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KONINKLIJKE AKADEMIE
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FROCBEDPINGS OF Wins sen
SECTION OF SCIENCES .

VOLUME X

JOHANNES MULLER :—: AMSTERDAM
JULY 1908

KONINKLIJKE AKADEMIE
VAN WETENSCHAPPEN
-- TE AMSTERDAM =-

BROGBEDINGS-OE TEE
SE@TION OF SCIENCES

VOLUME X
CS PART ES)

JOHANNES MULLER :—: AMSTERDAM
: DECEMBER 1907 :

of ays CA?

(Translated from: Verslagen van de Gewone Vergaderingen der Wis- en Natuurkundige
Afdeeling van 24 Mei 1907 tot 30 November 1907. DI XVI.)

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KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,

PROCEEDINGS OF THE MEETING

of Friday May 24, 1907.

SIC

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

Afdeeling van Vrijdag 24 Mei 1907, Dl. XVI).

GO AE EE NES:

L. Rurren: “On fossil Trichechids from Zealand and Belgium”, (Communicated by Profs
C. E. A. Wicumann), p. 2. (With one plate).

J. W. van Wine: “On the ‘existence of cartilaginous vertebrae in the development of the
skull of birds”, p. 14.

M. W. Bewerinck: “On lactic acid fermentation in milk”, p. 17.

J. J. van Laar: “On the course of the plaitpoint line and of the spinodal lines, also for the
case, that the mutual attraction of the molecules of one of the components of a binary mixture
of normal substances is slight”. (Communicated by Prof. H. A. Lorentz), p. 34.

W. pe Sirrer: “On periodic orbits of the type Hestia”. (Communicated by Prof. J. C. Kavreyy),
p. 47.

J. D. van DER Waats: “Contribution to the theory of binary mixtures”, IV, p. 56.

Proceedings Royal Acad. Amsterdam. Vol. X.

(2)

Palaeontology. — “On fossil Trichechids from Zealand and
Belgium.” By Mr. L. Rurren. Communicated by Prof. C. E.
A. WICHMANN.

(Communicated in the meeting of March 30, 1907).

Last summer a fisherman found opposite the village of Breskens
5. SCHOUTEN secured

in the West Scheldt a large skull, which Dr. S.
for the Geological Institute of Utrecht University.

The fragment belongs to an old Trichechus, but differs in some
respects from the now living Walrus. On closer examination it
appeared that the skull must be of the tertiary Trichechus Huxleyi,
of which until now only tusks were known, found in the “Red
Crag” of Suffolk. These were described by Ray LANKESTER. Of the
skull the description will be given here.

The plan suggests itself to compare the fragment first with the
walrus of recent times and then with the already known fossil

Trichechids.
1. Description of the skull and comparison with the walrus.

The most conspicuous point about the skull is its remarkably good
state of preservation. It has this in common with some remains of
diluvial mammals, also found in the river Scheldt. The skull, to be
sure, arrived here in several pieces, but the broken edges were absolutely
fresh and all parts fit perfectly together. Probably the fossil only broke
when it was being dredged. As to completeness the skull leaves nothing
to be desired, since only parts of the nasal, maxillary and frontal
bones, part of the vomer, the conchae and a few teeth are wanting.
The skull was filled with a fine-grained grey clay; the outer wall
of the cranium was overgrow with Balanids and Bryozoa. Although
the fossil is very heavy, a chemical analysis of a little piece of bone
revealed nothing particwar. It still contains pretty much organic
matter and consists for the rest especially of CaO and P,O,, while
a small quantity of ferrie hydroxide colours the bone dark brown.

That our Trichechus is full-grown, is proved by the fact that all
sutures are absent and by the strong development of all ridges.

As material for comparison we had at our disposal 24 recent skulls
and 26 pairs of tusks. Very unpleasaut was the great variability of
the recent walruses. Certain characteristics vary so strongly in
different individuals that with the limited material one always remains
uncertain whether the analogous characteristic in the fossil lies within

(3

the limit of variation of the recent animals. It will appear that in
most respects the fragment approaches the old walruses, but that
the tusks deviate considerably from those of the living animals.

Looking at the hind side of the fossil skull, one is at once struck
by its relatively great height. This is caused by the strong develop-
ment of the mastoid process and by a high ridge on the lambda
suture (crista lambdoidea).

Dividing the height of the skull and that of the mastoid process by
the breadth of the skull, we obtain two quotients, which for the fossil
are greater than for the walrus. In determining these quotients the
height of the mastoid process was measured by the vertical distance
between the lower edge of the foramen magnum and the base of the
mastoid process. The differences found are small, however; for this
characteristie the fossil stands consequently at the end of the variation
series of the walrus. The strong relief on the mastoid process and
the extraordinary size of the erista occipitalis externa as well as of
the crista lambdoidea are characteristies which the fossil skull has
in common with some old walruses.

Small deviations are also found in the vicinity of the foramen
magnum. The canalis hypoglossi always opens with the walrus into
the inside of the condyli of the cranium with two openings at each
side, whereas the fossil only shows a single small opening. But this
characteristic has not much value, since the aperture of the canalis
hypoglossi always varies strongly. The foramen magnum is much
more flattened dorsoventrally with the fossil than with the walrus,
but this too is a very variable characteristic. Comparable numbers
are here obtained again when the breadth of the foramen magnum
is divided by its height. The condyli occipitales are in the fossil less
strong than normally and present a shuttle-like appearance, while
in the walrus they project more and more when we proceed
upwards ; also they here project above the upper edge of the foramen
magnum, while there they remain below its upper edge.

Of all these small differences the shape of the condyli and of the
foramen magnum have the greatest importance, while the height-
ratios and the aperture of the canalis hypoglossi are of less value.

The base of the skull shows no more differences with the walrus
than the back part. The length of the two skulls compared with
their breadth, agrees entirely. The first difference concerns the position
of the foramen lacerum and of the canalis alisphenoideus. These
namely lie close behind each other with the walrus, while with
the fossil they are separated by a rather massive bony lamella,
extending from the os petrosum towards the pterygoid process. Also

1*

Ce)

the cup for the joint of the lower jaw is very broad and the result
of this is again that the pterygoid processes have approached each
other closely. Further changes appear at the frontal side of the skull-
base by the size of the alveoles of the tusks.

The alveolar outer wall shows a lateral projection as with the
walrus, only slightly more massive; the distance between the two
projections is consequently also somewhat greater than with the
walrus. We divide this distance again by the breadth of the skull :
the fossil les at the end of the variation series of the walrus. But
the size of the tusk-alveoles produces still another difference. It
‘auses namely the rows of teeth to be squeezed together, so that
the distance of the two incisors, compared with the breadth of the
skull, is extremely small. But this also occurs with some old wal-
ruses. Moreover the lower side of the upper jaw differs in shape:
in the walrus it is broad and hollowed, in the fossil narrow and flat.

The lateral face of the skull presents in more than one respect a
great difference with the walrus, namely in the shape of the tusks.
In all the former properties the fossil approached the old walruses
and if also the tusks had little deviated from theirs, the reasons for
making a distinction would have been rather feeble. But this is not
the case. The curvature of the tusks is with the fossil much stronger
than with the walrus. If we determine the radius of curvature
of all the tusks, we find it in the fossil to be 27 centimetres, for
the walrus never under 38 ems. It must be noted that such a small
radius of curvature only oceurs with young, female walruses with
relatively weak teeth. In older animals, however, with which we
must compare our skull, the radius of curvature was never under
45 ems. and mostly over 50 ems. Whereas in the former properties
the fossil resembles the old walruses, it deviates very strongly from
them in regard to the shape of the tusks. Also the tusks are more
elegant and the right tooth shows deep longitudinal grooves.

From the tusks we may also draw a conclusion as to the age of
the animal. With young individuals the pulp cavity is very deep ;
with advancing age it gradually fills with osteodentine. With the
fossil now the pulp cavity only had a depth of 3,5 em. Also the
thickness of the tusks is greater in the middle than at the base,
which points to the period of strongest growth for the teeth being
passed.

Again the considerable corrosion of the teeth point to an elderly
individual.

If we now summarise the results of the comparison of the fossil
with the walrus, we may state:

(5)

That the fossil skull belongs to a walrus-like animal, whose skull
in general differs only little from recent animals as to strength of deve-

Cross-section of the base of the tusks of Trichechus Huxleyi.
Found near Breskens in the West Scheldt.

lopment, but deviates entirely from them by the shape of the tusks,
It is a pity that for comparative anatomy the value of the frag-
ment is nil, for it presents many properties of Trichechus, such as
the strong crista occipitalis externa, the big mastoid process and the
massive bulla ossea still more typically than the recent animals.

2. Comparison of the skull with already known fossil Trichechids.

Fossil remains of Trichechids are known from North-America,
England and Belgium. Also skulls of Trichechus rosmarus have been
described from the subsoil of Paris (17), Hamburg (10) and Cologne
(25), but it has been proved that they were carried there by man.
The North-American finds seem to belong to the pleistocene and
miocene (21). The tertiary skull deviates in the number of molars
from Trichechus rosmarus (8); the pleistocene remains are identical
with Trichechus rosmarus, although Dr Kay has classed a skull
fragment from Accomac County in Virginia under a fossil species
Trichechus virginianus.

The English fossils were first found in the “Red Crag” of Suffolk,
where, however, they are in a secondary “Lagerstatte’; probably
they belong to the older pliocene. (19). Later they have also been
found in the “Cromer Forest Beds” (82). They are only tusks,
distinguished from the tusks of walruses by strong curvature,

(6)

smaller thickness and deeper longitfdinal grooves. Also Ray LANKESTER
is of opinion that in general they are bigger than those of the
walrus, although the maximum size of the two is the same. So these
tusks show a very good agreement with those of the Zealand fossil.
The Belgian Trichechids, occurring in the “Crag” of Antwerp,
have been described by P. J. vaN BeNepeN in a work of splendid
get up (26). The only pity is that the contents do not harmonise
at all with the exterior, since to a dangerous imagination more scope
has been given than to accurate description and careful criticism.
When the fortifications round Antwerp were dug, fossil remains of
Pinnipedia were found in very different places and at different times :
they were treated by van BENEDEN in the following manner:
“Voici, comment nous avons procédé: Apres avoir réuni tous les
os de phoque,.... nous avons réuni tous les os de même nature
c'est a dire, les humerus, les femurs ete... .. Apres cette premiere
opération nous avons reparti les os longs apres leur taille, ayant
devant nous les memes os des especes vivantes. Si l’on considere,
que la plupart des pieces se répete plusieurs fois, il n'est pas

difficile,.... d’établir parmi eux des groupes génériques et spécifiques.
Quand cette opération est faite pour les os comme les humérus et
les fémurs,.... on leur rapporte les autres os, en se guidant d’abord
d'apres leur dimension... Nous avons alors étalé les humerus, les

fémurs, les vertebres ete. des diverses espèces européennes et nous
nous sommes assurés, de quelles espèces vivantes nos phoques fossiles
se rapprochent le plus. En répétant la même opération pour les
autres Os, nous sommes arrivés ainsi a composer nos espèces eta en
établir un certain nombre avec une certitude entière.”

Hence when van BENEDEN had established a new species by means
of a single bone, he added to this bone what fitted best in size, a
method which theoretically has some good points, but which in
practice, with the very incomplete Antwerp material, presents so
many difficulties, that the determinations of van BENEDEN must a
priori be received with some misgivings. In any case, only the first
piece of bone, on which a species was founded, may be regarded
as having been definitely determined; all the other bones, added to
it, must be critically re-examined.

VAN BeNnepEN describes three species of Trichechids, which he refers
to three genera. Of these Trichechus rosmarus is supposed to be
diluvial; the two others, Trichecodon Koninekii and Alachtherium
Cretsii are tertiary.

Of the common walrus only a scaphoid and an incomplete vertebra
are described: “qui ont été quelque temps confondues.... avec les

ce)

animaux quaternaires terrestres. On les avait places a côté de Rhinocéros”!

The genus Trichecodon was based on a small fragment of a tusk
which has now even been lost and of which a cast only is left at
Brussels. This strongly rounded fragment, however, is not typefied
by a single characteristic, and so it will always be impossible to
ascertain whether later remains really belong to it. But in this way
the genus Trichechodon loses any right of existence and the bones,
referred to it, must be regarded as undetermined.

Alachtherium is first mentioned in an oration of Viscount pu Bus.
Of this Trichechid only half a mandible was known then. Also in
this case vAN BENEDEN has added to this lower jaw a whole series
of bones from the neighbourhood of Antwerp. Among these also a
fragment of a skull occurs, of which van BENEDEN gives the follow-
ing description, accompanied by some large, but not very happy
illustrations.

“En comparant la tête d’Alachtherium avec celle du Morse, nous
voyons des différences fort grandes dans la disposition de certains os.
Vu par devant, le crane est beaucoup plus élevé et les parties latérales,
formées par le temporal surtout, sont plus étendues en dehors et en
dessous. Il en résulte, que par la partie supérieure, le crane se
rapproche plus de celui des Otaries et par les parties latérales de
celui des Morses. Le crane est brisé en avant de maniere que la
boîte est restée entiere, et les os frontaux ne prennent qu'un faible
part a la formation de la cavité cranienne. Le crane, vu par la face
postérieure, montre los occipital s’élevant verticalement très haut
comme dans certaines Otaries adultes et les parties latérales et infé-
rieures, formées par le temporal, sont très massives en même temps
qu'elles descendent fort bas. Les deux condyles sont brisés. . . . Vu
sur le côté, le crane présente l’aspect d'un casque; il est beaucoup
plus élevé que dans le Morse et la conformation de toutes les régions
est complètement différente. . . . Tout le dessus du crane est aplati
et une bordure véritable sépare cette région supérieure en avant des
os de la face, sur le côté des os des tempes. Les pariétaux sont fort
bien indiqnés au devant de l’occipital et sont disposés de manière a
ressembler au premier abord, a des os nasaux’’.

Not to mention a few inaccuracies, the differences with the walrus
might have been indicated in less vague a manner, so that a new
comparison does not seem superfluous:

Looking at the skull in front, we notice several differences with
the walrus, which all have led to an alteration in the shape of the
parietal. For with the walrus this bone is clearly convex at both
sides while with Alachtherium a concavity is found which only for

GS")

a small part must be ascribed to decrease in size of the cranium.
It is chiefly caused by the development of a gigantic crista lambdoidea
and by the big mastoid process, as well as by the form of both.
The crista lambdoidea namely by its size draws the parietal upwards
and since in a median direction it extends far to the front, it exerts
this influence over a great part of the circumference of the parietal.
The strongly developed mastoid process, especially by its frontal
position, draws the lower edge of the parietal and the upper edge
of the squamosum outwards and therefore has the same effect at the
lower side of the parietal as the erista lambdoidea at the upper and
posterior side: the two together produce the concave shape of the parietal.
While now the strong development of the crista lambdoidea and the
increase in height of the mastoid process also cause an increase in
height of the skull as compared with the walrus, it is at the same
time broadened by the frontal position of the mastoid processes. For
these are placed with the walrus in a slanting forward direction
and are also smaller than with Alachtherium. So we cannot wonder
that the absolute height and breadth of the skull exceed the corresponding
dimensions of the walrus, but that their ratio lies within the limit
of variation of recent animals.

Other differences with Trichechus rosmarus are found at the base
of the skull. With the walrus a very large bulla ossea extends from
the external edge of the basioccipital and basisphenoid as far as the
mastoid process and as far forwards as the fossa glenoidea; a more
or less distinct groove separates this bulla ossea, in a rostral and a
caudal part. With Alachtherium, however, the bulla ossea is very
small and in this respect it deviates distinctly from the Trichechus
type. Corresponding to some extent to this cireumstance the fossa
elenoidea lies far backwards in Alachtherium: the space between
the articulation and the mastoid process is very small. While now
with the walrus the fossa glenoidea extends on the jugal process of
the squamosum, so that above it the squamosum rises in a slanting
upward direction, with Alachtherium it lies far less free and in front
of it the squamosum rises steeply. We shall see later on that this
is of importance when dealing with the mandibles to which the
cranial fragment was said to correspond by vaN BENEDEN.

A further difference is found at the border between basioccipital
and basisphenoid. Not to mention a frontally diverging crista and a
roughness on the oceipital on both sides behind it, these bones pass
gradually into each other in the walrus. In Alachtherium the outside
of the sphenoceipital suture is strongly thickened; a real knob has
formed which only at the left side has been preserved. The back of

(9)

the basisphenoid now rises at the left to a great height against this
knob and, instead of following the cranial base normally, it is situated
here almost sagittally: the complete basisphenoid must consequently
have shown a deep median groove. Analogous changes have occurred
at the basioecipital, which towards the knob shows a deep concavity.
By this the angle between basisphenoid and basioccipital has also
become more acute than in the walrus.

In order to compare the back of the skull with that of the walrus
we placed the fragment in such a position that the upper edge of
the parietal has a slight forward inclination, as this is also the case
in a walrus skull, placed on the table without tusks.

Then with both the basisphenoid rises slightly in a forward and
the basioccipital in a backward direction, so that their positions
may be considered as corresponding.

With Alachtherium the outline of the posterior part of the skull
then shows one important change, caused by the strong crista
lambdoidea and the broad mastoid processes. For this causes the
back of the skull to consist of a narrow supra-occipital and a very
broad temporal part, a phenomenon which also with old walruses
is sometimes indicated to some extent, but never so strongly as with
Alachtherium. Moreover Alachtherium has a very small cranium: all
bones are uncommonly thick. Further in Alachterium the crista
lambdoidea runs in a median direction far to the front and even
shows a tendency to pass into a sagittal ridge. As compared with
the walrus this phenomenon becomes very striking by the complete
absence of the crista occipitalis externa. Where consequently with
old walruses the occipital superius is strongly convex by the massive
crista occipitalis, it shows with Alachtherium a deep median fold.
Compared with Trichechus the hind skull of Alachtherium thus shows
three modifications: absence of the crista occipitalis externa, size of
the mastoid processes, and shape of the crista lambdoidea. The dif-
ferences at the side of the skull are not very great and we are
certainly not justified in stating, as VAN BENEDEN does: that “la
conformation de toutes les régions est completement différente.”’
Especially with the skulls of old male walruses Alachtherium shows
many points of resemblance and it would almost appear as if VAN
Benepen had only a small material for comparison at his disposal for
his description.

The many changes which the skull of Alachtherium shows when
compared with the skull of Trichechus, have not deprived it, though,
of its Trichechid character. But there are three phenomena which
bring it nearer the Otaridae: the smallness of the bulla ossea, the

(10)

absence of the erista occipitalis and the tendency of the erista
lambdoidea to develop on the skull into a sagittal ridge *).

What reasons had v. BeNppEN to coordinate the cranial fragment to
the mandible on which Alachtherium is based? He does not state
them anywhere:

“On ne possédait d'abord de ce curieux Amphitérien d'autre os
que le maxillaire . . . . Nous rapportons a ce meme animal . 3
… les vertebres cervicales etc.
ete... .. La forme du maxillaire inférieur indique une confor-
mation toute particuliere de tous les os en face i

le crane que nous réprésentons

The question now is whether on the contrary it cannot be shown
that cranial fragment and mandible do not belong to each other.
This seems indeed to be the case :

The lower jaw deviates strongly from that of Trichechus and
points in fact to a ‘conformation toute particuliere de tous les os
en face”. But as the hind skull of Alachtherium does entirely
conform to the Trichechus type, it is unjustifiable to assume for the
laeking part an entirely deviating shape, only in order to be able
to fit the skull to the lower jaw.

The hind skull has much more massive and coarse bones than
Trichechus, the mandible on the other hand is larger than that of
the walrus, but of a much more elegant and fine build: also in
their structure skull and lower jaw have consequently opposite
characters. Also the lower jaw is too big for the cranial fragment.
For the eranium belongs to an old animal and so the lower jaw
should certainly not be much too big for the skull. If we now
divide two dimensions of the walrus and of Alachtherium, we find:

Walrus Alachtherium Alacht.: Walrus

distance of the fossae glenvideae 13.5 14.5 107
length of the mandibie 24.7 35.7 144

Hence we here obtain again such abnormally great differences of
two dimensions between the walrus and Alachtherium that the
otherwise considerable analogy of the skulls does not permit us to
aseribe mandible and skull to one species. The principal argument,
however, is found in the shape of cranium and mandible.

We saw that with Alachtherium the fossa glenoidea has a much
less free situation than with Trichechus. With the latter the mandible
has a short, vertical coronoid process, which consequently easily
finds a place in front of the squamosum. The lower jaw of Alach-

1) J. A. Auten (30) states about Trichechus obesus that this also has a small
bulla ossea.

(eal)

therium, on the other hand, shows a long coronoid process, which
has a backward and slightly inward direction, and which on account
of the un-free situation of the articulation of the cranial fragment,
must inevitably come in collision with the squamosum; hence the
two bony pieces cannot possibly belong together. ,

So we may conclude that the skull described as Alachtherium
does not belong to this species. No more can it belong to Triche-
codon, since this genus must disappear from literature. So it must
be regarded as undetermined.

Finally the “Musée d’Histoire naturelle” at Brussels possesses still
another Trichechid skull, floated ashore near Heyst and considered
to be diluvial. It is the cranium of a very old male: the sutures
have all disappeared and the tusks are almost entirely used up.
The preservation is exactly as that of the Zealand fossil: the bones
have turned brown and the teeth entirely black; the skull is very
heavy and perhaps has become partly siliceous. Besides its shortness
and a strong development of the alveoles of the tusks, the fossil
shows no differences with the walrus: these two characteristics,
however, give it a very square appearance. But these small diffe-
rences give us no right to regard the skull as a new species: it
seems to be an ordinary Trichechus rosmarus. After having dealt
with the known skuils, we must assign a place in the system to
the Zealand fossil and to the Antwerp hind skull. They belong to
different species. The resemblance of the tusks of Trichechus Huxleyi
with those of the Zealand cranium was already pointed out. The
curvatures of the tusks of Trichechus Huxleyi, drawn by Ray LAN-
KESTER, are:

21, 27, 30; 38, Deo > 50) cms.

Hence they agree much better with the Zealand tusks than with
those of the walrus. Also the cross-sections of the tusks showed
analogies and so we may safely class the Zealand skull under
Trichechus Huxley. .

If we ask what age must be attributed to the skull from the
Scheldt, we must bear in mind that the good state of preservation
precludes a long transport. Hence the skull must have been dislodged
out of the bottom of the river. What sort of soil do we find there?
Formerly already Dr. pe Man has described remains of diluvial
terrestrial mammals (85), which were also fished from the Scheldt
and partly even very near the spot where also the Trichechus was
found (36). Now it is very improbable that the Trichechus and the
terrestrial mammals come from the same layer, since both are well
preserved. In the year 1879 Dr. Sretneim published some profiles

(12)

of Zealand, based on borings aiid showing that in the West Scheldt
it is of course impossible
the fossil got free, yet it
appears that the skull may belong to the tertiary pleiocene. Also in
this respect it would correspond to Trichechus Huxleyi.

The cranial fragment from Antwerp does not belong to Trichechus
Huxleyi, since it deviates considerably from the Zealand skull. Hence
it must be a new species. It does not seem desirable to establish
a new genus for a fragment, showing so much analogy with Tri-
chechus. The name of this Trichechid may be, after the spot where
it was found:

Since
to indicate the precise layer from which

occasionally tertiary layers occur.

Trichechus Antverpiensis.

The recent walrus skulls from the “Rijks Museum voor Natuurlijke
Historie” at Leyden and from the Zoological collections of the University
at Utrecht and Amsterdam were placed at my disposal through the
kindness of Dr. F. A. JeNriNK and Profs. A. A. W. Husrecat and
Max Weser. At Brussels I was enabled by the kindness of Dr. L.
Dorrò to study the fossil and recent material of the “Musée royal
d'Histoire naturelle de Belgique”. Finally I have to thank Prof.
WicuMaNnN who lent me the fossil for description and without whose

assistance I should certainly not have succeeded in collecting all
the literature.
FIGURES.

Hind view, base and side of the skull of Trichechus Huxleyi.
Find: opposite Breskens in the West Scheldt.

Hind view, base and side of the skull of Trichechus Antverpiensis.
Find: near Antwerp.

LITERATURE ON FOSSIL TRICHECHIDS.

ile 1823. Cuvier. Ossements fossiles 2e éd. le partie p.264, 2e partie p.521.

2. 1828. Mrrcuitt, SmirH and Cooper. Discovery of the fossil Walrus
in Virginia. Aum. Lyceum of Nat. Hist. of New-York II p. 271.

a 1834. R. Haran. Critical notices of various organic Remains, hitherto
discovered in North America. Edinb. New. Phil. Journ. XVII
p. 360.

4. 1835. R. Haran. Physical and medical Researches p. 255.

DE 1839. H. Ducroray DE BLAINVILLE. Ostéographie, IL, p. 45 et 49.

6. 1843. Cu. LyeLv. Edinb. New. Phil. Journ. p. 187.

7. 1842—1843. Cx. LyeLn. Proc. geol. Soc. IV p. 31.

8. 1844. Cu. Lyguu. On the tertiary strata of the Island of Marthas

Vineyard:

Amer. Journ. of Sc. XLVI. p. 319.

a ee Oey es (A
Hor ary DPR ANT

Number if 1 2 3 4 5 6 7 14) 45 | | 20 | ot | 29, 26 27 la || Fee RORE dee LEL
: : J en aa a ere alk = : = ——— - = a=:
= = = at an Te 3 pe ss ra | T | 1 |
- | 9 | |
Height . . od ON A900!) 46.7) 46.8) 16:5] 44:91) 16.4) 10.9) 45.9 19.7 | 16.6 10:89 2 A) — 16,4 | 18.8) 22.0) a |
Breadth. ..... If | 31.8) 98:0'| 96:0'] 95.9) 94:7) 99.7) Mdf 97.81) 924 28.5 | 26.6 U4 | 30.3] — | — 25.4 | 99.4| 30.2 1 i |
| a Ee E | |
Height occip. sup . I | 41.9 8.6 — 8.5 1.4) — 7.9) 9.9 ia 9.0 9.5 fe) 9.0) —| — | 85] 40.0 = | |
4 N MTA 5 re 5 5 i 3 9 3 5 aS 5 Er ae 44 | a = |
Height for. magnum IV, 4.3) 4.5 — kA} Aj = KAL 8.4) 6B) 5.4) 44] — 3.9| 4.6) 492] 3.6 | 3.9) 34) 42) 4.5] 5.0 45 | 44| 4.6 | 4.0 .
Breadth for. magnum V 54 45 4.0 4.4) — 3.8 3.8 4A 5A AAL — 4.3 4.6 4.6 | 3.9 Keke 1317 3.9 4A 5.0 | 4.2)}—|/—| — |} 4.6) 5.0 45 =|
| | {|
Length VI | 39.5 | 36:6) 33:6] 38.6) 32.4) — 317 | 39.8)) 30:4) 42,0!) 3 — $7.0 | 30:5] 87.5) 35.0} 33,7} 37.01) $7.7) 32.51) 330 ALO =| — 33:5\|| 37.5 | 38.0}
lengths « . 2.» | |
| | | | | | Vi « = 5
Curvature of the | vijl 96.0) — | 4910) >50) 47.0) >50) — | S50) 43 ho >50 | 48 | >50| >50)) 45 | 37 37 >50] 47 | 93 38 >50'| 43.) 46] >50 | >50 | 40 41 | >50| (21 | 27] 30} 38 | >50 | >50
tusk, exterior edge = | | | | | | | | |
; | | | | | | |
The same, interior | vu 28.0 — | 550) 45! | 50 >50 250, >50) >50) >50| 39 35 >50 | >50 | 47 | 50 |>50) >50|) 42 | 550] >50) | Ik 5
edge ) | : | | | | | | | | | | |
| | | | | | | | | |
+ | | |
Distance of the pro- | Ix | 22.0 18.0 | 43.4 | 23.0 | 44.5 | 16.9) 18:38 | 49.3] 17-4 | 16.0 | 42.8! 48.3 90.2} —|—| — | 21.0) 13.6) 47.7) 21.4]
cessus pracorbitales | | | | | | | | } | |
Distance of the incisors X 2.7 3.2] 3.0) 3.7) 3.2 | 3.4] 3.2 3a BLO || ALE 3.2 | 3.8 3.5, 26 | NE | 1.8 BEU S15) 9.7
| | |
Wl 1000, A 75.5 68.0} 69.0 | 71.9} 68.7 | GOA | 66.7 5 62.4 | 69.4 | 65.4 73.9 | — | A 65.5 | 64.5) 63.9 | 73.2 |
| | |
HII > 100%, 37.4 $2.8] 35.6) 33:00 97.0] 30.0] — | 35.7 | 2907) | — | —| — 32.6 | 33.3 | 39.0 = |
VAV>< 100%, . . ~ | 425.6 | 400 = | 97.6) 05.5) — 95.9) 100 | 100 — | 440 109.5 | 108.3 OEE NEN EUN EEN |
| | | | |
IX/IL >< 100 0/ ol 69.2) GIR} 56.9) 64:9) 57.5 | 55,4 i 62.2) 60.8) 60.7) 66.1 | 60.0 | 61.7} 6010} 57.9] GI.4 | 60.2) 54.2) 58.7 Dol == 64.3
| | |
XII 100% 8.5} 13:0} 44.0) 13.9} 45.8 | 15,8 | 40:8) 46.7) 9.9} 44.0} Anno 10,9 | 14.0} 43.3] 42:0) 46:4) 11.2 BON aia
/ | | | |
VI 00%... . | 194.9 | 80.7 | 199.9) 199.7) 131.2) — [aars | tesa | 497.6 | 120.7 | 492.5) — | rans | tats | tog | 1315 | 142.8 | 118.6 : = hh) alse
(IL >< 100 07, | | | | |
| i | | } | | |

All the measures are in centimeters.

f— Trichechus Huxley: from the Scheldt, Nr. 1—6 are walrus skulls from the Zoological Collection of Utrecht U; ersity.
Nr, 724 are walrus skulls from the State Natural History Museum at Leiden and from the collection of Natura Artis Magistra at Amsterdam,
Nr. 25—27 are walrus skulls. from the Musée d'Histoire naturelle at Brussels. 4 is the skull of Heyst
H are tusks of Trichechus Huxleyi (29), drawn by Ray LANKESTER.

iS
>

EL. RUTTEN. On fossil Trichechids from Zealand and Belgium.

Wig. 2.

Prooeedings Royal Acad Amsterdam. Vol. X.

Fig. 6.

le)

10.

Nie

20.

21.

33.
34.

1845.
1845.

1847,
1851.

1853.
1853—1856.
1853.
1857.

1891 —1893.
1898—1899.

(13 )

Cu. Lyern. Travels in North America | p. 257—258.

K. G ZiMMERMANN. Brief an den Geheimrath v. Leonhard.
Neues Jahrb. f. Min. p. 73. (The here described walrus skull
from the subsoil of Hamburg seems to have been carried
there by man; Communications of Prof. CG. Gorrscue).

GreBEL. Fauna der Vorwelt. I. p. 232.

Acassiz. Proceed. Amer. Assoc. f. the Adv. of science. p.
952, 348.

EicHwALp. Lethaea rossica. 3. p. 890.

Bronn. Lethaea geognostica. Thl. 6. p. 786.

Prerer. Paléontologie I. p. 233.

J. Lerpy. Notice on the Remains of the fossil walrus on the
coast of the United States. Transact. Phil. Soc. Philadelphia
New Series. vol. XI. p. 83.

GRATIOLET. Bull. Soc. géol. de France. 2e série. V.

P. Gervais. Zoölogie et Paléontologie francaise. Ile éd. p. 275.

E. Ray LANKESTER. On the Sources of the Mammalian Fauna
in the Red Crag and on the Discovery in that Deposits of
a new Mammal, allied to the Walrus. Proc. Geol. Soc. XXI.
p. 233—232.

Vicomte pu Bus. Sur quelques mammifères du Crag d'Anvers.
Bull. Acad. roy. Belgique. 2e serie 24. p. 562—577.

J. Lemmy. The extinct Fauna of Dakota and Nebraska Journ.
Acad. Nat. Science of Philadelphia VIL p. 416.

Le Hon. L'Homme fossile. p. 304.

P. J. v. BENEDEN. Les Phoques de la mer Scaldisienne. Bull.
Acad. roy. Belgique. 2e série 32. p. 5—18.

P. J. v. BENEDEN. Les Phoques du bassin d'Anvers. Bull. Acad.
roy. Belgique. 2e série T. 41. p. 783—812.

SCHAAFHAUSEN. Trichechus rosmarus in Cöln. Sitz. Ber.
Niederrh. Ges. f. Natur- und Heilk. S. 427.

P. J. v. BENEDEN. Description des ossements fossiles des environs
d'Anvers I. Pinnipedia Ann. Musée d’Hist. Nat. de Belg. T. I.

W. Davis. On a collection of pleistocene Mammals, dredged
off the Eastern Coast. Geol. Mag. (2). V. p. 97. 98.

E. T. Newton. Notes on the Vertebrata of the preglacial Forest
Beds of the Coast. of England. Geol. Mag. (2). VIL. p. 152—159.

Ik. Ray LANKESTER. On the Tusks of the fossil Walrus found
in the Red Crag of Suffolk. Transact. Linn. Soe (Zoology)
(2). I. p. 218—221.

J. A. ALLEN. History of North American Pinnipeds U. S. Geol.
Survey. Miscellaneous Publications 12.

E. Ray LANKESTER. Journ. Linn. Soc. (Zoology) XV London,
p. 144—146.

E. T. Newron. The vertebrata of the- pliocene Deposit of
Britain. Mem. Geol. Surv. of the United Kingdom, p. 17—18

K. Zivren. Handb. d. Paläontologie IV p. 680—685,

Trounssart. Catalogus Mammalium p- 375—376.

(ad)
LITERATURE ON THE FINDS OF TRICHECHUS HUXLEYI.

55 1875. J. CG. pe MAN. Beenderen van den mammouth en van het uil-
gestorven rund, opgevischt in den omtrek van Zeeland. Arch.
Zeeuwsch Genootsch. der Wetensch. Ill 2. p. 101—127.

36 1878. J. CG. pe Man. Een elandshoren, opgevischt in de Schelde.
Mededeeling over eenige beenderen, in of nabij Zeeland ge-
vonden. Arch. Zeeuwsch Gen, Ul 3. p. 1—22.

37 1879. F. SeELHEIM. Grondboringen in Zeeland. Verhand. Kon. Akad.
der Wetenschappen Afd. Natuurk. Amsterdam.
38 1889. J. G@ pe Max. Derde Mededeeling over in de Schelde gevon-

den beenderen. Arch. Zeeuwsch Genootsch. V. 1. p. 161—170.

Anatomy. — “On the existence of cartilaginous vertebrae in the
development of the skull of birds’. By Prof. J. W. vax Wisun.

(Communicated in the meeting of April 26, 1907).

It is a well-known fact that at a certain stage of development the
notochord in all vertebrates extends forward as far as the hypo-
physis cerebri and backwards as far as the tip of the tail.

Over the whole length of the trunk and also in the occipital
region of the head the dorsal part of the mesoderm is separated
into segments or somites.

In the lower vertebrates: Selachians and Petromyzontes, the somites
are not restricted to the occipital region, but extend forward as far
as the hypophysis, ie. equally far as the notochord.

The greater part of the voluntary muscular system is formed from
the somites and in Amphioxus the segmentation of this muscular
system is permanent and distinct from the anterior to the posterior
end of the body.

The original function of the somitie muscles of the Chordates
existed in my opinion) in the to and fro movement of the notochord
and so of the whole body during swimming.

In the Craniotes this muscular system is interrupted in the region
of the auricular organ and in my opinion the presence of the auricular
capsule is the cause of this. This capsule, which also encloses the
organ for equilibrium, needed a firmer attachment than could be
afforded by the connective tissue and found it in the parachordal
cartilage, through the stiffness of which the muscular fibres in this
region could no longer operate and consequently disappeared, partly
even in their origin.

1) Cf van Wine “Ueber die Homologisirung des Mundes und die primitive
Leibesgliederung der Wirbelthiere.” Perrus Camper, Vol. IV. 1906,

(15 )

The effect of this was also felt in the region in front of the
auricular organ, but bere part of the somitie muscles remained on
account of a change of function. They became attached to the here
developing eye-ball and now served for the movement of this latter
and no longer for the movement of the whole body. This was
accompanied by far-reaching shiftings, which can still be followed
in the individual development.

The cartilaginous skeleton forms a system which appears only late
in the development of the vertebrates and long after the appearance
of the muscular system. As soon as the first cartilage may be
observed, the muscular system in the head has undergone the
changes here indicated. In the auricular region the somitie muscles
have degenerated; partly they were not even indicated; in the region
in front of the auricular organ they have entirely changed in place
and shape and have entered into the service of the eye-ball. Only

in the region behind the auricular organ — the occipital region —
the myotomes — generally numbering three — still stand in the

original order, like the myotomes of the trunk.

Head and trunk are separated in the ontogeny — although the
border is later somewhat shifted in a caudal direction already
before the cartilaginous spinal chord appears, and I see no reason
for assuming that this separation should not have taken place also
in phylogeny before the appearance of the spinal chord.

The segmentation of the spinal chord. depends on that of the
muscular system. The boly of a vertebra is not formed opposite the
middle of a myotome, but opposite the border of two successive
myotomes. Barrour has given the explanation of this at first sight
curious phenomenon: the first muscular fibres occupy the whole
length of a myotome and lie laterally of the tissue, surrounding the
notochord. Now it is no more than natural that the solid points of
attachment which in this tissue are formed for the muscular fibres,
namely the origin of the vertebral bodies, are formed opposite the
borders of two successive myotomes.

If we now ask where the appearance of vertebral bodies in the head
must be expected, the answer must be that this cannot be in the
auricular region, since here the myotomes have disappeared at the
time of the appearance of the cartilage. No more can this be the
case in the region in front of the auricular organ, for here the
myotomes have entirely altered their place and have entered into
the service of the eye-ball.

Only in the occipital region one would expect the appearance of
two or three vertebrae. Yet until recently nobody has observed them

(16 )

here, although this region has been investigated not only by the
method of sectional series, but also by the methylene blue method,
by which the investigation is so much easier. By this method
Dr. Noorpensos did not tind them in the vertebrate skull any more
than myself in the skull of Selachians.

Instead of vertebrae we found the well-known parachordal cart-
ilage accompanying the notochord in the occipital and auricular regions.

Certain authors have indeed spoken of the origin of vertebrae
in the occiput, but the parts observed by them, were not cartila-
ginous but only badly outlined cell-heaps, not deserving the name
of vertebrae.

So I was greatly surprised when my former assistant, Mr. F.
Soxtes, discovered by the methylene blue method two cartilaginous
vertebral bodies in the occiput of embryos of the chick of the sixth
breeding day and of ducks in a corresponding stage.

It will be asked how it is possible that these vertebrae have not
been long known, since the embryos of the chick form the classical
material for investigation in all embryological laboratories. The
answer is that they were not discovered because the stage, in which
they appear, is of so very short duration. One has to hit the moment
in which the cartilage appears in the first two vertebrae of the neck.
Before the cartilage appears in the remaining vertebrae, the two
occipital vertebrae have already coalesced with the parachordal
cartilage.

It is impossible to indicate the hour of the breeding day, since
the development of the different eggs varies too much. By taking
a large quantity of material, however, it is always possible to obtain
the desired stage. It would require an immense expenditure of time
to work all this material by the sectional method. With the methylene
blue method, however, one is ready in a few days.

So the parachordal cartilage of birds does not originally form a
morphological unity. With Sontes we may distinguish two parts in
it: an anterior praevertebral part, situated in a region where the myo-
tomes are degenerate or abortive and a posterior or vertebral part,
occurring in the shape of two vertebral bodies, which soon coalesce
with the anterior part.

Corresponding to these two vertebral bodies later also two vertebral
arches appear on each side, which soon coalesce, but the locality of
which remains indicated by two openings for the two roots of the
hervus hypogiossus.

For further particulars and for several new discoveries about the
development of the cartilaginous skull and the spinal column of

eg)

birds, I refer to the academical thesis of Mr. Soxms, which is now
going through the press and will soon be published, also in “Petrus
Camper”. I will only mention that the small polar cartilage, discovered
by _NoorpuNBos in mammals and which also appears in Selachians,
was found by Sonins also in birds.

Microbiology. — “On Luctic acid fermentation in milk’. By
Professor Dr. M. W. Brtnrinck.

(Communicated in the meeting of April 26, 1907).

In milk left to itself, which in consequence of spontaneous infection,
contains the more generally distributed germs, with certain regula-
rity some special floras are observed, whose composition is chiefly
controlled by two factors: temperature and oxygen pressure. If the
latter is very slight, that is, if the microbes of the milk are reduced
to more or less anaërobie conditions, the floras become simple of
composition and produce certain fermentations. The three principal
of these are the Aérobacter-, the Butyrie acid- and the Lactic acid
fermentations, of which the two first are always characterised by the
evolution of hydrogen and carbonic acid, whilst in the lactic acid
fermentations, which may occur under different forms, beside the
lactic acid, no gas at all, or carbonic acid only is formed. Sometimes
this fermentation is accompanied by a vigorous slime formation,
which slime consists of the swollen cell walls of the inferred lactie
acid ferments.

For domestic purposes the lactic acid fermentation should be con-
sidered as useful; both the others as noxious.

The fermentation experiment the dairy industry applies to judge
of the purity of milk has for its object to determine the commonness
or the rarity of the germs of Aérobacter and of the butyric acid
ferment. To this end a high standing glass is filled with milk, placed in
a water bath of 40°C. and it is observed whether any fermentation
gas is evolved, and if so, after how much time. In good milk this
production of gas does not occur because then the lactic acid ferments
develop so quickly that the other microbes are expelled. Artificially
the Aérobacter fermentation is easily obtained by infecting non-
acidified milk with faeces, soil or canal water and cultivating at
about 37° to 40° C. After 6 to 12 hours production of gas is observed
originating from A?robacter coli or more rarely from A. aérogenes.
The nature of the thereby obtained varieties changes with the
temperature.

At temperatures beneath 40° the Aérobacter fermentation, after

2

Proceedings Royal Acad. Amsterdam. Vol. X.

(18)

lasting some hours, is replaced by a butyric acid fermentation which
again, after some time is succeeded by a lactic acid fermentation.
Externally the Aérobacter and the butyric acid fermentations cannot
be distinguished, but this can be done easily with the microscope.

If 3 to 5°/, chalk is added to a culture in a stoppered bottle at
35° to 40° C., the butyric acid fermentation can go on longer, and
by early transplanting, likewise in milk with chalk and with exelusion
of air, check the development of lactic acid ferments, without,
however, quite dispelling them.

Microscopically the butyric. acid fermentation may be recognised
by the long, thin, at neutral reaction highly motile rods, sometimes
mixed with elongated or more rounded clostridia, colouring blue by
iodium, all belonging to the species Granulobacter saccharobutyricum.

To: accumulate from such a crude butyric acid fermentation in
milk the lactic acid ferments, which hardly ever lack there, it will
suffice to transplant some drops into milk without chalk, and, if
necessary, to repeat this after the butyric acid fermentation, which
always sets in at first, is finished. Whether this be done in open or
closed bottles or tubes, at 37° to 40° C., lactic acid rods of the genus
Lactobacillus will be seen to appear, which by repeated transplantations
completely dispel the butyric acid ferments.

If in these experiments instead of using fresh, unheated infection
material, the soil, water, or faeces are previously heated to 80° or 95°C.,
by which only spore-forming microbes can develop in the milk, the
fermentations of Aérobacter and the lactic acid ferments do not arise,
their germs producing no spores, but a butyric acid fermentation is
obtained, from which the aërobie spore-formers may be dispelled by
repeated transplantation at exclusion of air.

1. Properties of the active lactic acid ferments.

As many bacteria of the most different groups can produce lactic
acid it seems not superfluous to indicate what are the characteristics
of the lactic acid ferments proper.

The active forms of dairy industries, yeast manufactories, distilleries,
tanneries, and breweries, although joined by transitions, may be
practically classified into the physiological genera Lactococcus, Lacto-
bacillus and Lactosarcina, of which the two first only occur in the
dairy products).

De In) the chief floras of milk- and dairy products occur, to my knowledge, no
species of Lactosarcina. When EMMERLING asserts to have founda yellow Sarcina
in Armenian mazun (Centralbl. f. Bacteriologie, 2t: Abt. Bd. 4, p. 418, 1898),
this can only have been a common infection from without. Also in butter sarcine

species may accidentally occur but they do not belong to the chief flora, which
consists of lactic acid ferments and lipophili.

(19 )

They are always immotile, no-spore forming bacteria, which bear
drying very well and which, by heating to 65° or 75° C., in which
they just remain alive, while these temperatures are deadly to most
other non sporeproducers, may be separated from these (“lacticisation”).
They require for nitrogentood peptones, such as are found in milk,
malt extract, or other juices of plant- or animal origin, and for carbon
food certain sugars,- which may differ for different species. They do not
peptonise proteids and, thus, do not liquefy gelatine; the secreted lactic
acid can dissolve a certain quantity of caseine, but chemically this
substance remains unchanged. These circumstances regulate their
distribution in nature, where they are by no means general, but may
rapidly multiply, especially under the influence of man. They are,
however, found in the soil and can, by methods mentioned below,
be accumulated and cultivated in a condition of pureness.

They are always more or less distinctly microaérophilous, some
species or varieties can, however, grow very well at the air; other
forms cannot and behave as real anaérobics. Access or absence of
air is commonly of no consequence to the acid formation, but in the
yeast industry a species is used, which at full atmospheric pressure
produces no acid, and in the dairy industry are also forms which
display the same property.

Always, even on good nutrient media, to which belong in particular
maltextract agar, and milk- or whey-agar, the growth of the colonies
remains limited, especially if the air and the produced acid can act
simultaneously. If the acid is neutralised by chalk the growth of the
colonies at the air may also become important. Yet, in most cases,
the recognition of these ferments may repose on the smallness of
their colonies compared with those of other bacteria.

Catalase is constantly absent, and hereupon an excellent diagnosis
can be based, for which it is only necessary that a culture plate, on
which all kinds of bacteria may occur, be flowed with strongly
diluted hydrogensuperoxyd which is by all microbic species, except
the lactic acid ferments, indifferently whether they belong to Lacto-
coccus, Lactobacillus or Lactosarcina, changed into a scum of little
oxygen bubbles.

Even the lately described *) large celled Sarcina, which in conse-
quence of continued research [ now consider as identie with the
stomach sareine (Sarcina ventriculi), and whose acid producing
power is very slight, — i.e. 3 ¢.c. of normal acid per 100 cc. of

1) These Proceedings 25 Februari 1905. Archives Néerlandaises T.1 and 2. T. ial
p. 200, 1906.

D*

( 20)

maltextract or glucose broth, — does not at all decompose hydrogen
superoxyd.

If we consider how generally catalase is met with in the animal
and vegetable kingdom, as also in the microbes, its very absence in
the lactic ferments appears in a peculiar light.

All active lactic acid ferments from milk invert sugar (invertase
reaction) and can more or less easily decompose esculine and indican
(emulsine reaction). The reaction on esculine is demonstrated by
- introducing, for example, 0.1°/, of this substance and a few drops
of ferricitrate solution into whey agar or whey gelatin. Streaks drawn
on it of species which decompose esculine produce intensely brown
or black diffusion fields of esculetiniron, brown at more alcaline,
black at more acid reaction, so that the lactic acid ferments become
recognisable by the black fields in the midst of which their colonies
are placed'). So long as esculine is present it is recognised by the
magnificent blue fluorescence of the whole plate at feeble alcaline
reaction. Indiean may be used in a corresponding way but then no
iron salt is wanted as the indoxyl produced from the glucosid
oxidises of itself at the air to indigo blue. The lactic acid ferments
decompose these two glucosides, slowly indeed, yet these reactions
are very characteristic and useful. Amygdaline is not decomposed by
the lactic acid ferments. *)

To the most remarkable properties of the lactie acid ferments
belongs their power of reducing levulose to mannite,*) which latter
substance may even in concentrated nutrient solutions be recognised
by its ready cristallisation at evaporation. A single drop dried on
the object glass, commonly gives at microscopical investigation full
certainty as to the existence of this reaction.

The lactic acid ferments thereby strongly contrast with the so
nearly allied vinegar bacteria, in as much as the latter do just the
reverse, i.e. they change by oxidation mannite into levulose.

Like so many other bacteria the lactic acid ferments possess,
also with regard to various pigments, a strongly reducing power,

1) The knowledge of this extremely sensitive reaction, which has been applied
for years in my laboratory, I owe to my colleague Mr. H. ter Meuten.

2) Amygdalin is decomposed with much more difficulty by the action of microbes
in general than the other glucosides named in the text. Moulds mostly decompose
it into amygdalinate of amonium; beer yeast into amygdalonitril glucosid and
glucose. Splitting under production of bitter almond oil, hydrocyanic acid and glucose
I detected hitherto only with Saccharomyces apiculatus and with the anaérobic
ferment of butyric acid fermentation, Granulobacter saccharobutyricum.

3) Ferments lactiques de l'industrie. Archives Néerlandaises 1901. Kayser, Fer-
mentation lactique. Annales de l'Institut agronomique 1904.

( 21 )

as is easily shown by inoculation into deep test-tubes of boiled
milk coloured with litmus. The red litmus is first in the depth,
later till near the surface quite discoloured, to turn red again by
shaking with air. The thickness of the red layer in the curdled
milk admits an accurate measure of the intensity of the growth and
of the reduction process. The thinner the red layer the more inten-
sive both functions must be.

2. Factors of variability.

Many, perhaps all lactic acid ferments display a high degree of
variability as well in physiological as in morphological properties.
Nevertheless this variability in different stocks, coming from different
isolations of the same species, is not always equal by far, which may
give rise to trouble in the study of the specitic properties. The cireum-
stances causing the variability are but partly known; decidedly
belongs to them an oxygen pressure, too far above or too far beneath
the optimum for the vital functions, which may, especially for the
bacterium of the long whey (Lactococcus hollandiae), be demonstrated
with exceeding clearness.

This remarkable species is characterised by a vigorous slime
formation when cultivated in milk or whey, but loses this power
at temperatures above 20° C., as well at the ordinary pressure of
the atmospheric oxygen, as at complete exclusion of it, if the changed
influence is allowed to act during some time on the growing microbes.
This is shown by cultivating the whey in a closed bottle; the upper layer,
just beneath the stopper, where a little air can find access, becomes quite
liquid and contains a hereditarily constant, common Lactococcus,
forming little acid and no slime. Also by cultivating the long whey
microbe in tubes of boiled milk with access of air, after one or two re-
inoculations, a Lactococcus is produced, which forms no slime at all.
If the material for the reinoculation is secured from the depth of the
cultures grown in closed flasks, at places where the access of air is
impossible, and the inoculation is repeated once or more in the same
way, a Lactococcus is likewise obtained which displays no trace of
slime production.

At some depth beneath the surface, however, is a zone in which
unchanged, slime forming, hereditarily constant material is found.

What in this case can be very easily ascertained, proves, at
accurate investigation, also to be true for the other species of lactic
acid ferments, namely, that they only then continue to display
constant specific characters, when they are continuously cultivated at

a certain pressure of the oxygen, else, these characters are seen
to disappear, whilst in fact, or apparently, new ones originate. Hence,
in some cases it may be proved, in others the probability is shown,
that each species must occur in three varieties, joined by intermediate
forms, i.e. the normal form, a “high pressure variant”, and a “low
pressure variant”.

As in wholly different groups of bacteria corresponding facts may
be observed, there is cause to assign a fundamental signification
to them.

A decisive factor which may cause the production of variants is
furthermore the temperature, for experience proves that a prolonged
cultivation above the optimum temperature of growth, gives rise
to the appearance of forms distinetly different from the original stock.

In other cases the cause of the variability is unknown; not seldom
for example, we find at the very first culture of a species taken from
nature, strongly varying colonies, which prove to belong to the same
species only because many colonies by sector-variation display the
genetic alliance of the variants to the wild stock.

But then, too, there is reason to admit that the new vital condi-
tions, to which the microbes are subjected just by the change of
oxygen pressure and temperature, are the chief factors of the variation
process which is, as it were, seen in action. This observation is of
so general a nature and is so closely related to the essence of life,
that it must be considered as probable, that also in higher plants
and animals, local changes in the access or exclusion of oxygen, in
connexion with temperature, play an important part in the morpho-
genesis.

As the examination of other species of microbes shows that the
absence of certain nutrient substances in the culture medium, at free
aération and during growth, may cause hereditary variation, for example
in Schizosaccharomyces octosporus, which in old cultures changes into
the spore-free variant, totally differing from the chief form, there is
reason also to believe, that also the said factor must be considered
to explain the great variability of the lactie acid ferments; but the
observations there about are not yet fit for definite conclusions.

3. Elective culture of the microbes of the slimy
lactic acid fermentation.

There is reason to assume that the slime producing lactic acid ferments
are the normal forms and the non-slime formers, species or variants
derived from them. Hence, the former deserve to be considered in
the first place.

(23)

To the typical slime producing species belongs the microbe of the
long whey (Lactococcus hollandiae), which particularly before the
introduction of pure cultures in the dairy industries, played.an
important part in the fight against cheese defects in North-Holland,
and is still here and there practically used to that end.

Further I have found that the popular food known in Norway
as “tjaette molken”, a sample of which I owe to the kindness of
Mr. Pennink of Rotterdam, consists of milk, in which the long whey
microbe, or at least a nearly allied form, secretes acid and slime.

Other materials in which these and allied microbes occur, were,
till now unknown, evidently because of the uncertainty about
culture conditions and the lack of a good accumulation method.
Taking the idea “species” in the broad sense, I think there is no
objection as to bringing the group of forms, found in the manner
described below, to the species just mentioned.

Starting from the following properties, the most characteristic for
the microbes ef the slimy lactic acid fermentation:

ist. The optimum temperature for their growth is at 20° or lower,

2nd. they can only compete in anaérobic cultures with the other
microbes, and

3rd, the medium must consist of substances containing peptones

as nitrogen and carbonhydrates as carbon source, I succeeded in
finding a method giving rise to their accumulation.
_ It is true that I only examined a single material in this way, the
common baker’s yeast, but the investigation of the soil of fermenting
or fermented substances, in short of materials of most varying de-
scription may be done in a corresponding way.

The experiment is arranged as follows.

Into a 30 ec. closed bottle, filled with maltextract, to which is
added */,°/, of peptone sieeum and which contains c.a. 10°/, extract,
a little pressed yeast is introduced, for instance '/, gram. Placed at
a temperature of 18 to 20°C. a quiet fermentation sets in, which is
allowed to continue 24 to 72 hours, whereby, because of the absence
of air the yeast hardly grows, but the various lactic acid ferments
reproduce quickly. Other microbes do not develop. Not seldom in
this first culture have the contents of the flask already become
somewhat slimy.

Whether this be the case or not, a not too small quantity from
it is transplanted into a bottle quite filled with boiled, air-free milk,
for instance */, ¢.c. into 30 e.c. of milk. At the same low or a some-
what higher temperature only a flora of lactic acid ferments can
develop, and if the slime-forming species is present, it is the most

vigorous. We then see that after 2 or 3 days the milk become
slimy and by inoculation into milk whey, a culture will start which
sometimes differs so little from the ordinary long whey, that we
may conclude to an identity of species.

Of course, I cannot foretell that such microbes occur in any yeast
sample taken at random, hence | must add that for my experiments
I used pressed yeast from the Yeast and Alcohol manufactory at Delft.

Such a culture in milk differs it is true in some respects from
„what is obtained by growing long whey from North Holland in milk,
as in the former case short rods or oblong cocci are observed, and
in the latter, shorter forms more reminding of the common micrococei.

I expect that by repeating this experiment various deviating
varieties will be found, and by application of the method to other
infection material perhaps new species of slime laetie acid ferments
may be discovered.

4. Elective culture of the lactococci of cream souring.

As the lactococei and lactobacilli, which both occur in spontaneously
or otherwise soured milk, in cheese, and various other dairy products,
seem to grow nowhere better than in milk,*) the culture experiments
here considered, should be taken with milk.

In order out of the innumerable microbes of the crude milk
practically to come to a pure culture of Lactococcus, the management
is as follows.

The optimum of growth is at 380° C. or lower, and as all species
of Lactococcus (like those of Lactobacillus) are strongly microaéro-
philous, sometimes even anaërobie (i.e. cannot grow at all at full
atmospheric pressure on plates), it is best to cultivate in absence of air.

A stoppered bottle is quite filled with commercial milk and placed
at 30 C. After 24 hours or somewhat later a Lactococcus-flora
begins to replace the other microbes, while not seldom a feeble
fermentation of B. coli or B. aërogenes has preceded.

After one or two re-inoculations under the same conditions, but

1) It is not impossible that there are *peptones’ which, together with glucose
or lactose, are still better food for the lactic acid ferments than milk itself, How
very differently peptones of dissimilar origin act on microbes is easily observed in
yeast species which in general grow better on “plant peptones” than on “animal
peptones’’. The introduction of the word “bios” to denote those nitrogen compounds
which are best fit as yeast food, is an attempt to circumscribe the peptoneproblem
has been given. The relation between “peptones’” and the lactic acid ferments is
still closer than between these substances and the different yeasts; but it is here
not the place to insist on this point.

(25)

into well boiled milk, which is done by transferring a trace of the
first culture to the second bottle, quite filled with boiled, air-free
milk, and so on, the lactococci free themselves completely from all
foreign microbes and a material is obtained, which displays a high
degree of purity and of practical usefulness. If the acidifying power
of the microbes obtained by the experiment is lower than wished
for, for example 5, whilst 8 to 10 ¢.c. of normal acid on 100 cc.
milk is desired, this must be attributed to the accidentally present
stock. It is necessary then to begin a new experiment, following the
same way as described, or it can be advisable to perform the first
inoculation with some good butter-milk.

As buttermilk, however, very often contains lactose yeast, in the
latter case a vigorous alcohol fermentation may at first be expected
in the bottles. But it soon disappears by inoculation into milk rendered
free from oxygen by boiling.

If in this way, thus in absence of air, the culture has been
prolonged, a fairly constant acid amount is obtained at each renewed
inoculation, which does not, however, rise above 10—12 ¢.c. normal
in 100¢.c. of milk. On whey agar or whey gelatin plates the growth
at the air of the thus obtained lactococci is different, as sometimes
a great many aêrobie colonies arise, which cause the same acidi-
fication as the cultures in the bottles, while in other cases nothing
is seen to grow.

The first gronp corresponds with the usual commercial forms
destined for the souring of cream, which commonly consist of
cultures of the microbes dried on milk sugar or starch; moreover
there are commercial aërobie pure cultures in milk or whey, which
are sold in bottles.

The second group, that is the cultures non-growing at the air,
may still better be used for the cream souring than the aërobic
stocks, as the anaërobic forms of Lactococcus show more aptness to
secrete the flavour desired in butter, than the more aérophilous
bacteria. *)

As well for this reason as for the great purity of the cultures made
after this “bottle method”, there is reason to prefer them in dairy
work to the commercial so-called pure cultures, which for the greater
part are by no means pure, but mostly contain, besides lactococci,
numerous contamination germs of the milk. In consequence of
frequent investigations I can therefore advise interested persons to
use the here described method. Best would be if these cultures were

1) Of late I have also met with such like anaërobie lactic acid bacteria in com-
mercial preparations,

( 26 )

prepared in the creameries themselves, but also the sellers of pure
cultures, by following the above prescriptions, will obtain a better
product than by the more usual way of selection of aërobie colonies.
Besides, the management is simpler and more scientific.

To my opinion there is no satisfying ground to class the aérobic
and anaërobie forms of Lactococcus, which can be produced after
the said method, in separate species. They are but variants of one
and the same species, whose oxygen requirements are different, which
also appears from the fact that in the course of time one and the
same stock shows considerable differences with regard to the said
relation. Moreover, by several isolations all transitions between the
more or less aërobie stocks may be obtained.

Finally it should be borne in mind, that by applying the “bottle
method’ at low temperature, in rare cases instead of a culture of
real Lactococcus a Lactobacillus is obtained, which may likewise be
had by colony selection from cheese. Using this Lactobacillus 1 did
not observe at all the pleasant flavour of the anaërobie lactococci,
so that I do not recommend these bacilli for cream souring.

5. Elective culture of the lactic acid bacilli.

If milk, soured spontaneously by Lactococcus lactis, or still better,
buttermilk,- is placed at exclusion of air in a thermostat of ca.
40° C., the original acid amount of 8 to 12 e.c. will in most cases
rise after some days to about 18 or 20 ee. per 100 ec. of milk.
For this experiment it is best to use a stoppered bottle of 250 to
300 ce. capacity quite filled with milk. If for the first experiment
a smaller quantity is used the result becomes uncertain, either by
the disturbing influence of the air, or by the scareity. of the inferred
bacteria.

The first change commonly observed in the sour milk is a mode-
rately vigorous alcoholic fermentation, caused by the hardly ever
lacking lactose yeast, and at the same time a complete separation
of the caseine, which is driven to the surface of the liquid by the
carbonic acid.

Microscopically we find that the lactocoeci present at first, are
succeeded by more lengthened forms, truncated at the ends and
united in chains, whereby the acid titer may considerably diminish,
for instance in 12 hours from 8 ec. to 6 @.¢., which should be
ascribed to the lactose yeast, for which the free lactic acid can
serve as carbon food. By transference, at exlusion of air, the lactose
yeast, as in the elective culture of lactococci, is rapidly dispelled
by the then stronger lactie acid ferments.

(20)

Real lactobacilli mostly appear after 2 or 3 days and then the
acid rises rapidly parallel to their multiplication to 20, even to
25 ee. normal per 100 ce. of milk. When this degree of souring
is reached, there is usually no further increase observed, not even
after several days, and whenever this does take place, there should
be thought of aération, by which the growth of vinegar bacteria
and acetic acid formation from alcohol, have become possible.

The pure culture of lactobacilli is sometimes easy, in other cases,
with more anaérobic stocks, it is more difficult. Always, however,
it is troublesome with these pure cultures to obtain a considerable
souring in milk and there is most chance of suecess (but even then
the success is not quite certain) by souring lactobacilli together with
Lactococcus which serves for the first souring to 8 ¢.c. If this amount
of acid is reached, and the pressure of the oxygen, sufficiently dimi-
nished, which in a stoppered bottle is likewise brought about by
the presence of the lactococei, the lactobacilli can develop and cause
further souring.

From the observation that by the deseribed experiment more or
less perfectly anaërobie lactobacilli are obtained, follows that here
as in the ease of Lactococcus different varieties may be expected.
At a continued research the differences prove to extend over other
characteristics also and may become so great, as well from a morpho-
logie as from a physiologic point of view, that it seems necessary
to create new species.

Especially the dimensions of the rods, the more or less branched
state of the colonies on agar plates, the slime formation, the either
or not originating of carbonic acid as fermentation gas beside the
lactic acid, and the action or non action on different sugars give
rise to this consideration. The deeper however we enter into these
distinctions, the more troublesome it becomes to devise such deserip-
tions as are wanted to present to other investigators an image of
the results of our own researches; so numerous become the forms
which nature, or better perhaps, which culture produces, and so
slight are the differences by which these forms are distinguished,
if we do not confine ourselves to the extremes of the groups. *)

If the latter is done, two distinct forms call attention, whieh ona
former occasion I named’) Lactobacillus caucasicus and L. longus.

1) For further information see W. Heyneserc, Zur Kenntniss der Milchsäure-
bakterien. Sonderabdruck aus Zeitschrift für Spiritusindustrie. No. 22--31, 1903;
Parey, Berlin.

2) Sur les ferments lactiques de l'industrie. Archives Néerlandaises. Sér. 2, T. 6,
p. 212, 1901.

( 28 )

Without attributing a special value to this classification I yet wish
to keep to it as I think that the facts to be mentioned are fairly
well comprised thereby.

The longusgroup is characterised by its not acting on maltose,
so that in maltextract no, or very little acid it formed, but it does
decompose milksugar. In milk the forms of this group, if grown
after a previous culture of Lactococcus which has produced 5 to 8 c.c.
of lactic acid per 100 ee. of milk, will once more produce a certain,
even a like quantity of acid so that ca. 16 c.c. may be titrated, the
latter amount being however an exception. Generally no evolution of
carbonic acid is observed but sometimes it is, and then so much gas
can arise that a milk beverage is acquired foaming like champagne.

By a series of transitions, the longus forms obtained at 40° C.,
are joined with lactobacilli which at a lower temperature find their
optimal vital conditions, but which are rarer in milk.

The caucasicus group comprises those lactobacilli, which are able,
independently of lactocoeci to produce in milk a very high acid
formation. At 37 to 40°C. it is possible after three days of their
action to titrate 20 to 25 ¢.c. of normal acid per 100 c.c. of milk.
When that amount is reached further acid formation stops. In this
case, too, there is a parallel form which, beside much lactic acid,
also evolves ecarbonic acid. What by-product is then formed from
the lactose molecule beside the carbonic acid is not yet clear; pro-
bably it is aethylalkohol. G. Brrrranp has proved that these ferments
can produce succinic acid. They greatly owe their notoriety to their
presence in kephir, which subject I have touched before'). Later
however I have come to the conclusion’) that their distribution is
by no means restricted to kephir only, but that they also oeeur in
our climate, sometimes in buttermilk, in cheese and even in common
baker’s yeast.

6. Yoghurt and maya.

The use of soured milk as drink and food is so familiar to many
Eastern countries, and dates from so remote an antiquity that there
can be no doubt as to its favourable effect on health, and the esta-
blishment of various societies which try to popularise new preparations
of that nature, seems to prove that the attention of the Western
nations begins to be drawn towards it.

Both in the preparations of the Eastern nations and in those of

1) Sur le Kefyr. Archives Néerlandaises. T. 23, p. 428, 1891.
2) Ferments lactiques de l'industrie |. c.

( 29 )

industry are always found lactic acid ferments of the genus Lacto-
bacillus, mostly of Lactococcus too. These lactic acid ferments alone
determine the character of the “leben raïb” of Egypt, ’) of the
“yoghurt” of Bulgary,*) and probably also that of the “prostokwacha”’
and the “véranetz”’ of Russia, which Mertcunikorr mentions. In the
“kephir” of the Caucasus, the “koumys” of Central Asia, *) and the
“mazun” of Armenia, *) occurs moreover, lactose yeast, which may,
however, under certain circumstances be wanting, without the
character of these beverages being lost. All other microbes, whieh
are mentioned in literature as occurring in the said beverages or
their ferments, such as Qidium, Mucor, other moulds, torula, red
yeast, vinegar bacteria, butyric acid ferment, proteolytic bacteria,
are only present by deficient preparation, so that it may be said
that in all examined cases a pure lactic acid fermentation proves to
be the wanted process, whilst eventually also an alcoholic ferment-
ation is wished for or suffered °).

Hence, in the commercial preparations which start from yoghurt,
only lactic acid ferments are cultivated. I have in particular inves-
tigated the products of “Le Ferment’, mentioned beneath, as also a
substance, sold as “maya” or Bulgarian ferment,") to which my
attention was drawn by Dr. De Lint at Scheveningen. Here I will
shortly describe the latter preparation.

It consists in a yellowish strongly acid reacting powder, composed,
after chemical, microscopical and bacteriological examination, of caseine
lactic acid, lactose, fat and lactic acid bacteria; it is evidently nothing

1) Annales de l'Institut Pasteur. T. 16. p. 65, 1902.

2) MassoL et Gricororr, Revue médicale de la Suisse romande 1905 p. 716.
Bertranp et Wersweirer, Action du ferment Bulgare sur le lait. Ann. de l'Institut
Pasteur, T. 20, p. 977, 1906.

3) For Kephir and Koumys see Weremann in Larar Technische Mykologie. Bd. 2.
p. 128. 1905.

4) Centralblatt für Bacteriologie, 2te Abt. Bd. 15, p. 577, 1906.

5) The study of literature leads at first view to a quite other result, as many
microbiological descriptions are made by beginners, not sufficiently acquainted with
the properties of lactic acid ferments, and who have attributed an exaggerated
weight to the different kinds of infections named above.

6) On the bottle stands: Maya bulgare, Société de la maya bulgare, GARNIER
& Co., Paris, 16 Rue Popincourt. The Société de Pury, Montreux, brings into
commerce a ferment of the same nature under the name of “maya bacilline”,
and the Société HenneBerG, Geneva, a liquid preparation as “lacticose”. Besides
there are to be had in Paris Lactobacilline de Mercunikorr in “Le Ferment”,
Fournisseur de |’Assistance publique, 77 Rue Denfert-Rochereau, who sells also, the
“Biolactyle” of Fournier and the “Bacilline paralactique” of Tisster (the preparations
of this firm make a very good impression).

(30 )

else but yoghurt evaporated at low temperature, perhaps in the
vacuum. As to the preparation of the “yoghurt” itself by means of
this ferment, it is done as follows and gives good results.

Milk is evaporated to half its volume, cooled to a (not nearer
indicated) temperature, for which 1 took 40°, as 45° proved too
high and 37° too low, and on a quantity of 250 cc, so much
ferment is strewn as can be put in a little spoon distributed with the
flacon containing the maya. After 6 hours already the eurdling of
the milk becomes perceptible, after 24 hours I titrated 12 c.e. and
after 3 >< 24 hours 20 to 23 ¢.c. of normal lactic acid per 100 ec.
of the evaporated milk, which by that time is changed into yoghurt.

As a titer of 10 ce. corresponds to 0.9°/, of lactic acid, the
titer 20 corresponds to somewhat less than 2°/, of the vanished
milk sugar. Supposing that the evaporated milk contains about 9.6 °/,
of milksugar it follows that 7°/, of milksugar has remained un-
decomposed. The caseine is of course curdled and the whole has
changed into a solid but soft, sweet tasting mass.

The evaporation of the milk is not necessary, but when prepared
from ordinary milk, the yoghurt remains more liquid, and as the
acid formation is equally strong as in evaporated material, there
remains about 2.5°/, of the original 4.8°/, milksugar, so that
in this case the taste is much less sweet.

If in the said way yoghurt has been prepared in the presence of
air and is re-inoculated into a new quantity of milk, then the result
is yoghurt of the same acidity as the first time. But after 3 or 4 trans-
ferrings difficulties arise and only with great quantities of infection
material further souring can be obtained. The experiment succeeded
much better when the yoghurt was prepared in a quite filled stop-
pered bottle; the transferring can then be longer continued, but I
do not know whether this will do in the long run. Evidently the
difficulty here, too, is the right choice of oxygen pressure, whereby
the inferred lactic acid bacteria preserve their properties unchanged ;
and this difficulty is still increased by the presence of two different
forms, with unequal optima as to temperature, and probably as to
oxygen pressure also.

One of these forms is again a Lactococcus, the other a Lactobacillus.

The former deviates somewhat from the common Lactococcus, in
as much as it is more extended, reminding of short rods, and further-
more by possessing a higher optimum as to the temperature whereby
the growth is quickest, which optimum proves nearer to 37° than
to 30° C. Hence, this form is as it were a transition to a Lactobacillus.
Isolation on milk agarplates was very easy, even at 30° U,

(31)

As to the second species, the Lactobacillus proper of yoghurt,
it was troublesome to grow its colonies on milk agar plates, but
on malt extract agar it was more easily obtained. In literature
it has been named Bacillus Massol by Gricororr, but I think that
name superfluous as the characters correspond fairly well with those
of the kephir bacilli which also oecur in our country; for instance,
as has been observed before, in yeast and buttermilk. Sown in
slightly soured milk this Lactobacillus can produce the strong acid
mentioned above, without the help of other bacteria. Evolution of
carbonic acid does not take place and the product has a very pure
taste, although a beginning of fat cleavage seems inevitable at such
a high amount of acid.

Metcunikorr ascribes a very favourable influence to the use of
yoghurt, as it diminishes the phenomena of autointoxication starting
from the intestinal canal, and he explains this effect by accepting
that the Lactobacillus, after passing the stomach, continues active
in the intestine, and checks ') the formation of the obnoxious products
which derive from other bacteria species. I do not doubt but this
may be brought about by the lactic acid, but I think it highly impro-
bable that the presence of the lactic acid bacteria from the yoghurt
themselves should be required in tbe intestine. I think this conclusion
is necessary, first because, without the use of yoghurt or other soured
milk preparations, there occur in the intestine lactic acid ferments
of different species, and second, because the conditions for lactic acid
formation by the active ferments are wanting or must at least be
very unfavourable there.

As to the first point I refer to the following experiments.

If sterile milk is infected with faeces of different origin (man,
cattle) and treated as described for the elective culture of Lactococcus,
without access of air and repeatedly reinoculated at a temperature
between 23° to 26° C., the said genus of microbes is indeed obtained
by which as good cream souring can be obtained as with the pure
cultures prepared in the before described way.

If sterile milk is infected in a corresponding way and exposed
to the conditions wanted for Lactobacillus, that is, if cultivated in
absence of air at 40 to 45°C., a fermentation of coli will first arise
and later or simultaneously a butyric acid and no lactic acid fermen-

1) Quelques remarques sur le lait aigri. Rémy, Paris, 1907. In this paper MercuntKorF
gives many assertions but no decisive experiments. Besides, his bacteriological
elucidation, p. 26, is not clear. The elaborate and interesting work of Dr. A. Compe,
L’autointoxication intestinale, Paris 1907, is neither quite convincing from a micro-
biological point of view.

(32)

tation, which latter would inevitably arise if the lactic acid ferments
were present in a rather considerable number. Only by repeated
transferences Lactobacillus is produced, which after some inoculations
forms 10 to 13 cc. of normal acid.

Hence, there is no doubt as to the presence of Lactobacillus and
Lactococcus in normal faeces. They are, however rare, and belong
by no means to the intestinal flora proper, like coli, but to the
accidental flora, which consists of all that is introduced and is able
to pass the stomach and intestines alive, without multiplying. There
seems to be no cause to attribute any important influence to this fact.

As to the second point, why in the intestinal canal the conditions
for the growth of the active lactic acid ferments are wanting, it is
that in the contents of the intestines an alcalic reaction exists, and
that the sugars which are formed or introduced there, in as much
as they are not absorbed by the intestinal wall, will surely be
attacked by col, which in these circumstances is the stronger and
dispels all competitors.

Why coli (and aërogenes) so completely defeat the lactic acid
ferments, should, to my opinion, be explained by the important
fact, not sufficiently considered in literature, that the first men-
tioned species can quite well live on peptone only, and multiply at
its expense, while the active lactic ferments completely lack this
faculty and, beside peptone, require a carbonhydrate for food.

If, moreover, it is borne in mind that coli in the presence of a
carbonhydrate can also feed on other sources of nitrogen than pep-
tone, for example on amines and ammonium salts, whereas the active
lactic acid ferments cannot, and decidedly want peptones for nitrogen
food, it is clear that for the different forms of col practically every
where in the intestinal contents a good feeding material is present,
and that in the few localities where it would also be sufficient for
the lactic acid ferments, it will be seized upon by col. Where
only peptones occur, coli will moreover increase the already alcalic
reaction of the contents and thus, not for itself but for the lactic
acid ferments, render the conditions of life more unfavourable.

Hence it seems evident why in the intestinal canal a coliflora can
exist but no lactic acid flora.

The yellow coloured faeces of babies during the lactation period
may be alleged to support this view. They consist microscopically
almost solely of bacteria, for far the greater part of common coli-
bacteria), among which there occur real lactic acid ferments, but

1) For different children not always the same varieties; sometimes, for instance
non-fermenting forms reminding of Lactobacillus, for which I before indeed took
such bacteria.

(33)

as in the case described before in quite an inferior number. This
fact acquires a special significance when we consider that EscHprIcH,
the discoverer of the colibacillus, has proved that this condition exists
directly behind the baby’s stomach, where coli and aërogenes are
predominant which, in reference to the preceding, necessitates the
conclusion that even at those portions of the intestines where a
lactie acid flora should first be looked for, it is evidently unable to
sustain itself.

There is no doubt but here too, the strongly disinfecting action
of the stomachal hydrochloric acid plays a part, as this acid, at a
much lower titer than the lactic acid checks the growth of the lactic
acid ferments, but hence can be neutralised by much less alcali,
which is not indifferent to coli, which produces aleali.

In so far as the theory of Mercunikorr and Compe is right, after
which yoghurt or other sour milk preparations counteract the auto-
intoxication from the intestinal canal, it seems certain that here
should more be thought of the influence of a milk diet and the free
acid taken up with the milk, than of a specific intestinal flora. But
in how far the apparently proved decrease of indol and phenol,
whose quantity is considered as determining the degree of auto-
intoxication, deviates, at a nutrition with soured milk preparations
instead of meat, from this decrease when non-soured milk is used,
— to my opinion the real core of the question, — has not been
considered by the said authors.

Admitting that the soured preparations really deserve to be
preferred, I think that especially in Holland, it must be possible
with good buttermilk in as simple a way to reach the wished for
end, as with the various exotic ferments, whose descriptions give
the impression that the preparators are but imperfectly acquainted
with the general phenomena of the lactic acid fermentation in milk.

Although J see no fundamental difference between the use of
buttermilk and yoghurt, it is certain that the latter may be prepared
in a very simple way under medical control, and hence, to my
meaning, deserves to be recommended in certain cases.

Summarising the preceding I come to the following conclusion.

In milk three chief forms of lactic acid fermentation, determined
by temperature, are to be distinguished, namely at very low tempe-
rature, the slimy lactic acid fermentation; at a middle temperature
the common lactic acid fermentation caused by Lactococcus; and at
higher temperature the lactic acid fermentation by Lactobacillus.

The elective culture of the microbes of the slimy fermentation,
succeeds by cultivating bakers yeast in absence of air between 15°

3

Proceedings Royal Acad. Amsterdam. Vol. X,

(34)

and 18° C. in malt extract and transferring to boiled milk or whey
at a somewhat higher temperature. The acidity obtained remains low
and amounts to 3 to 5 cc. of normal acid per 100 c.c. of milk.

The elective culture of Lactococcus takes place by allowing milk
to sour in a stoppered bottle at 20° to 25° C. and transfer it
repeatedly to boiled milk at that temperature. The thereby obtained
stocks of Lactococcus lactis are mostly anaérobic but specifically not
to be distinguished from the more aérobic forms which may be
produced by the same experiment. The acid mostly remains at about
8 cc. of normal acid per 100 c.c. of milk, but may become 10 to
dee:

The elective culture of Lactobacillus succeeds best by cultivating
buttermilk in absence of air at 37° to 40° C. and inoculating it into
boiled milk, at 30° C. and higher, the acidity can rise from 18 to
25 ¢.c. of normal acid per 100 e.c. of milk.

The active lactic acid ferments are very variable; as factors of
hereditary constant variation are recognised cultivation at too high
or too low oxygen pressure, and cultivation at a temperature above
the optimum of growth.

Lactic acid ferments do not lack in the intestinal flora, but play
there an inferior part.

A considerable difference between Eastern and Western lactic acid
ferments does not exist.

Yoghurt and other such like sour milk preparations deserve the
attention of hygienists.

Chemistry. — “On the course of the plaitpoint line and of the
spinodal lines, also for the case, that the mutual attraction of
the molecules of one of the components of a binary mixture
of normal substances is slight’, by Mr. J. J. van Laar. (Com-
municated by Prof. H. A. Lorentz).

(Communicated in the meeting of April 26, 1907).

1. In the latest volume of These Proceedings ') Dr. KrrsoM (also
in conjunction with Prof. KAMBRLINGH ONNrs) stated some important
results, inter alia concerning his investigation on the special case that
one, e.g. @,, of the two quantities a, and a, is very small; which is

1) KAMERLINGH Onnes and Keesom, These Proc., Dec. 29, 1906, p. 501—508 [On
the gas phase sinking in the liquid phase etc. (Comm. 965)]; Keesom, Ibid. p.
508—511 [On the conditions for the sinking etc. (Comm. 96c)]; Kresom, Ibid.
March 28, 1907, p. 660—664 (Comm. 96c continued); KAMERLINGH Onnes and
Keesom, Ibid. of April 25, 1907, p. 786—798 [The case that one component is
a gas without cohesion ete. (Suppl. N°. 15)].

(35)

realised, among others, for mixtures of He («,) and H, (a). In these
papers, particularly in the last, a particular kind of plaitpoint line
has been repeatedly mentioned, viz. one passing from the critical
temperature 7, called “third” by me (Krrsom’s 7), to the highest
of the two critical temperatures 7’, (Kersow’s 77, ).

Now the theoretical possibility of such a course of the plaitpoint
line, i.e. of one of its two branches, has been first brought to light
by me in a series of Discussions on this subject’). Not only for the
special case 6, = b,, for which among others, fig. 1 of June 21, 1905
holds, but for all possible cases (see specially TeyLer I and II). We
found that such a course will always be found, when the ratio of

gal

the two critical temperatures 6 = a is larger than the value of this

ratio, for which the plaitpoint line has a double point. This type was
called type I by me. (see also fig. 1 of Oct. 25, 1906).

The case that a plait starts from C, to C,, or also at the same
time from C, to C, (when there is a minimum temperature in the
plaitpoint line) is not new (see K. O. and Kresom, p. 788 below),
but has been before described and calculated by me in all particulars.

The double point in the plaitpoint line, discovered by me in 1905
(June 21), did not only give the key to the possibility of such a
course, which had already been ascertained for mixtures of water
and ether, of ethane and methylaleohol ’); but also the connection

1) These Proc. May 25, 1905, p. 646—657 ; Ibid. June 21, 1905, p. 33—48; Ibid. Aug
17, 1905, p. 144—152 (Cf. also Arch. Néerl. 1905, p. 373—413); Ibid. Jan 25, 1906, p.
578—590 (Also Arch. Néerl. 1906, p. 224—238) ; Ibid. Oct. 25, 1906, p. 226—235.
Further Arch. Teyrer (2) X, Première partie, p. 1—26 (1905); Ibid. Deuxième
partie, p. 1—54 (1906). Henceforth I shall refer to papers in these Proceedings
by mentioning the date, to papers in the Arch. Teyrer by putting Tryzer I or II.

2) I do not quite understand why in cases as for He Hg the plait considered
is particularly called a “gaspluit”. With exactly the same right the two coexisting
phases might be called liquid phases, expecially at the higher pressures in the
neighbourhood of the point Cp. With reference to water-ether, ete. we speak of a
gas phase and a liquid phase before the three phase equilibrium is reached, i.e. at
higher temperatures; and when at lower temperatures the equilibrium mentioned
has established itself, of two liquid phases. The “gas phase” is then determined
by the branch plait of the original transverse plait (which latter has now the
peculiar shape directed towards Cp in the neighbourhood of the axis « — 0. But
I acknowledge that this is perfectly arbitrary, it being difficult to indicate where
the pressure is high enough on such a plait to justify us in speaking of liquid
phases. Would it not be better to follow here van per Waats’ terminology, and
speak of fluid phases, and to call the two phases liquid phases at temperatures
where the three phase equilibrium is found? Otherwise in this latter case — keeping
to K. O. and Kegsom’s terminology — we should have to speak of three coexisting
gas phases, a rarefied one and two very dense ones, which latter, however, we
should never refer to as gas phases in the perfectly identical case of water + ether,

3%

(36 )

of the different series of hidden plaitpoints, etc. ete., as has, inter
alia, been indicated in Jan. 25, 1906 (cf. also Teytur II). Dr. Kersom
does not mention that in his figure I (loc. cit. p. 794) besides the
plaitpoint line from A, to A, drawn there, there always exists
also a second branch, which runs along the v-axis in the neighbour-
hood of «1 from the point where v=—=b to K, — and which
gives rise to a three phase equilibrium at lower temperatures, as this
has been explained by me. (also in Jan. 25, 1906 and Terrer II).

The fact whether a plait extends in the way mentioned, depends
therefore, as we said before, im the first place on the fact whether

1

b, a, 4 ihe Ps
the values of — and (~ of 6 = ander ) are such that 6

b, a I. Py
is larger than that value of 6 for which the plaitpoint line has a
double point with given value of a. The knowledge of this double
point, being therefore of so great importance for the distinction of the
different types, I have carried out in Teyrer I the lengthy calculations
required for this, and drawn up the results obtained in tables. [See
also Terrer II, where fig. 22 (p. 30) represents the results graph-
ically |.

Hence not the fact that Pr, > 7), [with perfect justice Kensom
says in a footnote (loc. cit. p. 794) that 7, may also be < Zijn
but only the fact that lies above the double point value, determines
the considered course of the plaitpoint line. (See also Oct. 25, 1906,
where I summed up most of the results obtained by me).')

It is true that Kresom mentions in a note (loc. cit. p. 786) that
I have examined the plaitpoint line for the case a, — 0, but this
statement is not quite complete, for I have not only examined such
a plaitpoint line for this particular case a, = 0, which I cursorily
mentioned in a note (June 21, 1905, p. 39), but for all cases. Quali-
tatively the plaitpoint line C, C, for the case a, = 0 is not distinguished
in anything from that for the case a, > 0 (provided it remain in
the case of type I), hence there was no call for a special investigation
of the form of the spinodal line and of the plait for a, — 0, this
having already been done for the general case. Moreover Krrsom
himself considers later on the case a, small, and no longer a, = 0,
which of course does not occur in practice.

Also the equation of the spinodal line (for molecular quantities) :

RTv? = 2 (1—2a) (v Wa, — 6, Va)’ + 2a (wv Wa, — b, Ya)’,

1

1) Prof. van perk Waats says (These Proc., March 28, 1907, p. 621), “that as yet no
one has succeeded in giving a satisfactory explanation of the different forms (of
plaits).”” 1 think I have done so to a certain degree in my papers of 1905—1906,

(37)

given by Krresom, had already been drawn up by me (May 25, 1905,
p. 652) in the identical form :

Relves, E (Le) (av — B Ya)? Ha (v—b)' |,
where a= Wa, — Va, and B=), — 4,.

2. The answer to the question whether the plait extends from
C, to C, with or without double point in the spinodal curve, i.e.
with or without minimum plaitpoint temperature, in other words the
answer to the question whether the plait passes from C, to C, un-
divided, or whether two plaits extend on the y-surface, one starting
from C,, the other from C,, which meet at the minimum tempera-

p ile . Ji
ture — depends on the value of IS (on which also ET
1

depends)

0
for given value of a The condition for this I derived in
Pi

Aug. 17, 1905, p. 150, and Jan. 25, 1906, p. 581. In the summer of
1906 I calculated the place of the minimum itself (Cf. Oct. 25, 1906,
234, line 18—16 from the bottom), but seeing that the paper, which at
that time had already been completed and sent to the editor of the
Arch. Teyler, has not yet been published (it may be even some time
before it is), | think it desirable to publish already now the calcu-
lation in question.

Like the calculations of Krrsom, VERSCHAFFELT and others, it starts
from the supposition that « and 5 do not depend on v or 7’, and
that these quantities may be represented by

a; =[—2) Vo, Heal’ ; be=(1—a)d, + eb,

So in conformity with BerrHeLor and others we assume that
a, = Va,a,. Some time ago Prof. van per Waars raised his voice
against this supposition '), and it seems to me that there is really
much to be said in favour of a,, being im general not = Va,a,.
But as a first approximation the equation put may be accep-
ted, the more so as also the variability of 6 with v and T is
neglected. That in consequence of the assumption a,,—=WVa,a, the
left region, mentioned by van per Waars, would be compressed to
an exceedingly small region, can hardly be adduced as an argument
against this supposition; rather the fact that the attractions are
specific quantities, and that therefore ¢,, need not be = Ve,e,.

