about 9.20;
the weighing of the first bough took place therefore about five
minutes, that of the other two fifteen and twenty minntes after
cutting. Whether the transpiration in the interval between cutting
off and the first weighing changed noticeably, cannot be ascer-
tained, but what is important is that the behaviour of the three
boughs agrees, for they all, */,;—1 hour after the cutting (when they
to 4°/, of their weight by.transpiration) show a

distinct vise in the intensity of transpiration, which about two hours

had lost from 1°/

1011

later (when the loss by transpiration of the boughs bad risen to from 6
to 10°/, of their original weight) reached a maximum and_ then
declined again.

Boughs of Pirus maius and Populus nigra which were investigated
in the same way at the same time as those of Vescum showed no
similar phenomena; the intensity of transpiration was here very
great and remained almost unchanged until the boughs had dried
up. In an experiment conducted some days later in precisely the
same way with some evergreens (Hedera helix, Pinus spec, Abies
spec. ete.) transpiration was at first also great, but gradually declined
until a minimum was reached. Therefore these evergreens showed
nothing of the irregularity which was noticed in Viscum.

The ready conclusion that in the experiment with Visewm it was
not a question of one or another disturbing factor, which had been
overlooked, but probably of some physiological peculiarity due to
the structure of the stomata, was further confirmed by the fact that
on looking throngh the protocols of my experiments IT found again
very clearly the same irregularity in an experiment conducted in
Brazil with Rhipsalixs Cassytha. The structure of the stomata of this
plant agrees in several very obvious characteristics with those of
Viscum album.

For the experiment, of which I give here the results only so far
as they bear upon the phenomenon in question, a large plant was
carefully loosened from the tree on which it grew, and hung up in
the laboratory. The weight of this plant was recorded at intervals
for a period of 136 days.

The following diminution in weight was observed :

during the first 24 hours dle gatoy. OF
ss » second A ZO So
es a tdayinzel < Dye Ol
3 , fourth - a CH
* » oth 6th and 7h , on the average 0,94 °/,
3 8's and 9th ie OODLE
is ,, LO and 11 Pg ee 1 0,86 °/,

3 pp hen Sad sates ee OLSone
”? 99 29th 33 oun > ”? 29 99 ”» 0,68 ie
+ Fe 38th 76th Ms oo. ae a 0,42 oy.
> ” tegen ”? 104° ” ” ” ” ” 0,23 ah
i Pel 5iht A OG at) We Neat odie es esta

of the original weight

9)

|
* » 12% to 16tinelusive,, ,, ,, . ALCO OH

1012

We see here also how the intensity of transpiration increases
when the plant investigated has lost + 1°/,°/, of its weight and
then later decreases (when the loss by transpiration has risen to
+ 6°/,). Simultaneously with this experiment on Rhipsalis Cassytha
some other plants (Pothos aurea, Philodendron spec., Aechmea spec.,
Vriesea spec. div.) were investigated by the same method, without
showing this peculiar irregularity in the transpiration.

It may clearly be assumed that in the case of Viscwm album and
Rhipsalis Cassytha we have to deal with the antagonism between
the guard-cells of the stomata and the adjacent epidermal cells,
which has been often mentioned in the literature, but nevertheless
remains the subject of controversy. The epidermal cells next to the
stomata are in both plants differentiated from the other epidermal
cells, and are developed as so-called subsidiary cells of the stoma

As my considerations and conclusions are limited to the plants
investigated, it would lead us too far afield to quote the whole
literature of the mechanism of the stomata; if will be enough to
characterise the current view of the antagonism between the guard-
cells and the adjacent epidermal cells.

Mont and Lrirces have assamed, partly on the evidence of expe-
riments with isolated pieces of epidermis, that the stomata are passively
closed through the turgor of the adjacent epidermal-cells.

SCHWENDENER and his school on the other hand defended the view
that the subsidiary cells are of little or no importance for the sto-
matal mechanism. ;

Prerrer’) in 1897 in a survey of these views pointed out that the
results of these various investigators only differed quantitatively and
that in experiments with isolated pieces of epidermis the different
rate of water-absorption in the various cells may have a great in-
fluence on the phenomena which are observed in the stoma.

Brnecke *) in 1892 published a special study of the subsidiary
cells of the stomata, and came to the conclusion that the subsidiary
cells have in Succulents the function of eliminating the influence on
the stomata of pressure and tension, which in consequence of the
crumpling of the leaves through loss of water, are set up in the
epidermis.

BENECKE scarcely touches on the question of the antagonism between
guard-cells and subsidiary cells: ‘“‘Wir verfolgen diese Streitfrage
“jiber die Bedeutung der Nebenzellen hier nicht weiter sondern

') Prerrer, Pflanzenphysiologie. Zweite Auflage 1897, Erster Band, S. 173.

®) Benecks, Die Nebenzellen der Spaltéffnungen, Botanische Zeitung 1892.

1018

“pracisiren nur noch unsere Stellungsnahme zu derselben, Es sei
“betont dass wir eine allgemein giiltige Loésung dieser Frage hier
‘nieht geben wollen noch kénnen. Unserer Ansicbt nach ist eben
“die Fragestellung nach der Rolle der Nebenzellen in dieser Allge-
“meinheit unrichtig, weil héchst wahrscheinlich diese eine von Fall
“zu Fall wechselnde ist. Im Allgemeinen richtig wird eine ver-
“mitielnde Stellungsnahme sein: Die Oeffnung des Spaltes wird durch
“der Turgor der Schliesszellen selbst bewirkt, die angrenzenden Epi-
“dermiszellen miissen in vielen Fallen zum Versehluss mit beitragen.”

In 1899 Wesrermaigr ') published an investigation on stomata
and their accessory-apparatus in which he does not deal at all with
the question of the antagonisin between guard-cells and adjacent
epidermal cells.

In 1902 CopgLanp *) published a detailed inquiry into the mecha-
nism of the stomata in which he takes the view that the turgor of
the adjacent epidermal cells can only play a passive part in bringing
about the movement of the stomata. ‘In stomata, whose outline changes
‘with their movements, and only in these, the turgescence of the
“contiguous cells must be a factor in determining the state of equilibrium,
“open, closed, or intermediate. But because the pore closes with excessive
“transpiration when turgescence in the leaf is least, because the
“contents of the guard-cells furnish a clue to changes in turgor
“which is wanting in the neighbouring cells, because some stomata
“do not change their outline (surface view) in their movements,
“because isolated stomata usually move like those on uninjured
“leaves, and because the forms and structures of the guard-cells are
“explicable and intelligible on this ground only, the conclusion cannot
“be escaped that the turgescence of the neighbourmg cells is a
“passive factor, the active one being, as SCHWENDENER and his students
“have maintained, the turgescence of the guard-cells”.

HapernanpT’) in the last edition of his handbook hardly says
anything about this question, but also clearly ascribes very little
importance to the turgor of the adjacent cells. The only reference
to the antagonism between the guard-cells and the epidermal cells
is as follows: ‘Bei einigen Grasern (Cynosurus echinatus, Aira capillita,
“Briza maxima) ist die Zentralspalte auch im turgorlosen Zustande
“der Schliesszellen, nach Tétune dieser, offen. In diesen Fallen miis-
“sen also, sofern die Spalt6ffnungen tiberhaupt noch funktionsfahig

1) WestermaieR, Ueber Spaltéffnungen und ihre Nebenapparate. Festschrift ftir
ScHwenvener. Berlin 1899.

2) CopeLanpd, The Mechanism of Stomata. Annals of Botany XVI 1902.

5) Hapertanpr. Physiologische Pflanzenanatomie. Dritte Auflage 1904.

1014

“sind, die beiden seitlich gelagerten Nebenzellen durch ihren Turgor-
“druck den Spaltenverschluss herbeifiihren”’.

Jost’) in a very recent handbook deals with the question in
the following way: “Die Offnungsweite der Spalte hangt tibrigens
‘nicht allein von dem Turgordruck der Schhesszellen ab sondern
“auch von dem Gegendruck der Nachbarzellen; wird dieser etwa
“durch Anstecken der Zellen aufgehoben, so sieht man sofort
“eine starke Spaltendffnung in den Schhesszellen eintreten, ohne
“dass in diesen der Druck gestiegen ware. Umgekehrt kann aber
“auch eine Druekzunahme in den Nachbarzellen einen passiven
“Versebluss der Spalt6ffning herbeifiihren. In wie weit indess die
“Kinwirkung der Nachbarzellen i der Natur eine Rolle spielt, dar-
“ber gehen die Meinungen der Autoren noch weit auseinander;
“SCHWENDENER “) schreibt den Nebenzellen gar keine, Lrrrees *) eine
“sehr grosse Wichtigkeit zu, Darwin *) vermittelt”’.

It seems to me that the peculiar irregularity in the regulation of
evaporation in Viscum album and Rhipsalis Cassytha may be simply
and naturally explained by assuming that when these plants begin
to wither the pore of the stoma first widens under the influence of
the antagonism of the guard-cells and subsidiary cells and is sub-
sequently constricted.

The stomata of Viscwm albuin are rather large and transverse to
the long axis of the stem and leaves. In order to survey the com-
plicated structure it is necessary to consider sections which have
been cut from the apparatus in different directions and at different levels.

A section which divides the stoma into two halves in a direction
perpendicular to the slit gives a view as represented in Fig. 4. The
thickened ventral side of the epidermal-cells is seen, the thick ridges
which surround the outer porch (‘Vorhof”’) of the stoma, the sub-
sidiary cells which to some extent surround the guard-cells above
and below, and the very thick collenchymatous ridge which surrounds
the inner cavity of the stoma. When a section of the stoma is made
in the same direction, not however through the middle, but close to
one of the extremities, the figure is different.

The lumen of the guard-cells is then (Fig. 5) seen to continue
upwards in the shape of a wedge. The dividing-wall between the
subsidiary cell and this wedge-shaped continuation of the guard-cell
is thickened. In the diagrammatic Fig. 1, the lines a, b, and ¢

1) Josv. Pflanzenphysiologie. Dritte Auflage 1915. Seite 58.

) Scuwenpenerk 1881. Monatsberichte Berliner Akademie. S. 833.

5) Lerrcer 1886. Mittheilungen aus dem botanischen Institut zu Graz 1.
‘) Darwin 1898. Philos. Transactions (B) 190.

«

7, Kamerling, ON THE REGULATION OF THE TRANSPIRATION OF VISCUM ALBUM AND RHIPSALIS CASSYTHA.

Proceedings Royal Academy, Amsterdam Vol. 1X.

1015

indicate three possible levels at whieh the stoma may be eut in
sections parallel to the surface; the lines @ and e indicate two
possible ways in which in a transverse section through the leaf a
razor directed more or less parallel to the slit opening of the stoma,
may hit the different parts.

In sections roughly corresponding to line a, the slit of the ‘“Vor-
hof” (Fig. 3) is seen to be bounded by two strong, very much
cuticularized ridges which continue on both sides as a non-cuticu-
larized strip united to the cell-wall of the adjacent epidermal-cells.
The razor has now passed above the guard-cells without touching
them; the cells seen in Fig. 3 on both sides of the opening, are
the subsidiary cells. When such preparations are treated with iodine
and zine chloride, the distinetion between the cuticularised ridge
and the non-cuticularised strip into which the latter passes on both
sides, becomes perfectly clear.

Such preparations suggest the comparison of the non-cuticularised
strip to a ligament of articulation. Preparations of this nature, treated
with iodine zine chloride show that the guardcells of the stoma,
wherever they border on the slit or on the respiratory’ cavity, are
covered with a thin cuticle.

When a similar preparation, as is seen in Fig. 3, is treated
with strong sulphuric acid, conditions such as those shown in
Fig. 9 may result. The non-cuticularised “ligaments of articula-
tion” are here dissolved; but the two cuticularised ridges which
occur in their normal condition in a and / are still seen, but in ¢
they are separated from one another and have fallen over outward.
The thin cuticle which covers the inner side of the guard-cells
adjoins these edges. The “ligaments of articulation” are simply the
thickened strips of membrane which in Fig. 5 are shown in trans-
verse section between the wedge-shaped continuation of the lumen
of the guard cell and the subsidiary cell.

When in preparations parallel to the surface, the stoma is cut at
a lower level corresponding roughly with the line 6 of Fig. 1, that
is to say about in the plane of the ‘central slit” a view is obtained
like that drawn in Fig. 2. The slit is here short and narrow, the
inner wall of the guard-cell is clearly thickened where it adjoins
the slit. The subsidiary-cells at this level surround the guard-cells
like a crescent. A section at a lower level, roughly corresponding
to line ¢ of Fig 1, passes under the lumina of the guard-cells with-
out touching them. It is then seen, as Fig. 6 represents, that the
inner cavity of the stoma is surrounded by two thick ridges of
cellulose. The ceil-cavities which are seen on either side of these

1016

ridges are not those of the guard-cells but of the subsidiary cells.

When a transverse section through the leaf, somewhere about the
line d of Fig. 1, cuts the stoma parallel to the long axis, a view
is obtained corresponding with Fig. 7. From above downwards the
much thiekened and ecuticularised outer-wall, the lumen of the sub-
sidiary cell, the wall dividing the subsidiary cell from the guard-
cell, the lumen of the latter and the thick ridge of cellulose here
follow each oiher. If on the other hand the razor follows the line e,
then as in Fig. 8, we see from above downwards the cuticularised
edge which adjoins the “Vorhof’, the lumen of the guard-cell, the
wall separating the guard-cell from the subsidiary cell, and the lumen
of the subsidiary cell. In similar longitudinal sections through the
stoma, the subsidiary cell can be seen either above or below the
euard-cell, according to the direction in which the section is made.
In Fig. 8 we may see also the peculiar shape of the guard cell,
somewhat like that of a dumb-bell, which can also be made out
by combining the sections of Fig. 4 and Fig. 5.

If we now wish to get an understanding of the functions of this
complicated apparatus, we must assume that the outer slit formed by
the ridges of the cuticle can be considerably narrowed and widened.
Perhaps the inner slit, bounded by the thick edges of cellulose
can also be narrowed and widened, though in all probability only
to a slight extent. Variations of turgor in the subsidiary cells, must,
as is at once clear from the structure, exert an influence on the
width of the outer shit.

The central slit (Centralspalte) is doubtless also capable of varia-
tion in width; it seems however that it is never wholly closed, but
that a small opening always remains, as represented in Fig. 2.

As long as the subsidiary cells are turgid, they offer resistance to
the pressure of the guard-cells; they cannot curve as strongly and
open the central shit as widely as would be the case if no counter-
pressure were exerted by the subsidiary cells.

When in consequence of transpiration. the turgor of the subsidiary
cells decreases before that of the guard-cells, a stronger curvature of
the latter and widening of the central slit must take place.

- It is likely that, when the plant first withers, the turgor indeed
decreases earlier in the subsidiary cells than in the guard-cells, because
the guard-cells are almost completely surrounded by the subsidiary-
cells and the small part of the wall of the guard-cells adjoining the
Opening is rather strongly cuticularised. I believe that in the first
place the chlorophyll-containing parenchyma loses water by trans-
piration, that these cells abstract water from the epidermal-cells and

1017

from the subsidiary cells of the stomata, and that finally the subsi-
diary cells draw water from the guard-cells.

The characteristic peculiarity of the stomata in question seems to
me to consist in: 1. That the guard-cells have only a small free
surface, the wall of which is fairly strongly cuticularised and 2. that
they adjoin no epidermal cells other than the subsidiary cells so that
the influx and efflux of water in the guard-cells is brought about
entirely through the medium of the subsidiary cells.

When indeed turgor decreases in the subsidiary cells before it does
in the guard cells there must therefore, when the plant begins to
wither, be a widening of the central slit of the stomata. In this first
stage when turgor in the subsidiary cells is already diminished, but
is still unchanged in the guard-cells, the subsidiary cells tend to
constrict the outer slit, the guard-cells tend to widen it.

When, at a later stage, turgor has also decreased in the guard-
cells, the subsidiary- and guard-cells cooperate to cause the outer
slit to contract and then the central slit also contracts.

In my investigation of the structure of the stomata of _Rhipsalis
Cassytha 1 had only at my disposal material from a hot-house, since
I had omitted to bring from Brazil spirit material of this plant

The stomata are here, just as in Loranthaceae mostly arranged
transversely to the long axis') of the stem.

A median longitudinal section through the stem shows that, as in
Viscum album, the subsidiary cells surround the guard-ceils above
and below. Fig. 10 represents such a section perpendicular to the
direction of the slit and approximately through the middle of a stoma
of Rhipsalis Cassytha.

In a transverse section through the stem, longitudinal sections of
the stoma can be obtained:as in Fig. 14 in which the bulging lower
part of the subsidiary cell can be seen under the dumb-bell-shaped
guard-cell and above the latter, in the background, the fold in
the wall of the subsidiary cell, which fold can be recognised in
Fig. 10 and projects above the level of the other epidermal cells.

A section which, parallel to the surface, passes through the plane
of the outer slit above the guard-cells without touching them, is
given in Fig. 12. The two folds of the cell-wall are seen and between
them the narrow outer slit which is bounded at either end by a
small curved fold which is not always equally distinet.

1) This peculiar orientation is somewhat rare. Low found it in Casuarina,
Pritzer, inter alia, in Colletia, the present writer observed it also in Cassytha
filiformis.

1018

The two large crescent-shaped cells which might at first sight be
faken for the guard-cells, are in reality the subsidiary cells. When
the stoma is similarly cut parallel to the surface but at a lower
level, at about the depth of the central slit, it may be represented
as in Fig. 11. The section was not completely parallel to the surface
of the stem; on one side (the upper one in the figure) the ordinary
epidermal cells are cut, on the other side (the lower one in the figure}
the section passes through sub-epidermal cells.

If the stoma is cut at a still lower level, a view may be
obtained as represented in Fig. 15. Those parts of the walls of the
surrounding parenchymatosis cells which border on the internal air
space are (generally though not always) somewhat considerably
thickened *) and in the channel thus formed the two subsidiary cells
are seen, separated by a long and very narrow slit. Fig. 13 was
drawn from a preparation viewed from the inner side.

It appears that in the stomata of Rhipsalis Cassytha constriction and
dilatation can take place in three places: 1. At the level of the central
slit between the relatively thin parts of the wall of the two guard-
cells, 2. at the level of the outer sht between the thick, strongly
cuticularised edges which bound this outer slit on both sides, 3. in
the plane beneath. the guard-cells between the thin-walled parts of
the subsidiary cells which bulge out downwards.

The assumption is obvious that in Rizpsalis Cassytha also, at the
first withering of the plant, turgor decreases earlier in the subsidiary
cells than in the e@uard-cells and that first, as in Viscum album,
dilatation of the central slit and increased amount of transpiration
per unit of time, vesults from this.

The characteristic peculiarity to which the observed irregularity
in transpiration is due in both plants investigated, lies, I consider,
principally in the manner in which each guard-cell is surrounded
by an epidermal-cell which is developed as a subsidiary cell and
separates the guard-cell from the other epidermal cells. It seems to
me probable that in other plants also, whenever the stomata are
constructed in a similar manner, this same irrigularily in the evaporation
will be found. In Loranthus dichrous of Brazil this same peculiarity
seems to occur, less clearly than in Viscum album and Rhipsalis
Cassytha, but nevertheless in a very similar manner as the following

figures show.

1) This point was brought out by Vdécutine, Beitriige zur Morphologie und
Anatomie der Rhipsalideén Pringsheim’s Jahrbticher IX. 1873—74.

Benecke and Westermarer (I. ¢.) also mention this peculiarity and state their
theory of its probable significance.

1019

Transpiration of two boughs of Loranthus dichrous Mart.
Exposed to the sun,

First bough Second bough
Ss = =e et : 22 See eee
observed weight| loss of weight |observed weight! loss of weight

1.9 29.9 grammes! 25.5 grammes

1.14 29.1 ; 0.8 gramme 24.9 5 0.6 gramme

i.19 204s 0.7 " 24.5 ‘ 0.4 5.

1.24 27.8 - 0.6 - 240505, 0.45 %

1.29 PAD 55 0.8 rS 23.6 0.45 “

1.34 26.5 7 0.5 5 23.1 ‘ 0.5 9

1.39 26) 05i-e. 0.45 -) 22 ROR Is 0.35 a

2.9 B50 ae 0.41 gr. 20M Tee 0.34 gr.

PaSOne 2028. a8 | ONaaeeerrtive |) 18.95". 0.29 , | Sit
| minutes \ minutes
3.9 1SS3 ae ere R042 1FOcu 0.325 ,,

|

These figures refer to a comparative experiment made in Campos
on transpiration in Loranthus dichrous and Psidium guajava;
regulation of transpiration took place regularly in the last species,
but in Loranthus dichrous it took a noticeably irregular course. We
see here also that at first the amount of transpiration per unit of
time decreases, later distinctly increases (when the boughs have
lost +5°/, in weight) and finally diminishes again (when the loss
in weight amounts to +10°/,). When the experiment was finished
at 3.9 both boughs already began to dry.

The results of this investigation may be summarised as follows:

When cut leafy boughs or whole plants are allowed to wither
and the transpiration is followed by means of periodical weighings,
it is found in most plants, either that the amount of transpiration
per unit of time remains approximately constant until the bough is
dried up or that these amounts decrease uniformly until the trans-
piration is reduced to a minimum.

In Viscum album and Rhipsalis Cassytha the peculiar phenomenon
is observable when the same experiments are made, namely, that
when the bough (or plant) under investigation has lost a certain

1020
proportion of its weight (varying from 1°/, to 4°/,) the amount of
transpiration per unit of time increases and then later, when the
loss in weight has increased (varying from 6 to 10°/,), the trans-
piration decreases again.

We may assume that this increase in the intensity of transpiration
when the plant first withers is caused by the dilatation of the
openings of the stomata, a dilatation which is however only of
comparatively short duration and is later again followed by constriction:

The dilatation of the stomata is probably caused by the antagonism
between the guard-cells and the subsidiary cells of the stomata in
such a way that turgor in the subsidiary cells begins to decrease
sooner than in the guard-cells, this phenomenon causing a stronger
curvature of the guard-cells and dilatation of the slit of the stomata.

The subsidiary cells of the stomata, in Viscum albwm as in
Rhipsalis Cassytha, surround the guard-cells in a peculiar manner ;
probably it is in this fact that the cause must be sought for the
irregularity of transpiration, with which this paper is concerned.

EXPLANATION OF THE FIGURES.

All drawings, except the diagrammatic figure 1 and figure 9, relating to a prepa-
ration treated with concentrated sulphuric acid, were made from unstained prepa-
rations of spirit material, cut by hand and treated in the usual way. The drawings
were made by means of a camera lucida. :
Kig. 1. Diagrammatic transverse section of a stoma of Viscum album. The lines
a, b, ¢, d, an e give the various directions and levels at which the stoma
was cut, line @ corresponds roughly with tig. 3, 6 with Kig. 2, ¢ with
Fig. 6, @ with Fig. 7, e with Fig. 8.

Nig. 2. Viscum album. From a section parallel to the surface of the leaf. The
level is roughly that of line D in Fig. 1.

Fig. 3. Viscum albnm. From a section parallel to the surface of the leaf. The
level is roughly that of lme a@ in Fig. 1.

Fig. 4. Viscum album. From a longitudinal section through the leaf. The stoma
in transverse section, the guard-cells roughly halved.

Kig. 5. Viseum album. From a longitudinal section through the leaf. Stoma cut
transversely, close to the extremity.

lig. G6. Viscum album. From a section parallel to the surface of the leaf. Level
about that of line ¢ in Fig. 1.

Le}
ca
~

Viscum album. From a transverse section through the leaf. The stoma
is cut parallel to the slit, roughly in the direction of the line @ in
Fig. 1.

Fig. 8. Visum album. From a transverse Section of the leaf. The stoma is cut
parallel to the slit, in the direction roughly of line e in Fig. 1. The
preparation was in such a position that the opening of the stoma
removed by the razor, would have been found on the upper edge,

Fig. 9. Visum album. From a section parallel to the surface, treated with
sulphuric acid. The cuticular ridges which are seen in Fig. 5 in relation
to the cell-wall net, have been loosened by the action of the sulphuric
acid. The “ligaments of articulation” are dissolved in the sulphuric acid;
a and b are in normal position, at c the ridges have fallen outwards.

Fig. 10. Rhipsalis Cassytha. From a median longitudinal section through the
stem. The stoma in transverse section, the guardcells roughly halved.
The section has been somewhat distorted in cutting and preparing, so
that the slit, especially in the middle and below, is wider than in the
intact plant.

Fig. 11. Rhipsalis Cassytha. From a section parallel to the surface. The level
is that of the central slit.

Fig. 12, Rhipsalis Cassytha. From a section parallel to the surface. The level is
above the guard-cells, the outer slit is seen

Fig. 15. Rhipsalis Cassytha. From a section parallel to the surface, placed in
an inverted position on the slide. The level is below the guard-cells,
the canal-shaped internal air space is seen, which is closed by the two
subsidiary cells.

Fig. 14. Rhipsalis Cassytha. From a transverse section through the stem. The
stoma in longitudinal section parallel to the slit, in a direction
roughly corresponding to line e in Fig. 1, the preparation is orientated
in a corresponding manner to the preparation of Viscum drawn in Fig. 8.

Leiden, December 19138. Botanical Laboratory.

Botany. — “The explanation of an apparent exception to Munvru’s
law of segregation.” By Miss Tine Tammus. (Communicated
bys Prof. J: Wee Monn):

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

In experiments on hybridisation in recent years various cases have
been observed in which the numerical proportion of different forms
occurring in the second generation does not agree with what might
be expected according to Menpet’s law. Among these there are very
many with respect to which there is no reason to assume that this law
does not apply, and in the greater number of these cases it has been
possible to show the causes of the discrepancy. These causes have been
found to be of two kinds. Firstly, there may be deviations which
are only the results of mistakes or wrong hypotieses on the part
of the observer. Secondly, there are cases in which the deviations
are due to the plant itself. The sources of error belonging to the
first class are chiefly as follows.

1. It may happen that the deviation is the result of making too
few observations.

1022

2. The observer may have wrongly estimated the difference in
the number of factors of the P-forms, so that the numerical pro-
portion he expects, is wrong.

3. Characters have to be dealt with, which cannot be seen at
the same moment in different individuals. If the observations in
such a case are extended over too short a period of time, then
wrong results are obtained.

4. In consequence of a strongly fluctuating variability of characters
the observer has failed to distinguish the different genotypes with
sufficient sharpness. ;

The known cases in which the cause of the deviation les in the
plant itself, are the following.

1. There are fewer gametes of a particular kind formed than
ought fo arise. The deviation then already arises in the formation
of the sexual-products.

2. The union of some kinds of gametes comes about with more
difficulty than that of others. The deviation then lies in the fertili-
sation-process.

3. Certain combinations of gametes are less capable of life than
others, so that the young individuals die off before the character
can be observed.

4. The different genes may be coupled or may repel one another.

Of all the various phenomena here enumerated examples are
known. Baur*) and especially Pratr*) give a survey of them in
their textbooks.

The ease, whieh I wish to deal with here, belongs io the second
group, in which the cause of the deviation lies in the plant itself.
The nature of this cause will be made clear below.

The phenomenon appeared on the crossing of a white- and a blue-
flowering variety of Linwmn usitatissimum and related to the colour
of the flower. The blue-flowering form was a variety obtained from
Keypt, and has been deseribed by me*) previously and named
Keyptian flax. The seed of the variety with white flowers was
obtained from Messrs. VitmMorin-Anprieux of Paris. Pure lines
of both varieties were used for the investigation and the reciprocal
crossings were carried out in 1908 and in 1911. The whole number

1) K. Baur, Vererbungslehre. 1911, p. 116.

*) L. Puatr, Vererbungslehre. 1913, p. 194.

‘) Der Flachsstengel, eine statistisch anatomische Monographie. Verh. vy. d. Holl
Maatsch. d. Wetensch. Haarlem, Verz. 3, Deel VI, Stuk 4, ,i907, p. 22.

Das Verhalten fluktuierend variierender Merkmale bei der Bastardierung Ree. d,
Trav. bot. Néerl. Vol. 8, 1911, p. 206,

of crossings amounted to 20; the first generation consisted of 30
plants, which all had blue flowers. In different years further cultures
of the 24, 34 and 4th generation were grown. The following table
gives a survey of the observations on both reciprocal crossings, since
the two sets agree. Circumstances prevented the second generation
from being cultivated in 1910; it was obtained for the first time
in 1911.

White Blue | Saale Deviation

0.871 : 3.129 + 0.129

Fo 1911 | 134 | 482

1912 146 | 481 0.931 : 3.069 + 0.069

» 1913 [Sela SHe sO:686 : 3.314 + 0.314

Fe 69 | 291 O16 7u3-233" |) 4240233
MP Oa ie 215 9,30 0.750 : 3.250 + 0.250
beekats 14} 44 | 0.966 : 3.034 += 0.034

34 130 0.829 : 3.171

+
=
SI

F3 1912 113 | 493 0.745 : 3.255 + 0.255

els OTS St 0.905 : 3.095 |

+ 0.095
a Re Se |
Fy 1913 Wi2 748 | OWM48i23),252 | + 0.252
| | |
Total | 800 | S106" 2 05819) 33. 181 + 0.181

In the second and third vertical column the number of white- and
of blue-flowering plants in each culture is given. It is seen from
this, that the proportion of these two deviates more or less from
the ratio 1:3. In order to make clear the extent of the deviation
the ratio for each culture is reckoned per four individuals. The figu-
res obtained are given in the fourth column and in that following
it the deviations of these from the theoretical ratio 1: 3.

In the second place, the table shows that the deviation in all
cases is in the same direction. The number of white-flowering plants

67

Proceedings Royal Acad. Aiusterduim. Vol, XVI

1024

is always less than was to be expected, ‘or as we may also consider
it, the number of blue-flowering ones is greater. Since here however
the former case obtains, as will be shown later, I shall indicate the
deviation in future as a deficiency of white-flowering plants. Further
it is seen from the table that the deviations, with the exception of
one small culture, are considerable. For the whole number of
observations on 800 white and 3106 blue ones the deviation calculated
for these figures amounts to + 0.181. The mean error for: this
number is 0.027; the deviation is therefore about 6.5 times greater.
This shows that the deviation from the ratio cannot be aseribed to
chance, but that a definite cause must exist. The question is now
what this cause is. Of the four causes mentioned above, whieh
result from errors or wrong suppositions, three do not here come
into consideration. With regard to the first, {he number of observations
is. very great, with regard to the second the flowering of all of the
plants was observed and with regard to the third cause fluctuating
variability plays no role here. The only remaining canse therefore
is a wrong hypothesis as to the number of factors in which the
Pforms differ. For it is possible that the numerical ratio to be
expected is not 1:3, and that therefore we have not to deal
with a monohybrid crossing or with a polyhybrid behaving as a
monohybrid, but that here several factors occur, which cause the
blue colour of the flower. The number of gametes in which the
factors for blue are wholly absent will then be relatively smaller
and white-flowering plants will arise in the second generation in
smaller proportion than in monohybrid crossing. In the ease in
which the number of factors for blue amounts to two, each by itself
producing the colour, the proportion of white and blue in F, is
1: 15, whilst with three factors for blue the proportion is already
1 : 68. These proportions differ so much from the observed ones,
that the cause must be different. Also when it is assumed that the
blue colour is caused by still more factors, which separately or in
definite groups can produce this colour, ratios are obtained which
do not in the ieast agree with that which was observed. If indeed
the existence is assumed of a very great number of factors which
only produce blue when combined in a certain way, a ratio may
be arrived at which sufficiently agrees with the given one. Such
an assumption would only have a reasonable basis, when the
phenomenon could not at all be explained in an other way. I have
found, however, that we are not dealing here with complicated
relations of factors, but that there are two other causes, which
together produce the deficiency of white-flowering plants.

1025

The first concerns the germinating-power of the seed.

I have repeatedly noticed that the seed of white-flowering varieties
has a germinating-power inferior to that of the blue ones, ie. a
relatively smaller number of seeds of the former germinate. This
difference existed also between the two forms which I crossed. The
seed of Egyptian blue flax, which I used for my cultures, had very
good power of germination; almost all its seed came up, as the
following figures show. Out of 706 seeds 701 germinated and
developed to plants, thus only 0.71 °/, failed. The white-flowering
flax, on the other hand, germinated badly and a number of seedlings
died at a very early stage. 682 seeds yielded 601 plants, that is a
loss of 11.9°/,. Now there are obtained from the /, plants and the
heterozygous plants of the following generation both seeds producing
white-flowering plants and seeds producing blue ones. If then a
higher percentage of this seed than of the blue flax does not
germinate, then it may safely be assumed that the loss almost entirely
arises through the failure of the seeds of the white-flowering plants.
I have not traced the proportion between the number of seeds sown
and the number of plants obtained for all the cultures of the whole
3906 plants to be found in the table, but only for about the half. From
these it was found that 1916 seeds yielded 1858 plants. There was
therefore for 1858 plants obtained a loss of 58. That will amount
to 122 for the 3906 plants reckoning all the cultures together.
Since of the 3906 plants 3106 had blue flowers and since we saw
that among the blue /?-form the 701 plants obtained, 5 seeds did
not germinate, we may assume that in this case out of the 122
seeds which did not germinate, there were 22 which should have
given blue-flowering plants and consequently 100 which should have
given the white-flowering ones. In this it is assumed that heterozygotes
behave as homozygous blues. I shall return to this point later.

Now we may inquire whether the number of 100 thus found is
sufficient to explain the whole deficiency of white-flowering plants.
3106 blue-flowering plants were observed, to which belong 22 seeds
which did not germinate. We may therefore assume, that among
the seeds which were sown, there were 3128 of them with a
predisposition towards the blue colour of the flower. Theoretically
‘/, of this number, that is 1042 7/,, or in round number 1043
seeds should have given white-flowering plants.

Only 800 are found, however. The deficiency amounts therefore to
243. Now we saw that by reason of the inferior germinating-
power of the seed 100 white-flowering plants will be wanting.
This is, however, much less than the observed deficiency, so much

67*

1026

less that the aberrant ratio of the number cannot be explained by
this means alone: some other cause must also be present which
acts in the same direction.

I have indeed succeeded in demonstrating this second cause of
the deficiency of white-flowering plants. It is connected with the
average number of seeds which are formed in the fruit of flax.
The flax-fruit may contain a maximum of ten seeds. The average
number, however is distinctly less, and in the white variety it is,
as I repeatedly observed, in general still smaller than in the blue one.

Now when the average number of seeds in the fruits of the
heterozygotes, which contain both seeds of white- and of blue-flowering
plants, is smaller than in the blue /-form, then the assumption is
plausible, that this is caused, by the formation of relatively fewer
seeds of white-flowering plants. If this seed is sown a progeny arises
with a deficiency of white-flowering plants.

The investigation was however not so simple in this case. In
contradistinction to the foregoing it was found that in the crossed
varieties the fruits of the white flax had on the average even a
greater number of seeds than those of the blue Egyptian flax. In
330 fruits of the white flax the number of seeds amounted to 2412,
an average of 7.31, while in 219 fruits of the Egyptian flax, there
were 824 seeds, an average of 3.76. In the white variety the average
number of seeds, is therefore almost twice as great as in the blue.

Now the seed of Hgyptian flax is, however, much larger than that
of the white flax and comparisons of different varieties had already
convinced me before that the average number of seeds is closely
connected with the size of the seed and in such a way that in
varieties with large seeds the average number is in general smaller
than in varieties with small seeds. It is therefore possible, that in
the white flax there is indeed a tendency to produce a smaller
number of seeds than the average number of the Egyptian flax,
but that this tendency is not revealed at all, because the difference
in size of the seed of the two varieties is accompanied by a much
greater difference in number in the opposite direction. In order
to make this out it is necessary therefore to eliminate the influence
of size. This is indeed possible in the case under consideration. My
earlier investigations’) have shown that the difference in size between
the seed of Egyptian flax and that of Linum angustifolium is caused
by several factors. Consequently there arise in the second generation
forms differing in the size of the seed, intermediate between that of

1) Das Verhallen fluktuierend variierender Merkmale bei der Bastardierung. Rec,
qd. Trav. bot. Néerl. Vol. 8, 1911, p. 212.

1027

the two P-forms. The majority however of the /’, plants show the
mean type. This also holds for the crossing of Egyptian with white-
flowering flax. Here also /’, shows, so far as size of seed is concerned,
a continuous series of forms in which the mean is most strongly
represented. It was therefore not difficult to find in /, and F, a
certain number of plants which agreed in size of seed. Among these
were blue-flowering ones which from investigation of their progeny
were found to be homozygous for the colour of the flower and
in this therefore were equal to the blue P-forms. At the same time
there were also white-flowering plants in this lot. These are always
homozygous and did not therefore require to be cultivated further.
Now since the size of the seed in these forms was the same, they
could independently of this point be compared as to their average
number of seeds.

An investigation of these plants gave the following results. 1100
fruits from 94 homozygous blue-flowering plants of /#’, and /’, were
examined. These yielded 6468 seeds, an average of 5.88. 71 white-
flowering plants from /’, and /’, yielded in 800 fruits 4112 seeds,
an average of 5.14. These two mean values are intermediate between
those of the P-forms, in connection with the size of the seed which
is also intermediate. But it further results that the white-flowering
plants have a smaller number of seeds in the fruits than the blue-
flowering ones, namely as 12.6°/, less than the blue ones. This
difference cannot, when the large number of the observations is taken
ito account, be ascribed to chance.

A second cause of the aberrant numerical proportion is in this
way demonstrated. The question mow remains to what extent
the deficiency in white-flowering plants can be explained by this
means.

As stated above, out of the whole number of cultures 1048 white-
flowering plants might be expected theoretically. The difference in
the average number of seeds formed between the white and the
blue varieties amounted to 12.6°/,, i.e., for every 100 seeds of white-
flowering plants 12.6 will be wanting. For 1048 seeds this would
amount to 10.43 % 12.6 — 1381, from which a corresponding
deficiency in white-flowering plants will arise.

By reason of both these causes together a deficiency of
100 + 1341 = 231 white-flowering plants can be explained. The
deficiency actually amounts to 243 plants. The difference between
these two values is insignificant. It may therefore be considered
proved that the lesser germinating-power and the lesser number
of seeds per fruit of the white-flowering variety are the causes

1028

of the aberrant numerical’ proportion. Although the deficieney is
not wholly accounted for by the two causes, yet I do not believe
that it is necessary to postulate a third cause for the absence of
white-flowering plants.

In the foregoing it has been assumed in all calculations that the
heterozygous blues behave as homozygous. | came to this conclusion
because of an investigation of the progeny of blue-flowering F,
individuals. Normally ‘, of the blue-flowering /’, plants are homo-
azygous and */, heterozygous. If, however, heterozygotism were to
exercise an influence, it would be noticeable in the number of seeds
and in their germinating-power. In proportion to the seeds which
are homozygous blue for the colour of flower there should be from
hybrid plants a smaller number of heterozygotes formed and this
seed should moreover have less germinating-power. The result
would be that in the succeeding generation too few heterozygous
blue-flowering plants occurred, which would be evident from the
investigation of the progeny.

This inquiry now showed that out of 48 /', plants, 13 were
homozygous and 30 heterozygous. Instead of a deficiency in hetero-
zygotes this number is even greater than it should be theoretically.
Although the figures are small, nevertheless I think that it may
be concluded, that the heterozygous blue plants behave in the same
way as homozygous ones.

As well as in the crossing between the blue Egyptian flax and
the white flax described above, 1 observed similar aberrant numerical
proportion in some other crossings between white- and blue-flowering
varieties. In the crossing between Vinmorin’s white flax mentioned
above and the blue flax commonly cultivated in Holland 318 white-
flowering and 1312 blue-flowering plants were obtained in F, that
is in the proportion 0.78 : 3.22. The deviation here observed,
+ 0.22 is even slightly greater than that found in the previous
crossing. The deviation here must also consist in a deficiency of
white-flowering plants, brought about by the causes mentioned above.
This is clear from the following. In 211 fruits of the common blue
flax the number of seeds amounted to 1851, an average of 8.78 ;
whilst the average for the white flax was seen to be 7.31. The
blue flax has therefore a higher average number of seeds in the
fruit. These two values are directly comparable because the size of
the seed is about the’ same. In connection with this, the average
number of seeds in the fruits of /’, lies between these two values
and amounts to 8.38. In these fruits therefore, in proportion a some-
what smaller number of seeds is produced for white-flowering plants

1029

than for blne-flowering ones. The germinating-power also shows a
difference capable of explaining a deficiency in white-flowering plants,
because the common blue flax that was used in my experiments,
germinates very well. Less than 1°/, fails, as in the blue Egyptian
flax, whilst the white flax, as has been said, shows a loss of 11,9 °/,.

Besides the white flax from the firm of Virmorr still another white
variety was crossed with the two blue forms mentioned. This was
cultivated as a pure line from a white-flowering form grown in the
province of Friesland.

By crossing this white with the blue Egyptian flax there were
obtained in /’, 60 white-flowering and 214 blue-flowering plants,
that is in the proportion of 0.876 : 3.124 with a deviation of
+ 0.124.

The crossing between the last mentioned white flax and the common
blue one gave 30 white- and 104° blue-flowering individuals, a
proportion of 0.895: 3.105 with a deviation of -F 0.105.

In both cases a deficiency in white-flowering plants appeared in
F,. Although the number of observations is not great, I think it
may nevertheless be concluded that we are here dealing with the
same phenomenon, because in comparison with the blue-flowering
varieties this white form also has a lower average number of seeds
and an inferior germinating-power. The differences are however not
so great as with the white flax obtained from Vriimorin.

The question now arises how the lesser number of seeds and _ the
lesser germinating-power of the seeds of the white-flowering variety
are caused. With respect to the number of seeds it is possible that
the cause lies in the number of gametes formed. Normally in /’, as
many gametes without the factor for blue should be formed as those
possessing this factor. Should there however be fewer gametes formed
in which the factor for blue is absent, then there will be after
fertilisation not only a relatively smaller number of homozygous
whites but also fewer heterozygous ones and /’, will necessarily have
a deficiency in heterozygous blues as well as in whites.

As I have shown, this is not the ease, there is here no deficiency
in heterozygous plants. Therefore the cause does not lie in a differing
number of the two kinds of gametes and can only be sought in
phenomena at or after fertilisation. It may be that the union of two
gametes, both devoid of the factor for blue, happens less easily so
that in some cases no fertilisation takes place. Or it is also possible
that the two gametes do unite and that a zygote is produced, but
that the embryo already dies off in the first stages. In both cases
there will be a deficiency of seed for white-flowering plants. Some-

1030

thing of this kind was observed by Correns ') on crossthe a blaék
sugar maize Zea Mais var. coeruleoduleis KcKr. and a common
white maize ‘“Popeorn’, Zea Mais var. leucoceras -Aunr. Here a
deficiency of sacchariferous granules occurred Correns showed by
crossing the /\-hybrid again with the sugar-containing P-form,
that the formation of an unequal number of the different gametes
was. not the cause of the phenomenon. He comes therefore to the
conclusion that the deficiency arises because the gametes-combination
of two sacchariferous ones happens less easily.

By crossing the varieties of flax a further deficiency was caused
through the seed of the white forms having less germinating-power.
It either does not germinate at all, the embryo has then already
died in the seed, or the seedlings die off early. The latter agrees
with the case observed by Baur’) in cultivating the aurea-variety
of Antirrhinum majus. From this form, which is heterozygous, there
are produced green- and aurea-plants in the proportion of 1: 2,
because the yellow individuals formed at the same time die off
very young.

It is clear from the inferior germinating-power of the seed of the
white varieties of flax that the gametes-combination of white with
white has less vitality. This suggests that very probably the smaller
number of seeds is also wholly or partly to be ascribed to the same
cause. I have not been able to ascertain whether seed is wanting
because fertilisation does not take place at all. It can however be
said in general, that the two phenomena, the smaller number of
seeds and their inferior germinating-power, which in the foregoing
have been always considered separately, are only the result of
a single cause, namely the smaller vitality of the gametes-com-
bination of white with white. Only because the death of certain
individuals as a result of this cause may take place at different
stages of development, two different phenomena can be observed
separately.

I will finally add a few words on a point resulting from these
observations. It is found that the number of seeds and their germi-
nating-power, therefore the vitality of the gametes-combination, is
connected with the colour of the flowers produced from such seed,
that is with the presence or absence of the factor for that colour.

1) C. Correns, Scheinbare Ausnahmen von der MENDEL’schen Spaltungsregel
fiir Bastarde. Ber. d. d. bot. Ges. Bd. XX, 1902, p. 159.

2) E. Baur, Untersuchungen tiber die Erblichkeitsverhaltnisse eimer nur in
Bastardform lebensfiihigen Sippe von Antirrhinum majus. Ber. d. d. bot. Ges.
Bd. 25, 1907, p. 442.

1031

The presence or absence of this factor is even more intimately con-
nected with the number of the seeds and their germinating-power
than the nature of the mother-plant which produces the seeds. For
seeds with the colour-factor and seeds without it are formed in F,
by the same plant, even in the same fruit and yet the number and
the germinating-power of those without the colour-factor is less. We
see therefore that the difference between the white and blue varieties
of flax, so far as concerns the number of seeds and their germina-
ting-power, is unconnected with the difference in nutritional relation-
ships between the plants, but only with the presence or absence in
the gametes of a factor for the colour of the flower.

The following is a summary of results.

In crossing white- and blue-flowering varieties of Linum usitatis-
sumum there are formed in the second and following generations
white and blue individuals in numerical proportions which are not
in agreement with those to be expected in accordance with Mrmnpet’s
law of segregation.

In all cases there is according to the proportion 1:3 a deficiency
in white-flowering plants.

The deticiency arises from two causes which act in the same
direction: 1. By F, and by the heterozygotes of the following
generation there is formed a relatively too small number of seeds
whieh will yield white-flowering plants. 2. The’ germinating-power
of the seed, that yields white-tlowering plants is less than that of
the seed which produces blue-flowering ones. The smaller number
of seeds which yield white-flowering plants and the inferior germi-
nating-power of these seeds are both the result of the lower vitality
of the combination of two gametes both devoid of the factor for
the blue colour.

The vitality of the gametes-combination and with it the average
number of seeds per fruit and the germinating-power of the seed
are more closely connected with the presence or absence in the
gametes of the factor for the floral colour than with the nature of
the plant, which produces the seed.

Groningen, 9 January 1914. Botanical Laboratory.

10382

Anatomy. — “The Arrangement of the motor roots and nuclei in
the brain of Acipenser ruthenus and Lepidosteus osseus.” By

F. Tuunissen. (Communicated by Prof. L. Boxk).

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

In the Folia Neurobiologica of 1912 Droocirnver Fortuyn ') described
the arrangement of the motor roots and nuclei in the brain of an
osseous Ganoid: Amia calva.

He came to the conclusion that Amia in many respects resembled
the Selachian type, though few points of analogy with the Teleosts
were found.

Of the other Ganoids as yet no adequate description exists as
far as concerns the motor roots and nuclei. Valuable descriptions
of the nervous system of Ganoids are given by GoronowitscH *) and
Jounston *) (Acipenser), Kinespury ‘) and Ariéns Kapprrs °) (Amia
calva and Lepidosteus), but these articles contain rather a general
account of the brain, the papers of Jonnsron and KinespurY more
specially of the sensory systems.

The Institute for Brainresearch possesses a complete series of the
brain of Acipenser ruthenus, which has enabled me to study the
relations of the motor system of this animal and to compare my
results with those obtained by Droocierver Fortruyn in Amia Calva.

We are greatly indebted to Prof. Miyor in Moskow for our
material of Acipenser ruthenus.

The results of my researches mapped out topographically after
Kapprrs’s method exhibit a striking resemblance with those obtained
by Droocienver Forruyn, and provide anew argument for classifying
Amia with the Ganoids.

My series, stained after Wericert-PaL with a contra-stain of para-
carmine and alternating with a van Gurson series, enabled me to

1) DROooGLEEVER FortruyNn, Notiz tiber den Eintritt der motorischen Nerven-
wurzeln. in die Medulla Oblongata and tiber die Lage der motorischen Kerne bei
Amia Calva, L. Folia Neurobiol. Bnd. VI, S. 27.

2) GoronowitscH Das Gehirn und die Cranialnerven von Acipenser ruthenus.
Morphologisches Jahrbuch. Bnd. 13, 13888.

3) Jounston, The Brain of Acipenser. G. FiscHer, Jena, 1901.

') Kinespury, The structure and morphology of the Oblongata in Fishes. Journ.
of Comp. Neur. Vol. VII. :

5) Arrins Kapprers, Untersuchungen tiber das Gehirn der Ganoiden Amia
Calva und Lepidosteus osseus. Abhandl der Senck. Naturf. Gesellschaft in Frank-
furt a. M. Bnd. 30, 1907.

10338

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( |SO9[9 |, ) Boul L

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Ss

NOLLVNVTd Xo

(g “Stq)

‘(sutqoydios snureyeo ay} Jo oovyd ay} sayvorpur More oJ.)

1034

trace with a great amount of exactness the course of the motor
roois and the position of their nuclei, which, brought in relation te
the sensory systems of this animal, provided new contributions to

the doctrine of neurobiotaxis,

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In Fig. 1 I give two reconstructions, one of a Selachian (Seyllium)
and one of a Teleost (Tinea), and in Fig. 2 I give the topographical
reproductions of the three Ganoids as yet examined.

1035
é

In Acipenser the IIT nerve enters the brain as usual directly bebind
the lobi inferiores. Its nucleus has a dorsal position, dorso-laterally
from and between the fascieuli longitudinales dorsales ; but very
few cells reach a somewhat more ventral position than in scyllium,
thus slightly indicating the process which in Teleosts gives’ rise to
the formation of a real ventro-median nucleus. The same was the
case in Amia. The dorso-lateral part of the nucleus extends some
distance in front of the entiance of the III root.

Some distance in front of it, new cells of a much larger type
appear, belonging to the large reticular type and probably con-
stituting the homologue of Casats') ‘foco intersticial” in mammals
and birds, also described by pe Lanen*) in Reptilia, which sends its
axones in the posterior longitudinal fascicle.

The IIL nueleus finishes caudally near the posterior limit of its
root entrance.

The IV nucleus lies some distance behind the III, separated
from it by the tractus cerebello-mesencefalicus dorsalis, which passes
here from the valvula cerebelli into the mesencephalon.

Such a separation has never yet been found in Selachii, but occurs
rather often in Teleosts. The nucleus is small and its root lies a
good deal farther caudad, as is also the case in Amia.

In the region of the trochlear nucleus large reticular cells are
rarely found, and I get the impression that these large cells in Aci-
penser, as in other animals (vy. H6nvenn)*), tend to group together
in definite regions.

Also the position of the motor V nucleus shows a great resem-
blance with that of Amia, in so far as in both the nucleus retains
a dorsal position over its entire length. The nucleus has moreover
the same length in the two, though in Amia it begins a little caudad
from the frontal line of entrance of its root and extends a little
behind the VII root entrance.

Next to the trigeminus nucleus, along the lateral border of the
fasciculus longitudinalis posterior, we find a great quantity of large

1) KE] sistema nervoso del hombre y de los verte brados, Tomo Il p. 551, Fig. 505
and Trabajos, Tomo VII: Ganglios de la substancia reticular del bulbo p 279 Fig. 9.

*) Das Zwischenhirn und das Mittelhirn der Reptilia. Folia Neurobiologica Vol.
VIII p..134, Fig. 57 and p. 135 Vig. 58.

Cyclostomes these large reticular cells have been found in front of the
Oculomotor nucleus (comp. a. others TRersaKxorr Arch. f. mikr, Anat. 1909, Bnd. 74).

3) J. J. L. D. Baron v. Héeveti. Remarks on the reticular cells of the oblon-
gata in different vertebrates. Proc. of the Kon. Akad. v. Wet. Amsterdam ;
April, 1911.

1086

reticular cells. Whether these cells are connected with secondary
neurones of the dese. V is difficult to tell. It seems as if several of
their dendrites reach into the region of the sensory Y.

It may be remembered that also van Hoékrvett found a large
quantity of reticular cells in the trigeminal and praetrigeminal region
in the classes of vertebrates which he examined.

The VII root of Acipenser enters the bulb directly behind the
motor V nueleus. After having reached the floor of the fourth
ventricle if pursues ifs course in a median direction and successively
shifts onto the lateral top of the fasciculus longitudinalis dorsalis, as
is also the case in sharks, Teleosts and several Reptilia.

Where the motor VII root makes its caudal curve, that is in the
region of the VIII, a group of large reticular cells is found next
and under the fasciculus longitudinalis posterior, corresponding to
vAN Hérveni’s nucleus reticularis medius.

The whole Vil nucleus is continuous with the IX and X, with
which it forms the posterior visceral column, as also oceurs im
Amia and in Selachii. A partial (Cyprinoidae, Pleuronectidae) or
total (Lophius) isolation of the VIL nucleus from the posterior
viscero-motor column as is found in Teleosts does not oceur in
Acipenser.

The posterior viscero-motor column has a dorsal position and
extends a good distance caudad beyond the frontal limit of the spino-
oceipital column. It reaches farther candad than in Amia, although
neither here nor there a muse. trapezius is developed (FURBRINGER)').
Consequently we may not consider the caudal part of this nucleus
as nucleus accessorius as is the case in sharks.

More ventrally and more medially — near the ventrolateral boyder
of the fasciculus longitudinalis posterior in and frontally from the
region of the facialis nucleus the abducens-nucleus is found,
which has three rootlets, whieh leave the brain between the VII and
IX root. Just as in Amia the nucleus does not lie so ventrally as
in Teleosts, nor is there a division into two chief groups as is fairly
constant in bony fishes. The nucleus does not however lie as dorsally
as in sharks.

The glossopharyngeus nucleus is continuous with the VII nucleus
frontad and the X nucleus caudad. All its cells remain near the
ventricle. The vagus nucleus has no special characteristics and resem-
bles in every respect the nucleus of the IX. The spino-oecipital
column is the direct continuation of the motor column of the spinal

1) Vergleichende Anatomie der Wirbeltiere mit Berticksichtigung der Wirbellosen,

1087

cord. The two frontal rootlets are thin and their cells remain very
dorsal, more as in Selachii than in Teleosts.

On the frontal level of the spino-occipital column a quantity of
large reticular cells is found, which we may compare with the
nucleus reticularis inferior in Rays. (Comp. vAN Hénveni). As in these
animals a central inferior reticular nucleus (lying in the raphe, as
occurs in all the higher vertebrates from Reptiles to Man) hardly
oceurs here: the cells keep a lateral position. Considering the differences
which Amia as well as Acipenser exhibits when compared with
Teleosts, we find as the most striking the less ventral position of the
oculomotor and abducens nucleus and the absence of a division of
the latter into two chief cell groups. A frontal isolation or ventral
displacement of the VII nucleus does not oceur.

All of these characteristics are easily understood if we compare
the sensory systems and their reflex paths in these animals.

Concerning the less ventral extension or position of the IIT and
VI nucleus, it may suffice to remark that the ventral tecto-bulbar
tracts are not nearly so well developed in Acipenser (and Amia) as
in bony fishes. The tectum opticum itself is relatively smaller (com-
pared with the underlying midbrain and thalamus) than in most otf
the bony fishes and reminds us more of the condition found in sharks.
No doubt this smaller development of the ventral teeto-bulbar paths
is the reason of the less ventral migration of the eye muscle-nuclei
mentioned above.

This fact may at the same time explain why the abducens nucleus
keeps a relatively caudal position.

We know that a hypertrophy of the ventral tecto-bulbar tracts
is not only correlated with a very ventral abducens nucleus, but
equally causes a more frontal position, at least of its frontal division
as is specially shown in Pleuronectidae ’).

Concerning the position of the facial nucleus in these Ganoids
and its resemblance in this respect with Selachiit the following ex-
planation must be given:

In his excellent paper on Acipenser (l.c. p. 31) JoHNston remarks
that from the sensory IX—X lobi (in whieh also the sensory VII
root finishes) a secondary ascending, fibres-traect rans along the de-
scending V. According to his description, this tract (Mayswr’s:
“vagotrigeminale Bahn’) is still unmyelinated in Acipenser, which

1) Compare Kaprers, The migrations of the V, VI, and VII nuclei and the

concomitating changes in tlieir root fibres. Verh der Kon. Akad. y. Wetensch.
1910, Deel 16, 2de Sectie, and Folia Neurobiol, Krgiinz. Heft Vol. VI, 1912.

10388

corresponds to our @xperience that this tract cannot be traced in
Weigert-preparations. ;

In most Teleosts this tract is very considerably developed and
Herrick has described it there in a masterly way under the name
of ascending secondary gustatory tract. :

It is this tract which has the greatest) influence on the ventral
shifting and perhaps on the frontal isolation of the VIL nucleus in
Teleosts. It can even be demonstrated that the ventral migration of
that nucleus (as well as of the V nucleus) is more conspicuous and
more complete in those Teleosts, where this gustatory tract is more
developed.

On account or this fact it is not astonishing that in animals where
the ascending gustatory system is only relatively poorly developed
a ventro-frontal migration of the VIL nucleus has not yet occurred.
It seems probable to me that in Ganoids as in Selachii the seeon-
dary neurones of the sensory VII—IX—X nuclei are partly short
intercalating neurones, while the longer seeondary neurones of the
viscerosensory nucleus may have chiefly a descending character.