For the calculation of the minimum we start from the equation
of the spinodal curve, derived by us (loc. cit.):

1) These Proc., March 28, 1907, p. 680—631,

( 38 )

9

RT = — | « (1-2) (er — BVO) Hale). OD
v
or
: Zi
Ee zij =( = ’

by a
which with — = ee = passes into

v v a

9 2 2 3
pov aed 5 nw ne (1—z) oe) Hp)? (tro) Jao

b, +2
Va Va, rea Eh and = tale hard wo + anw = (1+ne).
i 4 7

For

a
Now the spinodal curve must show a double point, in other words:
a == (0) inal ==),
when / represents the second member of (la). The first equation
gives:
(1-2) (1-2)? — 2 (1-2) (1-2) nw +2 (pF) (1-y)*-2 (p+)? (1-y) nw = 0,
when for the sake of brevity zw (y+) =< and (1427) = y is

put. Bearing in mind that nw = , we get for the last equation :

fa
2a (1-2)
gta

The second equation yields, when in (da) the factor w is brought
within [ |:

2 (1-2) a—sr ~ 20 (le) + “| A

(1-2) (1-2)? 2(1-z) + 2(p+a) (1-y)*?-2 (+e) (I-y)e-=0. (a)

+ (g+2)? la ONE ie no) =
or

« (l—e) ce = 22 | + (g+a)? ao — 2y | =
1. €.
e (le) (1—z)(1—82) + (p+2)? I—y) (1-39) =0...- B)
From (6) we solve:
(lL—y) A1—38y)

# (1a) = — (+2) a

(1—z) (1—8z) 2

Also from (a):

a(1-
1-26 =| — pe) (ly) +2 (pe) A) + | (1-2)

(39)
or

1-20= praten

He Laer
-32)

when for «(1—v) the value from @ is substituted. Further reduction
yields :

he 1—3y ds
Le =| — 2(y+-2)(1—y)* + pane = at kan ;

or

2 (y+) (1—y) nld
— 22 = — - 1 —3z ;
en aw nn A

or

1 — 2

_ 2(g+2) (1 —y) (ly) — 82 (12)
a=); ì ERE ‘
From (a) and (9) follows, as (1—2z)* = 1 — 42 (1—a):

. (a)

ag op EDA perl [Ate]
ine ZENE 0 (1—z)* ; (1—32)' k
iser
LE yy) cede |— 1—3y)\(1—2)? 135 |
[amat astra |
Arrangement according to the powers of z yields for { |:
(3y?—y*) —6z (y + 4°) + 827 (1 + Sy + 2y*) + 2*(—8—12y) + 62",
or
y°(3—y) — Oz (L+y) + 82°(1 + Sy + 29") — 42° (2 + 3y) + 62",
which may be reduced to

(y—z)?(6z?8z+3—y),

so that we find:

1 — Meta) 6282+ 8--y)
a (2 (132)

from which may be solved:

(1—2z)4(1—82)? @)

AL) (yab Ber Sj

through which p + 2 is expressed in the two parameters y and z.

In consequence of this (8) passes into

~~ (1—z)*(1 —32)(1—3y) (3)
4(y—z)*(62*—824+3—y)’

from which w, may be calculated with given values of y and z

Then p„ is also known through (2), ie. expressed in y and z.
Further we now find for RT, according to (1a):

(~+2)n =

Em (1 — Em) =

9

( 40 )

act
ah
Or

as nw (p + wv) =z and

Qe? (1 —z2)*(1—82)

2 | (1
nw | —
ey A(y -

2)*(62?—

2)*(1—3z)(1— 34)

8z4+3—y)

(lz eee |
A(y — -2)(62*

8243 —y
(1 + nv) o = y. Reduction yields:

(NS

Rl

The expression between [ | is = 2(y—2), hence, - 3 ‚being 5

RT » —

B A(y — 2) (62? —8z +34)

E 32) 1—y)—(1 mer

we get:

“ew (1 —2)*(1—3z)
b, (y—2)(62*—82+3—y)

Let us express this in 7, the critical temperature of one com-

ponent. (7 < Ai) Wie tind:
Des 8a, 8 ag!
en
as en gy was put. At last we get:
a
i ws 27 w (1—z)*(1—3<2) (4)
T, 8 go? (y—z)(62?—824+3—y)
Now
z=no(g+e) 3; y= (l + new,
Ro which we solve:
z aig UZ
NW 3 JSO 5
pre pre
hence :
tz 1 an
o=y— = (pe) —x (5)
pt n z

Now w and n have been expressed in y and 2, as (p + 2), and am
had already been expressed in y and z by (2) and (3).
As further :

Sr Pe
l+n=14—-—-=>-=-,
b, b, kad
and
1 6
reagan ea UA 5
p Va, Va, Va
5 Tr = ly 4, Pa CNE
when Odin IT anc WI tp We iave also:
ENE i
Cheers)
iere
oe EE i Aly (6)
1 +» (1 + x)?

so that also 6 and a can be expressed in y and z

(ar)

Reversely we may now also think the corresponding values of
w, v and A, to be solved for any given pair of values of a and 6,
though explicitly this is impossible, so that we shall have to be
satisfied with the set of equations from (2) to (6).

The further discussion of these equations, particularly with regard
to the branch C\A of the plaitpoint line, in connection with the
longitudinal plait, will be found in the paper, which will shortly
appear in the Arch. Teyler. There the course of the pressure is also
examined, which we no further discuss here. [t is only desirable to
calculate the data for the “third” critical temperature (,, viz. x,
and 7’, — not because these data are indispensable for the following
considerations, but because Krrsom includes them in his considerations,
and it is profitable in any case to know something concerning the

1

relation — or —.
di Tik
: 5 5 b 8
As vb for the point C,, so y= — =1, and the equation of the

v
v,«a-projection of the plaitpoint line (Aug. 17, 1905, p. 146; Teyler
I and ID), viz.

(l—2z)*(1—2a—3a(1—w)nw)4-3(g+2)(1 —y)?1—2)1—22)+
(¢+a)(1—y)(—3y)

0,
a(1—2)
is reduced to
1—22,—3z,(l1—2,)nw, = 0,
or as y= (1 + nz)w, and hence w, = —,, to

+ ne,
(1—22,)(1+nz,)—32,(l—a,)n = 0,
from which follows:

pie oie lect Alpaca tE (0)

n
From this is seen that the situation of C, depends only on the

2

value of n or 1 +n = a
1

The corresponding value of 7’

, Is found from (la). For y=1

we find:
2a?w
BE == . vy (l—z,)(1—z,)’,
b,
in which w, = — and z, = nw, (p + 2u,).
+ Nk,
8 ap?

As T, = (see above), we have:

27 6

1

( 42 )
diy ea Oy,

Via ri

1

MORNESE a

Hence we can immediately calculate 2, and 7’, from (7) and (8)
for any given set of values of 6 and a, or @ and n.

3. For our case (a, small) it is now important to know, when a
minimum occurs in the plaitpoint line C, C,, when not. For this
purpose we shall derive the condition that the minimum is to appear
exactly in the point C,. Evidently this condition will then indicate
the limit between the two cases that there occurs a minimum in
the neighbourhood of C, or not — in other words whether the line
of the plaitpoint temperatures in C, descends first and rises later
on to 7, in C,; or whether there is an immediate rise from 7, to
T,. (We call to mind that with us 7, is always the highest of the
two critical temperatures 7, and 7).

Now y= : =. in the point C,, while «1. Hence equation
(2) passes into

‘ (1 —z)* (1-32) 81 (1—z)*
(p+1 ==, 72] (1 __»\2 (R~2 2 DUN TE (oa
4 ?/, (*/;—z)? (62*— 82+ -27/,) 16(2—3z)
from which follows:
9 (1—z)?
Gali x aoe
hence
a, 1 Wz 2
Viti ay ey i) = (a)
Va, p (1 — 32)?
From
z=nw(g+ 2)
follows furtl Ld
ollows further, as w = 5 EN RD oper and @==1:
n ive 8 n (1—2z)?
Aen iE ert
This yields:
lin 3 (l—z)
Te 205)
or
b 3 (1—<)?
len ) (6)

When we put:

the simple relation

= x
BETZ
follows from (a) and (4) after some reduction, in which the sign >
refers to the existence of a minimum in the neighbourhood of C,.

The condition (c) found by us is quite identical with that, which

(e)

f dT,
we derived before from the formula for a (=) found by us
i\ dz],

(Aug. 17, 1905, p. 150 and Jan. 25, 1906, p. 580). This condition was:

Aaa
Jeen
(8Va—1)?
, : be : 1 (dTx
With this difference, however, that we then considered rg
1 at

at C, whereas we have now examined the branch of the plaitpoint
te it

; l fdTx
line which starts from C,, so that we have to calculate (5)

ihe ze
and to derive the condition of the minimum from this. But it is
4 : Eu ; nee 1
immediately seen that it is obtained by substituting zi for 6 and —
x
for aw in the above condition.
So we find:
4
1 an
cee ;
6 3 2
ees i
Vx
or
V2(3—V 2)’
And it appears immediately that (c) is identical with (c'), when
a 6
we substitute — for x* and — for 2 in (c).
Jt Jt

This furnishes a good test, both of the accuracy of the above
derived formula (c), and of the condition (c’), derived by us before.

Let us now examine what values of 2 and « correspond according
to the condition (c), so that the minimum still appears exactly in C,.
The corresponding values of z required for the calculation of 7,
may be found from (a), giving:

(C225)

The subjoined table combines the calculated values. We call
attention to the fact that the minimum in the neighbourhood of Cs
can only belong to the branch C,C, for type 1 (9 > the double
point value), and never to the branch C,C, for type I or HI
(6 < the double point value). For 7, > 7, being put, the minimum
on CLC, cannot possibly lie at C,, but it can lie in the neighbourhood
OEG

EEE ee ae TTE
| E b, ii: sb T, 1 T, 6
g=}/5 oo el o | @ 0 a) 1 (Case a, = 0)
IJs 25 | 4112/,, || 325 169 0,279 | 364 | 1,12
1/, AG) 48 Genie Od 0,365 | 209 1,19
0 9 1 81 81 0,500 108 1/,
] Sa
ij 4 Ve 28 49 0,694 | — Zs
Al ay, | % 131/, | 36 0,800 | 303, | 2),
Foo 1 1/, 5 25 || 0,896 = 4
5/, 1/, Wi, 1 16 0,968 | 9,30 9,30

_ That is to say: for a gas without cohesion as one of the components
of the mixture (a, =0,* =) 2 would have to be larger than the
limiting value o, for a minimum to appear in the line C, C, in the
neighbourhood of C,. (Then 4/7, <1 would be at the same time).
For finite values of 2 this cannot be satisfied, and the line C,C,
proceeds with 7, > 7, without a minimum.

: > . a NN
For a gas with feeble cohesion, where e.g. r=|/2 = 6!
a
1

b 7 ;
== a must be > 1°/,,, fora minimum to appear. 70/7, is then < 1,19.
1
1
For He — H, “ is about 175, hence’ x = 13,2 according to an
1
estimation of Kensom (These Proc., March 28, 1907, p. 661; Ibid.
‘April 25, 1907, p. 794). To this corresponds according to formula (c) the
limiting value 2 = 1,29. Now Kersom estimated (loc. cit.) this value
at about 2 for He —H,, and 2 being > 1,29, there is a minimum
in the plaitpoint line in the case of He —H,. This minimum can be
fully calculated by the aid of the formulae (2) to (8). The value of
Tof, is then smaller than about 1,25.

(+5)

For x = 2'/,, 4 must be > °/,, and then To/r, < 2'/,. Etc, etc.

The larger therefore the value of a, — the smaller in other words
the value of x — the smaller also the limiting value of 4, above

which a minimum is to be expected, the sooner this will therefore
appear, and at comparatively large corresponding values of Zo/r,.

But as we already observed in $ 1, all this refers only to the
existence or non-existence of a minimum in the line C, C,. That this
line has the shape in question, depends on quite different circumstances
— viz., as I already showed in June 21, 1905, p. 33—48 for 6, = 4,,
and further extended to the general case in later papers (particularly
Teyrer I), it depends only on this, whether for the given value of x
the value of @ is found above that at which the plaitpoint line has
a double point or not. And the criterion for this is fig. 1 of Oct. 25,
1906 (see also Terrer ID. If we are above the limiting line DBPAC’,
we are in the region of type 1, where one of the branches of the
plaitpoint line runs from C, to C, (the other from A to C, — see
e.g. fig. 1 of Juni 21, 1905 and fig. 1 of Jan. 25, 1906). And Below the
limiting line we are in the region of type II (or III), where the
branches of the plaitpoint line are C, C, and AC,. But for all this
consult the papers cited.

April 1907.

APPENDIX. After I had written the above considerations, the Con-
tinuation of the last cited paper by K. Onnes and Kersom appeared
in These Proceedings, April 25, 1907, p. 795—798. There a condi-
tion is derived for the appearance of a minimum plaitpoint tempera-
ture, which is identical with that which I published Jan. 25, 1906
(formula (3), p. 581), at which result also Verscuarrett (These Proc.,
April 24, 1906, p. 751) arrived a month later.

For on p. 796 K. O. and Kersou give the condition (see formula (2)):

4 fa 1 See ee.
VASE NVT +967, |
a, 3

/

Now in my notation %/,, = '/,, (see above; I denote viz. the
component with the smallest value of a by the index 1; Kersom
does the reverse). Further %/;, = !/5, so that the above formula

passes into
Ve 1 ; =
aim

from which follows:

being my above formula (c). And concerning this we have just
proved that it is identical with my relation and that of VurscHAFFELT
(Jan. and April 1906), viz.
daa
Ga’

“which is of general application, irrespective whether the branch of
the plaitpoint line starts from C, towards C, or towards C,. As we
already observed, this expression holds on the side of the component I,
when 6 = 72/7, and + =?P:/,,, so for the branch starting from what
is point C, with me. For C, (Kersom’s K,) 6 and a must simply
be replaced by '/) and '/; (see above in $ 8).

So in my opinion the footnote on p. 795 in the paper by K. O.
and K. of April 25, 1907 is not accurate, for according to the above
the conclusion of VeRSCHAFFELT (and mine) does not require any
qualification, because the formula’) given by us holds for any
course of the plaitpoint line, irrespective of the fact whether the
considered branch runs from C, to C, or to C,. For the transition of
the two types takes place gradually through the double point of the
plaitpoint line, and hence the two types are analytically included

all
in the same formula, so that only one expression exists for Ee
which holds equally for the two cases. And if any doubt should
remain, this must be removed, when from the above the identity is

seen between the relation derived last by K. O. and K., and the

general one of VeRSCHAFFELT and me.

It will be superfluous to observe that the so-called (homogeneous)
“double plaitpoint” in the branch of the plaitpoint line C,C,, of
which K. O. and K. speak, is identical with the fully discussed
minimum and with the double point in the spinodal line, and should
not be confounded with the “double poimt’, found by me in the
(whole) plaitpoint line, where the two branches of this line intersect,
and which separates the two types I and II (or HD, the data for
which double point can be calculated for the general case only with
great difficulty. (see Teyler I).

1) In the footnote on p. 795 it says maximum temperature; this must of course
be minimum temperature,

(4c)

Astronomy. — “On periodic orbits of the type Hestia. By Dr. W.
DE Sitter. (Communicated by Prof. J. C. Kapreryn).

The problem, of which some particular solutions will be treated
here, is the following. Two material points S and ./, having the
masses 1 and pw, move with uniform angular velocity ’ == 1 in
circles in one and the same plane round their centre of gravity.
The constant distance S.J is adopted as unit of length. Another
material point /?, with an infinitely small mass, moves in the same
plane under the influence of the Newtonian attractions of S and J.
This is the problem which has (for u — 0.1) been so exhaustively
treated by Darwin in Vol. XXI of the Acta Mathematica. The parti-
cular solutions which are treated below are those in which the orbit
of P is periodic and its limit for Lim. u = 0 is an ellipse with a
small excentricity, described round S as a foeus with a mean motion
not differing much from 3. If this limiting orbit (i.e. the undisturbed
orbit) is a circle, then the solution is, in Porncark’s phraseology, of the

2x
first sort (sorte), and its period is 7’= a If the excentricity of the

undisturbed orbit differs from zero, the solution is of the second
sort, and the limiting value of the period for Lim. «=O is Lim.
T’ = 2a. These solutions of the second sort are at the same time
of the second genus (genre) relatively to those of the first sort.

The solutions of the first sort are the orbits of Darwin’s “Planet
A”. This family of orbits undergoes within the range here considered
a transition from stability to instability, which has been discussed
by PorncarRK in an investigation contained in the articles 383 and
384 of his “Méthodes Nouvelles” (Vol. IH, p. 355—361). The
results there reached will be derived here by a different (and, as it
seems to me, simpler) reasoning.

Darwin’s work also presents an example of an orbit of the second
sort, viz. the orbit figured by him on page 281 and designated as

v, = — . 337. Although Porcaré proves the existence of solutions
of this kind, he seems to have overlooked the faet that Darwin had
actually computed one of them.

These solutions and their stability I wish to consider from the
point of view of the general theory developed by Porcaré in the
first and third volumes of the “Méthodes Nouvelles”. The following
is a summary of those general theorems, proved by Poincaré, which
will be used here. They are true for every problem capable of
being reduced to two degrees of freedom, containing one variable
parameter, and admitting for each value of this parameter a finite

( 48 )

number of periodic solutions. It need hardly be mentioned that
their valency is restricted to a certain domain of the several variable
quantities of the problem, of which it will however not be necessary
to transgress the limits.

A periodic solution is completely determined by the values of the
parameter and of one constant of integration or “element”. The
periodic solutions occur in families, the members of which are classi-
fied according to increasing or decreasing values of the parameter.
These families may be graphically represented by curves ® (% , 8) = 0,
where x is the parameter of the problem and 3 the determining
element.

The stability or instability is determined by a certain quantity a,
which is by Porncaré called the characteristic exponent. If the

9 1

. . 7, ” . . . . & d
period is 7, then values of « differing by a multiple of — —, must
i ) g by T

be considered as identical. The following three cases are possible:
aT purely imaginary . . . . . the solution is stable

aT real … 23s... « .» = 4 thesolutionas even byamstdbie
aT complex, with imaginary part =27: the solution is unevenly unstable’).

A solution having the period 7 can as well be conceived to have
the period 7” =2 7. If it is unevenly unstable with reference to
the period 7’, it is evenly unstable with reference to the period 7”.

Within each family the exponent « and the period 7 vary conti-
nuously with the parameter x. The product «7’ and the differential
coefficient = become equal to zero for the same values of x. The

dr
curve ¢=O then either has a multiple point, or is tangent to a
line «== const. The family splits into two branches, or, which
comes to the same thing, two families have one member in common.
If (x, 8,) is the point representing this common member, then we
have the following rules.

The number of branches of the curve ¢ =O (i.e. the number of
families of periodic solutions) for «>>, differs by an even number
from the number of branches for * < %,.

The branches which part from the point (x, 8,) towards the direction
of increasing x are alternately stable and evenly unstable *). The

1) The names even and uneven instability have been introduced by Darwin.
Poincaré distinguishes them as instability of the first and second “classe”. The
relation of Darwin’s quantity ¢ to the exponent z is given by the formula 27’ = ize.

2) To avoid circumlocution I speak of “stable and unstable branches”, meaning
branches whose points represent stable and unstable solutions respectively.

( 49 )

same thing is true of the branches on which # decreases. The two

branches between which lies the part of the line x =z, on which

B<p,, are either both stable, or both unstable, and similarly the
ee linea AS
the period of one of the branches and 7” of another, and if 7’, and
She
7’
multiple, then «, 7", =0. If e.g. 7”,
even with reference to the period 7”.

two branches enclosing the other half of the line x = x

are the values of these periods in the point (%, 3,), then 7, and

0

are mutually commensurable. If 7”, is their least common

0

‚—2 7, then the instability is

As an illustration of these general rules I may be allowed to
mention a few of the simplest cases.

1. The curve 6=O is tangent to the line x=~x,. There are
two families, springing from a common member, which come into
existence at this value of the parameter. One of them is stable, and
the other is evenly unstable. An example of this is presented by
Darwin’s families. B and C of satellites.

2. The curve has a double point. Two families are “crossing”
each other, at the same time exchanging their stability.

3. The curve consists of one branch tangent to the line x = z,
and another branch intersecting the first in the point of contact.
The two families which come into existence at this value of the
parameter are both stable or both unstable. The third family, which
exists both for #>z, and for «<<, becomes stable if it was
unstable and unstable if it was stable.

The cases 2 and 3 are the only ones occurring in the present
investigation.

The proof of the above supposes that the problem can be reduced
to the second order, so that there are only two characteristic exponents
(He and —a). The choice of the parameter is determined by the
way in which this reduction is effected, or is conceived to be effected.
Darwin uses the integral of Jacosr for this reduction. Consequently
his parameter is the constant C to which this integral is equal. This
constant Cis a function of the two elements « and e. The first of
these can be replaced by the mean motion 7, or by the period
7 2m
i ee
means of the integral of Jacobi one of these elements, say 7’, is

In consequence of the reduction of the problem by

eliminated. This therefore appears no longer as an arbitrary constant
of integration, but is entirely determined by C and ¢. On the other
hand Cis entirely determined by 7’and e. Now Darwty’s calculations
show that 7 continually increases if C decreases. It is therefore
irrevelant for our purpose whether we consider Cor 7’ as the
+
Proceedings Royal Acad. Amsterdam. Vol. X.

(50 )

parameter of the problem. The parameter which I will use here is
T’=2T. This change from C to 7” can also be conceived as no
more than a simplification of language. Instead of saying: “the
solution corresponding to the value of C for which the period of the
solution of the first sort is.*/, 7”, I say: “the solution corresponding
to the value 77”.

In Darwin’s work mw has the constant value 0.1. If now we
choose a convenient element § we can conceive the curves ¢(7”, §)
to be drawn. Next imagine the same thing to be done for other

values of u, and take w, 7” and § as rectangular coordinates. The
curves $(7”,&) belonging to the various values of mw then produce a
surface, every point of which represents a periodic solution.

If, on the other hand, we take for 7” a fixed value 7”,,
considering wu as the variable parameter, then we have another
problem, also admitting families of periodic solutions, which can be
represented by curves (u, §) = 0. If 7", varies these curves describe
again the same surface. The form of this surface will now be
investigated. Its section by the plane u — 0.1 then gives all periodic
solutions of Darwin’s problem.

The element which I will use is § =e, cosw,, where e, is the
excentricity and @, the longitude of the perihelion of the undisturbed
orbit, which is the limit of the orbit of P for lim. «=O. The
longitude @, is counted from a jived axis which at the beginning
of the period co-incides with S/. The orbit of P is not periodic
unless o, has one of the two values O or a. Moreover at the begin-
ning of the period P must be on the line S/, i.e. there must be
either opposition or conjunction.

Solutions of the first sort are characterised by 5 — 0. These solu-
tions can have any period, therefore the whole plane §=0O is a
part of our surface. The line §=0, u — 0.1 represents Darwin’s
family A. For a value of 7’ = 27, which lies between 330° and
354°, Le. between 1.88 at and 1.97 2, this family loses its stability
and becomes unevenly unstable. So there must be another family
which at this point has a member in common with the family A.
This new family must have the period 7”, and is therefore of the
second sort. If for the sake of argument we assume the change of
stability to take place at the value 7’ =1.92, then we know of
the branch of the curve ?=—O, which represents this family, that
for 7’ < 1.9 it is evenly unstable and for 7” > 1.9 2 it is stable.

Now there are only four possible periodic solutions of the second
sort, distinguished by the following positions of P at the beginning
of the period :

(51)

B : P in opposition in aphelion (#, =0, $= +e)
Daer x ,, perihelion (6, = 2, § = — €)
C : „ „conjunction ,, perihelion (o, = 0, § = -+ e,)
Cue a . , aphelion (Oo, =x7, §=—¢,)

With reference to rotating axes, of which the axis of vs co-incides
with SJ, the orbits B and B’ are identical, and similarly C

Orbit of family B or B
Fig. 1.

and (”. The orbits B and B’ are of the form represented in fig. 1.
The orbits C and C” are of the same form, rotated through 180°,
Le. with the double point away from ./.

The families B and B’ are stable C and C” are unstable. This is
easily found by considering the equation which determines the
exponent «. This equation is (see Porncaré, Acta Math. XIII, p. 134):

nn aut 2 3) ' | 2
ia SS SS (Gore bru Cnc == We Cn)

Now using the variables employed by Porscark le. pages 128

and 171, we find easily
| Le) Ci Car 10 CS oa.

If further in w (i.e. the average value of the perturbing function
over one period) we neglect the terms which contain a higher power
of e than the second, we find

w =u Ke? cos & EO, +30,
where ¢ is the mean longitude of P at the beginning of the period
and A is a positive constant.

We find thus

4*

(52)

ORNE Em COSTES
Thus, for positive values of w, a? is negative, and therefore the orbit
is stable, when there is opposition at the beginning of the period.

For positive values of u therefore DB’ is stable and CC” is unstable,
for negative values *) of u BA’ is unstable and CC’ is stable. It is
evident that, for § = 0, Band B’ co-incide, and similarly Cand C’. The
branch of @=0O which intersects §—O in the point 7” =1.9a
therefore represents either the family LA’ or the family CC’. In
the first case it is stable, and therefore it must on both sides of the
point of intersection bend round towards the right. In the other case
it is unstable and encloses the stable part of the line § = 0.

Now Darwin has, for C= 39.0, i.e. 7’ = 1.97 x, actually com-
puted and drawn an orbit, which shows the form of fig. 1, viz. :
the orbit w,=— —.387 which has already been quoted. This orbit
thus belongs te the family B, but it also belongs to 5’. It belongs
to B if P is in aphelion at the beginning of the period and in
perihelion in fae middle of the period (being at both times in opposi-
tion to /), aad to B’ in the opposite case. The branch of the curve
?=0 which passes through the point 7” — 1.9 a therefore represents
the family LB’, and not CC’. Consequently it is stable, and that
part of the section of our surface by the plane u — 0.1, which lies
to the left of the line 7” = 2a, is thereby completely determined.
This section is represented in Fig. 2. Stable families are there, and
in the following figures, represented by heavy full lines, unevenly
unstable families by broken lines, and evenly unstable ones by
dotted lines.

Nl.
5 :¢
eet
hae ae ae 50
4 a
a
ap
Fie. 2

We next consider the section of our surface by the plane u == 0.
1) The meaning of a negative value of g is that the force emanating from J
is repulsive, the force from S remaining attractive.

("53 )

We know then that there are stable periodic solutions of the first
sort with an arbitrary period, and of the second sort with the period
7’ =2-a and an arbitrary excentricity. The section therefore consists
of the line §=O and the part of the line 7” —2a between the
points §—-+ 1 and s=—1. I wish, however, to confine myself
to small values of &. This section is represented in Fig. 3.
Next consider the section
by a plane 7” = 77’, where
1.9%< T,'< 2m, and the curves
w(u, §) —=0 in that plane. The
line =O is a part of this
curve. The lower part of this
line is stable, the upper part is
unevenly unstable. In the point
where the transition to insta-
bility takes place the line §=0
oe is intersected by the branch of
Fig. 3. y—0 representing the family
BB’. This family being stable, that branch must on both sides of

the point of intersection bend upwards, as is represented in fig. 4a.

Consider now the section of our surface by a plane parallel to,
and at a very small distance from, §—= 0. The orbits represented by
the curves (u, 7”) in this plane are all of the second sort. We
can imagine these orbits to arise by a variation of u from the un-
disturbed periodic orbit of the second sort. They then appear as

Bin

ae
7<27 iy Baie

Fig. 4a. Fig. 40.

solutions of a problem, in which the parameter is u, § being kept
constant, and thus 7” (or C\ now is our element. These solutions
have been studied by Scnwarzscni_p (Astr. Nachr. 3506). For w= 0
the period is 27. For small values of w there are (for each value
of §) two solutions, viz. B and C when § is positive, B’ and C’

( 54°)

when it is negative. The curve y= 0 thus consists of two branches,
both passing through the point u=0, 7"’— 2, and there exchanging
their stability. Since now it has already been shown that the stable
branch B is, for positive values of «a, situated on the left side, the
unstable branch C must be on the right side. The eurves are
represented in fig. 9.

Our surface has thus been shown to consist
of the plane § = and of two sheets, which
pass through the line »=0, 7” = 22, and
then deviate to the left and to the right of
the plane 7’ =2z. The points of the left-
hand sheet represent the stable family BB’,
those of the right-hand sheet the unstable
family CC’. This latter sheet therefore inter-
sects the plane u =0O.1 in a eurve which on
both sides of its point of intersection with
the line S—=0 bends off towards the right.
In this same point of intersection the family

Fig. 5. A regains its stability, the stable part of the
line § =O, which represents this family, being enclosed between the

two unstable branches of the section just considered. This state of
things is rendered in the right-hand part of tig. 2. Also the form
of the section of the surface by a plane 7" — 7’) > 22, will need
no further explanation. It is represented in fig. 44. Whether this
right hand sheet does reach up to the plane u = 0.1, so as to pro-
duce a real section, cannot be decided by this reasoning. If there
is a point of intersection with the line w= 0.1, § =O, this must
correspond to a value of 7” exceeding 414.°3 = 2.23 2, since
for this value the family A is still unevenly unstable, as is shown
by Darwin’s work. That the left-hand sheet does actually intersect
the plane u=—=0.l is shown by the existence of Darwin’s orbit
wv, = — .337, belonging to the family 5’ (and also by the change

0
of stability of the family <A).

Thus all results have been derived which have been found by
PorscarÉ in the ‘‘Meéthodes Nouvelles”, already quoted. Naturally
PorscarÉ also must leave the question, whether his results still hold
for «= 0.1, unanswered.

It is not uminteresting to consider the solutions B and C from the
point of view of the theory of perturbations. This can, of course,
not teach us anything about their stability, but it will give information
about the form of the curves 7(u, 7”)=0O and w(u.s)=O0 for small
values of u and §. The period of the undisturbed solution is 2,

(55 )

By the perturbing influence of / this is changed to 7’ = 2” +1.
The conditions that the perturbed orbit shall be periodic are:

Gt Te

de 7 Gd 1 ei

Ef —_— dt =b 7 T
| dt dt :
0 0

where 2 is the mean longitude of P. For the computation of the
integrals ‘we must use the mean motion affected by perturbations,
i.e. n=3 + 06. The left-hand members of these equations of condition
are therefore functions of t and o, and these two unknowns can
be determined from them.

If in these equations of condition we neglect the square and higher
powers of e, they become

I= > (20 + 2) p [BY + (21 A® + 10 AD 4 2-4, a
62 + 1= (38 4 0) (Qa + 1) — na (20 4+ 1) ALO

The upper sign in these equations must be used for the family
CC’, the lower sign for BB’. The sum within the {?} being larger
than BD, we find that for the family 55’ + is negative, while for
CC’ it is positive, as has also been found above. Further the first equa-
tion shows that the numerical value of the differential coefficient ae

aut
for the tirst family (BB’) decreases if u increases, while for the
other family it increases. Thus the left-hand branch of x (u, 7") = 0
has its concave side towards the line 7” = 2z, and the right-hand
branch its convex side, as is shown in fig. 5.

In the numerical computation we must not forget that the formulas
(1) ean only be considered as approximatively true. The solution of
the equations is easily effected by means of the tables of RunKie, the
argument for the determination of the different functions A; being
computed by

10
nk
I find in this manner for the two families:

n=3+6 Boh Sj

Bee = 0085 PESSE
2n
T

(Gis = + 0.29 T'=2.58 x
2

These are the periods of those orbits of the two families, which
have §=0O, and which therefore co-incide with a member of the

family A, whose period is 7— — 7”. Darwiy’s computations show

that the value of 7” for which the. families A and B co-ineide
must lie between 1.886 a and 1,97 a. The point of co-incidence of
A and Cis outside the region explored by Darwin, the corresponding
value of 7” must therefore be larger than 2.23 a.

If in the equations (1) we take account of the square of e, the
right-hand member of the first must be multiplied by Ven
the second A, must be replaced by

1
OBS (a0 + {31 A,@ 4 24 AB + 6 Ae)

and */,e?T must be added to the second member. Now if we take

T’ = const. then t is constant and also 6 can be taken to be constant.
The second equation (1) then is of the form

const. = w(P QE) =>. = ae

Now we have 8? = ¢’, therefore (2) is approximately the equation
y(u,§)=O0. For the family BB’ P and Q are of opposite signs,
for CC’ they have the same sign. Thus the form of these curves

as drawn in the figures 4a and 4/ is confirmed. *)

Physics. — “Contribution to the theory of binary mixtures. IV

By Prof. J. D. vaN DER WAALS.
Continued, see p. 849 vol. IX.

THE BINODAL CURVE.

We might think that for the determination of the binodal curve
we could follow the following course. It is required for coexistence
that besides the temperature three other quantities are equal, 1. e.
p, q and Mu, If we now also trace the lines on which J/, u,, is
equal, we should have to seek in order to find a point of a binodal
curve, the points satisfying the condition that the p, q and JL, u,
lines passing through this point intersect in still another point of
the field. This search, however, being exceedingly difficult would
give moreover no clear survey of the results. We shall, therefore
not follow this course. Still I shall make some prefatory remarks
on the course of this third group of lines. For it is by no means
devoid of interest to know in which phases of a binary system the

E) This last paragraph has been added in the English translation,

(57)

molecular potential of one of the two components has the same
value. We shall call this third group of lines “potential lines”.

THE POTENTIAL LINES.

5 dp dp an 2
The value of ML, u, is equal to y— v in by differentia-
av ae
tion we find:
dw dup
dM pu, =— v on ad ae

or
d M, u, == Of) dp SHE dq.
If we want to know the shape of such a potential line, we must

dv ; 8 A
know — for such a line, which quantity we shall represent by

ad
dh & . B S. 5 2
— |. For the value of this quantity we find then the expression :
Pot

ede AN

i La
dv da dv dx?
neemen

1 a
dv? da dv
which may also be written:
v dv
dv dv a dary
a. ge de, 0 i dv :
0 de,

da
So there is a locus in whose points ( i e, and another in
av Pot

s dv v di
whose points ( jan The former takes place when ——— i.e.

dk J Pot AP de)
this locus is the series of points in which lines drawn from the
7 ; ‘dy 10) dv
origin touch the p-lines. On the other hand {— }=0 if -=—,
; de) Pot ip dag
: D ‚ B N dv dv dv
for the points of the spinodal curve in which ——=—., also =
pn we de) pot
4 / dv
IS equal 10! ——-
dap

dv
da

p-lines have the course as in the left region of the general p-figure,

The shape of the locus naa ) is different, according as the
P

or as is the case in the middle region or in the right region. The

(58 )

course of the p-lines being modified by the temperature, the value
of 7 will also influence this shape.

Let us first put a left region at a value of 7’ below 7;, and also
below 7. Then tangents may be drawn to all p-lines from the
origin. The points of contact on the side of the small volumes then
form a continuous series of points which begins in the point in which

eee: dp b
the liquid branch of the curve —=0O intersects the 1st axis, and
av
-moves further and further away from this curve as it approaches
the 2°¢ axis, remaining all the time at smaller volumes than those
of the curve mentioned. The points of contact on the side of the
large volumes also form a continuous series of point, which starts in

—() intersects

the point in which the vapour branch of the curve
av

the 1st axis, and also moves further and further away from this
curve as it draws near the 2rd axis. This series of points has always

dp : 2
larger volume than the curve — — 0. So when a potential line
av

passes through such a series of points it is direeted parallel to the
V-axis. The locus of the points in which a potential line runs parallel
to the X-axis, and which is found by drawing tangents from the
crigin to the g-lines, is a curve consisting of one single branch,
which at small volumes crosses the field from a certain point of the
first axis to the point » = 6 and «=1. But the shape of this curve
is very different, dependent on the more cr less complicated shape
of the g-lines. Without entering into further details we shall only
observe, that when gq-lines run as is the case in the absence of
dp ME
ae = 0, this curve will have no point in common with the preceding

he dy ; : dw
one; but if en 0 exisis: and intersects — — 0, the curve on
AX av

3 dv dp Sai:
which ie) = 0, passes round — = 0, and twice intersects the line,
AL J Pot an”

on which GE oo. These two points of intersection are again of
ALY Pot
importance for the shape of the potential lines. Then again a loop-
potential line passes through one of these two points. In this case the
double point is the point of intersection on the right, and the point
of intersection lying on the left serves then again as isolated point,
round which a series of potential lines run in closed figures. That
in this ease the point lying on the right is the double point, is in

(59)

connection with this that all potential lines terminate in the point
v=h and x=—1. My, is infinitely large on the line vp =b, and
on the second axis M,«, is negative infinite. In the point v= b and
r=l the value of the potential for the first component must there-
fore be indefinite. When arriving at this point all potential lines
touch the line v=b. In fig. 15 the course of the potential lines
has been schematically represented for this case of non-miscibility in
the liquid state. The first axis is cut or touched by the potential

( 60 )

lines of every degree. M/,u,—=—o for v=o. If» decreases, M, u,
increases till the potential has reached a highest value in the point

d , dp : } dl
of maximum pressure G =0). With further decrease of v the
av

potential diminishes, till the final point of the unstable state is reached,
dp. ‘ = ; fed : 5
where — is again equal to 0. There J/,u, is minimum. If the point
av
v=b is reached, M,p,—o. With very large volume Mu, is
“approximately equal to MRT log TE, in which also a function of
T is left out, which may generally be left out in the construction
of the y-surface for definite value of 7’; from this shape for Mu,
it is seen that the portions of the potential lines which start from
the tst axis for large volume, may almost be considered as straight
lines directed to the point «=1 and »=—0O. If the potential line
starts from the volume v,, the equation of the initial portion is
vy =v, (lez). If wv, should be =o, and so M,u, = — o, the value
of Mu, is negative infinite for every value of z for v=o, which
it is also all along the second axis. The rule that for very large
volumes the initial portions of the potential lines may be considered
as straight lines already follows from the law of Darron that each;
of the components in a mixture of gases behaves as if it alone was
present in the volume. If » =v, (1 —#), the density of the first
component has the same value, and the quantities determined by the
density, are the same; e.g. the pressure and the potential. If the
circumstances are as assumed in fig. 15, there is of course also a

dr
loous where C =| — 0, which is again a loop-line passing through
q Mijn

dv
the double point of the potential lines. If the locus vn 0
akg
; dv aa
does not intersect the other »—w«-——, all the potential lines have
dey

ihe simple shape which they have on the left side and on the right
side in fig. 15.
If we suppose a left region at a value of 7 above 7%, the locus

dv 5 5 el . 7
DE = 0 is subjected to a modification. Then the two branches
de),
_ dp = et B
of — 0 have joined, and in the same way the two branches of
dv

dp ‘
this locus will join; but both lying outside : = 0 the point of
av

(61)

junction will lie at larger x than the point of junction of the branches

of I) This junction must then take place in a point of inflec-
ave

tion of a p-line, as is immediately seen when in a p-figure the

tangents are drawn from the origin in the circumstances mentioned,

in which it also appears that the point of contact then lies on a

p-line of maximum value. So the point of junction mentioned is a

point in which the tangent of a p-line in its point of inflection passes

dv
through the origin. From the differential equation of v — « 7 0;
dk,
if » is taken as function of w and p, follows for this locus:
dr
(Le
dae dx di
i ae
dj Vr dp: Ie

The potential lines of low degree have then lost the points in
which they are directed vertically, and have then a very simple
shape. With decreasing volume they no longer run back to smaller
value of 2.

In the second place let us choose a region in the middie, where

dp

dp
the two points of intersection of — =O and P —( are found.
at av

‚dp : :
Even though the two branches of — — 0 remain entirely separated,
av

dv

this is not necessarily the case with the two branches of v—- «—-=0.

at
P
It is easy to see that the branch at the smaller volumes lies above

dp
Zed only from «=O to the double point of the p-lines. With

dv

higher value of z it lies below it. In the same way the branch of
dv ; dp 3

vp -~«— =O at larger volumes lies below —=O only from t=O
dep dv 7

to « of the double point. This lower branch passes through the
: p dp ; k F
double point, and lies above — =O with greater value of x. The
av
two branches join as soon as there exists a p-line, for which the
tangent in the point of inflection is directed to the origin. If at
De ae … dp Ee

minimum critical temperature the line — =O possesses a splitting

dv *

dev

point, the curve v—.« FF = 0 is restricted to the left part, and is
dup

(62)

closed for smaller value of than that of the splitting point. Tf,
however, the region extends far to the right, then also the right part
ip . . dv 8
— == 0 can again contain a closed part of v — r— =O, witha
dv dit,

top at a certain value of zv, and the open side at «=1. Also for

of

regions lying entirely on the right side it remains of force that

dv . A hap sn he
»y—x—=O0 lies within — =O; so that if —=0O no longer
de, dv dv
/
4 2 dv
extends over the entire width, » — cannot extend any longer
dey

over the entire width either.
If also in such middle region, and at the same time in a right

dy
region we examine the course of the locus »—.«—, where the
( vq
potential lines are directed horizontally, we see when consulting
figs. 5 and 6 that the locus mentioned remains restricted to smaller

; : dp 8
volumes than those of the line a) so long as the curve
Ivy
dp Bre ;
aa = 0 does not exist, or if it does, for all points outside this curve.
av
‚dp dp
It Ee cuts the curve — == 0, the loeus mentioned passes
Avy Av
y aa : en aap ; dv
through these points of intersection. Within — ==0 the line »—a«#—
: da? de,
3 3 dp d 5
lies at larger volumes than those of 5 =— 0. But then no intersection
dky
4 dv dv 7 x
of v — «— = 0 and v — « — = 0 inter seis to be expected. Hence
dig dep

there is no question of a loop-potential line. The result would have
been perfectly different, if we had also examined the course of M, u,
But this may be considered superfluous, now that we know the
course of the g-lines, so of J/, 4, — MW, u, and of JZ, u. This by no
means exhausts the properties of the course of the potential lines,
but as we are not going to avail ourselves of this third group of
lines for the determination of the binodal line, I think that it will
suffice to mention the above properties.

For the determination of the course of the binodal line we shall
make use of the equation of p. 57, viz. :

dM, w, =v dp — x dq.

3ut first some preliminary remarks. Among all the lines to be discussed

in a theory of mixtures the isobars and the binodal lines are to be

(65 )

considered as the most important ones, because they can be the
subject of experimental investigation. Though it is necessary for a
clear insight that for a simple substance we know that below certain
temperature the isotherm possesses unstable parts, and that we can
indicate the limits of these unstable parts, yet the determination of
the points of coexisting equilibrium is of the greatest importance
for the experiment. In the same way it is, indeed necessary for a
clear insight into a binary mixture that the existence of the unstable
phases and their limits are known, so the spinodal curve ; but
the knowledge of the binodal line is of still more importance, and
to determine the latter must be taken as the final end of all con-
siderations, because if can constitute the subject of experimental
investigation, and the results derived from our considerations can
only be tested by experience in so far as they refer to the binodal
line. If we are to admit an exception to this rule, this applies to
the plaitpoints to whose existence could be concluded without an
examination of the binodal curve being necessary. But moreover, it
deserves attention that not even the whole of the binodal line can
be realised by the experiment. The binodal line can possess portions
lying in the unstable region, and others which are metastable. This
has already been observed in the Théorie Moléculaire (Cont. p. 14),
but appears in an ampler and more complete measure from the
diagrams occurring in These Proc. March and June 1905. At the
same time it appears there how very complicated the binodal line
can be, when the spinodal curve hardly deviates from the usual
shape. Hence if the more or less complexity of a plait is to be judged
according to its spinodal curve or according to its binodal curve, a
very different opinion will be arrived at.

Thus paying attention to the properties of the binodal curve I
have been able to speak of a main plait and a branch plait in
the last cited paper. In the same way, regarding only the binodal
line and its nodal lines, we may speak of a transverse plait and a
longitudinal plait, whereas, regarding only the spinodal curve, we
shall have to consider these two as one single plait. However, to
prevent confusion, it is desirable to follow one and the same termi-
nology. At the moment it seems most desirable to me to consider
particularly the spinodal curve when choosing the name, leaving
that part out of account that may also sometimes exist, but which
then encloses the concave-concave part of the y-surface. If no plait-
point exists on the spinodal curve, or only one and then a reali-
sable one, such a plait might be called a normal one. If besides
there are a couple of heterogeneous plaitpoints found, we

( 64 )

might speak of an abnormal, or as I did in preceding pages of this

communication, of a complex plait. If the spinodal curve has split

up at certain value of 7, which may take place in consequence of
dp  5 e 7 ‘

the curve — =O having split up, there are two plaits, one of which
av

might be called the right plait, and the other the left plait. If it

has split up in consequence of a separation between the curves

dp dp 7 BAD > di

— =— 0 and —_— == 0, we might distinguish the two plaits by the names

dr av
“transverse plait and longitudinal plait”. Every time that the sepa-
ration into two plaits takes place, two homogeneous plaitpoints make
their appearance. With transition of a normal plait to a complex one
a couple of heterogeneous plaitpoints appear. If then we wish to
pay attention to properties of the binodal curve, other names might
be thought desirable, but then it would be advisable to state dis-
tinctly that this is done to call attention to the special shape of the
binodal line.

The equation d Mu, = vdp—edgq simplifies for a simple substance
to dM,u, =vdp, and may be considered in this form to lead to the
construction for the point of coexistence. This construction can be
carried out directly if as axes a p-axis and a M‚u,‚-axis is chosen,
in which case we get a curve intersecting itself (Cont. I p. 4 fig. 1),
or we can choose as axes a v-axis and a p-axis, and apply the
law of Maxwenn. In the latter case we think d Mu, =v dp writ-
ten in the form: d J/,u,=d(pv)—pdv, the integral of which is

b

(Mu) — Muda = (peo — (pra -{ pde. For coexistence we must
a

have (J/,u,)o = (M‚u)as and pa = ps = pCoer, $0 that we get:

vp
Ppe(ve—Va) =| pdv.
va

For a binary mixture we get for the determination of coexistence,
so for the determination of the points of the binodal curve, the same
simple equation :

dM u, == vdp,

when following the series of points for which dy —0 and so a
q-line, in the execution of the construction.

Let us assume that we wish to apply Maxwerr’s law. Then fol-
lowing a q-line, we draw the value of p at every value of v, and

( 65 )

seek how many times a straight line may be drawn parallel to the
b

v-axis, so that p(vy—va) = { pee. If this can take place only once,

a

the extremities of this straight line indicate the value of v of the
phases coexisting with each other, and the distance of this straight
line above the v-axis the value of the pressure for this pair of coexist-
ing phases, and the chosen q-line cuts then no other branches of
the binodal line. This may take place several times, when the chosen
gq-line passes + times through the binodal curve, or when there are
6 points of the binodal curve on the chosen q-line. To ascertain
whether this can take place O times, or 1, 2 or more times, we have
to pay attention in the first and foremost place whether or not the
chosen q-line intersects the spinodal curve, and if it does, how many
times. For every time when a g-line cuts the spinodal curve, there
is either maximum pressure or minimum pressure for the points of
this q-line. In the points of the spinodal curve a p-line touches the
chosen gq-line, and one and the same p-line, having either larger or
smaller value than the p-line which touches, will pass through two
points lying on either side of the spinodal line. Thus in fig. 7 (p. 738)
there is maximum pressure in point + of the g,-line, and minimum
pressure in point 2, but for larger volume than that of point 4 the
pressure is always smaller than in 4, and the smaller as v is larger,
and in points of the same g-line in which v is smaller, the pressure
is always larger than in 2, and the larger as we follow the g,-line
to its initial point, where p=. If we now construe p as function
of v, the p-line has a shape similar to that of an ordinary isotherm.
For v=oa, w=0O, there is a maximum and a minimum pressure,
and for vb, p=. Maxwe..’s rule may then be applied, but
only once.

So this q,-line will possess two points of the binodal curve. In
fig. 7 this will be the case for every g-line. For the line q = oo, or
for the first substance we find the coexisting phases of that substance,
and for ¢=—o or for the second substance, the coexisting phases
of the second substance. If starting from a certain point of the v,2-
diagram we draw both the p-curves as function of v, viz. the p-curve
when we follow the g-line which passes through the chosen point,
and the p-curve when we remain at constant value of w, then the
2ud curve has always greater value of p than the first for all values
of v smaller than that of the point chosen. Thus in fig. 7 the pressure
in a point lying more to the left to which the g-line moves is smaller
than is the case for constant value of w at the same value of v.

5
Proceedings Royal Acad. Amsterdam. Vol. X.

( 66 )

Now let the point from which we start be the point of the binodal
curve lying on the vapour side. Then, if we apply Maxwet1’s rule
to the two curves, it follows from the circumstance that p is always
larger for the curve at constant , in the first place that MaxweLL’s
line for this p-curve lies higher than that for the p-curve when we
follow the q-line, and in the second place that on the vapour side
the binodal curve for given « always lies at larger volumes than
the vapour volumes would be when every mixture was to be con-
sidered as homogeneous. In the same way on the liquid side at
smaller volumes. Just as the binodal line lies outside the line
dp ll)
dv

if every mixture should behave as a simple substance. Properties
which also immediately follow from the y-surface.

In fig. 75 only q-lines of lower degree intersect the spinodal
curve. The g-line of the highest degree which still has points in
common with the spinodal curve, which points are coinciding points
is that passing through the plaitpoint. When we follow this q-line
maximum and minimum pressure will have coincided, and drawing
p as function of v, we get a line which has an horizontal tangent
in the plaitpoint, and at the same time a point of inflection, just
as an ordinary isotherm in the critical point. This is a remark

which always holds for a plaitpoint, also for a hidden plaitpoint ;

Aas dp dp
but then the special point in the p-line where pe and is
q q

‚ the binodal line lies outside the phases which would coexist

dv dv?
equal to 0, lies on the unstable branch. There is a third possibility
for the situation of this special point, viz. that it lies on what we
might call the liquid branch of the p-line, as will presently appear.

Let us now consider the case of fig. 8, and let us choose there
a g-line which intersects the spinodal curve 4 times, as is the case
with one of the g-lines drawn. If starting at large volume we
follow this g-line, we meet, still at large volume, the spinodal line
in a point where p has a maximum value; in the second point
where the g-line leaves the unstable region for the first time, there
is maximum pressure. In the third point where this q-line enters
the unstable region again, there is again maximum pressure, and in
the fourth point when the unstable region is finally left there is
again minimum pressure. Now to draw p properly as function of

av

dp dp (du dp
Deet
dv), de» dv)g dor

dp
», we must know the value of (2). Now:
q

( 67 )

which equation may be written in the following form:

Py dw Pw?
(2) dv? de? \dadv

dv dw
q
dae
: ee dp\ . eee
From this form we see that yee positive in the unstable region
dv),
7
ED eee uae EAE. . DD os oat
only when —— is positive. If —— is negative, then {— | is again
dic? die 5 dv Jy ;

negative in the unstable region, and when the g-line intersects the

Pw dp i 5 :
curve: — 0); =o. In fig. 16 the course of p as function
q

da dv

of v when this g-line is followed, has been schematically represented.

Fig. 16.

Now we have to examine how many points of the binodal line
lie on this g-line. For this discussion I shall represent the branch
right of point 1 by a; the branch between 1 and 2 be then the
b-branch ete. The number of times that Maxwerr’s rule can now
be applied, is equal to the number of combinations in two of 4
quantities. Thus branch a could be combined, not with branch 4,
but with branches c, d and e. The branch 4 may be found combined
with d and e. And finally branch ¢ with e. We do not mean to
say that the application in those 6 cases is always actually feasible.
This will be discussed presently when we discuss other g-lines. But
for the g-line chosen here, it is really possible to trace those 6
MaxwerL lines. And then this g-line must cut the binodal curve
12 times. These 12 points of intersection are to be found in ole
In this figure the q-line has the shape of fig. 8. It intersects the

( 68 )

spinodal curve, which has also been drawn in this figure, four
times. It has a maximum and minimum volume. Between the

dy

U

points of largest and smallest volume the locus = 0 must be

thought.

bin

Vestel

Fig. 17.

In this fig. 17 the binodal line has further been drawn, and
on account of its intricate shape, it has been several times indicated
by the sign bi. We may consider this binodal curve as consisting

( 69 )

of two separate parts. First that part that we might call vapour-
liquid. binodal curve. The liquid branch of this part has a regular
course, but the vapour line branch has the well-known shape with
two cusps. The nodal line belonging to the cusp y, has its other
extremity in the point y, where the liquid branch of this binodal line
passes through the spinodal curve. In the same way the two points
indicated by d belong together as extremities of one same nodal line.
The remaining part of the binodal curve forms a curve closed in
itself. For this part of the binodal curve the two heterogeneous
plaitpoints P, and P, are in the first place of importance. The points
on the right and on the left of P, lie in the stable region, the points
on either side of P, in the unstable region. If we continue the branch
on the right of P,, and pass through the spinodal curve in the point
a, then to this point as an extremity of a nodal line belongs another
point « as the other extremity of this nodal line, and there must
again be a cusp for the binodal curve for this second point «. In
this second point « the binodal curve returns again to higher value
of w, and if it then meets the spinodal curve in the point indicated
by 8, another point 8 belongs to this, at which the right branch has
a cusp. From this point the remaining part of the binodal curve
has only points in the unstable region, and the points lying between
the two points 8 are extremities of nodal lines which approach each
other and coincide in P,.

To find the 12 points in which this g-line cuts the binodal curve,
let us apply Maxwrrr’s rule to that portion of the p-tigure with the
branches a, 6 and c, and determine the points denoted by 1. Let
us also add the branch d, then the equality between the areas above
and below the straight line would be disturbed, if the same straight
line is retained, i.e. in this sense that the total amount of the areas
above the straight line would be too large. From this follows that
we must trace the straight line higher. For the points of the binodal
curve which are determined by the combination of « with d, the
pressure is, therefore, larger, while, as the figure shows, the volumes
are both smaller than those of the corresponding points 1. The points
determined by this combination have been indicated by 3. If we
now also add the branch e, the pressure must again decrease. Then
we determine the points denoted by 2. It will presently appear that
the pressure in 2, though it is diminished, is still larger than in
the points 1. By means of the combination of 5 with d, both branches
in the unstable region, we determine the points 4; and after addition
of the branch e the points 5, which must have lower pressure than
the points +. Finally the combination of c with e remains. Now

(70 )

the situation of the g-line which we have chosen, is such, that the
branch e remains on the right of the points of three-phase-pressure.
From this ensues that if we have construed the p-line in fig. 16
correctly, the application of Maxwe.u’s rule to the combination (c, e)
must yield a larger pressure for the points 6 than for the points 1;
but it also follows from this that the pressure for the points 2
(combination of a, e) lies between p, and p, and so p, >p,
But not all these 12 points are realisable. Every time an unstable
‘branch occurs in the combination the nodes determined by this
combination are not to be realised. So the points 3 (combination
a,d), the points 4 (combination 6, d), and the points 5 (combination
b,e) are not to be realised under any circumstances. Thus already
6 of the 12 points are excluded as belonging to unstable coexisting
equilibria. Of the remaining 6 points 2 more are excluded, if meta-
stable states are set aside. So summarising we determine the following
points by means of the combination put by the side of it:

points combination
(ree Hen KOC he esta le:
7 de. metastable
3 aider = = unstable
4 bd sunstuble
5 b,e . . . unstable
6 Cyne) te eee astable

To construe all the points of the binodal curve we should have
to treat all the g-lines in a similar way. For the first component
(q = — ) the p-line is the ordinary isotherm, in the same way for
the second component (q = + o) the isotherm for this component.
So with increase of the value of q such a gradual change of the
qg-line must take place that it passes from the first shape to the second.
With very large volume these extreme shapes may be considered to
coincide. This is also the case with all intermediate forms. The modi-
fication remains chiefly restricted to the smaller volumes, and in the
case of b,=6, such a conclusion would be admissible also for the
exceedingly small volumes. So long as the q-line (see fig. 4 and fig. 8)
is still of so low a degree that it does not even pass through the

2

ih fi 8
lowest point of De = 0, the p-line has still the usual shape of an
ar

2

uw nn ae

~ == 0, does a special point
av

make its appearance in the unstable branch, For this point of contact

isotherm. Not before the q-line touches

(CAE)

dp dp . E ers 9
mn but {| — } still remains positive on the left and on the
v q ‚U q

right of that point. With somewhat higher degree of g,

intersected twice, and two points may be pointed out in the p-line
in the unstable branch where it is directed vertically. Between these

2 points is negative. But then too the p-line has but 3 branches,
and so Sherine rule can only be applied once ; then we find only
two points of the binodal curve, viz. a point indicating a liquid
volume lying in the left side of the figure, and a point indicating a
vapour volume, lying much more to the right side, but still remaining
sufficiently on the left of the double point of the vapour binodal
curve. Then the g-line cuts the binodal curve in no other points on
the vapour side. If the value of qg rises higher, a third special point
appears again on the unstable branch of the p-line, i.e. when the
g-line begins to have 4 points of intersection in common with the
spinodal curve. This will be the case when it passes through the
hidden plaitpoint P, (see fig. 17). Then it touches the spinodal curve,

2,

B ay : dv
but in such a way that 15) has the reversed sign of (S :
' q spin

da Ge
The rule that in a plaitpoint the p-line and the q-line envelop the
plait is, accordingly, restricted to the realisable plaitpoints. It must

run exactly the other way about for hidden plaitpoints. So there

dv dy 4 (dv dv

= | =| — | has the reversed sign of and of -} ,

dx’* da? CE ess dau? Jo;
p spin e bin

In this third special point of the unstable branch of the p-curve

(72)

dv dv
of fig. 18.

For q above this value the spinodal curve is cut in 4 points. The
two new points of intersection lie then on the left and on the right
of P,, and at the beginuing in the neighbourhood of this point. Then
a portion lying in the stable region has been added to the g-line,
from which we derive that p is smaller in the point of intersection
lying on the right than that lying on the left. Not until now has
the p-line the shape of fig. 16, but the branch c is still very small

dp a d*p
— J) =0, and also | — | =O, and then the p-curve has the shape
q 1

then, and the pressure of point 3 of this figure only little higher
than of point 2. From this moment there could be question of the
application of Maxwerr's rule to the 5 branches a, b, c, d and e,
and so of the determination of the 12 points of the binodal curve.
But at the beginning not all these 12 points are real. The application
for the combination of the first and the last branch is certainly
feasible, and it yields a couple of realisable points for the binodal
curve, and in contradiction with our result when we treated this
combination for the g-line in fig. 17, the points defined in this way
are not metastable but stable. No less is the application possible for
“the combination (b,d), and the two points determined then lie in the
unstable region, and can be represented by the points 4 of fig. 17,
provided they are shifted nearer the point P,. The rule cannot be
applied to the remaining + combinations. For the possibility of the
application to the combinations (a,c) it is required that the length
of branch c be such that the pressure of point 3 (fig. 19) be at least

P |

Fig. 19.

positive; and even this is not sufficient. If, namely, we have from
point 3 a line // v-axis, and if then the area between the branches

(73)

h and e and this line parallel to the v-axis is smaller than the area
between the branches « and 5 above this parallel line, Maxwe.u’s
line would have to lie higher, and hence is not possible. A fortiori
the combination (a, d), which would require a still higher value of
the pressure of Maxweir’s line, will be excluded. For similar reasons
the combinations (4, e) and (c,e) must be rejected. From this follows
that the q-line which is of somewhat higher degree than that passing
through P, must remain on the left side before the point « of fig. 1,
and on the right side of the ridge of the vapour branch of the
binodal line. If we continue to raise the value of g, the possibility
of the combinations (a,c) and (a, d), begin simultaneously, i. e. when
the pressure of the point 8, which may be considered as the top ot
c and d, has risen so high that the Maxwe tt line for the combination
(a,c) would just. go through point 3. In the same way the possi-
bility for the combinations (4, ¢) and (c, e) begins at the same time,
i.e. when the pressure of point 2, which is the lowest point of the
branches 4 and c, has descended so low, that the Maxwerr line for
the branches ¢ and e would just pass through point 2. If all these
possibilities exist, the twelve points can be pointed out on the g-line.

Which of these two simultaneously beginning possibilities presents
itself first on rise of the degree of the g-line, will probably not be
bound to a general rule. If we now follow such a q-line, beginning
at small volume on the left side of fig. 17, we first meet point 2
on the binodal curve, which proceeds regularly from left to right
on the liquid side; then 6 and 5 follow before we pass through the
‘spinodal curve. When the q-line rises again, we meet 4 and 3,
which have then to le more to the right than on the g-line, for
which fig. 17 has been drawn. When the g-line again descends we
first meet point I, then 6, afterwards 5 and 4, and at last on the
vapour side the points 8, 1 and 2 in this succession. But of all
these points only the points 2 are stable. The points 1 and 6 are
metastable. The others are unstable. And on further rise of q we
reach that special q-line which is to be considered as the principal
one for the phenomena of coexistence, and which, with three-phase-
equilibrium, passes through the three coexisting phases. This co-
existence of three phases is met with when (see fig. 16) the Maxwerr
line for the combination (a,c) is the continuation of the line for the
combination (c‚e). At the same time this line is also the Maxwerr line
for the combination (a, ¢). Then the points 1 and 2 or 2 and 1 coincide
on the vapour side. On the liquid side on the left the points 2 and 6
or 6 and 2 coincide, on the right on the liquid side the points 1
and 6 or 6 and 1. The points 3, 4 and 5 have remained; of them

(745)

3 and 4 are unstable coexisting equilibrium, and 5 is metastable.
In this case of three phase pressure the second component occurs
in the vapour in a greater measure than in the two liquids, in con-
nection with the circumstances which give rise to this figure, viz.
that the second component has higher value of 5 and lower 7% than
the first. In fig. 3 Cont. Hl, p. 11 the course of the pressure is
represented for the vapour-liquid binodal curve for this case.

With continued rise of the degree of g the p-curve, which entirely
deviates from the shape of a simple isotherm for the last chosen
values of g, must return to such a simple shape without abrupt
changes. Thus the existence of 5 branches ceases when the q-line
passes through P,. The branches c, d and e have then decreasing
pressure with increasing volume. Only there is then a point where
dp ap
and —
dv dv*g
higher value of q also this particularity has vanished, and we ap-
proach to the usual shape of an isotherm. Already beforehand the q-line

Zas

is equal to O on this descending branch. But with still

dy :
which above touches ae 0, was not found to run back to larger

ak
volumes in the unstable branch d *).

If we increase the temperature to 7), a new plaitpoint P, makes
its appearance at v= 1 and v = (w‚),. With further increase of the
temperature the characters of the two realisable plaitpoints P, and
P, begin to approach to each other. In fig. 17 the closed binodal
curve belongs to P,. Above a certain temperature, which I called
transformation temperature (These Proc. March 1905), this closed
binodal curve passes to P,. At this transformation temperature the

pairs of points 8 and y have coincided on the spinodal curve in

‘ 4 d*v
fig. 17, and two branches of the binodal curve touch, and —
u adv

is the same for these two branches. But for further particulars I
refer to the already frequently cited communication. We must only
bear in mind that in the case treated here 7).,< 7, whereas in
the figure which I gave before for this transformation it was assumed
that 7),>>7;,. Regarding the properties of the binodal curve we
may then speak of a principal plait and of a branch plait. At much
higher 7, P, and P, have coincided, and the binodal curve has
become a normal simple line. (To be continued).

1) Strictly speaking the change of the p-line with increasing value of q is not
a moving away from and then a return to the shape of an isotherm. It must be
regarded as a progressive development, which proceeds in the same sense. To the
last q-line belongs then also the infinitely large pressure along the line v =),
This portion is. however, not necessary for the description of the binodal curve,
at least when the plaitpomt P, exists.

(June 21, 1907),

iz

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,

PROCEEDINGS OF THE MEETING

of Saturday June 29, 1907.

IEC

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

Afdeeling van Zaterdag 29 Juni 1907, Dl. XVI).

CORNE ENEN SE

C. E. A. WicuManrN: “On ore veins in the province of Limburg”, p. 76

L. J. J. Muskens: “Nerve influence on the action of the heart. Ist Communication. Genesis
of the alternating pulse”. (Communicated by Prof. H. ZwAARDEMAKER), p78. (With one plate).

J. Borke: “On the structure of the nerve-cells in the central nervous system of Branchiostoma
lanceolatum”. Ist Communication. (Communicated by Prof. G. C. J. Vosmarr), p. 86. (With one
plate).

W. Eryruoven: “On a third heart sound”, p. 93.

W. pe Sirrer: “On some pvints in the theory of Jupiter’s satellites”.

(Communicated by Dr.
E. F. van DE SANDE BAKHUYZEN), p. 95.

P. Tescu: “Considerations on the Staringian “Zanddiluvium”. (Communicated by Prof. K.
Marry), p. 108.

H. ZWAARDEMAKER: “On the adsorption of the smell of muscon by surfaces of different
material”, p. 116. — Continued, p. 120.

J. D. van per Waars: “Contribution to the theory of binary mixtures” V. p. 123.

Proceedings Royal Acad. Amsterdam. Vol. X.

( 76 )

Geology. — “On ore veins in the province of Limburg”. By Prof.
A. WICHMANN.

(Communicated in the meeting of March 30, 1907.)

In the spring of 1856 the ex-colonel of the Dutch East-Indian
Army P. van SwrereN, at the Hague, founded a “Mining Society for
the Netherlands” *), which obtained the concession for the mining field
“Marie” in the southernmost part of the province of Limburg *), in
order to search for coal. After the first borings at Epen and Simpel-
veld had remained unsuccessful, the hamlet of Bommerig®), community
of Wittem, was taken, where on Oct. 11, 1856, a lode of ore was
discovered of 0,80 meter thickness, at a depth of 56,20 M. and
consisting chiefly of quartz and galena. Although it was suspected
at once that this lode communicated with the one worked at Bleiberg
in Belgium, situated to the SSE., yet the working of this lode was not
taken in hand because of the great expense, involved in sinking a shaft.
After this the Society continued its investigations in other parts of
the mining field with insufficient results until it was dissolved after
the available funds had been exhausted.

It has been known for a long time that the devonian and carboni-
ferous strata in the environs of Aachen (Aix-la-Chapelle), extending
mainly from the North-east to the South-west, are cleaved by faults
directed almost perpendicularly to them and which appeared to be
of great importance for the formation of ores *). These masses of
ores were found sparingly in the devonian system, mostly in those,

belonging to the carboniferous limestone and only once — it was
thought — in those of the coal-measures, namely at Bleiberg.

1) Nieuwe Rotterdamsche Courant, Thursday, May 22, 1856, N’. 140. The
foundation act dates from June 11, 1856 (Dutch State Gazette, Thursday, July 10,
1856 NO. 162).

2) Situated a little over a kilometer to the North-east of Epen and 2 kilometers
south of Mechelen.

8) Nieuwe Rotterdamsche Courant, Thursday, October 16, 1856; N°, 286.
P. van Swieten. Rapport sur les opérations de la Société de l'union minérale
pour la Néerlande de 1856 à 1857. Annales des Travaux publ. de Belgique XVI.

Bruxelles 1857—58 p. 266—267 PI. V.

4) C. Dantz. Der Kohlenkalk in der Umgebung von Aachen. Zeitschr. d. D. geolog.
Gesellsch. XLV. 1893 p. 599—683, Taf. 26. W.Scuutz. Führer des Berg- und Hütten-
Ingenieurs durch die Umgegend von Aachen. Aachen 1886, p. 37—41 m. Karte.
G. D. Uvyrenproek. Le sud-est du Limbourg néerlandais. Annales de la Soc.
géolog. de Belgique XXXII. Liége 1904—05. M. pag. 151—104., Pl. V.

G. Dewargve. Essai de carte tectonique l.c. Pl. IV.

(4)

On the most important fault — called by UiwreNBROEK the “Geul
Valley fault’ — lie the mines Fossey, near Hergenraed (Rhenish

Prussia), Moresnet (neutral territory) and Bleiberg (Belgium). Excepting
the contact seams, containing calamine, the ores are galena, being
the oldest formation as usual, zine-blende and pyrites. The vein,
found at Bommerig more than 50 years ago in the lowest stratum
of the productive carbon, shows that from the south-east to the
north-west the ores seek more and more the younger strata *) and
that the direction of the Geul valley fault begins to deviate more
towards the north-north-west after bleiberg.

For years numerous borings were made in a more northern
part of Limburg, which led to the sinking and working of some
coal-pits. In December 1905 Mr. L. Rurren at Utrecht found on
the dump of the mine ““Carl”*) some pieces of ore which he presented
to the Mineralogical-Geological Institute at Utrecht. Further investi-
gations, undertaken by him, showed that these ores originated from
a vein, met when sinking the shaft, at a depth of 278 metres, but
of which the dip and direction had not been determined. He
succeeded in securing a number of pieces, belonging to private
people. The vein has only a thickness of 0.20 M. On the clay-
containing salband pyrites has deposited. while the vein mass proper
consists of calcite, developed in the cavities in the form of crystals,
on which sometimes also crystals of pyrites are found. Beside this
vein ores were also found, likewise on joints of the sandstone
of the mine “Carl”, namely pyrites, but also zine-blende, copper,
pyrites, and galena. Moreover crystals of calcite are always found
and generally dolomite.

In the mine Oranje-Nassau, near Heerlen, similar formations seem
to occur, at any rate crystals of calcite, covered with pyrites, are
found here on joints. Peculiar is here the regular coalescence,
caused by the small cubes of pyrites accumulating at the poles, then
continuing themselves on the obtuse edges of the scalenohedra and
here gradually disappearing.

We finally point out that while in the Stolberg district the veins
of galena, pyrites, zinc-blende, and calcite are still mostly bound to
the carboniferous limestone these minerals occur in the more western
Worm district on joints of the carboniferous sandstone, which is
a more recent horizon, a phenomenon which repeats itself at Heerlen.

1) At Eupen they still occur in the devonian system.
*) Situated at 11/3 kilometers east of Heerlen.

( 78 )

Physiology. — “Nerve influence on the action of the heart. First
communication. Genesis of the alternating pulse.’ By Dr. L.
J. J. Muskens. (Communicated by Prof. H. ZwAARDEMAKER).

(Communicated in the meeting of April 26, 1907).

Whereas in 1897*) the writer has shown, that in the “pulsus
regulariter intermittens” of the frog we have to see a result of
slowed conduction between sinus and auricle *), or between auricle
and ventricle, which was later accepted by Wencknsacn’) and recently
proved by Mackrnzin*) for man, the problem of the pulsus alternans
did not profit by the application of physiology on the diseased heart.
It is true, that already years ago Traube directed the attention on
those types of P. A. in which the period between the weak beat,
and the next stronger one is smaller than between the larger and
the smaller contraction, where i.o. w. the greater contraction com-
mences too early. But until now only Ornrwarr®), W. Srraug ®) and
TRENDELENBURG *) have gone into the analysis of allied heart-curves
of the frog, following up the way which had led to the elucidation
of the intermittent pulse.

It is clear, that for this analysis we must not join those observers,
who think that the explanation of the P. A. by inotropic influence
amounts to something more than a simple periphrase of the fact,
that every other pulse is weaker. For this misconception brings
with it the additional drawback, that it cuts off the way for all
further analysis.

In the alternating contraction of the ventricle we have to do not
with a simple pathological phenomenon but rather with a general
physiological function that makes its appearance in many circum-
stances, which tends to appear as well in vertebrate as invertebrate
animals under uncommon conditions. We have here to deal with
a capacity of the cardiac muscle which enables the ventricle to go
on with rhythmical contractions even under those abnormal conditions.

Digitalis dyalisata, injected subcutaneously in the frog, brings
about after some time peculiar changes in the heart-beat, after a

1) Geneesk. Bladen. 1897. 4e Reeks. Bo. 4. p. 77.

2) American Journal of Physiology. Vol. I. 1895 p. 509.

*) Wencxepacu. Nederl. Tijdschr. v. Geneesk. 1899. I. Blz. 666.

4) Mackenzie. Britisch. Medical Journal. 24 October 1906.

5) OeHRwatt. Skandinavisches Arch. f. Physiologie. Bd. 8. 1898.

6) Srraug. Arch. f. experimentelle Pathologie u. Pharmakologie. B. 45.
1) TReNDeLENBURG. Arch. f. Physiologie. (Anat. u. Physiol.) 1903. p. 284.

( 79 )

cerfain period of normal contractions. In the transition of the normal
period into the period of slow contractions, regularly curves are
recorded, which together with curves formerly published of the living
frog-heart (loc. cit.) throw light, on one of the, at least four
varieties of P.A. which in my opinion must be distinguished, at
least in the physio-pathology of the frog-heart. As to the three
other types of P.A. I think, that the way may become clear to
explain them equally.

First form of P. A. with equal intervals.

The ventricle beats in regular rhythmus alternatingly stronger and
weaker, the beginning of the weak contraction is separated by the
same length of time from the preceding and following contraction
(fig. 1). This variety was described by ENGELMANN *) and ascribed to
momentaneously diminished conductivity. F.B. Hormann’) has shown,
that this form of P. A. is often dependent on slight changes of the
frequency of the heart-beat. SrTRAUB proved, that this P. A. under
influence of antiarine easily gives way to ‘Puls-halbirung’’, which I
often saw under influence of digitalis dyalisata.

Second form of P.A. with retarded small contraction.

In a former publication *) I deseribed an example of P.A. observed
in the dying frog-heart, where the interval between the greater and
smaller V, was longer than between the smaller and larger con-
traction. There it appeared, that the auricle continued to beat regu-
larly. By comparing the intervals A—V, preceding the greater and
smaller contractions, we concluded then, that the contractionwave in
the A—JV bundle, eventually in the ventricle itself, might be slowed,
which was the cause that the V, not only came too late, but was
also weaker.

The supposition, that this P. A. in certain cases might depend on
changes of conductivity within the ventricle, had right of discussion,
although this could not be strictly proved, as is remarked by
Wenckepacu. For one can never with certainty conclude to a change
of conduetivity within a heart cavity (e.g. within V) if the interval
between the contractions of two cavities (e. g. A—V) remained equal.
But with the same certainty this meritorious observer is mistaken,
when he, from the few curves (10a and 104) of ENcELMANN generalises
to the contrary i.e. to the exclusion of a similar relation in other

1) EMGELMANN, Arch, f. d. ges. Physiologie. Bd. 62. 1896. p. 556 seq.
*) Hormann. Arch. f. d. ges. Physiologie. Bd. 84. 1900. p. 165.
3) L. J. J. Muskens, Nederl. Tijdschr. v. Geneeskunde. 1902, No. IL. Blz. 591.

(80)

‘ases. These curves cannot be looked upon as deciding in this point,
because not there as in my cases, the auricle beass regularly,
and therefore entirely different factors must be present, which has
been overlooked by the writer. He appears to disregard, that in
different lower animals, it was proved, that under influence of the
vagus-nerve, at the same time the conductivity in one cavity can be
improved, in others can be inhibited, which was confirmed by
_ENGELMANN, when he observed, how on the three bridges, veins-
sinus, sinus-auricle, auricle-ventricle, independently of each other,
conductivity might be changed; sufficient to show, that only very
direct proofs could force us to admit, that under pathological cir-
cumstances this independence of conductivity in various parts should
be lost. As well here, as also there, where WeNCKrBACH explains
the early smaller contraction by the quicker course of the weaker
pulse-wave in the vessels, Wernckepacn’s conclusions appear to be
much exposed to discussion. Also his conclusion, that there is no
principal difference between P. A. with too early and retarded small
contraction wave does not appear to be warranted by any well-
known fact, certainly not by WenckrBacn’s suppositions. Sufficient
facts can be adduced now, that here in different ways the same
result can be arrived at.

To my former curves of P.A. brought about by poor nutrition,
I now can add similar curves of P.A. brought about by injeetion
of digitalis dyalisata (fig. 2).

In this case the interval S7— WV, can easily be determined. This
amounts to 20.6; 22.5; 20.9. In every case this interval is lengthened
where it precedes a smailer contraction; ie. the contraction-wave,
which culminates in a smaller J’., found more resistance on its
way from the sinus to the ventricle and there was an undoubtable
slowing of the conduction.

Looking carefully at the curve, one tinds that the sinus contraction
preceding a weak JV’, shows a flattened top. By measuring the
intervals of Sz, it becomes equally clear, that the sinus does not
contract regularly and that it is the sinus contraction that comes
too early, that is followed by a smaller WW. Also the A, preceding
the weak J’, appears to be diminished in size.

Although it is not the place here, to go into detail about the new
fact, that there exists a relation between the force of the sinus and
auricular contraction and the force of the ultimate WW, I will only
remark, that in many simular experiments this relation was found,
The question arises indeed, if in fact different parts of the three
principal heart-cavities do maintain a special relationship in such a

( 81 )

way, that a completer sinus and auricular contraction tends to give
rise to a completer ventricular contraction. If so, the next problem
appears to be, whether this relation is kept up by special muscular
arrangements or else whether nervous and ganglionic influence may
play a rôle in it.

Third Form of P.A. with retarded smaller contraction.

Figure 3 is an example, where we find moreover reappearance of
normal pulsation. Simple inspection of the pulsating heart made already
the impression, that we had to deal with an antiperistaltie contrac-
tion; that the contraction-wave reaching the ventricle from the auricle,
returned again to the auricle. BRANDENBURG *), also Pan ?), Herine 5,
VorHARD *), and Scumoi.*) have observed antiperistaltie contraction,
after the writer had long ago shown’), that antiperistaltie contrac-
tions are a very constant phenomenon in the sinus of the turtle-heart.

In this case of fig. 3 we have to deal for the interpretation with
2 possibilities, 1. we may have to do with a real extra-contraction
of auricle and ventricle, which results only in a very small elevation
of the lever, because of its appearing in the beginning of the diastole,
the ventricle being in the refractory period; or secondly we have
to do with an antiperistaltie contraction wave, which on account of
insufficient restoration of conduction in the A—J bundle and the
ventricular musculature, can only give rise to a weak V,.

Indeed, the first supposition could not be discarded if it were to be
admitted that spontaneously under similar conditions in the frog such an
extra-A,, followed by a very weak J’, could occur; an extra-contrac-
tion, which moreover was followed by an uncomplete compensatory
pause. This conception is however hardly acceptable, if we take note
of the systematical mode, in which this P. A., so to say, is prepared
by the two abnormal contractions, which precede the very small V’,.
Because these changes in the two ventricular contractions occur
regularly at least in so far, as in my curves I come across similar
eases, I think, that the other interpretation gains considerably in
probable correctness. This supposition is therefore as follows: Under
influence of the drug the conducting power within the ventricle is

1) K. BRANDENBURG. Arch. f. Anat. a. Physiol. Abt. 1904. Supp. p. 216.

2) O. Pan. Deutsche Zeitschr. f. klin. Medizin. Bd. 78. 1903. p. i28.

3) Hering. Priiiger’s Arch. Bd. 82. p. 1.

4) Votnarp. Zeitschr. f. klin. Medizin. 1904. Bd. 53. p. 574.

5) Scumott. Arch. f. klin. Medizin. 1907. p. 507.

8) Ned. Tijdschr. v. Geneesk. 1898. Deel Il. Blz. 568 and Americ. Jnl. of Phy-
siology; Vol. L. 1898. p. 504.

(82)

sensibly reduced. In the first only slightly weakened V, only a

part of the ventricular musculature could contract as a result of

this disturbance of conduction. In the following contraction of the
ventricle the wave spreads, however more slowly than in the
normal cases (hence the stretched form of JV.) over the entire
ventricular musculature. As the conduction of the contraction wave
can take place after the modern doctrine of GaskELL and ENGELMANN
in all directions, the contraction wave in this case winds its way
‘through this lengthened J’, to arrive antiperistaltically again at the
auricle. After this only a part of the ventricular musculature has
regained its conducting power sufficiently and a weakened J’, will
join the antiperistaltie Ay. It is clear, that on account of the
antiperistaltie contraction the wave from A to V, to A again; from A
returning to another limited part of J”; then again to A, ete. will
give rise to a pulsus alternans, in this case temporarily, whereby
the interval between the commencement of the great contraction
and that of the smaller one, is smaller than that between the
small contraction and the greater contraction. One can among the
dyalisata-experiments recognise these cases there, where after a
maximal toxie dose the frequency first became considerably slower,
but finally quicker again. Whereas in the vena cava curve previously
the pulsations of the sinus were easily visible, one does not find
any indication of sinus contraction after the premortal pulse accele-
ration has set in.

We find therefore here a form of cardiac activity, which shows
the same particularities as the P. A. formerly described by the
writer for the poorly nourished frog-heart (Loc. cit. 1902) of whieh
however the mode of origin was quite a different one.

The only objection, which can be adduced against this interpre-
tation, is a theoretical one. Until now, it was looked upon as a
dogma, that the unimpaired ventricular musculature under no cir-
cumstances shows the phenomena of dissociation. This dissociation
between the different heart cavities and in every one separately, was
explicitly deseribed by the writer in several publications *), especially
regarding the sinus; its significance for our understanding of nerve
influence on the heart, was more than once urged. Although in these
experiments and those of ENGELMANN the occurrence of similar dis-
sociations also of the unimpaired ventricle had to be acknowledged,
the direct proof of its existence as far as I know, has never been

1) Geneesk. bladen 1897. p. 75. Proceedings of the American Academy of Arts
and Sciences 1898. Vol. XXXIIL No. 71. p. 188. Americ. Jnl. of Physiol. 1898.
p. 503 seq. Ned. Tijdschr. y. Geneesk. 1898. Deel Il, Blz. 572 and 1902 Deel IL.
Blz. 583,

( 83 )

proved. Where under influence of digitalis dyalisata the tendency
of the cardiac muscle to dissociation, as we saw above, is accen-
tuated, there we could expect that if we combine this influence
with the equally dissociating vagus influence, the evidence of dis-
sociation also in the ventricle might come out. Indeed, during the
influence of the vagus nerve on such an intoxicated heart, I found
a curve which is apt to illustrate this dissociation. We have here
to deal with the transition of an alternating pulse into a normal one,
after a direct vagus stimulation and shortly after the inundation of
the entire heart by a physiological salt solution (In the ventricular
curve this is visible).

In my mind there is no doubt, that the smail elevation after the
reduced ventricular contraction cannot be interpreted, either as an
auricular contraction (because nowhere in this or other tracings an
A, of this considerable height was observed) nor as an ordinary
extra-systole of the ventricle. In the latter case it could not be
explained not only why here an extra systole arose, nor why the
preceding ventricular contraction coming at the right time, was so
exceedingly diminished in size. We have here undoubtedly to do with
a dissociation in time of two parts of the ventricular musculature
(eventually also of the “Reizleitungssystem”) and only when after
the pulsus alternans a not completely synchronic contraction of these
parts has taken place, and the entire musculature comes again at the
same time in the refractory period, normal contractions can follow.
According to this interpretation the difference between the great and
the small contractions of the preceding P. A. is to be ascribed to
the fact, that only in the great contractions a particular part of the
muscular mass is reached by the contraction wave; whereas this
part of the muscle is excluded from the contraction in the small |’,.

Fourth form of P. A. with retarded great contraction.

Of this type of P.A. I cannot adduce any curve met with in
lower animals. The only specimen I have come across, is registered
from a case of Basedow, who suffered from an exceedingly rapid
and at the same time irregular heartbeat, It appears to me that here
we have to deal with an automaticaliy beating ventricle or better
with a ventricle, in whom two divisions are beating independently,
only every other J’, (the greater one) causing an antiperistaltie con-
traction reaching the auricle. Comparable curves have been published
by Mackersiwe *) and Wenckesacu *), so that its occurrence in men can

1) Mackensie, British medical Journal, 1905, III. Comp. fig. 12 perhaps also fig. 5,
2) Wencxepacu, Arhythmie. 1903. P. 107.

( 84 )

be doubtlessly stated. In the latter curves no registration of the
jugular vein was added to the ventricular curve, so that L am not
in the situation to suppose or deny for these curves the same origin
as in my curve.

All in all it seems to me, that in these curves and their analysis
we have important arguments, which tend to prove, that from the
physiological side more special research is needed regarding the
conduction within the individual divisions of the heart. For the first
of the four deseribed types of P. A. we have shown, that from
physiological side the cause has to be sought in changed conductivity
by which in the weak contractions, the contraction wave is limited
to a part of V. For the second type of P. A. we thought we were able
to bring direct proofs, while it became probable for the third type
of P. A., that they are results of the conduction between the sinus and
the ventricle becoming slower; and for the third form of P. A. it
appeared probable that the P.A. is the result of the antiperistaltic
contraction wave, so that we had here not a quantitative, but a
qualitative change in the conductivity. Regarding the fact which
‘TRENDELENBURG stated, that by stimulating the ventricle artificially
the frequency of the ventricular rhythm may become much greater
if slowly the stimulation is quickened, before ‘‘Halbierung” of
the heart-beat. makes appearance, then if within a short period a
great frequency is attained, it is equally to be interpreted as follows :
that by slowly increasing frequency the conduetivity is enabled
to adapt itself to the great demands; so that the moment is
delayed where necessarily only partial contractions of the ventricle
arise. Regarding the pathology, it appears to me that it is of
importance for the knowledge of the pulsus trigeminus, discussed
by Wenckesacn, that from physiological side the importance of
dissociation of the ventricle under certain circumstances as also
the importance of the antiperistaltie contraction wave has been proved.
With the statement that partial contractions do occur, it appears to
me, that the necessity becomes evident, that the law of Bowditch
has to be limited, in so far, that certainly every ventricular muscle
fibre whieh contracts, does so with maximum force; but on the
other hand, we have not to accept that necessarily in every ventri-
cular contraction all muscular bundles contract equally.

Where we have to interprete curves like those of TscHirsEw *)
(cited by Wenckesacn) of O. Par ®), R. FINKELENBURG *) and Hay

1) Tscurrsew. Archiv fiir Physiologie. 1877.
2) O. Pan. Deutsche Zeitschrift. f. klin. Medizin. Bd. 78. 1905. p. 128.
3) R. FinkerenBure. Cited by WenckeBacH. 1905. Heft 1 and 2. p. 586.

L. J. J. MUSKENS. Nerve influence on the action of the heart. First communication. Genesis of the
alternating pulse.

RAIA AAA AA AAA AAA

PUA

Vena caya in

Proceedings Royal Acad, Amsterdam. Vol, X

( 85 )

and Moorn') we should not neglect the value of these phe-
nomena. For the absence of the compensatory pause (WENCKEBACH)
finds in the above interpretation its complete explication. At the
same time we can now regard Herina’s opinion, that all pulsus
bigemini should always depend on extra systoles as definitively
rejected.

With Funke I agree finally in this that a further discussion
about the question, whether apart from the pulsus alternans also the
existence of a pulsus bigeminus must be acknowledged, is completely
superfluous. On the other hand it might be desirable, if the experi-
mental results of KNout and those of HeriNG in warmblooded animals
about hemisystolia and heart-trigemini, should be taken up again,
also in regard to the recent anatomical data.

Regarding these questions three recent researches must be
regarded as important, firstly the observations of W. EINTHOVEN *),
whose accurate illustrations also of partial contractions, appear to
promise a good deal for further analysis. Moreover the important
researches of Tawara*) in AscaHor’s Laboratory, which has shown,
how far the division of functions in the ventricle of the warm- and
perhaps also of the cold-blooded animals has gone.

Finally the observations of MackKexzie ®) who has shown us the
possibility, to get information also in man about the movement of the
auricle under pathological circumstances, so that we may expect
also this field of work becoming fertile for scientific analysis.

The next thing should be, to bring also the sinus of man under the
scope of the graphical method. Wernckespacn’) thinks to have reason
to believe, that dissociation of the sinus deseribed by me in lower
animals") might be observed equally in men.

To physiology the task to examine what influences are able
to dissociate the two principal bundles of the “Reizleitung” system
and to get information about nerve influence as well regarding that
system itself as upon the muscular mass of the ventricle.

1) Hay and Moore. Lancet 1906. p. 1274.

2) Eirnoven. Tijdschr. v. Geneesk. I. No. 22.

3) Tawara. Das Herzleitungssystem. 1906.

4) Mackenzie. Britisch medical Jnl. 1902. Nov. p. 1411.

5) WerckeBacH. Arch. f. Physiologie. 1906. p. 361.

6) American Journal of Physiology. Vol. I. 1898. No. IV. p. 503.

( 86 )

Zoology. — “On the structure of the nerve-cells in the central
nervous system of Branchiostoma lanceolatum.” (First comm.)

By Dr. J. Borkr. (Communicated by Prof. G. C. J. Vosmarr).
(Communicated in the meeting of April-26, 1907).

The methods of staining the elements of the nervous system,
published in recent years by Ramon y CaJaL, Donacaio, and especially
by Bretscuowsky, have enabled us to study the minute structure ot
the ganglion-cells not only of the lower animals but also of the
vertebrates with more success than before. After having published
in These Proceedings, some years ago'), the results of my former
investigations on the structure of the nerve-cells of Branchiostoma,
then studied by means of the goldmethod of Aparny, it seemed ad-
visable to describe here too the results of my recent investigations
on the same subject by means of the methods mentioned above,
because they extend and complete my former results in several
directions.

Contradictory to the results of Epincer ©, the only author who
studied the central nervous system of amphioxus by means of the
method of Binischowsky, viz. that the method gave only scanty
results for the neurofibrillae in the cells, in my preparations, stained
after the method of BimtscHowskY—-PoLLAck, in a great number of
nerve-cells of several specimens of Branchiostoma a very clear and
distinct picture was obtained of the neurofibrillae, not only in the
nerve-fibres, but also in the body of the nerve-cells.

Preparations of material preserved in a mixture of platinum chloride-
osmic acid-acetie acid and corrosive sublimate *), and stained in thin
sections with iron-haematoxylin after Hemennain, were used as control
and for the study of the protoplasmic structures between the neuro-
fibrillae.

The different cell-forms of the central nervous system gave there,
where they were satisfactorily stained, as a rule the same mode of
arrangement of the neurofibrillae in the cell-body ; therefore I will
restrict myself to describe here only some cell-forms at length and
only refer briefly to the structure of other cells. At another place
I hope soon to give more and fuller details.

1) Proceedings Roy. Akad. of Sc. Amsterdam, of the meeting of Oct. 25, 1902.
2) Anat. Anzeiger, Bd. 28, No. 17, 18, 24 April 1905.
8) According to Dr. Lraros the best method for the preservation of the nervous
system of Branchiostoma. I can fully agree with him in this statement. This
mixture gives better results than all the others | tried.

(87)

1. As is well known, the very large nerve-cells (“Kolossalzellen’’)
lying at about equal distances from each other in the axis of the
spinal cord, possess a thick axonic fibre, that after leaving the cell-body
describes a characteristic curve and passes into one of the colossal
nerve-fibres that run in a longitudinal direction through the spinal
cord, and a number of dendrites, springing from the cell-body at
different points.

Sections of these cells, stained after the method of BirrscnowskKy,
give a very clear picture of the neurofibrillar structure. In a section
in which only some of the dendrites are to be seen, and not the
“(of which more later on)
these cells show an arrangement of the neurofibrillae as shown in
feels

The cell is surrounded by a glious capsule, composed of fine
interwoven fibrillae. The preservation of the nervous system in formol,
necessary for the BieLscHowsky-reaction, causes the cells to shrink a
little, so that the pericellular cavity is larger than it is in normal
life and in well-preserved specimens. Within the cell-body the
neurofibrillae form a very distinct and regular network. Everywhere
they anastomose with each other, nowhere I could discover free
running fibres. The meshes are regular, round or manysided, and
nearly all of about the same size. A subperipheral zone is formed,
where the meshes are somewhat smaller and the composing neuro-
fibrillae a little coarser. From this zone a few coarse neurofibrillae may
be followed in the network radiating to the central zone around the
nucleus. The nucleus itself is not coloured in these preparations, but
is only to be seen as a clear round or oval spot in the midst of the
darkly stained network of the neurofibrillae. There where a dendrite
leaves the cell-body, the meshes of the network are elongated in the
direction of the processus (fig. 1, 45, 6). In the dendrites themselves,
at least in the coarser ones, the anastomosing of the neurofibrillae
is to be seen still at some distance from the cell-body. In fig. 1 is
drawn a section of 7 u thick. In three of the following sections,

axonic fibre with its “cÔne d’entrance

passing through the dendrites, whose origin is shown in fig. 1, I
could still see the anastomosing of the composing neurofibrillae. In
fig. 2 is drawn one of the large dendrites of a similar colossal cell
there where it branches into two. The network of the neurofibrillae,
several coarser (and more darkly stained) fibrillae, and the continuity
of the network in both branches is clearly to be seen. In the finer
dendrites the neurofibrillae seem to become isolated sooner after
having left the cell-body (tig. | at 5). The same is to be seen in the
smaller nerve-cells of the spinal cord (figs. 45, 6).

(88 )

The axon of the colossal nerve-cells has a somewhat different
structure. As I described in my former paper '), the colossal nerve-
fibres contain a great number of closely set exceedingly fine separate
fibrillae, which in well-preserved preparations are distributed regularly
through the whole extent of the fibre. There where the axon enters
the cell, this bundle of neurofibrillae may be followed some way
into the cell-body; we see the fibres describe a curve or vortex
around the nucleus, and then the thin fibres melt into the somewhat
coarser network of the neurofibrillae described above.

The smaller, mediumsized and smallest nerve-cells of Branchiostoma,
such as those that are drawn in figg. 4, 5 and 6, at the same scale
as the cell figured in fig. 1, show the same arrangement of the
neurofibrillae as the colossal nerve-cells, viz. a regular network, the
meshes elongated there where a dendrite or axon leaves the cell,
more or less rounded in the centre of the cell-body. The subperi-
pheral zone with finer meshes and coarser fibrillae I could not find
here; the network seemed everywhere to be regular throughout the
cell-body. In fig. 4a and 44 two sections through the same medium-
sized nerve-cell are drawn. In fig. da the nucleus is to be seen, and
on it a very regular network of neurofibrillae, with only one layer
of meshes, and therefore giving a very clear idea of the regularity
of the network. This section passes through the centre of the cell-
body. Fig. 4 shows the peripheral part of the same cell. The
meshes are here more elongated in the direction of the processus,
and in the network some fibrillae are coarser and more darkly
stained; all of these run in the direction of the dendrite and leave
the cell-body there; inside the cell they form part of the general
network; in the dendrite they run more or less parallel to each other
and do not anastomose any more (see page 2). The same features
are to be seen very clearly in fig. 6, showing the neurofibrillar
structure of another mediumsized nerve-cell lying somewhat more
cephalad in the spinal cord.

In fig. 5 is drawn a very small ganglion cell (magnified to the
same scale as the foregoing figures). Here too the network of the
neurofibrillae is easily to be seen and the meshes are of about the
same size as in the mediumsized nerve-cells described above, though
smaller than in the colossal ganglion cells.

Fusiform cells, in which the neurofibrillae simply pass through
the cell-body from one processus to the other without interruption,
as I described them in my former paper, I was not able to find in

1) These proceedings. Meeting of Oct. 25, 1902.

(89)

the preparations stained after Brarscuowsky. Where the neurofibrillae
were visible, they formed a network. In my preparations stained
with chloride of gold after Aparny, which I looked over for these cells
I however found them again. The uninterrupted course of the neuro-
fibrillae was clearly to be seen. They are however only very rarely
met with.

So we find in nearly all the cells a network of neurofibrillae
with regular meshes. In full-grown animals the meshes in different
cells are of about the same size. But when we examine the same
kind of cells (for example the colossal ganglion cells) in very small
animals, we find a neurofibrillar network of the same regularity but
with much smaller meshes. So when we compare fig. 1, a colossal
ganglion cell of a fullgrown Branchiostoma of 48 m.m. in length,
with fig. 3, an analogue cell of an animal of 6 m.m. in length, we
find a much smaller-meshed network. Those small animals have
finished their metamorphosis already, and present nearly the same
organisation as the adult animal. The nerve-cells therefore seem to
have assumed already the definite arrangement of their neurofibrillar
structure, but the meshes are much smaller. During the following
growth of the nerve-cells the reticulum grows, but the structure
remains the same. In different adult specimens the size of the meshes
seemed always to be of the same order, and only to present the
slight differences mentioned above.

When we compare this with the neurofibrillar structure, described
for the ganglion cells of other animals, I will here especially call
attention to the description of Aparuy for Hirudineae and Vermes,
of Bocurnek for Helix, of Donaceio, Casa, MicHorre, LRGENDRE and
the many authors, who have studied the ganglioncells of the higher
vertebrates by means of the new elective histological methods. Among
the deseriptions by these authors of the neurofibrillar structure in
the nerve-cells of the representatives of different classes of the animal
kingdom, that of Branchiostoma takes just the place, we generally
give to that animal in the animal series. Is fig. 7 is drawn a
sensory cell of a Pontobdella, with the neurofibrillar structure stained
after ApatHy. We see a very coarse network around the nucleus,
with fibrillae radiating to the periphery and forming there a second
network. The ganglion cells of Helix give according to BocHENEK*)
a much finer network. The meshes of this network are still much
larger than those of the nerve-cells of Branchiostoma; these in their
turn are larger and the fibrillae coarser than the neurofibrillar struc-

1) Le Nevraxe, Vol. III, Fasc. 1. 1901. page 85.

(90)

ture, as it presents itself in well-stained preparations of the nerve-cells
of the higher vertebrates (as for example in the splendid figures of
Donaaaio). It seems that the higher is the organisation of the animal,
and in consequence that of the nerve-cells, the finer and more regular
is the network of the neurofibrillae in the nerve-cells. (ef. BOCHENEK).

The network of the neurofibrillae has no definite connection with the
protoplasma-reticulum. Im preparations, preserved in a mixture of
HERMANN’s fluid and corrosive sublimate, and stained with iron-
haematoxylin, the protoplasma has a very fine granular or fibrillar
structure, and in the centre of many cells are shown curious diversely-
shaped differentiations that remind us of the pseudochromosomes
described by HeiDeNHAIN, and of the rings, described in the ganglion
cells of vertebrates (Teleostei, Rana). But it would take us too far,
to describe these details here at some length.

2. An entirely different type of cells we find in the nerve-cells
which form the large group of ganglion cells lying dorsally in the
foremost part of the spinal cord just behind the brain ventricle, the
so-called oblongata, extending from the niveau of the infundibular
organ till beyond the first pigmented eye-cells. It is characteristic of
the peculiar difficulties, with which the investigation of the histology
of the nervous system of Branchiostoma is encumbered, that of the
large number of authors, who have studied the subject, only Josrpn’)
two years ago gave a nearly accurate account of the structure
of these cells. Even Hbymans and van ber Srricut in their very
elaborate study of the histology of the nervous system of Branebi-
ostoma, published in 1898, do not say a word about it, and only
in one of the many beautiful drawings, with which their paper is
illustrated, in two cells a slight indication of it is to be seen. Joseru
says of these cells, that they present at the surface a finely striated
border of minute rods, only at the side of the cell turned towards
the surface of the animal, and underneath this striated border a
coarsely granular darkly staining protoplasm. The same structure
JosepH described in the cells lying close to the central canal in the
spinal cord, covered by a pigment-cap, and being supposed to be
light-percepting cells. On these grounds JosrpH put forward the
suggestion, that the dorsal group of cells too consists of eye-cells,
light-percepting cells, differing only from the cells of Hesse by the
absence of a pigmented cap-shaped cell.

This far-reaching suggestion is, I think, not proved, nor even made
probable, by the facts. Even in the most carefully prepared sections

ay Labs Josepu: Ueber einige Zellstructuren im Zentralnervensystem von Amphioxus
Verh. d. Anatom. Gesellschaft. Jena 1904. p. 16—26,

(A)

in which the structure of both cells was very clearly to be seen,
the two types still present some marked differences, both in the
nuclei and in the structure of the protoplasm and the differentiations
on the surface of the cells. According to Josep the nuclei of the
dorsal cells and of the ventral eye-cells possessed a similar granular
structure, differing from that of the other nerve-cells. In some cases
this is true, but in other cases the same structure is found in the
nuclei of other cells, and, when we examine a number of prepara-
tions, the structure of the nuclei both of the dorsal cells, of the
ventral light-percepting cells and of the other nerve-cells presents
so many differences and varieties, that there cannot be drawn any
conclusion out of that. But the capital difference between the two
cell-forms lies in the absence of a pigmented cap-cell in the dorsal
cells and the totally different form and structure of the two types.

The light-percepting cells of the spinal cord possess a border of
short minute rods, lying close against the cap-shaped pigment cell.
The processus of the dorsal cells are much longer, and not rods,
but exactly shaped like hairs, or cilia. These hairs (fig. 8— 11) are
rather long, slender and thickly set and their course is often more
or less wavy. On the same cell they seem to be all of about the
same length; the hairs on different cells do not vary much in length.

The ventral light-percepting cells are all of the same regular form.
The dorsal cells however present the most different forms. *) Some
are rather regular (fig. 8), some are long and slender (fig. 9), some
are of a very irregular shape, but in most cases these cells, when
we reconstruct them from the thin sections, appear to have a very
typical cup-shape. In fig. 10 I have drawn the median section
through one of these cups, in which the central hole in the cell is
figured, in fig. 11 such a cup-shaped cell is cut vertically to the
axis of the cup.

These cells are surrounded by a glious basket of closely interwoven
fibres (in the figures this network is represented by a dark colour)
and the cells seem to fill up the room left by this basket so that
between the surface of the cell and the inside of the basket there
remains an open space, in which the hair-like processes of the cell-
‘surface are seen. In well-preserved sections this space has the same
width on all sides of the cell, where the surface carries the hair-like
structures. . The hairs reach from the surface of the cell nearly to

1) Only such cells are described here, which seemed to be perfectly preserved
All those cells, of which the irregular form seemed to be caused by bad preser-
vation, are left out of the discussion.

6
Proceedings Royal Acad. Amsterdam. Vol. X.

the inside of the basket, as may be seen in the figures. There where
no hairs are developed, the glious fibres lie close against the surface
of the cell-protoplasm (fig. 8, 10, 11).

Where JosrpH considers the hair-like processes to be only present
at that side of the cell which is turned towards the surface of the
animal, I cannot agree with him. When we compare horizontal and
transverse sections carefully with each other, we must draw the
conclusion, that the hairs may be developed on all sides of the cell,
except there where the cell-body sends a dendritical process through
the glious basket. Even there where the cell is shaped like a cup
or calix, at both sides of the cup the cilia may be present (figg. 10, 11).
The cilia at the inside of the cup are separated from each other by
an ingrowth of the fibres of the glious basket (fig. 10). When the
cell is cut at right angles to the axis of the calix, this may lead to
the appearance of a ring of protoplasm, at both sides covered with
the hairs, and surrounding a mass of coiled-up fibres, the ingrowing
fibres of the glious basket (fig. 11).

The protoplasm of these cells shows a regular network of neuro-
fibrillae, which differs from the network of the other cells of the
spinal cord by its much larger meshes (compare figg. 8—10 with
figg. 1—6); only at the periphery of the cell, under the hair-like
processes, a finer network of neurofibrillae is to be seen (fig. 8).
The hairs themselves seem to be implanted on a layer of small darkly
staining granules or small rods, of which the definite structure is
difficult to be seen. In many cases it is only represented by a some-
what more coarsely granular layer of protoplasm there where the
cell-body is covered with the hairs.

All these things seem to point to the conclusion that these cells
do not possess a light-percepting function, as suggested by Josnpn.
The shape of the cells and the peculiar structure at least are not
favourable to the hypothesis. But it is sure, that this group of cells,
all presenting the same peculiar structure, has a distinct and peculiar
function. The structure of the cells reminds us in the first place of
a statie organ, and especially cells as-drawn in fig. 9 and fig. 11,
seem to suggest such a function. The peculiar baskets of fibres sur-
rounding the cells remind us of the cells of Purkinse of the brain
of the craniotes, but bearing in mind the very little we know about
these cells and about the cells just described, it is more advisable to
stop at these general suggestions and not to try to go more into details.
The suggestion of JosepH at all events seems to me to be untenable.

A third type of cells differing from those which I deseribed here,
is that of the cells of the so-called infundibular organ in the ventral

J. BOEKE. On the structure of the nerve-cells in the central nervous system of Branchiostom

lanceolatum. (first communication).

A,
(enten EN
Ne

== 6 0,
* “xt

Proceedings Royal Acad. Amsterdam. Vol. X.

( 93 )

wall of the brain-vesicle. These cells I mean to describe in my
second paper.
Leiden, 25 April ’07.

DESCRIPTION OF FIGURES ON THE PLATE.

All the figures are magnified 1600 times, and are drawn with a camera lucida
of Asse directly after the preparations. Apochrom. oil-immersion lens of Zetss and
compens-ocular No. 8. :

Fig. 1. Colossal nerve-cell with neurofibrillar network, of a Branchiostoma of

4.8 cM. in length (BretscHowsky—Pottack’s method).
„ 2. Dendrites of a similar cell of an animal of 5 cM. in length (same method).
„ 3. Neurofibrillar network of a colossal nerve-cell of a Branchiostoma of

6 mM. in length.

a and b. Sections of a medium-sized nerve-cell of the same spinal cord

as fig. 2:

5. Section of a very small nerve-cell, with neurofibrillar network.

» 6. The same as in fig. 4.

7. Section of a sensory cell of Pontobdella, of 104, treated after the gold-
method of Aparny.

» S—11. Sections through different cells of the dorsal group of cells lying
behind the brain-vesicle, taken from preparations of several adult
specimens of Branchiostoma. In fig. 8 some of the adjoining cells are
drawn, to demonstrate the similarity of structure of the nuclei in the
two cell types.

In fig. 10 and fig. 11 are drawn two typical sections through cup-shaped
cells of the dorsal group of cells. The body contained in the centre
of the cell of fig. 11 is the prolongation of the glious basket sur-
rounding the cell. Compare fig. 10.

s
=

Physiology. — “On a third heart sound’. By W. E1xruoven, in
collaboration with Messrs. J. H. Wirrinca and E. P. Sxiopwrs,

assistents at the physiological laboratory at Leyden.

When continuing the investigation of the heart sounds by means
of the string galvanometer '), we noticed that in some cardiophono-
grams, especially with the apex sounds of Wi, recorded in February
last, shortly after the vibrations of the second sound still another
vibration was present, which admitted of no other interpretation than
by regarding it as a third heart sound.

We could not at once explain how this third sound was produced,
and we put off the closer investigation of this phenomenon, however

1) See: Die Registrirung der menschlichen Herztöne mittels des Saitengalvano-
meters. Prrücer’s Arch. f. d. gesammte Physiol. Vol. 117, p. 461, 1907,

6*

( 94)

interesting it seemed to us, since for the present our time was taken
up by other work.

A couple of months afterwards Dr. A. G. Gipson of Oxford —
to whom our former publications on the recording of heart sounds were
known, but who could not be acquainted with our later observations
asked whether in our collection of cardiophonograms of normal
persons there were any in which an extra sound was visible in the
diastolic phase. Gipson occupied himself with an investigation of the
venous pulse *) and had noticed that with some persons, without a
morbid affection of the heart, a low pitched sound could be heard
at the apex during the cardiac pause, something like a distant 24
sound, but feebler and much lower in pitch. The sound is clear and
nothing like a murmur. This particular sound is of varying intensity
being louder during the interval between the end of an expiration
and the beginning of the subsequent inspiration.

We hope elsewhere to publish in a more extensive paper the
cardiophonograms we obtained; here we shall only deal briefly with
them. When we try to predict from the shape and dimensions of
the curves what impression the third heart sound must make on the
ear of the observer, we cannot describe it otherwise than Gipson
did: a distant diastolic sound ef low pitch and clear tone, varying
in intensity, but always feeble.

There can be no doubt that the sound, heard by Gipson at Oxford,
is the same sound we recorded at Leyden.

The measurements made with some cardiophonograms, show that
with Wi the beginning of the third sound falls on the average
0.13 sec. (varying between 0.11 and 0.15 sec.) after the beginning
of the second sound and on the average 0.32 sec. before the beginning
of the following first sound. In the same curves the duration of
the first sound is about 0.08 sec. of the second about 0.05 sec. of
the third 0.02 to 0.03 sec. The first two sounds are murmurs, com-
posed of tones of irregular pitch. The mutual distance of some tops
in the curves shows that we have here tones of more than a hundred

double vibrations per second, whereas the third sound seems to be
built up of but one double vibration, the period of which amounts
to about 0.02 see.

The intensity of the third sound varies. While in some cardiac
beats it is entirely absent, the amplitude of its vibrations reaches in
other beats 1/7 of that of the first and second sounds. Putting the

1) Gteson’s investigation will shortly be published in “The Lancet” under the
title: “The significance of a hitherto undescribed wave in the jugular pulse”.

(95 )

ratio of the amplitudes of the first or second sound to that of the
third a —= 7, and the ratio of the frequencies ) —2, the ratio of the
intensities is a? 6° —= 196. Hence the third sound is at its maximum
still about 200 times feebler than the first or second.

While the above given figures refer to the objective intensities, a
comparison of the intensities of perception is still much less in favour
of the third sound, sinee a tone of frequeney 50 per second has
objectively to be a little over a hundred times stronger’) than a
tone of 100 vibrations a second, in order to produce an equally
strong auditory impression. Consequently, if the third sound attains
such an intensity that it is just audible still, the first and second
sounds may be 20.000 times weakened, before also the auditory
impression they produce, vanishes.

This explains the difficulty of the investigation by the method of
auscultation. GiBson *) emphasises this particularly and says that in
order to hear the sound, accidental sounds must be excluded as much
as possible, while one has to strain one’s attention during*the interval
in which the sound occurs. Although the cardiophonograms leave
no doubt as to the existence of the third heart sound with Wi, we
have been unable to hear it by means of a stethoscope.

Regarding the explanation of the third sound we refer to the
above mentioned more extensive paper which will shortlyfbe published
elsewhere. Here we will only state our conclusion that the sound
cannot be put on a line with a prae-systolic murmur of the mitral
valve, nor with a duplication of the second sound by non-simultaneous
action of the aortal and pulmonal valves, but that it is probably
caused by a second vibration of the valvulae semilunares aortae and
must be regarded as a phenomenon of pretty common occurrence.

Astronomy. — “On some points in the theory of Jupiter’s satellites.”
By Dr. W. pr Sitter. (Communicated by Dr. E. F. van pe
SANDE BAKHUYZEN).

The following pages contain a short account of some investigations,
which will soon be published, together with other results, in N°. 17
of the publications of the astronomical laboratory at Groningen.

A few words are necessary in explanation of the notations em-

1) Calculated according to Max Wren, Prrücer’s Arch. f. d. gesammte Physiol.
Bd. 97. p. 1. 1903. H. ZWAARDEMAKER and F. H. Qurx give in ENGELMANN’s
Arch. f. Physiol. p. 25. 1904, differences in the same sense, but of a different

order of magnitude.
*) Ic

(96)

ployed. The notations used by different writers on the theory of the
satellites are discordant in a most regrettable manner. The tables,
both those of Damoisnau and of DprAMBRE, distinguish the four
satellites by the numbers 1, 2, 3, 4. This example is followed by
Marrn, and I have also in all my previous work on the satellites
used this notation, as is also done by Mr. Cookson in the discussion
of his observations. The theoretical writers, on the other hand, LAPLACR,
TissERAND, SOUILLART use the suffixes 0, 1, 2, 3 or a corresponding
number of accents. Another fundamental difference is in the designation
of the perijoves. The letter © in the writings of Damotsnau, Marra,
Cookson and myself represents the ‘own’ perijove; SOUILLART and
TissrRAND use it for the osculating perijove. There are many more
differences of this kind, which need not be enumerated here. Though
thoroughly convinced of the great importance of a consistent notation,
I am, reluctantly, compelled in this communication to depart from
the notations employed by me elsewhere. In the first article of the
present communication, which treats of a theoretical point, I have, to
avoid the writing out at length of many well known formulas and
results, closely followed Tissrranp’s very clear argument in the
fourth volume of his Vraité de Mecanique Celeste. Accordingly in
tos first article, | will adopt Tissrranp’s notation, with one exception.
In the further articles I will return to the notation employed in my

previous work.

1. Theory of the libration. As has been explained, the notations
employed are TissmRAND’s excepting the mean longitudes, which I
denote by /,,/,,/, instead of by /, 7,7. In addition to the quantities
FI’ G, G’ defined by (19) page 11+) I wish to introduce

» | Ae OAC)
CS AQ) — aa —
a Oa
da! dA'D
G!'=— — 8a’ A) — ala! —_—
bl Bf = 4 As
a da
TisskRAND assumes Gr, == G and G,’ = G’, which is only approxi-

mately true. If it is not desired to introduce this approximation,
then on page 11, formula (20) we must in Rk, replace G by G, and
similarly in B,’ G’ by Gy’.

The only further difference from TisskrAND’s notation is in the
definition of the libration. [I put

1) The references of pages and formulas are to those of Tisseranp, volume IV,

(97)

a ANNEER 0
TisseRAND, however, has
o=l— sr 4 A".

The angle 9, as defined by [1] is the angle to which the name
libration was first applied by Larracp, and which is by him called ©.
(Mecanique Céleste, Livre VIII, art. 15, Oeuvres, tome IV pages 75
and 79 of the edition of 1845).

The differential equation determining the libration is

ay
dt?

NO rt B Soe lon ace, (741)

This equation is derived by the combination of the three equations

T?] \
a = — Q, sind
d?l, ‘
TE = — Q, sin 9 ae Oe pete, ed es aed)
ails ay
a = — Q, sin D
(
We have thus
RE 6 EE oo (ea

From these equations the whole theory of the libration is derived
in the well known manner, on which, however, I will not dwell,
my sole object being at present the determination of the quantities
Qc. and. Qs.

For that purpose we start from the formulas given by Tisseranp at
the top of page 20, which must however be complete] as follows:

Powe ns (ORS OR;
FS ar 2 ; i 4
dt a de de

and two similar equations for g' and 9".

Introducing the same auxiliary angles uw and w' that are used by
TisseRAND (formula (12) page 20), we get instead of TIsspRAND’s
equations (5):

/

(98)

dg 3 'g -! a ay, t À !
——=— mn | F (k sin u — h cos u) + — G, (k' sin u — cos u)
dt? 2 a

— 3n ie (ee — h?} sin 2u — 2kh cos 2)

ma 5 aa aes
jk’? — MV sin 2u — ZMK! cos 2u

mY a

— 2bo1 i — hh’ sin 2u — Wh’ + hk cos 2n) | :

d'o' a age ;
~ —= — Bnn? | G(R sin u — h' cos u) + — F (hk sin u — h cos u) \
dt? a ; \

|

3 a
+ = m''n'? | FR sin ul — h' cosa’) + — (U! sin u! — h" cos u') |

a a

+ Gn E 0 (: k? — h?? sin 2u — Zh cos 2)

mY a
—— ag} | {k? — h?} sin 2u — 2kh cos 2u
m Ya

— 2biv (we — hh’ sin 2u — Wh + hk’ cos 2n) |

== BY E (us — h'® sin 2u' — 2k'h' cos 2’)

Lid mn /

m a

+ ——— ag) | fh"? — h'?! sin Qu! — 2k"h" cos 2u |
m Wa

) [6]

— bio (wer — Wh? sin 2u' — Wh" + Ik" cos 2)

el "

do x 5 a

ee mine G (k"" sin ul — h"' cos ") + — Ff" (k' sin u —h' cos ")|
5

a

+ 6n" E (1 — hn sin 2u' — 2k"h" cos 20)

ma a ox
-+ ———_ajo{ fk’? — h'?} sin Qu! — kh cos 2u

" " =

mM a

— 2b24 (we — Whi sin Qu! — eh" +- hk} cos 2n') | -

To derive from these the formulas [3] we must for h, 4, h'
substitute the values
h= Bsinu + B, sinw

; ete. . . . . . ° [7]
k= Beosu + B, cos w',

which are given by TisseRAND at the bottom of page 21. In the

(99)

result we then reject-all terms which do not contain the argument
uo —u=d-+ 180°,

or its multiples. We thus find easily

@o 3

Fa Sie min] PB, oo = a | sin (u—w')
lrg
|

: GVA) A ;
— 3n 4,1 Be + a0 Jr east 2bo,1 BB, sin 2 (u—w)
mYa

m' ae

— 6n E | BB, he a o BB, — bo (BB +B 1B) fein (u!)

~— = — 3mn” Fen. + — = FB, | sin (u—u')
a

3 Tae
— 5 m'n? [rs + — au | sin (u'—u)
a

my a

m mwa
mY a

mal

-+ 6 E 0B,’ + Aon By? — 2b, 0 BB, fin 2 (u—uw')

+ 12n! | evo, ae aon BB, — b10(BB,' +B; |

sin (u—u')

m Ya

m'a" AR
— 67’ ao BB, = micah SE —b,9(B'B, 2,5) |

a

li "
m'a
— 7 J 9 Bl? — aa, B"* — 2b» ze sin 2 (u —u)

sin (u — u)
"

d'o : a"
= — mn | G'B" + — F'B' | sin (u'—u)
dt? a
me ma 4
+ 6n E LB" + —— ajo B® — 2bo) BB | sin 2 (u'— u)
mya
ji eum ma
4- 12n Eg B B, zhe "Va" 3,'— ban (BB, BB]
a

sin (u'—u)
We now put
sin (u—w') = sin 9
sin 2 (u—u') = — 2 sin 9,
Further we introduce the approximate values of B, BR’...
TisseRAND gives in the middle of page 22, viz.:

which

BOG Bn Bi Bil a S|
where C is a constant, the value of which is indifferent to our
argument, and can easily be derived by comparison with TISSERAND,

( 100 )

We then neglect the squares and products of B, B’..., and also
the difference of G, and G, and we put
ia =n tat Sn ha Soh sone ee en
which also is only approximately true, and
3 if YZYV Y
GSR
2 a

Introducing all these simplifications we find the equations (22) of
TISSERAND, VIZ. :

dl, mm)! f

= — — K sin 9
dt a’

dl mm!

2 ¢ .
== 3 —— K sin d
dt Oe
dl, Mmm

enn Ae:
dt Que

In comparing these with TissERAND it must not be forgotten that
our 9 differs 180° from TisspRAND’s. We have thus, if all the above
mentioned approximations are introduced

mm!’ mm! mm)

Kh Gek Q=2

a=

Ro. Tl

q''?

The values [9], however, are only approximately true; they contain
only the perturbations of the first order in the masses. Nevertheless
the deviations of the values of Q; from the truth caused by the
adoption of these approximate values, and similarly by [10] and by
the neglect of difference of G and G,, are not of a serious nature.
The neglect of the terms of the second degree in B, B’... on the
other hand, is very serious.

Now discarding all these simplifications, with the exception of
BB), which we continue to adopt, we find for the com-
plete values of Q,, Q., Qs:

At
Q, == 2 mn? = GAB — 6n [| ay 0(B,” — B'B,') bor po |

a
Qn = tem GBI a m'n? FB +
12
+ 12n' [aro(B*—BB,) + bio BB] + [12]
+ 6n' [ai2(B?—B'B,') + bie BB,"
" mi !
Q, = — 8m'n'” s HB — 2 Ew oy9(?—BB,) +b, BB, |
a m'a |

Using the numerical data adopted by Sovrmarrt, and putting
m, = 10000 m, m, = 10000 m', m, = 10000 m”.

( 101 )

we find from formula (411)
Q, = + 0.03201 m, m,
Q, = — 0.03794 m, m,
Q, = + 0.00994 m, m,,
From the formulas [12], on the other hand, we have:
Q, ={+ 0 03009 — -00460 m, — -01156 m, — -00958 m,}m, m, =
= + 0:01815 m, m,
Q, = {— 0:03436 + -00389 m, + 00933 m, + -00809 m,}m, m, =
= — 0:02438 m, m,
Q, = {+ 0-00794 — -00020 m, — -00016 m, — -00042 m,} m, m, =
= + 0:00751 m, m,.
The numerical coefficients depend almost exclusively on the ratios
of the major axes, i.e. on the mean motions, and they can be taken
as correct to the last figure given.

The corresponding periods, computed by the formula

Tr,
B
are, expressed in years:
inametormila: ELI tT 6 S18
from toemdan bape he. od ==, C985,

The difference is considerable.

The question naturally arises: why have these important terms of
the second degree been overlooked by Larracr and Soumiart? For
Larrace, the answer is very simple: he has neglected the part R,
of the perturbing function throughout. For Sovi_Larr it is different.
It is one of Soummart’'s great merits to have discovered the importance
of this same part of the perturbing function, especially for the
determination of the quantities B, B’... The corrections which have
been added by Soum.arr on this account to these coefficients, amount
to a considerable part of the whole. Also SourLLart evidently intended
to find the expression for the period of the libration as completely
‘as possible. On the pages 46 and 47 (Memoirs of the Royal Astro-
nomical Society, Vol. XLV) he considers the different parts of the
perturbing function, which can in the differential coefficients of the
mean longitudes introduce the argument /,— 3/,-+ 2/,. He, however,
rejects them all, as giving negligible coefficients, and retains only
the terms which had already been discovered by Lapiace. Among
the rejected terms are also the new terms treated above, which are
discarded by Sovittarr on the ground that they are of the second
degree in the excentricities (page 47, bottom). He here overlooks

( 102 )

that in these terms, for the same reason as in those of the first
degree, the excentricities must be replaced by their perturbations
with the arguments w and w’, in order to find the terms determining
the libration. These terms thus are of the second degree, not in
the excentricities, but in the quantities B, B’... and of these the
squares are not negligible, as we have seen.
The question further arises: do not the terms of the third degree

in the excentricities, i.e. those of the types

Pe? cos (2U — 1 —o), Qe ecos(2l' —l — 20+ 0),

Re? cos (61 — 31 — BO), Set cos (4l' —1— 3), ete.

also contribute appreciably towards the coefficients Q;? To find the
answer to this question I have computed all the terms of this kind
in Q,. These terms of the third degree, which are of the fourth order
in the masses, are:

dQ, =§+ :00012 m,* + :00079 m,? + 00034 m,? + 00061 m, m, +

+ -00050 m, m, + .00124 m, m,}m, m, = + .00071 m, m,.

They are thus not wholly negligible. I have, however, not carried
out the computation — which is rather complicated — for Q, and
Q,, nor have I computed the terms of the fourth degree (i. e. of the
fifth order in the masses). The development of the period 7’in powers
of the masses evidently converges very slowly, and the period com-
puted by the formulas [12] may very well be erroneous by a few
tenths of a year.

2. The equations of the centre. The large inequalities, which in
the integration by the method of variation of elements appear as
perturbations of the exeentricities and perijoves (formula [7] above),
are in practice added to the longitudes and radii-vectores, and the
excentricilies and perijoves are conceived to be affected by their
secular, but not by their periodic perturbations. I now return to the
notations used in all my other work on the satellites, and I denote
the excentricities and perijoves, defined in this way, by ZZ; and @;,
We have then *)

sin @; are

ba =D sn Qe SP =; Tij €
Q;

4)
k; = 2 E; COS =

Or EAR Ne
— Sj Tij ej COS wy

te be

The sums extend over the values of j from 1 to 4; e; and @; are
the “own” execentricities and perijoves of Lapiacr, the values of
e; are constant and o,; are linear functions of the time. Further

1) These h; and ki are thus not the same quantities as those denoted by h, k, h’...

by TissERAND,

( 103 )

4 7 dw; 4
ti = 1, the other ratios zj, and the motions ae depending on the

dt

masses. Thus if certain values of the masses are adopted, the ratios
tij are thereby determined. If then 4; and #; of the four satellites
are known from the observations, then from the eight linear equations
[13] (consisting of two sets of four each, with the same coefficients)
we can determine the eight unknowns e; sin ; and e; cos ;, and
from these again ¢ and w;. The method is exactly the same as the
one used by me for the determination of the inelinations and nodes
(see these Proceedings, 1906 March, pages 767—780). The values of
h; and k; have been determined from the heliometer-observations
made at the Cape Observatory, in 1891 by Sir Davin GiLr, and in
1901 and 1902 by Mr. Bryan Cooxson. The results from these
observations have been treated by the method just delineated, in two
different suppositions regarding the masses, i.e. regarding the ratios

e o 0,

2 = 900°O
= (3)
z 2 |
4 WO System | System System | System | System | System
n I Il IA I lie a) ae I I
| |
a le} le} 3 a ls) | Peat) _o oO le}
1891:75 0:036 | 0-036 | +:009 [158 157 + 15 248 [235
| |
I | 1901-6 “055| 055) + 22 [41386 |436 + 36 48 50
| |
1902-60 -022) -021) + 47 1262 |270 | + 27 120 _|131
| ar |
| | |
1 _1891-75 | 0-018, 0 020} +-006 |169 166 | +46 1300 | 274
= |
|
| 1901 -61 020 O19) + 14 |318 |315 +37 [292 | 294
II 4 | |
| 1902°60 026; 0% + 9 |302 [301 |+ 24 [961 | 967
| |
Mean 0-021 | 0-022 284 278
|
| | | |
! 4894-75 0:-086 | 0:086 | +:003 [179:7 |179°6 |E 2:0 f201:4 |200°4
| 1901 -61 100 101) + 9 [198:2 |198-1 + 5:6 [193:9 193-8
Ill / |
| 1902-60 -O80 ‘080; + 6 [219:0 8-8 | + 4-0 4212-2 | 919-3
| Mean | 0-089 | 0-089 202-5 | 202-2
{ 1891-75 |0°4284 |0-4280| +:0015 [142-28 | 142 29) + 0-20)148:19 | 147-83
| |
1901-61 -4298| -4216| + 30 [148-92] 149-05) + 40} 147-76 | 147: 96
IV |
4902-60 “4261 | -4262| + 25 |149:06/149:08 | + 34f147:20 | 147: 28
ï Mean 0° 4258 | 0-4253 147.72 | 1417-69

( 104 )

B do; = ; 5 .
Tj and the motions ——. The results are collected in the following
dt

table. The values of w; for 1900.0, given in the last two columns,
have been derived from those for the individual epochs for each
dw;

system separately by means of the motions En corresponding to the
assumed masses. The perijoves are counted from the assumed vernal
equinox of Jupiter, whose longitude in 1900.0 is 135°.45.

The values of these elements, on which Soummart's theory is
based, are: ‘

(1900-0)
Kom 4 o
e, = 0:001 wv, = 305
e, — 0-006 Ons 110
e, — 0-064 o, == PANO
e, = 0:4160 0, 5200

The results from the two systems are practically identical. The
corrections 10 SOUILLART’s values for the satellites IT, [IL and IV, are
considerable, and on the whole much larger than the deviations of
the three epochs inter se. These corrections are thus undoubtedly
real. The most remarkable of them is certainly the large own
excentricity of IL. The value of this element, assumed by DerAMBRE
and Damoisrau is zero. The value used by Sourrarr in his theory
is a pure arithmetical result, and has no weight whatever as a
determination of the element. Damoiseav, however, has suspected the
existence of an excentricity of practically the same amount as is
found here. This is shown by the following quotation from his un-
published memoir, written in explanation of the construction of his
tables, which I quote after Soumtart'). Damoiskau says there:
“Nous avons des motifs de soupconner dans lorbite du second
satellite une équation du centre propre de 325 en temps synodique
(ce qui correspondrait a une excentricité propre de 0.00032738),
mais notre incertitude sur la position du périjove, dont le mouvement
est encore a calculer par la théorie, nous a fait remettre cette re-
cherche à un autre temps.” This excentricity, expressed in arc is
0°.0188, and it is therefore practically the same as the value found
by me. The reason adduced by Daworsrau for not using it in his
tables sounds somewhat strange: as a matter of fact the motion of
the perijove had been determined long ago by Lapnace.

With regard to Satellite [ it is clear that the apparent equations

1) Mémoires des Savants ctrangers, tome XXX, page 28.

ne den RE an ate

(105 )

of the centre derived from the observations — which moreover are
only little larger than their probable errors — do not represent a

true excentricity. It is not impossible that they are produced by the
existence of surface markings on the dise of the satellite, causing the
centre of light, which is observed by the heliometer, to be displaced
relatively to the centre of gravity, the displacement being different
at different epochs. Any attempt to explain the observed /; and 4,
on this hypothesis would, however, necessarily involve so many
undeterminate quantities, that its success would be no proof of its
representing a true fact of nature.

3. Determination of the libration from the observations.

In a communication made by me in 1905 to the “Nederlandsch
Natuur- en Geneeskundig Congres”, *) I have shown:

that the libration probably has an appreciable coefficient,

that the determination from the observations, not only of the
phase and amplitude, but also of the period of the libration, is ot
the highest importance for the derivation of the masses, especially
of the mass of Satellite I,

that this determination is possible from the observations made at
the observatories at the Cape, Helsingfors and Pulkowa,

that most probably the period differs considerably from the value
adopted by LaprLacr and Soumrarrt, and

that this determination is intricately connected with an investigation
of the long-periodic inequalities in the longitudes of the satellites,
and that consequently the whole problem can only be solved by
successive approximations.

In number 17 of the Publications of the Astronomical Laboratory
at Groningen, which will soon be published, all these conclusions
are confirmed and the successive approximations are carried out. In
this communication I cannot dwell upon the details of this investiga-
tion, nor upon the difficulties which were encountered. I must confine
myself to a brief statement of the results.

The observations used are the heliometer-observations of the Cape
Observatory already quoted above, and further photographie plates
taken at Helsingfors in the years 1892—93, 1893—94, 1894—95,
1895—96 and 1897, at Pulkowa in 1895—96, 1897 and 1898, and
at the Cape in 1904. I thus had at my disposition ten oppositions

1) “Over de libratie der drie binnenste groote satellieten van Jupiter en eene
miewwe methode ter bepaling van de massa van Satelliet 1” Handelingen van
het 10de Congres, pages 125—128.

( 106 )

in all. For each of these corrections Al; to the assumed longitudes
of the satellites were derived. These direct results from the obser-
vations can, however, not be used as they stand. There are, as has
been mentioned above, in the longitude of each satellite four unequali-
ties, whose periods are between 400 and 500 days, and whose
coefficients are of the same order of magnitude as the libration.
These inequalities therefore, during the few months over which each
of the ten series of observations extends, are practically constant,
and the correction Al; derived from the observations consequently
contains, in addition to the correction Ae; to the mean longitude,
and the libration, also the correction to the assumed values of these
inequalities.

Now the coefficients of these inequalities are proportional to the
excentricities and depend on the masses, and are therefore incertain
to the same extent as these, i.e. to a very large extent. The periods
of the four inequalities are so nearly equal, that they cannot be
separated from each other. Further the period of the most important
of them — important both by its magnitude and by its uncertainty
— differs just so much from the average interval of one opposition
to the next that, when we consider only the values at the epochs of
opposition, the inequality presents itself as one having approximately
the period of the libration, and can therefore not be separated from
the libration itself. For all these reasons it was impossible to
determine the libration and he long-periodie inequalities from these
observations alone.

For the determination of the masses, leaving for the moment the
mass of IV out of consideration, we have the following data:

1. the large inequalities in the longitudes of the satellites I, II
and III,

2. the motion of the perijove of satellite IV,

3. the period of the libration.

The motion of the perijove of IV also depends on the compression
of the planet, which must thus also be investigated, and is deter-
mined by

4. the motion of the node of satellite IT.

The data mentioned under 1, 2 and 4 are those used by Lapnacs,
3 has for the first time been pointed out by me in the communi-
cation to the “Nederlandseh Natuur- en Geneeskundig Congres”,
quoted above.

The method by which the approximations have been conducted is
the following. Certain values of the masses, approximately verifying
he conditions 1, 2, and 4, are assumed, and the corresponding

(107 )

values of the long-periodic inequalities are computed. Let these
be dl’, and let dl” be the values used in computing the tabular
places which were compared with the observations. Then evidently
the correction to the mean longitude corresponding to the assumed
masses (and equations of the centre) is

Al; = Al; — (dl — dl;°).

From these Al/ we then determine the amplitude, the phase and
the period of the libration. If this period co-incides with the one
computed from the assumed masses, then the approximation is suffi-
cient, if not, then the whole process is repeated with different masses.

The communication of the different approximations and of the
residuals remaining after the substitution of the finally adopted values,
would exceed the limits set to this paper. The formula finally derived
for the libration is

oo . t— 1895-09
o = 0°.158 sex ———__—— .

The adopted masses are
m, = 0.0000 256
m, = 0.0000 231
m, = 9.0000 820
and the corresponding ratio of the distribution of the libration over
the longitudes of the three satellites is given by

ov 9 J
“1 — +4 0-175 “2? — _ 0-260 “* — 14 90-0225
‘ 9 a

The mean longitudes (excluding libration) on 1900 January 0,
Greenwich mean noon, are (counted from the point Aries)
1, = 142°-604
99 -534
= 167 -999
— 234 -372,

/ —
l
l

3
3
4

By a comparison of these with the values at the epoch 1750.0
the following sidereal mean daily motions) were derived

n, = 203°-4889 5652
n, = 101-3747 2411
N= 90-376 O0790°

Ny — .21 .5710 7132.
I have added no probable errors, which in the absence of the
details of the observational material can only have a subjective value.

1) i.e. sidereal mean motions in a mean solar day.

~l

Proceedings Royal Acad. Amsterdam. Vol. X.

( 108 )

EE)

Geology. — “Considerations on the Staringian “Zanddiluvium”

By P. Tescu. (Communicated by Prof. Kk. Mart).

The sandy areas form a great part of the Dutch land. When from
the so-called diluvial half of our country the gravelous diluvium
with the boulder-clay, the alluvial moors and river deposits and the
regions where the wind has influenced the bottom, are subtracted,
the districts are resting where the surface consists of sand without
or with little gravel and which are gathered by Srarine under the
collective name of “zanddiluvium’”. These districts have in the different
parts of our country a different appearance and a different fertility.
Therefore the neutral name of ‘“zanddiluvium” has been chosen by

STARING for a very good reason, in which name the origin rests”

undecided by this name. Yet he speaks on the pages 114 to 121
of the second volume of his “Bodem van Nederland” about the
origin of these sand deposits as follows:

“Evidently it has been formed in the last part of the diluvial
period or in the very first part of the alluvial period; for everywhere
where it is found, it rests upon the gravelous diluvium and is covered
by the alluvial beds.”

“This form (the horizontal position of the composing strata)
connected with its position upon the gravelous diluvium and at the
foot of the hills formed by this, permits to decide, with great
probability, about the presumptive origin of the “zanddiluvium’’. The
sand with boulders and gravel being transported to the places where
it is found now and having ‘taken its present form, still a long time
must have passed, before the surface was fastened by the vegetation
and the currents were streaming in their present beds. During this
period frost and. rain will have had a stronger influence on these
accumulations of sand and boulders than afterwards when their
surface was protected by a thick crust of humus. The rocks which
are capable of disintegration, many granites, mica slates, sand-stones
and grits, have been converted into gravel, sand and clay, and the
rain water has transported it for a great part to the valleys. These
valleys were filled up and at the same time the hills became lower
and took a more rounded form than was originally the case. That
this sand represents the detritus of the gravelous diluvium and has
been formed during the transition-time to the alluvial period, is also
to be concluded from the reflection that such a formation must exist
and that this formation cannot be pointed out in another than in

this sand.”

OO a

( 109 )

STARING was however not ignorant of the fact that still other
factors have contributed to the formation and the distribution of
this sand.

This may be sure when we see, how on his geological map on
some places along the great rivers alluvial sand-banks are placed on
the “zanddiluvium”’, isolated from the present river-bed and how on
the index of the colours “zanddiluvium” and “rivages diluviens” are
marked with different character Z and Z’ and yet this difference has
not been sustained on the map. Here the same colour and the same
character Z signifies “zanddiluvium’” as well as “diluvial sand-banks”
(map 19) and “river banks” (map 20). Apparently Srarinc would
not decide, though he was convinced that those formations are not
equivalent. He may not have said it clearly, yet the honour of
having first recognized the problem is due to him.

So STARING's point of view in the matter was as follows:

The “zanddiluvium” imeludes all sanddeposits which have been
formed after the glacial period and which are not surely alluvial.
It has been washed away by rain water from the gravel-hills in the
neighbourhood; yet on many places the possibility of another origin
may be taken into consideration.

After SrArING only three geologists, as far as is learned by the
literature I can dispose of, have been engaged in the study of the
postglacial “zanddiluvium”.

At the 7 Physical and Medical Congress in 1899 (Transactions
page 450) Dr. H. van Cappritin spoke on “de oorsprong van het
heide- of hellingzand”’.

In the Sraringian “zanddiluvium’ formations of a different age
must be represented. The orator observed on many places (West-
Drenthe, Gaasterland, Amersfoort ete.) between the sand which may
be considered with great probability as the product of the washing
from the gravel-hills, old surfaces which he connects with the inter-
glacial period by the following reasoning:

“the younger diluvial currents which have formed the level sand
of the valleys, have eroded this ““heidezand”. The sand of the
valleys being formed in the period of the melting away of the first
glacier, for the formation of the older “heidezand” only two sub-
sections of the diluvial period rest: Is*. the second glacial period
and 2". the period of the melting away of the first elacier.”

“The first age is possible for the sand which covers the mentioned
vegetable beds. So these vegetable beds must be interglacial. The
sand which covers the boulder-clay directly, may also be a deposit
of the first glacier.”

7*

( 110 )

Before continuing, [ will add some remarks. The old surfaces,
observed by Dr. van CAPPELLE, prove nothing else but the fact that
in the formation of this sand periods of rest have existed, in which
organic life could develop on the sand. But this fact does not yet
prove that two different geological periods are necessary. Indeed
Dr. vaN CaPpeLLE himself says that the vegetable beds lie between
the sand in the shape of wedge and so are very local. They have
not any value for a further determination of the age. I agree per-
fectly well with Dr. vaN CAPPELLE where he says on page 451:

“this author (Dr. J. Martin at Oldenburg) will not believe that
the interglacial period has passed without leaving behind traces in
our country, though a convincing proof is not to be given, because
the ground moraine of the second glacier fails’, and indeed it is
not to be thought otherwise that among our so-called postglacial
formations, deposits exist which are equivalent to such of the
second interglacial period and the third glacial period in Germany,
but a decisive proof is not to be given. Old surfaces between the
sand have not the least demonstrative power in this matter. To show
the point of view of Dr. van CapreLLe in 1899 in regard to the
origin of the “heidezand”, 1 will cite the conclusion at the end of
the mentioned communication :

The “heidezand” has been formed in part by the melting waters
of the retiring first glacier, in part after the interglacial period by
the brooks which were streaming from the gravelhills in the time
of the approaching of the second glacier; also the alluvial period
has contributed to the increase of the “heidezand” by the washing
of the hills.”

Dr. J. Lorré has laid stress upon the fact that the sandy plains
which accompany our great rivers and many smaller ones ought to
be considered as river-beds of the diluvial times. This sand has been
washed away from the banks and removed down the current. Two
examples will do.

At the 4th Physical and Medical Congress in 1893 (Transactions
page 393) Dr. Lori speaks about “the peat-moors of Brabant-
Limburg.” The speaker demonstrates that these moors owe their origin
to existing grooves in the surface which had no drainage. Those
grooves represent old branches of the Meuse. This whole region ought
to be considered as a diluvial delta of the Meuse.

“From the stadium of the “wild waters” when the Meuse was
still streaming without a definitive bed, a compound network was
born which decreased gradually, until only one current, the present

Meuse, remained.”

€ ey

In the communications on the geology of the Netherlands, col-
lected by the geological committee, number 35, Dr. Lorik shows
convincingly that the surface of the “Geldersche Vallei” represents
a terrace of a faded branch of the Rhine.

“The peat is followed by a thick layer of sand which has not been
washed away from the hills on either side, but has been supplied
by a branch of the Rhine which thus built a terrace”. (p. 95).

The fact, that the fluviatile sand reposes upon the marine fauna
of the ‘“Kemstelsel” with temperate character and is still separated
from it by peat and clay, proves in my opinion that the terraces
have been formed by the rivers in an old-alluvial period with our
present climate. I hope to revert soon to this subject.

The third examiner of the Dutch sand districts was Dr. J. L. C.
SCHROEDER VAN DER Kork, and it may be superfluous to draw out
his great merits another time, also in regard to this geological
problem. To his accurate sand inquiry we owe this division’).

I. Quartz-amfibol-sands :

a. quantity less than 0,4. Southern Diluvium.

4. quantity more than 0,4. Northern Diluvium.
II. Quartz-garnet-sands :

a. small quantity. Increase. Alluvium.

b. great quantity. Decrease. Alluvium.

He applied his rules to this study of the environs of Deventer
with much acuteness.

SCHROEDER VAN DER Kork could not continue his successful re-
searches because of his busy life in Delft and his feeble health, and
his death has put an end to all further expectations.

The difficulties are far from being conquered now. In general the
rules of SCHROEDER VAN DER Kork are quite right. Yet it is not
sufficient for the classification of each sand to determine the quantity
of heavy minerals. The activity of the forces of nature being too
much complicated, the effect cannot appear in a so simple form in
all cases. In each case all circumstances must be taken into con-
sideration or we shall often come to an erroneous conclusion. The
following example shows this necessity.

The lower parts of the Rhine-diluvium in Limburg are formed by
grey sands. In these sands grains of basalt are tolerably numerous.
Even when the grains larger than 2 mM. and those smaller than
0,2 mm. are removed, the quantity of heavy minerals is still 0,5 to
0,6, the specific weight of basalt being 2,9 to 3,1. The grains of

1) In this form Scuroeper van peR Kork gave his division at the 6‘ Physical
and Medical Congress in 1897 (Transactions page 409).

( 1412)

basalt not being considered as a imirfure of minerals, it would be
concluded that’ these sands belone to a glacial sheet whieh had
reached our country before the gravel of the Rhine-diluvium had
been deposed. Such a contradiction would give rise to many diffieulties.

There is still more. In the gravelous diluvium in situ, the practical
limit of 04°), will probably give good results, but in the “zand-
diluvium’, the materials of which must have been derived from the
eravelous diluvium, the quantity of heavy minerals must have been
changed, according to the different manners of derivation. Here the
greatest prudence is wanted.

When a characteristic can be pointed out which may be considered
as the effect of these different manners of derivation, a further step
has been made. | believe I have found a specifie which may aid in
some eases to take a decision, where the rules of SCHROEDER VAN
per Kork do not help. L add immediately that this specifie is nofat
all universal.

It will be necessary to tell in a very general manner how in my
opinion the beginning of the diluvial period found our country and
how our gravelous diluvium has been deposed.

As much as we know now, the tertiary base of our country is
marine (excepted South-Limburg). In the western part of Zeeuwsch-
Vlaanderen the base is formed by the “rupelleem’’, in the eastern part
it is the marine deposit of the Diestien. Along our southern frontiers
the marine deposits of the Poederlien, Diestien and Bolderien exist.
The sands of the Moséen appertain in my opinion to the old fluviatile
diluvium. The miocene land- and fresh-water deposits seem to be
restricted to South-Limbure. Along our eastern frontiers the base is
formed by upper-oligocene sea-sands, to the north these strata are
covered by miocene deposits. In Gelderland and Overyssel the ‘same
miocene clay forms the surface. In North-Brabant and North-Limburg
this miocene is still covered by sands which probably appertain to
the pliocene. To the north and west Lorif has shown a plioeene
sea-ground at several places (Grave, Arnhem, Goes, Gorkum, Bergen
op Zoom, Utrecht and Amsterdam) which deelines to the north-west.
So at the begining of the diluvial period the greater part of our
country was covered by the plioeene sea and only in the east and
south-east a coast existed.

Now the rivers Rhine and Meuse supplied the enormous quantity
of sand and gravel which form everywhere in our country the base
(excepted Zeeuwsch-Vlaanderen and South-Limburg). A delta was
built whieh filled up the basin of Holland and the Southern North-
sea as far as the chaik rocks of Norfolk aud Suffolk.

(050)

Then a part of this delta was covered by the northern glacier
which deposed its moraines on the surface of the delta. The glacial
sheet being retired, a new period begins. The river water remained
at the south of the morainal barrier Laren, Rhenen, Nymegen, Cleef,
Xanten, and the rivers came from the stadium of the “wild waters’
into the stadium of a compound network. The gravelous diluvium
has been deposed and we have to examine in what way the surface
‘an have been changed now.

In the sandy areas which are very numerous in our gravelous
dilivium, we may expect:

a. the sand which has been removed by the wind.

b. the sand washed away from the hills by rain water.

c. the sand deposed by a river in its bed.

How to distinguish these sands? The sand a must be deposed in
a depression and does not show a stratification. The composition
and the largeness of the grains do not offer a regularity and the
surface must be hilly. This origin may be possible for sand districts
which are surrounded by gravel-hills.

The sand c may be found. along the rivers or in a groove which
represents a faded river bed. In general the surface declines down
the current and the sand is stratified in a horizontal position. The
composition and the largeness of the grains give no difference in
the direction of the stream, neither in vertical direction.

The sand 5 may be found in depressions as well as in grooves,
has also to show a horizontal stratification, but in the composition
and the largeness of the grains differences may be expected :

1. in the direction of the groove, when the bordering hills differ
in composition, as in the case of the hills of Holten, Markelo and
Lochem.

2. in vertical direction. When grains of sand are washed down
the hills by rain water, the grains become smaller, while the incli-
nation decreases gradually. So the grains of the sand J has to become
smaller in the higher parts of the layer.

The next may show whether this characteristic can practically
be used.

In the last year the Dutch Government drilled at three places in
the Peel. As appeared the peat reposes on sand and then the gravelous
diluvium follows. The question is whether this sand is a sand / or
a sand c. When the lower parts have indeed a greater quantity of
large grains than the higher parts, it may be a sand 4, else we have
better consider it as a sand c.

(114 )

The hill-slope from Meyel to Deurne is about 18 K.M. long and
has a direction from N. N. W. to 8. S. E. At the east of this ridge
are situated the three places (at the station of Helenaveen, at the
village of Helenaveen and at the north of the village of Helden)
which I shall eall 1, 2 and 3, from the north to the south.

The position of the sand bed is as follows:

| Meters + A.P. 2.
= SSS | 5
from | to R
- - wn
at the first place | 31.32 | 24.92 | 6 40

at the second place 32.01 25.76 | 6.25

at the third place 30.19 | 23.54 | 6.65

geenen mmmmmmmmmsmmmmmmmmmsmmmsmsmmsmsmnmnmnmnnm

I accept four sorts of grains:
Sort A: grains larger than 2 mm.
Sort B: grains smaller than 2 mm. and larger than 1 mm.

Sort C: grains smaller than | mm. and larger than '/, mm.
+f

|

Sort D: grains smaller than mm.
The grains were separated by sieving and the quantity was weighed.

The results are found in the following tables:

FIRST PLACE.

oe of the | Sort | SOee |) Sterne Sorc
sample | |

en ear EMS Te ORE IPT 2)

|

A = a 7 |
31.12 0. IS 0.39 | 38-7 60.7
30.42 0.17 033 | 0D 64.0
29.38 | 0.43 0.66 | 41.2 | 57.7
98.38 | 0.45 | 0.75 | eg soe
07.62 | 0.87 | 0:74 |>49.9 | 52.5
26.52 0.93 | 4.58 | 47.5 | 50.0
25.42 2.80 | 1.88 | 46.0 | 49.3

| |

(115 )

SECOND PLACE.

Depth of the
sample, in

Sort Sort Sort | Sort

meters + A. P. Billie G D
21.36 0.25 | 0.56 | 39.2 | 60.0
20.56 0.58 | 0.58 37.8 | 61.0
28.56 0.61 | 0.92 | 423 | 56.2
97.56 183 | 2.80 | 44.3 | 514
26.56 3.50 9.78 44 5 | 50.2

THIRD PLACE.

Depth of the | Sort Sort Sort | Sort
sample, in | | |
meters + A.P.) A. | B. | C. D.
| | ’
98 04 0.09 0.52 | 29.8 69.6
27.04 155 O83) 20,5 66.4
|
25.04 9.79 9.99 34.6 | 59.6
|

These lists show that indeed in the higher parts of the sand bed
are more small grains and fewer large grains. So the question is
decided in favour of the sand 0.

It occurs to me that we may accept:

dst. that the groove originally was the bed of an old branch of
the Meuse. However this river did not wash away sand from the banks.

2nd. that afterwards the groove has been filled up with sand 5.
As I remarked already, this specitic is not at all universal, but can
only give an indication in some cases.

Finally a remark. The glacial sheet being retired the glacial
period ends for our country. Meanwhile we know that afterwards
another approach of the glacier came, which did not reach our
country. As Dr. van CapreLLe remarked already, interglacial deposits
must exist in our country. We do not know however deposits with
an arctic fauna and so the points of comparison fail to divide our
postglacial diluvium. Therefore we cannot give a further deter-
mination of the age for the deposits between our gravelous diluvium

( 146 )

and the modern formations. In my opinion it is not possible to
make a map of our country which is strictly geological. But it is
just for that reason that a geological survey would have to do good
work, by finding means to conquer the difficulties.

For the moment we must be content with a temporary division
which I propose as follows :

A. Glacial and fluviatile (fluvio-glacial) diluvium. The expression
“preglacial’”” can be applied only to the surface of the delta, where
the deposits of the northern glacier repose on it. At the south of
the glacial front the surface of the delta may be formed contem-
poraneously with the glacial diluvium.

B. Postglacial diluvium and old-alluvium.

Only in some: cases it will be possible to draw the line.

C. Recent formations.

Within these geological limits only petrographical and genetical
distinctions can be made.

Venlo, June 1907.

Physiology. — “On the adsorption of the smell of muscon by
surfaces of different material.” By Prof. H. ZWAARDRMAKRR.

(Communicated in the meeting of May 24, 1907).

In 1906 H. WarBaum discovered the odorous principle of muse
in a ketone of constitution C,, H,,O, to which the name muscon
was given'). Through the kindness of the firm Scnimmen & Co. I
was enabled to make some oifactological investigations with this
preparation, which at my request was mixed with myristie acid for
this purpose. With this fatty acid, melting at 54°C., it forms a
mixture, containing 0.627 °/, muscon which could easily be cast
into an olfactometrie cylinder of 8 millimetres lumen. Exposition of
0.15 cm. of such a cylinder to a passing air-current of 100 cubie
centimetres per second gives a just recognisable impression of the
smell of muscon, a soft perfume, not admitting of further definition
and soon grewing tiresome. With further dilution this perfume does
not change its character. Hence the odorimetric coefficient of the
mixture, used by us, was 6,7 *).

1) H. Waxeaum in Scuimmet & Co's Berichte, April 1906, p. 99.

2) The odorimetric coefficient of a smelling substance, offered in a certain con-
dition, is defined as the reciprocal value of the length in centimetres of the cylinder,
corresponding to the so-called “threshold value” (for olfactometric cylinders of 8 mm.

(AAS)

The olfactometrie measurements showed :

1. that the volatilised muscon adheres strongly to the glass walls
along which it passes.

2. that rubbing such a glass wall with cotton wool gives rise,
instead of an odour of musecon, to a smell, reminding of muse.

This smell of muse was also noticed with glass wool, cotton wool,
feathers or paper, placed in the path, but not with asbestos wool
and platinum sponge, the time of exposition in all these cases having
been about */, minute.

This led to a closer investigation, which I undertook the more
readily, since an investigation by J. ArrkeN in 1905 showed that
the odorous principle of muse must be regarded as a gas’). Thus
the above-mentioned olfactometrie cylinder, containing 0,627 °/,
muscon in myristie acid and having a length of 10 em. and a
diameter of 0.8 em., was connected by means of a short brass piece
with equally long and wide tubes of all sorts of material, in such
a way that these tubes could, if required, be kept at a pre-determined
temperature by a water-jacket. The thus formed canal passed into
an aerodromometer’), ie. a vertical glass tube in which an aluminium
dise is suspended between two spiral springs, the displacement of
which indicates the velocity of the air-current by means of an
empirical scale. After the aerodromometer finally followed a large tin
cone in which an electrically driven fan maintained a suction from
the narrow towards the wide end. The connection between the
different pieces could be removed and re-established in a moment.

The air, passing through this system, went successively through:

1. the olfaetometrie cylinder over its full length of 10 em.

2. the tube of which the adsorption is to be examined.

3. the aerodromometer.

In the experiments here mentioned the velocity of the air-current
was perfectly constant; 84¢m.* passed per second. Each exposition
lasted accurately 5 minutes. Between the experiments the olfactometric

lumen, i.e. 05 cM? cross-section). Cf. on this point Physiol. des Geruchs, Leipzig
1895, p. 185. The significance of this coefficient, which rises and falls with the
smelling power of a substance, is at once seen, when one recognises the close

relation between it and the quantity b in Frcuner’s celebrated formula y = k log =
)

(Psychophysik Il, p. 13). It deserves notice that the odorimetrie coefficient of
muscon in liquid paraffine is zero.

1) J. Airken. Evaporation of musk and other odorous substances. Proc. Roy. Soc.
Vol. 25, p. 894, 1905.

%) H. ZwWAARDEMAKER. Arch. f. Anat. u. Physiol. (Physiol Abth.). 1902, p. 417,

( 118 )

cylinder was always kept closed, while controlling experiments with
an entirely similar cylinder of pure myristie acid showed that by
this alone no lasting adsorption of odour is produced.

Adsorption of odour appeared to be entirely absent with some
materials (porous porcelain, carbon, ebonite, steel, iron), with others
to exist in a small degree (aluminium, silver, sulphur), with others
again to exist in a more or less considerable degree (tin, copper,
nickel, glass, lead alloyed with tin, lead). Judging by the impression
received immediately after the experiment, the substances may be
arranged in the following series of increasing condensation :

Porous porcelain *, are lamp carbon, ebonite *, steel, iron, alumi-
nium*, silver“, sulphur*, tin, copper, nickel, glass, lead alloyed with
tin, lead.

The substances marked with an asterisk are not entirely odourless
at the temperature of the room.

The first members of this series have no adsorption odour whatever
after the muscon-containing air has passed for five minutes, nor do
they acquire it by heating. The final members, especially tin, copper,
nickel, glass and lead have a distinct adsorption odour which during
the first minutes or even hours has an unmistakable muscon character.
At last, however, a change takes place, consisting in:

1. an alteration of the quality of the odour, so that finally it
resembles muse. This holds for tin, copper, nickel, glass, glazed
porcelain, lead alloyed with tin, lead. :

2. an increase in the smelling power of the adsorption odour,
so that for lead, at any rate, a maximum is obtained after about
3 >< 24 hours.

3. a subsequent decrease in the smelling power, so that finally
the tubes lose all odour.

Free from any acquired odour the tubes become:

For porous porcelain in O days

» carbon RO

,, steel OA dyes

iron , a few minutes

, sulphur „ less than 24 hour
„aluminium Ne A eo

,», glass Ps aa a: ea

„ Silver A - 2 days
„copper ee le op
Mn oy cs ap EAA

, nickel se os AOR ROAS
„ lead alloyed with tin „ „ » 6 days

„ lead segs | Gp) ene Wo Ee

(119 )

Meanwhile these figures have only an approximate value, since the
temperature of the room varied considerably during the last spring.
In the first place I investigated whether the adsorption of the muscon
odour must be explained as an electrical phenomenon. The muscon
gas, led over a sensitive electrometer, appeared to impart no charge
to it, but it is not impossible that the method was not sensitive
enough for this purpose. Therefore in the above described apparatus
numbered nickel-plated copper tubes were placed, facing an insulated
axially mounted steel rod of 3 millimetres thickness, so that an air
condenser was formed with a distance of 2.5 millimetres between
the cylindrical charged surfaces. The odd numbers are charged +,
the even ones — from the 220 volt continuous current main. Each
time, the exposition lasted a minute, the dielectric carrying the muscon
passing in the ordinary way at a rate of 84 em.” of air per second
The cylinders appeared to have assumed the odour of muscon with
about the same intensity, to acquire later an odour of muse in the
same manner and to lose this in about the same time. The com-
parisons between the tubes were made by three observers, trained in
these experiments and independently of each other. *)

Next the influence of temperature was investigated, first on the
adsorption and next on the change of the smell of muscon into that
of muse. For this purpose tubes of an alloy of lead and tin were
exposed for ten minutes at 0°, 13° and 100°.

immediate impression odourless in
exposition at 0° strong smell of muscon 5 days
5e = ale distinct smell of muscon Ohh a4
ae AIDE no smell of muscon 1 day

Then numbered, nickel-plated copper tubes were exposed during two
minutes to the ordinary air-current, passing over the muscon-myristic
acid. The odd numbers were placed in the ice-box, the even ones
were left to themselves at the temperature of the room, each placed
in a wide-necked glass stoppered bottle. After 24 hours there appears
to be no statistical difference of any importance. All cylinders whether
even or odd, appear to have assumed a smell of muse in a distinct
though feeble degree. So the temperature coefficient of the surface-
action, exerted by nickel on the phenomenon of the transition of
muscon into musc, cannot be great.

1) One of these observers has an ordinary acuteness of smell for the odour of
muscon, but cannot state with certainty the transition of muscon into musc. He
also has in other respects strongly deviating peculiarities of his organ of smell
which will soon be extensively communicated.

( 120 )

Finally I wish to state that capillary glass tubes of 1 mm.” eross-
section, after air, carrying muscon, had been passed through them
for five minutes, did not show a perceptible change of surface tension
with water (the tension being measured by the height of the water
column) and that repetition of the other experiments with tubes,
heated beforehand and with air that had been dried by means of
calcium chloride and cotton wool, gave no deviating results.

At present it is impossible to give a theory of these phenomena.
As a preliminary working hypothesis one might suppose the adsorbed
muscon to be dissolved in the layer of condensed water vapour and
air which covers all objects and it might be further assumed that
the change of muscon into muse only then takes place at a percep-
tible rate when the surface action of the metal, of the glass or of
the glazed porcelain produces a particularly great density of the
dissolved muscon in immediate contact with the surface in question.
This hypothesis is in harmony with equilibrium experiments, made
with dried air at O°, 10°, ete. These experiments are in progress
but not completed yet.

Physiology. — “On the adsorption of the smell of muscon by
surfaces of different material’. By Prof. H. ZWAARDEMAKER.

Continuation of a former communication.

When air, charged with muscon, is passed through tubes of an
alloy of lead and tin, in the manner described in the communication
of May 24, the inner surface of these tubes appears to adsorb
muscon in quantities, the amount of which may to some extent be
estimated from the time, during which the tubes preserve the odour
of muscon. This assumption is based on the supposition that the
adsorption takes place in one and the same dissolving substance,
namely the condensed layer which is said to cover all objeets.

The dilution at which the muscon is present in the air in these
experiments, can be kept constant when the current velocity is
controlled by means of an aerodromometer. Moreover, it may vary
between certain limits, since experiments, made to this purpose,
showed that it makes no difference in the results whether the muscon,
volatilised per second from the smelling source, is “contained in
42, 84 or 126 ce. of air. Tubes of lead, alloyed with tin, lose under
similar conditions the adsorption odour in the same degree and in
the same time, say 5 to 6 days.

(AM)

Under the just stated conditions the adsorption equilibrium is
reached at a temperature of the room of 19° centigrade in about
ten minutes, as will appear from the following table:

after 1 min. exposition odourless within 1 day

PE ze ss after 2
ems: Vy 5 5 » 2 days.
we ae es ‘ val Gun hss
oS en : 7 cree Bn
SOL ss, 2 EE eA rly ere
TOM 2 “2 Re 4 by

Preceding © | at 0? at 20° at 40° at 60° | at 1002
Exposition
5 min. 8 days 3 à 5 days 2 days | 1) days | 1 day
100 10 5 ze |3 » |2 „ | 2 days
15° alittleover 10days a littleoverSdays|4 , 2 ij Ante
| |

Nickel-plated copper tubes, treated in the same way, show saturation
after an exposition of about 5 minutes, it making no difference
whether this takes place at 0°, 20° or 40°. Complete loss of adsorp-
tion odour was found in these cases after respectively 4, 2 and 2 days.

From these experiments follows that a higher temperature during
the exposition causes the state of saturation to be reached only little
sooner, but that the degree of adsorption is much smaller at a higher
temperature. This proves that with higher temperatures the equilibrium
is shifted in the direction of minimum adsorption.

The facts, stated until now, agree very well with the hypothesis
of a solution of muscon in the layer of condensed water-vapour,
carbonic acid and air which covers all objects. Assuming this, we
are led to believe that on nickel-plated copper this layer is thinner
than on lead, alloyed with tin, and that consequently in the former
case the equilibrium during exposition is reached sooner than in the
latter, while temperature has the same influence on them both and in
the same degree. The fact that tubes, heated beforehand and treated
in dry air, give the same results, is not at variance with this since
we may not expect that the condensed layer will by this treatment
be completely removed. Also the transition of the smell of muscon
into that of muse must take place in this layer, the only curious
point being that temperature has so little influence on the rate of

(122)

this process of transition which yet must be of a chemical nature.

But a great difficulty to the theory arises from the fact that ad-
sorption of odour on metal surfaces appears to be a general pheno-
menon. This appears from similar systematic experiments as with
muse for two other characteristic smelling substances. I chose ionon,
a substance dissolving in water as well as in liquid air and scatol,
a substance for which this has not yet been investigated.

lonon, when diluted 1 to a million in an aqueous solution of
0,5 °/, antifebrin, and evaporating into a passing air-current which
in the well-known manner passes through cylinders of different
material, leaves an adsorption which disappears almost immediately
with porous porcelain, arc-lamp carbon, glass, silver, sticks to tin
for a very short time, to lead, containing tin, scarcely for a day
to nickel and copper for about two days, to aluminium for 2°/, days
and to iron and steel for about four days.

Seatol, when dissolved in .proportion of 1 to 1000 in liquid paraffin
and evaporating into passing air and passing in the well-known
manner through cylinders of different material, leaves an adsorption
which disappears almost at onee with porous porcelain and arc-lamp

carbon, in a few hours with glass, sticks to lead, containing tin, to -

lead, silver and tin for about a day, to copper 3 days, to iron 4 to
5 days, to steel 10 to 18 days, to aluminium over 10 days.

Hence ionon adheres most to the substance which does not take
up muscon at all, i.e. to steel; scatol most to aluminium which
shows a comparatively very small adsorptive power for muscon
(aluminium does not keep muscon for 24 hours).

In order to explain these deviations one is forced either to assume
a peculiar modification of the solubility, caused by the dissolution
of the specific metallic particles in the condensation layer, or to
assume an absorption in the metal itself. To me it would seem that
the collected facts do not at present admit of a choice between these
two possibilities, although the small influence of the muscon density
in the air would point to an adsorption compound with the metal.

EE ge a a ed nd

( 233:

Physics. — “Contribution to the theory of binary mixtures.” V.
By Prof. J. D. van DER WAALS.

Continued, See p. 74.

Up to now we have assumed in the determination of the binodal
line that the second component, for which the quantity > is larger
than for the first component, has a lower critical temperature, so
that we suppose (7%),<(7%),. In the opposite case, so (Ti), > (Ti),
we meet with some new complications, which we shall shortly
discuss. So we choose now a region from the general p-figure,

which lies more to the right, and in which the line eet is
AL Jy
found. Fig. 14 of These Proceedings April 26, 1907 may be ser-
viceable for this discussion. In this figure the points 1, 2, 3, 4, 5
and 6 are points of the spinodal line. If we had inserted the spinodal
line itself in the figure, this curve would have an ordinary shape
on the vapour side, remaining all the time at larger volumes than

1;
those of the line 2 =O. But on the liquid side the normal course
av] x

of the spinodal line has been strongly modified by the presence of

kl ) jaN . . . .
the line =0. On the left-hand side it begins in the point
at
dp f
me of the first component, proceeds then to smaller volumes,
av
‚dp
till the presence of =—0 forces it back to very small volumes,
ak
and is the cause that the distance between the spinodal line and the
dp : 7
line —0 is abnormally enlarged. In the points where ——- — 0 and
av adt
drf) ; Z dap
ae = 0 intersect, the spinodal curve touches the curve — = 0
da dv da

Two plaitpoints occur, viz. the realisable plaitpoint at very small
volume, and the hidden plaitpoint in the neighbourhood of the points
2 and 3. This hidden plaitpoint lies in this case on the left-hand
side in accordance with the shape of the q-lines. In fig. 17 this
hidden plaitpoint lies on the right-hand side, and the shape of the

AR: dp . ce
q-lines in the region where — is positive, is such that there is a
av

g-line which may be drawn tangent to the spinodal curve, the
hidden plaitpoint being the point of contact. In fig. 17 the q-lines
8

Proceedings Royal Acad. Amsterdam. Vol. X.

(124 )

in this region turn their concave side to the axis of the 1“t component.
In the case to be diseussed now they turn their convex side towards
the 1st component, and hence the hidden plaitpoint must lie on the
other side, as a point in which a q-line touches the spinodal line in
the unstable region. The drawn q-line intersects the spinodal line
in 6 points, and the p-line, thought as function of v, must have 3
maxima and 3 minima, when this g-line is followed; a maximum
value in the points 1, 3 and 5, a minimum value in the points 2,
4 and 6. In fig. 20 this p-curve is represented and the different

Fig. 20.

branches of this line are indicated by the letters a... g. The branches

d dp, :
d and f traverse the region where sale negative, and accordingly
Lv

dp aoe :
have two points each, where a The complication which the
‚Û
p-line presents in this case compared with the p-line of fig. 16,
consists only in this that the branch e, which before ran directly to
infinity and continually to smaller volumes, has now got a maximum
in the point 5, and as soon as the g-line passes into the region
aw
Lv
the minimum value has been reached, which however must be larger
than the maximum value of the pressure in the point 8. If the

where is negative, runs back to larger volumes. In the point 6

( 125 )

value of g is lowered, the points 6 and 3 draw nearer to each
other, and they coincide for the loop-q-line which passes through

; es. ; dats dp
the point of intersection of —— — 0 and
da? dx dv

=(. Then the bran-

ches ¢ and d intersect at an acute angle, just as the branches fand
g. When q is lowered further, and the g-line has split up into two
separate portions, the p-line too divides into two separate parts; the
branch gy is then the continuation of c, and the branch / the con-
tinuation of d. Fig. 21 illustrates the course of p as function of »

Fig. 21.

for such a g-line which has divided into two separate portions; then
the branches c, g, which have united to one branch cut the united
branch d, 7, and the branch e.

When applying Maxwerr’s rule for the determination of the binodal
line we are confronted with some difficulties, which I will now
discuss. Already when the p-line runs as is represented by the
branches ve, f and y in fig. 20, so when the middle one of the 3
branches cuts one of the outside lines, we must pay proper attention
to the sign of the areas when applying the rule for drawing MAXWELL’s
line. If the straight line is drawn lower than the point of intersection
of e and f, the area below this line, which according to the rule
must be equal to the area above this line, must of course be all
that is contained between the branches g and f below this line.
But the area ubove the line, which consists of two parts, viz. the
area of the loop, and the part that lies below the double point above
the line, must not be considered as the sum of these two parts. On
account of the branch f running back, the latter, part, must be taken

8*

( 126 )

negative. This may be considered to be sufficiently self-evident and
not to require an elaborate proof. But when the q-line has divided
into two separate parts, and when the p-line runs as is represented
in fig. 21, we meet with another difficulty, which indeed, calls for
a somewhat cioser discussion. The joined branches c and g form a
curve which cuts the branches d, e and /, which have joined to a
loop-like curve, in two points, but such a point of intersection must
really be considered as two altogether different points. Such a point
of intersection represents two perfectly different phases according as
it is considered as point of c, g or of d, e, f. Hence when drawing
the straight line we must bear in mind that the point of intersection
of c and d and of e and g does not represent the same phase, and
if the line is drawn as in fig. 21, where the two hatched areas are
equal, the points at the extremities of this line are not points of the
binodal line. To see how the straight line must be drawn in such
cases we revert to the general equation:

dM yp, = vdp — «dq.

Now to get from one point to the point with which it coexists,
we can no longer follow one g-line, but we shall partly have to
follow a way which joins the two separate branches of the q-line,
and for this we choose the isobar of the point of intersection that
the branches c, g and d, f have in common. We obtain then the
equation :

c c
(Mu)e — (Mu )e = Jvdp — Jadq,
e €

where in fran the value of v must be taken which corresponds to the

chosen value of g, and in raa the value of « which corresponds to

that p-line that passes through the point of intersection. Let us call the
value of the volume of the point of intersection v, and the values
of x for the points where the isobar of the point of intersection cuts
the two branches of the q-line, v, and w,. The above equation assumes
then the following form:

SC
(Mu de wis (Lue = E (ve — ve) — fra | De E (w,—2,) a aie | >
e 1

Cc
Now if (M,u,)- must be —=(M‚ue, then p (ve — ve) — [pao is

(127 )

not equal to 0, but to q (x, — 2,) — fade. For the loop-g-line the
1

length of the isobar along which foe must be taken, is equal to 0,

and x, and x, coincide. For a g-line of lower degree «, and «, differ.
In the above equation it is supposed that branch e is taken as starting
point, and that a course is followed necessary to reach branch c.
The point from which we start, lies on the closed circle of the q-line
and in the stable region. We now follow indifferently either the
lowest branch of this circle or the highest, but dependent on the
pair of coexisting phases that is to be determined. Let us suppose
that we follow the lowest course, then we get to branch d, and
meet the point of intersection of the isobar which we must follow
to meet the other branch of the q-line in a point which has equal

dj
volume v;. As this isobar must pass through the line (2) == (0),
AL) y

where maximum volume exists, the equality of the volumes wv, is
possible’), but the values of « which we have called wz, and 2,,
are different, viz. rz, <a. For x, the value of ¢ is the chosen one
and for 2, the value of g is again the same. Between 2, and 2,
this value is variable. Now:

dq ERN dp dv
da), dx? dadv day

or
Py dw db \?
dq da? dv? \da +.)
(a) = dp :
dv?
dp a dq\ . ne ;
aE (see fig. 14) being positive, @E positive outside the spino-

dal line, and negative inside it. Along the p-line, starting from smaller
value of zr, the value of q is, therefore, increasing, maximum on
the spinodal curve, then decreasing, minimum on the spinodal curve,
after which it increases continually, as represented in fig. 22.

1) The same observation holds for all points which are points of intersection
of different branches of the p-line in figs. 20 and 21. In such a point of inter-
section p and v are equal, and this could only occur when the phases denoted

‘ : oe
by such a point of intersection lie on either side of the line = 0)

da

( 128 ) .
Now: |
c 1
plee) — [pao=— Ja (en) —fo de)
e 2
or
c 1
fe dv — p Weve) = — | fs dx — q («,—2,) | 5
e 2

For the loop-g-line a, and w, coincide, and for a g-line but little

i
lower face is larger than q (7,—v«,). As 2, always lies on the left

2

1
of the value of « for which q has minimum value, i q dx > q (wt)
2

always holds. From this follows that for the lowest pair of coexisting
phases of fig. 21 the straight line must be drawn in such a way
that the area of the hatched part above this line, to which the area
of the hatehed part of fig. 22 is added, is equal to the hatched part
of fig 21 which would lie below this line. So the pressure of the
lowest pair of coexisting phases for this g-line is greater than would
follow from: the application of the rule if the point of intersection
of c,g and d,f was an identical point, or rather represented one
and the same phase. But we shall not pursue this course any further.

Now that we are obliged to include the quantity die dq in our con-

siderations, we can find the coexisting phases for the liquid volumes
in a simpler way by the aid of this quantity. For such volumes lie
on a p-line which can be followed without interruption when we
proceed from one point of the pair of coexisting phases to the second
point. And when we proceed along a p-line d M, u, = — a dq, and

4

so (A, u), — (Mu), = fe dq. Hence we need only choose two

2
points on the chosen p-line, satisfying the requirement that — za —

1
2
g (e,—e,) =f 4 dv.
l

Then we have to carry out the same construction on the g-line

or

(129)

as was carried out above on the p-line, and so for the p-line, for
which fig. 22 would represent the course of the g-line, we have to

Fig. 22.

draw a straight line in such a way that its height indicates the
middle value of the ordinates of the q-curve. That from the outset
we have not followed this course for the determination of the
coexisting phases in which the values of 2, and «x, for given value
of p are determined, is due to the fact, that this way of determina-
tion is again possible without correction term only when the whole
p-line is found between the two coexisting phases without interruption
in the v,#-diagram; and as for the equilibrium between vapour and
liquid phases as a rule this condition is not satisfied, and as it is
only by way of exception that the g-line has split up into two
branches, the determination of coexistence by the first mentioned
method may as a rule be considered as possible. But nevertheless,
in some cases the determination by means of the properties of the
value of q, following a p-line, is to be preferred. If we do so in
the case discussed for the determination of the coexistence of a liquid
phase with a second liquid phase, we must choose every time other
p-lines, and along each of these p-lines the course of q as function
of x is as drawn in fig. 22; and with the simple shape of such a
q-line there is only question of a single straight line along which

2
qe (#,—2#,) = jf qdx. The binodal curve for the coexistence of liquid
1

with liquid has therefore a simple shape and is restricted to the
stable region.

( 130 )

Indeed, this was also to be derived from the p-figure (fig. 20)
where the branches f and g must lie higher than the branches ec
and d, and therefore can never combine for the application of the
rule for coexistence; but then only for those g-lines which are or
higher degree than the loop-g-line; whereas the rule for finding the
conditions for coexistence from the values of gq when a p-line is
followed, holds for all p-values without exception. Let us consider
the case that this part of the plait has got quite detached from the
transverse plait as a closed longitudinal plait, and has the two
realisable plaitpoints, then a highest and a lowest p-line may be
drawn, along which the maximum and the minimum in the qg-line
have coincided, and in the point where they coincide they yield the
value of # for the two plaitpoints.

We had already repeatedly occasion to call attention to the reci-

2 2
procity between ae and as and between g and p or a and ia
da? dv? dx dv
Let us also do so in the case discussed. Here we have intersection
dy dp

in two points of ZN Ovand
da? dudv

= 0, and it appeared that then

separate portions of g-lines occur, so that it was not always possible
to pass without a leap from one part of a g-line to another part of
such a line. Then it is desirable for the determination of the coexisting
phases not to follow such a q-line, but on the contrary to go along
a p-line and to use the corresponding value of g. The reciprocal

Maa : ee i dy Pw
case is found in case of intersection of EE = 0 and
5

=O fn
vdar

which case the course of the p-lines is as is indicated in the middle
region of the general p-figure. Then there are p-lines, namely those
of higher degree than the loop-p-line, which have divided into two
separate parts: if we followed a p-line also then, in order to arrive
at the coexisting phases by means of the values of g, we should be
confronted by the same difficulties as we have met now when
following the g-line. If for a p-lme of lower degree than the loop-
p-line we draw the value of q, then such a course for g follows from

, as has been drawn in fig. 23, where

Pw dw yw \?
dq 2 dx? dv? \ dadv
de Pp = Pw

dx

dv*
the 1st, 3rd and 5'* branches lie in the stable region, and the 24
and 4 branches lie in the unstable region, if we take into account
that such a p-line passes £ times through the spinodal line, in which

( 131 )

é dq L ? dw :
points z=) —(, and also 4 times through the line — =O, in
Le p

dv?

d : - Poe
which points ee =o. Only for the loop-p-line the second minimum
del Pp

Fig. 23.

coincides with the first maximum, but for lower p-lines it lies higher,
as in the drawing. We have exactly the same shape for g as func-
tion of w, as in fig. 20 for p as function of v. Only one figure must
be turned over to cover the other, in accordance with the circum-
cht dw

: and p= — ma The combination ec, d and e
av dv

stance that g=
now yields a pair of coexisting phases, and the combination e, f
and g another pair. No other combinations are possible; and we
should be justified in concluding that the binodal line has a simple
course and remains limited to the stable region. But this conclusion
would be perfectly valid only for all pressures not higher than those
of the loop-p-line, though there are also coexisting phases with higher
value of p. In this case it is certainly preferable to follow a g-line,
and to construe p as function of v, which we have called preferable
already above for other reasons. We know that then a highest
pressure exists for the coexisting phases, viz. when «7, =,; this is

4 nd

only possible if the chosen g-line passes through the line ES
&

for only then this is the case for values of « within certain limits.