It seems useful to me to give here also the topographic reconstruc-
tion of a young specimen of Lepidosteus osseus which the Institute
received from Mr. Epw. Purtps ALiis in Menton.

I had at my disposition two specimens, of 5 and 10 e.m. The
specimen of 5 em. being better preserved, I shall only give the recon-
struction of this. I may add, however, that the 10 e.m. speeimen
did not differ in any principal point from this, so that I got the
conviction that the definite arrangement of the motor nuclei is already
present in the 5c. m. specimen as far as concerns its principal features.

Also in Lepidosteus the oculomotor nucleus extends a considerable
distance in front of the level of its root. The cells le on the
dorso-lateral border of the fasciculus longitudinalis, very near the
ventricle. There is a difference in so far that the slight indication
of a ventro-medial nucleus present in the fullgrown Amia and Aci-
penser fails in this young Lepidosteus. Perhaps this difference is due
to the young stage of development.

As in the other eanoids there is a considerable gap between the
II] and TV nueleus, although the tractus cerebello-mesencefalicus
dorsalis does not run between if.?) The trochlear root lies again a

eood deal behind its nucleus.

1) Not the only influence though. Some other tracts (e. g. an ascending sensory
tract from the cervical region) may also run near the descending V.
*) Since there is no real valvula cerebelli in Lepidosteus this tract, if present,

takes a more caudal couse.

10389

The trigeminus nucleus has the same dorsal position and length
as in Acipenser and Amia. Its sagittal topography recalls rather
that in Acipenser than in Amia.

The abducens leaves the same between the VII and IX roots
with four rootlets as was the case in Amia.

The location of its nucleus could not be stated with exactness,
the position of the cells being too diffuse amongst the reticular cells
of that region. It resembles, however, the position in the other Ganoids
in so far as its cells do not form two well defined groups as occurs
in bony fishes, nor do they have such a ventral position as in
Teleosts. The posterior viscero-motor column has the same position
as in the other ganoids. Its frontal limit is nearly the same, the
caudal extension seems a little shorter, which may be due to the
young stage of development.

It contains the motor VII, IX, and X nuclei, but the celis are not
equally large everywhere: groups of large cells alternate with groups
of smaller cells, of which the motor character is not so conspicuous.
It may be that this means a little discontinuity in this motor column.
It does not however give us sufficient evidence to speak of isolation
of different nuclei.

The position of the spino-occipital rootlets and cells resembles
very much that found in Amia.

On an average it may be said that Lepidosteus shows principally
the same type in the arrangement of its motor roots and nuclei as
the two other Ganoids.

A few words may be added concerning a structure at the base
of the medulla oblongata near the spino-occipital rootlets : the nucleus
paramedianus ov oliva inferior.

In this region the dark aspect of the tegmental part of the bulb
changes for a lighter one in the Weigert-Pal preparations, owing to an
enlargement of the grey matter consisting of small, more or less
spindle-shaped cells and a sort of ‘gelatinous’ substance. The caudal
and frontal limits of this structure are not sharp, but the bulk of it
extends in the places indicated at the base of my topographic schemes
by little crosses.

From this structure a crossed myelinated fibre tract runs along
the lateral border of the oblongata to the region where the cerebel-
lum joins the bulb. Also Jounston (1. c. p. 16) describes such crossed
fibrae arcuatae externae.

The character of this crossed cerebellar connection, the sort of
cells that constitute the nucleus paramedianus and its topographic
relation, prove that we have to consider it as a primitive oliva inferior.

65

Proceedings Royal Acad. Amsterdam. Vol. XVL.

1040

It seems as if ventral axones coming from the spinal cord end
in it. This caudal tract consists of thin fibres provided with only
a small myeline sheath and makes the impression of being ascending
in character.

Whether this can be a primitive homologue of HeLiwie’s triangular
tract, which oceupies a similar position in the mammalian cord and
oblongata, cannot be said.

It is interesting to see that this structure is already so well devel-
oped in the young Lepidosteus.

Droocierver Fortuyn has not indicated its limits in his map of
Amia. It has neither been possible to me to mark its limits with
any amount of exactness in this animal. The structure is so diffuse
and little cireumscript in Amia that its exact topography cannot be
given in Wericert or VAN Gibson preparations. It is certainly smaller
and less pronounced, which is not astonishing since Acipenser and
Lepidosteus are excellent swimmers and Amia leads a more quiet
life, as is also indieated by its name “mudfish’’. *)

Resuming my results concerning the arrangement of the motor
roots and nuclei in Acipenser and Lepidosteus, and comparing them
with Amia on one side and with Seyllium and Tinea on the other,
I may conclude:

Amia Calva, Acipenser and Lepidosteus osseus resemble each other
closely, and differ as well from the Selachii as specially from the
Teleosts.

They differ from the Teleosts by the very dorsal position of
the motor VII nucleus and by the continuity of the motor
column of the VII, IX, and X nuclei, by the less ventral position
and more diffuse’ structure of the abducens nucleus, the entirely
dorsal position of the V nucleus and the little ventro-medial migra-
tion of the oculomotor nucleus. On an average they resemble much

!) 1 will call attention to the possibility that the nucleus paramedianus of
fishes is rather the homologue of the ventro-medial accessory olive than of the
regular oliva inferior (comp. also Kaprers, Folia Neurobiologica Sommerergiin-
zungshell, Bnd. VI, 1912) on account of the fact, mentioned by Brouwer (Archiv.
Psych. Bnd. 51), that the ventro-medial accessory olive has connections with the
vermis cerebelli, not with its hemispheres, and that the cerebellum of sharks and
other fishes is probably the homologue of the vermis.

It is an interesting fact that this ventro-medial accessory olive of mammals
enlarges greatly in cetaceans, where it is again the dominating part of the inferior
olive (comp. Kanketer, Zur Vergl. Morphologie der unteren Siugetier-olive, Inaug.
Diss. Berlin 1913). ‘This, and the fact that in fishes it is probably the only part
of the inferior olive that occurs, might lead us to believe that the ventro-medial
accessory olive is chiefly related with the musculature of the trunk and the tail,

1041

more the selachian type of arrangement from which they only differ
by the constant gap between the oculomotor and trochlear nucleus,
the more dorsal position of the trigeminus nucleus and the less dorsal
extension of the abducens cells and roots.

Physiology. “On esophageal auscultation and the recording of
esophageal heart sounds’. By Dr. C. E. Bensamins. (Commu-
nicated by Prof. Dr. H. ZwaarbemMaKrr).

(Communicated in the meeting of February 28, 1914).
When performing an esophagoscopy our notice is surprisingly

attracted by distinct considerable pulsations at 32—85 e.m. from the

incisor teeth. Here an expansion may repeatedly be seen to appear
and to disappear rapidly after some complex to-and-fro motions.
Anatomically it has been shown that in this very place the left auricle
is located against the esophagus, from which it is separated only by
the pericardium, and, therefore, admits of immediate experimentation.

Following the lead of RavcrenperG’) and Minkowski”) I availed
myself of this circumstance by taking along this path cardiograms
as illustrated in Fig. 5. The results achieved in this investigation,
which was conducted in a way differing from the method generally
employed, will be given elsewhere. In this paper | propose to publish
my experience about the esophageal heart sounds.

I first wish to give some preliminary details of the technique
of examination. To the extremity of a strong grey india-rubber tube
(75 em. long; 5 m.m. bore; thickness of the rubber 1 m.m.), gra-
duated from 20—40 c.m., a knob-shaped appendage is fitted. Over
this appendage a rubber finger stall (from which the hard rim has
been removed) is tied so as to leave an elongaiion of 3—4 e.m.

The subject, whose pharynx had, or had not, been sprinkled
beforehand with a spray of a 5°/, cocain solution, to which some
drops of adrenalin had been added, swallows the lubricated tube
without difficulty, only being aided a little as at the insertion of a
stomach tube. When the tube is inserted as low as + 35 ¢.m. from
the labial curve, it is adjusted by means ofa T-piece to the binaural
stethoscope. (The T-piece has to protect the tympanic membranes
the moment the subject displays signs of choking). When he keeps
quiet, the T-piece is closed with the finger, so that we hear distinctly
1) RAUTENBERG. Die Registrierung der Vorhofpulsation yon der Speiserdhre aus.
Deutsches Arch. f. klin. Medicin 1907. Bd. 91. S. 251.

*, O. Minkowski. Die legistrierung der Herzbewegungen am linken Vorlol.
Berl. klin. Wochenschr. 1907. No. 21.

6S*

1042

all the sounds in the chest. In order to examine the heart sounds
the subject must hold his breath for a few seconds.

It requires some practice to distinguish the heart sounds. At first
a confusion of rustling, blowing, and crackling sounds is heard.
However, the moment the subject holds his breath only the well-
marked heart sounds can be made out, and then we become con-
scious of fowr murmzis, not two. When first listening to the two
loudest more defined sounds we distinetly hear one long, coarse
sound, and a second which is short and faint: the ordinary type of
the heart sounds over the apex. If we can divert our attention from
these sounds and try to single out the two much softer murmurs,
which seem to come from afar, we become aware that the first of
them commences before the first ventricular sound and undoubtedly
runs up till the latter is heard and even seems to coincide with it
for a short time. In the pause between the first and the second
ventricular sound an additional short and faint murmur is noticeable.

Passing the tube lower down or moving it a little higher up causes
the two faint murmurs to disappear, in order to re-appear again,
whenever contact with the auricle is again effected.

No doubt, we are here dealing with the auricular sounds that
have given rise to so much controversy. To raise the plausibility of
this assertion, | may add that, with persons subjected to esophagos-
copy, the site of the auricle was ascertained by measurement and that
it was always at this very spot that the auricular sounds occurred.
Besides the four murmurs under consideration one of our subjects
exhibited a fifth faint murmur, taking place after the second ven-
tricular sound. It may be typified as follows: rw,

ww

It appeared to me essential that these auricular sounds should be
recorded.

The chief obstacle was that, besides the sound vibrations impulses
arise from the movement of the heart, viz. at the apex beat, owing
to the impact against the chest-wall, and along the esophageal path
in consequence of the pressure on the rubber ball. Various methods
have been suggested to preclude the passage of these foreign im-
pulses. EirHoven’) and his pupils made the tube, connecting the

1) W. Enyrnoven and Getux. On the recording of heart sounds. Researches in
the physiol. lab. of Leyden. See. Series 1896.

G. Kaur. On simultaneous records of the heart sounds and the electro-cardiogram.
Heart. Vol. 4. No. 2. 1912.

P. Jo T. A. Barrarro, Further graphical experiments on the acoustic pheno-

mena of the heart.

1043

stethoscope with the recording apparatus, to communicate with the
ar of the room through a side opening, so that the impulses were
allowed to escape. GrrHARTZ') points out that, though this contri-
vance may enfeeble the sound as well as the extraneous impulses,
it does not eliminate the latter altogether. In the different heart-
sound figures he clearly sees indications of the apex-beat.

Still, considering the extremely beautiful curves taken in Eirno-
veNn’s laboratory, I daresay his method will do for recording heart
sounds through the chestwall; not, however, for registering them
along the esophagus. It soon became evident that the jerky com-
pressions of the rubber-ball could not be excluded from the curve.
For esophageal records the insertion of a stout stiff membrane serves
our purpose better. Various glass and mica membranes were tried,
but discarded as either enfeebling the sound or permitting the acci-
dental impnises to be recorded along with the heart sounds. Then
a common phonendoscope on a solid
ebonite plate was inserted; I chose
this material because it had proved
to transmit heart sounds. The phonen-
doscope P, in leaden case (0), was
attached hermetically to an afferent

tube and had thus been adapted for
72 mihropehow a cireuit with esophagus tube and
microphone. If the second aperture
was left open, no effect was produced
on the recording apparatus either by
Fig. 1. blowing into the tubes or by squeezing

them. It is certain, therefore, that the ebonite membrane is not
thrown into vibration by the impulsive beats of the air. Our greatest
obstacle was now overcome. It is true, the sounds were considerably
weaker, but what we wanted to hear, was clearly audible. For
further records we used a microphone (in camera plumbica) and a
small string galvanometer. This combination had in previous researches
proved suitable for recording the low sounds. (For the heart sounds
Weisz?) and Gurnarrz determined the number of vibrations at 5|0—100).
At the same time the electrocardiogram was taken in lead II by
means of the Jarge string galvanometer, with an are-light of its own.
With the aid of a screen the cone of either lamp was intercepted,

1) K. Gproarrz. Die Registrierung der Herzschalles. Berlin 1911.
2) O. Wetsz. Phono-kardiogramme. Gaupp und Naget’s Sammlung No. 7 Jena
1909.

1044

so that each lamp directed its light upon one half of the field,
Likewise the esophagogram was sometimes taken simultaneously.
Fie. 2. (a ecardiogram taken from Miss B.) is illustrative of the
slight oscillations of the heart sounds. Because we directed all our
attention to the heart sounds, no notice was taken of the electro-
cardiogram, which accounts for its unsatisfactory record. However,
for the present it serves our purpose. At /v we observe most distinctly
a constant, rather slow vibration of the string, which occurs before

the systolic portion of the electrocardiogram and is, therefore, of
auricular origin. (In the experiments, advisedly arranged, the recording
apparatus exhibired only a scarcely measurable slowing). Here then
we managed to record part of what is perceived by the ear. It
does not amount to much; the second auricular sound is wanting,
but the recording apparatus, on which moreover only weakened
sounds are directed, will ever be inferior to our highly sensitive
ear. It follows, that from these curves we cannot identify the real
commencement and the real termination of the heart sounds, the
initial and the terminal vibrations not having been well represented
in the tracing.

Of the first auricular sound only the loudest portion has been
traced. The ventricular sounds, which are much louder, yield much
better tracings and confirm EintHoven’s experience with regard to
the form of the heart sounds. They also point to his method being
perfectly reliable. for the sounds through the chestwall, since we
gather from them that the first auricular sound is made up of three
phases (a slow initial vibration, then the rapid main vibrations and
finally a slower terminal oscillation), whereas the second sound
consists of rapid vibrations only. We found the period of vibration
of the first auneular sound to be rather low, viz. 50 per second.
Further particulars are shown in Fig. 3, taken from subject t. D.;
however. here also the amplitudes are small, owing to considerable
damping. First of all we observe in one heart-rhythm three well-
defined groups of large vibrations. I and IL represent the ordinary
ventricular sounds and commence at the familiar spots, viz. some-
where about S and at the end of 7. The vibrations preceding I
start at a point some way from the foot Q of the A-peak, and must,
of course, be of ventricular origin. I marked them /v. A couple of
slight vibrations at Y indicate the real commencement. It will be
seen that the first sound like the first ventricular sounds is made
up of different parts, with differing vibration frequency. At the end
of the first ventricular sound we observe a couple of unlooked-for
slow vibrations (Ilv) with the shortest possible gap between them.

1045

Here | have been fortunate enough to record the short and faint
second auricular sound.

At the auscultation this subject often exhibited clearly Gupson-
Eintuoven’s third sound. In accordance with this I notice at | a
faint vibration of the string, which for the rest is perfectly quiet,
However the tracing is not clear enough to convince others.

I have also endeavoured to record the heart murmurs by taking
a superimposed curve, as suggested by Grraartz. If, for instance,
we leave the impulses to themselves, the recording apparatus will
take a cardiogram in which the more rapid vibrations of the heart
sounds are represented.

The esophagus tube being directly in ecirewt with the microphone,
with a side opening though, yielded the cardiogram (Fig. 4), taken
from subject P. In it we discern all the features of the so-called
complex esonhagogram as instanced in Fig. 5 for comparison.

The apex of the auricle is indicated by As; Vs is the ventricular
apex; D the diastolic portion of the third elevation,

The systolic apices I, IT, and III, which are so prominent in both
curves, I shall not discuss any further in this communication. The
points 1 to 5 are to be found in both tracings. A wave IV in the
diastole, visible only in Fig. 5, I shall revert to later.

Though, for the rest, the string is rather quiet, we observe, especially
with the aid of a magnifying glass, at the site of the first and the
_ second auricular sound, vibrations which have been superimposed in
the curve. Moreover at the anricle apex a good many fine oscillations
are discernable together with some bolder amplitudes. These are the
vibrations of the first auricular sound, which run up to the commence-
ment of the ventricular contraction. Though less prominent, some
vibrations, originating from the second auricular sound, are notice-
able in the descending limb of peak I.

Now, how are these auricular sounds produced ?

It has been generally admitted now, that heart sounds result from
muscle murmurs, from vibrations of membranes (valves or cell-walls)
and from eddies. An explanation for the first auricular sound is
soon found. Most likely it is chiefly due to muscular contraction,
but then the auricular contraction must last till the ventricular systole,
more particularly till the closure of the atrio-ventricular valves. The
continuance of the auricular systole in the isoelectric portion of the
electrocardiogram, between P? and (, is moreover demonstrated by
the fact that the largest vibrations of the auricular sound fall in this
portion, nay the systole is even prolonged for some time while the
R-peak is being formed (Fig. 3).

1046

When seanning the esophagogram ! was led to think that the
auricular systole runs into the ventricular systole without a previous
dilatation. This view is borne out by the auseultatory results and the
record of the auricular sounds.

Indeed, formerly it was taken for granted that only with cold-
blooded animals, e.g. the frog, the ventricular systole commences
only when the auricular systole has been completed, but that with
mammals the relations are more complex.

In Donpers’ Physiology 2°¢ Edition 1859 page 27 I read: ‘dasz
bei jedem Rhythmus zunichst die beiden stark ausgedehnten Vorbéfe
sich zusammenziehen und gleich darauf die beiden Kammern, ferner
die Vorhife sowohl wie die Kammern einen Augenblick im contra-
hirten Zustande verharren”. Donors holds that the old theory of
Haner, viz. that the auricular contraction and the ventricular systole
occur alternately, has been disproved. Scurrr’s experience coincides
with this view. It is remarkable that, in spite of this, HaLiEr’s
theory has found favour again in physiology. The second auricular
sound cannot be accounted for so easily; it may be that eddies come
into play; it has also been suggested by D. Grraarpr (cited by
WencokeBacn |. c.) that it may possibly proceed from muscular
movement at the auricular diastole.

The foregoing evidence has set the conjectures at rest concerning
the first avricular sound, which has long been a subject of dispute
in the literature. By what has been brought forward here Kreat’s *)
experience has been confirmed, Hirruie’s*) “Vorton’, recorded by
many researchers, has been substantiated; Fanr’s *) initial vibrations
have been transferred to the auricular systole; the discoveries of
auricular sounds by Barragre *), Wetsz*) and others have been
sustained, while moreover a second anricular sound has been added.

Finally I wish to return once more to the diastolic sound men-
tioned heretofore. 1 presume this to be the third sound of Gupson-
Erntuoven. Gipson *) detected in some individuals, with slow hearts,
an additional wave, called “b” in the diastolic portion of the curve
of the jugular vein and occasionally he heard a very feeble third

1) L. Kreau. Ueber den Herzmuskelton. Arch. f. (Anat. u) Physiol. 1889.

2) K. HiirrHir. Ueber die mechanische Registrierung der Herzténe. Pfliiger’:
Arch. Bd. 60 S. 263. c

3) G. Faur. le.

4) P. J. T. A. Batramrp. lic.

5) O. Werss. l.c.

5) A, Gipson. The significance of a hitherto undescribed wave in the jugular
puise. The Lancet, Nov. 16, 1907.

1047

sound. Erinrnoven ') found that third sound in his records as a faint
vibration, at a distance of 0,13 sec. from the commencement of the
second sound. In our subject, who has a slow heart (from 60 to 70
per minute) I, very | often, but not ahvays, noted this third sound
as a faint diastolic murmur, which got more distinct when the tube
was slipped as far down as 38 c.m. In fact the venous pulse of
this person often, though not always, yielded a beautiful Gipson
“b’-peak in the diastolic portion of the cardiac eyele.

Tt is evident, therefore, that it is of ventricular origin. If we return
again to Fig. 5, the esophagogram of the same subject, and look
at wave IV in the diastole at 0,135 sec. after line 4, the place of
the closure of the semilunar valves, we shall observe that this place
corresponds to the site of Ernraoven’s third sound.

Freépéricg *) also sometimes found a similar diastolic wave in the
auricular-pressure tracings.

When putting these facts together, viz. 1 ventricular origin; 2
inconstancy; 38 wave in the auricular-pressuwre tracings; 4 wave in
the esophagogram; 5 wave in the venous pulse curve; GIBSON’s
explanation seems to me the most plausible. He ascribes the origin
of this third sound to the fact that, at a high pressure or at a
copious ontlow of blood into the veins, the atrio-ventricular valves
will close for some moments just before the diastole, on account of
the blood rushing into the ventricle during the diastole, in conse-
quence of which the membranes are swung up by the eddies. They
produce a short sound and slightly check the blood in its passage
to the ventricles.

The evidence presented in this article will, | hope, support the
view that, together with the esophageal cardiography, the auscul-
tation and the recording of heart sounds through the esophagus
yields results not obtainable through the chestwall.

Physics. — “A new relation between the critical quantities, and on
the unity of all the substances in their thermic behaviour.”
(Continued.) By J. J. van Laar. (Communicated by Prof.
H. A.. Lorenz.)

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

13. If in the found*) expression 6 = f(r), viz.
4) W. Erruoven. A third heart sound. Ned. Tijdschrift voor Geneesk. 1907 Vol. 2
p. 470. ;

2) L. FrepericQ. La seconde ondulation positive (premiére ondulation systolique)
du pouls veineux physiologique chez le chien. Arch. intern. de Physiol. 1907.

3) These Proc. XVI, p. 924 to be cited as II.

atin ee SOI Rie be eee

, and 0, (=o)

in_ which «= (6—8,) : (v—»,) and which except 7,
only contains critical quantities which are (directly or indirectly)
experimentally determinable — we introduce again /,—0, instead

of b;—6,, then when (304) is taken into aecount, viz.

by! n b'>.
6 V1 - 2 Perr 0)

b—b, ey b'. wv y\n
yen) eee

In this is, also according to (300):

b—b n
ooo Lin( *) = on iO Aa

v—V,

(30) passes into

, 0

’

so that after substitution the equation (29), ie.

=) i a \r a
bb) = ed =. orn

is found back, from which we had started. In this we have found
for the exponent n [see (80a) and (31)]:

1 — x, 8y(y + 1) ie 2b} vz
"te = Oe Cys) > G= 2 eh
when for 4’, its value (4; —),)°:b;v~% is substituted, and further
for 47:6, the value 2y found in I’) (see §6, p. 817) and for vz: 2%,
the value 2(y+ 1). In this v, is the liquid volume extrapolated
from the equation of the straight diameter at 7’ = 0, y being the
reduced coéfficient of direction of the straight diameter.

In the two foregoing Papers the problem with which I have been
continually oceupied since 1901, has been brought to a provisional
solution. Already then I expressed (Arch. Teyler (2) VII, 3° partie:
“Sur Vinfluence des corrections etc.”) the critical quantities in the
values of 4’; and 4", at the critical point (see among others loc. cit.
§ 4), and verified the function = //(v) proposed by Kamer.incn
Onnes for H, and CO,. We now know that this function does not
fulfil the condition that at 7), the quantities 6), and 6"; must have
the values found by me. (See the preceding Paper II.)

In 1905 I went further, and expressed the different critical quan-
tities in two auxiliary quantities @ and «w, of which @ was in

relation with 7, and mw represented 1:s. (See particularly y 2 of

1) These Proc. XVI, p 808 to be cited as 1.

1049

the article in the Arch. Teyler (2) IX, 3° partie: “Quelques Remar-
ques sur l’équation d'état”).

This is therefore exactly the same as vAN DER WAALs continued
years later’), quite independently of the above investigations, and
in which. he found several remarkable approximate relations. These
were afterwards brought to a more accurate form by me, through
the introduction of the quantities 2, and /, into the expressions for
RT; and pz, in which it appeared that 7, = 4, for ordinary sub-
stances amounts to about 0,98, and approaches to 1 as the substances
approach more and more to so-called ‘ideal’? substances with 4
little variable or invariable. (See also I).

Thus all the quantities were expressed in 7 and s. But in con-
sequence of the equalization of 7%, and /, all of them could also
be expressed in the one quantity 7 (or rather // = /7:(1 +4) —
see I p. 811 and p. 814). This further step was followed by a still
more decisive one in consequence of a new relation being found
(See I, p. 815 et seq.), on account of which everything could be
expressed in the one quantity 7*), the reduced coefficient of direction
of the straight diameter’). For 4,:v, appeared to be = 2y (p. 816
loc. cit.). Of special importance is the simple relation 7’=8y (p. 818).

The table on p. 819 was the result of these new considerations.

And now that we have also an idea of the course of the function
SSvnOy — though of,course the found relation (30) or (29) is not
the only one that satisties all the imposed conditions, but certainly
one of the simplest relations that can be put — now the temperature-
influence neglected up to now, forces itself upon our attention. For
the found expression (29) only hoids for one temperature, viz. for the
critical. Here too we shall have to be satisfied for the present with
an empirical relation, leaving it to future investigation to give the
found equations 6 =/7(v) and )}=/(T) a theoretical foundation, in
which then the relations, found in I between 4; and v, (4,), and
those for 4’; and 6",, will find a natural explanation.

14. The variability with respect to T.
In the expression (30) the quantities 4,:4, and v;,: v, occur besides
in the. first member also in the second member because of 2; and

57, and the exponent vn. In this 4,:5, = 2y and ve: v, = 2(7 + 1).

1) These Proc. XIII, p. 118, 1216 et seq.

2) These Proc. XIV, p. 771 et seq.

8) And through which some approximate relations of v. p. W. (These Proc.
XV. p. 903, 971 and 1131) which were based on the approximate equality of s
and s’ (which quantities can, however, differ more than 12%) could be replaced
by more accurate ones.

1050

The value of b¢:6, (and of v;,:%,), i.e. of y, will depend on the
value of the critical temperature for different substances. But for
one and the same substance, considered at different temperatures,
hy: hb, (and vz: v,) loses of course its significance outside 7%. This

however, not the case with 4,:6,, which quantity is in relation
with 6:6, through (30°) at the critical temperature. We have namely :

Nie Be
(by —4,)r ——(b7 (hs) Va ie

ap—b yp

If in this we substitute the value 2y;—1 for (d,—4,) : b,, the value
(2v4—1): (2x + 1) for xz, = (b,-—0,) : (ve—v,) and the value (2y,—1)? :
4yn(vye+1) for 6%, — see above, and also I, p. 818 — we find

after some reductions :

by—b me / dyn (yet
sas) =Cr—0 [7 1a ea ees
Bi yee Ay, +1

in which nz = 8yx (yr-+1) : (2yz—) (472-41), according to (31) of I.

This naturally suggests the idea of making the above considerations
more general by putting },: 4, = 2y'; so that not only at the critical
temperature the equation (383) holds. in which y; represents the
reduced coefficient of direction of the straight diameter in the neigh-
bourhood of 7) — but quite general at any arbitrary temperature

i ee by (r+)
oa == ay = L=Qr—0 (7 ae ——, . . . (84)

in which, therefore, for an arbitrary substance y varies together

the relation

with y', when 7 changes.

Then outside 7; the quantity y is no longer in relation with any
bh, or with the reduced coefficient of direction of the straight
diameter in that point — but yet represents for any arbitrary tem-
perature: the value of */, (b¢:4,), or of the said coefficient of direction,
for another substance for which the critical temperature would corre-
spond with that temperature. Thus also outside 7; something is left
of the original meaning of y.

passing from 7’7=0 to =o for one and the same substance
all the types will be met with, which are found for different sub-
stances at their critical temperatures. Hvery substance approaches the
ideal type with constant 6, when only the temperature is made to
approach to OQ; every substance approaches the limiting type of the
substances with high molecular weight (y; = 1), if only the tempe-
rature be taken high enough. This has already been fully explained
in I (see § 7, p. 820—821), and there is no call to repeat the explana-

tion here.

1054

Remark.

Before proceeding to the discussion of the dependence on the tem-
perature of y' and y, a remark may be made in this context, con-
cerning the necessary consequences of the above considerations with
regard to the course of the ‘straight diameter”. When namely for a
substance we descend from the critical temperature to lower tem-
peratures, 6,—),, so also y, will continually descend ; so that the
slope of the straight diameter for an arbitrary temperature (which
slope at every temperature will depend on the type of the isotherm
at the considered temperature, determined there by 6,—4,), will also
have to decrease from the value y; measured at 7), down to the
lowest value, i.e, y='/,, holding for an ideal substance (7% = 0).
In other words the straight diameter cannot possibly remain straight,
but will exhibit such a curvature, that the final direction at 7’ =O

(supposing that liquid volumes could still be realized at these low
temperatures) approach to about 0,5.

It is self-evident that the /aw according to which this decrease
takes place need not be the same as the law that determines the
decrease of y' or y with the temperature, since for one and the
same substance v, at the critical temperature is, indeed, in direct
relation with the course of the straight diameter there, but this is no
longer the case, of course, below the critical temperature, where
b.: 6b, and y have lost their original meaning. A separate investigation
will have to decide later on, what the relation is of the real direction
of the straight diameter below 77, and the temperature.

That the change of direction for ordinary substances will never
be very great, however, at least not in the beginning, follows from
this that according to the law of variability of y to be drawn up

presently — with which the variation of direction of the straight
diameter in any case will run parallel —. a decrease of y of any

importance will not take place until at /ower temperature, i.e. at
temperatures which are considerably lower than the critical. For
substances as Hydrogen and Helium, where the critical temperature
lies so near the absolute zero, a more pronounced curvature of the
straight diameter will of course be expected.

15. A relation between yr and Tr.

It was then found by me that the quantity y;, at 7%, i.e. the
(reduced) coefficient of direction of the straight diameter, is in a
very simple relation to 7, namely aceording to the relation

bp—b,
Me

0

oO SS IA als, ocak fe (35)

1052

It may appear from the following table with what accuracy the
value of the quantity yz is given by this simple formula.

oe a ara | eines | eee
| | |
Helium 5a 2.28 0.0866 0.543 | a= (0556
Hydrogen 32.3 | 5.68 0.2158 0.608 | 0.604
Argon 150.65 | 12.27 0.4763 | 0.738 | 0.745
Xenon | 289.7 | 17.02 | 0.6468 | 0.823 | 0.813
Acetylene 308.5 | 17.56 0.6673 0.834 0.858
Isopentane 460.9 21.47 0.8159 | 0.908 0.914
Fluorbenzene, 559.6 | 23.66 | 0.8991 | 0.950 0.933

This table requires some elucidation, Of the many substances whose
values were at my disposal, I have only chosen some typical ones,
namely those substances which, just as in the table in I, p. 819,
represent a class as far as the value of y; is concerned. Oxygen
has not been inserted, because we know already from I, p. 819
that according to the values of s and / found for O, the value
of +; would have to be about (0,72, whereas 0,813 was found, just
as for Xenon. We have ascribed this to association. Also for CO,,
which belongs to the class of acetylene, the formula yields too low
a value of yz, viz. 0,85, whereas 0,9 was found. Whether here too
association of the liquid is the cause, is unknown to me. To the
iso-pentane group belongs also n-pentane and other substances, of
which 7). lies in the neighbourhood of 460° or 470° (absolute),
and y in the neighbourhood of 0,90 or 0,92. For iso-pentane yr = 0,916
according to Youne. The value given by us in the table, viz. 0,914,
is a mean value. Also C,H,, CCl,, and such substances with 7% in
the neighbourhood of 550° or 560° absolute, and y, = 0,98 or 0,94
belongs to the Fluorbenzene group. The given value 0,933 is again
a mean value.

For H,O, of which 7; = 6388, V 7; = 25,26, a value 0,98 would
follow for y, (2y, —1—= 0,96). It is unknown to me whether expe-
rimentally a sufficiently established value of yx for water is known ;
probably it will again be greater than 0,98, because also H,O is
associated, although it be at lower temperatures than the critical.

Even for a substance with. a critical temperature of 900° y, would

1058

be only 1,07 according to (35). However — at very high tempe-
ratures 6,:6, and so also 6,:6, will approach to a limiting value,
so that the coefficient 0,038 for y 7%, will probably gradually decrease
at higher temperatures. But as yet nothing is known about this, and
I shall therefore refrain from giving a more general expression derived
from theoretical considerations founded on the calculus of probabili-
ties (statistical mechanics), of which (35) or rather (36) would only
be a special case, holding only for temperatures up to about 606°
absolute. This expression too is characterized by particular simplicity.

Finally some indications of the sources of the given values of
7; and +; (found).

Helium. The value of 7; —=5,2 is that of KAMERLINGH ONNES in
Comm. 124 (see also Suppl. N° 21). The earlier values given in
Comm. 102a, 1412, and 119 deviate but little from this final value.
The value of y, (found) follows from that given for fin Comm. 124,
viz. 4,46 as lowest limit. If / is identified with 7’, which is certainly
permissible here on account of the slight variability of 4 for Helium,
7k = "/, f =9,56 would follow from, f'=4,5. I do not know a
direct determination of yz.

Hydrogen. In Comm. 119 is given 7), = 32,3. From f= 4,83
(see Kugnen, die Zustandsgleichung, p. 142) would follow y;,=0,604.
I do not know a direct determination of yz either.

Argon. According toComm. 115, 7% = --122,44+273,09—150,65.
By direct observation (Comm. 131) v;, = 0,7446 = 0,745') was found
here.

Xenon. Here | find given 77,=16,6 + 273,1 = 289,7, and further
yk = 0,818, as the boundary line coincides entirely with that of
O,, where yz; = 0,813.

We may therefore with close approximation draw up the formula
2yz —1= 0,088 V7; for substances, the eritical temperature of
which les no higher than + 600° absolute (330° C.), and: with
extension to arbitrary temperatures :

Cea 0 OO ae Ue eer ee ten (33.072)

For (bj — 6,): 6, = 2y'—1, also holding when a substance is

/

considered at arbitrary temperatures, and not only at the critical,
we may put:

Se ay, ae MONO Pelee ee titel! oan (80)

1) From s=8 yk: (1+ Vk) = 3,424 (Comm. 131) would follow yr = 0,748,
which is in perfect harmony with the found yalue.

1054

For every value of y we may caleulate the corresponding value

of (2y'—1):(2y— 1) from (34), bearing in mind that n=8y (y-+-1):
: (2y — 1) (4y +1). We shall then find the mean value 1,08 for that
ratio, so that the factor of }“ 7’ will get an average value of 0,038
(which also represents a mean value) x 1,08 = 0,041.
“In this it will no doubt follow from the nature of the thing that
the factor 0,041 in the formula for 4, — 4, is the same for all the
substances, but the factor 0,088 in the formula for 4; — 6, varies
somewhat with different substances, dependent on the value of the
ratio (5, b,): (6; — 5,). For by is, so to say, a natural point in
the series of values between the final points 4, and 4, — but by
only an accidental point, dependent on the situation of the critical
point. It follows, however, from this that now, for Helium e.g., the
factor for (6; — 6,): 6, will become greater than 0,038, viz. 0,041 :
: 1,004—0,041, because for He the value of (4,—4,) : (6;—b,)=1,004.
But this does not present any difficulty, for He can very well have
a somewhat greater value of the factor. With 0,041 2y,—1 would
namely become = 0,0931; so yr = 0,547, only little higher therefore ~
than 0,548, and still smaller than 0,56.

For the sake of completeness 1 shall just give the corrected values
of yz (ealeulated) for the other substances mentioned in the table.
For H, yx would become = 0,615. (Here the reduction factor
0 = (b,— b,) : (6. —b,) = 1,011). For Argon we find 7;= 0,739 (with
6=1,053); for Xenon with @=1,077 we find the value 0,824 —
both almost identical with the values in the original table. C,H,
yields -y; = 0,832 with — 1,084 ; Isopentane ys = 0,897 with
O=1,11; Fluorbenzene finally gives y;, = 0,933 with 6=1,12. The
last value of yz is now also equal to the “found” value of yz.

16. Calculation of the theoretical b-values. ;

The values of / can now be calculated from the reduced equation
of state in the form [see I, p. 812, equation (c)]:

y deo |
(e+ = Am oe oss Gan (37)

In this @ represents 6: vz. The values found thus can then be
compared with those which we can calculate from (80) and (35).
For equation (80) we may write:

t= =(2)
b—b, by—b,\" wk \ xk
Gee ea
i.e. with (6,—-6,):6,=2y—1, 6:=2y—1D? : 4y@+D);

0

1055

= (2y — 1): (27 +1), «= (06 — b,): w —»,):

pe OSS 4y?—]

4y(y+1)
In this equation 6—46, occurs both in the first and in the second
member, and cannot be solved from it (in consequence of 7" power).
We are therefore obliged to solve »—v, for the caleulation, and

treat ial = a ey
(= 1 ) pee ATs) Ciel
1

then we find after some reductions (v, = ¢,):
2y+1 b—b,
v—v 2y- eel b,
a a — ee (38)

Vy See +1) “dy yl "Ty (oon
4° 4y?—| Li |

in which n=8y(y-+-1) : (2y—1)(4y+1), 2y ime — OOS sal
In order to get an idea about the actual course of the curve b=/(v)

according to formula (88), I have taken the trouble — also with a view
to testing the caleulated values by those which the equation of state

will yield for Argon e.g. — to calculate the corresponding values
of (b,—4,):6, and (v— v,):v, for different values of y, i.e. of 7.

The limiting value 6, for v=o is evidently found by putting
the denominator of os = 0, from which follows:

uss yg 1)
sO (Dan eel SE ey eon 8 a
==\(2 oy ) dy +1 ( a)

And with regard to the limiting value (6—d,) : (v—v,) for b=4,,

is (6—6,) = rere 4y( y Ga iD
1G, ee Sh = THA a e 3]
um (=a) v Uh ne Dy ay? oye (38d)

0

agreeing with (34).

Vi),

follows immediately from (304) of I, ee instead of yz quite
generally again y is written.

a. y=0,9. (7 = + 450 absolute).
For n we find 171 :46:3,7174, so that (88) ete. passes into

Cea Orca ae SUS aaa se
Ss — ==
; b 56 SOL L 6 |

0 0 0

: nee
(b)—0,) 26, =0,8VI7T21I5 ; 2, =%/,V171: 56!
This yields the following survey (when for m not the shortened
value 3,7, but 38,7174 is taken).

69
Proceedings Royal Acad. Amsterdam, Vol, XVI,

1056

(by. — p):: &, = 90,8901 5° «, = 0,3858

|

(b—bp): bp = 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

(V—Up): V9 = 2.8:1 | 2.45: | 2.1: Sys |) theese ees || Was 0.35:

1.1719 1.2582 | 1.3057 | 1.3313 1.3438 | 1.3488 1.3502

=2.8 2.091 1.669 | 1.340 | 1.052 | 0.781 0.519 | 0.259

Hence we have for y= 0,9:

| im
b: by | 1.89 7 I [1.5 ne 11.3 “ae Iie
| | |
V2U9 | 0 hoe 3.09 so libeke kee am
= | 0 °. 2200 m0 0 200 0 Palin 380 | 0.384 | 0.385 0.986 | 0.36 386
Ta!)

It follows from this survey, what is of importance for practical
purposes, that the direction of the curve 6 = /(v) very soon — namely
at about v= 0,6 v7, — approaches the final direction given by
(6—b,) : (v—-v)) = 0,386. I observed already in II p. 935 that since
6", =0, the final part of the curve will have pretty much the shape
of a straight line. This is actually the case ; already for v: v, = 2,34,
where (6 — 6,):(v v,) = 0,373, the direction does not differ much
from the final direction. We introduced just now the quantity vj marked

in this and the following tables by an *; by this is meant the value
of v whieh would correspond with vz, if the considered substance
had its critical temperature at the assumed temperature (here + 450°).
0,9=yu, and hence vy: v, = 2 x —- 1) 38)
so that » = 2,34, is then = 0,6 2}. :

b. y= 0,75. (7 = + 150 absolute).

Kor mn we find 5,25, and further:

r—0, 1, b=), | 12D G/N
=.) . |)
v b [yA 5 5 b

Then “nauvely y=

elving

1057

(G;—6,)): 0) = 0;5266 4. x, = 052629

(6—by) by =0.5 | 0.4 0.3 0.2 0.1

Lae | ais | Weieye if: OLD:
| 1.2486 | 1.3010 | 1.3128 | 1.3143

osu wel OO2:, (1153 lar | 0.380

So we have for y = 0,75:

b: bo 1 S3h|etes 1.4 CEES Ba tee a 1
VV, Ea Seo mene 2 CON ib2e15) ai, WeGr |i 1.388 lal
| |
ae a " ae ae
See yl Osea | 0.250 | 0.260) 0.2625; 0.263) 0.263
ay |

Here too the curve /=/(v) is almost rectilinear for v = 0,6 vz,
nay even for v = 2,6 v,—0,75 vy’.

Just as for y= 0,9 we see also clearly in the above table, that
the greatest change of b will be in the neighbourhood of the eritical
(or = pseudo-critical) point; hence the comparatively large values of
by. and 6", through which += vp: b, is reduced from the ideal
value 3 to a much lower value, e.g. 2,1 (for yz—=0,9) or 2,33 (for
Yk = 0,75). We may’ say that the curve 6=/(v) at the beginning
and at the end runs almost rectilinearly (at the beginning, between
v=o and v =somewhat > vz, parallel to the v-axis), while in the
part somewhat before and somewhat past v; the change of direction
takes place from 0 to the final direction given by a
0,39 and 0,26).

Ca — OOM = + 100).

Now n=119:19 =6,2632, and further:

(above resp.

0

v—v, bb: bas 95 (_ _ b—b, \626 |
aa 2 Ge Se OH 8 |
v b 24 24 b )

9 0 0

]
6,26 \

6,26 f 5
(7 — bd )\iwo n= 054 VA OT I9 5) 3s CV On 24
from which follows ;

69%

1058

(b,- b, b, =i) 451A Oia mer AO nonlin

(b—bo) : bp = 0.4 0.3 | 0.2 0.1

ioe: 1.426 | 0.931

|
| |

(v—v 9): Vy = 2.4:1 | 1.8:1. lee le Doibs 2801 | 1.1: 1.2912
| | 0.465

In consequence of this we have for y = 0,70:

| |
bib) Las | 1.4 | re | 162] tena ea
vim | © | 3.4° L 2.43 | 1.93 | 1.465 | 1
oh icles | ieee Ae
i | |
Ee) 0 a 0.167 foie 0.215 | 0.215 | 0.215
U—WVp9 |

For v:v, = 2,43, hence v=0,7 v,, the final direction has already
been reached.

dy, —0 655 (i= 30):

For n we find the value 143 :18 = 7,9444. Further :

Oats bea 143 120 (10 b—8, |
lS a8 a ; 93° Dou an
7Oie Ss umietNe
(RRR = Obs) Vis A202 oe aloes
giving :
(b,—6,):b = 0,067 ; #, = 0,1642
= — tern

|

(v—09) : 0p = 2.3: 1 | 235: 1.2532 299: 1.2586
=2.3 | 1.2235 | 0.609
| |

Hence we have for y = 0,65:

bby 1-3tnlh 1-3 )1.2 | ee sin
| |

ViUg ce) Set 2422 Sophy eal

(6-bo):(Y Yo) 0 0.130 0.1635 0.164 | 0.164

|
|

L059
The final direction is again reached for v= 0,7 vp.
Cn — 0560) (CE = ==.25),

The value of » is 192:17 = 11,294. In consequence of this:

V—U, b—b, e796) We 85 =a 11,8
= 11 —— : 5 - ]
Ve b, bss ill b,
11,3 11,3 \

(8,—d,):3, = 0,2 V96:85 ; x, =1/,, V96:11

giving :

(Cob) oe — 020227 rer OOF

(b—bp) : by = 0.2 | 0.1

(v—v9): Uy =2.2:1=2.2 | 1.1:1.2114 = 0.908

so that for y = 0,60:

= (eee ee
V:U9 | o lites Shen | 1.91 oy 1

| | | E

(6—bp) : (Vv—vp) 0 | 0.091 0.110 | 0.110

A little beyond vj the deviation of the final direction is already
unimportant.
ie Oe Ue (Il SS eG)

Here n is = 341 : 16 = 21,3125, and further:

Ua b—b, (gue 320 / b—b, » 21,3
== Pil : 10
Uv b 21 21 b ) |]

0 0
21,3 A 21,8 :
(5, —0,) 10, One oo 2h920. sz, 9). 84n 2
from which follows:
(by— sor C1003; xv, = 0,05428,

so that we find (e.g. a a Helium isotherm at its critical temperature) ;

b: by fe1003: ae tee

ViU9 a) ee 1
|

(6—bp):(¥—0) 00.0476 | 0.0543

1060

And tinally for y=0,50(7’=0), where + is invariable, we should

find 4:6,=1 for all values of v:v,, (62—d,) : (v-—v,) always being = 0.
Let us in conclusion review according to what law or approxi-

mate law the found value of a, — i.e. of the final direction of the
curve b= f(v) — varies with y or 7.
d iT n 7 Aa (> Te)
From (884) follows 2, = (2y—1) *K — a Was i) We shall
2741 4y?—1

see that here the factor of 2y —1 is almost constant between
y= ONS Jand! 40) 55;

= 0:90!) 0575: 5 SOl7Or 50365) OF60> TOFSoR. 10250,

Xo = 0.386 "0.263 0.215 0.164 0.110 0.0543 | 0

Xo (2y—1) = 0.482| 0.526 0.538 0.547 0.551 0.543 | 0.5

If 0,482 for y=0,9 and 0,5 for ~—=0,5 is excepted, the mean
value of the other values is 0,541, and we may therefore write
with some accuracy :

b—b,
Lim ( -- ) = 0,04 (2y—1).
U—V y/o
But seeing that 2y—l = 0,038V 7, we have also:

b=6
Lim 2 ‘— 0,02 (Za; a cae | iia, +c Pau (39)

v v 0

which according to the above will therefore also hold all along the
jinal part of the curve 6= /(v), from values of v = 07 oy. tow o.
For Argon at temperatures < 7; only y=0,75 (7= 150) and
y= 0,70 (7=100) should practically be taken into account, be-
cause the observations have not been carried further than Z’= 90
(absolute). Uf we thus consider an isotherm for Argon below the
critical point, we may assume that (provided it be not too near 7%)
the value of 4 will practically agree with 6, at the vapour volume,
and that at the liquid volume the 6-value will satisfy the above
equation (39). ’
If (89) is written in the reduced form
i 2) = 0K 25 (elie
(v: vp) —(%, : Ur)
and if it is) taken into account that 6:2,= 8, v:vr—=n, and
Dos Vi = Ny = 8) = 1 idee e)s then) -foreArcon:
(8 —?*/,):(n —7/,)=0,02 YT, C1050)" ee 40)
when yz = 0,75 is taken.

1061

As 1— (8 —?*/,):(n—?*/,) also = (n-—§8):(n—7/,), we may
also write:

n— B=(n — 7/,)(1 — 0,02 7), (ici ONT) any un 40'a)
in which n—~ is determined by the equation of state (87). Equation
(40°) may serve among others to determine the dependence of the
reduced liquid volume on the temperature at low temperatures.

17. Calculation of the b-values from the isotherins of Argon.

In order to be able to draw up the reduced equation of state of
Argon, we must in the first place accurately know the critical data.
For the critical density oe, I took the value 0,53078 from Comm.
Leiden 131 (Marutas, KamuErnincu Onnus and Crommein). Abbreviated
therefore 0,531. In this it is assumed that the straight diameter remains
straight up to the critical point. The values of CrommELin in Comm.
115 (¢,=0,509) and Comm. 1187 (9; =0,496) are both too low.

For 7), has been taken — 122°,440 = 150,65 absolute, and for
pe the value 47,996, shortened to 48,0 — both from Comm. 115.

For s we assumed the value s=8,424 from Comm. 131. In Comm.
120a (KammrLINGH OnNES and CroMMpLIN) a too low value, viz. 3,283,
has been given (in connection with the too slight critical’ density).

At last the value of f. We derive from Comm. 120° f> 2,577
X< 2,8026, hence f >> 5,933. (Comm. 115 gives the too low value
5,712). From s= 8f': (8 + /’) -— see I, formula (7) — would follow

a 0:986. And frome /” = 8y see I, formula (17) — follows with
y= 0,;7446 the value f’ =5,957. Now f=/" (1+ 9) — see I,
formula (5) — hence, as 7 is small positive, / slightly greater than

jf’. We may therefore safely conclude to the value 6,00 for J from

the two values 5,99 and 5,96 for /’, which also fulfils the condition
i> 0,03.

Comm. 131 gives 0,0026235 7). : 0, as reduced coefficient of
direction for the straight diameter, giving with the above given
values of 77, and o; the value y= 0,7446. We saw just now that

this value yields a good value for /’. From s = 8y:(1 + y) would
follow y—0,748 for y. The former value from Comm. 120a, viz.
0,003050 7): o,=0,9027, is much too high, and would be quite in
contradiction with our temperature-relation 2 y— 1 = 0,028 // 7,
which yields 0,738, in good harmony with 0,745, but not in harmony
with 0,908, which high value of y would belong to substances of
the Isopentane type with a critical temperature of about 450 absolute,
i.e. three times as high as that of Argon.

We see from this how useful the above table in § 15, in con-

L062

junction with that in I, p. S19, can be for a first orientation con-
cerning the critical data.

Now the equation of state (87) passes into (assuming the value

6 also for 7”)
5
(« nt :) (iB) = 3,424 mn,
a

from which may be solved.

B=n— ——_ ,
é + 5:n?

The following values have all been derived from Comm. 1180,
p- 19 et seq. (KAmeRLINGH ONNES and Crommein) and from these
Proceedings of Oct. 1918 p. 477 et seq. (CromMELin). (See also
Comm. 138).

The value f% follows from 7 =vz: 6; =1: Br, hence 8 =1:7.
Now r=(1+y): 7 — see I, formula (14) —— so that B.=y:(1-+y)=0,427.
With r=1-+8:/" (see I, (7)) follows with /” =6 for r the value
2,33, hence for ®, the value */, = 0,429. As further 2y = 0,20, =
we have 8, = Br: 2¥ = 0,429 : 1,5 — 0,286.

We are not yet ready to carry out the calculations, as the given
volumes must all be changed into ‘veduced” volumes. Now e = 0,1073
corresponds with d4—= 60,21, (Comm. 118, p. 8), so y = 0,5308 (the
critical density, corresponding to n=1) would correspond to d4 =297,84,
i.e. to V4=1: 297,84. This is therefore the value of V4 at the
critical point. To reduce this to 1 (n= 1), this and all the other
volumes must be multiplied by the factor 297,84. .

a. The isotherm of 20°,39 C, i. e. (with 7, = 273,09) 7’= 293,48
absolute. From this follows m = 293,48 : 150,65 = 1,948, so 3,424 m =
= 6,670, so that ty ae

== 67h Oo}

o>

n— B= 6,670: (e + 5: n°).
Now e.g. d4 = 20,499 has been given (for p = 21,783). So the value
V4 is 1: 20,499, hence according to the above n = 297,84 : 20,499.
We must therefore divide 297,84 by all the given values of d4.
Thus we calculate the following survey.
————————————ee
p | a4 | E n ||: £5 :n2l n—a- ‘| 8
| I | |
th Nhe | \|
21.783 | 20.499 || 0.4538 | 14.529 || 0.4775 | 13.969 | 0.560
34.487 | 32.590 || 0.7185 | 9.139 || 0.7784 | 8.570 || 0.569
49.604 | 47.319 || 1.0334 | 6.294 || 1.1597 | 5.752 || 0.542

61.741 | 59.250 || 1.2863 | 5.027 || 1.4842 | 4.494 | 0.532
| | | 1
Mean 0.551

10638

From (85) with VT = /293,5 = 17,13 would follow y= 0,825,
referring to a substance which would have its critical temperature
at 293,5. Then (see above) 8, would be =~, K 2y = 0,471, while
By = 8, < 1,708 would be = 0,488. [See a. and bd. of § 16; 1,708
for y= 0,825 is the mean value of 1,8901 for y=0,9 and 1,5266
for y= 0,75].

The above found values of 3 (which will probably practically
agree with §,) are all higher than the value of 8, calculated from
our formula.

b= The isotherm) ote — 97-21, e, 2 = 215,37, m= 1,430) and
so 3,424 m = 4,895. From n— 3 = 4,895: (« + 5: n*) the following
table is calculated.

d irs 3
p 7 Tee nm jie-+5:n2| n—p 2

| |
17.872 23.509 | 0.3723 | 12.669 || 0.4035 | 12.131 0.538

35.127 | 48.116 || 0.7318 | 6.190 || 0.8623 | 5.677 0.513

46.209 | 64.948 || 0.9627 | 4.586 | 1.2005 | 4.078 0.508

62.079 90.695 | 1.2933 3.284 | 1.7569 | 2.786 | 0.498

Mean 0.514
Just as above we can again fix the limits of 8, corresponding to
a temperature of 215 absolute. With 7 714,68 corresponds y=0,779 ;
hence By = 0,445, 8, =8, « 1,597 = 0,456. Again 9, calculated from

the equation of state, is higher than the value calculated from our
formula.

ce. Isotherm of — 102°,54 = 170,58 absolute. Then m:1,132,
hence 3,424 mm = 3,8770.

72) dy } z n jje + 5:1? n—p | 5

14.864 | 25.571 0.3097 | 11.648 | 0.3466 | 11.188 || 0.460
32.394 | 62.240 | 0.6749 | 4.785 | 0.8932 | 4.340 0.445
40.976 | 84.002 || 0.8537 | 3.546 || 1.2513 | 3.099 0.447
51.398) |115.88 |) 1.0708 } 2.570 |! 1.8276 | 2.121 0.449

62.239 |158.01 || 1.2967 | 1.885

i)
a
©
Ww
ioe)
_

-434 0.451

Mean 0.450

With 7=170,6 corresponds 7 0,748, By = 0,427, 8, =8, X1,522—

1064

— 0,435. The p-values from the equation of state are still somewhat
too high.

d. The isotherm of — 116°,62 — 156,47 absolute. This yields
m = 1,039, hence 3,424 m = 3,556.

p | dy | n |le+5:n2| n—p || 2
| I I | ae i)

13.863 | 26.480 0.2888 | 11.248 | 0.3287 | 10.824 0.424
37.250 | | 0.7760 | 3.289 || 1.2429) 2.867 0.422
50.259 | 159.71 || 1.0471 | 1.865 I 2.4992 | 1.427 0.438
54.922 | 210.02 | 1.1442 | 1.418 | 3.6551 | 0.976 | 0.442
60.669 | 331.29 | 1.2639 0.8990) 7.5120 0.475 || 0.424

Mean 0.430

With 7'=156,5 corresponds y= 0,738, yielding By = 0,422,
B, = 8, < 1,500 = 0,429. As, just as in the above tables, n >2
(the last value is a little smaller), no appreciable diminution of the

limiting value 3, can be expected for 8 yet. Now that we approach
the critical temperature of Argon, however, the mean value 0,48
found in the table (calculated from the equation of state) agrees with
the theoretical value of 8, which can be calculated from our formula.

e. The isotherm of -— 121°,21 = 151,88 absolute, so slightly above

the critical temperature. Here m= 1,008, hence 3,424 im becomes

ord OA.
? dy nm \|:+5:n2} n—f 3

13.754 27.326) 0.2865 | 10.899 | 0.3290 | 10.497 | 0.402

30.122 |. 71.459)} 0.6275 4.168 || 0.9183 | 3.765 || 0.403

37.465 | 100.33 || 0.7805 2.969 | 1.3536 | 2.556 || 0.413

45.282 | 148.95 || 0.9434 2.000 || 2.2064 | 1.569 | 0.431

49.865 | 234.13 || 1.0389 L272 | 4.1596 | 0.833 0.439

50.885 | 333.75 | 1.0601 0.8924 7.4013 0.468 0.424
| Mean 0.419

With 7’ —151,88 corresponds y = 0,734, By =0,419, 8, =B8, X

S< 1,491 = 0,426. The found mean value, though slightly too small,
agrees pretty well with it.
Fontanivent sur Clarens, March 1914.

(To be concluded).

1065

Chemistry. — “The reciprocal pairs of salts KC1+ NaNO, 2
NaCl+ KNO, and the manufacture of conversion salpetre.”
By Prof. W. Retpers. (Communicated by Prof. F. A. H.

SCHREINEMAKERS.)
(Communicated in the meeting of February 28, 1914).

As is well known we understand by two reciprocal pairs of salts,
the two pairs that can be built up from two different cations and
two different anions and can be converted into each other by double
decomposition.

The instance of this mostly quoted is the system:

KCI + NaNO, = KNO, + NaCl,
known by the technical application of this transformation in the
manufacture of conversion salpetre.

Notwithstanding the technical importance of this system, a system-
atic research as to the equilibria occurring therein was still wanting.

Hence was started in 1909 by Miss J. Pu.. van Rees and myself
a research of this kind, which on account of the departure of the
first named could not be continued, but has since been completed in
cooperation with Mr. R. pr Laner. The results of these researches
will be communicated here briefly.

Meanwhile appeared in 1910 the publication of an investigation
of these equilibria at 25° by Kunsiro Uyepa'), to which our attention
was called by a communication thereon by E. JAnecky *). His
figures agree very well with our determinations at 25°. Besides at
25°, we have determined the equilibrium also at 5°, 50°, and 100°.