From this circumstance of the reciprocal case we conclude that in
dw : dp

== (is) Guts by) S= 0
a fame cha

the case under consideration, in which

( 132)
there is a minimum value of g for the coexisting phases, viz. if
v,—=v,. Then the line joining these phases runs parallel to the

z-axis, just as it runs parallel to the v-axis in the reciprocal case.
This too can only occur, if the coexisting phases lie on either side
of the line ge = 0; for the isobar that passes through the two points
av
of coexistence, can only have two equal values of v if between them
maximum or minimum value for the volume occurs. The equality
of v, and v, for minimum value of q, to which we have concluded
from the principle of reciprocity, follows from the simple equation,
whieh holds for two successive points of a binodal curve, viz. :
(v, — v,) dp = (a, — «,) dq.

For a pair of coexisting phases J/,, is the same, and for a following
pair of such phases dM,u, is also the same; now the above equation
follows from dM, = v,dp — x,dq = v,dp — «,dq. If x, —2,=0
and v,—v, is different from zero, then dp must be =0; in the
same way dq=O involves the equality of v, and v,, if dp is not
equal to 0. We can also derive from this equation, how the nodal
lines lie on either side of the special nodal line for which v, = «, or
p= vj, i.e. to which direction they diverge in a fanlike way. Let
us first consider the case ‚==, so maximum pressure on the
vapour-liquid binodal curve. On the left of this nodal line the sign
of v, —v, is positive on the vapour side, and the sign of dp, if we
do not limit ourselves to an infinitely small value of dp, negative.
Then also the sign of (w,—.2#,)dq must be negative, and the sign
of dq being negative, z, — xv, must be positive. On the right of this
nodal line the sign of »,—v, and of dp must be what it was in
the preceding case; but dq now being positive, 7, — 1, is negative.
So the nodal lines converge towards the vapour side. It would be
just the reverse if the pressure was minimum for w, ==, for then
dp is positive. Let us now consider the case v, ==v,, sO minimum
value of g on the liquid-liquid binodal curve. Let us choose the
right side, so where x, > .2,, and let us ascend, so put dp positive,
then q being minimum, dq will be positive. The second member is
positive, and so we find », —v, positive, whereas for negative dp
the value of v, — v, would be negative. So the nodal lines converge
towards the right side, and we may consider the nodal line for
which v, = 1,, as axis of such a converging pencil. This shows us
at the same time how and where the plaitpoints must lie. As the
tangent to the binodal curve in the plaitpoint is to be considered
as the limiting direction of the nodal lines, both the p-line and the

Tm ze

(133 )

g-line must have such a course in the upper plaitpoint that they
descend towards the right, which moreover could be put a priori.

dp
For every q-line when it still lies above the line a=) and does
7
2

d :
not pass through De, — 0, descends when it proceeds towards the
DT

right. But in the lower plaitpoint, i.e. in the plaitpoint with the
_ dp

larger volume that lies below the line — 0, the g-line which touches
U

in that plaitpoint, must descend as it proceeds to smaller value

of z, in accordance with the course of the nodal lines. We should

also have found this course of the nodal lines confirmed, if we had
paid attention to the eourse of the p-lines.

Everything we have discussed in this V‘* communication rests on

2

dp Mw
fig. 14; so we have thought that F0 and es =(interseet, There
AL ae

is, however, also a possibility, and it will even be the rule, that the
two curves exist, but do not intersect. Then two eases are to be
af: : : ay :
distinguished, viz. that — =O remains restricted to smaller volumes
av
dp 5
than those of 7 =0, or to larger ones’). When tracing the two

Lv

curves with respect to each other we must take care that the points

4 p dp ,
in which tangents may be drawn to —— —O parallel to the v-axis,
at”
b k d*p ch foe Leap
lie on the line — — 0, and that also the point in which — =O
dx’? da
ae 5 st = ; d*p
has minimum volume, lies on this line too. Now the line TE
at

dv , ete 3
has a simple course. The value of — for this line is equal to
at
ORS E ae ues dp p
——.. From this follows that this line —- == 0 consists of a single
da 1 b Age 5

v

branch, which from a point of the 1st axis moves regularly to the

5 ; 3 KA ‘ dp
right to points of continually larger volume. So if the line =
at
2

; d ;
cuts the line Ee =— 0, the two points in which tangents parallel to
at

1) See These Proceedings April 26, 1907, p. 833 seq.

( 134 )
a? dean
the v-axis can be drawn to De =— 0, and the point where = = ©
ar
has minimum volume must lie in such a way, that the last point
2

lies between the two first mentioned. If the line > — 0 is restricted
ue

2

d 9
to smaller volumes than Se then er = 0 must also lie at smal-
Hid We

ler « than the point where = O has the smallest volume and the

Fig. 24a Fig. 24b Fig. 24c

reverse; this has been represented in fig. 24a, fig. 245 and fig. 2de,
but has not always been kept in view in preceding schematical
figures, which were plotted for the representation of other particularities.

After these remarks we may examine more in details what happens

dp my 5 5 n
when (2) = 0 and ee = 0 intersect, and the temperature is raised.
at ar

ds

da?

With rise of 7

= 0 contracts to the point in which this curve

dp Se :
must disappear. Also the curve = = 0 contracts. If the point in which
ue
aw 5 5 dp
= QO must disappear, lies at smaller volume than aa 0, then
tite dv
: : ay : : :
with contraction Glen =0 the right-hand point where the latter curve is
na

directed // v-axis, will have to pass through the minimum volume of
dp : Sere ee hae :
= —(. Even then there is still intersection, but with further contraction
the two curves will touch, and get detached. Above the temperature at
which they touch, the complicated course of the q-lines has disappeared
in so far that no g-lines occur any more which have split up into
two separate branches; then we get a group of g-lines as drawn in

(135 )
fig. 3, These Proc. March 30, 1907 with a maximum and a mini-

dp
mum volume, but moreover when they afterwards cut — =0, with

de
. . . a? ) -
a maximum value of x. But when the point in which ~~ —0 must
adv

disappear lies at larger volume than “LE — 0, then with rise of 7’ the
LL
5 dp Ab ae 5
left-hand point where — — 0 is directed parallel to the v-axis, must
Ak

2 dp sal
pass through the point where — — 0 has minimum volume. Then
at .
intersection still takes place, but with further rise of 7’ the curves
touch and get detached and then the g-lines run as has been

at, Baty

ë A & me ay ay
drawn in fig. 5. So contact between —— —0O and — — — 0 may
at av av

take place in two ways and we may already conclude to this from

dv
the condition for contact. From the equality of ae for the two curves

de
dp d°p d*py?*
de dede \dz?)°
dp dp

being negative for the points of — = 0,
adv da Cae

follows namely :

dp

The value of

must be positive in the point of contact. That is to say, that for

d
the curve =0 the point of contact must lie to the right of the

line which joins the minimum and the maximum volume. Only with

the two kinds of contact which we have described, this condition

can be fulfilled. If the first described contact takes place, the mini-
d,

mum volume of BP —0 must lie to the right of the point of contact.
at

In the second case of contact this point must lie on the left, or

See 5 3 : do, a
even be entirely wanting in the figure, in which case — is positive
ae

: : Beel)
in all points of the line P — 0,
da
From all this follows that if the spinodal curve entirely envelops
2

Fae = 0 in a closed line, and the latter remains entirely
5 J

the curve

dp
restricted to smaller volume than the volumes of = = 0, there are
ve

( 136 )

indeed still two realisable plaitpoints on this spinodal line, but that
the course of the nodal lines in all this longitudinal plait is as was
the case in the upper half of the above discussed longitudinal plait
— so that in both plaitpoints the tangent p-line and the tangent

g-line descend to the right. All over this longitudinal plait v, > 7,
2

Er . . . . 5 ¢

if v, represents the right-hand point of coexistence. But if — — 0
av

dp
remains restricted to volumes larger than those Of the course
de
of the nodal lines is such that v, < v,, and the plaitpoint has such

ree. dv dv. ek Soh
a situation that — and — is negative for the p-line and the q-line

td Up ( Vg
which pass through the plaitpoint. I speak of the plaitpoint, because
I think I can demonstrate that then there cannot be question of two
realisable plaitpoints, nor of a detached closed longitudinal plait.
dv dv

For when a spinodal line splits up, not only aa AE in this split-
OLD 7

dv d*v
discussed this point (These Proc. April 26, 1907 p. 848), but on
account of the great importance of the question further elucidation
is perhaps not uncalled for. The following remarks may serve for
this purpose.

Let us in the first place consider a mixture represented by a
region of the general p-figure lying on the right side, and so much

ting point, but also = 0. Properly speaking I have already

; dp bf
to the right that the point where — == 0 has minimum volume, no
at

longer occurs, or lies at very small value of z. Then the point where
Pw
da?
pees _ dp
—- = 0, lies at smaller volume than those of the line —=0O; and
da? da

if this curve is still found at temperatures below 7,, the points in

=0 disappears at 1'= 7, because it must lie on the line

: : _ dp Zi: :
which this curve intersects the line 0, lie in the region where
av
dp , ; ;
— is negative. If we now suppose that the temperature rises, and
ak

the spinodal line might split up, this splitting point must lie between
[2

5 A ‚dp
the larger volumes of == 0 and the volumes of — == 0, so also
an av
RE sap EEE ae ee
in the region in which — is negative. Now the question is if in this
’ at

|
|

( 137 )

region a point of inflection of the p-lines and of the q-lines can lie.
It appears from what has been observed about the loci of these
points of inflection (These Proc. March 30, 1907 p. 736) that this
is possible for the g-lines. But fronr what has been observed on
the course of the locus of the points of inflection of the p-lines
(These Proc. Febr. 23, 1907 p. 628) appears that in the stable part
of that region no point of inflection can occur for these lines.

Let us now take the other case, viz. that the point with minimum
volume of = —0 exists, and is not found at very small value of 2.
If the spinodal line has split up into two parts, then there is a part

7 ; j : dp
which we might consider as belonging to — — 0, and another part

av
dp ae eee ae
that surrounds f= = 0. Now the splitting point lies again in the

E dp . : : ;

region where a negative, but in a part of that region where as
DT

well points of inflection of the p-lines as of the g-lines may occur,

2

d
at least if a= O still intersects the curve : = 0. Two branches

da Fi

P Ip = DN

on which = = 0, start from the point in which — =O cuts the
a ar
q

3
curve —-==0. One of these branches passes through the region

d?
where > is negative, and leaves this region only at the point where

v
dy
= =0 has the maximum volume. The second branch runs right
&
of the loop-g-line to larger volumes. But there is also a locus on

… dv ‚ dp

which = 0, which runs right of — =0, and passes through the

da? da
two following points. 1st the point where —=0O has minimum

dz
4 dp k dp
volume, and 2rd the point where — =O cuts the line — = 0. If
at dv

the spinodal line splits up, this will have to take place in the point
3,
=0 with the second men-

of intersection of the line on which
av p

]

dv

tioned branch on which =0. If this case of splitting occurs,

3
da?

(138 )

the detached closedZlongitudinal plait is cut by the line eet and
da

has the above discussed plaitpoints.

But though on the supposition of this way of splitting up we do
not meet with a definite contradiction, yet there is one circumstance
which makes me doubt whether it will occur frequently or universally.
If we draw the point of intersection of the mentioned loci on which

dy dy

ma = 0 and ——=0, we find a point which lies on the left side
(ahi ie Ax

ca) qd

of = 0, whereas after the detaching we should sooner expect

the place of the plaitpoint with the largest volume, according to the

5 d : : dw
course of the nodal lines, on the right side of Te =— 0. Indeed,
AL

another way of detaching is possible. The splitting may take place

va eR re aay
in a point on the left of ae =(. Then : = 0, which curve must
Ak at
‚dp
disappear in a point of ae = 0, must already have contracted so
ax
lee : dp. EN,
far that it lies entirely in the region where de is positive. As we
aX
j2
observed before, there runs a branch on which —- = 0 also there
7 du",
. . a )
and for the loop-line on which DE 0 (These Proc. March 30 1907
at”

p. 736) there must be a closed figure, which has got detached from

dp
the branch right of ‘ _— 0, because the double point, the point in
ax
dp dp
which ET 0 and —- == 0, no longer exists. Then we have again a
at at
detached closed longitudinal plait, but one which is not intersected

dp ; ne ae ;
by 7 — 0, and which has two plaitpoints in which the p- and
av
% 5 dv dv Ne B f
g-lines which touch have EME positive, in accordance with
dlp akg

the course of the nodal lines. In fig. 25 the circumstances after the
splitting have been represented for this case. First of all the lines

dp dp F : ; d*p :
LO and “’=0 occur in the figure; further <? — 0, which
da dv dx?
: dp page
passes through the point where ~-=0 has minimum volume.
we

( 139 )

Fig. 25.

yw ries

d,
D = 0 has

On the left of t=O and at smaller volumes also
dx dz?

3
: P :
been drawn. Where this curve passes through has tangents
ar

//v-axis. The spinodal line has split up and the two parts have been
drawn far apart for the sake of lucidity. One part surrounds

dw dp A aes H
aE = 0, and the other part touches al in the point in which
& av
dp
this curve is intersected by eel Further a p-line has been drawn
aL

with two points of inflection. The right-hand point of inflection is of

no importance for our case. And finally the detached branch of the

locus of the points of inflection of the g-lines has been drawn. Now
dv dv

— 0 and —

dx* da
expected on the left ae’ of the medal curve, which has got
detached. But for this case v, > v, for all nodal lines of the longi-
tudinal plait, and the second plaitpoint is really to be expected on
the left. I suspect these two ways of detaching to be connected with

too the point in which = 0 intersect, is to be

: : : : … ew 8 :
the two series of values of z,, for which ET 0 disappears in the
: av

9
Proceedings Reyal Acad. Amsterdam. Vol. X.

( 140 )

d
region where is positive (These Proc., April 26, 1907, p. 833)

ar
— either for a very great difference in tbe size of the molecules of
the components, or for a small difference. In the latter case the

2

1
: : =O are to be found at almost

highest and the lowest points of
&

the same value of z. But this is one of the many particularities
which is to be left to a later investigation.
Particularly the last described way of splitting up of the spinodal
Nee : dp :
curve takes place far to the left of the point where A has mi-
nimum volume, and so at a value of z, not very different from
that for which 2,—= 2, on the vapour binodal curve, and maximum
pressure exists; and so this leads to the opinion that this detaching
of a longitudinal plait is to be found for mixtures with minimum
pressure and very different size of the molecules; but also this sup-
position must be further defined by a fuller iuvestigation.
The following remarks may serve for a full characterization of
the course of the spinodal line before and after the splitting. Before

2 2

the splitting the curves on = 0 and a 3G) must be thought as
dx? dv?

intersecting, as in fig. 8 (These Proc. March 30, 1907), but the line

dw

dx?

for a left-hand region of the p-figure, but this figure would change little

= 0 as having moved to smaller volumes. This figure holds indeed

t

in its essential features if we also insert the line 7 =0 in it, but
place it on the right so that e= 0 is no longer intersected by it.
For a region of the left-hand side extended towards the right is the same
wo

da?

as a region of the right-hand side extended towards the left. If

2

and = 0 intersect there is a complicated plait, with the hidden

dv?
plaitpoint on the right side. If now with rise of temperature the two
curves get further apart, because they both contract, splitting up of
the spinodal curve does not always immediately follow. For this to
be brought about the curves must be pretty far apart, and intersection

2 2490
dv eae dv
de? dr’,
and the temperature must be reached at which this point of inter-

of =O must take place between the two curves,

(BEES)

section lies on the spinodal line. Then a point of the left-hand side
of the spinodal line coincides with a point of the right-hand side of
this line, but not in the hidden plaitpoint. Consult also fig. 17
(These Proc. May 24, 1907 p. 68). Then there are 4 plaitpoints,
viz. P,,P, and the double plaitpoint in the splitting point of the
spinodal line. The course of the binodal curve on the liquid side has
been represented in fig. 26. On the liquid side the binodal curve of

Fig. 26.

the vapour-liquid equilibria passes in two more points, y and d, through
the spinodal curve. And so nothing appears yet of the detaching of
the longitudinal plait for the experiment. Only at higher temperature
the detached binodal curve, and then with its newly obtained plait-
point, will pass through the binodal curve AB, and with still higher
value of 7’ the binodal line has split up into two quite separate
branches.
(To be continued).

(September 3, 1907),

i Ui aie

33. Fi ret oan

a

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,

PROCEEDINGS OF THE MEETING

of Saturday September 28, 1907.

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

Afdeeling van Zaterdag 28 September 1907, Dl. XVI).

ClO ENE EEE NaS:

H. J. HAMBURGER and E. Hexma: “Quantitative researches on Phagocytosis. A contribution
to the biology of phagocytes”, p. 144.

P. van RompurcH: “The decomposition of penta-erythritol tetraformate on heating”, p. 166.

J. van BrusEKOM: “On the influence of wound stimuli on the formation of adventitious buds
in the leaves of Gnetum Gnemon L.”. (Communicated by Prof. F. A. F. C. Went), p. 168.

A. L. W. E. van DER VEEN: “The system of crystallization of the diamond”. (Communicated
by Prof. G. A. F. MOLENGRAAFF), p. 182.

J. D. van DER Waars: “Contribution to the theory of binary mixtures. VI. The plaitpoint
line”, p. 183.

H. KAMERLINGH ONNES and J. Cray: “On the measurement of very low temperatures. XV-
Calibration of some platinum-resistance thermometers”, p. 200.

H. KAMERLINGH Onnes and C. Braak: “Isotherms of diatomic gases and their binary mix-
tures: VI. Isotherms of hydrogen between — 104° C. and — 217° C.”, p. 204.

H. KAMERLINGH Onnes and J. Cray: “On the change of the resistance of the metals at very
low temperatures and the influence exerted on it by small amounts of admixtures”, p. 207.

H. KAMERLINGH Onnes and G. H. Farivs: “Repetition of pe HEEN’s and Tr1cHNeEr’s experi-
ments on the critical state”, p. 215.

H. KAMERLINGE Onnes and W. H. Krrsom: “Contributions to the knowledge of the ¢-surface
of vAN DER Waars. XV. The case that one component is a gas without cohesion with molecules
which have extension. Limited miscibility of two gases”. (Second continuation), p. 231.

J. J. van Laar: “Some remarks on the last observations of Prof. H. KAMERLINGH ONNES and
W. H. Kersom”, p. 238.

Errata, p 239.

10
Proceedings Royal Acad. Amsterdam. Vol. X.

(144)

Physiology. — “Quantitative researches on phagocytosis. A contri-
bution to the biology of phagocytes.’ By Prof. H. J. HAMBURGER
and Dr. EB. Hrxma.

(Communicated in the meeting of June 29, 1907.)
1. Introduction and method of investigation.

The investigations of which an abridged account is given in this
paper *) are a continuation of those begun several years ago by one
of us’), with the object of ascertaining the influence exercised
by solutions of various concentration on the red corpuscles and
other cells. These researches had been for the greatest part
confined to the study of chemical and volumetrical alterations ex-
perienced by the cells through the modification of their media and
of their significance with regard to the functions of the body. But
until now, the influence of these agents on the life of the cell itself,
had not been the object of a systematic investigation, although the
plan had existed for some time and the expediency of the method
had been proved *). The importance of such an investigation will be
readily admitted. In the first place, because it enhances the value of
the chemical and volumetrical researches mentioned above, and
secondly, because the phenomena produced by the agency of solutions
undangerous to life, are in fact nothing else but the effects of reaction,
which finally will help us to penetrate farther into the chemical
structure of the living cell. The red corpuscles, which were mostly
used for the chemical and volumetrical researches, however, are no
suitable objects for the study of the influence of reagents upon life,
for they do not afford sure tests of vitality, nor is it possible to
measure the value of their life functions.

We therefore looked elsewhere for our material and our choice
fell on the phagocytes, for the twofold reason that they are simple,
isolated cells in which it is possible to follow the effect of the
chemical exchange with their natural medium, and to rate their very
life by quantity; besides the phagocytosis is an essential factor in
the functions of life. In support of this latter contention, we refer
to the important place assigned by Mercanrkorr to these cells in
the struggle of the body against disease; a theory which he has

1) For detailed account, see “Biochemische Zeitschrift”.

2) Hameuncer, Zittingsverslag der Koninkl. Akad. v. Wetensch. 29 December 1883.

5) Hampurcer, Het gedrag van witte bloedlichaampjes tegenover cyaankalium,
Bijdrage tot de kennis der celpermeabiliteit. Feestbundel voor Rosenstein, 1902.

(145 )

defended with such admirable acumen and unflagging energy.
According to the same investigator, the part they play in the healthy
body is no less important. The only thing therefore which remains
to be done with regard to these cells, is to get a nearer insight into
their conditions of life; as yet scarcely anything is known on this
subject, a fact mentioned with regret by Mrrcunixorr, in the paper
he read last year before the students of the University of Amsterdain,
on: “Réactions phagocytaires” *).

The method of investigation employed by us was the following:
White corpuscles from the blood of a horse, after having been trans-
ported into various media, were brought into contact with carbon
and afterwards it was ascertained what percentage of the leucocytes
had taken up particles of carbon. This percentage was the measure
for the degree of phagocytosis and gave the value of the influence
of various agents on that function of life.

These calculations were based on the principle that the phagacytorian
power of the phagocytes present in a suspension is of unequal
extent; i.e. the more detrimental the action of the agent is, the
„smaller must be the number of phagocytes able to take up
carbon.

Our selecting a neutral indifferent substance of bacteria, had
its ground in the fear that otherwise our work would have become
too complicated. We here refer to the recently established fact
that most kinds of bacteria, before they can be taken up by
the phagocytes, must undergo a certain amount of preparation *).
Hence it follows that not only will the intensity of phagocytosis
be influenced by the agent as such, but also by the degree of
preparation it has undergone. Another fact which had to be borne
in mind, is that the bacteria sometimes secrete poisons which have
an injurious effect on the phagocytosis.

1) “Nous ne sommes qu’an début. Lorsqu’on connaitra mieux la physiologie des
phagocytes (the italics are ours) on cherchera des méthodes pour augmenter l'activité
de ces éléments dans la lutte contre les microbes et on cherchera d’autres pour
préserver contre l’attaque des phagocytes les cellules nobles de notre corps. En
poursuivant ce but, il faudra tenir compte de ce que les phagocytes sont non
seulement les destructeurs des microbes, mais qu’ils sont capables aussi de s’en-
corporer des poisons solubles et de les rendre inoffensifs. Leur rôle n'en devient
que plus important.”

2) Wricut and Doveras, Proceed. of the Royal Society 72, 1903, p. 357 and
later studies prepared under Wricur. Further Hexroen and Rüpreer, Journ. of Infect.
diseases 2, 1905, p. 128 and other studies prepared under Hexrorn.

10*

( 146 )

The selection of the indifferent substance carbon, instead of the
usual grains of carmine was based on the greater facility and more
accurate certainty with which the taking up of carbon can be
ascertained. It was also for this reason that carbon had been the
substance selected in former investigations on the action of carbonic
acid’) and the action of cyanate of potassium’) on phagocytosis.

On the present, as well as on the former occasion, the leucocytes
used in our investigations, were taken from the blood of a horse *).
They were obtained by shaking blood with pieces of glass in a
closed bottle and straining the defibrinated blood through a piece
of muslin. The red corpuscles sink to the bottom, and the serum
which covers them holds all the leucocytes. When this turbid fluid
has been poured off we have a suspension of leucoeytes in serum ;
this suspension can be made richer in leucocytes, by centrifugalizing
it, removing part of the clear serum and mixing the leucocytes
which have fallen to the bottom, with the remaining serum. A detailed
description of this method, the process of preparing the carbon,
the mode of bringing it into contact with the leucocytes, and the
method of determining the percentage of the cells which have
taken up carbon, will be found in our article in the Biochemische
Zeitschrift’).

Il. The effects produced on phagocytosis by the addition of water.

Our first experiments were directed to the solution of the question
in how far phagocytosis is affected by the addition of water.

With this object in view, equal quantities of the suspension of
leucocytes were mixed with serum, previously diluted with known
quantities of water. The following table shows the results of one of
the series of experiments. It will need no further explanation.

1) Hampurcer. Vircuow's Archiv, 156, 1899. S. 329. Osmot. Druck u. Ionen-
lehre. 1. 5. 416.

2) Hampurcer. Het gedrag van witte bloedlichaampjes tegenover Cyaankalium in
Rosenstein’s Feestbundel. 1902.
3) At Groningen we experienced great difficulty in obtaining a regular supply
of horses’ blood. Mr. K. Horrnacer, the Director of the abattoir at Utrecht, had
the great kindness fully to meet our wants, for which we here beg to tender him

our best thanks.
4) Compare also Hampurcer, Osmot. Druck u. lonenlehre, Bd. 1. S. 401.

( 147 )
TABLE I.

Effect of lessening the concentration of the serum.

Number of white) Percentage of |
Senn __ Number of ‘corpuscles which number of white Decrease okie
with Ennes have taken up | corpuscles con- | P ee
: P 5 coal taining coal P
C0/, water 886 331 37
PAD 754 246 32 13 .50/p
Oe 732 154 24 43.2,
E100 636 81 123 66.2 „
140955 520 0 0
2005, 546 0 0

From this table it appears that in serum, to which no water has
been added, of the 886 examined leucocytes, 331 had taken up
carbon, i.e. 37 °/,. ,

We must here point out that in the circulating, and also in the coagulated
blood, the percentage of phagocytes is actually much smaller.

By a certain proceeding, however, we contrived that in our experiments, the
leucocytes used for examination should contain a great number of phagocytes.
This process is based on the fact that among the leucocytes, the phagocytes are
the cells which soonest sink to the bottom. After this explanation, it will cause
no surprise to find that, in normal serum, the percentage of the phagocytes
which have taken up carbon, continually varies in different series of our experiments.

An addition of 20°/, water, already lessens the phagocytarian
power with 13'/,°/,. In calculating this loss on an addition of
5 °/, water, supposing the diminution to be proportionate, the de-
crease of the phagocytarian capacity would have amounted to:

5 ‘
Si XxX 13.5 °/, = 3.4°/,. In other words, when the osmotic concen-

tration of the blood plasma is lessened by 5°/,, a loss which in a
healthy individual may be of daily occurrence *), the phaqocytarian
power falls about 3.4 °/,.

By the side of this great sensitiveness of the phagocytes to the
increase of their percentage of water, stands the fact, as shown from

1) Compare ao. Korerre. Prrücer’s Archiv. 62, 1896. S. 567, In his experim nts,
Korpre noticed a decline below the mean osmotic pressure of over 10 °/9.

( 148 )

the table, that on the other hand, there area great number of phago-
eytes which can stand a dilution of their serum with 100°/, of water.
Former experiments have proved that this dilution causes an increase
in the bulk of the cells, of considerably over 30 °/,.")

We will now pass on to the following question: Js. this decrease
in the phagocytosis of a permanent nature?

In order to find an answer, we brought the white corpuscles
which had been submitted to the action of diluted serum back into
the normal, undiluted serum, and then tested again their power
of taking up coal.

ACB BE IE

After exposure to the action of diluted serum, the phagocytes

are brought back into normal serum.

: Number of Number of white | Percentage of
sectimdilitted white corpuscles corpuscles which | white corpuscles
with : have taking up | containing carbon,
Ae carbon in normal serum
|
00, water | 500 | 105 21
2 ~«, | 500 99 19.8
u Nee 500 107 21.4
10) 3 500 96 19.2
400, | 500 78 15.6 |
|
200) es | 500 61 12.2 |

This table shows that phagocytes, which had some time remained
in serum, diluted with 20°/, or 50°/, water, dilutions which as
the former series of experiments indicates, caused a reduction of the
phagocytarian capacity of 13.5°/, and 48.2°/, respectively, after
having been brought back into normal serum, entirely recovered their
original phagocytarian power.

The addition to the serum of 100°/, water, has on part of the
phagocytes a lasting deleterious effect; the addition of 200°/, water is
even more detrimental. Still, itis interesting to observe that, although in
serum which had been diluted with 200 °/, water, all the phagocytes

1) HampurGer. Archiv. f. (Anat. u.) Physiol. 1898. S. 317.

( 149 )

had lost the power to take up carbon, after being replaced in the
normal serum, over 50°/, of the phagocytes recovered their original
capacity.

So, the greater part of the phagocytes can support a considerable
volume of water without permanent loss of their phagocytarian
capacity.

Here may be asked: On what does it depend, whether a phagocyte will
regain its phagocytarian power? It is not impossible, nay, it is even probable,
that here as well as in the case of the red corpuscles some lose their contents
in serum diluted with 70°, of water !). If the quantity of water added be raised to
100"/y,, the number of destroyed erythrocytes will be found considerably larger.
When the red corpuscles, which have not lost their haemoglobin, are removed
from the serum diluted with 100°/, of water into undiluted serum, they entirely
recover; they change from small globules into biconcave discs, which even arrange
themselves like piles of coins.

However, this only applies to the cells which have not lost their colouring matter,
These which have actually lost haemoglobin cannot recover. Now our microscopical
investigations have revealed the fact, that in serum + 70 °/¢ water, some of phago-
cytes lose a part of their contents: in that case we see a granular substance
lying by their sides. In serum to which 1000/, water has been added, the effect
is more apparent stilk Then the number of leucocytes which have expelled granular
matter is still larger. Il is easy to understand that these cells, when again placed
in normal serum, haye lost the power of taking up carbon. The difficulty of
ascertaining this with certainty however, is very great: in the transmission there is
every chance of disturbing the granular substance by the side of the cells, and it is
impossible to know whether one deals with a phagocyte which has lost part of its
contents or not. Anyhow, taking into consideration the striking analogy existing
between white and red corpuscles, both with regard to their permeability and to
the osmotic pressure of their interior substance, and even to the percentage of
the volume of their watery contents 2), we seem justified in our conjecture that the
same fluid, which causes a loss of colouring matter in the least resisting of red
corpuscles, also brings about the irremediate destruction of the phagocytarian
power of the least resisting phagocytes.

It is a fact worthy of notice that the resisting power of the
phagocytes reaches a higher maximum than that of the erythrocytes.
In serum diluted with 200°/, water, all the erythrocytes of the horse
are destroyed, and not quite half of the phagocytes.

Ill. Lifect on phagocytosis by the reduction of water.

A similar method as had been used for studying the effect on phago-
eytosis by dilution of the serum, was now applied to ascertain the

1) Hampurcer. Transactions of the Royal Academy of Sciences, 26th March 1885,
2) Osmot. Druck u. Jonenlehre I, S. 401—435.

influence of concentration.

(1

50 )

With this object in view, common salt

was dissolved in the serum in quantities of 0.1, 0.2, 0.3, 0.4 °/, and
more. The results of these experiments are shown in the following

table :

ABE NOG
Effects on phagocytosis by increased concentration of the serum.

. : The liquids in the, Procentage of Decrease of the
Serum in which preceding column | leucocytes which maren
diseerd are corresponding | have taken up pragocy
1S to: carbon power
208
0 % Sod. Chl.! Sod. Chl. 0.99/p 330 > 100 = 26 0/0
|
184
0.1 i 1 B74 <100 = 21.5 17.3%
184
5) Ae |= 100 = 18.3 29.6
0 ” ” | 1005 x
|
0.3 pa | eer 69.2
ce ” ” cy QA a
| |
| 43 E
0.4 a ee AS Sn SUIS DA 79.2
| (793
| |

Here we see that the injurious effect is very great, much greater
than is the case when the osmotic concentration has been diminished.
Then we observed that by diluting the serum with 20°/, water,
phagocytarian capacity fell 13.5°/,; here we find that by raising the
osmotic concentration by 10°/,, the phagocytarian power is lowered
bypali3'5/ 5.
siological boundaries in which the osmotic pressure of the blood
plasma usually varies in the normal body. For it may happen .
every day that in a normal individual the osmotic pressure of the
liquor sanguinis, a few hours after dinner, is still raised by that of
0.1 °/, common salt *).

Here again, as we did before when studying the decrease of
osmotic pressure, we ask whether the loss of phagocytarian power

1) Korppe, l.c.

D. ScHoure.
kliniek. Diss. Groningen 1903.

See also Osmot. Druck u. lonenlehre B. IS. 540 ff.; B. II S. 279 and 310 ff.

This effect must already be perceptible within the phy-

Het physisch-chemisch onderzoek van menschelijk bloed in de

4
a
Pca

(151 )

can be restored, by replacing the white corpuscles in the normal
serum. The answer will be found in the following table.

TAB, LE IVS

After being exposed to the action of increased concentration,

the leucocytes were replaced into normal serum.

Serum in which After replacement into normal serum, the
is dissolved | phagocytarian power stands at
273
0°/, Sod. Chl. = > 10018 9"/5
700
0, 26 JOOS
2 5 = 38.4
4 | 646 x
226
0.7 = 100 = 33
9 685 x
1.2 zb << 100 = 30
; 567 oat
15 19 400 = 21 |
f 5 713 X ger)
87
ea — < 100 = 14
625
3 at 100 = 9
Ve oe

From this table it may be seen that after exposure to the action
of serum in which 0.2 °/, common salt had been dissolved, a solution
which had lowered the phagocytarian capacity by 29.6 °/, (see
table III), replacement in normal serum brings it back to its original
value. The action of serum in which 0.7 °/, of salt had been dissolved,.
however, causes a permanent loss of phagocytosis. Still, this loss is
not so great considering that, in the serum with 0.7 °/,, not a single
cell has taken up carbon, — in other terms, the phagocytosis has been
entirely paralysed.

Now the phagocytes had only been exposed for half an hour to the
action of the concentrated media. This certainly may be considered
long enough for the small cells to readjust themselves to their new
medium. Still, it may be asked whether after a more prolonged exposure
the normal value of the phagocytarian power would be restored too. This
question is of great importance for the functions of normal.life, in

( 152 )

which the increase of osmotic concentration often lasts longer than
half an hour. For this reason, the experiments in which the leucocytes
were exposed to an action of much longer duration, were made
with serum containing only 0.1 and 0.2°/, NaCl; higher osmotic
concentration does not occur in the body; The leucocytes were placed in
the serum of increased osmotic concentration for 2, 24 and 48 hours,
and then transferred into normal serum.

The experiment showed that after an exposure of 24 and 48 hours,
the phagocytarian power had been diminished; but an equal decrease
of vitality was also observed in phagocytes which had remained for
24 and 48 hours respectively in normal serum. This proved that
the prolonged action of serum of increased osmotic concentration
had had no permanent injurious effect on the phagocytarian capacity.

Thus we may conclude that, in the living body an increase in the
osmotic concentration of the biood plasma, as well as a decrease of
the same, has a deleterious effect on the phagocytarian power, but
that the loss may be recovered; for as soon as the osmotic pressure
has been restored to the normal, the phagocytes also entirely regain
their inherent power.

If from these experiments we may conjecture, that what we have
observed in the phagocytes, will also be applicable to other cells with
semipermeable walls, it is reasonable to conclude from the results shown
in tables IL and IH, that the vital functions of the cell are in a large
measure influenced by slight oscillations in the osmotic concentration
of the environment and consequently of the cells themselves.

IV. Eject of simple solutions of Salt.

1. Solutions of Sodium Chloride.

Now the question arises whether the loss of vitality described
above, must be attributed to the variations of the quantity of water
as such, or to the modification in the concentration of one or
more of the substances.

In order to examine this question systematically, we might have
alternately reduced the several elements in the diluted serum to
their original concentration and then studied the extent of the improve-
ment. But as in the mean time it had been clearly demonstrated
to us that in a pure solution of Sodium Chloride of 0.9°/, the
phagocytes take up carbon in equal or almost equal quantities as
in normal serum, we decided to abandon this mode of investigation.

Here we must incidentally remark that, after all that has been said by

(153)

LorB') and others, of the injurious action of a pure solution of a simple salt on the
life of young moving larvae and the vital processes of higher animals, such as the
beating of the heart and the movements of the intestines, we were at first rather
astonished at the almost perfect innocuousness of similar solutions in regard to
the phagocytes. However, we can easily find an explanation for this seeming
inconsistency. Whenever a cell is surrounded by a simple isotonic solution of
salt, two things are likely to happen: an exchange of ions may take place, thus
causing a modification in the chemical structure of the cell, which interferes with
certain of its vital functions. This is the case with the larvae of fundulus.
with the muscle of the heart and that of the intestines. A supply of specified
ions is then required to restore the chemical structure of the cell to its normal
state. But — and this is the second possibility — if the permeability of the cell
to ions is highly limited, a pure isotonic solution of salt will not cause any, or
only a very slight alteration in the chemical structure of the cell. This is the
case with the white corpuscles, the slight permeability of which to ions of
salts has already been demonstrated in the most convincing manner.?)

Bearing this fact in mind, it can cause no surprise that, contrary to the results
of the observations on eggs and muscles, a pure solution of Sodium Chloride
leaves the phagocytarian power entirely or almost entirely intact.

Under these circumstances, for determining the influence of the
water as such, it was indicated to take solutions of Sodium Chloride
of various strength.

Table V shows the action of diluted solutions of Sodium Chloride
on phagocytosis.

TABLE V.
Effect of hyper-isotonie solutions of Sodium Chloride on phagocytosis.
Percentage
Solutions of Salt. | of leucocytes which
| have taken up carbon.
235
NaCl-sol. 0.9°/, 756 DOOS
J
208
NaCl 0.75%/, — NaCl 0.90 + 20%, water) — >X100— 28
‘ 221
EOC ge" OLON DOP 1 101g 6 100 = 21.8
U =” 10:9 1-400) — <100= 11.4
745

1) J. LoeB, American Journal of Physiol. 3 1900 p. 327 and 383; 5 1901 p. 362
Pfliiger’s Archiv 80 1900 S. 229.

Linete, Americ. of Journal of Physiol. 4 1900 p. 265.

Miss Moore, Ibid. 1900 p. 386 etc.

2) HampBurcer. Zeitschr. f. Biol. 35. 1897 S. 252 and S. 280; Proceed. of the
Royal Academy of Sciences 11 April 1897.

Archiv f. (Anat. u.) Physiol. 1898 S. 31 and S. 317.

Vircuow’s Archiv 156 1899 S. 329.

HampurcerR and VAN DER Scuroerr, Archiv f. (Anat. u.) Physiol. 1902, S. 251,

(154)

Here we see the marked effect of a diminution in the concentration
of the salt solution.

TABLE VI.

Effect of hyper-isotonic solutions of salt.

: 3 Decrease of the
F Percentage of leucocytes -
Solutions. al phagocytarian
containing carbon. power.
250
NaCl 0.9"/, 709 100 = 34.60, |_
293
pe 0.95 375 <100}—= 73325) 30/9:
1 a 100 = 11.84 60.6
n 302 >< sh :
105
‘ = = 1088) 69
5 lel 981 > 100
1.2 at 400° = 057 98
d A OR ae
VB) ae < 100 = 0
” : 200 a,
1.4 Ô 100 = 0
2 ‘ 150 x ve
0
rs 425 750 De 100 = 0

The surprisingly rapid decline of phagocytosis observed in serum
of increased concentration (table IIL) is again clearly demonstrated
in this instance.

Even the slight increase of 0.9 to 1°/, lowers the phagocytarian
power already 60.6°/,. Another illustration of this rapid decline is
afforded by the observation that in the 1°/, concentration of Sodium
Chloride, the amount of carbon present in the coal containing
phagocytes is far less than in those that have stayed in the solution

of 0.9°/,.

Now, by comparing tables VI and III, we see at a glance that,
when the experiments were made with a solution of Sodium Chloride
of 0.9°/,, to which afterwards salt had been added, the decline
in the phagocytarian power is more marked than when they are

(455 )

made in serum supplemented with an equal quantity of salt. This
proves that besides the osmotic pressure, which must principally
be made accountable for the decline, there is still another factor at
work, and this factor can be no other than the modification — however
slight — produced by a pure solution of NaCl in the chemical structure
of the phagocytes. Some time ago, one of us, in conjunction with
Dr. vAN DER Scurorrr'), already demonstrated that the leucocytes
the same as the red corpuscles are in any case permeable to anions.
It is therefore evident that, owing to their chemical structure being
interfered with, the cells most lose some of their vitality (phago-
cytarian power) under the action of pure salt solutions, — or
rather, that they should lose more than in an isosmotie serum.

We have submitted this hypothesis to further experiments, starting
from the following reasoning: If it is a fact that in a hyper-isotonic
solution of salt, the phagocytes undergo a chemical variation through
exchange of ions, it must be possible to restore this loss of phago-
cytarian capacity resulting from their modification in their structure,
by replacing them in normal serum, and that this recovery. will
not be complete by immersion in a 0.9°/, solution of salt. The
following table proves that we were correct in our surmise.

TABLE VII.

Effect of solutions of salt on the chemical structure

of the phagocytes.

White corpuscles | Phagocytarian power after being transferred into,
immersed for 2!/,
hours in the fol-
lowing solutions. Normal Serum Salt solutions of 0. 90/,
319 284
0.90 == 100 = 33.90 = = Jo
NaCl /o 942 De 33.9 lo Su DS 100 35 lo
258 251
4 == 400 = 33.3 Sn AOORSRS
7 775 x 760 x S
233 | 209
a a —— X 100 = 29.5 — X 100 = 28.6
790 735
202 175 |
12 = Se) SB == =D)
; 722 Bie ig emd

1) HAMBURGER and VAN DER SCHROEFF. |. c.

( 156)

It is clearly demonstrated that the phagocytes, which have been
exposed for two hours to the action of solutions of Sodium Chloride,
exhibit a greater phagocytarian power when they are transferred
into serum, than when they are placed into salt solution of 0.9 °/,.

No doubt the observation will strike the attentive reader as
contradictory, that this is only the case with the phagocytes which
had been exposed to the action of sodium chloride of 1°/,, 1.1 °/,
and 1.2°/,, but not with those which for the same space of time
had been immersed in a similar solution of 0.9°/,; then the effect
of this salt-solution and the serum is quite the reverse. This, however,
is not actually the case; for in serum the phagocytes are likely to
stick together and on this account do not offer as large a surface to
the carbon as in the salt-solutions in which they remain more isolated.
If then, as must be the case in an dsotonic solution, the injurious
effects of the Cl-ions of the pure salt solution are comparatively
small, they may easily be exceeded by the unfavourable position of
the cells caused by the serum.

When, however, by the use of Ayper-isotonic solution of sodium
chloride, the injurious action of the Cl-ions be increased, it may
exceed the detractory influence of the agglomeration of the cells,
and produce the results shown in the table.

With regard to these statements it may here be asked why, in
isotonic solutions of sodium chloride, the injurious effect on the
phagocytes cannot be determined, but is easily demonstrated when
hyper-isotonic solutions are used, and the more readily in proportion
as the concentration of the salt solutions are increased in strength.
This question is very natural, because it concerns such a small
increase in the considerable amount of ions of Cl or of Na
already present. Here we are involuntarily reminded of the fact
stated by Hepin') with regard to the red blood-corpuseles. The
minute investigations of this scientist have brought to light the fact,
that in isosmotie zsofonic solutions of salt, the corpuscles possess an
equal volume, but that in isosmotic anisotonie solutions their relative
volume is no longer equal. HepiN has not given an explanation of
this important fact; but anyhow, it proves that simple solutions of
salt, when anisotonie, exercise still another kind of action beyond that
of their osmotic pressure. We propose to investigate this matter
somewhat further: it is very probable that by a modification in the
dissociation of the contents of the cell, an altered condition for the
exchange of ions is produced.

1) Hepin. Skandinavisches Archiv f. Physiol, 1895 S. 377.

> fer op

(457 )

2. Solutions of Chloric Potash.

In our description of the influence of sodium chloride, we attri-
buted it to the ions of chlorine. This was based on the results of
investigations in which we compared the action of sodium chloride
and of potassium chloride, of which a few items here follow.

These investigations proved that isosmotic solutions of sodium
chloride and potassium chloride have almost the same effects on
phagocytosis.

TL ASBe tE NITE
Comparison of isosmotie quantities of sodium chloride
and potassium chloride.

Percentage of leucocytes
containing carbon.

253

Serum | ——><100 = 35 %
722
300 |
NaCl-sol, 0.90 —— 100/36
ai | 3367 )
: | 258 |
KCl-sol. 1.15°/, (isot. m. NaCl-sol. 0.9°/,) | as 100 = 34 |
| | 183 |
Serum+0.1 ®/ NaCl — >< 100 = 27

745
5
Noa NAC 100 = 7
= 7 630 <
bh
„ +0.38 , KCI ** 100 =

450.497 KCI | ~~ X100=95
|

184
» +0.3 „ NaCl afterwards 600 < 100 = 30
placed into
185
» +0.38 , KCl normal serum oat > 100 = 30

Two other parallel-experiments in solutions of 0.9°/, of sodium
chloride produced the following results:

198
acd X 100 = 23°/, of leucocytes containing carbon
146

and — X 100 = 21.5 °/, ,, a 53

677

( 158 )

in the isosmotic solution of KCl 1.15 °/,:

128
Fae x 100 = 21 °/, leucocytes containing carbon
165
d — x 100 = 22.5° 7 5 5
ae ea je

Hence we may conclude, that there is no difference between the
action of chloride of potassium and chloride of sodium.

3. Effect of chloride of calcium.

The great importance which, according to the most recent in-
vestigations must be ascribed to the ions of calcium,’) in the con-
stitution of the fluid-matter of the tissues, induced us to test also
the effect of this medium on phagocytes.

With this object in view, we dissolved various quantities of chloride
of calcium in the serum of the blood of a horse and mixed the
suspension of leucocytes thus obtained with carbon.

TASB i EXE

Effect of calcium chloride.

| Increase of the —
Serum ‘Percentage of leucocytes Ei
=F f containing carbon gaa
| ae
0/pCaCh Gag.) G45 XX 100 = 21.2%
| 0.010 a 1005726 29. .60/
„010, agi 100 = 2 22.60/o
180
0.1 — X 100 = 27.6 30.2
652
0.5 Bee 100 = 97 27.3
a War eS ria
1 D 100 0
724 * mt

An addition of 0.01 °/, of CaCl, 6 ag. to the serum already
produces an increase of the phagocytarian capacity of 22.6 °/,;
by the addition of 0.1°/, CaCl, 6 aq., the effect is somewhat

1) See especially the investigations of Loes. Publications of the University of
California and of Lancenporrr and Huecx. Pfliiger’s Archiv 96 1903 S. 473; for
the complete bibliography on the subject until 1904, see Osmotischer Druck und
Ionenlehre B. III, S. 107 etc. Comp. also A. Nerrer, Importance biologique du
Calcium. Paris. Masson et Cie. 1907.

(159 )

greater, and by the addition of 0.5 °/, Ca Cl, 6 aq, it again
decreases.

The result registered in the first instance, which is produced by
the addition of 0.01 °/, CaCl,, must be considered the most valuable,
for it denotes the nearest unalloyed effect of the calcium chloride.
In the experiments where quantities of 0.1°/,, 0.5°/, and 1°/, of Ca Cl,
were added, the increase of phagocytosis is counteracted by the
unfavourable influence of the raising of osmotic pressure.

This experience is in strict accordance with the observations made
by LANGENDORFF, who found that the injection of very small quantities
of calcium, causes the heart to beat with greater force. We ascribe
this manifestation to the action of the ion of calcium on the contractile
substance, and we may conclude that the muscular fibre and the
phagocytes aiso, are permeable to this cation.

4. Effect of citras natricus.

The frequent use which, in consequence of the experiments of
Wricut and Doveras, *) is made of this medium at the present day
by the bacteriologists, in order to prevent the coagulation of the blood,
actuated us also to experiment with this substance for the sake of
determining its action on the phagocytosis. The following table gives
a survey of the results.

The customary solutions of 1°/, and 2°/, of citras natricus in
0.9 °/, solution of sod. chl. were used in these experiments.

AN Bt be Epe Xe
Effect of citras natricus.

| Percentage of leucocytes
| containing carbon

(a) 1 ce. suspension of leucocytes + 2 cc. |
solution of 19/9 citras natr. in 0.90/) Sod.Chl. | 0

(6) 1 cc. suspension of leucocytes + 2 cc.
solution of 29/9 citras natr. in 0.90/, Sod.Chl. 0
| 56
i 260
(c) leucocytes from (a) transferred in con sag 100 — 38 0/,

(d) leucocytes from (6) transferred in Sod.Chl. 255 >< 100 = 35 0/,
734 2

0.9 0/, |
|
(e) 1 cc. suspension of leucocytes + 2 cc. | 369 ae
solution of 0.9 0/, Sod.Chl. (Control test) en meld

1) Wrieut and Doveras, Proceed. of the Roy. Soc. 72, 1903, p. 357; 78, 1904,
p. 128.
11
Proceedings Royal Acad. Amsterdam. Vol. X.

( 160 )

From the above table it is shown: 1. That in 1—2°/, solutions
of citras natricus in 0.9°/, of Sod. Chl. the phagocytarian power
is nil. ;

2. that the phagocytarian capacity again partially reappears, when
the cells are transferred into 0.9°/, solutions of Sod. Chl. The per-
manent decline of the phagocytarian power still amounts to 28 °/,.

5. Effect of Fluornatrium.

Fluornatrium being also much used for preventing the coagulation
of the blood, it seemed important to us also to study the effect of
this medium on the phagocytosis.

ASB BE meere
Effect of Fluornatrium.

Percentage of leucocytes containing

carbon
Before being trans- | After being trans-
ferred into 0.90, | ferred into 0.90/,
Sod. Chl. Sod. Chl.
xf 91
2ccsuspension of leucocytes +2cc NaF10.659/p U0/, == 100 — aa
(isot. with NaCl 0.9)/, 677
20
5 + 2ce NaFl 10/0 0 wm ODE RE
+ 2cc NaFl 20/, 0 0
369
+ 2cc NaCl 0.99%, zon < 100 = 50
+3)

Here we see that when the leucocytes have been exposed to
a solution of Fluornatrium of 2°/,, 1°/, or 0.65 °/, (isot. with
0.9°/, NaCl) the pbagocytarian power is entirely paralysed, yea,
that even after transferring of the phagocytes in a solution of 0.9 °/,
Sod. Chl. it shows to have been entirely destroyed for ever. Hence we
may conclude that NaFl is a powerful poison for the protoplasma
of the phagocytes.

V. Eject of acid and alkali.
1. Effect of acid.

The important part which the alkaline reaction of the blood-
plasma seems to play, not only in connexion with the degree of

( 161 )

oxydation taking place in the body, but also in infectious diseases,
induced us to study its effects on the increase or decrease of the
phagocytarian power.

The results of one of the experiment are shown in the following
table.

AGES aE xb]:

Diminution of the alkaline reaction of the serum.

l 5
lee /, n. H,SO, | Amount of acid Bae eerie
oes carbon |
9 ce serum ‘og norm. 0 |
(pe Sate 13 oe
14 cc 5 [ao je | 308 <100= 4.3%,
19 1/ | ee <100— 9
te ee /40 ne == <i
? | 398
2 465:
49 cc 5 “hoo 5 79k < 100 = 21.4
255 :
299 cc 7 e00 ” 612 pd 100 = 41.7
| | 256,
— | 499 cc ft "hooo = | 530 100 43.5
oe
| 297
normal serum =e OU —— 455
| 530
|

We observe that even the small addition of */,,, z-acid is injurious
to the phagocytosis.

Now, we know that according to titration with lacmoïde, 100 c.c.
horse serum in the mean is equivalent to 75.5 ee. */,, n-acid ') ; conse-
quently it is caleulated that serum represents an alkaline fluid of
1, normal.

The addition of */,,, r-acid, therefore lowers its alkaline reaction
bya):

Consequently, a diminution of the alkaline reaction of the serum
by 5°/, is already injurious to the phagocytes. °

This result is in strict accordance with the injurious effect experienced

1) Hampurcer, Verhandel. d. Koninkl. Akad. v. Wetensch. Second section, Vol.
MINOR SoT.

RS

( 162 )

by administering acid per os, and we are fully justified in aseribing
the poisonous effects of the acid, to a diminution in the process
of oxydation.

The results agree also with the observations recently published
by J. Loes, on the influence of the traces of NaOH (OH-ions) on
the artificial fructification of the eggs of sea-urchins. The author
has clearly demonstrated that the primary cause of this effect might
be found in the acceleration of chemical reactions. *).

DA a By ee se

Increase of the alkaline reaction of the serum.

Percentage of white
lee !/, n. NaOH Amount of os
2 : scles contain
Je alkali adaede | OE oen
| } 25 4
| 2ee Serum "oo re 100= 4
57
37 Is INA OO O RS
CEN, lr 840 x
49) ij B 100 =16
JCC ” 100 707 =
179 4
ee » ‘00 =e xX 100 = 25
716
ze ; 148 5
19% ce ” EN 531 < 100 — 27
9 1 100 = 95.7
3s 9 800 EENS IDS 95 A
cc » [so 580 0)
177 a
normal serum gea ”S 100 = 26.5

It is seen froin this table that, within a large margin, the addition of
OH-ions to the serum does not exercise a perceptible influence on
the phagocyterian power; it remains unaltered until the value is
increased by */,,, normal: ie, with 15°/, of the original alkaline
reaction. An additional supply of alkali causes a lessening of the
phagocytarian power.

More pronounced still is the effect of acid and alkali on the phago-
cytes, when these substances, instead of being added to serum, are

1) J. Lorp, Prrücer’s Archiev 118, 1907, H. 3/4, S. 181.

( 163 )

introduced in solutions of 0.9°/, sod. chl. A more detailed account
of the results of these investigations will follow later.

We also made a number of experiments to test the influence of
other media on the phagocytarian power, e.g. with ureum, chinine,
argentum colloidale, heterogenous serum, ete., the results of which
will appear in a subsequent paper.

Summary.

The following are the principal conclusions derived from the above
described experiments.

1. The action exercised by various media on the phagocyterian
power of white corpuscles, can be accurately determined by counting
the percentage of cells which have taken up particles of carbon.

2. The addition of water to the inherent medium of the phagocytes
de. to their own serum, acts injuriously on the phagocytarian power.

Ewen a decrease in the osmotic concentration as may daily occur
in a normal individual, causes a perceptible decline in the phago-
cytarian power.

So, it was shown in one of the experiments that, whilst in normal
undiluted serum 387°/, of the leucocytes had taken up carbon, in
serum which had been diluted with 20°,/, of water the amount of
cells containing carbon was only 32 °/,: this corresponds to a decline
37 --32

an STOOD

By the addition of 50°/, water, the percentage of phagocytes
containing carbon fell to 21°/,; thus in this case a decrease of

in the phagocytosis of

. , 87 —25 :
phagocytosis of Scere: XxX 100 = 48 °/,.

By addition of 140 and of 200°/, water, the percentage of the
carbon-containing leucocytes was lowered to nil, — in other words the
phagocytarian power had been suspended; but only temporarily, for

3. by replacing the cells damaged by the addition of water, into
their own serum, the phagocytarian power is entirely or partially
restored.

So the recovery was complete, when the serum had been diluted
with 20°/, or 50°/, of water, and only partial when 70 tot 100 °/,
water had been added. Even when it had been diluted with 200 °/,,

( 164 )

a figure at which, it is shown under 2, the phagocytosis had been
entirely suspended, — a recovery took place in the phagocytarian
power to half of its original amount.

4. The observations, here made with the phagocytes, correspond
with those previously observed in the red corpuscles.

1. The phagocytes, the same as the red corpuscles, can support
a considerable quantity of water (+ 60°/,) without a single cell
being destroyed ;

2. The modifications produced in the phagocytes by the addition
of water, unless they have led to their entire destruction, may,
judging from the phagocytarian capacity, be entirely obviated by
replacing them in normal serum.

dD. A heightening of the osmotic concentration of the serum, as
well as a lowering of the same, (comp. sub 2) has a very injurious
effect on the phagocytosis. It was obvious that an increase of the
osmotic concentration had even a more pronounced deleterious action
than the decrease at the same ratio. Already an addition of 0.1°/, NaCl
to the serum caused the phagocytarian power to decline 17.3°/,.

By the addition of 0.4°/, NaCl this decrease amounted to 79.2°/,
and by the addition of 0.5°/, Sod. Chl., the phagocytarian power was
reduced to nil; but this considerable loss was but temporary, for

6. when the cells which had been damaged by an addition of
sodium chloride to the serum, were replaced in their original blood-
serum, their phagocytarian capacity was again entirely or partially
restored; entirely when oniy from 0.1° ,—0.2°/, of the substance had
been added; partially when a greater amount had been used.

7. If thus, as shown under 2 and 5, the phagocytarian power
is specially impaired by modification of the normal osmotie concen-
tration of the blood-serum, this capacity will be entirely restored
as soon as the blood-plasma, principally owing to the activity of
the kidneys, has recovered its normal osmotic concentration. The
experiments have demonstrated that this recovery is still possible
after the agency of the anisotonic serum for 24 hours and more.

8. In solutions of 0.9°/, NaCl the phagacytarian power
is almost equal to that of serum. It considerably decreases under the
action of weaker and stronger solutions of this salt, even more so
than in serum which has been made isosmotie with these salt-solutions.

( 165 )

9. This result leads to the conclusion that the decline of the pha-
gocytarian capacity produced by anisotonic serum, has its cause
principally in the alteration of the amount of water in the cells.

10. Besides the modijication of the amount of water in the cells,
another factor comes into play, namely the chemical change, which takes
place consequently on the exchange of the contents of the cells with
those of their environment and which, as a matter of course, ts
greater when the cell is surrounded by a simple solution of NaCl
than when placed in an isosmotic serum. This accounts for the fact,
that phagocytes which have been submitted to the action of hyper-
isotonic solutions of NaCl, when replaced into serum, exhibit a
somewhat greater phagocytarian power, than when they are trans-
ferred to a 0.9°, solution of NaCl. In the latter case they have
not the opportunity, given them in the former, of regaining the
ions which they have lost in the anisotonic solutions of salt.

11. Jt is very probable that the ions of Ca and of OH belong
to this category.

With regard to calcium, it has been proved that by the addition
to the serum of the minute quantity of 0.01°/, CaCl, 6 aq, i.e. about
0.005 °), CaCl,, the phagocytarian power was raised by about
22.6°/,. The inference is that ions of calcium must have penetrated
into the phagocytes.

On the other hand it may be surmised that the phagocytes will
lose ions of calcium when the amount of calcium in the medium
is lower than that to which the phagocytes are accustomed. This
loss of ions of calcium must cause a diminution of the phagocytarian
power.

We observe a similar result in the case of the OH-ions; for our
experiments have demonstrated that decrease of these ions causes a
lowering of the phagocytarian power. A 5°/, diminution of the
alkaline veaction of the serum, which necessarily must lower the
amount of alkali in the phagocytes, produces a noticeable decline
in the phagocytarian capacity.

12. Lore and after him other investigators have pointed out,
that a pure solution of NaCl must be considered injurious to the
larvae of lower sea animals, the muscles of the heart, and those of
the intestines. his opinion does not hold for the phagecytes. The
proof of this assertion is found in the fact that in a solution of
NaCl isotonic with serum, the phagocytosis is almost as powerful as
in the serum itself.

( 166 )

This seeming contradiction may be met by the explanation that
the exchange of substance between the leucocytes and the solution
of NaCl, especially when the latter is isotonic with the serum, is very
small; whilst in the case of other cells (citiated cells, muscular fibre
cells) the conditions of the exchange of ions are not so restricted, and
consequently the chemical structure of these cells is more easily
modified. And it is obvious that a modification of their. chemical
structure causes a disturbance in their inherent functions.

13. From the facts here recorded, it is evident that in studying
the action of the phagocytes on bacteria im vitro, the degree of
Osmotic concentration and of the alkaline reaction of the. medium,
must be taken into account. This condition has been lost sight of
- in several of the experiments. They ought therefore to be repeated.

Groningen, June 1907.

Chemistry. — “The decomposition of penta-erythritol tetraformate
on heating.” By Prof. P. van Rompureu.

(Communicated in the meeting of June 29, 1907).

As the heating of the diformate of s. divinylglycol had led in such
a simple manner to hexatriene 1.3.5, investigations have been set on
foot in my laboratory for studying the decomposition of formic
esters of polyhydric alcohols, the results of which will be gradually

communicated.
If for penta-erythritol we accept the formula:

HOH,C. CH, OH
Sa”
HOH,C” CH, OH

and if the reaction took place in a similar manner as with s.
divinylglycol diformate, we might expect on heating the tetraformate *)
the formation of a hydrocarbon of the formula:

in which oceurs twice a 3-ring.’)

1) Gustavson C. R, 123 (1896) 242 obtained from the tetrabromide of penta-
erythritol, by the action of zinc and alcohol, vinyleyelopropan :

HC
l cH — CH=CH;
HC

instead of the above cited hydrocarbon.

( 167 )

The reaction, however, proceeds in quite a different sense, for
instead of the hydrocarbon we only obtain carbon monoxide, while
penta-erythritol is regenerated.

In order to prepare the tetraformate of penta-erythritol, this sub-
stance is heated with an excess (8 mols.) of concentrated formic
acid in a flask connected with a condenser, in such a manner that
the excess of acid distils over slowly with the water formed in the
reaction. When the thermometer placed in the liquid shows 120°,
the heating is stopped, and the distillation is repeated with a fresh
quantity of formic acid. After this the heating is repeated twice
with 100°/, acid. There then remains in the flask an oily liquid,
which, when placed in a dish over sulphuric acid, abundantly
deposits crystals after some time. These are collected at the pump,
and then thoroughly pressed between filterpaper.

The solid substance thus obtained, after having been recrystallised
from dry benzene, melts at 55°. After repeated recrystallisation from
that solvent, the melting point rose to 57° and then remained constant.

This formate is sparingly soluble in ether; from a solution in
benzene it is precipitated by ether. It has a slightly bitter taste.

On boiling with a titrated solution of potassium hydroxide the
formic acid formed may be readily estimated.

Found 74.21 and 74.16°/, formic acid
Caleulated = 74.18°/,.
The ultimate analysis gave the values expected for penta-erythritol
tetraformate :

Found Caleulated for C, H,, O,
C 43.6 48.75 43.57°/,
H °5.26. 5:16 4.88°/,

On heating this formate, a plainly visible evolution of gas com-
mences at 220°, which is fairly strong at 230°. The gas evolved
consists of pure carbon monoxide and when the evolution of gas
has ceased, there remains in the flask pure penta-erythritol, which may
be readily identified as such by its properties. The amount of gas
evolved is that required by theory.

I wish to express my thanks to Mr. van Enpt, who has assisted
me in these experiments with care and zeal.

Mr. Renter, who is engaged in the study of the formates of
glycols found that from 2.5 dimethyl-hexandiol 2.5, the well known
tetramethyldihydrofurane, is formed by simply heating with formic acid.

( 168 )

On the other hand the formic ester of pentandiol 2.4 is very stable
towards heat.

At about 400°, however, the ester is decomposed and a liquid
is formed boiling at 42° which is most probably 1.2 dimethyl-
cyclopropane.

Mr. vaN MAANEN, is engaged in the study of the decomposition
of the formic esters of mannitol.

Utrecht, Org. Chem. Lab. University.

Botany. — “On the influence of wound stimuli on the formation
of adventitious buds in the leaves of Gnetum Gnemon L.” By
Mr. J. van BEUSEKOM. Communicated by Prof. F. A. F. C. Went.

(Communicated in the meeting of June 29, 1907).

It had been observed for a long time already that adventitious
sprouts were formed on the leaves of a specimen of Gnetum Gne-
mon L., cultivated in the Botanic Garden at Utrecht.

In January 1906 my attention was drawn to this circumstance
by Prof. Went, who advised me to study the development of these
adventitious sprouts, and to try to discover the origin of their formation.

The results of this investigation will be concisely communicated here.

The adventitious buds appear on the tips of the leaves, while these
are still attached to the plant.

As far as I have been able to find out, the formation of these
adventitious buds has never before been observed with Gnetum
Gnemon, neither in its natural sites, nor in botanic gardens?) except
at Utrecht. The Utrecht Garden possesses three specimens of Gnetum
Gnemou. One of these has been continually cultivated in a hothouse
where in winter the temperature is kept at about 25° C., and the
air is very damp. The other two were, when I began my investi-
gation, in an other hothouse where the temperature is lower (in

winter on an average 15° C.), and the humidity less. Whereas of

the former I have always obtained leaves in different stages of bud-
formation, the other two showed the phenomenon only after they
had been conveyed to the warmer and damper hothouse.

Although all three plants, apart from the formation of adventitious
buds, are evidently healthy and do not make a morbid impression

1) On this point I gained information from the other botanic gardens in our
country, from that at Munich and also from that at Buitenzorg.

( 169 )

at all, they flower very rarely. Personally I only observed it with
one of the plants from the cooler hothouse. This latter plant produced
one single ¢ inflorescence, which enabled me to check the accuracy
of the determination.

The first external change, noticed with a leave which will form
adventitious buds, is that on the tip extremely small yellow dots
appear, which are seen best when light is falling through the leaf.
They remind us in this respect of the oil dots in the leaves of the
Rutaceae or Hypericum, but as a rule they are bigger and less
densely spread than these.

With the bigger ones a hand-magnifier will show that where the
dots are, the epiderm of the upper or lower side or of both together
is slightly bulged, so that we have to do with small vesicles.

It will be shown presently that these vesicles are caused by the
sting of a scale-insect Aspidiotus spec., and as such are not restricted
at all to the tip of the leaf. Normaily, however, it is only the tip
which can form adventitious buds. The remaining part of the leaf blade
can only form adventitious buds when the organic relation with the
tip has been disturbed in some way or other. But even then they
arise apically in this part. Hence only the vesicles which have
originated on the apical part of a leaf, form the introduction to the
process of bud-formation.

For the sake of simplicity we shall in what follows, only mention
‘the tip of the leaf, since the statements referring to the tip also
apply to the other cases.

After some time also the region, surrounding the vesicles, becomes
discoloured; as a rule the tip of the affected leaf soon becomes
distinctly yellow, although in some cases it long keeps a more or
less greenish tint.

At the same time with this discoloration the tip of the leaf becomes
thicker. This thickening is at first not easy to observe macroscopi-
cally; gradually, however, it becomes stronger and at last generally
advances so far that the tip becomes stiff and difficult to bend.

Of the yellow vesicles nothing can then be seen any longer.

The extent of this region of discoloration and thickening varies
much in a basal direction; along the edge it generally extends farther
basipetally than in the middle; always, however, the phenomenon
is restricted to the apical part of the leaf. A new stage sets in,
when the surface of the thickened leaf-tip which until now had
remained smooth, on account of the swelling being even, becomes
uneven: as well on the lower as on the upper surface this may as a
rule be observed; on the upper surface it is generally more pronounced.

( 170 )

During the first weeks generally no striking changes are observed
until after about a month a varying number of local elevations,
yellow like the leaf-tip that produces them, becomes prominent and
reveals the differentiation of special proliferating centres.

As a rule we see these grow to real knobs, especially in the
direction perpendicular to the surface of the leaf.

While the knobs are still relatively small, brownish grey streaks
begin to appear on their tops, which gradually extend, so that
finally the whole knobbed surface becomes brown.

For some time such a knob shows nothing particular, except that
it becomes larger and thicker. Next on a certain day a small opening
is formed in its top, through which a small green point projects,
which will grow out into a leafed sprout.

As well on the lower as on the upper surface of the leaf-tip
knobs may form. Mostly they form on the upper surface, though.
With some leaves I have observed knobs on both sides at the
same time.

The observations on the time, needed by a leaf in order to form
“ripe” knobs, after the yellow vesicles have appeared, have led to
somewhat diverging results. The shortest period was observed with
leaves on the upper branches or in the periphery of the crown,
which consequently occupied the most favourable position with regard
to light. On these good-sized, brown knobs had generally formed
half a year after the appearance of the yellow vesicles.

Also for the question, how old and bow large a knob must be in
order to open and give the adventitious bud an opportunity for
sprouting, no rule can be fixed. I saw one sprout five weeks after
the knob had first been observed as a special elevation, while others
were still closed after five to seven months.

About the size of the knobs we may state that some knobs,
scarcely rising more than a millimetre above the surface of the
leaf-tip, opened, while others of double and even treble the height
remained obstinately closed. Yet these latter contain as well an
adventitious bud and not seldom even more than one.

The microscopical investigation was for the greater part carried
out on microtome preparations. For fixing the material I used the
mixture: zinechloride-glacial acetic acid-aleohol, (2 grams of zinc-
chloride and 2 cem. of glacial acetic acid to 100 cem. of alcohol of
45—50 pCt), recommended by Jurr'). The particular hardness of

1) H O. Juet, Ueber den Pollenschlauch von Cupressus. (Flora. Bd. 93. 1904.
pag. 56—62).

——

(Gah sho)

the leaf tissue made it necessary to treat the material, before being
embedded in paraffin, during 3 to +X 24 hours with a 40 pCt.
aqueous solution of hydrofluoric acid. After this treatment it was
then washed for 8 to 10 hours in streaming water, dehydrated by
the usual method and after treatment with chloroform embedded in
paraffin (melting point 62° C.).

For staining the sections I used at first Haematoxylin-Delatield
and saffranin, according to the prescriptions given in CHAMBERLAIN’S
“Methods in Plant Histology” *); but this method proved unsatisfactory
for differentiating the very thin-walled meristem cells. Therefore I
afterwards always stained with methyl green and acid fuchsin ’), by
which very good results were obtained.

A consequence of the treatment with hydrofluoric acid was that
the microtome preparations were not suitable for all observations.
In these cases I used hand-cut preparations, if necessary stained with
Haematoxylin-Delafield.

The anatomy of the normal leaf, on which something may be
found in literature with BerrranD ®), De Bary‘), Scuerr °) and HaBer-
LANDT °), is as follows.

The epiderm of the lower and upper surface consists of relatively
small, cubical cells, the outer wall of which is strongly thickened
and provided with a strong cuticle and from which capriciously
shaped and ecanaliculate outgrowths project into the lumen of the
cell. (cf. Bertranp, Le. Pl. II fig. 6, 7, 8.). In the epiderm of the
lower side numerous, irregularly placed stomata are found.

Under the upper epiderm lies the palissade parenchyma, formed
by one continuous row of cells, slightly elongated in the direction
perpendicular to the leaf surface. (dimensions 13—21 u by 21—30 u).
Between the palissade cells and the lower epiderm lies the spongy
parenchyma, consisting of tubular cells, the diameter of which is on
the average 18 u, as a rule is not more than 9 u ata partition wall
between two tubes and does not reach more than 28 u. Between
the cells of the spongy parenchyma remains a system of large inter-

1, CG. J. Cuampertain, Methods in Plant Histology 2nd ed. Chicago. 1905.
pag. 30, 38 and 54.

2, CHAMBERLAIN. |. c. p. 40, 44 and 68.

3, CG. E. Berrranp, Anatomie comparée des tiges et des feuilles chez les
Gnétacées et les Coniféres. (Annales d. Se. nat. Botanique 5ieme série Tome XX. 1874).

4) A De Bary. Vergl. Anatomie der Vegetationsorgane der Phanerogamen und
Farne. (Handb. der Physiol. Botanik von \V. Hormetster. Leipzig. 1877.)

5, M. Scuerr, Die Tracheïden-Säume der Blattbündel der Coniferen etc. {Jenaische
Zeitschr. f. Naturw. Bd. XVI. Neue Folge Bd. IX. 1883.)

6) G. Hapertanpt, Physiologische Pflanzenanatomie 2te Aufl. Leipzig. 1886

(2107205)

cellular spaces. In the spongy parenchyma numerous thick-walled
sclerenchyma fibres are found, which are generally ramified and
often have an enormous length.

A section through a leaf-tip on which yellow vesicles are found,
shows that these vesicles are caused by hypertrophy of cells of the
spongy parenchyma which have there entirely lost their tubular shape
and among which specimens are found, measuring 91 by 109 u,
100 by 73 u, 100 by 113 u ete. Among the cells, constituting the
vesicle, some are always found which in unstained preparations are
conspicuous by their wall being more or less swollen and brown.
In preparations, treated with acid fuchsin and methyl green, the wall
of these cells is blue, those of the other cells red. Applying the
usual reactions we find that these walls have become suberized. Also
of the .palissade parenchyma some cells may have become larger,
but always in a small degree.

While in the vesicles themselves the process goes a little further
still on account of partition walls forming in some of the enlarged
cells, whose walls have not become suberized, also the region,
surrounding the vesicles, evidently answering to a stimulus, proceeding
from them, begins to undergo similar changes. Macroscopically we
detect this by the more or less yellow tint, assumed by the vicinity
of the vesicles. A microscopical examination of the section shows
that now also outside the vesicles the cells of the spongy parenchyma
are hypertrophical. As with the formation of the vesicles the chlo-
rophyl is disorganised in the hypertrophical cells.

At this stage no function of importance may be ascribed yet to
the cells belonging to the palissade parenchyma.

In most preparations now already the peculiar behaviour is noticed
of those spongy parenchyma cells which border immediately on the
palissade parenchyma. While the other cells of the spongy parenchyma
swell as evenly as possible in all directions, those which lie imme-
diately below the palissade parenchyma become enlarged especially
in a radial direction, thus making the impression of a second layer
of palissade cells. Since also in later stages they will repeatedly
draw our attention, I shall in what follows call these cells subpa-
lissade cells, instead of using the cumbrous longer definition.

This extension, especially in a radial direction, of the subpalissade
cells, is illustrated by the following two tables.

A Subpaliss. cells of a Height »:16} 16 | 14.5) 18 | 14.5} 16 | 14 | 14.5] 14.5} 22
normal leaf-tip | Breadthy.: 31 | 18 | 16 | 25.5} 27 | 27 | 18 | 25.5) 31 | 81
| | |
B Subpaliss. cells of a Height » : 33 | 26 | 38 | 44 | 47 | 42
yellow leaf-tip Breadthy : 31 | 29 | 18 | 31 | 33 | 33

—- 7

ee

In a leaf-tip which macroscopically is distinguished, besides by
the yellow colour, by a distinct thiekening, the intercellular cavities
of the spongy parenchyma are found to have entirely disappeared,
excepting a small corner here and there. The mutual pressure which
the cells consequently begin to exert on each other, causes them to
assume a more polygonal shape. The cells, bordering on the sub-
palissade cells and often also the rows, turned towards the lower
epiderm, show a tendency to stretch themselves in a direction per-
pendicular to the surface of the leaf. In many spongy parenchyma
cells partition walls have formed.

The part, played by the subpalissade cells in the process of thick-
ening, is generally a very important one. So I found in a leaf-tip
in a place, where it was 332 u thick (the section of a normal tip
is on the average 170 w), cell rows, formed of subpalissade cells,
partitioned by two or three walls and measuring 90, 110, 115 and
127 u in height. — The palissade rows were in these places not
sensibly enlarged.

That the different tissues also in the same leaf-tip do not every-
where play the same part in the process of thickening, appears from
the following figures, from measurements in two different places of
the same leaf-tip;

|

Height of the palissade cells, [36 to45 } Most sells with

2 or 3 partitions

| 27 » non-partitioned.
Height of the subpaliss. cells. |73 to 82 (mostly partitioned) |
|

AE | with numerous
ia partition walls.
Height of the spongy parench. 273 u.

The special thiekened outgrowths, mentioned on page 3, are caused
by the same processes of proliferation which cause the thickening
of the whole leaf-tip, and which in some places go on with particular
activity, while the surrounding region seems to come to rest.

On the upper surface they are formed by locally strong prolife-
ration of the subpalissade cells. Sometimes also the underlying cells,
originating from the spongy parenchyma contribute to them and then
it cannot be ascertained as a rule what part is derived from the
subpalissade cells and what from the original spongy parenchyma.
In most cases the contribution of the palissade parenchyma to the
formation of the special elevations is rather unimportant.

The special thickenings on the lower surface of the leaf are
entirely formed by cells which genetically belong to the spongy
parenchyma but for the rest in exactly the same way as those on
the upper surface. Since the cells from which they are built up,
divide parallelly to the surface of the leaf and the so-formed division-

(2)

cells stretch themselves again, these special thickenings, which at
first appear as small unevennesses, grow out into the knobs, already
mentioned on p. 3.

How has the epiderm been able to follow the inerease of surface,
accompanying these thickening processes?

In a normal leaf-tip we find for the dimensions of the epiderm
cells 9 to 18 u height and 9 to 29 u breadth, while in the epiderm,
covering a special thickening, amidst cells of normal dimensions
others are found which measured :

1 |

13 9
42 | 54.6

36

13
49

9
45.5

1
45.5

9
45.5

Height u: 9

lL | 13
Breadth » : 31

36 | 45.9

Hence some epiderm cells seem really to broaden; whether this
is only an extension or active growth, I dare not decide.

Besides, the epiderm soon gives way and is rent. Like the part
of the epiderm which gives way to the pressure, some cells of the
tissue underneath die off, the cell-walls turning brown. In this way
arise the brown streaks on the surface of the knobs which finally
by extension in tangential direction of this suberizing process becomes
entirely brown. A special suberizing meristem, a phellogen, is not
formed.

The regular structure of these cell-hills is lost as soon as the dif-
ferentiation of a meristem commences. Some cells, assembled in a
small group, then enter a new stage of strong growth, which makes
them conspicuous in the preparations by a more rounded form amidst
the adjoining cubical cells. A number of the surrounding cells are
compressed by the pressure which these primordial cells cause by
their growth, and die.

Soon the primordial cells divide into a number of small filial cells
with extremely thin walls and dense contents, after which the
primordium has become meristem.

For answering the question in what place in a knob the meristem
is formed and what is the descent of the initial cells, we have the
following data. An otherwise 415 to 450 u thick leaf-tip had by
local swelling to about 840 u, formed a knob, which by a small
depression in the middle was, so to speak, divided into two halves,
each of which contained a primordium of a meristem. The surface
of the knob was entirely suberized to a fairly considerable depth.
In one half the primordium lay 220 u below the top of the knob
and its cells in all probability descended from the subpalissade cells,
in the other half the primordium lay 180 u below the surface and
was of the same origin as in the former case.

(175)

While in another case a primordium was noticed which genetically
belonged to the original spongy parenchyma I found ina small knob
which was still covered by an intact epiderm, and did not rise more
than 85 u above its surroundings, and in this case had been formed
by special proliferation of the palissade parenchym, a distinct young
meristem immediately below the epiderm. The epiderm cells themselves
however, did not take part in the formation of the meristem.

In a word, meristem formation may take place as well by cells,
descending from the spongy parenchyma and the subpalissade cells,
as from such as have been formed by hyperplasia of the palissade
parenchyma, the epiderm, however, plays no part. In other words:
the adventitious buds on the leaves of Gnetum Gnemon are endogenic
formations.

In the beginning the young meristem increases in size by its own
active growth as well as by new cells from the immediate vicinity
becoming meristematic.

When the meristem has reached certain dimensions, it partly
becomes loose from the surrounding tissue. This is brought about
by some of the cells, forming the transition between the meristem
and the surrounding tissue, being dissolved and resorbed.

This dissolution process proceeds along the whole upper side of
the meristem, so that the growing point of the adventive bud comes
to be placed in a slit-shaped space.

The greater the depth at which the meristem was originally formed
inside the knob, the thicker is the layer of tissue which ultimately
separates the bud from the outer world and the further the develop-
ment within the enclosure proceeds. This explains how it is possible
that knobs, no larger than 1 millimetre, open, while much larger
ones remain persistently closed.

The appearance of two meristems within the same knob isa very
common occurrence; once I found as many as four meristems in
one knob.

The buds assume a green colour while they are still entirely
enclosed within the knob and hence must have the power, like the
germinating plants of Ephedra and the Coniferae, to form chlorophyl
independent of light.

The sprouts growing out of the adventitious buds always remain
short and tender. The biggest I observed reached a height of about
3,5 centimetres and consisted of a stem with 5 internodes (including
the basal part) of which the upper one reached the greatest length
(almost 2 centimetres), while the leaflets on the last node became

12

Proceedings Royal Acad. Amsterdam. Vol. X.

(176 )

largest (about 3 ems. long). The position of the leaves is alternating,
the innervation of the leaf the typical one for Gnetum Gnemon’).
The leaflets on the first node as a rule remain scale-shaped; in some
cases, however, they develop to leaflets, differentiated into stalk and
blade.

Although in the axils of the leaflets axillary buds are certainly
formed, I never saw the adventitious sprouts ramify themselves,
except in a single case, when, as I surmise, of the basal piece of
an adventitious sprout the terminal bud did not develop for some
reason or other, and instead the buds in the axils of the scale-leaves
sprouted.

On a differentiation of histogens at the vegetative cone I have not
been able to form a definite opinion from my preparations of ad-
ventitious sprouts.

The numerous attempts which I made, in order to induce the
adventious sprouts to produce roots, have all failed. This agrees with
the circumstance that in my preparations I have never been able to
discover anything that resembled root-formation. The sprout-carrying
leaves which had been planted in wet sand did not form roots either.
As far as I know formation of adventitious roots does not occur at
all with Gnetum Gnemon.

A connection between the vascular system of an adventitious
sprout and the nerve system of the mother leaf is established by
procambial bundles, formed by cells of the tissue, situated between
the meristem and a leaf bundle.

As a rule we find as the first indication of this vascular bundle
connection in the immediate vicinity of very young meristems even,
some tracheids and cells, changing into them. The degree of develop-
ment, reached at a certain moment by this vascular bundle connection,
is not directly dependent on the degree of development of the ad-
ventitious bud in question, but seems to me to stand in close relation
to the distance between meristem and leaf bundle and to the dia-
meter of this latter. When a complete connection has been established
we see the vascular bundles of the adventitious sprout within the
knob in which the bud has formed, bend towards each other and
unite with a more or less cylindrical group of locally formed vessels
and tracheids, the ramifications of which are connected with the
vascular bundles of the mother leaf.

When describing the changes, macroscopically observed with a

1) Viz. Nr. 3 of the leaf nervations, distinguished by Karsten for the species of

Gnetum [G. Karsten, Untersuchungen über die Gattung Gnetum. I. (Ann. du Jardin
Bot. de Buitenzorg Volume XI. 1893. p. 195—218)].

(177)

leaf in which adventitious buds are forming, it has already been
briefly stated that the yellow vesicles, initiating the process of bud-
formation, are caused by a scale-insect, Aspidiotus spec.

That suspicion fell on this Aspidiotus had a very simple reason.

Although not nearly all the leaves, showing yellow vesicles,
carried scale-insects, yet the reverse was generally true and it soon
became apparent that the leaves, carrying scale-insects generally also
had some yellow vesicles.

But unexpected difficulties were experienced when it was attempted
by means of microtome preparations to obtain certainty and a clearer
insight in what had been rendered probable by macroscopical obser-
vation. A great difficulty was that the majority of the insects refused
to stick to the bits of leaf from which the microtome preparations were
going to be made. While a great part already loosed their hold during
the treatment preceding the embedding itself, their example was
followed by most others when they were put into the melted paraffin.
It was supposed that perhaps the reason of this was that the scale-
insects, when coming into the fixing solution, withdrew their suction
organ from the tissue of the leaf, possibly on account of a pre-mortal
reactional movement. After this unfavourable result the leaves carrying
the insects were always treated before fixation with an anaesthetic,
namely aether. This precaution, however, did not materially improve
the results.

Among the microtome preparations which I obtained in spite of
these difficulties, there is not a single one in which a scale-insect
may be seen in a sucking position. But always in the places were
an insect was on the leaf, in the tissue the changes were found
which we described as characteristic for the yellow vesicles.

Here also hypertrophy, accompanied by disorganisation of the cholo-
rophyl, of cells, belonging to the mesophyl; some of these cells have
brown walls. Also in the epiderm on which the scale-insect is found,
some cells are found, the walls of which are suberized and which
besides are sometimes slightly swollen.

I was more fortunate with hand-made preparations, some of which
show the suction apparatus of the scale-insect inside the leaf tissue.
From these we see that in the yellow vesicles those cells, the wall
of which has become suberized, have been in direct contact with
the suction apparatus of the scale-insect and that the other cells,
which become hypertrophical, only react to a stimulus, exercised by
the wounded cells. On the character of this stimulant action we
shall speak presently.

That here the enlargement of the cell should take place at the

d Phe

(178 )

expense of its own contents, as is stated for many similar hypertro-
phical processes, is not the impression I received. Although in many
of the very strongly hypertrophical cells a large central vacuole may
be observed, yet I saw nowhere reduction of the protoplasm to a
very thin wall-lining. The nucleus does not show any deviation and
the cell-wall does not become perceptibly thinner.

That the sting of the scale-insect not only causes the formation of
the yellow vesicles but through them also all further changes, in-
cluding the formation of the adventitious buds, has become clear to
me by:

1. the microscopical examination of a very large number of
preparations, relating to these stages ;

2. the continued observation of a number of leaves on the tree,
showing that those leaves on which scale-insects or the yellow
vesicles caused by them, were seen, underwent the above described
changes, while the control leaves remained free from. them. On
Sept. 13, 1906, the top of that plant which forms adventitious buds
most strongly and one of its branches were each surrounded by a
muslin balloon, after they had first been carefully inspected and
cleaned. ~ These balloons were supported by skeletons of galvanised
iron wire and closed below by pulling them on to a pad of cotton
wool, placed round the sprout. At the top of the plant were then
only young leaves, on the branch full-grown ones, all of them free
from scale-insects and vesicles. The balloon, surrounding the top of
the plant had repeatedly to be replaced by a bigger one as the
top grew.

On January 22, 1907, the balloon was removed from the branch *
and the leaves were examined. Of two of these leaves the extreme
part of the top had turned yellow. A microscopical examination of
these leaf-tips showed, however, that here was no initial stage of
bud-formation. Hypertrophical cells, such as we ought to have found
in this ease in the mesophyl, were not present. The yellow colour
was caused by the dying of the tissue, the cell-contents then dis-
colouring.

On May 10 the top of the plant was liberated. A number of full-
grown leaves which at the beginning of the experiment were still
young and young leaves at lateral sprouts which during the isolation
had been formed by sprouting of the axillary buds, were now seen.
All these leaves were perfectly normal, healthy and strong with a
normal green colour; on none of them anything could be detected
of yellow vesicles or spots, of none the top showed any discolo-
ration or thickening. The isolation by means of the muslin balloon

4
|

(179 )

had not hindered these leaves at all in their normal development.
Only scale-insects and other animais had been prevented from settling
on the leaves with the formerly described result.

Similar tumours as the yellow, thickened leaf-tips of Gnetum
Gnemon really are, have also been repeatedly observed with other
plants and described under the name of “yellow specks” (Gelbflec-
kigkeit), oedemata or intumescences. The word “Intumescentia’”” was
introduced into phytopathological nomenclature by SorAvER with the
definition *): “Intumescentia” sind “diejenigen Erscheinungen, die das
gemeinsame Merkmal haben, als kleine knétchenformige oder drüsige
Auftreibungen der Blätter aufzutreten, die meist an diesen Stellen
gelb verfärbt erscheinen und eine aussergewölmliche Zellstreckung
ohne wesentliche Zellvermehrung zeigen’. That the thickened leaf-tips
of Gnetum Gnemon are not indeed “kleine Auftreibungen’’ and do
present “wesentliche Zellvermehrung” need not necessarily prevent
us from counting them among the intumescences, since as well very
large *) or mutually coalescent *) as typically hyperplastic *) intumes-
cences have been described for other plants.