We will indicate the composition of the solutions in the manner
proposed by E. JAnuckn*) according to the scheme:

ak, (1—-«2)Na, WNOs. (1 —y)Cl, mH,O
in which m is, therefore, the number of grm. mols. of water in
which 1 grm. mol. of salt is dissolved.

The graphic representation of the different solutions then becomes
a figure in space having as ground plane a quadrangle of the
side =1 of which two sides coincide with the « and the y-axis. The
four salts then form the apexes of this quadrangle, mixtures of two
salts with homonymous ions are placed at the borders of this quadrangle

1) Memoirs of the College of Science and Engineering, Kyoto Imperial University
1909/1910 Il, 245—251.

*) Zeitschr. f. anorg. Chem. 71, 1 (1911).

5) Zeitschr f. anorg Chem. 51, 132 (1908); 71, 1 (1911).

1066

and mixtures containing all four ions are represented by a point
within the quadrangle. If now, in the point indicating the proportion
of salts in the solution, we erect a perpendicular line of the length
m, the composition of this solutiou will then be fully determined
by the terminal point of the perpendicular line.

The equilibria at 25°.

The solutions saturated with one or more of the solid salts are
indicated in table I.
Fig. 1 is the horizontal projection of the spacial figure.

Na NO, G ko,

OTe VO? Een) Ves V6 Volz VaR 7019 KC
Fig. 1.

In addition to the lines indicating the equilibrium with two solid
salts are also projected therein the ¢sohydores, the lines that unite
saturated solutions with equal water contents.

In this figure are encompassed by the lines
AEP,P,HA the region of solutions in equilibrium with solid NaCl
EBFP,E 5: Pease, - es 3 ,», solid KCl
PE GCrAS Sie ¢ . % ,, solid KNO,
DGP,HD se A, s Fs “ a ,, solid NaNO,

TABLE I. Solubility at 25°.

Grms. of salt in 100 grms.

NO. of water. | Solid salt in equilibrium
SSS with the solution.
NaCl | KCI |NaNO;| KNO3

Pitss 08 C2 | es | NaCl
4113) || '5 = =) (|
32.28 10 = mA | f
30.27 | 15 sgl ti ietee .

E| 29.62 | 16.45) — = NaCl + KCI
20 9168) || <= on eae) KCI
15 24.66 | — os
12 9618) & :

B\ 0 35.98 | — = _

0 3580 — 5 5

a Soe 54alg el 10 5

|| C50 SS a ‘i
a= 9 )\6342920|| —— 189270 KCI + KNO;

ee 5 — | 28.93 | KNO,

22 10 — | 31.49 :

== |8 = -| 34.89)| '

Cl — | 38.85 .

= as 5 37.96 :

| Sa |= 10 37.49 5
_ == oie 37.42
ss = 20 37.54 :
ze => 40 39.39 “

(ee Ban 41.87 | 5

Ch — |100.90 | 46.15 KNO; ++ NaNO;

as ==) |orko5=|'s0r | NaNO,
=m — | 96.06 | 20 :
= — |94.47/10 | A
ak Sr 193839) 5 x

De) =. 91886. | 70 ,

5 Saesdeour | f
10 Se Cae Ge q
15 =e | F70K69N (oe ;

H | 23.62 | — 5801) = NaNO; +- NaCl
B25 Sie get 1D = NaCl
S31 00uie es 11010 = i
35407. |) = 5 — :

A} 36.04) — | — = es
bY valley OAs Ly a NaCl 4+ KCl
21.36 | 20,00} — | 32.9 KCI + KNO;
DAS =e | 61-3) | 17.2 KNO; + NaNO;
TO = 9 | 82 |43.15 NaNO, + NaCl

P,| 23.8 | — | 64.0 | 41.2 | NaCl+NaNO3+ KNO3

Pi) 41.5 | — | = [40.3 | NaCl+KCI--KNO,

xK

(Sy S33 SSS Se ea era SS ot es et ea ee) oh tes ey)
oS .
Oo

0.33
| 0.62
0.13
| 0.27
0,26
| 0.36

| yNO3

Se Sy SY SKS SS)

| Sol.: eK, (l—x) Na,
| yNO3 (1--v) Cl, 72 H,O.

mH,0

9.01
8.53
8.09
Hous
7.63
8.77
9.45
9.84
11.51
10.48
9.64
8.96
8.00
11.39

AAoOWMWHAHAAAaan ff fF FW WwW fH ©
oo

Qo
or nN
—-

1068

The lines of demareation between these planes: P,, /P,, GP,,
HP, and P,P, indicate the solutions which are in equilibrium with
two solid salts, and the points P, and P, the solutions saturated
with three solid salts.

We notice there are no solutions saturated with both KCl and
NaNO,. This pair of salts is, therefore the wnstable pair. If to a
solid mixture of these salts we add a little water a solution will
form in which one of the salts disappears and solid KNO,, solid
NaCl or both these solid phases are formed.

NaCl and KNO, are the stab/e pair and the line P,P, indicates
the solutions saturated with these salts.

The point P, which represents the solution saturated with the
three solid salts NaCl, NaNO, and KNO, lies entirely within the
triangle, whose points indicate the composition of these salts. The
solution is, therefore “congruent-saturated”. 7, lies just on the diagonal
NaCl—KNO,. Hence, this solution is still just “congruent-saturated”’.

The equilibrium at 5°, 50°, and 100°.

The result of the determinations at these temperatures is contained
in the tables 2, 3, and 4. In fig. 2 these equilibria are represented
graphically.

TABLE 2. Solubility at 5° C.

rr a

Grms. of salt in 100 grms. Sol.: xK, (lL—r) Na,

NO. of walker : Solid salt in equilibrium YNOs) (19) Eh ee
with the solution.

; NaCl | KCl |NaNO3| KNO3 xK | yNO3 | mH2O
Mis5 fia) eee =e NaCl 0° A] 00> 4) onee
E 31.50 | 10.40 | a NaCl + KCl 0.207 | 0 8.19

13.93 | 20.01 | — KCI 10.53 | 0 | 10.96
| 29.76 | — — KCl 1.00) | 08 |) 18%or
Fil = | 20 stile === Wierd KCI + KNOs 1.00 | 0.20 | 11.07

— | 16.32} — | 11.40 KNO3 | 1.00 | 0.34 | 16.74
Ci Se O283 KNO3 1.00 | 1.00 | 33.34

- — 22-30) 15:57 KNO; 0:37) | 1200) | |/ess4
a= — 82.10 | 18.1 KNO, + NaNO; 0.155 | 1.00 4.80
Diem — | 76.3 | — NaNO, 0] 1.00 .| 364s

10/493) == | 50 sien NaNO, 0 | 0.64 | 6.03
H| 27.6 Niches | = NaNO; + NaCl OF |O.5t |) sem

85 Alb) SalO gh cee lal Ont NaCl + KCl 0.22). 1'0.13. | weet

19.5 | 13.65| — | 13.88 KCI + KNO; 0.49 | 0.21 | 8.49

22100 |) =—0 1/256 .0hmimaeeo KNO, + NaNO; 0.12 | 0.68 | 4.72

91/50, | =) | 4215 9\ “3203 NaNO;-+NaCi | 0.03 | 0.53 | 5.55
P,| 29.1 44.3 14.0 NaCl, NaNO;,KNO; | 0.12 0.57 | 4.80
P;|38'5° | 10.64 | —" | 20,7 NaCl, KCl,KNO3 | 0.23 | 0.22 | 6.50

TABLE 3. Solubility at 50° C.

“Gah of salt fa 100 grms, | Sol.: xK, (1—x) Na,
No.| ae of woken: _|Solid salt in equilibrium INO3; (1-9) Ce:
with the solution. |
| NaCl | KCI | NaNO 3} KNOs | | xK | yNO3 | mH,0
—-—
FAN) S612) Pee | =| NaCl hac 0 | 8.85
Fal 26035) | 23409) || =a ans | NaCl + KCI 0.39 0 | 6.99
| 15.96 | 29.24; — | — | KCI | 0.59 0 | 8.35
Tees apg |, eee i a ‘ | e00° lo) orer
— | 41.39] — | 24.05 | p | 1.00 | 0.30 | 7.00
Fie SS. 75h a. 52.54 KCI + KNO, 1.00 | 0.50 | 5.34
Ci = See a5ei0r| KNO, 1.00 | 1.00 | 6.60
Pra), ieeon We57-80r| 81-53 | : | 0.56 | 1.c0 | 3.59
Gi | — 134.9 | 90.2 | KNO,-++ NaNO; * | 9.36 | 1.00 | 2.24
Der | i ee NaNO, | 0 | 1.00 | 4.14
F205 | = | eg |) =~ |; * NaNo,-++ NaCl | 0 | 0.74 | 4.12
|| ai ESO Ne | NaCl Oe NOEs RG
| 34.0 | 13.4 | — | 24.3. | NaCl + KCl | 0.42 | 0.24 | 5.55
12-1) 25-4 ees 58.6 | KCI + KNO; | 0.81 | 0.51 | 4.88
PO? al 104. o7sa NaCl +NaNO,; | 0.15 | 0.82 | 3.04
P,| 12.2 | — |110.7 | 82.2 | NaCl,NaNOs,KNO, | 0.35 /0.91 | 2.39
59.95 — 6.1 | 70.9 | NaCl,KCI.KNO; | 0.48 |0.53 | 3.80
TABLE 4. Solubility at 100°.
| Gee salt a 100 eae | i Sole deena,
<5 of water.“ _|Solid salt in equilibrium ”NOs (1—») Cl, mH,0.
| | with the solution. |
NaCl | KCl NaNO; | KNO; | ak NO, mH,0
5
A}39.2 | — | — | — NaCl iy | gi” 18.29
Fes 36:2 | = = NaCl + KCI | 0.51 0 | 5.83
iE) = er KCI 1.00 | 0 | 7.38
F| — | 41.6 | — | 199.0 | KCI -+ KNO; 1.00 | 0.78 | 2.20
(o) = = — | 246 | KNO; 1.00)" || 1800) 52/228
Ce — | 233.6 | 218.0} | KNO3-+NaNO, 0.44 | 1.00 | 1.13
Dike it = lie stl NaNO; 0 | 1.00 | 2.68
Poe |eeee 158-0; |- 01), 0 NaNGs = Neel 0 | 0.85 | 2.54
P,| 6.5 | — | 207.5| 194.6) NaCl,NaNOs,KNO; | 0.43 | 0.975 | 1.24
P,, 35.9 | Sel 47.0 | 192.2 NaCI, KCI, KNO, | 0.62 | 0.80 | 1.81
| |

1070

Nea Ch G7" G2 OS 18% 305), JOON OK OS LOO Kalen

The general character of the equilibrium line is not influenced by
ihe change in temperature. It appears, however, that at an elevation
of temperature the region of NaCl becomes much larger and that
of KNO, and NaNO, much smaller. Hence, P, and P, shift considerably
upwards.

P, always remains congruent saturated, P, is so also at 5°; at
50° and 100°, however it lies ontside the triangle NaCl, KCI, KNO,
and the solution is no longer congruent saturated. A solution is
formed with separation of solid KCl when NaCl and KNO, are
treated with water.

It further appears that at all temperatures the solubility of NaNO,
(per 100 grams of water) is not lowered by addition of KNO,,
as might be expected from a salt with a homonymous ion on the
ground of the theory of electrolytic dissociation, but increased. Ata
high temperature this behaviour is comprehensible, if we consider
that the eutecticum of the system NaNO,—KNO, lies at 218°. The
solubility of the eutectic mixture (49 mol. °/, NaNO, to 51 mol. °/,
KNO,) is then = whereas the solubility uf NaNO, and KNO, at
the temperatnre of 218° will still have definite values, As this

1071

eutecticum forms the terminus of the line indicating the change of
the point G with the temperature, the solution G, at temperatures
somewhat below the eutecticum will contain less water than the
solutions of pure NaNO, or KNO, saturated at the same temperature.

Uynpa’s idea that the increased solubility of NaNO, by addition
of KNO, would point to the formation of a double salt in solution
is, therefore, not confirmed.

Application to the conversion process.

Let us now see how from the figures obtained may be deduced
the most appropriate process for the preparation of potash salpetre
and let us calculate the yield of the conversion in the following
methods of working.

I. KCl and NaNO, are mixed in equimolecular quantities (say,
half a gram. mol. of each), dissolved in water and the liquid
evaporated at 100° isotherm. When the water content of the liquid
has sunk to m= 8,5 (point a in fig. 2) solid NaCl begins to deposit.
The composition of the liquid now changes in the direction ab. At
b (point of intersection with the line /’P,) the solution is also
saturated with KCl. A further evaporation would then cause KCl to
deposit as wel as NaCl so that the liquid would change its composition
in the direction 6P, (100°). As we only wish to separate NaCl, the
water content may, therefore, not fall below that of solution 4. The
solution 6 has the composition :

0,59 K , 0,41 Na , 0,59 NO, , 0,41 Cl , 2,83 H,O.

The change of liquid a (0,5 NaNO,, 0,5 KCI, 3,50 HO,) to liquid
6 and solid NaCl has then taken place according to the following
equation :

0,5 Na 0,5 K 50 | 0,59 KNO, |

0,5 CL0O,5 NO, ; = 0,153 NaCl + 1,10 H,O + , OAL NaCl

3,50 H,O 2,83 H,O
(2) ()

Let us now imagine the solution } separated from the solid sodium
chloride and cooled to 5°.

This solution lies in the diagram for 5° in the region of KNO,.
It is strongly supersaturated with KNO, and will allow this to
erystallise. Its composition then changes in the direction bac. The
most extreme solution attainable without depositing solid NaCl is
the solution c, the composition of which is 0,235 KNO,, 0,765 NaCl,
6,40 H,O.

; 70

Proceedings Royal Acad. Amsterdam. Vol. XVI

1072

As a rule, however, in order to attain this solution, a withdrawal
or addition of water wil! be necessary in addition to a withdrawal
of KNO,. The general equation thus becomes:

0,59 KNO, | ( Osis. KINO;
0,41 NaCl } =>w# H,O+y KNO,+ 2% 0,765 NaCl |
| Asses lal (@) | 6,40 H,O
If from this we calculate the values 2, y, and z, we find
i — A O1600 y = 0,464 A lp Sor

v is negative, that is to say that to the liquid 6 must be added
water so as to prevent the point ¢ to be surpassed. If this is not
done NaCl will deposit as well as KNO, and the salpetre obtained
will be impure.

In a continuous process the liquid obtained, .c, will be again
converted into the solution 6 by addition of fresh NaNO, and KCl
in which case separation of NaCl takes place.

The transformations of 6 to ¢ at 5° and from ¢ to 6 at 100° now
take place according to the subjoined equations :

0,59 KNO, {, 0,235 KNO, |
| 0.41 NaCl | + 0,600 H,O = 0,464 KNO, + 0,536 | 0,765 NaCl

2,83 H,O 6,40 H,O
and

0,235 KNO, | 0,59 KNO,
0,536 ; 0,765 NaCl ; + 0,464 KCl + 0,464 NaNO, = , 0,4) NaCl ; +
'640 H,O | | 2.83 H,O |
+ 0,464 NaCl + 0,600 H,O.

Hence, we have reverted to the initial condition, namely 1 gr.
mol. solution 6 of 100°, being 154,5 grams and during the circulation
process we have converted 0,464 grm. mols of NaNO, or 0,345 grm.
mols. per 100 grams of solution. On cooling, 0,6 mols. = 10,8 grams
of water had to be added to this solution which on raising the
temperature to 100° had again to be evaporated.

Il. If we start again from a solution in which equivalent quantities
of NaNO, and KCl are dissolved and allow the evaporation again to
take place at 100°, but the crystallisation of KNO, at 25°, the final
solution becomes c' (coinciding incidentally with P, at 25°) 0,64
NaCl, 0,36 KNO;, 5,01 H,O.

The reaction taking place when the liquid 4 is cooled, is then:
i (0.59 KNO, (0.64 NaCl
5G 0,41 NaCl ; + 0,321 H,O = 0,205 KNO, + 0,504 {0,36 KNO, ; -

a} 2063, On) 15.01 HO

0,500
For the continuous process the transformations at 25° and 100°

The yield is now 100

are expressed by the equations:
0,59 KNO, pone KNO,
0,41 NaCl ; + 0,379 H,O = 0,359 KNO, + 0,641 /0,64 NaCl ;

l2\s3 H,0 | 5,01 H,0
(0) (c’)
and
(0,36 KNO (0.59 KNO,

0,641 |0,64 NaCl ; + 0,359 NaNO, + 0,359 KCl = ;0,41 NaCl ; +
5,01 HO | lo.s3 H,O |
(c) (d)
+ 0,359 NaCl + 0,379 H,0.
Per 1 grm. mol. of solution ) only 0,859 grm. mol. of NaNO,
has now been converted into KNO, or 0.267 grm. mol. per LOO
grams of solution.

Hf. A solution in which KCl and NaNO, are present in equi-
valent quantities suffers from the defect that at the isothermie
evaporation at 100° the saturation with KCl is already attained when
only a comparatively small amount of NaCl has as yet deposited.
The point 6 lies close to a.

If to the solution is added a smail excess of NaNO, much more
NaCl can deposit at 100°. The most favourable proportion is present
in a solution which passes into the liquid P, (100°) with separation
of NaCl. As the composition of P, is:

0,38 Na, 0,62 K, 0,20Cl, 0,50NO,, 1,81 H;O
this solution must contain 0.80 grm.mol. of NaNO, and 0.62 grm.mol.
of KCI. During the isothermic evaporation at 100° it deposits 0.42
mols. of solid NaCl.

If now the solid NaCl is again removed and the liquid P, cools
to 5°, KNO, will erystallise out. The composition of the solution
then changes in the direction KNO,-—P,—d.

If no water is added, KNO, is deposited to such an extent that
the solution d is attained, afterwards, along the line dP, (5°) also
NaCl and finally in P, also NaNO,. The transformation takes place
according to the equation :

O62 Ker sy 0,12K
0,38 Na 0,88 Na
0,80 NO; }=0,575 KNO; + 0,038 NaCl +- 0,010 NaNO; + 0,377 ¢ 0,57 NO;
0,20 Cl 0,43 Cl
1,81 H,O 4,80 H,O
(P; 100°) (P; 5°)

70*

L074

If, however, water is added, the separation of solid NaCl and
NaNO, can be avoided and the solution d@ obtained as the final
liquid which has the composition 0,13 K, 0,87 Na, 0,54 NO, , 0,46 Cl,
4.99 H,O. This separation takes place according to the equation

0,62 K | (0,13 K
0,38 Na \os7 Na
‘0,80 NO, ? + 0,371 H,O = 0,568 KNO, + 0,437 ‘0,54 NO, >.

0.20 Cl 0,46 Cl
‘1,81 H,O 4,99 H,O
(P, 100) (d)

As the solution P, can be obtained from 0,80 mol. NaNO, and
0,62 erm. mol. of KCl the yield, in this method of working, is of
Dee 01568 Saab cy Gabor aa GS
NaNO, 0,800 xX 100 = 70,4°/, and of KCl 0,62

In a continuous process the final solution d must be again converted
into the solution P, (100°) which necessitates addition of fresh NaNO,
and KCl (in equivalent proportions). On heating at 100° these salts
pass into solution and NaCl is deposited. The entire decomposition

100 = 90,8°/,.

takes place according to the equation :

0,13 Kk 0,62 K
0,87 Na 0,38 Na
0.437 (0,54 NO, } + 0,563 KCl + 0,563 NaNO, = (0,80 NO,; +
0,46 Cl | 0,20 Cl |
4,99 H,O 1,81 H,O
(d) (P,:100)
+ 0,374 H,O + 0,563 NaCl.

We now have once more the original liquid P,, namely 1 grm.mol.

or 122.2 gram, whereas during the circulation process 0,565 grm.mols.
NaNO, have been transformed into KNO,. Per 100 grams of the
solution P, (100°) this is 0,461 erm.mols.
IV. If the lowest temperature we work at is not 5° but 25°
the final solution becomes :
d’ = 0.29 K, 0.71 Na, 0.627 NO,, 0.373 Cl, 3.87 H,O.

The transformation of P, (400°) into d’ takes place as follows:

0,62K | 0,29 K
0,38 Na 0,71 Na

+ 0,26 H,O = 0,465 KNO, + 0,535 (0,627 NO, ) .

(0,80 NO,

ip Cl pe Cl
1,81 H,O Sonia ll 0)
CP ALOOR) (d’)

1075

Conversely the solution d’ obtained will again have to take up
0,465 grm.mols. of KCl and NaNO, and deposit the same quantity
of NaCl in order to pass into 1 gram.mol. P, (100). In this method
of working 0,465 grm.mol. of salpetre are converted per grm.mol.
P, 100° (122,2 grams) that is 0,880 erm. mols. per 100 grams of
solution.

If we compare the yields of these four processes, it appears that,
in the continuous process, the transformation per 100 grams of
solutions ai 100° amounts to

0,345 grammolecules in the method of working |

0,267 ” ”? ” ” be) be) IL
0,461 319 ” 99 22 ) 9 II
0,380 fi oe meer 35 Li's

Hence, III and IV give the largest transformation.

This is in agreement with the practical experience in the con-
version. O. Dammpr') states about this, that, nowadays one does
not add together KCI and NaNO, in exactly equivalent quantities
but uses an excess of NaNO, so as to ensure a complete decomposi-
tion of the KCI.

We further notice that in all four processes, after heating at 100°
and removing the NaCl, an addition of water is necessary to prevent
simultaneous separation of NaCl with the KNO,. In practice, this
seems not to be done. The crude potash salpetre will, therefore,
contain NaCl-erystals which are removed by washing with cold
water.

Finally, I tender my sincere thanks to Miss J. Pa. van Rees and
Mr. R. pe Laner for their assistance and the care witb which they
have executed the analyses.

Laboratory for anorganic and physical chemistry

of the Technical High School.
Delft, January 1914.

1) Handbuch der chemischen Technologie. I, 307 (1905).

1076

Physies. — “On the critical density for associating substances.”
By Prof. J. D. van prr Waats.

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

For non-associating substances the critical density is determined
by the relation :

= Pk

28,84 RT),

We then understand by density the number of grams that 1 em*
weighs, by JM the molecular weight, and by s the factor introduced
by Sypnuy Youne, which denotes how many times the critical volume
is smaller than would be the case if the substance should have
followed the laws of Boyne and Gay-Lussac. So that s corresponds
to the relation:

Dy = 0,001293

sale Bah Ja A

Ripe

Or as p, = 4 “and Sh P= Ay to:
PRK

“RT,

Uns
If we imagine a quantity of substance present equal to J/, then
28,84
0,001293

nn.

Vy =

= 22305, and the given equation for D; becomes

duly :
AM

Di ==

Vie:

The determination of vj; is therefore sufficient for the determination
of Dy, and also, when 7% and pe are taken into account, for the
determination of the quantity s. We owe it chiefly to Sypnry Youne
that the value of D; and the corresponding value of s is known
for a great number of substances. If the observations do not allow
the direct determination of v;, one may avail oneself of other methods
to determine PD; for the caleulation of s, but not with the same
certainty, and determine the quantity s by the aid of this value and
the knowledge of J/, pr, and 7), according to the above given
formula. Now it is remarkable to how high a degree this quantity
is found the same for alle non-associating substances, and how little
it appears to differ from 3,77. Whether it really has this value for
all normal substances, whether a smaller value will exist particularly
for substances with small moiecules, I will not discuss again at

1077

present, but I will point out that the appreciably larger values of s,
which are given for associating substances by SypNey Youne, may
be perfectly accounted for with this value of s = 3,77.

Sypnry YounG (Proceedings Physical Society of Londen July 1894)
gives s=5 for acetic acid, s = 4,52 for methyl alcohol, s = 4,02
for ethyl alcohol, ete.

For associating substances a modification must be applied in the
formula for D;, which we have given above, namely in the value
of MW. Let there be present 1—.; single molecules, and 2, double
molecules, then the molecular weight present in the critical state
= M, (1 —az) + Ma, and M, being =2M,, the molecular weight
= M, (i + 2;). Hence we get:

0,001293 Pk
Soarameme 6°) eT,
which, if
dh es
RT; 8

is put again, agrees with:

ra Malte)
Vi}: OFF

The ratio between the critical density and that which would be
found when the laws of Boyte Gay-Lussac were followed,. is
therefore greater for two reasons. First because of the existence
of the quantity 2%, and secondly on account of the existence of
s>>1. And Sypney Youne’s value for acetic acid, viz. 5, is the
product s(1-+z;). And assuming again 3.77 for s, we determine

5
1+a4,= ae or 1+ 7 =—1,324. But we are only sure of this

value of a, if we may assume s—3,77 also in this case. And
though this is probable, a priori, because the value of s, deviating

8
from Ge the value obtained when 6 is put invariable, only depends

on the way in which #/ decreases, yet it seemed desirable to me
to investigate this more closely. For this purpose I have examined
the equation of state for an associating substance more accurately,
It has the form:

Ing ay

p=

v—b, v8

The numerator, whieh would be equal to Rk, 7M, d—a) + R, 7M,
may be written in this simple form, because M,Rk,7’= M,R,T.

1078

The value of 0, is 6,(4—2«)-+ 6,2; or as b,=26,, we find the
value 6, 1+) for 6, And the value of az consists of 3 terms,
viz. 1. a, (1—)’, the contribution yielded by the single molecules
present. 2. 2 2a,a(1-—a), the attraction of the single molecules
present exerted on the present double molecules and vice versa, and
3. the term. (2a,7)*. Joming these we find:

a, (l—a#+ 22)? =a, (1+2)’.
We can then reduce the equation of state to the following form:
/ayt lt

Bye b v \3
{22cm : =)

When we compare this shape of the equation of state of the
associating substance with that of the substance, when it would
contain only single molecules, we see, that with given pressure and

gal

temperature =T,, a volume V, of the associating substance

&
corresponds to a volume JV, of the single molecules, which volume
’, is (1+) times larger, and that over the entire region. Only the
value of w is variable. And as I may suppose known, another

equation, viz. (S)=0 is required for the determination of «2. But
Gh kes

at the moment we do not require the knowledge of the course of «.

A quantity J/, of a substance, consisting only of single molecules,
is in a volume v,, and a quantity J/,(1-+-2) of an associating
substance is in a volume v, (1+). The density is therefore the same

for given .p and mee in these cases. [ had expected this result,
and even pronounced it, though I may only consider this thesis as
proved by the foregoing.

Before proceeding further in the investigation of the value of s
for the associating substance, I will point out some particularities
about the critical circumstances. We find for (2 7%,)x by approximation :

8 a, (1+ <a;)° I @
(RT x) = 37 = a = 37 ae (1+-2%),
27 (6, )k wy) 27 (0, )k
and for (pre:
1 a, (1+ ax)? Is Ge

Pee = 37 Ce lpan 27)
CRE ;
and for ; the value 8 (4,),(1+.2;), and as (4,)¢ is smaller than
(Pk)a
(b,)4; about:

1079

(aT RT,
Cee ee ae)
(Pedr Ph

gal

k : rea
we find (see my preceding communication
Pk

p. 889, These Proce. Feb. 1914) the value of 10,415 much too large

For the quantity

4 Also by comparison of these values (1-+a;) might be deter-

mined, but with less certainty.

The critical temperature of an associating substance is therefore
greater than might be inferred from the molecular size of the single
molecule — but the critical pressure has not changed.

Ps So Fa a4
Let us now return to the determination of 3 for the critical

2 Ae p ae ek as
circumstances of the associating substance, and compare this with a for

the critical circumstances for permanent single molecules. For the
associating substance this value is equal to (ee If we replace
iia O
the value of (vz) by (1+ 2)v, for (px)x and (Ti), we have to
determine the value of = v,(1+.4,, and if we now substitute
‘a

(pk) for (pre, and (Tk,) +2) for (7), the required value
becomes equal to:

And now we have still to show that v, = (v,),.

If 6 is variable, the critical volume is, indeed, not 34,, but (Mobee
in which 7 is somewhat smaller than 2, or / br, when /' is somewhat
greater than 2, so that (v,)e=/b, (1-+2;). On the supposition that
/ has the same value for all substances, at least for substances with
not too small a number of atoms in the molecule, we have shown

by this that
(=) if ( =)
Tr Je flys Os

and that therefore the quantity s may be put equal to 3,77 also
for the associating substance.

The foregoing considerations are not confined to cases in which
real association exists, but may also be applied to cases in which
what I have called quasi association is found. This probably occurs
alrealy to an appreciable degree in the critical circumstances for
alcohols. In case of real association there are double and triple

1080

molecules present, the possibility of the existence of which chemistry
must be able to show by means of the construction of the molecule ;
in ease of quasi-association, however, there are local accumulations
of molecules, which may lead to the question if the cause why they
occur in a greater degree for one substance than for another, may
perhaps be found in the form of the molecules. But this question
cannot be answered with any certainty yet. Nor can the question
be answered as yet for real association why for acetic acid and for
aldehydes and perhaps. some other substances as nitriles, this asso-
ciation exists

The degree of aggregation for tne quasi-association will probably
not be the same for each of these aggregations, but to simplify the
calculation we may assume on an average the value 2 for it, which
I estimated already before at 8 or 9. It is, however, to be expected
that also the mean value will vary with pressure and temperature.
But. since we have only to examine the influence of the quasi
association on the critical circumstances here, we may confine
ourselves to an invariable value of n. Proceeding here as we did
above, we find for 1 — 2 non aggregated molecules, and 2 aggregations
the molecular weight equal to M,(1—2«-+ nz). For bk we find
b,(4—a2-+ nz) and for a, the value a, {1 —«x- nz}..

And we may write the equation of state:

RT
1+(rn—l)e a,
p= ——— — —— —.

v v J
et SET ie oats Soe

1+ (n—l)a 1+(n—1)a

ih a
Hence with given’ pressure and temperature - ==

1+(n-l)«
Uk

1 (n-1)a
would oceupy at the same pressure and corresponding temperature,

when it were not in quasi-association. The value of v=v, (1+-(n—1)a).

=v,, if we should call v, the volume which the substance

MM, :
In the first case the density is equal to — in the second to
Vv,

M (1 +(n—1)2) ;
a ea) . so of the same value. Thus we shall also find:

v

0,001293 (pk)x
— aaa M, (A+(n—1)ex] —

(RT)x
(Th)x = (Tr), (1+ (e—laz]
( pk)x = (Ph),

and

( | k)a: == (vx), {1 +(n—1) xz]

1081

(=) £5 ( tare
is es Tr 1

And so also:

According to the values given by Sypnny Youne@ s[1-+-(n—1)rp
has the value 4,52 for methy! alcohol, 4,02 for ethyl aleohol, and
also 4,02 for propyl alcohol. With s= 3.77 we found for:

Methyl aleohol 1 + (n—1)a, = 1,2
Ethyl aleohol 1 + (n—1)a;z, = 1,0668
Propy] alcohol 1+ (n—1)a, = 1.0663

‘ iN
Now for these three substances ( ) is respectively equal to:
PkJ x

Gr 2 os2eande LONG
By the aid of the value of 1 + (n—1)x;, for these three substances

my

k A
we calculate (=) or 6,, and then we find :

Pk
5,48, 7,69 and 10,03

The differences are almost equal, viz. 2.26 and 2.34, but they are
smaller than what we have found for CH, in the series of the saturated
hydrocarbons, and this seems inexplicable for the time being. Unless
we might assume that an atom C, when bound to O, is smaller
than when it is bound to H, and that besides it could also impart
this property to other atoms C to which it is bound. The value for
ethyl alcohol calculated here is, however, in perfect agreement with
the value for ether calculated in the preceding communication.
With 6 for ether equal to 13,12 follows the value 7.60 for
aleohol by subtraction of 2% 2.76. For methyl ether, for which
we found 6=7.55 before, we could now tind 5.43, by putting
OH, = 2.12. But this is possible, when C bound to O should be smaller
than C bound to C. The difference, however, is then greater than
could be expected. So that we are again confronted with the question
whether in case of quasi-association circumstances occur which we
have not yet duly taken into account in our discussion. This, how-
ever, is quite beside the subject of this communication which purposes
to show that we may consider the quantity s as entirely, or almost
entirely of the same value at least for polyatomic molecules. The

slight differences are then entirely subject to the relation given by
2

s
me_ before 7 | =a which, however, only holds unmodified for nor-

mal substances; the value of s for associating substances has been
discussed here, and a closer investigation about the value of / for
such substances would also be desirable.

1082

Physics. — “On the law of partition of energy.” V. By Prof-
J. D. van per Waats Jr. (Communicated by Prof. J. D: van
DER WAALS).

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

§ 10 bis. In § 10 of this series of communications") I have drawn
up a formula for the dissociation equilibrium of a di-atomie gas.
This formula, however, requires emendation. In the first place, namely,
the c, of the gas would not correspond with 5, but with 7 degrees
of freedom on the suppositions introduced l.c. And_ besides the
vibrations of the atom would consist of three equivalent degrees of
freedom, and there was no occasion to ascribe the ordinary equi-
partition amount to two of them (together xepresenting a rotation
round the other atom), and the amount (/ of PLANcK’s formula to
the third (the vibration in the direction of the radius vector).

To correct this we shall have to take care that the degrees of
freedom do not remain equivalent. Then it will no longer be permis-
sible to consider one atom’ as a point which moves in the quasi
elastic region of the other. We shall then introduce the following
suppositions. Every atom will have a point P, which we shall call
the pole. The line from the centre J/ to the pole will be called azvs.
There will be a quasi elastic region G round the pole. Two atoms
will now be .bound when they lie with their poles in each other’s
regions (7. The potential energy will be minimum when the poles
coincide, and when moreover the axes are one another’s continuation.

We shall introduce the following coordinates for the diatomic
inolecules :

1. The three coordinates of the centre of gravity a2, yz, 2z:. The
kinetic energy corresponding to them will be _ a.

2. The distance of the centres of the atoms, or rather the displace-
ment in the direction J/, ./, of the points P, and P, out of the
state of equilibrium (in which they coincided). This displacement
will be called 7; it will give rise to vibrations with the frequency v,

in which the potential and the kinetic energy are both equal to5 Ch

3. Displacements of P, and P, with respect to each other normal
to Jf, /,, or what comes to the same thing rotations of the axes
out of the position 7, J/,. These coordinates will give rise to rotative

1) These Proc. XVI, p. 88

| O83

vibrations. In agreement with Rurnerrorp, Perrin, and others | shall
assume the moment of inertia of the atom to be very small} even
in comparison with ma® (m= mass, a = radius of the atom). Then
the frequency of this rotative vibration will be great compared with
py. Im connection with this we shall put the energy of these vibra-
tions equal to zero, and entirely disregard possible atomic rotations.

4. The rotation of the molecule. Of this we may assume for all
the cases of equilibrium that have been experimentally investigated
that they represent two degrees of freedom, which present the equi-
partition amount, whereas the rotation round J/, M/, practically has
an energy zero. We shall represent the position of the axis of the
molecule by the aid of the angles ¢ and indicating the longitude
and the latitude. ,

Instead of equation (19) p. 88 loc. cit. we now find for the
number of dissociated pairs of atoms:

Ep

T= ZG G fe 6 du, dy, dz, (m) du ,dy dz, x<

x« te drde,(m) dx, dy ,dz., == Woe ma. (aise)

é

0

— 2 ‘ a
== N7¢ 4(200,4) aOX (22m, ) :

For the number of bound pairs of atoms we find, representing
the moment of inertia of the molecule by J:

ive)

1 Ep fa JT

in SINE e 6 Yrrv)dedydz(m, ao m,)dedy de S<
LO Re Sy Fo
dr — dr sin® adadgM*dads. =
m, +m, » (19%a)
intl -
79 a) 3 h 9
== INE \2ar (m, +-m,) B}'/2 rare An x 22 MO
Sey Re)
p : ame F
For «, depends on 7 through the term ~-———— r*, which term

2m,+m,
we shall call «,,. In connection with this equation (18) loe.eit. must
now be written as follows:

ee sie aya Wa Sn DLO. sag h
e 6 4 (rn vp) ——— dr dr = ——_—__
. m,+m, vh

This gives for the equilibrium constant: ;

al avi a)
Dae 0 Dio NAW | he 1 0 p
—— =e <= _ xX . (20
Ny (| Wie h ESS Qa (204)

§ 18. Zero point energy and chemical binding.

In the above given formula PLanck’s later supposition concerning
the existence of a zero point energy has not been taken into account.
We shall now examine some consequences of this supposition for the
chemical phenomena. In the first place we shall show that according to
this supposition the entropy of a number of particles does not change
at the absolute zero point, when they pass from a binding in which
they can vibrate with a definite period into another combined state,

in whieh they have another period. For this purpose we shall make
use of BoirzMaNn’s quantity H, which we shall represent as follows:

i — fri(e wsasdya: dudydez.

So we think here again of a three dimensional vibrator with three
equivalent degrees of freedom, though this case probably never
occurs in reality. If we had taken a linear vibrator, this would
have come to the saime thing. But then we should have had to
speak besides of vibrations, also of rotations of the molecule, which
would have rendered the question somewhat less simple.

According to PLanck’s supposition the value of # for 7=0 is
constant for an energy smaller than »/, equal to zero for a larger
energy. Let us put:

m® dudydz daedydz = do,
and

fre dadydz dadydz =
52 vh
then for 7 = 0:

{ Fdo = r{ dw = FG = N,
xv =
when NV represents the total number of particles, and further:

H = (FP) | Fdo =F). N = Nil(N)—1(@)}.

We may write for G:

1055

T= dz, dx, dv, dx, dv, dz,

e<vh
when we introduce a /m— 2,, y VA Hie zVm= Le Bl VAY meth
yV f =«, and z/f =2,, so thate = 2,’ + 2,7 +2, +27 + 2,?-+2,?.
The integral occurring in (, therefore, represents the content of
a sixdimensional sphere with a radius |/vrh, and is therefore pro-

: Hana : 1 if
portional to (v/)*’. Bearing in mind that » = >— Va we see that
ast m
G and with it also H, becomes an absolute constant.
If we assume for a linear vibrator that besides vibrations with
“ 4 h
a frequency pv rotations occur with a frequency »' = — mr’ it
ao’ J

appears here in the same way that G and H become absolute

constants.

Hence we see that on these simple suppositions PLANCR’s supposition
about the zero point energy directly leads to Nurnst’s heat theorem.

As known Pianck formulated Nernst’s theorem by assuming that
the entropy remains finite at 7’— 0, and does not become — o, as
it would have to do according to the older theory. According to
the older theory, e.g. according to Borrzmann, one would have to
come to the value —- «, because at 7’=—O the molecules would all
have a velocity zero, and there would, therefore, he only one
possible distribution of the points of velocity in the diagram of
velocity. At every higher temperature there would be o many
velocities possible for every molecule; there would therefore be
infinitely many possible distributions of the points of velocity. The
probability at higher temperature would therefore be a. times as
great as at 7’=0, which leads to an o difference of entropy.

It is interesting to observe how the two suppositions introduced
by Puranck into physics evade this difficulty and make the entropy
difference finite in the two only ways possible. The infinite entropy
difference could namely be evidently evaded in two ways; namely
1. by assuming that there is a finite number of distributions of the
points of velocity also at high temperature, and 2. by assuming that
there are infinitely many also at 7’—0O. The former hypothesis is
that of the energy quanta, the second that of the zero point energy.
Each of these two suppositions leads to a finite relation of the number
of possible distributions at 7’—O and at 7’ > 0, and hence to a
finite entropy difference.

Let us now examine the distribution of the energy at higher
temperature. We shall continue to assume that a number of mole-

1086

cules will possess an energy < vf, and that for them every value

of the energy is equally probable. So in this region the chance that

the energy lies between ¢ and «- de will be represented by #’(p) de.

In the region where ¢>r/ I shall continue to assume that the
é

function is represented by e 6 y(ev) dé*). If we now put:

vh 5 é
Taf P@)de+ foo 7 y(n) as ot). eee
0 vh
the equilibrium constant of a chemical conversion is represented by:
Ase
Viggen (20)

In this Ae represents the difference in potential energy which
would occur when the substances passed from the compounds of
the lefthand member of the reaction equation into those of the
righthand member. In order to obtain the energy amount Ae then,
it would however be necessary that the atoms in the compounds
always occupied the positions of minimum potential energy, so in
the centres of the quasi elastic regions. /// represents a fraction with
the product of the quantities /, referring to substances in the lefthand
member in the numerator, and with that in the righthand member
in the denominator. The equation is evidently nothing but a general-
isation of (20a), in which besides the /’s are determined in agreement
with the supposition of the zero point energy.

Now

HK hewn etl ae é
16 eth rag es )

On the other hand the law of the equilibrium change requires:
T

apr >| C.dT

wees Q = EIU Fell. (22a)
dé 0° G? . 3
Further we have:
Q, = (As + 2 47h) oe

1) Besides in my previous communications this function had~ already been
introduced by Enrenrest, Ann. d. Phys. IV, 36 p. 91, Ann. 1911, which paper
I have not sufficiently taken into account in my previous considerations; the same
refers to Porncars’s paper, Journal de Physique theor. et appl. V serie II p. 5.
Ann. 1912.

1087

tf,
ee eS, $3(Car SS) ee aa)
I do Be

In all these summations the quantities must have the sign + or
— according as they relate to the righthand or the lefthand member
of the reaction equation. The equations having to hold for every
chemical reaction, independent of the values of the »’s, we shall
be allowed to omit the signs in (28a), and write such an equation
for every coordinate separately.

We then get:

vh é

Ak e F (Ov) de + | ce 7 y(e,v)dé
ise Z avis Aue 2 Oe
i I dé
or
Come vh es é
(is, ae Seger.) ON eee "ene
5 (wh)? F(O,v) b fe 7 ¥(e,v)de = O° | ee de + Pe e 7 ¥(8,v) de
vh 0 yh
or
TON Oak
2 te ae) ee
from which follows:
vh
jC) Oe a an =. Mea ey'

It is evidently not impossible to assign such a value to the C

é
that #'(O,») and e O + (ev) continuously pass into each other at
more than a single temperature. In general a discontinuity will occur
in the function of probability at ¢—r/. I do not know a way to

determine C. The value (¢,r) 5 suggests itself most naturally.
&=vh

Then the function of probability becomes continuous at 6 = o ,

which is in accordance with the fact that at high temperatures the

deviations from classical mechanics become smaller. With this

value of C we see that the number of molecules having an energy

slightly smaller than vf, is greater that the number having a some-
: hr

what greater energy. The ratio is e279. This is in harmony with
Pianck’s theory according to which for vibrators which are absorbing
energy of radiation, only a part continues to absorb when «= vh
(i
Proceedings Royal Acad. Amsterdam. Vol. XVI.

1088

is reached, and passes therefore to the group for which s>yr,
whereas another part emits all the stored energy. For the chance
of emission we find another value than PLanck. This is not astonishing
as we assumed that for «> r/ the function of probability would be
continuous, whereas according to PLanck it exhibits new disconti-
nuities at ¢ = 2rh ete. At all events we see that PLANck’s hypothesis
concerning the zero-point energy can only be reconciled with the
thermodynomie law of the equilibrium change, when the function
of probability shows a discontinuity at ¢«—vh, of entirely the same
nature as had already been assumed by PLanck.

In conclusion we will calculate /, as this quantity occurs in the
formula for the equilibrium constant. Integration of (23e) with

i vh 1 f
Us — + — ph yields:
vh 2
eCreal
1 wh
he 29
f= ee
vh
eye
This expression differs from the value which we found without
1 vh
; / =e)
zero-point energy, and which we shall call /’ by the factor e ;
Hence we may write (200) in the following form:
aS: eee
-—— +
Kira ute! , So CLE
1
And Q, being = (Ae+ 2 = rh), we find the same expression

as without zero point energy, since then Q, = Aes, and we may,

therefore, always write:

Q,
C= e 6 ETS
Chemistry. -- “A new hydrocarbon from the pinacone of methyl

ethylketone’. By Prof. P. van RombBurcu and Miss D. W. WeENsINK.
(Communicated in the meeting of March 28, 1914).

When studying the action of formic acid on this pinacone this
seemed to take a course quite contrary to expectation. Whereas in
this reaction the ordinary pinacone is almost completely converted

1089

into pinacolin, a considerable quantity of a hydrocarbon is obtained
here in addition to a pinacolin. A formate of the pinacone could
not be isolated.

If we treat pinacone from methylethyiketone with an equal weight
of 97°/, formie acid, the liquid, particularly on warming, turns a
beautiful red colour and after about a quarter of an hour's heating
in a waterbath, the homogeneous mixture separates into two layers,
the upper one of which is nearly colourless. The bottom layer which
has a dark red colour gives, when diluted with water, a pale coloured
supernatant layer. The united layers were washed with water and
dried over potassium carbonate. On distilling at the ordinary pres-
sure up to 150° a liquid was obtained which proved to consist
mainly of the pinacolin (CH,), .C,H,.C.CO.C,H,.

The residue was distilied in vacuo when as main product was
obtained a pale yellow viscous liquid b. p. 130°. By fractionating
over metallic sodium a colourless distillate with an agreeable odour
was finally obtained. d1°> = 0.8741; n 135 = 1.4864. MRp = 72.3
calculated for C,, H,, 72.9.

The elementary analysis gave: C 86.96, 87.16; H 13.17, 12.82°/,.
Calculated for C,, H,,:C 87.27, H 12.72 °/,.

The determination of the molecular weight (by means of the
lowering of the freezing point of benzene) gave 216.5 and 207;
calculated for C,, H,, 220.

HerscHMann ') found that by the action of concentrated sulphurie

oO;

acid at O° pinacolin occurs only, but on heating with 5 °/, sulphurie
acid was formed, besides pinacolin, also a hydrocarbon C, H,, b. p.
117°—121°, which, as noticed by us, is converted on heating with

formic acid into a dimeride identical with our hydrocarbon C,, H,,.

Oe A hCHs CH, CH,

| | |

CHigte(OHa. «22s o0 ACH ACE

| | Seo || || — (C, 15 De Re
HOCH—— CHOH CH — CH

| | | |

GH) fC, CH, CH

One might imagine the structure of the hydrocarbon C,, H,, to
be like that of an octomethyleyclo-octadiene :

1) Monatshefte 14, 233 (1893).

1090
CH,CH, CH, CH,
(bn—dn—t
Aap ide creiiae

Ge veezao le x
|
CH,CH, CH, CH,
or in connexion with the researches of Lrsepry ') on polymeric
hydrocarbons, like:

| CH, CH, CH,
C= slr
GH, UZ = (SSS erg

ba

(oral
(CERIO ACSI) 31,
CH

CH,

In order to elucidate the structure we have already made a great
many experiments which, however, have not yet led to definite results.

If the hydrocarbon is treated with bromine there always takes
place, besides the addition, an evolution of hydrogen bromide even
in very strong dilution and cooling to —40°, and we did not
sueceed in isolating a well-defined compound. An effort was made
to reduce the dimeride with sodium and aleohol, but it did not take
up any hydrogen under those conditions. Reduction with hydrogen
under the influence of platinum or palladium was also applied by
us in vain, up to the present.

Oxidation with potassium permanganate has also failed to lead to
positive conclusions. Experiments intended to attain the desired result
with ozone are in progress.

Utrecht. Org. Chem. Lab. University.
Chemistry. — “1:3:5 Hevatriene.” By Prof. P. van Rompuren and

Dr. P. Murr.
(Communicated in the meeting of March 28, 1914).

One of us (v. R.) prepared in 1905, with Mr. van Dorssen,
the above hydrocarbon by heating the formate of s-divinylglycol.

rom this could be obtained by addition of bromine:

1. a dibromide C,H,Br, that proved identical with the. s-divinyl-
ethylene bromide prepared by Griner. *)

) Journ. Chem. Soe. 104 Abstr. 1285, (1913).

) Ann. d. Chimie et de phys. (6) 26, 367 (1892).

1091

2. a tetrabromide C,H,Br, also already described by Griner of
the formula CH,—CH-CHBr-CHBr-CHBr-CH, Br.

3. a hexabromide C,H,Br, having the formula of a1:2:3:4:5:6
hexabromohexane.

Addition of 6 atoms of hydrogen by the SaBatipr and SENDERENS
method gave normal hexane.

Although it was thus shown with certainty that by the process
employed the desired unsaturated hydrocarbon was obtained, there
remained some doubt as to its absolute purity, for instance, because the
physical constants of the different preparations did not quite agree.
{{ was, therefore, desirable to make efforts to get at a method that
could yield this compound, sc important from a theoretical point of
view, in a perfectly pure condition. After many tedious experiments
we have at last succeeded.

First of all we tried to gain our object by modifications in the
old method; after many experiments the following modus operandi
was found to give the best results.

s-divinylglycol is heated with an equal weight of 99°), formic
acid for half an hour at 105°, the excess of acid is then distilled
off in vacuo at 60° and the mixture of formates is decomposed
rapidly by heating at the ordinary pressure at 160°—220°. The
upper layer of the distillate is washed with water and distilled in
an atmosphere of carbon dioxide or hydrogen, so as to avoid oxida-
tion, up to 110° and the liquid obtained is dried over fused calcium
chloride. Owing to the modifications introduced the yield of hydro-
earbon is considerably larger and amounts to 40°/, of the glycol
used.

A careful fractionate distillation of the hydrocarbon obtained did
not, however, give even now a product with a constant boiling and
melting point.

Experiments made to purify the preparation by freezing, although
rising the initial fusion range’) could not be continued as the quantity
at disposal was not sufficient. Hence, another method of preparing
had to be looked for.

It was to be expected that by the action of dehydrating agents
on hexadiene 1.5-ol 1.4 the desired hydrocarbon might form. This
alcohol, obtained by Mr. Le Hevux*) according to Fourntmr’s method,
was treated with potassium pyrosulphate or pbthalie anhydride.
From 80 grams of the alcohol could be obtained by heating with
5—10 grams of potassium pyrosulphate 24 grams, and by heating

1) The initial fusion traject was —55° to — 470.5, the final — 47°.5 to —339,

This Proceedings, Febr. 1913, p. 1184.

SS

9

1092

with the theoretical quantity of phthalie anhydride 30 grams of a
product boiling below 100°, which, however, on continued purification,
yielded the same amount of hexatriene. The boiling point (80°.3—82°)
as well as the melting point (—34°.5 to —29°) was higher than
that of the hiydrocarbon prepared by the first method ; a pure product
could, however, not be obtained from the quantity at disposal.

Hence, we had recourse to the preparation from a crystallized
substance namely from the above mentioned dibromide C,H,Br,
prepared, according to Grinnr, by the action of phosphorus tribromide
on s.-divinylglycol. The bromide purified by reerystallisation gives,
on treating the boiling alcoholic solution with zine dust, a good yield
of pure hexatriene. This was placed over fused calcium chloride so
as to remove water and alcohol. After fractionating in an atmosphere
of carbon dioxide or hydrogen a liquid was obtained (b.p. 80°.5—82°
at 765 m.m.) which solidified in a mixture of ice and salt and
melted at —11°.5 to —9°.5 . di6" = 0.7855. nd}? = 1.5150.

MRp = 32.82. Calculated for C,H,/3 = 28.5.
For the specific exaltations were found:
Pps bl

Esp == 5a)
ES, ae ES, 11265 13625},

7 ») eS GytG = AN) .07/
Bs, — Esq = 2.23 = 152"/,

As will be noticed, the specitic exaltations of the refraction reach
a remarkably high figure.

If we allow bromine to act on a solution of the pure hexatriene
in carbon tetrachloride or carbon disulphide, s-divinyletiylenebromide,
m.p. 87°, is obtained quantitatively.

Hexatriene gets readily polymerised, particularly on warming. As
in the above mentioned preparation of the hydrocarbon a fractional
distillation at the ordinary pressure was applied for the purpose of puri-
fication, there was a chance that in this operation the distillate
also might be contaminated with the polymeride.

Therefore, a new supply was prepared which was dried, first
over calcium chloride and then over potassium hydroxide‘); it then
exhibited the following constants: m.p. =—11°; b.p. =80°—80°.5
(at 755 mim. idee —— (Rice We == DABS MIRine==to2-O8

After a distillation in vacuo at which the hydrocarbon passed over

1) If the hydrocarbon is pure, the KOH remains uncoloured. If, however, it
contains oxidation products, the latter turns brown at the surface.

1098

at the temperature of the room and was cooled in a mixture of solid
carbon dioxide and alcohol it gave the following results: m.p. —=—10°.5 ;
A 017105 en's on 2.;)M Rp = 32.7:

After standing for a week over potassium hydroxide this liquid
was again distilled at the ordinary pressure. Now was found :
m.p. —11° to—10°; d = 0.7396 ; nt P5167 MR 320

From this we notice that the distillation at the ordinary pressure
exerts no influence on the properties of the hydrocarbon so that the
above-cited constants may be really taken to be those of pure
hexatriene. The results mentioned here briefly, will be communicated
more fully elsewhere.

Utrecht. Org. Chem. Lab. University.
Chemistry. — “On dichloroacetylene’. (A warning). By Prof. J.
Borseken and J. F. Carritre. (Communicated by Prof. A. F.
HoLLEMAN).

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

Our object was to prepare di-trichlorovinylketone from thrichloro-
acrylic acid by elimination of carbon dioxide and water.

It was, therefore, first attempted to effect this decomposition by
a eareful dry distillation of the barium salt :

(CCl, : CCl.COO), Ba = Ba CO, + (CCI, : CCl), CO.

In a provisional investigation it appeared however, that a strong
charring took place, whilst the barium was left in the form of chloride

When the experiment was repeated much carbon dioxide was
evolved and further a gas with a disgustingly sweet odour, which

formed a strong nebula in contact with the air.

This nebula formation was coupled with a decided chemo-lumini-
ferous phenomenon, so that we suspected that the most simple carbon
chloride dichloroacetylene had formed according to the equation.

(CCl, : CCI1.COO), Ba = BaCl, + 2 CO, + 2C,Cl,

As we had to take into account the possibility of dealing with a
very explosive compound, a quantity of only one gram of the barium
salt was slowly heated in a dry current of hydrogen. After first
passing the gases through an empty suction tube, in which a fairly
large quantity of bye-product (with high b.p.) was retained, they
passed through a similar tube placed in a Dewar vessel in which
the temperature was brought to — 70°.

In this remained a little of a colourless, solid substance which
melted below — 50° to a mobile, colourless drop of liquid.

1094

In order to prove that this contained C,Cl, chlorine was passed
without opening the apparatus; after this had been able to act for
some time at — 50°, the tube was brought to the ordinary temperature;
C,Cl, was left behind, which by its odour and sublimation phenomena
was identified with the pure substance from the collection.

If the gas diluted with hydrogen was allowed to pass through a
layer of water into the air, the same phenomena were noticed as
with liquid hydrogen phosphide; each bubble coming into contact
with the air forms a nebulous ring.

In a second experiment we started with three grams of barium
trichloroacrylate; in the decomposition a more considerable secondary
reaction took place so that, finally, the quantity of C,Cl, collected
was estimated not to exceed half a gram.

When, however, the apparatus was removed, this quantity exploded
with the fatal result that one of us (Carriere) suffered a very serious
injury, to the eye.

Hence, dichloroacetylene is decidedly much more dangerous than
dibromoacetylene *), because it decomposes with explosion by slight
mechanical influences even without exposure to the air.

We have discontinued our researches in this direction and think
we must warn our colleagues against this exceedingly treacherous
compound.

The decomposition of barium trichloroacrylate is in agreement
with that of the p-halogenates in general where the elimination of
the metallic haloid salt must be considered as the first phase of
the reaction,

It is remarkable that also in the case of chlorine atoms combined
with unsaturated carbon, this tendency to form salts is so great that
an energetic compound such as dichloroacetylene can he formed in
considerable quantities.

Let us summarize the properties of dichloroacetylene :

It is a colourless gas with a disgustingly sweet odour. *) Ina very
diluted condition it exhibits chemo-luminosity ; in a somewhat more
concentrated form in admixture with H, and a little CO, it takes
fire in the air.

1) Lemoutt C. R. 186, 55 (1903); 187, 1333 (1908).

2) It is probable that Dr. Prins has already observed this substance in the
decomposition of one of the higher condensation products of CH Cl with C? Cl H;
there was then also formed from a hydrogen-free carbon chloride compound under
the influence of an alkali, a gas exploding in contact with the air having a
disgustingly sweet odour. (Dissertation H. J. Privs Delft 1912 p. 160—162).

1095

It may be readily condensed to a colourless, very mobile liquid
which solidifies below — 50°.
50° with chlorine

Liquid dichloroacetylene rapidly combines at
tot C,Cl,.

The gaseous compound, at least if diluted with H, or CO,, does
not seem to be dangerous, but the liquid substance explodes with
extreme violence.

Delft, 12 March 1914.

Chemistry. — “On the Isomorphy of the Ethylsulphates of the Metals
of the Rare Earths, and on the problem of eventual morpho-
tropic relations of these salts with analogous salts of Scandium,
Indium and Beryllium.’ By Prof. F. M. Janene. (Communi-
eated by Prof. P. van Rompurau.)