We cannot now deal with the very divergent views of different
investigators about the cause of the formation of intumescences; we
will only mention that in most cases it has been stated that a high
temperature and great humidity of the air are essential factors.

Experiments enabled me to form an idea about the character of
the stimulus exerted by the scale-insects on the tissue of the leaf of
Gnetum Gnemon, on which the formation of the intumescences is
the reaction. After I had tried artificially to produce intumescences
in leaves by mechanically wounding them in all sorts of ways and
treating them with poisons, without obtaining the desired result, I
arrived at the conclusion that either my method of wounding, com-
pared with that of the scale-insects, was too coarse or that the
insect injected some stimulating substance into the leaf. In order to
settle these points the following experiments were carried out: 1). In

1) P. Soraver, Die symptomatische Bedeutung der Intumescenzen (Bot. Zeitg.
48 Jahrg. 1890. p. 241).

2) H. v. Scurenx, Íntumescences formed as a result of chemical stimulation.
(Missouri botan. garden. 16th ann. report. 1905. p. 125).

5) Miss G. E. Doveras. The formation of intumescences in potatoplants. (Bot.
Gazette Vol XLII. 1907. p. 233.)

4) KE. Kiisrer, Uber experimentell erzeugte Intumescenzen. (Ber. deutsch. bot.
Ges. Bd. XXI. 1903. pag. 452). P. Soraver, Ueber Gelbfleckigkeit. (Forsch. a. d.
Geb. d. Agrik. Phys. h.v. Dr. E. Wottny. Bd. IX. 1886. pag. 387). and Intumescenz
bei Solanum floribundum. (Zeitschr. f. Pllanzenkrankh. Bd. VII. 1897. p. 122),

( 180 )

the leaf-tips extremely small wounds were made by means of the
sterilised, very fine point of an injection syringe. 2). The same was
done after the point had first been stuek into yellow vesicles, caused
by the scale-insects. 3). A number of yellow and thickened leaf-tips
were ground in a mortar and a very small portion of the so obtained
pulp, mixed with some diluted glycerin, injected in several places
in leaf-tips. 4). The same operation as in 3 was applied after the
pulp had tirst been heated to 100° C.

The result was exactly the same in al/ cases.

After some ten days small, brown specks were visible in the
wounded places, which afterwards could still increase somewhat in
size. A month after the wounding the brown specks had become
surrounded by a very thin, more or less transparent, yellow margin.
The brown specks were formed by tbe cells which had died in con-
sequence of the wounding, and the walls of which had turned brown.
In the yellow margin a complex was found of relatively small cells,
leaving no intercellular cavities. These cells had thick walls and
their protoplast still contained remnants of the chlorophyl grains.
The complex was formed by hyperplasia of the whole mesophyl.
On the border between this complex and the normal tissue some
cells of the spongy parenchyma had become greatly enlarged, their
chloroplasts having become disorganised. After another month it was
noticed that the leaf-tips in the neighbourhood of the wounded spots
assumed a somewhat yellow colour, which gradually became more
and more distinct. Microscopically it could be stated that where
externally this yellow discoloration was visible, the tissue round the
wounded spots had undergone precisely the same changes as take
place round the yellow vesicles, caused by the scale-insects, namely
a general hypertrophy of the cells of the spongy parenchyma, while
here and there even a partition wall had already been formed in
the enlarged cells.

As was stated above, this result was obtained in all eases, also
in those in which small wounds had been made without anything
else. From which we may conclude that the leaf of Gnetum Gnemon
may be stimulated to the formation of intumescences and hence of
adventitious buds by wounding, provided this is very light and that
consequently the process must be regarded as a reaction on a
wound stimulus.

In a disease of carnations which also consists in the formation of
a sort of intumescences') and for which it has been shown by

1) H. v. Scurenk |. c. p. 39.

I EE Ee ne

BED)

Woops *) that it is caused by the sting of aphides, among others,
Woops thinks the growth of the yellow, thickened spots must be
ascribed to the diffusion of an irritant, injected by the insect ®).

That a similar hypothesis is superfluous for the “stigmonose”’ of
Gnetum Gnemon, appears clearly enough from our experiments. The
“specific point about the wound, made by the suction organ of the
scale-insect is only that it is so trifling. Only a few cells, namely
those which are distinguished in the yellow vesieles by brown walls,
have undergone the direct consequences of it, while the whole
subsequent formation of the intumescences takes place as a reaction
on the stimulating action, proceeding from these few wounded cells.

Kusrer*) calls all cataplasms after vulneration, as far as they have
a parenchymatical character, callus. According to this terminology
also the tissue of which the thickened leaf-tips of Gnetum Gnemon
consist, is a “callus” and the buds, formed in them, are callus-buds *).

Why the two plants from the cooler hothouse did not form callus
or buds on their leaves, is now also clear. The Aspidiotus, playing
such an important part in this formation of callus, is also found in
the cooler hothouse; but for callus-formation the chief condition is
humidity. This condition was only to some extent fulfilled by the
cooler, but completely by the hotter house, while also the higher
temperature in this latter could not but favour the formation of
callus with these tropical plants.

Why only the apical part of a leaf is capable of forming callus
and buds, may be explained in the following manner. The small
wound causes an afflux of nutrient matter in an apical direction.
If now an accumulation of this matter, which is necessary for the
hyperplastic formation of callus, shall be possible, the afflux must
not be able to pass by, i.e. it must be stopped apically of the wound.
And this condition is normally only fulfilled in the tip of the leaf,
in another part of the blade only when the organic relation with
the tip has been disturbed.

Botanical laboratory at Utrecht.

1) A. F. Woops, Stigmonose: a disease of carnations and other pinks. (Bull.
no. 19. U. S. Dept. Agr. Div. Veg. Phys. and Path. 1900).

2) |. en ps 24

5) E. Küsrer, Pathologische Pflanzenanatomie. Jena. 1903, p. 154.

4) See also: E. Küster, Histologische und experimentelle Untersuchungen über
Intumescenzen. (Flora oder allgem. bot. Zeitg. 96 Bd. 1906, p. 527—537).

( 1835)

Crystallography. — “The system of crystallization of the diamond”
by Mr. A. L. W. E. van per Vern, candidate mining engineer.

(Comin. by Mr. MoLencraarr).

(Communicated in the meeting of June 29, 1907).

There still exists some doubt about the system of crystallization
of the diamond. Although the tetrahedral hemihedrism of the diamond
is pretty generally accepted, still the opinion that it belongs to the
regular system, also finds support.

The existing uncertainty is caused by the lack of physical research
with regard to this question. Such a research into the existence or
non-existence of polarity of the trigonal axes has now been made.
With that object in view the trigonal axes of the diamond were
tested for pyro-electricity according to P. P. Kocn’s method’).
Tourmaline, boracite and quartz, which evinced strongly pronounced
pyro-electrical characteristics, were used as testminerals. The result
arrived at is absolutely negative. The diamond is not pyro-electric,
and the trigonal axes do not possess polarity.

Besides, researches were made into the crystalline form of the
diamond out of a collection of 367 uncut diamonds collected by
Mr. Moueneraarr. Practically all types of crystallization were repre-
sented here, to explain which tetrahedral hemidedrism for the diamond
had been accepted in numerous writings of GROTH, SADEBECK, MARTIN
and others. The result of this investigation, which is not yet at an
end, is that a rational explanation of all irregular and apparently
tetrahedral-hemihedral crystalline forms of the diamond can be found
in the peculiar octahedral lamellar structure of the diamond.

On this ground it may be accepted that the diamond crystallizes
in the holohedral division of the regular system.

1) P. P. Koen, Ueber eine neue Methode zur Untersuchung auf Pyroëlektricität.
Inaug. Dissert. Miinchen, Mainz 1902.

(183 )

Physics. — “Contribution to the theory of binary mixtures. VI.
The plaitpoint line.” By Prof. J. D..van per WaAats.

Continued, See p. 123.

By the plaitpoint line we understand the continuous series of points,
in which the mixture is in the plaitpoint state. If we think the
points of the surface of saturation determined by the coordinates
T, p and z, then the plaitpoint line is a curve lying on this surface,
and its projections on the planes of coordinates are expressed by:
p=Sfi(T), p=, (2) and «=/,(7). If the surface of saturation
is given by the coordinates 7, v and wz, its projections have the
form: »=—/,(T), v=f,(@) and «=/,(7). The two surfaces of
saturation mentioned may be derived from each other by the aid of
the relation p= g(a, v, T). If we have the first mentioned surface,
the substitution of p leads to the second. However, we might also
have eliminated 7, and obtained a surface of saturation of the form
F (p,v,2)=0, also one of the form F, (p,v, T)=0. A point of
saturation being determined and known in all respects if the 4
quantities 7, x, v, and p are known and the equation of state giving
a relation between these + quantities, we may imagine as many
surfaces of saturation as the number of combinations of 4 quantities
three and three. The number of projections of the plaitpoint line
is then the number of combinations two and two. For the direction
dT dp dv dp dp dv :
ae har an” ap? mnd present themselves for
consideration, which of course, are not independent of each other.

The best known shape of the plaitpoint line is that for which the
initial point lies in the critical point of the first component, and the
final point in the eritical point of the second component.

In this case there is a point in which the plaitpoint line begins,
and another in which it terminates; but such initial and final points
lie necessarily in such places as are to be considered as natural
boundary points. Thus initial and final points might also occur for
boundary volumes (v6) — but a plaitpoint line can never have
an initial or final point for arbitrarily chosen value of v and z.
Thus in the case that there is minimum or maximum 7% the mentioned
well-known shape of the plaitpoint line will, it is true, make its
appearance only in a certain point with gradual increase or decrease
of the temperature for certain definite value of 7’ — but such a
point is then necessarily a double plaitpoint, and the plaitpoint line
itself retains its character of continuous series of points; the double

of the projections

( 184 )

plaitpoint mentioned is then an homogeneous double plaitpoint. If
then in the v, v-projection the plaitpoint line is drawn, it proceeds
again continuously from the left to the right side —- and this con-
tinues to be the case also when the plaitpoint line mentioned has
more intricate properties, e.g. when there are two heterogeneous
double plaitpoints, as discussed in “Contribution ete.” and also treated
in These Proc. March 25, 1905, p. 621 and These Proc. June 24,
1905, p. 184. However, besides this plaitpoint line, another is possible.
The latter does not cross from the left side to the opposite side. So
only the possibility is left either that it is a closed curve in the
v, x-projection, or that it begins and terminates on the borders v = 6.

We shall proceed to discuss some properties of the special points
of this line, particularly of the double points of this line. KorrEwne
has demonstrated that these double points are of two kinds. Either
it is a double point in which two homogeneous plaitpoints originate

or coincide — or it is a double point in which this is the cas2 for
two heterogeneous plaitpoints. Though physically such plaitpoints
bear such different characters — mathematically they satisfy the

same criteria, and on the plaitpoint line such an heterogeneous double
point is the transition point for a series of plaitpoints which might
be realized, and for a series of unrealisable plaitpoints.

Minimum or maximum temperature for the plaitpoint line.

If we suppose a double plaitpoint to originate or to disappear on
the w-surface at a certain value of 7, two plaitpoints are found at
somewhat higher or lower value of 7. This holds both for the case
that the double point is an homogeneous and an heterogeneous double

dT
point, as we shall briefly call them. For the plaitpoint line ae and
Hij

dT j ; : WOI
— = 0 in this case. But for an homogenous double point zE also
Ww

dv
d:
=0. This property follows from the shape of = which has been

derived in Verslag Kon. Ak. v. Wet. Deel IV p. 20 and p. 82 because
dv

te 0 in an homogeneous double point (Contribution ete. These Proc.
dx”,

March 30, 1907, p. 745). For an heterogeneous double point ag is
Pp

d
not equal to 0, as also appears from the value given for a as for such

gies ag i eee
== u em ==
dx*, z dz*y de’,

a double point . That in an heterogeneous

( 185 )
double point — is not equal to 0, is also immediately seen when we

E dT
consider that for such a point also dp = 0, and q Appears there-

ie
fore in an indefinite form, the value of which we shall presently

; dv dv , ; Gir
determine. Hence — =| — | for such a double point, which is not
dx z Jp
the case for an homogeneous double point.

Of the 6 differential quotients which come in for discussion, three
are equal to 0 for an homogeneous double point, and three are left

; 6 \ men edo. av dp
the value of which is still to be determined, viz. —,— and —.
de dp dx
If we write:
dT
dv dx
Tan er
dv
dT
dv dp
dp aT
dv
and
dil
dp da
dx aT’
5

in all these three expressions both numerator and denominator is
equal to 0. If in the first we differentiate numerator and denomi-
nator with respect to a2, in the second with respect to v, and in the
third with respect to p, we find:

dT
dv dx?
de PT dv
dv? de
dT dp
dv dp? dv
BAAT
dv?

and

( 186 )

dT dz

dp da? dp

En wel

dp’

or

One atk di
dor? dx? dv~\? dp? dp \’ dx?
Gy Sor 5 marit e Tm
dv? dv? dp?

We may verify these properties by writing for the immediate
neighbourhood of the minimum or maximum plaitpoint temperature:
T= T, ta (w Fr x,)? = iN, + Bv a v,)? = T, ty (p pd Ps
in which the sign + holds for minimum value of 7, and reversely
the sign — for maximum value.

From this follows:

ESC A AGD

or
+ («—z,) Va = + (v—v,) AES (pp) VY,
and
d ;
NE Wy enn eae eo
da B dv Y dp a
a dv _ dp_ de 1 totale: al Meee DE
S < — == V ave t AKC ¢ s1g i 5
s = x me x ap +1, we have to take all the signs positive, or

one positive and two negative. Thus in the case that there is mini-
mum or maximum plaitpoint temperature, and we choose the direction

db. i eee dp dp
of z such that — is positive, — > O and — <0, and so also —
dx da dx v

dp .
negative. It is, however, not always the case that zi negative.
v

. . . D 5 C
Thus for a plaitpoint line with maximum value of p, Ge )

d 8
also Oland ==) So in such a case reversal of the sign of
Hi (0)

dp
— must take place.
dv

If we examine the criteria for an heterogeneous double point, we

Al 7

a at.
have in the first place =0@0 and —= 0. Then — is nottequa
da dv dp

to 0. But in its stead there are two other differential quotients which

( 187 )

re eque to 0. i rom 5 : a | A t x d r
d z f ] OW Dy if we tal ein nsideré

f dp ee dz dp
tion that — has a finite value, and — == ow, that — must be
ID dT da

dp ;
= 0, and also ate That p has maximum or minimum value in
Vv

the case of an heterogeneous double point has already been repre-
sented by us in a drawing. (These Proc. March 25, 1905, p. 621,
and June 24, 1905, p. 184). So of the 6 differential quotients for
the projections of the plaitpointline 4 are zero. Two are left whose

; . dp dv
value is to be determined, viz. ae and a
dp
If we write: cn dey we find by differentiation of numerator
Chia Th :
da
and denominator :
dp
dp dx?
at er
dex?
dT
: : dv de ind
If we write: de aT’ we find:
dv
at
dv\? dx?
(3) TT
do?

What follows may serve as a verification. Let us again write as
holding in the immediate neighbourhood of the double point :
T =T, + a(e—z,)? = T, + B(v—»,)?
and
Pi Pa + y wa) == 1% + d (v—v,)’.
For minimum value of 7’ and p the positive sign must be chosen,
and reversely. So we have the following relations :
a (mz) = B (v—,)’,

and

( 188 )

y (wa)? =d (v—v,)*
from which

erp
ato aie
Further
sire i Se sore ay
a U6

In this last equation the sign -++ must be chosen, if, as is the
case, 7’ and p have at the same time either maximum or minimum
value. We find then:

dn
GIDS

dv DA a Y
EE es es =
de B Ve Jd

dv dv
That this value of z=(¢ es follows from the derivation.
de JT

and

_ 3 ry: NG
So we find a definite value for = and as no lower value of 7

exists for minimum value of 7, and no higher value for maximum
value, the p,7-projection of the plaitpoint curve must possess ‘cusps’.

d,
That this value of is positive, and so p and 7’ are at the same

time maximum or minimum, follows inter alia from the equation :
d d
Te) eet de +
dv ) rT de vr
dp
dx )y7 ‘ 5
, this equation reduces to:
dp
ae

dp _ (dp
OTN:

Other special points of the plaitpomt curve.

dv dv

For, as = = |

dx da pT

d
It appears from the form for = (Versl. Kon. Ak. Deel IV p. 20)

d,
that also the case that = 0 is possible, and for some mixtures a
q

maximum value of p in the p,7-projection has been experimentally

( 189 )

dp ds dp da sh dp dv

ET an ne derive that in this case also
ar a vd

shown. As

d dp É :
= O and 0, save in exceptional cases. Then p is the highest,
i v

or the lowest pressure that can occur on the plaitpoint curve. Of
the 6 differential quotients 3 are again equal to zero, and 3 others

de dv ik

av
are again to be determined, viz: —, — and —. We find then from:
Ser ad ar’ ar de

From

we find:

And from:

we find:

dv\? de?
(<.) ~ dp
dv*
which may be again verified from the equations:
De EUN eN mt A ie ME
For plaitpoint lines which do not run from x=0 to e= 1, and
which therefore either form a closed figure, or run from a point of

( 190 )

the line v= 6 to another point of this line, the value of « may be

: eh, oe da da da :
maximum or minimum. Then —, — and rs =, and the three re-

dT dv dp
maining differential quotients must be determined — and lastly also

dv dv dv
v might be maximum or minimum; then ~~, — and — would be
dT dp dz
dT dp
equal to zero, and —,

d
— and LD would have to be determined.
de da dT

Three phase pressure and jinal point of the three phase pressure
on the plaitpeint line.

If at a certain temperature three phase pressure exists, there must
be a hidden plaitpoint on the y-surface, as appears from the foregoing
remarks. If the spinodal curve is closed on the side of the small volumes
there is moreover a realisable plaitpoint, and there can even be another
realisable plaitpoint if the temperature is above the 7% of one of the
components. Let us call 2, and v,, 2, and v,, 2, and v, the com-
positions and volumes of the three phases, assuming the first two to
be liquid phases and the third to be a gas-phase, and let us put
z, >> x,. Now three cases may occur, viz.: 7, > 2, > 2,; 2, >#, > 4,
and 2, >a, >2,. The first case occurs when the gas phase contains
more of the second component than each of the liquid phases, and

dp : 5E
so when l= is always positive; the second case when the gas
AL /T

; d
phase contains less of the second component, and so when (2)
U Jor

5 ; F 4 : dp
is negative, and the third case requires that the line G ) = Oruns
di) yT

between the two liquid phases. Of the first case an example may
be found in the mixture water in SO,, mixtures of ethane and some
alcohols (above methylalecohol) constitute an example of the second
case, and of the third case the mixture water and phenol is an example.

As we have an equilibrium which is independent of the size of
the volume, when for a mixture of 2 substances there exists equili-
brium of 3 phases, the formula of CrAPEYRON may serve for the

d
computation of the value of a and we may put:

dp W

aT u

if W represents the heat which is released with decrease of volume
when part of the middle phase is converted into the state of the

(191 )

two other phases, and w the degree of this decrease of volume. We
arrive at the same result if we follow the course (Verslag Kon.
Akad. v. Wetensch. Deel V, p. 482) indicated there, viz. :

IL Lik
1
dp | lam | (#,—2,) (lj) — (eo 0) (MN)
Gre kl 0 Oy ~~ (@,—2#,) (v,—v,) — (#,—2;,) (vv)
WENDE
U 0

We find the same equation when we have three phase equilibrium
for a binary system of solid, liquid, and gaseous. And the course
of the line p= f (7) is then known. It is a line, consisting of two
branches lying above each other, which smoothly pass into each
other at a certain maximum temperature, and the upper branch of
which possesses maximum pressure. In this case, however, the course
is simpler. For the equilibrium of solid, liquid, and gaseous two
branches occur; on one branch the liquid is richer in one of the
components than the solid body, and on the other branch the reverse.
Where these branches meet, the value of « has the same amount
for the solid body and for the liquid, and in that point the line
p=f(T) has an element in common with the melting-point line.

d
This is seen from the value of a Heeren t= 2 18) put in it, in

d ”7,.—
which case Sek ay And it has, therefore, often been stated
dT v,—2,

as a fixed rule, that when two phases have the same concentration,
the variation of equilibrium with the temperature depends only on
these two phases, and is independent of the third. Also for equi-
librium of 2 liquid phases and one gas phase, however, equality of
concentration may occur between two phases. Thus one of the liquid
phases may get the same concentration as the gas phase, or the two
liquid phases may get the same value of z. Then the above mentioned
rule does not hold. When a solid body has the same concentration
as a liquid, and e.g. «,=2,, then 4, is not equal to 4,, and wv, not
equal to v,. Then there are, indeed, two phases of the same con-
centration, but not two identical phases. But when a liquid phase
has the same concentration as a gas phase this expression means
that in the three phase triangle one of the sides has been reduced
to zero, and these two phases have become identical. Then we find
13

Proceedings Royal Acad. Amsterdam. Vol. X.

( 192 )

after division of numerator and denominator by w, —a,:

dn,
dp se Mine ty (z,—2,) de, UT

an dv,
v,—v, — («,—2,) Age
Ly) pT

‚dp a Ws
dE 4

or

18

d
It appears from the form for = that this value is equal to

ae if a section is made through the surface of saturation for
Cie
In other words: The three phase triangle in its extreme position
touches the section mentioned and to this we might also at
once have concluded. It will also be immediately seen, that the
coinciding of the points 7, and 2, of the three phase triangle takes
place in a plaitpoint, and that therefore the final point of the line
p= (T) lies on the plaitpoint line. Then we have a plaitpoint in
the point where zx, and x, coincide, and the p, 7-projection of the
plaitpoiut line being the envelope of the p, 7-projection of the sections
of the surface of saturation for constant values of a, the plaitpoint
line and the p, 7-projection of the sections touch, and so also the
final point of the p, Z-projection of the three phase pressure, as in
that final point the last element of this pressure coincides with the
section mentioned. This contact has not yet been taken into con-
sideration in former diagrams. If there are two final points of the
three phase pressure, then there are two separate portions of the
realisable portion of the plaitpoint line, which are joined by the
three phase pressure, the meeting-points being again cusps, just as
is the case with the hidden portion of the plaitpoint line. Now,
however, rises the following question. We know from the shape of
the section of the surface of saturation at given value of a, that in
the simplest case it consists of two branches, and that on the upper
dp dp
branch the value of ap PA also be negative. Can now also i
be negative for the three phase pressure? As far as I know this
has never been observed; but the observations on the rise of the
three phase pressure with the temperature, and the other circum-

stances, viz. the values of a and v, have been only little examined

:
‘
4

( 193 )

d i
as yet. If it should be possible that = becomes negative, and for

the present I do not see any reason to consider this impossible, this
can only take place in the case of a plaitpoint line descending with the
temperature. Accordingly the final point of the three phase pressure,
so the plaitpoint, lies on that part of the section of the surface of
saturation which lies between minimum pressure and critical point
of contact, and it is known, that then also the plaitpoint line must
descend in its p, 7-projection, because it is the envelope of the
sections of the surface of saturation. If a is negative at the final
point, this value must have passed through O; this will then require
that no heat is released with conversion of the middle phase into
the two others, and so that if heat is released with conversion into
one of the two exireme phases, the conversion into the other extreme
phase is attended by heat-absorption *). And without further investi-
gation this cannot be pronounced as impossible.

Finally we point out that = cannot become infinite. For this it
would be required that the denominator is equal to zero without
this being the case with the numerator. Then the area of the three
phase triangle must be equal to zero or the 3 points must lie on a
straight line. This is the case when two points coincide, but then
the numerator is also equal to zero. Now a p-line — for the three
points always lie on the same isobar — can indeed be intersected
by a straight line in 3 points, but in this case this would have to
occur in the same three points with a q-line; this observation will
most likely suffice to put down this case as one that does not occur.

So we have in the p, T-projection of the threephase. pressure a
curve which, at least as a rule, ascends with the temperature; under
every point of this line is a point of the plaitpoint line (hidden
point) and above every point is a second point of this line (realisable
point). This second point is wanting if the plait should not be
closed at the bounding volume.

Shapes of plaitpoint lines (p, T-projection).
According to the above considerations I shall describe a possible
shape of plaitpoint line for the case of two components, for which

1) The diagrams p. 126 Cont. II, in which the value of vj, and wa; for coexisting
phases has been represented, must be supplemented, when also incomplete
miscibility is assumed.

13*

ner En en

( 194 )

the ratio ie is a high value, and for which the temperature, at
C1

A sre: ;
which [Ea O has contracted to a point, is much higher than 7%,.
As an example take the mixture helium and hydrogen investigated
by KAMERLINGH Onnes and Keresom partly experimentally and further
theoretically, or the mixture helium and water. As, however, there
are two shapes possible, I shall describe them both, not stating as
yet, which of these shapes is the correct one in these cases.

As 6 for hydrogen will be higher than 5 for helium, helium is
the first component. In the first place we observe that there must be
a complex plait for 7’< 7;,, which extends over the whole width.

2

2 d
ENO has closed on the helium side for 7 > Ti; but —-=0
dv* AE

d
is a closed curve, which extends outside er =0 on the helium
U

: de : dp dp
side, and so there is intersection of —- == 0 and — == 0. The
dv? da?
: : dp :
spinodal curve, which remains near Ae on the side of H,,
v

moves further away from this line as we approach the helium side,

‚dw 4
and remains also outside 7 = 0. I shall continue to assume that the
a

spinodal line remains closed on the side of the small volumes. The
changes which must be made if this should not be the case, will
be easily applied in the result at which we arrive. Then there are
three plaitpoints for this 7’> Ti. With very small difference of
T and Ty, there is first the ordinary plaitpoint on the helium side;
and further there are two heterogeneous plaitpoints, viz. a realisable
one at the very small volumes, and a hidden one (see inter alia
figs. 12 and 13 of the preceding communications).

If now the first mentioned plaitpoint should coincide with the hidden
one, as is assumed in the discussion of these figures, only one single
plaitpoint would remain; but another, more intricate case is possible.

aw dy : 5 ,
If ap 0 and a= 0 are quite detached, as will happen with
increasing temperature, the spinodal line may viz. either continue to
run round the two curves, as I have repeatedly drawn, or it may
split up between the two curves. For splitting it will be required
that they are so far apart that a point is found between them, in

(195 )

dw ay ve :
Fa and Pro positive, but the product is equal to
i

which not only

ad? d,
( ZE which may the sooner take place when the line 7) =i0
dedv du) »T

is in the neighbourhood. In this case there originate two new realisable
plaitpoints. Then there are 5 plaitpoints at somewhat higher tempe-
rature, because 2 new ones have been added to the three above
mentioned ones. And now, as I demonstrated when I discussed such
a splitting up, at somewhat higher temperature the hidden plaitpoint
will coincide with one of the newly formed realisable ones, and
vanish as a couple of heterogeneous plaitpoints. So there are 3 realisable
plaitpoints left viz. one that is the plaitpoint of the half of the plait
(transverse plait) on the hydrogen side. And the two others, which
are the upper and lower plaitpoint of the half of the plait which
has got detached (longitudinal plait). In other words: one half is a

d?
plait that surrounds the curve = 0, and the other half runs round
: av

iw
du?

d?
= 0. In this half = O performs in many respects the function
Hij

] h
Cc
WL

= 0 performs as a rule. The splitting up of the spinodal

line, so that a closed longitudinal plait detached itself, can, therefore,
take place in such a way that this longitudinal plait is found at

daw
temperatures at which Fi
v

= 0 still exists for the same value of a,

but is then restricted to very small volumes (mixtures of water and
2

: d
phenol); or it may take place in such a way that et
v

= 0 no longer

exists for the same value of z, but then the volumes need not be so
very small. We might say: the detaching might take place in such
a way that the two parts of the plait exist above or by the side of

each other.
3

d
Moreover the case may occur that ee has quite disappeared, and
v
d?
dx?
only take place for temperatures above 7;, and Zr, and if what
I have called 75, is larger than 7;, and T;,.
In fig. 27 I have drawn the p,7-projection of the plaitpoint line,
which in the v,a-plane is again a line which proceeds continuously
from the left to the right side. At 7; for H, there are three points

alone exists. Then only a longitudinal plait is found. This can

( 196 )

Hy BUF

0 T
Fig. 27.
of this line; the downmost is the hidden plaitpoint lying between
E and F. The place of the points # and F has been arbitrarily
chosen, so that it may also be possible that must lie more to the
right than 7%. At the value of 7p, the splitting temperature, 2 new
points appear. At Tr a couple of heterogeneous plaitpoints unite.
At Tc the detached longitudinal plait would disappear. Between
Tc and 7’p there are two plaitpoints for the detached plait. The
three phase pressure runs between G' and Z, the extremity Z having
been chosen such that the point D (splitting point) lies below the
three phase triangle, and can, therefore, not be observed. Hence only
the following 3 parts can be realized by means of the experiment:
1. H,G, 2. H,. ACL, 3. GL. And now, if the hypothesis that the
plait is closed on the side of the limiting volumes, should be incorrect,
we have only to open the upper part at A and C, and to make
the open branches run asymptotically towards infinitely high. So
this plaitpoint line is essentially the same as that with the double
point which I have drawn. Only one of the branches, i.e. the left
branch, has in addition got a maximum and a minimum pressure,
and a maximum and a minimum temperature. If we drew the T,a-
projection, there would be 2 maxima and two minima — also in
the p,v-projection. But the v,v-projection remains simple. If the plait
is closed at the limiting volumes, there is a minimum volume, in

1) In this figure the shape of the plaitpoint line has been drawn when really
é P aw aw 2 : me
the spinodal line could run between Agee and ye Further investigation
will have to decide whether or no this complication can occur. If it occurs, the
righthand side of the plait (transverse plait) will be much narrower, then when
this complication is not met with. In the latter case the righthand part of the
plait is a complex plait.

(KH)

the opposite case two points for which v= b, come in its stead.
For neither with an homogeneous double point, nor for an heteroge-

d dv
neous double point, Be = 0. And in the point in which i ==
dx pl dix pl

dx d
or (=) = 0, (see p. 185) a has not a value which presents any

dv
particularity.

The second form will differ from the one described here in so far
that the temperature at which the detaching of the longitudinal plait
takes place, is assumed to be equal to 7), (critical temperature of
the second component).

aw
This may take place if the temperature at which = 0 disappears,
at

is not only higher than 7%, but also higher than 7%, (a case to
which I alluded already before in these Contributions).

Tre Tyzo Trax

Fig, 28.
Then the p,7-projection is given by fig. 28. The highest tempera-

ne th :
ture which then occurs, is that at which —=0 disappears.
&

That for the mixture helium and hydrogen the second shape of
the plaitpoint line can occur, and that therefore 7, can be > Tr,
follows immediately from the formula for the value of 7, (These
Proc. May 24, 1907) viz.:

a, + a,—2a,
b é cay
For the case, namely, that a, and a,, may be neglected, and

1
b, <b, and dek we find really 7, > 7. Thus we find for

MRT, =2

b 8
x =0,4, which belongs to TEA = 0,3704, MRT, > aE For still

higher value of z, this value of ily would be found still higher, but

>

( 198 )

if a, + a, — 2a,, becomes appreciably smaller than a,, this may, of
course, be different. In this case the plait remains a complex plait

2

d
as far as T= Tj. At this value of 7’ has = = 0 disappeared,
Uv

2 ) f
and —- — 0 still exists. So above 7%, the complex plait is to be
ak

considered as a longitudinal plait.

If in the case described above we have a plaitpoint line that pro-
ceeds continuously in the v,v-plane, starting on the lefthand side in
the critical point of the first component, and terminating in the critical
point of the second component, though a maximum value of 2, and
then also a minimum value may be possible, still another case is
possible, and most likely this case is met with in the mixture water
and phenol. Of course the first mentioned line, which starts and
terminates in the critical point of the components, must continue to
exist, if we continue to assume that the plait remains closed on the
side of the limiting volumes. Else it splits up into 2 parts, which IJ,
however, consider as two parts of one and the same branch of the
plaitpoint curve. If another branch is possible, it must be a separate
closed curve — which, however, if the plait is supposed open on
the side of the limiting volumes, may be considered as starting in
a point of the line v4, and terminating in another point of this
line. We meet with this case when the longitudinal plait detaches
itself at a temperature which is lower than 7, and 7;,. As has
been described above, the longitudinal plait will have quite retreated
to volumes smaller than those of the liquid branch of the binodal line
of the transverse plait at a certain value of 7 higher than the tem-
perature of detaching. Then the three phase pressure no longer exists,
and the first mentioned branch of the plaitpoint line, which joins the
critical points of the components, has its simplest shape. In fig. 29
6

( 199 )

the p,7-projection has been drawn. At T= T4, which is lower
than 7, and 7, the detaching takes place, and there is an
homogeneous double point. At 7’= 7; there is an heterogeneous
double point, and at 74 again an homogeneous double point. If we
suppose the longitudinal plait to be open towards v= 6, pp must
be thought infinitely large, and the upper part of this second branch
disappears. Without doubt the three phase pressure line, which
terminates in LH, will have its other extremity, i.e. its initial point,
yr 7 O-

We should have a very simple and remarkable case of a closed
curve for the second branch of the plaitpoint line if the lowest
temperature at which an heterogeneous double point is formed, lies
little below the temperature at which this double point vanished
again — and this temperature lies below 7, and 7;,. Then also
the temperature at which again an heterogeneous double point exists,

B

mea
0 5 zt)

Ti, Tk,
Fig. 30.

will lie only little higher than the first. Fig. 80 gives then again
the p,7-projection for such a case. There can then be a phree phase
pressure indicated by a dotted line. Then the liquid begins to split
up into two phases at a temperature lying much below 7;, and 77, ,
becoming homogeneous again at somewhat higher temperature — at
least if the value of w has been chosen between that belonging to
the extremities of the three phase pressure. In the v,v-projection we
have then a small closed figure with maximum and minimum volume.

So many different shapes of plaitpoint lines, however, may be
deemed possible, that they would require a special study. If they
are found by the experiment, I expect that the rules given in these
contributions, will prove sufficient to render them intelligible.

However, I intend shortly to indicate the circumstances in which
the forms discussed are met with, more fully by means of some
mathematical developments.

( 200 )

Physics. — “On the measurement of very low temperatures. XV.
Calibration of some platinum-resistance thermometers.” By Prof.
H. KAMERLINGH Onnes and J. Cray. Communication N°. 99%
from the Physical Laboratory at Leiden.

(Communicated in the meeting of June 29, 1907).

§ 1. Introduction. The invgstigation on the variation of the
resistance of metals (pure ones and those with known admixtures)
set on foot many years ago (see Comm. N°. 77 $ 1 These Proc.
Febr. 1902) at Leiden, comprises besides the determination of the
galvanic resistance of conductors made of the different metals, also
the determination of the expansion for each of these metals. We
have only little advanced as yet with the latter part of this investi-
gation, the expansion has only been investigated for platinum, which
was chosen as standard metal, and then only down to — 182°. *)
We hope shortly to publish a Communication on the expansion
down to —252°C. For the present, however, the knowledge of
this expansion is not yet of much importance for the investigation
of the variation of the specific resistance with the temperature.
When in this investigation we descend to very low temperatures,
the correction for the expansion becomes so small compared with
the disturbance in consequence of other influences which are still
further to be investigated, that we may disregard it for the moment.’)

The investigation consists then in the calibration of different resi-
stance thermometers. The wires treated in this Communication being
chiefly of importance to us as resistance thermometers, we have
inserted their calibration in this series.

1) In Comm. N°. 85 (These Proc. April 1905) it was observed for the first time
that in order to represent the expansion of glass from — 180° to 0° a for-
mula of the second degree with other constants was required than for the range
from 0°? to + 100°. We found this confirmed in Comm. N°. 95% (These Proc.
Sept. ’06), and also applicable to platinum, for which a formula of the third
degree, as we gave one for glass, proved necessary between — 180° and + 100°.
Afterwards (Dec. ’07) Sereen, who was at first (Zeitschr. f. Instr.k. April ’06) of
opinion that a formula of the second degree could be found for platinum between
— 190° and + 100°, come to the same opinion as we, and gave the three constants for
platinum. Our formula of the second degree for platinum between 0° and —180° quoted
by Screen was used by us to prove, that for platinum between —180° and +100?
a formula of the second degree is not sufficient, but that a formula of the third
degree is required. In order to show this with given values at + 100°, 0° and
— 190° observations at a temperature about halfway between 0° and — 1909, as
our — 87°, are more suitable than observations at a temperature between 0°? and
-+ 100°, as those by Scuert at + 56°.

2) Here it is left entirely undecided whether the variation of the resistance with
the temperature is not in close connection with the expansion,

( 201 )

§ 2. Particulars on the comparison and on the investigated wires. In
these calibrations we have taken the platinum wire which was
compared with the hydrogen thermometer in Comm. N° 95° (These
Proc. Sept. ’06) and which we shall call Pt;, as standard. We
determined the variation of the resistance of the other wires by
bringing them together with P¢, at the desired temperature, and by
then comparing their resistance with that of Pt;. The two platinum
wires Ptj;; and Pty were brought in the same cryostat (see § 4
Comm. 95°) together with Pty, and whereas the temperature was
kept constant with one resistance according to the indication of the
Wueatstone-bridge, the ratio of the resistance of the other to Pt; was
determined by means of the differential galvanometer. Pty was also
measured separately with the Waeatsronr-bridge. The difference of
the results by the two methods amounted only to 0,02 °/, at the
lowest temperatures.

Just as Pt, Pty, and Pty were supplied by Heraxrus; they were
delivered at the same time, but later than P/. The diameter of all
three was 0.1 m.m. After having been treated and wound round
the glass (see Comm. N°. 95¢ § 3) in the same way, they were heated
for a long time in an annealing furnace for glass. Ptjj; and Pty
differed only in this respect that after being heated Py was partly
unwound, and then wound again, and was not heated in the annealing
furnace again.

To obtain also a resistance thermometer of very small dimensions
a platinum wire of 0,05 m.m. diameter was wound round a tube
of 1 e.m. diameter and about 8 ¢.m. long. The thin platinum wire
was welded to thick platinum wires which were fused in the glass.
Consequently the thermometer could be cleaned by means of acids
if necessary. The thin wire /¢, used for this thermometer, was also
furnished by Herarus.

A fourth wire was investigated to get an idea of the

§ 3. Invariability of the resistance thermometers for low tempe-
ratures with the time, viz. the resistance thermometer with which the
observations were made by MerrinK in 1902, and which we shall
call Pt);. The zero point appeared to have remained unchanged to
one 300000’). This was also the case with Pt, after measurements
had been made at very low temperatures with the resistance ther-
mometer for two years.

Repetition of the calibration at low temperatures of 1902 did not
give an equally good harmony. We found:

1) The thermometer had got defect in consequence of the bursting of the glass
cylindres. However carefully it was repaired, yet this gave rise to a diminution of
length of the wire of 3 mm. or 0,039 “/o, for which a correction was applied.

( 202 )

TABLE IV. KE:
| Deviation D viation |
Hydrogen th. 1902 1907 | in @ in ole
0° 110.045 110.048 — 0.003
—182.63 28.692 28.605 + 0.087 + 0. 95
—197.08 21 877 21.999 — 0.022 — 0.05
—209.93 16.025 15.934 + 0.089 + 0.25

We think that we cannot draw another conclusion from it than
that the reliability of the measurements with the hydrogen thermo-
meter in 1902 was not yet so great as it has become now as
appears from Comm. N°. 95".

§ 4. Results. The measurements have yielded for the resistance
of each of the wires expressed in that at O° as unity:

TABLE V. Comparison of different platinum resistance thermometers

Temperature Pt, Ptry Pty Pty Pty
(CoN ales le ile Ser: 4. Ie
— 30.53 „87892 0.87846 0.87799

0
— 58.58 0.76685 0.76632 0.76643

0.64991 0.64918 0.65039
—103.83 0.58345 0.58720
„56025 0.56126
12195 | 0.43182
„35240 0.35214 0.35979
„25141 0.25059 026022 0.27374

—109.09 0.56204
—140.19 0.43314
—159.41 0.35368
—182.75 0.25283
—195.10 0.20045 | 0.19894 0.19858 0.20812 0.22298
—204.68 0.15974 0.15816 0.45880 0.18355
—212.20 0.12816 0.12653 0.12625 0.13622 0.15285
—216.63 0.11024 0.10853 0.10824
—252.82 0.01424 0.040637

SS oe eS ©

— 255.18 0.01244 0.03766
—259.10 0.01053 0.03645

—_—!

( 203 )

It appears that wires delivered at the same time show the same course
with only small deviations. A considerable difference in deformation
of the wire has had only a slight influence for Pty. The great
difference with wires delivered at different times points to the fact that
the originally used material and the treatment in drawing the wires out
decide on the change of the resistance. How great the influence of
the treatment in drawing is appears from the comparison of P77 and
Pty. They were supplied by Hrrarvus about the same time and are
therefore probably made of platinum of the same degree of purity.
Yet the thinner wire Pt, decreases much less in resistance than the
thicker one. At the temperature of liquid hydrogen the differences
become very large. In view of the results obtained for gold, which
have been inserted in the following Communication (N°. 99°), the
most plausible explanation is this that the admixtures in the platinum
of the wires sent by Hrrarvs, either due to their being less pure by
nature or to the way of drawing, were less with the platinum sent
later than with that sent earlier. We come back to this in Comm.
N°. 99°. Here we may still mention that Drewar’s wire gave 0,30521
to ours 0,25344 at — 182°, and that only the thickest (0,2 m.M.) of
Hougorn’s wires gave a smaller value than ours, viz. 0,21253 to ours
0,21786 at — 191°.

§ 5. Calibration formulae for the new wires. Just as for Pt; we
have also calculated the constants for each of the wires Ptj77 and
Pty in a calibration formula which is adjusted down to — 217° and
does not give to great deviations at the hydrogen temperatures.
To be adjusted to the hydrogen temperatures too formulae of another
form are required. The above mentioned formulae of the form (A) :

nk B Oe 108 of oe au
— = a.t.10—? t.19—4 + ¢.t.10—- SS SS
W, T (273.09)?

give for the adjustment which we distinguish by A7:

| A 7 | a | b | c | d

| Pty | +40.401819 +-0.0007403 | +0.0052641 | +0.020666
| Pty 00020! —0.0026645 | +-0.0039442 qe cee

The mean error proved to be greater, for Pty even considerably
greater than in the calibration in Comm. 95°, which can be ascribed
only partly to the indirect method of the determination of the resistance.

( 204 )

Physics. — “Jsotherms of diatomic gases and their binary mixtures.
VI. Lsotherms of hydrogen between — 104° C. and — 217° C.”
(Continued). By Prof. H. KAMERLINGE Onnes and C. BRAAK.
Communication N°. 99e from the Physical Laboratory at Leiden.

(Communicated in the Meeting of June 29, 1907).

§ 14. Survey of the determinations.

The determinations mentioned in this Communication constitute
one whole with those of Communication N°. 97%. They may partly
serve to control the earlier determinations at — 104° and — 136°,
which, being the oldest observations, are not quite so reliable as the
others. For the determinations of isotherms at lower temperatures
they are a valuable supplement for the smaller densities from 70 to
100 times the normal one. With the exception of the isotherm of
— 217° the determinations communicated now may also be considered
as a whole in themselves. To complete this set of determinations a
part of the isotherm mentioned for the density at about 170 times
the normal one is still wanting. We hope soon to publish the
additional determinations referring to this. To the standard-tempera-
tures at which we determined the isotherms, we have still added
—164° C. From the data mentioned in Comm. N°. 974 may be
derived (see $ 13 of the communication mentioned) that the point
where the inclination of the pv-curve for exceedingly small densities
becomes zero, lies at about this temperature. The purpose of the
determinations at — 164° is to determine this point, which we shall
call the Boyle-point, more definitely.

The determinations, with the exception of that at — 140°, were
made at temperatures which differed little from the standard-tempe-
ratures of Comm. N°. 977. They may be reduced to these standard-
temperatures by a simple correction (See Comm. 97¢ §6). This
reduction has not yet been carried out for the isotherms mentioned
below. In Table XIX the temperatures are given at which the
measurements were made. They were determined and calculated in
exactly the same way as those of Comm. N°. 977; just as to these
latter temperatures the correction of Table XVII Comm. N°. 97% is
still to be applied to them.

We may still remark about the measurement of the pressure
(cf. § 3), that for the lowest pressures a direct connection with the
open manometer was required, because the closed auxiliary mano-
meter cannot be used below 20 atms.

§ 15. Remarks about the manometers and the piezometers.
When the determinations were finished, the auxiliary manometer

( 205 )

was once more compared with the open standard-manometer. It
proved that the normal volume had again undergone a slight dimi-
nution, i.e. of 0.00026 of the original value. This comparison was
made at about 22, 28 and 55 atmospheres. If the calculations of the
pressure are carried out with the corrected normal volume, the
remaining differences between the indications of the open and the
closed manometer are smaller than — of the total pressure.

The steeltube f, with hexagonal portion /, on the stem of the piezo-
meter 6, (cf. fig. 2 Pl. IL Comm. N°. 69, for the details at the top
of the tube compare fig. 4 ibid 7, /,, f,) was soldered to the glass
stem 0, in the way described in Comm. N°. 94°. Now the packing
could be pressed down more tightly (cf. § 4 Comm. N°. 97e) without
danger of the block sliding from the stem.

The dimensions of the different parts of the piezometer were
about the same as in the determinations of series I of Comm. N°. 97e,
The glass stem had a greater length and a volume of about 12 em’,
which enabled us to determine a greater part of the isotherms than
was possible in series I. The reservoir had the somewhat smaller
volume of 5.1583 em°.

§ 16. Second group of values of pva.
In table XIX the results of the determinations have been given
in the same way as in Table XII of Comm. N°. 974,

In conclusion we express our hearty thanks to Mr. J. Cray for
his valuable assistance in this investigation.

( 206 )

TABLE XIX. H Series IV. Values of pu, .

N°, | t P Puy | dy,
4 | —103°71 | 28.423 | 0.63208 44.967
2 38.154 | 0.63648 59.944
3 48.682 | 0.644143 75.897
4 58.217 | 0.64638 90.222
5 | —439:88 | 25.432 | 0.49459 51.428
6 33.774 | 0.49697 67.960
7 44.973 | 0.49967 82.600
8 48.558 | 0.50232 96.667
9 25.380 | 0.49466 51.308
10 | —46414 | 22.818 | 0.40065 56.952
u 28.688 | 0.40164 71.427
12 34.387 | 0.40253 85.427
13 39.947 | 0.40276 98.936
14 | —418318 | 20.409 | 0.32562 62.677
15 24.705 | 0.32550 75.898
16 98.374 | 0.39591 87.218
17 32.416 | 0.39599 99.673
18 20.400 | 0.39557 62.663
19 | —195-17 | 18.554 | 0.27867 66.581
20 23.337 | 0.27765 84.055
21 97.879 | 0.27622 | 100.932
22 | —20469 | 16.752 | 0.24040 69.684
23 20.456 | 0.23880 85.658
24 24.019 | 0.23695 | 401.367
25 | —49°82 | 15.416 | 0.20644 74.679
26 18.038 | 0.20430 88.296
27 20.643 | 0.20298 | 102.051
28 | —217°40 | 14.638 | 0.48742 78.103
29 46.787 | 0.48495 90.766
30 18.857 | 0.18293 103.080 q

( 207 )

Physics. — “On the change of the resistance of the metals at very
low temperatures and the influence exerted on it by small
amounts of admiztures”’ 1. By Prof. H. KaMeRLINGH ONNES
and J. Cray. Communication N°. 99° from the Physical
Laboratory at Leiden.

(Communicated in the meeting of June 29, 1907).

$ 1. Introduction. In Comm. N°. 99° we called attention to the
very large differences in the change of the galvanic resistance with
the temperature, which different platinum wires show when we
descend to the low temperatures which are to be reached with liquid
hydrogen. Such differences were still more pronounced for different
gold wires which we investigated. With this metal (see Comm. N°. 954
These Proc. Sept. 1906) we had taken in hand the investigation of
the influence of small amounts of admixture announced in Comm.
N°. 77, because the influence of admixing silver would probably be
important and the percentage of silver could be determined very
accurately, the possibility of drawing out wires of the different kinds
of gold and its high melting point moreover rendering this metal
preferable to the for the rest very suitable mercury.

Besides, the inquiry into the influence of small amounts of admixture
on the change of the resistance of gold with the temperature proved
at once useful as we thought that the gold resistance thermometer
would be preferable to the platinum resistance thermometer. Dr. C.
Hortsema, who already obliged us before (see Comm. N°. 95%) by putting
pure gold at our disposal, has had the kindness of supplying us
again with different samples of gold of high purity, further of pre-
paring for us different alloys with accurately known small percen-
tages of admixture, and of determining the impurity which was
finally left in the wires after they had been melted down. For all
this valuable help and for the information which Mr. HorrseMmA was
enabled to give us by his wide experience we express our hearty thanks.

The investigation of the different gold wires with very small
amounts of admixture may of course also be considered as the
calibration of different gold resistance thermometers. (Comp. Comm.
N°. 99% §1). We prefer, however, to consider it as a part of our more
general investigation (Comm. N°. 77) on the change of the resistance
with the temperature for pure metals, and on the influence which
small amounts of admixture exert on it.

As to the change of the specific resistance for the pure metals reduced
to the most normal state, attention is drawn to the temperature of the

14
Proceedings Royal Acad. Amsterdam. Vol. X.

( 208 )

2

r . , . .
= 0, the temperature of the point of proportionality

point of inflection 7s
G

dr

r ne d s
TT and the temperature of the minimum 7 = 0. It is clear that

the situation of these points, and the correspondence‘) and difference
of their situation and of the coefficient of variability of the resist-
ance with the temperature in general for different metals of different
classes must furnish important data for the theory of electrons.

The investigation of these points is only possible by the aid of

liquid hydrogen. Only in some cases — and even then the purity
of the metal is open to doubt — the point of inflection, whose

existence was indicated by Dewar, was found high enough to be
ascertained without measurements for hydrogen temperatures. For
metals in the purest and normal state the point of proportionality lies
probably still below the temperatures which are to be reached with
liquid hydrogen. It is true that Dewar derived from his measurements
at two hydrogen temperatures that it was surpassed for some of
his metal wires. Our measurements, however, point to this that as
a metal is brought to a purer and more normal state, the point of
proportionality is found to be lower. The metal wire which came
nearest to this ideal state, was one of our gold wires. Even at the
lowest temperature the point of proportionality was not yet reached
for that wire. Probably Drwar’s wires were further removed from
this ideal state.

With the low situation which we find for the point of proportionality
measurements at two hydrogen temperatures do not suffice, but we
have made determinations at at least three hydrogen temperatures,
because they were necessary to determine the probable situation of the

2

dr
point of proportionality by the aid Oe Until we have reached the pro-

portional point, we need not discuss the question of the minimum point.

In the inquiry into the properties of the metals in the ideal state
we must know first of all in how far the metal is in this state,
and else how we can derive what would be found in this state.
The influence of small deviations in the nature of the metals on
the change of the resistance with the temperature, becomes so ex-
ceedingly great for the -hydrogen temperatures, that a special investi-
gation is necessary for them. Here two things have to be paid
attention to: to small amounts of admixture, and to differences in

1) In this respect something is to be derived from the formulae given by us in
this and in the preceding communications.

a

( 209 )

hardness ete. For the present we have left the latter out of account;
in the investigation of the influence of the admixtures, however, the
influence of the hardness was as much as possible eliminated by
our treating the different samples of metals exactly in the same
way when comparing them, and by reducing them to the same state
of softness.

The most natural explanation of the whole of the results obtained
as yet (in this and the preceding Communication) is to ascribe the
deviations for the different wires of one and the same metal to
impurities in the metal, which may also come in during the drawing
if efficient precautions do not prevent it, and which even in very
small quantities exert a very great influence on the changes of the
resistance with tle temperature.

The influence of the drawing is altogether lost for mercury, in
which it is also easy to ensure uniform distribution of small quantities
of admixture. This enhances the importance of the study of this metal
for the investigation of the influence of admixture. In the first place
we have measured its resistance at hydrogen temperatures which
had not yet been determined; it is given in § 4. It proved that for
pure mercury *) the inflection point falls in the region of liquid hydrogen
temperatures. This is a drawback for the inquiry into the change of
the resistance with the temperature for pure metals.

Just as the gold wire Awy (see § 2), also the silver wire Ag; and
the platinum wires of the preceding Communication are probably
purer than Dewar’s wires of the same metals. For bismuth, on the
other hand, Dewar has most likely had a purer sample than we.
The change of the resistance at hydrogen temperatures for this metal,
which had not yet been measured by him, has been given in $ 5.
The observations for lead for those temperatures, which were still
wanting up to now, have been given in § 6.

The high degree of purity for some of the metals which were
at our disposal, and the lower temperatures to which we descended
(solid hydrogen evaporating at 2,5 m.m. pressure) render the decrease
of the resistance in some cases many times larger than was observed
by Dewar. To this it is also owing that we have observed the
great influence, which very small changes in the nature of the metal
obtain on the change of the resistance at hydrogen temperatures. We
may account for this by paying attention to the diilerence of the
resistance of a wire of pure metal at the temperature 7, 7;7, with

1) Perhaps in connection with the low melting point. Possibly the point of
proportionality is first reached for osmium.

14*

( 210 )

that of a wire of the same metal with a proportion of admixture #&
at the same temperature, 7,7. According to a theorem of MATTHIBSSEN *)
derived from observations between O° and 100°, this difference (the
theorem refers to a difference that is about the same as that con-
sidered here) is constant for different temperatures. FreMING®) found
this theorem about confirmed down to — 200°. As we have found,
this theorem “no longer holds for hydrogen temperatures. But the
deviation is not of such a nature as to affect our conclusions. So
if to form an idea of the influence of the admixtures, we put
rp=rir+pz, further p constant and large, then it is clear that
— when 7/7 becomes as small as is the case (see Table I Auy)
for pure metals and hydrogen temperatures — the resistance of a
metal for the case that w gets an appreciable amount, will be owing
almost exclusively to the admixture. The small amounts of admixture
obtain a remarkable influence *).

Analogues are easily found in the important influence of small
amounts of admixture on the density in the neighbourhood of the
critical temperature of a substance, in a space becoming opaque by
a cloud depositing on a minimum quantity of dust. But for a further
discussion the systematic investigation of the influence of small
amounts of admixture should be more advanced. At all events the
changes of the resistance with temperature at hydrogen tempera-
tures proves to be a highly sensitive criterion to decide about the
nature of a metal.

§ 2. Gold. The different samples of pure gold were all supplied
by Dr. C. Horrsema. With the exception of two the wires were all
treated in exactly the same way, drawn out by Hrrarvus to 0,1 mm.
diameter, and treated at every pull with diluted sulphurie acid and
nitrie acid. The gold wire Awy; was drawn in a different way and
made strongly impure. The exact amount has not yet been ascertained.

1) Pogg. Ann. Bd. CXXII.

2) Proc. Royal Institution June 1896 p. 9.
. 3) To a less degree of purity of the examined metal wires it is perhaps to be
ascribed that Nrecorar, Att. Line. 16, 1st sem. p. 906 finds a smaller decrease of resi-
stance at — 189° than we do, as appears by comparison with Tables I, III, V
of this communication and V of Comm. N°. 96%, Indeed Niccotar finds:

silver gold lead platinum
0° 1 1 1 1
— 189° 0.2784 0.3068 0.3357 0.3198

[Added in the translation].

( 211 )

Aug is the wire which was calibrated in Comm. N°. 95d. After melting it
down Dr. Horrtsrma found 0,03°/, impurities. As to the wires Awyj), Aujy
and Awy, Dr. Horrsema found about 0.015°/, admixture for Auj77,
about 0.005°/, admixture for Auyy and Auy. Aus; was made of an
alloy which after the wire had been remelted, contained 0.4 °/,
admixture (probably chiefly -silver). Wound round the same glass
cylinder all wires except Aug and Aw,j; were heated at the same
time in an annealing furnace for a long time, and slowly cooled, as had
also been done with Amp and Aw,,;, so that they were perfectly
malleable.

In table I the resistances have been given expressed in that at
0° as unity. These were about 92.

TABLE I.

Change of the resistance of different gold wires with the temperature.

Temperature, Au), Aupy Auy Auy, Au Au zer

—183.00 0.27653 0.27177 0.27096 0.37053 0.30070 | 0.387099
—197.87 0.21456 0.20963 6.20871 0.31659 0.23908
— 205.01 0.17897 0.20992

—215.34 0.14058 0.13407 0.13337 0.16822 0.16681

—252.93 | 0.01602 0.008743 | 0.008103 | 0.13669 0.04554 | 0.13942

255.13 0.005691
—258.81 | 0.01095 | 0.004265 | 0.003601 | 0.13241 | 0.03982 | 0.13288
[—261] 0.002713
[262] 0.003257 | 0.002526

02 1 1 1 1 1 1
—103.83 0.59601 0.59389 0.59306 0.64827 0.60545 | 0.64549

To facilitate comparison we may observe that Dewar found
0.03290, whereas we found 0.008103 at — 252°.93 for Auy.

$ 3. Mercury. It was doubly distilled and brought into a glass
spiral. The latter was protected by a bath of pentane, which was
slowly cooled from the bottom upwards before it was immersed into
the bath of the cryostat. We found:

(249)

TABLE II.

Change of the resistance of pure
mercury with the temperature

Temp. Resistance

0° | 97.126
— 183 00 7.2650
— 197.87 6.0103
— 205.01 5 3900
— 215.34 4,5057
— 252.93 1.2613
— 258.81 0.7534

§ 4. Silver. This was also supplied by Dr. C. Horrsema and drawn
to a wire of 0.1 m.m. by Hreraervs, during which operation it was
treated in exactly the same way as the gold and the platinum.
After the resistance had been determined, the composition was con-
trolled; the silver contained then 0.18°/, impurity. The zero point

TABLE Ill.
Change of t e resistance of silver with the temperature.

Temperature Se | OC O-Cayy

99°.76 1.41089 0 0

0 before 1 0 0

0 after 1.00037
— 103.81 | 0.58087 | — 0.00042 — 0.00042
— 139.87 | 0.43282 + 42 + 42
— 183.57 0 24679 | — 17 0
— 195.17 0.419703 +. 29 — 2
— 204.67 0.15528 — 31
— 252.92 0.008913 0
— 259.22 0.006.142 0

( 243 )

of the silver wire (resistance at 0°) changes slightly by being drawn
out in consequence of the difference in expansion of silver and glass.
The preceding table gives the resistance expressed in that at 0° as
unity. (The resistance at 0° was 21.519 2).

Column O—Cp contains the deviations from a formula adjusted
from + 100° to — 259° of the new form:

W,
—*=1+a.10-2.¢+510—-+# He 105
We

tay 10° 10° a To: TEE D
Nr enor) +a Teno) ©

which agreed best with the values:

—+0.004355

EK
ii

+0 .004806 | +0.00955 | —0.000013

For a comparison with platinum and gold the column O—C4 ,,,

gives the deviations from a formula of the form A (see Comm.
N°. 95e and 954):

Ba elo a me
aman ahem es OP A ENC

with values ‘which we distinguish by A7y on account of the other
way of adjusting the coefficients.

ee |

| 0.40355

+0,03968 | +40 005232 | —-0.008662

$ 5. Bismuth. The measured resistance, which we shall also
investigate in the magnetic field, was that of a bismuth spiral of
HARTMAN and Braun N°. 301. The resistance expressed in that at
0° as unity (the resistance at 0° was 17.3138 2) was:

( 214 )

TABLE IV.
Change of the resistance of Bismuth with the
temperature.
Temperature Resist nce Bij —C An
12°64 1.05148 0
42°70 1.05165
0 1
— 103.71 0.63649 + 0.00952
— 129.88 0.52865 — 127
— 164.05 0 46246 — 144
— 182.73 0 41435 — 69
— 195.17 0.38478 + 144
— 204 68 0.36064 + 127
— 216.01 0.33014 — 69
25301 0.22329 — 92
— 955.34 0.21388 — 2
— 258.86 0.19574 0 |

This column O—C'4 oe gives the differences with a formula of the
form A (see $ 4), with values which we shall indicate by 47/7 on
account of the adjustment at two hydrogen temperatures and over
the region to 0°:

d

+0.051928 | +0.0038155 | —0.0079700

| Anis | a | b | ce
|

| Bi, | 40. 399037

‘

§ 6. Lead. The knowledge of the resistance of lead is of particular
importance on account of the fact that this metal does not show
the Tuomson-effect. Probably the lead used by us, contained no more
than 0,015 °/, admixture.

The resistance of a narrow strip cut out from the flatted lead
and protected against chemical action by paraffine expressed in the
resistance at 0° (3.18114 2) as unity was- found to be:

(215 )

TABLE V.
Change of the resistance of lead with the temperature.
Temperature | Resistance
+ 16.33 1.0652
0e | 1

—103.63 | 0.59548 |
— 183.65 | 0. 29439

|, 495.45 0.25257
— 204.52 | 0.21742
—216.61 0.17129
—252.78 | 0.03039,
— 255.07 0.02314
—258.70 | 0.01314

Physics. Repetition of pe Hexn’s and TricHNer’s experiments on
the critical state’, by Prof. H. Kamertincn Onnes and G. H.
Fasius. Communication N°. 98 from the Physical Laboratory
at Leiden.

(Communicated in the meeting of April 26, 1907).

§ 1. Introduction. Experiments have been repeatedly made from
which the conclusion was drawn, that a substance can assume different
densities above its critical temperature with the same pressure and the
same temperature, which densities it can retain for hours according to
some investigators’). That in reality this is not the case, and that the

1) Travuse Ztschr. f. phys. Chem. 58 p. 477. 1907, cf. also Marmas, Le point
critique des corps purs p. 250.

When with change of density dissociations or variations of volume of the
molecules themselves should made their appearance which clearly require more time
than the establishment of temperature equilibrium through conduction of heat and
convection, we should when a phase was kept at constant volume after having
suffered variation of density, have to find an increase of the pressure both for
liquid and vapour phases and for phases above the critical temperature; thermo-
dynamically it follows from this that the density of liquid in equilibrium with
vapour would then have to be a function of the time.

. Cf. Travers and UsHER on variations of density in consequence of false equilibria.

( 216 )

differences found are to be ascribed to admixtures or to differences
in the pressure or the temperature of the phases compared appeared
already when Kurnen (Comm. n°. 11, Verslag Kon. Ak. v. Wet.
May and June 1894) repeated Gauirzinr’s experiments (Wied. Ann.
50, 1893), and found but trifling differences remaining. Afterwards
when pe HeeN (Bull. Ac. Belg. 3e S. t. XXXI 796) had again found
the differences of density in question by another way, it was shown
by repetition of his experiments at Leiden (Comm. N°. 68, These
Proc. April 1901 p. 628 and p. 691), that also these differences of
density vanish almost entirely for pure CO, when attention is paid
to the differences of temperature. In the last few years, however, it
has been particularly TeicHNeR’s *) experiments that have given new
support to the opinion that after all these differences of density really
exist (Drudes Ann. 13, 1904).

In the first place we have repeated pp HkxEn’s experiment in
different ways. Already with the earlier repetition (1901) thermo-
elements had been introduced for the determination of the difference
in temperature of the two metal reservoirs of the apparatus, which
were separated by a cock, the apparatus for the rest resembling that
of pr Herer as closely as possible. One of the thermo-elements, however,
was damaged during the experiments. Though it could be ascertained
that the differences in density even without correction for the tem-
perature were considerably smaller than those found by pe HreN,
probably on account of the greater purity of the CO,, the exact
amount of the difference remaining after temperature correction
could not be determined. To replace these measurements by better ones
a new, improved apparatus with thermo-elements was built, resembling
for the rest pr HeeN’s apparatus as closely as possible, and with
this apparatus we made the observations communicated in $ 3.
They confirm that the differences in density derived by pe Heen from
his experiments do not exist for a pure substance when temperature
and pressure are uniform’).

1) In the Tercuner’s tube the same differences of density which Gaurzine and
Wir (Congr. Intern. de Physique I 668, 1900) had found were shown by Gisert:
Farapay’s density-bulbs. What holds for TercaNer’s experiments applies therefore
also to those of Gaurrzine and Wip.

2) So if there exist processes as meant in p. 215 note 1, they pass so quickly that
it is not possible to demonstrate them by methods which require that the equili-
brium of pressure and temperature has first been established. As yet nothing
has been found that points to the fact that the establishment of the temperature
equilibrium is retarded an appreciable time on account of changes of energy which
increase in course of time to a definite limiting value, the volume remaining constant.

It was demonstrated in Comm. N°. 68 that admixtures and differences of tem-

(2009

Further we have repeated Teicaner’s experiment *) with more
precautions than had been taken by this observer. Especially a
thermoelement (platinum-platinum-iridium not to sacrifice the security
which the glass apparatus offers for the preservation of the purity
of the substance) was adjusted in the upper and in the lower end
of the TricHner tube, just as in pre Hren’s modified apparatus,
to enable us to follow the differences of temperature in the tube.’)
By using CO, for the experiment, a high degree of purity could be
reached, and we came into a region where the temperature could
be kept constant up to a very small amount.

If we wish to. prevent diffusion between the higher phases and
the lower ones, the modified TricuNner tube (at least when not a
capillary constriction has been made in it*) is inferior to the
modified apparatus of pe Hren. Moreover when we wish to reach
the equilibrium of temperature quickly, the bad conductivity of
heat of the glass is a drawback, but it has the great advantage, that
the changes of density can be observed at the same time with the
other phenomena for the critical state. With regard to these pheno-
mena Travers and Usner (Ztschr. f. phys. Chem. 57, p. 365, 1906)
and Youne (ibid p. 262) published important papers, after we had
made the experiments mentioned in § 7. In the main points our
observations agree with the descriptions given by Travers and

perature lead to systematic disturbances as in pe Heen’s experiments. Both give
rise to disturbances of the same character. In the discussion of the influence of
the differences of temperature the valuable paper by Virarp Ann. d. Ch. et d.
Phys (7) 10. 1897 has been overlooked there. That Trrcuyer’s results might be
ascribed to small admixtures has appeared in details from the calculations by
VerscHAFFELT (Comm. Suppl. n°. 10, (Dec. 1904).

To the influence of admixtures on phenomena in the neighbourhood of the
critical point attention has also been drawn by Youne Journ. de Chim. Phys. 4
(1906) p. 475. To this may be added that Krrsom, Comm. No. 88, These Proc.
Jan. 1904 p. 593 did not only consider the increase of the pressure during conden-
sation with constant temperature as a proof of the presence of admixtures, but
that it served him further to arrive at an opinion on the quantity of the admixture.

1) This was already mentioned Comm. Suppl. No. 10 These Proc. Dec. 1904,
Lately Trauge strongly urged the advisability of a repetition.

2) In a Caantarp-Latour tube thermometers were fused by Vittarp. Our tube
may just as well be called a Vittarp tube with density-bulbs as a Tetcuner tube
with thermo-elements.

3) Such an apparatus, if necessary provided with a valve which is worked
magnetically might be serviceable in the investigation of the variation of density
with temperature. [After this was printed we noticed that the device ofa capillary
constriction was used by Ramsay, Proc. Roy. Soc. 30 (1880) p. 327. Note added
in the translation].

(A8)

Usner and by Youre, and supplement them by giving the variations
of the densities.

After what the repetitions of pr Hren’s experiments had taught
us again about the asserted differences of density at the same pres-
sure and the same temperature above the critical temperature, our
repetition of TricHNer’s experiments has become rather a first con-
tribution to the study of the variations of density with temperature
and pressure by this way, than a refutation of the conclusions
derived from Tricuner’s experiments. We have, however, been able
to show sufficiently by our experiments that these conclusions are
erroneous.

§ 2. Repetition of one of DE HxxEn’s experiments. As we can refer

to Comm. n°. 68 with regard to the choice of the experiment which
is to be repeated (on account of the systematic character of the
deviations only one need be repeated), and as on another occasion
a full description of the apparatus used and the different operations will
be given, we think that the following remarks on the arrangement
of the experiments will suffice here.
„1. The pure carbonic acid was prepared by distillation. The
admixtures are to be estimated at no more than 0,00027 ( ef.
Kresom Comm. N°. 88 II, §2 and V § 10 These Proc. Jan. 1904). In
the apparatus it comes into contact only with metal, glass, and cork
(packings of this gave a perfect closure after having been repeatedly
tightened during a week.).

2. The apparatus, the conduits, and the further auxiliary arran-
gements, among which also two metal bottles with the purified
CO,, are all in connection with a mereury airpump. One of the
bottles with pure CO, serves for rinsing. From the second the
desired quantity is conveyed into the apparatus by distillation.

3. The density in every reservoir is determined by making -
the carbonic acid flow from it into a large reservoir with mercury
manometer kept at constant temperature. In the volumenometric
calculations the corrections are applied according to the empiric
equation of state V s. 1 of Comm. n°. 74 (Arch. Néerl. (2) 6,
1901). Errors in the density caused by leakages in the reservoirs
at high pressure are excluded. It was ascertained by separate
control experiments that the total amount of CO, in the apparatus
remained unchanged during the experiments.

4. The apparatus was kept at uniform constant temperature by
means of flowing water, a xylene thermoregulator (see Comm. N°. 70
III § 3 These Proc. May 1901) and a valve stirrer (see Comm.

( 219 )

N°. 83 III § + These Proc. Febr. 1903). Sufficient precautions were
taken to prevent conduction of heat from outside to parts of the apparatus.

§ 3. Variations of density found in the repetition of the expert-
ment of pr Heer after correction of the difference in temperature
of the reservoirs.

De Heer brings the temperature of the two reservoirs (see $ 2
beginning) from 28° to about 35° C, and opens the cock between
them 6 times four seconds during the heating; then when the
temperature has become constant at about 35°, he opens the
cock once more 6 times + seconds. Then he assumes that tempe-
rature and pressure are the same in the two reservoirs.

When repeating the experiment (being very careful to prevent
drops from being scattered from one reservoir into the other) we
found contirmed by reading the thermo-elements (nickel-iron), what
was observed in Comm. N°. 68 viz. that every time when the cock
between is opened for adjustment of pressure, a difference of tempe-
rature arises between the two reservoirs, and that when closing the
cock at the end of the experiment a difference of temperature remains,
which must be taken into account.

In order to find out in how far the equilibrium of temperature
and pressure has been reached, we have in the first place made
three determinations, in which the cock was opened respectively
2, 4, and 6 seconds every time (probably our cock allowed compara-
tively less substance to pass than that of De HreN). The results have
been given in the following table: v denotes the upper; / the lower
reservoir, so 9; is the density in the lower reservoir; the numbers of
times the cock was opened during the heating (distributed over
15 minutes) and then at constant temperature (distributed over half
an hour) have been separately given; 9; is g; corrected for ¢,—t.

SERIES I.
Establishment of the equili- Ker
brium by opening fm | P| Pil’y| fy) 15-4 femperatires.|
the cock | fee Bel
| Pu \Pufo

506 | 4.24 | 34°95 | 0°27 | 0.456 | 4.09
.495 | 4.47 | 34.40 | 0.22 | 0.454 | 1.08
„489 | 1.45 | 34.20 | 0.16 | 0.456 | 1.07
„501 | 1.45 | 34.30 | 0.20 | 0.466 | 4.07 ;

6 times 2 + 6times2sec. | 0.418 |
6 times 4 + 6 times 4sec. | 0.424
6 times 6 + 6 times 6 sec, | 0.427

6 times 6 4- 6 times 6sec. | 0.437
| |

Or ©

( 220 )

The temperature corrections have been borrowed from the graphical
representation derived in Comm. N°. 68 from Amacat’s determina-
tions. The uncertainty which still prevails with respect to the
correct course of the isotherms in the neighbourhood of the critical
state is, of course, also found in these corrections.

The rather rapid process of the heating from 28° to 35° prevents
further that the whole apparatus has already assumed the temperature
of the waterbath, so that also the observed differences of temperature
themselves are not quite Certain.

In the following series of determinations we proceeded in the
same way till the 12% opening (the 6" at constant temperature).
It was put off for 3 hours. When the cock was opened the course
of the deviations of the galvanometer appeared to be the same as
in the preceding series; the remaining temperature corrections,
however, were somewhat smaller than in the 1st series, which we
ascribe to this that all parts of the apparatus have had time to
assume the temperature of the waterbath. An increase of pressure
in the lower reservoir, which should have been found when e. g.
in this lower reservoir molecules were dissociated during these three
hours (see § 1, p. 216 footnote 2), and which should have given rise
to a greater galvanometer deviation when the cock was opened for
the last time, could not be traced. We found:

SERIES II.
Establishment of the | Correded a
equilibrium by fo | er | Peel oli temperature
opening the cock ey | Pipo

6 +5 +4 time 2 sec. | 0.430 | 0.497 | 1.16 | 34.55 | 0.20] 0.466 | 1.08
65 4 , 4sec. | 0.440 | 0.489 | 1.14 | 34.85 | 0.46 | 0.456 | 1.04
64+5+1 , 6sec. | 0.439 | 0.485 | 1.10 | 34.40 | 0.45 | 0.452] 1.03

In virtue of what the preceding determinations had taught us
as to the reaching of equilibrium of temperature and pressure the
cock was opened 12 times 12 seconds in a following determination,
and finally two more determinations were made in which the cock
was opened 12 times 4 seconds and at last once five minutes. We
found :

( 221 )

SERIES III.
Establishment of the En
equilibrium by Py Py ifPo i ty—t, |the ae
opening the cock Py Fito

| 6 + 6 times 12 seconds | 0.446 | 0.488 | 1.09 | 34.70 0.20 | 0.456 | 1.02
6 + 6 times 4 sec. 0.427 | 0.445 | 1.04 | 34.05 | 0.06 | 0.422 | 1.01
0.462 | 0.478 | 1.03 | 34.00 | 0.06 | 0.467 | 1.01

at last 5 minutes

From this follows that as the equilibrium of pressure and tempe-
rature is obtained better, the densities of the phases become more
and more equal, and that at last after the application of the tempe-
rature correction only very small differences remain.

The much more considerable deviations found by pe Heer
(ou/9: = 1.19, see Comm. No. 68) must, therefore, be attributed to
admixtures and differences of temperature. *) *).

§ 4. Example of differences of density as found by pr Heen,
caused by a slight impurity of the CO,

The great influence of small quantities of admixture is very con-
vineingly shown by the following results.

In a group of determinations ending with a repetition of experi-
ment 2 Series I we found:

PL Py

Establishment of the equilibrium
by opening the cock Py PL

| 646 times 4 sec.

>
le
de)
to
So
on

„531 | 1.35

It appeared that in consequence of carelessness in the cleaning
after it had been repaired, in the metal bottle in which the pure

1) That during the opening of the cock no important exchange of liquidogeneous
and gasogeneous molecules between the upper and the lower reservoir can have
taken place (to use the terminology of pe Heen), appears from this, that when the
upper reservoir was filled with air and the lower reservoir with air with 31 pCt.
CO, and the equilibrium was established without the cock being opened, after
the cock had been opened for 5 minutes, only 0,33 percent of CQ, had passed into
the upper reservoir.

2) They give both systematic errors of the same character (cf. § 1 p. 2 note 1
above).

( 222 )

carbonic acid was kept, a trace of oil had been left which had
diffused in the carbonic acid. When we thought that the whole
apparatus had been sufficiently cleaned by blowing pure carbonic
acid through it, we found:

Establishment of the
equilibrium by opening P

the cock 4 1 PilPo

Only 6 times 4 sec. during |

the rise of the 0.385 | 0.555
temperature.

6 + 3 times 4 sec. 013899) OE5 ESO

6 + 6 times 4 sec. 0.447 | 0.505 | 1.21

which by the side of Series I and II gives at the same time an idea
with what degree of approximation equilibrium of pressure is reached
by the repeated opening of the cock. Repeating the last determination
after continued blowing we found:

6+ Gtimes4sec. | 0.426 | 0.496 | 1.19

The last observation harmonizes pretty well with Series 1 N°. 2,
of which it is a repetition, the same deflections of the galvanometer
being moreover found. It leads to the same 9'//o,.

It appears how misleading even the presence of slight impurities
may be, and that in Comm. N°. 68 the leather packings have been
justly called a fundamental defect of pr HeeN’s apparatus (cf. 1 § 2
above).

§ 5 Correction for gravity and for slight admixtures in the ex-
periment of DE HreN. Kesult.

In order to be able to calculate the correction which is to be ap-
plied to ¢'//gy for gravity, we must know the density as function of
the level in a column of pure CO,. The accurate shape of the iso-
therms in the critical state being very uncertain '), this function is
not accurately known. Gouvy has taken Sarrav’s equation of state as
basis for his calculation. We have started from the equation of
state Vs. 1 of Comm. N°. 74. Only 0,0002 was found for the’
correction at 34° and 8 c.M. difference of level, so that it may be
neglected. As to the correction for the admixtures for the CO,, when
we put their amount as given in § 2, at 0,00027, it becomes

1) It is just to the knowledge of this shape that observations as made in § 3
and § 7 may contribute. ati

( 223 )

1°/, a 1,5°/, at 34°.5 according to the calculations of VERSCHAFFELT,
Comm. Suppl. N°. 10. If the uncertainty of this correction is taken
into account, we must come to the conclusion, the limit of accuracy
of our experiments not being higher than 1 °/, either, that the diffe-
rences of density derived by pr Hern from his experiments do not
exist for pure CO, when sufficient care is taken to ensure equili-

brium of pressure and temperature.

§ 6. Repetition of Teicungr’s experiment. An elaborate description
of the apparatus and the operations will be given on another occasion.
Here the following remarks may suffice:

1. Repetition with CO, was considered to be desirable also by
TEICHNER because it gives more warrants for purity.

2. A platinum-platinum-iridium thermo-element (used with a mag-
netically protected galvanometer of Dugois) was successfully fused
into TicnNner’s tube at the top and at the lower end, so that the
tube remained proof against a pressure of 150 atmospheres. However
we did not succeed in making the thermo-elements free from disturbing
electromotive forces, nor did they give with certainty the accuracy
of 0°.01 we wished. The places of contact were found at ‘/, and °/,
of the height of the tube. A third thermo-element to compare the
temperature in the tube with that in the bath would be desirable.

3. The critical density of CO,, 0.469 *), being smaller than that
of CCI, with which substance TricHNer worked, it was much more
difficult to obtain the required density-bulbs (small glass bulbs) of
0.365, 0.3890 and 0.405. We owe them as well as the fusion of the
thermo-elements to the skill of Mr. O. Kussenrine, chief of the glass-
blowing department of the laboratory. By means of CreBscr’s formula
it was found that the decrease of volume of the bulbs at the
highest pressures can only amount to from ‘/,,, to 1/,59-

4. Still greater care was devoted to the purification of the CO,
than in the repetition of pre Hren’s experiment. From a metal
bottle of CO, as used for the latter, '/, is once more blown off, and
then '/, distilled over into a second bottle from which under weighing,
so much is suffered to escape that a fixed quantity remains. This
second bottle is connected by glass tubes with the experimental tube,
a mercury manometer, a mercury airpump and an auxiliary bottle
(also of metal) with pure CO, for rinsing the conduits, after which
the fixed quantity which it contains, is quite distilled over into the

1) Derived by KeesoM Comm. NO. 88 These Proc, Jan. 1904, p. 574, from his
observations by means of the rule of the rectilinear diameter.

15
Proceedings Royal Acad. Amsterdam, Vol. X,

( 224 )

experimental tube, the latter being immersed in liquid air; at last
the experimental tube, still immersed in liquid air, is connected with
the mercury airpump, and fused off. By weighing it is ascertained
that the desired quantity has been transferred to the experimental tube.

5. A mode of heating which does not give rise to convection
currents inside the tube, is considered of great importance also by
Turcnner and TRAUBE, to prevent mixing of what is at the upper
end and what is at the lower end of the tube. TricHNer does not
accept Youne’s refutation of his experiments (see TxicHnrr, loc. cit.)
because in Youne’s apparatus convection currents are not so well
prevented as in that of himself. The thermostat used by us, however,
satisfies much higher demands than that of Tricuner. The tube is
immersed in a liquid bath in a double walled non-silvered vacuum-
glass which is hermetically closed with a badly conducting lid. The
glass is provided with a valve-stirrer and an arrangement to heat
the bath electrically from above, and is itself again immersed in a
bath with double glass walls, which is likewise provided with a
valve-stirrer. With the exception of two windows, the space between
these two walls is tilled with cotton wool, by which the outer wall
too is surrounded. Like the bath in which the improved apparatus of
pE Hern ($ 2) was placed, the outer bath was kept at constant
temperature (up to 0°,02) by flowing water with the aid of a xylene
thermoregulator (§ 2). In this way the temperature of the bath in
which the experimentaltube is, can be kept constant up to 0°,002. The
heating takes place according to the indication of thermometers divided
into 50% of a degree, which are placed in the inner and in the outer
bath, and is regulated in such a way that everything that might give
rise to convection currents is as much as possible avoided.

6. When manipulated the tube was always efficiently shielded
for the protection of the observer.

§ 7. Observations. The bulbs correspond with the densities 0.365,
0.390, 0.405, 0.421, 0.448, 0.450, 0.466, 0.483, and 0.510.

The position of the bulbs and that of the meniscus (indicated in
what follows by the read number of the mark of division between
[ ]) was read on a millimeter scale etched on the tube; in the middle
of the tube the mark 30 is found, the zero point is 20 mm. above
the bottom.

In the jirst experiment the heating took place very slowly; at
first also the inner bath was (electrically) heated, ¢ refers to the
outer bath, ¢; to the inner one. After three hours small gas bubbles
were seen to rise from the downmost thermo-element, probably

( 225 )

caused by conduction of heat along the threads, in consequence of
te having increased too much. We observed:

June 29 1906.

time

11h

dij
12
12
12

12
12

12

12

12

12

30
20
25
30
33
36

40

44

48

52

te t; men.
2199 27°15) [34]
27.92
30.00
30.4 30.39 the rising of the gas bubbles has finished,
the bulbs begin to show a tendency to divide
30.69 0.365 rises
30.83 0.365 at 33
30.88 [33] 0.510 begins to descend slowly to 25
30.94 0.510 at 5
30.99 0.510 on the bottom
the separate (electrical) heating of the inner bath is stopped,
31.00 31.00 0.365 at 36

0.483 begins to descend
31.00 [34] 0.365 between 38 and 39
0.483 Br 21 and 22
ti rises very slowly whereas f, was all the time kept some-
what higher to 2.50
0.483 between 10 and 11
0.365 rises to the top with accelerated
motion
0.483 continues to descend very slowly
[34.5] 0.483 has arrived at the bottom
all except 0.510, 0.483, and 0.365
in meniscus
(35] 0.390 begins to rise
0.390 between 37 and 38 with 0.405 by
its side somewhat lower
0.390 between 38 and 39 with 0.421
below it in a slanting direction
[35] 0.421 begins to rise, for the rest like
A 1107:

Looking from the top downward in a slanting direction
through the tube we observe a slight grey mist which is
denser in the part below the meniscus. When we look straight
through the tube, with a light behind the tube, the whole
shows a light brown colour, which is somewhat darker under
the meniscus.

The bulbs continue to move slowly apart, the rising ones

15%

2h15

2 20

2 50

8 10
8 30
35

40
8 50

Go oo

( 226 )

moving faster than the descending ones, and the velocity
of the rising bulbs increasing as they get higher, the same
thing taking place though in a smaller degree with the
descending ones.

31.032 the meniscus has gradually got fainter and
is hardly to be distinguished, only a slight constriction of
the light band is to be perceived at 35.

31.036 0.421 between 42 and 43

0.443 5 36 and 37
0.450 33 34 and 35
0.466 4 32 and 33
31.22 the outer bath is further kept at this temperature

31.050 the rise of the temperature of the inner bath

is now exceedingly regular

31.096 0.443 in the middle of 53

0.450 between 32 and 33
0.466 ee 24 and 25

The mist in the tube is now equally dense everywhere,
and beeomes gradually less, the moving apart of the three
still deseending bulbs continues slowly and regularly

31.210 0.466 lies just on the bottom

0.450 between 36 and 37; has risen
4 mm in 215’ and so shows a
tendency to move to the top.
The cooling takes place by reducing the outer bath to a
lower temperature
31.133 0.466 begins to rise from the bottom
0.450 at the same place
Throughout the tube a bluish mist appears
This mist gets denser
At [15| a thick milky white mist is formed,
which spreads rapidly upwards and downwards.

30.984 At [10] the meniscus appears. From the
upper place of contact of the thermo-elements drops fall
down, from the lower place of contact smaller gas bubbles
rise upwards. (The cooling proceeds too rapidly). The meniscus
rises, 3 bulbs fall quickly into it from above, and 1 rises
towards it from the bottom.

The differences of temperature within the tube were found
to be between 0°.02 and 0.03, but in consequence of dis-
turbances they were often not to be observed. In the obser-
vation of 8"7 they were no more than 0°.01.

( 227 )

July 5 1906.
In the second experiment the heating took place somewhat
more rapidly. In 1510’ the inner bath was brought at
gh 10’ 29°.99 The separation of the bulbs has, of course,
not advanced so far as in the first observation, and the
deflections of the galvanometer were larger. The tube re-
mained now farther behind the temperature of the waterbath.
9 40 31.60 [36] The meniscus is still dimly to be dis-
tinguished here, and a thin light mist is visible through the
whole tube. Under the meniscus a somewhat darker band
of a light brown colour is seen.
The position of the bulbs is now
0.365 at the top
0.390 between 43 and 44
0.405 5% 42 and 43
0.421 in the middle 41
0443 52°); is 40
0450 457 mA 39
0.466 between 37 and 38
0.483 and 0.510 on the bottom.
31.7 0.390 and 0.405 now go very rapidly to
the top followed by 0.421.
At the place of the meniscus now only a
slight constriction and a light brown mist band are to be

perceived.
10 45 31.900 The temperature is then kept constant till
11'37 with no greater deviation than 0°.004 and then from
4137 31.888 till 2"15 with no more deviation than 0°.002.

2 15 The mist has now entirely vanished and the bulbs are all apart.
0.510, 0.483, 0.466 on the bottom
0.450 and further ones in the top, none
of the bulbs remain suspended in the body
of the tube; the bulb 0.450 was the
last to go to the top, whereas 0.466 had
already been on the bottom for some time.

A difference of temperature is no longer to be perceived.
At first the cooling took place more slowly.

3 31.550 A slight mist is perceived
345 31.040 the mist has become distinctly denser.
5 10 30.985 [5]. In this position the meniscus originates

in a milky cloud in the lower part of the tube. Further the
lowering of the temperature proceeds too rapidly.

( 228 )

5 25 30.950 [1+4|. Three bulbs float in the meniscus.
A disturbance in the regulation of the temperature of the
outer bath put a stop to the experiment.

July 11 1906.

A third experiment did not give any difference with the
first with slow heating. The temperature was kept still closer
to the critical, and the heating went still more slowly. Now
the meniscus descended, and the brown colour under the
meniscus was particularly pronounced, it was darkest just
below the meniscus, and gradually faded downward. After
a slow heating which extended over 10'/, hours the menis-
cus disappeared at

6b 30°.986. The position of the bulbs was now
0.443 between 34 and 35
0.450 in the middle 27 ~
0.466 between 25 and 26.

In consequence of a slight disturbance in the regulation
of the outer bath ¢; descended to

6 45 30.984 [25] the meniscus appears, the position of
the highest bulb does not undergo any
change, the two others 0.450 and 0.466
float in the meniscus.