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

§ 1. In the following paper is given a short review of a comparative
study of crystallographical analogies within the series of the Hihyl-
sulphates of the metals: Yétriwm, Lanthanium, Cerium, Praseodymiuin,
Neodymium, Samarium, Europium, Gadolinium, Dysprosium, Tha-
lium, Erbium, Neoytterbium, Beryllium, Scandium, and Indium; and
also of some Acetylacetonates of the three last metals. These investiga-
tions were all executed, during the last two years, by means of
very small quantities (about 100 to 300 m.G.) of the oxides, which
for this purpose were kindly lent to me in the possibly highest
degree of purity, by the scientists: Professor G. Ursain in Paris,
Sir Winri1aAM Crookers in London, and Professor C. James in Durham,
New Hampshire (U.S. A.). It is an agreeable task to me to thank
the above mentioned chemists here once more for their kind help
in this matter. The complete description of these investigations will
be given in a full paper, which I hope to publish elsewhere ') within
a short time, with all the data and necessary figures.

§ 2. This research was started with respect to the question,
if it would be possible, to find out any relation between the changes
of the erystallographical parameters, which are caused by the sub-
stitution of the trivalent atom J/e- in the molecule:

Me, SO, : C,H,), + 18 0,0,
by any other atom of the series of elements here considered, and
between the changes in molecular weight, which are simultaneously
produced by this substitution. That im general a parallelism of the

1) In the: Recueil des Travaux d. Chim. des Pays-Bas, (1914).

1096

morphotropie influence of a substituent and its atomic weight or
atomic volume, may be supposed, is sufficiently proved by the
investigations of Mr. Turron on the similarly constituted salts (sul-
phates, selenates, ete.) of the alcali-metals. Possibly it could be stated
that within the series of the metals of the rare earths, whose atomic
weights differ from each other much less, a quantitative relation of
this kind would be found more easily than in the case of the
alcali-metals, or im that of other homologous elements of the same
group of the periodic system. Moreover, a more detailed investigation
of the molecular volumes of those crystallized salts would perhaps
give an opportunity to get some information about the parallelism,
— not yet sufficiently proved, but too many times advanced, — between
the changes of the atomic weights and those of the atomic or
molecular volumes of the rare earths or their analogous compounds.
Considerations of this kind are moreover closely connected with the
already often discussed problem, how. far the element scandium so
widely spread, but isolated only in small quantities and studied too
incompletely, must be placed among the metals of the rare earths *);
finally if could in my opinion hardly be considered superfluous, to
compare the crystallographical character of the element beryllium
once more with that of the metals of the rare earths, in connection
with the doubt upon this matter, which has existed during a long
time with some erystallographers and chemists. *)

§ 3. The choice of the etbylsulphates for these purposes was
suggested by the fact, that notwithstanding a number of tentatives
with other inorganic and organic acids, till now no derivatives of
the above mentioned oxides were obtained, which at the same time
fulfilled the following conditions :

a. To have the same number of water-molecules, if hydrated,
through the whole series of metais.

6. Not to be efflorescent in dry air, nor to be hygroscopical.

c. To give crystals, whose faces enabled very accurate measure-
ments of the angles, and whose angles showed a sufficient constancy
with different individuais of the same salt.

So these conditions are not fullfilled : with the beautifully crystallized
double nitrates of the bivalent metals Zn, Co, Ni, Mn, and Mq,
which always show curved and dull. faces, or at least will get them
very fast; nor with the platinum double-cyanides or with the
may G. Ursaty, Journ. de Chim. phys. 4. 32, 232, 321. (1906); UrBatn et
Lacompe, Chem. News 90. 319. (1904); W.,Brinrz, Zeits. f. anorg. Chem 82.
438. (1913); R. J. Meyer, Zeits. f. anorg. Chem. 86, 257. (1914).

2) Depray, Ann. de Chim. et Phys. (8). 44. 5. (1855); Wyrousorr, Bull. de
la Soc. Minér. de France, 19. 219. (1896).

1097

sulphates, which differ, like most other salts, in their content of water
of erystallisation with the successive elements of the series; ete.
Thus my choice was finally fixed on the ethylsulphates ; of these
only the salts of thuliwm and of neo-ytterbium were somewhat difficult
to obtain in a measurable form, because of their high solubility and
their tendency to form supersaturated solutions. However finally also
these salts were obtained in a well developed form.

From the borrowed salts (double nitrates, oxalates, bromates, ete.)
first the pure oxides were prepared, then the sulphates, and these
finally decomposed in aqueous solution by means of bariumethylsulphate
at a low temperature. To avoid any strong elevation of temperature
as much as possible, the solution was evaporated in vacuo or at a
strongly diminished pressure on the waterbath, at temperatures of
22° till 34° C; first the solution must stand for a long time to make
the finely divided bariumsulphate precipitate, and to separate it from
the mother-liquor by decanting and filtration. Only in this way it
was possible, to avoid an admixture of sulphate to the ethylsulphates,
formed by hydrolysis of these.

§ 4. The specific weights of the crystallized salts were determined
with the utmost care; I gratefully wish to remember here the valuable
assistance of Mr. M. J. Suir, cand. chem., in this tedious work. As well
by the pyenometrical method, with orthochlorotoluene as an immersion-
liquid, as also by means of heavy liquids (floating-method), we obtained
data, which were in full accordance with each other ; it need hardly
be said, that this was no easy task, regarding the very small quan-
tities of the salts at our disposal.

During this work we found, how far even the purest products
of the rare earths, sold in commerce (pi Hain, Dr. Drosspacn) for
scientific purposes, are suill removed from the spectroscopical purity
of Ursain’s preparations and those of the other mentioned scientists.
The following determinations of the specific weight may give an
impression of this :

Element : Specific weight of Spec. weight of the best

the pure salts : products in commerce :
Lanthanium 1,845 L801
Cerium 1,930 1,839
Praseodymium | 1,876 1,848
Neodymium | 1,883 1,866
Samarium 1,904 1,884
Gadolinium 1,919 1,905

Vtterbium 2,015 1,857

.

1098

§ 5. The following values for the atomic weights of these elements are
adopted in this paper: Vitriwm: 88,6; Lanthanium : 139,0 ; Cerium:
140,25; Praseodymium: 140,6; Neodymium: 144,83; Samarium :
150.4; Huropium : 152,0 ; Gadolinium : 157,38; Dysprosim : 62,5;
Exybium : 167,7; Thulium: 168,5; Neoytterbium :172,0; Beryllium :
91: Indium: 114,8; Scandium: 44,1.

Of each salt as large a number of crystals as possible was inves-
tigated; as many erystals possess more than seventy faces, the total
number of measurements is a very considerable one.

Highly remarkable is in first place the extraordinary variability of
eternal aspect of the crystals of these yet strictly isomorphous com-
pounds. Every substituting element seems to give some preference
to a special aspect in most cases, and under apparently the same
circumstances, although eventually a// the observed forms can be
present in a// cases; in the paper to be published at a later period
this fact will be discussed in detail.

The crystals are hevagonal; a combination of the predominant
forms and a stereographical projection of them, are reproduced in
fig. 1 and 2.

Stereographical Projection of the observed
erystal forms.

The exact determination of the class of symmetry was only possible
by combination of angular measurements and of Rén?eEN-photography’).

1) 1 was helped in the kindest manner in this work by the valuable assistance
of Prof. Haca and Lecturer Dr. ORNSTEIN, both of this University.

me r
ae Se ad
ea! 1
, i

Vas 2

=! :
| oh ah,
ilies a
- *" at ie 2 | | | |
2). ;
7"

mh ca Hi

1099

For the measurements of the angles enabled us only to state, that
a hexagonal or dihexagonal symmetry was present; the ROnrGEN-
pattern however, obtained by radiation through acrystalplate, cut perpen-
dicularly to an optical axis, showed immediately, that no binary
axes of symmetry, nor vertical symmetry-planes were present. There-
fore the true symmetry of the crystals could only be that of the
hexagonal-bipyramidal or of the hexagonal-pyramidal (hemimorphic)
class. The external aspect of the crystals could bring no decision in
the choice between these two possibilities ; the fact, that the faces at
both ends of the vertical axis showed always about the same degree
of development, could perhaps be considered as a very weak argu-
ment for the view, that no polarity of the vertical axis were really
present, and thus a single horizontal symmetry-plane must necessarily
exist. However the figures of corrosion which were obtained on the
faces of the prism (1010) by heating for a short time the crystals

Fig. 3.

Stereographical projection of the diffraction-pattern of the Erbium-aethylsulphate
(1 opt. axis) obtained by Ronreen-rays.

1100

of the ytiriwmsalt in their saturated mother-liquor, showed without
any doubt, that such a horizontal plane of symmetry is really
present. Thus all these salts belong to the hexagonal-bipyramidal
(bemiédric) class of the hexagonal system.

A stereograplncal projection of the pattern, produced by the
RonreEn-rays (erbiwmsalt), is reproduced in fig. 3; the differences
in intensity of the dark spots on the photographic plate, are
indicated here by means of larger and smaller dots. *)

Commonly the crystals are tabular parallel to two opposite faces
of the vertical prism; they make thus the impression of hexagonal
plates. The most interesting data are summarized in the subjoined
table.

§ 6. In the first instance this review of the obtained dates shows
clearly, that all these salts of the metals of the rare earths belong
to a series of perfectly isomorphous substances. Moreover it has been
proved by a great number, — i.e. several thousands, — of exact
measurements, that the deviations of the angles from the main value
with the different individuals of a same crystalspectes, must be con-
sidered to be of the same order as the deviations of the main values
of corresponding angles with the successive terms of the whole series.
Thus we can consider all those salts to have practically the same crystal-
form, whose parameters oscillate about the most probable main value:

a:¢=1:0,5062 + 0,0012

with deviations, which cannot be considered as typical for each kind
of crystals separately. Therefore the differences of the molecular
distances in the corresponding space-lattices of these crystals, can
be only of the same order, as the differences in molecular volumes
with the successive terms of the series. It must be considered a
rematkable fact in this respect, that, although the specific weights
of these salts are, generally speaking, gradually increasing with the
increase of atomic weight of the rare earth-metals — (with the
exception of the erbium-salt, which was prepared from not highly
pure oxide, and of the cerium-salt, whose isolated position in this
respect seems to be a real fact) — these molecular volumes, and
just so the calculated topic parameters, show a very evident perio-
dicity.*) This fact, which may be graphically represented in fig. 4

1) The stereographical projection is made upon a circular base, with a radius
of twice the distance between crystalplate and RGnreen-tube.

)

2) These topic parameters are calculated for the regular triangular prism

1101

and 5, may lead to the suspicion, that the atomic volumes of the

mM
=}
&
D =.
4 ae NYb
2,000] =< ¥
or Thu.”
1.975] de. 82
iso] ”

8 85 90 95 100 105 NO M5 120 125 130 135 140 145 150 155 160 165 170 175 180
Atomic weights.

mutually substituting elements in these salts, can no longer be con-
sidered as gradually increasing with the increase of the atomie weights
within this series of elements, if no better proof of this view is
brought forward than has been done up to this date. Possibly more
detailed accurate research with spectroscopically pure materials, and
extended over all terms of this remarkable group of elements, would
prove with full evidence, that the atomic-volume-curve of Loruar *
Meyer and MENDELEJEFF possesses also a single or double periodicity
within the group of the rare earth-metals.

That this fact was not shown previously in any clear way, may
be caused by the extreme difficulty of getting these elements in an
absolutely pure state. For they will form within the whole series
solid solutions with each other in all proportions; and as is well-
known from RpeteGeErs’ investigations, the specifie volume of such
mixed crystals will be in general continuously variable with their
chemical composition, and will be calculable in most cases from a
linear function cf this composition and the specific volumes of the
pure components.

(Bravais) as “unit” of the space-lattice, from the relations:
V 1s
¢ (Ve?)'s

4% => and » = ——_.,
"~~ 2 sin 60° sin 60°

1102

ee!
6100} ©
i
ie)
2s
6650) b> ;
: fr
‘ge! La "
6.600 oarit fal
i Nd sm Gd) Thu
iPr Eu Dys fr?
6.650 if nt
it bs
6.500 Ze ce- gud ; |
we Fr Sm ys |
: " ‘Thu
6450] Yt 3 i
Ce NYb
6.400
Fig.5.

443
139 1406 152 162.5 168.5
6.350 140,25 1504 157,3 167,7 172

80 90 100 110 120 130 140 180 160 170 180

Atomic weights

And even if this is not always the case, it must be clear, that
with chemically not quite homogeneous material, there will be
found quantitative data, from which must follow other relations
between different properties, as they would follow from observations
with absolutely pure substances.

Moreever the available data considering specific weights of corre-
sponding derivatives of the rare earth-metals, are highly rudimentary
and not very trustworthy, as will be shown later in the full paper
on these investigations. With respect to the available data it can
hardly be justified to suppose a general parallelism between atomic
weights and atomic volumes within this group of homologous elements.

[ may remind readers of the fact, that in a somewhat different
train of thought Mr. Urparn has shown just such a kind of periodicity
to exist with his spectroscopically pure oxides, with respect to some
other properties. He was able to show‘), that the coefficients of
magnetisation jw of the oxides of these metals, determined after the
method of Curte and Crennveat, and compared with the value of
uw of pure cobaltsulphate: CoSO,, 7 H,O,.were (X 10-):

for : Nd Sm Eu Gd Tb Dys

33,5 6,5 33,5 161 237 290
while these numbers are decreasing continually, passing holmiwm with
a not yet known, but probably very great value of mu, over erbium,

!) URBAIN el JANTSCH, Compt. rend. 174. 1286. (108),

1103

thulium, neoytterbium and /utetium. On the other side however,
lanthanium is diamagnetic, while praseodymium possesses a greater
value for j« than neodymium. ‘Thus the curve, showing the dependence
of w upon the atomic weight, must possess fo maxima: one in
the cerium-group, and the second, much steeper maximum, in the
yttrium-group.

There also exists such a periodicity in the basic properties of these
oxides; these seem to decrease from lanthaniuin to terbium, then to inerease
with holmium (yttrium) and erbium, and again to decrease to the side
of neoytterbium; the elements ave arranged in order of increasing
solubility of their ethylsulphates :

Ce : :
— La Pp Nd Sm (Cerium-group),
and: Hu Gd Th Dys Ho Yt Er Thu N-Yb (Yttrium-group)

An analagous periodicity seems to exist also for the solubility of
other ‘salts of these metals, e.g. for the ovalates, ete.

Finally all these facts may persuade us to some extent, that it
is really not at all justifiable, to deny the possibility of such a
periodicity a priori, even with respect to the relation between atomic
weight and volume, without accurate and extended investigations
with absolutely pure material; on the contrary : the facts here published
can be used as strong arguments in favour of the view of the
existence of such a periodical relationship. ‘)

§ 7. Now some more data about analogous investigations with
scandium-, beryllium- and indium-salts may find a place here. Originally
tentatives were made, to reach our scope also by means of the study
of the ethylsulphates. We succeeded in obtaining from scandium-,
and imdium-oxide, the corresponding ethylsulphates in the form of

1) In connection with this [ may remark once more, that an analogous abnor-
mality in the molecular volumes of the double nitrates of these same oxides of
Urpatn, was found a short time ago by Janrscu: Zeits. f anorg. Chemie 76, 303,
(1914)), with the salts of praseodymiwm and neodymium: the last compounds
always possess the greater molecular volume.

Moreover another argumentation for such a periodicity of properties within this
eroup of elements, can be derived from the available data of meltingpoints of these
metals or of their analogous compounds. For MurHMANN and Weiss (Lieb. Ann.
331. 1. (1904)) stated, that the mellingpoint of La is: 810° C.; of Ce: 623° C.;
of Pr: 940° C.; of Nd: 840° G. In the same way Bourton (Ann. de Chim. et
Phys. (8) 20. 547, (1910), showed, that the meltingpoints of the chlorides are:
of LaCl,: 890° C.; of CeCk: 848° C; of PrCly: 810° C.; of NdCl,: 784° C.;
of SmCl,: 686° C.; of GdCl,: 628° C.; of TOCl;: S88° C., but on’ the contiary,
for DysCl,: 680° C., — being thus about 100° higher.

72

Proceedings Royal Acad. Amsterdam. Vol XVI

1104

well-erystallized preparations ; however these crystals had microsco-
pical dimensions and were only little adapted for goniometrical measure-
ments, because they were intergrown with each other in a chaotie
mass. However it was possible to prove, that no relation in the
erystallographical architecture of these erystals with that of the ethyl-
sulphates of the also trivalent rare earth-metals exists. These salts
are of monoclinic symmetry, and they possess characteristic optical
properties, which can be considered as most typical for them. In the
subjoined table the principal data are put together.

From this review it follows, that the beryllium-ethylsulphate evidently
must be placed in an isolated place, with respect to all other
ethylsulphates. It is tetragonal and possesses a very deviating chemical
composition, being a basic salt of the formula: BeO. Be(SO,.C,H,) +
+ 4H,0O; analysis gave: 14,3°/, BeO.

§ 8. Because evidently the above mentioned salts of ¢mdiwm and
scandium were little adapted for measuring purposes, the corresponding
acetylacetonates were prepared. The acetylacetonates of the metals
of the rare earths crystallise always like felty, fine needles, which
are not exactly measurable. On the contrary, the acetylacetonates of
the trivalent metals: scandium, aluminium, indium and iron erystallise
in big, flat crystals, which immediately show themselves closely
related to each other, but widely different from tbe salts of the first
mentioned series. The measurements really prove, that the salts of
scandium, tron, and indium are directly isomorphous with each other,
while the alwminiwmsalt must stand to them in the relation of
zsodimorphy. With the trivalent gallium, all those metals must there-
fore be placed into the same group; evidently they are noé imme-
diately related to the rare earth-metals. Thus also the question, if
the element scandium must be placed among the rare earth-metals,
can be answered in the negative, as well with respect to arguments
formerly adduced from several sides, as with respect to the facts
described here *).

The beryllium-acetylacetonate is monoclinic, and, generally speaking,
very widely different from the other acetylacetonates. This substance
is a highly remarkable object for optical demonstrations : with enor-
mous values for its dispersion, it shows the phenomenon of the
crossing of axial planes, like the mineral brookite; but in agreement
with the monoclinic symmetry, the effect of the dispersion of the

') See about this question however the just published paper of R. J. Meyer,
doco cit). In my opimion the claimed analogy (p. 268) between scandiwm and

yllrimm can hardly be defended in a persuading way.

1105

bisectrices for different wave-lengths is here superposed upon it.
In this way a highly remarkable combination of crossed and hori-
zontal dispersions results from it, while the orthodiagonal is for some
wave-lengths the direction of the first bisectrix, for other ones that of the
second bisectrix. The very peculiar optical phenomena resulting from
this, will be deseribed in detail and explained in the paper to be
published lateron.
Laboratory for Inorganic and Physical Chemistry
of the University.
Groningen, 14 March 1914,

Paleontology. — ‘Contribution to the knowledge of the genus
Kloedenella, Utrtcn and Bassurr.” By J. H. Bonnema. (Com-
municated by Prof. J. W. Mot.)

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

When examining an erratic boulder, consisting of Chonetan or
Beyrichian limestone and originating from Vollenhove, I found some
remains of Ostracoda which, [ presumed, originated from the genus
which Kravsp has called Beyrichia hieroglyphica'), of which besides
an illustration (fig. 1) he gave the following description :

Beyrichia heroglyphica n. sp.

Lange 0,74 mm. Hohe 0,5 mm.

Die Schale ist annahernd rechteckig mit geradem Dorsal- und
Ventralrand und gerundeten Seitenrandern. Auf der Schalenober-
flache befinden sich 5 symmetrisch angeordnete grubenformige,
durch schmale Leisten von einander getrennte Vertiefungen, je eine
parallel den beiden Seitenrandern vom Dorsalrande bis zum Ventral-
rande verlaufend, in der Mitte zwischen diesen eine kiirzere, welche
vom Dorsalrande bis zur Mitte der Schale reieht, und unterhalb
derselben zwei rundliche Gruben am Ventralrande.

Die Art weicht von allen anderen Beyrichien unserer Geschiebe
weit ab. Am nachsten scheint sie noch der Beyrichia Halli Jonus aus
der Waterlime-Gruppe von Utica N.Y., zu stehen, nur dass bei dieser
die beiden unter der centralen Furche befindlichen Vertiefungen fehlen.

Ich . fand die eben beschriebene Form in einem grauen, fleckigen
Geschiebe zusammen mit Beyrichia Wilckensiana, B. aff. Kloedeni,

') Zeitschr. d. deutsch. geol. Gesellsch., XLII, p. 506, Taf. XXXII, Fig. 10, 1891.
72%

1106

Cypriden und Fisehresten. Die einzelnen Sechalen waren nur in
Bruchstiicken aus dem Gestein zu lésen. Fig. 10 ist ein ergéinztes
Bild eines der best erhaltenen Exemplare.”

In order to ascertain whether the remains of Ostracoda which I
had found, really originated from the genus described by Krause as
Beyrichia lieroglyphica, 1 looked for similar remains in an erratic
boulder consisting of Chonetan or Beyrichian limestone which I had
found some time ago when a pond was being dug near a villa,
called Hilghestede, between Groningen and Haren. This erratic
boulder is now in the collection of the Mineralogical Geological
Institute of the University of Groningen. I was then fortunate enough
to find not only a great number of separate valves, but also several
complete carapaces.

This latter erratic boulder is a dark grey somewhat crystalline
piece of Beyrichian limestone, in which among other things I found :
fish-remains, Aloedenca Wilckensiana Jonus, Beyrichia protuberans
Bou, Beyrichia tuberculata Kioprn sp. and Leperditia phaseolus His.
The first three fossils had also been found in the erratic boulder in
which Krause found remains of Beyrichia hieroglyphica, if at least
B. aff. Kloedenit may be identified with Beyrichia protuberans, which
seems almost certain ').

It appeared to me that the illustration given by Krause represents
a left valve, as the posterior of the two little furrows is always the
bigger one (the anterior may even be absent). This figure, however,
is very incomplete, for this author seems to have been ignorant of
the fact that the remains found by him, had only partly been
uncovered. Before the anterior lobe there is another sickle-shaped,
less convex part and behind the posterior lobe a similar part tapering
towards the lower end. The narrow inferior ends of the less convex
parts meet at the ventral side.

The lobe along the ventral edge, which joins the other lobes, is
nearly straight and not curved, as represented by Kravsr; in his
description, however, he calls it straight. The ventral edge of the
carapaces iS concave.

As the most striking feature of this Ostracod IT found, however,
that in the left valve the two anterior lobes unite at the top intoa
process, which lies in a notch of the right valve (tigs. 8 and 4). No
doubt the great number of complete carapaces which were found, is
due to this arrangement.

1) Wissenschaftliche Beilage zum Programm der Luisenstiidtischen Oberrealschule
zu Berlin. Ostern 1891, Berlin, R. Gaertners Verlagsbuchhanilung (HERMANN
HEYFELDER). p. 12.

J. H. BONNEMA: “Contribution to the knowledge of the genus Kloedenella,
Ulrich and Bassler.”

Fig. 1. Fig. 2. Fig. 3.
Left valve of Kloede- Kloedenella hieroglyphica Kloedenella hieroglyphica
nella hieroglyphica A. Krause sp. Left side A. KRAUSE sp. Right side view
A. Krause sp. (After view of complete carapace. of complete carapace 40>.

Krause). 20 X. 40 X.

Fig 4. Fig. 5. Fig. 6.
Kloedenella hierogly- Transverse section of a Left valve of Kloedenella
phica A. Krause sp. carapace of Kloedenella Halliit Jonrs. X15.
Dorsal view of com- hieroglyphica A KRAUSE (After Jones).
plete carapace. 40 X. through the part of the

muscle impression, as seen
from behind. 35 X.

Fig. 7.

Kloedenella pennsylvanica JONES

sp. Left side, end and ventral

views of complete carapace, 15 X.
(After Jonus).

Proceedings Royal Acad. Amsterdam. Vol. XVI.

1107
\

For the rest the hinge line is straight. Along the straight part
the right valve overlaps the left one. By making sections of complete
carapaces (fig. 5) I found that the sharp hinge line of the left valve
lies in a deep furrow of the right one.

On the other hand the free edges of the right valve are sharp
and when the carapaces are closed, these sharp edges lie in a furrow
on the free edges of the left valve. So the left valve overlaps the
right one except along the hinge line (fig. 2).

In the lower part of the middle-most of the three larger furrows
each valve has a round spot indicating the place where the adductor
was fastened.

When I had become better acquainted with Beyrichia hieroglyphica
Kravsr, the resemblance between this Ostracod and Beyrichia Hallit
Jones ') (fig. 6), to which Krause drew the attention, proved much
greater than the latter conld presume. Another thing that struck me
was that in the valve represented by Jones as a right one — though
in fact it is a left one — the two front lobes also seem to join
into a process. In order to see in how far I was right in my supposition
I applied to Dr. Basstrr, curator of the National Museum of
Washington, with the request to send me some material of this
Ostracod. This was kindly sent to me and | saw that the two
anterior lobes on. the left valve of Beyrichia Hallii Jonus indeed
unite dorsally into a process, similarly to those in Beyrichia hieroglyphica
KRAUSE.

On further examining the literature I found that Uneice and
BassLer*) had classified Leyrichia Halli Jonus among their genus
Kloedenella, of which they call the underdevonian Kloedenella
pennsylvanica Jonws (fig. 7) a typical representative.

Then I asked Dr. Basser to send me some material of this latter
Ostracod. In the complete carapace of Aloedenella pennsylvanica,
which was then sent me, I found the same characteristic way of
connecting the two valves, which is no doubt also found in other
Ostracoda, for which the two authors mentioned above have instituted
anew genus Kloedenella, for they make special mention of the
fact that of most of the representatives complete carapaces have
been found.

') The Quaterly Journal of the geological Society of London, Vol. XLVI, p. 15,
Pl. IV. fig. 21. 1889.

Jones has called this Ostracod B. Hallii and not B. Halli as Krause writes.

*) N°, 1646. — From the Proceedings of the United States National Museum.
Vol. XXXV. p. 317.

1108

Of the genus AZoedenclla Unricn and Basster give the following
diagnosis :

“Carapace small, strongly convex, elongate, somewhat barrel-shaped,
the length usually less than 1.5 m.m., dorsal edge nearly straight,
ventral edge usually somewhat concave, ends approximately equal
in height but differing in outline, the antero-dorsal angle often reet-
angular and always more distinct than the post-dorsal. Valves
unequal, the right overlapping the left around the ends and the
ventral side. Of the lobation the constant features are two sharply
impressed vertical or slightly oblique furrows, separated by a narrow
lobe, in the posterior half. In the move simple forms these furrows
extend only about half across the valve. Anterior half may be uni-
formly convex, but, as arule, is more or less clearly bisected vertically
by a straight or curved furrow. When present, this anterior furrow
often. produces an appearance suggesting the “loop” of a Bollia.
Surface generally smooth and polished and without ornamental
markings”.

Here the following remarks are to be made: first, that the way
in which the two valves are connected in Kloedenella hieroglyphica
Krause, as well as in Beyrichia tuberculata Kioven and Primitia
Tolli Bonnema, proves that what Unricn and Bassier called the
posterior end is to be looked upon as anterior.

Secondly “dorsal edge nearly straight’ ought to be replaced by
“Both valves have a straight dorsal edge, the sharp dorsal edge of
the left valve lies in a furrow on the dorsal edge of the right valve.
On the left valve there is a process before the right dorsal edge,
which fits into a notch of the right valve.”

To ‘valves unequal” may be added that the right valve overlaps
the left along the hinge-line. This is at least also the ease with
Kloedenella pennsylvanica as well as with Kloedenella hieroglphica.

The criteria of the genus Aloedenella ave accordingly :

Carapace elongate and small, the length usually less than 1.5 m.m.,
posterior half very convex, dorsal edge nearly straight, ventral edge
usually somewhat concave, ends equal in height, anterior edge
uniformly curved and passing almost invisibly into dorsal edge,
forming a very obtuse angle with it; posterior edge less curved,
forming a nearly rectangular angle with the dorsal edge. Valves
unequal, the anterior half of the right valve has a noteh in which
a process of the left valve lies; this latter is located before the straight
sharp hinge line, which is situated in the furrow on the straight
hinge line of the right valve. The right vaive overlaps the left along
the hinge line. The sharp free edges of the right valve lie in a

1109

furrow on the free edges of the left valve so that the left valve
overlaps the right along the free edges.

The surface of the carapaces is different, though furrows and
lobes are always present. Constant features on the anteridr half of
the valves are two more or less vertical furrows, separated by a
narrow lobe. The posterior half may also have a furrow. Else the
surface is generally smooth and without ornamental markings.

As may have been inferred from the above statements, the position
which I have given to this Ostracod corresponds to the position
which in my opinion *) is due to Beyrichia tuberculata KLévEN sp.,
in which there is. a furrow on the free edges of the left valve,
whereas the right has sharp edges. From Dr. Basser of Washing-
ton I received a letter the other day, in which he stated that he
and Dr. Unricu considered as posterior what I had assumed as the
anterior end in Primitia Toll: Bonnema, Beyrichia tuberculata K10-
pen sp. and Leyrichia protuberans Bout; but to this I cannot pos-
sibly agree. Their opinion is based on the fact that the lower of
the two nodes situated at one of the two ends, which in some
valves of Beyrichia tuberculata has widened into an “ovarian pouch”,
would be situated in the anterior half in the position suggested by
me, whereas in recent Ostracoda this node is found in the posterior
half. In my opinion, however, they disregard the fact that in the
position accepted by them, the eyes would be situated at the poste-
rior end of the animal, which seems very unlikely. They call upon
me to prove that the “ovarian pouch” has been at the anterior end
in paleozoic Ostracoda. I think I have sufficiently proved this with
my investigations into the location of the eyes.

Next I want to state that what ULricu and Basster ealled
“ovarian pouch” has to be considered as an incubation pouch, and
like Kirsow I have no objection to assume that in the paleozoic
Ostracoda this was located in the anterior half of the carapace,
whereas in the recent Cythere gibba MO11.. it is situated in the posterior
half of the carapace but near the centre.

Finally I tender my best thanks to Mr. Borxkr, teacher in the
“Middelbare Landbouwschool” (Secondary Agricultural School) of
Groningen, who has been kind enongh to make the drawings of
Kloedenella hieroglyphica Kravse sp., necessary for this paper.

1) These Proc. 16, 1913, p. 67—74.

1110

Physics. — “The effect of temperature and transverse magnetisation
on the continuous-current resistance of crystallized antimony.”
By Dr. W. J. pe Haas. Communication from the Bosscna-labo-
ratory. (Communicated by Prof. pu Bots).

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

Introduction. There exists an extensive literature on the effect of
transverse magnetisation on the electric conductivity of different
metals and metalloids. We may divide these into three groups i.e.

1. ferromagnetic, 2. paramagnetic, 3. diamagnetic substances. Other
phenomena also suggest this grouping.

As to our effect, the substances mentioned in section 1 show
distinctly measurable changes in the resistance. Those mentioned
in sect. 2 however have been less investigated and until now give
only exceedingly small effects’), the nature of which is very difficult
to determine. In contrast with the Hanr-effect, the ferromagnetic and
diamagnetic substances show in our case a change in the resistance
which is dependent on the direction of the field. For ferromagnetic
substances a decrease and an increase of the resistance have been
observed, while also the sign is dependent on the temperature”) at
least for Swedish iron.

By far the most measurements have been made with conglomerates.

The diamagnetic substances on the contrary

y always show an
increase of resistance with the temperature, not a change of this
increase into a decrease. The curves, which represent the resistance
as a function of the field have all the same character; sometimes
ihe effect is very large. For example for bismuth in a field of
37 K.G. at — 190°C. R’/R = 230%) and at hydrogen temperatures
in a field of 17 K.G. R’/R = 380"), while for graphite in a field
of 40 K.G. and at the temperature of liquid hydrogen R’/R = 130°).
Until now the diamagnetic elements have been investigated ; bismuth °),
antimony“), carbon‘) tellurium’) gold*’), silver *'), copper **), zine **)
lead **), cadmium ’*), mereury °°).

1) L. Grunmacw and F. Weiprert, Ann d. Phys. 22, p. 141, 1907.

2) H. KamertincH Onnes and B. Beckman, Comm. Leiden 12 N°. 132a, 1912.

3) H. pu Bors and A. P. Wuus, Verh. d. D. Phys. Ges. 1, p. 169, 1899.

‘) H, KamertineH Onnes, Comm. Leiden, 12 N?. 129, 1912.

5) D. E. Roperts, Ann. d. Phys. 40, p. 453, 1913

6) . CG. Brake, Ann. d. Phys. 28, p. 449, 1909.

6) 10) 12) 16) Hl. KamertingH Oxnes and Benet Beckman, Comm. Phys. Labor.
Leiden 12 N°. 129, 130, 1912.

7) A. v. ErringsHausen, Wien. Akad. Ber. 59, p. 714, 1887.

Pu. Lenarp, Wied. Ann. 39, p. 637, 1890.

10) 11) 12) 13) U4) 15) , Grunmacw and F. WeIpeErt, loc. cit.

15) 18) 8, 16) 12) 10) 11) J, Parrerson Phil. Mag. (6) 3, p. 643, 1902.

9) 15) 18) 10) G. W. Heaps, Phil. Mag. (6), 24, p. 813, 1912, VI, 22, p. 900. 1911.

8) 18) 15) $, C. Laws, Phil. Mag. (6) 19, p. 694, 1910.

1101

A list of the literature on bismuth up till L909 can be found in
a paper by F. C. Brake’). Of the more recent experiments must be
mentioned those of KamErRLINGH Onnes and Brockman *), who worked
at temperatures down to — 258° C. Carbon has been investigated
by Roserts, who also gives the literature.

There remains to be mentioned, that researches on crystallized
specimens have been made in the Leyden iaboratory on bismuth
and by Roperts on graphite. These are very important, as the orien-
tation of the principal axis has a great influence on the effect. It is
principally from this side that we can expect some lignt on the
otherwise unnecessarily complicated phenomena. However crystals
have been investigated insufficiently. A method to obtain large metal
crystals would certainly be of great use. So far reasonably large
crystals have only been made with bismuth.

§ 1. Investigation of antimony.

We shall use the following notations.

R Resistance in the field,

h'// Resistance in the field, when the axis of the erystal is parallel
to the field,

R's, The same with the axis perpendicular to the field,

R Resistance without a field, while the index at the foot indicates
the temperature, at which the measurements have been made,

SX) field.

Out of several antimony crystal conglomerates of Merck the best
specimens were selected; the material seemed to be very pure and
according to the analysis contained less than ‘/,,,,,°/, won. The
pieces were split into thin plates along the basic planes, which were
at the same time planes of perfect cleavage. These plates were then
immersed in shellac and carefully polished into small rods. At both
the ends of one of these rods (long 4 mm, broad 0.55 mm, thick
0.15 mm) two copperwires were soldered. These wires, were care-
fully insulated with shellac, and the two at one end were bent over
the rod so that they came into the same direction as the other two.
Then the whole, wires and rods, was slipped into a cylindrical glass »
tube of 0.8 mm diameter. The wires were then pulled through a
brass capillary, in the end of which the tube was fitted. Perpendi-
1) I. C. Buaxe, Ann. d. Phys. 28, p. 449, 1909.

a) ialance

1112

cular to the brass capillary a needle was soldered. When the apparatus
was mounted, so that it could be rotated, the needle passed a fixed
seale, indicating in this way the orientation of the crysfal axis in
the field. The resistances were measured with a TuHomson bridge. As
this method requires wire resistances small compared with the fixed
resistance, in the arms of the bridge (110 ohms in each arm), the
above mentioned wires, which were of necessity thin because the
four of them had to pass through the glass and brass capillary, were
kept as short as possible. When they had left the brass capillary
they were soldered to very thick wires, leading to the bridge.

In the bridge a galvanometer of the type of pu Bors and Ruspens
was used. The magnet most used was a small half ring magnet of
the newest type with water cooling. For some determinations a
large model magnet was used. This new type enables a long series
of measurements to be made without introducing an error due to
rise of the temperature in the field.

For the resistance measurements at the temperature of liquid air
the newly constructed vacuum cryoarmature on the immersion prin-
ciple has been very useful’). In fact the combination of the strong
fields up to 45 K.G. with low temperatures can easily be obtained ;
the field was only very slightly diminished by the gaps in the pole
pieces in which the Dewar vessel fitted. This strong field is partly
due to the use of ferrocobalt for the pole pieces.

The magnetic field was measured by the usual ballistic method ;
nothing particular has to be remarked on this subject. For the esti-
mation of the influence of the low temperatures on the field between
the ferro-cobalt pieces the Dewar vessel with the liquid air was
quickly taken away and immediately afterwards the field was measured.
This must be done very quickly, as the pole pieces become warm,
while also the search coil cools down and at the lower temperature
iis area is smaller, (and just on this area is based the measurement
of the field). Particularly the latter must be avoided as the coefficient
of expansion of the material (a hard kind of colophonium) was not
known. The coil had been compared previously with a carefully
polished glass standard coil. *) The influence of the temperature on
the field proved to be negligible.

The current through the magnet, was read on a precision instru-
ment of Simmpns and Hatske. The resistance measurements were
carried out at very short intervals. This was desirable to eliminate

1) H. pu Bots, Ann. der Physik. 42 p. 968, 1913.
2) See W. J. pe Haas and P. Drapier, Ann. der Physik. 42, p. 673, 1913.

ADS

the influence of fluetuations in the magnet current. The current was
taken from the central Berlin lighting cirewit net. The chief errors
in the measurements were due to the temperature and to a less
extent to the field measurement. An unfavourable circumstance 1s,
that’ the effect is roughly proportional to the square of the field, so
that an error in the field gets a double weight. When an accaracy
of */,°/, is desired, the magnetic field must be known to
this accuracy is not so easily attained as is often supposed.

The purpose of this research was not to make very accurate
measurements, but to see, whether in this case also the orientation

and

1/
/ 600

of the erystal axis has a great influence. For graphite this has
already been proved by D. E. Rosrrts (loc. cit.), for bismuth by
VAN Everpincen') and Lownps”’).

§ 2. Temperature curve without field. First the change of the
resistance of antimony in the basic plane was investigated. The
specific resistance was not determined because of the undefiniteness
of the soldering places, which much diminishes the accuracy of the
measurements. The different temperatures, were reached on the principle
of the Hnninc*) eryostate. In a vacuum vessel with petroleum ether
was put a tube, which was closed at the lower end. With a vacuum
siphon this tube was filled with liquid air. This filling was not
regulated automatically, but with the hand. The temperature was
read on a, pentane thermometer.

After some practice it was found that by good stirring the tempe-
rature could be kept sufficiently constant. Below — 140° the petro-
leum ether became thick, which made good stirring difficult and
for this reason the lowest points were measured in the liquid air
itself. At — 190° the curve R/R, = (A) (fig. 1) does not yet showa
point of inflexion. The greater the purity of the bismuth the lower
the temperature at which the point of inflexion occurs and_ the
weaker this poimt of inflexion. From this we may also conclude,
tliat the antimony from Merck was very pure‘). From the observed
values a formula R= &, (1 + «4+ 86) was calculated by the
method of least squares.

Such a formula holds within this range of temperature. The
formulae of Nernst, KAMERLINGH OnNes and Wien have not been

1) E. van Everpincen, Comm. Leiden N°. ¥6. 37. 40, 41. 42. 48. 53. 58. 61.
63, 72. Suppl. 2.

*) L. Lownps, Ann. der Phys. 6 p. 146, 1901; 9 p. 677, 1902.

3) F. Hennina, Zeitschr. f. Instrk. 33 p. 33, p. 1913.

4) F. C. Brake, loc. cit. Table 1.

1114

tried, partly because they do not refer to these low temperatures,
partly beeause we have not, as far as they have been derived from
ihe quantum theory, enough data, at least not for crystalline antimony.

Fie. 1 shows the curve R/R,; except at — 32.9° it coincides
very well with the experimental curve.

wy r T T 7

Ot

“

ia a et | | ett te He

|
|
ire 9g wUe- .0b- 4O9= .O8= LOUTH (OgI> (OFIF COUT CO8T= (00G5

Fig. 1.

The values have been collected in table 1. The differences between
the observed values and those calculated from the above mentioned
formula with two coefficients are about 1°/,; it would be possible
to get better agreement with a formula containing more coefficients
but this was of no value since on account of the indetiniteness of the
soldered joints an accuracy of 1°/, is as much as can be expected.

The values in table I have been calculated with the formula:

R= R, (1 + 0,005111 6 + 0,000005654 6°)... . - (1)

The linear coefficient of expansion is therefore somewhat greater
in the basic plane than in other directions.

The “Recueil de Constantes Physiques” gives @ 0,0039°*). This
agrees with the measurements of EUCKEN and GErHLHOFF *), who find
for the electric conductivity of a cast stick of antimony at

0° — 79° — 190°
2,565.104 3,968.10* 9,56.10*
1) Recueil de Const. Phys. p. 584, 1913.
2) A, Evexey und G. Gentuorr, Verh. d. D. Phys. Gesellsch. 14, p. 169, 1912.

TABLE 1
6c ue “IR G6 Og
Observation | Calculation
18° | 1.104 1.094 + 0.01 + 1%
0 | 1.000 1.000
=) Gil 962 971 = .01 =i |
= 10:8 942 951 == .009) slat
Ss 883 8925 E2009) ile
=» 991.9 851 | — .850 2.001) oNaaeais
fee 32.0 822 839 On | eee
= =43i5, || 2787 788 Se = ohh
= 2/61 684 683 001s pata
= 73 663 657 =e, 006) saps
=" SI 626 | .623 | + .003 | + I,
= 1 98y9 545 551 1 006m Pioaal
— 102.6 537 535 + .002 | + Ip
Fo 507 | .506 + eo |) hcp
1202 410 | 468 LAOD2 I geet)
— 120.9 473 465 TE WN ED
— 130 1443) | 439 Su. On ye stos2
isi =) 40a | 406 Je nie) | aE Sp,
Sari 235 240 £ 2° 5005) |, 52
191 228 .230 =F 002 tet

and with earlier experiments of von Bose and Marrarmsen') who

found for the conductivity between 10° and 100° :
A = 4,6172—0,018389 6 + 0,00004785 6?

§ 3. Orientation curve.

This was determined at 18° and about 28 K.G. The resistance of
the erystal was measured with the axis normal and parellel to the

1) ve Bose und Maruiessen, Pogg. Ann. 115, p. 353, 1862.

1116

field and in different positions between these two principal ones.
The current for the measurements was always normal to the field,
the direction of which is showr by the arrow in fig. 2. It was
found (see fig. 2) that in the maximum and minimum positions,

a >

did not differ
R

which were normal to each other, the values -

much, much less than in. the cases of graphite and bismuth. For
these conductors in one of these principal positions I the effect is
so much smaller than in the other one H, that Rogers *) thought
it possible, that in position I there does not exist an effect at all.
The small observed effect might be caused by an imperfect orienta-

A

Fig. 2.
tion in the field. In this case a small component of the effect belonging
to position H would be observed. For antimony the differences between
the results in the positions I and Hare so small, that this explana-
tion seems not to hold. It is therefore probable, that metal crystals
show for a definite direction of the current, normal both to the
principal axis and to the field, two independent magnetic resistance
changes, the one when the principal axis has the direction of the
field, the other when it is normal to it. Other cases for intermediate
positions can be reduced to these. The above observations, that for
bismuth and graphite, ie. for those crystals which show the greatest
resistance change in the field, the difference between the resistance
curves in the two principal positions is greatest, agree with a remark
of ©. W. Hears”). Heaps, who worked with conglomerates, points out
1) D. E. Ropers, loc. cit. p. 469.

2) C. W. Hears Phil. Mag, VI 24 p. 815. 1912.

sells

.

that those metals, whieh show the greatest resistance change also
give the most different resistance curves in a tranverse and a
longitudinal field. | hope to return to this point later. Fig 2 shows
the orientation curve.

The full line represents the formula:

Eisenia {0,519—0,510 sin 1,125 (81—-|.8 sin g))] )
R,. = keen (2)
+ [0,167—0,1696 sin 2,665 (30—|. cos y))]

where g is the angle between the direction of the field and the
principal axis of the crystal.

To represent the resistance change in the field in one of the two
principal directions, different types of formulae were tried. Finally
certain considerations, which may be omitted here, led to the form

;

a=? + h sinc (d—|}) (8). Because of the connexion between the

constants for the tield $ —O, this formula has three constants. The
above formula (2) is derived from (3) by resolving the J) under the
sin. into its components. As &’ — RF is very small compared with
fk and as there were no special precautions taken with regard to the
orientation, we may regard the agreement of the observed points ©
with the calculated ones as fairly satisfying.

§ 4. Isothermal curves. Fig 3.

As to these we may remark, that the quasi-linear part of the field
curves is already reached at 30 KG. Of earlier investigations must
be mentioned those of Lmnarp *), who used pressed antitnony wire,
0.2 mm. thick. This highest field was 6.6 KG. where he found
R ‘
~= 1.012 for a constant current; and also those of v. Ertines-
HAUSEN *), Lepret*) and Barrow *).

Fig. 3 shows the field curves for 18° and —188° in two principal
directions. The formulae used are:

R'yg0 a = F o:
Table 2. — = 1.519 — 0.510 sin 1.125.(81 — |, |)

1) In this and in the other formula © is expressed in degrees.
*) Pu. Lenarp, Wied. Ann. 39, p. 637, 1890.

3) A, v. ErrincsHausen, Wien. Akad. Ber. 59, p. 714, 1887.
*) A. Lesret, Diss. Leiden, 1895.

5) G. Bartow. Ann. d. Phys., 12, p. 916, 1903.

1118

ee + a Pa
°
SO) | 7 ~ = 1
|
42 =: + =
3 e/
34 r 4
2 -
2.6 7 /
1s = + oI
A
N
13)
aa St J
i 12 24 36 48
Fig. 3.
Table 3. = 1.167 — 0.1696 sin 2.665 (80 — |.1))
R_, ; :
4, ——18" — 2.742 — 1.80 sin 2.022 (38.55 — |.) |)
R_i880 :
De = 10.08 — 0.965 sin 1.069 (74.90 — |51)).
TA BIBES 2: TEN BisEss:
Antim. resist. as a funct. | Antim. resist. as a funct.
of § and of 9 and &.
axis |) field. axis | field.
ite 9 S188 | hee
Bh) Seer | By
| Kilogauss | R_ oe Kilogauss | _*’ 1G
R (O) R(C) R (O) | R(C)
\) wi2le4 1.0389 | 1.038 | 21.4 1.101 1.1015
| 23.2 1.047 1.048 23.2 iia | 1.114
|
) essa} | aeons | 1.0725 28.3 1.154 1.155
29°98:- }. 1079) i) 1082: 29.98 1.167 1.167
32.0 *

1.091 | 1.092

1419

The observed points have again been marked ©. In tabel 2, 3, 4,
and 5 the numbers are given.

;
IPA BIEE 4 | TAUB Eee):
| Antim. resist. as a funct. | Antim. resist. as a funct.
of § and . | of § and &.
axis |) field. | axis | field.
9 = — 198° | PT ye tee.
S Werte S| H ——
Kilogauss | R | | Kilogauss Re RG
R (O) R(C) | | R (O) R (C)
ea SES) | Cee ee aha dre Sid
= = - - = Fi are
6.7 Mei aes 6.6 e239 |) "12238
WEP? 1.310 1.297 12.4 | 1.620 1.607
19.8 1.630 1.633 19.8 | 2.210 2.192
| |
26.7 22013 2.010 26.7 le 2220371 2.920
BQH ||. 22200 pine 30.9 3.396 3.401
| | |
B32) 2= i) 25340 2.343, i || 133-0 3.664 3 666
33.0 2.392 2.392 43.3 5.195 | 5.105
43.3 3.060 3.045 aes eo

In order to test formula (3) still further it has been applied to
the observations of KAMpRLINGH ONNES and BrckMman.
The tables 6, 7, 8, 9 have been taken from Comm. N°. 129 and
R
130 Phys. Lab. Leiden. In the columns R,(0) are given the observed

0
'

values, while under R,(C) are (o be found the values calculated
0

from the formula at the head of the table.
R' bo th

TE == 15°: R= 08:4—68.76 sin 5.45 (15.05—|H])

TD Osoe. 5-74 —76.1 sin 5.09 (16.83—|

a)

~—

1

R
Tele. RB = 184 057 — 138.9 sin 2.166 (40 — |H)})

L

0
R
Th=—A9 ()\ Rp = 102.34 — 102 15 sin 2.04 (42.15 — |

0

Proceedings Royal Acad. Amsterdain, Vol. XVI,

1120

| TABEL 6.
|

Resistance of Bry, as a function of temperature and field.

Ry Ti NII IE i 20SONKG
Gauss R’ ARE R R’ | R R
Ro(O) RAC) RO) RC)
0 0.526 0.216 0.25 0.588 0.242 0.24
2760 1 tea) 4.73 4.74
3850 19.9 8.185 8.32
5540 34.9 14.35 14.38 32.8 13.50 13.69
7370 55.9 23.00 22.48 54.7 22.50 21.44
9200 80.8 33.25 32.14 76.7 31.55 30.86
11850 116.4 47.90 47.82 113.2 46.55 46.47
13600 143.1 58.85 58.95 141.5 58.20 57.69
15670 175.6 72.25 72.45 Ze 710.75 71.48
17080 199.3 82.00 81.18 196.5 80.85 81.00
TABLE i.
Resistance of Bi qj *S 4 function of temperature and field.
5 T= 12O Ke T= 927K,
Gauss i R’ R’ Re R’ LS Ss
Ro(O) RC) Ro(O) RoC)
| 0 | 0.989 0.407 | 0.407 1.075 0.442 0.490
2760 | 4.68 1.926 | 1.919 | 3.92 1.613 1.54
5540 | 12.28 | 5.052 | 4.957 | 9.24 3.80 | 3.86
7370 | 19.10 7.86 7.66 | 14.20 5.84 5.82
| 9200 26.6 10.94 11.01 19.74 8.12 8.14
| 11850 41.2 16.95 16.92 29.82 12.27 12.34
| 13600 52.4 21.6 PA vere) 38.60 15.88 15352
15670 | 67.2 | 27.65 21:57 | 48.05 =| 19.77 19.68
17080 717.8 32.0 32.03 | 55.80 | 22.96 | 22.79

1121

TRS i : : k
T 170°. = = 10.47 — 10.08 sin 2.46 (81.86 — |.))
R,
R'
1 SSO — = 1.657 — 0.749 sin 4.5 (12 — | §))
R, :
TABLE 8
Resistance of Big as a function of temperature and field.
“ T = 170° K. T = 290° K.
ve | |
Gaus ie Ro Re ee a | Re ey |
R(O) | RC) | | RO) RC) |
= == === = = — = = = ez =a a |
| | | |
0 | 1.570 | 0.646 0.630 2.570 1.057 | 1.051
2760 | 2.366 | 0.973 0.98 2.770 | 1.140 | 1.162
| 5540 | 3.657 1.504 HAT ld. AO, 1.280 | 1.294
lee 7370" |) 4.612) | 1.897 183 ile Se47See | PISS Boe
9200 5.613 | 2.310 2.25 3.635 | 1.495 1.494 |
11850 7.299 | 3.003 3.00 | 4.002 1.646 1.654 |
13600 8.506 | 3.500 | 3.51 4.248 1.746 1.750
15670 | 10.204 | 4.199 | 4.19 | 4.540 | 1.868 1.869
| | |
17080 | 11.412 | 4.695, | 4.69 |
|

§ 5. General remarks and conclusions. Referring to the existing obser-
vations we may make some remarks on the electron theory of metals.

The sign of the Hau.-effect shows, that the influence of the magnetic
field on the so-called “free” electrons is a complicated phenomenon.
The change of the resistance in the magnetic field can give us an
insight into the mechanism of the electric current. For it has been
found, that the resistance change of a crystal depended only on the
angle between the crystal axis and the field’); the angle between the
directions of the field and of the current is of no importance, at
least in a first approximation. From this we may conclude, that
although the electrons may be “free’” in passing from one molecule
to the other, the influence of the field on these free paths and the
resistance change caused by it, is negligible. Therefore theories as
eg. that of J. J. Tuomson, which try to calculate the phenomenon
from the direct effect of the field on the ‘free’ electrons cannot
possibly give the right result.

Dee Roserts, loc. cit, p. 468. Table Ll.

73%

The field produces the change of resistance through its effect on
the molecules and not on the ‘free’ electrons (when these indeed
exist) and it is natural to suppose that the field has also an orientating
influence on diamagnetic molecules. From the magnetic double refraction
Corron and Mouton have also concluded, that for diamagnetic sub-
stances too the field has a directing influence *). One can readily imagine,
that anisotropic molecules have, in general, a greater magnetic moment
than isotropic molecules; therefore, if the magnetic moment is already
present before the field is excited, the field will have a stronger
directing influence on anisotropic molecules. Similarly if we suppose,
as is generally done, that diamagnetism is an induced phenomenon,
we may assume that a bigger moment is produced in an anisotropic
molecule than in an isotropic one. We may therefore conclude that
the crystal system must have an influence on the phenomenon.

Now we find this to be really the case. All substances, which
show a large or rather large resistance change, belong to the hexa-
gonal system, while those which have a much smaller effeet belong
to the regular system.

Finally we may still remark, that those molecules, which have
a large susceptibility and which are besides anisotropic will undergo
the greatest influence of the magnetic field. And as the resistance
change is caused by a directing effect, there must be a connection
between susceptibility and resistance change. That this connection
really exists is proved by the experiments. It is from this connexion
that a large effect for graphite could be predicted 7’).

When we put the diamagnetic metals in a series in the order of
the values of (/’—2)/R, beginning with the largest value, we have first:

Bismuth.
Graphite.
Antimony.
Then according to:
GRUNMACH PATTERSON Harps
Cadmium Cadmium Tellurium
Zine Zine Cadmium
Silver Zine
Gold Gold Gold
Copper Copper
Lead

1) A. Corron and H. Mouron, Journal de Physique (5) ip. 40, 1911, P. Lanervin,
le Radium 7 p. 249, 1910.
2) D. E. Roserts, loc. cit.

The definite series is: Bismuth Graphite Antimony Tellurium
Cadmium Zine Silver Gold Copper Lead.

Hexagonal are : and regular :
Bismuth Silver
Graphite Gold
Antimony Copper
Tellurium Lead
Cadmium
Zine

The order of the diamagnetic susceptibilities is according to Morris
OweEN '): xX

Bismuth -—- 1.40 x 10-6

Graphite *)— 5 |

Antimony — 0.815 Pi

Tellurium — 0.303 Boxe ona

Cadmium — 0.185

Zine — 0151

Silver — 0.201

Gold — 0.152 | Regular

Lead — 0.120 |

Copper — 0.085 -

The division into two crystallographic groups and a remarkable
regularity in each of these groups are obvious.

CONCLUSION.

1. For all temperatures the resistance change of diamagnetic
substances in the magnetic field can be represented by a formula of
the form R’/R = a—b snc(d+ |H).

2. The field has a directing influence on the diamagnetic metal
molecules. ;

3. There exists a connexion between crystal system, resistance
change and diamagnetic susceptibility.

1) M. Owen. Ann. d. Phys. 37, p. 657, 1912.

2) As to the place of graphite one must take into account that different kinds
of graphite differ greatly in properties. Further, no account is taken of the influence
of temperature on the order in the series. All series are given for room tempe-
rature. It seems probable that in grouping at ‘corresponding’ temperatures and
“corresponding” states lead would also change its place.

L124

Mathematics. — “The theory? of Bravais (on errors im space) for
polydimensional space, with applications to Correlation.” By

Prof. M. J. van Uven. (Communicated by Prof. J.C. Kaprnyn).
(Communicated in the meeting of March 28, 1914).

In the original treatise of Bravais: “Analyse mathématique sur les
probabilités des erreurs de situation d’un point” *) as well as in the
articles that have afterwards appeared on this subject *) the problem
of the distribution of errors in space has only been investigated for
spaces of two and three dimensions. Only Prof. K. Pearson has also
treated the case of four-dimensional space *).

It may be interesting to treat this problem also for a space of an
arbitrary number of dimensions, not so much with a view to the
geometrical side of the problem, as in connection with the subject
of correlation. If we consider the problem from this point of view,
it comes to this :

A number (6) of variables w,,u,,...U-:, are given, each of which
follows Gauss’s exponential law :
h; 2
IWi= —— oi iu
Vn
and consequently may assume any value between — oo and + o.

Further we have a certain number (@) of linear functions 2, v,, ... @,
of the variables w;, viz.,
&y = yyy + agua +... + Ait,

@2 = a1, + aggug + .... + aacts,

ae = Gait + a@poue +... - + Aes Uc.

The probability that 2; ranges between ¢; and §; + 05; (j = 1, 2,..:0)
is then expressed by the formula

1) A. Bravais. “Anal. math. etc.” Paris: Mémoires preséntés par divers savants
a l’Académie royale des sciences de l'Institut de France; T. 9 (1846), p. 255.

2) E. Czuser. Theorie der Beobachtungsfehler. Leipzig, 1891, Teubner; p. 350.

M. p’Ocaane. Sur la composition des lois d’erreurs de situation d’un point;
Comptes Rendus T. 118 (1894), p. 512; Bulletin de la Soc. math. de France,
T. 23 (1895), p. 65; Annales de la Soc. scientif. de Bruxelles, T. 18 (1894) p. 86.

S. H. Bursury. On the Law of Error in the case of correlated variations; Report
of the British Assoc. (65th m.) (1895), p. 621.

V. Rema. Sulla probabilita degli errori di situazioni di un punto nello spazio;
Atti della R. Accad. dei Lincei, serie 5a, T. 6, sem. 1 (1897), p. 107.

5) K. Pearson. Mathematical contributions to the Theory of Evolution: Regression;
Phil. Trans. vol. 187 (1895), p. 253.

w= ey ge Hidsi dane Oar,

in which
Ie 6.48." == 2b, .51§. =r of gto -- bep§p"-
The aim of this paper is:
1. to express the coefficients 4); of the quadratic expression H
and the quantity # in the coefficients «;;,
2. to elucidate the notion of a coefjicient of correlation by means
of the expressions found.

The probability of the simultaneous occurrence of the values
Wn Wp ols ks

Z a
tah TS Ass G
JW =—e , IT Suj.
Wig 1
m2
We begin by writing
hu = v; (= 25s)
and
aij = hjaji (9; 1,85 Onn tear xO)
Thus we get
ae = Ore G
I~ e : IT dv;
1
2

and
&y = ayivy + ayove + ... + ayev,,

UZ = agivi + agqvq +.» + Ageda,

te = Go101 + pave -b «0. > Aas Uae

For the present we shall continue working with the coefficients
aj; only in the final result.

Like Bravais we moreover introduce 6—g auxiliary variables, viz,

c

Z
tei = = Aot1 i Vi

: - 0 5 e Uy & Us ;
The determinant of substitution of ( eae ) is then
Wr Uaareheaita

(41, 12, Ale |
| |
| | «
K= | et, 2225 ob |) = |a5i |.
es A: ese Acer
The algebraic complement of a;; we call Aji
> . . . v
By the substitution
As
/5[{ = D> ik
1
becomes
Le G i, Bj? + 2 = = biz Lj Lhe

1
Che functions v,,...v2 are given. We now dispose of the remaining
the following relations are

manner that

Oye aS ea (ee Bia
auxiliary variables

N

Mirai Gene, aby) SUC
satisfied :
bi ——=0) tor yi leo
In this way we attain that the introduced o—

occur only squared.
from the equations of substitution we find

Solving
= Ajj x;
= —_ ,
Uh ay (SS Aire) s

Consequently we find for H

vo + Ryans os eA 2a)e

a c 2
; = (2 Aja;) = (Ayia; + A, ae
op i=1\j=1 i=1
i — ve sh —— : = a
1 Le Le
Spee 5 of ah
= (Aj ty + 2Ay; Agiay we +... + Agi a.)
c—T
— A =
2 ao eee
— SA ay + 2 = > Ay; Ao; . x4 ave a se + SS Arraucs
— i=t 1 e.
o o °o 9 gi oe
=| 24; )2; +2 = ( > Aju ) Xj Xp
eo jt bi = jl sh —l
=¢ = A? ;
putting
Sy A => A ji Ake
— 7—I
AG = bj Ca ak = bik (= bxj)
Al Sb a2 ne, eS bane
i el) J ]
My —! Wy

11

i)

vi

We must now try to express the coefficients 4,; and 4,, for
3 | d j
i— 1. 2,5 Ck — a... 10, im? terms *ot-) the coefficients “of ‘the
given equations of substitution :
Bit Ui i,\- » «1 Bp =| 2 Api Vy «

The conditions 6;,=0 for h=o-+1,...6 are equivalent with
the conditions

SAA; —0 for h=o@- 1,...6;
i=!

but

= A;jajj—A

I!

Ajj o%;=0. for l=).
dl

are also always satisfied.
So we have the following set of equations,
ZAjiayi— 0, | Z Adi 0, 40 Aa == 0, Aa 7 — A,
= Ajjiaji1i=0,... AS Ajiag = 0, = Aji Api = L? bik,
yA Ape gO. wo, 22 jiAi= 0.

Hence
41 ; 12 p22 6 Ae ’ 0
ay > 22 Roca loc 0
Qj—1,1, %—1,2)---@j—1,0, 9
Opie Fi 1820 pine Gja 9B
Oily ly @j+1, 25 Aj+1, 0 0 =——a()
Getty ooh loyes.s Dect s tal LO
Apt ’ Ape peer Ap ’ LA?*bix
Aptijts Aptij2.-+-Aptia 0
As » AGS tieleAce nd)
or
a1 > 412 ge + Ate
a21 » 422 gees Q2¢
tice : 42 ’ A> : : :
| Gait ye Gao, Ayr. ae ed Re Fed ONL HFN

= Gy} 15 &@ 1,25--- @ lic
“thes = (-1)-ti| J, : J, It nel

| Ap+1, ly Ap +1, 25 see A-H, G Gel 1 42 omen sen pal
1 ' | Agi ’ Ape ypsae - Akg
ApH, rm Art, Pp Obs Act,

| Act , Aco ete Age

or
‘ — 74 .
Boje Ni (ets ae
Now the following relation holds good:
Q1r,5 Grgr-+> Aine | A,441, Toby? Ap+i, rte OG A441, i
N= pea ae tee Pe ie < Acts, Toty? Acts, (sel 15 Ate, Pe
Mor,» orgs 2+ Aor | Aan 9 ol FP Fis) ; Acs
in which 7,,7,,..-7,) %-44,---?, represents a permutation of numbers

1,2,...6 and the summation must be extended over all these
permutations.
As
A+, ales) = 2 A+, 7,

Ash iy

is the minor of the reciprocal determinant
| Aix, Ate, --. Ac

A=| Aai, As», renee Os

eee
c

ye 0 As. Satko A; | ’
which corresponds to the algebraic complement of
| Cir y +++ Air,

: ; F
Gory +++ Apr
p

we have the relation

| Ap441, Byes Acts, | Pace On yee Ur, |
: : : SSN : See
Acr 44 gece Agr | CFE, CO ND |

Consequently we find for NV

|@in» oe + Aly

Gon yes der |

ic. N is A’) times the sum of the squares of all determinants
of the o order of the matrix
\ayy 5 A12,-6. Q4>!
M= |
|Qet , Udy + +» os
which is formed from the coefficients of the given equations of
substitution.
If we represent such a determinant of the ot order in general
by D, we can write
N= A ee SD:
The numerator 7°, is reduced as follows:

A1r, Rieke Sirs, 1 Aer ; A kroay aM akeys Ale
at 17, An 4t4,7 3 Apttyr ing Ane,
Lit = ies an
Co ee :
pe eee ee Or 0

The determinant

Di (Ceara e—1)

belongs to the matrix
Ihbie apache |

: : |

Aj—1,15 +++ Aj—1,¢
M; — .
Gye, yee a1, 5
|@ot yee 2 Qog |
which is obtained by omitting the row a; (¢=1,2,...0) in the
matrix JM.
Besides
Akr ious Agr, |
Ap+1, ae pees Ati, r,

is the minor of the reciprocal determinant 4, which, apart from
the sign, corresponds to the algebraic complement of

aii |

Observing the sign, we have
|Agr. oe »- Abr

Aptian s-++ Apttyr,| =(—1P Ae”. Da,

AG; vaeketeAer:
P P

in which Dz, is obtained by omitting the row az; in the matrix J/.
So we find

Tin = (—1f A" SD; Dy,
in which the summation must be extended over all determinants of
the (g—1) order, resp. of the matrices M; and M;, and this in
such a way that the determinants D; and D, in the products are
built up from the same columns of M.
The coefficients 65; (j==1,2,...0; k=1,3,...0) are finally found
from

Ad jp. A’) SD? = (1 rt (— 1+ A? ESD;Dz,

=D Deve
bj = (— ste ——* ete 8):

so that

=D
and in particular

S72:
b; a (j= 1,2 0)
i) Sp’ J— tL, a,.--€

The determinant of the coefficients Dik (934 = 40 72,-. 7-6) SEs

| bi, bi2,..- dip, 0 ; 0 sec seen
bot, boo, . +» bao, 0 ; On Pane)
De alos aeade me) Reet)
Osea == lee :
Oe OM ee Oe botnets 0 ean 0)
0 ; 0 11-0 , 0 . Bepe,ef2r-+++ 0
Oi ce fiat See O ge 80 - 20 cue ibara|
or, if we write

| bi, dy2, . bie

| bo4, boo, ° bg. == E

| bet 5 boss > b,

| bik (SRS sa brass
: h=p+1
E is the determinant of the quadratic expression Hf in 2,, v,, ... @,
As the determinant quadratic expression in 7,,?,,...V; has the
value 1, we have
i
| on | = A?’

hence

Va - I brn
ett

de; = Alldy,,
1 1

Further we have

therefore
& i -(& guy $235 ne, vt) —D'bjjay?
Re 1 e 1 <e e+1 G
Ov =e 1 OO ——— =< = IMdxj}=
o i A 1 J
2 gu
I . 2
g(t je PLS Bins jee) i? H rh - > bineh?
= ae 1 Hide, i / —.e@ etl IT dv),
Fey Ad Cre e+1

In order to obtain the total probability 1’ we must integrate over ©
.a from —o to -+ o, and over 2,,2,,...2, resp. from

§1,5.>--- to §, + d§,,&, + d&,,...6-+d5,; i.e. the integration over

Wpiderssecp. consists in this, that in

replaced) by-6,55,,.2.s,, while dz,, dz,.:.. . dz;

Oe Oe 501. OS e:

So we find,

== S ers) Aen) =
, LT ae (: bij Sy + 2 = Oye §) se) ER cob con
ie eae G, 1 1 ld sj X
tr 1

the integrant 2,,2,,...@, are
are resp. replaced by

Wena, on. Sa ait,
x ile Vy er! Cun Fatal Sr hohe) a
Cais e+1
Th h=p+1

We have already calculated the coefficients ),,, that is to say,

expressed them in terms of the coefficients of the given equations
Their determinant / is consequently also known.

of substitution.
expression may be deduced. In

For this latter, however, a simpler
order to find it we start from the relation
Sen Moreh) eas
IT by, = A? TT by,
+1 etl

4132

1 1
Now 6;,=— = S\aAr and = An; Api =0 (for h=o-+-1....0)
Lea 1 ee

Consequently we have

better Octieper +++ betas
arlke eb eetls Oppeeter ++ Oetac |=
|b Ic,o+1 3 be ct2 quiets hee |

ERY Ae) » Octo ctor.
eH | :

bettctts 0 apnea) Le
0

|

[eesyatey, YS Apa Ape; jes Aes,
= A2e—?) 2A, +2, Apt+1,i , 2 Ap+2,i yore 2 Ante, Acie ||

SApAnat | 5, SAn Apis; So Ae:

Aztii, Apti2s AG » Aptis» 0 Ae) ae.) 2 \ Feat
Acta 5 A, cfeas-- Artes ; 0 : 0 hs -0 Rs
(—1)" As , ae qereue ae ) 0 ’ 0 Q019 0 R,
a A266) | —1 , 0 950° 0) , Anti ’ Apto1 pone Ag R;
Oia eee LON Aoi. Ap 42,2 eeeico R's
0 ‘ 0 Rtas ey 9 Diesel 6 cA 5% aeteks A. R',

or

ae Acti sy : Aptir is A Aptis,
= = A, 27 ’ A, 20 3. ol A, 27
A2(e—e) | ere, p+1 seal p+2 ° et?, c

| 4,

I brn =
o+1 :
ate Aer te dae
But
lie
Hrs }
| Aerg, ves Aer, |
is the minor of the ae ee determinant 4, which corresponds to

the complementary minor of

Gr, ; Mr, gee Ay

|

i]

| ie I
sl Az,» Ar, y+ + - Aer | ;

|

: g :
| Ger, » Gore 9- ++ Gor

'!) This reduction is easily controlled by first multiplying the rows R4, F’,...R’s
resp. by Agtia, Acti,2,...Ag+ti,e and adding all these products to A, ; then by
multiplying the same rows resp. by A¢+2,1, Az+2,2,..d4e+2,. and adding these
products to Fy, etc

11338

if 7,,7.,.--12Mef1,+-12 represents a permutation of the numbers
1,2,...0. Apparently this last minor is again a determinant D. of
the ot order of the matrix J/. Hence we have

| Aptis 4 gee Aetiy a

: : : | =Ar® x D
Acy_ Soyer A, |
and
a DSV/GE
4 Sie SS pot Sie Ser oe
fl bah oan ee (A Di Aa?
so that
1
B= = —
> 2

So our result is:

BE (4 bjjsj + 22 bn8s8r) ae
We — .é J 1 ITd3; ,
1

in which

>D;Dr. j
Dik = (-— 1)3-+-k — ce i = le Oa eks °)

Sp: k
and
; \
i —————
PDF

while D represents a determinant of the 9 order of the matrix

A115 (12,+++ Ae
|

Wii Sagi, 995, oe (9m |
\

(ila Uipeia om CHa
f f

and Dj; a determinant of the (e—A)" order of the matrix Mj, which
is obtained by omitting the row ajy, aj2,.-.aj, mm M.
Moreover the two determinants Dj; and Dr, in the products are
built up from the same columns of M.
Returning now to the coefficients @;; we have only to write
aja

aji = -
i

Denoting by PD, D;, Dy the determinants in the coefficients «;;,
corresponding to D, D; and Dy we have .

Mr, > Vr, 9 Ay D
S| (al a ca
oan pi an | hy Ny hy
| = o
eh (Uy Suen th.
| Any ’ Ir ’ rel |
| | —

7 Gm lira Cee, | D;
—= | u == a
|

| Aj +A» Oj +1,ros p44 r 1 hy, Tiere of
lees : er ees :
(mp Si. Ue Bis aa
rY ry as |
Dy
DD = ae
: h,. | h :
try Mg eee Rp

or, if we introduce the mean errors ¢; by means of the formulae

; 1
ieee
7 &; V2 b]
c p-1 p-1
DD a2 gr Epes é, D D2 2 8, Era- &, Dj 5 em oP ere ve

Before applying these results to questions concerning correlation
we shall first deduce simple expressions for the minors bj, of the
coefficients /j, in the determinant £L.

If we represent the minor of 4); in the determinant

| bi, die bi, | c IT by,
bie) =) ps 00 a a
i | Dies bez, ore L? e+l SSP):
by 8%, then for; <0,kSe:
Bik A
3 3
J P >p? Pjk
TT by,
e+1
Now
Swe ) As; Ag; yee Ari Aj_ 43 5 Ai; Aj4iji ts > Ay; Agi
= Ag; Ai; ’ > Ag; pe Agi A; —1,t ’ Adj Aj44,i ” 2 Ax; Asi

ATS; Ali; = Ap —1, Agis.:.2 Ak =1i Aj_1,i ; = Ap—1,i Asti pase eee A;
= “ at - F ta =e, 2
Ari Aj, = An+,i Apis 2 Ani Aj—1, = Ar i / $16 2 Appii Act
=F a AP
py: si Aj, ’ > Az; Ag; ees Aci Aj; 1, > PAS Aj44,i yeceeaes

1135
| Ay ’ Aye aoe Alt ’ 0 ’ 0 Seal) ,
eA ees As 0) M0 5.0
Ageia , lps eae : 0 , 0 0
+ l Arti ’ Ap+i,2 pe Apis) 0 ’ 0 0 ’ yet
C2) Ae ’ es pede ’ 0 ? 0 =o ? 0
aly 50) pees) » Ain, Agy,...A; =fetGs Apt 1 5-3

Se Sno =

a1
| 0 . =I yd , A1s, Az»,...Aj—12, Aj 412 5--Age

0 : 0 il ) Aes Age Apestin, Agtte Ae |

JAligl - eakiy (gee ey eeGy ein” Cosel.
Alt Gey dice yay °°, Aopiia 4. wd:

= | 4-11, 4%. 1,2, 4e—-14—1 At—1,441---Ap—ie |
Ag+iyt ) Aj qi; Ak+i—1; Akt t445---Ag pie

| Ag ; As : Anes ’ Anl44 EAS |
| |

| Ai 5 As, seca aasisI c Ajti1 weeded

| At2 Avg Aj—tje » Ajtiy 5--doe
Se A a FA maine Aly eT dy A eg eeAeae |
Aria 5 Axtpt ye bj—iitis Appa tps Aci
| Ae 7 Ase peo tc » Aji WS

+ = ajiapi
Bi 1
= aj) Ak] = — z

etc Ae g =
AxXe—1) ° l=1 /aXe}

Consequently we find
a
+ 2} ajiagi

Bye — —

LA?

By = Sp?

Sp :

and in particular

(To be continued).
74
Proceedings Royal Acad. Amsterdam. Vol. XVI.

1136

Chemistry. — “Equilibria in ternary systems. XIV. By Prof.
SCHREINEMAKERS.

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

After the previous discussion of the saturationcurves under their
own vapourpressure and of the boilingpointeurves of a component,
we must yet deduce its solutionpaths under its own vapour-pressure.
As, however, we discussed already formerly those of binary and
ternary compounds the reader may easily deduce those of a component.

In the previous communications VII—X we have discussed the
fourphase-equilibrium /’ + /” + £-+ G; for this we have assumed
that # and: #” are both ternary compounds. It is, however, easily
seen that these considerations apply also to binary and unary sub-
stances, provided that /’ and #” contain together the three com-
ponents; the line #/” is then situated, perhaps its extremities
excepted, completely within the componentstriangle. Then the
liquid contains aiso the three components, so that the quantity of
nene of them can approach to zero in it. When / and #” contain
together only two components, the line /’¥” coincides with one of
the sides of the componentstriangle. The quantity of one of the
components may then approach to zero in the liquid and in the
vapour, so that we must contemplate this case separately.

When we take e.g. the ternary equilibrium 6 + C+ L + G,, it is
evident that the quantity of A can become equal to zero in the
liquid and in the vapour. If the liquid and the vapour, in which
the quantity of one of the components becomes equal to zero, is
represented by £, and G,, then the binary equilibrium B+C+L,+G,
arises. Herein /, is the eutectical liquid under its own vapour-
pressure of the binary system B+ C; G, is the corresponding
vapour; the corresponding temperature and pressure we call 7, and
P,. The ternary equilibrium 5+ C+ L-+ G terminates, therefore,
when the quantity of A becomes zero, at the temperature 7” and
under the pressure /, in the binary eutectical point with the phases
B+C+L,+ G,.

Reversally we may also say that by addition of A the fourphase-
equilibrium 6+ C+ £-+G proceeds from the binary eutectical
point with the phases b+ C+ L, + G,.

When we take a eutectical point 6+ C+ ZL, under a constant
pressure, so that no vapour occurs, the threephaseequilibrium
b+ C+ L is formed on addition of A and the eutectical tempe-
rature is always lowered. From this naturally the question follows ;

1137

what influence has the addition of a new substance A on the
temperature 7’, and the pressure P, of the eutectical point under
its Own vapourpressure with the phases 6+ C+ L, + G,.

We may put this question also more generally ; for this we replace
the eutectical point with the phases B+ C+ L, + G, by a qua-
druplepoint with the phases “+ /#” + 1,+ G,; F and F” are
then either the components 4 and C’ or binary compounds of
B and C.

When we take a constant pressure so high, that the vapour
disappears, and when we add the substance A to the equilibrium
Ft +L, then the temperature is lowered. We may express
this also in the following way: the common meltingpoint or point
of inversion of two substances is lowered under a constant pressure
by addition of a third substance ‘).

We now must put the question: what influence has the addition
of a new substance A on the temperature 7’, and on the pressure

P, of the quadruplepoint with the phases /’+- 4’ + L, + G.

Firstly we shall consider the general case treated 2 communication
VILL more in detail. Instead of the equations (2), (3), and (4) (VIII)
we write:

[(@ a)r + (y —B)s| da + [(a@ —a)s + (y—)t] dy=AdP—BdT . (|)
[(w,-@)r + egy + [(v,-a)s + (y,-B)t]dy = (A+ C)dP-(B4+D)dT (2)

{(a'-a@)r + 3)s|da + [(a'-a)s + (p'-p)t|]dy = (A-A') dP- (B-B')dT . (3)
We find from (1) and (3), eliminating dy: ®

E(rt—s*)dx = [{(a’—a@)A + (ex—a)A}s + {(8'—y)A + (y—B) At] dP
[(a'—a#)B+ (a -a)Bis + (8'-yB+(y B)B't] a
We find from (2) and (3):
E, (rt—s*) da = |
[{(a'-a,) A+ (a ,-a)A'+ (a'—a) Cis +-{(8'-y,) A+ (y-B)A' + (8'-8)Cle]dP (5)
—[\(e'-«,)B + (w,-a)B'4-(a'-a) Dis + {(8'-y,) B+ (y-B) B+ (6'-8) Dit dT |

Herein £ is equal to:
(a! —2)(8—y) + («—a\(8'—) =(6' —8)(w—a) + (a —0)(8 y=
=(8'—8)(#— a') + (a'—a)(8'- 9).
We find /, by substituting in #2, and y, for x and y. For the sake
of abbreviation we put the following:

1) F. A. H. Scorernemaxers. Heterog. Gleichgewichte III’.

74*

1138

(a — a) V 4+ (a — a')v + (a—a2)v' + Feds 2 (z' —a) V,

Oy
f 7 I ! OV Y
aioe ie aU Misrm lsat) Serra (8) a) oh ee een
aH (6)
(a — a) H+ (e— a’) y 4+ (a— 2) + He = (c' — «) A,
Y
oH
(88) ELT 1B) ic et M0 crs sel td

When we replace #, V, H, « and y by #,, V,, H,, x, and y,
(= ee ete. rest unchanged we obtain the corresponding quantities
Vi» Vie, Hig and Ay,.

The following relations exist between these eight quantities, as
we may easily deduce.

E\V, = EViy = AV — EVig | (2)
E\@, — EM), == E\H, — EM,

We find another relation by eliminating /, and / from both
these equations.

Substituting in (4) and (5) their values for A, B ete., we find
with the aid of (6):

E (rt — s*) dv = [(a' —- a) V, .s + (6 — 8) Vz +t) dP | (8)
—[(@ —e«)H, .s+ (8 — 8) A, .t] dT

E, (ri — 3?) de = [(e' — ae) Viy-s +3 (8 — 8) Viget] dP | -)
— [(’ —a) My s4 (8 —B) Ma. t] aT

Eliminating de from (8) and (9) we find, when we make use of
the relations (7):

E, E,
Hy—=. Hy His — Hs

dP ee Hi
Mie eet eae Boe he
J Nii V, Vig ——. Vi;
i, EB ad EB
Herein //,, HH, ete. have the meaning indicated in (6); from (10)
it follows however, that this is also true when the term, in which

EE ov FE, occurs, is omitted in each of the eight relations (6).

Further we may deduce from (8) and (9):

Ei
IP (rope Hh IF 11, )

pee 11
da ia — ¢) a\(V Aisi y— V l yHy)s -- (8 Re Vy HD) ..— Vi, yoni Ce)

a Ne ee Te)

1139
In (12) N indicates the same denominator as in (11).

Let us now consider the case that both the solid substances of
the equilibrium # + #4” + L + G are binary compounds of 2 and C.
We must then. put a=Oandae’'=9. As E becomes = (f'— 8) a
and EL, = (@'— £) 2,, it follows from (10), (11) and (12):

a,
HN 4—— HA,
av

dP (13)
7 ar Tadd pt el Sen, ae ee
(rt—s*)a| Fy eu
APY) le Neda i ee 4
de (VeHz—VizHs)t ()
t—s*)al V: aby
ep a ee eae is
ie AED (ie)

Let us now consider the terminating point of the ternary equilibrium
F+k + L4G in the quadruplepoint &-+ £’ + L, + G,. For
this we make in the previous equations w and «, approach to zero.
As Limrz = RT it follows:

1
dT x Cs)
VYya— a V,,
x 0
R1| th,—(™) H, REN Vine 3 eve
dP \& F dT a), (17)

dz VA 2 — Viale da Ese ee Vics
Herein (2) is the value which a assumes for «=O and xv, =0.
z ), é
Further is :

(2) BV oo (Gp = Bie (iy) oe (8 8) Ve (18)
(@—s)V,+@%—8)» + @—y,) 7’ = ——8) Viz - (19)
@—sH + —8)1+6—y)v=C6 -B) ar - (20)
('— 6) 4, +%,—8)7+ @—y,) 7 =( —8) Mis . (21)
wherein to all quantities (y, 7,, V, V,, ete.) we must give the values,
which they have in the quadruplepoint #—+ #” + L, + G,. Herein
L, has the composition: y quantities of B+ (1 —y) quant. of C;

G, has the composition: y, quant. of B+ (1 —y,) quant. of C.
Between the three phases /’, /” and L, always may occur the reaction:

1140

(8’—) quant. of L,+(y—3’) quant. of #+(8—y) quant. of F7=0 (22)
in which always one of the coefficients is negative. This reaction
represents, according to the sign of the coefficients :

1. a congruent melting or solidification of 4+ /” viz. the reaction
F+h2L,.

2. an incongruent melting or solidification of #—+ H” viz. the
reaction FZ F’ +L, or MSF L,.

Consequently the incongruent melting or solidification of /”—-- /”
means: the inversion of / in /” or reversally, by the side of liquid
and vapour.

From (18) and (20) it follows that V, represents the change of
volume and //, the change of entropy, when one quantity of vapour
is formed at this reaction. Therefore, J”, is the increase of volume,
Hf, the increase of entropy at the congruent or incongruent melting
of F-+ Ff’.

Between the three phases /, /” and G, the reaction :

(8'—B) quant. of G, + (y,—') quant. of F + (8—y) quant. of F' =0 (23)
may take place. From (19) and (21) it follows that V1. represents
the increase of volume, //;, the increase of entropy when one quantity
of vapour is formed at the reaction (23). Vj, is, therefore, the
increase of volume, //), the increase of entropy at the congruent or
incongruent sublimation of + Ff”.

If we call W, the (congruent or incongruent) heat of melting, and
Wy. the (congruent or incongruent) heat of sublimation of #’-+ F”,

thene Hy == - and fa Further we put for the sake of
abbreviation
Vii Wea Vin Wiig = 2 KG, Ee coer. eee (A)
When V,, the change of volume on melting of /’ + /” is positive,
K is certainly positive; when, however V, is negative, this form
will nevertheless still be also positive, by reason of the great value
of Vy, with respect to V,. For this we shall assume A’ positive.
When we put further :

NV (=) Vseiid eA ae (“) Wy. . (25)
x), CHD

it follows:
CP > SAW. dP RT c dT Fuel 5
T —=— 7 -=——. AW ; —=—-——AV. (26)
CIN AAW dv IS da K
dl
( ‘) is the ratio of the quantity of A in the vapour to that in the
v 0

a

liquid when we add a little A to the binary equilibrium # + #” +

1141

+ L,+ G,; we may call this ratio the limitratio of A in + & +
+ L,+ G,.

Considering the cases (=) <1 and (=) > 1 in connection with
the values of Vj,, Vz, Wi, and W, (V can also be negative) it follows :

The P,7 curve of the ternary equilibrium #’-+ #” + LZ + G ends
in the quadruplepoint /’+ #” + £,+ G,; it is a curve ascendant
with the temperature, when the limitratio of A is smaller or only
a little larger than 1; it may have a point of maximumpressure
when the limitratio of A is much greater than 1; it may have,
besides the point of maxiniumpressure, also a point of maximum-
temperature, when the limitratio of A is very large (e. g. larger than
10000) and when the volume increases at the congruent or incon-
eruent melting of 4+ +”.

We may express the previous also in the following way :

The congruent or incongruent meltingpoint of two substances
(Ff -+- F’) is always lowered by addition of a new substance, when
we take the pressure constant; generally this is also the ease when
this addition takes place under its own vapourpressure. In the latter
case the temperature may however, before it decreases, yet first
rise a little. This can take place however only in the case that the
limitratio (=) of the new substance in #-+ H”’ + ZL, + G, is very

a ay
large and when the volume increases at the formation of liquid
from f+ F’.

The vapourpressure of the congruent or incongruent meltingpoint,

ean by addition of the new substance according to the value of

av y = ~ 5 : » 4
inh either decrease immediately or, before it decreases, firstly in-
a“ 0

crease. This latter is certainly the case when the temperature increases
also firstly, but it may also take place then, when the temperature
decreases immediately.

v

Let us now consider the case that ( ) is exceedingly small or
0

v
approaches to zero. This will be the case when the quantity of A
is exceedingly small in the vapour, therefore, e.g. when A isa salt,
very little or not volatile. From (25) and (26) then follows:

cE Wit aaa ey pack Te Hes die BRE:
‘a \ mt Py sain re K

As Wj, represents the (congruent or incongruent) heat of subli-

aad

Vie - (27)

1142

mation and Vy, the increase of volume at the (congruent or in-
congruent) sublimation of /-+-#”, W, and V,, are both positive.
Therefore, the equilibrium /’-+ #’ + 1+G proceeds from the
quadruplepoint immediately towards lower temperatures and pressures.
Let us imagine a P,7-diagram with the quadruplepoint 4’ —--} #”’ +
+ L,+G,. Four iriplecurves proceed from this point viz. the
(congruent or incongruent) binary meltingeurve #+ #” + L,, the
(congruent or incongruent) binary sublimationcurve # + #” + G,
and further the two binary solutioncurves under their own vapour-
pressure, viz. the curves /+ L,+ G, and #’ + L,+ G,. When
we draw in this P,7-diagram also the curve for the ternary
equilibrium /'+ /” + 1+ G, this touches, according to (27) the
binary sublimationcurve #’-+ #” + G, in the quadruplepoint.

An example of this case will be found when we add a third
substance, which is not volatile, to the equilibrium: /C7—-+- 707, +
+;,;+G, occurring at T, = 22,7°'and under P, = 42 m.m., in
which G, contains the two components /, and C/,. The same shall
also be the case when we add a substance, which is not volatile,
e.g. NaCl or NaNO, to the equilibrium Na,SO,.10H,O0-+ Na,SO,+
+4,+G, wherein G, consists only of water-vapour.

av

. 1 . . .
Let us now consider the case that is very large; as limit-
© fo)
v0

ve
av, Oak eto > fr
case we shall assume infinitely large. From (25) and (26) then
av
0

follows :
dP OW,
ary Ve

As W, represents the heat, required for the congruent or incon-
ernent melting of /’+ /”’, and V, the increase of volume at this
reaction, W, is positive, while V, may be as well positive as
negative. Imagining in a P,7-diagram the quadruplepoint #—+ #4” +
+,+G, and the binary (congruent or incongruent) meltingcurve
F+ Fk’ + L,, proceeding from this point the curve of the ternary
equilibrium A+ #” + + G will touch this binary meltingcurve
in the quadruplepoint.

In the quadruplepoint “+ #” + L,+ G, always between the
phases L,, G, and F the reaction: .
(y, —2) quant. of L, + (@—y) quant. of G@, + (y—y,) quant. of 7” = 0 (29)

(28)

may occur. The changes of entropy and of volume at this reaction are:
(y¥,—8) 2 (By) Ay G9) aie eo eo)
(,—8)V + (By) + G90? ay ie eo)

11438

It follows from the values of Vz, Viz, Hi, and M,, [(18)—(
that we may aiso write for (30) and (31):
(Beer ig = (eae) Eee ae Lae er (S2)

bo
=
=)

and
(8B—y) Vie —(8—y,) Vr . . . . . . (88)
(30) and therefore also (82) represent the increase of entropy,
when at the reaction between L,, G,, and F’ in all 8—y quantities
of vapour are formed; (31) and (33) represent the change of volume
at this reaction. From this it follows: when between the phases /,,
(., and #’ a reaction takes place, so that one quantity of vapour
is formed, the increase of entropy is:

NL Pe: ou diel ae oe)
B—y
consequently the heat which is to be added:
3S —1
ae a cn hubs dae tee (35)
B—y
and the increase of volume:
=
ee tt ae eta (ee)
B—y

Let us now imagine in a P, 7-diagram the quadruplepoint / -+--
+ /” + 2,4 G, and the binary solutioncurve of /’ under its own
vapourpressure, proceeding from this point, therefore, the curve
F4I1L,-+G,, its direction in the quadruplepoint is fixed by

r Un a
,— —— W,
Pcie Mee nevi a
dT p—y, ee ne \s
Vig — “ V;,
p-y

We imagine also in this P?, 7-diagram to be drawn the curve of
the ternary equilibrium /#’-++ /’ + 1+ G proceeding from this
quadruplepoint #’'4+ /” + 4,+ G,. Its direction is fixed in this
point. by (25) and (26). When accidentally :

cP B- “YM
= Sead Pat Cara hth Gee (ate
( wv ) Baa oe

both the curves will touch one another in the quadruplepoint.

The meaning of (38) is the following. We imagine in the con-
centration-diagram on the side SC’ the liquid of the quadruplepoint q.
Through this pot g runs a saturationcurve under its own vapour-
pressure and a boilingpointcurve of /. The meaning of (88) is that
the point of maximum or minimum pressure or temperature falls
exactly in gq.

1144

In the same way we find that in a P, 7-diagram the binary
solutioncurve under ifs own vapourpressure of /” proceeding from
the quadruplepoint, therefore, curve #” + L, + G,, and the curve of
the ternary equilibrium /’-+ /’ + L4G proceeding from this point

touch one another when
r Seay
2) Ge Be, Ne ire ee
& 0 p—y

We can summarise the previous results in the following way. We
imagine a P?, 7-diagram with the quadruplepoint + #” + LZ, + Gi,
the four triplecurves proceeding from this point and the curve of the
ternary equilibrium + #” + L4G proceeding from this point.
This last curve touches in the quadruplepoint :

the binary (congruent or incongruent) meltingcurve of # + F’

‘curve # + Ff” + L,) when G — oo :
x Jo

the binary (congruent or incongruent) sublimationcurve of #-+ F”
Ay

(curve + #” + G,) when i) (i
av

0
the binary solutioncurve under its own vapourpressure of F

(curve + LZ, + G,) when (38) is satisfied

the binary solutioneurve under its own vapourpressure of F”
(curve #’ + LZ, + G,) when (39) is satisfied.

The above considerations apply of course also to the ternary
eryohydrie curves under their own vapourpressure. As in a binary
cryohydric point under its own vapourpressure the equilibrium
F4+Icee+L,+G, oceurs and as from this point the ternary
eryohydric curve /'+ /ce-+ L-+ G proceeds, we have to replace
only £” by Jce in our previous considerations. Then we must equate
B’ to O in (18)—(21), (25) and (26); we then may summarise our
previous results in the following way : :

The cryohydric point of a substance is always lowered by addition
of a new substance when we keep the pressure constant; generally
this is also the case when this addition takes place under its own
vapourpressure. In the latter case the temperature, however, may
also firstly increase a little, before it decreases; this may take piace
however only then, when the limitratio = of the new substance
in F+ Iee+ L,+ G, is very large and when the volame increases
at the formation of liquid from /’ + Ice.

The vapourpressure of the eryohydric point, may, according to the

az a 3 : ;
value of ( ‘) by addition of a new substance either decrease im-
wv 0

1145

mediately or, before it decreases, first increase. This latter is
certainly the case when the temperature also increases a little at first,
but it may also take place then when the temperature decreases
immediately.

We have assumed in all our previous considerations of the equi-
librium + #7” + 24 G that the four phases have a different
composition; now we shall consider the case that two of these phases
have the same composition. This will amongst others be the case
when / and #” are modifications of the same solid substance or
also when F or #” is one of the components and when the vapour
consists only of this component. This latter is e.g. the case for the
eryohydric curve under its own vapourpressure /’ + /ce + L + G
when of the three components only the water is volatile and the
gasphase contains consequently only watervapour.

Let us first consider the latter case; we take, therefore, the
eryohydric curve under its own vapourpressure /’+ /ce + L + G
and we preassume that the gas contains only watervapour. The results,
therefore, of course remain also valid, when we replace the ice by
another component. Now we must equate in our previous consider-
gions 0, Bp’ ——0) 2, = 0'and 7,0; from ‘this: follows: 4 =
ay—Bx and FE, = 0, from (6) follows V,,—= V,—v’ and H,,—= H,— 1’.
Now it follows from (10):

ee tite Cee tal a @ al)

Herein H/, and J’, represent the entropy and the volume of the

/

gas, therefore of the watervapour; 2) and v’ are the entropy and
Oo}
. : 5 Gk .
the volume of the zce. From this follows, therefore, that — is the
¢

same for the ternary equilibrium / + /ce-+ £-+'G and for the
unary equilibrium /ce + watervapour. This is evident, also without
calculation; removing viz. from the ternary equilibrium / + /ce +
L+G the solid substance #’ and the liquid ZL, we retain, as G
consists only of watervapour, the unary equilibrium zce +- watervapour.

If we imagine the sublimationcurve of the ice and the eryohydric
curve /+ice+ L-+G to be drawn in a P,7-diagram the two
curves must, therefore, coincide. As the first curve is experimentally
known, we know, therefore, also the curve #+ ice + D+ G.

A cryohydric curve under constant pressure (consequently the
equilibrium /’-+ ice + L) has in the concentrationdiagram the point
of maximumtemperature in its point of intersection with the line,
which joins the two solid phases /” and ice. This is also the case

1146

with the eryohydric curve under its own vapourpressure. In the
point of intersection of this curve with the line /"— 7ce is viz. ey=B—e,
therefore H=0. From (11) and (12) it follows therefore, that dP=0
and ¢@7'’=0. In this point of intersection pressure and temperature
are, therefore, either maximum or minimum. In order to examine
more in detail whether a maximum ora minimum occurs, we assume
the conditions of equilibrium for the system /’+ ice + L + G.
These are:

WA OZ abies
Lay Ge gee Mak i
aU oaee ey)
a—+B—490—C=0andZ,—G=0
Ow Oy
Now it follows from the first of these conditions:

OV OV
wr + ys) dx + (ws 4- yt) dy + (« ae +y aaa V+ “) dP
x y

OH + 0H a a Wis ne or Os ae i
aG = + y ay —H+y7 ja +iirte ye = 5) 4- (42)

or Os Os Ot
+{s+te— + y- dady + 3(tte—+y—]ady’+ R=
dy ~~ OY : Oy “Ons
From the second it follows:

OV OV
(ar + Bs) da + (as + Bt) dy + (« > Bo -b vr) dP
2 Oy

OM ea AO as mdr KON ds :
as (« an -- Pp Oy sete 9] ) ar 2 a aa + 5.) da (43)

ab
-—
~
g
=
ar
eos)
| &
SS
Q
8
aS
eli
whe
a
~
g
Q| Q
S| &
i
coe
S|
SS,
Q
oS
S
od
S

Herein R and R' contain terms with dPdx, dTdx ete., which we
may neglect as will appear later. From the third condition follows:
(V0) dP — (Hi n)iaT = 0 ee

wherein the terms of higher order can also be neglected. As in the
point of intersection of the curve with the line /—J/ce ay = Bx, so

we may substitute in (43) @= adv and 6 = dy.
When we subtract (42) from (43) after having multiplied (42)
by 4, we find:
{A(V—v') +- v'—v} dP—}0(H—7') + 7'—7jdT |
= 3A(rdx* + 2sdedy + tdy’) + R" \°
Let us substitute the value of dy from (43) into (45); it is apparent
from (45) that it is sufficient that:
(as + Bt)dy = — (ar + Bs)da
and that we may neglect the terms with dP, d7’ ete. We may

(45)

1147

4

write then for the second term of (45): }4Q.d2*, wherein Q is
positive. From (6) it follows that we may write Vz and //, for the

coefficient of dP and d7’; (45) passes into:

VAREDOE,. dD e ONdn Vt , ayi gi che (48)
av
From (44) and (46) follows:
2e [H2(V,'—0')— Vx (H, —7')] dP = — a(,—7') Qda’? . (47)
2e [Hx V,—v')— Ve (H,—7')| d? = — al V, —v') Qda*?. . (48)

As V,—v’ = Vi, and H,—7’ = H).,, we see from (24) that the
coefficients of dP and d7’ in (47) and (48) are positive. Therefore,
dP and dT are zero at first approximation, at second approximation
negative so that pressure and temperature are maximum.

We may summarise the previous results in the following way: in
a P,T-diagram the sublimationcurve of the ce and the eryohydric
curve under its own yapourpressure (/’ + ice + L + G) coineide.
The eryohydric curve under a constant pressure has its maximum-
temperature in the pure solutionpoint of /’; the eryohydric curve
under its own vapourpressure bas in this point its maximumtempe-
rature and -pressure.

When F is a binary compound, we must in the previous consi-
derations “not only put e'—90, p'=0, «,=0 and y,—0, but

also «a'=9. From this follows: H=—@z, FE, =0, Viz.= V,—v'
and A, = H,—7'. From (10) again it follows that:
dP H,—1!'
7 ! (49)
dl a=

1
so that in a P,7-diagram again the sublimationcurve of the ice and
the cryohydrie curve /’-+ /ce + L + G@ coincide.

Considering the cryohydrie curve in the vicinity of the binary
eryohydric point #’+ ice + L,-+ G,, it follows from (25) and (26):

Bee ee eye eee ee (en mec)
dx K = K K

EE SEN od AN Tn i oh Bil Sey, aah (SIN
ao K : K a

From the binary ecryohydrie point, therefore, pressure and tempe-
rature decrease along the cryohydric curve.

We can also obtain these results by substituting 7= U+ RT x
log x in the three equations (41).

Now we shall suppose that /’ and /” are modifications of a same
substance, so that P+ #” + L + G represents the modificationcurve

1148

under its own vapourpressure and its corresponding vapourcurve.
We put in the formulae (2)—(4) (VIII) a’ =a and p’=8. We
then may write these :
(vw —a)r 4- PEs s| da +- [(@ —a)s + (y —B)t] dy = AdP—BdT. (52)
[(w,-—a)r + (y,—8)s] de + [(@,—-a@)s +- (y, —B)t] dy (53)
- (A +. C) dP—(B + D)aT
(=v) dP —(q7—=n) dl 2 (54)
Let us first take the substance /’. The P,7-diagram of this
substance was already discussed formerly and is drawn in_ fig.
(III) and 4 (IV). In fig. 1 ar represents the sublimationcurve,
Id the meltingeurve and KF’ a part of the limiteurve mM of
ihe substance /’. We find also in fig. 1 the P,7-diagram of the
substance #”; herein a’7rA’ is the sublimationcurve, /’d’ the melting
curve and A’ F” a part of the limiteurve m’ A’ FW’ of the substance /”.
The two sublimationcurves touch one another in 7; consequently
in 7 the equilibrium + /#” + G occurs, wherein G has the com-
position /”7 = /”. Therefore from 7 also a curve r/ proceeds, which
represents the. equilibrium /#’-+ /’. This curve may proceed from
ras well towards higher as towards lower temperatures; in fig. 1
ihe first case has been assumed. It is apparent from the position of
the different curves that we have assumed v/°> v, 7’ >, V >v
and V >’.
dP
From (54) it follows that ae for the equilibrium # + #’++L+G
and /’+-F” is the same. This is also apparent without more
explanation; when we remove viz. the liquid and the gas from

1149

Ft F’+ £L+G, then f+ F’ remains. Therefore, in fig. 1 curve
F+F+L+4G must coincide with +; it will, however, only
partly cover this curve. It is represented in fig. 1 by wv, wherein
w and w are the points of intersection of mA FM and mK’ PM’.

In order to see this we take any point 2 of the curve /-++ #”-+ L-+-G.
When we remove /” and when we keep further the quantity of
vapour always exceedingly small, the liquid JZ of the remaining
equilibrium’ /+-L+-G traces at change of temperature a solutionpath
of F under its own vapourpressure. The P,7-curve of this path is
represented in fig. 1 by yw. When we remove /’ and when we
keep again the quantity of vapour exceedingly small, the liquid 4
iraces a solutionpath of #” on. change of temperature ; this is indi-
cated in fig. 1 by y’ a’.

Only the part yx of the first solutionpath, only the part # /” of
the second represent stable conditions. Restricting ourselves to stable
conditions, we may say therefore: from each point of the modifi-
cationcurve “+ F’ + L + G one solutionpath of /’ proceeds towards
lower temperatures, and one of /” towards higher temperatures.
From this it follows that the one extremity of the modificationcurve
must be situated in w, and the other in w.

In order to deduce the modificationcurve and its corresponding
vapourcurve in the concentrationdiagram, we may act in a similar
way as e.g. at the deduction of the saturationcurves under their own
vapourpressure. When we take a definite 7 and P and when at
this 7’ and under this P a saturationcurve of F' exists, this is
circumphased ; the same applies to that of #”. When ai the assumed
T and P the modification /’ is the stable one, its saturationcurve
surrounds that of /”; when F” is the stable form, the saturation-
curve of /” surrounds that of F.

The two saturationcurves can never intersect each other, they can
completely coincide. This is the case when we choose P and 7’ in
such a way that they are in accordance with a point of curve rh
in fig. 1, so that the two modifications #’ and F’ may exist by the
side of one another. Then these two coinciding curves form the modifi-
cationcurve under a constant P and at a constant 7’; it represents
the liquid Z of the equilibrium / + #” 4- L.

Now we change not only the 7 or the P, but both together and
in such a way that they are always in accordance with a point of
the curve r/ in fig. 1; also we consider the vapourregion and the
heterogeneous region L—G. Then we find easily that the modifi-
cationcurve under its own vapourpressure and_ its corresponding
vapourcurve are circumphased.

1150

It follows amongst others from the formulas (52)—(54) that this
modificationcurve cannot go through the point #’"= /”; when we

put herein «=e and y= 8, it follows that

Bt ae aay re he eee

V—vy V—' v'—v

must be satisfied.

This means that the curves /d,F’d’ and rh of fig. 1 touch one
another in one point. Now it is apparent that these curves may
intersect one another in one point. When viz. two of these curves
intersect one another, necessarily the third goes also through this
point of intersection; only very accidentally they can, however,
touch one another. In the same way we find that also the corre-
sponding vapoureurve cannot go through the point #/= #”. From
(52)—(54) it follows that dP and d¢7’ become zero at the same time
and that this is the case when

JERE SAY (56)
&e—Ee t,—a

This means that the solid substance (/’— F”’), the liquid and the
vapour are situated on a straight line. It is evident that on each
closed modifieationcurve two such points « and w occur and on the
corresponding vapoureurve two corresponding points uw, and w,.
Pressure and temperature of the equilibrium # + #” + LZ, + Gi,
are in accordance with point w of fig. 1, pressure and temperature
of the equilibrium # + #” + ZL, 4- Gy,, with the point w of fig. 1.

From (54) it follows that the pressure can as well increase as
decrease at increase of temperature; therefore we may distinguish
two cases. :

1) P- and 7-maximum coincide and also P- and 7-minimum.

2) P-maximum and 7-minimum coincide and also P-minimum
and 7-maximum.

The case sub 1 oceurs when the pressure increases at increase
of temperature; curve r/ is then situated as in fig. 1. The case
sub 2 occurs when the pressure decreases at increase of temperature,
curve 7/ proceeds then in fig. 1 from 7 towards lower temperatures.

Now we shall assume that /’ and consequently also /’ is a binary
compound of B and C; to the P, 7’ diagram again then fig. 1 applies,
in which now however the solutionpaths no longer touch the melting-
curve in For Ff”.

In the concentrationdiagram the modificationcurve + #” + £-+ G
ends in two points on the side BC, the same applies to its corre-
sponding vapourcurve,

1151

Let us assume that point F’ in fig. 3 (XI) represents the two
modifications / and F” and that hafn is the modificationcurve and
h,a,b,n, the vapoureurve.

Therefore, in the binary system two temperatures and pressures
of inversion occur, viz. in the points / and n. Considering the equi-
libria under a constant pressure, 77, = 7’,; under their own vapour
pressure, however 7’, and 7), as wellas P, and P, are different. The
points / and n of fig. 3 (XI) resemble viz. w and vw of fig. 1. Although
solid substance, liquid and gas of the equilibrium #-+ F’+ L)-+G%,
and /# + F’ + L,-+ Gn are represented by points of a straight line,
yet in A and n dP—O and d7’—0 is not the case. In order to
see this, we substitute in (52)—(54) «@ = 0; from this we find:

1 dP £P. s y'—Yy i
rates oes BY)
RT \ da J=0 a“ s, J (y’—n)A V—(e'— v7) A

1 al a, 8 v'—v

a eset ea yea a a Ne ia (58)

RT lel a “aca V—('—v)AH
so that dP and d7’ in h and n are not zero. ATV is the increase of
volume and A/f/ is the increase of entropy when between F, ZL,
and G of the equilibrium /+-/"+-L,+G,, or F+F’+4 Li+Gi,
a reaction takes place, at which one volume of vapour is formed. | We
may also replace in (57) and (58) AV and 4H by AV’ and AH’,
which indicate then the same increases when the phases #”, L, and G
react]. When in fig. 8 (XI) / and n are situated not too close to
F, or in other words, when the temperatures of inversion 7, and 7’,
are situated not too close to the meltingpoint 77, 4 V is >0 and large
with respect to v’ —v; the denominator of (57) and (58) is then
generally positive.

That there may be accordance with fig. 1, we take first v’ >v.
In fig. 3 in the vicinity of h and h, (see A Faa,) s >s,; in the
vicinity of n and n, (see A bb.) s<s,. From (57) and (58) now
follows: ? and 7’ increase along the modificationcurve from n towards h.
When we take v’ << v then it follows: 7’ increases from / towards
n, P from n towards h.

At last we may still consider the case, that / and consequently
also F#” is one of the components, e.g. 4. The reader can easily draw
himself the P,7-diagram, which is now simpler~ than in fig. 4.
In the concentrationdiagram the modificationcurve ends then in two
points, the one on AC and the other on BA. If we determine the
modificationcurve under a constant pressure, 7’ is the same in each
point of this curve; in this case 7’ and P will change however again

75

Proceedings Royal Acad, Amsterdam, Vol, XVI,

1152

along the curve from point to point and either in the same or in
Opposite direction.

When we determine, therefore, e.g. the temperature of inversion
and pressure of inversion of rhombic in monoclinic sulfur, or of
two modifications of A.NO, ete. in a mixture of two solvents and
under its own vapourpressure, this 7’ and P of inversion change
with the composition of the solvent. These changes are, however,
very small, as it follows from the previous considerations.

(To be continued.)

Mathematics. — “On the singular solutions of ordinary and
partial differential equations of the first order”. By Prof. Hk. pe
Vries and G. SCHAAKE.
(Communicated in the meeting of March 28, 1914).
Inrropuction. If the complete integral of a partial differential
equation of the first order with two independent variables, /’ (7,y,2,p,q)
=( is represented by /(2,y,2,¢c,,c,) = 0, and if the result of the
elimination of c, and c, from the three equations

Ojai of
(0) ; —_=— 0 , —=0
J ae, de,

is called for the sake of brevity H=O, the following peculiar
phenomena may arise. If the general solution /(2,y,c) = 0, of an
ordinary differential equation of the first order / (v,y,p) = 0, possesses
a nodal locus, if belongs generally speaking to the result of elimination
of ¢ from the two equations

of =a

0c

and only in one particular case it does not belong to it; with the

te =="0) ;

partial equations it is just the reverse, at least if in this case the
locus of the nodes consists of one or more curves; if there is a
nodal surfuce, it does belong in general to =O, though there is
a possibility that it does not.

It is a matter of course that all possible cases may be arrived at
by a purely anatytical method; but it appears that considerations
derived from polydimensional geometry throw a vivid light on those
various analytical possibilities and so to say increase the differences
and render them more essential; to prove this is the aim of the
following paragraphs.

§ 1. Let in the first place be given an ordinary differential equation

of the 1st order
Pile, y, p= 0;

with the general solution / (v,y,w) = 0 (we represent, with a view
to the geometrical interpretation that is to follow, the arbitrary
constant by w), then the result of elimination 4’ = 0 of

ei Of 0

ieee hoi Maar
represents the locus of those points in the vy-plane, for which the
equation f(,y,u) = 0, considered as an equation in w, possesses a
double or multiple root, hence the locus of those points, through
which one particular integral less passes than through an arbitrary
point (if we restrict ourselves to a double root); it is obvious now
to surmise that a point which is node of a definite particular integral,
will belong to this locus, because the curve with the node passes
twice through that point, but in general this is incorrect, as may
appear from very simple instances. The equation

x? —y* — 2a (« —yp) = R?—2 («—yp)’

has as general solution

in which @ represents the arbitrary constant, consequently a system
of equilateral hyperbolae. The resalt of elimination / of a from
this last equation and its partial derivative with regard to a: gives,

H= a —2y7—2k? = 0,

and this is really the envelope of the equilateral hyperbolae.

Oy jit ee of

Let now — = 2#—2a=0, and — = — 2y = 0, then we find that

Ow Oy ‘
the point ea, y=O is a node for the particular integral which
is determined by giving to a e.g. the value #, thus for the pair
of straight lines

(e—RyY—y*? = 0;

but the node «= Rk, y=O0 does apparently not lie on #. And in
fact through the point «= Rk, y= 0 passes not only the particular
integral a= R, but also a=O («#’*—y’?= h?), viz. two, just as
through an arbitrary point.

What consequences has this for the differential equation ?

By solving it with regard to » we find for each point the tangents
of the integral curves passing through that point, so in our case 2;
but in the point «= Rk, y =O we must find 3 now, viz. the two
45°-lines, and the line parallel to the y-axis; hence the differential
equation must disappear identically in this case, which occurs at
once through substitution,

75*

1154

§ 2. A point satisfying the three equations

of o7
fimy==0 , 220 , 2=0
On

is a node for a definite integral curve; we ask when this point
satisfies moreover ;
of
Ou
consequently belongs to #—=
If we differentiate f=O partially with regard to a and y, we find:

Of Of du
ce)
Ow a Ou Ox | I
Of Opa \ \
dy Oudy ;
ire Oi oe wy 0
Now, if eee pel need of course not be zero, for vis and
Ou Oy Ou Ow

Ou
may be zero, and the latter is the normal case (ef. the geome-

Oy
trical explanation in § 3). Let us suppose viz. that in a particular

‘

case < is O, then we can easily determine another system of curves
u

where this is not the case; we have only to replace the equation
SF (ay,u) ==) by,

yp (a,y,u) = fey. + gu) = 9,
in’ which g(u) represents a function which is zero itself for that
particular value of « which produces the nodal curve in the system
f=O9, while its derivative g’(w) is not zero for the same value. It
is evident that the system of curves y=O has with f/=O0 the nodal

0, of
curve in common, because for the wu of this point isp = //, = rye)
av av
OY a Og of of op
—=—-: on the contrary — => — (uw), and if — =0;, — == 0:
Oy dy ey Sow Ou ard Ou Ou

We arrive, however, at quite different results if the system =O
contains a nodal locus. On this locus y and w are functions of 2,
because not only one or more points of this locus must be determined
by wv, but at the same time the values of w, by which the integral
curves are indicated for which those points are nodes. And as the
values of x, y, and uw, which are associated to each other by the
locus, satisfy at the same time #0, we can say that for each

point of that locus

1155

Of Ofdy . Of du

Aieies NIE Sp()
Ov dyde dude
Of es On .. dy
If now and. are both zero, and if se =E o«, which can occur
a y da

only in a few points, and may even there be avoided by rotation
of the axes of coordinates, then we must have

of du am
Ou di

if : : :
Now ~— =O will be the normal case, viz. the nodal locus will
Ou

as a rule belong to H—O; for if this is not so dy must be =O,
Av

and w consequently constant along the locus, which means that the

said locus is a particular integral to be reckoned twice. It is not
of du ‘

excluded, however, that 5, and aE are both zero; in that case too

there is a particular integral to be reckoned twice, which now does

belong to “=O, and the difference between this case and the

preceding one where there was also question of a particular integral

to be reckoned twice is not particularly striking. The geometrical

explanation in the following § will cast sufficient light on this case.

§ 3. If we consider the parameter w as a third coordinate, our
equation /(x,7,w) =O represents a surface; the sections «= constant
produce, if projected on the wy-plane, the various integral curves.
The curve “=O lying in the vy-plane contains apparently all the
points of the property that the straight lines, passing through those
points parallel to the w-axis, cut the surface in two coinciding points;
hence it contains:

Ist. the apparent contour of the surface for the point at infinity
of the w-axis as lighting point, and this is apparently the singular
integral ;

2d. the projection of an eventual double curve or cuspidal curve
of the surface, situated in such a way that any plane jw —= constant
cuts it in a certain number of points; the system of curves /= 0
then contains a locus of nodes or cusps in such a way that each
integral curve contains one or more of those points;

3°. the projection of an eventual double or cuspidal curve which
is lying in a plane w=constant; in that case one integral curve

1156

du

counts double, so that =() (see § 2), while at the same time
Av

Of

a)

Ou

4%. the projections of eventual conical points of the surface; in

: ae Of ae Oh
this case the two equations I of § 2 are satisfied by — =— =~ =
02" Oy © ou

0,

Ou Ou : . .
; and ——=|— 0, and the points under discussion are nodes of L.
Ox y

Generally speaking there are, however, a number of tangent planes
to be constructed to the surface perpendicularly to the w-axis ; they
cut the surface each along a curve with a node in the point of
contact, but as this node is not at the same time a node of the
surface itself, its projection will in general not lie on /#; so we
have now integral curves with nodes, not belonging to /; in the
Of ya Ou Ou of
= SS - > — =0, but SSE OM And
Ow Oy Ow Oy Ou
if such a node does belong to # after all, it is because the projecting
straight line of the point of contact on the surface touches that

equations I of § 2 is

surface e.g. in another place, or happens to cut if in a point of a
double or cuspidal curve; the node of the integral curve is then,
however, a simple point of L.