915 31.010 the meniscus disappeared somewhat lower,
the brown colour in the lower half is much more intense,
at last it contracted to a dark brown band of + 1 mM.
width just below the meniscus. Gradually it grew lighter
and shortly after the meniscus it also disappeared ;
0.443 between 41 and 42
0450-9 =. 23 and 24
0.466 in the middle 22.
The temperature at the top of the tube was 0°.01 higher
than at the bottom.

§ 8. Conclusions and remarks. An elaborate discussion of the ob-
servations in connection with other peculiarities of the net of isotherms
in the neighbourhood of the critical state (cf. Comm. n°. 74 and
Comm. n°. 88 IV $ 5, Jan. 1904 and Comm. Suppl. n°. 10), and as
to those on the mist in connection with the observations of Gour,

Travers and Usner and Youre *), must be deferred to a later occasion.
However, some conclusions are obvious.

As the temperature rises more slowly and the equilibrium in the
tube is better reached, we can get nearer to equality of density
of the vapour and liquid phases. We think we found a smaller dif-
ference in density in our measurements than any of the observers
before us *).

We did so in the third experiment. The critical temperature was then
fixed between 30°.984 and 30°.986 *). That at 30°.984 only a small dif-
ference in density existed between liquid and vapour appears as follows:
When the meniscus appeared we found 0.443 for the density of the
vapour at the height 35. So we estimate the density at 0.452 at the height
of the meniscus (25) according to the correction of §5 (doubtful);
bulb 0.450, however, floats on the meniscus. The density on the
bottom is < 0.483 (height (see § 7 beginning) 5 em. under 30), so
we estimate the density of the liquid at 0.468 at the height of the
meniscus; bulb 0.466 floats. Vapour and liquid differ, therefore,
certainly less than '/,,, and probably no more than ‘/,, in density. In
the first experiment we found 9, > 0.421, 9; < 0.483 from which
9, > 0.480 , 0, << 0.468 follow with the estimated correction for
gravity; so under these less favourable circumstances a difference
of less than */,, is most likely realized. These results concerning the
closer and closer approach of the density of liquid and vapour,
which quite agree with the views of ANDREWS-VAN DER WAALS,
deprive the much larger differences of phases at the same tempera-
ture and pressure above the critical temperature, which TrICHNER
derives from bis experiments, of all importance *).

1) This includes the discussion of the mist stage of von WESENDONCK, which
would constitute the transition stage in the neighbourhood of the critical state,

and which in any case can only extend over a small part of the region of density
and temperature where a mist can be seen.

2) Youre, Journ. Chem. Soc. 71 (1897) p. 455 stated at 0°.05 below the critical
temperature a difference of 14°/, between the liquid and vapour densities. [Note
added iu the translation].

3) The readings of the temperature have been reduced to those on a thermo-
meter which had been controlled with an air thermometer accurate up to 0°,01
by the Phys. Tech. Reichsanstalt. Our result agrees with that of Kersom, 30°.98
(Comm. N°. 88 see above), made with the same thermometer Moreover, besides
and after the determinations of the critical temperature of GO, cited in LANDOLT-
BORNSTEIN-MEYERHOFFER’S Phys. Chem. Tables are to be mentioned: VERSCHAFFELT
Zitt. Versl. Juni ’96 (31°.0), von WersrenponcK Verh. d. Destsch. Phys. Ges.
5 p. 238 (30°.95), BRINKMAN Diss. Amsterdam 1904 (31°.12).

4) It is true we might assume that the equilibrium of liquid and vapour with
so slight a difference of density as we observed, is only reached after so long a
time as was allowed in this experiment to obtain equilibrium of temperature and
that at first states with greater difference of density of liquid and vapour (ef.
note 1 p. 1 § 1) appear at the same temperature, which gradually pass into the final

( 230 )

It is in harmony with this that a tolerably sharply defined critical
density can be assigned. We derive 0.460 from the density of vapour
and liquid in the third experiment for it, which agrees with the
mean which would follow from experiment 1 at 2515, ie. 0.450,
and 0.470, derived from experiment 3 on account of the appearance
of the meniscus at 25 (ef. further $ 6 p. 228 footnote 1).

Differences of density as TricHner finds, were also found by us; it
was in the second experiment at the moment that the meniscus disappears
with comparatively rapidly rising temperature. However, after the tube
has been kept at the same temperature above the critical temperature
for 3 hours, and the temperature in the tube has become uniform
probably up to less than 0°,01 0’,9 above the critical temperature,
they have been reduced to less than 0,466 -— 0,450, or less than
3,5 °/,, i.e. after correction for gravity < 3,3°/, over 10 cm.

The remaining difference in the first experiment 0°,23 above the
critical temperature after 6 hours’ heating above the critical tempe-
rature can be derived from the fact that bulb 0.450 floats 5.6 em.
above 0,466. This difference is no more than 3,5 °/,, and corrected
for gravity 2,9 °/,.

From VERSCHAFFELT's calculations follows that at 0°,28 above the
critical temperature 0,0001 molecule of admixture may cause about
12°/, difference of density. Differences of temperature and admixtures
which may account for remaining differences such as those just treated
are scarcely to be avoided even with the precautions taken by us.

Nothing has been observed of an “Entmischung” by cooling when
the critical temperature is approached, as TrauBe Le. p. 477 mentions.

TricHNER observed that, after the disappearance of the meniscus, at
the place where it was found last a transition zone exists towards
which the differences of density concentrate, whereas outside it the
changes are only insignificant. In our observations the contrary
appeared, and the changes in density continue regularly with increase
of temperature, only the motion of the bulbs was slightly accelerated
as they approach the top of the tube, and they cover the last 1 or
2 em. very rapidly. In a less degree but in the same way this takes
place with the bulbs which descended. We consider these phenomena
to be connected with heating and cooling of phases by compression
and expansion *).
state with simultancous change of the pressure of coexistence (cf. note 1p. 1 §1).
But the absence of subsequent rise of pressure in the repetition of pe Heen's
experiment (see § 3) has taught us, that already after a very short time after-
changes of the density no longer occur.

1) They just as the “Entmischung” assign that the temperature differences within
the tube in the experiments of TetcHner were probably greater than in ours.
{Note added in the English translation].

€ 231)

Physics. — “Contributions to the knowledge of the w-surface of
van DER Waars. XV. The case that one component is a gas
without cohesion with molecules which have extension. Limited
miscibility of two gases.” (Continuation). By Prof. H. Kammr-
LINGH Onnes and Dr. W. H. Kersom. Supplement N°. 15
to the Communications from the Physical Laboratory at
Leiden.

(Communicated in the meeiing of May 24, 1907).

$ 8. On the temperatures and the pressures on the gas-gasplait. In
order to form a provisional opinion as to the experimental conditions
which must be satisfied that limited miscibility in the gas state may
be observed, and to be able to derive what pairs of substances
must be considered suitable for this purpose, it is desirable to examine
for some cases what temperatures and pressures occur on the gas-
gasplait’). In the case ($ 2, March °07) of a component without
cohesion’) or almost without cohesion (m< m,, see § 7), the gas-
gasplait will occur for all temperatures between the critical tempe-
rature of the less volatile component and the critical temperature
of complete miscibility *). Its pressures will then be larger than

1) In our opinion Mr. van LAAR (These Proc. May ‘07, p. 35, note 2) is
wrong in thinking that in the case of a three-phase-equilibrium, as e.g. in the
system water-ether, our terminology with regard to the distinction between gas
and liquid does not agree with that used by van peR Waars. According to what
has been said about this distinction in § 4, for a three phase equilibrium of a
system of the type water-ether the denser phase which is rich in water, must be
called liquid as belongirg to the liquid branch of the connode, just as the less
dense phase which is rich in ether, must be called gas phase; whether the denser
phase which is rich in ether is to be called liquid or gas, is not determined by
the principle of the continuity of the phase along the connode; if the reduced
temperatures at which this phase appears, are taken into account, also the last
menuoned phase will be called liquid for the system ether-water in accordance
with what has been said in § 4.

2) The second branch of the plaitpoint curve in Fig. 1 § 2 (These Proc. March ‘07,
p. 787), about which Van LAAR speaks in These Proc. May ’07, p. 36, has
there (@:. =O) contracted to a point c=1, v—dog. It is true that in the case
of our § 7 (Plate II, These Proc. March ’07) a second branch of the plaitpoint
curve occurs, but it has been explicitly stated there (p. 795 at the bottom and
p. 797) that we did not discuss the spinodal curves at the lower temperatures
at which this branch of the plaitpoint curve makes its influence felt, referring inter
alia with a view to these temperatures to VAN LAAR's papers.

3) As mentioned in § 1 this idea was introduced by VAN DER WAALS, who
also gave the formulae for the calculation of this temperature (VAN LAAR calls
it “third critical temperature’’).

( 232 )

the critical pressure of the least volatile component. If the sup-
positions mentioned in § 2 might be applied for this, and the
values of ay and Au for He might be borrowed from Comm. N°. 96¢,
Febr. 07, p. 660 footnote 2, so that ame = */;;; amu, = 0.0000024
and $Me = */, bmn, = 0.00044, this case would be realized for
mixtures of He and water‘). Then we should find 7), = 1.056 7;,,,
so that the gas-gasplait would occur over a range of temperature
of 36° above 365° C., and at pressures above 195 a 200 atms.

In the case that the molecules of the least volatile component act
on each other feebly, but still exert such an attraction that a double
plaitpoint *) occurs in the net of the spinodal curves, the pressure
in this plaitpoint and its temperature in connection with the critical
temperature of complete miscibility give important indications as to
the pressures and temperatures of the gas-gasplait.

In table II these data, calculated for the case that the suppositions

LA Be LB yw:

Pair of substances’ PkmlZe, | Pant De, api! "kx Paph Pie,
Hydrogen-helium | 0.933 | 0.915 | 444 41.6
Oxygen-helium 0.962 | 0.957 | 8.64 | 61.3
Argon-helium 0.970 | 0.962 | 7.90 64.5
Neon-helium 1.007 | 0.961 | 3.72 18.8
NO-helium 1.031 0.991 | 3.76 13.1
NH-helium 4.009 | 0.969 | 6.20 25.2
H.S-helium | 0.972 | 0.970 | 13.79 171

‚ CO,-helium | 0.9540 | 0.9536 | 45.89 | 104 |

|

1) The ay and by for water have been borrowed from LANDOLT-BÖRNSTEIN-
MEYERHOFFER’S Physik. Chem. Tabellen.

2) The appearance of a double plaitpoint near Kp was already observed by
van LAAR (These Proc. May 1905 p. 42). The conditions for its appearance,
however, were not correctly defined by him (cf.§9 IL). In view of this latter fact
we thought that we drew sufficient attention to this result of van LAAR by
referring the reader to vaN LAAR's papers. (see p. 797 footnote 1). The detaching
of a longitudinal plait at high temperatures, which leaves the d-surface with its
open side turned to v=), follows immediately (see These Proc. April ’07 p. 848
footnote) from the general considerations and calculations of vAN DER WAALS Cont. IL
§ 19 sqq. and vAN DER WAALS’ diagram in Zittingsverslag Kon. Akad. Nov,
1894 p. 133, when the case a) cf. § 9. I, a case which van LAAR has not
included in his considerations, does not occur.

( 238 )

mentioned in $ 2 might be applied, have been given for some helium
mixtures. 7%, has here been calculated according to vaN DER WAALS
Cont. II, p. 48 (ef. § 6), Ty, according to the formula mentioned

1 $ 7, papi from the equation of state with the just mentioned
Ta and the va, also represented in formula in § 7 *).

The reduced temperature of the double plaitpoint 74,1/7%;, men-
tioned in this table, gives an idea in how far the phases in its
neighbourhood behave as compressed gas-phases.

The values of a and 5 of the different components have been borrowed
from KOHNSTAMM, Lanpout-B6rNsTEIN-MEYERHOFFER’S Physik. Chem.
Tabellen; for those of helium see above; for neon we have made use
of the ratio of its refractive power *) to that of helium according to the
determinations of Ramsay and Travers *), and of the estimation con-
cerning the critical temperature by Travers, SENTER and JAQUEROD!).

It appears from table IL that when the gas-gasplait can make its
appearance, the range of temperature within which this is the case
between Phn and 74,/), on the mentioned suppositions is small for
most of these pairs of substances, for some even exceedingly narrow.

For the pressures on the gasplait higher values than pg,; will have

1) Though originally we did not consider the developments which led us to the
explicit expressions for the double plaitpoint mentioned These Proc. March °07
pp. 796 and 798 of sufficient importance, now that vaN Laar (see These Proc.
May ’07 p. 41) thinks the derivation of such like expressions im possible there
is a reason for communicating them on a following occasion.

2) HapprL, Habilitationsschrift Tübingen 1906, p. 30, found that the refractive
power for argon, crypton and xenon would yield values for b which greatly deviate
from the D's derived from the critical data. When according to the principle of
the corresponding states (cf. Harper loc. cit. p. 31, note 1) we compare the ratios
of the refractive powers for these gases with those of their critical volumes
(derived from pe and Fy) the deviations are far less considerable. So with regard
to this property, these one-atomic gases form a group, just as is the case with
the bi-atomic and with a great many more-atomic substances (Guye, Journ. de
phys. (2) 9 (1890) p. 312).

3) Ramsay and Travers, Phil. Trans. A197 (1900) p. 81. Yet we must
remark that when comparing this ratio for helium and argon according to RAMSAY
and TRAvERS with the ratio of Dae according to our estimation and ba derived
from pe and TP}, we should find an important deviation (cf. note 1), Also in
view of this the data concerning mixtures of helium and neon are very uncertain.

4) TRAVERS, SENTER and JAQUEROD, Phil. Trans. A 200 (1902) p. 177. Their
views, however, on a connection between atomic weight and critical temperature
lead to an unlikely result for the critical temperature of helium.

The determinations of isotherms of neon by Ramsay and Travers, loc. cit.
have been of as little use to us as those of helium for the determination of a and
b (different particulars in the course of the isotherms of the one-atomic gases
given by these scientists in plate 2 loc. cit. do not seem very probable to us).

( 234 )

to be expected as a rule. Thus it appears from table II that these
pressures become very high, if the circumstances are not very
favourable.

It would have a very favourable influence on the circumstances
of temperature and pressure at which limited miscibility in the gas
state might be observed, if it should prove that for mixtures of
helium with another gas ajom is smaller than is expressed by
Vain dom )-

$ 9. Mr. van Laar’s remarks, (These Proc. May ’07 p. 34—46)
which imply that we have set forth some of our results as new,
whereas they had been already derived and published by him
before, compel us to the following explanations in order to show the
incorrectness of these assertions.

I. As to part of these observations, they are best retuted by shortly
repeating the train of thought followed by us.

When we applied the equations laid down by van per WAALS
with regard to the spinodal curve’) in Cont. II, $ 19 sqq., trans-
ferred to the y-surface for the unity of weight, to the case that one
of the components is a gas without cohesion*) with molecules which
have extension, we arrived on the suppositions‘) mentioned in § 2
at a plait which starts from the side of the small volumes, comes

1) These Pree. March ‘07 p. 796 note 1, and van per Waats These Proc. April ’07
p. 831.

2) The equation for the spinodal curve of the molecular ¢-surface (cf. VAN LAAR
These Proc. May ‘07 p. 37 at the top) was given by VAN DER WAALS in Cont. II. p. 45,

da db d'a 3
—, —= and —— passes imme-
de’ dx da? P

diately into that used by van LAAR. (See VAN LAAR, These Proc. May ‘0d p. 33
at the bottom). The equation given by us p. 788 referred to and was derived from
the equation for the J-surface for the unity of weight (These Proc. Dec. 06 p. 510).
For the rest we differ from the opinion repeatedly expressed by Van LAAR (inter
alia These Proc. May ‘05 p. 34), that it would be more difficult and more elaborate
to derive the equation of the spinodal curve and also that of the plaitpoint curve
from the y-function than to do the same from the @function.
8) This investigation was announced in Comm. No. 965, Dec. ’06 p. 502.

equation (1) In a form which after substitution of

2

)
4) When we were not allowed to put ST =O for and in the immediate
u

neighbourhood of v —b, as we did (cf. Van per Waats Cont. II p. 42), the spinodal
curve will always be closed towards the side y= b as Van per Waars observes
Le. and These Proc. April ‘07 p. 848. It is then to be expected, at least for

076
small da”

maximum plaitpoint temperature, and for the rest extends to the large v’s in the
same way as the plait described here.

that the plait in question makes its appearance for the first time at a

SS

( 235 )

into contact with the line «=O at a certain temperature, and crosses
m a slanting direction from v =b to the side «=O at lower tempe-
rature ($ 2 These Proc. March ’07 p. 787). Comparison of this result
with vaN Laar’s papers induced us then to cite (p. 786 footnote 1) that
the latter already treated the projection of the plaitpoint curve on the
v,a-plane for the case of a gas without cohesion, but without
further investigating the shape of the spinodal curve and of the plait
for this case. Now that van Laar (These Proc. May ’07 p. 35) says:
“The case that a plait starts from C,*) to C,?), or also at the same
time from C, to C, (when there is a minimum temperature in the
plaitpoint line) is not new (see KAMERLINGH ONNes and Kerxsom, p. 788
below), but has been before described and caleulated by me in all
particulars’, we have once more looked through his papers.

It would have been good if Mr. van Laar had indicated the place
where we had to look for this description of the plait treated in
$2 and indicated by van Laar in the italicized words (the italics
are ours); we have not been able to find this deseription in his
preceding papers even on this renewed careful perusal *).

That the shape of the plait described by us occurs for tempera-
tures above the critical temperature of the least volatile component
led us to the considerations on limited miscibility in the gas state
mentioned in § 3 sqq.

Always availing ourselves of the above mentioned equations of
VAN DER WAALS, we examined then if also with «,, > 0 such a plait may
occur for values as they are to be expected for mixtures with helium.
We saw in § 7 (These Proc. March ’07 p. 795) that for the case of
the plaitpoint curve running from XK, to X,, (called type I by van Laar)
3 cases are to be distinguished: a) that with falling temperature the
plaitpoint gets from A, on the y-surface, and proceeds regularly
towards K,; 5) that with falling temperature a plaitpoint coming
from X,, and one coming from A, unite to a double plaitpoint ; c)
that the plaitpoint gets from K, on the y-surface and proceeds
regularly towards A, (without double plaitpoint with minimum

1) Our Km.

2) Our Ky.

3) On the contrary he says in his paper These Proc. Sept. 1906 p. 231 (cf. Van LAAR,
These Proc. May 1905, p. 42 at the bottom): ““: In former papers it has been demon-
strated that in the neighbourhood of C, a minimum plailpoint temperature makes its
appearance both with type I in the line C,C, and with type IL in the line CA, and
that therefore with decrease of temperature a separate plait begins to detach itself
starting from C, at a definite temperature 7, (the plailpoimt temperature in Co),
which plait will merge into the main plait (or its branch plait) later on in an
homogeneous double point.

( 236 )

plaitpoint temperature). The conditions for the occurrence of these
cases were defined by us by means of the equations (2) and (3)
there. From this appeared that with very feeble attraction the case
a) occurs, with greater attraction the case 6), whereas with still
greater attraction case c) occurs (supposing the system to belong to
type I).

We have found neither the case a) as we already observed above,
nor the case c) in vaN Laar. We did find the case 5), chiefly with
regard to the treatment of what takes place at lower temperatures,
when three-phase-equilibria occur. For this treatment we referred
to VAN Laar (cf. These Proc. March ’07 p. 797).

From the fact that vaN Laar has declared this shape b) to hold
universally for type I (cf. p. 235 footnote 3; see also van LAAR p. 36)
it appears in our opinion, that vaN Laar has not only left the cases
a) and c) unmentioned, but has decidedly overlooked them. *)

Il. One more remark remains to be discussed. In $ 7 we put
as the {wo criteria of the case b), the course of the plaitpoint
curve being from A, to K, (see above), in which case a minimum
plaitpoint temperature occurs’ (supposing boom < dim):

and
aom/aum < — (1 — beem/bum) + WL — b22u/biim + (622m/611M)?-

Mr. van Laar points out (These Proc. May ’07, p. 45, appendix),
that the first-mentioned condition corresponds with a condition for the
occurrence of a minimum plaitpoint temperature, derived by him These
Proc. Dee. ’05, p. 581 fand VerscnarreLT These Proc. March. ’06
p. 751). In our opinion, however, Mr. van Laar is mistaken when
he thinks that the one condition stated by him is sufficient in all
cases to decide as to the occurrence of a minimum plaitpoint tem-

1) We might consider the course of the spinodal curves in case 0), if this is
also extended to values of «>1 and <0, and of v<b, as a more general case,
from which the cases q@) and c) might be obtained, at least qualitatively and
when we restrict ourselves to the region of the g-surface (Ll >a >0 and v <b)
that is of importance for the treatment of mixtures, This might be done by cutting
out a region bounded by «=O and «=1, and a suitable line v =} in the same
way as vaN per Waats These Proc. Feb. ’07, p. 621 sqq. treats the course of the
isobars (cf. § 7 p. 796 of this Communication). We have not found a single indication
that van Laar’s description of case b) is to be interpreted in this way; from the
phrase, quoted p. 235 footnote 3 e.g. we should much sooner conclude to the contrary.

At any rate the distinctions which are of physical importance, have not been
made.

230)

perature. Nor can his considerations of Dee. 1905 give an indication
to conclude to the occurrence of a minimum plaitpoint temperature
in the branch A, X,, of the plaitpoint curve. For there van LAAR
starts from the value of df} dv at the critical temperature of the
most volatile component called 7%, by us. The condition that at
Ti, the lower of the critical temperatures of the components,
dT, /de <0, implies that if the plaitpoint curve crosses from K, to
K,, a minimum temperature must oecur in it) Van Laar (These
Proc. May ’O7 p. 48), considers now the value of d7’,,,/dxv for the
least volatile component (for A,). It is clear in our opinion, that at
the /ighest critical temperature the condition d7,,,; /de <0, which
coincides with the first of the inequalities mentioned (cf. p. 797
last sentence of the alinea at the top), does not give any indication to
conclude to the occurrence of a minimum plaitpoint temperature.
That if for K, dT,,;/de <0, really one of the conditions for the
occurrence of a minimum plaitpoint temperature in the branch A,X,
of the plaitpoint curve has been fulfilled, van Laar has, in our opinion,
only shown by his considerations on the situation of the double
plaitpoint, not given until April (translated in These Proc. of May)
at the same time with his remarks, which considerations agree with
those which had led us a month before to the statement of the two
conditions mentioned.

1) Only if the plaitpoint curve crosses from K, to Ko, this condition is sufficient
to conclude to the occurrence of the minimum plaitpoint temperature (cf. van
Laar p. 46); for if the branch of the plaitpoint curve starting from Kv bends
round to van Laar’s point A (zl, v= bs; in our notation), we cannot speak
of a minimum plaitpoint temperature in the sense which is generally attached to
this word.

A similar consideration gave rise to our remark in note 2 p. 795, which
remark we are obliged to maintain in spite of Mr. van Laar’s contradiction,
p 46. (Wrongly Mr. van Laar thinks there, note 1, that in our note instead of
“maximum-temp.” ‘‘minimum-temp.” should be read, which might also immediately
appear by comparison with the cited text of VERSCHAFFELT).

( 238 )

Physics. — “Some remarks on the last observations of Prof. H.
KAMERLINGH ONNes and Dr. W. H. Keresom.” By Mr. J. J.
vaN Laar. (Communicated by Prof. H. A. Lorentz).

In the Proceedings of May 24 (1907) Prof. KaMmeRLINGH ONNES
and Dr. Kresom answered some remarks which | published in the
Proceedings of April 26 (1907) (in reference to their last papers).

I may be allowed to revert briefly to the chief points of this
answer.

a. P. 235, line 14—18: “It would have been good”, ete.

In fact the course of the plait in the case referred to by Prof.
KAMERLINGH Onnes and Dr. Krersom has not been given by me. I
confined myself to investigating the course of the plaitpoint line in
general. The results which I obtained on this point harmonize fully
with what was found by KAMERLINGH Onnes and KersOM. *)

b. P. 236, line 7—15.

In my papers published in These Proceedings only the case 5
has been mentioned (in which a minimum temperature occurs on
the branch C,C, of the plaitpoint line). The reason of this is, that
I then (7 June 1905 and 10 January 1906) only worked ut
the case 6,—=6,, in which such a minimum always occurs. *)
The formulae which 1 developed afterwards for the general

case hb, SG (see Teyrer I, II and ID, [which last publication (viz.

III) was delayed by circumstances independent of my will], contained
the possibility of the three cases a, 6 and c. As a matter of
course Prof. KAMERLINGH Onnes and Dr. Krrsom could not take this
yet unpublished investigation into account, and I only mention the
fact to prove that the possibility of the cases a and e had not
escaped my notice.

c. P. 236. “In our opinion, however, Mr. van LAAR is mistaken
when he thinks that the one condition stated by him is sufficient in
all cases to decide as to the occurrence of a minimum plaitpoint
temperature.”

1) At the same time I am glad to declare that I completely acknowledge the
priority of Prof. KamertincH Onnes and Dr. Keesom in bringing to light the possi-
bility of plaits which proceed without minimum from C, to C, and inversely
(cases a. and c. of KamertincH Onnes and Kresom), the knowledge of which is
necessary for understanding the behaviour of binary mixtures, containing as one
component a substance with weak attraction.

(Note added in the English translation).

2) Afterwards I have seen that also for b,=bg the case a. does occur, when

it is not supposed that 7) < 7). (Note added in the English translation).

( 239 )

I may remark about this that T have meant nothing else — which
it seems, I ought to have set forth more clearly — but to conclude
to the existence of the minimum temperature, when the plaitpoint
temperature at the extremity of the branch of the plaitpoint line
where the condition in question is fulfilled, is lower than at the
other end of that branch, in which case this one condition is really
sufficient.)

Th dae Jee Zal alle yale
In the Proceedings of the meeting of February 1907:

p. 660 |. 5 from the bottom: for “least” read: “most”
p. 662 table II in the heading read M/M, = 2

In the Proceedings of the meeting of March 1907 ;

p. 765 1. 13 from the top: read:

| (pua)er — (pra)e | __ d pwd ju
| t! TE t : a dt uw

dpva

dt
p. 778 1. 13 and 14 from the top: for a, read: «
p. 785 1. 17 from the bottom: ae

For the temperatures in liquid hydrogen first the correction is to
be applied which will prove to be necessary according to Comm.
N°. 952 § 3b and § 8

table VII, for: ay read :

5 EM a
p. 796 the value for ane given in equation (1) is to be multiplied
— wey

by V ay y/Q2om .

1) But I readily concede that Prof. KAMeRLINGH Onnes and Dr. Keesom have been
the first to deduce both conditions for the minimum and to take in consideration
the cases a and c. (Note added in the English translation).

(October 31, 1907),

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS OF THE MEETING

of Saturday October 26, 1907.

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

Afdeeling van Zaterdag 26 October 1907, Dl. XVI.

ENE Nen

H. ZWAARDEMAKER: “About odour affinities’, p. 242.

H. J. HAMBURGER: “A method to extract enzymes and pro-enzymes from the mucous membrane
of the digestive tube and to establish the topic distribution of them”, p. 250.

J. A. Bagmav: “The extension of the configuration of KUMMER to spaces of 2’—1) dimensions”.
(Communicated by Prof. D. J. Kortewse), p. 263. (With one plate)

Lucien Gopraux: “The theorem of GRASSMANN in a space of x dimensions”. (Communicated
by Prof. P. H. Scrovre), p. 271.

H. KaMERLINGE ONNEs and W. H. Kessom: “Contributions to the knowledge of the g-surface
of vaN DER Waars. XVI. On the gas phase sinking in the liquid phase for binary mixtures in
the case that the molecules of one component exert only a feeble attraction”, p. 274. (With
one plate).

C. A. PEKELHARING: “An investigation of Mr. J. W. A. Grwny, on the relation of pepsin to
chymosin”, p. 283.

P. Zeeman: “The intensities of the components of spectral lines divided by magnetism”, p. 289.
(With one plate).

P. vax RoMBURGH: “On lupeol”, p. 292.

E. van EvERDINGEN dr.: “Relations between mortality of infants end high temperatures”. (Come
municated by Prof. C. H. Winn), p. 296.

R. A. WEERMAN: “Action of potassium hypochlorite on cinnamide”, (2nd communication),
(Communicated by Prof. S. HoOGEWERFF), p. 308.

J. P. van DER Stok: “The analysis of frequency-curves of the air-temperature”, p. 309.

L. Bork: “Is red hair a nuance or a variety ?”, p. S21.

Erratum, p. 329.

16
Proceedings Royal Acad. Amsterdam. Vol. X,

( 242 )
Physiology. — “About Odour-ajjinities’. By Prof. H. ZWAARDEMAKER.

(Communicated in the meeting of September 28, 1907).

The great number of odours occurring in nature and in technics
may, by virtue of the current opinions in literature, be divided into
9 classes, which may be indicated by historical names '), chiefly
borrowed from Linnaeus. These classes are: etherial odours, aromatic
odours, odores fragrantes, moschus odours, allyl odours, empyreu-
matic odours, capryl odours, narcotic odours, odores nauseosi. I
have selected from each class a representative which, chemically
well characterized, can in a very simple way be made fit for olfac-
tometric investigation (by dissolving the chemically pure odoriferous
material in paraffinum liquidum *), with one exception, viz. muscon,
which is odourless in by itself odourless paraffine, and which there-
fore has been used mixed with myristine acid. They are:

isoamylacetate 0.5°/,

nitrobenzol 5°/,
terpineol 2.5°/,
muscon 0.627°/,
aethylbisulfide 1°/,,,
guajacol Af
valerian acid 1°/,,,
pyridine 1e
scatol BO ae

If in the double olfactometer two of these materials are joined
together, there occur among the 36 combinations thus obtained no
real mixed odours, but because they are counterbalancing each
other, either an odourless mixture or rivalry is obtained. Odourlessness,
respectively indefiniteness of odour, with change into odourlessness
by rarefaction of the airmixture, is met with, when the stimuli are
weak; rivalry, i.e. the alternate preponderance of one or the other
of the two mixed odours is met with, when the stimuli are strong.
However, also in the last case the impression, made by the mixture,
is considerably weaker than the impression that every odour by itself
brings about.

As unit of smelling-power I take the olfaction, i.e. the smallest
quantity of odour of a definite quality, which can be recognized

1) H. ZwAARDEMAKER, Physiologie des Geruchs. Leipzig 1895 p. 207.
2) Not water, but paraffinum liquidum has been chosen as a solvent because it
is desirable to work for months at a stretch with the same cylinders without

alteration of the solution.

( 243 )

by a normal organ of smelling (“Erkennungsschwelle”, “recognizing-
limit”).

If the above mentioned paraffinie solutions are evaporated at a
temperature of 15° C. and give off smelling material to a current
of air brushing past with a velocity of 75 cub. em. per sec.,
one olfaction will be communicated to the latter per 50 a 100
cub. em. of air by shoving out the cylindric evaporating surface to
a definite cylinderlength. This cylinderlength amounted on an average:

for the isoamylacetate-solution to 0.2 em.

» », nhitrobenzol-solution x OUR
» 9 terpineol-solution mehr Lb Pe
» 9, Muscon-mixture ROES .
» >, aethylbisulfide-solution ,, 0.015 „„
» 9 guajacol-solution = (OS 5
» », valerian acid-solution ,, 0.03 „
»» >» pyridine-solution OO 2
» >» seatol-solution a OHOUBS oe

In judging of this table, it should be taken into consideration that
the numbers have sometimes been obtained by taking the cylinder-
lengths during the experiment actually 10 or 12 times longer and
by rarefying the air in the reservoir that is smelled at, 10 or 100
times. Thus the objection was obviated, on the one hand that small
eylinderlengths should not be capable of being read with precision,
on the other hand that the evaporation should not regularly take
place from very narrow strips.

The mixing of the odours, which are to be joined together two
by two, took place in a common reservoir, which, provided with
two stop-cocks had been placed downstream the double olfactometer.
The symmetry of the latter, in view of the resistance offered to the
current of air, was previously examined by means of a bridge of
Wheatstone applied to air-streams, while the purification of odours
adhering by absorption between each number of two experiments
has taken place by a permanent stream of air and electric warming
of the wall of the reservoir. The reservoir in which the mixture
takes place was smelled at by means of a separate tube, the down-
stream cock being opened.

The 36 combinations procured indefiniteness of odour o1 rivalry,
if p olfactions of one odour and 9 olfactions of the other showed
a proportion of p/g, of the following amount :

16*

(244 )

PoACB hh.
MheBuine JN Degree of completeness 5)
Pa of the compensation
isoamylacetate and nitrobenzol 0 44 indefiniteness *
‘A » terpineol Ae) moderately acid additional odour
A » muscon 0.0625 indefiniteness :
5 „ aethylbisulfide 0.244 complete compensation*
5 » guajacol 3 indefiniteness
5 » Valerian acid 0.01 rivalry
5 » pyridine 3.6 indefiniteness *
5 „ scatol 0.0037 | indefiniteness
nitrobenzol » terpineol 1.375 indefiniteness *
5 „ muscon | 0.434 ;
a „ aethylbisulfide} 0.111 | rs
> » guajacol 0.65 | ke
5 » Valerian acid 0.03 _
» pyridine 3e =
5 » scatol 0.012 indefiniteness *
terpineol » muscon 0.125 5
5 „_aethylbisulfide 0.067 somewhat aromatic remainder
9 » guajacol de rivalry
5 » Valerian acid 0.05 almost complete compensation
” ” pyridine 0.53 ” ” ”
” ” scatol 0 q 12 ” ” ”
muscon » aethylbisulfide 1 indefiniteness
5 » guajacol 0.03 tolerably satisfactory
* » valerian acid Oru almost complete compensation
Pr » pyridine 1.2 rivalry
: » scatol 0.2 indefiniteness *
aethylbisulfide , guajacol 0.056 rivalry *
7 » valerian acid 1.2 indefiniteness
4 » pyridine 3.2 very indefinite empyreum. odour
5 » scatol 0.0075 indefiniteness
guajacol » Valerian acid 0.03 5
és » pyridine 0.016 indefiteness *
5 » scatol 0.0007 ;
valerian acid ,, pyridine 4 i
= » scatol 1.2 5
pyridine „ scatol 0,42 indefiniteness

The details of these experiments and more particularly the absolute
quantities which were made to be the foundation of each combination
of odours, will soon be communicated elsewhere in a more extensive
treatise.

The proportional number given in the table holds good, besides
for a definite average combination, also for an adjacent group of
stronger, respectively weaker stimuli. For this zone holds good the
rule that if p olfactions of an odour are compensated by q olfactions
of another odour, this must likewise be the case for np and nq
olfactions. Frcuner called the intensities of stimulus and sensation,

ij p<4
2) Marked with an asterisk are those cases in which by an intentional experi-

ment it has been proved that the proportional number is applicable to a certain
zone of stimuli.

( 245 )

mutually increasing and decreasing in due proportion, the cardinal
values of stimulus and sensation. By analogy we might speak here
of cardinal values of the stimuli counterbalancing each other, leaving
altogether out of the question whether this proportion will prove as
easily explainable as that which Frcaner has in view. The zone for
which the proportional number of the table holds good, may therefore
be called the zone of cardinal proportions.

From the fact that at a simultaneous impression two odours can
neutralize each other, it follows that the action of these stimuli on
the organ may be represented by two vectors, standing as it were
for two forces, which in general act more or less in opposite direc-
tions, the direction of the vector of the strongest odour (answering
to g in the table) being chosen in such a way that the co-sine
of the angle that it forms with the continuation of the vector of the
weakest odour (answering to p in the table) is exactly equal to
the proportion found for p/q in the combination concerned. For in
this case the vector of the strongest odour may be thought to be
replaced by the sum of two other vectors: one in a direction opposite
to the vector of the weakest odour, and one at right angles to it (in
the plane of the original vectors). If, moreover, the two original vectors
are given equal length, each with such a unit of length as the propor-
tional number implies, i.e. for the vector q and its components of g/p
times more weight than for the vector p, the neutralization of actions
that has to be symbolized by the original vectors, will have been
accurately expressed. For the vector p and one of the components
of vector q will represent equal, but opposite forces. We shall ouly
have to consider the direction of the other component of vector q
as direction of odourlessness, in order to have duly accounted for
the complete lack of sensation.

A second set of vectors can be placed in the same system, pro-
vided the two sets have one vector in common. Starting from of a
new proportional number p'/g’ the new third odourvector that has
been introduced, may then be given a definite direction with regard
to the first odourvector; also the second and third vectors may be
given their relative directions by means of a third proportional
number p"/g". The latter, it is true, can be done in two ways,
according as the third vector is reached by a right- ora left-handed
rotation starting from the vector answering to p, but of these two one
may be chosen. To the combination p/q belongs a vector of odour-
lessness at right angles to the vector of weakest odour and to the
combination p"/g" a vector of odourlessness at right angles to the vector
of weakest odour. The units of length of these vectors will in general

( 246 )

never be the same and also differ according to the combination that
one has in view. As, however, we have never mutually combined three,
but always two odours at a time, it will never be necessary to occupy
ourselves with the units of length of the three at the same time, nor
does this change of units, depending on the case considered, raise any
objection. Even in our further demonstration this does not give rise
to any difficulty, as we are never going to mutually compare vectors
but when they have the same direction with regard to an independent
vector that is at the same time considered, in other words possess
with respect to the latter about the same units of length,*).

A third set of vectors can, speaking generally, not be placed in
the same system, even though it has one vector in common with
the two preceding systems, for the fourth vector will in general
have to be given different directions, according as it is considered
in connection with the first and second, with the first and third or
with the second and third. But what is in general impossible, may
in special cases prove quite practicable. Let us consider this.

If we number our nine standard-odours with the figures 1 to 9
and likewise the corresponding vectors, each time two of these
vectors can be fixed and the rest arranged with regard to these two
vectors, which are definite in their situation. The question we put
just now, comes to this: Is the mutual relation between the odours
perhaps so as to make some of these last seven vectors coincide ?
In consequence of mistakes in the experiment a complete coincidence
will no doubt be out of the question, but let us consider whether it
happens within a margin of error of at most 1°/, of 2x difference
of direction (—3.6°). For this purpose we have first combined 1
and 2, considering all the others with regard to these two; then 1
and 3 are fixed, the rest arranged according to this, ete. till all
combinations, 36, have occurred. In each of the combinations seven
vectors were met with, whose situation with regard to the two
vectors previously chosen had to be traced in order to see whether they
coincided or not. For each set of two previously determined vectors
this gives rise to 42 judgments, so that in all 1512 judgments have

1) The proportional numbers as they have been empirically composed and taken
together in our table, form 252 possible constellations of three vectors. Among
them there is only one which, also as to the unils, is completely satisfactory for
all three proportions at the same time. It is the constellation in which terpineol,
scatol and valerian acid are combined. The length of the vectors measured by
means of a joint unit of length amounts in this case to | for the terpineol-vector, 8
for the scatol-vector and 20 units for the valerian acid vector.

( 247 )

been necessary for 36 combinations. However, as each case is repeated
once, there are in reality 756 separate judgments.

Just now we said it was necessary that never other vectors than
those about equally directed, which accordingly possess about the
same unit of length, should be mutually compared. If we keep this in
view, the following constellations are identical within a limit of 1 °/, :

isoamylacetate and nitrobenzol

; : each four times
valerian acid and scatol |

isoamylacetate and guajacol

nitrobenzol and guajacol .
each three times

muscon and scatol 5

aethylbisulfide and valerian acid

isoamylacetate and terpineol

isoamylacetate and aethylbisulfide

nitrobenzol and terpineol

terpineol and guajacol > each once
muscon and aethylbisulfide

muscon and valerian acid

aethylbisulfide and scatol

together 27 constellations *).

Some of these 27 constellations give rise to reciprocity, in such a
way, that the vectors which are identical to two previously deter-
mined vectors, make the latter identical, when they themselves are
previously determined in their mutual situation. This occurs in:

thd — | muscon | — isoamylacetate
and with regard to’ and ; with regard to: and
terpineol — scatol — | guajacol

Though the coincidence of two odour-vectors, if considered with
respect to two other odour-vectors, is already very remarkable, a
coincidence of 3 vectors is still more interesting. This has been
realized in the following cases, if we extend the limit of error to 2°/,:

1) This figure rises to 42, if besides complete coincidences also coincidences
with reciprocal values are taken into consideration.

( 248 )

\

isoamy lacetaat
terpineol with regaid to musccn end scatcl
guajacol

nitrobenzol |

terpineol ' with regard to aethylbisulfide and scatol
guajacol |

muscon |

valerian acid | with regard to isoamylacetate and terpineol
scatol |

aethylbisulfide |

valerian acid | with regard to nitrobenzol and terpineol

seatol

Even a coincidence of 4 vectors, has been found once, and that for:
isoamy lacetate

nitrobenzol ; ;
with regard to valerian acid and scatol
terpineol

euajacol

The planes in which the vectors of odourlessness, belonging to these
odours, meet, have the form of a cone, respectively with the vector
of valerian acid and that of scatol for their axis.

If we cast a glance at the sum of the results arrived at, it
is especially the coincidence of several vectors at the same time
which draws our attention: 4 vectors with regard to valerian acid and
seatol, 4 sets of 3 vectors each time with regard to two others.
Evidently there exists between the coinciding vectors agreement in
action on our consciousness for those definite cases. But some of the
coinciding vectors are repeatedly found together. Their mutual agree-
ment must therefore be of a more intimate nature, otherwise it could
not reveal itself so frequently and in so many different circumstances.
This closer connection exists e.g. between isoamylacetate and nitro-
benzol, which in no less than 4 cases become reciprocally identical
to 1°), of the circumference of the circle; a connection only a little less
close between nitrobenzol and terpineol, nitrobenzol and guajacol and
isamylacetate and guajacol, which do the same in 3 cases; a connec-
tion not quite wanting between isoamylacetate and terpineol and
terpineol and guajacol, where also these appear to coincide to 1°/,.

But also the vectors with regard to which the coincidence of

J

( 249 )

‘several vectors comes about, are closely connected with each other.
Valerian acid and scatol, with regard to which no less than + vectors
become identical, have 4 mutual coincidences, to 1°/, and also the
vectors with regard to which the coincidence of three vectors takes
place, show in 3 cases out of 4, a plurality of identity. Considered
from certain definite points of view, therefore, they must have some-
thing in common in their action upon our consciousness.

If we ask ourselves what physical importance the relations found
might have, it must be this that odour-mixtures formed from the
coinciding vectors possess fixants in common and these fixants will
have to be found in the odour-classes to which the vectors with
regard to which they are placed, belong. In perfumery are known a
number of such fixants rendering useful services with regard to certain
definite perfume-mixtures, which otherwise would not be durable.
In my “Physiologie des Geruchs” I have given a series of such
examples. Here we quote one borrowed from G. Conn’s “die Riech-
stoffe’. Artificial jasmin is obtained by joining together benzylacetate,
linalylacetate, linalool and benzylalkohol, mixed with some indol,
which serves “als Fixiermittel und zur Auffrischung des Geruchs”,
and which may be replaced by methylketol, scatol, propyldi-
methylindol, propylaethylindol, allylmethylindol, ete. With the aid
of our table it must be possible to devise mixtures that will furnish
available bouquets with fixants to be specified beforehand. Their
practical fitness for the perfume-industry will depend, besides on the
pure compensation-proportions, also on the velocity of evaporation
and diffusion of the materials used. In a practically available perfume
the latter should not differ too much.

The multidimensional character of the organ of smelling prevents,
alas, projecting a clear representation of all proportions of the different
qualities im their action upon consciousness. This is only partially
possible, for separate vectors, isolated from the whole. Yet it appears
that in general there exists a contrast between

isoamy lacetate
i aethylbisulfide
nitrobenzol 4 ij
‘ with regard to valerian acid
terpineol |
d \_scatol
guajacol

From a phylogenetie point of view the first group might be called
the food-odours, the second the putrid odours, if not in many a case
also museon should be added to the last category, for which reason
it is perhaps safer to refrain from any denomination. The arrange-
ment in each group is governed by the above mentioned reciprocities,

( 250 )

Physiology. — “A method to extract enzymes and pro-enzymes from
the mucous membrane of the digestive tube and to establish
the topic distribution of them.” By Prof. H. J, Hampurerr.

II. INTRODUCTION ; PRINCIPLE OF THE METHOD.

The method applied as yet to extract enzymes and pro-enzymes
from the mucous membranes of the stomach and the intestines consists
in preparing the mucous membrane and extracting it in a fine state
of division, with or without the addition of antisepties; by repeated
precipitation and dissolution the body to be examined is finally
obtained in a more or less pure state. If we wish to be informed
as to the distribution of the enzyme over the various parts of the
mucous membrane, in other words to establish the topic distribution
of it, extracts are made of equal weights or of equal surfaces, and
of these the specific action is determined quantitatively.

It need hardly be said that these methods are rather complicated
and lengthy as well. A great drawback more especially is, that in
extracting, the enzyme is polluted with so many other substances of
the mucous membrane.

Now, we have occupied ourselves for some time with the question
by what force enzymes (pro-enzymes) are brought to the surface of
the mucous membrane, and more especially tried to determine whether
we have to do with kataphoresis, in other words whether in normal
life enzymes (pro-enzymes) are carried along by the electric current
arising when the secretory nerve fibres are stimulated in the natural
way.') We will not dwell on the results of these investigations
now. Let us only observe here that the method consisted in laying
on the mucous membrane a small column of solidified agar-agar,
into which a platinum electrode had been melted; then it was in-
vestigated whether under the influence of a weak electric current,
moving from the muscular side of the mucous membrane, to the
free surface of it, enzyme or pro-enzyme passed from the epithelium
cells into the agar agar.

That, if the enzyme or pro-enzyme was indeed moved by kata-
phoresis it would also pass into the agar-agar, we had a reason to
expect after the investigations of GRAHAM®), VoieTLANDER*) and others

1) HAMBURGER. Ocmotischer Druck u. lonenlehre. Bd. Il. S. 433 ff.

2) Granam, Liebig’s Annalen 121, 1862 S

8) VorerLÄnpeR, Zeitschr. f. physik. Chemie. 3, 1889 S. 316.

For the literature on this subject compare, Conen, Vorträge für Aerzte über
Physikalische Chemie 2e Aufl. 1907 S. 128.

(251)

according to which the velocity of diffusion in colloids is as great
as in the water in which the colloid is dissolved.

If it should be objected that these experiments were made only
with erystalloids, the investigations of C. ErkmaN*) have shown con-
clusively that colloids can diffuse into other colloids (gelatine into
agar-agar).

But before trying to establish the influence of a constant electric
current on the transition of enzyme into the agar-agar, we wished
to know to what extent the ferment would diffuse into the agar-agar
without the introduction of the electric current.

Evidently this transition took place. This fact seemed to suggest
a means of extracting in an easy manner enzymes and perhaps pro-
enzymes as well, from the mucous membrane in not too impure a
state. Perfect extraction would, it is true, be unattainable in this
way, but there was a likelihood that the method might be employed
to determine in a simple manner the relative amounts of enzyme
in the various parts of a mucous membrane.

II. EXPERIMENTAL METHOD.

Parts of a glass tube having in our experiments an internal dia-
meter of 22 mm. and a height of 30 mm., were ground flat at one
end by means of emery and placed with that side on a glass plate,
plate glass being the best for this purpose.

By means of a pipette 3ce. of liquid agar-agar were put into each
little cylinder. I shall not discuss the way to prepare this liquid: it
is to be found in ail handbooks on the technics of bacteriology. It
must be observed, however, that it is advisable to let the agar-agar
solution cool down to + 45° before measuring it in the pipette;
otherwise there is a danger of its flowing partly away from under-
neath the glass cylinder.

After some time the agar colums have become solid and are placed,
still surrounded by the glass tube, on the spread out parts of the
membrane which, if necessary, has been previously cleaned. For this”
cleaning which also may serve to remove the mucus, we take
NaCl 0,9°/,. Investigations especially made for this purpose on the
gastric mucous membrane have shown, however, that for this organ
at least washing with water gives satisfactory results.

On the mucous membrane, which if necessary has been cleaned,
the agar-agar colums remain for 8 hours or more, in order to enable
enzymes and pro-enzymes to diffuse into the agar-agar.

4) C. Erkuan, Centralbl. f. Bakteriol. 29, 1901, S 841.

( 252 )

If the experiment bears upon the pepsin incl. the pepsinogen of the
gastric mucous membrane, the agar columns which have been on it,
are cut fine and mixed with 3 cc. HCI of 0.4°/,. For this we use
cylindrical bottles with close fitting glass stoppers: they have a dia-
meter of 24 mm. and a height of 48 mm. Into these bottles we put
albumen columns prepared according to Mett’s method. When these
have been in contact with the agar-suspension for 10 hours or more
at 37.5 C., we determine by measurement how much has been
digested; then the albumen columns are placed in it again and the
measurements are repeated a few hours later. In each bottle we
generally had two albumen tubes. Perhaps it will be objected that
the presence of solid particles of agar-agar must impede the action
of the pepsin on the albumen. This proves not to be the case: in
the first place we observe that on all 4 sides of the 2 albumen
columns always about the same column of albumen has been digested,
which most likely would not be the case if now and then an agar-
particle prevented the entrance of the digesting fluid. And secondly
we noticed that when the experiment is made with a liquid, from
which the agar particles have been removed by filtration, the rate
of digestion is the same as when the agar particles were still in
the fluid.

If the experiment bears only upon the pepsinogen of the gastric
mucous membrane, we place alkalie instead of neutral agar-agar on
it, viz. a quantity of agar of 2°/, in Na, CO, of 3 p. mille. The
investigations of LANGLeY’) have shown that in this concentration
pepsin is decomposed by Na,CO,, pepsinogen on the other hand not.

It stands to reason that besides pepsin and pepsinogen, chymosin
and prochymosin will also be absorbed by the neutral agar-agar.
It was found indeed that the agar-mass had obtained the faculty of
coagulating milk.

In a similar way as the gastric mucous membrane the intestinal
mucous membrane may be experimented upon. We found that the
neutral agar absorbs both enterokinase and erepsin. The quantity of
enterokinase present in the agar is determined by cutting fine the
agar, mixing it with water, si/trating, and bringing the extract thus
obtained, into contact with inactive juice of a fresh pancreas gland
and two albumen tubes.

The attentive reader will notice that here no agar particles are
present at the digestion of the albumen as in the case of the gastric

') Lanetey Journal of Physiology 3 1882 p. 253.
Lanetey and Epxins Ibid 7 1886 p. 371.

( 253 )

juice. They were removed before the action of the fluid on the
albumen tubes, because it was observed that the conversion of albumen
by trypsin was greatly retarded by the presence of the agar-agar.

To determine the quantity of erepsin, drawn into the agar, we made
the clear extract act upon the peptone.

We here append the results of some experiments carried out in
accordance with the method described above. More explicit state-
ments will be published elsewhere. Some further particulars concerning
the method of investigation are mentioned below.

Ill. Some EXPERIMENTS.

1. Distribution of pepsin (incl. pepsinogen) over the

gastric mucous membrane.

A pig’s stomach was cut into two symmetrical halves along the
great and small curvature and washed with NaCl 0.9 °/,. Then both
halves were spread out flat and on the spots marked below A, B, C,
ete. columns of neutral agar-agar of 2 °/, were placed.

Duodenum

(2548)

As will be seen A is situated in the cardea region.

B in the border region between cardea and
fundus part

C in the fundus region

Din the border region between fundus and
pylorus part

HE in the pylorus region

F on the duodenum near to pylorus.

With respect to this figure we must point out that for all our
experiments with gastric mucous membrane, the letters have the same
meaning.

In the experiment of which table I gives the results, the agar
columns of 3 ec. remained during 14'/, hours on the mucous mem-
brane. Then the agar was cut fine and mixed with 3 ce 0.4°/, HCI
and each of the mixtures thus obtained was made to exert its digestive
influence on two tubes of albumen.

The four numbers which in the following table are connected by
+ represent the lengths of the four albumen columns, digested at
the 4 sides of the two tubes.

TABLE I.
Digested after 121 hrs.

tee We be EY, ke Uig M. VA SE Sa
se iy Sla Fe + N= Din Bt late tst lasten »
„ad oa ag, |e... 2 2 - oo
I= ED SY, ye
1, P42 Ss, RENE TPE
woe Ye tg Mie UA im | Fee oe 2

23) te) AS) (op def PS

From this table is seen:

1. That in the cardia region (A and A’) the amount of pepsin is
small, increases towards the fundus (B and B’), reaches its climax
there (Cand C’) and decreases towards the pylorus (D and D’).
In the duodenum we also meet with pepsin, but its quantity is small.

2. The table shows that in both halves of the stomach the quantity
of pepsin was equal in corresponding parts.

If we speak here of pepsin we mean pepsin and pepsinogen. As
has been said before and will further be demonstrated pepsinogen

( 255 )

too enters the agar. It is by mixing with HCl converted into pepsin
and so determined quantitatively with the pepsin.
2. Distribution of pepsinogen.

As has been said, the investigations of LANGLEY ') have shown
that, contrary to pepsin, pepsinogen is not destroyed by a solution
of Na,CO, 0.3°/,. We have made use of this fact to try if we could
withdraw pepsinogen from the mucous membrane.

For this purpose agar columns were placed upon the mucous
membrane containing 2°/, of agar in a Na,CO, solution of 0.3°/,.
The column again had a diameter of 22 mM., the contents being 3 cc.

It must be casually observed that separate experiments had shown
that in such an alkalic agar mass, pepsin at once loses irretrievably
its digestive power.

To the method of experimenting we have not much to add. Let
us only mention that the alkalic agar, after having been in contact
with the mucous membrane was cut fine, neutralized with diluted
hydrochloric acid, then mixed with 3 cc. HCl of 0.4°/,. The purpose
of this was, to liberate the pepsin from the pepsinogen. The digesting-
experiments with albumen-tubes gave the results tabulated below.
Here the lengths of the 4 digested albumen columns have each time
been added together.

TABLE III.

The agar columns were kept on the mucous membrane for 20 hours.

Digestion of albumen after 8 hours. | Digestion of albumen after 18 hours.

AS. 0) MM Srl 3. 0) mM; AERO mim Mece Alen. 0) mi ME
B ONB DIEN Oly Piss Velosprord Een ie tz <n ore At fee
C SN Geen Oe, CNN LORE OU
D AAS ree! NIE D meen PEAT NE OO),
E AED ZN italy b ih. Aa a El en 2
ja OM sey ech erg ON Siu Jin S09 Ml 58 Leno i 5

It will be seen that from the cardea part (A and A’) no pepsinogen
was extracted. This need not surprise us; for in several experiments
with neutral agar, no pepsin could be extracted from it either.

In the border region between cardea and fundus, pepsinogen
was found, but in a small quantity. It was considerable in the
fundus (C), gradually growing less towards the pylorus (D and E).

1) Lanetey, l.c

( 256 )

3. To what extent does the length of time during which the
agar columns are on the mucous membrane, influence

the quantity of enzyme and pro-enzyme absorbed ?

For these experiments the stomach was divided into two symme-
trical halves. On one half two neutral agar-columns were placed at
A, B, C ete, and on the corresponding places of the other half
A’, B’, C’ ete. two columns of alkalice agar. One of the two columns
near A, near B, near C ete. was taken away and treated, after
having been on the mucous membrane for 18 hours; the same was
done with those near A’, B’, C” ete. The other series A, B, Cete.
A’, B’, C’ ete. was left on the membrane for 36 hours. In both
series of experiments the thus activated agar was made to act for
20 hours on the albumen columns. The tables will be plain now
without further explanation.

TABLE IV.
Determination of the quantity of pepsin and pepsinogen which had passed into
the neutral agar, after the latter had been on the mucous membrane for-

18 hours | 36 hours
A 0 m.M.digested | 21/5 m.M. digested
B 1 4 Sans, 3
IAD yc
DIN SSI a 5 | 7 7 »
ak a a lenie e :
Je ® ; » | 2 5 ”

TABLE V.

Determination of the quantity of pepsinogen which had passed into the alkalic
agar, the latter having been on the mucous membrane during

18 hours 36 hours

A' | 0 m.M. albumen digested, 1} m.M. albumen digested

Bis | SO 55 7 » | 25 9 ” ”
CES: SN i y 10, ” ”
JOP |) EE 5 » SE » » »
ENC, > 43 3 yy ” »

Lel 0 ” ”» ” 1 ”» » »

(257)

Both tables show that after 36 hours more pepsin and also more
pepsinogen had passed into the agar than after 18 hours.

Further a comparison of tables TV and V makes it evident that
the digestion of albumen in experiments made with neutral agar,
is more considerable than where alkalic agar has been employed.
This result may also tend to confirm the reliability of tbe method;
for into the neutral agar pepsin and pepsinogen may enter, the
latter of which under the influence of hydrochloric acid produces
pepsin, whilst in the alkalie agar only pepsinogen is found. And as
we have seen invariably in all our experiments, the quantity of
enzyme and pro-enzyme at identical spots of the two symmetrical
parts of the stomach turns out to be the same.

I wish to observe here that the digestion of serum-albumen takes
place much more quickly than that of the egg-albumen used. GLAssNER
was the first to point out the advantage of coagulated serum, and I
may confirm it from my own experience. Serum albumen has
moreover the advantage that without preparation such as cutting
up and filtrating, it can be used after simply being coagulated in
glass tubes.

Owing to accidental circumstances no serum-albumen has been
used for the experiments described in this paper.

4. Distribution of rennet-ferment.

To demonstrate the presence of rennet-ferment and to know its
distribution in the gastrie mucous membrane, about the same method
was applied as that used for the investigations relating to pepsin
and pepsinogen. Only the agar-columns had a greater diameter than
in the pepsin experiments, viz. 85 instead of 22 mM. The contents
accordingly were 5 ce. instead of 3 ec. Moreover it was self-evident
that the quantitative determination of the rennet-ferment had to be
effected in another way. The columns having been on the mucous
membrane for some hours, the agar was cut fine and mixed in a
test-tube with */, ce. HCI 0.4°/, and afterwards with 10 ec. of milk.
Then the test tube was plunged into a bath of water at 37.5°, after
which it was noted down every half minute where coagulation had
taken place.

The presence of some hydro-chlorie acid did not impair the expe-
riment. Previous tests had shown that in a mixture of 5 ec. neutral
agar '/, ec. HCl of 0.4°/, and 10 ce. of milk coagulation did not
set in till more than an hour after. As the following series of expe-
riments demonstrates the addition of only '/, cc. of HCl can hardly

17

Proceedings Royal Acad. Amsterdam, Vol, X

( 258°)

have had any influence of the coagulative action of the rennet-
ferment.

TABLE VI.

Coagulation is visible:

by A after 3 minutes; by A! after 3 minutes.

ED 2 5 BE ge i
Fp UO AL ' 9 (CAR pial 5
me We WE wp nf OU 9:
reece » E , 2M »

This experiment shows that the distribution of chymosin (including
pro-chymosin) runs parallel with that of pepsin (including pro-pepsin),
a result agreeing with the researches of others.*)

Secondly the experiment shows the action of the rennet in corre-
sponding parts of the two symmetrical halves of the stomach to
be equal.

5. Distribution of enterokinase in the intestinal

mucous membrane.

On the mucous membrane of the duodenum, jejunum, ileum,
ecoecum and colon, cut open length-wise,agar-columns were placed,
their contents being 3 cc. These having been left on it for 24 hours,
the agar-agar was cut fine and extracted with 3 ec. of a Na Fl-
solution of 2°/,. Then 6 ec. of diluted pancreatic juice were added
to 2 ce. of the filtrate. The former had been obtained by pressing
the pancreas gland of a newly killed pig, mixing the thick juice
thus obtained with a NaFl-solution of 2°/,, and filtrating the
mixture.

In the mixture of 6 ce. diluted pancreatic juice thus obtained and
2 ce. agar-filtrate two albumen tubes were placed.

By the side of this, controlling-experiments were made with 2 ce.
agar-filtrate and 6 ec. of Na Fl solution, instead of 6 ec. of the diluted
pancreatic juice. The digestion of the albumen was noted down
after 19 and 44 hours.

1) Nenckr u. Sieger. Zeitschr. f. physiol. Chemie 32 1901 S. 291; PeKeLHaRine.
Ibid. 35 1902 S.8; Pawrow u. Parastscuux. Ibid 42 1904 S. 415; Sawvatow.
Ibid 46 1905 S. 307. ;

( 259 )

The following table gives the results of one of the series of ex-
periments made.

7 TABLE VII.
2ee duodenum-agar 2ee jejunum-agar 2 ce ileum-agar
extract extract extract

IEEE | ace SOES jae) SEE +6 cc

pancreatic | NaFl. pancreatic | NaFi. | pancreatic | NaFl.
juice ‚solution | juice | solution | juice solution

Albumen
digested after

19 hours 7.2 m.M. 0 m.M. | 6.4 m.M. 0 m.M. | 5.6 m.M. 0 m.M.

Albumen
digested after
44 hours 12.4 5 Os 11.2 4 Olek 10 Ss ORE

This series of experiments shows the quantity of enterokinase to
decrease gradually downward, a result agreeing with that obtained
by CHEPOWALNIKOW, DELEZENNE, FroviN and Farrorsr.

I shall not diseuss the experiments here, which show that in the
digestion of albumen by trypsin the presence of agar has a retarding
influence, nor the influence which the time during which the agar
has been in contact with the intestinal mucous membrane, has on
the transition of the enterokinase. These questions will be further
discussed in a more explicit account.

One experiment remains to be mentioned, showing how the
enterokinase diffused into the agar, distributes itself over agar and
water, after the agar has been cut up and mixed with water.

5 cc. of liquid agar are mixed with 2 cc. of watery extract of the intestinal
mucous membrane. Of this mixture 2>3cec. are taken and poured into the
above mentioned cylindrical tubes. When the agar has become solid it is cut
fine and mixed each time with 2 cc. of water. The mixture remains for an hour
exposed to the temperature of the body in order to enable the agar to give up
enterokinase.

After cooling down it is filtrated, twice lee. is taken and mixed with 2 cc. of
inactive pancreatic juice. In both mixtures I and II albumen tubes are placed.

Besides this experiment another one identical with it, is made; only instead of
5 ee. of agar, 5 cc. of water are taken of course. Cutting up is out of the anes-
tion here. The quantities, however, remain the same.

17*

( 260 )

TABLE VIII.

Liquid, ) |Dizesien Experiment I Experiment II

5ccagar-2c :

wet ate | 4hours |1+1--1+1=4mm, [Ill mm.
of this 2X 3 cc
cut up; each

3 cc mixed

with 2 ce | 16 hours | 34+ 41/43¥+4—=15'm.m,| 31/)+3\.4+3Yy44=14Y% mm.
water; of this
2><1 ee mixed
each with 2cc |

pancreatic |25 hours| 6+5+6+5=22mm. | 5454 64+5=21 mm.

juice

5cc water + | 4 hours | 1/, + 1/4, +1 + 14 mm.) 1*,+1+14%,+15,=5 m.m.
2cc intest.extr.
of this 2x3 cc;
each 3 cc
ae Water; {16 hours | 4+ 444+4-+4= 16% mm. | 443% +44+44= 17mm,
of this 2X1 cc
mixed each
with 2cc of
pancreatic | 25 hours} 6 +5 4-5 +622 m.m. 5+5+5+6=21 mm.
juice.

This table leaves no doubt, but the method of extracting the agar
with water, gives reliable results. They turn out to be the same as
if the agar itself were water. The enterokinase must distribute itself
equally over agar and water.

We observed the same with pepsin.

Finally we shall describe a series of experiments, showing that
erepsin too enters the agar, and that this supplies us with a means
of determining its distribution over the intestinal mucous membrane.

6. Distribution of Erepsin.

The 2°/, agar used was not dissolved in water, but in NaFl of
2°/, because the amount of erepsin, passing from the intestine into
the agar during the time taken up by the former experiments, was
not great enough.

Therefore it was expedient to leave the agar for at least 24 hours
on the mucous membrane, taking care to prevent putrefaction as
much as possible.

( 264 )

The action of erepsin consists as we know in its power to change
hemialbumose and peptone into products not giving the biuret-reaction.

Vernon *) has based on this a colorimetric method, to determine
the degree of conversion brought about by erepsin and Farrorse ?)
among others, has successfully used it. We too have applied this
method, in a somewhat modified form, however. It chiefly consisted
in a solution of CuSO, being mixed with a NaOH solution. The fluid
thus obtained imparts a violet-red colour to peptone. The more the
peptone solution from whieh we started is converted by erepsin, the
fainter the violet-red colour will be. It was now investigated, with
how much water the standard liquid had to be diluted to produce
the violet-red colour observed.

One of our experiments gave the following result.

In the peptone-solution (Wrrre) on which the duodenal-extract
has acted, are 46.2°/, of the original quantity of peptone left. In
the peptone-solution acted upon during the same time by the jejwnum-
agar-extract are still 16°/, of the original quality of peptone left,
and lastly where the c/ewm-agar-extract acted during the same time,
14°/, of the original amount.

It follows from this that in jejunum and ileum there was more
erepsin present than in duodenum, which corroborates so far FarLorse’s
results inasmuch as we too found much more erepsin in jejunum
than in duodenum. In the ileum, however, the amount of erepsin is
much greater than in the duodenum; Farrorse, indeed, notes a diffe-
rence in the same direction, but it is only slight. It must be kept
in mind though, that our experiments relate to the pig, FALLOISE’s
to the dog.

T may add that in Pryer’s plaques hardly any erepsin or entero-
kinase was found.

A number of experiments, made for the researches described above,
have been carried out by Mr. R. A. B. Oosrernuis, Med. eand.,
assistant at the physiological laboratory.

CoNcLUSION.

The above researches have shown:
1. That when agar columns are placed upon the mucous mem-
brane of stomach and intestines, enzymes and pro-enzymes are

1) Vernon. Journal of Physiology. 30, 1903, p. 330.
2) Fattoise. Archives internat. de Physiol. 2, 1903/4, p. 299,

( 262 )

absorbed from them and enter the agar. As such were examined
pepsin, including pepsinogen, chymosin and prochymosin, enterokinase
and erepsin.

2. The above-mentioned ferments can be extracted, partly at least,
by water from the agar-agar. Quantitative investigations have shown
even that pepsin + pepsinogen and enterokinase as well, distribute
themselves equally over the agar and water.

3. The facts mentioned sub 1 and 2 suggest a simple means of
extracting the above-named ferments from the mucous membrane,
and of determining quantitatively the distribution of them.

We have only to leave solid agar-agar columns of equal dimensions
on various parts of the mucous membrane for some time and make
subsequently a comparative quantitative determination of the specific
action of the watery agar extract.

4. The results obtained with this new method with respect to
the distribution of the above-named ferments in the digestive tube of
the pig confirm those obtained by most investigators with the usual
extraction methods on the dog. .

5. The advantages of the method over the usual one consist,
besides in its greater simplicity, also in the fact that the enzyme
under investigation is much less polluted by decomposition products
of the mucous membrane.

Especially for the investigation of the distribution of enzymes in
individuals who, when alive suffered from diseases of the stomach
or intestinal canal (ulcers in the stomach, the intestines, etc.) the
method seems to me likely to be of use.

Moreover it is to be expected that besides the ferments examined
till now, others will also pass into the agar-agar, which will enable
us to make quantitative determinations of them in a similar way.

Finally the method seems to me to deserve recommendation as it
can be applied in experiments at a lecture; at the same time, by
adding congo-red or a similar indicator to the agar, the amount of
acid or alkali can be demonstrated ocularly.

Groningen, September 1907.

— _—

( 263 )

Mathematics. — “The extension of the Configuration of Kummer
to spaces of (2?—1) dimensions.” By Mr. J. A. Barrav.
(Communicated by Prof. D. J. Kortewsc.)

(Communicated in the meeting of September 28, 1907).

. u a b . np
$ 1. If we represent by |S, the system Dt built up out of two
a
letters and by S, the same system in new letters c and d; if like-

wise we represent by 7’ the system of signs ee and by —T the

opposite ~ we obtain by connecting these
: Te He
and
or T —T

the two systems

Geode ee
ba de Se
and
cd abt IE
ae ba + —-— +

By giving each row of four letters in turn the signs of each row
of the system of signs sixteen quadruplets of algebraic quantities
appear which, as is known *), represent the elements of the Cf (16,)
of Kummer whether they are considered as homogeneous coordinates
of points or as coefficients of planes in Sp,. For, to each element
are incident the elements of another kind, represented by the three
permutated letter quadruplets and for each of them with half ofthe
sign combinations.

§ 2. If now we call S, and 7 the letter- and the sign-system
of 4 resp. and if we repeat the combination described above such-
like systems of 8 are formed of which that one of the letters
furnishes the permutations of a regular G, of order 8 *), consisting
exclusively of binary substitutions, whilst that of the signs is anallag-
matic*), i.e. every two rows show as many sign variations as

1) See a.o. Jessop Line-Complex p. 23 or Hupson Kwmmer’s Surface p. 5.

*) Compare Mitten Quart. Jowrn. 28 p. 255, group 8 No. 4.

3) Lucas Récréations Mathématiques Il p. 113; Nieuw Archief voor Wiskunde
7 p. 256.

sign-permanencies. The systems

differently arranged):

I a
IIb
Ill | c
IV d
Vv e
WAU Were
VII | g
Vill A

h
&

S

nc en

( 264 )

_

+ettt +

ou 9 oO fF WO ND
+

+4 +

EN)

become (that of the signs somew hat

+ +

++
=

|

|

|
|
En
ni
+++

3y providing each of the rows of letters with each of the sign-
combinations there appear sixty-four octuples of algebraic numbers
to which we assign the notations 11, 12,.... VIII8. Whether we
consider these numbers as homogeneous coordinates of points or as
coefficients of equations of Sp, in a Sp,, each element is incident to
7 < 4—= 28 of another sort, namely to half of the sign combinations
of each letter permutation; so a Cf. (64,,) appears, to be designated

by KYU,

As with KU it is possible to combine the Cf-elements to sim-
plexes A, B, C, D, E, F, G, H in various ways. Such an arrange-

ment is 1. a.:

The table indicates that eight vertices of e.g.

et {Gij teal (SS) eeh eS

1 2 3 4 5 6 7 8
11 14 | m5 | IV3 Vari VIS | VII6 | VIII2
12 117 16 | IV8 V4 VI3 | VII5 | VIILI
13 116 Td vA V5 VI 2 | VIl4 ; VII8
14 1 HIS | IV6 V2 VI5 | VII3 | VIIL7
15 118 1 | V7 V3 VI 4 | VII2 | VIII6
16 113 Wl2 | 1V4 V8 VI 7 | VIT1 | VIILS
17 112 3 | IV 5 VI VI6 | VIIS | VIII 4
18 115 OCS ey V6 VI1 | VII7 | VIS
|

the simplex A are

resp. the points 11, I14 ete, according to the former notation, whilst
at the same time the eight opposite side-Sp, of the simplex are

represented by those same notations.

( 265 )

The connection of Cf-elements can now be represented by a diagram
(pl. I) the rows of which indicate the Sp,, the columns the points,
whilst incidence of a Sp, with a point is indicated by hatching the
square common to the respective row and column.

We see that the diagram can be brought to a more condensed
shape :

A B C D E F G H

ke b (2 d Ne

Bae SEE f e ie Nee
€ ae Be AF ale Nina
Die aia Mali eee Sil) CZ b a \a
te aun ie 7 ee tae Ae
Pea |e po. tats reat at ae all
G allie at me a b g S e
onee essen? a6 ens,

Here |S indicates a simplex-filling; each of the other letters a system
(8,) denoting the incidence connection between the elements of two
simplexes. These systems (8,) have all degenerated into two (4,), each
pair of our simplexes is thus connected in an equal way and forms
a Cf (16,,) of the same type.

§ 3. Analogous to the well-known decomposition of AZ” into
four tetrahedra lying in pairs in a Moésius-position, it is obvieus
to call the position of two of the simplexes, e.g. A and B, by
that name. Each side-Sp, of one S contains three points, so a
face, of the other; each vertex of one lies in three side-Sp,, so
in a side-Sp, of the other; the correspondence is such that opposite
elements of A, e.g. vertex A, and side-space A, also furnish opposite
elements of B, namely resp. the side-Sp,: 5b,5,6,8,B, and the
face B,B,B,, just as this is the case with the tetrahedra in Mögrus-
position.

There exists already however, provided with the same property,
an extension of this notion, that of Brrzorarr *) where each side-Sp,
of one S contains one vertex of the other, and is generated by
operation with a focal system on an arbitrary simplex; let us call
this position MJ, then it is evident that the discussed more specialized
MII is to be regarded as a threefold M /.

1) Rendiconti del Circolo Matem. di Palermo 22.

( 266 )

The elements of two simplexes A and B in M [1 can be arranged
only in one other way to two suchlike simplexes, namely as
first simplex Ps: A, As Ay, AB BDR
second _ QED B B,, Be Aen
If we regard such a new simplex in connection with C, D,... H,
it then shows with each of these a new sort of position; for all
however of the same type, showing analogy to the pairs of tetrahedra
in STEINER-position which can be separated in the same way from
KU, We find for the cf (16,,) of two such simplexes a diagram
of the shape:
Soe
xX S,
where w again represents a system (8,) which however does not dege-
nerate now, but is identical to the cyclic system which is obtained
outsof. the initialorow: ARAS wonen
Opposite elements of one simplex furnish, as in Sp,, no opposite
ones of the other.

§ 4. The 28 operations determining in each c/-space the cf-points
incident to them and reciprocally, are focal-correlations; thus e.g.
the Sp,: A,

(Ha db, te dd, He Hfst 9 +4)
is transformed into the point A, situated in it
(+ 6,—a, + d,—e,+f,—e +h, — 9)
by operating with the skew-symmetrical determinant of transformation :
OET 0-00 0. 0 Oe nom

| Oe tO m0 VOU

{
|

0
0
reo
0
0

|
| OETROPE OM OO Oe Ole

These focalsystems are mutually in involution as the group of the
letter substitutions as well as that of the sign variations are ABEL groups.

The 36 remaining reciprocities are polarities with respect to some
36 quadratic Sp,, which serve for KVL as the 10 fundamental-
surfaces of order two for KU!

1) Martinerti, Rendic. Palermo 16 p. 196.

( 267 )

Their equations are of two types; namely eight of the form
Se es a ee Se ae ah ig ait Biden nt ae = are
where the combinations of signs must be derived from the sign
system; and twenty-eight of the form:
SE OF Gy SS SS ayy Sere =U

where the connection of the indices is given by the seven binary
substitutions of the regular (,, whilst the signs must be selected :
ee
oe — =
== — —

ee

|

++4+4

The sixty-three operations which transform an element into another
of the same sort are collineations; so we obtain, analogous to the
Kran G,, in Sp,, a geometrical Ase. group G,,,, consisting of the
identity and sixty-three collineations; twenty-eight focal systems in
involution and thirty-six polarities.

§ 5. The twenty-eight points in each Sp, of KV" lie on a qua-
dratic Q, and reciprocally.

To prove this we regard the determinant of the terms of order
two, formed of seven of the eight homogeneous coordinates; so this

9 see 5 .
is of order 7 + (7) = 28. The omission of a coordinate is geometri-

cally the projecting out of a vertex of the fundamental simplex on
the opposite Sp,; if the projections of 28 points lie in it quadrati-
cally, then the points themselves do so in their Sp,

Let us first restrict ourselves to Sp, : A,

The twenty-eight points are to be divided into seven quadruplets
of the same order of letters; the purely quadratic terms within such
a quadruplet are in each column alike, the mixed ones may differ
in sign. Let us call the four terms in a column p, q, 7, s, then the
substitution

Pompe gor ts rene BE att |
Q=pt+q—r—s |
R=p—qtr—s ’ oe 1 —1
Ip qr de fe ee, Vl

causes three of the four quadratic terms to disappear, the A,, breaks

up into the product of a A, of quadratic and a A,, of mixed
terms. Here

lof which is -- 0,

That in general A, =

=0 is evident i. a. from

hdi

The A,, gets after change of signs of some rows the form:

OM ON 0
OM KON 20
0 | bd |—be

ROMEO 0

leon 0.40

—cd, 0 | be
OF 0) 0
OF RKO RD
cd |—bd| 9
0 | 0 |—eh
0 |—eg) 0

—ef| 0 | 0
0 fal 0
Oh) WF ieee

lef | 0 | 0

—gh| 0 | 0
0 | 0 | fg
0 | eg | 0

| gh| 0 | 0
0 | fh| 0
0 | 0 | eh

0 | bh
—be, 0
0 | 0
ch, 0
0 |—ce
0 | 0
0} 0
dg |—df|
0 | 0
0 | 0
ON kee,
be | 0
0 | 0
0 | df
0 | 0
0 | 0
—dg| 0
OMO
0 —bh
—ch| 0
0 | 0

ORO 0) | =ak
0 |—af| ae | 0
CT OV OY)
0 |dg| 0 —de
0 | 0 |d| 0
OF MOR ROR S90
0) | 0. eg: Sch)
Omi cA) Ork
—ac, 0 | 0 | 0
On ONO
—fh| 0 | 0 | 0
0 |af| 0] 0
—eg) 0 | 0 | de
0| 0/070
0 | 0 |—ae, 0
0| 0! 0 | ah
0 |—ch| 0 | 0
fh | 0 —dr 0
o/o 00
eg |—-dg| 0 | 0
0 | O |—eg\ 0

0
0
0

df |—de| 0 |—cf\ ce | 0
0 | 0 | dh} 0 | O |—ch
OOF ONION MONO
0 ah 0 —be, 0 | be
—ag| 0 | ae} 0 —bh| 0
Oe Or Ow KON o
0 |—bg bf —ah| 0 | 0
—bh| 0 | 0 | 0 —ag af
OTO OM OM KONI ©
0 (bel 0 | ak} 0 | 0
ag || 0 |, 0) |) OD fons so
ORO | OF OR NOM Ke
0 ah| 0 |bg( 0 | 0
bh 0 | 0 | 0 | ag| 0
0 | 0 |—dh| 0 | 0 | O
0 |de| 0 | cf| 0] 0
0] 0] 0) 0 } 0 \=aF
0 | 0 |—ae 0; 0} 0
—df| 0 | 0 | O |—ce}| 0
OVEN Oe OON ONE
oy |) © —4f| OMO

fh

QO

| ac

bd

( 269 )

The sum of the numbers in each column amounts to zero; so
A a

As each element with the 28 incident to it can be transformed
into any other by means of a direct or reciprocal projectivity, the
quadratic position of every 28 is now proved.

§ 6. Each coupleof Sp, of the cf has twelve points in common lying-
thus in a Sp,. No other Sp, containing these twelve, all these Sp, differ

2
and their number is ce) = 2016. The cf-points form with them a

cf (64,,,, 2016,,).

There are triplets of Sp, which have six points in common, lying thus
in a Sp each cf-Sp, has namely in still 32 Sp, siz of its points.
Such a sextuple can be deduced from three groups of twelve, their

2016 x 32 8
number is thus En they form with the cf-Sp,
a cf (21504,, 2016,,).

There are quadruplets of Sp, having four points in common which
therefore determine a Sp,; each cf-Sp, has namely four of its six
points in fifteen other cf-Sp,. Every Sp, can be derived from four Sp,,

21504 « 15
their number is thus oa = 80640. They form with the ef Sp,

a cf (80640,, 21504, ,).

There are sextuplets of Sp, having three points of the cf in common,
which therefore determine a Sp,; each cf-Sp, has namely three of
its four points in eight other cfSp, more, these eight Sp, furnish two
by two however the same triplet; as furthermore each Sp, can be

2 4 … 80640 « 4
deduced from (5) = 15 Sp, their number is —————— = 21504.

15

€

This could be expected as the whole consideration starting from the
ef-points might have been put reciprocally, and would then have
led on account of the self-reciprocity of the system to the same
elements; so still 2016 Sp, are obtained, the right lines of con-
nection of the pairs of points.

The further amounts of incidences of the kinds of elements
mutually can now be easily deduced; the notation of AV
becomes finally:

Sp, SPee SP: Sp; Sp, Sp, SPs |
64 | 2016 | 21504 | 80640 | 21504 | 2016 | 64
incident to: | d |
Sp, = 2 3 4 6 12 | 98 |
Sp 63 Bc ill, dâ 15 | 66 | 378 |
Sp, 1ooen sane | a | 460 | 9016 |
Sp, 5040 | 240 | 45 | — | 15 | 240 | 5040 |
Sp, 2016 | 160 | A | 4 | — | 32 | 1008 |
Sp, 378 | 66 | 15 | 6 3) ||) ce
Sp (BNA Ghat a 3 2 a

By the method of intersecting and projecting triplets and doublets
of consecutive kinds of elements are to be transformed into elements
of Sp, or Sp,; thus are formed e.g. a cf (21504,,) of points and
planes, with 80640 cf-lines; and a plane cf (2016,,, 21504,) of
points and lines, or reciprocally.

§ 7. If we represent the system of letters and that of signs of 8
resp. by S, and 7 and if we repeat the combination

Sib) Si T —T,
we obtain systems for 16 belonging to each other, etc., the operation
allowing of indefinite continuation; one always arrives at a regular
ABEL substitution group Go? and a suitable anallagmatical system
for the signs.
These always furnish in Ze”, a cf, analogous to that of KUMMER

with the notation :
a 2p
Ch Car ;

arising from an arbitrary starting element by an operation with a
geometrical ABEL group :

the identity and 2%— 1 collineations on one hand

and (2p —1). 2e! focal systems mutually in involution with

(2e+! — 2 + 1). 2?—! polarities on the other hand.

The quadratic situation of the elements incident to one element
can always be proved by reduction of the determinant according
to the example of $ 5’).

1) A more extensive treatment also for spaces of other numbers of dimensions
will follow in the dissertation to be published: J. A. Barrau, Bijdragen tot de
theorie der cff. (Amsterdam 1907).

Proceed

J. A. BARRAU. “Analogon of the configuration of Kummrr in Sp,.”

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A B C D E F G A

Proceedings Royal Acad. Amsterdam. Vol. X.

(274)

Mathematics. — “The theorem of GRASSMANN in a space of n
dimensions” By Lvcmn Gopravx, at Morlanwelz (Hainault).
(Communicated by Prof. P. H. Scuoure).

We shall designate by the letter S a linear space and the number
of dimensions of this space shall be the index.

The notation VJ represents a variety, the locus of oo? elements
and of order j.

The order of a variety, locus of spaces Sj, occurring in an
(n—k) (kH1) —1 times infinite number in a space §,, is the number
of Sj, of an Sp, through an S,—, of this S;,41 and belonging to the
variety.

1. In an S, the theorem of GRASSMANN can be read thus:

The locus of S, for which the S, which unite it to
three fixed S, meet three fixed S, in three S, of the
same S, is a variety V3.

In an S, it has been given it the two following forms:

The locus of an S, for which the S, which unite it
fo tour. fixed .S; meet four fixed Sr in four S, of a
same S, is a V3. (Le Pater, Sur la génération de certaines
surfaces par des faisceaua quadrilintaires, Bul. de Belgique, 1884,
3e série, tome VIII).

The locus of an S, for which the S, which unite it
to four fixed S, meet four fixed S, in four S, of a
same S, is a V$.

2. Let there be in an S, & S,, which we shall designate by A; and
k Ss, which we shall designate by B;, “(= 1,...h).

Let p be a number satisfying the 2% inequalities

ie Pel See ees eis 8 wo Cy
Ope!) eles NA) (2

A space S, determines with the & spaces A; k spaces Sp
These spaces meet the corresponding spaces B; in k spaces
Srjsjtpntl

If these & spaces belong to an Sjn

Z (rite) + (pn t2)—1)

the space S, describes a variety V(n—»)(p4+1)—1 the order of which
is to be found.
Let us suppose we have
z = (ri +s) + k(p—n+2)=n4+1..... . (8)
Let C be an Sp: and Dan S,-_; of C.
Let us designate by A an S, passing through D and situated in C.

Let us take £— 1 spaces A and let us number them 1,...7—1,

7+1,..4
These £—1 spaces A determine with #—1 spaces A; suitably
chosen /;:— 1 spaces S,4,41. These spaces meet the corresponding
t

spaces B; in k—1 spaces S,4s.4)—np1,(=1,.-.,J—1,j+1,...%)

These spaces determine an Si=j—1
Sos (ribs) +01) (p n+2)—1

il
This space has in common with B; a Hee
Sijs 1 i=n .
re + 2) — An — 1
tl i=j+1 dell
In its turn this space determines with A; a space
Si=zjt

B ey) 4G pe eee

i=1

On account of the equality (8) the Jatter meets C in a single
point, which determines with D a space Aj

When j varies from 1 to #%, one obtains & series of spaces A
between which exists a (1,1,...1) correspondence. There are 4
coincidences.

X I
The variety described by the space Sj is Veena
The locus of a space S, for which the 5,4,41 which

unite it 10 # fixed spaces iS, meethk Sin &S, rekent

of a same B E(ritsi) Pk(p—n 2? C= 1 En is a va-

k
riety Vi—p) (pil -

The spaces A; are evidently principal spaces of the locus of Sy,
principal space having the same meaning as principal point or plane
of a complex of rays.

In S, we find the following theorem:

The locus of an S, for which the S, which join it to
four S, meet four S, in four S, of a same space 8, is
a variety V! (complex of order four).

3. If we regard the ordinary space as if generated by right lines
we have a geometry of four dimensions. We shall now show two
generalizations of the theory of GRASSMANN in this geometry.

Let us imagine & linear congruences G,,... Gx, and X plane pencils
(Pr), (Pe, rp). Let us imagine moreover to be given a linear
system C of linear complexes to the amount in number of oF.

An arbitrary right line g determines 4 linear complexes with the

5 congruences G. These have in common with the # corresponding
plane pencils & lines p,,.. . pk-

Let us now find the locus of the line g when the & lines p
belong to a same complex of the system C.

Let (A,a) be any plane pencil. Let us take £ —1 lines of this
pencil and let us number them 1,...7—1, i+1,...h.

Each of these lines determines with the corresponding congruence
G a linear complex, which has in common with the corresponding
plane pencil (P, 2) a line p. The &—1 lines p found in this way
determine a complex of the system C. This complex has a line
pi in common with the plane pencil (P;, 2;). This line determines
with G; a complex having a line a; in common with (A, a). When
z varies from 1 to & we have & series of lines a between which exists
a (1,1,...1) correspondence. There are & coincidences.

The locus of a right line for which the linear com-
plexes that it determines with k fixed linear con-
gruences meet & fixed plane pencils in & lines ofa
linear complex of a system of 6—% terms is a complex
of degree & (order and class) to which belong the given
k linear congruences.

If } = 6, we have a theorem of GRASSMANN.

4. Let us suppose five groups of three lines H,,...H, and five
nets of lines R,,... R,.

An arbitrary line g determines with H,,... H, five linear congru-
ences which meet the five corresponding nets in five lines. If these
five lines belong to a selfsame linear congruence the line g describes
a congruence.

Let z be a plane. Let us consider in this plane five series of lines p,,...ps.

Between the lines of these series it is easy to see that there is
such a correspondence that to four 1ight lines corresponds a fifth.

Let us suppose that three right lines are fixed, whilst the fourth
describes a pencil. It is then easy to verify that the fifth also de-
seribes a pencil. According to an extension of the principle of ZEUTHEN
there are fifteen coincidences.

The locus of a right line taken in sucha way that the
linear congruences which it determines with five
systems of three lines have in common with five nets
five lines of a same linear congruence is a congruence
of the fifteenth class.