Finally something else is possible. A tangent plane perpendicular
to the w-axis may, after the fashion of the two singular tangent
planes of a ring, have an infinite number of points of contact; in
that case a certain integral curve counts double, however without

Ny

there being the slightest cause for belonging to /#; for the points of

: : du
contact on the surface are simple points. We have then — = 0,
ve
Oy
but not as under 3), at the same time — = 0.
u

§ 4. Passing on to the partial differential equations we represent
the complete integral of (a, y, 2, p,q) =0 by 7 @,. 42, u,v) == 0
it determines a system of oo* integral surfaces.

Elimination of « and v from the four equations

f=0 , of Osha. eG : oie
; Ow Oy Oc

gives two relations between ww, 7.2, and so a twisted curve, locus of

0

the nodes of a surfaces out of the complete system ; this twisted
curve does not in general lie on the result of the elimination # = 0

Ilo yFy

of w and v from the equations

of df
(— 100 wee 5 cieiy
Ou dv

as appears e.g. at once from the example :
vw? + y? — kz? — 2ax — 2by = Rk? — 2a? — 20?,

representing a system of hyperboloids of revolution with vertical axes.

OF oF of

If spac a ; ae are: to. be =O} then, #=='a,.7, = 6, -z = Oland
if this point will lie on f=O, then a?-+ 6? must be = Rh?

The equation then assumes the form :

(c—a)? + (y--b)? — kz? = 0,

and consequently represents now a cone of revolution with its vertex

Re Os oa 5, 2=0, and the locus of those vertices is the circle
et —
On the ae hand we find easily that £ = 0 is represented here by
we? + y? — 2k2* = 2h;
it appears at once therefore that the eae x? + y? = RK does not

lie on # here. This is easy to understand. If we consider w as
independent variable, then y, 2, u,v become in consequence of the
nodal locus functions of w (ef. the analogous reasoning in § 2) and
as these functions must satisfy the equation f/=0O, we can write :

of Of dy , Of dz . Of du Of dv

de ' dy dx ' dz dx | Oude MCE
Of —0f5 “Of
de” dy Oe
Of du Of dv

Ou da dvde

Now for a point of the curve = 0, so that remains:

; , , of of
from which of course it need not ensue that a = >, = 0, though
u Vv
on the other hand this is not impossible.
of of : ;
That, however, oy = = QO is a particular, and not the general
A v
case, appears as follows (ef. § 2).
By elimination of w, y,2 from
of or of
=), =] =0 , — = 0, — 0
i Ow Oy ” Oz

we find a funetion,g (u,v) of uw and v, which becomes zero for
these systems of values of wu and v, which determine an integral
surface with a node. Conversely an infinite number of functions

1158

g(u,v) may be determined, which become zero for the said values of
Og Og

wand vo, wile 4 5=
Ou Ov

do not become zero for the same values.
If we consider now the system of surfaces :
p(@,y,2,4,v) = fla,y,2,u,v) + g(uv) = 0
where yg represents one of that infinite number of functions then
this new system has the same locus of nodes as the old one, while

Oy

> : f ye ;
for those nodes — and — are certainly not zero.
u Ov

Let there be a nodal locus, formed by a surface; then 2 and y
may both be chosen as independent variables, while z, «u,v become
functions of them, and as the equation #=O must always be
satisfied, we find by differentiation :

Ofa Oy df du df dv
PT Bude | 0 de
of of Of Ou Of dv

yt oy 12 ound as oneases
which equations reduce themselves into the last two terms, as in
Of MOL ueOF,

each point of the double surface — ===. =0. If the determinant
Ow Oy Oz

== (()

| Ou dv |
||
| Ow Oa |
| SSO

| Ou Ov |
— — |
oy Oy |

Of Sno : =i

then ea = 0, and the double surface consequently satisfies
Ou Ov

HO; in this case there exists no functional connection between
uw and v, i.e. the curves 2 econst., v= const. cut each other on
the double surface only in a limited number of points, or in other
words, each particular integral possesses a finite number of nodes.

Is on the contrary the determinant really zero, then v is a function
of w, so that on the double surface the curves w= const. and vy =
const., coincide; there are now only o' particular integrals possessing
nodes. but each of them possesses in that case a double curve and
its locus is the same surface as just mentioned, which need not,

of of
however, belong to = 0, because >, and need not be zero.
u v

They may be zero, though, and in that case the double surface
does belong to H= 0.
There is still another possibility. It may be that for the whole

1159

double surface 2—=const., but v not; this, however, is from a
geometrical point of view the same case as just mentioned, for
y=const. cuts the double surface now along a curye which is

of
double curve for a definite particular integral. a must be zero now,
Uv

Map OF :
it is true, but = must not, so that the double surface need not belong
Ut

to H=O either, though on the other hand it is quite possible, as

of
the case re is by no means excluded.
u

A very simple example of a system of surfaces with a double
surface not belonging to =O, gives the equation

(a7 + vy? +uyy+tu—2=0;
the double surface is z—O, locus of the secants of the pairs of
planes whieh are found by taking w zero. This plane z= 0 does

not satisfy, however, the result of elimination E: y? +42 = 0.
Finally w as well as v may be constant on the double surface ;
among the particular integrals there willbe one in that case, which
counts double, and which satisfies 470 or not, according to for
of Ofte
the particular w and v of the double surface 5 and , being zero
in each point of that surface or not; we have apparently to do then
with the singularsplane of contact at a surface (see the conclusion of § 3).
To wind up with, it is possible that any point of space is node
to some integral surface or other, this will e.g. be soif each integral
surface possesses a double curve, and these curves fill the whole
space; in that case / disappears identically.

§ 5. In order to illustrate the results of § 4 geometrically we
imagine the equation /(x,,2,u,v) = 0 in a space of five dimensions,
R,, interpreted as a twisted four-dimensional variety V,; for the
sake of distinctness we shall call it V,( f= 0). All points for
which w=const. lie in an &,, which is perpendicular to the
u-axis, and the same holds good for all points v = const., and these
two spaces FR, eut each other along an R,, which is absolutely
normal to the plane wr, and has a point in common with this
plane; this R, cuts V,( f= 0) along a surface 2, and if the points
of this surface are projected by means of planes parallel to the
plane wv on the space Ray: of the a, y and z-axis (by which to
each point of a one definite projection is associated), then a surface

,

x’, congruent with 2 arises as projection, because the space of a is

5)

1160

parallel with /t,y,, and the a’ is nothing but a particular integral
of the given differential equation.

Through the straight line 7, at infinity of the plane w pass x»*
planes; each of them cuts V,(f/=0) along a curve, and among
them are o? possessing a node, and whose plane touches therefore
the variety. Consequently o* planes of contact pass through /,
touching at V,(f=0); the locus of the points of contact P is
therefore a surface £2, but in general of course a surface that can
only occur in an F#,; the projection 2’ of 2 from /, on Ry, is
an ordinary surface, which might be called the “apparent contour”
of V,(f= 9) on R,,:, for the lighting axis /,.

The projection of 2 on R,,., takes place exactly through the
planes that have produced {2 itself, viz. the planes of contact
, touching at V,(f=0); now o% straight lines
pass through the point of contact P of such a plane, and conse-
quently o* that touch at V,(/=0) in P, and they determine the
tangent-R, in P at V, (f= 0); as this tangent-#, contains all tangents
through P at V,(f=0) it also contains the plane Pl; so it is
projecting, the consequence of which is that its projection on fy,-,
being nothing but its intersection with /,,., is only a plane, viz.
the plane of contact in P’ at Q’.

passing through /

Out of point P only one perpendicular line can be let Gown on
the plane we and through the foot of this perpendicular passes only
one ER, absolutely normal to we, from which it ensues that only
one surface a passes through 7. The plane of contact at this surface
in P coincides by no means with the one at 2, but does contain
tangents of V,(7—0), as a too belongs to this variety ; the plane
of contact in P at a lies therefore in the tangent-f, of P at V,(/=0)
and so projects itself, as the plane of contact at £2, in the plane of
contact in P’ at 2’, from which it ensues that a’ and &' touch
each other in P’; 2' is therefore the singular integral of our diffe-
rential equation.

In fact 2' is found analytically by making the (fourdimensional)
of the w-axis

of : takes :
first polar space 5 =O of the point at infinity CU,
u

of —
(7 =), and the first polar space , == OF Ofeaae
v

eut each other, in consequence of which the threedimensional
first polar space of the line U, V, =J/, arises; the latter cuts
V,(f =0) along the surface 2, and @' satisfies apparently the
oF ; of af
result of elimination H—O of wu and v from f=0, —=0,—-=0.

Ou Ov

with regard to V,

1161

§ 6. Among the »? spaces 2,, which are absolutely normal to
the plane wv, and according to what precedes, cut the surfaces 7 out
of V,( f= 0), there are o' for which that surface of intersection
possesses a node, and which touch V, accordingly in that point;
this node of a will in general, however, be only a simple point of
V4, i.e. the plane passing through /,, and that point will in general
eut V, along a curve that possesses no node in that point; and from
this it ensues that the projection of that point on &,,. will in
general not belong to /’=0O. With this we have proved that the
nodal curve, which in general is present in our system of surfaces 2’,
wili as a rule not belong to 4 = 0.

Conversely the possibility is, however, not excluded that V, (f= 0)
contains a double curve; now the plane passing through /

io}

and a
point P of this curve cuts V, along a eurve which does have a

aD

node in P, and the consequence of this is that the projection of the
double curve does belong this time to =O; and _ finally the
case is not excluded that both phenomena occur at a time, and
consequently the system of surfaces a’ contams two different
double curves, of which one does belong to #—O, the other
does not.

Let V,(f—=0) contain not a curve but a surface of nodes; as
any plane passing through /, and a point P of this double surface
cuts V,(f—0) along a curve with a node in P, the projection of
the double surface will belong to =O; and as an R,1 w cuts

io 2)

the double surface in general in a finite number of points we have
here to do with the case that each surface of the cx’
finite number of nodes (see § 4).

A double surface in the system a’, may, however, have a quite
different origin. Among the spaces Ah, 1 uv there may be some that

possesses a

touch Vy(f=0) not in one but in an infinite number of points,
so that the associated surface 2 possesses a double curve, which,
however, is not at the same time a double curve of JV’,; in that
case there are surfaces 2’ with a double curve not belonging to
H=0. And if all R, 4 w, which touch V,, have this property,
then we find in the system 2’ a double surface, locus of double
curves of om! surfaces a’, which does not belong tio H=0O. The
case is even not excluded that a certain R, 4 wv touches V, (f=0)
in all the points of a surface, the analogon of the singular planes

a)

of contact of a ring, then the difierential equation possesses a_par-
ticular integral counting double, not belonging to / = 0. If, however,
that integral counts double because the associated surface a in &, is
a real double surface of V,(/=0), which happens to lie in an

1162

R,1 uv, then the particular integral counting double does belong
again to H= 0; ete.
Finally V, (f= 0) may possess a double space, which then is
of of
common to the two polar spaces Wes 0, aa = 0 (ef. §5). Every
R, + uv cuts this double space along a curve, and every 2’ contains
a double curve, the latter of which fill the whole space R,,- ; the
result of the elimination /# lisappears now identically.

Observation. Following up this method, and without en-
countering other difficulties but those which arise from the increasing
number of dimensions, one can obtain an insight into the singular
solution of the partial differential equation of the first order with
an arbitrary number of independent , variables.

Physics. — “The diffusion-coef ficient of gases and the viscosity of
gas-mintures’. By Prof. J. P. Kurnen

(Communicated in the meeting cf Mareh 28, 1914).

In a previous communication ') on the diffusion-coefficient D of
gases it was shown, that the contradiction between O. EK. Meynr’s
theory .on the one hand and that of MAxweLi-STeran-LANGEVIN on
the other ean be largely removed by taking into account in the
former theory the persistence of molecular movement. By doing this
the limiting values for the two components, i. e. for , = O and
n, = 0, become equal. which involves a much smaller change in D
with the composition of the mixture than according to the incomplete
theory, while the second theory mentioned makes the coefficient
entirely independent of the composition; observation also gives only
a small variation of D.

{In order to further compare the improved theory with observation
I have ealeulated D for two pairs of gases viz. carbon dioxide—-
hydrogen and argon— helium, which seemed specially suitable for
this test owing to the great difference in the molecular masses. For
this purpose it is necessary to give a further modification to the
formulae in order to express the influence of the mutual attraction
of the molecules: in the former theoretical paper this influence had
to be left out of account, seeing that ii STrran’s theory the molecules
are likewise regarded as free from attraction.

Using Surnurtann’s well-known formulation of the attraction by

C aa ne
means of a factor (1 “ft =) the formulae become for 0° (7’= 273).

1) J. P. Kuenen, Proc. XV p. 1152. 1913.

i C, 2 m,+m, Cy,
SSS VV n, 18,7 te 373 +n, 10 a m, oN ete 273

= op 2 my - ms C, 2
= 1: van, ws (1 + a) eae: ve we (: MI 77)

TE y

; C ;
ale F —V2n, 98,2 (1 jh am) lL x< 0.406 —
mae [Aa i+ Ce 1 m,—9.188m,
= m, 273 m,+an,
f=: } = Vin, xe (1 a aE 0.406 —

ee m, +m, Cys m,—0.188m,
—n, 20 ——— {1+ —— ]|l, ——__
1 999 a
m 273 m,-+m,

1
D=—(n, 4,4 f, + 2, u,b fy:
onibane ; gt ee

Possibly in the last formula the coefficient a might be replaced by

a slightly different one, but the uncertainty involved in this has but
a small influence on the result.

A difficulty im the calculation arises from the constant C,,, which
measures the attraction of unlike molecules. Experiments on the
viscosity of mixtures have shown, that the influence of temperature
may in that case, as with pure substances, be represented by means

AY

of a factor (: = = but the constant Cin this faeter is not iden-

tical with the C\,-in the above formulae, for in the viscosity of a
mixture not only the attraction of unlike molecules but also that
between like molecules plays a part. If the observations could be
represented by a rigorous theoretical formula, the various attractions
could be separated and thus the C,, in question determined. As this
is not the case, however, an estimation has to be resorted to; it
seems simplest to take for C\, the value which holds for the mixture
of composition 1:1 as a whole: fortunately a small change in C,,
does not involve more than a small change in the result.

For the mixture of equal parts of CO, and H, (n,=n,=3n), | have
calculated from BrerrenBacn’s experiments *) C,, = 116.2.

The molecular diameters s, ands, were found from the viscosities
of the pure components at 0° using the formula

1) P. BREITENBACH, Wied, Ann. 67, p, 803, 1899,

1164

jon pees EN
C i ; C
ae 273 V2n ne(1 ale aa)
in whieh 7» was taken equal to 2.76 Xx 10** and further
d u Ns C

carbon-dioxide 0.00197 36250 0.0001388 239.7
hydrogen 0.0008987 169200 0.0000841 87
mixture ligeyal 0.0001423 116.2

The result of the calculation is s,=3.136 <10-8 and s,=

== 2.217 < 10-®, and hence
O46, Sh sy) OO Xa Oe Bes

For n, =n, =n I find Dy, = 0.458, whereas the limiting values
for pure CO, and H, become: D, = D, = 0.551. Observation has
given D =0.53.

The agreement with observation may be considered satisfactory.
The difference between D,, and D, or D, which was discussed in
the previous communication, is rather large: probably, as observed,
this is owing to the imperfections of the method of calculation by
averages followed in the theory.

For argon and helium the following constants hold ‘):

d u No C
Argon 0.001781 38080 0.0002119 164.1
Helium 0.0001784 120400 0.0001819 80.3
Mixture 3: 2 0.0002207
ioe 0.0002203 105

which give

Sua 2.074510 S885. le (oe Oe ehencemo 2.224 < 10-8
and

D*/, = 05385 Di = Di =0-597 Ditobserved)i 057700 a

The agreement with observation is less close here than in the
former case; it may be added, that Srmran’s formula (after correction
for the molecular attraction) would, as the previous communication
shows, give a result closely agreeing with D, = D, according to
our formula and therefore also differing from the experimental value.

1) K. Scumirt, Ann. d. Phys. (4) 30, p. 898, 1909.

2) R. Scumipt. Ann d. Phys. (4) 14 p. 801. 1904. A. Lonius ib. 29 p. 664
1909,

1165

The further question arises, whether the theory is capable of explaining
the viscosity of gas-mixtares, in particular the interesting fact, that,
e.g. for the two above combinations, the viscosity goes through a
maximum. In order to derive a formula for the viscosity of mixtures
it is necessary first to consider the case of a pure substance. The
coefficient 0.44 in the formula for 7, used above, is the result of the

multiplication of the factor 0.35 which is obtained, when the persistence

1
is left out of account, and a persistence-factor — ie where 9=0.406

1——#
2

represents the persistence.

: Le
The coefficient 5 in the denominator which is absent in the persist-

ence-factor of the diffusion-formula may be justified as follows ').
When a molecule is traced on its way from the moment that it
collides, it is found, that on the average it does not describe a distance
/ in the direction of motion, before its velocity in this direction is
exhausted and therefore all directions become equally probable, but
a distance :
l
EAT 9 EMTG2 Stas ip ee

1—o

In the case of viscosity however we are dealing with the transport
of momentum: it would on the one hand be incorrect to assume,
that the momentum of a molecule at each collision immediately
assumes the value belonging to the point where the collision occurs;
if that were the case, the persistence would have no influence on
the viscosity and would have to be left out of account. On the other
hand it cannot be assumed, that the molecule keeps its momentum
till the moment, when it has lost its velocity in the direction of
motion, and then suddenly, as regards momentum, goes into
equilibrium with the neighbouring molecules. It is much more reason-
able to assume, that at each collision the excess of momentum is
equally distributed over the two molecules: on this supposition the
persistence-factor will obviously be given by the series

EE) aes 1
1+ 9 oo + 4 et. oa T19.

by which Jxans’s result is obtained.

If we now apply this principle to mixtures, it seems natural to
suppose, that for collisions between unlike molecules the persistence

1) J. H. Jeans. Theory of gases p. 249—250. 1904,

1166

has to snultiplied, instead of by the factor */,, by the mass-ratio
m mM,
or =
m,+m, m,-+-m,
is impossible, but it would seem that an approximately correct result
will be obtained, if in the above formulae for / the first term in the
denominator which refers to collisions between like molecules is given

the factor

respectively. A rigorous treatment of the problem

‘/,, and the second term which depends on the unlike

collisions is multiplied by the aforesaid mass-ratio. In this manner
the persistence-factors 7” which apply in the case of viscosity assume
the following form

" ~ 3 Ca ;
] | ‘}1— 4 V2 maay( 4- ae ( x< 0.406 —
m m,+m, ( G! m,—0.188 m
= Be LASS n, 6" Aas i, Eb = l, ai “|
m, +m, m, 273 m,+m,
"= 1:/1l—3 y9 2( 1 = l, x 0.406
7 —— . mar 2 a Wass + 273 2 a. . —
mM, 4 m,+m, Sel One m,—0.188m,
a ROE ———| 1 + —— |l, ——————};
m, +m, m, ¢ 273 m, +m,
while the viscosity of the mixture is given by the formula
n, “y or Ny
ny = 0.35 — dul, f', + 0 35 — dul’,
n n

For CO, and H, with n,=n,="/,n calculation gives 7=0:0001482.
The theory therefore actually gives a maximum in the viscosity,
in accordance with observation which had not been explained hitherto.
The observed maximum lies at 70°/, CO, and is not quite so high viz,
about 0.000144, but a nearer agreement could not really be expected.
For argon and helium calenlation gives

for the mixture 3:2 4 = 0.0002294
oe 8 ‘ 1:1 47 = 0.0002321.

Observation gives a maximum near the first named mixture with
7) = 0.0002207 ; in this case the theory gives again too high a value.
Whereas therefore a numerical agreement is absent, we may conclude
from the investigation that the ordinary gas theory which treats the
molecules as mutually attracting elastic spheres can without being
strained explain the ocenrrence of a maximum in the viscosity of

the above mixtures.

1167

Chemistry. — “The metastable continuation of the mixed crystal
series of pseudo components in connection with the phenomenon
of allotropy’. By Profs A. Smits. (Communicated by Prof.
J. D. van DER WAALS).

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

1. For the case that a unary system is built up of two pseudo-
components the relation between the unary and the pseudo-binary
system has been derived by me by making use of Gripps’s principle
of equilibrium, which states that a system at constant temperature
and pressure tends to pass to such a state that the thermodynamic
potential (6-funetion) is a minimum. ’)

In this it has been assumed that when heterogeneous allotropy
occurs in the solid state, the ¢v-curve has a shape as indicated in
lig. 1. This assumption comes to this that there exists continuity in
the unstable region between the two mixed erystai series, which

ax KH i
Fig. 1.

1) Z. f. phys. Ghem.: 76, 421 (1911),

Proceedings Royal Acad. Amsterdam. Vol. XVI.

1168

start from the «@ and the 3-side, and in general possess a different
crystalline form.

As Herserte') has demonstrated by an experimental way that
such a continuous transition between mixed crystals of different
crystalline forms oceurs for potassiwm and thallium tartrate even in
the stable region, it must be admitted that the continuity in the
unstable region given in fig, 1, is a possibility, especially for mixed
crystals whose systems of crystallisation are closely allied to each other:

On the other hand it should be pointed out, that it is very probable,
that in many cases the continuity assumed here, does nof exist, and
the two halves of the $-z-line, which refer to mixed erystals of
different forms, are not related. We might imagine that in this case
two ¢-z-lines oecur, which proceed continuously from one axis to
another, as fig. 2 shows. The ¢-«-line cd would then relate to mixed
crystals of one kind, and ab to those of the second kind. The ¢-a-
line cd then indicates the §-values of different mixed crystals, in
which the pseudo-component « is compelled by ¢ to erystallize in

C

@)

ol # 2

1) Compt. rend, 140, 1649 (1905).

1169

the crystalline form of 3, whereas the line a/ refers to mixed crystals
in which p is forced by «@ to crystallize in the crystalline form of «.

These states would certainly be realisable when the pseudo compo-
nents presented the phenomenon of isodimorphy, but then we should
have to assume that the pseudo components can occur in different
crystalline forms, merely in consequence of a different arrangement
in the “Raumeitter” of a same kind of molecules.

Without the slightest doubt such a case is conceivable, but it is
by no means probable. We can hardly assume that when the pseudo-
components in the solid stable state are miscible to a limited extent,
the phenomenon of ¢sodimorphy always occurs. Besides it ts uv mi
opinion highly probable that a difference in composition is the cause
of the difference in crystalline form. It is now the question whether
another view is possible, which obviates the difficulty mentioned here.

It is clear that the stability of the ‘“Raumgitter” of the pseudo
component @ becomes smaller as there has been dissolved more of the
pseudo component $, and thus it wiil be possible that at a certain
concentration the “Raumegitter’” has become so unstable that it can

76*

1170

no longer maintain itself. It is now the question how this has to
be expressed in the $-2-figure.

There exist here two possibilities. It is possible that as fig. 3
indicates, the S-z-line a6 starting from the a-axis, approaches the
line pq asymptotically instead of running to the other axis, which
means that a mixed crystal of the concentration p is impossible, as
this mixed erystal would require an infinitely large value of $.

In the same way the ¢-2-line de would then approach asymp-
totically to 7s.

: 0g E as x ~ (dp
Then the expression { — = MRT log —— +{ = dv be-
dx) pq a ie dx v,

comes infinite at a definite value of «x, because then the second
term of the second member becomes = om.

Another possibility is this, that the ¢-v-line ends suddenly in the
figure, as fig. 4 shows. So this figure expresses that the possibility

x KH iE
Fig. 4.

of the existence of mixed crystals of the same crystalline form
suddenly ceases at 4 resp. c, and that the prolongations of the lines

A172

which might be imagined, have thermodynamically absolutely no

sense any more.

2. It is clear that as far as the metastable and unstable equilibria
are concerned, the pseudo 7-2-figure will be different according as
one view or the other is held.

The assumption of continuity in the unstable region would lead
to the 7’, 2-figures 5 and 6.

In Fig. 6 the lines pd and ime pass continuously into each other,
in the same way as in Fig. 5.

The

is less

assumption of isodimorphy of the pseudo components, which
probable than the two following, yields the figures 7 and: 8.

The assumption of an asymptouic course of the ¢-r-lines leads to
the figures 9 and 10.

Fig. 10.

0°$ Sins :
ar becoming = oo for a definite value of v, and
0x" / p 2

P
L
. == ee USL
aT) 0g
u.—wv =
( 0a?) pr
L

¢

=
-

'
\
'
|
\
|
|
I
\
'
|
|
|
'
|
|
|
I

\

: 11738

da
(F) assumes the value zero for that definite value of w.
¢ P

It appears at the same time from these figures that when the
temperature of the three phase equilibrium lies between the melting-
point temperatures of the pseudo-components, one of the metastably
produced meltingpoint lines must possess a maximum temperature.

When in conclusion we consider the ease that the S-2-lines for
solid suddenly terminate in the 6, .7-figures, we find what follows

for the corresponding 7’,v-figures,

Fig. 11.
We have treated here systems of two pseudo-components « and
8, but it is clear, that the same holds also for any other binary
system.
Amsterdam, 20 Mareh 1914.
Anorg. Chem. Laboratory of the University.

(To be continued.)

ii74

Chemistry. — “On the vapour pressure lines of the system phos-
phorus.” I. By Prof. A. Smits, S. C. Boxnorst, and J. W.

Terwen. (Communicated by Prof. J. D. van per Waats).
(Communicated in the meeting of March 28, 1913).

1. On a former occasion ') the result of a preliminary investi-
gation about the vapour pressure lines of liquid white and liquid
red phosphorus was communicated. It appeared already then that
the vapour pressure lines of these two colourless liquid phases of
the system phosphorus cannot be considered as two pieces of the
same vapour pressure line.

The question under discussion being of the utmost importance,
which ought to be decided with perfect certainty, it was resolved
to determine the vapour pressure lines of liquid white and liquid
red phosphorus as acenrately and as far as possible.

2. Determination of the vapour pressure line of liquid red phosphorus.

We again made use of Jackson’s glass spring manometer (see fig.
1 ah), which was now made of infusible glass, was filled with pure
red phosphorus, and then exhausted and sealed off. This glass spring
served as phosphorus reservoir and at the same time as indicator
of the pressure.

Round the glass spring a wider vessel c¢ had, namely, been sealed
on beforehand, which ended into a somewhat narrower tube, which
was electrolytically coated with copper at e, so that it could be
soldered to the copper mounting e.

This copper mounting consisted of a copper coupling piece, in
which a copper plate was used as packing. The said mounting was
in connection with the cocks A, A, by means of copper tubes, and
the pressure cylindre g, which was filled with glycerin, and was
connected with a Scuirrer and Bupensere’s hydrostatic press A
with closed air manometer J/,, and metal manometer ./,.

The cock A, could effect the communication between the space
round the glass spring and the carbonic acid cylindre , and the
cock A, could bring the same space into communication with the
open manometer M/,. A T-piece with the cocks A, and K, was
sealed to this open manometer, A’, being connected with the GarpE
pump. Before the beginning of every experiment the space round
the glass spring was exhausted through this cock, to have an oppor-
tunity to indicate the zero-position of the needle of the glass spring
on the tube d. This was effected by sticking two strips of paper

1) These Proc. XV, p. 885.

with marks put on them on the front and the back of the tube d,
but above each other, in such a way that the two marks are in the
same plane with the needle. When a vapour pressure determination
was made, a copper bath with a molten mixture of ANO, and
NaNO, was placed round the phosphorus manometer, in which a
stirrer was continually moved up and down. *)

1) In the preliminary experiments an air bath was used, with which no accurate
determinations could be made, however, on account of the unequal temperature.

Then a ganged thermo-element and a gauged very sensitive resist-
ance thermometer were placed in the bath for the temperature
measurement, so that the temperature could be measured in two
different ways. The bath was surrounded by a wider asbestos cylindre,
burners placed under it ensuring a uniform heating.

In the determination of the vapour pressure line of the liquid red
phosphorus the bath was slowly raised to a temperature above the
melting point of this modification.

In order to bring the needle of the glass spring manometer to its
zero position, the pressure in the space round this manometer had
to be continually increased. At first this was effected by slowly
adinitting air through A,, A, and A, being open, but afterwards
this was obtained by filling the tube between the valve V and the
cock A, with CO, of higher pressure, after A, had been closed, and
then carefully opening the cock K,. As the open manometer could
indicate at most an excess of pressure of + 4 atmospheres, AK, was
closed when this pressure had been reached, so that at higher
pressure only the closed air manometer J/, was used. In its turn
the airmanometer was closed at pressures of about 10 atmospheres,
and the metal manometer J/, was read. It had appeared in prelimi-
nary experiments that the three different manometers corresponded
with each other very satisfactorily.

When the red phosphorus was melted, the temperature was kept
constant for some time, the needle was brought exactly to its zero
position, and the pressure was read on the air manometer. Then
the temperature was slightly raised or lowered; then again put at
the same point, and the preceding operation was repeated to get
an idea of the accuracy of the method. The result was that the
error at these high temperatures and pressures amounted to less
than 0,1 atm.

In this way we could determine the vapour pressure line of the
molten red phosphorus up to a temperature of 634°, and a pressure
of 58.6 atm., which may, indeed, be called a surprising result, for
that a glass tube of a diameter of 2 em. and a thickness of wall
of 2 mm. can-resist a pressure of 58 atmospheres at a temperature
of 684°, was not expected by us, and in these experiments we were
fully prepared for a violent explosion, which, however, fortunately
did not take place. That the glass had not even been deformed was
proved by this that when the experiment was over, the zero position
appeared to have hardly changed.

We have been able to continue these vapour tension determina-
tions of the liquid red phosphorus up to + 85° below the triple

point, which lies at 589.5 and 43.1Laim. The supercooled phosphorus
then indeed was converted to the solid ved phosphorus, but we
succeeded in making the experiment in such a way that notwith-
standing, the vapour space remained saturate with vapour of the
liquid phase during the experiment. The method followed was this,

TABLE I.
C = 9.609
(aye a

cle | |

ee latmN ere 2? | ae | An) |par

ZOE | |
30 | 23.2) 504 | 777 | 2443.0 | 5023.2 | wir gs27|,2360
2 | 24.3 | 512 | 785 | 2504.5 | 5038.6 + 7.2 | 24.5
27 | 31.9 | 545.5) 818.5] 2834.1 | 5030.9 | — 0.5 | 31.9
30 | 32.4 | 548 | 821 | 2855.5 | 5033.5 | + 2.1 | 32.5
28 | 33.0 | 550. | 823 | 2877.6 | 5030.6 | — 0.8 | 33.0
21 | 33.6 | 553 | 826 | 2902.9 | 5034.2 | + 2.8 | 33.7
28 | 34.5 | 555.5) 828.5] 2934.0 | 5027.0 | — 4.4 | 34.4
2g | 35.4| 559 | 832 | 2967.4 | 5027.3 | — 4.3 | 35.3
30 | 35.5 | 560 | 833 2973.3 | 5030.9 — 0.5 | 35.5
98. | 35.9 | 562 | sas | 2980.9 | 5038.7 | + 2.3 | 36.0
27 | 37.6 | 569 | 842 | 3054.0 | 5036.8 | + 5.4 | 37.8
28 | 38.8 | 574 | 847 | 3098.6 | 5040.2 | + 8.8 | 39.2
28 | 40.3 | 578 | 851 | 3145.6 | 5031.7 | + 0.3 | 40.3
30 | 41.1 | 581 | 854 | 3173.4 | 5032.8 | +. 1.4 | 41.1
98 | 44.2| 503 | 866 | 3281.1 | 5040.4 | + 9.0 | 44.7
30 | 47.0 | 602 | 875 | 3368.8 | 5039.1 | a Re VC
28 | 48.6 | 606.5, 879.5 3415.6 | 5035.6 | + 4.2 | 48.8
28 | 49.0 | 608 | 881 | 3428.7 | 5036.9 | + 5.5 | 49.3
30 | 53.9 | 621 | 894 | 3564.5 | 5026.0 | — 5.4 | 53.6
30 | 55.6 | 625.5| 898.5| 3610.3 | 5023.5 | — 7.9 55.2
30 | 56.5 | 627.5| 900.5) 3632.7 | 5020.2 | — 11.2) 55.9
30 | 57.7 | 632 | 905 | 3669.9 | 5026.3 | — 5.1 | 57.4
30 | 58.6 | 634 | 907 | 3692.2 | 5023.3 | — 8.1 58.1

| | | | | |

1178

that for every determination the temperature was raised above the
triple point, and then was lowered as quickly as possible to a
definite temperature, which was then kept constant for some time,
till the vapour tension had become constant. Thus a constant vapour
tension could be observed even at the lowest point + 504° during
5 minutes. On continuation of the experiment pretty suddenly a.
decrease set in, which pointed to this that at that moment the liquid
phase had disappeared, and had been entirely converted to the solid
red phosphorus.

That these vapour tensions under the triple point really refer to
the saturate vapour could be proved by this that when after the
determination of the vapour tension at 550°, the temperature was
not first raised above the triple point temperature, but at once to
562°, a vapour tension was observed at this latter temperature, which
fitted exactly in the found vapour pressure line. After this deter-
mination at 562° we heated at onee to 574°, and also the vapour
tension observed at this temperature lay on the line already found.

It follows, therefore, from this that the vapour at 562° and 574°
was still saturated with the vapour of the liquid red phosphorus, so
that it is perfectly sure that this must also have been the case just
before and at the lower temperature 550°.

The results of the vapour tension determinations of the liquid red
phosphorus are given in the subjoined table. In the first column one
finds the number of the manometer, and in the second column the
temperature, the third giving the pressure in atmospheres.

In the PT representation Fig. 2 these results are graphically
represented by the line end, from which follows that the different
observations yield a very regular curve. Only the last point at 512°
lies too low.

The point » is the point where the vapour pressure line of the
solid red phosphorus mn (more about this later) intersects the vapour
pressure line of the’ liquid red phosphorus, so the triple point of
the red phosphorus.

When the saturation heat is no temperature function, the vapour
pressure formula

dnp Q
SOON IS os (1)
aL Wk
on integration yields the expression :
Q
lnp = — Gh Midge een ec,

or

Q
Li ——— Gr 8 fo he OS AS
np R + ( )

from which follows that Tinp, vepresented as function of T. will
yield a straight line.

H ¢
Fig. 2.

3 8 & S SS s 3 < & & =

It is now interesting fo examine what is found when 7np is
plotted against the temperature.

The points obtained in this way lay so nearly on a straight line
that it was possible to unite nearly all the points on the same
straight line, as the line hk shows; w proof therefore that the heat
of evaporation in the examined temperature range 1s practically no
temperature function.

This has the advantage that the constant C may be graphically

1180

determined in a simple way. For this purpose the line is drawn so
that as many points as possible lie on this line, and that the others,
which deviate lie regularly on the left or the right of it. In this
case the tangent of the angle a formed by this line and the tempera-
ture axis, will give the constant. This is immediately seen in the
following way.

For two different points on this line we get namely :

bs pas Spee
LG eee ai ak OL uh Se oi Ol) ex eee Co)
and
T inp, = = z Ot Pe enecteneee ls ts (O)
hence
Llnp, — Trp,
CS =n OF
T,—T, :
or

SS SE TY
ELIE

(6)

1181
In this way the constant C is now determined. If we calculate
Qe ke. : !
the quantity 7 with this value of C from the different observations,
?

we obtain the values given in the 6" column of table I. From this
follows as mean value for Q 9,96 Kk. Cal.
In connection with the deviations trom the mean value 5031,4

Q Ne

which the different values of = present (see column 7) it is to be
v

expected that the above value for the heat of evaporation is pretty

accurate. Finally the last column gives the calculated pressure when

Q
the values for C and z heading the table are used.

To give a better graphical survey of what has been found, the
discussed lines are once more separately represented in Fig. 3.
The upmost line again gives 7’/np as function of 7.

§ 3. Determination of the vapour pressure line of liquid white
phosphorus.

If the difficulties in the preceding experiments were great, because
many of the glass spring manometers already burst before the triple
point of the red phosphorus had been reached, the difficulties in the
following experiments were so great as to seem almost insuperable.

It is self-evident that the determination of the vapour tension of
the white phosphorus at temperatures at which the conversion to
solid red phosphorus still proceeds slowly, is attended with few diffi-
culties.

Up to 312° this line had already been determined by Jo.tsots ')
with pretty great accuracy.

For the purpose we had in view, it was, however, necessary to
carry these experiments up to as high temperatures as possible. In
this we meet, however, with different difficulties. In the first place
the molten white phosphorus begins rapidly to convert into the solid
red modification from + 280° on rise of temperature, in consequence
of which the liquid phase has disappeared in a comparatively short
time, and the prevailing vapour tension, therefore, no longer corre-
sponds with the vapour tension of the liquid phase at that temperature.

Hence to find points of the vapour pressure line of the liquid
white phosphorus at higher temperatures, one has to heat the glass
spring manometer as quickly as possible to a definite temperature,
and then to keep the temperature constant for some time.

1) Théses, Paris 1910.

1182

By this mode of procedure we have actually succeeded in determining
some pots with the glass spring manometer at higher temperatures,
but in the majority of the experiments the glass spring broke before
the required temperature had been reached. This circumstance was
owing to this that it often happens in case of rapid heating that
part of the liquid white phosphorus is enclosed by a wall of red
phosphorus. If now the tension in the space outside has become less
than the tension of the enclosed liquid phosphorus, the wall of red
phosphorus breaks at a certain difference of pressure, and the conse-
quent sudden increase of pressure bursts the glass spring manometer.

As all attempts to prevent this enclosure of the liquid phosphorus
failed, and with a few exceptions the experiments miscarried through
this circumstance, we have finally tried to reach our end by another
way, in which we have really succeeded. Instead of the statical
method we have namely introduced the dynamic method, in the
form given to it by Sarrn *). The difficulty was, however, to find
a suitable liquid, i. e. a liquid with a comparatively low melting-
point, high boiling-point (+ 360°) and besides indifferent with respect
to the phosphorus. We have succeeded in finding such a liquid, and
to this we owe the final success of our endeavours
in this direction. This liquid is melted stearin candle
material or a mixture of stearic acid and palmitic
acid. Instead of the glass spring manometer the
apparatus represented in Fig. 4 was now attached
to the apparatus Fig. 1.. The former consists of
EN a tube a, in which a vessel c¢ is placed with a
tube c, which is bent downward and part of which
is considerably widened, terminating in a capillary
placed in a small wider tube. This apparatus, 0i
which the vessel ¢ contains white phosphorus, is
quite immersed in the mixture of stearie acid and
palmitic acid; and in the same liquid column, at

the level of ¢ is the extremity of the glass tube 6

fused to at the bottom, in which a_ thermo-
element is placed. The tube a, which contains all

this, is fastened airtight by means of a rubber stopper
in the wider vessel d, also provided with the same
fatty acid mixture, the side tube e of which serves
Fig. 4, to enable us to compress the air in d somewhat,

LN WU

and to raise the boiling point of the mixture, if necessary. By means

1) Americ. Chem. Soc 32, 897 (1910).

1183

of this arrangement it was now possible to determine the boiling-
point of the liquid phosphorus under different pressures, and it is
in this way that we have supplied the deficiencies which had conti-
nued to exist when the static method was applied. The phenomenon
of inclosure of liquid phosphorus by solid red also often occurred
by this way of procedure with the result that when the wall of the
red phosphorus broke, a violent boiling of the liberated liquid took
place, in which often part of the contents were flung outside from
the vessel c.

However satisfactory this dynamic method was in the application,
the velocity of conversion of the white phosphorus becomes so
great above 360° that 366.4° is the highest temperature at which
reliable measurements could still be made.

The result of the statical and the dynamical investigation is combined
in the following table II, the results of JoLrpots’ statical investigation
being given in table III.

TABLE IL
. _—

Method FE a|patm.| ¢ | T Tinp

Bie | |

NS cer al |e
dyn 65 | 0.039 169.0 442.0 | — 1433.9
pel wes) | 0.070 fs 181 3 454.3 | — 1208.1
‘ 65 | 0.182 206.9 479.9) — 817.6
nm |, 65 | 0.320) 220.8 | 5028, == 572.9
nee | 265 | 0.542) 252.0] 525.0| — 321.6
Bol'65 | 0.686), :261-4 |) 534-4 201
Reman G5: 0.737 | 265.5 538.5| — 164.3
stat. and| dyn. | 1.— | 280.5 | 553.5 0.0
é 36 | 1.38 | 208.6| 571.6| + 184.9
: 35 | 2.36 | 324.5 | 597.5 | + 513.0
i 35) || S18) ule sadetuleolOnd 705.8
Re 36:11 S3350 | 344.9 | 617.9 840.9
dyn. | 54 3.94 343.9 616.9 845.8
- 59 | 4.38 | 347.5 | 620.5| 916.5
» | 60 | 5.39 | 353.9 | 626.9) 1056.0
stat. | 31 | 7.60 | 362.5 | 635.5 1291.8
dyn. | 56 | 9.56 | 366.4 639.4 1443.5

Uh
Proceedings Royal Acad. Amsterdam. Vol. XVI.

1184

TABLE III.

p atm.| ¢ | T Tinp

0.017 | 145 | 418 | — 1703.1
0.064 | 173 | 446 | — 1226.0
0.093 | 184 | 457 | — 1085.4
0.124 | 192 | 465 | — 970.7
0.157 | 200 | 473 | — 875.7
0.178 | 205 | 478 | — 825.0
0.253 | 219 | 492 | — 676.2
0.366 | 235 | 508 | — 510.6
0.418 | 239 | 512 | — 446.6
0.464 | 244 | 517 | — 397.0
0.499 | 247 | 520 | — 361.4
0.543 | 250 | 523 | — 319.4
0.591 | 254 | 527 ila 277.2
0.633 | 257 | 530 | — 242.2
0.675 | 259 | 532 | — 209.1
0.705 | 262 | 535 | — 187.0
0.797 | 268 | 541 | — 122.7
0.850 | 273 | 546 ies 88.7
0.925 | 275 | 548 |— 42.7
0.990 | 279 | 552 |— 5.5
1.034 | 281 | 554 | 4 18.5
1607142 283) 2550e| 1 easel
1.122-| 285 | 558 | -+ 64.2
1.329 | 205 | 568 | + 161.5
1.437 | 299 | 572 | + 207.4
1.650 | 307 | 580 | + 290.4
1.817 | 312 | 585 | + 349.3

Graphically represented the line ab Fig, 2 is obtained. As the
line ab shows, the higher temperatures are the most interesting, for
it is from the vapour pressures found at those temperatures that it

{4185

appears with the greatest clearness that the vapour pressure line of
liquid white phosphorus cannot be the prolongation of the vapour
pressure line of liquid red phosphorus.

This, however, follows still more clearly from the line efy, whick
gives Tinp as function of 7’.

In contrast with the line /é this line is not straight, but exhibits
an ever increasing slope at higher temperatures. So the heat of
evaporation is here undoubtedly a decided temperature function,
which we shall disenss on a following occasion. The most convincing
proof of the lack of correspondence of the vapour tension lines ab
and cd is this that when the line /h is prolonged towards lower
temperatures, it intersects the line v/y at a rather large angle, from
which it appears still more convincingly than from the lines a and
cd, that we have here certainly to do with two different curves in
the same way as for the system Cyanogen.

To set forth still more clearly the regular course of the vapour
pressure line a), it has, just as the curve for 7/np, been once more
separately represented in Fig. 5. In this figure also the points

J= Stat. Meth. Folibois.
= Dynam Jeth Smits & Bokhovst .
S= Stat Neth. _ Smits § Bokhout.

1186

determined by Joripors are indicated, who, as also follows from the
table, has only been able to continue his research up to 312°.

In a subsequent communication we shall give some theoretical
considerations in connection with the results stated here, and also
diseuss the vapour pressure line of the solid modification, which
we determined accurately already some time ago.

Anorg. Chem. Laboratory of the University.
Amsterdam, March 27, 1914.

Mathematics. — “A bilinear congruence of rational twisted quartics.”
By Professor Jan DE Vrips.

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

1. The base-curves of the pencils of cubic surfaces contained in
a net |®*| form a bilinear congruence. *)
If all the surfaces of the net have a twisted curve ¢*° of genus
one in common, and moreover pass through two fixed points H,, 1,,
every two * cut each other moreover along a rational curve 9%,

1

which rests on 0° in 10 points. *)

A third #* cuts y* in 12 points, of which 10 he on 0°; the
remaining 2 are H, and H,. Through an arbitrary point P passes
one o'; if P is chosen on a trisecant ¢ of 0°, then all ®* passing
through P contain the line ¢, and 0‘ is replaced by the figure com-
posed of ¢ and a t*, which cuts it, and meets 9° in 7 points.

2. In order to determine the order of the ruled surface of the
irisecants ¢, we observe that each point of 9° bears two trisecants,
so that @° is nodal curve of the ruled surface (4). We can now
prove that a bisecant 4, outside e°, cuts only one trisecant, from
which it ensues that (¢) must be of order five.

The bisecants 6, which rest on the bisecant 6,, form a ruled sur-
face (6) of order 7, on which 6, is a quadruple line. In a plane
passing through 6, lie three bisecants; as to each of those three lines
the point of intersection of the other two may be associated, by
which a correspondence (1,1) is brought about between the lines }
and the points of y*, (4) is of genus ene. A plane section of (6) has

1), See my communication in these Proceedings, volume XVI, p. 7383. There
| have considered the case that all ©’ have in common a twisted curve v° of genus
two, so that a bilinear congruence of elliptic quartics is formed.

2), See e.g. SturM, Synthetische Untersuchungen tiber Fldchen dritter Ordnung
(p.p. 215 and 233).

1187

therefore 14 nodes. Of these 5 lie on @°, 6 in the quadruple point
lying on 6,; the remaining 8 are represented by a triple point
originating from a trisecant resting on 4,. As 6, in each of its points

of intersection with o° meets two trisecants,‘(f) is consequently a
ruled surface of order jive. *)

3. A o* cutting ¢° in S forms with it the base of a pencil (*)
the surfaces of which touch in |S. We shall now consider two pencils
(W and (Q) in the net [*], and associate to each surface ¥* the
surface 2°, by which it is touched in S. The pencils having become
projective in consequence, produce a figure of order 6, which is
composed of the surface ®* common to both pencils and a surface
=*. On a line 7 passing through S a correspondence (2,2) is deter-
mined by (¥*) and (2); one of the coincidences lies in S, because
/ is touched in S by two corresponding surfaces. The remaining
three are intersections of / with the figure of order 6, mentioned
above; the latter has consequently a triple point in S, from which
it ensues that S is a node of >*. The curves e*, which meet 0° in
S, form therefore a cubic surface passing through 9’, which possesses
a node in S; 9° is therefore a singular curve of order three for the
congruence |o*).

Through S pass 6 lines of 2*; to them belong the two trisecants
t, meeting in S; the remaining four are singular bisecants of the
congruence. Such a line p is cut by o' curves g* in two points,
of which one coincides with \S, (singular biseeant of the jirst kind).

The o* rays 4, which may be drawn through the cardinal points
H,, H, possess the same property.

4. An arbitrary line 7 passing through a point P is cut by one
o* in a pair of points &,/’; the locus of those points is a surface
TT of order 5 with triple point P.

If P lies on 09°, then /° consists of the surface Y* belonging to
S= FP and a quadratic cone, of which the generatrices are singular
bisecants q. Hach line ¢ is bisecant of «' curves of the [9*}.

If, on the other hand, ¢ is bisecant of a v* and at the same time
secant of 9°, then the cubie surface passing through o*, e° and g
belongs to |®*|; consequently q is cut by the surfaces of this net
in the pairs of points of an /*, is therefore bisecant of o' curves 0'
(singular bisecant of the second kind).

The lines g meeting in a point P, belong to the common gene-

1) Other properties of the v® of genus 1 are to be found in my communication
“On twisted quintics of genus unity” (volume II, p. 374 of these Proceedings).

1188

rators of two cones, which have as curves of direction the oe! passing
through /, and the singular curve 9°. These cones pass through the
10 intersections of g* and 09°; of the 15 common generators 5 are
lying in lines g. As a plane contains 5 points S, consequently 10
lines q, the singular bisecants of the second kind form & congruence
(5, 10), which has v’ as singular curve of the second order.

The eubic cone 4*, which projects a e* out of one of its points
P, has a nodal line in the trisecant « of 9', which trisecant passes
through P. The latter is at the same time nodal line of the sur-
face I’. To the section of WZ’ and &* belongs in the first place the
curve o'; further the singular biseeants ,,2,, which connect H, and
H, with P, while uw represents four common lines; the rest of the
section consists of the 5 lines g, which meet in P.

As u with 9* and 9° determines a ®’, it is cut by the net {| ®*]
in the triplets of an involution /*, and is therefore singular trisecant
of the congruence (common bisecant of «' curves @°).

5. Let us now consider the quadruple involution (Q') in a plane ¢,
which is determined by the congruence |9*}. It has jive singular
points of the third order in the five intersections Se of the singular
curve 0°. The monoid *;, cuts g along the nodal curve o*;, the
points of which are arranged in the triplets of an /*, which form
with S; quadruples of (Q*); 6, also contains the remaining points S (§ 3).

If the point Q deseribes a line /, the remaining three points Q’
of its quadruple deseribe a curve 4, which passes three times through
each of the points S;. The curves 2 and 2* belonging to 7 and &,
have, besides the 45 intersections lying in the points S;, the three points
in common, which form a quadruple with /*; moreover as many
pairs of points as the order of 4 indicates. For, if / is cut by 4 in
L*, then / contains a point L of the quadruple determined by Z*,
and the remaining two points belonging to it are intersections of 2
and 4*. The order « of those curves is consequently found from
vw = 2Q¢+ 48; hence «—8.

The coincidences of the /* on the singular curve o,* are at the
same time coincidences of the (Q*). Each point S produces two
coincidences, the locus y of the coincidences has therefore in S 6
points in common with o,*; further two in each of the remaining 4
points |S and 4 in the coincidences of the /*. From this it ensues,
that the curve of coincidences y is of order six.

(Q*) consists of the quadruples of base-points of the pencils of
cubic curves belonging to a net with the jized base-points S;. Each

point of y° is node of a curve belonging to the net.

1189

6. The transformation (Q,Q’) changes a conic into a curve of
order 16, with sextuple points in S;. For the conie t* passing through
the five points S, this figure degenerates into the five curves o* and
a line w, which contains the triplets of points @’, corresponding to
the points Q of t*; consequently w is a singular trisecant of [9°].
On the other hand a bisecant w lying in g is transformed into a
figure of order 8, to which zw itself belongs twice; as the completing
figure must be counted three times and must contain the points .S;,
it is the come r°. Consequently ~ bears only one line wu, and the
singular trisecants of [@*| form @ congruence (1,1).

The surface of trisecants of 9° cuts ~ in a curve r* with 5 nodes
in S;. With wu,7° has five points 7% in common; each of these
points determines a quadruple (Q*), of which one point lies on 17,
while the remaining two are situated on w. By means of the trans-
formation (Q,Q’) t*° is therefore changed into a eurve of order 10,
t'". The latter is apparently the intersection of ~ with the surface
formed by the twisted cubics t*, which with the trisecants ¢ are
associated into degenerate curves of {9'}.

With o,*, 7° has, apart from the singular points S, three points in
common; for in S, lie 4 intersections and in each of the remaining
S, two; therefore S, is a triple point en the curve t”°,

The curves t* form therefore a surface of order ten with three-
fold curve 0°. .

Of the points of intersection of t* with y°,5 <2 2 = 20 lie
in the points S; in each of the remaining 10, a trisecant ¢ is cut
by the corresponding cubic curve t*. From this it ensues that the
locus of the points (¢,7*) is a twisted curve of order ten.

7. The pairs of points QQ’, which are collinear with a point P,
lie (§ 4) on a curve 2°, which passes through the points Sp. If Q
describes the line /, QQ' will envelop a curve of class 5. The points
@Q describe then (§ 5) a curve 2°, which passes three times through
the points S, consequently has still 25 points in common with 2°;
5 of them connect a point Q' of 4° with a point Q of /; the rest
form 10 pairs Q’',Q"; so that @Q’Q" passes through P. From this it
ensues that the triplets of the involution (Q’)’ lying on 4° form
triangles which are circumscribed to a curve (curve of wmvolution)
of class ten, (q),o-

For a point S, 2° degenerates into the curve 6,’ and two singular
lines sy; and s;,* (§ 4); such a line bears an involution /? of pairs
Q,Q’. A pair is formed by Sé and the intersection of s; with w;

1190

as the remaining two points ') of the quadruple lie on wu, the pairs
('.Q/’’ which complete the pairs Q,Q’’ into groups of (Q*), will
lie on a conic o,°. As sp with the curve o;,*, apart from .S;, has
two points in common, 6;*- passes through the four points S;. In
the transformation ((Q,Q’) s;, corresponds to the figure of order 8,
which is composed of s; itself, o,° and 6,” counted twice; this
figure, as it ought to do, passes three times through the points S.

Every singular line s, is bitangent of the curve of involution (q),,,
mentioned above, for it bears two pairs (’,Q’’, for which the point
( is intersection of «,? with /. The singular line w is septuple tangent
Of Gin » tor ehirst / euts the conic 1? in two points, which each
determine a triplet of the /* lying on «, on account of which w is
six times characterized as tangent; but w contains moreover the pair
of points Q’,Q’’ indicated by the intersection (Q of w with 7.

The curves (q),, and (q),,* belonging to / and /* have therefore

in common the line w, which represents 49 common tangents and
fo)

the 10 lines s, which each represent four of those tangents; the
| g ;

remaining 11 we find in the 8 lines indicated by the point //* and
the 8 which are determined by the intersections of /* with 4° (ef. § 5).

The curves 6,’ and 6,* have the points S,,S,,S, in common and
intersect twice in S, and S,, the remaining two intersections V,,
and V,,’ form with .S, and S, a quadruple. From this it ensues
that through each two points of @° passes only one curve of [9*].

The triangles of involution @Q’Q’’Q’’’ described in 6,* envelop a
curve of class four (for S, belongs to two of those triangles); this
eurve of involution has w as threefold tangent, for « bears a triplet
of points forming with S, a group of the (@Q'). So w represents nine
common tangents of the curves of involution belonging to S, and 8, ;
the line V,,V,,’ is also a common tangent; the remaining six are
appavently singular lines s and form three pairs, which respectively
pass through S,,5,,5,.

The singular line sz* is cut by the conic 67; in two points, which
form a quadruple with two points of s;; so they lie on 6**;. Conse-
quently s, and s; are opposite sides of one quadrangle of involution,
which has .S, as adjacent vertex. The two coincidences of the (Q*)
lying in S, also determine quadruples, for which S, is adjacent
vertex. It is easy to see that there are no other quadruples of which
{wo opposite sides intersect in S,. From this it is evident that an
arbitrary point is adjacent vertea of three quadrangles.

1), One of those points lies on sx* and forms with Sz a pair of the J? lying
on that line.

1191

8. -Let (/*) be a pencil belonging to the net [y*], which is pro-
duced by the intersection of the net [®*| with the plane vy. The
locus of the points which have the same polar line with regard to
a curve y? and the curves of a pencil (y”), is a curve w of order
2n + p—3"), hence a curve of order 9, if for y» the curve ot
coincidences y’ is taken. In the points S; w* like y*, has nodes
and there the same tangents as 7"; so the two curves have 30 points
in common in S; Further both of them pass through the 12 nodes
of the pencil |y*|. In each of the remaining 12 common points D
y°
belonging to [y*| have three-point contact. In ((*) occur therefore
twelve groups, in which every time three points have coincided.

In each of the 12 points D, 7° is touched by the complementary
curve y’*, into which y* is transformed by (Q,Q'); the latter is the
locus of the pairs of points which complete the coincidences of (Q*)
into quadruples. The figure of order 48, into which y° is transfor-

5)

is touched by w', which means that there the curves of a pencil

med, consists of ;° itself, of the 5 curves o;°, each counted twice,
and the complementary curve; the latter is consequently indeed
of order 12. With +* it has four points in common, arising from
the +4 coincidences of the /* lying on ~; the remaining 20 lie in
the points Sz From this it ensues that y'* has quadruple points in
the 5 singular points JS.

In S;, v'’, and y° have therefore 5 <4 >< 2 = 40 points in common,
they further touch in the 12 points ). The remaining 8 intersections
arise from quadruples of which twice two points have coincided ; so
(Q*) contains four groups, which consist each of fwo coincidences.

Mathematics. — ‘On Hermitrn’s functions.” By Prot. W. Kaprnyn.

(Communicated in the meetings of March 28 and April 24, 1913).

1. The n'® derivative of e~™ may be put in this form, first given
by Hermite

(ln
wy 0) = (1) eA, (2)
where
n(n —1) 3 n(n—1)(n—2)(n—3)
Ee (2) — (2a)" = it (2a)"—2 +- o oe (2a) ae (1)

These polynomia satisfy the following relations *)

1) See e.g. Cremona-Curtze, Hinleitung in eine geometrische Theorie der ebenen
Curven, p. 121.
2) Exerc. de Tisserand, 1877, p. 26, 27 and 140.

1192

dn

lik (@))= (—1)" ev (e—™) Se Meee Os is. hd (&)

da”

CH, ally

—= =— 24 —_ 1 on Ay =-0° 2 ) (B)
dx? dx
dH, ¢
er Os a Ger ipanee ie aoe ceo (45)
da
Ay eT a oe) (i) WE "Oe (2))
‘| TE (a) ly (@) ere dt —— 0) m = ee em 6 (3)

af H,,? (z)e—” daz = 29 .n! Ya 6) Sera)

ao
The object of this paper is to examine these polynomia and the
series connected with these, which also satisfy the differential equa-
tion (3).

2. To integrate the differential equation (3) by means of definite
integrals, put
H, =c€ z
then we have

a*z dz
+ 2 4+ 2(n+ 1)z=0
ax?

v
da
To solve this, we assume

Q
z =| ett T dt
P

where 7’ is a function of 4 and P and Q are constants. The result
of this substitution ts

z Q : iy dT Peer
2(¢7 ee) a | Ca [= 2t F + (#? + 2n) | av 0F
Now this equation will be satisfied, if we make
2
Tires
and
[2 ===") (OS Seok

Hence the general integral is

e - t
-xt+- —2xl-+—
Zi ACe | é 4 dt + “| e 4 tn dt

0 0

1193

2

ec, and c, being arbitrary constants.

Putting
t = tu
this takes the form

nl

ae fe tu” (A, cos wu +- B,, sin wu) du.
0
A, and &, being again arbitrary constants.
The general integral of
d’y =, dy
da? cas

therefore may be written

+ 2ny = 0

eo)
= e fe 4u" (A, cos au + B, sin vu) du.
<
0
Choosing
Cale ns (—1)r-+! | nx
A — cos sie
Va o Vn a
we get the particular integral
Bens Tes
1 ~C- na
y= — e Je fu cos| cu — = du
Vn e a
0
which for «=O, reduces to
Te 4
COS 5 eo) u2
9 aif
Yo—=0 — —-—— | é Virdu
Vn
v
where
n!
V ao (n even)
Vt
/]
See ue \2
fe 4urdu = 1 1
x DIN,
—— }! (x odd
0 [1 ( 5 (x odd)
Now we know that
Ul
d ni
\(—» (n even)
34 71.
HB, (0) = =! (8)

0 (n oda)

1194

therefore this particular integral is H, (v) and we have

1 ssp ne
(a) = <= || e +u cos (« — =) du. a. om)
Fay ~

0
Choosing again
(—1)" , nw (—1)" no
Ay = —— sin — B, = -————. cos —
Va 2 Va 2

the second particular integral may be written

2

eval sates f nm
L, (2) = Wee ve fe + unsin( au ——)du . . (10)
0

3. This second integral satisties also the relations (4) and (5).
For, differentiating, we have

NES ae sae nm
L'y (uw) = 2aLy (2) -- =e" Je 4 w+! cos |. eu — du
Va e 2
0
1 es n+1) x
= 221, (2) — y = er" fe 410+1 sin (« = a ) du
Kg ce

.
or
Eoin (@) = 2a, (@) Ep) (a) ieee eee eo) ee Ls)
Differentiating again, and remarking that ZL, (x) satisfies the differ-
ential equation (3), we find
(2n + 2) Ly — 2a Ln4) + Lnto = 0
or, changing n in n— 2
big — 20 T,—\ + 2 (n—=1) 2,2 = 10) es ee)
which is in accordance with (5).
If now we substitute the value
Ent OE Mo eT een
from (12) in (11), we get

iO ee oto Bs fo 0, (RLS)
which is in accordance with (4).
4. The function /,(v) may be expanded in series of ascending

powers of a.
If n is even, we have

1195

—* 3
IS beaty pe
Ibex (3) == (abe ex i e + uw" sin wu du
e

Vn
u
meh per Vee
= Ge er > (— 1) aif e 4 urktr+l dy
Vn 0 (2k-+-1)!/,
0
1)? w k: Dy)2k+!
ae re Eee, S(= ye each) (Gas
= ; 2 (2k-+1)/
or
1)n 2a)
Tee eg 22m, m! ex? ae (mn EE 4 (m+1)(m + (2) —... | (14)
Vx 5!

Proceeding in the same manner , n is odd, we get
Lyn 2 OD a)4
ieee ae — 22m lyn fer i. “mn cea (m+-1)(m+2 ot ae | (15)

Both these series*are converging for all finite values of the variable,
and show that

0 (n even)
| fais n—l1 .
Ln (0) = | (—1) 2 2 ( =a) NS)
a = eave (n odd)
Va

5. Te investigate the value of Z, (x) for large values of v, take
the differential equations

LE eae ey az eee
da? da yr coee:
rhe Dy dL
ow a@—+2nL, —9
da® dx
Multiply the former by Z,, the latter by /7, and subtract, so
aaa, a2, adLn a ahele
Views Logy, Nmke east (e pyay eta =)
dx? da? dx da
or integrating
afi, dH,
Te Ep ONY ge
da da

C’, being the arbitrary constant.
Introducing the relations (4) and (13). this may be written
Qn Gp) — Le Ay Ce.

1196

If c—0 we have
2n Hy, (0) Ly—1 (0) = C (n even)
— 2n Ly (0) Hn—1 (0) = €
therefore in both cases
Qn yn!

C= =—

Van

thus finally
Hy (2) Eqney(a) — La (ce) Hp) (2) = ———— , | aan

Now w having a large value, we may write approximately

Hf, (x) = (2a) Hy) (#) = (22)"—
Bnd ke
ee) Saar ex
and therefore
n! er &
En (2) Wes a (18)
6. Summation of some series containing the functions /7/,(2).
Let
S$ hap lt OF 2 aS (ie ee
0 (2k)! 0 (2k al)

and write Hs, and Ho,4, as definite integrals by means of (9),

then we have

1 Fes ae oo (uv)2*
f (2 fe teos avdv Je *cos eudu X (—1)* SAT
wu a 0 (2k)!
0 0
1 ae yp? se s ue a (uv)2k+1
QO a a fe 4 sin cnde fo 4 sin audu (— 1) ——_
M1 4 < 0 (2k +- 1)!
0 0
where
oO (wv)2* x uv)rk+l
= (—1)4 — == 0s uv =, (aye! ) — = sin uv.
0 (2k)! i) (2k -f 1)!
Now
ae Uk back Ty
fe 4 vos wu cos wwdu = 1 f- + [cos (w 4-0) uw + cos (w—v) u| du
0 0

and

119%

% 2
wo 2 a) uz

x
fe + sin-au sin urdu = 1 fe 4 [cos (v—v) wu — cos (w-+%) ul du
0 0

which may be reduced by means of the relation

ca = 42

Nea shes Va ——
e—P* cos Apudu = ——-e 4
2p

0
In this way we get

ao us

ae re Va eye
€ 4 cos cu cos uvdu = —— e—¥—™ (e2x» 4 e—2xv)
0
OS jue =
Sagiet: ; JU oie iat 5
e sin wu sin uvdu = —— Cmte Cs (C220 eme ate)
»
0
and
l ed
ee we e fe + cos av (et 4+ e—22r) du
“Via
0
1 CO 5y2
C= Sa Oe pe! A struey) (e2zP——e=aeee) do.
2V 2a e
0

(a)

To evaluate these integrals we may remark that the relation (@)
to} A \
holds for complex values of 4 Putting therefore 2=a-+ 7b and

equating the real and imaginary part in both members of the equation,

we obtain

w V5 a2 i b2 P
‘a9 Lt ap
fre cos apu (ebpe +- e—bpu)du==——e 4 4 cos a
5 p 2
0
ie ze aa A be ib
— — t
jee sin apu (ere — e—bvu) du = —-e 4 4 sin ;
P a
0
which reduce the values of P and Q to
4(a?4-2?) ;
1h ee ars 2 Eoj(a) Hop( a)
P=—e 5 cos— = & (1)k ——__—__..
; V5 5 0 (2k)!
4(a°-+-2?) .
a= 1 ees PSO a & (—1)k Hoj-41(w) Hon-41(@)
V5 5 0 (2k+1)/

Investigating in the same way a second series

(6)

(19)

(20)

1198

om g GO" 11, (n) IT, Ae)

!
0 Qn. n

where @ represents a value between O and 1, we get
A I, (x) IT, (2) nd Oe

DO uty? nae
= —____ e * wfy"cos
PO LY Sie oI ce.

nx
«“u —— |cos| av— dudv
2 Diy
0 0
and
2. OH, (a) He) hd 1

Guy \2k
OO O 42142 ===
aes ANS
— exext e 4 vos wu cos av
0 2r nt 14 ae
O80:

>>

_—

: UO
vo (2k)f
Guv \2k+1
u2+tv? rae
1 bia Pee)
— ete | e 4° sinwusinarv =
8 a a
0

= — dude
9 (2k+1)/

uv? bur mee
Gee =a 5 2
a Yom € 4 cosaucosav\e2 +e dudv
9
Qa :

1 2 0 uty? Gur buy
ie eaala e + sinwusinav \e
9
amt
0 0

2—¢ 2? Vege
means of (b), we may write
wo 2 >

uz fuv
[- 4+ cos wu
a

age ae
as 1 — x

et ae 2 dw? Vae
0

a)

Now, by

4+ cos Gav
ee u fur Juv 22
oO =e 2 ,
| e 4sinauie2 —e 2 Jdu=2V re + sin Axv
“0
therefore
1 &% (1—§3)y2
== VE ee [- 4 cos (a— Gu) vide (21)
Fy e
0
or
u—bar)*
1 pt wo ON, (x) H,(a
hfe NY: ee Re EEC) ve. US a(22)
V1—6? 0 ot ml
This result shows that the series is diverging when 6 = 1.
Ml

We shall next determine whether any function whatever of a
real variable can be expressed in a series of this form,

4199.
f(a) = A, H, («) + A, H, (w) + A, H, (#) 4
Supposing this expansion to be possible the coefficients A, may be
found by means of the relations (6) and (7)

1 ~
sa Qn. EN ~# f(a) Hy (a) da.

With these values the ous member reduces to

S= lin = S gn A, Hf, (z) *)

C—O)
where
ayy 2, 0" H, () Hy
> 0" A, A, («) =— fee 7 (a) da = — (*) («)
0 Va a 0 Qn SO
1 oy Fo Seer
=— | f(a) tu fo 4 cos (a—Gx) Bdp
uv vi
— © 0
Hence
© (1-0)
S = Lim f: 4 af J (a) cos (a—G2x)3 da
Gale
or

1
SS— fof (a) cos (a —x) B da.
a

Now the second member of this equation represents / (2),
this function satisfies fhe conditions of DiricHter between the limits
Every function of this kind may therefore be

when

—o and + o.
expanded in a series of the functions J&L.

8. We now proceed to give some examples of this expansion.
I. Let f(z) =a, then we have
ap=A,H,+ A, 4,+ A, a,+...

where
nm
ete Sears f
A — w! Hy, e—® da.
2. nlV a
5 —@
Evidently this integral is zero when wz 77, is an uneven function

The idea of introducing @ was suggested to me by Prof. P, Drsyr.
73

Proceedings Royal Acad. Amsterdam. Vol. XVI.

1200

or if n+p is an uneven number; the integral vanishes also

p <n. Supposing therefore p-- n even and n <p, we have
i) ao
> dn
fo Hi Neat de (1p: fiw (e—) dx
du?
—o —o
wo
Gofal
= (—1) | ep —| —— e-® | dz
dx \ dar—|
—o
i
= (1p fw See de
dan—i
or
2 a
| uP HH, e-* dx =p fe a) Gat da
—o ‘= o
Hence
% pl
fxr Hy ta = ATE
es (Dll
= op <i ee:
9
and
{, = — ate
2p Pesky nl
2
which gives
_ P(p—}) P(p—1)(p — 9)(p—8)
(22)? = Baa Se ane He
Il. In the second place expanding

287—

e2hx— 3 — A,4, 4 Alia +- A,H, = tects
the coefficients are given by

lan at
i

AME
= e-(@—8) H, (a) da.
Qn nt Va | :

a
or, putting «= y-+ 8B, by -

1 Wit esters
An = San a Calis FH, (y ar p) dy -
2 nl Va :. a
- 2
Now, expanding H, (y+ p) by Maciavrin’s theorem we have

(>)

Zn
Hy (y + 8) == Fy (y) + 8 Fh (y) +-. > Ay (y)
te

when

1201

where according to (4)
Hi, O) = 2n Hy y (y)
Hi," (y) = 2 n (x — 1) Hy-ofy)

HY) (y) = 22 nl HT, (y)
thus

(Q2

3 in
H, (y¥+8)= ET, (y) +-2n BH, 1 (y) ip n(n-1) 5 Holy) ap 42n.np' , Hly)-
oe! n!

Introducing this value, we get immediately

wo

pr eo) ; pr
A, = — e—-¥ dy = —
MV x ni

—

and
3 su
exer—A? — ] 4 ween (eee (Ge) 4 H, (2) 2 8
From this equation several others may Be: deduced, for instance
ye ‘ 3 B° B°
2 t
e—2pr— f° = | — HT (x = x2) — — v ware
1— 7 (@) tye ys +
e2Fx-— e—2xr é
[ae oe ih +6 dey oa
Ist e2Bz—. e—2hx 3 B a
EN 5 =F H, + a Er, Tey 4
Soe
eF 03 2 S (1k Fopla
= oN Y any) ()
% k yk!
er St. a) (— Al) op, v
y 0 ( ) (2k+1)/ +1 ( )

III. As a third example we will expand a discontinuous function.
Suppose 7 (2) 4 from’ #0) tor ai==1| “and 7 (@) — 0" for
1 << % < 0, we have

FA) Ay CAR pete Eine aoa

| TEE Oe cle tec
A, = On = / atl A af (a) da.
0

This coefficient may be determined in the following way.
Let

where

o |
Ik a 2—@ HI, (a) da = | (2a¢H,—,; — 2 (n—1) Hy—2) e-# da

then

x
18*

1202

eit l 1
{ 2ae-% H, da = — J H,1d (e-#) = — (e-# Hy) + [e-# H',1 da

0 0

]
= F,- ()— ya 0) £23) fee ae
0

e
0

and
[Ee (Oe en) (n > 0)
Now #H,,,(O) vanishes for odd values of n, therefore
Tee = a 0)
Top = — e—' Hox (1) + Hox (0) (k = 0)

The following relations hold between three successive values of /:
Topp) — 2Lo% + 2 (2k—1) Top (0) = 0 (k > 0).
(2k—2)/
Tox ~ 2 Tora 1. 2 (2h 2) Lor (0) = (—1)F2 =e (k > 1).
For
Topsy — 220% + 2 (2k-—1) Top = Hox (0) + 2 (2h—1) Hox_2 (0) —
— e-' [Hox (1) — 2p) (1) + 2'(2k—1) Hox Q)]

where the second member vanishes according to (5).

In the same way the second relation may be proved.

From this it is evident that all values of I depend upon the
values of /, and /,, and these may be obtained directly for

5
1
— @2 =<
| e (4e°—2) da = — 2¢
0
1

Seson —l1
in| e 2a da = 1—e
a
0
If «=O or w«=1 the expansion does not hold. For these values
however we may easily verify that the second member reduces to
i

the value 4.
Taking «= 0, the second member reduces to

1 tL 77) co An H, (0) H,, a
Lim | e da ae! = ()
6=1V me 1) 22. n!
0
or, according to (22), to
: 1 eal ca
Lim | =) NS aaa
4=1 V Ne Vi — @*
0

Assuming

we have

1 (“I La I ders
lim — alt os { a Ch — a
G1 Vn A Van «

In the same way the value for c=1 may be found.
SECOND SECTION.

9. Considering the functions
2
Pn (#) = Cr ae HI, (x)
and determining the value of the constant C, so that

ao

[oe (c)idai=11
we easily get
1
¢.=
we

2°ValW a

and
42
a
A= A)

n
22 Vania
Putting these values in the integral equation

Gn (a) = au fos (a) K (a, @) da
—o
we shall now determine the unknown function K (wv, @) and
unknown constant 4,, which verify this equation.
The expansion II from Art. 8 gave

REL ae are an
ee Oe nla é ) n (a) Oi = ay,

—o

thus, changing # into wu,

l w@
(2u)" = ge || (a—u)?? H,, (a) da.
VE (a)
—o

the

Substituting

1204
this value in (9) we hav
wo 5 les
Lee: - nm
Hi, (a) = —e™ Je +4 cos| wu — —
Qa A
0

00)
@ 5
%u— —u?
er” | e—% H, (a) da 4° cos| wu — —
2°74
—o 0
Changing @ into —a, this gives
(—1)"
H(i

*
Sones Pc # H,, (a)

da
—'@
and putting — w instead of

® 5
—2au— —u?
e 4 cos
=
0 \
es
Ee) La
n (v) = ——e" fe
ey d
which,

—# H, (a) da

—')

-

Uu

5
—2au—— uv
e 4. ‘cosil wt — | du
So
by the relation

ne NI
vos («"— =) = (—1)" cos Ga 9 )

is equivalent with
fi, (e) = Ge

— @
Ong

fe © TT, (a) da
Now

} 5
22U— — 42
fe 4 cos(
—n

nme
cu — — ) du . (d)
Sy
adding the equations (c) and (d) we find
|| n ~
(a) ( )

yL? o— x2 (
prema a H,, (a) de

nN
ane a
4

where, putting 7

5
2au— — uv? nN
4° cos| au— du
2
fe.)
"0 SS
5
=
oO
2 —2au—— 2
4
e cos
a

4
nIv
£u —= —
- 2

5
bee Pa ee
5 # 4 uw nN
du =e e cos | av — = es — — | aov=
2 5 2
iG
ae
4 te ¥
cos | — av cos av dv.

Aceording to formula (a) Art

9)
ve) 9
~ —2au—— u?
| 4
r 5
&

4
— 2

5
— @

6, we obtain therefore
4, -
no WVAiae Ga) mS
cos | au — — du = —— e
2 V5
io 3)

9 ie if —(4—u,? ET (a) da
1 - =)
— du.
9
vu —- =) du (e)

, the same equation leads to
0

1205

and finally

4 wo. &
Igri Phaiy: 4 m
F, («) = ———= e poke Hi, (a) cos | = ax — aN
WV 52 5 2
—o
a2
Multiplying this equation by C,e~2 we have
ow 3(a+27)
(«) 10 4 nm F
Pn (é Pn (a) € 0s | — ax — — | de
fp. (et) = mK Pn cos 5 € 9 aa
thus
i pisces
Ana K(e,e) = =e B wor (F ar — 2),
an Via 5 2

To make A(w,a) independent of n, we distinguish two cases:
1. n even = 2m, then

3(22-b2?)
Ge (—1)" yo 4 ;
om (a Pom (a) e cos — aa da
2m sd pam (a 5 av da
3(422)
—[)\n 1 aE
i ( = lis K, (« . a) =—— e th ecos=40ae
en Vix
2. n odd = 2m + 1, then
3(22+-22)
ee (—1)” | iOimbranct oF
P2m+1 (wv) = Bantex ) P2m-1 (4) € sim 5 ax da
3(a?—2?)
a = Gar K, (@ , «) =——e 10 : sin — aa
2m-1 = 92m-1 : 9 ’ Vox 5 °

According to the theory of integral equations we know that

D (Pam (4) Pram (a
TA eS ee
0

hom
K, (w VS ee SS P2m+1 (x) P2m+1 (a)
0 hemi
or
a2+22
———— Hey (w) Hon .(@) Hem (a)
Ke (ea) ———e 2 J (—1
1 (@,@) Wx ; he Snes
xitc
es Go Hom+1 (2) Hom+s (a
K, (#,a)=—~e 2 > (—1)» E ara ) +1 ( )

Va 0 (2m+-1)/

1206

which may be verified by the equations (19) and (20).

10. We shall now show that the function

Angi (v) + bk Lnqa (@)
; = TAG) SSG)

where & is an arbitrary constant, may be developed in a conti-
nuous fraction.

Differentiating and eliminating /, the differential equation for o,
takes the form

do dz, dz,
ORAS oe Nie Ta
dia da

dy, dz, dz, dy, dy, dy,
Zz + 4 —2z, — |o SS —— |= 0
+( * dx 2 dv Yo da 1 da om ce dx Ys dx

where

y, = An+1 (2) ¥, = Lats (*)
2, = Hn (2) Papi! Oe (9)

According to (17) the coefficients of this equation may be written

Yat, — U2, = Qn-+1 n! er?
dz, dz, 9 Cas
zy aa care = In (An Lai — Hn—1Ln) = 2 rane
Ly dz, dz d :
Zo : yy Yate 3 = Us Le fe Ys =2n (Ay Lni—An ily) =— 2+? nf xer*
dz dx dx dx
d d
yy, os — ¥, on = 2 (n+1) (Hntiln = HyLn41) — Qn+2 (n+1)! ox?
da dx
thus
do ; :
ae SSA SIs wiomag Goto =o (8!)
Substituting
2n
6= 2a — —
oO;

the function 6, satisties an equation of the same kind viz.

do,
de = 6,” —_ 220, + Qn.
ve
Substituting again
. 2 (n—1)
oO, al oe ==
6

the transformed equation is

16
eee 6,7 -— 2x6, + 2 (n—1).
da

1207

and so on, until

doy,
— = On? — 2x6, + 2.
dx
Putting now
On = GH + z
we have
d2 :
thus

hae (¢ —| ode

5 0
C being an arbitrary constant.
Hence
Die neat
Seer yin eens) Mid (aera) (22)
=> on a. 9
. 2a mn eu?
av au;
where
== er da
0
Thus for
2 H, (C—I) + 2ae”
ae 60) = 2a — = = 2 ils ee
7 CCD
at
CLT

=) P(e af 1B (Ge tee) ia

va 7 ~ HCD + Bae
Yioae rye SOI ace
I is ag ee a Ye Sees Cred cia ness
H, (C—1) + (42?—4) @

n= oo”) = ue An +1 (C4) ie Dn er

Th (C= eee
The following relation holds between three successive functions 7:
Ei == 20 \— 2nd n—9-

as appears from the substitution of the values of 6” and 6@—) in
pp

1208

Putting «=O in this relation, we obtain

n

T,(0) = (—1)2 2" Gi (n even)
2 (25)
(0) =10 (n odd)
If now we compare the two forms
a Aysi(C—L) + Tre" Pel Ay) + kLnti ()

Be (Cy ae ees a ee

we may determine the relation which exists between C and &. For
putting «= 0, we have /=0 and

T,(9)
Gr = kLn4i(0) (a even)
Cos mel dd
Tha(0) #E,00) “80
thus
Vx
k= — —.
2C

An+1

n

Therefore if Co the continued fraction (24) represents

Eis

From (e) we may deduce a new form for L,(«). For introducing

and if C—O the value of this fraction is

(' instead of 4, we have
B@e? (Hi T,—Havil 1) == V w(O—1) (Hanah eee
— Va (LnTn—Lri lr) =.
Now the relations
PO ei ea AO es
Ay4+1 = 2aH,—2nA,—4
Enti1 = 2aLyn —2nLy_4

lead easily to

ont

HD, ee
Lge = otha Toe ome On aieloe,
With these values, and (17) therefore, we find
OC on n) — (6=P) 2in Wan iO

or

ies pe AP SAT SB)

1209

This result leads also to a new form for all the functions Z,, (x), for

ew on 26°
L,=- — J. u cos cudu = 2aL, — ——
Va Va
0
and, according to (12)
9
Li Go COT a eo oa. ae ss a n OM)
a
where
Tr—1 = Hy—1 — 2(n—2) H,—3 + 23(n—8) (n—4) Hyp—5 — .... (28)

11. Applying the preceding expansion, the problem of the momenta
may be solved.
Let

a, = 4 I (y) yrdy
0

the question is to determine the function /(y) when «, is given for
all positive integral values of 7.
Putting
f(y) =e [0,H,(y) + 6,H,(y) +0,7,(y) +---]
we have to determine the coefficients 4 from

oe
7

wo
Cn = = bp foeutinay
0 «
—m

Here p-+n is an even number, for the integral vanishes for p + n
odd. Moreover the integral vanishes if p>>n therefore

oO

n i
OF = b fe Py Ay (y)dy
0
— 6

or, according to the expansion I Art. 8

= P
Oh! VV —
n—p
W 2Qn—p Band
2
which may be written
n
ee ——— A Psi iee
ni nu— ;
Vn 0 np Oem Y !

Solving these linear equations, we get immediately

1210

—

2
b= = 2(—1% Ay— —2k

92k , kl

and accordingly

| ee l =) He
——— p ) P =
iho) = VE: € du p UP cos { yu 9
0

where }, has the preceding values.
Writing this

uz

Ay) = Vm “all * du [cos yu S, + sin yu S,}

we have
p P
2 oy
S, = J (—1)? byw
0.2
joe

S, = = (—1) 2 bu :
1.3

or, expressing 4, in function of the values A

a A, 4 A, ae
S, — Al ——— eb AG = 924/ +- U A, = 931) 1 5a a °

ua u2

— et (A,— Ayu? + Ayut —...) = et S (—1)h Anjrk
0

u2
— —¢4 Se yee na a
Vn 0 (2k)!
and in the same way
2

a ac O2h+h1

Se A Se 1). Se eee
Vn 0 (2k+1)!

therefore

We % 2h: Ok
— d cos > (—1)k — u* 8 = —— y2k--l
A) — — fi u | »s yu : (-1l) (en! -urk + sin yu = (— Jk Qk +1)! u |

0
1 > pur G
p: Z COs @ a. =) du.
We 0 P ! 2

or finally

7) == 2 ep
0
Of course this is only a formal solution, which holds when the
values @, are such as to make this integral convergent. This is e.g.
the case if

Ho).(1
e2r41 = 0 a2, (—1)* aut)
for then
; 1 > wo Fyj.(1) ( w \2*
KD) = = fo yu = Dy (S) dh

or, according to the expansion II
1 Ge u2
FYy=— feosyue, * (e+ e-%) du,
20
0

which reduced by 6 Art. 6, gives

é
fy =—e-¥ cos ay .
Ei

Microbiology. — ‘On the nitrate ferment and the formation of
physiological species’. By Prof. Dr. M. W. Beterinck.

(Communicated in the meeting of March 28, 1913).

It is a well-known fact that in soil as well as in liquids containing
a great many individuals of the nitrate ferment, large amounts of
organic substances may be present without preventing nitratation,
which is the oxidation of nitrites to nitrates by that ferment.

On the other hand it is certain, that when only few germs of the
ferment are present, so that they must first grow and multiply in
order to exert a perceptible influence, extremely small quantities of
organic substance are already sufficient to make the experiments fail
altogether, the nitrite then remaining unchanged in the culture media.

It is generally supposed, that this latter circumstance must be
explained by accepting that the nitrate ferment can only then grow
and increase, when soluble organic substances are nearly or wholly
absent.

My own experiments, however, have led me to quite another
result, namely that the nitrate ferment very easily grows and increases
in presence of the most various organic substances. But in this case,
that is, when growing at the expense of organic food, it soon wholly
loses the power of oxidising nitrites to nitrates and then changes
into an apparently common saprophytic bacterium.

This change may be called the formation of a physiological
species, and the two conditions of the ferment thus resulting, respec-
tively the oligotrophic and the polytroplic form.

1212

Furthermore it is proved that the usual laboratory experiments
cannot give back to the polytrophic form, when it is kept in absence
of soluble organie matter and cultivated in a dilute nitrite solution,
the power of oxidising nitrites, not even in the course of 10 years.

Consequently the process of nitratation in pasture ground must
take place as follows.

When the soil contains a great deal of organic matter this need
not be exclusively oxidised and destroyed by other species of bacteria
in order to make the action of the nitrate germs possible, but if
may also be done in part of the germs themselves. It is true that
they get lost thereby as they pass into the polytrophie form, but in the
soil always places must be present without any considerable quantity of
organic substance, where unchanged oligotrophic germs occur. These,
after the destruction of the organic matter in their environment,
can multiply and again provide the soil with anew nitratating flora.

It is very difficult to obtain pure cultures of the nitrate ferment
in the nitratating or oligotrophic condition. The best way is as follows.
Kirst a erude nitratation is produced by bringing pasture soil into a
liquid of the composition: tapwater 100, sodiumnitrite 0,05 to OL,
bipotassiumfosfate 0,01, and cultivating at 30° C.

After about one or two weeks the nitrate ferment of the infection
material has strongly increased and all the nitrite may be converted
into nitrate.

A little of this nitratation, diluted with much water, is now sown
on the surface of a plate of the composition: tapwater 100, care-
fully extracted’) agar 2, sodiumnitrite 0,05, potassiumfosfate 0,01, and
again cultivated at 30° C. As the nitrate ferment and the other microbes
accumulating in the crude nitratations, do not attack the agar, the rate
of soluble organic food present is very low. The nitrate ferment can
grow upon such a plate without losing its faculty of nitratation and
forms very minute colonies of about '/, to I mill. in diameter, which,
being very transparent and = glassy little dises, are hardly visible.
With a greater percentage of water in the agar they are denditrically
branched, with a smaller percentage they remain unchanged circular,
or become somewhat crenate. In such a pure culture the distance
between the colonies must be so great, that they do not touch one
another and can be separately examined. In consequence their number
on the plates must be relatively small, the counteraction of the still
remaining soluble organic substances great, and the nitratative power

1) Por the extraction the agar is left many days in distilled water which is now
and then renewed.

1213

feeble. Hence the experiment takes much time, two or three weeks
or longer.

To obtain pure cultures on silica plates is much more troublesome
than on carefully extracted agar, although the nitratation takes place
very easily on that medium.

Some other species of bacteria, eventually oceurring in the crude
nitratations, may produce colonies on the agar much resembling those
of the nitrate ferment. Those species which in the crude nitratations
do not multiply at all or only very little, are to be recognised on
the plates by their relative rarity. But there exists a species, the
denitrifying, spore-forming Bacillus nitrovus*), which can increase in
the nitratating fluid and on the plates with the same intensity as
the nitrate ferment ifself and whose separation from the latter gives
rise to difficulties. But here the formation of a new physiological
species comes to our assistance, in as much as the nitrate ferment,
on broth- or peptone agar, produces very characteristic although no
more nitratating colonies. They are white-coloured, extensive and
thin; at first dry and flat, they later become thicker, slimy and
moist, and are easily distinguished from the small, semi-spherical,
moist Nitrovus colonies.

On the nitratating plates may further be found the colonies of
Bacillus oligocarbophilus, which are directly recognised by their
white colour and paperlike appearance, and to which I shall return.
later. Moreover a most characteristic species resembling Actinomyces,
but in fact nearly allied to 6. oligocarbophilus. So, in all four species
which should be considered as characteristic for the crude nitrata-
tions, because, after repeated transplantations they never dissappear,
whilst the numerous other species eventually obtained, are but
accidental inhabitants and at continued transferring to fresh media
may be quite expelled.

When the pure cultures of the nitrate ferment are kept in
continual contact with the above nitrite solutions, or on the nitrite
agar plates poor in soluble organic food, the faculty of oxidising
nitrites to nitrates remains unchanged, probably for an unlimited
length of time, that is, the ferment preserves its oligotrophic or
oligophagie condition. Microscopically it makes the impression of a
small Micrococcus but in reality consists of very short rodlets of
0.201 g, which in nitratating condition always seem non-motile.

If the ferment is now transferred to solid media or to culture
liquids richer in organic food, as for instance broth agar or agar

1) To compare: Bildung und Verbrauch von Stickoxydul durch Bakterien.
Centrabl. fiir Bakteriologie 2te Abt. Bd. 25, S. 30, 1910,

1214
dissolved in water with '/,,°/, peptone or more, it grows, as said,
vigorously and produces colonies of the above nature, im which i
is always possible to detect some few motile bacteria. The rodlets
now become somewhat longer and thicker than in the nitratating
state but for the greater part they remain very short; the ferment
has now changed into the polytrophie form.

In broth the same change takes place already on the second or third
day, at 30°., fairly rich cultures being obtained, whereby the broth beco-
mes distinctly turbid and is sometimes covered with a thin film,
perfectly resembling that of B. oligocarbophilus. In the liquid thin
rodlets and threads are found, many of which are moving. They
never ramify and their motility shows that they do not belong to
the family of the Actinomycetaceae, although their way of growing
might suggest it. Accordingly the statement in the manuals, that the
nitrate ferment may be recognised, by its not growing and increasing
in pure culture in broth, is quite erroneous, only nitratation is
excluded.

On broth-gelatin plates at room temperature the growth is at first
rather slow but very characteristic and finally fairly strong, where
by the gelatin quite liquefies and much ammonium carbonate is
produced.

On pure gelatin, dissolved in. distilled water, with nutrient salts,
hardly any development is visible, the nitratative power is never-
theless. rapidly destroyed.

The quantity of dissolved matter required to destroy this faculty,
is extremely small. Media with '/,,°/, of substances such as
glucose, mannite, asparagin, peptone, fyrosin, natriumacetate, or
calciumacetate, cause a vigorous growth and total loss of the nitra-
tative function. With a much smaller amount of soluble organie
substance in the medium, for example that of common non-extracted
agar, the nitrate ferment is able to assimilate that slight quantity
without losing the faculty of nitratation. But under these eireum-
stances weeks or months are required for the oxidation of the nitrite,
and many experiments fail altogether. Old dung, such as is found
in dung-heaps, does not destroy the faculty; vegetable juices, pressed
out from stems and roots of plants, convert the nitrate ferment
into the polytropbie, non-nitratative form, which conversion must,
under certain conditions, also take place in the soil.

Humates in the culture liquids or plates, even in rather great
quantities, are not assimilated and cause no change in the nitratation.

Addition of paraftinoil slackens the nitratation a little, but does
not at all prevent it.

1215

The very striking fact, that the nitrate ferment acts best when
organic substances are as far as possible kept out of the cultures,
has suggested the supposition that this microbe could feed by
chemosynthesis, whereby the energy, produced by the oxidation of
the nitrites should serve for the reduction of atmospheric carbonic acid.

For this hypothesis I have not, however, been able to find a
single proof.

When the pure nitrate ferment is cultivated in a liquid this remains
quite clear; only with the microscope many bacteria can be detected,
especially on the glass wall. A particle of cotton wool fallen from
the air into the cultures, represents a quantity of organic matter
equalling some millions of nitrate bacteria.

On silica plates soaked with solutions of 0,1°/, to 0,05°/, sodium
nitrite and 1,01°/, bipotassium fosfate, the nitrate ferment always forms
small but very active colonies only visible when magnified and the
smaller as the organic matter is better removed from the plates. So
there is also here ground to suppose that for the carbon requirement
of these extremely small colonies, always a sufficient amount of organic
substance is present in the impurities of the plates.

But the strongest argument against the existence of chemosynthesis
with regard to the nitrate ferment, is the following circumstance.

The crude cultures are always covered in the laboratory with a
thin, floating film, consisting of the above mentioned highly remark-
able -bacterium, described by me in 1903 under the name of Bacillus
oligocarbophilus.*) When the nitratation experiments are effected in
a hothouse this film also appears but later and then it always remains
much thinner. When such nitratations are sown out on agar- or silica-
plates, Bacillus oligocarbophilus likewise forms colonies, which at
first sight reveal their relation to the nitrate ferment, but they grow
out considerably larger and_ finally “have the appearance of snow-
white, dry, flat plates of one or more millimeters in diameter. As
B. oligocarbophilus is not able to oxidise nitrites, and hence, under
the said circumstances does certainly not possess the power of re-
ducing carbonic acid by chemosynthesis, there must evidently be
in the environment a sufficient amount of fixed organic carbon to
provide the carbon requirement of this species. As the nitrate ferment
not only lives in the same fluids as B. oligocarbophilus, but by the
nature of the colonies resembles it very much, and moreover quite
corresponds with it as regards its microscopic appearance, its motility

1) Farblose Bakterién deren Kohlenstoff aus der atmosferischen Luft herriihrt.
Centralbl, fiir Bakteriologie, 2e Abt. Bd. 10. S. 38. 1903.

ats)
Proceedings Royal Acad. Amsterdam. Vol. XVI.

1216

and its conditions for nutrition in the polyphagous state, it is quite
sure that these two bacteria are nearly allied. Consequently we
must conclude that the nitrate ferment can feed on the same organic
substances, which 4. oligocarbophilus finds at its disposal, as well in
the liquid as in the extracted agar and the silica plates. That those
substances are at least partly provided by the atmosphere of the
laboratory, I have pointed out in the above mentioned paper.

The nature of these substances is not yet stated, but it is very
probable that volatile products, given off by other bacterial cultures
occur among them.

In this relation I call to mind the experiment mentioned above
with paraffin oil, whose presence does not stop the nitratation. Perhaps
the nitrate ferment can feed on it, or on allied substances, whose
occurrence in the soil or the atmosphere seems not excluded.

From. the foregoing must be concluded, that chemosynthesis for
the nitrate ferment is unproved and that, as far as can be judged
at present, it is im this case a quite superfluous hypothesis.

Summarising we find, that the nitrate ferment represents a definite
state of a greater unity, a physiological species, which may be kept
constant in the nearly pure anorganic nitrite solutions, but which, at
better nutrition with organic substances, passes into an other state
of that unity, another physiological species much more constant.

If the former, that is the nitratating state of the ferment, is called
Nitribacillus cligotrophus, the latter, ron nitratating condition, may be
named Nitribacillus polytrophus. The conversion of the former into
the latter, that is in the direction

N. oligotrophus — N. polytrophus
easily takes place; the passage in opposite direction : V. polytrophus >
N. oligotrophus, cannot be effected by the usual laboratory experiments.

Although the nutrition of Nitribacillus oligotrophus requires an
almost total absence of organic food, there is no cause to ascribe to
this ferment the faculty of chemosynthesis.

The question, where the here described case of the formation of
a physiological species must be placed in the system of biology, is
to be answered as follows.

It cannot be an example of mutation, such as I have amply
described for a number of microbes, as the more or less constant
products of the mutation process arise at the side of the stock, and
continue to exist with it under the most different conditions.

But it is a new case of hereditary modification, in fact not much

1217

differing from the loss of virulence of many pathogenic bacteria, -
only much more evident as to the outward characteristics. Comparable
to, but not identic, with the pleomorphy of many Fungi; — com-
parable, too, to the differentiating process in the ontogenetic
development of the higher plants and animals, the result of which
we observe in the various cell-forms of one and the same indi-
vidual. By artificial nutrition, and independently of their relation
with the other cells, some of these cells can multiply without change
of properties, hence, also without returning to the state of the
mother-cell or the embryonal cell from which they sprung. The
increase of connective tissue and of the muscle cells of the embryonal
heart, cultivated in bloodplasm, are good examples.

Finally I wish to remark that the physiological formation of
species is not an isolated case for the nitrate ferment, but that it
same takes place in the life history of many microbes of soil and
water. To these other species, showing the same disposition,
belongs Bb. oligocarbophilus, which is, as said, nearly allied to the
nitrate ferment itself and on some media cannot even be distinguished
from it.

By the isolation of this bacterium on nitrite- or nitrate agar with-
out organic food, the floating films of crude nitratations, colonies
are obtained, which by their white, dry surface are perfectly lke
the films of the culture liquids, and which, when repeatedly
transferred on the same medium, without other organic food, can
preserve the film-character unchanged in the course of years. But
if these cultures are transferred to broth- or peptone agar, their
characteristic appearance gets lost, wet and glittering colonies
arise, semi-spherical, not extending sideways and seeming!ty belonging
to quite another species. When multiplying they, hereditarily transmit
their newly acquired properties, also when again transplanted on
media without organic food.

The thus obtained polytrophie form and the oligotrophic mother-
form, make a couple, quite comparable to the two conditions of the
nitrate ferment.

For a long time I considered the polytrophie form of 5. oligo-
carbophilus as a wholly different species, always mixed with the
primitive stock as an impurity. Erroneously I thought, that the
isolation could only be effected by means of a better nutrition, the
oligotrophic form thereby dying off. So, I had fallen into the same
error as my predecessors concerning the nitrate ferment, but the
recognition of the physiological formation of species now brings the
required light.

(May 29, 1914.) o

Rin

CONTENTS.

ABEL’s integralequation (Applications of Soninn’s extension of). 583.
ACID ANHYDRIDES and water (Pseudoternary systems of). I. Phthalic anhydride. 712.
ACID FORMATION (The mechanism of the) of aliphatic acid anhydrides in an excess
of water. 718.
Acitbs (Concerning combinations of urea with). 555,
ACIPENSER RUTHENUS (The arrangement of the motor roots and nuclei in the brain of)
and Lepidosteus osseus. 1032.
ADSORPTION-ZSOTHERM (Connexion between the) and the laws of Proust and Hmnry. 970.
ALCOHOL (Influence of) upon the respiratory exchange during rest and during muscular
exercise. 164,
ALDEHYDE (On the formation of an) from s. divinylglycol. 336.
ALGEBRAIC CURVES (Bilinear congruences and complexes of plane). 726.
aLLoTROPY (On the passivity of metals in the light of the theory of). 191.
— (The) of cadmium. I, 485.
— (The) of zine. I. 565.
— (The) of copper. I. 628.
— (The metastability of the metals in consequence of) and its significance for Chemistry,
Physics and Technics. 632.
— (The application of the theory of) to electromotive equilibria. 699.
— and electromotive equilibrium. 807. 1002.
— (The metastable continuation of the mixed crystal series of pseudo-components
in connection with the phenomenon of), 1167.
amipes (Contribution to the knowledge of the). 376.
AMIDO-OXALYLBIURET CONH, (On the synthesis of). 198.

CONH GONH CONHg
aAmpPHIBOLES (On zonal) in which the plane of optic axes of the margin is normal to
that of the central part. 275.
AMPHIOXUS LANCEOLATUS (On the metamorphosis of). 574.
Anatomy. ©. T. van Varkenbure and L. H. J. Mustrom: “On the visual centra in
the brain of an anophthalmos”. 186.
— P. Rérute: “Contributions upon Neurobiotaxis”. 296.
— H. A. Vermeunten: “Note on the size of the dorsal motor nucleus of the Ath

nerve in regard to the development of the stomach”. 305.

80
Proceedings Royal Acad. Amsterdam. Vol. XVI.

ii ClO NN ADSENSE

Anatomy. A. J. Hovy: “On the relation between the quantity of white and grey
substance in the central nervous system”. 311.
~ J. W. van Wisue: “Metamorphosis of Amphioxus lanceolatus”. 574.
— A. J. P. van ven Bronx: “On pteric sutures and pterie bones in the human
skull”. 634.
— V. Taruntssen: “The arrangement of the motor roofs and nuclei in the brain
of Acipenser ruthenus and Lepidosteus osseus”. 1032.
ANHYDRIDES (The mechanism of the acid formation of aliphatic acid) in an excess of
water, 718.
— (On a new method of preparing carboxylic). 959.

ANILINN (Concerning combinations of) with hydrochloric acid. 553.

ANIMALS (On the reflectorical influence of the thoracal autonomical nervous system

on the rigor mortis in cold-blooded), 952.
ANISOTROPOUS BopIFsS (On temperature-measurements of) by means of radiation-pyro-

meters. 799.
ANOPHTHALMOS (On the visual centra in the brain of an). 186.

antiBopiEs (On the formation of) after injection of sensitized antigens. 640.
ANTIGENS (On the formation of antibodies after injection of sensitized). 640.

antimony (The effect of temperature end transverse magnetisation on the continuous

current resistance of crystallized). 1110.

apparatus (An) for the determination of gas isotherms up to about 3000 atm. 754, 822.

argon (Lhe vapour pressure of solid and liquid) from the critical point down to —
206° C. 477.

ARIS4Z (t.), On the TynpaLL phenomenon in gelatin-solutions. 33).

— Variations of state of gelatin-solutions. 418.

ARISZ (W. 1). Positive and negative phototropy of the apexand base in oat-seedlings
(Avena sativa). 363.

— Adjustment to light in oats. 615.

Astronomy. J. £. pe Vos van Sreenwik: ‘Investigation of the inequalities of
approximately monthly period in the longitude of the moon, according to the
meridian observations at Greenwich”. 124 Part. 2. 141. Addendum. 890,

— H, I. van pe Sanpe Bakuuyzen: “On the significance of the term in the right
ascension of the moon, found by J. E. pe Vos van Sreenwixk”. 144.

— W. bbs Strrer: ‘On canonical elements”. 279.

— W. vr Sirrex: “On the constancy of the velocity of light’. 395.

ASCENSION of the moon, (On the significance of the term in the right) found by J. E.
DE Vos VAN STEENWIJK. 144

Atomic weicuts (The red lithium line and the spectroscopic determination of). 155.

AUSCULTATION (On esophsgeal) and the recording of esophageal heart sounds. 1041.

AVENA SATIVA (Positive and negative phototropy of the apex and base in oat-seedlings). 363.

axps of the margin (On zonal amphiboles in which the plane of optic) is normal to
that of the central part. 275.

BACKER (u. J-). On the nitration of methylarea. 770.

CG) OLN) TED Ni st 1

Baxuuyzen (E, F. van pp Sanpbe) presents a paper of Mr. J. E. pu Vos
VAN STEENWLK: “Investigation of the inequalities of approximately monthly period
in the longitude of the moon, according to the meridian observations at Green-
wich. 124. Part 2. 141. Addendum. 890.

— On the significance of the term in the right ascension of the moon. feund by
J. E. pg Vos van SrrEnwisk. 144.

BENJAMINS (c. E.). On esophageal auscultation and the recording of esophageal
heart sounds. 1041,

BERYLLIUM (On the isomorphy of the ethylsulphates of the metals of the rare earths,
and on the problem of eventual morphotropic relations of these salts with
analogous salts of Scandium, Indium and). 1095.

bevu (Hu. J. £.). The envelope of the osculating ellipses, which are described by the
representative point of a vibrating mechanism having two degrees of freedom. of
nearly equal frequencies. 938.

BEIJERINCK (M. W.). Oxidation of manganocarbonate by microbes. 397.

— presents a paper of Mr. Z. Kameruine: “On the regulation of the transpiration
of Viscum album and Rhipsalis cassytha”. 1008.

— The nitrate ferment and the formation of physiological species. 1211.

BEYRICHIA TUBERCULATA KLODEN sp. (The orientation of the shells of), 67.

BILINFAR CONGRUENCE (A) of twisted quartics of the first species. 733.

BILINEAR CONGRUENCES and complexes of plane algebraic curves, 726,

BINARY MIxTURES (Isothermals of di-atomic substances and their). XII. Liquid
densities of hydrogen between the boiling point and the triple point ; contraction
of hydrogen on freezing. 245,

— (Isothermals of monatomic substances and their), XV. The vapour pressure of

solid and liquid argon from the critical point down to —206°C, 477.
BLAAUW (a. H.). The primary photo-growthreaction and the cause of the positive
phototropism in Phycomyces nitens. 774.
BLOOD-COAGULATION PROBLEM (A contribution to our knowledge of the). 172.
BLOODCORPUSCLES (On the change in the permeability of the red) (also in man) 19.
Bopy (On the relation between the quantity of brain and the size of the) in vertebrates. 647.
BOER (s. DE). On the reflectorical influence of the thoracal autonsmical nervous
system on the rigor mortis in cold-blooded animals. 952.
BOESEKEN (J.) and J. F. Carriire. On dichloroacetylene. 1093.

— and W. D. Coney. On the reduction of aromatic ketones. 91. IL. 962.

—and K. H. A. Srixevis. The stability of eyelohydrocarbons in connection with
their configuration. The transformation of cyclo-hexene into benzene and cyclo-
hexane. 499.

— and P. E. Verxapr. The mechanism of the acid formation of aliphatic acid
anhydrides in an excess of water. 718.

BOIS (H. DU) presents a paper of Dr. P. Martin; “The magneto-optic Kerr-effect
in ferromagnetic compounds.” LV. 315,
BokuoRs?T (s. c.), A. Smirs and J. W. Terwen. On the vapour pressure lines of

the system phosphorus. I. 1174.

Iv GioeNG DE Nes:

Bouk (L.) presents a paper of Dr. P. Réture: “Contributions upon Neurobiotaxis”. 296.
— presents a paper of Mr. H. A. VermEuLen: “Note on the size of the dorsal
motor nucleus of the Xth nerve in regard to the development of the stomach”. 305.
-— presents a paper of Dr. A. J. Hovy: “On the relation between the quantity
of white and grey substanee in the central nervous system”. 311.
— presents a paper of Prof. A. J. P. van pen Brorx: ,On pieric sutures and
pteric bones in the human skull”. 634.
— presents a paper of F. Tununissnn: “The arrangement of the motor roots and
nuclei in the brain of Acipenser ruthenus and Lepidosteus osseus”, 1032.
BOLTZMANN (A mechanical theorem of) and its relation to the theory of energy
quanta. 591,
BONNEMA (J. H.). The orientation of the shells of Beyrichia tuberculata KL 6D EN
sp. 67.
— Contribution to the knowledge of the genus Kloedenella ULricu and Basser, 1105.
BORACITE (RONTGENpatterns of ) obtained above and below its inversion-temperature. 792.
BORNWATER (J. TH.). On the synthesis of amido-oxalylbiuret CoNnH, 98s

CONH CONH CONH
Botany. C. van Wissenincu: “On the nucleolus and karyokinesis in Zygnema’. 11,
— W. H. Arisz: “Positive and negative phototropy of the apex and base in oat-
seedlings (Avena sativa)”. 363.
— W. H. Arisz: “Adjustment to light in oats”. 615.
— A. H. Biaauw: “The primary photo-growth reaction and the cause of the
positive phototropism in Phycomyces nitens”. 774.
— J. A, Hoytnea: “Experiments on hybridisation with Canna indica”, 835.
— Z. Kamerwine: “Regulation of the transpiration of Viscum album and Rhipsalis
sassytha”. 1008.
— I. Tames: “The explanation of an apparent exception to MenpEL’s law of
segregation”. 1021,
BRAIN (On the relation between the quantity of) and the size of the body in verte-
brates. 647.
— (The arrangement of the motor roots and nuclei in the) of Acipenser ruthenus
and Lepidosteus osseus, 1032.
BRAVATS (The theory of) (on errors in space) for polydimensional space, with appli-
cations to correlation. 1124.
BROEK (A. J. P. VAN DEN). On pteric sutures and pteric bones in the human skull. 634.
BROUWER (. A.). On zonal amphiboles in which the plane of optic axes of the
margin is normal to that of the central part. 275.
— On homoeogeneors inclusions of Kawah Tdjen, Goentoer and Krakatau and their
connection with the surrounding eruptive rocks”. 995.
BRUIN (G. D¥) and Ernst Courn: On a new principle for the direct determination
of osmotic pressure. 160.
— The influence of pressure on the EMF of the lead-accumulator. 161.
BUCHNER (fb. H.). Colloids and the phase rule. 60.

BUTANE (The virial-coefficient & for normal). 350.

ClOSNE Talbaety sD (Ss vV

BUTANE (The viscosity of the vapour of normal). 355.
cabMiuM (The allotropy of). I. 485.
CANNA iNDICA (Hybridisation with). 835.
CANONICAL elements (On), 279.
CARBON DIOXIDE (Vapour pressures of) between —160° C. and —183° ©. 215.
— (Vapour pressure of) in the range from —140° C, to about 160° C. 445,
CARRIERE (J. PF.) and J. Boesexen. On dichloroacetylene. 1093.
Chemistry. A. Smits: “The systems phosphorus and cyane”, 27.
— A. Sirs and H, Vixsepoxse: “On the pseudo system methylrhodanide-methyl-
mustardoil”. 33,
— HE. H. Bicuner: “Colloids and the phase rule’. 60.
— J. Boesexen and W. 1. Couen: “On the reduction of aromatic ketones”, 91.
II. 962.
— VA. H. Scurermemakers: “Equilibria in ternary systems’. VIII. 99. JX. 385.
X. 540. XL. 597. XII. 739. XILI. 841. XIV. 1136.
— P. van Lrersum: “On the presence of quinine in the seed of Cinchona
Ledgeriana Moens’’. 153.
— Exnxsr Courn and G. pe Brurn: “On a new principle for the direct deter-
mination of osmotic pressure”. 160.
Ersnt Couen and G. ve Bruin: “The influence of pressure on the K.M.F. of
the lead-aecumulator”’. 161.
— A, Smits; “The passivity of metals in the light of the theory of allotropy”. 191.
— A, F. Honteman: “The nitration of toluols and its derivatives chlorated in the
side-chain”. 192.

— J. Ta. Bornwater: ‘On the synthesis of amido-oxalylbiuret conti,

CONH CONII CONH,”.

198.

— p. J. H. vay Giyneken: “Economie lixiviation”. 201.

— P. Mutuer: “On the formation of an aldehyde from s. divinilglycol”. 336.

— P. van Rompureu and J. H. Scunpsrs: ”2.3.4.6 Tetranitro~phenylmethyl- and
ethylnitramine”. 369.

— A. P. N. Francuimont;: "Contribution to the knowledge of the amides”. 376.

— W. Respers: “The distribution of a colloidally dissolved substance over two
layers”. 379.

— [Ernst Conen and W. D. Hetperman: “The allotropy of cadmium”. [. 485.

— J. Borsexen and K. H. A. Sruurvis: “Lhe stability of cyelohydrocarbons in
connection with their configuration. The transformation of cyclo-hexene into
benzene and cyclohexane”. 499.

— J. ©. Tsaonus: “Concerning combinations of aniline with hydrochloric acid”. 553.

— D. F. pu Torr: “Concerning combinations of urea with acids”. 555.

— A. Smits and ©. A. Losry pe Bruyn: “The occurrence of an upper critical
point of mixing of the coexistence of two mixed crystal phases”. 557.

— Ernst Couen and W. D. Henperman: “The allotropy of zinc”. I. 565.

— —: “The allotropy of copper”. I. 628.

VI CONTENTS.

Chemistry. Ernst couen; “The metastubility of the metals in consequence of allotropy

and its significance for Chemistry, Physics and Technies”. 632.

— A. Smivs: ‘The application of the theory of allotropy to electromotive equilibriw’.699.

— H. R. Kruyer: “Pseudoternary systems of acid anhydrides and water, I. Phtalie
anhydride”. 712.

— J. Borspken and P. E. Verkape: “The mechanism of the acid formation of
aliphatie acid anhydrides in an excess of water”. 718.

— H. J. Backer: “On the nitration of methylurea”. 770.

— Eenst Conen: ‘“Allotropy and electromotive equilibrium”. 807.

— ]. M. Jarcer and H. 8S. van Kiooster: “Studies in the field of silicate che-
mistry. I. On compounds of lithiumoxide and silica”. 857,

— A. J. van Peskr: “On a new method of preparing carboxylic anhydrides”. 969.

—. W. P. A. Jonker: “Connexion between the adsorption-isotherm and the laws
of Proust and Hrnry”, 970.

— A. Smurs, A. Kerrner and A. L. W. pe Gee: “On the pyrophoric phenomenon
in metals”, 999.

— A. Smirs: “Answer to Prof. E. Counn to his observations under the title of
“Allotropy and electromotive equilibrium”, L002.

— W. Respers: “The reciprocal pairs of salts KCl + NaNO Z NaCl+KNO,and

the manufacture of conversion salpeter”. 1065.

— P. van RomBurcu and Miss D. W. Wenstnx: “A new hydrocarbon from the
pinacone of methylethylketone”. LOSS.

— P. van Rompurcu and P. Muntpr: “On 1.3.5 hexatriene”. 1090.

— J. Borspken and J. F. Carritre: “On dichloroacetylene”. 1093.

— I. M. Jarcer: “On the isomorphy of the ethylsulphates of the metals of the
rare earths and on the problem of eventual morphotropic relations of these salts
with analogous salts of Scandium, Indium and Berylliam”. 1095.

— A. Smits: “The metastable continuation of the mixed crystal series of pseudo-
components in connection with the phenomenon of allotropy”. 1167.

— A. Smurrs, S C. Boxnorst and J. W. Terwen: “On the vapour pressure lines
of the system phosphorus”, I. 1174.

curMoraxis (The effect of subcutaneous terpentine-injections on the) of remote places. 609.

CINCHONA LEDGERIANA MOENS (On the presence of quinine in the seed of). 153.

cLouptNess of the sky (On the relation between the) and the duration of sunshine. 507.

COHEN (ERNST) presents a paper of Dr. P. J. H. VAN GINNEKEN: ‘Economic
Jixiviation”. 201.

— The metastibility of the metals in consequence of allotropy and its significance
for Chemistry, Physics and Technics. 632.

— presents a paper of Dr. H. R. Kruyr: *‘Pseudoternary systems of acid anhy-
drides and water. I Phthalic anhydride”. 712.

— Allotropy and electromotive equilibrium. 807 Answer of Prof. A. Smrrs. 1002.

cONEN (eERNsT) and G. pvp Bruin. On a new principle for the direct determj-
nation of osmotic pressure. 160.

GAOUN SEEN wes: Nir

COHEN (£RNS7) and G. ve Bruin. ‘The influence of pressure on the EMF of the
leadaccumulator, 161.

CONEN (eERNst) and W. D, Heiperman. The allotropy of cadmium, I. 485.

— The allotropy of zinc. I. 565.
— The allotropy of copper. I. 628.

COHEN (w. D.) and J. Borseken. On the reduction of aromatic ketones. 91. 1, 962.

CoLLoIps and the phase rule. 60.

COMPONENT ATOMS (The volume of molecules and the volume of the). 880.

compounDs (The magneto-optic Kerr effect in ferromagnetic). LV. 318.

CONVERSION SaLPETER (The reciprocal pairs of salts KC] -+- Na NO3 SS NaCl + KNO,
and the manufacture of). 1065.

correr (The allotropy of). [. 628.