In the same way we can verify that this congruence is also of
order fifteen and that it contains the generatrices of the same kind as
the given lines of the five quadratic surfaces determined by these lines.

18
Proceedings Royal Acad. Amsterdam. Vol. X.

(274)

Physics. — “Contributions to the knowledge of the y-surface of
vin DER Waats. XVI. On the gas phase sinking in the liquid
phase for binary mixtures in the case that the molecules of
one component evert only a feeble attraction.” By Prof. H.
KAMERLINGH ONNES and Dr. W. H. Kexsom. Supplement N°. 16
to the Communications from the Physical Laboratory at Leiden.

§ 1. Introduction. In Comm. N°. 96%, These Proc. Dee. 1906,
p. 501 a gas phase sinking in a liquid phase’), the barotropic pheno-
menon, was treated for binary mixtures for a gas liquid plait, which
crosses the y-surface as a transverse plait at lower temperature. Then the
treatment for temperatures, at which the appearance of a longitudinal
plait brings about a disturbance, was deferred to a later communi-
cation. Moreover, more special cases, as the appearance of minimum
or maximum Critical temperature or minimum or maximum pressure
of coexistence, were left out of consideration, and the discussion
was restricted to the case that retrograde condensation of the first
kind occurs.

When for binary mixtures the conditions for the sinking of a gas
phase in a liquid phase were treated in Comm. N°. 96°, These Proc.
Dec. ’06, p. 508 and Febr. ’07 p. 660, it appeared in the first place
that at least if the hypotheses mentioned there are valid, and pairs of
substances are found with proper aasa/aim, 022M/Oi1. and M,/M,
the theory of vaN per Waars’ yw-surface leads us io expect that
barotropic plaitpoints *) will occur. *) Further that for mixtures with

1) Considerations which are not in accord either with the limited compressibility
of a gas at high pressures, first stated by Natrerer in 1844, or with our present
views on the mixing of two substances, induced Jamin, C.R. 96 (1883) p. 1448,
Journ. de phys. (2) 2 (1883) p. 389 to raise the question whether it should be
possible that with compression of a mixture of GO, with air or with hydrogen, a
liquid phase would collect above the gas phase. Caituerer (Jamin |.c.) did not succeed
in realizing this.

2) On the peculiar phenomena which are met with in case of a barotropic
plaitpoint, we hope shortly to make a communication.

3) That the barotropic plaitpoit found in Comm. N’. 96c, Dec. "06 §5 belongs
‘o the gas liquid plait (cf. Comm. N°. 96c, Febr, '07, p. 660 footnote 1) was derived
rom the shape of the spinodal curve for this case, in connection with the course
of the plaitpoint curve. The same thing may appear as follows: By applying the
criterion (3) in Suppl. N°. 15, March ’07, p. 796, we find that mixtures of a pair of
substances of ratios indicated in the mentioned § belong to case (c), (cf. p. 276)
while we may derive from van Laar’s fig. 22, Arch. Teyrer (2) 10 (1907)
p. 138, These Proc. Sept. '06, p. 226, fig. 1, that the plaitpoint curve crosses from
the side =O to the side v=0 (van LAAR's type I).

( 275

certain ratio vzofvg: for not too large Tro/Tr (from O up to a certain
value, see Table I loc. cit. p. 662) only one barotropic plaitpoint
occurs, which in connection with Comm. N°. 96° p. 503 and 504
pointed to the fact that for the knowledge of the course of the
barotropic phenomena at lower temperature considerations in which
only the transverse plait is taken into account, are not sufficient
for these mixtures *) (see Comm. N°. 96° p. 663).

In Comm. N°. 96¢ p. 660 footnote 2 an estimation *) was derived
about the critical temperature of helium from the observation of
the barotropic phenomenon for a mixture of helium and hydrogen
described in Comm. N°. 962 These Proc. Nov. ’06, p. 459. In this
estimation the supposition already mentioned in Comm. N°. 967,
p. 460, that the molecules of helium exert only an exceedingly
slight mutual attraction, was found confirmed.

This suggested the investigation already announced in Comm.
N°. 96°, p. 502 on binary mixtures one of whose components is a
gas the molecules of which exert no or only feeble attraction (Suppl.
N°. 15, These Proc. March ’07, p 786). Here a plait was described
for the first time which at descending temperature appears on the

1) For mixtures of pairs of substances as meant in table I p. 662, for which
0.2'9 > Tx, /Tk, > 0.196, three barotropic plaitpoints will occur one of which,
however, does not belong to the absolutely stable region. At least for the larger
ones of the mentioned ratios 7%,/Tk,, the two others belong to a plait which
enters the y-surface from Ky, and crosses the {surface as a transverse plait at
lower temperature. For this the considerations of Comm. N’. 96% will hold at least
in so far as solid phases do not cause a disturbance. For the smaller ones of these
ratios one of these two barotropic plaitpoints will also fall in the not absolutely
stable fluid region, and so also for these we shall have to take the occurrence of
three phase equilibria into account.

2) For the calculations in note 2, p. 660 of Comm. NP. 96¢ we availed our-
selves for a and 6b of hydrogen of the values calculated for this by Konnstamm
(Lanpott-BérnstEmn-MeYeruHorrer’s Physik. Chem. Tables 1905), which values had
Tr = 38.6, pk = 20 according to OrszewsKr, Wied. Ann. Bd. 56, p. 133, 1895 as
starting point. If we derive the a and b for Hg from Tk —=29 a 32, pr =15
according to Dewar (B. A. Report 1902), the estimation for THe yields about 1°,
Ouszewski’s newer data, Ann. d. Phys. 17 (1905) p. 986: T= 32.3, pk = 14.2,
give it a value of more than 1° (the calculation according to note 2 l.c. yields
a22M/a11M= */s0, TkHe = 1.3).

This would bring about these modifications in the classification of the helium
mixtures mentioned in Suppl. NO. 15, Sept. 07, § 8, that mixtures of He with
H,0, Os, A, Ne, NO, NH; would belong to case (b), those with Hy, H,S, CO, to
case (c). For the modification which another assumption about ai2x (cf. p. 280)
would cause in the circumstances under which the plait starting from v =b occurs
see Suppl. N°. 15 le. p. 234. A smaller aizar might even again bring about a
shifting in the classification in the direction from (c) towards (a).

18%

( 276 )

w-surface from the side of the small volumes, reaches the side z=0
at 7’= T;,, and then passes into a plait crossing in a slanting
direction from v—=b to e=0O. ‘This description was accompanied
by remarks about limited miscibility in the gas state.

In Suppl. N°. 15 § 7 These Proc. March ’07, p. 795 three cases
were distinguished for mixtures in which one component is a gas
with a feeble attraction. They are indicated as cases (a), (0) and (c)
in § 9, These Proc. Sept. ’O7, p. 235. Case (a) corresponds with the
above mentioned one; in case ()) a plait coming from v= 6 and
one coming from «=O join to a single plait in a double plaitpoint *) ;
in case (c) a plait starts from «=O, comes in contact with v= 6

1) On the suppositions mentioned in Comm, N°. 96c p. 509 and p. 510 the
data for the two double points in the net of spinodal curves, of which this double
plaitpoint is one (a node) may be found in the following way (cf. Comm. Suppl.
N’. 15, p. 233, note 1):

The equation for the v,a-projection of the spinodal curve on the molecular

W-surface : :
RT v3 = (1 ea) Cu euu-bumV au)? + 2eu(euV @22M-b2uVam)* (1)

(cf. Suppl. N°. 15, March '07, p. 788) gives as conditions for the appearance of
a double point after some obvious reductions:

vanum bum Waar)? = 20 uVauim-(l—em) (CMV aum—biuVay) +
+ boon anar emu aam beenen). . . « (2)

and
(vauWaaoar —beomWam)? = 2m Wase - (L—em)(eMV eum— bimVam) +
+ 2b.21V am …em(vMW asem breman). « . -« (8)

From (2) and (3) follows:
QiVairm—biuVanu)? — (UMV azom— borman)?
Vaua = Vaal

Extracting the root from this equation, we may (2) and (3) reduce to:

(4)

vaan Pun VOM on ll San) + bir EN
Vaum
and
vm Was —beom Van ,
Vaxam
By eliminating var from (5) and (6) we obtain for x the equation (1) of Suppl.
NO. 15, March ’07, p. 796 (cf. errata Proc. Sept. ’07, p. 239).
The further derivation of var and 7' (see Suppl. N°. 15, March ’07, p. 798)
may be left to the reader (compare with these developments van Laar, These
Proc. May '07, p. 38 sqq. and Arch. Teyrer (2) 11 (1907) 1re partie § 5).

boomen + 2b\\y(l_—em) Maiim/ar2m. (6)

(377)

at lower temperature, and passes then into a plait crossing in a slanting
direction *).

For this distinction ds2y/di1y4 was always supposed so small in
connection with the value of bs.44/h;,y, that the plaitpoint curve crosses
from K, to the line »=é and that three phase equilibria not yet
occur at the temperatures under consideration ’).

Now that the estimations concerning the a and 5 of helium justify
the supposition that the plaitpoint curve’) crosses from w= 0 to the

1) Kunpt, Berl. Sitzb. Oct. 1880, S. 812—824 was of opinion that it would
always be possible to convert a liquid to the gas state by pressing in a gas.
This view was maintained in van Erpi’s thesis (Leiden 1898, p. 7, cf. Comm.
Phys. Lab. Leiden, Suppl. N’. 3, p. 45), where it says that the operation mentioned,
if it is realized, would be the determination of the plaitpoint pressure corresponding
to the temperature of observation of the pair of substances which is subjected to
the experiment. There it was tacitly assumed that with sufficiently high pressure
the plaitpoint state could be reached for every temperature between the critical
temperatures of the components as e.g. for mixtures of methyl chloride and carbonic
acid, even though it would have to be found above 750 atmospheres for hydrogen
and ether, as van Erpik derived taking into account the diminution which with increasing
pressure is found in the decrease of the surface tension caused by one and the
same increase of pressure (Kunp? loc. cit. p. 818, van Erpik Thesis, p. 5, cf Suppl.
N°. 3, p. 52). If we pay attention to the possibility now foreseen by the theory,
that this diminution continues outside the rezion of observation, it seems probable
in the light of the observations mentioned, that it would not be possible — here
we treat as infinite, pressures which exert forces on the molecules greater than
those joining the parts of them — to reduce the surface tension to O for the
pair of substances mentioned (and the same remark applies to hydrogen and -
etnylalcohol) at the temperature of observation (Kunpt 21°, van Erpik 9°.5), so
that already at that temperature a plait crossing obliquely from z=0 to v=b
would exist on the d-surface.

In fact we should also derive from van Laanr’s figure cited p. 274 footnote 3 that ether-
hydrogen (and also alcohol-hydrogen) belong to van Laar’s type I, while according to
the criteria laid down by us, they should belong to case (c) of this type. Van DER WAALS’
equations Contin. II p 43, however, would point out a critical temperature of complete
miscibility of about — 200°C. in the supposition of aizar= “ dui ar d22m, so that according
to these suppositions an obliquely crossing plait would only make its appearance
below this temperature. If the existence of an obliquely crossing plait at the tem-
perature of the above mentioned experiments should be confirmed, this might,
among other things point to the fact that aizs would be considerably smaller than
Vaid for the pair of substances mentioned (cf. p. 280).

2) According to this restriction case (c) cannot occur e.g. for boeu/bnar larger
than a certain value (cf. Suppl. N°. 15 These Proc. March ’07, p. 797).

8) Kuenen, These Proc. Febr. ‘03, p. 473 was the first to find experimentally
a plaitpoint curve starting from #—0, and directed to the side v — b for mixtures
of ethane and methylalcohol.

(278)

line v==b for mixtures of helium and hydrogen‘), it is desirable to
subject the barotropic phenomena for the cases mentioned to a closer
examination. In this discussion for mixtures one component of which
is a gas with feeble attraction, we shall again restrict ourselves
and suppose that in the considered cases at the considered temperatures
the second branch of the plaitpoint curve (van Laar, These Proc.
May ’05 p. 37), starting from K,, does not make its influence felt,
so that three phase equilibria do not yet make their appearance.

§ 2. The course of the barotropic phenomena for binary mixtures,
one component of which is a gas whose molecules exert only a feeble
attraction.

In this discussion we shall have to distinguish the cases a, 6, and
e mentioned in § 1.

a. In this case a plait starting from v= dé and closed towards
the side of the large v’s, appears for Tim > 7 >> T;,, which plait
we have called gas-gasplait in Suppl. N°. 15, March ’07, p. 793. If

b,,< 6,,, then 9, will be >= for T > Tits (see Comm. N°, 96°

p. 504); at 7 = 7,1, a barotropic plaitpoint occurs (ef. Suppl. N°. 15
March ’07 PL I, fig. 1); at 7’< Topis we find a barotropic nodal
line on the gas-gasplait (cf. Suppl. N°.15, Pl. I, fig. 2). At 7= 7;,
the gas-gasplait passes into an obliquely crossing gas liquid plait. A
barotropic nodal line will exist on it (see fig. 1) till it disappears
under the three phase triangle, and so passes into the not absolutely
stable region. As mentioned in § 1 we shall not give the description
of what happens when three phase equilibria have appeared. In the
same way we shall for the present disregard more complicated cases,
as the appearance of two barotropic nodal lines on the gas-gasplait,
three on the obliquely crossing plait ete., till further investigation
may teach that these cases are possible.

If 6,, >6,,, the plait coming from v = b may reach the side z = 0,
and pass into an oblique plait without it being necessary that a
barotropic tangent chord occurs.

6. For 6,,<4,, a barotropic plaitpoint will occur at Typis > Tayi
(cf. Suppl. N°. 15, March ’O7 p. 798). This barotropic plaitpoint,
and also at 7%,1, > 77> Ta, the barotropic tangent chord, may

1) This follows also from van Laar’s fig. 22, Arch. Teyter (2) 10 (1907) p. 38
with the mentioned estimations on the critical temperature and pressure of helium
(cf. p. 275 note 2) and on the suppositions made (cf. These Proc. Dec. 06 p. 509
and 510).

(279)

occur both on the plait starting from v ==b and on that starting
from z=—0 (figs. 2 and 3). If in the homogeneous double plaitpoint
the isobar should run parallel to the z-axis, 7%), would coincide
with Tj. For 7 < Ty, a barotropic chord exists on the obliquely
crossing plait, just as in case («)*).

For 6,, > ,,, as in this case for a, the existence of barotropic
tangent chords is not required.

ce. If 6,,<C6,,, a barotropic plaitpoint will make its appearance for
Tote < Tr, and > Ty; at lower temperatures a barotropic tangent
chord is found on the plait starting from «=O and closed on the
side of the small v’s, and at 7’< Tym on the obliquely crossing plait
(fig. 4). For 6,, > 0,, as for a and 6.

In fig. 5 the course of the spinodal curves (continuous) and of the
connodal curves (lines consisting of dashes) on the w-surface for the
unity of weight has been more fully represented for a case c. The
figure has been construed with a view to mixtures of helium and
hydrogen. In this we adopted the hypotheses mentioned in Comm.
N°. 96°, Dee. °06, p. 509 and 510, and put for hydrogen ti mi Pe
Pu = 14.2, for helium 7;,,= 1,3, Omme = } bmu, (p. 275 note 2) ?).
The volume v is expressed in the theoretical normal volume of a
molecular quantity as unity. The point A, has been calculated
according to VAN DER Waats Cont. Il, p. 48. The spinodal curves
have been constructed as in Suppl. N°. 15, March ’07, p. 788.
P, is the barotropic plaitpoint, calculated in the way indicated in
Comm. N°. 96°, Dec. ’06, p. 510. Further the plaitpoint curve
KK calculated according to the equation given by van Laar,

1) In the light of our present knowledge of the behaviour of mixtures and divested
of the considerations which are incompatible with it (cf. p. 274 footnote 1) the
phenomenon deemed possible by Jami, C. R. 96 (1883) p. 1451, Journ. phys. (2)
2 (1883) p. 383, would be described as follows: On compression of a gas above a
suitable quantity of liquid (see p. 281 note 2), this liquid is made to dissolve at first
under plaitpoint circumstances, after which on further pressing in of the gas
into the thus formed homogeneous phase a phase richer in the least volatile
component (called by Jamin liquid, by us in certain cases, cf. Suppl. No. 15,
March 07, § 4, second gas phase) may separate above the phase which is richer
in the most volatile component. If this phenomenon could be realized, we should
have to deal with a case b for a temperature Z’> Tu, and in which the line
RQ (see fig. 6) intersects the plait starting from v=06 in such a way that for
ld
2

3) However, on account of the uncertainty which still prevails about Tkre and
pkHe, and in view of the probability that dior < Vauar dom (see p. 280) it is
still to be considered as quite possible that He—Hy, belongs to case (0), as was
supposed in Suppl. N°, 15.

the intersected connodal tangent chords 6 >

( 280 )

These Proc. April ’05 p. 652 has been included in the diagram.
The second branch of the plaitpoint curve is not to be distinguished
from the straight line HA, on the scale on which the diagram has
been drawn.

For the connodal curves the points of intersection with the line
z =O representing the points of saturation for pure hydrogen have
been calculated. For this purpose the constants of saturation have
been used, which have been calculated by Darron*) for a substance
that follows the equation of state of vaN DER Waa.s with constant
a and 4. For the rest the course of the connodal curves for which
for 7’> Tin also the plaitpoints are known, has been represented

schematically. This applies particularly to the points of intersection
of the connodal curve for Z’=20 with the line v=6, so that
also the course of the connodal curve, particularly of the gas branch,
is uncertain in the neighbourhood of the line v == b. The line CD
represents the experimentally determined barotropic tangent chord for
T = 20 (see Comms. N°. 96% and N°. 96° Febr. 07 p. 660 footnote 2).

The situation of the line CD with respect to the connodal curves
might point to 7%, being higher than was calculated by us, which
may be due either to the critical temperature of helium being lower
than was assumed by us here, or to dys being < Vandy for
mixtures of He—H,’).

The course of the barotropic plaitpoints and barotropic tangent
chords in case (c), and also in case (4), if they oceur on the plait
starting from xO, corresponds for the higher temperatures with
that for the case that the branch of the plaitpoint curve starting
from A, crosses the w-surface from «=O to x=—=1, for which case
the course was described in Comm. N°. 96°. For the lower tempe-
ratures we meet with this difference that in the cases considered in
this comm. the barotropie tangent chord continues to exist on the
plait, till it disappears under the three phase triangle, whereas
in the cases considered in Comm. N°. 96% the barotropic tangent
chord may also vanish from the plait through a barotropie plaitpoint
(lower barotropic plaitpoint temperature, see Comm. N°. 96% p. 504).
The latter must even be the case if for 72 7, no three phase
equilibria appear as yet (cf. p. 275 note 1).

1) J. P. Darron, Phil. Mag. April 1907, p. 520.

2) The same remark concerning aio” for mixtures of H, with other substances
might be derived as follows: for CO, — Hz (the same holds for CO,—-O,) from
a comparison of the experimentally determined portion of the plaitpoint curve with
that calculated in the same way as above for He—H,; for H, — ether and
H, — alcohol see § | p. 277 note 1 ).

( 281 )

Van per Waars, These Proc. Jan. ’07 p. 528 calls attention to the
influence of 6,,,, on the oceurrence of barotropic phenomena by
stating this rule: “When the most volatile substance has the greatest
limiting density, the gas phase can be specifically heavier than the
liquid phase.” In connection with what was discussed above we
may now supplement this rule as follows: If of a binary mixture
the more volatile component has the greater limiting density, the
gas phase will be made to sink in the liquid phase by compression
with suitable concentration and temperature, provided the more
volatile component has so feeble an attraction that pressing in of
this latter component cannot make the liquid phase of the less volatile
component dissolve in the gas phase at detinite*) temperatures even
at the highest (comp. p. 277 note 1) pressures. *) It is implied in the
terms of this rule that it has been supposed that no two liquid phases
occur.

It is not excluded that also in other cases sinking of the gas phase
in the liquid phase might occur. *)

If we apply this rule to pairs of substances of which data are
available for aso, anar and boy, bi, it appears that only for
He—H, it may be expected on reasonable grounds ‘) that barotropic
phenomena occur at not too high pressures‘). Further investigations will
have to reveal whether for mixtures of pairs of substances as nitrogen

1) Also at higher temperatures than these barotropic phenomena may then occur.

2) In the case of compression of a gas above a liquid, slarting from the pure
substance in the way as was done in Kunpr’s experiments we describe on the
Y-surface a curve the v, z-projection of which is a straight line joining a point of
the line «= 0 with the point »=0, «=1. For the liquid phase to disappear at
a definite, suitable temperature just under plaitpoint circumstances, we must start
from a definite quantity of liquid so that the volume is represented by SQ (see
fig. 6). If the quantily of liquid from which we start, is smaller, the liquid phase
will evaporate (be dissolved in the gas phase), if it is larger the gas is dissolved
in the liquid phase (cf. van per Waats, Cont. Il, p 136). Only if the diffusion
is not rapid enough to ensure equilibrium all through the tube, solution of the
liquid under plaitpoint phenomena may be observed also with~other quantities of
liquid as corresponding with vg, as has been set forth by Kuenen’s experiments
on the influence of phenomena of retardation.

8) See e.g. § 1, p 275, note 1.

4) Though for mixtures of e.g. helium and acetonitril the available data with
application of the special hypotheses assumed in this § (concerning the equation
of state ete.) would point to the fact that at high pressures barotropic phenomena
might still just occur, it is impossible to express a definite expectation with regard
to this on account of the influence of the uncertainties, both in the data and in
the validity of the mentioned suppositions.

9) This was mentioned in Comm. No. 965 Dec. '06 p. 504.

( 282 )

and a light oil with high critical temperature '), nitrogen-lithium,
argon-kalium, mercury-iron etc. sinking of the gas phase in the
liquid phase could be realized.

§ 3. On the conditions for the occurrence of barotropic phenomena.

It appeared in § 2 that with a suitable ratio of the limiting densities
the occurrence of the barotropic phenomena depends to a great extent
on the ratio of the attractions of the molecules of the two compo-
nents, hence on the ratio of the critical temperatures. The same thing
may also be derived in the following way, more independent of the
particular hypotheses which have led to the consideration of obliquely
crossing plaits.

To bring about the phenomenon of the gas phase sinking in the
liquid phase, the gas phase will have to be much more compressible
than the liquid phase, and even on compression the gas phase must
not dissolve in the liquid phase. For this the temperature will have
to be pretty far below the critical temperature of the least volatile
component (7%), but still far above that of the second component
(Tr). This points to a large difference between the critical tempe-
ratures of the components.

If for the pair of substances considered retrograde condensation of
the first kind occurs, the coexisting phases indicated by the points
L and G on the y-surface for the molecular quantity (see fig. 7)”,
can only have the same density if M, > ™,.

Only when on the plait on the molecular y-surface connodal
tangent chords appear for which the angle with the axis z= 0:

wu
0 > the coexisting phases can have equal density for M‚, << M,.

As the difference between x, and 2, is larger, and so the connodal
tangent chords deflect more rapidly from the side =O, a smaller
difference between J/, and M, will suffice to establish equal densities
in G and L.

This will be the more the case the more the plait extends towards
the side v=).

The latter is particularly furthered by a small ratio asoy/ana (cf.
Comm. Suppl. N°. 15 Pl. 1 fig. 1 and Pl. II), so by a small ratio of
the critical temperatures, bj: smaller than bij also tending in this
direction.

1) Mr. F. M. Guttey of Boston drew our attention to mixtures of air and oil.

2) The dotted lines indicate that the considerations of this § hold both for the
case that at lower temperature the plait crosses the /-surface asa transverse plait,
and for the case that it extends towards v=b.

H. KAMERL
of VAI

in the

Proceedin

. KAMERLINGH ONNES and W. H. KEESOM. ‘Contributions to the knowledge of the J-surface

of VAN DER WAALS. XVI. On the gasphase sinking in the liquid phase for binary mixtures
in the case that the molecules of one component exert only a feeble attraction.”

Proceedings Royal Acad. Amsterdam Vol. X.

Fig. 7.

‘ ( 283 )

Hence we get as conditions for the possibility of the occurrence
of barotropic phenomena:

The second component must have: 7%, small compared with 7%,,
and by preference also: M, > M, and boy < Ou.

This becomes still clearer by the application of equations (2) and
(4) of Comm. N°. 79, April ’02, p. 659:

Ey — PU
MRT
Cc, == Ty é
got |T dpm 4) Paley — 0)
MRE S SMD EE \_ MRT

which determine the ratio of the concentrations of gas and liquid
phases of a binary mixture in which the quantity of one component
is small, if the law of the corresponding states may be applied.
The connodal tangent chord will rapidly deflect from the side z= 0,
if the exponent of e assumes a considerable negative value. The

‘ 1 i hee
greatest influence on this exerts « = — 5 ‚ on account of
Ef ky dz 2=0
i. LENS 7 EA
the value of the coefficient — AT (> 7); so 7, will have to be small
Pm C
1 dus

with respect to 7. The influence of B=a—y, if y= — a

UE, da
(ef. Comm. N°. 81, Oct. 02 p. 325) is only of secondary importance.
To tend at least in the right direction, y would have to be negative,

so bom < bim’)

Physiology. — “An investigation of Mr. J. W. A. Grwin, on the
relation of pepsin to chymosin.” By Prof. C. A. PEKELHARING.

That gastric juice possesses the power, on the one hand to digest
proteins under acid reaction, on the other hand, to curdle milk under
neutral or scarcely acid reaction, is generally attributed to the pres-
ence of two different enzymes in the gastric juice, viz. pepsin and
chymosin. ‘This opinion is chiefly based upon an observation of
HAMMARSTEN, who was the first to throw light on the changes that
take place in milk when it is coagulated by means of rennet.
HAMMARSTEN found that an extract from the mucous membrane of
the stomach, which, when prepared fresh, could digest proteins as well

1) The more elaborate mathematical treatment of the conditions for the occurrence
of barotropic phenomena, as sequel to Comm. N°, 96e, will be postponed till
further experiments call for a further discussion.

( 284 )

as curdle milk, after having been digested for a few days with hydro-
chloric acid at a temperature of 37° C., no longer showed the action
of rennet, but had preserved its peptic action. From this it could
not but follow that each of these actions depended upon a separate
agent.

Meantime doubts have gradually arisen as to the correctness of this
opinion. That there must at any rate be a very close connection
between the proteolytic action of pepsin and the enzym of rennet,
was made probable by the experience that all enzym-solutions with
a proteolytic action, no matter whether they are of animal or of
vegetable origin, can also act like rennet. And, as I communicated
some years ago in this Academy, and as was afterwards corroborated
by Nenckt and Sreper, it could also be proved that all kinds of
preparations of pepsin, also when a long digestion with hydrochloric
acid and a purification as careful as possible had preceded, are able
to act like rennet.

In 1904 there appeared an investigation by PawLow and Parast-
SCHUK '), in which they demonstrated that pepsin and chymosin must
be considered as the same substance. These investigators found that
in different liquids containing enzym not only the proteolytic and
the curdling power are always found side by side, but that also a
proportionately greater curdling power corresponds to a greater
proteolytic action. That this is not found in some enzym-solutions
of commerce appeared to be owing to the presence of other sub-
stances; as soon as their effect was destroyed, the proportionality
came to light. A solution of rennet, according to HAMMARSTEN
prepared by means of carbonate of magnesia from gastric juice,
which, in his opinion, no longer contained any pepsin at all, appeared
to be a very good digester of albumen, if only the noxious influence
of magnesia-salts was taken away. No more was it proved by
HAMMARSTEN, — as Pawrow explained — that a pepsin-solution can be
freed from rennet by digestion with hydrochloric acid, as the pro-
teolytic action had been examiued, while the liquid still had an acid
reaction; the curdling action, on the other hand, after neutralization,
by which the enzym might be easily destroged.

Against Pawrow’s explanation objections have been raised. Especially
two Swedish investigators, BANG *) and ScHMipr-NIELSEN *), have
defended HamMarsten’s point of view. The investigation of Mr. Gerwin

1) Zeitschr. f Physiol. Chemie, Bd. XLII, S. 415.
*) Zeitschr f. Physiol. Chemie, Bd. XLIII, S. 358.
3) Ibid. Bd. XLVII[, S. 92.

4) Pritiaer’s Archiv. Bd. LXXIX, S. 425.

( 285 )

refers principally to the grounds alleged by these two authors for
the duality-hy pothesis.

In the first place he has occupied himself with an inquiry into
the correctness of the conclusion previously drawn by Bane *) from
a number of experiments, that there is not only a difference between
pepsin and rennet, but also that even the enzym of rennet does not
possess the same qualities in different kinds of animals. Bane con-
tinued to apply the old name, chymosin, to the enzym of rennet,
as it is found in the calf. From this he distinguished by the name
of parachymosin the enzym that can be got from the mucous mem-
brane of the pig-stomach. The difference showed itself in the fact
that parachymosin, when diluted, became sooner inactive than chy-
mosin, that it showed a greater activity by the addition of chlor-
calcium, was more proof against heating to 70° C. and less so against
the action of alkali.

With reference to extracts from the mucous membrane of the
stomach of calf or pig Gerwin could corroborate these differences;
only he did uot find the difference in the promotion of the activity
by adding chlorcalcium as important as Bane. However, it was a
different thing, if not the extracts themselves were examined but the
enzym extracted therefrom by dialysis, and purified as much as
possible in the way formerly communicated by me. The better the
purification had taken place, the smaller the difference became. The
extract from the mucous membrane of the calf-stomach loses its
power to curdle milk when, neutralized, it is heated for 10 minutes
to 70° C.; however, its power is but little reduced, if it is mixed
with caustic soda to 0.01 °/, and neutralized again after half an hour.
With the extract of the mucous membrane of a pig-stomach it is just
the reverse. With the enzym of the calf, purified as much as possible,
the resistance against heating appeared to have become great, against
alkali small. From this it must therefore be deduced that the dif-
ference does not lie in the enzym itself, but that it is caused by
other substances occurring in the extract. Indeed, it could be proved
experimentally that the extract from the membrane of the calf-stomach
contains substances which protect the enzym against the action of
alkali, but make it the more sensitive to heat. Of a solution of
purified pig-enzym (which possesses the qualities of Bane’s para-
chymosin) one half was diluted with water, the other with an
extract from the mucous membrane of a calf-stomach, which extract
had been deprived of all enzym by heating it for one hour to 80° C.
and then neutralized. Of both solutions 2 ec. mixed with 8 cc. of
milk caused curdling in 30 sec. A part of each was heated for

( 286 )

10 minutes to 70° C., another part for half an hour left in contact
with 0.01 °/, Na HO and then neutralized again. Now the result was:

| After heating | After action of alkali
2 ee. enzym with water +8 ce. milk} curdling in 2/)min.}no curdling
De 7 , extract +8 , , [no curdling |curdling in 11 min.

Gewin also examined two rennet-preparations of commerce, one
Dutch of van Hasserr and one Danish of Hansen. Both showed the
qualities of Bane’s chymosin. But when, by dialysis and precipitation
with acetic acid, the enzym had been isolated and at least for the
greater part been freed from impurities, they had become much more
susceptible to alkali and much less so to heating.

That the enzym is destroyed not only by alkaline, but gradually
also by neutral reaction has been made clear by Pawrow and
corroborated by GEWIN in numerous experiments. From this GEwin
explains the difference found by Bana between chymosin and para-
chymosin, the solution being diluted. What Bane calls chymosin is
the enzym mixed with substances protecting it from alkali. When
those substances are present, it may be assumed that the enzym is
better proof against the dilution with water, by which the number
of hydroxyl- and metal-ions increases. A solution of purified enzym
(parachymosin), possessing the same curdling power as a not purified
solution of calf-enzym (chymosin), shows, when diluted, sooner a
decrease in action, and consequently must, also sooner, show the
promoting influence of the addition of chlorealcium.

So there is no reason for assuming different rennet-enzymes in
different kinds of animals. The difference does not lie in the enzym
but in other substances originating from the mucous membrane of the
stomach. If it is necessary to give a separate name to the enzym of
the gastric juice that can curdle milk, it is sufficient to use the word
chymosin for it.

But is even this necessary? Should it be assumed that chymosin
is different from pepsin?

To the solution of this question Gerwin has devoted the second
part of his investigation. It was tried in vain to divide the enzym
into a proteolytic and a curdling part. It is a well-known fact that
proteins, undissolved and at a temperature of 15° C. put into a
pepsin-solution, take up and keep baek this enzym, so that it is not
to be separated from it by washing it out. Coagulated and minced hen’s
albumen was put in a solution of purified pepsin in 0.2 °/, HCI.
Now, if chymosin were a different matter from pepsin, only the last
mentioned would perhaps be extracted from the solution by the
albumen. It appeared, however, that the liquid filtered from the

(28)

albumen after some hours, had lost not only the peptic but also the
curdling power. Indeed, the same negative result had already been
arrived at by Jacosy, who for these experiments did not use hen’s
albumen but caseine *).

In the second place it was examined whether a separation into two
enzymes could be brought about by dialysis. When pepsin, dissolved
in hydrochloric acid, is dialyzed against distilled water, it is partly
precipitated, most completely at a low temperature, as soon as the
quantity of acid has gone down to about 0.02°/, HCl. Always, however,
a considerable part remains dissolved, which, with the aid of ammo-
nium-sulfate — if the solution does not contain much albumose
through 50°/, saturation with this salt — can be precipitated. If pepsin
and chymosin are different matters, it cannot be deemed improbable
that they also differ in solubility, that therefore the precipitate in
the dialyser should contain more of either one or the other matter
than the liquid filtered from it. Also in this way, however, a sepa-
ration into two enzymes, did not succeed.

SCHMIDT— NIELSEN, however, has communicated experiments from
which it appears that, though not a complete, still a partial separation
of pepsin and chymosin is possible. A strongly active extract from
the mucous membrane of the calf-stomach, prepared with hydrochloric
acid, was divided into two parts. One was preserved at a low tem-
_ perature, the other at 37° C. After some days the heated part had
for the greater part lost its power to curdle milk, under a neutral
reaction; at acid reaction, however, protein was still strongly digested.
Now both liquids were neutralized and the one not heated so much
diluted that the curdling power had become as weak as that of the
one heated. After that the two liquids were rendered equally acid
with hydrochloric acid and digested with fibrine. The fibrine was
much quicker dissolved by the heated liquid than by the diluted
one, not heated. During the process of heating, therefore, the chymosin
had been chiefly lost, the pepsin however not.

This experiment would certainly be convincing, if the neutralization
had the same effect on the heated liquid as on the one not heated.
This, however, is not the case. The extract contains substances
protecting the enzym from the action of alkali; also when no more
of this is added than what is necessary to attain a neutral reaction.
If the extract is preserved at a low temperature, these substances
remain for a long time undisturbed, but if the acid extract is heated
to 37° C., they are destroyed. Grwin has proved this by ample
experiments, of which a detailed account is given elsewhere. At the

1) Biochem. Zeitschr. Bd. I, S. 66.

( 288)

outset the enzym in the extract of rennet is quite proof against
neutralizing, but after having been digested for a few days at 37° C.
this power of resistance becomes smaller, and then diminishes quickly.
Now, if the neutralized liquid, in order to determine the curdling
power, is mixed with milk, the reaction remains neutral and no
curdling arises. However, if it is rendered acid again, soon after the
neutralisation, a sufficient quantity of enzym is left to digest protein.
Also if the not heated solution of the enzym, before being neutra-
lized, is sufficiently diluted with 0.2°/, HCl, neutralisation herein
causes a rapid decrease and at last an annihilating of the curdling
power. Thus the curdling time of such a solution was, 8 times
diluted, 10 seconds, directly after the neutralisation 2'/, to 4 minutes,
whilst the milk, mixed in the same proportion with the solution
half an hour after the neutralisation, was not yet curdled after 20
minutes.

In all experiments, on the other hand, at which the noxious action
of alkali was avoided, the curdling and proteolytic power of the
enzym solutions appeared to keep pace with each other.

Summing up the result is therefore that not a single reason is left
to assume a difference between pepsin and chymosin.

No more is there any reason to stick to the opinion of NeNckr
and Steger, which I formerly shared, according to which pepsin
should be considered as a molecule, which, through different groups
of atoms, on the one hand should have a proteolytic, on the other
band a curdling action. The basis for such an idea, the opinion
that the activity in one direction could be preserved, whilst that in
the other direction was lost, I must now consider as having lost its
foundation. The opinion defended by Sawsatorr, is far more acceptable,
who considers the alteration of caseine, of which the formation of
cheese is the consequence, as the beginning of digestion, of proteolysis *).
This opinion has, I believe, become more probable by the experiments
made of late about the alterations caseine undergoes under the
influence of rennet, particularly by the investigation made some time
ago in my laboratory by Miss Van HeERWERDEN!). From these it
has appeared that caseine, at a very weak acid or neutral reaction
and at a temperature not much lower than 37° C. in a solution
of rennet — either a preparation of commerce or pepsin purified
as well as possible — soon falls asunder into paracaseine, which
when it does not directly become insoluble as a lime-compound,
cheese, continues to change, and other substances, among which

1) Zeitschr. f. Physiol. Chem. Bd. XLVI, S. 307.
2) Ibid, Bd. LII, S. 184.

a protein, provisionally called substance C by Miss van HeRWERDEN.
Not until the enzym has been able for a long time to influence
these substances, does it form primary albumose from them. At
the same time, however, the enzym also appeared at neutral
reaction to form from coagulated albumen primary albumose, though
in a small quantity. So there is every reason to consider curdling
of milk as a proof of the first stage of proteolysis.

Taking this into consideration, it is not so wonderful, as it has
been regarded, that all kinds of proteolytic enzymes possess the
power of curdling milk, though in natural circumstances they never
come in contact with caseine. For then the peculiarity is not to be
sought for in the enzyme, but in the caseine, the splitting of which
already can be observed in a stage of the digestion, in which with
other proteins alteration is still quite imperceptible.

Physics. — “The intensities of the components of spectral lines

divided by magnetism’. By Prof. P. Zeeman.

If a spectral line is resolved into a triplet by the application
of a magnetic field, the two outer components and the middle line
will generally differ in intensity. According to the elementary theory
of Lorentz of the phenomenon of magnetic resolution there exists a
simple relation between these intensities.

Let /, and /, be the intensities of the outer components and J,
that of the middle line then we may expect that

Weep Ni Ee Ae ee ke Ss a(t)

It has been often asserted, that generally this relation is not ful-
filled, and that triplets frequently have in contradiction with (1) a
weak middle line and strong outer components.

Really some cases *) can be cited, in which the intensities differ
from what may be inferred from equation (1). In numerous cases
however this contradiction is only apparent, no attention having been
paid to a circumstance presently to be mentioned and not yet exa-
mined in connexion with our present subject.

In the very important investigation by Rurer and PASCHEN?) a
calespar prism was placed before the tube placed in the magnetic
field. By means of a quartz lens the two images given by the cale-

1) The lines exhibiting the partial polarization observed by Ecororr and Grorarewsky
(C.R. 124, 125. 1897) are meant here.
*) G. Runes u. F. PAscuen Abb. der Berl. Akad. Anhang. 1902.

Proceedings Royal Acad. Amsterdam. Vol. X.

( 290 )

spar are projected in the plane of the slit of the spectroscope. The
two images could be examined separately.

“Bei richtiger Stellung des Kalkspaths bestand das eine Bild aus
Licht, dessen elektrische Schwingungen in der Lichtquelle parallel
den Kraftlinien vor sich gehen, das andere Bild aus Licht, dessen
elektrische Schwingungen in der Lichtquelle auf den Kraftlinien
senkrecht stehen. Dass die Ebene der Schwingungen nach dem
Durchsetzen des Kalkspaths durch die Quarzlinse gedreht wird, thut
nichts zur Sache”.

Bij means of this arrangement the components with vertical vibra-
tions are undoubtedly separated from those with horizontal ones. The
main object of RuNee and PascrHeN's investigation being the connexion
between series and magnetic separation there is no objection to be
made. The case is changed however as soon as the relative inten-
sities of the components in the emitted light are under investigation,
for these under certain circumstances could be essentially altered. If
vertical and horizontal vibrations are reflected differently by the
erating, the rotation of the direction of vibration in the beams
passing through the quartz lens of course will be apparent in the
observed intensity. ;

Polarizing effects of gratings are well known and generally the
direction of vibrations relatively to the grooves must be of importance.

I had not anticipated that this circumstance would give rise to
such striking effects as were observed by me in some experiments
with a large Rownanp grating. | have only made some observations
with the yellow mercury lines, observing in the spectrum of the first
order. The incident rays made an angle of about 19° with the nor-
mal to the grating, and in this latter direction observations were
made or photographs taken. A vacuum tube charged with some
mercury ') was placed in the magnetic field and by means of a
glass lens an image was projected on the slit of the spectroscope.
The light emitted at right angles to the horizontal magnetic lines of
force was investigated.

In figure 1. a reproduction is given of the triplet in which the
line 5769.4 is resolved. The distribution of intensities is in absolute
contradiction with equation (1).

Observations with a calespar and a sodium flame, the light of
Which was incident on the grating at about the same angle as
above specified, the direction of observation being normal to the
erating, showed at once that the light reflected from the grating

1) F. Pascuen, Physik. Zeitschr. Jahrg. 1 p. 478. 1900.

( 291 )

was strongly polarized. The vertical vibrations were strongly
preponderating.

The influence of a rotation of the plane of polarisation of the
yellow mercury light on the distribution of intensities in the triplet
was then examined. The plane of polarization was rotated by
means of quartz plates with faces perpendicular to the axis placed
in front of the slit. L had at my disposal two small plates of 2.15
resp. 4.17 mm. thick. According to GuMiicH *) the rotation for mercury
light of wavelength 5769 in a quartz plate 1 mm. thick, is at
f= 20° 22°.718 and hence the rotation in my plates amounted to

22.72 << 2.15 = 48°.90 en 22.72 K 417 = 94°.7.

The change in the distribution of light is at once apparent. In
figure 3 the outer components are hardly visible. The negative
reproduced corresponds to the case in which the plate rotating the
plane of polarization 94°.7 is in front of the slit.

Figure 2 corresponds to the case in which the incident vibrations
are inclined at about 45° to the slit. It may be remarked that in
this case the real distribution of intensities between the components,
as existing in the emitted light, is observed.

Vertical and horizontal vibrations now being equally present in
each of the components, and hence the circumstances as to vibrations
being the same for the three components, the polarization by the
erating is eliminated.

The distribution of light in figure 2 is certainly not in contradiction
with equation (1) and eye observation seems to confirm it numerically
also. Of course a photographie reproduction is not sufficient for a
comparison of intensities and a numerical test must be reserved for
a future paper.

For an estimation of the real ratio of intensities of the components
of a divided spectral line henceforth care must be taken that for the
region of the spectrum under review the vibrations in the incident
light are inclined at an angle of 45° C. to the slit.

If in the case of a complicated division of a spectral line some
components are weak, it will sometimes be possible to streng-
then these components by placing a quartz plate of suitable thickness
in front of the slit. This will be feasible in all cases in which the
incident vibrations are not those most favoured by the grating.

Of course also with other spectroscopes this device does apply

') Gumrien. Wied. Ann. Bd. 64 p. 333. 1898.
19%

( 292 )

e.g. in the case of a MricuersoN echelon spectroscope, if the incident
light has been previously analyzed by means of an auxiliary
spectroscope. Reflection and refraction in the glass prisms of course
weakens to different amounts vertical and horizontal vibrations.

Cases in which relation (1) fails are to be observed in some
spectra with many lines (e. g. iron). Among adjacent magnetic triplets
some are to be detected in which the distribution of intensity in
one resembles figure 1, in the other figure 2. Without further
analysis one may conclude that for the one or for the other relation
(1) fails.

EXPLANATION OF THE PLATE.

The figures are thirtyfold enlargements of negatives concerning the mercury line
5769, 4.

In all cases the image of the source was projected on the slit with a glass lens.

Fig. 1. No quartz plate in front of slit.

Fig. 2. Quartz plate, rotating plane of polarization 45° in front of slit. The
distribution of light corresponds to that in source.

Fig. 3. Quartz plate, rotating plane of polarization 90° in front of shit. Though
the time of exposition was thrice that used with the other figures, there appear
cnly traces of the outer components in the original negatives.

Chemistry. — “On lupeol.’ By Prof. P. van RoMBURGH.

In the Comptes rendus of June 24, 1907, JuNerLeiscH and LEROUX
state that lupeol cinnamate occurs in the gutta percha of Palaguium
Treubti Brox.

I have demonstrated previously that cinnamic acid may be obtained
from this species of gutta, whereas lupeol cinnamate proved to be a
constituent of different commercial varieties of gutta percha *).

JUNGFLEISCH and Leroux have now studied the lupeol obtained by them
and state that this substance on heating suddenly on the “bloe Maquenne”
melts at 190°—192°, then immediately solidifies and melts again at
212°. They explain this phenomenon by assuming that lupeol loses
water and is converted into a hydrocarbon, melting at 212°, to which
they give the name of lupeylene. At 130° lupeol would lose water
slowly, very rapidly so at 150°—160° and suddenly at 190°.

h B.B. 37 (1904) 3442.
*) Diss. Utrecht 1906.

P. ZEEMAN. The intensities of the components of spectral lines
divided by magnetism.

Proceedings Royal Acad. Amsterdam. Vol. X.

1. No quartz plate in front of
slit.

2. Quartz plate, rotating plane of
polarization 45° in front
of slit.

Intensities as in source.

3. Quartz plate, rotating plane of
polarization 90° in front
of slit.

( 293 )

On treating lupeol with acetic anhydride and sodium acetate at
170°, they did not obtain lupeol acetate, but lupeylene, and they
argue that the acetate cannot be obtained by the ordinary methods
owing to the lupeol losing water so readily.

But some time ago (loc. cit.) I obtained with Dr. v. p. LINDEN
an acetate, by acetylating lupeol; whilst Dr. Conen also prepared
this ester and studied several of its reactions.

It, therefore, did not seem to me superfluous to repeat the expe-
riments of these French chemists, and to again prepare and analyse
the lupeol acetate, so as to make sure that this substance really
exists; and that Dr. Conen, who did not analyse it, because the
properties coincided with those of my preparation, and because a
mixture of his acetate with lupeol exhibited a considerable lowering
of the melting point, was really in possession of the substance.

In order to observe readily an eventual separation of water, and
to see and weigh the same, I, first of all, heated lupeol for many
hours in one of the limbs of a reverted U vacuum tube placed in
an oilbath at 190°, whilst the other limb was cooled in a Weinhold’s
glass containing liquefied ammonia. In the limb containing the lupeol
a sublimate of beautiful crystals had deposited above the oil surface
whilst a slight deposit had also formed in the cooled limb.

The weight of the lupeol was 0.5403 gram.

The deposit in the cooled limb weighed 0.0065 gram.

On heating the same at 100° there remained 0.0046 gram.

Therefore only traces of water could have been present in the
cooled limb.

The sublimate in the heated limb melted at 212°—213°.

In another experiment, 1.0806 gram of lupeol was weighed in a
glass boat and placed in a horizontal tube which could be heated
in an airbath. The tube was connected to a reservoir with sulphuric
acid and the whole apparatus was evacuated by means of a water-
airpump. First I heated the apparatus for ten hours at 140°—160°;
the loss of weight amounted only to 0.0066 gram, but it must be
observed, however, that a sublimate had formed in the tube just
above the boat. Then the substance was heated in the same manner
for six hours at 190°—200°. The total loss in weight then amounted
to 0.041 gram, but as the sublimate weighed 0.039 gram it was in
reality only 0.002 gram. A separation of water, which would have
amounted to 0.040 gram, was therefore again out of the question.

The residue of the two experiments, after being reerystallised from

( 294 )

acetone, was combusted with lead chromate and the result showed

that the lupeol had remained unaltered.

0.1991 gram yielded 0.2147 gram H,O and 0.6172 gram CO,

EI GE
Found : 12.08 84.54
Caleulated : 11.49 84.85 (for C,, H,,0)*).

On boiling with acetic anhydride (10 parts) and sodium acetate
(1 part), the residue could be converted readily into an acetate
melting at 213° as shown by the analysis :

0.2191 gram yielded 0.2251 gram H,O and 0.6588 gram CO,

H. C.
Found : 11.51 82.04
Calculated : 10.93 82.41 (for Cy Os

For the purpose of comparison the acetate of non-heated lupeol
was prepared and analysed in the same manner. It melted at 212°.

0.2113 gram yielded 0.2169 gram H,O and 0.6362 gram CO,

H. GC:
Found : 11.5 82.11
Calculated : 10.93 82.41

A mixture of the two acetates analysed also melted at 212’, whilst
the acetate mixed with lupeol gave a strong depression of the melting
point.

In another experiment, lupeol was heated at 200° for 2'/, hours
in a current of dry earbon dioxide. A small calcium chloride-tube
attached showed a slight increase of weight, but it appeared that a
little solid matter had again volatilised with the current. The heating
was then continued for six hours and the residue heated finally
until the mass began to melt. On treating the same with benzoyl
chloride and pyridine it was easy to obtain the lupeol benzoate,
(m.p. 264°) proving that the lupeol has not passed into the hydro-

carbon.

Finally I have also heated lupeol with acetic anhydride and sodium
acetate in a sealed tube for three hours at 170°. The reaction product

after being treated with water was recrystallised from a mixture of

acetone and alcohol. The melting point of the product obtained was

') | will not go into the question whether it would be better to assign to lupeol
the formula C39 Hs O.

ee ee

( 295 )

212°. An addition of lupeol acetate from a previous preparation did
not affect the melting point. If, however, it was mixed with lupeol
or with lupeol which had been heated for some time at 190° a
serious depression (about 20°) of the melting point could be observed.

The experiments described, therefore, prove convincingly that lupeol
(obtained from bresk) is not converted into lupeylene under the
circumstances mentioned by JUNGFLEISCH and Lrrovx.

As lupeol might perhaps exist in two modifications, Dr. F. M. JALGER,
to whom I wish to convey my best thanks, was kind enough to
study the behaviour of lupeol on melting. Dr. JARGER communicates
to the following particulars me:

“If lupeol is melted to a singly-refracting liquid £, which takes
place very sharply, the mass, on cooling, solidifies partly to an

aggregate of broad pointed needles

A, glittering in high interference

colours, partly to a horny singly-

So refracting mass A’, which fre-

quently exhibits globular sphero-

lites, resembling liquid droplets,

which are very feebly doubly-refracting. The needles A at once

show a tremendous number of transversal clefts, whilst the splendour

of the colours diminishes strongly; A passes here into a second

modification B, the common form of lupeol. Meanwhile the horny

mass has also burst and exhibits here and there a strained double

refraction besides an increase in the number of droplets, that is

to say, crystallisation nuclei in an embryonal condition. If heated

carefully for a moment, it erystallises into the needles A, which pass

immediately into B (by bursting ete.); the horny mass A’ is iden-
tical with the needles A: it is A in a supercooled condition.

The crystallisation velocity is here nearly = 0, and by heating
it is increased to such an extent (owing to the diminution of the
internal friction ete.) that the mass begins to crystallise. This is
a phenomenon well known to me; beautiful instances of erystal-
lisation on heating are usnic acid and many cholesterol esters of
fatty acids.

On remelting B, A is formed some times for a few short moments,
afterwards L. The two modifications therefore appear to be related
by enantiotropy.”

Utrecht, Org. Chem. Lab. Univers,

( 296 )

Statistics. “Relations between mortality of infants and high
temperatures.” By Dr. BE. van EvERDINGEN. (Communicated by

Prof. C. H. Winp.)

In the “Statistische mededeelingen uitgegeven door het bureau van
statistiek der gemeente Amsterdam” the other day a treatise appeared
as N° 19: “Kindersterfte in Nederland (in de jaren 1881—1905)” by
Prof. Dr. R. H. Sanrer and Mr. Pu. Fanxunpure.’) The authors point
to the fact of the existence of a distinct maximum in the mortality of
children under one year of age in the summer-months, and try to
find among others a relation between the amplitude of this maximum
in different places and in different periods, and the monthly means
of temperature at neighbouring places in the same periods. The
result is rather negative; hence they write as follows:

“Also from the chronological comparison of the mortality of
infants and temperatures, as given by us here for Zealand and the
town of Groningen, we are only able to draw a negative conclusion.
If in a single case we may speak of parallelism, in the majority of
the cases no direct relation between temperatures and mortality or
infants can be traced. In so saying we do not imply that we have
proved tbe statement, that the mortality of infants should be in-
dependent of the condition of the air. On the contrary, the diagrams
we gave furnish the most evident proofs of a relation between the
condition of the air in the summer and the mortality of infants.
But it is not the height of the temperature which regulates this
mortality. As we remarked before, in our opinion the probability
remains, that the temperature-fluctuations of the summer — diurn
or interdiurn are the causes which exert an obnoxious influence.
The data concerning these fluctuations fail however and cannot in
our opinion be replaced by data about temperature-frequencies, which
the Meteorological Institute would be able to furnish. We cannot
but with a single word refer here to the theory which connects the
summer mortality of babies with the presence in this season of a
larger number of insects, bearers of disease-germs. Positive facts
enabling to further investigate this matter are lacking at present.

Hence there is reserved here a vast field of research for the
zealous investigator of the future.

1) A german translation of this treatise appeared under the title: “Statistische
Mitteilungen des Statistischen Amtes der Stadt Amsterdam N°. 19, Kindersterblich-
keit besonders in den Niederlanden, bearbeitet von Prof. Dr. R. H. Satrer and
Dr. Pu, FALKENBURG.

( 297 )

2. We think we can show that the writers have expressed them-
selves here in too definite terms, and that a distinetly positive result is
obtained if another method of research is followed.

Already in furnishing the mean monthly temperatures for periods
of 5 years, which the writers used for their research, the present
writer expressed his doubt as to whether these data were fitted for
the purpose aimed at. If the fluctuations of the mortality of infants
were merely directly proportional to the fluctuations of the mean
monthly temperature, the relation sought for ought indeed to appear
also in this way. As soon however as these data are otherwise

connected — e.g. the increased mortality occurs only after the tem-
perature exceeding a certain limit — it is no longer allowed to use

mean values without further inquiry.

The research of Prof. Savrer and Mr. FarkeNBere did indeed not,
as we saw before, reveal any relation between mean monthly tem-
peratures and mortality of infants. We will demonstrate this here
clearly once more by giving for a single town, Groningen, the
deviations from the mean for 25 years of the 5-annual means of
the mortality of infants in the summer months May-September, and
by their side, in italies, the same deviations for the temperature.
The former are given in hundredths per diem, the latter in tenths
of a degree Celsius.

GRONINGEN 4881—1905.

Period | May | June July | Aug. Sept.

|
18811885 | 10 —5| 12 —9| 32 Dee EE
{886—1890 | 9 3 | 17 1 | U —t11 | == 9 =2
haden aie westertoren zl Aas Me 2D > 4
1896—1900 | A4 —5 | —5 15 | =20 6 © 4 8
foots een 3 eae ate | 6 —2 | —4 —2
| |

If high temperature-means for 5-year-periods were accompanied by
high mortalities of infants, at least the signs of the two kinds of
deviations ought to agree generally. We find however 12 concordances,
12 discrepancies and 1 undecided case; hence in this way no relation
is apparent.

3. It might be supposed that this very unfavourable result is
caused partly by adding up the numbers for five years. In this con-
nection we might mention that Dr. OrraND *) formerly traced a

VAG. OrLanD, Invloed van het weer op het sterftecijfer. Thesis, Utrecht. 1896.

( 298 )

difference in the general mortality by comparing very hot and very
cold summermonths. The principal causes however are different.

We now take as an example the mean mortality of infants at
Groningen over the whole period 1891—1905, expressed for every
month in percentages of one twelfth of the year-mortality ; then we
find in round percentages (le. p. 74, Table XLI B).

April May June July Aug. Sept. Oct.
103 93 100 110 133 103 83

We will compare these numbers with the mean monthly tempe-
ratures, and moreover with the number of days with excessively
high temperatures, which occurred during a similar period. In this
respect we think in the first place of the days with maximum tem-
peratures above 25°C., for which the normals oceur in the ‘“Maand-
overzicht der weersgesteldheid in Nederland” *).

We thus find for the total number during the period 1894—1906.

April May June July Aug. Sept. Oct.
2 20 64 100 Dl 22 1
whereas the mean monthly temperatures in the period 1891—1905 are
8.6 15.0 16.6 18.4 17.6 EN 9.6
omy 5 UW 8 © There is much more resemblance between

the form of the maxima in the first two
series of numbers than between those of
the first and third series, as is clearly
shown by fig. 1. (S mortality, Z number
of days with max. temp. > 25°, 7 mean
monthly temperature); but also for the
second series the epoch of the maximum does
not coincide with that of the first: it seems

as if there is a retardation of the mortality
as compared with the high temperatures.

In itself this does not look improbable.
Though the writer enters here a field where
he is searcely entitled to a judgment, he
thinks he may risk the supposition, that
perhaps the high temperatures favour the

development of diseases which only after
a certain lapse of time cause death. If this

be the ease, then a better agreement between
the fluctuations of temperature and mor-

1) (Monthly weather review in the Netherlands) Publ. N°. 94 Kon. Ned. Meteor, Inst,

( 299 )

tality must be obtained if the latter are compared with mean tem-
peratures or numbers of days with high temperatures for a period
which begins and ends a little earlier.

We have tested this conclusion by calculating the mean tempera-
tures as well as the numbers of days with temperature above 25° —
which, in accordance with a terminology used in meteorology, we
will call henceforth “summer days” — once for the calendar months,
once for periods from the 16 of one month till the 15" of the
next month.

Both the choice of the “shift? of 15 days and that of the tem-
perature-limit 25° are somewhat arbitrary. For a preliminary research
like ours there is however no objection to this. From the table below
it appears that at least for some parts of our country the shift has
about the size which serves the purpose; by S are indicated the
mean values of the mortality of infants for calendarmonths during
the period mentioned in the first column, given in percentages of
one twelfth of the yearly death-rate, as we will continue doing in
the following pages; by 7’ the mean numbers of summerdays in 5
years, for periods of one month shifted over 15 days.

Period Place of observation May-June | June-July | July-Aug. Aur. Sept

100 110 133 103
1891—1905 Groningen ||

E Ie 40 Nt 16

| | |
S Utrecht ij 4102 130 133 | 97

1881 —1905 | | |
T Utrecht—de Bilt | KE 5) 22 15

| |
S Zealand | TA 159 } 459

1881 — 1905 | | | |
T Flushing I 4 12 12 | 7

\| | | |

For Groningen and Utrecht the maxima now coincide wholly or
almost so. For the province of Zealand, only partially well represented
as to its climate by Flushing, a difference of a month in the epoch
of the maximum remains.

4. We first give here the results of the investigation for Groningen,
in which we compare successively with the deviation of the mortality
in 5-year periods the deviations of:

( 300 )

a. the common mean monthly temperatures ;
bh. the means for the periods May 16%— June L5'" ete. ;
c. the numbers of summerdays for calendarmonths;

d. the number of summerdays for the periods May 16'*—June 15" ete.

GRONINGEN 1881—1905,

Period | June July Aug. | Sept:

a. Mean temperatures for calendarmonths

1891—1895 3 13 5 5 | —28 OAT
| |

1896—1900 7 12 | —6 2 10 ANT

1901—1905 || —4 1| 414 2 19 ee oe

b. Mean temperatures May 16th — June 15th etc.

EEN — 5 ONE 7 ee
| |

1896—1900 7 3 —~6 —2 | 10 8 | 5 5)

1981-1905 || —5 3 | 41 2 ON)

c. Summerdays calendarmonths.

IEN Ee || Ge i |) HE ii
| |
1896—1900 7 ale 6| 40 2° |, Saas
|
19 —1905 || —4 — 2] M 65 49 SSN omen

d. Summerdays May 16th —June 15th etc.

1891—1895 || —3 A 1 98 us| de 5
1856—1900 7 Bk =D AD GE 5 2
190t—t03 || A —2 | 11 B 70 7 OSE
First regarding only the signs, we find:
concordances discrepancies Undecided
a 6 5 |
b d 1

oe
a
|

d 10

( 301 )

The differences between « and /, and between c and d give the
effect of the substitution of number of summerdays for mean-tempe-
ratures, the differences between « and /, and between c and d the
effect of a shift of 15 days. It appears that the improvement in the
concordance of the signs is largest for the transition from 5 to d;
in the transition from c to d in the first place the improvement also
in the quantitative agreement of the deviations of mortality and
number of summerdays is remarkable. Finally the agreement in case
d may be called so satisfactory, that but little doubt remains whether
the high temperatures must be considered as the cause of the increased
mortality of infants.

Hence the negative result arrived at by Prof. Sarrer and Mr. FaLKEN-
BURG was due partly to the use of mean temperatures instead of
temperature frequencies, partly to their non considering a retardation
of the mortality with respect to the cause of death.

We will now test the agreement in case d also for Utrecht and
Zealand.

UTRECHT (de Bilt).

Period June | July | Aug. Sept.
| | | gu
18811885 | 16 —7| 17 10/299 — 3) A3 —4
deser 4eon || edo td A Soya og
IRE SM — Zal SS SSN ij 1
1896—1900 | — 7 8 | 7 4 8 21 15 8
NE | 7 | HC | 8

Period June | July | Aug. ee Sept:

[ ]
1881—1885 | ted |. 9} 21 3 | iQ. 223
18861890) 4 2 MEE RE paar, Bee
ieee a, Gok eid 10 |= 8
1806 1000-), AB AA —5| A (7 |. Ent 7

1901—1905 | 4 OA == 0 1 ae

( 302 )

Hence so far as the signs are concerned we find :

Concordance Discrepancy Undecided
Utrecht: 13 a —
Zealand : 12 4 4

The number of econcordances in these cases is large enough to
show that the fluctuations in the number of summerdays play an
important part in the matter of the mortality of infants, especially
if we consider that at Utrecht as well as in Zealand most concord-
ances occur in the months of large mortality of infants: July and
August for Utrecht, August and September for Zealand. Doubtless
there are besides them other important circumstances, not connected
with temperature, the influence of which even in means for 5 years
is not yet eliminated. This need not surprise us — it rather may
be called remarkable that in the case of Groningen not more is
shown of such circumstances. Whether a better agreement might be
obtained by assuming a higher temperature limit for Utrecht, for
Zealand a lower temperature limit and another value for the shift
we have not tried so far.

The mean temperatures for the periods May 16%— June 15% etc.
were not calculated for Utrecht—de Bilt and Flushing; a comparison
of the methods «a, c and d however favours the view, that no impro-
vement would ensue. For, the result for Utrecht was :

Concordance Discrepancy Undecided
al 15 7 =
c 13 6 1
d 13 if —
for Flushing
a i a 6
c 12 7 1
d 12 4 4

It would seem as if the result for Utrecht is practically the same
in the three cases. If however also the quantitative agreement is
considered, this appears to be wholly lacking in the case c¢, but
to be much better in case d than in case « ; hence the results obtained
for Groningen are also here, though not so generally, valid.

5. A drawback of the use of means or sums for periods of 5

( 303 )

vears is this, that the total number of data for comparison is rather
small, and that there remains an uncertainty as to whether really
the increased mortality, appearing from these means, occurred in the
same years in which also the number of summerdays was largest.
For this reason we have compiled from the “Ned. Staatscourant”
the numbers expressing the death-rate of children less than one year
of age for the period 1881— 1905, both for Utrecht and Groningen;
we have expressed the monthly values in percentages of one twelfth
of the yearly death-rate, and compared these data after the method
of the preceding §§, by comparing the deviations from the means
for the period 1881—1905 respectively 1891—1905, with the
deviations of the number of summerdays between May 16% and
June 15 ete.
The results are given in the following tables.

GRONINGEN 1891—1905.

Year June | July | Aug. | Sept.
1891 | —4 A4 | B AA =| ONE
92 | 35 DE Ald | 2 2
| |
Dn EN EE = Sa hg
er EE le 1 eal Gy Seca) Sap” eee,
95 9 sld 0 in 13 5
| |
96 Al >| 48 2 | =p oen BSS
Oe ae pl Toe ey Ts
98 —7 —1|—67 —6 42° —2) |_— 9 5
EE
1900 12 zis 2 Pest 5 61 2
Oe ere See 0 3 De MEAN 0
02 48 Dl On aen
03 —Il1 0|--15 —3 1 —# oT
Ol en En ZE BANE

( 304. )

UTRECHT 1881— 1905,

TE ä B 7 a |

Year June | July | Aug. | Sept.

1881 9 — 3 | —14 2 12 1|—9 — 8
82 |} —17 —3 3 — 349 — 2 10 —3
83 35 — 2 0 3\;—61 —3/;—9 —1
84 9 — 4 35 7 qi 6 | —40 5
85 39 3 12 1} —3|—15 —e2
86 96 —1)—3 — 3)/—15 — 2 43 10
87 B —4| A7 —1)|)—9 Ol —2 —1
88 —9 —1}]—21 —1|2 —2|—297 —3
89 27 Á 16 —1|—8 —4 10 — 2
90 21 — 40 —5|)—3 —2|—15 — 2
91 —21 — 4] —28 --3 | —15 —2/]—8& —2
92 3 4)—22 —4]-—42 — 3 16 2
93 i 0 18 4 40 0 | —24 2
94 —12 — 2 10 — 1 0 —1| A7 — 3
95 —4 26 —2| -144 —2 21 2
96 3 0 0 4 | —13 il 8 —3
97 17 6 19 4 0 6|—6 — 2
98 3 2)—33 — 5 15 — 1 57 8
99 —4 — 1 27 2 14 8 13 3

1900 — 8 3} 41 — 1 18 9|—5 2
Ot —17 0 20 1 21 9 | —12 0
02 — 9 1 | —40 1|—48 —3 11 — 1
05 — 25 3 | —18 1 18 — 5 27 0
04 —45 — 1 35 — 2 174 7 —2
05 — 8 0 44 5 36 Ol A7 —3

For comparison we give the same table, with the mean tempera-
tures at Groningen for the periods May 16%— June 15 ete. (case
6 § 4). The deviations for these temperatures are given in tenths
of degrees.

( 305 )

GRONINGEN 1891—1905 (6).

}

Year June July Aug.

1804, | 14) 29> Riga tte) | ag eg oz) 45
92 | 35 Ol (Ae El EN 4 10
le El 49 ad og
9% | —39 —18 Si) at Se he GH ee
95 AE OE EE Baa ise ee
96 Mog | 48 el | ee
EA RC ay 4 ESTE a 9 —8
98 —7—9 | —67 —22 42 — 5 0 25
go? ==. ge 73 Bra vo aa AE | 6 5

1900 CD ET DN DE A = 3

ONE Ek NOTE EN EN
2 PE EN VE EEN
gepsaag [5 Se ú Ei | 35 —13
4 | a al Bie ee eee
Bent A0) ee ier | Me jd Bei

| ol | |

It was to be expected that in these tables more cases would be
found where the signs do not agree, or the magnitude of the devia-
tion in one series of numbers is not proportional to that in the
other series; indeed, all disturbing causes exert their full influence
here. If however we leave out of consideration those cases where
one of the deviations is zero, and those where the deviation of the
number of summerdays is but one, or the deviation of the mean
temperature not more than @.°2 (Groningen 4) then we obtain the
following résume :

Signs equal. Signs opposite.
Number of Sums Number of Sums
cases Groningen cases

wi S 1 S

31 114 927 13 42 191
Utrecht
50 186 1275 19 54 308
Groningen (b)
31 38,4 836 17 14,9 366
20

Proceedings Royal Acad. Amsterdam. Vol. X.

( 306 )

Henee in the two first tables the number of coneordances is much
larger than that of the discrepancies, and, moreover, in the favourable
eases the mean deviations of number of summerdays and mortality
are greater, so that in our opininion no doubt remains concerning
the relation between the two phenomena.

The résumé for the third table clearly shows that the parallelism
with the deviations of the mean monthly temperatures is not so
good as with the number of summerdays.

We may now try to find the factor, which can expressethis relation
approximately. For this purpose we take the sum of all positive
deviations of the number of summerdays, and compute the algebraic
sum of the corresponding deviations of the mortality of infants. Likewise
for the negative deviations of the summerdays. We thus find:

Sum pos. dev. 7’ Sum $ Sum neg. dev. 7 Sum S
Groningen + 81 + 463 — 83 352
Utrecht (town) — 120 + 502 — 120 — 465

Without giving all numbers in detail we may add here the result
for the province of Utrecht, where 54 concordances occur against
17 discrepancies :

Utrecht (prov.) + 1383 + 543 — 118 — 433

The difference between sum S for positive and negative deviations
of 7, rather large for Groningen, is probably an indication of a
non linear relation. If we overlook this and combine the two kinds
of deviations, we find for the factor sought for Groningen about
5.0, for Utrecht (town) about 4.0, Utrecht (prov.) about 3.9.

6. What precedes still leaves open to doubt whether the high
temperatures themselves cause the increased mortality, or, as Prof.
Satter and Mr. FArKeNBURG supposed, temperature-fluctuations con-
nected with them. It might indeed be imagined that, as a rule,
numerous high temperatures would be accompanied by numerous
large temperature fluctuations. Though, from a meteorological point
of view, this supposition did not look very probable, we have tested
it likewise, for which purpose the annals of the Royal Netherlands
Meteor. Institute are quite sufficient. For the same periods from the
middle of one month to the middle of the next for which the sum-
merdays had been counted, we computed for Groningen the sum of
the differences of the maximum temperature from one day to another,
for simplicity neglecting the tenths of degrees. The results were
dealt with in the same way as before: hence the deviations of the

gn

De

temperature fluctuation sums are expressed in entire degrees. The
result follows here:

GRONINGEN 1891—1905.

Period June July | Aug. Sept:
1891—1895 | — 3 —19 | — 5 22 | —28 —16 | — 7 20
1896—1900 7 31 | — 6 9 10 45 5 — 1
19004905 | — 4 —11 11 —31 19 —30 2 —18

Among 12 cases there is concordance in 5, discrepancy in 7 cases,
so that in this way no relation between the temperature-fluctuations froni
day to day and the fluctuations of the mortality of infants is shown,
Also the annual range of the mean amplitude of the temperature-
fluctuations from day to day has another character than that of the
frequency of high temperatures; the maximum of the temperature-
fluctuations falls in June, not in August. Therefore we thought it
useless to separately investigate the /arge or the diurn temperature-
fluctuations.

7. In coneluding our investigation we are well aware that it is
far from complete and leaves room for various questions. If we
succeeded in convincing the reader that one of the prominent causes
of increased mortality of infants is an increase of the number of
very hot days, we express a hope that others, may it he competent
in medical matters, will feel inclined to trace the more direct
relations, to explain the different character of the phenomenon in
various parts of the country, perhaps with the aid of other tem-
perature limits and other shifts. The data the Meteorological Institute
is able to furnish for this purpose, also concerning other elements
than temperature, will readily be put at the disposal of the future
investigator.

The results obtained so far may be summed up as follows:

1st. The fluctuations of the mortality of infants bear hardly any
relation to those of the mean monthly temperatures in the same
months, neither with those of the mean amplitude of the temperature-
fluctuations from day to day.

2"? The number of days with maximum temperature above

20*

( 308 )

25° C. (“summerdays’’) counted for periods from May 16" to June 15,
June 16—July 15 ete shows fluctuations, which in a large majority
of cases agree in sign with those of the mortality of infants in June,
July ete.

Bd If a simple proportionality is assumed between the deviation
from the normal of the number of ‘‘summerdays” and that of the
mortality in a period beginning and ending 15 days later, then for
each summerday above or below the normal number the mortality
of infants is increased or diminished at Groningen with 5, at Utrecht
with 4°/, of the mean monthly death-rate.

Chemistry. — “Action of potassium hypochlorite on cinnamide”,
(2nd communication). By Dr. R. A. Wrerman. (Communicated
by Prof. 5. HOOGEWERrFF).

It has been stated in a previous communication *) that from cin-
namide and potassium hypochlorite was obtained cinnamoylstyrylurea.

(@ HCcuS CH == NH
+z . aS CO
C,H,C# = CH— 00 — NES

This proved that in the action of potassium hypochlorite on cin-
namide an intramolecular rearrangement of atoms takes place, and
that it therefore becomes possible to arrive from a compound with
the atomic grouping:

C,H,C = C— C—N
at one with the atomic grouping:
CERN

A compound of this structure may be very readily obtained from
cinnamide by treating this in methylaleoholie solution with an alkaline
solution of potassium hypochlorite. In this way a yield of about
70°/, of the urethane is obtained :

C,H,c2= CSS N= Cocn,
styrylaminoformic methyl ester.

B. p. 181°—182° at 14 mm. M.p. 122°—123° (corr.)
0,1674 gr. yielded 0,0914 gr. H,O and 0,4141 gr. CO,
Oo Sm 53 12 ce. N, at 14° and 761 mm.

Found: 67,45 °/, C;. 6,11°/, H. and 82 eae

Calculated for C,,H,,0,N: 67,76°/,C; 6,27°/, H and 7,91 °/, N.

1) Proc. 1906, 303.

(-309 )

A substance of the same structure has been deseribed by Tumre
and Pickard’), who prepared it from the potassium salt of the
acetylated cinnamo-hydroxamic acid. As they give the melting point
as 115°, and as, in another respect, their observations do not quite
agree with mine, the urethane was prepared by Mr. W. OcrTMaN,
in the manner indicated by Trieste and Pickarp for the purpose of
comparison.

The two substances appeared to be quite identical; the melting
point was found to be 122°—123° and a mixture of the two melted
at the same temperature.

C‚H, CH=CH Cy, Ts

C,H,CH=CH—COH _ _C,H,CH CH-COK —7

\ N
NOH NO-—C°—CH,

This ready formation of urethane in an aqueous-alcoholic aikaline

C,H,CH=CH—NH-— Coocq,

medium is remarkable.

I ascertained that this reaction also takes place with a derivative
of einnamie acid. From o-nitro-cinnamide is formed the o-nitrostyryl-
aminoformiemethyl ester :

C,H,xo, — CE= CH= N= Go OCH,

This erystallises in bright yellow needles mp. 149’— 150’.
0,2009 gr. yielded 0,3956 gr. CO, and 0,0781 er. H,O.
Osim 5 dooreen Ne at don and) 758) mM.

Found : © 53,70 °/, C; 4,36 °/, H and 12,60 °/, N.
Calculated for C,,H,,O,N,: 54,03 °/, C; 4,55 °/; H and 12,61 °/, N.
A fuller communication will follow in the Receuil.

; ans Chemical Laboratory of the
Delft, July 1907. ; y
den Technical High School.

Meteorology. — “The analysis of frequency-curves of the au-
temperature.” By Dr. J. P. VAN DER STOK.

1. The question in what way the characteristic details of frequency-
curves of different kinds may be pointed out in a striking way ina
pliant, analytical form has again been treated extensively in a recent
work”).

The aim of this communication is to fix the attention on the

1) Ann. 309, 197.

*) H, Bruns, Wahrscheinlichkeitsrechnung und Kollektivmasslehre, Leipzig und
Berlin, Tevpner, 1906,

( 310 )

method of treatment suggested in it and to give some applications
of it to frequency-numbers concerning air-temperature, deduced from
observations made on board the lightship “Schouwenbank’”’.

2. The method suggested by Bruns deserves the more the con-
sideration of all who are occupied with the treatment of frequencies
as it is based on the classical works of Besser and FrCHNER and
can be regarded as a logical outcome of the principles indicated by
these investigators.

As a basis is taken the well-known function =

mofo. se Sr

for which in various works tables are given; the first derivative of
this function :

2
Pe ya ear MEA ols oo (()

assumes after substitution of iv for x and multiplication by h the
form of the specific probability of a deviation x according to the
law of errors of Gauss in its simplest form. The derivatives of
higher order can be written thus:

O32

oz) = A en Wd

T

2° EN HE 1
AE arf 0121 17072

4 x av
= >
NO to <a, (sale
2° —x? If a Cite 4
KOS Ze mal oai Man aon
Ln 2 m5) El Bs 5 |
P, (x) anon oft rr TRUE.

etc.

Now Bruns’ suggestion is as follows: the specific probability (sum
of the numbers —=1) of a deviation from a groundvalue assumed
arbitrarily be represented by the series:

y =hLD,®,(ha) + D,®,(he) + D,D(he) +... . . &

( 311.)

from which ensues, that the integral of this equation, called the
curve of the sums, is expressed by the form

D,®, + DD, + D,0,+ ete. . . . . . (5)

where ® means D(hr). as is the case in what follows.

From (4) it is immediately evident when regarded in connection
with (3) that the suggested analysis of the curve (called by Bruns
not frequency-curve but curve of distribution) shows a resemblance
to the development of a function in terms of a Fourier series.

In the different , terms appear polynomial functions of order
p—l; the ®, curve shows p maxima and minima and intersects
the x axis in p—1 points and alternately will be found for «= 0
either an extreme value (order uneven) or a point of intersection
(order even).

The constants D are determined in the well-known way by
evaluating the moments of various orders with respect to the y-axis
through the origin of coordinates; if we take for this origin the
value of «x corresponding to the arithmetical mean and if we put:

le 2]
{ ary dz = Un,
* ——6O

we find evidently D,=4 on account of u, being equal to 1; further-
more u, must be — 0 on account of the choice of the origin, so
D, must be put equal to 0, whilst, if one defines the value of the
constant 4 in such a way that

id 1,

it is then easy to deduce that also D, must be 0.
The expressions (4) and (5) can thus be simplified and they become

Alk IDD. als a)
and
IDE DD inn ih an UR (58)

The constants D,, D,, ete. can easily be calculated by means of
the formula (3) where, with a view to this, the above mentioned
form is given.

To caleulate 2D, we have namely, to consider the form appearing
between square brackets in the expression for ®,4; and to substitute
in it Anu, for 2”.

Our finding in this way 2D, instead of D, is due to the same
reason why D, must be put equal to }; namely to the form of (1)
in which the number 2 stands as coefficient.

Air temperature

. Schouwenbank. Frequencies

( 312 )

TABLE I.

of Daily-means.

a 5 sis DR 3 5
Celsius 2/5 55 Ei SIE bo 5 ©
See 7 | Pals ees

lp}
EO hy ltl eae Ces eer an eae os st
7-8) EN EE ee ee
—6.9 Sa fermentable sees (Meare Pe ey
—5.9 =O) 2) | — = en
—4.9 —4.0| 2 See eee AES
— 3.9 SON EN
— 9.9 ON ASN AAN || ee |e ee
5416) = 10) |) 8) | Oey || =F 22 =
—0.9 FO] SSS |i | | en
01 .0 | 56 | 48 | 25 En = a=
1.1 220077 89" 50m A B Nn
Ord EON 23 OON TEN ema Wk
3.1 AAO SANSA LAAN Gilet | |] —
4A 5EONLSON TON ASOR KSO IN =| ee en ee
5.4 60/471 420202 BN | 22 | |
6.1 ONES Oe WB IGT all |E
7141 RON ONE EE PONNE ZA IE
Sl 9.0) | 24 | 40 | 69 A86 149 3e =) = ator
9A WOON Anes | Oy FANT Bal | Se | 75
10.4 AEON SSA aly KOTA AS ON 5) — |) ALO
Ml TOON) NN RL GON 70 eN ENG O
12.1 1320) GH BENSON GS |) Sel SNE
ASA VON AST SON OTA KaG TANS?
14.4 15.0; — | — | — | — | 46 |218 | 85 | 49 149 | 87
15.1 16.0 | — | — | — | — | 32 [160 [170 152 292 | 53
16.4 A701 = SR SLA 9451975 1195419301) 418
17 A ONE EDE ze 3}
18.4 HCHO) || eit EAO NEON A7 |) Fle
4971 20.0}; —} — | —}| —] - 7 | 64 106 | 29 | —
20.4 PO |) |) == a |] OF EED SS ||) —
214 DONE Nm pe Pe | a | als Bi ==
921 A lh eS ala ie
93.4 MW as | | S| = | = | =| S| Bl a | =

\

November |

December |

—

( 313 )

For the values of ®,, ®, .., Bruns has given tables, so there
are no further difficulties about the calculations which can easily be
done after some practice.

We must suffice with this short and for that reason incomplete
survey of the method; for further details we must refer to the above-
mentioned work, where all questions which may arise are discussed
extensively.

3. When applying this method to observations of air-temperature
it has been assumed that the series need not be continued farther
than to the third term, so that only asymmetrical (D,) deviations
and symmetrical ones (D,) of order one of the simple law are
regarded, which, with these kinds of curves not differing much from
the bell-shape, proves to be sufficient. When introducing terms or
higher order the disadvantage moreover appears that with the evaluation
of the higher moments the single extreme deviations, therefore in-
accurately determined, play an unduly important part. As first example
have been selected the daily-means of the air-temperature, because with
these frequeney-curves their obliquity changes sign along with the
season and ean therefore be regarded as a climatological factor. The
daily-means are calculated from observations on temperature taken six
times a day during the years 1882—1904.

In Table I the frequencies are given from degree to degree,
calculated at a total of 1000; the number of data amounts of course
for every month to about:

23 < 30 = 690 or 23 31 = 713.

The obliquity is immediately evident; in winter we find extreme
temperatures or negative deviations whieh are not compensated by
equally large positive deviatious; in summer we find on the contrary
important positive deviations not contrasted by negative ones. The
constants of the curve, namely, the mean temperature WM indicating
the origin of coordinates, the factor of consistency / and the coeffi-
cients D, and D, by which the deviations of the curve from the regular
bell-shape are determined are found in survey in Table II; the last
two quantities having reference to u,—=1, so that they must still
be multiplied by 1000 for the calculation of the numbers comparable
to the frequencies of Table I.

(314 )

TABLE II.

Constants of the frequency-curves.

Daily-means of air-temperature.

| M h D, D,

| =
January STONE 0.2587 + 0.01657 — 0.00043
February | 3.842 0.2773 + 0.01959 + 0.00048
March | 5.324 0.2908 + 0.00214 + 0.00213
April | 7.953 0 3738 + 0 00313 — 0.00115
May 11.068 0.3540 | — 0.00847 | — 0.00166
June 14,320 0.3708 — (0.00015 + 0.00114
July 16.871 0.4442 — 0.00216 + 0.00007
August 17.367 0.4380 — 0.01170 — (00026
September 16.032 0.3893 — 0 00634 ++ 0.00106
October | 12.142 | 0.3335 + 0.00470 — 0.00002
November 8.399 | 9.2662 | + 0.09657 | + 0.00659
December | 5.174 0.2377 + 0.02463 + 0.00390 ©

From these results of the calculation it is evident that in contrast
to most frequency-curves, the J, deviations from the simple ex-
ponential law for the frequency-curve of the daily-means of the air-
temperature are slight and may be regarded as being within the

limits of the errors of observation.

In order to investigate how far the calculation agrees with the
observation, the numbers of Table I for the months of January and
December are taken together as being the most asymmetrical. The
numbers obtained in this way are indicated in Table HI by O

(observed).

The constants of these curve are:
4,469 C°
0.2403

== (0.01764

+ 0.00130

TABLE III.

(315 )

Analysis of the frequencies Jan. + Dec. of Table I.

O Gs OG ë | OSE & OE
1 0 10 01 09 =~ 1
0 01 01 ead ZE: 04 0
0 0.2 0.3 0.3 0.0 0.2 0
1 0.4 0.6 ES ile" OR a
Qs 1.4 11 | AAN EEDE of
6 3.4 BG ie Re a= 44 Opa se
14 8.4 5.6 | 5.0 | 0.6 0.1 1
29 17.5 12.0 0) 3.7 8.3 0.9 9
37 32 9 BA - 0.3 had 2.0 6
415 54.9 AE EN IT aa = 9
58 81.5 — 835 |—160 | — 7.5 he eee
985 108.0 a 0.6 15
1055 127.9 NE 41.9) — 10.5 34 — 13
1255 134.9 ate it eeu | — 9.8 4A = tt
155 127.0 28.0 12.6 15.4 2.9 13
138 106.6 31.4 18.2 13.2 0.5 13
96 79.7 16.3 15.7 0.6 1.8 2
57 53.3 42 | 82 | — 4.0 26 | =a
26 81.7 — 57 | 06 | — 63 19 | — 4
7 16.9 hy | ee mens OB e=
a 8.4 REU | ek 01 zr
= 3.0 ROR e320 0.9 0.4 1
= 1.2 See 1.2 0.5 1
— 0.3 ORS 0.9 0.3 4
== 0.3 — 03 |— 0.5 0.2 0.1 0
= 0.4 Oven), aed 0.4 0.1 0
|
= = 1000 5 =244.6 z=118.4 SHUT

( 316 )

In the second column is given under (', (calculated) the distribu-
tion derived according to the simple exponential law; in the fourth
column we find the values of the second term in the series having
D, as factor; from the third and fourth columns is evident that the
sum of the differences is lessened by this term from 215 to 118 a
thousand. As has been noticed before, the influence of the third term
with D, is slight.

The sum of the differences remains 12°/,, also after introducing
this term, which can be called satisfactory considering that the total

number of observations is not more than :
2 >< 3) x 23 = 1426

and that the most unfavourable months have been taken as an example.
In fact, from the regular course of the differences it is evident that
there might be a possibility of making the differences smaller still
by addition of a fourth or a fifth term with D, and D,.

For D, we find the value — 0.00036, from which ensues that of
by far the greater part the differences are due to incompleteness of
the material af observation, so that extension of the series would
avail but little.

4. As fitting material for a second application of the method to
meteorological quantities all the observations of temperature have
been chosen, taken six times a day in the month of July on the
same lightship during the years 18821906. The number of obser-
vations is now six times greater than for the daily-means and amounts
to 4516.

On account of this greater number the frequency-curve will have
a more regular shape and the obliquity which was easily discernible
for the daily-means also for the summer months, will now come
more clearly to the front.

The -observations are arranged according to the different quarters
of the wind, so that we obtain (Table IV) frequencies of the so-called
thermic windrose. On board the lightships the direction of the wind
is determined in accordance with the indications of the compass ;
for the period 1882—1906 we can assume that these observed diree-
tions of the wind can be reduced to the proper direction by applying
as correction the mean deviation, — 15°.

Ca)

Ors 687 | VOG Wwe | o46| S8e | 99 | LEE | SGV | vor LL OET <6 C8 bor | SLE | 896] 67E ung

iy zr = = nay 7 = a = ae = = = 8 EE En = a COG SG
5 b = > I = En 9 Ei TT =F ae a J | | Sr EE G S6>9° 46
Ol | Si Te 0 ST, = 6 [ =a oe = b G 0 J | = GTE EG
VG V4 b 6 0 7 == | 0 b b 6 0 | t t G G G SCT GS
va ci b 6 J 2 6 % | 6 & y v G t L G G GEE V6
86 | L t 9 J 9 os G Y, G 9 9 J OF OF bal Vi y Gre 006
LIG 8 9 6 9 VG Ly 61 Ob G Ve cea 9 al 9 66 OF 6 6059 6h
617 | LG Ol 1G el Ge L9 Ge val vb L 91 eh LG OF | 87 tel 9G CGI Dt 7
GVL LO % Wy Ie 6h) | OVE | 69 GG GG Gh CG 66 Ge che IE 6G is tS fet amet) 412
896 LE LS Va VS LVV | G8 | 76 Ve LE cl 86 kad cS 66 | 6L St 9S GL 9b
66 YG GY 0e €L GSI OV | OL LG 6h SI sh yi LG W OS 99 LY G'9)—9 Sb
£69 | SI 61 ci GL 69 99 Os 6 eh a el 6 BT VG cs 67 VL Cele aE
LOG | 5 1S keld 0G 6 VV Gr y 5 Vi = V6 Vb G cl 9G YY KEA amet là
CO |= SG eh 6 0 G 6 | | EE G G | G LI 66 CO Sma GP
£6 — ta tS 0 1 = or 0 0 = = == ad Ee I [ y Gor VI
Wi = a V =H | = | | = = == = = = ne b DS VES 9.08
TIO || D |MNN| MN MNM) M |MSM| MS |MSS| S [ASS | IS | ASA | SL NEMEN EA | N

‘9061—zasl ‘Ang ‘yuequemnoyps (onouZew) pulMm aug Jo sJoptenb yussIyIP JO} sainyeiadwia}-11e jo salouanbas4

“AI ATEVL

( 318 )

More clearly than in the numbers of Table IV does the influence
of the direction of the wind on the temperature show itself in the
mean temperature Jf and the factor of consistency Jh, arranged in
Table V.