CORRELATION (The theory of Bravais (on errors in space) for polydimensional space,
with application to). 1124.

CRITICAL DENSITY (On the) for associating substances. 1076.

CRITICAL QUANTITIES (A new relation between the) and on the unity of all the sub-
stances in their thermic behaviour. 808, 924. 1047.

CROMMELIN (C, A.). Isothermals of monatomic substances and their binary mixtures.
XV. The vapour pressure of solid and liquid argon from the critical point down
to —206°C. 477.

CROMMELIN (Cc. a.) and H. Kameruincu Onnts. Isothermals of di-atomic substances
and their binary mixtures. XIII. Liquid-densities of hydrogen between the boiiing
point and the triple point; contraction of hydrogen on freezing. 245.

CRYOMAGNETIC APPARATUS (Modification in the) of KamERLINGH ONNEs and Perrier, 892.

CRYOMAGNETIC investigation of substances (Apparatus for the general) of small suscep-
tibility. 689. 786.

CRYSTAL PHAsEs (The occurrence of an upper critical point of mixing at the coexistence
of two mixed). 557.

CRYsTAL sERIEs (The metastable continuation of the mixed) of pseudo-components in
connection with the phenomenon of allotropy. 1167.

CUBIC INVOLUTIONS in the plane. 974.

CURIE’s Law (The deviations from) in connection with the zero-point energy. 432.

cyaNe& (The systems phosphorus and). 27.

CYCLOHYDROCARBONS (The stability of) in connection with their configuration. The
transformation of cyclo-hexene into benzene and cyclo-hexane. 499.

DICHLOROACETYLENE (On). 1093,

DIFFERENTIAL EQUATIONS (On the singular solutions of ordinary and partial) of the
first order, 1152.

DIFFUSION-COEFFICIENT (The) of gases and the viscosity of gas-mixtures. 1162.

DIVINYLGLYCOL (On the formation of an aldehyde from s.). 336.

DUBOIS (EUG.). On the relation between the quantity of brain and the size of the
body in vertebrates. 647.

EHRENFES?T (P.). A mechanical theorem of BoLtzMann and its relation to the

theory of energy quanta. 591.

VIE CeOSNTTAESN Doss

EINSTEIN’S theory of gravita‘ion (On a system of curves occurring in). 40.

ELECTROCARDIOGRAMS Of surviving human embryos. 992.

ELFCPROMOTIVE EQUILIBRIA (The application of the theory of allotropy to). 699,

ELECTROMOTIVE EQUILtBRIUM (Allotropy and). 807. 1002.

ELECTRONS (On the theory of free) in metals. 236.

ELEPHAS ANTIQUUS ALC. from the river Waal near Nijmegen. 769.

ELLIPsps (The envelope of the osculating) which are described by the representative
point of a vibrating mechanism having two degrees of freedom of nearly equal
frequencies. 938.

embryos ([lectrocardiograms of surviving human). 992. >

ENERGY (On the law of the partition of). IM. 84. IV. 491. V. 1082.

ENERGY QUANTA (A mechanical theorem of BotrzMann and its relation to the theory
of). 591.

EQUATION OF sTATE (Some difficulties and contradictions met with in the drawing up
of the). 44.

— (On the) of an ideal monatomic gas according to the quantumtheory, 227.

EQUILIBRIA in ternary systems. VIIT. 99. 1X. 385. X. 540. XI. 597. XIL. 739. XIII.
S41. XIV. 1136.

ERRATUM, 336 490.

ERRORS in space (The theory of Bravars on) for polydimensional space, with appli-
cation to correlation. 1124.

PPAYLNICRAMINE (2.3.4.6 Tetranitro-phenylmethyl- and). 369.

ETHYLSULPHATES (On the isomorphy of the) of the metals of the rare earths, and on
the problem of eventual morphotropic relations of these salts with analogous salts
of Scandium, Indium and Beryllium. 1095.

HY KMAN (c.) presents a paper of Dr. C. J. C. Hoogennuyze and J. Nreuwennuyse:
“Influence of aleohol upon the respiratory exchange during rest and during
muscular exercise”. 164,

— presents a paper of Mr, L. K. Woxrr: “On the formation of antibodies after

injection of sensitized antigens”. 640,

i

PASCICULUS DEITERS ASCENDENS (Rolling movements and the «ascending vestibulary
connections), 338.

ripktN (On) in sol and gel state. Likewise a contribution to our knowledge of the
blood-coagulation problem, 172.

FRANCHIMONT (A. P. N.) presents a paper of Dr. J. To. Bornwarer: “On the

synthesis of amido-oxalylbiuret CONH, eS:

CONH CONH CONHg
— Contribution to the knowledge of the amides”. 576.
— presents a paper of Dr. H. J. Backer: “On the nitration of methylurea”. 770.
GALVANOMETER (A quick coil-). 149.
— (Contribution to the knowledge of the string). 522.
Gas (On the equation of state of an ideal monatomic) according to the quantum-
theory. 227.

CO NAL aN Des: IX

GAS-IsoTHERMS (An apparatus for the determination of) up to about 3000 atm. 754. $22.
Gas-MixTuRES (The diflusion-coefficient of gases and the viscosity of). 1162.
GEE (a. L. W. DE), A. Smits and A. Kerrner: On the pyrophoric phenomenon ir
metals. 999. ,
GELATIN-SOLUTIONS (On the TyNDALL-phenomenon in). 331.
— (Variations of state of). 418.
Geology. H. A Brouwer: “On zonal amphiboles, in which the plane ef optic axes
of the margin is normal to that of the central part”. 275.
— L. Rurren: “Elephas antiquus Fale. from the river Waal near Nijmegen”. 769.
— k. Marty: “At what time the Indian Archipelago is separated from the
Tethys?” 921.
— H. A. Brouwer: “On homoeogeneous inclusions cf Kawah Idjen, Goentoer and
Krakatau and their connection with the surrounding eruptive rocks”, 995.
GINNEKEN (P. J. H. van). Economic lixiviation. 201.
GOENTOER (On homoeogeneous inclusions of Kawah Idjen,) and Krakatau and their
connection with the surrounding eruptive rocks, 995.
GRAVITATION (On a system of curves occurring in Ernsrein’s theory of). 40.
GREENWICH (Investigation of the inequalities of approximately monthly period in the
longitude of the moon, according to the meridian cbservations al). 124. Part 2.
141, Addendum. 890.
WaAsS (wW. a. DE). The effect of temperature and transverse magnetisation on the con-
tinuous-current resistance of crystallized antimony. 1110.

WAGA (H) presents a paper of Prof. F. M. Jarapr and Ant. Srupk ; «On temperature-
measurements of anisotropous bodies by means of radiation-pyrometers”. 799.
HAGA (H.) and F. M. Jarger. RoénrcENpatterns of Boracite, obtained above and

below its inversion-temperature. 792.
HAMBURGER (H. J.) presents a puper of Mr. I. Snapper: “On the change in the
permeability of the red blood corpuscles (also in man)’. 19.
— presents a paper of Dr FE. Laqurur and W. BR. van per Meer: “Velocity of
the intestinal movements in different mammals”. 65.
— presents a paper of Dr. E, Hexma: “On fibrin in sol- and gel-state. Likewise a
contribution to our knowledge of the blood-coagulation problem”. 172.
— The effect of subcutaneous terpentine-injections on the chemotaxis of remote
places. 609.
HEARING-APPARATUS (On) examined after Lord Raytpicu’s mode of arrangement. 492.
HEART soUNDS (On) esophageal auscultation and the recording of esophageal). LO41.
HEKMA (k.). On fibrin in sol and gel state. Likewise a contribution to our knowledge
of the blood-coagulation problem, 172.
HELDERMAN (w. b.) and Ernst Coen. The allotropy of cadmium. I. 455,
— The allotropy of zinc. [. 565.
— The allotropy of copper. I. 628.
HELIUM (Further experiments with liquid). H. 113. 673. 1. 987.
HERMITE’s functions (On). 1191.

HEXANE-water (On the system). 404.
HEXATRIENE (On 1,3,5), 1090.

x CxOLN TENS Lass

HOLLEMAN (A. PF.) presents a paper of Dr. E. IL. Biicuner: “Colloids and the
phase rule”. 60.
— presents a paper of Prof. A. Smirs: “The passivity of metals in the light of the
theory of allotropy”. 191.
— The nitration of toluols and its derivatives chlorated in the side-chain, 192.
— presents a paper of Prof. J. Borsexen and K, H. A. Sruveyis: “The stability
of cyclo hydrocarbons in connection with their configuration. The transformation
of cyclo-hexene into benzene and cyclo-hexane”. 499.
— presents a paper of Prof. J, Borsmxen and P. EB. Verxape: “The mechanism
of the acid formation of aliphatic acid anhydrides in an excess of water”. 718.
—- presents a paper of Prof. J. BonsEKEN and J. F. Carriire; “On dichloroacetylene”.
1098.
— presents a paper of Prof. J. Bérsrxken and W. D. Comrn: “On the reduction
of aromatic ketones”. 91. II. 962.
HONING (J. a.). Hybridisation with Canna indica, 835.
HOOGENHUYZE (fc. J. C. VAN) and J. Nreuwenuuyse. Influence of alcohol upon
the respiratory exchange during rest and during muscular exercise. 164.
HOOGEWERFF (s.) presents «a paper of Mr. A. J. van Pesxi: “On a new
method of preparing carboxylic anhydrides”, 969.
Hovy (a. J.), On the relation between the quantity of white and grey substance in
the central nervous system. 311.
HUMAN SKULL (On pteric sutures and pteric bones in the). 634.
HYBRIDISATION with Canna indica 835.
HYDROCARBON (A new) from the pinacone of methylethylketone. 1088.
HYDROCHLORIC AcID (Concerning combinations of aniline with). 553.
HyDROGEN (Liquid-densities of) between the boiling point and the triple point. 245.
— (The vapour pressures of) from the boiling point down to near the triple point. 440,
1@as? in Livonia (On the pseudometeorite of). 292.
INDIAN ARCHIPELAGO (At what time the) is separated from the Tethys? 921.
tnp1uM and Beryllium (On the isomorphy of the ethylsulphates of the metals of the
rare earths, and on the problem of eventual morphotropic relations of these
salts with analogous salts of Scandium). 1095.
INJECTION (On the formation of antibodies after) with sensitized antigens. 640.
INTEGRALEQUATION (Applications of Sonrne’s extension of ABEL’s). 583.
INTESTINAL MOVEMENTS (Velocity of the) in different mammals. 65.
INVERSTON=TEMPERATURE (RONTGENpatterns of boracite, obtained above and below its). 792.
ISOTHERMALS of di-atomic substances and their binary mixtures. XIII. Liquid-densities
of hydrogen between the boiling point and the triple point; contraction of hydrogen
on freezing. 245,

— of monatomie substances and their binary mixtures. XV. The vapour pressure
of solid and liquid argon from the critical point down to — 206° C. 477.
JAEGER (F. M.). On the isomorphy of tne ethylsulphates of the metals of the rare

earths, and on the problem of eventual morphotropie relations of these salts with

analogous salts of Scandium, Indium and Beryllium, 1098.

CiOONe 2 VEEN TDS: XI

JAEGER (ry. M.) and H. Haca. Ronreunpatterns of Boracite, obtained above and
below its inversion-temperature. 792.
— and H. 8. van Kuoostmr, Studies in the field of silicate-chemistry. [. On com-
pounds of lithiumoxide and silica, 857.
— and Ant. Simek. On temperature-measurements of anisotropous bodies by means
of radiation-pyrometers. 799.
JONKER (Ww. P, A.). Connexion between the adsorption-isotherm and the laws of
Proust and Henry. 970.
JULIUS (W. H.) presents a paper of Dr. W. J. H. Moti: “A quick coil galvano-
meter”. 149.
— On the interpretation of photospheric phenomena. 264.
— presents a paper of Dr. W. J. H. Monn: “A rapid thermopile”. 568.
KAMERLING (2). On the regulation of the transpiration of Viscum album and
Rhipsalis Cassytha, 1008.
KAMERLINGH ONNEsS (H.). v. Onnes (H. KAMpRLINGH).
KAPTEYN (J. Cc.) presents a paper of Prof. M. J. van Uven: “The theory of
Bravats (on errors in space) for polydimensional space, with applications to

correlation, 1124.

KAPTEYN (w.) presents a paper of Dr. J. G. Rurcurs: “Applications of Soyxine’s
extension of ABBL’s integralequation”. 583.
— On Uermiry’s functions. 1191.
KARYOKINESIS (On the nucleolus and) in Zygnema. 1).
KAWAH IDJEN (On homoeogeneous inclusions of), Goentoer and Krakatau and their
connection with the surrounding eruptive rocks. 995.
KEESOM (Ww. H.). On the equation of state of an ideal monatomic gas according to
the quantum theory. 227.
— On the theory of free electrons in metals. 236.
— On the magnetization of ferromagnetic substances considered in connection with

the assumption of a zero-point energy. 454, IT. 468.

— On the question whether at the absolute zero entropy changes on mixing. 669.

KEESOM (w. H.) and H. Kamertmncn Onnes Vapour pressures of hydrogen from
the boiling point @own to near the triple-point. 440.

KBRR-EFFECT (The magneto-optic) in ferromagnetic compounds), IV. 318.

KETONES (On the reduction of aromatic). 91. II. 962.

KETTNER (a), A. Smits and A. L. W. pe Ger. On the pyrophoric phenomenon
in metals, 999.

KLOEDENELLA Uxricu and Basster (Contribution to the knowledge of the genus). 1105.

K LOOSTER (H 8s. VAN) and F. M, Jarcer. Studies in the field of Silicate-Chemistry.
I. On compounds of lithiumoxide and silica. 857.

KOHNSTAMM (PH.) and K. W. Watsrra. An apparatus for the determination of
gas isotherms up to about 3000 atm. 754. $22.

KORTEWEG (D. J.) presents a paper of Dr. H. J. KE. Bern: “The envelope of the
osculating ellipses, which are described by the representative point of a vibrating

mechanism having two degrees of freedom of nearly equal frequencies”, 938.

XIf CONTEN TS.

KRAKATAU (On homceogeneous inclusions of Kawah Idjen, Goentoer and) and their
connection with the surrounding eruptive rocks. 995,

KRUYT (H. R.) Pseudoternary systems of acid anhydrides and water. I. Phthalic
anhydride. 712.

KUENEN (J. P.). The diflusion-coefficient of gases and the viscosity of gas-mixtures.
1162.

— and 8. W. Visser. Viscosimeter and volatile liquids. 75.

— The virialeoefficient B for normal butane. 350.

— The viscosity of the vapour of normal butane. 355.

LAAR (J. J. VAN). Some difficulties and contradictions met with in the drawing up
of the equation of state. 44.

— A new relation between the critical quantities and on the unity of all the

substances in their thermic behaviour, 808. 924. 1047.

LAQUEUR (e.) and W. R. van per Mesr. Velocity of the intestinal movements
in different mammals. 65.

LANGELAAN (J. w.). Experiments on the atonical muscle. 336. IL. 571.

Law of the partition of energy (On the). ILL. 84. IV. 401. V. 1082.

— of segregation (The explanation of an apparent exception to Menpun’s). 1021.
Laws of Proust and Henry (Connexion between the adsorption-isotherm and the). 970.
LEAD-accuMuULATOR (The influence of pressure on the MF of the). 161.

LEERSUM (be. VAN). On the presence of quinine in the seed of Cinchona Ledgeriana
Moens. 153.

LEPIDOSTEUs OssEUs (The arrangement of the motor roots and nuclei in the brain of
Acipenser ruthenus and). 1032.

LiGHt (On the constancy of the velocity of). 395.

— (Adjustment to) in oats. 615.

LIiQuip-pENstniEs of hydrogen between the boiling point and the triple point. 245.

LIQuIDs (Viscosimeter and volatile). 75.

LITHIUMLINE (The red) and the spectroscopic determination of atomic weights, 155.

LITHIUMOXTDE and Silica (On compounds of). 857.

LIXIVIATION (Lconomic). 201.

LOBRY DE BRUYN (c. A.) and A, Smits, The occurrence of an upper critical point
of mixing at the coexistence of two mixed crystal phases. 557.

LONGITUDE OF THE MOON, (Investigation of the inequalities of approximately monthly
period in the), according to the meridian observations at Greenwich. 124. Part 2.
141. Addendum. 890.

LORENTZ (H. A.) presents a paper of Mr. Cu. H. van Os: “On a system of curves
occurring in Einsrrin’s theory of gravitation”. 40.

— presents a paper of Mr. J. J. van Laar: “Some difficulties and contradictions

met with in the drawing up of the equation of state”. 44.
— presents a paper of Prof. P. Eurmxrest: “A mechanical theorem of BoLTZMANN

and its relation to the theory of energy quanta”. 591.
— presents a paper of Mr. J. J. van Laar: “A new relation between the critical

quantities, and on the unity of all the substances in their thermic behaviour”,
808. 924. 1047.

CONDEN®?S. xn

LORENTZ (H. 4.) presents a paper of Dr. W. J. pe Haas. “The effect of temperature
and transverse magnetization on the continuous-current resistance of crystallized
antimony”. 1110.

MAGNETIC RESEARCHES. IX. The deviations from Curib’s law in connection with the
zero-point energy. 432. X. Apparatus for the general cryomagnetic investigation
of substances of small susceptibility. 689. 786. XI. Modification of the eryomag-
netic apparatus of Kameritnen Onnes and Perrine 892. XII. The susceptibility
of solid oxygen in two forms. 894. XII[. The susceptibility of liquid mixtures of
oxygen and nitrogen and the influence of the mutual distance of the molecules
upon paramagnetism. 901, On paramagnetism at low temperatures. 917.

MAGNETIC RESOLUTION of spectrum lines and temperature. 158.

MAGNETIZATION (On the) of ferro-magnetic substances considered in connection of a
zero-point energy. 454. IT. 468.
— (The effect of temperature and transverse) on the continuous-current resistance
of crystallized antimony. 1110.
MAMMALS (Velocity of the intestinal movements in different). 65.
MAN (On the change in the permeability of the red bloodcorpuscles also in). 19.
MANGANOCARBONATE (Oxidation of) by microbes. 397.
MARTIN (Kk). At what time the Indian Archipelago is separated from the Tethys? 921.
MARTIN (PIERRE). The magneto-optic Kerr-eflect in ferromagnetic compounds,
IV. 318.
Mathematics. J. G. Rueers: ‘Applications of Sonine’s extension of ABEL’s integral-
equation”. 583.
— Jan pe Vrizs: “Bilinear congruences aud complexes of plane algebraic curves.” 726.
— Jan ve Vrigs: “A bilinear congruence of twisted quartics of the first species”. 733.
— H. J. EH. Bera: “The envelope of the osculating ellipses, which are described
by the representative point of a vibrating mechanism having two degrees of
freedom of nearly equal frequencies”. 938.
— Jan pe Vrigs: “Cubic involutions in the plane”. 974.
— M. J. van Uven: “The theory of Bravats (on errors in space) for polydimen=
sional space with application to correlation”. 1124.
— Hk. ve Vates and G. Scuaake: “On the singular solutions of ordinary and
partial differential equations of the first order’. 1152.
— Jan pre Vrizs: “A bilinear congruence of rational twisted quarties”. 1186.
— W. Kapreyn: “On Hermire’s functions”. 1191.
MEER (W. R. VAN DER) and E, Laqueur. Velocity of the intestinal movements in
mammals, 65,
MENDEL law of segregation (The explanation of an apparent exception to). 1021.
MERIDIAN OBSERVATIONS at Greenwich (Investigation of the inequalities of approxi-
mately monthly period in the longitude of the moon, according to the), 124. Part 2.
141. Addendum. 890.
MESTROM (L. H. J.) and ©. T, van VaLkenpurG. On the visual centra in the brain
of an anophthalmos, 186,

metaLs (The passivity of) in the light of the theory of allotropy. 191.

XIV CON DE Ns;

METALS (On the theory of free electrons in). 236.

— (On the metastability of the) in consequence of allotropy and its significance
for Chemistry, Physics and Technics, 6382.

— (On the pyrophoric phenomenon in). 999.

METAMORPHOSIS (On the) of Amphioxus lanceolatus. 574.

MPTASTABILITY (On the) of the metals in consequence of allotropy and its significance
for Chemistry, Physies and Technies. 632,

Meteorology. J. P. van per Srox: “On the relation between the cloudiness of the sky
and the duration of sunshine”. 507.

MEVTHYLETHYLKETONE (A new hydrocarbon from the pinacone of). 1088,

MBTHYLRUODANIDE-methyl-mustardoil (On the pseudo-system). 33.

MpTuyYLUREA (On the nitration of). 770.

Microbiology. M. W. Bryerinck: “Oxidation of manganocarbonate by microbes’. 397.

— M. W. Beyerinck: “The nitrate ferment and the formation of physiological
species”. 1211.

MICROTELEPHONE-APPARATUS (On reinforcement of sound and sound-seleetion by
means of). 194,
Mineralogy. A. Wicumaxn: “On the pseudometeorite of Igast in Livonia”, 292.

- Hl. Haga and F. M. Jagger: “RontGeNnpatterns of Boracite, obtained above and
below its inversion-temperature’. 792.

— F. M. Jancer and Ant, Simex: “On temperature-measurements of anisotropous
bodies by means of radiation-pyrometers”. 799.

MIXING (On the question whether at the absolute zero entropy changes on). 669.

Mixturrs of oxygen and nitrogen (The susceptibility of liquid) and the influence of
the mutual distance of the molecules upon paramagnetism. 901,

MOLECULES (The susceptibility of liquid mixtures of oxygen and nitrogen and the
influence of the mutual distance of the) upon paramagnetism. 901.

— (The volume of) and the volume of the component atoms. 880.

MOLENGRAAFF (G A. F.) presents a paper of Dr. H. A. Brouwer: “On zonal
amphiboles in which the plane of optic axes of the margin is normal to that of the
central part, 275.

— presents a paper of Dr. H. A. Brouwer: “On homoeogeneous inclusions of
Kawah Idjen, Goentoer and Krakatan and their connection with the surrounding
eruptive rocks’. 995.

MOLL (J. W.) presents a paper of Prof. C. van WisseLincu: “On the nucleolus and
karyokinesis in Zygnema”. 11.

— presents a paper of Prof. J. H. Boxnema: “The orientation of the shells o
Beyrichia tuberculata Kléden sp.”. 67.

— present a paper of Miss Tine Tammers: “The explanation of an apparent excep-
tion to MEnpEL’s law of segregation”. 1021.

—- presents a paper of Prof. J, H. Bonnema: “Contribution to the knowledge of
the genus Kloedenella Ubrici and Bassuer”. 1105.

MOLL (W. J. m). A quick coil galvanometer. 149.

— A rapid thermopile. 568.

CONTENTS * XV
MONTHLY PERIOD (Investigation of the inequalities of approximately) in the longitude
of the moon, according to the meridian observations at Greenwich, 124, Part 2.
141, Addendum. 890.
moon, (On the significance of the term in the right ascension of the) found by
J. E. pe Vos van Sreenwisk. 144.
motor roots and nuclei (The arrangement of the) in the brain of Acipenser ruthenus
and Lepidosteus osseus. 1032.
MULLER (P.). On the formation of an aldehyde from s, divinylglycol. 336.
— and P. van Romburen. On 1.3.5 hexatriene. 1090,
MuscLE (Experiments on the atonical). 336. [l. 571.
MUSKENS (L. J. J.). “Rolling movements, and the ascending vestibulary connec-
tions”. 338.
NERVE (Note on the size of the dorsal motor nucleus of the Xth) in regard to the
development of the stomach. 305.
NERVOUS sysTEM (On the relation between the quantity of white and grey substance
in the central) 311.
— (On the reflectorical influence of the thoracal autonomical) on the rigor mortis
in cold-blooded animals. 952.
NEUROBIOTASIS (Contributions upon) 296.
NIEUWENHUYSE (J) and C. J. C. Hoocrnnuyze. Influence of aleohol upon the
respiratory exchange during rest and during muscular exercise. 164.
NITRATE FERMENT (The) and the formation of physiological species. 1211.
NITRATION (The) of toluo!s and its derivatives chlorated in the side-chain. 192.
— (On the) of methylurea. 770.
NUCLEI (The arrangement of the motor roots and) in the brain of Acipenser ruihenus
and Lepidosteus osseus). 1032.
NUCLEOLUS (On the) and karyokinesis in Zygnema. 11.
NucLEus (Note on the size of the dorsal motor) of the Xth nerve in regard to the
development of the stomach. 505.
OAT-SEEDLINGS (Avena sativa) (Positive and negative phototropy of the apex and
base in). 363.
oats (Adjustment to light in). 615.
ONNES (H. KAMERLINGH). Further experiments with liquid helium. H, 115,
673. I. 987.

— presents a paper of Dr. W. H. Kersom: “On the equation of state of an ideal
monatomie gas according to the quantum theory”. 227.

— presents a paper of Dr. W. H. Kresom: “On the theory of free electrons in
metals’. 236.

— presents a paper of Mr. E, Oosrernuts: “Magnetic researches. [X. The devia-
tions from Curie’s law in connection with the zero-point energy”. 432.

— presents a paper of Mr. Sopnus Wrsrr: “Vapour pressures at very low reduced
temperatures. IT. The vapour pressure of carbon dioxide in the range from — 140° C,
to about 160° C.? 445.

— presents a paper of Dr. W. H. Kersom: “On the magnetization of ferromagnetic
substances considered in connection with the assumption of a zero-point energy”.
454. IL. 468.

XVI CON TEN DS

ONNES (H. KAMERLINGRH) presents a paper of Dr. C. A, Cromme.in: “Isother-
mals of monatomic substances and their binary mixtures. XV. The vapour pressure

of solid and liquid argon, from the critical point down to — 206° C.” 4177.

— presents a paper of Dr. W. H. Kersom: ‘On the question whether at the
absolute zero entropy changes on mixing’’. 669.

— presents a paper of Mr. Ei. Gosrermuis: “Magnetic researches. XI. Modification
in the eryomagnetic apparatus of KaMeRLINGH ONNEs and Perrine”. $92.

— and ©. A. Crommettn. Isothermals of di-atomie substances and their binary
mixtures. XLIL. Liquid-densities of hydrogen between the boiling point and the
triple point; contraction of hydrogen on freezing. 245.

— and W. H. Kresom. The vapour pressures of hydrogen from the boiling point
down to near the triple point. 440. :

— and KE. Oosrprnuis. Magnetic researches. XIV. On paramagnetism at low
ten:peratures, 917.

— and Apert Perrier. Magnetic researches. X. Apparatus for the general
cryomagnetic investigation of substances of small susceptibility. 689. 786. XII.
The susceptibility of solid oxygen in two forms. 894. XIIT. The susceptibility of
liquid mixtures of oxygen and nitrogen and the influence of the mutual distance
of the moleeules upon paramagnetism. 901.

— and Sorputs Weer, Vapour pressures of substances of low critical temperature
at low reduced temperatures. I. Vapour pressures of carbon dioxide between
—160° C. and —183° C. 215.

oOosTERUUIS (8). Magnetic researches. IX. The deviations from Curtn’s law in
connection with the zero-point energy. 432, XI. Modification in the eryomaguetic
apparatus of KamerLincu Onnes and Perrier, 892.

— and H, Kamertineu Onnes. Magnetie’researches. XIV. On paramagnetism at
low temperatures. 917,

o8 (Gu. u. VAN). On asystem of curves occurring in Einsrety’s theory of gravitation. 40,
osMOTIC PRESSURE (On a new principle for the direct determination of). 160.
OxiDaTION of manganocarbonate by microbes. 397.

oxyGEN (The susceptibility of solid) in two forms. 894.

Paleontology. J. H. Bonnema: “Lhe orientation of the shelis of Beyrichia tuber-
culata KLOpEN sp.”. 67.
— J. H. Bonnema: “Contribution to the knowledge of the genus Kloedenella
Uric and Bassupr”’. 1105.
pancreas (Investigations into the internal secretion of the). 2.
— (Further experimental investigations of the internal secretion of the). 248.
P\RAMAGNEIISM (Lhe susceptibility of liquid mixtures of oxygen and nitrogen, and
the influence of the mutual distance of the molecules upon). 901.
— (On) at low temperatures. 917.
partition of energy (On the law of the). Ht. 84. 1V. 401. V. 1082.
PPRMEABLLITY (On the change in the) of the red bloodcorpuscles (also in man). LY.
PEKELMARING (c A.) presents a paper of Mr. N. Waterman : “Investigations

into the internal secretion of the pancreas”. 2.

CONTENTS XVIt

PEKELHARING (©, a.) presents a paper of Mr. N. Warerman: “Further expe-
Yimental investigations of the internal secretion of the pancreas”. 248.

— presents a paper of Mr. S. ve Bomr: “On the reflectorical influence of the
thoracal autonomical nervous system on the rigor mortis in cold-blooded ani-
mals”. 952.

PERRIER (ALB.) and H. Kameriincu Onnes. Magnetic researches. X. Apparatus
for the general ecryomagnetic investigation of substances of small susceptibility.
689. 786. XII. The susceptibility of solid oxygen in two forms, 894. XIII. The
susceptibility of liquid mixtures of oxygen and nitrogen and the influence of the
mutual distance of the molecules upon paramagnetism. 901.

PESKI (A. J. VAN). On a new method of preparing carboxylic anhydrides. 969.

PHASE RULE (Colloids and the). 60.

PHOSPHORUS (On the vapour pressure lines of the system). I. 1174.

PHOSPHORUS and cyane (The systems). 27.

PHOTO-GROWTHREACTION (Ibe primary) and the cause of the positive phototropism in
Phycomyces nitens. 774.

pHototrorisM (Lhe primary photo-growthreaction and the cause of the: positive) in
Phycomyces nitens. 774.

PHoTOTROPY (Positive and negative) of the apex and base in oat-seedlings (Avena
sativa). 363.

PHOTOSPHERIC PHENOMENA (On the interpretation of). 264.

PHTHALIC ANHYDRIDE. 712.

PHYCOMYCES NITENS (The primary photo-growthreaction and the cause of the positive
phototropism in). 774.

Physics. J. D. van per Waats: “On the point in which the solid state disappears
as an answer to the question in how far this point can be compared to the
critical point of a liquid. The easiest way to do this is by means of the curve”. 39,

— On. H. van Os: “On a system of curves occurring in Erysrern’s theory of
gravitation”. 40.

=— J. J. van Laan: “Some difficulties and contradictions met with in the drawing
up of the equation of state”. 44.

— J. P. Kuenen and 8S. W. Visser: “Viscosimeter for volatile liquids”. 75.

— J. D. van per Waats Jr.: “On the law of the partition of energy”. IIL. 84.
IV. 401. V. 1082.

— H. KameruinecH Onnes: “Further experiments with liquid helium”, H. 113,
673. I. 987.

— W. J. H. Moun: “A quick coil galvanometer”. 149.

— P. Zevman: “The red lithium line and the spectroscopic determination of
atomic weights”. 155.

— H. R. Worrser and P. Zeeman: “Magnetic resolution of spectrum lines and
temperature”, 158.

— H. Kamertinen Owners and Sopuus Weber: “Vapour pressures of substances
of low critical temperature at low reduced temperatures. 1. Vapour pressures of
carbon dioxide between — 160° C. and — 183° ©.” 215.

fol
Proceedings Royal Acad. Amsterdam. Vol. XVI.

XVIIL CUO IN WDE NL ss

Physics. W. H. Kensom: “On the equation of state of an ideal monatomic gas accor.
ding to the quantum-theory”. 227.

— W. H. Kersom: “On the theory of free electrons in metals”, 236.

— H. Kamerntingu Onnes and C. A. CromMetin: “Isothermals of di-atomic
substances and their binary mixtures. XIII. Liquid densities of hydrogen between
the boiling point and the triple point ; contraction of hydrogen on freezing”. 245.

— W. H. Juntus: “On the interpretation of photospheric phenomena”, 264.

— P. Martin: “The magneto-optic Krrr-etfect in ferro magnetic compounds”. [V. 318.

— J. P. Kupnen and 8, W. VissEr: “The virial coefficient B for normal butane”. 350.

— J. P. Kurnnn and 8. W. Visser; “The viscosity of the vapour of norma
butane”. 355.

— IF. BE. C. Scuerrer: “On the system hexane-water”. 404.

— KE. Oosrrruuis: “Magnetic researches. IX. The deviations from Curie’s law in
connection with the zero-point energy”. 432.

— H. Kameriinen Onnes and W. H. Kersom: “The vapour pressures of hydrogen
from the: boiling point down to near the triple point”. 440.

— S. Weber: ‘‘Vapour-pressures at very low reduced temperatures. IL. The vapour
pressure of carbon dioxide in the range from — 140° ©. to about 160°C.” 445,

— W. H. Kersom: “On the magnetization of ferro magnetic substances considered
dn connection with the assumption of a zero-point energy”. 454. IT. 468.

-- C, A. CromMetin: “lsothermals of monatomic substances and their binary
mixtures. XV. The vapour pressure of solid and liquid argon, from_the critical
point down to — 206° C.” 477.

— J. K. A. Werrurm Satomonson : “Contribution to the knowledge of the string
galvanometer”. 522.

— W. J. H. Mout: “A rapid thermopile”. 568.

— P. Eurenresr: “A mechanical theorem of BoLtzmann and its relation to the
theory of energy quanta”. 591.

— W. H. Keesom: “On the question whether at the absolute zero entropy changes
on mixing”. 669.

— H. Kameriinew Onnes and Anpert Perrier: “Magnetic Researches. X. Appas
ratus for the general cryomagnetic investigation of substances of small suscepti-
bility.” 689. 786.

— Pu. Konunstamm and kK, W. Watsrra: “An apparatus for the determination of
gas isotherms up to about 3000 atm.” 754. 822.

— J.

unity of all the substances in their thermic behaviour’. 808. 924. 1047.

— J. D. van per Waans: “The volume of molecules and the volume of the

J. van Laar: “A new relation between the critical quantities and on the

component atoms”. 880.

— KE. Oosreruuts: “Magnetic researches. XI. Modification in the ecryomagnetic
apparatus of KAMERLINGH OnNnes and Perrier.” 892.

— Apert Perrier and H. KaMERLINGH ONNES : “Magnetic researches, XII. The
susceptibility of solid oxygen in two forms”. 894, XIIL. The susceptibility of liquid

CAOPNS LT Sha Ne UES: XIX

mixtures of oxygen and nitrogen and the influence of the mutual distance of
the molecules upon paramagnetism’”. 901. 2
Paysics. H. Kamertincu Onnes and E. Oosteruurs: “Magnetic researches. XIV.
Gn paramagnetism at low temperatures”. 917.
— J. D. van per Waats: “On the critical density for associating substances”. 1076.
— W. J. pe Haas: “The effect of temperature and transverse magnetisation on
the continuous-current resistance of crystallized antimony”. 1110.
— J. P. Kupxen: “The diffusion-coefficient of gases and the viscosity of gas-mix-
tures”. 1162.
PHYSIOLOGICAL SPECIES (‘The nitrate ferment and the formation of). 1211.
Physiology. N. Warerman: “Investigations into the internal secretion of the panereas’’, 2.
I. Snapper: “On the change in the permeability of the red bloedeorpuscles (also
in man)”. 19,
— E. Laaurur and W. R. vax per Meer: “Velocity of the intestinal movements
in different mammals”. 65. -
— C. J. C. van Hoocenauisze and J. Ninuwennuise: “Influence of alcohol
upon the respiratory exchange during rest and during muscular exercise’, 164,
— E. Hexma: “On fibrin in sol and gel state. Likewise a contribution to our
knowledge of the blood-coagulation-problem”, 172.
— H. Zwaarvemaker: “On reinforcement of sound and soundselection by means
of micro-telephone apparatus”. 194.
— N. Waterman: “Further experimental investigations of the internal secretion
of the pancreas”. 248.
— L. Artsz: “On the Tynpa1i phenomenon in gelatin-solutions”, 331.
— J. W. Laneenaan: “Experiments on the atonical muscle”. 336. IL. 571.
— L, J. J. Muskens. “Rolling movements and the ascending vestibulary connec-
tions. (Fasciculus Deiters Ascendens). 338.
— L. Arisz: “Variations of state in gelatin-solutions”. 418.
— H. Zwaarpemaker: “On hearing-apparatus examined after Lord Ravyuercu’s
mode of arrangement”. 492.
—H. J. Hampurcer: “The effect of subcutaneous terpentine-injections on the
chemotaxis of remote places’. 609.
— Eve, Dusots: “On the relation between the quantity of brain and the size of
body in vertebrates”. 647.
— 8. pe Borr: ‘On the reflectorical influence of the thoracal autonomical nervous
system on the rigor mortis in cold-blooded animals”. 952.
— J. K. A. Werturim Satomonson: “Electrocardiograms of surviving human
embryos”. 992.
— L. k. Wourr: “On the formation of antibodies after injection. of sensitized
antigens”. 640.
— C. E. Bensamins: “On esophageal auscultation and the recording of esophageal
heart sounds”, 1041,
POINT OF MIxING (The occurrence of an upper critical) at the coexistence of two
mixed crystal phases, 557.

XX CONTENTS.

pressurn (The influence of) on the EME of the lead-accumulator. 161.

PSEUDO-COMPONE

vs (The metastable continuation of the mixed crystal series of) in
connection with the phenomenon of allotropy). 1167.

PSEUDOMETEORITE of Igast in Livonia (On the). 292.

psrubo-systemM (On the) methylrhodanide-methylmustard oil. 33.

prpeRIc suTURES (On) and pteric bones in the human skull. 634.

PYROPHORIC PHENOMENON (On the) in metals. 999.

QUANTUM THEORY (On the equation of state of an ideal monatomic gas according to
the). 227.

quarrics (A bilinear congruence of twisted) of the first species. 733.

— (A bilinear congruence of rational twisted). 1186.

QUININE (On the presence of) in the seed of Cinchona Ledgeriana Moens, 153.

RADIATION-pyrometers (On temperature-measurements of anisotropous bodies by means
of). 799,

RAYLEIGH’s mode of arrangement (On hearing-apparatus examined after Lord). 492.

RETNDERS (w.). The distribution of a colloidally dissolved substance over two
layers. 379.

— The reciprocal pairs of salts KCl + NaNO; = NaCl + KNO3; and the manufac-
ture of conversion salpeter. 1065.

REINFORCEMENT OF soUND (On) and soundselection by means of microtelephone-
apparatus. 194.

REPRESENTATIVE Porn (The envelope of the osculating ellipses which are deseribed
by the) of a vibrating mechanism having two degrees of freedom of nearly equal
frequencies. 938.

RESPIRATORY PXCHANGE (Influence of alcohol upon the) during rest and during mus-
cular exercise. 164.

RHIPSALIS CassytHaA (On the regulation of the transpiration of Viscum album and)
1008.

RIGOR MORTIS (On the reflectorical influence of the thoracal autonomical nervous system
on the) in cold-blooded animals. 952.

rocks (On homoeogeneous inclusions of Kawah Idjen, Goentoer and Krakatau and their
connection with the surrounding eruptive). 995.

ROLLING MOVEM*NTs and the ascending vestibulary connections (Fasciculus Deiters
Ascendens). 338.

ROMBURGA (P, VAN) presents a paper of Dr. P. Munier: “On the formation ot
an aldehyde from s. divinylglycol”. 336.

— presents a paper of Prof. F. M. Jazcer: “On the isomorphy of the ethylsulphates
of the metals of the rare earths, and on the problem of eventual morphotropic
relations of these salts with analogous salts of Scandium, Indium and Beryllium.”
1095.

— presents a paper of Prof, Dr, F. M. Jarcer and Dr. H. 8. van Knooster:
“Studies in the field of silicate-chemistry: I. On compounds of lithiumoxide and
silica”. 857.

ROMBURGH (pe. VAN) and P, Muuuer. On 1.3,5 hexatriene. 1090.

COON DE Nis: XX1

ROMBURGH (re. vAN) and J. H. Scuepers, 2.3.4.6 Tetranitro-phenylmethyl- and
ethylnitramine. 369.

ROMBURGH (Pp. vAN) and Miss D. W. Wensinx. A new hydrocarbon from the
pinacone of methylethylketone. 1088.
RONTGENPATTERNS of Boracite, obtained above and below its inversion-temperature. 792.
ROTHTIG (e.). Contributions upon Neurobiotaxis. 296.
RUTGERS (J. G.). Applications of Sonryn’s extension of ABEL’s integralequation. 583.
RUTTEN (L.). Elephas antiquus Fale. from the river Waal near Nijmegen. 769.
SALOMONSON (I, K. A WERTHEIM) presents a paper of Dr. L.J.J. Muskens:
“Rolling movements and the ascending vestibulary connections (Fasciculus Deiters
Ascendens). 338.
— Contribution to the knowledge of the string galvanometer. 522.
— Electrocardiograms of surviving human embryos. 992.
saLts (The reciprocal pairs of) KCl + NaNO, ZZ NaCl-+- KNOg and the manufacture
of conversion salpeter. 1065.
SANDE BAKHUIJZEN (E. fF. VAN DE). v. BAKHUIJZEN (EK. F. vAN DE SanDe).
scaNnbIuM, Indium and Berylliam (On the isomorphy of the ethylsulphates of the metals
of the rare earths, and on the problem of eventual morphotropic relations of these
salts with analogous salts of). 1095.
SCHAAKE (G.) and Hk. pe Vries. On the singular solutions of ordinary and partial
differential equations of the first order. 1152.
SCHEFFER (Ff. BE. C.). On the system hexane-water. 404.
SCHEPERS (J, H.) and P. van Romsurau. 2.3.4.6 Tetranitro-phenylmethyl- and
ethylnitramine. 369.
SCHREINEMAKERS (Ff, A. H.). Equilibria in ternary systems. VIII, 99. IX. 385.
X. 540. XI. 597. XII. 739. XIII. 841. XTV. 1136.
— presents a paper of Prof. W. Retnpers: “The distribution of a colloidally
dissolved substance over two layers’. 379.
— presents a paper of Mr. J. C. Tuonus: “Concerning combinations of aniline
with hydrochloric acid”, 553,
— presents a paper of Mr. D. F. pu Torr: “Concerning combinations of urea
with acids”. 555.
— presents a paper of Dr. W. P. A, JonKER: “Connexion between the adsorption-
isotherm and the laws of Proust and Henry”. 970.
— presents a paper of Prof. W. Reinpers: “The reciprocal pairs of salts
KCl-+ NaNO, Z NaCl + KNO, and the manufacture of conversion salpeter”. 1065.
SECRETION (Further experimental investigations of the internal) of the pancreas. 248.
— (Investigations into the interna!) of the pancreas, 2.
SEGREGATION (The explanation of an apparent exception to MeNDEL’s law of). 1021,
SILICATE-CHEMISTRY (Studies in the field of). I. On compounds of lithiumoxide and
silica. 857.
SILLEVIs (k. H. A.) and J. Bogsexen. The stability of cyclohydrocarbons in con-
nection with their configuration. The transformation of cyclc-hexene into benzene
and eyclo-hexane, 499,

XXII CONTENTS.

sIMEK (ant) and F. M. Jancer. On temperature-measurements of anisotropous

bodies by means of radiation-pyrometers. 799.
SITTER (Ww. DE). On canonical elements. 279.

— On the constancy of the velocity of light. 395.
sM.iTs (a.). The systems phosphorus and cyane. 27.
— The passivity of metals in the light of the theory of allotropy. 191.
— The application of the theory of allotropy to electromotive equilibria. 699.
— Answer to Prof. £, ConEn to his observations under the title ‘“Allotropy and
electromotive equilibriuin”’. 1002.
— The metastable continuation of the mixed crystal series of pseudo components
in connection with the phenomenon of allotropy. 1167.
— §. C. Boxuorsr and J, W. Terwen. On the vapour pressure lines of the system
phosphorus. I. 1174.
— A. Kerrrner and A. L. W. pr Gue, On the pyrophoric phenomenon in metals. 999,
—and C. A. Losry pe Bruyn. The occurrence of an upper critical point ot
mixing at the coexistence of two mixed crystal phases. 557.
— and H. Vixsrpoxse: “On the pseudosystem methylrhodanide-methyl—mustard—
oil”. 33.
SNAPPER (1.) On the change in the permeability of the red bloodcorpuscles (also
in man). 19.
soLIp staTr (On the point in which the) disappears as an answer to the question in
how far this point can be compared to the critical point of a liquid. The easiest
way to do this is by means of the y-curve. 39.
S$ ONINE’s extension (Applications of) of ABnL’s integralequation. 583.
SOUNDSELECTION (On reinforcement of sound and) by means of microtelephone-appa-
ratus. 194.
SPECTRUM LINES (Magnetic resolution of) and temperature. 158.
svapiuiry (The) of cyclohydrocarbons in connection with their configuration. The
transformation of cyclo-hexene into benzene and cyclo-hexane. 499.
s1TOK (J. P. VAN DER). On the relation between the cloudiness of the sky and the
duration of sunshine). 507.
stomacu (Note on the size of the dorsal motor nucleus of the Xth nerve in regard
to the development of the). 305.
suBsTANCE (On the relation between the quantity of white and grey) in the central
nervous system. aylale

— (The distribution of a colloidally dissolved) over two layers. 379.
substances (lsothermals of di-atomic) and their binary mixtures. XIII. Liquid-densities

of hydrogen between the boiling point and the triple point; contraction of hydrogen
on freezing. 245.

— (Vapour pressures of) of low critical temperature at low reduced temperatures.
[. Vapour pressures of carbon dioxide between — 160°C. and — 183°C, 215.

— (On the magnetization of ferro-magnetic) considered in connection with the
assumption of a zero-point energy. 454. Il. 468.

— (Isothermals of monatomic) and their binary mixtures. XV. The vapour pressure
of solid and liquid argon from the critical point down to — 206° C. 477.

CyOFN TE NT; S: XXUT

suBsTaNces (Apparatus for ihe general cryomagnetic investigation of) of small sus-
ceptibility 689. 786.

— (On the critical density for associating). 1076.

SUNSHINE (On the relation between the cloudiness of the sky and the duration of). 607.
SUSCEPTIBILITY (On the) in the excited ferromagnetic state. 468.
-- (The) of solid argon in two forms. 894.

—- (The) of liquid mixtures of oxygen and nitrogen and the influence of the mutual
distance of the molecules upon paramagnetism. 901.
SYSTEM hexane-water (On the). 404.
— phosphorus (On the vapour pressure lines of the). I. 1174.
— of curves (On a) occurring in Ernstrin’s theory of gravitation. 40.
systems (The) phosphorus and cyane. 27.
— (Pseudoternary) of acid anhydrides and water. I, Phthalic anhydride. 712.
TAMMES (TINE). The explanation of an apparent exception to MrnpEt’s law of
segregation. 1021,
TEMPERATURE (Magnetic resolution of spectrum lines and), 158.
— (The effect of) and transverse magnetisation on the continuous-current resistance
of crystallized antimony. 1110.
TEMPERATURE-measurements (On) of anisotropous bodies of radiation-pyrometers. 799.
TERNARY sysTEMS (Equilibria in). VIII. 99. IX. 385. X. 540. XL 597. XID. 739.
XIII. 841. XIV. 1136.
TERPENTINE-injections (The effect of subcutaneous) on the chemotaxis of remote places. 609.
TERWEN (J. w.), A. Smrrs and S. ©. Boxuorsr. On the vapour pressure lines of
the system phosphorus. 1. 1174.
TETHYS (At what time the Indian Archipelago is separated from the). 921.
TETRANITRO PHENYLMETHYL and ethylnitramine (2.3.4.6). 869.
THEORY of Bravats (The) (on errors in space) for polydimensional space, with applica-
tions to correlation. 1124.
— of energy quanta (A mechanical theorem of Bottzmann and its relation to
the). 591.
THEORY of allotropy (On the passivity of metals in the light of the). 191,
— (The application of the) to electromotive equilibria. 699.
— of free electrons (On the) in metals. 236.
THERMOPILE (A rapid). 568.
THEUNISSEN (f.). The arrangement of the motor roots and nuclei in the brain
of Acipenser ruthenus and Lepidosteus osseus. 1032.
TH ONUs (J. c.) Concerning combinations of aniline with hydrochloric acid. 553.
TOIT (D. F. DU). Concerning combinations of urea with acids. 555.
TOLUOLS (The nitration of) and its derivatives chlorated in the side-chain. 192.
TRANSFORMATION (The) of cyclo-hexene into benzene and cyclo-hexane. 499.
TRANSPIRATION (On the regulation of the) of Viscum album and Rhipsalis Cassytha. 1008,
TYNDALL-phenomenon (On the) in gelatin-solutions. 331.

XXIV CHOSN, TeESNe es.

untty of all the substances (A new relation between the critical quantities and on the)
in their thermic behaviour. 808. 924. 1047.

urEA (Concerning combinations of) with acids, 555.

UVEN (M. J. VAN). The theory of Bravats (on errors in space) for polydimensional
space, with applications to correlation. 1124.
VALKENBURG (c. T. VAN) and L. H. J. Mustrom. On the visual centra in the
brain of an anophthalmos. 186.
VAPOUR PRESSURE (Thie) of solid and liquid argon from the critical point down to-206°C. 477.
VAPOUR PRESSURE LINES (On the) of the system phosphorus. I. 1174.
VAPOUR PRESSURES of substances of low critical temperature at low reduced tempera-
tures. I. Vapour pressure of carbon dioxide between —160° C.and —183° C, 215,
— at very low reduced temperatures. IJ. Vapour pressure of carbon dioxide in
the range from —140° C, to about 160° C. 445.
— (The) of hydrogen from the boiling point down to near the triple point. 440.
VARIATIONS OF STATE in gelatin-solutions. 418.
veLociry of light (On the constancy of the). 395.
VERKADE (pe. £E.) and J. Borsexen. The mechanism of the acid formation of
aliphatic acid anhydrides in an excess of water. 718.
VERMEULEN (H. A.). Note on the size of the dorsal motor nucleus of the Xth
nerve in regard to the development of the stomach. 305.
VERTEBRATES (On the relation between the quantity of brain and the size of the
body in). 647.
VESTIBULARY CONNECTIONS (Rolling movements and the ascending) (Fasciculus Deiters
Ascendens). 338.
VIRIALCOEFFICIENT B (The) for normal butane. 250.
VISCOSIMETER and volatile liquids. 75.
viscosity of gas-mixtures (The diffusion-coefficient of gases and the). 1162.
—- of the vapour (The) of normal butane. 355.
viscUM ALBUM (On the regulation of the transpiration of) and Rhipsalis cassytha. 1008.
VISSER (s. w.) and J. P. KuENnEN. Viscosimeter and volatile liquids. 75.
— The virial coefficient B for normal butane. 350.
— The viscosity of the vapour of normal butane. 355.
VISUAL CENTRA (On the) in the brain of an anophthalmos, 186.
VIXSEBOXE (nH). “On the pseudo system methylrhodanide-methyl-mustard oil”. 33.
VOS VAN STEENWIK (J. E. DB). Investigation of the inequalities of approxi-
mately monthly period in the longitude of the moon, according to the meridian
observations at Greenwich, 124. Part 2. 141. Addendum. 890.
— (On the significance of the term in the right ascension of the moon, found by). 144.
VRIES (HK. DE) and G. Scuaake, On the singular solutions of ordinary and partial
differentialequations of the first order. 1152.
VRIES (JAN DE). Bilinear congruences and complexes of plane algebraic curves. 726.
— A bilinear congruence of twisted quartics of the first species, 733.
— Cubic involutions in the plane. 974.

— A bilinear congruence of rational twisted quartics, 1186.

“ CONTEN Ts XXV

WAALS (J. D. VAN DER) presents a paper of Prof. A. Smivs: “The systems phos-
phorus and cyane”. 27.
— presents a paper of Prof. A. Smrrs and H. Vixsepoxse: “On the pseudo-system
methylrhodanide-methyl-mustardoil”. 33.

WAALS (J. D. VAN DER). On the point in which the solid state disappears as an
answer to the question in how far this point can be compared to the critical
point of a liquid. The easiest way to do this is by means of the ¥ curve. 39.

— presents a paper of Prof. J. D. van per Waats Jr.: ‘On the law of partition
of energy”. IIL. 84. LV. 401. V. 1082.

— presents a paper of Dr. F. EB. C. Scuurrer: “On the system hexane-water”. 404.

— presents a paper of Prof. A, Smirs and ©. A. Losey pe Bruin: “The occur-
rence of an upper critical point of mixing at the coexistence of two mixed crystal
phases’. 557.

— presents a paper of Prof. A. Smits: “The application of the theory of allotropy
to electromotive equilibria”. 699.

— presents a paper of Prof. Pu. Kounsramm and Mr. K. W. Waustra: “An
apparatus for the determination of gas isotherms up to about 3000 atm’. 754. $22.

— The volume of molecules and the volume of the component atoms. 880.

— presents a paper of Prof. A. Smits, A. Kerrner and A. L. W. pe Ger: “On
the pyrophoric phenomenon in metals”. 999.

~- presents a paper of Prof. A. Sars: “Answer to Prof. KE. Cohen to his obser-
vations under the title of ‘“Allotropy and electromotive equilibrium”. L002.

— On the critical density for associating substances. 1076.

— presents a paper of Prof. A. Smrrs: ‘The metastable continuation of the mixed
erystal series of pseudo components in connection with the phenomenon of allo-
tropy”. 1167.

— presents a paper of Prof. A. Smrvs, S. C. Bokuorst and J. W. TErwen: “On

the vapour pressure lines of the system phosphorus”. [. 1174.

WAALS JR. (J. D. VAN DER). On the Jaw of partition of energy. ILL 84. IV. 401.
V. 1082.

WALSTRA (kK. W.) and Pu. Kounstamm. An apparatus for the determination of gas
isotherms up to about 3000 atm. 754, $22.

waTeR (On the system hexane-). 404,
— (Pseudoternary systems of acid anhydrides and), [. Phthalic anhidryde, 712.
WATERMAN (nN). Investigations into the internal secretion of the pancreas. 2.
— Further experimental investigations of the internal secretion of the pancreas. 248.
WEBER (SOPHUsS). Vapour pressures at very low reduced temperatures. II. ‘The
vapour pressure of carbon dioxide in the range from —140° C, to about 160° C. 445.
— and H. Kameriincu Onnes. Vapour pressures of substances of low critical
temperature at low reduced temperatures. I. Vapour pressures of carbon-
dioxide between —160°C, and —183°C. 215.
W ENSINK (Miss p. w.) and P. van Rompureu. A new hydrocarbon from the pina~
cone of methylethylketone. 1088,

XNVI CONTE N TS. ®

WENT (f. A. FC.) presents a paper of Mr. W. H. Arisa: “Positive and negative
phototropy of the apex and base in oat-seedlings (Avena sativa)”, 363.
— presents a paper of Mr. W. H. Artsz: “Adjustment to light in oats”. 615.
— presents a paper of Dr. A. H. Buaauw: “The primary photo-growthreaction
and the cause of the positive phototropism in Phycomyces nitens”. 774.
— presents a paper of Mr, J. A. Hownine: “Hybridisation with Canna indica”. $33.
WERTHEIM SALOMONSON (tI. K. A.). v. Satomonson ([. K. A. WertuEm).
WICHMANN (a.). On the pseudometeorite of Igast in Livonia. 292.
— presents a paper of Dr. L. Rurren: “Elephas antiquus Fale, from the river
Waal near Nijmegen’. 769.
WINKLER (C.) presents a paper of Dr. C. T. vaw Vatkensure and L. H. J. Mestrom:
“On the visual centra in the brain of an anophthalmos.” 186.
WISSELINGH (Cc. VAN). On the nucleolus and karyokinesis in Zygnema, 11.
WOLFF (L. K.). On the formation of antibodies after injection of sensitized antigens. 640.
WOL’TJER (a. k.) and P. Zeeman. Magnetic resolution of spectrum lines and
temperature. 158.
WiJ HE (J. W. VAN). On the metamorphosis of Amphioxis lanceolatus. 574.
ZEEMAN (p.). The red lithium line and the spectroscopic determination of atomic
weights. 155.
ZBDMAN (P.) and H, R. Wotrser. Magnetic resolution of spectrum lines and
temperature. 158.
zeERO PNTROPY (On the question whether at the absolute) changes on mixing. 669,
ZERO-POINT ENERGY (On the magnetization of ferro-magnetic substances considered
in connection with the assumption of a). 454. IL. 468.
ZERO-POINT ENERGY (The deviations from Curte’s law in connection with the), 432.
zinc (The allotropy of). I. 565.
ZWAARDEMAKER (tH). On reinforcement of sound and sound-selection by means
of microtelephone-apparatus, 194.
— presents a paper of Mr. ©. Antsz: ‘Variations of state in gelatin-solutions”. 418.
— On hearing apparatus examined after Lord Rayieieu’s mode of arrangement. 492.
— presents a paper of Prof. J, W. Laneruaan: “Experiments on the atonical
muscle”. 336. II. 571.

— presents a paper of Prof. Eve Dusors: ‘On the relation between the quantity
of brain and the size of the body in vertebrates’. 647.

— presents a paper of Dr. C. EK. Bengamins: “On esophageal auscultation and
the recording of esophageal heart sounds”. 1041.

— presents a paper of Mr. L. Arisa: “On the TynpaLL phenomenon in gelatin-
solutions”. 331.

ZY GNEMA (On the nucleolus and karyokinesis in). 11.

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