TABLE V.

Direction en ae | 5

Magn. observ.

N | 349 13:10 | 0.3485
NNE | %8 | 16.33 | 0.3478
NE 375 47.50 | 0.3477
ENE | 191 | 17.61 | 0.3564
E | 485 | 17:68 | 0.3155
ESE al eos | 47.53 | 0.3494
SE SIC Aeon Ann | 0.3527
SSE Tip) | ATCT | _0-3436
s | 41% | 47.30 | 0.373
ssw | 195 17.38 | 0.3754
sw | 337 | 417.93 | 0.4037
wsw | 656 | 47.08 | 0.519%
W | 585 17.10 | 0.4685
wNw | 272 | 16.32 | 0.4301
NW 314 16.97 | 0.3519
NNW | 64 15.65 | 0.348
Calm | 18218756 0.3295

From this table is evident that in this summermonth by far the
highest temperatures are observed when there are calms; for the
rest we have the lowest temperatures with the northerly seawind,
the highest with a landwind; the transition from NNE (W 7°.5 E
prop. dir.) to NE (N 30° E prop. dir.) is sharp, much sharper than
that from SW (N 210° E prop. dir. landwind) to WNW (N 277°.5
E proper dir. seawind).

This sharp difference we do not find for the factor of consistency,
which shows for WSW wind a distinct maximum and for calm a
minimum.

The numbers of observations being rather slight for many directions

a

( 319 )

of the wind, the numbers of Table IV have been arranged in
Table VI to five groups where as much as possible comparable series
have been added together.

TABLE VI.
Frequencies deduced from Table IV.
WNW| NE | ESE \WSW| C ||
— — — — Total

NNE| E | SW| W |

= ! |
ESR DEN 2 | 4
11.6—12.5 A Oey | 23
19.6—13.5 Seal) eee | a |=. Il a9
13561415 aga | 25 | 35 | 2 | 3 || 267
14 615,5 318 | 74 | 78 |435 | 18 || 698
15.6—16.5 298 | 148 | 466 | 316 | 24 || 959
16.6—17.5 996 | 153 | 293 | 329 | 37 || 968
17.6—18.5 161 | 126 | 469 | 250 | 27 || 742
18.6—19.5 83 | 9 | 99 [419 | 27 || 49
19.6—20.5 4 | 61 | 57 | a | 48 | 7
20.6—21.5 18 | 38 | 4 | a] 7 98
1 .6—22.5 goed age ie cers A5 Het
29. 6—23.5 ol Bol See | Ae ON Od
23.6—24.5 flow ceed al) Ae
24.6—25.5 etl ae lhe aM ne | 5
95 .6—26.5 NT | poe | las

||
Sum 1454 | 751 | ess liga | 182 || 4516

The comparatively low temperatures for WNW—NNE winds with
a small factor of consistency (great distribution) in contrast to the
high temperatures and small distribution for WSW—W winds is
very clear from this table.

At the same time is evident from these data how the combination
of series with different mean values decreases the obliquity in the
total, so that we can expect that the obliquity factor D, will be
considerably smaller for the total series than D,, calculated for the
various series, which is confirmed by the following table.

( 320 )

TABLE VII.

Constants of the frequency-numbers of Table VI.

M beh D,

WNW—NNE | 16.135 | 0.3576 | — 0.01778 | 0.00385

NE-E 17.589 | 0.3498 | — 0.01657 | 0.00343
ESE-SW | 17.430 | 0.3710 | — 0.01540 | 0.00477
WSW W | 17.089 | 0.4869 | — 0.01300 | 0.00297
C | 18.585 | 0.3295 | — 0.01153 | 0.00108
Total 16.971 | 0.3603 | — 0 01116 | 0.00331

The (negative) obliquity D, is therefore strongest for the northerly
seawinds with low temperature and decreases further regularly with
the azimuth counted from North through East. The symmetrical
deviation D, is greatest for southerly winds and smallest for calms.

TABLE VIII.
Analysis of the frequencies of Table VI.

OM LHe, | OC) | C, | O-Cy-C, | C, | 0=s€
{ Neale sel EEN aeee
Beel ET ST EN 0.7 | 1.0 0
93° <| 9780" a SB nono ema 3
Opel) Goren |e | 5 MO |—88| —2
138 | 1229.7 15.1 45.4 6 |= 64 6
aA | 478.4 32.6 14.7 47.9: | SN
14 | 201.2 19S. 075 13.3 | 14) =2
(Ge. TES || ese 5 eS 3.5 624 | 8
93 | 119.2 | —2.2 |—4145 |— 41.7 |
18 627) | A4 (= 40 = 4007. IO ane
22 A 3.6 |=: 74 0
14 ca chic 5.9 43 | 1.6 14 1
5 25008 3.0 | 203 (O7, | al il
2 | 0.4 | 1e | os 0.8 0.8 0
4 | 0.0 1-0 0.2 | 0.8 0.3 4
RE ted aot
== 1000 | l= 444.2. | E=82.6 | z=42

(321 3

Let us remark bere that a negative D, refers to the ascending
slope. of the curves on the left being steeper than the descending
slope on the right and that a positive sign of D, means that small
deviations appear in greater number than would be the case in
accordance with the simple exponential law.

In order to show clearly the part played by the various terms
of the series in the composition of the curve of distribution a
comparison has been given in table VIII, as in table VI, of the observed
and calculated frequency-numbers of the last series of table IV;
the number of observations 4516 has here been reduced in the first
column under © to 1000.

From this table is evident that if only a great number of
observations is at hand, the frequency-curve of the air-temperature
can be very satisfactorily determined by the three constants of the
series of Bruns, the total of the differences between observation
and calculation amounting in round numbers to 4 °/,.

Anthropology. — “/s red hair a nuance or a variety?’ By Prof.
L. Bork.

Concerning the anthropological importance of red hair the literature
relating to it contains up till now little more than opinions based
upon general impressions or suppositions, founded on statistical data,
which when looked at more closely are open to more or less un-
favourable criticism. There is in those opinions and suppositions a
definite main current according to which it is generally assumed
that a closer affinity of redhairiness exists to what, for the sake of
brevity, I shall indicate as the blonde race, characterized as to the
pigmentation by blonde hair and blue eyes.

The nature of the relation between blonde and red-haired people
is expressed by Topinarp ') as follows: the red-haired type has arisen
from the blonde type “par une action des milieux”. Also Brppor
and RipLey, to mention the principal English and the best known
American anthropologist, assume a closer connection between blonde
and red hair. VircHow looks upon the subject from a somewhat
different standpoint, when he says that redhairiness probably arises
in two manners, viz. by a decrease of pigment in brown hair or an
increase in blonde hair’). This opinion of VircHow is based upon

1) Eléments d’Anthropologie générale. Paris 1885 p. 334

2) Das jedoch scheint mir nicht unwahrscheinlich zu sein, dass es eine doppelte
Art von Rothharigkeit giebt, von denen die eine als eine Steigerung des Pigments
bei den Blonden, die andere als eine Verminderung desselben bei den Braunen
anzusehen ist. Archiv für Anthrop. XVI Bnd. p. 338.

21

Proceedings Royal Acad. Amsterdam. Vol. X.

( 322 )

his statistics of the extension of redhaired people in Germany. Now
it would not be difficult to prove that VircHow was in no way
entitled to such a conclusion on the ground of his statistics; his
data were very incomplete and the relations found by him he him-
self calls “ganz unzutreffend”. I intend to revert to this in another
place, but would like to examine another side of Vircnow’s conclusion
somewhat more closely. For where he says that redhairiness arises,
either by an inerease or by a decrease of the hair-pigment, this
implies that in VircHow’s opinion redhairiness is the consequence of
quantitative difference, and that, in other words, this quality is con-
sequently only a question of gradation. Moreover I do not wish to
enter into the question whether VircHow has a right to place blonde
or brown over against each other as primary or pure hair-colours.
Let it suffice for the present to state that VircHow sees no contrast
between red and blonde hair, but that the former is only anuance,
either of blonde or of brown. I know only one anthropologist who,
in contradistinction to the great majority, raises his voice against the
existence of a closer relationship between red and blonde hair, viz.
Ammon, who in his Anthropology of the Baden population hazards
the suggestion that the difference between blonde and red hair is
not founded on a quantitative difference of the pigment, but on a
qualitative distinction. So Ammon is more inclined to the opinion that
in redhairiness not a nuance, but a variety renders itself manifest *).

In working up my anthropological material concerning the population
of Holland I have naturally come to the question about the importance
of redhairiness, and the conclusion at which I have arrived deviates
from the general opinion. The extension of redhairiness in our country
causes me to deny every closer relationship with the blonde race.

Let me begin by pointing out that the composition of our popula-
tion is very favourable for an answer to this question. A few
years ago I had the pleasure in this meeting to throw light upon
the main features of the composition of our population from the
so-called blonde and brown-haired race. And I could then establish
how the composition of our population differs, if the northern part
of our country is compared with the southern. The blonde type
decreases regularly in a southern direction, going hand in hand with
an increase of mixed types, and though of course in a smaller
proportion, an increase of the pure brown type. The differences

2) Die von manchen Anthropologen beliebte Vereinigung der roten Haare mit
den blonden, halten wir fiir unzulässig, dern die roten stehen in vielen Fallen den
braunen näher und sind jedenfalls stärker pigmentiert, haben vielleicht ein Pigment
von anderer Beschaffenheit. Zur Anthropologie der Badener. blz. 129.

(328)

between the northern and southernmost parts of our country are
in the end rather considerable, and it is for this very reason that
our population is so extremely fit to answer a question like this.
If it should after all be true that redhairiness is more closely related
to blondness, then the variation in the number of blondes cannot but
cause a similar change in the number of redhaired people.

The materials for the following illustration have again been bor-
rowed from my inquiry made at the time into the distribution of the
colour of hair and eyes among the population of Dutch schools. On
the schedules that were distributed for that purpose I distinguished
four colours of hair: blonde, brown, red and black, and four colours
of eyes: blue, grey, brown and brownish-green. The total number
of children examined, amounted, with the exception of the Israelites,
to 478.976. The total number of redhaired individuals among them
is 11772, so that there are on an average 2.45°/, redhaired children.
The figures from which this proportion has been borrowed, are high
enough to consider this as the exact average.

The first question we shall answer is: in what proportion do
red-haired persons occur in the different provinces of our country,
This appears from Table I. In the first column is found the total
number of the children examined in each province, in the last the
number of red-haired ones among them, also in the proportion
expressed by the percentage. What appears from this last column?
Suppose that in round numbers the general average is 25 red-haired
individuals in 1000 inhabitants, then we see that in four provinces:
Friesland, Gelderland, N. Holland and Utrecht the same proportional
number appears, that there occurs in Z. Holland only one in 1000,
in Groningen 2 in 1000 and in Overijsel and Limburg 3 in 1000
less — in N. Brabant 1 and in Drenthe 2 more in 1000 inhabitants.
These figures differ so little, also from the general average, that we
are in my opinion fully entitled to conclude that in the provinces
mentioned the extension of red-haired persons is much the same
every where.

This slight difference in the percentage of redhaired persons in our
country is corroborated by Table II in which the absolute numbers
and the proportions are mentioned of all the places in our country
in which the number of the children examined was more than 2500.
It was to be expected that where the absolute numbers are sometimes
relatively low here, the variation of the percentage would be greater.
But yet nowhere does the proportion fall below 2°/, and only once
a percentage of 2.9 is reached as the most favourable proportion.
Where the absolute figures are high, as in Amsterdam and Rotter-

( 324 )

TABLE I.
: Blondhaired- Blackhaired :
Province Total blue-eyed brown-eyed Redhaired
Friesland 33.053 | 14.282—43.20/, 566=1.7°/, 857=2.50/,
Groningen . 32.223 | 13.401—=41.3 446=1 .4 LEES)
Drenthe . lS GIDI 205183 429—9 .7
Overijsel . 44.389 | 14.713=35.5 6891.6 919—2 .2

Gelderland .
Zuid Holland .
Noord Holland
Utrecht .
Zeeland .
Noord Brabant

Limburg.

41.155 |

21.902

ES
3
oe)
ee)
Ss
in

4.790—=2 8

TABLE II.

1240=2.8
2.712=2.5
Wilts
528=2.4
834—4.1
16614. —

1013=4.7

Municipality | Total | Redhaired | Percent.
| |
the Hague. . | 13.184 | 276 | 2.01
Enschede . . | 3.667 77 | OA
Maastricht. 3.812 86 2.2
Utrecht . 8.668 205 2.3
Haarlem 9.908 229 2.3
Hengelo. | 9.876 68 2.3
Rotterdam. 25.898 | 647 9.5
Amsterdam | 44.118 | 1164 | 8226
Dordrecht. see ne 493 2.6
Zwolle. .,. | 3.618 | 101 | 27
Deventer | 3.754 | 105 | 2.7
Leeuwarden. | 3.502 | 1022 | 2.8
Leiden. … . | 5.68 eaten ain eto:
Gouda . ‚| 3.640 102 | 2.8
Groningen. . | 5.039 149 2.8
Arnhem. 179 249)

6.269

1198=2.5
26402. 4
2472—2.5

545=2.

So ow
~l1 (Jo)
to oot
tl
to —
OD 00 U

( 325 )

dam, the general figure of proportion, which has been found, reappears
again.

Thus far I have left one province out of consideration, Zeeland.
There is no denying that this province takes up a place somewhat
separated from the others, since here the number of redhaired persons
falls suddenly to 1.8°/,. This contrast with the other provinces is too
great not to see here the influence of a definite cause. Yet this decrease
in redhairiness in Zeeland, as will be proved higher up, cannot be
attributed to a rise in the number of brunettes, which really occurs
here, for N. Brabant, which is no less brunette than Zeeland, does
not show this decrease. 1 will not enter into the cause of this decrease,
I only wish to point out that already repeatedly both by Belgian
and Dutch investigators attention has been drawn to the fact that
from an anthropological point of view our Zeeland population takes
up quite a peculiar place among the inhabitants of our country. It
seems to me that this opinion is corroborated by the proportion
found for the redhaired persons.

This much concerning the extension of redhaired persons in our
country in general. The general conclusion to which we come, may be
expressed thus, that with the exception of Zeeland this extension is a
very regular one all through the country. This fact was really contrary
to my expectation, as I myself, when beginning to work up my
data, held the general opinion that there was a closer relationship
between redhairiness and blondness. So I expected that, where in
our country the blonde type varies so strongly, the influence of this
would also come forth in the variation of redhairiness. Let us now,
in order to prove the independence of the two phenomena, pay some
more attention to Table I. For through this table we also get an
insight into the decrease of the blonde and the increase of the brunette
race, in a direction from North to South. As I said before, I dis-
tinguished on the schedules sent round four colours of hair and
four of the eyes, making together 16 combinations. Of these combi-
nations there are two which are really characteristical for the race,
namely the combination blonde hair and blue eyes for the blonde
race and the combination black hair and brown eyes for the brunette
race. The other 14 combinations may be considered as mixed forms
between the two races. Now, in order to keep the foundation of my
reasoning as pure as possible, I have inserted in Table I only these
two combinations to mutually compare them.

In the third column we find the number and percentage of blond-
haired blue-eyed individuals in the different provinces. Now it appears
that the number of pure blondes decreases very regularly from North

( 326 )

to South. The number is greatest in Friesland, viz. 43.8°/,, smallest
in Limburg 21.8°/,, so reduced to half of the number for Friesland.
The fourth column affords a survey of the increase of pure brunettes.
Herein Drente shows the smallest number, 1.3°/,, Limburg the
greatest 4.6°/,. The figures in this column point to a distinct increase
in a southern direction. From this table something else appears that
is important for the characterisation of redhairiness. If namely the per-
centages of the “pure” types are added up, so the blondes and the
brunettes, this gives for Friesland a total of 44.9°/,, for Limburg
only 26.4°/,, while between these two numbers those of the other
provinces are regularly grouped. So the number of mixed types is
in the south of our country nearly 20°/, higher than in the north.
As a general result we may state a decrease of the pure blondes,
an increase of the pure brunettes and the mixed types in a southern
direction.

And notwithstanding in Friesland twice as many pure blondes are
found as in Limburg, a change in the number of redhaired individ-
uals is not perceptible. Therefore 1 think I am entitled to deny
the existence of any relation between the two phenomena on the
ground of the figures found. But my table also induces me to reject
the opinion which is sometimes given, that redhairiness should be
a consequence of a crossing between a blonde and a brunette indi-
vidual. If this were the case, an increase might be expected of the
number of redhaired persons in a southern direction in connection
with the increase of mixed types.

Have I therefore to deny relationship between the blonde and the
redhaired type on the ground of the data mentioned, a still stronger
proof for this is afforded by another fact, which I had expected as
little as the others which have been explained. It is namely the
extension of redhairiness among the Jewish school-population. The
total number of Jewish children examined at Amsterdam, the Hague
and Rotterdam amounted to 9155. Of these 228 were redhaired,
ie. 2.47°/,, whilst for the not Jewish population a proportion of
2.45 °/, had been found. The agreement between the two figures is
surprising and the importance of the fact for the question put by us,
shows itself clearly, when I point out the fact that pure blondes i.e.
blondhaired blue-eyed Jews occur only in a proportion of 8.2 °/,
pure brunettes, i.e. black-baired brown-eyed in 18.1 °/,. From this
it proceeds that in our country among the Jewish schoolpopulation
with 8.2°/, pure blondes, there occur as many redhaired persons as in
Friesland with 43.2 °/, pure blondes. A stronger proof that there is no
direct relation between redhairiness and blondness cannot be desired.

( 327 )

Thus far we examined redhairiness with regard to the increase
or decrease of the number of blondes among our population, and we
came to the conclusion that the two phenomena are independent of
each other. We can now look upon the phenomena from another
point of view. If it were true that redhairiness showed a preference
for the blond race, the consequence of this must needs be that among
the children who, as to pigmentation, belong to the blonde race, ac-
cordingly such as have blue or grey eyes, there are more redhaired
individuals than among those with brown or brownishgreen eyes.

How far this is true is shown by Table III.

TABLE III.

ree of Total (Ploudhatred | Brown Black | Red

. | |

Blue. . . | 186.033 83.340/, 41.819/, 2.380/, 2.479,

Gnreyaen <0). 152.072 719 67 14.66 3.06 2.63

Brownish- 9 =
green 58.531 60.68 28.64 8.— 2.55

Brown . . 82.338 45.05 38.61 14.28 2.03

The first column mentions the total number of children with one
of the four different iris-colours, and in the four following columns
we find consecutively the percentage of the combination of the iris-
colour with one of the four haircolours. Phenomena make them-
selves manifest therein, which were to be expected beforehand. Of
the blue-eyed individuals for example, 83 °/, have blonde hair, of the
brown-eyed only 45°/,; on the other hand the number of brown-
haired persons with the last is more than three times as large as
with the blue-eyed, and a relatively still stronger rise is found with
the blackhaired. Generally speaking, it appears that with an increase
of the pigmentation of the iris also the pigmentation of the hair
increases. This holds good for blonde, brown and black hair. But in
contradistinction to this there appears to be no relation between the
degree of pigmentation of the iris and the hair with redhaired in-
dividuals. For of the blue-eyed 2.47 °/, are redhaired, of the grey-
eyed 2.63 °/,, of the brownish-green-eyed 2.55 °/, and of the brown-
eyed 2.03°/,. It is true, this last figure is the lowest, but it seems
to me that the difference is not so great that therein the proof may
be seen that redhairiness shows less relationship to the brunette race.
Moreover, this opinion could directly be refuted by the fact that I

( 328 )

find a somewhat lower percentage of redhaired individuals among
the blue-eyed ‘children than with the grey or brownish-greeneyed.
Red hair is therefore a quality altogether independent of the degree
of pigmentation of the iris. No matter from what side we look
upon the redhairiness with regard to the other phenomena of pig-

mentation of hair or eyes, there is — at least on the score of my
researches --- not a single proportion to be alleged on behalf of the

opinion that redhairiness should by preference occur in the blonde
race. So I cannot but reject as incorrect the opinion of those who,
reducing redhairiness to a quantitative difference of pigment, see in
it nothing but a nuance. And these results of our investigation
naturally lead to considering red bair as a variety, in which the
pigment is qualitatively different from that in blonde and black hair.
Between these two last there is properly speaking no real difference;
gradually, through numerous shades, flax-blonde hair passes into
jet-black, by an increase of the quantity of pigment; also in red hair
a great number of shades can be distinguished; in proportion to the
quantity of pigment the colour varies between gold-blonde and
fiery red.

How is the appearance and the regular extension of redhaired
individuals among our population to be accounted for? It need
hardly be said that, on the ground of the proportions found, I am
not entitled to give any explanation. For this purpose anthropological
researches of another nature would be necessary. Only for the sake
of completeness I mention the opinion of Topinarp, who explains
redhairiness from a former mixing with an originally redhaired race,
which in pre-historic times is said to have inhabited the plains of
Russia, Siberia and Turkistan and of which one of the groups of
the Finnish population (the Letts and the Esths) are said to be tbe
purest descendants *).

1) L'histoire de cette race est à faire. Jusqu'à nouvel ordre j’admets qu'elle a
occupé le sol de la Russie aux époques préhistoriques, antérieurement à invasion
des Asiatiques, répondant à l'un des deux types finnois actuels, je n’ose dire de
celui qui a apporté la langue du Kalevala. Elle est représentée dans la plupart
des kourgans anciens de la Russie. Le type en est signalé dans les annales des
Han antérieurement à l'ère chrétienne en Sibérie et dans le Turkestan Chinois. —
Kléments d’Anthrop. générale. p. 334.

(November 28, 1907).

( 329 )
BER RAY +A.
Proceedings of the meeting of September 1907.

229 1. 1 and p. 230 |. 7 from the bottom: for p. 1 read p. 215

Proceedings of the meeting of March 1907.
788 |. 6 from the bottom: for 1.299< r< 1.040
read 1.299 > 1 > 1.040

| es eee ME 5 for 1.040 <1 <1
read 1.040 >1 > 1

Le E B for “becomes” read “comes”

ale AS a for “united” read “unite”

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM,

PROCEEDINGS OF THE MEETING

of Saturday November 30, 1997.

DOC

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

Afdeeling van Zaterdag 30 November 1907, Dl. XVI.

ClO WN) SEEN aS:

G. van Rignperk: “On the segmental skin-innervation by the sympathetic nervous system in
vertebrates, based on experimental researches about the innervation of the pigment-cells in flat
fishes and of the pilo-motor muscles in cats”. (Communicated by Prof. C. Wink Er), p. 332.

H. KAMERLINGH ONNES and J. Cray: “Some remarks on the expansion of platinum at low
temperatures”, p. 342.

J. W. LANGELAAN: “On the development of the Corpus callosum in the human brain”.
(Communieated by Prof. T. Prace), p. 344. (With one plate)

W. Karreyn: “On an infinite product, represented by a definite integral”, p. 347.

P. ZEEMAN: “Magnetic revolution of spectral lines and magnetie force”, (2nd part), p. 351.
(With 2 plates).

Mr. and Mrs. Docters van LEEUWEN-REYNVAAN: “On a double reduction of the number
of chromosomes during the formation of the sexual cells and on a subsequent double fertilisation
in some species of Polytrichum”. (Communicated by Prof. F. A. F. C. Went), p. 359.

Erratum, p. 366.

22
Proceedings Royal Acad. Amsterdam: Vol. X.

( 332 )

Physiology. — “On the segmental shin-innervation by the sym-
\ q A K
pathetic nervous system in vertebrates, based on experimental
researches about the innervation of the pigment-cells in flat
fishes and of the pilo-motor muscles in cats.” By Dr. G. van
RIJNBERK. (Communicated by Prof. C. WINKLER.
y

(Communicated in the meeting of October 26, 1907.)

We possess numerous, though dispersed, data, obtained either by
means of experiments on animals or founded on clinical observations,
tending all to confirm the opinion, that in vertebrates and in man,
the efferent nervefibres, intended for the skin, which are conducted by
the grey connecting branches from the lateral column of the N.
sympathicus towards the mixed spinal nerves, are distributed within
the area of the skin that is supplied with afferent fibres by the
spinal nerve. As moreover, in general, save slight deviations, the
efferent sympathetic fibres of the grey connecting branches have
their origin in the ganglia of the column in which these branches
apparently originate, we may assume that the zones of the skin,
innervated by the ganglia of the sympathetic column are nearly
identical in their distribution with the zones of the skin, supplied
by the different corresponding spinal ganglia. Less numerous are
the data about the relative extent of the sympathetic and spinal
zones of the skin; but indirect indications apparently support the
view that the zones of the skin innervated by the spinal gangiia
are more extensive than the zones of the different corresponding
sympathetic ganglia. With this reservation however we apparently
may hold it very probable, that the innervation of the skin both by
the sympathetic and by the spinal ganglia is taking place according
to the self-same morphological scheme. Hitherto nevertheless no
direct proofs have been given by demonstrating on the self-same
object the relative distribution and extent of these innervation-areas.
It has been my purpose to do this now by means of a few simple
experiments.

A. The sympathetic innervation of the pigment-cells and the
spinal innervation for sensibility of the skin in flat fishes.
Since the elaborate researches of G. Poucuwr') we know that in
several species of fishes the phenomenon of the variability of colouring
IG. Povener. Des changements de coloration sous l’influence des nerfs. —
Journal de l’anatomie et de la physiologie. Tome 12 p. 1—90, and p. 113—165,
Parijs 1876. >

( 333 )

in the skin is directly influenced by the sympathetic nervous system.
If in a turbot the connecting branches of some spinal nerves or
these nerves themselves, in that upward turned half of the body
containing the eyes, are cut through, there appears on the skin a
more or less sharply defined dark zone. Povcner considered this
phenomenon to be caused by a paralysis of the pigment-cells in
consequence of the section of the nerves, and he called the dark
zones appearing after section, ‘paralytic’ zones. He made however
no further researches as to the significance of these zones, when
considered as innervation-areas of sympathetic ganglia, and since,
to my knowledge, nobody has taken up again these yet so extremely
interesting researches. I have done so at the present time, and added
unto this a comparative investigation about the sensible innervation
of the skin.

For objects I got numerous specimens of Solea (impar, vulgaris,
monochir) and Rhomboidichthys (mancus seu podas). This latter
species in particular, and likewise Solea impar, have furnished me
with excellent results, and the more detailed demonstration is prin-
cipally based on experiments made on these animals. The operative
part of these experiments was very simple. By a longitudinal incision,
cleaving skin and muscles, and passing along the lateral line of the
organ of sense in the ventral portion of the skin of the caudal part
of the pigmented half of the body bearing the eyes, the origins of
a few haemal vertebral spinous processes were laid bare and the

Fig. 1.

Scheme of course and distribution of the main trunks of the spinal nerves in
the caudal portion of the Pleuronectidi (taken from a preparation of Rhombus
laevis), 1, body of vertebra, 2, neutral spinous process, 3, haemal spinous process,
4'd, 4"d, bw, 4"v, first and second lonzitudinal septum of the dorsal and ventral
muscles, — cr, ca, cranial and caudal boundaries of the preparation. — r.d., r.m.,
r.v., ramus dorsalis, medius and ventralis of the spinal nerves — 7.¢.d., 1.8, ramus
comunieans and ramus spinosus of the dorsal nerve-lrunks. — 7.c.s., left sympathetic
connecting branch.

22*

( 334 )

ventral branches of the spinal nerves were sought. In most cases
these were caught up and torn off together with the connecting
branches of the N. sympathicus.

In all cases the visible consequence of these operations consisted
constantly in the appearance on the skin of a more or less sharply
defined dark field, i.e. darker than the surrounding skin. Distribution
and extent of these dark fields were dependent on the place in the
segmental arrangement of the sectioned nerves and on their number.
The shape of these fields was always identical, being that ofa band,
beginning in the dorsal marginal fin, going somewhat obliquely
cranialward to the lateral line of the organ of sense, and thence
somewhat obliquely caudalward towards the ventral marginal fin,
wherein it terminated. Thus much for the shape and the general
distribution of these zones. As regards thei extent, the following
may be stated. After destroying the connecting branch of one single
spinal nerve I never observed any plainly visible change in the
colouring of the skin. After destroying the connecting branches of
two consecutive nerves, usually a narrow, not very dark zone was
observed, that might be not easily defined. Only when three conse-
cutive branches were destroyed, there appeared a plainly visible,
sharply defined dark zone.

wrr UY,
PII DIS Y a ;
ell

\\

INN
\
SS

nn ANN
Sod MQQ\aeYy
SQQQu
Fig. 2. })
Rhomboidichthys mancus, dark zone appearing alter cutting through three
spinal nerves and the sympathetic connecting branches.

If more than three branches were destroyed, there was found a
dark zone, identical as to shape and position, only broader. If after
a first section of viz. three branches, still another couple of branches,

rz

1) This figure and fig. 3, 4, 6, 7, 8, 9 are reproductions of photographies
counterdrawn in outline.

( 335 )

lying next to these first ones either cranially or caudally, were
destroyed, the originally observed dark zone was afterwards con-
stantly found uniformly broadened, either the cranial boundary being
removed cranialward or the caudal boundary being removed caudal-
ward, according to the case. By these means a series of indications
was furnished, tending to prove that the skin-areas supplied with
pigmento-motor fibres by each connecting branch or by the ganglia
of the sympathetic column, are themselves likewise uninterrupted,
zone-shaped fields. Still further data on this subject were obtained
in the following manner.

a
—
ce

C 22
Sarron ORS
„err OT PY af
Fig. 3.
Solea impar. Isolation of four spinal nerves between four nerves cut through
cranially and four other ones cut through caudally of them.

Se EVEN TUS Oe
<< DN my

7

SS

Fig. 4.
Another solea, on which a similar operation had been made.

If a few, viz. four connecting branches were destroyed, and again
also four other ones eranially or caudally from these, leaving intact
e.g. four branches between the two, two dark zones appeared of about
equal breadth, enclosing between them a somewhat broader zone of
lighter colouring, corresponding to the uninjured branches. (Fig. 3
and 4). By means of similar experiments the supposition that the
ganglia of the sympathetic column innervate zone-shaped skin-areas
becomes nearly a certainty. Some results too were obtained as to
the extent of these areas. Comparative calculations, as shown before,
starting from measurements of the darker and lighter zones, made
with as much accuracy as was possible, have shown that the cranial-

( 336 )

caudalward breadth of a skin-area innervated by a ganglion of the
sympathetic column, having an average length of 20 em. may be
approximated at 7 mm., and that the areas overlap one another
somewhat more than half.

The foregoing having been duly stated, a comparison between
the scheme of the spinal and that of the sympathetic innervation of
the skin lay very near indeed. Once the ventral (and dorsal) branches
of a couple of spinal nerves having been cut through together with
the sympathetic connecting branches, it is easy enough to define the
extent and the distribution of the insensible zone of the skin resulting
from this operation, and to establish a comparison between these
and those of the dark zone. In order to facilitate this definition, I
augmented the irritability for reflex actions in the animals by
intoxicating them with a small quantity of a solution of the sulphuric
salt of strychnia in sea-water (1 : 10.000). After this a slight scratching
of the skin by means of a pin’s point was sufficient to produce a
plainly visible general reaction, making it possible to define the
boundaries between the sensible and insensible areas- with great
precision. I found the results of a series of experiments to be nearly
invariable, so that I may communicate them here with sufficient
certainty.

Generally then the anaesthetic areas and the dark zones, observed
after the section of spinal nerves and their corresponding sympathetic
connecting branches are found to accord completely as regards their
extent, distribution and arrangement. Consequently the pigmento-motor
sympathetic fibres, originating in a certain ganglion of the N.sympa-
thieus and its connecting branch, are distributed precisely within
that area of the skin that is supplied with sensory fibres by the
corresponding spinal ganglion. Both schemes therefore cover one
another completely, and the above given particulars about the inner-
vation of the pigment-cells, holds good likewise for the sensory
innervation of the skin. Thus the central innervation of the skin in
Pleuronectidae is divided into a series of segmental areas, which
considered in their functional significance, may be distinguished in
sensory and pigmento-motor skin segments, but according completely
as regards their distribution and extent.

B. The sympathetic innervation of the pilo-motor muscles and
the spinal sensory innervation of the skin in cats.
The well-known researches of Lanainy (1893) *) have shown that

1) J. N. Lanerey. — Preliminary account of the arrangement of the sympathetic
nervous system, based chiefly on observations upon pilomotor nerves. Proceedings

( 337)

the sympathetic nerve-fibres, intended for the pilo-motor muscles of
the skin of the trunk in eats, originate in the series of ganglia of
the column of the N. sympathicus, that they are conducted along
the grey connecting branches towards the relative corresponding
spinal nerves, thence following the primary dorsal nerve-trunks and
the (dorsal) skin branches of these, to terminate in the pilo-motor
muscles of the dorsal portion of the skin. Besides he has demonstrated
that by far the greater number of the nerve-fibres, originating in
the sympathetic ganglion, the ‘‘pilo-motor” nerves as he called them
were conducted along the selfsame grey connecting branch towards
the one spinal nerve segmentally corresponding with it, and that
along the dorsal skin-branch or branches of this nerve, they jointly
reach the skin, where they are distributed within one uninterrupted
area, that may be sharply defined. He found further more, that these
skin-areas, supplied with pilo-motor nerve-fibres by the series of
sympathetic ganglia form a regular series, arranged on both sides of
the mid-dorsal line of the body. As regards the relation between
the innervation of the skin by fibres for the pilo-motor muscles
from the sympathetic ganglia, and the innervation by sensory fibres
from the spinal ganglia, he confined himself to comparing the arran-
gement of the pilo-motor skin-areas innervated by the sympathetic
ganglia with the results of the researches made by TüreK and
SHERRINGTON about the spinal innervation in the dog and the monkey.
Direct comparisons between the sensory and the pilo-motor inner-
vation of the skin were not made by him. These have been made
recently by me.

The way in which to do this was clearly indicated. At present,
especially after the anatomical studies of BoLK on man, we may
take it for granted, that there does not occur an interchange of
nerve-fibres destined for the skin between the spinal nerves in the
trunk-area in mammalia. Consequently the serially arranged skin-
branches of the dorsal portion of the body represent separately the
different spinal and sympathetic nerve-fibres intended for the dorsal
portion of the skin of the trunk from the spinal nerves and sympa-
thetic connecting branches in which they originate. In order therefore
to obtain a knowledge of the innervation of the dorsal skin-portion
relatively by the spinal and by the sympathetic ganglia, it is sufficient
to define separately and then to compare the different areas of dis-

of the R. Society of London, vol. 52, n°. 320, p. 547—556 Februari 1893. London.
J. N. LaneLey. The arrangement of the sympathetic nervous system based chiefly
upon pilomotor nerves. Journal of Physiology (Foster) vol. 15 n’. 3 p. 176—244,
1893. Cambridge.

( 338 )

tribution of the pilo-motor and of the sensory fibres having their
course in the dorsal nerve-branches of the skin. This may be done
in a very simple way.

Fig. 5.

Scheme of the course of the (post ganglionic) pilomotor- and of the sensory
nerve-fibres toward the skin of the trunk-area in eats.

M.S.= medulla spinalis. — 7.d-7.v= dorsal and ventral root. — N.S. = mixed
spinal nerve. — d.p.d.-d.p.v.=dorsal and ventral trunk of the spinal nerve. —
r.e.d. = dorsal ramus cutaneus. — C.L.= lateral column of the N. Sympathicus. —
y.sp.-g.si. = ganglion spinale, sympathie ganglion. — r.c. = grey connecting branch
— — — — define the course of the spinal sensible fibres .... that of the pilo-
motor fibres.

I obtained this scheme by defining first by means of SHERRINGTON’s
method of isolation the surface of the sensible area innervated by a
certain skin-branch and next by the stimulus of an induced current
applied to the same branch, causing the surface of the skin-area,
innervated by the pilomotor fibres from this branch, to become visible.
In order to do so, the hair on the trunk of the cats I made use
of, were first cut uniformly by means of a so-called tondeuse to a
length of about half a c.M. Afterwards, under narcotics and with
aseptie precautions (as far as possible, the skin not being shorn) a
longitudinal incision was made in the skin along the mid-dorsal
line, and the skin was folded back to both sides. The connective
tissue having been prepared the series of dorsal skin-nerves was in
most cases pretty plainly distinguishable, and it was very easy to
choose a definite branch for isolating and to section the three branches
lying next to this one both cranialward and caudalward, either after

( 339 )

having loosened them from the adjacent blood-vessels that mostly
follow the same course, or else together with the bloodvessels
between a double ligature. The skin was then skitehed and the
animal was allowed a few days quiet. After this the sensible and
the insensible areas to be found in the skin were defined and their
boundaries carefully indicated by means of coloured demareation-
lines. Finally the animal was again brought under narcosis, the
incision in the skin was reopened and the isolated nerves were laid
bare and stimulated. The area-field, on which the hair was rising,
was demarcated by another colour.

Fig. 6.
Pilomotor area of the 7th thoracal nerve.

Z
a aan

Fig. 7.
Pilomotor area of the 8th ea nerve in the same cat.

As regards the pilomoter nerves I can be short, as I have hardly
anything to add to the very accurate communications of LANGLEY
on this subject. Like him I found in my experiments that the
areas in which during the irritation of different skin-branches
and on different animals the hair rose, showed rather important

( 340 )

differences, both as to their extent, shape and boundaries and as to
the intensity of the phenomenon itself. Usually the field, in whieh
the hair rose, was nearly rectangular, and save for a slight
deviation eaudal-ward, it was lying vertically on the mid-dorsal line.
In the most successful experiments the pilo-motor areas extended nearly
unto the dorsal axilla-inguinal line over a dorso-ventral surface of
almost 60 m.M. The cranio-caudal breadth amounted on the average
to 26 m.M. For an instance of the proportions of the pilomotor
areas in an exceptionally favourable case [ refer to the photographs
represented in fig. 6 and 7.

The isolated sensible areas usually presented a shape not greatly
different from that of the pilomotor areas described above. Like these
they were generally nearly rectangular, lying almost vertically on the
mid-dorsal line, and they showed likewise a slight deviation caudal-
ward, perhaps even somewhat more marked. Cranially and candally
they were bounded by the insensible areas; ventrally they passed
without any distinct boundaries into the lateral part of the body,
where sensibility was retained wholly intact. The cranio-caudal
breadth of the sensible areas was on the average 30 m.M., their
dorso-ventral extent of course was not to be defined; that of the
insensible areas was on the average 60 m.M.

We may now pass on to a comparison between the sensible and
the pilomotor skin-areas. On account of what I remarked before
about the variability both as to shape and extent of these latter ones,
it may be inferred already that the results of this comparison presented
likewise great differences. On one important point however the results
of all my experiments are in accord: the pilomotor skin-area was
always to be found within the sensible area of the isolated nerve-
branch. In this respect the principal problem I had put before me
in all my experiments, may be considered to have been solved, at
least for that portion of the skin of the trunk on which I made my
experiments. As regards further the relative extent of the sensible
and of the pilomotor skin-areas, and the exact situation of the latter
within the former, E found, as remarked before, great differences.
Sometimes the pilomotor field area had an extent nearly equal to
that of the sensible field, both fields being consequently almost
identical. In the majority of cases however the pilomotor skin-area
was less extensive in all directions than the sensible area. The place,
occupied by the pilomotor field within the sensible field differed
greatly in different cases. Generally it was lying almost in the midst
of it, as is shown in the cats, photographies of which are represented
in fig. 8 and 9.

nd a

( 341 )

Fig. 8.
Situation of the pilomotor skin-area (white) within the sensible area nearly
isolated by insensible areas (hatched transversally).

Fig. 9.

The same in another cat.

In another case however it lay nearer to the cranial or caudal
boundary of the sensible area, I have not been able to state a definite
rule in this respect.

Returning now to the principal problem aimed at by my researches,
we find that from the above statements it has become evident that
the pilomotor nerve-fibres and the sensory fibres having their course
in the dorsal skin-branches of the skin of the trunk in cats, are
distributed within areas of the skin that are in accordance as to
situation and arrangement but not as regards their extent. Thence
it follows that the sympathetic ganglia and the spinal ganglia inner-
vate the skin after the same scheme, and although the relations in
cats are less simple than those found in flat fishes, still I believe
that here likewise the scheme of the pilomotor innervation of the
skin by means of the marginal column of the sympathetic nervous
system may be called a ‘segmental’ scheme.

(342 )

Physies. — “Some remarks on the expansion of platinum at low
temperatures’. By Prof. H. KaAMBRLINGH Onnes and J. Cray.
Supplement N°. 17 to the Communications from the Physical

Laboratory at Leiden.

(Communicated in the meeting of September 28, 1907).

The communication from the “Physikalisch-technische Reichsanstalt”
by K. Score, in the meeting of Jan. 11, 1907 of the “Deutsche
physikalische Gesellschaft” led us to make a remark already
in the Meeting of June 29, 1907 (These Proc. Sept. 1907 p. 200).
In Communication N°. 95% (These Proc. Sept. ‘06 p. 199) we had
given a quadratic formula for the expansion of platinum below 0°,
from which followed that, as was remarked in the Introduction of
that Communication, a formula of the third degree is required if we
wish to represent the expansion of platinum from — 180° to + 100°
by one polynomial with increasing powers of ¢, and if we have to
deal with observations which if repeated a sufficient number of
times, allow us to reach an accuracy (comp. § | of Comm. N°. 85,
June ’08, These Proc. April ’05) of */,,. in the expansion. We found
this confirmed by the measurements of ScneeL, who arrived at the
same result by determining a quadratic formula for the expansion
of platinum above 0°, and by measuring the length at — 190°.

We now consider the striking difference of the expansion at low
temperatures according to the formula given by us, and that according
to SCHEEL’s formula, viz.: 43 u for the expansion of a bar of 1 meter
between — 183° and + 16°, (cf. ScureL loc. cit. p. 19, note 1), a
difference much greater than could be accounted for by the inaccuracy
of the observations.

For an explanation of this discrepancy we call attention to the
difference of the observations of Dec. 16 1904 and Febr. 3, 1905
in Table Il of Comm. N°. 95°, which give as length of the platinum
bar provided with the two glass extremities, at 16°") before it had
ever been reduced to low temperature, 1027.460 m.m., and a long
time after it had been reduced to low temperature for the last time,
1027.457 m.m., mean 1027.458 m.m., with that of Dec.19, 21 and
23 in the same table which yield the mean value 1027.441 mm.
(from 1027.441, 1027.442 and 1027.440) for the length at 16°,
which was observed on return to the ordinary temperature a day after

1) In Table Il of this communication under L16° for the ordinary temperatures
the length of the bar at 16° reduced on the measuring rod at 16° has been
given and not the length at S as in the tables of Comm. N°, 85.

EE —

( 343 )

the cooling. Indeed this former mean value is 17 w larger than the latter.

Now this difference of 17 u, which refers to a bar of platinum
of 840 mm. (for a bar of 1 M. it would be 20 u) exceeds the
errors which may be ascribed to the inaccuracy of the observation
by about half the difference which exists between ScHrrr’s formula
and our formula of June 1906.

As basis for the calculation of our formula the mean’, of the
two lengths has been taken. We arrive at values for the expansion
nearer to those of ScueeL when for the length at the ordinary tem-
perature we take that which was found immediately after cooling,
instead of the mean of this length and the length which was found
long before and after the cooling, as was done in the calculation
of our formula of June 1907. If we now make use of the first-
mentioned length, that which was found immediately after cooling,
in order to find the coefficients now distinguished by (a) and (/)
from the former a and 5 in the formula:

e= (1 je Na (oo) + (b) (ro) ot)

we find:
(a) 877.7, KAMERLINGE ONNES
(b) 35.7 | and Cray (1905)
Platinum ;
= 183° to == 16°) { wher eas
| (5) aera ScHEEL (1906)

It is true that the now remaining difference of 34u per M. with
an expansion of — 183° to + 16° remains considerably larger than
the accuracy of the observations would lead us to expect, but it is
considerably smaller than that found originally, and taking into
consideration the different sources of uneertainty whether we observe
really what we think we observe, the small number of measurements,
and the difference of the methods applied at low temperatures for
the first time, it is not great.

We had hoped to obtain further information on the difference in
length of our bar at ordinary temperature immediately after the
cooling and long after it, but have not yet been able to do so.

Differences as the one discussed now have more occurred in our
measurements. We have pointed this out in Comm. N°. 95? and

1) In the calculations for the glass the values of the length immediately after
the cooling, Dec. 23 in Table I, and April 15 and 16 in Table Ill, have been left
out of account in connection with the further observations.

( 344 )

for glass we have expressly investigated the possibility of thermical
hysteresis on cooling to the lowest temperatures. In connection with
what has been said in Comm. N°. 95% we fear that for the above
treated difference an irregularity in the behaviour of the place of
fusion of the glass points to the platinum bar has played a part, to
prevent which further experiments ought to be made with still
greater care. If what we now think probable, is verified, observations
in which a difference as the one considered just now, manifests itself,
should be rejected.

Besides the formula of the second degree for temperatures below
0°, we have also calculated a formula of the third degree

cone Re Nee ee
ir a + 550 bh w() + ©) (50) [zo |

for the expansion of platinum between — 183° and + 80° by the
aid of Brvyoir’s observations from 0° to + 80°, in which formula
(a), (6), (c’) refer to the length at the ordinary temperature imme-
diately after the cooling.

The agreement of

(a’) 875.3 | Brnorr and

Re (b’) 316 | KaMERLINGH ONNms
2 (c’) —1.49 | and Cray (1905)

Platinum
(a’) 874.9 |

(b’) 31.41
(c’) — 6.94

+ 100°

"490° ScHEEL (1906)

is pretty satisfactory. Substitution of Scuwer’s values for those of
Benoit would bring about only a slight change in the first group
of coefficients.

Anatomy. — “On the Development of the Corpus callosum in the
human Brain.’ By Prof. J. W. Laneenaan. (Communicated by
Profs ly eT ACH):

The points that at this moment seem of interest in the history
of the development of the corpus callosum have been clearly for-
mulated by Rerzivs*) in the form of questions. Two of these are:
1. Where does the corpus callosum originate? 2. Of what

1) Rerztus. Das Menschenhirn. Stockholm 1896. p. 6.

( 345 )

elements is it composed at its first appearance? The third question
of Rerzius has been amplified by ZvcKeRKANDL *) and may be formu-
lated as follows: what are the changes occurring in the mesial wall
of the pallium in consequence of the development of the corpus
callosum ?

For the answering of the first question a human embryo of the
beginning of the fourth month was at my disposal. The fronto-
occipital diameter of the corpus callosum amounted to but 0.5 m.m.
Figure | shows a frontal section through the more posterior part of
the lamina terminalis.

The plane of section deviating a little from the frontal plane, that
which is shown in the right part of the drawing is more frontally
placed than that which is shown in the left part.

As appears from the drawing the corpus callosum lies in the
lamina terminalis; especially on the left this is clearly evident, where
the underborder of the pallium goes over into a taenia (7) which
is bent in and passes over into the lamina terminalis (/.¢.). The fact
that the ependyma of the lamina terminalis, which is continued into
the ependyma of the taenia, also spreads underneath the corpus
callosum, obviates all doubt as to the existence of this relation. If
now the sections are examined more frontally, it will be seen, that
the more frontal part of the corpus callosum no longer lies in the
lamina terminalis. This part of the corpus callosum exceeds the
limits of the lamina and is situated in the zone of union of the
mesial walls of the pallium. This zone is built up of glia-tissue and
in immediate continuity with the glia-layer covering the fore-side of
the lamina terminalis.

On the ground of this observation I believe that the corpus cal-
losum originates in the lamina terminalis, very soon, however, in
consequence of the enlargement of the commissure, preponderantly
in a frontal direction, it encroaches on the lamina and lies partially
in the zone of union of the pallia.

Another embryo, of the middle of the fourth month, exhibits a
corpus callosum with a maximum diameter of 2.5 m.m. Here the
commissure is still entirely situated in front of the foramen Monroi.
Figure Il shows a frontal section through the more posterior part
of the corpus callosum. In this section the corpus callosum (C.c.)
hes most dorsally, laterally going over into the mesial wall of the
pallium. In this wall, aside from the callosum, we find the fornix

1) ZuekeRKANDL. Sitzb. K. Acad. der W. Math. Naturw. cl. Bd. CX. h. VII,
Wien 1901. p. 234.

( 346 )

(F.) which, in the mesial wall of the pallium, is not clearly dis-
tinguishable from the corpus callosum. Downwards, the fornix may
be followed as far as the anterior commissure (Ca). In the angle,
where callosum and fornix meet, lies a bundle of fibres (Ps.)
ventrally from the corpus callosum and coming from behind. This
bundle crosses in the middle-line anotber bundle of the same kind
coming from the opposite direction. This crossing-system is the
fornix-commissure. More frontally this commissure is wanting and
only the callosum and the fornix are present in the relation I just
now described.

From the topographical relation of the corpus callosum to the
fornix-commissure the deduction may be made that the more posterior
part of the callosum is equivalent to the splenium. In the same way
it follows from the relation of the callosum to the fornix-bundle that
the more anterior part of the callosum corresponds with the genu
of that structure. The origin of the: corpus callosum therefore
comprises the whole commissure, and consequently the growth of
the corpus callosum does not take place by means of the apposition
of new systems of fibres, but by an equable enlargement in corre-
spondence with the growth of the pallium.

The most preponderant change in the structure of the mesial wall
of the pallium at the place of origin of the callosum consists in the
cortex-layer bending a little inward and ending with a sharp edge.
The middle-layer of the wall of the pallium gets richer in nuclei; .
these nuclei surround the callosum and the fornix like acap. Along
the lower edge of the cortex-layer they penetrate into the marginal-
zone of the wall of the pallium. By this process the marginal-zone
disappears as a separate layer.

In the zone of union of the mesial walls of the pallium the changes
in the structure of this wall are more considerable; the observation,
that the most mesial bundles of the fornix pass through the glia-
tissue of this zone of union, seems of importance here, as from this
fact may be derived, that the re-constructed mesial wall of the
pallium — the later septum lucidum — comprises more than the
original mesial wall.

Fig. I.
Frontal section of the more posterior part of the lamina terminalis.
Section 20 u stained with haematoxylin and eosin. Enl 16.5 diam.

Ca. Anterior commissure. L.t. Lamina terminalis.
Cc. Corpus callosum. L.tr. Lamina trapezoidea.

C.ch. Corpus chorioideum. T. Taenia.

a NEN A Sane

Sen get ye
Spit

rof. J. W. LANGELAAN. “On the Development of the Corpus callosum in the human Brain.”

Verslagen der Afdeeling Natuurk. Dl. XVI. AC. 1907/8.

%

#

f

( 347 )

FE. Fornix. Vl. Lateral ventricle.
Lc. Limbus corticalis. V.t. Third ventricle.
L.m. Limbus medullaris.

Fig. IL.
Frontal section through the more posterior part of the corpus
callosum. Section 15 u stained with haematoxylin and eosin. Enl.
13 diam.

C. Zone of union of the pallia. Lc. Limbus corticalis.

C.a. Anterior commissure. Lm. Limbus medullaris.

C.c. Corpus callosum. Ltr. Lamina trapezoidea.

C.ch. Corpus chorioidenm. Ps. Fornix commmissure.

C.str. Corpus striatum. Vl. Lateral ventricle.

F. Fornix. V.t. Third ventricle.
Mathematics. — “On an infinite product, represented by a definite

integral.” By Prof. W. Kapreyn.

The object of this paper is to write the infinite product

een
At)

in the form of a definite integral.
This product is connected with mod. Fu + w), for
mod. F(u + iv) = F(u).ePUw) (u > 0)

where
1 a py?
IC) == Up dl — z
(wn) = 5 = if +.) )
thus
mod. _F(u + w)= Ee) ; .
oo v
HI 1
Al a a)
and

(14 v = T° (u)
s=0 (w+ s) mod? T'(u + iv)

To write the second member of this equation in the form of a
definite integral, we start from Wetersrrass’ definition

1 iL ff
= ll et t= dt
(2) zoue

W
where the integral is taken along a curve JI’ commencing at negative

') Nielsen. Handbuch der Theorie der Gammafunctionen p. 23.

Proceedings Royal Acad. Amsterdam. Vol. X.

( 348 ) /

infinity, cireulating around the origin in the positive direction, and
returning to negative infinity again; thus

2ti lin Lely (Sas
== | e—tt—2 dt — eze f e—tt = dt
TG)

0 0

and if z=u—+w

ao
= GT (en (ru) Hi sin (a) f e—! (on (vlg t)—7 sin (vlg 4) dt
0

= co(om (au)—i sin (a of e—tt-u G (vlg t)—7 sin (vlg 0) dt.

201

Pui)

0
Writing
if e—tt—4 cos (vlg t) dt = M
0
Af e—tt—* sin (vlg t) dt = N
0

2n Bhd 3
TEE) =a-+iq
we obtain
a = (erv + ere) sin (au) M + (er! — e—7) cos (au) N
8 = (em — e—*) cos (ru) M — (er? + e—*") sin (au) N
and
a? + p> = (Pr? — 2 cos 2au + e—27) (M* + N?).

Now we have
oo 00

M= ee wt cos (vg x) du fe y 4 cos (vlg y) dy

0 0

oo) 0
N? = fe a—" sin (vlg v) da fo y—" sin (vla y) dy
(

) 0

M? + N? =i) footy (yy) cos (wu 5) dady
1
0 @

or in polar coordinates, putting

His 0, y= ris oO

12 pe
Me Ae =| fe —7 (cos 8 +- sin 4) (2? sin 6 cos A)—" cos (vlg tg 0) rard.
O10

This double integral may be reduced to a single one, for

( 349 )

(2 — 2u)
(cos 0 + sin 02 2u

len 9) p—2u++! dp = (u < 1)
0
therefore

ns

72 (sin 6 cos 0)
M+ N° =T(2— 20) f cos (vlg tg 6)
0

: dé
(cos O + sin Gu

or

M? 4+ N?=2r(2—2 if (anny ey et are:
i — = CA COs (VLJ tq = iO.
ease (cos O +- sin @)2—2u
0
If in this integral, we change the variable by the substitution
tg @ = e—t
it takes the form:
MLN =4 re f
0

cos (2vt) dt

(et + e—t)2—2u

With this value we find
An © cos (2vt) dt
ee = 4 (2 = 2u) (27? — 2 cos 2 xu He?) LEN,
mod* Pu Hiv) (et Het) 2-24

and finally

d :
v T (u) P(2—2u cos (2vt)dt
H | 1+ -— |= ne - Oe Zeos 2au-+ e—27") Uae
s=0 (ws)? n° (et + e—t)2—2u

0

which holds for all vaiues of », and for values of « between 0 and 1.

Seen Me 2 1 3
If for instance we put v = —, u=-— and — we obtain
Zar 1 4

42? 42? 42?
(: By =I ze aie a sale =

wu
+ et

z 3 1 zt
rT (5) r(,) @ COS 6 dt
— _ a (dt Hee Ki:
Ce Arn
0
23

t
*

( 350 )

Writing «= 1—w' we may also conclude from the as that

1 F(2u' ) ae Fs Cos _cos (2vt) dt
SS AE ST zE —
mod? P(l—u' + iv) n (et He +e teu zu!

or, because

fa
E(u) a a)
(eee has | bara) sin (ul + iv)
* cos (ot) dt
mod? P(u + iv) = 41 (2w) EE
(et + e—t)eu
which formula holds not only for 0< wv’ <1, but also for u’ > 1
Introducing in this equation, the infinite product, we have

i cos (2vt)dt T° (w) 1

et Het’ AT (U) o v?
0 ne le BEES: cu =

a formula which enables us to write the integral in a finite form in

1
two cases viz. u’ =n and uw’ =>n——

If u’ =n= positive number

oo v? oo v?
iT 1 == SS SIN = 1/3
nl +o) Al ee

bo

with
TV — TTU ow v?
ne
2av zel Se
this gives
n—1 vy?
mii+—
se (2vt) dt __ mv I DN) een 3?
A Het) Jm SA 2T'(2n) eve

Wi A iP zj we have

ra

oee YE a eee
s=0 (a 4+ 9) s=n-1 (4 + 5)?

which gives with

ere CT py?

eee
2 s=0 (3+s)
this result

n--2

v?
I
~® cos (2 vt) dt a4 i? (x — 2) a ap (4 + oe
| (et + e121 He oly ero i ge :
0

( 351 )

Physics. — “Magnetic resolution of spectral lines and magnetic
force.” By Prof. P. Zunman. (Second part). *)

Asymmetry in strong fields.

2. By means of the method of the non-uniform field, described
in the first part of this communication, it is possible to survey at
one glance a phenomenon dependent upon the intensity of the
magnetic field for a series of different intensities, all other ci:cum-
stances surely being the same.

I there proposed to use this method for a more minute study
concerning an asymmetry of the resolution of spectral lines first
predicted from theory by Voier *) and lately considered by Lorentz *)
from another point of view.

The theoretical result of Voier, applying to the case of resolution
into a triplet, may be given in his own words: “dass das normal
zu den Kraftlinien wahrnehmbare Duplet der parallel zu & | magnetic
force] polarisirten Componenten bei kleineren Feldstarken in der
Weise unsymmetrisch ist, dass die nach Rot liegende Componente die
grössere Intensitdit, die nach Violett hin liegende aber den grisseren
Abstand von der urspriinglichen Absorptionslinie besitzt.” Vorer here
mentions an absorption line because he considers the so called in-
verse effect, by reason however of the parallellism of the pheno-
mena of emission and absorption, the emission lines show analogous
phenomena.

The amount of the asymmetry of the distances, i. e. the difference
of the distances of the outer components from the middle line, ought
to be on Voier’s theory independent of the strength of the magnetic
field. Moreover it is to be inferred that the described asymmetry
must be scarcely observable.

On a former occasion *) I have given some examples of asymme-
trical resolution and measurements since published by other physicists
undoubtedly go far towards confirming these results.

A more minute investigation of the course of the magnetic separa-
tion, when the scale of field intensities from large to small values
is traversed, is I think still of great theoretical interest. The most
interesting parts of the scale are of course the very strong and the
weak fields.

1) Continued from Proceedings of April 1906.

2) Vorer. Ann. d. Phys 1. p. 376. 1900.

5) Lorentz. These Proceedings November, December 1905.

4) ZEEMAN. ibid. December 1899. Archiv. Neerl. (2) T, 5. 237—242. 1900,

( 352 )

The most. striking example of asymmetrical resolution that 1 know
of, occurs in the ease of one of the yellow mercury Tines (5791).
The structure of a line like this one cannot be made out by means
of MicueLsoN’s interferometer. Indeed the assumption of symmetry,
which is, as has been proved by Lord Rarrrieu *), necessary to
deduce the structure from the visibility curve in this case certainly
is unjustified.

3. Following the method described in the first part of this paper
I have made some experiments concerning the mentioned spectral
line in strong fields. For the Rowranp grating used in my obser-
vations I am indebted to the dutch Society of Sciences at Haarlem.
Presently I hope to give an account of results obtained in weak
fields by means of an interference method.

The grating has 10.000 lines to the inch and a radius of curvature
of 6.5 M., the divided part being of 14 em. width. In the use of
my method the grating necessarily should be mounted in such a
manner that to every point of the slit corresponds only one point
of the spectral image. RowLaNp’s concave grating can be mounted
in a non-astigmatic manner as has been remarked by Rurer and
PAscHeN ?) and this arrangement was made use of in former inves-
tigations by myself, *) Harro and Guess. *)

All observations recorded in the present paper were made with
the spectrum of the first order.

4. Whereas the mercury line 5791 is resolved asymmetrically, the
neighbouring line 5770 is resolved by the magnetic field into a
perfectly symmetrical triplet, or at least very approximately so. I
have used this circumstance for applying the optical method of
measurement of field (see § 1), the mentioned yellow lines being
easily photographed simultaneously.

Fig. 1 represents a ninefold enlargement of one of the negatives.
According to measurements of Fasry and Prror the difference of
wavelength of the yellow mercury lines is 5790.66 — 5769.60 = 21.06
A.U., hence 1 m.m. in Fig. 1 corresponds to 0.551 A.U. Inspection
of Fig. 1 clearly shows that line 5791 is asymmetrically resolved.
Perhaps this is still more evident in the enlargements Figures 2 and
3 of parts of Fig. 1.

1) Rayreien. Phil. Mag. November 1892.

2) Runge and Pascuen. Wied. Ann. Bd. 61. p. 641. 1897.

8) Zeeman. Archiv. Néerl. (2) T. 5. 237. 1900, T. 7. 465. 1902. These Proc.
May 1902, May 1903, Dee. 1904.

tj Harro. Archiv. Néerl. (2) T. 10. p. 148., Geest. (2) T. 10 p. 291. 1905.

( 353 )

Our object of investigation is the relation between asymmetry and
strength of field.

The measurements were made in the following way. The negative
was placed on the comparator, in such a manner, that the middle
line of one of the triplets was contained between the two parallel
Wires in the reading microscope. The parallel wires had been placed
previously at right angles to the direction of motion of the negative.
It appeared that if with one of the triplets the desired coincidence
had been obtained, this was also the case with the other. An extra
system of cross wires, crossing under an angle of about 50°, was
used in the measurements and made it possible to determine the
resolution in the selected point of the lines.

The resolution of one line having been measured for a definite
value of the magnetic foree, the corresponding resolution in the
corresponding point of the second line was determined immediately
afterwards.

The line 5770 appeared to be divided almost exactly symmetri-
cally, so that the resolution could be taken as a measure of the
magnetic force.

On the obtained negatives 54 series of measurements were made.
They relate to different points of 10 negatives made at different times.

The vacuum tubes used were intentionally made somewhat dissimilar.

In order to control the results the negatives were taken with
different maximum intensity of field.

Finally the negatives obtained can be distributed into two groups,
differing by the position of the grating. After taking 7 negatives I
resolved to rotate the grating in its own plane through 180 in order
to see whether this had some influence on the asymmetry.

This appeared to be not the case, but the apparent distribution of
intensities changed in a remarkable manner. Whereas in one position
of the grating figures 1—5 were obtained, the middle line being
strong and the outer components: rather weak, the distribution of
light after rotation became reversed. In this position of the grating
Fig. 1 of my last paper was taken. (See these Proceedings October
1907). The middle line is very weak and the outer components
predominate.

5. The results of the measurements are dealed with in the following
way. The amounts of separation of line 5791 towards the red and
towards the violet are supposed to be functions of the separation
of line 5770, which may be treated as proportional to the magnetic
force. The separations of line 5770 may be taken as abscissae, the
two other separations as ordinates.

( 354 )

Groups of four or five single proximate results simply were com-
bined by assigning to each mean abscissa the mean ordinate.

The 2 > 7 principal values thus obtained are given in the first
three columns of the following table.

Mean Separation 5791 Intensity of
separation | omvatte srs) | Asymmetry field
aa red violet in Gauss
270 234 | 259 | 25 | 44800
328 283 312 29 {18020
362 313 345 32 19860
399 353 388 35 21910
440 394 431 37 24140
453 404 442, 38. 24880
532 475 523 48 29220

All these differences of wavelength are given in thousandths of
an AnasrröÖM unit.

The fourth column in like manner gives the amount of the
asymmetry.

6. The last column contains the field intensity in Gauss. In cal-
eulating it I have assumed proportionality between separation and
magnetic force.

Increasing accuracy of the measurements has furnished continually
increasing arguments for this proportionality and the investigations of
FárBer '), Weiss and Corron *), PascHen*) and STETTENHEIMER *) have
given a high degree of certainty to this simple law.

The numbers in the fifth column are deduced from those in the
first by means of the separations of line 5770 4 0.414 and —0.415
given by Runew and Pascnen for the field used in their investigation.

The measurements of Ruxer and Pascnen concerning the mercury
lines refer, as Prof. PascueN has kindly commmunicated to me, to
a field of 22750 Gauss according to measurements made in his
laboratory by Frl. _STETTENHEIMER, and of 22780 Gauss according

1) Pärger. Diss. Tübingen, 1902; Ann. d. Phys. 9, 886, 1902,

2) Weiss and Corroy. Journal de Physique. Juin 1907.

3) Pascnen. Physik. Zeitschr. 8 Jahrgang N’. 16. 522, 1907.

4) STETTENHEIMER. Diss. Tübingen, 1907; Ann. d. Phys. 24, 384 1907.

(355 )

to measurements, not hitherto published, by Gareiin. In reducing
my observations I have therefore taken 22765 as the value of the
magnetic force belonging to the mean of the two numbers mentioned
for the separation.

7. The results are graphically represented in the following dia-
gram. The abscissae are the separations of line 5770 in A.U., and
the corresponding field intensities in Gauss, the ordinates the corre-
sponding separations of 5791. The small crosses represent the obser-
vations of the table in $ 5.

The full freehand lines give the best mean result of the observa-
tions. (See § 9).

The signification of the upper dotted straight line is the following.

fasooAU A
py
pen ay ees) wa

The mean of the 34 single values of the asymmetry is 0.036 A.U.
The straight dotted line has been traced parallel to the lower line
at a distance of 36 thousandths of an ANGsTROM unit, measured
along the ordinate.

8. We may infer from our observations that with the fields used,
from 15000 to 30000 Gauss, an asymmetry undoubtedly exists which

to say the least bears a very striking resemblance to the one deduced
from theory by Voicr.

In both cases, the theoretical one and that following from our
experiments, there is a difference of the distances between the central
line and the two outer components, in this sense that the component
towards the red is nearer to the middle line than that towards the
violet, just as predicted by theory.

There exists also an asymmetry of the intensities of the outer
components in the sense indicated by theory.

An inspection e.g. of the original negative of which Fig. 1 is a
nine-fold reproduction, or of the reproduction Fig. 1, or better of
reprints on photographie paper of the 29-fold enlargement given in
Fig. 2 or even of that figure reveals the existence of a very small
asymmetry of intensity. This is perhaps most clearly seen by looking
at the figure from a not too small distance, covering the central line
with a small strip of paper. No trace of asymmetry can be seen in
the triplet of line 5770, see also the enlargements Fig. + and Fig. 5
of the middle and outer parts of the right of Fig. I.

On the other hand there seems to be a difference between theory
and observation in this respect, that the amount of asymmetry appears
to be not constant. The table of § 5 and the graphical representation
clearly indicate that when the magnetic force decreases from 30000
to 15000 Gauss the asymmetry also is nearly halved. *).

An error of an amount sufficient to bring a single point of the
upper line on the dotted one is not absolutely excluded (see § 9).
‚For the right part of the diagram the error ought to be three times
the probable error of one single of the principal values (see § 5) and
would happen therefore on the average in one out of every twenty
three cases |.

We have however reasonable security against a combination of
errors which would move all the points of the full line to the
dotted one.

Of course we cannot deduce from the now determined part of
the upper line whether or not it will approach asymptotically to a
finite distance of the lower one.

9. We may now consider the question as to the best fitting
straight lines to our two systems of points.

Measuring the divergencies at right angles to the line the best fit
will be obtained if we make the sum of the squares of the perpen-

1) An excellent series of measurements made after the writing of this article
gives a somewhat lower rate of decrease, the mean value of the asymmetry
being the same.

( 357 )

diculars from the system of points to the line a minimum. The line
thus determined will be the principal axis of inertia of the system
of points ®).

Performing this calculation we find that the best fitting lower line
passes through the point with the coordinates 398, 351, at a slope
determined by 6, = 48°6'. For the upper line these numbers become
398, 386, whereas 6, = 45°35’.

In order to judge of the accuracy obtained in the representation
of the observations by these straight lines the following table may
The third fourth column, the sixth and seventh
column contain the errors of the abscissae and ordinates of the two
point systems to be assumed, if the straight lines are supposed correct.

serve. and resp.

Mean Separation | | Separation | IE
separation 5791 NCA pent | Ae AA | AO
5770) towards red violet
270 | 934 | H1.6 | — 1.8 259 (aire a as
38 | 283 AD | + 4.4 | 312 ek SET
362 13 | — 2.4 | 4+ 2.2 345 ONE 0
399 353 | (Dat || (ual 388 0 0
440 ST ct tS =A oo 431 | +1.0| —09
453 40% Alki les oon ee eel Mar
532 415 iet AEON RE NO 523 0 0

It appears from this table that the lines completely represent the
observations, if we admit mean uncertainty of 0.0013 A. U. in
the observations concerning line 5770 and of 0.0014 A. U. resp.
of 0.0011 A. U. in the determination of the components towards the
red resp. towards the violet in the case of line 5791; we must
admit these as appears from the distribution of deviations.

10. The position of one point of each line may still be checked
by the observations of Runge and PascuHeN. They give for the separa-
tion in the case of line 5770 towards the red resp. towards the
violet + 414+ 1.7 resp. — 415 + 1.7, whereas for the same magnetic

*) Kart Pearson. On Lines and Planes of closest Fit to Systems of Points in
space. Phil. Mag. p. 559. Vol. 2. 1901. Here we read: “The best fitting straight
line for a system of points in a space of any order goes through the centroid
of the system” cf. Keesou. These Proceedings 31 May, 1902.

( 358 )

force these numbers for line 5791 become + 366 + 6.7 resp. 399 + 6.7,
the values preceded by + indicating the mean error. According to
our observations to the abscissa 415 correspond the ordinates 368
and 403, hence a very good agreement.

11. From the extremely small amount of the asymmetry viz.
0.036 A.U. one might infer after comparison with the width of the
spectral lines in our figures that the asymmetry is only a small part
of the real width of the line. Such a conclusion would however be
too rash,

It is true that from our figures and from their originals follows
an apparent width of the outer components of about 0.190 A. U.
The negative of Fig. 1 was not taken however with extremely narrow
slit, but with a width of slit of 0.08 m.m. Other photographs taken
with a width of slit of 0.02 m.m. gave a somewhat smaller apparent
width of the spectral line as the first result.

To be sure however of the real width of the line, which is of
some importance here, I made an independent determination by means
of an echelon spectroscope of high resolving power, the mercury tube
being under the same circumstances, as in the experiments under
review. The width of the spectral line appeared to be the */,, part
of the distance of two successive orders of the echelon. In the
vicinity of the yellow mercury lines this distance is 0.694 A. U.

jC

©

hence the width of these lines is about n= 0.0683 ACE

We may compare this result with a value we may deduce from
results obtained by Mrcuerson. MicHeLsoN’s analysis ') by means of the
interferometer shows that in a field of 10000 Gauss the whole sepa-
ration of the yellow mercury lines is 0.36 A. U. From his diagram
on pag. 354 |. ce. we infer that the width of the spectral line was
under the circumstances of the case one fourth part of the separation
or 0.09 A. U.

Hence taking a mean value for the width of 0.07 A. U. we
conclude that the asymmetry amounts to about one half of the
width of the line or at any rate that width and asymmetry are of
the same order of magnitude.

1) Mrcnerson. Phil. mag. Vol. 45, p. 348. 1898.

TAR
Sitel ns

P. ZEEMAN. “Magnetic resolution of spectral lines and magnetic force.’ (Second part).

Fig. 2.

5791
Enlargement of middle part of
DAE AE
Fig. 4,
ee CEN enn
ip EEN | (U
5770

Enlargement of middle part of
5770. Fig. 1.

Proceedings Royal Acad. Amsterdam. Vol. X

Fig. 3.

5791
Enlargement of point of
5791. Ing. 1.

Fig. 5.

5770
Enlargement of point of
5770. Fig. 1.

1

P. ZEEMAN. “Magnetic resolution of spectral lines and magnetic force.’

(Second part.)
Plate IL.

Fig. 1.

5791 ; 5770

5791 asymmetric separation.
5770 symmetric separation.

Proceedings Royal. Acad. Amsterdam. Vol. X,

( 359 )
EXPLANATION OF PLATES IL AND III.

Plate IL. Fig. 1. The figure is an enlargement (about nine-fold) of the original
negative. The yellow mercury lines 5791 and 5770 in a non-uniform field. 1 mm.
in figure is 0.551 A. U.

Plate Ill. Fig. 2—5 enlarged 29 times after the original.

Fig. 2. Middle part of line 5791 in Fig. 1. { asymmetrical
Fig. 3. Point of line 5791 in Fig. 1. ) separation.
Fig. 4. Middle part of line 5770 in Fig. 1. ‚ symmetrical
Fig 5. Point of line 5770 in Fig. 1. separation.

The letters r and »v indicate the parts towards the red and towards the violet
ends of the spectrum.

Botany. — “On a double reduction of the number of chromosomes
during the formation of the seaual cells and on a subsequent
double fertilisation in some species of Polytrichum.” By Dr. W.
Docters VAN LEEUWEN and Mrs. J. Docrers van LEEUWEN-
REYNVAAN. (Communicated by Prof. F. A. F. C. Went).

In 1904 there appeared an investigation by IKENO *) on spermato-
genesis in Marchantia polymorpha. Since then quite a number of
researches on this subject have been carried out with liverworts.
Here and there an occasional reference to the true Mosses has been
made, but, as far as we are aware, nothing has been published
on their spermatogenesis since the appearance of IKENO’s paper.

The older publications, e.g. those of GuieNarp*) and of Srras-
BURGER*), treat exclusively of the final changes of the spermatids to
spermatozoids. For this reason we began the present investigation
in 1904 soon after the publication of IKENo’s memoir; we obtained
results, differing so widely from the ordinary conceptions, that we
investigated, not only the spermatogenesis, but also the development
and the fertilisation of the ovum.

The material was fixed at a suitable time, mostly in the field, by
a sublimate mixture, and was afterwards stained with iron-haema-
toxylin according to Hermennain. We used Polytrichum piliferum,
P. juniperinum and P. formosum. It is our intention to give a
more detailed account of the work and of the methods which we
have employed, in the Recueil des Travaux Botaniques Néerlandais.

IkeNo made the remarkable discovery that in the antheridial cells,
immediately before division, a small round body passed out of the

1) Ikeno Beihefte zum Botan. Centra!blatt. Bd. 16, 1903.
*) Guienarp. Revue gén. de botanique I, 1889.
5) Srraspurcer. Hist. Beitr. Heft IV, 1892.

( 360 )

nucleus into the cytoplasm and divided itself into two parts, whieh
during mitosis wandered to the poles of the spindle, like true centro-
somes. Since then these centrosomes have been found again in many
other liverworts, but according to some observers, they seem to be
absent from the divisions in the antheridia of Pellia.

At the diaster stage the centrosome disappeared, only to emerge
again from the nucleus at a subsequent division. At the last division
only of the antheridial cells it remained in the cytoplasm and was
transformed into the blepharoplast. For this reason IKeNo considers
the blepharoplast of the liverworts to be homologous with the
centrosome.

Many arguments, both for and against this view, have afterwards
been advanced, which we will not discuss further. Without a detailed
review of the literature such a discussion would scarcely be possible.

Our results with Polytrichum agree in part with those published
by IkeNo and others, but also at the same time differ from them in
certain respects.

I. On the growth of the antheridial cells and on spermatogenesis.

In the antheridia the cells are closely packed. The nuclei are
spherical and contain at their centre a substance, which is deeply
stained by iron-haematoxylin. We do not propose to diseuss whether
this is, or is not, a nucleolus. There is no agreement in the literature
on this point and different investigators designate by nucleolus the
most widely different structures. It is, however, usual in botanical
literature to call such a body a nucleolus, though it also takes up
the other chromatin stains very readily. However this may be, the
dark mass lies in the middle of the nucleus, and slightly more to-
wards the periphery there is, in addition, another fairly large, black
corpuscle.

If nuclei are examined in various stages of rest and mitosis, those,
which are furthest removed from their next division only show the
central black mass. A little later the corpuscle also appears, at first
connected to the central mass by a thin black thread. Soon this
connexion disappears and the corpuscle approaches more and more
the nuclear membrane. After some time it emerges from the nucleus
and remains imbedded in the cytoplasm, in contact with the nuclear
membrane. The corpuscle which was at first round, now becomes
rod-shaped and afterwards undergoes constriction in the middle, thus
assuming a dumb-bell shape. It subsequently divides into small spheres,
which move along the nuclear membrane and which become more

( 361 )

and more widely separated. At this stage each little corpuscle is
surrounded by a light border, which becomes especially noticeable,
when the corpuscles separate from the nucleus.

During mitosis the two corpuscles are found at the tops of the
spindle and hence may well be called centrosomes. There are,
especially during division, many black granules in the cytoplasm.
This always renders the investigation more difficult, but in the first
place the two centrosomes are larger than the other granules and
secondly they are surrounded by a lightborder. In the case of
animal cells their centrosome nature would not be doubted, but with
vegetable cells a certain amount of reserve is still very desirable.
We do not hesitate, however, to call these bodies centrosomes. Of
course they do not stain well in all mitoses. Any one who has
searched for centrosomes in animal tissues, knows, that the staining
of these corpuscles is difficult, even in objects which are famous for
them. The centrosomes of Polytrichum accordingly have achromatic
origin. They originate in the nucleus and divide into two in the
cytoplasm.

Ikeno describes these corpuscles as disappearing in the diaster
stage. This is not the case in Polytrichum. They do not remain in
their places, but may be found in various cells moving more and
more to the other side of the chromosomes, so that at last they lie
opposite each other among the spindle threads, which unite the two
chromosome masses. When the daughter nuclei have only just been
formed and the chromosomes are therefore still more or less clearly
visible, the corpuscle lies between them; afterwards everything be-
comes a black mass. At the last division of the antheridial cells the
centrosome is also taken up in the nucleus and there is here no
deviation from what is found in liverworts.

After this, such changes begin, as finally lead to the formation ot
the spermatozoids.

We did not succeed in finding young sporogonia with many young
spore mother-cells undergoing division.

We found, however, numerous dividing nuclei in the vegetative
cells of young sporogonia and hence it was not difficult to make
out the actual number of the chromosomes. The chromosomes are
small, but they are sharply differentiated and may be especially well
recognised in the equatorial plane. We found that the cells of the
sporogonium have 12 chromosomes.

Judging from analogy with what is known of liverworts and
vascular eryptogams, it was safe to assume that in the formation of
the spores a reduction of the chromosomes would take place, and

( 362 )

that their number in the gametophyte would hence be six. We did
in fact, always find six chromosomes in the cells of the antheridium
and in those of the female plants.

When the antheridia have arrived at the end of their development,
the chromosomes assume a different appearance. At first they are,
relatively to their length, fairly thick rodlets. At the last but one
division, however, they have the same length, but become much
thinner and are no longer so smooth. At this stage six chromosomes
can always still be clearly observed. At the last division, and there-
fore immediately before the actual formation of the spermatozoids,
three of the six chromosomes go to one pole and three to the other pole.

The nuclei of the spermatozoids therefore do not contain six, but
three chromosomes, i. e. a quarter of the number contained in the
nuclei of the vegetative generation.

The cells, in which the reducing division has taken place, and
which therefore are about to develop into spermatozoids, may be
recognized by their almost invisible cell wall and by their beginning
to round themselves off. The nucleus has again a central mass of
chromatin, which is, however, appreciably smaller than that in the
younger cells.

This mass again extrudes a chromatin granule in the usual manner
which travels to the periphery and then emerges from the nucleus.
The corpuscle arises therefore in the same way as the centrosome
in the cells undergoing division. It does not, however, divide but
goes at once to the periphery of the cell. Meanwhile a piece is
again separated from the mass of chromatin in the nucleus, and this
time the part separated off is so large, that it is often almost equal
to the remainder. At first the two portions remain connected, but
afterwards they become completely separated and finally the part
of the chromatin which has been split off, wanders out of the nucleus.

IKENO also describes in the changed spermatids of Marchantia the
occurrence of a chromatin body by the side of the nucleus, when
the centrosome has already quite reached the periphery.

Where it comes from, he does not know, nor what subsequently
happens to it; he only says that the organ disappears again later
and calls it “chromatoïde Nebenkérper’, which name we may retain.

Having arrived outside the nucleus, it changes its shape in Poly-
trichum and extends itself to a bent rodlet. This rodlet grows further,
till at last it becomes a closed circular body. Afterwards it again
becomes indistinct and in subsequent stages it can only be seen as
a dotted ring, which finally disappears completely. We have not
been able to discover anything about the significance of this body.

( 363 )

Meanwhile the centrosome has also changed its form. It has become
somewhat longer and more or less endgel-shaped. At the obtuse end
a thin band then becomes visible, which goes along the periphery
of the cell. The progressive differentiation of this band starts from
the centrosome and proceeds in the direction of the nucleus. The
latter has also travelled to the periphery, at that side, which is
opposite the centrosome.

A similar band, which extends from the blepharoplast to the
nucleus, has also been described by IkeNo. According to him it
originates in the cytoplasm and is stained in the same way as the
latter, but more intensely.

In our preparations which were stained with iron-haematoxylin,
it is very clearly visible and sharply marked out in black, but a
difference from the staining of the chromatin may nevertheless be
observed.

While this band slowly grows out and the “echromatoïde Neben-
kérper” disappears, a quantity of chromatin is separated off for the
third time from the chromatin mass of the nucleus. This time however,
only a very small body is formed, which also emerges from the
nucleus, but mostly remains very close to the nuclear membrane ;
the latter can only be seen very indistinetly.

In a somewhat later stage the band extends along half the circum-
ference of the cell and has therefore nearly reached the nucleus.
The third chromatin body is found at the end of the band and in
contact with the nucleus, so that in the spermatozoid it lies between
the band and the modified nucleus.

The changes which the nucleus itself undergoes in the formation
of the spermatozoid have already been described in detail by Srras-
BURGER and others; it seems to us therefore unnecessary to investi-
gate this matter further.

Il. Development of the Ovum and Fertilisation.

In the young archegonia the mother cell of the ovum is especially
large. During the further development of the archegonium this cell
divides into two and thus gives rise to an ovum and a ventral
canal-cell. A point of difference from many other mosses is, that in
the species of Polytrichum, which we have examined, the two
cells are of exactly the same size. These cells now round themselves
off and then lie loose in the venter of the archegonium. The venter
increases in size and the cells which have been rounded off, separate
from each other, till one lies at the base of the venter, and the

24

Proceedings Royal Acad. Amsterdam. Vol. X.

( 364 )

other close to the first of the neck canal-cells. Meanwhile these
latter degenerate, i.e. their walls disappear and they become some-
what rounded, so that they lie detached in the neck.

The top of the neck opens and through the opening the neck
canal-cells pass out. This could be seen in living specimens with
mature archegonia; when they were placed in water, the neck soon
opened and the cells appeared one by one.

At the stage when the neck-cells have become separated and the
neck itself is about to open, a large number of the neck-cells may
be found, in fixed preparations, in the venter of the archegonium.
They lie loose round the ovum and the ventral canal-cell.

The ventral canal-cell now approaches the ovum and appliesitself
to the latter. No demarcation between the cytoplasm of the two cells
can then be observed. The two nuclei lie side by side and gradually
fuse. This was observed by us several times and in all the successive
stages. The rest of the ventral canal-cell sbrivels up and is extruded
like the neck canal-cells.

Finally the ovum lies by itself in the venter with a large, normal,
round nucleus.

A transformation of the neck canal-cells into mucilage, as described
by Gaver?) and others, does not occur. Mucilage may indeed be
found later in the neck, and may serve to attract spermatozoids,
but it is probably secreted by the neck-cells themselves.

It now became of great importance to know the number of
chromosomes in the nucleus of the ovum. Unfortunately, as has
already been remarked, only a very limited number of nuclear
divisions can be found in the tissues of Mosses, (except in the anthe-
ridia) and hence most of the ova were either in a stage before, or
in a stage after that of nuclear division. In the other dividing cells
of the archegonium there were always six chromosomes. At the stage
immediately preceding mitosis, the nucleus of a young cell, which
after division would form an ovum, showed six pieces of chromatin.
Happily we found one very good mitotic stage. Here there was a
large spindle, parallel to the axis of the archegonium, which proved
that we had lighted on the division of the egg mother-cell. There
were six chromosomes, and though they were still in contact with
each other in pairs by one end, the other end was already directed
to the top of the spindle. It was highly probable, that of the six
chromosomes three were going to one and three to the other pole.
The discovery of a nuclear fusion also leads to the supposition, that

1) L, Gaver. Ann. des Se. nat. Bot. Série 8, T. Ill, 1897.

——o

( 365 )

the number of chromosomes was again doubled in the ovum, which
now awaited fertilisation in the venter; the latter already communi-
cated with the exterior.

These two discoveries seem to us to justify the conclusion that
before fertilisation the ovum contains six chromosomes.

We next had to attempt to find how there could be again twelve
chromosomes after fertilisation. There were six chromosomes in the
ovum and three in the spermatozoid. If fecundation were to take
place in the ordinary manner, there would still only be nine chromo-
somes, whereas the sporogonia have twelve.

For this purpose we fixed and cut several hundred female plants
of Polytrichum. There was of course only a small chance, that a
given plant would contain a fertilized archegonium, fixed at the right
moment. In a number of cases we found, however, the desired stages
and so now possess a fine series of preparations, illustrating in regular
succession, the fertilisation process from the penetration and modi-
fication of the spermatozoid onwards.

The number of spermatozoids which enter the venter of the arche-
gonium is sometimes very great, but after some have penetrated into
the ovum, the others no longer closely surround the ovum, but lie
more in the direction of the neck. Hence it would appear that here
also the fertilized egg exerts a repulsive action.

The youngest stage, which we now possess, and which has been
observed several times, shows near the periphery, but without a
doubt imbedded in the cytoplasm of the ovum, two spermatozoids ;
their length, their shape, everything agrees with that view.

In a later stage both are in contact with the nucleus; they have
become thicker and shorter. This thickening and shortening proceeds
until there are two oblong corpuscles, containing a few dark granules
in their interior, and lying against the nucleus.

We also found a few examples of the next stage, namely an ovum
which clearly showed three nuclei, each with a thick mass of chro-
matin, and another ovum, in which the demarcation between the
three nuclei was no longer so obvious; the circumference of the
nucleus in the latter case was, however, still indented and inside the
nucleus there were three dark masses of chromatin. We find there-
fore, that the cells of the sporophyte contain twelve chromosomes,
that those of the gametophyte have six, and that the spermatozoids
have three. The ovum has again six chromosomes after fusion with
the ventral canal-cell, and after fecundation by two spermatozoids
there are once more twelve chromosomes.

( 366 )
ERRATUM.

In the Proceedings of the meeting of September 1907.
p. 201 1. 8 from the bottom: for 300.000 read 30.000.

Pa

(December 24, 1907). red

KONINKLIJKE AKADEMIE
VAN WETENSCHAPPEN
-- TE AMSTERDAM -:-

PROCEEDINGS OE THE
SECTION OF. SCIENCES

VOLUME xX
( — IST PART — )

JOHANNES MULLER :—: AMSTERDAM
: DECEMBER 1907 :

MP nai ie ney. ke
ie © Hh SNe Dot a aa nr
; PEP RA Le „5 DO:
7 AE ges
MAU ak Avy igi pe a oe =< a
= ial L > a

(Transiated from: Verslagen van de Gewone Vergaderingen der Wis- en Natuurkundige i
Afdeeling van 24 May 1907 tot 30 November 1907. DI, XVI)

igst

Bn

10013914